Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [862,2,Mod(1,862)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(862, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("862.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 862 = 2 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 862.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: | \(6.88310465423\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.11017801.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 13x^{3} + 3x^{2} - 10x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.32324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 862.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.32324 | −0.763974 | −0.381987 | − | 0.924168i | \(-0.624760\pi\) | ||||
−0.381987 | + | 0.924168i | \(0.624760\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.36571 | 1.05798 | 0.528989 | − | 0.848629i | \(-0.322571\pi\) | ||||
0.528989 | + | 0.848629i | \(0.322571\pi\) | |||||||
\(6\) | 1.32324 | 0.540211 | ||||||||
\(7\) | 2.18258 | 0.824937 | 0.412469 | − | 0.910972i | \(-0.364667\pi\) | ||||
0.412469 | + | 0.910972i | \(0.364667\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.24903 | −0.416344 | ||||||||
\(10\) | −2.36571 | −0.748103 | ||||||||
\(11\) | −5.72343 | −1.72568 | −0.862839 | − | 0.505479i | \(-0.831316\pi\) | ||||
−0.862839 | + | 0.505479i | \(0.831316\pi\) | |||||||
\(12\) | −1.32324 | −0.381987 | ||||||||
\(13\) | 0.593025 | 0.164475 | 0.0822377 | − | 0.996613i | \(-0.473793\pi\) | ||||
0.0822377 | + | 0.996613i | \(0.473793\pi\) | |||||||
\(14\) | −2.18258 | −0.583319 | ||||||||
\(15\) | −3.13040 | −0.808267 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.42893 | −1.80178 | −0.900890 | − | 0.434048i | \(-0.857085\pi\) | ||||
−0.900890 | + | 0.434048i | \(0.857085\pi\) | |||||||
\(18\) | 1.24903 | 0.294400 | ||||||||
\(19\) | −3.56128 | −0.817015 | −0.408507 | − | 0.912755i | \(-0.633951\pi\) | ||||
−0.408507 | + | 0.912755i | \(0.633951\pi\) | |||||||
\(20\) | 2.36571 | 0.528989 | ||||||||
\(21\) | −2.88808 | −0.630230 | ||||||||
\(22\) | 5.72343 | 1.22024 | ||||||||
\(23\) | 4.42537 | 0.922754 | 0.461377 | − | 0.887204i | \(-0.347356\pi\) | ||||
0.461377 | + | 0.887204i | \(0.347356\pi\) | |||||||
\(24\) | 1.32324 | 0.270105 | ||||||||
\(25\) | 0.596577 | 0.119315 | ||||||||
\(26\) | −0.593025 | −0.116302 | ||||||||
\(27\) | 5.62250 | 1.08205 | ||||||||
\(28\) | 2.18258 | 0.412469 | ||||||||
\(29\) | −3.86409 | −0.717544 | −0.358772 | − | 0.933425i | \(-0.616804\pi\) | ||||
−0.358772 | + | 0.933425i | \(0.616804\pi\) | |||||||
\(30\) | 3.13040 | 0.571531 | ||||||||
\(31\) | 8.47915 | 1.52290 | 0.761450 | − | 0.648224i | \(-0.224488\pi\) | ||||
0.761450 | + | 0.648224i | \(0.224488\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.57347 | 1.31837 | ||||||||
\(34\) | 7.42893 | 1.27405 | ||||||||
\(35\) | 5.16334 | 0.872764 | ||||||||
\(36\) | −1.24903 | −0.208172 | ||||||||
\(37\) | −7.14962 | −1.17539 | −0.587695 | − | 0.809083i | \(-0.699964\pi\) | ||||
−0.587695 | + | 0.809083i | \(0.699964\pi\) | |||||||
\(38\) | 3.56128 | 0.577717 | ||||||||
\(39\) | −0.784714 | −0.125655 | ||||||||
\(40\) | −2.36571 | −0.374051 | ||||||||
\(41\) | −12.6822 | −1.98062 | −0.990310 | − | 0.138872i | \(-0.955652\pi\) | ||||
−0.990310 | + | 0.138872i | \(0.955652\pi\) | |||||||
\(42\) | 2.88808 | 0.445640 | ||||||||
\(43\) | 1.56872 | 0.239228 | 0.119614 | − | 0.992820i | \(-0.461834\pi\) | ||||
0.119614 | + | 0.992820i | \(0.461834\pi\) | |||||||
\(44\) | −5.72343 | −0.862839 | ||||||||
\(45\) | −2.95485 | −0.440483 | ||||||||
\(46\) | −4.42537 | −0.652486 | ||||||||
\(47\) | −4.71439 | −0.687665 | −0.343832 | − | 0.939031i | \(-0.611725\pi\) | ||||
−0.343832 | + | 0.939031i | \(0.611725\pi\) | |||||||
\(48\) | −1.32324 | −0.190993 | ||||||||
\(49\) | −2.23635 | −0.319479 | ||||||||
\(50\) | −0.596577 | −0.0843687 | ||||||||
\(51\) | 9.83026 | 1.37651 | ||||||||
\(52\) | 0.593025 | 0.0822377 | ||||||||
\(53\) | 2.42851 | 0.333582 | 0.166791 | − | 0.985992i | \(-0.446660\pi\) | ||||
0.166791 | + | 0.985992i | \(0.446660\pi\) | |||||||
\(54\) | −5.62250 | −0.765125 | ||||||||
\(55\) | −13.5400 | −1.82573 | ||||||||
\(56\) | −2.18258 | −0.291659 | ||||||||
\(57\) | 4.71244 | 0.624178 | ||||||||
\(58\) | 3.86409 | 0.507380 | ||||||||
\(59\) | 12.6925 | 1.65242 | 0.826210 | − | 0.563363i | \(-0.190493\pi\) | ||||
0.826210 | + | 0.563363i | \(0.190493\pi\) | |||||||
\(60\) | −3.13040 | −0.404133 | ||||||||
\(61\) | −3.35111 | −0.429066 | −0.214533 | − | 0.976717i | \(-0.568823\pi\) | ||||
−0.214533 | + | 0.976717i | \(0.568823\pi\) | |||||||
\(62\) | −8.47915 | −1.07685 | ||||||||
\(63\) | −2.72611 | −0.343458 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.40292 | 0.174011 | ||||||||
\(66\) | −7.57347 | −0.932230 | ||||||||
\(67\) | 8.04239 | 0.982534 | 0.491267 | − | 0.871009i | \(-0.336534\pi\) | ||||
0.491267 | + | 0.871009i | \(0.336534\pi\) | |||||||
\(68\) | −7.42893 | −0.900890 | ||||||||
\(69\) | −5.85584 | −0.704960 | ||||||||
\(70\) | −5.16334 | −0.617138 | ||||||||
\(71\) | −7.37588 | −0.875356 | −0.437678 | − | 0.899132i | \(-0.644199\pi\) | ||||
−0.437678 | + | 0.899132i | \(0.644199\pi\) | |||||||
\(72\) | 1.24903 | 0.147200 | ||||||||
\(73\) | −15.2546 | −1.78541 | −0.892706 | − | 0.450639i | \(-0.851196\pi\) | ||||
−0.892706 | + | 0.450639i | \(0.851196\pi\) | |||||||
\(74\) | 7.14962 | 0.831126 | ||||||||
\(75\) | −0.789415 | −0.0911538 | ||||||||
\(76\) | −3.56128 | −0.408507 | ||||||||
\(77\) | −12.4918 | −1.42358 | ||||||||
\(78\) | 0.784714 | 0.0888514 | ||||||||
\(79\) | −8.80507 | −0.990648 | −0.495324 | − | 0.868708i | \(-0.664951\pi\) | ||||
−0.495324 | + | 0.868708i | \(0.664951\pi\) | |||||||
\(80\) | 2.36571 | 0.264494 | ||||||||
\(81\) | −3.69282 | −0.410313 | ||||||||
\(82\) | 12.6822 | 1.40051 | ||||||||
\(83\) | −11.5468 | −1.26742 | −0.633710 | − | 0.773570i | \(-0.718469\pi\) | ||||
−0.633710 | + | 0.773570i | \(0.718469\pi\) | |||||||
\(84\) | −2.88808 | −0.315115 | ||||||||
\(85\) | −17.5747 | −1.90624 | ||||||||
\(86\) | −1.56872 | −0.169160 | ||||||||
\(87\) | 5.11312 | 0.548184 | ||||||||
\(88\) | 5.72343 | 0.610119 | ||||||||
\(89\) | 12.3809 | 1.31237 | 0.656185 | − | 0.754600i | \(-0.272169\pi\) | ||||
0.656185 | + | 0.754600i | \(0.272169\pi\) | |||||||
\(90\) | 2.95485 | 0.311468 | ||||||||
\(91\) | 1.29432 | 0.135682 | ||||||||
\(92\) | 4.42537 | 0.461377 | ||||||||
\(93\) | −11.2200 | −1.16346 | ||||||||
\(94\) | 4.71439 | 0.486252 | ||||||||
\(95\) | −8.42496 | −0.864383 | ||||||||
\(96\) | 1.32324 | 0.135053 | ||||||||
\(97\) | 0.965753 | 0.0980574 | 0.0490287 | − | 0.998797i | \(-0.484387\pi\) | ||||
0.0490287 | + | 0.998797i | \(0.484387\pi\) | |||||||
\(98\) | 2.23635 | 0.225906 | ||||||||
\(99\) | 7.14875 | 0.718476 | ||||||||
\(100\) | 0.596577 | 0.0596577 | ||||||||
\(101\) | 3.52582 | 0.350832 | 0.175416 | − | 0.984494i | \(-0.443873\pi\) | ||||
0.175416 | + | 0.984494i | \(0.443873\pi\) | |||||||
\(102\) | −9.83026 | −0.973341 | ||||||||
\(103\) | −1.91457 | −0.188648 | −0.0943239 | − | 0.995542i | \(-0.530069\pi\) | ||||
−0.0943239 | + | 0.995542i | \(0.530069\pi\) | |||||||
\(104\) | −0.593025 | −0.0581508 | ||||||||
\(105\) | −6.83235 | −0.666769 | ||||||||
\(106\) | −2.42851 | −0.235878 | ||||||||
\(107\) | −17.7035 | −1.71146 | −0.855732 | − | 0.517420i | \(-0.826893\pi\) | ||||
−0.855732 | + | 0.517420i | \(0.826893\pi\) | |||||||
\(108\) | 5.62250 | 0.541025 | ||||||||
\(109\) | 19.7191 | 1.88874 | 0.944372 | − | 0.328879i | \(-0.106671\pi\) | ||||
0.944372 | + | 0.328879i | \(0.106671\pi\) | |||||||
\(110\) | 13.5400 | 1.29098 | ||||||||
\(111\) | 9.46067 | 0.897967 | ||||||||
\(112\) | 2.18258 | 0.206234 | ||||||||
\(113\) | −3.94098 | −0.370737 | −0.185368 | − | 0.982669i | \(-0.559348\pi\) | ||||
−0.185368 | + | 0.982669i | \(0.559348\pi\) | |||||||
\(114\) | −4.71244 | −0.441360 | ||||||||
\(115\) | 10.4691 | 0.976253 | ||||||||
\(116\) | −3.86409 | −0.358772 | ||||||||
\(117\) | −0.740707 | −0.0684784 | ||||||||
\(118\) | −12.6925 | −1.16844 | ||||||||
\(119\) | −16.2142 | −1.48635 | ||||||||
\(120\) | 3.13040 | 0.285765 | ||||||||
\(121\) | 21.7576 | 1.97797 | ||||||||
\(122\) | 3.35111 | 0.303396 | ||||||||
\(123\) | 16.7816 | 1.51314 | ||||||||
\(124\) | 8.47915 | 0.761450 | ||||||||
\(125\) | −10.4172 | −0.931744 | ||||||||
\(126\) | 2.72611 | 0.242861 | ||||||||
\(127\) | −22.2288 | −1.97249 | −0.986245 | − | 0.165292i | \(-0.947143\pi\) | ||||
−0.986245 | + | 0.165292i | \(0.947143\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.07580 | −0.182764 | ||||||||
\(130\) | −1.40292 | −0.123045 | ||||||||
\(131\) | 14.6039 | 1.27594 | 0.637972 | − | 0.770059i | \(-0.279773\pi\) | ||||
0.637972 | + | 0.770059i | \(0.279773\pi\) | |||||||
\(132\) | 7.57347 | 0.659186 | ||||||||
\(133\) | −7.77278 | −0.673986 | ||||||||
\(134\) | −8.04239 | −0.694756 | ||||||||
\(135\) | 13.3012 | 1.14478 | ||||||||
\(136\) | 7.42893 | 0.637025 | ||||||||
\(137\) | 12.2027 | 1.04255 | 0.521275 | − | 0.853389i | \(-0.325457\pi\) | ||||
0.521275 | + | 0.853389i | \(0.325457\pi\) | |||||||
\(138\) | 5.85584 | 0.498482 | ||||||||
\(139\) | 8.96165 | 0.760118 | 0.380059 | − | 0.924962i | \(-0.375904\pi\) | ||||
0.380059 | + | 0.924962i | \(0.375904\pi\) | |||||||
\(140\) | 5.16334 | 0.436382 | ||||||||
\(141\) | 6.23828 | 0.525358 | ||||||||
\(142\) | 7.37588 | 0.618970 | ||||||||
\(143\) | −3.39413 | −0.283832 | ||||||||
\(144\) | −1.24903 | −0.104086 | ||||||||
\(145\) | −9.14131 | −0.759145 | ||||||||
\(146\) | 15.2546 | 1.26248 | ||||||||
\(147\) | 2.95923 | 0.244073 | ||||||||
\(148\) | −7.14962 | −0.587695 | ||||||||
\(149\) | −8.36208 | −0.685048 | −0.342524 | − | 0.939509i | \(-0.611282\pi\) | ||||
−0.342524 | + | 0.939509i | \(0.611282\pi\) | |||||||
\(150\) | 0.789415 | 0.0644555 | ||||||||
\(151\) | 6.26793 | 0.510077 | 0.255039 | − | 0.966931i | \(-0.417912\pi\) | ||||
0.255039 | + | 0.966931i | \(0.417912\pi\) | |||||||
\(152\) | 3.56128 | 0.288858 | ||||||||
\(153\) | 9.27897 | 0.750161 | ||||||||
\(154\) | 12.4918 | 1.00662 | ||||||||
\(155\) | 20.0592 | 1.61119 | ||||||||
\(156\) | −0.784714 | −0.0628274 | ||||||||
\(157\) | 22.9217 | 1.82935 | 0.914676 | − | 0.404187i | \(-0.132445\pi\) | ||||
0.914676 | + | 0.404187i | \(0.132445\pi\) | |||||||
\(158\) | 8.80507 | 0.700494 | ||||||||
\(159\) | −3.21351 | −0.254848 | ||||||||
\(160\) | −2.36571 | −0.187026 | ||||||||
\(161\) | 9.65873 | 0.761214 | ||||||||
\(162\) | 3.69282 | 0.290135 | ||||||||
\(163\) | −19.9480 | −1.56245 | −0.781224 | − | 0.624251i | \(-0.785404\pi\) | ||||
−0.781224 | + | 0.624251i | \(0.785404\pi\) | |||||||
\(164\) | −12.6822 | −0.990310 | ||||||||
\(165\) | 17.9166 | 1.39481 | ||||||||
\(166\) | 11.5468 | 0.896202 | ||||||||
\(167\) | −4.57145 | −0.353750 | −0.176875 | − | 0.984233i | \(-0.556599\pi\) | ||||
−0.176875 | + | 0.984233i | \(0.556599\pi\) | |||||||
\(168\) | 2.88808 | 0.222820 | ||||||||
\(169\) | −12.6483 | −0.972948 | ||||||||
\(170\) | 17.5747 | 1.34792 | ||||||||
\(171\) | 4.44816 | 0.340159 | ||||||||
\(172\) | 1.56872 | 0.119614 | ||||||||
\(173\) | −8.83938 | −0.672046 | −0.336023 | − | 0.941854i | \(-0.609082\pi\) | ||||
−0.336023 | + | 0.941854i | \(0.609082\pi\) | |||||||
\(174\) | −5.11312 | −0.387625 | ||||||||
\(175\) | 1.30208 | 0.0984277 | ||||||||
\(176\) | −5.72343 | −0.431420 | ||||||||
\(177\) | −16.7952 | −1.26240 | ||||||||
\(178\) | −12.3809 | −0.927985 | ||||||||
\(179\) | −5.09347 | −0.380704 | −0.190352 | − | 0.981716i | \(-0.560963\pi\) | ||||
−0.190352 | + | 0.981716i | \(0.560963\pi\) | |||||||
\(180\) | −2.95485 | −0.220241 | ||||||||
\(181\) | −12.1346 | −0.901957 | −0.450978 | − | 0.892535i | \(-0.648925\pi\) | ||||
−0.450978 | + | 0.892535i | \(0.648925\pi\) | |||||||
\(182\) | −1.29432 | −0.0959416 | ||||||||
\(183\) | 4.43433 | 0.327795 | ||||||||
\(184\) | −4.42537 | −0.326243 | ||||||||
\(185\) | −16.9139 | −1.24354 | ||||||||
\(186\) | 11.2200 | 0.822687 | ||||||||
\(187\) | 42.5189 | 3.10929 | ||||||||
\(188\) | −4.71439 | −0.343832 | ||||||||
\(189\) | 12.2715 | 0.892623 | ||||||||
\(190\) | 8.42496 | 0.611211 | ||||||||
\(191\) | 1.18950 | 0.0860693 | 0.0430347 | − | 0.999074i | \(-0.486297\pi\) | ||||
0.0430347 | + | 0.999074i | \(0.486297\pi\) | |||||||
\(192\) | −1.32324 | −0.0954967 | ||||||||
\(193\) | 3.45647 | 0.248802 | 0.124401 | − | 0.992232i | \(-0.460299\pi\) | ||||
0.124401 | + | 0.992232i | \(0.460299\pi\) | |||||||
\(194\) | −0.965753 | −0.0693370 | ||||||||
\(195\) | −1.85641 | −0.132940 | ||||||||
\(196\) | −2.23635 | −0.159739 | ||||||||
\(197\) | −20.6176 | −1.46895 | −0.734473 | − | 0.678638i | \(-0.762571\pi\) | ||||
−0.734473 | + | 0.678638i | \(0.762571\pi\) | |||||||
\(198\) | −7.14875 | −0.508039 | ||||||||
\(199\) | 5.29993 | 0.375702 | 0.187851 | − | 0.982198i | \(-0.439848\pi\) | ||||
0.187851 | + | 0.982198i | \(0.439848\pi\) | |||||||
\(200\) | −0.596577 | −0.0421844 | ||||||||
\(201\) | −10.6420 | −0.750630 | ||||||||
\(202\) | −3.52582 | −0.248076 | ||||||||
\(203\) | −8.43368 | −0.591928 | ||||||||
\(204\) | 9.83026 | 0.688256 | ||||||||
\(205\) | −30.0023 | −2.09545 | ||||||||
\(206\) | 1.91457 | 0.133394 | ||||||||
\(207\) | −5.52744 | −0.384183 | ||||||||
\(208\) | 0.593025 | 0.0411189 | ||||||||
\(209\) | 20.3827 | 1.40990 | ||||||||
\(210\) | 6.83235 | 0.471477 | ||||||||
\(211\) | −3.18579 | −0.219319 | −0.109660 | − | 0.993969i | \(-0.534976\pi\) | ||||
−0.109660 | + | 0.993969i | \(0.534976\pi\) | |||||||
\(212\) | 2.42851 | 0.166791 | ||||||||
\(213\) | 9.76007 | 0.668749 | ||||||||
\(214\) | 17.7035 | 1.21019 | ||||||||
\(215\) | 3.71114 | 0.253098 | ||||||||
\(216\) | −5.62250 | −0.382562 | ||||||||
\(217\) | 18.5064 | 1.25630 | ||||||||
\(218\) | −19.7191 | −1.33554 | ||||||||
\(219\) | 20.1855 | 1.36401 | ||||||||
\(220\) | −13.5400 | −0.912864 | ||||||||
\(221\) | −4.40554 | −0.296348 | ||||||||
\(222\) | −9.46067 | −0.634958 | ||||||||
\(223\) | 19.7205 | 1.32058 | 0.660290 | − | 0.751010i | \(-0.270433\pi\) | ||||
0.660290 | + | 0.751010i | \(0.270433\pi\) | |||||||
\(224\) | −2.18258 | −0.145830 | ||||||||
\(225\) | −0.745144 | −0.0496763 | ||||||||
\(226\) | 3.94098 | 0.262150 | ||||||||
\(227\) | 17.9668 | 1.19250 | 0.596248 | − | 0.802800i | \(-0.296657\pi\) | ||||
0.596248 | + | 0.802800i | \(0.296657\pi\) | |||||||
\(228\) | 4.71244 | 0.312089 | ||||||||
\(229\) | 17.6093 | 1.16366 | 0.581829 | − | 0.813311i | \(-0.302337\pi\) | ||||
0.581829 | + | 0.813311i | \(0.302337\pi\) | |||||||
\(230\) | −10.4691 | −0.690315 | ||||||||
\(231\) | 16.5297 | 1.08757 | ||||||||
\(232\) | 3.86409 | 0.253690 | ||||||||
\(233\) | 11.8245 | 0.774650 | 0.387325 | − | 0.921943i | \(-0.373399\pi\) | ||||
0.387325 | + | 0.921943i | \(0.373399\pi\) | |||||||
\(234\) | 0.740707 | 0.0484215 | ||||||||
\(235\) | −11.1529 | −0.727533 | ||||||||
\(236\) | 12.6925 | 0.826210 | ||||||||
\(237\) | 11.6512 | 0.756829 | ||||||||
\(238\) | 16.2142 | 1.05101 | ||||||||
\(239\) | 12.3656 | 0.799865 | 0.399933 | − | 0.916545i | \(-0.369034\pi\) | ||||
0.399933 | + | 0.916545i | \(0.369034\pi\) | |||||||
\(240\) | −3.13040 | −0.202067 | ||||||||
\(241\) | −13.7153 | −0.883481 | −0.441741 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441741 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(242\) | −21.7576 | −1.39863 | ||||||||
\(243\) | −11.9810 | −0.768581 | ||||||||
\(244\) | −3.35111 | −0.214533 | ||||||||
\(245\) | −5.29056 | −0.338001 | ||||||||
\(246\) | −16.7816 | −1.06995 | ||||||||
\(247\) | −2.11193 | −0.134379 | ||||||||
\(248\) | −8.47915 | −0.538426 | ||||||||
\(249\) | 15.2791 | 0.968276 | ||||||||
\(250\) | 10.4172 | 0.658843 | ||||||||
\(251\) | −2.70050 | −0.170454 | −0.0852269 | − | 0.996362i | \(-0.527162\pi\) | ||||
−0.0852269 | + | 0.996362i | \(0.527162\pi\) | |||||||
\(252\) | −2.72611 | −0.171729 | ||||||||
\(253\) | −25.3283 | −1.59238 | ||||||||
\(254\) | 22.2288 | 1.39476 | ||||||||
\(255\) | 23.2555 | 1.45632 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.3529 | 0.645798 | 0.322899 | − | 0.946433i | \(-0.395343\pi\) | ||||
0.322899 | + | 0.946433i | \(0.395343\pi\) | |||||||
\(258\) | 2.07580 | 0.129233 | ||||||||
\(259\) | −15.6046 | −0.969623 | ||||||||
\(260\) | 1.40292 | 0.0870056 | ||||||||
\(261\) | 4.82638 | 0.298745 | ||||||||
\(262\) | −14.6039 | −0.902229 | ||||||||
\(263\) | 3.77652 | 0.232870 | 0.116435 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116435 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(264\) | −7.57347 | −0.466115 | ||||||||
\(265\) | 5.74515 | 0.352922 | ||||||||
\(266\) | 7.77278 | 0.476580 | ||||||||
\(267\) | −16.3829 | −1.00262 | ||||||||
\(268\) | 8.04239 | 0.491267 | ||||||||
\(269\) | −4.24877 | −0.259052 | −0.129526 | − | 0.991576i | \(-0.541346\pi\) | ||||
−0.129526 | + | 0.991576i | \(0.541346\pi\) | |||||||
\(270\) | −13.3012 | −0.809484 | ||||||||
\(271\) | 24.6332 | 1.49636 | 0.748179 | − | 0.663497i | \(-0.230928\pi\) | ||||
0.748179 | + | 0.663497i | \(0.230928\pi\) | |||||||
\(272\) | −7.42893 | −0.450445 | ||||||||
\(273\) | −1.71270 | −0.103657 | ||||||||
\(274\) | −12.2027 | −0.737194 | ||||||||
\(275\) | −3.41447 | −0.205900 | ||||||||
\(276\) | −5.85584 | −0.352480 | ||||||||
\(277\) | 23.1348 | 1.39004 | 0.695018 | − | 0.718992i | \(-0.255396\pi\) | ||||
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(278\) | −8.96165 | −0.537484 | ||||||||
\(279\) | −10.5907 | −0.634051 | ||||||||
\(280\) | −5.16334 | −0.308569 | ||||||||
\(281\) | −18.9945 | −1.13312 | −0.566558 | − | 0.824022i | \(-0.691725\pi\) | ||||
−0.566558 | + | 0.824022i | \(0.691725\pi\) | |||||||
\(282\) | −6.23828 | −0.371484 | ||||||||
\(283\) | −1.54158 | −0.0916376 | −0.0458188 | − | 0.998950i | \(-0.514590\pi\) | ||||
−0.0458188 | + | 0.998950i | \(0.514590\pi\) | |||||||
\(284\) | −7.37588 | −0.437678 | ||||||||
\(285\) | 11.1483 | 0.660366 | ||||||||
\(286\) | 3.39413 | 0.200699 | ||||||||
\(287\) | −27.6798 | −1.63389 | ||||||||
\(288\) | 1.24903 | 0.0736000 | ||||||||
\(289\) | 38.1889 | 2.24641 | ||||||||
\(290\) | 9.14131 | 0.536796 | ||||||||
\(291\) | −1.27792 | −0.0749132 | ||||||||
\(292\) | −15.2546 | −0.892706 | ||||||||
\(293\) | −12.0162 | −0.701991 | −0.350996 | − | 0.936377i | \(-0.614157\pi\) | ||||
−0.350996 | + | 0.936377i | \(0.614157\pi\) | |||||||
\(294\) | −2.95923 | −0.172586 | ||||||||
\(295\) | 30.0267 | 1.74822 | ||||||||
\(296\) | 7.14962 | 0.415563 | ||||||||
\(297\) | −32.1799 | −1.86727 | ||||||||
\(298\) | 8.36208 | 0.484402 | ||||||||
\(299\) | 2.62436 | 0.151770 | ||||||||
\(300\) | −0.789415 | −0.0455769 | ||||||||
\(301\) | 3.42386 | 0.197348 | ||||||||
\(302\) | −6.26793 | −0.360679 | ||||||||
\(303\) | −4.66550 | −0.268026 | ||||||||
\(304\) | −3.56128 | −0.204254 | ||||||||
\(305\) | −7.92776 | −0.453942 | ||||||||
\(306\) | −9.27897 | −0.530444 | ||||||||
\(307\) | 21.2277 | 1.21153 | 0.605763 | − | 0.795645i | \(-0.292868\pi\) | ||||
0.605763 | + | 0.795645i | \(0.292868\pi\) | |||||||
\(308\) | −12.4918 | −0.711788 | ||||||||
\(309\) | 2.53343 | 0.144122 | ||||||||
\(310\) | −20.0592 | −1.13929 | ||||||||
\(311\) | 2.44107 | 0.138420 | 0.0692101 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692101 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(312\) | 0.784714 | 0.0444257 | ||||||||
\(313\) | −25.8091 | −1.45882 | −0.729409 | − | 0.684078i | \(-0.760205\pi\) | ||||
−0.729409 | + | 0.684078i | \(0.760205\pi\) | |||||||
\(314\) | −22.9217 | −1.29355 | ||||||||
\(315\) | −6.44919 | −0.363371 | ||||||||
\(316\) | −8.80507 | −0.495324 | ||||||||
\(317\) | −9.80038 | −0.550444 | −0.275222 | − | 0.961381i | \(-0.588751\pi\) | ||||
−0.275222 | + | 0.961381i | \(0.588751\pi\) | |||||||
\(318\) | 3.21351 | 0.180205 | ||||||||
\(319\) | 22.1158 | 1.23825 | ||||||||
\(320\) | 2.36571 | 0.132247 | ||||||||
\(321\) | 23.4260 | 1.30751 | ||||||||
\(322\) | −9.65873 | −0.538260 | ||||||||
\(323\) | 26.4565 | 1.47208 | ||||||||
\(324\) | −3.69282 | −0.205157 | ||||||||
\(325\) | 0.353785 | 0.0196245 | ||||||||
\(326\) | 19.9480 | 1.10482 | ||||||||
\(327\) | −26.0931 | −1.44295 | ||||||||
\(328\) | 12.6822 | 0.700255 | ||||||||
\(329\) | −10.2895 | −0.567280 | ||||||||
\(330\) | −17.9166 | −0.986278 | ||||||||
\(331\) | 8.07682 | 0.443942 | 0.221971 | − | 0.975053i | \(-0.428751\pi\) | ||||
0.221971 | + | 0.975053i | \(0.428751\pi\) | |||||||
\(332\) | −11.5468 | −0.633710 | ||||||||
\(333\) | 8.93011 | 0.489367 | ||||||||
\(334\) | 4.57145 | 0.250139 | ||||||||
\(335\) | 19.0259 | 1.03950 | ||||||||
\(336\) | −2.88808 | −0.157558 | ||||||||
\(337\) | 18.9338 | 1.03139 | 0.515696 | − | 0.856772i | \(-0.327533\pi\) | ||||
0.515696 | + | 0.856772i | \(0.327533\pi\) | |||||||
\(338\) | 12.6483 | 0.687978 | ||||||||
\(339\) | 5.21487 | 0.283233 | ||||||||
\(340\) | −17.5747 | −0.953121 | ||||||||
\(341\) | −48.5298 | −2.62804 | ||||||||
\(342\) | −4.44816 | −0.240529 | ||||||||
\(343\) | −20.1591 | −1.08849 | ||||||||
\(344\) | −1.56872 | −0.0845798 | ||||||||
\(345\) | −13.8532 | −0.745831 | ||||||||
\(346\) | 8.83938 | 0.475208 | ||||||||
\(347\) | 5.40719 | 0.290273 | 0.145137 | − | 0.989412i | \(-0.453638\pi\) | ||||
0.145137 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(348\) | 5.11312 | 0.274092 | ||||||||
\(349\) | 15.9428 | 0.853396 | 0.426698 | − | 0.904394i | \(-0.359677\pi\) | ||||
0.426698 | + | 0.904394i | \(0.359677\pi\) | |||||||
\(350\) | −1.30208 | −0.0695989 | ||||||||
\(351\) | 3.33428 | 0.177971 | ||||||||
\(352\) | 5.72343 | 0.305060 | ||||||||
\(353\) | −29.7808 | −1.58507 | −0.792536 | − | 0.609825i | \(-0.791240\pi\) | ||||
−0.792536 | + | 0.609825i | \(0.791240\pi\) | |||||||
\(354\) | 16.7952 | 0.892655 | ||||||||
\(355\) | −17.4492 | −0.926107 | ||||||||
\(356\) | 12.3809 | 0.656185 | ||||||||
\(357\) | 21.4553 | 1.13554 | ||||||||
\(358\) | 5.09347 | 0.269198 | ||||||||
\(359\) | −6.81817 | −0.359849 | −0.179925 | − | 0.983680i | \(-0.557585\pi\) | ||||
−0.179925 | + | 0.983680i | \(0.557585\pi\) | |||||||
\(360\) | 2.95485 | 0.155734 | ||||||||
\(361\) | −6.31726 | −0.332487 | ||||||||
\(362\) | 12.1346 | 0.637780 | ||||||||
\(363\) | −28.7906 | −1.51111 | ||||||||
\(364\) | 1.29432 | 0.0678409 | ||||||||
\(365\) | −36.0879 | −1.88893 | ||||||||
\(366\) | −4.43433 | −0.231786 | ||||||||
\(367\) | −7.69745 | −0.401803 | −0.200902 | − | 0.979611i | \(-0.564387\pi\) | ||||
−0.200902 | + | 0.979611i | \(0.564387\pi\) | |||||||
\(368\) | 4.42537 | 0.230689 | ||||||||
\(369\) | 15.8404 | 0.824620 | ||||||||
\(370\) | 16.9139 | 0.879312 | ||||||||
\(371\) | 5.30042 | 0.275184 | ||||||||
\(372\) | −11.2200 | −0.581728 | ||||||||
\(373\) | 20.9846 | 1.08654 | 0.543271 | − | 0.839557i | \(-0.317185\pi\) | ||||
0.543271 | + | 0.839557i | \(0.317185\pi\) | |||||||
\(374\) | −42.5189 | −2.19860 | ||||||||
\(375\) | 13.7845 | 0.711828 | ||||||||
\(376\) | 4.71439 | 0.243126 | ||||||||
\(377\) | −2.29150 | −0.118018 | ||||||||
\(378\) | −12.2715 | −0.631180 | ||||||||
\(379\) | 12.4153 | 0.637730 | 0.318865 | − | 0.947800i | \(-0.396698\pi\) | ||||
0.318865 | + | 0.947800i | \(0.396698\pi\) | |||||||
\(380\) | −8.42496 | −0.432191 | ||||||||
\(381\) | 29.4141 | 1.50693 | ||||||||
\(382\) | −1.18950 | −0.0608602 | ||||||||
\(383\) | −23.3716 | −1.19423 | −0.597116 | − | 0.802155i | \(-0.703687\pi\) | ||||
−0.597116 | + | 0.802155i | \(0.703687\pi\) | |||||||
\(384\) | 1.32324 | 0.0675264 | ||||||||
\(385\) | −29.5520 | −1.50611 | ||||||||
\(386\) | −3.45647 | −0.175929 | ||||||||
\(387\) | −1.95938 | −0.0996011 | ||||||||
\(388\) | 0.965753 | 0.0490287 | ||||||||
\(389\) | 5.61282 | 0.284581 | 0.142291 | − | 0.989825i | \(-0.454553\pi\) | ||||
0.142291 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(390\) | 1.85641 | 0.0940028 | ||||||||
\(391\) | −32.8758 | −1.66260 | ||||||||
\(392\) | 2.23635 | 0.112953 | ||||||||
\(393\) | −19.3244 | −0.974788 | ||||||||
\(394\) | 20.6176 | 1.03870 | ||||||||
\(395\) | −20.8302 | −1.04808 | ||||||||
\(396\) | 7.14875 | 0.359238 | ||||||||
\(397\) | 36.8075 | 1.84731 | 0.923657 | − | 0.383219i | \(-0.125185\pi\) | ||||
0.923657 | + | 0.383219i | \(0.125185\pi\) | |||||||
\(398\) | −5.29993 | −0.265661 | ||||||||
\(399\) | 10.2853 | 0.514907 | ||||||||
\(400\) | 0.596577 | 0.0298289 | ||||||||
\(401\) | 14.0637 | 0.702306 | 0.351153 | − | 0.936318i | \(-0.385790\pi\) | ||||
0.351153 | + | 0.936318i | \(0.385790\pi\) | |||||||
\(402\) | 10.6420 | 0.530775 | ||||||||
\(403\) | 5.02834 | 0.250480 | ||||||||
\(404\) | 3.52582 | 0.175416 | ||||||||
\(405\) | −8.73613 | −0.434102 | ||||||||
\(406\) | 8.43368 | 0.418556 | ||||||||
\(407\) | 40.9203 | 2.02834 | ||||||||
\(408\) | −9.83026 | −0.486670 | ||||||||
\(409\) | −11.0305 | −0.545422 | −0.272711 | − | 0.962096i | \(-0.587920\pi\) | ||||
−0.272711 | + | 0.962096i | \(0.587920\pi\) | |||||||
\(410\) | 30.0023 | 1.48171 | ||||||||
\(411\) | −16.1472 | −0.796480 | ||||||||
\(412\) | −1.91457 | −0.0943239 | ||||||||
\(413\) | 27.7023 | 1.36314 | ||||||||
\(414\) | 5.52744 | 0.271659 | ||||||||
\(415\) | −27.3162 | −1.34090 | ||||||||
\(416\) | −0.593025 | −0.0290754 | ||||||||
\(417\) | −11.8584 | −0.580710 | ||||||||
\(418\) | −20.3827 | −0.996953 | ||||||||
\(419\) | 21.0666 | 1.02917 | 0.514586 | − | 0.857439i | \(-0.327945\pi\) | ||||
0.514586 | + | 0.857439i | \(0.327945\pi\) | |||||||
\(420\) | −6.83235 | −0.333385 | ||||||||
\(421\) | −29.5821 | −1.44174 | −0.720871 | − | 0.693069i | \(-0.756258\pi\) | ||||
−0.720871 | + | 0.693069i | \(0.756258\pi\) | |||||||
\(422\) | 3.18579 | 0.155082 | ||||||||
\(423\) | 5.88843 | 0.286305 | ||||||||
\(424\) | −2.42851 | −0.117939 | ||||||||
\(425\) | −4.43193 | −0.214980 | ||||||||
\(426\) | −9.76007 | −0.472877 | ||||||||
\(427\) | −7.31407 | −0.353953 | ||||||||
\(428\) | −17.7035 | −0.855732 | ||||||||
\(429\) | 4.49126 | 0.216840 | ||||||||
\(430\) | −3.71114 | −0.178967 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 5.62250 | 0.270512 | ||||||||
\(433\) | −9.98168 | −0.479689 | −0.239844 | − | 0.970811i | \(-0.577096\pi\) | ||||
−0.239844 | + | 0.970811i | \(0.577096\pi\) | |||||||
\(434\) | −18.5064 | −0.888336 | ||||||||
\(435\) | 12.0962 | 0.579966 | ||||||||
\(436\) | 19.7191 | 0.944372 | ||||||||
\(437\) | −15.7600 | −0.753904 | ||||||||
\(438\) | −20.1855 | −0.964499 | ||||||||
\(439\) | −27.2149 | −1.29890 | −0.649448 | − | 0.760406i | \(-0.725000\pi\) | ||||
−0.649448 | + | 0.760406i | \(0.725000\pi\) | |||||||
\(440\) | 13.5400 | 0.645492 | ||||||||
\(441\) | 2.79328 | 0.133013 | ||||||||
\(442\) | 4.40554 | 0.209550 | ||||||||
\(443\) | 24.2809 | 1.15362 | 0.576809 | − | 0.816879i | \(-0.304298\pi\) | ||||
0.576809 | + | 0.816879i | \(0.304298\pi\) | |||||||
\(444\) | 9.46067 | 0.448983 | ||||||||
\(445\) | 29.2895 | 1.38846 | ||||||||
\(446\) | −19.7205 | −0.933792 | ||||||||
\(447\) | 11.0650 | 0.523359 | ||||||||
\(448\) | 2.18258 | 0.103117 | ||||||||
\(449\) | 26.3995 | 1.24587 | 0.622935 | − | 0.782273i | \(-0.285940\pi\) | ||||
0.622935 | + | 0.782273i | \(0.285940\pi\) | |||||||
\(450\) | 0.745144 | 0.0351264 | ||||||||
\(451\) | 72.5854 | 3.41791 | ||||||||
\(452\) | −3.94098 | −0.185368 | ||||||||
\(453\) | −8.29398 | −0.389685 | ||||||||
\(454\) | −17.9668 | −0.843222 | ||||||||
\(455\) | 3.06199 | 0.143548 | ||||||||
\(456\) | −4.71244 | −0.220680 | ||||||||
\(457\) | 10.6999 | 0.500519 | 0.250259 | − | 0.968179i | \(-0.419484\pi\) | ||||
0.250259 | + | 0.968179i | \(0.419484\pi\) | |||||||
\(458\) | −17.6093 | −0.822830 | ||||||||
\(459\) | −41.7691 | −1.94961 | ||||||||
\(460\) | 10.4691 | 0.488126 | ||||||||
\(461\) | −18.6750 | −0.869782 | −0.434891 | − | 0.900483i | \(-0.643213\pi\) | ||||
−0.434891 | + | 0.900483i | \(0.643213\pi\) | |||||||
\(462\) | −16.5297 | −0.769031 | ||||||||
\(463\) | −14.4416 | −0.671159 | −0.335580 | − | 0.942012i | \(-0.608932\pi\) | ||||
−0.335580 | + | 0.942012i | \(0.608932\pi\) | |||||||
\(464\) | −3.86409 | −0.179386 | ||||||||
\(465\) | −26.5431 | −1.23091 | ||||||||
\(466\) | −11.8245 | −0.547760 | ||||||||
\(467\) | −30.2858 | −1.40146 | −0.700730 | − | 0.713427i | \(-0.747142\pi\) | ||||
−0.700730 | + | 0.713427i | \(0.747142\pi\) | |||||||
\(468\) | −0.740707 | −0.0342392 | ||||||||
\(469\) | 17.5531 | 0.810529 | ||||||||
\(470\) | 11.1529 | 0.514444 | ||||||||
\(471\) | −30.3310 | −1.39758 | ||||||||
\(472\) | −12.6925 | −0.584218 | ||||||||
\(473\) | −8.97846 | −0.412830 | ||||||||
\(474\) | −11.6512 | −0.535159 | ||||||||
\(475\) | −2.12458 | −0.0974824 | ||||||||
\(476\) | −16.2142 | −0.743177 | ||||||||
\(477\) | −3.03329 | −0.138885 | ||||||||
\(478\) | −12.3656 | −0.565590 | ||||||||
\(479\) | 0.0429468 | 0.00196229 | 0.000981144 | − | 1.00000i | \(-0.499688\pi\) | ||||
0.000981144 | 1.00000i | \(0.499688\pi\) | ||||||||
\(480\) | 3.13040 | 0.142883 | ||||||||
\(481\) | −4.23990 | −0.193323 | ||||||||
\(482\) | 13.7153 | 0.624716 | ||||||||
\(483\) | −12.7808 | −0.581548 | ||||||||
\(484\) | 21.7576 | 0.988983 | ||||||||
\(485\) | 2.28469 | 0.103742 | ||||||||
\(486\) | 11.9810 | 0.543469 | ||||||||
\(487\) | −41.6315 | −1.88650 | −0.943251 | − | 0.332082i | \(-0.892249\pi\) | ||||
−0.943251 | + | 0.332082i | \(0.892249\pi\) | |||||||
\(488\) | 3.35111 | 0.151698 | ||||||||
\(489\) | 26.3960 | 1.19367 | ||||||||
\(490\) | 5.29056 | 0.239003 | ||||||||
\(491\) | −1.62707 | −0.0734288 | −0.0367144 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367144 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(492\) | 16.7816 | 0.756571 | ||||||||
\(493\) | 28.7060 | 1.29286 | ||||||||
\(494\) | 2.11193 | 0.0950202 | ||||||||
\(495\) | 16.9119 | 0.760131 | ||||||||
\(496\) | 8.47915 | 0.380725 | ||||||||
\(497\) | −16.0984 | −0.722114 | ||||||||
\(498\) | −15.2791 | −0.684674 | ||||||||
\(499\) | 4.86937 | 0.217983 | 0.108992 | − | 0.994043i | \(-0.465238\pi\) | ||||
0.108992 | + | 0.994043i | \(0.465238\pi\) | |||||||
\(500\) | −10.4172 | −0.465872 | ||||||||
\(501\) | 6.04913 | 0.270255 | ||||||||
\(502\) | 2.70050 | 0.120529 | ||||||||
\(503\) | 20.7085 | 0.923345 | 0.461672 | − | 0.887050i | \(-0.347250\pi\) | ||||
0.461672 | + | 0.887050i | \(0.347250\pi\) | |||||||
\(504\) | 2.72611 | 0.121431 | ||||||||
\(505\) | 8.34105 | 0.371172 | ||||||||
\(506\) | 25.3283 | 1.12598 | ||||||||
\(507\) | 16.7368 | 0.743306 | ||||||||
\(508\) | −22.2288 | −0.986245 | ||||||||
\(509\) | 23.7710 | 1.05363 | 0.526815 | − | 0.849980i | \(-0.323386\pi\) | ||||
0.526815 | + | 0.849980i | \(0.323386\pi\) | |||||||
\(510\) | −23.2555 | −1.02977 | ||||||||
\(511\) | −33.2943 | −1.47285 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −20.0233 | −0.884050 | ||||||||
\(514\) | −10.3529 | −0.456648 | ||||||||
\(515\) | −4.52930 | −0.199585 | ||||||||
\(516\) | −2.07580 | −0.0913819 | ||||||||
\(517\) | 26.9825 | 1.18669 | ||||||||
\(518\) | 15.6046 | 0.685627 | ||||||||
\(519\) | 11.6966 | 0.513425 | ||||||||
\(520\) | −1.40292 | −0.0615223 | ||||||||
\(521\) | −3.43809 | −0.150625 | −0.0753126 | − | 0.997160i | \(-0.523995\pi\) | ||||
−0.0753126 | + | 0.997160i | \(0.523995\pi\) | |||||||
\(522\) | −4.82638 | −0.211245 | ||||||||
\(523\) | 0.672956 | 0.0294263 | 0.0147131 | − | 0.999892i | \(-0.495316\pi\) | ||||
0.0147131 | + | 0.999892i | \(0.495316\pi\) | |||||||
\(524\) | 14.6039 | 0.637972 | ||||||||
\(525\) | −1.72296 | −0.0751962 | ||||||||
\(526\) | −3.77652 | −0.164664 | ||||||||
\(527\) | −62.9910 | −2.74393 | ||||||||
\(528\) | 7.57347 | 0.329593 | ||||||||
\(529\) | −3.41606 | −0.148525 | ||||||||
\(530\) | −5.74515 | −0.249553 | ||||||||
\(531\) | −15.8533 | −0.687975 | ||||||||
\(532\) | −7.77278 | −0.336993 | ||||||||
\(533\) | −7.52083 | −0.325763 | ||||||||
\(534\) | 16.3829 | 0.708956 | ||||||||
\(535\) | −41.8814 | −1.81069 | ||||||||
\(536\) | −8.04239 | −0.347378 | ||||||||
\(537\) | 6.73990 | 0.290848 | ||||||||
\(538\) | 4.24877 | 0.183178 | ||||||||
\(539\) | 12.7996 | 0.551318 | ||||||||
\(540\) | 13.3012 | 0.572392 | ||||||||
\(541\) | 15.9853 | 0.687261 | 0.343631 | − | 0.939105i | \(-0.388343\pi\) | ||||
0.343631 | + | 0.939105i | \(0.388343\pi\) | |||||||
\(542\) | −24.6332 | −1.05808 | ||||||||
\(543\) | 16.0570 | 0.689071 | ||||||||
\(544\) | 7.42893 | 0.318513 | ||||||||
\(545\) | 46.6496 | 1.99825 | ||||||||
\(546\) | 1.71270 | 0.0732968 | ||||||||
\(547\) | −28.7279 | −1.22831 | −0.614157 | − | 0.789184i | \(-0.710504\pi\) | ||||
−0.614157 | + | 0.789184i | \(0.710504\pi\) | |||||||
\(548\) | 12.2027 | 0.521275 | ||||||||
\(549\) | 4.18565 | 0.178639 | ||||||||
\(550\) | 3.41447 | 0.145593 | ||||||||
\(551\) | 13.7611 | 0.586244 | ||||||||
\(552\) | 5.85584 | 0.249241 | ||||||||
\(553\) | −19.2178 | −0.817222 | ||||||||
\(554\) | −23.1348 | −0.982904 | ||||||||
\(555\) | 22.3812 | 0.950028 | ||||||||
\(556\) | 8.96165 | 0.380059 | ||||||||
\(557\) | 3.90284 | 0.165369 | 0.0826844 | − | 0.996576i | \(-0.473651\pi\) | ||||
0.0826844 | + | 0.996576i | \(0.473651\pi\) | |||||||
\(558\) | 10.5907 | 0.448342 | ||||||||
\(559\) | 0.930290 | 0.0393471 | ||||||||
\(560\) | 5.16334 | 0.218191 | ||||||||
\(561\) | −56.2628 | −2.37542 | ||||||||
\(562\) | 18.9945 | 0.801234 | ||||||||
\(563\) | −4.35913 | −0.183715 | −0.0918576 | − | 0.995772i | \(-0.529280\pi\) | ||||
−0.0918576 | + | 0.995772i | \(0.529280\pi\) | |||||||
\(564\) | 6.23828 | 0.262679 | ||||||||
\(565\) | −9.32322 | −0.392231 | ||||||||
\(566\) | 1.54158 | 0.0647976 | ||||||||
\(567\) | −8.05986 | −0.338482 | ||||||||
\(568\) | 7.37588 | 0.309485 | ||||||||
\(569\) | −20.2849 | −0.850388 | −0.425194 | − | 0.905102i | \(-0.639794\pi\) | ||||
−0.425194 | + | 0.905102i | \(0.639794\pi\) | |||||||
\(570\) | −11.1483 | −0.466949 | ||||||||
\(571\) | 22.4985 | 0.941535 | 0.470767 | − | 0.882257i | \(-0.343977\pi\) | ||||
0.470767 | + | 0.882257i | \(0.343977\pi\) | |||||||
\(572\) | −3.39413 | −0.141916 | ||||||||
\(573\) | −1.57400 | −0.0657547 | ||||||||
\(574\) | 27.6798 | 1.15533 | ||||||||
\(575\) | 2.64008 | 0.110099 | ||||||||
\(576\) | −1.24903 | −0.0520430 | ||||||||
\(577\) | −16.7727 | −0.698257 | −0.349128 | − | 0.937075i | \(-0.613522\pi\) | ||||
−0.349128 | + | 0.937075i | \(0.613522\pi\) | |||||||
\(578\) | −38.1889 | −1.58845 | ||||||||
\(579\) | −4.57374 | −0.190078 | ||||||||
\(580\) | −9.14131 | −0.379572 | ||||||||
\(581\) | −25.2017 | −1.04554 | ||||||||
\(582\) | 1.27792 | 0.0529717 | ||||||||
\(583\) | −13.8994 | −0.575655 | ||||||||
\(584\) | 15.2546 | 0.631239 | ||||||||
\(585\) | −1.75230 | −0.0724486 | ||||||||
\(586\) | 12.0162 | 0.496383 | ||||||||
\(587\) | 14.1911 | 0.585728 | 0.292864 | − | 0.956154i | \(-0.405392\pi\) | ||||
0.292864 | + | 0.956154i | \(0.405392\pi\) | |||||||
\(588\) | 2.95923 | 0.122037 | ||||||||
\(589\) | −30.1967 | −1.24423 | ||||||||
\(590\) | −30.0267 | −1.23618 | ||||||||
\(591\) | 27.2821 | 1.12224 | ||||||||
\(592\) | −7.14962 | −0.293847 | ||||||||
\(593\) | 13.6825 | 0.561874 | 0.280937 | − | 0.959726i | \(-0.409355\pi\) | ||||
0.280937 | + | 0.959726i | \(0.409355\pi\) | |||||||
\(594\) | 32.1799 | 1.32036 | ||||||||
\(595\) | −38.3581 | −1.57253 | ||||||||
\(596\) | −8.36208 | −0.342524 | ||||||||
\(597\) | −7.01308 | −0.287026 | ||||||||
\(598\) | −2.62436 | −0.107318 | ||||||||
\(599\) | 17.5662 | 0.717734 | 0.358867 | − | 0.933389i | \(-0.383163\pi\) | ||||
0.358867 | + | 0.933389i | \(0.383163\pi\) | |||||||
\(600\) | 0.789415 | 0.0322277 | ||||||||
\(601\) | −33.7469 | −1.37657 | −0.688283 | − | 0.725442i | \(-0.741635\pi\) | ||||
−0.688283 | + | 0.725442i | \(0.741635\pi\) | |||||||
\(602\) | −3.42386 | −0.139546 | ||||||||
\(603\) | −10.0452 | −0.409072 | ||||||||
\(604\) | 6.26793 | 0.255039 | ||||||||
\(605\) | 51.4722 | 2.09264 | ||||||||
\(606\) | 4.66550 | 0.189523 | ||||||||
\(607\) | 30.9610 | 1.25667 | 0.628334 | − | 0.777944i | \(-0.283737\pi\) | ||||
0.628334 | + | 0.777944i | \(0.283737\pi\) | |||||||
\(608\) | 3.56128 | 0.144429 | ||||||||
\(609\) | 11.1598 | 0.452218 | ||||||||
\(610\) | 7.92776 | 0.320986 | ||||||||
\(611\) | −2.79575 | −0.113104 | ||||||||
\(612\) | 9.27897 | 0.375080 | ||||||||
\(613\) | 25.8630 | 1.04460 | 0.522298 | − | 0.852763i | \(-0.325075\pi\) | ||||
0.522298 | + | 0.852763i | \(0.325075\pi\) | |||||||
\(614\) | −21.2277 | −0.856679 | ||||||||
\(615\) | 39.7003 | 1.60087 | ||||||||
\(616\) | 12.4918 | 0.503310 | ||||||||
\(617\) | 0.765560 | 0.0308203 | 0.0154101 | − | 0.999881i | \(-0.495095\pi\) | ||||
0.0154101 | + | 0.999881i | \(0.495095\pi\) | |||||||
\(618\) | −2.53343 | −0.101910 | ||||||||
\(619\) | 36.1339 | 1.45234 | 0.726172 | − | 0.687513i | \(-0.241298\pi\) | ||||
0.726172 | + | 0.687513i | \(0.241298\pi\) | |||||||
\(620\) | 20.0592 | 0.805597 | ||||||||
\(621\) | 24.8816 | 0.998466 | ||||||||
\(622\) | −2.44107 | −0.0978778 | ||||||||
\(623\) | 27.0222 | 1.08262 | ||||||||
\(624\) | −0.784714 | −0.0314137 | ||||||||
\(625\) | −27.6270 | −1.10508 | ||||||||
\(626\) | 25.8091 | 1.03154 | ||||||||
\(627\) | −26.9713 | −1.07713 | ||||||||
\(628\) | 22.9217 | 0.914676 | ||||||||
\(629\) | 53.1140 | 2.11779 | ||||||||
\(630\) | 6.44919 | 0.256942 | ||||||||
\(631\) | −15.0437 | −0.598880 | −0.299440 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299440 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(632\) | 8.80507 | 0.350247 | ||||||||
\(633\) | 4.21557 | 0.167554 | ||||||||
\(634\) | 9.80038 | 0.389223 | ||||||||
\(635\) | −52.5869 | −2.08685 | ||||||||
\(636\) | −3.21351 | −0.127424 | ||||||||
\(637\) | −1.32621 | −0.0525464 | ||||||||
\(638\) | −22.1158 | −0.875574 | ||||||||
\(639\) | 9.21272 | 0.364450 | ||||||||
\(640\) | −2.36571 | −0.0935128 | ||||||||
\(641\) | 21.3475 | 0.843177 | 0.421588 | − | 0.906787i | \(-0.361473\pi\) | ||||
0.421588 | + | 0.906787i | \(0.361473\pi\) | |||||||
\(642\) | −23.4260 | −0.924551 | ||||||||
\(643\) | −7.76561 | −0.306246 | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||||
−0.153123 | + | 0.988207i | \(0.548933\pi\) | |||||||
\(644\) | 9.65873 | 0.380607 | ||||||||
\(645\) | −4.91073 | −0.193360 | ||||||||
\(646\) | −26.4565 | −1.04092 | ||||||||
\(647\) | −35.7626 | −1.40597 | −0.702987 | − | 0.711202i | \(-0.748151\pi\) | ||||
−0.702987 | + | 0.711202i | \(0.748151\pi\) | |||||||
\(648\) | 3.69282 | 0.145068 | ||||||||
\(649\) | −72.6444 | −2.85154 | ||||||||
\(650\) | −0.353785 | −0.0138766 | ||||||||
\(651\) | −24.4884 | −0.959777 | ||||||||
\(652\) | −19.9480 | −0.781224 | ||||||||
\(653\) | 3.14562 | 0.123098 | 0.0615489 | − | 0.998104i | \(-0.480396\pi\) | ||||
0.0615489 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(654\) | 26.0931 | 1.02032 | ||||||||
\(655\) | 34.5485 | 1.34992 | ||||||||
\(656\) | −12.6822 | −0.495155 | ||||||||
\(657\) | 19.0535 | 0.743346 | ||||||||
\(658\) | 10.2895 | 0.401128 | ||||||||
\(659\) | 44.1737 | 1.72076 | 0.860381 | − | 0.509652i | \(-0.170226\pi\) | ||||
0.860381 | + | 0.509652i | \(0.170226\pi\) | |||||||
\(660\) | 17.9166 | 0.697404 | ||||||||
\(661\) | −37.4340 | −1.45602 | −0.728008 | − | 0.685569i | \(-0.759554\pi\) | ||||
−0.728008 | + | 0.685569i | \(0.759554\pi\) | |||||||
\(662\) | −8.07682 | −0.313915 | ||||||||
\(663\) | 5.82959 | 0.226402 | ||||||||
\(664\) | 11.5468 | 0.448101 | ||||||||
\(665\) | −18.3881 | −0.713061 | ||||||||
\(666\) | −8.93011 | −0.346035 | ||||||||
\(667\) | −17.1000 | −0.662116 | ||||||||
\(668\) | −4.57145 | −0.176875 | ||||||||
\(669\) | −26.0949 | −1.00889 | ||||||||
\(670\) | −19.0259 | −0.735036 | ||||||||
\(671\) | 19.1799 | 0.740430 | ||||||||
\(672\) | 2.88808 | 0.111410 | ||||||||
\(673\) | −26.4710 | −1.02038 | −0.510192 | − | 0.860061i | \(-0.670426\pi\) | ||||
−0.510192 | + | 0.860061i | \(0.670426\pi\) | |||||||
\(674\) | −18.9338 | −0.729304 | ||||||||
\(675\) | 3.35425 | 0.129105 | ||||||||
\(676\) | −12.6483 | −0.486474 | ||||||||
\(677\) | −9.66859 | −0.371594 | −0.185797 | − | 0.982588i | \(-0.559487\pi\) | ||||
−0.185797 | + | 0.982588i | \(0.559487\pi\) | |||||||
\(678\) | −5.21487 | −0.200276 | ||||||||
\(679\) | 2.10783 | 0.0808911 | ||||||||
\(680\) | 17.5747 | 0.673958 | ||||||||
\(681\) | −23.7744 | −0.911036 | ||||||||
\(682\) | 48.5298 | 1.85830 | ||||||||
\(683\) | −12.9638 | −0.496046 | −0.248023 | − | 0.968754i | \(-0.579781\pi\) | ||||
−0.248023 | + | 0.968754i | \(0.579781\pi\) | |||||||
\(684\) | 4.44816 | 0.170080 | ||||||||
\(685\) | 28.8681 | 1.10299 | ||||||||
\(686\) | 20.1591 | 0.769677 | ||||||||
\(687\) | −23.3014 | −0.889004 | ||||||||
\(688\) | 1.56872 | 0.0598069 | ||||||||
\(689\) | 1.44017 | 0.0548660 | ||||||||
\(690\) | 13.8532 | 0.527382 | ||||||||
\(691\) | −36.6557 | −1.39445 | −0.697224 | − | 0.716853i | \(-0.745582\pi\) | ||||
−0.697224 | + | 0.716853i | \(0.745582\pi\) | |||||||
\(692\) | −8.83938 | −0.336023 | ||||||||
\(693\) | 15.6027 | 0.592698 | ||||||||
\(694\) | −5.40719 | −0.205254 | ||||||||
\(695\) | 21.2007 | 0.804187 | ||||||||
\(696\) | −5.11312 | −0.193812 | ||||||||
\(697\) | 94.2148 | 3.56864 | ||||||||
\(698\) | −15.9428 | −0.603442 | ||||||||
\(699\) | −15.6467 | −0.591812 | ||||||||
\(700\) | 1.30208 | 0.0492139 | ||||||||
\(701\) | 12.1479 | 0.458819 | 0.229409 | − | 0.973330i | \(-0.426321\pi\) | ||||
0.229409 | + | 0.973330i | \(0.426321\pi\) | |||||||
\(702\) | −3.33428 | −0.125844 | ||||||||
\(703\) | 25.4618 | 0.960311 | ||||||||
\(704\) | −5.72343 | −0.215710 | ||||||||
\(705\) | 14.7579 | 0.555816 | ||||||||
\(706\) | 29.7808 | 1.12082 | ||||||||
\(707\) | 7.69537 | 0.289414 | ||||||||
\(708\) | −16.7952 | −0.631202 | ||||||||
\(709\) | −23.8247 | −0.894757 | −0.447378 | − | 0.894345i | \(-0.647642\pi\) | ||||
−0.447378 | + | 0.894345i | \(0.647642\pi\) | |||||||
\(710\) | 17.4492 | 0.654856 | ||||||||
\(711\) | 10.9978 | 0.412451 | ||||||||
\(712\) | −12.3809 | −0.463993 | ||||||||
\(713\) | 37.5234 | 1.40526 | ||||||||
\(714\) | −21.4553 | −0.802945 | ||||||||
\(715\) | −8.02953 | −0.300287 | ||||||||
\(716\) | −5.09347 | −0.190352 | ||||||||
\(717\) | −16.3627 | −0.611076 | ||||||||
\(718\) | 6.81817 | 0.254452 | ||||||||
\(719\) | 51.7817 | 1.93113 | 0.965566 | − | 0.260157i | \(-0.0837742\pi\) | ||||
0.965566 | + | 0.260157i | \(0.0837742\pi\) | |||||||
\(720\) | −2.95485 | −0.110121 | ||||||||
\(721\) | −4.17869 | −0.155623 | ||||||||
\(722\) | 6.31726 | 0.235104 | ||||||||
\(723\) | 18.1487 | 0.674957 | ||||||||
\(724\) | −12.1346 | −0.450978 | ||||||||
\(725\) | −2.30523 | −0.0856140 | ||||||||
\(726\) | 28.7906 | 1.06852 | ||||||||
\(727\) | −33.7167 | −1.25048 | −0.625242 | − | 0.780431i | \(-0.715000\pi\) | ||||
−0.625242 | + | 0.780431i | \(0.715000\pi\) | |||||||
\(728\) | −1.29432 | −0.0479708 | ||||||||
\(729\) | 26.9322 | 0.997489 | ||||||||
\(730\) | 36.0879 | 1.33567 | ||||||||
\(731\) | −11.6539 | −0.431036 | ||||||||
\(732\) | 4.43433 | 0.163898 | ||||||||
\(733\) | 8.77700 | 0.324186 | 0.162093 | − | 0.986775i | \(-0.448176\pi\) | ||||
0.162093 | + | 0.986775i | \(0.448176\pi\) | |||||||
\(734\) | 7.69745 | 0.284118 | ||||||||
\(735\) | 7.00068 | 0.258224 | ||||||||
\(736\) | −4.42537 | −0.163121 | ||||||||
\(737\) | −46.0300 | −1.69554 | ||||||||
\(738\) | −15.8404 | −0.583095 | ||||||||
\(739\) | −26.4394 | −0.972590 | −0.486295 | − | 0.873795i | \(-0.661652\pi\) | ||||
−0.486295 | + | 0.873795i | \(0.661652\pi\) | |||||||
\(740\) | −16.9139 | −0.621768 | ||||||||
\(741\) | 2.79459 | 0.102662 | ||||||||
\(742\) | −5.30042 | −0.194584 | ||||||||
\(743\) | −13.4713 | −0.494213 | −0.247106 | − | 0.968988i | \(-0.579480\pi\) | ||||
−0.247106 | + | 0.968988i | \(0.579480\pi\) | |||||||
\(744\) | 11.2200 | 0.411344 | ||||||||
\(745\) | −19.7822 | −0.724765 | ||||||||
\(746\) | −20.9846 | −0.768302 | ||||||||
\(747\) | 14.4223 | 0.527683 | ||||||||
\(748\) | 42.5189 | 1.55465 | ||||||||
\(749\) | −38.6393 | −1.41185 | ||||||||
\(750\) | −13.7845 | −0.503338 | ||||||||
\(751\) | 16.7382 | 0.610786 | 0.305393 | − | 0.952226i | \(-0.401212\pi\) | ||||
0.305393 | + | 0.952226i | \(0.401212\pi\) | |||||||
\(752\) | −4.71439 | −0.171916 | ||||||||
\(753\) | 3.57341 | 0.130222 | ||||||||
\(754\) | 2.29150 | 0.0834515 | ||||||||
\(755\) | 14.8281 | 0.539650 | ||||||||
\(756\) | 12.2715 | 0.446311 | ||||||||
\(757\) | −32.9806 | −1.19870 | −0.599349 | − | 0.800488i | \(-0.704574\pi\) | ||||
−0.599349 | + | 0.800488i | \(0.704574\pi\) | |||||||
\(758\) | −12.4153 | −0.450943 | ||||||||
\(759\) | 33.5155 | 1.21653 | ||||||||
\(760\) | 8.42496 | 0.305605 | ||||||||
\(761\) | −8.96721 | −0.325061 | −0.162531 | − | 0.986704i | \(-0.551966\pi\) | ||||
−0.162531 | + | 0.986704i | \(0.551966\pi\) | |||||||
\(762\) | −29.4141 | −1.06556 | ||||||||
\(763\) | 43.0384 | 1.55810 | ||||||||
\(764\) | 1.18950 | 0.0430347 | ||||||||
\(765\) | 21.9513 | 0.793653 | ||||||||
\(766\) | 23.3716 | 0.844450 | ||||||||
\(767\) | 7.52695 | 0.271782 | ||||||||
\(768\) | −1.32324 | −0.0477484 | ||||||||
\(769\) | 29.6941 | 1.07080 | 0.535399 | − | 0.844600i | \(-0.320161\pi\) | ||||
0.535399 | + | 0.844600i | \(0.320161\pi\) | |||||||
\(770\) | 29.5520 | 1.06498 | ||||||||
\(771\) | −13.6994 | −0.493372 | ||||||||
\(772\) | 3.45647 | 0.124401 | ||||||||
\(773\) | −35.8550 | −1.28962 | −0.644808 | − | 0.764345i | \(-0.723063\pi\) | ||||
−0.644808 | + | 0.764345i | \(0.723063\pi\) | |||||||
\(774\) | 1.95938 | 0.0704286 | ||||||||
\(775\) | 5.05846 | 0.181705 | ||||||||
\(776\) | −0.965753 | −0.0346685 | ||||||||
\(777\) | 20.6486 | 0.740766 | ||||||||
\(778\) | −5.61282 | −0.201229 | ||||||||
\(779\) | 45.1648 | 1.61820 | ||||||||
\(780\) | −1.85641 | −0.0664700 | ||||||||
\(781\) | 42.2153 | 1.51058 | ||||||||
\(782\) | 32.8758 | 1.17564 | ||||||||
\(783\) | −21.7258 | −0.776418 | ||||||||
\(784\) | −2.23635 | −0.0798697 | ||||||||
\(785\) | 54.2261 | 1.93541 | ||||||||
\(786\) | 19.3244 | 0.689279 | ||||||||
\(787\) | −26.6006 | −0.948209 | −0.474105 | − | 0.880469i | \(-0.657228\pi\) | ||||
−0.474105 | + | 0.880469i | \(0.657228\pi\) | |||||||
\(788\) | −20.6176 | −0.734473 | ||||||||
\(789\) | −4.99724 | −0.177907 | ||||||||
\(790\) | 20.8302 | 0.741107 | ||||||||
\(791\) | −8.60150 | −0.305834 | ||||||||
\(792\) | −7.14875 | −0.254020 | ||||||||
\(793\) | −1.98729 | −0.0705708 | ||||||||
\(794\) | −36.8075 | −1.30625 | ||||||||
\(795\) | −7.60222 | −0.269623 | ||||||||
\(796\) | 5.29993 | 0.187851 | ||||||||
\(797\) | −8.86760 | −0.314106 | −0.157053 | − | 0.987590i | \(-0.550199\pi\) | ||||
−0.157053 | + | 0.987590i | \(0.550199\pi\) | |||||||
\(798\) | −10.2853 | −0.364094 | ||||||||
\(799\) | 35.0229 | 1.23902 | ||||||||
\(800\) | −0.596577 | −0.0210922 | ||||||||
\(801\) | −15.4641 | −0.546398 | ||||||||
\(802\) | −14.0637 | −0.496605 | ||||||||
\(803\) | 87.3084 | 3.08105 | ||||||||
\(804\) | −10.6420 | −0.375315 | ||||||||
\(805\) | 22.8497 | 0.805347 | ||||||||
\(806\) | −5.02834 | −0.177116 | ||||||||
\(807\) | 5.62215 | 0.197909 | ||||||||
\(808\) | −3.52582 | −0.124038 | ||||||||
\(809\) | 45.4475 | 1.59785 | 0.798924 | − | 0.601432i | \(-0.205403\pi\) | ||||
0.798924 | + | 0.601432i | \(0.205403\pi\) | |||||||
\(810\) | 8.73613 | 0.306956 | ||||||||
\(811\) | 5.95170 | 0.208992 | 0.104496 | − | 0.994525i | \(-0.466677\pi\) | ||||
0.104496 | + | 0.994525i | \(0.466677\pi\) | |||||||
\(812\) | −8.43368 | −0.295964 | ||||||||
\(813\) | −32.5956 | −1.14318 | ||||||||
\(814\) | −40.9203 | −1.43426 | ||||||||
\(815\) | −47.1911 | −1.65303 | ||||||||
\(816\) | 9.83026 | 0.344128 | ||||||||
\(817\) | −5.58666 | −0.195453 | ||||||||
\(818\) | 11.0305 | 0.385672 | ||||||||
\(819\) | −1.61665 | −0.0564904 | ||||||||
\(820\) | −30.0023 | −1.04773 | ||||||||
\(821\) | 8.02465 | 0.280062 | 0.140031 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140031 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(822\) | 16.1472 | 0.563197 | ||||||||
\(823\) | 32.4142 | 1.12989 | 0.564944 | − | 0.825129i | \(-0.308898\pi\) | ||||
0.564944 | + | 0.825129i | \(0.308898\pi\) | |||||||
\(824\) | 1.91457 | 0.0666970 | ||||||||
\(825\) | 4.51816 | 0.157302 | ||||||||
\(826\) | −27.7023 | −0.963887 | ||||||||
\(827\) | 21.4478 | 0.745815 | 0.372907 | − | 0.927869i | \(-0.378361\pi\) | ||||
0.372907 | + | 0.927869i | \(0.378361\pi\) | |||||||
\(828\) | −5.52744 | −0.192092 | ||||||||
\(829\) | −5.93889 | −0.206266 | −0.103133 | − | 0.994668i | \(-0.532887\pi\) | ||||
−0.103133 | + | 0.994668i | \(0.532887\pi\) | |||||||
\(830\) | 27.3162 | 0.948161 | ||||||||
\(831\) | −30.6129 | −1.06195 | ||||||||
\(832\) | 0.593025 | 0.0205594 | ||||||||
\(833\) | 16.6137 | 0.575630 | ||||||||
\(834\) | 11.8584 | 0.410624 | ||||||||
\(835\) | −10.8147 | −0.374259 | ||||||||
\(836\) | 20.3827 | 0.704952 | ||||||||
\(837\) | 47.6740 | 1.64785 | ||||||||
\(838\) | −21.0666 | −0.727735 | ||||||||
\(839\) | 7.56223 | 0.261077 | 0.130539 | − | 0.991443i | \(-0.458329\pi\) | ||||
0.130539 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(840\) | 6.83235 | 0.235738 | ||||||||
\(841\) | −14.0688 | −0.485131 | ||||||||
\(842\) | 29.5821 | 1.01947 | ||||||||
\(843\) | 25.1343 | 0.865671 | ||||||||
\(844\) | −3.18579 | −0.109660 | ||||||||
\(845\) | −29.9222 | −1.02936 | ||||||||
\(846\) | −5.88843 | −0.202448 | ||||||||
\(847\) | 47.4877 | 1.63170 | ||||||||
\(848\) | 2.42851 | 0.0833954 | ||||||||
\(849\) | 2.03989 | 0.0700087 | ||||||||
\(850\) | 4.43193 | 0.152014 | ||||||||
\(851\) | −31.6397 | −1.08460 | ||||||||
\(852\) | 9.76007 | 0.334375 | ||||||||
\(853\) | −5.84755 | −0.200216 | −0.100108 | − | 0.994977i | \(-0.531919\pi\) | ||||
−0.100108 | + | 0.994977i | \(0.531919\pi\) | |||||||
\(854\) | 7.31407 | 0.250282 | ||||||||
\(855\) | 10.5231 | 0.359881 | ||||||||
\(856\) | 17.7035 | 0.605094 | ||||||||
\(857\) | 0.0905027 | 0.00309151 | 0.00154576 | − | 0.999999i | \(-0.499508\pi\) | ||||
0.00154576 | + | 0.999999i | \(0.499508\pi\) | |||||||
\(858\) | −4.49126 | −0.153329 | ||||||||
\(859\) | 48.3590 | 1.64999 | 0.824994 | − | 0.565142i | \(-0.191179\pi\) | ||||
0.824994 | + | 0.565142i | \(0.191179\pi\) | |||||||
\(860\) | 3.71114 | 0.126549 | ||||||||
\(861\) | 36.6271 | 1.24825 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −50.2436 | −1.71031 | −0.855155 | − | 0.518372i | \(-0.826538\pi\) | ||||
−0.855155 | + | 0.518372i | \(0.826538\pi\) | |||||||
\(864\) | −5.62250 | −0.191281 | ||||||||
\(865\) | −20.9114 | −0.711009 | ||||||||
\(866\) | 9.98168 | 0.339191 | ||||||||
\(867\) | −50.5332 | −1.71620 | ||||||||
\(868\) | 18.5064 | 0.628148 | ||||||||
\(869\) | 50.3952 | 1.70954 | ||||||||
\(870\) | −12.0962 | −0.410098 | ||||||||
\(871\) | 4.76933 | 0.161603 | ||||||||
\(872\) | −19.7191 | −0.667772 | ||||||||
\(873\) | −1.20626 | −0.0408256 | ||||||||
\(874\) | 15.7600 | 0.533090 | ||||||||
\(875\) | −22.7364 | −0.768630 | ||||||||
\(876\) | 20.1855 | 0.682004 | ||||||||
\(877\) | −39.2087 | −1.32398 | −0.661992 | − | 0.749511i | \(-0.730289\pi\) | ||||
−0.661992 | + | 0.749511i | \(0.730289\pi\) | |||||||
\(878\) | 27.2149 | 0.918458 | ||||||||
\(879\) | 15.9003 | 0.536303 | ||||||||
\(880\) | −13.5400 | −0.456432 | ||||||||
\(881\) | −53.7477 | −1.81081 | −0.905403 | − | 0.424554i | \(-0.860431\pi\) | ||||
−0.905403 | + | 0.424554i | \(0.860431\pi\) | |||||||
\(882\) | −2.79328 | −0.0940545 | ||||||||
\(883\) | 2.65639 | 0.0893947 | 0.0446973 | − | 0.999001i | \(-0.485768\pi\) | ||||
0.0446973 | + | 0.999001i | \(0.485768\pi\) | |||||||
\(884\) | −4.40554 | −0.148174 | ||||||||
\(885\) | −39.7326 | −1.33560 | ||||||||
\(886\) | −24.2809 | −0.815732 | ||||||||
\(887\) | −24.4649 | −0.821451 | −0.410725 | − | 0.911759i | \(-0.634725\pi\) | ||||
−0.410725 | + | 0.911759i | \(0.634725\pi\) | |||||||
\(888\) | −9.46067 | −0.317479 | ||||||||
\(889\) | −48.5162 | −1.62718 | ||||||||
\(890\) | −29.2895 | −0.981787 | ||||||||
\(891\) | 21.1356 | 0.708068 | ||||||||
\(892\) | 19.7205 | 0.660290 | ||||||||
\(893\) | 16.7893 | 0.561832 | ||||||||
\(894\) | −11.0650 | −0.370071 | ||||||||
\(895\) | −12.0497 | −0.402776 | ||||||||
\(896\) | −2.18258 | −0.0729148 | ||||||||
\(897\) | −3.47265 | −0.115949 | ||||||||
\(898\) | −26.3995 | −0.880963 | ||||||||
\(899\) | −32.7642 | −1.09275 | ||||||||
\(900\) | −0.745144 | −0.0248381 | ||||||||
\(901\) | −18.0412 | −0.601041 | ||||||||
\(902\) | −72.5854 | −2.41683 | ||||||||
\(903\) | −4.53059 | −0.150769 | ||||||||
\(904\) | 3.94098 | 0.131075 | ||||||||
\(905\) | −28.7069 | −0.954249 | ||||||||
\(906\) | 8.29398 | 0.275549 | ||||||||
\(907\) | 5.42034 | 0.179979 | 0.0899897 | − | 0.995943i | \(-0.471317\pi\) | ||||
0.0899897 | + | 0.995943i | \(0.471317\pi\) | |||||||
\(908\) | 17.9668 | 0.596248 | ||||||||
\(909\) | −4.40386 | −0.146067 | ||||||||
\(910\) | −3.06199 | −0.101504 | ||||||||
\(911\) | −13.5809 | −0.449955 | −0.224977 | − | 0.974364i | \(-0.572231\pi\) | ||||
−0.224977 | + | 0.974364i | \(0.572231\pi\) | |||||||
\(912\) | 4.71244 | 0.156044 | ||||||||
\(913\) | 66.0870 | 2.18716 | ||||||||
\(914\) | −10.6999 | −0.353920 | ||||||||
\(915\) | 10.4903 | 0.346800 | ||||||||
\(916\) | 17.6093 | 0.581829 | ||||||||
\(917\) | 31.8741 | 1.05257 | ||||||||
\(918\) | 41.7691 | 1.37859 | ||||||||
\(919\) | 43.6751 | 1.44071 | 0.720354 | − | 0.693607i | \(-0.243979\pi\) | ||||
0.720354 | + | 0.693607i | \(0.243979\pi\) | |||||||
\(920\) | −10.4691 | −0.345157 | ||||||||
\(921\) | −28.0893 | −0.925575 | ||||||||
\(922\) | 18.6750 | 0.615029 | ||||||||
\(923\) | −4.37408 | −0.143975 | ||||||||
\(924\) | 16.5297 | 0.543787 | ||||||||
\(925\) | −4.26530 | −0.140242 | ||||||||
\(926\) | 14.4416 | 0.474581 | ||||||||
\(927\) | 2.39136 | 0.0785424 | ||||||||
\(928\) | 3.86409 | 0.126845 | ||||||||
\(929\) | −37.0724 | −1.21631 | −0.608154 | − | 0.793819i | \(-0.708090\pi\) | ||||
−0.608154 | + | 0.793819i | \(0.708090\pi\) | |||||||
\(930\) | 26.5431 | 0.870384 | ||||||||
\(931\) | 7.96428 | 0.261019 | ||||||||
\(932\) | 11.8245 | 0.387325 | ||||||||
\(933\) | −3.23012 | −0.105749 | ||||||||
\(934\) | 30.2858 | 0.990981 | ||||||||
\(935\) | 100.587 | 3.28956 | ||||||||
\(936\) | 0.740707 | 0.0242108 | ||||||||
\(937\) | −49.9019 | −1.63022 | −0.815111 | − | 0.579304i | \(-0.803324\pi\) | ||||
−0.815111 | + | 0.579304i | \(0.803324\pi\) | |||||||
\(938\) | −17.5531 | −0.573130 | ||||||||
\(939\) | 34.1517 | 1.11450 | ||||||||
\(940\) | −11.1529 | −0.363767 | ||||||||
\(941\) | −40.2104 | −1.31082 | −0.655410 | − | 0.755273i | \(-0.727504\pi\) | ||||
−0.655410 | + | 0.755273i | \(0.727504\pi\) | |||||||
\(942\) | 30.3310 | 0.988236 | ||||||||
\(943\) | −56.1233 | −1.82763 | ||||||||
\(944\) | 12.6925 | 0.413105 | ||||||||
\(945\) | 29.0309 | 0.944375 | ||||||||
\(946\) | 8.97846 | 0.291915 | ||||||||
\(947\) | −16.0286 | −0.520861 | −0.260430 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260430 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(948\) | 11.6512 | 0.378415 | ||||||||
\(949\) | −9.04634 | −0.293656 | ||||||||
\(950\) | 2.12458 | 0.0689305 | ||||||||
\(951\) | 12.9683 | 0.420525 | ||||||||
\(952\) | 16.2142 | 0.525506 | ||||||||
\(953\) | 15.7956 | 0.511671 | 0.255836 | − | 0.966720i | \(-0.417649\pi\) | ||||
0.255836 | + | 0.966720i | \(0.417649\pi\) | |||||||
\(954\) | 3.03329 | 0.0982064 | ||||||||
\(955\) | 2.81401 | 0.0910593 | ||||||||
\(956\) | 12.3656 | 0.399933 | ||||||||
\(957\) | −29.2646 | −0.945990 | ||||||||
\(958\) | −0.0429468 | −0.00138755 | ||||||||
\(959\) | 26.6334 | 0.860038 | ||||||||
\(960\) | −3.13040 | −0.101033 | ||||||||
\(961\) | 40.8959 | 1.31922 | ||||||||
\(962\) | 4.23990 | 0.136700 | ||||||||
\(963\) | 22.1123 | 0.712558 | ||||||||
\(964\) | −13.7153 | −0.441741 | ||||||||
\(965\) | 8.17699 | 0.263227 | ||||||||
\(966\) | 12.7808 | 0.411216 | ||||||||
\(967\) | −52.7366 | −1.69590 | −0.847948 | − | 0.530080i | \(-0.822162\pi\) | ||||
−0.847948 | + | 0.530080i | \(0.822162\pi\) | |||||||
\(968\) | −21.7576 | −0.699316 | ||||||||
\(969\) | −35.0083 | −1.12463 | ||||||||
\(970\) | −2.28469 | −0.0733570 | ||||||||
\(971\) | 39.5003 | 1.26762 | 0.633812 | − | 0.773487i | \(-0.281489\pi\) | ||||
0.633812 | + | 0.773487i | \(0.281489\pi\) | |||||||
\(972\) | −11.9810 | −0.384291 | ||||||||
\(973\) | 19.5595 | 0.627049 | ||||||||
\(974\) | 41.6315 | 1.33396 | ||||||||
\(975\) | −0.468143 | −0.0149926 | ||||||||
\(976\) | −3.35111 | −0.107267 | ||||||||
\(977\) | −22.9090 | −0.732923 | −0.366462 | − | 0.930433i | \(-0.619431\pi\) | ||||
−0.366462 | + | 0.930433i | \(0.619431\pi\) | |||||||
\(978\) | −26.3960 | −0.844051 | ||||||||
\(979\) | −70.8610 | −2.26473 | ||||||||
\(980\) | −5.29056 | −0.169001 | ||||||||
\(981\) | −24.6298 | −0.786368 | ||||||||
\(982\) | 1.62707 | 0.0519220 | ||||||||
\(983\) | 12.2582 | 0.390976 | 0.195488 | − | 0.980706i | \(-0.437371\pi\) | ||||
0.195488 | + | 0.980706i | \(0.437371\pi\) | |||||||
\(984\) | −16.7816 | −0.534976 | ||||||||
\(985\) | −48.7753 | −1.55411 | ||||||||
\(986\) | −28.7060 | −0.914187 | ||||||||
\(987\) | 13.6155 | 0.433387 | ||||||||
\(988\) | −2.11193 | −0.0671894 | ||||||||
\(989\) | 6.94218 | 0.220748 | ||||||||
\(990\) | −16.9119 | −0.537494 | ||||||||
\(991\) | −39.3982 | −1.25152 | −0.625762 | − | 0.780014i | \(-0.715212\pi\) | ||||
−0.625762 | + | 0.780014i | \(0.715212\pi\) | |||||||
\(992\) | −8.47915 | −0.269213 | ||||||||
\(993\) | −10.6876 | −0.339160 | ||||||||
\(994\) | 16.0984 | 0.510612 | ||||||||
\(995\) | 12.5381 | 0.397484 | ||||||||
\(996\) | 15.2791 | 0.484138 | ||||||||
\(997\) | −10.6266 | −0.336549 | −0.168275 | − | 0.985740i | \(-0.553820\pi\) | ||||
−0.168275 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(998\) | −4.86937 | −0.154137 | ||||||||
\(999\) | −40.1987 | −1.27183 |
(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 | 862.2.a.i.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 7758.2.a.t.1.1 | 6 | |||
4.3 | odd | 2 | 6896.2.a.q.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
862.2.a.i.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
6896.2.a.q.1.4 | 6 | 4.3 | odd | 2 | |||
7758.2.a.t.1.1 | 6 | 3.2 | odd | 2 |