Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6038,2,Mod(1,6038)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6038, 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("6038.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6038 = 2 \cdot 3019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6038.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: | \(48.2136727404\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6038.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.29973 | −1.32775 | −0.663876 | − | 0.747843i | \(-0.731090\pi\) | ||||
−0.663876 | + | 0.747843i | \(0.731090\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.30527 | 1.92537 | 0.962687 | − | 0.270619i | \(-0.0872283\pi\) | ||||
0.962687 | + | 0.270619i | \(0.0872283\pi\) | |||||||
\(6\) | 2.29973 | 0.938862 | ||||||||
\(7\) | −2.14109 | −0.809255 | −0.404627 | − | 0.914482i | \(-0.632599\pi\) | ||||
−0.404627 | + | 0.914482i | \(0.632599\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.28878 | 0.762925 | ||||||||
\(10\) | −4.30527 | −1.36144 | ||||||||
\(11\) | 3.89862 | 1.17548 | 0.587740 | − | 0.809050i | \(-0.300018\pi\) | ||||
0.587740 | + | 0.809050i | \(0.300018\pi\) | |||||||
\(12\) | −2.29973 | −0.663876 | ||||||||
\(13\) | 5.85266 | 1.62324 | 0.811618 | − | 0.584189i | \(-0.198587\pi\) | ||||
0.811618 | + | 0.584189i | \(0.198587\pi\) | |||||||
\(14\) | 2.14109 | 0.572229 | ||||||||
\(15\) | −9.90096 | −2.55642 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.43093 | −1.80226 | −0.901132 | − | 0.433544i | \(-0.857263\pi\) | ||||
−0.901132 | + | 0.433544i | \(0.857263\pi\) | |||||||
\(18\) | −2.28878 | −0.539469 | ||||||||
\(19\) | −4.19092 | −0.961462 | −0.480731 | − | 0.876868i | \(-0.659629\pi\) | ||||
−0.480731 | + | 0.876868i | \(0.659629\pi\) | |||||||
\(20\) | 4.30527 | 0.962687 | ||||||||
\(21\) | 4.92393 | 1.07449 | ||||||||
\(22\) | −3.89862 | −0.831189 | ||||||||
\(23\) | −2.89167 | −0.602955 | −0.301477 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301477 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(24\) | 2.29973 | 0.469431 | ||||||||
\(25\) | 13.5353 | 2.70706 | ||||||||
\(26\) | −5.85266 | −1.14780 | ||||||||
\(27\) | 1.63563 | 0.314777 | ||||||||
\(28\) | −2.14109 | −0.404627 | ||||||||
\(29\) | 0.280020 | 0.0519983 | 0.0259992 | − | 0.999662i | \(-0.491723\pi\) | ||||
0.0259992 | + | 0.999662i | \(0.491723\pi\) | |||||||
\(30\) | 9.90096 | 1.80766 | ||||||||
\(31\) | −1.81691 | −0.326326 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.96579 | −1.56074 | ||||||||
\(34\) | 7.43093 | 1.27439 | ||||||||
\(35\) | −9.21795 | −1.55812 | ||||||||
\(36\) | 2.28878 | 0.381463 | ||||||||
\(37\) | 4.64283 | 0.763276 | 0.381638 | − | 0.924312i | \(-0.375360\pi\) | ||||
0.381638 | + | 0.924312i | \(0.375360\pi\) | |||||||
\(38\) | 4.19092 | 0.679857 | ||||||||
\(39\) | −13.4596 | −2.15525 | ||||||||
\(40\) | −4.30527 | −0.680722 | ||||||||
\(41\) | −5.26094 | −0.821621 | −0.410811 | − | 0.911721i | \(-0.634754\pi\) | ||||
−0.410811 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(42\) | −4.92393 | −0.759779 | ||||||||
\(43\) | 7.25858 | 1.10692 | 0.553461 | − | 0.832875i | \(-0.313307\pi\) | ||||
0.553461 | + | 0.832875i | \(0.313307\pi\) | |||||||
\(44\) | 3.89862 | 0.587740 | ||||||||
\(45\) | 9.85378 | 1.46892 | ||||||||
\(46\) | 2.89167 | 0.426353 | ||||||||
\(47\) | −8.27119 | −1.20648 | −0.603238 | − | 0.797561i | \(-0.706123\pi\) | ||||
−0.603238 | + | 0.797561i | \(0.706123\pi\) | |||||||
\(48\) | −2.29973 | −0.331938 | ||||||||
\(49\) | −2.41575 | −0.345107 | ||||||||
\(50\) | −13.5353 | −1.91418 | ||||||||
\(51\) | 17.0892 | 2.39296 | ||||||||
\(52\) | 5.85266 | 0.811618 | ||||||||
\(53\) | 8.63037 | 1.18547 | 0.592736 | − | 0.805397i | \(-0.298048\pi\) | ||||
0.592736 | + | 0.805397i | \(0.298048\pi\) | |||||||
\(54\) | −1.63563 | −0.222581 | ||||||||
\(55\) | 16.7846 | 2.26324 | ||||||||
\(56\) | 2.14109 | 0.286115 | ||||||||
\(57\) | 9.63799 | 1.27658 | ||||||||
\(58\) | −0.280020 | −0.0367684 | ||||||||
\(59\) | 1.39283 | 0.181330 | 0.0906652 | − | 0.995881i | \(-0.471101\pi\) | ||||
0.0906652 | + | 0.995881i | \(0.471101\pi\) | |||||||
\(60\) | −9.90096 | −1.27821 | ||||||||
\(61\) | −4.72509 | −0.604986 | −0.302493 | − | 0.953152i | \(-0.597819\pi\) | ||||
−0.302493 | + | 0.953152i | \(0.597819\pi\) | |||||||
\(62\) | 1.81691 | 0.230747 | ||||||||
\(63\) | −4.90047 | −0.617401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 25.1973 | 3.12533 | ||||||||
\(66\) | 8.96579 | 1.10361 | ||||||||
\(67\) | 11.6766 | 1.42653 | 0.713264 | − | 0.700895i | \(-0.247216\pi\) | ||||
0.713264 | + | 0.700895i | \(0.247216\pi\) | |||||||
\(68\) | −7.43093 | −0.901132 | ||||||||
\(69\) | 6.65007 | 0.800574 | ||||||||
\(70\) | 9.21795 | 1.10176 | ||||||||
\(71\) | −3.22774 | −0.383062 | −0.191531 | − | 0.981487i | \(-0.561345\pi\) | ||||
−0.191531 | + | 0.981487i | \(0.561345\pi\) | |||||||
\(72\) | −2.28878 | −0.269735 | ||||||||
\(73\) | 14.8491 | 1.73795 | 0.868976 | − | 0.494854i | \(-0.164778\pi\) | ||||
0.868976 | + | 0.494854i | \(0.164778\pi\) | |||||||
\(74\) | −4.64283 | −0.539718 | ||||||||
\(75\) | −31.1276 | −3.59431 | ||||||||
\(76\) | −4.19092 | −0.480731 | ||||||||
\(77\) | −8.34729 | −0.951262 | ||||||||
\(78\) | 13.4596 | 1.52400 | ||||||||
\(79\) | 4.69214 | 0.527907 | 0.263953 | − | 0.964535i | \(-0.414973\pi\) | ||||
0.263953 | + | 0.964535i | \(0.414973\pi\) | |||||||
\(80\) | 4.30527 | 0.481343 | ||||||||
\(81\) | −10.6278 | −1.18087 | ||||||||
\(82\) | 5.26094 | 0.580974 | ||||||||
\(83\) | −2.93193 | −0.321821 | −0.160910 | − | 0.986969i | \(-0.551443\pi\) | ||||
−0.160910 | + | 0.986969i | \(0.551443\pi\) | |||||||
\(84\) | 4.92393 | 0.537245 | ||||||||
\(85\) | −31.9921 | −3.47003 | ||||||||
\(86\) | −7.25858 | −0.782713 | ||||||||
\(87\) | −0.643970 | −0.0690409 | ||||||||
\(88\) | −3.89862 | −0.415595 | ||||||||
\(89\) | 7.89771 | 0.837155 | 0.418578 | − | 0.908181i | \(-0.362529\pi\) | ||||
0.418578 | + | 0.908181i | \(0.362529\pi\) | |||||||
\(90\) | −9.85378 | −1.03868 | ||||||||
\(91\) | −12.5311 | −1.31361 | ||||||||
\(92\) | −2.89167 | −0.301477 | ||||||||
\(93\) | 4.17840 | 0.433280 | ||||||||
\(94\) | 8.27119 | 0.853108 | ||||||||
\(95\) | −18.0430 | −1.85117 | ||||||||
\(96\) | 2.29973 | 0.234716 | ||||||||
\(97\) | 15.0883 | 1.53199 | 0.765994 | − | 0.642847i | \(-0.222247\pi\) | ||||
0.765994 | + | 0.642847i | \(0.222247\pi\) | |||||||
\(98\) | 2.41575 | 0.244027 | ||||||||
\(99\) | 8.92307 | 0.896802 | ||||||||
\(100\) | 13.5353 | 1.35353 | ||||||||
\(101\) | 17.0591 | 1.69744 | 0.848722 | − | 0.528839i | \(-0.177372\pi\) | ||||
0.848722 | + | 0.528839i | \(0.177372\pi\) | |||||||
\(102\) | −17.0892 | −1.69208 | ||||||||
\(103\) | 5.57578 | 0.549398 | 0.274699 | − | 0.961530i | \(-0.411422\pi\) | ||||
0.274699 | + | 0.961530i | \(0.411422\pi\) | |||||||
\(104\) | −5.85266 | −0.573901 | ||||||||
\(105\) | 21.1988 | 2.06879 | ||||||||
\(106\) | −8.63037 | −0.838256 | ||||||||
\(107\) | −2.17223 | −0.209997 | −0.104999 | − | 0.994472i | \(-0.533484\pi\) | ||||
−0.104999 | + | 0.994472i | \(0.533484\pi\) | |||||||
\(108\) | 1.63563 | 0.157388 | ||||||||
\(109\) | −10.9597 | −1.04975 | −0.524874 | − | 0.851180i | \(-0.675888\pi\) | ||||
−0.524874 | + | 0.851180i | \(0.675888\pi\) | |||||||
\(110\) | −16.7846 | −1.60035 | ||||||||
\(111\) | −10.6773 | −1.01344 | ||||||||
\(112\) | −2.14109 | −0.202314 | ||||||||
\(113\) | −10.4854 | −0.986381 | −0.493191 | − | 0.869921i | \(-0.664169\pi\) | ||||
−0.493191 | + | 0.869921i | \(0.664169\pi\) | |||||||
\(114\) | −9.63799 | −0.902681 | ||||||||
\(115\) | −12.4494 | −1.16091 | ||||||||
\(116\) | 0.280020 | 0.0259992 | ||||||||
\(117\) | 13.3954 | 1.23841 | ||||||||
\(118\) | −1.39283 | −0.128220 | ||||||||
\(119\) | 15.9103 | 1.45849 | ||||||||
\(120\) | 9.90096 | 0.903830 | ||||||||
\(121\) | 4.19926 | 0.381751 | ||||||||
\(122\) | 4.72509 | 0.427790 | ||||||||
\(123\) | 12.0988 | 1.09091 | ||||||||
\(124\) | −1.81691 | −0.163163 | ||||||||
\(125\) | 36.7468 | 3.28673 | ||||||||
\(126\) | 4.90047 | 0.436568 | ||||||||
\(127\) | 17.4195 | 1.54573 | 0.772864 | − | 0.634572i | \(-0.218823\pi\) | ||||
0.772864 | + | 0.634572i | \(0.218823\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −16.6928 | −1.46972 | ||||||||
\(130\) | −25.1973 | −2.20995 | ||||||||
\(131\) | −22.0261 | −1.92443 | −0.962216 | − | 0.272288i | \(-0.912220\pi\) | ||||
−0.962216 | + | 0.272288i | \(0.912220\pi\) | |||||||
\(132\) | −8.96579 | −0.780372 | ||||||||
\(133\) | 8.97312 | 0.778068 | ||||||||
\(134\) | −11.6766 | −1.00871 | ||||||||
\(135\) | 7.04181 | 0.606063 | ||||||||
\(136\) | 7.43093 | 0.637197 | ||||||||
\(137\) | 6.39282 | 0.546175 | 0.273088 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273088 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(138\) | −6.65007 | −0.566092 | ||||||||
\(139\) | −7.88978 | −0.669203 | −0.334601 | − | 0.942360i | \(-0.608602\pi\) | ||||
−0.334601 | + | 0.942360i | \(0.608602\pi\) | |||||||
\(140\) | −9.21795 | −0.779059 | ||||||||
\(141\) | 19.0215 | 1.60190 | ||||||||
\(142\) | 3.22774 | 0.270866 | ||||||||
\(143\) | 22.8173 | 1.90808 | ||||||||
\(144\) | 2.28878 | 0.190731 | ||||||||
\(145\) | 1.20556 | 0.100116 | ||||||||
\(146\) | −14.8491 | −1.22892 | ||||||||
\(147\) | 5.55558 | 0.458216 | ||||||||
\(148\) | 4.64283 | 0.381638 | ||||||||
\(149\) | 2.83546 | 0.232290 | 0.116145 | − | 0.993232i | \(-0.462946\pi\) | ||||
0.116145 | + | 0.993232i | \(0.462946\pi\) | |||||||
\(150\) | 31.1276 | 2.54156 | ||||||||
\(151\) | −8.12924 | −0.661548 | −0.330774 | − | 0.943710i | \(-0.607310\pi\) | ||||
−0.330774 | + | 0.943710i | \(0.607310\pi\) | |||||||
\(152\) | 4.19092 | 0.339928 | ||||||||
\(153\) | −17.0077 | −1.37499 | ||||||||
\(154\) | 8.34729 | 0.672644 | ||||||||
\(155\) | −7.82226 | −0.628299 | ||||||||
\(156\) | −13.4596 | −1.07763 | ||||||||
\(157\) | −8.03302 | −0.641105 | −0.320552 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320552 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(158\) | −4.69214 | −0.373287 | ||||||||
\(159\) | −19.8476 | −1.57401 | ||||||||
\(160\) | −4.30527 | −0.340361 | ||||||||
\(161\) | 6.19131 | 0.487944 | ||||||||
\(162\) | 10.6278 | 0.835001 | ||||||||
\(163\) | 3.51694 | 0.275468 | 0.137734 | − | 0.990469i | \(-0.456018\pi\) | ||||
0.137734 | + | 0.990469i | \(0.456018\pi\) | |||||||
\(164\) | −5.26094 | −0.410811 | ||||||||
\(165\) | −38.6001 | −3.00502 | ||||||||
\(166\) | 2.93193 | 0.227562 | ||||||||
\(167\) | 23.0013 | 1.77989 | 0.889947 | − | 0.456065i | \(-0.150742\pi\) | ||||
0.889947 | + | 0.456065i | \(0.150742\pi\) | |||||||
\(168\) | −4.92393 | −0.379889 | ||||||||
\(169\) | 21.2536 | 1.63490 | ||||||||
\(170\) | 31.9921 | 2.45368 | ||||||||
\(171\) | −9.59207 | −0.733524 | ||||||||
\(172\) | 7.25858 | 0.553461 | ||||||||
\(173\) | 20.5463 | 1.56211 | 0.781053 | − | 0.624465i | \(-0.214683\pi\) | ||||
0.781053 | + | 0.624465i | \(0.214683\pi\) | |||||||
\(174\) | 0.643970 | 0.0488193 | ||||||||
\(175\) | −28.9803 | −2.19070 | ||||||||
\(176\) | 3.89862 | 0.293870 | ||||||||
\(177\) | −3.20313 | −0.240762 | ||||||||
\(178\) | −7.89771 | −0.591958 | ||||||||
\(179\) | 23.6137 | 1.76497 | 0.882487 | − | 0.470337i | \(-0.155868\pi\) | ||||
0.882487 | + | 0.470337i | \(0.155868\pi\) | |||||||
\(180\) | 9.85378 | 0.734458 | ||||||||
\(181\) | 6.20711 | 0.461371 | 0.230686 | − | 0.973028i | \(-0.425903\pi\) | ||||
0.230686 | + | 0.973028i | \(0.425903\pi\) | |||||||
\(182\) | 12.5311 | 0.928863 | ||||||||
\(183\) | 10.8665 | 0.803271 | ||||||||
\(184\) | 2.89167 | 0.213177 | ||||||||
\(185\) | 19.9886 | 1.46959 | ||||||||
\(186\) | −4.17840 | −0.306375 | ||||||||
\(187\) | −28.9704 | −2.11852 | ||||||||
\(188\) | −8.27119 | −0.603238 | ||||||||
\(189\) | −3.50202 | −0.254735 | ||||||||
\(190\) | 18.0430 | 1.30898 | ||||||||
\(191\) | 1.54240 | 0.111604 | 0.0558022 | − | 0.998442i | \(-0.482228\pi\) | ||||
0.0558022 | + | 0.998442i | \(0.482228\pi\) | |||||||
\(192\) | −2.29973 | −0.165969 | ||||||||
\(193\) | −16.0416 | −1.15470 | −0.577349 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577349 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(194\) | −15.0883 | −1.08328 | ||||||||
\(195\) | −57.9470 | −4.14967 | ||||||||
\(196\) | −2.41575 | −0.172553 | ||||||||
\(197\) | −1.14901 | −0.0818638 | −0.0409319 | − | 0.999162i | \(-0.513033\pi\) | ||||
−0.0409319 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(198\) | −8.92307 | −0.634135 | ||||||||
\(199\) | −12.0770 | −0.856117 | −0.428058 | − | 0.903751i | \(-0.640802\pi\) | ||||
−0.428058 | + | 0.903751i | \(0.640802\pi\) | |||||||
\(200\) | −13.5353 | −0.957091 | ||||||||
\(201\) | −26.8532 | −1.89408 | ||||||||
\(202\) | −17.0591 | −1.20027 | ||||||||
\(203\) | −0.599546 | −0.0420799 | ||||||||
\(204\) | 17.0892 | 1.19648 | ||||||||
\(205\) | −22.6498 | −1.58193 | ||||||||
\(206\) | −5.57578 | −0.388483 | ||||||||
\(207\) | −6.61838 | −0.460009 | ||||||||
\(208\) | 5.85266 | 0.405809 | ||||||||
\(209\) | −16.3388 | −1.13018 | ||||||||
\(210\) | −21.1988 | −1.46286 | ||||||||
\(211\) | −25.8902 | −1.78236 | −0.891178 | − | 0.453653i | \(-0.850120\pi\) | ||||
−0.891178 | + | 0.453653i | \(0.850120\pi\) | |||||||
\(212\) | 8.63037 | 0.592736 | ||||||||
\(213\) | 7.42294 | 0.508611 | ||||||||
\(214\) | 2.17223 | 0.148490 | ||||||||
\(215\) | 31.2501 | 2.13124 | ||||||||
\(216\) | −1.63563 | −0.111290 | ||||||||
\(217\) | 3.89015 | 0.264081 | ||||||||
\(218\) | 10.9597 | 0.742284 | ||||||||
\(219\) | −34.1489 | −2.30757 | ||||||||
\(220\) | 16.7846 | 1.13162 | ||||||||
\(221\) | −43.4907 | −2.92550 | ||||||||
\(222\) | 10.6773 | 0.716612 | ||||||||
\(223\) | −10.6083 | −0.710381 | −0.355191 | − | 0.934794i | \(-0.615584\pi\) | ||||
−0.355191 | + | 0.934794i | \(0.615584\pi\) | |||||||
\(224\) | 2.14109 | 0.143057 | ||||||||
\(225\) | 30.9793 | 2.06529 | ||||||||
\(226\) | 10.4854 | 0.697477 | ||||||||
\(227\) | −18.8647 | −1.25209 | −0.626046 | − | 0.779786i | \(-0.715328\pi\) | ||||
−0.626046 | + | 0.779786i | \(0.715328\pi\) | |||||||
\(228\) | 9.63799 | 0.638292 | ||||||||
\(229\) | 16.8459 | 1.11321 | 0.556605 | − | 0.830777i | \(-0.312104\pi\) | ||||
0.556605 | + | 0.830777i | \(0.312104\pi\) | |||||||
\(230\) | 12.4494 | 0.820889 | ||||||||
\(231\) | 19.1965 | 1.26304 | ||||||||
\(232\) | −0.280020 | −0.0183842 | ||||||||
\(233\) | −3.84736 | −0.252049 | −0.126024 | − | 0.992027i | \(-0.540222\pi\) | ||||
−0.126024 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(234\) | −13.3954 | −0.875686 | ||||||||
\(235\) | −35.6097 | −2.32292 | ||||||||
\(236\) | 1.39283 | 0.0906652 | ||||||||
\(237\) | −10.7907 | −0.700929 | ||||||||
\(238\) | −15.9103 | −1.03131 | ||||||||
\(239\) | −17.4034 | −1.12573 | −0.562867 | − | 0.826548i | \(-0.690302\pi\) | ||||
−0.562867 | + | 0.826548i | \(0.690302\pi\) | |||||||
\(240\) | −9.90096 | −0.639104 | ||||||||
\(241\) | 16.4594 | 1.06024 | 0.530122 | − | 0.847921i | \(-0.322146\pi\) | ||||
0.530122 | + | 0.847921i | \(0.322146\pi\) | |||||||
\(242\) | −4.19926 | −0.269939 | ||||||||
\(243\) | 19.5343 | 1.25313 | ||||||||
\(244\) | −4.72509 | −0.302493 | ||||||||
\(245\) | −10.4004 | −0.664459 | ||||||||
\(246\) | −12.0988 | −0.771389 | ||||||||
\(247\) | −24.5280 | −1.56068 | ||||||||
\(248\) | 1.81691 | 0.115374 | ||||||||
\(249\) | 6.74265 | 0.427298 | ||||||||
\(250\) | −36.7468 | −2.32407 | ||||||||
\(251\) | −18.7120 | −1.18109 | −0.590544 | − | 0.807005i | \(-0.701087\pi\) | ||||
−0.590544 | + | 0.807005i | \(0.701087\pi\) | |||||||
\(252\) | −4.90047 | −0.308700 | ||||||||
\(253\) | −11.2735 | −0.708761 | ||||||||
\(254\) | −17.4195 | −1.09299 | ||||||||
\(255\) | 73.5733 | 4.60734 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.0436 | 0.938395 | 0.469198 | − | 0.883093i | \(-0.344543\pi\) | ||||
0.469198 | + | 0.883093i | \(0.344543\pi\) | |||||||
\(258\) | 16.6928 | 1.03925 | ||||||||
\(259\) | −9.94070 | −0.617685 | ||||||||
\(260\) | 25.1973 | 1.56267 | ||||||||
\(261\) | 0.640902 | 0.0396708 | ||||||||
\(262\) | 22.0261 | 1.36078 | ||||||||
\(263\) | −3.06598 | −0.189056 | −0.0945282 | − | 0.995522i | \(-0.530134\pi\) | ||||
−0.0945282 | + | 0.995522i | \(0.530134\pi\) | |||||||
\(264\) | 8.96579 | 0.551807 | ||||||||
\(265\) | 37.1560 | 2.28248 | ||||||||
\(266\) | −8.97312 | −0.550177 | ||||||||
\(267\) | −18.1626 | −1.11153 | ||||||||
\(268\) | 11.6766 | 0.713264 | ||||||||
\(269\) | 6.91528 | 0.421632 | 0.210816 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210816 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(270\) | −7.04181 | −0.428551 | ||||||||
\(271\) | −15.9621 | −0.969626 | −0.484813 | − | 0.874618i | \(-0.661112\pi\) | ||||
−0.484813 | + | 0.874618i | \(0.661112\pi\) | |||||||
\(272\) | −7.43093 | −0.450566 | ||||||||
\(273\) | 28.8181 | 1.74415 | ||||||||
\(274\) | −6.39282 | −0.386204 | ||||||||
\(275\) | 52.7691 | 3.18209 | ||||||||
\(276\) | 6.65007 | 0.400287 | ||||||||
\(277\) | −3.73209 | −0.224240 | −0.112120 | − | 0.993695i | \(-0.535764\pi\) | ||||
−0.112120 | + | 0.993695i | \(0.535764\pi\) | |||||||
\(278\) | 7.88978 | 0.473198 | ||||||||
\(279\) | −4.15849 | −0.248962 | ||||||||
\(280\) | 9.21795 | 0.550878 | ||||||||
\(281\) | −3.92086 | −0.233899 | −0.116950 | − | 0.993138i | \(-0.537312\pi\) | ||||
−0.116950 | + | 0.993138i | \(0.537312\pi\) | |||||||
\(282\) | −19.0215 | −1.13272 | ||||||||
\(283\) | 21.4635 | 1.27587 | 0.637935 | − | 0.770090i | \(-0.279789\pi\) | ||||
0.637935 | + | 0.770090i | \(0.279789\pi\) | |||||||
\(284\) | −3.22774 | −0.191531 | ||||||||
\(285\) | 41.4941 | 2.45790 | ||||||||
\(286\) | −22.8173 | −1.34922 | ||||||||
\(287\) | 11.2641 | 0.664901 | ||||||||
\(288\) | −2.28878 | −0.134867 | ||||||||
\(289\) | 38.2187 | 2.24816 | ||||||||
\(290\) | −1.20556 | −0.0707928 | ||||||||
\(291\) | −34.6992 | −2.03410 | ||||||||
\(292\) | 14.8491 | 0.868976 | ||||||||
\(293\) | −15.5987 | −0.911284 | −0.455642 | − | 0.890163i | \(-0.650590\pi\) | ||||
−0.455642 | + | 0.890163i | \(0.650590\pi\) | |||||||
\(294\) | −5.55558 | −0.324008 | ||||||||
\(295\) | 5.99648 | 0.349129 | ||||||||
\(296\) | −4.64283 | −0.269859 | ||||||||
\(297\) | 6.37670 | 0.370013 | ||||||||
\(298\) | −2.83546 | −0.164254 | ||||||||
\(299\) | −16.9240 | −0.978738 | ||||||||
\(300\) | −31.1276 | −1.79715 | ||||||||
\(301\) | −15.5412 | −0.895782 | ||||||||
\(302\) | 8.12924 | 0.467785 | ||||||||
\(303\) | −39.2314 | −2.25379 | ||||||||
\(304\) | −4.19092 | −0.240366 | ||||||||
\(305\) | −20.3428 | −1.16482 | ||||||||
\(306\) | 17.0077 | 0.972267 | ||||||||
\(307\) | 1.62354 | 0.0926606 | 0.0463303 | − | 0.998926i | \(-0.485247\pi\) | ||||
0.0463303 | + | 0.998926i | \(0.485247\pi\) | |||||||
\(308\) | −8.34729 | −0.475631 | ||||||||
\(309\) | −12.8228 | −0.729464 | ||||||||
\(310\) | 7.82226 | 0.444275 | ||||||||
\(311\) | 10.5682 | 0.599267 | 0.299634 | − | 0.954054i | \(-0.403136\pi\) | ||||
0.299634 | + | 0.954054i | \(0.403136\pi\) | |||||||
\(312\) | 13.4596 | 0.761998 | ||||||||
\(313\) | 26.4726 | 1.49632 | 0.748159 | − | 0.663520i | \(-0.230938\pi\) | ||||
0.748159 | + | 0.663520i | \(0.230938\pi\) | |||||||
\(314\) | 8.03302 | 0.453330 | ||||||||
\(315\) | −21.0978 | −1.18873 | ||||||||
\(316\) | 4.69214 | 0.263953 | ||||||||
\(317\) | −2.80286 | −0.157424 | −0.0787122 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787122 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(318\) | 19.8476 | 1.11300 | ||||||||
\(319\) | 1.09169 | 0.0611229 | ||||||||
\(320\) | 4.30527 | 0.240672 | ||||||||
\(321\) | 4.99555 | 0.278824 | ||||||||
\(322\) | −6.19131 | −0.345028 | ||||||||
\(323\) | 31.1424 | 1.73281 | ||||||||
\(324\) | −10.6278 | −0.590435 | ||||||||
\(325\) | 79.2176 | 4.39420 | ||||||||
\(326\) | −3.51694 | −0.194785 | ||||||||
\(327\) | 25.2044 | 1.39381 | ||||||||
\(328\) | 5.26094 | 0.290487 | ||||||||
\(329\) | 17.7093 | 0.976347 | ||||||||
\(330\) | 38.6001 | 2.12487 | ||||||||
\(331\) | −1.78735 | −0.0982418 | −0.0491209 | − | 0.998793i | \(-0.515642\pi\) | ||||
−0.0491209 | + | 0.998793i | \(0.515642\pi\) | |||||||
\(332\) | −2.93193 | −0.160910 | ||||||||
\(333\) | 10.6264 | 0.582323 | ||||||||
\(334\) | −23.0013 | −1.25857 | ||||||||
\(335\) | 50.2710 | 2.74660 | ||||||||
\(336\) | 4.92393 | 0.268622 | ||||||||
\(337\) | −22.8434 | −1.24436 | −0.622181 | − | 0.782874i | \(-0.713753\pi\) | ||||
−0.622181 | + | 0.782874i | \(0.713753\pi\) | |||||||
\(338\) | −21.2536 | −1.15605 | ||||||||
\(339\) | 24.1136 | 1.30967 | ||||||||
\(340\) | −31.9921 | −1.73502 | ||||||||
\(341\) | −7.08343 | −0.383589 | ||||||||
\(342\) | 9.59207 | 0.518680 | ||||||||
\(343\) | 20.1599 | 1.08853 | ||||||||
\(344\) | −7.25858 | −0.391356 | ||||||||
\(345\) | 28.6303 | 1.54140 | ||||||||
\(346\) | −20.5463 | −1.10458 | ||||||||
\(347\) | 1.28394 | 0.0689254 | 0.0344627 | − | 0.999406i | \(-0.489028\pi\) | ||||
0.0344627 | + | 0.999406i | \(0.489028\pi\) | |||||||
\(348\) | −0.643970 | −0.0345204 | ||||||||
\(349\) | 8.58415 | 0.459499 | 0.229749 | − | 0.973250i | \(-0.426209\pi\) | ||||
0.229749 | + | 0.973250i | \(0.426209\pi\) | |||||||
\(350\) | 28.9803 | 1.54906 | ||||||||
\(351\) | 9.57277 | 0.510957 | ||||||||
\(352\) | −3.89862 | −0.207797 | ||||||||
\(353\) | 10.3829 | 0.552628 | 0.276314 | − | 0.961067i | \(-0.410887\pi\) | ||||
0.276314 | + | 0.961067i | \(0.410887\pi\) | |||||||
\(354\) | 3.20313 | 0.170244 | ||||||||
\(355\) | −13.8963 | −0.737537 | ||||||||
\(356\) | 7.89771 | 0.418578 | ||||||||
\(357\) | −36.5894 | −1.93651 | ||||||||
\(358\) | −23.6137 | −1.24803 | ||||||||
\(359\) | −22.8669 | −1.20687 | −0.603435 | − | 0.797412i | \(-0.706202\pi\) | ||||
−0.603435 | + | 0.797412i | \(0.706202\pi\) | |||||||
\(360\) | −9.85378 | −0.519340 | ||||||||
\(361\) | −1.43621 | −0.0755902 | ||||||||
\(362\) | −6.20711 | −0.326239 | ||||||||
\(363\) | −9.65718 | −0.506871 | ||||||||
\(364\) | −12.5311 | −0.656806 | ||||||||
\(365\) | 63.9292 | 3.34621 | ||||||||
\(366\) | −10.8665 | −0.567999 | ||||||||
\(367\) | 23.2295 | 1.21257 | 0.606284 | − | 0.795248i | \(-0.292659\pi\) | ||||
0.606284 | + | 0.795248i | \(0.292659\pi\) | |||||||
\(368\) | −2.89167 | −0.150739 | ||||||||
\(369\) | −12.0411 | −0.626836 | ||||||||
\(370\) | −19.9886 | −1.03916 | ||||||||
\(371\) | −18.4784 | −0.959349 | ||||||||
\(372\) | 4.17840 | 0.216640 | ||||||||
\(373\) | −2.21307 | −0.114588 | −0.0572942 | − | 0.998357i | \(-0.518247\pi\) | ||||
−0.0572942 | + | 0.998357i | \(0.518247\pi\) | |||||||
\(374\) | 28.9704 | 1.49802 | ||||||||
\(375\) | −84.5078 | −4.36396 | ||||||||
\(376\) | 8.27119 | 0.426554 | ||||||||
\(377\) | 1.63886 | 0.0844055 | ||||||||
\(378\) | 3.50202 | 0.180125 | ||||||||
\(379\) | 29.8174 | 1.53162 | 0.765810 | − | 0.643067i | \(-0.222339\pi\) | ||||
0.765810 | + | 0.643067i | \(0.222339\pi\) | |||||||
\(380\) | −18.0430 | −0.925587 | ||||||||
\(381\) | −40.0601 | −2.05234 | ||||||||
\(382\) | −1.54240 | −0.0789162 | ||||||||
\(383\) | 0.812538 | 0.0415187 | 0.0207594 | − | 0.999785i | \(-0.493392\pi\) | ||||
0.0207594 | + | 0.999785i | \(0.493392\pi\) | |||||||
\(384\) | 2.29973 | 0.117358 | ||||||||
\(385\) | −35.9373 | −1.83153 | ||||||||
\(386\) | 16.0416 | 0.816495 | ||||||||
\(387\) | 16.6133 | 0.844499 | ||||||||
\(388\) | 15.0883 | 0.765994 | ||||||||
\(389\) | 34.6668 | 1.75768 | 0.878839 | − | 0.477119i | \(-0.158319\pi\) | ||||
0.878839 | + | 0.477119i | \(0.158319\pi\) | |||||||
\(390\) | 57.9470 | 2.93426 | ||||||||
\(391\) | 21.4878 | 1.08668 | ||||||||
\(392\) | 2.41575 | 0.122014 | ||||||||
\(393\) | 50.6542 | 2.55517 | ||||||||
\(394\) | 1.14901 | 0.0578864 | ||||||||
\(395\) | 20.2009 | 1.01642 | ||||||||
\(396\) | 8.92307 | 0.448401 | ||||||||
\(397\) | −2.02605 | −0.101684 | −0.0508422 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508422 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(398\) | 12.0770 | 0.605366 | ||||||||
\(399\) | −20.6358 | −1.03308 | ||||||||
\(400\) | 13.5353 | 0.676765 | ||||||||
\(401\) | −25.3333 | −1.26508 | −0.632541 | − | 0.774527i | \(-0.717988\pi\) | ||||
−0.632541 | + | 0.774527i | \(0.717988\pi\) | |||||||
\(402\) | 26.8532 | 1.33931 | ||||||||
\(403\) | −10.6337 | −0.529704 | ||||||||
\(404\) | 17.0591 | 0.848722 | ||||||||
\(405\) | −45.7556 | −2.27362 | ||||||||
\(406\) | 0.599546 | 0.0297550 | ||||||||
\(407\) | 18.1006 | 0.897215 | ||||||||
\(408\) | −17.0892 | −0.846039 | ||||||||
\(409\) | −4.66049 | −0.230447 | −0.115223 | − | 0.993340i | \(-0.536758\pi\) | ||||
−0.115223 | + | 0.993340i | \(0.536758\pi\) | |||||||
\(410\) | 22.6498 | 1.11859 | ||||||||
\(411\) | −14.7018 | −0.725185 | ||||||||
\(412\) | 5.57578 | 0.274699 | ||||||||
\(413\) | −2.98216 | −0.146742 | ||||||||
\(414\) | 6.61838 | 0.325276 | ||||||||
\(415\) | −12.6227 | −0.619625 | ||||||||
\(416\) | −5.85266 | −0.286950 | ||||||||
\(417\) | 18.1444 | 0.888535 | ||||||||
\(418\) | 16.3388 | 0.799157 | ||||||||
\(419\) | 28.2376 | 1.37950 | 0.689748 | − | 0.724050i | \(-0.257721\pi\) | ||||
0.689748 | + | 0.724050i | \(0.257721\pi\) | |||||||
\(420\) | 21.1988 | 1.03440 | ||||||||
\(421\) | −26.7983 | −1.30607 | −0.653034 | − | 0.757328i | \(-0.726504\pi\) | ||||
−0.653034 | + | 0.757328i | \(0.726504\pi\) | |||||||
\(422\) | 25.8902 | 1.26032 | ||||||||
\(423\) | −18.9309 | −0.920451 | ||||||||
\(424\) | −8.63037 | −0.419128 | ||||||||
\(425\) | −100.580 | −4.87884 | ||||||||
\(426\) | −7.42294 | −0.359643 | ||||||||
\(427\) | 10.1168 | 0.489588 | ||||||||
\(428\) | −2.17223 | −0.104999 | ||||||||
\(429\) | −52.4738 | −2.53346 | ||||||||
\(430\) | −31.2501 | −1.50701 | ||||||||
\(431\) | 7.29725 | 0.351496 | 0.175748 | − | 0.984435i | \(-0.443766\pi\) | ||||
0.175748 | + | 0.984435i | \(0.443766\pi\) | |||||||
\(432\) | 1.63563 | 0.0786942 | ||||||||
\(433\) | −4.31925 | −0.207570 | −0.103785 | − | 0.994600i | \(-0.533095\pi\) | ||||
−0.103785 | + | 0.994600i | \(0.533095\pi\) | |||||||
\(434\) | −3.89015 | −0.186733 | ||||||||
\(435\) | −2.77246 | −0.132929 | ||||||||
\(436\) | −10.9597 | −0.524874 | ||||||||
\(437\) | 12.1187 | 0.579718 | ||||||||
\(438\) | 34.1489 | 1.63170 | ||||||||
\(439\) | 41.0464 | 1.95904 | 0.979519 | − | 0.201351i | \(-0.0645333\pi\) | ||||
0.979519 | + | 0.201351i | \(0.0645333\pi\) | |||||||
\(440\) | −16.7846 | −0.800175 | ||||||||
\(441\) | −5.52910 | −0.263291 | ||||||||
\(442\) | 43.4907 | 2.06864 | ||||||||
\(443\) | 5.76790 | 0.274041 | 0.137021 | − | 0.990568i | \(-0.456247\pi\) | ||||
0.137021 | + | 0.990568i | \(0.456247\pi\) | |||||||
\(444\) | −10.6773 | −0.506721 | ||||||||
\(445\) | 34.0017 | 1.61184 | ||||||||
\(446\) | 10.6083 | 0.502315 | ||||||||
\(447\) | −6.52080 | −0.308423 | ||||||||
\(448\) | −2.14109 | −0.101157 | ||||||||
\(449\) | −15.6905 | −0.740478 | −0.370239 | − | 0.928936i | \(-0.620724\pi\) | ||||
−0.370239 | + | 0.928936i | \(0.620724\pi\) | |||||||
\(450\) | −30.9793 | −1.46038 | ||||||||
\(451\) | −20.5104 | −0.965799 | ||||||||
\(452\) | −10.4854 | −0.493191 | ||||||||
\(453\) | 18.6951 | 0.878371 | ||||||||
\(454\) | 18.8647 | 0.885362 | ||||||||
\(455\) | −53.9495 | −2.52919 | ||||||||
\(456\) | −9.63799 | −0.451340 | ||||||||
\(457\) | 23.2567 | 1.08790 | 0.543952 | − | 0.839116i | \(-0.316927\pi\) | ||||
0.543952 | + | 0.839116i | \(0.316927\pi\) | |||||||
\(458\) | −16.8459 | −0.787158 | ||||||||
\(459\) | −12.1542 | −0.567311 | ||||||||
\(460\) | −12.4494 | −0.580456 | ||||||||
\(461\) | 34.5518 | 1.60924 | 0.804619 | − | 0.593791i | \(-0.202369\pi\) | ||||
0.804619 | + | 0.593791i | \(0.202369\pi\) | |||||||
\(462\) | −19.1965 | −0.893104 | ||||||||
\(463\) | −2.86618 | −0.133202 | −0.0666012 | − | 0.997780i | \(-0.521216\pi\) | ||||
−0.0666012 | + | 0.997780i | \(0.521216\pi\) | |||||||
\(464\) | 0.280020 | 0.0129996 | ||||||||
\(465\) | 17.9891 | 0.834225 | ||||||||
\(466\) | 3.84736 | 0.178225 | ||||||||
\(467\) | −12.4586 | −0.576513 | −0.288257 | − | 0.957553i | \(-0.593076\pi\) | ||||
−0.288257 | + | 0.957553i | \(0.593076\pi\) | |||||||
\(468\) | 13.3954 | 0.619204 | ||||||||
\(469\) | −25.0007 | −1.15442 | ||||||||
\(470\) | 35.6097 | 1.64255 | ||||||||
\(471\) | 18.4738 | 0.851228 | ||||||||
\(472\) | −1.39283 | −0.0641100 | ||||||||
\(473\) | 28.2985 | 1.30116 | ||||||||
\(474\) | 10.7907 | 0.495632 | ||||||||
\(475\) | −56.7254 | −2.60274 | ||||||||
\(476\) | 15.9103 | 0.729246 | ||||||||
\(477\) | 19.7530 | 0.904427 | ||||||||
\(478\) | 17.4034 | 0.796014 | ||||||||
\(479\) | 6.58838 | 0.301031 | 0.150515 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150515 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(480\) | 9.90096 | 0.451915 | ||||||||
\(481\) | 27.1729 | 1.23898 | ||||||||
\(482\) | −16.4594 | −0.749706 | ||||||||
\(483\) | −14.2384 | −0.647868 | ||||||||
\(484\) | 4.19926 | 0.190876 | ||||||||
\(485\) | 64.9593 | 2.94965 | ||||||||
\(486\) | −19.5343 | −0.886094 | ||||||||
\(487\) | 36.8423 | 1.66948 | 0.834742 | − | 0.550641i | \(-0.185617\pi\) | ||||
0.834742 | + | 0.550641i | \(0.185617\pi\) | |||||||
\(488\) | 4.72509 | 0.213895 | ||||||||
\(489\) | −8.08802 | −0.365753 | ||||||||
\(490\) | 10.4004 | 0.469844 | ||||||||
\(491\) | 27.2499 | 1.22977 | 0.614884 | − | 0.788617i | \(-0.289203\pi\) | ||||
0.614884 | + | 0.788617i | \(0.289203\pi\) | |||||||
\(492\) | 12.0988 | 0.545455 | ||||||||
\(493\) | −2.08080 | −0.0937147 | ||||||||
\(494\) | 24.5280 | 1.10357 | ||||||||
\(495\) | 38.4162 | 1.72668 | ||||||||
\(496\) | −1.81691 | −0.0815815 | ||||||||
\(497\) | 6.91087 | 0.309995 | ||||||||
\(498\) | −6.74265 | −0.302146 | ||||||||
\(499\) | 11.0765 | 0.495853 | 0.247927 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247927 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(500\) | 36.7468 | 1.64337 | ||||||||
\(501\) | −52.8968 | −2.36326 | ||||||||
\(502\) | 18.7120 | 0.835155 | ||||||||
\(503\) | 39.9675 | 1.78206 | 0.891032 | − | 0.453940i | \(-0.149982\pi\) | ||||
0.891032 | + | 0.453940i | \(0.149982\pi\) | |||||||
\(504\) | 4.90047 | 0.218284 | ||||||||
\(505\) | 73.4440 | 3.26821 | ||||||||
\(506\) | 11.2735 | 0.501169 | ||||||||
\(507\) | −48.8777 | −2.17073 | ||||||||
\(508\) | 17.4195 | 0.772864 | ||||||||
\(509\) | −12.0712 | −0.535046 | −0.267523 | − | 0.963551i | \(-0.586205\pi\) | ||||
−0.267523 | + | 0.963551i | \(0.586205\pi\) | |||||||
\(510\) | −73.5733 | −3.25788 | ||||||||
\(511\) | −31.7932 | −1.40645 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.85478 | −0.302646 | ||||||||
\(514\) | −15.0436 | −0.663546 | ||||||||
\(515\) | 24.0052 | 1.05780 | ||||||||
\(516\) | −16.6928 | −0.734859 | ||||||||
\(517\) | −32.2462 | −1.41819 | ||||||||
\(518\) | 9.94070 | 0.436769 | ||||||||
\(519\) | −47.2510 | −2.07409 | ||||||||
\(520\) | −25.1973 | −1.10497 | ||||||||
\(521\) | 19.7906 | 0.867042 | 0.433521 | − | 0.901143i | \(-0.357271\pi\) | ||||
0.433521 | + | 0.901143i | \(0.357271\pi\) | |||||||
\(522\) | −0.640902 | −0.0280515 | ||||||||
\(523\) | −21.9793 | −0.961088 | −0.480544 | − | 0.876971i | \(-0.659561\pi\) | ||||
−0.480544 | + | 0.876971i | \(0.659561\pi\) | |||||||
\(524\) | −22.0261 | −0.962216 | ||||||||
\(525\) | 66.6469 | 2.90871 | ||||||||
\(526\) | 3.06598 | 0.133683 | ||||||||
\(527\) | 13.5013 | 0.588126 | ||||||||
\(528\) | −8.96579 | −0.390186 | ||||||||
\(529\) | −14.6382 | −0.636446 | ||||||||
\(530\) | −37.1560 | −1.61396 | ||||||||
\(531\) | 3.18786 | 0.138342 | ||||||||
\(532\) | 8.97312 | 0.389034 | ||||||||
\(533\) | −30.7905 | −1.33369 | ||||||||
\(534\) | 18.1626 | 0.785974 | ||||||||
\(535\) | −9.35202 | −0.404323 | ||||||||
\(536\) | −11.6766 | −0.504354 | ||||||||
\(537\) | −54.3053 | −2.34345 | ||||||||
\(538\) | −6.91528 | −0.298139 | ||||||||
\(539\) | −9.41809 | −0.405666 | ||||||||
\(540\) | 7.04181 | 0.303031 | ||||||||
\(541\) | 2.16876 | 0.0932421 | 0.0466210 | − | 0.998913i | \(-0.485155\pi\) | ||||
0.0466210 | + | 0.998913i | \(0.485155\pi\) | |||||||
\(542\) | 15.9621 | 0.685629 | ||||||||
\(543\) | −14.2747 | −0.612586 | ||||||||
\(544\) | 7.43093 | 0.318598 | ||||||||
\(545\) | −47.1844 | −2.02116 | ||||||||
\(546\) | −28.8181 | −1.23330 | ||||||||
\(547\) | −3.51556 | −0.150314 | −0.0751572 | − | 0.997172i | \(-0.523946\pi\) | ||||
−0.0751572 | + | 0.997172i | \(0.523946\pi\) | |||||||
\(548\) | 6.39282 | 0.273088 | ||||||||
\(549\) | −10.8147 | −0.461559 | ||||||||
\(550\) | −52.7691 | −2.25008 | ||||||||
\(551\) | −1.17354 | −0.0499944 | ||||||||
\(552\) | −6.65007 | −0.283046 | ||||||||
\(553\) | −10.0463 | −0.427211 | ||||||||
\(554\) | 3.73209 | 0.158561 | ||||||||
\(555\) | −45.9685 | −1.95125 | ||||||||
\(556\) | −7.88978 | −0.334601 | ||||||||
\(557\) | −25.1086 | −1.06389 | −0.531943 | − | 0.846780i | \(-0.678538\pi\) | ||||
−0.531943 | + | 0.846780i | \(0.678538\pi\) | |||||||
\(558\) | 4.15849 | 0.176043 | ||||||||
\(559\) | 42.4820 | 1.79680 | ||||||||
\(560\) | −9.21795 | −0.389529 | ||||||||
\(561\) | 66.6242 | 2.81287 | ||||||||
\(562\) | 3.92086 | 0.165392 | ||||||||
\(563\) | −13.6667 | −0.575984 | −0.287992 | − | 0.957633i | \(-0.592988\pi\) | ||||
−0.287992 | + | 0.957633i | \(0.592988\pi\) | |||||||
\(564\) | 19.0215 | 0.800951 | ||||||||
\(565\) | −45.1423 | −1.89915 | ||||||||
\(566\) | −21.4635 | −0.902177 | ||||||||
\(567\) | 22.7551 | 0.955625 | ||||||||
\(568\) | 3.22774 | 0.135433 | ||||||||
\(569\) | 28.6430 | 1.20078 | 0.600389 | − | 0.799708i | \(-0.295012\pi\) | ||||
0.600389 | + | 0.799708i | \(0.295012\pi\) | |||||||
\(570\) | −41.4941 | −1.73800 | ||||||||
\(571\) | 16.8022 | 0.703151 | 0.351576 | − | 0.936160i | \(-0.385646\pi\) | ||||
0.351576 | + | 0.936160i | \(0.385646\pi\) | |||||||
\(572\) | 22.8173 | 0.954040 | ||||||||
\(573\) | −3.54712 | −0.148183 | ||||||||
\(574\) | −11.2641 | −0.470156 | ||||||||
\(575\) | −39.1396 | −1.63224 | ||||||||
\(576\) | 2.28878 | 0.0953656 | ||||||||
\(577\) | −41.7611 | −1.73854 | −0.869269 | − | 0.494340i | \(-0.835410\pi\) | ||||
−0.869269 | + | 0.494340i | \(0.835410\pi\) | |||||||
\(578\) | −38.2187 | −1.58969 | ||||||||
\(579\) | 36.8914 | 1.53315 | ||||||||
\(580\) | 1.20556 | 0.0500581 | ||||||||
\(581\) | 6.27751 | 0.260435 | ||||||||
\(582\) | 34.6992 | 1.43833 | ||||||||
\(583\) | 33.6466 | 1.39350 | ||||||||
\(584\) | −14.8491 | −0.614459 | ||||||||
\(585\) | 57.6709 | 2.38440 | ||||||||
\(586\) | 15.5987 | 0.644375 | ||||||||
\(587\) | 43.3782 | 1.79041 | 0.895204 | − | 0.445656i | \(-0.147030\pi\) | ||||
0.895204 | + | 0.445656i | \(0.147030\pi\) | |||||||
\(588\) | 5.55558 | 0.229108 | ||||||||
\(589\) | 7.61450 | 0.313750 | ||||||||
\(590\) | −5.99648 | −0.246871 | ||||||||
\(591\) | 2.64242 | 0.108695 | ||||||||
\(592\) | 4.64283 | 0.190819 | ||||||||
\(593\) | 34.7457 | 1.42683 | 0.713417 | − | 0.700740i | \(-0.247147\pi\) | ||||
0.713417 | + | 0.700740i | \(0.247147\pi\) | |||||||
\(594\) | −6.37670 | −0.261639 | ||||||||
\(595\) | 68.4979 | 2.80814 | ||||||||
\(596\) | 2.83546 | 0.116145 | ||||||||
\(597\) | 27.7739 | 1.13671 | ||||||||
\(598\) | 16.9240 | 0.692072 | ||||||||
\(599\) | −26.0543 | −1.06455 | −0.532274 | − | 0.846572i | \(-0.678662\pi\) | ||||
−0.532274 | + | 0.846572i | \(0.678662\pi\) | |||||||
\(600\) | 31.1276 | 1.27078 | ||||||||
\(601\) | 35.6867 | 1.45569 | 0.727846 | − | 0.685741i | \(-0.240522\pi\) | ||||
0.727846 | + | 0.685741i | \(0.240522\pi\) | |||||||
\(602\) | 15.5412 | 0.633414 | ||||||||
\(603\) | 26.7252 | 1.08833 | ||||||||
\(604\) | −8.12924 | −0.330774 | ||||||||
\(605\) | 18.0789 | 0.735013 | ||||||||
\(606\) | 39.2314 | 1.59367 | ||||||||
\(607\) | 13.7086 | 0.556415 | 0.278208 | − | 0.960521i | \(-0.410260\pi\) | ||||
0.278208 | + | 0.960521i | \(0.410260\pi\) | |||||||
\(608\) | 4.19092 | 0.169964 | ||||||||
\(609\) | 1.37880 | 0.0558716 | ||||||||
\(610\) | 20.3428 | 0.823655 | ||||||||
\(611\) | −48.4085 | −1.95840 | ||||||||
\(612\) | −17.0077 | −0.687496 | ||||||||
\(613\) | 25.5036 | 1.03008 | 0.515041 | − | 0.857165i | \(-0.327777\pi\) | ||||
0.515041 | + | 0.857165i | \(0.327777\pi\) | |||||||
\(614\) | −1.62354 | −0.0655209 | ||||||||
\(615\) | 52.0884 | 2.10041 | ||||||||
\(616\) | 8.34729 | 0.336322 | ||||||||
\(617\) | −13.5322 | −0.544788 | −0.272394 | − | 0.962186i | \(-0.587815\pi\) | ||||
−0.272394 | + | 0.962186i | \(0.587815\pi\) | |||||||
\(618\) | 12.8228 | 0.515809 | ||||||||
\(619\) | 41.7586 | 1.67842 | 0.839210 | − | 0.543807i | \(-0.183018\pi\) | ||||
0.839210 | + | 0.543807i | \(0.183018\pi\) | |||||||
\(620\) | −7.82226 | −0.314150 | ||||||||
\(621\) | −4.72969 | −0.189796 | ||||||||
\(622\) | −10.5682 | −0.423746 | ||||||||
\(623\) | −16.9097 | −0.677472 | ||||||||
\(624\) | −13.4596 | −0.538814 | ||||||||
\(625\) | 90.5280 | 3.62112 | ||||||||
\(626\) | −26.4726 | −1.05806 | ||||||||
\(627\) | 37.5749 | 1.50060 | ||||||||
\(628\) | −8.03302 | −0.320552 | ||||||||
\(629\) | −34.5005 | −1.37563 | ||||||||
\(630\) | 21.0978 | 0.840557 | ||||||||
\(631\) | 35.8980 | 1.42908 | 0.714539 | − | 0.699596i | \(-0.246637\pi\) | ||||
0.714539 | + | 0.699596i | \(0.246637\pi\) | |||||||
\(632\) | −4.69214 | −0.186643 | ||||||||
\(633\) | 59.5406 | 2.36653 | ||||||||
\(634\) | 2.80286 | 0.111316 | ||||||||
\(635\) | 74.9954 | 2.97610 | ||||||||
\(636\) | −19.8476 | −0.787007 | ||||||||
\(637\) | −14.1386 | −0.560190 | ||||||||
\(638\) | −1.09169 | −0.0432204 | ||||||||
\(639\) | −7.38757 | −0.292248 | ||||||||
\(640\) | −4.30527 | −0.170181 | ||||||||
\(641\) | −11.1701 | −0.441193 | −0.220597 | − | 0.975365i | \(-0.570800\pi\) | ||||
−0.220597 | + | 0.975365i | \(0.570800\pi\) | |||||||
\(642\) | −4.99555 | −0.197158 | ||||||||
\(643\) | 38.1131 | 1.50304 | 0.751518 | − | 0.659713i | \(-0.229322\pi\) | ||||
0.751518 | + | 0.659713i | \(0.229322\pi\) | |||||||
\(644\) | 6.19131 | 0.243972 | ||||||||
\(645\) | −71.8669 | −2.82976 | ||||||||
\(646\) | −31.1424 | −1.22528 | ||||||||
\(647\) | 31.6345 | 1.24368 | 0.621841 | − | 0.783143i | \(-0.286385\pi\) | ||||
0.621841 | + | 0.783143i | \(0.286385\pi\) | |||||||
\(648\) | 10.6278 | 0.417501 | ||||||||
\(649\) | 5.43010 | 0.213150 | ||||||||
\(650\) | −79.2176 | −3.10717 | ||||||||
\(651\) | −8.94632 | −0.350634 | ||||||||
\(652\) | 3.51694 | 0.137734 | ||||||||
\(653\) | −46.7416 | −1.82914 | −0.914570 | − | 0.404427i | \(-0.867471\pi\) | ||||
−0.914570 | + | 0.404427i | \(0.867471\pi\) | |||||||
\(654\) | −25.2044 | −0.985569 | ||||||||
\(655\) | −94.8283 | −3.70525 | ||||||||
\(656\) | −5.26094 | −0.205405 | ||||||||
\(657\) | 33.9862 | 1.32593 | ||||||||
\(658\) | −17.7093 | −0.690382 | ||||||||
\(659\) | −5.72371 | −0.222964 | −0.111482 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111482 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(660\) | −38.6001 | −1.50251 | ||||||||
\(661\) | 6.55187 | 0.254838 | 0.127419 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127419 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(662\) | 1.78735 | 0.0694674 | ||||||||
\(663\) | 100.017 | 3.88434 | ||||||||
\(664\) | 2.93193 | 0.113781 | ||||||||
\(665\) | 38.6316 | 1.49807 | ||||||||
\(666\) | −10.6264 | −0.411764 | ||||||||
\(667\) | −0.809724 | −0.0313526 | ||||||||
\(668\) | 23.0013 | 0.889947 | ||||||||
\(669\) | 24.3962 | 0.943210 | ||||||||
\(670\) | −50.2710 | −1.94214 | ||||||||
\(671\) | −18.4213 | −0.711148 | ||||||||
\(672\) | −4.92393 | −0.189945 | ||||||||
\(673\) | −6.88356 | −0.265342 | −0.132671 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132671 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(674\) | 22.8434 | 0.879896 | ||||||||
\(675\) | 22.1387 | 0.852120 | ||||||||
\(676\) | 21.2536 | 0.817448 | ||||||||
\(677\) | 22.0692 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360593\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360593\pi\) | |||||||
\(678\) | −24.1136 | −0.926076 | ||||||||
\(679\) | −32.3054 | −1.23977 | ||||||||
\(680\) | 31.9921 | 1.22684 | ||||||||
\(681\) | 43.3837 | 1.66247 | ||||||||
\(682\) | 7.08343 | 0.271239 | ||||||||
\(683\) | −7.77409 | −0.297467 | −0.148734 | − | 0.988877i | \(-0.547520\pi\) | ||||
−0.148734 | + | 0.988877i | \(0.547520\pi\) | |||||||
\(684\) | −9.59207 | −0.366762 | ||||||||
\(685\) | 27.5228 | 1.05159 | ||||||||
\(686\) | −20.1599 | −0.769710 | ||||||||
\(687\) | −38.7411 | −1.47807 | ||||||||
\(688\) | 7.25858 | 0.276731 | ||||||||
\(689\) | 50.5106 | 1.92430 | ||||||||
\(690\) | −28.6303 | −1.08994 | ||||||||
\(691\) | 17.8552 | 0.679243 | 0.339622 | − | 0.940562i | \(-0.389701\pi\) | ||||
0.339622 | + | 0.940562i | \(0.389701\pi\) | |||||||
\(692\) | 20.5463 | 0.781053 | ||||||||
\(693\) | −19.1051 | −0.725742 | ||||||||
\(694\) | −1.28394 | −0.0487376 | ||||||||
\(695\) | −33.9676 | −1.28846 | ||||||||
\(696\) | 0.643970 | 0.0244096 | ||||||||
\(697\) | 39.0937 | 1.48078 | ||||||||
\(698\) | −8.58415 | −0.324915 | ||||||||
\(699\) | 8.84790 | 0.334658 | ||||||||
\(700\) | −28.9803 | −1.09535 | ||||||||
\(701\) | −10.1830 | −0.384607 | −0.192304 | − | 0.981335i | \(-0.561596\pi\) | ||||
−0.192304 | + | 0.981335i | \(0.561596\pi\) | |||||||
\(702\) | −9.57277 | −0.361301 | ||||||||
\(703\) | −19.4577 | −0.733862 | ||||||||
\(704\) | 3.89862 | 0.146935 | ||||||||
\(705\) | 81.8927 | 3.08426 | ||||||||
\(706\) | −10.3829 | −0.390767 | ||||||||
\(707\) | −36.5250 | −1.37367 | ||||||||
\(708\) | −3.20313 | −0.120381 | ||||||||
\(709\) | −4.60367 | −0.172894 | −0.0864471 | − | 0.996256i | \(-0.527551\pi\) | ||||
−0.0864471 | + | 0.996256i | \(0.527551\pi\) | |||||||
\(710\) | 13.8963 | 0.521518 | ||||||||
\(711\) | 10.7393 | 0.402753 | ||||||||
\(712\) | −7.89771 | −0.295979 | ||||||||
\(713\) | 5.25389 | 0.196760 | ||||||||
\(714\) | 36.5894 | 1.36932 | ||||||||
\(715\) | 98.2346 | 3.67377 | ||||||||
\(716\) | 23.6137 | 0.882487 | ||||||||
\(717\) | 40.0232 | 1.49469 | ||||||||
\(718\) | 22.8669 | 0.853386 | ||||||||
\(719\) | −34.6283 | −1.29142 | −0.645708 | − | 0.763584i | \(-0.723438\pi\) | ||||
−0.645708 | + | 0.763584i | \(0.723438\pi\) | |||||||
\(720\) | 9.85378 | 0.367229 | ||||||||
\(721\) | −11.9382 | −0.444603 | ||||||||
\(722\) | 1.43621 | 0.0534503 | ||||||||
\(723\) | −37.8523 | −1.40774 | ||||||||
\(724\) | 6.20711 | 0.230686 | ||||||||
\(725\) | 3.79015 | 0.140763 | ||||||||
\(726\) | 9.65718 | 0.358412 | ||||||||
\(727\) | −21.4295 | −0.794775 | −0.397388 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397388 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(728\) | 12.5311 | 0.464432 | ||||||||
\(729\) | −13.0402 | −0.482970 | ||||||||
\(730\) | −63.9292 | −2.36613 | ||||||||
\(731\) | −53.9380 | −1.99497 | ||||||||
\(732\) | 10.8665 | 0.401636 | ||||||||
\(733\) | 40.3462 | 1.49022 | 0.745111 | − | 0.666940i | \(-0.232396\pi\) | ||||
0.745111 | + | 0.666940i | \(0.232396\pi\) | |||||||
\(734\) | −23.2295 | −0.857415 | ||||||||
\(735\) | 23.9182 | 0.882237 | ||||||||
\(736\) | 2.89167 | 0.106588 | ||||||||
\(737\) | 45.5228 | 1.67685 | ||||||||
\(738\) | 12.0411 | 0.443240 | ||||||||
\(739\) | −24.4528 | −0.899509 | −0.449755 | − | 0.893152i | \(-0.648489\pi\) | ||||
−0.449755 | + | 0.893152i | \(0.648489\pi\) | |||||||
\(740\) | 19.9886 | 0.734796 | ||||||||
\(741\) | 56.4079 | 2.07220 | ||||||||
\(742\) | 18.4784 | 0.678362 | ||||||||
\(743\) | −10.8968 | −0.399767 | −0.199883 | − | 0.979820i | \(-0.564056\pi\) | ||||
−0.199883 | + | 0.979820i | \(0.564056\pi\) | |||||||
\(744\) | −4.17840 | −0.153188 | ||||||||
\(745\) | 12.2074 | 0.447245 | ||||||||
\(746\) | 2.21307 | 0.0810262 | ||||||||
\(747\) | −6.71052 | −0.245525 | ||||||||
\(748\) | −28.9704 | −1.05926 | ||||||||
\(749\) | 4.65093 | 0.169941 | ||||||||
\(750\) | 84.5078 | 3.08579 | ||||||||
\(751\) | 8.10066 | 0.295597 | 0.147799 | − | 0.989017i | \(-0.452781\pi\) | ||||
0.147799 | + | 0.989017i | \(0.452781\pi\) | |||||||
\(752\) | −8.27119 | −0.301619 | ||||||||
\(753\) | 43.0325 | 1.56819 | ||||||||
\(754\) | −1.63886 | −0.0596837 | ||||||||
\(755\) | −34.9985 | −1.27373 | ||||||||
\(756\) | −3.50202 | −0.127367 | ||||||||
\(757\) | −41.3597 | −1.50325 | −0.751623 | − | 0.659593i | \(-0.770729\pi\) | ||||
−0.751623 | + | 0.659593i | \(0.770729\pi\) | |||||||
\(758\) | −29.8174 | −1.08302 | ||||||||
\(759\) | 25.9261 | 0.941058 | ||||||||
\(760\) | 18.0430 | 0.654489 | ||||||||
\(761\) | 20.8524 | 0.755897 | 0.377949 | − | 0.925827i | \(-0.376630\pi\) | ||||
0.377949 | + | 0.925827i | \(0.376630\pi\) | |||||||
\(762\) | 40.0601 | 1.45123 | ||||||||
\(763\) | 23.4657 | 0.849514 | ||||||||
\(764\) | 1.54240 | 0.0558022 | ||||||||
\(765\) | −73.2228 | −2.64737 | ||||||||
\(766\) | −0.812538 | −0.0293582 | ||||||||
\(767\) | 8.15173 | 0.294342 | ||||||||
\(768\) | −2.29973 | −0.0829845 | ||||||||
\(769\) | 22.8569 | 0.824240 | 0.412120 | − | 0.911130i | \(-0.364788\pi\) | ||||
0.412120 | + | 0.911130i | \(0.364788\pi\) | |||||||
\(770\) | 35.9373 | 1.29509 | ||||||||
\(771\) | −34.5963 | −1.24596 | ||||||||
\(772\) | −16.0416 | −0.577349 | ||||||||
\(773\) | 7.34957 | 0.264346 | 0.132173 | − | 0.991227i | \(-0.457805\pi\) | ||||
0.132173 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(774\) | −16.6133 | −0.597151 | ||||||||
\(775\) | −24.5924 | −0.883384 | ||||||||
\(776\) | −15.0883 | −0.541640 | ||||||||
\(777\) | 22.8610 | 0.820132 | ||||||||
\(778\) | −34.6668 | −1.24287 | ||||||||
\(779\) | 22.0482 | 0.789958 | ||||||||
\(780\) | −57.9470 | −2.07483 | ||||||||
\(781\) | −12.5837 | −0.450281 | ||||||||
\(782\) | −21.4878 | −0.768402 | ||||||||
\(783\) | 0.458008 | 0.0163679 | ||||||||
\(784\) | −2.41575 | −0.0862767 | ||||||||
\(785\) | −34.5843 | −1.23437 | ||||||||
\(786\) | −50.6542 | −1.80678 | ||||||||
\(787\) | 23.6963 | 0.844682 | 0.422341 | − | 0.906437i | \(-0.361208\pi\) | ||||
0.422341 | + | 0.906437i | \(0.361208\pi\) | |||||||
\(788\) | −1.14901 | −0.0409319 | ||||||||
\(789\) | 7.05094 | 0.251020 | ||||||||
\(790\) | −20.2009 | −0.718716 | ||||||||
\(791\) | 22.4501 | 0.798234 | ||||||||
\(792\) | −8.92307 | −0.317068 | ||||||||
\(793\) | −27.6544 | −0.982035 | ||||||||
\(794\) | 2.02605 | 0.0719018 | ||||||||
\(795\) | −85.4490 | −3.03056 | ||||||||
\(796\) | −12.0770 | −0.428058 | ||||||||
\(797\) | −43.4409 | −1.53876 | −0.769378 | − | 0.638793i | \(-0.779434\pi\) | ||||
−0.769378 | + | 0.638793i | \(0.779434\pi\) | |||||||
\(798\) | 20.6358 | 0.730499 | ||||||||
\(799\) | 61.4626 | 2.17439 | ||||||||
\(800\) | −13.5353 | −0.478545 | ||||||||
\(801\) | 18.0761 | 0.638687 | ||||||||
\(802\) | 25.3333 | 0.894549 | ||||||||
\(803\) | 57.8909 | 2.04293 | ||||||||
\(804\) | −26.8532 | −0.947038 | ||||||||
\(805\) | 26.6553 | 0.939474 | ||||||||
\(806\) | 10.6337 | 0.374557 | ||||||||
\(807\) | −15.9033 | −0.559823 | ||||||||
\(808\) | −17.0591 | −0.600137 | ||||||||
\(809\) | 20.5117 | 0.721151 | 0.360576 | − | 0.932730i | \(-0.382580\pi\) | ||||
0.360576 | + | 0.932730i | \(0.382580\pi\) | |||||||
\(810\) | 45.7556 | 1.60769 | ||||||||
\(811\) | −30.4952 | −1.07083 | −0.535415 | − | 0.844589i | \(-0.679845\pi\) | ||||
−0.535415 | + | 0.844589i | \(0.679845\pi\) | |||||||
\(812\) | −0.599546 | −0.0210399 | ||||||||
\(813\) | 36.7085 | 1.28742 | ||||||||
\(814\) | −18.1006 | −0.634427 | ||||||||
\(815\) | 15.1414 | 0.530379 | ||||||||
\(816\) | 17.0892 | 0.598240 | ||||||||
\(817\) | −30.4201 | −1.06426 | ||||||||
\(818\) | 4.66049 | 0.162950 | ||||||||
\(819\) | −28.6808 | −1.00219 | ||||||||
\(820\) | −22.6498 | −0.790964 | ||||||||
\(821\) | −15.3526 | −0.535808 | −0.267904 | − | 0.963446i | \(-0.586331\pi\) | ||||
−0.267904 | + | 0.963446i | \(0.586331\pi\) | |||||||
\(822\) | 14.7018 | 0.512783 | ||||||||
\(823\) | 40.2115 | 1.40168 | 0.700842 | − | 0.713316i | \(-0.252808\pi\) | ||||
0.700842 | + | 0.713316i | \(0.252808\pi\) | |||||||
\(824\) | −5.57578 | −0.194241 | ||||||||
\(825\) | −121.355 | −4.22503 | ||||||||
\(826\) | 2.98216 | 0.103763 | ||||||||
\(827\) | −35.1509 | −1.22232 | −0.611159 | − | 0.791508i | \(-0.709296\pi\) | ||||
−0.611159 | + | 0.791508i | \(0.709296\pi\) | |||||||
\(828\) | −6.61838 | −0.230005 | ||||||||
\(829\) | −4.26109 | −0.147994 | −0.0739969 | − | 0.997258i | \(-0.523575\pi\) | ||||
−0.0739969 | + | 0.997258i | \(0.523575\pi\) | |||||||
\(830\) | 12.6227 | 0.438141 | ||||||||
\(831\) | 8.58282 | 0.297735 | ||||||||
\(832\) | 5.85266 | 0.202904 | ||||||||
\(833\) | 17.9513 | 0.621974 | ||||||||
\(834\) | −18.1444 | −0.628289 | ||||||||
\(835\) | 99.0266 | 3.42696 | ||||||||
\(836\) | −16.3388 | −0.565089 | ||||||||
\(837\) | −2.97178 | −0.102720 | ||||||||
\(838\) | −28.2376 | −0.975451 | ||||||||
\(839\) | 44.6142 | 1.54025 | 0.770126 | − | 0.637892i | \(-0.220193\pi\) | ||||
0.770126 | + | 0.637892i | \(0.220193\pi\) | |||||||
\(840\) | −21.1988 | −0.731429 | ||||||||
\(841\) | −28.9216 | −0.997296 | ||||||||
\(842\) | 26.7983 | 0.923530 | ||||||||
\(843\) | 9.01694 | 0.310560 | ||||||||
\(844\) | −25.8902 | −0.891178 | ||||||||
\(845\) | 91.5025 | 3.14778 | ||||||||
\(846\) | 18.9309 | 0.650857 | ||||||||
\(847\) | −8.99098 | −0.308934 | ||||||||
\(848\) | 8.63037 | 0.296368 | ||||||||
\(849\) | −49.3603 | −1.69404 | ||||||||
\(850\) | 100.580 | 3.44986 | ||||||||
\(851\) | −13.4255 | −0.460221 | ||||||||
\(852\) | 7.42294 | 0.254306 | ||||||||
\(853\) | −8.26990 | −0.283156 | −0.141578 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141578 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(854\) | −10.1168 | −0.346191 | ||||||||
\(855\) | −41.2964 | −1.41231 | ||||||||
\(856\) | 2.17223 | 0.0742452 | ||||||||
\(857\) | −37.8927 | −1.29439 | −0.647195 | − | 0.762324i | \(-0.724058\pi\) | ||||
−0.647195 | + | 0.762324i | \(0.724058\pi\) | |||||||
\(858\) | 52.4738 | 1.79142 | ||||||||
\(859\) | 3.31060 | 0.112956 | 0.0564780 | − | 0.998404i | \(-0.482013\pi\) | ||||
0.0564780 | + | 0.998404i | \(0.482013\pi\) | |||||||
\(860\) | 31.2501 | 1.06562 | ||||||||
\(861\) | −25.9045 | −0.882824 | ||||||||
\(862\) | −7.29725 | −0.248545 | ||||||||
\(863\) | −13.3775 | −0.455376 | −0.227688 | − | 0.973734i | \(-0.573117\pi\) | ||||
−0.227688 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(864\) | −1.63563 | −0.0556452 | ||||||||
\(865\) | 88.4572 | 3.00764 | ||||||||
\(866\) | 4.31925 | 0.146774 | ||||||||
\(867\) | −87.8928 | −2.98500 | ||||||||
\(868\) | 3.89015 | 0.132040 | ||||||||
\(869\) | 18.2929 | 0.620544 | ||||||||
\(870\) | 2.77246 | 0.0939953 | ||||||||
\(871\) | 68.3394 | 2.31559 | ||||||||
\(872\) | 10.9597 | 0.371142 | ||||||||
\(873\) | 34.5338 | 1.16879 | ||||||||
\(874\) | −12.1187 | −0.409923 | ||||||||
\(875\) | −78.6780 | −2.65980 | ||||||||
\(876\) | −34.1489 | −1.15378 | ||||||||
\(877\) | −51.1512 | −1.72725 | −0.863627 | − | 0.504131i | \(-0.831813\pi\) | ||||
−0.863627 | + | 0.504131i | \(0.831813\pi\) | |||||||
\(878\) | −41.0464 | −1.38525 | ||||||||
\(879\) | 35.8728 | 1.20996 | ||||||||
\(880\) | 16.7846 | 0.565809 | ||||||||
\(881\) | 14.7329 | 0.496364 | 0.248182 | − | 0.968713i | \(-0.420167\pi\) | ||||
0.248182 | + | 0.968713i | \(0.420167\pi\) | |||||||
\(882\) | 5.52910 | 0.186175 | ||||||||
\(883\) | −2.22046 | −0.0747244 | −0.0373622 | − | 0.999302i | \(-0.511896\pi\) | ||||
−0.0373622 | + | 0.999302i | \(0.511896\pi\) | |||||||
\(884\) | −43.4907 | −1.46275 | ||||||||
\(885\) | −13.7903 | −0.463556 | ||||||||
\(886\) | −5.76790 | −0.193776 | ||||||||
\(887\) | −5.41606 | −0.181853 | −0.0909267 | − | 0.995858i | \(-0.528983\pi\) | ||||
−0.0909267 | + | 0.995858i | \(0.528983\pi\) | |||||||
\(888\) | 10.6773 | 0.358306 | ||||||||
\(889\) | −37.2966 | −1.25089 | ||||||||
\(890\) | −34.0017 | −1.13974 | ||||||||
\(891\) | −41.4339 | −1.38809 | ||||||||
\(892\) | −10.6083 | −0.355191 | ||||||||
\(893\) | 34.6639 | 1.15998 | ||||||||
\(894\) | 6.52080 | 0.218088 | ||||||||
\(895\) | 101.663 | 3.39823 | ||||||||
\(896\) | 2.14109 | 0.0715287 | ||||||||
\(897\) | 38.9206 | 1.29952 | ||||||||
\(898\) | 15.6905 | 0.523597 | ||||||||
\(899\) | −0.508769 | −0.0169684 | ||||||||
\(900\) | 30.9793 | 1.03264 | ||||||||
\(901\) | −64.1317 | −2.13654 | ||||||||
\(902\) | 20.5104 | 0.682923 | ||||||||
\(903\) | 35.7407 | 1.18938 | ||||||||
\(904\) | 10.4854 | 0.348738 | ||||||||
\(905\) | 26.7233 | 0.888312 | ||||||||
\(906\) | −18.6951 | −0.621102 | ||||||||
\(907\) | −34.6455 | −1.15039 | −0.575193 | − | 0.818018i | \(-0.695073\pi\) | ||||
−0.575193 | + | 0.818018i | \(0.695073\pi\) | |||||||
\(908\) | −18.8647 | −0.626046 | ||||||||
\(909\) | 39.0445 | 1.29502 | ||||||||
\(910\) | 53.9495 | 1.78841 | ||||||||
\(911\) | −5.96343 | −0.197577 | −0.0987886 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987886 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(912\) | 9.63799 | 0.319146 | ||||||||
\(913\) | −11.4305 | −0.378294 | ||||||||
\(914\) | −23.2567 | −0.769265 | ||||||||
\(915\) | 46.7830 | 1.54660 | ||||||||
\(916\) | 16.8459 | 0.556605 | ||||||||
\(917\) | 47.1598 | 1.55736 | ||||||||
\(918\) | 12.1542 | 0.401149 | ||||||||
\(919\) | −22.9004 | −0.755413 | −0.377707 | − | 0.925925i | \(-0.623287\pi\) | ||||
−0.377707 | + | 0.925925i | \(0.623287\pi\) | |||||||
\(920\) | 12.4494 | 0.410445 | ||||||||
\(921\) | −3.73372 | −0.123030 | ||||||||
\(922\) | −34.5518 | −1.13790 | ||||||||
\(923\) | −18.8909 | −0.621800 | ||||||||
\(924\) | 19.1965 | 0.631520 | ||||||||
\(925\) | 62.8421 | 2.06624 | ||||||||
\(926\) | 2.86618 | 0.0941884 | ||||||||
\(927\) | 12.7617 | 0.419149 | ||||||||
\(928\) | −0.280020 | −0.00919209 | ||||||||
\(929\) | −25.5399 | −0.837937 | −0.418968 | − | 0.908001i | \(-0.637608\pi\) | ||||
−0.418968 | + | 0.908001i | \(0.637608\pi\) | |||||||
\(930\) | −17.9891 | −0.589886 | ||||||||
\(931\) | 10.1242 | 0.331807 | ||||||||
\(932\) | −3.84736 | −0.126024 | ||||||||
\(933\) | −24.3040 | −0.795678 | ||||||||
\(934\) | 12.4586 | 0.407657 | ||||||||
\(935\) | −124.725 | −4.07895 | ||||||||
\(936\) | −13.3954 | −0.437843 | ||||||||
\(937\) | −11.0308 | −0.360360 | −0.180180 | − | 0.983634i | \(-0.557668\pi\) | ||||
−0.180180 | + | 0.983634i | \(0.557668\pi\) | |||||||
\(938\) | 25.0007 | 0.816301 | ||||||||
\(939\) | −60.8798 | −1.98674 | ||||||||
\(940\) | −35.6097 | −1.16146 | ||||||||
\(941\) | 32.9011 | 1.07255 | 0.536273 | − | 0.844044i | \(-0.319832\pi\) | ||||
0.536273 | + | 0.844044i | \(0.319832\pi\) | |||||||
\(942\) | −18.4738 | −0.601909 | ||||||||
\(943\) | 15.2129 | 0.495401 | ||||||||
\(944\) | 1.39283 | 0.0453326 | ||||||||
\(945\) | −15.0771 | −0.490459 | ||||||||
\(946\) | −28.2985 | −0.920062 | ||||||||
\(947\) | −32.2923 | −1.04936 | −0.524680 | − | 0.851300i | \(-0.675815\pi\) | ||||
−0.524680 | + | 0.851300i | \(0.675815\pi\) | |||||||
\(948\) | −10.7907 | −0.350465 | ||||||||
\(949\) | 86.9066 | 2.82111 | ||||||||
\(950\) | 56.7254 | 1.84041 | ||||||||
\(951\) | 6.44583 | 0.209020 | ||||||||
\(952\) | −15.9103 | −0.515655 | ||||||||
\(953\) | −7.13993 | −0.231285 | −0.115643 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115643 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(954\) | −19.7530 | −0.639526 | ||||||||
\(955\) | 6.64045 | 0.214880 | ||||||||
\(956\) | −17.4034 | −0.562867 | ||||||||
\(957\) | −2.51060 | −0.0811561 | ||||||||
\(958\) | −6.58838 | −0.212861 | ||||||||
\(959\) | −13.6876 | −0.441995 | ||||||||
\(960\) | −9.90096 | −0.319552 | ||||||||
\(961\) | −27.6989 | −0.893511 | ||||||||
\(962\) | −27.1729 | −0.876090 | ||||||||
\(963\) | −4.97174 | −0.160212 | ||||||||
\(964\) | 16.4594 | 0.530122 | ||||||||
\(965\) | −69.0633 | −2.22322 | ||||||||
\(966\) | 14.2384 | 0.458112 | ||||||||
\(967\) | 46.4553 | 1.49390 | 0.746952 | − | 0.664878i | \(-0.231517\pi\) | ||||
0.746952 | + | 0.664878i | \(0.231517\pi\) | |||||||
\(968\) | −4.19926 | −0.134969 | ||||||||
\(969\) | −71.6192 | −2.30074 | ||||||||
\(970\) | −64.9593 | −2.08572 | ||||||||
\(971\) | −37.4217 | −1.20092 | −0.600459 | − | 0.799656i | \(-0.705015\pi\) | ||||
−0.600459 | + | 0.799656i | \(0.705015\pi\) | |||||||
\(972\) | 19.5343 | 0.626563 | ||||||||
\(973\) | 16.8927 | 0.541555 | ||||||||
\(974\) | −36.8423 | −1.18050 | ||||||||
\(975\) | −182.179 | −5.83441 | ||||||||
\(976\) | −4.72509 | −0.151246 | ||||||||
\(977\) | 51.9228 | 1.66116 | 0.830579 | − | 0.556902i | \(-0.188010\pi\) | ||||
0.830579 | + | 0.556902i | \(0.188010\pi\) | |||||||
\(978\) | 8.08802 | 0.258627 | ||||||||
\(979\) | 30.7902 | 0.984059 | ||||||||
\(980\) | −10.4004 | −0.332230 | ||||||||
\(981\) | −25.0843 | −0.800879 | ||||||||
\(982\) | −27.2499 | −0.869578 | ||||||||
\(983\) | −37.2095 | −1.18680 | −0.593399 | − | 0.804908i | \(-0.702214\pi\) | ||||
−0.593399 | + | 0.804908i | \(0.702214\pi\) | |||||||
\(984\) | −12.0988 | −0.385695 | ||||||||
\(985\) | −4.94681 | −0.157618 | ||||||||
\(986\) | 2.08080 | 0.0662663 | ||||||||
\(987\) | −40.7267 | −1.29635 | ||||||||
\(988\) | −24.5280 | −0.780340 | ||||||||
\(989\) | −20.9894 | −0.667424 | ||||||||
\(990\) | −38.4162 | −1.22095 | ||||||||
\(991\) | −33.3346 | −1.05891 | −0.529454 | − | 0.848339i | \(-0.677603\pi\) | ||||
−0.529454 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(992\) | 1.81691 | 0.0576868 | ||||||||
\(993\) | 4.11044 | 0.130441 | ||||||||
\(994\) | −6.91087 | −0.219199 | ||||||||
\(995\) | −51.9947 | −1.64834 | ||||||||
\(996\) | 6.74265 | 0.213649 | ||||||||
\(997\) | 41.8887 | 1.32663 | 0.663315 | − | 0.748340i | \(-0.269149\pi\) | ||||
0.663315 | + | 0.748340i | \(0.269149\pi\) | |||||||
\(998\) | −11.0765 | −0.350621 | ||||||||
\(999\) | 7.59394 | 0.240262 |
(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 | 6038.2.a.d.1.10 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6038.2.a.d.1.10 | ✓ | 69 | 1.1 | even | 1 | trivial |