Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, 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("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(0\) |
Dimension: | \(98\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 | ||||||||
\(3\) | −2.67018 | −1.54163 | −0.770814 | − | 0.637060i | \(-0.780150\pi\) | ||||
−0.770814 | + | 0.637060i | \(0.780150\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0387933 | 0.0173489 | 0.00867445 | − | 0.999962i | \(-0.497239\pi\) | ||||
0.00867445 | + | 0.999962i | \(0.497239\pi\) | |||||||
\(6\) | −2.67018 | −1.09010 | ||||||||
\(7\) | −0.245209 | −0.0926803 | −0.0463402 | − | 0.998926i | \(-0.514756\pi\) | ||||
−0.0463402 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.12985 | 1.37662 | ||||||||
\(10\) | 0.0387933 | 0.0122675 | ||||||||
\(11\) | 0.614227 | 0.185196 | 0.0925982 | − | 0.995704i | \(-0.470483\pi\) | ||||
0.0925982 | + | 0.995704i | \(0.470483\pi\) | |||||||
\(12\) | −2.67018 | −0.770814 | ||||||||
\(13\) | 5.44648 | 1.51058 | 0.755290 | − | 0.655390i | \(-0.227496\pi\) | ||||
0.755290 | + | 0.655390i | \(0.227496\pi\) | |||||||
\(14\) | −0.245209 | −0.0655349 | ||||||||
\(15\) | −0.103585 | −0.0267456 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.52679 | 1.09791 | 0.548954 | − | 0.835852i | \(-0.315026\pi\) | ||||
0.548954 | + | 0.835852i | \(0.315026\pi\) | |||||||
\(18\) | 4.12985 | 0.973416 | ||||||||
\(19\) | 6.26006 | 1.43616 | 0.718079 | − | 0.695962i | \(-0.245022\pi\) | ||||
0.718079 | + | 0.695962i | \(0.245022\pi\) | |||||||
\(20\) | 0.0387933 | 0.00867445 | ||||||||
\(21\) | 0.654752 | 0.142879 | ||||||||
\(22\) | 0.614227 | 0.130954 | ||||||||
\(23\) | −5.73257 | −1.19532 | −0.597662 | − | 0.801748i | \(-0.703903\pi\) | ||||
−0.597662 | + | 0.801748i | \(0.703903\pi\) | |||||||
\(24\) | −2.67018 | −0.545048 | ||||||||
\(25\) | −4.99850 | −0.999699 | ||||||||
\(26\) | 5.44648 | 1.06814 | ||||||||
\(27\) | −3.01691 | −0.580604 | ||||||||
\(28\) | −0.245209 | −0.0463402 | ||||||||
\(29\) | −3.88297 | −0.721049 | −0.360524 | − | 0.932750i | \(-0.617402\pi\) | ||||
−0.360524 | + | 0.932750i | \(0.617402\pi\) | |||||||
\(30\) | −0.103585 | −0.0189120 | ||||||||
\(31\) | 2.99444 | 0.537817 | 0.268908 | − | 0.963166i | \(-0.413337\pi\) | ||||
0.268908 | + | 0.963166i | \(0.413337\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.64010 | −0.285504 | ||||||||
\(34\) | 4.52679 | 0.776339 | ||||||||
\(35\) | −0.00951248 | −0.00160790 | ||||||||
\(36\) | 4.12985 | 0.688309 | ||||||||
\(37\) | 5.06219 | 0.832219 | 0.416109 | − | 0.909315i | \(-0.363393\pi\) | ||||
0.416109 | + | 0.909315i | \(0.363393\pi\) | |||||||
\(38\) | 6.26006 | 1.01552 | ||||||||
\(39\) | −14.5431 | −2.32875 | ||||||||
\(40\) | 0.0387933 | 0.00613376 | ||||||||
\(41\) | 7.74952 | 1.21027 | 0.605136 | − | 0.796122i | \(-0.293119\pi\) | ||||
0.605136 | + | 0.796122i | \(0.293119\pi\) | |||||||
\(42\) | 0.654752 | 0.101030 | ||||||||
\(43\) | 6.14495 | 0.937096 | 0.468548 | − | 0.883438i | \(-0.344777\pi\) | ||||
0.468548 | + | 0.883438i | \(0.344777\pi\) | |||||||
\(44\) | 0.614227 | 0.0925982 | ||||||||
\(45\) | 0.160211 | 0.0238828 | ||||||||
\(46\) | −5.73257 | −0.845221 | ||||||||
\(47\) | 13.2172 | 1.92793 | 0.963967 | − | 0.266022i | \(-0.0857094\pi\) | ||||
0.963967 | + | 0.266022i | \(0.0857094\pi\) | |||||||
\(48\) | −2.67018 | −0.385407 | ||||||||
\(49\) | −6.93987 | −0.991410 | ||||||||
\(50\) | −4.99850 | −0.706894 | ||||||||
\(51\) | −12.0873 | −1.69257 | ||||||||
\(52\) | 5.44648 | 0.755290 | ||||||||
\(53\) | −10.8002 | −1.48353 | −0.741764 | − | 0.670661i | \(-0.766010\pi\) | ||||
−0.741764 | + | 0.670661i | \(0.766010\pi\) | |||||||
\(54\) | −3.01691 | −0.410549 | ||||||||
\(55\) | 0.0238279 | 0.00321296 | ||||||||
\(56\) | −0.245209 | −0.0327674 | ||||||||
\(57\) | −16.7155 | −2.21402 | ||||||||
\(58\) | −3.88297 | −0.509858 | ||||||||
\(59\) | 11.5393 | 1.50229 | 0.751144 | − | 0.660139i | \(-0.229503\pi\) | ||||
0.751144 | + | 0.660139i | \(0.229503\pi\) | |||||||
\(60\) | −0.103585 | −0.0133728 | ||||||||
\(61\) | −3.95778 | −0.506741 | −0.253371 | − | 0.967369i | \(-0.581539\pi\) | ||||
−0.253371 | + | 0.967369i | \(0.581539\pi\) | |||||||
\(62\) | 2.99444 | 0.380294 | ||||||||
\(63\) | −1.01268 | −0.127585 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.211287 | 0.0262069 | ||||||||
\(66\) | −1.64010 | −0.201882 | ||||||||
\(67\) | 13.0393 | 1.59300 | 0.796502 | − | 0.604636i | \(-0.206681\pi\) | ||||
0.796502 | + | 0.604636i | \(0.206681\pi\) | |||||||
\(68\) | 4.52679 | 0.548954 | ||||||||
\(69\) | 15.3070 | 1.84274 | ||||||||
\(70\) | −0.00951248 | −0.00113696 | ||||||||
\(71\) | 3.91350 | 0.464447 | 0.232224 | − | 0.972662i | \(-0.425400\pi\) | ||||
0.232224 | + | 0.972662i | \(0.425400\pi\) | |||||||
\(72\) | 4.12985 | 0.486708 | ||||||||
\(73\) | 8.12008 | 0.950383 | 0.475192 | − | 0.879882i | \(-0.342379\pi\) | ||||
0.475192 | + | 0.879882i | \(0.342379\pi\) | |||||||
\(74\) | 5.06219 | 0.588467 | ||||||||
\(75\) | 13.3469 | 1.54116 | ||||||||
\(76\) | 6.26006 | 0.718079 | ||||||||
\(77\) | −0.150614 | −0.0171641 | ||||||||
\(78\) | −14.5431 | −1.64668 | ||||||||
\(79\) | −12.9813 | −1.46051 | −0.730256 | − | 0.683173i | \(-0.760599\pi\) | ||||
−0.730256 | + | 0.683173i | \(0.760599\pi\) | |||||||
\(80\) | 0.0387933 | 0.00433723 | ||||||||
\(81\) | −4.33388 | −0.481542 | ||||||||
\(82\) | 7.74952 | 0.855791 | ||||||||
\(83\) | −16.1098 | −1.76828 | −0.884139 | − | 0.467225i | \(-0.845254\pi\) | ||||
−0.884139 | + | 0.467225i | \(0.845254\pi\) | |||||||
\(84\) | 0.654752 | 0.0714393 | ||||||||
\(85\) | 0.175609 | 0.0190475 | ||||||||
\(86\) | 6.14495 | 0.662627 | ||||||||
\(87\) | 10.3682 | 1.11159 | ||||||||
\(88\) | 0.614227 | 0.0654768 | ||||||||
\(89\) | −0.876082 | −0.0928645 | −0.0464322 | − | 0.998921i | \(-0.514785\pi\) | ||||
−0.0464322 | + | 0.998921i | \(0.514785\pi\) | |||||||
\(90\) | 0.160211 | 0.0168877 | ||||||||
\(91\) | −1.33553 | −0.140001 | ||||||||
\(92\) | −5.73257 | −0.597662 | ||||||||
\(93\) | −7.99568 | −0.829113 | ||||||||
\(94\) | 13.2172 | 1.36326 | ||||||||
\(95\) | 0.242849 | 0.0249158 | ||||||||
\(96\) | −2.67018 | −0.272524 | ||||||||
\(97\) | −4.05879 | −0.412107 | −0.206054 | − | 0.978541i | \(-0.566062\pi\) | ||||
−0.206054 | + | 0.978541i | \(0.566062\pi\) | |||||||
\(98\) | −6.93987 | −0.701033 | ||||||||
\(99\) | 2.53667 | 0.254945 | ||||||||
\(100\) | −4.99850 | −0.499850 | ||||||||
\(101\) | −16.4040 | −1.63226 | −0.816130 | − | 0.577868i | \(-0.803885\pi\) | ||||
−0.816130 | + | 0.577868i | \(0.803885\pi\) | |||||||
\(102\) | −12.0873 | −1.19683 | ||||||||
\(103\) | −10.2928 | −1.01418 | −0.507090 | − | 0.861893i | \(-0.669279\pi\) | ||||
−0.507090 | + | 0.861893i | \(0.669279\pi\) | |||||||
\(104\) | 5.44648 | 0.534071 | ||||||||
\(105\) | 0.0254000 | 0.00247879 | ||||||||
\(106\) | −10.8002 | −1.04901 | ||||||||
\(107\) | −4.20498 | −0.406511 | −0.203256 | − | 0.979126i | \(-0.565152\pi\) | ||||
−0.203256 | + | 0.979126i | \(0.565152\pi\) | |||||||
\(108\) | −3.01691 | −0.290302 | ||||||||
\(109\) | −9.55077 | −0.914798 | −0.457399 | − | 0.889262i | \(-0.651219\pi\) | ||||
−0.457399 | + | 0.889262i | \(0.651219\pi\) | |||||||
\(110\) | 0.0238279 | 0.00227190 | ||||||||
\(111\) | −13.5169 | −1.28297 | ||||||||
\(112\) | −0.245209 | −0.0231701 | ||||||||
\(113\) | −11.0791 | −1.04223 | −0.521116 | − | 0.853486i | \(-0.674484\pi\) | ||||
−0.521116 | + | 0.853486i | \(0.674484\pi\) | |||||||
\(114\) | −16.7155 | −1.56555 | ||||||||
\(115\) | −0.222385 | −0.0207376 | ||||||||
\(116\) | −3.88297 | −0.360524 | ||||||||
\(117\) | 22.4931 | 2.07949 | ||||||||
\(118\) | 11.5393 | 1.06228 | ||||||||
\(119\) | −1.11001 | −0.101755 | ||||||||
\(120\) | −0.103585 | −0.00945598 | ||||||||
\(121\) | −10.6227 | −0.965702 | ||||||||
\(122\) | −3.95778 | −0.358320 | ||||||||
\(123\) | −20.6926 | −1.86579 | ||||||||
\(124\) | 2.99444 | 0.268908 | ||||||||
\(125\) | −0.387875 | −0.0346926 | ||||||||
\(126\) | −1.01268 | −0.0902165 | ||||||||
\(127\) | 2.32324 | 0.206154 | 0.103077 | − | 0.994673i | \(-0.467131\pi\) | ||||
0.103077 | + | 0.994673i | \(0.467131\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −16.4081 | −1.44465 | ||||||||
\(130\) | 0.211287 | 0.0185311 | ||||||||
\(131\) | 14.1634 | 1.23746 | 0.618732 | − | 0.785602i | \(-0.287647\pi\) | ||||
0.618732 | + | 0.785602i | \(0.287647\pi\) | |||||||
\(132\) | −1.64010 | −0.142752 | ||||||||
\(133\) | −1.53502 | −0.133104 | ||||||||
\(134\) | 13.0393 | 1.12642 | ||||||||
\(135\) | −0.117036 | −0.0100728 | ||||||||
\(136\) | 4.52679 | 0.388169 | ||||||||
\(137\) | 1.99119 | 0.170119 | 0.0850594 | − | 0.996376i | \(-0.472892\pi\) | ||||
0.0850594 | + | 0.996376i | \(0.472892\pi\) | |||||||
\(138\) | 15.3070 | 1.30302 | ||||||||
\(139\) | 4.98502 | 0.422824 | 0.211412 | − | 0.977397i | \(-0.432194\pi\) | ||||
0.211412 | + | 0.977397i | \(0.432194\pi\) | |||||||
\(140\) | −0.00951248 | −0.000803951 0 | ||||||||
\(141\) | −35.2924 | −2.97216 | ||||||||
\(142\) | 3.91350 | 0.328414 | ||||||||
\(143\) | 3.34537 | 0.279754 | ||||||||
\(144\) | 4.12985 | 0.344154 | ||||||||
\(145\) | −0.150633 | −0.0125094 | ||||||||
\(146\) | 8.12008 | 0.672023 | ||||||||
\(147\) | 18.5307 | 1.52839 | ||||||||
\(148\) | 5.06219 | 0.416109 | ||||||||
\(149\) | 10.3669 | 0.849290 | 0.424645 | − | 0.905360i | \(-0.360399\pi\) | ||||
0.424645 | + | 0.905360i | \(0.360399\pi\) | |||||||
\(150\) | 13.3469 | 1.08977 | ||||||||
\(151\) | 18.0604 | 1.46973 | 0.734866 | − | 0.678212i | \(-0.237245\pi\) | ||||
0.734866 | + | 0.678212i | \(0.237245\pi\) | |||||||
\(152\) | 6.26006 | 0.507758 | ||||||||
\(153\) | 18.6950 | 1.51140 | ||||||||
\(154\) | −0.150614 | −0.0121368 | ||||||||
\(155\) | 0.116164 | 0.00933053 | ||||||||
\(156\) | −14.5431 | −1.16438 | ||||||||
\(157\) | 2.96996 | 0.237028 | 0.118514 | − | 0.992952i | \(-0.462187\pi\) | ||||
0.118514 | + | 0.992952i | \(0.462187\pi\) | |||||||
\(158\) | −12.9813 | −1.03274 | ||||||||
\(159\) | 28.8386 | 2.28705 | ||||||||
\(160\) | 0.0387933 | 0.00306688 | ||||||||
\(161\) | 1.40568 | 0.110783 | ||||||||
\(162\) | −4.33388 | −0.340501 | ||||||||
\(163\) | 8.25223 | 0.646364 | 0.323182 | − | 0.946337i | \(-0.395247\pi\) | ||||
0.323182 | + | 0.946337i | \(0.395247\pi\) | |||||||
\(164\) | 7.74952 | 0.605136 | ||||||||
\(165\) | −0.0636248 | −0.00495318 | ||||||||
\(166\) | −16.1098 | −1.25036 | ||||||||
\(167\) | −7.38164 | −0.571208 | −0.285604 | − | 0.958348i | \(-0.592194\pi\) | ||||
−0.285604 | + | 0.958348i | \(0.592194\pi\) | |||||||
\(168\) | 0.654752 | 0.0505152 | ||||||||
\(169\) | 16.6641 | 1.28185 | ||||||||
\(170\) | 0.175609 | 0.0134686 | ||||||||
\(171\) | 25.8531 | 1.97704 | ||||||||
\(172\) | 6.14495 | 0.468548 | ||||||||
\(173\) | −10.5712 | −0.803714 | −0.401857 | − | 0.915702i | \(-0.631635\pi\) | ||||
−0.401857 | + | 0.915702i | \(0.631635\pi\) | |||||||
\(174\) | 10.3682 | 0.786012 | ||||||||
\(175\) | 1.22568 | 0.0926524 | ||||||||
\(176\) | 0.614227 | 0.0462991 | ||||||||
\(177\) | −30.8120 | −2.31597 | ||||||||
\(178\) | −0.876082 | −0.0656651 | ||||||||
\(179\) | 8.50968 | 0.636043 | 0.318022 | − | 0.948083i | \(-0.396982\pi\) | ||||
0.318022 | + | 0.948083i | \(0.396982\pi\) | |||||||
\(180\) | 0.160211 | 0.0119414 | ||||||||
\(181\) | 23.7885 | 1.76818 | 0.884092 | − | 0.467314i | \(-0.154778\pi\) | ||||
0.884092 | + | 0.467314i | \(0.154778\pi\) | |||||||
\(182\) | −1.33553 | −0.0989957 | ||||||||
\(183\) | 10.5680 | 0.781207 | ||||||||
\(184\) | −5.73257 | −0.422611 | ||||||||
\(185\) | 0.196379 | 0.0144381 | ||||||||
\(186\) | −7.99568 | −0.586272 | ||||||||
\(187\) | 2.78048 | 0.203329 | ||||||||
\(188\) | 13.2172 | 0.963967 | ||||||||
\(189\) | 0.739773 | 0.0538106 | ||||||||
\(190\) | 0.242849 | 0.0176181 | ||||||||
\(191\) | −9.69339 | −0.701389 | −0.350695 | − | 0.936490i | \(-0.614054\pi\) | ||||
−0.350695 | + | 0.936490i | \(0.614054\pi\) | |||||||
\(192\) | −2.67018 | −0.192704 | ||||||||
\(193\) | −12.9799 | −0.934312 | −0.467156 | − | 0.884175i | \(-0.654721\pi\) | ||||
−0.467156 | + | 0.884175i | \(0.654721\pi\) | |||||||
\(194\) | −4.05879 | −0.291404 | ||||||||
\(195\) | −0.564174 | −0.0404013 | ||||||||
\(196\) | −6.93987 | −0.495705 | ||||||||
\(197\) | 7.79852 | 0.555622 | 0.277811 | − | 0.960636i | \(-0.410391\pi\) | ||||
0.277811 | + | 0.960636i | \(0.410391\pi\) | |||||||
\(198\) | 2.53667 | 0.180273 | ||||||||
\(199\) | −23.1244 | −1.63924 | −0.819621 | − | 0.572905i | \(-0.805816\pi\) | ||||
−0.819621 | + | 0.572905i | \(0.805816\pi\) | |||||||
\(200\) | −4.99850 | −0.353447 | ||||||||
\(201\) | −34.8173 | −2.45582 | ||||||||
\(202\) | −16.4040 | −1.15418 | ||||||||
\(203\) | 0.952139 | 0.0668270 | ||||||||
\(204\) | −12.0873 | −0.846284 | ||||||||
\(205\) | 0.300630 | 0.0209969 | ||||||||
\(206\) | −10.2928 | −0.717133 | ||||||||
\(207\) | −23.6747 | −1.64550 | ||||||||
\(208\) | 5.44648 | 0.377645 | ||||||||
\(209\) | 3.84510 | 0.265971 | ||||||||
\(210\) | 0.0254000 | 0.00175277 | ||||||||
\(211\) | 22.6794 | 1.56131 | 0.780657 | − | 0.624960i | \(-0.214885\pi\) | ||||
0.780657 | + | 0.624960i | \(0.214885\pi\) | |||||||
\(212\) | −10.8002 | −0.741764 | ||||||||
\(213\) | −10.4497 | −0.716005 | ||||||||
\(214\) | −4.20498 | −0.287447 | ||||||||
\(215\) | 0.238383 | 0.0162576 | ||||||||
\(216\) | −3.01691 | −0.205275 | ||||||||
\(217\) | −0.734263 | −0.0498450 | ||||||||
\(218\) | −9.55077 | −0.646860 | ||||||||
\(219\) | −21.6821 | −1.46514 | ||||||||
\(220\) | 0.0238279 | 0.00160648 | ||||||||
\(221\) | 24.6551 | 1.65848 | ||||||||
\(222\) | −13.5169 | −0.907198 | ||||||||
\(223\) | 11.2807 | 0.755413 | 0.377707 | − | 0.925925i | \(-0.376713\pi\) | ||||
0.377707 | + | 0.925925i | \(0.376713\pi\) | |||||||
\(224\) | −0.245209 | −0.0163837 | ||||||||
\(225\) | −20.6430 | −1.37620 | ||||||||
\(226\) | −11.0791 | −0.736969 | ||||||||
\(227\) | 26.0937 | 1.73190 | 0.865951 | − | 0.500129i | \(-0.166714\pi\) | ||||
0.865951 | + | 0.500129i | \(0.166714\pi\) | |||||||
\(228\) | −16.7155 | −1.10701 | ||||||||
\(229\) | 9.06761 | 0.599205 | 0.299602 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299602 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(230\) | −0.222385 | −0.0146637 | ||||||||
\(231\) | 0.402166 | 0.0264606 | ||||||||
\(232\) | −3.88297 | −0.254929 | ||||||||
\(233\) | 17.1795 | 1.12547 | 0.562734 | − | 0.826638i | \(-0.309750\pi\) | ||||
0.562734 | + | 0.826638i | \(0.309750\pi\) | |||||||
\(234\) | 22.4931 | 1.47042 | ||||||||
\(235\) | 0.512741 | 0.0334475 | ||||||||
\(236\) | 11.5393 | 0.751144 | ||||||||
\(237\) | 34.6624 | 2.25157 | ||||||||
\(238\) | −1.11001 | −0.0719513 | ||||||||
\(239\) | −11.7483 | −0.759935 | −0.379967 | − | 0.925000i | \(-0.624065\pi\) | ||||
−0.379967 | + | 0.925000i | \(0.624065\pi\) | |||||||
\(240\) | −0.103585 | −0.00668639 | ||||||||
\(241\) | 9.55671 | 0.615602 | 0.307801 | − | 0.951451i | \(-0.400407\pi\) | ||||
0.307801 | + | 0.951451i | \(0.400407\pi\) | |||||||
\(242\) | −10.6227 | −0.682855 | ||||||||
\(243\) | 20.6229 | 1.32296 | ||||||||
\(244\) | −3.95778 | −0.253371 | ||||||||
\(245\) | −0.269221 | −0.0171999 | ||||||||
\(246\) | −20.6926 | −1.31931 | ||||||||
\(247\) | 34.0953 | 2.16943 | ||||||||
\(248\) | 2.99444 | 0.190147 | ||||||||
\(249\) | 43.0160 | 2.72603 | ||||||||
\(250\) | −0.387875 | −0.0245314 | ||||||||
\(251\) | 3.22576 | 0.203608 | 0.101804 | − | 0.994804i | \(-0.467538\pi\) | ||||
0.101804 | + | 0.994804i | \(0.467538\pi\) | |||||||
\(252\) | −1.01268 | −0.0637927 | ||||||||
\(253\) | −3.52110 | −0.221370 | ||||||||
\(254\) | 2.32324 | 0.145773 | ||||||||
\(255\) | −0.468908 | −0.0293642 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.92975 | 0.245131 | 0.122566 | − | 0.992460i | \(-0.460888\pi\) | ||||
0.122566 | + | 0.992460i | \(0.460888\pi\) | |||||||
\(258\) | −16.4081 | −1.02152 | ||||||||
\(259\) | −1.24129 | −0.0771303 | ||||||||
\(260\) | 0.211287 | 0.0131035 | ||||||||
\(261\) | −16.0361 | −0.992608 | ||||||||
\(262\) | 14.1634 | 0.875020 | ||||||||
\(263\) | 14.9787 | 0.923627 | 0.461814 | − | 0.886977i | \(-0.347199\pi\) | ||||
0.461814 | + | 0.886977i | \(0.347199\pi\) | |||||||
\(264\) | −1.64010 | −0.100941 | ||||||||
\(265\) | −0.418977 | −0.0257376 | ||||||||
\(266\) | −1.53502 | −0.0941184 | ||||||||
\(267\) | 2.33929 | 0.143163 | ||||||||
\(268\) | 13.0393 | 0.796502 | ||||||||
\(269\) | −17.5697 | −1.07124 | −0.535622 | − | 0.844458i | \(-0.679923\pi\) | ||||
−0.535622 | + | 0.844458i | \(0.679923\pi\) | |||||||
\(270\) | −0.117036 | −0.00712258 | ||||||||
\(271\) | 25.9833 | 1.57837 | 0.789186 | − | 0.614154i | \(-0.210503\pi\) | ||||
0.789186 | + | 0.614154i | \(0.210503\pi\) | |||||||
\(272\) | 4.52679 | 0.274477 | ||||||||
\(273\) | 3.56609 | 0.215830 | ||||||||
\(274\) | 1.99119 | 0.120292 | ||||||||
\(275\) | −3.07021 | −0.185141 | ||||||||
\(276\) | 15.3070 | 0.921372 | ||||||||
\(277\) | −12.3616 | −0.742735 | −0.371368 | − | 0.928486i | \(-0.621111\pi\) | ||||
−0.371368 | + | 0.928486i | \(0.621111\pi\) | |||||||
\(278\) | 4.98502 | 0.298982 | ||||||||
\(279\) | 12.3666 | 0.740368 | ||||||||
\(280\) | −0.00951248 | −0.000568479 0 | ||||||||
\(281\) | 19.5555 | 1.16658 | 0.583290 | − | 0.812264i | \(-0.301765\pi\) | ||||
0.583290 | + | 0.812264i | \(0.301765\pi\) | |||||||
\(282\) | −35.2924 | −2.10163 | ||||||||
\(283\) | 6.32929 | 0.376237 | 0.188119 | − | 0.982146i | \(-0.439761\pi\) | ||||
0.188119 | + | 0.982146i | \(0.439761\pi\) | |||||||
\(284\) | 3.91350 | 0.232224 | ||||||||
\(285\) | −0.648449 | −0.0384108 | ||||||||
\(286\) | 3.34537 | 0.197816 | ||||||||
\(287\) | −1.90025 | −0.112168 | ||||||||
\(288\) | 4.12985 | 0.243354 | ||||||||
\(289\) | 3.49187 | 0.205404 | ||||||||
\(290\) | −0.150633 | −0.00884549 | ||||||||
\(291\) | 10.8377 | 0.635317 | ||||||||
\(292\) | 8.12008 | 0.475192 | ||||||||
\(293\) | −23.6910 | −1.38404 | −0.692021 | − | 0.721878i | \(-0.743279\pi\) | ||||
−0.692021 | + | 0.721878i | \(0.743279\pi\) | |||||||
\(294\) | 18.5307 | 1.08073 | ||||||||
\(295\) | 0.447647 | 0.0260630 | ||||||||
\(296\) | 5.06219 | 0.294234 | ||||||||
\(297\) | −1.85307 | −0.107526 | ||||||||
\(298\) | 10.3669 | 0.600539 | ||||||||
\(299\) | −31.2223 | −1.80563 | ||||||||
\(300\) | 13.3469 | 0.770582 | ||||||||
\(301\) | −1.50680 | −0.0868504 | ||||||||
\(302\) | 18.0604 | 1.03926 | ||||||||
\(303\) | 43.8017 | 2.51634 | ||||||||
\(304\) | 6.26006 | 0.359039 | ||||||||
\(305\) | −0.153535 | −0.00879141 | ||||||||
\(306\) | 18.6950 | 1.06872 | ||||||||
\(307\) | 21.6283 | 1.23439 | 0.617197 | − | 0.786809i | \(-0.288268\pi\) | ||||
0.617197 | + | 0.786809i | \(0.288268\pi\) | |||||||
\(308\) | −0.150614 | −0.00858203 | ||||||||
\(309\) | 27.4836 | 1.56349 | ||||||||
\(310\) | 0.116164 | 0.00659768 | ||||||||
\(311\) | −0.398441 | −0.0225935 | −0.0112968 | − | 0.999936i | \(-0.503596\pi\) | ||||
−0.0112968 | + | 0.999936i | \(0.503596\pi\) | |||||||
\(312\) | −14.5431 | −0.823339 | ||||||||
\(313\) | 4.54967 | 0.257162 | 0.128581 | − | 0.991699i | \(-0.458958\pi\) | ||||
0.128581 | + | 0.991699i | \(0.458958\pi\) | |||||||
\(314\) | 2.96996 | 0.167604 | ||||||||
\(315\) | −0.0392851 | −0.00221347 | ||||||||
\(316\) | −12.9813 | −0.730256 | ||||||||
\(317\) | −27.8929 | −1.56662 | −0.783311 | − | 0.621630i | \(-0.786471\pi\) | ||||
−0.783311 | + | 0.621630i | \(0.786471\pi\) | |||||||
\(318\) | 28.8386 | 1.61719 | ||||||||
\(319\) | −2.38502 | −0.133536 | ||||||||
\(320\) | 0.0387933 | 0.00216861 | ||||||||
\(321\) | 11.2281 | 0.626689 | ||||||||
\(322\) | 1.40568 | 0.0783354 | ||||||||
\(323\) | 28.3380 | 1.57677 | ||||||||
\(324\) | −4.33388 | −0.240771 | ||||||||
\(325\) | −27.2242 | −1.51013 | ||||||||
\(326\) | 8.25223 | 0.457049 | ||||||||
\(327\) | 25.5023 | 1.41028 | ||||||||
\(328\) | 7.74952 | 0.427895 | ||||||||
\(329\) | −3.24099 | −0.178682 | ||||||||
\(330\) | −0.0636248 | −0.00350243 | ||||||||
\(331\) | 15.1509 | 0.832767 | 0.416384 | − | 0.909189i | \(-0.363297\pi\) | ||||
0.416384 | + | 0.909189i | \(0.363297\pi\) | |||||||
\(332\) | −16.1098 | −0.884139 | ||||||||
\(333\) | 20.9061 | 1.14565 | ||||||||
\(334\) | −7.38164 | −0.403905 | ||||||||
\(335\) | 0.505838 | 0.0276369 | ||||||||
\(336\) | 0.654752 | 0.0357196 | ||||||||
\(337\) | 20.1118 | 1.09556 | 0.547780 | − | 0.836623i | \(-0.315473\pi\) | ||||
0.547780 | + | 0.836623i | \(0.315473\pi\) | |||||||
\(338\) | 16.6641 | 0.906408 | ||||||||
\(339\) | 29.5831 | 1.60673 | ||||||||
\(340\) | 0.175609 | 0.00952376 | ||||||||
\(341\) | 1.83926 | 0.0996017 | ||||||||
\(342\) | 25.8531 | 1.39798 | ||||||||
\(343\) | 3.41818 | 0.184565 | ||||||||
\(344\) | 6.14495 | 0.331314 | ||||||||
\(345\) | 0.593809 | 0.0319696 | ||||||||
\(346\) | −10.5712 | −0.568312 | ||||||||
\(347\) | −24.3117 | −1.30512 | −0.652559 | − | 0.757738i | \(-0.726305\pi\) | ||||
−0.652559 | + | 0.757738i | \(0.726305\pi\) | |||||||
\(348\) | 10.3682 | 0.555795 | ||||||||
\(349\) | 8.10640 | 0.433926 | 0.216963 | − | 0.976180i | \(-0.430385\pi\) | ||||
0.216963 | + | 0.976180i | \(0.430385\pi\) | |||||||
\(350\) | 1.22568 | 0.0655152 | ||||||||
\(351\) | −16.4315 | −0.877050 | ||||||||
\(352\) | 0.614227 | 0.0327384 | ||||||||
\(353\) | −20.3427 | −1.08273 | −0.541367 | − | 0.840787i | \(-0.682093\pi\) | ||||
−0.541367 | + | 0.840787i | \(0.682093\pi\) | |||||||
\(354\) | −30.8120 | −1.63764 | ||||||||
\(355\) | 0.151818 | 0.00805765 | ||||||||
\(356\) | −0.876082 | −0.0464322 | ||||||||
\(357\) | 2.96393 | 0.156868 | ||||||||
\(358\) | 8.50968 | 0.449750 | ||||||||
\(359\) | 26.7484 | 1.41173 | 0.705864 | − | 0.708347i | \(-0.250559\pi\) | ||||
0.705864 | + | 0.708347i | \(0.250559\pi\) | |||||||
\(360\) | 0.160211 | 0.00844385 | ||||||||
\(361\) | 20.1884 | 1.06255 | ||||||||
\(362\) | 23.7885 | 1.25029 | ||||||||
\(363\) | 28.3646 | 1.48875 | ||||||||
\(364\) | −1.33553 | −0.0700006 | ||||||||
\(365\) | 0.315005 | 0.0164881 | ||||||||
\(366\) | 10.5680 | 0.552397 | ||||||||
\(367\) | 26.4394 | 1.38012 | 0.690062 | − | 0.723750i | \(-0.257583\pi\) | ||||
0.690062 | + | 0.723750i | \(0.257583\pi\) | |||||||
\(368\) | −5.73257 | −0.298831 | ||||||||
\(369\) | 32.0044 | 1.66608 | ||||||||
\(370\) | 0.196379 | 0.0102093 | ||||||||
\(371\) | 2.64832 | 0.137494 | ||||||||
\(372\) | −7.99568 | −0.414557 | ||||||||
\(373\) | −16.9400 | −0.877119 | −0.438560 | − | 0.898702i | \(-0.644511\pi\) | ||||
−0.438560 | + | 0.898702i | \(0.644511\pi\) | |||||||
\(374\) | 2.78048 | 0.143775 | ||||||||
\(375\) | 1.03570 | 0.0534831 | ||||||||
\(376\) | 13.2172 | 0.681628 | ||||||||
\(377\) | −21.1485 | −1.08920 | ||||||||
\(378\) | 0.739773 | 0.0380498 | ||||||||
\(379\) | −37.2869 | −1.91530 | −0.957651 | − | 0.287932i | \(-0.907032\pi\) | ||||
−0.957651 | + | 0.287932i | \(0.907032\pi\) | |||||||
\(380\) | 0.242849 | 0.0124579 | ||||||||
\(381\) | −6.20346 | −0.317813 | ||||||||
\(382\) | −9.69339 | −0.495957 | ||||||||
\(383\) | −24.1208 | −1.23252 | −0.616258 | − | 0.787544i | \(-0.711352\pi\) | ||||
−0.616258 | + | 0.787544i | \(0.711352\pi\) | |||||||
\(384\) | −2.67018 | −0.136262 | ||||||||
\(385\) | −0.00584282 | −0.000297778 0 | ||||||||
\(386\) | −12.9799 | −0.660658 | ||||||||
\(387\) | 25.3777 | 1.29002 | ||||||||
\(388\) | −4.05879 | −0.206054 | ||||||||
\(389\) | 21.2138 | 1.07558 | 0.537792 | − | 0.843078i | \(-0.319259\pi\) | ||||
0.537792 | + | 0.843078i | \(0.319259\pi\) | |||||||
\(390\) | −0.564174 | −0.0285681 | ||||||||
\(391\) | −25.9502 | −1.31236 | ||||||||
\(392\) | −6.93987 | −0.350516 | ||||||||
\(393\) | −37.8189 | −1.90771 | ||||||||
\(394\) | 7.79852 | 0.392884 | ||||||||
\(395\) | −0.503588 | −0.0253383 | ||||||||
\(396\) | 2.53667 | 0.127472 | ||||||||
\(397\) | 25.1165 | 1.26056 | 0.630281 | − | 0.776367i | \(-0.282940\pi\) | ||||
0.630281 | + | 0.776367i | \(0.282940\pi\) | |||||||
\(398\) | −23.1244 | −1.15912 | ||||||||
\(399\) | 4.09879 | 0.205196 | ||||||||
\(400\) | −4.99850 | −0.249925 | ||||||||
\(401\) | 23.0519 | 1.15116 | 0.575580 | − | 0.817746i | \(-0.304777\pi\) | ||||
0.575580 | + | 0.817746i | \(0.304777\pi\) | |||||||
\(402\) | −34.8173 | −1.73653 | ||||||||
\(403\) | 16.3091 | 0.812415 | ||||||||
\(404\) | −16.4040 | −0.816130 | ||||||||
\(405\) | −0.168125 | −0.00835422 | ||||||||
\(406\) | 0.952139 | 0.0472538 | ||||||||
\(407\) | 3.10933 | 0.154124 | ||||||||
\(408\) | −12.0873 | −0.598413 | ||||||||
\(409\) | −30.8180 | −1.52385 | −0.761926 | − | 0.647664i | \(-0.775746\pi\) | ||||
−0.761926 | + | 0.647664i | \(0.775746\pi\) | |||||||
\(410\) | 0.300630 | 0.0148470 | ||||||||
\(411\) | −5.31683 | −0.262260 | ||||||||
\(412\) | −10.2928 | −0.507090 | ||||||||
\(413\) | −2.82954 | −0.139232 | ||||||||
\(414\) | −23.6747 | −1.16355 | ||||||||
\(415\) | −0.624952 | −0.0306777 | ||||||||
\(416\) | 5.44648 | 0.267036 | ||||||||
\(417\) | −13.3109 | −0.651837 | ||||||||
\(418\) | 3.84510 | 0.188070 | ||||||||
\(419\) | −1.65891 | −0.0810428 | −0.0405214 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405214 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(420\) | 0.0254000 | 0.00123939 | ||||||||
\(421\) | −9.64421 | −0.470030 | −0.235015 | − | 0.971992i | \(-0.575514\pi\) | ||||
−0.235015 | + | 0.971992i | \(0.575514\pi\) | |||||||
\(422\) | 22.6794 | 1.10402 | ||||||||
\(423\) | 54.5853 | 2.65403 | ||||||||
\(424\) | −10.8002 | −0.524506 | ||||||||
\(425\) | −22.6272 | −1.09758 | ||||||||
\(426\) | −10.4497 | −0.506292 | ||||||||
\(427\) | 0.970483 | 0.0469649 | ||||||||
\(428\) | −4.20498 | −0.203256 | ||||||||
\(429\) | −8.93275 | −0.431277 | ||||||||
\(430\) | 0.238383 | 0.0114959 | ||||||||
\(431\) | 6.07992 | 0.292859 | 0.146430 | − | 0.989221i | \(-0.453222\pi\) | ||||
0.146430 | + | 0.989221i | \(0.453222\pi\) | |||||||
\(432\) | −3.01691 | −0.145151 | ||||||||
\(433\) | 20.5245 | 0.986343 | 0.493172 | − | 0.869932i | \(-0.335837\pi\) | ||||
0.493172 | + | 0.869932i | \(0.335837\pi\) | |||||||
\(434\) | −0.734263 | −0.0352457 | ||||||||
\(435\) | 0.402218 | 0.0192849 | ||||||||
\(436\) | −9.55077 | −0.457399 | ||||||||
\(437\) | −35.8863 | −1.71667 | ||||||||
\(438\) | −21.6821 | −1.03601 | ||||||||
\(439\) | 4.24562 | 0.202633 | 0.101316 | − | 0.994854i | \(-0.467695\pi\) | ||||
0.101316 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(440\) | 0.0238279 | 0.00113595 | ||||||||
\(441\) | −28.6606 | −1.36479 | ||||||||
\(442\) | 24.6551 | 1.17272 | ||||||||
\(443\) | 25.2000 | 1.19729 | 0.598645 | − | 0.801014i | \(-0.295706\pi\) | ||||
0.598645 | + | 0.801014i | \(0.295706\pi\) | |||||||
\(444\) | −13.5169 | −0.641486 | ||||||||
\(445\) | −0.0339861 | −0.00161110 | ||||||||
\(446\) | 11.2807 | 0.534158 | ||||||||
\(447\) | −27.6815 | −1.30929 | ||||||||
\(448\) | −0.245209 | −0.0115850 | ||||||||
\(449\) | 19.0875 | 0.900796 | 0.450398 | − | 0.892828i | \(-0.351282\pi\) | ||||
0.450398 | + | 0.892828i | \(0.351282\pi\) | |||||||
\(450\) | −20.6430 | −0.973123 | ||||||||
\(451\) | 4.75996 | 0.224138 | ||||||||
\(452\) | −11.0791 | −0.521116 | ||||||||
\(453\) | −48.2244 | −2.26578 | ||||||||
\(454\) | 26.0937 | 1.22464 | ||||||||
\(455\) | −0.0518095 | −0.00242887 | ||||||||
\(456\) | −16.7155 | −0.782775 | ||||||||
\(457\) | 28.5928 | 1.33752 | 0.668758 | − | 0.743480i | \(-0.266826\pi\) | ||||
0.668758 | + | 0.743480i | \(0.266826\pi\) | |||||||
\(458\) | 9.06761 | 0.423702 | ||||||||
\(459\) | −13.6569 | −0.637450 | ||||||||
\(460\) | −0.222385 | −0.0103688 | ||||||||
\(461\) | 8.59595 | 0.400354 | 0.200177 | − | 0.979760i | \(-0.435848\pi\) | ||||
0.200177 | + | 0.979760i | \(0.435848\pi\) | |||||||
\(462\) | 0.402166 | 0.0187105 | ||||||||
\(463\) | 23.6207 | 1.09775 | 0.548873 | − | 0.835906i | \(-0.315057\pi\) | ||||
0.548873 | + | 0.835906i | \(0.315057\pi\) | |||||||
\(464\) | −3.88297 | −0.180262 | ||||||||
\(465\) | −0.310179 | −0.0143842 | ||||||||
\(466\) | 17.1795 | 0.795826 | ||||||||
\(467\) | −16.0747 | −0.743849 | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(468\) | 22.4931 | 1.03975 | ||||||||
\(469\) | −3.19735 | −0.147640 | ||||||||
\(470\) | 0.512741 | 0.0236510 | ||||||||
\(471\) | −7.93032 | −0.365410 | ||||||||
\(472\) | 11.5393 | 0.531139 | ||||||||
\(473\) | 3.77440 | 0.173547 | ||||||||
\(474\) | 34.6624 | 1.59210 | ||||||||
\(475\) | −31.2909 | −1.43573 | ||||||||
\(476\) | −1.11001 | −0.0508773 | ||||||||
\(477\) | −44.6034 | −2.04225 | ||||||||
\(478\) | −11.7483 | −0.537355 | ||||||||
\(479\) | −4.74526 | −0.216816 | −0.108408 | − | 0.994106i | \(-0.534575\pi\) | ||||
−0.108408 | + | 0.994106i | \(0.534575\pi\) | |||||||
\(480\) | −0.103585 | −0.00472799 | ||||||||
\(481\) | 27.5711 | 1.25713 | ||||||||
\(482\) | 9.55671 | 0.435296 | ||||||||
\(483\) | −3.75341 | −0.170786 | ||||||||
\(484\) | −10.6227 | −0.482851 | ||||||||
\(485\) | −0.157454 | −0.00714961 | ||||||||
\(486\) | 20.6229 | 0.935476 | ||||||||
\(487\) | −9.08566 | −0.411710 | −0.205855 | − | 0.978582i | \(-0.565998\pi\) | ||||
−0.205855 | + | 0.978582i | \(0.565998\pi\) | |||||||
\(488\) | −3.95778 | −0.179160 | ||||||||
\(489\) | −22.0349 | −0.996454 | ||||||||
\(490\) | −0.269221 | −0.0121622 | ||||||||
\(491\) | 6.41519 | 0.289513 | 0.144757 | − | 0.989467i | \(-0.453760\pi\) | ||||
0.144757 | + | 0.989467i | \(0.453760\pi\) | |||||||
\(492\) | −20.6926 | −0.932894 | ||||||||
\(493\) | −17.5774 | −0.791646 | ||||||||
\(494\) | 34.0953 | 1.53402 | ||||||||
\(495\) | 0.0984058 | 0.00442301 | ||||||||
\(496\) | 2.99444 | 0.134454 | ||||||||
\(497\) | −0.959626 | −0.0430451 | ||||||||
\(498\) | 43.0160 | 1.92759 | ||||||||
\(499\) | −34.9687 | −1.56541 | −0.782707 | − | 0.622390i | \(-0.786162\pi\) | ||||
−0.782707 | + | 0.622390i | \(0.786162\pi\) | |||||||
\(500\) | −0.387875 | −0.0173463 | ||||||||
\(501\) | 19.7103 | 0.880591 | ||||||||
\(502\) | 3.22576 | 0.143973 | ||||||||
\(503\) | 1.26728 | 0.0565054 | 0.0282527 | − | 0.999601i | \(-0.491006\pi\) | ||||
0.0282527 | + | 0.999601i | \(0.491006\pi\) | |||||||
\(504\) | −1.01268 | −0.0451082 | ||||||||
\(505\) | −0.636366 | −0.0283179 | ||||||||
\(506\) | −3.52110 | −0.156532 | ||||||||
\(507\) | −44.4962 | −1.97614 | ||||||||
\(508\) | 2.32324 | 0.103077 | ||||||||
\(509\) | −7.47595 | −0.331366 | −0.165683 | − | 0.986179i | \(-0.552983\pi\) | ||||
−0.165683 | + | 0.986179i | \(0.552983\pi\) | |||||||
\(510\) | −0.468908 | −0.0207636 | ||||||||
\(511\) | −1.99112 | −0.0880818 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −18.8860 | −0.833839 | ||||||||
\(514\) | 3.92975 | 0.173334 | ||||||||
\(515\) | −0.399292 | −0.0175949 | ||||||||
\(516\) | −16.4081 | −0.722327 | ||||||||
\(517\) | 8.11839 | 0.357047 | ||||||||
\(518\) | −1.24129 | −0.0545393 | ||||||||
\(519\) | 28.2270 | 1.23903 | ||||||||
\(520\) | 0.211287 | 0.00926555 | ||||||||
\(521\) | 0.840534 | 0.0368245 | 0.0184122 | − | 0.999830i | \(-0.494139\pi\) | ||||
0.0184122 | + | 0.999830i | \(0.494139\pi\) | |||||||
\(522\) | −16.0361 | −0.701880 | ||||||||
\(523\) | 14.4486 | 0.631792 | 0.315896 | − | 0.948794i | \(-0.397695\pi\) | ||||
0.315896 | + | 0.948794i | \(0.397695\pi\) | |||||||
\(524\) | 14.1634 | 0.618732 | ||||||||
\(525\) | −3.27277 | −0.142836 | ||||||||
\(526\) | 14.9787 | 0.653103 | ||||||||
\(527\) | 13.5552 | 0.590474 | ||||||||
\(528\) | −1.64010 | −0.0713760 | ||||||||
\(529\) | 9.86237 | 0.428799 | ||||||||
\(530\) | −0.418977 | −0.0181992 | ||||||||
\(531\) | 47.6556 | 2.06807 | ||||||||
\(532\) | −1.53502 | −0.0665518 | ||||||||
\(533\) | 42.2076 | 1.82821 | ||||||||
\(534\) | 2.33929 | 0.101231 | ||||||||
\(535\) | −0.163125 | −0.00705252 | ||||||||
\(536\) | 13.0393 | 0.563212 | ||||||||
\(537\) | −22.7224 | −0.980542 | ||||||||
\(538\) | −17.5697 | −0.757484 | ||||||||
\(539\) | −4.26266 | −0.183606 | ||||||||
\(540\) | −0.117036 | −0.00503642 | ||||||||
\(541\) | −10.1803 | −0.437684 | −0.218842 | − | 0.975760i | \(-0.570228\pi\) | ||||
−0.218842 | + | 0.975760i | \(0.570228\pi\) | |||||||
\(542\) | 25.9833 | 1.11608 | ||||||||
\(543\) | −63.5195 | −2.72588 | ||||||||
\(544\) | 4.52679 | 0.194085 | ||||||||
\(545\) | −0.370506 | −0.0158707 | ||||||||
\(546\) | 3.56609 | 0.152615 | ||||||||
\(547\) | −29.4273 | −1.25822 | −0.629109 | − | 0.777317i | \(-0.716580\pi\) | ||||
−0.629109 | + | 0.777317i | \(0.716580\pi\) | |||||||
\(548\) | 1.99119 | 0.0850594 | ||||||||
\(549\) | −16.3450 | −0.697589 | ||||||||
\(550\) | −3.07021 | −0.130914 | ||||||||
\(551\) | −24.3076 | −1.03554 | ||||||||
\(552\) | 15.3070 | 0.651509 | ||||||||
\(553\) | 3.18314 | 0.135361 | ||||||||
\(554\) | −12.3616 | −0.525193 | ||||||||
\(555\) | −0.524367 | −0.0222582 | ||||||||
\(556\) | 4.98502 | 0.211412 | ||||||||
\(557\) | 4.29434 | 0.181957 | 0.0909784 | − | 0.995853i | \(-0.471001\pi\) | ||||
0.0909784 | + | 0.995853i | \(0.471001\pi\) | |||||||
\(558\) | 12.3666 | 0.523519 | ||||||||
\(559\) | 33.4683 | 1.41556 | ||||||||
\(560\) | −0.00951248 | −0.000401975 0 | ||||||||
\(561\) | −7.42438 | −0.313457 | ||||||||
\(562\) | 19.5555 | 0.824897 | ||||||||
\(563\) | −7.70744 | −0.324830 | −0.162415 | − | 0.986723i | \(-0.551928\pi\) | ||||
−0.162415 | + | 0.986723i | \(0.551928\pi\) | |||||||
\(564\) | −35.2924 | −1.48608 | ||||||||
\(565\) | −0.429794 | −0.0180816 | ||||||||
\(566\) | 6.32929 | 0.266040 | ||||||||
\(567\) | 1.06271 | 0.0446294 | ||||||||
\(568\) | 3.91350 | 0.164207 | ||||||||
\(569\) | −32.9066 | −1.37951 | −0.689757 | − | 0.724040i | \(-0.742283\pi\) | ||||
−0.689757 | + | 0.724040i | \(0.742283\pi\) | |||||||
\(570\) | −0.648449 | −0.0271606 | ||||||||
\(571\) | 33.9154 | 1.41931 | 0.709657 | − | 0.704547i | \(-0.248850\pi\) | ||||
0.709657 | + | 0.704547i | \(0.248850\pi\) | |||||||
\(572\) | 3.34537 | 0.139877 | ||||||||
\(573\) | 25.8831 | 1.08128 | ||||||||
\(574\) | −1.90025 | −0.0793150 | ||||||||
\(575\) | 28.6542 | 1.19496 | ||||||||
\(576\) | 4.12985 | 0.172077 | ||||||||
\(577\) | 42.5789 | 1.77258 | 0.886291 | − | 0.463128i | \(-0.153273\pi\) | ||||
0.886291 | + | 0.463128i | \(0.153273\pi\) | |||||||
\(578\) | 3.49187 | 0.145242 | ||||||||
\(579\) | 34.6586 | 1.44036 | ||||||||
\(580\) | −0.150633 | −0.00625470 | ||||||||
\(581\) | 3.95026 | 0.163884 | ||||||||
\(582\) | 10.8377 | 0.449237 | ||||||||
\(583\) | −6.63380 | −0.274744 | ||||||||
\(584\) | 8.12008 | 0.336011 | ||||||||
\(585\) | 0.872584 | 0.0360769 | ||||||||
\(586\) | −23.6910 | −0.978665 | ||||||||
\(587\) | −16.6455 | −0.687034 | −0.343517 | − | 0.939146i | \(-0.611618\pi\) | ||||
−0.343517 | + | 0.939146i | \(0.611618\pi\) | |||||||
\(588\) | 18.5307 | 0.764193 | ||||||||
\(589\) | 18.7454 | 0.772389 | ||||||||
\(590\) | 0.447647 | 0.0184294 | ||||||||
\(591\) | −20.8235 | −0.856562 | ||||||||
\(592\) | 5.06219 | 0.208055 | ||||||||
\(593\) | 31.7189 | 1.30254 | 0.651270 | − | 0.758846i | \(-0.274236\pi\) | ||||
0.651270 | + | 0.758846i | \(0.274236\pi\) | |||||||
\(594\) | −1.85307 | −0.0760323 | ||||||||
\(595\) | −0.0430610 | −0.00176533 | ||||||||
\(596\) | 10.3669 | 0.424645 | ||||||||
\(597\) | 61.7462 | 2.52710 | ||||||||
\(598\) | −31.2223 | −1.27678 | ||||||||
\(599\) | −8.33948 | −0.340742 | −0.170371 | − | 0.985380i | \(-0.554497\pi\) | ||||
−0.170371 | + | 0.985380i | \(0.554497\pi\) | |||||||
\(600\) | 13.3469 | 0.544884 | ||||||||
\(601\) | 40.0492 | 1.63364 | 0.816820 | − | 0.576893i | \(-0.195735\pi\) | ||||
0.816820 | + | 0.576893i | \(0.195735\pi\) | |||||||
\(602\) | −1.50680 | −0.0614125 | ||||||||
\(603\) | 53.8504 | 2.19296 | ||||||||
\(604\) | 18.0604 | 0.734866 | ||||||||
\(605\) | −0.412091 | −0.0167539 | ||||||||
\(606\) | 43.8017 | 1.77932 | ||||||||
\(607\) | −46.5892 | −1.89100 | −0.945498 | − | 0.325628i | \(-0.894424\pi\) | ||||
−0.945498 | + | 0.325628i | \(0.894424\pi\) | |||||||
\(608\) | 6.26006 | 0.253879 | ||||||||
\(609\) | −2.54238 | −0.103022 | ||||||||
\(610\) | −0.153535 | −0.00621646 | ||||||||
\(611\) | 71.9874 | 2.91230 | ||||||||
\(612\) | 18.6950 | 0.755700 | ||||||||
\(613\) | −20.3636 | −0.822479 | −0.411240 | − | 0.911527i | \(-0.634904\pi\) | ||||
−0.411240 | + | 0.911527i | \(0.634904\pi\) | |||||||
\(614\) | 21.6283 | 0.872848 | ||||||||
\(615\) | −0.802734 | −0.0323694 | ||||||||
\(616\) | −0.150614 | −0.00606841 | ||||||||
\(617\) | −4.26438 | −0.171677 | −0.0858387 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858387 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(618\) | 27.4836 | 1.10555 | ||||||||
\(619\) | −32.4660 | −1.30492 | −0.652460 | − | 0.757823i | \(-0.726263\pi\) | ||||
−0.652460 | + | 0.757823i | \(0.726263\pi\) | |||||||
\(620\) | 0.116164 | 0.00466526 | ||||||||
\(621\) | 17.2946 | 0.694010 | ||||||||
\(622\) | −0.398441 | −0.0159760 | ||||||||
\(623\) | 0.214823 | 0.00860671 | ||||||||
\(624\) | −14.5431 | −0.582189 | ||||||||
\(625\) | 24.9774 | 0.999097 | ||||||||
\(626\) | 4.54967 | 0.181841 | ||||||||
\(627\) | −10.2671 | −0.410029 | ||||||||
\(628\) | 2.96996 | 0.118514 | ||||||||
\(629\) | 22.9155 | 0.913700 | ||||||||
\(630\) | −0.0392851 | −0.00156516 | ||||||||
\(631\) | 12.9019 | 0.513616 | 0.256808 | − | 0.966462i | \(-0.417329\pi\) | ||||
0.256808 | + | 0.966462i | \(0.417329\pi\) | |||||||
\(632\) | −12.9813 | −0.516369 | ||||||||
\(633\) | −60.5580 | −2.40697 | ||||||||
\(634\) | −27.8929 | −1.10777 | ||||||||
\(635\) | 0.0901262 | 0.00357655 | ||||||||
\(636\) | 28.8386 | 1.14352 | ||||||||
\(637\) | −37.7979 | −1.49761 | ||||||||
\(638\) | −2.38502 | −0.0944240 | ||||||||
\(639\) | 16.1622 | 0.639366 | ||||||||
\(640\) | 0.0387933 | 0.00153344 | ||||||||
\(641\) | −4.86586 | −0.192190 | −0.0960949 | − | 0.995372i | \(-0.530635\pi\) | ||||
−0.0960949 | + | 0.995372i | \(0.530635\pi\) | |||||||
\(642\) | 11.2281 | 0.443136 | ||||||||
\(643\) | 2.11293 | 0.0833260 | 0.0416630 | − | 0.999132i | \(-0.486734\pi\) | ||||
0.0416630 | + | 0.999132i | \(0.486734\pi\) | |||||||
\(644\) | 1.40568 | 0.0553915 | ||||||||
\(645\) | −0.636525 | −0.0250632 | ||||||||
\(646\) | 28.3380 | 1.11494 | ||||||||
\(647\) | −43.1312 | −1.69566 | −0.847831 | − | 0.530266i | \(-0.822092\pi\) | ||||
−0.847831 | + | 0.530266i | \(0.822092\pi\) | |||||||
\(648\) | −4.33388 | −0.170251 | ||||||||
\(649\) | 7.08774 | 0.278218 | ||||||||
\(650\) | −27.2242 | −1.06782 | ||||||||
\(651\) | 1.96061 | 0.0768425 | ||||||||
\(652\) | 8.25223 | 0.323182 | ||||||||
\(653\) | −14.8454 | −0.580945 | −0.290473 | − | 0.956883i | \(-0.593813\pi\) | ||||
−0.290473 | + | 0.956883i | \(0.593813\pi\) | |||||||
\(654\) | 25.5023 | 0.997217 | ||||||||
\(655\) | 0.549447 | 0.0214687 | ||||||||
\(656\) | 7.74952 | 0.302568 | ||||||||
\(657\) | 33.5347 | 1.30831 | ||||||||
\(658\) | −3.24099 | −0.126347 | ||||||||
\(659\) | −30.7917 | −1.19948 | −0.599738 | − | 0.800196i | \(-0.704729\pi\) | ||||
−0.599738 | + | 0.800196i | \(0.704729\pi\) | |||||||
\(660\) | −0.0636248 | −0.00247659 | ||||||||
\(661\) | −13.5504 | −0.527049 | −0.263525 | − | 0.964653i | \(-0.584885\pi\) | ||||
−0.263525 | + | 0.964653i | \(0.584885\pi\) | |||||||
\(662\) | 15.1509 | 0.588855 | ||||||||
\(663\) | −65.8335 | −2.55676 | ||||||||
\(664\) | −16.1098 | −0.625180 | ||||||||
\(665\) | −0.0595487 | −0.00230920 | ||||||||
\(666\) | 20.9061 | 0.810095 | ||||||||
\(667\) | 22.2594 | 0.861887 | ||||||||
\(668\) | −7.38164 | −0.285604 | ||||||||
\(669\) | −30.1216 | −1.16457 | ||||||||
\(670\) | 0.505838 | 0.0195422 | ||||||||
\(671\) | −2.43097 | −0.0938467 | ||||||||
\(672\) | 0.654752 | 0.0252576 | ||||||||
\(673\) | −8.10403 | −0.312387 | −0.156194 | − | 0.987726i | \(-0.549922\pi\) | ||||
−0.156194 | + | 0.987726i | \(0.549922\pi\) | |||||||
\(674\) | 20.1118 | 0.774678 | ||||||||
\(675\) | 15.0800 | 0.580429 | ||||||||
\(676\) | 16.6641 | 0.640927 | ||||||||
\(677\) | 16.9160 | 0.650134 | 0.325067 | − | 0.945691i | \(-0.394613\pi\) | ||||
0.325067 | + | 0.945691i | \(0.394613\pi\) | |||||||
\(678\) | 29.5831 | 1.13613 | ||||||||
\(679\) | 0.995252 | 0.0381942 | ||||||||
\(680\) | 0.175609 | 0.00673431 | ||||||||
\(681\) | −69.6749 | −2.66995 | ||||||||
\(682\) | 1.83926 | 0.0704291 | ||||||||
\(683\) | 25.0868 | 0.959921 | 0.479960 | − | 0.877290i | \(-0.340651\pi\) | ||||
0.479960 | + | 0.877290i | \(0.340651\pi\) | |||||||
\(684\) | 25.8531 | 0.988520 | ||||||||
\(685\) | 0.0772449 | 0.00295137 | ||||||||
\(686\) | 3.41818 | 0.130507 | ||||||||
\(687\) | −24.2121 | −0.923751 | ||||||||
\(688\) | 6.14495 | 0.234274 | ||||||||
\(689\) | −58.8233 | −2.24099 | ||||||||
\(690\) | 0.593809 | 0.0226059 | ||||||||
\(691\) | −20.1568 | −0.766803 | −0.383401 | − | 0.923582i | \(-0.625247\pi\) | ||||
−0.383401 | + | 0.923582i | \(0.625247\pi\) | |||||||
\(692\) | −10.5712 | −0.401857 | ||||||||
\(693\) | −0.622014 | −0.0236284 | ||||||||
\(694\) | −24.3117 | −0.922858 | ||||||||
\(695\) | 0.193386 | 0.00733553 | ||||||||
\(696\) | 10.3682 | 0.393006 | ||||||||
\(697\) | 35.0805 | 1.32877 | ||||||||
\(698\) | 8.10640 | 0.306832 | ||||||||
\(699\) | −45.8724 | −1.73505 | ||||||||
\(700\) | 1.22568 | 0.0463262 | ||||||||
\(701\) | 48.7422 | 1.84097 | 0.920484 | − | 0.390780i | \(-0.127795\pi\) | ||||
0.920484 | + | 0.390780i | \(0.127795\pi\) | |||||||
\(702\) | −16.4315 | −0.620168 | ||||||||
\(703\) | 31.6896 | 1.19520 | ||||||||
\(704\) | 0.614227 | 0.0231496 | ||||||||
\(705\) | −1.36911 | −0.0515637 | ||||||||
\(706\) | −20.3427 | −0.765608 | ||||||||
\(707\) | 4.02241 | 0.151278 | ||||||||
\(708\) | −30.8120 | −1.15798 | ||||||||
\(709\) | 23.0709 | 0.866447 | 0.433223 | − | 0.901287i | \(-0.357376\pi\) | ||||
0.433223 | + | 0.901287i | \(0.357376\pi\) | |||||||
\(710\) | 0.151818 | 0.00569762 | ||||||||
\(711\) | −53.6109 | −2.01057 | ||||||||
\(712\) | −0.876082 | −0.0328326 | ||||||||
\(713\) | −17.1658 | −0.642865 | ||||||||
\(714\) | 2.96393 | 0.110922 | ||||||||
\(715\) | 0.129778 | 0.00485343 | ||||||||
\(716\) | 8.50968 | 0.318022 | ||||||||
\(717\) | 31.3701 | 1.17154 | ||||||||
\(718\) | 26.7484 | 0.998243 | ||||||||
\(719\) | −10.8499 | −0.404632 | −0.202316 | − | 0.979320i | \(-0.564847\pi\) | ||||
−0.202316 | + | 0.979320i | \(0.564847\pi\) | |||||||
\(720\) | 0.160211 | 0.00597070 | ||||||||
\(721\) | 2.52389 | 0.0939944 | ||||||||
\(722\) | 20.1884 | 0.751335 | ||||||||
\(723\) | −25.5181 | −0.949029 | ||||||||
\(724\) | 23.7885 | 0.884092 | ||||||||
\(725\) | 19.4090 | 0.720832 | ||||||||
\(726\) | 28.3646 | 1.05271 | ||||||||
\(727\) | −22.4701 | −0.833371 | −0.416686 | − | 0.909051i | \(-0.636808\pi\) | ||||
−0.416686 | + | 0.909051i | \(0.636808\pi\) | |||||||
\(728\) | −1.33553 | −0.0494979 | ||||||||
\(729\) | −42.0653 | −1.55797 | ||||||||
\(730\) | 0.315005 | 0.0116589 | ||||||||
\(731\) | 27.8169 | 1.02885 | ||||||||
\(732\) | 10.5680 | 0.390603 | ||||||||
\(733\) | −17.7389 | −0.655201 | −0.327600 | − | 0.944816i | \(-0.606240\pi\) | ||||
−0.327600 | + | 0.944816i | \(0.606240\pi\) | |||||||
\(734\) | 26.4394 | 0.975895 | ||||||||
\(735\) | 0.718867 | 0.0265158 | ||||||||
\(736\) | −5.73257 | −0.211305 | ||||||||
\(737\) | 8.00909 | 0.295019 | ||||||||
\(738\) | 32.0044 | 1.17810 | ||||||||
\(739\) | 18.9612 | 0.697500 | 0.348750 | − | 0.937216i | \(-0.386606\pi\) | ||||
0.348750 | + | 0.937216i | \(0.386606\pi\) | |||||||
\(740\) | 0.196379 | 0.00721904 | ||||||||
\(741\) | −91.0405 | −3.34446 | ||||||||
\(742\) | 2.64832 | 0.0972228 | ||||||||
\(743\) | −27.2233 | −0.998727 | −0.499364 | − | 0.866392i | \(-0.666433\pi\) | ||||
−0.499364 | + | 0.866392i | \(0.666433\pi\) | |||||||
\(744\) | −7.99568 | −0.293136 | ||||||||
\(745\) | 0.402167 | 0.0147343 | ||||||||
\(746\) | −16.9400 | −0.620217 | ||||||||
\(747\) | −66.5310 | −2.43424 | ||||||||
\(748\) | 2.78048 | 0.101664 | ||||||||
\(749\) | 1.03110 | 0.0376756 | ||||||||
\(750\) | 1.03570 | 0.0378182 | ||||||||
\(751\) | −21.0078 | −0.766585 | −0.383292 | − | 0.923627i | \(-0.625210\pi\) | ||||
−0.383292 | + | 0.923627i | \(0.625210\pi\) | |||||||
\(752\) | 13.2172 | 0.481983 | ||||||||
\(753\) | −8.61336 | −0.313888 | ||||||||
\(754\) | −21.1485 | −0.770183 | ||||||||
\(755\) | 0.700622 | 0.0254982 | ||||||||
\(756\) | 0.739773 | 0.0269053 | ||||||||
\(757\) | −13.9970 | −0.508729 | −0.254364 | − | 0.967108i | \(-0.581866\pi\) | ||||
−0.254364 | + | 0.967108i | \(0.581866\pi\) | |||||||
\(758\) | −37.2869 | −1.35432 | ||||||||
\(759\) | 9.40197 | 0.341270 | ||||||||
\(760\) | 0.242849 | 0.00880905 | ||||||||
\(761\) | 29.3070 | 1.06238 | 0.531188 | − | 0.847254i | \(-0.321746\pi\) | ||||
0.531188 | + | 0.847254i | \(0.321746\pi\) | |||||||
\(762\) | −6.20346 | −0.224728 | ||||||||
\(763\) | 2.34194 | 0.0847837 | ||||||||
\(764\) | −9.69339 | −0.350695 | ||||||||
\(765\) | 0.725241 | 0.0262211 | ||||||||
\(766\) | −24.1208 | −0.871520 | ||||||||
\(767\) | 62.8485 | 2.26933 | ||||||||
\(768\) | −2.67018 | −0.0963518 | ||||||||
\(769\) | 4.66718 | 0.168303 | 0.0841514 | − | 0.996453i | \(-0.473182\pi\) | ||||
0.0841514 | + | 0.996453i | \(0.473182\pi\) | |||||||
\(770\) | −0.00584282 | −0.000210561 0 | ||||||||
\(771\) | −10.4931 | −0.377901 | ||||||||
\(772\) | −12.9799 | −0.467156 | ||||||||
\(773\) | 12.0542 | 0.433558 | 0.216779 | − | 0.976221i | \(-0.430445\pi\) | ||||
0.216779 | + | 0.976221i | \(0.430445\pi\) | |||||||
\(774\) | 25.3777 | 0.912184 | ||||||||
\(775\) | −14.9677 | −0.537655 | ||||||||
\(776\) | −4.05879 | −0.145702 | ||||||||
\(777\) | 3.31448 | 0.118906 | ||||||||
\(778\) | 21.2138 | 0.760553 | ||||||||
\(779\) | 48.5125 | 1.73814 | ||||||||
\(780\) | −0.564174 | −0.0202007 | ||||||||
\(781\) | 2.40378 | 0.0860140 | ||||||||
\(782\) | −25.9502 | −0.927976 | ||||||||
\(783\) | 11.7146 | 0.418644 | ||||||||
\(784\) | −6.93987 | −0.247853 | ||||||||
\(785\) | 0.115215 | 0.00411218 | ||||||||
\(786\) | −37.8189 | −1.34895 | ||||||||
\(787\) | 44.0561 | 1.57043 | 0.785215 | − | 0.619223i | \(-0.212552\pi\) | ||||
0.785215 | + | 0.619223i | \(0.212552\pi\) | |||||||
\(788\) | 7.79852 | 0.277811 | ||||||||
\(789\) | −39.9958 | −1.42389 | ||||||||
\(790\) | −0.503588 | −0.0179169 | ||||||||
\(791\) | 2.71669 | 0.0965944 | ||||||||
\(792\) | 2.53667 | 0.0901366 | ||||||||
\(793\) | −21.5559 | −0.765474 | ||||||||
\(794\) | 25.1165 | 0.891352 | ||||||||
\(795\) | 1.11874 | 0.0396778 | ||||||||
\(796\) | −23.1244 | −0.819621 | ||||||||
\(797\) | −7.00035 | −0.247965 | −0.123983 | − | 0.992284i | \(-0.539567\pi\) | ||||
−0.123983 | + | 0.992284i | \(0.539567\pi\) | |||||||
\(798\) | 4.09879 | 0.145096 | ||||||||
\(799\) | 59.8318 | 2.11670 | ||||||||
\(800\) | −4.99850 | −0.176723 | ||||||||
\(801\) | −3.61809 | −0.127839 | ||||||||
\(802\) | 23.0519 | 0.813992 | ||||||||
\(803\) | 4.98757 | 0.176008 | ||||||||
\(804\) | −34.8173 | −1.22791 | ||||||||
\(805\) | 0.0545309 | 0.00192196 | ||||||||
\(806\) | 16.3091 | 0.574464 | ||||||||
\(807\) | 46.9143 | 1.65146 | ||||||||
\(808\) | −16.4040 | −0.577091 | ||||||||
\(809\) | −21.2848 | −0.748335 | −0.374168 | − | 0.927361i | \(-0.622072\pi\) | ||||
−0.374168 | + | 0.927361i | \(0.622072\pi\) | |||||||
\(810\) | −0.168125 | −0.00590733 | ||||||||
\(811\) | −3.97132 | −0.139452 | −0.0697260 | − | 0.997566i | \(-0.522213\pi\) | ||||
−0.0697260 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(812\) | 0.952139 | 0.0334135 | ||||||||
\(813\) | −69.3800 | −2.43326 | ||||||||
\(814\) | 3.10933 | 0.108982 | ||||||||
\(815\) | 0.320131 | 0.0112137 | ||||||||
\(816\) | −12.0873 | −0.423142 | ||||||||
\(817\) | 38.4678 | 1.34582 | ||||||||
\(818\) | −30.8180 | −1.07753 | ||||||||
\(819\) | −5.51552 | −0.192728 | ||||||||
\(820\) | 0.300630 | 0.0104984 | ||||||||
\(821\) | 9.80769 | 0.342291 | 0.171145 | − | 0.985246i | \(-0.445253\pi\) | ||||
0.171145 | + | 0.985246i | \(0.445253\pi\) | |||||||
\(822\) | −5.31683 | −0.185446 | ||||||||
\(823\) | −29.2818 | −1.02070 | −0.510349 | − | 0.859967i | \(-0.670484\pi\) | ||||
−0.510349 | + | 0.859967i | \(0.670484\pi\) | |||||||
\(824\) | −10.2928 | −0.358567 | ||||||||
\(825\) | 8.19801 | 0.285418 | ||||||||
\(826\) | −2.82954 | −0.0984522 | ||||||||
\(827\) | −15.6278 | −0.543431 | −0.271716 | − | 0.962378i | \(-0.587591\pi\) | ||||
−0.271716 | + | 0.962378i | \(0.587591\pi\) | |||||||
\(828\) | −23.6747 | −0.822752 | ||||||||
\(829\) | −12.1408 | −0.421667 | −0.210833 | − | 0.977522i | \(-0.567618\pi\) | ||||
−0.210833 | + | 0.977522i | \(0.567618\pi\) | |||||||
\(830\) | −0.624952 | −0.0216924 | ||||||||
\(831\) | 33.0076 | 1.14502 | ||||||||
\(832\) | 5.44648 | 0.188823 | ||||||||
\(833\) | −31.4154 | −1.08848 | ||||||||
\(834\) | −13.3109 | −0.460919 | ||||||||
\(835\) | −0.286358 | −0.00990984 | ||||||||
\(836\) | 3.84510 | 0.132986 | ||||||||
\(837\) | −9.03394 | −0.312259 | ||||||||
\(838\) | −1.65891 | −0.0573059 | ||||||||
\(839\) | −3.99697 | −0.137991 | −0.0689953 | − | 0.997617i | \(-0.521979\pi\) | ||||
−0.0689953 | + | 0.997617i | \(0.521979\pi\) | |||||||
\(840\) | 0.0254000 | 0.000876383 0 | ||||||||
\(841\) | −13.9226 | −0.480089 | ||||||||
\(842\) | −9.64421 | −0.332361 | ||||||||
\(843\) | −52.2166 | −1.79843 | ||||||||
\(844\) | 22.6794 | 0.780657 | ||||||||
\(845\) | 0.646456 | 0.0222388 | ||||||||
\(846\) | 54.5853 | 1.87668 | ||||||||
\(847\) | 2.60479 | 0.0895016 | ||||||||
\(848\) | −10.8002 | −0.370882 | ||||||||
\(849\) | −16.9003 | −0.580018 | ||||||||
\(850\) | −22.6272 | −0.776105 | ||||||||
\(851\) | −29.0194 | −0.994771 | ||||||||
\(852\) | −10.4497 | −0.358002 | ||||||||
\(853\) | −8.45459 | −0.289480 | −0.144740 | − | 0.989470i | \(-0.546235\pi\) | ||||
−0.144740 | + | 0.989470i | \(0.546235\pi\) | |||||||
\(854\) | 0.970483 | 0.0332092 | ||||||||
\(855\) | 1.00293 | 0.0342995 | ||||||||
\(856\) | −4.20498 | −0.143723 | ||||||||
\(857\) | 13.0534 | 0.445895 | 0.222948 | − | 0.974830i | \(-0.428432\pi\) | ||||
0.222948 | + | 0.974830i | \(0.428432\pi\) | |||||||
\(858\) | −8.93275 | −0.304959 | ||||||||
\(859\) | 47.9735 | 1.63684 | 0.818418 | − | 0.574624i | \(-0.194852\pi\) | ||||
0.818418 | + | 0.574624i | \(0.194852\pi\) | |||||||
\(860\) | 0.238383 | 0.00812880 | ||||||||
\(861\) | 5.07401 | 0.172922 | ||||||||
\(862\) | 6.07992 | 0.207083 | ||||||||
\(863\) | 13.0411 | 0.443924 | 0.221962 | − | 0.975055i | \(-0.428754\pi\) | ||||
0.221962 | + | 0.975055i | \(0.428754\pi\) | |||||||
\(864\) | −3.01691 | −0.102637 | ||||||||
\(865\) | −0.410092 | −0.0139436 | ||||||||
\(866\) | 20.5245 | 0.697450 | ||||||||
\(867\) | −9.32390 | −0.316656 | ||||||||
\(868\) | −0.734263 | −0.0249225 | ||||||||
\(869\) | −7.97348 | −0.270482 | ||||||||
\(870\) | 0.402218 | 0.0136365 | ||||||||
\(871\) | 71.0182 | 2.40636 | ||||||||
\(872\) | −9.55077 | −0.323430 | ||||||||
\(873\) | −16.7622 | −0.567314 | ||||||||
\(874\) | −35.8863 | −1.21387 | ||||||||
\(875\) | 0.0951104 | 0.00321532 | ||||||||
\(876\) | −21.6821 | −0.732569 | ||||||||
\(877\) | −17.9480 | −0.606062 | −0.303031 | − | 0.952981i | \(-0.597999\pi\) | ||||
−0.303031 | + | 0.952981i | \(0.597999\pi\) | |||||||
\(878\) | 4.24562 | 0.143283 | ||||||||
\(879\) | 63.2591 | 2.13368 | ||||||||
\(880\) | 0.0238279 | 0.000803239 0 | ||||||||
\(881\) | 35.8679 | 1.20842 | 0.604211 | − | 0.796825i | \(-0.293489\pi\) | ||||
0.604211 | + | 0.796825i | \(0.293489\pi\) | |||||||
\(882\) | −28.6606 | −0.965054 | ||||||||
\(883\) | −5.14535 | −0.173155 | −0.0865773 | − | 0.996245i | \(-0.527593\pi\) | ||||
−0.0865773 | + | 0.996245i | \(0.527593\pi\) | |||||||
\(884\) | 24.6551 | 0.829240 | ||||||||
\(885\) | −1.19530 | −0.0401795 | ||||||||
\(886\) | 25.2000 | 0.846612 | ||||||||
\(887\) | −11.8793 | −0.398868 | −0.199434 | − | 0.979911i | \(-0.563910\pi\) | ||||
−0.199434 | + | 0.979911i | \(0.563910\pi\) | |||||||
\(888\) | −13.5169 | −0.453599 | ||||||||
\(889\) | −0.569679 | −0.0191064 | ||||||||
\(890\) | −0.0339861 | −0.00113922 | ||||||||
\(891\) | −2.66198 | −0.0891798 | ||||||||
\(892\) | 11.2807 | 0.377707 | ||||||||
\(893\) | 82.7408 | 2.76882 | ||||||||
\(894\) | −27.6815 | −0.925807 | ||||||||
\(895\) | 0.330119 | 0.0110346 | ||||||||
\(896\) | −0.245209 | −0.00819186 | ||||||||
\(897\) | 83.3691 | 2.78361 | ||||||||
\(898\) | 19.0875 | 0.636959 | ||||||||
\(899\) | −11.6273 | −0.387792 | ||||||||
\(900\) | −20.6430 | −0.688102 | ||||||||
\(901\) | −48.8905 | −1.62878 | ||||||||
\(902\) | 4.75996 | 0.158489 | ||||||||
\(903\) | 4.02342 | 0.133891 | ||||||||
\(904\) | −11.0791 | −0.368485 | ||||||||
\(905\) | 0.922834 | 0.0306760 | ||||||||
\(906\) | −48.2244 | −1.60215 | ||||||||
\(907\) | −16.3792 | −0.543863 | −0.271931 | − | 0.962317i | \(-0.587662\pi\) | ||||
−0.271931 | + | 0.962317i | \(0.587662\pi\) | |||||||
\(908\) | 26.0937 | 0.865951 | ||||||||
\(909\) | −67.7462 | −2.24700 | ||||||||
\(910\) | −0.0518095 | −0.00171747 | ||||||||
\(911\) | 12.1555 | 0.402730 | 0.201365 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201365 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(912\) | −16.7155 | −0.553505 | ||||||||
\(913\) | −9.89506 | −0.327479 | ||||||||
\(914\) | 28.5928 | 0.945767 | ||||||||
\(915\) | 0.409967 | 0.0135531 | ||||||||
\(916\) | 9.06761 | 0.299602 | ||||||||
\(917\) | −3.47300 | −0.114689 | ||||||||
\(918\) | −13.6569 | −0.450746 | ||||||||
\(919\) | 12.2556 | 0.404275 | 0.202137 | − | 0.979357i | \(-0.435211\pi\) | ||||
0.202137 | + | 0.979357i | \(0.435211\pi\) | |||||||
\(920\) | −0.222385 | −0.00733183 | ||||||||
\(921\) | −57.7515 | −1.90298 | ||||||||
\(922\) | 8.59595 | 0.283093 | ||||||||
\(923\) | 21.3148 | 0.701585 | ||||||||
\(924\) | 0.402166 | 0.0132303 | ||||||||
\(925\) | −25.3033 | −0.831968 | ||||||||
\(926\) | 23.6207 | 0.776224 | ||||||||
\(927\) | −42.5077 | −1.39614 | ||||||||
\(928\) | −3.88297 | −0.127465 | ||||||||
\(929\) | −29.0287 | −0.952400 | −0.476200 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476200 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(930\) | −0.310179 | −0.0101712 | ||||||||
\(931\) | −43.4441 | −1.42382 | ||||||||
\(932\) | 17.1795 | 0.562734 | ||||||||
\(933\) | 1.06391 | 0.0348308 | ||||||||
\(934\) | −16.0747 | −0.525981 | ||||||||
\(935\) | 0.107864 | 0.00352753 | ||||||||
\(936\) | 22.4931 | 0.735211 | ||||||||
\(937\) | −11.9568 | −0.390613 | −0.195306 | − | 0.980742i | \(-0.562570\pi\) | ||||
−0.195306 | + | 0.980742i | \(0.562570\pi\) | |||||||
\(938\) | −3.19735 | −0.104397 | ||||||||
\(939\) | −12.1484 | −0.396449 | ||||||||
\(940\) | 0.512741 | 0.0167238 | ||||||||
\(941\) | 48.7480 | 1.58914 | 0.794569 | − | 0.607174i | \(-0.207697\pi\) | ||||
0.794569 | + | 0.607174i | \(0.207697\pi\) | |||||||
\(942\) | −7.93032 | −0.258384 | ||||||||
\(943\) | −44.4246 | −1.44667 | ||||||||
\(944\) | 11.5393 | 0.375572 | ||||||||
\(945\) | 0.0286983 | 0.000933554 0 | ||||||||
\(946\) | 3.77440 | 0.122716 | ||||||||
\(947\) | 44.7818 | 1.45521 | 0.727606 | − | 0.685995i | \(-0.240633\pi\) | ||||
0.727606 | + | 0.685995i | \(0.240633\pi\) | |||||||
\(948\) | 34.6624 | 1.12578 | ||||||||
\(949\) | 44.2258 | 1.43563 | ||||||||
\(950\) | −31.2909 | −1.01521 | ||||||||
\(951\) | 74.4790 | 2.41515 | ||||||||
\(952\) | −1.11001 | −0.0359757 | ||||||||
\(953\) | −4.49735 | −0.145684 | −0.0728418 | − | 0.997344i | \(-0.523207\pi\) | ||||
−0.0728418 | + | 0.997344i | \(0.523207\pi\) | |||||||
\(954\) | −44.6034 | −1.44409 | ||||||||
\(955\) | −0.376039 | −0.0121683 | ||||||||
\(956\) | −11.7483 | −0.379967 | ||||||||
\(957\) | 6.36844 | 0.205862 | ||||||||
\(958\) | −4.74526 | −0.153312 | ||||||||
\(959\) | −0.488258 | −0.0157667 | ||||||||
\(960\) | −0.103585 | −0.00334319 | ||||||||
\(961\) | −22.0334 | −0.710753 | ||||||||
\(962\) | 27.5711 | 0.888928 | ||||||||
\(963\) | −17.3660 | −0.559610 | ||||||||
\(964\) | 9.55671 | 0.307801 | ||||||||
\(965\) | −0.503533 | −0.0162093 | ||||||||
\(966\) | −3.75341 | −0.120764 | ||||||||
\(967\) | 40.2014 | 1.29279 | 0.646395 | − | 0.763003i | \(-0.276276\pi\) | ||||
0.646395 | + | 0.763003i | \(0.276276\pi\) | |||||||
\(968\) | −10.6227 | −0.341427 | ||||||||
\(969\) | −75.6676 | −2.43079 | ||||||||
\(970\) | −0.157454 | −0.00505554 | ||||||||
\(971\) | 38.9525 | 1.25005 | 0.625023 | − | 0.780607i | \(-0.285090\pi\) | ||||
0.625023 | + | 0.780607i | \(0.285090\pi\) | |||||||
\(972\) | 20.6229 | 0.661481 | ||||||||
\(973\) | −1.22237 | −0.0391875 | ||||||||
\(974\) | −9.08566 | −0.291123 | ||||||||
\(975\) | 72.6934 | 2.32805 | ||||||||
\(976\) | −3.95778 | −0.126685 | ||||||||
\(977\) | 11.2106 | 0.358657 | 0.179329 | − | 0.983789i | \(-0.442607\pi\) | ||||
0.179329 | + | 0.983789i | \(0.442607\pi\) | |||||||
\(978\) | −22.0349 | −0.704599 | ||||||||
\(979\) | −0.538113 | −0.0171982 | ||||||||
\(980\) | −0.269221 | −0.00859994 | ||||||||
\(981\) | −39.4433 | −1.25933 | ||||||||
\(982\) | 6.41519 | 0.204717 | ||||||||
\(983\) | −24.7558 | −0.789587 | −0.394793 | − | 0.918770i | \(-0.629184\pi\) | ||||
−0.394793 | + | 0.918770i | \(0.629184\pi\) | |||||||
\(984\) | −20.6926 | −0.659656 | ||||||||
\(985\) | 0.302531 | 0.00963943 | ||||||||
\(986\) | −17.5774 | −0.559778 | ||||||||
\(987\) | 8.65402 | 0.275460 | ||||||||
\(988\) | 34.0953 | 1.08472 | ||||||||
\(989\) | −35.2264 | −1.12013 | ||||||||
\(990\) | 0.0984058 | 0.00312754 | ||||||||
\(991\) | −23.3731 | −0.742473 | −0.371236 | − | 0.928538i | \(-0.621066\pi\) | ||||
−0.371236 | + | 0.928538i | \(0.621066\pi\) | |||||||
\(992\) | 2.99444 | 0.0950734 | ||||||||
\(993\) | −40.4555 | −1.28382 | ||||||||
\(994\) | −0.959626 | −0.0304375 | ||||||||
\(995\) | −0.897071 | −0.0284391 | ||||||||
\(996\) | 43.0160 | 1.36301 | ||||||||
\(997\) | −54.1021 | −1.71343 | −0.856716 | − | 0.515788i | \(-0.827499\pi\) | ||||
−0.856716 | + | 0.515788i | \(0.827499\pi\) | |||||||
\(998\) | −34.9687 | −1.10692 | ||||||||
\(999\) | −15.2722 | −0.483190 |
(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 | 8006.2.a.d.1.12 | ✓ | 98 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.d.1.12 | ✓ | 98 | 1.1 | even | 1 | trivial |