Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(1,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.31743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58181 | −1.82561 | −0.912807 | − | 0.408392i | \(-0.866090\pi\) | ||||
−0.912807 | + | 0.408392i | \(0.866090\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.66573 | 2.33286 | ||||||||
\(5\) | −2.71878 | −1.21588 | −0.607938 | − | 0.793984i | \(-0.708003\pi\) | ||||
−0.607938 | + | 0.793984i | \(0.708003\pi\) | |||||||
\(6\) | 2.58181 | 1.05402 | ||||||||
\(7\) | −4.30059 | −1.62547 | −0.812735 | − | 0.582633i | \(-0.802022\pi\) | ||||
−0.812735 | + | 0.582633i | \(0.802022\pi\) | |||||||
\(8\) | −6.88240 | −2.43329 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.01937 | 2.21972 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.66573 | −1.34688 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 11.1033 | 2.96748 | ||||||||
\(15\) | 2.71878 | 0.701987 | ||||||||
\(16\) | 8.43756 | 2.10939 | ||||||||
\(17\) | −6.11056 | −1.48203 | −0.741014 | − | 0.671489i | \(-0.765655\pi\) | ||||
−0.741014 | + | 0.671489i | \(0.765655\pi\) | |||||||
\(18\) | −2.58181 | −0.608538 | ||||||||
\(19\) | −0.300590 | −0.0689600 | −0.0344800 | − | 0.999405i | \(-0.510977\pi\) | ||||
−0.0344800 | + | 0.999405i | \(0.510977\pi\) | |||||||
\(20\) | −12.6851 | −2.83647 | ||||||||
\(21\) | 4.30059 | 0.938466 | ||||||||
\(22\) | 2.58181 | 0.550443 | ||||||||
\(23\) | 1.49789 | 0.312331 | 0.156165 | − | 0.987731i | \(-0.450087\pi\) | ||||
0.156165 | + | 0.987731i | \(0.450087\pi\) | |||||||
\(24\) | 6.88240 | 1.40486 | ||||||||
\(25\) | 2.39178 | 0.478356 | ||||||||
\(26\) | −2.58181 | −0.506334 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −20.0654 | −3.79200 | ||||||||
\(29\) | −0.312085 | −0.0579527 | −0.0289763 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289763 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(30\) | −7.01937 | −1.28156 | ||||||||
\(31\) | 4.55094 | 0.817373 | 0.408686 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408686 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(32\) | −8.01937 | −1.41764 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 15.7763 | 2.70561 | ||||||||
\(35\) | 11.6924 | 1.97637 | ||||||||
\(36\) | 4.66573 | 0.777621 | ||||||||
\(37\) | −7.96632 | −1.30965 | −0.654827 | − | 0.755779i | \(-0.727259\pi\) | ||||
−0.654827 | + | 0.755779i | \(0.727259\pi\) | |||||||
\(38\) | 0.776064 | 0.125894 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 18.7117 | 2.95859 | ||||||||
\(41\) | 1.03087 | 0.160994 | 0.0804972 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804972 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(42\) | −11.1033 | −1.71328 | ||||||||
\(43\) | 12.4906 | 1.90480 | 0.952401 | − | 0.304849i | \(-0.0986059\pi\) | ||||
0.952401 | + | 0.304849i | \(0.0986059\pi\) | |||||||
\(44\) | −4.66573 | −0.703385 | ||||||||
\(45\) | −2.71878 | −0.405292 | ||||||||
\(46\) | −3.86725 | −0.570195 | ||||||||
\(47\) | 13.1299 | 1.91520 | 0.957599 | − | 0.288105i | \(-0.0930253\pi\) | ||||
0.957599 | + | 0.288105i | \(0.0930253\pi\) | |||||||
\(48\) | −8.43756 | −1.21786 | ||||||||
\(49\) | 11.4951 | 1.64215 | ||||||||
\(50\) | −6.17511 | −0.873292 | ||||||||
\(51\) | 6.11056 | 0.855650 | ||||||||
\(52\) | 4.66573 | 0.647020 | ||||||||
\(53\) | 8.49507 | 1.16689 | 0.583444 | − | 0.812153i | \(-0.301705\pi\) | ||||
0.583444 | + | 0.812153i | \(0.301705\pi\) | |||||||
\(54\) | 2.58181 | 0.351339 | ||||||||
\(55\) | 2.71878 | 0.366601 | ||||||||
\(56\) | 29.5984 | 3.95525 | ||||||||
\(57\) | 0.300590 | 0.0398141 | ||||||||
\(58\) | 0.805743 | 0.105799 | ||||||||
\(59\) | 9.22535 | 1.20104 | 0.600519 | − | 0.799610i | \(-0.294961\pi\) | ||||
0.600519 | + | 0.799610i | \(0.294961\pi\) | |||||||
\(60\) | 12.6851 | 1.63764 | ||||||||
\(61\) | −9.86021 | −1.26247 | −0.631235 | − | 0.775591i | \(-0.717452\pi\) | ||||
−0.631235 | + | 0.775591i | \(0.717452\pi\) | |||||||
\(62\) | −11.7496 | −1.49221 | ||||||||
\(63\) | −4.30059 | −0.541823 | ||||||||
\(64\) | 3.82934 | 0.478668 | ||||||||
\(65\) | −2.71878 | −0.337223 | ||||||||
\(66\) | −2.58181 | −0.317798 | ||||||||
\(67\) | −8.05024 | −0.983493 | −0.491747 | − | 0.870738i | \(-0.663641\pi\) | ||||
−0.491747 | + | 0.870738i | \(0.663641\pi\) | |||||||
\(68\) | −28.5102 | −3.45737 | ||||||||
\(69\) | −1.49789 | −0.180324 | ||||||||
\(70\) | −30.1874 | −3.60809 | ||||||||
\(71\) | −0.696596 | −0.0826707 | −0.0413353 | − | 0.999145i | \(-0.513161\pi\) | ||||
−0.0413353 | + | 0.999145i | \(0.513161\pi\) | |||||||
\(72\) | −6.88240 | −0.811098 | ||||||||
\(73\) | 4.57454 | 0.535409 | 0.267705 | − | 0.963501i | \(-0.413735\pi\) | ||||
0.267705 | + | 0.963501i | \(0.413735\pi\) | |||||||
\(74\) | 20.5675 | 2.39092 | ||||||||
\(75\) | −2.39178 | −0.276179 | ||||||||
\(76\) | −1.40247 | −0.160874 | ||||||||
\(77\) | 4.30059 | 0.490098 | ||||||||
\(78\) | 2.58181 | 0.292332 | ||||||||
\(79\) | −17.0918 | −1.92298 | −0.961489 | − | 0.274844i | \(-0.911374\pi\) | ||||
−0.961489 | + | 0.274844i | \(0.911374\pi\) | |||||||
\(80\) | −22.9399 | −2.56476 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.66150 | −0.293914 | ||||||||
\(83\) | 8.76902 | 0.962525 | 0.481263 | − | 0.876576i | \(-0.340178\pi\) | ||||
0.481263 | + | 0.876576i | \(0.340178\pi\) | |||||||
\(84\) | 20.0654 | 2.18931 | ||||||||
\(85\) | 16.6133 | 1.80196 | ||||||||
\(86\) | −32.2484 | −3.47743 | ||||||||
\(87\) | 0.312085 | 0.0334590 | ||||||||
\(88\) | 6.88240 | 0.733666 | ||||||||
\(89\) | −3.24754 | −0.344238 | −0.172119 | − | 0.985076i | \(-0.555061\pi\) | ||||
−0.172119 | + | 0.985076i | \(0.555061\pi\) | |||||||
\(90\) | 7.01937 | 0.739907 | ||||||||
\(91\) | −4.30059 | −0.450824 | ||||||||
\(92\) | 6.98873 | 0.728625 | ||||||||
\(93\) | −4.55094 | −0.471910 | ||||||||
\(94\) | −33.8990 | −3.49641 | ||||||||
\(95\) | 0.817238 | 0.0838468 | ||||||||
\(96\) | 8.01937 | 0.818474 | ||||||||
\(97\) | 7.63063 | 0.774773 | 0.387387 | − | 0.921917i | \(-0.373378\pi\) | ||||
0.387387 | + | 0.921917i | \(0.373378\pi\) | |||||||
\(98\) | −29.6781 | −2.99794 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 11.1594 | 1.11594 | ||||||||
\(101\) | 3.83661 | 0.381757 | 0.190878 | − | 0.981614i | \(-0.438866\pi\) | ||||
0.190878 | + | 0.981614i | \(0.438866\pi\) | |||||||
\(102\) | −15.7763 | −1.56209 | ||||||||
\(103\) | 11.3315 | 1.11652 | 0.558261 | − | 0.829666i | \(-0.311469\pi\) | ||||
0.558261 | + | 0.829666i | \(0.311469\pi\) | |||||||
\(104\) | −6.88240 | −0.674875 | ||||||||
\(105\) | −11.6924 | −1.14106 | ||||||||
\(106\) | −21.9326 | −2.13029 | ||||||||
\(107\) | −15.5526 | −1.50352 | −0.751762 | − | 0.659434i | \(-0.770796\pi\) | ||||
−0.751762 | + | 0.659434i | \(0.770796\pi\) | |||||||
\(108\) | −4.66573 | −0.448960 | ||||||||
\(109\) | −0.0266392 | −0.00255157 | −0.00127578 | − | 0.999999i | \(-0.500406\pi\) | ||||
−0.00127578 | + | 0.999999i | \(0.500406\pi\) | |||||||
\(110\) | −7.01937 | −0.669271 | ||||||||
\(111\) | 7.96632 | 0.756129 | ||||||||
\(112\) | −36.2865 | −3.42875 | ||||||||
\(113\) | −18.4333 | −1.73406 | −0.867031 | − | 0.498254i | \(-0.833975\pi\) | ||||
−0.867031 | + | 0.498254i | \(0.833975\pi\) | |||||||
\(114\) | −0.776064 | −0.0726851 | ||||||||
\(115\) | −4.07243 | −0.379756 | ||||||||
\(116\) | −1.45610 | −0.135196 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −23.8181 | −2.19263 | ||||||||
\(119\) | 26.2790 | 2.40899 | ||||||||
\(120\) | −18.7117 | −1.70814 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 25.4572 | 2.30478 | ||||||||
\(123\) | −1.03087 | −0.0929502 | ||||||||
\(124\) | 21.2335 | 1.90682 | ||||||||
\(125\) | 7.09119 | 0.634255 | ||||||||
\(126\) | 11.1033 | 0.989160 | ||||||||
\(127\) | −8.01514 | −0.711229 | −0.355615 | − | 0.934633i | \(-0.615728\pi\) | ||||
−0.355615 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(128\) | 6.15212 | 0.543776 | ||||||||
\(129\) | −12.4906 | −1.09974 | ||||||||
\(130\) | 7.01937 | 0.615640 | ||||||||
\(131\) | 11.5437 | 1.00858 | 0.504288 | − | 0.863536i | \(-0.331755\pi\) | ||||
0.504288 | + | 0.863536i | \(0.331755\pi\) | |||||||
\(132\) | 4.66573 | 0.406100 | ||||||||
\(133\) | 1.29271 | 0.112092 | ||||||||
\(134\) | 20.7842 | 1.79548 | ||||||||
\(135\) | 2.71878 | 0.233996 | ||||||||
\(136\) | 42.0553 | 3.60621 | ||||||||
\(137\) | −5.97781 | −0.510719 | −0.255360 | − | 0.966846i | \(-0.582194\pi\) | ||||
−0.255360 | + | 0.966846i | \(0.582194\pi\) | |||||||
\(138\) | 3.86725 | 0.329202 | ||||||||
\(139\) | 9.85576 | 0.835954 | 0.417977 | − | 0.908458i | \(-0.362739\pi\) | ||||
0.417977 | + | 0.908458i | \(0.362739\pi\) | |||||||
\(140\) | 54.5534 | 4.61060 | ||||||||
\(141\) | −13.1299 | −1.10574 | ||||||||
\(142\) | 1.79848 | 0.150925 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 8.43756 | 0.703130 | ||||||||
\(145\) | 0.848491 | 0.0704633 | ||||||||
\(146\) | −11.8106 | −0.977451 | ||||||||
\(147\) | −11.4951 | −0.948097 | ||||||||
\(148\) | −37.1687 | −3.05525 | ||||||||
\(149\) | −11.5703 | −0.947877 | −0.473938 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473938 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(150\) | 6.17511 | 0.504196 | ||||||||
\(151\) | −3.24308 | −0.263918 | −0.131959 | − | 0.991255i | \(-0.542127\pi\) | ||||
−0.131959 | + | 0.991255i | \(0.542127\pi\) | |||||||
\(152\) | 2.06878 | 0.167800 | ||||||||
\(153\) | −6.11056 | −0.494010 | ||||||||
\(154\) | −11.1033 | −0.894729 | ||||||||
\(155\) | −12.3730 | −0.993825 | ||||||||
\(156\) | −4.66573 | −0.373557 | ||||||||
\(157\) | 8.21363 | 0.655519 | 0.327759 | − | 0.944761i | \(-0.393706\pi\) | ||||
0.327759 | + | 0.944761i | \(0.393706\pi\) | |||||||
\(158\) | 44.1277 | 3.51061 | ||||||||
\(159\) | −8.49507 | −0.673703 | ||||||||
\(160\) | 21.8029 | 1.72367 | ||||||||
\(161\) | −6.44179 | −0.507684 | ||||||||
\(162\) | −2.58181 | −0.202846 | ||||||||
\(163\) | −2.80574 | −0.219763 | −0.109881 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(164\) | 4.80975 | 0.375578 | ||||||||
\(165\) | −2.71878 | −0.211657 | ||||||||
\(166\) | −22.6399 | −1.75720 | ||||||||
\(167\) | −1.93827 | −0.149987 | −0.0749937 | − | 0.997184i | \(-0.523894\pi\) | ||||
−0.0749937 | + | 0.997184i | \(0.523894\pi\) | |||||||
\(168\) | −29.5984 | −2.28356 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −42.8923 | −3.28969 | ||||||||
\(171\) | −0.300590 | −0.0229867 | ||||||||
\(172\) | 58.2778 | 4.44364 | ||||||||
\(173\) | −8.55235 | −0.650223 | −0.325112 | − | 0.945676i | \(-0.605402\pi\) | ||||
−0.325112 | + | 0.945676i | \(0.605402\pi\) | |||||||
\(174\) | −0.805743 | −0.0610832 | ||||||||
\(175\) | −10.2861 | −0.777553 | ||||||||
\(176\) | −8.43756 | −0.636005 | ||||||||
\(177\) | −9.22535 | −0.693420 | ||||||||
\(178\) | 8.38451 | 0.628446 | ||||||||
\(179\) | 17.9312 | 1.34024 | 0.670121 | − | 0.742252i | \(-0.266242\pi\) | ||||
0.670121 | + | 0.742252i | \(0.266242\pi\) | |||||||
\(180\) | −12.6851 | −0.945492 | ||||||||
\(181\) | 0.334272 | 0.0248462 | 0.0124231 | − | 0.999923i | \(-0.496046\pi\) | ||||
0.0124231 | + | 0.999923i | \(0.496046\pi\) | |||||||
\(182\) | 11.1033 | 0.823031 | ||||||||
\(183\) | 9.86021 | 0.728888 | ||||||||
\(184\) | −10.3090 | −0.759993 | ||||||||
\(185\) | 21.6587 | 1.59238 | ||||||||
\(186\) | 11.7496 | 0.861526 | ||||||||
\(187\) | 6.11056 | 0.446848 | ||||||||
\(188\) | 61.2607 | 4.46790 | ||||||||
\(189\) | 4.30059 | 0.312822 | ||||||||
\(190\) | −2.10995 | −0.153072 | ||||||||
\(191\) | −20.1538 | −1.45827 | −0.729137 | − | 0.684367i | \(-0.760078\pi\) | ||||
−0.729137 | + | 0.684367i | \(0.760078\pi\) | |||||||
\(192\) | −3.82934 | −0.276359 | ||||||||
\(193\) | 22.5689 | 1.62455 | 0.812273 | − | 0.583278i | \(-0.198230\pi\) | ||||
0.812273 | + | 0.583278i | \(0.198230\pi\) | |||||||
\(194\) | −19.7008 | −1.41444 | ||||||||
\(195\) | 2.71878 | 0.194696 | ||||||||
\(196\) | 53.6329 | 3.83092 | ||||||||
\(197\) | −26.6133 | −1.89612 | −0.948059 | − | 0.318095i | \(-0.896957\pi\) | ||||
−0.948059 | + | 0.318095i | \(0.896957\pi\) | |||||||
\(198\) | 2.58181 | 0.183481 | ||||||||
\(199\) | 4.81340 | 0.341213 | 0.170606 | − | 0.985339i | \(-0.445427\pi\) | ||||
0.170606 | + | 0.985339i | \(0.445427\pi\) | |||||||
\(200\) | −16.4612 | −1.16398 | ||||||||
\(201\) | 8.05024 | 0.567820 | ||||||||
\(202\) | −9.90539 | −0.696941 | ||||||||
\(203\) | 1.34215 | 0.0942004 | ||||||||
\(204\) | 28.5102 | 1.99611 | ||||||||
\(205\) | −2.80270 | −0.195749 | ||||||||
\(206\) | −29.2556 | −2.03834 | ||||||||
\(207\) | 1.49789 | 0.104110 | ||||||||
\(208\) | 8.43756 | 0.585040 | ||||||||
\(209\) | 0.300590 | 0.0207922 | ||||||||
\(210\) | 30.1874 | 2.08313 | ||||||||
\(211\) | 25.2596 | 1.73895 | 0.869473 | − | 0.493981i | \(-0.164459\pi\) | ||||
0.869473 | + | 0.493981i | \(0.164459\pi\) | |||||||
\(212\) | 39.6357 | 2.72219 | ||||||||
\(213\) | 0.696596 | 0.0477299 | ||||||||
\(214\) | 40.1538 | 2.74485 | ||||||||
\(215\) | −33.9593 | −2.31600 | ||||||||
\(216\) | 6.88240 | 0.468288 | ||||||||
\(217\) | −19.5717 | −1.32862 | ||||||||
\(218\) | 0.0687772 | 0.00465818 | ||||||||
\(219\) | −4.57454 | −0.309119 | ||||||||
\(220\) | 12.6851 | 0.855229 | ||||||||
\(221\) | −6.11056 | −0.411041 | ||||||||
\(222\) | −20.5675 | −1.38040 | ||||||||
\(223\) | −11.8291 | −0.792136 | −0.396068 | − | 0.918221i | \(-0.629626\pi\) | ||||
−0.396068 | + | 0.918221i | \(0.629626\pi\) | |||||||
\(224\) | 34.4880 | 2.30433 | ||||||||
\(225\) | 2.39178 | 0.159452 | ||||||||
\(226\) | 47.5913 | 3.16573 | ||||||||
\(227\) | 21.1370 | 1.40291 | 0.701455 | − | 0.712714i | \(-0.252534\pi\) | ||||
0.701455 | + | 0.712714i | \(0.252534\pi\) | |||||||
\(228\) | 1.40247 | 0.0928808 | ||||||||
\(229\) | −11.6778 | −0.771693 | −0.385846 | − | 0.922563i | \(-0.626091\pi\) | ||||
−0.385846 | + | 0.922563i | \(0.626091\pi\) | |||||||
\(230\) | 10.5142 | 0.693287 | ||||||||
\(231\) | −4.30059 | −0.282958 | ||||||||
\(232\) | 2.14789 | 0.141016 | ||||||||
\(233\) | 10.1156 | 0.662696 | 0.331348 | − | 0.943509i | \(-0.392497\pi\) | ||||
0.331348 | + | 0.943509i | \(0.392497\pi\) | |||||||
\(234\) | −2.58181 | −0.168778 | ||||||||
\(235\) | −35.6974 | −2.32864 | ||||||||
\(236\) | 43.0430 | 2.80186 | ||||||||
\(237\) | 17.0918 | 1.11023 | ||||||||
\(238\) | −67.8473 | −4.39789 | ||||||||
\(239\) | 2.65081 | 0.171467 | 0.0857333 | − | 0.996318i | \(-0.472677\pi\) | ||||
0.0857333 | + | 0.996318i | \(0.472677\pi\) | |||||||
\(240\) | 22.9399 | 1.48076 | ||||||||
\(241\) | 4.15939 | 0.267930 | 0.133965 | − | 0.990986i | \(-0.457229\pi\) | ||||
0.133965 | + | 0.990986i | \(0.457229\pi\) | |||||||
\(242\) | −2.58181 | −0.165965 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −46.0051 | −2.94517 | ||||||||
\(245\) | −31.2526 | −1.99666 | ||||||||
\(246\) | 2.66150 | 0.169691 | ||||||||
\(247\) | −0.300590 | −0.0191261 | ||||||||
\(248\) | −31.3214 | −1.98891 | ||||||||
\(249\) | −8.76902 | −0.555714 | ||||||||
\(250\) | −18.3081 | −1.15790 | ||||||||
\(251\) | 15.7115 | 0.991702 | 0.495851 | − | 0.868408i | \(-0.334856\pi\) | ||||
0.495851 | + | 0.868408i | \(0.334856\pi\) | |||||||
\(252\) | −20.0654 | −1.26400 | ||||||||
\(253\) | −1.49789 | −0.0941713 | ||||||||
\(254\) | 20.6936 | 1.29843 | ||||||||
\(255\) | −16.6133 | −1.04036 | ||||||||
\(256\) | −23.5423 | −1.47139 | ||||||||
\(257\) | 4.53944 | 0.283163 | 0.141581 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141581 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(258\) | 32.2484 | 2.00770 | ||||||||
\(259\) | 34.2599 | 2.12880 | ||||||||
\(260\) | −12.6851 | −0.786697 | ||||||||
\(261\) | −0.312085 | −0.0193176 | ||||||||
\(262\) | −29.8035 | −1.84127 | ||||||||
\(263\) | 8.38006 | 0.516737 | 0.258368 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258368 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(264\) | −6.88240 | −0.423582 | ||||||||
\(265\) | −23.0963 | −1.41879 | ||||||||
\(266\) | −3.33753 | −0.204637 | ||||||||
\(267\) | 3.24754 | 0.198746 | ||||||||
\(268\) | −37.5602 | −2.29436 | ||||||||
\(269\) | −4.95140 | −0.301892 | −0.150946 | − | 0.988542i | \(-0.548232\pi\) | ||||
−0.150946 | + | 0.988542i | \(0.548232\pi\) | |||||||
\(270\) | −7.01937 | −0.427185 | ||||||||
\(271\) | −24.5750 | −1.49282 | −0.746412 | − | 0.665484i | \(-0.768225\pi\) | ||||
−0.746412 | + | 0.665484i | \(0.768225\pi\) | |||||||
\(272\) | −51.5582 | −3.12618 | ||||||||
\(273\) | 4.30059 | 0.260284 | ||||||||
\(274\) | 15.4336 | 0.932376 | ||||||||
\(275\) | −2.39178 | −0.144230 | ||||||||
\(276\) | −6.98873 | −0.420672 | ||||||||
\(277\) | 27.5913 | 1.65780 | 0.828901 | − | 0.559395i | \(-0.188967\pi\) | ||||
0.828901 | + | 0.559395i | \(0.188967\pi\) | |||||||
\(278\) | −25.4457 | −1.52613 | ||||||||
\(279\) | 4.55094 | 0.272458 | ||||||||
\(280\) | −80.4715 | −4.80909 | ||||||||
\(281\) | 10.3478 | 0.617297 | 0.308649 | − | 0.951176i | \(-0.400123\pi\) | ||||
0.308649 | + | 0.951176i | \(0.400123\pi\) | |||||||
\(282\) | 33.8990 | 2.01865 | ||||||||
\(283\) | −1.97640 | −0.117485 | −0.0587424 | − | 0.998273i | \(-0.518709\pi\) | ||||
−0.0587424 | + | 0.998273i | \(0.518709\pi\) | |||||||
\(284\) | −3.25013 | −0.192859 | ||||||||
\(285\) | −0.817238 | −0.0484090 | ||||||||
\(286\) | 2.58181 | 0.152665 | ||||||||
\(287\) | −4.43334 | −0.261692 | ||||||||
\(288\) | −8.01937 | −0.472546 | ||||||||
\(289\) | 20.3389 | 1.19641 | ||||||||
\(290\) | −2.19064 | −0.128639 | ||||||||
\(291\) | −7.63063 | −0.447316 | ||||||||
\(292\) | 21.3436 | 1.24904 | ||||||||
\(293\) | 13.5877 | 0.793800 | 0.396900 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396900 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(294\) | 29.6781 | 1.73086 | ||||||||
\(295\) | −25.0817 | −1.46031 | ||||||||
\(296\) | 54.8274 | 3.18678 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 29.8723 | 1.73046 | ||||||||
\(299\) | 1.49789 | 0.0866250 | ||||||||
\(300\) | −11.1594 | −0.644287 | ||||||||
\(301\) | −53.7170 | −3.09620 | ||||||||
\(302\) | 8.37302 | 0.481813 | ||||||||
\(303\) | −3.83661 | −0.220407 | ||||||||
\(304\) | −2.53624 | −0.145464 | ||||||||
\(305\) | 26.8078 | 1.53501 | ||||||||
\(306\) | 15.7763 | 0.901870 | ||||||||
\(307\) | 31.8302 | 1.81664 | 0.908322 | − | 0.418271i | \(-0.137364\pi\) | ||||
0.908322 | + | 0.418271i | \(0.137364\pi\) | |||||||
\(308\) | 20.0654 | 1.14333 | ||||||||
\(309\) | −11.3315 | −0.644624 | ||||||||
\(310\) | 31.9447 | 1.81434 | ||||||||
\(311\) | 6.64697 | 0.376915 | 0.188457 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188457 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(312\) | 6.88240 | 0.389639 | ||||||||
\(313\) | −22.6171 | −1.27840 | −0.639198 | − | 0.769042i | \(-0.720733\pi\) | ||||
−0.639198 | + | 0.769042i | \(0.720733\pi\) | |||||||
\(314\) | −21.2060 | −1.19672 | ||||||||
\(315\) | 11.6924 | 0.658790 | ||||||||
\(316\) | −79.7457 | −4.48605 | ||||||||
\(317\) | 26.3971 | 1.48261 | 0.741303 | − | 0.671170i | \(-0.234208\pi\) | ||||
0.741303 | + | 0.671170i | \(0.234208\pi\) | |||||||
\(318\) | 21.9326 | 1.22992 | ||||||||
\(319\) | 0.312085 | 0.0174734 | ||||||||
\(320\) | −10.4112 | −0.582001 | ||||||||
\(321\) | 15.5526 | 0.868060 | ||||||||
\(322\) | 16.6315 | 0.926835 | ||||||||
\(323\) | 1.83677 | 0.102201 | ||||||||
\(324\) | 4.66573 | 0.259207 | ||||||||
\(325\) | 2.39178 | 0.132672 | ||||||||
\(326\) | 7.24389 | 0.401202 | ||||||||
\(327\) | 0.0266392 | 0.00147315 | ||||||||
\(328\) | −7.09484 | −0.391747 | ||||||||
\(329\) | −56.4665 | −3.11310 | ||||||||
\(330\) | 7.01937 | 0.386404 | ||||||||
\(331\) | 20.1227 | 1.10604 | 0.553021 | − | 0.833167i | \(-0.313475\pi\) | ||||
0.553021 | + | 0.833167i | \(0.313475\pi\) | |||||||
\(332\) | 40.9139 | 2.24544 | ||||||||
\(333\) | −7.96632 | −0.436552 | ||||||||
\(334\) | 5.00423 | 0.273819 | ||||||||
\(335\) | 21.8868 | 1.19581 | ||||||||
\(336\) | 36.2865 | 1.97959 | ||||||||
\(337\) | 13.5526 | 0.738256 | 0.369128 | − | 0.929379i | \(-0.379656\pi\) | ||||
0.369128 | + | 0.929379i | \(0.379656\pi\) | |||||||
\(338\) | −2.58181 | −0.140432 | ||||||||
\(339\) | 18.4333 | 1.00116 | ||||||||
\(340\) | 77.5131 | 4.20374 | ||||||||
\(341\) | −4.55094 | −0.246447 | ||||||||
\(342\) | 0.776064 | 0.0419648 | ||||||||
\(343\) | −19.3315 | −1.04380 | ||||||||
\(344\) | −85.9654 | −4.63494 | ||||||||
\(345\) | 4.07243 | 0.219252 | ||||||||
\(346\) | 22.0805 | 1.18706 | ||||||||
\(347\) | −2.24590 | −0.120566 | −0.0602831 | − | 0.998181i | \(-0.519200\pi\) | ||||
−0.0602831 | + | 0.998181i | \(0.519200\pi\) | |||||||
\(348\) | 1.45610 | 0.0780553 | ||||||||
\(349\) | 28.7634 | 1.53967 | 0.769835 | − | 0.638244i | \(-0.220339\pi\) | ||||
0.769835 | + | 0.638244i | \(0.220339\pi\) | |||||||
\(350\) | 26.5566 | 1.41951 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 8.01937 | 0.427434 | ||||||||
\(353\) | −24.4920 | −1.30358 | −0.651790 | − | 0.758400i | \(-0.725982\pi\) | ||||
−0.651790 | + | 0.758400i | \(0.725982\pi\) | |||||||
\(354\) | 23.8181 | 1.26592 | ||||||||
\(355\) | 1.89389 | 0.100517 | ||||||||
\(356\) | −15.1521 | −0.803061 | ||||||||
\(357\) | −26.2790 | −1.39083 | ||||||||
\(358\) | −46.2950 | −2.44676 | ||||||||
\(359\) | 7.12852 | 0.376229 | 0.188114 | − | 0.982147i | \(-0.439762\pi\) | ||||
0.188114 | + | 0.982147i | \(0.439762\pi\) | |||||||
\(360\) | 18.7117 | 0.986195 | ||||||||
\(361\) | −18.9096 | −0.995245 | ||||||||
\(362\) | −0.863025 | −0.0453596 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −20.0654 | −1.05171 | ||||||||
\(365\) | −12.4372 | −0.650992 | ||||||||
\(366\) | −25.4572 | −1.33067 | ||||||||
\(367\) | 6.56244 | 0.342556 | 0.171278 | − | 0.985223i | \(-0.445210\pi\) | ||||
0.171278 | + | 0.985223i | \(0.445210\pi\) | |||||||
\(368\) | 12.6385 | 0.658828 | ||||||||
\(369\) | 1.03087 | 0.0536648 | ||||||||
\(370\) | −55.9186 | −2.90707 | ||||||||
\(371\) | −36.5338 | −1.89674 | ||||||||
\(372\) | −21.2335 | −1.10090 | ||||||||
\(373\) | 19.0345 | 0.985570 | 0.492785 | − | 0.870151i | \(-0.335979\pi\) | ||||
0.492785 | + | 0.870151i | \(0.335979\pi\) | |||||||
\(374\) | −15.7763 | −0.815772 | ||||||||
\(375\) | −7.09119 | −0.366187 | ||||||||
\(376\) | −90.3654 | −4.66024 | ||||||||
\(377\) | −0.312085 | −0.0160732 | ||||||||
\(378\) | −11.1033 | −0.571092 | ||||||||
\(379\) | 9.46866 | 0.486372 | 0.243186 | − | 0.969980i | \(-0.421807\pi\) | ||||
0.243186 | + | 0.969980i | \(0.421807\pi\) | |||||||
\(380\) | 3.81301 | 0.195603 | ||||||||
\(381\) | 8.01514 | 0.410628 | ||||||||
\(382\) | 52.0331 | 2.66225 | ||||||||
\(383\) | 1.89389 | 0.0967734 | 0.0483867 | − | 0.998829i | \(-0.484592\pi\) | ||||
0.0483867 | + | 0.998829i | \(0.484592\pi\) | |||||||
\(384\) | −6.15212 | −0.313949 | ||||||||
\(385\) | −11.6924 | −0.595898 | ||||||||
\(386\) | −58.2686 | −2.96579 | ||||||||
\(387\) | 12.4906 | 0.634934 | ||||||||
\(388\) | 35.6025 | 1.80744 | ||||||||
\(389\) | −6.31269 | −0.320066 | −0.160033 | − | 0.987112i | \(-0.551160\pi\) | ||||
−0.160033 | + | 0.987112i | \(0.551160\pi\) | |||||||
\(390\) | −7.01937 | −0.355440 | ||||||||
\(391\) | −9.15292 | −0.462883 | ||||||||
\(392\) | −79.1136 | −3.99584 | ||||||||
\(393\) | −11.5437 | −0.582301 | ||||||||
\(394\) | 68.7104 | 3.46158 | ||||||||
\(395\) | 46.4689 | 2.33810 | ||||||||
\(396\) | −4.66573 | −0.234462 | ||||||||
\(397\) | −15.2949 | −0.767631 | −0.383816 | − | 0.923410i | \(-0.625390\pi\) | ||||
−0.383816 | + | 0.923410i | \(0.625390\pi\) | |||||||
\(398\) | −12.4273 | −0.622922 | ||||||||
\(399\) | −1.29271 | −0.0647166 | ||||||||
\(400\) | 20.1808 | 1.00904 | ||||||||
\(401\) | 2.45329 | 0.122511 | 0.0612557 | − | 0.998122i | \(-0.480489\pi\) | ||||
0.0612557 | + | 0.998122i | \(0.480489\pi\) | |||||||
\(402\) | −20.7842 | −1.03662 | ||||||||
\(403\) | 4.55094 | 0.226698 | ||||||||
\(404\) | 17.9006 | 0.890587 | ||||||||
\(405\) | −2.71878 | −0.135097 | ||||||||
\(406\) | −3.46517 | −0.171973 | ||||||||
\(407\) | 7.96632 | 0.394876 | ||||||||
\(408\) | −42.0553 | −2.08205 | ||||||||
\(409\) | −3.76114 | −0.185977 | −0.0929883 | − | 0.995667i | \(-0.529642\pi\) | ||||
−0.0929883 | + | 0.995667i | \(0.529642\pi\) | |||||||
\(410\) | 7.23604 | 0.357363 | ||||||||
\(411\) | 5.97781 | 0.294864 | ||||||||
\(412\) | 52.8695 | 2.60469 | ||||||||
\(413\) | −39.6744 | −1.95225 | ||||||||
\(414\) | −3.86725 | −0.190065 | ||||||||
\(415\) | −23.8411 | −1.17031 | ||||||||
\(416\) | −8.01937 | −0.393182 | ||||||||
\(417\) | −9.85576 | −0.482639 | ||||||||
\(418\) | −0.776064 | −0.0379586 | ||||||||
\(419\) | 32.2080 | 1.57346 | 0.786732 | − | 0.617295i | \(-0.211771\pi\) | ||||
0.786732 | + | 0.617295i | \(0.211771\pi\) | |||||||
\(420\) | −54.5534 | −2.66193 | ||||||||
\(421\) | −26.3216 | −1.28284 | −0.641418 | − | 0.767191i | \(-0.721654\pi\) | ||||
−0.641418 | + | 0.767191i | \(0.721654\pi\) | |||||||
\(422\) | −65.2155 | −3.17464 | ||||||||
\(423\) | 13.1299 | 0.638399 | ||||||||
\(424\) | −58.4665 | −2.83938 | ||||||||
\(425\) | −14.6151 | −0.708937 | ||||||||
\(426\) | −1.79848 | −0.0871364 | ||||||||
\(427\) | 42.4047 | 2.05211 | ||||||||
\(428\) | −72.5641 | −3.50752 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 87.6763 | 4.22813 | ||||||||
\(431\) | 2.71619 | 0.130834 | 0.0654172 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654172 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(432\) | −8.43756 | −0.405953 | ||||||||
\(433\) | 6.54790 | 0.314672 | 0.157336 | − | 0.987545i | \(-0.449709\pi\) | ||||
0.157336 | + | 0.987545i | \(0.449709\pi\) | |||||||
\(434\) | 50.5304 | 2.42554 | ||||||||
\(435\) | −0.848491 | −0.0406820 | ||||||||
\(436\) | −0.124291 | −0.00595246 | ||||||||
\(437\) | −0.450249 | −0.0215383 | ||||||||
\(438\) | 11.8106 | 0.564331 | ||||||||
\(439\) | 18.9413 | 0.904020 | 0.452010 | − | 0.892013i | \(-0.350707\pi\) | ||||
0.452010 | + | 0.892013i | \(0.350707\pi\) | |||||||
\(440\) | −18.7117 | −0.892047 | ||||||||
\(441\) | 11.4951 | 0.547384 | ||||||||
\(442\) | 15.7763 | 0.750402 | ||||||||
\(443\) | −33.8568 | −1.60859 | −0.804293 | − | 0.594233i | \(-0.797456\pi\) | ||||
−0.804293 | + | 0.594233i | \(0.797456\pi\) | |||||||
\(444\) | 37.1687 | 1.76395 | ||||||||
\(445\) | 8.82934 | 0.418551 | ||||||||
\(446\) | 30.5405 | 1.44613 | ||||||||
\(447\) | 11.5703 | 0.547257 | ||||||||
\(448\) | −16.4684 | −0.778060 | ||||||||
\(449\) | −2.62721 | −0.123986 | −0.0619928 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619928 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(450\) | −6.17511 | −0.291097 | ||||||||
\(451\) | −1.03087 | −0.0485416 | ||||||||
\(452\) | −86.0049 | −4.04533 | ||||||||
\(453\) | 3.24308 | 0.152373 | ||||||||
\(454\) | −54.5716 | −2.56117 | ||||||||
\(455\) | 11.6924 | 0.548147 | ||||||||
\(456\) | −2.06878 | −0.0968794 | ||||||||
\(457\) | 19.3230 | 0.903892 | 0.451946 | − | 0.892045i | \(-0.350730\pi\) | ||||
0.451946 | + | 0.892045i | \(0.350730\pi\) | |||||||
\(458\) | 30.1499 | 1.40881 | ||||||||
\(459\) | 6.11056 | 0.285217 | ||||||||
\(460\) | −19.0008 | −0.885918 | ||||||||
\(461\) | −6.17995 | −0.287829 | −0.143914 | − | 0.989590i | \(-0.545969\pi\) | ||||
−0.143914 | + | 0.989590i | \(0.545969\pi\) | |||||||
\(462\) | 11.1033 | 0.516572 | ||||||||
\(463\) | −3.36773 | −0.156512 | −0.0782558 | − | 0.996933i | \(-0.524935\pi\) | ||||
−0.0782558 | + | 0.996933i | \(0.524935\pi\) | |||||||
\(464\) | −2.63324 | −0.122245 | ||||||||
\(465\) | 12.3730 | 0.573785 | ||||||||
\(466\) | −26.1166 | −1.20983 | ||||||||
\(467\) | 37.3632 | 1.72896 | 0.864480 | − | 0.502667i | \(-0.167648\pi\) | ||||
0.864480 | + | 0.502667i | \(0.167648\pi\) | |||||||
\(468\) | 4.66573 | 0.215673 | ||||||||
\(469\) | 34.6208 | 1.59864 | ||||||||
\(470\) | 92.1639 | 4.25120 | ||||||||
\(471\) | −8.21363 | −0.378464 | ||||||||
\(472\) | −63.4925 | −2.92248 | ||||||||
\(473\) | −12.4906 | −0.574319 | ||||||||
\(474\) | −44.1277 | −2.02685 | ||||||||
\(475\) | −0.718944 | −0.0329874 | ||||||||
\(476\) | 122.611 | 5.61985 | ||||||||
\(477\) | 8.49507 | 0.388963 | ||||||||
\(478\) | −6.84388 | −0.313032 | ||||||||
\(479\) | −20.6133 | −0.941845 | −0.470922 | − | 0.882175i | \(-0.656079\pi\) | ||||
−0.470922 | + | 0.882175i | \(0.656079\pi\) | |||||||
\(480\) | −21.8029 | −0.995163 | ||||||||
\(481\) | −7.96632 | −0.363233 | ||||||||
\(482\) | −10.7387 | −0.489136 | ||||||||
\(483\) | 6.44179 | 0.293112 | ||||||||
\(484\) | 4.66573 | 0.212079 | ||||||||
\(485\) | −20.7460 | −0.942029 | ||||||||
\(486\) | 2.58181 | 0.117113 | ||||||||
\(487\) | 7.47711 | 0.338820 | 0.169410 | − | 0.985546i | \(-0.445814\pi\) | ||||
0.169410 | + | 0.985546i | \(0.445814\pi\) | |||||||
\(488\) | 67.8619 | 3.07196 | ||||||||
\(489\) | 2.80574 | 0.126880 | ||||||||
\(490\) | 80.6882 | 3.64512 | ||||||||
\(491\) | −11.6250 | −0.524629 | −0.262315 | − | 0.964982i | \(-0.584486\pi\) | ||||
−0.262315 | + | 0.964982i | \(0.584486\pi\) | |||||||
\(492\) | −4.80975 | −0.216840 | ||||||||
\(493\) | 1.90701 | 0.0858875 | ||||||||
\(494\) | 0.776064 | 0.0349168 | ||||||||
\(495\) | 2.71878 | 0.122200 | ||||||||
\(496\) | 38.3989 | 1.72416 | ||||||||
\(497\) | 2.99577 | 0.134379 | ||||||||
\(498\) | 22.6399 | 1.01452 | ||||||||
\(499\) | 24.2714 | 1.08654 | 0.543268 | − | 0.839560i | \(-0.317187\pi\) | ||||
0.543268 | + | 0.839560i | \(0.317187\pi\) | |||||||
\(500\) | 33.0856 | 1.47963 | ||||||||
\(501\) | 1.93827 | 0.0865953 | ||||||||
\(502\) | −40.5641 | −1.81046 | ||||||||
\(503\) | −31.7648 | −1.41632 | −0.708161 | − | 0.706051i | \(-0.750475\pi\) | ||||
−0.708161 | + | 0.706051i | \(0.750475\pi\) | |||||||
\(504\) | 29.5984 | 1.31842 | ||||||||
\(505\) | −10.4309 | −0.464169 | ||||||||
\(506\) | 3.86725 | 0.171920 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −37.3965 | −1.65920 | ||||||||
\(509\) | −8.06984 | −0.357689 | −0.178845 | − | 0.983877i | \(-0.557236\pi\) | ||||
−0.178845 | + | 0.983877i | \(0.557236\pi\) | |||||||
\(510\) | 42.8923 | 1.89930 | ||||||||
\(511\) | −19.6732 | −0.870292 | ||||||||
\(512\) | 48.4774 | 2.14242 | ||||||||
\(513\) | 0.300590 | 0.0132714 | ||||||||
\(514\) | −11.7200 | −0.516946 | ||||||||
\(515\) | −30.8078 | −1.35755 | ||||||||
\(516\) | −58.2778 | −2.56554 | ||||||||
\(517\) | −13.1299 | −0.577454 | ||||||||
\(518\) | −88.4524 | −3.88637 | ||||||||
\(519\) | 8.55235 | 0.375407 | ||||||||
\(520\) | 18.7117 | 0.820564 | ||||||||
\(521\) | 16.9986 | 0.744722 | 0.372361 | − | 0.928088i | \(-0.378548\pi\) | ||||
0.372361 | + | 0.928088i | \(0.378548\pi\) | |||||||
\(522\) | 0.805743 | 0.0352664 | ||||||||
\(523\) | 7.38591 | 0.322963 | 0.161482 | − | 0.986876i | \(-0.448373\pi\) | ||||
0.161482 | + | 0.986876i | \(0.448373\pi\) | |||||||
\(524\) | 53.8596 | 2.35287 | ||||||||
\(525\) | 10.2861 | 0.448920 | ||||||||
\(526\) | −21.6357 | −0.943361 | ||||||||
\(527\) | −27.8088 | −1.21137 | ||||||||
\(528\) | 8.43756 | 0.367198 | ||||||||
\(529\) | −20.7563 | −0.902449 | ||||||||
\(530\) | 59.6301 | 2.59016 | ||||||||
\(531\) | 9.22535 | 0.400346 | ||||||||
\(532\) | 6.03145 | 0.261496 | ||||||||
\(533\) | 1.03087 | 0.0446518 | ||||||||
\(534\) | −8.38451 | −0.362833 | ||||||||
\(535\) | 42.2841 | 1.82810 | ||||||||
\(536\) | 55.4049 | 2.39313 | ||||||||
\(537\) | −17.9312 | −0.773789 | ||||||||
\(538\) | 12.7836 | 0.551138 | ||||||||
\(539\) | −11.4951 | −0.495128 | ||||||||
\(540\) | 12.6851 | 0.545880 | ||||||||
\(541\) | 34.9901 | 1.50434 | 0.752172 | − | 0.658967i | \(-0.229006\pi\) | ||||
0.752172 | + | 0.658967i | \(0.229006\pi\) | |||||||
\(542\) | 63.4479 | 2.72532 | ||||||||
\(543\) | −0.334272 | −0.0143450 | ||||||||
\(544\) | 49.0029 | 2.10098 | ||||||||
\(545\) | 0.0724261 | 0.00310239 | ||||||||
\(546\) | −11.1033 | −0.475177 | ||||||||
\(547\) | 9.93203 | 0.424663 | 0.212331 | − | 0.977198i | \(-0.431894\pi\) | ||||
0.212331 | + | 0.977198i | \(0.431894\pi\) | |||||||
\(548\) | −27.8909 | −1.19144 | ||||||||
\(549\) | −9.86021 | −0.420824 | ||||||||
\(550\) | 6.17511 | 0.263308 | ||||||||
\(551\) | 0.0938094 | 0.00399642 | ||||||||
\(552\) | 10.3090 | 0.438782 | ||||||||
\(553\) | 73.5048 | 3.12574 | ||||||||
\(554\) | −71.2355 | −3.02651 | ||||||||
\(555\) | −21.6587 | −0.919360 | ||||||||
\(556\) | 45.9843 | 1.95017 | ||||||||
\(557\) | 4.53624 | 0.192207 | 0.0961034 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961034 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(558\) | −11.7496 | −0.497402 | ||||||||
\(559\) | 12.4906 | 0.528297 | ||||||||
\(560\) | 98.6551 | 4.16894 | ||||||||
\(561\) | −6.11056 | −0.257988 | ||||||||
\(562\) | −26.7160 | −1.12695 | ||||||||
\(563\) | −24.0916 | −1.01534 | −0.507669 | − | 0.861552i | \(-0.669493\pi\) | ||||
−0.507669 | + | 0.861552i | \(0.669493\pi\) | |||||||
\(564\) | −61.2607 | −2.57954 | ||||||||
\(565\) | 50.1162 | 2.10841 | ||||||||
\(566\) | 5.10268 | 0.214482 | ||||||||
\(567\) | −4.30059 | −0.180608 | ||||||||
\(568\) | 4.79425 | 0.201162 | ||||||||
\(569\) | 2.72583 | 0.114273 | 0.0571363 | − | 0.998366i | \(-0.481803\pi\) | ||||
0.0571363 | + | 0.998366i | \(0.481803\pi\) | |||||||
\(570\) | 2.10995 | 0.0883761 | ||||||||
\(571\) | 37.1221 | 1.55351 | 0.776755 | − | 0.629802i | \(-0.216864\pi\) | ||||
0.776755 | + | 0.629802i | \(0.216864\pi\) | |||||||
\(572\) | −4.66573 | −0.195084 | ||||||||
\(573\) | 20.1538 | 0.841935 | ||||||||
\(574\) | 11.4460 | 0.477748 | ||||||||
\(575\) | 3.58261 | 0.149405 | ||||||||
\(576\) | 3.82934 | 0.159556 | ||||||||
\(577\) | 8.06173 | 0.335614 | 0.167807 | − | 0.985820i | \(-0.446331\pi\) | ||||
0.167807 | + | 0.985820i | \(0.446331\pi\) | |||||||
\(578\) | −52.5112 | −2.18418 | ||||||||
\(579\) | −22.5689 | −0.937932 | ||||||||
\(580\) | 3.95883 | 0.164381 | ||||||||
\(581\) | −37.7120 | −1.56456 | ||||||||
\(582\) | 19.7008 | 0.816625 | ||||||||
\(583\) | −8.49507 | −0.351830 | ||||||||
\(584\) | −31.4838 | −1.30281 | ||||||||
\(585\) | −2.71878 | −0.112408 | ||||||||
\(586\) | −35.0808 | −1.44917 | ||||||||
\(587\) | 1.16924 | 0.0482599 | 0.0241299 | − | 0.999709i | \(-0.492318\pi\) | ||||
0.0241299 | + | 0.999709i | \(0.492318\pi\) | |||||||
\(588\) | −53.6329 | −2.21178 | ||||||||
\(589\) | −1.36797 | −0.0563660 | ||||||||
\(590\) | 64.7562 | 2.66597 | ||||||||
\(591\) | 26.6133 | 1.09472 | ||||||||
\(592\) | −67.2163 | −2.76257 | ||||||||
\(593\) | 13.6550 | 0.560745 | 0.280373 | − | 0.959891i | \(-0.409542\pi\) | ||||
0.280373 | + | 0.959891i | \(0.409542\pi\) | |||||||
\(594\) | −2.58181 | −0.105933 | ||||||||
\(595\) | −71.4469 | −2.92904 | ||||||||
\(596\) | −53.9839 | −2.21127 | ||||||||
\(597\) | −4.81340 | −0.196999 | ||||||||
\(598\) | −3.86725 | −0.158144 | ||||||||
\(599\) | −23.0289 | −0.940935 | −0.470467 | − | 0.882417i | \(-0.655915\pi\) | ||||
−0.470467 | + | 0.882417i | \(0.655915\pi\) | |||||||
\(600\) | 16.4612 | 0.672024 | ||||||||
\(601\) | 1.70261 | 0.0694509 | 0.0347255 | − | 0.999397i | \(-0.488944\pi\) | ||||
0.0347255 | + | 0.999397i | \(0.488944\pi\) | |||||||
\(602\) | 138.687 | 5.65246 | ||||||||
\(603\) | −8.05024 | −0.327831 | ||||||||
\(604\) | −15.1313 | −0.615686 | ||||||||
\(605\) | −2.71878 | −0.110534 | ||||||||
\(606\) | 9.90539 | 0.402379 | ||||||||
\(607\) | 8.51584 | 0.345647 | 0.172824 | − | 0.984953i | \(-0.444711\pi\) | ||||
0.172824 | + | 0.984953i | \(0.444711\pi\) | |||||||
\(608\) | 2.41054 | 0.0977603 | ||||||||
\(609\) | −1.34215 | −0.0543866 | ||||||||
\(610\) | −69.2125 | −2.80233 | ||||||||
\(611\) | 13.1299 | 0.531180 | ||||||||
\(612\) | −28.5102 | −1.15246 | ||||||||
\(613\) | −0.185577 | −0.00749538 | −0.00374769 | − | 0.999993i | \(-0.501193\pi\) | ||||
−0.00374769 | + | 0.999993i | \(0.501193\pi\) | |||||||
\(614\) | −82.1794 | −3.31649 | ||||||||
\(615\) | 2.80270 | 0.113016 | ||||||||
\(616\) | −29.5984 | −1.19255 | ||||||||
\(617\) | −11.7230 | −0.471951 | −0.235975 | − | 0.971759i | \(-0.575828\pi\) | ||||
−0.235975 | + | 0.971759i | \(0.575828\pi\) | |||||||
\(618\) | 29.2556 | 1.17683 | ||||||||
\(619\) | −44.5649 | −1.79121 | −0.895607 | − | 0.444845i | \(-0.853259\pi\) | ||||
−0.895607 | + | 0.444845i | \(0.853259\pi\) | |||||||
\(620\) | −57.7291 | −2.31846 | ||||||||
\(621\) | −1.49789 | −0.0601081 | ||||||||
\(622\) | −17.1612 | −0.688101 | ||||||||
\(623\) | 13.9663 | 0.559549 | ||||||||
\(624\) | −8.43756 | −0.337773 | ||||||||
\(625\) | −31.2383 | −1.24953 | ||||||||
\(626\) | 58.3931 | 2.33386 | ||||||||
\(627\) | −0.300590 | −0.0120044 | ||||||||
\(628\) | 38.3226 | 1.52924 | ||||||||
\(629\) | 48.6787 | 1.94095 | ||||||||
\(630\) | −30.1874 | −1.20270 | ||||||||
\(631\) | −5.29191 | −0.210668 | −0.105334 | − | 0.994437i | \(-0.533591\pi\) | ||||
−0.105334 | + | 0.994437i | \(0.533591\pi\) | |||||||
\(632\) | 117.633 | 4.67917 | ||||||||
\(633\) | −25.2596 | −1.00398 | ||||||||
\(634\) | −68.1521 | −2.70667 | ||||||||
\(635\) | 21.7914 | 0.864767 | ||||||||
\(636\) | −39.6357 | −1.57166 | ||||||||
\(637\) | 11.4951 | 0.455451 | ||||||||
\(638\) | −0.805743 | −0.0318997 | ||||||||
\(639\) | −0.696596 | −0.0275569 | ||||||||
\(640\) | −16.7263 | −0.661164 | ||||||||
\(641\) | 13.1406 | 0.519023 | 0.259512 | − | 0.965740i | \(-0.416438\pi\) | ||||
0.259512 | + | 0.965740i | \(0.416438\pi\) | |||||||
\(642\) | −40.1538 | −1.58474 | ||||||||
\(643\) | 23.8594 | 0.940923 | 0.470462 | − | 0.882420i | \(-0.344087\pi\) | ||||
0.470462 | + | 0.882420i | \(0.344087\pi\) | |||||||
\(644\) | −30.0557 | −1.18436 | ||||||||
\(645\) | 33.9593 | 1.33715 | ||||||||
\(646\) | −4.74219 | −0.186579 | ||||||||
\(647\) | −12.0472 | −0.473624 | −0.236812 | − | 0.971555i | \(-0.576103\pi\) | ||||
−0.236812 | + | 0.971555i | \(0.576103\pi\) | |||||||
\(648\) | −6.88240 | −0.270366 | ||||||||
\(649\) | −9.22535 | −0.362127 | ||||||||
\(650\) | −6.17511 | −0.242208 | ||||||||
\(651\) | 19.5717 | 0.767076 | ||||||||
\(652\) | −13.0908 | −0.512677 | ||||||||
\(653\) | 2.21222 | 0.0865707 | 0.0432854 | − | 0.999063i | \(-0.486218\pi\) | ||||
0.0432854 | + | 0.999063i | \(0.486218\pi\) | |||||||
\(654\) | −0.0687772 | −0.00268940 | ||||||||
\(655\) | −31.3847 | −1.22630 | ||||||||
\(656\) | 8.69801 | 0.339600 | ||||||||
\(657\) | 4.57454 | 0.178470 | ||||||||
\(658\) | 145.785 | 5.68331 | ||||||||
\(659\) | 28.6764 | 1.11708 | 0.558538 | − | 0.829479i | \(-0.311363\pi\) | ||||
0.558538 | + | 0.829479i | \(0.311363\pi\) | |||||||
\(660\) | −12.6851 | −0.493767 | ||||||||
\(661\) | −27.9500 | −1.08713 | −0.543564 | − | 0.839367i | \(-0.682926\pi\) | ||||
−0.543564 | + | 0.839367i | \(0.682926\pi\) | |||||||
\(662\) | −51.9528 | −2.01920 | ||||||||
\(663\) | 6.11056 | 0.237315 | ||||||||
\(664\) | −60.3519 | −2.34211 | ||||||||
\(665\) | −3.51460 | −0.136291 | ||||||||
\(666\) | 20.5675 | 0.796974 | ||||||||
\(667\) | −0.467467 | −0.0181004 | ||||||||
\(668\) | −9.04342 | −0.349900 | ||||||||
\(669\) | 11.8291 | 0.457340 | ||||||||
\(670\) | −56.5076 | −2.18308 | ||||||||
\(671\) | 9.86021 | 0.380649 | ||||||||
\(672\) | −34.4880 | −1.33040 | ||||||||
\(673\) | −28.5534 | −1.10065 | −0.550327 | − | 0.834949i | \(-0.685497\pi\) | ||||
−0.550327 | + | 0.834949i | \(0.685497\pi\) | |||||||
\(674\) | −34.9901 | −1.34777 | ||||||||
\(675\) | −2.39178 | −0.0920596 | ||||||||
\(676\) | 4.66573 | 0.179451 | ||||||||
\(677\) | 7.52290 | 0.289129 | 0.144564 | − | 0.989495i | \(-0.453822\pi\) | ||||
0.144564 | + | 0.989495i | \(0.453822\pi\) | |||||||
\(678\) | −47.5913 | −1.82773 | ||||||||
\(679\) | −32.8162 | −1.25937 | ||||||||
\(680\) | −114.339 | −4.38471 | ||||||||
\(681\) | −21.1370 | −0.809971 | ||||||||
\(682\) | 11.7496 | 0.449917 | ||||||||
\(683\) | −1.33324 | −0.0510152 | −0.0255076 | − | 0.999675i | \(-0.508120\pi\) | ||||
−0.0255076 | + | 0.999675i | \(0.508120\pi\) | |||||||
\(684\) | −1.40247 | −0.0536248 | ||||||||
\(685\) | 16.2524 | 0.620971 | ||||||||
\(686\) | 49.9101 | 1.90558 | ||||||||
\(687\) | 11.6778 | 0.445537 | ||||||||
\(688\) | 105.390 | 4.01797 | ||||||||
\(689\) | 8.49507 | 0.323636 | ||||||||
\(690\) | −10.5142 | −0.400269 | ||||||||
\(691\) | 8.96796 | 0.341157 | 0.170579 | − | 0.985344i | \(-0.445436\pi\) | ||||
0.170579 | + | 0.985344i | \(0.445436\pi\) | |||||||
\(692\) | −39.9030 | −1.51688 | ||||||||
\(693\) | 4.30059 | 0.163366 | ||||||||
\(694\) | 5.79848 | 0.220107 | ||||||||
\(695\) | −26.7957 | −1.01642 | ||||||||
\(696\) | −2.14789 | −0.0814156 | ||||||||
\(697\) | −6.29918 | −0.238598 | ||||||||
\(698\) | −74.2615 | −2.81084 | ||||||||
\(699\) | −10.1156 | −0.382608 | ||||||||
\(700\) | −47.9919 | −1.81392 | ||||||||
\(701\) | 7.66269 | 0.289416 | 0.144708 | − | 0.989474i | \(-0.453776\pi\) | ||||
0.144708 | + | 0.989474i | \(0.453776\pi\) | |||||||
\(702\) | 2.58181 | 0.0974440 | ||||||||
\(703\) | 2.39459 | 0.0903138 | ||||||||
\(704\) | −3.82934 | −0.144324 | ||||||||
\(705\) | 35.6974 | 1.34444 | ||||||||
\(706\) | 63.2337 | 2.37983 | ||||||||
\(707\) | −16.4997 | −0.620535 | ||||||||
\(708\) | −43.0430 | −1.61765 | ||||||||
\(709\) | 17.4253 | 0.654420 | 0.327210 | − | 0.944952i | \(-0.393892\pi\) | ||||
0.327210 | + | 0.944952i | \(0.393892\pi\) | |||||||
\(710\) | −4.88966 | −0.183506 | ||||||||
\(711\) | −17.0918 | −0.640993 | ||||||||
\(712\) | 22.3508 | 0.837633 | ||||||||
\(713\) | 6.81679 | 0.255291 | ||||||||
\(714\) | 67.8473 | 2.53912 | ||||||||
\(715\) | 2.71878 | 0.101677 | ||||||||
\(716\) | 83.6622 | 3.12660 | ||||||||
\(717\) | −2.65081 | −0.0989963 | ||||||||
\(718\) | −18.4045 | −0.686848 | ||||||||
\(719\) | 6.79764 | 0.253509 | 0.126755 | − | 0.991934i | \(-0.459544\pi\) | ||||
0.126755 | + | 0.991934i | \(0.459544\pi\) | |||||||
\(720\) | −22.9399 | −0.854920 | ||||||||
\(721\) | −48.7319 | −1.81487 | ||||||||
\(722\) | 48.8211 | 1.81693 | ||||||||
\(723\) | −4.15939 | −0.154689 | ||||||||
\(724\) | 1.55962 | 0.0579628 | ||||||||
\(725\) | −0.746437 | −0.0277220 | ||||||||
\(726\) | 2.58181 | 0.0958199 | ||||||||
\(727\) | −30.6932 | −1.13835 | −0.569174 | − | 0.822217i | \(-0.692737\pi\) | ||||
−0.569174 | + | 0.822217i | \(0.692737\pi\) | |||||||
\(728\) | 29.5984 | 1.09699 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 32.1104 | 1.18846 | ||||||||
\(731\) | −76.3247 | −2.82297 | ||||||||
\(732\) | 46.0051 | 1.70040 | ||||||||
\(733\) | −16.3482 | −0.603836 | −0.301918 | − | 0.953334i | \(-0.597627\pi\) | ||||
−0.301918 | + | 0.953334i | \(0.597627\pi\) | |||||||
\(734\) | −16.9429 | −0.625375 | ||||||||
\(735\) | 31.2526 | 1.15277 | ||||||||
\(736\) | −12.0121 | −0.442772 | ||||||||
\(737\) | 8.05024 | 0.296534 | ||||||||
\(738\) | −2.66150 | −0.0979712 | ||||||||
\(739\) | −19.9677 | −0.734525 | −0.367262 | − | 0.930117i | \(-0.619705\pi\) | ||||
−0.367262 | + | 0.930117i | \(0.619705\pi\) | |||||||
\(740\) | 101.054 | 3.71480 | ||||||||
\(741\) | 0.300590 | 0.0110424 | ||||||||
\(742\) | 94.3233 | 3.46272 | ||||||||
\(743\) | 18.9756 | 0.696148 | 0.348074 | − | 0.937467i | \(-0.386836\pi\) | ||||
0.348074 | + | 0.937467i | \(0.386836\pi\) | |||||||
\(744\) | 31.3214 | 1.14830 | ||||||||
\(745\) | 31.4572 | 1.15250 | ||||||||
\(746\) | −49.1435 | −1.79927 | ||||||||
\(747\) | 8.76902 | 0.320842 | ||||||||
\(748\) | 28.5102 | 1.04244 | ||||||||
\(749\) | 66.8853 | 2.44393 | ||||||||
\(750\) | 18.3081 | 0.668517 | ||||||||
\(751\) | 5.94717 | 0.217015 | 0.108508 | − | 0.994096i | \(-0.465393\pi\) | ||||
0.108508 | + | 0.994096i | \(0.465393\pi\) | |||||||
\(752\) | 110.785 | 4.03990 | ||||||||
\(753\) | −15.7115 | −0.572559 | ||||||||
\(754\) | 0.805743 | 0.0293434 | ||||||||
\(755\) | 8.81724 | 0.320892 | ||||||||
\(756\) | 20.0654 | 0.729771 | ||||||||
\(757\) | −21.7275 | −0.789698 | −0.394849 | − | 0.918746i | \(-0.629203\pi\) | ||||
−0.394849 | + | 0.918746i | \(0.629203\pi\) | |||||||
\(758\) | −24.4462 | −0.887928 | ||||||||
\(759\) | 1.49789 | 0.0543698 | ||||||||
\(760\) | −5.62456 | −0.204024 | ||||||||
\(761\) | −11.7241 | −0.424997 | −0.212499 | − | 0.977161i | \(-0.568160\pi\) | ||||
−0.212499 | + | 0.977161i | \(0.568160\pi\) | |||||||
\(762\) | −20.6936 | −0.749648 | ||||||||
\(763\) | 0.114564 | 0.00414750 | ||||||||
\(764\) | −94.0320 | −3.40196 | ||||||||
\(765\) | 16.6133 | 0.600655 | ||||||||
\(766\) | −4.88966 | −0.176671 | ||||||||
\(767\) | 9.22535 | 0.333108 | ||||||||
\(768\) | 23.5423 | 0.849509 | ||||||||
\(769\) | 27.0676 | 0.976084 | 0.488042 | − | 0.872820i | \(-0.337711\pi\) | ||||
0.488042 | + | 0.872820i | \(0.337711\pi\) | |||||||
\(770\) | 30.1874 | 1.08788 | ||||||||
\(771\) | −4.53944 | −0.163484 | ||||||||
\(772\) | 105.300 | 3.78984 | ||||||||
\(773\) | 17.6574 | 0.635094 | 0.317547 | − | 0.948243i | \(-0.397141\pi\) | ||||
0.317547 | + | 0.948243i | \(0.397141\pi\) | |||||||
\(774\) | −32.2484 | −1.15914 | ||||||||
\(775\) | 10.8848 | 0.390995 | ||||||||
\(776\) | −52.5170 | −1.88525 | ||||||||
\(777\) | −34.2599 | −1.22907 | ||||||||
\(778\) | 16.2982 | 0.584317 | ||||||||
\(779\) | −0.309868 | −0.0111022 | ||||||||
\(780\) | 12.6851 | 0.454199 | ||||||||
\(781\) | 0.696596 | 0.0249262 | ||||||||
\(782\) | 23.6311 | 0.845046 | ||||||||
\(783\) | 0.312085 | 0.0111530 | ||||||||
\(784\) | 96.9904 | 3.46394 | ||||||||
\(785\) | −22.3311 | −0.797030 | ||||||||
\(786\) | 29.8035 | 1.06306 | ||||||||
\(787\) | −19.9677 | −0.711773 | −0.355886 | − | 0.934529i | \(-0.615821\pi\) | ||||
−0.355886 | + | 0.934529i | \(0.615821\pi\) | |||||||
\(788\) | −124.170 | −4.42339 | ||||||||
\(789\) | −8.38006 | −0.298338 | ||||||||
\(790\) | −119.974 | −4.26847 | ||||||||
\(791\) | 79.2742 | 2.81867 | ||||||||
\(792\) | 6.88240 | 0.244555 | ||||||||
\(793\) | −9.86021 | −0.350146 | ||||||||
\(794\) | 39.4886 | 1.40140 | ||||||||
\(795\) | 23.0963 | 0.819140 | ||||||||
\(796\) | 22.4580 | 0.796003 | ||||||||
\(797\) | 15.2343 | 0.539625 | 0.269812 | − | 0.962913i | \(-0.413038\pi\) | ||||
0.269812 | + | 0.962913i | \(0.413038\pi\) | |||||||
\(798\) | 3.33753 | 0.118147 | ||||||||
\(799\) | −80.2312 | −2.83838 | ||||||||
\(800\) | −19.1806 | −0.678135 | ||||||||
\(801\) | −3.24754 | −0.114746 | ||||||||
\(802\) | −6.33392 | −0.223658 | ||||||||
\(803\) | −4.57454 | −0.161432 | ||||||||
\(804\) | 37.5602 | 1.32465 | ||||||||
\(805\) | 17.5138 | 0.617282 | ||||||||
\(806\) | −11.7496 | −0.413864 | ||||||||
\(807\) | 4.95140 | 0.174297 | ||||||||
\(808\) | −26.4051 | −0.928927 | ||||||||
\(809\) | −34.4551 | −1.21138 | −0.605689 | − | 0.795701i | \(-0.707103\pi\) | ||||
−0.605689 | + | 0.795701i | \(0.707103\pi\) | |||||||
\(810\) | 7.01937 | 0.246636 | ||||||||
\(811\) | 4.75409 | 0.166939 | 0.0834693 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834693 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(812\) | 6.26210 | 0.219757 | ||||||||
\(813\) | 24.5750 | 0.861882 | ||||||||
\(814\) | −20.5675 | −0.720890 | ||||||||
\(815\) | 7.62820 | 0.267204 | ||||||||
\(816\) | 51.5582 | 1.80490 | ||||||||
\(817\) | −3.75455 | −0.131355 | ||||||||
\(818\) | 9.71055 | 0.339521 | ||||||||
\(819\) | −4.30059 | −0.150275 | ||||||||
\(820\) | −13.0767 | −0.456657 | ||||||||
\(821\) | 7.36700 | 0.257110 | 0.128555 | − | 0.991702i | \(-0.458966\pi\) | ||||
0.128555 | + | 0.991702i | \(0.458966\pi\) | |||||||
\(822\) | −15.4336 | −0.538307 | ||||||||
\(823\) | 35.5385 | 1.23879 | 0.619397 | − | 0.785078i | \(-0.287377\pi\) | ||||
0.619397 | + | 0.785078i | \(0.287377\pi\) | |||||||
\(824\) | −77.9876 | −2.71683 | ||||||||
\(825\) | 2.39178 | 0.0832710 | ||||||||
\(826\) | 102.432 | 3.56406 | ||||||||
\(827\) | −16.1506 | −0.561610 | −0.280805 | − | 0.959765i | \(-0.590601\pi\) | ||||
−0.280805 | + | 0.959765i | \(0.590601\pi\) | |||||||
\(828\) | 6.98873 | 0.242875 | ||||||||
\(829\) | 28.9986 | 1.00716 | 0.503581 | − | 0.863948i | \(-0.332015\pi\) | ||||
0.503581 | + | 0.863948i | \(0.332015\pi\) | |||||||
\(830\) | 61.5530 | 2.13654 | ||||||||
\(831\) | −27.5913 | −0.957132 | ||||||||
\(832\) | 3.82934 | 0.132759 | ||||||||
\(833\) | −70.2413 | −2.43372 | ||||||||
\(834\) | 25.4457 | 0.881111 | ||||||||
\(835\) | 5.26972 | 0.182366 | ||||||||
\(836\) | 1.40247 | 0.0485054 | ||||||||
\(837\) | −4.55094 | −0.157303 | ||||||||
\(838\) | −83.1548 | −2.87254 | ||||||||
\(839\) | −12.7246 | −0.439304 | −0.219652 | − | 0.975578i | \(-0.570492\pi\) | ||||
−0.219652 | + | 0.975578i | \(0.570492\pi\) | |||||||
\(840\) | 80.4715 | 2.77653 | ||||||||
\(841\) | −28.9026 | −0.996641 | ||||||||
\(842\) | 67.9573 | 2.34196 | ||||||||
\(843\) | −10.3478 | −0.356397 | ||||||||
\(844\) | 117.855 | 4.05672 | ||||||||
\(845\) | −2.71878 | −0.0935290 | ||||||||
\(846\) | −33.8990 | −1.16547 | ||||||||
\(847\) | −4.30059 | −0.147770 | ||||||||
\(848\) | 71.6777 | 2.46142 | ||||||||
\(849\) | 1.97640 | 0.0678299 | ||||||||
\(850\) | 37.7334 | 1.29424 | ||||||||
\(851\) | −11.9326 | −0.409045 | ||||||||
\(852\) | 3.25013 | 0.111347 | ||||||||
\(853\) | 31.0434 | 1.06291 | 0.531453 | − | 0.847088i | \(-0.321646\pi\) | ||||
0.531453 | + | 0.847088i | \(0.321646\pi\) | |||||||
\(854\) | −109.481 | −3.74636 | ||||||||
\(855\) | 0.817238 | 0.0279489 | ||||||||
\(856\) | 107.039 | 3.65852 | ||||||||
\(857\) | 36.4658 | 1.24565 | 0.622825 | − | 0.782361i | \(-0.285985\pi\) | ||||
0.622825 | + | 0.782361i | \(0.285985\pi\) | |||||||
\(858\) | −2.58181 | −0.0881414 | ||||||||
\(859\) | −44.3200 | −1.51218 | −0.756089 | − | 0.654468i | \(-0.772892\pi\) | ||||
−0.756089 | + | 0.654468i | \(0.772892\pi\) | |||||||
\(860\) | −158.445 | −5.40292 | ||||||||
\(861\) | 4.43334 | 0.151088 | ||||||||
\(862\) | −7.01268 | −0.238853 | ||||||||
\(863\) | −35.1467 | −1.19641 | −0.598204 | − | 0.801344i | \(-0.704119\pi\) | ||||
−0.598204 | + | 0.801344i | \(0.704119\pi\) | |||||||
\(864\) | 8.01937 | 0.272825 | ||||||||
\(865\) | 23.2520 | 0.790591 | ||||||||
\(866\) | −16.9054 | −0.574469 | ||||||||
\(867\) | −20.3389 | −0.690747 | ||||||||
\(868\) | −91.3164 | −3.09948 | ||||||||
\(869\) | 17.0918 | 0.579800 | ||||||||
\(870\) | 2.19064 | 0.0742696 | ||||||||
\(871\) | −8.05024 | −0.272772 | ||||||||
\(872\) | 0.183341 | 0.00620872 | ||||||||
\(873\) | 7.63063 | 0.258258 | ||||||||
\(874\) | 1.16246 | 0.0393207 | ||||||||
\(875\) | −30.4963 | −1.03096 | ||||||||
\(876\) | −21.3436 | −0.721132 | ||||||||
\(877\) | −11.2927 | −0.381328 | −0.190664 | − | 0.981655i | \(-0.561064\pi\) | ||||
−0.190664 | + | 0.981655i | \(0.561064\pi\) | |||||||
\(878\) | −48.9028 | −1.65039 | ||||||||
\(879\) | −13.5877 | −0.458301 | ||||||||
\(880\) | 22.9399 | 0.773304 | ||||||||
\(881\) | 31.7503 | 1.06969 | 0.534847 | − | 0.844949i | \(-0.320369\pi\) | ||||
0.534847 | + | 0.844949i | \(0.320369\pi\) | |||||||
\(882\) | −29.6781 | −0.999312 | ||||||||
\(883\) | 42.8824 | 1.44311 | 0.721554 | − | 0.692358i | \(-0.243428\pi\) | ||||
0.721554 | + | 0.692358i | \(0.243428\pi\) | |||||||
\(884\) | −28.5102 | −0.958902 | ||||||||
\(885\) | 25.0817 | 0.843113 | ||||||||
\(886\) | 87.4118 | 2.93666 | ||||||||
\(887\) | 32.8290 | 1.10229 | 0.551144 | − | 0.834410i | \(-0.314191\pi\) | ||||
0.551144 | + | 0.834410i | \(0.314191\pi\) | |||||||
\(888\) | −54.8274 | −1.83989 | ||||||||
\(889\) | 34.4698 | 1.15608 | ||||||||
\(890\) | −22.7957 | −0.764112 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −55.1915 | −1.84795 | ||||||||
\(893\) | −3.94672 | −0.132072 | ||||||||
\(894\) | −29.8723 | −0.999080 | ||||||||
\(895\) | −48.7511 | −1.62957 | ||||||||
\(896\) | −26.4577 | −0.883891 | ||||||||
\(897\) | −1.49789 | −0.0500130 | ||||||||
\(898\) | 6.78295 | 0.226350 | ||||||||
\(899\) | −1.42028 | −0.0473690 | ||||||||
\(900\) | 11.1594 | 0.371980 | ||||||||
\(901\) | −51.9096 | −1.72936 | ||||||||
\(902\) | 2.66150 | 0.0886183 | ||||||||
\(903\) | 53.7170 | 1.78759 | ||||||||
\(904\) | 126.866 | 4.21949 | ||||||||
\(905\) | −0.908812 | −0.0302099 | ||||||||
\(906\) | −8.37302 | −0.278175 | ||||||||
\(907\) | 43.1597 | 1.43309 | 0.716546 | − | 0.697539i | \(-0.245722\pi\) | ||||
0.716546 | + | 0.697539i | \(0.245722\pi\) | |||||||
\(908\) | 98.6194 | 3.27280 | ||||||||
\(909\) | 3.83661 | 0.127252 | ||||||||
\(910\) | −30.1874 | −1.00070 | ||||||||
\(911\) | −28.7690 | −0.953160 | −0.476580 | − | 0.879131i | \(-0.658124\pi\) | ||||
−0.476580 | + | 0.879131i | \(0.658124\pi\) | |||||||
\(912\) | 2.53624 | 0.0839835 | ||||||||
\(913\) | −8.76902 | −0.290212 | ||||||||
\(914\) | −49.8883 | −1.65016 | ||||||||
\(915\) | −26.8078 | −0.886237 | ||||||||
\(916\) | −54.4856 | −1.80025 | ||||||||
\(917\) | −49.6446 | −1.63941 | ||||||||
\(918\) | −15.7763 | −0.520695 | ||||||||
\(919\) | 26.5804 | 0.876807 | 0.438403 | − | 0.898778i | \(-0.355544\pi\) | ||||
0.438403 | + | 0.898778i | \(0.355544\pi\) | |||||||
\(920\) | 28.0281 | 0.924058 | ||||||||
\(921\) | −31.8302 | −1.04884 | ||||||||
\(922\) | 15.9554 | 0.525464 | ||||||||
\(923\) | −0.696596 | −0.0229287 | ||||||||
\(924\) | −20.0654 | −0.660103 | ||||||||
\(925\) | −19.0537 | −0.626481 | ||||||||
\(926\) | 8.69483 | 0.285730 | ||||||||
\(927\) | 11.3315 | 0.372174 | ||||||||
\(928\) | 2.50272 | 0.0821559 | ||||||||
\(929\) | 28.1614 | 0.923946 | 0.461973 | − | 0.886894i | \(-0.347142\pi\) | ||||
0.461973 | + | 0.886894i | \(0.347142\pi\) | |||||||
\(930\) | −31.9447 | −1.04751 | ||||||||
\(931\) | −3.45530 | −0.113243 | ||||||||
\(932\) | 47.1967 | 1.54598 | ||||||||
\(933\) | −6.64697 | −0.217612 | ||||||||
\(934\) | −96.4645 | −3.15641 | ||||||||
\(935\) | −16.6133 | −0.543312 | ||||||||
\(936\) | −6.88240 | −0.224958 | ||||||||
\(937\) | −35.6727 | −1.16537 | −0.582687 | − | 0.812696i | \(-0.697999\pi\) | ||||
−0.582687 | + | 0.812696i | \(0.697999\pi\) | |||||||
\(938\) | −89.3842 | −2.91850 | ||||||||
\(939\) | 22.6171 | 0.738082 | ||||||||
\(940\) | −166.555 | −5.43241 | ||||||||
\(941\) | 18.0210 | 0.587468 | 0.293734 | − | 0.955887i | \(-0.405102\pi\) | ||||
0.293734 | + | 0.955887i | \(0.405102\pi\) | |||||||
\(942\) | 21.2060 | 0.690929 | ||||||||
\(943\) | 1.54412 | 0.0502835 | ||||||||
\(944\) | 77.8395 | 2.53346 | ||||||||
\(945\) | −11.6924 | −0.380353 | ||||||||
\(946\) | 32.2484 | 1.04848 | ||||||||
\(947\) | −25.0093 | −0.812693 | −0.406346 | − | 0.913719i | \(-0.633197\pi\) | ||||
−0.406346 | + | 0.913719i | \(0.633197\pi\) | |||||||
\(948\) | 79.7457 | 2.59002 | ||||||||
\(949\) | 4.57454 | 0.148496 | ||||||||
\(950\) | 1.85617 | 0.0602222 | ||||||||
\(951\) | −26.3971 | −0.855983 | ||||||||
\(952\) | −180.863 | −5.86179 | ||||||||
\(953\) | 18.2302 | 0.590534 | 0.295267 | − | 0.955415i | \(-0.404591\pi\) | ||||
0.295267 | + | 0.955415i | \(0.404591\pi\) | |||||||
\(954\) | −21.9326 | −0.710095 | ||||||||
\(955\) | 54.7937 | 1.77308 | ||||||||
\(956\) | 12.3680 | 0.400008 | ||||||||
\(957\) | −0.312085 | −0.0100883 | ||||||||
\(958\) | 53.2195 | 1.71944 | ||||||||
\(959\) | 25.7081 | 0.830159 | ||||||||
\(960\) | 10.4112 | 0.336018 | ||||||||
\(961\) | −10.2889 | −0.331901 | ||||||||
\(962\) | 20.5675 | 0.663123 | ||||||||
\(963\) | −15.5526 | −0.501175 | ||||||||
\(964\) | 19.4066 | 0.625043 | ||||||||
\(965\) | −61.3600 | −1.97525 | ||||||||
\(966\) | −16.6315 | −0.535109 | ||||||||
\(967\) | 21.5792 | 0.693941 | 0.346970 | − | 0.937876i | \(-0.387210\pi\) | ||||
0.346970 | + | 0.937876i | \(0.387210\pi\) | |||||||
\(968\) | −6.88240 | −0.221209 | ||||||||
\(969\) | −1.83677 | −0.0590056 | ||||||||
\(970\) | 53.5623 | 1.71978 | ||||||||
\(971\) | 52.4263 | 1.68244 | 0.841220 | − | 0.540693i | \(-0.181838\pi\) | ||||
0.841220 | + | 0.540693i | \(0.181838\pi\) | |||||||
\(972\) | −4.66573 | −0.149653 | ||||||||
\(973\) | −42.3856 | −1.35882 | ||||||||
\(974\) | −19.3045 | −0.618555 | ||||||||
\(975\) | −2.39178 | −0.0765982 | ||||||||
\(976\) | −83.1962 | −2.66304 | ||||||||
\(977\) | 50.5189 | 1.61624 | 0.808122 | − | 0.589015i | \(-0.200484\pi\) | ||||
0.808122 | + | 0.589015i | \(0.200484\pi\) | |||||||
\(978\) | −7.24389 | −0.231634 | ||||||||
\(979\) | 3.24754 | 0.103792 | ||||||||
\(980\) | −145.816 | −4.65793 | ||||||||
\(981\) | −0.0266392 | −0.000850523 0 | ||||||||
\(982\) | 30.0135 | 0.957770 | ||||||||
\(983\) | −29.2556 | −0.933110 | −0.466555 | − | 0.884492i | \(-0.654505\pi\) | ||||
−0.466555 | + | 0.884492i | \(0.654505\pi\) | |||||||
\(984\) | 7.09484 | 0.226175 | ||||||||
\(985\) | 72.3557 | 2.30545 | ||||||||
\(986\) | −4.92354 | −0.156797 | ||||||||
\(987\) | 56.4665 | 1.79735 | ||||||||
\(988\) | −1.40247 | −0.0446185 | ||||||||
\(989\) | 18.7095 | 0.594928 | ||||||||
\(990\) | −7.01937 | −0.223090 | ||||||||
\(991\) | −12.1117 | −0.384742 | −0.192371 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192371 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(992\) | −36.4957 | −1.15874 | ||||||||
\(993\) | −20.1227 | −0.638573 | ||||||||
\(994\) | −7.73451 | −0.245324 | ||||||||
\(995\) | −13.0866 | −0.414872 | ||||||||
\(996\) | −40.9139 | −1.29641 | ||||||||
\(997\) | −47.9395 | −1.51826 | −0.759129 | − | 0.650940i | \(-0.774375\pi\) | ||||
−0.759129 | + | 0.650940i | \(0.774375\pi\) | |||||||
\(998\) | −62.6640 | −1.98359 | ||||||||
\(999\) | 7.96632 | 0.252043 |
(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 | 429.2.a.h.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 1287.2.a.m.1.4 | 4 | |||
4.3 | odd | 2 | 6864.2.a.bz.1.1 | 4 | |||
11.10 | odd | 2 | 4719.2.a.z.1.4 | 4 | |||
13.12 | even | 2 | 5577.2.a.m.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.a.h.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1287.2.a.m.1.4 | 4 | 3.2 | odd | 2 | |||
4719.2.a.z.1.4 | 4 | 11.10 | odd | 2 | |||
5577.2.a.m.1.4 | 4 | 13.12 | even | 2 | |||
6864.2.a.bz.1.1 | 4 | 4.3 | odd | 2 |