Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(1\) |
Dimension: | \(149\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85239 | −1.30984 | −0.654920 | − | 0.755698i | \(-0.727298\pi\) | ||||
−0.654920 | + | 0.755698i | \(0.727298\pi\) | |||||||
\(3\) | −0.815947 | −0.471087 | −0.235544 | − | 0.971864i | \(-0.575687\pi\) | ||||
−0.235544 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(4\) | 1.43137 | 0.715683 | ||||||||
\(5\) | −2.54029 | −1.13605 | −0.568025 | − | 0.823011i | \(-0.692292\pi\) | ||||
−0.568025 | + | 0.823011i | \(0.692292\pi\) | |||||||
\(6\) | 1.51146 | 0.617049 | ||||||||
\(7\) | 1.66105 | 0.627819 | 0.313910 | − | 0.949453i | \(-0.398361\pi\) | ||||
0.313910 | + | 0.949453i | \(0.398361\pi\) | |||||||
\(8\) | 1.05333 | 0.372410 | ||||||||
\(9\) | −2.33423 | −0.778077 | ||||||||
\(10\) | 4.70561 | 1.48805 | ||||||||
\(11\) | 1.16811 | 0.352198 | 0.176099 | − | 0.984372i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984372i | \(0.443652\pi\) | |||||||
\(12\) | −1.16792 | −0.337149 | ||||||||
\(13\) | −2.37094 | −0.657581 | −0.328790 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328790 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(14\) | −3.07693 | −0.822343 | ||||||||
\(15\) | 2.07274 | 0.535179 | ||||||||
\(16\) | −4.81392 | −1.20348 | ||||||||
\(17\) | 3.97585 | 0.964284 | 0.482142 | − | 0.876093i | \(-0.339859\pi\) | ||||
0.482142 | + | 0.876093i | \(0.339859\pi\) | |||||||
\(18\) | 4.32392 | 1.01916 | ||||||||
\(19\) | 0.254652 | 0.0584213 | 0.0292106 | − | 0.999573i | \(-0.490701\pi\) | ||||
0.0292106 | + | 0.999573i | \(0.490701\pi\) | |||||||
\(20\) | −3.63608 | −0.813052 | ||||||||
\(21\) | −1.35533 | −0.295757 | ||||||||
\(22\) | −2.16380 | −0.461323 | ||||||||
\(23\) | −4.22841 | −0.881685 | −0.440842 | − | 0.897585i | \(-0.645320\pi\) | ||||
−0.440842 | + | 0.897585i | \(0.645320\pi\) | |||||||
\(24\) | −0.859465 | −0.175437 | ||||||||
\(25\) | 1.45305 | 0.290611 | ||||||||
\(26\) | 4.39192 | 0.861326 | ||||||||
\(27\) | 4.35245 | 0.837629 | ||||||||
\(28\) | 2.37758 | 0.449320 | ||||||||
\(29\) | −1.45058 | −0.269366 | −0.134683 | − | 0.990889i | \(-0.543002\pi\) | ||||
−0.134683 | + | 0.990889i | \(0.543002\pi\) | |||||||
\(30\) | −3.83953 | −0.700999 | ||||||||
\(31\) | 5.30439 | 0.952697 | 0.476348 | − | 0.879257i | \(-0.341960\pi\) | ||||
0.476348 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(32\) | 6.81062 | 1.20396 | ||||||||
\(33\) | −0.953114 | −0.165916 | ||||||||
\(34\) | −7.36484 | −1.26306 | ||||||||
\(35\) | −4.21955 | −0.713234 | ||||||||
\(36\) | −3.34114 | −0.556857 | ||||||||
\(37\) | −6.57184 | −1.08040 | −0.540202 | − | 0.841535i | \(-0.681652\pi\) | ||||
−0.540202 | + | 0.841535i | \(0.681652\pi\) | |||||||
\(38\) | −0.471717 | −0.0765225 | ||||||||
\(39\) | 1.93456 | 0.309778 | ||||||||
\(40\) | −2.67577 | −0.423076 | ||||||||
\(41\) | 0.319902 | 0.0499603 | 0.0249801 | − | 0.999688i | \(-0.492048\pi\) | ||||
0.0249801 | + | 0.999688i | \(0.492048\pi\) | |||||||
\(42\) | 2.51061 | 0.387395 | ||||||||
\(43\) | 6.89324 | 1.05121 | 0.525604 | − | 0.850729i | \(-0.323839\pi\) | ||||
0.525604 | + | 0.850729i | \(0.323839\pi\) | |||||||
\(44\) | 1.67199 | 0.252062 | ||||||||
\(45\) | 5.92961 | 0.883935 | ||||||||
\(46\) | 7.83269 | 1.15487 | ||||||||
\(47\) | 3.12577 | 0.455941 | 0.227971 | − | 0.973668i | \(-0.426791\pi\) | ||||
0.227971 | + | 0.973668i | \(0.426791\pi\) | |||||||
\(48\) | 3.92790 | 0.566944 | ||||||||
\(49\) | −4.24090 | −0.605843 | ||||||||
\(50\) | −2.69163 | −0.380654 | ||||||||
\(51\) | −3.24408 | −0.454262 | ||||||||
\(52\) | −3.39368 | −0.470619 | ||||||||
\(53\) | −3.91108 | −0.537228 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(54\) | −8.06245 | −1.09716 | ||||||||
\(55\) | −2.96733 | −0.400115 | ||||||||
\(56\) | 1.74964 | 0.233806 | ||||||||
\(57\) | −0.207783 | −0.0275215 | ||||||||
\(58\) | 2.68705 | 0.352827 | ||||||||
\(59\) | 11.0273 | 1.43563 | 0.717814 | − | 0.696235i | \(-0.245143\pi\) | ||||
0.717814 | + | 0.696235i | \(0.245143\pi\) | |||||||
\(60\) | 2.96685 | 0.383018 | ||||||||
\(61\) | −5.60537 | −0.717694 | −0.358847 | − | 0.933396i | \(-0.616830\pi\) | ||||
−0.358847 | + | 0.933396i | \(0.616830\pi\) | |||||||
\(62\) | −9.82583 | −1.24788 | ||||||||
\(63\) | −3.87728 | −0.488492 | ||||||||
\(64\) | −2.98811 | −0.373513 | ||||||||
\(65\) | 6.02287 | 0.747045 | ||||||||
\(66\) | 1.76554 | 0.217323 | ||||||||
\(67\) | −7.74173 | −0.945803 | −0.472901 | − | 0.881115i | \(-0.656793\pi\) | ||||
−0.472901 | + | 0.881115i | \(0.656793\pi\) | |||||||
\(68\) | 5.69089 | 0.690122 | ||||||||
\(69\) | 3.45016 | 0.415350 | ||||||||
\(70\) | 7.81627 | 0.934223 | ||||||||
\(71\) | −5.61399 | −0.666258 | −0.333129 | − | 0.942881i | \(-0.608105\pi\) | ||||
−0.333129 | + | 0.942881i | \(0.608105\pi\) | |||||||
\(72\) | −2.45873 | −0.289764 | ||||||||
\(73\) | 3.59707 | 0.421005 | 0.210503 | − | 0.977593i | \(-0.432490\pi\) | ||||
0.210503 | + | 0.977593i | \(0.432490\pi\) | |||||||
\(74\) | 12.1737 | 1.41516 | ||||||||
\(75\) | −1.18561 | −0.136903 | ||||||||
\(76\) | 0.364501 | 0.0418111 | ||||||||
\(77\) | 1.94029 | 0.221117 | ||||||||
\(78\) | −3.58357 | −0.405759 | ||||||||
\(79\) | 12.1156 | 1.36311 | 0.681555 | − | 0.731767i | \(-0.261304\pi\) | ||||
0.681555 | + | 0.731767i | \(0.261304\pi\) | |||||||
\(80\) | 12.2287 | 1.36721 | ||||||||
\(81\) | 3.45133 | 0.383481 | ||||||||
\(82\) | −0.592585 | −0.0654400 | ||||||||
\(83\) | 4.34313 | 0.476721 | 0.238360 | − | 0.971177i | \(-0.423390\pi\) | ||||
0.238360 | + | 0.971177i | \(0.423390\pi\) | |||||||
\(84\) | −1.93998 | −0.211669 | ||||||||
\(85\) | −10.0998 | −1.09548 | ||||||||
\(86\) | −12.7690 | −1.37692 | ||||||||
\(87\) | 1.18360 | 0.126895 | ||||||||
\(88\) | 1.23041 | 0.131162 | ||||||||
\(89\) | 4.01262 | 0.425337 | 0.212668 | − | 0.977124i | \(-0.431785\pi\) | ||||
0.212668 | + | 0.977124i | \(0.431785\pi\) | |||||||
\(90\) | −10.9840 | −1.15781 | ||||||||
\(91\) | −3.93826 | −0.412842 | ||||||||
\(92\) | −6.05241 | −0.631007 | ||||||||
\(93\) | −4.32810 | −0.448803 | ||||||||
\(94\) | −5.79017 | −0.597210 | ||||||||
\(95\) | −0.646890 | −0.0663695 | ||||||||
\(96\) | −5.55710 | −0.567169 | ||||||||
\(97\) | 8.84155 | 0.897723 | 0.448862 | − | 0.893601i | \(-0.351830\pi\) | ||||
0.448862 | + | 0.893601i | \(0.351830\pi\) | |||||||
\(98\) | 7.85582 | 0.793558 | ||||||||
\(99\) | −2.72664 | −0.274037 | ||||||||
\(100\) | 2.07985 | 0.207985 | ||||||||
\(101\) | 15.5402 | 1.54631 | 0.773155 | − | 0.634218i | \(-0.218678\pi\) | ||||
0.773155 | + | 0.634218i | \(0.218678\pi\) | |||||||
\(102\) | 6.00931 | 0.595011 | ||||||||
\(103\) | −7.19792 | −0.709232 | −0.354616 | − | 0.935012i | \(-0.615388\pi\) | ||||
−0.354616 | + | 0.935012i | \(0.615388\pi\) | |||||||
\(104\) | −2.49739 | −0.244890 | ||||||||
\(105\) | 3.44293 | 0.335995 | ||||||||
\(106\) | 7.24486 | 0.703683 | ||||||||
\(107\) | 6.81066 | 0.658411 | 0.329205 | − | 0.944258i | \(-0.393219\pi\) | ||||
0.329205 | + | 0.944258i | \(0.393219\pi\) | |||||||
\(108\) | 6.22995 | 0.599477 | ||||||||
\(109\) | −3.83985 | −0.367791 | −0.183895 | − | 0.982946i | \(-0.558871\pi\) | ||||
−0.183895 | + | 0.982946i | \(0.558871\pi\) | |||||||
\(110\) | 5.49667 | 0.524087 | ||||||||
\(111\) | 5.36227 | 0.508965 | ||||||||
\(112\) | −7.99618 | −0.755568 | ||||||||
\(113\) | −8.11474 | −0.763371 | −0.381685 | − | 0.924292i | \(-0.624656\pi\) | ||||
−0.381685 | + | 0.924292i | \(0.624656\pi\) | |||||||
\(114\) | 0.384896 | 0.0360488 | ||||||||
\(115\) | 10.7414 | 1.00164 | ||||||||
\(116\) | −2.07631 | −0.192781 | ||||||||
\(117\) | 5.53432 | 0.511648 | ||||||||
\(118\) | −20.4269 | −1.88044 | ||||||||
\(119\) | 6.60409 | 0.605396 | ||||||||
\(120\) | 2.18329 | 0.199306 | ||||||||
\(121\) | −9.63552 | −0.875957 | ||||||||
\(122\) | 10.3834 | 0.940065 | ||||||||
\(123\) | −0.261023 | −0.0235356 | ||||||||
\(124\) | 7.59253 | 0.681829 | ||||||||
\(125\) | 9.01026 | 0.805902 | ||||||||
\(126\) | 7.18226 | 0.639846 | ||||||||
\(127\) | −16.5173 | −1.46567 | −0.732836 | − | 0.680406i | \(-0.761804\pi\) | ||||
−0.732836 | + | 0.680406i | \(0.761804\pi\) | |||||||
\(128\) | −8.08608 | −0.714716 | ||||||||
\(129\) | −5.62451 | −0.495211 | ||||||||
\(130\) | −11.1567 | −0.978510 | ||||||||
\(131\) | 18.5454 | 1.62032 | 0.810161 | − | 0.586207i | \(-0.199379\pi\) | ||||
0.810161 | + | 0.586207i | \(0.199379\pi\) | |||||||
\(132\) | −1.36426 | −0.118743 | ||||||||
\(133\) | 0.422991 | 0.0366780 | ||||||||
\(134\) | 14.3407 | 1.23885 | ||||||||
\(135\) | −11.0565 | −0.951589 | ||||||||
\(136\) | 4.18789 | 0.359109 | ||||||||
\(137\) | 9.78396 | 0.835900 | 0.417950 | − | 0.908470i | \(-0.362749\pi\) | ||||
0.417950 | + | 0.908470i | \(0.362749\pi\) | |||||||
\(138\) | −6.39106 | −0.544043 | ||||||||
\(139\) | 21.8853 | 1.85629 | 0.928144 | − | 0.372221i | \(-0.121404\pi\) | ||||
0.928144 | + | 0.372221i | \(0.121404\pi\) | |||||||
\(140\) | −6.03972 | −0.510450 | ||||||||
\(141\) | −2.55047 | −0.214788 | ||||||||
\(142\) | 10.3993 | 0.872692 | ||||||||
\(143\) | −2.76952 | −0.231599 | ||||||||
\(144\) | 11.2368 | 0.936401 | ||||||||
\(145\) | 3.68489 | 0.306014 | ||||||||
\(146\) | −6.66319 | −0.551450 | ||||||||
\(147\) | 3.46035 | 0.285405 | ||||||||
\(148\) | −9.40672 | −0.773227 | ||||||||
\(149\) | −21.1938 | −1.73626 | −0.868131 | − | 0.496335i | \(-0.834679\pi\) | ||||
−0.868131 | + | 0.496335i | \(0.834679\pi\) | |||||||
\(150\) | 2.19623 | 0.179321 | ||||||||
\(151\) | −2.65216 | −0.215829 | −0.107915 | − | 0.994160i | \(-0.534417\pi\) | ||||
−0.107915 | + | 0.994160i | \(0.534417\pi\) | |||||||
\(152\) | 0.268234 | 0.0217567 | ||||||||
\(153\) | −9.28054 | −0.750287 | ||||||||
\(154\) | −3.59418 | −0.289628 | ||||||||
\(155\) | −13.4747 | −1.08231 | ||||||||
\(156\) | 2.76907 | 0.221703 | ||||||||
\(157\) | 6.08920 | 0.485971 | 0.242986 | − | 0.970030i | \(-0.421873\pi\) | ||||
0.242986 | + | 0.970030i | \(0.421873\pi\) | |||||||
\(158\) | −22.4429 | −1.78546 | ||||||||
\(159\) | 3.19123 | 0.253081 | ||||||||
\(160\) | −17.3009 | −1.36776 | ||||||||
\(161\) | −7.02362 | −0.553539 | ||||||||
\(162\) | −6.39322 | −0.502299 | ||||||||
\(163\) | 11.2215 | 0.878933 | 0.439467 | − | 0.898259i | \(-0.355167\pi\) | ||||
0.439467 | + | 0.898259i | \(0.355167\pi\) | |||||||
\(164\) | 0.457897 | 0.0357557 | ||||||||
\(165\) | 2.42118 | 0.188489 | ||||||||
\(166\) | −8.04520 | −0.624429 | ||||||||
\(167\) | 24.9029 | 1.92704 | 0.963522 | − | 0.267630i | \(-0.0862403\pi\) | ||||
0.963522 | + | 0.267630i | \(0.0862403\pi\) | |||||||
\(168\) | −1.42762 | −0.110143 | ||||||||
\(169\) | −7.37864 | −0.567588 | ||||||||
\(170\) | 18.7088 | 1.43490 | ||||||||
\(171\) | −0.594417 | −0.0454562 | ||||||||
\(172\) | 9.86675 | 0.752332 | ||||||||
\(173\) | 3.26411 | 0.248166 | 0.124083 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124083 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(174\) | −2.19249 | −0.166212 | ||||||||
\(175\) | 2.41360 | 0.182451 | ||||||||
\(176\) | −5.62319 | −0.423864 | ||||||||
\(177\) | −8.99766 | −0.676306 | ||||||||
\(178\) | −7.43295 | −0.557123 | ||||||||
\(179\) | −11.9544 | −0.893511 | −0.446755 | − | 0.894656i | \(-0.647421\pi\) | ||||
−0.446755 | + | 0.894656i | \(0.647421\pi\) | |||||||
\(180\) | 8.48745 | 0.632617 | ||||||||
\(181\) | −23.3767 | −1.73758 | −0.868790 | − | 0.495181i | \(-0.835102\pi\) | ||||
−0.868790 | + | 0.495181i | \(0.835102\pi\) | |||||||
\(182\) | 7.29521 | 0.540757 | ||||||||
\(183\) | 4.57368 | 0.338097 | ||||||||
\(184\) | −4.45393 | −0.328348 | ||||||||
\(185\) | 16.6944 | 1.22739 | ||||||||
\(186\) | 8.01735 | 0.587861 | ||||||||
\(187\) | 4.64422 | 0.339619 | ||||||||
\(188\) | 4.47413 | 0.326309 | ||||||||
\(189\) | 7.22965 | 0.525880 | ||||||||
\(190\) | 1.19830 | 0.0869335 | ||||||||
\(191\) | −7.39886 | −0.535363 | −0.267682 | − | 0.963507i | \(-0.586258\pi\) | ||||
−0.267682 | + | 0.963507i | \(0.586258\pi\) | |||||||
\(192\) | 2.43814 | 0.175957 | ||||||||
\(193\) | −19.7294 | −1.42015 | −0.710076 | − | 0.704125i | \(-0.751339\pi\) | ||||
−0.710076 | + | 0.704125i | \(0.751339\pi\) | |||||||
\(194\) | −16.3780 | −1.17587 | ||||||||
\(195\) | −4.91434 | −0.351923 | ||||||||
\(196\) | −6.07028 | −0.433592 | ||||||||
\(197\) | −5.61916 | −0.400348 | −0.200174 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200174 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(198\) | 5.05081 | 0.358945 | ||||||||
\(199\) | 19.9656 | 1.41533 | 0.707663 | − | 0.706550i | \(-0.249749\pi\) | ||||
0.707663 | + | 0.706550i | \(0.249749\pi\) | |||||||
\(200\) | 1.53055 | 0.108226 | ||||||||
\(201\) | 6.31684 | 0.445555 | ||||||||
\(202\) | −28.7866 | −2.02542 | ||||||||
\(203\) | −2.40949 | −0.169113 | ||||||||
\(204\) | −4.64346 | −0.325108 | ||||||||
\(205\) | −0.812642 | −0.0567574 | ||||||||
\(206\) | 13.3334 | 0.928981 | ||||||||
\(207\) | 9.87009 | 0.686019 | ||||||||
\(208\) | 11.4135 | 0.791386 | ||||||||
\(209\) | 0.297462 | 0.0205758 | ||||||||
\(210\) | −6.37766 | −0.440101 | ||||||||
\(211\) | 25.7972 | 1.77595 | 0.887976 | − | 0.459889i | \(-0.152111\pi\) | ||||
0.887976 | + | 0.459889i | \(0.152111\pi\) | |||||||
\(212\) | −5.59819 | −0.384485 | ||||||||
\(213\) | 4.58072 | 0.313866 | ||||||||
\(214\) | −12.6160 | −0.862414 | ||||||||
\(215\) | −17.5108 | −1.19423 | ||||||||
\(216\) | 4.58458 | 0.311941 | ||||||||
\(217\) | 8.81088 | 0.598121 | ||||||||
\(218\) | 7.11291 | 0.481747 | ||||||||
\(219\) | −2.93502 | −0.198330 | ||||||||
\(220\) | −4.24734 | −0.286355 | ||||||||
\(221\) | −9.42649 | −0.634095 | ||||||||
\(222\) | −9.93305 | −0.666663 | ||||||||
\(223\) | −11.9595 | −0.800869 | −0.400434 | − | 0.916325i | \(-0.631141\pi\) | ||||
−0.400434 | + | 0.916325i | \(0.631141\pi\) | |||||||
\(224\) | 11.3128 | 0.755868 | ||||||||
\(225\) | −3.39176 | −0.226117 | ||||||||
\(226\) | 15.0317 | 0.999894 | ||||||||
\(227\) | 16.2793 | 1.08049 | 0.540246 | − | 0.841507i | \(-0.318331\pi\) | ||||
0.540246 | + | 0.841507i | \(0.318331\pi\) | |||||||
\(228\) | −0.297413 | −0.0196967 | ||||||||
\(229\) | −21.2115 | −1.40170 | −0.700849 | − | 0.713310i | \(-0.747195\pi\) | ||||
−0.700849 | + | 0.713310i | \(0.747195\pi\) | |||||||
\(230\) | −19.8973 | −1.31199 | ||||||||
\(231\) | −1.58317 | −0.104165 | ||||||||
\(232\) | −1.52795 | −0.100315 | ||||||||
\(233\) | −7.51719 | −0.492468 | −0.246234 | − | 0.969210i | \(-0.579193\pi\) | ||||
−0.246234 | + | 0.969210i | \(0.579193\pi\) | |||||||
\(234\) | −10.2518 | −0.670178 | ||||||||
\(235\) | −7.94036 | −0.517972 | ||||||||
\(236\) | 15.7841 | 1.02745 | ||||||||
\(237\) | −9.88568 | −0.642144 | ||||||||
\(238\) | −12.2334 | −0.792973 | ||||||||
\(239\) | −21.6746 | −1.40201 | −0.701006 | − | 0.713155i | \(-0.747265\pi\) | ||||
−0.701006 | + | 0.713155i | \(0.747265\pi\) | |||||||
\(240\) | −9.97800 | −0.644077 | ||||||||
\(241\) | −20.5138 | −1.32141 | −0.660705 | − | 0.750646i | \(-0.729743\pi\) | ||||
−0.660705 | + | 0.750646i | \(0.729743\pi\) | |||||||
\(242\) | 17.8488 | 1.14736 | ||||||||
\(243\) | −15.8734 | −1.01828 | ||||||||
\(244\) | −8.02334 | −0.513642 | ||||||||
\(245\) | 10.7731 | 0.688268 | ||||||||
\(246\) | 0.483517 | 0.0308279 | ||||||||
\(247\) | −0.603766 | −0.0384167 | ||||||||
\(248\) | 5.58730 | 0.354794 | ||||||||
\(249\) | −3.54377 | −0.224577 | ||||||||
\(250\) | −16.6906 | −1.05560 | ||||||||
\(251\) | 1.31732 | 0.0831488 | 0.0415744 | − | 0.999135i | \(-0.486763\pi\) | ||||
0.0415744 | + | 0.999135i | \(0.486763\pi\) | |||||||
\(252\) | −5.54981 | −0.349605 | ||||||||
\(253\) | −4.93924 | −0.310528 | ||||||||
\(254\) | 30.5965 | 1.91980 | ||||||||
\(255\) | 8.24089 | 0.516064 | ||||||||
\(256\) | 20.9548 | 1.30968 | ||||||||
\(257\) | −19.8531 | −1.23840 | −0.619202 | − | 0.785232i | \(-0.712544\pi\) | ||||
−0.619202 | + | 0.785232i | \(0.712544\pi\) | |||||||
\(258\) | 10.4188 | 0.648647 | ||||||||
\(259\) | −10.9162 | −0.678299 | ||||||||
\(260\) | 8.62093 | 0.534647 | ||||||||
\(261\) | 3.38599 | 0.209588 | ||||||||
\(262\) | −34.3535 | −2.12236 | ||||||||
\(263\) | −10.8515 | −0.669135 | −0.334567 | − | 0.942372i | \(-0.608590\pi\) | ||||
−0.334567 | + | 0.942372i | \(0.608590\pi\) | |||||||
\(264\) | −1.00395 | −0.0617887 | ||||||||
\(265\) | 9.93526 | 0.610318 | ||||||||
\(266\) | −0.783547 | −0.0480423 | ||||||||
\(267\) | −3.27408 | −0.200371 | ||||||||
\(268\) | −11.0812 | −0.676895 | ||||||||
\(269\) | 19.0762 | 1.16310 | 0.581548 | − | 0.813512i | \(-0.302447\pi\) | ||||
0.581548 | + | 0.813512i | \(0.302447\pi\) | |||||||
\(270\) | 20.4809 | 1.24643 | ||||||||
\(271\) | −22.1187 | −1.34362 | −0.671808 | − | 0.740726i | \(-0.734482\pi\) | ||||
−0.671808 | + | 0.740726i | \(0.734482\pi\) | |||||||
\(272\) | −19.1394 | −1.16050 | ||||||||
\(273\) | 3.21341 | 0.194484 | ||||||||
\(274\) | −18.1237 | −1.09490 | ||||||||
\(275\) | 1.69732 | 0.102352 | ||||||||
\(276\) | 4.93844 | 0.297259 | ||||||||
\(277\) | −17.6959 | −1.06324 | −0.531622 | − | 0.846982i | \(-0.678417\pi\) | ||||
−0.531622 | + | 0.846982i | \(0.678417\pi\) | |||||||
\(278\) | −40.5402 | −2.43144 | ||||||||
\(279\) | −12.3817 | −0.741272 | ||||||||
\(280\) | −4.44460 | −0.265615 | ||||||||
\(281\) | −15.1604 | −0.904394 | −0.452197 | − | 0.891918i | \(-0.649360\pi\) | ||||
−0.452197 | + | 0.891918i | \(0.649360\pi\) | |||||||
\(282\) | 4.72447 | 0.281338 | ||||||||
\(283\) | 3.74481 | 0.222606 | 0.111303 | − | 0.993787i | \(-0.464498\pi\) | ||||
0.111303 | + | 0.993787i | \(0.464498\pi\) | |||||||
\(284\) | −8.03568 | −0.476830 | ||||||||
\(285\) | 0.527828 | 0.0312658 | ||||||||
\(286\) | 5.13024 | 0.303357 | ||||||||
\(287\) | 0.531374 | 0.0313660 | ||||||||
\(288\) | −15.8976 | −0.936772 | ||||||||
\(289\) | −1.19265 | −0.0701559 | ||||||||
\(290\) | −6.82587 | −0.400829 | ||||||||
\(291\) | −7.21423 | −0.422906 | ||||||||
\(292\) | 5.14872 | 0.301306 | ||||||||
\(293\) | 2.25853 | 0.131945 | 0.0659723 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659723 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(294\) | −6.40993 | −0.373835 | ||||||||
\(295\) | −28.0124 | −1.63095 | ||||||||
\(296\) | −6.92235 | −0.402353 | ||||||||
\(297\) | 5.08413 | 0.295011 | ||||||||
\(298\) | 39.2593 | 2.27423 | ||||||||
\(299\) | 10.0253 | 0.579779 | ||||||||
\(300\) | −1.69705 | −0.0979791 | ||||||||
\(301\) | 11.4500 | 0.659969 | ||||||||
\(302\) | 4.91284 | 0.282702 | ||||||||
\(303\) | −12.6800 | −0.728446 | ||||||||
\(304\) | −1.22588 | −0.0703089 | ||||||||
\(305\) | 14.2392 | 0.815337 | ||||||||
\(306\) | 17.1912 | 0.982757 | ||||||||
\(307\) | −23.4159 | −1.33642 | −0.668208 | − | 0.743975i | \(-0.732938\pi\) | ||||
−0.668208 | + | 0.743975i | \(0.732938\pi\) | |||||||
\(308\) | 2.77727 | 0.158249 | ||||||||
\(309\) | 5.87311 | 0.334110 | ||||||||
\(310\) | 24.9604 | 1.41766 | ||||||||
\(311\) | 6.90315 | 0.391442 | 0.195721 | − | 0.980660i | \(-0.437295\pi\) | ||||
0.195721 | + | 0.980660i | \(0.437295\pi\) | |||||||
\(312\) | 2.03774 | 0.115364 | ||||||||
\(313\) | −14.0162 | −0.792245 | −0.396122 | − | 0.918198i | \(-0.629644\pi\) | ||||
−0.396122 | + | 0.918198i | \(0.629644\pi\) | |||||||
\(314\) | −11.2796 | −0.636545 | ||||||||
\(315\) | 9.84941 | 0.554951 | ||||||||
\(316\) | 17.3418 | 0.975555 | ||||||||
\(317\) | 9.72672 | 0.546307 | 0.273154 | − | 0.961970i | \(-0.411933\pi\) | ||||
0.273154 | + | 0.961970i | \(0.411933\pi\) | |||||||
\(318\) | −5.91142 | −0.331496 | ||||||||
\(319\) | −1.69444 | −0.0948702 | ||||||||
\(320\) | 7.59064 | 0.424330 | ||||||||
\(321\) | −5.55713 | −0.310169 | ||||||||
\(322\) | 13.0105 | 0.725048 | ||||||||
\(323\) | 1.01246 | 0.0563347 | ||||||||
\(324\) | 4.94011 | 0.274451 | ||||||||
\(325\) | −3.44510 | −0.191100 | ||||||||
\(326\) | −20.7866 | −1.15126 | ||||||||
\(327\) | 3.13311 | 0.173261 | ||||||||
\(328\) | 0.336964 | 0.0186057 | ||||||||
\(329\) | 5.19208 | 0.286249 | ||||||||
\(330\) | −4.48499 | −0.246890 | ||||||||
\(331\) | 31.1716 | 1.71335 | 0.856674 | − | 0.515859i | \(-0.172527\pi\) | ||||
0.856674 | + | 0.515859i | \(0.172527\pi\) | |||||||
\(332\) | 6.21662 | 0.341181 | ||||||||
\(333\) | 15.3402 | 0.840638 | ||||||||
\(334\) | −46.1300 | −2.52412 | ||||||||
\(335\) | 19.6662 | 1.07448 | ||||||||
\(336\) | 6.52446 | 0.355938 | ||||||||
\(337\) | −4.89621 | −0.266713 | −0.133357 | − | 0.991068i | \(-0.542576\pi\) | ||||
−0.133357 | + | 0.991068i | \(0.542576\pi\) | |||||||
\(338\) | 13.6682 | 0.743450 | ||||||||
\(339\) | 6.62120 | 0.359614 | ||||||||
\(340\) | −14.4565 | −0.784013 | ||||||||
\(341\) | 6.19611 | 0.335538 | ||||||||
\(342\) | 1.10110 | 0.0595404 | ||||||||
\(343\) | −18.6717 | −1.00818 | ||||||||
\(344\) | 7.26088 | 0.391480 | ||||||||
\(345\) | −8.76439 | −0.471859 | ||||||||
\(346\) | −6.04642 | −0.325058 | ||||||||
\(347\) | 23.8370 | 1.27963 | 0.639817 | − | 0.768527i | \(-0.279010\pi\) | ||||
0.639817 | + | 0.768527i | \(0.279010\pi\) | |||||||
\(348\) | 1.69416 | 0.0908166 | ||||||||
\(349\) | −31.6470 | −1.69402 | −0.847012 | − | 0.531574i | \(-0.821601\pi\) | ||||
−0.847012 | + | 0.531574i | \(0.821601\pi\) | |||||||
\(350\) | −4.47094 | −0.238982 | ||||||||
\(351\) | −10.3194 | −0.550809 | ||||||||
\(352\) | 7.95554 | 0.424032 | ||||||||
\(353\) | 6.22861 | 0.331516 | 0.165758 | − | 0.986166i | \(-0.446993\pi\) | ||||
0.165758 | + | 0.986166i | \(0.446993\pi\) | |||||||
\(354\) | 16.6672 | 0.885853 | ||||||||
\(355\) | 14.2611 | 0.756903 | ||||||||
\(356\) | 5.74353 | 0.304406 | ||||||||
\(357\) | −5.38859 | −0.285194 | ||||||||
\(358\) | 22.1442 | 1.17036 | ||||||||
\(359\) | 22.6052 | 1.19306 | 0.596529 | − | 0.802591i | \(-0.296546\pi\) | ||||
0.596529 | + | 0.802591i | \(0.296546\pi\) | |||||||
\(360\) | 6.24587 | 0.329186 | ||||||||
\(361\) | −18.9352 | −0.996587 | ||||||||
\(362\) | 43.3030 | 2.27595 | ||||||||
\(363\) | 7.86207 | 0.412652 | ||||||||
\(364\) | −5.63709 | −0.295464 | ||||||||
\(365\) | −9.13759 | −0.478283 | ||||||||
\(366\) | −8.47227 | −0.442853 | ||||||||
\(367\) | −14.3808 | −0.750670 | −0.375335 | − | 0.926889i | \(-0.622472\pi\) | ||||
−0.375335 | + | 0.926889i | \(0.622472\pi\) | |||||||
\(368\) | 20.3552 | 1.06109 | ||||||||
\(369\) | −0.746725 | −0.0388729 | ||||||||
\(370\) | −30.9246 | −1.60769 | ||||||||
\(371\) | −6.49651 | −0.337282 | ||||||||
\(372\) | −6.19510 | −0.321201 | ||||||||
\(373\) | 6.56346 | 0.339843 | 0.169922 | − | 0.985458i | \(-0.445649\pi\) | ||||
0.169922 | + | 0.985458i | \(0.445649\pi\) | |||||||
\(374\) | −8.60293 | −0.444847 | ||||||||
\(375\) | −7.35189 | −0.379650 | ||||||||
\(376\) | 3.29248 | 0.169797 | ||||||||
\(377\) | 3.43924 | 0.177130 | ||||||||
\(378\) | −13.3922 | −0.688819 | ||||||||
\(379\) | −30.9806 | −1.59136 | −0.795682 | − | 0.605714i | \(-0.792888\pi\) | ||||
−0.795682 | + | 0.605714i | \(0.792888\pi\) | |||||||
\(380\) | −0.925936 | −0.0474995 | ||||||||
\(381\) | 13.4772 | 0.690459 | ||||||||
\(382\) | 13.7056 | 0.701240 | ||||||||
\(383\) | −23.4879 | −1.20017 | −0.600087 | − | 0.799935i | \(-0.704867\pi\) | ||||
−0.600087 | + | 0.799935i | \(0.704867\pi\) | |||||||
\(384\) | 6.59781 | 0.336693 | ||||||||
\(385\) | −4.92889 | −0.251200 | ||||||||
\(386\) | 36.5466 | 1.86017 | ||||||||
\(387\) | −16.0904 | −0.817921 | ||||||||
\(388\) | 12.6555 | 0.642485 | ||||||||
\(389\) | 3.36780 | 0.170754 | 0.0853772 | − | 0.996349i | \(-0.472790\pi\) | ||||
0.0853772 | + | 0.996349i | \(0.472790\pi\) | |||||||
\(390\) | 9.10330 | 0.460963 | ||||||||
\(391\) | −16.8115 | −0.850195 | ||||||||
\(392\) | −4.46709 | −0.225622 | ||||||||
\(393\) | −15.1321 | −0.763313 | ||||||||
\(394\) | 10.4089 | 0.524393 | ||||||||
\(395\) | −30.7771 | −1.54856 | ||||||||
\(396\) | −3.90281 | −0.196124 | ||||||||
\(397\) | 8.88272 | 0.445811 | 0.222905 | − | 0.974840i | \(-0.428446\pi\) | ||||
0.222905 | + | 0.974840i | \(0.428446\pi\) | |||||||
\(398\) | −36.9842 | −1.85385 | ||||||||
\(399\) | −0.345138 | −0.0172785 | ||||||||
\(400\) | −6.99489 | −0.349744 | ||||||||
\(401\) | 11.7056 | 0.584547 | 0.292274 | − | 0.956335i | \(-0.405588\pi\) | ||||
0.292274 | + | 0.956335i | \(0.405588\pi\) | |||||||
\(402\) | −11.7013 | −0.583607 | ||||||||
\(403\) | −12.5764 | −0.626475 | ||||||||
\(404\) | 22.2437 | 1.10667 | ||||||||
\(405\) | −8.76736 | −0.435654 | ||||||||
\(406\) | 4.46333 | 0.221511 | ||||||||
\(407\) | −7.67663 | −0.380516 | ||||||||
\(408\) | −3.41710 | −0.169172 | ||||||||
\(409\) | −29.1511 | −1.44143 | −0.720715 | − | 0.693231i | \(-0.756186\pi\) | ||||
−0.720715 | + | 0.693231i | \(0.756186\pi\) | |||||||
\(410\) | 1.50533 | 0.0743432 | ||||||||
\(411\) | −7.98319 | −0.393782 | ||||||||
\(412\) | −10.3029 | −0.507585 | ||||||||
\(413\) | 18.3169 | 0.901315 | ||||||||
\(414\) | −18.2833 | −0.898575 | ||||||||
\(415\) | −11.0328 | −0.541579 | ||||||||
\(416\) | −16.1476 | −0.791700 | ||||||||
\(417\) | −17.8573 | −0.874473 | ||||||||
\(418\) | −0.551016 | −0.0269511 | ||||||||
\(419\) | −13.2516 | −0.647384 | −0.323692 | − | 0.946162i | \(-0.604924\pi\) | ||||
−0.323692 | + | 0.946162i | \(0.604924\pi\) | |||||||
\(420\) | 4.92809 | 0.240466 | ||||||||
\(421\) | −17.8129 | −0.868145 | −0.434073 | − | 0.900878i | \(-0.642924\pi\) | ||||
−0.434073 | + | 0.900878i | \(0.642924\pi\) | |||||||
\(422\) | −47.7866 | −2.32622 | ||||||||
\(423\) | −7.29628 | −0.354757 | ||||||||
\(424\) | −4.11967 | −0.200069 | ||||||||
\(425\) | 5.77712 | 0.280231 | ||||||||
\(426\) | −8.48530 | −0.411114 | ||||||||
\(427\) | −9.31082 | −0.450582 | ||||||||
\(428\) | 9.74854 | 0.471214 | ||||||||
\(429\) | 2.25978 | 0.109103 | ||||||||
\(430\) | 32.4369 | 1.56425 | ||||||||
\(431\) | 10.7414 | 0.517395 | 0.258697 | − | 0.965958i | \(-0.416707\pi\) | ||||
0.258697 | + | 0.965958i | \(0.416707\pi\) | |||||||
\(432\) | −20.9524 | −1.00807 | ||||||||
\(433\) | 10.4424 | 0.501829 | 0.250915 | − | 0.968009i | \(-0.419269\pi\) | ||||
0.250915 | + | 0.968009i | \(0.419269\pi\) | |||||||
\(434\) | −16.3212 | −0.783444 | ||||||||
\(435\) | −3.00667 | −0.144159 | ||||||||
\(436\) | −5.49623 | −0.263222 | ||||||||
\(437\) | −1.07678 | −0.0515091 | ||||||||
\(438\) | 5.43681 | 0.259781 | ||||||||
\(439\) | −11.3551 | −0.541947 | −0.270974 | − | 0.962587i | \(-0.587346\pi\) | ||||
−0.270974 | + | 0.962587i | \(0.587346\pi\) | |||||||
\(440\) | −3.12559 | −0.149007 | ||||||||
\(441\) | 9.89924 | 0.471393 | ||||||||
\(442\) | 17.4616 | 0.830563 | ||||||||
\(443\) | −13.7769 | −0.654562 | −0.327281 | − | 0.944927i | \(-0.606132\pi\) | ||||
−0.327281 | + | 0.944927i | \(0.606132\pi\) | |||||||
\(444\) | 7.67538 | 0.364257 | ||||||||
\(445\) | −10.1932 | −0.483204 | ||||||||
\(446\) | 22.1538 | 1.04901 | ||||||||
\(447\) | 17.2930 | 0.817931 | ||||||||
\(448\) | −4.96340 | −0.234499 | ||||||||
\(449\) | −3.68194 | −0.173762 | −0.0868808 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868808 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(450\) | 6.28288 | 0.296178 | ||||||||
\(451\) | 0.373680 | 0.0175959 | ||||||||
\(452\) | −11.6152 | −0.546332 | ||||||||
\(453\) | 2.16402 | 0.101674 | ||||||||
\(454\) | −30.1556 | −1.41527 | ||||||||
\(455\) | 10.0043 | 0.469009 | ||||||||
\(456\) | −0.218865 | −0.0102493 | ||||||||
\(457\) | 18.7280 | 0.876061 | 0.438031 | − | 0.898960i | \(-0.355676\pi\) | ||||
0.438031 | + | 0.898960i | \(0.355676\pi\) | |||||||
\(458\) | 39.2921 | 1.83600 | ||||||||
\(459\) | 17.3047 | 0.807712 | ||||||||
\(460\) | 15.3748 | 0.716856 | ||||||||
\(461\) | −2.42289 | −0.112845 | −0.0564225 | − | 0.998407i | \(-0.517969\pi\) | ||||
−0.0564225 | + | 0.998407i | \(0.517969\pi\) | |||||||
\(462\) | 2.93266 | 0.136440 | ||||||||
\(463\) | 25.4090 | 1.18086 | 0.590429 | − | 0.807089i | \(-0.298958\pi\) | ||||
0.590429 | + | 0.807089i | \(0.298958\pi\) | |||||||
\(464\) | 6.98299 | 0.324177 | ||||||||
\(465\) | 10.9946 | 0.509863 | ||||||||
\(466\) | 13.9248 | 0.645054 | ||||||||
\(467\) | −29.6416 | −1.37165 | −0.685825 | − | 0.727766i | \(-0.740559\pi\) | ||||
−0.685825 | + | 0.727766i | \(0.740559\pi\) | |||||||
\(468\) | 7.92164 | 0.366178 | ||||||||
\(469\) | −12.8594 | −0.593793 | ||||||||
\(470\) | 14.7087 | 0.678461 | ||||||||
\(471\) | −4.96846 | −0.228935 | ||||||||
\(472\) | 11.6154 | 0.534642 | ||||||||
\(473\) | 8.05205 | 0.370234 | ||||||||
\(474\) | 18.3122 | 0.841106 | ||||||||
\(475\) | 0.370023 | 0.0169778 | ||||||||
\(476\) | 9.45288 | 0.433272 | ||||||||
\(477\) | 9.12936 | 0.418005 | ||||||||
\(478\) | 40.1499 | 1.83641 | ||||||||
\(479\) | −22.0854 | −1.00911 | −0.504553 | − | 0.863380i | \(-0.668343\pi\) | ||||
−0.504553 | + | 0.863380i | \(0.668343\pi\) | |||||||
\(480\) | 14.1166 | 0.644333 | ||||||||
\(481\) | 15.5815 | 0.710453 | ||||||||
\(482\) | 37.9997 | 1.73084 | ||||||||
\(483\) | 5.73090 | 0.260765 | ||||||||
\(484\) | −13.7920 | −0.626907 | ||||||||
\(485\) | −22.4601 | −1.01986 | ||||||||
\(486\) | 29.4039 | 1.33379 | ||||||||
\(487\) | −14.4410 | −0.654383 | −0.327192 | − | 0.944958i | \(-0.606102\pi\) | ||||
−0.327192 | + | 0.944958i | \(0.606102\pi\) | |||||||
\(488\) | −5.90433 | −0.267276 | ||||||||
\(489\) | −9.15612 | −0.414054 | ||||||||
\(490\) | −19.9560 | −0.901522 | ||||||||
\(491\) | 2.06866 | 0.0933574 | 0.0466787 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466787 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(492\) | −0.373619 | −0.0168441 | ||||||||
\(493\) | −5.76729 | −0.259746 | ||||||||
\(494\) | 1.11841 | 0.0503197 | ||||||||
\(495\) | 6.92643 | 0.311320 | ||||||||
\(496\) | −25.5349 | −1.14655 | ||||||||
\(497\) | −9.32514 | −0.418290 | ||||||||
\(498\) | 6.56445 | 0.294160 | ||||||||
\(499\) | −6.30743 | −0.282359 | −0.141180 | − | 0.989984i | \(-0.545090\pi\) | ||||
−0.141180 | + | 0.989984i | \(0.545090\pi\) | |||||||
\(500\) | 12.8970 | 0.576771 | ||||||||
\(501\) | −20.3194 | −0.907805 | ||||||||
\(502\) | −2.44021 | −0.108912 | ||||||||
\(503\) | −4.33810 | −0.193426 | −0.0967132 | − | 0.995312i | \(-0.530833\pi\) | ||||
−0.0967132 | + | 0.995312i | \(0.530833\pi\) | |||||||
\(504\) | −4.08407 | −0.181919 | ||||||||
\(505\) | −39.4766 | −1.75669 | ||||||||
\(506\) | 9.14943 | 0.406742 | ||||||||
\(507\) | 6.02058 | 0.267383 | ||||||||
\(508\) | −23.6423 | −1.04896 | ||||||||
\(509\) | −13.9230 | −0.617126 | −0.308563 | − | 0.951204i | \(-0.599848\pi\) | ||||
−0.308563 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(510\) | −15.2654 | −0.675962 | ||||||||
\(511\) | 5.97493 | 0.264315 | ||||||||
\(512\) | −22.6445 | −1.00075 | ||||||||
\(513\) | 1.10836 | 0.0489353 | ||||||||
\(514\) | 36.7758 | 1.62211 | ||||||||
\(515\) | 18.2848 | 0.805723 | ||||||||
\(516\) | −8.05074 | −0.354414 | ||||||||
\(517\) | 3.65124 | 0.160582 | ||||||||
\(518\) | 20.2211 | 0.888463 | ||||||||
\(519\) | −2.66334 | −0.116908 | ||||||||
\(520\) | 6.34409 | 0.278207 | ||||||||
\(521\) | −31.2382 | −1.36857 | −0.684284 | − | 0.729215i | \(-0.739885\pi\) | ||||
−0.684284 | + | 0.729215i | \(0.739885\pi\) | |||||||
\(522\) | −6.27219 | −0.274526 | ||||||||
\(523\) | −3.42781 | −0.149888 | −0.0749438 | − | 0.997188i | \(-0.523878\pi\) | ||||
−0.0749438 | + | 0.997188i | \(0.523878\pi\) | |||||||
\(524\) | 26.5453 | 1.15964 | ||||||||
\(525\) | −1.96937 | −0.0859503 | ||||||||
\(526\) | 20.1013 | 0.876460 | ||||||||
\(527\) | 21.0894 | 0.918671 | ||||||||
\(528\) | 4.58822 | 0.199677 | ||||||||
\(529\) | −5.12053 | −0.222632 | ||||||||
\(530\) | −18.4040 | −0.799420 | ||||||||
\(531\) | −25.7402 | −1.11703 | ||||||||
\(532\) | 0.605455 | 0.0262498 | ||||||||
\(533\) | −0.758468 | −0.0328529 | ||||||||
\(534\) | 6.06489 | 0.262454 | ||||||||
\(535\) | −17.3010 | −0.747988 | ||||||||
\(536\) | −8.15463 | −0.352226 | ||||||||
\(537\) | 9.75412 | 0.420921 | ||||||||
\(538\) | −35.3366 | −1.52347 | ||||||||
\(539\) | −4.95383 | −0.213377 | ||||||||
\(540\) | −15.8258 | −0.681036 | ||||||||
\(541\) | −33.0652 | −1.42158 | −0.710792 | − | 0.703402i | \(-0.751663\pi\) | ||||
−0.710792 | + | 0.703402i | \(0.751663\pi\) | |||||||
\(542\) | 40.9726 | 1.75992 | ||||||||
\(543\) | 19.0742 | 0.818551 | ||||||||
\(544\) | 27.0780 | 1.16096 | ||||||||
\(545\) | 9.75431 | 0.417829 | ||||||||
\(546\) | −5.95250 | −0.254744 | ||||||||
\(547\) | 39.5966 | 1.69303 | 0.846514 | − | 0.532366i | \(-0.178697\pi\) | ||||
0.846514 | + | 0.532366i | \(0.178697\pi\) | |||||||
\(548\) | 14.0044 | 0.598239 | ||||||||
\(549\) | 13.0842 | 0.558421 | ||||||||
\(550\) | −3.14411 | −0.134065 | ||||||||
\(551\) | −0.369394 | −0.0157367 | ||||||||
\(552\) | 3.63417 | 0.154681 | ||||||||
\(553\) | 20.1246 | 0.855787 | ||||||||
\(554\) | 32.7798 | 1.39268 | ||||||||
\(555\) | −13.6217 | −0.578209 | ||||||||
\(556\) | 31.3259 | 1.32851 | ||||||||
\(557\) | −16.9161 | −0.716760 | −0.358380 | − | 0.933576i | \(-0.616671\pi\) | ||||
−0.358380 | + | 0.933576i | \(0.616671\pi\) | |||||||
\(558\) | 22.9357 | 0.970948 | ||||||||
\(559\) | −16.3435 | −0.691254 | ||||||||
\(560\) | 20.3126 | 0.858364 | ||||||||
\(561\) | −3.78944 | −0.159990 | ||||||||
\(562\) | 28.0831 | 1.18461 | ||||||||
\(563\) | 15.9657 | 0.672873 | 0.336436 | − | 0.941706i | \(-0.390778\pi\) | ||||
0.336436 | + | 0.941706i | \(0.390778\pi\) | |||||||
\(564\) | −3.65065 | −0.153720 | ||||||||
\(565\) | 20.6138 | 0.867228 | ||||||||
\(566\) | −6.93686 | −0.291578 | ||||||||
\(567\) | 5.73284 | 0.240757 | ||||||||
\(568\) | −5.91341 | −0.248121 | ||||||||
\(569\) | 6.38371 | 0.267619 | 0.133810 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133810 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(570\) | −0.977745 | −0.0409532 | ||||||||
\(571\) | −9.08461 | −0.380179 | −0.190090 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190090 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(572\) | −3.96419 | −0.165751 | ||||||||
\(573\) | 6.03708 | 0.252203 | ||||||||
\(574\) | −0.984315 | −0.0410845 | ||||||||
\(575\) | −6.14411 | −0.256227 | ||||||||
\(576\) | 6.97493 | 0.290622 | ||||||||
\(577\) | −10.6019 | −0.441361 | −0.220681 | − | 0.975346i | \(-0.570828\pi\) | ||||
−0.220681 | + | 0.975346i | \(0.570828\pi\) | |||||||
\(578\) | 2.20926 | 0.0918930 | ||||||||
\(579\) | 16.0981 | 0.669015 | ||||||||
\(580\) | 5.27443 | 0.219009 | ||||||||
\(581\) | 7.21418 | 0.299295 | ||||||||
\(582\) | 13.3636 | 0.553939 | ||||||||
\(583\) | −4.56857 | −0.189211 | ||||||||
\(584\) | 3.78892 | 0.156786 | ||||||||
\(585\) | −14.0588 | −0.581258 | ||||||||
\(586\) | −4.18368 | −0.172826 | ||||||||
\(587\) | 40.7823 | 1.68326 | 0.841632 | − | 0.540051i | \(-0.181595\pi\) | ||||
0.841632 | + | 0.540051i | \(0.181595\pi\) | |||||||
\(588\) | 4.95303 | 0.204259 | ||||||||
\(589\) | 1.35078 | 0.0556577 | ||||||||
\(590\) | 51.8900 | 2.13628 | ||||||||
\(591\) | 4.58493 | 0.188599 | ||||||||
\(592\) | 31.6364 | 1.30025 | ||||||||
\(593\) | −30.0020 | −1.23204 | −0.616018 | − | 0.787732i | \(-0.711255\pi\) | ||||
−0.616018 | + | 0.787732i | \(0.711255\pi\) | |||||||
\(594\) | −9.41782 | −0.386418 | ||||||||
\(595\) | −16.7763 | −0.687761 | ||||||||
\(596\) | −30.3361 | −1.24261 | ||||||||
\(597\) | −16.2909 | −0.666742 | ||||||||
\(598\) | −18.5708 | −0.759418 | ||||||||
\(599\) | −2.97212 | −0.121438 | −0.0607189 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607189 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(600\) | −1.24885 | −0.0509840 | ||||||||
\(601\) | −27.8131 | −1.13452 | −0.567260 | − | 0.823539i | \(-0.691996\pi\) | ||||
−0.567260 | + | 0.823539i | \(0.691996\pi\) | |||||||
\(602\) | −21.2100 | −0.864454 | ||||||||
\(603\) | 18.0710 | 0.735907 | ||||||||
\(604\) | −3.79621 | −0.154465 | ||||||||
\(605\) | 24.4770 | 0.995131 | ||||||||
\(606\) | 23.4883 | 0.954149 | ||||||||
\(607\) | −16.9174 | −0.686655 | −0.343328 | − | 0.939216i | \(-0.611554\pi\) | ||||
−0.343328 | + | 0.939216i | \(0.611554\pi\) | |||||||
\(608\) | 1.73434 | 0.0703368 | ||||||||
\(609\) | 1.96602 | 0.0796671 | ||||||||
\(610\) | −26.3767 | −1.06796 | ||||||||
\(611\) | −7.41103 | −0.299818 | ||||||||
\(612\) | −13.2839 | −0.536968 | ||||||||
\(613\) | 13.7662 | 0.556013 | 0.278006 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278006 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(614\) | 43.3755 | 1.75049 | ||||||||
\(615\) | 0.663073 | 0.0267377 | ||||||||
\(616\) | 2.04377 | 0.0823460 | ||||||||
\(617\) | 28.7183 | 1.15616 | 0.578078 | − | 0.815981i | \(-0.303803\pi\) | ||||
0.578078 | + | 0.815981i | \(0.303803\pi\) | |||||||
\(618\) | −10.8793 | −0.437631 | ||||||||
\(619\) | 21.8205 | 0.877041 | 0.438521 | − | 0.898721i | \(-0.355503\pi\) | ||||
0.438521 | + | 0.898721i | \(0.355503\pi\) | |||||||
\(620\) | −19.2872 | −0.774592 | ||||||||
\(621\) | −18.4039 | −0.738525 | ||||||||
\(622\) | −12.7874 | −0.512726 | ||||||||
\(623\) | 6.66517 | 0.267035 | ||||||||
\(624\) | −9.31283 | −0.372812 | ||||||||
\(625\) | −30.1539 | −1.20616 | ||||||||
\(626\) | 25.9636 | 1.03771 | ||||||||
\(627\) | −0.242713 | −0.00969302 | ||||||||
\(628\) | 8.71587 | 0.347801 | ||||||||
\(629\) | −26.1286 | −1.04182 | ||||||||
\(630\) | −18.2450 | −0.726898 | ||||||||
\(631\) | −48.4687 | −1.92951 | −0.964755 | − | 0.263149i | \(-0.915239\pi\) | ||||
−0.964755 | + | 0.263149i | \(0.915239\pi\) | |||||||
\(632\) | 12.7618 | 0.507636 | ||||||||
\(633\) | −21.0491 | −0.836628 | ||||||||
\(634\) | −18.0177 | −0.715576 | ||||||||
\(635\) | 41.9586 | 1.66508 | ||||||||
\(636\) | 4.56782 | 0.181126 | ||||||||
\(637\) | 10.0549 | 0.398391 | ||||||||
\(638\) | 3.13877 | 0.124265 | ||||||||
\(639\) | 13.1044 | 0.518400 | ||||||||
\(640\) | 20.5410 | 0.811953 | ||||||||
\(641\) | −4.01689 | −0.158658 | −0.0793288 | − | 0.996849i | \(-0.525278\pi\) | ||||
−0.0793288 | + | 0.996849i | \(0.525278\pi\) | |||||||
\(642\) | 10.2940 | 0.406272 | ||||||||
\(643\) | −25.8159 | −1.01808 | −0.509040 | − | 0.860743i | \(-0.669999\pi\) | ||||
−0.509040 | + | 0.860743i | \(0.669999\pi\) | |||||||
\(644\) | −10.0534 | −0.396158 | ||||||||
\(645\) | 14.2879 | 0.562584 | ||||||||
\(646\) | −1.87547 | −0.0737895 | ||||||||
\(647\) | 16.4825 | 0.647993 | 0.323996 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323996 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(648\) | 3.63540 | 0.142812 | ||||||||
\(649\) | 12.8810 | 0.505625 | ||||||||
\(650\) | 6.38169 | 0.250311 | ||||||||
\(651\) | −7.18921 | −0.281767 | ||||||||
\(652\) | 16.0620 | 0.629038 | ||||||||
\(653\) | 1.80207 | 0.0705204 | 0.0352602 | − | 0.999378i | \(-0.488774\pi\) | ||||
0.0352602 | + | 0.999378i | \(0.488774\pi\) | |||||||
\(654\) | −5.80376 | −0.226945 | ||||||||
\(655\) | −47.1107 | −1.84077 | ||||||||
\(656\) | −1.53998 | −0.0601262 | ||||||||
\(657\) | −8.39639 | −0.327574 | ||||||||
\(658\) | −9.61778 | −0.374940 | ||||||||
\(659\) | −51.0630 | −1.98913 | −0.994567 | − | 0.104103i | \(-0.966803\pi\) | ||||
−0.994567 | + | 0.104103i | \(0.966803\pi\) | |||||||
\(660\) | 3.46560 | 0.134898 | ||||||||
\(661\) | −37.8703 | −1.47298 | −0.736492 | − | 0.676446i | \(-0.763519\pi\) | ||||
−0.736492 | + | 0.676446i | \(0.763519\pi\) | |||||||
\(662\) | −57.7421 | −2.24421 | ||||||||
\(663\) | 7.69152 | 0.298714 | ||||||||
\(664\) | 4.57477 | 0.177536 | ||||||||
\(665\) | −1.07452 | −0.0416680 | ||||||||
\(666\) | −28.4161 | −1.10110 | ||||||||
\(667\) | 6.13366 | 0.237496 | ||||||||
\(668\) | 35.6452 | 1.37915 | ||||||||
\(669\) | 9.75833 | 0.377279 | ||||||||
\(670\) | −36.4296 | −1.40740 | ||||||||
\(671\) | −6.54768 | −0.252771 | ||||||||
\(672\) | −9.23064 | −0.356080 | ||||||||
\(673\) | 41.7302 | 1.60858 | 0.804291 | − | 0.594236i | \(-0.202545\pi\) | ||||
0.804291 | + | 0.594236i | \(0.202545\pi\) | |||||||
\(674\) | 9.06971 | 0.349352 | ||||||||
\(675\) | 6.32434 | 0.243424 | ||||||||
\(676\) | −10.5615 | −0.406213 | ||||||||
\(677\) | −17.8698 | −0.686793 | −0.343396 | − | 0.939191i | \(-0.611577\pi\) | ||||
−0.343396 | + | 0.939191i | \(0.611577\pi\) | |||||||
\(678\) | −12.2651 | −0.471037 | ||||||||
\(679\) | 14.6863 | 0.563608 | ||||||||
\(680\) | −10.6384 | −0.407966 | ||||||||
\(681\) | −13.2830 | −0.509006 | ||||||||
\(682\) | −11.4776 | −0.439501 | ||||||||
\(683\) | −50.5914 | −1.93583 | −0.967913 | − | 0.251285i | \(-0.919147\pi\) | ||||
−0.967913 | + | 0.251285i | \(0.919147\pi\) | |||||||
\(684\) | −0.850829 | −0.0325323 | ||||||||
\(685\) | −24.8540 | −0.949624 | ||||||||
\(686\) | 34.5874 | 1.32055 | ||||||||
\(687\) | 17.3075 | 0.660321 | ||||||||
\(688\) | −33.1835 | −1.26511 | ||||||||
\(689\) | 9.27294 | 0.353271 | ||||||||
\(690\) | 16.2351 | 0.618060 | ||||||||
\(691\) | −8.32596 | −0.316735 | −0.158367 | − | 0.987380i | \(-0.550623\pi\) | ||||
−0.158367 | + | 0.987380i | \(0.550623\pi\) | |||||||
\(692\) | 4.67214 | 0.177608 | ||||||||
\(693\) | −4.52909 | −0.172046 | ||||||||
\(694\) | −44.1554 | −1.67612 | ||||||||
\(695\) | −55.5950 | −2.10884 | ||||||||
\(696\) | 1.24672 | 0.0472569 | ||||||||
\(697\) | 1.27188 | 0.0481759 | ||||||||
\(698\) | 58.6227 | 2.21890 | ||||||||
\(699\) | 6.13363 | 0.231995 | ||||||||
\(700\) | 3.45474 | 0.130577 | ||||||||
\(701\) | −21.3209 | −0.805278 | −0.402639 | − | 0.915359i | \(-0.631907\pi\) | ||||
−0.402639 | + | 0.915359i | \(0.631907\pi\) | |||||||
\(702\) | 19.1156 | 0.721472 | ||||||||
\(703\) | −1.67354 | −0.0631186 | ||||||||
\(704\) | −3.49043 | −0.131551 | ||||||||
\(705\) | 6.47891 | 0.244010 | ||||||||
\(706\) | −11.5379 | −0.434233 | ||||||||
\(707\) | 25.8131 | 0.970803 | ||||||||
\(708\) | −12.8789 | −0.484021 | ||||||||
\(709\) | 41.0157 | 1.54038 | 0.770188 | − | 0.637817i | \(-0.220163\pi\) | ||||
0.770188 | + | 0.637817i | \(0.220163\pi\) | |||||||
\(710\) | −26.4173 | −0.991423 | ||||||||
\(711\) | −28.2806 | −1.06060 | ||||||||
\(712\) | 4.22663 | 0.158400 | ||||||||
\(713\) | −22.4292 | −0.839978 | ||||||||
\(714\) | 9.98179 | 0.373559 | ||||||||
\(715\) | 7.03536 | 0.263108 | ||||||||
\(716\) | −17.1111 | −0.639471 | ||||||||
\(717\) | 17.6853 | 0.660470 | ||||||||
\(718\) | −41.8738 | −1.56272 | ||||||||
\(719\) | −33.7158 | −1.25739 | −0.628694 | − | 0.777653i | \(-0.716410\pi\) | ||||
−0.628694 | + | 0.777653i | \(0.716410\pi\) | |||||||
\(720\) | −28.5447 | −1.06380 | ||||||||
\(721\) | −11.9561 | −0.445269 | ||||||||
\(722\) | 35.0754 | 1.30537 | ||||||||
\(723\) | 16.7382 | 0.622499 | ||||||||
\(724\) | −33.4607 | −1.24356 | ||||||||
\(725\) | −2.10777 | −0.0782807 | ||||||||
\(726\) | −14.5637 | −0.540508 | ||||||||
\(727\) | 50.8204 | 1.88483 | 0.942413 | − | 0.334453i | \(-0.108551\pi\) | ||||
0.942413 | + | 0.334453i | \(0.108551\pi\) | |||||||
\(728\) | −4.14830 | −0.153746 | ||||||||
\(729\) | 2.59790 | 0.0962185 | ||||||||
\(730\) | 16.9264 | 0.626475 | ||||||||
\(731\) | 27.4064 | 1.01366 | ||||||||
\(732\) | 6.54662 | 0.241970 | ||||||||
\(733\) | −48.0098 | −1.77328 | −0.886642 | − | 0.462456i | \(-0.846968\pi\) | ||||
−0.886642 | + | 0.462456i | \(0.846968\pi\) | |||||||
\(734\) | 26.6389 | 0.983258 | ||||||||
\(735\) | −8.79028 | −0.324234 | ||||||||
\(736\) | −28.7981 | −1.06151 | ||||||||
\(737\) | −9.04318 | −0.333110 | ||||||||
\(738\) | 1.38323 | 0.0509174 | ||||||||
\(739\) | 27.1000 | 0.996891 | 0.498446 | − | 0.866921i | \(-0.333904\pi\) | ||||
0.498446 | + | 0.866921i | \(0.333904\pi\) | |||||||
\(740\) | 23.8958 | 0.878425 | ||||||||
\(741\) | 0.492641 | 0.0180976 | ||||||||
\(742\) | 12.0341 | 0.441786 | ||||||||
\(743\) | −20.4902 | −0.751711 | −0.375856 | − | 0.926678i | \(-0.622651\pi\) | ||||
−0.375856 | + | 0.926678i | \(0.622651\pi\) | |||||||
\(744\) | −4.55894 | −0.167139 | ||||||||
\(745\) | 53.8383 | 1.97248 | ||||||||
\(746\) | −12.1581 | −0.445140 | ||||||||
\(747\) | −10.1379 | −0.370926 | ||||||||
\(748\) | 6.64758 | 0.243060 | ||||||||
\(749\) | 11.3129 | 0.413363 | ||||||||
\(750\) | 13.6186 | 0.497281 | ||||||||
\(751\) | 28.4132 | 1.03681 | 0.518407 | − | 0.855134i | \(-0.326525\pi\) | ||||
0.518407 | + | 0.855134i | \(0.326525\pi\) | |||||||
\(752\) | −15.0472 | −0.548716 | ||||||||
\(753\) | −1.07487 | −0.0391703 | ||||||||
\(754\) | −6.37083 | −0.232012 | ||||||||
\(755\) | 6.73724 | 0.245193 | ||||||||
\(756\) | 10.3483 | 0.376363 | ||||||||
\(757\) | 20.7910 | 0.755663 | 0.377831 | − | 0.925874i | \(-0.376670\pi\) | ||||
0.377831 | + | 0.925874i | \(0.376670\pi\) | |||||||
\(758\) | 57.3882 | 2.08443 | ||||||||
\(759\) | 4.03016 | 0.146286 | ||||||||
\(760\) | −0.681391 | −0.0247167 | ||||||||
\(761\) | −28.7206 | −1.04112 | −0.520560 | − | 0.853825i | \(-0.674277\pi\) | ||||
−0.520560 | + | 0.853825i | \(0.674277\pi\) | |||||||
\(762\) | −24.9651 | −0.904391 | ||||||||
\(763\) | −6.37819 | −0.230906 | ||||||||
\(764\) | −10.5905 | −0.383150 | ||||||||
\(765\) | 23.5752 | 0.852364 | ||||||||
\(766\) | 43.5088 | 1.57204 | ||||||||
\(767\) | −26.1450 | −0.944041 | ||||||||
\(768\) | −17.0980 | −0.616972 | ||||||||
\(769\) | 13.0742 | 0.471468 | 0.235734 | − | 0.971818i | \(-0.424251\pi\) | ||||
0.235734 | + | 0.971818i | \(0.424251\pi\) | |||||||
\(770\) | 9.13026 | 0.329032 | ||||||||
\(771\) | 16.1991 | 0.583396 | ||||||||
\(772\) | −28.2400 | −1.01638 | ||||||||
\(773\) | 32.9239 | 1.18419 | 0.592095 | − | 0.805868i | \(-0.298301\pi\) | ||||
0.592095 | + | 0.805868i | \(0.298301\pi\) | |||||||
\(774\) | 29.8058 | 1.07135 | ||||||||
\(775\) | 7.70756 | 0.276864 | ||||||||
\(776\) | 9.31310 | 0.334321 | ||||||||
\(777\) | 8.90703 | 0.319538 | ||||||||
\(778\) | −6.23850 | −0.223661 | ||||||||
\(779\) | 0.0814638 | 0.00291874 | ||||||||
\(780\) | −7.03422 | −0.251865 | ||||||||
\(781\) | −6.55775 | −0.234655 | ||||||||
\(782\) | 31.1416 | 1.11362 | ||||||||
\(783\) | −6.31358 | −0.225629 | ||||||||
\(784\) | 20.4154 | 0.729120 | ||||||||
\(785\) | −15.4683 | −0.552088 | ||||||||
\(786\) | 28.0306 | 0.999818 | ||||||||
\(787\) | −22.5117 | −0.802454 | −0.401227 | − | 0.915979i | \(-0.631416\pi\) | ||||
−0.401227 | + | 0.915979i | \(0.631416\pi\) | |||||||
\(788\) | −8.04307 | −0.286523 | ||||||||
\(789\) | 8.85428 | 0.315221 | ||||||||
\(790\) | 57.0113 | 2.02837 | ||||||||
\(791\) | −13.4790 | −0.479259 | ||||||||
\(792\) | −2.87206 | −0.102054 | ||||||||
\(793\) | 13.2900 | 0.471942 | ||||||||
\(794\) | −16.4543 | −0.583941 | ||||||||
\(795\) | −8.10664 | −0.287513 | ||||||||
\(796\) | 28.5781 | 1.01293 | ||||||||
\(797\) | 7.50958 | 0.266003 | 0.133002 | − | 0.991116i | \(-0.457538\pi\) | ||||
0.133002 | + | 0.991116i | \(0.457538\pi\) | |||||||
\(798\) | 0.639332 | 0.0226321 | ||||||||
\(799\) | 12.4276 | 0.439657 | ||||||||
\(800\) | 9.89619 | 0.349883 | ||||||||
\(801\) | −9.36638 | −0.330945 | ||||||||
\(802\) | −21.6833 | −0.765664 | ||||||||
\(803\) | 4.20177 | 0.148277 | ||||||||
\(804\) | 9.04171 | 0.318876 | ||||||||
\(805\) | 17.8420 | 0.628848 | ||||||||
\(806\) | 23.2965 | 0.820583 | ||||||||
\(807\) | −15.5652 | −0.547919 | ||||||||
\(808\) | 16.3690 | 0.575861 | ||||||||
\(809\) | 21.6984 | 0.762876 | 0.381438 | − | 0.924395i | \(-0.375429\pi\) | ||||
0.381438 | + | 0.924395i | \(0.375429\pi\) | |||||||
\(810\) | 16.2406 | 0.570637 | ||||||||
\(811\) | 21.6926 | 0.761731 | 0.380865 | − | 0.924631i | \(-0.375626\pi\) | ||||
0.380865 | + | 0.924631i | \(0.375626\pi\) | |||||||
\(812\) | −3.44887 | −0.121032 | ||||||||
\(813\) | 18.0477 | 0.632960 | ||||||||
\(814\) | 14.2201 | 0.498416 | ||||||||
\(815\) | −28.5057 | −0.998513 | ||||||||
\(816\) | 15.6167 | 0.546695 | ||||||||
\(817\) | 1.75538 | 0.0614129 | ||||||||
\(818\) | 53.9994 | 1.88804 | ||||||||
\(819\) | 9.19281 | 0.321223 | ||||||||
\(820\) | −1.16319 | −0.0406203 | ||||||||
\(821\) | 14.6517 | 0.511348 | 0.255674 | − | 0.966763i | \(-0.417703\pi\) | ||||
0.255674 | + | 0.966763i | \(0.417703\pi\) | |||||||
\(822\) | 14.7880 | 0.515791 | ||||||||
\(823\) | 28.4594 | 0.992031 | 0.496016 | − | 0.868314i | \(-0.334796\pi\) | ||||
0.496016 | + | 0.868314i | \(0.334796\pi\) | |||||||
\(824\) | −7.58181 | −0.264125 | ||||||||
\(825\) | −1.38493 | −0.0482169 | ||||||||
\(826\) | −33.9301 | −1.18058 | ||||||||
\(827\) | 10.8438 | 0.377075 | 0.188538 | − | 0.982066i | \(-0.439625\pi\) | ||||
0.188538 | + | 0.982066i | \(0.439625\pi\) | |||||||
\(828\) | 14.1277 | 0.490972 | ||||||||
\(829\) | 8.15262 | 0.283152 | 0.141576 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141576 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(830\) | 20.4371 | 0.709382 | ||||||||
\(831\) | 14.4389 | 0.500880 | ||||||||
\(832\) | 7.08462 | 0.245615 | ||||||||
\(833\) | −16.8612 | −0.584205 | ||||||||
\(834\) | 33.0787 | 1.14542 | ||||||||
\(835\) | −63.2605 | −2.18922 | ||||||||
\(836\) | 0.425777 | 0.0147258 | ||||||||
\(837\) | 23.0871 | 0.798007 | ||||||||
\(838\) | 24.5472 | 0.847971 | ||||||||
\(839\) | 54.6201 | 1.88569 | 0.942847 | − | 0.333225i | \(-0.108137\pi\) | ||||
0.942847 | + | 0.333225i | \(0.108137\pi\) | |||||||
\(840\) | 3.62655 | 0.125128 | ||||||||
\(841\) | −26.8958 | −0.927442 | ||||||||
\(842\) | 32.9964 | 1.13713 | ||||||||
\(843\) | 12.3701 | 0.426048 | ||||||||
\(844\) | 36.9252 | 1.27102 | ||||||||
\(845\) | 18.7439 | 0.644808 | ||||||||
\(846\) | 13.5156 | 0.464676 | ||||||||
\(847\) | −16.0051 | −0.549942 | ||||||||
\(848\) | 18.8276 | 0.646544 | ||||||||
\(849\) | −3.05556 | −0.104867 | ||||||||
\(850\) | −10.7015 | −0.367058 | ||||||||
\(851\) | 27.7885 | 0.952576 | ||||||||
\(852\) | 6.55669 | 0.224628 | ||||||||
\(853\) | −14.6519 | −0.501673 | −0.250836 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250836 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(854\) | 17.2473 | 0.590191 | ||||||||
\(855\) | 1.50999 | 0.0516406 | ||||||||
\(856\) | 7.17390 | 0.245199 | ||||||||
\(857\) | 5.39325 | 0.184230 | 0.0921150 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921150 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(858\) | −4.18600 | −0.142908 | ||||||||
\(859\) | −2.38156 | −0.0812577 | −0.0406289 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406289 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(860\) | −25.0644 | −0.854687 | ||||||||
\(861\) | −0.433573 | −0.0147761 | ||||||||
\(862\) | −19.8973 | −0.677705 | ||||||||
\(863\) | 22.2287 | 0.756675 | 0.378337 | − | 0.925668i | \(-0.376496\pi\) | ||||
0.378337 | + | 0.925668i | \(0.376496\pi\) | |||||||
\(864\) | 29.6429 | 1.00847 | ||||||||
\(865\) | −8.29177 | −0.281929 | ||||||||
\(866\) | −19.3434 | −0.657316 | ||||||||
\(867\) | 0.973138 | 0.0330495 | ||||||||
\(868\) | 12.6116 | 0.428065 | ||||||||
\(869\) | 14.1523 | 0.480085 | ||||||||
\(870\) | 5.56955 | 0.188825 | ||||||||
\(871\) | 18.3552 | 0.621942 | ||||||||
\(872\) | −4.04464 | −0.136969 | ||||||||
\(873\) | −20.6382 | −0.698498 | ||||||||
\(874\) | 1.99461 | 0.0674688 | ||||||||
\(875\) | 14.9665 | 0.505961 | ||||||||
\(876\) | −4.20108 | −0.141941 | ||||||||
\(877\) | 8.26649 | 0.279139 | 0.139570 | − | 0.990212i | \(-0.455428\pi\) | ||||
0.139570 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(878\) | 21.0340 | 0.709865 | ||||||||
\(879\) | −1.84284 | −0.0621574 | ||||||||
\(880\) | 14.2845 | 0.481530 | ||||||||
\(881\) | −35.2806 | −1.18863 | −0.594317 | − | 0.804231i | \(-0.702578\pi\) | ||||
−0.594317 | + | 0.804231i | \(0.702578\pi\) | |||||||
\(882\) | −18.3373 | −0.617449 | ||||||||
\(883\) | 11.3172 | 0.380856 | 0.190428 | − | 0.981701i | \(-0.439012\pi\) | ||||
0.190428 | + | 0.981701i | \(0.439012\pi\) | |||||||
\(884\) | −13.4928 | −0.453811 | ||||||||
\(885\) | 22.8566 | 0.768317 | ||||||||
\(886\) | 25.5203 | 0.857372 | ||||||||
\(887\) | 27.1504 | 0.911622 | 0.455811 | − | 0.890077i | \(-0.349349\pi\) | ||||
0.455811 | + | 0.890077i | \(0.349349\pi\) | |||||||
\(888\) | 5.64827 | 0.189543 | ||||||||
\(889\) | −27.4361 | −0.920177 | ||||||||
\(890\) | 18.8818 | 0.632920 | ||||||||
\(891\) | 4.03153 | 0.135061 | ||||||||
\(892\) | −17.1185 | −0.573168 | ||||||||
\(893\) | 0.795986 | 0.0266366 | ||||||||
\(894\) | −32.0335 | −1.07136 | ||||||||
\(895\) | 30.3675 | 1.01507 | ||||||||
\(896\) | −13.4314 | −0.448712 | ||||||||
\(897\) | −8.18012 | −0.273126 | ||||||||
\(898\) | 6.82041 | 0.227600 | ||||||||
\(899\) | −7.69445 | −0.256624 | ||||||||
\(900\) | −4.85485 | −0.161828 | ||||||||
\(901\) | −15.5498 | −0.518041 | ||||||||
\(902\) | −0.692203 | −0.0230478 | ||||||||
\(903\) | −9.34262 | −0.310903 | ||||||||
\(904\) | −8.54753 | −0.284287 | ||||||||
\(905\) | 59.3836 | 1.97398 | ||||||||
\(906\) | −4.00862 | −0.133177 | ||||||||
\(907\) | 33.8524 | 1.12405 | 0.562025 | − | 0.827120i | \(-0.310022\pi\) | ||||
0.562025 | + | 0.827120i | \(0.310022\pi\) | |||||||
\(908\) | 23.3016 | 0.773290 | ||||||||
\(909\) | −36.2745 | −1.20315 | ||||||||
\(910\) | −18.5319 | −0.614327 | ||||||||
\(911\) | 2.77307 | 0.0918760 | 0.0459380 | − | 0.998944i | \(-0.485372\pi\) | ||||
0.0459380 | + | 0.998944i | \(0.485372\pi\) | |||||||
\(912\) | 1.00025 | 0.0331216 | ||||||||
\(913\) | 5.07325 | 0.167900 | ||||||||
\(914\) | −34.6917 | −1.14750 | ||||||||
\(915\) | −11.6185 | −0.384095 | ||||||||
\(916\) | −30.3615 | −1.00317 | ||||||||
\(917\) | 30.8050 | 1.01727 | ||||||||
\(918\) | −32.0551 | −1.05797 | ||||||||
\(919\) | 8.74425 | 0.288446 | 0.144223 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144223 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(920\) | 11.3143 | 0.373020 | ||||||||
\(921\) | 19.1061 | 0.629568 | ||||||||
\(922\) | 4.48814 | 0.147809 | ||||||||
\(923\) | 13.3104 | 0.438119 | ||||||||
\(924\) | −2.26610 | −0.0745493 | ||||||||
\(925\) | −9.54924 | −0.313977 | ||||||||
\(926\) | −47.0676 | −1.54674 | ||||||||
\(927\) | 16.8016 | 0.551837 | ||||||||
\(928\) | −9.87935 | −0.324306 | ||||||||
\(929\) | 26.0141 | 0.853496 | 0.426748 | − | 0.904371i | \(-0.359659\pi\) | ||||
0.426748 | + | 0.904371i | \(0.359659\pi\) | |||||||
\(930\) | −20.3664 | −0.667839 | ||||||||
\(931\) | −1.07996 | −0.0353941 | ||||||||
\(932\) | −10.7599 | −0.352451 | ||||||||
\(933\) | −5.63260 | −0.184403 | ||||||||
\(934\) | 54.9080 | 1.79664 | ||||||||
\(935\) | −11.7976 | −0.385824 | ||||||||
\(936\) | 5.82949 | 0.190543 | ||||||||
\(937\) | 5.81652 | 0.190017 | 0.0950087 | − | 0.995476i | \(-0.469712\pi\) | ||||
0.0950087 | + | 0.995476i | \(0.469712\pi\) | |||||||
\(938\) | 23.8207 | 0.777774 | ||||||||
\(939\) | 11.4365 | 0.373216 | ||||||||
\(940\) | −11.3656 | −0.370704 | ||||||||
\(941\) | 0.883221 | 0.0287922 | 0.0143961 | − | 0.999896i | \(-0.495417\pi\) | ||||
0.0143961 | + | 0.999896i | \(0.495417\pi\) | |||||||
\(942\) | 9.20355 | 0.299868 | ||||||||
\(943\) | −1.35268 | −0.0440492 | ||||||||
\(944\) | −53.0844 | −1.72775 | ||||||||
\(945\) | −18.3654 | −0.597426 | ||||||||
\(946\) | −14.9156 | −0.484947 | ||||||||
\(947\) | −32.2064 | −1.04657 | −0.523284 | − | 0.852159i | \(-0.675293\pi\) | ||||
−0.523284 | + | 0.852159i | \(0.675293\pi\) | |||||||
\(948\) | −14.1500 | −0.459571 | ||||||||
\(949\) | −8.52844 | −0.276845 | ||||||||
\(950\) | −0.685429 | −0.0222383 | ||||||||
\(951\) | −7.93649 | −0.257358 | ||||||||
\(952\) | 6.95632 | 0.225456 | ||||||||
\(953\) | −22.5641 | −0.730924 | −0.365462 | − | 0.930826i | \(-0.619089\pi\) | ||||
−0.365462 | + | 0.930826i | \(0.619089\pi\) | |||||||
\(954\) | −16.9112 | −0.547520 | ||||||||
\(955\) | 18.7952 | 0.608199 | ||||||||
\(956\) | −31.0243 | −1.00340 | ||||||||
\(957\) | 1.38257 | 0.0446921 | ||||||||
\(958\) | 40.9108 | 1.32177 | ||||||||
\(959\) | 16.2517 | 0.524794 | ||||||||
\(960\) | −6.19356 | −0.199896 | ||||||||
\(961\) | −2.86343 | −0.0923687 | ||||||||
\(962\) | −28.8630 | −0.930581 | ||||||||
\(963\) | −15.8976 | −0.512294 | ||||||||
\(964\) | −29.3628 | −0.945711 | ||||||||
\(965\) | 50.1183 | 1.61336 | ||||||||
\(966\) | −10.6159 | −0.341561 | ||||||||
\(967\) | 25.3183 | 0.814182 | 0.407091 | − | 0.913388i | \(-0.366543\pi\) | ||||
0.407091 | + | 0.913388i | \(0.366543\pi\) | |||||||
\(968\) | −10.1494 | −0.326215 | ||||||||
\(969\) | −0.826112 | −0.0265385 | ||||||||
\(970\) | 41.6049 | 1.33585 | ||||||||
\(971\) | 32.5555 | 1.04475 | 0.522377 | − | 0.852715i | \(-0.325045\pi\) | ||||
0.522377 | + | 0.852715i | \(0.325045\pi\) | |||||||
\(972\) | −22.7207 | −0.728767 | ||||||||
\(973\) | 36.3527 | 1.16541 | ||||||||
\(974\) | 26.7504 | 0.857138 | ||||||||
\(975\) | 2.81102 | 0.0900247 | ||||||||
\(976\) | 26.9838 | 0.863731 | ||||||||
\(977\) | 30.4021 | 0.972649 | 0.486324 | − | 0.873778i | \(-0.338337\pi\) | ||||
0.486324 | + | 0.873778i | \(0.338337\pi\) | |||||||
\(978\) | 16.9608 | 0.542345 | ||||||||
\(979\) | 4.68717 | 0.149803 | ||||||||
\(980\) | 15.4203 | 0.492582 | ||||||||
\(981\) | 8.96309 | 0.286169 | ||||||||
\(982\) | −3.83198 | −0.122283 | ||||||||
\(983\) | −51.0478 | −1.62817 | −0.814086 | − | 0.580744i | \(-0.802762\pi\) | ||||
−0.814086 | + | 0.580744i | \(0.802762\pi\) | |||||||
\(984\) | −0.274944 | −0.00876490 | ||||||||
\(985\) | 14.2743 | 0.454816 | ||||||||
\(986\) | 10.6833 | 0.340225 | ||||||||
\(987\) | −4.23646 | −0.134848 | ||||||||
\(988\) | −0.864210 | −0.0274942 | ||||||||
\(989\) | −29.1474 | −0.926835 | ||||||||
\(990\) | −12.8305 | −0.407780 | ||||||||
\(991\) | −2.05724 | −0.0653503 | −0.0326752 | − | 0.999466i | \(-0.510403\pi\) | ||||
−0.0326752 | + | 0.999466i | \(0.510403\pi\) | |||||||
\(992\) | 36.1262 | 1.14701 | ||||||||
\(993\) | −25.4344 | −0.807136 | ||||||||
\(994\) | 17.2738 | 0.547893 | ||||||||
\(995\) | −50.7184 | −1.60788 | ||||||||
\(996\) | −5.07243 | −0.160726 | ||||||||
\(997\) | −38.5108 | −1.21965 | −0.609824 | − | 0.792537i | \(-0.708760\pi\) | ||||
−0.609824 | + | 0.792537i | \(0.708760\pi\) | |||||||
\(998\) | 11.6839 | 0.369846 | ||||||||
\(999\) | −28.6036 | −0.904978 |
(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 | 4001.2.a.a.1.29 | ✓ | 149 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.a.1.29 | ✓ | 149 | 1.1 | even | 1 | trivial |