Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, 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("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.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: | \(32.1078466528\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37064 | −1.67629 | −0.838147 | − | 0.545444i | \(-0.816361\pi\) | ||||
−0.838147 | + | 0.545444i | \(0.816361\pi\) | |||||||
\(3\) | −0.181119 | −0.104569 | −0.0522847 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522847 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(4\) | 3.61993 | 1.80996 | ||||||||
\(5\) | 1.77155 | 0.792262 | 0.396131 | − | 0.918194i | \(-0.370353\pi\) | ||||
0.396131 | + | 0.918194i | \(0.370353\pi\) | |||||||
\(6\) | 0.429369 | 0.175289 | ||||||||
\(7\) | −0.953276 | −0.360304 | −0.180152 | − | 0.983639i | \(-0.557659\pi\) | ||||
−0.180152 | + | 0.983639i | \(0.557659\pi\) | |||||||
\(8\) | −3.84026 | −1.35774 | ||||||||
\(9\) | −2.96720 | −0.989065 | ||||||||
\(10\) | −4.19971 | −1.32806 | ||||||||
\(11\) | 3.10092 | 0.934962 | 0.467481 | − | 0.884003i | \(-0.345162\pi\) | ||||
0.467481 | + | 0.884003i | \(0.345162\pi\) | |||||||
\(12\) | −0.655639 | −0.189267 | ||||||||
\(13\) | −2.76366 | −0.766502 | −0.383251 | − | 0.923644i | \(-0.625196\pi\) | ||||
−0.383251 | + | 0.923644i | \(0.625196\pi\) | |||||||
\(14\) | 2.25987 | 0.603976 | ||||||||
\(15\) | −0.320862 | −0.0828463 | ||||||||
\(16\) | 1.86402 | 0.466005 | ||||||||
\(17\) | −1.69260 | −0.410515 | −0.205258 | − | 0.978708i | \(-0.565803\pi\) | ||||
−0.205258 | + | 0.978708i | \(0.565803\pi\) | |||||||
\(18\) | 7.03415 | 1.65796 | ||||||||
\(19\) | −2.33313 | −0.535257 | −0.267628 | − | 0.963522i | \(-0.586240\pi\) | ||||
−0.267628 | + | 0.963522i | \(0.586240\pi\) | |||||||
\(20\) | 6.41289 | 1.43397 | ||||||||
\(21\) | 0.172657 | 0.0376768 | ||||||||
\(22\) | −7.35116 | −1.56727 | ||||||||
\(23\) | 2.41355 | 0.503260 | 0.251630 | − | 0.967824i | \(-0.419033\pi\) | ||||
0.251630 | + | 0.967824i | \(0.419033\pi\) | |||||||
\(24\) | 0.695546 | 0.141978 | ||||||||
\(25\) | −1.86161 | −0.372321 | ||||||||
\(26\) | 6.55164 | 1.28488 | ||||||||
\(27\) | 1.08078 | 0.207995 | ||||||||
\(28\) | −3.45079 | −0.652138 | ||||||||
\(29\) | 6.33499 | 1.17638 | 0.588189 | − | 0.808724i | \(-0.299841\pi\) | ||||
0.588189 | + | 0.808724i | \(0.299841\pi\) | |||||||
\(30\) | 0.760649 | 0.138875 | ||||||||
\(31\) | −2.67778 | −0.480944 | −0.240472 | − | 0.970656i | \(-0.577302\pi\) | ||||
−0.240472 | + | 0.970656i | \(0.577302\pi\) | |||||||
\(32\) | 3.26161 | 0.576576 | ||||||||
\(33\) | −0.561637 | −0.0977684 | ||||||||
\(34\) | 4.01254 | 0.688145 | ||||||||
\(35\) | −1.68878 | −0.285455 | ||||||||
\(36\) | −10.7410 | −1.79017 | ||||||||
\(37\) | 7.83933 | 1.28878 | 0.644389 | − | 0.764698i | \(-0.277112\pi\) | ||||
0.644389 | + | 0.764698i | \(0.277112\pi\) | |||||||
\(38\) | 5.53101 | 0.897248 | ||||||||
\(39\) | 0.500553 | 0.0801526 | ||||||||
\(40\) | −6.80322 | −1.07568 | ||||||||
\(41\) | −1.91690 | −0.299370 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(42\) | −0.409307 | −0.0631574 | ||||||||
\(43\) | 7.68521 | 1.17198 | 0.585992 | − | 0.810317i | \(-0.300705\pi\) | ||||
0.585992 | + | 0.810317i | \(0.300705\pi\) | |||||||
\(44\) | 11.2251 | 1.69225 | ||||||||
\(45\) | −5.25654 | −0.783599 | ||||||||
\(46\) | −5.72165 | −0.843612 | ||||||||
\(47\) | 3.92709 | 0.572825 | 0.286412 | − | 0.958106i | \(-0.407537\pi\) | ||||
0.286412 | + | 0.958106i | \(0.407537\pi\) | |||||||
\(48\) | −0.337610 | −0.0487298 | ||||||||
\(49\) | −6.09127 | −0.870181 | ||||||||
\(50\) | 4.41320 | 0.624120 | ||||||||
\(51\) | 0.306562 | 0.0429273 | ||||||||
\(52\) | −10.0043 | −1.38734 | ||||||||
\(53\) | −8.91148 | −1.22409 | −0.612043 | − | 0.790824i | \(-0.709652\pi\) | ||||
−0.612043 | + | 0.790824i | \(0.709652\pi\) | |||||||
\(54\) | −2.56213 | −0.348661 | ||||||||
\(55\) | 5.49344 | 0.740735 | ||||||||
\(56\) | 3.66083 | 0.489199 | ||||||||
\(57\) | 0.422575 | 0.0559714 | ||||||||
\(58\) | −15.0180 | −1.97196 | ||||||||
\(59\) | 8.29463 | 1.07987 | 0.539935 | − | 0.841707i | \(-0.318449\pi\) | ||||
0.539935 | + | 0.841707i | \(0.318449\pi\) | |||||||
\(60\) | −1.16150 | −0.149949 | ||||||||
\(61\) | −1.58369 | −0.202770 | −0.101385 | − | 0.994847i | \(-0.532327\pi\) | ||||
−0.101385 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(62\) | 6.34806 | 0.806204 | ||||||||
\(63\) | 2.82856 | 0.356365 | ||||||||
\(64\) | −11.4601 | −1.43252 | ||||||||
\(65\) | −4.89597 | −0.607270 | ||||||||
\(66\) | 1.33144 | 0.163889 | ||||||||
\(67\) | −11.6908 | −1.42826 | −0.714130 | − | 0.700013i | \(-0.753177\pi\) | ||||
−0.714130 | + | 0.700013i | \(0.753177\pi\) | |||||||
\(68\) | −6.12708 | −0.743018 | ||||||||
\(69\) | −0.437141 | −0.0526256 | ||||||||
\(70\) | 4.00348 | 0.478507 | ||||||||
\(71\) | 0.457924 | 0.0543456 | 0.0271728 | − | 0.999631i | \(-0.491350\pi\) | ||||
0.0271728 | + | 0.999631i | \(0.491350\pi\) | |||||||
\(72\) | 11.3948 | 1.34289 | ||||||||
\(73\) | 9.82549 | 1.14999 | 0.574994 | − | 0.818158i | \(-0.305005\pi\) | ||||
0.574994 | + | 0.818158i | \(0.305005\pi\) | |||||||
\(74\) | −18.5842 | −2.16037 | ||||||||
\(75\) | 0.337173 | 0.0389334 | ||||||||
\(76\) | −8.44576 | −0.968795 | ||||||||
\(77\) | −2.95603 | −0.336871 | ||||||||
\(78\) | −1.18663 | −0.134359 | ||||||||
\(79\) | 6.39444 | 0.719431 | 0.359715 | − | 0.933062i | \(-0.382874\pi\) | ||||
0.359715 | + | 0.933062i | \(0.382874\pi\) | |||||||
\(80\) | 3.30221 | 0.369198 | ||||||||
\(81\) | 8.70584 | 0.967315 | ||||||||
\(82\) | 4.54428 | 0.501832 | ||||||||
\(83\) | −4.34921 | −0.477388 | −0.238694 | − | 0.971095i | \(-0.576719\pi\) | ||||
−0.238694 | + | 0.971095i | \(0.576719\pi\) | |||||||
\(84\) | 0.625005 | 0.0681936 | ||||||||
\(85\) | −2.99852 | −0.325236 | ||||||||
\(86\) | −18.2189 | −1.96459 | ||||||||
\(87\) | −1.14739 | −0.123013 | ||||||||
\(88\) | −11.9083 | −1.26943 | ||||||||
\(89\) | −5.61886 | −0.595598 | −0.297799 | − | 0.954629i | \(-0.596253\pi\) | ||||
−0.297799 | + | 0.954629i | \(0.596253\pi\) | |||||||
\(90\) | 12.4614 | 1.31354 | ||||||||
\(91\) | 2.63453 | 0.276174 | ||||||||
\(92\) | 8.73687 | 0.910882 | ||||||||
\(93\) | 0.484999 | 0.0502920 | ||||||||
\(94\) | −9.30971 | −0.960223 | ||||||||
\(95\) | −4.13326 | −0.424063 | ||||||||
\(96\) | −0.590741 | −0.0602922 | ||||||||
\(97\) | −6.65009 | −0.675214 | −0.337607 | − | 0.941287i | \(-0.609618\pi\) | ||||
−0.337607 | + | 0.941287i | \(0.609618\pi\) | |||||||
\(98\) | 14.4402 | 1.45868 | ||||||||
\(99\) | −9.20103 | −0.924739 | ||||||||
\(100\) | −6.73888 | −0.673888 | ||||||||
\(101\) | −19.2858 | −1.91901 | −0.959505 | − | 0.281691i | \(-0.909105\pi\) | ||||
−0.959505 | + | 0.281691i | \(0.909105\pi\) | |||||||
\(102\) | −0.726749 | −0.0719588 | ||||||||
\(103\) | 12.2732 | 1.20931 | 0.604656 | − | 0.796487i | \(-0.293311\pi\) | ||||
0.604656 | + | 0.796487i | \(0.293311\pi\) | |||||||
\(104\) | 10.6132 | 1.04071 | ||||||||
\(105\) | 0.305870 | 0.0298499 | ||||||||
\(106\) | 21.1259 | 2.05193 | ||||||||
\(107\) | 0.337182 | 0.0325967 | 0.0162983 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162983 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(108\) | 3.91233 | 0.376464 | ||||||||
\(109\) | −13.7850 | −1.32036 | −0.660182 | − | 0.751106i | \(-0.729521\pi\) | ||||
−0.660182 | + | 0.751106i | \(0.729521\pi\) | |||||||
\(110\) | −13.0230 | −1.24169 | ||||||||
\(111\) | −1.41985 | −0.134767 | ||||||||
\(112\) | −1.77692 | −0.167904 | ||||||||
\(113\) | −4.75007 | −0.446849 | −0.223424 | − | 0.974721i | \(-0.571724\pi\) | ||||
−0.223424 | + | 0.974721i | \(0.571724\pi\) | |||||||
\(114\) | −1.00177 | −0.0938246 | ||||||||
\(115\) | 4.27573 | 0.398714 | ||||||||
\(116\) | 22.9322 | 2.12920 | ||||||||
\(117\) | 8.20032 | 0.758120 | ||||||||
\(118\) | −19.6636 | −1.81018 | ||||||||
\(119\) | 1.61351 | 0.147910 | ||||||||
\(120\) | 1.23220 | 0.112484 | ||||||||
\(121\) | −1.38430 | −0.125846 | ||||||||
\(122\) | 3.75435 | 0.339903 | ||||||||
\(123\) | 0.347188 | 0.0313049 | ||||||||
\(124\) | −9.69338 | −0.870492 | ||||||||
\(125\) | −12.1557 | −1.08724 | ||||||||
\(126\) | −6.70548 | −0.597372 | ||||||||
\(127\) | −12.8518 | −1.14041 | −0.570206 | − | 0.821502i | \(-0.693136\pi\) | ||||
−0.570206 | + | 0.821502i | \(0.693136\pi\) | |||||||
\(128\) | 20.6446 | 1.82474 | ||||||||
\(129\) | −1.39194 | −0.122554 | ||||||||
\(130\) | 11.6066 | 1.01796 | ||||||||
\(131\) | −19.5908 | −1.71165 | −0.855827 | − | 0.517262i | \(-0.826951\pi\) | ||||
−0.855827 | + | 0.517262i | \(0.826951\pi\) | |||||||
\(132\) | −2.03308 | −0.176957 | ||||||||
\(133\) | 2.22412 | 0.192855 | ||||||||
\(134\) | 27.7147 | 2.39418 | ||||||||
\(135\) | 1.91465 | 0.164787 | ||||||||
\(136\) | 6.50002 | 0.557372 | ||||||||
\(137\) | −8.10114 | −0.692127 | −0.346064 | − | 0.938211i | \(-0.612482\pi\) | ||||
−0.346064 | + | 0.938211i | \(0.612482\pi\) | |||||||
\(138\) | 1.03630 | 0.0882160 | ||||||||
\(139\) | 7.33058 | 0.621771 | 0.310886 | − | 0.950447i | \(-0.399374\pi\) | ||||
0.310886 | + | 0.950447i | \(0.399374\pi\) | |||||||
\(140\) | −6.11325 | −0.516664 | ||||||||
\(141\) | −0.711272 | −0.0598999 | ||||||||
\(142\) | −1.08557 | −0.0910993 | ||||||||
\(143\) | −8.56989 | −0.716650 | ||||||||
\(144\) | −5.53091 | −0.460909 | ||||||||
\(145\) | 11.2228 | 0.931999 | ||||||||
\(146\) | −23.2927 | −1.92772 | ||||||||
\(147\) | 1.10325 | 0.0909942 | ||||||||
\(148\) | 28.3778 | 2.33264 | ||||||||
\(149\) | −5.17227 | −0.423728 | −0.211864 | − | 0.977299i | \(-0.567953\pi\) | ||||
−0.211864 | + | 0.977299i | \(0.567953\pi\) | |||||||
\(150\) | −0.799316 | −0.0652639 | ||||||||
\(151\) | −9.32418 | −0.758791 | −0.379396 | − | 0.925235i | \(-0.623868\pi\) | ||||
−0.379396 | + | 0.925235i | \(0.623868\pi\) | |||||||
\(152\) | 8.95983 | 0.726738 | ||||||||
\(153\) | 5.02227 | 0.406026 | ||||||||
\(154\) | 7.00768 | 0.564695 | ||||||||
\(155\) | −4.74383 | −0.381034 | ||||||||
\(156\) | 1.81196 | 0.145073 | ||||||||
\(157\) | 22.9694 | 1.83316 | 0.916580 | − | 0.399851i | \(-0.130938\pi\) | ||||
0.916580 | + | 0.399851i | \(0.130938\pi\) | |||||||
\(158\) | −15.1589 | −1.20598 | ||||||||
\(159\) | 1.61404 | 0.128002 | ||||||||
\(160\) | 5.77811 | 0.456799 | ||||||||
\(161\) | −2.30078 | −0.181327 | ||||||||
\(162\) | −20.6384 | −1.62151 | ||||||||
\(163\) | 1.05812 | 0.0828786 | 0.0414393 | − | 0.999141i | \(-0.486806\pi\) | ||||
0.0414393 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(164\) | −6.93905 | −0.541849 | ||||||||
\(165\) | −0.994968 | −0.0774582 | ||||||||
\(166\) | 10.3104 | 0.800243 | ||||||||
\(167\) | −16.9648 | −1.31277 | −0.656387 | − | 0.754424i | \(-0.727916\pi\) | ||||
−0.656387 | + | 0.754424i | \(0.727916\pi\) | |||||||
\(168\) | −0.663047 | −0.0511552 | ||||||||
\(169\) | −5.36218 | −0.412475 | ||||||||
\(170\) | 7.10842 | 0.545191 | ||||||||
\(171\) | 6.92285 | 0.529404 | ||||||||
\(172\) | 27.8199 | 2.12125 | ||||||||
\(173\) | 3.64897 | 0.277426 | 0.138713 | − | 0.990333i | \(-0.455703\pi\) | ||||
0.138713 | + | 0.990333i | \(0.455703\pi\) | |||||||
\(174\) | 2.72005 | 0.206206 | ||||||||
\(175\) | 1.77462 | 0.134149 | ||||||||
\(176\) | 5.78017 | 0.435697 | ||||||||
\(177\) | −1.50232 | −0.112921 | ||||||||
\(178\) | 13.3203 | 0.998398 | ||||||||
\(179\) | −3.69440 | −0.276133 | −0.138066 | − | 0.990423i | \(-0.544089\pi\) | ||||
−0.138066 | + | 0.990423i | \(0.544089\pi\) | |||||||
\(180\) | −19.0283 | −1.41828 | ||||||||
\(181\) | −0.875066 | −0.0650431 | −0.0325216 | − | 0.999471i | \(-0.510354\pi\) | ||||
−0.0325216 | + | 0.999471i | \(0.510354\pi\) | |||||||
\(182\) | −6.24552 | −0.462949 | ||||||||
\(183\) | 0.286836 | 0.0212036 | ||||||||
\(184\) | −9.26866 | −0.683295 | ||||||||
\(185\) | 13.8878 | 1.02105 | ||||||||
\(186\) | −1.14976 | −0.0843043 | ||||||||
\(187\) | −5.24861 | −0.383816 | ||||||||
\(188\) | 14.2158 | 1.03679 | ||||||||
\(189\) | −1.03028 | −0.0749416 | ||||||||
\(190\) | 9.79846 | 0.710855 | ||||||||
\(191\) | −2.00117 | −0.144799 | −0.0723996 | − | 0.997376i | \(-0.523066\pi\) | ||||
−0.0723996 | + | 0.997376i | \(0.523066\pi\) | |||||||
\(192\) | 2.07565 | 0.149797 | ||||||||
\(193\) | 24.7896 | 1.78439 | 0.892197 | − | 0.451646i | \(-0.149163\pi\) | ||||
0.892197 | + | 0.451646i | \(0.149163\pi\) | |||||||
\(194\) | 15.7650 | 1.13186 | ||||||||
\(195\) | 0.886755 | 0.0635018 | ||||||||
\(196\) | −22.0499 | −1.57500 | ||||||||
\(197\) | 17.3859 | 1.23869 | 0.619346 | − | 0.785118i | \(-0.287398\pi\) | ||||
0.619346 | + | 0.785118i | \(0.287398\pi\) | |||||||
\(198\) | 21.8123 | 1.55013 | ||||||||
\(199\) | −12.9673 | −0.919227 | −0.459613 | − | 0.888119i | \(-0.652012\pi\) | ||||
−0.459613 | + | 0.888119i | \(0.652012\pi\) | |||||||
\(200\) | 7.14906 | 0.505515 | ||||||||
\(201\) | 2.11743 | 0.149352 | ||||||||
\(202\) | 45.7197 | 3.21683 | ||||||||
\(203\) | −6.03899 | −0.423854 | ||||||||
\(204\) | 1.10973 | 0.0776969 | ||||||||
\(205\) | −3.39589 | −0.237179 | ||||||||
\(206\) | −29.0952 | −2.02716 | ||||||||
\(207\) | −7.16147 | −0.497757 | ||||||||
\(208\) | −5.15152 | −0.357194 | ||||||||
\(209\) | −7.23485 | −0.500445 | ||||||||
\(210\) | −0.725108 | −0.0500372 | ||||||||
\(211\) | 19.4139 | 1.33651 | 0.668255 | − | 0.743933i | \(-0.267042\pi\) | ||||
0.668255 | + | 0.743933i | \(0.267042\pi\) | |||||||
\(212\) | −32.2589 | −2.21555 | ||||||||
\(213\) | −0.0829390 | −0.00568289 | ||||||||
\(214\) | −0.799338 | −0.0546416 | ||||||||
\(215\) | 13.6147 | 0.928518 | ||||||||
\(216\) | −4.15046 | −0.282403 | ||||||||
\(217\) | 2.55267 | 0.173286 | ||||||||
\(218\) | 32.6793 | 2.21332 | ||||||||
\(219\) | −1.77959 | −0.120253 | ||||||||
\(220\) | 19.8858 | 1.34070 | ||||||||
\(221\) | 4.67777 | 0.314661 | ||||||||
\(222\) | 3.36596 | 0.225909 | ||||||||
\(223\) | −20.2865 | −1.35849 | −0.679243 | − | 0.733913i | \(-0.737692\pi\) | ||||
−0.679243 | + | 0.733913i | \(0.737692\pi\) | |||||||
\(224\) | −3.10921 | −0.207743 | ||||||||
\(225\) | 5.52375 | 0.368250 | ||||||||
\(226\) | 11.2607 | 0.749050 | ||||||||
\(227\) | 2.27392 | 0.150926 | 0.0754628 | − | 0.997149i | \(-0.475957\pi\) | ||||
0.0754628 | + | 0.997149i | \(0.475957\pi\) | |||||||
\(228\) | 1.52969 | 0.101306 | ||||||||
\(229\) | 4.53366 | 0.299593 | 0.149796 | − | 0.988717i | \(-0.452138\pi\) | ||||
0.149796 | + | 0.988717i | \(0.452138\pi\) | |||||||
\(230\) | −10.1362 | −0.668361 | ||||||||
\(231\) | 0.535395 | 0.0352264 | ||||||||
\(232\) | −24.3280 | −1.59721 | ||||||||
\(233\) | 24.5448 | 1.60798 | 0.803992 | − | 0.594640i | \(-0.202705\pi\) | ||||
0.803992 | + | 0.594640i | \(0.202705\pi\) | |||||||
\(234\) | −19.4400 | −1.27083 | ||||||||
\(235\) | 6.95704 | 0.453827 | ||||||||
\(236\) | 30.0260 | 1.95452 | ||||||||
\(237\) | −1.15816 | −0.0752304 | ||||||||
\(238\) | −3.82506 | −0.247942 | ||||||||
\(239\) | 6.47840 | 0.419053 | 0.209526 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209526 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(240\) | −0.598094 | −0.0386068 | ||||||||
\(241\) | −7.62545 | −0.491198 | −0.245599 | − | 0.969371i | \(-0.578985\pi\) | ||||
−0.245599 | + | 0.969371i | \(0.578985\pi\) | |||||||
\(242\) | 3.28168 | 0.210955 | ||||||||
\(243\) | −4.81912 | −0.309147 | ||||||||
\(244\) | −5.73283 | −0.367007 | ||||||||
\(245\) | −10.7910 | −0.689411 | ||||||||
\(246\) | −0.823058 | −0.0524763 | ||||||||
\(247\) | 6.44798 | 0.410275 | ||||||||
\(248\) | 10.2834 | 0.652996 | ||||||||
\(249\) | 0.787727 | 0.0499202 | ||||||||
\(250\) | 28.8167 | 1.82253 | ||||||||
\(251\) | −1.23544 | −0.0779805 | −0.0389903 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389903 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(252\) | 10.2392 | 0.645007 | ||||||||
\(253\) | 7.48422 | 0.470529 | ||||||||
\(254\) | 30.4669 | 1.91167 | ||||||||
\(255\) | 0.543091 | 0.0340097 | ||||||||
\(256\) | −26.0207 | −1.62629 | ||||||||
\(257\) | −0.607426 | −0.0378902 | −0.0189451 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189451 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(258\) | 3.29979 | 0.205436 | ||||||||
\(259\) | −7.47304 | −0.464352 | ||||||||
\(260\) | −17.7230 | −1.09914 | ||||||||
\(261\) | −18.7971 | −1.16351 | ||||||||
\(262\) | 46.4426 | 2.86924 | ||||||||
\(263\) | −25.7861 | −1.59004 | −0.795019 | − | 0.606584i | \(-0.792539\pi\) | ||||
−0.795019 | + | 0.606584i | \(0.792539\pi\) | |||||||
\(264\) | 2.15683 | 0.132744 | ||||||||
\(265\) | −15.7871 | −0.969797 | ||||||||
\(266\) | −5.27258 | −0.323282 | ||||||||
\(267\) | 1.01769 | 0.0622813 | ||||||||
\(268\) | −42.3199 | −2.58510 | ||||||||
\(269\) | 22.8107 | 1.39080 | 0.695398 | − | 0.718625i | \(-0.255228\pi\) | ||||
0.695398 | + | 0.718625i | \(0.255228\pi\) | |||||||
\(270\) | −4.53894 | −0.276231 | ||||||||
\(271\) | 4.17703 | 0.253736 | 0.126868 | − | 0.991920i | \(-0.459507\pi\) | ||||
0.126868 | + | 0.991920i | \(0.459507\pi\) | |||||||
\(272\) | −3.15504 | −0.191302 | ||||||||
\(273\) | −0.477165 | −0.0288793 | ||||||||
\(274\) | 19.2049 | 1.16021 | ||||||||
\(275\) | −5.77269 | −0.348106 | ||||||||
\(276\) | −1.58242 | −0.0952504 | ||||||||
\(277\) | 9.06109 | 0.544428 | 0.272214 | − | 0.962237i | \(-0.412244\pi\) | ||||
0.272214 | + | 0.962237i | \(0.412244\pi\) | |||||||
\(278\) | −17.3781 | −1.04227 | ||||||||
\(279\) | 7.94551 | 0.475685 | ||||||||
\(280\) | 6.48535 | 0.387574 | ||||||||
\(281\) | −30.0583 | −1.79313 | −0.896565 | − | 0.442912i | \(-0.853945\pi\) | ||||
−0.896565 | + | 0.442912i | \(0.853945\pi\) | |||||||
\(282\) | 1.68617 | 0.100410 | ||||||||
\(283\) | −0.613366 | −0.0364608 | −0.0182304 | − | 0.999834i | \(-0.505803\pi\) | ||||
−0.0182304 | + | 0.999834i | \(0.505803\pi\) | |||||||
\(284\) | 1.65765 | 0.0983636 | ||||||||
\(285\) | 0.748614 | 0.0443440 | ||||||||
\(286\) | 20.3161 | 1.20132 | ||||||||
\(287\) | 1.82734 | 0.107864 | ||||||||
\(288\) | −9.67783 | −0.570272 | ||||||||
\(289\) | −14.1351 | −0.831477 | ||||||||
\(290\) | −26.6051 | −1.56230 | ||||||||
\(291\) | 1.20446 | 0.0706067 | ||||||||
\(292\) | 35.5676 | 2.08143 | ||||||||
\(293\) | −10.8221 | −0.632236 | −0.316118 | − | 0.948720i | \(-0.602379\pi\) | ||||
−0.316118 | + | 0.948720i | \(0.602379\pi\) | |||||||
\(294\) | −2.61540 | −0.152533 | ||||||||
\(295\) | 14.6944 | 0.855539 | ||||||||
\(296\) | −30.1051 | −1.74982 | ||||||||
\(297\) | 3.35140 | 0.194468 | ||||||||
\(298\) | 12.2616 | 0.710294 | ||||||||
\(299\) | −6.67023 | −0.385750 | ||||||||
\(300\) | 1.22054 | 0.0704680 | ||||||||
\(301\) | −7.32613 | −0.422271 | ||||||||
\(302\) | 22.1043 | 1.27196 | ||||||||
\(303\) | 3.49304 | 0.200670 | ||||||||
\(304\) | −4.34900 | −0.249432 | ||||||||
\(305\) | −2.80558 | −0.160647 | ||||||||
\(306\) | −11.9060 | −0.680620 | ||||||||
\(307\) | −12.8336 | −0.732455 | −0.366227 | − | 0.930525i | \(-0.619351\pi\) | ||||
−0.366227 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(308\) | −10.7006 | −0.609724 | ||||||||
\(309\) | −2.22291 | −0.126457 | ||||||||
\(310\) | 11.2459 | 0.638725 | ||||||||
\(311\) | −4.87295 | −0.276320 | −0.138160 | − | 0.990410i | \(-0.544119\pi\) | ||||
−0.138160 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(312\) | −1.92225 | −0.108826 | ||||||||
\(313\) | −27.4070 | −1.54914 | −0.774569 | − | 0.632489i | \(-0.782033\pi\) | ||||
−0.774569 | + | 0.632489i | \(0.782033\pi\) | |||||||
\(314\) | −54.4522 | −3.07292 | ||||||||
\(315\) | 5.01093 | 0.282334 | ||||||||
\(316\) | 23.1474 | 1.30214 | ||||||||
\(317\) | −5.47432 | −0.307469 | −0.153734 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153734 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(318\) | −3.82631 | −0.214569 | ||||||||
\(319\) | 19.6443 | 1.09987 | ||||||||
\(320\) | −20.3022 | −1.13493 | ||||||||
\(321\) | −0.0610703 | −0.00340861 | ||||||||
\(322\) | 5.45431 | 0.303957 | ||||||||
\(323\) | 3.94905 | 0.219731 | ||||||||
\(324\) | 31.5145 | 1.75081 | ||||||||
\(325\) | 5.14485 | 0.285385 | ||||||||
\(326\) | −2.50843 | −0.138929 | ||||||||
\(327\) | 2.49673 | 0.138070 | ||||||||
\(328\) | 7.36141 | 0.406466 | ||||||||
\(329\) | −3.74360 | −0.206391 | ||||||||
\(330\) | 2.35871 | 0.129843 | ||||||||
\(331\) | 19.9632 | 1.09728 | 0.548638 | − | 0.836060i | \(-0.315146\pi\) | ||||
0.548638 | + | 0.836060i | \(0.315146\pi\) | |||||||
\(332\) | −15.7438 | −0.864055 | ||||||||
\(333\) | −23.2608 | −1.27469 | ||||||||
\(334\) | 40.2174 | 2.20060 | ||||||||
\(335\) | −20.7109 | −1.13156 | ||||||||
\(336\) | 0.321836 | 0.0175576 | ||||||||
\(337\) | −0.257107 | −0.0140055 | −0.00700276 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700276 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(338\) | 12.7118 | 0.691430 | ||||||||
\(339\) | 0.860330 | 0.0467267 | ||||||||
\(340\) | −10.8544 | −0.588665 | ||||||||
\(341\) | −8.30359 | −0.449665 | ||||||||
\(342\) | −16.4116 | −0.887437 | ||||||||
\(343\) | 12.4796 | 0.673834 | ||||||||
\(344\) | −29.5132 | −1.59125 | ||||||||
\(345\) | −0.774417 | −0.0416932 | ||||||||
\(346\) | −8.65039 | −0.465048 | ||||||||
\(347\) | −9.47879 | −0.508848 | −0.254424 | − | 0.967093i | \(-0.581886\pi\) | ||||
−0.254424 | + | 0.967093i | \(0.581886\pi\) | |||||||
\(348\) | −4.15347 | −0.222649 | ||||||||
\(349\) | −31.9053 | −1.70785 | −0.853927 | − | 0.520394i | \(-0.825785\pi\) | ||||
−0.853927 | + | 0.520394i | \(0.825785\pi\) | |||||||
\(350\) | −4.20699 | −0.224873 | ||||||||
\(351\) | −2.98690 | −0.159429 | ||||||||
\(352\) | 10.1140 | 0.539077 | ||||||||
\(353\) | 24.9653 | 1.32877 | 0.664384 | − | 0.747391i | \(-0.268694\pi\) | ||||
0.664384 | + | 0.747391i | \(0.268694\pi\) | |||||||
\(354\) | 3.56146 | 0.189289 | ||||||||
\(355\) | 0.811236 | 0.0430560 | ||||||||
\(356\) | −20.3399 | −1.07801 | ||||||||
\(357\) | −0.292239 | −0.0154669 | ||||||||
\(358\) | 8.75809 | 0.462880 | ||||||||
\(359\) | −30.5887 | −1.61441 | −0.807204 | − | 0.590273i | \(-0.799020\pi\) | ||||
−0.807204 | + | 0.590273i | \(0.799020\pi\) | |||||||
\(360\) | 20.1865 | 1.06392 | ||||||||
\(361\) | −13.5565 | −0.713500 | ||||||||
\(362\) | 2.07447 | 0.109031 | ||||||||
\(363\) | 0.250724 | 0.0131596 | ||||||||
\(364\) | 9.53681 | 0.499865 | ||||||||
\(365\) | 17.4064 | 0.911091 | ||||||||
\(366\) | −0.679986 | −0.0355434 | ||||||||
\(367\) | −19.9193 | −1.03978 | −0.519890 | − | 0.854233i | \(-0.674027\pi\) | ||||
−0.519890 | + | 0.854233i | \(0.674027\pi\) | |||||||
\(368\) | 4.49890 | 0.234522 | ||||||||
\(369\) | 5.68782 | 0.296096 | ||||||||
\(370\) | −32.9229 | −1.71158 | ||||||||
\(371\) | 8.49510 | 0.441044 | ||||||||
\(372\) | 1.75566 | 0.0910267 | ||||||||
\(373\) | −34.7446 | −1.79901 | −0.899503 | − | 0.436914i | \(-0.856072\pi\) | ||||
−0.899503 | + | 0.436914i | \(0.856072\pi\) | |||||||
\(374\) | 12.4426 | 0.643389 | ||||||||
\(375\) | 2.20163 | 0.113692 | ||||||||
\(376\) | −15.0811 | −0.777746 | ||||||||
\(377\) | −17.5078 | −0.901695 | ||||||||
\(378\) | 2.44241 | 0.125624 | ||||||||
\(379\) | 16.6281 | 0.854128 | 0.427064 | − | 0.904222i | \(-0.359548\pi\) | ||||
0.427064 | + | 0.904222i | \(0.359548\pi\) | |||||||
\(380\) | −14.9621 | −0.767539 | ||||||||
\(381\) | 2.32771 | 0.119252 | ||||||||
\(382\) | 4.74404 | 0.242726 | ||||||||
\(383\) | −34.9864 | −1.78772 | −0.893860 | − | 0.448345i | \(-0.852014\pi\) | ||||
−0.893860 | + | 0.448345i | \(0.852014\pi\) | |||||||
\(384\) | −3.73914 | −0.190812 | ||||||||
\(385\) | −5.23676 | −0.266890 | ||||||||
\(386\) | −58.7672 | −2.99117 | ||||||||
\(387\) | −22.8035 | −1.15917 | ||||||||
\(388\) | −24.0728 | −1.22211 | ||||||||
\(389\) | 15.8376 | 0.803000 | 0.401500 | − | 0.915859i | \(-0.368489\pi\) | ||||
0.401500 | + | 0.915859i | \(0.368489\pi\) | |||||||
\(390\) | −2.10218 | −0.106448 | ||||||||
\(391\) | −4.08517 | −0.206596 | ||||||||
\(392\) | 23.3921 | 1.18148 | ||||||||
\(393\) | 3.54827 | 0.178987 | ||||||||
\(394\) | −41.2156 | −2.07641 | ||||||||
\(395\) | 11.3281 | 0.569977 | ||||||||
\(396\) | −33.3071 | −1.67374 | ||||||||
\(397\) | −2.34761 | −0.117823 | −0.0589116 | − | 0.998263i | \(-0.518763\pi\) | ||||
−0.0589116 | + | 0.998263i | \(0.518763\pi\) | |||||||
\(398\) | 30.7408 | 1.54090 | ||||||||
\(399\) | −0.402831 | −0.0201668 | ||||||||
\(400\) | −3.47007 | −0.173504 | ||||||||
\(401\) | −25.4144 | −1.26913 | −0.634566 | − | 0.772868i | \(-0.718821\pi\) | ||||
−0.634566 | + | 0.772868i | \(0.718821\pi\) | |||||||
\(402\) | −5.01967 | −0.250358 | ||||||||
\(403\) | 7.40049 | 0.368645 | ||||||||
\(404\) | −69.8133 | −3.47334 | ||||||||
\(405\) | 15.4228 | 0.766367 | ||||||||
\(406\) | 14.3163 | 0.710504 | ||||||||
\(407\) | 24.3091 | 1.20496 | ||||||||
\(408\) | −1.17728 | −0.0582841 | ||||||||
\(409\) | 13.4957 | 0.667319 | 0.333659 | − | 0.942694i | \(-0.391717\pi\) | ||||
0.333659 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(410\) | 8.05043 | 0.397582 | ||||||||
\(411\) | 1.46727 | 0.0723753 | ||||||||
\(412\) | 44.4280 | 2.18881 | ||||||||
\(413\) | −7.90707 | −0.389082 | ||||||||
\(414\) | 16.9773 | 0.834387 | ||||||||
\(415\) | −7.70485 | −0.378216 | ||||||||
\(416\) | −9.01398 | −0.441947 | ||||||||
\(417\) | −1.32771 | −0.0650182 | ||||||||
\(418\) | 17.1512 | 0.838893 | ||||||||
\(419\) | −5.67009 | −0.277002 | −0.138501 | − | 0.990362i | \(-0.544228\pi\) | ||||
−0.138501 | + | 0.990362i | \(0.544228\pi\) | |||||||
\(420\) | 1.10723 | 0.0540272 | ||||||||
\(421\) | −33.8168 | −1.64813 | −0.824064 | − | 0.566496i | \(-0.808299\pi\) | ||||
−0.824064 | + | 0.566496i | \(0.808299\pi\) | |||||||
\(422\) | −46.0234 | −2.24038 | ||||||||
\(423\) | −11.6524 | −0.566561 | ||||||||
\(424\) | 34.2224 | 1.66199 | ||||||||
\(425\) | 3.15095 | 0.152844 | ||||||||
\(426\) | 0.196618 | 0.00952619 | ||||||||
\(427\) | 1.50969 | 0.0730590 | ||||||||
\(428\) | 1.22058 | 0.0589988 | ||||||||
\(429\) | 1.55217 | 0.0749396 | ||||||||
\(430\) | −32.2756 | −1.55647 | ||||||||
\(431\) | −20.9507 | −1.00916 | −0.504581 | − | 0.863364i | \(-0.668353\pi\) | ||||
−0.504581 | + | 0.863364i | \(0.668353\pi\) | |||||||
\(432\) | 2.01459 | 0.0969268 | ||||||||
\(433\) | 27.2153 | 1.30789 | 0.653943 | − | 0.756544i | \(-0.273114\pi\) | ||||
0.653943 | + | 0.756544i | \(0.273114\pi\) | |||||||
\(434\) | −6.05145 | −0.290479 | ||||||||
\(435\) | −2.03266 | −0.0974585 | ||||||||
\(436\) | −49.9007 | −2.38981 | ||||||||
\(437\) | −5.63112 | −0.269373 | ||||||||
\(438\) | 4.21876 | 0.201580 | ||||||||
\(439\) | −10.3784 | −0.495333 | −0.247667 | − | 0.968845i | \(-0.579664\pi\) | ||||
−0.247667 | + | 0.968845i | \(0.579664\pi\) | |||||||
\(440\) | −21.0962 | −1.00572 | ||||||||
\(441\) | 18.0740 | 0.860666 | ||||||||
\(442\) | −11.0893 | −0.527464 | ||||||||
\(443\) | −31.8810 | −1.51471 | −0.757356 | − | 0.653002i | \(-0.773509\pi\) | ||||
−0.757356 | + | 0.653002i | \(0.773509\pi\) | |||||||
\(444\) | −5.13977 | −0.243923 | ||||||||
\(445\) | −9.95410 | −0.471870 | ||||||||
\(446\) | 48.0920 | 2.27722 | ||||||||
\(447\) | 0.936798 | 0.0443090 | ||||||||
\(448\) | 10.9247 | 0.516142 | ||||||||
\(449\) | −26.7452 | −1.26218 | −0.631092 | − | 0.775708i | \(-0.717393\pi\) | ||||
−0.631092 | + | 0.775708i | \(0.717393\pi\) | |||||||
\(450\) | −13.0948 | −0.617296 | ||||||||
\(451\) | −5.94416 | −0.279899 | ||||||||
\(452\) | −17.1949 | −0.808780 | ||||||||
\(453\) | 1.68879 | 0.0793463 | ||||||||
\(454\) | −5.39065 | −0.252996 | ||||||||
\(455\) | 4.66721 | 0.218802 | ||||||||
\(456\) | −1.62280 | −0.0759945 | ||||||||
\(457\) | 21.0590 | 0.985101 | 0.492550 | − | 0.870284i | \(-0.336065\pi\) | ||||
0.492550 | + | 0.870284i | \(0.336065\pi\) | |||||||
\(458\) | −10.7477 | −0.502206 | ||||||||
\(459\) | −1.82932 | −0.0853852 | ||||||||
\(460\) | 15.4778 | 0.721657 | ||||||||
\(461\) | 16.3333 | 0.760719 | 0.380359 | − | 0.924839i | \(-0.375800\pi\) | ||||
0.380359 | + | 0.924839i | \(0.375800\pi\) | |||||||
\(462\) | −1.26923 | −0.0590498 | ||||||||
\(463\) | −23.1742 | −1.07700 | −0.538498 | − | 0.842627i | \(-0.681008\pi\) | ||||
−0.538498 | + | 0.842627i | \(0.681008\pi\) | |||||||
\(464\) | 11.8085 | 0.548198 | ||||||||
\(465\) | 0.859200 | 0.0398445 | ||||||||
\(466\) | −58.1869 | −2.69546 | ||||||||
\(467\) | −22.9556 | −1.06226 | −0.531130 | − | 0.847290i | \(-0.678233\pi\) | ||||
−0.531130 | + | 0.847290i | \(0.678233\pi\) | |||||||
\(468\) | 29.6846 | 1.37217 | ||||||||
\(469\) | 11.1446 | 0.514608 | ||||||||
\(470\) | −16.4926 | −0.760748 | ||||||||
\(471\) | −4.16021 | −0.191692 | ||||||||
\(472\) | −31.8536 | −1.46618 | ||||||||
\(473\) | 23.8312 | 1.09576 | ||||||||
\(474\) | 2.74557 | 0.126108 | ||||||||
\(475\) | 4.34337 | 0.199287 | ||||||||
\(476\) | 5.84080 | 0.267713 | ||||||||
\(477\) | 26.4421 | 1.21070 | ||||||||
\(478\) | −15.3579 | −0.702456 | ||||||||
\(479\) | −0.0771714 | −0.00352605 | −0.00176303 | − | 0.999998i | \(-0.500561\pi\) | ||||
−0.00176303 | + | 0.999998i | \(0.500561\pi\) | |||||||
\(480\) | −1.04653 | −0.0477672 | ||||||||
\(481\) | −21.6652 | −0.987850 | ||||||||
\(482\) | 18.0772 | 0.823393 | ||||||||
\(483\) | 0.416716 | 0.0189612 | ||||||||
\(484\) | −5.01108 | −0.227776 | ||||||||
\(485\) | −11.7810 | −0.534947 | ||||||||
\(486\) | 11.4244 | 0.518221 | ||||||||
\(487\) | 30.5714 | 1.38532 | 0.692661 | − | 0.721263i | \(-0.256438\pi\) | ||||
0.692661 | + | 0.721263i | \(0.256438\pi\) | |||||||
\(488\) | 6.08177 | 0.275309 | ||||||||
\(489\) | −0.191647 | −0.00866656 | ||||||||
\(490\) | 25.5815 | 1.15566 | ||||||||
\(491\) | 23.3870 | 1.05544 | 0.527719 | − | 0.849419i | \(-0.323047\pi\) | ||||
0.527719 | + | 0.849419i | \(0.323047\pi\) | |||||||
\(492\) | 1.25680 | 0.0566608 | ||||||||
\(493\) | −10.7226 | −0.482921 | ||||||||
\(494\) | −15.2858 | −0.687742 | ||||||||
\(495\) | −16.3001 | −0.732635 | ||||||||
\(496\) | −4.99144 | −0.224122 | ||||||||
\(497\) | −0.436528 | −0.0195810 | ||||||||
\(498\) | −1.86742 | −0.0836809 | ||||||||
\(499\) | −35.8812 | −1.60626 | −0.803132 | − | 0.595802i | \(-0.796834\pi\) | ||||
−0.803132 | + | 0.595802i | \(0.796834\pi\) | |||||||
\(500\) | −44.0027 | −1.96786 | ||||||||
\(501\) | 3.07265 | 0.137276 | ||||||||
\(502\) | 2.92879 | 0.130718 | ||||||||
\(503\) | −9.34711 | −0.416767 | −0.208384 | − | 0.978047i | \(-0.566820\pi\) | ||||
−0.208384 | + | 0.978047i | \(0.566820\pi\) | |||||||
\(504\) | −10.8624 | −0.483850 | ||||||||
\(505\) | −34.1658 | −1.52036 | ||||||||
\(506\) | −17.7424 | −0.788745 | ||||||||
\(507\) | 0.971194 | 0.0431323 | ||||||||
\(508\) | −46.5225 | −2.06410 | ||||||||
\(509\) | 1.20262 | 0.0533052 | 0.0266526 | − | 0.999645i | \(-0.491515\pi\) | ||||
0.0266526 | + | 0.999645i | \(0.491515\pi\) | |||||||
\(510\) | −1.28747 | −0.0570102 | ||||||||
\(511\) | −9.36641 | −0.414345 | ||||||||
\(512\) | 20.3963 | 0.901400 | ||||||||
\(513\) | −2.52159 | −0.111331 | ||||||||
\(514\) | 1.43999 | 0.0635152 | ||||||||
\(515\) | 21.7425 | 0.958091 | ||||||||
\(516\) | −5.03873 | −0.221818 | ||||||||
\(517\) | 12.1776 | 0.535570 | ||||||||
\(518\) | 17.7159 | 0.778391 | ||||||||
\(519\) | −0.660899 | −0.0290103 | ||||||||
\(520\) | 18.8018 | 0.824513 | ||||||||
\(521\) | −0.253487 | −0.0111055 | −0.00555273 | − | 0.999985i | \(-0.501767\pi\) | ||||
−0.00555273 | + | 0.999985i | \(0.501767\pi\) | |||||||
\(522\) | 44.5612 | 1.95039 | ||||||||
\(523\) | 22.7182 | 0.993399 | 0.496700 | − | 0.867923i | \(-0.334545\pi\) | ||||
0.496700 | + | 0.867923i | \(0.334545\pi\) | |||||||
\(524\) | −70.9172 | −3.09803 | ||||||||
\(525\) | −0.321419 | −0.0140279 | ||||||||
\(526\) | 61.1295 | 2.66537 | ||||||||
\(527\) | 4.53241 | 0.197435 | ||||||||
\(528\) | −1.04690 | −0.0455605 | ||||||||
\(529\) | −17.1748 | −0.746729 | ||||||||
\(530\) | 37.4256 | 1.62567 | ||||||||
\(531\) | −24.6118 | −1.06806 | ||||||||
\(532\) | 8.05114 | 0.349061 | ||||||||
\(533\) | 5.29767 | 0.229468 | ||||||||
\(534\) | −2.41256 | −0.104402 | ||||||||
\(535\) | 0.597336 | 0.0258251 | ||||||||
\(536\) | 44.8958 | 1.93920 | ||||||||
\(537\) | 0.669128 | 0.0288750 | ||||||||
\(538\) | −54.0760 | −2.33138 | ||||||||
\(539\) | −18.8885 | −0.813586 | ||||||||
\(540\) | 6.93089 | 0.298258 | ||||||||
\(541\) | −16.7625 | −0.720677 | −0.360339 | − | 0.932822i | \(-0.617339\pi\) | ||||
−0.360339 | + | 0.932822i | \(0.617339\pi\) | |||||||
\(542\) | −9.90222 | −0.425337 | ||||||||
\(543\) | 0.158491 | 0.00680152 | ||||||||
\(544\) | −5.52059 | −0.236693 | ||||||||
\(545\) | −24.4208 | −1.04607 | ||||||||
\(546\) | 1.13119 | 0.0484103 | ||||||||
\(547\) | 13.2498 | 0.566522 | 0.283261 | − | 0.959043i | \(-0.408584\pi\) | ||||
0.283261 | + | 0.959043i | \(0.408584\pi\) | |||||||
\(548\) | −29.3255 | −1.25273 | ||||||||
\(549\) | 4.69911 | 0.200553 | ||||||||
\(550\) | 13.6850 | 0.583529 | ||||||||
\(551\) | −14.7803 | −0.629664 | ||||||||
\(552\) | 1.67874 | 0.0714517 | ||||||||
\(553\) | −6.09566 | −0.259214 | ||||||||
\(554\) | −21.4806 | −0.912622 | ||||||||
\(555\) | −2.51535 | −0.106770 | ||||||||
\(556\) | 26.5362 | 1.12538 | ||||||||
\(557\) | 1.88308 | 0.0797888 | 0.0398944 | − | 0.999204i | \(-0.487298\pi\) | ||||
0.0398944 | + | 0.999204i | \(0.487298\pi\) | |||||||
\(558\) | −18.8359 | −0.797389 | ||||||||
\(559\) | −21.2393 | −0.898328 | ||||||||
\(560\) | −3.14791 | −0.133024 | ||||||||
\(561\) | 0.950625 | 0.0401354 | ||||||||
\(562\) | 71.2574 | 3.00581 | ||||||||
\(563\) | 37.2453 | 1.56970 | 0.784851 | − | 0.619684i | \(-0.212739\pi\) | ||||
0.784851 | + | 0.619684i | \(0.212739\pi\) | |||||||
\(564\) | −2.57475 | −0.108417 | ||||||||
\(565\) | −8.41499 | −0.354021 | ||||||||
\(566\) | 1.45407 | 0.0611190 | ||||||||
\(567\) | −8.29907 | −0.348528 | ||||||||
\(568\) | −1.75855 | −0.0737871 | ||||||||
\(569\) | −17.6538 | −0.740085 | −0.370043 | − | 0.929015i | \(-0.620657\pi\) | ||||
−0.370043 | + | 0.929015i | \(0.620657\pi\) | |||||||
\(570\) | −1.77469 | −0.0743337 | ||||||||
\(571\) | 40.7896 | 1.70699 | 0.853495 | − | 0.521101i | \(-0.174479\pi\) | ||||
0.853495 | + | 0.521101i | \(0.174479\pi\) | |||||||
\(572\) | −31.0224 | −1.29711 | ||||||||
\(573\) | 0.362450 | 0.0151416 | ||||||||
\(574\) | −4.33196 | −0.180812 | ||||||||
\(575\) | −4.49308 | −0.187374 | ||||||||
\(576\) | 34.0045 | 1.41685 | ||||||||
\(577\) | 28.5791 | 1.18976 | 0.594881 | − | 0.803814i | \(-0.297199\pi\) | ||||
0.594881 | + | 0.803814i | \(0.297199\pi\) | |||||||
\(578\) | 33.5092 | 1.39380 | ||||||||
\(579\) | −4.48988 | −0.186593 | ||||||||
\(580\) | 40.6255 | 1.68688 | ||||||||
\(581\) | 4.14600 | 0.172005 | ||||||||
\(582\) | −2.85534 | −0.118358 | ||||||||
\(583\) | −27.6338 | −1.14447 | ||||||||
\(584\) | −37.7325 | −1.56138 | ||||||||
\(585\) | 14.5273 | 0.600630 | ||||||||
\(586\) | 25.6554 | 1.05981 | ||||||||
\(587\) | −28.6256 | −1.18151 | −0.590753 | − | 0.806852i | \(-0.701169\pi\) | ||||
−0.590753 | + | 0.806852i | \(0.701169\pi\) | |||||||
\(588\) | 3.99367 | 0.164696 | ||||||||
\(589\) | 6.24762 | 0.257429 | ||||||||
\(590\) | −34.8350 | −1.43414 | ||||||||
\(591\) | −3.14892 | −0.129529 | ||||||||
\(592\) | 14.6127 | 0.600577 | ||||||||
\(593\) | 11.3825 | 0.467423 | 0.233712 | − | 0.972306i | \(-0.424913\pi\) | ||||
0.233712 | + | 0.972306i | \(0.424913\pi\) | |||||||
\(594\) | −7.94495 | −0.325985 | ||||||||
\(595\) | 2.85842 | 0.117184 | ||||||||
\(596\) | −18.7232 | −0.766933 | ||||||||
\(597\) | 2.34863 | 0.0961230 | ||||||||
\(598\) | 15.8127 | 0.646630 | ||||||||
\(599\) | −25.6843 | −1.04943 | −0.524717 | − | 0.851277i | \(-0.675829\pi\) | ||||
−0.524717 | + | 0.851277i | \(0.675829\pi\) | |||||||
\(600\) | −1.29483 | −0.0528613 | ||||||||
\(601\) | −4.70524 | −0.191931 | −0.0959654 | − | 0.995385i | \(-0.530594\pi\) | ||||
−0.0959654 | + | 0.995385i | \(0.530594\pi\) | |||||||
\(602\) | 17.3676 | 0.707851 | ||||||||
\(603\) | 34.6889 | 1.41264 | ||||||||
\(604\) | −33.7529 | −1.37338 | ||||||||
\(605\) | −2.45237 | −0.0997028 | ||||||||
\(606\) | −8.28073 | −0.336382 | ||||||||
\(607\) | 17.6769 | 0.717481 | 0.358741 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358741 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(608\) | −7.60975 | −0.308616 | ||||||||
\(609\) | 1.09378 | 0.0443221 | ||||||||
\(610\) | 6.65102 | 0.269292 | ||||||||
\(611\) | −10.8531 | −0.439071 | ||||||||
\(612\) | 18.1803 | 0.734893 | ||||||||
\(613\) | 45.3400 | 1.83127 | 0.915633 | − | 0.402015i | \(-0.131690\pi\) | ||||
0.915633 | + | 0.402015i | \(0.131690\pi\) | |||||||
\(614\) | 30.4239 | 1.22781 | ||||||||
\(615\) | 0.615062 | 0.0248017 | ||||||||
\(616\) | 11.3519 | 0.457382 | ||||||||
\(617\) | −29.9150 | −1.20433 | −0.602166 | − | 0.798371i | \(-0.705696\pi\) | ||||
−0.602166 | + | 0.798371i | \(0.705696\pi\) | |||||||
\(618\) | 5.26971 | 0.211979 | ||||||||
\(619\) | 44.0915 | 1.77219 | 0.886093 | − | 0.463508i | \(-0.153410\pi\) | ||||
0.886093 | + | 0.463508i | \(0.153410\pi\) | |||||||
\(620\) | −17.1723 | −0.689657 | ||||||||
\(621\) | 2.60850 | 0.104676 | ||||||||
\(622\) | 11.5520 | 0.463193 | ||||||||
\(623\) | 5.35633 | 0.214597 | ||||||||
\(624\) | 0.933040 | 0.0373515 | ||||||||
\(625\) | −12.2264 | −0.489056 | ||||||||
\(626\) | 64.9722 | 2.59681 | ||||||||
\(627\) | 1.31037 | 0.0523312 | ||||||||
\(628\) | 83.1477 | 3.31795 | ||||||||
\(629\) | −13.2688 | −0.529063 | ||||||||
\(630\) | −11.8791 | −0.473275 | ||||||||
\(631\) | −26.5892 | −1.05850 | −0.529249 | − | 0.848466i | \(-0.677526\pi\) | ||||
−0.529249 | + | 0.848466i | \(0.677526\pi\) | |||||||
\(632\) | −24.5563 | −0.976798 | ||||||||
\(633\) | −3.51624 | −0.139758 | ||||||||
\(634\) | 12.9776 | 0.515408 | ||||||||
\(635\) | −22.7676 | −0.903504 | ||||||||
\(636\) | 5.84272 | 0.231679 | ||||||||
\(637\) | 16.8342 | 0.666995 | ||||||||
\(638\) | −46.5695 | −1.84370 | ||||||||
\(639\) | −1.35875 | −0.0537514 | ||||||||
\(640\) | 36.5730 | 1.44567 | ||||||||
\(641\) | −9.93314 | −0.392336 | −0.196168 | − | 0.980570i | \(-0.562850\pi\) | ||||
−0.196168 | + | 0.980570i | \(0.562850\pi\) | |||||||
\(642\) | 0.144776 | 0.00571384 | ||||||||
\(643\) | −0.926771 | −0.0365483 | −0.0182741 | − | 0.999833i | \(-0.505817\pi\) | ||||
−0.0182741 | + | 0.999833i | \(0.505817\pi\) | |||||||
\(644\) | −8.32865 | −0.328195 | ||||||||
\(645\) | −2.46590 | −0.0970945 | ||||||||
\(646\) | −9.36177 | −0.368334 | ||||||||
\(647\) | −2.57708 | −0.101315 | −0.0506577 | − | 0.998716i | \(-0.516132\pi\) | ||||
−0.0506577 | + | 0.998716i | \(0.516132\pi\) | |||||||
\(648\) | −33.4327 | −1.31336 | ||||||||
\(649\) | 25.7210 | 1.00964 | ||||||||
\(650\) | −12.1966 | −0.478389 | ||||||||
\(651\) | −0.462338 | −0.0181204 | ||||||||
\(652\) | 3.83033 | 0.150007 | ||||||||
\(653\) | −30.4848 | −1.19296 | −0.596482 | − | 0.802626i | \(-0.703435\pi\) | ||||
−0.596482 | + | 0.802626i | \(0.703435\pi\) | |||||||
\(654\) | −5.91885 | −0.231445 | ||||||||
\(655\) | −34.7061 | −1.35608 | ||||||||
\(656\) | −3.57314 | −0.139508 | ||||||||
\(657\) | −29.1542 | −1.13741 | ||||||||
\(658\) | 8.87472 | 0.345973 | ||||||||
\(659\) | 37.1021 | 1.44529 | 0.722647 | − | 0.691218i | \(-0.242925\pi\) | ||||
0.722647 | + | 0.691218i | \(0.242925\pi\) | |||||||
\(660\) | −3.60171 | −0.140196 | ||||||||
\(661\) | −2.33331 | −0.0907551 | −0.0453775 | − | 0.998970i | \(-0.514449\pi\) | ||||
−0.0453775 | + | 0.998970i | \(0.514449\pi\) | |||||||
\(662\) | −47.3255 | −1.83936 | ||||||||
\(663\) | −0.847235 | −0.0329039 | ||||||||
\(664\) | 16.7021 | 0.648168 | ||||||||
\(665\) | 3.94014 | 0.152792 | ||||||||
\(666\) | 55.1430 | 2.13675 | ||||||||
\(667\) | 15.2898 | 0.592024 | ||||||||
\(668\) | −61.4113 | −2.37607 | ||||||||
\(669\) | 3.67429 | 0.142056 | ||||||||
\(670\) | 49.0980 | 1.89682 | ||||||||
\(671\) | −4.91088 | −0.189583 | ||||||||
\(672\) | 0.563139 | 0.0217236 | ||||||||
\(673\) | −35.8433 | −1.38166 | −0.690829 | − | 0.723018i | \(-0.742754\pi\) | ||||
−0.690829 | + | 0.723018i | \(0.742754\pi\) | |||||||
\(674\) | 0.609508 | 0.0234774 | ||||||||
\(675\) | −2.01198 | −0.0774411 | ||||||||
\(676\) | −19.4107 | −0.746565 | ||||||||
\(677\) | 42.8400 | 1.64647 | 0.823237 | − | 0.567697i | \(-0.192166\pi\) | ||||
0.823237 | + | 0.567697i | \(0.192166\pi\) | |||||||
\(678\) | −2.03953 | −0.0783277 | ||||||||
\(679\) | 6.33937 | 0.243283 | ||||||||
\(680\) | 11.5151 | 0.441585 | ||||||||
\(681\) | −0.411852 | −0.0157822 | ||||||||
\(682\) | 19.6848 | 0.753770 | ||||||||
\(683\) | 2.24546 | 0.0859200 | 0.0429600 | − | 0.999077i | \(-0.486321\pi\) | ||||
0.0429600 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(684\) | 25.0602 | 0.958202 | ||||||||
\(685\) | −14.3516 | −0.548346 | ||||||||
\(686\) | −29.5846 | −1.12954 | ||||||||
\(687\) | −0.821135 | −0.0313282 | ||||||||
\(688\) | 14.3254 | 0.546150 | ||||||||
\(689\) | 24.6283 | 0.938264 | ||||||||
\(690\) | 1.83586 | 0.0698901 | ||||||||
\(691\) | −12.4776 | −0.474671 | −0.237336 | − | 0.971428i | \(-0.576274\pi\) | ||||
−0.237336 | + | 0.971428i | \(0.576274\pi\) | |||||||
\(692\) | 13.2090 | 0.502131 | ||||||||
\(693\) | 8.77112 | 0.333187 | ||||||||
\(694\) | 22.4708 | 0.852980 | ||||||||
\(695\) | 12.9865 | 0.492606 | ||||||||
\(696\) | 4.40628 | 0.167019 | ||||||||
\(697\) | 3.24455 | 0.122896 | ||||||||
\(698\) | 75.6360 | 2.86286 | ||||||||
\(699\) | −4.44554 | −0.168146 | ||||||||
\(700\) | 6.42401 | 0.242805 | ||||||||
\(701\) | −19.7583 | −0.746262 | −0.373131 | − | 0.927779i | \(-0.621716\pi\) | ||||
−0.373131 | + | 0.927779i | \(0.621716\pi\) | |||||||
\(702\) | 7.08085 | 0.267250 | ||||||||
\(703\) | −18.2902 | −0.689827 | ||||||||
\(704\) | −35.5369 | −1.33935 | ||||||||
\(705\) | −1.26006 | −0.0474564 | ||||||||
\(706\) | −59.1837 | −2.22741 | ||||||||
\(707\) | 18.3847 | 0.691428 | ||||||||
\(708\) | −5.43829 | −0.204383 | ||||||||
\(709\) | 17.5081 | 0.657531 | 0.328765 | − | 0.944412i | \(-0.393367\pi\) | ||||
0.328765 | + | 0.944412i | \(0.393367\pi\) | |||||||
\(710\) | −1.92315 | −0.0721745 | ||||||||
\(711\) | −18.9736 | −0.711564 | ||||||||
\(712\) | 21.5779 | 0.808666 | ||||||||
\(713\) | −6.46296 | −0.242040 | ||||||||
\(714\) | 0.692792 | 0.0259271 | ||||||||
\(715\) | −15.1820 | −0.567774 | ||||||||
\(716\) | −13.3735 | −0.499790 | ||||||||
\(717\) | −1.17336 | −0.0438201 | ||||||||
\(718\) | 72.5147 | 2.70622 | ||||||||
\(719\) | 30.8017 | 1.14871 | 0.574355 | − | 0.818607i | \(-0.305253\pi\) | ||||
0.574355 | + | 0.818607i | \(0.305253\pi\) | |||||||
\(720\) | −9.79829 | −0.365161 | ||||||||
\(721\) | −11.6997 | −0.435720 | ||||||||
\(722\) | 32.1376 | 1.19604 | ||||||||
\(723\) | 1.38112 | 0.0513643 | ||||||||
\(724\) | −3.16768 | −0.117726 | ||||||||
\(725\) | −11.7933 | −0.437990 | ||||||||
\(726\) | −0.594377 | −0.0220594 | ||||||||
\(727\) | 1.43952 | 0.0533888 | 0.0266944 | − | 0.999644i | \(-0.491502\pi\) | ||||
0.0266944 | + | 0.999644i | \(0.491502\pi\) | |||||||
\(728\) | −10.1173 | −0.374972 | ||||||||
\(729\) | −25.2447 | −0.934988 | ||||||||
\(730\) | −41.2642 | −1.52726 | ||||||||
\(731\) | −13.0080 | −0.481117 | ||||||||
\(732\) | 1.03833 | 0.0383777 | ||||||||
\(733\) | 46.0606 | 1.70129 | 0.850643 | − | 0.525743i | \(-0.176213\pi\) | ||||
0.850643 | + | 0.525743i | \(0.176213\pi\) | |||||||
\(734\) | 47.2215 | 1.74298 | ||||||||
\(735\) | 1.95446 | 0.0720913 | ||||||||
\(736\) | 7.87205 | 0.290168 | ||||||||
\(737\) | −36.2523 | −1.33537 | ||||||||
\(738\) | −13.4838 | −0.496345 | ||||||||
\(739\) | −53.2450 | −1.95865 | −0.979325 | − | 0.202294i | \(-0.935160\pi\) | ||||
−0.979325 | + | 0.202294i | \(0.935160\pi\) | |||||||
\(740\) | 50.2727 | 1.84806 | ||||||||
\(741\) | −1.16785 | −0.0429022 | ||||||||
\(742\) | −20.1388 | −0.739319 | ||||||||
\(743\) | −22.3241 | −0.818991 | −0.409496 | − | 0.912312i | \(-0.634295\pi\) | ||||
−0.409496 | + | 0.912312i | \(0.634295\pi\) | |||||||
\(744\) | −1.86252 | −0.0682834 | ||||||||
\(745\) | −9.16293 | −0.335704 | ||||||||
\(746\) | 82.3669 | 3.01567 | ||||||||
\(747\) | 12.9050 | 0.472168 | ||||||||
\(748\) | −18.9996 | −0.694694 | ||||||||
\(749\) | −0.321428 | −0.0117447 | ||||||||
\(750\) | −5.21927 | −0.190581 | ||||||||
\(751\) | 9.25668 | 0.337781 | 0.168891 | − | 0.985635i | \(-0.445982\pi\) | ||||
0.168891 | + | 0.985635i | \(0.445982\pi\) | |||||||
\(752\) | 7.32017 | 0.266939 | ||||||||
\(753\) | 0.223763 | 0.00815437 | ||||||||
\(754\) | 41.5046 | 1.51151 | ||||||||
\(755\) | −16.5183 | −0.601161 | ||||||||
\(756\) | −3.72953 | −0.135642 | ||||||||
\(757\) | 13.2985 | 0.483343 | 0.241672 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241672 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(758\) | −39.4192 | −1.43177 | ||||||||
\(759\) | −1.35554 | −0.0492029 | ||||||||
\(760\) | 15.8728 | 0.575767 | ||||||||
\(761\) | −19.0709 | −0.691321 | −0.345660 | − | 0.938360i | \(-0.612345\pi\) | ||||
−0.345660 | + | 0.938360i | \(0.612345\pi\) | |||||||
\(762\) | −5.51815 | −0.199902 | ||||||||
\(763\) | 13.1409 | 0.475733 | ||||||||
\(764\) | −7.24408 | −0.262081 | ||||||||
\(765\) | 8.89721 | 0.321679 | ||||||||
\(766\) | 82.9401 | 2.99675 | ||||||||
\(767\) | −22.9236 | −0.827722 | ||||||||
\(768\) | 4.71285 | 0.170060 | ||||||||
\(769\) | 12.0504 | 0.434550 | 0.217275 | − | 0.976110i | \(-0.430283\pi\) | ||||
0.217275 | + | 0.976110i | \(0.430283\pi\) | |||||||
\(770\) | 12.4145 | 0.447386 | ||||||||
\(771\) | 0.110017 | 0.00396216 | ||||||||
\(772\) | 89.7366 | 3.22969 | ||||||||
\(773\) | 39.9603 | 1.43727 | 0.718635 | − | 0.695387i | \(-0.244767\pi\) | ||||
0.718635 | + | 0.695387i | \(0.244767\pi\) | |||||||
\(774\) | 54.0589 | 1.94311 | ||||||||
\(775\) | 4.98498 | 0.179066 | ||||||||
\(776\) | 25.5381 | 0.916764 | ||||||||
\(777\) | 1.35351 | 0.0485570 | ||||||||
\(778\) | −37.5453 | −1.34606 | ||||||||
\(779\) | 4.47238 | 0.160240 | ||||||||
\(780\) | 3.20999 | 0.114936 | ||||||||
\(781\) | 1.41999 | 0.0508111 | ||||||||
\(782\) | 9.68446 | 0.346316 | ||||||||
\(783\) | 6.84670 | 0.244681 | ||||||||
\(784\) | −11.3542 | −0.405508 | ||||||||
\(785\) | 40.6915 | 1.45234 | ||||||||
\(786\) | −8.41166 | −0.300034 | ||||||||
\(787\) | −22.4812 | −0.801367 | −0.400683 | − | 0.916217i | \(-0.631227\pi\) | ||||
−0.400683 | + | 0.916217i | \(0.631227\pi\) | |||||||
\(788\) | 62.9356 | 2.24199 | ||||||||
\(789\) | 4.67036 | 0.166269 | ||||||||
\(790\) | −26.8548 | −0.955450 | ||||||||
\(791\) | 4.52813 | 0.161002 | ||||||||
\(792\) | 35.3344 | 1.25555 | ||||||||
\(793\) | 4.37677 | 0.155424 | ||||||||
\(794\) | 5.56533 | 0.197506 | ||||||||
\(795\) | 2.85936 | 0.101411 | ||||||||
\(796\) | −46.9407 | −1.66377 | ||||||||
\(797\) | −2.66718 | −0.0944763 | −0.0472382 | − | 0.998884i | \(-0.515042\pi\) | ||||
−0.0472382 | + | 0.998884i | \(0.515042\pi\) | |||||||
\(798\) | 0.954966 | 0.0338054 | ||||||||
\(799\) | −6.64698 | −0.235153 | ||||||||
\(800\) | −6.07183 | −0.214672 | ||||||||
\(801\) | 16.6723 | 0.589086 | ||||||||
\(802\) | 60.2483 | 2.12744 | ||||||||
\(803\) | 30.4681 | 1.07519 | ||||||||
\(804\) | 7.66496 | 0.270322 | ||||||||
\(805\) | −4.07595 | −0.143658 | ||||||||
\(806\) | −17.5439 | −0.617957 | ||||||||
\(807\) | −4.13147 | −0.145435 | ||||||||
\(808\) | 74.0626 | 2.60551 | ||||||||
\(809\) | 2.22276 | 0.0781481 | 0.0390741 | − | 0.999236i | \(-0.487559\pi\) | ||||
0.0390741 | + | 0.999236i | \(0.487559\pi\) | |||||||
\(810\) | −36.5620 | −1.28466 | ||||||||
\(811\) | 27.9050 | 0.979878 | 0.489939 | − | 0.871757i | \(-0.337019\pi\) | ||||
0.489939 | + | 0.871757i | \(0.337019\pi\) | |||||||
\(812\) | −21.8607 | −0.767160 | ||||||||
\(813\) | −0.756541 | −0.0265330 | ||||||||
\(814\) | −57.6281 | −2.01986 | ||||||||
\(815\) | 1.87452 | 0.0656615 | ||||||||
\(816\) | 0.571438 | 0.0200043 | ||||||||
\(817\) | −17.9306 | −0.627312 | ||||||||
\(818\) | −31.9934 | −1.11862 | ||||||||
\(819\) | −7.81717 | −0.273154 | ||||||||
\(820\) | −12.2929 | −0.429286 | ||||||||
\(821\) | 7.67411 | 0.267828 | 0.133914 | − | 0.990993i | \(-0.457245\pi\) | ||||
0.133914 | + | 0.990993i | \(0.457245\pi\) | |||||||
\(822\) | −3.47838 | −0.121322 | ||||||||
\(823\) | 47.7600 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186964\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186964\pi\) | |||||||
\(824\) | −47.1322 | −1.64193 | ||||||||
\(825\) | 1.04555 | 0.0364013 | ||||||||
\(826\) | 18.7448 | 0.652216 | ||||||||
\(827\) | 18.6901 | 0.649917 | 0.324958 | − | 0.945728i | \(-0.394650\pi\) | ||||
0.324958 | + | 0.945728i | \(0.394650\pi\) | |||||||
\(828\) | −25.9240 | −0.900922 | ||||||||
\(829\) | −0.843871 | −0.0293088 | −0.0146544 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146544 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(830\) | 18.2654 | 0.634002 | ||||||||
\(831\) | −1.64114 | −0.0569305 | ||||||||
\(832\) | 31.6719 | 1.09803 | ||||||||
\(833\) | 10.3101 | 0.357223 | ||||||||
\(834\) | 3.14752 | 0.108990 | ||||||||
\(835\) | −30.0540 | −1.04006 | ||||||||
\(836\) | −26.1896 | −0.905787 | ||||||||
\(837\) | −2.89408 | −0.100034 | ||||||||
\(838\) | 13.4417 | 0.464337 | ||||||||
\(839\) | 53.8824 | 1.86023 | 0.930113 | − | 0.367274i | \(-0.119709\pi\) | ||||
0.930113 | + | 0.367274i | \(0.119709\pi\) | |||||||
\(840\) | −1.17462 | −0.0405283 | ||||||||
\(841\) | 11.1321 | 0.383864 | ||||||||
\(842\) | 80.1674 | 2.76275 | ||||||||
\(843\) | 5.44415 | 0.187506 | ||||||||
\(844\) | 70.2770 | 2.41903 | ||||||||
\(845\) | −9.49937 | −0.326788 | ||||||||
\(846\) | 27.6237 | 0.949724 | ||||||||
\(847\) | 1.31962 | 0.0453428 | ||||||||
\(848\) | −16.6112 | −0.570430 | ||||||||
\(849\) | 0.111092 | 0.00381268 | ||||||||
\(850\) | −7.46977 | −0.256211 | ||||||||
\(851\) | 18.9206 | 0.648590 | ||||||||
\(852\) | −0.300233 | −0.0102858 | ||||||||
\(853\) | 4.28689 | 0.146780 | 0.0733902 | − | 0.997303i | \(-0.476618\pi\) | ||||
0.0733902 | + | 0.997303i | \(0.476618\pi\) | |||||||
\(854\) | −3.57893 | −0.122468 | ||||||||
\(855\) | 12.2642 | 0.419426 | ||||||||
\(856\) | −1.29487 | −0.0442577 | ||||||||
\(857\) | 35.5916 | 1.21579 | 0.607894 | − | 0.794019i | \(-0.292015\pi\) | ||||
0.607894 | + | 0.794019i | \(0.292015\pi\) | |||||||
\(858\) | −3.67964 | −0.125621 | ||||||||
\(859\) | −38.4568 | −1.31213 | −0.656064 | − | 0.754705i | \(-0.727780\pi\) | ||||
−0.656064 | + | 0.754705i | \(0.727780\pi\) | |||||||
\(860\) | 49.2844 | 1.68058 | ||||||||
\(861\) | −0.330966 | −0.0112793 | ||||||||
\(862\) | 49.6666 | 1.69165 | ||||||||
\(863\) | −49.1038 | −1.67151 | −0.835757 | − | 0.549100i | \(-0.814971\pi\) | ||||
−0.835757 | + | 0.549100i | \(0.814971\pi\) | |||||||
\(864\) | 3.52507 | 0.119925 | ||||||||
\(865\) | 6.46434 | 0.219794 | ||||||||
\(866\) | −64.5177 | −2.19240 | ||||||||
\(867\) | 2.56014 | 0.0869470 | ||||||||
\(868\) | 9.24047 | 0.313642 | ||||||||
\(869\) | 19.8286 | 0.672640 | ||||||||
\(870\) | 4.81870 | 0.163369 | ||||||||
\(871\) | 32.3094 | 1.09476 | ||||||||
\(872\) | 52.9381 | 1.79271 | ||||||||
\(873\) | 19.7321 | 0.667831 | ||||||||
\(874\) | 13.3494 | 0.451549 | ||||||||
\(875\) | 11.5877 | 0.391737 | ||||||||
\(876\) | −6.44198 | −0.217654 | ||||||||
\(877\) | −26.6763 | −0.900794 | −0.450397 | − | 0.892828i | \(-0.648718\pi\) | ||||
−0.450397 | + | 0.892828i | \(0.648718\pi\) | |||||||
\(878\) | 24.6034 | 0.830324 | ||||||||
\(879\) | 1.96010 | 0.0661125 | ||||||||
\(880\) | 10.2399 | 0.345186 | ||||||||
\(881\) | −1.98755 | −0.0669624 | −0.0334812 | − | 0.999439i | \(-0.510659\pi\) | ||||
−0.0334812 | + | 0.999439i | \(0.510659\pi\) | |||||||
\(882\) | −42.8469 | −1.44273 | ||||||||
\(883\) | −28.4545 | −0.957571 | −0.478785 | − | 0.877932i | \(-0.658923\pi\) | ||||
−0.478785 | + | 0.877932i | \(0.658923\pi\) | |||||||
\(884\) | 16.9332 | 0.569524 | ||||||||
\(885\) | −2.66144 | −0.0894632 | ||||||||
\(886\) | 75.5783 | 2.53910 | ||||||||
\(887\) | 23.3548 | 0.784178 | 0.392089 | − | 0.919927i | \(-0.371752\pi\) | ||||
0.392089 | + | 0.919927i | \(0.371752\pi\) | |||||||
\(888\) | 5.45261 | 0.182978 | ||||||||
\(889\) | 12.2513 | 0.410895 | ||||||||
\(890\) | 23.5976 | 0.790993 | ||||||||
\(891\) | 26.9961 | 0.904403 | ||||||||
\(892\) | −73.4358 | −2.45881 | ||||||||
\(893\) | −9.16241 | −0.306608 | ||||||||
\(894\) | −2.22081 | −0.0742750 | ||||||||
\(895\) | −6.54482 | −0.218769 | ||||||||
\(896\) | −19.6800 | −0.657463 | ||||||||
\(897\) | 1.20811 | 0.0403376 | ||||||||
\(898\) | 63.4032 | 2.11579 | ||||||||
\(899\) | −16.9637 | −0.565772 | ||||||||
\(900\) | 19.9956 | 0.666519 | ||||||||
\(901\) | 15.0836 | 0.502506 | ||||||||
\(902\) | 14.0915 | 0.469194 | ||||||||
\(903\) | 1.32690 | 0.0441566 | ||||||||
\(904\) | 18.2415 | 0.606704 | ||||||||
\(905\) | −1.55022 | −0.0515312 | ||||||||
\(906\) | −4.00351 | −0.133008 | ||||||||
\(907\) | 4.13188 | 0.137197 | 0.0685983 | − | 0.997644i | \(-0.478147\pi\) | ||||
0.0685983 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(908\) | 8.23144 | 0.273170 | ||||||||
\(909\) | 57.2248 | 1.89803 | ||||||||
\(910\) | −11.0643 | −0.366777 | ||||||||
\(911\) | −35.7070 | −1.18303 | −0.591513 | − | 0.806296i | \(-0.701469\pi\) | ||||
−0.591513 | + | 0.806296i | \(0.701469\pi\) | |||||||
\(912\) | 0.787688 | 0.0260830 | ||||||||
\(913\) | −13.4866 | −0.446340 | ||||||||
\(914\) | −49.9234 | −1.65132 | ||||||||
\(915\) | 0.508146 | 0.0167988 | ||||||||
\(916\) | 16.4115 | 0.542252 | ||||||||
\(917\) | 18.6754 | 0.616716 | ||||||||
\(918\) | 4.33665 | 0.143131 | ||||||||
\(919\) | −44.2652 | −1.46017 | −0.730087 | − | 0.683355i | \(-0.760520\pi\) | ||||
−0.730087 | + | 0.683355i | \(0.760520\pi\) | |||||||
\(920\) | −16.4199 | −0.541348 | ||||||||
\(921\) | 2.32442 | 0.0765923 | ||||||||
\(922\) | −38.7204 | −1.27519 | ||||||||
\(923\) | −1.26555 | −0.0416560 | ||||||||
\(924\) | 1.93809 | 0.0637585 | ||||||||
\(925\) | −14.5937 | −0.479839 | ||||||||
\(926\) | 54.9377 | 1.80536 | ||||||||
\(927\) | −36.4169 | −1.19609 | ||||||||
\(928\) | 20.6622 | 0.678271 | ||||||||
\(929\) | 16.5049 | 0.541507 | 0.270754 | − | 0.962649i | \(-0.412727\pi\) | ||||
0.270754 | + | 0.962649i | \(0.412727\pi\) | |||||||
\(930\) | −2.03685 | −0.0667910 | ||||||||
\(931\) | 14.2117 | 0.465770 | ||||||||
\(932\) | 88.8505 | 2.91039 | ||||||||
\(933\) | 0.882586 | 0.0288946 | ||||||||
\(934\) | 54.4195 | 1.78066 | ||||||||
\(935\) | −9.29818 | −0.304083 | ||||||||
\(936\) | −31.4914 | −1.02933 | ||||||||
\(937\) | −32.4305 | −1.05946 | −0.529729 | − | 0.848167i | \(-0.677706\pi\) | ||||
−0.529729 | + | 0.848167i | \(0.677706\pi\) | |||||||
\(938\) | −26.4197 | −0.862635 | ||||||||
\(939\) | 4.96395 | 0.161992 | ||||||||
\(940\) | 25.1840 | 0.821411 | ||||||||
\(941\) | −49.3511 | −1.60880 | −0.804400 | − | 0.594088i | \(-0.797513\pi\) | ||||
−0.804400 | + | 0.594088i | \(0.797513\pi\) | |||||||
\(942\) | 9.86236 | 0.321333 | ||||||||
\(943\) | −4.62654 | −0.150661 | ||||||||
\(944\) | 15.4614 | 0.503224 | ||||||||
\(945\) | −1.82519 | −0.0593734 | ||||||||
\(946\) | −56.4952 | −1.83682 | ||||||||
\(947\) | −30.6757 | −0.996825 | −0.498413 | − | 0.866940i | \(-0.666084\pi\) | ||||
−0.498413 | + | 0.866940i | \(0.666084\pi\) | |||||||
\(948\) | −4.19244 | −0.136164 | ||||||||
\(949\) | −27.1543 | −0.881467 | ||||||||
\(950\) | −10.2966 | −0.334064 | ||||||||
\(951\) | 0.991506 | 0.0321518 | ||||||||
\(952\) | −6.19631 | −0.200824 | ||||||||
\(953\) | −3.63547 | −0.117764 | −0.0588822 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588822 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(954\) | −62.6847 | −2.02949 | ||||||||
\(955\) | −3.54517 | −0.114719 | ||||||||
\(956\) | 23.4513 | 0.758470 | ||||||||
\(957\) | −3.55796 | −0.115013 | ||||||||
\(958\) | 0.182946 | 0.00591070 | ||||||||
\(959\) | 7.72262 | 0.249377 | ||||||||
\(960\) | 3.67713 | 0.118679 | ||||||||
\(961\) | −23.8295 | −0.768693 | ||||||||
\(962\) | 51.3605 | 1.65593 | ||||||||
\(963\) | −1.00049 | −0.0322402 | ||||||||
\(964\) | −27.6036 | −0.889051 | ||||||||
\(965\) | 43.9160 | 1.41371 | ||||||||
\(966\) | −0.987882 | −0.0317846 | ||||||||
\(967\) | 20.2103 | 0.649920 | 0.324960 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324960 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(968\) | 5.31609 | 0.170866 | ||||||||
\(969\) | −0.715250 | −0.0229771 | ||||||||
\(970\) | 27.9284 | 0.896728 | ||||||||
\(971\) | 27.4648 | 0.881388 | 0.440694 | − | 0.897657i | \(-0.354732\pi\) | ||||
0.440694 | + | 0.897657i | \(0.354732\pi\) | |||||||
\(972\) | −17.4449 | −0.559545 | ||||||||
\(973\) | −6.98806 | −0.224027 | ||||||||
\(974\) | −72.4737 | −2.32221 | ||||||||
\(975\) | −0.931832 | −0.0298425 | ||||||||
\(976\) | −2.95202 | −0.0944920 | ||||||||
\(977\) | −27.1733 | −0.869351 | −0.434676 | − | 0.900587i | \(-0.643137\pi\) | ||||
−0.434676 | + | 0.900587i | \(0.643137\pi\) | |||||||
\(978\) | 0.454325 | 0.0145277 | ||||||||
\(979\) | −17.4236 | −0.556862 | ||||||||
\(980\) | −39.0626 | −1.24781 | ||||||||
\(981\) | 40.9028 | 1.30593 | ||||||||
\(982\) | −55.4420 | −1.76923 | ||||||||
\(983\) | 40.0402 | 1.27708 | 0.638542 | − | 0.769587i | \(-0.279538\pi\) | ||||
0.638542 | + | 0.769587i | \(0.279538\pi\) | |||||||
\(984\) | −1.33329 | −0.0425039 | ||||||||
\(985\) | 30.7999 | 0.981368 | ||||||||
\(986\) | 25.4194 | 0.809518 | ||||||||
\(987\) | 0.678039 | 0.0215822 | ||||||||
\(988\) | 23.3412 | 0.742583 | ||||||||
\(989\) | 18.5486 | 0.589812 | ||||||||
\(990\) | 38.6416 | 1.22811 | ||||||||
\(991\) | −29.3816 | −0.933339 | −0.466669 | − | 0.884432i | \(-0.654546\pi\) | ||||
−0.466669 | + | 0.884432i | \(0.654546\pi\) | |||||||
\(992\) | −8.73388 | −0.277301 | ||||||||
\(993\) | −3.61572 | −0.114741 | ||||||||
\(994\) | 1.03485 | 0.0328235 | ||||||||
\(995\) | −22.9722 | −0.728268 | ||||||||
\(996\) | 2.85151 | 0.0903537 | ||||||||
\(997\) | −18.5995 | −0.589052 | −0.294526 | − | 0.955643i | \(-0.595162\pi\) | ||||
−0.294526 | + | 0.955643i | \(0.595162\pi\) | |||||||
\(998\) | 85.0614 | 2.69257 | ||||||||
\(999\) | 8.47255 | 0.268060 |
(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 | 4021.2.a.b.1.16 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.b.1.16 | ✓ | 151 | 1.1 | even | 1 | trivial |