Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1577774590\) |
Analytic rank: | \(1\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17795 | −1.54005 | −0.770023 | − | 0.638017i | \(-0.779755\pi\) | ||||
−0.770023 | + | 0.638017i | \(0.779755\pi\) | |||||||
\(3\) | 2.23759 | 1.29187 | 0.645937 | − | 0.763391i | \(-0.276467\pi\) | ||||
0.645937 | + | 0.763391i | \(0.276467\pi\) | |||||||
\(4\) | 2.74348 | 1.37174 | ||||||||
\(5\) | 1.66421 | 0.744257 | 0.372128 | − | 0.928181i | \(-0.378628\pi\) | ||||
0.372128 | + | 0.928181i | \(0.378628\pi\) | |||||||
\(6\) | −4.87337 | −1.98954 | ||||||||
\(7\) | −3.06154 | −1.15715 | −0.578577 | − | 0.815628i | \(-0.696392\pi\) | ||||
−0.578577 | + | 0.815628i | \(0.696392\pi\) | |||||||
\(8\) | −1.61926 | −0.572496 | ||||||||
\(9\) | 2.00681 | 0.668937 | ||||||||
\(10\) | −3.62457 | −1.14619 | ||||||||
\(11\) | −1.57786 | −0.475742 | −0.237871 | − | 0.971297i | \(-0.576450\pi\) | ||||
−0.237871 | + | 0.971297i | \(0.576450\pi\) | |||||||
\(12\) | 6.13878 | 1.77211 | ||||||||
\(13\) | −0.211680 | −0.0587094 | −0.0293547 | − | 0.999569i | \(-0.509345\pi\) | ||||
−0.0293547 | + | 0.999569i | \(0.509345\pi\) | |||||||
\(14\) | 6.66790 | 1.78207 | ||||||||
\(15\) | 3.72382 | 0.961485 | ||||||||
\(16\) | −1.96028 | −0.490070 | ||||||||
\(17\) | 2.77554 | 0.673167 | 0.336583 | − | 0.941654i | \(-0.390729\pi\) | ||||
0.336583 | + | 0.941654i | \(0.390729\pi\) | |||||||
\(18\) | −4.37074 | −1.03019 | ||||||||
\(19\) | −6.50524 | −1.49240 | −0.746202 | − | 0.665719i | \(-0.768125\pi\) | ||||
−0.746202 | + | 0.665719i | \(0.768125\pi\) | |||||||
\(20\) | 4.56572 | 1.02093 | ||||||||
\(21\) | −6.85048 | −1.49490 | ||||||||
\(22\) | 3.43650 | 0.732664 | ||||||||
\(23\) | 3.87991 | 0.809017 | 0.404509 | − | 0.914534i | \(-0.367443\pi\) | ||||
0.404509 | + | 0.914534i | \(0.367443\pi\) | |||||||
\(24\) | −3.62325 | −0.739592 | ||||||||
\(25\) | −2.23041 | −0.446082 | ||||||||
\(26\) | 0.461028 | 0.0904151 | ||||||||
\(27\) | −2.22235 | −0.427692 | ||||||||
\(28\) | −8.39928 | −1.58731 | ||||||||
\(29\) | 2.19193 | 0.407031 | 0.203516 | − | 0.979072i | \(-0.434763\pi\) | ||||
0.203516 | + | 0.979072i | \(0.434763\pi\) | |||||||
\(30\) | −8.11030 | −1.48073 | ||||||||
\(31\) | 6.91264 | 1.24155 | 0.620774 | − | 0.783990i | \(-0.286819\pi\) | ||||
0.620774 | + | 0.783990i | \(0.286819\pi\) | |||||||
\(32\) | 7.50792 | 1.32723 | ||||||||
\(33\) | −3.53060 | −0.614598 | ||||||||
\(34\) | −6.04499 | −1.03671 | ||||||||
\(35\) | −5.09504 | −0.861220 | ||||||||
\(36\) | 5.50564 | 0.917607 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 14.1681 | 2.29837 | ||||||||
\(39\) | −0.473652 | −0.0758451 | ||||||||
\(40\) | −2.69479 | −0.426084 | ||||||||
\(41\) | 1.14950 | 0.179522 | 0.0897610 | − | 0.995963i | \(-0.471390\pi\) | ||||
0.0897610 | + | 0.995963i | \(0.471390\pi\) | |||||||
\(42\) | 14.9200 | 2.30221 | ||||||||
\(43\) | 6.19271 | 0.944379 | 0.472189 | − | 0.881497i | \(-0.343464\pi\) | ||||
0.472189 | + | 0.881497i | \(0.343464\pi\) | |||||||
\(44\) | −4.32882 | −0.652594 | ||||||||
\(45\) | 3.33975 | 0.497861 | ||||||||
\(46\) | −8.45026 | −1.24592 | ||||||||
\(47\) | −0.352658 | −0.0514405 | −0.0257202 | − | 0.999669i | \(-0.508188\pi\) | ||||
−0.0257202 | + | 0.999669i | \(0.508188\pi\) | |||||||
\(48\) | −4.38630 | −0.633108 | ||||||||
\(49\) | 2.37304 | 0.339006 | ||||||||
\(50\) | 4.85773 | 0.686986 | ||||||||
\(51\) | 6.21051 | 0.869646 | ||||||||
\(52\) | −0.580739 | −0.0805339 | ||||||||
\(53\) | −13.5084 | −1.85552 | −0.927761 | − | 0.373175i | \(-0.878269\pi\) | ||||
−0.927761 | + | 0.373175i | \(0.878269\pi\) | |||||||
\(54\) | 4.84018 | 0.658664 | ||||||||
\(55\) | −2.62588 | −0.354074 | ||||||||
\(56\) | 4.95744 | 0.662466 | ||||||||
\(57\) | −14.5561 | −1.92800 | ||||||||
\(58\) | −4.77392 | −0.626846 | ||||||||
\(59\) | 3.36630 | 0.438255 | 0.219128 | − | 0.975696i | \(-0.429679\pi\) | ||||
0.219128 | + | 0.975696i | \(0.429679\pi\) | |||||||
\(60\) | 10.2162 | 1.31891 | ||||||||
\(61\) | 1.43260 | 0.183426 | 0.0917131 | − | 0.995785i | \(-0.470766\pi\) | ||||
0.0917131 | + | 0.995785i | \(0.470766\pi\) | |||||||
\(62\) | −15.0554 | −1.91204 | ||||||||
\(63\) | −6.14394 | −0.774063 | ||||||||
\(64\) | −12.4313 | −1.55392 | ||||||||
\(65\) | −0.352279 | −0.0436948 | ||||||||
\(66\) | 7.68948 | 0.946509 | ||||||||
\(67\) | −1.92342 | −0.234983 | −0.117492 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117492 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(68\) | 7.61463 | 0.923409 | ||||||||
\(69\) | 8.68165 | 1.04515 | ||||||||
\(70\) | 11.0968 | 1.32632 | ||||||||
\(71\) | 6.00523 | 0.712689 | 0.356345 | − | 0.934355i | \(-0.384023\pi\) | ||||
0.356345 | + | 0.934355i | \(0.384023\pi\) | |||||||
\(72\) | −3.24955 | −0.382964 | ||||||||
\(73\) | −8.32780 | −0.974696 | −0.487348 | − | 0.873208i | \(-0.662036\pi\) | ||||
−0.487348 | + | 0.873208i | \(0.662036\pi\) | |||||||
\(74\) | 2.17795 | 0.253182 | ||||||||
\(75\) | −4.99074 | −0.576281 | ||||||||
\(76\) | −17.8470 | −2.04719 | ||||||||
\(77\) | 4.83068 | 0.550507 | ||||||||
\(78\) | 1.03159 | 0.116805 | ||||||||
\(79\) | −7.66645 | −0.862543 | −0.431271 | − | 0.902222i | \(-0.641935\pi\) | ||||
−0.431271 | + | 0.902222i | \(0.641935\pi\) | |||||||
\(80\) | −3.26231 | −0.364738 | ||||||||
\(81\) | −10.9931 | −1.22146 | ||||||||
\(82\) | −2.50356 | −0.276472 | ||||||||
\(83\) | 2.04666 | 0.224651 | 0.112325 | − | 0.993671i | \(-0.464170\pi\) | ||||
0.112325 | + | 0.993671i | \(0.464170\pi\) | |||||||
\(84\) | −18.7941 | −2.05061 | ||||||||
\(85\) | 4.61907 | 0.501009 | ||||||||
\(86\) | −13.4874 | −1.45439 | ||||||||
\(87\) | 4.90464 | 0.525833 | ||||||||
\(88\) | 2.55497 | 0.272360 | ||||||||
\(89\) | 13.6855 | 1.45066 | 0.725331 | − | 0.688400i | \(-0.241687\pi\) | ||||
0.725331 | + | 0.688400i | \(0.241687\pi\) | |||||||
\(90\) | −7.27382 | −0.766728 | ||||||||
\(91\) | 0.648066 | 0.0679358 | ||||||||
\(92\) | 10.6445 | 1.10976 | ||||||||
\(93\) | 15.4677 | 1.60392 | ||||||||
\(94\) | 0.768073 | 0.0792207 | ||||||||
\(95\) | −10.8261 | −1.11073 | ||||||||
\(96\) | 16.7997 | 1.71461 | ||||||||
\(97\) | −4.63698 | −0.470814 | −0.235407 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235407 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(98\) | −5.16837 | −0.522085 | ||||||||
\(99\) | −3.16646 | −0.318241 | ||||||||
\(100\) | −6.11908 | −0.611908 | ||||||||
\(101\) | 4.50301 | 0.448066 | 0.224033 | − | 0.974582i | \(-0.428078\pi\) | ||||
0.224033 | + | 0.974582i | \(0.428078\pi\) | |||||||
\(102\) | −13.5262 | −1.33929 | ||||||||
\(103\) | −1.91684 | −0.188872 | −0.0944358 | − | 0.995531i | \(-0.530105\pi\) | ||||
−0.0944358 | + | 0.995531i | \(0.530105\pi\) | |||||||
\(104\) | 0.342765 | 0.0336109 | ||||||||
\(105\) | −11.4006 | −1.11259 | ||||||||
\(106\) | 29.4207 | 2.85759 | ||||||||
\(107\) | 4.59889 | 0.444592 | 0.222296 | − | 0.974979i | \(-0.428645\pi\) | ||||
0.222296 | + | 0.974979i | \(0.428645\pi\) | |||||||
\(108\) | −6.09697 | −0.586681 | ||||||||
\(109\) | −12.5070 | −1.19796 | −0.598978 | − | 0.800765i | \(-0.704426\pi\) | ||||
−0.598978 | + | 0.800765i | \(0.704426\pi\) | |||||||
\(110\) | 5.71905 | 0.545290 | ||||||||
\(111\) | −2.23759 | −0.212383 | ||||||||
\(112\) | 6.00148 | 0.567087 | ||||||||
\(113\) | 10.7719 | 1.01334 | 0.506668 | − | 0.862141i | \(-0.330877\pi\) | ||||
0.506668 | + | 0.862141i | \(0.330877\pi\) | |||||||
\(114\) | 31.7024 | 2.96920 | ||||||||
\(115\) | 6.45698 | 0.602116 | ||||||||
\(116\) | 6.01351 | 0.558341 | ||||||||
\(117\) | −0.424801 | −0.0392729 | ||||||||
\(118\) | −7.33165 | −0.674933 | ||||||||
\(119\) | −8.49742 | −0.778958 | ||||||||
\(120\) | −6.02984 | −0.550446 | ||||||||
\(121\) | −8.51037 | −0.773670 | ||||||||
\(122\) | −3.12015 | −0.282485 | ||||||||
\(123\) | 2.57211 | 0.231920 | ||||||||
\(124\) | 18.9647 | 1.70308 | ||||||||
\(125\) | −12.0329 | −1.07626 | ||||||||
\(126\) | 13.3812 | 1.19209 | ||||||||
\(127\) | −17.9311 | −1.59113 | −0.795566 | − | 0.605867i | \(-0.792826\pi\) | ||||
−0.795566 | + | 0.605867i | \(0.792826\pi\) | |||||||
\(128\) | 12.0590 | 1.06588 | ||||||||
\(129\) | 13.8567 | 1.22002 | ||||||||
\(130\) | 0.767247 | 0.0672920 | ||||||||
\(131\) | −10.8428 | −0.947336 | −0.473668 | − | 0.880703i | \(-0.657070\pi\) | ||||
−0.473668 | + | 0.880703i | \(0.657070\pi\) | |||||||
\(132\) | −9.68612 | −0.843069 | ||||||||
\(133\) | 19.9161 | 1.72694 | ||||||||
\(134\) | 4.18912 | 0.361885 | ||||||||
\(135\) | −3.69845 | −0.318312 | ||||||||
\(136\) | −4.49432 | −0.385385 | ||||||||
\(137\) | 17.1676 | 1.46673 | 0.733364 | − | 0.679836i | \(-0.237949\pi\) | ||||
0.733364 | + | 0.679836i | \(0.237949\pi\) | |||||||
\(138\) | −18.9082 | −1.60958 | ||||||||
\(139\) | −17.2896 | −1.46648 | −0.733242 | − | 0.679967i | \(-0.761994\pi\) | ||||
−0.733242 | + | 0.679967i | \(0.761994\pi\) | |||||||
\(140\) | −13.9782 | −1.18137 | ||||||||
\(141\) | −0.789104 | −0.0664546 | ||||||||
\(142\) | −13.0791 | −1.09757 | ||||||||
\(143\) | 0.334000 | 0.0279305 | ||||||||
\(144\) | −3.93391 | −0.327826 | ||||||||
\(145\) | 3.64783 | 0.302936 | ||||||||
\(146\) | 18.1376 | 1.50108 | ||||||||
\(147\) | 5.30990 | 0.437953 | ||||||||
\(148\) | −2.74348 | −0.225513 | ||||||||
\(149\) | −11.4017 | −0.934065 | −0.467032 | − | 0.884240i | \(-0.654677\pi\) | ||||
−0.467032 | + | 0.884240i | \(0.654677\pi\) | |||||||
\(150\) | 10.8696 | 0.887500 | ||||||||
\(151\) | 1.31952 | 0.107381 | 0.0536906 | − | 0.998558i | \(-0.482902\pi\) | ||||
0.0536906 | + | 0.998558i | \(0.482902\pi\) | |||||||
\(152\) | 10.5337 | 0.854396 | ||||||||
\(153\) | 5.56998 | 0.450306 | ||||||||
\(154\) | −10.5210 | −0.847805 | ||||||||
\(155\) | 11.5041 | 0.924030 | ||||||||
\(156\) | −1.29946 | −0.104040 | ||||||||
\(157\) | −16.2682 | −1.29834 | −0.649172 | − | 0.760641i | \(-0.724885\pi\) | ||||
−0.649172 | + | 0.760641i | \(0.724885\pi\) | |||||||
\(158\) | 16.6972 | 1.32835 | ||||||||
\(159\) | −30.2263 | −2.39710 | ||||||||
\(160\) | 12.4948 | 0.987797 | ||||||||
\(161\) | −11.8785 | −0.936158 | ||||||||
\(162\) | 23.9425 | 1.88110 | ||||||||
\(163\) | −1.00000 | −0.0783260 | ||||||||
\(164\) | 3.15363 | 0.246257 | ||||||||
\(165\) | −5.87565 | −0.457419 | ||||||||
\(166\) | −4.45754 | −0.345972 | ||||||||
\(167\) | −11.9549 | −0.925101 | −0.462551 | − | 0.886593i | \(-0.653066\pi\) | ||||
−0.462551 | + | 0.886593i | \(0.653066\pi\) | |||||||
\(168\) | 11.0927 | 0.855822 | ||||||||
\(169\) | −12.9552 | −0.996553 | ||||||||
\(170\) | −10.0601 | −0.771576 | ||||||||
\(171\) | −13.0548 | −0.998325 | ||||||||
\(172\) | 16.9896 | 1.29544 | ||||||||
\(173\) | −17.6997 | −1.34569 | −0.672843 | − | 0.739786i | \(-0.734927\pi\) | ||||
−0.672843 | + | 0.739786i | \(0.734927\pi\) | |||||||
\(174\) | −10.6821 | −0.809806 | ||||||||
\(175\) | 6.82849 | 0.516186 | ||||||||
\(176\) | 3.09304 | 0.233147 | ||||||||
\(177\) | 7.53240 | 0.566170 | ||||||||
\(178\) | −29.8064 | −2.23408 | ||||||||
\(179\) | −14.9414 | −1.11678 | −0.558388 | − | 0.829580i | \(-0.688580\pi\) | ||||
−0.558388 | + | 0.829580i | \(0.688580\pi\) | |||||||
\(180\) | 9.16254 | 0.682935 | ||||||||
\(181\) | 5.94801 | 0.442112 | 0.221056 | − | 0.975261i | \(-0.429050\pi\) | ||||
0.221056 | + | 0.975261i | \(0.429050\pi\) | |||||||
\(182\) | −1.41146 | −0.104624 | ||||||||
\(183\) | 3.20558 | 0.236963 | ||||||||
\(184\) | −6.28259 | −0.463159 | ||||||||
\(185\) | −1.66421 | −0.122355 | ||||||||
\(186\) | −33.6878 | −2.47011 | ||||||||
\(187\) | −4.37940 | −0.320253 | ||||||||
\(188\) | −0.967510 | −0.0705629 | ||||||||
\(189\) | 6.80382 | 0.494905 | ||||||||
\(190\) | 23.5787 | 1.71058 | ||||||||
\(191\) | −16.2068 | −1.17268 | −0.586340 | − | 0.810065i | \(-0.699432\pi\) | ||||
−0.586340 | + | 0.810065i | \(0.699432\pi\) | |||||||
\(192\) | −27.8163 | −2.00747 | ||||||||
\(193\) | −13.3399 | −0.960227 | −0.480114 | − | 0.877206i | \(-0.659405\pi\) | ||||
−0.480114 | + | 0.877206i | \(0.659405\pi\) | |||||||
\(194\) | 10.0991 | 0.725076 | ||||||||
\(195\) | −0.788256 | −0.0564482 | ||||||||
\(196\) | 6.51039 | 0.465028 | ||||||||
\(197\) | −13.6324 | −0.971267 | −0.485634 | − | 0.874162i | \(-0.661411\pi\) | ||||
−0.485634 | + | 0.874162i | \(0.661411\pi\) | |||||||
\(198\) | 6.89640 | 0.490106 | ||||||||
\(199\) | 18.0998 | 1.28306 | 0.641532 | − | 0.767096i | \(-0.278299\pi\) | ||||
0.641532 | + | 0.767096i | \(0.278299\pi\) | |||||||
\(200\) | 3.61162 | 0.255380 | ||||||||
\(201\) | −4.30383 | −0.303569 | ||||||||
\(202\) | −9.80733 | −0.690042 | ||||||||
\(203\) | −6.71069 | −0.470998 | ||||||||
\(204\) | 17.0384 | 1.19293 | ||||||||
\(205\) | 1.91301 | 0.133610 | ||||||||
\(206\) | 4.17478 | 0.290871 | ||||||||
\(207\) | 7.78625 | 0.541181 | ||||||||
\(208\) | 0.414951 | 0.0287717 | ||||||||
\(209\) | 10.2643 | 0.709999 | ||||||||
\(210\) | 24.8300 | 1.71343 | ||||||||
\(211\) | 2.46892 | 0.169967 | 0.0849837 | − | 0.996382i | \(-0.472916\pi\) | ||||
0.0849837 | + | 0.996382i | \(0.472916\pi\) | |||||||
\(212\) | −37.0600 | −2.54529 | ||||||||
\(213\) | 13.4372 | 0.920704 | ||||||||
\(214\) | −10.0162 | −0.684691 | ||||||||
\(215\) | 10.3060 | 0.702860 | ||||||||
\(216\) | 3.59857 | 0.244852 | ||||||||
\(217\) | −21.1634 | −1.43666 | ||||||||
\(218\) | 27.2397 | 1.84491 | ||||||||
\(219\) | −18.6342 | −1.25918 | ||||||||
\(220\) | −7.20406 | −0.485697 | ||||||||
\(221\) | −0.587525 | −0.0395212 | ||||||||
\(222\) | 4.87337 | 0.327079 | ||||||||
\(223\) | 9.70937 | 0.650187 | 0.325094 | − | 0.945682i | \(-0.394604\pi\) | ||||
0.325094 | + | 0.945682i | \(0.394604\pi\) | |||||||
\(224\) | −22.9858 | −1.53581 | ||||||||
\(225\) | −4.47601 | −0.298401 | ||||||||
\(226\) | −23.4607 | −1.56058 | ||||||||
\(227\) | −24.5150 | −1.62712 | −0.813559 | − | 0.581482i | \(-0.802473\pi\) | ||||
−0.813559 | + | 0.581482i | \(0.802473\pi\) | |||||||
\(228\) | −39.9343 | −2.64471 | ||||||||
\(229\) | −25.7628 | −1.70246 | −0.851228 | − | 0.524797i | \(-0.824141\pi\) | ||||
−0.851228 | + | 0.524797i | \(0.824141\pi\) | |||||||
\(230\) | −14.0630 | −0.927287 | ||||||||
\(231\) | 10.8091 | 0.711185 | ||||||||
\(232\) | −3.54931 | −0.233024 | ||||||||
\(233\) | 3.31972 | 0.217482 | 0.108741 | − | 0.994070i | \(-0.465318\pi\) | ||||
0.108741 | + | 0.994070i | \(0.465318\pi\) | |||||||
\(234\) | 0.925196 | 0.0604820 | ||||||||
\(235\) | −0.586897 | −0.0382849 | ||||||||
\(236\) | 9.23538 | 0.601172 | ||||||||
\(237\) | −17.1544 | −1.11430 | ||||||||
\(238\) | 18.5070 | 1.19963 | ||||||||
\(239\) | −27.8008 | −1.79828 | −0.899142 | − | 0.437658i | \(-0.855808\pi\) | ||||
−0.899142 | + | 0.437658i | \(0.855808\pi\) | |||||||
\(240\) | −7.29972 | −0.471195 | ||||||||
\(241\) | 11.6947 | 0.753325 | 0.376662 | − | 0.926351i | \(-0.377072\pi\) | ||||
0.376662 | + | 0.926351i | \(0.377072\pi\) | |||||||
\(242\) | 18.5352 | 1.19149 | ||||||||
\(243\) | −17.9311 | −1.15028 | ||||||||
\(244\) | 3.93032 | 0.251613 | ||||||||
\(245\) | 3.94924 | 0.252307 | ||||||||
\(246\) | −5.60194 | −0.357167 | ||||||||
\(247\) | 1.37703 | 0.0876181 | ||||||||
\(248\) | −11.1934 | −0.710781 | ||||||||
\(249\) | 4.57960 | 0.290220 | ||||||||
\(250\) | 26.2071 | 1.65748 | ||||||||
\(251\) | 5.45539 | 0.344341 | 0.172171 | − | 0.985067i | \(-0.444922\pi\) | ||||
0.172171 | + | 0.985067i | \(0.444922\pi\) | |||||||
\(252\) | −16.8558 | −1.06181 | ||||||||
\(253\) | −6.12194 | −0.384883 | ||||||||
\(254\) | 39.0532 | 2.45042 | ||||||||
\(255\) | 10.3356 | 0.647240 | ||||||||
\(256\) | −1.40133 | −0.0875829 | ||||||||
\(257\) | −21.7313 | −1.35556 | −0.677780 | − | 0.735265i | \(-0.737058\pi\) | ||||
−0.677780 | + | 0.735265i | \(0.737058\pi\) | |||||||
\(258\) | −30.1793 | −1.87888 | ||||||||
\(259\) | 3.06154 | 0.190235 | ||||||||
\(260\) | −0.966470 | −0.0599379 | ||||||||
\(261\) | 4.39879 | 0.272278 | ||||||||
\(262\) | 23.6150 | 1.45894 | ||||||||
\(263\) | −13.2484 | −0.816930 | −0.408465 | − | 0.912774i | \(-0.633936\pi\) | ||||
−0.408465 | + | 0.912774i | \(0.633936\pi\) | |||||||
\(264\) | 5.71697 | 0.351855 | ||||||||
\(265\) | −22.4808 | −1.38098 | ||||||||
\(266\) | −43.3763 | −2.65957 | ||||||||
\(267\) | 30.6226 | 1.87407 | ||||||||
\(268\) | −5.27687 | −0.322336 | ||||||||
\(269\) | 19.6607 | 1.19874 | 0.599368 | − | 0.800474i | \(-0.295419\pi\) | ||||
0.599368 | + | 0.800474i | \(0.295419\pi\) | |||||||
\(270\) | 8.05506 | 0.490215 | ||||||||
\(271\) | 22.2540 | 1.35184 | 0.675918 | − | 0.736976i | \(-0.263747\pi\) | ||||
0.675918 | + | 0.736976i | \(0.263747\pi\) | |||||||
\(272\) | −5.44083 | −0.329899 | ||||||||
\(273\) | 1.45011 | 0.0877644 | ||||||||
\(274\) | −37.3903 | −2.25883 | ||||||||
\(275\) | 3.51927 | 0.212220 | ||||||||
\(276\) | 23.8179 | 1.43367 | ||||||||
\(277\) | 2.32516 | 0.139705 | 0.0698527 | − | 0.997557i | \(-0.477747\pi\) | ||||
0.0698527 | + | 0.997557i | \(0.477747\pi\) | |||||||
\(278\) | 37.6559 | 2.25845 | ||||||||
\(279\) | 13.8724 | 0.830517 | ||||||||
\(280\) | 8.25022 | 0.493045 | ||||||||
\(281\) | 18.3593 | 1.09522 | 0.547612 | − | 0.836733i | \(-0.315537\pi\) | ||||
0.547612 | + | 0.836733i | \(0.315537\pi\) | |||||||
\(282\) | 1.71863 | 0.102343 | ||||||||
\(283\) | −5.84818 | −0.347638 | −0.173819 | − | 0.984778i | \(-0.555611\pi\) | ||||
−0.173819 | + | 0.984778i | \(0.555611\pi\) | |||||||
\(284\) | 16.4752 | 0.977624 | ||||||||
\(285\) | −24.2243 | −1.43493 | ||||||||
\(286\) | −0.727437 | −0.0430142 | ||||||||
\(287\) | −3.51925 | −0.207735 | ||||||||
\(288\) | 15.0670 | 0.887830 | ||||||||
\(289\) | −9.29639 | −0.546847 | ||||||||
\(290\) | −7.94480 | −0.466535 | ||||||||
\(291\) | −10.3757 | −0.608233 | ||||||||
\(292\) | −22.8472 | −1.33703 | ||||||||
\(293\) | −20.4865 | −1.19683 | −0.598416 | − | 0.801186i | \(-0.704203\pi\) | ||||
−0.598416 | + | 0.801186i | \(0.704203\pi\) | |||||||
\(294\) | −11.5647 | −0.674467 | ||||||||
\(295\) | 5.60223 | 0.326174 | ||||||||
\(296\) | 1.61926 | 0.0941177 | ||||||||
\(297\) | 3.50655 | 0.203471 | ||||||||
\(298\) | 24.8324 | 1.43850 | ||||||||
\(299\) | −0.821298 | −0.0474969 | ||||||||
\(300\) | −13.6920 | −0.790508 | ||||||||
\(301\) | −18.9592 | −1.09279 | ||||||||
\(302\) | −2.87386 | −0.165372 | ||||||||
\(303\) | 10.0759 | 0.578844 | ||||||||
\(304\) | 12.7521 | 0.731383 | ||||||||
\(305\) | 2.38415 | 0.136516 | ||||||||
\(306\) | −12.1311 | −0.693492 | ||||||||
\(307\) | −13.3681 | −0.762957 | −0.381478 | − | 0.924378i | \(-0.624585\pi\) | ||||
−0.381478 | + | 0.924378i | \(0.624585\pi\) | |||||||
\(308\) | 13.2529 | 0.755152 | ||||||||
\(309\) | −4.28910 | −0.243998 | ||||||||
\(310\) | −25.0553 | −1.42305 | ||||||||
\(311\) | 14.0947 | 0.799236 | 0.399618 | − | 0.916682i | \(-0.369143\pi\) | ||||
0.399618 | + | 0.916682i | \(0.369143\pi\) | |||||||
\(312\) | 0.766967 | 0.0434210 | ||||||||
\(313\) | 16.6098 | 0.938839 | 0.469419 | − | 0.882975i | \(-0.344463\pi\) | ||||
0.469419 | + | 0.882975i | \(0.344463\pi\) | |||||||
\(314\) | 35.4314 | 1.99951 | ||||||||
\(315\) | −10.2248 | −0.576102 | ||||||||
\(316\) | −21.0327 | −1.18318 | ||||||||
\(317\) | −0.563916 | −0.0316727 | −0.0158363 | − | 0.999875i | \(-0.505041\pi\) | ||||
−0.0158363 | + | 0.999875i | \(0.505041\pi\) | |||||||
\(318\) | 65.8314 | 3.69164 | ||||||||
\(319\) | −3.45855 | −0.193642 | ||||||||
\(320\) | −20.6884 | −1.15651 | ||||||||
\(321\) | 10.2904 | 0.574356 | ||||||||
\(322\) | 25.8708 | 1.44173 | ||||||||
\(323\) | −18.0555 | −1.00464 | ||||||||
\(324\) | −30.1595 | −1.67553 | ||||||||
\(325\) | 0.472132 | 0.0261892 | ||||||||
\(326\) | 2.17795 | 0.120626 | ||||||||
\(327\) | −27.9856 | −1.54761 | ||||||||
\(328\) | −1.86135 | −0.102776 | ||||||||
\(329\) | 1.07968 | 0.0595246 | ||||||||
\(330\) | 12.7969 | 0.704446 | ||||||||
\(331\) | 24.1833 | 1.32924 | 0.664618 | − | 0.747183i | \(-0.268594\pi\) | ||||
0.664618 | + | 0.747183i | \(0.268594\pi\) | |||||||
\(332\) | 5.61498 | 0.308162 | ||||||||
\(333\) | −2.00681 | −0.109973 | ||||||||
\(334\) | 26.0373 | 1.42470 | ||||||||
\(335\) | −3.20097 | −0.174888 | ||||||||
\(336\) | 13.4289 | 0.732604 | ||||||||
\(337\) | 13.8672 | 0.755394 | 0.377697 | − | 0.925929i | \(-0.376716\pi\) | ||||
0.377697 | + | 0.925929i | \(0.376716\pi\) | |||||||
\(338\) | 28.2158 | 1.53474 | ||||||||
\(339\) | 24.1031 | 1.30910 | ||||||||
\(340\) | 12.6723 | 0.687254 | ||||||||
\(341\) | −10.9072 | −0.590656 | ||||||||
\(342\) | 28.4327 | 1.53747 | ||||||||
\(343\) | 14.1656 | 0.764872 | ||||||||
\(344\) | −10.0276 | −0.540653 | ||||||||
\(345\) | 14.4481 | 0.777858 | ||||||||
\(346\) | 38.5492 | 2.07242 | ||||||||
\(347\) | 8.73119 | 0.468715 | 0.234357 | − | 0.972150i | \(-0.424701\pi\) | ||||
0.234357 | + | 0.972150i | \(0.424701\pi\) | |||||||
\(348\) | 13.4558 | 0.721306 | ||||||||
\(349\) | 25.6201 | 1.37141 | 0.685706 | − | 0.727879i | \(-0.259494\pi\) | ||||
0.685706 | + | 0.727879i | \(0.259494\pi\) | |||||||
\(350\) | −14.8721 | −0.794949 | ||||||||
\(351\) | 0.470426 | 0.0251095 | ||||||||
\(352\) | −11.8464 | −0.631417 | ||||||||
\(353\) | 15.3174 | 0.815260 | 0.407630 | − | 0.913147i | \(-0.366355\pi\) | ||||
0.407630 | + | 0.913147i | \(0.366355\pi\) | |||||||
\(354\) | −16.4052 | −0.871928 | ||||||||
\(355\) | 9.99395 | 0.530424 | ||||||||
\(356\) | 37.5459 | 1.98993 | ||||||||
\(357\) | −19.0138 | −1.00631 | ||||||||
\(358\) | 32.5418 | 1.71989 | ||||||||
\(359\) | −10.2809 | −0.542604 | −0.271302 | − | 0.962494i | \(-0.587454\pi\) | ||||
−0.271302 | + | 0.962494i | \(0.587454\pi\) | |||||||
\(360\) | −5.40794 | −0.285023 | ||||||||
\(361\) | 23.3182 | 1.22727 | ||||||||
\(362\) | −12.9545 | −0.680873 | ||||||||
\(363\) | −19.0427 | −0.999483 | ||||||||
\(364\) | 1.77796 | 0.0931902 | ||||||||
\(365\) | −13.8592 | −0.725424 | ||||||||
\(366\) | −6.98161 | −0.364934 | ||||||||
\(367\) | −7.14373 | −0.372900 | −0.186450 | − | 0.982464i | \(-0.559698\pi\) | ||||
−0.186450 | + | 0.982464i | \(0.559698\pi\) | |||||||
\(368\) | −7.60571 | −0.396475 | ||||||||
\(369\) | 2.30683 | 0.120089 | ||||||||
\(370\) | 3.62457 | 0.188432 | ||||||||
\(371\) | 41.3565 | 2.14712 | ||||||||
\(372\) | 42.4352 | 2.20016 | ||||||||
\(373\) | −3.14111 | −0.162640 | −0.0813202 | − | 0.996688i | \(-0.525914\pi\) | ||||
−0.0813202 | + | 0.996688i | \(0.525914\pi\) | |||||||
\(374\) | 9.53813 | 0.493205 | ||||||||
\(375\) | −26.9247 | −1.39039 | ||||||||
\(376\) | 0.571046 | 0.0294495 | ||||||||
\(377\) | −0.463987 | −0.0238965 | ||||||||
\(378\) | −14.8184 | −0.762176 | ||||||||
\(379\) | 8.36914 | 0.429894 | 0.214947 | − | 0.976626i | \(-0.431042\pi\) | ||||
0.214947 | + | 0.976626i | \(0.431042\pi\) | |||||||
\(380\) | −29.7011 | −1.52364 | ||||||||
\(381\) | −40.1226 | −2.05554 | ||||||||
\(382\) | 35.2976 | 1.80598 | ||||||||
\(383\) | 13.2778 | 0.678462 | 0.339231 | − | 0.940703i | \(-0.389833\pi\) | ||||
0.339231 | + | 0.940703i | \(0.389833\pi\) | |||||||
\(384\) | 26.9832 | 1.37698 | ||||||||
\(385\) | 8.03925 | 0.409718 | ||||||||
\(386\) | 29.0537 | 1.47879 | ||||||||
\(387\) | 12.4276 | 0.631730 | ||||||||
\(388\) | −12.7215 | −0.645835 | ||||||||
\(389\) | −32.2691 | −1.63611 | −0.818053 | − | 0.575143i | \(-0.804947\pi\) | ||||
−0.818053 | + | 0.575143i | \(0.804947\pi\) | |||||||
\(390\) | 1.71678 | 0.0869328 | ||||||||
\(391\) | 10.7688 | 0.544603 | ||||||||
\(392\) | −3.84258 | −0.194080 | ||||||||
\(393\) | −24.2617 | −1.22384 | ||||||||
\(394\) | 29.6907 | 1.49580 | ||||||||
\(395\) | −12.7586 | −0.641953 | ||||||||
\(396\) | −8.68712 | −0.436544 | ||||||||
\(397\) | 33.3729 | 1.67494 | 0.837468 | − | 0.546486i | \(-0.184035\pi\) | ||||
0.837468 | + | 0.546486i | \(0.184035\pi\) | |||||||
\(398\) | −39.4206 | −1.97598 | ||||||||
\(399\) | 44.5640 | 2.23099 | ||||||||
\(400\) | 4.37223 | 0.218611 | ||||||||
\(401\) | −19.7770 | −0.987615 | −0.493808 | − | 0.869571i | \(-0.664395\pi\) | ||||
−0.493808 | + | 0.869571i | \(0.664395\pi\) | |||||||
\(402\) | 9.37354 | 0.467510 | ||||||||
\(403\) | −1.46327 | −0.0728905 | ||||||||
\(404\) | 12.3539 | 0.614630 | ||||||||
\(405\) | −18.2949 | −0.909080 | ||||||||
\(406\) | 14.6156 | 0.725358 | ||||||||
\(407\) | 1.57786 | 0.0782115 | ||||||||
\(408\) | −10.0565 | −0.497869 | ||||||||
\(409\) | −35.8166 | −1.77102 | −0.885508 | − | 0.464625i | \(-0.846189\pi\) | ||||
−0.885508 | + | 0.464625i | \(0.846189\pi\) | |||||||
\(410\) | −4.16645 | −0.205766 | ||||||||
\(411\) | 38.4141 | 1.89483 | ||||||||
\(412\) | −5.25881 | −0.259083 | ||||||||
\(413\) | −10.3061 | −0.507129 | ||||||||
\(414\) | −16.9581 | −0.833444 | ||||||||
\(415\) | 3.40608 | 0.167198 | ||||||||
\(416\) | −1.58927 | −0.0779206 | ||||||||
\(417\) | −38.6870 | −1.89451 | ||||||||
\(418\) | −22.3553 | −1.09343 | ||||||||
\(419\) | 5.47375 | 0.267410 | 0.133705 | − | 0.991021i | \(-0.457313\pi\) | ||||
0.133705 | + | 0.991021i | \(0.457313\pi\) | |||||||
\(420\) | −31.2774 | −1.52618 | ||||||||
\(421\) | −1.44517 | −0.0704333 | −0.0352167 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352167 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(422\) | −5.37719 | −0.261757 | ||||||||
\(423\) | −0.707718 | −0.0344104 | ||||||||
\(424\) | 21.8737 | 1.06228 | ||||||||
\(425\) | −6.19059 | −0.300287 | ||||||||
\(426\) | −29.2657 | −1.41793 | ||||||||
\(427\) | −4.38598 | −0.212252 | ||||||||
\(428\) | 12.6170 | 0.609864 | ||||||||
\(429\) | 0.747356 | 0.0360827 | ||||||||
\(430\) | −22.4459 | −1.08244 | ||||||||
\(431\) | 2.66243 | 0.128245 | 0.0641224 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641224 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(432\) | 4.35643 | 0.209599 | ||||||||
\(433\) | 21.1460 | 1.01621 | 0.508106 | − | 0.861295i | \(-0.330346\pi\) | ||||
0.508106 | + | 0.861295i | \(0.330346\pi\) | |||||||
\(434\) | 46.0928 | 2.21252 | ||||||||
\(435\) | 8.16235 | 0.391355 | ||||||||
\(436\) | −34.3128 | −1.64328 | ||||||||
\(437\) | −25.2398 | −1.20738 | ||||||||
\(438\) | 40.5844 | 1.93920 | ||||||||
\(439\) | −0.970109 | −0.0463008 | −0.0231504 | − | 0.999732i | \(-0.507370\pi\) | ||||
−0.0231504 | + | 0.999732i | \(0.507370\pi\) | |||||||
\(440\) | 4.25200 | 0.202706 | ||||||||
\(441\) | 4.76225 | 0.226774 | ||||||||
\(442\) | 1.27960 | 0.0608644 | ||||||||
\(443\) | 6.05898 | 0.287871 | 0.143935 | − | 0.989587i | \(-0.454024\pi\) | ||||
0.143935 | + | 0.989587i | \(0.454024\pi\) | |||||||
\(444\) | −6.13878 | −0.291334 | ||||||||
\(445\) | 22.7756 | 1.07966 | ||||||||
\(446\) | −21.1465 | −1.00132 | ||||||||
\(447\) | −25.5124 | −1.20669 | ||||||||
\(448\) | 38.0591 | 1.79812 | ||||||||
\(449\) | −20.2042 | −0.953496 | −0.476748 | − | 0.879040i | \(-0.658185\pi\) | ||||
−0.476748 | + | 0.879040i | \(0.658185\pi\) | |||||||
\(450\) | 9.74854 | 0.459551 | ||||||||
\(451\) | −1.81375 | −0.0854061 | ||||||||
\(452\) | 29.5525 | 1.39003 | ||||||||
\(453\) | 2.95255 | 0.138723 | ||||||||
\(454\) | 53.3925 | 2.50584 | ||||||||
\(455\) | 1.07852 | 0.0505617 | ||||||||
\(456\) | 23.5701 | 1.10377 | ||||||||
\(457\) | −34.6527 | −1.62098 | −0.810492 | − | 0.585750i | \(-0.800800\pi\) | ||||
−0.810492 | + | 0.585750i | \(0.800800\pi\) | |||||||
\(458\) | 56.1102 | 2.62186 | ||||||||
\(459\) | −6.16822 | −0.287908 | ||||||||
\(460\) | 17.7146 | 0.825947 | ||||||||
\(461\) | 28.2054 | 1.31365 | 0.656827 | − | 0.754041i | \(-0.271898\pi\) | ||||
0.656827 | + | 0.754041i | \(0.271898\pi\) | |||||||
\(462\) | −23.5417 | −1.09526 | ||||||||
\(463\) | −11.8701 | −0.551650 | −0.275825 | − | 0.961208i | \(-0.588951\pi\) | ||||
−0.275825 | + | 0.961208i | \(0.588951\pi\) | |||||||
\(464\) | −4.29680 | −0.199474 | ||||||||
\(465\) | 25.7414 | 1.19373 | ||||||||
\(466\) | −7.23019 | −0.334932 | ||||||||
\(467\) | −16.8305 | −0.778822 | −0.389411 | − | 0.921064i | \(-0.627321\pi\) | ||||
−0.389411 | + | 0.921064i | \(0.627321\pi\) | |||||||
\(468\) | −1.16543 | −0.0538721 | ||||||||
\(469\) | 5.88864 | 0.271912 | ||||||||
\(470\) | 1.27823 | 0.0589605 | ||||||||
\(471\) | −36.4016 | −1.67730 | ||||||||
\(472\) | −5.45093 | −0.250899 | ||||||||
\(473\) | −9.77121 | −0.449281 | ||||||||
\(474\) | 37.3614 | 1.71607 | ||||||||
\(475\) | 14.5094 | 0.665735 | ||||||||
\(476\) | −23.3125 | −1.06853 | ||||||||
\(477\) | −27.1088 | −1.24123 | ||||||||
\(478\) | 60.5488 | 2.76944 | ||||||||
\(479\) | 21.0644 | 0.962459 | 0.481229 | − | 0.876595i | \(-0.340190\pi\) | ||||
0.481229 | + | 0.876595i | \(0.340190\pi\) | |||||||
\(480\) | 27.9581 | 1.27611 | ||||||||
\(481\) | 0.211680 | 0.00965176 | ||||||||
\(482\) | −25.4706 | −1.16015 | ||||||||
\(483\) | −26.5792 | −1.20940 | ||||||||
\(484\) | −23.3480 | −1.06127 | ||||||||
\(485\) | −7.71691 | −0.350407 | ||||||||
\(486\) | 39.0531 | 1.77148 | ||||||||
\(487\) | 4.03781 | 0.182971 | 0.0914853 | − | 0.995806i | \(-0.470839\pi\) | ||||
0.0914853 | + | 0.995806i | \(0.470839\pi\) | |||||||
\(488\) | −2.31976 | −0.105011 | ||||||||
\(489\) | −2.23759 | −0.101187 | ||||||||
\(490\) | −8.60125 | −0.388565 | ||||||||
\(491\) | −9.68684 | −0.437161 | −0.218580 | − | 0.975819i | \(-0.570143\pi\) | ||||
−0.218580 | + | 0.975819i | \(0.570143\pi\) | |||||||
\(492\) | 7.05654 | 0.318133 | ||||||||
\(493\) | 6.08378 | 0.274000 | ||||||||
\(494\) | −2.99910 | −0.134936 | ||||||||
\(495\) | −5.26965 | −0.236853 | ||||||||
\(496\) | −13.5507 | −0.608445 | ||||||||
\(497\) | −18.3853 | −0.824692 | ||||||||
\(498\) | −9.97415 | −0.446952 | ||||||||
\(499\) | 15.0909 | 0.675562 | 0.337781 | − | 0.941225i | \(-0.390324\pi\) | ||||
0.337781 | + | 0.941225i | \(0.390324\pi\) | |||||||
\(500\) | −33.0120 | −1.47634 | ||||||||
\(501\) | −26.7503 | −1.19511 | ||||||||
\(502\) | −11.8816 | −0.530301 | ||||||||
\(503\) | 18.0593 | 0.805223 | 0.402611 | − | 0.915371i | \(-0.368103\pi\) | ||||
0.402611 | + | 0.915371i | \(0.368103\pi\) | |||||||
\(504\) | 9.94865 | 0.443148 | ||||||||
\(505\) | 7.49394 | 0.333476 | ||||||||
\(506\) | 13.3333 | 0.592738 | ||||||||
\(507\) | −28.9884 | −1.28742 | ||||||||
\(508\) | −49.1937 | −2.18262 | ||||||||
\(509\) | 16.0031 | 0.709327 | 0.354663 | − | 0.934994i | \(-0.384596\pi\) | ||||
0.354663 | + | 0.934994i | \(0.384596\pi\) | |||||||
\(510\) | −22.5104 | −0.996779 | ||||||||
\(511\) | 25.4959 | 1.12787 | ||||||||
\(512\) | −21.0660 | −0.930997 | ||||||||
\(513\) | 14.4569 | 0.638289 | ||||||||
\(514\) | 47.3297 | 2.08762 | ||||||||
\(515\) | −3.19002 | −0.140569 | ||||||||
\(516\) | 38.0157 | 1.67355 | ||||||||
\(517\) | 0.556444 | 0.0244724 | ||||||||
\(518\) | −6.66790 | −0.292971 | ||||||||
\(519\) | −39.6047 | −1.73846 | ||||||||
\(520\) | 0.570432 | 0.0250151 | ||||||||
\(521\) | −29.4987 | −1.29236 | −0.646180 | − | 0.763185i | \(-0.723635\pi\) | ||||
−0.646180 | + | 0.763185i | \(0.723635\pi\) | |||||||
\(522\) | −9.58035 | −0.419321 | ||||||||
\(523\) | 20.1316 | 0.880295 | 0.440148 | − | 0.897925i | \(-0.354926\pi\) | ||||
0.440148 | + | 0.897925i | \(0.354926\pi\) | |||||||
\(524\) | −29.7469 | −1.29950 | ||||||||
\(525\) | 15.2794 | 0.666847 | ||||||||
\(526\) | 28.8543 | 1.25811 | ||||||||
\(527\) | 19.1863 | 0.835768 | ||||||||
\(528\) | 6.92096 | 0.301196 | ||||||||
\(529\) | −7.94630 | −0.345491 | ||||||||
\(530\) | 48.9621 | 2.12678 | ||||||||
\(531\) | 6.75553 | 0.293165 | ||||||||
\(532\) | 54.6393 | 2.36892 | ||||||||
\(533\) | −0.243326 | −0.0105396 | ||||||||
\(534\) | −66.6945 | −2.88615 | ||||||||
\(535\) | 7.65351 | 0.330890 | ||||||||
\(536\) | 3.11452 | 0.134527 | ||||||||
\(537\) | −33.4328 | −1.44273 | ||||||||
\(538\) | −42.8201 | −1.84611 | ||||||||
\(539\) | −3.74432 | −0.161279 | ||||||||
\(540\) | −10.1466 | −0.436642 | ||||||||
\(541\) | 20.4381 | 0.878704 | 0.439352 | − | 0.898315i | \(-0.355208\pi\) | ||||
0.439352 | + | 0.898315i | \(0.355208\pi\) | |||||||
\(542\) | −48.4683 | −2.08189 | ||||||||
\(543\) | 13.3092 | 0.571153 | ||||||||
\(544\) | 20.8385 | 0.893444 | ||||||||
\(545\) | −20.8143 | −0.891587 | ||||||||
\(546\) | −3.15826 | −0.135161 | ||||||||
\(547\) | 44.5050 | 1.90290 | 0.951448 | − | 0.307810i | \(-0.0995960\pi\) | ||||
0.951448 | + | 0.307810i | \(0.0995960\pi\) | |||||||
\(548\) | 47.0990 | 2.01197 | ||||||||
\(549\) | 2.87497 | 0.122701 | ||||||||
\(550\) | −7.66480 | −0.326828 | ||||||||
\(551\) | −14.2590 | −0.607455 | ||||||||
\(552\) | −14.0579 | −0.598343 | ||||||||
\(553\) | 23.4711 | 0.998095 | ||||||||
\(554\) | −5.06410 | −0.215153 | ||||||||
\(555\) | −3.72382 | −0.158067 | ||||||||
\(556\) | −47.4337 | −2.01164 | ||||||||
\(557\) | 18.7315 | 0.793679 | 0.396839 | − | 0.917888i | \(-0.370107\pi\) | ||||
0.396839 | + | 0.917888i | \(0.370107\pi\) | |||||||
\(558\) | −30.2134 | −1.27903 | ||||||||
\(559\) | −1.31087 | −0.0554439 | ||||||||
\(560\) | 9.98771 | 0.422058 | ||||||||
\(561\) | −9.79930 | −0.413727 | ||||||||
\(562\) | −39.9857 | −1.68669 | ||||||||
\(563\) | 1.82548 | 0.0769348 | 0.0384674 | − | 0.999260i | \(-0.487752\pi\) | ||||
0.0384674 | + | 0.999260i | \(0.487752\pi\) | |||||||
\(564\) | −2.16489 | −0.0911584 | ||||||||
\(565\) | 17.9267 | 0.754183 | ||||||||
\(566\) | 12.7371 | 0.535379 | ||||||||
\(567\) | 33.6560 | 1.41342 | ||||||||
\(568\) | −9.72404 | −0.408012 | ||||||||
\(569\) | −27.0464 | −1.13384 | −0.566922 | − | 0.823772i | \(-0.691866\pi\) | ||||
−0.566922 | + | 0.823772i | \(0.691866\pi\) | |||||||
\(570\) | 52.7595 | 2.20985 | ||||||||
\(571\) | 30.8653 | 1.29167 | 0.645835 | − | 0.763477i | \(-0.276509\pi\) | ||||
0.645835 | + | 0.763477i | \(0.276509\pi\) | |||||||
\(572\) | 0.916322 | 0.0383134 | ||||||||
\(573\) | −36.2641 | −1.51495 | ||||||||
\(574\) | 7.66476 | 0.319921 | ||||||||
\(575\) | −8.65379 | −0.360888 | ||||||||
\(576\) | −24.9474 | −1.03947 | ||||||||
\(577\) | 30.3918 | 1.26523 | 0.632614 | − | 0.774467i | \(-0.281982\pi\) | ||||
0.632614 | + | 0.774467i | \(0.281982\pi\) | |||||||
\(578\) | 20.2471 | 0.842169 | ||||||||
\(579\) | −29.8492 | −1.24049 | ||||||||
\(580\) | 10.0077 | 0.415549 | ||||||||
\(581\) | −6.26595 | −0.259955 | ||||||||
\(582\) | 22.5977 | 0.936706 | ||||||||
\(583\) | 21.3143 | 0.882749 | ||||||||
\(584\) | 13.4849 | 0.558009 | ||||||||
\(585\) | −0.706957 | −0.0292291 | ||||||||
\(586\) | 44.6185 | 1.84317 | ||||||||
\(587\) | 44.9641 | 1.85587 | 0.927934 | − | 0.372745i | \(-0.121584\pi\) | ||||
0.927934 | + | 0.372745i | \(0.121584\pi\) | |||||||
\(588\) | 14.5676 | 0.600757 | ||||||||
\(589\) | −44.9684 | −1.85289 | ||||||||
\(590\) | −12.2014 | −0.502323 | ||||||||
\(591\) | −30.5037 | −1.25475 | ||||||||
\(592\) | 1.96028 | 0.0805670 | ||||||||
\(593\) | 41.0025 | 1.68377 | 0.841885 | − | 0.539657i | \(-0.181446\pi\) | ||||
0.841885 | + | 0.539657i | \(0.181446\pi\) | |||||||
\(594\) | −7.63711 | −0.313354 | ||||||||
\(595\) | −14.1415 | −0.579744 | ||||||||
\(596\) | −31.2804 | −1.28129 | ||||||||
\(597\) | 40.5001 | 1.65756 | ||||||||
\(598\) | 1.78875 | 0.0731473 | ||||||||
\(599\) | 5.24433 | 0.214278 | 0.107139 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107139 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(600\) | 8.08133 | 0.329919 | ||||||||
\(601\) | −23.9038 | −0.975057 | −0.487528 | − | 0.873107i | \(-0.662101\pi\) | ||||
−0.487528 | + | 0.873107i | \(0.662101\pi\) | |||||||
\(602\) | 41.2923 | 1.68295 | ||||||||
\(603\) | −3.85994 | −0.157189 | ||||||||
\(604\) | 3.62008 | 0.147299 | ||||||||
\(605\) | −14.1630 | −0.575809 | ||||||||
\(606\) | −21.9448 | −0.891446 | ||||||||
\(607\) | −47.8565 | −1.94244 | −0.971218 | − | 0.238193i | \(-0.923445\pi\) | ||||
−0.971218 | + | 0.238193i | \(0.923445\pi\) | |||||||
\(608\) | −48.8409 | −1.98076 | ||||||||
\(609\) | −15.0158 | −0.608470 | ||||||||
\(610\) | −5.19257 | −0.210241 | ||||||||
\(611\) | 0.0746505 | 0.00302004 | ||||||||
\(612\) | 15.2811 | 0.617703 | ||||||||
\(613\) | −35.4248 | −1.43080 | −0.715398 | − | 0.698717i | \(-0.753754\pi\) | ||||
−0.715398 | + | 0.698717i | \(0.753754\pi\) | |||||||
\(614\) | 29.1151 | 1.17499 | ||||||||
\(615\) | 4.28053 | 0.172608 | ||||||||
\(616\) | −7.82214 | −0.315163 | ||||||||
\(617\) | −47.0432 | −1.89389 | −0.946944 | − | 0.321400i | \(-0.895847\pi\) | ||||
−0.946944 | + | 0.321400i | \(0.895847\pi\) | |||||||
\(618\) | 9.34145 | 0.375768 | ||||||||
\(619\) | 11.8891 | 0.477862 | 0.238931 | − | 0.971037i | \(-0.423203\pi\) | ||||
0.238931 | + | 0.971037i | \(0.423203\pi\) | |||||||
\(620\) | 31.5612 | 1.26753 | ||||||||
\(621\) | −8.62252 | −0.346010 | ||||||||
\(622\) | −30.6976 | −1.23086 | ||||||||
\(623\) | −41.8988 | −1.67864 | ||||||||
\(624\) | 0.928491 | 0.0371694 | ||||||||
\(625\) | −8.87322 | −0.354929 | ||||||||
\(626\) | −36.1753 | −1.44585 | ||||||||
\(627\) | 22.9674 | 0.917229 | ||||||||
\(628\) | −44.6315 | −1.78099 | ||||||||
\(629\) | −2.77554 | −0.110668 | ||||||||
\(630\) | 22.2691 | 0.887223 | ||||||||
\(631\) | 20.8728 | 0.830932 | 0.415466 | − | 0.909609i | \(-0.363618\pi\) | ||||
0.415466 | + | 0.909609i | \(0.363618\pi\) | |||||||
\(632\) | 12.4140 | 0.493802 | ||||||||
\(633\) | 5.52443 | 0.219576 | ||||||||
\(634\) | 1.22818 | 0.0487774 | ||||||||
\(635\) | −29.8412 | −1.18421 | ||||||||
\(636\) | −82.9251 | −3.28820 | ||||||||
\(637\) | −0.502324 | −0.0199028 | ||||||||
\(638\) | 7.53256 | 0.298217 | ||||||||
\(639\) | 12.0514 | 0.476744 | ||||||||
\(640\) | 20.0688 | 0.793287 | ||||||||
\(641\) | 6.55250 | 0.258808 | 0.129404 | − | 0.991592i | \(-0.458694\pi\) | ||||
0.129404 | + | 0.991592i | \(0.458694\pi\) | |||||||
\(642\) | −22.4121 | −0.884534 | ||||||||
\(643\) | 0.298843 | 0.0117852 | 0.00589260 | − | 0.999983i | \(-0.498124\pi\) | ||||
0.00589260 | + | 0.999983i | \(0.498124\pi\) | |||||||
\(644\) | −32.5884 | −1.28416 | ||||||||
\(645\) | 23.0605 | 0.908007 | ||||||||
\(646\) | 39.3241 | 1.54719 | ||||||||
\(647\) | −27.4302 | −1.07839 | −0.539196 | − | 0.842180i | \(-0.681272\pi\) | ||||
−0.539196 | + | 0.842180i | \(0.681272\pi\) | |||||||
\(648\) | 17.8008 | 0.699281 | ||||||||
\(649\) | −5.31154 | −0.208496 | ||||||||
\(650\) | −1.02828 | −0.0403325 | ||||||||
\(651\) | −47.3549 | −1.85599 | ||||||||
\(652\) | −2.74348 | −0.107443 | ||||||||
\(653\) | 16.8664 | 0.660032 | 0.330016 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330016 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(654\) | 60.9514 | 2.38339 | ||||||||
\(655\) | −18.0446 | −0.705061 | ||||||||
\(656\) | −2.25335 | −0.0879784 | ||||||||
\(657\) | −16.7123 | −0.652010 | ||||||||
\(658\) | −2.35149 | −0.0916705 | ||||||||
\(659\) | 14.9053 | 0.580629 | 0.290314 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290314 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(660\) | −16.1197 | −0.627460 | ||||||||
\(661\) | 28.9641 | 1.12657 | 0.563287 | − | 0.826261i | \(-0.309536\pi\) | ||||
0.563287 | + | 0.826261i | \(0.309536\pi\) | |||||||
\(662\) | −52.6702 | −2.04708 | ||||||||
\(663\) | −1.31464 | −0.0510564 | ||||||||
\(664\) | −3.31409 | −0.128612 | ||||||||
\(665\) | 33.1445 | 1.28529 | ||||||||
\(666\) | 4.37074 | 0.169363 | ||||||||
\(667\) | 8.50449 | 0.329295 | ||||||||
\(668\) | −32.7981 | −1.26900 | ||||||||
\(669\) | 21.7256 | 0.839960 | ||||||||
\(670\) | 6.97157 | 0.269335 | ||||||||
\(671\) | −2.26045 | −0.0872635 | ||||||||
\(672\) | −51.4329 | −1.98407 | ||||||||
\(673\) | −22.1710 | −0.854629 | −0.427314 | − | 0.904103i | \(-0.640540\pi\) | ||||
−0.427314 | + | 0.904103i | \(0.640540\pi\) | |||||||
\(674\) | −30.2021 | −1.16334 | ||||||||
\(675\) | 4.95675 | 0.190786 | ||||||||
\(676\) | −35.5423 | −1.36701 | ||||||||
\(677\) | −7.24291 | −0.278368 | −0.139184 | − | 0.990267i | \(-0.544448\pi\) | ||||
−0.139184 | + | 0.990267i | \(0.544448\pi\) | |||||||
\(678\) | −52.4955 | −2.01608 | ||||||||
\(679\) | 14.1963 | 0.544805 | ||||||||
\(680\) | −7.47949 | −0.286825 | ||||||||
\(681\) | −54.8545 | −2.10203 | ||||||||
\(682\) | 23.7553 | 0.909637 | ||||||||
\(683\) | −30.9066 | −1.18261 | −0.591305 | − | 0.806448i | \(-0.701387\pi\) | ||||
−0.591305 | + | 0.806448i | \(0.701387\pi\) | |||||||
\(684\) | −35.8155 | −1.36944 | ||||||||
\(685\) | 28.5705 | 1.09162 | ||||||||
\(686\) | −30.8521 | −1.17794 | ||||||||
\(687\) | −57.6466 | −2.19936 | ||||||||
\(688\) | −12.1394 | −0.462812 | ||||||||
\(689\) | 2.85945 | 0.108936 | ||||||||
\(690\) | −31.4672 | −1.19794 | ||||||||
\(691\) | −25.6614 | −0.976206 | −0.488103 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488103 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(692\) | −48.5588 | −1.84593 | ||||||||
\(693\) | 9.69425 | 0.368254 | ||||||||
\(694\) | −19.0161 | −0.721842 | ||||||||
\(695\) | −28.7735 | −1.09144 | ||||||||
\(696\) | −7.94190 | −0.301037 | ||||||||
\(697\) | 3.19048 | 0.120848 | ||||||||
\(698\) | −55.7994 | −2.11204 | ||||||||
\(699\) | 7.42817 | 0.280959 | ||||||||
\(700\) | 18.7338 | 0.708072 | ||||||||
\(701\) | 2.09900 | 0.0792781 | 0.0396390 | − | 0.999214i | \(-0.487379\pi\) | ||||
0.0396390 | + | 0.999214i | \(0.487379\pi\) | |||||||
\(702\) | −1.02457 | −0.0386698 | ||||||||
\(703\) | 6.50524 | 0.245350 | ||||||||
\(704\) | 19.6149 | 0.739264 | ||||||||
\(705\) | −1.31323 | −0.0494593 | ||||||||
\(706\) | −33.3605 | −1.25554 | ||||||||
\(707\) | −13.7861 | −0.518481 | ||||||||
\(708\) | 20.6650 | 0.776638 | ||||||||
\(709\) | −5.27148 | −0.197974 | −0.0989872 | − | 0.995089i | \(-0.531560\pi\) | ||||
−0.0989872 | + | 0.995089i | \(0.531560\pi\) | |||||||
\(710\) | −21.7664 | −0.816877 | ||||||||
\(711\) | −15.3851 | −0.576987 | ||||||||
\(712\) | −22.1604 | −0.830498 | ||||||||
\(713\) | 26.8204 | 1.00443 | ||||||||
\(714\) | 41.4111 | 1.54977 | ||||||||
\(715\) | 0.555846 | 0.0207875 | ||||||||
\(716\) | −40.9915 | −1.53193 | ||||||||
\(717\) | −62.2068 | −2.32315 | ||||||||
\(718\) | 22.3913 | 0.835634 | ||||||||
\(719\) | 19.7331 | 0.735920 | 0.367960 | − | 0.929842i | \(-0.380056\pi\) | ||||
0.367960 | + | 0.929842i | \(0.380056\pi\) | |||||||
\(720\) | −6.54685 | −0.243987 | ||||||||
\(721\) | 5.86848 | 0.218554 | ||||||||
\(722\) | −50.7859 | −1.89006 | ||||||||
\(723\) | 26.1680 | 0.973200 | ||||||||
\(724\) | 16.3183 | 0.606463 | ||||||||
\(725\) | −4.88890 | −0.181569 | ||||||||
\(726\) | 41.4741 | 1.53925 | ||||||||
\(727\) | 11.9747 | 0.444118 | 0.222059 | − | 0.975033i | \(-0.428722\pi\) | ||||
0.222059 | + | 0.975033i | \(0.428722\pi\) | |||||||
\(728\) | −1.04939 | −0.0388930 | ||||||||
\(729\) | −7.14303 | −0.264557 | ||||||||
\(730\) | 30.1847 | 1.11719 | ||||||||
\(731\) | 17.1881 | 0.635724 | ||||||||
\(732\) | 8.79445 | 0.325052 | ||||||||
\(733\) | 44.7076 | 1.65131 | 0.825656 | − | 0.564174i | \(-0.190805\pi\) | ||||
0.825656 | + | 0.564174i | \(0.190805\pi\) | |||||||
\(734\) | 15.5587 | 0.574282 | ||||||||
\(735\) | 8.83677 | 0.325949 | ||||||||
\(736\) | 29.1301 | 1.07375 | ||||||||
\(737\) | 3.03488 | 0.111791 | ||||||||
\(738\) | −5.02417 | −0.184942 | ||||||||
\(739\) | 37.9602 | 1.39639 | 0.698194 | − | 0.715908i | \(-0.253987\pi\) | ||||
0.698194 | + | 0.715908i | \(0.253987\pi\) | |||||||
\(740\) | −4.56572 | −0.167839 | ||||||||
\(741\) | 3.08122 | 0.113192 | ||||||||
\(742\) | −90.0726 | −3.30667 | ||||||||
\(743\) | −5.70078 | −0.209141 | −0.104571 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104571 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(744\) | −25.0462 | −0.918239 | ||||||||
\(745\) | −18.9748 | −0.695184 | ||||||||
\(746\) | 6.84118 | 0.250473 | ||||||||
\(747\) | 4.10727 | 0.150277 | ||||||||
\(748\) | −12.0148 | −0.439304 | ||||||||
\(749\) | −14.0797 | −0.514461 | ||||||||
\(750\) | 58.6408 | 2.14126 | ||||||||
\(751\) | −20.6289 | −0.752760 | −0.376380 | − | 0.926465i | \(-0.622831\pi\) | ||||
−0.376380 | + | 0.926465i | \(0.622831\pi\) | |||||||
\(752\) | 0.691309 | 0.0252094 | ||||||||
\(753\) | 12.2069 | 0.444846 | ||||||||
\(754\) | 1.01054 | 0.0368017 | ||||||||
\(755\) | 2.19596 | 0.0799192 | ||||||||
\(756\) | 18.6661 | 0.678881 | ||||||||
\(757\) | 18.2338 | 0.662720 | 0.331360 | − | 0.943504i | \(-0.392493\pi\) | ||||
0.331360 | + | 0.943504i | \(0.392493\pi\) | |||||||
\(758\) | −18.2276 | −0.662056 | ||||||||
\(759\) | −13.6984 | −0.497221 | ||||||||
\(760\) | 17.5303 | 0.635890 | ||||||||
\(761\) | −27.4534 | −0.995184 | −0.497592 | − | 0.867411i | \(-0.665782\pi\) | ||||
−0.497592 | + | 0.867411i | \(0.665782\pi\) | |||||||
\(762\) | 87.3851 | 3.16563 | ||||||||
\(763\) | 38.2908 | 1.38622 | ||||||||
\(764\) | −44.4629 | −1.60861 | ||||||||
\(765\) | 9.26960 | 0.335143 | ||||||||
\(766\) | −28.9183 | −1.04486 | ||||||||
\(767\) | −0.712577 | −0.0257297 | ||||||||
\(768\) | −3.13560 | −0.113146 | ||||||||
\(769\) | −31.0418 | −1.11940 | −0.559699 | − | 0.828696i | \(-0.689083\pi\) | ||||
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(770\) | −17.5091 | −0.630985 | ||||||||
\(771\) | −48.6257 | −1.75121 | ||||||||
\(772\) | −36.5978 | −1.31718 | ||||||||
\(773\) | 21.1360 | 0.760210 | 0.380105 | − | 0.924943i | \(-0.375888\pi\) | ||||
0.380105 | + | 0.924943i | \(0.375888\pi\) | |||||||
\(774\) | −27.0667 | −0.972893 | ||||||||
\(775\) | −15.4180 | −0.553832 | ||||||||
\(776\) | 7.50850 | 0.269539 | ||||||||
\(777\) | 6.85048 | 0.245760 | ||||||||
\(778\) | 70.2805 | 2.51968 | ||||||||
\(779\) | −7.47779 | −0.267920 | ||||||||
\(780\) | −2.16256 | −0.0774322 | ||||||||
\(781\) | −9.47539 | −0.339056 | ||||||||
\(782\) | −23.4540 | −0.838714 | ||||||||
\(783\) | −4.87124 | −0.174084 | ||||||||
\(784\) | −4.65183 | −0.166137 | ||||||||
\(785\) | −27.0737 | −0.966302 | ||||||||
\(786\) | 52.8407 | 1.88477 | ||||||||
\(787\) | 39.9800 | 1.42513 | 0.712567 | − | 0.701604i | \(-0.247532\pi\) | ||||
0.712567 | + | 0.701604i | \(0.247532\pi\) | |||||||
\(788\) | −37.4002 | −1.33233 | ||||||||
\(789\) | −29.6444 | −1.05537 | ||||||||
\(790\) | 27.7876 | 0.988637 | ||||||||
\(791\) | −32.9787 | −1.17259 | ||||||||
\(792\) | 5.12733 | 0.182192 | ||||||||
\(793\) | −0.303253 | −0.0107688 | ||||||||
\(794\) | −72.6845 | −2.57948 | ||||||||
\(795\) | −50.3028 | −1.78406 | ||||||||
\(796\) | 49.6566 | 1.76003 | ||||||||
\(797\) | −50.5254 | −1.78970 | −0.894850 | − | 0.446367i | \(-0.852718\pi\) | ||||
−0.894850 | + | 0.446367i | \(0.852718\pi\) | |||||||
\(798\) | −97.0583 | −3.43583 | ||||||||
\(799\) | −0.978816 | −0.0346280 | ||||||||
\(800\) | −16.7457 | −0.592052 | ||||||||
\(801\) | 27.4642 | 0.970401 | ||||||||
\(802\) | 43.0733 | 1.52097 | ||||||||
\(803\) | 13.1401 | 0.463704 | ||||||||
\(804\) | −11.8075 | −0.416417 | ||||||||
\(805\) | −19.7683 | −0.696742 | ||||||||
\(806\) | 3.18692 | 0.112255 | ||||||||
\(807\) | 43.9926 | 1.54861 | ||||||||
\(808\) | −7.29155 | −0.256516 | ||||||||
\(809\) | −14.8578 | −0.522371 | −0.261186 | − | 0.965289i | \(-0.584113\pi\) | ||||
−0.261186 | + | 0.965289i | \(0.584113\pi\) | |||||||
\(810\) | 39.8454 | 1.40002 | ||||||||
\(811\) | −9.81834 | −0.344769 | −0.172384 | − | 0.985030i | \(-0.555147\pi\) | ||||
−0.172384 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(812\) | −18.4106 | −0.646086 | ||||||||
\(813\) | 49.7954 | 1.74640 | ||||||||
\(814\) | −3.43650 | −0.120449 | ||||||||
\(815\) | −1.66421 | −0.0582947 | ||||||||
\(816\) | −12.1743 | −0.426187 | ||||||||
\(817\) | −40.2851 | −1.40940 | ||||||||
\(818\) | 78.0068 | 2.72744 | ||||||||
\(819\) | 1.30055 | 0.0454448 | ||||||||
\(820\) | 5.24831 | 0.183279 | ||||||||
\(821\) | −46.2810 | −1.61522 | −0.807609 | − | 0.589719i | \(-0.799239\pi\) | ||||
−0.807609 | + | 0.589719i | \(0.799239\pi\) | |||||||
\(822\) | −83.6641 | −2.91812 | ||||||||
\(823\) | −37.3876 | −1.30325 | −0.651624 | − | 0.758542i | \(-0.725912\pi\) | ||||
−0.651624 | + | 0.758542i | \(0.725912\pi\) | |||||||
\(824\) | 3.10386 | 0.108128 | ||||||||
\(825\) | 7.87468 | 0.274161 | ||||||||
\(826\) | 22.4461 | 0.781001 | ||||||||
\(827\) | 20.1688 | 0.701340 | 0.350670 | − | 0.936499i | \(-0.385954\pi\) | ||||
0.350670 | + | 0.936499i | \(0.385954\pi\) | |||||||
\(828\) | 21.3614 | 0.742360 | ||||||||
\(829\) | −23.9360 | −0.831331 | −0.415665 | − | 0.909518i | \(-0.636451\pi\) | ||||
−0.415665 | + | 0.909518i | \(0.636451\pi\) | |||||||
\(830\) | −7.41827 | −0.257492 | ||||||||
\(831\) | 5.20276 | 0.180482 | ||||||||
\(832\) | 2.63146 | 0.0912295 | ||||||||
\(833\) | 6.58646 | 0.228207 | ||||||||
\(834\) | 84.2586 | 2.91764 | ||||||||
\(835\) | −19.8955 | −0.688513 | ||||||||
\(836\) | 28.1600 | 0.973934 | ||||||||
\(837\) | −15.3623 | −0.530999 | ||||||||
\(838\) | −11.9216 | −0.411824 | ||||||||
\(839\) | −23.9225 | −0.825895 | −0.412948 | − | 0.910755i | \(-0.635501\pi\) | ||||
−0.412948 | + | 0.910755i | \(0.635501\pi\) | |||||||
\(840\) | 18.4606 | 0.636951 | ||||||||
\(841\) | −24.1954 | −0.834326 | ||||||||
\(842\) | 3.14752 | 0.108471 | ||||||||
\(843\) | 41.0806 | 1.41489 | ||||||||
\(844\) | 6.77343 | 0.233151 | ||||||||
\(845\) | −21.5601 | −0.741691 | ||||||||
\(846\) | 1.54138 | 0.0529936 | ||||||||
\(847\) | 26.0548 | 0.895255 | ||||||||
\(848\) | 26.4802 | 0.909335 | ||||||||
\(849\) | −13.0858 | −0.449105 | ||||||||
\(850\) | 13.4828 | 0.462456 | ||||||||
\(851\) | −3.87991 | −0.133002 | ||||||||
\(852\) | 36.8648 | 1.26297 | ||||||||
\(853\) | 36.5859 | 1.25268 | 0.626339 | − | 0.779551i | \(-0.284553\pi\) | ||||
0.626339 | + | 0.779551i | \(0.284553\pi\) | |||||||
\(854\) | 9.55246 | 0.326878 | ||||||||
\(855\) | −21.7259 | −0.743010 | ||||||||
\(856\) | −7.44681 | −0.254527 | ||||||||
\(857\) | −2.64142 | −0.0902292 | −0.0451146 | − | 0.998982i | \(-0.514365\pi\) | ||||
−0.0451146 | + | 0.998982i | \(0.514365\pi\) | |||||||
\(858\) | −1.62771 | −0.0555689 | ||||||||
\(859\) | −25.5410 | −0.871447 | −0.435723 | − | 0.900081i | \(-0.643507\pi\) | ||||
−0.435723 | + | 0.900081i | \(0.643507\pi\) | |||||||
\(860\) | 28.2742 | 0.964141 | ||||||||
\(861\) | −7.87464 | −0.268367 | ||||||||
\(862\) | −5.79865 | −0.197503 | ||||||||
\(863\) | 16.9554 | 0.577168 | 0.288584 | − | 0.957455i | \(-0.406816\pi\) | ||||
0.288584 | + | 0.957455i | \(0.406816\pi\) | |||||||
\(864\) | −16.6852 | −0.567643 | ||||||||
\(865\) | −29.4560 | −1.00154 | ||||||||
\(866\) | −46.0550 | −1.56501 | ||||||||
\(867\) | −20.8015 | −0.706457 | ||||||||
\(868\) | −58.0612 | −1.97073 | ||||||||
\(869\) | 12.0966 | 0.410348 | ||||||||
\(870\) | −17.7772 | −0.602704 | ||||||||
\(871\) | 0.407149 | 0.0137957 | ||||||||
\(872\) | 20.2522 | 0.685825 | ||||||||
\(873\) | −9.30555 | −0.314945 | ||||||||
\(874\) | 54.9710 | 1.85942 | ||||||||
\(875\) | 36.8393 | 1.24539 | ||||||||
\(876\) | −51.1226 | −1.72727 | ||||||||
\(877\) | 25.8789 | 0.873868 | 0.436934 | − | 0.899494i | \(-0.356064\pi\) | ||||
0.436934 | + | 0.899494i | \(0.356064\pi\) | |||||||
\(878\) | 2.11285 | 0.0713053 | ||||||||
\(879\) | −45.8403 | −1.54615 | ||||||||
\(880\) | 5.14747 | 0.173521 | ||||||||
\(881\) | −21.4890 | −0.723984 | −0.361992 | − | 0.932181i | \(-0.617903\pi\) | ||||
−0.361992 | + | 0.932181i | \(0.617903\pi\) | |||||||
\(882\) | −10.3719 | −0.349242 | ||||||||
\(883\) | −27.4683 | −0.924383 | −0.462192 | − | 0.886780i | \(-0.652937\pi\) | ||||
−0.462192 | + | 0.886780i | \(0.652937\pi\) | |||||||
\(884\) | −1.61186 | −0.0542128 | ||||||||
\(885\) | 12.5355 | 0.421376 | ||||||||
\(886\) | −13.1962 | −0.443334 | ||||||||
\(887\) | −23.2596 | −0.780980 | −0.390490 | − | 0.920607i | \(-0.627694\pi\) | ||||
−0.390490 | + | 0.920607i | \(0.627694\pi\) | |||||||
\(888\) | 3.62325 | 0.121588 | ||||||||
\(889\) | 54.8970 | 1.84119 | ||||||||
\(890\) | −49.6041 | −1.66273 | ||||||||
\(891\) | 17.3456 | 0.581100 | ||||||||
\(892\) | 26.6375 | 0.891888 | ||||||||
\(893\) | 2.29413 | 0.0767700 | ||||||||
\(894\) | 55.5647 | 1.85836 | ||||||||
\(895\) | −24.8657 | −0.831168 | ||||||||
\(896\) | −36.9193 | −1.23339 | ||||||||
\(897\) | −1.83773 | −0.0613600 | ||||||||
\(898\) | 44.0039 | 1.46843 | ||||||||
\(899\) | 15.1520 | 0.505349 | ||||||||
\(900\) | −12.2798 | −0.409328 | ||||||||
\(901\) | −37.4931 | −1.24908 | ||||||||
\(902\) | 3.95026 | 0.131529 | ||||||||
\(903\) | −42.4230 | −1.41175 | ||||||||
\(904\) | −17.4426 | −0.580131 | ||||||||
\(905\) | 9.89873 | 0.329045 | ||||||||
\(906\) | −6.43052 | −0.213640 | ||||||||
\(907\) | 20.6327 | 0.685099 | 0.342550 | − | 0.939500i | \(-0.388710\pi\) | ||||
0.342550 | + | 0.939500i | \(0.388710\pi\) | |||||||
\(908\) | −67.2564 | −2.23198 | ||||||||
\(909\) | 9.03668 | 0.299728 | ||||||||
\(910\) | −2.34896 | −0.0778672 | ||||||||
\(911\) | 8.48694 | 0.281185 | 0.140592 | − | 0.990068i | \(-0.455099\pi\) | ||||
0.140592 | + | 0.990068i | \(0.455099\pi\) | |||||||
\(912\) | 28.5340 | 0.944854 | ||||||||
\(913\) | −3.22934 | −0.106876 | ||||||||
\(914\) | 75.4719 | 2.49639 | ||||||||
\(915\) | 5.33476 | 0.176362 | ||||||||
\(916\) | −70.6798 | −2.33533 | ||||||||
\(917\) | 33.1956 | 1.09621 | ||||||||
\(918\) | 13.4341 | 0.443391 | ||||||||
\(919\) | −45.0377 | −1.48566 | −0.742829 | − | 0.669481i | \(-0.766516\pi\) | ||||
−0.742829 | + | 0.669481i | \(0.766516\pi\) | |||||||
\(920\) | −10.4555 | −0.344709 | ||||||||
\(921\) | −29.9123 | −0.985644 | ||||||||
\(922\) | −61.4299 | −2.02309 | ||||||||
\(923\) | −1.27118 | −0.0418415 | ||||||||
\(924\) | 29.6545 | 0.975561 | ||||||||
\(925\) | 2.23041 | 0.0733354 | ||||||||
\(926\) | 25.8525 | 0.849566 | ||||||||
\(927\) | −3.84673 | −0.126343 | ||||||||
\(928\) | 16.4568 | 0.540222 | ||||||||
\(929\) | 18.5910 | 0.609950 | 0.304975 | − | 0.952360i | \(-0.401352\pi\) | ||||
0.304975 | + | 0.952360i | \(0.401352\pi\) | |||||||
\(930\) | −56.0636 | −1.83840 | ||||||||
\(931\) | −15.4372 | −0.505934 | ||||||||
\(932\) | 9.10757 | 0.298329 | ||||||||
\(933\) | 31.5381 | 1.03251 | ||||||||
\(934\) | 36.6560 | 1.19942 | ||||||||
\(935\) | −7.28824 | −0.238351 | ||||||||
\(936\) | 0.687864 | 0.0224835 | ||||||||
\(937\) | −0.172970 | −0.00565069 | −0.00282534 | − | 0.999996i | \(-0.500899\pi\) | ||||
−0.00282534 | + | 0.999996i | \(0.500899\pi\) | |||||||
\(938\) | −12.8252 | −0.418757 | ||||||||
\(939\) | 37.1658 | 1.21286 | ||||||||
\(940\) | −1.61014 | −0.0525169 | ||||||||
\(941\) | −36.8477 | −1.20120 | −0.600601 | − | 0.799549i | \(-0.705072\pi\) | ||||
−0.600601 | + | 0.799549i | \(0.705072\pi\) | |||||||
\(942\) | 79.2810 | 2.58311 | ||||||||
\(943\) | 4.45996 | 0.145236 | ||||||||
\(944\) | −6.59889 | −0.214776 | ||||||||
\(945\) | 11.3230 | 0.368336 | ||||||||
\(946\) | 21.2812 | 0.691912 | ||||||||
\(947\) | 57.3352 | 1.86314 | 0.931572 | − | 0.363558i | \(-0.118438\pi\) | ||||
0.931572 | + | 0.363558i | \(0.118438\pi\) | |||||||
\(948\) | −47.0626 | −1.52852 | ||||||||
\(949\) | 1.76283 | 0.0572238 | ||||||||
\(950\) | −31.6007 | −1.02526 | ||||||||
\(951\) | −1.26181 | −0.0409171 | ||||||||
\(952\) | 13.7596 | 0.445950 | ||||||||
\(953\) | −12.9136 | −0.418312 | −0.209156 | − | 0.977882i | \(-0.567072\pi\) | ||||
−0.209156 | + | 0.977882i | \(0.567072\pi\) | |||||||
\(954\) | 59.0417 | 1.91155 | ||||||||
\(955\) | −26.9714 | −0.872775 | ||||||||
\(956\) | −76.2709 | −2.46678 | ||||||||
\(957\) | −7.73882 | −0.250161 | ||||||||
\(958\) | −45.8774 | −1.48223 | ||||||||
\(959\) | −52.5594 | −1.69723 | ||||||||
\(960\) | −46.2921 | −1.49407 | ||||||||
\(961\) | 16.7846 | 0.541440 | ||||||||
\(962\) | −0.461028 | −0.0148641 | ||||||||
\(963\) | 9.22910 | 0.297404 | ||||||||
\(964\) | 32.0843 | 1.03337 | ||||||||
\(965\) | −22.2004 | −0.714656 | ||||||||
\(966\) | 57.8883 | 1.86253 | ||||||||
\(967\) | −18.3592 | −0.590392 | −0.295196 | − | 0.955437i | \(-0.595385\pi\) | ||||
−0.295196 | + | 0.955437i | \(0.595385\pi\) | |||||||
\(968\) | 13.7805 | 0.442923 | ||||||||
\(969\) | −40.4009 | −1.29786 | ||||||||
\(970\) | 16.8071 | 0.539642 | ||||||||
\(971\) | −41.6272 | −1.33588 | −0.667941 | − | 0.744214i | \(-0.732824\pi\) | ||||
−0.667941 | + | 0.744214i | \(0.732824\pi\) | |||||||
\(972\) | −49.1936 | −1.57789 | ||||||||
\(973\) | 52.9328 | 1.69695 | ||||||||
\(974\) | −8.79416 | −0.281783 | ||||||||
\(975\) | 1.05644 | 0.0338331 | ||||||||
\(976\) | −2.80831 | −0.0898917 | ||||||||
\(977\) | 31.8934 | 1.02036 | 0.510180 | − | 0.860068i | \(-0.329579\pi\) | ||||
0.510180 | + | 0.860068i | \(0.329579\pi\) | |||||||
\(978\) | 4.87337 | 0.155833 | ||||||||
\(979\) | −21.5938 | −0.690140 | ||||||||
\(980\) | 10.8346 | 0.346100 | ||||||||
\(981\) | −25.0992 | −0.801357 | ||||||||
\(982\) | 21.0975 | 0.673247 | ||||||||
\(983\) | 41.1876 | 1.31368 | 0.656840 | − | 0.754030i | \(-0.271893\pi\) | ||||
0.656840 | + | 0.754030i | \(0.271893\pi\) | |||||||
\(984\) | −4.16493 | −0.132773 | ||||||||
\(985\) | −22.6871 | −0.722872 | ||||||||
\(986\) | −13.2502 | −0.421972 | ||||||||
\(987\) | 2.41588 | 0.0768982 | ||||||||
\(988\) | 3.77785 | 0.120189 | ||||||||
\(989\) | 24.0271 | 0.764019 | ||||||||
\(990\) | 11.4771 | 0.364765 | ||||||||
\(991\) | −16.4554 | −0.522723 | −0.261362 | − | 0.965241i | \(-0.584171\pi\) | ||||
−0.261362 | + | 0.965241i | \(0.584171\pi\) | |||||||
\(992\) | 51.8996 | 1.64781 | ||||||||
\(993\) | 54.1124 | 1.71720 | ||||||||
\(994\) | 40.0422 | 1.27006 | ||||||||
\(995\) | 30.1219 | 0.954929 | ||||||||
\(996\) | 12.5640 | 0.398106 | ||||||||
\(997\) | −55.5583 | −1.75955 | −0.879775 | − | 0.475391i | \(-0.842307\pi\) | ||||
−0.879775 | + | 0.475391i | \(0.842307\pi\) | |||||||
\(998\) | −32.8673 | −1.04040 | ||||||||
\(999\) | 2.22235 | 0.0703121 |
(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 | 6031.2.a.c.1.16 | ✓ | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.c.1.16 | ✓ | 110 | 1.1 | even | 1 | trivial |