Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48308 | −1.75581 | −0.877903 | − | 0.478839i | \(-0.841058\pi\) | ||||
−0.877903 | + | 0.478839i | \(0.841058\pi\) | |||||||
\(3\) | 1.22996 | 0.710116 | 0.355058 | − | 0.934844i | \(-0.384461\pi\) | ||||
0.355058 | + | 0.934844i | \(0.384461\pi\) | |||||||
\(4\) | 4.16571 | 2.08285 | ||||||||
\(5\) | 3.96003 | 1.77098 | 0.885489 | − | 0.464661i | \(-0.153824\pi\) | ||||
0.885489 | + | 0.464661i | \(0.153824\pi\) | |||||||
\(6\) | −3.05409 | −1.24683 | ||||||||
\(7\) | −1.52214 | −0.575315 | −0.287657 | − | 0.957733i | \(-0.592876\pi\) | ||||
−0.287657 | + | 0.957733i | \(0.592876\pi\) | |||||||
\(8\) | −5.37763 | −1.90128 | ||||||||
\(9\) | −1.48721 | −0.495736 | ||||||||
\(10\) | −9.83308 | −3.10949 | ||||||||
\(11\) | 3.53545 | 1.06598 | 0.532989 | − | 0.846122i | \(-0.321069\pi\) | ||||
0.532989 | + | 0.846122i | \(0.321069\pi\) | |||||||
\(12\) | 5.12364 | 1.47907 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.77960 | 1.01014 | ||||||||
\(15\) | 4.87066 | 1.25760 | ||||||||
\(16\) | 5.02170 | 1.25542 | ||||||||
\(17\) | −4.34507 | −1.05383 | −0.526917 | − | 0.849917i | \(-0.676652\pi\) | ||||
−0.526917 | + | 0.849917i | \(0.676652\pi\) | |||||||
\(18\) | 3.69286 | 0.870416 | ||||||||
\(19\) | −4.22546 | −0.969387 | −0.484693 | − | 0.874684i | \(-0.661069\pi\) | ||||
−0.484693 | + | 0.874684i | \(0.661069\pi\) | |||||||
\(20\) | 16.4963 | 3.68869 | ||||||||
\(21\) | −1.87217 | −0.408540 | ||||||||
\(22\) | −8.77881 | −1.87165 | ||||||||
\(23\) | −2.12271 | −0.442616 | −0.221308 | − | 0.975204i | \(-0.571033\pi\) | ||||
−0.221308 | + | 0.975204i | \(0.571033\pi\) | |||||||
\(24\) | −6.61425 | −1.35013 | ||||||||
\(25\) | 10.6818 | 2.13636 | ||||||||
\(26\) | −2.48308 | −0.486973 | ||||||||
\(27\) | −5.51907 | −1.06215 | ||||||||
\(28\) | −6.34079 | −1.19830 | ||||||||
\(29\) | 3.03990 | 0.564496 | 0.282248 | − | 0.959342i | \(-0.408920\pi\) | ||||
0.282248 | + | 0.959342i | \(0.408920\pi\) | |||||||
\(30\) | −12.0943 | −2.20810 | ||||||||
\(31\) | −3.99192 | −0.716970 | −0.358485 | − | 0.933535i | \(-0.616707\pi\) | ||||
−0.358485 | + | 0.933535i | \(0.616707\pi\) | |||||||
\(32\) | −1.71403 | −0.303001 | ||||||||
\(33\) | 4.34845 | 0.756967 | ||||||||
\(34\) | 10.7892 | 1.85033 | ||||||||
\(35\) | −6.02771 | −1.01887 | ||||||||
\(36\) | −6.19527 | −1.03254 | ||||||||
\(37\) | 1.67262 | 0.274976 | 0.137488 | − | 0.990503i | \(-0.456097\pi\) | ||||
0.137488 | + | 0.990503i | \(0.456097\pi\) | |||||||
\(38\) | 10.4922 | 1.70205 | ||||||||
\(39\) | 1.22996 | 0.196951 | ||||||||
\(40\) | −21.2956 | −3.36712 | ||||||||
\(41\) | −4.58133 | −0.715484 | −0.357742 | − | 0.933820i | \(-0.616453\pi\) | ||||
−0.357742 | + | 0.933820i | \(0.616453\pi\) | |||||||
\(42\) | 4.64875 | 0.717317 | ||||||||
\(43\) | 0.939516 | 0.143275 | 0.0716375 | − | 0.997431i | \(-0.477178\pi\) | ||||
0.0716375 | + | 0.997431i | \(0.477178\pi\) | |||||||
\(44\) | 14.7276 | 2.22027 | ||||||||
\(45\) | −5.88938 | −0.877937 | ||||||||
\(46\) | 5.27087 | 0.777147 | ||||||||
\(47\) | −7.91434 | −1.15443 | −0.577213 | − | 0.816594i | \(-0.695860\pi\) | ||||
−0.577213 | + | 0.816594i | \(0.695860\pi\) | |||||||
\(48\) | 6.17647 | 0.891496 | ||||||||
\(49\) | −4.68309 | −0.669013 | ||||||||
\(50\) | −26.5238 | −3.75103 | ||||||||
\(51\) | −5.34425 | −0.748344 | ||||||||
\(52\) | 4.16571 | 0.577680 | ||||||||
\(53\) | −3.48634 | −0.478885 | −0.239443 | − | 0.970911i | \(-0.576965\pi\) | ||||
−0.239443 | + | 0.970911i | \(0.576965\pi\) | |||||||
\(54\) | 13.7043 | 1.86492 | ||||||||
\(55\) | 14.0005 | 1.88782 | ||||||||
\(56\) | 8.18551 | 1.09383 | ||||||||
\(57\) | −5.19713 | −0.688377 | ||||||||
\(58\) | −7.54833 | −0.991144 | ||||||||
\(59\) | −6.34877 | −0.826540 | −0.413270 | − | 0.910609i | \(-0.635613\pi\) | ||||
−0.413270 | + | 0.910609i | \(0.635613\pi\) | |||||||
\(60\) | 20.2897 | 2.61939 | ||||||||
\(61\) | 5.63188 | 0.721088 | 0.360544 | − | 0.932742i | \(-0.382591\pi\) | ||||
0.360544 | + | 0.932742i | \(0.382591\pi\) | |||||||
\(62\) | 9.91227 | 1.25886 | ||||||||
\(63\) | 2.26374 | 0.285204 | ||||||||
\(64\) | −5.78731 | −0.723413 | ||||||||
\(65\) | 3.96003 | 0.491181 | ||||||||
\(66\) | −10.7976 | −1.32909 | ||||||||
\(67\) | −11.1244 | −1.35907 | −0.679534 | − | 0.733644i | \(-0.737818\pi\) | ||||
−0.679534 | + | 0.733644i | \(0.737818\pi\) | |||||||
\(68\) | −18.1003 | −2.19498 | ||||||||
\(69\) | −2.61084 | −0.314308 | ||||||||
\(70\) | 14.9673 | 1.78894 | ||||||||
\(71\) | −11.6419 | −1.38164 | −0.690818 | − | 0.723028i | \(-0.742750\pi\) | ||||
−0.690818 | + | 0.723028i | \(0.742750\pi\) | |||||||
\(72\) | 7.99765 | 0.942532 | ||||||||
\(73\) | 7.26666 | 0.850498 | 0.425249 | − | 0.905076i | \(-0.360187\pi\) | ||||
0.425249 | + | 0.905076i | \(0.360187\pi\) | |||||||
\(74\) | −4.15325 | −0.482805 | ||||||||
\(75\) | 13.1382 | 1.51706 | ||||||||
\(76\) | −17.6020 | −2.01909 | ||||||||
\(77\) | −5.38145 | −0.613273 | ||||||||
\(78\) | −3.05409 | −0.345807 | ||||||||
\(79\) | −3.57287 | −0.401980 | −0.200990 | − | 0.979593i | \(-0.564416\pi\) | ||||
−0.200990 | + | 0.979593i | \(0.564416\pi\) | |||||||
\(80\) | 19.8860 | 2.22333 | ||||||||
\(81\) | −2.32659 | −0.258510 | ||||||||
\(82\) | 11.3758 | 1.25625 | ||||||||
\(83\) | 6.26776 | 0.687976 | 0.343988 | − | 0.938974i | \(-0.388222\pi\) | ||||
0.343988 | + | 0.938974i | \(0.388222\pi\) | |||||||
\(84\) | −7.79889 | −0.850929 | ||||||||
\(85\) | −17.2066 | −1.86632 | ||||||||
\(86\) | −2.33290 | −0.251563 | ||||||||
\(87\) | 3.73895 | 0.400857 | ||||||||
\(88\) | −19.0123 | −2.02672 | ||||||||
\(89\) | −6.28391 | −0.666093 | −0.333047 | − | 0.942910i | \(-0.608077\pi\) | ||||
−0.333047 | + | 0.942910i | \(0.608077\pi\) | |||||||
\(90\) | 14.6238 | 1.54149 | ||||||||
\(91\) | −1.52214 | −0.159564 | ||||||||
\(92\) | −8.84259 | −0.921903 | ||||||||
\(93\) | −4.90989 | −0.509132 | ||||||||
\(94\) | 19.6520 | 2.02695 | ||||||||
\(95\) | −16.7329 | −1.71676 | ||||||||
\(96\) | −2.10818 | −0.215166 | ||||||||
\(97\) | −1.35998 | −0.138085 | −0.0690423 | − | 0.997614i | \(-0.521994\pi\) | ||||
−0.0690423 | + | 0.997614i | \(0.521994\pi\) | |||||||
\(98\) | 11.6285 | 1.17466 | ||||||||
\(99\) | −5.25794 | −0.528443 | ||||||||
\(100\) | 44.4973 | 4.44973 | ||||||||
\(101\) | 19.3491 | 1.92530 | 0.962651 | − | 0.270744i | \(-0.0872697\pi\) | ||||
0.962651 | + | 0.270744i | \(0.0872697\pi\) | |||||||
\(102\) | 13.2702 | 1.31395 | ||||||||
\(103\) | 11.3555 | 1.11889 | 0.559447 | − | 0.828866i | \(-0.311013\pi\) | ||||
0.559447 | + | 0.828866i | \(0.311013\pi\) | |||||||
\(104\) | −5.37763 | −0.527320 | ||||||||
\(105\) | −7.41383 | −0.723515 | ||||||||
\(106\) | 8.65687 | 0.840829 | ||||||||
\(107\) | 3.44688 | 0.333222 | 0.166611 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166611 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(108\) | −22.9908 | −2.21229 | ||||||||
\(109\) | 9.86710 | 0.945097 | 0.472548 | − | 0.881305i | \(-0.343334\pi\) | ||||
0.472548 | + | 0.881305i | \(0.343334\pi\) | |||||||
\(110\) | −34.7643 | −3.31465 | ||||||||
\(111\) | 2.05724 | 0.195265 | ||||||||
\(112\) | −7.64373 | −0.722264 | ||||||||
\(113\) | −2.66934 | −0.251111 | −0.125555 | − | 0.992087i | \(-0.540071\pi\) | ||||
−0.125555 | + | 0.992087i | \(0.540071\pi\) | |||||||
\(114\) | 12.9049 | 1.20866 | ||||||||
\(115\) | −8.40599 | −0.783862 | ||||||||
\(116\) | 12.6633 | 1.17576 | ||||||||
\(117\) | −1.48721 | −0.137492 | ||||||||
\(118\) | 15.7645 | 1.45124 | ||||||||
\(119\) | 6.61380 | 0.606286 | ||||||||
\(120\) | −26.1926 | −2.39105 | ||||||||
\(121\) | 1.49939 | 0.136308 | ||||||||
\(122\) | −13.9844 | −1.26609 | ||||||||
\(123\) | −5.63484 | −0.508076 | ||||||||
\(124\) | −16.6292 | −1.49334 | ||||||||
\(125\) | 22.5001 | 2.01247 | ||||||||
\(126\) | −5.62105 | −0.500763 | ||||||||
\(127\) | 5.89144 | 0.522781 | 0.261391 | − | 0.965233i | \(-0.415819\pi\) | ||||
0.261391 | + | 0.965233i | \(0.415819\pi\) | |||||||
\(128\) | 17.7984 | 1.57317 | ||||||||
\(129\) | 1.15556 | 0.101742 | ||||||||
\(130\) | −9.83308 | −0.862418 | ||||||||
\(131\) | −5.59868 | −0.489159 | −0.244580 | − | 0.969629i | \(-0.578650\pi\) | ||||
−0.244580 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(132\) | 18.1143 | 1.57665 | ||||||||
\(133\) | 6.43174 | 0.557703 | ||||||||
\(134\) | 27.6229 | 2.38626 | ||||||||
\(135\) | −21.8557 | −1.88104 | ||||||||
\(136\) | 23.3662 | 2.00363 | ||||||||
\(137\) | −14.2111 | −1.21414 | −0.607068 | − | 0.794650i | \(-0.707654\pi\) | ||||
−0.607068 | + | 0.794650i | \(0.707654\pi\) | |||||||
\(138\) | 6.48294 | 0.551864 | ||||||||
\(139\) | −15.5376 | −1.31788 | −0.658940 | − | 0.752196i | \(-0.728995\pi\) | ||||
−0.658940 | + | 0.752196i | \(0.728995\pi\) | |||||||
\(140\) | −25.1097 | −2.12216 | ||||||||
\(141\) | −9.73430 | −0.819776 | ||||||||
\(142\) | 28.9078 | 2.42589 | ||||||||
\(143\) | 3.53545 | 0.295649 | ||||||||
\(144\) | −7.46830 | −0.622359 | ||||||||
\(145\) | 12.0381 | 0.999709 | ||||||||
\(146\) | −18.0437 | −1.49331 | ||||||||
\(147\) | −5.76000 | −0.475076 | ||||||||
\(148\) | 6.96763 | 0.572735 | ||||||||
\(149\) | −20.7384 | −1.69895 | −0.849477 | − | 0.527625i | \(-0.823083\pi\) | ||||
−0.849477 | + | 0.527625i | \(0.823083\pi\) | |||||||
\(150\) | −32.6231 | −2.66367 | ||||||||
\(151\) | −10.6197 | −0.864218 | −0.432109 | − | 0.901821i | \(-0.642230\pi\) | ||||
−0.432109 | + | 0.901821i | \(0.642230\pi\) | |||||||
\(152\) | 22.7230 | 1.84308 | ||||||||
\(153\) | 6.46202 | 0.522423 | ||||||||
\(154\) | 13.3626 | 1.07679 | ||||||||
\(155\) | −15.8081 | −1.26974 | ||||||||
\(156\) | 5.12364 | 0.410219 | ||||||||
\(157\) | −24.9115 | −1.98815 | −0.994077 | − | 0.108681i | \(-0.965337\pi\) | ||||
−0.994077 | + | 0.108681i | \(0.965337\pi\) | |||||||
\(158\) | 8.87175 | 0.705798 | ||||||||
\(159\) | −4.28804 | −0.340064 | ||||||||
\(160\) | −6.78761 | −0.536608 | ||||||||
\(161\) | 3.23106 | 0.254643 | ||||||||
\(162\) | 5.77713 | 0.453894 | ||||||||
\(163\) | 21.7326 | 1.70223 | 0.851116 | − | 0.524978i | \(-0.175926\pi\) | ||||
0.851116 | + | 0.524978i | \(0.175926\pi\) | |||||||
\(164\) | −19.0845 | −1.49025 | ||||||||
\(165\) | 17.2200 | 1.34057 | ||||||||
\(166\) | −15.5634 | −1.20795 | ||||||||
\(167\) | 10.3024 | 0.797224 | 0.398612 | − | 0.917120i | \(-0.369492\pi\) | ||||
0.398612 | + | 0.917120i | \(0.369492\pi\) | |||||||
\(168\) | 10.0678 | 0.776749 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 42.7254 | 3.27689 | ||||||||
\(171\) | 6.28413 | 0.480560 | ||||||||
\(172\) | 3.91375 | 0.298421 | ||||||||
\(173\) | −16.1482 | −1.22773 | −0.613863 | − | 0.789413i | \(-0.710385\pi\) | ||||
−0.613863 | + | 0.789413i | \(0.710385\pi\) | |||||||
\(174\) | −9.28412 | −0.703827 | ||||||||
\(175\) | −16.2592 | −1.22908 | ||||||||
\(176\) | 17.7539 | 1.33825 | ||||||||
\(177\) | −7.80871 | −0.586939 | ||||||||
\(178\) | 15.6035 | 1.16953 | ||||||||
\(179\) | −0.973105 | −0.0727333 | −0.0363667 | − | 0.999339i | \(-0.511578\pi\) | ||||
−0.0363667 | + | 0.999339i | \(0.511578\pi\) | |||||||
\(180\) | −24.5334 | −1.82861 | ||||||||
\(181\) | −3.35889 | −0.249664 | −0.124832 | − | 0.992178i | \(-0.539839\pi\) | ||||
−0.124832 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(182\) | 3.77960 | 0.280163 | ||||||||
\(183\) | 6.92697 | 0.512056 | ||||||||
\(184\) | 11.4152 | 0.841536 | ||||||||
\(185\) | 6.62360 | 0.486977 | ||||||||
\(186\) | 12.1917 | 0.893936 | ||||||||
\(187\) | −15.3618 | −1.12336 | ||||||||
\(188\) | −32.9688 | −2.40450 | ||||||||
\(189\) | 8.40080 | 0.611068 | ||||||||
\(190\) | 41.5493 | 3.01430 | ||||||||
\(191\) | −1.88438 | −0.136349 | −0.0681745 | − | 0.997673i | \(-0.521717\pi\) | ||||
−0.0681745 | + | 0.997673i | \(0.521717\pi\) | |||||||
\(192\) | −7.11814 | −0.513707 | ||||||||
\(193\) | 10.4790 | 0.754292 | 0.377146 | − | 0.926154i | \(-0.376905\pi\) | ||||
0.377146 | + | 0.926154i | \(0.376905\pi\) | |||||||
\(194\) | 3.37693 | 0.242450 | ||||||||
\(195\) | 4.87066 | 0.348795 | ||||||||
\(196\) | −19.5084 | −1.39346 | ||||||||
\(197\) | 11.7830 | 0.839504 | 0.419752 | − | 0.907639i | \(-0.362117\pi\) | ||||
0.419752 | + | 0.907639i | \(0.362117\pi\) | |||||||
\(198\) | 13.0559 | 0.927843 | ||||||||
\(199\) | −19.8094 | −1.40425 | −0.702126 | − | 0.712053i | \(-0.747766\pi\) | ||||
−0.702126 | + | 0.712053i | \(0.747766\pi\) | |||||||
\(200\) | −57.4428 | −4.06182 | ||||||||
\(201\) | −13.6826 | −0.965095 | ||||||||
\(202\) | −48.0453 | −3.38046 | ||||||||
\(203\) | −4.62716 | −0.324763 | ||||||||
\(204\) | −22.2626 | −1.55869 | ||||||||
\(205\) | −18.1422 | −1.26711 | ||||||||
\(206\) | −28.1968 | −1.96456 | ||||||||
\(207\) | 3.15691 | 0.219420 | ||||||||
\(208\) | 5.02170 | 0.348192 | ||||||||
\(209\) | −14.9389 | −1.03334 | ||||||||
\(210\) | 18.4092 | 1.27035 | ||||||||
\(211\) | −16.4613 | −1.13324 | −0.566622 | − | 0.823978i | \(-0.691750\pi\) | ||||
−0.566622 | + | 0.823978i | \(0.691750\pi\) | |||||||
\(212\) | −14.5231 | −0.997448 | ||||||||
\(213\) | −14.3190 | −0.981122 | ||||||||
\(214\) | −8.55889 | −0.585074 | ||||||||
\(215\) | 3.72051 | 0.253737 | ||||||||
\(216\) | 29.6795 | 2.01944 | ||||||||
\(217\) | 6.07626 | 0.412484 | ||||||||
\(218\) | −24.5008 | −1.65941 | ||||||||
\(219\) | 8.93767 | 0.603952 | ||||||||
\(220\) | 58.3218 | 3.93206 | ||||||||
\(221\) | −4.34507 | −0.292281 | ||||||||
\(222\) | −5.10831 | −0.342847 | ||||||||
\(223\) | 8.94287 | 0.598859 | 0.299429 | − | 0.954118i | \(-0.403204\pi\) | ||||
0.299429 | + | 0.954118i | \(0.403204\pi\) | |||||||
\(224\) | 2.60900 | 0.174321 | ||||||||
\(225\) | −15.8861 | −1.05907 | ||||||||
\(226\) | 6.62820 | 0.440902 | ||||||||
\(227\) | −17.1723 | −1.13977 | −0.569883 | − | 0.821726i | \(-0.693012\pi\) | ||||
−0.569883 | + | 0.821726i | \(0.693012\pi\) | |||||||
\(228\) | −21.6497 | −1.43379 | ||||||||
\(229\) | −7.31679 | −0.483507 | −0.241754 | − | 0.970338i | \(-0.577723\pi\) | ||||
−0.241754 | + | 0.970338i | \(0.577723\pi\) | |||||||
\(230\) | 20.8728 | 1.37631 | ||||||||
\(231\) | −6.61894 | −0.435495 | ||||||||
\(232\) | −16.3475 | −1.07326 | ||||||||
\(233\) | −1.34734 | −0.0882669 | −0.0441335 | − | 0.999026i | \(-0.514053\pi\) | ||||
−0.0441335 | + | 0.999026i | \(0.514053\pi\) | |||||||
\(234\) | 3.69286 | 0.241410 | ||||||||
\(235\) | −31.3410 | −2.04446 | ||||||||
\(236\) | −26.4471 | −1.72156 | ||||||||
\(237\) | −4.39448 | −0.285452 | ||||||||
\(238\) | −16.4226 | −1.06452 | ||||||||
\(239\) | 0.469954 | 0.0303988 | 0.0151994 | − | 0.999884i | \(-0.495162\pi\) | ||||
0.0151994 | + | 0.999884i | \(0.495162\pi\) | |||||||
\(240\) | 24.4590 | 1.57882 | ||||||||
\(241\) | 28.8992 | 1.86156 | 0.930780 | − | 0.365580i | \(-0.119129\pi\) | ||||
0.930780 | + | 0.365580i | \(0.119129\pi\) | |||||||
\(242\) | −3.72310 | −0.239330 | ||||||||
\(243\) | 13.6956 | 0.878573 | ||||||||
\(244\) | 23.4608 | 1.50192 | ||||||||
\(245\) | −18.5452 | −1.18481 | ||||||||
\(246\) | 13.9918 | 0.892084 | ||||||||
\(247\) | −4.22546 | −0.268860 | ||||||||
\(248\) | 21.4671 | 1.36316 | ||||||||
\(249\) | 7.70907 | 0.488543 | ||||||||
\(250\) | −55.8696 | −3.53350 | ||||||||
\(251\) | 6.52086 | 0.411593 | 0.205797 | − | 0.978595i | \(-0.434021\pi\) | ||||
0.205797 | + | 0.978595i | \(0.434021\pi\) | |||||||
\(252\) | 9.43007 | 0.594038 | ||||||||
\(253\) | −7.50473 | −0.471818 | ||||||||
\(254\) | −14.6290 | −0.917902 | ||||||||
\(255\) | −21.1633 | −1.32530 | ||||||||
\(256\) | −32.6204 | −2.03877 | ||||||||
\(257\) | 15.2444 | 0.950918 | 0.475459 | − | 0.879738i | \(-0.342282\pi\) | ||||
0.475459 | + | 0.879738i | \(0.342282\pi\) | |||||||
\(258\) | −2.86936 | −0.178639 | ||||||||
\(259\) | −2.54596 | −0.158198 | ||||||||
\(260\) | 16.4963 | 1.02306 | ||||||||
\(261\) | −4.52096 | −0.279841 | ||||||||
\(262\) | 13.9020 | 0.858869 | ||||||||
\(263\) | −31.6443 | −1.95127 | −0.975637 | − | 0.219392i | \(-0.929593\pi\) | ||||
−0.975637 | + | 0.219392i | \(0.929593\pi\) | |||||||
\(264\) | −23.3843 | −1.43921 | ||||||||
\(265\) | −13.8060 | −0.848095 | ||||||||
\(266\) | −15.9706 | −0.979217 | ||||||||
\(267\) | −7.72894 | −0.473003 | ||||||||
\(268\) | −46.3412 | −2.83074 | ||||||||
\(269\) | −10.7238 | −0.653844 | −0.326922 | − | 0.945051i | \(-0.606011\pi\) | ||||
−0.326922 | + | 0.945051i | \(0.606011\pi\) | |||||||
\(270\) | 54.2694 | 3.30273 | ||||||||
\(271\) | −30.2525 | −1.83771 | −0.918854 | − | 0.394599i | \(-0.870884\pi\) | ||||
−0.918854 | + | 0.394599i | \(0.870884\pi\) | |||||||
\(272\) | −21.8196 | −1.32301 | ||||||||
\(273\) | −1.87217 | −0.113309 | ||||||||
\(274\) | 35.2874 | 2.13179 | ||||||||
\(275\) | 37.7650 | 2.27731 | ||||||||
\(276\) | −10.8760 | −0.654658 | ||||||||
\(277\) | −26.2097 | −1.57479 | −0.787393 | − | 0.616452i | \(-0.788570\pi\) | ||||
−0.787393 | + | 0.616452i | \(0.788570\pi\) | |||||||
\(278\) | 38.5811 | 2.31394 | ||||||||
\(279\) | 5.93681 | 0.355428 | ||||||||
\(280\) | 32.4148 | 1.93716 | ||||||||
\(281\) | −12.6806 | −0.756460 | −0.378230 | − | 0.925712i | \(-0.623467\pi\) | ||||
−0.378230 | + | 0.925712i | \(0.623467\pi\) | |||||||
\(282\) | 24.1711 | 1.43937 | ||||||||
\(283\) | −6.31162 | −0.375187 | −0.187593 | − | 0.982247i | \(-0.560069\pi\) | ||||
−0.187593 | + | 0.982247i | \(0.560069\pi\) | |||||||
\(284\) | −48.4966 | −2.87775 | ||||||||
\(285\) | −20.5808 | −1.21910 | ||||||||
\(286\) | −8.77881 | −0.519102 | ||||||||
\(287\) | 6.97343 | 0.411629 | ||||||||
\(288\) | 2.54912 | 0.150208 | ||||||||
\(289\) | 1.87962 | 0.110566 | ||||||||
\(290\) | −29.8916 | −1.75529 | ||||||||
\(291\) | −1.67271 | −0.0980560 | ||||||||
\(292\) | 30.2708 | 1.77146 | ||||||||
\(293\) | 7.91731 | 0.462534 | 0.231267 | − | 0.972890i | \(-0.425713\pi\) | ||||
0.231267 | + | 0.972890i | \(0.425713\pi\) | |||||||
\(294\) | 14.3026 | 0.834142 | ||||||||
\(295\) | −25.1413 | −1.46378 | ||||||||
\(296\) | −8.99471 | −0.522807 | ||||||||
\(297\) | −19.5124 | −1.13222 | ||||||||
\(298\) | 51.4952 | 2.98303 | ||||||||
\(299\) | −2.12271 | −0.122759 | ||||||||
\(300\) | 54.7297 | 3.15982 | ||||||||
\(301\) | −1.43008 | −0.0824282 | ||||||||
\(302\) | 26.3696 | 1.51740 | ||||||||
\(303\) | 23.7985 | 1.36719 | ||||||||
\(304\) | −21.2190 | −1.21699 | ||||||||
\(305\) | 22.3024 | 1.27703 | ||||||||
\(306\) | −16.0457 | −0.917273 | ||||||||
\(307\) | −8.25869 | −0.471348 | −0.235674 | − | 0.971832i | \(-0.575730\pi\) | ||||
−0.235674 | + | 0.971832i | \(0.575730\pi\) | |||||||
\(308\) | −22.4175 | −1.27736 | ||||||||
\(309\) | 13.9668 | 0.794545 | ||||||||
\(310\) | 39.2529 | 2.22941 | ||||||||
\(311\) | −11.4474 | −0.649125 | −0.324562 | − | 0.945864i | \(-0.605217\pi\) | ||||
−0.324562 | + | 0.945864i | \(0.605217\pi\) | |||||||
\(312\) | −6.61425 | −0.374458 | ||||||||
\(313\) | 18.9042 | 1.06853 | 0.534264 | − | 0.845318i | \(-0.320589\pi\) | ||||
0.534264 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(314\) | 61.8573 | 3.49081 | ||||||||
\(315\) | 8.96446 | 0.505090 | ||||||||
\(316\) | −14.8835 | −0.837265 | ||||||||
\(317\) | 31.3944 | 1.76328 | 0.881642 | − | 0.471919i | \(-0.156439\pi\) | ||||
0.881642 | + | 0.471919i | \(0.156439\pi\) | |||||||
\(318\) | 10.6476 | 0.597086 | ||||||||
\(319\) | 10.7474 | 0.601739 | ||||||||
\(320\) | −22.9179 | −1.28115 | ||||||||
\(321\) | 4.23951 | 0.236626 | ||||||||
\(322\) | −8.02300 | −0.447104 | ||||||||
\(323\) | 18.3599 | 1.02157 | ||||||||
\(324\) | −9.69191 | −0.538439 | ||||||||
\(325\) | 10.6818 | 0.592520 | ||||||||
\(326\) | −53.9640 | −2.98879 | ||||||||
\(327\) | 12.1361 | 0.671128 | ||||||||
\(328\) | 24.6367 | 1.36034 | ||||||||
\(329\) | 12.0467 | 0.664158 | ||||||||
\(330\) | −42.7586 | −2.35378 | ||||||||
\(331\) | 23.5685 | 1.29544 | 0.647722 | − | 0.761877i | \(-0.275722\pi\) | ||||
0.647722 | + | 0.761877i | \(0.275722\pi\) | |||||||
\(332\) | 26.1097 | 1.43295 | ||||||||
\(333\) | −2.48753 | −0.136316 | ||||||||
\(334\) | −25.5817 | −1.39977 | ||||||||
\(335\) | −44.0531 | −2.40688 | ||||||||
\(336\) | −9.40145 | −0.512891 | ||||||||
\(337\) | −34.0654 | −1.85566 | −0.927832 | − | 0.373000i | \(-0.878329\pi\) | ||||
−0.927832 | + | 0.373000i | \(0.878329\pi\) | |||||||
\(338\) | −2.48308 | −0.135062 | ||||||||
\(339\) | −3.28318 | −0.178318 | ||||||||
\(340\) | −71.6776 | −3.88726 | ||||||||
\(341\) | −14.1132 | −0.764274 | ||||||||
\(342\) | −15.6040 | −0.843769 | ||||||||
\(343\) | 17.7833 | 0.960208 | ||||||||
\(344\) | −5.05237 | −0.272406 | ||||||||
\(345\) | −10.3390 | −0.556633 | ||||||||
\(346\) | 40.0974 | 2.15565 | ||||||||
\(347\) | 20.1030 | 1.07919 | 0.539593 | − | 0.841926i | \(-0.318578\pi\) | ||||
0.539593 | + | 0.841926i | \(0.318578\pi\) | |||||||
\(348\) | 15.5754 | 0.834927 | ||||||||
\(349\) | 16.6339 | 0.890391 | 0.445195 | − | 0.895433i | \(-0.353134\pi\) | ||||
0.445195 | + | 0.895433i | \(0.353134\pi\) | |||||||
\(350\) | 40.3730 | 2.15803 | ||||||||
\(351\) | −5.51907 | −0.294586 | ||||||||
\(352\) | −6.05987 | −0.322992 | ||||||||
\(353\) | 2.56768 | 0.136664 | 0.0683320 | − | 0.997663i | \(-0.478232\pi\) | ||||
0.0683320 | + | 0.997663i | \(0.478232\pi\) | |||||||
\(354\) | 19.3897 | 1.03055 | ||||||||
\(355\) | −46.1021 | −2.44685 | ||||||||
\(356\) | −26.1769 | −1.38737 | ||||||||
\(357\) | 8.13469 | 0.430534 | ||||||||
\(358\) | 2.41630 | 0.127706 | ||||||||
\(359\) | −17.9408 | −0.946880 | −0.473440 | − | 0.880826i | \(-0.656988\pi\) | ||||
−0.473440 | + | 0.880826i | \(0.656988\pi\) | |||||||
\(360\) | 31.6709 | 1.66920 | ||||||||
\(361\) | −1.14550 | −0.0602894 | ||||||||
\(362\) | 8.34040 | 0.438362 | ||||||||
\(363\) | 1.84418 | 0.0967943 | ||||||||
\(364\) | −6.34079 | −0.332348 | ||||||||
\(365\) | 28.7761 | 1.50621 | ||||||||
\(366\) | −17.2002 | −0.899071 | ||||||||
\(367\) | 3.44745 | 0.179955 | 0.0899777 | − | 0.995944i | \(-0.471320\pi\) | ||||
0.0899777 | + | 0.995944i | \(0.471320\pi\) | |||||||
\(368\) | −10.6596 | −0.555670 | ||||||||
\(369\) | 6.81339 | 0.354691 | ||||||||
\(370\) | −16.4470 | −0.855037 | ||||||||
\(371\) | 5.30669 | 0.275510 | ||||||||
\(372\) | −20.4532 | −1.06045 | ||||||||
\(373\) | 8.98400 | 0.465174 | 0.232587 | − | 0.972576i | \(-0.425281\pi\) | ||||
0.232587 | + | 0.972576i | \(0.425281\pi\) | |||||||
\(374\) | 38.1445 | 1.97241 | ||||||||
\(375\) | 27.6741 | 1.42909 | ||||||||
\(376\) | 42.5604 | 2.19489 | ||||||||
\(377\) | 3.03990 | 0.156563 | ||||||||
\(378\) | −20.8599 | −1.07292 | ||||||||
\(379\) | −14.5587 | −0.747828 | −0.373914 | − | 0.927463i | \(-0.621984\pi\) | ||||
−0.373914 | + | 0.927463i | \(0.621984\pi\) | |||||||
\(380\) | −69.7045 | −3.57576 | ||||||||
\(381\) | 7.24622 | 0.371235 | ||||||||
\(382\) | 4.67908 | 0.239402 | ||||||||
\(383\) | −4.91235 | −0.251010 | −0.125505 | − | 0.992093i | \(-0.540055\pi\) | ||||
−0.125505 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(384\) | 21.8913 | 1.11714 | ||||||||
\(385\) | −21.3107 | −1.08609 | ||||||||
\(386\) | −26.0201 | −1.32439 | ||||||||
\(387\) | −1.39726 | −0.0710265 | ||||||||
\(388\) | −5.66526 | −0.287610 | ||||||||
\(389\) | 17.5598 | 0.890315 | 0.445157 | − | 0.895452i | \(-0.353148\pi\) | ||||
0.445157 | + | 0.895452i | \(0.353148\pi\) | |||||||
\(390\) | −12.0943 | −0.612416 | ||||||||
\(391\) | 9.22332 | 0.466443 | ||||||||
\(392\) | 25.1839 | 1.27198 | ||||||||
\(393\) | −6.88614 | −0.347360 | ||||||||
\(394\) | −29.2582 | −1.47401 | ||||||||
\(395\) | −14.1487 | −0.711897 | ||||||||
\(396\) | −21.9030 | −1.10067 | ||||||||
\(397\) | −17.6111 | −0.883873 | −0.441937 | − | 0.897046i | \(-0.645708\pi\) | ||||
−0.441937 | + | 0.897046i | \(0.645708\pi\) | |||||||
\(398\) | 49.1884 | 2.46559 | ||||||||
\(399\) | 7.91076 | 0.396033 | ||||||||
\(400\) | 53.6408 | 2.68204 | ||||||||
\(401\) | 19.4817 | 0.972872 | 0.486436 | − | 0.873716i | \(-0.338297\pi\) | ||||
0.486436 | + | 0.873716i | \(0.338297\pi\) | |||||||
\(402\) | 33.9750 | 1.69452 | ||||||||
\(403\) | −3.99192 | −0.198852 | ||||||||
\(404\) | 80.6025 | 4.01012 | ||||||||
\(405\) | −9.21337 | −0.457816 | ||||||||
\(406\) | 11.4896 | 0.570220 | ||||||||
\(407\) | 5.91344 | 0.293119 | ||||||||
\(408\) | 28.7394 | 1.42281 | ||||||||
\(409\) | 32.4828 | 1.60617 | 0.803084 | − | 0.595865i | \(-0.203191\pi\) | ||||
0.803084 | + | 0.595865i | \(0.203191\pi\) | |||||||
\(410\) | 45.0486 | 2.22479 | ||||||||
\(411\) | −17.4790 | −0.862177 | ||||||||
\(412\) | 47.3038 | 2.33049 | ||||||||
\(413\) | 9.66372 | 0.475521 | ||||||||
\(414\) | −7.83887 | −0.385260 | ||||||||
\(415\) | 24.8205 | 1.21839 | ||||||||
\(416\) | −1.71403 | −0.0840373 | ||||||||
\(417\) | −19.1105 | −0.935847 | ||||||||
\(418\) | 37.0945 | 1.81435 | ||||||||
\(419\) | −14.4814 | −0.707461 | −0.353730 | − | 0.935347i | \(-0.615087\pi\) | ||||
−0.353730 | + | 0.935347i | \(0.615087\pi\) | |||||||
\(420\) | −30.8838 | −1.50698 | ||||||||
\(421\) | 5.24430 | 0.255592 | 0.127796 | − | 0.991801i | \(-0.459210\pi\) | ||||
0.127796 | + | 0.991801i | \(0.459210\pi\) | |||||||
\(422\) | 40.8749 | 1.98976 | ||||||||
\(423\) | 11.7703 | 0.572290 | ||||||||
\(424\) | 18.7482 | 0.910495 | ||||||||
\(425\) | −46.4132 | −2.25137 | ||||||||
\(426\) | 35.5553 | 1.72266 | ||||||||
\(427\) | −8.57251 | −0.414853 | ||||||||
\(428\) | 14.3587 | 0.694053 | ||||||||
\(429\) | 4.34845 | 0.209945 | ||||||||
\(430\) | −9.23834 | −0.445512 | ||||||||
\(431\) | 35.5231 | 1.71109 | 0.855544 | − | 0.517731i | \(-0.173223\pi\) | ||||
0.855544 | + | 0.517731i | \(0.173223\pi\) | |||||||
\(432\) | −27.7151 | −1.33344 | ||||||||
\(433\) | −8.67821 | −0.417048 | −0.208524 | − | 0.978017i | \(-0.566866\pi\) | ||||
−0.208524 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(434\) | −15.0879 | −0.724241 | ||||||||
\(435\) | 14.8063 | 0.709909 | ||||||||
\(436\) | 41.1034 | 1.96850 | ||||||||
\(437\) | 8.96942 | 0.429066 | ||||||||
\(438\) | −22.1930 | −1.06042 | ||||||||
\(439\) | −18.1770 | −0.867541 | −0.433770 | − | 0.901023i | \(-0.642817\pi\) | ||||
−0.433770 | + | 0.901023i | \(0.642817\pi\) | |||||||
\(440\) | −75.2893 | −3.58928 | ||||||||
\(441\) | 6.96472 | 0.331654 | ||||||||
\(442\) | 10.7892 | 0.513189 | ||||||||
\(443\) | 21.6124 | 1.02684 | 0.513418 | − | 0.858138i | \(-0.328379\pi\) | ||||
0.513418 | + | 0.858138i | \(0.328379\pi\) | |||||||
\(444\) | 8.56988 | 0.406708 | ||||||||
\(445\) | −24.8845 | −1.17964 | ||||||||
\(446\) | −22.2059 | −1.05148 | ||||||||
\(447\) | −25.5073 | −1.20645 | ||||||||
\(448\) | 8.80909 | 0.416190 | ||||||||
\(449\) | −2.77970 | −0.131182 | −0.0655910 | − | 0.997847i | \(-0.520893\pi\) | ||||
−0.0655910 | + | 0.997847i | \(0.520893\pi\) | |||||||
\(450\) | 39.4464 | 1.85952 | ||||||||
\(451\) | −16.1971 | −0.762690 | ||||||||
\(452\) | −11.1197 | −0.523027 | ||||||||
\(453\) | −13.0618 | −0.613695 | ||||||||
\(454\) | 42.6403 | 2.00121 | ||||||||
\(455\) | −6.02771 | −0.282584 | ||||||||
\(456\) | 27.9482 | 1.30880 | ||||||||
\(457\) | 2.30183 | 0.107675 | 0.0538375 | − | 0.998550i | \(-0.482855\pi\) | ||||
0.0538375 | + | 0.998550i | \(0.482855\pi\) | |||||||
\(458\) | 18.1682 | 0.848944 | ||||||||
\(459\) | 23.9807 | 1.11932 | ||||||||
\(460\) | −35.0169 | −1.63267 | ||||||||
\(461\) | 27.2955 | 1.27128 | 0.635639 | − | 0.771987i | \(-0.280737\pi\) | ||||
0.635639 | + | 0.771987i | \(0.280737\pi\) | |||||||
\(462\) | 16.4354 | 0.764644 | ||||||||
\(463\) | 1.07563 | 0.0499887 | 0.0249944 | − | 0.999688i | \(-0.492043\pi\) | ||||
0.0249944 | + | 0.999688i | \(0.492043\pi\) | |||||||
\(464\) | 15.2655 | 0.708681 | ||||||||
\(465\) | −19.4433 | −0.901661 | ||||||||
\(466\) | 3.34555 | 0.154980 | ||||||||
\(467\) | −35.1459 | −1.62636 | −0.813179 | − | 0.582013i | \(-0.802265\pi\) | ||||
−0.813179 | + | 0.582013i | \(0.802265\pi\) | |||||||
\(468\) | −6.19527 | −0.286376 | ||||||||
\(469\) | 16.9330 | 0.781892 | ||||||||
\(470\) | 77.8224 | 3.58968 | ||||||||
\(471\) | −30.6400 | −1.41182 | ||||||||
\(472\) | 34.1413 | 1.57148 | ||||||||
\(473\) | 3.32161 | 0.152728 | ||||||||
\(474\) | 10.9119 | 0.501198 | ||||||||
\(475\) | −45.1355 | −2.07096 | ||||||||
\(476\) | 27.5512 | 1.26281 | ||||||||
\(477\) | 5.18491 | 0.237401 | ||||||||
\(478\) | −1.16694 | −0.0533744 | ||||||||
\(479\) | 20.8085 | 0.950764 | 0.475382 | − | 0.879779i | \(-0.342310\pi\) | ||||
0.475382 | + | 0.879779i | \(0.342310\pi\) | |||||||
\(480\) | −8.34847 | −0.381054 | ||||||||
\(481\) | 1.67262 | 0.0762647 | ||||||||
\(482\) | −71.7591 | −3.26854 | ||||||||
\(483\) | 3.97407 | 0.180826 | ||||||||
\(484\) | 6.24600 | 0.283909 | ||||||||
\(485\) | −5.38554 | −0.244545 | ||||||||
\(486\) | −34.0073 | −1.54260 | ||||||||
\(487\) | 26.0142 | 1.17882 | 0.589408 | − | 0.807835i | \(-0.299361\pi\) | ||||
0.589408 | + | 0.807835i | \(0.299361\pi\) | |||||||
\(488\) | −30.2862 | −1.37099 | ||||||||
\(489\) | 26.7302 | 1.20878 | ||||||||
\(490\) | 46.0492 | 2.08029 | ||||||||
\(491\) | 31.6352 | 1.42767 | 0.713837 | − | 0.700312i | \(-0.246956\pi\) | ||||
0.713837 | + | 0.700312i | \(0.246956\pi\) | |||||||
\(492\) | −23.4731 | −1.05825 | ||||||||
\(493\) | −13.2086 | −0.594885 | ||||||||
\(494\) | 10.4922 | 0.472065 | ||||||||
\(495\) | −20.8216 | −0.935861 | ||||||||
\(496\) | −20.0462 | −0.900102 | ||||||||
\(497\) | 17.7206 | 0.794876 | ||||||||
\(498\) | −19.1423 | −0.857786 | ||||||||
\(499\) | −25.9286 | −1.16072 | −0.580361 | − | 0.814359i | \(-0.697089\pi\) | ||||
−0.580361 | + | 0.814359i | \(0.697089\pi\) | |||||||
\(500\) | 93.7288 | 4.19168 | ||||||||
\(501\) | 12.6715 | 0.566121 | ||||||||
\(502\) | −16.1918 | −0.722677 | ||||||||
\(503\) | 20.2039 | 0.900847 | 0.450424 | − | 0.892815i | \(-0.351273\pi\) | ||||
0.450424 | + | 0.892815i | \(0.351273\pi\) | |||||||
\(504\) | −12.1735 | −0.542253 | ||||||||
\(505\) | 76.6228 | 3.40967 | ||||||||
\(506\) | 18.6349 | 0.828421 | ||||||||
\(507\) | 1.22996 | 0.0546243 | ||||||||
\(508\) | 24.5420 | 1.08888 | ||||||||
\(509\) | −35.4402 | −1.57086 | −0.785430 | − | 0.618951i | \(-0.787558\pi\) | ||||
−0.785430 | + | 0.618951i | \(0.787558\pi\) | |||||||
\(510\) | 52.5504 | 2.32697 | ||||||||
\(511\) | −11.0609 | −0.489304 | ||||||||
\(512\) | 45.4023 | 2.00652 | ||||||||
\(513\) | 23.3206 | 1.02963 | ||||||||
\(514\) | −37.8531 | −1.66963 | ||||||||
\(515\) | 44.9682 | 1.98154 | ||||||||
\(516\) | 4.81374 | 0.211913 | ||||||||
\(517\) | −27.9807 | −1.23059 | ||||||||
\(518\) | 6.32182 | 0.277765 | ||||||||
\(519\) | −19.8616 | −0.871827 | ||||||||
\(520\) | −21.2956 | −0.933872 | ||||||||
\(521\) | 29.2589 | 1.28186 | 0.640929 | − | 0.767601i | \(-0.278549\pi\) | ||||
0.640929 | + | 0.767601i | \(0.278549\pi\) | |||||||
\(522\) | 11.2259 | 0.491346 | ||||||||
\(523\) | 2.29827 | 0.100496 | 0.0502482 | − | 0.998737i | \(-0.483999\pi\) | ||||
0.0502482 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(524\) | −23.3225 | −1.01885 | ||||||||
\(525\) | −19.9981 | −0.872789 | ||||||||
\(526\) | 78.5756 | 3.42606 | ||||||||
\(527\) | 17.3452 | 0.755568 | ||||||||
\(528\) | 21.8366 | 0.950315 | ||||||||
\(529\) | −18.4941 | −0.804091 | ||||||||
\(530\) | 34.2814 | 1.48909 | ||||||||
\(531\) | 9.44194 | 0.409745 | ||||||||
\(532\) | 26.7927 | 1.16161 | ||||||||
\(533\) | −4.58133 | −0.198440 | ||||||||
\(534\) | 19.1916 | 0.830502 | ||||||||
\(535\) | 13.6497 | 0.590129 | ||||||||
\(536\) | 59.8232 | 2.58397 | ||||||||
\(537\) | −1.19688 | −0.0516491 | ||||||||
\(538\) | 26.6282 | 1.14802 | ||||||||
\(539\) | −16.5568 | −0.713152 | ||||||||
\(540\) | −91.0442 | −3.91792 | ||||||||
\(541\) | −1.78231 | −0.0766275 | −0.0383138 | − | 0.999266i | \(-0.512199\pi\) | ||||
−0.0383138 | + | 0.999266i | \(0.512199\pi\) | |||||||
\(542\) | 75.1194 | 3.22666 | ||||||||
\(543\) | −4.13129 | −0.177290 | ||||||||
\(544\) | 7.44759 | 0.319313 | ||||||||
\(545\) | 39.0740 | 1.67375 | ||||||||
\(546\) | 4.64875 | 0.198948 | ||||||||
\(547\) | 29.0846 | 1.24357 | 0.621785 | − | 0.783188i | \(-0.286408\pi\) | ||||
0.621785 | + | 0.783188i | \(0.286408\pi\) | |||||||
\(548\) | −59.1993 | −2.52887 | ||||||||
\(549\) | −8.37577 | −0.357469 | ||||||||
\(550\) | −93.7735 | −3.99852 | ||||||||
\(551\) | −12.8450 | −0.547214 | ||||||||
\(552\) | 14.0401 | 0.597588 | ||||||||
\(553\) | 5.43842 | 0.231265 | ||||||||
\(554\) | 65.0808 | 2.76502 | ||||||||
\(555\) | 8.14674 | 0.345810 | ||||||||
\(556\) | −64.7249 | −2.74495 | ||||||||
\(557\) | 12.9814 | 0.550039 | 0.275020 | − | 0.961439i | \(-0.411316\pi\) | ||||
0.275020 | + | 0.961439i | \(0.411316\pi\) | |||||||
\(558\) | −14.7416 | −0.624062 | ||||||||
\(559\) | 0.939516 | 0.0397373 | ||||||||
\(560\) | −30.2693 | −1.27911 | ||||||||
\(561\) | −18.8943 | −0.797718 | ||||||||
\(562\) | 31.4869 | 1.32820 | ||||||||
\(563\) | −2.69123 | −0.113422 | −0.0567109 | − | 0.998391i | \(-0.518061\pi\) | ||||
−0.0567109 | + | 0.998391i | \(0.518061\pi\) | |||||||
\(564\) | −40.5502 | −1.70747 | ||||||||
\(565\) | −10.5707 | −0.444711 | ||||||||
\(566\) | 15.6723 | 0.658755 | ||||||||
\(567\) | 3.54140 | 0.148725 | ||||||||
\(568\) | 62.6057 | 2.62688 | ||||||||
\(569\) | 41.6096 | 1.74436 | 0.872182 | − | 0.489182i | \(-0.162705\pi\) | ||||
0.872182 | + | 0.489182i | \(0.162705\pi\) | |||||||
\(570\) | 51.1038 | 2.14050 | ||||||||
\(571\) | −3.39647 | −0.142138 | −0.0710690 | − | 0.997471i | \(-0.522641\pi\) | ||||
−0.0710690 | + | 0.997471i | \(0.522641\pi\) | |||||||
\(572\) | 14.7276 | 0.615793 | ||||||||
\(573\) | −2.31771 | −0.0968236 | ||||||||
\(574\) | −17.3156 | −0.722740 | ||||||||
\(575\) | −22.6744 | −0.945587 | ||||||||
\(576\) | 8.60692 | 0.358622 | ||||||||
\(577\) | 24.7277 | 1.02943 | 0.514715 | − | 0.857361i | \(-0.327898\pi\) | ||||
0.514715 | + | 0.857361i | \(0.327898\pi\) | |||||||
\(578\) | −4.66726 | −0.194133 | ||||||||
\(579\) | 12.8887 | 0.535635 | ||||||||
\(580\) | 50.1471 | 2.08225 | ||||||||
\(581\) | −9.54041 | −0.395803 | ||||||||
\(582\) | 4.15348 | 0.172167 | ||||||||
\(583\) | −12.3258 | −0.510481 | ||||||||
\(584\) | −39.0774 | −1.61703 | ||||||||
\(585\) | −5.88938 | −0.243496 | ||||||||
\(586\) | −19.6593 | −0.812120 | ||||||||
\(587\) | 36.8507 | 1.52099 | 0.760496 | − | 0.649343i | \(-0.224956\pi\) | ||||
0.760496 | + | 0.649343i | \(0.224956\pi\) | |||||||
\(588\) | −23.9944 | −0.989514 | ||||||||
\(589\) | 16.8677 | 0.695021 | ||||||||
\(590\) | 62.4280 | 2.57012 | ||||||||
\(591\) | 14.4926 | 0.596145 | ||||||||
\(592\) | 8.39937 | 0.345212 | ||||||||
\(593\) | −28.5530 | −1.17253 | −0.586265 | − | 0.810119i | \(-0.699402\pi\) | ||||
−0.586265 | + | 0.810119i | \(0.699402\pi\) | |||||||
\(594\) | 48.4509 | 1.98796 | ||||||||
\(595\) | 26.1908 | 1.07372 | ||||||||
\(596\) | −86.3900 | −3.53867 | ||||||||
\(597\) | −24.3647 | −0.997181 | ||||||||
\(598\) | 5.27087 | 0.215542 | ||||||||
\(599\) | −13.7645 | −0.562400 | −0.281200 | − | 0.959649i | \(-0.590732\pi\) | ||||
−0.281200 | + | 0.959649i | \(0.590732\pi\) | |||||||
\(600\) | −70.6521 | −2.88436 | ||||||||
\(601\) | −35.5295 | −1.44928 | −0.724639 | − | 0.689129i | \(-0.757993\pi\) | ||||
−0.724639 | + | 0.689129i | \(0.757993\pi\) | |||||||
\(602\) | 3.55100 | 0.144728 | ||||||||
\(603\) | 16.5444 | 0.673738 | ||||||||
\(604\) | −44.2385 | −1.80004 | ||||||||
\(605\) | 5.93761 | 0.241398 | ||||||||
\(606\) | −59.0937 | −2.40052 | ||||||||
\(607\) | −3.90470 | −0.158487 | −0.0792434 | − | 0.996855i | \(-0.525250\pi\) | ||||
−0.0792434 | + | 0.996855i | \(0.525250\pi\) | |||||||
\(608\) | 7.24257 | 0.293725 | ||||||||
\(609\) | −5.69120 | −0.230619 | ||||||||
\(610\) | −55.3787 | −2.24222 | ||||||||
\(611\) | −7.91434 | −0.320180 | ||||||||
\(612\) | 26.9189 | 1.08813 | ||||||||
\(613\) | −21.4663 | −0.867015 | −0.433507 | − | 0.901150i | \(-0.642724\pi\) | ||||
−0.433507 | + | 0.901150i | \(0.642724\pi\) | |||||||
\(614\) | 20.5070 | 0.827596 | ||||||||
\(615\) | −22.3141 | −0.899792 | ||||||||
\(616\) | 28.9394 | 1.16600 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −34.6808 | −1.39507 | ||||||||
\(619\) | −30.7152 | −1.23455 | −0.617274 | − | 0.786748i | \(-0.711763\pi\) | ||||
−0.617274 | + | 0.786748i | \(0.711763\pi\) | |||||||
\(620\) | −65.8519 | −2.64468 | ||||||||
\(621\) | 11.7154 | 0.470122 | ||||||||
\(622\) | 28.4249 | 1.13974 | ||||||||
\(623\) | 9.56499 | 0.383213 | ||||||||
\(624\) | 6.17647 | 0.247257 | ||||||||
\(625\) | 35.6919 | 1.42768 | ||||||||
\(626\) | −46.9407 | −1.87613 | ||||||||
\(627\) | −18.3742 | −0.733794 | ||||||||
\(628\) | −103.774 | −4.14103 | ||||||||
\(629\) | −7.26763 | −0.289779 | ||||||||
\(630\) | −22.2595 | −0.886840 | ||||||||
\(631\) | −10.8137 | −0.430486 | −0.215243 | − | 0.976560i | \(-0.569054\pi\) | ||||
−0.215243 | + | 0.976560i | \(0.569054\pi\) | |||||||
\(632\) | 19.2136 | 0.764276 | ||||||||
\(633\) | −20.2467 | −0.804735 | ||||||||
\(634\) | −77.9549 | −3.09598 | ||||||||
\(635\) | 23.3303 | 0.925834 | ||||||||
\(636\) | −17.8627 | −0.708303 | ||||||||
\(637\) | −4.68309 | −0.185551 | ||||||||
\(638\) | −26.6867 | −1.05654 | ||||||||
\(639\) | 17.3139 | 0.684927 | ||||||||
\(640\) | 70.4822 | 2.78606 | ||||||||
\(641\) | −19.8380 | −0.783553 | −0.391777 | − | 0.920060i | \(-0.628139\pi\) | ||||
−0.391777 | + | 0.920060i | \(0.628139\pi\) | |||||||
\(642\) | −10.5271 | −0.415470 | ||||||||
\(643\) | −7.91369 | −0.312085 | −0.156043 | − | 0.987750i | \(-0.549874\pi\) | ||||
−0.156043 | + | 0.987750i | \(0.549874\pi\) | |||||||
\(644\) | 13.4597 | 0.530385 | ||||||||
\(645\) | 4.57606 | 0.180182 | ||||||||
\(646\) | −45.5892 | −1.79368 | ||||||||
\(647\) | −24.1382 | −0.948972 | −0.474486 | − | 0.880263i | \(-0.657366\pi\) | ||||
−0.474486 | + | 0.880263i | \(0.657366\pi\) | |||||||
\(648\) | 12.5116 | 0.491501 | ||||||||
\(649\) | −22.4457 | −0.881073 | ||||||||
\(650\) | −26.5238 | −1.04035 | ||||||||
\(651\) | 7.47354 | 0.292911 | ||||||||
\(652\) | 90.5318 | 3.54550 | ||||||||
\(653\) | 17.5062 | 0.685070 | 0.342535 | − | 0.939505i | \(-0.388714\pi\) | ||||
0.342535 | + | 0.939505i | \(0.388714\pi\) | |||||||
\(654\) | −30.1350 | −1.17837 | ||||||||
\(655\) | −22.1709 | −0.866290 | ||||||||
\(656\) | −23.0061 | −0.898236 | ||||||||
\(657\) | −10.8070 | −0.421622 | ||||||||
\(658\) | −29.9131 | −1.16613 | ||||||||
\(659\) | −7.67864 | −0.299117 | −0.149559 | − | 0.988753i | \(-0.547785\pi\) | ||||
−0.149559 | + | 0.988753i | \(0.547785\pi\) | |||||||
\(660\) | 71.7333 | 2.79221 | ||||||||
\(661\) | −27.6520 | −1.07554 | −0.537769 | − | 0.843092i | \(-0.680733\pi\) | ||||
−0.537769 | + | 0.843092i | \(0.680733\pi\) | |||||||
\(662\) | −58.5227 | −2.27455 | ||||||||
\(663\) | −5.34425 | −0.207553 | ||||||||
\(664\) | −33.7057 | −1.30804 | ||||||||
\(665\) | 25.4699 | 0.987679 | ||||||||
\(666\) | 6.17674 | 0.239344 | ||||||||
\(667\) | −6.45283 | −0.249855 | ||||||||
\(668\) | 42.9168 | 1.66050 | ||||||||
\(669\) | 10.9993 | 0.425259 | ||||||||
\(670\) | 109.388 | 4.22601 | ||||||||
\(671\) | 19.9112 | 0.768664 | ||||||||
\(672\) | 3.20895 | 0.123788 | ||||||||
\(673\) | 0.863984 | 0.0333041 | 0.0166521 | − | 0.999861i | \(-0.494699\pi\) | ||||
0.0166521 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(674\) | 84.5874 | 3.25818 | ||||||||
\(675\) | −58.9536 | −2.26913 | ||||||||
\(676\) | 4.16571 | 0.160219 | ||||||||
\(677\) | −35.4038 | −1.36068 | −0.680340 | − | 0.732897i | \(-0.738168\pi\) | ||||
−0.680340 | + | 0.732897i | \(0.738168\pi\) | |||||||
\(678\) | 8.15240 | 0.313091 | ||||||||
\(679\) | 2.07007 | 0.0794421 | ||||||||
\(680\) | 92.5307 | 3.54839 | ||||||||
\(681\) | −21.1212 | −0.809366 | ||||||||
\(682\) | 35.0443 | 1.34192 | ||||||||
\(683\) | 18.2982 | 0.700160 | 0.350080 | − | 0.936720i | \(-0.386154\pi\) | ||||
0.350080 | + | 0.936720i | \(0.386154\pi\) | |||||||
\(684\) | 26.1778 | 1.00094 | ||||||||
\(685\) | −56.2763 | −2.15021 | ||||||||
\(686\) | −44.1574 | −1.68594 | ||||||||
\(687\) | −8.99933 | −0.343346 | ||||||||
\(688\) | 4.71797 | 0.179871 | ||||||||
\(689\) | −3.48634 | −0.132819 | ||||||||
\(690\) | 25.6726 | 0.977339 | ||||||||
\(691\) | 17.0566 | 0.648865 | 0.324433 | − | 0.945909i | \(-0.394827\pi\) | ||||
0.324433 | + | 0.945909i | \(0.394827\pi\) | |||||||
\(692\) | −67.2687 | −2.55717 | ||||||||
\(693\) | 8.00333 | 0.304021 | ||||||||
\(694\) | −49.9174 | −1.89484 | ||||||||
\(695\) | −61.5292 | −2.33393 | ||||||||
\(696\) | −20.1067 | −0.762141 | ||||||||
\(697\) | 19.9062 | 0.754001 | ||||||||
\(698\) | −41.3033 | −1.56335 | ||||||||
\(699\) | −1.65716 | −0.0626797 | ||||||||
\(700\) | −67.7311 | −2.55999 | ||||||||
\(701\) | −0.324257 | −0.0122470 | −0.00612351 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612351 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(702\) | 13.7043 | 0.517236 | ||||||||
\(703\) | −7.06757 | −0.266558 | ||||||||
\(704\) | −20.4607 | −0.771142 | ||||||||
\(705\) | −38.5481 | −1.45180 | ||||||||
\(706\) | −6.37577 | −0.239955 | ||||||||
\(707\) | −29.4520 | −1.10766 | ||||||||
\(708\) | −32.5288 | −1.22251 | ||||||||
\(709\) | 16.7721 | 0.629888 | 0.314944 | − | 0.949110i | \(-0.398014\pi\) | ||||
0.314944 | + | 0.949110i | \(0.398014\pi\) | |||||||
\(710\) | 114.475 | 4.29619 | ||||||||
\(711\) | 5.31360 | 0.199276 | ||||||||
\(712\) | 33.7926 | 1.26643 | ||||||||
\(713\) | 8.47369 | 0.317342 | ||||||||
\(714\) | −20.1991 | −0.755933 | ||||||||
\(715\) | 14.0005 | 0.523588 | ||||||||
\(716\) | −4.05367 | −0.151493 | ||||||||
\(717\) | 0.578023 | 0.0215867 | ||||||||
\(718\) | 44.5486 | 1.66254 | ||||||||
\(719\) | −10.7300 | −0.400160 | −0.200080 | − | 0.979780i | \(-0.564120\pi\) | ||||
−0.200080 | + | 0.979780i | \(0.564120\pi\) | |||||||
\(720\) | −29.5747 | −1.10218 | ||||||||
\(721\) | −17.2847 | −0.643717 | ||||||||
\(722\) | 2.84437 | 0.105856 | ||||||||
\(723\) | 35.5447 | 1.32192 | ||||||||
\(724\) | −13.9921 | −0.520014 | ||||||||
\(725\) | 32.4716 | 1.20597 | ||||||||
\(726\) | −4.57925 | −0.169952 | ||||||||
\(727\) | 33.4686 | 1.24128 | 0.620641 | − | 0.784095i | \(-0.286872\pi\) | ||||
0.620641 | + | 0.784095i | \(0.286872\pi\) | |||||||
\(728\) | 8.18551 | 0.303375 | ||||||||
\(729\) | 23.8248 | 0.882399 | ||||||||
\(730\) | −71.4536 | −2.64462 | ||||||||
\(731\) | −4.08226 | −0.150988 | ||||||||
\(732\) | 28.8557 | 1.06654 | ||||||||
\(733\) | 30.5277 | 1.12757 | 0.563784 | − | 0.825922i | \(-0.309345\pi\) | ||||
0.563784 | + | 0.825922i | \(0.309345\pi\) | |||||||
\(734\) | −8.56031 | −0.315967 | ||||||||
\(735\) | −22.8097 | −0.841350 | ||||||||
\(736\) | 3.63839 | 0.134113 | ||||||||
\(737\) | −39.3299 | −1.44874 | ||||||||
\(738\) | −16.9182 | −0.622768 | ||||||||
\(739\) | −42.5417 | −1.56492 | −0.782461 | − | 0.622700i | \(-0.786036\pi\) | ||||
−0.782461 | + | 0.622700i | \(0.786036\pi\) | |||||||
\(740\) | 27.5920 | 1.01430 | ||||||||
\(741\) | −5.19713 | −0.190921 | ||||||||
\(742\) | −13.1770 | −0.483742 | ||||||||
\(743\) | 31.0324 | 1.13847 | 0.569235 | − | 0.822175i | \(-0.307240\pi\) | ||||
0.569235 | + | 0.822175i | \(0.307240\pi\) | |||||||
\(744\) | 26.4036 | 0.968002 | ||||||||
\(745\) | −82.1245 | −3.00881 | ||||||||
\(746\) | −22.3080 | −0.816755 | ||||||||
\(747\) | −9.32146 | −0.341054 | ||||||||
\(748\) | −63.9926 | −2.33980 | ||||||||
\(749\) | −5.24663 | −0.191708 | ||||||||
\(750\) | −68.7172 | −2.50920 | ||||||||
\(751\) | −9.39012 | −0.342651 | −0.171325 | − | 0.985215i | \(-0.554805\pi\) | ||||
−0.171325 | + | 0.985215i | \(0.554805\pi\) | |||||||
\(752\) | −39.7434 | −1.44929 | ||||||||
\(753\) | 8.02038 | 0.292279 | ||||||||
\(754\) | −7.54833 | −0.274894 | ||||||||
\(755\) | −42.0542 | −1.53051 | ||||||||
\(756\) | 34.9953 | 1.27277 | ||||||||
\(757\) | −5.33256 | −0.193815 | −0.0969077 | − | 0.995293i | \(-0.530895\pi\) | ||||
−0.0969077 | + | 0.995293i | \(0.530895\pi\) | |||||||
\(758\) | 36.1504 | 1.31304 | ||||||||
\(759\) | −9.23049 | −0.335046 | ||||||||
\(760\) | 89.9835 | 3.26404 | ||||||||
\(761\) | 21.0320 | 0.762411 | 0.381205 | − | 0.924490i | \(-0.375509\pi\) | ||||
0.381205 | + | 0.924490i | \(0.375509\pi\) | |||||||
\(762\) | −17.9930 | −0.651817 | ||||||||
\(763\) | −15.0191 | −0.543728 | ||||||||
\(764\) | −7.84978 | −0.283995 | ||||||||
\(765\) | 25.5898 | 0.925200 | ||||||||
\(766\) | 12.1978 | 0.440724 | ||||||||
\(767\) | −6.34877 | −0.229241 | ||||||||
\(768\) | −40.1217 | −1.44777 | ||||||||
\(769\) | 4.86203 | 0.175329 | 0.0876646 | − | 0.996150i | \(-0.472060\pi\) | ||||
0.0876646 | + | 0.996150i | \(0.472060\pi\) | |||||||
\(770\) | 52.9162 | 1.90697 | ||||||||
\(771\) | 18.7499 | 0.675262 | ||||||||
\(772\) | 43.6523 | 1.57108 | ||||||||
\(773\) | −20.8518 | −0.749988 | −0.374994 | − | 0.927027i | \(-0.622355\pi\) | ||||
−0.374994 | + | 0.927027i | \(0.622355\pi\) | |||||||
\(774\) | 3.46950 | 0.124709 | ||||||||
\(775\) | −42.6409 | −1.53171 | ||||||||
\(776\) | 7.31344 | 0.262537 | ||||||||
\(777\) | −3.13141 | −0.112339 | ||||||||
\(778\) | −43.6023 | −1.56322 | ||||||||
\(779\) | 19.3582 | 0.693581 | ||||||||
\(780\) | 20.2897 | 0.726489 | ||||||||
\(781\) | −41.1592 | −1.47279 | ||||||||
\(782\) | −22.9023 | −0.818984 | ||||||||
\(783\) | −16.7774 | −0.599576 | ||||||||
\(784\) | −23.5170 | −0.839895 | ||||||||
\(785\) | −98.6501 | −3.52097 | ||||||||
\(786\) | 17.0989 | 0.609896 | ||||||||
\(787\) | −3.99080 | −0.142257 | −0.0711284 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711284 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(788\) | 49.0845 | 1.74856 | ||||||||
\(789\) | −38.9212 | −1.38563 | ||||||||
\(790\) | 35.1323 | 1.24995 | ||||||||
\(791\) | 4.06311 | 0.144468 | ||||||||
\(792\) | 28.2753 | 1.00472 | ||||||||
\(793\) | 5.63188 | 0.199994 | ||||||||
\(794\) | 43.7297 | 1.55191 | ||||||||
\(795\) | −16.9808 | −0.602246 | ||||||||
\(796\) | −82.5202 | −2.92485 | ||||||||
\(797\) | 3.98593 | 0.141189 | 0.0705944 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705944 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(798\) | −19.6431 | −0.695358 | ||||||||
\(799\) | 34.3884 | 1.21657 | ||||||||
\(800\) | −18.3090 | −0.647319 | ||||||||
\(801\) | 9.34548 | 0.330206 | ||||||||
\(802\) | −48.3748 | −1.70817 | ||||||||
\(803\) | 25.6909 | 0.906611 | ||||||||
\(804\) | −56.9976 | −2.01015 | ||||||||
\(805\) | 12.7951 | 0.450968 | ||||||||
\(806\) | 9.91227 | 0.349145 | ||||||||
\(807\) | −13.1899 | −0.464305 | ||||||||
\(808\) | −104.052 | −3.66054 | ||||||||
\(809\) | −15.8877 | −0.558581 | −0.279291 | − | 0.960207i | \(-0.590099\pi\) | ||||
−0.279291 | + | 0.960207i | \(0.590099\pi\) | |||||||
\(810\) | 22.8776 | 0.803836 | ||||||||
\(811\) | 22.1132 | 0.776501 | 0.388251 | − | 0.921554i | \(-0.373080\pi\) | ||||
0.388251 | + | 0.921554i | \(0.373080\pi\) | |||||||
\(812\) | −19.2754 | −0.676433 | ||||||||
\(813\) | −37.2092 | −1.30498 | ||||||||
\(814\) | −14.6836 | −0.514659 | ||||||||
\(815\) | 86.0618 | 3.01461 | ||||||||
\(816\) | −26.8372 | −0.939489 | ||||||||
\(817\) | −3.96989 | −0.138889 | ||||||||
\(818\) | −80.6574 | −2.82012 | ||||||||
\(819\) | 2.26374 | 0.0791014 | ||||||||
\(820\) | −75.5751 | −2.63920 | ||||||||
\(821\) | 37.4035 | 1.30539 | 0.652696 | − | 0.757620i | \(-0.273638\pi\) | ||||
0.652696 | + | 0.757620i | \(0.273638\pi\) | |||||||
\(822\) | 43.4019 | 1.51382 | ||||||||
\(823\) | −3.04770 | −0.106236 | −0.0531181 | − | 0.998588i | \(-0.516916\pi\) | ||||
−0.0531181 | + | 0.998588i | \(0.516916\pi\) | |||||||
\(824\) | −61.0659 | −2.12733 | ||||||||
\(825\) | 46.4492 | 1.61716 | ||||||||
\(826\) | −23.9958 | −0.834922 | ||||||||
\(827\) | 25.5190 | 0.887381 | 0.443691 | − | 0.896180i | \(-0.353669\pi\) | ||||
0.443691 | + | 0.896180i | \(0.353669\pi\) | |||||||
\(828\) | 13.1508 | 0.457020 | ||||||||
\(829\) | −34.0425 | −1.18235 | −0.591173 | − | 0.806545i | \(-0.701335\pi\) | ||||
−0.591173 | + | 0.806545i | \(0.701335\pi\) | |||||||
\(830\) | −61.6314 | −2.13926 | ||||||||
\(831\) | −32.2367 | −1.11828 | ||||||||
\(832\) | −5.78731 | −0.200639 | ||||||||
\(833\) | 20.3483 | 0.705028 | ||||||||
\(834\) | 47.4531 | 1.64316 | ||||||||
\(835\) | 40.7978 | 1.41186 | ||||||||
\(836\) | −62.2310 | −2.15230 | ||||||||
\(837\) | 22.0317 | 0.761527 | ||||||||
\(838\) | 35.9584 | 1.24216 | ||||||||
\(839\) | −23.1980 | −0.800882 | −0.400441 | − | 0.916322i | \(-0.631143\pi\) | ||||
−0.400441 | + | 0.916322i | \(0.631143\pi\) | |||||||
\(840\) | 39.8688 | 1.37560 | ||||||||
\(841\) | −19.7590 | −0.681345 | ||||||||
\(842\) | −13.0220 | −0.448769 | ||||||||
\(843\) | −15.5966 | −0.537174 | ||||||||
\(844\) | −68.5731 | −2.36038 | ||||||||
\(845\) | 3.96003 | 0.136229 | ||||||||
\(846\) | −29.2266 | −1.00483 | ||||||||
\(847\) | −2.28228 | −0.0784199 | ||||||||
\(848\) | −17.5073 | −0.601204 | ||||||||
\(849\) | −7.76301 | −0.266426 | ||||||||
\(850\) | 115.248 | 3.95297 | ||||||||
\(851\) | −3.55048 | −0.121709 | ||||||||
\(852\) | −59.6488 | −2.04353 | ||||||||
\(853\) | −44.9518 | −1.53912 | −0.769560 | − | 0.638575i | \(-0.779524\pi\) | ||||
−0.769560 | + | 0.638575i | \(0.779524\pi\) | |||||||
\(854\) | 21.2863 | 0.728401 | ||||||||
\(855\) | 24.8853 | 0.851060 | ||||||||
\(856\) | −18.5360 | −0.633549 | ||||||||
\(857\) | 23.5718 | 0.805198 | 0.402599 | − | 0.915376i | \(-0.368107\pi\) | ||||
0.402599 | + | 0.915376i | \(0.368107\pi\) | |||||||
\(858\) | −10.7976 | −0.368623 | ||||||||
\(859\) | −32.1256 | −1.09611 | −0.548056 | − | 0.836442i | \(-0.684632\pi\) | ||||
−0.548056 | + | 0.836442i | \(0.684632\pi\) | |||||||
\(860\) | 15.4985 | 0.528496 | ||||||||
\(861\) | 8.57702 | 0.292304 | ||||||||
\(862\) | −88.2068 | −3.00434 | ||||||||
\(863\) | −0.0589951 | −0.00200821 | −0.00100411 | − | 0.999999i | \(-0.500320\pi\) | ||||
−0.00100411 | + | 0.999999i | \(0.500320\pi\) | |||||||
\(864\) | 9.45986 | 0.321831 | ||||||||
\(865\) | −63.9473 | −2.17427 | ||||||||
\(866\) | 21.5487 | 0.732256 | ||||||||
\(867\) | 2.31186 | 0.0785147 | ||||||||
\(868\) | 25.3119 | 0.859143 | ||||||||
\(869\) | −12.6317 | −0.428501 | ||||||||
\(870\) | −36.7653 | −1.24646 | ||||||||
\(871\) | −11.1244 | −0.376938 | ||||||||
\(872\) | −53.0616 | −1.79689 | ||||||||
\(873\) | 2.02257 | 0.0684535 | ||||||||
\(874\) | −22.2718 | −0.753356 | ||||||||
\(875\) | −34.2483 | −1.15780 | ||||||||
\(876\) | 37.2317 | 1.25794 | ||||||||
\(877\) | −37.4177 | −1.26350 | −0.631752 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631752 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(878\) | 45.1350 | 1.52323 | ||||||||
\(879\) | 9.73794 | 0.328453 | ||||||||
\(880\) | 70.3061 | 2.37002 | ||||||||
\(881\) | 25.2264 | 0.849899 | 0.424949 | − | 0.905217i | \(-0.360292\pi\) | ||||
0.424949 | + | 0.905217i | \(0.360292\pi\) | |||||||
\(882\) | −17.2940 | −0.582319 | ||||||||
\(883\) | −12.8827 | −0.433539 | −0.216769 | − | 0.976223i | \(-0.569552\pi\) | ||||
−0.216769 | + | 0.976223i | \(0.569552\pi\) | |||||||
\(884\) | −18.1003 | −0.608778 | ||||||||
\(885\) | −30.9227 | −1.03946 | ||||||||
\(886\) | −53.6655 | −1.80293 | ||||||||
\(887\) | 35.8572 | 1.20397 | 0.601983 | − | 0.798509i | \(-0.294377\pi\) | ||||
0.601983 | + | 0.798509i | \(0.294377\pi\) | |||||||
\(888\) | −11.0631 | −0.371253 | ||||||||
\(889\) | −8.96760 | −0.300764 | ||||||||
\(890\) | 61.7902 | 2.07121 | ||||||||
\(891\) | −8.22555 | −0.275566 | ||||||||
\(892\) | 37.2534 | 1.24734 | ||||||||
\(893\) | 33.4417 | 1.11909 | ||||||||
\(894\) | 63.3368 | 2.11830 | ||||||||
\(895\) | −3.85352 | −0.128809 | ||||||||
\(896\) | −27.0917 | −0.905071 | ||||||||
\(897\) | −2.61084 | −0.0871734 | ||||||||
\(898\) | 6.90222 | 0.230330 | ||||||||
\(899\) | −12.1350 | −0.404726 | ||||||||
\(900\) | −66.1766 | −2.20589 | ||||||||
\(901\) | 15.1484 | 0.504666 | ||||||||
\(902\) | 40.2187 | 1.33914 | ||||||||
\(903\) | −1.75893 | −0.0585336 | ||||||||
\(904\) | 14.3547 | 0.477432 | ||||||||
\(905\) | −13.3013 | −0.442150 | ||||||||
\(906\) | 32.4334 | 1.07753 | ||||||||
\(907\) | −5.40074 | −0.179329 | −0.0896643 | − | 0.995972i | \(-0.528579\pi\) | ||||
−0.0896643 | + | 0.995972i | \(0.528579\pi\) | |||||||
\(908\) | −71.5348 | −2.37397 | ||||||||
\(909\) | −28.7761 | −0.954441 | ||||||||
\(910\) | 14.9673 | 0.496162 | ||||||||
\(911\) | −11.6188 | −0.384947 | −0.192473 | − | 0.981302i | \(-0.561651\pi\) | ||||
−0.192473 | + | 0.981302i | \(0.561651\pi\) | |||||||
\(912\) | −26.0984 | −0.864205 | ||||||||
\(913\) | 22.1593 | 0.733367 | ||||||||
\(914\) | −5.71564 | −0.189056 | ||||||||
\(915\) | 27.4310 | 0.906840 | ||||||||
\(916\) | −30.4796 | −1.00707 | ||||||||
\(917\) | 8.52198 | 0.281421 | ||||||||
\(918\) | −59.5462 | −1.96532 | ||||||||
\(919\) | 4.53266 | 0.149519 | 0.0747593 | − | 0.997202i | \(-0.476181\pi\) | ||||
0.0747593 | + | 0.997202i | \(0.476181\pi\) | |||||||
\(920\) | 45.2043 | 1.49034 | ||||||||
\(921\) | −10.1578 | −0.334712 | ||||||||
\(922\) | −67.7770 | −2.23212 | ||||||||
\(923\) | −11.6419 | −0.383197 | ||||||||
\(924\) | −27.5726 | −0.907071 | ||||||||
\(925\) | 17.8666 | 0.587449 | ||||||||
\(926\) | −2.67088 | −0.0877705 | ||||||||
\(927\) | −16.8880 | −0.554676 | ||||||||
\(928\) | −5.21049 | −0.171043 | ||||||||
\(929\) | −2.49965 | −0.0820110 | −0.0410055 | − | 0.999159i | \(-0.513056\pi\) | ||||
−0.0410055 | + | 0.999159i | \(0.513056\pi\) | |||||||
\(930\) | 48.2793 | 1.58314 | ||||||||
\(931\) | 19.7882 | 0.648532 | ||||||||
\(932\) | −5.61261 | −0.183847 | ||||||||
\(933\) | −14.0798 | −0.460954 | ||||||||
\(934\) | 87.2702 | 2.85557 | ||||||||
\(935\) | −60.8330 | −1.98945 | ||||||||
\(936\) | 7.99765 | 0.261411 | ||||||||
\(937\) | −38.7035 | −1.26439 | −0.632193 | − | 0.774811i | \(-0.717845\pi\) | ||||
−0.632193 | + | 0.774811i | \(0.717845\pi\) | |||||||
\(938\) | −42.0460 | −1.37285 | ||||||||
\(939\) | 23.2513 | 0.758779 | ||||||||
\(940\) | −130.557 | −4.25831 | ||||||||
\(941\) | 30.2123 | 0.984893 | 0.492447 | − | 0.870343i | \(-0.336103\pi\) | ||||
0.492447 | + | 0.870343i | \(0.336103\pi\) | |||||||
\(942\) | 76.0818 | 2.47888 | ||||||||
\(943\) | 9.72484 | 0.316684 | ||||||||
\(944\) | −31.8816 | −1.03766 | ||||||||
\(945\) | 33.2674 | 1.08219 | ||||||||
\(946\) | −8.24784 | −0.268160 | ||||||||
\(947\) | 47.4280 | 1.54120 | 0.770601 | − | 0.637318i | \(-0.219956\pi\) | ||||
0.770601 | + | 0.637318i | \(0.219956\pi\) | |||||||
\(948\) | −18.3061 | −0.594555 | ||||||||
\(949\) | 7.26666 | 0.235886 | ||||||||
\(950\) | 112.075 | 3.63620 | ||||||||
\(951\) | 38.6137 | 1.25214 | ||||||||
\(952\) | −35.5666 | −1.15272 | ||||||||
\(953\) | −6.24219 | −0.202204 | −0.101102 | − | 0.994876i | \(-0.532237\pi\) | ||||
−0.101102 | + | 0.994876i | \(0.532237\pi\) | |||||||
\(954\) | −12.8746 | −0.416829 | ||||||||
\(955\) | −7.46220 | −0.241471 | ||||||||
\(956\) | 1.95769 | 0.0633163 | ||||||||
\(957\) | 13.2188 | 0.427305 | ||||||||
\(958\) | −51.6692 | −1.66936 | ||||||||
\(959\) | 21.6313 | 0.698511 | ||||||||
\(960\) | −28.1880 | −0.909764 | ||||||||
\(961\) | −15.0646 | −0.485954 | ||||||||
\(962\) | −4.15325 | −0.133906 | ||||||||
\(963\) | −5.12622 | −0.165190 | ||||||||
\(964\) | 120.386 | 3.87736 | ||||||||
\(965\) | 41.4970 | 1.33583 | ||||||||
\(966\) | −9.86794 | −0.317496 | ||||||||
\(967\) | −29.5912 | −0.951588 | −0.475794 | − | 0.879557i | \(-0.657839\pi\) | ||||
−0.475794 | + | 0.879557i | \(0.657839\pi\) | |||||||
\(968\) | −8.06315 | −0.259159 | ||||||||
\(969\) | 22.5819 | 0.725435 | ||||||||
\(970\) | 13.3727 | 0.429373 | ||||||||
\(971\) | 52.9660 | 1.69976 | 0.849879 | − | 0.526978i | \(-0.176675\pi\) | ||||
0.849879 | + | 0.526978i | \(0.176675\pi\) | |||||||
\(972\) | 57.0518 | 1.82994 | ||||||||
\(973\) | 23.6504 | 0.758196 | ||||||||
\(974\) | −64.5955 | −2.06977 | ||||||||
\(975\) | 13.1382 | 0.420758 | ||||||||
\(976\) | 28.2816 | 0.905271 | ||||||||
\(977\) | −57.4832 | −1.83905 | −0.919525 | − | 0.393031i | \(-0.871426\pi\) | ||||
−0.919525 | + | 0.393031i | \(0.871426\pi\) | |||||||
\(978\) | −66.3734 | −2.12239 | ||||||||
\(979\) | −22.2164 | −0.710040 | ||||||||
\(980\) | −77.2537 | −2.46778 | ||||||||
\(981\) | −14.6744 | −0.468518 | ||||||||
\(982\) | −78.5527 | −2.50672 | ||||||||
\(983\) | 10.4191 | 0.332317 | 0.166159 | − | 0.986099i | \(-0.446864\pi\) | ||||
0.166159 | + | 0.986099i | \(0.446864\pi\) | |||||||
\(984\) | 30.3021 | 0.965995 | ||||||||
\(985\) | 46.6610 | 1.48674 | ||||||||
\(986\) | 32.7980 | 1.04450 | ||||||||
\(987\) | 14.8170 | 0.471629 | ||||||||
\(988\) | −17.6020 | −0.559995 | ||||||||
\(989\) | −1.99432 | −0.0634157 | ||||||||
\(990\) | 51.7017 | 1.64319 | ||||||||
\(991\) | −26.4505 | −0.840226 | −0.420113 | − | 0.907472i | \(-0.638010\pi\) | ||||
−0.420113 | + | 0.907472i | \(0.638010\pi\) | |||||||
\(992\) | 6.84228 | 0.217243 | ||||||||
\(993\) | 28.9883 | 0.919915 | ||||||||
\(994\) | −44.0017 | −1.39565 | ||||||||
\(995\) | −78.4458 | −2.48690 | ||||||||
\(996\) | 32.1137 | 1.01756 | ||||||||
\(997\) | 34.8309 | 1.10311 | 0.551553 | − | 0.834140i | \(-0.314035\pi\) | ||||
0.551553 | + | 0.834140i | \(0.314035\pi\) | |||||||
\(998\) | 64.3828 | 2.03800 | ||||||||
\(999\) | −9.23128 | −0.292065 |
(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 | 8021.2.a.a.1.9 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.a.1.9 | ✓ | 134 | 1.1 | even | 1 | trivial |