Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0439663311\) |
Analytic rank: | \(1\) |
Dimension: | \(157\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51870 | −1.78099 | −0.890495 | − | 0.454992i | \(-0.849642\pi\) | ||||
−0.890495 | + | 0.454992i | \(0.849642\pi\) | |||||||
\(3\) | −2.55292 | −1.47393 | −0.736965 | − | 0.675931i | \(-0.763742\pi\) | ||||
−0.736965 | + | 0.675931i | \(0.763742\pi\) | |||||||
\(4\) | 4.34385 | 2.17193 | ||||||||
\(5\) | 0.976255 | 0.436595 | 0.218297 | − | 0.975882i | \(-0.429950\pi\) | ||||
0.218297 | + | 0.975882i | \(0.429950\pi\) | |||||||
\(6\) | 6.43005 | 2.62506 | ||||||||
\(7\) | 1.70978 | 0.646235 | 0.323117 | − | 0.946359i | \(-0.395269\pi\) | ||||
0.323117 | + | 0.946359i | \(0.395269\pi\) | |||||||
\(8\) | −5.90347 | −2.08719 | ||||||||
\(9\) | 3.51742 | 1.17247 | ||||||||
\(10\) | −2.45890 | −0.777571 | ||||||||
\(11\) | 4.17377 | 1.25844 | 0.629220 | − | 0.777228i | \(-0.283375\pi\) | ||||
0.629220 | + | 0.777228i | \(0.283375\pi\) | |||||||
\(12\) | −11.0895 | −3.20127 | ||||||||
\(13\) | −1.21071 | −0.335791 | −0.167895 | − | 0.985805i | \(-0.553697\pi\) | ||||
−0.167895 | + | 0.985805i | \(0.553697\pi\) | |||||||
\(14\) | −4.30641 | −1.15094 | ||||||||
\(15\) | −2.49230 | −0.643510 | ||||||||
\(16\) | 6.18136 | 1.54534 | ||||||||
\(17\) | −0.279831 | −0.0678691 | −0.0339345 | − | 0.999424i | \(-0.510804\pi\) | ||||
−0.0339345 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(18\) | −8.85932 | −2.08816 | ||||||||
\(19\) | 6.13525 | 1.40752 | 0.703762 | − | 0.710436i | \(-0.251502\pi\) | ||||
0.703762 | + | 0.710436i | \(0.251502\pi\) | |||||||
\(20\) | 4.24071 | 0.948252 | ||||||||
\(21\) | −4.36493 | −0.952505 | ||||||||
\(22\) | −10.5125 | −2.24127 | ||||||||
\(23\) | 2.44051 | 0.508881 | 0.254440 | − | 0.967088i | \(-0.418109\pi\) | ||||
0.254440 | + | 0.967088i | \(0.418109\pi\) | |||||||
\(24\) | 15.0711 | 3.07638 | ||||||||
\(25\) | −4.04693 | −0.809385 | ||||||||
\(26\) | 3.04942 | 0.598040 | ||||||||
\(27\) | −1.32092 | −0.254211 | ||||||||
\(28\) | 7.42702 | 1.40357 | ||||||||
\(29\) | 3.74203 | 0.694877 | 0.347439 | − | 0.937703i | \(-0.387051\pi\) | ||||
0.347439 | + | 0.937703i | \(0.387051\pi\) | |||||||
\(30\) | 6.27737 | 1.14609 | ||||||||
\(31\) | −2.71974 | −0.488479 | −0.244240 | − | 0.969715i | \(-0.578538\pi\) | ||||
−0.244240 | + | 0.969715i | \(0.578538\pi\) | |||||||
\(32\) | −3.76207 | −0.665046 | ||||||||
\(33\) | −10.6553 | −1.85485 | ||||||||
\(34\) | 0.704812 | 0.120874 | ||||||||
\(35\) | 1.66918 | 0.282143 | ||||||||
\(36\) | 15.2791 | 2.54652 | ||||||||
\(37\) | −6.09875 | −1.00263 | −0.501314 | − | 0.865265i | \(-0.667150\pi\) | ||||
−0.501314 | + | 0.865265i | \(0.667150\pi\) | |||||||
\(38\) | −15.4529 | −2.50679 | ||||||||
\(39\) | 3.09085 | 0.494932 | ||||||||
\(40\) | −5.76329 | −0.911257 | ||||||||
\(41\) | −6.40081 | −0.999639 | −0.499819 | − | 0.866130i | \(-0.666600\pi\) | ||||
−0.499819 | + | 0.866130i | \(0.666600\pi\) | |||||||
\(42\) | 10.9939 | 1.69640 | ||||||||
\(43\) | 6.04242 | 0.921460 | 0.460730 | − | 0.887540i | \(-0.347588\pi\) | ||||
0.460730 | + | 0.887540i | \(0.347588\pi\) | |||||||
\(44\) | 18.1303 | 2.73324 | ||||||||
\(45\) | 3.43390 | 0.511895 | ||||||||
\(46\) | −6.14690 | −0.906311 | ||||||||
\(47\) | −11.7029 | −1.70705 | −0.853525 | − | 0.521052i | \(-0.825540\pi\) | ||||
−0.853525 | + | 0.521052i | \(0.825540\pi\) | |||||||
\(48\) | −15.7805 | −2.27773 | ||||||||
\(49\) | −4.07667 | −0.582381 | ||||||||
\(50\) | 10.1930 | 1.44151 | ||||||||
\(51\) | 0.714388 | 0.100034 | ||||||||
\(52\) | −5.25915 | −0.729313 | ||||||||
\(53\) | 3.51186 | 0.482392 | 0.241196 | − | 0.970476i | \(-0.422460\pi\) | ||||
0.241196 | + | 0.970476i | \(0.422460\pi\) | |||||||
\(54\) | 3.32701 | 0.452748 | ||||||||
\(55\) | 4.07467 | 0.549428 | ||||||||
\(56\) | −10.0936 | −1.34882 | ||||||||
\(57\) | −15.6628 | −2.07459 | ||||||||
\(58\) | −9.42505 | −1.23757 | ||||||||
\(59\) | −10.0019 | −1.30213 | −0.651066 | − | 0.759021i | \(-0.725678\pi\) | ||||
−0.651066 | + | 0.759021i | \(0.725678\pi\) | |||||||
\(60\) | −10.8262 | −1.39766 | ||||||||
\(61\) | −7.38514 | −0.945570 | −0.472785 | − | 0.881178i | \(-0.656751\pi\) | ||||
−0.472785 | + | 0.881178i | \(0.656751\pi\) | |||||||
\(62\) | 6.85020 | 0.869977 | ||||||||
\(63\) | 6.01399 | 0.757692 | ||||||||
\(64\) | −2.88720 | −0.360900 | ||||||||
\(65\) | −1.18196 | −0.146604 | ||||||||
\(66\) | 26.8375 | 3.30347 | ||||||||
\(67\) | −9.43644 | −1.15285 | −0.576423 | − | 0.817152i | \(-0.695552\pi\) | ||||
−0.576423 | + | 0.817152i | \(0.695552\pi\) | |||||||
\(68\) | −1.21555 | −0.147407 | ||||||||
\(69\) | −6.23042 | −0.750055 | ||||||||
\(70\) | −4.20416 | −0.502493 | ||||||||
\(71\) | 1.52496 | 0.180980 | 0.0904899 | − | 0.995897i | \(-0.471157\pi\) | ||||
0.0904899 | + | 0.995897i | \(0.471157\pi\) | |||||||
\(72\) | −20.7650 | −2.44717 | ||||||||
\(73\) | −7.27110 | −0.851018 | −0.425509 | − | 0.904954i | \(-0.639905\pi\) | ||||
−0.425509 | + | 0.904954i | \(0.639905\pi\) | |||||||
\(74\) | 15.3609 | 1.78567 | ||||||||
\(75\) | 10.3315 | 1.19298 | ||||||||
\(76\) | 26.6507 | 3.05704 | ||||||||
\(77\) | 7.13621 | 0.813247 | ||||||||
\(78\) | −7.78493 | −0.881470 | ||||||||
\(79\) | −7.03448 | −0.791441 | −0.395720 | − | 0.918371i | \(-0.629505\pi\) | ||||
−0.395720 | + | 0.918371i | \(0.629505\pi\) | |||||||
\(80\) | 6.03459 | 0.674688 | ||||||||
\(81\) | −7.18004 | −0.797782 | ||||||||
\(82\) | 16.1217 | 1.78035 | ||||||||
\(83\) | −11.2907 | −1.23932 | −0.619660 | − | 0.784870i | \(-0.712730\pi\) | ||||
−0.619660 | + | 0.784870i | \(0.712730\pi\) | |||||||
\(84\) | −18.9606 | −2.06877 | ||||||||
\(85\) | −0.273187 | −0.0296313 | ||||||||
\(86\) | −15.2190 | −1.64111 | ||||||||
\(87\) | −9.55311 | −1.02420 | ||||||||
\(88\) | −24.6397 | −2.62660 | ||||||||
\(89\) | 13.8931 | 1.47266 | 0.736332 | − | 0.676620i | \(-0.236556\pi\) | ||||
0.736332 | + | 0.676620i | \(0.236556\pi\) | |||||||
\(90\) | −8.64896 | −0.911680 | ||||||||
\(91\) | −2.07004 | −0.217000 | ||||||||
\(92\) | 10.6012 | 1.10525 | ||||||||
\(93\) | 6.94328 | 0.719984 | ||||||||
\(94\) | 29.4762 | 3.04024 | ||||||||
\(95\) | 5.98957 | 0.614517 | ||||||||
\(96\) | 9.60427 | 0.980232 | ||||||||
\(97\) | 5.32653 | 0.540827 | 0.270414 | − | 0.962744i | \(-0.412840\pi\) | ||||
0.270414 | + | 0.962744i | \(0.412840\pi\) | |||||||
\(98\) | 10.2679 | 1.03721 | ||||||||
\(99\) | 14.6809 | 1.47548 | ||||||||
\(100\) | −17.5793 | −1.75793 | ||||||||
\(101\) | −0.652201 | −0.0648964 | −0.0324482 | − | 0.999473i | \(-0.510330\pi\) | ||||
−0.0324482 | + | 0.999473i | \(0.510330\pi\) | |||||||
\(102\) | −1.79933 | −0.178160 | ||||||||
\(103\) | −18.0137 | −1.77494 | −0.887471 | − | 0.460864i | \(-0.847539\pi\) | ||||
−0.887471 | + | 0.460864i | \(0.847539\pi\) | |||||||
\(104\) | 7.14739 | 0.700860 | ||||||||
\(105\) | −4.26128 | −0.415859 | ||||||||
\(106\) | −8.84534 | −0.859135 | ||||||||
\(107\) | −12.3239 | −1.19140 | −0.595700 | − | 0.803207i | \(-0.703125\pi\) | ||||
−0.595700 | + | 0.803207i | \(0.703125\pi\) | |||||||
\(108\) | −5.73789 | −0.552129 | ||||||||
\(109\) | 6.67066 | 0.638934 | 0.319467 | − | 0.947597i | \(-0.396496\pi\) | ||||
0.319467 | + | 0.947597i | \(0.396496\pi\) | |||||||
\(110\) | −10.2629 | −0.978526 | ||||||||
\(111\) | 15.5696 | 1.47781 | ||||||||
\(112\) | 10.5687 | 0.998653 | ||||||||
\(113\) | −14.3371 | −1.34872 | −0.674361 | − | 0.738402i | \(-0.735581\pi\) | ||||
−0.674361 | + | 0.738402i | \(0.735581\pi\) | |||||||
\(114\) | 39.4500 | 3.69483 | ||||||||
\(115\) | 2.38256 | 0.222175 | ||||||||
\(116\) | 16.2548 | 1.50922 | ||||||||
\(117\) | −4.25857 | −0.393705 | ||||||||
\(118\) | 25.1917 | 2.31909 | ||||||||
\(119\) | −0.478449 | −0.0438594 | ||||||||
\(120\) | 14.7132 | 1.34313 | ||||||||
\(121\) | 6.42036 | 0.583669 | ||||||||
\(122\) | 18.6010 | 1.68405 | ||||||||
\(123\) | 16.3408 | 1.47340 | ||||||||
\(124\) | −11.8141 | −1.06094 | ||||||||
\(125\) | −8.83211 | −0.789968 | ||||||||
\(126\) | −15.1474 | −1.34944 | ||||||||
\(127\) | −10.6880 | −0.948407 | −0.474203 | − | 0.880415i | \(-0.657264\pi\) | ||||
−0.474203 | + | 0.880415i | \(0.657264\pi\) | |||||||
\(128\) | 14.7961 | 1.30781 | ||||||||
\(129\) | −15.4258 | −1.35817 | ||||||||
\(130\) | 2.97701 | 0.261101 | ||||||||
\(131\) | 14.8696 | 1.29916 | 0.649580 | − | 0.760293i | \(-0.274945\pi\) | ||||
0.649580 | + | 0.760293i | \(0.274945\pi\) | |||||||
\(132\) | −46.2851 | −4.02860 | ||||||||
\(133\) | 10.4899 | 0.909591 | ||||||||
\(134\) | 23.7676 | 2.05321 | ||||||||
\(135\) | −1.28956 | −0.110987 | ||||||||
\(136\) | 1.65198 | 0.141656 | ||||||||
\(137\) | 5.83326 | 0.498369 | 0.249184 | − | 0.968456i | \(-0.419838\pi\) | ||||
0.249184 | + | 0.968456i | \(0.419838\pi\) | |||||||
\(138\) | 15.6926 | 1.33584 | ||||||||
\(139\) | 18.0239 | 1.52876 | 0.764382 | − | 0.644763i | \(-0.223044\pi\) | ||||
0.764382 | + | 0.644763i | \(0.223044\pi\) | |||||||
\(140\) | 7.25067 | 0.612793 | ||||||||
\(141\) | 29.8767 | 2.51607 | ||||||||
\(142\) | −3.84093 | −0.322323 | ||||||||
\(143\) | −5.05323 | −0.422572 | ||||||||
\(144\) | 21.7424 | 1.81187 | ||||||||
\(145\) | 3.65318 | 0.303380 | ||||||||
\(146\) | 18.3137 | 1.51566 | ||||||||
\(147\) | 10.4074 | 0.858389 | ||||||||
\(148\) | −26.4921 | −2.17764 | ||||||||
\(149\) | 20.8920 | 1.71154 | 0.855771 | − | 0.517355i | \(-0.173083\pi\) | ||||
0.855771 | + | 0.517355i | \(0.173083\pi\) | |||||||
\(150\) | −26.0219 | −2.12468 | ||||||||
\(151\) | −6.25912 | −0.509360 | −0.254680 | − | 0.967025i | \(-0.581970\pi\) | ||||
−0.254680 | + | 0.967025i | \(0.581970\pi\) | |||||||
\(152\) | −36.2193 | −2.93777 | ||||||||
\(153\) | −0.984283 | −0.0795746 | ||||||||
\(154\) | −17.9740 | −1.44839 | ||||||||
\(155\) | −2.65516 | −0.213267 | ||||||||
\(156\) | 13.4262 | 1.07496 | ||||||||
\(157\) | −9.76999 | −0.779730 | −0.389865 | − | 0.920872i | \(-0.627478\pi\) | ||||
−0.389865 | + | 0.920872i | \(0.627478\pi\) | |||||||
\(158\) | 17.7177 | 1.40955 | ||||||||
\(159\) | −8.96552 | −0.711012 | ||||||||
\(160\) | −3.67274 | −0.290356 | ||||||||
\(161\) | 4.17272 | 0.328856 | ||||||||
\(162\) | 18.0844 | 1.42084 | ||||||||
\(163\) | −0.736362 | −0.0576763 | −0.0288381 | − | 0.999584i | \(-0.509181\pi\) | ||||
−0.0288381 | + | 0.999584i | \(0.509181\pi\) | |||||||
\(164\) | −27.8042 | −2.17114 | ||||||||
\(165\) | −10.4023 | −0.809818 | ||||||||
\(166\) | 28.4380 | 2.20722 | ||||||||
\(167\) | 15.6615 | 1.21192 | 0.605961 | − | 0.795494i | \(-0.292789\pi\) | ||||
0.605961 | + | 0.795494i | \(0.292789\pi\) | |||||||
\(168\) | 25.7682 | 1.98806 | ||||||||
\(169\) | −11.5342 | −0.887245 | ||||||||
\(170\) | 0.688076 | 0.0527730 | ||||||||
\(171\) | 21.5802 | 1.65028 | ||||||||
\(172\) | 26.2474 | 2.00134 | ||||||||
\(173\) | −18.8153 | −1.43050 | −0.715249 | − | 0.698870i | \(-0.753687\pi\) | ||||
−0.715249 | + | 0.698870i | \(0.753687\pi\) | |||||||
\(174\) | 24.0614 | 1.82409 | ||||||||
\(175\) | −6.91934 | −0.523053 | ||||||||
\(176\) | 25.7996 | 1.94472 | ||||||||
\(177\) | 25.5340 | 1.91925 | ||||||||
\(178\) | −34.9925 | −2.62280 | ||||||||
\(179\) | 11.6867 | 0.873505 | 0.436753 | − | 0.899582i | \(-0.356129\pi\) | ||||
0.436753 | + | 0.899582i | \(0.356129\pi\) | |||||||
\(180\) | 14.9163 | 1.11180 | ||||||||
\(181\) | −18.4778 | −1.37345 | −0.686723 | − | 0.726919i | \(-0.740951\pi\) | ||||
−0.686723 | + | 0.726919i | \(0.740951\pi\) | |||||||
\(182\) | 5.21382 | 0.386474 | ||||||||
\(183\) | 18.8537 | 1.39371 | ||||||||
\(184\) | −14.4074 | −1.06213 | ||||||||
\(185\) | −5.95394 | −0.437742 | ||||||||
\(186\) | −17.4880 | −1.28229 | ||||||||
\(187\) | −1.16795 | −0.0854091 | ||||||||
\(188\) | −50.8359 | −3.70759 | ||||||||
\(189\) | −2.25848 | −0.164280 | ||||||||
\(190\) | −15.0859 | −1.09445 | ||||||||
\(191\) | 18.0667 | 1.30726 | 0.653631 | − | 0.756814i | \(-0.273245\pi\) | ||||
0.653631 | + | 0.756814i | \(0.273245\pi\) | |||||||
\(192\) | 7.37080 | 0.531941 | ||||||||
\(193\) | −10.2747 | −0.739591 | −0.369796 | − | 0.929113i | \(-0.620572\pi\) | ||||
−0.369796 | + | 0.929113i | \(0.620572\pi\) | |||||||
\(194\) | −13.4159 | −0.963208 | ||||||||
\(195\) | 3.01746 | 0.216085 | ||||||||
\(196\) | −17.7084 | −1.26489 | ||||||||
\(197\) | 13.8174 | 0.984445 | 0.492223 | − | 0.870469i | \(-0.336185\pi\) | ||||
0.492223 | + | 0.870469i | \(0.336185\pi\) | |||||||
\(198\) | −36.9768 | −2.62782 | ||||||||
\(199\) | 16.0122 | 1.13507 | 0.567536 | − | 0.823349i | \(-0.307897\pi\) | ||||
0.567536 | + | 0.823349i | \(0.307897\pi\) | |||||||
\(200\) | 23.8909 | 1.68934 | ||||||||
\(201\) | 24.0905 | 1.69921 | ||||||||
\(202\) | 1.64270 | 0.115580 | ||||||||
\(203\) | 6.39803 | 0.449054 | ||||||||
\(204\) | 3.10320 | 0.217267 | ||||||||
\(205\) | −6.24882 | −0.436437 | ||||||||
\(206\) | 45.3711 | 3.16115 | ||||||||
\(207\) | 8.58427 | 0.596648 | ||||||||
\(208\) | −7.48384 | −0.518911 | ||||||||
\(209\) | 25.6071 | 1.77128 | ||||||||
\(210\) | 10.7329 | 0.740640 | ||||||||
\(211\) | −15.9583 | −1.09862 | −0.549308 | − | 0.835620i | \(-0.685108\pi\) | ||||
−0.549308 | + | 0.835620i | \(0.685108\pi\) | |||||||
\(212\) | 15.2550 | 1.04772 | ||||||||
\(213\) | −3.89311 | −0.266752 | ||||||||
\(214\) | 31.0403 | 2.12187 | ||||||||
\(215\) | 5.89894 | 0.402305 | ||||||||
\(216\) | 7.79802 | 0.530588 | ||||||||
\(217\) | −4.65014 | −0.315672 | ||||||||
\(218\) | −16.8014 | −1.13794 | ||||||||
\(219\) | 18.5626 | 1.25434 | ||||||||
\(220\) | 17.6998 | 1.19332 | ||||||||
\(221\) | 0.338795 | 0.0227898 | ||||||||
\(222\) | −39.2153 | −2.63196 | ||||||||
\(223\) | −6.62629 | −0.443729 | −0.221864 | − | 0.975078i | \(-0.571214\pi\) | ||||
−0.221864 | + | 0.975078i | \(0.571214\pi\) | |||||||
\(224\) | −6.43230 | −0.429776 | ||||||||
\(225\) | −14.2347 | −0.948981 | ||||||||
\(226\) | 36.1109 | 2.40206 | ||||||||
\(227\) | −10.3331 | −0.685835 | −0.342917 | − | 0.939366i | \(-0.611415\pi\) | ||||
−0.342917 | + | 0.939366i | \(0.611415\pi\) | |||||||
\(228\) | −68.0371 | −4.50586 | ||||||||
\(229\) | −0.785016 | −0.0518753 | −0.0259376 | − | 0.999664i | \(-0.508257\pi\) | ||||
−0.0259376 | + | 0.999664i | \(0.508257\pi\) | |||||||
\(230\) | −6.00095 | −0.395691 | ||||||||
\(231\) | −18.2182 | −1.19867 | ||||||||
\(232\) | −22.0910 | −1.45034 | ||||||||
\(233\) | 19.3574 | 1.26814 | 0.634072 | − | 0.773274i | \(-0.281382\pi\) | ||||
0.634072 | + | 0.773274i | \(0.281382\pi\) | |||||||
\(234\) | 10.7261 | 0.701185 | ||||||||
\(235\) | −11.4251 | −0.745289 | ||||||||
\(236\) | −43.4467 | −2.82814 | ||||||||
\(237\) | 17.9585 | 1.16653 | ||||||||
\(238\) | 1.20507 | 0.0781131 | ||||||||
\(239\) | −8.76454 | −0.566931 | −0.283466 | − | 0.958982i | \(-0.591484\pi\) | ||||
−0.283466 | + | 0.958982i | \(0.591484\pi\) | |||||||
\(240\) | −15.4058 | −0.994443 | ||||||||
\(241\) | −14.9234 | −0.961304 | −0.480652 | − | 0.876911i | \(-0.659600\pi\) | ||||
−0.480652 | + | 0.876911i | \(0.659600\pi\) | |||||||
\(242\) | −16.1710 | −1.03951 | ||||||||
\(243\) | 22.2928 | 1.43009 | ||||||||
\(244\) | −32.0800 | −2.05371 | ||||||||
\(245\) | −3.97987 | −0.254264 | ||||||||
\(246\) | −41.1575 | −2.62411 | ||||||||
\(247\) | −7.42802 | −0.472633 | ||||||||
\(248\) | 16.0559 | 1.01955 | ||||||||
\(249\) | 28.8244 | 1.82667 | ||||||||
\(250\) | 22.2454 | 1.40693 | ||||||||
\(251\) | −9.29744 | −0.586849 | −0.293424 | − | 0.955982i | \(-0.594795\pi\) | ||||
−0.293424 | + | 0.955982i | \(0.594795\pi\) | |||||||
\(252\) | 26.1239 | 1.64565 | ||||||||
\(253\) | 10.1861 | 0.640395 | ||||||||
\(254\) | 26.9199 | 1.68910 | ||||||||
\(255\) | 0.697425 | 0.0436745 | ||||||||
\(256\) | −31.4926 | −1.96829 | ||||||||
\(257\) | −1.54505 | −0.0963777 | −0.0481889 | − | 0.998838i | \(-0.515345\pi\) | ||||
−0.0481889 | + | 0.998838i | \(0.515345\pi\) | |||||||
\(258\) | 38.8531 | 2.41889 | ||||||||
\(259\) | −10.4275 | −0.647934 | ||||||||
\(260\) | −5.13427 | −0.318414 | ||||||||
\(261\) | 13.1623 | 0.814724 | ||||||||
\(262\) | −37.4520 | −2.31379 | ||||||||
\(263\) | 4.65951 | 0.287318 | 0.143659 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143659 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(264\) | 62.9033 | 3.87143 | ||||||||
\(265\) | 3.42848 | 0.210610 | ||||||||
\(266\) | −26.4209 | −1.61997 | ||||||||
\(267\) | −35.4680 | −2.17061 | ||||||||
\(268\) | −40.9905 | −2.50390 | ||||||||
\(269\) | −10.1262 | −0.617403 | −0.308701 | − | 0.951159i | \(-0.599894\pi\) | ||||
−0.308701 | + | 0.951159i | \(0.599894\pi\) | |||||||
\(270\) | 3.24801 | 0.197667 | ||||||||
\(271\) | −1.82245 | −0.110706 | −0.0553529 | − | 0.998467i | \(-0.517628\pi\) | ||||
−0.0553529 | + | 0.998467i | \(0.517628\pi\) | |||||||
\(272\) | −1.72974 | −0.104881 | ||||||||
\(273\) | 5.28466 | 0.319842 | ||||||||
\(274\) | −14.6922 | −0.887590 | ||||||||
\(275\) | −16.8909 | −1.01856 | ||||||||
\(276\) | −27.0640 | −1.62906 | ||||||||
\(277\) | 0.423590 | 0.0254511 | 0.0127255 | − | 0.999919i | \(-0.495949\pi\) | ||||
0.0127255 | + | 0.999919i | \(0.495949\pi\) | |||||||
\(278\) | −45.3967 | −2.72272 | ||||||||
\(279\) | −9.56644 | −0.572728 | ||||||||
\(280\) | −9.85394 | −0.588886 | ||||||||
\(281\) | 11.0799 | 0.660972 | 0.330486 | − | 0.943811i | \(-0.392787\pi\) | ||||
0.330486 | + | 0.943811i | \(0.392787\pi\) | |||||||
\(282\) | −75.2505 | −4.48110 | ||||||||
\(283\) | 21.4721 | 1.27638 | 0.638192 | − | 0.769878i | \(-0.279683\pi\) | ||||
0.638192 | + | 0.769878i | \(0.279683\pi\) | |||||||
\(284\) | 6.62422 | 0.393075 | ||||||||
\(285\) | −15.2909 | −0.905756 | ||||||||
\(286\) | 12.7276 | 0.752597 | ||||||||
\(287\) | −10.9440 | −0.646001 | ||||||||
\(288\) | −13.2328 | −0.779748 | ||||||||
\(289\) | −16.9217 | −0.995394 | ||||||||
\(290\) | −9.20126 | −0.540316 | ||||||||
\(291\) | −13.5982 | −0.797142 | ||||||||
\(292\) | −31.5846 | −1.84835 | ||||||||
\(293\) | 3.52390 | 0.205869 | 0.102934 | − | 0.994688i | \(-0.467177\pi\) | ||||
0.102934 | + | 0.994688i | \(0.467177\pi\) | |||||||
\(294\) | −26.2132 | −1.52878 | ||||||||
\(295\) | −9.76438 | −0.568504 | ||||||||
\(296\) | 36.0038 | 2.09268 | ||||||||
\(297\) | −5.51322 | −0.319910 | ||||||||
\(298\) | −52.6208 | −3.04824 | ||||||||
\(299\) | −2.95475 | −0.170877 | ||||||||
\(300\) | 44.8785 | 2.59106 | ||||||||
\(301\) | 10.3312 | 0.595480 | ||||||||
\(302\) | 15.7648 | 0.907165 | ||||||||
\(303\) | 1.66502 | 0.0956528 | ||||||||
\(304\) | 37.9242 | 2.17510 | ||||||||
\(305\) | −7.20978 | −0.412831 | ||||||||
\(306\) | 2.47912 | 0.141722 | ||||||||
\(307\) | 13.7615 | 0.785410 | 0.392705 | − | 0.919664i | \(-0.371539\pi\) | ||||
0.392705 | + | 0.919664i | \(0.371539\pi\) | |||||||
\(308\) | 30.9987 | 1.76631 | ||||||||
\(309\) | 45.9876 | 2.61614 | ||||||||
\(310\) | 6.68755 | 0.379827 | ||||||||
\(311\) | −10.9347 | −0.620050 | −0.310025 | − | 0.950728i | \(-0.600337\pi\) | ||||
−0.310025 | + | 0.950728i | \(0.600337\pi\) | |||||||
\(312\) | −18.2467 | −1.03302 | ||||||||
\(313\) | −21.7170 | −1.22752 | −0.613758 | − | 0.789494i | \(-0.710343\pi\) | ||||
−0.613758 | + | 0.789494i | \(0.710343\pi\) | |||||||
\(314\) | 24.6077 | 1.38869 | ||||||||
\(315\) | 5.87119 | 0.330804 | ||||||||
\(316\) | −30.5567 | −1.71895 | ||||||||
\(317\) | −12.4820 | −0.701058 | −0.350529 | − | 0.936552i | \(-0.613998\pi\) | ||||
−0.350529 | + | 0.936552i | \(0.613998\pi\) | |||||||
\(318\) | 22.5815 | 1.26631 | ||||||||
\(319\) | 15.6184 | 0.874461 | ||||||||
\(320\) | −2.81864 | −0.157567 | ||||||||
\(321\) | 31.4621 | 1.75604 | ||||||||
\(322\) | −10.5098 | −0.585690 | ||||||||
\(323\) | −1.71684 | −0.0955274 | ||||||||
\(324\) | −31.1890 | −1.73272 | ||||||||
\(325\) | 4.89966 | 0.271784 | ||||||||
\(326\) | 1.85467 | 0.102721 | ||||||||
\(327\) | −17.0297 | −0.941744 | ||||||||
\(328\) | 37.7870 | 2.08644 | ||||||||
\(329\) | −20.0094 | −1.10315 | ||||||||
\(330\) | 26.2003 | 1.44228 | ||||||||
\(331\) | −22.2289 | −1.22181 | −0.610904 | − | 0.791704i | \(-0.709194\pi\) | ||||
−0.610904 | + | 0.791704i | \(0.709194\pi\) | |||||||
\(332\) | −49.0454 | −2.69171 | ||||||||
\(333\) | −21.4519 | −1.17555 | ||||||||
\(334\) | −39.4466 | −2.15842 | ||||||||
\(335\) | −9.21238 | −0.503326 | ||||||||
\(336\) | −26.9812 | −1.47195 | ||||||||
\(337\) | 3.88116 | 0.211420 | 0.105710 | − | 0.994397i | \(-0.466288\pi\) | ||||
0.105710 | + | 0.994397i | \(0.466288\pi\) | |||||||
\(338\) | 29.0512 | 1.58017 | ||||||||
\(339\) | 36.6015 | 1.98792 | ||||||||
\(340\) | −1.18668 | −0.0643570 | ||||||||
\(341\) | −11.3516 | −0.614721 | ||||||||
\(342\) | −54.3542 | −2.93914 | ||||||||
\(343\) | −18.9386 | −1.02259 | ||||||||
\(344\) | −35.6712 | −1.92326 | ||||||||
\(345\) | −6.08248 | −0.327470 | ||||||||
\(346\) | 47.3900 | 2.54770 | ||||||||
\(347\) | −13.1607 | −0.706505 | −0.353253 | − | 0.935528i | \(-0.614924\pi\) | ||||
−0.353253 | + | 0.935528i | \(0.614924\pi\) | |||||||
\(348\) | −41.4973 | −2.22449 | ||||||||
\(349\) | 7.05730 | 0.377768 | 0.188884 | − | 0.981999i | \(-0.439513\pi\) | ||||
0.188884 | + | 0.981999i | \(0.439513\pi\) | |||||||
\(350\) | 17.4277 | 0.931552 | ||||||||
\(351\) | 1.59925 | 0.0853618 | ||||||||
\(352\) | −15.7020 | −0.836920 | ||||||||
\(353\) | 29.9439 | 1.59376 | 0.796878 | − | 0.604141i | \(-0.206484\pi\) | ||||
0.796878 | + | 0.604141i | \(0.206484\pi\) | |||||||
\(354\) | −64.3125 | −3.41817 | ||||||||
\(355\) | 1.48875 | 0.0790148 | ||||||||
\(356\) | 60.3496 | 3.19852 | ||||||||
\(357\) | 1.22144 | 0.0646457 | ||||||||
\(358\) | −29.4353 | −1.55570 | ||||||||
\(359\) | −33.2601 | −1.75540 | −0.877700 | − | 0.479211i | \(-0.840923\pi\) | ||||
−0.877700 | + | 0.479211i | \(0.840923\pi\) | |||||||
\(360\) | −20.2719 | −1.06842 | ||||||||
\(361\) | 18.6413 | 0.981123 | ||||||||
\(362\) | 46.5401 | 2.44609 | ||||||||
\(363\) | −16.3907 | −0.860288 | ||||||||
\(364\) | −8.99197 | −0.471307 | ||||||||
\(365\) | −7.09845 | −0.371550 | ||||||||
\(366\) | −47.4868 | −2.48218 | ||||||||
\(367\) | −5.16226 | −0.269468 | −0.134734 | − | 0.990882i | \(-0.543018\pi\) | ||||
−0.134734 | + | 0.990882i | \(0.543018\pi\) | |||||||
\(368\) | 15.0857 | 0.786394 | ||||||||
\(369\) | −22.5143 | −1.17205 | ||||||||
\(370\) | 14.9962 | 0.779615 | ||||||||
\(371\) | 6.00450 | 0.311738 | ||||||||
\(372\) | 30.1606 | 1.56375 | ||||||||
\(373\) | 26.1863 | 1.35587 | 0.677937 | − | 0.735120i | \(-0.262874\pi\) | ||||
0.677937 | + | 0.735120i | \(0.262874\pi\) | |||||||
\(374\) | 2.94172 | 0.152113 | ||||||||
\(375\) | 22.5477 | 1.16436 | ||||||||
\(376\) | 69.0880 | 3.56294 | ||||||||
\(377\) | −4.53051 | −0.233333 | ||||||||
\(378\) | 5.68844 | 0.292582 | ||||||||
\(379\) | 3.33316 | 0.171213 | 0.0856064 | − | 0.996329i | \(-0.472717\pi\) | ||||
0.0856064 | + | 0.996329i | \(0.472717\pi\) | |||||||
\(380\) | 26.0178 | 1.33469 | ||||||||
\(381\) | 27.2856 | 1.39789 | ||||||||
\(382\) | −45.5046 | −2.32822 | ||||||||
\(383\) | −17.9774 | −0.918600 | −0.459300 | − | 0.888281i | \(-0.651900\pi\) | ||||
−0.459300 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(384\) | −37.7734 | −1.92761 | ||||||||
\(385\) | 6.96677 | 0.355059 | ||||||||
\(386\) | 25.8790 | 1.31721 | ||||||||
\(387\) | 21.2537 | 1.08039 | ||||||||
\(388\) | 23.1377 | 1.17464 | ||||||||
\(389\) | 23.0793 | 1.17017 | 0.585083 | − | 0.810973i | \(-0.301062\pi\) | ||||
0.585083 | + | 0.810973i | \(0.301062\pi\) | |||||||
\(390\) | −7.60008 | −0.384845 | ||||||||
\(391\) | −0.682930 | −0.0345373 | ||||||||
\(392\) | 24.0665 | 1.21554 | ||||||||
\(393\) | −37.9609 | −1.91487 | ||||||||
\(394\) | −34.8018 | −1.75329 | ||||||||
\(395\) | −6.86745 | −0.345539 | ||||||||
\(396\) | 63.7716 | 3.20464 | ||||||||
\(397\) | 18.0210 | 0.904449 | 0.452224 | − | 0.891904i | \(-0.350631\pi\) | ||||
0.452224 | + | 0.891904i | \(0.350631\pi\) | |||||||
\(398\) | −40.3298 | −2.02155 | ||||||||
\(399\) | −26.7799 | −1.34067 | ||||||||
\(400\) | −25.0155 | −1.25078 | ||||||||
\(401\) | 29.4307 | 1.46970 | 0.734848 | − | 0.678231i | \(-0.237253\pi\) | ||||
0.734848 | + | 0.678231i | \(0.237253\pi\) | |||||||
\(402\) | −60.6768 | −3.02628 | ||||||||
\(403\) | 3.29281 | 0.164027 | ||||||||
\(404\) | −2.83306 | −0.140950 | ||||||||
\(405\) | −7.00955 | −0.348307 | ||||||||
\(406\) | −16.1147 | −0.799761 | ||||||||
\(407\) | −25.4548 | −1.26175 | ||||||||
\(408\) | −4.21737 | −0.208791 | ||||||||
\(409\) | 6.01634 | 0.297489 | 0.148744 | − | 0.988876i | \(-0.452477\pi\) | ||||
0.148744 | + | 0.988876i | \(0.452477\pi\) | |||||||
\(410\) | 15.7389 | 0.777290 | ||||||||
\(411\) | −14.8919 | −0.734561 | ||||||||
\(412\) | −78.2488 | −3.85504 | ||||||||
\(413\) | −17.1010 | −0.841483 | ||||||||
\(414\) | −21.6212 | −1.06262 | ||||||||
\(415\) | −11.0227 | −0.541081 | ||||||||
\(416\) | 4.55478 | 0.223316 | ||||||||
\(417\) | −46.0136 | −2.25329 | ||||||||
\(418\) | −64.4967 | −3.15464 | ||||||||
\(419\) | −22.7558 | −1.11169 | −0.555847 | − | 0.831285i | \(-0.687606\pi\) | ||||
−0.555847 | + | 0.831285i | \(0.687606\pi\) | |||||||
\(420\) | −18.5104 | −0.903215 | ||||||||
\(421\) | −23.5312 | −1.14684 | −0.573421 | − | 0.819261i | \(-0.694384\pi\) | ||||
−0.573421 | + | 0.819261i | \(0.694384\pi\) | |||||||
\(422\) | 40.1942 | 1.95662 | ||||||||
\(423\) | −41.1641 | −2.00147 | ||||||||
\(424\) | −20.7322 | −1.00684 | ||||||||
\(425\) | 1.13246 | 0.0549322 | ||||||||
\(426\) | 9.80559 | 0.475082 | ||||||||
\(427\) | −12.6269 | −0.611060 | ||||||||
\(428\) | −53.5334 | −2.58763 | ||||||||
\(429\) | 12.9005 | 0.622842 | ||||||||
\(430\) | −14.8577 | −0.716501 | ||||||||
\(431\) | 17.1113 | 0.824222 | 0.412111 | − | 0.911134i | \(-0.364792\pi\) | ||||
0.412111 | + | 0.911134i | \(0.364792\pi\) | |||||||
\(432\) | −8.16510 | −0.392843 | ||||||||
\(433\) | −6.20289 | −0.298092 | −0.149046 | − | 0.988830i | \(-0.547620\pi\) | ||||
−0.149046 | + | 0.988830i | \(0.547620\pi\) | |||||||
\(434\) | 11.7123 | 0.562209 | ||||||||
\(435\) | −9.32628 | −0.447161 | ||||||||
\(436\) | 28.9764 | 1.38772 | ||||||||
\(437\) | 14.9731 | 0.716261 | ||||||||
\(438\) | −46.7536 | −2.23397 | ||||||||
\(439\) | −27.6279 | −1.31861 | −0.659303 | − | 0.751877i | \(-0.729149\pi\) | ||||
−0.659303 | + | 0.751877i | \(0.729149\pi\) | |||||||
\(440\) | −24.0547 | −1.14676 | ||||||||
\(441\) | −14.3393 | −0.682825 | ||||||||
\(442\) | −0.853323 | −0.0405884 | ||||||||
\(443\) | −19.8160 | −0.941487 | −0.470744 | − | 0.882270i | \(-0.656014\pi\) | ||||
−0.470744 | + | 0.882270i | \(0.656014\pi\) | |||||||
\(444\) | 67.6323 | 3.20969 | ||||||||
\(445\) | 13.5632 | 0.642958 | ||||||||
\(446\) | 16.6896 | 0.790277 | ||||||||
\(447\) | −53.3358 | −2.52269 | ||||||||
\(448\) | −4.93646 | −0.233226 | ||||||||
\(449\) | −14.6224 | −0.690075 | −0.345037 | − | 0.938589i | \(-0.612134\pi\) | ||||
−0.345037 | + | 0.938589i | \(0.612134\pi\) | |||||||
\(450\) | 35.8530 | 1.69013 | ||||||||
\(451\) | −26.7155 | −1.25798 | ||||||||
\(452\) | −62.2783 | −2.92933 | ||||||||
\(453\) | 15.9790 | 0.750761 | ||||||||
\(454\) | 26.0261 | 1.22147 | ||||||||
\(455\) | −2.02089 | −0.0947409 | ||||||||
\(456\) | 92.4650 | 4.33007 | ||||||||
\(457\) | 7.28335 | 0.340701 | 0.170350 | − | 0.985384i | \(-0.445510\pi\) | ||||
0.170350 | + | 0.985384i | \(0.445510\pi\) | |||||||
\(458\) | 1.97722 | 0.0923894 | ||||||||
\(459\) | 0.369635 | 0.0172531 | ||||||||
\(460\) | 10.3495 | 0.482547 | ||||||||
\(461\) | 2.30732 | 0.107463 | 0.0537313 | − | 0.998555i | \(-0.482889\pi\) | ||||
0.0537313 | + | 0.998555i | \(0.482889\pi\) | |||||||
\(462\) | 45.8862 | 2.13482 | ||||||||
\(463\) | 18.6412 | 0.866331 | 0.433166 | − | 0.901314i | \(-0.357397\pi\) | ||||
0.433166 | + | 0.901314i | \(0.357397\pi\) | |||||||
\(464\) | 23.1308 | 1.07382 | ||||||||
\(465\) | 6.77841 | 0.314341 | ||||||||
\(466\) | −48.7554 | −2.25855 | ||||||||
\(467\) | −10.6130 | −0.491112 | −0.245556 | − | 0.969382i | \(-0.578971\pi\) | ||||
−0.245556 | + | 0.969382i | \(0.578971\pi\) | |||||||
\(468\) | −18.4986 | −0.855099 | ||||||||
\(469\) | −16.1342 | −0.745008 | ||||||||
\(470\) | 28.7763 | 1.32735 | ||||||||
\(471\) | 24.9420 | 1.14927 | ||||||||
\(472\) | 59.0457 | 2.71780 | ||||||||
\(473\) | 25.2197 | 1.15960 | ||||||||
\(474\) | −45.2320 | −2.07758 | ||||||||
\(475\) | −24.8289 | −1.13923 | ||||||||
\(476\) | −2.07831 | −0.0952593 | ||||||||
\(477\) | 12.3527 | 0.565591 | ||||||||
\(478\) | 22.0753 | 1.00970 | ||||||||
\(479\) | −30.5907 | −1.39772 | −0.698861 | − | 0.715257i | \(-0.746310\pi\) | ||||
−0.698861 | + | 0.715257i | \(0.746310\pi\) | |||||||
\(480\) | 9.37622 | 0.427964 | ||||||||
\(481\) | 7.38383 | 0.336674 | ||||||||
\(482\) | 37.5877 | 1.71207 | ||||||||
\(483\) | −10.6526 | −0.484711 | ||||||||
\(484\) | 27.8891 | 1.26769 | ||||||||
\(485\) | 5.20005 | 0.236122 | ||||||||
\(486\) | −56.1490 | −2.54697 | ||||||||
\(487\) | −8.66128 | −0.392480 | −0.196240 | − | 0.980556i | \(-0.562873\pi\) | ||||
−0.196240 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(488\) | 43.5979 | 1.97359 | ||||||||
\(489\) | 1.87987 | 0.0850109 | ||||||||
\(490\) | 10.0241 | 0.452842 | ||||||||
\(491\) | 5.06921 | 0.228770 | 0.114385 | − | 0.993436i | \(-0.463510\pi\) | ||||
0.114385 | + | 0.993436i | \(0.463510\pi\) | |||||||
\(492\) | 70.9819 | 3.20011 | ||||||||
\(493\) | −1.04714 | −0.0471607 | ||||||||
\(494\) | 18.7090 | 0.841756 | ||||||||
\(495\) | 14.3323 | 0.644189 | ||||||||
\(496\) | −16.8117 | −0.754867 | ||||||||
\(497\) | 2.60735 | 0.116955 | ||||||||
\(498\) | −72.6001 | −3.25329 | ||||||||
\(499\) | 23.8025 | 1.06554 | 0.532772 | − | 0.846259i | \(-0.321150\pi\) | ||||
0.532772 | + | 0.846259i | \(0.321150\pi\) | |||||||
\(500\) | −38.3654 | −1.71575 | ||||||||
\(501\) | −39.9826 | −1.78629 | ||||||||
\(502\) | 23.4175 | 1.04517 | ||||||||
\(503\) | 4.87344 | 0.217296 | 0.108648 | − | 0.994080i | \(-0.465348\pi\) | ||||
0.108648 | + | 0.994080i | \(0.465348\pi\) | |||||||
\(504\) | −35.5034 | −1.58145 | ||||||||
\(505\) | −0.636714 | −0.0283334 | ||||||||
\(506\) | −25.6558 | −1.14054 | ||||||||
\(507\) | 29.4459 | 1.30774 | ||||||||
\(508\) | −46.4271 | −2.05987 | ||||||||
\(509\) | −38.5669 | −1.70945 | −0.854724 | − | 0.519083i | \(-0.826273\pi\) | ||||
−0.854724 | + | 0.519083i | \(0.826273\pi\) | |||||||
\(510\) | −1.75661 | −0.0777838 | ||||||||
\(511\) | −12.4320 | −0.549958 | ||||||||
\(512\) | 49.7283 | 2.19770 | ||||||||
\(513\) | −8.10419 | −0.357809 | ||||||||
\(514\) | 3.89153 | 0.171648 | ||||||||
\(515\) | −17.5860 | −0.774930 | ||||||||
\(516\) | −67.0076 | −2.94984 | ||||||||
\(517\) | −48.8454 | −2.14822 | ||||||||
\(518\) | 26.2638 | 1.15396 | ||||||||
\(519\) | 48.0339 | 2.10845 | ||||||||
\(520\) | 6.97768 | 0.305992 | ||||||||
\(521\) | 33.6265 | 1.47321 | 0.736603 | − | 0.676325i | \(-0.236429\pi\) | ||||
0.736603 | + | 0.676325i | \(0.236429\pi\) | |||||||
\(522\) | −33.1518 | −1.45102 | ||||||||
\(523\) | −27.3723 | −1.19691 | −0.598453 | − | 0.801158i | \(-0.704218\pi\) | ||||
−0.598453 | + | 0.801158i | \(0.704218\pi\) | |||||||
\(524\) | 64.5913 | 2.82168 | ||||||||
\(525\) | 17.6645 | 0.770943 | ||||||||
\(526\) | −11.7359 | −0.511710 | ||||||||
\(527\) | 0.761068 | 0.0331526 | ||||||||
\(528\) | −65.8644 | −2.86638 | ||||||||
\(529\) | −17.0439 | −0.741041 | ||||||||
\(530\) | −8.63531 | −0.375094 | ||||||||
\(531\) | −35.1807 | −1.52671 | ||||||||
\(532\) | 45.5666 | 1.97556 | ||||||||
\(533\) | 7.74953 | 0.335669 | ||||||||
\(534\) | 89.3333 | 3.86583 | ||||||||
\(535\) | −12.0313 | −0.520159 | ||||||||
\(536\) | 55.7078 | 2.40621 | ||||||||
\(537\) | −29.8352 | −1.28749 | ||||||||
\(538\) | 25.5048 | 1.09959 | ||||||||
\(539\) | −17.0151 | −0.732891 | ||||||||
\(540\) | −5.60165 | −0.241056 | ||||||||
\(541\) | −12.0840 | −0.519530 | −0.259765 | − | 0.965672i | \(-0.583645\pi\) | ||||
−0.259765 | + | 0.965672i | \(0.583645\pi\) | |||||||
\(542\) | 4.59020 | 0.197166 | ||||||||
\(543\) | 47.1725 | 2.02436 | ||||||||
\(544\) | 1.05275 | 0.0451361 | ||||||||
\(545\) | 6.51227 | 0.278955 | ||||||||
\(546\) | −13.3105 | −0.569636 | ||||||||
\(547\) | −21.9258 | −0.937481 | −0.468741 | − | 0.883336i | \(-0.655292\pi\) | ||||
−0.468741 | + | 0.883336i | \(0.655292\pi\) | |||||||
\(548\) | 25.3388 | 1.08242 | ||||||||
\(549\) | −25.9766 | −1.10865 | ||||||||
\(550\) | 42.5432 | 1.81405 | ||||||||
\(551\) | 22.9583 | 0.978056 | ||||||||
\(552\) | 36.7811 | 1.56551 | ||||||||
\(553\) | −12.0274 | −0.511456 | ||||||||
\(554\) | −1.06690 | −0.0453281 | ||||||||
\(555\) | 15.2000 | 0.645202 | ||||||||
\(556\) | 78.2931 | 3.32037 | ||||||||
\(557\) | 11.1586 | 0.472806 | 0.236403 | − | 0.971655i | \(-0.424032\pi\) | ||||
0.236403 | + | 0.971655i | \(0.424032\pi\) | |||||||
\(558\) | 24.0950 | 1.02002 | ||||||||
\(559\) | −7.31562 | −0.309418 | ||||||||
\(560\) | 10.3178 | 0.436006 | ||||||||
\(561\) | 2.98169 | 0.125887 | ||||||||
\(562\) | −27.9070 | −1.17718 | ||||||||
\(563\) | −18.5865 | −0.783330 | −0.391665 | − | 0.920108i | \(-0.628101\pi\) | ||||
−0.391665 | + | 0.920108i | \(0.628101\pi\) | |||||||
\(564\) | 129.780 | 5.46473 | ||||||||
\(565\) | −13.9967 | −0.588845 | ||||||||
\(566\) | −54.0818 | −2.27323 | ||||||||
\(567\) | −12.2763 | −0.515554 | ||||||||
\(568\) | −9.00258 | −0.377740 | ||||||||
\(569\) | 32.0351 | 1.34298 | 0.671490 | − | 0.741013i | \(-0.265655\pi\) | ||||
0.671490 | + | 0.741013i | \(0.265655\pi\) | |||||||
\(570\) | 38.5133 | 1.61314 | ||||||||
\(571\) | −24.3165 | −1.01761 | −0.508807 | − | 0.860881i | \(-0.669913\pi\) | ||||
−0.508807 | + | 0.860881i | \(0.669913\pi\) | |||||||
\(572\) | −21.9505 | −0.917796 | ||||||||
\(573\) | −46.1229 | −1.92681 | ||||||||
\(574\) | 27.5645 | 1.15052 | ||||||||
\(575\) | −9.87654 | −0.411880 | ||||||||
\(576\) | −10.1555 | −0.423145 | ||||||||
\(577\) | 6.44589 | 0.268346 | 0.134173 | − | 0.990958i | \(-0.457162\pi\) | ||||
0.134173 | + | 0.990958i | \(0.457162\pi\) | |||||||
\(578\) | 42.6207 | 1.77279 | ||||||||
\(579\) | 26.2306 | 1.09011 | ||||||||
\(580\) | 15.8689 | 0.658919 | ||||||||
\(581\) | −19.3046 | −0.800892 | ||||||||
\(582\) | 34.2499 | 1.41970 | ||||||||
\(583\) | 14.6577 | 0.607060 | ||||||||
\(584\) | 42.9247 | 1.77624 | ||||||||
\(585\) | −4.15745 | −0.171890 | ||||||||
\(586\) | −8.87565 | −0.366650 | ||||||||
\(587\) | −1.84073 | −0.0759752 | −0.0379876 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379876 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(588\) | 45.2083 | 1.86436 | ||||||||
\(589\) | −16.6863 | −0.687546 | ||||||||
\(590\) | 24.5935 | 1.01250 | ||||||||
\(591\) | −35.2746 | −1.45100 | ||||||||
\(592\) | −37.6986 | −1.54940 | ||||||||
\(593\) | −11.1782 | −0.459034 | −0.229517 | − | 0.973305i | \(-0.573715\pi\) | ||||
−0.229517 | + | 0.973305i | \(0.573715\pi\) | |||||||
\(594\) | 13.8862 | 0.569756 | ||||||||
\(595\) | −0.467088 | −0.0191488 | ||||||||
\(596\) | 90.7520 | 3.71735 | ||||||||
\(597\) | −40.8778 | −1.67302 | ||||||||
\(598\) | 7.44212 | 0.304331 | ||||||||
\(599\) | −19.5645 | −0.799383 | −0.399691 | − | 0.916650i | \(-0.630883\pi\) | ||||
−0.399691 | + | 0.916650i | \(0.630883\pi\) | |||||||
\(600\) | −60.9916 | −2.48997 | ||||||||
\(601\) | 39.0613 | 1.59334 | 0.796671 | − | 0.604413i | \(-0.206592\pi\) | ||||
0.796671 | + | 0.604413i | \(0.206592\pi\) | |||||||
\(602\) | −26.0212 | −1.06054 | ||||||||
\(603\) | −33.1919 | −1.35168 | ||||||||
\(604\) | −27.1887 | −1.10629 | ||||||||
\(605\) | 6.26791 | 0.254827 | ||||||||
\(606\) | −4.19368 | −0.170357 | ||||||||
\(607\) | 35.5059 | 1.44114 | 0.720571 | − | 0.693381i | \(-0.243880\pi\) | ||||
0.720571 | + | 0.693381i | \(0.243880\pi\) | |||||||
\(608\) | −23.0813 | −0.936068 | ||||||||
\(609\) | −16.3337 | −0.661874 | ||||||||
\(610\) | 18.1593 | 0.735248 | ||||||||
\(611\) | 14.1689 | 0.573211 | ||||||||
\(612\) | −4.27558 | −0.172830 | ||||||||
\(613\) | 18.6224 | 0.752152 | 0.376076 | − | 0.926589i | \(-0.377273\pi\) | ||||
0.376076 | + | 0.926589i | \(0.377273\pi\) | |||||||
\(614\) | −34.6611 | −1.39881 | ||||||||
\(615\) | 15.9528 | 0.643278 | ||||||||
\(616\) | −42.1284 | −1.69740 | ||||||||
\(617\) | −38.8603 | −1.56446 | −0.782229 | − | 0.622991i | \(-0.785917\pi\) | ||||
−0.782229 | + | 0.622991i | \(0.785917\pi\) | |||||||
\(618\) | −115.829 | −4.65932 | ||||||||
\(619\) | −45.1865 | −1.81620 | −0.908100 | − | 0.418753i | \(-0.862467\pi\) | ||||
−0.908100 | + | 0.418753i | \(0.862467\pi\) | |||||||
\(620\) | −11.5336 | −0.463201 | ||||||||
\(621\) | −3.22372 | −0.129363 | ||||||||
\(622\) | 27.5412 | 1.10430 | ||||||||
\(623\) | 23.7541 | 0.951687 | ||||||||
\(624\) | 19.1057 | 0.764839 | ||||||||
\(625\) | 11.6122 | 0.464489 | ||||||||
\(626\) | 54.6986 | 2.18619 | ||||||||
\(627\) | −65.3731 | −2.61075 | ||||||||
\(628\) | −42.4394 | −1.69352 | ||||||||
\(629\) | 1.70662 | 0.0680475 | ||||||||
\(630\) | −14.7878 | −0.589159 | ||||||||
\(631\) | 19.3404 | 0.769928 | 0.384964 | − | 0.922932i | \(-0.374214\pi\) | ||||
0.384964 | + | 0.922932i | \(0.374214\pi\) | |||||||
\(632\) | 41.5278 | 1.65189 | ||||||||
\(633\) | 40.7403 | 1.61928 | ||||||||
\(634\) | 31.4384 | 1.24858 | ||||||||
\(635\) | −10.4342 | −0.414069 | ||||||||
\(636\) | −38.9449 | −1.54427 | ||||||||
\(637\) | 4.93566 | 0.195558 | ||||||||
\(638\) | −39.3380 | −1.55741 | ||||||||
\(639\) | 5.36393 | 0.212194 | ||||||||
\(640\) | 14.4448 | 0.570981 | ||||||||
\(641\) | 20.9738 | 0.828414 | 0.414207 | − | 0.910183i | \(-0.364059\pi\) | ||||
0.414207 | + | 0.910183i | \(0.364059\pi\) | |||||||
\(642\) | −79.2435 | −3.12749 | ||||||||
\(643\) | 28.2448 | 1.11387 | 0.556933 | − | 0.830557i | \(-0.311978\pi\) | ||||
0.556933 | + | 0.830557i | \(0.311978\pi\) | |||||||
\(644\) | 18.1257 | 0.714252 | ||||||||
\(645\) | −15.0595 | −0.592969 | ||||||||
\(646\) | 4.32420 | 0.170133 | ||||||||
\(647\) | −19.2848 | −0.758164 | −0.379082 | − | 0.925363i | \(-0.623760\pi\) | ||||
−0.379082 | + | 0.925363i | \(0.623760\pi\) | |||||||
\(648\) | 42.3871 | 1.66512 | ||||||||
\(649\) | −41.7455 | −1.63865 | ||||||||
\(650\) | −12.3408 | −0.484045 | ||||||||
\(651\) | 11.8715 | 0.465279 | ||||||||
\(652\) | −3.19865 | −0.125269 | ||||||||
\(653\) | 21.0938 | 0.825465 | 0.412732 | − | 0.910852i | \(-0.364574\pi\) | ||||
0.412732 | + | 0.910852i | \(0.364574\pi\) | |||||||
\(654\) | 42.8927 | 1.67724 | ||||||||
\(655\) | 14.5165 | 0.567206 | ||||||||
\(656\) | −39.5657 | −1.54478 | ||||||||
\(657\) | −25.5755 | −0.997795 | ||||||||
\(658\) | 50.3977 | 1.96471 | ||||||||
\(659\) | 26.2056 | 1.02082 | 0.510412 | − | 0.859930i | \(-0.329493\pi\) | ||||
0.510412 | + | 0.859930i | \(0.329493\pi\) | |||||||
\(660\) | −45.1861 | −1.75887 | ||||||||
\(661\) | 33.0047 | 1.28373 | 0.641867 | − | 0.766816i | \(-0.278160\pi\) | ||||
0.641867 | + | 0.766816i | \(0.278160\pi\) | |||||||
\(662\) | 55.9879 | 2.17603 | ||||||||
\(663\) | −0.864917 | −0.0335906 | ||||||||
\(664\) | 66.6546 | 2.58670 | ||||||||
\(665\) | 10.2408 | 0.397122 | ||||||||
\(666\) | 54.0308 | 2.09365 | ||||||||
\(667\) | 9.13244 | 0.353610 | ||||||||
\(668\) | 68.0312 | 2.63221 | ||||||||
\(669\) | 16.9164 | 0.654026 | ||||||||
\(670\) | 23.2032 | 0.896419 | ||||||||
\(671\) | −30.8239 | −1.18994 | ||||||||
\(672\) | 16.4212 | 0.633460 | ||||||||
\(673\) | 10.3076 | 0.397328 | 0.198664 | − | 0.980068i | \(-0.436340\pi\) | ||||
0.198664 | + | 0.980068i | \(0.436340\pi\) | |||||||
\(674\) | −9.77549 | −0.376538 | ||||||||
\(675\) | 5.34567 | 0.205755 | ||||||||
\(676\) | −50.1028 | −1.92703 | ||||||||
\(677\) | 43.8215 | 1.68420 | 0.842098 | − | 0.539325i | \(-0.181320\pi\) | ||||
0.842098 | + | 0.539325i | \(0.181320\pi\) | |||||||
\(678\) | −92.1883 | −3.54047 | ||||||||
\(679\) | 9.10718 | 0.349501 | ||||||||
\(680\) | 1.61275 | 0.0618462 | ||||||||
\(681\) | 26.3797 | 1.01087 | ||||||||
\(682\) | 28.5912 | 1.09481 | ||||||||
\(683\) | 1.49346 | 0.0571457 | 0.0285729 | − | 0.999592i | \(-0.490904\pi\) | ||||
0.0285729 | + | 0.999592i | \(0.490904\pi\) | |||||||
\(684\) | 93.7414 | 3.58429 | ||||||||
\(685\) | 5.69475 | 0.217585 | ||||||||
\(686\) | 47.7007 | 1.82122 | ||||||||
\(687\) | 2.00408 | 0.0764606 | ||||||||
\(688\) | 37.3504 | 1.42397 | ||||||||
\(689\) | −4.25185 | −0.161983 | ||||||||
\(690\) | 15.3200 | 0.583221 | ||||||||
\(691\) | −21.6368 | −0.823103 | −0.411551 | − | 0.911387i | \(-0.635013\pi\) | ||||
−0.411551 | + | 0.911387i | \(0.635013\pi\) | |||||||
\(692\) | −81.7308 | −3.10694 | ||||||||
\(693\) | 25.1010 | 0.953509 | ||||||||
\(694\) | 33.1480 | 1.25828 | ||||||||
\(695\) | 17.5959 | 0.667451 | ||||||||
\(696\) | 56.3965 | 2.13770 | ||||||||
\(697\) | 1.79115 | 0.0678446 | ||||||||
\(698\) | −17.7752 | −0.672802 | ||||||||
\(699\) | −49.4179 | −1.86915 | ||||||||
\(700\) | −30.0566 | −1.13603 | ||||||||
\(701\) | 39.4637 | 1.49052 | 0.745262 | − | 0.666772i | \(-0.232325\pi\) | ||||
0.745262 | + | 0.666772i | \(0.232325\pi\) | |||||||
\(702\) | −4.02804 | −0.152029 | ||||||||
\(703\) | −37.4174 | −1.41122 | ||||||||
\(704\) | −12.0505 | −0.454170 | ||||||||
\(705\) | 29.1673 | 1.09850 | ||||||||
\(706\) | −75.4198 | −2.83846 | ||||||||
\(707\) | −1.11512 | −0.0419383 | ||||||||
\(708\) | 110.916 | 4.16848 | ||||||||
\(709\) | 27.1583 | 1.01995 | 0.509975 | − | 0.860189i | \(-0.329655\pi\) | ||||
0.509975 | + | 0.860189i | \(0.329655\pi\) | |||||||
\(710\) | −3.74973 | −0.140725 | ||||||||
\(711\) | −24.7432 | −0.927942 | ||||||||
\(712\) | −82.0174 | −3.07373 | ||||||||
\(713\) | −6.63753 | −0.248578 | ||||||||
\(714\) | −3.07645 | −0.115133 | ||||||||
\(715\) | −4.93324 | −0.184493 | ||||||||
\(716\) | 50.7653 | 1.89719 | ||||||||
\(717\) | 22.3752 | 0.835617 | ||||||||
\(718\) | 83.7722 | 3.12635 | ||||||||
\(719\) | −15.7274 | −0.586532 | −0.293266 | − | 0.956031i | \(-0.594742\pi\) | ||||
−0.293266 | + | 0.956031i | \(0.594742\pi\) | |||||||
\(720\) | 21.2262 | 0.791052 | ||||||||
\(721\) | −30.7994 | −1.14703 | ||||||||
\(722\) | −46.9520 | −1.74737 | ||||||||
\(723\) | 38.0984 | 1.41690 | ||||||||
\(724\) | −80.2650 | −2.98302 | ||||||||
\(725\) | −15.1437 | −0.562423 | ||||||||
\(726\) | 41.2832 | 1.53216 | ||||||||
\(727\) | 26.6803 | 0.989519 | 0.494759 | − | 0.869030i | \(-0.335256\pi\) | ||||
0.494759 | + | 0.869030i | \(0.335256\pi\) | |||||||
\(728\) | 12.2204 | 0.452920 | ||||||||
\(729\) | −35.3718 | −1.31007 | ||||||||
\(730\) | 17.8789 | 0.661727 | ||||||||
\(731\) | −1.69086 | −0.0625387 | ||||||||
\(732\) | 81.8977 | 3.02703 | ||||||||
\(733\) | −39.8165 | −1.47066 | −0.735328 | − | 0.677711i | \(-0.762972\pi\) | ||||
−0.735328 | + | 0.677711i | \(0.762972\pi\) | |||||||
\(734\) | 13.0022 | 0.479919 | ||||||||
\(735\) | 10.1603 | 0.374768 | ||||||||
\(736\) | −9.18135 | −0.338429 | ||||||||
\(737\) | −39.3856 | −1.45079 | ||||||||
\(738\) | 56.7068 | 2.08741 | ||||||||
\(739\) | −32.1444 | −1.18245 | −0.591226 | − | 0.806506i | \(-0.701356\pi\) | ||||
−0.591226 | + | 0.806506i | \(0.701356\pi\) | |||||||
\(740\) | −25.8631 | −0.950745 | ||||||||
\(741\) | 18.9632 | 0.696629 | ||||||||
\(742\) | −15.1235 | −0.555203 | ||||||||
\(743\) | 44.7205 | 1.64064 | 0.820319 | − | 0.571907i | \(-0.193796\pi\) | ||||
0.820319 | + | 0.571907i | \(0.193796\pi\) | |||||||
\(744\) | −40.9894 | −1.50275 | ||||||||
\(745\) | 20.3960 | 0.747250 | ||||||||
\(746\) | −65.9554 | −2.41480 | ||||||||
\(747\) | −39.7142 | −1.45307 | ||||||||
\(748\) | −5.07341 | −0.185502 | ||||||||
\(749\) | −21.0712 | −0.769924 | ||||||||
\(750\) | −56.7909 | −2.07371 | ||||||||
\(751\) | 2.21974 | 0.0809995 | 0.0404998 | − | 0.999180i | \(-0.487105\pi\) | ||||
0.0404998 | + | 0.999180i | \(0.487105\pi\) | |||||||
\(752\) | −72.3402 | −2.63797 | ||||||||
\(753\) | 23.7356 | 0.864975 | ||||||||
\(754\) | 11.4110 | 0.415565 | ||||||||
\(755\) | −6.11049 | −0.222384 | ||||||||
\(756\) | −9.81051 | −0.356805 | ||||||||
\(757\) | −0.203274 | −0.00738811 | −0.00369406 | − | 0.999993i | \(-0.501176\pi\) | ||||
−0.00369406 | + | 0.999993i | \(0.501176\pi\) | |||||||
\(758\) | −8.39522 | −0.304928 | ||||||||
\(759\) | −26.0043 | −0.943898 | ||||||||
\(760\) | −35.3593 | −1.28262 | ||||||||
\(761\) | 46.5798 | 1.68852 | 0.844259 | − | 0.535936i | \(-0.180041\pi\) | ||||
0.844259 | + | 0.535936i | \(0.180041\pi\) | |||||||
\(762\) | −68.7244 | −2.48962 | ||||||||
\(763\) | 11.4053 | 0.412901 | ||||||||
\(764\) | 78.4792 | 2.83928 | ||||||||
\(765\) | −0.960912 | −0.0347418 | ||||||||
\(766\) | 45.2796 | 1.63602 | ||||||||
\(767\) | 12.1094 | 0.437244 | ||||||||
\(768\) | 80.3983 | 2.90112 | ||||||||
\(769\) | −51.7065 | −1.86458 | −0.932291 | − | 0.361708i | \(-0.882194\pi\) | ||||
−0.932291 | + | 0.361708i | \(0.882194\pi\) | |||||||
\(770\) | −17.5472 | −0.632357 | ||||||||
\(771\) | 3.94440 | 0.142054 | ||||||||
\(772\) | −44.6319 | −1.60634 | ||||||||
\(773\) | −18.9385 | −0.681171 | −0.340586 | − | 0.940213i | \(-0.610625\pi\) | ||||
−0.340586 | + | 0.940213i | \(0.610625\pi\) | |||||||
\(774\) | −53.5317 | −1.92416 | ||||||||
\(775\) | 11.0066 | 0.395368 | ||||||||
\(776\) | −31.4450 | −1.12881 | ||||||||
\(777\) | 26.6206 | 0.955009 | ||||||||
\(778\) | −58.1298 | −2.08406 | ||||||||
\(779\) | −39.2706 | −1.40701 | ||||||||
\(780\) | 13.1074 | 0.469320 | ||||||||
\(781\) | 6.36485 | 0.227752 | ||||||||
\(782\) | 1.72010 | 0.0615105 | ||||||||
\(783\) | −4.94293 | −0.176646 | ||||||||
\(784\) | −25.1994 | −0.899977 | ||||||||
\(785\) | −9.53801 | −0.340426 | ||||||||
\(786\) | 95.6121 | 3.41037 | ||||||||
\(787\) | −49.9533 | −1.78064 | −0.890322 | − | 0.455332i | \(-0.849521\pi\) | ||||
−0.890322 | + | 0.455332i | \(0.849521\pi\) | |||||||
\(788\) | 60.0206 | 2.13814 | ||||||||
\(789\) | −11.8954 | −0.423487 | ||||||||
\(790\) | 17.2970 | 0.615401 | ||||||||
\(791\) | −24.5132 | −0.871591 | ||||||||
\(792\) | −86.6681 | −3.07962 | ||||||||
\(793\) | 8.94127 | 0.317514 | ||||||||
\(794\) | −45.3896 | −1.61081 | ||||||||
\(795\) | −8.75263 | −0.310424 | ||||||||
\(796\) | 69.5545 | 2.46529 | ||||||||
\(797\) | −1.86555 | −0.0660811 | −0.0330405 | − | 0.999454i | \(-0.510519\pi\) | ||||
−0.0330405 | + | 0.999454i | \(0.510519\pi\) | |||||||
\(798\) | 67.4506 | 2.38773 | ||||||||
\(799\) | 3.27485 | 0.115856 | ||||||||
\(800\) | 15.2248 | 0.538279 | ||||||||
\(801\) | 48.8678 | 1.72666 | ||||||||
\(802\) | −74.1270 | −2.61752 | ||||||||
\(803\) | −30.3479 | −1.07095 | ||||||||
\(804\) | 104.646 | 3.69057 | ||||||||
\(805\) | 4.07364 | 0.143577 | ||||||||
\(806\) | −8.29361 | −0.292130 | ||||||||
\(807\) | 25.8513 | 0.910009 | ||||||||
\(808\) | 3.85025 | 0.135451 | ||||||||
\(809\) | 1.92498 | 0.0676786 | 0.0338393 | − | 0.999427i | \(-0.489227\pi\) | ||||
0.0338393 | + | 0.999427i | \(0.489227\pi\) | |||||||
\(810\) | 17.6550 | 0.620332 | ||||||||
\(811\) | 12.0173 | 0.421984 | 0.210992 | − | 0.977488i | \(-0.432331\pi\) | ||||
0.210992 | + | 0.977488i | \(0.432331\pi\) | |||||||
\(812\) | 27.7921 | 0.975312 | ||||||||
\(813\) | 4.65257 | 0.163173 | ||||||||
\(814\) | 64.1130 | 2.24716 | ||||||||
\(815\) | −0.718877 | −0.0251812 | ||||||||
\(816\) | 4.41589 | 0.154587 | ||||||||
\(817\) | 37.0718 | 1.29698 | ||||||||
\(818\) | −15.1534 | −0.529825 | ||||||||
\(819\) | −7.28120 | −0.254426 | ||||||||
\(820\) | −27.1440 | −0.947909 | ||||||||
\(821\) | 43.7978 | 1.52855 | 0.764276 | − | 0.644889i | \(-0.223096\pi\) | ||||
0.764276 | + | 0.644889i | \(0.223096\pi\) | |||||||
\(822\) | 37.5081 | 1.30825 | ||||||||
\(823\) | −6.62175 | −0.230820 | −0.115410 | − | 0.993318i | \(-0.536818\pi\) | ||||
−0.115410 | + | 0.993318i | \(0.536818\pi\) | |||||||
\(824\) | 106.343 | 3.70464 | ||||||||
\(825\) | 43.1213 | 1.50129 | ||||||||
\(826\) | 43.0722 | 1.49867 | ||||||||
\(827\) | −54.8145 | −1.90609 | −0.953043 | − | 0.302836i | \(-0.902066\pi\) | ||||
−0.953043 | + | 0.302836i | \(0.902066\pi\) | |||||||
\(828\) | 37.2888 | 1.29588 | ||||||||
\(829\) | 8.66582 | 0.300976 | 0.150488 | − | 0.988612i | \(-0.451915\pi\) | ||||
0.150488 | + | 0.988612i | \(0.451915\pi\) | |||||||
\(830\) | 27.7628 | 0.963659 | ||||||||
\(831\) | −1.08139 | −0.0375131 | ||||||||
\(832\) | 3.49556 | 0.121187 | ||||||||
\(833\) | 1.14078 | 0.0395257 | ||||||||
\(834\) | 115.894 | 4.01309 | ||||||||
\(835\) | 15.2896 | 0.529119 | ||||||||
\(836\) | 111.234 | 3.84710 | ||||||||
\(837\) | 3.59256 | 0.124177 | ||||||||
\(838\) | 57.3151 | 1.97992 | ||||||||
\(839\) | −22.4667 | −0.775638 | −0.387819 | − | 0.921736i | \(-0.626771\pi\) | ||||
−0.387819 | + | 0.921736i | \(0.626771\pi\) | |||||||
\(840\) | 25.1564 | 0.867977 | ||||||||
\(841\) | −14.9972 | −0.517145 | ||||||||
\(842\) | 59.2681 | 2.04251 | ||||||||
\(843\) | −28.2862 | −0.974227 | ||||||||
\(844\) | −69.3206 | −2.38611 | ||||||||
\(845\) | −11.2603 | −0.387366 | ||||||||
\(846\) | 103.680 | 3.56460 | ||||||||
\(847\) | 10.9774 | 0.377187 | ||||||||
\(848\) | 21.7081 | 0.745460 | ||||||||
\(849\) | −54.8166 | −1.88130 | ||||||||
\(850\) | −2.85232 | −0.0978338 | ||||||||
\(851\) | −14.8840 | −0.510218 | ||||||||
\(852\) | −16.9111 | −0.579366 | ||||||||
\(853\) | 20.4107 | 0.698848 | 0.349424 | − | 0.936965i | \(-0.386377\pi\) | ||||
0.349424 | + | 0.936965i | \(0.386377\pi\) | |||||||
\(854\) | 31.8035 | 1.08829 | ||||||||
\(855\) | 21.0678 | 0.720504 | ||||||||
\(856\) | 72.7540 | 2.48668 | ||||||||
\(857\) | 44.8013 | 1.53038 | 0.765192 | − | 0.643802i | \(-0.222644\pi\) | ||||
0.765192 | + | 0.643802i | \(0.222644\pi\) | |||||||
\(858\) | −32.4925 | −1.10928 | ||||||||
\(859\) | −7.23373 | −0.246812 | −0.123406 | − | 0.992356i | \(-0.539382\pi\) | ||||
−0.123406 | + | 0.992356i | \(0.539382\pi\) | |||||||
\(860\) | 25.6242 | 0.873776 | ||||||||
\(861\) | 27.9391 | 0.952161 | ||||||||
\(862\) | −43.0982 | −1.46793 | ||||||||
\(863\) | 34.6798 | 1.18051 | 0.590257 | − | 0.807215i | \(-0.299026\pi\) | ||||
0.590257 | + | 0.807215i | \(0.299026\pi\) | |||||||
\(864\) | 4.96940 | 0.169062 | ||||||||
\(865\) | −18.3685 | −0.624548 | ||||||||
\(866\) | 15.6232 | 0.530899 | ||||||||
\(867\) | 43.1998 | 1.46714 | ||||||||
\(868\) | −20.1995 | −0.685617 | ||||||||
\(869\) | −29.3603 | −0.995980 | ||||||||
\(870\) | 23.4901 | 0.796389 | ||||||||
\(871\) | 11.4248 | 0.387115 | ||||||||
\(872\) | −39.3801 | −1.33358 | ||||||||
\(873\) | 18.7356 | 0.634105 | ||||||||
\(874\) | −37.7128 | −1.27565 | ||||||||
\(875\) | −15.1009 | −0.510505 | ||||||||
\(876\) | 80.6331 | 2.72434 | ||||||||
\(877\) | 2.02177 | 0.0682702 | 0.0341351 | − | 0.999417i | \(-0.489132\pi\) | ||||
0.0341351 | + | 0.999417i | \(0.489132\pi\) | |||||||
\(878\) | 69.5864 | 2.34843 | ||||||||
\(879\) | −8.99625 | −0.303436 | ||||||||
\(880\) | 25.1870 | 0.849053 | ||||||||
\(881\) | −51.1992 | −1.72494 | −0.862472 | − | 0.506105i | \(-0.831085\pi\) | ||||
−0.862472 | + | 0.506105i | \(0.831085\pi\) | |||||||
\(882\) | 36.1165 | 1.21610 | ||||||||
\(883\) | 39.6191 | 1.33329 | 0.666645 | − | 0.745375i | \(-0.267730\pi\) | ||||
0.666645 | + | 0.745375i | \(0.267730\pi\) | |||||||
\(884\) | 1.47168 | 0.0494978 | ||||||||
\(885\) | 24.9277 | 0.837936 | ||||||||
\(886\) | 49.9106 | 1.67678 | ||||||||
\(887\) | −59.1273 | −1.98530 | −0.992651 | − | 0.121016i | \(-0.961385\pi\) | ||||
−0.992651 | + | 0.121016i | \(0.961385\pi\) | |||||||
\(888\) | −91.9149 | −3.08446 | ||||||||
\(889\) | −18.2741 | −0.612893 | ||||||||
\(890\) | −34.1617 | −1.14510 | ||||||||
\(891\) | −29.9678 | −1.00396 | ||||||||
\(892\) | −28.7836 | −0.963747 | ||||||||
\(893\) | −71.8005 | −2.40271 | ||||||||
\(894\) | 134.337 | 4.49290 | ||||||||
\(895\) | 11.4092 | 0.381368 | ||||||||
\(896\) | 25.2981 | 0.845149 | ||||||||
\(897\) | 7.54324 | 0.251861 | ||||||||
\(898\) | 36.8295 | 1.22902 | ||||||||
\(899\) | −10.1773 | −0.339433 | ||||||||
\(900\) | −61.8335 | −2.06112 | ||||||||
\(901\) | −0.982730 | −0.0327395 | ||||||||
\(902\) | 67.2884 | 2.24046 | ||||||||
\(903\) | −26.3747 | −0.877696 | ||||||||
\(904\) | 84.6387 | 2.81504 | ||||||||
\(905\) | −18.0391 | −0.599639 | ||||||||
\(906\) | −40.2464 | −1.33710 | ||||||||
\(907\) | 51.0329 | 1.69452 | 0.847259 | − | 0.531180i | \(-0.178251\pi\) | ||||
0.847259 | + | 0.531180i | \(0.178251\pi\) | |||||||
\(908\) | −44.8857 | −1.48958 | ||||||||
\(909\) | −2.29406 | −0.0760892 | ||||||||
\(910\) | 5.09002 | 0.168733 | ||||||||
\(911\) | −5.02620 | −0.166525 | −0.0832627 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832627 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(912\) | −96.8177 | −3.20595 | ||||||||
\(913\) | −47.1250 | −1.55961 | ||||||||
\(914\) | −18.3446 | −0.606785 | ||||||||
\(915\) | 18.4060 | 0.608484 | ||||||||
\(916\) | −3.40999 | −0.112669 | ||||||||
\(917\) | 25.4236 | 0.839562 | ||||||||
\(918\) | −0.931001 | −0.0307276 | ||||||||
\(919\) | 23.6453 | 0.779987 | 0.389994 | − | 0.920818i | \(-0.372477\pi\) | ||||
0.389994 | + | 0.920818i | \(0.372477\pi\) | |||||||
\(920\) | −14.0653 | −0.463721 | ||||||||
\(921\) | −35.1320 | −1.15764 | ||||||||
\(922\) | −5.81145 | −0.191390 | ||||||||
\(923\) | −1.84629 | −0.0607714 | ||||||||
\(924\) | −79.1372 | −2.60342 | ||||||||
\(925\) | 24.6812 | 0.811513 | ||||||||
\(926\) | −46.9517 | −1.54293 | ||||||||
\(927\) | −63.3616 | −2.08107 | ||||||||
\(928\) | −14.0778 | −0.462126 | ||||||||
\(929\) | −40.4994 | −1.32874 | −0.664372 | − | 0.747402i | \(-0.731301\pi\) | ||||
−0.664372 | + | 0.747402i | \(0.731301\pi\) | |||||||
\(930\) | −17.0728 | −0.559839 | ||||||||
\(931\) | −25.0114 | −0.819715 | ||||||||
\(932\) | 84.0856 | 2.75431 | ||||||||
\(933\) | 27.9154 | 0.913910 | ||||||||
\(934\) | 26.7310 | 0.874666 | ||||||||
\(935\) | −1.14022 | −0.0372892 | ||||||||
\(936\) | 25.1403 | 0.821738 | ||||||||
\(937\) | 14.1534 | 0.462373 | 0.231187 | − | 0.972909i | \(-0.425739\pi\) | ||||
0.231187 | + | 0.972909i | \(0.425739\pi\) | |||||||
\(938\) | 40.6372 | 1.32685 | ||||||||
\(939\) | 55.4418 | 1.80927 | ||||||||
\(940\) | −49.6288 | −1.61871 | ||||||||
\(941\) | −9.87614 | −0.321953 | −0.160976 | − | 0.986958i | \(-0.551464\pi\) | ||||
−0.160976 | + | 0.986958i | \(0.551464\pi\) | |||||||
\(942\) | −62.8215 | −2.04684 | ||||||||
\(943\) | −15.6212 | −0.508697 | ||||||||
\(944\) | −61.8252 | −2.01224 | ||||||||
\(945\) | −2.20485 | −0.0717239 | ||||||||
\(946\) | −63.5208 | −2.06524 | ||||||||
\(947\) | 7.85653 | 0.255303 | 0.127652 | − | 0.991819i | \(-0.459256\pi\) | ||||
0.127652 | + | 0.991819i | \(0.459256\pi\) | |||||||
\(948\) | 78.0090 | 2.53362 | ||||||||
\(949\) | 8.80320 | 0.285764 | ||||||||
\(950\) | 62.5366 | 2.02896 | ||||||||
\(951\) | 31.8655 | 1.03331 | ||||||||
\(952\) | 2.82451 | 0.0915429 | ||||||||
\(953\) | 49.2263 | 1.59460 | 0.797299 | − | 0.603585i | \(-0.206262\pi\) | ||||
0.797299 | + | 0.603585i | \(0.206262\pi\) | |||||||
\(954\) | −31.1127 | −1.00731 | ||||||||
\(955\) | 17.6377 | 0.570743 | ||||||||
\(956\) | −38.0719 | −1.23133 | ||||||||
\(957\) | −39.8725 | −1.28889 | ||||||||
\(958\) | 77.0487 | 2.48933 | ||||||||
\(959\) | 9.97356 | 0.322063 | ||||||||
\(960\) | 7.19578 | 0.232243 | ||||||||
\(961\) | −23.6030 | −0.761388 | ||||||||
\(962\) | −18.5977 | −0.599612 | ||||||||
\(963\) | −43.3484 | −1.39688 | ||||||||
\(964\) | −64.8253 | −2.08788 | ||||||||
\(965\) | −10.0308 | −0.322902 | ||||||||
\(966\) | 26.8308 | 0.863266 | ||||||||
\(967\) | 20.3902 | 0.655706 | 0.327853 | − | 0.944729i | \(-0.393675\pi\) | ||||
0.327853 | + | 0.944729i | \(0.393675\pi\) | |||||||
\(968\) | −37.9024 | −1.21823 | ||||||||
\(969\) | 4.38295 | 0.140801 | ||||||||
\(970\) | −13.0974 | −0.420532 | ||||||||
\(971\) | −19.6085 | −0.629266 | −0.314633 | − | 0.949213i | \(-0.601881\pi\) | ||||
−0.314633 | + | 0.949213i | \(0.601881\pi\) | |||||||
\(972\) | 96.8369 | 3.10604 | ||||||||
\(973\) | 30.8168 | 0.987941 | ||||||||
\(974\) | 21.8152 | 0.699004 | ||||||||
\(975\) | −12.5084 | −0.400591 | ||||||||
\(976\) | −45.6502 | −1.46123 | ||||||||
\(977\) | −39.0408 | −1.24903 | −0.624513 | − | 0.781015i | \(-0.714702\pi\) | ||||
−0.624513 | + | 0.781015i | \(0.714702\pi\) | |||||||
\(978\) | −4.73484 | −0.151404 | ||||||||
\(979\) | 57.9866 | 1.85326 | ||||||||
\(980\) | −17.2880 | −0.552244 | ||||||||
\(981\) | 23.4635 | 0.749132 | ||||||||
\(982\) | −12.7678 | −0.407438 | ||||||||
\(983\) | −2.07574 | −0.0662059 | −0.0331029 | − | 0.999452i | \(-0.510539\pi\) | ||||
−0.0331029 | + | 0.999452i | \(0.510539\pi\) | |||||||
\(984\) | −96.4673 | −3.07526 | ||||||||
\(985\) | 13.4893 | 0.429804 | ||||||||
\(986\) | 2.63743 | 0.0839928 | ||||||||
\(987\) | 51.0825 | 1.62597 | ||||||||
\(988\) | −32.2662 | −1.02653 | ||||||||
\(989\) | 14.7466 | 0.468913 | ||||||||
\(990\) | −36.0988 | −1.14729 | ||||||||
\(991\) | 37.5684 | 1.19340 | 0.596700 | − | 0.802465i | \(-0.296478\pi\) | ||||
0.596700 | + | 0.802465i | \(0.296478\pi\) | |||||||
\(992\) | 10.2318 | 0.324861 | ||||||||
\(993\) | 56.7486 | 1.80086 | ||||||||
\(994\) | −6.56713 | −0.208297 | ||||||||
\(995\) | 15.6320 | 0.495566 | ||||||||
\(996\) | 125.209 | 3.96740 | ||||||||
\(997\) | 8.93943 | 0.283114 | 0.141557 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141557 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(998\) | −59.9513 | −1.89773 | ||||||||
\(999\) | 8.05597 | 0.254880 |
(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 | 4013.2.a.b.1.12 | ✓ | 157 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.b.1.12 | ✓ | 157 | 1.1 | even | 1 | trivial |