Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40042 | −1.69736 | −0.848678 | − | 0.528910i | \(-0.822601\pi\) | ||||
−0.848678 | + | 0.528910i | \(0.822601\pi\) | |||||||
\(3\) | −0.672797 | −0.388440 | −0.194220 | − | 0.980958i | \(-0.562218\pi\) | ||||
−0.194220 | + | 0.980958i | \(0.562218\pi\) | |||||||
\(4\) | 3.76203 | 1.88101 | ||||||||
\(5\) | −3.90458 | −1.74618 | −0.873091 | − | 0.487558i | \(-0.837888\pi\) | ||||
−0.873091 | + | 0.487558i | \(0.837888\pi\) | |||||||
\(6\) | 1.61500 | 0.659320 | ||||||||
\(7\) | −3.05635 | −1.15519 | −0.577595 | − | 0.816323i | \(-0.696009\pi\) | ||||
−0.577595 | + | 0.816323i | \(0.696009\pi\) | |||||||
\(8\) | −4.22962 | −1.49539 | ||||||||
\(9\) | −2.54734 | −0.849115 | ||||||||
\(10\) | 9.37264 | 2.96389 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.53108 | −0.730661 | ||||||||
\(13\) | −5.54437 | −1.53773 | −0.768865 | − | 0.639411i | \(-0.779178\pi\) | ||||
−0.768865 | + | 0.639411i | \(0.779178\pi\) | |||||||
\(14\) | 7.33653 | 1.96077 | ||||||||
\(15\) | 2.62699 | 0.678286 | ||||||||
\(16\) | 2.62881 | 0.657202 | ||||||||
\(17\) | −5.45989 | −1.32422 | −0.662109 | − | 0.749408i | \(-0.730338\pi\) | ||||
−0.662109 | + | 0.749408i | \(0.730338\pi\) | |||||||
\(18\) | 6.11470 | 1.44125 | ||||||||
\(19\) | 5.83487 | 1.33861 | 0.669306 | − | 0.742987i | \(-0.266592\pi\) | ||||
0.669306 | + | 0.742987i | \(0.266592\pi\) | |||||||
\(20\) | −14.6891 | −3.28459 | ||||||||
\(21\) | 2.05630 | 0.448722 | ||||||||
\(22\) | 2.40042 | 0.511772 | ||||||||
\(23\) | −7.83643 | −1.63401 | −0.817004 | − | 0.576632i | \(-0.804367\pi\) | ||||
−0.817004 | + | 0.576632i | \(0.804367\pi\) | |||||||
\(24\) | 2.84567 | 0.580871 | ||||||||
\(25\) | 10.2458 | 2.04915 | ||||||||
\(26\) | 13.3088 | 2.61008 | ||||||||
\(27\) | 3.73224 | 0.718270 | ||||||||
\(28\) | −11.4981 | −2.17293 | ||||||||
\(29\) | −3.45552 | −0.641673 | −0.320837 | − | 0.947135i | \(-0.603964\pi\) | ||||
−0.320837 | + | 0.947135i | \(0.603964\pi\) | |||||||
\(30\) | −6.30589 | −1.15129 | ||||||||
\(31\) | −0.504688 | −0.0906446 | −0.0453223 | − | 0.998972i | \(-0.514431\pi\) | ||||
−0.0453223 | + | 0.998972i | \(0.514431\pi\) | |||||||
\(32\) | 2.14898 | 0.379890 | ||||||||
\(33\) | 0.672797 | 0.117119 | ||||||||
\(34\) | 13.1060 | 2.24767 | ||||||||
\(35\) | 11.9338 | 2.01717 | ||||||||
\(36\) | −9.58318 | −1.59720 | ||||||||
\(37\) | −5.34533 | −0.878767 | −0.439384 | − | 0.898299i | \(-0.644803\pi\) | ||||
−0.439384 | + | 0.898299i | \(0.644803\pi\) | |||||||
\(38\) | −14.0062 | −2.27210 | ||||||||
\(39\) | 3.73024 | 0.597316 | ||||||||
\(40\) | 16.5149 | 2.61123 | ||||||||
\(41\) | −12.1681 | −1.90034 | −0.950171 | − | 0.311731i | \(-0.899091\pi\) | ||||
−0.950171 | + | 0.311731i | \(0.899091\pi\) | |||||||
\(42\) | −4.93600 | −0.761641 | ||||||||
\(43\) | −4.71869 | −0.719594 | −0.359797 | − | 0.933031i | \(-0.617154\pi\) | ||||
−0.359797 | + | 0.933031i | \(0.617154\pi\) | |||||||
\(44\) | −3.76203 | −0.567147 | ||||||||
\(45\) | 9.94631 | 1.48271 | ||||||||
\(46\) | 18.8107 | 2.77349 | ||||||||
\(47\) | 3.26502 | 0.476252 | 0.238126 | − | 0.971234i | \(-0.423467\pi\) | ||||
0.238126 | + | 0.971234i | \(0.423467\pi\) | |||||||
\(48\) | −1.76865 | −0.255283 | ||||||||
\(49\) | 2.34126 | 0.334466 | ||||||||
\(50\) | −24.5941 | −3.47814 | ||||||||
\(51\) | 3.67340 | 0.514379 | ||||||||
\(52\) | −20.8581 | −2.89249 | ||||||||
\(53\) | 7.66741 | 1.05320 | 0.526600 | − | 0.850113i | \(-0.323466\pi\) | ||||
0.526600 | + | 0.850113i | \(0.323466\pi\) | |||||||
\(54\) | −8.95895 | −1.21916 | ||||||||
\(55\) | 3.90458 | 0.526494 | ||||||||
\(56\) | 12.9272 | 1.72747 | ||||||||
\(57\) | −3.92569 | −0.519970 | ||||||||
\(58\) | 8.29470 | 1.08915 | ||||||||
\(59\) | 2.01048 | 0.261742 | 0.130871 | − | 0.991399i | \(-0.458223\pi\) | ||||
0.130871 | + | 0.991399i | \(0.458223\pi\) | |||||||
\(60\) | 9.88282 | 1.27587 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 1.21146 | 0.153856 | ||||||||
\(63\) | 7.78557 | 0.980890 | ||||||||
\(64\) | −10.4161 | −1.30201 | ||||||||
\(65\) | 21.6484 | 2.68516 | ||||||||
\(66\) | −1.61500 | −0.198793 | ||||||||
\(67\) | 5.54815 | 0.677814 | 0.338907 | − | 0.940820i | \(-0.389943\pi\) | ||||
0.338907 | + | 0.940820i | \(0.389943\pi\) | |||||||
\(68\) | −20.5403 | −2.49087 | ||||||||
\(69\) | 5.27233 | 0.634714 | ||||||||
\(70\) | −28.6461 | −3.42386 | ||||||||
\(71\) | 5.61256 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(72\) | 10.7743 | 1.26976 | ||||||||
\(73\) | 4.97921 | 0.582773 | 0.291386 | − | 0.956605i | \(-0.405883\pi\) | ||||
0.291386 | + | 0.956605i | \(0.405883\pi\) | |||||||
\(74\) | 12.8311 | 1.49158 | ||||||||
\(75\) | −6.89331 | −0.795971 | ||||||||
\(76\) | 21.9510 | 2.51795 | ||||||||
\(77\) | 3.05635 | 0.348303 | ||||||||
\(78\) | −8.95414 | −1.01386 | ||||||||
\(79\) | 2.08461 | 0.234537 | 0.117269 | − | 0.993100i | \(-0.462586\pi\) | ||||
0.117269 | + | 0.993100i | \(0.462586\pi\) | |||||||
\(80\) | −10.2644 | −1.14759 | ||||||||
\(81\) | 5.13099 | 0.570110 | ||||||||
\(82\) | 29.2086 | 3.22555 | ||||||||
\(83\) | −4.20087 | −0.461105 | −0.230553 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230553 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(84\) | 7.73587 | 0.844053 | ||||||||
\(85\) | 21.3186 | 2.31232 | ||||||||
\(86\) | 11.3269 | 1.22141 | ||||||||
\(87\) | 2.32486 | 0.249251 | ||||||||
\(88\) | 4.22962 | 0.450879 | ||||||||
\(89\) | −4.09744 | −0.434328 | −0.217164 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217164 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(90\) | −23.8753 | −2.51668 | ||||||||
\(91\) | 16.9455 | 1.77637 | ||||||||
\(92\) | −29.4809 | −3.07359 | ||||||||
\(93\) | 0.339553 | 0.0352100 | ||||||||
\(94\) | −7.83742 | −0.808368 | ||||||||
\(95\) | −22.7827 | −2.33746 | ||||||||
\(96\) | −1.44583 | −0.147564 | ||||||||
\(97\) | 7.15422 | 0.726401 | 0.363201 | − | 0.931711i | \(-0.381684\pi\) | ||||
0.363201 | + | 0.931711i | \(0.381684\pi\) | |||||||
\(98\) | −5.62002 | −0.567708 | ||||||||
\(99\) | 2.54734 | 0.256018 | ||||||||
\(100\) | 38.5448 | 3.85448 | ||||||||
\(101\) | −6.28383 | −0.625264 | −0.312632 | − | 0.949874i | \(-0.601211\pi\) | ||||
−0.312632 | + | 0.949874i | \(0.601211\pi\) | |||||||
\(102\) | −8.81771 | −0.873083 | ||||||||
\(103\) | −5.04101 | −0.496706 | −0.248353 | − | 0.968670i | \(-0.579889\pi\) | ||||
−0.248353 | + | 0.968670i | \(0.579889\pi\) | |||||||
\(104\) | 23.4505 | 2.29951 | ||||||||
\(105\) | −8.02900 | −0.783550 | ||||||||
\(106\) | −18.4050 | −1.78766 | ||||||||
\(107\) | −15.0276 | −1.45278 | −0.726389 | − | 0.687284i | \(-0.758803\pi\) | ||||
−0.726389 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(108\) | 14.0408 | 1.35108 | ||||||||
\(109\) | −10.9249 | −1.04642 | −0.523210 | − | 0.852204i | \(-0.675266\pi\) | ||||
−0.523210 | + | 0.852204i | \(0.675266\pi\) | |||||||
\(110\) | −9.37264 | −0.893647 | ||||||||
\(111\) | 3.59633 | 0.341348 | ||||||||
\(112\) | −8.03455 | −0.759194 | ||||||||
\(113\) | 6.36396 | 0.598671 | 0.299335 | − | 0.954148i | \(-0.403235\pi\) | ||||
0.299335 | + | 0.954148i | \(0.403235\pi\) | |||||||
\(114\) | 9.42330 | 0.882573 | ||||||||
\(115\) | 30.5980 | 2.85328 | ||||||||
\(116\) | −12.9998 | −1.20700 | ||||||||
\(117\) | 14.1234 | 1.30571 | ||||||||
\(118\) | −4.82600 | −0.444269 | ||||||||
\(119\) | 16.6873 | 1.52972 | ||||||||
\(120\) | −11.1112 | −1.01431 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.40042 | −0.217324 | ||||||||
\(123\) | 8.18668 | 0.738168 | ||||||||
\(124\) | −1.89865 | −0.170504 | ||||||||
\(125\) | −20.4825 | −1.83201 | ||||||||
\(126\) | −18.6887 | −1.66492 | ||||||||
\(127\) | −8.82634 | −0.783211 | −0.391606 | − | 0.920133i | \(-0.628080\pi\) | ||||
−0.391606 | + | 0.920133i | \(0.628080\pi\) | |||||||
\(128\) | 20.7050 | 1.83008 | ||||||||
\(129\) | 3.17472 | 0.279519 | ||||||||
\(130\) | −51.9654 | −4.55767 | ||||||||
\(131\) | 5.63711 | 0.492517 | 0.246258 | − | 0.969204i | \(-0.420799\pi\) | ||||
0.246258 | + | 0.969204i | \(0.420799\pi\) | |||||||
\(132\) | 2.53108 | 0.220303 | ||||||||
\(133\) | −17.8334 | −1.54635 | ||||||||
\(134\) | −13.3179 | −1.15049 | ||||||||
\(135\) | −14.5728 | −1.25423 | ||||||||
\(136\) | 23.0932 | 1.98023 | ||||||||
\(137\) | −6.63735 | −0.567067 | −0.283533 | − | 0.958962i | \(-0.591507\pi\) | ||||
−0.283533 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(138\) | −12.6558 | −1.07733 | ||||||||
\(139\) | −16.6192 | −1.40962 | −0.704812 | − | 0.709395i | \(-0.748968\pi\) | ||||
−0.704812 | + | 0.709395i | \(0.748968\pi\) | |||||||
\(140\) | 44.8951 | 3.79433 | ||||||||
\(141\) | −2.19669 | −0.184995 | ||||||||
\(142\) | −13.4725 | −1.13059 | ||||||||
\(143\) | 5.54437 | 0.463643 | ||||||||
\(144\) | −6.69648 | −0.558040 | ||||||||
\(145\) | 13.4923 | 1.12048 | ||||||||
\(146\) | −11.9522 | −0.989172 | ||||||||
\(147\) | −1.57520 | −0.129920 | ||||||||
\(148\) | −20.1093 | −1.65297 | ||||||||
\(149\) | −9.73673 | −0.797664 | −0.398832 | − | 0.917024i | \(-0.630584\pi\) | ||||
−0.398832 | + | 0.917024i | \(0.630584\pi\) | |||||||
\(150\) | 16.5469 | 1.35105 | ||||||||
\(151\) | −4.86318 | −0.395760 | −0.197880 | − | 0.980226i | \(-0.563406\pi\) | ||||
−0.197880 | + | 0.980226i | \(0.563406\pi\) | |||||||
\(152\) | −24.6793 | −2.00175 | ||||||||
\(153\) | 13.9082 | 1.12441 | ||||||||
\(154\) | −7.33653 | −0.591194 | ||||||||
\(155\) | 1.97059 | 0.158282 | ||||||||
\(156\) | 14.0333 | 1.12356 | ||||||||
\(157\) | −20.7193 | −1.65358 | −0.826790 | − | 0.562510i | \(-0.809836\pi\) | ||||
−0.826790 | + | 0.562510i | \(0.809836\pi\) | |||||||
\(158\) | −5.00395 | −0.398093 | ||||||||
\(159\) | −5.15862 | −0.409105 | ||||||||
\(160\) | −8.39088 | −0.663357 | ||||||||
\(161\) | 23.9509 | 1.88759 | ||||||||
\(162\) | −12.3165 | −0.967680 | ||||||||
\(163\) | 7.33960 | 0.574882 | 0.287441 | − | 0.957798i | \(-0.407195\pi\) | ||||
0.287441 | + | 0.957798i | \(0.407195\pi\) | |||||||
\(164\) | −45.7768 | −3.57457 | ||||||||
\(165\) | −2.62699 | −0.204511 | ||||||||
\(166\) | 10.0839 | 0.782660 | ||||||||
\(167\) | −16.3048 | −1.26171 | −0.630853 | − | 0.775902i | \(-0.717295\pi\) | ||||
−0.630853 | + | 0.775902i | \(0.717295\pi\) | |||||||
\(168\) | −8.69737 | −0.671017 | ||||||||
\(169\) | 17.7400 | 1.36462 | ||||||||
\(170\) | −51.1736 | −3.92484 | ||||||||
\(171\) | −14.8634 | −1.13663 | ||||||||
\(172\) | −17.7519 | −1.35357 | ||||||||
\(173\) | −25.3219 | −1.92519 | −0.962593 | − | 0.270950i | \(-0.912662\pi\) | ||||
−0.962593 | + | 0.270950i | \(0.912662\pi\) | |||||||
\(174\) | −5.58065 | −0.423068 | ||||||||
\(175\) | −31.3146 | −2.36716 | ||||||||
\(176\) | −2.62881 | −0.198154 | ||||||||
\(177\) | −1.35264 | −0.101671 | ||||||||
\(178\) | 9.83559 | 0.737208 | ||||||||
\(179\) | −3.11194 | −0.232597 | −0.116299 | − | 0.993214i | \(-0.537103\pi\) | ||||
−0.116299 | + | 0.993214i | \(0.537103\pi\) | |||||||
\(180\) | 37.4183 | 2.78900 | ||||||||
\(181\) | −6.22703 | −0.462851 | −0.231426 | − | 0.972853i | \(-0.574339\pi\) | ||||
−0.231426 | + | 0.972853i | \(0.574339\pi\) | |||||||
\(182\) | −40.6764 | −3.01514 | ||||||||
\(183\) | −0.672797 | −0.0497346 | ||||||||
\(184\) | 33.1451 | 2.44349 | ||||||||
\(185\) | 20.8713 | 1.53449 | ||||||||
\(186\) | −0.815070 | −0.0597638 | ||||||||
\(187\) | 5.45989 | 0.399267 | ||||||||
\(188\) | 12.2831 | 0.895836 | ||||||||
\(189\) | −11.4070 | −0.829738 | ||||||||
\(190\) | 54.6882 | 3.96750 | ||||||||
\(191\) | 23.1436 | 1.67461 | 0.837305 | − | 0.546736i | \(-0.184130\pi\) | ||||
0.837305 | + | 0.546736i | \(0.184130\pi\) | |||||||
\(192\) | 7.00791 | 0.505752 | ||||||||
\(193\) | 12.6861 | 0.913162 | 0.456581 | − | 0.889682i | \(-0.349074\pi\) | ||||
0.456581 | + | 0.889682i | \(0.349074\pi\) | |||||||
\(194\) | −17.1732 | −1.23296 | ||||||||
\(195\) | −14.5650 | −1.04302 | ||||||||
\(196\) | 8.80790 | 0.629136 | ||||||||
\(197\) | 22.0266 | 1.56933 | 0.784664 | − | 0.619922i | \(-0.212836\pi\) | ||||
0.784664 | + | 0.619922i | \(0.212836\pi\) | |||||||
\(198\) | −6.11470 | −0.434553 | ||||||||
\(199\) | −15.1778 | −1.07592 | −0.537962 | − | 0.842969i | \(-0.680806\pi\) | ||||
−0.537962 | + | 0.842969i | \(0.680806\pi\) | |||||||
\(200\) | −43.3356 | −3.06429 | ||||||||
\(201\) | −3.73278 | −0.263290 | ||||||||
\(202\) | 15.0838 | 1.06130 | ||||||||
\(203\) | 10.5613 | 0.741255 | ||||||||
\(204\) | 13.8194 | 0.967554 | ||||||||
\(205\) | 47.5114 | 3.31834 | ||||||||
\(206\) | 12.1006 | 0.843086 | ||||||||
\(207\) | 19.9621 | 1.38746 | ||||||||
\(208\) | −14.5751 | −1.01060 | ||||||||
\(209\) | −5.83487 | −0.403606 | ||||||||
\(210\) | 19.2730 | 1.32996 | ||||||||
\(211\) | −25.7691 | −1.77402 | −0.887008 | − | 0.461754i | \(-0.847220\pi\) | ||||
−0.887008 | + | 0.461754i | \(0.847220\pi\) | |||||||
\(212\) | 28.8450 | 1.98109 | ||||||||
\(213\) | −3.77612 | −0.258735 | ||||||||
\(214\) | 36.0727 | 2.46588 | ||||||||
\(215\) | 18.4245 | 1.25654 | ||||||||
\(216\) | −15.7859 | −1.07410 | ||||||||
\(217\) | 1.54250 | 0.104712 | ||||||||
\(218\) | 26.2245 | 1.77615 | ||||||||
\(219\) | −3.35000 | −0.226372 | ||||||||
\(220\) | 14.6891 | 0.990342 | ||||||||
\(221\) | 30.2716 | 2.03629 | ||||||||
\(222\) | −8.63270 | −0.579389 | ||||||||
\(223\) | −28.1180 | −1.88292 | −0.941459 | − | 0.337127i | \(-0.890545\pi\) | ||||
−0.941459 | + | 0.337127i | \(0.890545\pi\) | |||||||
\(224\) | −6.56804 | −0.438846 | ||||||||
\(225\) | −26.0994 | −1.73996 | ||||||||
\(226\) | −15.2762 | −1.01616 | ||||||||
\(227\) | −0.658880 | −0.0437314 | −0.0218657 | − | 0.999761i | \(-0.506961\pi\) | ||||
−0.0218657 | + | 0.999761i | \(0.506961\pi\) | |||||||
\(228\) | −14.7685 | −0.978071 | ||||||||
\(229\) | −8.51326 | −0.562572 | −0.281286 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281286 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(230\) | −73.4481 | −4.84302 | ||||||||
\(231\) | −2.05630 | −0.135295 | ||||||||
\(232\) | 14.6155 | 0.959555 | ||||||||
\(233\) | −6.97393 | −0.456877 | −0.228439 | − | 0.973558i | \(-0.573362\pi\) | ||||
−0.228439 | + | 0.973558i | \(0.573362\pi\) | |||||||
\(234\) | −33.9022 | −2.21625 | ||||||||
\(235\) | −12.7485 | −0.831622 | ||||||||
\(236\) | 7.56348 | 0.492340 | ||||||||
\(237\) | −1.40252 | −0.0911035 | ||||||||
\(238\) | −40.0566 | −2.59649 | ||||||||
\(239\) | −1.06405 | −0.0688276 | −0.0344138 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344138 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(240\) | 6.90585 | 0.445771 | ||||||||
\(241\) | 22.8037 | 1.46891 | 0.734456 | − | 0.678656i | \(-0.237437\pi\) | ||||
0.734456 | + | 0.678656i | \(0.237437\pi\) | |||||||
\(242\) | −2.40042 | −0.154305 | ||||||||
\(243\) | −14.6488 | −0.939723 | ||||||||
\(244\) | 3.76203 | 0.240839 | ||||||||
\(245\) | −9.14165 | −0.584039 | ||||||||
\(246\) | −19.6515 | −1.25293 | ||||||||
\(247\) | −32.3507 | −2.05842 | ||||||||
\(248\) | 2.13464 | 0.135549 | ||||||||
\(249\) | 2.82633 | 0.179112 | ||||||||
\(250\) | 49.1666 | 3.10957 | ||||||||
\(251\) | 22.7712 | 1.43730 | 0.718651 | − | 0.695370i | \(-0.244760\pi\) | ||||
0.718651 | + | 0.695370i | \(0.244760\pi\) | |||||||
\(252\) | 29.2895 | 1.84507 | ||||||||
\(253\) | 7.83643 | 0.492672 | ||||||||
\(254\) | 21.1870 | 1.32939 | ||||||||
\(255\) | −14.3431 | −0.898199 | ||||||||
\(256\) | −28.8687 | −1.80429 | ||||||||
\(257\) | 12.0057 | 0.748896 | 0.374448 | − | 0.927248i | \(-0.377832\pi\) | ||||
0.374448 | + | 0.927248i | \(0.377832\pi\) | |||||||
\(258\) | −7.62068 | −0.474443 | ||||||||
\(259\) | 16.3372 | 1.01514 | ||||||||
\(260\) | 81.4420 | 5.05082 | ||||||||
\(261\) | 8.80239 | 0.544854 | ||||||||
\(262\) | −13.5315 | −0.835976 | ||||||||
\(263\) | −15.8133 | −0.975092 | −0.487546 | − | 0.873097i | \(-0.662108\pi\) | ||||
−0.487546 | + | 0.873097i | \(0.662108\pi\) | |||||||
\(264\) | −2.84567 | −0.175139 | ||||||||
\(265\) | −29.9380 | −1.83908 | ||||||||
\(266\) | 42.8077 | 2.62471 | ||||||||
\(267\) | 2.75675 | 0.168710 | ||||||||
\(268\) | 20.8723 | 1.27498 | ||||||||
\(269\) | −19.0522 | −1.16164 | −0.580818 | − | 0.814033i | \(-0.697267\pi\) | ||||
−0.580818 | + | 0.814033i | \(0.697267\pi\) | |||||||
\(270\) | 34.9809 | 2.12887 | ||||||||
\(271\) | 20.4576 | 1.24271 | 0.621356 | − | 0.783528i | \(-0.286582\pi\) | ||||
0.621356 | + | 0.783528i | \(0.286582\pi\) | |||||||
\(272\) | −14.3530 | −0.870278 | ||||||||
\(273\) | −11.4009 | −0.690014 | ||||||||
\(274\) | 15.9324 | 0.962514 | ||||||||
\(275\) | −10.2458 | −0.617842 | ||||||||
\(276\) | 19.8347 | 1.19391 | ||||||||
\(277\) | −11.0227 | −0.662291 | −0.331146 | − | 0.943580i | \(-0.607435\pi\) | ||||
−0.331146 | + | 0.943580i | \(0.607435\pi\) | |||||||
\(278\) | 39.8931 | 2.39263 | ||||||||
\(279\) | 1.28561 | 0.0769677 | ||||||||
\(280\) | −50.4752 | −3.01647 | ||||||||
\(281\) | −12.9918 | −0.775029 | −0.387514 | − | 0.921864i | \(-0.626666\pi\) | ||||
−0.387514 | + | 0.921864i | \(0.626666\pi\) | |||||||
\(282\) | 5.27300 | 0.314002 | ||||||||
\(283\) | −28.7769 | −1.71061 | −0.855305 | − | 0.518125i | \(-0.826630\pi\) | ||||
−0.855305 | + | 0.518125i | \(0.826630\pi\) | |||||||
\(284\) | 21.1146 | 1.25292 | ||||||||
\(285\) | 15.3282 | 0.907962 | ||||||||
\(286\) | −13.3088 | −0.786967 | ||||||||
\(287\) | 37.1900 | 2.19526 | ||||||||
\(288\) | −5.47420 | −0.322570 | ||||||||
\(289\) | 12.8104 | 0.753553 | ||||||||
\(290\) | −32.3873 | −1.90185 | ||||||||
\(291\) | −4.81334 | −0.282163 | ||||||||
\(292\) | 18.7319 | 1.09620 | ||||||||
\(293\) | 21.8789 | 1.27818 | 0.639088 | − | 0.769134i | \(-0.279312\pi\) | ||||
0.639088 | + | 0.769134i | \(0.279312\pi\) | |||||||
\(294\) | 3.78114 | 0.220520 | ||||||||
\(295\) | −7.85007 | −0.457049 | ||||||||
\(296\) | 22.6087 | 1.31410 | ||||||||
\(297\) | −3.73224 | −0.216566 | ||||||||
\(298\) | 23.3723 | 1.35392 | ||||||||
\(299\) | 43.4480 | 2.51267 | ||||||||
\(300\) | −25.9328 | −1.49723 | ||||||||
\(301\) | 14.4220 | 0.831268 | ||||||||
\(302\) | 11.6737 | 0.671745 | ||||||||
\(303\) | 4.22774 | 0.242877 | ||||||||
\(304\) | 15.3387 | 0.879738 | ||||||||
\(305\) | −3.90458 | −0.223576 | ||||||||
\(306\) | −33.3856 | −1.90853 | ||||||||
\(307\) | −21.4140 | −1.22216 | −0.611080 | − | 0.791569i | \(-0.709265\pi\) | ||||
−0.611080 | + | 0.791569i | \(0.709265\pi\) | |||||||
\(308\) | 11.4981 | 0.655163 | ||||||||
\(309\) | 3.39158 | 0.192940 | ||||||||
\(310\) | −4.73026 | −0.268661 | ||||||||
\(311\) | 12.1431 | 0.688574 | 0.344287 | − | 0.938864i | \(-0.388121\pi\) | ||||
0.344287 | + | 0.938864i | \(0.388121\pi\) | |||||||
\(312\) | −15.7775 | −0.893223 | ||||||||
\(313\) | 11.4623 | 0.647886 | 0.323943 | − | 0.946077i | \(-0.394991\pi\) | ||||
0.323943 | + | 0.946077i | \(0.394991\pi\) | |||||||
\(314\) | 49.7351 | 2.80671 | ||||||||
\(315\) | −30.3994 | −1.71281 | ||||||||
\(316\) | 7.84237 | 0.441168 | ||||||||
\(317\) | 23.7449 | 1.33365 | 0.666824 | − | 0.745215i | \(-0.267653\pi\) | ||||
0.666824 | + | 0.745215i | \(0.267653\pi\) | |||||||
\(318\) | 12.3829 | 0.694396 | ||||||||
\(319\) | 3.45552 | 0.193472 | ||||||||
\(320\) | 40.6704 | 2.27355 | ||||||||
\(321\) | 10.1106 | 0.564316 | ||||||||
\(322\) | −57.4922 | −3.20391 | ||||||||
\(323\) | −31.8578 | −1.77261 | ||||||||
\(324\) | 19.3029 | 1.07239 | ||||||||
\(325\) | −56.8062 | −3.15104 | ||||||||
\(326\) | −17.6182 | −0.975779 | ||||||||
\(327\) | 7.35028 | 0.406471 | ||||||||
\(328\) | 51.4665 | 2.84176 | ||||||||
\(329\) | −9.97903 | −0.550162 | ||||||||
\(330\) | 6.30589 | 0.347128 | ||||||||
\(331\) | −4.65951 | −0.256110 | −0.128055 | − | 0.991767i | \(-0.540873\pi\) | ||||
−0.128055 | + | 0.991767i | \(0.540873\pi\) | |||||||
\(332\) | −15.8038 | −0.867346 | ||||||||
\(333\) | 13.6164 | 0.746174 | ||||||||
\(334\) | 39.1385 | 2.14156 | ||||||||
\(335\) | −21.6632 | −1.18359 | ||||||||
\(336\) | 5.40562 | 0.294901 | ||||||||
\(337\) | 1.69410 | 0.0922838 | 0.0461419 | − | 0.998935i | \(-0.485307\pi\) | ||||
0.0461419 | + | 0.998935i | \(0.485307\pi\) | |||||||
\(338\) | −42.5835 | −2.31624 | ||||||||
\(339\) | −4.28165 | −0.232547 | ||||||||
\(340\) | 80.2011 | 4.34952 | ||||||||
\(341\) | 0.504688 | 0.0273304 | ||||||||
\(342\) | 35.6785 | 1.92927 | ||||||||
\(343\) | 14.2387 | 0.768819 | ||||||||
\(344\) | 19.9583 | 1.07608 | ||||||||
\(345\) | −20.5862 | −1.10833 | ||||||||
\(346\) | 60.7832 | 3.26773 | ||||||||
\(347\) | 6.77085 | 0.363478 | 0.181739 | − | 0.983347i | \(-0.441827\pi\) | ||||
0.181739 | + | 0.983347i | \(0.441827\pi\) | |||||||
\(348\) | 8.74620 | 0.468846 | ||||||||
\(349\) | −28.2464 | −1.51200 | −0.755999 | − | 0.654573i | \(-0.772848\pi\) | ||||
−0.755999 | + | 0.654573i | \(0.772848\pi\) | |||||||
\(350\) | 75.1682 | 4.01791 | ||||||||
\(351\) | −20.6929 | −1.10451 | ||||||||
\(352\) | −2.14898 | −0.114541 | ||||||||
\(353\) | 22.2759 | 1.18563 | 0.592814 | − | 0.805339i | \(-0.298017\pi\) | ||||
0.592814 | + | 0.805339i | \(0.298017\pi\) | |||||||
\(354\) | 3.24692 | 0.172572 | ||||||||
\(355\) | −21.9147 | −1.16311 | ||||||||
\(356\) | −15.4147 | −0.816977 | ||||||||
\(357\) | −11.2272 | −0.594206 | ||||||||
\(358\) | 7.46998 | 0.394800 | ||||||||
\(359\) | 17.0196 | 0.898261 | 0.449130 | − | 0.893466i | \(-0.351734\pi\) | ||||
0.449130 | + | 0.893466i | \(0.351734\pi\) | |||||||
\(360\) | −42.0691 | −2.21723 | ||||||||
\(361\) | 15.0457 | 0.791880 | ||||||||
\(362\) | 14.9475 | 0.785623 | ||||||||
\(363\) | −0.672797 | −0.0353127 | ||||||||
\(364\) | 63.7495 | 3.34138 | ||||||||
\(365\) | −19.4417 | −1.01763 | ||||||||
\(366\) | 1.61500 | 0.0844173 | ||||||||
\(367\) | 21.8660 | 1.14140 | 0.570699 | − | 0.821159i | \(-0.306672\pi\) | ||||
0.570699 | + | 0.821159i | \(0.306672\pi\) | |||||||
\(368\) | −20.6005 | −1.07387 | ||||||||
\(369\) | 30.9964 | 1.61361 | ||||||||
\(370\) | −50.0999 | −2.60457 | ||||||||
\(371\) | −23.4343 | −1.21665 | ||||||||
\(372\) | 1.27741 | 0.0662305 | ||||||||
\(373\) | −5.98827 | −0.310061 | −0.155030 | − | 0.987910i | \(-0.549548\pi\) | ||||
−0.155030 | + | 0.987910i | \(0.549548\pi\) | |||||||
\(374\) | −13.1060 | −0.677697 | ||||||||
\(375\) | 13.7805 | 0.711624 | ||||||||
\(376\) | −13.8098 | −0.712184 | ||||||||
\(377\) | 19.1587 | 0.986721 | ||||||||
\(378\) | 27.3817 | 1.40836 | ||||||||
\(379\) | −8.87032 | −0.455638 | −0.227819 | − | 0.973704i | \(-0.573159\pi\) | ||||
−0.227819 | + | 0.973704i | \(0.573159\pi\) | |||||||
\(380\) | −85.7093 | −4.39679 | ||||||||
\(381\) | 5.93834 | 0.304230 | ||||||||
\(382\) | −55.5543 | −2.84241 | ||||||||
\(383\) | −25.0388 | −1.27942 | −0.639712 | − | 0.768614i | \(-0.720947\pi\) | ||||
−0.639712 | + | 0.768614i | \(0.720947\pi\) | |||||||
\(384\) | −13.9303 | −0.710877 | ||||||||
\(385\) | −11.9338 | −0.608201 | ||||||||
\(386\) | −30.4519 | −1.54996 | ||||||||
\(387\) | 12.0201 | 0.611018 | ||||||||
\(388\) | 26.9144 | 1.36637 | ||||||||
\(389\) | −17.1937 | −0.871756 | −0.435878 | − | 0.900006i | \(-0.643562\pi\) | ||||
−0.435878 | + | 0.900006i | \(0.643562\pi\) | |||||||
\(390\) | 34.9622 | 1.77038 | ||||||||
\(391\) | 42.7860 | 2.16378 | ||||||||
\(392\) | −9.90265 | −0.500159 | ||||||||
\(393\) | −3.79263 | −0.191313 | ||||||||
\(394\) | −52.8731 | −2.66371 | ||||||||
\(395\) | −8.13953 | −0.409544 | ||||||||
\(396\) | 9.58318 | 0.481573 | ||||||||
\(397\) | −24.0795 | −1.20851 | −0.604257 | − | 0.796790i | \(-0.706530\pi\) | ||||
−0.604257 | + | 0.796790i | \(0.706530\pi\) | |||||||
\(398\) | 36.4331 | 1.82623 | ||||||||
\(399\) | 11.9983 | 0.600664 | ||||||||
\(400\) | 26.9341 | 1.34671 | ||||||||
\(401\) | −0.0181059 | −0.000904168 0 | −0.000452084 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000452084 | 1.00000i | \(0.500144\pi\) | ||||||||
\(402\) | 8.96025 | 0.446897 | ||||||||
\(403\) | 2.79817 | 0.139387 | ||||||||
\(404\) | −23.6399 | −1.17613 | ||||||||
\(405\) | −20.0344 | −0.995516 | ||||||||
\(406\) | −25.3515 | −1.25817 | ||||||||
\(407\) | 5.34533 | 0.264958 | ||||||||
\(408\) | −15.5371 | −0.769199 | ||||||||
\(409\) | 22.1873 | 1.09709 | 0.548546 | − | 0.836120i | \(-0.315181\pi\) | ||||
0.548546 | + | 0.836120i | \(0.315181\pi\) | |||||||
\(410\) | −114.047 | −5.63240 | ||||||||
\(411\) | 4.46559 | 0.220271 | ||||||||
\(412\) | −18.9644 | −0.934311 | ||||||||
\(413\) | −6.14472 | −0.302362 | ||||||||
\(414\) | −47.9174 | −2.35501 | ||||||||
\(415\) | 16.4026 | 0.805174 | ||||||||
\(416\) | −11.9148 | −0.584169 | ||||||||
\(417\) | 11.1814 | 0.547554 | ||||||||
\(418\) | 14.0062 | 0.685064 | ||||||||
\(419\) | −29.2309 | −1.42802 | −0.714012 | − | 0.700133i | \(-0.753124\pi\) | ||||
−0.714012 | + | 0.700133i | \(0.753124\pi\) | |||||||
\(420\) | −30.2053 | −1.47387 | ||||||||
\(421\) | 13.7237 | 0.668853 | 0.334426 | − | 0.942422i | \(-0.391457\pi\) | ||||
0.334426 | + | 0.942422i | \(0.391457\pi\) | |||||||
\(422\) | 61.8567 | 3.01114 | ||||||||
\(423\) | −8.31712 | −0.404392 | ||||||||
\(424\) | −32.4302 | −1.57495 | ||||||||
\(425\) | −55.9407 | −2.71352 | ||||||||
\(426\) | 9.06428 | 0.439166 | ||||||||
\(427\) | −3.05635 | −0.147907 | ||||||||
\(428\) | −56.5344 | −2.73270 | ||||||||
\(429\) | −3.73024 | −0.180097 | ||||||||
\(430\) | −44.2266 | −2.13280 | ||||||||
\(431\) | 5.92420 | 0.285359 | 0.142679 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142679 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(432\) | 9.81133 | 0.472048 | ||||||||
\(433\) | −15.6146 | −0.750392 | −0.375196 | − | 0.926946i | \(-0.622425\pi\) | ||||
−0.375196 | + | 0.926946i | \(0.622425\pi\) | |||||||
\(434\) | −3.70266 | −0.177733 | ||||||||
\(435\) | −9.07761 | −0.435238 | ||||||||
\(436\) | −41.1000 | −1.96833 | ||||||||
\(437\) | −45.7246 | −2.18730 | ||||||||
\(438\) | 8.04142 | 0.384234 | ||||||||
\(439\) | 11.4705 | 0.547457 | 0.273728 | − | 0.961807i | \(-0.411743\pi\) | ||||
0.273728 | + | 0.961807i | \(0.411743\pi\) | |||||||
\(440\) | −16.5149 | −0.787316 | ||||||||
\(441\) | −5.96400 | −0.284000 | ||||||||
\(442\) | −72.6647 | −3.45631 | ||||||||
\(443\) | 34.4924 | 1.63878 | 0.819391 | − | 0.573235i | \(-0.194312\pi\) | ||||
0.819391 | + | 0.573235i | \(0.194312\pi\) | |||||||
\(444\) | 13.5295 | 0.642081 | ||||||||
\(445\) | 15.9988 | 0.758415 | ||||||||
\(446\) | 67.4950 | 3.19598 | ||||||||
\(447\) | 6.55084 | 0.309844 | ||||||||
\(448\) | 31.8352 | 1.50407 | ||||||||
\(449\) | −9.16375 | −0.432464 | −0.216232 | − | 0.976342i | \(-0.569377\pi\) | ||||
−0.216232 | + | 0.976342i | \(0.569377\pi\) | |||||||
\(450\) | 62.6497 | 2.95334 | ||||||||
\(451\) | 12.1681 | 0.572974 | ||||||||
\(452\) | 23.9414 | 1.12611 | ||||||||
\(453\) | 3.27193 | 0.153729 | ||||||||
\(454\) | 1.58159 | 0.0742277 | ||||||||
\(455\) | −66.1651 | −3.10187 | ||||||||
\(456\) | 16.6041 | 0.777560 | ||||||||
\(457\) | 10.5400 | 0.493040 | 0.246520 | − | 0.969138i | \(-0.420713\pi\) | ||||
0.246520 | + | 0.969138i | \(0.420713\pi\) | |||||||
\(458\) | 20.4354 | 0.954884 | ||||||||
\(459\) | −20.3776 | −0.951145 | ||||||||
\(460\) | 115.110 | 5.36705 | ||||||||
\(461\) | 38.3015 | 1.78388 | 0.891939 | − | 0.452157i | \(-0.149345\pi\) | ||||
0.891939 | + | 0.452157i | \(0.149345\pi\) | |||||||
\(462\) | 4.93600 | 0.229643 | ||||||||
\(463\) | 1.10261 | 0.0512428 | 0.0256214 | − | 0.999672i | \(-0.491844\pi\) | ||||
0.0256214 | + | 0.999672i | \(0.491844\pi\) | |||||||
\(464\) | −9.08389 | −0.421709 | ||||||||
\(465\) | −1.32581 | −0.0614830 | ||||||||
\(466\) | 16.7404 | 0.775483 | ||||||||
\(467\) | 0.840580 | 0.0388974 | 0.0194487 | − | 0.999811i | \(-0.493809\pi\) | ||||
0.0194487 | + | 0.999811i | \(0.493809\pi\) | |||||||
\(468\) | 53.1327 | 2.45606 | ||||||||
\(469\) | −16.9571 | −0.783005 | ||||||||
\(470\) | 30.6018 | 1.41156 | ||||||||
\(471\) | 13.9399 | 0.642316 | ||||||||
\(472\) | −8.50355 | −0.391408 | ||||||||
\(473\) | 4.71869 | 0.216966 | ||||||||
\(474\) | 3.36664 | 0.154635 | ||||||||
\(475\) | 59.7826 | 2.74302 | ||||||||
\(476\) | 62.7782 | 2.87743 | ||||||||
\(477\) | −19.5315 | −0.894288 | ||||||||
\(478\) | 2.55417 | 0.116825 | ||||||||
\(479\) | −35.4273 | −1.61871 | −0.809357 | − | 0.587317i | \(-0.800184\pi\) | ||||
−0.809357 | + | 0.587317i | \(0.800184\pi\) | |||||||
\(480\) | 5.64536 | 0.257674 | ||||||||
\(481\) | 29.6365 | 1.35131 | ||||||||
\(482\) | −54.7384 | −2.49327 | ||||||||
\(483\) | −16.1141 | −0.733216 | ||||||||
\(484\) | 3.76203 | 0.171001 | ||||||||
\(485\) | −27.9342 | −1.26843 | ||||||||
\(486\) | 35.1634 | 1.59504 | ||||||||
\(487\) | −5.22639 | −0.236830 | −0.118415 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118415 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(488\) | −4.22962 | −0.191466 | ||||||||
\(489\) | −4.93807 | −0.223307 | ||||||||
\(490\) | 21.9438 | 0.991321 | ||||||||
\(491\) | 15.4077 | 0.695338 | 0.347669 | − | 0.937617i | \(-0.386973\pi\) | ||||
0.347669 | + | 0.937617i | \(0.386973\pi\) | |||||||
\(492\) | 30.7985 | 1.38850 | ||||||||
\(493\) | 18.8667 | 0.849715 | ||||||||
\(494\) | 77.6553 | 3.49388 | ||||||||
\(495\) | −9.94631 | −0.447053 | ||||||||
\(496\) | −1.32673 | −0.0595718 | ||||||||
\(497\) | −17.1540 | −0.769460 | ||||||||
\(498\) | −6.78440 | −0.304016 | ||||||||
\(499\) | −3.91959 | −0.175465 | −0.0877326 | − | 0.996144i | \(-0.527962\pi\) | ||||
−0.0877326 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(500\) | −77.0556 | −3.44603 | ||||||||
\(501\) | 10.9699 | 0.490097 | ||||||||
\(502\) | −54.6604 | −2.43961 | ||||||||
\(503\) | 17.9435 | 0.800061 | 0.400030 | − | 0.916502i | \(-0.369000\pi\) | ||||
0.400030 | + | 0.916502i | \(0.369000\pi\) | |||||||
\(504\) | −32.9300 | −1.46682 | ||||||||
\(505\) | 24.5357 | 1.09182 | ||||||||
\(506\) | −18.8107 | −0.836240 | ||||||||
\(507\) | −11.9354 | −0.530071 | ||||||||
\(508\) | −33.2050 | −1.47323 | ||||||||
\(509\) | −20.0890 | −0.890431 | −0.445216 | − | 0.895423i | \(-0.646873\pi\) | ||||
−0.445216 | + | 0.895423i | \(0.646873\pi\) | |||||||
\(510\) | 34.4295 | 1.52456 | ||||||||
\(511\) | −15.2182 | −0.673214 | ||||||||
\(512\) | 27.8869 | 1.23244 | ||||||||
\(513\) | 21.7771 | 0.961484 | ||||||||
\(514\) | −28.8188 | −1.27114 | ||||||||
\(515\) | 19.6830 | 0.867338 | ||||||||
\(516\) | 11.9434 | 0.525779 | ||||||||
\(517\) | −3.26502 | −0.143595 | ||||||||
\(518\) | −39.2162 | −1.72306 | ||||||||
\(519\) | 17.0365 | 0.747819 | ||||||||
\(520\) | −91.5645 | −4.01537 | ||||||||
\(521\) | −18.6827 | −0.818506 | −0.409253 | − | 0.912421i | \(-0.634211\pi\) | ||||
−0.409253 | + | 0.912421i | \(0.634211\pi\) | |||||||
\(522\) | −21.1295 | −0.924811 | ||||||||
\(523\) | −25.5801 | −1.11854 | −0.559270 | − | 0.828986i | \(-0.688918\pi\) | ||||
−0.559270 | + | 0.828986i | \(0.688918\pi\) | |||||||
\(524\) | 21.2070 | 0.926431 | ||||||||
\(525\) | 21.0684 | 0.919499 | ||||||||
\(526\) | 37.9587 | 1.65508 | ||||||||
\(527\) | 2.75554 | 0.120033 | ||||||||
\(528\) | 1.76865 | 0.0769708 | ||||||||
\(529\) | 38.4096 | 1.66998 | ||||||||
\(530\) | 71.8640 | 3.12157 | ||||||||
\(531\) | −5.12138 | −0.222249 | ||||||||
\(532\) | −67.0898 | −2.90871 | ||||||||
\(533\) | 67.4645 | 2.92221 | ||||||||
\(534\) | −6.61736 | −0.286361 | ||||||||
\(535\) | 58.6767 | 2.53681 | ||||||||
\(536\) | −23.4665 | −1.01360 | ||||||||
\(537\) | 2.09371 | 0.0903501 | ||||||||
\(538\) | 45.7334 | 1.97171 | ||||||||
\(539\) | −2.34126 | −0.100845 | ||||||||
\(540\) | −54.8234 | −2.35922 | ||||||||
\(541\) | 18.0242 | 0.774919 | 0.387460 | − | 0.921887i | \(-0.373353\pi\) | ||||
0.387460 | + | 0.921887i | \(0.373353\pi\) | |||||||
\(542\) | −49.1069 | −2.10932 | ||||||||
\(543\) | 4.18953 | 0.179790 | ||||||||
\(544\) | −11.7332 | −0.503057 | ||||||||
\(545\) | 42.6573 | 1.82724 | ||||||||
\(546\) | 27.3670 | 1.17120 | ||||||||
\(547\) | 6.47617 | 0.276901 | 0.138451 | − | 0.990369i | \(-0.455788\pi\) | ||||
0.138451 | + | 0.990369i | \(0.455788\pi\) | |||||||
\(548\) | −24.9699 | −1.06666 | ||||||||
\(549\) | −2.54734 | −0.108718 | ||||||||
\(550\) | 24.5941 | 1.04870 | ||||||||
\(551\) | −20.1625 | −0.858951 | ||||||||
\(552\) | −22.2999 | −0.949148 | ||||||||
\(553\) | −6.37130 | −0.270935 | ||||||||
\(554\) | 26.4592 | 1.12414 | ||||||||
\(555\) | −14.0421 | −0.596056 | ||||||||
\(556\) | −62.5220 | −2.65152 | ||||||||
\(557\) | 29.5658 | 1.25274 | 0.626372 | − | 0.779524i | \(-0.284539\pi\) | ||||
0.626372 | + | 0.779524i | \(0.284539\pi\) | |||||||
\(558\) | −3.08602 | −0.130641 | ||||||||
\(559\) | 26.1622 | 1.10654 | ||||||||
\(560\) | 31.3715 | 1.32569 | ||||||||
\(561\) | −3.67340 | −0.155091 | ||||||||
\(562\) | 31.1859 | 1.31550 | ||||||||
\(563\) | 25.7670 | 1.08595 | 0.542976 | − | 0.839748i | \(-0.317298\pi\) | ||||
0.542976 | + | 0.839748i | \(0.317298\pi\) | |||||||
\(564\) | −8.26403 | −0.347978 | ||||||||
\(565\) | −24.8486 | −1.04539 | ||||||||
\(566\) | 69.0767 | 2.90351 | ||||||||
\(567\) | −15.6821 | −0.658586 | ||||||||
\(568\) | −23.7390 | −0.996066 | ||||||||
\(569\) | −16.5438 | −0.693554 | −0.346777 | − | 0.937948i | \(-0.612724\pi\) | ||||
−0.346777 | + | 0.937948i | \(0.612724\pi\) | |||||||
\(570\) | −36.7941 | −1.54113 | ||||||||
\(571\) | 0.633532 | 0.0265125 | 0.0132562 | − | 0.999912i | \(-0.495780\pi\) | ||||
0.0132562 | + | 0.999912i | \(0.495780\pi\) | |||||||
\(572\) | 20.8581 | 0.872120 | ||||||||
\(573\) | −15.5709 | −0.650485 | ||||||||
\(574\) | −89.2717 | −3.72613 | ||||||||
\(575\) | −80.2901 | −3.34833 | ||||||||
\(576\) | 26.5333 | 1.10556 | ||||||||
\(577\) | −5.75419 | −0.239550 | −0.119775 | − | 0.992801i | \(-0.538217\pi\) | ||||
−0.119775 | + | 0.992801i | \(0.538217\pi\) | |||||||
\(578\) | −30.7504 | −1.27905 | ||||||||
\(579\) | −8.53514 | −0.354709 | ||||||||
\(580\) | 50.7586 | 2.10764 | ||||||||
\(581\) | 12.8393 | 0.532665 | ||||||||
\(582\) | 11.5541 | 0.478931 | ||||||||
\(583\) | −7.66741 | −0.317552 | ||||||||
\(584\) | −21.0602 | −0.871475 | ||||||||
\(585\) | −55.1460 | −2.28001 | ||||||||
\(586\) | −52.5185 | −2.16952 | ||||||||
\(587\) | −16.9735 | −0.700573 | −0.350286 | − | 0.936643i | \(-0.613916\pi\) | ||||
−0.350286 | + | 0.936643i | \(0.613916\pi\) | |||||||
\(588\) | −5.92593 | −0.244381 | ||||||||
\(589\) | −2.94479 | −0.121338 | ||||||||
\(590\) | 18.8435 | 0.775774 | ||||||||
\(591\) | −14.8194 | −0.609589 | ||||||||
\(592\) | −14.0518 | −0.577527 | ||||||||
\(593\) | 26.2600 | 1.07837 | 0.539185 | − | 0.842187i | \(-0.318732\pi\) | ||||
0.539185 | + | 0.842187i | \(0.318732\pi\) | |||||||
\(594\) | 8.95895 | 0.367590 | ||||||||
\(595\) | −65.1570 | −2.67118 | ||||||||
\(596\) | −36.6299 | −1.50042 | ||||||||
\(597\) | 10.2116 | 0.417932 | ||||||||
\(598\) | −104.294 | −4.26489 | ||||||||
\(599\) | 6.49896 | 0.265540 | 0.132770 | − | 0.991147i | \(-0.457613\pi\) | ||||
0.132770 | + | 0.991147i | \(0.457613\pi\) | |||||||
\(600\) | 29.1561 | 1.19029 | ||||||||
\(601\) | 4.36919 | 0.178223 | 0.0891115 | − | 0.996022i | \(-0.471597\pi\) | ||||
0.0891115 | + | 0.996022i | \(0.471597\pi\) | |||||||
\(602\) | −34.6188 | −1.41096 | ||||||||
\(603\) | −14.1330 | −0.575542 | ||||||||
\(604\) | −18.2954 | −0.744431 | ||||||||
\(605\) | −3.90458 | −0.158744 | ||||||||
\(606\) | −10.1484 | −0.412249 | ||||||||
\(607\) | 5.74264 | 0.233087 | 0.116543 | − | 0.993186i | \(-0.462819\pi\) | ||||
0.116543 | + | 0.993186i | \(0.462819\pi\) | |||||||
\(608\) | 12.5390 | 0.508525 | ||||||||
\(609\) | −7.10559 | −0.287933 | ||||||||
\(610\) | 9.37264 | 0.379487 | ||||||||
\(611\) | −18.1025 | −0.732347 | ||||||||
\(612\) | 52.3231 | 2.11504 | ||||||||
\(613\) | 48.0137 | 1.93926 | 0.969629 | − | 0.244582i | \(-0.0786509\pi\) | ||||
0.969629 | + | 0.244582i | \(0.0786509\pi\) | |||||||
\(614\) | 51.4026 | 2.07444 | ||||||||
\(615\) | −31.9655 | −1.28898 | ||||||||
\(616\) | −12.9272 | −0.520851 | ||||||||
\(617\) | 22.3596 | 0.900165 | 0.450083 | − | 0.892987i | \(-0.351395\pi\) | ||||
0.450083 | + | 0.892987i | \(0.351395\pi\) | |||||||
\(618\) | −8.14122 | −0.327488 | ||||||||
\(619\) | −29.2776 | −1.17677 | −0.588384 | − | 0.808582i | \(-0.700236\pi\) | ||||
−0.588384 | + | 0.808582i | \(0.700236\pi\) | |||||||
\(620\) | 7.41343 | 0.297731 | ||||||||
\(621\) | −29.2474 | −1.17366 | ||||||||
\(622\) | −29.1487 | −1.16875 | ||||||||
\(623\) | 12.5232 | 0.501731 | ||||||||
\(624\) | 9.80607 | 0.392557 | ||||||||
\(625\) | 28.7467 | 1.14987 | ||||||||
\(626\) | −27.5143 | −1.09969 | ||||||||
\(627\) | 3.92569 | 0.156777 | ||||||||
\(628\) | −77.9466 | −3.11041 | ||||||||
\(629\) | 29.1849 | 1.16368 | ||||||||
\(630\) | 72.9714 | 2.90725 | ||||||||
\(631\) | −44.1200 | −1.75639 | −0.878195 | − | 0.478303i | \(-0.841252\pi\) | ||||
−0.878195 | + | 0.478303i | \(0.841252\pi\) | |||||||
\(632\) | −8.81710 | −0.350726 | ||||||||
\(633\) | 17.3374 | 0.689098 | ||||||||
\(634\) | −56.9979 | −2.26368 | ||||||||
\(635\) | 34.4632 | 1.36763 | ||||||||
\(636\) | −19.4069 | −0.769532 | ||||||||
\(637\) | −12.9808 | −0.514319 | ||||||||
\(638\) | −8.29470 | −0.328390 | ||||||||
\(639\) | −14.2971 | −0.565586 | ||||||||
\(640\) | −80.8445 | −3.19566 | ||||||||
\(641\) | −25.1861 | −0.994790 | −0.497395 | − | 0.867524i | \(-0.665710\pi\) | ||||
−0.497395 | + | 0.867524i | \(0.665710\pi\) | |||||||
\(642\) | −24.2696 | −0.957845 | ||||||||
\(643\) | −27.5892 | −1.08801 | −0.544005 | − | 0.839082i | \(-0.683093\pi\) | ||||
−0.544005 | + | 0.839082i | \(0.683093\pi\) | |||||||
\(644\) | 90.1038 | 3.55059 | ||||||||
\(645\) | −12.3960 | −0.488091 | ||||||||
\(646\) | 76.4721 | 3.00875 | ||||||||
\(647\) | 1.45014 | 0.0570108 | 0.0285054 | − | 0.999594i | \(-0.490925\pi\) | ||||
0.0285054 | + | 0.999594i | \(0.490925\pi\) | |||||||
\(648\) | −21.7021 | −0.852540 | ||||||||
\(649\) | −2.01048 | −0.0789181 | ||||||||
\(650\) | 136.359 | 5.34844 | ||||||||
\(651\) | −1.03779 | −0.0406742 | ||||||||
\(652\) | 27.6118 | 1.08136 | ||||||||
\(653\) | 3.86759 | 0.151350 | 0.0756752 | − | 0.997133i | \(-0.475889\pi\) | ||||
0.0756752 | + | 0.997133i | \(0.475889\pi\) | |||||||
\(654\) | −17.6438 | −0.689926 | ||||||||
\(655\) | −22.0106 | −0.860024 | ||||||||
\(656\) | −31.9876 | −1.24891 | ||||||||
\(657\) | −12.6838 | −0.494841 | ||||||||
\(658\) | 23.9539 | 0.933820 | ||||||||
\(659\) | −8.00713 | −0.311914 | −0.155957 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155957 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(660\) | −9.88282 | −0.384688 | ||||||||
\(661\) | −9.68056 | −0.376530 | −0.188265 | − | 0.982118i | \(-0.560286\pi\) | ||||
−0.188265 | + | 0.982118i | \(0.560286\pi\) | |||||||
\(662\) | 11.1848 | 0.434709 | ||||||||
\(663\) | −20.3667 | −0.790976 | ||||||||
\(664\) | 17.7681 | 0.689535 | ||||||||
\(665\) | 69.6319 | 2.70021 | ||||||||
\(666\) | −32.6851 | −1.26652 | ||||||||
\(667\) | 27.0789 | 1.04850 | ||||||||
\(668\) | −61.3393 | −2.37329 | ||||||||
\(669\) | 18.9177 | 0.731400 | ||||||||
\(670\) | 52.0008 | 2.00897 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 4.41896 | 0.170465 | ||||||||
\(673\) | 36.2068 | 1.39567 | 0.697834 | − | 0.716259i | \(-0.254147\pi\) | ||||
0.697834 | + | 0.716259i | \(0.254147\pi\) | |||||||
\(674\) | −4.06657 | −0.156638 | ||||||||
\(675\) | 38.2396 | 1.47184 | ||||||||
\(676\) | 66.7384 | 2.56686 | ||||||||
\(677\) | −9.72560 | −0.373785 | −0.186893 | − | 0.982380i | \(-0.559842\pi\) | ||||
−0.186893 | + | 0.982380i | \(0.559842\pi\) | |||||||
\(678\) | 10.2778 | 0.394716 | ||||||||
\(679\) | −21.8658 | −0.839132 | ||||||||
\(680\) | −90.1694 | −3.45784 | ||||||||
\(681\) | 0.443293 | 0.0169870 | ||||||||
\(682\) | −1.21146 | −0.0463894 | ||||||||
\(683\) | −30.8902 | −1.18198 | −0.590991 | − | 0.806678i | \(-0.701263\pi\) | ||||
−0.590991 | + | 0.806678i | \(0.701263\pi\) | |||||||
\(684\) | −55.9166 | −2.13803 | ||||||||
\(685\) | 25.9161 | 0.990202 | ||||||||
\(686\) | −34.1789 | −1.30496 | ||||||||
\(687\) | 5.72770 | 0.218525 | ||||||||
\(688\) | −12.4045 | −0.472918 | ||||||||
\(689\) | −42.5110 | −1.61954 | ||||||||
\(690\) | 49.4157 | 1.88122 | ||||||||
\(691\) | 19.0958 | 0.726439 | 0.363219 | − | 0.931704i | \(-0.381678\pi\) | ||||
0.363219 | + | 0.931704i | \(0.381678\pi\) | |||||||
\(692\) | −95.2616 | −3.62130 | ||||||||
\(693\) | −7.78557 | −0.295749 | ||||||||
\(694\) | −16.2529 | −0.616952 | ||||||||
\(695\) | 64.8911 | 2.46146 | ||||||||
\(696\) | −9.83328 | −0.372729 | ||||||||
\(697\) | 66.4366 | 2.51647 | ||||||||
\(698\) | 67.8034 | 2.56640 | ||||||||
\(699\) | 4.69204 | 0.177469 | ||||||||
\(700\) | −117.806 | −4.45266 | ||||||||
\(701\) | 21.4093 | 0.808618 | 0.404309 | − | 0.914623i | \(-0.367512\pi\) | ||||
0.404309 | + | 0.914623i | \(0.367512\pi\) | |||||||
\(702\) | 49.6717 | 1.87474 | ||||||||
\(703\) | −31.1893 | −1.17633 | ||||||||
\(704\) | 10.4161 | 0.392571 | ||||||||
\(705\) | 8.57717 | 0.323035 | ||||||||
\(706\) | −53.4717 | −2.01243 | ||||||||
\(707\) | 19.2056 | 0.722300 | ||||||||
\(708\) | −5.08869 | −0.191245 | ||||||||
\(709\) | 29.4953 | 1.10772 | 0.553860 | − | 0.832610i | \(-0.313154\pi\) | ||||
0.553860 | + | 0.832610i | \(0.313154\pi\) | |||||||
\(710\) | 52.6046 | 1.97421 | ||||||||
\(711\) | −5.31022 | −0.199149 | ||||||||
\(712\) | 17.3306 | 0.649492 | ||||||||
\(713\) | 3.95495 | 0.148114 | ||||||||
\(714\) | 26.9500 | 1.00858 | ||||||||
\(715\) | −21.6484 | −0.809605 | ||||||||
\(716\) | −11.7072 | −0.437519 | ||||||||
\(717\) | 0.715890 | 0.0267354 | ||||||||
\(718\) | −40.8543 | −1.52467 | ||||||||
\(719\) | −25.0362 | −0.933694 | −0.466847 | − | 0.884338i | \(-0.654610\pi\) | ||||
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(720\) | 26.1469 | 0.974438 | ||||||||
\(721\) | 15.4071 | 0.573790 | ||||||||
\(722\) | −36.1161 | −1.34410 | ||||||||
\(723\) | −15.3422 | −0.570584 | ||||||||
\(724\) | −23.4263 | −0.870630 | ||||||||
\(725\) | −35.4044 | −1.31489 | ||||||||
\(726\) | 1.61500 | 0.0599382 | ||||||||
\(727\) | −16.7702 | −0.621971 | −0.310986 | − | 0.950415i | \(-0.600659\pi\) | ||||
−0.310986 | + | 0.950415i | \(0.600659\pi\) | |||||||
\(728\) | −71.6730 | −2.65638 | ||||||||
\(729\) | −5.53728 | −0.205085 | ||||||||
\(730\) | 46.6684 | 1.72727 | ||||||||
\(731\) | 25.7635 | 0.952899 | ||||||||
\(732\) | −2.53108 | −0.0935515 | ||||||||
\(733\) | −32.1830 | −1.18871 | −0.594354 | − | 0.804204i | \(-0.702592\pi\) | ||||
−0.594354 | + | 0.804204i | \(0.702592\pi\) | |||||||
\(734\) | −52.4877 | −1.93736 | ||||||||
\(735\) | 6.15048 | 0.226864 | ||||||||
\(736\) | −16.8404 | −0.620744 | ||||||||
\(737\) | −5.54815 | −0.204369 | ||||||||
\(738\) | −74.4044 | −2.73886 | ||||||||
\(739\) | 2.77895 | 0.102225 | 0.0511126 | − | 0.998693i | \(-0.483723\pi\) | ||||
0.0511126 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(740\) | 78.5184 | 2.88639 | ||||||||
\(741\) | 21.7654 | 0.799573 | ||||||||
\(742\) | 56.2522 | 2.06508 | ||||||||
\(743\) | 12.3289 | 0.452302 | 0.226151 | − | 0.974092i | \(-0.427386\pi\) | ||||
0.226151 | + | 0.974092i | \(0.427386\pi\) | |||||||
\(744\) | −1.43618 | −0.0526528 | ||||||||
\(745\) | 38.0178 | 1.39287 | ||||||||
\(746\) | 14.3744 | 0.526283 | ||||||||
\(747\) | 10.7011 | 0.391531 | ||||||||
\(748\) | 20.5403 | 0.751027 | ||||||||
\(749\) | 45.9297 | 1.67824 | ||||||||
\(750\) | −33.0791 | −1.20788 | ||||||||
\(751\) | 1.48325 | 0.0541245 | 0.0270622 | − | 0.999634i | \(-0.491385\pi\) | ||||
0.0270622 | + | 0.999634i | \(0.491385\pi\) | |||||||
\(752\) | 8.58310 | 0.312993 | ||||||||
\(753\) | −15.3204 | −0.558305 | ||||||||
\(754\) | −45.9889 | −1.67482 | ||||||||
\(755\) | 18.9887 | 0.691069 | ||||||||
\(756\) | −42.9135 | −1.56075 | ||||||||
\(757\) | −6.42481 | −0.233514 | −0.116757 | − | 0.993161i | \(-0.537250\pi\) | ||||
−0.116757 | + | 0.993161i | \(0.537250\pi\) | |||||||
\(758\) | 21.2925 | 0.773379 | ||||||||
\(759\) | −5.27233 | −0.191373 | ||||||||
\(760\) | 96.3622 | 3.49542 | ||||||||
\(761\) | −4.70734 | −0.170641 | −0.0853204 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853204 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(762\) | −14.2545 | −0.516387 | ||||||||
\(763\) | 33.3904 | 1.20882 | ||||||||
\(764\) | 87.0668 | 3.14997 | ||||||||
\(765\) | −54.3058 | −1.96343 | ||||||||
\(766\) | 60.1038 | 2.17164 | ||||||||
\(767\) | −11.1468 | −0.402489 | ||||||||
\(768\) | 19.4228 | 0.700859 | ||||||||
\(769\) | 31.7419 | 1.14464 | 0.572321 | − | 0.820030i | \(-0.306043\pi\) | ||||
0.572321 | + | 0.820030i | \(0.306043\pi\) | |||||||
\(770\) | 28.6461 | 1.03233 | ||||||||
\(771\) | −8.07741 | −0.290901 | ||||||||
\(772\) | 47.7253 | 1.71767 | ||||||||
\(773\) | 33.7048 | 1.21228 | 0.606139 | − | 0.795359i | \(-0.292718\pi\) | ||||
0.606139 | + | 0.795359i | \(0.292718\pi\) | |||||||
\(774\) | −28.8534 | −1.03711 | ||||||||
\(775\) | −5.17091 | −0.185744 | ||||||||
\(776\) | −30.2596 | −1.08626 | ||||||||
\(777\) | −10.9916 | −0.394322 | ||||||||
\(778\) | 41.2722 | 1.47968 | ||||||||
\(779\) | −70.9994 | −2.54382 | ||||||||
\(780\) | −54.7940 | −1.96194 | ||||||||
\(781\) | −5.61256 | −0.200833 | ||||||||
\(782\) | −102.705 | −3.67271 | ||||||||
\(783\) | −12.8968 | −0.460894 | ||||||||
\(784\) | 6.15473 | 0.219812 | ||||||||
\(785\) | 80.9002 | 2.88745 | ||||||||
\(786\) | 9.10393 | 0.324726 | ||||||||
\(787\) | 10.6021 | 0.377922 | 0.188961 | − | 0.981985i | \(-0.439488\pi\) | ||||
0.188961 | + | 0.981985i | \(0.439488\pi\) | |||||||
\(788\) | 82.8646 | 2.95193 | ||||||||
\(789\) | 10.6392 | 0.378765 | ||||||||
\(790\) | 19.5383 | 0.695142 | ||||||||
\(791\) | −19.4505 | −0.691579 | ||||||||
\(792\) | −10.7743 | −0.382848 | ||||||||
\(793\) | −5.54437 | −0.196886 | ||||||||
\(794\) | 57.8009 | 2.05128 | ||||||||
\(795\) | 20.1422 | 0.714371 | ||||||||
\(796\) | −57.0993 | −2.02383 | ||||||||
\(797\) | −5.19312 | −0.183950 | −0.0919749 | − | 0.995761i | \(-0.529318\pi\) | ||||
−0.0919749 | + | 0.995761i | \(0.529318\pi\) | |||||||
\(798\) | −28.8009 | −1.01954 | ||||||||
\(799\) | −17.8266 | −0.630661 | ||||||||
\(800\) | 22.0179 | 0.778452 | ||||||||
\(801\) | 10.4376 | 0.368794 | ||||||||
\(802\) | 0.0434619 | 0.00153469 | ||||||||
\(803\) | −4.97921 | −0.175713 | ||||||||
\(804\) | −14.0428 | −0.495252 | ||||||||
\(805\) | −93.5181 | −3.29608 | ||||||||
\(806\) | −6.71680 | −0.236589 | ||||||||
\(807\) | 12.8183 | 0.451225 | ||||||||
\(808\) | 26.5782 | 0.935017 | ||||||||
\(809\) | 26.1862 | 0.920657 | 0.460328 | − | 0.887749i | \(-0.347732\pi\) | ||||
0.460328 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(810\) | 48.0910 | 1.68974 | ||||||||
\(811\) | −26.7395 | −0.938950 | −0.469475 | − | 0.882946i | \(-0.655557\pi\) | ||||
−0.469475 | + | 0.882946i | \(0.655557\pi\) | |||||||
\(812\) | 39.7318 | 1.39431 | ||||||||
\(813\) | −13.7638 | −0.482719 | ||||||||
\(814\) | −12.8311 | −0.449728 | ||||||||
\(815\) | −28.6581 | −1.00385 | ||||||||
\(816\) | 9.65666 | 0.338051 | ||||||||
\(817\) | −27.5330 | −0.963256 | ||||||||
\(818\) | −53.2589 | −1.86216 | ||||||||
\(819\) | −43.1661 | −1.50834 | ||||||||
\(820\) | 178.739 | 6.24185 | ||||||||
\(821\) | −44.8895 | −1.56665 | −0.783327 | − | 0.621610i | \(-0.786479\pi\) | ||||
−0.783327 | + | 0.621610i | \(0.786479\pi\) | |||||||
\(822\) | −10.7193 | −0.373879 | ||||||||
\(823\) | 12.5123 | 0.436152 | 0.218076 | − | 0.975932i | \(-0.430022\pi\) | ||||
0.218076 | + | 0.975932i | \(0.430022\pi\) | |||||||
\(824\) | 21.3215 | 0.742771 | ||||||||
\(825\) | 6.89331 | 0.239994 | ||||||||
\(826\) | 14.7499 | 0.513216 | ||||||||
\(827\) | −12.4709 | −0.433657 | −0.216829 | − | 0.976210i | \(-0.569571\pi\) | ||||
−0.216829 | + | 0.976210i | \(0.569571\pi\) | |||||||
\(828\) | 75.0979 | 2.60983 | ||||||||
\(829\) | 13.7328 | 0.476959 | 0.238480 | − | 0.971148i | \(-0.423351\pi\) | ||||
0.238480 | + | 0.971148i | \(0.423351\pi\) | |||||||
\(830\) | −39.3733 | −1.36667 | ||||||||
\(831\) | 7.41606 | 0.257260 | ||||||||
\(832\) | 57.7506 | 2.00214 | ||||||||
\(833\) | −12.7830 | −0.442906 | ||||||||
\(834\) | −26.8400 | −0.929393 | ||||||||
\(835\) | 63.6636 | 2.20317 | ||||||||
\(836\) | −21.9510 | −0.759190 | ||||||||
\(837\) | −1.88361 | −0.0651073 | ||||||||
\(838\) | 70.1666 | 2.42387 | ||||||||
\(839\) | 25.7292 | 0.888270 | 0.444135 | − | 0.895960i | \(-0.353511\pi\) | ||||
0.444135 | + | 0.895960i | \(0.353511\pi\) | |||||||
\(840\) | 33.9596 | 1.17172 | ||||||||
\(841\) | −17.0594 | −0.588255 | ||||||||
\(842\) | −32.9427 | −1.13528 | ||||||||
\(843\) | 8.74088 | 0.301052 | ||||||||
\(844\) | −96.9440 | −3.33695 | ||||||||
\(845\) | −69.2673 | −2.38287 | ||||||||
\(846\) | 19.9646 | 0.686397 | ||||||||
\(847\) | −3.05635 | −0.105017 | ||||||||
\(848\) | 20.1562 | 0.692165 | ||||||||
\(849\) | 19.3610 | 0.664469 | ||||||||
\(850\) | 134.281 | 4.60581 | ||||||||
\(851\) | 41.8883 | 1.43591 | ||||||||
\(852\) | −14.2059 | −0.486685 | ||||||||
\(853\) | −18.4750 | −0.632572 | −0.316286 | − | 0.948664i | \(-0.602436\pi\) | ||||
−0.316286 | + | 0.948664i | \(0.602436\pi\) | |||||||
\(854\) | 7.33653 | 0.251051 | ||||||||
\(855\) | 58.0354 | 1.98477 | ||||||||
\(856\) | 63.5612 | 2.17248 | ||||||||
\(857\) | −29.9179 | −1.02197 | −0.510987 | − | 0.859588i | \(-0.670720\pi\) | ||||
−0.510987 | + | 0.859588i | \(0.670720\pi\) | |||||||
\(858\) | 8.95414 | 0.305689 | ||||||||
\(859\) | −6.91499 | −0.235936 | −0.117968 | − | 0.993017i | \(-0.537638\pi\) | ||||
−0.117968 | + | 0.993017i | \(0.537638\pi\) | |||||||
\(860\) | 69.3136 | 2.36357 | ||||||||
\(861\) | −25.0213 | −0.852725 | ||||||||
\(862\) | −14.2206 | −0.484355 | ||||||||
\(863\) | 39.9338 | 1.35936 | 0.679681 | − | 0.733508i | \(-0.262118\pi\) | ||||
0.679681 | + | 0.733508i | \(0.262118\pi\) | |||||||
\(864\) | 8.02052 | 0.272864 | ||||||||
\(865\) | 98.8713 | 3.36173 | ||||||||
\(866\) | 37.4817 | 1.27368 | ||||||||
\(867\) | −8.61880 | −0.292710 | ||||||||
\(868\) | 5.80294 | 0.196965 | ||||||||
\(869\) | −2.08461 | −0.0707156 | ||||||||
\(870\) | 21.7901 | 0.738754 | ||||||||
\(871\) | −30.7610 | −1.04230 | ||||||||
\(872\) | 46.2083 | 1.56481 | ||||||||
\(873\) | −18.2243 | −0.616798 | ||||||||
\(874\) | 109.758 | 3.71263 | ||||||||
\(875\) | 62.6015 | 2.11632 | ||||||||
\(876\) | −12.6028 | −0.425809 | ||||||||
\(877\) | −48.6939 | −1.64428 | −0.822139 | − | 0.569287i | \(-0.807219\pi\) | ||||
−0.822139 | + | 0.569287i | \(0.807219\pi\) | |||||||
\(878\) | −27.5340 | −0.929229 | ||||||||
\(879\) | −14.7200 | −0.496494 | ||||||||
\(880\) | 10.2644 | 0.346012 | ||||||||
\(881\) | −25.0353 | −0.843460 | −0.421730 | − | 0.906721i | \(-0.638577\pi\) | ||||
−0.421730 | + | 0.906721i | \(0.638577\pi\) | |||||||
\(882\) | 14.3161 | 0.482049 | ||||||||
\(883\) | 41.3439 | 1.39133 | 0.695667 | − | 0.718364i | \(-0.255109\pi\) | ||||
0.695667 | + | 0.718364i | \(0.255109\pi\) | |||||||
\(884\) | 113.883 | 3.83029 | ||||||||
\(885\) | 5.28151 | 0.177536 | ||||||||
\(886\) | −82.7963 | −2.78160 | ||||||||
\(887\) | −22.9598 | −0.770913 | −0.385457 | − | 0.922726i | \(-0.625956\pi\) | ||||
−0.385457 | + | 0.922726i | \(0.625956\pi\) | |||||||
\(888\) | −15.2111 | −0.510450 | ||||||||
\(889\) | 26.9764 | 0.904759 | ||||||||
\(890\) | −38.4038 | −1.28730 | ||||||||
\(891\) | −5.13099 | −0.171895 | ||||||||
\(892\) | −105.781 | −3.54180 | ||||||||
\(893\) | 19.0510 | 0.637516 | ||||||||
\(894\) | −15.7248 | −0.525916 | ||||||||
\(895\) | 12.1508 | 0.406157 | ||||||||
\(896\) | −63.2818 | −2.11410 | ||||||||
\(897\) | −29.2317 | −0.976019 | ||||||||
\(898\) | 21.9969 | 0.734046 | ||||||||
\(899\) | 1.74396 | 0.0581642 | ||||||||
\(900\) | −98.1869 | −3.27290 | ||||||||
\(901\) | −41.8632 | −1.39467 | ||||||||
\(902\) | −29.2086 | −0.972541 | ||||||||
\(903\) | −9.70306 | −0.322898 | ||||||||
\(904\) | −26.9171 | −0.895249 | ||||||||
\(905\) | 24.3139 | 0.808222 | ||||||||
\(906\) | −7.85403 | −0.260933 | ||||||||
\(907\) | 54.1257 | 1.79722 | 0.898608 | − | 0.438753i | \(-0.144580\pi\) | ||||
0.898608 | + | 0.438753i | \(0.144580\pi\) | |||||||
\(908\) | −2.47873 | −0.0822594 | ||||||||
\(909\) | 16.0071 | 0.530921 | ||||||||
\(910\) | 158.824 | 5.26497 | ||||||||
\(911\) | 13.9020 | 0.460594 | 0.230297 | − | 0.973120i | \(-0.426030\pi\) | ||||
0.230297 | + | 0.973120i | \(0.426030\pi\) | |||||||
\(912\) | −10.3199 | −0.341725 | ||||||||
\(913\) | 4.20087 | 0.139029 | ||||||||
\(914\) | −25.3004 | −0.836864 | ||||||||
\(915\) | 2.62699 | 0.0868457 | ||||||||
\(916\) | −32.0271 | −1.05821 | ||||||||
\(917\) | −17.2290 | −0.568951 | ||||||||
\(918\) | 48.9149 | 1.61443 | ||||||||
\(919\) | −42.6331 | −1.40634 | −0.703168 | − | 0.711023i | \(-0.748232\pi\) | ||||
−0.703168 | + | 0.711023i | \(0.748232\pi\) | |||||||
\(920\) | −129.418 | −4.26677 | ||||||||
\(921\) | 14.4073 | 0.474735 | ||||||||
\(922\) | −91.9397 | −3.02787 | ||||||||
\(923\) | −31.1181 | −1.02427 | ||||||||
\(924\) | −7.73587 | −0.254491 | ||||||||
\(925\) | −54.7670 | −1.80073 | ||||||||
\(926\) | −2.64674 | −0.0869772 | ||||||||
\(927\) | 12.8412 | 0.421760 | ||||||||
\(928\) | −7.42585 | −0.243765 | ||||||||
\(929\) | −45.6604 | −1.49807 | −0.749034 | − | 0.662531i | \(-0.769482\pi\) | ||||
−0.749034 | + | 0.662531i | \(0.769482\pi\) | |||||||
\(930\) | 3.18251 | 0.104358 | ||||||||
\(931\) | 13.6610 | 0.447720 | ||||||||
\(932\) | −26.2361 | −0.859393 | ||||||||
\(933\) | −8.16987 | −0.267469 | ||||||||
\(934\) | −2.01775 | −0.0660227 | ||||||||
\(935\) | −21.3186 | −0.697192 | ||||||||
\(936\) | −59.7366 | −1.95255 | ||||||||
\(937\) | 30.8463 | 1.00770 | 0.503852 | − | 0.863790i | \(-0.331916\pi\) | ||||
0.503852 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(938\) | 40.7041 | 1.32904 | ||||||||
\(939\) | −7.71178 | −0.251664 | ||||||||
\(940\) | −47.9603 | −1.56429 | ||||||||
\(941\) | −4.21276 | −0.137332 | −0.0686660 | − | 0.997640i | \(-0.521874\pi\) | ||||
−0.0686660 | + | 0.997640i | \(0.521874\pi\) | |||||||
\(942\) | −33.4616 | −1.09024 | ||||||||
\(943\) | 95.3546 | 3.10517 | ||||||||
\(944\) | 5.28516 | 0.172017 | ||||||||
\(945\) | 44.5396 | 1.44887 | ||||||||
\(946\) | −11.3269 | −0.368268 | ||||||||
\(947\) | 9.29055 | 0.301902 | 0.150951 | − | 0.988541i | \(-0.451766\pi\) | ||||
0.150951 | + | 0.988541i | \(0.451766\pi\) | |||||||
\(948\) | −5.27632 | −0.171367 | ||||||||
\(949\) | −27.6066 | −0.896148 | ||||||||
\(950\) | −143.504 | −4.65587 | ||||||||
\(951\) | −15.9755 | −0.518042 | ||||||||
\(952\) | −70.5810 | −2.28754 | ||||||||
\(953\) | −42.1444 | −1.36519 | −0.682595 | − | 0.730797i | \(-0.739149\pi\) | ||||
−0.682595 | + | 0.730797i | \(0.739149\pi\) | |||||||
\(954\) | 46.8840 | 1.51792 | ||||||||
\(955\) | −90.3659 | −2.92417 | ||||||||
\(956\) | −4.00299 | −0.129466 | ||||||||
\(957\) | −2.32486 | −0.0751521 | ||||||||
\(958\) | 85.0405 | 2.74753 | ||||||||
\(959\) | 20.2860 | 0.655070 | ||||||||
\(960\) | −27.3630 | −0.883136 | ||||||||
\(961\) | −30.7453 | −0.991784 | ||||||||
\(962\) | −71.1401 | −2.29365 | ||||||||
\(963\) | 38.2806 | 1.23357 | ||||||||
\(964\) | 85.7880 | 2.76305 | ||||||||
\(965\) | −49.5337 | −1.59455 | ||||||||
\(966\) | 38.6806 | 1.24453 | ||||||||
\(967\) | −9.83390 | −0.316237 | −0.158119 | − | 0.987420i | \(-0.550543\pi\) | ||||
−0.158119 | + | 0.987420i | \(0.550543\pi\) | |||||||
\(968\) | −4.22962 | −0.135945 | ||||||||
\(969\) | 21.4338 | 0.688553 | ||||||||
\(970\) | 67.0540 | 2.15297 | ||||||||
\(971\) | 14.8073 | 0.475190 | 0.237595 | − | 0.971364i | \(-0.423641\pi\) | ||||
0.237595 | + | 0.971364i | \(0.423641\pi\) | |||||||
\(972\) | −55.1093 | −1.76763 | ||||||||
\(973\) | 50.7941 | 1.62838 | ||||||||
\(974\) | 12.5456 | 0.401985 | ||||||||
\(975\) | 38.2191 | 1.22399 | ||||||||
\(976\) | 2.62881 | 0.0841461 | ||||||||
\(977\) | 46.6744 | 1.49325 | 0.746623 | − | 0.665247i | \(-0.231674\pi\) | ||||
0.746623 | + | 0.665247i | \(0.231674\pi\) | |||||||
\(978\) | 11.8534 | 0.379031 | ||||||||
\(979\) | 4.09744 | 0.130955 | ||||||||
\(980\) | −34.3912 | −1.09859 | ||||||||
\(981\) | 27.8296 | 0.888531 | ||||||||
\(982\) | −36.9849 | −1.18023 | ||||||||
\(983\) | 43.9079 | 1.40044 | 0.700222 | − | 0.713925i | \(-0.253084\pi\) | ||||
0.700222 | + | 0.713925i | \(0.253084\pi\) | |||||||
\(984\) | −34.6265 | −1.10385 | ||||||||
\(985\) | −86.0045 | −2.74033 | ||||||||
\(986\) | −45.2882 | −1.44227 | ||||||||
\(987\) | 6.71386 | 0.213705 | ||||||||
\(988\) | −121.704 | −3.87193 | ||||||||
\(989\) | 36.9777 | 1.17582 | ||||||||
\(990\) | 23.8753 | 0.758808 | ||||||||
\(991\) | 51.8812 | 1.64806 | 0.824031 | − | 0.566545i | \(-0.191720\pi\) | ||||
0.824031 | + | 0.566545i | \(0.191720\pi\) | |||||||
\(992\) | −1.08457 | −0.0344350 | ||||||||
\(993\) | 3.13490 | 0.0994832 | ||||||||
\(994\) | 41.1767 | 1.30605 | ||||||||
\(995\) | 59.2629 | 1.87876 | ||||||||
\(996\) | 10.6328 | 0.336912 | ||||||||
\(997\) | 17.3273 | 0.548760 | 0.274380 | − | 0.961621i | \(-0.411527\pi\) | ||||
0.274380 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(998\) | 9.40868 | 0.297827 | ||||||||
\(999\) | −19.9501 | −0.631192 |
(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 | 671.2.a.d.1.4 | ✓ | 21 | |
3.2 | odd | 2 | 6039.2.a.l.1.18 | 21 | |||
11.10 | odd | 2 | 7381.2.a.j.1.18 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.d.1.4 | ✓ | 21 | 1.1 | even | 1 | trivial | |
6039.2.a.l.1.18 | 21 | 3.2 | odd | 2 | |||
7381.2.a.j.1.18 | 21 | 11.10 | odd | 2 |