Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67732 | −1.18605 | −0.593023 | − | 0.805185i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805185i | \(0.702066\pi\) | |||||||
\(3\) | −1.15146 | −0.664797 | −0.332399 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332399 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(4\) | 0.813414 | 0.406707 | ||||||||
\(5\) | 0.864739 | 0.386723 | 0.193362 | − | 0.981128i | \(-0.438061\pi\) | ||||
0.193362 | + | 0.981128i | \(0.438061\pi\) | |||||||
\(6\) | 1.93138 | 0.788481 | ||||||||
\(7\) | 4.27290 | 1.61501 | 0.807503 | − | 0.589864i | \(-0.200819\pi\) | ||||
0.807503 | + | 0.589864i | \(0.200819\pi\) | |||||||
\(8\) | 1.99029 | 0.703673 | ||||||||
\(9\) | −1.67413 | −0.558045 | ||||||||
\(10\) | −1.45045 | −0.458672 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.936615 | −0.270378 | ||||||||
\(13\) | −3.63737 | −1.00883 | −0.504413 | − | 0.863463i | \(-0.668291\pi\) | ||||
−0.504413 | + | 0.863463i | \(0.668291\pi\) | |||||||
\(14\) | −7.16704 | −1.91547 | ||||||||
\(15\) | −0.995715 | −0.257092 | ||||||||
\(16\) | −4.96519 | −1.24130 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.80806 | 0.661867 | ||||||||
\(19\) | −5.18808 | −1.19023 | −0.595114 | − | 0.803641i | \(-0.702893\pi\) | ||||
−0.595114 | + | 0.803641i | \(0.702893\pi\) | |||||||
\(20\) | 0.703391 | 0.157283 | ||||||||
\(21\) | −4.92009 | −1.07365 | ||||||||
\(22\) | 1.67732 | 0.357607 | ||||||||
\(23\) | 6.08938 | 1.26972 | 0.634862 | − | 0.772625i | \(-0.281057\pi\) | ||||
0.634862 | + | 0.772625i | \(0.281057\pi\) | |||||||
\(24\) | −2.29174 | −0.467800 | ||||||||
\(25\) | −4.25223 | −0.850445 | ||||||||
\(26\) | 6.10105 | 1.19651 | ||||||||
\(27\) | 5.38209 | 1.03578 | ||||||||
\(28\) | 3.47564 | 0.656834 | ||||||||
\(29\) | 6.16986 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(30\) | 1.67014 | 0.304924 | ||||||||
\(31\) | −8.85311 | −1.59007 | −0.795033 | − | 0.606566i | \(-0.792547\pi\) | ||||
−0.795033 | + | 0.606566i | \(0.792547\pi\) | |||||||
\(32\) | 4.34764 | 0.768562 | ||||||||
\(33\) | 1.15146 | 0.200444 | ||||||||
\(34\) | −1.67732 | −0.287659 | ||||||||
\(35\) | 3.69495 | 0.624560 | ||||||||
\(36\) | −1.36176 | −0.226961 | ||||||||
\(37\) | 3.85625 | 0.633963 | 0.316981 | − | 0.948432i | \(-0.397331\pi\) | ||||
0.316981 | + | 0.948432i | \(0.397331\pi\) | |||||||
\(38\) | 8.70209 | 1.41167 | ||||||||
\(39\) | 4.18830 | 0.670665 | ||||||||
\(40\) | 1.72108 | 0.272127 | ||||||||
\(41\) | 5.22332 | 0.815746 | 0.407873 | − | 0.913039i | \(-0.366271\pi\) | ||||
0.407873 | + | 0.913039i | \(0.366271\pi\) | |||||||
\(42\) | 8.25258 | 1.27340 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −0.813414 | −0.122627 | ||||||||
\(45\) | −1.44769 | −0.215809 | ||||||||
\(46\) | −10.2139 | −1.50595 | ||||||||
\(47\) | 2.34464 | 0.342001 | 0.171000 | − | 0.985271i | \(-0.445300\pi\) | ||||
0.171000 | + | 0.985271i | \(0.445300\pi\) | |||||||
\(48\) | 5.71723 | 0.825210 | ||||||||
\(49\) | 11.2577 | 1.60824 | ||||||||
\(50\) | 7.13236 | 1.00867 | ||||||||
\(51\) | −1.15146 | −0.161237 | ||||||||
\(52\) | −2.95869 | −0.410296 | ||||||||
\(53\) | −11.6657 | −1.60241 | −0.801205 | − | 0.598391i | \(-0.795807\pi\) | ||||
−0.801205 | + | 0.598391i | \(0.795807\pi\) | |||||||
\(54\) | −9.02751 | −1.22849 | ||||||||
\(55\) | −0.864739 | −0.116601 | ||||||||
\(56\) | 8.50431 | 1.13644 | ||||||||
\(57\) | 5.97389 | 0.791260 | ||||||||
\(58\) | −10.3488 | −1.35887 | ||||||||
\(59\) | −5.41617 | −0.705125 | −0.352562 | − | 0.935788i | \(-0.614690\pi\) | ||||
−0.352562 | + | 0.935788i | \(0.614690\pi\) | |||||||
\(60\) | −0.809928 | −0.104561 | ||||||||
\(61\) | 8.78057 | 1.12424 | 0.562118 | − | 0.827057i | \(-0.309987\pi\) | ||||
0.562118 | + | 0.827057i | \(0.309987\pi\) | |||||||
\(62\) | 14.8495 | 1.88589 | ||||||||
\(63\) | −7.15341 | −0.901245 | ||||||||
\(64\) | 2.63797 | 0.329746 | ||||||||
\(65\) | −3.14538 | −0.390136 | ||||||||
\(66\) | −1.93138 | −0.237736 | ||||||||
\(67\) | 4.24084 | 0.518101 | 0.259050 | − | 0.965864i | \(-0.416590\pi\) | ||||
0.259050 | + | 0.965864i | \(0.416590\pi\) | |||||||
\(68\) | 0.813414 | 0.0986409 | ||||||||
\(69\) | −7.01170 | −0.844109 | ||||||||
\(70\) | −6.19762 | −0.740757 | ||||||||
\(71\) | 9.07897 | 1.07747 | 0.538737 | − | 0.842474i | \(-0.318901\pi\) | ||||
0.538737 | + | 0.842474i | \(0.318901\pi\) | |||||||
\(72\) | −3.33201 | −0.392681 | ||||||||
\(73\) | −9.81684 | −1.14897 | −0.574487 | − | 0.818514i | \(-0.694798\pi\) | ||||
−0.574487 | + | 0.818514i | \(0.694798\pi\) | |||||||
\(74\) | −6.46817 | −0.751910 | ||||||||
\(75\) | 4.89628 | 0.565374 | ||||||||
\(76\) | −4.22006 | −0.484074 | ||||||||
\(77\) | −4.27290 | −0.486942 | ||||||||
\(78\) | −7.02513 | −0.795440 | ||||||||
\(79\) | −12.8691 | −1.44789 | −0.723946 | − | 0.689857i | \(-0.757673\pi\) | ||||
−0.723946 | + | 0.689857i | \(0.757673\pi\) | |||||||
\(80\) | −4.29359 | −0.480038 | ||||||||
\(81\) | −1.17487 | −0.130542 | ||||||||
\(82\) | −8.76120 | −0.967513 | ||||||||
\(83\) | 11.8943 | 1.30557 | 0.652784 | − | 0.757544i | \(-0.273601\pi\) | ||||
0.652784 | + | 0.757544i | \(0.273601\pi\) | |||||||
\(84\) | −4.00207 | −0.436661 | ||||||||
\(85\) | 0.864739 | 0.0937941 | ||||||||
\(86\) | −1.67732 | −0.180870 | ||||||||
\(87\) | −7.10436 | −0.761667 | ||||||||
\(88\) | −1.99029 | −0.212166 | ||||||||
\(89\) | 0.950347 | 0.100737 | 0.0503683 | − | 0.998731i | \(-0.483960\pi\) | ||||
0.0503683 | + | 0.998731i | \(0.483960\pi\) | |||||||
\(90\) | 2.42824 | 0.255959 | ||||||||
\(91\) | −15.5421 | −1.62926 | ||||||||
\(92\) | 4.95319 | 0.516405 | ||||||||
\(93\) | 10.1940 | 1.05707 | ||||||||
\(94\) | −3.93272 | −0.405629 | ||||||||
\(95\) | −4.48634 | −0.460289 | ||||||||
\(96\) | −5.00615 | −0.510938 | ||||||||
\(97\) | 4.39615 | 0.446362 | 0.223181 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223181 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(98\) | −18.8828 | −1.90745 | ||||||||
\(99\) | 1.67413 | 0.168257 | ||||||||
\(100\) | −3.45882 | −0.345882 | ||||||||
\(101\) | 7.01478 | 0.697997 | 0.348998 | − | 0.937123i | \(-0.386522\pi\) | ||||
0.348998 | + | 0.937123i | \(0.386522\pi\) | |||||||
\(102\) | 1.93138 | 0.191235 | ||||||||
\(103\) | −15.2667 | −1.50427 | −0.752137 | − | 0.659007i | \(-0.770977\pi\) | ||||
−0.752137 | + | 0.659007i | \(0.770977\pi\) | |||||||
\(104\) | −7.23943 | −0.709884 | ||||||||
\(105\) | −4.25459 | −0.415206 | ||||||||
\(106\) | 19.5672 | 1.90053 | ||||||||
\(107\) | −11.1033 | −1.07340 | −0.536700 | − | 0.843773i | \(-0.680329\pi\) | ||||
−0.536700 | + | 0.843773i | \(0.680329\pi\) | |||||||
\(108\) | 4.37787 | 0.421260 | ||||||||
\(109\) | 15.3496 | 1.47023 | 0.735113 | − | 0.677944i | \(-0.237129\pi\) | ||||
0.735113 | + | 0.677944i | \(0.237129\pi\) | |||||||
\(110\) | 1.45045 | 0.138295 | ||||||||
\(111\) | −4.44032 | −0.421457 | ||||||||
\(112\) | −21.2158 | −2.00470 | ||||||||
\(113\) | −6.36107 | −0.598399 | −0.299199 | − | 0.954191i | \(-0.596720\pi\) | ||||
−0.299199 | + | 0.954191i | \(0.596720\pi\) | |||||||
\(114\) | −10.0201 | −0.938472 | ||||||||
\(115\) | 5.26573 | 0.491032 | ||||||||
\(116\) | 5.01865 | 0.465970 | ||||||||
\(117\) | 6.08945 | 0.562970 | ||||||||
\(118\) | 9.08466 | 0.836311 | ||||||||
\(119\) | 4.27290 | 0.391696 | ||||||||
\(120\) | −1.98176 | −0.180909 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.7278 | −1.33340 | ||||||||
\(123\) | −6.01446 | −0.542306 | ||||||||
\(124\) | −7.20124 | −0.646691 | ||||||||
\(125\) | −8.00076 | −0.715610 | ||||||||
\(126\) | 11.9986 | 1.06892 | ||||||||
\(127\) | −17.3234 | −1.53720 | −0.768602 | − | 0.639728i | \(-0.779047\pi\) | ||||
−0.768602 | + | 0.639728i | \(0.779047\pi\) | |||||||
\(128\) | −13.1200 | −1.15966 | ||||||||
\(129\) | −1.15146 | −0.101381 | ||||||||
\(130\) | 5.27582 | 0.462720 | ||||||||
\(131\) | −14.0079 | −1.22388 | −0.611939 | − | 0.790905i | \(-0.709610\pi\) | ||||
−0.611939 | + | 0.790905i | \(0.709610\pi\) | |||||||
\(132\) | 0.936615 | 0.0815219 | ||||||||
\(133\) | −22.1682 | −1.92222 | ||||||||
\(134\) | −7.11325 | −0.614492 | ||||||||
\(135\) | 4.65410 | 0.400562 | ||||||||
\(136\) | 1.99029 | 0.170666 | ||||||||
\(137\) | −5.28457 | −0.451491 | −0.225745 | − | 0.974186i | \(-0.572482\pi\) | ||||
−0.225745 | + | 0.974186i | \(0.572482\pi\) | |||||||
\(138\) | 11.7609 | 1.00115 | ||||||||
\(139\) | 6.72632 | 0.570519 | 0.285259 | − | 0.958450i | \(-0.407920\pi\) | ||||
0.285259 | + | 0.958450i | \(0.407920\pi\) | |||||||
\(140\) | 3.00552 | 0.254013 | ||||||||
\(141\) | −2.69976 | −0.227361 | ||||||||
\(142\) | −15.2284 | −1.27794 | ||||||||
\(143\) | 3.63737 | 0.304172 | ||||||||
\(144\) | 8.31238 | 0.692699 | ||||||||
\(145\) | 5.33532 | 0.443074 | ||||||||
\(146\) | 16.4660 | 1.36274 | ||||||||
\(147\) | −12.9628 | −1.06915 | ||||||||
\(148\) | 3.13672 | 0.257837 | ||||||||
\(149\) | −13.4692 | −1.10344 | −0.551720 | − | 0.834030i | \(-0.686028\pi\) | ||||
−0.551720 | + | 0.834030i | \(0.686028\pi\) | |||||||
\(150\) | −8.21264 | −0.670560 | ||||||||
\(151\) | 10.8352 | 0.881754 | 0.440877 | − | 0.897567i | \(-0.354667\pi\) | ||||
0.440877 | + | 0.897567i | \(0.354667\pi\) | |||||||
\(152\) | −10.3258 | −0.837532 | ||||||||
\(153\) | −1.67413 | −0.135346 | ||||||||
\(154\) | 7.16704 | 0.577536 | ||||||||
\(155\) | −7.65563 | −0.614915 | ||||||||
\(156\) | 3.40682 | 0.272764 | ||||||||
\(157\) | −18.8229 | −1.50223 | −0.751115 | − | 0.660172i | \(-0.770484\pi\) | ||||
−0.751115 | + | 0.660172i | \(0.770484\pi\) | |||||||
\(158\) | 21.5857 | 1.71727 | ||||||||
\(159\) | 13.4326 | 1.06528 | ||||||||
\(160\) | 3.75958 | 0.297221 | ||||||||
\(161\) | 26.0193 | 2.05061 | ||||||||
\(162\) | 1.97064 | 0.154828 | ||||||||
\(163\) | 11.1814 | 0.875796 | 0.437898 | − | 0.899025i | \(-0.355723\pi\) | ||||
0.437898 | + | 0.899025i | \(0.355723\pi\) | |||||||
\(164\) | 4.24872 | 0.331769 | ||||||||
\(165\) | 0.995715 | 0.0775163 | ||||||||
\(166\) | −19.9506 | −1.54846 | ||||||||
\(167\) | 17.5563 | 1.35855 | 0.679274 | − | 0.733884i | \(-0.262295\pi\) | ||||
0.679274 | + | 0.733884i | \(0.262295\pi\) | |||||||
\(168\) | −9.79240 | −0.755500 | ||||||||
\(169\) | 0.230488 | 0.0177298 | ||||||||
\(170\) | −1.45045 | −0.111244 | ||||||||
\(171\) | 8.68555 | 0.664200 | ||||||||
\(172\) | 0.813414 | 0.0620222 | ||||||||
\(173\) | −9.34971 | −0.710845 | −0.355423 | − | 0.934706i | \(-0.615663\pi\) | ||||
−0.355423 | + | 0.934706i | \(0.615663\pi\) | |||||||
\(174\) | 11.9163 | 0.903373 | ||||||||
\(175\) | −18.1693 | −1.37347 | ||||||||
\(176\) | 4.96519 | 0.374265 | ||||||||
\(177\) | 6.23651 | 0.468765 | ||||||||
\(178\) | −1.59404 | −0.119478 | ||||||||
\(179\) | −13.3130 | −0.995059 | −0.497529 | − | 0.867447i | \(-0.665759\pi\) | ||||
−0.497529 | + | 0.867447i | \(0.665759\pi\) | |||||||
\(180\) | −1.17757 | −0.0877709 | ||||||||
\(181\) | 1.56808 | 0.116554 | 0.0582772 | − | 0.998300i | \(-0.481439\pi\) | ||||
0.0582772 | + | 0.998300i | \(0.481439\pi\) | |||||||
\(182\) | 26.0692 | 1.93238 | ||||||||
\(183\) | −10.1105 | −0.747389 | ||||||||
\(184\) | 12.1196 | 0.893471 | ||||||||
\(185\) | 3.33465 | 0.245168 | ||||||||
\(186\) | −17.0987 | −1.25374 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 1.90716 | 0.139094 | ||||||||
\(189\) | 22.9971 | 1.67280 | ||||||||
\(190\) | 7.52504 | 0.545924 | ||||||||
\(191\) | 14.1536 | 1.02412 | 0.512059 | − | 0.858950i | \(-0.328883\pi\) | ||||
0.512059 | + | 0.858950i | \(0.328883\pi\) | |||||||
\(192\) | −3.03752 | −0.219214 | ||||||||
\(193\) | 0.170964 | 0.0123062 | 0.00615311 | − | 0.999981i | \(-0.498041\pi\) | ||||
0.00615311 | + | 0.999981i | \(0.498041\pi\) | |||||||
\(194\) | −7.37377 | −0.529406 | ||||||||
\(195\) | 3.62179 | 0.259362 | ||||||||
\(196\) | 9.15716 | 0.654083 | ||||||||
\(197\) | 9.57856 | 0.682444 | 0.341222 | − | 0.939983i | \(-0.389159\pi\) | ||||
0.341222 | + | 0.939983i | \(0.389159\pi\) | |||||||
\(198\) | −2.80806 | −0.199560 | ||||||||
\(199\) | −9.03919 | −0.640771 | −0.320386 | − | 0.947287i | \(-0.603813\pi\) | ||||
−0.320386 | + | 0.947287i | \(0.603813\pi\) | |||||||
\(200\) | −8.46316 | −0.598436 | ||||||||
\(201\) | −4.88316 | −0.344432 | ||||||||
\(202\) | −11.7661 | −0.827857 | ||||||||
\(203\) | 26.3632 | 1.85033 | ||||||||
\(204\) | −0.936615 | −0.0655762 | ||||||||
\(205\) | 4.51681 | 0.315468 | ||||||||
\(206\) | 25.6072 | 1.78414 | ||||||||
\(207\) | −10.1944 | −0.708563 | ||||||||
\(208\) | 18.0602 | 1.25225 | ||||||||
\(209\) | 5.18808 | 0.358867 | ||||||||
\(210\) | 7.13633 | 0.492453 | ||||||||
\(211\) | 24.8770 | 1.71260 | 0.856302 | − | 0.516475i | \(-0.172756\pi\) | ||||
0.856302 | + | 0.516475i | \(0.172756\pi\) | |||||||
\(212\) | −9.48905 | −0.651711 | ||||||||
\(213\) | −10.4541 | −0.716302 | ||||||||
\(214\) | 18.6239 | 1.27310 | ||||||||
\(215\) | 0.864739 | 0.0589747 | ||||||||
\(216\) | 10.7119 | 0.728854 | ||||||||
\(217\) | −37.8285 | −2.56797 | ||||||||
\(218\) | −25.7463 | −1.74376 | ||||||||
\(219\) | 11.3037 | 0.763835 | ||||||||
\(220\) | −0.703391 | −0.0474226 | ||||||||
\(221\) | −3.63737 | −0.244676 | ||||||||
\(222\) | 7.44786 | 0.499867 | ||||||||
\(223\) | −7.15198 | −0.478932 | −0.239466 | − | 0.970905i | \(-0.576972\pi\) | ||||
−0.239466 | + | 0.970905i | \(0.576972\pi\) | |||||||
\(224\) | 18.5771 | 1.24123 | ||||||||
\(225\) | 7.11880 | 0.474586 | ||||||||
\(226\) | 10.6696 | 0.709729 | ||||||||
\(227\) | −5.08228 | −0.337323 | −0.168661 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168661 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(228\) | 4.85924 | 0.321811 | ||||||||
\(229\) | −21.0669 | −1.39214 | −0.696071 | − | 0.717973i | \(-0.745070\pi\) | ||||
−0.696071 | + | 0.717973i | \(0.745070\pi\) | |||||||
\(230\) | −8.83233 | −0.582387 | ||||||||
\(231\) | 4.92009 | 0.323718 | ||||||||
\(232\) | 12.2798 | 0.806208 | ||||||||
\(233\) | −9.41555 | −0.616833 | −0.308417 | − | 0.951251i | \(-0.599799\pi\) | ||||
−0.308417 | + | 0.951251i | \(0.599799\pi\) | |||||||
\(234\) | −10.2140 | −0.667709 | ||||||||
\(235\) | 2.02750 | 0.132260 | ||||||||
\(236\) | −4.40558 | −0.286779 | ||||||||
\(237\) | 14.8183 | 0.962554 | ||||||||
\(238\) | −7.16704 | −0.464570 | ||||||||
\(239\) | −9.63432 | −0.623192 | −0.311596 | − | 0.950215i | \(-0.600864\pi\) | ||||
−0.311596 | + | 0.950215i | \(0.600864\pi\) | |||||||
\(240\) | 4.94391 | 0.319128 | ||||||||
\(241\) | 13.6007 | 0.876100 | 0.438050 | − | 0.898951i | \(-0.355669\pi\) | ||||
0.438050 | + | 0.898951i | \(0.355669\pi\) | |||||||
\(242\) | −1.67732 | −0.107822 | ||||||||
\(243\) | −14.7934 | −0.949000 | ||||||||
\(244\) | 7.14223 | 0.457234 | ||||||||
\(245\) | 9.73497 | 0.621944 | ||||||||
\(246\) | 10.0882 | 0.643200 | ||||||||
\(247\) | 18.8710 | 1.20073 | ||||||||
\(248\) | −17.6203 | −1.11889 | ||||||||
\(249\) | −13.6958 | −0.867937 | ||||||||
\(250\) | 13.4199 | 0.848747 | ||||||||
\(251\) | 16.9772 | 1.07159 | 0.535796 | − | 0.844348i | \(-0.320012\pi\) | ||||
0.535796 | + | 0.844348i | \(0.320012\pi\) | |||||||
\(252\) | −5.81868 | −0.366542 | ||||||||
\(253\) | −6.08938 | −0.382836 | ||||||||
\(254\) | 29.0569 | 1.82319 | ||||||||
\(255\) | −0.995715 | −0.0623541 | ||||||||
\(256\) | 16.7306 | 1.04566 | ||||||||
\(257\) | −20.9979 | −1.30981 | −0.654907 | − | 0.755710i | \(-0.727292\pi\) | ||||
−0.654907 | + | 0.755710i | \(0.727292\pi\) | |||||||
\(258\) | 1.93138 | 0.120242 | ||||||||
\(259\) | 16.4774 | 1.02385 | ||||||||
\(260\) | −2.55849 | −0.158671 | ||||||||
\(261\) | −10.3292 | −0.639359 | ||||||||
\(262\) | 23.4958 | 1.45158 | ||||||||
\(263\) | 1.58540 | 0.0977598 | 0.0488799 | − | 0.998805i | \(-0.484435\pi\) | ||||
0.0488799 | + | 0.998805i | \(0.484435\pi\) | |||||||
\(264\) | 2.29174 | 0.141047 | ||||||||
\(265\) | −10.0878 | −0.619689 | ||||||||
\(266\) | 37.1832 | 2.27985 | ||||||||
\(267\) | −1.09429 | −0.0669694 | ||||||||
\(268\) | 3.44955 | 0.210715 | ||||||||
\(269\) | −5.84899 | −0.356619 | −0.178310 | − | 0.983974i | \(-0.557063\pi\) | ||||
−0.178310 | + | 0.983974i | \(0.557063\pi\) | |||||||
\(270\) | −7.80644 | −0.475085 | ||||||||
\(271\) | 29.8039 | 1.81046 | 0.905229 | − | 0.424923i | \(-0.139699\pi\) | ||||
0.905229 | + | 0.424923i | \(0.139699\pi\) | |||||||
\(272\) | −4.96519 | −0.301059 | ||||||||
\(273\) | 17.8962 | 1.08313 | ||||||||
\(274\) | 8.86393 | 0.535489 | ||||||||
\(275\) | 4.25223 | 0.256419 | ||||||||
\(276\) | −5.70341 | −0.343305 | ||||||||
\(277\) | −16.4703 | −0.989604 | −0.494802 | − | 0.869006i | \(-0.664759\pi\) | ||||
−0.494802 | + | 0.869006i | \(0.664759\pi\) | |||||||
\(278\) | −11.2822 | −0.676662 | ||||||||
\(279\) | 14.8213 | 0.887328 | ||||||||
\(280\) | 7.35401 | 0.439486 | ||||||||
\(281\) | −11.8918 | −0.709403 | −0.354702 | − | 0.934980i | \(-0.615418\pi\) | ||||
−0.354702 | + | 0.934980i | \(0.615418\pi\) | |||||||
\(282\) | 4.52838 | 0.269661 | ||||||||
\(283\) | 19.3990 | 1.15315 | 0.576576 | − | 0.817044i | \(-0.304388\pi\) | ||||
0.576576 | + | 0.817044i | \(0.304388\pi\) | |||||||
\(284\) | 7.38495 | 0.438216 | ||||||||
\(285\) | 5.16585 | 0.305999 | ||||||||
\(286\) | −6.10105 | −0.360763 | ||||||||
\(287\) | 22.3187 | 1.31743 | ||||||||
\(288\) | −7.27854 | −0.428892 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −8.94905 | −0.525506 | ||||||||
\(291\) | −5.06201 | −0.296740 | ||||||||
\(292\) | −7.98515 | −0.467295 | ||||||||
\(293\) | 0.229983 | 0.0134357 | 0.00671787 | − | 0.999977i | \(-0.497862\pi\) | ||||
0.00671787 | + | 0.999977i | \(0.497862\pi\) | |||||||
\(294\) | 21.7428 | 1.26807 | ||||||||
\(295\) | −4.68357 | −0.272688 | ||||||||
\(296\) | 7.67505 | 0.446103 | ||||||||
\(297\) | −5.38209 | −0.312301 | ||||||||
\(298\) | 22.5922 | 1.30873 | ||||||||
\(299\) | −22.1494 | −1.28093 | ||||||||
\(300\) | 3.98270 | 0.229941 | ||||||||
\(301\) | 4.27290 | 0.246286 | ||||||||
\(302\) | −18.1741 | −1.04580 | ||||||||
\(303\) | −8.07726 | −0.464026 | ||||||||
\(304\) | 25.7598 | 1.47743 | ||||||||
\(305\) | 7.59290 | 0.434768 | ||||||||
\(306\) | 2.80806 | 0.160526 | ||||||||
\(307\) | 31.5765 | 1.80217 | 0.901083 | − | 0.433648i | \(-0.142774\pi\) | ||||
0.901083 | + | 0.433648i | \(0.142774\pi\) | |||||||
\(308\) | −3.47564 | −0.198043 | ||||||||
\(309\) | 17.5790 | 1.00004 | ||||||||
\(310\) | 12.8410 | 0.729318 | ||||||||
\(311\) | −14.9980 | −0.850459 | −0.425230 | − | 0.905086i | \(-0.639807\pi\) | ||||
−0.425230 | + | 0.905086i | \(0.639807\pi\) | |||||||
\(312\) | 8.33593 | 0.471929 | ||||||||
\(313\) | −8.09259 | −0.457420 | −0.228710 | − | 0.973495i | \(-0.573451\pi\) | ||||
−0.228710 | + | 0.973495i | \(0.573451\pi\) | |||||||
\(314\) | 31.5721 | 1.78171 | ||||||||
\(315\) | −6.18583 | −0.348532 | ||||||||
\(316\) | −10.4679 | −0.588867 | ||||||||
\(317\) | −18.3538 | −1.03085 | −0.515425 | − | 0.856935i | \(-0.672366\pi\) | ||||
−0.515425 | + | 0.856935i | \(0.672366\pi\) | |||||||
\(318\) | −22.5309 | −1.26347 | ||||||||
\(319\) | −6.16986 | −0.345446 | ||||||||
\(320\) | 2.28115 | 0.127520 | ||||||||
\(321\) | 12.7851 | 0.713593 | ||||||||
\(322\) | −43.6428 | −2.43212 | ||||||||
\(323\) | −5.18808 | −0.288673 | ||||||||
\(324\) | −0.955659 | −0.0530922 | ||||||||
\(325\) | 15.4669 | 0.857951 | ||||||||
\(326\) | −18.7548 | −1.03873 | ||||||||
\(327\) | −17.6745 | −0.977402 | ||||||||
\(328\) | 10.3959 | 0.574019 | ||||||||
\(329\) | 10.0184 | 0.552333 | ||||||||
\(330\) | −1.67014 | −0.0919379 | ||||||||
\(331\) | 20.9775 | 1.15303 | 0.576514 | − | 0.817088i | \(-0.304413\pi\) | ||||
0.576514 | + | 0.817088i | \(0.304413\pi\) | |||||||
\(332\) | 9.67497 | 0.530983 | ||||||||
\(333\) | −6.45587 | −0.353780 | ||||||||
\(334\) | −29.4476 | −1.61130 | ||||||||
\(335\) | 3.66722 | 0.200361 | ||||||||
\(336\) | 24.4291 | 1.33272 | ||||||||
\(337\) | 6.12489 | 0.333644 | 0.166822 | − | 0.985987i | \(-0.446649\pi\) | ||||
0.166822 | + | 0.985987i | \(0.446649\pi\) | |||||||
\(338\) | −0.386603 | −0.0210284 | ||||||||
\(339\) | 7.32453 | 0.397814 | ||||||||
\(340\) | 0.703391 | 0.0381467 | ||||||||
\(341\) | 8.85311 | 0.479423 | ||||||||
\(342\) | −14.5685 | −0.787773 | ||||||||
\(343\) | 18.1927 | 0.982314 | ||||||||
\(344\) | 1.99029 | 0.107309 | ||||||||
\(345\) | −6.06329 | −0.326437 | ||||||||
\(346\) | 15.6825 | 0.843096 | ||||||||
\(347\) | 2.02113 | 0.108500 | 0.0542499 | − | 0.998527i | \(-0.482723\pi\) | ||||
0.0542499 | + | 0.998527i | \(0.482723\pi\) | |||||||
\(348\) | −5.77878 | −0.309775 | ||||||||
\(349\) | 21.1727 | 1.13335 | 0.566675 | − | 0.823941i | \(-0.308229\pi\) | ||||
0.566675 | + | 0.823941i | \(0.308229\pi\) | |||||||
\(350\) | 30.4759 | 1.62900 | ||||||||
\(351\) | −19.5767 | −1.04493 | ||||||||
\(352\) | −4.34764 | −0.231730 | ||||||||
\(353\) | 31.0972 | 1.65514 | 0.827568 | − | 0.561365i | \(-0.189724\pi\) | ||||
0.827568 | + | 0.561365i | \(0.189724\pi\) | |||||||
\(354\) | −10.4606 | −0.555977 | ||||||||
\(355\) | 7.85094 | 0.416684 | ||||||||
\(356\) | 0.773025 | 0.0409703 | ||||||||
\(357\) | −4.92009 | −0.260399 | ||||||||
\(358\) | 22.3302 | 1.18019 | ||||||||
\(359\) | −11.8162 | −0.623635 | −0.311818 | − | 0.950142i | \(-0.600938\pi\) | ||||
−0.311818 | + | 0.950142i | \(0.600938\pi\) | |||||||
\(360\) | −2.88132 | −0.151859 | ||||||||
\(361\) | 7.91622 | 0.416643 | ||||||||
\(362\) | −2.63018 | −0.138239 | ||||||||
\(363\) | −1.15146 | −0.0604361 | ||||||||
\(364\) | −12.6422 | −0.662631 | ||||||||
\(365\) | −8.48900 | −0.444335 | ||||||||
\(366\) | 16.9586 | 0.886439 | ||||||||
\(367\) | −3.77522 | −0.197065 | −0.0985325 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985325 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(368\) | −30.2349 | −1.57610 | ||||||||
\(369\) | −8.74454 | −0.455223 | ||||||||
\(370\) | −5.59328 | −0.290781 | ||||||||
\(371\) | −49.8465 | −2.58790 | ||||||||
\(372\) | 8.29196 | 0.429918 | ||||||||
\(373\) | 3.50210 | 0.181332 | 0.0906658 | − | 0.995881i | \(-0.471100\pi\) | ||||
0.0906658 | + | 0.995881i | \(0.471100\pi\) | |||||||
\(374\) | 1.67732 | 0.0867323 | ||||||||
\(375\) | 9.21258 | 0.475736 | ||||||||
\(376\) | 4.66651 | 0.240657 | ||||||||
\(377\) | −22.4421 | −1.15583 | ||||||||
\(378\) | −38.5736 | −1.98401 | ||||||||
\(379\) | −3.67954 | −0.189005 | −0.0945026 | − | 0.995525i | \(-0.530126\pi\) | ||||
−0.0945026 | + | 0.995525i | \(0.530126\pi\) | |||||||
\(380\) | −3.64925 | −0.187203 | ||||||||
\(381\) | 19.9472 | 1.02193 | ||||||||
\(382\) | −23.7401 | −1.21465 | ||||||||
\(383\) | −16.7645 | −0.856626 | −0.428313 | − | 0.903631i | \(-0.640892\pi\) | ||||
−0.428313 | + | 0.903631i | \(0.640892\pi\) | |||||||
\(384\) | 15.1072 | 0.770936 | ||||||||
\(385\) | −3.69495 | −0.188312 | ||||||||
\(386\) | −0.286761 | −0.0145958 | ||||||||
\(387\) | −1.67413 | −0.0851010 | ||||||||
\(388\) | 3.57589 | 0.181538 | ||||||||
\(389\) | −30.4907 | −1.54594 | −0.772970 | − | 0.634442i | \(-0.781230\pi\) | ||||
−0.772970 | + | 0.634442i | \(0.781230\pi\) | |||||||
\(390\) | −6.07491 | −0.307615 | ||||||||
\(391\) | 6.08938 | 0.307953 | ||||||||
\(392\) | 22.4061 | 1.13168 | ||||||||
\(393\) | 16.1296 | 0.813631 | ||||||||
\(394\) | −16.0663 | −0.809411 | ||||||||
\(395\) | −11.1285 | −0.559933 | ||||||||
\(396\) | 1.36176 | 0.0684312 | ||||||||
\(397\) | 8.46300 | 0.424746 | 0.212373 | − | 0.977189i | \(-0.431881\pi\) | ||||
0.212373 | + | 0.977189i | \(0.431881\pi\) | |||||||
\(398\) | 15.1616 | 0.759985 | ||||||||
\(399\) | 25.5258 | 1.27789 | ||||||||
\(400\) | 21.1131 | 1.05565 | ||||||||
\(401\) | −26.6014 | −1.32841 | −0.664205 | − | 0.747550i | \(-0.731230\pi\) | ||||
−0.664205 | + | 0.747550i | \(0.731230\pi\) | |||||||
\(402\) | 8.19065 | 0.408512 | ||||||||
\(403\) | 32.2021 | 1.60410 | ||||||||
\(404\) | 5.70592 | 0.283880 | ||||||||
\(405\) | −1.01596 | −0.0504835 | ||||||||
\(406\) | −44.2196 | −2.19458 | ||||||||
\(407\) | −3.85625 | −0.191147 | ||||||||
\(408\) | −2.29174 | −0.113458 | ||||||||
\(409\) | −3.42813 | −0.169510 | −0.0847551 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847551 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(410\) | −7.57615 | −0.374160 | ||||||||
\(411\) | 6.08498 | 0.300150 | ||||||||
\(412\) | −12.4181 | −0.611798 | ||||||||
\(413\) | −23.1428 | −1.13878 | ||||||||
\(414\) | 17.0994 | 0.840388 | ||||||||
\(415\) | 10.2855 | 0.504893 | ||||||||
\(416\) | −15.8140 | −0.775345 | ||||||||
\(417\) | −7.74510 | −0.379279 | ||||||||
\(418\) | −8.70209 | −0.425633 | ||||||||
\(419\) | −26.7252 | −1.30561 | −0.652806 | − | 0.757525i | \(-0.726408\pi\) | ||||
−0.652806 | + | 0.757525i | \(0.726408\pi\) | |||||||
\(420\) | −3.46074 | −0.168867 | ||||||||
\(421\) | 16.6101 | 0.809525 | 0.404762 | − | 0.914422i | \(-0.367354\pi\) | ||||
0.404762 | + | 0.914422i | \(0.367354\pi\) | |||||||
\(422\) | −41.7268 | −2.03123 | ||||||||
\(423\) | −3.92524 | −0.190852 | ||||||||
\(424\) | −23.2181 | −1.12757 | ||||||||
\(425\) | −4.25223 | −0.206263 | ||||||||
\(426\) | 17.5349 | 0.849568 | ||||||||
\(427\) | 37.5185 | 1.81565 | ||||||||
\(428\) | −9.03160 | −0.436559 | ||||||||
\(429\) | −4.18830 | −0.202213 | ||||||||
\(430\) | −1.45045 | −0.0699468 | ||||||||
\(431\) | 1.36297 | 0.0656517 | 0.0328259 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328259 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(432\) | −26.7231 | −1.28571 | ||||||||
\(433\) | −31.6453 | −1.52078 | −0.760389 | − | 0.649468i | \(-0.774992\pi\) | ||||
−0.760389 | + | 0.649468i | \(0.774992\pi\) | |||||||
\(434\) | 63.4506 | 3.04573 | ||||||||
\(435\) | −6.14342 | −0.294554 | ||||||||
\(436\) | 12.4856 | 0.597951 | ||||||||
\(437\) | −31.5922 | −1.51126 | ||||||||
\(438\) | −18.9600 | −0.905944 | ||||||||
\(439\) | −6.83218 | −0.326082 | −0.163041 | − | 0.986619i | \(-0.552130\pi\) | ||||
−0.163041 | + | 0.986619i | \(0.552130\pi\) | |||||||
\(440\) | −1.72108 | −0.0820493 | ||||||||
\(441\) | −18.8469 | −0.897471 | ||||||||
\(442\) | 6.10105 | 0.290197 | ||||||||
\(443\) | 20.0838 | 0.954208 | 0.477104 | − | 0.878847i | \(-0.341686\pi\) | ||||
0.477104 | + | 0.878847i | \(0.341686\pi\) | |||||||
\(444\) | −3.61182 | −0.171409 | ||||||||
\(445\) | 0.821803 | 0.0389572 | ||||||||
\(446\) | 11.9962 | 0.568035 | ||||||||
\(447\) | 15.5093 | 0.733564 | ||||||||
\(448\) | 11.2718 | 0.532542 | ||||||||
\(449\) | 0.204759 | 0.00966317 | 0.00483158 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483158 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(450\) | −11.9405 | −0.562882 | ||||||||
\(451\) | −5.22332 | −0.245957 | ||||||||
\(452\) | −5.17418 | −0.243373 | ||||||||
\(453\) | −12.4763 | −0.586188 | ||||||||
\(454\) | 8.52462 | 0.400080 | ||||||||
\(455\) | −13.4399 | −0.630072 | ||||||||
\(456\) | 11.8898 | 0.556789 | ||||||||
\(457\) | −0.622232 | −0.0291068 | −0.0145534 | − | 0.999894i | \(-0.504633\pi\) | ||||
−0.0145534 | + | 0.999894i | \(0.504633\pi\) | |||||||
\(458\) | 35.3361 | 1.65115 | ||||||||
\(459\) | 5.38209 | 0.251214 | ||||||||
\(460\) | 4.28321 | 0.199706 | ||||||||
\(461\) | −24.2058 | −1.12738 | −0.563689 | − | 0.825987i | \(-0.690618\pi\) | ||||
−0.563689 | + | 0.825987i | \(0.690618\pi\) | |||||||
\(462\) | −8.25258 | −0.383945 | ||||||||
\(463\) | 2.35716 | 0.109547 | 0.0547733 | − | 0.998499i | \(-0.482556\pi\) | ||||
0.0547733 | + | 0.998499i | \(0.482556\pi\) | |||||||
\(464\) | −30.6345 | −1.42217 | ||||||||
\(465\) | 8.81518 | 0.408794 | ||||||||
\(466\) | 15.7929 | 0.731593 | ||||||||
\(467\) | 7.43362 | 0.343987 | 0.171993 | − | 0.985098i | \(-0.444979\pi\) | ||||
0.171993 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(468\) | 4.95324 | 0.228964 | ||||||||
\(469\) | 18.1207 | 0.836735 | ||||||||
\(470\) | −3.40078 | −0.156866 | ||||||||
\(471\) | 21.6738 | 0.998678 | ||||||||
\(472\) | −10.7797 | −0.496178 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −24.8551 | −1.14163 | ||||||||
\(475\) | 22.0609 | 1.01222 | ||||||||
\(476\) | 3.47564 | 0.159306 | ||||||||
\(477\) | 19.5300 | 0.894216 | ||||||||
\(478\) | 16.1599 | 0.739135 | ||||||||
\(479\) | −34.7011 | −1.58553 | −0.792767 | − | 0.609525i | \(-0.791360\pi\) | ||||
−0.792767 | + | 0.609525i | \(0.791360\pi\) | |||||||
\(480\) | −4.32901 | −0.197591 | ||||||||
\(481\) | −14.0266 | −0.639558 | ||||||||
\(482\) | −22.8128 | −1.03910 | ||||||||
\(483\) | −29.9603 | −1.36324 | ||||||||
\(484\) | 0.813414 | 0.0369733 | ||||||||
\(485\) | 3.80153 | 0.172618 | ||||||||
\(486\) | 24.8134 | 1.12556 | ||||||||
\(487\) | 14.0865 | 0.638320 | 0.319160 | − | 0.947701i | \(-0.396599\pi\) | ||||
0.319160 | + | 0.947701i | \(0.396599\pi\) | |||||||
\(488\) | 17.4759 | 0.791095 | ||||||||
\(489\) | −12.8750 | −0.582227 | ||||||||
\(490\) | −16.3287 | −0.737655 | ||||||||
\(491\) | −29.6256 | −1.33699 | −0.668493 | − | 0.743719i | \(-0.733060\pi\) | ||||
−0.668493 | + | 0.743719i | \(0.733060\pi\) | |||||||
\(492\) | −4.89224 | −0.220559 | ||||||||
\(493\) | 6.16986 | 0.277876 | ||||||||
\(494\) | −31.6528 | −1.42413 | ||||||||
\(495\) | 1.44769 | 0.0650688 | ||||||||
\(496\) | 43.9574 | 1.97374 | ||||||||
\(497\) | 38.7935 | 1.74013 | ||||||||
\(498\) | 22.9723 | 1.02941 | ||||||||
\(499\) | −31.1634 | −1.39506 | −0.697532 | − | 0.716554i | \(-0.745718\pi\) | ||||
−0.697532 | + | 0.716554i | \(0.745718\pi\) | |||||||
\(500\) | −6.50793 | −0.291043 | ||||||||
\(501\) | −20.2154 | −0.903160 | ||||||||
\(502\) | −28.4762 | −1.27096 | ||||||||
\(503\) | 8.86786 | 0.395398 | 0.197699 | − | 0.980263i | \(-0.436653\pi\) | ||||
0.197699 | + | 0.980263i | \(0.436653\pi\) | |||||||
\(504\) | −14.2374 | −0.634182 | ||||||||
\(505\) | 6.06596 | 0.269932 | ||||||||
\(506\) | 10.2139 | 0.454062 | ||||||||
\(507\) | −0.265398 | −0.0117867 | ||||||||
\(508\) | −14.0911 | −0.625191 | ||||||||
\(509\) | −24.8705 | −1.10236 | −0.551182 | − | 0.834385i | \(-0.685823\pi\) | ||||
−0.551182 | + | 0.834385i | \(0.685823\pi\) | |||||||
\(510\) | 1.67014 | 0.0739549 | ||||||||
\(511\) | −41.9464 | −1.85560 | ||||||||
\(512\) | −1.82254 | −0.0805458 | ||||||||
\(513\) | −27.9227 | −1.23282 | ||||||||
\(514\) | 35.2203 | 1.55350 | ||||||||
\(515\) | −13.2017 | −0.581737 | ||||||||
\(516\) | −0.936615 | −0.0412322 | ||||||||
\(517\) | −2.34464 | −0.103117 | ||||||||
\(518\) | −27.6379 | −1.21434 | ||||||||
\(519\) | 10.7658 | 0.472568 | ||||||||
\(520\) | −6.26022 | −0.274529 | ||||||||
\(521\) | −2.89692 | −0.126916 | −0.0634582 | − | 0.997984i | \(-0.520213\pi\) | ||||
−0.0634582 | + | 0.997984i | \(0.520213\pi\) | |||||||
\(522\) | 17.3254 | 0.758310 | ||||||||
\(523\) | −31.1372 | −1.36154 | −0.680768 | − | 0.732499i | \(-0.738354\pi\) | ||||
−0.680768 | + | 0.732499i | \(0.738354\pi\) | |||||||
\(524\) | −11.3942 | −0.497760 | ||||||||
\(525\) | 20.9213 | 0.913081 | ||||||||
\(526\) | −2.65922 | −0.115948 | ||||||||
\(527\) | −8.85311 | −0.385648 | ||||||||
\(528\) | −5.71723 | −0.248810 | ||||||||
\(529\) | 14.0806 | 0.612200 | ||||||||
\(530\) | 16.9205 | 0.734980 | ||||||||
\(531\) | 9.06739 | 0.393491 | ||||||||
\(532\) | −18.0319 | −0.781782 | ||||||||
\(533\) | −18.9992 | −0.822946 | ||||||||
\(534\) | 1.83548 | 0.0794289 | ||||||||
\(535\) | −9.60148 | −0.415108 | ||||||||
\(536\) | 8.44049 | 0.364574 | ||||||||
\(537\) | 15.3294 | 0.661512 | ||||||||
\(538\) | 9.81065 | 0.422967 | ||||||||
\(539\) | −11.2577 | −0.484903 | ||||||||
\(540\) | 3.78571 | 0.162911 | ||||||||
\(541\) | −45.2449 | −1.94523 | −0.972616 | − | 0.232417i | \(-0.925336\pi\) | ||||
−0.972616 | + | 0.232417i | \(0.925336\pi\) | |||||||
\(542\) | −49.9908 | −2.14729 | ||||||||
\(543\) | −1.80558 | −0.0774851 | ||||||||
\(544\) | 4.34764 | 0.186404 | ||||||||
\(545\) | 13.2734 | 0.568571 | ||||||||
\(546\) | −30.0177 | −1.28464 | ||||||||
\(547\) | −27.0170 | −1.15516 | −0.577582 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577582 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(548\) | −4.29854 | −0.183624 | ||||||||
\(549\) | −14.6998 | −0.627374 | ||||||||
\(550\) | −7.13236 | −0.304125 | ||||||||
\(551\) | −32.0097 | −1.36366 | ||||||||
\(552\) | −13.9553 | −0.593977 | ||||||||
\(553\) | −54.9886 | −2.33835 | ||||||||
\(554\) | 27.6260 | 1.17372 | ||||||||
\(555\) | −3.83972 | −0.162987 | ||||||||
\(556\) | 5.47128 | 0.232034 | ||||||||
\(557\) | −0.490211 | −0.0207709 | −0.0103855 | − | 0.999946i | \(-0.503306\pi\) | ||||
−0.0103855 | + | 0.999946i | \(0.503306\pi\) | |||||||
\(558\) | −24.8601 | −1.05241 | ||||||||
\(559\) | −3.63737 | −0.153845 | ||||||||
\(560\) | −18.3461 | −0.775264 | ||||||||
\(561\) | 1.15146 | 0.0486148 | ||||||||
\(562\) | 19.9463 | 0.841385 | ||||||||
\(563\) | −16.8842 | −0.711586 | −0.355793 | − | 0.934565i | \(-0.615789\pi\) | ||||
−0.355793 | + | 0.934565i | \(0.615789\pi\) | |||||||
\(564\) | −2.19602 | −0.0924693 | ||||||||
\(565\) | −5.50066 | −0.231415 | ||||||||
\(566\) | −32.5384 | −1.36769 | ||||||||
\(567\) | −5.02012 | −0.210825 | ||||||||
\(568\) | 18.0698 | 0.758191 | ||||||||
\(569\) | −1.70745 | −0.0715800 | −0.0357900 | − | 0.999359i | \(-0.511395\pi\) | ||||
−0.0357900 | + | 0.999359i | \(0.511395\pi\) | |||||||
\(570\) | −8.66481 | −0.362929 | ||||||||
\(571\) | 0.331367 | 0.0138673 | 0.00693365 | − | 0.999976i | \(-0.497793\pi\) | ||||
0.00693365 | + | 0.999976i | \(0.497793\pi\) | |||||||
\(572\) | 2.95869 | 0.123709 | ||||||||
\(573\) | −16.2973 | −0.680831 | ||||||||
\(574\) | −37.4357 | −1.56254 | ||||||||
\(575\) | −25.8934 | −1.07983 | ||||||||
\(576\) | −4.41631 | −0.184013 | ||||||||
\(577\) | 0.506196 | 0.0210732 | 0.0105366 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105366 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(578\) | −1.67732 | −0.0697675 | ||||||||
\(579\) | −0.196858 | −0.00818115 | ||||||||
\(580\) | 4.33982 | 0.180201 | ||||||||
\(581\) | 50.8231 | 2.10850 | ||||||||
\(582\) | 8.49062 | 0.351948 | ||||||||
\(583\) | 11.6657 | 0.483144 | ||||||||
\(584\) | −19.5383 | −0.808502 | ||||||||
\(585\) | 5.26579 | 0.217713 | ||||||||
\(586\) | −0.385755 | −0.0159354 | ||||||||
\(587\) | 11.9171 | 0.491872 | 0.245936 | − | 0.969286i | \(-0.420905\pi\) | ||||
0.245936 | + | 0.969286i | \(0.420905\pi\) | |||||||
\(588\) | −10.5441 | −0.434833 | ||||||||
\(589\) | 45.9307 | 1.89254 | ||||||||
\(590\) | 7.85586 | 0.323421 | ||||||||
\(591\) | −11.0294 | −0.453687 | ||||||||
\(592\) | −19.1470 | −0.786936 | ||||||||
\(593\) | 43.7935 | 1.79838 | 0.899192 | − | 0.437555i | \(-0.144156\pi\) | ||||
0.899192 | + | 0.437555i | \(0.144156\pi\) | |||||||
\(594\) | 9.02751 | 0.370403 | ||||||||
\(595\) | 3.69495 | 0.151478 | ||||||||
\(596\) | −10.9560 | −0.448776 | ||||||||
\(597\) | 10.4083 | 0.425983 | ||||||||
\(598\) | 37.1516 | 1.51924 | ||||||||
\(599\) | 12.3121 | 0.503058 | 0.251529 | − | 0.967850i | \(-0.419067\pi\) | ||||
0.251529 | + | 0.967850i | \(0.419067\pi\) | |||||||
\(600\) | 9.74501 | 0.397838 | ||||||||
\(601\) | −31.1109 | −1.26904 | −0.634520 | − | 0.772906i | \(-0.718802\pi\) | ||||
−0.634520 | + | 0.772906i | \(0.718802\pi\) | |||||||
\(602\) | −7.16704 | −0.292107 | ||||||||
\(603\) | −7.09973 | −0.289123 | ||||||||
\(604\) | 8.81348 | 0.358616 | ||||||||
\(605\) | 0.864739 | 0.0351566 | ||||||||
\(606\) | 13.5482 | 0.550357 | ||||||||
\(607\) | −19.2929 | −0.783077 | −0.391538 | − | 0.920162i | \(-0.628057\pi\) | ||||
−0.391538 | + | 0.920162i | \(0.628057\pi\) | |||||||
\(608\) | −22.5559 | −0.914764 | ||||||||
\(609\) | −30.3562 | −1.23010 | ||||||||
\(610\) | −12.7357 | −0.515655 | ||||||||
\(611\) | −8.52833 | −0.345019 | ||||||||
\(612\) | −1.36176 | −0.0550460 | ||||||||
\(613\) | −40.0560 | −1.61785 | −0.808923 | − | 0.587914i | \(-0.799949\pi\) | ||||
−0.808923 | + | 0.587914i | \(0.799949\pi\) | |||||||
\(614\) | −52.9640 | −2.13745 | ||||||||
\(615\) | −5.20094 | −0.209722 | ||||||||
\(616\) | −8.50431 | −0.342648 | ||||||||
\(617\) | 2.64543 | 0.106501 | 0.0532505 | − | 0.998581i | \(-0.483042\pi\) | ||||
0.0532505 | + | 0.998581i | \(0.483042\pi\) | |||||||
\(618\) | −29.4857 | −1.18609 | ||||||||
\(619\) | −19.5240 | −0.784734 | −0.392367 | − | 0.919809i | \(-0.628344\pi\) | ||||
−0.392367 | + | 0.919809i | \(0.628344\pi\) | |||||||
\(620\) | −6.22720 | −0.250090 | ||||||||
\(621\) | 32.7736 | 1.31516 | ||||||||
\(622\) | 25.1565 | 1.00868 | ||||||||
\(623\) | 4.06074 | 0.162690 | ||||||||
\(624\) | −20.7957 | −0.832494 | ||||||||
\(625\) | 14.3426 | 0.573702 | ||||||||
\(626\) | 13.5739 | 0.542522 | ||||||||
\(627\) | −5.97389 | −0.238574 | ||||||||
\(628\) | −15.3108 | −0.610967 | ||||||||
\(629\) | 3.85625 | 0.153759 | ||||||||
\(630\) | 10.3756 | 0.413376 | ||||||||
\(631\) | −35.7479 | −1.42310 | −0.711551 | − | 0.702634i | \(-0.752007\pi\) | ||||
−0.711551 | + | 0.702634i | \(0.752007\pi\) | |||||||
\(632\) | −25.6133 | −1.01884 | ||||||||
\(633\) | −28.6450 | −1.13853 | ||||||||
\(634\) | 30.7852 | 1.22264 | ||||||||
\(635\) | −14.9802 | −0.594472 | ||||||||
\(636\) | 10.9263 | 0.433255 | ||||||||
\(637\) | −40.9484 | −1.62244 | ||||||||
\(638\) | 10.3488 | 0.409715 | ||||||||
\(639\) | −15.1994 | −0.601279 | ||||||||
\(640\) | −11.3454 | −0.448466 | ||||||||
\(641\) | 21.0910 | 0.833044 | 0.416522 | − | 0.909126i | \(-0.363249\pi\) | ||||
0.416522 | + | 0.909126i | \(0.363249\pi\) | |||||||
\(642\) | −21.4447 | −0.846355 | ||||||||
\(643\) | −18.2420 | −0.719396 | −0.359698 | − | 0.933069i | \(-0.617120\pi\) | ||||
−0.359698 | + | 0.933069i | \(0.617120\pi\) | |||||||
\(644\) | 21.1645 | 0.833997 | ||||||||
\(645\) | −0.995715 | −0.0392062 | ||||||||
\(646\) | 8.70209 | 0.342379 | ||||||||
\(647\) | 21.5489 | 0.847176 | 0.423588 | − | 0.905855i | \(-0.360770\pi\) | ||||
0.423588 | + | 0.905855i | \(0.360770\pi\) | |||||||
\(648\) | −2.33834 | −0.0918587 | ||||||||
\(649\) | 5.41617 | 0.212603 | ||||||||
\(650\) | −25.9431 | −1.01757 | ||||||||
\(651\) | 43.5581 | 1.70718 | ||||||||
\(652\) | 9.09511 | 0.356192 | ||||||||
\(653\) | −7.69137 | −0.300987 | −0.150493 | − | 0.988611i | \(-0.548086\pi\) | ||||
−0.150493 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(654\) | 29.6459 | 1.15924 | ||||||||
\(655\) | −12.1132 | −0.473302 | ||||||||
\(656\) | −25.9348 | −1.01258 | ||||||||
\(657\) | 16.4347 | 0.641179 | ||||||||
\(658\) | −16.8041 | −0.655093 | ||||||||
\(659\) | −16.0265 | −0.624304 | −0.312152 | − | 0.950032i | \(-0.601050\pi\) | ||||
−0.312152 | + | 0.950032i | \(0.601050\pi\) | |||||||
\(660\) | 0.809928 | 0.0315264 | ||||||||
\(661\) | 24.9762 | 0.971461 | 0.485730 | − | 0.874109i | \(-0.338554\pi\) | ||||
0.485730 | + | 0.874109i | \(0.338554\pi\) | |||||||
\(662\) | −35.1860 | −1.36754 | ||||||||
\(663\) | 4.18830 | 0.162660 | ||||||||
\(664\) | 23.6731 | 0.918693 | ||||||||
\(665\) | −19.1697 | −0.743369 | ||||||||
\(666\) | 10.8286 | 0.419599 | ||||||||
\(667\) | 37.5706 | 1.45474 | ||||||||
\(668\) | 14.2805 | 0.552531 | ||||||||
\(669\) | 8.23523 | 0.318393 | ||||||||
\(670\) | −6.15111 | −0.237638 | ||||||||
\(671\) | −8.78057 | −0.338970 | ||||||||
\(672\) | −21.3908 | −0.825167 | ||||||||
\(673\) | −43.1325 | −1.66264 | −0.831319 | − | 0.555796i | \(-0.812414\pi\) | ||||
−0.831319 | + | 0.555796i | \(0.812414\pi\) | |||||||
\(674\) | −10.2734 | −0.395718 | ||||||||
\(675\) | −22.8859 | −0.880877 | ||||||||
\(676\) | 0.187482 | 0.00721084 | ||||||||
\(677\) | 45.8118 | 1.76069 | 0.880345 | − | 0.474334i | \(-0.157311\pi\) | ||||
0.880345 | + | 0.474334i | \(0.157311\pi\) | |||||||
\(678\) | −12.2856 | −0.471826 | ||||||||
\(679\) | 18.7843 | 0.720877 | ||||||||
\(680\) | 1.72108 | 0.0660004 | ||||||||
\(681\) | 5.85205 | 0.224251 | ||||||||
\(682\) | −14.8495 | −0.568618 | ||||||||
\(683\) | 4.62756 | 0.177069 | 0.0885344 | − | 0.996073i | \(-0.471782\pi\) | ||||
0.0885344 | + | 0.996073i | \(0.471782\pi\) | |||||||
\(684\) | 7.06494 | 0.270135 | ||||||||
\(685\) | −4.56977 | −0.174602 | ||||||||
\(686\) | −30.5151 | −1.16507 | ||||||||
\(687\) | 24.2578 | 0.925493 | ||||||||
\(688\) | −4.96519 | −0.189296 | ||||||||
\(689\) | 42.4326 | 1.61655 | ||||||||
\(690\) | 10.1701 | 0.387169 | ||||||||
\(691\) | −38.8612 | −1.47835 | −0.739174 | − | 0.673514i | \(-0.764784\pi\) | ||||
−0.739174 | + | 0.673514i | \(0.764784\pi\) | |||||||
\(692\) | −7.60518 | −0.289106 | ||||||||
\(693\) | 7.15341 | 0.271736 | ||||||||
\(694\) | −3.39008 | −0.128686 | ||||||||
\(695\) | 5.81651 | 0.220633 | ||||||||
\(696\) | −14.1397 | −0.535965 | ||||||||
\(697\) | 5.22332 | 0.197847 | ||||||||
\(698\) | −35.5135 | −1.34421 | ||||||||
\(699\) | 10.8417 | 0.410069 | ||||||||
\(700\) | −14.7792 | −0.558601 | ||||||||
\(701\) | −17.3203 | −0.654181 | −0.327090 | − | 0.944993i | \(-0.606068\pi\) | ||||
−0.327090 | + | 0.944993i | \(0.606068\pi\) | |||||||
\(702\) | 32.8364 | 1.23933 | ||||||||
\(703\) | −20.0065 | −0.754561 | ||||||||
\(704\) | −2.63797 | −0.0994222 | ||||||||
\(705\) | −2.33459 | −0.0879258 | ||||||||
\(706\) | −52.1601 | −1.96307 | ||||||||
\(707\) | 29.9735 | 1.12727 | ||||||||
\(708\) | 5.07286 | 0.190650 | ||||||||
\(709\) | 37.6808 | 1.41513 | 0.707567 | − | 0.706646i | \(-0.249793\pi\) | ||||
0.707567 | + | 0.706646i | \(0.249793\pi\) | |||||||
\(710\) | −13.1686 | −0.494207 | ||||||||
\(711\) | 21.5447 | 0.807988 | ||||||||
\(712\) | 1.89147 | 0.0708857 | ||||||||
\(713\) | −53.9100 | −2.01895 | ||||||||
\(714\) | 8.25258 | 0.308845 | ||||||||
\(715\) | 3.14538 | 0.117631 | ||||||||
\(716\) | −10.8290 | −0.404697 | ||||||||
\(717\) | 11.0936 | 0.414297 | ||||||||
\(718\) | 19.8196 | 0.739661 | ||||||||
\(719\) | −14.5962 | −0.544347 | −0.272173 | − | 0.962248i | \(-0.587742\pi\) | ||||
−0.272173 | + | 0.962248i | \(0.587742\pi\) | |||||||
\(720\) | 7.18805 | 0.267883 | ||||||||
\(721\) | −65.2332 | −2.42941 | ||||||||
\(722\) | −13.2781 | −0.494158 | ||||||||
\(723\) | −15.6607 | −0.582429 | ||||||||
\(724\) | 1.27550 | 0.0474035 | ||||||||
\(725\) | −26.2356 | −0.974367 | ||||||||
\(726\) | 1.93138 | 0.0716801 | ||||||||
\(727\) | −17.1624 | −0.636518 | −0.318259 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318259 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(728\) | −30.9334 | −1.14647 | ||||||||
\(729\) | 20.5587 | 0.761434 | ||||||||
\(730\) | 14.2388 | 0.527002 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −8.22401 | −0.303968 | ||||||||
\(733\) | 38.8930 | 1.43655 | 0.718273 | − | 0.695761i | \(-0.244933\pi\) | ||||
0.718273 | + | 0.695761i | \(0.244933\pi\) | |||||||
\(734\) | 6.33227 | 0.233728 | ||||||||
\(735\) | −11.2095 | −0.413467 | ||||||||
\(736\) | 26.4745 | 0.975862 | ||||||||
\(737\) | −4.24084 | −0.156213 | ||||||||
\(738\) | 14.6674 | 0.539915 | ||||||||
\(739\) | 23.5168 | 0.865079 | 0.432539 | − | 0.901615i | \(-0.357618\pi\) | ||||
0.432539 | + | 0.901615i | \(0.357618\pi\) | |||||||
\(740\) | 2.71245 | 0.0997115 | ||||||||
\(741\) | −21.7293 | −0.798244 | ||||||||
\(742\) | 83.6086 | 3.06937 | ||||||||
\(743\) | −47.7068 | −1.75019 | −0.875096 | − | 0.483950i | \(-0.839202\pi\) | ||||
−0.875096 | + | 0.483950i | \(0.839202\pi\) | |||||||
\(744\) | 20.2891 | 0.743833 | ||||||||
\(745\) | −11.6473 | −0.426726 | ||||||||
\(746\) | −5.87415 | −0.215068 | ||||||||
\(747\) | −19.9126 | −0.728565 | ||||||||
\(748\) | −0.813414 | −0.0297413 | ||||||||
\(749\) | −47.4434 | −1.73355 | ||||||||
\(750\) | −15.4525 | −0.564245 | ||||||||
\(751\) | −35.1586 | −1.28296 | −0.641478 | − | 0.767141i | \(-0.721678\pi\) | ||||
−0.641478 | + | 0.767141i | \(0.721678\pi\) | |||||||
\(752\) | −11.6416 | −0.424524 | ||||||||
\(753\) | −19.5486 | −0.712391 | ||||||||
\(754\) | 37.6426 | 1.37086 | ||||||||
\(755\) | 9.36961 | 0.340995 | ||||||||
\(756\) | 18.7062 | 0.680338 | ||||||||
\(757\) | 17.0524 | 0.619781 | 0.309890 | − | 0.950772i | \(-0.399708\pi\) | ||||
0.309890 | + | 0.950772i | \(0.399708\pi\) | |||||||
\(758\) | 6.17178 | 0.224169 | ||||||||
\(759\) | 7.01170 | 0.254508 | ||||||||
\(760\) | −8.92911 | −0.323893 | ||||||||
\(761\) | 16.2250 | 0.588155 | 0.294077 | − | 0.955782i | \(-0.404988\pi\) | ||||
0.294077 | + | 0.955782i | \(0.404988\pi\) | |||||||
\(762\) | −33.4580 | −1.21205 | ||||||||
\(763\) | 65.5874 | 2.37442 | ||||||||
\(764\) | 11.5127 | 0.416516 | ||||||||
\(765\) | −1.44769 | −0.0523413 | ||||||||
\(766\) | 28.1195 | 1.01600 | ||||||||
\(767\) | 19.7006 | 0.711348 | ||||||||
\(768\) | −19.2646 | −0.695152 | ||||||||
\(769\) | 17.4922 | 0.630784 | 0.315392 | − | 0.948962i | \(-0.397864\pi\) | ||||
0.315392 | + | 0.948962i | \(0.397864\pi\) | |||||||
\(770\) | 6.19762 | 0.223347 | ||||||||
\(771\) | 24.1783 | 0.870760 | ||||||||
\(772\) | 0.139064 | 0.00500503 | ||||||||
\(773\) | 44.6653 | 1.60650 | 0.803249 | − | 0.595643i | \(-0.203103\pi\) | ||||
0.803249 | + | 0.595643i | \(0.203103\pi\) | |||||||
\(774\) | 2.80806 | 0.100934 | ||||||||
\(775\) | 37.6454 | 1.35226 | ||||||||
\(776\) | 8.74962 | 0.314093 | ||||||||
\(777\) | −18.9731 | −0.680655 | ||||||||
\(778\) | 51.1428 | 1.83356 | ||||||||
\(779\) | −27.0990 | −0.970924 | ||||||||
\(780\) | 2.94601 | 0.105484 | ||||||||
\(781\) | −9.07897 | −0.324871 | ||||||||
\(782\) | −10.2139 | −0.365247 | ||||||||
\(783\) | 33.2067 | 1.18671 | ||||||||
\(784\) | −55.8965 | −1.99630 | ||||||||
\(785\) | −16.2769 | −0.580947 | ||||||||
\(786\) | −27.0546 | −0.965005 | ||||||||
\(787\) | −25.7516 | −0.917947 | −0.458973 | − | 0.888450i | \(-0.651783\pi\) | ||||
−0.458973 | + | 0.888450i | \(0.651783\pi\) | |||||||
\(788\) | 7.79133 | 0.277555 | ||||||||
\(789\) | −1.82553 | −0.0649905 | ||||||||
\(790\) | 18.6660 | 0.664107 | ||||||||
\(791\) | −27.1802 | −0.966417 | ||||||||
\(792\) | 3.33201 | 0.118398 | ||||||||
\(793\) | −31.9382 | −1.13416 | ||||||||
\(794\) | −14.1952 | −0.503768 | ||||||||
\(795\) | 11.6157 | 0.411967 | ||||||||
\(796\) | −7.35260 | −0.260606 | ||||||||
\(797\) | 14.5972 | 0.517061 | 0.258530 | − | 0.966003i | \(-0.416762\pi\) | ||||
0.258530 | + | 0.966003i | \(0.416762\pi\) | |||||||
\(798\) | −42.8151 | −1.51564 | ||||||||
\(799\) | 2.34464 | 0.0829474 | ||||||||
\(800\) | −18.4872 | −0.653620 | ||||||||
\(801\) | −1.59101 | −0.0562155 | ||||||||
\(802\) | 44.6191 | 1.57556 | ||||||||
\(803\) | 9.81684 | 0.346429 | ||||||||
\(804\) | −3.97203 | −0.140083 | ||||||||
\(805\) | 22.4999 | 0.793019 | ||||||||
\(806\) | −54.0133 | −1.90254 | ||||||||
\(807\) | 6.73489 | 0.237079 | ||||||||
\(808\) | 13.9614 | 0.491162 | ||||||||
\(809\) | 25.6232 | 0.900865 | 0.450432 | − | 0.892811i | \(-0.351270\pi\) | ||||
0.450432 | + | 0.892811i | \(0.351270\pi\) | |||||||
\(810\) | 1.70409 | 0.0598757 | ||||||||
\(811\) | −4.82738 | −0.169512 | −0.0847562 | − | 0.996402i | \(-0.527011\pi\) | ||||
−0.0847562 | + | 0.996402i | \(0.527011\pi\) | |||||||
\(812\) | 21.4442 | 0.752543 | ||||||||
\(813\) | −34.3181 | −1.20359 | ||||||||
\(814\) | 6.46817 | 0.226709 | ||||||||
\(815\) | 9.66901 | 0.338691 | ||||||||
\(816\) | 5.71723 | 0.200143 | ||||||||
\(817\) | −5.18808 | −0.181508 | ||||||||
\(818\) | 5.75009 | 0.201047 | ||||||||
\(819\) | 26.0196 | 0.909199 | ||||||||
\(820\) | 3.67404 | 0.128303 | ||||||||
\(821\) | 0.259077 | 0.00904187 | 0.00452093 | − | 0.999990i | \(-0.498561\pi\) | ||||
0.00452093 | + | 0.999990i | \(0.498561\pi\) | |||||||
\(822\) | −10.2065 | −0.355992 | ||||||||
\(823\) | −3.15977 | −0.110143 | −0.0550713 | − | 0.998482i | \(-0.517539\pi\) | ||||
−0.0550713 | + | 0.998482i | \(0.517539\pi\) | |||||||
\(824\) | −30.3852 | −1.05852 | ||||||||
\(825\) | −4.89628 | −0.170467 | ||||||||
\(826\) | 38.8179 | 1.35065 | ||||||||
\(827\) | 10.2275 | 0.355646 | 0.177823 | − | 0.984062i | \(-0.443095\pi\) | ||||
0.177823 | + | 0.984062i | \(0.443095\pi\) | |||||||
\(828\) | −8.29230 | −0.288177 | ||||||||
\(829\) | −13.5436 | −0.470387 | −0.235194 | − | 0.971949i | \(-0.575572\pi\) | ||||
−0.235194 | + | 0.971949i | \(0.575572\pi\) | |||||||
\(830\) | −17.2520 | −0.598827 | ||||||||
\(831\) | 18.9649 | 0.657886 | ||||||||
\(832\) | −9.59528 | −0.332656 | ||||||||
\(833\) | 11.2577 | 0.390056 | ||||||||
\(834\) | 12.9910 | 0.449843 | ||||||||
\(835\) | 15.1816 | 0.525382 | ||||||||
\(836\) | 4.22006 | 0.145954 | ||||||||
\(837\) | −47.6483 | −1.64696 | ||||||||
\(838\) | 44.8268 | 1.54852 | ||||||||
\(839\) | 8.04702 | 0.277814 | 0.138907 | − | 0.990305i | \(-0.455641\pi\) | ||||
0.138907 | + | 0.990305i | \(0.455641\pi\) | |||||||
\(840\) | −8.46787 | −0.292169 | ||||||||
\(841\) | 9.06714 | 0.312660 | ||||||||
\(842\) | −27.8604 | −0.960134 | ||||||||
\(843\) | 13.6929 | 0.471609 | ||||||||
\(844\) | 20.2353 | 0.696528 | ||||||||
\(845\) | 0.199312 | 0.00685654 | ||||||||
\(846\) | 6.58390 | 0.226359 | ||||||||
\(847\) | 4.27290 | 0.146819 | ||||||||
\(848\) | 57.9224 | 1.98906 | ||||||||
\(849\) | −22.3372 | −0.766612 | ||||||||
\(850\) | 7.13236 | 0.244638 | ||||||||
\(851\) | 23.4822 | 0.804958 | ||||||||
\(852\) | −8.50350 | −0.291325 | ||||||||
\(853\) | 27.8307 | 0.952903 | 0.476452 | − | 0.879201i | \(-0.341923\pi\) | ||||
0.476452 | + | 0.879201i | \(0.341923\pi\) | |||||||
\(854\) | −62.9307 | −2.15344 | ||||||||
\(855\) | 7.51073 | 0.256862 | ||||||||
\(856\) | −22.0988 | −0.755323 | ||||||||
\(857\) | 50.1440 | 1.71289 | 0.856444 | − | 0.516241i | \(-0.172669\pi\) | ||||
0.856444 | + | 0.516241i | \(0.172669\pi\) | |||||||
\(858\) | 7.02513 | 0.239834 | ||||||||
\(859\) | 52.1920 | 1.78077 | 0.890384 | − | 0.455210i | \(-0.150436\pi\) | ||||
0.890384 | + | 0.455210i | \(0.150436\pi\) | |||||||
\(860\) | 0.703391 | 0.0239854 | ||||||||
\(861\) | −25.6992 | −0.875826 | ||||||||
\(862\) | −2.28613 | −0.0778660 | ||||||||
\(863\) | −51.2681 | −1.74519 | −0.872593 | − | 0.488448i | \(-0.837563\pi\) | ||||
−0.872593 | + | 0.488448i | \(0.837563\pi\) | |||||||
\(864\) | 23.3994 | 0.796064 | ||||||||
\(865\) | −8.08506 | −0.274900 | ||||||||
\(866\) | 53.0795 | 1.80371 | ||||||||
\(867\) | −1.15146 | −0.0391057 | ||||||||
\(868\) | −30.7702 | −1.04441 | ||||||||
\(869\) | 12.8691 | 0.436556 | ||||||||
\(870\) | 10.3045 | 0.349355 | ||||||||
\(871\) | −15.4255 | −0.522673 | ||||||||
\(872\) | 30.5502 | 1.03456 | ||||||||
\(873\) | −7.35975 | −0.249090 | ||||||||
\(874\) | 52.9904 | 1.79243 | ||||||||
\(875\) | −34.1865 | −1.15571 | ||||||||
\(876\) | 9.19460 | 0.310657 | ||||||||
\(877\) | −9.60183 | −0.324231 | −0.162115 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162115 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(878\) | 11.4598 | 0.386749 | ||||||||
\(879\) | −0.264816 | −0.00893204 | ||||||||
\(880\) | 4.29359 | 0.144737 | ||||||||
\(881\) | −9.41947 | −0.317350 | −0.158675 | − | 0.987331i | \(-0.550722\pi\) | ||||
−0.158675 | + | 0.987331i | \(0.550722\pi\) | |||||||
\(882\) | 31.6123 | 1.06444 | ||||||||
\(883\) | −5.21504 | −0.175500 | −0.0877500 | − | 0.996143i | \(-0.527968\pi\) | ||||
−0.0877500 | + | 0.996143i | \(0.527968\pi\) | |||||||
\(884\) | −2.95869 | −0.0995115 | ||||||||
\(885\) | 5.39296 | 0.181282 | ||||||||
\(886\) | −33.6870 | −1.13174 | ||||||||
\(887\) | −32.9155 | −1.10520 | −0.552598 | − | 0.833448i | \(-0.686363\pi\) | ||||
−0.552598 | + | 0.833448i | \(0.686363\pi\) | |||||||
\(888\) | −8.83753 | −0.296568 | ||||||||
\(889\) | −74.0212 | −2.48259 | ||||||||
\(890\) | −1.37843 | −0.0462050 | ||||||||
\(891\) | 1.17487 | 0.0393598 | ||||||||
\(892\) | −5.81751 | −0.194785 | ||||||||
\(893\) | −12.1642 | −0.407059 | ||||||||
\(894\) | −26.0141 | −0.870041 | ||||||||
\(895\) | −11.5123 | −0.384812 | ||||||||
\(896\) | −56.0605 | −1.87285 | ||||||||
\(897\) | 25.5042 | 0.851559 | ||||||||
\(898\) | −0.343447 | −0.0114610 | ||||||||
\(899\) | −54.6225 | −1.82176 | ||||||||
\(900\) | 5.79052 | 0.193017 | ||||||||
\(901\) | −11.6657 | −0.388641 | ||||||||
\(902\) | 8.76120 | 0.291716 | ||||||||
\(903\) | −4.92009 | −0.163730 | ||||||||
\(904\) | −12.6604 | −0.421077 | ||||||||
\(905\) | 1.35598 | 0.0450743 | ||||||||
\(906\) | 20.9268 | 0.695246 | ||||||||
\(907\) | −32.0727 | −1.06496 | −0.532479 | − | 0.846443i | \(-0.678739\pi\) | ||||
−0.532479 | + | 0.846443i | \(0.678739\pi\) | |||||||
\(908\) | −4.13399 | −0.137191 | ||||||||
\(909\) | −11.7437 | −0.389513 | ||||||||
\(910\) | 22.5431 | 0.747295 | ||||||||
\(911\) | −42.7210 | −1.41541 | −0.707705 | − | 0.706508i | \(-0.750269\pi\) | ||||
−0.707705 | + | 0.706508i | \(0.750269\pi\) | |||||||
\(912\) | −29.6614 | −0.982189 | ||||||||
\(913\) | −11.8943 | −0.393643 | ||||||||
\(914\) | 1.04369 | 0.0345220 | ||||||||
\(915\) | −8.74294 | −0.289033 | ||||||||
\(916\) | −17.1361 | −0.566194 | ||||||||
\(917\) | −59.8545 | −1.97657 | ||||||||
\(918\) | −9.02751 | −0.297952 | ||||||||
\(919\) | 45.2298 | 1.49199 | 0.745997 | − | 0.665950i | \(-0.231974\pi\) | ||||
0.745997 | + | 0.665950i | \(0.231974\pi\) | |||||||
\(920\) | 10.4803 | 0.345526 | ||||||||
\(921\) | −36.3591 | −1.19807 | ||||||||
\(922\) | 40.6010 | 1.33712 | ||||||||
\(923\) | −33.0236 | −1.08698 | ||||||||
\(924\) | 4.00207 | 0.131658 | ||||||||
\(925\) | −16.3976 | −0.539151 | ||||||||
\(926\) | −3.95373 | −0.129927 | ||||||||
\(927\) | 25.5585 | 0.839452 | ||||||||
\(928\) | 26.8243 | 0.880552 | ||||||||
\(929\) | 44.2355 | 1.45132 | 0.725659 | − | 0.688054i | \(-0.241535\pi\) | ||||
0.725659 | + | 0.688054i | \(0.241535\pi\) | |||||||
\(930\) | −14.7859 | −0.484849 | ||||||||
\(931\) | −58.4059 | −1.91417 | ||||||||
\(932\) | −7.65873 | −0.250870 | ||||||||
\(933\) | 17.2696 | 0.565383 | ||||||||
\(934\) | −12.4686 | −0.407984 | ||||||||
\(935\) | −0.864739 | −0.0282800 | ||||||||
\(936\) | 12.1198 | 0.396147 | ||||||||
\(937\) | 3.74517 | 0.122349 | 0.0611747 | − | 0.998127i | \(-0.480515\pi\) | ||||
0.0611747 | + | 0.998127i | \(0.480515\pi\) | |||||||
\(938\) | −30.3942 | −0.992407 | ||||||||
\(939\) | 9.31832 | 0.304092 | ||||||||
\(940\) | 1.64920 | 0.0537909 | ||||||||
\(941\) | 36.3145 | 1.18382 | 0.591909 | − | 0.806005i | \(-0.298374\pi\) | ||||
0.591909 | + | 0.806005i | \(0.298374\pi\) | |||||||
\(942\) | −36.3541 | −1.18448 | ||||||||
\(943\) | 31.8068 | 1.03577 | ||||||||
\(944\) | 26.8923 | 0.875269 | ||||||||
\(945\) | 19.8865 | 0.646909 | ||||||||
\(946\) | 1.67732 | 0.0545345 | ||||||||
\(947\) | 42.9674 | 1.39625 | 0.698126 | − | 0.715975i | \(-0.254017\pi\) | ||||
0.698126 | + | 0.715975i | \(0.254017\pi\) | |||||||
\(948\) | 12.0534 | 0.391477 | ||||||||
\(949\) | 35.7075 | 1.15911 | ||||||||
\(950\) | −37.0033 | −1.20054 | ||||||||
\(951\) | 21.1337 | 0.685306 | ||||||||
\(952\) | 8.50431 | 0.275626 | ||||||||
\(953\) | −53.7341 | −1.74062 | −0.870310 | − | 0.492505i | \(-0.836081\pi\) | ||||
−0.870310 | + | 0.492505i | \(0.836081\pi\) | |||||||
\(954\) | −32.7581 | −1.06058 | ||||||||
\(955\) | 12.2392 | 0.396050 | ||||||||
\(956\) | −7.83669 | −0.253457 | ||||||||
\(957\) | 7.10436 | 0.229651 | ||||||||
\(958\) | 58.2050 | 1.88052 | ||||||||
\(959\) | −22.5804 | −0.729160 | ||||||||
\(960\) | −2.62666 | −0.0847752 | ||||||||
\(961\) | 47.3776 | 1.52831 | ||||||||
\(962\) | 23.5272 | 0.758546 | ||||||||
\(963\) | 18.5885 | 0.599005 | ||||||||
\(964\) | 11.0630 | 0.356316 | ||||||||
\(965\) | 0.147839 | 0.00475910 | ||||||||
\(966\) | 50.2531 | 1.61687 | ||||||||
\(967\) | −27.3361 | −0.879071 | −0.439535 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439535 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(968\) | 1.99029 | 0.0639703 | ||||||||
\(969\) | 5.97389 | 0.191909 | ||||||||
\(970\) | −6.37639 | −0.204734 | ||||||||
\(971\) | 12.0804 | 0.387677 | 0.193839 | − | 0.981033i | \(-0.437906\pi\) | ||||
0.193839 | + | 0.981033i | \(0.437906\pi\) | |||||||
\(972\) | −12.0332 | −0.385965 | ||||||||
\(973\) | 28.7409 | 0.921391 | ||||||||
\(974\) | −23.6276 | −0.757077 | ||||||||
\(975\) | −17.8096 | −0.570364 | ||||||||
\(976\) | −43.5971 | −1.39551 | ||||||||
\(977\) | 15.7842 | 0.504982 | 0.252491 | − | 0.967599i | \(-0.418750\pi\) | ||||
0.252491 | + | 0.967599i | \(0.418750\pi\) | |||||||
\(978\) | 21.5955 | 0.690548 | ||||||||
\(979\) | −0.950347 | −0.0303732 | ||||||||
\(980\) | 7.91856 | 0.252949 | ||||||||
\(981\) | −25.6973 | −0.820452 | ||||||||
\(982\) | 49.6917 | 1.58573 | ||||||||
\(983\) | −51.0876 | −1.62944 | −0.814721 | − | 0.579854i | \(-0.803110\pi\) | ||||
−0.814721 | + | 0.579854i | \(0.803110\pi\) | |||||||
\(984\) | −11.9705 | −0.381606 | ||||||||
\(985\) | 8.28296 | 0.263917 | ||||||||
\(986\) | −10.3488 | −0.329574 | ||||||||
\(987\) | −11.5358 | −0.367189 | ||||||||
\(988\) | 15.3499 | 0.488346 | ||||||||
\(989\) | 6.08938 | 0.193631 | ||||||||
\(990\) | −2.42824 | −0.0771746 | ||||||||
\(991\) | 38.4437 | 1.22120 | 0.610602 | − | 0.791938i | \(-0.290928\pi\) | ||||
0.610602 | + | 0.791938i | \(0.290928\pi\) | |||||||
\(992\) | −38.4902 | −1.22206 | ||||||||
\(993\) | −24.1548 | −0.766529 | ||||||||
\(994\) | −65.0693 | −2.06387 | ||||||||
\(995\) | −7.81654 | −0.247801 | ||||||||
\(996\) | −11.1404 | −0.352996 | ||||||||
\(997\) | −40.8881 | −1.29494 | −0.647469 | − | 0.762092i | \(-0.724172\pi\) | ||||
−0.647469 | + | 0.762092i | \(0.724172\pi\) | |||||||
\(998\) | 52.2710 | 1.65461 | ||||||||
\(999\) | 20.7547 | 0.656649 |
(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 | 8041.2.a.g.1.19 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.19 | ✓ | 69 | 1.1 | even | 1 | trivial |