Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.46231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46231 | −1.03401 | −0.517004 | − | 0.855983i | \(-0.672953\pi\) | ||||
−0.517004 | + | 0.855983i | \(0.672953\pi\) | |||||||
\(3\) | 1.51036 | 0.872004 | 0.436002 | − | 0.899946i | \(-0.356394\pi\) | ||||
0.436002 | + | 0.899946i | \(0.356394\pi\) | |||||||
\(4\) | 0.138346 | 0.0691728 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.20860 | −0.901659 | ||||||||
\(7\) | 4.07172 | 1.53897 | 0.769484 | − | 0.638667i | \(-0.220514\pi\) | ||||
0.769484 | + | 0.638667i | \(0.220514\pi\) | |||||||
\(8\) | 2.72231 | 0.962483 | ||||||||
\(9\) | −0.718827 | −0.239609 | ||||||||
\(10\) | 1.46231 | 0.462422 | ||||||||
\(11\) | −0.621006 | −0.187240 | −0.0936201 | − | 0.995608i | \(-0.529844\pi\) | ||||
−0.0936201 | + | 0.995608i | \(0.529844\pi\) | |||||||
\(12\) | 0.208951 | 0.0603189 | ||||||||
\(13\) | −5.09329 | −1.41262 | −0.706312 | − | 0.707901i | \(-0.749642\pi\) | ||||
−0.706312 | + | 0.707901i | \(0.749642\pi\) | |||||||
\(14\) | −5.95412 | −1.59130 | ||||||||
\(15\) | −1.51036 | −0.389972 | ||||||||
\(16\) | −4.25755 | −1.06439 | ||||||||
\(17\) | −0.266483 | −0.0646317 | −0.0323159 | − | 0.999478i | \(-0.510288\pi\) | ||||
−0.0323159 | + | 0.999478i | \(0.510288\pi\) | |||||||
\(18\) | 1.05115 | 0.247758 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.138346 | −0.0309350 | ||||||||
\(21\) | 6.14975 | 1.34199 | ||||||||
\(22\) | 0.908102 | 0.193608 | ||||||||
\(23\) | −5.84174 | −1.21809 | −0.609043 | − | 0.793137i | \(-0.708446\pi\) | ||||
−0.609043 | + | 0.793137i | \(0.708446\pi\) | |||||||
\(24\) | 4.11166 | 0.839289 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.44796 | 1.46066 | ||||||||
\(27\) | −5.61675 | −1.08094 | ||||||||
\(28\) | 0.563305 | 0.106455 | ||||||||
\(29\) | 4.07754 | 0.757181 | 0.378591 | − | 0.925564i | \(-0.376409\pi\) | ||||
0.378591 | + | 0.925564i | \(0.376409\pi\) | |||||||
\(30\) | 2.20860 | 0.403234 | ||||||||
\(31\) | −6.48991 | −1.16562 | −0.582811 | − | 0.812608i | \(-0.698047\pi\) | ||||
−0.582811 | + | 0.812608i | \(0.698047\pi\) | |||||||
\(32\) | 0.781227 | 0.138103 | ||||||||
\(33\) | −0.937939 | −0.163274 | ||||||||
\(34\) | 0.389681 | 0.0668297 | ||||||||
\(35\) | −4.07172 | −0.688247 | ||||||||
\(36\) | −0.0994465 | −0.0165744 | ||||||||
\(37\) | −8.83927 | −1.45317 | −0.726584 | − | 0.687078i | \(-0.758893\pi\) | ||||
−0.726584 | + | 0.687078i | \(0.758893\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.69267 | −1.23181 | ||||||||
\(40\) | −2.72231 | −0.430435 | ||||||||
\(41\) | −4.48083 | −0.699788 | −0.349894 | − | 0.936789i | \(-0.613782\pi\) | ||||
−0.349894 | + | 0.936789i | \(0.613782\pi\) | |||||||
\(42\) | −8.99283 | −1.38762 | ||||||||
\(43\) | −1.80073 | −0.274608 | −0.137304 | − | 0.990529i | \(-0.543844\pi\) | ||||
−0.137304 | + | 0.990529i | \(0.543844\pi\) | |||||||
\(44\) | −0.0859133 | −0.0129519 | ||||||||
\(45\) | 0.718827 | 0.107156 | ||||||||
\(46\) | 8.54242 | 1.25951 | ||||||||
\(47\) | 11.5465 | 1.68423 | 0.842113 | − | 0.539301i | \(-0.181312\pi\) | ||||
0.842113 | + | 0.539301i | \(0.181312\pi\) | |||||||
\(48\) | −6.43041 | −0.928150 | ||||||||
\(49\) | 9.57894 | 1.36842 | ||||||||
\(50\) | −1.46231 | −0.206802 | ||||||||
\(51\) | −0.402485 | −0.0563591 | ||||||||
\(52\) | −0.704633 | −0.0977151 | ||||||||
\(53\) | −2.52292 | −0.346550 | −0.173275 | − | 0.984873i | \(-0.555435\pi\) | ||||
−0.173275 | + | 0.984873i | \(0.555435\pi\) | |||||||
\(54\) | 8.21342 | 1.11770 | ||||||||
\(55\) | 0.621006 | 0.0837364 | ||||||||
\(56\) | 11.0845 | 1.48123 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.96263 | −0.782931 | ||||||||
\(59\) | 0.890444 | 0.115926 | 0.0579630 | − | 0.998319i | \(-0.481539\pi\) | ||||
0.0579630 | + | 0.998319i | \(0.481539\pi\) | |||||||
\(60\) | −0.208951 | −0.0269754 | ||||||||
\(61\) | 2.16991 | 0.277828 | 0.138914 | − | 0.990304i | \(-0.455639\pi\) | ||||
0.138914 | + | 0.990304i | \(0.455639\pi\) | |||||||
\(62\) | 9.49025 | 1.20526 | ||||||||
\(63\) | −2.92687 | −0.368751 | ||||||||
\(64\) | 7.37271 | 0.921588 | ||||||||
\(65\) | 5.09329 | 0.631744 | ||||||||
\(66\) | 1.37156 | 0.168827 | ||||||||
\(67\) | −14.0788 | −1.72000 | −0.859999 | − | 0.510296i | \(-0.829536\pi\) | ||||
−0.859999 | + | 0.510296i | \(0.829536\pi\) | |||||||
\(68\) | −0.0368668 | −0.00447075 | ||||||||
\(69\) | −8.82310 | −1.06218 | ||||||||
\(70\) | 5.95412 | 0.711653 | ||||||||
\(71\) | −1.64668 | −0.195425 | −0.0977125 | − | 0.995215i | \(-0.531153\pi\) | ||||
−0.0977125 | + | 0.995215i | \(0.531153\pi\) | |||||||
\(72\) | −1.95687 | −0.230620 | ||||||||
\(73\) | 1.79675 | 0.210294 | 0.105147 | − | 0.994457i | \(-0.466469\pi\) | ||||
0.105147 | + | 0.994457i | \(0.466469\pi\) | |||||||
\(74\) | 12.9257 | 1.50259 | ||||||||
\(75\) | 1.51036 | 0.174401 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.52856 | −0.288157 | ||||||||
\(78\) | 11.2491 | 1.27371 | ||||||||
\(79\) | 5.14647 | 0.579023 | 0.289511 | − | 0.957175i | \(-0.406507\pi\) | ||||
0.289511 | + | 0.957175i | \(0.406507\pi\) | |||||||
\(80\) | 4.25755 | 0.476009 | ||||||||
\(81\) | −6.32681 | −0.702978 | ||||||||
\(82\) | 6.55236 | 0.723587 | ||||||||
\(83\) | 13.7833 | 1.51292 | 0.756459 | − | 0.654041i | \(-0.226928\pi\) | ||||
0.756459 | + | 0.654041i | \(0.226928\pi\) | |||||||
\(84\) | 0.850790 | 0.0928288 | ||||||||
\(85\) | 0.266483 | 0.0289042 | ||||||||
\(86\) | 2.63322 | 0.283947 | ||||||||
\(87\) | 6.15854 | 0.660265 | ||||||||
\(88\) | −1.69057 | −0.180216 | ||||||||
\(89\) | −0.000747238 0 | −7.92071e−5 0 | −3.96035e−5 | − | 1.00000i | \(-0.500013\pi\) | ||||
−3.96035e−5 | 1.00000i | \(0.500013\pi\) | ||||||||
\(90\) | −1.05115 | −0.110801 | ||||||||
\(91\) | −20.7385 | −2.17398 | ||||||||
\(92\) | −0.808178 | −0.0842584 | ||||||||
\(93\) | −9.80207 | −1.01643 | ||||||||
\(94\) | −16.8845 | −1.74150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.17993 | 0.120426 | ||||||||
\(97\) | −10.4225 | −1.05825 | −0.529123 | − | 0.848545i | \(-0.677479\pi\) | ||||
−0.529123 | + | 0.848545i | \(0.677479\pi\) | |||||||
\(98\) | −14.0074 | −1.41496 | ||||||||
\(99\) | 0.446396 | 0.0448645 | ||||||||
\(100\) | 0.138346 | 0.0138346 | ||||||||
\(101\) | −12.2197 | −1.21591 | −0.607955 | − | 0.793972i | \(-0.708010\pi\) | ||||
−0.607955 | + | 0.793972i | \(0.708010\pi\) | |||||||
\(102\) | 0.588557 | 0.0582758 | ||||||||
\(103\) | −7.80372 | −0.768924 | −0.384462 | − | 0.923141i | \(-0.625613\pi\) | ||||
−0.384462 | + | 0.923141i | \(0.625613\pi\) | |||||||
\(104\) | −13.8655 | −1.35963 | ||||||||
\(105\) | −6.14975 | −0.600154 | ||||||||
\(106\) | 3.68929 | 0.358336 | ||||||||
\(107\) | 5.70414 | 0.551440 | 0.275720 | − | 0.961238i | \(-0.411084\pi\) | ||||
0.275720 | + | 0.961238i | \(0.411084\pi\) | |||||||
\(108\) | −0.777052 | −0.0747719 | ||||||||
\(109\) | −6.73318 | −0.644922 | −0.322461 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322461 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(110\) | −0.908102 | −0.0865841 | ||||||||
\(111\) | −13.3504 | −1.26717 | ||||||||
\(112\) | −17.3356 | −1.63806 | ||||||||
\(113\) | −4.78878 | −0.450490 | −0.225245 | − | 0.974302i | \(-0.572318\pi\) | ||||
−0.225245 | + | 0.974302i | \(0.572318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.84174 | 0.544745 | ||||||||
\(116\) | 0.564110 | 0.0523763 | ||||||||
\(117\) | 3.66119 | 0.338477 | ||||||||
\(118\) | −1.30210 | −0.119868 | ||||||||
\(119\) | −1.08505 | −0.0994661 | ||||||||
\(120\) | −4.11166 | −0.375341 | ||||||||
\(121\) | −10.6144 | −0.964941 | ||||||||
\(122\) | −3.17308 | −0.287277 | ||||||||
\(123\) | −6.76765 | −0.610218 | ||||||||
\(124\) | −0.897850 | −0.0806293 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.27998 | 0.381291 | ||||||||
\(127\) | 18.4967 | 1.64131 | 0.820656 | − | 0.571422i | \(-0.193608\pi\) | ||||
0.820656 | + | 0.571422i | \(0.193608\pi\) | |||||||
\(128\) | −12.3436 | −1.09103 | ||||||||
\(129\) | −2.71974 | −0.239459 | ||||||||
\(130\) | −7.44796 | −0.653229 | ||||||||
\(131\) | −19.5844 | −1.71110 | −0.855549 | − | 0.517721i | \(-0.826780\pi\) | ||||
−0.855549 | + | 0.517721i | \(0.826780\pi\) | |||||||
\(132\) | −0.129760 | −0.0112941 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20.5875 | 1.77849 | ||||||||
\(135\) | 5.61675 | 0.483413 | ||||||||
\(136\) | −0.725451 | −0.0622069 | ||||||||
\(137\) | −2.35667 | −0.201343 | −0.100672 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100672 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(138\) | 12.9021 | 1.09830 | ||||||||
\(139\) | 3.83050 | 0.324899 | 0.162449 | − | 0.986717i | \(-0.448061\pi\) | ||||
0.162449 | + | 0.986717i | \(0.448061\pi\) | |||||||
\(140\) | −0.563305 | −0.0476079 | ||||||||
\(141\) | 17.4393 | 1.46865 | ||||||||
\(142\) | 2.40795 | 0.202071 | ||||||||
\(143\) | 3.16296 | 0.264500 | ||||||||
\(144\) | 3.06044 | 0.255037 | ||||||||
\(145\) | −4.07754 | −0.338622 | ||||||||
\(146\) | −2.62741 | −0.217446 | ||||||||
\(147\) | 14.4676 | 1.19327 | ||||||||
\(148\) | −1.22287 | −0.100520 | ||||||||
\(149\) | 18.1856 | 1.48982 | 0.744910 | − | 0.667165i | \(-0.232492\pi\) | ||||
0.744910 | + | 0.667165i | \(0.232492\pi\) | |||||||
\(150\) | −2.20860 | −0.180332 | ||||||||
\(151\) | −2.29340 | −0.186634 | −0.0933170 | − | 0.995636i | \(-0.529747\pi\) | ||||
−0.0933170 | + | 0.995636i | \(0.529747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.191556 | 0.0154863 | ||||||||
\(154\) | 3.69754 | 0.297956 | ||||||||
\(155\) | 6.48991 | 0.521282 | ||||||||
\(156\) | −1.06425 | −0.0852079 | ||||||||
\(157\) | −20.8445 | −1.66357 | −0.831787 | − | 0.555095i | \(-0.812682\pi\) | ||||
−0.831787 | + | 0.555095i | \(0.812682\pi\) | |||||||
\(158\) | −7.52572 | −0.598714 | ||||||||
\(159\) | −3.81051 | −0.302193 | ||||||||
\(160\) | −0.781227 | −0.0617614 | ||||||||
\(161\) | −23.7859 | −1.87460 | ||||||||
\(162\) | 9.25174 | 0.726885 | ||||||||
\(163\) | −7.91691 | −0.620100 | −0.310050 | − | 0.950720i | \(-0.600346\pi\) | ||||
−0.310050 | + | 0.950720i | \(0.600346\pi\) | |||||||
\(164\) | −0.619903 | −0.0484063 | ||||||||
\(165\) | 0.937939 | 0.0730184 | ||||||||
\(166\) | −20.1555 | −1.56437 | ||||||||
\(167\) | 14.0935 | 1.09059 | 0.545293 | − | 0.838246i | \(-0.316418\pi\) | ||||
0.545293 | + | 0.838246i | \(0.316418\pi\) | |||||||
\(168\) | 16.7415 | 1.29164 | ||||||||
\(169\) | 12.9416 | 0.995505 | ||||||||
\(170\) | −0.389681 | −0.0298872 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.249122 | −0.0189954 | ||||||||
\(173\) | −10.5128 | −0.799273 | −0.399636 | − | 0.916674i | \(-0.630864\pi\) | ||||
−0.399636 | + | 0.916674i | \(0.630864\pi\) | |||||||
\(174\) | −9.00569 | −0.682719 | ||||||||
\(175\) | 4.07172 | 0.307793 | ||||||||
\(176\) | 2.64396 | 0.199296 | ||||||||
\(177\) | 1.34489 | 0.101088 | ||||||||
\(178\) | 0.00109269 | 8.19008e−5 0 | ||||||||
\(179\) | 5.00329 | 0.373963 | 0.186982 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186982 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(180\) | 0.0994465 | 0.00741231 | ||||||||
\(181\) | −26.4916 | −1.96911 | −0.984553 | − | 0.175089i | \(-0.943979\pi\) | ||||
−0.984553 | + | 0.175089i | \(0.943979\pi\) | |||||||
\(182\) | 30.3260 | 2.24791 | ||||||||
\(183\) | 3.27733 | 0.242267 | ||||||||
\(184\) | −15.9030 | −1.17239 | ||||||||
\(185\) | 8.83927 | 0.649876 | ||||||||
\(186\) | 14.3337 | 1.05099 | ||||||||
\(187\) | 0.165488 | 0.0121017 | ||||||||
\(188\) | 1.59740 | 0.116503 | ||||||||
\(189\) | −22.8699 | −1.66354 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.143815 | −0.0104061 | −0.00520303 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520303 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(192\) | 11.1354 | 0.803629 | ||||||||
\(193\) | 2.06115 | 0.148365 | 0.0741823 | − | 0.997245i | \(-0.476365\pi\) | ||||
0.0741823 | + | 0.997245i | \(0.476365\pi\) | |||||||
\(194\) | 15.2409 | 1.09423 | ||||||||
\(195\) | 7.69267 | 0.550884 | ||||||||
\(196\) | 1.32520 | 0.0946574 | ||||||||
\(197\) | 18.2483 | 1.30014 | 0.650068 | − | 0.759876i | \(-0.274741\pi\) | ||||
0.650068 | + | 0.759876i | \(0.274741\pi\) | |||||||
\(198\) | −0.652768 | −0.0463902 | ||||||||
\(199\) | 8.00301 | 0.567318 | 0.283659 | − | 0.958925i | \(-0.408452\pi\) | ||||
0.283659 | + | 0.958925i | \(0.408452\pi\) | |||||||
\(200\) | 2.72231 | 0.192497 | ||||||||
\(201\) | −21.2640 | −1.49984 | ||||||||
\(202\) | 17.8690 | 1.25726 | ||||||||
\(203\) | 16.6026 | 1.16528 | ||||||||
\(204\) | −0.0556819 | −0.00389851 | ||||||||
\(205\) | 4.48083 | 0.312955 | ||||||||
\(206\) | 11.4115 | 0.795073 | ||||||||
\(207\) | 4.19920 | 0.291865 | ||||||||
\(208\) | 21.6849 | 1.50358 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 8.99283 | 0.620564 | ||||||||
\(211\) | −14.0828 | −0.969501 | −0.484750 | − | 0.874653i | \(-0.661090\pi\) | ||||
−0.484750 | + | 0.874653i | \(0.661090\pi\) | |||||||
\(212\) | −0.349035 | −0.0239718 | ||||||||
\(213\) | −2.48707 | −0.170411 | ||||||||
\(214\) | −8.34121 | −0.570193 | ||||||||
\(215\) | 1.80073 | 0.122808 | ||||||||
\(216\) | −15.2906 | −1.04039 | ||||||||
\(217\) | −26.4251 | −1.79386 | ||||||||
\(218\) | 9.84599 | 0.666855 | ||||||||
\(219\) | 2.71374 | 0.183377 | ||||||||
\(220\) | 0.0859133 | 0.00579228 | ||||||||
\(221\) | 1.35728 | 0.0913003 | ||||||||
\(222\) | 19.5225 | 1.31026 | ||||||||
\(223\) | 4.90610 | 0.328537 | 0.164268 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164268 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(224\) | 3.18094 | 0.212536 | ||||||||
\(225\) | −0.718827 | −0.0479218 | ||||||||
\(226\) | 7.00267 | 0.465811 | ||||||||
\(227\) | 2.65246 | 0.176050 | 0.0880250 | − | 0.996118i | \(-0.471944\pi\) | ||||
0.0880250 | + | 0.996118i | \(0.471944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.1372 | −1.52895 | −0.764473 | − | 0.644655i | \(-0.777001\pi\) | ||||
−0.764473 | + | 0.644655i | \(0.777001\pi\) | |||||||
\(230\) | −8.54242 | −0.563271 | ||||||||
\(231\) | −3.81903 | −0.251274 | ||||||||
\(232\) | 11.1004 | 0.728774 | ||||||||
\(233\) | −28.9098 | −1.89394 | −0.946971 | − | 0.321319i | \(-0.895874\pi\) | ||||
−0.946971 | + | 0.321319i | \(0.895874\pi\) | |||||||
\(234\) | −5.35379 | −0.349988 | ||||||||
\(235\) | −11.5465 | −0.753209 | ||||||||
\(236\) | 0.123189 | 0.00801892 | ||||||||
\(237\) | 7.77299 | 0.504910 | ||||||||
\(238\) | 1.58667 | 0.102849 | ||||||||
\(239\) | −20.7473 | −1.34203 | −0.671016 | − | 0.741443i | \(-0.734142\pi\) | ||||
−0.671016 | + | 0.741443i | \(0.734142\pi\) | |||||||
\(240\) | 6.43041 | 0.415082 | ||||||||
\(241\) | 6.19740 | 0.399209 | 0.199605 | − | 0.979877i | \(-0.436034\pi\) | ||||
0.199605 | + | 0.979877i | \(0.436034\pi\) | |||||||
\(242\) | 15.5215 | 0.997757 | ||||||||
\(243\) | 7.29453 | 0.467944 | ||||||||
\(244\) | 0.300197 | 0.0192182 | ||||||||
\(245\) | −9.57894 | −0.611976 | ||||||||
\(246\) | 9.89639 | 0.630971 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −17.6676 | −1.12189 | ||||||||
\(249\) | 20.8177 | 1.31927 | ||||||||
\(250\) | 1.46231 | 0.0924845 | ||||||||
\(251\) | 7.78995 | 0.491697 | 0.245849 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245849 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(252\) | −0.404919 | −0.0255075 | ||||||||
\(253\) | 3.62775 | 0.228075 | ||||||||
\(254\) | −27.0478 | −1.69713 | ||||||||
\(255\) | 0.402485 | 0.0252046 | ||||||||
\(256\) | 3.30477 | 0.206548 | ||||||||
\(257\) | 20.1572 | 1.25737 | 0.628686 | − | 0.777659i | \(-0.283593\pi\) | ||||
0.628686 | + | 0.777659i | \(0.283593\pi\) | |||||||
\(258\) | 3.97709 | 0.247603 | ||||||||
\(259\) | −35.9911 | −2.23638 | ||||||||
\(260\) | 0.704633 | 0.0436995 | ||||||||
\(261\) | −2.93105 | −0.181427 | ||||||||
\(262\) | 28.6385 | 1.76929 | ||||||||
\(263\) | 10.6858 | 0.658914 | 0.329457 | − | 0.944171i | \(-0.393134\pi\) | ||||
0.329457 | + | 0.944171i | \(0.393134\pi\) | |||||||
\(264\) | −2.55336 | −0.157149 | ||||||||
\(265\) | 2.52292 | 0.154982 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.00112860 | −6.90689e−5 0 | ||||||||
\(268\) | −1.94774 | −0.118977 | ||||||||
\(269\) | −23.9260 | −1.45879 | −0.729396 | − | 0.684092i | \(-0.760199\pi\) | ||||
−0.729396 | + | 0.684092i | \(0.760199\pi\) | |||||||
\(270\) | −8.21342 | −0.499853 | ||||||||
\(271\) | 25.9701 | 1.57757 | 0.788787 | − | 0.614667i | \(-0.210709\pi\) | ||||
0.788787 | + | 0.614667i | \(0.210709\pi\) | |||||||
\(272\) | 1.13457 | 0.0687932 | ||||||||
\(273\) | −31.3224 | −1.89572 | ||||||||
\(274\) | 3.44617 | 0.208191 | ||||||||
\(275\) | −0.621006 | −0.0374480 | ||||||||
\(276\) | −1.22064 | −0.0734737 | ||||||||
\(277\) | −1.83370 | −0.110176 | −0.0550882 | − | 0.998481i | \(-0.517544\pi\) | ||||
−0.0550882 | + | 0.998481i | \(0.517544\pi\) | |||||||
\(278\) | −5.60137 | −0.335948 | ||||||||
\(279\) | 4.66513 | 0.279294 | ||||||||
\(280\) | −11.0845 | −0.662426 | ||||||||
\(281\) | −13.6844 | −0.816345 | −0.408173 | − | 0.912905i | \(-0.633834\pi\) | ||||
−0.408173 | + | 0.912905i | \(0.633834\pi\) | |||||||
\(282\) | −25.5016 | −1.51860 | ||||||||
\(283\) | 10.5363 | 0.626319 | 0.313159 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313159 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(284\) | −0.227811 | −0.0135181 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.62522 | −0.273495 | ||||||||
\(287\) | −18.2447 | −1.07695 | ||||||||
\(288\) | −0.561567 | −0.0330907 | ||||||||
\(289\) | −16.9290 | −0.995823 | ||||||||
\(290\) | 5.96263 | 0.350138 | ||||||||
\(291\) | −15.7417 | −0.922794 | ||||||||
\(292\) | 0.248573 | 0.0145466 | ||||||||
\(293\) | 23.9043 | 1.39650 | 0.698251 | − | 0.715853i | \(-0.253962\pi\) | ||||
0.698251 | + | 0.715853i | \(0.253962\pi\) | |||||||
\(294\) | −21.1561 | −1.23385 | ||||||||
\(295\) | −0.890444 | −0.0518437 | ||||||||
\(296\) | −24.0633 | −1.39865 | ||||||||
\(297\) | 3.48803 | 0.202396 | ||||||||
\(298\) | −26.5929 | −1.54049 | ||||||||
\(299\) | 29.7536 | 1.72070 | ||||||||
\(300\) | 0.208951 | 0.0120638 | ||||||||
\(301\) | −7.33206 | −0.422613 | ||||||||
\(302\) | 3.35366 | 0.192981 | ||||||||
\(303\) | −18.4561 | −1.06028 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.16991 | −0.124249 | ||||||||
\(306\) | −0.280113 | −0.0160130 | ||||||||
\(307\) | 15.6686 | 0.894256 | 0.447128 | − | 0.894470i | \(-0.352447\pi\) | ||||
0.447128 | + | 0.894470i | \(0.352447\pi\) | |||||||
\(308\) | −0.349815 | −0.0199326 | ||||||||
\(309\) | −11.7864 | −0.670505 | ||||||||
\(310\) | −9.49025 | −0.539010 | ||||||||
\(311\) | −3.51210 | −0.199153 | −0.0995764 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995764 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(312\) | −20.9419 | −1.18560 | ||||||||
\(313\) | 1.17307 | 0.0663061 | 0.0331530 | − | 0.999450i | \(-0.489445\pi\) | ||||
0.0331530 | + | 0.999450i | \(0.489445\pi\) | |||||||
\(314\) | 30.4811 | 1.72015 | ||||||||
\(315\) | 2.92687 | 0.164910 | ||||||||
\(316\) | 0.711991 | 0.0400526 | ||||||||
\(317\) | −1.31161 | −0.0736673 | −0.0368336 | − | 0.999321i | \(-0.511727\pi\) | ||||
−0.0368336 | + | 0.999321i | \(0.511727\pi\) | |||||||
\(318\) | 5.57214 | 0.312470 | ||||||||
\(319\) | −2.53218 | −0.141775 | ||||||||
\(320\) | −7.37271 | −0.412147 | ||||||||
\(321\) | 8.61527 | 0.480858 | ||||||||
\(322\) | 34.7824 | 1.93835 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.875285 | −0.0486270 | ||||||||
\(325\) | −5.09329 | −0.282525 | ||||||||
\(326\) | 11.5770 | 0.641189 | ||||||||
\(327\) | −10.1695 | −0.562375 | ||||||||
\(328\) | −12.1982 | −0.673534 | ||||||||
\(329\) | 47.0140 | 2.59197 | ||||||||
\(330\) | −1.37156 | −0.0755017 | ||||||||
\(331\) | −12.7249 | −0.699423 | −0.349712 | − | 0.936857i | \(-0.613720\pi\) | ||||
−0.349712 | + | 0.936857i | \(0.613720\pi\) | |||||||
\(332\) | 1.90686 | 0.104653 | ||||||||
\(333\) | 6.35391 | 0.348192 | ||||||||
\(334\) | −20.6090 | −1.12767 | ||||||||
\(335\) | 14.0788 | 0.769206 | ||||||||
\(336\) | −26.1829 | −1.42839 | ||||||||
\(337\) | 15.2196 | 0.829064 | 0.414532 | − | 0.910035i | \(-0.363945\pi\) | ||||
0.414532 | + | 0.910035i | \(0.363945\pi\) | |||||||
\(338\) | −18.9246 | −1.02936 | ||||||||
\(339\) | −7.23276 | −0.392829 | ||||||||
\(340\) | 0.0368668 | 0.00199938 | ||||||||
\(341\) | 4.03027 | 0.218251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5007 | 0.566987 | ||||||||
\(344\) | −4.90214 | −0.264306 | ||||||||
\(345\) | 8.82310 | 0.475020 | ||||||||
\(346\) | 15.3729 | 0.826455 | ||||||||
\(347\) | 20.0179 | 1.07462 | 0.537308 | − | 0.843386i | \(-0.319441\pi\) | ||||
0.537308 | + | 0.843386i | \(0.319441\pi\) | |||||||
\(348\) | 0.852006 | 0.0456723 | ||||||||
\(349\) | 22.2816 | 1.19271 | 0.596353 | − | 0.802722i | \(-0.296616\pi\) | ||||
0.596353 | + | 0.802722i | \(0.296616\pi\) | |||||||
\(350\) | −5.95412 | −0.318261 | ||||||||
\(351\) | 28.6077 | 1.52697 | ||||||||
\(352\) | −0.485146 | −0.0258584 | ||||||||
\(353\) | −26.2150 | −1.39528 | −0.697642 | − | 0.716447i | \(-0.745767\pi\) | ||||
−0.697642 | + | 0.716447i | \(0.745767\pi\) | |||||||
\(354\) | −1.96664 | −0.104526 | ||||||||
\(355\) | 1.64668 | 0.0873967 | ||||||||
\(356\) | −0.000103377 0 | −5.47897e−6 0 | ||||||||
\(357\) | −1.63881 | −0.0867348 | ||||||||
\(358\) | −7.31635 | −0.386681 | ||||||||
\(359\) | 28.2782 | 1.49247 | 0.746234 | − | 0.665683i | \(-0.231860\pi\) | ||||
0.746234 | + | 0.665683i | \(0.231860\pi\) | |||||||
\(360\) | 1.95687 | 0.103136 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 38.7389 | 2.03607 | ||||||||
\(363\) | −16.0314 | −0.841432 | ||||||||
\(364\) | −2.86907 | −0.150380 | ||||||||
\(365\) | −1.79675 | −0.0940464 | ||||||||
\(366\) | −4.79247 | −0.250507 | ||||||||
\(367\) | −9.59488 | −0.500848 | −0.250424 | − | 0.968136i | \(-0.580570\pi\) | ||||
−0.250424 | + | 0.968136i | \(0.580570\pi\) | |||||||
\(368\) | 24.8715 | 1.29652 | ||||||||
\(369\) | 3.22094 | 0.167676 | ||||||||
\(370\) | −12.9257 | −0.671977 | ||||||||
\(371\) | −10.2727 | −0.533330 | ||||||||
\(372\) | −1.35607 | −0.0703091 | ||||||||
\(373\) | 13.0401 | 0.675189 | 0.337595 | − | 0.941292i | \(-0.390387\pi\) | ||||
0.337595 | + | 0.941292i | \(0.390387\pi\) | |||||||
\(374\) | −0.241994 | −0.0125132 | ||||||||
\(375\) | −1.51036 | −0.0779944 | ||||||||
\(376\) | 31.4331 | 1.62104 | ||||||||
\(377\) | −20.7681 | −1.06961 | ||||||||
\(378\) | 33.4428 | 1.72011 | ||||||||
\(379\) | 9.93895 | 0.510530 | 0.255265 | − | 0.966871i | \(-0.417837\pi\) | ||||
0.255265 | + | 0.966871i | \(0.417837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.9365 | 1.43123 | ||||||||
\(382\) | 0.210301 | 0.0107599 | ||||||||
\(383\) | −18.0285 | −0.921212 | −0.460606 | − | 0.887605i | \(-0.652368\pi\) | ||||
−0.460606 | + | 0.887605i | \(0.652368\pi\) | |||||||
\(384\) | −18.6433 | −0.951385 | ||||||||
\(385\) | 2.52856 | 0.128868 | ||||||||
\(386\) | −3.01403 | −0.153410 | ||||||||
\(387\) | 1.29441 | 0.0657986 | ||||||||
\(388\) | −1.44191 | −0.0732017 | ||||||||
\(389\) | 24.3511 | 1.23465 | 0.617325 | − | 0.786708i | \(-0.288216\pi\) | ||||
0.617325 | + | 0.786708i | \(0.288216\pi\) | |||||||
\(390\) | −11.2491 | −0.569618 | ||||||||
\(391\) | 1.55673 | 0.0787270 | ||||||||
\(392\) | 26.0769 | 1.31708 | ||||||||
\(393\) | −29.5794 | −1.49208 | ||||||||
\(394\) | −26.6846 | −1.34435 | ||||||||
\(395\) | −5.14647 | −0.258947 | ||||||||
\(396\) | 0.0617568 | 0.00310340 | ||||||||
\(397\) | −19.9719 | −1.00236 | −0.501180 | − | 0.865343i | \(-0.667100\pi\) | ||||
−0.501180 | + | 0.865343i | \(0.667100\pi\) | |||||||
\(398\) | −11.7029 | −0.586611 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.25755 | −0.212878 | ||||||||
\(401\) | −16.4037 | −0.819163 | −0.409581 | − | 0.912274i | \(-0.634325\pi\) | ||||
−0.409581 | + | 0.912274i | \(0.634325\pi\) | |||||||
\(402\) | 31.0945 | 1.55085 | ||||||||
\(403\) | 33.0550 | 1.64659 | ||||||||
\(404\) | −1.69055 | −0.0841078 | ||||||||
\(405\) | 6.32681 | 0.314381 | ||||||||
\(406\) | −24.2782 | −1.20491 | ||||||||
\(407\) | 5.48924 | 0.272091 | ||||||||
\(408\) | −1.09569 | −0.0542447 | ||||||||
\(409\) | 8.33303 | 0.412042 | 0.206021 | − | 0.978548i | \(-0.433948\pi\) | ||||
0.206021 | + | 0.978548i | \(0.433948\pi\) | |||||||
\(410\) | −6.55236 | −0.323598 | ||||||||
\(411\) | −3.55940 | −0.175572 | ||||||||
\(412\) | −1.07961 | −0.0531886 | ||||||||
\(413\) | 3.62564 | 0.178406 | ||||||||
\(414\) | −6.14053 | −0.301790 | ||||||||
\(415\) | −13.7833 | −0.676597 | ||||||||
\(416\) | −3.97901 | −0.195087 | ||||||||
\(417\) | 5.78542 | 0.283313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6553 | −0.569397 | −0.284698 | − | 0.958617i | \(-0.591893\pi\) | ||||
−0.284698 | + | 0.958617i | \(0.591893\pi\) | |||||||
\(420\) | −0.850790 | −0.0415143 | ||||||||
\(421\) | 21.1916 | 1.03282 | 0.516408 | − | 0.856343i | \(-0.327269\pi\) | ||||
0.516408 | + | 0.856343i | \(0.327269\pi\) | |||||||
\(422\) | 20.5934 | 1.00247 | ||||||||
\(423\) | −8.29992 | −0.403556 | ||||||||
\(424\) | −6.86819 | −0.333549 | ||||||||
\(425\) | −0.266483 | −0.0129263 | ||||||||
\(426\) | 3.63687 | 0.176207 | ||||||||
\(427\) | 8.83527 | 0.427569 | ||||||||
\(428\) | 0.789142 | 0.0381446 | ||||||||
\(429\) | 4.77719 | 0.230645 | ||||||||
\(430\) | −2.63322 | −0.126985 | ||||||||
\(431\) | 0.392264 | 0.0188947 | 0.00944734 | − | 0.999955i | \(-0.496993\pi\) | ||||
0.00944734 | + | 0.999955i | \(0.496993\pi\) | |||||||
\(432\) | 23.9136 | 1.15054 | ||||||||
\(433\) | 12.9711 | 0.623354 | 0.311677 | − | 0.950188i | \(-0.399109\pi\) | ||||
0.311677 | + | 0.950188i | \(0.399109\pi\) | |||||||
\(434\) | 38.6417 | 1.85486 | ||||||||
\(435\) | −6.15854 | −0.295279 | ||||||||
\(436\) | −0.931506 | −0.0446110 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.96832 | −0.189614 | ||||||||
\(439\) | −5.44800 | −0.260019 | −0.130009 | − | 0.991513i | \(-0.541501\pi\) | ||||
−0.130009 | + | 0.991513i | \(0.541501\pi\) | |||||||
\(440\) | 1.69057 | 0.0805948 | ||||||||
\(441\) | −6.88560 | −0.327886 | ||||||||
\(442\) | −1.98476 | −0.0944052 | ||||||||
\(443\) | 24.7427 | 1.17556 | 0.587780 | − | 0.809021i | \(-0.300002\pi\) | ||||
0.587780 | + | 0.809021i | \(0.300002\pi\) | |||||||
\(444\) | −1.84697 | −0.0876535 | ||||||||
\(445\) | 0.000747238 0 | 3.54225e−5 0 | ||||||||
\(446\) | −7.17423 | −0.339710 | ||||||||
\(447\) | 27.4667 | 1.29913 | ||||||||
\(448\) | 30.0196 | 1.41829 | ||||||||
\(449\) | 34.5619 | 1.63108 | 0.815538 | − | 0.578704i | \(-0.196441\pi\) | ||||
0.815538 | + | 0.578704i | \(0.196441\pi\) | |||||||
\(450\) | 1.05115 | 0.0495515 | ||||||||
\(451\) | 2.78262 | 0.131029 | ||||||||
\(452\) | −0.662506 | −0.0311617 | ||||||||
\(453\) | −3.46385 | −0.162746 | ||||||||
\(454\) | −3.87872 | −0.182037 | ||||||||
\(455\) | 20.7385 | 0.972234 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6425 | −0.544613 | −0.272307 | − | 0.962211i | \(-0.587786\pi\) | ||||
−0.272307 | + | 0.962211i | \(0.587786\pi\) | |||||||
\(458\) | 33.8337 | 1.58094 | ||||||||
\(459\) | 1.49677 | 0.0698633 | ||||||||
\(460\) | 0.808178 | 0.0376815 | ||||||||
\(461\) | 2.98973 | 0.139246 | 0.0696228 | − | 0.997573i | \(-0.477820\pi\) | ||||
0.0696228 | + | 0.997573i | \(0.477820\pi\) | |||||||
\(462\) | 5.58460 | 0.259819 | ||||||||
\(463\) | −8.48715 | −0.394431 | −0.197216 | − | 0.980360i | \(-0.563190\pi\) | ||||
−0.197216 | + | 0.980360i | \(0.563190\pi\) | |||||||
\(464\) | −17.3604 | −0.805934 | ||||||||
\(465\) | 9.80207 | 0.454560 | ||||||||
\(466\) | 42.2750 | 1.95835 | ||||||||
\(467\) | 17.9302 | 0.829712 | 0.414856 | − | 0.909887i | \(-0.363832\pi\) | ||||
0.414856 | + | 0.909887i | \(0.363832\pi\) | |||||||
\(468\) | 0.506510 | 0.0234134 | ||||||||
\(469\) | −57.3249 | −2.64702 | ||||||||
\(470\) | 16.8845 | 0.778824 | ||||||||
\(471\) | −31.4826 | −1.45064 | ||||||||
\(472\) | 2.42407 | 0.111577 | ||||||||
\(473\) | 1.11826 | 0.0514177 | ||||||||
\(474\) | −11.3665 | −0.522081 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.150111 | −0.00688034 | ||||||||
\(477\) | 1.81355 | 0.0830366 | ||||||||
\(478\) | 30.3389 | 1.38767 | ||||||||
\(479\) | 3.38955 | 0.154873 | 0.0774363 | − | 0.996997i | \(-0.475327\pi\) | ||||
0.0774363 | + | 0.996997i | \(0.475327\pi\) | |||||||
\(480\) | −1.17993 | −0.0538562 | ||||||||
\(481\) | 45.0210 | 2.05278 | ||||||||
\(482\) | −9.06250 | −0.412786 | ||||||||
\(483\) | −35.9252 | −1.63465 | ||||||||
\(484\) | −1.46845 | −0.0667476 | ||||||||
\(485\) | 10.4225 | 0.473262 | ||||||||
\(486\) | −10.6668 | −0.483858 | ||||||||
\(487\) | −11.1620 | −0.505797 | −0.252899 | − | 0.967493i | \(-0.581384\pi\) | ||||
−0.252899 | + | 0.967493i | \(0.581384\pi\) | |||||||
\(488\) | 5.90717 | 0.267405 | ||||||||
\(489\) | −11.9573 | −0.540730 | ||||||||
\(490\) | 14.0074 | 0.632788 | ||||||||
\(491\) | 22.9830 | 1.03721 | 0.518604 | − | 0.855015i | \(-0.326452\pi\) | ||||
0.518604 | + | 0.855015i | \(0.326452\pi\) | |||||||
\(492\) | −0.936274 | −0.0422105 | ||||||||
\(493\) | −1.08660 | −0.0489379 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.446396 | −0.0200640 | ||||||||
\(496\) | 27.6311 | 1.24067 | ||||||||
\(497\) | −6.70483 | −0.300753 | ||||||||
\(498\) | −30.4419 | −1.36414 | ||||||||
\(499\) | 0.980732 | 0.0439036 | 0.0219518 | − | 0.999759i | \(-0.493012\pi\) | ||||
0.0219518 | + | 0.999759i | \(0.493012\pi\) | |||||||
\(500\) | −0.138346 | −0.00618700 | ||||||||
\(501\) | 21.2862 | 0.950995 | ||||||||
\(502\) | −11.3913 | −0.508419 | ||||||||
\(503\) | 3.57195 | 0.159265 | 0.0796326 | − | 0.996824i | \(-0.474625\pi\) | ||||
0.0796326 | + | 0.996824i | \(0.474625\pi\) | |||||||
\(504\) | −7.96785 | −0.354916 | ||||||||
\(505\) | 12.2197 | 0.543771 | ||||||||
\(506\) | −5.30489 | −0.235831 | ||||||||
\(507\) | 19.5464 | 0.868085 | ||||||||
\(508\) | 2.55893 | 0.113534 | ||||||||
\(509\) | −12.9903 | −0.575783 | −0.287892 | − | 0.957663i | \(-0.592954\pi\) | ||||
−0.287892 | + | 0.957663i | \(0.592954\pi\) | |||||||
\(510\) | −0.588557 | −0.0260617 | ||||||||
\(511\) | 7.31589 | 0.323636 | ||||||||
\(512\) | 19.8547 | 0.877460 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.4761 | −1.30013 | ||||||||
\(515\) | 7.80372 | 0.343873 | ||||||||
\(516\) | −0.376263 | −0.0165641 | ||||||||
\(517\) | −7.17042 | −0.315355 | ||||||||
\(518\) | 52.6301 | 2.31243 | ||||||||
\(519\) | −15.8781 | −0.696969 | ||||||||
\(520\) | 13.8655 | 0.608043 | ||||||||
\(521\) | 22.9197 | 1.00413 | 0.502064 | − | 0.864830i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864830i | \(0.332574\pi\) | |||||||
\(522\) | 4.28610 | 0.187597 | ||||||||
\(523\) | 1.97236 | 0.0862455 | 0.0431227 | − | 0.999070i | \(-0.486269\pi\) | ||||
0.0431227 | + | 0.999070i | \(0.486269\pi\) | |||||||
\(524\) | −2.70942 | −0.118361 | ||||||||
\(525\) | 6.14975 | 0.268397 | ||||||||
\(526\) | −15.6259 | −0.681323 | ||||||||
\(527\) | 1.72945 | 0.0753362 | ||||||||
\(528\) | 3.99332 | 0.173787 | ||||||||
\(529\) | 11.1259 | 0.483735 | ||||||||
\(530\) | −3.68929 | −0.160253 | ||||||||
\(531\) | −0.640075 | −0.0277769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.8222 | 0.988538 | ||||||||
\(534\) | 0.00165035 | 7.14178e−5 0 | ||||||||
\(535\) | −5.70414 | −0.246611 | ||||||||
\(536\) | −38.3269 | −1.65547 | ||||||||
\(537\) | 7.55674 | 0.326098 | ||||||||
\(538\) | 34.9871 | 1.50840 | ||||||||
\(539\) | −5.94858 | −0.256223 | ||||||||
\(540\) | 0.777052 | 0.0334390 | ||||||||
\(541\) | −27.5270 | −1.18348 | −0.591739 | − | 0.806129i | \(-0.701559\pi\) | ||||
−0.591739 | + | 0.806129i | \(0.701559\pi\) | |||||||
\(542\) | −37.9764 | −1.63122 | ||||||||
\(543\) | −40.0117 | −1.71707 | ||||||||
\(544\) | −0.208184 | −0.00892582 | ||||||||
\(545\) | 6.73318 | 0.288418 | ||||||||
\(546\) | 45.8031 | 1.96019 | ||||||||
\(547\) | 8.34646 | 0.356869 | 0.178434 | − | 0.983952i | \(-0.442897\pi\) | ||||
0.178434 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(548\) | −0.326034 | −0.0139275 | ||||||||
\(549\) | −1.55979 | −0.0665702 | ||||||||
\(550\) | 0.908102 | 0.0387216 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −24.0192 | −1.02233 | ||||||||
\(553\) | 20.9550 | 0.891097 | ||||||||
\(554\) | 2.68144 | 0.113923 | ||||||||
\(555\) | 13.3504 | 0.566695 | ||||||||
\(556\) | 0.529933 | 0.0224742 | ||||||||
\(557\) | 23.8334 | 1.00985 | 0.504926 | − | 0.863163i | \(-0.331520\pi\) | ||||
0.504926 | + | 0.863163i | \(0.331520\pi\) | |||||||
\(558\) | −6.82185 | −0.288792 | ||||||||
\(559\) | 9.17161 | 0.387918 | ||||||||
\(560\) | 17.3356 | 0.732562 | ||||||||
\(561\) | 0.249945 | 0.0105527 | ||||||||
\(562\) | 20.0109 | 0.844108 | ||||||||
\(563\) | −19.6274 | −0.827198 | −0.413599 | − | 0.910459i | \(-0.635728\pi\) | ||||
−0.413599 | + | 0.910459i | \(0.635728\pi\) | |||||||
\(564\) | 2.41264 | 0.101591 | ||||||||
\(565\) | 4.78878 | 0.201465 | ||||||||
\(566\) | −15.4073 | −0.647618 | ||||||||
\(567\) | −25.7610 | −1.08186 | ||||||||
\(568\) | −4.48278 | −0.188093 | ||||||||
\(569\) | 23.7705 | 0.996510 | 0.498255 | − | 0.867030i | \(-0.333974\pi\) | ||||
0.498255 | + | 0.867030i | \(0.333974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5361 | −0.733865 | −0.366933 | − | 0.930248i | \(-0.619592\pi\) | ||||
−0.366933 | + | 0.930248i | \(0.619592\pi\) | |||||||
\(572\) | 0.437581 | 0.0182962 | ||||||||
\(573\) | −0.217211 | −0.00907412 | ||||||||
\(574\) | 26.6794 | 1.11358 | ||||||||
\(575\) | −5.84174 | −0.243617 | ||||||||
\(576\) | −5.29970 | −0.220821 | ||||||||
\(577\) | −25.9280 | −1.07940 | −0.539699 | − | 0.841858i | \(-0.681462\pi\) | ||||
−0.539699 | + | 0.841858i | \(0.681462\pi\) | |||||||
\(578\) | 24.7554 | 1.02969 | ||||||||
\(579\) | 3.11306 | 0.129375 | ||||||||
\(580\) | −0.564110 | −0.0234234 | ||||||||
\(581\) | 56.1220 | 2.32833 | ||||||||
\(582\) | 23.0192 | 0.954177 | ||||||||
\(583\) | 1.56675 | 0.0648882 | ||||||||
\(584\) | 4.89133 | 0.202405 | ||||||||
\(585\) | −3.66119 | −0.151372 | ||||||||
\(586\) | −34.9554 | −1.44399 | ||||||||
\(587\) | −4.04205 | −0.166833 | −0.0834166 | − | 0.996515i | \(-0.526583\pi\) | ||||
−0.0834166 | + | 0.996515i | \(0.526583\pi\) | |||||||
\(588\) | 2.00153 | 0.0825416 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.30210 | 0.0536068 | ||||||||
\(591\) | 27.5614 | 1.13372 | ||||||||
\(592\) | 37.6337 | 1.54673 | ||||||||
\(593\) | 18.8561 | 0.774329 | 0.387165 | − | 0.922011i | \(-0.373455\pi\) | ||||
0.387165 | + | 0.922011i | \(0.373455\pi\) | |||||||
\(594\) | −5.10058 | −0.209279 | ||||||||
\(595\) | 1.08505 | 0.0444826 | ||||||||
\(596\) | 2.51589 | 0.103055 | ||||||||
\(597\) | 12.0874 | 0.494704 | ||||||||
\(598\) | −43.5090 | −1.77922 | ||||||||
\(599\) | −38.8211 | −1.58619 | −0.793094 | − | 0.609099i | \(-0.791531\pi\) | ||||
−0.793094 | + | 0.609099i | \(0.791531\pi\) | |||||||
\(600\) | 4.11166 | 0.167858 | ||||||||
\(601\) | 0.358419 | 0.0146202 | 0.00731011 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00731011 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(602\) | 10.7217 | 0.436985 | ||||||||
\(603\) | 10.1202 | 0.412127 | ||||||||
\(604\) | −0.317281 | −0.0129100 | ||||||||
\(605\) | 10.6144 | 0.431535 | ||||||||
\(606\) | 26.9886 | 1.09634 | ||||||||
\(607\) | 4.56885 | 0.185444 | 0.0927219 | − | 0.995692i | \(-0.470443\pi\) | ||||
0.0927219 | + | 0.995692i | \(0.470443\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.0759 | 1.01613 | ||||||||
\(610\) | 3.17308 | 0.128474 | ||||||||
\(611\) | −58.8095 | −2.37918 | ||||||||
\(612\) | 0.0265008 | 0.00107123 | ||||||||
\(613\) | 16.8926 | 0.682287 | 0.341143 | − | 0.940011i | \(-0.389186\pi\) | ||||
0.341143 | + | 0.940011i | \(0.389186\pi\) | |||||||
\(614\) | −22.9124 | −0.924668 | ||||||||
\(615\) | 6.76765 | 0.272898 | ||||||||
\(616\) | −6.88354 | −0.277346 | ||||||||
\(617\) | 24.3654 | 0.980914 | 0.490457 | − | 0.871465i | \(-0.336830\pi\) | ||||
0.490457 | + | 0.871465i | \(0.336830\pi\) | |||||||
\(618\) | 17.2353 | 0.693307 | ||||||||
\(619\) | −33.3232 | −1.33937 | −0.669687 | − | 0.742644i | \(-0.733572\pi\) | ||||
−0.669687 | + | 0.742644i | \(0.733572\pi\) | |||||||
\(620\) | 0.897850 | 0.0360585 | ||||||||
\(621\) | 32.8116 | 1.31668 | ||||||||
\(622\) | 5.13577 | 0.205926 | ||||||||
\(623\) | −0.00304255 | −0.000121897 0 | ||||||||
\(624\) | 32.7519 | 1.31113 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −1.71540 | −0.0685610 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88375 | −0.115074 | ||||||||
\(629\) | 2.35552 | 0.0939207 | ||||||||
\(630\) | −4.27998 | −0.170519 | ||||||||
\(631\) | 37.5315 | 1.49411 | 0.747053 | − | 0.664765i | \(-0.231468\pi\) | ||||
0.747053 | + | 0.664765i | \(0.231468\pi\) | |||||||
\(632\) | 14.0103 | 0.557300 | ||||||||
\(633\) | −21.2701 | −0.845409 | ||||||||
\(634\) | 1.91798 | 0.0761725 | ||||||||
\(635\) | −18.4967 | −0.734017 | ||||||||
\(636\) | −0.527167 | −0.0209035 | ||||||||
\(637\) | −48.7883 | −1.93306 | ||||||||
\(638\) | 3.70282 | 0.146596 | ||||||||
\(639\) | 1.18368 | 0.0468256 | ||||||||
\(640\) | 12.3436 | 0.487925 | ||||||||
\(641\) | −7.04598 | −0.278300 | −0.139150 | − | 0.990271i | \(-0.544437\pi\) | ||||
−0.139150 | + | 0.990271i | \(0.544437\pi\) | |||||||
\(642\) | −12.5982 | −0.497211 | ||||||||
\(643\) | 15.2815 | 0.602645 | 0.301323 | − | 0.953522i | \(-0.402572\pi\) | ||||
0.301323 | + | 0.953522i | \(0.402572\pi\) | |||||||
\(644\) | −3.29068 | −0.129671 | ||||||||
\(645\) | 2.71974 | 0.107089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.8972 | 0.939495 | 0.469748 | − | 0.882801i | \(-0.344345\pi\) | ||||
0.469748 | + | 0.882801i | \(0.344345\pi\) | |||||||
\(648\) | −17.2235 | −0.676605 | ||||||||
\(649\) | −0.552971 | −0.0217060 | ||||||||
\(650\) | 7.44796 | 0.292133 | ||||||||
\(651\) | −39.9113 | −1.56425 | ||||||||
\(652\) | −1.09527 | −0.0428940 | ||||||||
\(653\) | −27.1407 | −1.06210 | −0.531050 | − | 0.847341i | \(-0.678202\pi\) | ||||
−0.531050 | + | 0.847341i | \(0.678202\pi\) | |||||||
\(654\) | 14.8709 | 0.581500 | ||||||||
\(655\) | 19.5844 | 0.765227 | ||||||||
\(656\) | 19.0774 | 0.744846 | ||||||||
\(657\) | −1.29156 | −0.0503884 | ||||||||
\(658\) | −68.7490 | −2.68012 | ||||||||
\(659\) | −45.8304 | −1.78530 | −0.892650 | − | 0.450750i | \(-0.851156\pi\) | ||||
−0.892650 | + | 0.450750i | \(0.851156\pi\) | |||||||
\(660\) | 0.129760 | 0.00505089 | ||||||||
\(661\) | 18.3884 | 0.715226 | 0.357613 | − | 0.933870i | \(-0.383591\pi\) | ||||
0.357613 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(662\) | 18.6077 | 0.723209 | ||||||||
\(663\) | 2.04997 | 0.0796142 | ||||||||
\(664\) | 37.5226 | 1.45616 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.29138 | −0.360034 | ||||||||
\(667\) | −23.8199 | −0.922312 | ||||||||
\(668\) | 1.94977 | 0.0754388 | ||||||||
\(669\) | 7.40995 | 0.286485 | ||||||||
\(670\) | −20.5875 | −0.795366 | ||||||||
\(671\) | −1.34753 | −0.0520207 | ||||||||
\(672\) | 4.80435 | 0.185332 | ||||||||
\(673\) | −5.81977 | −0.224336 | −0.112168 | − | 0.993689i | \(-0.535779\pi\) | ||||
−0.112168 | + | 0.993689i | \(0.535779\pi\) | |||||||
\(674\) | −22.2557 | −0.857259 | ||||||||
\(675\) | −5.61675 | −0.216189 | ||||||||
\(676\) | 1.79041 | 0.0688619 | ||||||||
\(677\) | 17.8836 | 0.687324 | 0.343662 | − | 0.939093i | \(-0.388332\pi\) | ||||
0.343662 | + | 0.939093i | \(0.388332\pi\) | |||||||
\(678\) | 10.5765 | 0.406189 | ||||||||
\(679\) | −42.4376 | −1.62861 | ||||||||
\(680\) | 0.725451 | 0.0278198 | ||||||||
\(681\) | 4.00616 | 0.153516 | ||||||||
\(682\) | −5.89350 | −0.225674 | ||||||||
\(683\) | −13.4534 | −0.514779 | −0.257390 | − | 0.966308i | \(-0.582862\pi\) | ||||
−0.257390 | + | 0.966308i | \(0.582862\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.35667 | 0.0900435 | ||||||||
\(686\) | −15.3553 | −0.586269 | ||||||||
\(687\) | −34.9453 | −1.33325 | ||||||||
\(688\) | 7.66668 | 0.292290 | ||||||||
\(689\) | 12.8500 | 0.489545 | ||||||||
\(690\) | −12.9021 | −0.491174 | ||||||||
\(691\) | 2.31515 | 0.0880724 | 0.0440362 | − | 0.999030i | \(-0.485978\pi\) | ||||
0.0440362 | + | 0.999030i | \(0.485978\pi\) | |||||||
\(692\) | −1.45440 | −0.0552879 | ||||||||
\(693\) | 1.81760 | 0.0690449 | ||||||||
\(694\) | −29.2723 | −1.11116 | ||||||||
\(695\) | −3.83050 | −0.145299 | ||||||||
\(696\) | 16.7655 | 0.635494 | ||||||||
\(697\) | 1.19407 | 0.0452285 | ||||||||
\(698\) | −32.5825 | −1.23327 | ||||||||
\(699\) | −43.6640 | −1.65152 | ||||||||
\(700\) | 0.563305 | 0.0212909 | ||||||||
\(701\) | 3.12614 | 0.118073 | 0.0590364 | − | 0.998256i | \(-0.481197\pi\) | ||||
0.0590364 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(702\) | −41.8333 | −1.57890 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4.57849 | −0.172558 | ||||||||
\(705\) | −17.4393 | −0.656801 | ||||||||
\(706\) | 38.3344 | 1.44273 | ||||||||
\(707\) | −49.7554 | −1.87124 | ||||||||
\(708\) | 0.186059 | 0.00699253 | ||||||||
\(709\) | −28.1738 | −1.05809 | −0.529045 | − | 0.848594i | \(-0.677450\pi\) | ||||
−0.529045 | + | 0.848594i | \(0.677450\pi\) | |||||||
\(710\) | −2.40795 | −0.0903689 | ||||||||
\(711\) | −3.69942 | −0.138739 | ||||||||
\(712\) | −0.00203422 | −7.62355e−5 0 | ||||||||
\(713\) | 37.9124 | 1.41983 | ||||||||
\(714\) | 2.39644 | 0.0896845 | ||||||||
\(715\) | −3.16296 | −0.118288 | ||||||||
\(716\) | 0.692183 | 0.0258681 | ||||||||
\(717\) | −31.3358 | −1.17026 | ||||||||
\(718\) | −41.3515 | −1.54322 | ||||||||
\(719\) | −1.21291 | −0.0452338 | −0.0226169 | − | 0.999744i | \(-0.507200\pi\) | ||||
−0.0226169 | + | 0.999744i | \(0.507200\pi\) | |||||||
\(720\) | −3.06044 | −0.114056 | ||||||||
\(721\) | −31.7746 | −1.18335 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.36027 | 0.348112 | ||||||||
\(724\) | −3.66499 | −0.136208 | ||||||||
\(725\) | 4.07754 | 0.151436 | ||||||||
\(726\) | 23.4429 | 0.870048 | ||||||||
\(727\) | 35.7719 | 1.32671 | 0.663354 | − | 0.748306i | \(-0.269132\pi\) | ||||
0.663354 | + | 0.748306i | \(0.269132\pi\) | |||||||
\(728\) | −56.4566 | −2.09242 | ||||||||
\(729\) | 29.9977 | 1.11103 | ||||||||
\(730\) | 2.62741 | 0.0972447 | ||||||||
\(731\) | 0.479864 | 0.0177484 | ||||||||
\(732\) | 0.453404 | 0.0167583 | ||||||||
\(733\) | 37.8471 | 1.39791 | 0.698957 | − | 0.715164i | \(-0.253648\pi\) | ||||
0.698957 | + | 0.715164i | \(0.253648\pi\) | |||||||
\(734\) | 14.0307 | 0.517881 | ||||||||
\(735\) | −14.4676 | −0.533646 | ||||||||
\(736\) | −4.56373 | −0.168221 | ||||||||
\(737\) | 8.74301 | 0.322053 | ||||||||
\(738\) | −4.71001 | −0.173378 | ||||||||
\(739\) | 7.54675 | 0.277612 | 0.138806 | − | 0.990320i | \(-0.455674\pi\) | ||||
0.138806 | + | 0.990320i | \(0.455674\pi\) | |||||||
\(740\) | 1.22287 | 0.0449537 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0218 | 0.551467 | ||||||||
\(743\) | −9.17584 | −0.336629 | −0.168314 | − | 0.985733i | \(-0.553832\pi\) | ||||
−0.168314 | + | 0.985733i | \(0.553832\pi\) | |||||||
\(744\) | −26.6843 | −0.978294 | ||||||||
\(745\) | −18.1856 | −0.666268 | ||||||||
\(746\) | −19.0686 | −0.698151 | ||||||||
\(747\) | −9.90784 | −0.362509 | ||||||||
\(748\) | 0.0228945 | 0.000837105 0 | ||||||||
\(749\) | 23.2257 | 0.848648 | ||||||||
\(750\) | 2.20860 | 0.0806468 | ||||||||
\(751\) | 10.4714 | 0.382105 | 0.191053 | − | 0.981580i | \(-0.438810\pi\) | ||||
0.191053 | + | 0.981580i | \(0.438810\pi\) | |||||||
\(752\) | −49.1597 | −1.79267 | ||||||||
\(753\) | 11.7656 | 0.428762 | ||||||||
\(754\) | 30.3694 | 1.10599 | ||||||||
\(755\) | 2.29340 | 0.0834653 | ||||||||
\(756\) | −3.16394 | −0.115071 | ||||||||
\(757\) | −53.0755 | −1.92906 | −0.964532 | − | 0.263967i | \(-0.914969\pi\) | ||||
−0.964532 | + | 0.263967i | \(0.914969\pi\) | |||||||
\(758\) | −14.5338 | −0.527892 | ||||||||
\(759\) | 5.47919 | 0.198882 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6886 | −0.604960 | −0.302480 | − | 0.953156i | \(-0.597815\pi\) | ||||
−0.302480 | + | 0.953156i | \(0.597815\pi\) | |||||||
\(762\) | −40.8518 | −1.47990 | ||||||||
\(763\) | −27.4157 | −0.992514 | ||||||||
\(764\) | −0.0198961 | −0.000719816 0 | ||||||||
\(765\) | −0.191556 | −0.00692570 | ||||||||
\(766\) | 26.3632 | 0.952541 | ||||||||
\(767\) | −4.53529 | −0.163760 | ||||||||
\(768\) | 4.99138 | 0.180111 | ||||||||
\(769\) | −6.17780 | −0.222777 | −0.111389 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111389 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(770\) | −3.69754 | −0.133250 | ||||||||
\(771\) | 30.4445 | 1.09643 | ||||||||
\(772\) | 0.285150 | 0.0102628 | ||||||||
\(773\) | 28.1558 | 1.01270 | 0.506348 | − | 0.862330i | \(-0.330995\pi\) | ||||
0.506348 | + | 0.862330i | \(0.330995\pi\) | |||||||
\(774\) | −1.89283 | −0.0680363 | ||||||||
\(775\) | −6.48991 | −0.233125 | ||||||||
\(776\) | −28.3733 | −1.01854 | ||||||||
\(777\) | −54.3593 | −1.95013 | ||||||||
\(778\) | −35.6088 | −1.27664 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.06425 | 0.0381061 | ||||||||
\(781\) | 1.02260 | 0.0365914 | ||||||||
\(782\) | −2.27641 | −0.0814044 | ||||||||
\(783\) | −22.9025 | −0.818470 | ||||||||
\(784\) | −40.7828 | −1.45653 | ||||||||
\(785\) | 20.8445 | 0.743973 | ||||||||
\(786\) | 43.2542 | 1.54283 | ||||||||
\(787\) | 5.46867 | 0.194937 | 0.0974685 | − | 0.995239i | \(-0.468925\pi\) | ||||
0.0974685 | + | 0.995239i | \(0.468925\pi\) | |||||||
\(788\) | 2.52457 | 0.0899339 | ||||||||
\(789\) | 16.1393 | 0.574576 | ||||||||
\(790\) | 7.52572 | 0.267753 | ||||||||
\(791\) | −19.4986 | −0.693290 | ||||||||
\(792\) | 1.21523 | 0.0431813 | ||||||||
\(793\) | −11.0520 | −0.392467 | ||||||||
\(794\) | 29.2050 | 1.03645 | ||||||||
\(795\) | 3.81051 | 0.135145 | ||||||||
\(796\) | 1.10718 | 0.0392429 | ||||||||
\(797\) | −47.2273 | −1.67288 | −0.836439 | − | 0.548061i | \(-0.815366\pi\) | ||||
−0.836439 | + | 0.548061i | \(0.815366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.07694 | −0.108854 | ||||||||
\(800\) | 0.781227 | 0.0276206 | ||||||||
\(801\) | 0.000537135 0 | 1.89787e−5 0 | ||||||||
\(802\) | 23.9873 | 0.847021 | ||||||||
\(803\) | −1.11579 | −0.0393755 | ||||||||
\(804\) | −2.94177 | −0.103748 | ||||||||
\(805\) | 23.7859 | 0.838345 | ||||||||
\(806\) | −48.3366 | −1.70258 | ||||||||
\(807\) | −36.1367 | −1.27207 | ||||||||
\(808\) | −33.2659 | −1.17029 | ||||||||
\(809\) | −6.13382 | −0.215654 | −0.107827 | − | 0.994170i | \(-0.534389\pi\) | ||||
−0.107827 | + | 0.994170i | \(0.534389\pi\) | |||||||
\(810\) | −9.25174 | −0.325073 | ||||||||
\(811\) | 26.9998 | 0.948093 | 0.474046 | − | 0.880500i | \(-0.342793\pi\) | ||||
0.474046 | + | 0.880500i | \(0.342793\pi\) | |||||||
\(812\) | 2.29690 | 0.0806054 | ||||||||
\(813\) | 39.2241 | 1.37565 | ||||||||
\(814\) | −8.02696 | −0.281345 | ||||||||
\(815\) | 7.91691 | 0.277317 | ||||||||
\(816\) | 1.71360 | 0.0599880 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −12.1855 | −0.426055 | ||||||||
\(819\) | 14.9074 | 0.520906 | ||||||||
\(820\) | 0.619903 | 0.0216480 | ||||||||
\(821\) | −45.2474 | −1.57914 | −0.789572 | − | 0.613658i | \(-0.789697\pi\) | ||||
−0.789572 | + | 0.613658i | \(0.789697\pi\) | |||||||
\(822\) | 5.20494 | 0.181543 | ||||||||
\(823\) | 30.1438 | 1.05075 | 0.525373 | − | 0.850872i | \(-0.323926\pi\) | ||||
0.525373 | + | 0.850872i | \(0.323926\pi\) | |||||||
\(824\) | −21.2442 | −0.740076 | ||||||||
\(825\) | −0.937939 | −0.0326548 | ||||||||
\(826\) | −5.30181 | −0.184473 | ||||||||
\(827\) | −20.4710 | −0.711846 | −0.355923 | − | 0.934515i | \(-0.615833\pi\) | ||||
−0.355923 | + | 0.934515i | \(0.615833\pi\) | |||||||
\(828\) | 0.580941 | 0.0201891 | ||||||||
\(829\) | −20.9207 | −0.726606 | −0.363303 | − | 0.931671i | \(-0.618351\pi\) | ||||
−0.363303 | + | 0.931671i | \(0.618351\pi\) | |||||||
\(830\) | 20.1555 | 0.699607 | ||||||||
\(831\) | −2.76954 | −0.0960743 | ||||||||
\(832\) | −37.5513 | −1.30186 | ||||||||
\(833\) | −2.55263 | −0.0884433 | ||||||||
\(834\) | −8.46006 | −0.292948 | ||||||||
\(835\) | −14.0935 | −0.487725 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.4522 | 1.25997 | ||||||||
\(838\) | 17.0436 | 0.588761 | ||||||||
\(839\) | 4.24739 | 0.146636 | 0.0733180 | − | 0.997309i | \(-0.476641\pi\) | ||||
0.0733180 | + | 0.997309i | \(0.476641\pi\) | |||||||
\(840\) | −16.7415 | −0.577638 | ||||||||
\(841\) | −12.3736 | −0.426677 | ||||||||
\(842\) | −30.9887 | −1.06794 | ||||||||
\(843\) | −20.6684 | −0.711856 | ||||||||
\(844\) | −1.94829 | −0.0670630 | ||||||||
\(845\) | −12.9416 | −0.445204 | ||||||||
\(846\) | 12.1370 | 0.417280 | ||||||||
\(847\) | −43.2187 | −1.48501 | ||||||||
\(848\) | 10.7415 | 0.368864 | ||||||||
\(849\) | 15.9136 | 0.546152 | ||||||||
\(850\) | 0.389681 | 0.0133659 | ||||||||
\(851\) | 51.6367 | 1.77008 | ||||||||
\(852\) | −0.344075 | −0.0117878 | ||||||||
\(853\) | −1.66945 | −0.0571610 | −0.0285805 | − | 0.999591i | \(-0.509099\pi\) | ||||
−0.0285805 | + | 0.999591i | \(0.509099\pi\) | |||||||
\(854\) | −12.9199 | −0.442110 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.5284 | 0.530751 | ||||||||
\(857\) | 0.856668 | 0.0292632 | 0.0146316 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146316 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(858\) | −6.98573 | −0.238489 | ||||||||
\(859\) | −53.1009 | −1.81178 | −0.905889 | − | 0.423515i | \(-0.860796\pi\) | ||||
−0.905889 | + | 0.423515i | \(0.860796\pi\) | |||||||
\(860\) | 0.249122 | 0.00849500 | ||||||||
\(861\) | −27.5560 | −0.939106 | ||||||||
\(862\) | −0.573611 | −0.0195373 | ||||||||
\(863\) | 29.5608 | 1.00626 | 0.503130 | − | 0.864211i | \(-0.332182\pi\) | ||||
0.503130 | + | 0.864211i | \(0.332182\pi\) | |||||||
\(864\) | −4.38796 | −0.149281 | ||||||||
\(865\) | 10.5128 | 0.357446 | ||||||||
\(866\) | −18.9678 | −0.644553 | ||||||||
\(867\) | −25.5688 | −0.868361 | ||||||||
\(868\) | −3.65580 | −0.124086 | ||||||||
\(869\) | −3.19598 | −0.108416 | ||||||||
\(870\) | 9.00569 | 0.305321 | ||||||||
\(871\) | 71.7073 | 2.42971 | ||||||||
\(872\) | −18.3298 | −0.620727 | ||||||||
\(873\) | 7.49198 | 0.253565 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.07172 | −0.137649 | ||||||||
\(876\) | 0.375433 | 0.0126847 | ||||||||
\(877\) | 8.79077 | 0.296843 | 0.148422 | − | 0.988924i | \(-0.452581\pi\) | ||||
0.148422 | + | 0.988924i | \(0.452581\pi\) | |||||||
\(878\) | 7.96665 | 0.268861 | ||||||||
\(879\) | 36.1039 | 1.21776 | ||||||||
\(880\) | −2.64396 | −0.0891280 | ||||||||
\(881\) | 27.2670 | 0.918647 | 0.459324 | − | 0.888269i | \(-0.348092\pi\) | ||||
0.459324 | + | 0.888269i | \(0.348092\pi\) | |||||||
\(882\) | 10.0689 | 0.339037 | ||||||||
\(883\) | −8.65079 | −0.291122 | −0.145561 | − | 0.989349i | \(-0.546499\pi\) | ||||
−0.145561 | + | 0.989349i | \(0.546499\pi\) | |||||||
\(884\) | 0.187773 | 0.00631549 | ||||||||
\(885\) | −1.34489 | −0.0452079 | ||||||||
\(886\) | −36.1814 | −1.21554 | ||||||||
\(887\) | 39.6495 | 1.33130 | 0.665651 | − | 0.746263i | \(-0.268154\pi\) | ||||
0.665651 | + | 0.746263i | \(0.268154\pi\) | |||||||
\(888\) | −36.3441 | −1.21963 | ||||||||
\(889\) | 75.3133 | 2.52593 | ||||||||
\(890\) | −0.00109269 | −3.66271e−5 0 | ||||||||
\(891\) | 3.92898 | 0.131626 | ||||||||
\(892\) | 0.678737 | 0.0227258 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −40.1648 | −1.34331 | ||||||||
\(895\) | −5.00329 | −0.167242 | ||||||||
\(896\) | −50.2598 | −1.67906 | ||||||||
\(897\) | 44.9386 | 1.50046 | ||||||||
\(898\) | −50.5401 | −1.68655 | ||||||||
\(899\) | −26.4629 | −0.882587 | ||||||||
\(900\) | −0.0994465 | −0.00331488 | ||||||||
\(901\) | 0.672317 | 0.0223981 | ||||||||
\(902\) | −4.06905 | −0.135485 | ||||||||
\(903\) | −11.0740 | −0.368520 | ||||||||
\(904\) | −13.0366 | −0.433589 | ||||||||
\(905\) | 26.4916 | 0.880611 | ||||||||
\(906\) | 5.06521 | 0.168280 | ||||||||
\(907\) | −33.3774 | −1.10828 | −0.554139 | − | 0.832424i | \(-0.686952\pi\) | ||||
−0.554139 | + | 0.832424i | \(0.686952\pi\) | |||||||
\(908\) | 0.366956 | 0.0121779 | ||||||||
\(909\) | 8.78388 | 0.291343 | ||||||||
\(910\) | −30.3260 | −1.00530 | ||||||||
\(911\) | −46.3977 | −1.53722 | −0.768611 | − | 0.639716i | \(-0.779052\pi\) | ||||
−0.768611 | + | 0.639716i | \(0.779052\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.55953 | −0.283279 | ||||||||
\(914\) | 17.0249 | 0.563134 | ||||||||
\(915\) | −3.27733 | −0.108345 | ||||||||
\(916\) | −3.20092 | −0.105761 | ||||||||
\(917\) | −79.7424 | −2.63333 | ||||||||
\(918\) | −2.18874 | −0.0722392 | ||||||||
\(919\) | 8.51995 | 0.281047 | 0.140524 | − | 0.990077i | \(-0.455121\pi\) | ||||
0.140524 | + | 0.990077i | \(0.455121\pi\) | |||||||
\(920\) | 15.9030 | 0.524308 | ||||||||
\(921\) | 23.6652 | 0.779795 | ||||||||
\(922\) | −4.37191 | −0.143981 | ||||||||
\(923\) | 8.38701 | 0.276062 | ||||||||
\(924\) | −0.528345 | −0.0173813 | ||||||||
\(925\) | −8.83927 | −0.290634 | ||||||||
\(926\) | 12.4108 | 0.407845 | ||||||||
\(927\) | 5.60953 | 0.184241 | ||||||||
\(928\) | 3.18549 | 0.104569 | ||||||||
\(929\) | −47.1584 | −1.54722 | −0.773608 | − | 0.633665i | \(-0.781550\pi\) | ||||
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(930\) | −14.3337 | −0.470019 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.99954 | −0.131009 | ||||||||
\(933\) | −5.30452 | −0.173662 | ||||||||
\(934\) | −26.2195 | −0.857929 | ||||||||
\(935\) | −0.165488 | −0.00541203 | ||||||||
\(936\) | 9.96691 | 0.325779 | ||||||||
\(937\) | −29.5004 | −0.963735 | −0.481867 | − | 0.876244i | \(-0.660041\pi\) | ||||
−0.481867 | + | 0.876244i | \(0.660041\pi\) | |||||||
\(938\) | 83.8267 | 2.73704 | ||||||||
\(939\) | 1.77176 | 0.0578192 | ||||||||
\(940\) | −1.59740 | −0.0521015 | ||||||||
\(941\) | −9.49895 | −0.309657 | −0.154829 | − | 0.987941i | \(-0.549483\pi\) | ||||
−0.154829 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(942\) | 46.0373 | 1.49998 | ||||||||
\(943\) | 26.1759 | 0.852403 | ||||||||
\(944\) | −3.79111 | −0.123390 | ||||||||
\(945\) | 22.8699 | 0.743957 | ||||||||
\(946\) | −1.63524 | −0.0531663 | ||||||||
\(947\) | −9.85963 | −0.320395 | −0.160198 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160198 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(948\) | 1.07536 | 0.0349260 | ||||||||
\(949\) | −9.15138 | −0.297066 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.98099 | −0.0642381 | ||||||||
\(952\) | −2.95384 | −0.0957344 | ||||||||
\(953\) | 53.6746 | 1.73869 | 0.869346 | − | 0.494204i | \(-0.164540\pi\) | ||||
0.869346 | + | 0.494204i | \(0.164540\pi\) | |||||||
\(954\) | −2.65196 | −0.0858605 | ||||||||
\(955\) | 0.143815 | 0.00465373 | ||||||||
\(956\) | −2.87030 | −0.0928320 | ||||||||
\(957\) | −3.82449 | −0.123628 | ||||||||
\(958\) | −4.95657 | −0.160139 | ||||||||
\(959\) | −9.59569 | −0.309861 | ||||||||
\(960\) | −11.1354 | −0.359394 | ||||||||
\(961\) | 11.1190 | 0.358676 | ||||||||
\(962\) | −65.8345 | −2.12259 | ||||||||
\(963\) | −4.10029 | −0.132130 | ||||||||
\(964\) | 0.857382 | 0.0276144 | ||||||||
\(965\) | −2.06115 | −0.0663507 | ||||||||
\(966\) | 52.5338 | 1.69025 | ||||||||
\(967\) | 34.2375 | 1.10100 | 0.550502 | − | 0.834834i | \(-0.314436\pi\) | ||||
0.550502 | + | 0.834834i | \(0.314436\pi\) | |||||||
\(968\) | −28.8956 | −0.928739 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.2409 | −0.489356 | ||||||||
\(971\) | 14.1698 | 0.454730 | 0.227365 | − | 0.973810i | \(-0.426989\pi\) | ||||
0.227365 | + | 0.973810i | \(0.426989\pi\) | |||||||
\(972\) | 1.00916 | 0.0323690 | ||||||||
\(973\) | 15.5967 | 0.500009 | ||||||||
\(974\) | 16.3222 | 0.522998 | ||||||||
\(975\) | −7.69267 | −0.246363 | ||||||||
\(976\) | −9.23850 | −0.295717 | ||||||||
\(977\) | 45.6175 | 1.45943 | 0.729717 | − | 0.683749i | \(-0.239652\pi\) | ||||
0.729717 | + | 0.683749i | \(0.239652\pi\) | |||||||
\(978\) | 17.4853 | 0.559119 | ||||||||
\(979\) | 0.000464039 0 | 1.48308e−5 0 | ||||||||
\(980\) | −1.32520 | −0.0423321 | ||||||||
\(981\) | 4.84000 | 0.154529 | ||||||||
\(982\) | −33.6082 | −1.07248 | ||||||||
\(983\) | 20.1860 | 0.643832 | 0.321916 | − | 0.946768i | \(-0.395673\pi\) | ||||
0.321916 | + | 0.946768i | \(0.395673\pi\) | |||||||
\(984\) | −18.4237 | −0.587325 | ||||||||
\(985\) | −18.2483 | −0.581438 | ||||||||
\(986\) | 1.58894 | 0.0506022 | ||||||||
\(987\) | 71.0079 | 2.26021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.5194 | 0.334496 | ||||||||
\(990\) | 0.652768 | 0.0207463 | ||||||||
\(991\) | −11.0566 | −0.351226 | −0.175613 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175613 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(992\) | −5.07010 | −0.160976 | ||||||||
\(993\) | −19.2191 | −0.609900 | ||||||||
\(994\) | 9.80452 | 0.310981 | ||||||||
\(995\) | −8.00301 | −0.253712 | ||||||||
\(996\) | 2.88004 | 0.0912576 | ||||||||
\(997\) | 31.2270 | 0.988969 | 0.494485 | − | 0.869186i | \(-0.335357\pi\) | ||||
0.494485 | + | 0.869186i | \(0.335357\pi\) | |||||||
\(998\) | −1.43413 | −0.0453967 | ||||||||
\(999\) | 49.6480 | 1.57079 |
(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 | 1805.2.a.t.1.3 | 9 | ||
5.4 | even | 2 | 9025.2.a.ce.1.7 | 9 | |||
19.6 | even | 9 | 95.2.k.b.36.1 | ✓ | 18 | ||
19.16 | even | 9 | 95.2.k.b.66.1 | yes | 18 | ||
19.18 | odd | 2 | 1805.2.a.u.1.7 | 9 | |||
57.35 | odd | 18 | 855.2.bs.b.541.3 | 18 | |||
57.44 | odd | 18 | 855.2.bs.b.226.3 | 18 | |||
95.44 | even | 18 | 475.2.l.b.226.3 | 18 | |||
95.54 | even | 18 | 475.2.l.b.351.3 | 18 | |||
95.63 | odd | 36 | 475.2.u.c.74.5 | 36 | |||
95.73 | odd | 36 | 475.2.u.c.199.2 | 36 | |||
95.82 | odd | 36 | 475.2.u.c.74.2 | 36 | |||
95.92 | odd | 36 | 475.2.u.c.199.5 | 36 | |||
95.94 | odd | 2 | 9025.2.a.cd.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.36.1 | ✓ | 18 | 19.6 | even | 9 | ||
95.2.k.b.66.1 | yes | 18 | 19.16 | even | 9 | ||
475.2.l.b.226.3 | 18 | 95.44 | even | 18 | |||
475.2.l.b.351.3 | 18 | 95.54 | even | 18 | |||
475.2.u.c.74.2 | 36 | 95.82 | odd | 36 | |||
475.2.u.c.74.5 | 36 | 95.63 | odd | 36 | |||
475.2.u.c.199.2 | 36 | 95.73 | odd | 36 | |||
475.2.u.c.199.5 | 36 | 95.92 | odd | 36 | |||
855.2.bs.b.226.3 | 18 | 57.44 | odd | 18 | |||
855.2.bs.b.541.3 | 18 | 57.35 | odd | 18 | |||
1805.2.a.t.1.3 | 9 | 1.1 | even | 1 | trivial | ||
1805.2.a.u.1.7 | 9 | 19.18 | odd | 2 | |||
9025.2.a.cd.1.3 | 9 | 95.94 | odd | 2 | |||
9025.2.a.ce.1.7 | 9 | 5.4 | even | 2 |