Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} + \cdots + 281 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-2.61511\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61511 | 1.84916 | 0.924581 | − | 0.380986i | \(-0.124415\pi\) | ||||
0.924581 | + | 0.380986i | \(0.124415\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.83880 | 2.41940 | ||||||||
\(5\) | 4.09685 | 1.83217 | 0.916083 | − | 0.400988i | \(-0.131333\pi\) | ||||
0.916083 | + | 0.400988i | \(0.131333\pi\) | |||||||
\(6\) | 2.61511 | 1.06761 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 7.42376 | 2.62470 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 10.7137 | 3.38797 | ||||||||
\(11\) | −5.70245 | −1.71935 | −0.859677 | − | 0.510838i | \(-0.829335\pi\) | ||||
−0.859677 | + | 0.510838i | \(0.829335\pi\) | |||||||
\(12\) | 4.83880 | 1.39684 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.61511 | 0.698917 | ||||||||
\(15\) | 4.09685 | 1.05780 | ||||||||
\(16\) | 9.73635 | 2.43409 | ||||||||
\(17\) | −4.37843 | −1.06192 | −0.530962 | − | 0.847395i | \(-0.678169\pi\) | ||||
−0.530962 | + | 0.847395i | \(0.678169\pi\) | |||||||
\(18\) | 2.61511 | 0.616387 | ||||||||
\(19\) | −3.61201 | −0.828652 | −0.414326 | − | 0.910128i | \(-0.635983\pi\) | ||||
−0.414326 | + | 0.910128i | \(0.635983\pi\) | |||||||
\(20\) | 19.8238 | 4.43274 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −14.9125 | −3.17936 | ||||||||
\(23\) | 1.52889 | 0.318796 | 0.159398 | − | 0.987214i | \(-0.449045\pi\) | ||||
0.159398 | + | 0.987214i | \(0.449045\pi\) | |||||||
\(24\) | 7.42376 | 1.51537 | ||||||||
\(25\) | 11.7842 | 2.35683 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.83880 | 0.914446 | ||||||||
\(29\) | −8.65363 | −1.60694 | −0.803470 | − | 0.595346i | \(-0.797015\pi\) | ||||
−0.803470 | + | 0.595346i | \(0.797015\pi\) | |||||||
\(30\) | 10.7137 | 1.95605 | ||||||||
\(31\) | 2.53755 | 0.455758 | 0.227879 | − | 0.973689i | \(-0.426821\pi\) | ||||
0.227879 | + | 0.973689i | \(0.426821\pi\) | |||||||
\(32\) | 10.6141 | 1.87633 | ||||||||
\(33\) | −5.70245 | −0.992669 | ||||||||
\(34\) | −11.4501 | −1.96367 | ||||||||
\(35\) | 4.09685 | 0.692494 | ||||||||
\(36\) | 4.83880 | 0.806466 | ||||||||
\(37\) | −0.399662 | −0.0657040 | −0.0328520 | − | 0.999460i | \(-0.510459\pi\) | ||||
−0.0328520 | + | 0.999460i | \(0.510459\pi\) | |||||||
\(38\) | −9.44580 | −1.53231 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 30.4140 | 4.80888 | ||||||||
\(41\) | −3.49412 | −0.545689 | −0.272845 | − | 0.962058i | \(-0.587965\pi\) | ||||
−0.272845 | + | 0.962058i | \(0.587965\pi\) | |||||||
\(42\) | 2.61511 | 0.403520 | ||||||||
\(43\) | 10.0663 | 1.53510 | 0.767552 | − | 0.640987i | \(-0.221475\pi\) | ||||
0.767552 | + | 0.640987i | \(0.221475\pi\) | |||||||
\(44\) | −27.5930 | −4.15980 | ||||||||
\(45\) | 4.09685 | 0.610722 | ||||||||
\(46\) | 3.99822 | 0.589505 | ||||||||
\(47\) | −2.38790 | −0.348311 | −0.174156 | − | 0.984718i | \(-0.555720\pi\) | ||||
−0.174156 | + | 0.984718i | \(0.555720\pi\) | |||||||
\(48\) | 9.73635 | 1.40532 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 30.8169 | 4.35817 | ||||||||
\(51\) | −4.37843 | −0.613102 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.72536 | −0.649078 | −0.324539 | − | 0.945872i | \(-0.605209\pi\) | ||||
−0.324539 | + | 0.945872i | \(0.605209\pi\) | |||||||
\(54\) | 2.61511 | 0.355871 | ||||||||
\(55\) | −23.3621 | −3.15014 | ||||||||
\(56\) | 7.42376 | 0.992042 | ||||||||
\(57\) | −3.61201 | −0.478423 | ||||||||
\(58\) | −22.6302 | −2.97149 | ||||||||
\(59\) | 3.98709 | 0.519074 | 0.259537 | − | 0.965733i | \(-0.416430\pi\) | ||||
0.259537 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(60\) | 19.8238 | 2.55924 | ||||||||
\(61\) | −1.11129 | −0.142287 | −0.0711433 | − | 0.997466i | \(-0.522665\pi\) | ||||
−0.0711433 | + | 0.997466i | \(0.522665\pi\) | |||||||
\(62\) | 6.63598 | 0.842770 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.28433 | 1.03554 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.9125 | −1.83561 | ||||||||
\(67\) | 8.84355 | 1.08041 | 0.540206 | − | 0.841533i | \(-0.318346\pi\) | ||||
0.540206 | + | 0.841533i | \(0.318346\pi\) | |||||||
\(68\) | −21.1863 | −2.56922 | ||||||||
\(69\) | 1.52889 | 0.184057 | ||||||||
\(70\) | 10.7137 | 1.28053 | ||||||||
\(71\) | 4.15260 | 0.492823 | 0.246411 | − | 0.969165i | \(-0.420749\pi\) | ||||
0.246411 | + | 0.969165i | \(0.420749\pi\) | |||||||
\(72\) | 7.42376 | 0.874899 | ||||||||
\(73\) | 6.08083 | 0.711707 | 0.355854 | − | 0.934542i | \(-0.384190\pi\) | ||||
0.355854 | + | 0.934542i | \(0.384190\pi\) | |||||||
\(74\) | −1.04516 | −0.121497 | ||||||||
\(75\) | 11.7842 | 1.36072 | ||||||||
\(76\) | −17.4778 | −2.00484 | ||||||||
\(77\) | −5.70245 | −0.649855 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.225699 | −0.0253931 | −0.0126965 | − | 0.999919i | \(-0.504042\pi\) | ||||
−0.0126965 | + | 0.999919i | \(0.504042\pi\) | |||||||
\(80\) | 39.8884 | 4.45965 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.13750 | −1.00907 | ||||||||
\(83\) | −9.32245 | −1.02327 | −0.511636 | − | 0.859202i | \(-0.670960\pi\) | ||||
−0.511636 | + | 0.859202i | \(0.670960\pi\) | |||||||
\(84\) | 4.83880 | 0.527956 | ||||||||
\(85\) | −17.9378 | −1.94562 | ||||||||
\(86\) | 26.3246 | 2.83865 | ||||||||
\(87\) | −8.65363 | −0.927767 | ||||||||
\(88\) | −42.3336 | −4.51278 | ||||||||
\(89\) | −9.60970 | −1.01863 | −0.509313 | − | 0.860581i | \(-0.670101\pi\) | ||||
−0.509313 | + | 0.860581i | \(0.670101\pi\) | |||||||
\(90\) | 10.7137 | 1.12932 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.39799 | 0.771294 | ||||||||
\(93\) | 2.53755 | 0.263132 | ||||||||
\(94\) | −6.24463 | −0.644084 | ||||||||
\(95\) | −14.7979 | −1.51823 | ||||||||
\(96\) | 10.6141 | 1.08330 | ||||||||
\(97\) | 14.1480 | 1.43651 | 0.718254 | − | 0.695781i | \(-0.244942\pi\) | ||||
0.718254 | + | 0.695781i | \(0.244942\pi\) | |||||||
\(98\) | 2.61511 | 0.264166 | ||||||||
\(99\) | −5.70245 | −0.573118 | ||||||||
\(100\) | 57.0212 | 5.70212 | ||||||||
\(101\) | −10.1307 | −1.00804 | −0.504022 | − | 0.863691i | \(-0.668147\pi\) | ||||
−0.504022 | + | 0.863691i | \(0.668147\pi\) | |||||||
\(102\) | −11.4501 | −1.13373 | ||||||||
\(103\) | 1.94213 | 0.191363 | 0.0956817 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956817 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.09685 | 0.399811 | ||||||||
\(106\) | −12.3573 | −1.20025 | ||||||||
\(107\) | −4.11614 | −0.397922 | −0.198961 | − | 0.980007i | \(-0.563757\pi\) | ||||
−0.198961 | + | 0.980007i | \(0.563757\pi\) | |||||||
\(108\) | 4.83880 | 0.465613 | ||||||||
\(109\) | −6.52500 | −0.624981 | −0.312491 | − | 0.949921i | \(-0.601163\pi\) | ||||
−0.312491 | + | 0.949921i | \(0.601163\pi\) | |||||||
\(110\) | −61.0944 | −5.82512 | ||||||||
\(111\) | −0.399662 | −0.0379342 | ||||||||
\(112\) | 9.73635 | 0.919999 | ||||||||
\(113\) | 0.829620 | 0.0780440 | 0.0390220 | − | 0.999238i | \(-0.487576\pi\) | ||||
0.0390220 | + | 0.999238i | \(0.487576\pi\) | |||||||
\(114\) | −9.44580 | −0.884681 | ||||||||
\(115\) | 6.26363 | 0.584087 | ||||||||
\(116\) | −41.8732 | −3.88782 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4267 | 0.959852 | ||||||||
\(119\) | −4.37843 | −0.401370 | ||||||||
\(120\) | 30.4140 | 2.77641 | ||||||||
\(121\) | 21.5180 | 1.95618 | ||||||||
\(122\) | −2.90616 | −0.263111 | ||||||||
\(123\) | −3.49412 | −0.315054 | ||||||||
\(124\) | 12.2787 | 1.10266 | ||||||||
\(125\) | 27.7937 | 2.48594 | ||||||||
\(126\) | 2.61511 | 0.232972 | ||||||||
\(127\) | −11.8157 | −1.04848 | −0.524239 | − | 0.851571i | \(-0.675650\pi\) | ||||
−0.524239 | + | 0.851571i | \(0.675650\pi\) | |||||||
\(128\) | 0.436221 | 0.0385569 | ||||||||
\(129\) | 10.0663 | 0.886292 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9488 | 1.39345 | 0.696726 | − | 0.717338i | \(-0.254640\pi\) | ||||
0.696726 | + | 0.717338i | \(0.254640\pi\) | |||||||
\(132\) | −27.5930 | −2.40166 | ||||||||
\(133\) | −3.61201 | −0.313201 | ||||||||
\(134\) | 23.1268 | 1.99785 | ||||||||
\(135\) | 4.09685 | 0.352601 | ||||||||
\(136\) | −32.5044 | −2.78723 | ||||||||
\(137\) | −13.2254 | −1.12992 | −0.564962 | − | 0.825117i | \(-0.691109\pi\) | ||||
−0.564962 | + | 0.825117i | \(0.691109\pi\) | |||||||
\(138\) | 3.99822 | 0.340351 | ||||||||
\(139\) | −3.88051 | −0.329141 | −0.164570 | − | 0.986365i | \(-0.552624\pi\) | ||||
−0.164570 | + | 0.986365i | \(0.552624\pi\) | |||||||
\(140\) | 19.8238 | 1.67542 | ||||||||
\(141\) | −2.38790 | −0.201098 | ||||||||
\(142\) | 10.8595 | 0.911308 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.73635 | 0.811363 | ||||||||
\(145\) | −35.4526 | −2.94418 | ||||||||
\(146\) | 15.9020 | 1.31606 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −1.93388 | −0.158964 | ||||||||
\(149\) | −16.8716 | −1.38218 | −0.691089 | − | 0.722769i | \(-0.742869\pi\) | ||||
−0.691089 | + | 0.722769i | \(0.742869\pi\) | |||||||
\(150\) | 30.8169 | 2.51619 | ||||||||
\(151\) | −19.7463 | −1.60693 | −0.803467 | − | 0.595349i | \(-0.797014\pi\) | ||||
−0.803467 | + | 0.595349i | \(0.797014\pi\) | |||||||
\(152\) | −26.8147 | −2.17496 | ||||||||
\(153\) | −4.37843 | −0.353975 | ||||||||
\(154\) | −14.9125 | −1.20169 | ||||||||
\(155\) | 10.3960 | 0.835024 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9869 | 1.43551 | 0.717756 | − | 0.696294i | \(-0.245169\pi\) | ||||
0.717756 | + | 0.696294i | \(0.245169\pi\) | |||||||
\(158\) | −0.590227 | −0.0469559 | ||||||||
\(159\) | −4.72536 | −0.374746 | ||||||||
\(160\) | 43.4844 | 3.43774 | ||||||||
\(161\) | 1.52889 | 0.120493 | ||||||||
\(162\) | 2.61511 | 0.205462 | ||||||||
\(163\) | −2.92694 | −0.229256 | −0.114628 | − | 0.993408i | \(-0.536568\pi\) | ||||
−0.114628 | + | 0.993408i | \(0.536568\pi\) | |||||||
\(164\) | −16.9073 | −1.32024 | ||||||||
\(165\) | −23.3621 | −1.81874 | ||||||||
\(166\) | −24.3792 | −1.89220 | ||||||||
\(167\) | 15.6431 | 1.21050 | 0.605250 | − | 0.796036i | \(-0.293073\pi\) | ||||
0.605250 | + | 0.796036i | \(0.293073\pi\) | |||||||
\(168\) | 7.42376 | 0.572756 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −46.9092 | −3.59777 | ||||||||
\(171\) | −3.61201 | −0.276217 | ||||||||
\(172\) | 48.7090 | 3.71403 | ||||||||
\(173\) | −21.5961 | −1.64192 | −0.820959 | − | 0.570986i | \(-0.806561\pi\) | ||||
−0.820959 | + | 0.570986i | \(0.806561\pi\) | |||||||
\(174\) | −22.6302 | −1.71559 | ||||||||
\(175\) | 11.7842 | 0.890799 | ||||||||
\(176\) | −55.5211 | −4.18506 | ||||||||
\(177\) | 3.98709 | 0.299688 | ||||||||
\(178\) | −25.1304 | −1.88360 | ||||||||
\(179\) | 3.42054 | 0.255663 | 0.127831 | − | 0.991796i | \(-0.459198\pi\) | ||||
0.127831 | + | 0.991796i | \(0.459198\pi\) | |||||||
\(180\) | 19.8238 | 1.47758 | ||||||||
\(181\) | 11.5344 | 0.857346 | 0.428673 | − | 0.903460i | \(-0.358981\pi\) | ||||
0.428673 | + | 0.903460i | \(0.358981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.11129 | −0.0821493 | ||||||||
\(184\) | 11.3501 | 0.836742 | ||||||||
\(185\) | −1.63736 | −0.120381 | ||||||||
\(186\) | 6.63598 | 0.486574 | ||||||||
\(187\) | 24.9678 | 1.82582 | ||||||||
\(188\) | −11.5546 | −0.842704 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −38.6980 | −2.80745 | ||||||||
\(191\) | 5.79542 | 0.419342 | 0.209671 | − | 0.977772i | \(-0.432761\pi\) | ||||
0.209671 | + | 0.977772i | \(0.432761\pi\) | |||||||
\(192\) | 8.28433 | 0.597870 | ||||||||
\(193\) | 15.8937 | 1.14405 | 0.572026 | − | 0.820236i | \(-0.306158\pi\) | ||||
0.572026 | + | 0.820236i | \(0.306158\pi\) | |||||||
\(194\) | 36.9985 | 2.65634 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.83880 | 0.345628 | ||||||||
\(197\) | 1.57741 | 0.112386 | 0.0561929 | − | 0.998420i | \(-0.482104\pi\) | ||||
0.0561929 | + | 0.998420i | \(0.482104\pi\) | |||||||
\(198\) | −14.9125 | −1.05979 | ||||||||
\(199\) | 4.31559 | 0.305924 | 0.152962 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152962 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(200\) | 87.4828 | 6.18597 | ||||||||
\(201\) | 8.84355 | 0.623776 | ||||||||
\(202\) | −26.4929 | −1.86404 | ||||||||
\(203\) | −8.65363 | −0.607366 | ||||||||
\(204\) | −21.1863 | −1.48334 | ||||||||
\(205\) | −14.3149 | −0.999794 | ||||||||
\(206\) | 5.07887 | 0.353862 | ||||||||
\(207\) | 1.52889 | 0.106265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.5973 | 1.42475 | ||||||||
\(210\) | 10.7137 | 0.739316 | ||||||||
\(211\) | −7.84846 | −0.540310 | −0.270155 | − | 0.962817i | \(-0.587075\pi\) | ||||
−0.270155 | + | 0.962817i | \(0.587075\pi\) | |||||||
\(212\) | −22.8651 | −1.57038 | ||||||||
\(213\) | 4.15260 | 0.284531 | ||||||||
\(214\) | −10.7642 | −0.735822 | ||||||||
\(215\) | 41.2403 | 2.81256 | ||||||||
\(216\) | 7.42376 | 0.505123 | ||||||||
\(217\) | 2.53755 | 0.172260 | ||||||||
\(218\) | −17.0636 | −1.15569 | ||||||||
\(219\) | 6.08083 | 0.410904 | ||||||||
\(220\) | −113.044 | −7.62145 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.04516 | −0.0701465 | ||||||||
\(223\) | −5.21856 | −0.349461 | −0.174730 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174730 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(224\) | 10.6141 | 0.709184 | ||||||||
\(225\) | 11.7842 | 0.785611 | ||||||||
\(226\) | 2.16955 | 0.144316 | ||||||||
\(227\) | 17.3482 | 1.15144 | 0.575720 | − | 0.817647i | \(-0.304722\pi\) | ||||
0.575720 | + | 0.817647i | \(0.304722\pi\) | |||||||
\(228\) | −17.4778 | −1.15749 | ||||||||
\(229\) | −8.20358 | −0.542108 | −0.271054 | − | 0.962564i | \(-0.587372\pi\) | ||||
−0.271054 | + | 0.962564i | \(0.587372\pi\) | |||||||
\(230\) | 16.3801 | 1.08007 | ||||||||
\(231\) | −5.70245 | −0.375194 | ||||||||
\(232\) | −64.2425 | −4.21773 | ||||||||
\(233\) | 13.3917 | 0.877320 | 0.438660 | − | 0.898653i | \(-0.355453\pi\) | ||||
0.438660 | + | 0.898653i | \(0.355453\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.78288 | −0.638164 | ||||||||
\(236\) | 19.2927 | 1.25585 | ||||||||
\(237\) | −0.225699 | −0.0146607 | ||||||||
\(238\) | −11.4501 | −0.742197 | ||||||||
\(239\) | 14.9556 | 0.967400 | 0.483700 | − | 0.875234i | \(-0.339293\pi\) | ||||
0.483700 | + | 0.875234i | \(0.339293\pi\) | |||||||
\(240\) | 39.8884 | 2.57478 | ||||||||
\(241\) | −23.0567 | −1.48521 | −0.742607 | − | 0.669727i | \(-0.766411\pi\) | ||||
−0.742607 | + | 0.669727i | \(0.766411\pi\) | |||||||
\(242\) | 56.2718 | 3.61729 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.37733 | −0.344248 | ||||||||
\(245\) | 4.09685 | 0.261738 | ||||||||
\(246\) | −9.13750 | −0.582586 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 18.8382 | 1.19623 | ||||||||
\(249\) | −9.32245 | −0.590786 | ||||||||
\(250\) | 72.6836 | 4.59691 | ||||||||
\(251\) | 18.9733 | 1.19759 | 0.598793 | − | 0.800904i | \(-0.295647\pi\) | ||||
0.598793 | + | 0.800904i | \(0.295647\pi\) | |||||||
\(252\) | 4.83880 | 0.304815 | ||||||||
\(253\) | −8.71843 | −0.548123 | ||||||||
\(254\) | −30.8994 | −1.93880 | ||||||||
\(255\) | −17.9378 | −1.12331 | ||||||||
\(256\) | −15.4279 | −0.964243 | ||||||||
\(257\) | 18.1751 | 1.13373 | 0.566867 | − | 0.823809i | \(-0.308155\pi\) | ||||
0.566867 | + | 0.823809i | \(0.308155\pi\) | |||||||
\(258\) | 26.3246 | 1.63890 | ||||||||
\(259\) | −0.399662 | −0.0248338 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.65363 | −0.535646 | ||||||||
\(262\) | 41.7078 | 2.57672 | ||||||||
\(263\) | 30.0127 | 1.85066 | 0.925331 | − | 0.379160i | \(-0.123787\pi\) | ||||
0.925331 | + | 0.379160i | \(0.123787\pi\) | |||||||
\(264\) | −42.3336 | −2.60545 | ||||||||
\(265\) | −19.3591 | −1.18922 | ||||||||
\(266\) | −9.44580 | −0.579159 | ||||||||
\(267\) | −9.60970 | −0.588104 | ||||||||
\(268\) | 42.7921 | 2.61394 | ||||||||
\(269\) | 15.2181 | 0.927864 | 0.463932 | − | 0.885871i | \(-0.346438\pi\) | ||||
0.463932 | + | 0.885871i | \(0.346438\pi\) | |||||||
\(270\) | 10.7137 | 0.652015 | ||||||||
\(271\) | 1.39762 | 0.0848995 | 0.0424497 | − | 0.999099i | \(-0.486484\pi\) | ||||
0.0424497 | + | 0.999099i | \(0.486484\pi\) | |||||||
\(272\) | −42.6299 | −2.58482 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −34.5859 | −2.08941 | ||||||||
\(275\) | −67.1986 | −4.05223 | ||||||||
\(276\) | 7.39799 | 0.445307 | ||||||||
\(277\) | 9.68781 | 0.582084 | 0.291042 | − | 0.956710i | \(-0.405998\pi\) | ||||
0.291042 | + | 0.956710i | \(0.405998\pi\) | |||||||
\(278\) | −10.1480 | −0.608634 | ||||||||
\(279\) | 2.53755 | 0.151919 | ||||||||
\(280\) | 30.4140 | 1.81759 | ||||||||
\(281\) | −29.5572 | −1.76324 | −0.881619 | − | 0.471962i | \(-0.843546\pi\) | ||||
−0.881619 | + | 0.471962i | \(0.843546\pi\) | |||||||
\(282\) | −6.24463 | −0.371862 | ||||||||
\(283\) | 9.80289 | 0.582721 | 0.291361 | − | 0.956613i | \(-0.405892\pi\) | ||||
0.291361 | + | 0.956613i | \(0.405892\pi\) | |||||||
\(284\) | 20.0936 | 1.19233 | ||||||||
\(285\) | −14.7979 | −0.876550 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.49412 | −0.206251 | ||||||||
\(288\) | 10.6141 | 0.625442 | ||||||||
\(289\) | 2.17062 | 0.127684 | ||||||||
\(290\) | −92.7125 | −5.44426 | ||||||||
\(291\) | 14.1480 | 0.829368 | ||||||||
\(292\) | 29.4239 | 1.72190 | ||||||||
\(293\) | 9.92535 | 0.579845 | 0.289923 | − | 0.957050i | \(-0.406370\pi\) | ||||
0.289923 | + | 0.957050i | \(0.406370\pi\) | |||||||
\(294\) | 2.61511 | 0.152516 | ||||||||
\(295\) | 16.3345 | 0.951031 | ||||||||
\(296\) | −2.96700 | −0.172453 | ||||||||
\(297\) | −5.70245 | −0.330890 | ||||||||
\(298\) | −44.1212 | −2.55587 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 57.0212 | 3.29212 | ||||||||
\(301\) | 10.0663 | 0.580214 | ||||||||
\(302\) | −51.6388 | −2.97148 | ||||||||
\(303\) | −10.1307 | −0.581995 | ||||||||
\(304\) | −35.1678 | −2.01701 | ||||||||
\(305\) | −4.55281 | −0.260693 | ||||||||
\(306\) | −11.4501 | −0.654557 | ||||||||
\(307\) | 33.7537 | 1.92643 | 0.963213 | − | 0.268738i | \(-0.0866065\pi\) | ||||
0.963213 | + | 0.268738i | \(0.0866065\pi\) | |||||||
\(308\) | −27.5930 | −1.57226 | ||||||||
\(309\) | 1.94213 | 0.110484 | ||||||||
\(310\) | 27.1866 | 1.54409 | ||||||||
\(311\) | 27.3331 | 1.54992 | 0.774959 | − | 0.632011i | \(-0.217770\pi\) | ||||
0.774959 | + | 0.632011i | \(0.217770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6286 | −0.713813 | −0.356907 | − | 0.934140i | \(-0.616169\pi\) | ||||
−0.356907 | + | 0.934140i | \(0.616169\pi\) | |||||||
\(314\) | 47.0378 | 2.65450 | ||||||||
\(315\) | 4.09685 | 0.230831 | ||||||||
\(316\) | −1.09211 | −0.0614360 | ||||||||
\(317\) | −13.9653 | −0.784370 | −0.392185 | − | 0.919886i | \(-0.628281\pi\) | ||||
−0.392185 | + | 0.919886i | \(0.628281\pi\) | |||||||
\(318\) | −12.3573 | −0.692965 | ||||||||
\(319\) | 49.3469 | 2.76290 | ||||||||
\(320\) | 33.9396 | 1.89728 | ||||||||
\(321\) | −4.11614 | −0.229740 | ||||||||
\(322\) | 3.99822 | 0.222812 | ||||||||
\(323\) | 15.8149 | 0.879966 | ||||||||
\(324\) | 4.83880 | 0.268822 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.65428 | −0.423931 | ||||||||
\(327\) | −6.52500 | −0.360833 | ||||||||
\(328\) | −25.9395 | −1.43227 | ||||||||
\(329\) | −2.38790 | −0.131649 | ||||||||
\(330\) | −61.0944 | −3.36314 | ||||||||
\(331\) | −4.67384 | −0.256898 | −0.128449 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128449 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(332\) | −45.1094 | −2.47570 | ||||||||
\(333\) | −0.399662 | −0.0219013 | ||||||||
\(334\) | 40.9084 | 2.23841 | ||||||||
\(335\) | 36.2307 | 1.97949 | ||||||||
\(336\) | 9.73635 | 0.531162 | ||||||||
\(337\) | 19.4462 | 1.05930 | 0.529652 | − | 0.848215i | \(-0.322323\pi\) | ||||
0.529652 | + | 0.848215i | \(0.322323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.829620 | 0.0450588 | ||||||||
\(340\) | −86.7971 | −4.70723 | ||||||||
\(341\) | −14.4703 | −0.783609 | ||||||||
\(342\) | −9.44580 | −0.510771 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 74.7301 | 4.02918 | ||||||||
\(345\) | 6.26363 | 0.337223 | ||||||||
\(346\) | −56.4761 | −3.03617 | ||||||||
\(347\) | −23.9395 | −1.28514 | −0.642569 | − | 0.766228i | \(-0.722131\pi\) | ||||
−0.642569 | + | 0.766228i | \(0.722131\pi\) | |||||||
\(348\) | −41.8732 | −2.24464 | ||||||||
\(349\) | 5.12046 | 0.274092 | 0.137046 | − | 0.990565i | \(-0.456239\pi\) | ||||
0.137046 | + | 0.990565i | \(0.456239\pi\) | |||||||
\(350\) | 30.8169 | 1.64723 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −60.5264 | −3.22607 | ||||||||
\(353\) | 7.74166 | 0.412047 | 0.206023 | − | 0.978547i | \(-0.433948\pi\) | ||||
0.206023 | + | 0.978547i | \(0.433948\pi\) | |||||||
\(354\) | 10.4267 | 0.554171 | ||||||||
\(355\) | 17.0126 | 0.902933 | ||||||||
\(356\) | −46.4994 | −2.46446 | ||||||||
\(357\) | −4.37843 | −0.231731 | ||||||||
\(358\) | 8.94507 | 0.472762 | ||||||||
\(359\) | −31.7337 | −1.67484 | −0.837420 | − | 0.546559i | \(-0.815937\pi\) | ||||
−0.837420 | + | 0.546559i | \(0.815937\pi\) | |||||||
\(360\) | 30.4140 | 1.60296 | ||||||||
\(361\) | −5.95337 | −0.313335 | ||||||||
\(362\) | 30.1637 | 1.58537 | ||||||||
\(363\) | 21.5180 | 1.12940 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.9122 | 1.30397 | ||||||||
\(366\) | −2.90616 | −0.151907 | ||||||||
\(367\) | 13.1949 | 0.688769 | 0.344384 | − | 0.938829i | \(-0.388088\pi\) | ||||
0.344384 | + | 0.938829i | \(0.388088\pi\) | |||||||
\(368\) | 14.8858 | 0.775977 | ||||||||
\(369\) | −3.49412 | −0.181896 | ||||||||
\(370\) | −4.28186 | −0.222603 | ||||||||
\(371\) | −4.72536 | −0.245329 | ||||||||
\(372\) | 12.2787 | 0.636621 | ||||||||
\(373\) | 30.9479 | 1.60242 | 0.801212 | − | 0.598381i | \(-0.204189\pi\) | ||||
0.801212 | + | 0.598381i | \(0.204189\pi\) | |||||||
\(374\) | 65.2934 | 3.37624 | ||||||||
\(375\) | 27.7937 | 1.43526 | ||||||||
\(376\) | −17.7272 | −0.914211 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.61511 | 0.134507 | ||||||||
\(379\) | 0.0568165 | 0.00291847 | 0.00145923 | − | 0.999999i | \(-0.499536\pi\) | ||||
0.00145923 | + | 0.999999i | \(0.499536\pi\) | |||||||
\(380\) | −71.6038 | −3.67320 | ||||||||
\(381\) | −11.8157 | −0.605339 | ||||||||
\(382\) | 15.1557 | 0.775431 | ||||||||
\(383\) | 2.47372 | 0.126401 | 0.0632005 | − | 0.998001i | \(-0.479869\pi\) | ||||
0.0632005 | + | 0.998001i | \(0.479869\pi\) | |||||||
\(384\) | 0.436221 | 0.0222608 | ||||||||
\(385\) | −23.3621 | −1.19064 | ||||||||
\(386\) | 41.5637 | 2.11554 | ||||||||
\(387\) | 10.0663 | 0.511701 | ||||||||
\(388\) | 68.4591 | 3.47548 | ||||||||
\(389\) | 20.1130 | 1.01977 | 0.509884 | − | 0.860243i | \(-0.329688\pi\) | ||||
0.509884 | + | 0.860243i | \(0.329688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.69414 | −0.338537 | ||||||||
\(392\) | 7.42376 | 0.374957 | ||||||||
\(393\) | 15.9488 | 0.804509 | ||||||||
\(394\) | 4.12510 | 0.207819 | ||||||||
\(395\) | −0.924653 | −0.0465244 | ||||||||
\(396\) | −27.5930 | −1.38660 | ||||||||
\(397\) | −38.5811 | −1.93633 | −0.968164 | − | 0.250317i | \(-0.919465\pi\) | ||||
−0.968164 | + | 0.250317i | \(0.919465\pi\) | |||||||
\(398\) | 11.2857 | 0.565703 | ||||||||
\(399\) | −3.61201 | −0.180827 | ||||||||
\(400\) | 114.735 | 5.73674 | ||||||||
\(401\) | −32.4962 | −1.62278 | −0.811390 | − | 0.584505i | \(-0.801289\pi\) | ||||
−0.811390 | + | 0.584505i | \(0.801289\pi\) | |||||||
\(402\) | 23.1268 | 1.15346 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −49.0205 | −2.43886 | ||||||||
\(405\) | 4.09685 | 0.203574 | ||||||||
\(406\) | −22.6302 | −1.12312 | ||||||||
\(407\) | 2.27905 | 0.112968 | ||||||||
\(408\) | −32.5044 | −1.60921 | ||||||||
\(409\) | 0.690530 | 0.0341445 | 0.0170723 | − | 0.999854i | \(-0.494565\pi\) | ||||
0.0170723 | + | 0.999854i | \(0.494565\pi\) | |||||||
\(410\) | −37.4349 | −1.84878 | ||||||||
\(411\) | −13.2254 | −0.652362 | ||||||||
\(412\) | 9.39755 | 0.462984 | ||||||||
\(413\) | 3.98709 | 0.196192 | ||||||||
\(414\) | 3.99822 | 0.196502 | ||||||||
\(415\) | −38.1927 | −1.87480 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.88051 | −0.190029 | ||||||||
\(418\) | 53.8642 | 2.63459 | ||||||||
\(419\) | 30.5802 | 1.49394 | 0.746971 | − | 0.664857i | \(-0.231507\pi\) | ||||
0.746971 | + | 0.664857i | \(0.231507\pi\) | |||||||
\(420\) | 19.8238 | 0.967303 | ||||||||
\(421\) | 12.5119 | 0.609792 | 0.304896 | − | 0.952386i | \(-0.401378\pi\) | ||||
0.304896 | + | 0.952386i | \(0.401378\pi\) | |||||||
\(422\) | −20.5246 | −0.999121 | ||||||||
\(423\) | −2.38790 | −0.116104 | ||||||||
\(424\) | −35.0800 | −1.70363 | ||||||||
\(425\) | −51.5961 | −2.50278 | ||||||||
\(426\) | 10.8595 | 0.526144 | ||||||||
\(427\) | −1.11129 | −0.0537793 | ||||||||
\(428\) | −19.9172 | −0.962732 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 107.848 | 5.20089 | ||||||||
\(431\) | −24.2411 | −1.16765 | −0.583827 | − | 0.811878i | \(-0.698446\pi\) | ||||
−0.583827 | + | 0.811878i | \(0.698446\pi\) | |||||||
\(432\) | 9.73635 | 0.468440 | ||||||||
\(433\) | −14.7727 | −0.709930 | −0.354965 | − | 0.934880i | \(-0.615507\pi\) | ||||
−0.354965 | + | 0.934880i | \(0.615507\pi\) | |||||||
\(434\) | 6.63598 | 0.318537 | ||||||||
\(435\) | −35.4526 | −1.69982 | ||||||||
\(436\) | −31.5731 | −1.51208 | ||||||||
\(437\) | −5.52237 | −0.264171 | ||||||||
\(438\) | 15.9020 | 0.759828 | ||||||||
\(439\) | −28.9217 | −1.38036 | −0.690178 | − | 0.723639i | \(-0.742468\pi\) | ||||
−0.690178 | + | 0.723639i | \(0.742468\pi\) | |||||||
\(440\) | −173.434 | −8.26816 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.5183 | 1.83006 | 0.915030 | − | 0.403385i | \(-0.132166\pi\) | ||||
0.915030 | + | 0.403385i | \(0.132166\pi\) | |||||||
\(444\) | −1.93388 | −0.0917780 | ||||||||
\(445\) | −39.3695 | −1.86629 | ||||||||
\(446\) | −13.6471 | −0.646210 | ||||||||
\(447\) | −16.8716 | −0.798001 | ||||||||
\(448\) | 8.28433 | 0.391398 | ||||||||
\(449\) | −25.5939 | −1.20785 | −0.603926 | − | 0.797040i | \(-0.706398\pi\) | ||||
−0.603926 | + | 0.797040i | \(0.706398\pi\) | |||||||
\(450\) | 30.8169 | 1.45272 | ||||||||
\(451\) | 19.9250 | 0.938233 | ||||||||
\(452\) | 4.01436 | 0.188820 | ||||||||
\(453\) | −19.7463 | −0.927764 | ||||||||
\(454\) | 45.3674 | 2.12920 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −26.8147 | −1.25571 | ||||||||
\(457\) | 5.16777 | 0.241738 | 0.120869 | − | 0.992668i | \(-0.461432\pi\) | ||||
0.120869 | + | 0.992668i | \(0.461432\pi\) | |||||||
\(458\) | −21.4532 | −1.00244 | ||||||||
\(459\) | −4.37843 | −0.204367 | ||||||||
\(460\) | 30.3084 | 1.41314 | ||||||||
\(461\) | 26.8777 | 1.25182 | 0.625909 | − | 0.779896i | \(-0.284728\pi\) | ||||
0.625909 | + | 0.779896i | \(0.284728\pi\) | |||||||
\(462\) | −14.9125 | −0.693794 | ||||||||
\(463\) | −15.0113 | −0.697633 | −0.348817 | − | 0.937191i | \(-0.613416\pi\) | ||||
−0.348817 | + | 0.937191i | \(0.613416\pi\) | |||||||
\(464\) | −84.2548 | −3.91143 | ||||||||
\(465\) | 10.3960 | 0.482102 | ||||||||
\(466\) | 35.0208 | 1.62231 | ||||||||
\(467\) | −26.6991 | −1.23549 | −0.617744 | − | 0.786379i | \(-0.711953\pi\) | ||||
−0.617744 | + | 0.786379i | \(0.711953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.84355 | 0.408357 | ||||||||
\(470\) | −25.5833 | −1.18007 | ||||||||
\(471\) | 17.9869 | 0.828794 | ||||||||
\(472\) | 29.5992 | 1.36241 | ||||||||
\(473\) | −57.4028 | −2.63939 | ||||||||
\(474\) | −0.590227 | −0.0271100 | ||||||||
\(475\) | −42.5645 | −1.95300 | ||||||||
\(476\) | −21.1863 | −0.971073 | ||||||||
\(477\) | −4.72536 | −0.216359 | ||||||||
\(478\) | 39.1106 | 1.78888 | ||||||||
\(479\) | 8.99953 | 0.411199 | 0.205599 | − | 0.978636i | \(-0.434086\pi\) | ||||
0.205599 | + | 0.978636i | \(0.434086\pi\) | |||||||
\(480\) | 43.4844 | 1.98478 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −60.2959 | −2.74640 | ||||||||
\(483\) | 1.52889 | 0.0695669 | ||||||||
\(484\) | 104.121 | 4.73277 | ||||||||
\(485\) | 57.9621 | 2.63192 | ||||||||
\(486\) | 2.61511 | 0.118624 | ||||||||
\(487\) | 15.9943 | 0.724772 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(488\) | −8.24998 | −0.373459 | ||||||||
\(489\) | −2.92694 | −0.132361 | ||||||||
\(490\) | 10.7137 | 0.483996 | ||||||||
\(491\) | 18.8654 | 0.851382 | 0.425691 | − | 0.904869i | \(-0.360031\pi\) | ||||
0.425691 | + | 0.904869i | \(0.360031\pi\) | |||||||
\(492\) | −16.9073 | −0.762241 | ||||||||
\(493\) | 37.8893 | 1.70645 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.3621 | −1.05005 | ||||||||
\(496\) | 24.7065 | 1.10935 | ||||||||
\(497\) | 4.15260 | 0.186269 | ||||||||
\(498\) | −24.3792 | −1.09246 | ||||||||
\(499\) | −30.6858 | −1.37368 | −0.686841 | − | 0.726807i | \(-0.741003\pi\) | ||||
−0.686841 | + | 0.726807i | \(0.741003\pi\) | |||||||
\(500\) | 134.488 | 6.01449 | ||||||||
\(501\) | 15.6431 | 0.698882 | ||||||||
\(502\) | 49.6173 | 2.21453 | ||||||||
\(503\) | −22.4254 | −0.999897 | −0.499948 | − | 0.866055i | \(-0.666648\pi\) | ||||
−0.499948 | + | 0.866055i | \(0.666648\pi\) | |||||||
\(504\) | 7.42376 | 0.330681 | ||||||||
\(505\) | −41.5040 | −1.84691 | ||||||||
\(506\) | −22.7996 | −1.01357 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57.1739 | −2.53668 | ||||||||
\(509\) | 24.6562 | 1.09287 | 0.546434 | − | 0.837502i | \(-0.315985\pi\) | ||||
0.546434 | + | 0.837502i | \(0.315985\pi\) | |||||||
\(510\) | −46.9092 | −2.07717 | ||||||||
\(511\) | 6.08083 | 0.269000 | ||||||||
\(512\) | −41.2181 | −1.82160 | ||||||||
\(513\) | −3.61201 | −0.159474 | ||||||||
\(514\) | 47.5300 | 2.09646 | ||||||||
\(515\) | 7.95660 | 0.350610 | ||||||||
\(516\) | 48.7090 | 2.14429 | ||||||||
\(517\) | 13.6169 | 0.598870 | ||||||||
\(518\) | −1.04516 | −0.0459217 | ||||||||
\(519\) | −21.5961 | −0.947962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.20050 | −0.359271 | −0.179635 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179635 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(522\) | −22.6302 | −0.990497 | ||||||||
\(523\) | −33.0519 | −1.44526 | −0.722630 | − | 0.691235i | \(-0.757067\pi\) | ||||
−0.722630 | + | 0.691235i | \(0.757067\pi\) | |||||||
\(524\) | 77.1729 | 3.37131 | ||||||||
\(525\) | 11.7842 | 0.514303 | ||||||||
\(526\) | 78.4865 | 3.42217 | ||||||||
\(527\) | −11.1105 | −0.483981 | ||||||||
\(528\) | −55.5211 | −2.41624 | ||||||||
\(529\) | −20.6625 | −0.898369 | ||||||||
\(530\) | −50.6261 | −2.19906 | ||||||||
\(531\) | 3.98709 | 0.173025 | ||||||||
\(532\) | −17.4778 | −0.757758 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −25.1304 | −1.08750 | ||||||||
\(535\) | −16.8632 | −0.729060 | ||||||||
\(536\) | 65.6524 | 2.83575 | ||||||||
\(537\) | 3.42054 | 0.147607 | ||||||||
\(538\) | 39.7970 | 1.71577 | ||||||||
\(539\) | −5.70245 | −0.245622 | ||||||||
\(540\) | 19.8238 | 0.853081 | ||||||||
\(541\) | −1.79997 | −0.0773867 | −0.0386933 | − | 0.999251i | \(-0.512320\pi\) | ||||
−0.0386933 | + | 0.999251i | \(0.512320\pi\) | |||||||
\(542\) | 3.65493 | 0.156993 | ||||||||
\(543\) | 11.5344 | 0.494989 | ||||||||
\(544\) | −46.4731 | −1.99252 | ||||||||
\(545\) | −26.7319 | −1.14507 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.55618 | −0.280322 | −0.140161 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140161 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(548\) | −63.9952 | −2.73374 | ||||||||
\(549\) | −1.11129 | −0.0474289 | ||||||||
\(550\) | −175.732 | −7.49323 | ||||||||
\(551\) | 31.2570 | 1.33159 | ||||||||
\(552\) | 11.3501 | 0.483093 | ||||||||
\(553\) | −0.225699 | −0.00959768 | ||||||||
\(554\) | 25.3347 | 1.07637 | ||||||||
\(555\) | −1.63736 | −0.0695019 | ||||||||
\(556\) | −18.7770 | −0.796322 | ||||||||
\(557\) | −15.2943 | −0.648039 | −0.324019 | − | 0.946050i | \(-0.605034\pi\) | ||||
−0.324019 | + | 0.946050i | \(0.605034\pi\) | |||||||
\(558\) | 6.63598 | 0.280923 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 39.8884 | 1.68559 | ||||||||
\(561\) | 24.9678 | 1.05414 | ||||||||
\(562\) | −77.2954 | −3.26051 | ||||||||
\(563\) | 45.2000 | 1.90495 | 0.952477 | − | 0.304612i | \(-0.0985267\pi\) | ||||
0.952477 | + | 0.304612i | \(0.0985267\pi\) | |||||||
\(564\) | −11.5546 | −0.486535 | ||||||||
\(565\) | 3.39883 | 0.142990 | ||||||||
\(566\) | 25.6356 | 1.07755 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 30.8279 | 1.29351 | ||||||||
\(569\) | −9.68102 | −0.405850 | −0.202925 | − | 0.979194i | \(-0.565045\pi\) | ||||
−0.202925 | + | 0.979194i | \(0.565045\pi\) | |||||||
\(570\) | −38.6980 | −1.62088 | ||||||||
\(571\) | 27.8363 | 1.16491 | 0.582457 | − | 0.812861i | \(-0.302091\pi\) | ||||
0.582457 | + | 0.812861i | \(0.302091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.79542 | 0.242107 | ||||||||
\(574\) | −9.13750 | −0.381392 | ||||||||
\(575\) | 18.0167 | 0.751349 | ||||||||
\(576\) | 8.28433 | 0.345180 | ||||||||
\(577\) | 10.2332 | 0.426016 | 0.213008 | − | 0.977051i | \(-0.431674\pi\) | ||||
0.213008 | + | 0.977051i | \(0.431674\pi\) | |||||||
\(578\) | 5.67641 | 0.236108 | ||||||||
\(579\) | 15.8937 | 0.660518 | ||||||||
\(580\) | −171.548 | −7.12314 | ||||||||
\(581\) | −9.32245 | −0.386761 | ||||||||
\(582\) | 36.9985 | 1.53364 | ||||||||
\(583\) | 26.9461 | 1.11600 | ||||||||
\(584\) | 45.1426 | 1.86801 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.9559 | 1.07223 | ||||||||
\(587\) | 29.9645 | 1.23677 | 0.618383 | − | 0.785877i | \(-0.287788\pi\) | ||||
0.618383 | + | 0.785877i | \(0.287788\pi\) | |||||||
\(588\) | 4.83880 | 0.199549 | ||||||||
\(589\) | −9.16567 | −0.377665 | ||||||||
\(590\) | 42.7165 | 1.75861 | ||||||||
\(591\) | 1.57741 | 0.0648860 | ||||||||
\(592\) | −3.89125 | −0.159929 | ||||||||
\(593\) | −12.9516 | −0.531857 | −0.265928 | − | 0.963993i | \(-0.585679\pi\) | ||||
−0.265928 | + | 0.963993i | \(0.585679\pi\) | |||||||
\(594\) | −14.9125 | −0.611869 | ||||||||
\(595\) | −17.9378 | −0.735376 | ||||||||
\(596\) | −81.6384 | −3.34404 | ||||||||
\(597\) | 4.31559 | 0.176625 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1867 | 0.457075 | 0.228538 | − | 0.973535i | \(-0.426606\pi\) | ||||
0.228538 | + | 0.973535i | \(0.426606\pi\) | |||||||
\(600\) | 87.4828 | 3.57147 | ||||||||
\(601\) | −7.68718 | −0.313566 | −0.156783 | − | 0.987633i | \(-0.550112\pi\) | ||||
−0.156783 | + | 0.987633i | \(0.550112\pi\) | |||||||
\(602\) | 26.3246 | 1.07291 | ||||||||
\(603\) | 8.84355 | 0.360137 | ||||||||
\(604\) | −95.5485 | −3.88781 | ||||||||
\(605\) | 88.1558 | 3.58404 | ||||||||
\(606\) | −26.4929 | −1.07620 | ||||||||
\(607\) | −20.3771 | −0.827082 | −0.413541 | − | 0.910485i | \(-0.635708\pi\) | ||||
−0.413541 | + | 0.910485i | \(0.635708\pi\) | |||||||
\(608\) | −38.3383 | −1.55482 | ||||||||
\(609\) | −8.65363 | −0.350663 | ||||||||
\(610\) | −11.9061 | −0.482063 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −21.1863 | −0.856406 | ||||||||
\(613\) | −40.7493 | −1.64585 | −0.822925 | − | 0.568150i | \(-0.807659\pi\) | ||||
−0.822925 | + | 0.568150i | \(0.807659\pi\) | |||||||
\(614\) | 88.2697 | 3.56227 | ||||||||
\(615\) | −14.3149 | −0.577231 | ||||||||
\(616\) | −42.3336 | −1.70567 | ||||||||
\(617\) | −25.3049 | −1.01874 | −0.509368 | − | 0.860549i | \(-0.670121\pi\) | ||||
−0.509368 | + | 0.860549i | \(0.670121\pi\) | |||||||
\(618\) | 5.07887 | 0.204302 | ||||||||
\(619\) | 21.6724 | 0.871086 | 0.435543 | − | 0.900168i | \(-0.356556\pi\) | ||||
0.435543 | + | 0.900168i | \(0.356556\pi\) | |||||||
\(620\) | 50.3040 | 2.02026 | ||||||||
\(621\) | 1.52889 | 0.0613523 | ||||||||
\(622\) | 71.4791 | 2.86605 | ||||||||
\(623\) | −9.60970 | −0.385005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 54.9458 | 2.19783 | ||||||||
\(626\) | −33.0253 | −1.31996 | ||||||||
\(627\) | 20.5973 | 0.822578 | ||||||||
\(628\) | 87.0351 | 3.47308 | ||||||||
\(629\) | 1.74989 | 0.0697727 | ||||||||
\(630\) | 10.7137 | 0.426844 | ||||||||
\(631\) | 29.7618 | 1.18480 | 0.592400 | − | 0.805644i | \(-0.298181\pi\) | ||||
0.592400 | + | 0.805644i | \(0.298181\pi\) | |||||||
\(632\) | −1.67553 | −0.0666491 | ||||||||
\(633\) | −7.84846 | −0.311948 | ||||||||
\(634\) | −36.5208 | −1.45043 | ||||||||
\(635\) | −48.4073 | −1.92098 | ||||||||
\(636\) | −22.8651 | −0.906659 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 129.048 | 5.10904 | ||||||||
\(639\) | 4.15260 | 0.164274 | ||||||||
\(640\) | 1.78713 | 0.0706426 | ||||||||
\(641\) | −15.7964 | −0.623920 | −0.311960 | − | 0.950095i | \(-0.600986\pi\) | ||||
−0.311960 | + | 0.950095i | \(0.600986\pi\) | |||||||
\(642\) | −10.7642 | −0.424827 | ||||||||
\(643\) | 15.9937 | 0.630732 | 0.315366 | − | 0.948970i | \(-0.397873\pi\) | ||||
0.315366 | + | 0.948970i | \(0.397873\pi\) | |||||||
\(644\) | 7.39799 | 0.291522 | ||||||||
\(645\) | 41.2403 | 1.62383 | ||||||||
\(646\) | 41.3578 | 1.62720 | ||||||||
\(647\) | 34.3302 | 1.34966 | 0.674829 | − | 0.737974i | \(-0.264217\pi\) | ||||
0.674829 | + | 0.737974i | \(0.264217\pi\) | |||||||
\(648\) | 7.42376 | 0.291633 | ||||||||
\(649\) | −22.7362 | −0.892473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.53755 | 0.0994545 | ||||||||
\(652\) | −14.1629 | −0.554661 | ||||||||
\(653\) | 17.5804 | 0.687975 | 0.343988 | − | 0.938974i | \(-0.388222\pi\) | ||||
0.343988 | + | 0.938974i | \(0.388222\pi\) | |||||||
\(654\) | −17.0636 | −0.667239 | ||||||||
\(655\) | 65.3397 | 2.55303 | ||||||||
\(656\) | −34.0200 | −1.32826 | ||||||||
\(657\) | 6.08083 | 0.237236 | ||||||||
\(658\) | −6.24463 | −0.243441 | ||||||||
\(659\) | −29.9239 | −1.16567 | −0.582835 | − | 0.812591i | \(-0.698056\pi\) | ||||
−0.582835 | + | 0.812591i | \(0.698056\pi\) | |||||||
\(660\) | −113.044 | −4.40024 | ||||||||
\(661\) | −9.86053 | −0.383530 | −0.191765 | − | 0.981441i | \(-0.561421\pi\) | ||||
−0.191765 | + | 0.981441i | \(0.561421\pi\) | |||||||
\(662\) | −12.2226 | −0.475045 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −69.2077 | −2.68578 | ||||||||
\(665\) | −14.7979 | −0.573837 | ||||||||
\(666\) | −1.04516 | −0.0404991 | ||||||||
\(667\) | −13.2305 | −0.512285 | ||||||||
\(668\) | 75.6938 | 2.92868 | ||||||||
\(669\) | −5.21856 | −0.201761 | ||||||||
\(670\) | 94.7472 | 3.66040 | ||||||||
\(671\) | 6.33710 | 0.244641 | ||||||||
\(672\) | 10.6141 | 0.409448 | ||||||||
\(673\) | 40.3380 | 1.55492 | 0.777458 | − | 0.628935i | \(-0.216509\pi\) | ||||
0.777458 | + | 0.628935i | \(0.216509\pi\) | |||||||
\(674\) | 50.8540 | 1.95882 | ||||||||
\(675\) | 11.7842 | 0.453573 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.8234 | 1.14621 | 0.573103 | − | 0.819483i | \(-0.305739\pi\) | ||||
0.573103 | + | 0.819483i | \(0.305739\pi\) | |||||||
\(678\) | 2.16955 | 0.0833209 | ||||||||
\(679\) | 14.1480 | 0.542949 | ||||||||
\(680\) | −133.166 | −5.10667 | ||||||||
\(681\) | 17.3482 | 0.664784 | ||||||||
\(682\) | −37.8413 | −1.44902 | ||||||||
\(683\) | −12.8508 | −0.491722 | −0.245861 | − | 0.969305i | \(-0.579071\pi\) | ||||
−0.245861 | + | 0.969305i | \(0.579071\pi\) | |||||||
\(684\) | −17.4778 | −0.668280 | ||||||||
\(685\) | −54.1826 | −2.07021 | ||||||||
\(686\) | 2.61511 | 0.0998453 | ||||||||
\(687\) | −8.20358 | −0.312986 | ||||||||
\(688\) | 98.0095 | 3.73658 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.3801 | 0.623579 | ||||||||
\(691\) | −16.4674 | −0.626451 | −0.313225 | − | 0.949679i | \(-0.601410\pi\) | ||||
−0.313225 | + | 0.949679i | \(0.601410\pi\) | |||||||
\(692\) | −104.499 | −3.97246 | ||||||||
\(693\) | −5.70245 | −0.216618 | ||||||||
\(694\) | −62.6043 | −2.37643 | ||||||||
\(695\) | −15.8979 | −0.603040 | ||||||||
\(696\) | −64.2425 | −2.43511 | ||||||||
\(697\) | 15.2987 | 0.579481 | ||||||||
\(698\) | 13.3906 | 0.506840 | ||||||||
\(699\) | 13.3917 | 0.506521 | ||||||||
\(700\) | 57.0212 | 2.15520 | ||||||||
\(701\) | −38.7459 | −1.46341 | −0.731705 | − | 0.681621i | \(-0.761275\pi\) | ||||
−0.731705 | + | 0.681621i | \(0.761275\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.44358 | 0.0544458 | ||||||||
\(704\) | −47.2410 | −1.78046 | ||||||||
\(705\) | −9.78288 | −0.368444 | ||||||||
\(706\) | 20.2453 | 0.761941 | ||||||||
\(707\) | −10.1307 | −0.381005 | ||||||||
\(708\) | 19.2927 | 0.725064 | ||||||||
\(709\) | −51.1868 | −1.92236 | −0.961181 | − | 0.275918i | \(-0.911018\pi\) | ||||
−0.961181 | + | 0.275918i | \(0.911018\pi\) | |||||||
\(710\) | 44.4897 | 1.66967 | ||||||||
\(711\) | −0.225699 | −0.00846436 | ||||||||
\(712\) | −71.3401 | −2.67358 | ||||||||
\(713\) | 3.87964 | 0.145294 | ||||||||
\(714\) | −11.4501 | −0.428508 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.5513 | 0.618550 | ||||||||
\(717\) | 14.9556 | 0.558529 | ||||||||
\(718\) | −82.9871 | −3.09705 | ||||||||
\(719\) | −39.5817 | −1.47615 | −0.738074 | − | 0.674719i | \(-0.764265\pi\) | ||||
−0.738074 | + | 0.674719i | \(0.764265\pi\) | |||||||
\(720\) | 39.8884 | 1.48655 | ||||||||
\(721\) | 1.94213 | 0.0723286 | ||||||||
\(722\) | −15.5687 | −0.579408 | ||||||||
\(723\) | −23.0567 | −0.857489 | ||||||||
\(724\) | 55.8126 | 2.07426 | ||||||||
\(725\) | −101.976 | −3.78729 | ||||||||
\(726\) | 56.2718 | 2.08844 | ||||||||
\(727\) | 21.6125 | 0.801564 | 0.400782 | − | 0.916173i | \(-0.368738\pi\) | ||||
0.400782 | + | 0.916173i | \(0.368738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 65.1482 | 2.41124 | ||||||||
\(731\) | −44.0748 | −1.63016 | ||||||||
\(732\) | −5.37733 | −0.198752 | ||||||||
\(733\) | 11.8544 | 0.437853 | 0.218926 | − | 0.975741i | \(-0.429745\pi\) | ||||
0.218926 | + | 0.975741i | \(0.429745\pi\) | |||||||
\(734\) | 34.5061 | 1.27364 | ||||||||
\(735\) | 4.09685 | 0.151115 | ||||||||
\(736\) | 16.2278 | 0.598165 | ||||||||
\(737\) | −50.4299 | −1.85761 | ||||||||
\(738\) | −9.13750 | −0.336356 | ||||||||
\(739\) | 4.16606 | 0.153251 | 0.0766255 | − | 0.997060i | \(-0.475585\pi\) | ||||
0.0766255 | + | 0.997060i | \(0.475585\pi\) | |||||||
\(740\) | −7.92283 | −0.291249 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.3573 | −0.453652 | ||||||||
\(743\) | −20.4996 | −0.752059 | −0.376029 | − | 0.926608i | \(-0.622711\pi\) | ||||
−0.376029 | + | 0.926608i | \(0.622711\pi\) | |||||||
\(744\) | 18.8382 | 0.690641 | ||||||||
\(745\) | −69.1205 | −2.53238 | ||||||||
\(746\) | 80.9322 | 2.96314 | ||||||||
\(747\) | −9.32245 | −0.341091 | ||||||||
\(748\) | 120.814 | 4.41739 | ||||||||
\(749\) | −4.11614 | −0.150400 | ||||||||
\(750\) | 72.6836 | 2.65403 | ||||||||
\(751\) | −9.35235 | −0.341272 | −0.170636 | − | 0.985334i | \(-0.554582\pi\) | ||||
−0.170636 | + | 0.985334i | \(0.554582\pi\) | |||||||
\(752\) | −23.2495 | −0.847821 | ||||||||
\(753\) | 18.9733 | 0.691426 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −80.8978 | −2.94417 | ||||||||
\(756\) | 4.83880 | 0.175985 | ||||||||
\(757\) | −24.3988 | −0.886789 | −0.443394 | − | 0.896327i | \(-0.646226\pi\) | ||||
−0.443394 | + | 0.896327i | \(0.646226\pi\) | |||||||
\(758\) | 0.148581 | 0.00539671 | ||||||||
\(759\) | −8.71843 | −0.316459 | ||||||||
\(760\) | −109.856 | −3.98489 | ||||||||
\(761\) | −48.1163 | −1.74421 | −0.872107 | − | 0.489316i | \(-0.837246\pi\) | ||||
−0.872107 | + | 0.489316i | \(0.837246\pi\) | |||||||
\(762\) | −30.8994 | −1.11937 | ||||||||
\(763\) | −6.52500 | −0.236221 | ||||||||
\(764\) | 28.0429 | 1.01456 | ||||||||
\(765\) | −17.9378 | −0.648541 | ||||||||
\(766\) | 6.46904 | 0.233736 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −15.4279 | −0.556706 | ||||||||
\(769\) | −17.9764 | −0.648247 | −0.324123 | − | 0.946015i | \(-0.605069\pi\) | ||||
−0.324123 | + | 0.946015i | \(0.605069\pi\) | |||||||
\(770\) | −61.0944 | −2.20169 | ||||||||
\(771\) | 18.1751 | 0.654562 | ||||||||
\(772\) | 76.9062 | 2.76792 | ||||||||
\(773\) | −0.803670 | −0.0289060 | −0.0144530 | − | 0.999896i | \(-0.504601\pi\) | ||||
−0.0144530 | + | 0.999896i | \(0.504601\pi\) | |||||||
\(774\) | 26.3246 | 0.946218 | ||||||||
\(775\) | 29.9030 | 1.07415 | ||||||||
\(776\) | 105.031 | 3.77040 | ||||||||
\(777\) | −0.399662 | −0.0143378 | ||||||||
\(778\) | 52.5976 | 1.88572 | ||||||||
\(779\) | 12.6208 | 0.452187 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.6800 | −0.847336 | ||||||||
\(782\) | −17.5059 | −0.626010 | ||||||||
\(783\) | −8.65363 | −0.309256 | ||||||||
\(784\) | 9.73635 | 0.347727 | ||||||||
\(785\) | 73.6897 | 2.63010 | ||||||||
\(786\) | 41.7078 | 1.48767 | ||||||||
\(787\) | 21.4970 | 0.766286 | 0.383143 | − | 0.923689i | \(-0.374842\pi\) | ||||
0.383143 | + | 0.923689i | \(0.374842\pi\) | |||||||
\(788\) | 7.63276 | 0.271906 | ||||||||
\(789\) | 30.0127 | 1.06848 | ||||||||
\(790\) | −2.41807 | −0.0860310 | ||||||||
\(791\) | 0.829620 | 0.0294979 | ||||||||
\(792\) | −42.3336 | −1.50426 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −100.894 | −3.58058 | ||||||||
\(795\) | −19.3591 | −0.686596 | ||||||||
\(796\) | 20.8822 | 0.740152 | ||||||||
\(797\) | 1.61335 | 0.0571477 | 0.0285739 | − | 0.999592i | \(-0.490903\pi\) | ||||
0.0285739 | + | 0.999592i | \(0.490903\pi\) | |||||||
\(798\) | −9.44580 | −0.334378 | ||||||||
\(799\) | 10.4553 | 0.369880 | ||||||||
\(800\) | 125.078 | 4.42219 | ||||||||
\(801\) | −9.60970 | −0.339542 | ||||||||
\(802\) | −84.9810 | −3.00078 | ||||||||
\(803\) | −34.6756 | −1.22368 | ||||||||
\(804\) | 42.7921 | 1.50916 | ||||||||
\(805\) | 6.26363 | 0.220764 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.2181 | 0.535703 | ||||||||
\(808\) | −75.2081 | −2.64581 | ||||||||
\(809\) | 4.21432 | 0.148168 | 0.0740838 | − | 0.997252i | \(-0.476397\pi\) | ||||
0.0740838 | + | 0.997252i | \(0.476397\pi\) | |||||||
\(810\) | 10.7137 | 0.376441 | ||||||||
\(811\) | −18.3325 | −0.643741 | −0.321871 | − | 0.946784i | \(-0.604312\pi\) | ||||
−0.321871 | + | 0.946784i | \(0.604312\pi\) | |||||||
\(812\) | −41.8732 | −1.46946 | ||||||||
\(813\) | 1.39762 | 0.0490167 | ||||||||
\(814\) | 5.95997 | 0.208897 | ||||||||
\(815\) | −11.9912 | −0.420035 | ||||||||
\(816\) | −42.6299 | −1.49235 | ||||||||
\(817\) | −36.3598 | −1.27207 | ||||||||
\(818\) | 1.80581 | 0.0631387 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −69.2667 | −2.41890 | ||||||||
\(821\) | 38.1069 | 1.32994 | 0.664970 | − | 0.746870i | \(-0.268445\pi\) | ||||
0.664970 | + | 0.746870i | \(0.268445\pi\) | |||||||
\(822\) | −34.5859 | −1.20632 | ||||||||
\(823\) | 11.3478 | 0.395559 | 0.197780 | − | 0.980246i | \(-0.436627\pi\) | ||||
0.197780 | + | 0.980246i | \(0.436627\pi\) | |||||||
\(824\) | 14.4179 | 0.502271 | ||||||||
\(825\) | −67.1986 | −2.33956 | ||||||||
\(826\) | 10.4267 | 0.362790 | ||||||||
\(827\) | 26.1746 | 0.910181 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(828\) | 7.39799 | 0.257098 | ||||||||
\(829\) | 25.6170 | 0.889716 | 0.444858 | − | 0.895601i | \(-0.353254\pi\) | ||||
0.444858 | + | 0.895601i | \(0.353254\pi\) | |||||||
\(830\) | −99.8780 | −3.46682 | ||||||||
\(831\) | 9.68781 | 0.336066 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.37843 | −0.151704 | ||||||||
\(834\) | −10.1480 | −0.351395 | ||||||||
\(835\) | 64.0874 | 2.21784 | ||||||||
\(836\) | 99.6662 | 3.44703 | ||||||||
\(837\) | 2.53755 | 0.0877107 | ||||||||
\(838\) | 79.9706 | 2.76254 | ||||||||
\(839\) | −6.23099 | −0.215118 | −0.107559 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107559 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(840\) | 30.4140 | 1.04938 | ||||||||
\(841\) | 45.8853 | 1.58225 | ||||||||
\(842\) | 32.7200 | 1.12760 | ||||||||
\(843\) | −29.5572 | −1.01801 | ||||||||
\(844\) | −37.9771 | −1.30722 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.24463 | −0.214695 | ||||||||
\(847\) | 21.5180 | 0.739366 | ||||||||
\(848\) | −46.0078 | −1.57991 | ||||||||
\(849\) | 9.80289 | 0.336434 | ||||||||
\(850\) | −134.929 | −4.62804 | ||||||||
\(851\) | −0.611040 | −0.0209462 | ||||||||
\(852\) | 20.0936 | 0.688394 | ||||||||
\(853\) | 14.8238 | 0.507558 | 0.253779 | − | 0.967262i | \(-0.418326\pi\) | ||||
0.253779 | + | 0.967262i | \(0.418326\pi\) | |||||||
\(854\) | −2.90616 | −0.0994466 | ||||||||
\(855\) | −14.7979 | −0.506076 | ||||||||
\(856\) | −30.5572 | −1.04442 | ||||||||
\(857\) | −48.0811 | −1.64242 | −0.821210 | − | 0.570626i | \(-0.806701\pi\) | ||||
−0.821210 | + | 0.570626i | \(0.806701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.03561 | 0.308291 | 0.154146 | − | 0.988048i | \(-0.450738\pi\) | ||||
0.154146 | + | 0.988048i | \(0.450738\pi\) | |||||||
\(860\) | 199.553 | 6.80471 | ||||||||
\(861\) | −3.49412 | −0.119079 | ||||||||
\(862\) | −63.3932 | −2.15918 | ||||||||
\(863\) | −27.4629 | −0.934848 | −0.467424 | − | 0.884033i | \(-0.654818\pi\) | ||||
−0.467424 | + | 0.884033i | \(0.654818\pi\) | |||||||
\(864\) | 10.6141 | 0.361099 | ||||||||
\(865\) | −88.4758 | −3.00827 | ||||||||
\(866\) | −38.6322 | −1.31278 | ||||||||
\(867\) | 2.17062 | 0.0737182 | ||||||||
\(868\) | 12.2787 | 0.416766 | ||||||||
\(869\) | 1.28704 | 0.0436597 | ||||||||
\(870\) | −92.7125 | −3.14325 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −48.4400 | −1.64039 | ||||||||
\(873\) | 14.1480 | 0.478836 | ||||||||
\(874\) | −14.4416 | −0.488495 | ||||||||
\(875\) | 27.7937 | 0.939599 | ||||||||
\(876\) | 29.4239 | 0.994141 | ||||||||
\(877\) | −19.3933 | −0.654865 | −0.327433 | − | 0.944875i | \(-0.606183\pi\) | ||||
−0.327433 | + | 0.944875i | \(0.606183\pi\) | |||||||
\(878\) | −75.6334 | −2.55250 | ||||||||
\(879\) | 9.92535 | 0.334774 | ||||||||
\(880\) | −227.461 | −7.66772 | ||||||||
\(881\) | −2.10868 | −0.0710431 | −0.0355215 | − | 0.999369i | \(-0.511309\pi\) | ||||
−0.0355215 | + | 0.999369i | \(0.511309\pi\) | |||||||
\(882\) | 2.61511 | 0.0880553 | ||||||||
\(883\) | −7.70898 | −0.259428 | −0.129714 | − | 0.991551i | \(-0.541406\pi\) | ||||
−0.129714 | + | 0.991551i | \(0.541406\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3345 | 0.549078 | ||||||||
\(886\) | 100.730 | 3.38408 | ||||||||
\(887\) | −3.93091 | −0.131987 | −0.0659936 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659936 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(888\) | −2.96700 | −0.0995659 | ||||||||
\(889\) | −11.8157 | −0.396287 | ||||||||
\(890\) | −102.956 | −3.45108 | ||||||||
\(891\) | −5.70245 | −0.191039 | ||||||||
\(892\) | −25.2516 | −0.845485 | ||||||||
\(893\) | 8.62513 | 0.288629 | ||||||||
\(894\) | −44.1212 | −1.47563 | ||||||||
\(895\) | 14.0134 | 0.468417 | ||||||||
\(896\) | 0.436221 | 0.0145731 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −66.9309 | −2.23351 | ||||||||
\(899\) | −21.9591 | −0.732375 | ||||||||
\(900\) | 57.0212 | 1.90071 | ||||||||
\(901\) | 20.6897 | 0.689272 | ||||||||
\(902\) | 52.1061 | 1.73494 | ||||||||
\(903\) | 10.0663 | 0.334987 | ||||||||
\(904\) | 6.15890 | 0.204842 | ||||||||
\(905\) | 47.2547 | 1.57080 | ||||||||
\(906\) | −51.6388 | −1.71559 | ||||||||
\(907\) | 19.4487 | 0.645784 | 0.322892 | − | 0.946436i | \(-0.395345\pi\) | ||||
0.322892 | + | 0.946436i | \(0.395345\pi\) | |||||||
\(908\) | 83.9444 | 2.78579 | ||||||||
\(909\) | −10.1307 | −0.336015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.5453 | −1.87343 | −0.936714 | − | 0.350095i | \(-0.886149\pi\) | ||||
−0.936714 | + | 0.350095i | \(0.886149\pi\) | |||||||
\(912\) | −35.1678 | −1.16452 | ||||||||
\(913\) | 53.1608 | 1.75937 | ||||||||
\(914\) | 13.5143 | 0.447012 | ||||||||
\(915\) | −4.55281 | −0.150511 | ||||||||
\(916\) | −39.6954 | −1.31157 | ||||||||
\(917\) | 15.9488 | 0.526675 | ||||||||
\(918\) | −11.4501 | −0.377908 | ||||||||
\(919\) | −6.22782 | −0.205437 | −0.102718 | − | 0.994710i | \(-0.532754\pi\) | ||||
−0.102718 | + | 0.994710i | \(0.532754\pi\) | |||||||
\(920\) | 46.4997 | 1.53305 | ||||||||
\(921\) | 33.7537 | 1.11222 | ||||||||
\(922\) | 70.2880 | 2.31481 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −27.5930 | −0.907743 | ||||||||
\(925\) | −4.70969 | −0.154853 | ||||||||
\(926\) | −39.2561 | −1.29004 | ||||||||
\(927\) | 1.94213 | 0.0637878 | ||||||||
\(928\) | −91.8505 | −3.01514 | ||||||||
\(929\) | −28.7107 | −0.941969 | −0.470985 | − | 0.882141i | \(-0.656101\pi\) | ||||
−0.470985 | + | 0.882141i | \(0.656101\pi\) | |||||||
\(930\) | 27.1866 | 0.891484 | ||||||||
\(931\) | −3.61201 | −0.118379 | ||||||||
\(932\) | 64.7997 | 2.12259 | ||||||||
\(933\) | 27.3331 | 0.894846 | ||||||||
\(934\) | −69.8211 | −2.28462 | ||||||||
\(935\) | 102.289 | 3.34521 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.1310 | 1.63771 | 0.818855 | − | 0.574001i | \(-0.194609\pi\) | ||||
0.818855 | + | 0.574001i | \(0.194609\pi\) | |||||||
\(938\) | 23.1268 | 0.755118 | ||||||||
\(939\) | −12.6286 | −0.412120 | ||||||||
\(940\) | −47.3373 | −1.54397 | ||||||||
\(941\) | 12.7241 | 0.414795 | 0.207398 | − | 0.978257i | \(-0.433501\pi\) | ||||
0.207398 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(942\) | 47.0378 | 1.53257 | ||||||||
\(943\) | −5.34212 | −0.173963 | ||||||||
\(944\) | 38.8197 | 1.26347 | ||||||||
\(945\) | 4.09685 | 0.133270 | ||||||||
\(946\) | −150.115 | −4.88065 | ||||||||
\(947\) | 37.7169 | 1.22564 | 0.612818 | − | 0.790224i | \(-0.290036\pi\) | ||||
0.612818 | + | 0.790224i | \(0.290036\pi\) | |||||||
\(948\) | −1.09211 | −0.0354701 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −111.311 | −3.61140 | ||||||||
\(951\) | −13.9653 | −0.452856 | ||||||||
\(952\) | −32.5044 | −1.05347 | ||||||||
\(953\) | 40.0863 | 1.29852 | 0.649261 | − | 0.760566i | \(-0.275078\pi\) | ||||
0.649261 | + | 0.760566i | \(0.275078\pi\) | |||||||
\(954\) | −12.3573 | −0.400084 | ||||||||
\(955\) | 23.7430 | 0.768304 | ||||||||
\(956\) | 72.3673 | 2.34053 | ||||||||
\(957\) | 49.3469 | 1.59516 | ||||||||
\(958\) | 23.5348 | 0.760373 | ||||||||
\(959\) | −13.2254 | −0.427071 | ||||||||
\(960\) | 33.9396 | 1.09540 | ||||||||
\(961\) | −24.5608 | −0.792285 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.11614 | −0.132641 | ||||||||
\(964\) | −111.567 | −3.59333 | ||||||||
\(965\) | 65.1139 | 2.09609 | ||||||||
\(966\) | 3.99822 | 0.128641 | ||||||||
\(967\) | −13.1830 | −0.423937 | −0.211968 | − | 0.977277i | \(-0.567987\pi\) | ||||
−0.211968 | + | 0.977277i | \(0.567987\pi\) | |||||||
\(968\) | 159.744 | 5.13437 | ||||||||
\(969\) | 15.8149 | 0.508049 | ||||||||
\(970\) | 151.577 | 4.86685 | ||||||||
\(971\) | 7.28316 | 0.233728 | 0.116864 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116864 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(972\) | 4.83880 | 0.155204 | ||||||||
\(973\) | −3.88051 | −0.124403 | ||||||||
\(974\) | 41.8269 | 1.34022 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8200 | −0.346338 | ||||||||
\(977\) | 14.3070 | 0.457721 | 0.228860 | − | 0.973459i | \(-0.426500\pi\) | ||||
0.228860 | + | 0.973459i | \(0.426500\pi\) | |||||||
\(978\) | −7.65428 | −0.244757 | ||||||||
\(979\) | 54.7989 | 1.75138 | ||||||||
\(980\) | 19.8238 | 0.633248 | ||||||||
\(981\) | −6.52500 | −0.208327 | ||||||||
\(982\) | 49.3350 | 1.57434 | ||||||||
\(983\) | −25.9689 | −0.828280 | −0.414140 | − | 0.910213i | \(-0.635918\pi\) | ||||
−0.414140 | + | 0.910213i | \(0.635918\pi\) | |||||||
\(984\) | −25.9395 | −0.826921 | ||||||||
\(985\) | 6.46241 | 0.205909 | ||||||||
\(986\) | 99.0846 | 3.15550 | ||||||||
\(987\) | −2.38790 | −0.0760078 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.3903 | 0.489384 | ||||||||
\(990\) | −61.0944 | −1.94171 | ||||||||
\(991\) | −27.5093 | −0.873862 | −0.436931 | − | 0.899495i | \(-0.643935\pi\) | ||||
−0.436931 | + | 0.899495i | \(0.643935\pi\) | |||||||
\(992\) | 26.9338 | 0.855150 | ||||||||
\(993\) | −4.67384 | −0.148320 | ||||||||
\(994\) | 10.8595 | 0.344442 | ||||||||
\(995\) | 17.6803 | 0.560504 | ||||||||
\(996\) | −45.1094 | −1.42935 | ||||||||
\(997\) | 37.8645 | 1.19918 | 0.599590 | − | 0.800308i | \(-0.295330\pi\) | ||||
0.599590 | + | 0.800308i | \(0.295330\pi\) | |||||||
\(998\) | −80.2466 | −2.54016 | ||||||||
\(999\) | −0.399662 | −0.0126447 |
(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 | 3549.2.a.bg.1.15 | ✓ | 15 | |
13.12 | even | 2 | 3549.2.a.bh.1.1 | yes | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.bg.1.15 | ✓ | 15 | 1.1 | even | 1 | trivial | |
3549.2.a.bh.1.1 | yes | 15 | 13.12 | even | 2 |