Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7942,2,Mod(1,7942)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7942, 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("7942.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7942 = 2 \cdot 11 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7942.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: | \(63.4171892853\) |
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: | \( x^{15} - 3 x^{14} - 33 x^{13} + 101 x^{12} + 408 x^{11} - 1314 x^{10} - 2271 x^{9} + 8292 x^{8} + \cdots - 3592 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.14157\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7942.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.14157 | −1.81379 | −0.906894 | − | 0.421360i | \(-0.861553\pi\) | ||||
−0.906894 | + | 0.421360i | \(0.861553\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.25314 | 1.90206 | 0.951032 | − | 0.309093i | \(-0.100026\pi\) | ||||
0.951032 | + | 0.309093i | \(0.100026\pi\) | |||||||
\(6\) | 3.14157 | 1.28254 | ||||||||
\(7\) | −0.789032 | −0.298226 | −0.149113 | − | 0.988820i | \(-0.547642\pi\) | ||||
−0.149113 | + | 0.988820i | \(0.547642\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.86947 | 2.28982 | ||||||||
\(10\) | −4.25314 | −1.34496 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.14157 | −0.906894 | ||||||||
\(13\) | 2.86562 | 0.794781 | 0.397391 | − | 0.917650i | \(-0.369916\pi\) | ||||
0.397391 | + | 0.917650i | \(0.369916\pi\) | |||||||
\(14\) | 0.789032 | 0.210878 | ||||||||
\(15\) | −13.3616 | −3.44994 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.87274 | −1.18181 | −0.590906 | − | 0.806740i | \(-0.701230\pi\) | ||||
−0.590906 | + | 0.806740i | \(0.701230\pi\) | |||||||
\(18\) | −6.86947 | −1.61915 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 4.25314 | 0.951032 | ||||||||
\(21\) | 2.47880 | 0.540919 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.00362 | −0.626298 | −0.313149 | − | 0.949704i | \(-0.601384\pi\) | ||||
−0.313149 | + | 0.949704i | \(0.601384\pi\) | |||||||
\(24\) | 3.14157 | 0.641271 | ||||||||
\(25\) | 13.0892 | 2.61785 | ||||||||
\(26\) | −2.86562 | −0.561995 | ||||||||
\(27\) | −12.1562 | −2.33947 | ||||||||
\(28\) | −0.789032 | −0.149113 | ||||||||
\(29\) | −6.79350 | −1.26152 | −0.630760 | − | 0.775978i | \(-0.717257\pi\) | ||||
−0.630760 | + | 0.775978i | \(0.717257\pi\) | |||||||
\(30\) | 13.3616 | 2.43947 | ||||||||
\(31\) | −10.2935 | −1.84876 | −0.924380 | − | 0.381473i | \(-0.875417\pi\) | ||||
−0.924380 | + | 0.381473i | \(0.875417\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.14157 | 0.546877 | ||||||||
\(34\) | 4.87274 | 0.835668 | ||||||||
\(35\) | −3.35587 | −0.567245 | ||||||||
\(36\) | 6.86947 | 1.14491 | ||||||||
\(37\) | 0.927122 | 0.152418 | 0.0762089 | − | 0.997092i | \(-0.475718\pi\) | ||||
0.0762089 | + | 0.997092i | \(0.475718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00256 | −1.44156 | ||||||||
\(40\) | −4.25314 | −0.672481 | ||||||||
\(41\) | 0.0787280 | 0.0122952 | 0.00614762 | − | 0.999981i | \(-0.498043\pi\) | ||||
0.00614762 | + | 0.999981i | \(0.498043\pi\) | |||||||
\(42\) | −2.47880 | −0.382487 | ||||||||
\(43\) | −4.27932 | −0.652590 | −0.326295 | − | 0.945268i | \(-0.605800\pi\) | ||||
−0.326295 | + | 0.945268i | \(0.605800\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 29.2169 | 4.35539 | ||||||||
\(46\) | 3.00362 | 0.442860 | ||||||||
\(47\) | 1.10688 | 0.161455 | 0.0807275 | − | 0.996736i | \(-0.474276\pi\) | ||||
0.0807275 | + | 0.996736i | \(0.474276\pi\) | |||||||
\(48\) | −3.14157 | −0.453447 | ||||||||
\(49\) | −6.37743 | −0.911061 | ||||||||
\(50\) | −13.0892 | −1.85110 | ||||||||
\(51\) | 15.3081 | 2.14356 | ||||||||
\(52\) | 2.86562 | 0.397391 | ||||||||
\(53\) | 1.13808 | 0.156327 | 0.0781636 | − | 0.996941i | \(-0.475094\pi\) | ||||
0.0781636 | + | 0.996941i | \(0.475094\pi\) | |||||||
\(54\) | 12.1562 | 1.65425 | ||||||||
\(55\) | −4.25314 | −0.573494 | ||||||||
\(56\) | 0.789032 | 0.105439 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.79350 | 0.892030 | ||||||||
\(59\) | −2.50283 | −0.325840 | −0.162920 | − | 0.986639i | \(-0.552091\pi\) | ||||
−0.162920 | + | 0.986639i | \(0.552091\pi\) | |||||||
\(60\) | −13.3616 | −1.72497 | ||||||||
\(61\) | −7.07049 | −0.905283 | −0.452642 | − | 0.891693i | \(-0.649518\pi\) | ||||
−0.452642 | + | 0.891693i | \(0.649518\pi\) | |||||||
\(62\) | 10.2935 | 1.30727 | ||||||||
\(63\) | −5.42023 | −0.682885 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.1879 | 1.51172 | ||||||||
\(66\) | −3.14157 | −0.386701 | ||||||||
\(67\) | 0.0387536 | 0.00473451 | 0.00236726 | − | 0.999997i | \(-0.499246\pi\) | ||||
0.00236726 | + | 0.999997i | \(0.499246\pi\) | |||||||
\(68\) | −4.87274 | −0.590906 | ||||||||
\(69\) | 9.43609 | 1.13597 | ||||||||
\(70\) | 3.35587 | 0.401103 | ||||||||
\(71\) | 14.8810 | 1.76605 | 0.883027 | − | 0.469323i | \(-0.155502\pi\) | ||||
0.883027 | + | 0.469323i | \(0.155502\pi\) | |||||||
\(72\) | −6.86947 | −0.809575 | ||||||||
\(73\) | 9.08659 | 1.06350 | 0.531752 | − | 0.846900i | \(-0.321534\pi\) | ||||
0.531752 | + | 0.846900i | \(0.321534\pi\) | |||||||
\(74\) | −0.927122 | −0.107776 | ||||||||
\(75\) | −41.1207 | −4.74821 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.789032 | 0.0899185 | ||||||||
\(78\) | 9.00256 | 1.01934 | ||||||||
\(79\) | 1.40495 | 0.158069 | 0.0790344 | − | 0.996872i | \(-0.474816\pi\) | ||||
0.0790344 | + | 0.996872i | \(0.474816\pi\) | |||||||
\(80\) | 4.25314 | 0.475516 | ||||||||
\(81\) | 17.5812 | 1.95347 | ||||||||
\(82\) | −0.0787280 | −0.00869405 | ||||||||
\(83\) | 11.0728 | 1.21539 | 0.607696 | − | 0.794169i | \(-0.292094\pi\) | ||||
0.607696 | + | 0.794169i | \(0.292094\pi\) | |||||||
\(84\) | 2.47880 | 0.270459 | ||||||||
\(85\) | −20.7245 | −2.24788 | ||||||||
\(86\) | 4.27932 | 0.461451 | ||||||||
\(87\) | 21.3423 | 2.28813 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 0.532856 | 0.0564826 | 0.0282413 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282413 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(90\) | −29.2169 | −3.07973 | ||||||||
\(91\) | −2.26107 | −0.237024 | ||||||||
\(92\) | −3.00362 | −0.313149 | ||||||||
\(93\) | 32.3376 | 3.35326 | ||||||||
\(94\) | −1.10688 | −0.114166 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.14157 | 0.320635 | ||||||||
\(97\) | 11.9267 | 1.21097 | 0.605487 | − | 0.795855i | \(-0.292978\pi\) | ||||
0.605487 | + | 0.795855i | \(0.292978\pi\) | |||||||
\(98\) | 6.37743 | 0.644218 | ||||||||
\(99\) | −6.86947 | −0.690408 | ||||||||
\(100\) | 13.0892 | 1.30892 | ||||||||
\(101\) | −16.0343 | −1.59547 | −0.797736 | − | 0.603007i | \(-0.793969\pi\) | ||||
−0.797736 | + | 0.603007i | \(0.793969\pi\) | |||||||
\(102\) | −15.3081 | −1.51572 | ||||||||
\(103\) | 7.04010 | 0.693682 | 0.346841 | − | 0.937924i | \(-0.387254\pi\) | ||||
0.346841 | + | 0.937924i | \(0.387254\pi\) | |||||||
\(104\) | −2.86562 | −0.280998 | ||||||||
\(105\) | 10.5427 | 1.02886 | ||||||||
\(106\) | −1.13808 | −0.110540 | ||||||||
\(107\) | 14.5660 | 1.40815 | 0.704076 | − | 0.710124i | \(-0.251361\pi\) | ||||
0.704076 | + | 0.710124i | \(0.251361\pi\) | |||||||
\(108\) | −12.1562 | −1.16973 | ||||||||
\(109\) | 1.32900 | 0.127295 | 0.0636474 | − | 0.997972i | \(-0.479727\pi\) | ||||
0.0636474 | + | 0.997972i | \(0.479727\pi\) | |||||||
\(110\) | 4.25314 | 0.405521 | ||||||||
\(111\) | −2.91262 | −0.276454 | ||||||||
\(112\) | −0.789032 | −0.0745565 | ||||||||
\(113\) | 5.13343 | 0.482913 | 0.241456 | − | 0.970412i | \(-0.422375\pi\) | ||||
0.241456 | + | 0.970412i | \(0.422375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7748 | −1.19126 | ||||||||
\(116\) | −6.79350 | −0.630760 | ||||||||
\(117\) | 19.6853 | 1.81991 | ||||||||
\(118\) | 2.50283 | 0.230404 | ||||||||
\(119\) | 3.84475 | 0.352447 | ||||||||
\(120\) | 13.3616 | 1.21974 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.07049 | 0.640132 | ||||||||
\(123\) | −0.247330 | −0.0223010 | ||||||||
\(124\) | −10.2935 | −0.924380 | ||||||||
\(125\) | 34.4046 | 3.07724 | ||||||||
\(126\) | 5.42023 | 0.482873 | ||||||||
\(127\) | −0.480932 | −0.0426758 | −0.0213379 | − | 0.999772i | \(-0.506793\pi\) | ||||
−0.0213379 | + | 0.999772i | \(0.506793\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 13.4438 | 1.18366 | ||||||||
\(130\) | −12.1879 | −1.06895 | ||||||||
\(131\) | 19.3980 | 1.69482 | 0.847408 | − | 0.530943i | \(-0.178162\pi\) | ||||
0.847408 | + | 0.530943i | \(0.178162\pi\) | |||||||
\(132\) | 3.14157 | 0.273439 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.0387536 | −0.00334781 | ||||||||
\(135\) | −51.7022 | −4.44982 | ||||||||
\(136\) | 4.87274 | 0.417834 | ||||||||
\(137\) | 13.3184 | 1.13786 | 0.568932 | − | 0.822384i | \(-0.307357\pi\) | ||||
0.568932 | + | 0.822384i | \(0.307357\pi\) | |||||||
\(138\) | −9.43609 | −0.803253 | ||||||||
\(139\) | −1.65530 | −0.140400 | −0.0702002 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702002 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(140\) | −3.35587 | −0.283622 | ||||||||
\(141\) | −3.47734 | −0.292845 | ||||||||
\(142\) | −14.8810 | −1.24879 | ||||||||
\(143\) | −2.86562 | −0.239635 | ||||||||
\(144\) | 6.86947 | 0.572456 | ||||||||
\(145\) | −28.8937 | −2.39949 | ||||||||
\(146\) | −9.08659 | −0.752011 | ||||||||
\(147\) | 20.0352 | 1.65247 | ||||||||
\(148\) | 0.927122 | 0.0762089 | ||||||||
\(149\) | 11.9696 | 0.980588 | 0.490294 | − | 0.871557i | \(-0.336889\pi\) | ||||
0.490294 | + | 0.871557i | \(0.336889\pi\) | |||||||
\(150\) | 41.1207 | 3.35749 | ||||||||
\(151\) | −9.55950 | −0.777941 | −0.388970 | − | 0.921250i | \(-0.627169\pi\) | ||||
−0.388970 | + | 0.921250i | \(0.627169\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −33.4732 | −2.70614 | ||||||||
\(154\) | −0.789032 | −0.0635820 | ||||||||
\(155\) | −43.7796 | −3.51646 | ||||||||
\(156\) | −9.00256 | −0.720782 | ||||||||
\(157\) | 15.0603 | 1.20194 | 0.600970 | − | 0.799272i | \(-0.294781\pi\) | ||||
0.600970 | + | 0.799272i | \(0.294781\pi\) | |||||||
\(158\) | −1.40495 | −0.111771 | ||||||||
\(159\) | −3.57536 | −0.283544 | ||||||||
\(160\) | −4.25314 | −0.336240 | ||||||||
\(161\) | 2.36995 | 0.186778 | ||||||||
\(162\) | −17.5812 | −1.38131 | ||||||||
\(163\) | 9.68699 | 0.758744 | 0.379372 | − | 0.925244i | \(-0.376140\pi\) | ||||
0.379372 | + | 0.925244i | \(0.376140\pi\) | |||||||
\(164\) | 0.0787280 | 0.00614762 | ||||||||
\(165\) | 13.3616 | 1.04020 | ||||||||
\(166\) | −11.0728 | −0.859413 | ||||||||
\(167\) | −10.1358 | −0.784335 | −0.392168 | − | 0.919894i | \(-0.628275\pi\) | ||||
−0.392168 | + | 0.919894i | \(0.628275\pi\) | |||||||
\(168\) | −2.47880 | −0.191244 | ||||||||
\(169\) | −4.78820 | −0.368323 | ||||||||
\(170\) | 20.7245 | 1.58949 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.27932 | −0.326295 | ||||||||
\(173\) | 19.3926 | 1.47439 | 0.737197 | − | 0.675677i | \(-0.236149\pi\) | ||||
0.737197 | + | 0.675677i | \(0.236149\pi\) | |||||||
\(174\) | −21.3423 | −1.61795 | ||||||||
\(175\) | −10.3278 | −0.780710 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 7.86281 | 0.591005 | ||||||||
\(178\) | −0.532856 | −0.0399392 | ||||||||
\(179\) | −3.17158 | −0.237055 | −0.118527 | − | 0.992951i | \(-0.537817\pi\) | ||||
−0.118527 | + | 0.992951i | \(0.537817\pi\) | |||||||
\(180\) | 29.2169 | 2.17770 | ||||||||
\(181\) | 16.1966 | 1.20388 | 0.601942 | − | 0.798540i | \(-0.294394\pi\) | ||||
0.601942 | + | 0.798540i | \(0.294394\pi\) | |||||||
\(182\) | 2.26107 | 0.167602 | ||||||||
\(183\) | 22.2124 | 1.64199 | ||||||||
\(184\) | 3.00362 | 0.221430 | ||||||||
\(185\) | 3.94318 | 0.289908 | ||||||||
\(186\) | −32.3376 | −2.37111 | ||||||||
\(187\) | 4.87274 | 0.356330 | ||||||||
\(188\) | 1.10688 | 0.0807275 | ||||||||
\(189\) | 9.59165 | 0.697690 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.789906 | −0.0571556 | −0.0285778 | − | 0.999592i | \(-0.509098\pi\) | ||||
−0.0285778 | + | 0.999592i | \(0.509098\pi\) | |||||||
\(192\) | −3.14157 | −0.226723 | ||||||||
\(193\) | 6.02776 | 0.433888 | 0.216944 | − | 0.976184i | \(-0.430391\pi\) | ||||
0.216944 | + | 0.976184i | \(0.430391\pi\) | |||||||
\(194\) | −11.9267 | −0.856288 | ||||||||
\(195\) | −38.2892 | −2.74195 | ||||||||
\(196\) | −6.37743 | −0.455531 | ||||||||
\(197\) | 10.7225 | 0.763950 | 0.381975 | − | 0.924173i | \(-0.375244\pi\) | ||||
0.381975 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(198\) | 6.86947 | 0.488192 | ||||||||
\(199\) | −8.73696 | −0.619347 | −0.309673 | − | 0.950843i | \(-0.600220\pi\) | ||||
−0.309673 | + | 0.950843i | \(0.600220\pi\) | |||||||
\(200\) | −13.0892 | −0.925548 | ||||||||
\(201\) | −0.121747 | −0.00858740 | ||||||||
\(202\) | 16.0343 | 1.12817 | ||||||||
\(203\) | 5.36029 | 0.376218 | ||||||||
\(204\) | 15.3081 | 1.07178 | ||||||||
\(205\) | 0.334841 | 0.0233863 | ||||||||
\(206\) | −7.04010 | −0.490507 | ||||||||
\(207\) | −20.6333 | −1.43411 | ||||||||
\(208\) | 2.86562 | 0.198695 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −10.5427 | −0.727515 | ||||||||
\(211\) | −1.55294 | −0.106909 | −0.0534544 | − | 0.998570i | \(-0.517023\pi\) | ||||
−0.0534544 | + | 0.998570i | \(0.517023\pi\) | |||||||
\(212\) | 1.13808 | 0.0781636 | ||||||||
\(213\) | −46.7498 | −3.20325 | ||||||||
\(214\) | −14.5660 | −0.995714 | ||||||||
\(215\) | −18.2005 | −1.24127 | ||||||||
\(216\) | 12.1562 | 0.827127 | ||||||||
\(217\) | 8.12187 | 0.551348 | ||||||||
\(218\) | −1.32900 | −0.0900110 | ||||||||
\(219\) | −28.5462 | −1.92897 | ||||||||
\(220\) | −4.25314 | −0.286747 | ||||||||
\(221\) | −13.9634 | −0.939282 | ||||||||
\(222\) | 2.91262 | 0.195482 | ||||||||
\(223\) | 10.1442 | 0.679306 | 0.339653 | − | 0.940551i | \(-0.389690\pi\) | ||||
0.339653 | + | 0.940551i | \(0.389690\pi\) | |||||||
\(224\) | 0.789032 | 0.0527194 | ||||||||
\(225\) | 89.9161 | 5.99441 | ||||||||
\(226\) | −5.13343 | −0.341471 | ||||||||
\(227\) | 18.0026 | 1.19487 | 0.597436 | − | 0.801917i | \(-0.296186\pi\) | ||||
0.597436 | + | 0.801917i | \(0.296186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0845 | 1.39330 | 0.696652 | − | 0.717409i | \(-0.254672\pi\) | ||||
0.696652 | + | 0.717409i | \(0.254672\pi\) | |||||||
\(230\) | 12.7748 | 0.842347 | ||||||||
\(231\) | −2.47880 | −0.163093 | ||||||||
\(232\) | 6.79350 | 0.446015 | ||||||||
\(233\) | −0.852182 | −0.0558283 | −0.0279142 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279142 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(234\) | −19.6853 | −1.28687 | ||||||||
\(235\) | 4.70772 | 0.307098 | ||||||||
\(236\) | −2.50283 | −0.162920 | ||||||||
\(237\) | −4.41374 | −0.286703 | ||||||||
\(238\) | −3.84475 | −0.249218 | ||||||||
\(239\) | −27.7837 | −1.79718 | −0.898588 | − | 0.438793i | \(-0.855406\pi\) | ||||
−0.898588 | + | 0.438793i | \(0.855406\pi\) | |||||||
\(240\) | −13.3616 | −0.862485 | ||||||||
\(241\) | 14.7320 | 0.948972 | 0.474486 | − | 0.880263i | \(-0.342634\pi\) | ||||
0.474486 | + | 0.880263i | \(0.342634\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −18.7641 | −1.20371 | ||||||||
\(244\) | −7.07049 | −0.452642 | ||||||||
\(245\) | −27.1241 | −1.73290 | ||||||||
\(246\) | 0.247330 | 0.0157692 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.2935 | 0.653635 | ||||||||
\(249\) | −34.7859 | −2.20446 | ||||||||
\(250\) | −34.4046 | −2.17594 | ||||||||
\(251\) | −14.1660 | −0.894151 | −0.447076 | − | 0.894496i | \(-0.647534\pi\) | ||||
−0.447076 | + | 0.894496i | \(0.647534\pi\) | |||||||
\(252\) | −5.42023 | −0.341443 | ||||||||
\(253\) | 3.00362 | 0.188836 | ||||||||
\(254\) | 0.480932 | 0.0301764 | ||||||||
\(255\) | 65.1074 | 4.07718 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.8309 | 1.61128 | 0.805642 | − | 0.592402i | \(-0.201820\pi\) | ||||
0.805642 | + | 0.592402i | \(0.201820\pi\) | |||||||
\(258\) | −13.4438 | −0.836973 | ||||||||
\(259\) | −0.731529 | −0.0454550 | ||||||||
\(260\) | 12.1879 | 0.755862 | ||||||||
\(261\) | −46.6677 | −2.88866 | ||||||||
\(262\) | −19.3980 | −1.19842 | ||||||||
\(263\) | 2.52559 | 0.155735 | 0.0778673 | − | 0.996964i | \(-0.475189\pi\) | ||||
0.0778673 | + | 0.996964i | \(0.475189\pi\) | |||||||
\(264\) | −3.14157 | −0.193350 | ||||||||
\(265\) | 4.84041 | 0.297344 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.67400 | −0.102447 | ||||||||
\(268\) | 0.0387536 | 0.00236726 | ||||||||
\(269\) | −6.20436 | −0.378287 | −0.189143 | − | 0.981949i | \(-0.560571\pi\) | ||||
−0.189143 | + | 0.981949i | \(0.560571\pi\) | |||||||
\(270\) | 51.7022 | 3.14649 | ||||||||
\(271\) | −21.4449 | −1.30268 | −0.651342 | − | 0.758785i | \(-0.725793\pi\) | ||||
−0.651342 | + | 0.758785i | \(0.725793\pi\) | |||||||
\(272\) | −4.87274 | −0.295453 | ||||||||
\(273\) | 7.10331 | 0.429912 | ||||||||
\(274\) | −13.3184 | −0.804592 | ||||||||
\(275\) | −13.0892 | −0.789310 | ||||||||
\(276\) | 9.43609 | 0.567986 | ||||||||
\(277\) | −16.5444 | −0.994055 | −0.497027 | − | 0.867735i | \(-0.665575\pi\) | ||||
−0.497027 | + | 0.867735i | \(0.665575\pi\) | |||||||
\(278\) | 1.65530 | 0.0992781 | ||||||||
\(279\) | −70.7106 | −4.23334 | ||||||||
\(280\) | 3.35587 | 0.200551 | ||||||||
\(281\) | 7.17752 | 0.428175 | 0.214087 | − | 0.976815i | \(-0.431322\pi\) | ||||
0.214087 | + | 0.976815i | \(0.431322\pi\) | |||||||
\(282\) | 3.47734 | 0.207073 | ||||||||
\(283\) | −18.0992 | −1.07588 | −0.537942 | − | 0.842982i | \(-0.680798\pi\) | ||||
−0.537942 | + | 0.842982i | \(0.680798\pi\) | |||||||
\(284\) | 14.8810 | 0.883027 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.86562 | 0.169448 | ||||||||
\(287\) | −0.0621189 | −0.00366676 | ||||||||
\(288\) | −6.86947 | −0.404788 | ||||||||
\(289\) | 6.74359 | 0.396681 | ||||||||
\(290\) | 28.8937 | 1.69670 | ||||||||
\(291\) | −37.4686 | −2.19645 | ||||||||
\(292\) | 9.08659 | 0.531752 | ||||||||
\(293\) | −28.4730 | −1.66341 | −0.831706 | − | 0.555217i | \(-0.812635\pi\) | ||||
−0.831706 | + | 0.555217i | \(0.812635\pi\) | |||||||
\(294\) | −20.0352 | −1.16847 | ||||||||
\(295\) | −10.6449 | −0.619769 | ||||||||
\(296\) | −0.927122 | −0.0538879 | ||||||||
\(297\) | 12.1562 | 0.705376 | ||||||||
\(298\) | −11.9696 | −0.693380 | ||||||||
\(299\) | −8.60725 | −0.497770 | ||||||||
\(300\) | −41.1207 | −2.37411 | ||||||||
\(301\) | 3.37652 | 0.194619 | ||||||||
\(302\) | 9.55950 | 0.550087 | ||||||||
\(303\) | 50.3729 | 2.89385 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.0718 | −1.72191 | ||||||||
\(306\) | 33.4732 | 1.91353 | ||||||||
\(307\) | 0.660887 | 0.0377188 | 0.0188594 | − | 0.999822i | \(-0.493997\pi\) | ||||
0.0188594 | + | 0.999822i | \(0.493997\pi\) | |||||||
\(308\) | 0.789032 | 0.0449593 | ||||||||
\(309\) | −22.1170 | −1.25819 | ||||||||
\(310\) | 43.7796 | 2.48651 | ||||||||
\(311\) | 26.1008 | 1.48004 | 0.740019 | − | 0.672586i | \(-0.234816\pi\) | ||||
0.740019 | + | 0.672586i | \(0.234816\pi\) | |||||||
\(312\) | 9.00256 | 0.509670 | ||||||||
\(313\) | −6.18994 | −0.349876 | −0.174938 | − | 0.984579i | \(-0.555972\pi\) | ||||
−0.174938 | + | 0.984579i | \(0.555972\pi\) | |||||||
\(314\) | −15.0603 | −0.849900 | ||||||||
\(315\) | −23.0530 | −1.29889 | ||||||||
\(316\) | 1.40495 | 0.0790344 | ||||||||
\(317\) | −30.5155 | −1.71392 | −0.856961 | − | 0.515381i | \(-0.827650\pi\) | ||||
−0.856961 | + | 0.515381i | \(0.827650\pi\) | |||||||
\(318\) | 3.57536 | 0.200496 | ||||||||
\(319\) | 6.79350 | 0.380363 | ||||||||
\(320\) | 4.25314 | 0.237758 | ||||||||
\(321\) | −45.7603 | −2.55409 | ||||||||
\(322\) | −2.36995 | −0.132072 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.5812 | 0.976736 | ||||||||
\(325\) | 37.5088 | 2.08061 | ||||||||
\(326\) | −9.68699 | −0.536513 | ||||||||
\(327\) | −4.17514 | −0.230886 | ||||||||
\(328\) | −0.0787280 | −0.00434703 | ||||||||
\(329\) | −0.873363 | −0.0481501 | ||||||||
\(330\) | −13.3616 | −0.735529 | ||||||||
\(331\) | −9.69672 | −0.532980 | −0.266490 | − | 0.963838i | \(-0.585864\pi\) | ||||
−0.266490 | + | 0.963838i | \(0.585864\pi\) | |||||||
\(332\) | 11.0728 | 0.607696 | ||||||||
\(333\) | 6.36884 | 0.349010 | ||||||||
\(334\) | 10.1358 | 0.554609 | ||||||||
\(335\) | 0.164825 | 0.00900534 | ||||||||
\(336\) | 2.47880 | 0.135230 | ||||||||
\(337\) | 20.9048 | 1.13876 | 0.569379 | − | 0.822075i | \(-0.307184\pi\) | ||||
0.569379 | + | 0.822075i | \(0.307184\pi\) | |||||||
\(338\) | 4.78820 | 0.260444 | ||||||||
\(339\) | −16.1270 | −0.875901 | ||||||||
\(340\) | −20.7245 | −1.12394 | ||||||||
\(341\) | 10.2935 | 0.557422 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5552 | 0.569928 | ||||||||
\(344\) | 4.27932 | 0.230725 | ||||||||
\(345\) | 40.1330 | 2.16069 | ||||||||
\(346\) | −19.3926 | −1.04255 | ||||||||
\(347\) | −13.5329 | −0.726485 | −0.363243 | − | 0.931695i | \(-0.618330\pi\) | ||||
−0.363243 | + | 0.931695i | \(0.618330\pi\) | |||||||
\(348\) | 21.3423 | 1.14406 | ||||||||
\(349\) | 0.617963 | 0.0330788 | 0.0165394 | − | 0.999863i | \(-0.494735\pi\) | ||||
0.0165394 | + | 0.999863i | \(0.494735\pi\) | |||||||
\(350\) | 10.3278 | 0.552045 | ||||||||
\(351\) | −34.8352 | −1.85936 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −10.7603 | −0.572714 | −0.286357 | − | 0.958123i | \(-0.592444\pi\) | ||||
−0.286357 | + | 0.958123i | \(0.592444\pi\) | |||||||
\(354\) | −7.86281 | −0.417904 | ||||||||
\(355\) | 63.2912 | 3.35915 | ||||||||
\(356\) | 0.532856 | 0.0282413 | ||||||||
\(357\) | −12.0785 | −0.639265 | ||||||||
\(358\) | 3.17158 | 0.167623 | ||||||||
\(359\) | 21.1931 | 1.11853 | 0.559265 | − | 0.828989i | \(-0.311084\pi\) | ||||
0.559265 | + | 0.828989i | \(0.311084\pi\) | |||||||
\(360\) | −29.2169 | −1.53986 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −16.1966 | −0.851274 | ||||||||
\(363\) | −3.14157 | −0.164890 | ||||||||
\(364\) | −2.26107 | −0.118512 | ||||||||
\(365\) | 38.6466 | 2.02285 | ||||||||
\(366\) | −22.2124 | −1.16106 | ||||||||
\(367\) | 10.1420 | 0.529408 | 0.264704 | − | 0.964330i | \(-0.414726\pi\) | ||||
0.264704 | + | 0.964330i | \(0.414726\pi\) | |||||||
\(368\) | −3.00362 | −0.156575 | ||||||||
\(369\) | 0.540820 | 0.0281540 | ||||||||
\(370\) | −3.94318 | −0.204996 | ||||||||
\(371\) | −0.897981 | −0.0466209 | ||||||||
\(372\) | 32.3376 | 1.67663 | ||||||||
\(373\) | −7.87532 | −0.407769 | −0.203884 | − | 0.978995i | \(-0.565357\pi\) | ||||
−0.203884 | + | 0.978995i | \(0.565357\pi\) | |||||||
\(374\) | −4.87274 | −0.251963 | ||||||||
\(375\) | −108.085 | −5.58147 | ||||||||
\(376\) | −1.10688 | −0.0570830 | ||||||||
\(377\) | −19.4676 | −1.00263 | ||||||||
\(378\) | −9.59165 | −0.493341 | ||||||||
\(379\) | −14.8933 | −0.765016 | −0.382508 | − | 0.923952i | \(-0.624940\pi\) | ||||
−0.382508 | + | 0.923952i | \(0.624940\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.51088 | 0.0774049 | ||||||||
\(382\) | 0.789906 | 0.0404151 | ||||||||
\(383\) | 9.65125 | 0.493156 | 0.246578 | − | 0.969123i | \(-0.420694\pi\) | ||||
0.246578 | + | 0.969123i | \(0.420694\pi\) | |||||||
\(384\) | 3.14157 | 0.160318 | ||||||||
\(385\) | 3.35587 | 0.171031 | ||||||||
\(386\) | −6.02776 | −0.306805 | ||||||||
\(387\) | −29.3967 | −1.49432 | ||||||||
\(388\) | 11.9267 | 0.605487 | ||||||||
\(389\) | −9.10826 | −0.461807 | −0.230904 | − | 0.972977i | \(-0.574168\pi\) | ||||
−0.230904 | + | 0.972977i | \(0.574168\pi\) | |||||||
\(390\) | 38.2892 | 1.93885 | ||||||||
\(391\) | 14.6359 | 0.740167 | ||||||||
\(392\) | 6.37743 | 0.322109 | ||||||||
\(393\) | −60.9404 | −3.07403 | ||||||||
\(394\) | −10.7225 | −0.540194 | ||||||||
\(395\) | 5.97544 | 0.300657 | ||||||||
\(396\) | −6.86947 | −0.345204 | ||||||||
\(397\) | 1.57061 | 0.0788266 | 0.0394133 | − | 0.999223i | \(-0.487451\pi\) | ||||
0.0394133 | + | 0.999223i | \(0.487451\pi\) | |||||||
\(398\) | 8.73696 | 0.437944 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0892 | 0.654461 | ||||||||
\(401\) | 7.96088 | 0.397547 | 0.198774 | − | 0.980045i | \(-0.436304\pi\) | ||||
0.198774 | + | 0.980045i | \(0.436304\pi\) | |||||||
\(402\) | 0.121747 | 0.00607221 | ||||||||
\(403\) | −29.4972 | −1.46936 | ||||||||
\(404\) | −16.0343 | −0.797736 | ||||||||
\(405\) | 74.7755 | 3.71563 | ||||||||
\(406\) | −5.36029 | −0.266026 | ||||||||
\(407\) | −0.927122 | −0.0459557 | ||||||||
\(408\) | −15.3081 | −0.757862 | ||||||||
\(409\) | 4.38108 | 0.216630 | 0.108315 | − | 0.994117i | \(-0.465454\pi\) | ||||
0.108315 | + | 0.994117i | \(0.465454\pi\) | |||||||
\(410\) | −0.334841 | −0.0165366 | ||||||||
\(411\) | −41.8406 | −2.06384 | ||||||||
\(412\) | 7.04010 | 0.346841 | ||||||||
\(413\) | 1.97481 | 0.0971740 | ||||||||
\(414\) | 20.6333 | 1.01407 | ||||||||
\(415\) | 47.0940 | 2.31175 | ||||||||
\(416\) | −2.86562 | −0.140499 | ||||||||
\(417\) | 5.20023 | 0.254656 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.1059 | −0.640266 | −0.320133 | − | 0.947373i | \(-0.603728\pi\) | ||||
−0.320133 | + | 0.947373i | \(0.603728\pi\) | |||||||
\(420\) | 10.5427 | 0.514431 | ||||||||
\(421\) | 35.0448 | 1.70798 | 0.853990 | − | 0.520289i | \(-0.174176\pi\) | ||||
0.853990 | + | 0.520289i | \(0.174176\pi\) | |||||||
\(422\) | 1.55294 | 0.0755960 | ||||||||
\(423\) | 7.60368 | 0.369704 | ||||||||
\(424\) | −1.13808 | −0.0552700 | ||||||||
\(425\) | −63.7804 | −3.09380 | ||||||||
\(426\) | 46.7498 | 2.26504 | ||||||||
\(427\) | 5.57884 | 0.269979 | ||||||||
\(428\) | 14.5660 | 0.704076 | ||||||||
\(429\) | 9.00256 | 0.434648 | ||||||||
\(430\) | 18.2005 | 0.877708 | ||||||||
\(431\) | 15.0634 | 0.725581 | 0.362790 | − | 0.931871i | \(-0.381824\pi\) | ||||
0.362790 | + | 0.931871i | \(0.381824\pi\) | |||||||
\(432\) | −12.1562 | −0.584867 | ||||||||
\(433\) | −20.4220 | −0.981420 | −0.490710 | − | 0.871323i | \(-0.663263\pi\) | ||||
−0.490710 | + | 0.871323i | \(0.663263\pi\) | |||||||
\(434\) | −8.12187 | −0.389862 | ||||||||
\(435\) | 90.7717 | 4.35217 | ||||||||
\(436\) | 1.32900 | 0.0636474 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 28.5462 | 1.36399 | ||||||||
\(439\) | 32.9051 | 1.57048 | 0.785238 | − | 0.619194i | \(-0.212541\pi\) | ||||
0.785238 | + | 0.619194i | \(0.212541\pi\) | |||||||
\(440\) | 4.25314 | 0.202761 | ||||||||
\(441\) | −43.8096 | −2.08617 | ||||||||
\(442\) | 13.9634 | 0.664173 | ||||||||
\(443\) | 34.9998 | 1.66289 | 0.831446 | − | 0.555606i | \(-0.187514\pi\) | ||||
0.831446 | + | 0.555606i | \(0.187514\pi\) | |||||||
\(444\) | −2.91262 | −0.138227 | ||||||||
\(445\) | 2.26631 | 0.107433 | ||||||||
\(446\) | −10.1442 | −0.480342 | ||||||||
\(447\) | −37.6034 | −1.77858 | ||||||||
\(448\) | −0.789032 | −0.0372783 | ||||||||
\(449\) | −12.2917 | −0.580080 | −0.290040 | − | 0.957015i | \(-0.593669\pi\) | ||||
−0.290040 | + | 0.957015i | \(0.593669\pi\) | |||||||
\(450\) | −89.9161 | −4.23869 | ||||||||
\(451\) | −0.0787280 | −0.00370716 | ||||||||
\(452\) | 5.13343 | 0.241456 | ||||||||
\(453\) | 30.0318 | 1.41102 | ||||||||
\(454\) | −18.0026 | −0.844902 | ||||||||
\(455\) | −9.61665 | −0.450835 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.8163 | 1.90931 | 0.954653 | − | 0.297721i | \(-0.0962264\pi\) | ||||
0.954653 | + | 0.297721i | \(0.0962264\pi\) | |||||||
\(458\) | −21.0845 | −0.985215 | ||||||||
\(459\) | 59.2341 | 2.76481 | ||||||||
\(460\) | −12.7748 | −0.595629 | ||||||||
\(461\) | 11.6324 | 0.541776 | 0.270888 | − | 0.962611i | \(-0.412683\pi\) | ||||
0.270888 | + | 0.962611i | \(0.412683\pi\) | |||||||
\(462\) | 2.47880 | 0.115324 | ||||||||
\(463\) | 19.2052 | 0.892540 | 0.446270 | − | 0.894898i | \(-0.352752\pi\) | ||||
0.446270 | + | 0.894898i | \(0.352752\pi\) | |||||||
\(464\) | −6.79350 | −0.315380 | ||||||||
\(465\) | 137.537 | 6.37811 | ||||||||
\(466\) | 0.852182 | 0.0394766 | ||||||||
\(467\) | 9.52417 | 0.440726 | 0.220363 | − | 0.975418i | \(-0.429276\pi\) | ||||
0.220363 | + | 0.975418i | \(0.429276\pi\) | |||||||
\(468\) | 19.6853 | 0.909954 | ||||||||
\(469\) | −0.0305779 | −0.00141195 | ||||||||
\(470\) | −4.70772 | −0.217151 | ||||||||
\(471\) | −47.3129 | −2.18006 | ||||||||
\(472\) | 2.50283 | 0.115202 | ||||||||
\(473\) | 4.27932 | 0.196763 | ||||||||
\(474\) | 4.41374 | 0.202730 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.84475 | 0.176224 | ||||||||
\(477\) | 7.81801 | 0.357962 | ||||||||
\(478\) | 27.7837 | 1.27080 | ||||||||
\(479\) | 25.8981 | 1.18331 | 0.591656 | − | 0.806190i | \(-0.298474\pi\) | ||||
0.591656 | + | 0.806190i | \(0.298474\pi\) | |||||||
\(480\) | 13.3616 | 0.609869 | ||||||||
\(481\) | 2.65678 | 0.121139 | ||||||||
\(482\) | −14.7320 | −0.671025 | ||||||||
\(483\) | −7.44538 | −0.338776 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 50.7260 | 2.30335 | ||||||||
\(486\) | 18.7641 | 0.851155 | ||||||||
\(487\) | 1.13302 | 0.0513418 | 0.0256709 | − | 0.999670i | \(-0.491828\pi\) | ||||
0.0256709 | + | 0.999670i | \(0.491828\pi\) | |||||||
\(488\) | 7.07049 | 0.320066 | ||||||||
\(489\) | −30.4324 | −1.37620 | ||||||||
\(490\) | 27.1241 | 1.22534 | ||||||||
\(491\) | −2.02215 | −0.0912582 | −0.0456291 | − | 0.998958i | \(-0.514529\pi\) | ||||
−0.0456291 | + | 0.998958i | \(0.514529\pi\) | |||||||
\(492\) | −0.247330 | −0.0111505 | ||||||||
\(493\) | 33.1029 | 1.49088 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.2169 | −1.31320 | ||||||||
\(496\) | −10.2935 | −0.462190 | ||||||||
\(497\) | −11.7416 | −0.526683 | ||||||||
\(498\) | 34.7859 | 1.55879 | ||||||||
\(499\) | 39.8484 | 1.78386 | 0.891930 | − | 0.452173i | \(-0.149351\pi\) | ||||
0.891930 | + | 0.452173i | \(0.149351\pi\) | |||||||
\(500\) | 34.4046 | 1.53862 | ||||||||
\(501\) | 31.8425 | 1.42262 | ||||||||
\(502\) | 14.1660 | 0.632260 | ||||||||
\(503\) | 43.6692 | 1.94711 | 0.973556 | − | 0.228447i | \(-0.0733648\pi\) | ||||
0.973556 | + | 0.228447i | \(0.0733648\pi\) | |||||||
\(504\) | 5.42023 | 0.241436 | ||||||||
\(505\) | −68.1961 | −3.03469 | ||||||||
\(506\) | −3.00362 | −0.133527 | ||||||||
\(507\) | 15.0425 | 0.668060 | ||||||||
\(508\) | −0.480932 | −0.0213379 | ||||||||
\(509\) | 24.4491 | 1.08369 | 0.541844 | − | 0.840479i | \(-0.317726\pi\) | ||||
0.541844 | + | 0.840479i | \(0.317726\pi\) | |||||||
\(510\) | −65.1074 | −2.88300 | ||||||||
\(511\) | −7.16961 | −0.317165 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.8309 | −1.13935 | ||||||||
\(515\) | 29.9425 | 1.31943 | ||||||||
\(516\) | 13.4438 | 0.591829 | ||||||||
\(517\) | −1.10688 | −0.0486805 | ||||||||
\(518\) | 0.731529 | 0.0321415 | ||||||||
\(519\) | −60.9234 | −2.67424 | ||||||||
\(520\) | −12.1879 | −0.534475 | ||||||||
\(521\) | 22.6422 | 0.991972 | 0.495986 | − | 0.868330i | \(-0.334807\pi\) | ||||
0.495986 | + | 0.868330i | \(0.334807\pi\) | |||||||
\(522\) | 46.6677 | 2.04259 | ||||||||
\(523\) | −24.7889 | −1.08394 | −0.541972 | − | 0.840397i | \(-0.682322\pi\) | ||||
−0.541972 | + | 0.840397i | \(0.682322\pi\) | |||||||
\(524\) | 19.3980 | 0.847408 | ||||||||
\(525\) | 32.4456 | 1.41604 | ||||||||
\(526\) | −2.52559 | −0.110121 | ||||||||
\(527\) | 50.1573 | 2.18489 | ||||||||
\(528\) | 3.14157 | 0.136719 | ||||||||
\(529\) | −13.9783 | −0.607751 | ||||||||
\(530\) | −4.84041 | −0.210254 | ||||||||
\(531\) | −17.1931 | −0.746117 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.225605 | 0.00977203 | ||||||||
\(534\) | 1.67400 | 0.0724412 | ||||||||
\(535\) | 61.9515 | 2.67840 | ||||||||
\(536\) | −0.0387536 | −0.00167390 | ||||||||
\(537\) | 9.96374 | 0.429967 | ||||||||
\(538\) | 6.20436 | 0.267489 | ||||||||
\(539\) | 6.37743 | 0.274695 | ||||||||
\(540\) | −51.7022 | −2.22491 | ||||||||
\(541\) | −1.68305 | −0.0723598 | −0.0361799 | − | 0.999345i | \(-0.511519\pi\) | ||||
−0.0361799 | + | 0.999345i | \(0.511519\pi\) | |||||||
\(542\) | 21.4449 | 0.921136 | ||||||||
\(543\) | −50.8828 | −2.18359 | ||||||||
\(544\) | 4.87274 | 0.208917 | ||||||||
\(545\) | 5.65241 | 0.242123 | ||||||||
\(546\) | −7.10331 | −0.303994 | ||||||||
\(547\) | −1.39005 | −0.0594341 | −0.0297170 | − | 0.999558i | \(-0.509461\pi\) | ||||
−0.0297170 | + | 0.999558i | \(0.509461\pi\) | |||||||
\(548\) | 13.3184 | 0.568932 | ||||||||
\(549\) | −48.5705 | −2.07294 | ||||||||
\(550\) | 13.0892 | 0.558126 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −9.43609 | −0.401627 | ||||||||
\(553\) | −1.10855 | −0.0471402 | ||||||||
\(554\) | 16.5444 | 0.702903 | ||||||||
\(555\) | −12.3878 | −0.525832 | ||||||||
\(556\) | −1.65530 | −0.0702002 | ||||||||
\(557\) | 10.1719 | 0.430995 | 0.215498 | − | 0.976504i | \(-0.430863\pi\) | ||||
0.215498 | + | 0.976504i | \(0.430863\pi\) | |||||||
\(558\) | 70.7106 | 2.99342 | ||||||||
\(559\) | −12.2629 | −0.518666 | ||||||||
\(560\) | −3.35587 | −0.141811 | ||||||||
\(561\) | −15.3081 | −0.646307 | ||||||||
\(562\) | −7.17752 | −0.302765 | ||||||||
\(563\) | −11.4443 | −0.482319 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(564\) | −3.47734 | −0.146423 | ||||||||
\(565\) | 21.8332 | 0.918530 | ||||||||
\(566\) | 18.0992 | 0.760764 | ||||||||
\(567\) | −13.8722 | −0.582576 | ||||||||
\(568\) | −14.8810 | −0.624394 | ||||||||
\(569\) | 25.3528 | 1.06285 | 0.531423 | − | 0.847107i | \(-0.321657\pi\) | ||||
0.531423 | + | 0.847107i | \(0.321657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.6040 | −1.32259 | −0.661293 | − | 0.750128i | \(-0.729992\pi\) | ||||
−0.661293 | + | 0.750128i | \(0.729992\pi\) | |||||||
\(572\) | −2.86562 | −0.119818 | ||||||||
\(573\) | 2.48155 | 0.103668 | ||||||||
\(574\) | 0.0621189 | 0.00259279 | ||||||||
\(575\) | −39.3151 | −1.63955 | ||||||||
\(576\) | 6.86947 | 0.286228 | ||||||||
\(577\) | 20.2670 | 0.843726 | 0.421863 | − | 0.906660i | \(-0.361376\pi\) | ||||
0.421863 | + | 0.906660i | \(0.361376\pi\) | |||||||
\(578\) | −6.74359 | −0.280496 | ||||||||
\(579\) | −18.9366 | −0.786980 | ||||||||
\(580\) | −28.8937 | −1.19975 | ||||||||
\(581\) | −8.73676 | −0.362462 | ||||||||
\(582\) | 37.4686 | 1.55312 | ||||||||
\(583\) | −1.13808 | −0.0471344 | ||||||||
\(584\) | −9.08659 | −0.376006 | ||||||||
\(585\) | 83.7245 | 3.46158 | ||||||||
\(586\) | 28.4730 | 1.17621 | ||||||||
\(587\) | 13.3771 | 0.552132 | 0.276066 | − | 0.961139i | \(-0.410969\pi\) | ||||
0.276066 | + | 0.961139i | \(0.410969\pi\) | |||||||
\(588\) | 20.0352 | 0.826236 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 10.6449 | 0.438243 | ||||||||
\(591\) | −33.6856 | −1.38564 | ||||||||
\(592\) | 0.927122 | 0.0381045 | ||||||||
\(593\) | −21.7005 | −0.891134 | −0.445567 | − | 0.895249i | \(-0.646998\pi\) | ||||
−0.445567 | + | 0.895249i | \(0.646998\pi\) | |||||||
\(594\) | −12.1562 | −0.498776 | ||||||||
\(595\) | 16.3523 | 0.670377 | ||||||||
\(596\) | 11.9696 | 0.490294 | ||||||||
\(597\) | 27.4478 | 1.12336 | ||||||||
\(598\) | 8.60725 | 0.351976 | ||||||||
\(599\) | 43.5240 | 1.77834 | 0.889171 | − | 0.457574i | \(-0.151282\pi\) | ||||
0.889171 | + | 0.457574i | \(0.151282\pi\) | |||||||
\(600\) | 41.1207 | 1.67875 | ||||||||
\(601\) | −37.3107 | −1.52193 | −0.760967 | − | 0.648790i | \(-0.775275\pi\) | ||||
−0.760967 | + | 0.648790i | \(0.775275\pi\) | |||||||
\(602\) | −3.37652 | −0.137617 | ||||||||
\(603\) | 0.266217 | 0.0108412 | ||||||||
\(604\) | −9.55950 | −0.388970 | ||||||||
\(605\) | 4.25314 | 0.172915 | ||||||||
\(606\) | −50.3729 | −2.04626 | ||||||||
\(607\) | 1.12996 | 0.0458635 | 0.0229318 | − | 0.999737i | \(-0.492700\pi\) | ||||
0.0229318 | + | 0.999737i | \(0.492700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.8397 | −0.682380 | ||||||||
\(610\) | 30.0718 | 1.21757 | ||||||||
\(611\) | 3.17190 | 0.128321 | ||||||||
\(612\) | −33.4732 | −1.35307 | ||||||||
\(613\) | −10.0991 | −0.407899 | −0.203950 | − | 0.978981i | \(-0.565378\pi\) | ||||
−0.203950 | + | 0.978981i | \(0.565378\pi\) | |||||||
\(614\) | −0.660887 | −0.0266712 | ||||||||
\(615\) | −1.05193 | −0.0424178 | ||||||||
\(616\) | −0.789032 | −0.0317910 | ||||||||
\(617\) | −36.7553 | −1.47971 | −0.739857 | − | 0.672764i | \(-0.765107\pi\) | ||||
−0.739857 | + | 0.672764i | \(0.765107\pi\) | |||||||
\(618\) | 22.1170 | 0.889675 | ||||||||
\(619\) | 23.7732 | 0.955526 | 0.477763 | − | 0.878489i | \(-0.341448\pi\) | ||||
0.477763 | + | 0.878489i | \(0.341448\pi\) | |||||||
\(620\) | −43.7796 | −1.75823 | ||||||||
\(621\) | 36.5127 | 1.46520 | ||||||||
\(622\) | −26.1008 | −1.04655 | ||||||||
\(623\) | −0.420440 | −0.0168446 | ||||||||
\(624\) | −9.00256 | −0.360391 | ||||||||
\(625\) | 80.8817 | 3.23527 | ||||||||
\(626\) | 6.18994 | 0.247400 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.0603 | 0.600970 | ||||||||
\(629\) | −4.51762 | −0.180129 | ||||||||
\(630\) | 23.0530 | 0.918455 | ||||||||
\(631\) | 25.9645 | 1.03363 | 0.516815 | − | 0.856097i | \(-0.327118\pi\) | ||||
0.516815 | + | 0.856097i | \(0.327118\pi\) | |||||||
\(632\) | −1.40495 | −0.0558857 | ||||||||
\(633\) | 4.87867 | 0.193910 | ||||||||
\(634\) | 30.5155 | 1.21193 | ||||||||
\(635\) | −2.04547 | −0.0811721 | ||||||||
\(636\) | −3.57536 | −0.141772 | ||||||||
\(637\) | −18.2753 | −0.724094 | ||||||||
\(638\) | −6.79350 | −0.268957 | ||||||||
\(639\) | 102.225 | 4.04395 | ||||||||
\(640\) | −4.25314 | −0.168120 | ||||||||
\(641\) | 0.942753 | 0.0372365 | 0.0186183 | − | 0.999827i | \(-0.494073\pi\) | ||||
0.0186183 | + | 0.999827i | \(0.494073\pi\) | |||||||
\(642\) | 45.7603 | 1.80601 | ||||||||
\(643\) | 24.9667 | 0.984591 | 0.492296 | − | 0.870428i | \(-0.336158\pi\) | ||||
0.492296 | + | 0.870428i | \(0.336158\pi\) | |||||||
\(644\) | 2.36995 | 0.0933892 | ||||||||
\(645\) | 57.1783 | 2.25139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.15151 | 0.241841 | 0.120920 | − | 0.992662i | \(-0.461415\pi\) | ||||
0.120920 | + | 0.992662i | \(0.461415\pi\) | |||||||
\(648\) | −17.5812 | −0.690657 | ||||||||
\(649\) | 2.50283 | 0.0982445 | ||||||||
\(650\) | −37.5088 | −1.47122 | ||||||||
\(651\) | −25.5154 | −1.00003 | ||||||||
\(652\) | 9.68699 | 0.379372 | ||||||||
\(653\) | −40.1091 | −1.56959 | −0.784795 | − | 0.619756i | \(-0.787232\pi\) | ||||
−0.784795 | + | 0.619756i | \(0.787232\pi\) | |||||||
\(654\) | 4.17514 | 0.163261 | ||||||||
\(655\) | 82.5027 | 3.22365 | ||||||||
\(656\) | 0.0787280 | 0.00307381 | ||||||||
\(657\) | 62.4201 | 2.43524 | ||||||||
\(658\) | 0.873363 | 0.0340473 | ||||||||
\(659\) | 2.57003 | 0.100114 | 0.0500570 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500570 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(660\) | 13.3616 | 0.520098 | ||||||||
\(661\) | 14.3037 | 0.556348 | 0.278174 | − | 0.960531i | \(-0.410271\pi\) | ||||
0.278174 | + | 0.960531i | \(0.410271\pi\) | |||||||
\(662\) | 9.69672 | 0.376874 | ||||||||
\(663\) | 43.8671 | 1.70366 | ||||||||
\(664\) | −11.0728 | −0.429706 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.36884 | −0.246787 | ||||||||
\(667\) | 20.4051 | 0.790088 | ||||||||
\(668\) | −10.1358 | −0.392168 | ||||||||
\(669\) | −31.8687 | −1.23212 | ||||||||
\(670\) | −0.164825 | −0.00636774 | ||||||||
\(671\) | 7.07049 | 0.272953 | ||||||||
\(672\) | −2.47880 | −0.0956218 | ||||||||
\(673\) | −30.6801 | −1.18263 | −0.591315 | − | 0.806441i | \(-0.701391\pi\) | ||||
−0.591315 | + | 0.806441i | \(0.701391\pi\) | |||||||
\(674\) | −20.9048 | −0.805224 | ||||||||
\(675\) | −159.116 | −6.12436 | ||||||||
\(676\) | −4.78820 | −0.184162 | ||||||||
\(677\) | −23.3072 | −0.895768 | −0.447884 | − | 0.894092i | \(-0.647822\pi\) | ||||
−0.447884 | + | 0.894092i | \(0.647822\pi\) | |||||||
\(678\) | 16.1270 | 0.619355 | ||||||||
\(679\) | −9.41056 | −0.361144 | ||||||||
\(680\) | 20.7245 | 0.794747 | ||||||||
\(681\) | −56.5564 | −2.16724 | ||||||||
\(682\) | −10.2935 | −0.394157 | ||||||||
\(683\) | 16.6896 | 0.638609 | 0.319304 | − | 0.947652i | \(-0.396551\pi\) | ||||
0.319304 | + | 0.947652i | \(0.396551\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 56.6449 | 2.16429 | ||||||||
\(686\) | −10.5552 | −0.403000 | ||||||||
\(687\) | −66.2385 | −2.52716 | ||||||||
\(688\) | −4.27932 | −0.163147 | ||||||||
\(689\) | 3.26131 | 0.124246 | ||||||||
\(690\) | −40.1330 | −1.52784 | ||||||||
\(691\) | −2.39287 | −0.0910289 | −0.0455145 | − | 0.998964i | \(-0.514493\pi\) | ||||
−0.0455145 | + | 0.998964i | \(0.514493\pi\) | |||||||
\(692\) | 19.3926 | 0.737197 | ||||||||
\(693\) | 5.42023 | 0.205898 | ||||||||
\(694\) | 13.5329 | 0.513703 | ||||||||
\(695\) | −7.04021 | −0.267050 | ||||||||
\(696\) | −21.3423 | −0.808976 | ||||||||
\(697\) | −0.383621 | −0.0145307 | ||||||||
\(698\) | −0.617963 | −0.0233903 | ||||||||
\(699\) | 2.67719 | 0.101261 | ||||||||
\(700\) | −10.3278 | −0.390355 | ||||||||
\(701\) | −29.2046 | −1.10304 | −0.551522 | − | 0.834161i | \(-0.685953\pi\) | ||||
−0.551522 | + | 0.834161i | \(0.685953\pi\) | |||||||
\(702\) | 34.8352 | 1.31477 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −14.7896 | −0.557010 | ||||||||
\(706\) | 10.7603 | 0.404970 | ||||||||
\(707\) | 12.6516 | 0.475811 | ||||||||
\(708\) | 7.86281 | 0.295502 | ||||||||
\(709\) | −10.3287 | −0.387902 | −0.193951 | − | 0.981011i | \(-0.562130\pi\) | ||||
−0.193951 | + | 0.981011i | \(0.562130\pi\) | |||||||
\(710\) | −63.2912 | −2.37527 | ||||||||
\(711\) | 9.65124 | 0.361950 | ||||||||
\(712\) | −0.532856 | −0.0199696 | ||||||||
\(713\) | 30.9176 | 1.15787 | ||||||||
\(714\) | 12.0785 | 0.452028 | ||||||||
\(715\) | −12.1879 | −0.455802 | ||||||||
\(716\) | −3.17158 | −0.118527 | ||||||||
\(717\) | 87.2844 | 3.25970 | ||||||||
\(718\) | −21.1931 | −0.790920 | ||||||||
\(719\) | 10.5567 | 0.393698 | 0.196849 | − | 0.980434i | \(-0.436929\pi\) | ||||
0.196849 | + | 0.980434i | \(0.436929\pi\) | |||||||
\(720\) | 29.2169 | 1.08885 | ||||||||
\(721\) | −5.55486 | −0.206874 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.2817 | −1.72123 | ||||||||
\(724\) | 16.1966 | 0.601942 | ||||||||
\(725\) | −88.9216 | −3.30247 | ||||||||
\(726\) | 3.14157 | 0.116595 | ||||||||
\(727\) | 10.0662 | 0.373337 | 0.186668 | − | 0.982423i | \(-0.440231\pi\) | ||||
0.186668 | + | 0.982423i | \(0.440231\pi\) | |||||||
\(728\) | 2.26107 | 0.0838008 | ||||||||
\(729\) | 6.20490 | 0.229811 | ||||||||
\(730\) | −38.6466 | −1.43037 | ||||||||
\(731\) | 20.8520 | 0.771239 | ||||||||
\(732\) | 22.2124 | 0.820995 | ||||||||
\(733\) | −7.05178 | −0.260464 | −0.130232 | − | 0.991484i | \(-0.541572\pi\) | ||||
−0.130232 | + | 0.991484i | \(0.541572\pi\) | |||||||
\(734\) | −10.1420 | −0.374348 | ||||||||
\(735\) | 85.2124 | 3.14311 | ||||||||
\(736\) | 3.00362 | 0.110715 | ||||||||
\(737\) | −0.0387536 | −0.00142751 | ||||||||
\(738\) | −0.540820 | −0.0199079 | ||||||||
\(739\) | 5.21930 | 0.191995 | 0.0959975 | − | 0.995382i | \(-0.469396\pi\) | ||||
0.0959975 | + | 0.995382i | \(0.469396\pi\) | |||||||
\(740\) | 3.94318 | 0.144954 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.897981 | 0.0329659 | ||||||||
\(743\) | −7.24624 | −0.265839 | −0.132919 | − | 0.991127i | \(-0.542435\pi\) | ||||
−0.132919 | + | 0.991127i | \(0.542435\pi\) | |||||||
\(744\) | −32.3376 | −1.18556 | ||||||||
\(745\) | 50.9084 | 1.86514 | ||||||||
\(746\) | 7.87532 | 0.288336 | ||||||||
\(747\) | 76.0640 | 2.78304 | ||||||||
\(748\) | 4.87274 | 0.178165 | ||||||||
\(749\) | −11.4931 | −0.419948 | ||||||||
\(750\) | 108.085 | 3.94669 | ||||||||
\(751\) | 9.15541 | 0.334086 | 0.167043 | − | 0.985950i | \(-0.446578\pi\) | ||||
0.167043 | + | 0.985950i | \(0.446578\pi\) | |||||||
\(752\) | 1.10688 | 0.0403638 | ||||||||
\(753\) | 44.5036 | 1.62180 | ||||||||
\(754\) | 19.4676 | 0.708968 | ||||||||
\(755\) | −40.6579 | −1.47969 | ||||||||
\(756\) | 9.59165 | 0.348845 | ||||||||
\(757\) | 8.64501 | 0.314208 | 0.157104 | − | 0.987582i | \(-0.449784\pi\) | ||||
0.157104 | + | 0.987582i | \(0.449784\pi\) | |||||||
\(758\) | 14.8933 | 0.540948 | ||||||||
\(759\) | −9.43609 | −0.342508 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.2300 | −1.63959 | −0.819793 | − | 0.572659i | \(-0.805912\pi\) | ||||
−0.819793 | + | 0.572659i | \(0.805912\pi\) | |||||||
\(762\) | −1.51088 | −0.0547335 | ||||||||
\(763\) | −1.04862 | −0.0379626 | ||||||||
\(764\) | −0.789906 | −0.0285778 | ||||||||
\(765\) | −142.366 | −5.14726 | ||||||||
\(766\) | −9.65125 | −0.348714 | ||||||||
\(767\) | −7.17216 | −0.258972 | ||||||||
\(768\) | −3.14157 | −0.113362 | ||||||||
\(769\) | 0.255007 | 0.00919579 | 0.00459789 | − | 0.999989i | \(-0.498536\pi\) | ||||
0.00459789 | + | 0.999989i | \(0.498536\pi\) | |||||||
\(770\) | −3.35587 | −0.120937 | ||||||||
\(771\) | −81.1495 | −2.92253 | ||||||||
\(772\) | 6.02776 | 0.216944 | ||||||||
\(773\) | 30.5492 | 1.09878 | 0.549389 | − | 0.835567i | \(-0.314861\pi\) | ||||
0.549389 | + | 0.835567i | \(0.314861\pi\) | |||||||
\(774\) | 29.3967 | 1.05664 | ||||||||
\(775\) | −134.733 | −4.83977 | ||||||||
\(776\) | −11.9267 | −0.428144 | ||||||||
\(777\) | 2.29815 | 0.0824457 | ||||||||
\(778\) | 9.10826 | 0.326547 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −38.2892 | −1.37097 | ||||||||
\(781\) | −14.8810 | −0.532485 | ||||||||
\(782\) | −14.6359 | −0.523377 | ||||||||
\(783\) | 82.5833 | 2.95129 | ||||||||
\(784\) | −6.37743 | −0.227765 | ||||||||
\(785\) | 64.0534 | 2.28617 | ||||||||
\(786\) | 60.9404 | 2.17367 | ||||||||
\(787\) | −15.3750 | −0.548058 | −0.274029 | − | 0.961721i | \(-0.588356\pi\) | ||||
−0.274029 | + | 0.961721i | \(0.588356\pi\) | |||||||
\(788\) | 10.7225 | 0.381975 | ||||||||
\(789\) | −7.93433 | −0.282470 | ||||||||
\(790\) | −5.97544 | −0.212596 | ||||||||
\(791\) | −4.05044 | −0.144017 | ||||||||
\(792\) | 6.86947 | 0.244096 | ||||||||
\(793\) | −20.2614 | −0.719502 | ||||||||
\(794\) | −1.57061 | −0.0557389 | ||||||||
\(795\) | −15.2065 | −0.539319 | ||||||||
\(796\) | −8.73696 | −0.309673 | ||||||||
\(797\) | 12.5306 | 0.443858 | 0.221929 | − | 0.975063i | \(-0.428765\pi\) | ||||
0.221929 | + | 0.975063i | \(0.428765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.39354 | −0.190810 | ||||||||
\(800\) | −13.0892 | −0.462774 | ||||||||
\(801\) | 3.66044 | 0.129335 | ||||||||
\(802\) | −7.96088 | −0.281108 | ||||||||
\(803\) | −9.08659 | −0.320659 | ||||||||
\(804\) | −0.121747 | −0.00429370 | ||||||||
\(805\) | 10.0797 | 0.355264 | ||||||||
\(806\) | 29.4972 | 1.03899 | ||||||||
\(807\) | 19.4915 | 0.686132 | ||||||||
\(808\) | 16.0343 | 0.564084 | ||||||||
\(809\) | 20.8700 | 0.733751 | 0.366876 | − | 0.930270i | \(-0.380427\pi\) | ||||
0.366876 | + | 0.930270i | \(0.380427\pi\) | |||||||
\(810\) | −74.7755 | −2.62735 | ||||||||
\(811\) | −43.5142 | −1.52799 | −0.763995 | − | 0.645222i | \(-0.776765\pi\) | ||||
−0.763995 | + | 0.645222i | \(0.776765\pi\) | |||||||
\(812\) | 5.36029 | 0.188109 | ||||||||
\(813\) | 67.3706 | 2.36279 | ||||||||
\(814\) | 0.927122 | 0.0324956 | ||||||||
\(815\) | 41.2002 | 1.44318 | ||||||||
\(816\) | 15.3081 | 0.535889 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −4.38108 | −0.153181 | ||||||||
\(819\) | −15.5324 | −0.542744 | ||||||||
\(820\) | 0.334841 | 0.0116932 | ||||||||
\(821\) | −31.3062 | −1.09259 | −0.546297 | − | 0.837592i | \(-0.683963\pi\) | ||||
−0.546297 | + | 0.837592i | \(0.683963\pi\) | |||||||
\(822\) | 41.8406 | 1.45936 | ||||||||
\(823\) | 5.93510 | 0.206884 | 0.103442 | − | 0.994635i | \(-0.467014\pi\) | ||||
0.103442 | + | 0.994635i | \(0.467014\pi\) | |||||||
\(824\) | −7.04010 | −0.245253 | ||||||||
\(825\) | 41.1207 | 1.43164 | ||||||||
\(826\) | −1.97481 | −0.0687124 | ||||||||
\(827\) | −2.38933 | −0.0830853 | −0.0415426 | − | 0.999137i | \(-0.513227\pi\) | ||||
−0.0415426 | + | 0.999137i | \(0.513227\pi\) | |||||||
\(828\) | −20.6333 | −0.717056 | ||||||||
\(829\) | 7.02302 | 0.243920 | 0.121960 | − | 0.992535i | \(-0.461082\pi\) | ||||
0.121960 | + | 0.992535i | \(0.461082\pi\) | |||||||
\(830\) | −47.0940 | −1.63466 | ||||||||
\(831\) | 51.9753 | 1.80300 | ||||||||
\(832\) | 2.86562 | 0.0993476 | ||||||||
\(833\) | 31.0755 | 1.07670 | ||||||||
\(834\) | −5.20023 | −0.180069 | ||||||||
\(835\) | −43.1092 | −1.49185 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 125.130 | 4.32511 | ||||||||
\(838\) | 13.1059 | 0.452737 | ||||||||
\(839\) | −12.5878 | −0.434579 | −0.217289 | − | 0.976107i | \(-0.569722\pi\) | ||||
−0.217289 | + | 0.976107i | \(0.569722\pi\) | |||||||
\(840\) | −10.5427 | −0.363757 | ||||||||
\(841\) | 17.1516 | 0.591434 | ||||||||
\(842\) | −35.0448 | −1.20772 | ||||||||
\(843\) | −22.5487 | −0.776618 | ||||||||
\(844\) | −1.55294 | −0.0534544 | ||||||||
\(845\) | −20.3649 | −0.700574 | ||||||||
\(846\) | −7.60368 | −0.261420 | ||||||||
\(847\) | −0.789032 | −0.0271115 | ||||||||
\(848\) | 1.13808 | 0.0390818 | ||||||||
\(849\) | 56.8598 | 1.95142 | ||||||||
\(850\) | 63.7804 | 2.18765 | ||||||||
\(851\) | −2.78472 | −0.0954591 | ||||||||
\(852\) | −46.7498 | −1.60162 | ||||||||
\(853\) | −46.4032 | −1.58882 | −0.794408 | − | 0.607385i | \(-0.792219\pi\) | ||||
−0.794408 | + | 0.607385i | \(0.792219\pi\) | |||||||
\(854\) | −5.57884 | −0.190904 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.5660 | −0.497857 | ||||||||
\(857\) | −53.0866 | −1.81340 | −0.906702 | − | 0.421772i | \(-0.861408\pi\) | ||||
−0.906702 | + | 0.421772i | \(0.861408\pi\) | |||||||
\(858\) | −9.00256 | −0.307342 | ||||||||
\(859\) | −27.8557 | −0.950424 | −0.475212 | − | 0.879871i | \(-0.657629\pi\) | ||||
−0.475212 | + | 0.879871i | \(0.657629\pi\) | |||||||
\(860\) | −18.2005 | −0.620633 | ||||||||
\(861\) | 0.195151 | 0.00665073 | ||||||||
\(862\) | −15.0634 | −0.513063 | ||||||||
\(863\) | −4.59189 | −0.156310 | −0.0781549 | − | 0.996941i | \(-0.524903\pi\) | ||||
−0.0781549 | + | 0.996941i | \(0.524903\pi\) | |||||||
\(864\) | 12.1562 | 0.413563 | ||||||||
\(865\) | 82.4797 | 2.80439 | ||||||||
\(866\) | 20.4220 | 0.693969 | ||||||||
\(867\) | −21.1855 | −0.719496 | ||||||||
\(868\) | 8.12187 | 0.275674 | ||||||||
\(869\) | −1.40495 | −0.0476595 | ||||||||
\(870\) | −90.7717 | −3.07745 | ||||||||
\(871\) | 0.111053 | 0.00376290 | ||||||||
\(872\) | −1.32900 | −0.0450055 | ||||||||
\(873\) | 81.9303 | 2.77292 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.1464 | −0.917714 | ||||||||
\(876\) | −28.5462 | −0.964486 | ||||||||
\(877\) | −24.7295 | −0.835057 | −0.417529 | − | 0.908664i | \(-0.637104\pi\) | ||||
−0.417529 | + | 0.908664i | \(0.637104\pi\) | |||||||
\(878\) | −32.9051 | −1.11049 | ||||||||
\(879\) | 89.4500 | 3.01707 | ||||||||
\(880\) | −4.25314 | −0.143373 | ||||||||
\(881\) | −35.6142 | −1.19987 | −0.599937 | − | 0.800047i | \(-0.704808\pi\) | ||||
−0.599937 | + | 0.800047i | \(0.704808\pi\) | |||||||
\(882\) | 43.8096 | 1.47515 | ||||||||
\(883\) | −30.3291 | −1.02065 | −0.510327 | − | 0.859980i | \(-0.670476\pi\) | ||||
−0.510327 | + | 0.859980i | \(0.670476\pi\) | |||||||
\(884\) | −13.9634 | −0.469641 | ||||||||
\(885\) | 33.4416 | 1.12413 | ||||||||
\(886\) | −34.9998 | −1.17584 | ||||||||
\(887\) | −24.6424 | −0.827412 | −0.413706 | − | 0.910410i | \(-0.635766\pi\) | ||||
−0.413706 | + | 0.910410i | \(0.635766\pi\) | |||||||
\(888\) | 2.91262 | 0.0977411 | ||||||||
\(889\) | 0.379471 | 0.0127270 | ||||||||
\(890\) | −2.26631 | −0.0759669 | ||||||||
\(891\) | −17.5812 | −0.588994 | ||||||||
\(892\) | 10.1442 | 0.339653 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 37.6034 | 1.25764 | ||||||||
\(895\) | −13.4892 | −0.450893 | ||||||||
\(896\) | 0.789032 | 0.0263597 | ||||||||
\(897\) | 27.0403 | 0.902849 | ||||||||
\(898\) | 12.2917 | 0.410178 | ||||||||
\(899\) | 69.9286 | 2.33225 | ||||||||
\(900\) | 89.9161 | 2.99720 | ||||||||
\(901\) | −5.54556 | −0.184750 | ||||||||
\(902\) | 0.0787280 | 0.00262136 | ||||||||
\(903\) | −10.6076 | −0.352998 | ||||||||
\(904\) | −5.13343 | −0.170735 | ||||||||
\(905\) | 68.8864 | 2.28986 | ||||||||
\(906\) | −30.0318 | −0.997741 | ||||||||
\(907\) | −32.5163 | −1.07969 | −0.539843 | − | 0.841766i | \(-0.681516\pi\) | ||||
−0.539843 | + | 0.841766i | \(0.681516\pi\) | |||||||
\(908\) | 18.0026 | 0.597436 | ||||||||
\(909\) | −110.147 | −3.65335 | ||||||||
\(910\) | 9.61665 | 0.318789 | ||||||||
\(911\) | −25.5544 | −0.846654 | −0.423327 | − | 0.905977i | \(-0.639138\pi\) | ||||
−0.423327 | + | 0.905977i | \(0.639138\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0728 | −0.366455 | ||||||||
\(914\) | −40.8163 | −1.35008 | ||||||||
\(915\) | 94.4727 | 3.12317 | ||||||||
\(916\) | 21.0845 | 0.696652 | ||||||||
\(917\) | −15.3057 | −0.505438 | ||||||||
\(918\) | −59.2341 | −1.95502 | ||||||||
\(919\) | −16.7964 | −0.554061 | −0.277031 | − | 0.960861i | \(-0.589350\pi\) | ||||
−0.277031 | + | 0.960861i | \(0.589350\pi\) | |||||||
\(920\) | 12.7748 | 0.421174 | ||||||||
\(921\) | −2.07622 | −0.0684139 | ||||||||
\(922\) | −11.6324 | −0.383094 | ||||||||
\(923\) | 42.6434 | 1.40363 | ||||||||
\(924\) | −2.47880 | −0.0815465 | ||||||||
\(925\) | 12.1353 | 0.399006 | ||||||||
\(926\) | −19.2052 | −0.631121 | ||||||||
\(927\) | 48.3618 | 1.58841 | ||||||||
\(928\) | 6.79350 | 0.223007 | ||||||||
\(929\) | 48.8769 | 1.60360 | 0.801799 | − | 0.597594i | \(-0.203876\pi\) | ||||
0.801799 | + | 0.597594i | \(0.203876\pi\) | |||||||
\(930\) | −137.537 | −4.51000 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.852182 | −0.0279142 | ||||||||
\(933\) | −81.9974 | −2.68448 | ||||||||
\(934\) | −9.52417 | −0.311640 | ||||||||
\(935\) | 20.7245 | 0.677762 | ||||||||
\(936\) | −19.6853 | −0.643435 | ||||||||
\(937\) | −9.21994 | −0.301202 | −0.150601 | − | 0.988595i | \(-0.548121\pi\) | ||||
−0.150601 | + | 0.988595i | \(0.548121\pi\) | |||||||
\(938\) | 0.0305779 | 0.000998403 0 | ||||||||
\(939\) | 19.4461 | 0.634601 | ||||||||
\(940\) | 4.70772 | 0.153549 | ||||||||
\(941\) | 46.9982 | 1.53210 | 0.766049 | − | 0.642782i | \(-0.222220\pi\) | ||||
0.766049 | + | 0.642782i | \(0.222220\pi\) | |||||||
\(942\) | 47.3129 | 1.54154 | ||||||||
\(943\) | −0.236469 | −0.00770049 | ||||||||
\(944\) | −2.50283 | −0.0814601 | ||||||||
\(945\) | 40.7947 | 1.32705 | ||||||||
\(946\) | −4.27932 | −0.139133 | ||||||||
\(947\) | 45.8260 | 1.48914 | 0.744572 | − | 0.667542i | \(-0.232654\pi\) | ||||
0.744572 | + | 0.667542i | \(0.232654\pi\) | |||||||
\(948\) | −4.41374 | −0.143352 | ||||||||
\(949\) | 26.0387 | 0.845253 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 95.8667 | 3.10869 | ||||||||
\(952\) | −3.84475 | −0.124609 | ||||||||
\(953\) | −2.80221 | −0.0907726 | −0.0453863 | − | 0.998970i | \(-0.514452\pi\) | ||||
−0.0453863 | + | 0.998970i | \(0.514452\pi\) | |||||||
\(954\) | −7.81801 | −0.253117 | ||||||||
\(955\) | −3.35958 | −0.108714 | ||||||||
\(956\) | −27.7837 | −0.898588 | ||||||||
\(957\) | −21.3423 | −0.689897 | ||||||||
\(958\) | −25.8981 | −0.836728 | ||||||||
\(959\) | −10.5086 | −0.339341 | ||||||||
\(960\) | −13.3616 | −0.431242 | ||||||||
\(961\) | 74.9553 | 2.41791 | ||||||||
\(962\) | −2.65678 | −0.0856581 | ||||||||
\(963\) | 100.061 | 3.22442 | ||||||||
\(964\) | 14.7320 | 0.474486 | ||||||||
\(965\) | 25.6369 | 0.825282 | ||||||||
\(966\) | 7.44538 | 0.239551 | ||||||||
\(967\) | 28.8507 | 0.927776 | 0.463888 | − | 0.885894i | \(-0.346454\pi\) | ||||
0.463888 | + | 0.885894i | \(0.346454\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −50.7260 | −1.62871 | ||||||||
\(971\) | 18.5452 | 0.595145 | 0.297572 | − | 0.954699i | \(-0.403823\pi\) | ||||
0.297572 | + | 0.954699i | \(0.403823\pi\) | |||||||
\(972\) | −18.7641 | −0.601857 | ||||||||
\(973\) | 1.30608 | 0.0418711 | ||||||||
\(974\) | −1.13302 | −0.0363042 | ||||||||
\(975\) | −117.837 | −3.77379 | ||||||||
\(976\) | −7.07049 | −0.226321 | ||||||||
\(977\) | −39.6590 | −1.26880 | −0.634401 | − | 0.773004i | \(-0.718753\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(978\) | 30.4324 | 0.973120 | ||||||||
\(979\) | −0.532856 | −0.0170301 | ||||||||
\(980\) | −27.1241 | −0.866448 | ||||||||
\(981\) | 9.12950 | 0.291483 | ||||||||
\(982\) | 2.02215 | 0.0645293 | ||||||||
\(983\) | 13.0948 | 0.417660 | 0.208830 | − | 0.977952i | \(-0.433034\pi\) | ||||
0.208830 | + | 0.977952i | \(0.433034\pi\) | |||||||
\(984\) | 0.247330 | 0.00788458 | ||||||||
\(985\) | 45.6045 | 1.45308 | ||||||||
\(986\) | −33.1029 | −1.05421 | ||||||||
\(987\) | 2.74373 | 0.0873340 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.8534 | 0.408716 | ||||||||
\(990\) | 29.2169 | 0.928573 | ||||||||
\(991\) | −7.87788 | −0.250249 | −0.125125 | − | 0.992141i | \(-0.539933\pi\) | ||||
−0.125125 | + | 0.992141i | \(0.539933\pi\) | |||||||
\(992\) | 10.2935 | 0.326818 | ||||||||
\(993\) | 30.4629 | 0.966712 | ||||||||
\(994\) | 11.7416 | 0.372421 | ||||||||
\(995\) | −37.1595 | −1.17804 | ||||||||
\(996\) | −34.7859 | −1.10223 | ||||||||
\(997\) | 46.9150 | 1.48581 | 0.742906 | − | 0.669396i | \(-0.233447\pi\) | ||||
0.742906 | + | 0.669396i | \(0.233447\pi\) | |||||||
\(998\) | −39.8484 | −1.26138 | ||||||||
\(999\) | −11.2703 | −0.356577 |
(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 | 7942.2.a.by.1.2 | 15 | ||
19.3 | odd | 18 | 418.2.j.d.199.5 | ✓ | 30 | ||
19.13 | odd | 18 | 418.2.j.d.397.5 | yes | 30 | ||
19.18 | odd | 2 | 7942.2.a.ca.1.14 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.j.d.199.5 | ✓ | 30 | 19.3 | odd | 18 | ||
418.2.j.d.397.5 | yes | 30 | 19.13 | odd | 18 | ||
7942.2.a.by.1.2 | 15 | 1.1 | even | 1 | trivial | ||
7942.2.a.ca.1.14 | 15 | 19.18 | odd | 2 |