Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [381,2,Mod(1,381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(381, 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("381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 381 = 3 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 381.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: | \(3.04230031701\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.246832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 \) |
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 | 1.5 | ||
Root | \(2.71457\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 381.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.65432 | 1.87689 | 0.938443 | − | 0.345435i | \(-0.112268\pi\) | ||||
0.938443 | + | 0.345435i | \(0.112268\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.04540 | 2.52270 | ||||||||
\(5\) | 0.121872 | 0.0545028 | 0.0272514 | − | 0.999629i | \(-0.491325\pi\) | ||||
0.0272514 | + | 0.999629i | \(0.491325\pi\) | |||||||
\(6\) | −2.65432 | −1.08362 | ||||||||
\(7\) | −0.0602522 | −0.0227732 | −0.0113866 | − | 0.999935i | \(-0.503625\pi\) | ||||
−0.0113866 | + | 0.999935i | \(0.503625\pi\) | |||||||
\(8\) | 8.08346 | 2.85793 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.323487 | 0.102296 | ||||||||
\(11\) | −0.159928 | −0.0482202 | −0.0241101 | − | 0.999709i | \(-0.507675\pi\) | ||||
−0.0241101 | + | 0.999709i | \(0.507675\pi\) | |||||||
\(12\) | −5.04540 | −1.45648 | ||||||||
\(13\) | −1.06025 | −0.294061 | −0.147031 | − | 0.989132i | \(-0.546972\pi\) | ||||
−0.147031 | + | 0.989132i | \(0.546972\pi\) | |||||||
\(14\) | −0.159928 | −0.0427427 | ||||||||
\(15\) | −0.121872 | −0.0314672 | ||||||||
\(16\) | 11.3653 | 2.84131 | ||||||||
\(17\) | −3.67288 | −0.890805 | −0.445402 | − | 0.895330i | \(-0.646939\pi\) | ||||
−0.445402 | + | 0.895330i | \(0.646939\pi\) | |||||||
\(18\) | 2.65432 | 0.625629 | ||||||||
\(19\) | −2.41792 | −0.554708 | −0.277354 | − | 0.960768i | \(-0.589457\pi\) | ||||
−0.277354 | + | 0.960768i | \(0.589457\pi\) | |||||||
\(20\) | 0.614893 | 0.137494 | ||||||||
\(21\) | 0.0602522 | 0.0131481 | ||||||||
\(22\) | −0.424501 | −0.0905038 | ||||||||
\(23\) | 3.62748 | 0.756383 | 0.378191 | − | 0.925727i | \(-0.376546\pi\) | ||||
0.378191 | + | 0.925727i | \(0.376546\pi\) | |||||||
\(24\) | −8.08346 | −1.65003 | ||||||||
\(25\) | −4.98515 | −0.997029 | ||||||||
\(26\) | −2.81425 | −0.551919 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.303996 | −0.0574499 | ||||||||
\(29\) | 5.54367 | 1.02943 | 0.514717 | − | 0.857360i | \(-0.327897\pi\) | ||||
0.514717 | + | 0.857360i | \(0.327897\pi\) | |||||||
\(30\) | −0.323487 | −0.0590604 | ||||||||
\(31\) | 4.40965 | 0.791996 | 0.395998 | − | 0.918251i | \(-0.370399\pi\) | ||||
0.395998 | + | 0.918251i | \(0.370399\pi\) | |||||||
\(32\) | 14.0001 | 2.47489 | ||||||||
\(33\) | 0.159928 | 0.0278400 | ||||||||
\(34\) | −9.74900 | −1.67194 | ||||||||
\(35\) | −0.00734305 | −0.00124120 | ||||||||
\(36\) | 5.04540 | 0.840900 | ||||||||
\(37\) | −7.01586 | −1.15340 | −0.576700 | − | 0.816956i | \(-0.695660\pi\) | ||||
−0.576700 | + | 0.816956i | \(0.695660\pi\) | |||||||
\(38\) | −6.41792 | −1.04112 | ||||||||
\(39\) | 1.06025 | 0.169776 | ||||||||
\(40\) | 0.985147 | 0.155765 | ||||||||
\(41\) | −9.62849 | −1.50372 | −0.751859 | − | 0.659324i | \(-0.770843\pi\) | ||||
−0.751859 | + | 0.659324i | \(0.770843\pi\) | |||||||
\(42\) | 0.159928 | 0.0246775 | ||||||||
\(43\) | −7.54875 | −1.15117 | −0.575587 | − | 0.817741i | \(-0.695226\pi\) | ||||
−0.575587 | + | 0.817741i | \(0.695226\pi\) | |||||||
\(44\) | −0.806902 | −0.121645 | ||||||||
\(45\) | 0.121872 | 0.0181676 | ||||||||
\(46\) | 9.62849 | 1.41964 | ||||||||
\(47\) | −0.250645 | −0.0365603 | −0.0182801 | − | 0.999833i | \(-0.505819\pi\) | ||||
−0.0182801 | + | 0.999833i | \(0.505819\pi\) | |||||||
\(48\) | −11.3653 | −1.64043 | ||||||||
\(49\) | −6.99637 | −0.999481 | ||||||||
\(50\) | −13.2322 | −1.87131 | ||||||||
\(51\) | 3.67288 | 0.514306 | ||||||||
\(52\) | −5.34940 | −0.741828 | ||||||||
\(53\) | 1.64173 | 0.225509 | 0.112754 | − | 0.993623i | \(-0.464033\pi\) | ||||
0.112754 | + | 0.993623i | \(0.464033\pi\) | |||||||
\(54\) | −2.65432 | −0.361207 | ||||||||
\(55\) | −0.0194908 | −0.00262814 | ||||||||
\(56\) | −0.487046 | −0.0650842 | ||||||||
\(57\) | 2.41792 | 0.320261 | ||||||||
\(58\) | 14.7147 | 1.93213 | ||||||||
\(59\) | −3.71828 | −0.484079 | −0.242040 | − | 0.970266i | \(-0.577816\pi\) | ||||
−0.242040 | + | 0.970266i | \(0.577816\pi\) | |||||||
\(60\) | −0.614893 | −0.0793824 | ||||||||
\(61\) | 11.6109 | 1.48662 | 0.743312 | − | 0.668945i | \(-0.233254\pi\) | ||||
0.743312 | + | 0.668945i | \(0.233254\pi\) | |||||||
\(62\) | 11.7046 | 1.48649 | ||||||||
\(63\) | −0.0602522 | −0.00759106 | ||||||||
\(64\) | 14.4301 | 1.80377 | ||||||||
\(65\) | −0.129215 | −0.0160272 | ||||||||
\(66\) | 0.424501 | 0.0522524 | ||||||||
\(67\) | 13.9415 | 1.70322 | 0.851612 | − | 0.524173i | \(-0.175626\pi\) | ||||
0.851612 | + | 0.524173i | \(0.175626\pi\) | |||||||
\(68\) | −18.5312 | −2.24723 | ||||||||
\(69\) | −3.62748 | −0.436698 | ||||||||
\(70\) | −0.0194908 | −0.00232960 | ||||||||
\(71\) | 8.57784 | 1.01800 | 0.509001 | − | 0.860766i | \(-0.330015\pi\) | ||||
0.509001 | + | 0.860766i | \(0.330015\pi\) | |||||||
\(72\) | 8.08346 | 0.952644 | ||||||||
\(73\) | −11.0944 | −1.29850 | −0.649252 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649252 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(74\) | −18.6223 | −2.16480 | ||||||||
\(75\) | 4.98515 | 0.575635 | ||||||||
\(76\) | −12.1994 | −1.39936 | ||||||||
\(77\) | 0.00963603 | 0.00109813 | ||||||||
\(78\) | 2.81425 | 0.318651 | ||||||||
\(79\) | 7.67288 | 0.863267 | 0.431633 | − | 0.902049i | \(-0.357937\pi\) | ||||
0.431633 | + | 0.902049i | \(0.357937\pi\) | |||||||
\(80\) | 1.38511 | 0.154860 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −25.5571 | −2.82231 | ||||||||
\(83\) | 7.42087 | 0.814546 | 0.407273 | − | 0.913306i | \(-0.366480\pi\) | ||||
0.407273 | + | 0.913306i | \(0.366480\pi\) | |||||||
\(84\) | 0.303996 | 0.0331687 | ||||||||
\(85\) | −0.447622 | −0.0485514 | ||||||||
\(86\) | −20.0368 | −2.16062 | ||||||||
\(87\) | −5.54367 | −0.594344 | ||||||||
\(88\) | −1.29277 | −0.137810 | ||||||||
\(89\) | 11.9941 | 1.27137 | 0.635686 | − | 0.771947i | \(-0.280717\pi\) | ||||
0.635686 | + | 0.771947i | \(0.280717\pi\) | |||||||
\(90\) | 0.323487 | 0.0340985 | ||||||||
\(91\) | 0.0638825 | 0.00669670 | ||||||||
\(92\) | 18.3021 | 1.90813 | ||||||||
\(93\) | −4.40965 | −0.457259 | ||||||||
\(94\) | −0.665290 | −0.0686195 | ||||||||
\(95\) | −0.294676 | −0.0302332 | ||||||||
\(96\) | −14.0001 | −1.42888 | ||||||||
\(97\) | −0.974091 | −0.0989040 | −0.0494520 | − | 0.998777i | \(-0.515747\pi\) | ||||
−0.0494520 | + | 0.998777i | \(0.515747\pi\) | |||||||
\(98\) | −18.5706 | −1.87591 | ||||||||
\(99\) | −0.159928 | −0.0160734 | ||||||||
\(100\) | −25.1521 | −2.51521 | ||||||||
\(101\) | −0.153953 | −0.0153189 | −0.00765945 | − | 0.999971i | \(-0.502438\pi\) | ||||
−0.00765945 | + | 0.999971i | \(0.502438\pi\) | |||||||
\(102\) | 9.74900 | 0.965294 | ||||||||
\(103\) | −14.7525 | −1.45360 | −0.726801 | − | 0.686848i | \(-0.758994\pi\) | ||||
−0.726801 | + | 0.686848i | \(0.758994\pi\) | |||||||
\(104\) | −8.57050 | −0.840407 | ||||||||
\(105\) | 0.00734305 | 0.000716609 0 | ||||||||
\(106\) | 4.35766 | 0.423254 | ||||||||
\(107\) | 9.26460 | 0.895643 | 0.447821 | − | 0.894123i | \(-0.352200\pi\) | ||||
0.447821 | + | 0.894123i | \(0.352200\pi\) | |||||||
\(108\) | −5.04540 | −0.485494 | ||||||||
\(109\) | −0.135190 | −0.0129489 | −0.00647445 | − | 0.999979i | \(-0.502061\pi\) | ||||
−0.00647445 | + | 0.999979i | \(0.502061\pi\) | |||||||
\(110\) | −0.0517347 | −0.00493271 | ||||||||
\(111\) | 7.01586 | 0.665916 | ||||||||
\(112\) | −0.684781 | −0.0647058 | ||||||||
\(113\) | 10.5609 | 0.993483 | 0.496741 | − | 0.867899i | \(-0.334530\pi\) | ||||
0.496741 | + | 0.867899i | \(0.334530\pi\) | |||||||
\(114\) | 6.41792 | 0.601093 | ||||||||
\(115\) | 0.442089 | 0.0412250 | ||||||||
\(116\) | 27.9700 | 2.59695 | ||||||||
\(117\) | −1.06025 | −0.0980203 | ||||||||
\(118\) | −9.86950 | −0.908561 | ||||||||
\(119\) | 0.221299 | 0.0202865 | ||||||||
\(120\) | −0.985147 | −0.0899312 | ||||||||
\(121\) | −10.9744 | −0.997675 | ||||||||
\(122\) | 30.8190 | 2.79022 | ||||||||
\(123\) | 9.62849 | 0.868172 | ||||||||
\(124\) | 22.2484 | 1.99797 | ||||||||
\(125\) | −1.21691 | −0.108844 | ||||||||
\(126\) | −0.159928 | −0.0142476 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 10.3020 | 0.910578 | ||||||||
\(129\) | 7.54875 | 0.664630 | ||||||||
\(130\) | −0.342978 | −0.0300811 | ||||||||
\(131\) | 11.3916 | 0.995293 | 0.497646 | − | 0.867380i | \(-0.334198\pi\) | ||||
0.497646 | + | 0.867380i | \(0.334198\pi\) | |||||||
\(132\) | 0.806902 | 0.0702318 | ||||||||
\(133\) | 0.145685 | 0.0126325 | ||||||||
\(134\) | 37.0051 | 3.19676 | ||||||||
\(135\) | −0.121872 | −0.0104891 | ||||||||
\(136\) | −29.6896 | −2.54586 | ||||||||
\(137\) | 20.5766 | 1.75797 | 0.878987 | − | 0.476846i | \(-0.158220\pi\) | ||||
0.878987 | + | 0.476846i | \(0.158220\pi\) | |||||||
\(138\) | −9.62849 | −0.819632 | ||||||||
\(139\) | 14.8583 | 1.26026 | 0.630131 | − | 0.776489i | \(-0.283001\pi\) | ||||
0.630131 | + | 0.776489i | \(0.283001\pi\) | |||||||
\(140\) | −0.0370486 | −0.00313118 | ||||||||
\(141\) | 0.250645 | 0.0211081 | ||||||||
\(142\) | 22.7683 | 1.91067 | ||||||||
\(143\) | 0.169564 | 0.0141797 | ||||||||
\(144\) | 11.3653 | 0.947105 | ||||||||
\(145\) | 0.675618 | 0.0561070 | ||||||||
\(146\) | −29.4481 | −2.43714 | ||||||||
\(147\) | 6.99637 | 0.577051 | ||||||||
\(148\) | −35.3978 | −2.90968 | ||||||||
\(149\) | −2.64424 | −0.216624 | −0.108312 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108312 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(150\) | 13.2322 | 1.08040 | ||||||||
\(151\) | −7.40875 | −0.602916 | −0.301458 | − | 0.953479i | \(-0.597473\pi\) | ||||
−0.301458 | + | 0.953479i | \(0.597473\pi\) | |||||||
\(152\) | −19.5451 | −1.58532 | ||||||||
\(153\) | −3.67288 | −0.296935 | ||||||||
\(154\) | 0.0255771 | 0.00206106 | ||||||||
\(155\) | 0.537413 | 0.0431660 | ||||||||
\(156\) | 5.34940 | 0.428294 | ||||||||
\(157\) | 8.13184 | 0.648991 | 0.324496 | − | 0.945887i | \(-0.394805\pi\) | ||||
0.324496 | + | 0.945887i | \(0.394805\pi\) | |||||||
\(158\) | 20.3663 | 1.62025 | ||||||||
\(159\) | −1.64173 | −0.130197 | ||||||||
\(160\) | 1.70622 | 0.134888 | ||||||||
\(161\) | −0.218564 | −0.0172252 | ||||||||
\(162\) | 2.65432 | 0.208543 | ||||||||
\(163\) | −1.99447 | −0.156219 | −0.0781094 | − | 0.996945i | \(-0.524888\pi\) | ||||
−0.0781094 | + | 0.996945i | \(0.524888\pi\) | |||||||
\(164\) | −48.5796 | −3.79343 | ||||||||
\(165\) | 0.0194908 | 0.00151736 | ||||||||
\(166\) | 19.6973 | 1.52881 | ||||||||
\(167\) | 15.9154 | 1.23157 | 0.615786 | − | 0.787914i | \(-0.288839\pi\) | ||||
0.615786 | + | 0.787914i | \(0.288839\pi\) | |||||||
\(168\) | 0.487046 | 0.0375764 | ||||||||
\(169\) | −11.8759 | −0.913528 | ||||||||
\(170\) | −1.18813 | −0.0911254 | ||||||||
\(171\) | −2.41792 | −0.184903 | ||||||||
\(172\) | −38.0864 | −2.90406 | ||||||||
\(173\) | −8.46195 | −0.643350 | −0.321675 | − | 0.946850i | \(-0.604246\pi\) | ||||
−0.321675 | + | 0.946850i | \(0.604246\pi\) | |||||||
\(174\) | −14.7147 | −1.11551 | ||||||||
\(175\) | 0.300366 | 0.0227055 | ||||||||
\(176\) | −1.81763 | −0.137009 | ||||||||
\(177\) | 3.71828 | 0.279483 | ||||||||
\(178\) | 31.8362 | 2.38622 | ||||||||
\(179\) | −0.828932 | −0.0619573 | −0.0309786 | − | 0.999520i | \(-0.509862\pi\) | ||||
−0.0309786 | + | 0.999520i | \(0.509862\pi\) | |||||||
\(180\) | 0.614893 | 0.0458314 | ||||||||
\(181\) | −17.0055 | −1.26401 | −0.632004 | − | 0.774965i | \(-0.717767\pi\) | ||||
−0.632004 | + | 0.774965i | \(0.717767\pi\) | |||||||
\(182\) | 0.169564 | 0.0125689 | ||||||||
\(183\) | −11.6109 | −0.858303 | ||||||||
\(184\) | 29.3226 | 2.16169 | ||||||||
\(185\) | −0.855037 | −0.0628636 | ||||||||
\(186\) | −11.7046 | −0.858223 | ||||||||
\(187\) | 0.587398 | 0.0429548 | ||||||||
\(188\) | −1.26460 | −0.0922306 | ||||||||
\(189\) | 0.0602522 | 0.00438270 | ||||||||
\(190\) | −0.782165 | −0.0567442 | ||||||||
\(191\) | 10.0074 | 0.724112 | 0.362056 | − | 0.932156i | \(-0.382075\pi\) | ||||
0.362056 | + | 0.932156i | \(0.382075\pi\) | |||||||
\(192\) | −14.4301 | −1.04141 | ||||||||
\(193\) | −19.2597 | −1.38634 | −0.693172 | − | 0.720772i | \(-0.743788\pi\) | ||||
−0.693172 | + | 0.720772i | \(0.743788\pi\) | |||||||
\(194\) | −2.58555 | −0.185631 | ||||||||
\(195\) | 0.129215 | 0.00925328 | ||||||||
\(196\) | −35.2995 | −2.52139 | ||||||||
\(197\) | 7.85481 | 0.559632 | 0.279816 | − | 0.960054i | \(-0.409726\pi\) | ||||
0.279816 | + | 0.960054i | \(0.409726\pi\) | |||||||
\(198\) | −0.424501 | −0.0301679 | ||||||||
\(199\) | 16.7433 | 1.18690 | 0.593451 | − | 0.804870i | \(-0.297765\pi\) | ||||
0.593451 | + | 0.804870i | \(0.297765\pi\) | |||||||
\(200\) | −40.2972 | −2.84944 | ||||||||
\(201\) | −13.9415 | −0.983356 | ||||||||
\(202\) | −0.408640 | −0.0287518 | ||||||||
\(203\) | −0.334018 | −0.0234435 | ||||||||
\(204\) | 18.5312 | 1.29744 | ||||||||
\(205\) | −1.17344 | −0.0819569 | ||||||||
\(206\) | −39.1577 | −2.72825 | ||||||||
\(207\) | 3.62748 | 0.252128 | ||||||||
\(208\) | −12.0500 | −0.835520 | ||||||||
\(209\) | 0.386693 | 0.0267481 | ||||||||
\(210\) | 0.0194908 | 0.00134499 | ||||||||
\(211\) | −6.90368 | −0.475269 | −0.237634 | − | 0.971355i | \(-0.576372\pi\) | ||||
−0.237634 | + | 0.971355i | \(0.576372\pi\) | |||||||
\(212\) | 8.28317 | 0.568890 | ||||||||
\(213\) | −8.57784 | −0.587744 | ||||||||
\(214\) | 24.5912 | 1.68102 | ||||||||
\(215\) | −0.919981 | −0.0627422 | ||||||||
\(216\) | −8.08346 | −0.550009 | ||||||||
\(217\) | −0.265691 | −0.0180363 | ||||||||
\(218\) | −0.358838 | −0.0243036 | ||||||||
\(219\) | 11.0944 | 0.749692 | ||||||||
\(220\) | −0.0983388 | −0.00663000 | ||||||||
\(221\) | 3.89418 | 0.261951 | ||||||||
\(222\) | 18.6223 | 1.24985 | ||||||||
\(223\) | −25.0408 | −1.67685 | −0.838427 | − | 0.545014i | \(-0.816524\pi\) | ||||
−0.838427 | + | 0.545014i | \(0.816524\pi\) | |||||||
\(224\) | −0.843535 | −0.0563611 | ||||||||
\(225\) | −4.98515 | −0.332343 | ||||||||
\(226\) | 28.0319 | 1.86465 | ||||||||
\(227\) | −16.5898 | −1.10110 | −0.550552 | − | 0.834801i | \(-0.685583\pi\) | ||||
−0.550552 | + | 0.834801i | \(0.685583\pi\) | |||||||
\(228\) | 12.1994 | 0.807922 | ||||||||
\(229\) | 23.4458 | 1.54934 | 0.774672 | − | 0.632363i | \(-0.217915\pi\) | ||||
0.774672 | + | 0.632363i | \(0.217915\pi\) | |||||||
\(230\) | 1.17344 | 0.0773746 | ||||||||
\(231\) | −0.00963603 | −0.000634004 0 | ||||||||
\(232\) | 44.8120 | 2.94205 | ||||||||
\(233\) | 25.6658 | 1.68142 | 0.840710 | − | 0.541485i | \(-0.182138\pi\) | ||||
0.840710 | + | 0.541485i | \(0.182138\pi\) | |||||||
\(234\) | −2.81425 | −0.183973 | ||||||||
\(235\) | −0.0305466 | −0.00199264 | ||||||||
\(236\) | −18.7602 | −1.22119 | ||||||||
\(237\) | −7.67288 | −0.498407 | ||||||||
\(238\) | 0.587398 | 0.0380754 | ||||||||
\(239\) | −19.1324 | −1.23757 | −0.618786 | − | 0.785560i | \(-0.712375\pi\) | ||||
−0.618786 | + | 0.785560i | \(0.712375\pi\) | |||||||
\(240\) | −1.38511 | −0.0894083 | ||||||||
\(241\) | 18.8973 | 1.21728 | 0.608640 | − | 0.793447i | \(-0.291715\pi\) | ||||
0.608640 | + | 0.793447i | \(0.291715\pi\) | |||||||
\(242\) | −29.1296 | −1.87252 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 58.5816 | 3.75031 | ||||||||
\(245\) | −0.852662 | −0.0544746 | ||||||||
\(246\) | 25.5571 | 1.62946 | ||||||||
\(247\) | 2.56360 | 0.163118 | ||||||||
\(248\) | 35.6452 | 2.26347 | ||||||||
\(249\) | −7.42087 | −0.470279 | ||||||||
\(250\) | −3.23007 | −0.204287 | ||||||||
\(251\) | 24.0758 | 1.51965 | 0.759825 | − | 0.650128i | \(-0.225285\pi\) | ||||
0.759825 | + | 0.650128i | \(0.225285\pi\) | |||||||
\(252\) | −0.303996 | −0.0191500 | ||||||||
\(253\) | −0.580137 | −0.0364729 | ||||||||
\(254\) | 2.65432 | 0.166547 | ||||||||
\(255\) | 0.447622 | 0.0280312 | ||||||||
\(256\) | −1.51547 | −0.0947166 | ||||||||
\(257\) | −21.1973 | −1.32225 | −0.661127 | − | 0.750274i | \(-0.729921\pi\) | ||||
−0.661127 | + | 0.750274i | \(0.729921\pi\) | |||||||
\(258\) | 20.0368 | 1.24743 | ||||||||
\(259\) | 0.422721 | 0.0262666 | ||||||||
\(260\) | −0.651942 | −0.0404317 | ||||||||
\(261\) | 5.54367 | 0.343144 | ||||||||
\(262\) | 30.2370 | 1.86805 | ||||||||
\(263\) | −30.1230 | −1.85746 | −0.928731 | − | 0.370755i | \(-0.879099\pi\) | ||||
−0.928731 | + | 0.370755i | \(0.879099\pi\) | |||||||
\(264\) | 1.29277 | 0.0795647 | ||||||||
\(265\) | 0.200081 | 0.0122909 | ||||||||
\(266\) | 0.386693 | 0.0237097 | ||||||||
\(267\) | −11.9941 | −0.734027 | ||||||||
\(268\) | 70.3404 | 4.29672 | ||||||||
\(269\) | −7.96482 | −0.485624 | −0.242812 | − | 0.970073i | \(-0.578070\pi\) | ||||
−0.242812 | + | 0.970073i | \(0.578070\pi\) | |||||||
\(270\) | −0.323487 | −0.0196868 | ||||||||
\(271\) | 11.7971 | 0.716625 | 0.358312 | − | 0.933602i | \(-0.383352\pi\) | ||||
0.358312 | + | 0.933602i | \(0.383352\pi\) | |||||||
\(272\) | −41.7433 | −2.53106 | ||||||||
\(273\) | −0.0638825 | −0.00386634 | ||||||||
\(274\) | 54.6167 | 3.29952 | ||||||||
\(275\) | 0.797266 | 0.0480770 | ||||||||
\(276\) | −18.3021 | −1.10166 | ||||||||
\(277\) | −30.6509 | −1.84164 | −0.920818 | − | 0.389992i | \(-0.872478\pi\) | ||||
−0.920818 | + | 0.389992i | \(0.872478\pi\) | |||||||
\(278\) | 39.4386 | 2.36537 | ||||||||
\(279\) | 4.40965 | 0.263999 | ||||||||
\(280\) | −0.0593573 | −0.00354727 | ||||||||
\(281\) | −17.6965 | −1.05568 | −0.527842 | − | 0.849343i | \(-0.676999\pi\) | ||||
−0.527842 | + | 0.849343i | \(0.676999\pi\) | |||||||
\(282\) | 0.665290 | 0.0396175 | ||||||||
\(283\) | 16.0146 | 0.951972 | 0.475986 | − | 0.879453i | \(-0.342091\pi\) | ||||
0.475986 | + | 0.879453i | \(0.342091\pi\) | |||||||
\(284\) | 43.2787 | 2.56812 | ||||||||
\(285\) | 0.294676 | 0.0174551 | ||||||||
\(286\) | 0.450078 | 0.0266136 | ||||||||
\(287\) | 0.580137 | 0.0342444 | ||||||||
\(288\) | 14.0001 | 0.824963 | ||||||||
\(289\) | −3.50993 | −0.206467 | ||||||||
\(290\) | 1.79330 | 0.105306 | ||||||||
\(291\) | 0.974091 | 0.0571023 | ||||||||
\(292\) | −55.9758 | −3.27574 | ||||||||
\(293\) | −19.9488 | −1.16542 | −0.582710 | − | 0.812680i | \(-0.698008\pi\) | ||||
−0.582710 | + | 0.812680i | \(0.698008\pi\) | |||||||
\(294\) | 18.5706 | 1.08306 | ||||||||
\(295\) | −0.453155 | −0.0263837 | ||||||||
\(296\) | −56.7124 | −3.29634 | ||||||||
\(297\) | 0.159928 | 0.00927998 | ||||||||
\(298\) | −7.01865 | −0.406579 | ||||||||
\(299\) | −3.84605 | −0.222423 | ||||||||
\(300\) | 25.1521 | 1.45215 | ||||||||
\(301\) | 0.454828 | 0.0262159 | ||||||||
\(302\) | −19.6652 | −1.13160 | ||||||||
\(303\) | 0.153953 | 0.00884437 | ||||||||
\(304\) | −27.4802 | −1.57610 | ||||||||
\(305\) | 1.41504 | 0.0810252 | ||||||||
\(306\) | −9.74900 | −0.557313 | ||||||||
\(307\) | 1.74509 | 0.0995973 | 0.0497986 | − | 0.998759i | \(-0.484142\pi\) | ||||
0.0497986 | + | 0.998759i | \(0.484142\pi\) | |||||||
\(308\) | 0.0486176 | 0.00277025 | ||||||||
\(309\) | 14.7525 | 0.839238 | ||||||||
\(310\) | 1.42646 | 0.0810177 | ||||||||
\(311\) | 16.3942 | 0.929632 | 0.464816 | − | 0.885407i | \(-0.346120\pi\) | ||||
0.464816 | + | 0.885407i | \(0.346120\pi\) | |||||||
\(312\) | 8.57050 | 0.485209 | ||||||||
\(313\) | −3.25949 | −0.184237 | −0.0921187 | − | 0.995748i | \(-0.529364\pi\) | ||||
−0.0921187 | + | 0.995748i | \(0.529364\pi\) | |||||||
\(314\) | 21.5845 | 1.21808 | ||||||||
\(315\) | −0.00734305 | −0.000413734 0 | ||||||||
\(316\) | 38.7128 | 2.17776 | ||||||||
\(317\) | −3.81807 | −0.214444 | −0.107222 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107222 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(318\) | −4.35766 | −0.244366 | ||||||||
\(319\) | −0.886590 | −0.0496395 | ||||||||
\(320\) | 1.75863 | 0.0983105 | ||||||||
\(321\) | −9.26460 | −0.517100 | ||||||||
\(322\) | −0.580137 | −0.0323298 | ||||||||
\(323\) | 8.88072 | 0.494137 | ||||||||
\(324\) | 5.04540 | 0.280300 | ||||||||
\(325\) | 5.28551 | 0.293188 | ||||||||
\(326\) | −5.29395 | −0.293205 | ||||||||
\(327\) | 0.135190 | 0.00747605 | ||||||||
\(328\) | −77.8315 | −4.29752 | ||||||||
\(329\) | 0.0151019 | 0.000832594 0 | ||||||||
\(330\) | 0.0517347 | 0.00284790 | ||||||||
\(331\) | 13.9352 | 0.765949 | 0.382975 | − | 0.923759i | \(-0.374900\pi\) | ||||
0.382975 | + | 0.923759i | \(0.374900\pi\) | |||||||
\(332\) | 37.4413 | 2.05486 | ||||||||
\(333\) | −7.01586 | −0.384467 | ||||||||
\(334\) | 42.2445 | 2.31152 | ||||||||
\(335\) | 1.69908 | 0.0928305 | ||||||||
\(336\) | 0.684781 | 0.0373579 | ||||||||
\(337\) | −2.48928 | −0.135600 | −0.0677998 | − | 0.997699i | \(-0.521598\pi\) | ||||
−0.0677998 | + | 0.997699i | \(0.521598\pi\) | |||||||
\(338\) | −31.5223 | −1.71459 | ||||||||
\(339\) | −10.5609 | −0.573587 | ||||||||
\(340\) | −2.25843 | −0.122481 | ||||||||
\(341\) | −0.705228 | −0.0381902 | ||||||||
\(342\) | −6.41792 | −0.347041 | ||||||||
\(343\) | 0.843312 | 0.0455345 | ||||||||
\(344\) | −61.0200 | −3.28998 | ||||||||
\(345\) | −0.442089 | −0.0238013 | ||||||||
\(346\) | −22.4607 | −1.20749 | ||||||||
\(347\) | 10.2540 | 0.550462 | 0.275231 | − | 0.961378i | \(-0.411246\pi\) | ||||
0.275231 | + | 0.961378i | \(0.411246\pi\) | |||||||
\(348\) | −27.9700 | −1.49935 | ||||||||
\(349\) | −23.4312 | −1.25424 | −0.627120 | − | 0.778922i | \(-0.715767\pi\) | ||||
−0.627120 | + | 0.778922i | \(0.715767\pi\) | |||||||
\(350\) | 0.797266 | 0.0426157 | ||||||||
\(351\) | 1.06025 | 0.0565921 | ||||||||
\(352\) | −2.23901 | −0.119340 | ||||||||
\(353\) | −9.26151 | −0.492940 | −0.246470 | − | 0.969150i | \(-0.579271\pi\) | ||||
−0.246470 | + | 0.969150i | \(0.579271\pi\) | |||||||
\(354\) | 9.86950 | 0.524558 | ||||||||
\(355\) | 1.04540 | 0.0554840 | ||||||||
\(356\) | 60.5151 | 3.20729 | ||||||||
\(357\) | −0.221299 | −0.0117124 | ||||||||
\(358\) | −2.20025 | −0.116287 | ||||||||
\(359\) | −1.52535 | −0.0805048 | −0.0402524 | − | 0.999190i | \(-0.512816\pi\) | ||||
−0.0402524 | + | 0.999190i | \(0.512816\pi\) | |||||||
\(360\) | 0.985147 | 0.0519218 | ||||||||
\(361\) | −13.1537 | −0.692299 | ||||||||
\(362\) | −45.1379 | −2.37240 | ||||||||
\(363\) | 10.9744 | 0.576008 | ||||||||
\(364\) | 0.322313 | 0.0168938 | ||||||||
\(365\) | −1.35210 | −0.0707722 | ||||||||
\(366\) | −30.8190 | −1.61094 | ||||||||
\(367\) | −28.9807 | −1.51278 | −0.756389 | − | 0.654122i | \(-0.773038\pi\) | ||||
−0.756389 | + | 0.654122i | \(0.773038\pi\) | |||||||
\(368\) | 41.2273 | 2.14912 | ||||||||
\(369\) | −9.62849 | −0.501239 | ||||||||
\(370\) | −2.26954 | −0.117988 | ||||||||
\(371\) | −0.0989176 | −0.00513555 | ||||||||
\(372\) | −22.2484 | −1.15353 | ||||||||
\(373\) | 1.07773 | 0.0558025 | 0.0279013 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0279013 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(374\) | 1.55914 | 0.0806213 | ||||||||
\(375\) | 1.21691 | 0.0628410 | ||||||||
\(376\) | −2.02608 | −0.104487 | ||||||||
\(377\) | −5.87769 | −0.302716 | ||||||||
\(378\) | 0.159928 | 0.00822583 | ||||||||
\(379\) | −0.694276 | −0.0356626 | −0.0178313 | − | 0.999841i | \(-0.505676\pi\) | ||||
−0.0178313 | + | 0.999841i | \(0.505676\pi\) | |||||||
\(380\) | −1.48676 | −0.0762692 | ||||||||
\(381\) | −1.00000 | −0.0512316 | ||||||||
\(382\) | 26.5629 | 1.35908 | ||||||||
\(383\) | −24.2426 | −1.23874 | −0.619369 | − | 0.785100i | \(-0.712612\pi\) | ||||
−0.619369 | + | 0.785100i | \(0.712612\pi\) | |||||||
\(384\) | −10.3020 | −0.525723 | ||||||||
\(385\) | 0.00117436 | 5.98511e−5 0 | ||||||||
\(386\) | −51.1214 | −2.60201 | ||||||||
\(387\) | −7.54875 | −0.383724 | ||||||||
\(388\) | −4.91468 | −0.249505 | ||||||||
\(389\) | 38.4127 | 1.94760 | 0.973800 | − | 0.227407i | \(-0.0730247\pi\) | ||||
0.973800 | + | 0.227407i | \(0.0730247\pi\) | |||||||
\(390\) | 0.342978 | 0.0173674 | ||||||||
\(391\) | −13.3233 | −0.673789 | ||||||||
\(392\) | −56.5548 | −2.85645 | ||||||||
\(393\) | −11.3916 | −0.574633 | ||||||||
\(394\) | 20.8492 | 1.05037 | ||||||||
\(395\) | 0.935110 | 0.0470505 | ||||||||
\(396\) | −0.806902 | −0.0405484 | ||||||||
\(397\) | 29.9092 | 1.50110 | 0.750549 | − | 0.660815i | \(-0.229789\pi\) | ||||
0.750549 | + | 0.660815i | \(0.229789\pi\) | |||||||
\(398\) | 44.4420 | 2.22768 | ||||||||
\(399\) | −0.145685 | −0.00729336 | ||||||||
\(400\) | −56.6575 | −2.83287 | ||||||||
\(401\) | 0.194391 | 0.00970743 | 0.00485371 | − | 0.999988i | \(-0.498455\pi\) | ||||
0.00485371 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(402\) | −37.0051 | −1.84565 | ||||||||
\(403\) | −4.67534 | −0.232895 | ||||||||
\(404\) | −0.776754 | −0.0386450 | ||||||||
\(405\) | 0.121872 | 0.00605587 | ||||||||
\(406\) | −0.886590 | −0.0440007 | ||||||||
\(407\) | 1.12204 | 0.0556172 | ||||||||
\(408\) | 29.6896 | 1.46985 | ||||||||
\(409\) | −6.01049 | −0.297200 | −0.148600 | − | 0.988897i | \(-0.547477\pi\) | ||||
−0.148600 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(410\) | −3.11469 | −0.153824 | ||||||||
\(411\) | −20.5766 | −1.01497 | ||||||||
\(412\) | −74.4320 | −3.66700 | ||||||||
\(413\) | 0.224035 | 0.0110240 | ||||||||
\(414\) | 9.62849 | 0.473215 | ||||||||
\(415\) | 0.904397 | 0.0443951 | ||||||||
\(416\) | −14.8436 | −0.727768 | ||||||||
\(417\) | −14.8583 | −0.727613 | ||||||||
\(418\) | 1.02641 | 0.0502032 | ||||||||
\(419\) | −2.47049 | −0.120691 | −0.0603456 | − | 0.998178i | \(-0.519220\pi\) | ||||
−0.0603456 | + | 0.998178i | \(0.519220\pi\) | |||||||
\(420\) | 0.0370486 | 0.00180779 | ||||||||
\(421\) | −1.47555 | −0.0719137 | −0.0359568 | − | 0.999353i | \(-0.511448\pi\) | ||||
−0.0359568 | + | 0.999353i | \(0.511448\pi\) | |||||||
\(422\) | −18.3245 | −0.892025 | ||||||||
\(423\) | −0.250645 | −0.0121868 | ||||||||
\(424\) | 13.2708 | 0.644488 | ||||||||
\(425\) | 18.3099 | 0.888159 | ||||||||
\(426\) | −22.7683 | −1.10313 | ||||||||
\(427\) | −0.699582 | −0.0338551 | ||||||||
\(428\) | 46.7436 | 2.25944 | ||||||||
\(429\) | −0.169564 | −0.00818665 | ||||||||
\(430\) | −2.44192 | −0.117760 | ||||||||
\(431\) | −24.6705 | −1.18834 | −0.594168 | − | 0.804341i | \(-0.702519\pi\) | ||||
−0.594168 | + | 0.804341i | \(0.702519\pi\) | |||||||
\(432\) | −11.3653 | −0.546811 | ||||||||
\(433\) | −11.4334 | −0.549456 | −0.274728 | − | 0.961522i | \(-0.588588\pi\) | ||||
−0.274728 | + | 0.961522i | \(0.588588\pi\) | |||||||
\(434\) | −0.705228 | −0.0338520 | ||||||||
\(435\) | −0.675618 | −0.0323934 | ||||||||
\(436\) | −0.682090 | −0.0326662 | ||||||||
\(437\) | −8.77095 | −0.419571 | ||||||||
\(438\) | 29.4481 | 1.40709 | ||||||||
\(439\) | 20.2215 | 0.965118 | 0.482559 | − | 0.875863i | \(-0.339707\pi\) | ||||
0.482559 | + | 0.875863i | \(0.339707\pi\) | |||||||
\(440\) | −0.157553 | −0.00751104 | ||||||||
\(441\) | −6.99637 | −0.333160 | ||||||||
\(442\) | 10.3364 | 0.491652 | ||||||||
\(443\) | −12.2600 | −0.582490 | −0.291245 | − | 0.956648i | \(-0.594070\pi\) | ||||
−0.291245 | + | 0.956648i | \(0.594070\pi\) | |||||||
\(444\) | 35.3978 | 1.67991 | ||||||||
\(445\) | 1.46175 | 0.0692934 | ||||||||
\(446\) | −66.4661 | −3.14726 | ||||||||
\(447\) | 2.64424 | 0.125068 | ||||||||
\(448\) | −0.869448 | −0.0410775 | ||||||||
\(449\) | −23.0518 | −1.08788 | −0.543941 | − | 0.839123i | \(-0.683069\pi\) | ||||
−0.543941 | + | 0.839123i | \(0.683069\pi\) | |||||||
\(450\) | −13.2322 | −0.623770 | ||||||||
\(451\) | 1.53987 | 0.0725096 | ||||||||
\(452\) | 53.2838 | 2.50626 | ||||||||
\(453\) | 7.40875 | 0.348094 | ||||||||
\(454\) | −44.0346 | −2.06665 | ||||||||
\(455\) | 0.00778549 | 0.000364989 0 | ||||||||
\(456\) | 19.5451 | 0.915284 | ||||||||
\(457\) | 22.9884 | 1.07535 | 0.537676 | − | 0.843152i | \(-0.319302\pi\) | ||||
0.537676 | + | 0.843152i | \(0.319302\pi\) | |||||||
\(458\) | 62.2327 | 2.90794 | ||||||||
\(459\) | 3.67288 | 0.171435 | ||||||||
\(460\) | 2.23051 | 0.103998 | ||||||||
\(461\) | −22.2984 | −1.03854 | −0.519269 | − | 0.854611i | \(-0.673796\pi\) | ||||
−0.519269 | + | 0.854611i | \(0.673796\pi\) | |||||||
\(462\) | −0.0255771 | −0.00118995 | ||||||||
\(463\) | −4.52005 | −0.210065 | −0.105032 | − | 0.994469i | \(-0.533495\pi\) | ||||
−0.105032 | + | 0.994469i | \(0.533495\pi\) | |||||||
\(464\) | 63.0052 | 2.92494 | ||||||||
\(465\) | −0.537413 | −0.0249219 | ||||||||
\(466\) | 68.1251 | 3.15583 | ||||||||
\(467\) | −3.44014 | −0.159191 | −0.0795954 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795954 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(468\) | −5.34940 | −0.247276 | ||||||||
\(469\) | −0.840005 | −0.0387878 | ||||||||
\(470\) | −0.0810803 | −0.00373996 | ||||||||
\(471\) | −8.13184 | −0.374695 | ||||||||
\(472\) | −30.0566 | −1.38347 | ||||||||
\(473\) | 1.20726 | 0.0555098 | ||||||||
\(474\) | −20.3663 | −0.935453 | ||||||||
\(475\) | 12.0537 | 0.553060 | ||||||||
\(476\) | 1.11654 | 0.0511766 | ||||||||
\(477\) | 1.64173 | 0.0751695 | ||||||||
\(478\) | −50.7835 | −2.32278 | ||||||||
\(479\) | −16.4602 | −0.752084 | −0.376042 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376042 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(480\) | −1.70622 | −0.0778779 | ||||||||
\(481\) | 7.43858 | 0.339170 | ||||||||
\(482\) | 50.1593 | 2.28469 | ||||||||
\(483\) | 0.218564 | 0.00994499 | ||||||||
\(484\) | −55.3703 | −2.51683 | ||||||||
\(485\) | −0.118715 | −0.00539055 | ||||||||
\(486\) | −2.65432 | −0.120402 | ||||||||
\(487\) | 28.0787 | 1.27237 | 0.636183 | − | 0.771538i | \(-0.280512\pi\) | ||||
0.636183 | + | 0.771538i | \(0.280512\pi\) | |||||||
\(488\) | 93.8562 | 4.24867 | ||||||||
\(489\) | 1.99447 | 0.0901929 | ||||||||
\(490\) | −2.26323 | −0.102243 | ||||||||
\(491\) | 5.02776 | 0.226900 | 0.113450 | − | 0.993544i | \(-0.463810\pi\) | ||||
0.113450 | + | 0.993544i | \(0.463810\pi\) | |||||||
\(492\) | 48.5796 | 2.19014 | ||||||||
\(493\) | −20.3612 | −0.917024 | ||||||||
\(494\) | 6.80461 | 0.306154 | ||||||||
\(495\) | −0.0194908 | −0.000876046 0 | ||||||||
\(496\) | 50.1168 | 2.25031 | ||||||||
\(497\) | −0.516834 | −0.0231832 | ||||||||
\(498\) | −19.6973 | −0.882659 | ||||||||
\(499\) | 23.2126 | 1.03914 | 0.519570 | − | 0.854428i | \(-0.326092\pi\) | ||||
0.519570 | + | 0.854428i | \(0.326092\pi\) | |||||||
\(500\) | −6.13980 | −0.274580 | ||||||||
\(501\) | −15.9154 | −0.711048 | ||||||||
\(502\) | 63.9048 | 2.85221 | ||||||||
\(503\) | 15.9960 | 0.713228 | 0.356614 | − | 0.934252i | \(-0.383931\pi\) | ||||
0.356614 | + | 0.934252i | \(0.383931\pi\) | |||||||
\(504\) | −0.487046 | −0.0216947 | ||||||||
\(505\) | −0.0187626 | −0.000834923 0 | ||||||||
\(506\) | −1.53987 | −0.0684555 | ||||||||
\(507\) | 11.8759 | 0.527426 | ||||||||
\(508\) | 5.04540 | 0.223853 | ||||||||
\(509\) | 24.2158 | 1.07335 | 0.536674 | − | 0.843790i | \(-0.319681\pi\) | ||||
0.536674 | + | 0.843790i | \(0.319681\pi\) | |||||||
\(510\) | 1.18813 | 0.0526113 | ||||||||
\(511\) | 0.668463 | 0.0295711 | ||||||||
\(512\) | −24.6266 | −1.08835 | ||||||||
\(513\) | 2.41792 | 0.106754 | ||||||||
\(514\) | −56.2645 | −2.48172 | ||||||||
\(515\) | −1.79791 | −0.0792255 | ||||||||
\(516\) | 38.0864 | 1.67666 | ||||||||
\(517\) | 0.0400852 | 0.00176294 | ||||||||
\(518\) | 1.12204 | 0.0492994 | ||||||||
\(519\) | 8.46195 | 0.371438 | ||||||||
\(520\) | −1.04450 | −0.0458046 | ||||||||
\(521\) | 35.8187 | 1.56925 | 0.784624 | − | 0.619972i | \(-0.212856\pi\) | ||||
0.784624 | + | 0.619972i | \(0.212856\pi\) | |||||||
\(522\) | 14.7147 | 0.644043 | ||||||||
\(523\) | 7.47258 | 0.326753 | 0.163377 | − | 0.986564i | \(-0.447761\pi\) | ||||
0.163377 | + | 0.986564i | \(0.447761\pi\) | |||||||
\(524\) | 57.4754 | 2.51082 | ||||||||
\(525\) | −0.300366 | −0.0131090 | ||||||||
\(526\) | −79.9559 | −3.48624 | ||||||||
\(527\) | −16.1961 | −0.705514 | ||||||||
\(528\) | 1.81763 | 0.0791020 | ||||||||
\(529\) | −9.84137 | −0.427885 | ||||||||
\(530\) | 0.531077 | 0.0230685 | ||||||||
\(531\) | −3.71828 | −0.161360 | ||||||||
\(532\) | 0.735037 | 0.0318679 | ||||||||
\(533\) | 10.2086 | 0.442185 | ||||||||
\(534\) | −31.8362 | −1.37769 | ||||||||
\(535\) | 1.12910 | 0.0488151 | ||||||||
\(536\) | 112.695 | 4.86770 | ||||||||
\(537\) | 0.828932 | 0.0357710 | ||||||||
\(538\) | −21.1412 | −0.911460 | ||||||||
\(539\) | 1.11892 | 0.0481952 | ||||||||
\(540\) | −0.614893 | −0.0264608 | ||||||||
\(541\) | −25.3744 | −1.09093 | −0.545466 | − | 0.838133i | \(-0.683647\pi\) | ||||
−0.545466 | + | 0.838133i | \(0.683647\pi\) | |||||||
\(542\) | 31.3133 | 1.34502 | ||||||||
\(543\) | 17.0055 | 0.729775 | ||||||||
\(544\) | −51.4207 | −2.20464 | ||||||||
\(545\) | −0.0164759 | −0.000705751 0 | ||||||||
\(546\) | −0.169564 | −0.00725669 | ||||||||
\(547\) | 19.2589 | 0.823450 | 0.411725 | − | 0.911308i | \(-0.364926\pi\) | ||||
0.411725 | + | 0.911308i | \(0.364926\pi\) | |||||||
\(548\) | 103.817 | 4.43484 | ||||||||
\(549\) | 11.6109 | 0.495541 | ||||||||
\(550\) | 2.11620 | 0.0902350 | ||||||||
\(551\) | −13.4041 | −0.571035 | ||||||||
\(552\) | −29.3226 | −1.24805 | ||||||||
\(553\) | −0.462308 | −0.0196593 | ||||||||
\(554\) | −81.3573 | −3.45654 | ||||||||
\(555\) | 0.855037 | 0.0362943 | ||||||||
\(556\) | 74.9659 | 3.17926 | ||||||||
\(557\) | 31.0604 | 1.31607 | 0.658035 | − | 0.752987i | \(-0.271388\pi\) | ||||
0.658035 | + | 0.752987i | \(0.271388\pi\) | |||||||
\(558\) | 11.7046 | 0.495495 | ||||||||
\(559\) | 8.00358 | 0.338515 | ||||||||
\(560\) | −0.0834557 | −0.00352665 | ||||||||
\(561\) | −0.587398 | −0.0248000 | ||||||||
\(562\) | −46.9721 | −1.98140 | ||||||||
\(563\) | −33.1705 | −1.39797 | −0.698986 | − | 0.715136i | \(-0.746365\pi\) | ||||
−0.698986 | + | 0.715136i | \(0.746365\pi\) | |||||||
\(564\) | 1.26460 | 0.0532494 | ||||||||
\(565\) | 1.28707 | 0.0541476 | ||||||||
\(566\) | 42.5079 | 1.78674 | ||||||||
\(567\) | −0.0602522 | −0.00253035 | ||||||||
\(568\) | 69.3386 | 2.90938 | ||||||||
\(569\) | −34.7023 | −1.45479 | −0.727397 | − | 0.686217i | \(-0.759270\pi\) | ||||
−0.727397 | + | 0.686217i | \(0.759270\pi\) | |||||||
\(570\) | 0.782165 | 0.0327613 | ||||||||
\(571\) | −20.5890 | −0.861621 | −0.430810 | − | 0.902442i | \(-0.641772\pi\) | ||||
−0.430810 | + | 0.902442i | \(0.641772\pi\) | |||||||
\(572\) | 0.855520 | 0.0357711 | ||||||||
\(573\) | −10.0074 | −0.418066 | ||||||||
\(574\) | 1.53987 | 0.0642729 | ||||||||
\(575\) | −18.0835 | −0.754136 | ||||||||
\(576\) | 14.4301 | 0.601256 | ||||||||
\(577\) | −23.6592 | −0.984946 | −0.492473 | − | 0.870328i | \(-0.663907\pi\) | ||||
−0.492473 | + | 0.870328i | \(0.663907\pi\) | |||||||
\(578\) | −9.31648 | −0.387514 | ||||||||
\(579\) | 19.2597 | 0.800407 | ||||||||
\(580\) | 3.40876 | 0.141541 | ||||||||
\(581\) | −0.447124 | −0.0185498 | ||||||||
\(582\) | 2.58555 | 0.107174 | ||||||||
\(583\) | −0.262559 | −0.0108741 | ||||||||
\(584\) | −89.6813 | −3.71104 | ||||||||
\(585\) | −0.129215 | −0.00534239 | ||||||||
\(586\) | −52.9504 | −2.18736 | ||||||||
\(587\) | −31.9623 | −1.31922 | −0.659612 | − | 0.751606i | \(-0.729279\pi\) | ||||
−0.659612 | + | 0.751606i | \(0.729279\pi\) | |||||||
\(588\) | 35.2995 | 1.45573 | ||||||||
\(589\) | −10.6622 | −0.439327 | ||||||||
\(590\) | −1.20282 | −0.0495192 | ||||||||
\(591\) | −7.85481 | −0.323104 | ||||||||
\(592\) | −79.7371 | −3.27717 | ||||||||
\(593\) | 26.0212 | 1.06856 | 0.534282 | − | 0.845306i | \(-0.320582\pi\) | ||||
0.534282 | + | 0.845306i | \(0.320582\pi\) | |||||||
\(594\) | 0.424501 | 0.0174175 | ||||||||
\(595\) | 0.0269702 | 0.00110567 | ||||||||
\(596\) | −13.3412 | −0.546478 | ||||||||
\(597\) | −16.7433 | −0.685258 | ||||||||
\(598\) | −10.2086 | −0.417462 | ||||||||
\(599\) | −14.6966 | −0.600485 | −0.300243 | − | 0.953863i | \(-0.597068\pi\) | ||||
−0.300243 | + | 0.953863i | \(0.597068\pi\) | |||||||
\(600\) | 40.2972 | 1.64513 | ||||||||
\(601\) | −6.64010 | −0.270855 | −0.135428 | − | 0.990787i | \(-0.543241\pi\) | ||||
−0.135428 | + | 0.990787i | \(0.543241\pi\) | |||||||
\(602\) | 1.20726 | 0.0492042 | ||||||||
\(603\) | 13.9415 | 0.567741 | ||||||||
\(604\) | −37.3801 | −1.52098 | ||||||||
\(605\) | −1.33748 | −0.0543761 | ||||||||
\(606\) | 0.408640 | 0.0165999 | ||||||||
\(607\) | 30.2066 | 1.22605 | 0.613023 | − | 0.790065i | \(-0.289953\pi\) | ||||
0.613023 | + | 0.790065i | \(0.289953\pi\) | |||||||
\(608\) | −33.8510 | −1.37284 | ||||||||
\(609\) | 0.334018 | 0.0135351 | ||||||||
\(610\) | 3.75598 | 0.152075 | ||||||||
\(611\) | 0.265747 | 0.0107510 | ||||||||
\(612\) | −18.5312 | −0.749078 | ||||||||
\(613\) | 43.6245 | 1.76198 | 0.880989 | − | 0.473136i | \(-0.156878\pi\) | ||||
0.880989 | + | 0.473136i | \(0.156878\pi\) | |||||||
\(614\) | 4.63201 | 0.186933 | ||||||||
\(615\) | 1.17344 | 0.0473178 | ||||||||
\(616\) | 0.0778924 | 0.00313838 | ||||||||
\(617\) | −34.1094 | −1.37319 | −0.686596 | − | 0.727039i | \(-0.740896\pi\) | ||||
−0.686596 | + | 0.727039i | \(0.740896\pi\) | |||||||
\(618\) | 39.1577 | 1.57515 | ||||||||
\(619\) | 5.16120 | 0.207446 | 0.103723 | − | 0.994606i | \(-0.466924\pi\) | ||||
0.103723 | + | 0.994606i | \(0.466924\pi\) | |||||||
\(620\) | 2.71146 | 0.108895 | ||||||||
\(621\) | −3.62748 | −0.145566 | ||||||||
\(622\) | 43.5155 | 1.74481 | ||||||||
\(623\) | −0.722671 | −0.0289532 | ||||||||
\(624\) | 12.0500 | 0.482388 | ||||||||
\(625\) | 24.7774 | 0.991097 | ||||||||
\(626\) | −8.65172 | −0.345792 | ||||||||
\(627\) | −0.386693 | −0.0154430 | ||||||||
\(628\) | 41.0284 | 1.63721 | ||||||||
\(629\) | 25.7684 | 1.02745 | ||||||||
\(630\) | −0.0194908 | −0.000776532 0 | ||||||||
\(631\) | 44.1665 | 1.75824 | 0.879121 | − | 0.476599i | \(-0.158131\pi\) | ||||
0.879121 | + | 0.476599i | \(0.158131\pi\) | |||||||
\(632\) | 62.0234 | 2.46716 | ||||||||
\(633\) | 6.90368 | 0.274397 | ||||||||
\(634\) | −10.1344 | −0.402487 | ||||||||
\(635\) | 0.121872 | 0.00483634 | ||||||||
\(636\) | −8.28317 | −0.328449 | ||||||||
\(637\) | 7.41792 | 0.293909 | ||||||||
\(638\) | −2.35329 | −0.0931676 | ||||||||
\(639\) | 8.57784 | 0.339334 | ||||||||
\(640\) | 1.25553 | 0.0496291 | ||||||||
\(641\) | 35.9696 | 1.42071 | 0.710357 | − | 0.703842i | \(-0.248534\pi\) | ||||
0.710357 | + | 0.703842i | \(0.248534\pi\) | |||||||
\(642\) | −24.5912 | −0.970537 | ||||||||
\(643\) | −46.3358 | −1.82731 | −0.913654 | − | 0.406494i | \(-0.866751\pi\) | ||||
−0.913654 | + | 0.406494i | \(0.866751\pi\) | |||||||
\(644\) | −1.10274 | −0.0434541 | ||||||||
\(645\) | 0.919981 | 0.0362242 | ||||||||
\(646\) | 23.5723 | 0.927438 | ||||||||
\(647\) | −37.8776 | −1.48912 | −0.744561 | − | 0.667554i | \(-0.767341\pi\) | ||||
−0.744561 | + | 0.667554i | \(0.767341\pi\) | |||||||
\(648\) | 8.08346 | 0.317548 | ||||||||
\(649\) | 0.594659 | 0.0233424 | ||||||||
\(650\) | 14.0294 | 0.550279 | ||||||||
\(651\) | 0.265691 | 0.0104132 | ||||||||
\(652\) | −10.0629 | −0.394093 | ||||||||
\(653\) | −21.7248 | −0.850156 | −0.425078 | − | 0.905157i | \(-0.639753\pi\) | ||||
−0.425078 | + | 0.905157i | \(0.639753\pi\) | |||||||
\(654\) | 0.358838 | 0.0140317 | ||||||||
\(655\) | 1.38832 | 0.0542463 | ||||||||
\(656\) | −109.430 | −4.27253 | ||||||||
\(657\) | −11.0944 | −0.432835 | ||||||||
\(658\) | 0.0400852 | 0.00156268 | ||||||||
\(659\) | 1.43232 | 0.0557954 | 0.0278977 | − | 0.999611i | \(-0.491119\pi\) | ||||
0.0278977 | + | 0.999611i | \(0.491119\pi\) | |||||||
\(660\) | 0.0983388 | 0.00382783 | ||||||||
\(661\) | 38.3355 | 1.49108 | 0.745539 | − | 0.666462i | \(-0.232192\pi\) | ||||
0.745539 | + | 0.666462i | \(0.232192\pi\) | |||||||
\(662\) | 36.9885 | 1.43760 | ||||||||
\(663\) | −3.89418 | −0.151237 | ||||||||
\(664\) | 59.9863 | 2.32792 | ||||||||
\(665\) | 0.0177549 | 0.000688505 0 | ||||||||
\(666\) | −18.6223 | −0.721600 | ||||||||
\(667\) | 20.1096 | 0.778645 | ||||||||
\(668\) | 80.2996 | 3.10688 | ||||||||
\(669\) | 25.0408 | 0.968132 | ||||||||
\(670\) | 4.50989 | 0.174232 | ||||||||
\(671\) | −1.85691 | −0.0716853 | ||||||||
\(672\) | 0.843535 | 0.0325401 | ||||||||
\(673\) | −4.23191 | −0.163128 | −0.0815640 | − | 0.996668i | \(-0.525991\pi\) | ||||
−0.0815640 | + | 0.996668i | \(0.525991\pi\) | |||||||
\(674\) | −6.60733 | −0.254505 | ||||||||
\(675\) | 4.98515 | 0.191878 | ||||||||
\(676\) | −59.9185 | −2.30456 | ||||||||
\(677\) | 3.17305 | 0.121950 | 0.0609751 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609751 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(678\) | −28.0319 | −1.07656 | ||||||||
\(679\) | 0.0586911 | 0.00225236 | ||||||||
\(680\) | −3.61833 | −0.138757 | ||||||||
\(681\) | 16.5898 | 0.635722 | ||||||||
\(682\) | −1.87190 | −0.0716787 | ||||||||
\(683\) | 44.4169 | 1.69956 | 0.849782 | − | 0.527134i | \(-0.176734\pi\) | ||||
0.849782 | + | 0.527134i | \(0.176734\pi\) | |||||||
\(684\) | −12.1994 | −0.466454 | ||||||||
\(685\) | 2.50771 | 0.0958146 | ||||||||
\(686\) | 2.23842 | 0.0854631 | ||||||||
\(687\) | −23.4458 | −0.894515 | ||||||||
\(688\) | −85.7935 | −3.27084 | ||||||||
\(689\) | −1.74064 | −0.0663133 | ||||||||
\(690\) | −1.17344 | −0.0446722 | ||||||||
\(691\) | 35.3985 | 1.34662 | 0.673312 | − | 0.739359i | \(-0.264871\pi\) | ||||
0.673312 | + | 0.739359i | \(0.264871\pi\) | |||||||
\(692\) | −42.6939 | −1.62298 | ||||||||
\(693\) | 0.00963603 | 0.000366043 0 | ||||||||
\(694\) | 27.2173 | 1.03315 | ||||||||
\(695\) | 1.81081 | 0.0686879 | ||||||||
\(696\) | −44.8120 | −1.69859 | ||||||||
\(697\) | 35.3643 | 1.33952 | ||||||||
\(698\) | −62.1937 | −2.35407 | ||||||||
\(699\) | −25.6658 | −0.970769 | ||||||||
\(700\) | 1.51547 | 0.0572792 | ||||||||
\(701\) | −8.50547 | −0.321247 | −0.160624 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160624 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(702\) | 2.81425 | 0.106217 | ||||||||
\(703\) | 16.9638 | 0.639800 | ||||||||
\(704\) | −2.30779 | −0.0869781 | ||||||||
\(705\) | 0.0305466 | 0.00115045 | ||||||||
\(706\) | −24.5830 | −0.925193 | ||||||||
\(707\) | 0.00927600 | 0.000348860 0 | ||||||||
\(708\) | 18.7602 | 0.705052 | ||||||||
\(709\) | −24.4835 | −0.919498 | −0.459749 | − | 0.888049i | \(-0.652061\pi\) | ||||
−0.459749 | + | 0.888049i | \(0.652061\pi\) | |||||||
\(710\) | 2.77482 | 0.104137 | ||||||||
\(711\) | 7.67288 | 0.287756 | ||||||||
\(712\) | 96.9538 | 3.63350 | ||||||||
\(713\) | 15.9959 | 0.599052 | ||||||||
\(714\) | −0.587398 | −0.0219828 | ||||||||
\(715\) | 0.0206652 | 0.000772833 0 | ||||||||
\(716\) | −4.18229 | −0.156300 | ||||||||
\(717\) | 19.1324 | 0.714513 | ||||||||
\(718\) | −4.04876 | −0.151098 | ||||||||
\(719\) | 42.5741 | 1.58775 | 0.793874 | − | 0.608083i | \(-0.208061\pi\) | ||||
0.793874 | + | 0.608083i | \(0.208061\pi\) | |||||||
\(720\) | 1.38511 | 0.0516199 | ||||||||
\(721\) | 0.888868 | 0.0331032 | ||||||||
\(722\) | −34.9140 | −1.29937 | ||||||||
\(723\) | −18.8973 | −0.702797 | ||||||||
\(724\) | −85.7994 | −3.18871 | ||||||||
\(725\) | −27.6360 | −1.02638 | ||||||||
\(726\) | 29.1296 | 1.08110 | ||||||||
\(727\) | 6.89992 | 0.255904 | 0.127952 | − | 0.991780i | \(-0.459160\pi\) | ||||
0.127952 | + | 0.991780i | \(0.459160\pi\) | |||||||
\(728\) | 0.516391 | 0.0191387 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −3.58890 | −0.132831 | ||||||||
\(731\) | 27.7257 | 1.02547 | ||||||||
\(732\) | −58.5816 | −2.16524 | ||||||||
\(733\) | −8.87156 | −0.327679 | −0.163839 | − | 0.986487i | \(-0.552388\pi\) | ||||
−0.163839 | + | 0.986487i | \(0.552388\pi\) | |||||||
\(734\) | −76.9239 | −2.83931 | ||||||||
\(735\) | 0.852662 | 0.0314509 | ||||||||
\(736\) | 50.7851 | 1.87196 | ||||||||
\(737\) | −2.22964 | −0.0821298 | ||||||||
\(738\) | −25.5571 | −0.940769 | ||||||||
\(739\) | 20.1269 | 0.740381 | 0.370190 | − | 0.928956i | \(-0.379292\pi\) | ||||
0.370190 | + | 0.928956i | \(0.379292\pi\) | |||||||
\(740\) | −4.31400 | −0.158586 | ||||||||
\(741\) | −2.56360 | −0.0941762 | ||||||||
\(742\) | −0.262559 | −0.00963883 | ||||||||
\(743\) | −18.0241 | −0.661240 | −0.330620 | − | 0.943764i | \(-0.607258\pi\) | ||||
−0.330620 | + | 0.943764i | \(0.607258\pi\) | |||||||
\(744\) | −35.6452 | −1.30682 | ||||||||
\(745\) | −0.322259 | −0.0118066 | ||||||||
\(746\) | 2.86063 | 0.104735 | ||||||||
\(747\) | 7.42087 | 0.271515 | ||||||||
\(748\) | 2.96366 | 0.108362 | ||||||||
\(749\) | −0.558212 | −0.0203966 | ||||||||
\(750\) | 3.23007 | 0.117945 | ||||||||
\(751\) | −27.8187 | −1.01512 | −0.507560 | − | 0.861616i | \(-0.669452\pi\) | ||||
−0.507560 | + | 0.861616i | \(0.669452\pi\) | |||||||
\(752\) | −2.84864 | −0.103879 | ||||||||
\(753\) | −24.0758 | −0.877370 | ||||||||
\(754\) | −15.6012 | −0.568164 | ||||||||
\(755\) | −0.902920 | −0.0328606 | ||||||||
\(756\) | 0.303996 | 0.0110562 | ||||||||
\(757\) | 13.2283 | 0.480792 | 0.240396 | − | 0.970675i | \(-0.422723\pi\) | ||||
0.240396 | + | 0.970675i | \(0.422723\pi\) | |||||||
\(758\) | −1.84283 | −0.0669346 | ||||||||
\(759\) | 0.580137 | 0.0210577 | ||||||||
\(760\) | −2.38200 | −0.0864043 | ||||||||
\(761\) | 13.8717 | 0.502848 | 0.251424 | − | 0.967877i | \(-0.419101\pi\) | ||||
0.251424 | + | 0.967877i | \(0.419101\pi\) | |||||||
\(762\) | −2.65432 | −0.0961558 | ||||||||
\(763\) | 0.00814552 | 0.000294888 0 | ||||||||
\(764\) | 50.4915 | 1.82672 | ||||||||
\(765\) | −0.447622 | −0.0161838 | ||||||||
\(766\) | −64.3475 | −2.32497 | ||||||||
\(767\) | 3.94232 | 0.142349 | ||||||||
\(768\) | 1.51547 | 0.0546847 | ||||||||
\(769\) | −11.3251 | −0.408394 | −0.204197 | − | 0.978930i | \(-0.565458\pi\) | ||||
−0.204197 | + | 0.978930i | \(0.565458\pi\) | |||||||
\(770\) | 0.00311713 | 0.000112334 0 | ||||||||
\(771\) | 21.1973 | 0.763404 | ||||||||
\(772\) | −97.1730 | −3.49733 | ||||||||
\(773\) | 21.9384 | 0.789068 | 0.394534 | − | 0.918881i | \(-0.370906\pi\) | ||||
0.394534 | + | 0.918881i | \(0.370906\pi\) | |||||||
\(774\) | −20.0368 | −0.720207 | ||||||||
\(775\) | −21.9827 | −0.789643 | ||||||||
\(776\) | −7.87402 | −0.282661 | ||||||||
\(777\) | −0.422721 | −0.0151650 | ||||||||
\(778\) | 101.959 | 3.65542 | ||||||||
\(779\) | 23.2809 | 0.834124 | ||||||||
\(780\) | 0.651942 | 0.0233433 | ||||||||
\(781\) | −1.37184 | −0.0490883 | ||||||||
\(782\) | −35.3643 | −1.26463 | ||||||||
\(783\) | −5.54367 | −0.198115 | ||||||||
\(784\) | −79.5155 | −2.83984 | ||||||||
\(785\) | 0.991044 | 0.0353719 | ||||||||
\(786\) | −30.2370 | −1.07852 | ||||||||
\(787\) | 27.2535 | 0.971484 | 0.485742 | − | 0.874102i | \(-0.338550\pi\) | ||||
0.485742 | + | 0.874102i | \(0.338550\pi\) | |||||||
\(788\) | 39.6307 | 1.41178 | ||||||||
\(789\) | 30.1230 | 1.07241 | ||||||||
\(790\) | 2.48208 | 0.0883084 | ||||||||
\(791\) | −0.636315 | −0.0226248 | ||||||||
\(792\) | −1.29277 | −0.0459367 | ||||||||
\(793\) | −12.3105 | −0.437158 | ||||||||
\(794\) | 79.3884 | 2.81739 | ||||||||
\(795\) | −0.200081 | −0.00709613 | ||||||||
\(796\) | 84.4767 | 2.99420 | ||||||||
\(797\) | 25.8283 | 0.914887 | 0.457443 | − | 0.889239i | \(-0.348765\pi\) | ||||
0.457443 | + | 0.889239i | \(0.348765\pi\) | |||||||
\(798\) | −0.386693 | −0.0136888 | ||||||||
\(799\) | 0.920589 | 0.0325681 | ||||||||
\(800\) | −69.7925 | −2.46754 | ||||||||
\(801\) | 11.9941 | 0.423791 | ||||||||
\(802\) | 0.515975 | 0.0182197 | ||||||||
\(803\) | 1.77431 | 0.0626142 | ||||||||
\(804\) | −70.3404 | −2.48071 | ||||||||
\(805\) | −0.0266368 | −0.000938824 0 | ||||||||
\(806\) | −12.4098 | −0.437118 | ||||||||
\(807\) | 7.96482 | 0.280375 | ||||||||
\(808\) | −1.24447 | −0.0437804 | ||||||||
\(809\) | 35.8182 | 1.25930 | 0.629651 | − | 0.776878i | \(-0.283198\pi\) | ||||
0.629651 | + | 0.776878i | \(0.283198\pi\) | |||||||
\(810\) | 0.323487 | 0.0113662 | ||||||||
\(811\) | 13.5766 | 0.476739 | 0.238370 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238370 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(812\) | −1.68525 | −0.0591408 | ||||||||
\(813\) | −11.7971 | −0.413743 | ||||||||
\(814\) | 2.97824 | 0.104387 | ||||||||
\(815\) | −0.243070 | −0.00851436 | ||||||||
\(816\) | 41.7433 | 1.46131 | ||||||||
\(817\) | 18.2522 | 0.638565 | ||||||||
\(818\) | −15.9538 | −0.557810 | ||||||||
\(819\) | 0.0638825 | 0.00223223 | ||||||||
\(820\) | −5.92049 | −0.206753 | ||||||||
\(821\) | −22.3923 | −0.781495 | −0.390748 | − | 0.920498i | \(-0.627783\pi\) | ||||
−0.390748 | + | 0.920498i | \(0.627783\pi\) | |||||||
\(822\) | −54.6167 | −1.90498 | ||||||||
\(823\) | −46.2161 | −1.61099 | −0.805495 | − | 0.592602i | \(-0.798101\pi\) | ||||
−0.805495 | + | 0.592602i | \(0.798101\pi\) | |||||||
\(824\) | −119.251 | −4.15430 | ||||||||
\(825\) | −0.797266 | −0.0277573 | ||||||||
\(826\) | 0.594659 | 0.0206908 | ||||||||
\(827\) | −43.3279 | −1.50666 | −0.753329 | − | 0.657644i | \(-0.771553\pi\) | ||||
−0.753329 | + | 0.657644i | \(0.771553\pi\) | |||||||
\(828\) | 18.3021 | 0.636042 | ||||||||
\(829\) | 30.7055 | 1.06645 | 0.533223 | − | 0.845975i | \(-0.320981\pi\) | ||||
0.533223 | + | 0.845975i | \(0.320981\pi\) | |||||||
\(830\) | 2.40056 | 0.0833245 | ||||||||
\(831\) | 30.6509 | 1.06327 | ||||||||
\(832\) | −15.2996 | −0.530418 | ||||||||
\(833\) | 25.6968 | 0.890343 | ||||||||
\(834\) | −39.4386 | −1.36565 | ||||||||
\(835\) | 1.93964 | 0.0671241 | ||||||||
\(836\) | 1.95102 | 0.0674775 | ||||||||
\(837\) | −4.40965 | −0.152420 | ||||||||
\(838\) | −6.55746 | −0.226524 | ||||||||
\(839\) | −1.04914 | −0.0362202 | −0.0181101 | − | 0.999836i | \(-0.505765\pi\) | ||||
−0.0181101 | + | 0.999836i | \(0.505765\pi\) | |||||||
\(840\) | 0.0593573 | 0.00204802 | ||||||||
\(841\) | 1.73225 | 0.0597328 | ||||||||
\(842\) | −3.91657 | −0.134974 | ||||||||
\(843\) | 17.6965 | 0.609499 | ||||||||
\(844\) | −34.8318 | −1.19896 | ||||||||
\(845\) | −1.44734 | −0.0497899 | ||||||||
\(846\) | −0.665290 | −0.0228732 | ||||||||
\(847\) | 0.661233 | 0.0227202 | ||||||||
\(848\) | 18.6586 | 0.640741 | ||||||||
\(849\) | −16.0146 | −0.549621 | ||||||||
\(850\) | 48.6002 | 1.66697 | ||||||||
\(851\) | −25.4499 | −0.872412 | ||||||||
\(852\) | −43.2787 | −1.48270 | ||||||||
\(853\) | −21.7655 | −0.745238 | −0.372619 | − | 0.927984i | \(-0.621540\pi\) | ||||
−0.372619 | + | 0.927984i | \(0.621540\pi\) | |||||||
\(854\) | −1.85691 | −0.0635422 | ||||||||
\(855\) | −0.294676 | −0.0100777 | ||||||||
\(856\) | 74.8900 | 2.55969 | ||||||||
\(857\) | 1.31119 | 0.0447895 | 0.0223948 | − | 0.999749i | \(-0.492871\pi\) | ||||
0.0223948 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(858\) | −0.450078 | −0.0153654 | ||||||||
\(859\) | −22.6717 | −0.773549 | −0.386774 | − | 0.922174i | \(-0.626411\pi\) | ||||
−0.386774 | + | 0.922174i | \(0.626411\pi\) | |||||||
\(860\) | −4.64167 | −0.158280 | ||||||||
\(861\) | −0.580137 | −0.0197710 | ||||||||
\(862\) | −65.4834 | −2.23037 | ||||||||
\(863\) | −52.8484 | −1.79898 | −0.899490 | − | 0.436941i | \(-0.856062\pi\) | ||||
−0.899490 | + | 0.436941i | \(0.856062\pi\) | |||||||
\(864\) | −14.0001 | −0.476292 | ||||||||
\(865\) | −1.03127 | −0.0350644 | ||||||||
\(866\) | −30.3480 | −1.03127 | ||||||||
\(867\) | 3.50993 | 0.119204 | ||||||||
\(868\) | −1.34052 | −0.0455001 | ||||||||
\(869\) | −1.22711 | −0.0416269 | ||||||||
\(870\) | −1.79330 | −0.0607987 | ||||||||
\(871\) | −14.7815 | −0.500852 | ||||||||
\(872\) | −1.09281 | −0.0370071 | ||||||||
\(873\) | −0.974091 | −0.0329680 | ||||||||
\(874\) | −23.2809 | −0.787488 | ||||||||
\(875\) | 0.0733215 | 0.00247872 | ||||||||
\(876\) | 55.9758 | 1.89125 | ||||||||
\(877\) | 19.1137 | 0.645423 | 0.322712 | − | 0.946497i | \(-0.395406\pi\) | ||||
0.322712 | + | 0.946497i | \(0.395406\pi\) | |||||||
\(878\) | 53.6742 | 1.81142 | ||||||||
\(879\) | 19.9488 | 0.672856 | ||||||||
\(880\) | −0.221518 | −0.00746737 | ||||||||
\(881\) | −10.8265 | −0.364756 | −0.182378 | − | 0.983229i | \(-0.558379\pi\) | ||||
−0.182378 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(882\) | −18.5706 | −0.625304 | ||||||||
\(883\) | 28.4711 | 0.958128 | 0.479064 | − | 0.877780i | \(-0.340976\pi\) | ||||
0.479064 | + | 0.877780i | \(0.340976\pi\) | |||||||
\(884\) | 19.6477 | 0.660824 | ||||||||
\(885\) | 0.453155 | 0.0152326 | ||||||||
\(886\) | −32.5419 | −1.09327 | ||||||||
\(887\) | −9.46381 | −0.317763 | −0.158882 | − | 0.987298i | \(-0.550789\pi\) | ||||
−0.158882 | + | 0.987298i | \(0.550789\pi\) | |||||||
\(888\) | 56.7124 | 1.90314 | ||||||||
\(889\) | −0.0602522 | −0.00202079 | ||||||||
\(890\) | 3.87994 | 0.130056 | ||||||||
\(891\) | −0.159928 | −0.00535780 | ||||||||
\(892\) | −126.341 | −4.23020 | ||||||||
\(893\) | 0.606038 | 0.0202803 | ||||||||
\(894\) | 7.01865 | 0.234739 | ||||||||
\(895\) | −0.101024 | −0.00337685 | ||||||||
\(896\) | −0.620719 | −0.0207368 | ||||||||
\(897\) | 3.84605 | 0.128416 | ||||||||
\(898\) | −61.1869 | −2.04183 | ||||||||
\(899\) | 24.4456 | 0.815307 | ||||||||
\(900\) | −25.1521 | −0.838402 | ||||||||
\(901\) | −6.02987 | −0.200884 | ||||||||
\(902\) | 4.08730 | 0.136092 | ||||||||
\(903\) | −0.454828 | −0.0151357 | ||||||||
\(904\) | 85.3683 | 2.83931 | ||||||||
\(905\) | −2.07249 | −0.0688920 | ||||||||
\(906\) | 19.6652 | 0.653332 | ||||||||
\(907\) | 21.5831 | 0.716655 | 0.358327 | − | 0.933596i | \(-0.383347\pi\) | ||||
0.358327 | + | 0.933596i | \(0.383347\pi\) | |||||||
\(908\) | −83.7021 | −2.77775 | ||||||||
\(909\) | −0.153953 | −0.00510630 | ||||||||
\(910\) | 0.0206652 | 0.000685043 0 | ||||||||
\(911\) | 32.1087 | 1.06381 | 0.531904 | − | 0.846805i | \(-0.321477\pi\) | ||||
0.531904 | + | 0.846805i | \(0.321477\pi\) | |||||||
\(912\) | 27.4802 | 0.909962 | ||||||||
\(913\) | −1.18681 | −0.0392776 | ||||||||
\(914\) | 61.0185 | 2.01831 | ||||||||
\(915\) | −1.41504 | −0.0467799 | ||||||||
\(916\) | 118.294 | 3.90853 | ||||||||
\(917\) | −0.686371 | −0.0226660 | ||||||||
\(918\) | 9.74900 | 0.321765 | ||||||||
\(919\) | −34.2000 | −1.12815 | −0.564077 | − | 0.825722i | \(-0.690768\pi\) | ||||
−0.564077 | + | 0.825722i | \(0.690768\pi\) | |||||||
\(920\) | 3.57361 | 0.117818 | ||||||||
\(921\) | −1.74509 | −0.0575025 | ||||||||
\(922\) | −59.1869 | −1.94922 | ||||||||
\(923\) | −9.09468 | −0.299355 | ||||||||
\(924\) | −0.0486176 | −0.00159940 | ||||||||
\(925\) | 34.9751 | 1.14997 | ||||||||
\(926\) | −11.9977 | −0.394267 | ||||||||
\(927\) | −14.7525 | −0.484534 | ||||||||
\(928\) | 77.6118 | 2.54773 | ||||||||
\(929\) | 29.2758 | 0.960508 | 0.480254 | − | 0.877129i | \(-0.340544\pi\) | ||||
0.480254 | + | 0.877129i | \(0.340544\pi\) | |||||||
\(930\) | −1.42646 | −0.0467756 | ||||||||
\(931\) | 16.9166 | 0.554420 | ||||||||
\(932\) | 129.494 | 4.24172 | ||||||||
\(933\) | −16.3942 | −0.536723 | ||||||||
\(934\) | −9.13123 | −0.298783 | ||||||||
\(935\) | 0.0715874 | 0.00234116 | ||||||||
\(936\) | −8.57050 | −0.280136 | ||||||||
\(937\) | 28.7035 | 0.937704 | 0.468852 | − | 0.883277i | \(-0.344668\pi\) | ||||
0.468852 | + | 0.883277i | \(0.344668\pi\) | |||||||
\(938\) | −2.22964 | −0.0728003 | ||||||||
\(939\) | 3.25949 | 0.106369 | ||||||||
\(940\) | −0.154120 | −0.00502683 | ||||||||
\(941\) | −3.41244 | −0.111242 | −0.0556211 | − | 0.998452i | \(-0.517714\pi\) | ||||
−0.0556211 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(942\) | −21.5845 | −0.703260 | ||||||||
\(943\) | −34.9272 | −1.13739 | ||||||||
\(944\) | −42.2592 | −1.37542 | ||||||||
\(945\) | 0.00734305 | 0.000238870 0 | ||||||||
\(946\) | 3.20445 | 0.104186 | ||||||||
\(947\) | 15.1032 | 0.490789 | 0.245395 | − | 0.969423i | \(-0.421082\pi\) | ||||
0.245395 | + | 0.969423i | \(0.421082\pi\) | |||||||
\(948\) | −38.7128 | −1.25733 | ||||||||
\(949\) | 11.7629 | 0.381840 | ||||||||
\(950\) | 31.9943 | 1.03803 | ||||||||
\(951\) | 3.81807 | 0.123809 | ||||||||
\(952\) | 1.78886 | 0.0579773 | ||||||||
\(953\) | −32.9900 | −1.06865 | −0.534326 | − | 0.845279i | \(-0.679434\pi\) | ||||
−0.534326 | + | 0.845279i | \(0.679434\pi\) | |||||||
\(954\) | 4.35766 | 0.141085 | ||||||||
\(955\) | 1.21963 | 0.0394661 | ||||||||
\(956\) | −96.5306 | −3.12202 | ||||||||
\(957\) | 0.886590 | 0.0286594 | ||||||||
\(958\) | −43.6905 | −1.41158 | ||||||||
\(959\) | −1.23978 | −0.0400347 | ||||||||
\(960\) | −1.75863 | −0.0567596 | ||||||||
\(961\) | −11.5550 | −0.372742 | ||||||||
\(962\) | 19.7444 | 0.636584 | ||||||||
\(963\) | 9.26460 | 0.298548 | ||||||||
\(964\) | 95.3442 | 3.07083 | ||||||||
\(965\) | −2.34722 | −0.0755597 | ||||||||
\(966\) | 0.580137 | 0.0186656 | ||||||||
\(967\) | −31.9734 | −1.02819 | −0.514097 | − | 0.857732i | \(-0.671873\pi\) | ||||
−0.514097 | + | 0.857732i | \(0.671873\pi\) | |||||||
\(968\) | −88.7113 | −2.85129 | ||||||||
\(969\) | −8.88072 | −0.285290 | ||||||||
\(970\) | −0.315106 | −0.0101174 | ||||||||
\(971\) | 9.23119 | 0.296243 | 0.148122 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148122 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(972\) | −5.04540 | −0.161831 | ||||||||
\(973\) | −0.895243 | −0.0287002 | ||||||||
\(974\) | 74.5297 | 2.38809 | ||||||||
\(975\) | −5.28551 | −0.169272 | ||||||||
\(976\) | 131.961 | 4.22396 | ||||||||
\(977\) | 9.34029 | 0.298822 | 0.149411 | − | 0.988775i | \(-0.452262\pi\) | ||||
0.149411 | + | 0.988775i | \(0.452262\pi\) | |||||||
\(978\) | 5.29395 | 0.169282 | ||||||||
\(979\) | −1.91820 | −0.0613059 | ||||||||
\(980\) | −4.30202 | −0.137423 | ||||||||
\(981\) | −0.135190 | −0.00431630 | ||||||||
\(982\) | 13.3453 | 0.425865 | ||||||||
\(983\) | 22.9545 | 0.732135 | 0.366068 | − | 0.930588i | \(-0.380704\pi\) | ||||
0.366068 | + | 0.930588i | \(0.380704\pi\) | |||||||
\(984\) | 77.8315 | 2.48118 | ||||||||
\(985\) | 0.957282 | 0.0305015 | ||||||||
\(986\) | −54.0452 | −1.72115 | ||||||||
\(987\) | −0.0151019 | −0.000480698 0 | ||||||||
\(988\) | 12.9344 | 0.411498 | ||||||||
\(989\) | −27.3830 | −0.870727 | ||||||||
\(990\) | −0.0517347 | −0.00164424 | ||||||||
\(991\) | 7.38759 | 0.234674 | 0.117337 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117337 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(992\) | 61.7354 | 1.96010 | ||||||||
\(993\) | −13.9352 | −0.442221 | ||||||||
\(994\) | −1.37184 | −0.0435121 | ||||||||
\(995\) | 2.04054 | 0.0646895 | ||||||||
\(996\) | −37.4413 | −1.18637 | ||||||||
\(997\) | −21.8910 | −0.693296 | −0.346648 | − | 0.937995i | \(-0.612680\pi\) | ||||
−0.346648 | + | 0.937995i | \(0.612680\pi\) | |||||||
\(998\) | 61.6137 | 1.95035 | ||||||||
\(999\) | 7.01586 | 0.221972 |
(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 | 381.2.a.d.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 1143.2.a.g.1.1 | 5 | |||
4.3 | odd | 2 | 6096.2.a.bf.1.3 | 5 | |||
5.4 | even | 2 | 9525.2.a.j.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
381.2.a.d.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1143.2.a.g.1.1 | 5 | 3.2 | odd | 2 | |||
6096.2.a.bf.1.3 | 5 | 4.3 | odd | 2 | |||
9525.2.a.j.1.1 | 5 | 5.4 | even | 2 |