Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + 5778 x^{8} - 5124 x^{7} - 9405 x^{6} + 8288 x^{5} + 6405 x^{4} - 6032 x^{3} + \cdots - 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-2.00482\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00482 | 1.41762 | 0.708812 | − | 0.705397i | \(-0.249231\pi\) | ||||
0.708812 | + | 0.705397i | \(0.249231\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.01932 | 1.00966 | ||||||||
\(5\) | 3.94433 | 1.76396 | 0.881978 | − | 0.471290i | \(-0.156212\pi\) | ||||
0.881978 | + | 0.471290i | \(0.156212\pi\) | |||||||
\(6\) | 2.00482 | 0.818466 | ||||||||
\(7\) | −2.43681 | −0.921026 | −0.460513 | − | 0.887653i | \(-0.652335\pi\) | ||||
−0.460513 | + | 0.887653i | \(0.652335\pi\) | |||||||
\(8\) | 0.0387322 | 0.0136939 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.90768 | 2.50063 | ||||||||
\(11\) | 5.06353 | 1.52671 | 0.763356 | − | 0.645977i | \(-0.223550\pi\) | ||||
0.763356 | + | 0.645977i | \(0.223550\pi\) | |||||||
\(12\) | 2.01932 | 0.582927 | ||||||||
\(13\) | 0.849677 | 0.235658 | 0.117829 | − | 0.993034i | \(-0.462407\pi\) | ||||
0.117829 | + | 0.993034i | \(0.462407\pi\) | |||||||
\(14\) | −4.88537 | −1.30567 | ||||||||
\(15\) | 3.94433 | 1.01842 | ||||||||
\(16\) | −3.96099 | −0.990247 | ||||||||
\(17\) | −3.54469 | −0.859713 | −0.429857 | − | 0.902897i | \(-0.641436\pi\) | ||||
−0.429857 | + | 0.902897i | \(0.641436\pi\) | |||||||
\(18\) | 2.00482 | 0.472542 | ||||||||
\(19\) | 2.59053 | 0.594309 | 0.297155 | − | 0.954829i | \(-0.403962\pi\) | ||||
0.297155 | + | 0.954829i | \(0.403962\pi\) | |||||||
\(20\) | 7.96485 | 1.78100 | ||||||||
\(21\) | −2.43681 | −0.531755 | ||||||||
\(22\) | 10.1515 | 2.16431 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.0387322 | 0.00790619 | ||||||||
\(25\) | 10.5577 | 2.11154 | ||||||||
\(26\) | 1.70345 | 0.334075 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.92069 | −0.929923 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 7.90768 | 1.44374 | ||||||||
\(31\) | −0.555799 | −0.0998244 | −0.0499122 | − | 0.998754i | \(-0.515894\pi\) | ||||
−0.0499122 | + | 0.998754i | \(0.515894\pi\) | |||||||
\(32\) | −8.01855 | −1.41749 | ||||||||
\(33\) | 5.06353 | 0.881448 | ||||||||
\(34\) | −7.10648 | −1.21875 | ||||||||
\(35\) | −9.61156 | −1.62465 | ||||||||
\(36\) | 2.01932 | 0.336553 | ||||||||
\(37\) | −2.47840 | −0.407446 | −0.203723 | − | 0.979029i | \(-0.565304\pi\) | ||||
−0.203723 | + | 0.979029i | \(0.565304\pi\) | |||||||
\(38\) | 5.19356 | 0.842507 | ||||||||
\(39\) | 0.849677 | 0.136057 | ||||||||
\(40\) | 0.152773 | 0.0241555 | ||||||||
\(41\) | 2.45770 | 0.383829 | 0.191914 | − | 0.981412i | \(-0.438530\pi\) | ||||
0.191914 | + | 0.981412i | \(0.438530\pi\) | |||||||
\(42\) | −4.88537 | −0.753828 | ||||||||
\(43\) | −7.48299 | −1.14114 | −0.570572 | − | 0.821247i | \(-0.693279\pi\) | ||||
−0.570572 | + | 0.821247i | \(0.693279\pi\) | |||||||
\(44\) | 10.2249 | 1.54146 | ||||||||
\(45\) | 3.94433 | 0.587985 | ||||||||
\(46\) | −2.00482 | −0.295595 | ||||||||
\(47\) | 4.02053 | 0.586454 | 0.293227 | − | 0.956043i | \(-0.405271\pi\) | ||||
0.293227 | + | 0.956043i | \(0.405271\pi\) | |||||||
\(48\) | −3.96099 | −0.571719 | ||||||||
\(49\) | −1.06198 | −0.151711 | ||||||||
\(50\) | 21.1663 | 2.99337 | ||||||||
\(51\) | −3.54469 | −0.496356 | ||||||||
\(52\) | 1.71577 | 0.237934 | ||||||||
\(53\) | 3.73104 | 0.512498 | 0.256249 | − | 0.966611i | \(-0.417513\pi\) | ||||
0.256249 | + | 0.966611i | \(0.417513\pi\) | |||||||
\(54\) | 2.00482 | 0.272822 | ||||||||
\(55\) | 19.9722 | 2.69305 | ||||||||
\(56\) | −0.0943829 | −0.0126125 | ||||||||
\(57\) | 2.59053 | 0.343125 | ||||||||
\(58\) | −2.00482 | −0.263246 | ||||||||
\(59\) | 9.66773 | 1.25863 | 0.629316 | − | 0.777150i | \(-0.283335\pi\) | ||||
0.629316 | + | 0.777150i | \(0.283335\pi\) | |||||||
\(60\) | 7.96485 | 1.02826 | ||||||||
\(61\) | −6.98014 | −0.893716 | −0.446858 | − | 0.894605i | \(-0.647457\pi\) | ||||
−0.446858 | + | 0.894605i | \(0.647457\pi\) | |||||||
\(62\) | −1.11428 | −0.141514 | ||||||||
\(63\) | −2.43681 | −0.307009 | ||||||||
\(64\) | −8.15380 | −1.01923 | ||||||||
\(65\) | 3.35140 | 0.415691 | ||||||||
\(66\) | 10.1515 | 1.24956 | ||||||||
\(67\) | −13.0703 | −1.59679 | −0.798394 | − | 0.602135i | \(-0.794317\pi\) | ||||
−0.798394 | + | 0.602135i | \(0.794317\pi\) | |||||||
\(68\) | −7.15786 | −0.868018 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −19.2695 | −2.30314 | ||||||||
\(71\) | 6.82458 | 0.809929 | 0.404964 | − | 0.914332i | \(-0.367284\pi\) | ||||
0.404964 | + | 0.914332i | \(0.367284\pi\) | |||||||
\(72\) | 0.0387322 | 0.00456464 | ||||||||
\(73\) | −15.2749 | −1.78779 | −0.893894 | − | 0.448279i | \(-0.852037\pi\) | ||||
−0.893894 | + | 0.448279i | \(0.852037\pi\) | |||||||
\(74\) | −4.96875 | −0.577606 | ||||||||
\(75\) | 10.5577 | 1.21910 | ||||||||
\(76\) | 5.23112 | 0.600050 | ||||||||
\(77\) | −12.3388 | −1.40614 | ||||||||
\(78\) | 1.70345 | 0.192878 | ||||||||
\(79\) | 8.57302 | 0.964541 | 0.482270 | − | 0.876022i | \(-0.339812\pi\) | ||||
0.482270 | + | 0.876022i | \(0.339812\pi\) | |||||||
\(80\) | −15.6234 | −1.74675 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.92726 | 0.544125 | ||||||||
\(83\) | 8.09331 | 0.888356 | 0.444178 | − | 0.895939i | \(-0.353496\pi\) | ||||
0.444178 | + | 0.895939i | \(0.353496\pi\) | |||||||
\(84\) | −4.92069 | −0.536891 | ||||||||
\(85\) | −13.9814 | −1.51650 | ||||||||
\(86\) | −15.0021 | −1.61771 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0.196122 | 0.0209067 | ||||||||
\(89\) | 3.09574 | 0.328147 | 0.164074 | − | 0.986448i | \(-0.447537\pi\) | ||||
0.164074 | + | 0.986448i | \(0.447537\pi\) | |||||||
\(90\) | 7.90768 | 0.833543 | ||||||||
\(91\) | −2.07050 | −0.217047 | ||||||||
\(92\) | −2.01932 | −0.210529 | ||||||||
\(93\) | −0.555799 | −0.0576336 | ||||||||
\(94\) | 8.06045 | 0.831372 | ||||||||
\(95\) | 10.2179 | 1.04834 | ||||||||
\(96\) | −8.01855 | −0.818390 | ||||||||
\(97\) | 0.381632 | 0.0387488 | 0.0193744 | − | 0.999812i | \(-0.493833\pi\) | ||||
0.0193744 | + | 0.999812i | \(0.493833\pi\) | |||||||
\(98\) | −2.12908 | −0.215070 | ||||||||
\(99\) | 5.06353 | 0.508904 | ||||||||
\(100\) | 21.3194 | 2.13194 | ||||||||
\(101\) | −7.72348 | −0.768514 | −0.384257 | − | 0.923226i | \(-0.625542\pi\) | ||||
−0.384257 | + | 0.923226i | \(0.625542\pi\) | |||||||
\(102\) | −7.10648 | −0.703646 | ||||||||
\(103\) | −12.1128 | −1.19351 | −0.596756 | − | 0.802423i | \(-0.703544\pi\) | ||||
−0.596756 | + | 0.802423i | \(0.703544\pi\) | |||||||
\(104\) | 0.0329099 | 0.00322708 | ||||||||
\(105\) | −9.61156 | −0.937992 | ||||||||
\(106\) | 7.48008 | 0.726529 | ||||||||
\(107\) | −12.7158 | −1.22928 | −0.614640 | − | 0.788808i | \(-0.710699\pi\) | ||||
−0.614640 | + | 0.788808i | \(0.710699\pi\) | |||||||
\(108\) | 2.01932 | 0.194309 | ||||||||
\(109\) | −4.06457 | −0.389315 | −0.194657 | − | 0.980871i | \(-0.562360\pi\) | ||||
−0.194657 | + | 0.980871i | \(0.562360\pi\) | |||||||
\(110\) | 40.0408 | 3.81774 | ||||||||
\(111\) | −2.47840 | −0.235239 | ||||||||
\(112\) | 9.65216 | 0.912043 | ||||||||
\(113\) | 10.3389 | 0.972601 | 0.486301 | − | 0.873792i | \(-0.338346\pi\) | ||||
0.486301 | + | 0.873792i | \(0.338346\pi\) | |||||||
\(114\) | 5.19356 | 0.486422 | ||||||||
\(115\) | −3.94433 | −0.367810 | ||||||||
\(116\) | −2.01932 | −0.187489 | ||||||||
\(117\) | 0.849677 | 0.0785527 | ||||||||
\(118\) | 19.3821 | 1.78427 | ||||||||
\(119\) | 8.63772 | 0.791818 | ||||||||
\(120\) | 0.152773 | 0.0139462 | ||||||||
\(121\) | 14.6394 | 1.33085 | ||||||||
\(122\) | −13.9940 | −1.26695 | ||||||||
\(123\) | 2.45770 | 0.221604 | ||||||||
\(124\) | −1.12234 | −0.100789 | ||||||||
\(125\) | 21.9214 | 1.96071 | ||||||||
\(126\) | −4.88537 | −0.435223 | ||||||||
\(127\) | 4.63744 | 0.411507 | 0.205753 | − | 0.978604i | \(-0.434036\pi\) | ||||
0.205753 | + | 0.978604i | \(0.434036\pi\) | |||||||
\(128\) | −0.309843 | −0.0273866 | ||||||||
\(129\) | −7.48299 | −0.658840 | ||||||||
\(130\) | 6.71898 | 0.589293 | ||||||||
\(131\) | −11.3178 | −0.988838 | −0.494419 | − | 0.869224i | \(-0.664619\pi\) | ||||
−0.494419 | + | 0.869224i | \(0.664619\pi\) | |||||||
\(132\) | 10.2249 | 0.889963 | ||||||||
\(133\) | −6.31263 | −0.547374 | ||||||||
\(134\) | −26.2036 | −2.26365 | ||||||||
\(135\) | 3.94433 | 0.339474 | ||||||||
\(136\) | −0.137294 | −0.0117728 | ||||||||
\(137\) | 8.44177 | 0.721229 | 0.360614 | − | 0.932715i | \(-0.382567\pi\) | ||||
0.360614 | + | 0.932715i | \(0.382567\pi\) | |||||||
\(138\) | −2.00482 | −0.170662 | ||||||||
\(139\) | 0.788881 | 0.0669120 | 0.0334560 | − | 0.999440i | \(-0.489349\pi\) | ||||
0.0334560 | + | 0.999440i | \(0.489349\pi\) | |||||||
\(140\) | −19.4088 | −1.64034 | ||||||||
\(141\) | 4.02053 | 0.338590 | ||||||||
\(142\) | 13.6821 | 1.14817 | ||||||||
\(143\) | 4.30237 | 0.359782 | ||||||||
\(144\) | −3.96099 | −0.330082 | ||||||||
\(145\) | −3.94433 | −0.327558 | ||||||||
\(146\) | −30.6234 | −2.53441 | ||||||||
\(147\) | −1.06198 | −0.0875905 | ||||||||
\(148\) | −5.00468 | −0.411382 | ||||||||
\(149\) | −7.78451 | −0.637732 | −0.318866 | − | 0.947800i | \(-0.603302\pi\) | ||||
−0.318866 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(150\) | 21.1663 | 1.72822 | ||||||||
\(151\) | −19.2856 | −1.56944 | −0.784719 | − | 0.619851i | \(-0.787193\pi\) | ||||
−0.784719 | + | 0.619851i | \(0.787193\pi\) | |||||||
\(152\) | 0.100337 | 0.00813842 | ||||||||
\(153\) | −3.54469 | −0.286571 | ||||||||
\(154\) | −24.7372 | −1.99338 | ||||||||
\(155\) | −2.19225 | −0.176086 | ||||||||
\(156\) | 1.71577 | 0.137372 | ||||||||
\(157\) | −11.9533 | −0.953979 | −0.476989 | − | 0.878909i | \(-0.658272\pi\) | ||||
−0.476989 | + | 0.878909i | \(0.658272\pi\) | |||||||
\(158\) | 17.1874 | 1.36736 | ||||||||
\(159\) | 3.73104 | 0.295891 | ||||||||
\(160\) | −31.6278 | −2.50039 | ||||||||
\(161\) | 2.43681 | 0.192047 | ||||||||
\(162\) | 2.00482 | 0.157514 | ||||||||
\(163\) | 13.9184 | 1.09018 | 0.545088 | − | 0.838379i | \(-0.316496\pi\) | ||||
0.545088 | + | 0.838379i | \(0.316496\pi\) | |||||||
\(164\) | 4.96289 | 0.387536 | ||||||||
\(165\) | 19.9722 | 1.55484 | ||||||||
\(166\) | 16.2257 | 1.25936 | ||||||||
\(167\) | 11.6350 | 0.900343 | 0.450171 | − | 0.892942i | \(-0.351363\pi\) | ||||
0.450171 | + | 0.892942i | \(0.351363\pi\) | |||||||
\(168\) | −0.0943829 | −0.00728180 | ||||||||
\(169\) | −12.2780 | −0.944465 | ||||||||
\(170\) | −28.0303 | −2.14982 | ||||||||
\(171\) | 2.59053 | 0.198103 | ||||||||
\(172\) | −15.1105 | −1.15217 | ||||||||
\(173\) | −15.0093 | −1.14114 | −0.570569 | − | 0.821250i | \(-0.693277\pi\) | ||||
−0.570569 | + | 0.821250i | \(0.693277\pi\) | |||||||
\(174\) | −2.00482 | −0.151985 | ||||||||
\(175\) | −25.7271 | −1.94478 | ||||||||
\(176\) | −20.0566 | −1.51182 | ||||||||
\(177\) | 9.66773 | 0.726671 | ||||||||
\(178\) | 6.20641 | 0.465190 | ||||||||
\(179\) | 0.558696 | 0.0417589 | 0.0208794 | − | 0.999782i | \(-0.493353\pi\) | ||||
0.0208794 | + | 0.999782i | \(0.493353\pi\) | |||||||
\(180\) | 7.96485 | 0.593665 | ||||||||
\(181\) | 13.6021 | 1.01104 | 0.505518 | − | 0.862816i | \(-0.331301\pi\) | ||||
0.505518 | + | 0.862816i | \(0.331301\pi\) | |||||||
\(182\) | −4.15098 | −0.307691 | ||||||||
\(183\) | −6.98014 | −0.515987 | ||||||||
\(184\) | −0.0387322 | −0.00285538 | ||||||||
\(185\) | −9.77562 | −0.718718 | ||||||||
\(186\) | −1.11428 | −0.0817029 | ||||||||
\(187\) | −17.9486 | −1.31254 | ||||||||
\(188\) | 8.11873 | 0.592119 | ||||||||
\(189\) | −2.43681 | −0.177252 | ||||||||
\(190\) | 20.4851 | 1.48615 | ||||||||
\(191\) | 18.5494 | 1.34219 | 0.671093 | − | 0.741373i | \(-0.265825\pi\) | ||||
0.671093 | + | 0.741373i | \(0.265825\pi\) | |||||||
\(192\) | −8.15380 | −0.588450 | ||||||||
\(193\) | 2.30044 | 0.165589 | 0.0827947 | − | 0.996567i | \(-0.473615\pi\) | ||||
0.0827947 | + | 0.996567i | \(0.473615\pi\) | |||||||
\(194\) | 0.765104 | 0.0549313 | ||||||||
\(195\) | 3.35140 | 0.239999 | ||||||||
\(196\) | −2.14447 | −0.153177 | ||||||||
\(197\) | −23.7251 | −1.69035 | −0.845173 | − | 0.534492i | \(-0.820503\pi\) | ||||
−0.845173 | + | 0.534492i | \(0.820503\pi\) | |||||||
\(198\) | 10.1515 | 0.721435 | ||||||||
\(199\) | 10.1146 | 0.717005 | 0.358503 | − | 0.933529i | \(-0.383287\pi\) | ||||
0.358503 | + | 0.933529i | \(0.383287\pi\) | |||||||
\(200\) | 0.408924 | 0.0289153 | ||||||||
\(201\) | −13.0703 | −0.921906 | ||||||||
\(202\) | −15.4842 | −1.08947 | ||||||||
\(203\) | 2.43681 | 0.171030 | ||||||||
\(204\) | −7.15786 | −0.501150 | ||||||||
\(205\) | 9.69398 | 0.677057 | ||||||||
\(206\) | −24.2841 | −1.69195 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −3.36556 | −0.233360 | ||||||||
\(209\) | 13.1173 | 0.907340 | ||||||||
\(210\) | −19.2695 | −1.32972 | ||||||||
\(211\) | −21.6952 | −1.49356 | −0.746778 | − | 0.665073i | \(-0.768400\pi\) | ||||
−0.746778 | + | 0.665073i | \(0.768400\pi\) | |||||||
\(212\) | 7.53416 | 0.517448 | ||||||||
\(213\) | 6.82458 | 0.467613 | ||||||||
\(214\) | −25.4929 | −1.74266 | ||||||||
\(215\) | −29.5153 | −2.01293 | ||||||||
\(216\) | 0.0387322 | 0.00263540 | ||||||||
\(217\) | 1.35437 | 0.0919409 | ||||||||
\(218\) | −8.14874 | −0.551902 | ||||||||
\(219\) | −15.2749 | −1.03218 | ||||||||
\(220\) | 40.3303 | 2.71907 | ||||||||
\(221\) | −3.01184 | −0.202598 | ||||||||
\(222\) | −4.96875 | −0.333481 | ||||||||
\(223\) | −9.48165 | −0.634938 | −0.317469 | − | 0.948269i | \(-0.602833\pi\) | ||||
−0.317469 | + | 0.948269i | \(0.602833\pi\) | |||||||
\(224\) | 19.5396 | 1.30555 | ||||||||
\(225\) | 10.5577 | 0.703847 | ||||||||
\(226\) | 20.7277 | 1.37878 | ||||||||
\(227\) | 19.8447 | 1.31714 | 0.658568 | − | 0.752521i | \(-0.271162\pi\) | ||||
0.658568 | + | 0.752521i | \(0.271162\pi\) | |||||||
\(228\) | 5.23112 | 0.346439 | ||||||||
\(229\) | 19.1534 | 1.26569 | 0.632847 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632847 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(230\) | −7.90768 | −0.521417 | ||||||||
\(231\) | −12.3388 | −0.811837 | ||||||||
\(232\) | −0.0387322 | −0.00254290 | ||||||||
\(233\) | 0.846581 | 0.0554613 | 0.0277307 | − | 0.999615i | \(-0.491172\pi\) | ||||
0.0277307 | + | 0.999615i | \(0.491172\pi\) | |||||||
\(234\) | 1.70345 | 0.111358 | ||||||||
\(235\) | 15.8583 | 1.03448 | ||||||||
\(236\) | 19.5222 | 1.27079 | ||||||||
\(237\) | 8.57302 | 0.556878 | ||||||||
\(238\) | 17.3171 | 1.12250 | ||||||||
\(239\) | −0.968657 | −0.0626572 | −0.0313286 | − | 0.999509i | \(-0.509974\pi\) | ||||
−0.0313286 | + | 0.999509i | \(0.509974\pi\) | |||||||
\(240\) | −15.6234 | −1.00849 | ||||||||
\(241\) | −1.03734 | −0.0668212 | −0.0334106 | − | 0.999442i | \(-0.510637\pi\) | ||||
−0.0334106 | + | 0.999442i | \(0.510637\pi\) | |||||||
\(242\) | 29.3494 | 1.88665 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.0951 | −0.902349 | ||||||||
\(245\) | −4.18879 | −0.267612 | ||||||||
\(246\) | 4.92726 | 0.314151 | ||||||||
\(247\) | 2.20112 | 0.140054 | ||||||||
\(248\) | −0.0215273 | −0.00136699 | ||||||||
\(249\) | 8.09331 | 0.512892 | ||||||||
\(250\) | 43.9486 | 2.77955 | ||||||||
\(251\) | −27.7696 | −1.75280 | −0.876399 | − | 0.481585i | \(-0.840061\pi\) | ||||
−0.876399 | + | 0.481585i | \(0.840061\pi\) | |||||||
\(252\) | −4.92069 | −0.309974 | ||||||||
\(253\) | −5.06353 | −0.318342 | ||||||||
\(254\) | 9.29726 | 0.583362 | ||||||||
\(255\) | −13.9814 | −0.875550 | ||||||||
\(256\) | 15.6864 | 0.980401 | ||||||||
\(257\) | −15.0573 | −0.939251 | −0.469625 | − | 0.882866i | \(-0.655611\pi\) | ||||
−0.469625 | + | 0.882866i | \(0.655611\pi\) | |||||||
\(258\) | −15.0021 | −0.933988 | ||||||||
\(259\) | 6.03938 | 0.375269 | ||||||||
\(260\) | 6.76756 | 0.419706 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −22.6901 | −1.40180 | ||||||||
\(263\) | 16.2360 | 1.00115 | 0.500577 | − | 0.865692i | \(-0.333121\pi\) | ||||
0.500577 | + | 0.865692i | \(0.333121\pi\) | |||||||
\(264\) | 0.196122 | 0.0120705 | ||||||||
\(265\) | 14.7164 | 0.904023 | ||||||||
\(266\) | −12.6557 | −0.775971 | ||||||||
\(267\) | 3.09574 | 0.189456 | ||||||||
\(268\) | −26.3931 | −1.61221 | ||||||||
\(269\) | 19.5471 | 1.19180 | 0.595902 | − | 0.803057i | \(-0.296795\pi\) | ||||
0.595902 | + | 0.803057i | \(0.296795\pi\) | |||||||
\(270\) | 7.90768 | 0.481246 | ||||||||
\(271\) | 16.0743 | 0.976444 | 0.488222 | − | 0.872719i | \(-0.337646\pi\) | ||||
0.488222 | + | 0.872719i | \(0.337646\pi\) | |||||||
\(272\) | 14.0405 | 0.851328 | ||||||||
\(273\) | −2.07050 | −0.125312 | ||||||||
\(274\) | 16.9243 | 1.02243 | ||||||||
\(275\) | 53.4593 | 3.22372 | ||||||||
\(276\) | −2.01932 | −0.121549 | ||||||||
\(277\) | 11.5689 | 0.695105 | 0.347553 | − | 0.937660i | \(-0.387013\pi\) | ||||
0.347553 | + | 0.937660i | \(0.387013\pi\) | |||||||
\(278\) | 1.58157 | 0.0948561 | ||||||||
\(279\) | −0.555799 | −0.0332748 | ||||||||
\(280\) | −0.372277 | −0.0222478 | ||||||||
\(281\) | 1.08577 | 0.0647716 | 0.0323858 | − | 0.999475i | \(-0.489689\pi\) | ||||
0.0323858 | + | 0.999475i | \(0.489689\pi\) | |||||||
\(282\) | 8.06045 | 0.479993 | ||||||||
\(283\) | 10.9798 | 0.652680 | 0.326340 | − | 0.945252i | \(-0.394185\pi\) | ||||
0.326340 | + | 0.945252i | \(0.394185\pi\) | |||||||
\(284\) | 13.7810 | 0.817752 | ||||||||
\(285\) | 10.2179 | 0.605257 | ||||||||
\(286\) | 8.62549 | 0.510036 | ||||||||
\(287\) | −5.98894 | −0.353516 | ||||||||
\(288\) | −8.01855 | −0.472497 | ||||||||
\(289\) | −4.43519 | −0.260893 | ||||||||
\(290\) | −7.90768 | −0.464355 | ||||||||
\(291\) | 0.381632 | 0.0223716 | ||||||||
\(292\) | −30.8448 | −1.80506 | ||||||||
\(293\) | 3.35385 | 0.195934 | 0.0979670 | − | 0.995190i | \(-0.468766\pi\) | ||||
0.0979670 | + | 0.995190i | \(0.468766\pi\) | |||||||
\(294\) | −2.12908 | −0.124170 | ||||||||
\(295\) | 38.1327 | 2.22017 | ||||||||
\(296\) | −0.0959940 | −0.00557954 | ||||||||
\(297\) | 5.06353 | 0.293816 | ||||||||
\(298\) | −15.6066 | −0.904064 | ||||||||
\(299\) | −0.849677 | −0.0491381 | ||||||||
\(300\) | 21.3194 | 1.23088 | ||||||||
\(301\) | 18.2346 | 1.05102 | ||||||||
\(302\) | −38.6642 | −2.22488 | ||||||||
\(303\) | −7.72348 | −0.443702 | ||||||||
\(304\) | −10.2611 | −0.588513 | ||||||||
\(305\) | −27.5320 | −1.57648 | ||||||||
\(306\) | −7.10648 | −0.406250 | ||||||||
\(307\) | 11.0025 | 0.627945 | 0.313972 | − | 0.949432i | \(-0.398340\pi\) | ||||
0.313972 | + | 0.949432i | \(0.398340\pi\) | |||||||
\(308\) | −24.9161 | −1.41973 | ||||||||
\(309\) | −12.1128 | −0.689074 | ||||||||
\(310\) | −4.39508 | −0.249624 | ||||||||
\(311\) | 32.0112 | 1.81519 | 0.907594 | − | 0.419849i | \(-0.137917\pi\) | ||||
0.907594 | + | 0.419849i | \(0.137917\pi\) | |||||||
\(312\) | 0.0329099 | 0.00186316 | ||||||||
\(313\) | −13.3302 | −0.753467 | −0.376734 | − | 0.926322i | \(-0.622953\pi\) | ||||
−0.376734 | + | 0.926322i | \(0.622953\pi\) | |||||||
\(314\) | −23.9643 | −1.35238 | ||||||||
\(315\) | −9.61156 | −0.541550 | ||||||||
\(316\) | 17.3117 | 0.973858 | ||||||||
\(317\) | −2.22126 | −0.124758 | −0.0623792 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623792 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(318\) | 7.48008 | 0.419462 | ||||||||
\(319\) | −5.06353 | −0.283503 | ||||||||
\(320\) | −32.1613 | −1.79787 | ||||||||
\(321\) | −12.7158 | −0.709725 | ||||||||
\(322\) | 4.88537 | 0.272251 | ||||||||
\(323\) | −9.18263 | −0.510935 | ||||||||
\(324\) | 2.01932 | 0.112184 | ||||||||
\(325\) | 8.97064 | 0.497602 | ||||||||
\(326\) | 27.9040 | 1.54546 | ||||||||
\(327\) | −4.06457 | −0.224771 | ||||||||
\(328\) | 0.0951923 | 0.00525611 | ||||||||
\(329\) | −9.79725 | −0.540140 | ||||||||
\(330\) | 40.0408 | 2.20417 | ||||||||
\(331\) | −6.00619 | −0.330130 | −0.165065 | − | 0.986283i | \(-0.552783\pi\) | ||||
−0.165065 | + | 0.986283i | \(0.552783\pi\) | |||||||
\(332\) | 16.3430 | 0.896937 | ||||||||
\(333\) | −2.47840 | −0.135815 | ||||||||
\(334\) | 23.3261 | 1.27635 | ||||||||
\(335\) | −51.5534 | −2.81666 | ||||||||
\(336\) | 9.65216 | 0.526568 | ||||||||
\(337\) | 2.98109 | 0.162390 | 0.0811952 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811952 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(338\) | −24.6153 | −1.33890 | ||||||||
\(339\) | 10.3389 | 0.561532 | ||||||||
\(340\) | −28.2329 | −1.53115 | ||||||||
\(341\) | −2.81431 | −0.152403 | ||||||||
\(342\) | 5.19356 | 0.280836 | ||||||||
\(343\) | 19.6455 | 1.06076 | ||||||||
\(344\) | −0.289833 | −0.0156267 | ||||||||
\(345\) | −3.94433 | −0.212355 | ||||||||
\(346\) | −30.0911 | −1.61771 | ||||||||
\(347\) | −32.2077 | −1.72900 | −0.864499 | − | 0.502634i | \(-0.832364\pi\) | ||||
−0.864499 | + | 0.502634i | \(0.832364\pi\) | |||||||
\(348\) | −2.01932 | −0.108247 | ||||||||
\(349\) | 26.3675 | 1.41142 | 0.705711 | − | 0.708500i | \(-0.250628\pi\) | ||||
0.705711 | + | 0.708500i | \(0.250628\pi\) | |||||||
\(350\) | −51.5783 | −2.75697 | ||||||||
\(351\) | 0.849677 | 0.0453524 | ||||||||
\(352\) | −40.6022 | −2.16410 | ||||||||
\(353\) | −28.3671 | −1.50983 | −0.754914 | − | 0.655824i | \(-0.772321\pi\) | ||||
−0.754914 | + | 0.655824i | \(0.772321\pi\) | |||||||
\(354\) | 19.3821 | 1.03015 | ||||||||
\(355\) | 26.9184 | 1.42868 | ||||||||
\(356\) | 6.25128 | 0.331317 | ||||||||
\(357\) | 8.63772 | 0.457156 | ||||||||
\(358\) | 1.12009 | 0.0591984 | ||||||||
\(359\) | 33.8035 | 1.78408 | 0.892041 | − | 0.451955i | \(-0.149273\pi\) | ||||
0.892041 | + | 0.451955i | \(0.149273\pi\) | |||||||
\(360\) | 0.152773 | 0.00805182 | ||||||||
\(361\) | −12.2891 | −0.646797 | ||||||||
\(362\) | 27.2698 | 1.43327 | ||||||||
\(363\) | 14.6394 | 0.768368 | ||||||||
\(364\) | −4.18100 | −0.219144 | ||||||||
\(365\) | −60.2490 | −3.15358 | ||||||||
\(366\) | −13.9940 | −0.731476 | ||||||||
\(367\) | −25.5711 | −1.33480 | −0.667399 | − | 0.744700i | \(-0.732593\pi\) | ||||
−0.667399 | + | 0.744700i | \(0.732593\pi\) | |||||||
\(368\) | 3.96099 | 0.206481 | ||||||||
\(369\) | 2.45770 | 0.127943 | ||||||||
\(370\) | −19.5984 | −1.01887 | ||||||||
\(371\) | −9.09182 | −0.472024 | ||||||||
\(372\) | −1.12234 | −0.0581904 | ||||||||
\(373\) | 0.179366 | 0.00928724 | 0.00464362 | − | 0.999989i | \(-0.498522\pi\) | ||||
0.00464362 | + | 0.999989i | \(0.498522\pi\) | |||||||
\(374\) | −35.9839 | −1.86068 | ||||||||
\(375\) | 21.9214 | 1.13202 | ||||||||
\(376\) | 0.155724 | 0.00803086 | ||||||||
\(377\) | −0.849677 | −0.0437606 | ||||||||
\(378\) | −4.88537 | −0.251276 | ||||||||
\(379\) | −9.59910 | −0.493073 | −0.246536 | − | 0.969134i | \(-0.579292\pi\) | ||||
−0.246536 | + | 0.969134i | \(0.579292\pi\) | |||||||
\(380\) | 20.6332 | 1.05846 | ||||||||
\(381\) | 4.63744 | 0.237583 | ||||||||
\(382\) | 37.1882 | 1.90272 | ||||||||
\(383\) | 26.0551 | 1.33136 | 0.665678 | − | 0.746239i | \(-0.268143\pi\) | ||||
0.665678 | + | 0.746239i | \(0.268143\pi\) | |||||||
\(384\) | −0.309843 | −0.0158116 | ||||||||
\(385\) | −48.6684 | −2.48037 | ||||||||
\(386\) | 4.61198 | 0.234744 | ||||||||
\(387\) | −7.48299 | −0.380382 | ||||||||
\(388\) | 0.770636 | 0.0391231 | ||||||||
\(389\) | −9.42577 | −0.477905 | −0.238953 | − | 0.971031i | \(-0.576804\pi\) | ||||
−0.238953 | + | 0.971031i | \(0.576804\pi\) | |||||||
\(390\) | 6.71898 | 0.340229 | ||||||||
\(391\) | 3.54469 | 0.179263 | ||||||||
\(392\) | −0.0411328 | −0.00207752 | ||||||||
\(393\) | −11.3178 | −0.570906 | ||||||||
\(394\) | −47.5647 | −2.39628 | ||||||||
\(395\) | 33.8148 | 1.70141 | ||||||||
\(396\) | 10.2249 | 0.513820 | ||||||||
\(397\) | −7.25375 | −0.364055 | −0.182028 | − | 0.983293i | \(-0.558266\pi\) | ||||
−0.182028 | + | 0.983293i | \(0.558266\pi\) | |||||||
\(398\) | 20.2780 | 1.01644 | ||||||||
\(399\) | −6.31263 | −0.316027 | ||||||||
\(400\) | −41.8189 | −2.09095 | ||||||||
\(401\) | −4.37364 | −0.218409 | −0.109205 | − | 0.994019i | \(-0.534830\pi\) | ||||
−0.109205 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(402\) | −26.2036 | −1.30692 | ||||||||
\(403\) | −0.472250 | −0.0235244 | ||||||||
\(404\) | −15.5962 | −0.775938 | ||||||||
\(405\) | 3.94433 | 0.195995 | ||||||||
\(406\) | 4.88537 | 0.242457 | ||||||||
\(407\) | −12.5495 | −0.622054 | ||||||||
\(408\) | −0.137294 | −0.00679705 | ||||||||
\(409\) | −17.3026 | −0.855556 | −0.427778 | − | 0.903884i | \(-0.640704\pi\) | ||||
−0.427778 | + | 0.903884i | \(0.640704\pi\) | |||||||
\(410\) | 19.4347 | 0.959812 | ||||||||
\(411\) | 8.44177 | 0.416402 | ||||||||
\(412\) | −24.4597 | −1.20504 | ||||||||
\(413\) | −23.5584 | −1.15923 | ||||||||
\(414\) | −2.00482 | −0.0985317 | ||||||||
\(415\) | 31.9226 | 1.56702 | ||||||||
\(416\) | −6.81318 | −0.334044 | ||||||||
\(417\) | 0.788881 | 0.0386317 | ||||||||
\(418\) | 26.2978 | 1.28627 | ||||||||
\(419\) | 36.6204 | 1.78902 | 0.894512 | − | 0.447044i | \(-0.147523\pi\) | ||||
0.894512 | + | 0.447044i | \(0.147523\pi\) | |||||||
\(420\) | −19.4088 | −0.947053 | ||||||||
\(421\) | −29.6292 | −1.44404 | −0.722019 | − | 0.691873i | \(-0.756786\pi\) | ||||
−0.722019 | + | 0.691873i | \(0.756786\pi\) | |||||||
\(422\) | −43.4950 | −2.11730 | ||||||||
\(423\) | 4.02053 | 0.195485 | ||||||||
\(424\) | 0.144511 | 0.00701810 | ||||||||
\(425\) | −37.4238 | −1.81532 | ||||||||
\(426\) | 13.6821 | 0.662899 | ||||||||
\(427\) | 17.0092 | 0.823135 | ||||||||
\(428\) | −25.6772 | −1.24115 | ||||||||
\(429\) | 4.30237 | 0.207720 | ||||||||
\(430\) | −59.1731 | −2.85358 | ||||||||
\(431\) | 12.4234 | 0.598413 | 0.299207 | − | 0.954188i | \(-0.403278\pi\) | ||||
0.299207 | + | 0.954188i | \(0.403278\pi\) | |||||||
\(432\) | −3.96099 | −0.190573 | ||||||||
\(433\) | −37.4749 | −1.80093 | −0.900463 | − | 0.434932i | \(-0.856772\pi\) | ||||
−0.900463 | + | 0.434932i | \(0.856772\pi\) | |||||||
\(434\) | 2.71528 | 0.130338 | ||||||||
\(435\) | −3.94433 | −0.189116 | ||||||||
\(436\) | −8.20766 | −0.393076 | ||||||||
\(437\) | −2.59053 | −0.123922 | ||||||||
\(438\) | −30.6234 | −1.46324 | ||||||||
\(439\) | −33.9757 | −1.62157 | −0.810787 | − | 0.585342i | \(-0.800960\pi\) | ||||
−0.810787 | + | 0.585342i | \(0.800960\pi\) | |||||||
\(440\) | 0.773569 | 0.0368785 | ||||||||
\(441\) | −1.06198 | −0.0505704 | ||||||||
\(442\) | −6.03821 | −0.287208 | ||||||||
\(443\) | −14.2272 | −0.675954 | −0.337977 | − | 0.941154i | \(-0.609743\pi\) | ||||
−0.337977 | + | 0.941154i | \(0.609743\pi\) | |||||||
\(444\) | −5.00468 | −0.237512 | ||||||||
\(445\) | 12.2106 | 0.578838 | ||||||||
\(446\) | −19.0090 | −0.900104 | ||||||||
\(447\) | −7.78451 | −0.368195 | ||||||||
\(448\) | 19.8692 | 0.938733 | ||||||||
\(449\) | 23.8102 | 1.12367 | 0.561835 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561835 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(450\) | 21.1663 | 0.997791 | ||||||||
\(451\) | 12.4447 | 0.585996 | ||||||||
\(452\) | 20.8775 | 0.981996 | ||||||||
\(453\) | −19.2856 | −0.906116 | ||||||||
\(454\) | 39.7850 | 1.86720 | ||||||||
\(455\) | −8.16672 | −0.382862 | ||||||||
\(456\) | 0.100337 | 0.00469872 | ||||||||
\(457\) | 9.04233 | 0.422982 | 0.211491 | − | 0.977380i | \(-0.432168\pi\) | ||||
0.211491 | + | 0.977380i | \(0.432168\pi\) | |||||||
\(458\) | 38.3992 | 1.79428 | ||||||||
\(459\) | −3.54469 | −0.165452 | ||||||||
\(460\) | −7.96485 | −0.371363 | ||||||||
\(461\) | −24.9696 | −1.16295 | −0.581475 | − | 0.813565i | \(-0.697524\pi\) | ||||
−0.581475 | + | 0.813565i | \(0.697524\pi\) | |||||||
\(462\) | −24.7372 | −1.15088 | ||||||||
\(463\) | 30.2988 | 1.40810 | 0.704051 | − | 0.710149i | \(-0.251372\pi\) | ||||
0.704051 | + | 0.710149i | \(0.251372\pi\) | |||||||
\(464\) | 3.96099 | 0.183884 | ||||||||
\(465\) | −2.19225 | −0.101663 | ||||||||
\(466\) | 1.69725 | 0.0786234 | ||||||||
\(467\) | 35.3513 | 1.63586 | 0.817930 | − | 0.575317i | \(-0.195121\pi\) | ||||
0.817930 | + | 0.575317i | \(0.195121\pi\) | |||||||
\(468\) | 1.71577 | 0.0793115 | ||||||||
\(469\) | 31.8497 | 1.47068 | ||||||||
\(470\) | 31.7930 | 1.46650 | ||||||||
\(471\) | −11.9533 | −0.550780 | ||||||||
\(472\) | 0.374453 | 0.0172356 | ||||||||
\(473\) | −37.8904 | −1.74220 | ||||||||
\(474\) | 17.1874 | 0.789444 | ||||||||
\(475\) | 27.3501 | 1.25491 | ||||||||
\(476\) | 17.4423 | 0.799467 | ||||||||
\(477\) | 3.73104 | 0.170833 | ||||||||
\(478\) | −1.94199 | −0.0888244 | ||||||||
\(479\) | 10.1693 | 0.464648 | 0.232324 | − | 0.972638i | \(-0.425367\pi\) | ||||
0.232324 | + | 0.972638i | \(0.425367\pi\) | |||||||
\(480\) | −31.6278 | −1.44360 | ||||||||
\(481\) | −2.10584 | −0.0960180 | ||||||||
\(482\) | −2.07969 | −0.0947274 | ||||||||
\(483\) | 2.43681 | 0.110878 | ||||||||
\(484\) | 29.5616 | 1.34371 | ||||||||
\(485\) | 1.50528 | 0.0683512 | ||||||||
\(486\) | 2.00482 | 0.0909407 | ||||||||
\(487\) | −6.68801 | −0.303063 | −0.151531 | − | 0.988452i | \(-0.548420\pi\) | ||||
−0.151531 | + | 0.988452i | \(0.548420\pi\) | |||||||
\(488\) | −0.270357 | −0.0122385 | ||||||||
\(489\) | 13.9184 | 0.629414 | ||||||||
\(490\) | −8.39779 | −0.379373 | ||||||||
\(491\) | −9.85750 | −0.444863 | −0.222431 | − | 0.974948i | \(-0.571399\pi\) | ||||
−0.222431 | + | 0.974948i | \(0.571399\pi\) | |||||||
\(492\) | 4.96289 | 0.223744 | ||||||||
\(493\) | 3.54469 | 0.159645 | ||||||||
\(494\) | 4.41285 | 0.198544 | ||||||||
\(495\) | 19.9722 | 0.897685 | ||||||||
\(496\) | 2.20151 | 0.0988508 | ||||||||
\(497\) | −16.6302 | −0.745965 | ||||||||
\(498\) | 16.2257 | 0.727089 | ||||||||
\(499\) | 22.8453 | 1.02270 | 0.511348 | − | 0.859374i | \(-0.329146\pi\) | ||||
0.511348 | + | 0.859374i | \(0.329146\pi\) | |||||||
\(500\) | 44.2663 | 1.97965 | ||||||||
\(501\) | 11.6350 | 0.519813 | ||||||||
\(502\) | −55.6731 | −2.48481 | ||||||||
\(503\) | 6.17445 | 0.275305 | 0.137652 | − | 0.990481i | \(-0.456044\pi\) | ||||
0.137652 | + | 0.990481i | \(0.456044\pi\) | |||||||
\(504\) | −0.0943829 | −0.00420415 | ||||||||
\(505\) | −30.4639 | −1.35563 | ||||||||
\(506\) | −10.1515 | −0.451289 | ||||||||
\(507\) | −12.2780 | −0.545287 | ||||||||
\(508\) | 9.36448 | 0.415482 | ||||||||
\(509\) | 15.9641 | 0.707595 | 0.353798 | − | 0.935322i | \(-0.384890\pi\) | ||||
0.353798 | + | 0.935322i | \(0.384890\pi\) | |||||||
\(510\) | −28.0303 | −1.24120 | ||||||||
\(511\) | 37.2219 | 1.64660 | ||||||||
\(512\) | 32.0682 | 1.41723 | ||||||||
\(513\) | 2.59053 | 0.114375 | ||||||||
\(514\) | −30.1873 | −1.33151 | ||||||||
\(515\) | −47.7769 | −2.10530 | ||||||||
\(516\) | −15.1105 | −0.665204 | ||||||||
\(517\) | 20.3581 | 0.895347 | ||||||||
\(518\) | 12.1079 | 0.531990 | ||||||||
\(519\) | −15.0093 | −0.658837 | ||||||||
\(520\) | 0.129807 | 0.00569243 | ||||||||
\(521\) | 31.0979 | 1.36243 | 0.681213 | − | 0.732086i | \(-0.261453\pi\) | ||||
0.681213 | + | 0.732086i | \(0.261453\pi\) | |||||||
\(522\) | −2.00482 | −0.0877488 | ||||||||
\(523\) | 29.9735 | 1.31065 | 0.655325 | − | 0.755347i | \(-0.272532\pi\) | ||||
0.655325 | + | 0.755347i | \(0.272532\pi\) | |||||||
\(524\) | −22.8542 | −0.998390 | ||||||||
\(525\) | −25.7271 | −1.12282 | ||||||||
\(526\) | 32.5503 | 1.41926 | ||||||||
\(527\) | 1.97013 | 0.0858204 | ||||||||
\(528\) | −20.0566 | −0.872851 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 29.5039 | 1.28157 | ||||||||
\(531\) | 9.66773 | 0.419544 | ||||||||
\(532\) | −12.7472 | −0.552662 | ||||||||
\(533\) | 2.08825 | 0.0904523 | ||||||||
\(534\) | 6.20641 | 0.268578 | ||||||||
\(535\) | −50.1552 | −2.16840 | ||||||||
\(536\) | −0.506241 | −0.0218663 | ||||||||
\(537\) | 0.558696 | 0.0241095 | ||||||||
\(538\) | 39.1884 | 1.68953 | ||||||||
\(539\) | −5.37736 | −0.231619 | ||||||||
\(540\) | 7.96485 | 0.342753 | ||||||||
\(541\) | −25.1201 | −1.08000 | −0.539998 | − | 0.841666i | \(-0.681575\pi\) | ||||
−0.539998 | + | 0.841666i | \(0.681575\pi\) | |||||||
\(542\) | 32.2261 | 1.38423 | ||||||||
\(543\) | 13.6021 | 0.583722 | ||||||||
\(544\) | 28.4233 | 1.21864 | ||||||||
\(545\) | −16.0320 | −0.686734 | ||||||||
\(546\) | −4.15098 | −0.177646 | ||||||||
\(547\) | 29.3028 | 1.25290 | 0.626448 | − | 0.779463i | \(-0.284508\pi\) | ||||
0.626448 | + | 0.779463i | \(0.284508\pi\) | |||||||
\(548\) | 17.0466 | 0.728196 | ||||||||
\(549\) | −6.98014 | −0.297905 | ||||||||
\(550\) | 107.177 | 4.57002 | ||||||||
\(551\) | −2.59053 | −0.110360 | ||||||||
\(552\) | −0.0387322 | −0.00164855 | ||||||||
\(553\) | −20.8908 | −0.888367 | ||||||||
\(554\) | 23.1935 | 0.985398 | ||||||||
\(555\) | −9.77562 | −0.414952 | ||||||||
\(556\) | 1.59300 | 0.0675584 | ||||||||
\(557\) | 15.0301 | 0.636846 | 0.318423 | − | 0.947949i | \(-0.396847\pi\) | ||||
0.318423 | + | 0.947949i | \(0.396847\pi\) | |||||||
\(558\) | −1.11428 | −0.0471712 | ||||||||
\(559\) | −6.35812 | −0.268920 | ||||||||
\(560\) | 38.0713 | 1.60880 | ||||||||
\(561\) | −17.9486 | −0.757793 | ||||||||
\(562\) | 2.17678 | 0.0918218 | ||||||||
\(563\) | −28.7347 | −1.21102 | −0.605511 | − | 0.795837i | \(-0.707031\pi\) | ||||
−0.605511 | + | 0.795837i | \(0.707031\pi\) | |||||||
\(564\) | 8.11873 | 0.341860 | ||||||||
\(565\) | 40.7800 | 1.71563 | ||||||||
\(566\) | 22.0125 | 0.925256 | ||||||||
\(567\) | −2.43681 | −0.102336 | ||||||||
\(568\) | 0.264331 | 0.0110911 | ||||||||
\(569\) | −13.5827 | −0.569418 | −0.284709 | − | 0.958614i | \(-0.591897\pi\) | ||||
−0.284709 | + | 0.958614i | \(0.591897\pi\) | |||||||
\(570\) | 20.4851 | 0.858027 | ||||||||
\(571\) | 1.44552 | 0.0604932 | 0.0302466 | − | 0.999542i | \(-0.490371\pi\) | ||||
0.0302466 | + | 0.999542i | \(0.490371\pi\) | |||||||
\(572\) | 8.68786 | 0.363258 | ||||||||
\(573\) | 18.5494 | 0.774911 | ||||||||
\(574\) | −12.0068 | −0.501153 | ||||||||
\(575\) | −10.5577 | −0.440287 | ||||||||
\(576\) | −8.15380 | −0.339742 | ||||||||
\(577\) | 4.53867 | 0.188947 | 0.0944736 | − | 0.995527i | \(-0.469883\pi\) | ||||
0.0944736 | + | 0.995527i | \(0.469883\pi\) | |||||||
\(578\) | −8.89177 | −0.369849 | ||||||||
\(579\) | 2.30044 | 0.0956031 | ||||||||
\(580\) | −7.96485 | −0.330723 | ||||||||
\(581\) | −19.7218 | −0.818199 | ||||||||
\(582\) | 0.765104 | 0.0317146 | ||||||||
\(583\) | 18.8922 | 0.782437 | ||||||||
\(584\) | −0.591630 | −0.0244818 | ||||||||
\(585\) | 3.35140 | 0.138564 | ||||||||
\(586\) | 6.72388 | 0.277761 | ||||||||
\(587\) | −47.3036 | −1.95243 | −0.976214 | − | 0.216810i | \(-0.930435\pi\) | ||||
−0.976214 | + | 0.216810i | \(0.930435\pi\) | |||||||
\(588\) | −2.14447 | −0.0884366 | ||||||||
\(589\) | −1.43982 | −0.0593266 | ||||||||
\(590\) | 76.4493 | 3.14737 | ||||||||
\(591\) | −23.7251 | −0.975922 | ||||||||
\(592\) | 9.81691 | 0.403473 | ||||||||
\(593\) | −8.55983 | −0.351510 | −0.175755 | − | 0.984434i | \(-0.556237\pi\) | ||||
−0.175755 | + | 0.984434i | \(0.556237\pi\) | |||||||
\(594\) | 10.1515 | 0.416521 | ||||||||
\(595\) | 34.0700 | 1.39673 | ||||||||
\(596\) | −15.7194 | −0.643892 | ||||||||
\(597\) | 10.1146 | 0.413963 | ||||||||
\(598\) | −1.70345 | −0.0696594 | ||||||||
\(599\) | −4.50642 | −0.184127 | −0.0920637 | − | 0.995753i | \(-0.529346\pi\) | ||||
−0.0920637 | + | 0.995753i | \(0.529346\pi\) | |||||||
\(600\) | 0.408924 | 0.0166942 | ||||||||
\(601\) | 21.1749 | 0.863742 | 0.431871 | − | 0.901935i | \(-0.357854\pi\) | ||||
0.431871 | + | 0.901935i | \(0.357854\pi\) | |||||||
\(602\) | 36.5571 | 1.48996 | ||||||||
\(603\) | −13.0703 | −0.532263 | ||||||||
\(604\) | −38.9438 | −1.58460 | ||||||||
\(605\) | 57.7425 | 2.34757 | ||||||||
\(606\) | −15.4842 | −0.629003 | ||||||||
\(607\) | −31.5614 | −1.28104 | −0.640519 | − | 0.767942i | \(-0.721281\pi\) | ||||
−0.640519 | + | 0.767942i | \(0.721281\pi\) | |||||||
\(608\) | −20.7723 | −0.842429 | ||||||||
\(609\) | 2.43681 | 0.0987443 | ||||||||
\(610\) | −55.1967 | −2.23485 | ||||||||
\(611\) | 3.41615 | 0.138203 | ||||||||
\(612\) | −7.15786 | −0.289339 | ||||||||
\(613\) | 17.3406 | 0.700379 | 0.350189 | − | 0.936679i | \(-0.386117\pi\) | ||||
0.350189 | + | 0.936679i | \(0.386117\pi\) | |||||||
\(614\) | 22.0580 | 0.890190 | ||||||||
\(615\) | 9.69398 | 0.390899 | ||||||||
\(616\) | −0.477911 | −0.0192556 | ||||||||
\(617\) | −13.0619 | −0.525853 | −0.262927 | − | 0.964816i | \(-0.584688\pi\) | ||||
−0.262927 | + | 0.964816i | \(0.584688\pi\) | |||||||
\(618\) | −24.2841 | −0.976849 | ||||||||
\(619\) | −34.4145 | −1.38324 | −0.691618 | − | 0.722263i | \(-0.743102\pi\) | ||||
−0.691618 | + | 0.722263i | \(0.743102\pi\) | |||||||
\(620\) | −4.42686 | −0.177787 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 64.1768 | 2.57325 | ||||||||
\(623\) | −7.54371 | −0.302232 | ||||||||
\(624\) | −3.36556 | −0.134730 | ||||||||
\(625\) | 33.6766 | 1.34707 | ||||||||
\(626\) | −26.7247 | −1.06813 | ||||||||
\(627\) | 13.1173 | 0.523853 | ||||||||
\(628\) | −24.1376 | −0.963194 | ||||||||
\(629\) | 8.78515 | 0.350287 | ||||||||
\(630\) | −19.2695 | −0.767714 | ||||||||
\(631\) | 40.9589 | 1.63055 | 0.815275 | − | 0.579075i | \(-0.196586\pi\) | ||||
0.815275 | + | 0.579075i | \(0.196586\pi\) | |||||||
\(632\) | 0.332052 | 0.0132083 | ||||||||
\(633\) | −21.6952 | −0.862305 | ||||||||
\(634\) | −4.45324 | −0.176861 | ||||||||
\(635\) | 18.2916 | 0.725880 | ||||||||
\(636\) | 7.53416 | 0.298749 | ||||||||
\(637\) | −0.902339 | −0.0357520 | ||||||||
\(638\) | −10.1515 | −0.401902 | ||||||||
\(639\) | 6.82458 | 0.269976 | ||||||||
\(640\) | −1.22212 | −0.0483087 | ||||||||
\(641\) | −12.7161 | −0.502255 | −0.251127 | − | 0.967954i | \(-0.580801\pi\) | ||||
−0.251127 | + | 0.967954i | \(0.580801\pi\) | |||||||
\(642\) | −25.4929 | −1.00612 | ||||||||
\(643\) | −1.86413 | −0.0735143 | −0.0367571 | − | 0.999324i | \(-0.511703\pi\) | ||||
−0.0367571 | + | 0.999324i | \(0.511703\pi\) | |||||||
\(644\) | 4.92069 | 0.193902 | ||||||||
\(645\) | −29.5153 | −1.16217 | ||||||||
\(646\) | −18.4096 | −0.724315 | ||||||||
\(647\) | 40.0695 | 1.57529 | 0.787647 | − | 0.616126i | \(-0.211299\pi\) | ||||
0.787647 | + | 0.616126i | \(0.211299\pi\) | |||||||
\(648\) | 0.0387322 | 0.00152155 | ||||||||
\(649\) | 48.9529 | 1.92157 | ||||||||
\(650\) | 17.9846 | 0.705413 | ||||||||
\(651\) | 1.35437 | 0.0530821 | ||||||||
\(652\) | 28.1058 | 1.10071 | ||||||||
\(653\) | −12.7936 | −0.500651 | −0.250326 | − | 0.968162i | \(-0.580538\pi\) | ||||
−0.250326 | + | 0.968162i | \(0.580538\pi\) | |||||||
\(654\) | −8.14874 | −0.318641 | ||||||||
\(655\) | −44.6410 | −1.74427 | ||||||||
\(656\) | −9.73493 | −0.380085 | ||||||||
\(657\) | −15.2749 | −0.595929 | ||||||||
\(658\) | −19.6418 | −0.765715 | ||||||||
\(659\) | 37.7280 | 1.46967 | 0.734836 | − | 0.678245i | \(-0.237259\pi\) | ||||
0.734836 | + | 0.678245i | \(0.237259\pi\) | |||||||
\(660\) | 40.3303 | 1.56986 | ||||||||
\(661\) | 44.0649 | 1.71393 | 0.856963 | − | 0.515378i | \(-0.172348\pi\) | ||||
0.856963 | + | 0.515378i | \(0.172348\pi\) | |||||||
\(662\) | −12.0414 | −0.468001 | ||||||||
\(663\) | −3.01184 | −0.116970 | ||||||||
\(664\) | 0.313472 | 0.0121651 | ||||||||
\(665\) | −24.8991 | −0.965544 | ||||||||
\(666\) | −4.96875 | −0.192535 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 23.4948 | 0.909040 | ||||||||
\(669\) | −9.48165 | −0.366582 | ||||||||
\(670\) | −103.356 | −3.99297 | ||||||||
\(671\) | −35.3442 | −1.36445 | ||||||||
\(672\) | 19.5396 | 0.753758 | ||||||||
\(673\) | −10.9482 | −0.422023 | −0.211011 | − | 0.977484i | \(-0.567676\pi\) | ||||
−0.211011 | + | 0.977484i | \(0.567676\pi\) | |||||||
\(674\) | 5.97657 | 0.230209 | ||||||||
\(675\) | 10.5577 | 0.406366 | ||||||||
\(676\) | −24.7933 | −0.953589 | ||||||||
\(677\) | −13.1905 | −0.506954 | −0.253477 | − | 0.967341i | \(-0.581574\pi\) | ||||
−0.253477 | + | 0.967341i | \(0.581574\pi\) | |||||||
\(678\) | 20.7277 | 0.796041 | ||||||||
\(679\) | −0.929962 | −0.0356887 | ||||||||
\(680\) | −0.541531 | −0.0207668 | ||||||||
\(681\) | 19.8447 | 0.760449 | ||||||||
\(682\) | −5.64219 | −0.216051 | ||||||||
\(683\) | 36.1584 | 1.38356 | 0.691782 | − | 0.722107i | \(-0.256826\pi\) | ||||
0.691782 | + | 0.722107i | \(0.256826\pi\) | |||||||
\(684\) | 5.23112 | 0.200017 | ||||||||
\(685\) | 33.2971 | 1.27222 | ||||||||
\(686\) | 39.3857 | 1.50375 | ||||||||
\(687\) | 19.1534 | 0.730749 | ||||||||
\(688\) | 29.6400 | 1.13001 | ||||||||
\(689\) | 3.17018 | 0.120774 | ||||||||
\(690\) | −7.90768 | −0.301040 | ||||||||
\(691\) | 39.3807 | 1.49811 | 0.749056 | − | 0.662507i | \(-0.230507\pi\) | ||||
0.749056 | + | 0.662507i | \(0.230507\pi\) | |||||||
\(692\) | −30.3086 | −1.15216 | ||||||||
\(693\) | −12.3388 | −0.468714 | ||||||||
\(694\) | −64.5707 | −2.45107 | ||||||||
\(695\) | 3.11160 | 0.118030 | ||||||||
\(696\) | −0.0387322 | −0.00146814 | ||||||||
\(697\) | −8.71179 | −0.329982 | ||||||||
\(698\) | 52.8623 | 2.00087 | ||||||||
\(699\) | 0.846581 | 0.0320206 | ||||||||
\(700\) | −51.9512 | −1.96357 | ||||||||
\(701\) | −16.2919 | −0.615336 | −0.307668 | − | 0.951494i | \(-0.599549\pi\) | ||||
−0.307668 | + | 0.951494i | \(0.599549\pi\) | |||||||
\(702\) | 1.70345 | 0.0642927 | ||||||||
\(703\) | −6.42038 | −0.242149 | ||||||||
\(704\) | −41.2871 | −1.55606 | ||||||||
\(705\) | 15.8583 | 0.597257 | ||||||||
\(706\) | −56.8710 | −2.14037 | ||||||||
\(707\) | 18.8206 | 0.707822 | ||||||||
\(708\) | 19.5222 | 0.733691 | ||||||||
\(709\) | −10.2677 | −0.385610 | −0.192805 | − | 0.981237i | \(-0.561758\pi\) | ||||
−0.192805 | + | 0.981237i | \(0.561758\pi\) | |||||||
\(710\) | 53.9666 | 2.02533 | ||||||||
\(711\) | 8.57302 | 0.321514 | ||||||||
\(712\) | 0.119905 | 0.00449362 | ||||||||
\(713\) | 0.555799 | 0.0208148 | ||||||||
\(714\) | 17.3171 | 0.648076 | ||||||||
\(715\) | 16.9699 | 0.634640 | ||||||||
\(716\) | 1.12819 | 0.0421623 | ||||||||
\(717\) | −0.968657 | −0.0361752 | ||||||||
\(718\) | 67.7701 | 2.52916 | ||||||||
\(719\) | −35.4359 | −1.32154 | −0.660768 | − | 0.750590i | \(-0.729769\pi\) | ||||
−0.660768 | + | 0.750590i | \(0.729769\pi\) | |||||||
\(720\) | −15.6234 | −0.582251 | ||||||||
\(721\) | 29.5166 | 1.09926 | ||||||||
\(722\) | −24.6376 | −0.916915 | ||||||||
\(723\) | −1.03734 | −0.0385793 | ||||||||
\(724\) | 27.4670 | 1.02080 | ||||||||
\(725\) | −10.5577 | −0.392103 | ||||||||
\(726\) | 29.3494 | 1.08926 | ||||||||
\(727\) | 45.3897 | 1.68341 | 0.841706 | − | 0.539937i | \(-0.181552\pi\) | ||||
0.841706 | + | 0.539937i | \(0.181552\pi\) | |||||||
\(728\) | −0.0801950 | −0.00297223 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −120.789 | −4.47059 | ||||||||
\(731\) | 26.5249 | 0.981057 | ||||||||
\(732\) | −14.0951 | −0.520971 | ||||||||
\(733\) | 41.6542 | 1.53853 | 0.769266 | − | 0.638928i | \(-0.220622\pi\) | ||||
0.769266 | + | 0.638928i | \(0.220622\pi\) | |||||||
\(734\) | −51.2655 | −1.89224 | ||||||||
\(735\) | −4.18879 | −0.154506 | ||||||||
\(736\) | 8.01855 | 0.295568 | ||||||||
\(737\) | −66.1818 | −2.43784 | ||||||||
\(738\) | 4.92726 | 0.181375 | ||||||||
\(739\) | 23.7060 | 0.872038 | 0.436019 | − | 0.899937i | \(-0.356388\pi\) | ||||
0.436019 | + | 0.899937i | \(0.356388\pi\) | |||||||
\(740\) | −19.7401 | −0.725660 | ||||||||
\(741\) | 2.20112 | 0.0808601 | ||||||||
\(742\) | −18.2275 | −0.669152 | ||||||||
\(743\) | −35.7954 | −1.31321 | −0.656603 | − | 0.754236i | \(-0.728007\pi\) | ||||
−0.656603 | + | 0.754236i | \(0.728007\pi\) | |||||||
\(744\) | −0.0215273 | −0.000789230 0 | ||||||||
\(745\) | −30.7046 | −1.12493 | ||||||||
\(746\) | 0.359598 | 0.0131658 | ||||||||
\(747\) | 8.09331 | 0.296119 | ||||||||
\(748\) | −36.2441 | −1.32521 | ||||||||
\(749\) | 30.9859 | 1.13220 | ||||||||
\(750\) | 43.9486 | 1.60477 | ||||||||
\(751\) | 20.2739 | 0.739806 | 0.369903 | − | 0.929070i | \(-0.379391\pi\) | ||||
0.369903 | + | 0.929070i | \(0.379391\pi\) | |||||||
\(752\) | −15.9253 | −0.580735 | ||||||||
\(753\) | −27.7696 | −1.01198 | ||||||||
\(754\) | −1.70345 | −0.0620361 | ||||||||
\(755\) | −76.0686 | −2.76842 | ||||||||
\(756\) | −4.92069 | −0.178964 | ||||||||
\(757\) | 15.6157 | 0.567563 | 0.283781 | − | 0.958889i | \(-0.408411\pi\) | ||||
0.283781 | + | 0.958889i | \(0.408411\pi\) | |||||||
\(758\) | −19.2445 | −0.698992 | ||||||||
\(759\) | −5.06353 | −0.183795 | ||||||||
\(760\) | 0.395762 | 0.0143558 | ||||||||
\(761\) | 47.2992 | 1.71460 | 0.857298 | − | 0.514821i | \(-0.172142\pi\) | ||||
0.857298 | + | 0.514821i | \(0.172142\pi\) | |||||||
\(762\) | 9.29726 | 0.336804 | ||||||||
\(763\) | 9.90456 | 0.358569 | ||||||||
\(764\) | 37.4571 | 1.35515 | ||||||||
\(765\) | −13.9814 | −0.505499 | ||||||||
\(766\) | 52.2360 | 1.88736 | ||||||||
\(767\) | 8.21445 | 0.296607 | ||||||||
\(768\) | 15.6864 | 0.566035 | ||||||||
\(769\) | −10.2077 | −0.368098 | −0.184049 | − | 0.982917i | \(-0.558920\pi\) | ||||
−0.184049 | + | 0.982917i | \(0.558920\pi\) | |||||||
\(770\) | −97.5717 | −3.51624 | ||||||||
\(771\) | −15.0573 | −0.542277 | ||||||||
\(772\) | 4.64533 | 0.167189 | ||||||||
\(773\) | −25.6587 | −0.922880 | −0.461440 | − | 0.887171i | \(-0.652667\pi\) | ||||
−0.461440 | + | 0.887171i | \(0.652667\pi\) | |||||||
\(774\) | −15.0021 | −0.539238 | ||||||||
\(775\) | −5.86796 | −0.210783 | ||||||||
\(776\) | 0.0147814 | 0.000530623 0 | ||||||||
\(777\) | 6.03938 | 0.216661 | ||||||||
\(778\) | −18.8970 | −0.677490 | ||||||||
\(779\) | 6.36676 | 0.228113 | ||||||||
\(780\) | 6.76756 | 0.242317 | ||||||||
\(781\) | 34.5565 | 1.23653 | ||||||||
\(782\) | 7.10648 | 0.254127 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 4.20648 | 0.150232 | ||||||||
\(785\) | −47.1478 | −1.68278 | ||||||||
\(786\) | −22.6901 | −0.809330 | ||||||||
\(787\) | −0.441263 | −0.0157293 | −0.00786466 | − | 0.999969i | \(-0.502503\pi\) | ||||
−0.00786466 | + | 0.999969i | \(0.502503\pi\) | |||||||
\(788\) | −47.9087 | −1.70668 | ||||||||
\(789\) | 16.2360 | 0.578016 | ||||||||
\(790\) | 67.7927 | 2.41196 | ||||||||
\(791\) | −25.1939 | −0.895791 | ||||||||
\(792\) | 0.196122 | 0.00696889 | ||||||||
\(793\) | −5.93087 | −0.210611 | ||||||||
\(794\) | −14.5425 | −0.516094 | ||||||||
\(795\) | 14.7164 | 0.521938 | ||||||||
\(796\) | 20.4246 | 0.723931 | ||||||||
\(797\) | −41.1212 | −1.45659 | −0.728295 | − | 0.685264i | \(-0.759687\pi\) | ||||
−0.728295 | + | 0.685264i | \(0.759687\pi\) | |||||||
\(798\) | −12.6557 | −0.448007 | ||||||||
\(799\) | −14.2515 | −0.504183 | ||||||||
\(800\) | −84.6575 | −2.99309 | ||||||||
\(801\) | 3.09574 | 0.109382 | ||||||||
\(802\) | −8.76838 | −0.309622 | ||||||||
\(803\) | −77.3448 | −2.72944 | ||||||||
\(804\) | −26.3931 | −0.930811 | ||||||||
\(805\) | 9.61156 | 0.338763 | ||||||||
\(806\) | −0.946777 | −0.0333488 | ||||||||
\(807\) | 19.5471 | 0.688089 | ||||||||
\(808\) | −0.299147 | −0.0105240 | ||||||||
\(809\) | 28.4603 | 1.00061 | 0.500306 | − | 0.865849i | \(-0.333221\pi\) | ||||
0.500306 | + | 0.865849i | \(0.333221\pi\) | |||||||
\(810\) | 7.90768 | 0.277848 | ||||||||
\(811\) | −39.4573 | −1.38553 | −0.692767 | − | 0.721161i | \(-0.743609\pi\) | ||||
−0.692767 | + | 0.721161i | \(0.743609\pi\) | |||||||
\(812\) | 4.92069 | 0.172682 | ||||||||
\(813\) | 16.0743 | 0.563750 | ||||||||
\(814\) | −25.1595 | −0.881839 | ||||||||
\(815\) | 54.8989 | 1.92302 | ||||||||
\(816\) | 14.0405 | 0.491515 | ||||||||
\(817\) | −19.3849 | −0.678193 | ||||||||
\(818\) | −34.6886 | −1.21286 | ||||||||
\(819\) | −2.07050 | −0.0723491 | ||||||||
\(820\) | 19.5752 | 0.683597 | ||||||||
\(821\) | 31.1954 | 1.08873 | 0.544364 | − | 0.838849i | \(-0.316771\pi\) | ||||
0.544364 | + | 0.838849i | \(0.316771\pi\) | |||||||
\(822\) | 16.9243 | 0.590301 | ||||||||
\(823\) | −19.8791 | −0.692940 | −0.346470 | − | 0.938061i | \(-0.612620\pi\) | ||||
−0.346470 | + | 0.938061i | \(0.612620\pi\) | |||||||
\(824\) | −0.469157 | −0.0163438 | ||||||||
\(825\) | 53.4593 | 1.86121 | ||||||||
\(826\) | −47.2304 | −1.64336 | ||||||||
\(827\) | 33.4931 | 1.16467 | 0.582335 | − | 0.812949i | \(-0.302139\pi\) | ||||
0.582335 | + | 0.812949i | \(0.302139\pi\) | |||||||
\(828\) | −2.01932 | −0.0701762 | ||||||||
\(829\) | 36.8317 | 1.27922 | 0.639610 | − | 0.768700i | \(-0.279096\pi\) | ||||
0.639610 | + | 0.768700i | \(0.279096\pi\) | |||||||
\(830\) | 63.9993 | 2.22145 | ||||||||
\(831\) | 11.5689 | 0.401319 | ||||||||
\(832\) | −6.92810 | −0.240189 | ||||||||
\(833\) | 3.76438 | 0.130428 | ||||||||
\(834\) | 1.58157 | 0.0547652 | ||||||||
\(835\) | 45.8922 | 1.58817 | ||||||||
\(836\) | 26.4879 | 0.916104 | ||||||||
\(837\) | −0.555799 | −0.0192112 | ||||||||
\(838\) | 73.4175 | 2.53617 | ||||||||
\(839\) | 38.3930 | 1.32547 | 0.662737 | − | 0.748853i | \(-0.269395\pi\) | ||||
0.662737 | + | 0.748853i | \(0.269395\pi\) | |||||||
\(840\) | −0.372277 | −0.0128448 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −59.4013 | −2.04711 | ||||||||
\(843\) | 1.08577 | 0.0373959 | ||||||||
\(844\) | −43.8095 | −1.50798 | ||||||||
\(845\) | −48.4286 | −1.66600 | ||||||||
\(846\) | 8.06045 | 0.277124 | ||||||||
\(847\) | −35.6733 | −1.22575 | ||||||||
\(848\) | −14.7786 | −0.507499 | ||||||||
\(849\) | 10.9798 | 0.376825 | ||||||||
\(850\) | −75.0281 | −2.57344 | ||||||||
\(851\) | 2.47840 | 0.0849584 | ||||||||
\(852\) | 13.7810 | 0.472130 | ||||||||
\(853\) | 45.8492 | 1.56985 | 0.784923 | − | 0.619593i | \(-0.212702\pi\) | ||||
0.784923 | + | 0.619593i | \(0.212702\pi\) | |||||||
\(854\) | 34.1006 | 1.16690 | ||||||||
\(855\) | 10.2179 | 0.349445 | ||||||||
\(856\) | −0.492510 | −0.0168337 | ||||||||
\(857\) | 25.3677 | 0.866544 | 0.433272 | − | 0.901263i | \(-0.357359\pi\) | ||||
0.433272 | + | 0.901263i | \(0.357359\pi\) | |||||||
\(858\) | 8.62549 | 0.294470 | ||||||||
\(859\) | 52.6817 | 1.79748 | 0.898738 | − | 0.438486i | \(-0.144485\pi\) | ||||
0.898738 | + | 0.438486i | \(0.144485\pi\) | |||||||
\(860\) | −59.6009 | −2.03237 | ||||||||
\(861\) | −5.98894 | −0.204103 | ||||||||
\(862\) | 24.9067 | 0.848325 | ||||||||
\(863\) | −24.0843 | −0.819839 | −0.409920 | − | 0.912122i | \(-0.634443\pi\) | ||||
−0.409920 | + | 0.912122i | \(0.634443\pi\) | |||||||
\(864\) | −8.01855 | −0.272797 | ||||||||
\(865\) | −59.2017 | −2.01292 | ||||||||
\(866\) | −75.1305 | −2.55304 | ||||||||
\(867\) | −4.43519 | −0.150627 | ||||||||
\(868\) | 2.73491 | 0.0928290 | ||||||||
\(869\) | 43.4098 | 1.47258 | ||||||||
\(870\) | −7.90768 | −0.268095 | ||||||||
\(871\) | −11.1055 | −0.376296 | ||||||||
\(872\) | −0.157430 | −0.00533124 | ||||||||
\(873\) | 0.381632 | 0.0129163 | ||||||||
\(874\) | −5.19356 | −0.175675 | ||||||||
\(875\) | −53.4182 | −1.80586 | ||||||||
\(876\) | −30.8448 | −1.04215 | ||||||||
\(877\) | 48.6597 | 1.64312 | 0.821560 | − | 0.570122i | \(-0.193104\pi\) | ||||
0.821560 | + | 0.570122i | \(0.193104\pi\) | |||||||
\(878\) | −68.1154 | −2.29878 | ||||||||
\(879\) | 3.35385 | 0.113122 | ||||||||
\(880\) | −79.1098 | −2.66679 | ||||||||
\(881\) | 4.21156 | 0.141891 | 0.0709455 | − | 0.997480i | \(-0.477398\pi\) | ||||
0.0709455 | + | 0.997480i | \(0.477398\pi\) | |||||||
\(882\) | −2.12908 | −0.0716899 | ||||||||
\(883\) | −31.2259 | −1.05083 | −0.525417 | − | 0.850845i | \(-0.676091\pi\) | ||||
−0.525417 | + | 0.850845i | \(0.676091\pi\) | |||||||
\(884\) | −6.08187 | −0.204555 | ||||||||
\(885\) | 38.1327 | 1.28182 | ||||||||
\(886\) | −28.5230 | −0.958249 | ||||||||
\(887\) | −10.9743 | −0.368480 | −0.184240 | − | 0.982881i | \(-0.558982\pi\) | ||||
−0.184240 | + | 0.982881i | \(0.558982\pi\) | |||||||
\(888\) | −0.0959940 | −0.00322135 | ||||||||
\(889\) | −11.3006 | −0.379008 | ||||||||
\(890\) | 24.4801 | 0.820575 | ||||||||
\(891\) | 5.06353 | 0.169635 | ||||||||
\(892\) | −19.1465 | −0.641071 | ||||||||
\(893\) | 10.4153 | 0.348535 | ||||||||
\(894\) | −15.6066 | −0.521962 | ||||||||
\(895\) | 2.20368 | 0.0736609 | ||||||||
\(896\) | 0.755028 | 0.0252237 | ||||||||
\(897\) | −0.849677 | −0.0283699 | ||||||||
\(898\) | 47.7352 | 1.59294 | ||||||||
\(899\) | 0.555799 | 0.0185369 | ||||||||
\(900\) | 21.3194 | 0.710646 | ||||||||
\(901\) | −13.2254 | −0.440601 | ||||||||
\(902\) | 24.9493 | 0.830722 | ||||||||
\(903\) | 18.2346 | 0.606809 | ||||||||
\(904\) | 0.400448 | 0.0133187 | ||||||||
\(905\) | 53.6511 | 1.78342 | ||||||||
\(906\) | −38.6642 | −1.28453 | ||||||||
\(907\) | −6.75010 | −0.224133 | −0.112067 | − | 0.993701i | \(-0.535747\pi\) | ||||
−0.112067 | + | 0.993701i | \(0.535747\pi\) | |||||||
\(908\) | 40.0727 | 1.32986 | ||||||||
\(909\) | −7.72348 | −0.256171 | ||||||||
\(910\) | −16.3728 | −0.542754 | ||||||||
\(911\) | 2.35100 | 0.0778921 | 0.0389460 | − | 0.999241i | \(-0.487600\pi\) | ||||
0.0389460 | + | 0.999241i | \(0.487600\pi\) | |||||||
\(912\) | −10.2611 | −0.339778 | ||||||||
\(913\) | 40.9807 | 1.35626 | ||||||||
\(914\) | 18.1283 | 0.599630 | ||||||||
\(915\) | −27.5320 | −0.910178 | ||||||||
\(916\) | 38.6769 | 1.27792 | ||||||||
\(917\) | 27.5792 | 0.910745 | ||||||||
\(918\) | −7.10648 | −0.234549 | ||||||||
\(919\) | 57.2879 | 1.88975 | 0.944876 | − | 0.327427i | \(-0.106182\pi\) | ||||
0.944876 | + | 0.327427i | \(0.106182\pi\) | |||||||
\(920\) | −0.152773 | −0.00503676 | ||||||||
\(921\) | 11.0025 | 0.362544 | ||||||||
\(922\) | −50.0596 | −1.64863 | ||||||||
\(923\) | 5.79869 | 0.190866 | ||||||||
\(924\) | −24.9161 | −0.819679 | ||||||||
\(925\) | −26.1662 | −0.860340 | ||||||||
\(926\) | 60.7437 | 1.99616 | ||||||||
\(927\) | −12.1128 | −0.397837 | ||||||||
\(928\) | 8.01855 | 0.263222 | ||||||||
\(929\) | 13.5839 | 0.445672 | 0.222836 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222836 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(930\) | −4.39508 | −0.144120 | ||||||||
\(931\) | −2.75109 | −0.0901634 | ||||||||
\(932\) | 1.70952 | 0.0559971 | ||||||||
\(933\) | 32.0112 | 1.04800 | ||||||||
\(934\) | 70.8730 | 2.31904 | ||||||||
\(935\) | −70.7953 | −2.31525 | ||||||||
\(936\) | 0.0329099 | 0.00107569 | ||||||||
\(937\) | −15.0191 | −0.490651 | −0.245326 | − | 0.969441i | \(-0.578895\pi\) | ||||
−0.245326 | + | 0.969441i | \(0.578895\pi\) | |||||||
\(938\) | 63.8531 | 2.08488 | ||||||||
\(939\) | −13.3302 | −0.435015 | ||||||||
\(940\) | 32.0229 | 1.04447 | ||||||||
\(941\) | 10.4773 | 0.341550 | 0.170775 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170775 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(942\) | −23.9643 | −0.780799 | ||||||||
\(943\) | −2.45770 | −0.0800338 | ||||||||
\(944\) | −38.2938 | −1.24636 | ||||||||
\(945\) | −9.61156 | −0.312664 | ||||||||
\(946\) | −75.9635 | −2.46979 | ||||||||
\(947\) | 41.9689 | 1.36381 | 0.681903 | − | 0.731442i | \(-0.261152\pi\) | ||||
0.681903 | + | 0.731442i | \(0.261152\pi\) | |||||||
\(948\) | 17.3117 | 0.562257 | ||||||||
\(949\) | −12.9787 | −0.421307 | ||||||||
\(950\) | 54.8321 | 1.77899 | ||||||||
\(951\) | −2.22126 | −0.0720293 | ||||||||
\(952\) | 0.334558 | 0.0108431 | ||||||||
\(953\) | −1.88809 | −0.0611613 | −0.0305807 | − | 0.999532i | \(-0.509736\pi\) | ||||
−0.0305807 | + | 0.999532i | \(0.509736\pi\) | |||||||
\(954\) | 7.48008 | 0.242176 | ||||||||
\(955\) | 73.1648 | 2.36756 | ||||||||
\(956\) | −1.95603 | −0.0632625 | ||||||||
\(957\) | −5.06353 | −0.163681 | ||||||||
\(958\) | 20.3877 | 0.658697 | ||||||||
\(959\) | −20.5709 | −0.664270 | ||||||||
\(960\) | −32.1613 | −1.03800 | ||||||||
\(961\) | −30.6911 | −0.990035 | ||||||||
\(962\) | −4.22184 | −0.136118 | ||||||||
\(963\) | −12.7158 | −0.409760 | ||||||||
\(964\) | −2.09473 | −0.0674667 | ||||||||
\(965\) | 9.07369 | 0.292092 | ||||||||
\(966\) | 4.88537 | 0.157184 | ||||||||
\(967\) | 30.5244 | 0.981599 | 0.490800 | − | 0.871272i | \(-0.336705\pi\) | ||||
0.490800 | + | 0.871272i | \(0.336705\pi\) | |||||||
\(968\) | 0.567016 | 0.0182246 | ||||||||
\(969\) | −9.18263 | −0.294989 | ||||||||
\(970\) | 3.01782 | 0.0968964 | ||||||||
\(971\) | 10.0716 | 0.323212 | 0.161606 | − | 0.986855i | \(-0.448333\pi\) | ||||
0.161606 | + | 0.986855i | \(0.448333\pi\) | |||||||
\(972\) | 2.01932 | 0.0647697 | ||||||||
\(973\) | −1.92235 | −0.0616277 | ||||||||
\(974\) | −13.4083 | −0.429629 | ||||||||
\(975\) | 8.97064 | 0.287291 | ||||||||
\(976\) | 27.6483 | 0.884999 | ||||||||
\(977\) | 23.5545 | 0.753576 | 0.376788 | − | 0.926300i | \(-0.377029\pi\) | ||||
0.376788 | + | 0.926300i | \(0.377029\pi\) | |||||||
\(978\) | 27.9040 | 0.892272 | ||||||||
\(979\) | 15.6754 | 0.500987 | ||||||||
\(980\) | −8.45850 | −0.270197 | ||||||||
\(981\) | −4.06457 | −0.129772 | ||||||||
\(982\) | −19.7626 | −0.630649 | ||||||||
\(983\) | 17.1703 | 0.547647 | 0.273823 | − | 0.961780i | \(-0.411712\pi\) | ||||
0.273823 | + | 0.961780i | \(0.411712\pi\) | |||||||
\(984\) | 0.0951923 | 0.00303462 | ||||||||
\(985\) | −93.5797 | −2.98170 | ||||||||
\(986\) | 7.10648 | 0.226316 | ||||||||
\(987\) | −9.79725 | −0.311850 | ||||||||
\(988\) | 4.44476 | 0.141407 | ||||||||
\(989\) | 7.48299 | 0.237945 | ||||||||
\(990\) | 40.0408 | 1.27258 | ||||||||
\(991\) | −9.28729 | −0.295020 | −0.147510 | − | 0.989061i | \(-0.547126\pi\) | ||||
−0.147510 | + | 0.989061i | \(0.547126\pi\) | |||||||
\(992\) | 4.45670 | 0.141500 | ||||||||
\(993\) | −6.00619 | −0.190601 | ||||||||
\(994\) | −33.3406 | −1.05750 | ||||||||
\(995\) | 39.8953 | 1.26477 | ||||||||
\(996\) | 16.3430 | 0.517847 | ||||||||
\(997\) | 19.7598 | 0.625800 | 0.312900 | − | 0.949786i | \(-0.398700\pi\) | ||||
0.312900 | + | 0.949786i | \(0.398700\pi\) | |||||||
\(998\) | 45.8008 | 1.44980 | ||||||||
\(999\) | −2.47840 | −0.0784131 |
(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 | 2001.2.a.n.1.13 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.r.1.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.n.1.13 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.r.1.4 | 16 | 3.2 | odd | 2 |