Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.691575 | −0.399281 | −0.199641 | − | 0.979869i | \(-0.563977\pi\) | ||||
−0.199641 | + | 0.979869i | \(0.563977\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.88995 | −0.845210 | −0.422605 | − | 0.906314i | \(-0.638884\pi\) | ||||
−0.422605 | + | 0.906314i | \(0.638884\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.98805 | 1.88531 | 0.942653 | − | 0.333775i | \(-0.108323\pi\) | ||||
0.942653 | + | 0.333775i | \(0.108323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52172 | −0.840575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24294 | −1.27930 | −0.639648 | − | 0.768668i | \(-0.720920\pi\) | ||||
−0.639648 | + | 0.768668i | \(0.720920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.255617 | 0.0708955 | 0.0354477 | − | 0.999372i | \(-0.488714\pi\) | ||||
0.0354477 | + | 0.999372i | \(0.488714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30704 | 0.337476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.15886 | −1.97881 | −0.989407 | − | 0.145170i | \(-0.953627\pi\) | ||||
−0.989407 | + | 0.145170i | \(0.953627\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0286100 | −0.00656358 | −0.00328179 | − | 0.999995i | \(-0.501045\pi\) | ||||
−0.00328179 | + | 0.999995i | \(0.501045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.44961 | −0.752767 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.59610 | 1.37538 | 0.687691 | − | 0.726004i | \(-0.258624\pi\) | ||||
0.687691 | + | 0.726004i | \(0.258624\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.42810 | −0.285620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.81869 | 0.734907 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.26352 | −0.420325 | −0.210163 | − | 0.977666i | \(-0.567399\pi\) | ||||
−0.210163 | + | 0.977666i | \(0.567399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.18850 | −0.752277 | −0.376139 | − | 0.926563i | \(-0.622748\pi\) | ||||
−0.376139 | + | 0.926563i | \(0.622748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.93431 | 0.510798 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.42715 | −1.59348 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.27456 | −0.702733 | −0.351366 | − | 0.936238i | \(-0.614283\pi\) | ||||
−0.351366 | + | 0.936238i | \(0.614283\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.176779 | −0.0283072 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.77543 | −1.21432 | −0.607159 | − | 0.794580i | \(-0.707691\pi\) | ||||
−0.607159 | + | 0.794580i | \(0.707691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.8738 | 1.81075 | 0.905373 | − | 0.424618i | \(-0.139592\pi\) | ||||
0.905373 | + | 0.424618i | \(0.139592\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.76593 | 0.710462 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0979024 | 0.0142805 | 0.00714027 | − | 0.999975i | \(-0.497727\pi\) | ||||
0.00714027 | + | 0.999975i | \(0.497727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.8806 | 2.55438 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.64246 | 0.790103 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.31292 | 0.317703 | 0.158852 | − | 0.987302i | \(-0.449221\pi\) | ||||
0.158852 | + | 0.987302i | \(0.449221\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.01894 | 1.08127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0197859 | 0.00262071 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.83165 | 0.629027 | 0.314514 | − | 0.949253i | \(-0.398159\pi\) | ||||
0.314514 | + | 0.949253i | \(0.398159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40707 | 0.436230 | 0.218115 | − | 0.975923i | \(-0.430009\pi\) | ||||
0.218115 | + | 0.975923i | \(0.430009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.5785 | −1.58474 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.483103 | −0.0599216 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2867 | 1.50107 | 0.750533 | − | 0.660833i | \(-0.229797\pi\) | ||||
0.750533 | + | 0.660833i | \(0.229797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.56170 | −0.549164 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4325 | −1.35679 | −0.678393 | − | 0.734699i | \(-0.737323\pi\) | ||||
−0.678393 | + | 0.734699i | \(0.737323\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.63184 | −0.659158 | −0.329579 | − | 0.944128i | \(-0.606907\pi\) | ||||
−0.329579 | + | 0.944128i | \(0.606907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.987638 | 0.114043 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.1640 | −2.41186 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.59380 | 0.854369 | 0.427184 | − | 0.904165i | \(-0.359506\pi\) | ||||
0.427184 | + | 0.904165i | \(0.359506\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.92426 | 0.547140 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0138 | 1.31869 | 0.659345 | − | 0.751841i | \(-0.270834\pi\) | ||||
0.659345 | + | 0.751841i | \(0.270834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.4198 | 1.67251 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.56539 | 0.167828 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.68427 | −0.284533 | −0.142266 | − | 0.989828i | \(-0.545439\pi\) | ||||
−0.142266 | + | 0.989828i | \(0.545439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.27503 | 0.133660 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.89666 | 0.300370 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0540713 | 0.00554760 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.68885 | −0.171477 | −0.0857386 | − | 0.996318i | \(-0.527325\pi\) | ||||
−0.0857386 | + | 0.996318i | \(0.527325\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6995 | 1.07534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6186 | 1.35510 | 0.677551 | − | 0.735476i | \(-0.263041\pi\) | ||||
0.677551 | + | 0.735476i | \(0.263041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.91857 | 0.484641 | 0.242320 | − | 0.970196i | \(-0.422091\pi\) | ||||
0.242320 | + | 0.970196i | \(0.422091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.51958 | 0.636246 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.92934 | −0.476537 | −0.238268 | − | 0.971199i | \(-0.576580\pi\) | ||||
−0.238268 | + | 0.971199i | \(0.576580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.25276 | 0.311557 | 0.155779 | − | 0.987792i | \(-0.450211\pi\) | ||||
0.155779 | + | 0.987792i | \(0.450211\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.95618 | 0.280588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.6477 | −1.94237 | −0.971187 | − | 0.238320i | \(-0.923403\pi\) | ||||
−0.971187 | + | 0.238320i | \(0.923403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.4663 | −1.16249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.644596 | −0.0595929 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −40.6968 | −3.73067 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00257 | 0.636597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.37729 | 0.484854 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1488 | 1.08662 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8670 | −1.05303 | −0.526513 | − | 0.850167i | \(-0.676501\pi\) | ||||
−0.526513 | + | 0.850167i | \(0.676501\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.21166 | −0.722996 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3654 | 0.993002 | 0.496501 | − | 0.868036i | \(-0.334618\pi\) | ||||
0.496501 | + | 0.868036i | \(0.334618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.142708 | −0.0123743 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.21712 | −0.621151 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5731 | 1.67224 | 0.836121 | − | 0.548545i | \(-0.184818\pi\) | ||||
0.836121 | + | 0.548545i | \(0.184818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.3930 | 1.05116 | 0.525580 | − | 0.850744i | \(-0.323848\pi\) | ||||
0.525580 | + | 0.850744i | \(0.323848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0677069 | −0.00570195 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.08457 | −0.0906963 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.27793 | 0.355263 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.3658 | −1.01991 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.77070 | −0.308908 | −0.154454 | − | 0.988000i | \(-0.549362\pi\) | ||||
−0.154454 | + | 0.988000i | \(0.549362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.819040 | −0.0666526 | −0.0333263 | − | 0.999445i | \(-0.510610\pi\) | ||||
−0.0333263 | + | 0.999445i | \(0.510610\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.5744 | 1.66334 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.91605 | 0.635832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.9452 | −1.75142 | −0.875709 | − | 0.482839i | \(-0.839605\pi\) | ||||
−0.875709 | + | 0.482839i | \(0.839605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.59955 | −0.126853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.9017 | 2.59301 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.46062 | −0.349383 | −0.174691 | − | 0.984623i | \(-0.555893\pi\) | ||||
−0.174691 | + | 0.984623i | \(0.555893\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.54570 | −0.431732 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.98379 | −0.385658 | −0.192829 | − | 0.981232i | \(-0.561766\pi\) | ||||
−0.192829 | + | 0.981232i | \(0.561766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9347 | −0.994974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0721464 | 0.00551718 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.3664 | 1.92857 | 0.964287 | − | 0.264861i | \(-0.0853260\pi\) | ||||
0.964287 | + | 0.264861i | \(0.0853260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.12343 | −0.538481 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.34145 | −0.251159 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2611 | 0.991182 | 0.495591 | − | 0.868556i | \(-0.334951\pi\) | ||||
0.495591 | + | 0.868556i | \(0.334951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.86567 | 0.138674 | 0.0693372 | − | 0.997593i | \(-0.477912\pi\) | ||||
0.0693372 | + | 0.997593i | \(0.477912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.35624 | −0.174178 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.07869 | 0.593957 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.6176 | 2.53149 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.0478 | 1.38552 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.8772 | 1.29355 | 0.646773 | − | 0.762682i | \(-0.276118\pi\) | ||||
0.646773 | + | 0.762682i | \(0.276118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.12261 | 0.368734 | 0.184367 | − | 0.982857i | \(-0.440977\pi\) | ||||
0.184367 | + | 0.982857i | \(0.440977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.334102 | 0.0239256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8588 | −0.916152 | −0.458076 | − | 0.888913i | \(-0.651461\pi\) | ||||
−0.458076 | + | 0.888913i | \(0.651461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.73338 | 0.548205 | 0.274103 | − | 0.961700i | \(-0.411619\pi\) | ||||
0.274103 | + | 0.961700i | \(0.411619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.49721 | −0.599347 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.2906 | −0.792441 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.6952 | 1.02635 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.6335 | −1.15611 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.121390 | 0.00839675 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74255 | −0.119962 | −0.0599810 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599810 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.90642 | 0.541739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.4410 | −1.53046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.8925 | −1.41827 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.89484 | 0.263189 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.08555 | −0.140289 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.25485 | −0.284926 | −0.142463 | − | 0.989800i | \(-0.545502\pi\) | ||||
−0.142463 | + | 0.989800i | \(0.545502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.60127 | 0.240085 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.2454 | 1.34373 | 0.671866 | − | 0.740673i | \(-0.265493\pi\) | ||||
0.671866 | + | 0.740673i | \(0.265493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.96675 | 0.262130 | 0.131065 | − | 0.991374i | \(-0.458160\pi\) | ||||
0.131065 | + | 0.991374i | \(0.458160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.6365 | 0.963011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4979 | −1.14633 | −0.573164 | − | 0.819441i | \(-0.694284\pi\) | ||||
−0.573164 | + | 0.819441i | \(0.694284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.185030 | −0.0120701 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.25168 | −0.341133 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.8325 | −1.47691 | −0.738456 | − | 0.674301i | \(-0.764445\pi\) | ||||
−0.738456 | + | 0.674301i | \(0.764445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.9795 | 1.80232 | 0.901160 | − | 0.433486i | \(-0.142717\pi\) | ||||
0.901160 | + | 0.433486i | \(0.142717\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.8616 | −0.953369 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −33.7935 | −2.15899 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.00731320 | −0.000465328 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.30847 | −0.526528 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.2334 | −1.02464 | −0.512320 | − | 0.858794i | \(-0.671214\pi\) | ||||
−0.512320 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.9869 | −1.75952 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6640 | −0.667803 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.22214 | −0.512883 | −0.256442 | − | 0.966560i | \(-0.582550\pi\) | ||||
−0.256442 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.3217 | −1.32487 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.70797 | 0.353315 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.2834 | 1.00408 | 0.502038 | − | 0.864846i | \(-0.332584\pi\) | ||||
0.502038 | + | 0.864846i | \(0.332584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.37129 | −0.268526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.85638 | 0.113608 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7345 | −0.654495 | −0.327248 | − | 0.944939i | \(-0.606121\pi\) | ||||
−0.327248 | + | 0.944939i | \(0.606121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5461 | −1.06585 | −0.532925 | − | 0.846163i | \(-0.678907\pi\) | ||||
−0.532925 | + | 0.846163i | \(0.678907\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.881780 | −0.0533678 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.05934 | 0.365392 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.6792 | −0.821906 | −0.410953 | − | 0.911657i | \(-0.634804\pi\) | ||||
−0.410953 | + | 0.911657i | \(0.634804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.5622 | 0.632345 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.60169 | 0.572789 | 0.286394 | − | 0.958112i | \(-0.407543\pi\) | ||||
0.286394 | + | 0.958112i | \(0.407543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.4532 | 1.15638 | 0.578188 | − | 0.815904i | \(-0.303760\pi\) | ||||
0.578188 | + | 0.815904i | \(0.303760\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0373944 | −0.00221505 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −38.7842 | −2.28936 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.5670 | 2.91570 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.16797 | 0.0684676 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.99532 | 0.525512 | 0.262756 | − | 0.964862i | \(-0.415369\pi\) | ||||
0.262756 | + | 0.964862i | \(0.415369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.13157 | −0.531660 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.2025 | −0.940163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.68608 | 0.0975084 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 59.2274 | 3.41381 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.41828 | −0.541066 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.43918 | −0.368706 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7568 | 0.899285 | 0.449643 | − | 0.893209i | \(-0.351551\pi\) | ||||
0.449643 | + | 0.893209i | \(0.351551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.40156 | −0.193508 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2569 | 1.31878 | 0.659388 | − | 0.751803i | \(-0.270816\pi\) | ||||
0.659388 | + | 0.751803i | \(0.270816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0317 | 1.41488 | 0.707438 | − | 0.706775i | \(-0.249851\pi\) | ||||
0.707438 | + | 0.706775i | \(0.249851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.7727 | 1.33944 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.7785 | 0.942375 | 0.471188 | − | 0.882033i | \(-0.343825\pi\) | ||||
0.471188 | + | 0.882033i | \(0.343825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.60399 | 0.537720 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.40901 | 0.190272 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.233425 | 0.0129881 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.365047 | −0.0202492 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.24952 | −0.124399 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.488342 | 0.0269232 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.53931 | −0.194538 | −0.0972690 | − | 0.995258i | \(-0.531011\pi\) | ||||
−0.0972690 | + | 0.995258i | \(0.531011\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.7793 | 0.590699 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.2213 | −1.26872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0094 | 1.85261 | 0.926305 | − | 0.376776i | \(-0.122967\pi\) | ||||
0.926305 | + | 0.376776i | \(0.122967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.2794 | 0.775553 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.7716 | 0.962385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 54.2732 | 2.93048 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.62137 | 0.464159 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5553 | −0.566636 | −0.283318 | − | 0.959026i | \(-0.591435\pi\) | ||||
−0.283318 | + | 0.959026i | \(0.591435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0269 | 0.750842 | 0.375421 | − | 0.926854i | \(-0.377498\pi\) | ||||
0.375421 | + | 0.926854i | \(0.377498\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.976122 | 0.0521016 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.8192 | −1.42744 | −0.713721 | − | 0.700430i | \(-0.752992\pi\) | ||||
−0.713721 | + | 0.700430i | \(0.752992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.6068 | 1.14677 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.1449 | 1.48959 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7200 | 0.829672 | 0.414836 | − | 0.909896i | \(-0.363839\pi\) | ||||
0.414836 | + | 0.909896i | \(0.363839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9992 | −0.999957 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.84280 | −0.254181 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.6439 | 0.557127 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6533 | 1.02589 | 0.512947 | − | 0.858420i | \(-0.328554\pi\) | ||||
0.512947 | + | 0.858420i | \(0.328554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.6075 | 1.02073 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5369 | 0.598968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2903 | −0.532811 | −0.266406 | − | 0.963861i | \(-0.585836\pi\) | ||||
−0.266406 | + | 0.963861i | \(0.585836\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.40179 | −0.433866 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.578595 | −0.0297992 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7445 | 0.706008 | 0.353004 | − | 0.935622i | \(-0.385160\pi\) | ||||
0.353004 | + | 0.935622i | \(0.385160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.20691 | 0.420453 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.82959 | 0.451171 | 0.225585 | − | 0.974223i | \(-0.427571\pi\) | ||||
0.225585 | + | 0.974223i | \(0.427571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 39.9989 | 2.03853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −29.9426 | −1.52207 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.9808 | −1.11447 | −0.557235 | − | 0.830355i | \(-0.688138\pi\) | ||||
−0.557235 | + | 0.830355i | \(0.688138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.8166 | −2.72162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.86005 | −0.396487 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3519 | −0.722121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.2475 | 0.966003 | 0.483002 | − | 0.875620i | \(-0.339547\pi\) | ||||
0.483002 | + | 0.875620i | \(0.339547\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0986932 | 0.00494084 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.85175 | 0.142410 | 0.0712049 | − | 0.997462i | \(-0.477316\pi\) | ||||
0.0712049 | + | 0.997462i | \(0.477316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.07065 | −0.0533331 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.30660 | −0.462449 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.1367 | 0.899003 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.1676 | −0.799435 | −0.399717 | − | 0.916638i | \(-0.630892\pi\) | ||||
−0.399717 | + | 0.916638i | \(0.630892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.5363 | −0.667695 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.1005 | 1.18591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.7055 | −1.11457 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.57069 | −0.419709 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7360 | −0.622195 | −0.311097 | − | 0.950378i | \(-0.600697\pi\) | ||||
−0.311097 | + | 0.950378i | \(0.600697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2736 | 0.988074 | 0.494037 | − | 0.869441i | \(-0.335521\pi\) | ||||
0.494037 | + | 0.869441i | \(0.335521\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.246883 | −0.0120039 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6517 | 0.565188 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.9946 | 0.822427 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.750061 | 0.0362133 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.82368 | −0.328685 | −0.164343 | − | 0.986403i | \(-0.552550\pi\) | ||||
−0.164343 | + | 0.986403i | \(0.552550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9063 | 0.812467 | 0.406234 | − | 0.913769i | \(-0.366842\pi\) | ||||
0.406234 | + | 0.913769i | \(0.366842\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.95851 | −0.141850 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.188714 | −0.00902742 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.1028 | 1.38900 | 0.694501 | − | 0.719492i | \(-0.255625\pi\) | ||||
0.694501 | + | 0.719492i | \(0.255625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −45.0900 | −2.14714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.52297 | 0.452450 | 0.226225 | − | 0.974075i | \(-0.427362\pi\) | ||||
0.226225 | + | 0.974075i | \(0.427362\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.07314 | 0.240490 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.60772 | 0.123341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.5773 | 1.86777 | 0.933884 | − | 0.357575i | \(-0.116396\pi\) | ||||
0.933884 | + | 0.357575i | \(0.116396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.9907 | 1.55347 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.566428 | 0.0266131 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.40974 | −0.112970 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.83127 | 0.413110 | 0.206555 | − | 0.978435i | \(-0.433775\pi\) | ||||
0.206555 | + | 0.978435i | \(0.433775\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.1561 | −1.45424 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.2058 | 1.87257 | 0.936285 | − | 0.351242i | \(-0.114241\pi\) | ||||
0.936285 | + | 0.351242i | \(0.114241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.7668 | −1.05806 | −0.529031 | − | 0.848603i | \(-0.677444\pi\) | ||||
−0.529031 | + | 0.848603i | \(0.677444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.47454 | −0.253876 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.17948 | −0.100854 | −0.0504272 | − | 0.998728i | \(-0.516058\pi\) | ||||
−0.0504272 | + | 0.998728i | \(0.516058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 61.2869 | 2.82997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.1768 | 0.699308 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.3801 | −2.31648 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0408579 | 0.00187469 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.83253 | −0.267053 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.4534 | 0.980232 | 0.490116 | − | 0.871657i | \(-0.336954\pi\) | ||||
0.490116 | + | 0.871657i | \(0.336954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.09265 | −0.0498206 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.7540 | −1.03534 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.19185 | 0.144934 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8786 | −0.538269 | −0.269134 | − | 0.963103i | \(-0.586738\pi\) | ||||
−0.269134 | + | 0.963103i | \(0.586738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.08485 | 0.139502 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.35041 | −0.241461 | −0.120730 | − | 0.992685i | \(-0.538524\pi\) | ||||
−0.120730 | + | 0.992685i | \(0.538524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.4677 | 0.831745 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.2215 | −0.908891 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −57.0258 | −2.55796 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.43138 | 0.287908 | 0.143954 | − | 0.989584i | \(-0.454018\pi\) | ||||
0.143954 | + | 0.989584i | \(0.454018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.44667 | 0.153986 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.1140 | −1.29813 | −0.649064 | − | 0.760734i | \(-0.724839\pi\) | ||||
−0.649064 | + | 0.760734i | \(0.724839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.7384 | −1.14535 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.94529 | 0.397274 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.1478 | 0.715737 | 0.357869 | − | 0.933772i | \(-0.383504\pi\) | ||||
0.357869 | + | 0.933772i | \(0.383504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0919 | −1.24271 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.109252 | −0.00482362 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.29583 | −0.409623 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.415394 | −0.0182690 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.5428 | −0.770043 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.7289 | 1.47769 | 0.738845 | − | 0.673876i | \(-0.235372\pi\) | ||||
0.738845 | + | 0.673876i | \(0.235372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.4235 | −0.543242 | −0.271621 | − | 0.962404i | \(-0.587560\pi\) | ||||
−0.271621 | + | 0.962404i | \(0.587560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.92639 | 0.215005 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.1734 | 1.48862 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5085 | 0.891675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.1841 | −0.528744 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.98753 | −0.0860897 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.31619 | 0.402774 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.17106 | −0.395760 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −75.8665 | −3.26780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.64455 | −0.199685 | −0.0998423 | − | 0.995003i | \(-0.531834\pi\) | ||||
−0.0998423 | + | 0.995003i | \(0.531834\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.29025 | −0.0553700 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.14754 | −0.263332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.77503 | −0.375193 | −0.187597 | − | 0.982246i | \(-0.560070\pi\) | ||||
−0.187597 | + | 0.982246i | \(0.560070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.59168 | −0.366684 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0647592 | 0.00275884 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.8782 | 1.61075 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.58702 | −0.237156 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.7624 | 0.964475 | 0.482238 | − | 0.876040i | \(-0.339824\pi\) | ||||
0.482238 | + | 0.876040i | \(0.339824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.03516 | 0.128374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.9406 | −1.01077 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.5518 | −1.07688 | −0.538441 | − | 0.842664i | \(-0.680986\pi\) | ||||
−0.538441 | + | 0.842664i | \(0.680986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.0231 | 1.64171 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.5625 | 1.03153 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.2344 | 1.77056 | 0.885278 | − | 0.465062i | \(-0.153968\pi\) | ||||
0.885278 | + | 0.465062i | \(0.153968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.50536 | 0.355938 | 0.177969 | − | 0.984036i | \(-0.443047\pi\) | ||||
0.177969 | + | 0.984036i | \(0.443047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.3634 | −0.516489 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.41988 | −0.392836 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.547439 | −0.0227902 | −0.0113951 | − | 0.999935i | \(-0.503627\pi\) | ||||
−0.0113951 | + | 0.999935i | \(0.503627\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.54267 | −0.147228 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 59.9256 | 2.48613 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.81357 | −0.406436 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.21825 | 0.0503686 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.52515 | −0.351871 | −0.175935 | − | 0.984402i | \(-0.556295\pi\) | ||||
−0.175935 | + | 0.984402i | \(0.556295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.119833 | 0.00493763 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.89283 | 0.365802 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.7567 | 0.934504 | 0.467252 | − | 0.884124i | \(-0.345244\pi\) | ||||
0.467252 | + | 0.884124i | \(0.345244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 76.9148 | 3.15320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.34822 | −0.218888 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.10721 | −0.290393 | −0.145196 | − | 0.989403i | \(-0.546381\pi\) | ||||
−0.145196 | + | 0.989403i | \(0.546381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5116 | −0.510359 | −0.255180 | − | 0.966894i | \(-0.582135\pi\) | ||||
−0.255180 | + | 0.966894i | \(0.582135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.9838 | −1.26176 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.2345 | −0.538058 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.6990 | −1.04309 | −0.521545 | − | 0.853224i | \(-0.674644\pi\) | ||||
−0.521545 | + | 0.853224i | \(0.674644\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.80826 | 0.316407 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0250256 | 0.00101243 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.43544 | −0.138756 | −0.0693780 | − | 0.997590i | \(-0.522101\pi\) | ||||
−0.0693780 | + | 0.997590i | \(0.522101\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.1628 | −0.409804 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.1933 | −0.732436 | −0.366218 | − | 0.930529i | \(-0.619348\pi\) | ||||
−0.366218 | + | 0.930529i | \(0.619348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.9770 | 0.883329 | 0.441665 | − | 0.897180i | \(-0.354388\pi\) | ||||
0.441665 | + | 0.897180i | \(0.354388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.1884 | 1.01078 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.3893 | −0.536431 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.8200 | −0.632801 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0839506 | −0.00335266 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.8755 | 1.39058 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.6174 | −0.422670 | −0.211335 | − | 0.977414i | \(-0.567781\pi\) | ||||
−0.211335 | + | 0.977414i | \(0.567781\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.20510 | 0.0478986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.4280 | 0.890027 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.57060 | 0.181094 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.8296 | 1.14048 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1469 | −0.440274 | −0.220137 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220137 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.25517 | −0.246680 | −0.123340 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123340 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.5196 | 0.611084 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9942 | −0.510854 | −0.255427 | − | 0.966828i | \(-0.582216\pi\) | ||||
−0.255427 | + | 0.966828i | \(0.582216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.5004 | −0.804712 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.4487 | 0.566289 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.6494 | −1.43420 | −0.717100 | − | 0.696970i | \(-0.754531\pi\) | ||||
−0.717100 | + | 0.696970i | \(0.754531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4801 | −0.839296 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.2020 | 0.554071 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5912 | 1.19166 | 0.595831 | − | 0.803110i | \(-0.296823\pi\) | ||||
0.595831 | + | 0.803110i | \(0.296823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3480 | −1.10261 | −0.551305 | − | 0.834304i | \(-0.685870\pi\) | ||||
−0.551305 | + | 0.834304i | \(0.685870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.44231 | 0.0560147 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.269710 | 0.0104589 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.9304 | −0.578108 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.94255 | 0.113765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.4560 | −0.558067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9364 | 0.614304 | 0.307152 | − | 0.951661i | \(-0.400624\pi\) | ||||
0.307152 | + | 0.951661i | \(0.400624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.45346 | −0.209904 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.8347 | −1.06977 | −0.534887 | − | 0.844923i | \(-0.679646\pi\) | ||||
−0.534887 | + | 0.844923i | \(0.679646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.42409 | −0.323287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0012 | −0.536526 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.7950 | −1.48445 | −0.742225 | − | 0.670150i | \(-0.766230\pi\) | ||||
−0.742225 | + | 0.670150i | \(0.766230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.9921 | −1.41340 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.74331 | −0.104664 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.591221 | 0.0225237 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.98620 | −0.189684 | −0.0948420 | − | 0.995492i | \(-0.530235\pi\) | ||||
−0.0948420 | + | 0.995492i | \(0.530235\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 53.3698 | 2.02735 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.4221 | −0.888452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 63.4386 | 2.40291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.1011 | 0.457707 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.35330 | −0.126652 | −0.0633262 | − | 0.997993i | \(-0.520171\pi\) | ||||
−0.0633262 | + | 0.997993i | \(0.520171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.122295 | 0.00461244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.127962 | 0.00481934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 67.9302 | 2.55478 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8302 | −0.444291 | −0.222145 | − | 0.975014i | \(-0.571306\pi\) | ||||
−0.222145 | + | 0.975014i | \(0.571306\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.1495 | −0.718161 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.6278 | −1.03467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.04978 | 0.0766574 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.7904 | 0.589703 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0120 | 0.559853 | 0.279926 | − | 0.960021i | \(-0.409690\pi\) | ||||
0.279926 | + | 0.960021i | \(0.409690\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.5341 | 0.913696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.3500 | −0.719632 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.23253 | 0.120053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.4234 | 1.68466 | 0.842331 | − | 0.538961i | \(-0.181183\pi\) | ||||
0.842331 | + | 0.538961i | \(0.181183\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.49490 | −0.166478 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −96.8770 | −3.58313 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.7212 | −1.09778 | −0.548889 | − | 0.835895i | \(-0.684949\pi\) | ||||
−0.548889 | + | 0.835895i | \(0.684949\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.3707 | 0.862042 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −52.1320 | −1.92031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.4850 | 1.41569 | 0.707847 | − | 0.706366i | \(-0.249667\pi\) | ||||
0.707847 | + | 0.706366i | \(0.249667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.00505763 | 0.000185797 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2057 | 0.888022 | 0.444011 | − | 0.896021i | \(-0.353555\pi\) | ||||
0.444011 | + | 0.896021i | \(0.353555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.12643 | 0.261092 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.2956 | −1.10846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.5878 | −0.898418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.2266 | 0.409120 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.54794 | 0.0563354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.0242 | −1.85451 | −0.927253 | − | 0.374435i | \(-0.877837\pi\) | ||||
−0.927253 | + | 0.374435i | \(0.877837\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.3550 | 0.702543 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.22601 | 0.116943 | 0.0584715 | − | 0.998289i | \(-0.481377\pi\) | ||||
0.0584715 | + | 0.998289i | \(0.481377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.2249 | 0.587381 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.8845 | −1.40587 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.23505 | 0.0445952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.9237 | −1.61999 | −0.809994 | − | 0.586437i | \(-0.800530\pi\) | ||||
−0.809994 | + | 0.586437i | \(0.800530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.68623 | 0.204785 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.3400 | −1.63077 | −0.815384 | − | 0.578921i | \(-0.803474\pi\) | ||||
−0.815384 | + | 0.578921i | \(0.803474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.98160 | 0.214865 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.7456 | 0.528994 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.222455 | 0.00797027 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.5074 | 1.73573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.64367 | −0.308900 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.4753 | 1.48032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.44124 | −0.122667 | −0.0613334 | − | 0.998117i | \(-0.519535\pi\) | ||||
−0.0613334 | + | 0.998117i | \(0.519535\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.2612 | −0.400908 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −102.992 | −3.66197 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.870905 | 0.0309268 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.02307 | 0.107217 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.1118 | 0.889507 | 0.444754 | − | 0.895653i | \(-0.353291\pi\) | ||||
0.444754 | + | 0.895653i | \(0.353291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.798772 | −0.0282585 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.76900 | 0.239171 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.8956 | 0.843257 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −62.1824 | −2.19164 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.42373 | 0.261328 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.0871 | −1.40939 | −0.704693 | − | 0.709512i | \(-0.748915\pi\) | ||||
−0.704693 | + | 0.709512i | \(0.748915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.4538 | −0.999148 | −0.499574 | − | 0.866271i | \(-0.666510\pi\) | ||||
−0.499574 | + | 0.866271i | \(0.666510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.1344 | 0.425573 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.43034 | 0.295302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.339710 | −0.0118850 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.21528 | −0.112351 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5338 | 0.716636 | 0.358318 | − | 0.933600i | \(-0.383350\pi\) | ||||
0.358318 | + | 0.933600i | \(0.383350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3222 | −0.429526 | −0.214763 | − | 0.976666i | \(-0.568898\pi\) | ||||
−0.214763 | + | 0.976666i | \(0.568898\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.19049 | −0.145894 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.5681 | 1.51501 | 0.757505 | − | 0.652829i | \(-0.226418\pi\) | ||||
0.757505 | + | 0.652829i | \(0.226418\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.7521 | −0.894409 | −0.447204 | − | 0.894432i | \(-0.647580\pi\) | ||||
−0.447204 | + | 0.894432i | \(0.647580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.46022 | 0.328171 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −145.886 | −5.05464 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.41911 | 0.325962 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.9946 | −0.552853 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.2700 | 1.11408 | 0.557042 | − | 0.830484i | \(-0.311936\pi\) | ||||
0.557042 | + | 0.830484i | \(0.311936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8765 | −0.823327 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.64029 | −0.228704 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.4458 | 0.840962 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.9291 | 1.20018 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.4534 | −0.461719 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.1954 | −0.966526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.6516 | 1.56308 | 0.781540 | − | 0.623855i | \(-0.214434\pi\) | ||||
0.781540 | + | 0.623855i | \(0.214434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.136353 | −0.00466317 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7515 | −0.811336 | −0.405668 | − | 0.914020i | \(-0.632961\pi\) | ||||
−0.405668 | + | 0.914020i | \(0.632961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.30524 | −0.249252 | −0.124626 | − | 0.992204i | \(-0.539773\pi\) | ||||
−0.124626 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.8222 | 0.914098 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8543 | 1.35666 | 0.678329 | − | 0.734759i | \(-0.262705\pi\) | ||||
0.678329 | + | 0.734759i | \(0.262705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.9412 | −1.63005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.2793 | −1.16419 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.2200 | −1.09299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.14071 | 0.106419 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.25882 | 0.144139 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 60.5987 | 2.04861 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.1439 | 1.86208 | 0.931038 | − | 0.364922i | \(-0.118904\pi\) | ||||
0.931038 | + | 0.364922i | \(0.118904\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.22094 | −0.209827 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.8420 | −1.20755 | −0.603774 | − | 0.797156i | \(-0.706337\pi\) | ||||
−0.603774 | + | 0.797156i | \(0.706337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.0233 | −1.07767 | −0.538835 | − | 0.842411i | \(-0.681135\pi\) | ||||
−0.538835 | + | 0.842411i | \(0.681135\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.31516 | 0.212282 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.9790 | 1.00660 | 0.503298 | − | 0.864113i | \(-0.332120\pi\) | ||||
0.503298 | + | 0.864113i | \(0.332120\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.1931 | −1.98527 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.8934 | −0.699954 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.00280098 | −9.37314e−5 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.0628 | −0.837757 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.16605 | −0.0389332 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.48076 | 0.316201 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.8707 | −0.628676 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.9602 | −1.36307 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.52602 | −0.117209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.4473 | 0.512919 | 0.256460 | − | 0.966555i | \(-0.417444\pi\) | ||||
0.256460 | + | 0.966555i | \(0.417444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.3423 | −1.13906 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3375 | 0.905732 | 0.452866 | − | 0.891579i | \(-0.350402\pi\) | ||||
0.452866 | + | 0.891579i | \(0.350402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.9740 | −1.68699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.45317 | 0.147217 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 56.6913 | 1.87211 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.3324 | −0.769665 | −0.384833 | − | 0.922986i | \(-0.625741\pi\) | ||||
−0.384833 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8970 | −0.359068 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.92234 | −0.0961900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.10449 | 0.200714 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4033 | −0.407377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.6280 | −1.26734 | −0.633671 | − | 0.773602i | \(-0.718453\pi\) | ||||
−0.633671 | + | 0.773602i | \(0.718453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.511564 | −0.0167658 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.0839 | −0.526562 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −65.4254 | −2.13964 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.8195 | −1.82354 | −0.911772 | − | 0.410696i | \(-0.865286\pi\) | ||||
−0.911772 | + | 0.410696i | \(0.865286\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.3113 | −0.564933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.2474 | −1.27943 | −0.639714 | − | 0.768613i | \(-0.720947\pi\) | ||||
−0.639714 | + | 0.768613i | \(0.720947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51.2875 | −1.67015 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −35.9993 | −1.17106 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.4075 | 1.31307 | 0.656534 | − | 0.754297i | \(-0.272022\pi\) | ||||
0.656534 | + | 0.754297i | \(0.272022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.43960 | −0.0467313 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.6036 | −0.376273 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.6187 | −1.08902 | −0.544508 | − | 0.838756i | \(-0.683283\pi\) | ||||
−0.544508 | + | 0.838756i | \(0.683283\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.7869 | −1.09332 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.64188 | −0.214701 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 97.6316 | 3.15269 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4564 | −0.434079 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4304 | 0.400565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.68147 | −0.311658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.7754 | −1.34341 | −0.671704 | − | 0.740820i | \(-0.734437\pi\) | ||||
−0.671704 | + | 0.740820i | \(0.734437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.161431 | −0.00518590 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.9780 | 1.50760 | 0.753798 | − | 0.657107i | \(-0.228220\pi\) | ||||
0.753798 | + | 0.657107i | \(0.228220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 61.8169 | 1.98176 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.252457 | 0.00808511 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.7190 | 0.854816 | 0.427408 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427408 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3892 | 0.364001 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.20255 | −0.261887 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.71854 | 0.246183 | 0.123092 | − | 0.992395i | \(-0.460719\pi\) | ||||
0.123092 | + | 0.992395i | \(0.460719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.3025 | 0.774341 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.337725 | −0.0107499 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.3211 | 2.49047 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7678 | 1.45386 | 0.726931 | − | 0.686710i | \(-0.240946\pi\) | ||||
0.726931 | + | 0.686710i | \(0.240946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.44770 | 0.0776753 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.6157 | −0.463348 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.69495 | −0.275372 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.3232 | −0.516443 |
(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 | 6008.2.a.e.1.18 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.18 | ✓ | 50 | 1.1 | even | 1 | trivial |