Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(168\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59593 | −1.83560 | −0.917801 | − | 0.397041i | \(-0.870037\pi\) | ||||
−0.917801 | + | 0.397041i | \(0.870037\pi\) | |||||||
\(3\) | −2.11181 | −1.21926 | −0.609628 | − | 0.792688i | \(-0.708681\pi\) | ||||
−0.609628 | + | 0.792688i | \(0.708681\pi\) | |||||||
\(4\) | 4.73887 | 2.36943 | ||||||||
\(5\) | −0.212258 | −0.0949248 | −0.0474624 | − | 0.998873i | \(-0.515113\pi\) | ||||
−0.0474624 | + | 0.998873i | \(0.515113\pi\) | |||||||
\(6\) | 5.48213 | 2.23807 | ||||||||
\(7\) | 0.982044 | 0.371178 | 0.185589 | − | 0.982627i | \(-0.440581\pi\) | ||||
0.185589 | + | 0.982627i | \(0.440581\pi\) | |||||||
\(8\) | −7.10991 | −2.51373 | ||||||||
\(9\) | 1.45976 | 0.486585 | ||||||||
\(10\) | 0.551008 | 0.174244 | ||||||||
\(11\) | 5.95551 | 1.79565 | 0.897826 | − | 0.440350i | \(-0.145146\pi\) | ||||
0.897826 | + | 0.440350i | \(0.145146\pi\) | |||||||
\(12\) | −10.0076 | −2.88895 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.54932 | −0.681335 | ||||||||
\(15\) | 0.448250 | 0.115738 | ||||||||
\(16\) | 8.97913 | 2.24478 | ||||||||
\(17\) | 3.91829 | 0.950325 | 0.475162 | − | 0.879898i | \(-0.342389\pi\) | ||||
0.475162 | + | 0.879898i | \(0.342389\pi\) | |||||||
\(18\) | −3.78943 | −0.893177 | ||||||||
\(19\) | 0.758524 | 0.174017 | 0.0870087 | − | 0.996208i | \(-0.472269\pi\) | ||||
0.0870087 | + | 0.996208i | \(0.472269\pi\) | |||||||
\(20\) | −1.00586 | −0.224918 | ||||||||
\(21\) | −2.07389 | −0.452561 | ||||||||
\(22\) | −15.4601 | −3.29610 | ||||||||
\(23\) | −0.567071 | −0.118243 | −0.0591213 | − | 0.998251i | \(-0.518830\pi\) | ||||
−0.0591213 | + | 0.998251i | \(0.518830\pi\) | |||||||
\(24\) | 15.0148 | 3.06489 | ||||||||
\(25\) | −4.95495 | −0.990989 | ||||||||
\(26\) | −2.59593 | −0.509104 | ||||||||
\(27\) | 3.25271 | 0.625984 | ||||||||
\(28\) | 4.65378 | 0.879481 | ||||||||
\(29\) | −7.16674 | −1.33083 | −0.665415 | − | 0.746474i | \(-0.731745\pi\) | ||||
−0.665415 | + | 0.746474i | \(0.731745\pi\) | |||||||
\(30\) | −1.16363 | −0.212448 | ||||||||
\(31\) | 1.08405 | 0.194700 | 0.0973502 | − | 0.995250i | \(-0.468963\pi\) | ||||
0.0973502 | + | 0.995250i | \(0.468963\pi\) | |||||||
\(32\) | −9.08938 | −1.60679 | ||||||||
\(33\) | −12.5769 | −2.18936 | ||||||||
\(34\) | −10.1716 | −1.74442 | ||||||||
\(35\) | −0.208447 | −0.0352340 | ||||||||
\(36\) | 6.91759 | 1.15293 | ||||||||
\(37\) | −1.14642 | −0.188471 | −0.0942354 | − | 0.995550i | \(-0.530041\pi\) | ||||
−0.0942354 | + | 0.995550i | \(0.530041\pi\) | |||||||
\(38\) | −1.96908 | −0.319427 | ||||||||
\(39\) | −2.11181 | −0.338161 | ||||||||
\(40\) | 1.50914 | 0.238616 | ||||||||
\(41\) | −5.10519 | −0.797297 | −0.398648 | − | 0.917104i | \(-0.630521\pi\) | ||||
−0.398648 | + | 0.917104i | \(0.630521\pi\) | |||||||
\(42\) | 5.38369 | 0.830722 | ||||||||
\(43\) | 11.4748 | 1.74989 | 0.874947 | − | 0.484219i | \(-0.160896\pi\) | ||||
0.874947 | + | 0.484219i | \(0.160896\pi\) | |||||||
\(44\) | 28.2223 | 4.25468 | ||||||||
\(45\) | −0.309845 | −0.0461890 | ||||||||
\(46\) | 1.47208 | 0.217046 | ||||||||
\(47\) | −1.47661 | −0.215386 | −0.107693 | − | 0.994184i | \(-0.534346\pi\) | ||||
−0.107693 | + | 0.994184i | \(0.534346\pi\) | |||||||
\(48\) | −18.9622 | −2.73696 | ||||||||
\(49\) | −6.03559 | −0.862227 | ||||||||
\(50\) | 12.8627 | 1.81906 | ||||||||
\(51\) | −8.27470 | −1.15869 | ||||||||
\(52\) | 4.73887 | 0.657163 | ||||||||
\(53\) | 11.0659 | 1.52002 | 0.760011 | − | 0.649910i | \(-0.225193\pi\) | ||||
0.760011 | + | 0.649910i | \(0.225193\pi\) | |||||||
\(54\) | −8.44381 | −1.14906 | ||||||||
\(55\) | −1.26411 | −0.170452 | ||||||||
\(56\) | −6.98225 | −0.933043 | ||||||||
\(57\) | −1.60186 | −0.212172 | ||||||||
\(58\) | 18.6044 | 2.44287 | ||||||||
\(59\) | 6.24324 | 0.812800 | 0.406400 | − | 0.913695i | \(-0.366784\pi\) | ||||
0.406400 | + | 0.913695i | \(0.366784\pi\) | |||||||
\(60\) | 2.12420 | 0.274233 | ||||||||
\(61\) | 6.94738 | 0.889520 | 0.444760 | − | 0.895650i | \(-0.353289\pi\) | ||||
0.444760 | + | 0.895650i | \(0.353289\pi\) | |||||||
\(62\) | −2.81411 | −0.357392 | ||||||||
\(63\) | 1.43355 | 0.180610 | ||||||||
\(64\) | 5.63716 | 0.704646 | ||||||||
\(65\) | −0.212258 | −0.0263274 | ||||||||
\(66\) | 32.6488 | 4.01879 | ||||||||
\(67\) | 7.94727 | 0.970914 | 0.485457 | − | 0.874261i | \(-0.338653\pi\) | ||||
0.485457 | + | 0.874261i | \(0.338653\pi\) | |||||||
\(68\) | 18.5683 | 2.25173 | ||||||||
\(69\) | 1.19755 | 0.144168 | ||||||||
\(70\) | 0.541115 | 0.0646756 | ||||||||
\(71\) | 5.45408 | 0.647280 | 0.323640 | − | 0.946180i | \(-0.395093\pi\) | ||||
0.323640 | + | 0.946180i | \(0.395093\pi\) | |||||||
\(72\) | −10.3787 | −1.22315 | ||||||||
\(73\) | −5.30789 | −0.621242 | −0.310621 | − | 0.950534i | \(-0.600537\pi\) | ||||
−0.310621 | + | 0.950534i | \(0.600537\pi\) | |||||||
\(74\) | 2.97604 | 0.345957 | ||||||||
\(75\) | 10.4639 | 1.20827 | ||||||||
\(76\) | 3.59455 | 0.412323 | ||||||||
\(77\) | 5.84857 | 0.666507 | ||||||||
\(78\) | 5.48213 | 0.620728 | ||||||||
\(79\) | −13.4571 | −1.51405 | −0.757023 | − | 0.653389i | \(-0.773347\pi\) | ||||
−0.757023 | + | 0.653389i | \(0.773347\pi\) | |||||||
\(80\) | −1.90589 | −0.213085 | ||||||||
\(81\) | −11.2484 | −1.24982 | ||||||||
\(82\) | 13.2527 | 1.46352 | ||||||||
\(83\) | 10.1226 | 1.11110 | 0.555549 | − | 0.831484i | \(-0.312508\pi\) | ||||
0.555549 | + | 0.831484i | \(0.312508\pi\) | |||||||
\(84\) | −9.82791 | −1.07231 | ||||||||
\(85\) | −0.831690 | −0.0902094 | ||||||||
\(86\) | −29.7879 | −3.21211 | ||||||||
\(87\) | 15.1348 | 1.62262 | ||||||||
\(88\) | −42.3431 | −4.51379 | ||||||||
\(89\) | 0.0604180 | 0.00640429 | 0.00320215 | − | 0.999995i | \(-0.498981\pi\) | ||||
0.00320215 | + | 0.999995i | \(0.498981\pi\) | |||||||
\(90\) | 0.804338 | 0.0847846 | ||||||||
\(91\) | 0.982044 | 0.102946 | ||||||||
\(92\) | −2.68728 | −0.280168 | ||||||||
\(93\) | −2.28930 | −0.237390 | ||||||||
\(94\) | 3.83319 | 0.395363 | ||||||||
\(95\) | −0.161003 | −0.0165186 | ||||||||
\(96\) | 19.1951 | 1.95909 | ||||||||
\(97\) | 5.01786 | 0.509487 | 0.254743 | − | 0.967009i | \(-0.418009\pi\) | ||||
0.254743 | + | 0.967009i | \(0.418009\pi\) | |||||||
\(98\) | 15.6680 | 1.58271 | ||||||||
\(99\) | 8.69358 | 0.873738 | ||||||||
\(100\) | −23.4808 | −2.34808 | ||||||||
\(101\) | −8.65114 | −0.860821 | −0.430410 | − | 0.902633i | \(-0.641631\pi\) | ||||
−0.430410 | + | 0.902633i | \(0.641631\pi\) | |||||||
\(102\) | 21.4806 | 2.12689 | ||||||||
\(103\) | 3.43622 | 0.338581 | 0.169291 | − | 0.985566i | \(-0.445852\pi\) | ||||
0.169291 | + | 0.985566i | \(0.445852\pi\) | |||||||
\(104\) | −7.10991 | −0.697184 | ||||||||
\(105\) | 0.440201 | 0.0429593 | ||||||||
\(106\) | −28.7264 | −2.79016 | ||||||||
\(107\) | 3.69234 | 0.356952 | 0.178476 | − | 0.983944i | \(-0.442883\pi\) | ||||
0.178476 | + | 0.983944i | \(0.442883\pi\) | |||||||
\(108\) | 15.4142 | 1.48323 | ||||||||
\(109\) | −14.8541 | −1.42277 | −0.711384 | − | 0.702804i | \(-0.751931\pi\) | ||||
−0.711384 | + | 0.702804i | \(0.751931\pi\) | |||||||
\(110\) | 3.28153 | 0.312882 | ||||||||
\(111\) | 2.42103 | 0.229794 | ||||||||
\(112\) | 8.81790 | 0.833213 | ||||||||
\(113\) | −8.18130 | −0.769632 | −0.384816 | − | 0.922993i | \(-0.625735\pi\) | ||||
−0.384816 | + | 0.922993i | \(0.625735\pi\) | |||||||
\(114\) | 4.15833 | 0.389463 | ||||||||
\(115\) | 0.120366 | 0.0112242 | ||||||||
\(116\) | −33.9622 | −3.15331 | ||||||||
\(117\) | 1.45976 | 0.134954 | ||||||||
\(118\) | −16.2070 | −1.49198 | ||||||||
\(119\) | 3.84793 | 0.352740 | ||||||||
\(120\) | −3.18702 | −0.290934 | ||||||||
\(121\) | 24.4680 | 2.22437 | ||||||||
\(122\) | −18.0349 | −1.63281 | ||||||||
\(123\) | 10.7812 | 0.972109 | ||||||||
\(124\) | 5.13715 | 0.461330 | ||||||||
\(125\) | 2.11302 | 0.188994 | ||||||||
\(126\) | −3.72139 | −0.331527 | ||||||||
\(127\) | −3.49070 | −0.309749 | −0.154875 | − | 0.987934i | \(-0.549497\pi\) | ||||
−0.154875 | + | 0.987934i | \(0.549497\pi\) | |||||||
\(128\) | 3.54506 | 0.313342 | ||||||||
\(129\) | −24.2327 | −2.13357 | ||||||||
\(130\) | 0.551008 | 0.0483266 | ||||||||
\(131\) | 21.9797 | 1.92038 | 0.960188 | − | 0.279355i | \(-0.0901206\pi\) | ||||
0.960188 | + | 0.279355i | \(0.0901206\pi\) | |||||||
\(132\) | −59.6003 | −5.18754 | ||||||||
\(133\) | 0.744905 | 0.0645914 | ||||||||
\(134\) | −20.6306 | −1.78221 | ||||||||
\(135\) | −0.690414 | −0.0594214 | ||||||||
\(136\) | −27.8587 | −2.38886 | ||||||||
\(137\) | 14.3449 | 1.22557 | 0.612785 | − | 0.790249i | \(-0.290049\pi\) | ||||
0.612785 | + | 0.790249i | \(0.290049\pi\) | |||||||
\(138\) | −3.10876 | −0.264635 | ||||||||
\(139\) | 20.2106 | 1.71424 | 0.857122 | − | 0.515114i | \(-0.172250\pi\) | ||||
0.857122 | + | 0.515114i | \(0.172250\pi\) | |||||||
\(140\) | −0.987803 | −0.0834846 | ||||||||
\(141\) | 3.11833 | 0.262611 | ||||||||
\(142\) | −14.1584 | −1.18815 | ||||||||
\(143\) | 5.95551 | 0.498024 | ||||||||
\(144\) | 13.1073 | 1.09228 | ||||||||
\(145\) | 1.52120 | 0.126329 | ||||||||
\(146\) | 13.7789 | 1.14035 | ||||||||
\(147\) | 12.7460 | 1.05128 | ||||||||
\(148\) | −5.43274 | −0.446569 | ||||||||
\(149\) | 20.0144 | 1.63965 | 0.819823 | − | 0.572617i | \(-0.194072\pi\) | ||||
0.819823 | + | 0.572617i | \(0.194072\pi\) | |||||||
\(150\) | −27.1636 | −2.21790 | ||||||||
\(151\) | −4.07723 | −0.331800 | −0.165900 | − | 0.986143i | \(-0.553053\pi\) | ||||
−0.165900 | + | 0.986143i | \(0.553053\pi\) | |||||||
\(152\) | −5.39304 | −0.437434 | ||||||||
\(153\) | 5.71975 | 0.462414 | ||||||||
\(154\) | −15.1825 | −1.22344 | ||||||||
\(155\) | −0.230098 | −0.0184819 | ||||||||
\(156\) | −10.0076 | −0.801249 | ||||||||
\(157\) | −0.543734 | −0.0433947 | −0.0216973 | − | 0.999765i | \(-0.506907\pi\) | ||||
−0.0216973 | + | 0.999765i | \(0.506907\pi\) | |||||||
\(158\) | 34.9338 | 2.77918 | ||||||||
\(159\) | −23.3692 | −1.85330 | ||||||||
\(160\) | 1.92930 | 0.152524 | ||||||||
\(161\) | −0.556889 | −0.0438890 | ||||||||
\(162\) | 29.2000 | 2.29417 | ||||||||
\(163\) | 11.6629 | 0.913508 | 0.456754 | − | 0.889593i | \(-0.349012\pi\) | ||||
0.456754 | + | 0.889593i | \(0.349012\pi\) | |||||||
\(164\) | −24.1928 | −1.88914 | ||||||||
\(165\) | 2.66956 | 0.207825 | ||||||||
\(166\) | −26.2776 | −2.03953 | ||||||||
\(167\) | 6.07425 | 0.470039 | 0.235020 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235020 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(168\) | 14.7452 | 1.13762 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.15901 | 0.165589 | ||||||||
\(171\) | 1.10726 | 0.0846743 | ||||||||
\(172\) | 54.3777 | 4.14626 | ||||||||
\(173\) | −18.3402 | −1.39438 | −0.697191 | − | 0.716886i | \(-0.745567\pi\) | ||||
−0.697191 | + | 0.716886i | \(0.745567\pi\) | |||||||
\(174\) | −39.2890 | −2.97849 | ||||||||
\(175\) | −4.86598 | −0.367833 | ||||||||
\(176\) | 53.4752 | 4.03085 | ||||||||
\(177\) | −13.1846 | −0.991012 | ||||||||
\(178\) | −0.156841 | −0.0117557 | ||||||||
\(179\) | 4.73828 | 0.354155 | 0.177078 | − | 0.984197i | \(-0.443336\pi\) | ||||
0.177078 | + | 0.984197i | \(0.443336\pi\) | |||||||
\(180\) | −1.46832 | −0.109442 | ||||||||
\(181\) | 2.71067 | 0.201482 | 0.100741 | − | 0.994913i | \(-0.467879\pi\) | ||||
0.100741 | + | 0.994913i | \(0.467879\pi\) | |||||||
\(182\) | −2.54932 | −0.188968 | ||||||||
\(183\) | −14.6716 | −1.08455 | ||||||||
\(184\) | 4.03183 | 0.297230 | ||||||||
\(185\) | 0.243338 | 0.0178905 | ||||||||
\(186\) | 5.94288 | 0.435753 | ||||||||
\(187\) | 23.3354 | 1.70645 | ||||||||
\(188\) | −6.99748 | −0.510344 | ||||||||
\(189\) | 3.19430 | 0.232351 | ||||||||
\(190\) | 0.417953 | 0.0303215 | ||||||||
\(191\) | 3.66012 | 0.264837 | 0.132418 | − | 0.991194i | \(-0.457726\pi\) | ||||
0.132418 | + | 0.991194i | \(0.457726\pi\) | |||||||
\(192\) | −11.9046 | −0.859143 | ||||||||
\(193\) | 6.31340 | 0.454448 | 0.227224 | − | 0.973842i | \(-0.427035\pi\) | ||||
0.227224 | + | 0.973842i | \(0.427035\pi\) | |||||||
\(194\) | −13.0260 | −0.935215 | ||||||||
\(195\) | 0.448250 | 0.0320998 | ||||||||
\(196\) | −28.6019 | −2.04299 | ||||||||
\(197\) | 12.8232 | 0.913618 | 0.456809 | − | 0.889565i | \(-0.348992\pi\) | ||||
0.456809 | + | 0.889565i | \(0.348992\pi\) | |||||||
\(198\) | −22.5680 | −1.60383 | ||||||||
\(199\) | −21.8014 | −1.54546 | −0.772731 | − | 0.634733i | \(-0.781110\pi\) | ||||
−0.772731 | + | 0.634733i | \(0.781110\pi\) | |||||||
\(200\) | 35.2292 | 2.49108 | ||||||||
\(201\) | −16.7832 | −1.18379 | ||||||||
\(202\) | 22.4578 | 1.58012 | ||||||||
\(203\) | −7.03806 | −0.493975 | ||||||||
\(204\) | −39.2127 | −2.74544 | ||||||||
\(205\) | 1.08362 | 0.0756832 | ||||||||
\(206\) | −8.92021 | −0.621500 | ||||||||
\(207\) | −0.827786 | −0.0575351 | ||||||||
\(208\) | 8.97913 | 0.622590 | ||||||||
\(209\) | 4.51740 | 0.312475 | ||||||||
\(210\) | −1.14273 | −0.0788561 | ||||||||
\(211\) | −20.7232 | −1.42664 | −0.713322 | − | 0.700836i | \(-0.752810\pi\) | ||||
−0.713322 | + | 0.700836i | \(0.752810\pi\) | |||||||
\(212\) | 52.4400 | 3.60159 | ||||||||
\(213\) | −11.5180 | −0.789200 | ||||||||
\(214\) | −9.58507 | −0.655222 | ||||||||
\(215\) | −2.43563 | −0.166108 | ||||||||
\(216\) | −23.1265 | −1.57356 | ||||||||
\(217\) | 1.06458 | 0.0722685 | ||||||||
\(218\) | 38.5603 | 2.61164 | ||||||||
\(219\) | 11.2093 | 0.757452 | ||||||||
\(220\) | −5.99043 | −0.403875 | ||||||||
\(221\) | 3.91829 | 0.263573 | ||||||||
\(222\) | −6.28483 | −0.421810 | ||||||||
\(223\) | 2.05448 | 0.137578 | 0.0687890 | − | 0.997631i | \(-0.478086\pi\) | ||||
0.0687890 | + | 0.997631i | \(0.478086\pi\) | |||||||
\(224\) | −8.92617 | −0.596405 | ||||||||
\(225\) | −7.23301 | −0.482201 | ||||||||
\(226\) | 21.2381 | 1.41274 | ||||||||
\(227\) | 3.44064 | 0.228363 | 0.114182 | − | 0.993460i | \(-0.463575\pi\) | ||||
0.114182 | + | 0.993460i | \(0.463575\pi\) | |||||||
\(228\) | −7.59101 | −0.502727 | ||||||||
\(229\) | 1.41176 | 0.0932918 | 0.0466459 | − | 0.998911i | \(-0.485147\pi\) | ||||
0.0466459 | + | 0.998911i | \(0.485147\pi\) | |||||||
\(230\) | −0.312461 | −0.0206031 | ||||||||
\(231\) | −12.3511 | −0.812642 | ||||||||
\(232\) | 50.9549 | 3.34535 | ||||||||
\(233\) | 25.4986 | 1.67047 | 0.835234 | − | 0.549894i | \(-0.185332\pi\) | ||||
0.835234 | + | 0.549894i | \(0.185332\pi\) | |||||||
\(234\) | −3.78943 | −0.247723 | ||||||||
\(235\) | 0.313424 | 0.0204455 | ||||||||
\(236\) | 29.5859 | 1.92588 | ||||||||
\(237\) | 28.4189 | 1.84601 | ||||||||
\(238\) | −9.98898 | −0.647489 | ||||||||
\(239\) | −27.6219 | −1.78671 | −0.893357 | − | 0.449348i | \(-0.851656\pi\) | ||||
−0.893357 | + | 0.449348i | \(0.851656\pi\) | |||||||
\(240\) | 4.02489 | 0.259806 | ||||||||
\(241\) | −8.85500 | −0.570401 | −0.285200 | − | 0.958468i | \(-0.592060\pi\) | ||||
−0.285200 | + | 0.958468i | \(0.592060\pi\) | |||||||
\(242\) | −63.5174 | −4.08305 | ||||||||
\(243\) | 13.9964 | 0.897867 | ||||||||
\(244\) | 32.9227 | 2.10766 | ||||||||
\(245\) | 1.28110 | 0.0818467 | ||||||||
\(246\) | −27.9873 | −1.78440 | ||||||||
\(247\) | 0.758524 | 0.0482638 | ||||||||
\(248\) | −7.70748 | −0.489425 | ||||||||
\(249\) | −21.3770 | −1.35471 | ||||||||
\(250\) | −5.48526 | −0.346918 | ||||||||
\(251\) | 28.6762 | 1.81003 | 0.905013 | − | 0.425384i | \(-0.139861\pi\) | ||||
0.905013 | + | 0.425384i | \(0.139861\pi\) | |||||||
\(252\) | 6.79338 | 0.427943 | ||||||||
\(253\) | −3.37720 | −0.212323 | ||||||||
\(254\) | 9.06162 | 0.568577 | ||||||||
\(255\) | 1.75637 | 0.109988 | ||||||||
\(256\) | −20.4771 | −1.27982 | ||||||||
\(257\) | 11.1245 | 0.693927 | 0.346963 | − | 0.937879i | \(-0.387213\pi\) | ||||
0.346963 | + | 0.937879i | \(0.387213\pi\) | |||||||
\(258\) | 62.9064 | 3.91638 | ||||||||
\(259\) | −1.12584 | −0.0699562 | ||||||||
\(260\) | −1.00586 | −0.0623810 | ||||||||
\(261\) | −10.4617 | −0.647562 | ||||||||
\(262\) | −57.0578 | −3.52505 | ||||||||
\(263\) | −21.5525 | −1.32899 | −0.664493 | − | 0.747295i | \(-0.731352\pi\) | ||||
−0.664493 | + | 0.747295i | \(0.731352\pi\) | |||||||
\(264\) | 89.4208 | 5.50347 | ||||||||
\(265\) | −2.34884 | −0.144288 | ||||||||
\(266\) | −1.93372 | −0.118564 | ||||||||
\(267\) | −0.127591 | −0.00780847 | ||||||||
\(268\) | 37.6611 | 2.30052 | ||||||||
\(269\) | −13.6804 | −0.834108 | −0.417054 | − | 0.908882i | \(-0.636937\pi\) | ||||
−0.417054 | + | 0.908882i | \(0.636937\pi\) | |||||||
\(270\) | 1.79227 | 0.109074 | ||||||||
\(271\) | −15.9341 | −0.967928 | −0.483964 | − | 0.875088i | \(-0.660803\pi\) | ||||
−0.483964 | + | 0.875088i | \(0.660803\pi\) | |||||||
\(272\) | 35.1828 | 2.13327 | ||||||||
\(273\) | −2.07389 | −0.125518 | ||||||||
\(274\) | −37.2385 | −2.24966 | ||||||||
\(275\) | −29.5092 | −1.77947 | ||||||||
\(276\) | 5.67503 | 0.341596 | ||||||||
\(277\) | −28.8414 | −1.73291 | −0.866455 | − | 0.499255i | \(-0.833607\pi\) | ||||
−0.866455 | + | 0.499255i | \(0.833607\pi\) | |||||||
\(278\) | −52.4655 | −3.14667 | ||||||||
\(279\) | 1.58244 | 0.0947384 | ||||||||
\(280\) | 1.48204 | 0.0885689 | ||||||||
\(281\) | −12.1811 | −0.726662 | −0.363331 | − | 0.931660i | \(-0.618361\pi\) | ||||
−0.363331 | + | 0.931660i | \(0.618361\pi\) | |||||||
\(282\) | −8.09498 | −0.482049 | ||||||||
\(283\) | −25.7489 | −1.53061 | −0.765306 | − | 0.643667i | \(-0.777412\pi\) | ||||
−0.765306 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(284\) | 25.8461 | 1.53369 | ||||||||
\(285\) | 0.340009 | 0.0201404 | ||||||||
\(286\) | −15.4601 | −0.914174 | ||||||||
\(287\) | −5.01352 | −0.295939 | ||||||||
\(288\) | −13.2683 | −0.781840 | ||||||||
\(289\) | −1.64701 | −0.0968828 | ||||||||
\(290\) | −3.94893 | −0.231889 | ||||||||
\(291\) | −10.5968 | −0.621195 | ||||||||
\(292\) | −25.1534 | −1.47199 | ||||||||
\(293\) | −11.2296 | −0.656040 | −0.328020 | − | 0.944671i | \(-0.606381\pi\) | ||||
−0.328020 | + | 0.944671i | \(0.606381\pi\) | |||||||
\(294\) | −33.0879 | −1.92972 | ||||||||
\(295\) | −1.32518 | −0.0771549 | ||||||||
\(296\) | 8.15097 | 0.473765 | ||||||||
\(297\) | 19.3715 | 1.12405 | ||||||||
\(298\) | −51.9561 | −3.00974 | ||||||||
\(299\) | −0.567071 | −0.0327946 | ||||||||
\(300\) | 49.5871 | 2.86291 | ||||||||
\(301\) | 11.2688 | 0.649522 | ||||||||
\(302\) | 10.5842 | 0.609053 | ||||||||
\(303\) | 18.2696 | 1.04956 | ||||||||
\(304\) | 6.81089 | 0.390631 | ||||||||
\(305\) | −1.47464 | −0.0844375 | ||||||||
\(306\) | −14.8481 | −0.848808 | ||||||||
\(307\) | −32.0278 | −1.82792 | −0.913962 | − | 0.405800i | \(-0.866993\pi\) | ||||
−0.913962 | + | 0.405800i | \(0.866993\pi\) | |||||||
\(308\) | 27.7156 | 1.57924 | ||||||||
\(309\) | −7.25667 | −0.412817 | ||||||||
\(310\) | 0.597319 | 0.0339254 | ||||||||
\(311\) | −18.2853 | −1.03687 | −0.518433 | − | 0.855118i | \(-0.673484\pi\) | ||||
−0.518433 | + | 0.855118i | \(0.673484\pi\) | |||||||
\(312\) | 15.0148 | 0.850046 | ||||||||
\(313\) | 11.3189 | 0.639785 | 0.319892 | − | 0.947454i | \(-0.396353\pi\) | ||||
0.319892 | + | 0.947454i | \(0.396353\pi\) | |||||||
\(314\) | 1.41150 | 0.0796554 | ||||||||
\(315\) | −0.304282 | −0.0171443 | ||||||||
\(316\) | −63.7715 | −3.58743 | ||||||||
\(317\) | 13.2211 | 0.742571 | 0.371286 | − | 0.928519i | \(-0.378917\pi\) | ||||
0.371286 | + | 0.928519i | \(0.378917\pi\) | |||||||
\(318\) | 60.6648 | 3.40191 | ||||||||
\(319\) | −42.6815 | −2.38971 | ||||||||
\(320\) | −1.19654 | −0.0668883 | ||||||||
\(321\) | −7.79754 | −0.435216 | ||||||||
\(322\) | 1.44565 | 0.0805628 | ||||||||
\(323\) | 2.97212 | 0.165373 | ||||||||
\(324\) | −53.3046 | −2.96137 | ||||||||
\(325\) | −4.95495 | −0.274851 | ||||||||
\(326\) | −30.2761 | −1.67684 | ||||||||
\(327\) | 31.3692 | 1.73472 | ||||||||
\(328\) | 36.2975 | 2.00419 | ||||||||
\(329\) | −1.45010 | −0.0799466 | ||||||||
\(330\) | −6.92999 | −0.381483 | ||||||||
\(331\) | 17.7265 | 0.974338 | 0.487169 | − | 0.873308i | \(-0.338030\pi\) | ||||
0.487169 | + | 0.873308i | \(0.338030\pi\) | |||||||
\(332\) | 47.9696 | 2.63267 | ||||||||
\(333\) | −1.67350 | −0.0917071 | ||||||||
\(334\) | −15.7683 | −0.862805 | ||||||||
\(335\) | −1.68687 | −0.0921638 | ||||||||
\(336\) | −18.6218 | −1.01590 | ||||||||
\(337\) | 26.7991 | 1.45984 | 0.729921 | − | 0.683531i | \(-0.239557\pi\) | ||||
0.729921 | + | 0.683531i | \(0.239557\pi\) | |||||||
\(338\) | −2.59593 | −0.141200 | ||||||||
\(339\) | 17.2774 | 0.938378 | ||||||||
\(340\) | −3.94127 | −0.213745 | ||||||||
\(341\) | 6.45604 | 0.349614 | ||||||||
\(342\) | −2.87437 | −0.155428 | ||||||||
\(343\) | −12.8015 | −0.691218 | ||||||||
\(344\) | −81.5850 | −4.39877 | ||||||||
\(345\) | −0.254190 | −0.0136851 | ||||||||
\(346\) | 47.6100 | 2.55953 | ||||||||
\(347\) | 18.8462 | 1.01172 | 0.505859 | − | 0.862616i | \(-0.331176\pi\) | ||||
0.505859 | + | 0.862616i | \(0.331176\pi\) | |||||||
\(348\) | 71.7219 | 3.84470 | ||||||||
\(349\) | 25.1581 | 1.34668 | 0.673341 | − | 0.739332i | \(-0.264859\pi\) | ||||
0.673341 | + | 0.739332i | \(0.264859\pi\) | |||||||
\(350\) | 12.6318 | 0.675196 | ||||||||
\(351\) | 3.25271 | 0.173617 | ||||||||
\(352\) | −54.1318 | −2.88524 | ||||||||
\(353\) | 6.14325 | 0.326972 | 0.163486 | − | 0.986546i | \(-0.447726\pi\) | ||||
0.163486 | + | 0.986546i | \(0.447726\pi\) | |||||||
\(354\) | 34.2262 | 1.81910 | ||||||||
\(355\) | −1.15767 | −0.0614429 | ||||||||
\(356\) | 0.286313 | 0.0151745 | ||||||||
\(357\) | −8.12612 | −0.430080 | ||||||||
\(358\) | −12.3002 | −0.650088 | ||||||||
\(359\) | 35.1218 | 1.85366 | 0.926829 | − | 0.375484i | \(-0.122523\pi\) | ||||
0.926829 | + | 0.375484i | \(0.122523\pi\) | |||||||
\(360\) | 2.20297 | 0.116107 | ||||||||
\(361\) | −18.4246 | −0.969718 | ||||||||
\(362\) | −7.03671 | −0.369841 | ||||||||
\(363\) | −51.6719 | −2.71207 | ||||||||
\(364\) | 4.65378 | 0.243924 | ||||||||
\(365\) | 1.12664 | 0.0589712 | ||||||||
\(366\) | 38.0864 | 1.99081 | ||||||||
\(367\) | 37.0472 | 1.93385 | 0.966923 | − | 0.255068i | \(-0.0820977\pi\) | ||||
0.966923 | + | 0.255068i | \(0.0820977\pi\) | |||||||
\(368\) | −5.09181 | −0.265429 | ||||||||
\(369\) | −7.45233 | −0.387953 | ||||||||
\(370\) | −0.631688 | −0.0328399 | ||||||||
\(371\) | 10.8672 | 0.564199 | ||||||||
\(372\) | −10.8487 | −0.562479 | ||||||||
\(373\) | 15.8011 | 0.818151 | 0.409076 | − | 0.912500i | \(-0.365851\pi\) | ||||
0.409076 | + | 0.912500i | \(0.365851\pi\) | |||||||
\(374\) | −60.5771 | −3.13237 | ||||||||
\(375\) | −4.46230 | −0.230432 | ||||||||
\(376\) | 10.4986 | 0.541424 | ||||||||
\(377\) | −7.16674 | −0.369106 | ||||||||
\(378\) | −8.29220 | −0.426505 | ||||||||
\(379\) | −7.85370 | −0.403418 | −0.201709 | − | 0.979446i | \(-0.564649\pi\) | ||||
−0.201709 | + | 0.979446i | \(0.564649\pi\) | |||||||
\(380\) | −0.762972 | −0.0391397 | ||||||||
\(381\) | 7.37170 | 0.377664 | ||||||||
\(382\) | −9.50142 | −0.486135 | ||||||||
\(383\) | −30.9635 | −1.58216 | −0.791081 | − | 0.611712i | \(-0.790481\pi\) | ||||
−0.791081 | + | 0.611712i | \(0.790481\pi\) | |||||||
\(384\) | −7.48650 | −0.382044 | ||||||||
\(385\) | −1.24141 | −0.0632680 | ||||||||
\(386\) | −16.3892 | −0.834186 | ||||||||
\(387\) | 16.7504 | 0.851473 | ||||||||
\(388\) | 23.7790 | 1.20719 | ||||||||
\(389\) | 18.9823 | 0.962439 | 0.481219 | − | 0.876600i | \(-0.340194\pi\) | ||||
0.481219 | + | 0.876600i | \(0.340194\pi\) | |||||||
\(390\) | −1.16363 | −0.0589225 | ||||||||
\(391\) | −2.22195 | −0.112369 | ||||||||
\(392\) | 42.9125 | 2.16741 | ||||||||
\(393\) | −46.4170 | −2.34143 | ||||||||
\(394\) | −33.2883 | −1.67704 | ||||||||
\(395\) | 2.85639 | 0.143720 | ||||||||
\(396\) | 41.1977 | 2.07026 | ||||||||
\(397\) | −34.6265 | −1.73785 | −0.868926 | − | 0.494942i | \(-0.835189\pi\) | ||||
−0.868926 | + | 0.494942i | \(0.835189\pi\) | |||||||
\(398\) | 56.5951 | 2.83685 | ||||||||
\(399\) | −1.57310 | −0.0787535 | ||||||||
\(400\) | −44.4911 | −2.22455 | ||||||||
\(401\) | −32.7088 | −1.63340 | −0.816701 | − | 0.577062i | \(-0.804199\pi\) | ||||
−0.816701 | + | 0.577062i | \(0.804199\pi\) | |||||||
\(402\) | 43.5679 | 2.17297 | ||||||||
\(403\) | 1.08405 | 0.0540002 | ||||||||
\(404\) | −40.9966 | −2.03966 | ||||||||
\(405\) | 2.38756 | 0.118639 | ||||||||
\(406\) | 18.2703 | 0.906741 | ||||||||
\(407\) | −6.82753 | −0.338428 | ||||||||
\(408\) | 58.8324 | 2.91264 | ||||||||
\(409\) | −14.5354 | −0.718730 | −0.359365 | − | 0.933197i | \(-0.617007\pi\) | ||||
−0.359365 | + | 0.933197i | \(0.617007\pi\) | |||||||
\(410\) | −2.81300 | −0.138924 | ||||||||
\(411\) | −30.2938 | −1.49428 | ||||||||
\(412\) | 16.2838 | 0.802246 | ||||||||
\(413\) | 6.13114 | 0.301694 | ||||||||
\(414\) | 2.14888 | 0.105611 | ||||||||
\(415\) | −2.14860 | −0.105471 | ||||||||
\(416\) | −9.08938 | −0.445643 | ||||||||
\(417\) | −42.6811 | −2.09010 | ||||||||
\(418\) | −11.7269 | −0.573579 | ||||||||
\(419\) | −22.1553 | −1.08236 | −0.541179 | − | 0.840907i | \(-0.682022\pi\) | ||||
−0.541179 | + | 0.840907i | \(0.682022\pi\) | |||||||
\(420\) | 2.08606 | 0.101789 | ||||||||
\(421\) | −18.8034 | −0.916420 | −0.458210 | − | 0.888844i | \(-0.651509\pi\) | ||||
−0.458210 | + | 0.888844i | \(0.651509\pi\) | |||||||
\(422\) | 53.7960 | 2.61875 | ||||||||
\(423\) | −2.15550 | −0.104804 | ||||||||
\(424\) | −78.6778 | −3.82093 | ||||||||
\(425\) | −19.4149 | −0.941762 | ||||||||
\(426\) | 29.8999 | 1.44866 | ||||||||
\(427\) | 6.82263 | 0.330170 | ||||||||
\(428\) | 17.4975 | 0.845775 | ||||||||
\(429\) | −12.5769 | −0.607219 | ||||||||
\(430\) | 6.32272 | 0.304909 | ||||||||
\(431\) | 30.7966 | 1.48342 | 0.741710 | − | 0.670721i | \(-0.234015\pi\) | ||||
0.741710 | + | 0.670721i | \(0.234015\pi\) | |||||||
\(432\) | 29.2065 | 1.40520 | ||||||||
\(433\) | −26.5124 | −1.27411 | −0.637053 | − | 0.770820i | \(-0.719847\pi\) | ||||
−0.637053 | + | 0.770820i | \(0.719847\pi\) | |||||||
\(434\) | −2.76358 | −0.132656 | ||||||||
\(435\) | −3.21249 | −0.154027 | ||||||||
\(436\) | −70.3918 | −3.37115 | ||||||||
\(437\) | −0.430137 | −0.0205763 | ||||||||
\(438\) | −29.0985 | −1.39038 | ||||||||
\(439\) | 18.9193 | 0.902971 | 0.451486 | − | 0.892278i | \(-0.350894\pi\) | ||||
0.451486 | + | 0.892278i | \(0.350894\pi\) | |||||||
\(440\) | 8.98768 | 0.428471 | ||||||||
\(441\) | −8.81049 | −0.419547 | ||||||||
\(442\) | −10.1716 | −0.483814 | ||||||||
\(443\) | −15.5275 | −0.737732 | −0.368866 | − | 0.929483i | \(-0.620254\pi\) | ||||
−0.368866 | + | 0.929483i | \(0.620254\pi\) | |||||||
\(444\) | 11.4729 | 0.544482 | ||||||||
\(445\) | −0.0128242 | −0.000607926 0 | ||||||||
\(446\) | −5.33329 | −0.252538 | ||||||||
\(447\) | −42.2667 | −1.99915 | ||||||||
\(448\) | 5.53595 | 0.261549 | ||||||||
\(449\) | 29.0060 | 1.36888 | 0.684439 | − | 0.729070i | \(-0.260047\pi\) | ||||
0.684439 | + | 0.729070i | \(0.260047\pi\) | |||||||
\(450\) | 18.7764 | 0.885129 | ||||||||
\(451\) | −30.4040 | −1.43167 | ||||||||
\(452\) | −38.7701 | −1.82359 | ||||||||
\(453\) | 8.61034 | 0.404549 | ||||||||
\(454\) | −8.93167 | −0.419184 | ||||||||
\(455\) | −0.208447 | −0.00977215 | ||||||||
\(456\) | 11.3891 | 0.533344 | ||||||||
\(457\) | 38.3281 | 1.79291 | 0.896456 | − | 0.443134i | \(-0.146133\pi\) | ||||
0.896456 | + | 0.443134i | \(0.146133\pi\) | |||||||
\(458\) | −3.66484 | −0.171247 | ||||||||
\(459\) | 12.7451 | 0.594888 | ||||||||
\(460\) | 0.570397 | 0.0265949 | ||||||||
\(461\) | 1.79473 | 0.0835889 | 0.0417944 | − | 0.999126i | \(-0.486693\pi\) | ||||
0.0417944 | + | 0.999126i | \(0.486693\pi\) | |||||||
\(462\) | 32.0626 | 1.49169 | ||||||||
\(463\) | 1.06332 | 0.0494166 | 0.0247083 | − | 0.999695i | \(-0.492134\pi\) | ||||
0.0247083 | + | 0.999695i | \(0.492134\pi\) | |||||||
\(464\) | −64.3510 | −2.98742 | ||||||||
\(465\) | 0.485924 | 0.0225342 | ||||||||
\(466\) | −66.1926 | −3.06631 | ||||||||
\(467\) | −23.5543 | −1.08996 | −0.544981 | − | 0.838449i | \(-0.683463\pi\) | ||||
−0.544981 | + | 0.838449i | \(0.683463\pi\) | |||||||
\(468\) | 6.91759 | 0.319766 | ||||||||
\(469\) | 7.80457 | 0.360382 | ||||||||
\(470\) | −0.813627 | −0.0375298 | ||||||||
\(471\) | 1.14826 | 0.0529092 | ||||||||
\(472\) | −44.3889 | −2.04316 | ||||||||
\(473\) | 68.3384 | 3.14220 | ||||||||
\(474\) | −73.7737 | −3.38854 | ||||||||
\(475\) | −3.75845 | −0.172449 | ||||||||
\(476\) | 18.2348 | 0.835793 | ||||||||
\(477\) | 16.1536 | 0.739621 | ||||||||
\(478\) | 71.7046 | 3.27969 | ||||||||
\(479\) | −34.1377 | −1.55979 | −0.779895 | − | 0.625911i | \(-0.784727\pi\) | ||||
−0.779895 | + | 0.625911i | \(0.784727\pi\) | |||||||
\(480\) | −4.07431 | −0.185966 | ||||||||
\(481\) | −1.14642 | −0.0522724 | ||||||||
\(482\) | 22.9870 | 1.04703 | ||||||||
\(483\) | 1.17605 | 0.0535120 | ||||||||
\(484\) | 115.951 | 5.27049 | ||||||||
\(485\) | −1.06508 | −0.0483629 | ||||||||
\(486\) | −36.3336 | −1.64813 | ||||||||
\(487\) | −16.4760 | −0.746599 | −0.373300 | − | 0.927711i | \(-0.621774\pi\) | ||||
−0.373300 | + | 0.927711i | \(0.621774\pi\) | |||||||
\(488\) | −49.3952 | −2.23602 | ||||||||
\(489\) | −24.6298 | −1.11380 | ||||||||
\(490\) | −3.32566 | −0.150238 | ||||||||
\(491\) | 25.6367 | 1.15697 | 0.578484 | − | 0.815694i | \(-0.303645\pi\) | ||||
0.578484 | + | 0.815694i | \(0.303645\pi\) | |||||||
\(492\) | 51.0907 | 2.30335 | ||||||||
\(493\) | −28.0814 | −1.26472 | ||||||||
\(494\) | −1.96908 | −0.0885930 | ||||||||
\(495\) | −1.84529 | −0.0829394 | ||||||||
\(496\) | 9.73379 | 0.437060 | ||||||||
\(497\) | 5.35614 | 0.240256 | ||||||||
\(498\) | 55.4933 | 2.48671 | ||||||||
\(499\) | 1.52661 | 0.0683405 | 0.0341702 | − | 0.999416i | \(-0.489121\pi\) | ||||
0.0341702 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(500\) | 10.0133 | 0.447809 | ||||||||
\(501\) | −12.8277 | −0.573098 | ||||||||
\(502\) | −74.4415 | −3.32249 | ||||||||
\(503\) | −7.90478 | −0.352457 | −0.176228 | − | 0.984349i | \(-0.556390\pi\) | ||||
−0.176228 | + | 0.984349i | \(0.556390\pi\) | |||||||
\(504\) | −10.1924 | −0.454005 | ||||||||
\(505\) | 1.83628 | 0.0817133 | ||||||||
\(506\) | 8.76698 | 0.389740 | ||||||||
\(507\) | −2.11181 | −0.0937889 | ||||||||
\(508\) | −16.5420 | −0.733931 | ||||||||
\(509\) | −0.349493 | −0.0154910 | −0.00774550 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774550 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(510\) | −4.55943 | −0.201895 | ||||||||
\(511\) | −5.21258 | −0.230591 | ||||||||
\(512\) | 46.0670 | 2.03589 | ||||||||
\(513\) | 2.46726 | 0.108932 | ||||||||
\(514\) | −28.8784 | −1.27377 | ||||||||
\(515\) | −0.729367 | −0.0321398 | ||||||||
\(516\) | −114.835 | −5.05535 | ||||||||
\(517\) | −8.79398 | −0.386759 | ||||||||
\(518\) | 2.92260 | 0.128412 | ||||||||
\(519\) | 38.7311 | 1.70011 | ||||||||
\(520\) | 1.50914 | 0.0661801 | ||||||||
\(521\) | 38.2101 | 1.67401 | 0.837007 | − | 0.547193i | \(-0.184303\pi\) | ||||
0.837007 | + | 0.547193i | \(0.184303\pi\) | |||||||
\(522\) | 27.1578 | 1.18867 | ||||||||
\(523\) | 30.1059 | 1.31644 | 0.658221 | − | 0.752825i | \(-0.271309\pi\) | ||||
0.658221 | + | 0.752825i | \(0.271309\pi\) | |||||||
\(524\) | 104.159 | 4.55020 | ||||||||
\(525\) | 10.2760 | 0.448483 | ||||||||
\(526\) | 55.9489 | 2.43949 | ||||||||
\(527\) | 4.24761 | 0.185029 | ||||||||
\(528\) | −112.930 | −4.91464 | ||||||||
\(529\) | −22.6784 | −0.986019 | ||||||||
\(530\) | 6.09742 | 0.264855 | ||||||||
\(531\) | 9.11360 | 0.395497 | ||||||||
\(532\) | 3.53000 | 0.153045 | ||||||||
\(533\) | −5.10519 | −0.221130 | ||||||||
\(534\) | 0.331219 | 0.0143332 | ||||||||
\(535\) | −0.783731 | −0.0338836 | ||||||||
\(536\) | −56.5044 | −2.44062 | ||||||||
\(537\) | −10.0064 | −0.431806 | ||||||||
\(538\) | 35.5134 | 1.53109 | ||||||||
\(539\) | −35.9450 | −1.54826 | ||||||||
\(540\) | −3.27178 | −0.140795 | ||||||||
\(541\) | 8.14455 | 0.350162 | 0.175081 | − | 0.984554i | \(-0.443981\pi\) | ||||
0.175081 | + | 0.984554i | \(0.443981\pi\) | |||||||
\(542\) | 41.3639 | 1.77673 | ||||||||
\(543\) | −5.72443 | −0.245659 | ||||||||
\(544\) | −35.6148 | −1.52697 | ||||||||
\(545\) | 3.15291 | 0.135056 | ||||||||
\(546\) | 5.38369 | 0.230401 | ||||||||
\(547\) | 25.4303 | 1.08732 | 0.543660 | − | 0.839306i | \(-0.317038\pi\) | ||||
0.543660 | + | 0.839306i | \(0.317038\pi\) | |||||||
\(548\) | 67.9787 | 2.90391 | ||||||||
\(549\) | 10.1415 | 0.432827 | ||||||||
\(550\) | 76.6039 | 3.26640 | ||||||||
\(551\) | −5.43615 | −0.231588 | ||||||||
\(552\) | −8.51447 | −0.362400 | ||||||||
\(553\) | −13.2155 | −0.561980 | ||||||||
\(554\) | 74.8703 | 3.18093 | ||||||||
\(555\) | −0.513884 | −0.0218132 | ||||||||
\(556\) | 95.7755 | 4.06179 | ||||||||
\(557\) | −1.29288 | −0.0547811 | −0.0273906 | − | 0.999625i | \(-0.508720\pi\) | ||||
−0.0273906 | + | 0.999625i | \(0.508720\pi\) | |||||||
\(558\) | −4.10791 | −0.173902 | ||||||||
\(559\) | 11.4748 | 0.485333 | ||||||||
\(560\) | −1.87167 | −0.0790926 | ||||||||
\(561\) | −49.2800 | −2.08060 | ||||||||
\(562\) | 31.6213 | 1.33386 | ||||||||
\(563\) | 19.6499 | 0.828146 | 0.414073 | − | 0.910244i | \(-0.364106\pi\) | ||||
0.414073 | + | 0.910244i | \(0.364106\pi\) | |||||||
\(564\) | 14.7774 | 0.622239 | ||||||||
\(565\) | 1.73655 | 0.0730571 | ||||||||
\(566\) | 66.8424 | 2.80959 | ||||||||
\(567\) | −11.0464 | −0.463906 | ||||||||
\(568\) | −38.7780 | −1.62709 | ||||||||
\(569\) | −17.0337 | −0.714091 | −0.357046 | − | 0.934087i | \(-0.616216\pi\) | ||||
−0.357046 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(570\) | −0.882639 | −0.0369697 | ||||||||
\(571\) | −10.2598 | −0.429361 | −0.214680 | − | 0.976684i | \(-0.568871\pi\) | ||||
−0.214680 | + | 0.976684i | \(0.568871\pi\) | |||||||
\(572\) | 28.2223 | 1.18004 | ||||||||
\(573\) | −7.72949 | −0.322904 | ||||||||
\(574\) | 13.0148 | 0.543226 | ||||||||
\(575\) | 2.80981 | 0.117177 | ||||||||
\(576\) | 8.22888 | 0.342870 | ||||||||
\(577\) | −39.8243 | −1.65791 | −0.828954 | − | 0.559316i | \(-0.811064\pi\) | ||||
−0.828954 | + | 0.559316i | \(0.811064\pi\) | |||||||
\(578\) | 4.27552 | 0.177838 | ||||||||
\(579\) | −13.3327 | −0.554089 | ||||||||
\(580\) | 7.20876 | 0.299328 | ||||||||
\(581\) | 9.94083 | 0.412415 | ||||||||
\(582\) | 27.5086 | 1.14027 | ||||||||
\(583\) | 65.9032 | 2.72943 | ||||||||
\(584\) | 37.7386 | 1.56164 | ||||||||
\(585\) | −0.309845 | −0.0128105 | ||||||||
\(586\) | 29.1513 | 1.20423 | ||||||||
\(587\) | −4.34058 | −0.179155 | −0.0895774 | − | 0.995980i | \(-0.528552\pi\) | ||||
−0.0895774 | + | 0.995980i | \(0.528552\pi\) | |||||||
\(588\) | 60.4018 | 2.49093 | ||||||||
\(589\) | 0.822276 | 0.0338813 | ||||||||
\(590\) | 3.44008 | 0.141626 | ||||||||
\(591\) | −27.0803 | −1.11393 | ||||||||
\(592\) | −10.2939 | −0.423076 | ||||||||
\(593\) | −17.3634 | −0.713027 | −0.356514 | − | 0.934290i | \(-0.616035\pi\) | ||||
−0.356514 | + | 0.934290i | \(0.616035\pi\) | |||||||
\(594\) | −50.2872 | −2.06331 | ||||||||
\(595\) | −0.816756 | −0.0334837 | ||||||||
\(596\) | 94.8457 | 3.88503 | ||||||||
\(597\) | 46.0406 | 1.88431 | ||||||||
\(598\) | 1.47208 | 0.0601978 | ||||||||
\(599\) | −4.88829 | −0.199730 | −0.0998650 | − | 0.995001i | \(-0.531841\pi\) | ||||
−0.0998650 | + | 0.995001i | \(0.531841\pi\) | |||||||
\(600\) | −74.3976 | −3.03727 | ||||||||
\(601\) | −7.64495 | −0.311844 | −0.155922 | − | 0.987769i | \(-0.549835\pi\) | ||||
−0.155922 | + | 0.987769i | \(0.549835\pi\) | |||||||
\(602\) | −29.2530 | −1.19226 | ||||||||
\(603\) | 11.6011 | 0.472432 | ||||||||
\(604\) | −19.3214 | −0.786178 | ||||||||
\(605\) | −5.19355 | −0.211148 | ||||||||
\(606\) | −47.4267 | −1.92658 | ||||||||
\(607\) | −0.625947 | −0.0254064 | −0.0127032 | − | 0.999919i | \(-0.504044\pi\) | ||||
−0.0127032 | + | 0.999919i | \(0.504044\pi\) | |||||||
\(608\) | −6.89452 | −0.279610 | ||||||||
\(609\) | 14.8631 | 0.602282 | ||||||||
\(610\) | 3.82806 | 0.154994 | ||||||||
\(611\) | −1.47661 | −0.0597374 | ||||||||
\(612\) | 27.1051 | 1.09566 | ||||||||
\(613\) | 2.43573 | 0.0983780 | 0.0491890 | − | 0.998789i | \(-0.484336\pi\) | ||||
0.0491890 | + | 0.998789i | \(0.484336\pi\) | |||||||
\(614\) | 83.1420 | 3.35534 | ||||||||
\(615\) | −2.28840 | −0.0922772 | ||||||||
\(616\) | −41.5828 | −1.67542 | ||||||||
\(617\) | −35.5416 | −1.43085 | −0.715426 | − | 0.698689i | \(-0.753767\pi\) | ||||
−0.715426 | + | 0.698689i | \(0.753767\pi\) | |||||||
\(618\) | 18.8378 | 0.757768 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | −1.09040 | −0.0437916 | ||||||||
\(621\) | −1.84452 | −0.0740180 | ||||||||
\(622\) | 47.4675 | 1.90327 | ||||||||
\(623\) | 0.0593331 | 0.00237713 | ||||||||
\(624\) | −18.9622 | −0.759097 | ||||||||
\(625\) | 24.3262 | 0.973049 | ||||||||
\(626\) | −29.3832 | −1.17439 | ||||||||
\(627\) | −9.53990 | −0.380987 | ||||||||
\(628\) | −2.57668 | −0.102821 | ||||||||
\(629\) | −4.49202 | −0.179108 | ||||||||
\(630\) | 0.789895 | 0.0314702 | ||||||||
\(631\) | 5.90919 | 0.235241 | 0.117621 | − | 0.993059i | \(-0.462473\pi\) | ||||
0.117621 | + | 0.993059i | \(0.462473\pi\) | |||||||
\(632\) | 95.6790 | 3.80591 | ||||||||
\(633\) | 43.7635 | 1.73944 | ||||||||
\(634\) | −34.3211 | −1.36307 | ||||||||
\(635\) | 0.740930 | 0.0294029 | ||||||||
\(636\) | −110.743 | −4.39126 | ||||||||
\(637\) | −6.03559 | −0.239139 | ||||||||
\(638\) | 110.798 | 4.38655 | ||||||||
\(639\) | 7.96162 | 0.314957 | ||||||||
\(640\) | −0.752468 | −0.0297439 | ||||||||
\(641\) | 27.3766 | 1.08131 | 0.540654 | − | 0.841245i | \(-0.318177\pi\) | ||||
0.540654 | + | 0.841245i | \(0.318177\pi\) | |||||||
\(642\) | 20.2419 | 0.798884 | ||||||||
\(643\) | 15.5152 | 0.611858 | 0.305929 | − | 0.952054i | \(-0.401033\pi\) | ||||
0.305929 | + | 0.952054i | \(0.401033\pi\) | |||||||
\(644\) | −2.63902 | −0.103992 | ||||||||
\(645\) | 5.14359 | 0.202529 | ||||||||
\(646\) | −7.71542 | −0.303559 | ||||||||
\(647\) | 30.9475 | 1.21667 | 0.608336 | − | 0.793679i | \(-0.291837\pi\) | ||||
0.608336 | + | 0.793679i | \(0.291837\pi\) | |||||||
\(648\) | 79.9750 | 3.14172 | ||||||||
\(649\) | 37.1816 | 1.45951 | ||||||||
\(650\) | 12.8627 | 0.504517 | ||||||||
\(651\) | −2.24820 | −0.0881138 | ||||||||
\(652\) | 55.2689 | 2.16450 | ||||||||
\(653\) | 29.3171 | 1.14726 | 0.573632 | − | 0.819113i | \(-0.305534\pi\) | ||||
0.573632 | + | 0.819113i | \(0.305534\pi\) | |||||||
\(654\) | −81.4322 | −3.18425 | ||||||||
\(655\) | −4.66538 | −0.182291 | ||||||||
\(656\) | −45.8401 | −1.78976 | ||||||||
\(657\) | −7.74822 | −0.302287 | ||||||||
\(658\) | 3.76436 | 0.146750 | ||||||||
\(659\) | 0.501103 | 0.0195202 | 0.00976011 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976011 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(660\) | 12.6507 | 0.492427 | ||||||||
\(661\) | 41.4726 | 1.61310 | 0.806548 | − | 0.591169i | \(-0.201333\pi\) | ||||
0.806548 | + | 0.591169i | \(0.201333\pi\) | |||||||
\(662\) | −46.0169 | −1.78850 | ||||||||
\(663\) | −8.27470 | −0.321363 | ||||||||
\(664\) | −71.9707 | −2.79301 | ||||||||
\(665\) | −0.158112 | −0.00613133 | ||||||||
\(666\) | 4.34429 | 0.168338 | ||||||||
\(667\) | 4.06405 | 0.157361 | ||||||||
\(668\) | 28.7851 | 1.11373 | ||||||||
\(669\) | −4.33867 | −0.167743 | ||||||||
\(670\) | 4.37901 | 0.169176 | ||||||||
\(671\) | 41.3751 | 1.59727 | ||||||||
\(672\) | 18.8504 | 0.727171 | ||||||||
\(673\) | 23.3727 | 0.900951 | 0.450476 | − | 0.892789i | \(-0.351254\pi\) | ||||
0.450476 | + | 0.892789i | \(0.351254\pi\) | |||||||
\(674\) | −69.5688 | −2.67969 | ||||||||
\(675\) | −16.1170 | −0.620343 | ||||||||
\(676\) | 4.73887 | 0.182264 | ||||||||
\(677\) | 23.0344 | 0.885285 | 0.442642 | − | 0.896698i | \(-0.354041\pi\) | ||||
0.442642 | + | 0.896698i | \(0.354041\pi\) | |||||||
\(678\) | −44.8509 | −1.72249 | ||||||||
\(679\) | 4.92776 | 0.189110 | ||||||||
\(680\) | 5.91324 | 0.226762 | ||||||||
\(681\) | −7.26599 | −0.278433 | ||||||||
\(682\) | −16.7595 | −0.641753 | ||||||||
\(683\) | 23.2621 | 0.890101 | 0.445050 | − | 0.895506i | \(-0.353186\pi\) | ||||
0.445050 | + | 0.895506i | \(0.353186\pi\) | |||||||
\(684\) | 5.24716 | 0.200630 | ||||||||
\(685\) | −3.04483 | −0.116337 | ||||||||
\(686\) | 33.2319 | 1.26880 | ||||||||
\(687\) | −2.98138 | −0.113747 | ||||||||
\(688\) | 103.034 | 3.92813 | ||||||||
\(689\) | 11.0659 | 0.421578 | ||||||||
\(690\) | 0.659859 | 0.0251204 | ||||||||
\(691\) | 4.26416 | 0.162216 | 0.0811081 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811081 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(692\) | −86.9119 | −3.30389 | ||||||||
\(693\) | 8.53749 | 0.324312 | ||||||||
\(694\) | −48.9235 | −1.85711 | ||||||||
\(695\) | −4.28988 | −0.162724 | ||||||||
\(696\) | −107.607 | −4.07884 | ||||||||
\(697\) | −20.0036 | −0.757691 | ||||||||
\(698\) | −65.3087 | −2.47197 | ||||||||
\(699\) | −53.8483 | −2.03673 | ||||||||
\(700\) | −23.0592 | −0.871557 | ||||||||
\(701\) | 13.4000 | 0.506111 | 0.253055 | − | 0.967452i | \(-0.418565\pi\) | ||||
0.253055 | + | 0.967452i | \(0.418565\pi\) | |||||||
\(702\) | −8.44381 | −0.318691 | ||||||||
\(703\) | −0.869589 | −0.0327972 | ||||||||
\(704\) | 33.5722 | 1.26530 | ||||||||
\(705\) | −0.661892 | −0.0249283 | ||||||||
\(706\) | −15.9475 | −0.600191 | ||||||||
\(707\) | −8.49581 | −0.319518 | ||||||||
\(708\) | −62.4798 | −2.34814 | ||||||||
\(709\) | −44.1210 | −1.65700 | −0.828500 | − | 0.559989i | \(-0.810805\pi\) | ||||
−0.828500 | + | 0.559989i | \(0.810805\pi\) | |||||||
\(710\) | 3.00524 | 0.112785 | ||||||||
\(711\) | −19.6441 | −0.736712 | ||||||||
\(712\) | −0.429567 | −0.0160987 | ||||||||
\(713\) | −0.614732 | −0.0230219 | ||||||||
\(714\) | 21.0949 | 0.789455 | ||||||||
\(715\) | −1.26411 | −0.0472749 | ||||||||
\(716\) | 22.4541 | 0.839147 | ||||||||
\(717\) | 58.3323 | 2.17846 | ||||||||
\(718\) | −91.1738 | −3.40258 | ||||||||
\(719\) | 20.8621 | 0.778026 | 0.389013 | − | 0.921232i | \(-0.372816\pi\) | ||||
0.389013 | + | 0.921232i | \(0.372816\pi\) | |||||||
\(720\) | −2.78214 | −0.103684 | ||||||||
\(721\) | 3.37453 | 0.125674 | ||||||||
\(722\) | 47.8291 | 1.78002 | ||||||||
\(723\) | 18.7001 | 0.695465 | ||||||||
\(724\) | 12.8455 | 0.477399 | ||||||||
\(725\) | 35.5108 | 1.31884 | ||||||||
\(726\) | 134.137 | 4.97829 | ||||||||
\(727\) | −21.0850 | −0.782000 | −0.391000 | − | 0.920391i | \(-0.627871\pi\) | ||||
−0.391000 | + | 0.920391i | \(0.627871\pi\) | |||||||
\(728\) | −6.98225 | −0.258779 | ||||||||
\(729\) | 4.18745 | 0.155091 | ||||||||
\(730\) | −2.92469 | −0.108248 | ||||||||
\(731\) | 44.9617 | 1.66297 | ||||||||
\(732\) | −69.5266 | −2.56978 | ||||||||
\(733\) | 13.7852 | 0.509170 | 0.254585 | − | 0.967050i | \(-0.418061\pi\) | ||||
0.254585 | + | 0.967050i | \(0.418061\pi\) | |||||||
\(734\) | −96.1720 | −3.54977 | ||||||||
\(735\) | −2.70545 | −0.0997921 | ||||||||
\(736\) | 5.15433 | 0.189991 | ||||||||
\(737\) | 47.3300 | 1.74342 | ||||||||
\(738\) | 19.3457 | 0.712127 | ||||||||
\(739\) | 17.8872 | 0.657992 | 0.328996 | − | 0.944331i | \(-0.393290\pi\) | ||||
0.328996 | + | 0.944331i | \(0.393290\pi\) | |||||||
\(740\) | 1.15315 | 0.0423905 | ||||||||
\(741\) | −1.60186 | −0.0588459 | ||||||||
\(742\) | −28.2106 | −1.03564 | ||||||||
\(743\) | −15.7558 | −0.578023 | −0.289012 | − | 0.957326i | \(-0.593327\pi\) | ||||
−0.289012 | + | 0.957326i | \(0.593327\pi\) | |||||||
\(744\) | 16.2768 | 0.596735 | ||||||||
\(745\) | −4.24823 | −0.155643 | ||||||||
\(746\) | −41.0187 | −1.50180 | ||||||||
\(747\) | 14.7765 | 0.540644 | ||||||||
\(748\) | 110.583 | 4.04333 | ||||||||
\(749\) | 3.62605 | 0.132493 | ||||||||
\(750\) | 11.5838 | 0.422982 | ||||||||
\(751\) | −10.2173 | −0.372834 | −0.186417 | − | 0.982471i | \(-0.559687\pi\) | ||||
−0.186417 | + | 0.982471i | \(0.559687\pi\) | |||||||
\(752\) | −13.2587 | −0.483495 | ||||||||
\(753\) | −60.5588 | −2.20689 | ||||||||
\(754\) | 18.6044 | 0.677531 | ||||||||
\(755\) | 0.865426 | 0.0314961 | ||||||||
\(756\) | 15.1374 | 0.550541 | ||||||||
\(757\) | −12.3155 | −0.447616 | −0.223808 | − | 0.974633i | \(-0.571849\pi\) | ||||
−0.223808 | + | 0.974633i | \(0.571849\pi\) | |||||||
\(758\) | 20.3877 | 0.740514 | ||||||||
\(759\) | 7.13201 | 0.258876 | ||||||||
\(760\) | 1.14472 | 0.0415233 | ||||||||
\(761\) | 31.9899 | 1.15963 | 0.579817 | − | 0.814747i | \(-0.303124\pi\) | ||||
0.579817 | + | 0.814747i | \(0.303124\pi\) | |||||||
\(762\) | −19.1364 | −0.693240 | ||||||||
\(763\) | −14.5874 | −0.528100 | ||||||||
\(764\) | 17.3448 | 0.627513 | ||||||||
\(765\) | −1.21406 | −0.0438946 | ||||||||
\(766\) | 80.3792 | 2.90422 | ||||||||
\(767\) | 6.24324 | 0.225430 | ||||||||
\(768\) | 43.2437 | 1.56042 | ||||||||
\(769\) | −39.6147 | −1.42854 | −0.714272 | − | 0.699868i | \(-0.753242\pi\) | ||||
−0.714272 | + | 0.699868i | \(0.753242\pi\) | |||||||
\(770\) | 3.22261 | 0.116135 | ||||||||
\(771\) | −23.4928 | −0.846074 | ||||||||
\(772\) | 29.9183 | 1.07678 | ||||||||
\(773\) | −50.8767 | −1.82991 | −0.914954 | − | 0.403559i | \(-0.867773\pi\) | ||||
−0.914954 | + | 0.403559i | \(0.867773\pi\) | |||||||
\(774\) | −43.4830 | −1.56296 | ||||||||
\(775\) | −5.37139 | −0.192946 | ||||||||
\(776\) | −35.6766 | −1.28071 | ||||||||
\(777\) | 2.37756 | 0.0852945 | ||||||||
\(778\) | −49.2767 | −1.76665 | ||||||||
\(779\) | −3.87241 | −0.138744 | ||||||||
\(780\) | 2.12420 | 0.0760585 | ||||||||
\(781\) | 32.4818 | 1.16229 | ||||||||
\(782\) | 5.76803 | 0.206264 | ||||||||
\(783\) | −23.3113 | −0.833078 | ||||||||
\(784\) | −54.1943 | −1.93551 | ||||||||
\(785\) | 0.115412 | 0.00411923 | ||||||||
\(786\) | 120.496 | 4.29793 | ||||||||
\(787\) | −24.2460 | −0.864277 | −0.432138 | − | 0.901807i | \(-0.642241\pi\) | ||||
−0.432138 | + | 0.901807i | \(0.642241\pi\) | |||||||
\(788\) | 60.7676 | 2.16476 | ||||||||
\(789\) | 45.5149 | 1.62037 | ||||||||
\(790\) | −7.41499 | −0.263813 | ||||||||
\(791\) | −8.03440 | −0.285670 | ||||||||
\(792\) | −61.8106 | −2.19635 | ||||||||
\(793\) | 6.94738 | 0.246709 | ||||||||
\(794\) | 89.8880 | 3.19000 | ||||||||
\(795\) | 4.96030 | 0.175924 | ||||||||
\(796\) | −103.314 | −3.66187 | ||||||||
\(797\) | −4.99338 | −0.176875 | −0.0884373 | − | 0.996082i | \(-0.528187\pi\) | ||||
−0.0884373 | + | 0.996082i | \(0.528187\pi\) | |||||||
\(798\) | 4.08366 | 0.144560 | ||||||||
\(799\) | −5.78580 | −0.204687 | ||||||||
\(800\) | 45.0374 | 1.59231 | ||||||||
\(801\) | 0.0881955 | 0.00311623 | ||||||||
\(802\) | 84.9099 | 2.99827 | ||||||||
\(803\) | −31.6112 | −1.11553 | ||||||||
\(804\) | −79.5331 | −2.80492 | ||||||||
\(805\) | 0.118204 | 0.00416616 | ||||||||
\(806\) | −2.81411 | −0.0991228 | ||||||||
\(807\) | 28.8904 | 1.01699 | ||||||||
\(808\) | 61.5089 | 2.16388 | ||||||||
\(809\) | −2.27929 | −0.0801356 | −0.0400678 | − | 0.999197i | \(-0.512757\pi\) | ||||
−0.0400678 | + | 0.999197i | \(0.512757\pi\) | |||||||
\(810\) | −6.19795 | −0.217774 | ||||||||
\(811\) | 6.13788 | 0.215530 | 0.107765 | − | 0.994176i | \(-0.465631\pi\) | ||||
0.107765 | + | 0.994176i | \(0.465631\pi\) | |||||||
\(812\) | −33.3524 | −1.17044 | ||||||||
\(813\) | 33.6499 | 1.18015 | ||||||||
\(814\) | 17.7238 | 0.621219 | ||||||||
\(815\) | −2.47554 | −0.0867145 | ||||||||
\(816\) | −74.2995 | −2.60100 | ||||||||
\(817\) | 8.70393 | 0.304512 | ||||||||
\(818\) | 37.7329 | 1.31930 | ||||||||
\(819\) | 1.43355 | 0.0500921 | ||||||||
\(820\) | 5.13513 | 0.179326 | ||||||||
\(821\) | 7.10551 | 0.247984 | 0.123992 | − | 0.992283i | \(-0.460430\pi\) | ||||
0.123992 | + | 0.992283i | \(0.460430\pi\) | |||||||
\(822\) | 78.6407 | 2.74291 | ||||||||
\(823\) | 26.4610 | 0.922372 | 0.461186 | − | 0.887304i | \(-0.347424\pi\) | ||||
0.461186 | + | 0.887304i | \(0.347424\pi\) | |||||||
\(824\) | −24.4313 | −0.851103 | ||||||||
\(825\) | 62.3179 | 2.16963 | ||||||||
\(826\) | −15.9160 | −0.553789 | ||||||||
\(827\) | −18.5744 | −0.645894 | −0.322947 | − | 0.946417i | \(-0.604673\pi\) | ||||
−0.322947 | + | 0.946417i | \(0.604673\pi\) | |||||||
\(828\) | −3.92277 | −0.136326 | ||||||||
\(829\) | −7.17700 | −0.249268 | −0.124634 | − | 0.992203i | \(-0.539776\pi\) | ||||
−0.124634 | + | 0.992203i | \(0.539776\pi\) | |||||||
\(830\) | 5.57763 | 0.193602 | ||||||||
\(831\) | 60.9076 | 2.11286 | ||||||||
\(832\) | 5.63716 | 0.195434 | ||||||||
\(833\) | −23.6492 | −0.819396 | ||||||||
\(834\) | 110.797 | 3.83659 | ||||||||
\(835\) | −1.28931 | −0.0446184 | ||||||||
\(836\) | 21.4073 | 0.740388 | ||||||||
\(837\) | 3.52609 | 0.121879 | ||||||||
\(838\) | 57.5138 | 1.98678 | ||||||||
\(839\) | 16.7380 | 0.577862 | 0.288931 | − | 0.957350i | \(-0.406700\pi\) | ||||
0.288931 | + | 0.957350i | \(0.406700\pi\) | |||||||
\(840\) | −3.12979 | −0.107988 | ||||||||
\(841\) | 22.3621 | 0.771108 | ||||||||
\(842\) | 48.8123 | 1.68218 | ||||||||
\(843\) | 25.7242 | 0.885987 | ||||||||
\(844\) | −98.2045 | −3.38034 | ||||||||
\(845\) | −0.212258 | −0.00730191 | ||||||||
\(846\) | 5.59552 | 0.192378 | ||||||||
\(847\) | 24.0287 | 0.825636 | ||||||||
\(848\) | 99.3624 | 3.41212 | ||||||||
\(849\) | 54.3768 | 1.86621 | ||||||||
\(850\) | 50.3998 | 1.72870 | ||||||||
\(851\) | 0.650103 | 0.0222853 | ||||||||
\(852\) | −54.5822 | −1.86996 | ||||||||
\(853\) | −19.0758 | −0.653143 | −0.326572 | − | 0.945172i | \(-0.605893\pi\) | ||||
−0.326572 | + | 0.945172i | \(0.605893\pi\) | |||||||
\(854\) | −17.7111 | −0.606061 | ||||||||
\(855\) | −0.235025 | −0.00803769 | ||||||||
\(856\) | −26.2522 | −0.897283 | ||||||||
\(857\) | 35.0510 | 1.19732 | 0.598660 | − | 0.801003i | \(-0.295700\pi\) | ||||
0.598660 | + | 0.801003i | \(0.295700\pi\) | |||||||
\(858\) | 32.6488 | 1.11461 | ||||||||
\(859\) | 1.37456 | 0.0468995 | 0.0234498 | − | 0.999725i | \(-0.492535\pi\) | ||||
0.0234498 | + | 0.999725i | \(0.492535\pi\) | |||||||
\(860\) | −11.5421 | −0.393583 | ||||||||
\(861\) | 10.5876 | 0.360825 | ||||||||
\(862\) | −79.9459 | −2.72297 | ||||||||
\(863\) | −3.56863 | −0.121478 | −0.0607388 | − | 0.998154i | \(-0.519346\pi\) | ||||
−0.0607388 | + | 0.998154i | \(0.519346\pi\) | |||||||
\(864\) | −29.5651 | −1.00583 | ||||||||
\(865\) | 3.89287 | 0.132361 | ||||||||
\(866\) | 68.8245 | 2.33875 | ||||||||
\(867\) | 3.47817 | 0.118125 | ||||||||
\(868\) | 5.04491 | 0.171235 | ||||||||
\(869\) | −80.1440 | −2.71870 | ||||||||
\(870\) | 8.33941 | 0.282732 | ||||||||
\(871\) | 7.94727 | 0.269283 | ||||||||
\(872\) | 105.612 | 3.57646 | ||||||||
\(873\) | 7.32485 | 0.247909 | ||||||||
\(874\) | 1.11661 | 0.0377698 | ||||||||
\(875\) | 2.07508 | 0.0701505 | ||||||||
\(876\) | 53.1193 | 1.79473 | ||||||||
\(877\) | −42.7850 | −1.44475 | −0.722374 | − | 0.691503i | \(-0.756949\pi\) | ||||
−0.722374 | + | 0.691503i | \(0.756949\pi\) | |||||||
\(878\) | −49.1133 | −1.65750 | ||||||||
\(879\) | 23.7148 | 0.799880 | ||||||||
\(880\) | −11.3506 | −0.382627 | ||||||||
\(881\) | 45.3084 | 1.52648 | 0.763240 | − | 0.646115i | \(-0.223608\pi\) | ||||
0.763240 | + | 0.646115i | \(0.223608\pi\) | |||||||
\(882\) | 22.8714 | 0.770121 | ||||||||
\(883\) | −9.85097 | −0.331512 | −0.165756 | − | 0.986167i | \(-0.553006\pi\) | ||||
−0.165756 | + | 0.986167i | \(0.553006\pi\) | |||||||
\(884\) | 18.5683 | 0.624518 | ||||||||
\(885\) | 2.79853 | 0.0940716 | ||||||||
\(886\) | 40.3082 | 1.35418 | ||||||||
\(887\) | 50.4173 | 1.69285 | 0.846423 | − | 0.532511i | \(-0.178752\pi\) | ||||
0.846423 | + | 0.532511i | \(0.178752\pi\) | |||||||
\(888\) | −17.2133 | −0.577641 | ||||||||
\(889\) | −3.42802 | −0.114972 | ||||||||
\(890\) | 0.0332908 | 0.00111591 | ||||||||
\(891\) | −66.9898 | −2.24424 | ||||||||
\(892\) | 9.73590 | 0.325982 | ||||||||
\(893\) | −1.12005 | −0.0374810 | ||||||||
\(894\) | 109.722 | 3.66964 | ||||||||
\(895\) | −1.00574 | −0.0336181 | ||||||||
\(896\) | 3.48140 | 0.116306 | ||||||||
\(897\) | 1.19755 | 0.0399850 | ||||||||
\(898\) | −75.2977 | −2.51272 | ||||||||
\(899\) | −7.76908 | −0.259113 | ||||||||
\(900\) | −34.2763 | −1.14254 | ||||||||
\(901\) | 43.3595 | 1.44452 | ||||||||
\(902\) | 78.9267 | 2.62797 | ||||||||
\(903\) | −23.7976 | −0.791934 | ||||||||
\(904\) | 58.1683 | 1.93465 | ||||||||
\(905\) | −0.575362 | −0.0191257 | ||||||||
\(906\) | −22.3519 | −0.742591 | ||||||||
\(907\) | −33.9009 | −1.12566 | −0.562831 | − | 0.826572i | \(-0.690288\pi\) | ||||
−0.562831 | + | 0.826572i | \(0.690288\pi\) | |||||||
\(908\) | 16.3047 | 0.541092 | ||||||||
\(909\) | −12.6286 | −0.418863 | ||||||||
\(910\) | 0.541115 | 0.0179378 | ||||||||
\(911\) | −12.5356 | −0.415324 | −0.207662 | − | 0.978201i | \(-0.566585\pi\) | ||||
−0.207662 | + | 0.978201i | \(0.566585\pi\) | |||||||
\(912\) | −14.3833 | −0.476279 | ||||||||
\(913\) | 60.2851 | 1.99515 | ||||||||
\(914\) | −99.4971 | −3.29107 | ||||||||
\(915\) | 3.11416 | 0.102951 | ||||||||
\(916\) | 6.69015 | 0.221049 | ||||||||
\(917\) | 21.5850 | 0.712801 | ||||||||
\(918\) | −33.0853 | −1.09198 | ||||||||
\(919\) | 6.36020 | 0.209804 | 0.104902 | − | 0.994483i | \(-0.466547\pi\) | ||||
0.104902 | + | 0.994483i | \(0.466547\pi\) | |||||||
\(920\) | −0.855789 | −0.0282145 | ||||||||
\(921\) | 67.6367 | 2.22871 | ||||||||
\(922\) | −4.65900 | −0.153436 | ||||||||
\(923\) | 5.45408 | 0.179523 | ||||||||
\(924\) | −58.5302 | −1.92550 | ||||||||
\(925\) | 5.68046 | 0.186772 | ||||||||
\(926\) | −2.76030 | −0.0907092 | ||||||||
\(927\) | 5.01605 | 0.164749 | ||||||||
\(928\) | 65.1412 | 2.13836 | ||||||||
\(929\) | 10.7769 | 0.353578 | 0.176789 | − | 0.984249i | \(-0.443429\pi\) | ||||
0.176789 | + | 0.984249i | \(0.443429\pi\) | |||||||
\(930\) | −1.26143 | −0.0413638 | ||||||||
\(931\) | −4.57814 | −0.150043 | ||||||||
\(932\) | 120.834 | 3.95806 | ||||||||
\(933\) | 38.6152 | 1.26420 | ||||||||
\(934\) | 61.1453 | 2.00073 | ||||||||
\(935\) | −4.95313 | −0.161985 | ||||||||
\(936\) | −10.3787 | −0.339240 | ||||||||
\(937\) | 47.7347 | 1.55943 | 0.779713 | − | 0.626137i | \(-0.215365\pi\) | ||||
0.779713 | + | 0.626137i | \(0.215365\pi\) | |||||||
\(938\) | −20.2601 | −0.661517 | ||||||||
\(939\) | −23.9035 | −0.780061 | ||||||||
\(940\) | 1.48527 | 0.0484443 | ||||||||
\(941\) | −30.1957 | −0.984350 | −0.492175 | − | 0.870496i | \(-0.663798\pi\) | ||||
−0.492175 | + | 0.870496i | \(0.663798\pi\) | |||||||
\(942\) | −2.98082 | −0.0971203 | ||||||||
\(943\) | 2.89501 | 0.0942744 | ||||||||
\(944\) | 56.0588 | 1.82456 | ||||||||
\(945\) | −0.678018 | −0.0220559 | ||||||||
\(946\) | −177.402 | −5.76783 | ||||||||
\(947\) | 44.3394 | 1.44084 | 0.720419 | − | 0.693539i | \(-0.243950\pi\) | ||||
0.720419 | + | 0.693539i | \(0.243950\pi\) | |||||||
\(948\) | 134.674 | 4.37399 | ||||||||
\(949\) | −5.30789 | −0.172301 | ||||||||
\(950\) | 9.75668 | 0.316548 | ||||||||
\(951\) | −27.9205 | −0.905385 | ||||||||
\(952\) | −27.3585 | −0.886694 | ||||||||
\(953\) | 22.2007 | 0.719151 | 0.359575 | − | 0.933116i | \(-0.382922\pi\) | ||||
0.359575 | + | 0.933116i | \(0.382922\pi\) | |||||||
\(954\) | −41.9335 | −1.35765 | ||||||||
\(955\) | −0.776891 | −0.0251396 | ||||||||
\(956\) | −130.897 | −4.23350 | ||||||||
\(957\) | 90.1355 | 2.91367 | ||||||||
\(958\) | 88.6190 | 2.86315 | ||||||||
\(959\) | 14.0874 | 0.454905 | ||||||||
\(960\) | 2.52686 | 0.0815540 | ||||||||
\(961\) | −29.8248 | −0.962092 | ||||||||
\(962\) | 2.97604 | 0.0959512 | ||||||||
\(963\) | 5.38992 | 0.173688 | ||||||||
\(964\) | −41.9627 | −1.35153 | ||||||||
\(965\) | −1.34007 | −0.0431384 | ||||||||
\(966\) | −3.05294 | −0.0982266 | ||||||||
\(967\) | −1.21693 | −0.0391338 | −0.0195669 | − | 0.999809i | \(-0.506229\pi\) | ||||
−0.0195669 | + | 0.999809i | \(0.506229\pi\) | |||||||
\(968\) | −173.966 | −5.59147 | ||||||||
\(969\) | −6.27656 | −0.201632 | ||||||||
\(970\) | 2.76488 | 0.0887751 | ||||||||
\(971\) | 32.2158 | 1.03385 | 0.516927 | − | 0.856029i | \(-0.327076\pi\) | ||||
0.516927 | + | 0.856029i | \(0.327076\pi\) | |||||||
\(972\) | 66.3269 | 2.12744 | ||||||||
\(973\) | 19.8477 | 0.636289 | ||||||||
\(974\) | 42.7706 | 1.37046 | ||||||||
\(975\) | 10.4639 | 0.335114 | ||||||||
\(976\) | 62.3814 | 1.99678 | ||||||||
\(977\) | −10.6458 | −0.340591 | −0.170295 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170295 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(978\) | 63.9374 | 2.04449 | ||||||||
\(979\) | 0.359820 | 0.0114999 | ||||||||
\(980\) | 6.07098 | 0.193930 | ||||||||
\(981\) | −21.6834 | −0.692298 | ||||||||
\(982\) | −66.5511 | −2.12373 | ||||||||
\(983\) | 43.2404 | 1.37915 | 0.689577 | − | 0.724213i | \(-0.257797\pi\) | ||||
0.689577 | + | 0.724213i | \(0.257797\pi\) | |||||||
\(984\) | −76.6535 | −2.44362 | ||||||||
\(985\) | −2.72184 | −0.0867250 | ||||||||
\(986\) | 72.8973 | 2.32152 | ||||||||
\(987\) | 3.06234 | 0.0974754 | ||||||||
\(988\) | 3.59455 | 0.114358 | ||||||||
\(989\) | −6.50704 | −0.206912 | ||||||||
\(990\) | 4.79024 | 0.152244 | ||||||||
\(991\) | 5.17909 | 0.164519 | 0.0822597 | − | 0.996611i | \(-0.473786\pi\) | ||||
0.0822597 | + | 0.996611i | \(0.473786\pi\) | |||||||
\(992\) | −9.85331 | −0.312843 | ||||||||
\(993\) | −37.4351 | −1.18797 | ||||||||
\(994\) | −13.9042 | −0.441014 | ||||||||
\(995\) | 4.62754 | 0.146703 | ||||||||
\(996\) | −101.303 | −3.20990 | ||||||||
\(997\) | 37.7823 | 1.19658 | 0.598288 | − | 0.801281i | \(-0.295848\pi\) | ||||
0.598288 | + | 0.801281i | \(0.295848\pi\) | |||||||
\(998\) | −3.96298 | −0.125446 | ||||||||
\(999\) | −3.72898 | −0.117980 |
(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 | 8047.2.a.e.1.5 | ✓ | 168 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.e.1.5 | ✓ | 168 | 1.1 | even | 1 | trivial |