Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1681,2,Mod(1,1681)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1681, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1681.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1681 = 41^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1681.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: | \(13.4228525798\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 41) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1681.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71427 | −1.21217 | −0.606087 | − | 0.795399i | \(-0.707261\pi\) | ||||
−0.606087 | + | 0.795399i | \(0.707261\pi\) | |||||||
\(3\) | −3.15154 | −1.81954 | −0.909771 | − | 0.415110i | \(-0.863743\pi\) | ||||
−0.909771 | + | 0.415110i | \(0.863743\pi\) | |||||||
\(4\) | 0.938727 | 0.469364 | ||||||||
\(5\) | −2.70948 | −1.21172 | −0.605859 | − | 0.795572i | \(-0.707171\pi\) | ||||
−0.605859 | + | 0.795572i | \(0.707171\pi\) | |||||||
\(6\) | 5.40260 | 2.20560 | ||||||||
\(7\) | −1.61292 | −0.609625 | −0.304813 | − | 0.952412i | \(-0.598594\pi\) | ||||
−0.304813 | + | 0.952412i | \(0.598594\pi\) | |||||||
\(8\) | 1.81931 | 0.643223 | ||||||||
\(9\) | 6.93221 | 2.31074 | ||||||||
\(10\) | 4.64479 | 1.46881 | ||||||||
\(11\) | −0.692944 | −0.208930 | −0.104465 | − | 0.994529i | \(-0.533313\pi\) | ||||
−0.104465 | + | 0.994529i | \(0.533313\pi\) | |||||||
\(12\) | −2.95844 | −0.854027 | ||||||||
\(13\) | −1.52612 | −0.423269 | −0.211635 | − | 0.977349i | \(-0.567879\pi\) | ||||
−0.211635 | + | 0.977349i | \(0.567879\pi\) | |||||||
\(14\) | 2.76498 | 0.738972 | ||||||||
\(15\) | 8.53905 | 2.20477 | ||||||||
\(16\) | −4.99625 | −1.24906 | ||||||||
\(17\) | −1.05794 | −0.256588 | −0.128294 | − | 0.991736i | \(-0.540950\pi\) | ||||
−0.128294 | + | 0.991736i | \(0.540950\pi\) | |||||||
\(18\) | −11.8837 | −2.80101 | ||||||||
\(19\) | −0.128551 | −0.0294916 | −0.0147458 | − | 0.999891i | \(-0.504694\pi\) | ||||
−0.0147458 | + | 0.999891i | \(0.504694\pi\) | |||||||
\(20\) | −2.54347 | −0.568736 | ||||||||
\(21\) | 5.08317 | 1.10924 | ||||||||
\(22\) | 1.18789 | 0.253260 | ||||||||
\(23\) | 1.88345 | 0.392727 | 0.196363 | − | 0.980531i | \(-0.437087\pi\) | ||||
0.196363 | + | 0.980531i | \(0.437087\pi\) | |||||||
\(24\) | −5.73363 | −1.17037 | ||||||||
\(25\) | 2.34131 | 0.468261 | ||||||||
\(26\) | 2.61618 | 0.513076 | ||||||||
\(27\) | −12.3925 | −2.38494 | ||||||||
\(28\) | −1.51409 | −0.286136 | ||||||||
\(29\) | −8.29648 | −1.54062 | −0.770309 | − | 0.637671i | \(-0.779898\pi\) | ||||
−0.770309 | + | 0.637671i | \(0.779898\pi\) | |||||||
\(30\) | −14.6383 | −2.67257 | ||||||||
\(31\) | −1.20736 | −0.216848 | −0.108424 | − | 0.994105i | \(-0.534580\pi\) | ||||
−0.108424 | + | 0.994105i | \(0.534580\pi\) | |||||||
\(32\) | 4.92630 | 0.870855 | ||||||||
\(33\) | 2.18384 | 0.380158 | ||||||||
\(34\) | 1.81360 | 0.311029 | ||||||||
\(35\) | 4.37017 | 0.738694 | ||||||||
\(36\) | 6.50745 | 1.08457 | ||||||||
\(37\) | −6.04786 | −0.994262 | −0.497131 | − | 0.867675i | \(-0.665613\pi\) | ||||
−0.497131 | + | 0.867675i | \(0.665613\pi\) | |||||||
\(38\) | 0.220371 | 0.0357489 | ||||||||
\(39\) | 4.80963 | 0.770157 | ||||||||
\(40\) | −4.92939 | −0.779405 | ||||||||
\(41\) | 0 | 0 | ||||||||
\(42\) | −8.71394 | −1.34459 | ||||||||
\(43\) | −10.5792 | −1.61331 | −0.806655 | − | 0.591022i | \(-0.798724\pi\) | ||||
−0.806655 | + | 0.591022i | \(0.798724\pi\) | |||||||
\(44\) | −0.650485 | −0.0980643 | ||||||||
\(45\) | −18.7827 | −2.79996 | ||||||||
\(46\) | −3.22875 | −0.476053 | ||||||||
\(47\) | −6.34015 | −0.924806 | −0.462403 | − | 0.886670i | \(-0.653013\pi\) | ||||
−0.462403 | + | 0.886670i | \(0.653013\pi\) | |||||||
\(48\) | 15.7459 | 2.27272 | ||||||||
\(49\) | −4.39850 | −0.628357 | ||||||||
\(50\) | −4.01364 | −0.567614 | ||||||||
\(51\) | 3.33414 | 0.466873 | ||||||||
\(52\) | −1.43261 | −0.198667 | ||||||||
\(53\) | −12.4903 | −1.71567 | −0.857835 | − | 0.513925i | \(-0.828191\pi\) | ||||
−0.857835 | + | 0.513925i | \(0.828191\pi\) | |||||||
\(54\) | 21.2441 | 2.89096 | ||||||||
\(55\) | 1.87752 | 0.253165 | ||||||||
\(56\) | −2.93440 | −0.392125 | ||||||||
\(57\) | 0.405133 | 0.0536612 | ||||||||
\(58\) | 14.2224 | 1.86749 | ||||||||
\(59\) | 8.17953 | 1.06488 | 0.532442 | − | 0.846467i | \(-0.321274\pi\) | ||||
0.532442 | + | 0.846467i | \(0.321274\pi\) | |||||||
\(60\) | 8.01584 | 1.03484 | ||||||||
\(61\) | 2.63308 | 0.337131 | 0.168566 | − | 0.985690i | \(-0.446087\pi\) | ||||
0.168566 | + | 0.985690i | \(0.446087\pi\) | |||||||
\(62\) | 2.06974 | 0.262857 | ||||||||
\(63\) | −11.1811 | −1.40868 | ||||||||
\(64\) | 1.54747 | 0.193434 | ||||||||
\(65\) | 4.13500 | 0.512883 | ||||||||
\(66\) | −3.74369 | −0.460817 | ||||||||
\(67\) | −8.49003 | −1.03722 | −0.518611 | − | 0.855010i | \(-0.673551\pi\) | ||||
−0.518611 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(68\) | −0.993116 | −0.120433 | ||||||||
\(69\) | −5.93577 | −0.714583 | ||||||||
\(70\) | −7.49167 | −0.895425 | ||||||||
\(71\) | 4.29060 | 0.509201 | 0.254600 | − | 0.967046i | \(-0.418056\pi\) | ||||
0.254600 | + | 0.967046i | \(0.418056\pi\) | |||||||
\(72\) | 12.6118 | 1.48632 | ||||||||
\(73\) | −12.1957 | −1.42739 | −0.713697 | − | 0.700455i | \(-0.752981\pi\) | ||||
−0.713697 | + | 0.700455i | \(0.752981\pi\) | |||||||
\(74\) | 10.3677 | 1.20522 | ||||||||
\(75\) | −7.37872 | −0.852021 | ||||||||
\(76\) | −0.120674 | −0.0138423 | ||||||||
\(77\) | 1.11766 | 0.127369 | ||||||||
\(78\) | −8.24501 | −0.933563 | ||||||||
\(79\) | −11.5144 | −1.29547 | −0.647736 | − | 0.761865i | \(-0.724284\pi\) | ||||
−0.647736 | + | 0.761865i | \(0.724284\pi\) | |||||||
\(80\) | 13.5373 | 1.51351 | ||||||||
\(81\) | 18.2589 | 2.02876 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.49090 | 0.712469 | 0.356235 | − | 0.934397i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934397i | \(0.384060\pi\) | |||||||
\(84\) | 4.77171 | 0.520637 | ||||||||
\(85\) | 2.86647 | 0.310912 | ||||||||
\(86\) | 18.1356 | 1.95561 | ||||||||
\(87\) | 26.1467 | 2.80322 | ||||||||
\(88\) | −1.26068 | −0.134389 | ||||||||
\(89\) | 2.88381 | 0.305684 | 0.152842 | − | 0.988251i | \(-0.451157\pi\) | ||||
0.152842 | + | 0.988251i | \(0.451157\pi\) | |||||||
\(90\) | 32.1987 | 3.39404 | ||||||||
\(91\) | 2.46150 | 0.258036 | ||||||||
\(92\) | 1.76805 | 0.184332 | ||||||||
\(93\) | 3.80504 | 0.394564 | ||||||||
\(94\) | 10.8687 | 1.12103 | ||||||||
\(95\) | 0.348306 | 0.0357355 | ||||||||
\(96\) | −15.5254 | −1.58456 | ||||||||
\(97\) | −1.20901 | −0.122756 | −0.0613781 | − | 0.998115i | \(-0.519550\pi\) | ||||
−0.0613781 | + | 0.998115i | \(0.519550\pi\) | |||||||
\(98\) | 7.54022 | 0.761677 | ||||||||
\(99\) | −4.80363 | −0.482783 | ||||||||
\(100\) | 2.19785 | 0.219785 | ||||||||
\(101\) | −5.30173 | −0.527541 | −0.263771 | − | 0.964585i | \(-0.584966\pi\) | ||||
−0.263771 | + | 0.964585i | \(0.584966\pi\) | |||||||
\(102\) | −5.71562 | −0.565931 | ||||||||
\(103\) | 13.8765 | 1.36730 | 0.683648 | − | 0.729812i | \(-0.260392\pi\) | ||||
0.683648 | + | 0.729812i | \(0.260392\pi\) | |||||||
\(104\) | −2.77648 | −0.272257 | ||||||||
\(105\) | −13.7728 | −1.34409 | ||||||||
\(106\) | 21.4117 | 2.07969 | ||||||||
\(107\) | −9.53341 | −0.921630 | −0.460815 | − | 0.887496i | \(-0.652443\pi\) | ||||
−0.460815 | + | 0.887496i | \(0.652443\pi\) | |||||||
\(108\) | −11.6332 | −1.11940 | ||||||||
\(109\) | −2.35650 | −0.225712 | −0.112856 | − | 0.993611i | \(-0.536000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(110\) | −3.21858 | −0.306880 | ||||||||
\(111\) | 19.0601 | 1.80910 | ||||||||
\(112\) | 8.05853 | 0.761460 | ||||||||
\(113\) | 7.67722 | 0.722212 | 0.361106 | − | 0.932525i | \(-0.382399\pi\) | ||||
0.361106 | + | 0.932525i | \(0.382399\pi\) | |||||||
\(114\) | −0.694508 | −0.0650466 | ||||||||
\(115\) | −5.10318 | −0.475874 | ||||||||
\(116\) | −7.78813 | −0.723110 | ||||||||
\(117\) | −10.5794 | −0.978064 | ||||||||
\(118\) | −14.0219 | −1.29082 | ||||||||
\(119\) | 1.70637 | 0.156423 | ||||||||
\(120\) | 15.5352 | 1.41816 | ||||||||
\(121\) | −10.5198 | −0.956348 | ||||||||
\(122\) | −4.51381 | −0.408661 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.13338 | −0.101781 | ||||||||
\(125\) | 7.20369 | 0.644317 | ||||||||
\(126\) | 19.1674 | 1.70757 | ||||||||
\(127\) | 6.23197 | 0.552998 | 0.276499 | − | 0.961014i | \(-0.410826\pi\) | ||||
0.276499 | + | 0.961014i | \(0.410826\pi\) | |||||||
\(128\) | −12.5054 | −1.10533 | ||||||||
\(129\) | 33.3407 | 2.93549 | ||||||||
\(130\) | −7.08851 | −0.621703 | ||||||||
\(131\) | −0.725340 | −0.0633732 | −0.0316866 | − | 0.999498i | \(-0.510088\pi\) | ||||
−0.0316866 | + | 0.999498i | \(0.510088\pi\) | |||||||
\(132\) | 2.05003 | 0.178432 | ||||||||
\(133\) | 0.207342 | 0.0179788 | ||||||||
\(134\) | 14.5542 | 1.25729 | ||||||||
\(135\) | 33.5773 | 2.88987 | ||||||||
\(136\) | −1.92472 | −0.165043 | ||||||||
\(137\) | −18.6603 | −1.59426 | −0.797131 | − | 0.603807i | \(-0.793650\pi\) | ||||
−0.797131 | + | 0.603807i | \(0.793650\pi\) | |||||||
\(138\) | 10.1755 | 0.866199 | ||||||||
\(139\) | 6.34313 | 0.538017 | 0.269009 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269009 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(140\) | 4.10240 | 0.346716 | ||||||||
\(141\) | 19.9812 | 1.68272 | ||||||||
\(142\) | −7.35526 | −0.617240 | ||||||||
\(143\) | 1.05751 | 0.0884338 | ||||||||
\(144\) | −34.6350 | −2.88625 | ||||||||
\(145\) | 22.4792 | 1.86679 | ||||||||
\(146\) | 20.9067 | 1.73025 | ||||||||
\(147\) | 13.8620 | 1.14332 | ||||||||
\(148\) | −5.67729 | −0.466670 | ||||||||
\(149\) | 12.9287 | 1.05916 | 0.529579 | − | 0.848261i | \(-0.322350\pi\) | ||||
0.529579 | + | 0.848261i | \(0.322350\pi\) | |||||||
\(150\) | 12.6491 | 1.03280 | ||||||||
\(151\) | 1.39618 | 0.113620 | 0.0568098 | − | 0.998385i | \(-0.481907\pi\) | ||||
0.0568098 | + | 0.998385i | \(0.481907\pi\) | |||||||
\(152\) | −0.233874 | −0.0189697 | ||||||||
\(153\) | −7.33385 | −0.592907 | ||||||||
\(154\) | −1.91597 | −0.154394 | ||||||||
\(155\) | 3.27132 | 0.262759 | ||||||||
\(156\) | 4.51493 | 0.361483 | ||||||||
\(157\) | −17.5611 | −1.40153 | −0.700763 | − | 0.713394i | \(-0.747157\pi\) | ||||
−0.700763 | + | 0.713394i | \(0.747157\pi\) | |||||||
\(158\) | 19.7388 | 1.57034 | ||||||||
\(159\) | 39.3636 | 3.12174 | ||||||||
\(160\) | −13.3477 | −1.05523 | ||||||||
\(161\) | −3.03785 | −0.239416 | ||||||||
\(162\) | −31.3006 | −2.45921 | ||||||||
\(163\) | −17.6081 | −1.37918 | −0.689588 | − | 0.724202i | \(-0.742208\pi\) | ||||
−0.689588 | + | 0.724202i | \(0.742208\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.91708 | −0.460644 | ||||||||
\(166\) | −11.1272 | −0.863636 | ||||||||
\(167\) | 2.77606 | 0.214818 | 0.107409 | − | 0.994215i | \(-0.465745\pi\) | ||||
0.107409 | + | 0.994215i | \(0.465745\pi\) | |||||||
\(168\) | 9.24787 | 0.713489 | ||||||||
\(169\) | −10.6710 | −0.820843 | ||||||||
\(170\) | −4.91391 | −0.376880 | ||||||||
\(171\) | −0.891141 | −0.0681472 | ||||||||
\(172\) | −9.93097 | −0.757229 | ||||||||
\(173\) | −11.7096 | −0.890265 | −0.445132 | − | 0.895465i | \(-0.646843\pi\) | ||||
−0.445132 | + | 0.895465i | \(0.646843\pi\) | |||||||
\(174\) | −44.8225 | −3.39799 | ||||||||
\(175\) | −3.77633 | −0.285464 | ||||||||
\(176\) | 3.46212 | 0.260967 | ||||||||
\(177\) | −25.7781 | −1.93760 | ||||||||
\(178\) | −4.94364 | −0.370542 | ||||||||
\(179\) | −4.25363 | −0.317932 | −0.158966 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158966 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(180\) | −17.6318 | −1.31420 | ||||||||
\(181\) | −4.63621 | −0.344606 | −0.172303 | − | 0.985044i | \(-0.555121\pi\) | ||||
−0.172303 | + | 0.985044i | \(0.555121\pi\) | |||||||
\(182\) | −4.21969 | −0.312784 | ||||||||
\(183\) | −8.29825 | −0.613425 | ||||||||
\(184\) | 3.42658 | 0.252611 | ||||||||
\(185\) | 16.3866 | 1.20477 | ||||||||
\(186\) | −6.52287 | −0.478280 | ||||||||
\(187\) | 0.733093 | 0.0536090 | ||||||||
\(188\) | −5.95167 | −0.434070 | ||||||||
\(189\) | 19.9881 | 1.45392 | ||||||||
\(190\) | −0.597092 | −0.0433176 | ||||||||
\(191\) | 22.3688 | 1.61855 | 0.809275 | − | 0.587430i | \(-0.199860\pi\) | ||||
0.809275 | + | 0.587430i | \(0.199860\pi\) | |||||||
\(192\) | −4.87692 | −0.351962 | ||||||||
\(193\) | −14.5740 | −1.04906 | −0.524530 | − | 0.851392i | \(-0.675759\pi\) | ||||
−0.524530 | + | 0.851392i | \(0.675759\pi\) | |||||||
\(194\) | 2.07257 | 0.148802 | ||||||||
\(195\) | −13.0316 | −0.933213 | ||||||||
\(196\) | −4.12899 | −0.294928 | ||||||||
\(197\) | 0.930554 | 0.0662992 | 0.0331496 | − | 0.999450i | \(-0.489446\pi\) | ||||
0.0331496 | + | 0.999450i | \(0.489446\pi\) | |||||||
\(198\) | 8.23472 | 0.585216 | ||||||||
\(199\) | −0.412246 | −0.0292233 | −0.0146117 | − | 0.999893i | \(-0.504651\pi\) | ||||
−0.0146117 | + | 0.999893i | \(0.504651\pi\) | |||||||
\(200\) | 4.25956 | 0.301197 | ||||||||
\(201\) | 26.7567 | 1.88727 | ||||||||
\(202\) | 9.08860 | 0.639472 | ||||||||
\(203\) | 13.3815 | 0.939199 | ||||||||
\(204\) | 3.12985 | 0.219133 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −23.7881 | −1.65740 | ||||||||
\(207\) | 13.0565 | 0.907488 | ||||||||
\(208\) | 7.62487 | 0.528689 | ||||||||
\(209\) | 0.0890785 | 0.00616169 | ||||||||
\(210\) | 23.6103 | 1.62926 | ||||||||
\(211\) | −22.4233 | −1.54369 | −0.771843 | − | 0.635813i | \(-0.780665\pi\) | ||||
−0.771843 | + | 0.635813i | \(0.780665\pi\) | |||||||
\(212\) | −11.7250 | −0.805273 | ||||||||
\(213\) | −13.5220 | −0.926513 | ||||||||
\(214\) | 16.3429 | 1.11717 | ||||||||
\(215\) | 28.6641 | 1.95488 | ||||||||
\(216\) | −22.5458 | −1.53405 | ||||||||
\(217\) | 1.94737 | 0.132196 | ||||||||
\(218\) | 4.03969 | 0.273602 | ||||||||
\(219\) | 38.4351 | 2.59720 | ||||||||
\(220\) | 1.76248 | 0.118826 | ||||||||
\(221\) | 1.61454 | 0.108606 | ||||||||
\(222\) | −32.6741 | −2.19295 | ||||||||
\(223\) | −4.07615 | −0.272959 | −0.136480 | − | 0.990643i | \(-0.543579\pi\) | ||||
−0.136480 | + | 0.990643i | \(0.543579\pi\) | |||||||
\(224\) | −7.94572 | −0.530896 | ||||||||
\(225\) | 16.2304 | 1.08203 | ||||||||
\(226\) | −13.1608 | −0.875446 | ||||||||
\(227\) | 21.5929 | 1.43317 | 0.716584 | − | 0.697501i | \(-0.245705\pi\) | ||||
0.716584 | + | 0.697501i | \(0.245705\pi\) | |||||||
\(228\) | 0.380309 | 0.0251866 | ||||||||
\(229\) | 9.90746 | 0.654703 | 0.327352 | − | 0.944903i | \(-0.393844\pi\) | ||||
0.327352 | + | 0.944903i | \(0.393844\pi\) | |||||||
\(230\) | 8.74824 | 0.576842 | ||||||||
\(231\) | −3.52235 | −0.231754 | ||||||||
\(232\) | −15.0939 | −0.990961 | ||||||||
\(233\) | 1.28663 | 0.0842899 | 0.0421449 | − | 0.999112i | \(-0.486581\pi\) | ||||
0.0421449 | + | 0.999112i | \(0.486581\pi\) | |||||||
\(234\) | 18.1359 | 1.18558 | ||||||||
\(235\) | 17.1785 | 1.12060 | ||||||||
\(236\) | 7.67834 | 0.499818 | ||||||||
\(237\) | 36.2881 | 2.35717 | ||||||||
\(238\) | −2.92518 | −0.189611 | ||||||||
\(239\) | 7.09666 | 0.459045 | 0.229522 | − | 0.973303i | \(-0.426284\pi\) | ||||
0.229522 | + | 0.973303i | \(0.426284\pi\) | |||||||
\(240\) | −42.6632 | −2.75390 | ||||||||
\(241\) | −10.7877 | −0.694899 | −0.347449 | − | 0.937699i | \(-0.612952\pi\) | ||||
−0.347449 | + | 0.937699i | \(0.612952\pi\) | |||||||
\(242\) | 18.0338 | 1.15926 | ||||||||
\(243\) | −20.3660 | −1.30648 | ||||||||
\(244\) | 2.47174 | 0.158237 | ||||||||
\(245\) | 11.9177 | 0.761391 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.196184 | 0.0124829 | ||||||||
\(248\) | −2.19656 | −0.139482 | ||||||||
\(249\) | −20.4563 | −1.29637 | ||||||||
\(250\) | −12.3491 | −0.781024 | ||||||||
\(251\) | 5.62542 | 0.355073 | 0.177537 | − | 0.984114i | \(-0.443187\pi\) | ||||
0.177537 | + | 0.984114i | \(0.443187\pi\) | |||||||
\(252\) | −10.4960 | −0.661184 | ||||||||
\(253\) | −1.30513 | −0.0820526 | ||||||||
\(254\) | −10.6833 | −0.670329 | ||||||||
\(255\) | −9.03380 | −0.565718 | ||||||||
\(256\) | 18.3427 | 1.14642 | ||||||||
\(257\) | 21.9844 | 1.37135 | 0.685675 | − | 0.727908i | \(-0.259507\pi\) | ||||
0.685675 | + | 0.727908i | \(0.259507\pi\) | |||||||
\(258\) | −57.1551 | −3.55832 | ||||||||
\(259\) | 9.75470 | 0.606128 | ||||||||
\(260\) | 3.88163 | 0.240729 | ||||||||
\(261\) | −57.5129 | −3.55996 | ||||||||
\(262\) | 1.24343 | 0.0768193 | ||||||||
\(263\) | −5.86109 | −0.361410 | −0.180705 | − | 0.983537i | \(-0.557838\pi\) | ||||
−0.180705 | + | 0.983537i | \(0.557838\pi\) | |||||||
\(264\) | 3.97308 | 0.244526 | ||||||||
\(265\) | 33.8422 | 2.07891 | ||||||||
\(266\) | −0.355440 | −0.0217934 | ||||||||
\(267\) | −9.08846 | −0.556205 | ||||||||
\(268\) | −7.96982 | −0.486834 | ||||||||
\(269\) | −13.7302 | −0.837146 | −0.418573 | − | 0.908183i | \(-0.637470\pi\) | ||||
−0.418573 | + | 0.908183i | \(0.637470\pi\) | |||||||
\(270\) | −57.5606 | −3.50303 | ||||||||
\(271\) | 15.9129 | 0.966638 | 0.483319 | − | 0.875444i | \(-0.339431\pi\) | ||||
0.483319 | + | 0.875444i | \(0.339431\pi\) | |||||||
\(272\) | 5.28573 | 0.320494 | ||||||||
\(273\) | −7.75753 | −0.469507 | ||||||||
\(274\) | 31.9889 | 1.93252 | ||||||||
\(275\) | −1.62239 | −0.0978340 | ||||||||
\(276\) | −5.57207 | −0.335399 | ||||||||
\(277\) | 19.1964 | 1.15340 | 0.576699 | − | 0.816957i | \(-0.304341\pi\) | ||||
0.576699 | + | 0.816957i | \(0.304341\pi\) | |||||||
\(278\) | −10.8738 | −0.652170 | ||||||||
\(279\) | −8.36966 | −0.501078 | ||||||||
\(280\) | 7.95070 | 0.475145 | ||||||||
\(281\) | 1.45103 | 0.0865611 | 0.0432806 | − | 0.999063i | \(-0.486219\pi\) | ||||
0.0432806 | + | 0.999063i | \(0.486219\pi\) | |||||||
\(282\) | −34.2533 | −2.03975 | ||||||||
\(283\) | −9.42328 | −0.560156 | −0.280078 | − | 0.959977i | \(-0.590360\pi\) | ||||
−0.280078 | + | 0.959977i | \(0.590360\pi\) | |||||||
\(284\) | 4.02771 | 0.239000 | ||||||||
\(285\) | −1.09770 | −0.0650222 | ||||||||
\(286\) | −1.81287 | −0.107197 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 34.1501 | 2.01232 | ||||||||
\(289\) | −15.8808 | −0.934163 | ||||||||
\(290\) | −38.5354 | −2.26288 | ||||||||
\(291\) | 3.81024 | 0.223360 | ||||||||
\(292\) | −11.4484 | −0.669967 | ||||||||
\(293\) | 1.08492 | 0.0633820 | 0.0316910 | − | 0.999498i | \(-0.489911\pi\) | ||||
0.0316910 | + | 0.999498i | \(0.489911\pi\) | |||||||
\(294\) | −23.7633 | −1.38590 | ||||||||
\(295\) | −22.1623 | −1.29034 | ||||||||
\(296\) | −11.0029 | −0.639533 | ||||||||
\(297\) | 8.58731 | 0.498286 | ||||||||
\(298\) | −22.1633 | −1.28388 | ||||||||
\(299\) | −2.87437 | −0.166229 | ||||||||
\(300\) | −6.92661 | −0.399908 | ||||||||
\(301\) | 17.0633 | 0.983515 | ||||||||
\(302\) | −2.39343 | −0.137727 | ||||||||
\(303\) | 16.7086 | 0.959884 | ||||||||
\(304\) | 0.642271 | 0.0368368 | ||||||||
\(305\) | −7.13429 | −0.408508 | ||||||||
\(306\) | 12.5722 | 0.718706 | ||||||||
\(307\) | −29.6465 | −1.69202 | −0.846008 | − | 0.533170i | \(-0.821000\pi\) | ||||
−0.846008 | + | 0.533170i | \(0.821000\pi\) | |||||||
\(308\) | 1.04918 | 0.0597825 | ||||||||
\(309\) | −43.7325 | −2.48785 | ||||||||
\(310\) | −5.60793 | −0.318509 | ||||||||
\(311\) | −17.2471 | −0.977994 | −0.488997 | − | 0.872286i | \(-0.662637\pi\) | ||||
−0.488997 | + | 0.872286i | \(0.662637\pi\) | |||||||
\(312\) | 8.75020 | 0.495383 | ||||||||
\(313\) | −1.62235 | −0.0917008 | −0.0458504 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458504 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(314\) | 30.1045 | 1.69889 | ||||||||
\(315\) | 30.2949 | 1.70693 | ||||||||
\(316\) | −10.8089 | −0.608047 | ||||||||
\(317\) | −16.2930 | −0.915105 | −0.457552 | − | 0.889183i | \(-0.651274\pi\) | ||||
−0.457552 | + | 0.889183i | \(0.651274\pi\) | |||||||
\(318\) | −67.4799 | −3.78408 | ||||||||
\(319\) | 5.74899 | 0.321882 | ||||||||
\(320\) | −4.19285 | −0.234388 | ||||||||
\(321\) | 30.0449 | 1.67694 | ||||||||
\(322\) | 5.20770 | 0.290214 | ||||||||
\(323\) | 0.135999 | 0.00756719 | ||||||||
\(324\) | 17.1401 | 0.952227 | ||||||||
\(325\) | −3.57311 | −0.198201 | ||||||||
\(326\) | 30.1851 | 1.67180 | ||||||||
\(327\) | 7.42662 | 0.410693 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.2261 | 0.563786 | ||||||||
\(330\) | 10.1435 | 0.558380 | ||||||||
\(331\) | 25.3548 | 1.39362 | 0.696812 | − | 0.717254i | \(-0.254601\pi\) | ||||
0.696812 | + | 0.717254i | \(0.254601\pi\) | |||||||
\(332\) | 6.09318 | 0.334407 | ||||||||
\(333\) | −41.9250 | −2.29748 | ||||||||
\(334\) | −4.75893 | −0.260397 | ||||||||
\(335\) | 23.0036 | 1.25682 | ||||||||
\(336\) | −25.3968 | −1.38551 | ||||||||
\(337\) | 26.2434 | 1.42957 | 0.714785 | − | 0.699344i | \(-0.246525\pi\) | ||||
0.714785 | + | 0.699344i | \(0.246525\pi\) | |||||||
\(338\) | 18.2929 | 0.995004 | ||||||||
\(339\) | −24.1951 | −1.31410 | ||||||||
\(340\) | 2.69083 | 0.145931 | ||||||||
\(341\) | 0.836631 | 0.0453061 | ||||||||
\(342\) | 1.52766 | 0.0826062 | ||||||||
\(343\) | 18.3848 | 0.992688 | ||||||||
\(344\) | −19.2468 | −1.03772 | ||||||||
\(345\) | 16.0829 | 0.865874 | ||||||||
\(346\) | 20.0734 | 1.07915 | ||||||||
\(347\) | −16.6674 | −0.894751 | −0.447375 | − | 0.894346i | \(-0.647641\pi\) | ||||
−0.447375 | + | 0.894346i | \(0.647641\pi\) | |||||||
\(348\) | 24.5446 | 1.31573 | ||||||||
\(349\) | 8.65063 | 0.463058 | 0.231529 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231529 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(350\) | 6.47366 | 0.346032 | ||||||||
\(351\) | 18.9124 | 1.00947 | ||||||||
\(352\) | −3.41365 | −0.181948 | ||||||||
\(353\) | −13.7928 | −0.734115 | −0.367058 | − | 0.930198i | \(-0.619635\pi\) | ||||
−0.367058 | + | 0.930198i | \(0.619635\pi\) | |||||||
\(354\) | 44.1907 | 2.34871 | ||||||||
\(355\) | −11.6253 | −0.617008 | ||||||||
\(356\) | 2.70711 | 0.143477 | ||||||||
\(357\) | −5.37769 | −0.284618 | ||||||||
\(358\) | 7.29188 | 0.385388 | ||||||||
\(359\) | 18.1150 | 0.956075 | 0.478038 | − | 0.878339i | \(-0.341348\pi\) | ||||
0.478038 | + | 0.878339i | \(0.341348\pi\) | |||||||
\(360\) | −34.1716 | −1.80100 | ||||||||
\(361\) | −18.9835 | −0.999130 | ||||||||
\(362\) | 7.94772 | 0.417723 | ||||||||
\(363\) | 33.1537 | 1.74012 | ||||||||
\(364\) | 2.31068 | 0.121113 | ||||||||
\(365\) | 33.0439 | 1.72960 | ||||||||
\(366\) | 14.2255 | 0.743577 | ||||||||
\(367\) | −23.0926 | −1.20543 | −0.602713 | − | 0.797958i | \(-0.705913\pi\) | ||||
−0.602713 | + | 0.797958i | \(0.705913\pi\) | |||||||
\(368\) | −9.41019 | −0.490540 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.0911 | −1.46038 | ||||||||
\(371\) | 20.1458 | 1.04592 | ||||||||
\(372\) | 3.57189 | 0.185194 | ||||||||
\(373\) | −14.1402 | −0.732151 | −0.366076 | − | 0.930585i | \(-0.619299\pi\) | ||||
−0.366076 | + | 0.930585i | \(0.619299\pi\) | |||||||
\(374\) | −1.25672 | −0.0649834 | ||||||||
\(375\) | −22.7027 | −1.17236 | ||||||||
\(376\) | −11.5347 | −0.594857 | ||||||||
\(377\) | 12.6614 | 0.652096 | ||||||||
\(378\) | −34.2650 | −1.76240 | ||||||||
\(379\) | −37.1747 | −1.90953 | −0.954767 | − | 0.297354i | \(-0.903896\pi\) | ||||
−0.954767 | + | 0.297354i | \(0.903896\pi\) | |||||||
\(380\) | 0.326965 | 0.0167729 | ||||||||
\(381\) | −19.6403 | −1.00620 | ||||||||
\(382\) | −38.3462 | −1.96196 | ||||||||
\(383\) | 6.92178 | 0.353686 | 0.176843 | − | 0.984239i | \(-0.443411\pi\) | ||||
0.176843 | + | 0.984239i | \(0.443411\pi\) | |||||||
\(384\) | 39.4112 | 2.01120 | ||||||||
\(385\) | −3.02828 | −0.154336 | ||||||||
\(386\) | 24.9838 | 1.27164 | ||||||||
\(387\) | −73.3371 | −3.72793 | ||||||||
\(388\) | −1.13493 | −0.0576173 | ||||||||
\(389\) | −2.36723 | −0.120023 | −0.0600117 | − | 0.998198i | \(-0.519114\pi\) | ||||
−0.0600117 | + | 0.998198i | \(0.519114\pi\) | |||||||
\(390\) | 22.3397 | 1.13122 | ||||||||
\(391\) | −1.99258 | −0.100769 | ||||||||
\(392\) | −8.00223 | −0.404174 | ||||||||
\(393\) | 2.28594 | 0.115310 | ||||||||
\(394\) | −1.59522 | −0.0803661 | ||||||||
\(395\) | 31.1981 | 1.56975 | ||||||||
\(396\) | −4.50930 | −0.226601 | ||||||||
\(397\) | −16.1503 | −0.810559 | −0.405279 | − | 0.914193i | \(-0.632826\pi\) | ||||
−0.405279 | + | 0.914193i | \(0.632826\pi\) | |||||||
\(398\) | 0.706702 | 0.0354238 | ||||||||
\(399\) | −0.653446 | −0.0327132 | ||||||||
\(400\) | −11.6977 | −0.584887 | ||||||||
\(401\) | 4.77242 | 0.238323 | 0.119162 | − | 0.992875i | \(-0.461979\pi\) | ||||
0.119162 | + | 0.992875i | \(0.461979\pi\) | |||||||
\(402\) | −45.8682 | −2.28770 | ||||||||
\(403\) | 1.84257 | 0.0917851 | ||||||||
\(404\) | −4.97687 | −0.247609 | ||||||||
\(405\) | −49.4721 | −2.45829 | ||||||||
\(406\) | −22.9396 | −1.13847 | ||||||||
\(407\) | 4.19083 | 0.207732 | ||||||||
\(408\) | 6.06583 | 0.300303 | ||||||||
\(409\) | 9.57331 | 0.473370 | 0.236685 | − | 0.971586i | \(-0.423939\pi\) | ||||
0.236685 | + | 0.971586i | \(0.423939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 58.8088 | 2.90083 | ||||||||
\(412\) | 13.0263 | 0.641759 | ||||||||
\(413\) | −13.1929 | −0.649180 | ||||||||
\(414\) | −22.3823 | −1.10003 | ||||||||
\(415\) | −17.5870 | −0.863312 | ||||||||
\(416\) | −7.51813 | −0.368606 | ||||||||
\(417\) | −19.9906 | −0.978945 | ||||||||
\(418\) | −0.152705 | −0.00746903 | ||||||||
\(419\) | 8.06247 | 0.393878 | 0.196939 | − | 0.980416i | \(-0.436900\pi\) | ||||
0.196939 | + | 0.980416i | \(0.436900\pi\) | |||||||
\(420\) | −12.9289 | −0.630865 | ||||||||
\(421\) | 17.6577 | 0.860585 | 0.430292 | − | 0.902690i | \(-0.358410\pi\) | ||||
0.430292 | + | 0.902690i | \(0.358410\pi\) | |||||||
\(422\) | 38.4397 | 1.87121 | ||||||||
\(423\) | −43.9512 | −2.13698 | ||||||||
\(424\) | −22.7237 | −1.10356 | ||||||||
\(425\) | −2.47696 | −0.120150 | ||||||||
\(426\) | 23.1804 | 1.12309 | ||||||||
\(427\) | −4.24694 | −0.205524 | ||||||||
\(428\) | −8.94927 | −0.432579 | ||||||||
\(429\) | −3.33280 | −0.160909 | ||||||||
\(430\) | −49.1381 | −2.36965 | ||||||||
\(431\) | −10.1535 | −0.489075 | −0.244537 | − | 0.969640i | \(-0.578636\pi\) | ||||
−0.244537 | + | 0.969640i | \(0.578636\pi\) | |||||||
\(432\) | 61.9160 | 2.97893 | ||||||||
\(433\) | 33.2213 | 1.59651 | 0.798256 | − | 0.602318i | \(-0.205756\pi\) | ||||
0.798256 | + | 0.602318i | \(0.205756\pi\) | |||||||
\(434\) | −3.33832 | −0.160244 | ||||||||
\(435\) | −70.8440 | −3.39671 | ||||||||
\(436\) | −2.21211 | −0.105941 | ||||||||
\(437\) | −0.242119 | −0.0115821 | ||||||||
\(438\) | −65.8882 | −3.14826 | ||||||||
\(439\) | 36.8515 | 1.75883 | 0.879413 | − | 0.476060i | \(-0.157935\pi\) | ||||
0.879413 | + | 0.476060i | \(0.157935\pi\) | |||||||
\(440\) | 3.41579 | 0.162841 | ||||||||
\(441\) | −30.4913 | −1.45197 | ||||||||
\(442\) | −2.76776 | −0.131649 | ||||||||
\(443\) | 30.8429 | 1.46539 | 0.732694 | − | 0.680558i | \(-0.238262\pi\) | ||||
0.732694 | + | 0.680558i | \(0.238262\pi\) | |||||||
\(444\) | 17.8922 | 0.849127 | ||||||||
\(445\) | −7.81365 | −0.370403 | ||||||||
\(446\) | 6.98763 | 0.330874 | ||||||||
\(447\) | −40.7452 | −1.92718 | ||||||||
\(448\) | −2.49595 | −0.117922 | ||||||||
\(449\) | −29.6350 | −1.39856 | −0.699282 | − | 0.714846i | \(-0.746497\pi\) | ||||
−0.699282 | + | 0.714846i | \(0.746497\pi\) | |||||||
\(450\) | −27.8233 | −1.31161 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.20681 | 0.338980 | ||||||||
\(453\) | −4.40012 | −0.206736 | ||||||||
\(454\) | −37.0160 | −1.73725 | ||||||||
\(455\) | −6.66941 | −0.312667 | ||||||||
\(456\) | 0.737063 | 0.0345161 | ||||||||
\(457\) | −7.59375 | −0.355221 | −0.177610 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177610 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(458\) | −16.9841 | −0.793614 | ||||||||
\(459\) | 13.1105 | 0.611947 | ||||||||
\(460\) | −4.79050 | −0.223358 | ||||||||
\(461\) | −25.2841 | −1.17760 | −0.588800 | − | 0.808279i | \(-0.700399\pi\) | ||||
−0.588800 | + | 0.808279i | \(0.700399\pi\) | |||||||
\(462\) | 6.03827 | 0.280926 | ||||||||
\(463\) | 14.7447 | 0.685246 | 0.342623 | − | 0.939473i | \(-0.388685\pi\) | ||||
0.342623 | + | 0.939473i | \(0.388685\pi\) | |||||||
\(464\) | 41.4512 | 1.92433 | ||||||||
\(465\) | −10.3097 | −0.478101 | ||||||||
\(466\) | −2.20563 | −0.102174 | ||||||||
\(467\) | −22.1233 | −1.02374 | −0.511872 | − | 0.859062i | \(-0.671048\pi\) | ||||
−0.511872 | + | 0.859062i | \(0.671048\pi\) | |||||||
\(468\) | −9.93114 | −0.459067 | ||||||||
\(469\) | 13.6937 | 0.632317 | ||||||||
\(470\) | −29.4487 | −1.35837 | ||||||||
\(471\) | 55.3445 | 2.55014 | ||||||||
\(472\) | 14.8811 | 0.684958 | ||||||||
\(473\) | 7.33078 | 0.337070 | ||||||||
\(474\) | −62.2077 | −2.85729 | ||||||||
\(475\) | −0.300977 | −0.0138098 | ||||||||
\(476\) | 1.60181 | 0.0734191 | ||||||||
\(477\) | −86.5851 | −3.96446 | ||||||||
\(478\) | −12.1656 | −0.556441 | ||||||||
\(479\) | 15.8848 | 0.725795 | 0.362898 | − | 0.931829i | \(-0.381787\pi\) | ||||
0.362898 | + | 0.931829i | \(0.381787\pi\) | |||||||
\(480\) | 42.0659 | 1.92004 | ||||||||
\(481\) | 9.22976 | 0.420841 | ||||||||
\(482\) | 18.4931 | 0.842337 | ||||||||
\(483\) | 9.57391 | 0.435628 | ||||||||
\(484\) | −9.87525 | −0.448875 | ||||||||
\(485\) | 3.27579 | 0.148746 | ||||||||
\(486\) | 34.9129 | 1.58368 | ||||||||
\(487\) | −21.0380 | −0.953323 | −0.476662 | − | 0.879087i | \(-0.658153\pi\) | ||||
−0.476662 | + | 0.879087i | \(0.658153\pi\) | |||||||
\(488\) | 4.79039 | 0.216851 | ||||||||
\(489\) | 55.4928 | 2.50947 | ||||||||
\(490\) | −20.4301 | −0.922938 | ||||||||
\(491\) | 0.0541126 | 0.00244207 | 0.00122103 | − | 0.999999i | \(-0.499611\pi\) | ||||
0.00122103 | + | 0.999999i | \(0.499611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.77717 | 0.395304 | ||||||||
\(494\) | −0.336312 | −0.0151314 | ||||||||
\(495\) | 13.0154 | 0.584997 | ||||||||
\(496\) | 6.03226 | 0.270856 | ||||||||
\(497\) | −6.92039 | −0.310422 | ||||||||
\(498\) | 35.0677 | 1.57142 | ||||||||
\(499\) | 32.5037 | 1.45507 | 0.727533 | − | 0.686073i | \(-0.240667\pi\) | ||||
0.727533 | + | 0.686073i | \(0.240667\pi\) | |||||||
\(500\) | 6.76230 | 0.302419 | ||||||||
\(501\) | −8.74887 | −0.390871 | ||||||||
\(502\) | −9.64350 | −0.430410 | ||||||||
\(503\) | 32.2851 | 1.43952 | 0.719760 | − | 0.694223i | \(-0.244252\pi\) | ||||
0.719760 | + | 0.694223i | \(0.244252\pi\) | |||||||
\(504\) | −20.3418 | −0.906098 | ||||||||
\(505\) | 14.3649 | 0.639232 | ||||||||
\(506\) | 2.23734 | 0.0994619 | ||||||||
\(507\) | 33.6300 | 1.49356 | ||||||||
\(508\) | 5.85011 | 0.259557 | ||||||||
\(509\) | 28.8657 | 1.27945 | 0.639724 | − | 0.768604i | \(-0.279049\pi\) | ||||
0.639724 | + | 0.768604i | \(0.279049\pi\) | |||||||
\(510\) | 15.4864 | 0.685749 | ||||||||
\(511\) | 19.6706 | 0.870176 | ||||||||
\(512\) | −6.43357 | −0.284326 | ||||||||
\(513\) | 1.59307 | 0.0703356 | ||||||||
\(514\) | −37.6872 | −1.66231 | ||||||||
\(515\) | −37.5983 | −1.65678 | ||||||||
\(516\) | 31.2978 | 1.37781 | ||||||||
\(517\) | 4.39337 | 0.193220 | ||||||||
\(518\) | −16.7222 | −0.734731 | ||||||||
\(519\) | 36.9033 | 1.61987 | ||||||||
\(520\) | 7.52284 | 0.329898 | ||||||||
\(521\) | −17.5099 | −0.767121 | −0.383560 | − | 0.923516i | \(-0.625302\pi\) | ||||
−0.383560 | + | 0.923516i | \(0.625302\pi\) | |||||||
\(522\) | 98.5927 | 4.31529 | ||||||||
\(523\) | −7.28359 | −0.318489 | −0.159245 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159245 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(524\) | −0.680896 | −0.0297451 | ||||||||
\(525\) | 11.9013 | 0.519414 | ||||||||
\(526\) | 10.0475 | 0.438092 | ||||||||
\(527\) | 1.27731 | 0.0556406 | ||||||||
\(528\) | −10.9110 | −0.474840 | ||||||||
\(529\) | −19.4526 | −0.845766 | ||||||||
\(530\) | −58.0147 | −2.52000 | ||||||||
\(531\) | 56.7022 | 2.46066 | ||||||||
\(532\) | 0.194637 | 0.00843860 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 15.5801 | 0.674216 | ||||||||
\(535\) | 25.8306 | 1.11676 | ||||||||
\(536\) | −15.4460 | −0.667165 | ||||||||
\(537\) | 13.4055 | 0.578490 | ||||||||
\(538\) | 23.5373 | 1.01477 | ||||||||
\(539\) | 3.04791 | 0.131283 | ||||||||
\(540\) | 31.5199 | 1.35640 | ||||||||
\(541\) | 30.4703 | 1.31002 | 0.655011 | − | 0.755620i | \(-0.272664\pi\) | ||||
0.655011 | + | 0.755620i | \(0.272664\pi\) | |||||||
\(542\) | −27.2790 | −1.17173 | ||||||||
\(543\) | 14.6112 | 0.627026 | ||||||||
\(544\) | −5.21173 | −0.223451 | ||||||||
\(545\) | 6.38491 | 0.273500 | ||||||||
\(546\) | 13.2985 | 0.569124 | ||||||||
\(547\) | 32.4922 | 1.38927 | 0.694634 | − | 0.719364i | \(-0.255566\pi\) | ||||
0.694634 | + | 0.719364i | \(0.255566\pi\) | |||||||
\(548\) | −17.5170 | −0.748288 | ||||||||
\(549\) | 18.2530 | 0.779021 | ||||||||
\(550\) | 2.78122 | 0.118592 | ||||||||
\(551\) | 1.06652 | 0.0454352 | ||||||||
\(552\) | −10.7990 | −0.459637 | ||||||||
\(553\) | 18.5718 | 0.789753 | ||||||||
\(554\) | −32.9078 | −1.39812 | ||||||||
\(555\) | −51.6430 | −2.19212 | ||||||||
\(556\) | 5.95447 | 0.252526 | ||||||||
\(557\) | −24.8381 | −1.05242 | −0.526211 | − | 0.850354i | \(-0.676388\pi\) | ||||
−0.526211 | + | 0.850354i | \(0.676388\pi\) | |||||||
\(558\) | 14.3479 | 0.607394 | ||||||||
\(559\) | 16.1451 | 0.682865 | ||||||||
\(560\) | −21.8345 | −0.922675 | ||||||||
\(561\) | −2.31037 | −0.0975439 | ||||||||
\(562\) | −2.48746 | −0.104927 | ||||||||
\(563\) | 24.9154 | 1.05006 | 0.525029 | − | 0.851085i | \(-0.324055\pi\) | ||||
0.525029 | + | 0.851085i | \(0.324055\pi\) | |||||||
\(564\) | 18.7569 | 0.789810 | ||||||||
\(565\) | −20.8013 | −0.875118 | ||||||||
\(566\) | 16.1541 | 0.679006 | ||||||||
\(567\) | −29.4500 | −1.23679 | ||||||||
\(568\) | 7.80594 | 0.327530 | ||||||||
\(569\) | 14.0530 | 0.589131 | 0.294565 | − | 0.955631i | \(-0.404825\pi\) | ||||
0.294565 | + | 0.955631i | \(0.404825\pi\) | |||||||
\(570\) | 1.88176 | 0.0788182 | ||||||||
\(571\) | −30.7133 | −1.28531 | −0.642657 | − | 0.766154i | \(-0.722168\pi\) | ||||
−0.642657 | + | 0.766154i | \(0.722168\pi\) | |||||||
\(572\) | 0.992718 | 0.0415076 | ||||||||
\(573\) | −70.4962 | −2.94502 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.40974 | 0.183899 | ||||||||
\(576\) | 10.7274 | 0.446975 | ||||||||
\(577\) | −0.149336 | −0.00621693 | −0.00310846 | − | 0.999995i | \(-0.500989\pi\) | ||||
−0.00310846 | + | 0.999995i | \(0.500989\pi\) | |||||||
\(578\) | 27.2239 | 1.13237 | ||||||||
\(579\) | 45.9306 | 1.90881 | ||||||||
\(580\) | 21.1018 | 0.876205 | ||||||||
\(581\) | −10.4693 | −0.434339 | ||||||||
\(582\) | −6.53178 | −0.270751 | ||||||||
\(583\) | 8.65505 | 0.358456 | ||||||||
\(584\) | −22.1877 | −0.918133 | ||||||||
\(585\) | 28.6647 | 1.18514 | ||||||||
\(586\) | −1.85985 | −0.0768299 | ||||||||
\(587\) | 16.0049 | 0.660593 | 0.330296 | − | 0.943877i | \(-0.392851\pi\) | ||||
0.330296 | + | 0.943877i | \(0.392851\pi\) | |||||||
\(588\) | 13.0127 | 0.536634 | ||||||||
\(589\) | 0.155207 | 0.00639519 | ||||||||
\(590\) | 37.9922 | 1.56411 | ||||||||
\(591\) | −2.93268 | −0.120634 | ||||||||
\(592\) | 30.2166 | 1.24189 | ||||||||
\(593\) | 1.96819 | 0.0808239 | 0.0404120 | − | 0.999183i | \(-0.487133\pi\) | ||||
0.0404120 | + | 0.999183i | \(0.487133\pi\) | |||||||
\(594\) | −14.7210 | −0.604009 | ||||||||
\(595\) | −4.62338 | −0.189540 | ||||||||
\(596\) | 12.1365 | 0.497130 | ||||||||
\(597\) | 1.29921 | 0.0531731 | ||||||||
\(598\) | 4.92746 | 0.201499 | ||||||||
\(599\) | 18.6180 | 0.760712 | 0.380356 | − | 0.924840i | \(-0.375801\pi\) | ||||
0.380356 | + | 0.924840i | \(0.375801\pi\) | |||||||
\(600\) | −13.4242 | −0.548040 | ||||||||
\(601\) | 10.0007 | 0.407939 | 0.203970 | − | 0.978977i | \(-0.434616\pi\) | ||||
0.203970 | + | 0.978977i | \(0.434616\pi\) | |||||||
\(602\) | −29.2512 | −1.19219 | ||||||||
\(603\) | −58.8546 | −2.39675 | ||||||||
\(604\) | 1.31063 | 0.0533289 | ||||||||
\(605\) | 28.5033 | 1.15882 | ||||||||
\(606\) | −28.6431 | −1.16355 | ||||||||
\(607\) | 37.9289 | 1.53948 | 0.769742 | − | 0.638355i | \(-0.220385\pi\) | ||||
0.769742 | + | 0.638355i | \(0.220385\pi\) | |||||||
\(608\) | −0.633280 | −0.0256829 | ||||||||
\(609\) | −42.1724 | −1.70891 | ||||||||
\(610\) | 12.2301 | 0.495182 | ||||||||
\(611\) | 9.67583 | 0.391442 | ||||||||
\(612\) | −6.88449 | −0.278289 | ||||||||
\(613\) | 27.0143 | 1.09110 | 0.545549 | − | 0.838079i | \(-0.316321\pi\) | ||||
0.545549 | + | 0.838079i | \(0.316321\pi\) | |||||||
\(614\) | 50.8222 | 2.05102 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.03337 | 0.0819269 | ||||||||
\(617\) | −10.0246 | −0.403574 | −0.201787 | − | 0.979429i | \(-0.564675\pi\) | ||||
−0.201787 | + | 0.979429i | \(0.564675\pi\) | |||||||
\(618\) | 74.9693 | 3.01571 | ||||||||
\(619\) | −33.3272 | −1.33953 | −0.669766 | − | 0.742572i | \(-0.733606\pi\) | ||||
−0.669766 | + | 0.742572i | \(0.733606\pi\) | |||||||
\(620\) | 3.07088 | 0.123329 | ||||||||
\(621\) | −23.3407 | −0.936629 | ||||||||
\(622\) | 29.5662 | 1.18550 | ||||||||
\(623\) | −4.65135 | −0.186353 | ||||||||
\(624\) | −24.0301 | −0.961973 | ||||||||
\(625\) | −31.2248 | −1.24899 | ||||||||
\(626\) | 2.78115 | 0.111157 | ||||||||
\(627\) | −0.280734 | −0.0112115 | ||||||||
\(628\) | −16.4851 | −0.657826 | ||||||||
\(629\) | 6.39827 | 0.255116 | ||||||||
\(630\) | −51.9338 | −2.06909 | ||||||||
\(631\) | −10.5324 | −0.419289 | −0.209644 | − | 0.977778i | \(-0.567231\pi\) | ||||
−0.209644 | + | 0.977778i | \(0.567231\pi\) | |||||||
\(632\) | −20.9483 | −0.833278 | ||||||||
\(633\) | 70.6680 | 2.80880 | ||||||||
\(634\) | 27.9306 | 1.10927 | ||||||||
\(635\) | −16.8854 | −0.670077 | ||||||||
\(636\) | 36.9517 | 1.46523 | ||||||||
\(637\) | 6.71263 | 0.265964 | ||||||||
\(638\) | −9.85533 | −0.390176 | ||||||||
\(639\) | 29.7433 | 1.17663 | ||||||||
\(640\) | 33.8832 | 1.33935 | ||||||||
\(641\) | −4.64277 | −0.183379 | −0.0916893 | − | 0.995788i | \(-0.529227\pi\) | ||||
−0.0916893 | + | 0.995788i | \(0.529227\pi\) | |||||||
\(642\) | −51.5052 | −2.03275 | ||||||||
\(643\) | 30.0438 | 1.18481 | 0.592407 | − | 0.805639i | \(-0.298178\pi\) | ||||
0.592407 | + | 0.805639i | \(0.298178\pi\) | |||||||
\(644\) | −2.85171 | −0.112373 | ||||||||
\(645\) | −90.3362 | −3.55698 | ||||||||
\(646\) | −0.233139 | −0.00917274 | ||||||||
\(647\) | 16.4853 | 0.648104 | 0.324052 | − | 0.946039i | \(-0.394955\pi\) | ||||
0.324052 | + | 0.946039i | \(0.394955\pi\) | |||||||
\(648\) | 33.2185 | 1.30495 | ||||||||
\(649\) | −5.66795 | −0.222487 | ||||||||
\(650\) | 6.12529 | 0.240254 | ||||||||
\(651\) | −6.13721 | −0.240536 | ||||||||
\(652\) | −16.5292 | −0.647335 | ||||||||
\(653\) | 33.3959 | 1.30688 | 0.653441 | − | 0.756977i | \(-0.273325\pi\) | ||||
0.653441 | + | 0.756977i | \(0.273325\pi\) | |||||||
\(654\) | −12.7312 | −0.497831 | ||||||||
\(655\) | 1.96530 | 0.0767905 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −84.5428 | −3.29833 | ||||||||
\(658\) | −17.5304 | −0.683406 | ||||||||
\(659\) | 4.77185 | 0.185885 | 0.0929425 | − | 0.995671i | \(-0.470373\pi\) | ||||
0.0929425 | + | 0.995671i | \(0.470373\pi\) | |||||||
\(660\) | −5.55452 | −0.216210 | ||||||||
\(661\) | 12.9311 | 0.502962 | 0.251481 | − | 0.967862i | \(-0.419082\pi\) | ||||
0.251481 | + | 0.967862i | \(0.419082\pi\) | |||||||
\(662\) | −43.4650 | −1.68931 | ||||||||
\(663\) | −5.08829 | −0.197613 | ||||||||
\(664\) | 11.8090 | 0.458277 | ||||||||
\(665\) | −0.561789 | −0.0217853 | ||||||||
\(666\) | 71.8709 | 2.78494 | ||||||||
\(667\) | −15.6260 | −0.605042 | ||||||||
\(668\) | 2.60597 | 0.100828 | ||||||||
\(669\) | 12.8462 | 0.496661 | ||||||||
\(670\) | −39.4344 | −1.52348 | ||||||||
\(671\) | −1.82458 | −0.0704369 | ||||||||
\(672\) | 25.0412 | 0.965987 | ||||||||
\(673\) | −6.35874 | −0.245111 | −0.122556 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122556 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(674\) | −44.9883 | −1.73289 | ||||||||
\(675\) | −29.0147 | −1.11677 | ||||||||
\(676\) | −10.0171 | −0.385274 | ||||||||
\(677\) | −34.9105 | −1.34172 | −0.670859 | − | 0.741585i | \(-0.734074\pi\) | ||||
−0.670859 | + | 0.741585i | \(0.734074\pi\) | |||||||
\(678\) | 41.4769 | 1.59291 | ||||||||
\(679\) | 1.95003 | 0.0748353 | ||||||||
\(680\) | 5.21500 | 0.199986 | ||||||||
\(681\) | −68.0508 | −2.60771 | ||||||||
\(682\) | −1.43421 | −0.0549189 | ||||||||
\(683\) | 25.0272 | 0.957641 | 0.478820 | − | 0.877913i | \(-0.341065\pi\) | ||||
0.478820 | + | 0.877913i | \(0.341065\pi\) | |||||||
\(684\) | −0.836538 | −0.0319858 | ||||||||
\(685\) | 50.5599 | 1.93180 | ||||||||
\(686\) | −31.5166 | −1.20331 | ||||||||
\(687\) | −31.2238 | −1.19126 | ||||||||
\(688\) | 52.8562 | 2.01512 | ||||||||
\(689\) | 19.0616 | 0.726191 | ||||||||
\(690\) | −27.5704 | −1.04959 | ||||||||
\(691\) | −26.6246 | −1.01285 | −0.506424 | − | 0.862285i | \(-0.669033\pi\) | ||||
−0.506424 | + | 0.862285i | \(0.669033\pi\) | |||||||
\(692\) | −10.9921 | −0.417858 | ||||||||
\(693\) | 7.74786 | 0.294317 | ||||||||
\(694\) | 28.5724 | 1.08459 | ||||||||
\(695\) | −17.1866 | −0.651925 | ||||||||
\(696\) | 47.5689 | 1.80310 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14.8295 | −0.561306 | ||||||||
\(699\) | −4.05486 | −0.153369 | ||||||||
\(700\) | −3.54495 | −0.133986 | ||||||||
\(701\) | −20.7971 | −0.785497 | −0.392749 | − | 0.919646i | \(-0.628476\pi\) | ||||
−0.392749 | + | 0.919646i | \(0.628476\pi\) | |||||||
\(702\) | −32.4211 | −1.22365 | ||||||||
\(703\) | 0.777457 | 0.0293224 | ||||||||
\(704\) | −1.07231 | −0.0404143 | ||||||||
\(705\) | −54.1389 | −2.03899 | ||||||||
\(706\) | 23.6446 | 0.889874 | ||||||||
\(707\) | 8.55125 | 0.321603 | ||||||||
\(708\) | −24.1986 | −0.909439 | ||||||||
\(709\) | 8.79271 | 0.330217 | 0.165109 | − | 0.986275i | \(-0.447203\pi\) | ||||
0.165109 | + | 0.986275i | \(0.447203\pi\) | |||||||
\(710\) | 19.9290 | 0.747921 | ||||||||
\(711\) | −79.8202 | −2.99349 | ||||||||
\(712\) | 5.24655 | 0.196623 | ||||||||
\(713\) | −2.27400 | −0.0851620 | ||||||||
\(714\) | 9.21882 | 0.345006 | ||||||||
\(715\) | −2.86532 | −0.107157 | ||||||||
\(716\) | −3.99300 | −0.149225 | ||||||||
\(717\) | −22.3654 | −0.835251 | ||||||||
\(718\) | −31.0541 | −1.15893 | ||||||||
\(719\) | −13.0553 | −0.486880 | −0.243440 | − | 0.969916i | \(-0.578276\pi\) | ||||
−0.243440 | + | 0.969916i | \(0.578276\pi\) | |||||||
\(720\) | 93.8430 | 3.49732 | ||||||||
\(721\) | −22.3817 | −0.833538 | ||||||||
\(722\) | 32.5428 | 1.21112 | ||||||||
\(723\) | 33.9980 | 1.26440 | ||||||||
\(724\) | −4.35213 | −0.161746 | ||||||||
\(725\) | −19.4246 | −0.721412 | ||||||||
\(726\) | −56.8344 | −2.10932 | ||||||||
\(727\) | −27.6930 | −1.02708 | −0.513538 | − | 0.858067i | \(-0.671665\pi\) | ||||
−0.513538 | + | 0.858067i | \(0.671665\pi\) | |||||||
\(728\) | 4.47824 | 0.165975 | ||||||||
\(729\) | 9.40774 | 0.348435 | ||||||||
\(730\) | −56.6463 | −2.09657 | ||||||||
\(731\) | 11.1921 | 0.413956 | ||||||||
\(732\) | −7.78979 | −0.287919 | ||||||||
\(733\) | 24.4503 | 0.903091 | 0.451545 | − | 0.892248i | \(-0.350873\pi\) | ||||
0.451545 | + | 0.892248i | \(0.350873\pi\) | |||||||
\(734\) | 39.5870 | 1.46118 | ||||||||
\(735\) | −37.5590 | −1.38538 | ||||||||
\(736\) | 9.27845 | 0.342008 | ||||||||
\(737\) | 5.88311 | 0.216707 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1342 | −1.29243 | −0.646215 | − | 0.763155i | \(-0.723649\pi\) | ||||
−0.646215 | + | 0.763155i | \(0.723649\pi\) | |||||||
\(740\) | 15.3825 | 0.565473 | ||||||||
\(741\) | −0.618281 | −0.0227131 | ||||||||
\(742\) | −34.5353 | −1.26783 | ||||||||
\(743\) | 5.72093 | 0.209881 | 0.104940 | − | 0.994479i | \(-0.466535\pi\) | ||||
0.104940 | + | 0.994479i | \(0.466535\pi\) | |||||||
\(744\) | 6.92254 | 0.253793 | ||||||||
\(745\) | −35.0300 | −1.28340 | ||||||||
\(746\) | 24.2401 | 0.887494 | ||||||||
\(747\) | 44.9963 | 1.64633 | ||||||||
\(748\) | 0.688174 | 0.0251621 | ||||||||
\(749\) | 15.3766 | 0.561849 | ||||||||
\(750\) | 38.9186 | 1.42111 | ||||||||
\(751\) | −11.6727 | −0.425943 | −0.212972 | − | 0.977058i | \(-0.568314\pi\) | ||||
−0.212972 | + | 0.977058i | \(0.568314\pi\) | |||||||
\(752\) | 31.6770 | 1.15514 | ||||||||
\(753\) | −17.7287 | −0.646071 | ||||||||
\(754\) | −21.7051 | −0.790453 | ||||||||
\(755\) | −3.78293 | −0.137675 | ||||||||
\(756\) | 18.7634 | 0.682417 | ||||||||
\(757\) | 38.3826 | 1.39504 | 0.697519 | − | 0.716566i | \(-0.254287\pi\) | ||||
0.697519 | + | 0.716566i | \(0.254287\pi\) | |||||||
\(758\) | 63.7275 | 2.31469 | ||||||||
\(759\) | 4.11316 | 0.149298 | ||||||||
\(760\) | 0.633677 | 0.0229859 | ||||||||
\(761\) | 48.2836 | 1.75028 | 0.875140 | − | 0.483871i | \(-0.160769\pi\) | ||||
0.875140 | + | 0.483871i | \(0.160769\pi\) | |||||||
\(762\) | 33.6688 | 1.21969 | ||||||||
\(763\) | 3.80085 | 0.137600 | ||||||||
\(764\) | 20.9982 | 0.759689 | ||||||||
\(765\) | 19.8710 | 0.718436 | ||||||||
\(766\) | −11.8658 | −0.428729 | ||||||||
\(767\) | −12.4829 | −0.450733 | ||||||||
\(768\) | −57.8077 | −2.08596 | ||||||||
\(769\) | −3.92461 | −0.141525 | −0.0707625 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707625 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(770\) | 5.19130 | 0.187082 | ||||||||
\(771\) | −69.2847 | −2.49523 | ||||||||
\(772\) | −13.6810 | −0.492391 | ||||||||
\(773\) | 33.3650 | 1.20005 | 0.600027 | − | 0.799979i | \(-0.295156\pi\) | ||||
0.600027 | + | 0.799979i | \(0.295156\pi\) | |||||||
\(774\) | 125.720 | 4.51890 | ||||||||
\(775\) | −2.82680 | −0.101542 | ||||||||
\(776\) | −2.19956 | −0.0789596 | ||||||||
\(777\) | −30.7423 | −1.10287 | ||||||||
\(778\) | 4.05808 | 0.145489 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −12.2331 | −0.438016 | ||||||||
\(781\) | −2.97315 | −0.106388 | ||||||||
\(782\) | 3.41582 | 0.122149 | ||||||||
\(783\) | 102.814 | 3.67428 | ||||||||
\(784\) | 21.9760 | 0.784856 | ||||||||
\(785\) | 47.5815 | 1.69826 | ||||||||
\(786\) | −3.91872 | −0.139776 | ||||||||
\(787\) | 11.2780 | 0.402018 | 0.201009 | − | 0.979589i | \(-0.435578\pi\) | ||||
0.201009 | + | 0.979589i | \(0.435578\pi\) | |||||||
\(788\) | 0.873536 | 0.0311184 | ||||||||
\(789\) | 18.4715 | 0.657602 | ||||||||
\(790\) | −53.4820 | −1.90280 | ||||||||
\(791\) | −12.3827 | −0.440279 | ||||||||
\(792\) | −8.73929 | −0.310537 | ||||||||
\(793\) | −4.01839 | −0.142697 | ||||||||
\(794\) | 27.6859 | 0.982538 | ||||||||
\(795\) | −106.655 | −3.78266 | ||||||||
\(796\) | −0.386986 | −0.0137164 | ||||||||
\(797\) | −28.5583 | −1.01159 | −0.505793 | − | 0.862655i | \(-0.668800\pi\) | ||||
−0.505793 | + | 0.862655i | \(0.668800\pi\) | |||||||
\(798\) | 1.12018 | 0.0396541 | ||||||||
\(799\) | 6.70750 | 0.237294 | ||||||||
\(800\) | 11.5340 | 0.407788 | ||||||||
\(801\) | 19.9912 | 0.706354 | ||||||||
\(802\) | −8.18122 | −0.288889 | ||||||||
\(803\) | 8.45090 | 0.298226 | ||||||||
\(804\) | 25.1172 | 0.885816 | ||||||||
\(805\) | 8.23101 | 0.290105 | ||||||||
\(806\) | −3.15867 | −0.111259 | ||||||||
\(807\) | 43.2713 | 1.52322 | ||||||||
\(808\) | −9.64548 | −0.339327 | ||||||||
\(809\) | 10.6581 | 0.374717 | 0.187359 | − | 0.982292i | \(-0.440007\pi\) | ||||
0.187359 | + | 0.982292i | \(0.440007\pi\) | |||||||
\(810\) | 84.8086 | 2.97987 | ||||||||
\(811\) | −33.8780 | −1.18962 | −0.594809 | − | 0.803867i | \(-0.702772\pi\) | ||||
−0.594809 | + | 0.803867i | \(0.702772\pi\) | |||||||
\(812\) | 12.5616 | 0.440826 | ||||||||
\(813\) | −50.1500 | −1.75884 | ||||||||
\(814\) | −7.18422 | −0.251807 | ||||||||
\(815\) | 47.7090 | 1.67117 | ||||||||
\(816\) | −16.6582 | −0.583153 | ||||||||
\(817\) | 1.35996 | 0.0475791 | ||||||||
\(818\) | −16.4113 | −0.573806 | ||||||||
\(819\) | 17.0637 | 0.596252 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.1853 | 1.75148 | 0.875739 | − | 0.482785i | \(-0.160375\pi\) | ||||
0.875739 | + | 0.482785i | \(0.160375\pi\) | |||||||
\(822\) | −100.814 | −3.51630 | ||||||||
\(823\) | 45.0545 | 1.57050 | 0.785251 | − | 0.619178i | \(-0.212534\pi\) | ||||
0.785251 | + | 0.619178i | \(0.212534\pi\) | |||||||
\(824\) | 25.2457 | 0.879476 | ||||||||
\(825\) | 5.11304 | 0.178013 | ||||||||
\(826\) | 22.6162 | 0.786919 | ||||||||
\(827\) | −3.57914 | −0.124459 | −0.0622295 | − | 0.998062i | \(-0.519821\pi\) | ||||
−0.0622295 | + | 0.998062i | \(0.519821\pi\) | |||||||
\(828\) | 12.2565 | 0.425942 | ||||||||
\(829\) | 18.5904 | 0.645672 | 0.322836 | − | 0.946455i | \(-0.395364\pi\) | ||||
0.322836 | + | 0.946455i | \(0.395364\pi\) | |||||||
\(830\) | 30.1489 | 1.04648 | ||||||||
\(831\) | −60.4981 | −2.09866 | ||||||||
\(832\) | −2.36163 | −0.0818747 | ||||||||
\(833\) | 4.65334 | 0.161229 | ||||||||
\(834\) | 34.2694 | 1.18665 | ||||||||
\(835\) | −7.52170 | −0.260299 | ||||||||
\(836\) | 0.0836204 | 0.00289207 | ||||||||
\(837\) | 14.9622 | 0.517169 | ||||||||
\(838\) | −13.8213 | −0.477448 | ||||||||
\(839\) | −36.2824 | −1.25261 | −0.626304 | − | 0.779579i | \(-0.715433\pi\) | ||||
−0.626304 | + | 0.779579i | \(0.715433\pi\) | |||||||
\(840\) | −25.0570 | −0.864547 | ||||||||
\(841\) | 39.8315 | 1.37350 | ||||||||
\(842\) | −30.2701 | −1.04318 | ||||||||
\(843\) | −4.57297 | −0.157502 | ||||||||
\(844\) | −21.0494 | −0.724550 | ||||||||
\(845\) | 28.9128 | 0.994631 | ||||||||
\(846\) | 75.3444 | 2.59039 | ||||||||
\(847\) | 16.9676 | 0.583014 | ||||||||
\(848\) | 62.4045 | 2.14298 | ||||||||
\(849\) | 29.6979 | 1.01923 | ||||||||
\(850\) | 4.24618 | 0.145643 | ||||||||
\(851\) | −11.3909 | −0.390473 | ||||||||
\(852\) | −12.6935 | −0.434871 | ||||||||
\(853\) | −16.0614 | −0.549933 | −0.274966 | − | 0.961454i | \(-0.588667\pi\) | ||||
−0.274966 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(854\) | 7.28041 | 0.249130 | ||||||||
\(855\) | 2.41453 | 0.0825752 | ||||||||
\(856\) | −17.3442 | −0.592814 | ||||||||
\(857\) | −15.8027 | −0.539809 | −0.269904 | − | 0.962887i | \(-0.586992\pi\) | ||||
−0.269904 | + | 0.962887i | \(0.586992\pi\) | |||||||
\(858\) | 5.71333 | 0.195050 | ||||||||
\(859\) | 20.2212 | 0.689937 | 0.344969 | − | 0.938614i | \(-0.387890\pi\) | ||||
0.344969 | + | 0.938614i | \(0.387890\pi\) | |||||||
\(860\) | 26.9078 | 0.917548 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.4058 | 0.592843 | ||||||||
\(863\) | −10.7247 | −0.365074 | −0.182537 | − | 0.983199i | \(-0.558431\pi\) | ||||
−0.182537 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(864\) | −61.0492 | −2.07694 | ||||||||
\(865\) | 31.7270 | 1.07875 | ||||||||
\(866\) | −56.9503 | −1.93525 | ||||||||
\(867\) | 50.0489 | 1.69975 | ||||||||
\(868\) | 1.82805 | 0.0620480 | ||||||||
\(869\) | 7.97883 | 0.270663 | ||||||||
\(870\) | 121.446 | 4.11740 | ||||||||
\(871\) | 12.9568 | 0.439024 | ||||||||
\(872\) | −4.28721 | −0.145183 | ||||||||
\(873\) | −8.38109 | −0.283657 | ||||||||
\(874\) | 0.415058 | 0.0140396 | ||||||||
\(875\) | −11.6190 | −0.392792 | ||||||||
\(876\) | 36.0801 | 1.21903 | ||||||||
\(877\) | −12.0861 | −0.408120 | −0.204060 | − | 0.978958i | \(-0.565414\pi\) | ||||
−0.204060 | + | 0.978958i | \(0.565414\pi\) | |||||||
\(878\) | −63.1735 | −2.13200 | ||||||||
\(879\) | −3.41918 | −0.115326 | ||||||||
\(880\) | −9.38055 | −0.316218 | ||||||||
\(881\) | −9.42951 | −0.317688 | −0.158844 | − | 0.987304i | \(-0.550777\pi\) | ||||
−0.158844 | + | 0.987304i | \(0.550777\pi\) | |||||||
\(882\) | 52.2704 | 1.76003 | ||||||||
\(883\) | 23.5030 | 0.790938 | 0.395469 | − | 0.918479i | \(-0.370582\pi\) | ||||
0.395469 | + | 0.918479i | \(0.370582\pi\) | |||||||
\(884\) | 1.51561 | 0.0509756 | ||||||||
\(885\) | 69.8454 | 2.34783 | ||||||||
\(886\) | −52.8730 | −1.77630 | ||||||||
\(887\) | −48.5055 | −1.62866 | −0.814328 | − | 0.580405i | \(-0.802894\pi\) | ||||
−0.814328 | + | 0.580405i | \(0.802894\pi\) | |||||||
\(888\) | 34.6762 | 1.16366 | ||||||||
\(889\) | −10.0516 | −0.337121 | ||||||||
\(890\) | 13.3947 | 0.448992 | ||||||||
\(891\) | −12.6524 | −0.423870 | ||||||||
\(892\) | −3.82639 | −0.128117 | ||||||||
\(893\) | 0.815032 | 0.0272740 | ||||||||
\(894\) | 69.8484 | 2.33608 | ||||||||
\(895\) | 11.5252 | 0.385243 | ||||||||
\(896\) | 20.1702 | 0.673838 | ||||||||
\(897\) | 9.05870 | 0.302461 | ||||||||
\(898\) | 50.8025 | 1.69530 | ||||||||
\(899\) | 10.0168 | 0.334080 | ||||||||
\(900\) | 15.2359 | 0.507864 | ||||||||
\(901\) | 13.2140 | 0.440221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.7758 | −1.78955 | ||||||||
\(904\) | 13.9672 | 0.464544 | ||||||||
\(905\) | 12.5617 | 0.417566 | ||||||||
\(906\) | 7.54300 | 0.250599 | ||||||||
\(907\) | −8.58540 | −0.285074 | −0.142537 | − | 0.989790i | \(-0.545526\pi\) | ||||
−0.142537 | + | 0.989790i | \(0.545526\pi\) | |||||||
\(908\) | 20.2698 | 0.672677 | ||||||||
\(909\) | −36.7527 | −1.21901 | ||||||||
\(910\) | 11.4332 | 0.379006 | ||||||||
\(911\) | −21.0427 | −0.697176 | −0.348588 | − | 0.937276i | \(-0.613339\pi\) | ||||
−0.348588 | + | 0.937276i | \(0.613339\pi\) | |||||||
\(912\) | −2.02414 | −0.0670261 | ||||||||
\(913\) | −4.49783 | −0.148856 | ||||||||
\(914\) | 13.0178 | 0.430589 | ||||||||
\(915\) | 22.4840 | 0.743298 | ||||||||
\(916\) | 9.30040 | 0.307294 | ||||||||
\(917\) | 1.16991 | 0.0386339 | ||||||||
\(918\) | −22.4750 | −0.741785 | ||||||||
\(919\) | −47.8628 | −1.57885 | −0.789424 | − | 0.613848i | \(-0.789621\pi\) | ||||
−0.789424 | + | 0.613848i | \(0.789621\pi\) | |||||||
\(920\) | −9.28427 | −0.306093 | ||||||||
\(921\) | 93.4322 | 3.07869 | ||||||||
\(922\) | 43.3439 | 1.42746 | ||||||||
\(923\) | −6.54797 | −0.215529 | ||||||||
\(924\) | −3.30653 | −0.108777 | ||||||||
\(925\) | −14.1599 | −0.465575 | ||||||||
\(926\) | −25.2765 | −0.830637 | ||||||||
\(927\) | 96.1950 | 3.15946 | ||||||||
\(928\) | −40.8710 | −1.34165 | ||||||||
\(929\) | −52.1656 | −1.71150 | −0.855748 | − | 0.517392i | \(-0.826903\pi\) | ||||
−0.855748 | + | 0.517392i | \(0.826903\pi\) | |||||||
\(930\) | 17.6736 | 0.579541 | ||||||||
\(931\) | 0.565430 | 0.0185312 | ||||||||
\(932\) | 1.20779 | 0.0395626 | ||||||||
\(933\) | 54.3549 | 1.77950 | ||||||||
\(934\) | 37.9253 | 1.24096 | ||||||||
\(935\) | −1.98630 | −0.0649591 | ||||||||
\(936\) | −19.2472 | −0.629113 | ||||||||
\(937\) | −15.2606 | −0.498543 | −0.249271 | − | 0.968434i | \(-0.580191\pi\) | ||||
−0.249271 | + | 0.968434i | \(0.580191\pi\) | |||||||
\(938\) | −23.4747 | −0.766478 | ||||||||
\(939\) | 5.11291 | 0.166854 | ||||||||
\(940\) | 16.1260 | 0.525971 | ||||||||
\(941\) | −55.3336 | −1.80382 | −0.901912 | − | 0.431919i | \(-0.857837\pi\) | ||||
−0.901912 | + | 0.431919i | \(0.857837\pi\) | |||||||
\(942\) | −94.8754 | −3.09121 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −40.8669 | −1.33011 | ||||||||
\(945\) | −54.1574 | −1.76174 | ||||||||
\(946\) | −12.5669 | −0.408587 | ||||||||
\(947\) | 1.57167 | 0.0510723 | 0.0255362 | − | 0.999674i | \(-0.491871\pi\) | ||||
0.0255362 | + | 0.999674i | \(0.491871\pi\) | |||||||
\(948\) | 34.0646 | 1.10637 | ||||||||
\(949\) | 18.6120 | 0.604172 | ||||||||
\(950\) | 0.515956 | 0.0167398 | ||||||||
\(951\) | 51.3480 | 1.66507 | ||||||||
\(952\) | 3.10441 | 0.100615 | ||||||||
\(953\) | 42.6660 | 1.38209 | 0.691044 | − | 0.722812i | \(-0.257151\pi\) | ||||
0.691044 | + | 0.722812i | \(0.257151\pi\) | |||||||
\(954\) | 148.430 | 4.80561 | ||||||||
\(955\) | −60.6080 | −1.96123 | ||||||||
\(956\) | 6.66182 | 0.215459 | ||||||||
\(957\) | −18.1182 | −0.585678 | ||||||||
\(958\) | −27.2309 | −0.879789 | ||||||||
\(959\) | 30.0976 | 0.971902 | ||||||||
\(960\) | 13.2139 | 0.426478 | ||||||||
\(961\) | −29.5423 | −0.952977 | ||||||||
\(962\) | −15.8223 | −0.510132 | ||||||||
\(963\) | −66.0876 | −2.12964 | ||||||||
\(964\) | −10.1267 | −0.326160 | ||||||||
\(965\) | 39.4881 | 1.27117 | ||||||||
\(966\) | −16.4123 | −0.528057 | ||||||||
\(967\) | 4.13912 | 0.133105 | 0.0665525 | − | 0.997783i | \(-0.478800\pi\) | ||||
0.0665525 | + | 0.997783i | \(0.478800\pi\) | |||||||
\(968\) | −19.1388 | −0.615145 | ||||||||
\(969\) | −0.428606 | −0.0137688 | ||||||||
\(970\) | −5.61559 | −0.180306 | ||||||||
\(971\) | −16.0357 | −0.514611 | −0.257306 | − | 0.966330i | \(-0.582835\pi\) | ||||
−0.257306 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(972\) | −19.1181 | −0.613214 | ||||||||
\(973\) | −10.2309 | −0.327989 | ||||||||
\(974\) | 36.0649 | 1.15559 | ||||||||
\(975\) | 11.2608 | 0.360635 | ||||||||
\(976\) | −13.1555 | −0.421098 | ||||||||
\(977\) | −42.7852 | −1.36882 | −0.684410 | − | 0.729098i | \(-0.739940\pi\) | ||||
−0.684410 | + | 0.729098i | \(0.739940\pi\) | |||||||
\(978\) | −95.1297 | −3.04191 | ||||||||
\(979\) | −1.99832 | −0.0638666 | ||||||||
\(980\) | 11.1874 | 0.357369 | ||||||||
\(981\) | −16.3358 | −0.521561 | ||||||||
\(982\) | −0.0927636 | −0.00296021 | ||||||||
\(983\) | 31.6046 | 1.00803 | 0.504015 | − | 0.863695i | \(-0.331856\pi\) | ||||
0.504015 | + | 0.863695i | \(0.331856\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.52132 | −0.0803360 | ||||||||
\(986\) | −15.0465 | −0.479177 | ||||||||
\(987\) | −32.2281 | −1.02583 | ||||||||
\(988\) | 0.184163 | 0.00585901 | ||||||||
\(989\) | −19.9254 | −0.633590 | ||||||||
\(990\) | −22.3119 | −0.709117 | ||||||||
\(991\) | 27.4148 | 0.870858 | 0.435429 | − | 0.900223i | \(-0.356597\pi\) | ||||
0.435429 | + | 0.900223i | \(0.356597\pi\) | |||||||
\(992\) | −5.94781 | −0.188843 | ||||||||
\(993\) | −79.9066 | −2.53576 | ||||||||
\(994\) | 11.8634 | 0.376285 | ||||||||
\(995\) | 1.11697 | 0.0354105 | ||||||||
\(996\) | −19.2029 | −0.608468 | ||||||||
\(997\) | 24.8267 | 0.786270 | 0.393135 | − | 0.919481i | \(-0.371391\pi\) | ||||
0.393135 | + | 0.919481i | \(0.371391\pi\) | |||||||
\(998\) | −55.7202 | −1.76379 | ||||||||
\(999\) | 74.9481 | 2.37125 |
(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 | 1681.2.a.m.1.3 | 24 | ||
41.13 | odd | 40 | 41.2.g.a.5.1 | ✓ | 24 | ||
41.19 | odd | 40 | 41.2.g.a.33.1 | yes | 24 | ||
41.40 | even | 2 | inner | 1681.2.a.m.1.4 | 24 | ||
123.95 | even | 40 | 369.2.u.a.46.3 | 24 | |||
123.101 | even | 40 | 369.2.u.a.361.3 | 24 | |||
164.19 | even | 40 | 656.2.bs.d.33.1 | 24 | |||
164.95 | even | 40 | 656.2.bs.d.497.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.2.g.a.5.1 | ✓ | 24 | 41.13 | odd | 40 | ||
41.2.g.a.33.1 | yes | 24 | 41.19 | odd | 40 | ||
369.2.u.a.46.3 | 24 | 123.95 | even | 40 | |||
369.2.u.a.361.3 | 24 | 123.101 | even | 40 | |||
656.2.bs.d.33.1 | 24 | 164.19 | even | 40 | |||
656.2.bs.d.497.1 | 24 | 164.95 | even | 40 | |||
1681.2.a.m.1.3 | 24 | 1.1 | even | 1 | trivial | ||
1681.2.a.m.1.4 | 24 | 41.40 | even | 2 | inner |