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: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.78532 | −1.96952 | −0.984758 | − | 0.173930i | \(-0.944353\pi\) | ||||
−0.984758 | + | 0.173930i | \(0.944353\pi\) | |||||||
\(3\) | −0.218444 | −0.126119 | −0.0630595 | − | 0.998010i | \(-0.520086\pi\) | ||||
−0.0630595 | + | 0.998010i | \(0.520086\pi\) | |||||||
\(4\) | 5.75799 | 2.87899 | ||||||||
\(5\) | 3.30077 | 1.47615 | 0.738074 | − | 0.674719i | \(-0.235735\pi\) | ||||
0.738074 | + | 0.674719i | \(0.235735\pi\) | |||||||
\(6\) | 0.608437 | 0.248393 | ||||||||
\(7\) | −0.196953 | −0.0744413 | −0.0372206 | − | 0.999307i | \(-0.511850\pi\) | ||||
−0.0372206 | + | 0.999307i | \(0.511850\pi\) | |||||||
\(8\) | −10.4672 | −3.70071 | ||||||||
\(9\) | −2.95228 | −0.984094 | ||||||||
\(10\) | −9.19368 | −2.90730 | ||||||||
\(11\) | −0.112785 | −0.0340059 | −0.0170030 | − | 0.999855i | \(-0.505412\pi\) | ||||
−0.0170030 | + | 0.999855i | \(0.505412\pi\) | |||||||
\(12\) | −1.25780 | −0.363096 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.548577 | 0.146613 | ||||||||
\(15\) | −0.721034 | −0.186170 | ||||||||
\(16\) | 17.6384 | 4.40961 | ||||||||
\(17\) | 1.07399 | 0.260480 | 0.130240 | − | 0.991483i | \(-0.458425\pi\) | ||||
0.130240 | + | 0.991483i | \(0.458425\pi\) | |||||||
\(18\) | 8.22304 | 1.93819 | ||||||||
\(19\) | 2.45645 | 0.563548 | 0.281774 | − | 0.959481i | \(-0.409077\pi\) | ||||
0.281774 | + | 0.959481i | \(0.409077\pi\) | |||||||
\(20\) | 19.0058 | 4.24982 | ||||||||
\(21\) | 0.0430233 | 0.00938845 | ||||||||
\(22\) | 0.314141 | 0.0669752 | ||||||||
\(23\) | −2.79072 | −0.581906 | −0.290953 | − | 0.956737i | \(-0.593972\pi\) | ||||
−0.290953 | + | 0.956737i | \(0.593972\pi\) | |||||||
\(24\) | 2.28650 | 0.466729 | ||||||||
\(25\) | 5.89507 | 1.17901 | ||||||||
\(26\) | −2.78532 | −0.546245 | ||||||||
\(27\) | 1.30024 | 0.250232 | ||||||||
\(28\) | −1.13405 | −0.214316 | ||||||||
\(29\) | −4.40077 | −0.817203 | −0.408601 | − | 0.912713i | \(-0.633983\pi\) | ||||
−0.408601 | + | 0.912713i | \(0.633983\pi\) | |||||||
\(30\) | 2.00831 | 0.366665 | ||||||||
\(31\) | 9.82701 | 1.76498 | 0.882492 | − | 0.470328i | \(-0.155864\pi\) | ||||
0.882492 | + | 0.470328i | \(0.155864\pi\) | |||||||
\(32\) | −28.1943 | −4.98409 | ||||||||
\(33\) | 0.0246372 | 0.00428879 | ||||||||
\(34\) | −2.99139 | −0.513019 | ||||||||
\(35\) | −0.650097 | −0.109886 | ||||||||
\(36\) | −16.9992 | −2.83320 | ||||||||
\(37\) | −1.84834 | −0.303865 | −0.151932 | − | 0.988391i | \(-0.548550\pi\) | ||||
−0.151932 | + | 0.988391i | \(0.548550\pi\) | |||||||
\(38\) | −6.84199 | −1.10992 | ||||||||
\(39\) | −0.218444 | −0.0349791 | ||||||||
\(40\) | −34.5497 | −5.46279 | ||||||||
\(41\) | −7.55605 | −1.18006 | −0.590028 | − | 0.807383i | \(-0.700883\pi\) | ||||
−0.590028 | + | 0.807383i | \(0.700883\pi\) | |||||||
\(42\) | −0.119833 | −0.0184907 | ||||||||
\(43\) | 0.395497 | 0.0603128 | 0.0301564 | − | 0.999545i | \(-0.490399\pi\) | ||||
0.0301564 | + | 0.999545i | \(0.490399\pi\) | |||||||
\(44\) | −0.649414 | −0.0979028 | ||||||||
\(45\) | −9.74480 | −1.45267 | ||||||||
\(46\) | 7.77305 | 1.14607 | ||||||||
\(47\) | −7.12697 | −1.03958 | −0.519788 | − | 0.854295i | \(-0.673989\pi\) | ||||
−0.519788 | + | 0.854295i | \(0.673989\pi\) | |||||||
\(48\) | −3.85302 | −0.556135 | ||||||||
\(49\) | −6.96121 | −0.994458 | ||||||||
\(50\) | −16.4196 | −2.32209 | ||||||||
\(51\) | −0.234606 | −0.0328514 | ||||||||
\(52\) | 5.75799 | 0.798489 | ||||||||
\(53\) | 3.72379 | 0.511503 | 0.255751 | − | 0.966743i | \(-0.417677\pi\) | ||||
0.255751 | + | 0.966743i | \(0.417677\pi\) | |||||||
\(54\) | −3.62159 | −0.492836 | ||||||||
\(55\) | −0.372277 | −0.0501978 | ||||||||
\(56\) | 2.06154 | 0.275485 | ||||||||
\(57\) | −0.536597 | −0.0710741 | ||||||||
\(58\) | 12.2575 | 1.60949 | ||||||||
\(59\) | −8.99756 | −1.17138 | −0.585691 | − | 0.810534i | \(-0.699177\pi\) | ||||
−0.585691 | + | 0.810534i | \(0.699177\pi\) | |||||||
\(60\) | −4.15171 | −0.535983 | ||||||||
\(61\) | 4.26565 | 0.546160 | 0.273080 | − | 0.961991i | \(-0.411958\pi\) | ||||
0.273080 | + | 0.961991i | \(0.411958\pi\) | |||||||
\(62\) | −27.3713 | −3.47616 | ||||||||
\(63\) | 0.581461 | 0.0732572 | ||||||||
\(64\) | 43.2531 | 5.40663 | ||||||||
\(65\) | 3.30077 | 0.409410 | ||||||||
\(66\) | −0.0686224 | −0.00844684 | ||||||||
\(67\) | −9.82507 | −1.20032 | −0.600162 | − | 0.799879i | \(-0.704897\pi\) | ||||
−0.600162 | + | 0.799879i | \(0.704897\pi\) | |||||||
\(68\) | 6.18400 | 0.749920 | ||||||||
\(69\) | 0.609618 | 0.0733894 | ||||||||
\(70\) | 1.81072 | 0.216423 | ||||||||
\(71\) | 2.31105 | 0.274271 | 0.137136 | − | 0.990552i | \(-0.456210\pi\) | ||||
0.137136 | + | 0.990552i | \(0.456210\pi\) | |||||||
\(72\) | 30.9021 | 3.64184 | ||||||||
\(73\) | −0.109087 | −0.0127677 | −0.00638384 | − | 0.999980i | \(-0.502032\pi\) | ||||
−0.00638384 | + | 0.999980i | \(0.502032\pi\) | |||||||
\(74\) | 5.14820 | 0.598466 | ||||||||
\(75\) | −1.28775 | −0.148696 | ||||||||
\(76\) | 14.1442 | 1.62245 | ||||||||
\(77\) | 0.0222133 | 0.00253144 | ||||||||
\(78\) | 0.608437 | 0.0688919 | ||||||||
\(79\) | −12.1736 | −1.36963 | −0.684816 | − | 0.728716i | \(-0.740118\pi\) | ||||
−0.684816 | + | 0.728716i | \(0.740118\pi\) | |||||||
\(80\) | 58.2204 | 6.50924 | ||||||||
\(81\) | 8.57282 | 0.952535 | ||||||||
\(82\) | 21.0460 | 2.32414 | ||||||||
\(83\) | −2.73580 | −0.300293 | −0.150146 | − | 0.988664i | \(-0.547975\pi\) | ||||
−0.150146 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(84\) | 0.247728 | 0.0270293 | ||||||||
\(85\) | 3.54498 | 0.384507 | ||||||||
\(86\) | −1.10158 | −0.118787 | ||||||||
\(87\) | 0.961323 | 0.103065 | ||||||||
\(88\) | 1.18054 | 0.125846 | ||||||||
\(89\) | −3.45780 | −0.366526 | −0.183263 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183263 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(90\) | 27.1423 | 2.86105 | ||||||||
\(91\) | −0.196953 | −0.0206463 | ||||||||
\(92\) | −16.0690 | −1.67530 | ||||||||
\(93\) | −2.14666 | −0.222598 | ||||||||
\(94\) | 19.8509 | 2.04746 | ||||||||
\(95\) | 8.10817 | 0.831881 | ||||||||
\(96\) | 6.15888 | 0.628588 | ||||||||
\(97\) | −7.59364 | −0.771017 | −0.385509 | − | 0.922704i | \(-0.625974\pi\) | ||||
−0.385509 | + | 0.922704i | \(0.625974\pi\) | |||||||
\(98\) | 19.3892 | 1.95860 | ||||||||
\(99\) | 0.332973 | 0.0334650 | ||||||||
\(100\) | 33.9438 | 3.39438 | ||||||||
\(101\) | 10.1958 | 1.01452 | 0.507259 | − | 0.861794i | \(-0.330659\pi\) | ||||
0.507259 | + | 0.861794i | \(0.330659\pi\) | |||||||
\(102\) | 0.653453 | 0.0647014 | ||||||||
\(103\) | −6.55370 | −0.645755 | −0.322878 | − | 0.946441i | \(-0.604650\pi\) | ||||
−0.322878 | + | 0.946441i | \(0.604650\pi\) | |||||||
\(104\) | −10.4672 | −1.02639 | ||||||||
\(105\) | 0.142010 | 0.0138588 | ||||||||
\(106\) | −10.3719 | −1.00741 | ||||||||
\(107\) | −1.31620 | −0.127242 | −0.0636210 | − | 0.997974i | \(-0.520265\pi\) | ||||
−0.0636210 | + | 0.997974i | \(0.520265\pi\) | |||||||
\(108\) | 7.48678 | 0.720416 | ||||||||
\(109\) | 15.6413 | 1.49816 | 0.749082 | − | 0.662477i | \(-0.230495\pi\) | ||||
0.749082 | + | 0.662477i | \(0.230495\pi\) | |||||||
\(110\) | 1.03691 | 0.0988653 | ||||||||
\(111\) | 0.403759 | 0.0383231 | ||||||||
\(112\) | −3.47394 | −0.328257 | ||||||||
\(113\) | 11.4392 | 1.07611 | 0.538055 | − | 0.842910i | \(-0.319159\pi\) | ||||
0.538055 | + | 0.842910i | \(0.319159\pi\) | |||||||
\(114\) | 1.49459 | 0.139981 | ||||||||
\(115\) | −9.21153 | −0.858980 | ||||||||
\(116\) | −25.3396 | −2.35272 | ||||||||
\(117\) | −2.95228 | −0.272939 | ||||||||
\(118\) | 25.0610 | 2.30706 | ||||||||
\(119\) | −0.211525 | −0.0193905 | ||||||||
\(120\) | 7.54720 | 0.688962 | ||||||||
\(121\) | −10.9873 | −0.998844 | ||||||||
\(122\) | −11.8812 | −1.07567 | ||||||||
\(123\) | 1.65058 | 0.148827 | ||||||||
\(124\) | 56.5838 | 5.08137 | ||||||||
\(125\) | 2.95443 | 0.264252 | ||||||||
\(126\) | −1.61955 | −0.144281 | ||||||||
\(127\) | −1.82365 | −0.161822 | −0.0809112 | − | 0.996721i | \(-0.525783\pi\) | ||||
−0.0809112 | + | 0.996721i | \(0.525783\pi\) | |||||||
\(128\) | −64.0849 | −5.66436 | ||||||||
\(129\) | −0.0863941 | −0.00760658 | ||||||||
\(130\) | −9.19368 | −0.806339 | ||||||||
\(131\) | 13.8527 | 1.21032 | 0.605158 | − | 0.796106i | \(-0.293110\pi\) | ||||
0.605158 | + | 0.796106i | \(0.293110\pi\) | |||||||
\(132\) | 0.141861 | 0.0123474 | ||||||||
\(133\) | −0.483805 | −0.0419512 | ||||||||
\(134\) | 27.3659 | 2.36406 | ||||||||
\(135\) | 4.29180 | 0.369379 | ||||||||
\(136\) | −11.2416 | −0.963960 | ||||||||
\(137\) | −10.8697 | −0.928658 | −0.464329 | − | 0.885663i | \(-0.653704\pi\) | ||||
−0.464329 | + | 0.885663i | \(0.653704\pi\) | |||||||
\(138\) | −1.69798 | −0.144542 | ||||||||
\(139\) | 9.04896 | 0.767523 | 0.383761 | − | 0.923432i | \(-0.374629\pi\) | ||||
0.383761 | + | 0.923432i | \(0.374629\pi\) | |||||||
\(140\) | −3.74325 | −0.316362 | ||||||||
\(141\) | 1.55685 | 0.131110 | ||||||||
\(142\) | −6.43701 | −0.540182 | ||||||||
\(143\) | −0.112785 | −0.00943154 | ||||||||
\(144\) | −52.0736 | −4.33947 | ||||||||
\(145\) | −14.5259 | −1.20631 | ||||||||
\(146\) | 0.303842 | 0.0251462 | ||||||||
\(147\) | 1.52064 | 0.125420 | ||||||||
\(148\) | −10.6427 | −0.874824 | ||||||||
\(149\) | −21.4379 | −1.75626 | −0.878129 | − | 0.478425i | \(-0.841208\pi\) | ||||
−0.878129 | + | 0.478425i | \(0.841208\pi\) | |||||||
\(150\) | 3.58678 | 0.292859 | ||||||||
\(151\) | 12.0105 | 0.977398 | 0.488699 | − | 0.872453i | \(-0.337472\pi\) | ||||
0.488699 | + | 0.872453i | \(0.337472\pi\) | |||||||
\(152\) | −25.7121 | −2.08553 | ||||||||
\(153\) | −3.17071 | −0.256337 | ||||||||
\(154\) | −0.0618711 | −0.00498572 | ||||||||
\(155\) | 32.4367 | 2.60538 | ||||||||
\(156\) | −1.25780 | −0.100705 | ||||||||
\(157\) | −22.2264 | −1.77386 | −0.886929 | − | 0.461906i | \(-0.847166\pi\) | ||||
−0.886929 | + | 0.461906i | \(0.847166\pi\) | |||||||
\(158\) | 33.9072 | 2.69751 | ||||||||
\(159\) | −0.813442 | −0.0645101 | ||||||||
\(160\) | −93.0627 | −7.35725 | ||||||||
\(161\) | 0.549642 | 0.0433178 | ||||||||
\(162\) | −23.8780 | −1.87603 | ||||||||
\(163\) | −17.3689 | −1.36044 | −0.680218 | − | 0.733010i | \(-0.738115\pi\) | ||||
−0.680218 | + | 0.733010i | \(0.738115\pi\) | |||||||
\(164\) | −43.5076 | −3.39737 | ||||||||
\(165\) | 0.0813217 | 0.00633089 | ||||||||
\(166\) | 7.62007 | 0.591432 | ||||||||
\(167\) | 18.9693 | 1.46789 | 0.733943 | − | 0.679211i | \(-0.237678\pi\) | ||||
0.733943 | + | 0.679211i | \(0.237678\pi\) | |||||||
\(168\) | −0.450333 | −0.0347439 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −9.87389 | −0.757293 | ||||||||
\(171\) | −7.25213 | −0.554584 | ||||||||
\(172\) | 2.27727 | 0.173640 | ||||||||
\(173\) | 4.92266 | 0.374263 | 0.187131 | − | 0.982335i | \(-0.440081\pi\) | ||||
0.187131 | + | 0.982335i | \(0.440081\pi\) | |||||||
\(174\) | −2.67759 | −0.202988 | ||||||||
\(175\) | −1.16105 | −0.0877673 | ||||||||
\(176\) | −1.98935 | −0.149953 | ||||||||
\(177\) | 1.96547 | 0.147733 | ||||||||
\(178\) | 9.63106 | 0.721878 | ||||||||
\(179\) | −7.75093 | −0.579332 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(180\) | −56.1104 | −4.18222 | ||||||||
\(181\) | −2.32461 | −0.172787 | −0.0863933 | − | 0.996261i | \(-0.527534\pi\) | ||||
−0.0863933 | + | 0.996261i | \(0.527534\pi\) | |||||||
\(182\) | 0.548577 | 0.0406632 | ||||||||
\(183\) | −0.931807 | −0.0688811 | ||||||||
\(184\) | 29.2110 | 2.15346 | ||||||||
\(185\) | −6.10093 | −0.448549 | ||||||||
\(186\) | 5.97911 | 0.438410 | ||||||||
\(187\) | −0.121129 | −0.00885786 | ||||||||
\(188\) | −41.0370 | −2.99293 | ||||||||
\(189\) | −0.256087 | −0.0186276 | ||||||||
\(190\) | −22.5838 | −1.63840 | ||||||||
\(191\) | −21.6777 | −1.56854 | −0.784271 | − | 0.620419i | \(-0.786963\pi\) | ||||
−0.784271 | + | 0.620419i | \(0.786963\pi\) | |||||||
\(192\) | −9.44839 | −0.681879 | ||||||||
\(193\) | 16.4639 | 1.18510 | 0.592549 | − | 0.805534i | \(-0.298121\pi\) | ||||
0.592549 | + | 0.805534i | \(0.298121\pi\) | |||||||
\(194\) | 21.1507 | 1.51853 | ||||||||
\(195\) | −0.721034 | −0.0516343 | ||||||||
\(196\) | −40.0826 | −2.86304 | ||||||||
\(197\) | −25.2251 | −1.79721 | −0.898607 | − | 0.438754i | \(-0.855420\pi\) | ||||
−0.898607 | + | 0.438754i | \(0.855420\pi\) | |||||||
\(198\) | −0.927434 | −0.0659099 | ||||||||
\(199\) | −18.8149 | −1.33376 | −0.666878 | − | 0.745167i | \(-0.732370\pi\) | ||||
−0.666878 | + | 0.745167i | \(0.732370\pi\) | |||||||
\(200\) | −61.7048 | −4.36319 | ||||||||
\(201\) | 2.14623 | 0.151384 | ||||||||
\(202\) | −28.3985 | −1.99811 | ||||||||
\(203\) | 0.866745 | 0.0608336 | ||||||||
\(204\) | −1.35086 | −0.0945791 | ||||||||
\(205\) | −24.9408 | −1.74194 | ||||||||
\(206\) | 18.2541 | 1.27183 | ||||||||
\(207\) | 8.23901 | 0.572650 | ||||||||
\(208\) | 17.6384 | 1.22301 | ||||||||
\(209\) | −0.277050 | −0.0191640 | ||||||||
\(210\) | −0.395543 | −0.0272950 | ||||||||
\(211\) | −10.6244 | −0.731412 | −0.365706 | − | 0.930730i | \(-0.619172\pi\) | ||||
−0.365706 | + | 0.930730i | \(0.619172\pi\) | |||||||
\(212\) | 21.4416 | 1.47261 | ||||||||
\(213\) | −0.504836 | −0.0345908 | ||||||||
\(214\) | 3.66604 | 0.250605 | ||||||||
\(215\) | 1.30544 | 0.0890306 | ||||||||
\(216\) | −13.6099 | −0.926035 | ||||||||
\(217\) | −1.93546 | −0.131388 | ||||||||
\(218\) | −43.5659 | −2.95066 | ||||||||
\(219\) | 0.0238295 | 0.00161025 | ||||||||
\(220\) | −2.14356 | −0.144519 | ||||||||
\(221\) | 1.07399 | 0.0722441 | ||||||||
\(222\) | −1.12460 | −0.0754779 | ||||||||
\(223\) | 9.63034 | 0.644895 | 0.322448 | − | 0.946587i | \(-0.395494\pi\) | ||||
0.322448 | + | 0.946587i | \(0.395494\pi\) | |||||||
\(224\) | 5.55295 | 0.371022 | ||||||||
\(225\) | −17.4039 | −1.16026 | ||||||||
\(226\) | −31.8618 | −2.11942 | ||||||||
\(227\) | 10.8519 | 0.720264 | 0.360132 | − | 0.932901i | \(-0.382732\pi\) | ||||
0.360132 | + | 0.932901i | \(0.382732\pi\) | |||||||
\(228\) | −3.08972 | −0.204622 | ||||||||
\(229\) | 25.6843 | 1.69727 | 0.848635 | − | 0.528980i | \(-0.177425\pi\) | ||||
0.848635 | + | 0.528980i | \(0.177425\pi\) | |||||||
\(230\) | 25.6570 | 1.69177 | ||||||||
\(231\) | −0.00485238 | −0.000319263 0 | ||||||||
\(232\) | 46.0637 | 3.02423 | ||||||||
\(233\) | −13.7275 | −0.899321 | −0.449660 | − | 0.893200i | \(-0.648455\pi\) | ||||
−0.449660 | + | 0.893200i | \(0.648455\pi\) | |||||||
\(234\) | 8.22304 | 0.537557 | ||||||||
\(235\) | −23.5245 | −1.53457 | ||||||||
\(236\) | −51.8078 | −3.37240 | ||||||||
\(237\) | 2.65925 | 0.172737 | ||||||||
\(238\) | 0.589164 | 0.0381898 | ||||||||
\(239\) | 21.3946 | 1.38390 | 0.691950 | − | 0.721946i | \(-0.256752\pi\) | ||||
0.691950 | + | 0.721946i | \(0.256752\pi\) | |||||||
\(240\) | −12.7179 | −0.820938 | ||||||||
\(241\) | 20.1886 | 1.30046 | 0.650232 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650232 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(242\) | 30.6030 | 1.96724 | ||||||||
\(243\) | −5.77341 | −0.370364 | ||||||||
\(244\) | 24.5615 | 1.57239 | ||||||||
\(245\) | −22.9773 | −1.46797 | ||||||||
\(246\) | −4.59738 | −0.293118 | ||||||||
\(247\) | 2.45645 | 0.156300 | ||||||||
\(248\) | −102.861 | −6.53169 | ||||||||
\(249\) | 0.597620 | 0.0378726 | ||||||||
\(250\) | −8.22902 | −0.520449 | ||||||||
\(251\) | 3.32965 | 0.210166 | 0.105083 | − | 0.994463i | \(-0.466489\pi\) | ||||
0.105083 | + | 0.994463i | \(0.466489\pi\) | |||||||
\(252\) | 3.34805 | 0.210907 | ||||||||
\(253\) | 0.314751 | 0.0197882 | ||||||||
\(254\) | 5.07943 | 0.318712 | ||||||||
\(255\) | −0.774381 | −0.0484936 | ||||||||
\(256\) | 91.9907 | 5.74942 | ||||||||
\(257\) | −15.4478 | −0.963605 | −0.481802 | − | 0.876280i | \(-0.660018\pi\) | ||||
−0.481802 | + | 0.876280i | \(0.660018\pi\) | |||||||
\(258\) | 0.240635 | 0.0149813 | ||||||||
\(259\) | 0.364036 | 0.0226201 | ||||||||
\(260\) | 19.0058 | 1.17869 | ||||||||
\(261\) | 12.9923 | 0.804204 | ||||||||
\(262\) | −38.5841 | −2.38374 | ||||||||
\(263\) | −0.409596 | −0.0252568 | −0.0126284 | − | 0.999920i | \(-0.504020\pi\) | ||||
−0.0126284 | + | 0.999920i | \(0.504020\pi\) | |||||||
\(264\) | −0.257882 | −0.0158715 | ||||||||
\(265\) | 12.2914 | 0.755054 | ||||||||
\(266\) | 1.34755 | 0.0826236 | ||||||||
\(267\) | 0.755336 | 0.0462258 | ||||||||
\(268\) | −56.5726 | −3.45572 | ||||||||
\(269\) | −9.23392 | −0.563002 | −0.281501 | − | 0.959561i | \(-0.590832\pi\) | ||||
−0.281501 | + | 0.959561i | \(0.590832\pi\) | |||||||
\(270\) | −11.9540 | −0.727498 | ||||||||
\(271\) | −21.0588 | −1.27923 | −0.639616 | − | 0.768694i | \(-0.720907\pi\) | ||||
−0.639616 | + | 0.768694i | \(0.720907\pi\) | |||||||
\(272\) | 18.9434 | 1.14861 | ||||||||
\(273\) | 0.0430233 | 0.00260389 | ||||||||
\(274\) | 30.2754 | 1.82901 | ||||||||
\(275\) | −0.664875 | −0.0400935 | ||||||||
\(276\) | 3.51017 | 0.211288 | ||||||||
\(277\) | −15.3968 | −0.925105 | −0.462552 | − | 0.886592i | \(-0.653066\pi\) | ||||
−0.462552 | + | 0.886592i | \(0.653066\pi\) | |||||||
\(278\) | −25.2042 | −1.51165 | ||||||||
\(279\) | −29.0121 | −1.73691 | ||||||||
\(280\) | 6.80468 | 0.406657 | ||||||||
\(281\) | 20.3336 | 1.21300 | 0.606499 | − | 0.795084i | \(-0.292573\pi\) | ||||
0.606499 | + | 0.795084i | \(0.292573\pi\) | |||||||
\(282\) | −4.33631 | −0.258224 | ||||||||
\(283\) | 7.80832 | 0.464157 | 0.232078 | − | 0.972697i | \(-0.425447\pi\) | ||||
0.232078 | + | 0.972697i | \(0.425447\pi\) | |||||||
\(284\) | 13.3070 | 0.789626 | ||||||||
\(285\) | −1.77118 | −0.104916 | ||||||||
\(286\) | 0.314141 | 0.0185756 | ||||||||
\(287\) | 1.48819 | 0.0878449 | ||||||||
\(288\) | 83.2374 | 4.90481 | ||||||||
\(289\) | −15.8466 | −0.932150 | ||||||||
\(290\) | 40.4593 | 2.37585 | ||||||||
\(291\) | 1.65879 | 0.0972399 | ||||||||
\(292\) | −0.628122 | −0.0367581 | ||||||||
\(293\) | 15.5609 | 0.909077 | 0.454539 | − | 0.890727i | \(-0.349804\pi\) | ||||
0.454539 | + | 0.890727i | \(0.349804\pi\) | |||||||
\(294\) | −4.23546 | −0.247017 | ||||||||
\(295\) | −29.6989 | −1.72913 | ||||||||
\(296\) | 19.3469 | 1.12451 | ||||||||
\(297\) | −0.146648 | −0.00850936 | ||||||||
\(298\) | 59.7112 | 3.45898 | ||||||||
\(299\) | −2.79072 | −0.161392 | ||||||||
\(300\) | −7.41482 | −0.428095 | ||||||||
\(301\) | −0.0778944 | −0.00448976 | ||||||||
\(302\) | −33.4529 | −1.92500 | ||||||||
\(303\) | −2.22721 | −0.127950 | ||||||||
\(304\) | 43.3279 | 2.48503 | ||||||||
\(305\) | 14.0799 | 0.806214 | ||||||||
\(306\) | 8.83143 | 0.504859 | ||||||||
\(307\) | −8.34124 | −0.476060 | −0.238030 | − | 0.971258i | \(-0.576502\pi\) | ||||
−0.238030 | + | 0.971258i | \(0.576502\pi\) | |||||||
\(308\) | 0.127904 | 0.00728801 | ||||||||
\(309\) | 1.43162 | 0.0814420 | ||||||||
\(310\) | −90.3464 | −5.13133 | ||||||||
\(311\) | −8.32549 | −0.472095 | −0.236047 | − | 0.971742i | \(-0.575852\pi\) | ||||
−0.236047 | + | 0.971742i | \(0.575852\pi\) | |||||||
\(312\) | 2.28650 | 0.129447 | ||||||||
\(313\) | 22.8449 | 1.29127 | 0.645636 | − | 0.763645i | \(-0.276592\pi\) | ||||
0.645636 | + | 0.763645i | \(0.276592\pi\) | |||||||
\(314\) | 61.9075 | 3.49364 | ||||||||
\(315\) | 1.91927 | 0.108139 | ||||||||
\(316\) | −70.0952 | −3.94316 | ||||||||
\(317\) | −31.3137 | −1.75875 | −0.879376 | − | 0.476127i | \(-0.842040\pi\) | ||||
−0.879376 | + | 0.476127i | \(0.842040\pi\) | |||||||
\(318\) | 2.26569 | 0.127054 | ||||||||
\(319\) | 0.496340 | 0.0277897 | ||||||||
\(320\) | 142.768 | 7.98099 | ||||||||
\(321\) | 0.287517 | 0.0160476 | ||||||||
\(322\) | −1.53093 | −0.0853152 | ||||||||
\(323\) | 2.63819 | 0.146793 | ||||||||
\(324\) | 49.3622 | 2.74234 | ||||||||
\(325\) | 5.89507 | 0.327000 | ||||||||
\(326\) | 48.3778 | 2.67940 | ||||||||
\(327\) | −3.41675 | −0.188947 | ||||||||
\(328\) | 79.0905 | 4.36704 | ||||||||
\(329\) | 1.40368 | 0.0773874 | ||||||||
\(330\) | −0.226507 | −0.0124688 | ||||||||
\(331\) | 21.2173 | 1.16621 | 0.583104 | − | 0.812398i | \(-0.301838\pi\) | ||||
0.583104 | + | 0.812398i | \(0.301838\pi\) | |||||||
\(332\) | −15.7527 | −0.864541 | ||||||||
\(333\) | 5.45681 | 0.299031 | ||||||||
\(334\) | −52.8354 | −2.89103 | ||||||||
\(335\) | −32.4303 | −1.77186 | ||||||||
\(336\) | 0.758864 | 0.0413994 | ||||||||
\(337\) | 3.17707 | 0.173066 | 0.0865330 | − | 0.996249i | \(-0.472421\pi\) | ||||
0.0865330 | + | 0.996249i | \(0.472421\pi\) | |||||||
\(338\) | −2.78532 | −0.151501 | ||||||||
\(339\) | −2.49883 | −0.135718 | ||||||||
\(340\) | 20.4119 | 1.10699 | ||||||||
\(341\) | −1.10834 | −0.0600198 | ||||||||
\(342\) | 20.1995 | 1.09226 | ||||||||
\(343\) | 2.74970 | 0.148470 | ||||||||
\(344\) | −4.13974 | −0.223200 | ||||||||
\(345\) | 2.01221 | 0.108334 | ||||||||
\(346\) | −13.7112 | −0.737116 | ||||||||
\(347\) | 1.16585 | 0.0625862 | 0.0312931 | − | 0.999510i | \(-0.490037\pi\) | ||||
0.0312931 | + | 0.999510i | \(0.490037\pi\) | |||||||
\(348\) | 5.53529 | 0.296723 | ||||||||
\(349\) | 25.1005 | 1.34360 | 0.671798 | − | 0.740734i | \(-0.265522\pi\) | ||||
0.671798 | + | 0.740734i | \(0.265522\pi\) | |||||||
\(350\) | 3.23390 | 0.172859 | ||||||||
\(351\) | 1.30024 | 0.0694018 | ||||||||
\(352\) | 3.17988 | 0.169488 | ||||||||
\(353\) | −29.0400 | −1.54564 | −0.772822 | − | 0.634622i | \(-0.781156\pi\) | ||||
−0.772822 | + | 0.634622i | \(0.781156\pi\) | |||||||
\(354\) | −5.47444 | −0.290963 | ||||||||
\(355\) | 7.62825 | 0.404865 | ||||||||
\(356\) | −19.9099 | −1.05523 | ||||||||
\(357\) | 0.0462064 | 0.00244550 | ||||||||
\(358\) | 21.5888 | 1.14100 | ||||||||
\(359\) | 0.382166 | 0.0201700 | 0.0100850 | − | 0.999949i | \(-0.496790\pi\) | ||||
0.0100850 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(360\) | 102.001 | 5.37590 | ||||||||
\(361\) | −12.9659 | −0.682414 | ||||||||
\(362\) | 6.47477 | 0.340306 | ||||||||
\(363\) | 2.40011 | 0.125973 | ||||||||
\(364\) | −1.13405 | −0.0594405 | ||||||||
\(365\) | −0.360071 | −0.0188470 | ||||||||
\(366\) | 2.59538 | 0.135662 | ||||||||
\(367\) | −24.6922 | −1.28892 | −0.644461 | − | 0.764637i | \(-0.722918\pi\) | ||||
−0.644461 | + | 0.764637i | \(0.722918\pi\) | |||||||
\(368\) | −49.2240 | −2.56598 | ||||||||
\(369\) | 22.3076 | 1.16129 | ||||||||
\(370\) | 16.9930 | 0.883425 | ||||||||
\(371\) | −0.733413 | −0.0380769 | ||||||||
\(372\) | −12.3604 | −0.640857 | ||||||||
\(373\) | −2.33779 | −0.121046 | −0.0605231 | − | 0.998167i | \(-0.519277\pi\) | ||||
−0.0605231 | + | 0.998167i | \(0.519277\pi\) | |||||||
\(374\) | 0.337384 | 0.0174457 | ||||||||
\(375\) | −0.645378 | −0.0333272 | ||||||||
\(376\) | 74.5993 | 3.84717 | ||||||||
\(377\) | −4.40077 | −0.226651 | ||||||||
\(378\) | 0.713283 | 0.0366873 | ||||||||
\(379\) | 9.20946 | 0.473058 | 0.236529 | − | 0.971624i | \(-0.423990\pi\) | ||||
0.236529 | + | 0.971624i | \(0.423990\pi\) | |||||||
\(380\) | 46.6867 | 2.39498 | ||||||||
\(381\) | 0.398365 | 0.0204089 | ||||||||
\(382\) | 60.3792 | 3.08927 | ||||||||
\(383\) | −18.3727 | −0.938802 | −0.469401 | − | 0.882985i | \(-0.655530\pi\) | ||||
−0.469401 | + | 0.882985i | \(0.655530\pi\) | |||||||
\(384\) | 13.9990 | 0.714383 | ||||||||
\(385\) | 0.0733210 | 0.00373679 | ||||||||
\(386\) | −45.8572 | −2.33407 | ||||||||
\(387\) | −1.16762 | −0.0593534 | ||||||||
\(388\) | −43.7241 | −2.21975 | ||||||||
\(389\) | −2.39605 | −0.121484 | −0.0607422 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607422 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(390\) | 2.00831 | 0.101695 | ||||||||
\(391\) | −2.99720 | −0.151575 | ||||||||
\(392\) | 72.8642 | 3.68020 | ||||||||
\(393\) | −3.02604 | −0.152644 | ||||||||
\(394\) | 70.2599 | 3.53964 | ||||||||
\(395\) | −40.1821 | −2.02178 | ||||||||
\(396\) | 1.91725 | 0.0963455 | ||||||||
\(397\) | 29.8137 | 1.49630 | 0.748152 | − | 0.663527i | \(-0.230941\pi\) | ||||
0.748152 | + | 0.663527i | \(0.230941\pi\) | |||||||
\(398\) | 52.4056 | 2.62685 | ||||||||
\(399\) | 0.105685 | 0.00529084 | ||||||||
\(400\) | 103.980 | 5.19899 | ||||||||
\(401\) | 11.0203 | 0.550328 | 0.275164 | − | 0.961397i | \(-0.411268\pi\) | ||||
0.275164 | + | 0.961397i | \(0.411268\pi\) | |||||||
\(402\) | −5.97793 | −0.298152 | ||||||||
\(403\) | 9.82701 | 0.489518 | ||||||||
\(404\) | 58.7072 | 2.92079 | ||||||||
\(405\) | 28.2969 | 1.40608 | ||||||||
\(406\) | −2.41416 | −0.119813 | ||||||||
\(407\) | 0.208464 | 0.0103332 | ||||||||
\(408\) | 2.45567 | 0.121574 | ||||||||
\(409\) | 2.40843 | 0.119089 | 0.0595446 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595446 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(410\) | 69.4679 | 3.43078 | ||||||||
\(411\) | 2.37442 | 0.117121 | ||||||||
\(412\) | −37.7361 | −1.85913 | ||||||||
\(413\) | 1.77210 | 0.0871992 | ||||||||
\(414\) | −22.9482 | −1.12784 | ||||||||
\(415\) | −9.03024 | −0.443277 | ||||||||
\(416\) | −28.1943 | −1.38234 | ||||||||
\(417\) | −1.97669 | −0.0967991 | ||||||||
\(418\) | 0.771672 | 0.0377437 | ||||||||
\(419\) | −9.91740 | −0.484497 | −0.242248 | − | 0.970214i | \(-0.577885\pi\) | ||||
−0.242248 | + | 0.970214i | \(0.577885\pi\) | |||||||
\(420\) | 0.817691 | 0.0398993 | ||||||||
\(421\) | −32.5450 | −1.58615 | −0.793073 | − | 0.609126i | \(-0.791520\pi\) | ||||
−0.793073 | + | 0.609126i | \(0.791520\pi\) | |||||||
\(422\) | 29.5922 | 1.44053 | ||||||||
\(423\) | 21.0408 | 1.02304 | ||||||||
\(424\) | −38.9776 | −1.89292 | ||||||||
\(425\) | 6.33123 | 0.307110 | ||||||||
\(426\) | 1.40613 | 0.0681272 | ||||||||
\(427\) | −0.840132 | −0.0406569 | ||||||||
\(428\) | −7.57867 | −0.366329 | ||||||||
\(429\) | 0.0246372 | 0.00118950 | ||||||||
\(430\) | −3.63608 | −0.175347 | ||||||||
\(431\) | 6.13703 | 0.295610 | 0.147805 | − | 0.989016i | \(-0.452779\pi\) | ||||
0.147805 | + | 0.989016i | \(0.452779\pi\) | |||||||
\(432\) | 22.9342 | 1.10342 | ||||||||
\(433\) | 14.5672 | 0.700054 | 0.350027 | − | 0.936740i | \(-0.386172\pi\) | ||||
0.350027 | + | 0.936740i | \(0.386172\pi\) | |||||||
\(434\) | 5.39087 | 0.258770 | ||||||||
\(435\) | 3.17311 | 0.152139 | ||||||||
\(436\) | 90.0623 | 4.31320 | ||||||||
\(437\) | −6.85527 | −0.327932 | ||||||||
\(438\) | −0.0663726 | −0.00317141 | ||||||||
\(439\) | 11.4353 | 0.545779 | 0.272890 | − | 0.962045i | \(-0.412021\pi\) | ||||
0.272890 | + | 0.962045i | \(0.412021\pi\) | |||||||
\(440\) | 3.89669 | 0.185767 | ||||||||
\(441\) | 20.5515 | 0.978641 | ||||||||
\(442\) | −2.99139 | −0.142286 | ||||||||
\(443\) | −0.389132 | −0.0184882 | −0.00924411 | − | 0.999957i | \(-0.502943\pi\) | ||||
−0.00924411 | + | 0.999957i | \(0.502943\pi\) | |||||||
\(444\) | 2.32484 | 0.110332 | ||||||||
\(445\) | −11.4134 | −0.541046 | ||||||||
\(446\) | −26.8235 | −1.27013 | ||||||||
\(447\) | 4.68298 | 0.221497 | ||||||||
\(448\) | −8.51882 | −0.402477 | ||||||||
\(449\) | 17.1628 | 0.809963 | 0.404982 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404982 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(450\) | 48.4754 | 2.28515 | ||||||||
\(451\) | 0.852207 | 0.0401289 | ||||||||
\(452\) | 65.8668 | 3.09811 | ||||||||
\(453\) | −2.62362 | −0.123268 | ||||||||
\(454\) | −30.2259 | −1.41857 | ||||||||
\(455\) | −0.650097 | −0.0304770 | ||||||||
\(456\) | 5.61666 | 0.263024 | ||||||||
\(457\) | −35.6845 | −1.66925 | −0.834626 | − | 0.550818i | \(-0.814316\pi\) | ||||
−0.834626 | + | 0.550818i | \(0.814316\pi\) | |||||||
\(458\) | −71.5390 | −3.34280 | ||||||||
\(459\) | 1.39644 | 0.0651804 | ||||||||
\(460\) | −53.0399 | −2.47300 | ||||||||
\(461\) | 20.7104 | 0.964580 | 0.482290 | − | 0.876012i | \(-0.339805\pi\) | ||||
0.482290 | + | 0.876012i | \(0.339805\pi\) | |||||||
\(462\) | 0.0135154 | 0.000628793 0 | ||||||||
\(463\) | 24.5900 | 1.14279 | 0.571397 | − | 0.820674i | \(-0.306402\pi\) | ||||
0.571397 | + | 0.820674i | \(0.306402\pi\) | |||||||
\(464\) | −77.6227 | −3.60354 | ||||||||
\(465\) | −7.08561 | −0.328587 | ||||||||
\(466\) | 38.2355 | 1.77123 | ||||||||
\(467\) | −15.5851 | −0.721191 | −0.360596 | − | 0.932722i | \(-0.617427\pi\) | ||||
−0.360596 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(468\) | −16.9992 | −0.785788 | ||||||||
\(469\) | 1.93508 | 0.0893536 | ||||||||
\(470\) | 65.5231 | 3.02236 | ||||||||
\(471\) | 4.85523 | 0.223717 | ||||||||
\(472\) | 94.1791 | 4.33494 | ||||||||
\(473\) | −0.0446061 | −0.00205099 | ||||||||
\(474\) | −7.40684 | −0.340207 | ||||||||
\(475\) | 14.4809 | 0.664431 | ||||||||
\(476\) | −1.21796 | −0.0558250 | ||||||||
\(477\) | −10.9937 | −0.503367 | ||||||||
\(478\) | −59.5906 | −2.72561 | ||||||||
\(479\) | −33.7281 | −1.54108 | −0.770538 | − | 0.637394i | \(-0.780012\pi\) | ||||
−0.770538 | + | 0.637394i | \(0.780012\pi\) | |||||||
\(480\) | 20.3290 | 0.927889 | ||||||||
\(481\) | −1.84834 | −0.0842769 | ||||||||
\(482\) | −56.2317 | −2.56128 | ||||||||
\(483\) | −0.120066 | −0.00546320 | ||||||||
\(484\) | −63.2646 | −2.87566 | ||||||||
\(485\) | −25.0648 | −1.13814 | ||||||||
\(486\) | 16.0808 | 0.729439 | ||||||||
\(487\) | 23.5252 | 1.06603 | 0.533015 | − | 0.846106i | \(-0.321059\pi\) | ||||
0.533015 | + | 0.846106i | \(0.321059\pi\) | |||||||
\(488\) | −44.6493 | −2.02118 | ||||||||
\(489\) | 3.79413 | 0.171577 | ||||||||
\(490\) | 63.9992 | 2.89119 | ||||||||
\(491\) | 15.2704 | 0.689143 | 0.344572 | − | 0.938760i | \(-0.388024\pi\) | ||||
0.344572 | + | 0.938760i | \(0.388024\pi\) | |||||||
\(492\) | 9.50399 | 0.428473 | ||||||||
\(493\) | −4.72637 | −0.212865 | ||||||||
\(494\) | −6.84199 | −0.307836 | ||||||||
\(495\) | 1.09907 | 0.0493993 | ||||||||
\(496\) | 173.333 | 7.78289 | ||||||||
\(497\) | −0.455169 | −0.0204171 | ||||||||
\(498\) | −1.66456 | −0.0745907 | ||||||||
\(499\) | 24.3679 | 1.09086 | 0.545429 | − | 0.838157i | \(-0.316367\pi\) | ||||
0.545429 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(500\) | 17.0116 | 0.760780 | ||||||||
\(501\) | −4.14373 | −0.185128 | ||||||||
\(502\) | −9.27412 | −0.413924 | ||||||||
\(503\) | −32.2446 | −1.43772 | −0.718858 | − | 0.695156i | \(-0.755335\pi\) | ||||
−0.718858 | + | 0.695156i | \(0.755335\pi\) | |||||||
\(504\) | −6.08626 | −0.271104 | ||||||||
\(505\) | 33.6539 | 1.49758 | ||||||||
\(506\) | −0.876682 | −0.0389733 | ||||||||
\(507\) | −0.218444 | −0.00970146 | ||||||||
\(508\) | −10.5005 | −0.465886 | ||||||||
\(509\) | −33.3970 | −1.48030 | −0.740148 | − | 0.672444i | \(-0.765245\pi\) | ||||
−0.740148 | + | 0.672444i | \(0.765245\pi\) | |||||||
\(510\) | 2.15690 | 0.0955089 | ||||||||
\(511\) | 0.0214850 | 0.000950443 0 | ||||||||
\(512\) | −128.053 | −5.65921 | ||||||||
\(513\) | 3.19398 | 0.141018 | ||||||||
\(514\) | 43.0269 | 1.89783 | ||||||||
\(515\) | −21.6323 | −0.953231 | ||||||||
\(516\) | −0.497456 | −0.0218993 | ||||||||
\(517\) | 0.803814 | 0.0353517 | ||||||||
\(518\) | −1.01395 | −0.0445506 | ||||||||
\(519\) | −1.07533 | −0.0472016 | ||||||||
\(520\) | −34.5497 | −1.51511 | ||||||||
\(521\) | −34.9871 | −1.53281 | −0.766405 | − | 0.642357i | \(-0.777957\pi\) | ||||
−0.766405 | + | 0.642357i | \(0.777957\pi\) | |||||||
\(522\) | −36.1877 | −1.58389 | ||||||||
\(523\) | −17.9117 | −0.783225 | −0.391612 | − | 0.920130i | \(-0.628083\pi\) | ||||
−0.391612 | + | 0.920130i | \(0.628083\pi\) | |||||||
\(524\) | 79.7636 | 3.48449 | ||||||||
\(525\) | 0.253625 | 0.0110691 | ||||||||
\(526\) | 1.14085 | 0.0497436 | ||||||||
\(527\) | 10.5541 | 0.459743 | ||||||||
\(528\) | 0.434562 | 0.0189119 | ||||||||
\(529\) | −15.2119 | −0.661385 | ||||||||
\(530\) | −34.2354 | −1.48709 | ||||||||
\(531\) | 26.5633 | 1.15275 | ||||||||
\(532\) | −2.78574 | −0.120777 | ||||||||
\(533\) | −7.55605 | −0.327289 | ||||||||
\(534\) | −2.10385 | −0.0910425 | ||||||||
\(535\) | −4.34448 | −0.187828 | ||||||||
\(536\) | 102.841 | 4.44205 | ||||||||
\(537\) | 1.69315 | 0.0730647 | ||||||||
\(538\) | 25.7194 | 1.10884 | ||||||||
\(539\) | 0.785119 | 0.0338175 | ||||||||
\(540\) | 24.7121 | 1.06344 | ||||||||
\(541\) | 15.5408 | 0.668151 | 0.334076 | − | 0.942546i | \(-0.391576\pi\) | ||||
0.334076 | + | 0.942546i | \(0.391576\pi\) | |||||||
\(542\) | 58.6555 | 2.51947 | ||||||||
\(543\) | 0.507797 | 0.0217917 | ||||||||
\(544\) | −30.2802 | −1.29825 | ||||||||
\(545\) | 51.6283 | 2.21151 | ||||||||
\(546\) | −0.119833 | −0.00512840 | ||||||||
\(547\) | −33.0512 | −1.41317 | −0.706583 | − | 0.707631i | \(-0.749764\pi\) | ||||
−0.706583 | + | 0.707631i | \(0.749764\pi\) | |||||||
\(548\) | −62.5874 | −2.67360 | ||||||||
\(549\) | −12.5934 | −0.537473 | ||||||||
\(550\) | 1.85189 | 0.0789647 | ||||||||
\(551\) | −10.8103 | −0.460533 | ||||||||
\(552\) | −6.38098 | −0.271593 | ||||||||
\(553\) | 2.39762 | 0.101957 | ||||||||
\(554\) | 42.8850 | 1.82201 | ||||||||
\(555\) | 1.33271 | 0.0565706 | ||||||||
\(556\) | 52.1038 | 2.20969 | ||||||||
\(557\) | −24.7518 | −1.04877 | −0.524383 | − | 0.851483i | \(-0.675704\pi\) | ||||
−0.524383 | + | 0.851483i | \(0.675704\pi\) | |||||||
\(558\) | 80.8079 | 3.42087 | ||||||||
\(559\) | 0.395497 | 0.0167277 | ||||||||
\(560\) | −11.4667 | −0.484556 | ||||||||
\(561\) | 0.0264600 | 0.00111714 | ||||||||
\(562\) | −56.6354 | −2.38902 | ||||||||
\(563\) | 15.4964 | 0.653093 | 0.326547 | − | 0.945181i | \(-0.394115\pi\) | ||||
0.326547 | + | 0.945181i | \(0.394115\pi\) | |||||||
\(564\) | 8.96431 | 0.377465 | ||||||||
\(565\) | 37.7582 | 1.58850 | ||||||||
\(566\) | −21.7486 | −0.914164 | ||||||||
\(567\) | −1.68844 | −0.0709079 | ||||||||
\(568\) | −24.1902 | −1.01500 | ||||||||
\(569\) | −3.24444 | −0.136014 | −0.0680070 | − | 0.997685i | \(-0.521664\pi\) | ||||
−0.0680070 | + | 0.997685i | \(0.521664\pi\) | |||||||
\(570\) | 4.93331 | 0.206633 | ||||||||
\(571\) | −7.80474 | −0.326618 | −0.163309 | − | 0.986575i | \(-0.552217\pi\) | ||||
−0.163309 | + | 0.986575i | \(0.552217\pi\) | |||||||
\(572\) | −0.649414 | −0.0271533 | ||||||||
\(573\) | 4.73536 | 0.197823 | ||||||||
\(574\) | −4.14507 | −0.173012 | ||||||||
\(575\) | −16.4515 | −0.686076 | ||||||||
\(576\) | −127.695 | −5.32063 | ||||||||
\(577\) | −5.80806 | −0.241793 | −0.120896 | − | 0.992665i | \(-0.538577\pi\) | ||||
−0.120896 | + | 0.992665i | \(0.538577\pi\) | |||||||
\(578\) | 44.1377 | 1.83588 | ||||||||
\(579\) | −3.59645 | −0.149463 | ||||||||
\(580\) | −83.6401 | −3.47297 | ||||||||
\(581\) | 0.538824 | 0.0223542 | ||||||||
\(582\) | −4.62025 | −0.191515 | ||||||||
\(583\) | −0.419988 | −0.0173941 | ||||||||
\(584\) | 1.14183 | 0.0472495 | ||||||||
\(585\) | −9.74480 | −0.402898 | ||||||||
\(586\) | −43.3420 | −1.79044 | ||||||||
\(587\) | 12.4736 | 0.514841 | 0.257421 | − | 0.966299i | \(-0.417127\pi\) | ||||
0.257421 | + | 0.966299i | \(0.417127\pi\) | |||||||
\(588\) | 8.75581 | 0.361083 | ||||||||
\(589\) | 24.1395 | 0.994653 | ||||||||
\(590\) | 82.7207 | 3.40556 | ||||||||
\(591\) | 5.51028 | 0.226663 | ||||||||
\(592\) | −32.6018 | −1.33992 | ||||||||
\(593\) | 3.99777 | 0.164169 | 0.0820843 | − | 0.996625i | \(-0.473842\pi\) | ||||
0.0820843 | + | 0.996625i | \(0.473842\pi\) | |||||||
\(594\) | 0.408460 | 0.0167593 | ||||||||
\(595\) | −0.698195 | −0.0286232 | ||||||||
\(596\) | −123.439 | −5.05625 | ||||||||
\(597\) | 4.11002 | 0.168212 | ||||||||
\(598\) | 7.77305 | 0.317864 | ||||||||
\(599\) | 15.6207 | 0.638246 | 0.319123 | − | 0.947713i | \(-0.396612\pi\) | ||||
0.319123 | + | 0.947713i | \(0.396612\pi\) | |||||||
\(600\) | 13.4791 | 0.550281 | ||||||||
\(601\) | −23.5181 | −0.959324 | −0.479662 | − | 0.877453i | \(-0.659241\pi\) | ||||
−0.479662 | + | 0.877453i | \(0.659241\pi\) | |||||||
\(602\) | 0.216961 | 0.00884265 | ||||||||
\(603\) | 29.0064 | 1.18123 | ||||||||
\(604\) | 69.1561 | 2.81392 | ||||||||
\(605\) | −36.2665 | −1.47444 | ||||||||
\(606\) | 6.20349 | 0.251999 | ||||||||
\(607\) | 41.4881 | 1.68395 | 0.841974 | − | 0.539518i | \(-0.181394\pi\) | ||||
0.841974 | + | 0.539518i | \(0.181394\pi\) | |||||||
\(608\) | −69.2578 | −2.80877 | ||||||||
\(609\) | −0.189336 | −0.00767227 | ||||||||
\(610\) | −39.2170 | −1.58785 | ||||||||
\(611\) | −7.12697 | −0.288326 | ||||||||
\(612\) | −18.2569 | −0.737992 | ||||||||
\(613\) | 6.75731 | 0.272925 | 0.136463 | − | 0.990645i | \(-0.456427\pi\) | ||||
0.136463 | + | 0.990645i | \(0.456427\pi\) | |||||||
\(614\) | 23.2330 | 0.937607 | ||||||||
\(615\) | 5.44817 | 0.219691 | ||||||||
\(616\) | −0.232511 | −0.00936813 | ||||||||
\(617\) | 0.0751672 | 0.00302612 | 0.00151306 | − | 0.999999i | \(-0.499518\pi\) | ||||
0.00151306 | + | 0.999999i | \(0.499518\pi\) | |||||||
\(618\) | −3.98751 | −0.160401 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 186.770 | 7.50086 | ||||||||
\(621\) | −3.62862 | −0.145611 | ||||||||
\(622\) | 23.1891 | 0.929799 | ||||||||
\(623\) | 0.681024 | 0.0272846 | ||||||||
\(624\) | −3.85302 | −0.154244 | ||||||||
\(625\) | −19.7235 | −0.788939 | ||||||||
\(626\) | −63.6303 | −2.54318 | ||||||||
\(627\) | 0.0605200 | 0.00241694 | ||||||||
\(628\) | −127.979 | −5.10692 | ||||||||
\(629\) | −1.98509 | −0.0791506 | ||||||||
\(630\) | −5.34577 | −0.212981 | ||||||||
\(631\) | 6.82304 | 0.271621 | 0.135811 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135811 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(632\) | 127.423 | 5.06861 | ||||||||
\(633\) | 2.32083 | 0.0922449 | ||||||||
\(634\) | 87.2186 | 3.46389 | ||||||||
\(635\) | −6.01944 | −0.238874 | ||||||||
\(636\) | −4.68379 | −0.185724 | ||||||||
\(637\) | −6.96121 | −0.275813 | ||||||||
\(638\) | −1.38246 | −0.0547323 | ||||||||
\(639\) | −6.82288 | −0.269909 | ||||||||
\(640\) | −211.530 | −8.36144 | ||||||||
\(641\) | −20.6467 | −0.815494 | −0.407747 | − | 0.913095i | \(-0.633685\pi\) | ||||
−0.407747 | + | 0.913095i | \(0.633685\pi\) | |||||||
\(642\) | −0.800826 | −0.0316061 | ||||||||
\(643\) | −15.9420 | −0.628693 | −0.314347 | − | 0.949308i | \(-0.601785\pi\) | ||||
−0.314347 | + | 0.949308i | \(0.601785\pi\) | |||||||
\(644\) | 3.16483 | 0.124712 | ||||||||
\(645\) | −0.285167 | −0.0112284 | ||||||||
\(646\) | −7.34820 | −0.289111 | ||||||||
\(647\) | −17.8798 | −0.702926 | −0.351463 | − | 0.936202i | \(-0.614316\pi\) | ||||
−0.351463 | + | 0.936202i | \(0.614316\pi\) | |||||||
\(648\) | −89.7332 | −3.52505 | ||||||||
\(649\) | 1.01479 | 0.0398339 | ||||||||
\(650\) | −16.4196 | −0.644031 | ||||||||
\(651\) | 0.422790 | 0.0165705 | ||||||||
\(652\) | −100.010 | −3.91669 | ||||||||
\(653\) | −15.6763 | −0.613459 | −0.306730 | − | 0.951797i | \(-0.599235\pi\) | ||||
−0.306730 | + | 0.951797i | \(0.599235\pi\) | |||||||
\(654\) | 9.51673 | 0.372134 | ||||||||
\(655\) | 45.7245 | 1.78661 | ||||||||
\(656\) | −133.277 | −5.20359 | ||||||||
\(657\) | 0.322056 | 0.0125646 | ||||||||
\(658\) | −3.90969 | −0.152416 | ||||||||
\(659\) | 24.7991 | 0.966037 | 0.483018 | − | 0.875610i | \(-0.339540\pi\) | ||||
0.483018 | + | 0.875610i | \(0.339540\pi\) | |||||||
\(660\) | 0.468249 | 0.0182266 | ||||||||
\(661\) | −8.16894 | −0.317735 | −0.158867 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158867 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(662\) | −59.0969 | −2.29686 | ||||||||
\(663\) | −0.234606 | −0.00911135 | ||||||||
\(664\) | 28.6361 | 1.11130 | ||||||||
\(665\) | −1.59693 | −0.0619262 | ||||||||
\(666\) | −15.1989 | −0.588947 | ||||||||
\(667\) | 12.2813 | 0.475535 | ||||||||
\(668\) | 109.225 | 4.22604 | ||||||||
\(669\) | −2.10369 | −0.0813335 | ||||||||
\(670\) | 90.3286 | 3.48970 | ||||||||
\(671\) | −0.481100 | −0.0185727 | ||||||||
\(672\) | −1.21301 | −0.0467929 | ||||||||
\(673\) | −24.2244 | −0.933781 | −0.466890 | − | 0.884315i | \(-0.654626\pi\) | ||||
−0.466890 | + | 0.884315i | \(0.654626\pi\) | |||||||
\(674\) | −8.84915 | −0.340856 | ||||||||
\(675\) | 7.66502 | 0.295027 | ||||||||
\(676\) | 5.75799 | 0.221461 | ||||||||
\(677\) | −36.5211 | −1.40362 | −0.701810 | − | 0.712364i | \(-0.747624\pi\) | ||||
−0.701810 | + | 0.712364i | \(0.747624\pi\) | |||||||
\(678\) | 6.96003 | 0.267298 | ||||||||
\(679\) | 1.49559 | 0.0573955 | ||||||||
\(680\) | −37.1059 | −1.42295 | ||||||||
\(681\) | −2.37053 | −0.0908389 | ||||||||
\(682\) | 3.08707 | 0.118210 | ||||||||
\(683\) | −48.2973 | −1.84804 | −0.924022 | − | 0.382339i | \(-0.875119\pi\) | ||||
−0.924022 | + | 0.382339i | \(0.875119\pi\) | |||||||
\(684\) | −41.7577 | −1.59664 | ||||||||
\(685\) | −35.8782 | −1.37084 | ||||||||
\(686\) | −7.65879 | −0.292414 | ||||||||
\(687\) | −5.61060 | −0.214058 | ||||||||
\(688\) | 6.97595 | 0.265956 | ||||||||
\(689\) | 3.72379 | 0.141865 | ||||||||
\(690\) | −5.60464 | −0.213365 | ||||||||
\(691\) | 7.55277 | 0.287321 | 0.143660 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143660 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(692\) | 28.3446 | 1.07750 | ||||||||
\(693\) | −0.0655800 | −0.00249118 | ||||||||
\(694\) | −3.24726 | −0.123264 | ||||||||
\(695\) | 29.8685 | 1.13298 | ||||||||
\(696\) | −10.0623 | −0.381412 | ||||||||
\(697\) | −8.11509 | −0.307381 | ||||||||
\(698\) | −69.9127 | −2.64624 | ||||||||
\(699\) | 2.99870 | 0.113421 | ||||||||
\(700\) | −6.68533 | −0.252682 | ||||||||
\(701\) | −14.6796 | −0.554441 | −0.277221 | − | 0.960806i | \(-0.589413\pi\) | ||||
−0.277221 | + | 0.960806i | \(0.589413\pi\) | |||||||
\(702\) | −3.62159 | −0.136688 | ||||||||
\(703\) | −4.54034 | −0.171242 | ||||||||
\(704\) | −4.87829 | −0.183857 | ||||||||
\(705\) | 5.13879 | 0.193538 | ||||||||
\(706\) | 80.8857 | 3.04417 | ||||||||
\(707\) | −2.00809 | −0.0755220 | ||||||||
\(708\) | 11.3171 | 0.425324 | ||||||||
\(709\) | 22.9673 | 0.862553 | 0.431277 | − | 0.902220i | \(-0.358063\pi\) | ||||
0.431277 | + | 0.902220i | \(0.358063\pi\) | |||||||
\(710\) | −21.2471 | −0.797389 | ||||||||
\(711\) | 35.9398 | 1.34785 | ||||||||
\(712\) | 36.1934 | 1.35640 | ||||||||
\(713\) | −27.4245 | −1.02705 | ||||||||
\(714\) | −0.128700 | −0.00481646 | ||||||||
\(715\) | −0.372277 | −0.0139224 | ||||||||
\(716\) | −44.6298 | −1.66789 | ||||||||
\(717\) | −4.67352 | −0.174536 | ||||||||
\(718\) | −1.06445 | −0.0397251 | ||||||||
\(719\) | 19.2914 | 0.719446 | 0.359723 | − | 0.933059i | \(-0.382871\pi\) | ||||
0.359723 | + | 0.933059i | \(0.382871\pi\) | |||||||
\(720\) | −171.883 | −6.40570 | ||||||||
\(721\) | 1.29077 | 0.0480709 | ||||||||
\(722\) | 36.1140 | 1.34402 | ||||||||
\(723\) | −4.41009 | −0.164013 | ||||||||
\(724\) | −13.3851 | −0.497452 | ||||||||
\(725\) | −25.9429 | −0.963494 | ||||||||
\(726\) | −6.68506 | −0.248106 | ||||||||
\(727\) | −20.7186 | −0.768409 | −0.384204 | − | 0.923248i | \(-0.625524\pi\) | ||||
−0.384204 | + | 0.923248i | \(0.625524\pi\) | |||||||
\(728\) | 2.06154 | 0.0764059 | ||||||||
\(729\) | −24.4573 | −0.905825 | ||||||||
\(730\) | 1.00291 | 0.0371195 | ||||||||
\(731\) | 0.424759 | 0.0157103 | ||||||||
\(732\) | −5.36533 | −0.198308 | ||||||||
\(733\) | −2.60035 | −0.0960462 | −0.0480231 | − | 0.998846i | \(-0.515292\pi\) | ||||
−0.0480231 | + | 0.998846i | \(0.515292\pi\) | |||||||
\(734\) | 68.7756 | 2.53855 | ||||||||
\(735\) | 5.01927 | 0.185139 | ||||||||
\(736\) | 78.6824 | 2.90027 | ||||||||
\(737\) | 1.10812 | 0.0408181 | ||||||||
\(738\) | −62.1337 | −2.28717 | ||||||||
\(739\) | −36.4001 | −1.33900 | −0.669499 | − | 0.742813i | \(-0.733491\pi\) | ||||
−0.669499 | + | 0.742813i | \(0.733491\pi\) | |||||||
\(740\) | −35.1291 | −1.29137 | ||||||||
\(741\) | −0.536597 | −0.0197124 | ||||||||
\(742\) | 2.04279 | 0.0749931 | ||||||||
\(743\) | 40.7197 | 1.49386 | 0.746930 | − | 0.664903i | \(-0.231527\pi\) | ||||
0.746930 | + | 0.664903i | \(0.231527\pi\) | |||||||
\(744\) | 22.4694 | 0.823769 | ||||||||
\(745\) | −70.7614 | −2.59250 | ||||||||
\(746\) | 6.51148 | 0.238402 | ||||||||
\(747\) | 8.07685 | 0.295517 | ||||||||
\(748\) | −0.697461 | −0.0255017 | ||||||||
\(749\) | 0.259230 | 0.00947206 | ||||||||
\(750\) | 1.79758 | 0.0656384 | ||||||||
\(751\) | 10.7050 | 0.390630 | 0.195315 | − | 0.980741i | \(-0.437427\pi\) | ||||
0.195315 | + | 0.980741i | \(0.437427\pi\) | |||||||
\(752\) | −125.709 | −4.58412 | ||||||||
\(753\) | −0.727343 | −0.0265059 | ||||||||
\(754\) | 12.2575 | 0.446393 | ||||||||
\(755\) | 39.6438 | 1.44278 | ||||||||
\(756\) | −1.47454 | −0.0536287 | ||||||||
\(757\) | 2.57150 | 0.0934627 | 0.0467314 | − | 0.998907i | \(-0.485120\pi\) | ||||
0.0467314 | + | 0.998907i | \(0.485120\pi\) | |||||||
\(758\) | −25.6513 | −0.931696 | ||||||||
\(759\) | −0.0687557 | −0.00249567 | ||||||||
\(760\) | −84.8697 | −3.07855 | ||||||||
\(761\) | −38.7869 | −1.40602 | −0.703011 | − | 0.711179i | \(-0.748162\pi\) | ||||
−0.703011 | + | 0.711179i | \(0.748162\pi\) | |||||||
\(762\) | −1.10957 | −0.0401956 | ||||||||
\(763\) | −3.08060 | −0.111525 | ||||||||
\(764\) | −124.820 | −4.51582 | ||||||||
\(765\) | −10.4658 | −0.378391 | ||||||||
\(766\) | 51.1738 | 1.84899 | ||||||||
\(767\) | −8.99756 | −0.324883 | ||||||||
\(768\) | −20.0948 | −0.725110 | ||||||||
\(769\) | −12.9522 | −0.467070 | −0.233535 | − | 0.972348i | \(-0.575029\pi\) | ||||
−0.233535 | + | 0.972348i | \(0.575029\pi\) | |||||||
\(770\) | −0.204222 | −0.00735966 | ||||||||
\(771\) | 3.37448 | 0.121529 | ||||||||
\(772\) | 94.7990 | 3.41189 | ||||||||
\(773\) | 13.1192 | 0.471866 | 0.235933 | − | 0.971769i | \(-0.424185\pi\) | ||||
0.235933 | + | 0.971769i | \(0.424185\pi\) | |||||||
\(774\) | 3.25219 | 0.116898 | ||||||||
\(775\) | 57.9309 | 2.08094 | ||||||||
\(776\) | 79.4840 | 2.85331 | ||||||||
\(777\) | −0.0795215 | −0.00285282 | ||||||||
\(778\) | 6.67375 | 0.239266 | ||||||||
\(779\) | −18.5610 | −0.665018 | ||||||||
\(780\) | −4.15171 | −0.148655 | ||||||||
\(781\) | −0.260652 | −0.00932685 | ||||||||
\(782\) | 8.34815 | 0.298529 | ||||||||
\(783\) | −5.72207 | −0.204490 | ||||||||
\(784\) | −122.785 | −4.38517 | ||||||||
\(785\) | −73.3641 | −2.61848 | ||||||||
\(786\) | 8.42849 | 0.300634 | ||||||||
\(787\) | 19.5051 | 0.695282 | 0.347641 | − | 0.937628i | \(-0.386983\pi\) | ||||
0.347641 | + | 0.937628i | \(0.386983\pi\) | |||||||
\(788\) | −145.246 | −5.17417 | ||||||||
\(789\) | 0.0894740 | 0.00318536 | ||||||||
\(790\) | 111.920 | 3.98193 | ||||||||
\(791\) | −2.25299 | −0.0801070 | ||||||||
\(792\) | −3.48528 | −0.123844 | ||||||||
\(793\) | 4.26565 | 0.151478 | ||||||||
\(794\) | −83.0405 | −2.94700 | ||||||||
\(795\) | −2.68498 | −0.0952266 | ||||||||
\(796\) | −108.336 | −3.83987 | ||||||||
\(797\) | −22.2545 | −0.788294 | −0.394147 | − | 0.919047i | \(-0.628960\pi\) | ||||
−0.394147 | + | 0.919047i | \(0.628960\pi\) | |||||||
\(798\) | −0.294365 | −0.0104204 | ||||||||
\(799\) | −7.65427 | −0.270789 | ||||||||
\(800\) | −166.207 | −5.87631 | ||||||||
\(801\) | 10.2084 | 0.360696 | ||||||||
\(802\) | −30.6951 | −1.08388 | ||||||||
\(803\) | 0.0123034 | 0.000434177 0 | ||||||||
\(804\) | 12.3580 | 0.435832 | ||||||||
\(805\) | 1.81424 | 0.0639436 | ||||||||
\(806\) | −27.3713 | −0.964114 | ||||||||
\(807\) | 2.01710 | 0.0710052 | ||||||||
\(808\) | −106.721 | −3.75443 | ||||||||
\(809\) | 11.0616 | 0.388906 | 0.194453 | − | 0.980912i | \(-0.437707\pi\) | ||||
0.194453 | + | 0.980912i | \(0.437707\pi\) | |||||||
\(810\) | −78.8158 | −2.76930 | ||||||||
\(811\) | −7.94801 | −0.279092 | −0.139546 | − | 0.990216i | \(-0.544564\pi\) | ||||
−0.139546 | + | 0.990216i | \(0.544564\pi\) | |||||||
\(812\) | 4.99071 | 0.175140 | ||||||||
\(813\) | 4.60018 | 0.161335 | ||||||||
\(814\) | −0.580639 | −0.0203514 | ||||||||
\(815\) | −57.3307 | −2.00821 | ||||||||
\(816\) | −4.13809 | −0.144862 | ||||||||
\(817\) | 0.971519 | 0.0339891 | ||||||||
\(818\) | −6.70824 | −0.234548 | ||||||||
\(819\) | 0.581461 | 0.0203179 | ||||||||
\(820\) | −143.609 | −5.01503 | ||||||||
\(821\) | −6.66062 | −0.232457 | −0.116229 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116229 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(822\) | −6.61350 | −0.230672 | ||||||||
\(823\) | 18.8733 | 0.657882 | 0.328941 | − | 0.944350i | \(-0.393308\pi\) | ||||
0.328941 | + | 0.944350i | \(0.393308\pi\) | |||||||
\(824\) | 68.5988 | 2.38975 | ||||||||
\(825\) | 0.145238 | 0.00505654 | ||||||||
\(826\) | −4.93585 | −0.171740 | ||||||||
\(827\) | −16.8673 | −0.586532 | −0.293266 | − | 0.956031i | \(-0.594742\pi\) | ||||
−0.293266 | + | 0.956031i | \(0.594742\pi\) | |||||||
\(828\) | 47.4401 | 1.64866 | ||||||||
\(829\) | 29.9562 | 1.04042 | 0.520211 | − | 0.854038i | \(-0.325853\pi\) | ||||
0.520211 | + | 0.854038i | \(0.325853\pi\) | |||||||
\(830\) | 25.1521 | 0.873041 | ||||||||
\(831\) | 3.36335 | 0.116673 | ||||||||
\(832\) | 43.2531 | 1.49953 | ||||||||
\(833\) | −7.47624 | −0.259036 | ||||||||
\(834\) | 5.50572 | 0.190647 | ||||||||
\(835\) | 62.6132 | 2.16682 | ||||||||
\(836\) | −1.59525 | −0.0551729 | ||||||||
\(837\) | 12.7775 | 0.441655 | ||||||||
\(838\) | 27.6231 | 0.954224 | ||||||||
\(839\) | −0.370000 | −0.0127738 | −0.00638691 | − | 0.999980i | \(-0.502033\pi\) | ||||
−0.00638691 | + | 0.999980i | \(0.502033\pi\) | |||||||
\(840\) | −1.48644 | −0.0512872 | ||||||||
\(841\) | −9.63322 | −0.332180 | ||||||||
\(842\) | 90.6481 | 3.12394 | ||||||||
\(843\) | −4.44175 | −0.152982 | ||||||||
\(844\) | −61.1750 | −2.10573 | ||||||||
\(845\) | 3.30077 | 0.113550 | ||||||||
\(846\) | −58.6054 | −2.01489 | ||||||||
\(847\) | 2.16398 | 0.0743552 | ||||||||
\(848\) | 65.6819 | 2.25553 | ||||||||
\(849\) | −1.70568 | −0.0585389 | ||||||||
\(850\) | −17.6345 | −0.604857 | ||||||||
\(851\) | 5.15820 | 0.176821 | ||||||||
\(852\) | −2.90684 | −0.0995867 | ||||||||
\(853\) | −39.2122 | −1.34260 | −0.671300 | − | 0.741186i | \(-0.734264\pi\) | ||||
−0.671300 | + | 0.741186i | \(0.734264\pi\) | |||||||
\(854\) | 2.34003 | 0.0800743 | ||||||||
\(855\) | −23.9376 | −0.818649 | ||||||||
\(856\) | 13.7769 | 0.470886 | ||||||||
\(857\) | 24.7901 | 0.846814 | 0.423407 | − | 0.905940i | \(-0.360834\pi\) | ||||
0.423407 | + | 0.905940i | \(0.360834\pi\) | |||||||
\(858\) | −0.0686224 | −0.00234273 | ||||||||
\(859\) | 31.9652 | 1.09064 | 0.545319 | − | 0.838228i | \(-0.316408\pi\) | ||||
0.545319 | + | 0.838228i | \(0.316408\pi\) | |||||||
\(860\) | 7.51673 | 0.256318 | ||||||||
\(861\) | −0.325086 | −0.0110789 | ||||||||
\(862\) | −17.0936 | −0.582209 | ||||||||
\(863\) | −6.90151 | −0.234930 | −0.117465 | − | 0.993077i | \(-0.537477\pi\) | ||||
−0.117465 | + | 0.993077i | \(0.537477\pi\) | |||||||
\(864\) | −36.6594 | −1.24718 | ||||||||
\(865\) | 16.2485 | 0.552467 | ||||||||
\(866\) | −40.5742 | −1.37877 | ||||||||
\(867\) | 3.46159 | 0.117562 | ||||||||
\(868\) | −11.1444 | −0.378264 | ||||||||
\(869\) | 1.37299 | 0.0465756 | ||||||||
\(870\) | −8.83810 | −0.299640 | ||||||||
\(871\) | −9.82507 | −0.332910 | ||||||||
\(872\) | −163.720 | −5.54427 | ||||||||
\(873\) | 22.4186 | 0.758753 | ||||||||
\(874\) | 19.0941 | 0.645867 | ||||||||
\(875\) | −0.581884 | −0.0196713 | ||||||||
\(876\) | 0.137210 | 0.00463589 | ||||||||
\(877\) | −7.53594 | −0.254471 | −0.127235 | − | 0.991873i | \(-0.540610\pi\) | ||||
−0.127235 | + | 0.991873i | \(0.540610\pi\) | |||||||
\(878\) | −31.8510 | −1.07492 | ||||||||
\(879\) | −3.39919 | −0.114652 | ||||||||
\(880\) | −6.56638 | −0.221353 | ||||||||
\(881\) | 21.9387 | 0.739133 | 0.369566 | − | 0.929204i | \(-0.379506\pi\) | ||||
0.369566 | + | 0.929204i | \(0.379506\pi\) | |||||||
\(882\) | −57.2423 | −1.92745 | ||||||||
\(883\) | 0.345527 | 0.0116279 | 0.00581395 | − | 0.999983i | \(-0.498149\pi\) | ||||
0.00581395 | + | 0.999983i | \(0.498149\pi\) | |||||||
\(884\) | 6.18400 | 0.207990 | ||||||||
\(885\) | 6.48755 | 0.218077 | ||||||||
\(886\) | 1.08386 | 0.0364128 | ||||||||
\(887\) | −38.9942 | −1.30930 | −0.654649 | − | 0.755933i | \(-0.727184\pi\) | ||||
−0.654649 | + | 0.755933i | \(0.727184\pi\) | |||||||
\(888\) | −4.22622 | −0.141823 | ||||||||
\(889\) | 0.359173 | 0.0120463 | ||||||||
\(890\) | 31.7899 | 1.06560 | ||||||||
\(891\) | −0.966884 | −0.0323918 | ||||||||
\(892\) | 55.4514 | 1.85665 | ||||||||
\(893\) | −17.5070 | −0.585851 | ||||||||
\(894\) | −13.0436 | −0.436242 | ||||||||
\(895\) | −25.5840 | −0.855180 | ||||||||
\(896\) | 12.6217 | 0.421662 | ||||||||
\(897\) | 0.609618 | 0.0203546 | ||||||||
\(898\) | −47.8039 | −1.59524 | ||||||||
\(899\) | −43.2464 | −1.44235 | ||||||||
\(900\) | −100.212 | −3.34038 | ||||||||
\(901\) | 3.99930 | 0.133236 | ||||||||
\(902\) | −2.37367 | −0.0790345 | ||||||||
\(903\) | 0.0170156 | 0.000566244 0 | ||||||||
\(904\) | −119.736 | −3.98237 | ||||||||
\(905\) | −7.67299 | −0.255059 | ||||||||
\(906\) | 7.30761 | 0.242779 | ||||||||
\(907\) | 56.2085 | 1.86637 | 0.933186 | − | 0.359393i | \(-0.117016\pi\) | ||||
0.933186 | + | 0.359393i | \(0.117016\pi\) | |||||||
\(908\) | 62.4849 | 2.07364 | ||||||||
\(909\) | −30.1008 | −0.998381 | ||||||||
\(910\) | 1.81072 | 0.0600249 | ||||||||
\(911\) | 52.8425 | 1.75075 | 0.875376 | − | 0.483443i | \(-0.160614\pi\) | ||||
0.875376 | + | 0.483443i | \(0.160614\pi\) | |||||||
\(912\) | −9.46474 | −0.313409 | ||||||||
\(913\) | 0.308557 | 0.0102117 | ||||||||
\(914\) | 99.3926 | 3.28762 | ||||||||
\(915\) | −3.07568 | −0.101679 | ||||||||
\(916\) | 147.890 | 4.88643 | ||||||||
\(917\) | −2.72833 | −0.0900974 | ||||||||
\(918\) | −3.88953 | −0.128374 | ||||||||
\(919\) | −5.50777 | −0.181685 | −0.0908423 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908423 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(920\) | 96.4188 | 3.17883 | ||||||||
\(921\) | 1.82210 | 0.0600401 | ||||||||
\(922\) | −57.6850 | −1.89975 | ||||||||
\(923\) | 2.31105 | 0.0760692 | ||||||||
\(924\) | −0.0279399 | −0.000919156 0 | ||||||||
\(925\) | −10.8961 | −0.358261 | ||||||||
\(926\) | −68.4909 | −2.25075 | ||||||||
\(927\) | 19.3484 | 0.635484 | ||||||||
\(928\) | 124.076 | 4.07301 | ||||||||
\(929\) | −31.1379 | −1.02160 | −0.510801 | − | 0.859699i | \(-0.670651\pi\) | ||||
−0.510801 | + | 0.859699i | \(0.670651\pi\) | |||||||
\(930\) | 19.7357 | 0.647158 | ||||||||
\(931\) | −17.0999 | −0.560425 | ||||||||
\(932\) | −79.0430 | −2.58914 | ||||||||
\(933\) | 1.81866 | 0.0595401 | ||||||||
\(934\) | 43.4094 | 1.42040 | ||||||||
\(935\) | −0.399820 | −0.0130755 | ||||||||
\(936\) | 30.9021 | 1.01007 | ||||||||
\(937\) | −29.3654 | −0.959325 | −0.479663 | − | 0.877453i | \(-0.659241\pi\) | ||||
−0.479663 | + | 0.877453i | \(0.659241\pi\) | |||||||
\(938\) | −5.38981 | −0.175983 | ||||||||
\(939\) | −4.99035 | −0.162854 | ||||||||
\(940\) | −135.454 | −4.41801 | ||||||||
\(941\) | −21.4960 | −0.700751 | −0.350376 | − | 0.936609i | \(-0.613946\pi\) | ||||
−0.350376 | + | 0.936609i | \(0.613946\pi\) | |||||||
\(942\) | −13.5233 | −0.440614 | ||||||||
\(943\) | 21.0868 | 0.686682 | ||||||||
\(944\) | −158.703 | −5.16534 | ||||||||
\(945\) | −0.845283 | −0.0274971 | ||||||||
\(946\) | 0.124242 | 0.00403946 | ||||||||
\(947\) | 34.1868 | 1.11092 | 0.555461 | − | 0.831543i | \(-0.312542\pi\) | ||||
0.555461 | + | 0.831543i | \(0.312542\pi\) | |||||||
\(948\) | 15.3119 | 0.497307 | ||||||||
\(949\) | −0.109087 | −0.00354112 | ||||||||
\(950\) | −40.3340 | −1.30861 | ||||||||
\(951\) | 6.84030 | 0.221812 | ||||||||
\(952\) | 2.21407 | 0.0717584 | ||||||||
\(953\) | 12.0807 | 0.391333 | 0.195667 | − | 0.980670i | \(-0.437313\pi\) | ||||
0.195667 | + | 0.980670i | \(0.437313\pi\) | |||||||
\(954\) | 30.6209 | 0.991389 | ||||||||
\(955\) | −71.5530 | −2.31540 | ||||||||
\(956\) | 123.190 | 3.98424 | ||||||||
\(957\) | −0.108423 | −0.00350481 | ||||||||
\(958\) | 93.9434 | 3.03517 | ||||||||
\(959\) | 2.14081 | 0.0691305 | ||||||||
\(960\) | −31.1869 | −1.00655 | ||||||||
\(961\) | 65.5701 | 2.11517 | ||||||||
\(962\) | 5.14820 | 0.165985 | ||||||||
\(963\) | 3.88580 | 0.125218 | ||||||||
\(964\) | 116.246 | 3.74403 | ||||||||
\(965\) | 54.3436 | 1.74938 | ||||||||
\(966\) | 0.334422 | 0.0107599 | ||||||||
\(967\) | 31.1851 | 1.00284 | 0.501422 | − | 0.865203i | \(-0.332810\pi\) | ||||
0.501422 | + | 0.865203i | \(0.332810\pi\) | |||||||
\(968\) | 115.006 | 3.69643 | ||||||||
\(969\) | −0.576298 | −0.0185134 | ||||||||
\(970\) | 69.8135 | 2.24158 | ||||||||
\(971\) | 3.92415 | 0.125932 | 0.0629660 | − | 0.998016i | \(-0.479944\pi\) | ||||
0.0629660 | + | 0.998016i | \(0.479944\pi\) | |||||||
\(972\) | −33.2432 | −1.06628 | ||||||||
\(973\) | −1.78222 | −0.0571354 | ||||||||
\(974\) | −65.5252 | −2.09956 | ||||||||
\(975\) | −1.28775 | −0.0412409 | ||||||||
\(976\) | 75.2393 | 2.40835 | ||||||||
\(977\) | −27.9425 | −0.893959 | −0.446979 | − | 0.894544i | \(-0.647500\pi\) | ||||
−0.446979 | + | 0.894544i | \(0.647500\pi\) | |||||||
\(978\) | −10.5679 | −0.337923 | ||||||||
\(979\) | 0.389987 | 0.0124640 | ||||||||
\(980\) | −132.303 | −4.22627 | ||||||||
\(981\) | −46.1775 | −1.47433 | ||||||||
\(982\) | −42.5329 | −1.35728 | ||||||||
\(983\) | −16.7077 | −0.532892 | −0.266446 | − | 0.963850i | \(-0.585849\pi\) | ||||
−0.266446 | + | 0.963850i | \(0.585849\pi\) | |||||||
\(984\) | −17.2769 | −0.550767 | ||||||||
\(985\) | −83.2622 | −2.65295 | ||||||||
\(986\) | 13.1644 | 0.419241 | ||||||||
\(987\) | −0.306626 | −0.00976001 | ||||||||
\(988\) | 14.1442 | 0.449987 | ||||||||
\(989\) | −1.10372 | −0.0350964 | ||||||||
\(990\) | −3.06125 | −0.0972928 | ||||||||
\(991\) | 22.9017 | 0.727496 | 0.363748 | − | 0.931497i | \(-0.381497\pi\) | ||||
0.363748 | + | 0.931497i | \(0.381497\pi\) | |||||||
\(992\) | −277.065 | −8.79683 | ||||||||
\(993\) | −4.63480 | −0.147081 | ||||||||
\(994\) | 1.26779 | 0.0402118 | ||||||||
\(995\) | −62.1038 | −1.96882 | ||||||||
\(996\) | 3.44109 | 0.109035 | ||||||||
\(997\) | 26.0098 | 0.823737 | 0.411869 | − | 0.911243i | \(-0.364876\pi\) | ||||
0.411869 | + | 0.911243i | \(0.364876\pi\) | |||||||
\(998\) | −67.8724 | −2.14846 | ||||||||
\(999\) | −2.40329 | −0.0760366 |
(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.b.1.1 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.1 | ✓ | 142 | 1.1 | even | 1 | trivial |