Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 11x^{8} + 56x^{7} + 26x^{6} - 266x^{5} + 52x^{4} + 526x^{3} - 255x^{2} - 372x + 239 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.80657\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.80657 | 1.98454 | 0.992271 | − | 0.124090i | \(-0.0396011\pi\) | ||||
0.992271 | + | 0.124090i | \(0.0396011\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.87681 | 2.93841 | ||||||||
\(5\) | 4.11270 | 1.83926 | 0.919628 | − | 0.392790i | \(-0.128490\pi\) | ||||
0.919628 | + | 0.392790i | \(0.128490\pi\) | |||||||
\(6\) | 2.80657 | 1.14578 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 10.8805 | 3.84685 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 11.5426 | 3.65008 | ||||||||
\(11\) | −4.01832 | −1.21157 | −0.605785 | − | 0.795628i | \(-0.707141\pi\) | ||||
−0.605785 | + | 0.795628i | \(0.707141\pi\) | |||||||
\(12\) | 5.87681 | 1.69649 | ||||||||
\(13\) | 0.753718 | 0.209044 | 0.104522 | − | 0.994523i | \(-0.466669\pi\) | ||||
0.104522 | + | 0.994523i | \(0.466669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.11270 | 1.06190 | ||||||||
\(16\) | 18.7833 | 4.69583 | ||||||||
\(17\) | −2.86815 | −0.695629 | −0.347815 | − | 0.937563i | \(-0.613076\pi\) | ||||
−0.347815 | + | 0.937563i | \(0.613076\pi\) | |||||||
\(18\) | 2.80657 | 0.661514 | ||||||||
\(19\) | −8.05398 | −1.84771 | −0.923855 | − | 0.382744i | \(-0.874979\pi\) | ||||
−0.923855 | + | 0.382744i | \(0.874979\pi\) | |||||||
\(20\) | 24.1696 | 5.40448 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −11.2777 | −2.40441 | ||||||||
\(23\) | −6.62187 | −1.38075 | −0.690377 | − | 0.723449i | \(-0.742555\pi\) | ||||
−0.690377 | + | 0.723449i | \(0.742555\pi\) | |||||||
\(24\) | 10.8805 | 2.22098 | ||||||||
\(25\) | 11.9143 | 2.38286 | ||||||||
\(26\) | 2.11536 | 0.414856 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.55799 | −0.660702 | −0.330351 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330351 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(30\) | 11.5426 | 2.10738 | ||||||||
\(31\) | −1.91801 | −0.344485 | −0.172242 | − | 0.985055i | \(-0.555101\pi\) | ||||
−0.172242 | + | 0.985055i | \(0.555101\pi\) | |||||||
\(32\) | 30.9555 | 5.47222 | ||||||||
\(33\) | −4.01832 | −0.699500 | ||||||||
\(34\) | −8.04966 | −1.38051 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.87681 | 0.979469 | ||||||||
\(37\) | 5.80800 | 0.954829 | 0.477414 | − | 0.878678i | \(-0.341574\pi\) | ||||
0.477414 | + | 0.878678i | \(0.341574\pi\) | |||||||
\(38\) | −22.6040 | −3.66686 | ||||||||
\(39\) | 0.753718 | 0.120691 | ||||||||
\(40\) | 44.7484 | 7.07534 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.59707 | −0.396049 | −0.198025 | − | 0.980197i | \(-0.563453\pi\) | ||||
−0.198025 | + | 0.980197i | \(0.563453\pi\) | |||||||
\(44\) | −23.6149 | −3.56009 | ||||||||
\(45\) | 4.11270 | 0.613085 | ||||||||
\(46\) | −18.5847 | −2.74017 | ||||||||
\(47\) | −1.45654 | −0.212458 | −0.106229 | − | 0.994342i | \(-0.533878\pi\) | ||||
−0.106229 | + | 0.994342i | \(0.533878\pi\) | |||||||
\(48\) | 18.7833 | 2.71114 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 33.4383 | 4.72889 | ||||||||
\(51\) | −2.86815 | −0.401622 | ||||||||
\(52\) | 4.42946 | 0.614255 | ||||||||
\(53\) | 7.12681 | 0.978943 | 0.489471 | − | 0.872019i | \(-0.337190\pi\) | ||||
0.489471 | + | 0.872019i | \(0.337190\pi\) | |||||||
\(54\) | 2.80657 | 0.381925 | ||||||||
\(55\) | −16.5262 | −2.22839 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.05398 | −1.06678 | ||||||||
\(58\) | −9.98574 | −1.31119 | ||||||||
\(59\) | 2.95445 | 0.384637 | 0.192318 | − | 0.981333i | \(-0.438399\pi\) | ||||
0.192318 | + | 0.981333i | \(0.438399\pi\) | |||||||
\(60\) | 24.1696 | 3.12028 | ||||||||
\(61\) | −5.68932 | −0.728443 | −0.364222 | − | 0.931312i | \(-0.618665\pi\) | ||||
−0.364222 | + | 0.931312i | \(0.618665\pi\) | |||||||
\(62\) | −5.38302 | −0.683644 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 49.3121 | 6.16402 | ||||||||
\(65\) | 3.09982 | 0.384485 | ||||||||
\(66\) | −11.2777 | −1.38819 | ||||||||
\(67\) | 4.99671 | 0.610446 | 0.305223 | − | 0.952281i | \(-0.401269\pi\) | ||||
0.305223 | + | 0.952281i | \(0.401269\pi\) | |||||||
\(68\) | −16.8556 | −2.04404 | ||||||||
\(69\) | −6.62187 | −0.797179 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.96041 | 0.707370 | 0.353685 | − | 0.935365i | \(-0.384928\pi\) | ||||
0.353685 | + | 0.935365i | \(0.384928\pi\) | |||||||
\(72\) | 10.8805 | 1.28228 | ||||||||
\(73\) | −14.7998 | −1.73218 | −0.866092 | − | 0.499885i | \(-0.833375\pi\) | ||||
−0.866092 | + | 0.499885i | \(0.833375\pi\) | |||||||
\(74\) | 16.3005 | 1.89490 | ||||||||
\(75\) | 11.9143 | 1.37575 | ||||||||
\(76\) | −47.3317 | −5.42932 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.11536 | 0.239517 | ||||||||
\(79\) | 8.86055 | 0.996890 | 0.498445 | − | 0.866921i | \(-0.333905\pi\) | ||||
0.498445 | + | 0.866921i | \(0.333905\pi\) | |||||||
\(80\) | 77.2502 | 8.63683 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.80657 | 0.309933 | ||||||||
\(83\) | −1.22105 | −0.134028 | −0.0670141 | − | 0.997752i | \(-0.521347\pi\) | ||||
−0.0670141 | + | 0.997752i | \(0.521347\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7959 | −1.27944 | ||||||||
\(86\) | −7.28885 | −0.785977 | ||||||||
\(87\) | −3.55799 | −0.381457 | ||||||||
\(88\) | −43.7215 | −4.66073 | ||||||||
\(89\) | 6.89799 | 0.731186 | 0.365593 | − | 0.930775i | \(-0.380866\pi\) | ||||
0.365593 | + | 0.930775i | \(0.380866\pi\) | |||||||
\(90\) | 11.5426 | 1.21669 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −38.9155 | −4.05722 | ||||||||
\(93\) | −1.91801 | −0.198888 | ||||||||
\(94\) | −4.08787 | −0.421632 | ||||||||
\(95\) | −33.1236 | −3.39841 | ||||||||
\(96\) | 30.9555 | 3.15939 | ||||||||
\(97\) | −1.83652 | −0.186471 | −0.0932353 | − | 0.995644i | \(-0.529721\pi\) | ||||
−0.0932353 | + | 0.995644i | \(0.529721\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.01832 | −0.403857 | ||||||||
\(100\) | 70.0182 | 7.00182 | ||||||||
\(101\) | −16.4538 | −1.63722 | −0.818609 | − | 0.574351i | \(-0.805255\pi\) | ||||
−0.818609 | + | 0.574351i | \(0.805255\pi\) | |||||||
\(102\) | −8.04966 | −0.797035 | ||||||||
\(103\) | 7.19377 | 0.708823 | 0.354412 | − | 0.935090i | \(-0.384681\pi\) | ||||
0.354412 | + | 0.935090i | \(0.384681\pi\) | |||||||
\(104\) | 8.20085 | 0.804160 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.0019 | 1.94275 | ||||||||
\(107\) | 8.56687 | 0.828191 | 0.414095 | − | 0.910234i | \(-0.364098\pi\) | ||||
0.414095 | + | 0.910234i | \(0.364098\pi\) | |||||||
\(108\) | 5.87681 | 0.565497 | ||||||||
\(109\) | 13.9372 | 1.33494 | 0.667469 | − | 0.744638i | \(-0.267378\pi\) | ||||
0.667469 | + | 0.744638i | \(0.267378\pi\) | |||||||
\(110\) | −46.3818 | −4.42233 | ||||||||
\(111\) | 5.80800 | 0.551271 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8482 | −1.02051 | −0.510256 | − | 0.860022i | \(-0.670449\pi\) | ||||
−0.510256 | + | 0.860022i | \(0.670449\pi\) | |||||||
\(114\) | −22.6040 | −2.11706 | ||||||||
\(115\) | −27.2338 | −2.53956 | ||||||||
\(116\) | −20.9097 | −1.94141 | ||||||||
\(117\) | 0.753718 | 0.0696812 | ||||||||
\(118\) | 8.29186 | 0.763327 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 44.7484 | 4.08495 | ||||||||
\(121\) | 5.14693 | 0.467903 | ||||||||
\(122\) | −15.9675 | −1.44563 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −11.2718 | −1.01224 | ||||||||
\(125\) | 28.4365 | 2.54344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.7606 | −1.22106 | −0.610530 | − | 0.791993i | \(-0.709043\pi\) | ||||
−0.610530 | + | 0.791993i | \(0.709043\pi\) | |||||||
\(128\) | 76.4867 | 6.76053 | ||||||||
\(129\) | −2.59707 | −0.228659 | ||||||||
\(130\) | 8.69984 | 0.763027 | ||||||||
\(131\) | 7.79788 | 0.681304 | 0.340652 | − | 0.940190i | \(-0.389352\pi\) | ||||
0.340652 | + | 0.940190i | \(0.389352\pi\) | |||||||
\(132\) | −23.6149 | −2.05542 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.0236 | 1.21145 | ||||||||
\(135\) | 4.11270 | 0.353965 | ||||||||
\(136\) | −31.2070 | −2.67598 | ||||||||
\(137\) | 9.01085 | 0.769849 | 0.384924 | − | 0.922948i | \(-0.374227\pi\) | ||||
0.384924 | + | 0.922948i | \(0.374227\pi\) | |||||||
\(138\) | −18.5847 | −1.58204 | ||||||||
\(139\) | −14.5224 | −1.23177 | −0.615885 | − | 0.787836i | \(-0.711202\pi\) | ||||
−0.615885 | + | 0.787836i | \(0.711202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.45654 | −0.122663 | ||||||||
\(142\) | 16.7283 | 1.40381 | ||||||||
\(143\) | −3.02868 | −0.253271 | ||||||||
\(144\) | 18.7833 | 1.56528 | ||||||||
\(145\) | −14.6330 | −1.21520 | ||||||||
\(146\) | −41.5366 | −3.43759 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 34.1325 | 2.80568 | ||||||||
\(149\) | 5.01078 | 0.410499 | 0.205249 | − | 0.978710i | \(-0.434199\pi\) | ||||
0.205249 | + | 0.978710i | \(0.434199\pi\) | |||||||
\(150\) | 33.4383 | 2.73023 | ||||||||
\(151\) | −13.6609 | −1.11171 | −0.555853 | − | 0.831280i | \(-0.687608\pi\) | ||||
−0.555853 | + | 0.831280i | \(0.687608\pi\) | |||||||
\(152\) | −87.6316 | −7.10786 | ||||||||
\(153\) | −2.86815 | −0.231876 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.88820 | −0.633596 | ||||||||
\(156\) | 4.42946 | 0.354641 | ||||||||
\(157\) | −2.36196 | −0.188505 | −0.0942526 | − | 0.995548i | \(-0.530046\pi\) | ||||
−0.0942526 | + | 0.995548i | \(0.530046\pi\) | |||||||
\(158\) | 24.8677 | 1.97837 | ||||||||
\(159\) | 7.12681 | 0.565193 | ||||||||
\(160\) | 127.311 | 10.0648 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.80657 | 0.220505 | ||||||||
\(163\) | 0.595417 | 0.0466367 | 0.0233183 | − | 0.999728i | \(-0.492577\pi\) | ||||
0.0233183 | + | 0.999728i | \(0.492577\pi\) | |||||||
\(164\) | 5.87681 | 0.458902 | ||||||||
\(165\) | −16.5262 | −1.28656 | ||||||||
\(166\) | −3.42697 | −0.265985 | ||||||||
\(167\) | 3.69545 | 0.285963 | 0.142981 | − | 0.989725i | \(-0.454331\pi\) | ||||
0.142981 | + | 0.989725i | \(0.454331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4319 | −0.956301 | ||||||||
\(170\) | −33.1059 | −2.53910 | ||||||||
\(171\) | −8.05398 | −0.615903 | ||||||||
\(172\) | −15.2625 | −1.16375 | ||||||||
\(173\) | −8.93647 | −0.679427 | −0.339714 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339714 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(174\) | −9.98574 | −0.757017 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −75.4774 | −5.68933 | ||||||||
\(177\) | 2.95445 | 0.222070 | ||||||||
\(178\) | 19.3597 | 1.45107 | ||||||||
\(179\) | −7.70618 | −0.575987 | −0.287994 | − | 0.957632i | \(-0.592988\pi\) | ||||
−0.287994 | + | 0.957632i | \(0.592988\pi\) | |||||||
\(180\) | 24.1696 | 1.80149 | ||||||||
\(181\) | −9.67962 | −0.719480 | −0.359740 | − | 0.933053i | \(-0.617135\pi\) | ||||
−0.359740 | + | 0.933053i | \(0.617135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.68932 | −0.420567 | ||||||||
\(184\) | −72.0494 | −5.31156 | ||||||||
\(185\) | 23.8866 | 1.75617 | ||||||||
\(186\) | −5.38302 | −0.394702 | ||||||||
\(187\) | 11.5252 | 0.842804 | ||||||||
\(188\) | −8.55981 | −0.624288 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −92.9636 | −6.74429 | ||||||||
\(191\) | 20.9409 | 1.51523 | 0.757614 | − | 0.652702i | \(-0.226365\pi\) | ||||
0.757614 | + | 0.652702i | \(0.226365\pi\) | |||||||
\(192\) | 49.3121 | 3.55880 | ||||||||
\(193\) | 6.85788 | 0.493641 | 0.246821 | − | 0.969061i | \(-0.420614\pi\) | ||||
0.246821 | + | 0.969061i | \(0.420614\pi\) | |||||||
\(194\) | −5.15432 | −0.370059 | ||||||||
\(195\) | 3.09982 | 0.221982 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.85575 | 0.417205 | 0.208603 | − | 0.978001i | \(-0.433109\pi\) | ||||
0.208603 | + | 0.978001i | \(0.433109\pi\) | |||||||
\(198\) | −11.2777 | −0.801471 | ||||||||
\(199\) | −9.49177 | −0.672854 | −0.336427 | − | 0.941710i | \(-0.609219\pi\) | ||||
−0.336427 | + | 0.941710i | \(0.609219\pi\) | |||||||
\(200\) | 129.634 | 9.16652 | ||||||||
\(201\) | 4.99671 | 0.352441 | ||||||||
\(202\) | −46.1788 | −3.24913 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.8556 | −1.18013 | ||||||||
\(205\) | 4.11270 | 0.287244 | ||||||||
\(206\) | 20.1898 | 1.40669 | ||||||||
\(207\) | −6.62187 | −0.460252 | ||||||||
\(208\) | 14.1573 | 0.981633 | ||||||||
\(209\) | 32.3635 | 2.23863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9337 | −1.37229 | −0.686146 | − | 0.727464i | \(-0.740699\pi\) | ||||
−0.686146 | + | 0.727464i | \(0.740699\pi\) | |||||||
\(212\) | 41.8829 | 2.87653 | ||||||||
\(213\) | 5.96041 | 0.408400 | ||||||||
\(214\) | 24.0435 | 1.64358 | ||||||||
\(215\) | −10.6810 | −0.728436 | ||||||||
\(216\) | 10.8805 | 0.740327 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 39.1156 | 2.64924 | ||||||||
\(219\) | −14.7998 | −1.00008 | ||||||||
\(220\) | −97.1212 | −6.54791 | ||||||||
\(221\) | −2.16178 | −0.145417 | ||||||||
\(222\) | 16.3005 | 1.09402 | ||||||||
\(223\) | 2.16735 | 0.145136 | 0.0725682 | − | 0.997363i | \(-0.476880\pi\) | ||||
0.0725682 | + | 0.997363i | \(0.476880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.9143 | 0.794288 | ||||||||
\(226\) | −30.4462 | −2.02525 | ||||||||
\(227\) | −27.4094 | −1.81923 | −0.909613 | − | 0.415457i | \(-0.863622\pi\) | ||||
−0.909613 | + | 0.415457i | \(0.863622\pi\) | |||||||
\(228\) | −47.3317 | −3.13462 | ||||||||
\(229\) | 12.3463 | 0.815867 | 0.407933 | − | 0.913012i | \(-0.366250\pi\) | ||||
0.407933 | + | 0.913012i | \(0.366250\pi\) | |||||||
\(230\) | −76.4334 | −5.03987 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −38.7128 | −2.54162 | ||||||||
\(233\) | −11.9621 | −0.783664 | −0.391832 | − | 0.920037i | \(-0.628159\pi\) | ||||
−0.391832 | + | 0.920037i | \(0.628159\pi\) | |||||||
\(234\) | 2.11536 | 0.138285 | ||||||||
\(235\) | −5.99031 | −0.390765 | ||||||||
\(236\) | 17.3627 | 1.13022 | ||||||||
\(237\) | 8.86055 | 0.575555 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4914 | −0.743320 | −0.371660 | − | 0.928369i | \(-0.621211\pi\) | ||||
−0.371660 | + | 0.928369i | \(0.621211\pi\) | |||||||
\(240\) | 77.2502 | 4.98648 | ||||||||
\(241\) | 24.4262 | 1.57343 | 0.786715 | − | 0.617317i | \(-0.211780\pi\) | ||||
0.786715 | + | 0.617317i | \(0.211780\pi\) | |||||||
\(242\) | 14.4452 | 0.928573 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −33.4351 | −2.14046 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.80657 | 0.178940 | ||||||||
\(247\) | −6.07043 | −0.386252 | ||||||||
\(248\) | −20.8690 | −1.32518 | ||||||||
\(249\) | −1.22105 | −0.0773812 | ||||||||
\(250\) | 79.8090 | 5.04757 | ||||||||
\(251\) | −17.3618 | −1.09587 | −0.547935 | − | 0.836521i | \(-0.684586\pi\) | ||||
−0.547935 | + | 0.836521i | \(0.684586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.6088 | 1.67288 | ||||||||
\(254\) | −38.6201 | −2.42324 | ||||||||
\(255\) | −11.7959 | −0.738686 | ||||||||
\(256\) | 116.041 | 7.25254 | ||||||||
\(257\) | 15.9782 | 0.996693 | 0.498347 | − | 0.866978i | \(-0.333941\pi\) | ||||
0.498347 | + | 0.866978i | \(0.333941\pi\) | |||||||
\(258\) | −7.28885 | −0.453784 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 18.2170 | 1.12977 | ||||||||
\(261\) | −3.55799 | −0.220234 | ||||||||
\(262\) | 21.8853 | 1.35208 | ||||||||
\(263\) | −3.35156 | −0.206666 | −0.103333 | − | 0.994647i | \(-0.532951\pi\) | ||||
−0.103333 | + | 0.994647i | \(0.532951\pi\) | |||||||
\(264\) | −43.7215 | −2.69087 | ||||||||
\(265\) | 29.3104 | 1.80053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.89799 | 0.422150 | ||||||||
\(268\) | 29.3647 | 1.79374 | ||||||||
\(269\) | 8.96079 | 0.546349 | 0.273174 | − | 0.961965i | \(-0.411926\pi\) | ||||
0.273174 | + | 0.961965i | \(0.411926\pi\) | |||||||
\(270\) | 11.5426 | 0.702458 | ||||||||
\(271\) | −2.53831 | −0.154191 | −0.0770957 | − | 0.997024i | \(-0.524565\pi\) | ||||
−0.0770957 | + | 0.997024i | \(0.524565\pi\) | |||||||
\(272\) | −53.8734 | −3.26656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.2896 | 1.52780 | ||||||||
\(275\) | −47.8756 | −2.88701 | ||||||||
\(276\) | −38.9155 | −2.34244 | ||||||||
\(277\) | 19.0038 | 1.14183 | 0.570914 | − | 0.821010i | \(-0.306589\pi\) | ||||
0.570914 | + | 0.821010i | \(0.306589\pi\) | |||||||
\(278\) | −40.7580 | −2.44450 | ||||||||
\(279\) | −1.91801 | −0.114828 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.50424 | −0.328356 | −0.164178 | − | 0.986431i | \(-0.552497\pi\) | ||||
−0.164178 | + | 0.986431i | \(0.552497\pi\) | |||||||
\(282\) | −4.08787 | −0.243429 | ||||||||
\(283\) | 25.6985 | 1.52762 | 0.763809 | − | 0.645443i | \(-0.223327\pi\) | ||||
0.763809 | + | 0.645443i | \(0.223327\pi\) | |||||||
\(284\) | 35.0282 | 2.07854 | ||||||||
\(285\) | −33.1236 | −1.96207 | ||||||||
\(286\) | −8.50020 | −0.502627 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 30.9555 | 1.82407 | ||||||||
\(289\) | −8.77369 | −0.516100 | ||||||||
\(290\) | −41.0684 | −2.41162 | ||||||||
\(291\) | −1.83652 | −0.107659 | ||||||||
\(292\) | −86.9755 | −5.08986 | ||||||||
\(293\) | −15.9943 | −0.934395 | −0.467197 | − | 0.884153i | \(-0.654736\pi\) | ||||
−0.467197 | + | 0.884153i | \(0.654736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1508 | 0.707445 | ||||||||
\(296\) | 63.1941 | 3.67308 | ||||||||
\(297\) | −4.01832 | −0.233167 | ||||||||
\(298\) | 14.0631 | 0.814652 | ||||||||
\(299\) | −4.99102 | −0.288638 | ||||||||
\(300\) | 70.0182 | 4.04250 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −38.3402 | −2.20623 | ||||||||
\(303\) | −16.4538 | −0.945249 | ||||||||
\(304\) | −151.280 | −8.67652 | ||||||||
\(305\) | −23.3985 | −1.33979 | ||||||||
\(306\) | −8.04966 | −0.460169 | ||||||||
\(307\) | 20.1627 | 1.15075 | 0.575373 | − | 0.817891i | \(-0.304857\pi\) | ||||
0.575373 | + | 0.817891i | \(0.304857\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.19377 | 0.409239 | ||||||||
\(310\) | −22.1388 | −1.25740 | ||||||||
\(311\) | 23.6861 | 1.34312 | 0.671558 | − | 0.740952i | \(-0.265626\pi\) | ||||
0.671558 | + | 0.740952i | \(0.265626\pi\) | |||||||
\(312\) | 8.20085 | 0.464282 | ||||||||
\(313\) | 25.9892 | 1.46900 | 0.734499 | − | 0.678610i | \(-0.237417\pi\) | ||||
0.734499 | + | 0.678610i | \(0.237417\pi\) | |||||||
\(314\) | −6.62901 | −0.374097 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 52.0718 | 2.92927 | ||||||||
\(317\) | 12.9378 | 0.726659 | 0.363329 | − | 0.931661i | \(-0.381640\pi\) | ||||
0.363329 | + | 0.931661i | \(0.381640\pi\) | |||||||
\(318\) | 20.0019 | 1.12165 | ||||||||
\(319\) | 14.2972 | 0.800487 | ||||||||
\(320\) | 202.806 | 11.3372 | ||||||||
\(321\) | 8.56687 | 0.478156 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.1000 | 1.28532 | ||||||||
\(324\) | 5.87681 | 0.326490 | ||||||||
\(325\) | 8.98003 | 0.498123 | ||||||||
\(326\) | 1.67108 | 0.0925524 | ||||||||
\(327\) | 13.9372 | 0.770727 | ||||||||
\(328\) | 10.8805 | 0.600777 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −46.3818 | −2.55323 | ||||||||
\(331\) | −15.8948 | −0.873655 | −0.436827 | − | 0.899545i | \(-0.643898\pi\) | ||||
−0.436827 | + | 0.899545i | \(0.643898\pi\) | |||||||
\(332\) | −7.17591 | −0.393829 | ||||||||
\(333\) | 5.80800 | 0.318276 | ||||||||
\(334\) | 10.3715 | 0.567505 | ||||||||
\(335\) | 20.5500 | 1.12277 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.73799 | −0.421515 | −0.210758 | − | 0.977538i | \(-0.567593\pi\) | ||||
−0.210758 | + | 0.977538i | \(0.567593\pi\) | |||||||
\(338\) | −34.8910 | −1.89782 | ||||||||
\(339\) | −10.8482 | −0.589193 | ||||||||
\(340\) | −69.3221 | −3.75952 | ||||||||
\(341\) | 7.70719 | 0.417368 | ||||||||
\(342\) | −22.6040 | −1.22229 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −28.2575 | −1.52354 | ||||||||
\(345\) | −27.2338 | −1.46622 | ||||||||
\(346\) | −25.0808 | −1.34835 | ||||||||
\(347\) | −6.92049 | −0.371511 | −0.185756 | − | 0.982596i | \(-0.559473\pi\) | ||||
−0.185756 | + | 0.982596i | \(0.559473\pi\) | |||||||
\(348\) | −20.9097 | −1.12087 | ||||||||
\(349\) | 33.9500 | 1.81730 | 0.908651 | − | 0.417556i | \(-0.137113\pi\) | ||||
0.908651 | + | 0.417556i | \(0.137113\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.753718 | 0.0402305 | ||||||||
\(352\) | −124.389 | −6.62998 | ||||||||
\(353\) | 19.8577 | 1.05692 | 0.528460 | − | 0.848958i | \(-0.322770\pi\) | ||||
0.528460 | + | 0.848958i | \(0.322770\pi\) | |||||||
\(354\) | 8.29186 | 0.440707 | ||||||||
\(355\) | 24.5134 | 1.30104 | ||||||||
\(356\) | 40.5382 | 2.14852 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.6279 | −1.14307 | ||||||||
\(359\) | 5.95353 | 0.314216 | 0.157108 | − | 0.987581i | \(-0.449783\pi\) | ||||
0.157108 | + | 0.987581i | \(0.449783\pi\) | |||||||
\(360\) | 44.7484 | 2.35845 | ||||||||
\(361\) | 45.8666 | 2.41403 | ||||||||
\(362\) | −27.1665 | −1.42784 | ||||||||
\(363\) | 5.14693 | 0.270144 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −60.8671 | −3.18593 | ||||||||
\(366\) | −15.9675 | −0.834633 | ||||||||
\(367\) | −29.4136 | −1.53538 | −0.767690 | − | 0.640822i | \(-0.778594\pi\) | ||||
−0.767690 | + | 0.640822i | \(0.778594\pi\) | |||||||
\(368\) | −124.381 | −6.48379 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 67.0392 | 3.48520 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.2718 | −0.584415 | ||||||||
\(373\) | −1.46339 | −0.0757715 | −0.0378857 | − | 0.999282i | \(-0.512062\pi\) | ||||
−0.0378857 | + | 0.999282i | \(0.512062\pi\) | |||||||
\(374\) | 32.3462 | 1.67258 | ||||||||
\(375\) | 28.4365 | 1.46846 | ||||||||
\(376\) | −15.8479 | −0.817294 | ||||||||
\(377\) | −2.68172 | −0.138116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.8794 | −1.48343 | −0.741717 | − | 0.670713i | \(-0.765988\pi\) | ||||
−0.741717 | + | 0.670713i | \(0.765988\pi\) | |||||||
\(380\) | −194.661 | −9.98591 | ||||||||
\(381\) | −13.7606 | −0.704979 | ||||||||
\(382\) | 58.7720 | 3.00704 | ||||||||
\(383\) | −9.31702 | −0.476077 | −0.238039 | − | 0.971256i | \(-0.576505\pi\) | ||||
−0.238039 | + | 0.971256i | \(0.576505\pi\) | |||||||
\(384\) | 76.4867 | 3.90320 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.2471 | 0.979652 | ||||||||
\(387\) | −2.59707 | −0.132016 | ||||||||
\(388\) | −10.7929 | −0.547926 | ||||||||
\(389\) | 14.1181 | 0.715816 | 0.357908 | − | 0.933757i | \(-0.383490\pi\) | ||||
0.357908 | + | 0.933757i | \(0.383490\pi\) | |||||||
\(390\) | 8.69984 | 0.440534 | ||||||||
\(391\) | 18.9925 | 0.960494 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.79788 | 0.393351 | ||||||||
\(394\) | 16.4346 | 0.827961 | ||||||||
\(395\) | 36.4408 | 1.83354 | ||||||||
\(396\) | −23.6149 | −1.18670 | ||||||||
\(397\) | −32.9826 | −1.65535 | −0.827674 | − | 0.561209i | \(-0.810336\pi\) | ||||
−0.827674 | + | 0.561209i | \(0.810336\pi\) | |||||||
\(398\) | −26.6393 | −1.33531 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 223.790 | 11.1895 | ||||||||
\(401\) | 20.1923 | 1.00836 | 0.504178 | − | 0.863600i | \(-0.331796\pi\) | ||||
0.504178 | + | 0.863600i | \(0.331796\pi\) | |||||||
\(402\) | 14.0236 | 0.699434 | ||||||||
\(403\) | −1.44564 | −0.0720124 | ||||||||
\(404\) | −96.6962 | −4.81081 | ||||||||
\(405\) | 4.11270 | 0.204362 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.3384 | −1.15684 | ||||||||
\(408\) | −31.2070 | −1.54498 | ||||||||
\(409\) | 8.05070 | 0.398082 | 0.199041 | − | 0.979991i | \(-0.436217\pi\) | ||||
0.199041 | + | 0.979991i | \(0.436217\pi\) | |||||||
\(410\) | 11.5426 | 0.570047 | ||||||||
\(411\) | 9.01085 | 0.444473 | ||||||||
\(412\) | 42.2764 | 2.08281 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.5847 | −0.913388 | ||||||||
\(415\) | −5.02183 | −0.246512 | ||||||||
\(416\) | 23.3317 | 1.14393 | ||||||||
\(417\) | −14.5224 | −0.711163 | ||||||||
\(418\) | 90.8303 | 4.44265 | ||||||||
\(419\) | 14.8930 | 0.727570 | 0.363785 | − | 0.931483i | \(-0.381484\pi\) | ||||
0.363785 | + | 0.931483i | \(0.381484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.32962 | 0.113539 | 0.0567695 | − | 0.998387i | \(-0.481920\pi\) | ||||
0.0567695 | + | 0.998387i | \(0.481920\pi\) | |||||||
\(422\) | −55.9452 | −2.72337 | ||||||||
\(423\) | −1.45654 | −0.0708194 | ||||||||
\(424\) | 77.5435 | 3.76585 | ||||||||
\(425\) | −34.1721 | −1.65759 | ||||||||
\(426\) | 16.7283 | 0.810488 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 50.3459 | 2.43356 | ||||||||
\(429\) | −3.02868 | −0.146226 | ||||||||
\(430\) | −29.9769 | −1.44561 | ||||||||
\(431\) | 11.9770 | 0.576914 | 0.288457 | − | 0.957493i | \(-0.406858\pi\) | ||||
0.288457 | + | 0.957493i | \(0.406858\pi\) | |||||||
\(432\) | 18.7833 | 0.903712 | ||||||||
\(433\) | 28.6259 | 1.37568 | 0.687838 | − | 0.725865i | \(-0.258560\pi\) | ||||
0.687838 | + | 0.725865i | \(0.258560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.6330 | −0.701597 | ||||||||
\(436\) | 81.9061 | 3.92259 | ||||||||
\(437\) | 53.3324 | 2.55123 | ||||||||
\(438\) | −41.5366 | −1.98469 | ||||||||
\(439\) | 14.2078 | 0.678102 | 0.339051 | − | 0.940768i | \(-0.389894\pi\) | ||||
0.339051 | + | 0.940768i | \(0.389894\pi\) | |||||||
\(440\) | −179.814 | −8.57228 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.06717 | −0.288586 | ||||||||
\(443\) | −9.29302 | −0.441525 | −0.220762 | − | 0.975328i | \(-0.570855\pi\) | ||||
−0.220762 | + | 0.975328i | \(0.570855\pi\) | |||||||
\(444\) | 34.1325 | 1.61986 | ||||||||
\(445\) | 28.3694 | 1.34484 | ||||||||
\(446\) | 6.08281 | 0.288029 | ||||||||
\(447\) | 5.01078 | 0.237002 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.3303 | −1.76173 | −0.880864 | − | 0.473369i | \(-0.843038\pi\) | ||||
−0.880864 | + | 0.473369i | \(0.843038\pi\) | |||||||
\(450\) | 33.4383 | 1.57630 | ||||||||
\(451\) | −4.01832 | −0.189216 | ||||||||
\(452\) | −63.7528 | −2.99868 | ||||||||
\(453\) | −13.6609 | −0.641844 | ||||||||
\(454\) | −76.9263 | −3.61033 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −87.6316 | −4.10372 | ||||||||
\(457\) | 12.5438 | 0.586776 | 0.293388 | − | 0.955993i | \(-0.405217\pi\) | ||||
0.293388 | + | 0.955993i | \(0.405217\pi\) | |||||||
\(458\) | 34.6507 | 1.61912 | ||||||||
\(459\) | −2.86815 | −0.133874 | ||||||||
\(460\) | −160.048 | −7.46227 | ||||||||
\(461\) | −16.7456 | −0.779919 | −0.389959 | − | 0.920832i | \(-0.627511\pi\) | ||||
−0.389959 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.4001 | −0.762176 | −0.381088 | − | 0.924539i | \(-0.624451\pi\) | ||||
−0.381088 | + | 0.924539i | \(0.624451\pi\) | |||||||
\(464\) | −66.8309 | −3.10254 | ||||||||
\(465\) | −7.88820 | −0.365807 | ||||||||
\(466\) | −33.5725 | −1.55521 | ||||||||
\(467\) | 16.4957 | 0.763331 | 0.381666 | − | 0.924300i | \(-0.375351\pi\) | ||||
0.381666 | + | 0.924300i | \(0.375351\pi\) | |||||||
\(468\) | 4.42946 | 0.204752 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.8122 | −0.775489 | ||||||||
\(471\) | −2.36196 | −0.108834 | ||||||||
\(472\) | 32.1460 | 1.47964 | ||||||||
\(473\) | 10.4359 | 0.479842 | ||||||||
\(474\) | 24.8677 | 1.14221 | ||||||||
\(475\) | −95.9577 | −4.40284 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.12681 | 0.326314 | ||||||||
\(478\) | −32.2515 | −1.47515 | ||||||||
\(479\) | 13.3546 | 0.610185 | 0.305093 | − | 0.952323i | \(-0.401313\pi\) | ||||
0.305093 | + | 0.952323i | \(0.401313\pi\) | |||||||
\(480\) | 127.311 | 5.81092 | ||||||||
\(481\) | 4.37759 | 0.199601 | ||||||||
\(482\) | 68.5537 | 3.12254 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.2476 | 1.37489 | ||||||||
\(485\) | −7.55307 | −0.342967 | ||||||||
\(486\) | 2.80657 | 0.127308 | ||||||||
\(487\) | 3.34242 | 0.151460 | 0.0757298 | − | 0.997128i | \(-0.475871\pi\) | ||||
0.0757298 | + | 0.997128i | \(0.475871\pi\) | |||||||
\(488\) | −61.9029 | −2.80221 | ||||||||
\(489\) | 0.595417 | 0.0269257 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.1104 | 0.952699 | 0.476349 | − | 0.879256i | \(-0.341960\pi\) | ||||
0.476349 | + | 0.879256i | \(0.341960\pi\) | |||||||
\(492\) | 5.87681 | 0.264947 | ||||||||
\(493\) | 10.2049 | 0.459604 | ||||||||
\(494\) | −17.0371 | −0.766533 | ||||||||
\(495\) | −16.5262 | −0.742796 | ||||||||
\(496\) | −36.0266 | −1.61764 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.42697 | −0.153566 | ||||||||
\(499\) | −0.109003 | −0.00487963 | −0.00243981 | − | 0.999997i | \(-0.500777\pi\) | ||||
−0.00243981 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(500\) | 167.116 | 7.47366 | ||||||||
\(501\) | 3.69545 | 0.165101 | ||||||||
\(502\) | −48.7271 | −2.17480 | ||||||||
\(503\) | 3.20557 | 0.142930 | 0.0714648 | − | 0.997443i | \(-0.477233\pi\) | ||||
0.0714648 | + | 0.997443i | \(0.477233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67.6698 | −3.01127 | ||||||||
\(506\) | 74.6794 | 3.31990 | ||||||||
\(507\) | −12.4319 | −0.552120 | ||||||||
\(508\) | −80.8687 | −3.58797 | ||||||||
\(509\) | −13.9817 | −0.619727 | −0.309863 | − | 0.950781i | \(-0.600283\pi\) | ||||
−0.309863 | + | 0.950781i | \(0.600283\pi\) | |||||||
\(510\) | −33.1059 | −1.46595 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 172.703 | 7.63245 | ||||||||
\(513\) | −8.05398 | −0.355592 | ||||||||
\(514\) | 44.8439 | 1.97798 | ||||||||
\(515\) | 29.5858 | 1.30371 | ||||||||
\(516\) | −15.2625 | −0.671894 | ||||||||
\(517\) | 5.85285 | 0.257408 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.93647 | −0.392268 | ||||||||
\(520\) | 33.7277 | 1.47906 | ||||||||
\(521\) | −11.6932 | −0.512288 | −0.256144 | − | 0.966639i | \(-0.582452\pi\) | ||||
−0.256144 | + | 0.966639i | \(0.582452\pi\) | |||||||
\(522\) | −9.98574 | −0.437064 | ||||||||
\(523\) | 11.6517 | 0.509492 | 0.254746 | − | 0.967008i | \(-0.418008\pi\) | ||||
0.254746 | + | 0.967008i | \(0.418008\pi\) | |||||||
\(524\) | 45.8267 | 2.00195 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.40637 | −0.410137 | ||||||||
\(527\) | 5.50115 | 0.239634 | ||||||||
\(528\) | −75.4774 | −3.28473 | ||||||||
\(529\) | 20.8491 | 0.906483 | ||||||||
\(530\) | 82.2617 | 3.57322 | ||||||||
\(531\) | 2.95445 | 0.128212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.753718 | 0.0326471 | ||||||||
\(534\) | 19.3597 | 0.837775 | ||||||||
\(535\) | 35.2330 | 1.52325 | ||||||||
\(536\) | 54.3669 | 2.34829 | ||||||||
\(537\) | −7.70618 | −0.332546 | ||||||||
\(538\) | 25.1490 | 1.08425 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 24.1696 | 1.04009 | ||||||||
\(541\) | 23.6914 | 1.01857 | 0.509285 | − | 0.860598i | \(-0.329910\pi\) | ||||
0.509285 | + | 0.860598i | \(0.329910\pi\) | |||||||
\(542\) | −7.12393 | −0.305999 | ||||||||
\(543\) | −9.67962 | −0.415392 | ||||||||
\(544\) | −88.7852 | −3.80664 | ||||||||
\(545\) | 57.3194 | 2.45529 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.3071 | 1.93719 | 0.968597 | − | 0.248637i | \(-0.0799826\pi\) | ||||
0.968597 | + | 0.248637i | \(0.0799826\pi\) | |||||||
\(548\) | 52.9551 | 2.26213 | ||||||||
\(549\) | −5.68932 | −0.242814 | ||||||||
\(550\) | −134.366 | −5.72939 | ||||||||
\(551\) | 28.6560 | 1.22079 | ||||||||
\(552\) | −72.0494 | −3.06663 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 53.3355 | 2.26601 | ||||||||
\(555\) | 23.8866 | 1.01393 | ||||||||
\(556\) | −85.3452 | −3.61944 | ||||||||
\(557\) | 20.3869 | 0.863820 | 0.431910 | − | 0.901917i | \(-0.357840\pi\) | ||||
0.431910 | + | 0.901917i | \(0.357840\pi\) | |||||||
\(558\) | −5.38302 | −0.227881 | ||||||||
\(559\) | −1.95746 | −0.0827916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.5252 | 0.486593 | ||||||||
\(562\) | −15.4480 | −0.651635 | ||||||||
\(563\) | −25.8965 | −1.09141 | −0.545703 | − | 0.837978i | \(-0.683737\pi\) | ||||
−0.545703 | + | 0.837978i | \(0.683737\pi\) | |||||||
\(564\) | −8.55981 | −0.360433 | ||||||||
\(565\) | −44.6154 | −1.87698 | ||||||||
\(566\) | 72.1246 | 3.03162 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 64.8524 | 2.72115 | ||||||||
\(569\) | 17.4999 | 0.733632 | 0.366816 | − | 0.930293i | \(-0.380448\pi\) | ||||
0.366816 | + | 0.930293i | \(0.380448\pi\) | |||||||
\(570\) | −92.9636 | −3.89382 | ||||||||
\(571\) | 23.4334 | 0.980656 | 0.490328 | − | 0.871538i | \(-0.336877\pi\) | ||||
0.490328 | + | 0.871538i | \(0.336877\pi\) | |||||||
\(572\) | −17.7990 | −0.744214 | ||||||||
\(573\) | 20.9409 | 0.874818 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −78.8950 | −3.29015 | ||||||||
\(576\) | 49.3121 | 2.05467 | ||||||||
\(577\) | 27.6328 | 1.15037 | 0.575184 | − | 0.818024i | \(-0.304930\pi\) | ||||
0.575184 | + | 0.818024i | \(0.304930\pi\) | |||||||
\(578\) | −24.6240 | −1.02422 | ||||||||
\(579\) | 6.85788 | 0.285004 | ||||||||
\(580\) | −85.9952 | −3.57076 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.15432 | −0.213653 | ||||||||
\(583\) | −28.6378 | −1.18606 | ||||||||
\(584\) | −161.029 | −6.66345 | ||||||||
\(585\) | 3.09982 | 0.128162 | ||||||||
\(586\) | −44.8889 | −1.85435 | ||||||||
\(587\) | 3.95052 | 0.163056 | 0.0815278 | − | 0.996671i | \(-0.474020\pi\) | ||||
0.0815278 | + | 0.996671i | \(0.474020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.4476 | 0.636508 | ||||||||
\(590\) | 34.1019 | 1.40395 | ||||||||
\(591\) | 5.85575 | 0.240873 | ||||||||
\(592\) | 109.093 | 4.48371 | ||||||||
\(593\) | 30.9520 | 1.27105 | 0.635523 | − | 0.772082i | \(-0.280785\pi\) | ||||
0.635523 | + | 0.772082i | \(0.280785\pi\) | |||||||
\(594\) | −11.2777 | −0.462729 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.4474 | 1.20621 | ||||||||
\(597\) | −9.49177 | −0.388472 | ||||||||
\(598\) | −14.0076 | −0.572814 | ||||||||
\(599\) | 0.0709266 | 0.00289798 | 0.00144899 | − | 0.999999i | \(-0.499539\pi\) | ||||
0.00144899 | + | 0.999999i | \(0.499539\pi\) | |||||||
\(600\) | 129.634 | 5.29229 | ||||||||
\(601\) | −24.8758 | −1.01471 | −0.507353 | − | 0.861738i | \(-0.669376\pi\) | ||||
−0.507353 | + | 0.861738i | \(0.669376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.99671 | 0.203482 | ||||||||
\(604\) | −80.2825 | −3.26665 | ||||||||
\(605\) | 21.1678 | 0.860593 | ||||||||
\(606\) | −46.1788 | −1.87589 | ||||||||
\(607\) | −14.5138 | −0.589096 | −0.294548 | − | 0.955637i | \(-0.595169\pi\) | ||||
−0.294548 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(608\) | −249.315 | −10.1111 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −65.6694 | −2.65888 | ||||||||
\(611\) | −1.09782 | −0.0444130 | ||||||||
\(612\) | −16.8556 | −0.681347 | ||||||||
\(613\) | −22.0987 | −0.892559 | −0.446279 | − | 0.894894i | \(-0.647251\pi\) | ||||
−0.446279 | + | 0.894894i | \(0.647251\pi\) | |||||||
\(614\) | 56.5879 | 2.28370 | ||||||||
\(615\) | 4.11270 | 0.165840 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.7730 | 0.554482 | 0.277241 | − | 0.960800i | \(-0.410580\pi\) | ||||
0.277241 | + | 0.960800i | \(0.410580\pi\) | |||||||
\(618\) | 20.1898 | 0.812153 | ||||||||
\(619\) | 7.60818 | 0.305799 | 0.152899 | − | 0.988242i | \(-0.451139\pi\) | ||||
0.152899 | + | 0.988242i | \(0.451139\pi\) | |||||||
\(620\) | −46.3575 | −1.86176 | ||||||||
\(621\) | −6.62187 | −0.265726 | ||||||||
\(622\) | 66.4766 | 2.66547 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.1573 | 0.566746 | ||||||||
\(625\) | 57.3794 | 2.29518 | ||||||||
\(626\) | 72.9405 | 2.91529 | ||||||||
\(627\) | 32.3635 | 1.29247 | ||||||||
\(628\) | −13.8808 | −0.553905 | ||||||||
\(629\) | −16.6582 | −0.664207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7825 | −0.787530 | −0.393765 | − | 0.919211i | \(-0.628828\pi\) | ||||
−0.393765 | + | 0.919211i | \(0.628828\pi\) | |||||||
\(632\) | 96.4075 | 3.83489 | ||||||||
\(633\) | −19.9337 | −0.792293 | ||||||||
\(634\) | 36.3108 | 1.44209 | ||||||||
\(635\) | −56.5934 | −2.24584 | ||||||||
\(636\) | 41.8829 | 1.66077 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 40.1259 | 1.58860 | ||||||||
\(639\) | 5.96041 | 0.235790 | ||||||||
\(640\) | 314.567 | 12.4344 | ||||||||
\(641\) | −2.29745 | −0.0907439 | −0.0453719 | − | 0.998970i | \(-0.514447\pi\) | ||||
−0.0453719 | + | 0.998970i | \(0.514447\pi\) | |||||||
\(642\) | 24.0435 | 0.948921 | ||||||||
\(643\) | −32.2860 | −1.27323 | −0.636617 | − | 0.771180i | \(-0.719667\pi\) | ||||
−0.636617 | + | 0.771180i | \(0.719667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.6810 | −0.420563 | ||||||||
\(646\) | 64.8318 | 2.55077 | ||||||||
\(647\) | −38.0027 | −1.49404 | −0.747019 | − | 0.664802i | \(-0.768516\pi\) | ||||
−0.747019 | + | 0.664802i | \(0.768516\pi\) | |||||||
\(648\) | 10.8805 | 0.427428 | ||||||||
\(649\) | −11.8719 | −0.466014 | ||||||||
\(650\) | 25.2031 | 0.988545 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.49915 | 0.137037 | ||||||||
\(653\) | −5.33327 | −0.208707 | −0.104354 | − | 0.994540i | \(-0.533277\pi\) | ||||
−0.104354 | + | 0.994540i | \(0.533277\pi\) | |||||||
\(654\) | 39.1156 | 1.52954 | ||||||||
\(655\) | 32.0703 | 1.25309 | ||||||||
\(656\) | 18.7833 | 0.733365 | ||||||||
\(657\) | −14.7998 | −0.577394 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9072 | 1.47665 | 0.738327 | − | 0.674443i | \(-0.235616\pi\) | ||||
0.738327 | + | 0.674443i | \(0.235616\pi\) | |||||||
\(660\) | −97.1212 | −3.78044 | ||||||||
\(661\) | −23.6532 | −0.920004 | −0.460002 | − | 0.887918i | \(-0.652151\pi\) | ||||
−0.460002 | + | 0.887918i | \(0.652151\pi\) | |||||||
\(662\) | −44.6097 | −1.73380 | ||||||||
\(663\) | −2.16178 | −0.0839565 | ||||||||
\(664\) | −13.2857 | −0.515586 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.3005 | 0.631633 | ||||||||
\(667\) | 23.5605 | 0.912268 | ||||||||
\(668\) | 21.7175 | 0.840275 | ||||||||
\(669\) | 2.16735 | 0.0837946 | ||||||||
\(670\) | 57.6749 | 2.22818 | ||||||||
\(671\) | 22.8615 | 0.882560 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.8125 | −1.45757 | −0.728783 | − | 0.684745i | \(-0.759914\pi\) | ||||
−0.728783 | + | 0.684745i | \(0.759914\pi\) | |||||||
\(674\) | −21.7172 | −0.836515 | ||||||||
\(675\) | 11.9143 | 0.458582 | ||||||||
\(676\) | −73.0600 | −2.81000 | ||||||||
\(677\) | −46.9680 | −1.80513 | −0.902563 | − | 0.430557i | \(-0.858317\pi\) | ||||
−0.902563 | + | 0.430557i | \(0.858317\pi\) | |||||||
\(678\) | −30.4462 | −1.16928 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −128.345 | −4.92182 | ||||||||
\(681\) | −27.4094 | −1.05033 | ||||||||
\(682\) | 21.6307 | 0.828283 | ||||||||
\(683\) | 6.20097 | 0.237274 | 0.118637 | − | 0.992938i | \(-0.462148\pi\) | ||||
0.118637 | + | 0.992938i | \(0.462148\pi\) | |||||||
\(684\) | −47.3317 | −1.80977 | ||||||||
\(685\) | 37.0589 | 1.41595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.3463 | 0.471041 | ||||||||
\(688\) | −48.7816 | −1.85978 | ||||||||
\(689\) | 5.37160 | 0.204642 | ||||||||
\(690\) | −76.4334 | −2.90977 | ||||||||
\(691\) | −2.33309 | −0.0887548 | −0.0443774 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443774 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(692\) | −52.5180 | −1.99643 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.4228 | −0.737280 | ||||||||
\(695\) | −59.7262 | −2.26554 | ||||||||
\(696\) | −38.7128 | −1.46741 | ||||||||
\(697\) | −2.86815 | −0.108639 | ||||||||
\(698\) | 95.2830 | 3.60651 | ||||||||
\(699\) | −11.9621 | −0.452449 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.8503 | 0.636427 | 0.318213 | − | 0.948019i | \(-0.396917\pi\) | ||||
0.318213 | + | 0.948019i | \(0.396917\pi\) | |||||||
\(702\) | 2.11536 | 0.0798391 | ||||||||
\(703\) | −46.7775 | −1.76425 | ||||||||
\(704\) | −198.152 | −7.46814 | ||||||||
\(705\) | −5.99031 | −0.225608 | ||||||||
\(706\) | 55.7320 | 2.09750 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.3627 | 0.652532 | ||||||||
\(709\) | −12.6657 | −0.475670 | −0.237835 | − | 0.971306i | \(-0.576438\pi\) | ||||
−0.237835 | + | 0.971306i | \(0.576438\pi\) | |||||||
\(710\) | 68.7984 | 2.58196 | ||||||||
\(711\) | 8.86055 | 0.332297 | ||||||||
\(712\) | 75.0538 | 2.81276 | ||||||||
\(713\) | 12.7008 | 0.475649 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.4561 | −0.465831 | ||||||||
\(716\) | −45.2878 | −1.69248 | ||||||||
\(717\) | −11.4914 | −0.429156 | ||||||||
\(718\) | 16.7090 | 0.623574 | ||||||||
\(719\) | 21.7824 | 0.812348 | 0.406174 | − | 0.913796i | \(-0.366863\pi\) | ||||
0.406174 | + | 0.913796i | \(0.366863\pi\) | |||||||
\(720\) | 77.2502 | 2.87894 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 128.728 | 4.79074 | ||||||||
\(723\) | 24.4262 | 0.908420 | ||||||||
\(724\) | −56.8853 | −2.11413 | ||||||||
\(725\) | −42.3910 | −1.57436 | ||||||||
\(726\) | 14.4452 | 0.536112 | ||||||||
\(727\) | −3.60601 | −0.133739 | −0.0668697 | − | 0.997762i | \(-0.521301\pi\) | ||||
−0.0668697 | + | 0.997762i | \(0.521301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −170.827 | −6.32261 | ||||||||
\(731\) | 7.44879 | 0.275504 | ||||||||
\(732\) | −33.4351 | −1.23580 | ||||||||
\(733\) | 44.4399 | 1.64143 | 0.820713 | − | 0.571341i | \(-0.193576\pi\) | ||||
0.820713 | + | 0.571341i | \(0.193576\pi\) | |||||||
\(734\) | −82.5513 | −3.04702 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −204.983 | −7.55579 | ||||||||
\(737\) | −20.0784 | −0.739598 | ||||||||
\(738\) | 2.80657 | 0.103311 | ||||||||
\(739\) | −23.7944 | −0.875291 | −0.437646 | − | 0.899148i | \(-0.644188\pi\) | ||||
−0.437646 | + | 0.899148i | \(0.644188\pi\) | |||||||
\(740\) | 140.377 | 5.16036 | ||||||||
\(741\) | −6.07043 | −0.223003 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.0075 | −1.79791 | −0.898956 | − | 0.438038i | \(-0.855673\pi\) | ||||
−0.898956 | + | 0.438038i | \(0.855673\pi\) | |||||||
\(744\) | −20.8690 | −0.765094 | ||||||||
\(745\) | 20.6078 | 0.755012 | ||||||||
\(746\) | −4.10710 | −0.150372 | ||||||||
\(747\) | −1.22105 | −0.0446761 | ||||||||
\(748\) | 67.7313 | 2.47650 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 79.8090 | 2.91421 | ||||||||
\(751\) | 1.45799 | 0.0532030 | 0.0266015 | − | 0.999646i | \(-0.491531\pi\) | ||||
0.0266015 | + | 0.999646i | \(0.491531\pi\) | |||||||
\(752\) | −27.3586 | −0.997667 | ||||||||
\(753\) | −17.3618 | −0.632700 | ||||||||
\(754\) | −7.52643 | −0.274096 | ||||||||
\(755\) | −56.1831 | −2.04471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.3969 | 1.25018 | 0.625089 | − | 0.780554i | \(-0.285063\pi\) | ||||
0.625089 | + | 0.780554i | \(0.285063\pi\) | |||||||
\(758\) | −81.0518 | −2.94394 | ||||||||
\(759\) | 26.6088 | 0.965839 | ||||||||
\(760\) | −360.403 | −13.0732 | ||||||||
\(761\) | −39.2505 | −1.42283 | −0.711415 | − | 0.702772i | \(-0.751945\pi\) | ||||
−0.711415 | + | 0.702772i | \(0.751945\pi\) | |||||||
\(762\) | −38.6201 | −1.39906 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 123.066 | 4.45236 | ||||||||
\(765\) | −11.7959 | −0.426480 | ||||||||
\(766\) | −26.1488 | −0.944796 | ||||||||
\(767\) | 2.22682 | 0.0804058 | ||||||||
\(768\) | 116.041 | 4.18726 | ||||||||
\(769\) | −47.5049 | −1.71307 | −0.856535 | − | 0.516089i | \(-0.827387\pi\) | ||||
−0.856535 | + | 0.516089i | \(0.827387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.9782 | 0.575441 | ||||||||
\(772\) | 40.3025 | 1.45052 | ||||||||
\(773\) | 18.5442 | 0.666989 | 0.333494 | − | 0.942752i | \(-0.391772\pi\) | ||||
0.333494 | + | 0.942752i | \(0.391772\pi\) | |||||||
\(774\) | −7.28885 | −0.261992 | ||||||||
\(775\) | −22.8518 | −0.820860 | ||||||||
\(776\) | −19.9823 | −0.717324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.6234 | 1.42057 | ||||||||
\(779\) | −8.05398 | −0.288564 | ||||||||
\(780\) | 18.2170 | 0.652275 | ||||||||
\(781\) | −23.9509 | −0.857029 | ||||||||
\(782\) | 53.3038 | 1.90614 | ||||||||
\(783\) | −3.55799 | −0.127152 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.71406 | −0.346710 | ||||||||
\(786\) | 21.8853 | 0.780621 | ||||||||
\(787\) | 38.9277 | 1.38762 | 0.693812 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693812 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(788\) | 34.4132 | 1.22592 | ||||||||
\(789\) | −3.35156 | −0.119319 | ||||||||
\(790\) | 102.274 | 3.63873 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −43.7215 | −1.55358 | ||||||||
\(793\) | −4.28814 | −0.152276 | ||||||||
\(794\) | −92.5678 | −3.28511 | ||||||||
\(795\) | 29.3104 | 1.03953 | ||||||||
\(796\) | −55.7814 | −1.97712 | ||||||||
\(797\) | 4.22206 | 0.149553 | 0.0747766 | − | 0.997200i | \(-0.476176\pi\) | ||||
0.0747766 | + | 0.997200i | \(0.476176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.17758 | 0.147792 | ||||||||
\(800\) | 368.814 | 13.0395 | ||||||||
\(801\) | 6.89799 | 0.243729 | ||||||||
\(802\) | 56.6711 | 2.00112 | ||||||||
\(803\) | 59.4703 | 2.09866 | ||||||||
\(804\) | 29.3647 | 1.03561 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.05728 | −0.142912 | ||||||||
\(807\) | 8.96079 | 0.315435 | ||||||||
\(808\) | −179.027 | −6.29813 | ||||||||
\(809\) | −18.3897 | −0.646548 | −0.323274 | − | 0.946305i | \(-0.604784\pi\) | ||||
−0.323274 | + | 0.946305i | \(0.604784\pi\) | |||||||
\(810\) | 11.5426 | 0.405565 | ||||||||
\(811\) | 17.8646 | 0.627311 | 0.313656 | − | 0.949537i | \(-0.398446\pi\) | ||||
0.313656 | + | 0.949537i | \(0.398446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.53831 | −0.0890224 | ||||||||
\(814\) | −65.5008 | −2.29580 | ||||||||
\(815\) | 2.44877 | 0.0857768 | ||||||||
\(816\) | −53.8734 | −1.88595 | ||||||||
\(817\) | 20.9167 | 0.731784 | ||||||||
\(818\) | 22.5948 | 0.790010 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.1696 | 0.844038 | ||||||||
\(821\) | 22.7936 | 0.795502 | 0.397751 | − | 0.917493i | \(-0.369791\pi\) | ||||
0.397751 | + | 0.917493i | \(0.369791\pi\) | |||||||
\(822\) | 25.2896 | 0.882074 | ||||||||
\(823\) | 26.6506 | 0.928983 | 0.464491 | − | 0.885578i | \(-0.346237\pi\) | ||||
0.464491 | + | 0.885578i | \(0.346237\pi\) | |||||||
\(824\) | 78.2721 | 2.72674 | ||||||||
\(825\) | −47.8756 | −1.66681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.0514 | −1.39272 | −0.696361 | − | 0.717692i | \(-0.745199\pi\) | ||||
−0.696361 | + | 0.717692i | \(0.745199\pi\) | |||||||
\(828\) | −38.9155 | −1.35241 | ||||||||
\(829\) | 29.9196 | 1.03915 | 0.519576 | − | 0.854424i | \(-0.326090\pi\) | ||||
0.519576 | + | 0.854424i | \(0.326090\pi\) | |||||||
\(830\) | −14.0941 | −0.489214 | ||||||||
\(831\) | 19.0038 | 0.659235 | ||||||||
\(832\) | 37.1674 | 1.28855 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −40.7580 | −1.41133 | ||||||||
\(835\) | 15.1983 | 0.525959 | ||||||||
\(836\) | 190.194 | 6.57800 | ||||||||
\(837\) | −1.91801 | −0.0662961 | ||||||||
\(838\) | 41.7981 | 1.44389 | ||||||||
\(839\) | 46.0646 | 1.59033 | 0.795163 | − | 0.606396i | \(-0.207385\pi\) | ||||
0.795163 | + | 0.606396i | \(0.207385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3407 | −0.563472 | ||||||||
\(842\) | 6.53824 | 0.225323 | ||||||||
\(843\) | −5.50424 | −0.189576 | ||||||||
\(844\) | −117.147 | −4.03235 | ||||||||
\(845\) | −51.1287 | −1.75888 | ||||||||
\(846\) | −4.08787 | −0.140544 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 133.865 | 4.59695 | ||||||||
\(849\) | 25.6985 | 0.881970 | ||||||||
\(850\) | −95.9063 | −3.28956 | ||||||||
\(851\) | −38.4598 | −1.31838 | ||||||||
\(852\) | 35.0282 | 1.20005 | ||||||||
\(853\) | −6.91770 | −0.236858 | −0.118429 | − | 0.992963i | \(-0.537786\pi\) | ||||
−0.118429 | + | 0.992963i | \(0.537786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.1236 | −1.13280 | ||||||||
\(856\) | 93.2121 | 3.18592 | ||||||||
\(857\) | −21.5052 | −0.734603 | −0.367302 | − | 0.930102i | \(-0.619718\pi\) | ||||
−0.367302 | + | 0.930102i | \(0.619718\pi\) | |||||||
\(858\) | −8.50020 | −0.290192 | ||||||||
\(859\) | 18.6568 | 0.636562 | 0.318281 | − | 0.947996i | \(-0.396894\pi\) | ||||
0.318281 | + | 0.947996i | \(0.396894\pi\) | |||||||
\(860\) | −62.7701 | −2.14044 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.6144 | 1.14491 | ||||||||
\(863\) | 31.7858 | 1.08200 | 0.541001 | − | 0.841022i | \(-0.318046\pi\) | ||||
0.541001 | + | 0.841022i | \(0.318046\pi\) | |||||||
\(864\) | 30.9555 | 1.05313 | ||||||||
\(865\) | −36.7530 | −1.24964 | ||||||||
\(866\) | 80.3406 | 2.73009 | ||||||||
\(867\) | −8.77369 | −0.297970 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −35.6046 | −1.20780 | ||||||||
\(870\) | −41.0684 | −1.39235 | ||||||||
\(871\) | 3.76611 | 0.127610 | ||||||||
\(872\) | 151.644 | 5.13531 | ||||||||
\(873\) | −1.83652 | −0.0621569 | ||||||||
\(874\) | 149.681 | 5.06303 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −86.9755 | −2.93863 | ||||||||
\(877\) | −19.4115 | −0.655480 | −0.327740 | − | 0.944768i | \(-0.606287\pi\) | ||||
−0.327740 | + | 0.944768i | \(0.606287\pi\) | |||||||
\(878\) | 39.8752 | 1.34572 | ||||||||
\(879\) | −15.9943 | −0.539473 | ||||||||
\(880\) | −310.416 | −10.4641 | ||||||||
\(881\) | 28.9178 | 0.974265 | 0.487133 | − | 0.873328i | \(-0.338043\pi\) | ||||
0.487133 | + | 0.873328i | \(0.338043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.0790 | 1.44972 | 0.724862 | − | 0.688894i | \(-0.241903\pi\) | ||||
0.724862 | + | 0.688894i | \(0.241903\pi\) | |||||||
\(884\) | −12.7044 | −0.427294 | ||||||||
\(885\) | 12.1508 | 0.408444 | ||||||||
\(886\) | −26.0815 | −0.876225 | ||||||||
\(887\) | −38.8059 | −1.30297 | −0.651487 | − | 0.758660i | \(-0.725854\pi\) | ||||
−0.651487 | + | 0.758660i | \(0.725854\pi\) | |||||||
\(888\) | 63.1941 | 2.12066 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 79.6206 | 2.66889 | ||||||||
\(891\) | −4.01832 | −0.134619 | ||||||||
\(892\) | 12.7371 | 0.426470 | ||||||||
\(893\) | 11.7309 | 0.392561 | ||||||||
\(894\) | 14.0631 | 0.470340 | ||||||||
\(895\) | −31.6932 | −1.05939 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.99102 | −0.166645 | ||||||||
\(898\) | −104.770 | −3.49622 | ||||||||
\(899\) | 6.82426 | 0.227602 | ||||||||
\(900\) | 70.0182 | 2.33394 | ||||||||
\(901\) | −20.4408 | −0.680981 | ||||||||
\(902\) | −11.2777 | −0.375506 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −118.034 | −3.92576 | ||||||||
\(905\) | −39.8094 | −1.32331 | ||||||||
\(906\) | −38.3402 | −1.27377 | ||||||||
\(907\) | 10.6255 | 0.352815 | 0.176407 | − | 0.984317i | \(-0.443552\pi\) | ||||
0.176407 | + | 0.984317i | \(0.443552\pi\) | |||||||
\(908\) | −161.080 | −5.34562 | ||||||||
\(909\) | −16.4538 | −0.545740 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7405 | 0.521505 | 0.260753 | − | 0.965406i | \(-0.416029\pi\) | ||||
0.260753 | + | 0.965406i | \(0.416029\pi\) | |||||||
\(912\) | −151.280 | −5.00939 | ||||||||
\(913\) | 4.90659 | 0.162385 | ||||||||
\(914\) | 35.2051 | 1.16448 | ||||||||
\(915\) | −23.3985 | −0.773530 | ||||||||
\(916\) | 72.5569 | 2.39735 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.04966 | −0.265678 | ||||||||
\(919\) | 55.3915 | 1.82720 | 0.913599 | − | 0.406617i | \(-0.133292\pi\) | ||||
0.913599 | + | 0.406617i | \(0.133292\pi\) | |||||||
\(920\) | −296.318 | −9.76931 | ||||||||
\(921\) | 20.1627 | 0.664384 | ||||||||
\(922\) | −46.9975 | −1.54778 | ||||||||
\(923\) | 4.49247 | 0.147871 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.1983 | 2.27523 | ||||||||
\(926\) | −46.0279 | −1.51257 | ||||||||
\(927\) | 7.19377 | 0.236274 | ||||||||
\(928\) | −110.140 | −3.61551 | ||||||||
\(929\) | 59.4411 | 1.95020 | 0.975099 | − | 0.221769i | \(-0.0711831\pi\) | ||||
0.975099 | + | 0.221769i | \(0.0711831\pi\) | |||||||
\(930\) | −22.1388 | −0.725959 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −70.2991 | −2.30272 | ||||||||
\(933\) | 23.6861 | 0.775448 | ||||||||
\(934\) | 46.2963 | 1.51486 | ||||||||
\(935\) | 47.3996 | 1.55013 | ||||||||
\(936\) | 8.20085 | 0.268053 | ||||||||
\(937\) | 12.7418 | 0.416258 | 0.208129 | − | 0.978101i | \(-0.433263\pi\) | ||||
0.208129 | + | 0.978101i | \(0.433263\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.9892 | 0.848127 | ||||||||
\(940\) | −35.2040 | −1.14823 | ||||||||
\(941\) | −53.0284 | −1.72868 | −0.864338 | − | 0.502912i | \(-0.832262\pi\) | ||||
−0.864338 | + | 0.502912i | \(0.832262\pi\) | |||||||
\(942\) | −6.62901 | −0.215985 | ||||||||
\(943\) | −6.62187 | −0.215638 | ||||||||
\(944\) | 55.4943 | 1.80619 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.2890 | 0.952266 | ||||||||
\(947\) | 33.9701 | 1.10388 | 0.551940 | − | 0.833884i | \(-0.313888\pi\) | ||||
0.551940 | + | 0.833884i | \(0.313888\pi\) | |||||||
\(948\) | 52.0718 | 1.69121 | ||||||||
\(949\) | −11.1549 | −0.362102 | ||||||||
\(950\) | −269.312 | −8.73762 | ||||||||
\(951\) | 12.9378 | 0.419537 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9729 | 0.679378 | 0.339689 | − | 0.940538i | \(-0.389678\pi\) | ||||
0.339689 | + | 0.940538i | \(0.389678\pi\) | |||||||
\(954\) | 20.0019 | 0.647584 | ||||||||
\(955\) | 86.1236 | 2.78689 | ||||||||
\(956\) | −67.5331 | −2.18418 | ||||||||
\(957\) | 14.2972 | 0.462162 | ||||||||
\(958\) | 37.4804 | 1.21094 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 202.806 | 6.54554 | ||||||||
\(961\) | −27.3212 | −0.881330 | ||||||||
\(962\) | 12.2860 | 0.396116 | ||||||||
\(963\) | 8.56687 | 0.276064 | ||||||||
\(964\) | 143.548 | 4.62338 | ||||||||
\(965\) | 28.2044 | 0.907933 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.4462 | −1.01124 | −0.505621 | − | 0.862756i | \(-0.668737\pi\) | ||||
−0.505621 | + | 0.862756i | \(0.668737\pi\) | |||||||
\(968\) | 56.0013 | 1.79995 | ||||||||
\(969\) | 23.1000 | 0.742080 | ||||||||
\(970\) | −21.1982 | −0.680633 | ||||||||
\(971\) | 38.8183 | 1.24574 | 0.622869 | − | 0.782326i | \(-0.285967\pi\) | ||||
0.622869 | + | 0.782326i | \(0.285967\pi\) | |||||||
\(972\) | 5.87681 | 0.188499 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.38073 | 0.300578 | ||||||||
\(975\) | 8.98003 | 0.287591 | ||||||||
\(976\) | −106.864 | −3.42064 | ||||||||
\(977\) | 34.6293 | 1.10789 | 0.553945 | − | 0.832554i | \(-0.313122\pi\) | ||||
0.553945 | + | 0.832554i | \(0.313122\pi\) | |||||||
\(978\) | 1.67108 | 0.0534352 | ||||||||
\(979\) | −27.7184 | −0.885883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.9372 | 0.444979 | ||||||||
\(982\) | 59.2477 | 1.89067 | ||||||||
\(983\) | 52.6484 | 1.67922 | 0.839612 | − | 0.543187i | \(-0.182783\pi\) | ||||
0.839612 | + | 0.543187i | \(0.182783\pi\) | |||||||
\(984\) | 10.8805 | 0.346859 | ||||||||
\(985\) | 24.0830 | 0.767347 | ||||||||
\(986\) | 28.6406 | 0.912104 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −35.6748 | −1.13497 | ||||||||
\(989\) | 17.1974 | 0.546847 | ||||||||
\(990\) | −46.3818 | −1.47411 | ||||||||
\(991\) | 17.1185 | 0.543788 | 0.271894 | − | 0.962327i | \(-0.412350\pi\) | ||||
0.271894 | + | 0.962327i | \(0.412350\pi\) | |||||||
\(992\) | −59.3730 | −1.88510 | ||||||||
\(993\) | −15.8948 | −0.504405 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.0368 | −1.23755 | ||||||||
\(996\) | −7.17591 | −0.227377 | ||||||||
\(997\) | −23.0058 | −0.728601 | −0.364301 | − | 0.931281i | \(-0.618692\pi\) | ||||
−0.364301 | + | 0.931281i | \(0.618692\pi\) | |||||||
\(998\) | −0.305923 | −0.00968383 | ||||||||
\(999\) | 5.80800 | 0.183757 |
(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 | 6027.2.a.be.1.10 | yes | 10 | |
7.6 | odd | 2 | 6027.2.a.bd.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bd.1.10 | ✓ | 10 | 7.6 | odd | 2 | ||
6027.2.a.be.1.10 | yes | 10 | 1.1 | even | 1 | trivial |