Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9251,2,Mod(1,9251)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9251, 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("9251.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9251 = 11 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9251.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: | \(73.8696069099\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.78145\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9251.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.78145 | 1.25967 | 0.629837 | − | 0.776727i | \(-0.283122\pi\) | ||||
0.629837 | + | 0.776727i | \(0.283122\pi\) | |||||||
\(3\) | 1.92907 | 1.11375 | 0.556875 | − | 0.830597i | \(-0.312000\pi\) | ||||
0.556875 | + | 0.830597i | \(0.312000\pi\) | |||||||
\(4\) | 1.17356 | 0.586779 | ||||||||
\(5\) | −0.848076 | −0.379271 | −0.189636 | − | 0.981855i | \(-0.560731\pi\) | ||||
−0.189636 | + | 0.981855i | \(0.560731\pi\) | |||||||
\(6\) | 3.43654 | 1.40296 | ||||||||
\(7\) | 2.45497 | 0.927891 | 0.463945 | − | 0.885864i | \(-0.346433\pi\) | ||||
0.463945 | + | 0.885864i | \(0.346433\pi\) | |||||||
\(8\) | −1.47226 | −0.520523 | ||||||||
\(9\) | 0.721313 | 0.240438 | ||||||||
\(10\) | −1.51080 | −0.477758 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.26388 | 0.653525 | ||||||||
\(13\) | −2.27043 | −0.629705 | −0.314852 | − | 0.949141i | \(-0.601955\pi\) | ||||
−0.314852 | + | 0.949141i | \(0.601955\pi\) | |||||||
\(14\) | 4.37340 | 1.16884 | ||||||||
\(15\) | −1.63600 | −0.422413 | ||||||||
\(16\) | −4.96988 | −1.24247 | ||||||||
\(17\) | 6.53754 | 1.58559 | 0.792793 | − | 0.609491i | \(-0.208626\pi\) | ||||
0.792793 | + | 0.609491i | \(0.208626\pi\) | |||||||
\(18\) | 1.28498 | 0.302873 | ||||||||
\(19\) | −7.80252 | −1.79002 | −0.895010 | − | 0.446046i | \(-0.852832\pi\) | ||||
−0.895010 | + | 0.446046i | \(0.852832\pi\) | |||||||
\(20\) | −0.995267 | −0.222549 | ||||||||
\(21\) | 4.73581 | 1.03344 | ||||||||
\(22\) | −1.78145 | −0.379806 | ||||||||
\(23\) | −2.66317 | −0.555309 | −0.277655 | − | 0.960681i | \(-0.589557\pi\) | ||||
−0.277655 | + | 0.960681i | \(0.589557\pi\) | |||||||
\(24\) | −2.84010 | −0.579733 | ||||||||
\(25\) | −4.28077 | −0.856153 | ||||||||
\(26\) | −4.04466 | −0.793223 | ||||||||
\(27\) | −4.39575 | −0.845962 | ||||||||
\(28\) | 2.88105 | 0.544467 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | −2.91445 | −0.532103 | ||||||||
\(31\) | 2.88571 | 0.518289 | 0.259144 | − | 0.965839i | \(-0.416559\pi\) | ||||
0.259144 | + | 0.965839i | \(0.416559\pi\) | |||||||
\(32\) | −5.90906 | −1.04458 | ||||||||
\(33\) | −1.92907 | −0.335808 | ||||||||
\(34\) | 11.6463 | 1.99732 | ||||||||
\(35\) | −2.08200 | −0.351922 | ||||||||
\(36\) | 0.846503 | 0.141084 | ||||||||
\(37\) | −6.95308 | −1.14308 | −0.571540 | − | 0.820574i | \(-0.693654\pi\) | ||||
−0.571540 | + | 0.820574i | \(0.693654\pi\) | |||||||
\(38\) | −13.8998 | −2.25484 | ||||||||
\(39\) | −4.37983 | −0.701333 | ||||||||
\(40\) | 1.24859 | 0.197420 | ||||||||
\(41\) | −7.15083 | −1.11677 | −0.558386 | − | 0.829581i | \(-0.688579\pi\) | ||||
−0.558386 | + | 0.829581i | \(0.688579\pi\) | |||||||
\(42\) | 8.43660 | 1.30180 | ||||||||
\(43\) | 1.97256 | 0.300812 | 0.150406 | − | 0.988624i | \(-0.451942\pi\) | ||||
0.150406 | + | 0.988624i | \(0.451942\pi\) | |||||||
\(44\) | −1.17356 | −0.176921 | ||||||||
\(45\) | −0.611729 | −0.0911911 | ||||||||
\(46\) | −4.74430 | −0.699509 | ||||||||
\(47\) | −8.46322 | −1.23449 | −0.617244 | − | 0.786772i | \(-0.711751\pi\) | ||||
−0.617244 | + | 0.786772i | \(0.711751\pi\) | |||||||
\(48\) | −9.58724 | −1.38380 | ||||||||
\(49\) | −0.973131 | −0.139019 | ||||||||
\(50\) | −7.62597 | −1.07847 | ||||||||
\(51\) | 12.6114 | 1.76595 | ||||||||
\(52\) | −2.66449 | −0.369498 | ||||||||
\(53\) | 10.0192 | 1.37625 | 0.688125 | − | 0.725593i | \(-0.258434\pi\) | ||||
0.688125 | + | 0.725593i | \(0.258434\pi\) | |||||||
\(54\) | −7.83080 | −1.06564 | ||||||||
\(55\) | 0.848076 | 0.114355 | ||||||||
\(56\) | −3.61436 | −0.482989 | ||||||||
\(57\) | −15.0516 | −1.99363 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.67078 | −0.217517 | −0.108759 | − | 0.994068i | \(-0.534688\pi\) | ||||
−0.108759 | + | 0.994068i | \(0.534688\pi\) | |||||||
\(60\) | −1.91994 | −0.247863 | ||||||||
\(61\) | −7.62442 | −0.976207 | −0.488103 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488103 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(62\) | 5.14074 | 0.652875 | ||||||||
\(63\) | 1.77080 | 0.223100 | ||||||||
\(64\) | −0.586923 | −0.0733653 | ||||||||
\(65\) | 1.92550 | 0.238829 | ||||||||
\(66\) | −3.43654 | −0.423009 | ||||||||
\(67\) | −6.65145 | −0.812604 | −0.406302 | − | 0.913739i | \(-0.633182\pi\) | ||||
−0.406302 | + | 0.913739i | \(0.633182\pi\) | |||||||
\(68\) | 7.67219 | 0.930389 | ||||||||
\(69\) | −5.13744 | −0.618475 | ||||||||
\(70\) | −3.70898 | −0.443307 | ||||||||
\(71\) | −16.3246 | −1.93737 | −0.968687 | − | 0.248285i | \(-0.920133\pi\) | ||||
−0.968687 | + | 0.248285i | \(0.920133\pi\) | |||||||
\(72\) | −1.06196 | −0.125153 | ||||||||
\(73\) | 13.3077 | 1.55755 | 0.778774 | − | 0.627305i | \(-0.215842\pi\) | ||||
0.778774 | + | 0.627305i | \(0.215842\pi\) | |||||||
\(74\) | −12.3866 | −1.43991 | ||||||||
\(75\) | −8.25790 | −0.953540 | ||||||||
\(76\) | −9.15671 | −1.05035 | ||||||||
\(77\) | −2.45497 | −0.279770 | ||||||||
\(78\) | −7.80243 | −0.883452 | ||||||||
\(79\) | 14.2486 | 1.60309 | 0.801545 | − | 0.597935i | \(-0.204012\pi\) | ||||
0.801545 | + | 0.597935i | \(0.204012\pi\) | |||||||
\(80\) | 4.21484 | 0.471233 | ||||||||
\(81\) | −10.6436 | −1.18263 | ||||||||
\(82\) | −12.7388 | −1.40677 | ||||||||
\(83\) | 5.56435 | 0.610766 | 0.305383 | − | 0.952230i | \(-0.401215\pi\) | ||||
0.305383 | + | 0.952230i | \(0.401215\pi\) | |||||||
\(84\) | 5.55775 | 0.606400 | ||||||||
\(85\) | −5.54433 | −0.601367 | ||||||||
\(86\) | 3.51401 | 0.378925 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.47226 | 0.156944 | ||||||||
\(89\) | 5.14212 | 0.545064 | 0.272532 | − | 0.962147i | \(-0.412139\pi\) | ||||
0.272532 | + | 0.962147i | \(0.412139\pi\) | |||||||
\(90\) | −1.08976 | −0.114871 | ||||||||
\(91\) | −5.57384 | −0.584297 | ||||||||
\(92\) | −3.12539 | −0.325844 | ||||||||
\(93\) | 5.56674 | 0.577244 | ||||||||
\(94\) | −15.0768 | −1.55505 | ||||||||
\(95\) | 6.61713 | 0.678903 | ||||||||
\(96\) | −11.3990 | −1.16340 | ||||||||
\(97\) | 18.0058 | 1.82821 | 0.914104 | − | 0.405479i | \(-0.132895\pi\) | ||||
0.914104 | + | 0.405479i | \(0.132895\pi\) | |||||||
\(98\) | −1.73358 | −0.175118 | ||||||||
\(99\) | −0.721313 | −0.0724947 | ||||||||
\(100\) | −5.02373 | −0.502373 | ||||||||
\(101\) | 2.22234 | 0.221131 | 0.110566 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110566 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(102\) | 22.4665 | 2.22452 | ||||||||
\(103\) | −6.13391 | −0.604392 | −0.302196 | − | 0.953246i | \(-0.597720\pi\) | ||||
−0.302196 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(104\) | 3.34267 | 0.327776 | ||||||||
\(105\) | −4.01633 | −0.391953 | ||||||||
\(106\) | 17.8488 | 1.73363 | ||||||||
\(107\) | 6.66721 | 0.644543 | 0.322272 | − | 0.946647i | \(-0.395554\pi\) | ||||
0.322272 | + | 0.946647i | \(0.395554\pi\) | |||||||
\(108\) | −5.15867 | −0.496393 | ||||||||
\(109\) | 6.96016 | 0.666662 | 0.333331 | − | 0.942810i | \(-0.391827\pi\) | ||||
0.333331 | + | 0.942810i | \(0.391827\pi\) | |||||||
\(110\) | 1.51080 | 0.144050 | ||||||||
\(111\) | −13.4130 | −1.27310 | ||||||||
\(112\) | −12.2009 | −1.15288 | ||||||||
\(113\) | −12.8702 | −1.21073 | −0.605366 | − | 0.795948i | \(-0.706973\pi\) | ||||
−0.605366 | + | 0.795948i | \(0.706973\pi\) | |||||||
\(114\) | −26.8137 | −2.51133 | ||||||||
\(115\) | 2.25857 | 0.210613 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.63769 | −0.151405 | ||||||||
\(118\) | −2.97641 | −0.274001 | ||||||||
\(119\) | 16.0495 | 1.47125 | ||||||||
\(120\) | 2.40862 | 0.219876 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.5825 | −1.22970 | ||||||||
\(123\) | −13.7945 | −1.24380 | ||||||||
\(124\) | 3.38655 | 0.304121 | ||||||||
\(125\) | 7.87080 | 0.703986 | ||||||||
\(126\) | 3.15459 | 0.281033 | ||||||||
\(127\) | 1.79718 | 0.159474 | 0.0797369 | − | 0.996816i | \(-0.474592\pi\) | ||||
0.0797369 | + | 0.996816i | \(0.474592\pi\) | |||||||
\(128\) | 10.7725 | 0.952167 | ||||||||
\(129\) | 3.80520 | 0.335029 | ||||||||
\(130\) | 3.43018 | 0.300847 | ||||||||
\(131\) | −9.92738 | −0.867360 | −0.433680 | − | 0.901067i | \(-0.642785\pi\) | ||||
−0.433680 | + | 0.901067i | \(0.642785\pi\) | |||||||
\(132\) | −2.26388 | −0.197045 | ||||||||
\(133\) | −19.1549 | −1.66094 | ||||||||
\(134\) | −11.8492 | −1.02362 | ||||||||
\(135\) | 3.72793 | 0.320849 | ||||||||
\(136\) | −9.62498 | −0.825335 | ||||||||
\(137\) | −11.2435 | −0.960598 | −0.480299 | − | 0.877105i | \(-0.659472\pi\) | ||||
−0.480299 | + | 0.877105i | \(0.659472\pi\) | |||||||
\(138\) | −9.15209 | −0.779077 | ||||||||
\(139\) | −7.85311 | −0.666092 | −0.333046 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333046 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(140\) | −2.44335 | −0.206501 | ||||||||
\(141\) | −16.3262 | −1.37491 | ||||||||
\(142\) | −29.0814 | −2.44046 | ||||||||
\(143\) | 2.27043 | 0.189863 | ||||||||
\(144\) | −3.58484 | −0.298736 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.7070 | 1.96200 | ||||||||
\(147\) | −1.87724 | −0.154832 | ||||||||
\(148\) | −8.15985 | −0.670735 | ||||||||
\(149\) | −1.28162 | −0.104994 | −0.0524971 | − | 0.998621i | \(-0.516718\pi\) | ||||
−0.0524971 | + | 0.998621i | \(0.516718\pi\) | |||||||
\(150\) | −14.7110 | −1.20115 | ||||||||
\(151\) | 6.34789 | 0.516584 | 0.258292 | − | 0.966067i | \(-0.416840\pi\) | ||||
0.258292 | + | 0.966067i | \(0.416840\pi\) | |||||||
\(152\) | 11.4874 | 0.931747 | ||||||||
\(153\) | 4.71561 | 0.381235 | ||||||||
\(154\) | −4.37340 | −0.352419 | ||||||||
\(155\) | −2.44730 | −0.196572 | ||||||||
\(156\) | −5.13998 | −0.411528 | ||||||||
\(157\) | −19.7780 | −1.57845 | −0.789227 | − | 0.614102i | \(-0.789519\pi\) | ||||
−0.789227 | + | 0.614102i | \(0.789519\pi\) | |||||||
\(158\) | 25.3831 | 2.01937 | ||||||||
\(159\) | 19.3278 | 1.53280 | ||||||||
\(160\) | 5.01133 | 0.396180 | ||||||||
\(161\) | −6.53800 | −0.515266 | ||||||||
\(162\) | −18.9611 | −1.48973 | ||||||||
\(163\) | 0.717552 | 0.0562030 | 0.0281015 | − | 0.999605i | \(-0.491054\pi\) | ||||
0.0281015 | + | 0.999605i | \(0.491054\pi\) | |||||||
\(164\) | −8.39192 | −0.655299 | ||||||||
\(165\) | 1.63600 | 0.127362 | ||||||||
\(166\) | 9.91260 | 0.769367 | ||||||||
\(167\) | 20.2382 | 1.56608 | 0.783039 | − | 0.621973i | \(-0.213669\pi\) | ||||
0.783039 | + | 0.621973i | \(0.213669\pi\) | |||||||
\(168\) | −6.97235 | −0.537929 | ||||||||
\(169\) | −7.84513 | −0.603472 | ||||||||
\(170\) | −9.87694 | −0.757527 | ||||||||
\(171\) | −5.62806 | −0.430388 | ||||||||
\(172\) | 2.31491 | 0.176510 | ||||||||
\(173\) | 7.29179 | 0.554384 | 0.277192 | − | 0.960814i | \(-0.410596\pi\) | ||||
0.277192 | + | 0.960814i | \(0.410596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.5091 | −0.794417 | ||||||||
\(176\) | 4.96988 | 0.374619 | ||||||||
\(177\) | −3.22306 | −0.242260 | ||||||||
\(178\) | 9.16043 | 0.686603 | ||||||||
\(179\) | −5.63972 | −0.421532 | −0.210766 | − | 0.977537i | \(-0.567596\pi\) | ||||
−0.210766 | + | 0.977537i | \(0.567596\pi\) | |||||||
\(180\) | −0.717899 | −0.0535091 | ||||||||
\(181\) | 20.4124 | 1.51725 | 0.758623 | − | 0.651530i | \(-0.225873\pi\) | ||||
0.758623 | + | 0.651530i | \(0.225873\pi\) | |||||||
\(182\) | −9.92951 | −0.736024 | ||||||||
\(183\) | −14.7080 | −1.08725 | ||||||||
\(184\) | 3.92088 | 0.289051 | ||||||||
\(185\) | 5.89674 | 0.433537 | ||||||||
\(186\) | 9.91686 | 0.727139 | ||||||||
\(187\) | −6.53754 | −0.478072 | ||||||||
\(188\) | −9.93209 | −0.724372 | ||||||||
\(189\) | −10.7914 | −0.784960 | ||||||||
\(190\) | 11.7881 | 0.855197 | ||||||||
\(191\) | −5.94507 | −0.430170 | −0.215085 | − | 0.976595i | \(-0.569003\pi\) | ||||
−0.215085 | + | 0.976595i | \(0.569003\pi\) | |||||||
\(192\) | −1.13222 | −0.0817106 | ||||||||
\(193\) | −1.86066 | −0.133933 | −0.0669666 | − | 0.997755i | \(-0.521332\pi\) | ||||
−0.0669666 | + | 0.997755i | \(0.521332\pi\) | |||||||
\(194\) | 32.0763 | 2.30295 | ||||||||
\(195\) | 3.71443 | 0.265996 | ||||||||
\(196\) | −1.14203 | −0.0815733 | ||||||||
\(197\) | −10.5367 | −0.750706 | −0.375353 | − | 0.926882i | \(-0.622479\pi\) | ||||
−0.375353 | + | 0.926882i | \(0.622479\pi\) | |||||||
\(198\) | −1.28498 | −0.0913197 | ||||||||
\(199\) | −9.88442 | −0.700688 | −0.350344 | − | 0.936621i | \(-0.613935\pi\) | ||||
−0.350344 | + | 0.936621i | \(0.613935\pi\) | |||||||
\(200\) | 6.30241 | 0.445648 | ||||||||
\(201\) | −12.8311 | −0.905038 | ||||||||
\(202\) | 3.95899 | 0.278553 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 14.8002 | 1.03622 | ||||||||
\(205\) | 6.06445 | 0.423560 | ||||||||
\(206\) | −10.9272 | −0.761337 | ||||||||
\(207\) | −1.92098 | −0.133517 | ||||||||
\(208\) | 11.2838 | 0.782389 | ||||||||
\(209\) | 7.80252 | 0.539711 | ||||||||
\(210\) | −7.15488 | −0.493733 | ||||||||
\(211\) | 19.6653 | 1.35381 | 0.676906 | − | 0.736069i | \(-0.263320\pi\) | ||||
0.676906 | + | 0.736069i | \(0.263320\pi\) | |||||||
\(212\) | 11.7582 | 0.807555 | ||||||||
\(213\) | −31.4913 | −2.15775 | ||||||||
\(214\) | 11.8773 | 0.811914 | ||||||||
\(215\) | −1.67288 | −0.114089 | ||||||||
\(216\) | 6.47170 | 0.440343 | ||||||||
\(217\) | 7.08433 | 0.480915 | ||||||||
\(218\) | 12.3992 | 0.839777 | ||||||||
\(219\) | 25.6715 | 1.73472 | ||||||||
\(220\) | 0.995267 | 0.0671009 | ||||||||
\(221\) | −14.8430 | −0.998451 | ||||||||
\(222\) | −23.8945 | −1.60370 | ||||||||
\(223\) | 15.2289 | 1.01980 | 0.509901 | − | 0.860233i | \(-0.329682\pi\) | ||||
0.509901 | + | 0.860233i | \(0.329682\pi\) | |||||||
\(224\) | −14.5065 | −0.969259 | ||||||||
\(225\) | −3.08777 | −0.205852 | ||||||||
\(226\) | −22.9277 | −1.52513 | ||||||||
\(227\) | −5.95105 | −0.394985 | −0.197492 | − | 0.980304i | \(-0.563280\pi\) | ||||
−0.197492 | + | 0.980304i | \(0.563280\pi\) | |||||||
\(228\) | −17.6639 | −1.16982 | ||||||||
\(229\) | −18.8853 | −1.24798 | −0.623989 | − | 0.781433i | \(-0.714489\pi\) | ||||
−0.623989 | + | 0.781433i | \(0.714489\pi\) | |||||||
\(230\) | 4.02353 | 0.265304 | ||||||||
\(231\) | −4.73581 | −0.311593 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.1830 | −1.32223 | −0.661115 | − | 0.750284i | \(-0.729917\pi\) | ||||
−0.661115 | + | 0.750284i | \(0.729917\pi\) | |||||||
\(234\) | −2.91747 | −0.190721 | ||||||||
\(235\) | 7.17746 | 0.468206 | ||||||||
\(236\) | −1.96076 | −0.127635 | ||||||||
\(237\) | 27.4865 | 1.78544 | ||||||||
\(238\) | 28.5913 | 1.85330 | ||||||||
\(239\) | −10.0674 | −0.651206 | −0.325603 | − | 0.945507i | \(-0.605567\pi\) | ||||
−0.325603 | + | 0.945507i | \(0.605567\pi\) | |||||||
\(240\) | 8.13071 | 0.524835 | ||||||||
\(241\) | −24.1592 | −1.55623 | −0.778116 | − | 0.628121i | \(-0.783824\pi\) | ||||
−0.778116 | + | 0.628121i | \(0.783824\pi\) | |||||||
\(242\) | 1.78145 | 0.114516 | ||||||||
\(243\) | −7.34510 | −0.471189 | ||||||||
\(244\) | −8.94770 | −0.572818 | ||||||||
\(245\) | 0.825289 | 0.0527258 | ||||||||
\(246\) | −24.5741 | −1.56679 | ||||||||
\(247\) | 17.7151 | 1.12718 | ||||||||
\(248\) | −4.24852 | −0.269781 | ||||||||
\(249\) | 10.7340 | 0.680241 | ||||||||
\(250\) | 14.0214 | 0.886793 | ||||||||
\(251\) | −4.74546 | −0.299531 | −0.149765 | − | 0.988722i | \(-0.547852\pi\) | ||||
−0.149765 | + | 0.988722i | \(0.547852\pi\) | |||||||
\(252\) | 2.07814 | 0.130910 | ||||||||
\(253\) | 2.66317 | 0.167432 | ||||||||
\(254\) | 3.20158 | 0.200885 | ||||||||
\(255\) | −10.6954 | −0.669772 | ||||||||
\(256\) | 20.3646 | 1.27279 | ||||||||
\(257\) | 14.4146 | 0.899159 | 0.449579 | − | 0.893240i | \(-0.351574\pi\) | ||||
0.449579 | + | 0.893240i | \(0.351574\pi\) | |||||||
\(258\) | 6.77877 | 0.422028 | ||||||||
\(259\) | −17.0696 | −1.06065 | ||||||||
\(260\) | 2.25969 | 0.140140 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.6851 | −1.09259 | ||||||||
\(263\) | 1.64890 | 0.101676 | 0.0508378 | − | 0.998707i | \(-0.483811\pi\) | ||||
0.0508378 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(264\) | 2.84010 | 0.174796 | ||||||||
\(265\) | −8.49708 | −0.521972 | ||||||||
\(266\) | −34.1235 | −2.09225 | ||||||||
\(267\) | 9.91952 | 0.607065 | ||||||||
\(268\) | −7.80587 | −0.476819 | ||||||||
\(269\) | 2.23892 | 0.136509 | 0.0682547 | − | 0.997668i | \(-0.478257\pi\) | ||||
0.0682547 | + | 0.997668i | \(0.478257\pi\) | |||||||
\(270\) | 6.64111 | 0.404165 | ||||||||
\(271\) | −23.3206 | −1.41663 | −0.708314 | − | 0.705898i | \(-0.750544\pi\) | ||||
−0.708314 | + | 0.705898i | \(0.750544\pi\) | |||||||
\(272\) | −32.4908 | −1.97004 | ||||||||
\(273\) | −10.7523 | −0.650761 | ||||||||
\(274\) | −20.0297 | −1.21004 | ||||||||
\(275\) | 4.28077 | 0.258140 | ||||||||
\(276\) | −6.02909 | −0.362909 | ||||||||
\(277\) | −6.13143 | −0.368402 | −0.184201 | − | 0.982889i | \(-0.558970\pi\) | ||||
−0.184201 | + | 0.982889i | \(0.558970\pi\) | |||||||
\(278\) | −13.9899 | −0.839059 | ||||||||
\(279\) | 2.08150 | 0.124616 | ||||||||
\(280\) | 3.06525 | 0.183184 | ||||||||
\(281\) | 17.6475 | 1.05276 | 0.526381 | − | 0.850249i | \(-0.323548\pi\) | ||||
0.526381 | + | 0.850249i | \(0.323548\pi\) | |||||||
\(282\) | −29.0842 | −1.73194 | ||||||||
\(283\) | 12.7175 | 0.755974 | 0.377987 | − | 0.925811i | \(-0.376616\pi\) | ||||
0.377987 | + | 0.925811i | \(0.376616\pi\) | |||||||
\(284\) | −19.1579 | −1.13681 | ||||||||
\(285\) | 12.7649 | 0.756128 | ||||||||
\(286\) | 4.04466 | 0.239166 | ||||||||
\(287\) | −17.5551 | −1.03624 | ||||||||
\(288\) | −4.26228 | −0.251157 | ||||||||
\(289\) | 25.7394 | 1.51408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.7344 | 2.03617 | ||||||||
\(292\) | 15.6174 | 0.913937 | ||||||||
\(293\) | −25.3501 | −1.48097 | −0.740483 | − | 0.672075i | \(-0.765403\pi\) | ||||
−0.740483 | + | 0.672075i | \(0.765403\pi\) | |||||||
\(294\) | −3.34420 | −0.195038 | ||||||||
\(295\) | 1.41695 | 0.0824981 | ||||||||
\(296\) | 10.2368 | 0.595000 | ||||||||
\(297\) | 4.39575 | 0.255067 | ||||||||
\(298\) | −2.28314 | −0.132259 | ||||||||
\(299\) | 6.04655 | 0.349681 | ||||||||
\(300\) | −9.69113 | −0.559518 | ||||||||
\(301\) | 4.84256 | 0.279121 | ||||||||
\(302\) | 11.3084 | 0.650728 | ||||||||
\(303\) | 4.28705 | 0.246285 | ||||||||
\(304\) | 38.7776 | 2.22405 | ||||||||
\(305\) | 6.46609 | 0.370247 | ||||||||
\(306\) | 8.40062 | 0.480232 | ||||||||
\(307\) | 6.70484 | 0.382665 | 0.191333 | − | 0.981525i | \(-0.438719\pi\) | ||||
0.191333 | + | 0.981525i | \(0.438719\pi\) | |||||||
\(308\) | −2.88105 | −0.164163 | ||||||||
\(309\) | −11.8327 | −0.673141 | ||||||||
\(310\) | −4.35974 | −0.247617 | ||||||||
\(311\) | 7.62827 | 0.432560 | 0.216280 | − | 0.976331i | \(-0.430608\pi\) | ||||
0.216280 | + | 0.976331i | \(0.430608\pi\) | |||||||
\(312\) | 6.44825 | 0.365060 | ||||||||
\(313\) | −20.4075 | −1.15350 | −0.576750 | − | 0.816921i | \(-0.695679\pi\) | ||||
−0.576750 | + | 0.816921i | \(0.695679\pi\) | |||||||
\(314\) | −35.2334 | −1.98834 | ||||||||
\(315\) | −1.50177 | −0.0846154 | ||||||||
\(316\) | 16.7215 | 0.940660 | ||||||||
\(317\) | −17.3671 | −0.975432 | −0.487716 | − | 0.873002i | \(-0.662170\pi\) | ||||
−0.487716 | + | 0.873002i | \(0.662170\pi\) | |||||||
\(318\) | 34.4315 | 1.93082 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.497755 | 0.0278254 | ||||||||
\(321\) | 12.8615 | 0.717860 | ||||||||
\(322\) | −11.6471 | −0.649068 | ||||||||
\(323\) | −51.0093 | −2.83823 | ||||||||
\(324\) | −12.4909 | −0.693941 | ||||||||
\(325\) | 9.71919 | 0.539124 | ||||||||
\(326\) | 1.27828 | 0.0707975 | ||||||||
\(327\) | 13.4266 | 0.742495 | ||||||||
\(328\) | 10.5279 | 0.581306 | ||||||||
\(329\) | −20.7769 | −1.14547 | ||||||||
\(330\) | 2.91445 | 0.160435 | ||||||||
\(331\) | 7.05722 | 0.387900 | 0.193950 | − | 0.981011i | \(-0.437870\pi\) | ||||
0.193950 | + | 0.981011i | \(0.437870\pi\) | |||||||
\(332\) | 6.53009 | 0.358385 | ||||||||
\(333\) | −5.01535 | −0.274839 | ||||||||
\(334\) | 36.0533 | 1.97275 | ||||||||
\(335\) | 5.64094 | 0.308197 | ||||||||
\(336\) | −23.5364 | −1.28401 | ||||||||
\(337\) | 7.74779 | 0.422049 | 0.211024 | − | 0.977481i | \(-0.432320\pi\) | ||||
0.211024 | + | 0.977481i | \(0.432320\pi\) | |||||||
\(338\) | −13.9757 | −0.760178 | ||||||||
\(339\) | −24.8276 | −1.34845 | ||||||||
\(340\) | −6.50660 | −0.352870 | ||||||||
\(341\) | −2.88571 | −0.156270 | ||||||||
\(342\) | −10.0261 | −0.542149 | ||||||||
\(343\) | −19.5738 | −1.05688 | ||||||||
\(344\) | −2.90412 | −0.156580 | ||||||||
\(345\) | 4.35694 | 0.234570 | ||||||||
\(346\) | 12.9899 | 0.698344 | ||||||||
\(347\) | −25.4257 | −1.36492 | −0.682461 | − | 0.730922i | \(-0.739090\pi\) | ||||
−0.682461 | + | 0.730922i | \(0.739090\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0704 | −1.12787 | −0.563936 | − | 0.825818i | \(-0.690714\pi\) | ||||
−0.563936 | + | 0.825818i | \(0.690714\pi\) | |||||||
\(350\) | −18.7215 | −1.00071 | ||||||||
\(351\) | 9.98025 | 0.532706 | ||||||||
\(352\) | 5.90906 | 0.314954 | ||||||||
\(353\) | 15.1578 | 0.806768 | 0.403384 | − | 0.915031i | \(-0.367834\pi\) | ||||
0.403384 | + | 0.915031i | \(0.367834\pi\) | |||||||
\(354\) | −5.74171 | −0.305169 | ||||||||
\(355\) | 13.8445 | 0.734790 | ||||||||
\(356\) | 6.03458 | 0.319832 | ||||||||
\(357\) | 30.9605 | 1.63860 | ||||||||
\(358\) | −10.0469 | −0.530993 | ||||||||
\(359\) | −4.19544 | −0.221427 | −0.110714 | − | 0.993852i | \(-0.535314\pi\) | ||||
−0.110714 | + | 0.993852i | \(0.535314\pi\) | |||||||
\(360\) | 0.900625 | 0.0474671 | ||||||||
\(361\) | 41.8793 | 2.20417 | ||||||||
\(362\) | 36.3637 | 1.91123 | ||||||||
\(363\) | 1.92907 | 0.101250 | ||||||||
\(364\) | −6.54123 | −0.342854 | ||||||||
\(365\) | −11.2859 | −0.590733 | ||||||||
\(366\) | −26.2016 | −1.36958 | ||||||||
\(367\) | 6.66570 | 0.347947 | 0.173973 | − | 0.984750i | \(-0.444339\pi\) | ||||
0.173973 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(368\) | 13.2356 | 0.689955 | ||||||||
\(369\) | −5.15799 | −0.268514 | ||||||||
\(370\) | 10.5047 | 0.546116 | ||||||||
\(371\) | 24.5969 | 1.27701 | ||||||||
\(372\) | 6.53289 | 0.338715 | ||||||||
\(373\) | 20.3265 | 1.05246 | 0.526232 | − | 0.850341i | \(-0.323604\pi\) | ||||
0.526232 | + | 0.850341i | \(0.323604\pi\) | |||||||
\(374\) | −11.6463 | −0.602215 | ||||||||
\(375\) | 15.1833 | 0.784064 | ||||||||
\(376\) | 12.4601 | 0.642580 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −19.2244 | −0.988794 | ||||||||
\(379\) | −7.00197 | −0.359667 | −0.179833 | − | 0.983697i | \(-0.557556\pi\) | ||||
−0.179833 | + | 0.983697i | \(0.557556\pi\) | |||||||
\(380\) | 7.76559 | 0.398366 | ||||||||
\(381\) | 3.46688 | 0.177614 | ||||||||
\(382\) | −10.5908 | −0.541874 | ||||||||
\(383\) | 29.1043 | 1.48716 | 0.743581 | − | 0.668646i | \(-0.233126\pi\) | ||||
0.743581 | + | 0.668646i | \(0.233126\pi\) | |||||||
\(384\) | 20.7810 | 1.06048 | ||||||||
\(385\) | 2.08200 | 0.106109 | ||||||||
\(386\) | −3.31467 | −0.168712 | ||||||||
\(387\) | 1.42283 | 0.0723265 | ||||||||
\(388\) | 21.1308 | 1.07276 | ||||||||
\(389\) | 17.1971 | 0.871928 | 0.435964 | − | 0.899964i | \(-0.356408\pi\) | ||||
0.435964 | + | 0.899964i | \(0.356408\pi\) | |||||||
\(390\) | 6.61706 | 0.335068 | ||||||||
\(391\) | −17.4106 | −0.880491 | ||||||||
\(392\) | 1.43270 | 0.0723625 | ||||||||
\(393\) | −19.1506 | −0.966021 | ||||||||
\(394\) | −18.7705 | −0.945645 | ||||||||
\(395\) | −12.0839 | −0.608006 | ||||||||
\(396\) | −0.846503 | −0.0425384 | ||||||||
\(397\) | −8.40364 | −0.421767 | −0.210883 | − | 0.977511i | \(-0.567634\pi\) | ||||
−0.210883 | + | 0.977511i | \(0.567634\pi\) | |||||||
\(398\) | −17.6086 | −0.882638 | ||||||||
\(399\) | −36.9512 | −1.84987 | ||||||||
\(400\) | 21.2749 | 1.06374 | ||||||||
\(401\) | −21.5339 | −1.07535 | −0.537677 | − | 0.843151i | \(-0.680698\pi\) | ||||
−0.537677 | + | 0.843151i | \(0.680698\pi\) | |||||||
\(402\) | −22.8580 | −1.14005 | ||||||||
\(403\) | −6.55181 | −0.326369 | ||||||||
\(404\) | 2.60805 | 0.129755 | ||||||||
\(405\) | 9.02662 | 0.448537 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.95308 | 0.344651 | ||||||||
\(408\) | −18.5673 | −0.919216 | ||||||||
\(409\) | 26.6309 | 1.31681 | 0.658405 | − | 0.752663i | \(-0.271231\pi\) | ||||
0.658405 | + | 0.752663i | \(0.271231\pi\) | |||||||
\(410\) | 10.8035 | 0.533547 | ||||||||
\(411\) | −21.6895 | −1.06987 | ||||||||
\(412\) | −7.19850 | −0.354645 | ||||||||
\(413\) | −4.10172 | −0.201832 | ||||||||
\(414\) | −3.42213 | −0.168188 | ||||||||
\(415\) | −4.71899 | −0.231646 | ||||||||
\(416\) | 13.4161 | 0.657779 | ||||||||
\(417\) | −15.1492 | −0.741859 | ||||||||
\(418\) | 13.8998 | 0.679861 | ||||||||
\(419\) | 7.39201 | 0.361123 | 0.180562 | − | 0.983564i | \(-0.442208\pi\) | ||||
0.180562 | + | 0.983564i | \(0.442208\pi\) | |||||||
\(420\) | −4.71339 | −0.229990 | ||||||||
\(421\) | −21.6379 | −1.05456 | −0.527282 | − | 0.849690i | \(-0.676789\pi\) | ||||
−0.527282 | + | 0.849690i | \(0.676789\pi\) | |||||||
\(422\) | 35.0326 | 1.70536 | ||||||||
\(423\) | −6.10463 | −0.296817 | ||||||||
\(424\) | −14.7510 | −0.716370 | ||||||||
\(425\) | −27.9857 | −1.35750 | ||||||||
\(426\) | −56.1001 | −2.71806 | ||||||||
\(427\) | −18.7177 | −0.905813 | ||||||||
\(428\) | 7.82436 | 0.378205 | ||||||||
\(429\) | 4.37983 | 0.211460 | ||||||||
\(430\) | −2.98015 | −0.143715 | ||||||||
\(431\) | 14.5472 | 0.700715 | 0.350358 | − | 0.936616i | \(-0.386060\pi\) | ||||
0.350358 | + | 0.936616i | \(0.386060\pi\) | |||||||
\(432\) | 21.8463 | 1.05108 | ||||||||
\(433\) | −0.496922 | −0.0238806 | −0.0119403 | − | 0.999929i | \(-0.503801\pi\) | ||||
−0.0119403 | + | 0.999929i | \(0.503801\pi\) | |||||||
\(434\) | 12.6204 | 0.605797 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.16816 | 0.391184 | ||||||||
\(437\) | 20.7794 | 0.994015 | ||||||||
\(438\) | 45.7324 | 2.18518 | ||||||||
\(439\) | −37.5541 | −1.79236 | −0.896180 | − | 0.443691i | \(-0.853669\pi\) | ||||
−0.896180 | + | 0.443691i | \(0.853669\pi\) | |||||||
\(440\) | −1.24859 | −0.0595242 | ||||||||
\(441\) | −0.701932 | −0.0334253 | ||||||||
\(442\) | −26.4421 | −1.25772 | ||||||||
\(443\) | 31.0408 | 1.47479 | 0.737396 | − | 0.675461i | \(-0.236055\pi\) | ||||
0.737396 | + | 0.675461i | \(0.236055\pi\) | |||||||
\(444\) | −15.7409 | −0.747031 | ||||||||
\(445\) | −4.36091 | −0.206727 | ||||||||
\(446\) | 27.1295 | 1.28462 | ||||||||
\(447\) | −2.47233 | −0.116937 | ||||||||
\(448\) | −1.44088 | −0.0680750 | ||||||||
\(449\) | −23.4475 | −1.10655 | −0.553277 | − | 0.832997i | \(-0.686623\pi\) | ||||
−0.553277 | + | 0.832997i | \(0.686623\pi\) | |||||||
\(450\) | −5.50071 | −0.259306 | ||||||||
\(451\) | 7.15083 | 0.336720 | ||||||||
\(452\) | −15.1040 | −0.710432 | ||||||||
\(453\) | 12.2455 | 0.575345 | ||||||||
\(454\) | −10.6015 | −0.497552 | ||||||||
\(455\) | 4.72704 | 0.221607 | ||||||||
\(456\) | 22.1599 | 1.03773 | ||||||||
\(457\) | 6.53081 | 0.305498 | 0.152749 | − | 0.988265i | \(-0.451187\pi\) | ||||
0.152749 | + | 0.988265i | \(0.451187\pi\) | |||||||
\(458\) | −33.6433 | −1.57205 | ||||||||
\(459\) | −28.7374 | −1.34135 | ||||||||
\(460\) | 2.65057 | 0.123583 | ||||||||
\(461\) | 33.9899 | 1.58307 | 0.791535 | − | 0.611124i | \(-0.209283\pi\) | ||||
0.791535 | + | 0.611124i | \(0.209283\pi\) | |||||||
\(462\) | −8.43660 | −0.392506 | ||||||||
\(463\) | 9.24762 | 0.429773 | 0.214887 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214887 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.72102 | −0.218932 | ||||||||
\(466\) | −35.9549 | −1.66558 | ||||||||
\(467\) | −27.5893 | −1.27668 | −0.638341 | − | 0.769754i | \(-0.720379\pi\) | ||||
−0.638341 | + | 0.769754i | \(0.720379\pi\) | |||||||
\(468\) | −1.92193 | −0.0888412 | ||||||||
\(469\) | −16.3291 | −0.754008 | ||||||||
\(470\) | 12.7863 | 0.589787 | ||||||||
\(471\) | −38.1531 | −1.75800 | ||||||||
\(472\) | 2.45983 | 0.113223 | ||||||||
\(473\) | −1.97256 | −0.0906982 | ||||||||
\(474\) | 48.9658 | 2.24907 | ||||||||
\(475\) | 33.4008 | 1.53253 | ||||||||
\(476\) | 18.8350 | 0.863300 | ||||||||
\(477\) | 7.22701 | 0.330902 | ||||||||
\(478\) | −17.9346 | −0.820308 | ||||||||
\(479\) | 16.3173 | 0.745557 | 0.372778 | − | 0.927920i | \(-0.378405\pi\) | ||||
0.372778 | + | 0.927920i | \(0.378405\pi\) | |||||||
\(480\) | 9.66721 | 0.441246 | ||||||||
\(481\) | 15.7865 | 0.719803 | ||||||||
\(482\) | −43.0384 | −1.96035 | ||||||||
\(483\) | −12.6123 | −0.573877 | ||||||||
\(484\) | 1.17356 | 0.0533436 | ||||||||
\(485\) | −15.2703 | −0.693387 | ||||||||
\(486\) | −13.0849 | −0.593544 | ||||||||
\(487\) | 22.8961 | 1.03752 | 0.518760 | − | 0.854920i | \(-0.326394\pi\) | ||||
0.518760 | + | 0.854920i | \(0.326394\pi\) | |||||||
\(488\) | 11.2251 | 0.508139 | ||||||||
\(489\) | 1.38421 | 0.0625961 | ||||||||
\(490\) | 1.47021 | 0.0664173 | ||||||||
\(491\) | 22.7150 | 1.02511 | 0.512556 | − | 0.858654i | \(-0.328699\pi\) | ||||
0.512556 | + | 0.858654i | \(0.328699\pi\) | |||||||
\(492\) | −16.1886 | −0.729839 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 31.5585 | 1.41989 | ||||||||
\(495\) | 0.611729 | 0.0274952 | ||||||||
\(496\) | −14.3416 | −0.643958 | ||||||||
\(497\) | −40.0764 | −1.79767 | ||||||||
\(498\) | 19.1221 | 0.856882 | ||||||||
\(499\) | 2.60721 | 0.116715 | 0.0583574 | − | 0.998296i | \(-0.481414\pi\) | ||||
0.0583574 | + | 0.998296i | \(0.481414\pi\) | |||||||
\(500\) | 9.23684 | 0.413084 | ||||||||
\(501\) | 39.0409 | 1.74422 | ||||||||
\(502\) | −8.45379 | −0.377311 | ||||||||
\(503\) | 9.64698 | 0.430137 | 0.215069 | − | 0.976599i | \(-0.431002\pi\) | ||||
0.215069 | + | 0.976599i | \(0.431002\pi\) | |||||||
\(504\) | −2.60708 | −0.116129 | ||||||||
\(505\) | −1.88472 | −0.0838687 | ||||||||
\(506\) | 4.74430 | 0.210910 | ||||||||
\(507\) | −15.1338 | −0.672116 | ||||||||
\(508\) | 2.10909 | 0.0935759 | ||||||||
\(509\) | 8.80063 | 0.390081 | 0.195040 | − | 0.980795i | \(-0.437516\pi\) | ||||
0.195040 | + | 0.980795i | \(0.437516\pi\) | |||||||
\(510\) | −19.0533 | −0.843695 | ||||||||
\(511\) | 32.6700 | 1.44523 | ||||||||
\(512\) | 14.7334 | 0.651128 | ||||||||
\(513\) | 34.2979 | 1.51429 | ||||||||
\(514\) | 25.6789 | 1.13265 | ||||||||
\(515\) | 5.20202 | 0.229229 | ||||||||
\(516\) | 4.46563 | 0.196588 | ||||||||
\(517\) | 8.46322 | 0.372212 | ||||||||
\(518\) | −30.4086 | −1.33608 | ||||||||
\(519\) | 14.0664 | 0.617445 | ||||||||
\(520\) | −2.83484 | −0.124316 | ||||||||
\(521\) | −36.8285 | −1.61349 | −0.806744 | − | 0.590901i | \(-0.798772\pi\) | ||||
−0.806744 | + | 0.590901i | \(0.798772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3453 | 1.06455 | 0.532273 | − | 0.846573i | \(-0.321338\pi\) | ||||
0.532273 | + | 0.846573i | \(0.321338\pi\) | |||||||
\(524\) | −11.6504 | −0.508949 | ||||||||
\(525\) | −20.2729 | −0.884781 | ||||||||
\(526\) | 2.93743 | 0.128078 | ||||||||
\(527\) | 18.8654 | 0.821791 | ||||||||
\(528\) | 9.58724 | 0.417231 | ||||||||
\(529\) | −15.9075 | −0.691632 | ||||||||
\(530\) | −15.1371 | −0.657514 | ||||||||
\(531\) | −1.20516 | −0.0522994 | ||||||||
\(532\) | −22.4794 | −0.974607 | ||||||||
\(533\) | 16.2355 | 0.703237 | ||||||||
\(534\) | 17.6711 | 0.764704 | ||||||||
\(535\) | −5.65430 | −0.244457 | ||||||||
\(536\) | 9.79269 | 0.422980 | ||||||||
\(537\) | −10.8794 | −0.469481 | ||||||||
\(538\) | 3.98852 | 0.171957 | ||||||||
\(539\) | 0.973131 | 0.0419157 | ||||||||
\(540\) | 4.37494 | 0.188268 | ||||||||
\(541\) | 17.6971 | 0.760856 | 0.380428 | − | 0.924810i | \(-0.375777\pi\) | ||||
0.380428 | + | 0.924810i | \(0.375777\pi\) | |||||||
\(542\) | −41.5445 | −1.78449 | ||||||||
\(543\) | 39.3770 | 1.68983 | ||||||||
\(544\) | −38.6307 | −1.65628 | ||||||||
\(545\) | −5.90275 | −0.252846 | ||||||||
\(546\) | −19.1547 | −0.819747 | ||||||||
\(547\) | 9.86507 | 0.421800 | 0.210900 | − | 0.977508i | \(-0.432361\pi\) | ||||
0.210900 | + | 0.977508i | \(0.432361\pi\) | |||||||
\(548\) | −13.1949 | −0.563659 | ||||||||
\(549\) | −5.49959 | −0.234717 | ||||||||
\(550\) | 7.62597 | 0.325172 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 7.56366 | 0.321931 | ||||||||
\(553\) | 34.9798 | 1.48749 | ||||||||
\(554\) | −10.9228 | −0.464066 | ||||||||
\(555\) | 11.3752 | 0.482852 | ||||||||
\(556\) | −9.21608 | −0.390849 | ||||||||
\(557\) | −15.7332 | −0.666636 | −0.333318 | − | 0.942814i | \(-0.608168\pi\) | ||||
−0.333318 | + | 0.942814i | \(0.608168\pi\) | |||||||
\(558\) | 3.70809 | 0.156976 | ||||||||
\(559\) | −4.47856 | −0.189423 | ||||||||
\(560\) | 10.3473 | 0.437253 | ||||||||
\(561\) | −12.6114 | −0.532453 | ||||||||
\(562\) | 31.4381 | 1.32614 | ||||||||
\(563\) | −42.5873 | −1.79484 | −0.897420 | − | 0.441177i | \(-0.854561\pi\) | ||||
−0.897420 | + | 0.441177i | \(0.854561\pi\) | |||||||
\(564\) | −19.1597 | −0.806769 | ||||||||
\(565\) | 10.9150 | 0.459196 | ||||||||
\(566\) | 22.6555 | 0.952281 | ||||||||
\(567\) | −26.1298 | −1.09735 | ||||||||
\(568\) | 24.0341 | 1.00845 | ||||||||
\(569\) | −39.4283 | −1.65292 | −0.826459 | − | 0.562997i | \(-0.809648\pi\) | ||||
−0.826459 | + | 0.562997i | \(0.809648\pi\) | |||||||
\(570\) | 22.7400 | 0.952475 | ||||||||
\(571\) | 40.4567 | 1.69306 | 0.846530 | − | 0.532342i | \(-0.178688\pi\) | ||||
0.846530 | + | 0.532342i | \(0.178688\pi\) | |||||||
\(572\) | 2.66449 | 0.111408 | ||||||||
\(573\) | −11.4685 | −0.479102 | ||||||||
\(574\) | −31.2734 | −1.30533 | ||||||||
\(575\) | 11.4004 | 0.475430 | ||||||||
\(576\) | −0.423355 | −0.0176398 | ||||||||
\(577\) | 18.6305 | 0.775597 | 0.387798 | − | 0.921744i | \(-0.373236\pi\) | ||||
0.387798 | + | 0.921744i | \(0.373236\pi\) | |||||||
\(578\) | 45.8535 | 1.90725 | ||||||||
\(579\) | −3.58934 | −0.149168 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6603 | 0.566724 | ||||||||
\(582\) | 61.8775 | 2.56491 | ||||||||
\(583\) | −10.0192 | −0.414955 | ||||||||
\(584\) | −19.5924 | −0.810740 | ||||||||
\(585\) | 1.38889 | 0.0574235 | ||||||||
\(586\) | −45.1598 | −1.86554 | ||||||||
\(587\) | −28.2511 | −1.16605 | −0.583024 | − | 0.812455i | \(-0.698130\pi\) | ||||
−0.583024 | + | 0.812455i | \(0.698130\pi\) | |||||||
\(588\) | −2.20305 | −0.0908522 | ||||||||
\(589\) | −22.5158 | −0.927747 | ||||||||
\(590\) | 2.52423 | 0.103921 | ||||||||
\(591\) | −20.3260 | −0.836098 | ||||||||
\(592\) | 34.5560 | 1.42024 | ||||||||
\(593\) | −21.8860 | −0.898749 | −0.449374 | − | 0.893344i | \(-0.648353\pi\) | ||||
−0.449374 | + | 0.893344i | \(0.648353\pi\) | |||||||
\(594\) | 7.83080 | 0.321302 | ||||||||
\(595\) | −13.6112 | −0.558003 | ||||||||
\(596\) | −1.50405 | −0.0616084 | ||||||||
\(597\) | −19.0677 | −0.780391 | ||||||||
\(598\) | 10.7716 | 0.440484 | ||||||||
\(599\) | 4.19515 | 0.171409 | 0.0857046 | − | 0.996321i | \(-0.472686\pi\) | ||||
0.0857046 | + | 0.996321i | \(0.472686\pi\) | |||||||
\(600\) | 12.1578 | 0.496340 | ||||||||
\(601\) | 27.4535 | 1.11985 | 0.559927 | − | 0.828542i | \(-0.310829\pi\) | ||||
0.559927 | + | 0.828542i | \(0.310829\pi\) | |||||||
\(602\) | 8.62678 | 0.351601 | ||||||||
\(603\) | −4.79778 | −0.195381 | ||||||||
\(604\) | 7.44962 | 0.303121 | ||||||||
\(605\) | −0.848076 | −0.0344792 | ||||||||
\(606\) | 7.63716 | 0.310239 | ||||||||
\(607\) | 33.8834 | 1.37529 | 0.687643 | − | 0.726049i | \(-0.258645\pi\) | ||||
0.687643 | + | 0.726049i | \(0.258645\pi\) | |||||||
\(608\) | 46.1055 | 1.86983 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.5190 | 0.466391 | ||||||||
\(611\) | 19.2152 | 0.777363 | ||||||||
\(612\) | 5.53405 | 0.223701 | ||||||||
\(613\) | 3.94951 | 0.159519 | 0.0797597 | − | 0.996814i | \(-0.474585\pi\) | ||||
0.0797597 | + | 0.996814i | \(0.474585\pi\) | |||||||
\(614\) | 11.9443 | 0.482034 | ||||||||
\(615\) | 11.6988 | 0.471739 | ||||||||
\(616\) | 3.61436 | 0.145627 | ||||||||
\(617\) | 17.3211 | 0.697320 | 0.348660 | − | 0.937249i | \(-0.386637\pi\) | ||||
0.348660 | + | 0.937249i | \(0.386637\pi\) | |||||||
\(618\) | −21.0794 | −0.847939 | ||||||||
\(619\) | 26.6581 | 1.07148 | 0.535740 | − | 0.844383i | \(-0.320033\pi\) | ||||
0.535740 | + | 0.844383i | \(0.320033\pi\) | |||||||
\(620\) | −2.87205 | −0.115344 | ||||||||
\(621\) | 11.7066 | 0.469770 | ||||||||
\(622\) | 13.5894 | 0.544884 | ||||||||
\(623\) | 12.6237 | 0.505760 | ||||||||
\(624\) | 21.7672 | 0.871385 | ||||||||
\(625\) | 14.7288 | 0.589152 | ||||||||
\(626\) | −36.3549 | −1.45303 | ||||||||
\(627\) | 15.0516 | 0.601103 | ||||||||
\(628\) | −23.2106 | −0.926204 | ||||||||
\(629\) | −45.4560 | −1.81245 | ||||||||
\(630\) | −2.67533 | −0.106588 | ||||||||
\(631\) | 29.0215 | 1.15533 | 0.577663 | − | 0.816275i | \(-0.303965\pi\) | ||||
0.577663 | + | 0.816275i | \(0.303965\pi\) | |||||||
\(632\) | −20.9776 | −0.834446 | ||||||||
\(633\) | 37.9357 | 1.50781 | ||||||||
\(634\) | −30.9385 | −1.22873 | ||||||||
\(635\) | −1.52414 | −0.0604838 | ||||||||
\(636\) | 22.6823 | 0.899413 | ||||||||
\(637\) | 2.20943 | 0.0875408 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.7751 | −0.465818 | ||||||||
\(640\) | −9.13593 | −0.361130 | ||||||||
\(641\) | −38.1853 | −1.50823 | −0.754114 | − | 0.656743i | \(-0.771934\pi\) | ||||
−0.754114 | + | 0.656743i | \(0.771934\pi\) | |||||||
\(642\) | 22.9121 | 0.904269 | ||||||||
\(643\) | −47.9079 | −1.88930 | −0.944652 | − | 0.328075i | \(-0.893600\pi\) | ||||
−0.944652 | + | 0.328075i | \(0.893600\pi\) | |||||||
\(644\) | −7.67272 | −0.302348 | ||||||||
\(645\) | −3.22710 | −0.127067 | ||||||||
\(646\) | −90.8704 | −3.57525 | ||||||||
\(647\) | −0.128175 | −0.00503907 | −0.00251954 | − | 0.999997i | \(-0.500802\pi\) | ||||
−0.00251954 | + | 0.999997i | \(0.500802\pi\) | |||||||
\(648\) | 15.6702 | 0.615585 | ||||||||
\(649\) | 1.67078 | 0.0655840 | ||||||||
\(650\) | 17.3142 | 0.679120 | ||||||||
\(651\) | 13.6662 | 0.535619 | ||||||||
\(652\) | 0.842089 | 0.0329788 | ||||||||
\(653\) | −36.1102 | −1.41310 | −0.706550 | − | 0.707663i | \(-0.749749\pi\) | ||||
−0.706550 | + | 0.707663i | \(0.749749\pi\) | |||||||
\(654\) | 23.9189 | 0.935302 | ||||||||
\(655\) | 8.41918 | 0.328965 | ||||||||
\(656\) | 35.5388 | 1.38756 | ||||||||
\(657\) | 9.59902 | 0.374493 | ||||||||
\(658\) | −37.0131 | −1.44292 | ||||||||
\(659\) | 30.0440 | 1.17035 | 0.585173 | − | 0.810908i | \(-0.301026\pi\) | ||||
0.585173 | + | 0.810908i | \(0.301026\pi\) | |||||||
\(660\) | 1.91994 | 0.0747336 | ||||||||
\(661\) | 35.5408 | 1.38238 | 0.691188 | − | 0.722675i | \(-0.257088\pi\) | ||||
0.691188 | + | 0.722675i | \(0.257088\pi\) | |||||||
\(662\) | 12.5721 | 0.488628 | ||||||||
\(663\) | −28.6333 | −1.11202 | ||||||||
\(664\) | −8.19218 | −0.317918 | ||||||||
\(665\) | 16.2448 | 0.629948 | ||||||||
\(666\) | −8.93458 | −0.346208 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 23.7507 | 0.918942 | ||||||||
\(669\) | 29.3776 | 1.13580 | ||||||||
\(670\) | 10.0490 | 0.388228 | ||||||||
\(671\) | 7.62442 | 0.294337 | ||||||||
\(672\) | −27.9841 | −1.07951 | ||||||||
\(673\) | 17.2593 | 0.665298 | 0.332649 | − | 0.943051i | \(-0.392058\pi\) | ||||
0.332649 | + | 0.943051i | \(0.392058\pi\) | |||||||
\(674\) | 13.8023 | 0.531644 | ||||||||
\(675\) | 18.8172 | 0.724273 | ||||||||
\(676\) | −9.20672 | −0.354105 | ||||||||
\(677\) | 40.7109 | 1.56465 | 0.782324 | − | 0.622871i | \(-0.214034\pi\) | ||||
0.782324 | + | 0.622871i | \(0.214034\pi\) | |||||||
\(678\) | −44.2291 | −1.69861 | ||||||||
\(679\) | 44.2036 | 1.69638 | ||||||||
\(680\) | 8.16271 | 0.313026 | ||||||||
\(681\) | −11.4800 | −0.439914 | ||||||||
\(682\) | −5.14074 | −0.196849 | ||||||||
\(683\) | 3.01801 | 0.115481 | 0.0577404 | − | 0.998332i | \(-0.481610\pi\) | ||||
0.0577404 | + | 0.998332i | \(0.481610\pi\) | |||||||
\(684\) | −6.60486 | −0.252543 | ||||||||
\(685\) | 9.53536 | 0.364327 | ||||||||
\(686\) | −34.8697 | −1.33133 | ||||||||
\(687\) | −36.4311 | −1.38993 | ||||||||
\(688\) | −9.80336 | −0.373750 | ||||||||
\(689\) | −22.7480 | −0.866631 | ||||||||
\(690\) | 7.76167 | 0.295482 | ||||||||
\(691\) | −32.0386 | −1.21881 | −0.609403 | − | 0.792860i | \(-0.708591\pi\) | ||||
−0.609403 | + | 0.792860i | \(0.708591\pi\) | |||||||
\(692\) | 8.55734 | 0.325301 | ||||||||
\(693\) | −1.77080 | −0.0672672 | ||||||||
\(694\) | −45.2945 | −1.71936 | ||||||||
\(695\) | 6.66003 | 0.252629 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.7488 | −1.77074 | ||||||||
\(698\) | −37.5358 | −1.42075 | ||||||||
\(699\) | −38.9344 | −1.47263 | ||||||||
\(700\) | −12.3331 | −0.466147 | ||||||||
\(701\) | −34.4196 | −1.30001 | −0.650005 | − | 0.759930i | \(-0.725233\pi\) | ||||
−0.650005 | + | 0.759930i | \(0.725233\pi\) | |||||||
\(702\) | 17.7793 | 0.671037 | ||||||||
\(703\) | 54.2515 | 2.04613 | ||||||||
\(704\) | 0.586923 | 0.0221205 | ||||||||
\(705\) | 13.8458 | 0.521464 | ||||||||
\(706\) | 27.0028 | 1.01626 | ||||||||
\(707\) | 5.45578 | 0.205186 | ||||||||
\(708\) | −3.78245 | −0.142153 | ||||||||
\(709\) | −44.7279 | −1.67979 | −0.839896 | − | 0.542747i | \(-0.817384\pi\) | ||||
−0.839896 | + | 0.542747i | \(0.817384\pi\) | |||||||
\(710\) | 24.6633 | 0.925596 | ||||||||
\(711\) | 10.2777 | 0.385443 | ||||||||
\(712\) | −7.57055 | −0.283719 | ||||||||
\(713\) | −7.68513 | −0.287810 | ||||||||
\(714\) | 55.1546 | 2.06411 | ||||||||
\(715\) | −1.92550 | −0.0720096 | ||||||||
\(716\) | −6.61854 | −0.247346 | ||||||||
\(717\) | −19.4207 | −0.725280 | ||||||||
\(718\) | −7.47397 | −0.278926 | ||||||||
\(719\) | 18.8534 | 0.703115 | 0.351557 | − | 0.936166i | \(-0.385652\pi\) | ||||
0.351557 | + | 0.936166i | \(0.385652\pi\) | |||||||
\(720\) | 3.04022 | 0.113302 | ||||||||
\(721\) | −15.0586 | −0.560810 | ||||||||
\(722\) | 74.6058 | 2.77654 | ||||||||
\(723\) | −46.6048 | −1.73325 | ||||||||
\(724\) | 23.9552 | 0.890288 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.43654 | 0.127542 | ||||||||
\(727\) | −18.6087 | −0.690158 | −0.345079 | − | 0.938574i | \(-0.612148\pi\) | ||||
−0.345079 | + | 0.938574i | \(0.612148\pi\) | |||||||
\(728\) | 8.20616 | 0.304140 | ||||||||
\(729\) | 17.7617 | 0.657841 | ||||||||
\(730\) | −20.1053 | −0.744131 | ||||||||
\(731\) | 12.8957 | 0.476963 | ||||||||
\(732\) | −17.2607 | −0.637976 | ||||||||
\(733\) | −21.9510 | −0.810777 | −0.405388 | − | 0.914145i | \(-0.632864\pi\) | ||||
−0.405388 | + | 0.914145i | \(0.632864\pi\) | |||||||
\(734\) | 11.8746 | 0.438300 | ||||||||
\(735\) | 1.59204 | 0.0587233 | ||||||||
\(736\) | 15.7368 | 0.580067 | ||||||||
\(737\) | 6.65145 | 0.245009 | ||||||||
\(738\) | −9.18869 | −0.338240 | ||||||||
\(739\) | −22.2525 | −0.818573 | −0.409286 | − | 0.912406i | \(-0.634222\pi\) | ||||
−0.409286 | + | 0.912406i | \(0.634222\pi\) | |||||||
\(740\) | 6.92017 | 0.254391 | ||||||||
\(741\) | 34.1737 | 1.25540 | ||||||||
\(742\) | 43.8182 | 1.60862 | ||||||||
\(743\) | 2.12726 | 0.0780417 | 0.0390208 | − | 0.999238i | \(-0.487576\pi\) | ||||
0.0390208 | + | 0.999238i | \(0.487576\pi\) | |||||||
\(744\) | −8.19570 | −0.300469 | ||||||||
\(745\) | 1.08691 | 0.0398213 | ||||||||
\(746\) | 36.2105 | 1.32576 | ||||||||
\(747\) | 4.01364 | 0.146851 | ||||||||
\(748\) | −7.67219 | −0.280523 | ||||||||
\(749\) | 16.3678 | 0.598066 | ||||||||
\(750\) | 27.0483 | 0.987665 | ||||||||
\(751\) | −48.9374 | −1.78575 | −0.892876 | − | 0.450303i | \(-0.851316\pi\) | ||||
−0.892876 | + | 0.450303i | \(0.851316\pi\) | |||||||
\(752\) | 42.0612 | 1.53381 | ||||||||
\(753\) | −9.15433 | −0.333602 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.38350 | −0.195926 | ||||||||
\(756\) | −12.6644 | −0.460599 | ||||||||
\(757\) | −28.7611 | −1.04534 | −0.522671 | − | 0.852535i | \(-0.675064\pi\) | ||||
−0.522671 | + | 0.852535i | \(0.675064\pi\) | |||||||
\(758\) | −12.4736 | −0.453063 | ||||||||
\(759\) | 5.13744 | 0.186477 | ||||||||
\(760\) | −9.74215 | −0.353385 | ||||||||
\(761\) | 13.7023 | 0.496709 | 0.248354 | − | 0.968669i | \(-0.420110\pi\) | ||||
0.248354 | + | 0.968669i | \(0.420110\pi\) | |||||||
\(762\) | 6.17607 | 0.223736 | ||||||||
\(763\) | 17.0870 | 0.618590 | ||||||||
\(764\) | −6.97689 | −0.252415 | ||||||||
\(765\) | −3.99920 | −0.144591 | ||||||||
\(766\) | 51.8479 | 1.87334 | ||||||||
\(767\) | 3.79340 | 0.136972 | ||||||||
\(768\) | 39.2847 | 1.41756 | ||||||||
\(769\) | −30.1249 | −1.08633 | −0.543166 | − | 0.839625i | \(-0.682775\pi\) | ||||
−0.543166 | + | 0.839625i | \(0.682775\pi\) | |||||||
\(770\) | 3.70898 | 0.133662 | ||||||||
\(771\) | 27.8068 | 1.00144 | ||||||||
\(772\) | −2.18359 | −0.0785892 | ||||||||
\(773\) | 31.1971 | 1.12208 | 0.561041 | − | 0.827788i | \(-0.310401\pi\) | ||||
0.561041 | + | 0.827788i | \(0.310401\pi\) | |||||||
\(774\) | 2.53470 | 0.0911079 | ||||||||
\(775\) | −12.3530 | −0.443735 | ||||||||
\(776\) | −26.5092 | −0.951626 | ||||||||
\(777\) | −32.9284 | −1.18130 | ||||||||
\(778\) | 30.6357 | 1.09834 | ||||||||
\(779\) | 55.7945 | 1.99904 | ||||||||
\(780\) | 4.35910 | 0.156081 | ||||||||
\(781\) | 16.3246 | 0.584140 | ||||||||
\(782\) | −31.0160 | −1.10913 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.83634 | 0.172727 | ||||||||
\(785\) | 16.7732 | 0.598662 | ||||||||
\(786\) | −34.1158 | −1.21687 | ||||||||
\(787\) | −16.7312 | −0.596404 | −0.298202 | − | 0.954503i | \(-0.596387\pi\) | ||||
−0.298202 | + | 0.954503i | \(0.596387\pi\) | |||||||
\(788\) | −12.3654 | −0.440499 | ||||||||
\(789\) | 3.18085 | 0.113241 | ||||||||
\(790\) | −21.5268 | −0.765889 | ||||||||
\(791\) | −31.5961 | −1.12343 | ||||||||
\(792\) | 1.06196 | 0.0377352 | ||||||||
\(793\) | 17.3107 | 0.614722 | ||||||||
\(794\) | −14.9707 | −0.531289 | ||||||||
\(795\) | −16.3915 | −0.581346 | ||||||||
\(796\) | −11.5999 | −0.411149 | ||||||||
\(797\) | −9.08294 | −0.321734 | −0.160867 | − | 0.986976i | \(-0.551429\pi\) | ||||
−0.160867 | + | 0.986976i | \(0.551429\pi\) | |||||||
\(798\) | −65.8267 | −2.33024 | ||||||||
\(799\) | −55.3287 | −1.95739 | ||||||||
\(800\) | 25.2953 | 0.894323 | ||||||||
\(801\) | 3.70908 | 0.131054 | ||||||||
\(802\) | −38.3616 | −1.35460 | ||||||||
\(803\) | −13.3077 | −0.469618 | ||||||||
\(804\) | −15.0581 | −0.531057 | ||||||||
\(805\) | 5.54472 | 0.195426 | ||||||||
\(806\) | −11.6717 | −0.411119 | ||||||||
\(807\) | 4.31904 | 0.152037 | ||||||||
\(808\) | −3.27187 | −0.115104 | ||||||||
\(809\) | −31.8513 | −1.11983 | −0.559915 | − | 0.828550i | \(-0.689166\pi\) | ||||
−0.559915 | + | 0.828550i | \(0.689166\pi\) | |||||||
\(810\) | 16.0805 | 0.565010 | ||||||||
\(811\) | −9.46359 | −0.332312 | −0.166156 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166156 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −44.9871 | −1.57777 | ||||||||
\(814\) | 12.3866 | 0.434148 | ||||||||
\(815\) | −0.608539 | −0.0213162 | ||||||||
\(816\) | −62.6770 | −2.19413 | ||||||||
\(817\) | −15.3909 | −0.538459 | ||||||||
\(818\) | 47.4415 | 1.65875 | ||||||||
\(819\) | −4.02048 | −0.140487 | ||||||||
\(820\) | 7.11699 | 0.248536 | ||||||||
\(821\) | 45.9200 | 1.60262 | 0.801310 | − | 0.598249i | \(-0.204137\pi\) | ||||
0.801310 | + | 0.598249i | \(0.204137\pi\) | |||||||
\(822\) | −38.6388 | −1.34768 | ||||||||
\(823\) | 34.5510 | 1.20437 | 0.602187 | − | 0.798355i | \(-0.294296\pi\) | ||||
0.602187 | + | 0.798355i | \(0.294296\pi\) | |||||||
\(824\) | 9.03073 | 0.314600 | ||||||||
\(825\) | 8.25790 | 0.287503 | ||||||||
\(826\) | −7.30700 | −0.254243 | ||||||||
\(827\) | −5.54741 | −0.192902 | −0.0964512 | − | 0.995338i | \(-0.530749\pi\) | ||||
−0.0964512 | + | 0.995338i | \(0.530749\pi\) | |||||||
\(828\) | −2.25438 | −0.0783452 | ||||||||
\(829\) | −11.7610 | −0.408476 | −0.204238 | − | 0.978921i | \(-0.565472\pi\) | ||||
−0.204238 | + | 0.978921i | \(0.565472\pi\) | |||||||
\(830\) | −8.40664 | −0.291799 | ||||||||
\(831\) | −11.8280 | −0.410307 | ||||||||
\(832\) | 1.33257 | 0.0461985 | ||||||||
\(833\) | −6.36188 | −0.220426 | ||||||||
\(834\) | −26.9875 | −0.934501 | ||||||||
\(835\) | −17.1635 | −0.593968 | ||||||||
\(836\) | 9.15671 | 0.316691 | ||||||||
\(837\) | −12.6849 | −0.438453 | ||||||||
\(838\) | 13.1685 | 0.454898 | ||||||||
\(839\) | −21.8446 | −0.754159 | −0.377080 | − | 0.926181i | \(-0.623072\pi\) | ||||
−0.377080 | + | 0.926181i | \(0.623072\pi\) | |||||||
\(840\) | 5.91309 | 0.204021 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | −38.5467 | −1.32841 | ||||||||
\(843\) | 34.0433 | 1.17251 | ||||||||
\(844\) | 23.0783 | 0.794389 | ||||||||
\(845\) | 6.65327 | 0.228880 | ||||||||
\(846\) | −10.8751 | −0.373893 | ||||||||
\(847\) | 2.45497 | 0.0843537 | ||||||||
\(848\) | −49.7944 | −1.70995 | ||||||||
\(849\) | 24.5329 | 0.841966 | ||||||||
\(850\) | −49.8550 | −1.71001 | ||||||||
\(851\) | 18.5172 | 0.634762 | ||||||||
\(852\) | −36.9569 | −1.26612 | ||||||||
\(853\) | 18.0234 | 0.617110 | 0.308555 | − | 0.951206i | \(-0.400155\pi\) | ||||
0.308555 | + | 0.951206i | \(0.400155\pi\) | |||||||
\(854\) | −33.3446 | −1.14103 | ||||||||
\(855\) | 4.77302 | 0.163234 | ||||||||
\(856\) | −9.81588 | −0.335500 | ||||||||
\(857\) | 36.3010 | 1.24002 | 0.620009 | − | 0.784595i | \(-0.287129\pi\) | ||||
0.620009 | + | 0.784595i | \(0.287129\pi\) | |||||||
\(858\) | 7.80243 | 0.266371 | ||||||||
\(859\) | 4.89319 | 0.166953 | 0.0834767 | − | 0.996510i | \(-0.473398\pi\) | ||||
0.0834767 | + | 0.996510i | \(0.473398\pi\) | |||||||
\(860\) | −1.96322 | −0.0669453 | ||||||||
\(861\) | −33.8650 | −1.15411 | ||||||||
\(862\) | 25.9151 | 0.882673 | ||||||||
\(863\) | −3.46670 | −0.118008 | −0.0590038 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590038 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(864\) | 25.9747 | 0.883678 | ||||||||
\(865\) | −6.18399 | −0.210262 | ||||||||
\(866\) | −0.885241 | −0.0300817 | ||||||||
\(867\) | 49.6532 | 1.68631 | ||||||||
\(868\) | 8.31387 | 0.282191 | ||||||||
\(869\) | −14.2486 | −0.483350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1017 | 0.511701 | ||||||||
\(872\) | −10.2472 | −0.347013 | ||||||||
\(873\) | 12.9878 | 0.439570 | ||||||||
\(874\) | 37.0175 | 1.25213 | ||||||||
\(875\) | 19.3226 | 0.653222 | ||||||||
\(876\) | 30.1270 | 1.01790 | ||||||||
\(877\) | 18.5138 | 0.625168 | 0.312584 | − | 0.949890i | \(-0.398805\pi\) | ||||
0.312584 | + | 0.949890i | \(0.398805\pi\) | |||||||
\(878\) | −66.9007 | −2.25779 | ||||||||
\(879\) | −48.9021 | −1.64943 | ||||||||
\(880\) | −4.21484 | −0.142082 | ||||||||
\(881\) | 34.6831 | 1.16850 | 0.584252 | − | 0.811572i | \(-0.301388\pi\) | ||||
0.584252 | + | 0.811572i | \(0.301388\pi\) | |||||||
\(882\) | −1.25046 | −0.0421050 | ||||||||
\(883\) | −51.6039 | −1.73661 | −0.868305 | − | 0.496030i | \(-0.834791\pi\) | ||||
−0.868305 | + | 0.496030i | \(0.834791\pi\) | |||||||
\(884\) | −17.4192 | −0.585871 | ||||||||
\(885\) | 2.73340 | 0.0918822 | ||||||||
\(886\) | 55.2975 | 1.85776 | ||||||||
\(887\) | 42.4340 | 1.42479 | 0.712397 | − | 0.701777i | \(-0.247610\pi\) | ||||
0.712397 | + | 0.701777i | \(0.247610\pi\) | |||||||
\(888\) | 19.7474 | 0.662680 | ||||||||
\(889\) | 4.41201 | 0.147974 | ||||||||
\(890\) | −7.76874 | −0.260409 | ||||||||
\(891\) | 10.6436 | 0.356576 | ||||||||
\(892\) | 17.8720 | 0.598398 | ||||||||
\(893\) | 66.0344 | 2.20976 | ||||||||
\(894\) | −4.40433 | −0.147303 | ||||||||
\(895\) | 4.78291 | 0.159875 | ||||||||
\(896\) | 26.4462 | 0.883507 | ||||||||
\(897\) | 11.6642 | 0.389457 | ||||||||
\(898\) | −41.7704 | −1.39390 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.62368 | −0.120789 | ||||||||
\(901\) | 65.5012 | 2.18216 | ||||||||
\(902\) | 12.7388 | 0.424157 | ||||||||
\(903\) | 9.34164 | 0.310870 | ||||||||
\(904\) | 18.9484 | 0.630214 | ||||||||
\(905\) | −17.3113 | −0.575447 | ||||||||
\(906\) | 21.8148 | 0.724748 | ||||||||
\(907\) | 49.1581 | 1.63227 | 0.816133 | − | 0.577864i | \(-0.196113\pi\) | ||||
0.816133 | + | 0.577864i | \(0.196113\pi\) | |||||||
\(908\) | −6.98390 | −0.231769 | ||||||||
\(909\) | 1.60300 | 0.0531683 | ||||||||
\(910\) | 8.42098 | 0.279153 | ||||||||
\(911\) | −30.5305 | −1.01152 | −0.505760 | − | 0.862674i | \(-0.668788\pi\) | ||||
−0.505760 | + | 0.862674i | \(0.668788\pi\) | |||||||
\(912\) | 74.8046 | 2.47703 | ||||||||
\(913\) | −5.56435 | −0.184153 | ||||||||
\(914\) | 11.6343 | 0.384829 | ||||||||
\(915\) | 12.4735 | 0.412363 | ||||||||
\(916\) | −22.1630 | −0.732288 | ||||||||
\(917\) | −24.3714 | −0.804815 | ||||||||
\(918\) | −51.1942 | −1.68966 | ||||||||
\(919\) | −37.8847 | −1.24970 | −0.624850 | − | 0.780745i | \(-0.714840\pi\) | ||||
−0.624850 | + | 0.780745i | \(0.714840\pi\) | |||||||
\(920\) | −3.32521 | −0.109629 | ||||||||
\(921\) | 12.9341 | 0.426193 | ||||||||
\(922\) | 60.5513 | 1.99415 | ||||||||
\(923\) | 37.0639 | 1.21997 | ||||||||
\(924\) | −5.55775 | −0.182836 | ||||||||
\(925\) | 29.7645 | 0.978651 | ||||||||
\(926\) | 16.4742 | 0.541374 | ||||||||
\(927\) | −4.42447 | −0.145319 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.0388 | 1.01835 | 0.509176 | − | 0.860663i | \(-0.329950\pi\) | ||||
0.509176 | + | 0.860663i | \(0.329950\pi\) | |||||||
\(930\) | −8.41025 | −0.275783 | ||||||||
\(931\) | 7.59287 | 0.248846 | ||||||||
\(932\) | −23.6859 | −0.775857 | ||||||||
\(933\) | 14.7155 | 0.481763 | ||||||||
\(934\) | −49.1490 | −1.60820 | ||||||||
\(935\) | 5.54433 | 0.181319 | ||||||||
\(936\) | 2.41111 | 0.0788097 | ||||||||
\(937\) | −14.1913 | −0.463608 | −0.231804 | − | 0.972762i | \(-0.574463\pi\) | ||||
−0.231804 | + | 0.972762i | \(0.574463\pi\) | |||||||
\(938\) | −29.0895 | −0.949804 | ||||||||
\(939\) | −39.3675 | −1.28471 | ||||||||
\(940\) | 8.42317 | 0.274733 | ||||||||
\(941\) | −39.6260 | −1.29177 | −0.645885 | − | 0.763434i | \(-0.723512\pi\) | ||||
−0.645885 | + | 0.763434i | \(0.723512\pi\) | |||||||
\(942\) | −67.9678 | −2.21451 | ||||||||
\(943\) | 19.0439 | 0.620154 | ||||||||
\(944\) | 8.30359 | 0.270259 | ||||||||
\(945\) | 9.15195 | 0.297713 | ||||||||
\(946\) | −3.51401 | −0.114250 | ||||||||
\(947\) | 43.2822 | 1.40648 | 0.703240 | − | 0.710952i | \(-0.251736\pi\) | ||||
0.703240 | + | 0.710952i | \(0.251736\pi\) | |||||||
\(948\) | 32.2570 | 1.04766 | ||||||||
\(949\) | −30.2142 | −0.980796 | ||||||||
\(950\) | 59.5017 | 1.93049 | ||||||||
\(951\) | −33.5023 | −1.08639 | ||||||||
\(952\) | −23.6290 | −0.765821 | ||||||||
\(953\) | 1.66999 | 0.0540964 | 0.0270482 | − | 0.999634i | \(-0.491389\pi\) | ||||
0.0270482 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(954\) | 12.8746 | 0.416829 | ||||||||
\(955\) | 5.04187 | 0.163151 | ||||||||
\(956\) | −11.8147 | −0.382114 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.0684 | 0.939159 | ||||||||
\(959\) | −27.6025 | −0.891330 | ||||||||
\(960\) | 0.960205 | 0.0309905 | ||||||||
\(961\) | −22.6727 | −0.731377 | ||||||||
\(962\) | 28.1228 | 0.906717 | ||||||||
\(963\) | 4.80914 | 0.154972 | ||||||||
\(964\) | −28.3523 | −0.913165 | ||||||||
\(965\) | 1.57798 | 0.0507970 | ||||||||
\(966\) | −22.4681 | −0.722899 | ||||||||
\(967\) | −54.4782 | −1.75190 | −0.875950 | − | 0.482401i | \(-0.839765\pi\) | ||||
−0.875950 | + | 0.482401i | \(0.839765\pi\) | |||||||
\(968\) | −1.47226 | −0.0473203 | ||||||||
\(969\) | −98.4005 | −3.16108 | ||||||||
\(970\) | −27.2032 | −0.873442 | ||||||||
\(971\) | 51.2275 | 1.64397 | 0.821984 | − | 0.569511i | \(-0.192867\pi\) | ||||
0.821984 | + | 0.569511i | \(0.192867\pi\) | |||||||
\(972\) | −8.61991 | −0.276484 | ||||||||
\(973\) | −19.2791 | −0.618060 | ||||||||
\(974\) | 40.7882 | 1.30694 | ||||||||
\(975\) | 18.7490 | 0.600449 | ||||||||
\(976\) | 37.8924 | 1.21291 | ||||||||
\(977\) | −43.7917 | −1.40102 | −0.700510 | − | 0.713642i | \(-0.747044\pi\) | ||||
−0.700510 | + | 0.713642i | \(0.747044\pi\) | |||||||
\(978\) | 2.46590 | 0.0788507 | ||||||||
\(979\) | −5.14212 | −0.164343 | ||||||||
\(980\) | 0.968526 | 0.0309384 | ||||||||
\(981\) | 5.02045 | 0.160291 | ||||||||
\(982\) | 40.4655 | 1.29131 | ||||||||
\(983\) | 36.5283 | 1.16507 | 0.582535 | − | 0.812805i | \(-0.302061\pi\) | ||||
0.582535 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(984\) | 20.3091 | 0.647429 | ||||||||
\(985\) | 8.93589 | 0.284721 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −40.0802 | −1.27577 | ||||||||
\(988\) | 20.7897 | 0.661408 | ||||||||
\(989\) | −5.25325 | −0.167044 | ||||||||
\(990\) | 1.08976 | 0.0346349 | ||||||||
\(991\) | −14.8345 | −0.471232 | −0.235616 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235616 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(992\) | −17.0518 | −0.541396 | ||||||||
\(993\) | 13.6139 | 0.432023 | ||||||||
\(994\) | −71.3940 | −2.26448 | ||||||||
\(995\) | 8.38274 | 0.265751 | ||||||||
\(996\) | 12.5970 | 0.399151 | ||||||||
\(997\) | −49.8939 | −1.58015 | −0.790077 | − | 0.613007i | \(-0.789960\pi\) | ||||
−0.790077 | + | 0.613007i | \(0.789960\pi\) | |||||||
\(998\) | 4.64461 | 0.147023 | ||||||||
\(999\) | 30.5640 | 0.967002 |
(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 | 9251.2.a.t.1.16 | yes | 18 | |
29.28 | even | 2 | 9251.2.a.s.1.3 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9251.2.a.s.1.3 | ✓ | 18 | 29.28 | even | 2 | ||
9251.2.a.t.1.16 | yes | 18 | 1.1 | even | 1 | trivial |