Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, 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("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.637875\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.637875 | −0.451045 | −0.225523 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225523 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(3\) | −2.56771 | −1.48247 | −0.741233 | − | 0.671248i | \(-0.765759\pi\) | ||||
−0.741233 | + | 0.671248i | \(0.765759\pi\) | |||||||
\(4\) | −1.59312 | −0.796558 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.63787 | 0.668659 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.29196 | 0.810329 | ||||||||
\(9\) | 3.59312 | 1.19771 | ||||||||
\(10\) | −0.637875 | −0.201714 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 4.09065 | 1.18087 | ||||||||
\(13\) | −2.09065 | −0.579843 | −0.289922 | − | 0.957050i | \(-0.593629\pi\) | ||||
−0.289922 | + | 0.957050i | \(0.593629\pi\) | |||||||
\(14\) | 0.637875 | 0.170479 | ||||||||
\(15\) | −2.56771 | −0.662979 | ||||||||
\(16\) | 1.72425 | 0.431063 | ||||||||
\(17\) | 6.47819 | 1.57119 | 0.785596 | − | 0.618740i | \(-0.212357\pi\) | ||||
0.785596 | + | 0.618740i | \(0.212357\pi\) | |||||||
\(18\) | −2.29196 | −0.540220 | ||||||||
\(19\) | 1.61246 | 0.369925 | 0.184962 | − | 0.982746i | \(-0.440784\pi\) | ||||
0.184962 | + | 0.982746i | \(0.440784\pi\) | |||||||
\(20\) | −1.59312 | −0.356232 | ||||||||
\(21\) | 2.56771 | 0.560319 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.929832 | 0.193883 | 0.0969417 | − | 0.995290i | \(-0.469094\pi\) | ||||
0.0969417 | + | 0.995290i | \(0.469094\pi\) | |||||||
\(24\) | −5.88507 | −1.20129 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.33358 | 0.261536 | ||||||||
\(27\) | −1.52295 | −0.293091 | ||||||||
\(28\) | 1.59312 | 0.301071 | ||||||||
\(29\) | −2.41116 | −0.447742 | −0.223871 | − | 0.974619i | \(-0.571869\pi\) | ||||
−0.223871 | + | 0.974619i | \(0.571869\pi\) | |||||||
\(30\) | 1.63787 | 0.299034 | ||||||||
\(31\) | −0.749661 | −0.134643 | −0.0673215 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673215 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(32\) | −5.68377 | −1.00476 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.13227 | −0.708679 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −5.72425 | −0.954042 | ||||||||
\(37\) | 1.51375 | 0.248858 | 0.124429 | − | 0.992228i | \(-0.460290\pi\) | ||||
0.124429 | + | 0.992228i | \(0.460290\pi\) | |||||||
\(38\) | −1.02855 | −0.166853 | ||||||||
\(39\) | 5.36819 | 0.859598 | ||||||||
\(40\) | 2.29196 | 0.362390 | ||||||||
\(41\) | 10.4366 | 1.62992 | 0.814959 | − | 0.579518i | \(-0.196759\pi\) | ||||
0.814959 | + | 0.579518i | \(0.196759\pi\) | |||||||
\(42\) | −1.63787 | −0.252730 | ||||||||
\(43\) | −2.78950 | −0.425394 | −0.212697 | − | 0.977118i | \(-0.568225\pi\) | ||||
−0.212697 | + | 0.977118i | \(0.568225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.59312 | 0.535630 | ||||||||
\(46\) | −0.593116 | −0.0874502 | ||||||||
\(47\) | 0.403743 | 0.0588920 | 0.0294460 | − | 0.999566i | \(-0.490626\pi\) | ||||
0.0294460 | + | 0.999566i | \(0.490626\pi\) | |||||||
\(48\) | −4.42737 | −0.639036 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.637875 | −0.0902091 | ||||||||
\(51\) | −16.6341 | −2.32924 | ||||||||
\(52\) | 3.33065 | 0.461879 | ||||||||
\(53\) | 5.79442 | 0.795925 | 0.397962 | − | 0.917402i | \(-0.369717\pi\) | ||||
0.397962 | + | 0.917402i | \(0.369717\pi\) | |||||||
\(54\) | 0.971450 | 0.132198 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.29196 | −0.306276 | ||||||||
\(57\) | −4.14034 | −0.548401 | ||||||||
\(58\) | 1.53802 | 0.201952 | ||||||||
\(59\) | 8.93097 | 1.16271 | 0.581357 | − | 0.813649i | \(-0.302522\pi\) | ||||
0.581357 | + | 0.813649i | \(0.302522\pi\) | |||||||
\(60\) | 4.09065 | 0.528101 | ||||||||
\(61\) | −8.13227 | −1.04123 | −0.520615 | − | 0.853791i | \(-0.674297\pi\) | ||||
−0.520615 | + | 0.853791i | \(0.674297\pi\) | |||||||
\(62\) | 0.478189 | 0.0607301 | ||||||||
\(63\) | −3.59312 | −0.452690 | ||||||||
\(64\) | 0.177031 | 0.0221288 | ||||||||
\(65\) | −2.09065 | −0.259314 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.789495 | −0.0964522 | −0.0482261 | − | 0.998836i | \(-0.515357\pi\) | ||||
−0.0482261 | + | 0.998836i | \(0.515357\pi\) | |||||||
\(68\) | −10.3205 | −1.25155 | ||||||||
\(69\) | −2.38754 | −0.287425 | ||||||||
\(70\) | 0.637875 | 0.0762406 | ||||||||
\(71\) | −10.9056 | −1.29425 | −0.647126 | − | 0.762383i | \(-0.724029\pi\) | ||||
−0.647126 | + | 0.762383i | \(0.724029\pi\) | |||||||
\(72\) | 8.23527 | 0.970536 | ||||||||
\(73\) | −3.89427 | −0.455790 | −0.227895 | − | 0.973686i | \(-0.573184\pi\) | ||||
−0.227895 | + | 0.973686i | \(0.573184\pi\) | |||||||
\(74\) | −0.965580 | −0.112246 | ||||||||
\(75\) | −2.56771 | −0.296493 | ||||||||
\(76\) | −2.56884 | −0.294667 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.42423 | −0.387718 | ||||||||
\(79\) | −5.86887 | −0.660299 | −0.330149 | − | 0.943929i | \(-0.607099\pi\) | ||||
−0.330149 | + | 0.943929i | \(0.607099\pi\) | |||||||
\(80\) | 1.72425 | 0.192777 | ||||||||
\(81\) | −6.86887 | −0.763207 | ||||||||
\(82\) | −6.65722 | −0.735167 | ||||||||
\(83\) | −17.6534 | −1.93772 | −0.968858 | − | 0.247616i | \(-0.920353\pi\) | ||||
−0.968858 | + | 0.247616i | \(0.920353\pi\) | |||||||
\(84\) | −4.09065 | −0.446327 | ||||||||
\(85\) | 6.47819 | 0.702658 | ||||||||
\(86\) | 1.77935 | 0.191872 | ||||||||
\(87\) | 6.19116 | 0.663762 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2099 | 1.40024 | 0.700121 | − | 0.714024i | \(-0.253129\pi\) | ||||
0.700121 | + | 0.714024i | \(0.253129\pi\) | |||||||
\(90\) | −2.29196 | −0.241594 | ||||||||
\(91\) | 2.09065 | 0.219160 | ||||||||
\(92\) | −1.48133 | −0.154439 | ||||||||
\(93\) | 1.92491 | 0.199604 | ||||||||
\(94\) | −0.257538 | −0.0265630 | ||||||||
\(95\) | 1.61246 | 0.165435 | ||||||||
\(96\) | 14.5943 | 1.48952 | ||||||||
\(97\) | −16.6584 | −1.69140 | −0.845700 | − | 0.533658i | \(-0.820817\pi\) | ||||
−0.845700 | + | 0.533658i | \(0.820817\pi\) | |||||||
\(98\) | −0.637875 | −0.0644351 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.59312 | −0.159312 | ||||||||
\(101\) | 8.52609 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(102\) | 10.6105 | 1.05059 | ||||||||
\(103\) | −20.1975 | −1.99012 | −0.995060 | − | 0.0992731i | \(-0.968348\pi\) | ||||
−0.995060 | + | 0.0992731i | \(0.968348\pi\) | |||||||
\(104\) | −4.79169 | −0.469864 | ||||||||
\(105\) | 2.56771 | 0.250582 | ||||||||
\(106\) | −3.69611 | −0.358998 | ||||||||
\(107\) | −7.32657 | −0.708286 | −0.354143 | − | 0.935191i | \(-0.615227\pi\) | ||||
−0.354143 | + | 0.935191i | \(0.615227\pi\) | |||||||
\(108\) | 2.42623 | 0.233464 | ||||||||
\(109\) | 16.9564 | 1.62413 | 0.812063 | − | 0.583569i | \(-0.198344\pi\) | ||||
0.812063 | + | 0.583569i | \(0.198344\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.88686 | −0.368924 | ||||||||
\(112\) | −1.72425 | −0.162926 | ||||||||
\(113\) | −6.55150 | −0.616313 | −0.308157 | − | 0.951336i | \(-0.599712\pi\) | ||||
−0.308157 | + | 0.951336i | \(0.599712\pi\) | |||||||
\(114\) | 2.64102 | 0.247354 | ||||||||
\(115\) | 0.929832 | 0.0867073 | ||||||||
\(116\) | 3.84126 | 0.356652 | ||||||||
\(117\) | −7.51196 | −0.694481 | ||||||||
\(118\) | −5.69684 | −0.524436 | ||||||||
\(119\) | −6.47819 | −0.593855 | ||||||||
\(120\) | −5.88507 | −0.537231 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.18737 | 0.469642 | ||||||||
\(123\) | −26.7981 | −2.41630 | ||||||||
\(124\) | 1.19430 | 0.107251 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.29196 | 0.204184 | ||||||||
\(127\) | 10.4944 | 0.931227 | 0.465614 | − | 0.884988i | \(-0.345834\pi\) | ||||
0.465614 | + | 0.884988i | \(0.345834\pi\) | |||||||
\(128\) | 11.2546 | 0.994777 | ||||||||
\(129\) | 7.16261 | 0.630632 | ||||||||
\(130\) | 1.33358 | 0.116962 | ||||||||
\(131\) | 15.7193 | 1.37340 | 0.686702 | − | 0.726939i | \(-0.259058\pi\) | ||||
0.686702 | + | 0.726939i | \(0.259058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.61246 | −0.139818 | ||||||||
\(134\) | 0.503599 | 0.0435043 | ||||||||
\(135\) | −1.52295 | −0.131074 | ||||||||
\(136\) | 14.8477 | 1.27318 | ||||||||
\(137\) | 14.7184 | 1.25748 | 0.628738 | − | 0.777617i | \(-0.283572\pi\) | ||||
0.628738 | + | 0.777617i | \(0.283572\pi\) | |||||||
\(138\) | 1.52295 | 0.129642 | ||||||||
\(139\) | −2.58391 | −0.219165 | −0.109582 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109582 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(140\) | 1.59312 | 0.134643 | ||||||||
\(141\) | −1.03669 | −0.0873054 | ||||||||
\(142\) | 6.95638 | 0.583766 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.19543 | 0.516286 | ||||||||
\(145\) | −2.41116 | −0.200236 | ||||||||
\(146\) | 2.48406 | 0.205582 | ||||||||
\(147\) | −2.56771 | −0.211781 | ||||||||
\(148\) | −2.41157 | −0.198230 | ||||||||
\(149\) | 6.05082 | 0.495702 | 0.247851 | − | 0.968798i | \(-0.420276\pi\) | ||||
0.247851 | + | 0.968798i | \(0.420276\pi\) | |||||||
\(150\) | 1.63787 | 0.133732 | ||||||||
\(151\) | 12.8252 | 1.04370 | 0.521852 | − | 0.853036i | \(-0.325241\pi\) | ||||
0.521852 | + | 0.853036i | \(0.325241\pi\) | |||||||
\(152\) | 3.69570 | 0.299761 | ||||||||
\(153\) | 23.2769 | 1.88182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.749661 | −0.0602142 | ||||||||
\(156\) | −8.55214 | −0.684720 | ||||||||
\(157\) | −8.65836 | −0.691012 | −0.345506 | − | 0.938416i | \(-0.612293\pi\) | ||||
−0.345506 | + | 0.938416i | \(0.612293\pi\) | |||||||
\(158\) | 3.74360 | 0.297825 | ||||||||
\(159\) | −14.8784 | −1.17993 | ||||||||
\(160\) | −5.68377 | −0.449341 | ||||||||
\(161\) | −0.929832 | −0.0732810 | ||||||||
\(162\) | 4.38147 | 0.344241 | ||||||||
\(163\) | 18.2079 | 1.42615 | 0.713075 | − | 0.701088i | \(-0.247302\pi\) | ||||
0.713075 | + | 0.701088i | \(0.247302\pi\) | |||||||
\(164\) | −16.6267 | −1.29832 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.2607 | 0.873998 | ||||||||
\(167\) | −5.55536 | −0.429887 | −0.214943 | − | 0.976626i | \(-0.568957\pi\) | ||||
−0.214943 | + | 0.976626i | \(0.568957\pi\) | |||||||
\(168\) | 5.88507 | 0.454043 | ||||||||
\(169\) | −8.62916 | −0.663782 | ||||||||
\(170\) | −4.13227 | −0.316931 | ||||||||
\(171\) | 5.79377 | 0.443061 | ||||||||
\(172\) | 4.44399 | 0.338851 | ||||||||
\(173\) | 0.618526 | 0.0470256 | 0.0235128 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235128 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(174\) | −3.94918 | −0.299387 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.9321 | −1.72368 | ||||||||
\(178\) | −8.42623 | −0.631573 | ||||||||
\(179\) | 6.27083 | 0.468704 | 0.234352 | − | 0.972152i | \(-0.424703\pi\) | ||||
0.234352 | + | 0.972152i | \(0.424703\pi\) | |||||||
\(180\) | −5.72425 | −0.426660 | ||||||||
\(181\) | −18.6584 | −1.38687 | −0.693433 | − | 0.720522i | \(-0.743902\pi\) | ||||
−0.693433 | + | 0.720522i | \(0.743902\pi\) | |||||||
\(182\) | −1.33358 | −0.0988512 | ||||||||
\(183\) | 20.8813 | 1.54359 | ||||||||
\(184\) | 2.13113 | 0.157109 | ||||||||
\(185\) | 1.51375 | 0.111293 | ||||||||
\(186\) | −1.22785 | −0.0900303 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.643210 | −0.0469109 | ||||||||
\(189\) | 1.52295 | 0.110778 | ||||||||
\(190\) | −1.02855 | −0.0746189 | ||||||||
\(191\) | −1.96758 | −0.142369 | −0.0711847 | − | 0.997463i | \(-0.522678\pi\) | ||||
−0.0711847 | + | 0.997463i | \(0.522678\pi\) | |||||||
\(192\) | −0.454563 | −0.0328052 | ||||||||
\(193\) | −20.1246 | −1.44860 | −0.724301 | − | 0.689484i | \(-0.757837\pi\) | ||||
−0.724301 | + | 0.689484i | \(0.757837\pi\) | |||||||
\(194\) | 10.6259 | 0.762898 | ||||||||
\(195\) | 5.36819 | 0.384424 | ||||||||
\(196\) | −1.59312 | −0.113794 | ||||||||
\(197\) | 20.7981 | 1.48180 | 0.740900 | − | 0.671615i | \(-0.234399\pi\) | ||||
0.740900 | + | 0.671615i | \(0.234399\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.189373 | 0.0134243 | 0.00671214 | − | 0.999977i | \(-0.497863\pi\) | ||||
0.00671214 | + | 0.999977i | \(0.497863\pi\) | |||||||
\(200\) | 2.29196 | 0.162066 | ||||||||
\(201\) | 2.02719 | 0.142987 | ||||||||
\(202\) | −5.43857 | −0.382657 | ||||||||
\(203\) | 2.41116 | 0.169230 | ||||||||
\(204\) | 26.5000 | 1.85537 | ||||||||
\(205\) | 10.4366 | 0.728922 | ||||||||
\(206\) | 12.8835 | 0.897635 | ||||||||
\(207\) | 3.34099 | 0.232215 | ||||||||
\(208\) | −3.60481 | −0.249949 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.63787 | −0.113024 | ||||||||
\(211\) | 10.8547 | 0.747271 | 0.373636 | − | 0.927576i | \(-0.378111\pi\) | ||||
0.373636 | + | 0.927576i | \(0.378111\pi\) | |||||||
\(212\) | −9.23118 | −0.634000 | ||||||||
\(213\) | 28.0023 | 1.91868 | ||||||||
\(214\) | 4.67343 | 0.319469 | ||||||||
\(215\) | −2.78950 | −0.190242 | ||||||||
\(216\) | −3.49053 | −0.237501 | ||||||||
\(217\) | 0.749661 | 0.0508903 | ||||||||
\(218\) | −10.8160 | −0.732555 | ||||||||
\(219\) | 9.99935 | 0.675694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.5437 | −0.911045 | ||||||||
\(222\) | 2.47933 | 0.166402 | ||||||||
\(223\) | −12.5106 | −0.837772 | −0.418886 | − | 0.908039i | \(-0.637579\pi\) | ||||
−0.418886 | + | 0.908039i | \(0.637579\pi\) | |||||||
\(224\) | 5.68377 | 0.379763 | ||||||||
\(225\) | 3.59312 | 0.239541 | ||||||||
\(226\) | 4.17903 | 0.277985 | ||||||||
\(227\) | 24.3154 | 1.61387 | 0.806934 | − | 0.590642i | \(-0.201125\pi\) | ||||
0.806934 | + | 0.590642i | \(0.201125\pi\) | |||||||
\(228\) | 6.59604 | 0.436833 | ||||||||
\(229\) | −19.8619 | −1.31251 | −0.656257 | − | 0.754538i | \(-0.727861\pi\) | ||||
−0.656257 | + | 0.754538i | \(0.727861\pi\) | |||||||
\(230\) | −0.593116 | −0.0391089 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.52628 | −0.362818 | ||||||||
\(233\) | −2.32751 | −0.152481 | −0.0762403 | − | 0.997089i | \(-0.524292\pi\) | ||||
−0.0762403 | + | 0.997089i | \(0.524292\pi\) | |||||||
\(234\) | 4.79169 | 0.313243 | ||||||||
\(235\) | 0.403743 | 0.0263373 | ||||||||
\(236\) | −14.2281 | −0.926168 | ||||||||
\(237\) | 15.0695 | 0.978871 | ||||||||
\(238\) | 4.13227 | 0.267855 | ||||||||
\(239\) | 4.32164 | 0.279544 | 0.139772 | − | 0.990184i | \(-0.455363\pi\) | ||||
0.139772 | + | 0.990184i | \(0.455363\pi\) | |||||||
\(240\) | −4.42737 | −0.285786 | ||||||||
\(241\) | 29.5621 | 1.90426 | 0.952132 | − | 0.305686i | \(-0.0988858\pi\) | ||||
0.952132 | + | 0.305686i | \(0.0988858\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2061 | 1.42452 | ||||||||
\(244\) | 12.9557 | 0.829401 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 17.0938 | 1.08986 | ||||||||
\(247\) | −3.37111 | −0.214498 | ||||||||
\(248\) | −1.71819 | −0.109105 | ||||||||
\(249\) | 45.3288 | 2.87260 | ||||||||
\(250\) | −0.637875 | −0.0403427 | ||||||||
\(251\) | 7.48247 | 0.472289 | 0.236145 | − | 0.971718i | \(-0.424116\pi\) | ||||
0.236145 | + | 0.971718i | \(0.424116\pi\) | |||||||
\(252\) | 5.72425 | 0.360594 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.69411 | −0.420026 | ||||||||
\(255\) | −16.6341 | −1.04167 | ||||||||
\(256\) | −7.53310 | −0.470818 | ||||||||
\(257\) | −22.6669 | −1.41392 | −0.706962 | − | 0.707252i | \(-0.749935\pi\) | ||||
−0.706962 | + | 0.707252i | \(0.749935\pi\) | |||||||
\(258\) | −4.56884 | −0.284444 | ||||||||
\(259\) | −1.51375 | −0.0940596 | ||||||||
\(260\) | 3.33065 | 0.206558 | ||||||||
\(261\) | −8.66358 | −0.536262 | ||||||||
\(262\) | −10.0270 | −0.619468 | ||||||||
\(263\) | −5.45706 | −0.336497 | −0.168248 | − | 0.985745i | \(-0.553811\pi\) | ||||
−0.168248 | + | 0.985745i | \(0.553811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.79442 | 0.355948 | ||||||||
\(266\) | 1.02855 | 0.0630645 | ||||||||
\(267\) | −33.9190 | −2.07581 | ||||||||
\(268\) | 1.25776 | 0.0768298 | ||||||||
\(269\) | 17.2121 | 1.04944 | 0.524721 | − | 0.851274i | \(-0.324170\pi\) | ||||
0.524721 | + | 0.851274i | \(0.324170\pi\) | |||||||
\(270\) | 0.971450 | 0.0591205 | ||||||||
\(271\) | −12.2829 | −0.746136 | −0.373068 | − | 0.927804i | \(-0.621694\pi\) | ||||
−0.373068 | + | 0.927804i | \(0.621694\pi\) | |||||||
\(272\) | 11.1700 | 0.677282 | ||||||||
\(273\) | −5.36819 | −0.324897 | ||||||||
\(274\) | −9.38848 | −0.567179 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.80362 | 0.228951 | ||||||||
\(277\) | 18.1895 | 1.09290 | 0.546449 | − | 0.837492i | \(-0.315979\pi\) | ||||
0.546449 | + | 0.837492i | \(0.315979\pi\) | |||||||
\(278\) | 1.64821 | 0.0988533 | ||||||||
\(279\) | −2.69362 | −0.161263 | ||||||||
\(280\) | −2.29196 | −0.136971 | ||||||||
\(281\) | 8.03870 | 0.479548 | 0.239774 | − | 0.970829i | \(-0.422927\pi\) | ||||
0.239774 | + | 0.970829i | \(0.422927\pi\) | |||||||
\(282\) | 0.661281 | 0.0393787 | ||||||||
\(283\) | −13.3675 | −0.794618 | −0.397309 | − | 0.917685i | \(-0.630056\pi\) | ||||
−0.397309 | + | 0.917685i | \(0.630056\pi\) | |||||||
\(284\) | 17.3738 | 1.03095 | ||||||||
\(285\) | −4.14034 | −0.245252 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4366 | −0.616051 | ||||||||
\(288\) | −20.4224 | −1.20340 | ||||||||
\(289\) | 24.9669 | 1.46864 | ||||||||
\(290\) | 1.53802 | 0.0903156 | ||||||||
\(291\) | 42.7738 | 2.50744 | ||||||||
\(292\) | 6.20403 | 0.363063 | ||||||||
\(293\) | 29.6222 | 1.73054 | 0.865272 | − | 0.501302i | \(-0.167145\pi\) | ||||
0.865272 | + | 0.501302i | \(0.167145\pi\) | |||||||
\(294\) | 1.63787 | 0.0955228 | ||||||||
\(295\) | 8.93097 | 0.519981 | ||||||||
\(296\) | 3.46944 | 0.201657 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.85966 | −0.223584 | ||||||||
\(299\) | −1.94396 | −0.112422 | ||||||||
\(300\) | 4.09065 | 0.236174 | ||||||||
\(301\) | 2.78950 | 0.160784 | ||||||||
\(302\) | −8.18090 | −0.470758 | ||||||||
\(303\) | −21.8925 | −1.25769 | ||||||||
\(304\) | 2.78029 | 0.159461 | ||||||||
\(305\) | −8.13227 | −0.465653 | ||||||||
\(306\) | −14.8477 | −0.848788 | ||||||||
\(307\) | 33.1613 | 1.89262 | 0.946308 | − | 0.323266i | \(-0.104781\pi\) | ||||
0.946308 | + | 0.323266i | \(0.104781\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.8613 | 2.95029 | ||||||||
\(310\) | 0.478189 | 0.0271593 | ||||||||
\(311\) | 18.2303 | 1.03375 | 0.516874 | − | 0.856061i | \(-0.327096\pi\) | ||||
0.516874 | + | 0.856061i | \(0.327096\pi\) | |||||||
\(312\) | 12.3037 | 0.696557 | ||||||||
\(313\) | −1.66851 | −0.0943096 | −0.0471548 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471548 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(314\) | 5.52295 | 0.311678 | ||||||||
\(315\) | −3.59312 | −0.202449 | ||||||||
\(316\) | 9.34978 | 0.525966 | ||||||||
\(317\) | 25.9699 | 1.45861 | 0.729306 | − | 0.684187i | \(-0.239843\pi\) | ||||
0.729306 | + | 0.684187i | \(0.239843\pi\) | |||||||
\(318\) | 9.49053 | 0.532203 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.177031 | 0.00989631 | ||||||||
\(321\) | 18.8125 | 1.05001 | ||||||||
\(322\) | 0.593116 | 0.0330531 | ||||||||
\(323\) | 10.4459 | 0.581223 | ||||||||
\(324\) | 10.9429 | 0.607939 | ||||||||
\(325\) | −2.09065 | −0.115969 | ||||||||
\(326\) | −11.6143 | −0.643258 | ||||||||
\(327\) | −43.5390 | −2.40771 | ||||||||
\(328\) | 23.9202 | 1.32077 | ||||||||
\(329\) | −0.403743 | −0.0222591 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1053 | −1.05012 | −0.525060 | − | 0.851065i | \(-0.675957\pi\) | ||||
−0.525060 | + | 0.851065i | \(0.675957\pi\) | |||||||
\(332\) | 28.1240 | 1.54350 | ||||||||
\(333\) | 5.43907 | 0.298059 | ||||||||
\(334\) | 3.54363 | 0.193899 | ||||||||
\(335\) | −0.789495 | −0.0431347 | ||||||||
\(336\) | 4.42737 | 0.241533 | ||||||||
\(337\) | −13.2515 | −0.721854 | −0.360927 | − | 0.932594i | \(-0.617540\pi\) | ||||
−0.360927 | + | 0.932594i | \(0.617540\pi\) | |||||||
\(338\) | 5.50432 | 0.299396 | ||||||||
\(339\) | 16.8223 | 0.913663 | ||||||||
\(340\) | −10.3205 | −0.559708 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.69570 | −0.199841 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.39340 | −0.344709 | ||||||||
\(345\) | −2.38754 | −0.128541 | ||||||||
\(346\) | −0.394542 | −0.0212107 | ||||||||
\(347\) | −23.2839 | −1.24994 | −0.624972 | − | 0.780647i | \(-0.714890\pi\) | ||||
−0.624972 | + | 0.780647i | \(0.714890\pi\) | |||||||
\(348\) | −9.86323 | −0.528725 | ||||||||
\(349\) | 25.6464 | 1.37282 | 0.686411 | − | 0.727214i | \(-0.259185\pi\) | ||||
0.686411 | + | 0.727214i | \(0.259185\pi\) | |||||||
\(350\) | 0.637875 | 0.0340958 | ||||||||
\(351\) | 3.18396 | 0.169947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.17638 | −0.488410 | −0.244205 | − | 0.969724i | \(-0.578527\pi\) | ||||
−0.244205 | + | 0.969724i | \(0.578527\pi\) | |||||||
\(354\) | 14.6278 | 0.777459 | ||||||||
\(355\) | −10.9056 | −0.578807 | ||||||||
\(356\) | −21.0448 | −1.11537 | ||||||||
\(357\) | 16.6341 | 0.880369 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | 29.8203 | 1.57386 | 0.786928 | − | 0.617045i | \(-0.211670\pi\) | ||||
0.786928 | + | 0.617045i | \(0.211670\pi\) | |||||||
\(360\) | 8.23527 | 0.434037 | ||||||||
\(361\) | −16.4000 | −0.863156 | ||||||||
\(362\) | 11.9017 | 0.625539 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.33065 | −0.174574 | ||||||||
\(365\) | −3.89427 | −0.203836 | ||||||||
\(366\) | −13.3196 | −0.696229 | ||||||||
\(367\) | −6.51394 | −0.340025 | −0.170012 | − | 0.985442i | \(-0.554381\pi\) | ||||
−0.170012 | + | 0.985442i | \(0.554381\pi\) | |||||||
\(368\) | 1.60326 | 0.0835759 | ||||||||
\(369\) | 37.4998 | 1.95216 | ||||||||
\(370\) | −0.965580 | −0.0501981 | ||||||||
\(371\) | −5.79442 | −0.300831 | ||||||||
\(372\) | −3.06660 | −0.158996 | ||||||||
\(373\) | 19.0702 | 0.987416 | 0.493708 | − | 0.869628i | \(-0.335641\pi\) | ||||
0.493708 | + | 0.869628i | \(0.335641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.56771 | −0.132596 | ||||||||
\(376\) | 0.925362 | 0.0477219 | ||||||||
\(377\) | 5.04091 | 0.259620 | ||||||||
\(378\) | −0.971450 | −0.0499660 | ||||||||
\(379\) | 14.1305 | 0.725834 | 0.362917 | − | 0.931821i | \(-0.381781\pi\) | ||||
0.362917 | + | 0.931821i | \(0.381781\pi\) | |||||||
\(380\) | −2.56884 | −0.131779 | ||||||||
\(381\) | −26.9465 | −1.38051 | ||||||||
\(382\) | 1.25507 | 0.0642150 | ||||||||
\(383\) | −0.380117 | −0.0194231 | −0.00971153 | − | 0.999953i | \(-0.503091\pi\) | ||||
−0.00971153 | + | 0.999953i | \(0.503091\pi\) | |||||||
\(384\) | −28.8986 | −1.47472 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.8370 | 0.653385 | ||||||||
\(387\) | −10.0230 | −0.509497 | ||||||||
\(388\) | 26.5387 | 1.34730 | ||||||||
\(389\) | 17.1827 | 0.871196 | 0.435598 | − | 0.900141i | \(-0.356537\pi\) | ||||
0.435598 | + | 0.900141i | \(0.356537\pi\) | |||||||
\(390\) | −3.42423 | −0.173393 | ||||||||
\(391\) | 6.02363 | 0.304628 | ||||||||
\(392\) | 2.29196 | 0.115761 | ||||||||
\(393\) | −40.3626 | −2.03602 | ||||||||
\(394\) | −13.2665 | −0.668359 | ||||||||
\(395\) | −5.86887 | −0.295295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2049 | 0.512171 | 0.256086 | − | 0.966654i | \(-0.417567\pi\) | ||||
0.256086 | + | 0.966654i | \(0.417567\pi\) | |||||||
\(398\) | −0.120796 | −0.00605496 | ||||||||
\(399\) | 4.14034 | 0.207276 | ||||||||
\(400\) | 1.72425 | 0.0862125 | ||||||||
\(401\) | 16.6636 | 0.832140 | 0.416070 | − | 0.909333i | \(-0.363407\pi\) | ||||
0.416070 | + | 0.909333i | \(0.363407\pi\) | |||||||
\(402\) | −1.29309 | −0.0644937 | ||||||||
\(403\) | 1.56728 | 0.0780718 | ||||||||
\(404\) | −13.5830 | −0.675782 | ||||||||
\(405\) | −6.86887 | −0.341317 | ||||||||
\(406\) | −1.53802 | −0.0763306 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −38.1246 | −1.88745 | ||||||||
\(409\) | 25.1844 | 1.24529 | 0.622645 | − | 0.782504i | \(-0.286058\pi\) | ||||
0.622645 | + | 0.782504i | \(0.286058\pi\) | |||||||
\(410\) | −6.65722 | −0.328777 | ||||||||
\(411\) | −37.7925 | −1.86417 | ||||||||
\(412\) | 32.1770 | 1.58525 | ||||||||
\(413\) | −8.93097 | −0.439464 | ||||||||
\(414\) | −2.13113 | −0.104740 | ||||||||
\(415\) | −17.6534 | −0.866573 | ||||||||
\(416\) | 11.8828 | 0.582602 | ||||||||
\(417\) | 6.63473 | 0.324904 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.1916 | −1.76808 | −0.884039 | − | 0.467413i | \(-0.845186\pi\) | ||||
−0.884039 | + | 0.467413i | \(0.845186\pi\) | |||||||
\(420\) | −4.09065 | −0.199603 | ||||||||
\(421\) | −15.6327 | −0.761893 | −0.380946 | − | 0.924597i | \(-0.624402\pi\) | ||||
−0.380946 | + | 0.924597i | \(0.624402\pi\) | |||||||
\(422\) | −6.92396 | −0.337053 | ||||||||
\(423\) | 1.45070 | 0.0705353 | ||||||||
\(424\) | 13.2806 | 0.644961 | ||||||||
\(425\) | 6.47819 | 0.314238 | ||||||||
\(426\) | −17.8619 | −0.865414 | ||||||||
\(427\) | 8.13227 | 0.393548 | ||||||||
\(428\) | 11.6721 | 0.564191 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.77935 | 0.0858078 | ||||||||
\(431\) | −20.6525 | −0.994795 | −0.497398 | − | 0.867523i | \(-0.665711\pi\) | ||||
−0.497398 | + | 0.867523i | \(0.665711\pi\) | |||||||
\(432\) | −2.62594 | −0.126341 | ||||||||
\(433\) | −21.0158 | −1.00995 | −0.504976 | − | 0.863133i | \(-0.668499\pi\) | ||||
−0.504976 | + | 0.863133i | \(0.668499\pi\) | |||||||
\(434\) | −0.478189 | −0.0229538 | ||||||||
\(435\) | 6.19116 | 0.296843 | ||||||||
\(436\) | −27.0135 | −1.29371 | ||||||||
\(437\) | 1.49932 | 0.0717223 | ||||||||
\(438\) | −6.37833 | −0.304769 | ||||||||
\(439\) | 7.55642 | 0.360648 | 0.180324 | − | 0.983607i | \(-0.442285\pi\) | ||||
0.180324 | + | 0.983607i | \(0.442285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.59312 | 0.171101 | ||||||||
\(442\) | 8.63915 | 0.410923 | ||||||||
\(443\) | 28.8876 | 1.37249 | 0.686245 | − | 0.727371i | \(-0.259258\pi\) | ||||
0.686245 | + | 0.727371i | \(0.259258\pi\) | |||||||
\(444\) | 6.19221 | 0.293869 | ||||||||
\(445\) | 13.2099 | 0.626207 | ||||||||
\(446\) | 7.98020 | 0.377873 | ||||||||
\(447\) | −15.5367 | −0.734862 | ||||||||
\(448\) | −0.177031 | −0.00836391 | ||||||||
\(449\) | 30.5594 | 1.44219 | 0.721094 | − | 0.692837i | \(-0.243640\pi\) | ||||
0.721094 | + | 0.692837i | \(0.243640\pi\) | |||||||
\(450\) | −2.29196 | −0.108044 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.4373 | 0.490929 | ||||||||
\(453\) | −32.9315 | −1.54725 | ||||||||
\(454\) | −15.5102 | −0.727927 | ||||||||
\(455\) | 2.09065 | 0.0980114 | ||||||||
\(456\) | −9.48947 | −0.444385 | ||||||||
\(457\) | −14.2177 | −0.665076 | −0.332538 | − | 0.943090i | \(-0.607905\pi\) | ||||
−0.332538 | + | 0.943090i | \(0.607905\pi\) | |||||||
\(458\) | 12.6694 | 0.592003 | ||||||||
\(459\) | −9.86594 | −0.460503 | ||||||||
\(460\) | −1.48133 | −0.0690674 | ||||||||
\(461\) | 23.9831 | 1.11701 | 0.558503 | − | 0.829502i | \(-0.311376\pi\) | ||||
0.558503 | + | 0.829502i | \(0.311376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.3680 | 1.55074 | 0.775370 | − | 0.631507i | \(-0.217563\pi\) | ||||
0.775370 | + | 0.631507i | \(0.217563\pi\) | |||||||
\(464\) | −4.15745 | −0.193005 | ||||||||
\(465\) | 1.92491 | 0.0892655 | ||||||||
\(466\) | 1.48466 | 0.0687756 | ||||||||
\(467\) | −35.1440 | −1.62627 | −0.813136 | − | 0.582073i | \(-0.802242\pi\) | ||||
−0.813136 | + | 0.582073i | \(0.802242\pi\) | |||||||
\(468\) | 11.9674 | 0.553195 | ||||||||
\(469\) | 0.789495 | 0.0364555 | ||||||||
\(470\) | −0.257538 | −0.0118793 | ||||||||
\(471\) | 22.2321 | 1.02440 | ||||||||
\(472\) | 20.4694 | 0.942180 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −9.61246 | −0.441515 | ||||||||
\(475\) | 1.61246 | 0.0739850 | ||||||||
\(476\) | 10.3205 | 0.473040 | ||||||||
\(477\) | 20.8200 | 0.953283 | ||||||||
\(478\) | −2.75667 | −0.126087 | ||||||||
\(479\) | 12.4977 | 0.571036 | 0.285518 | − | 0.958373i | \(-0.407834\pi\) | ||||
0.285518 | + | 0.958373i | \(0.407834\pi\) | |||||||
\(480\) | 14.5943 | 0.666133 | ||||||||
\(481\) | −3.16472 | −0.144299 | ||||||||
\(482\) | −18.8569 | −0.858910 | ||||||||
\(483\) | 2.38754 | 0.108637 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.6584 | −0.756417 | ||||||||
\(486\) | −14.1647 | −0.642523 | ||||||||
\(487\) | 22.6577 | 1.02672 | 0.513360 | − | 0.858174i | \(-0.328401\pi\) | ||||
0.513360 | + | 0.858174i | \(0.328401\pi\) | |||||||
\(488\) | −18.6388 | −0.843740 | ||||||||
\(489\) | −46.7524 | −2.11422 | ||||||||
\(490\) | −0.637875 | −0.0288162 | ||||||||
\(491\) | −8.70104 | −0.392672 | −0.196336 | − | 0.980537i | \(-0.562904\pi\) | ||||
−0.196336 | + | 0.980537i | \(0.562904\pi\) | |||||||
\(492\) | 42.6924 | 1.92472 | ||||||||
\(493\) | −15.6200 | −0.703488 | ||||||||
\(494\) | 2.15034 | 0.0967485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.29260 | −0.0580396 | ||||||||
\(497\) | 10.9056 | 0.489181 | ||||||||
\(498\) | −28.9141 | −1.29567 | ||||||||
\(499\) | 15.3351 | 0.686494 | 0.343247 | − | 0.939245i | \(-0.388473\pi\) | ||||
0.343247 | + | 0.939245i | \(0.388473\pi\) | |||||||
\(500\) | −1.59312 | −0.0712463 | ||||||||
\(501\) | 14.2645 | 0.637293 | ||||||||
\(502\) | −4.77288 | −0.213024 | ||||||||
\(503\) | −15.4820 | −0.690307 | −0.345154 | − | 0.938546i | \(-0.612173\pi\) | ||||
−0.345154 | + | 0.938546i | \(0.612173\pi\) | |||||||
\(504\) | −8.23527 | −0.366828 | ||||||||
\(505\) | 8.52609 | 0.379406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.1572 | 0.984034 | ||||||||
\(508\) | −16.7188 | −0.741777 | ||||||||
\(509\) | 21.5587 | 0.955572 | 0.477786 | − | 0.878476i | \(-0.341439\pi\) | ||||
0.477786 | + | 0.878476i | \(0.341439\pi\) | |||||||
\(510\) | 10.6105 | 0.469839 | ||||||||
\(511\) | 3.89427 | 0.172273 | ||||||||
\(512\) | −17.7041 | −0.782417 | ||||||||
\(513\) | −2.45570 | −0.108422 | ||||||||
\(514\) | 14.4586 | 0.637744 | ||||||||
\(515\) | −20.1975 | −0.890009 | ||||||||
\(516\) | −11.4109 | −0.502335 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.965580 | 0.0424252 | ||||||||
\(519\) | −1.58819 | −0.0697139 | ||||||||
\(520\) | −4.79169 | −0.210130 | ||||||||
\(521\) | 1.43971 | 0.0630749 | 0.0315375 | − | 0.999503i | \(-0.489960\pi\) | ||||
0.0315375 | + | 0.999503i | \(0.489960\pi\) | |||||||
\(522\) | 5.52628 | 0.241879 | ||||||||
\(523\) | −45.0273 | −1.96890 | −0.984452 | − | 0.175652i | \(-0.943797\pi\) | ||||
−0.984452 | + | 0.175652i | \(0.943797\pi\) | |||||||
\(524\) | −25.0427 | −1.09400 | ||||||||
\(525\) | 2.56771 | 0.112064 | ||||||||
\(526\) | 3.48092 | 0.151775 | ||||||||
\(527\) | −4.85644 | −0.211550 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1354 | −0.962409 | ||||||||
\(530\) | −3.69611 | −0.160549 | ||||||||
\(531\) | 32.0900 | 1.39259 | ||||||||
\(532\) | 2.56884 | 0.111373 | ||||||||
\(533\) | −21.8193 | −0.945097 | ||||||||
\(534\) | 21.6361 | 0.936285 | ||||||||
\(535\) | −7.32657 | −0.316755 | ||||||||
\(536\) | −1.80949 | −0.0781581 | ||||||||
\(537\) | −16.1016 | −0.694837 | ||||||||
\(538\) | −10.9792 | −0.473346 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.42623 | 0.104408 | ||||||||
\(541\) | 19.9577 | 0.858050 | 0.429025 | − | 0.903293i | \(-0.358857\pi\) | ||||
0.429025 | + | 0.903293i | \(0.358857\pi\) | |||||||
\(542\) | 7.83498 | 0.336541 | ||||||||
\(543\) | 47.9092 | 2.05598 | ||||||||
\(544\) | −36.8205 | −1.57867 | ||||||||
\(545\) | 16.9564 | 0.726331 | ||||||||
\(546\) | 3.42423 | 0.146543 | ||||||||
\(547\) | −12.7180 | −0.543781 | −0.271891 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271891 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(548\) | −23.4481 | −1.00165 | ||||||||
\(549\) | −29.2202 | −1.24709 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.88791 | −0.165631 | ||||||||
\(552\) | −5.47213 | −0.232909 | ||||||||
\(553\) | 5.86887 | 0.249570 | ||||||||
\(554\) | −11.6026 | −0.492947 | ||||||||
\(555\) | −3.88686 | −0.164988 | ||||||||
\(556\) | 4.11648 | 0.174577 | ||||||||
\(557\) | 0.445281 | 0.0188672 | 0.00943359 | − | 0.999956i | \(-0.496997\pi\) | ||||
0.00943359 | + | 0.999956i | \(0.496997\pi\) | |||||||
\(558\) | 1.71819 | 0.0727368 | ||||||||
\(559\) | 5.83187 | 0.246662 | ||||||||
\(560\) | −1.72425 | −0.0728629 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.12768 | −0.216298 | ||||||||
\(563\) | 13.2186 | 0.557100 | 0.278550 | − | 0.960422i | \(-0.410146\pi\) | ||||
0.278550 | + | 0.960422i | \(0.410146\pi\) | |||||||
\(564\) | 1.65157 | 0.0695438 | ||||||||
\(565\) | −6.55150 | −0.275624 | ||||||||
\(566\) | 8.52681 | 0.358409 | ||||||||
\(567\) | 6.86887 | 0.288465 | ||||||||
\(568\) | −24.9951 | −1.04877 | ||||||||
\(569\) | 32.9020 | 1.37932 | 0.689662 | − | 0.724132i | \(-0.257759\pi\) | ||||
0.689662 | + | 0.724132i | \(0.257759\pi\) | |||||||
\(570\) | 2.64102 | 0.110620 | ||||||||
\(571\) | 8.04097 | 0.336504 | 0.168252 | − | 0.985744i | \(-0.446188\pi\) | ||||
0.168252 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.05218 | 0.211058 | ||||||||
\(574\) | 6.65722 | 0.277867 | ||||||||
\(575\) | 0.929832 | 0.0387767 | ||||||||
\(576\) | 0.636092 | 0.0265038 | ||||||||
\(577\) | 36.6548 | 1.52596 | 0.762980 | − | 0.646423i | \(-0.223736\pi\) | ||||
0.762980 | + | 0.646423i | \(0.223736\pi\) | |||||||
\(578\) | −15.9258 | −0.662425 | ||||||||
\(579\) | 51.6741 | 2.14750 | ||||||||
\(580\) | 3.84126 | 0.159500 | ||||||||
\(581\) | 17.6534 | 0.732388 | ||||||||
\(582\) | −27.2843 | −1.13097 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.92551 | −0.369340 | ||||||||
\(585\) | −7.51196 | −0.310581 | ||||||||
\(586\) | −18.8952 | −0.780554 | ||||||||
\(587\) | −8.45979 | −0.349173 | −0.174586 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174586 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(588\) | 4.09065 | 0.168696 | ||||||||
\(589\) | −1.20880 | −0.0498078 | ||||||||
\(590\) | −5.69684 | −0.234535 | ||||||||
\(591\) | −53.4033 | −2.19672 | ||||||||
\(592\) | 2.61008 | 0.107274 | ||||||||
\(593\) | −23.3601 | −0.959285 | −0.479643 | − | 0.877464i | \(-0.659234\pi\) | ||||
−0.479643 | + | 0.877464i | \(0.659234\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.47819 | −0.265580 | ||||||||
\(596\) | −9.63966 | −0.394856 | ||||||||
\(597\) | −0.486254 | −0.0199010 | ||||||||
\(598\) | 1.24000 | 0.0507074 | ||||||||
\(599\) | −5.52401 | −0.225705 | −0.112852 | − | 0.993612i | \(-0.535999\pi\) | ||||
−0.112852 | + | 0.993612i | \(0.535999\pi\) | |||||||
\(600\) | −5.88507 | −0.240257 | ||||||||
\(601\) | −33.2675 | −1.35701 | −0.678504 | − | 0.734597i | \(-0.737371\pi\) | ||||
−0.678504 | + | 0.734597i | \(0.737371\pi\) | |||||||
\(602\) | −1.77935 | −0.0725208 | ||||||||
\(603\) | −2.83675 | −0.115521 | ||||||||
\(604\) | −20.4321 | −0.831370 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.9647 | 0.567276 | ||||||||
\(607\) | −15.0511 | −0.610906 | −0.305453 | − | 0.952207i | \(-0.598808\pi\) | ||||
−0.305453 | + | 0.952207i | \(0.598808\pi\) | |||||||
\(608\) | −9.16488 | −0.371685 | ||||||||
\(609\) | −6.19116 | −0.250878 | ||||||||
\(610\) | 5.18737 | 0.210030 | ||||||||
\(611\) | −0.844088 | −0.0341481 | ||||||||
\(612\) | −37.0828 | −1.49898 | ||||||||
\(613\) | 30.7859 | 1.24343 | 0.621716 | − | 0.783243i | \(-0.286436\pi\) | ||||
0.621716 | + | 0.783243i | \(0.286436\pi\) | |||||||
\(614\) | −21.1528 | −0.853656 | ||||||||
\(615\) | −26.7981 | −1.08060 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.31442 | −0.133433 | −0.0667167 | − | 0.997772i | \(-0.521252\pi\) | ||||
−0.0667167 | + | 0.997772i | \(0.521252\pi\) | |||||||
\(618\) | −33.0810 | −1.33071 | ||||||||
\(619\) | 13.8215 | 0.555531 | 0.277766 | − | 0.960649i | \(-0.410406\pi\) | ||||
0.277766 | + | 0.960649i | \(0.410406\pi\) | |||||||
\(620\) | 1.19430 | 0.0479641 | ||||||||
\(621\) | −1.41609 | −0.0568256 | ||||||||
\(622\) | −11.6287 | −0.466267 | ||||||||
\(623\) | −13.2099 | −0.529242 | ||||||||
\(624\) | 9.25610 | 0.370541 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.06430 | 0.0425379 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.7938 | 0.550431 | ||||||||
\(629\) | 9.80634 | 0.391004 | ||||||||
\(630\) | 2.29196 | 0.0913138 | ||||||||
\(631\) | 29.6806 | 1.18157 | 0.590784 | − | 0.806830i | \(-0.298819\pi\) | ||||
0.590784 | + | 0.806830i | \(0.298819\pi\) | |||||||
\(632\) | −13.4512 | −0.535060 | ||||||||
\(633\) | −27.8718 | −1.10780 | ||||||||
\(634\) | −16.5655 | −0.657901 | ||||||||
\(635\) | 10.4944 | 0.416457 | ||||||||
\(636\) | 23.7030 | 0.939884 | ||||||||
\(637\) | −2.09065 | −0.0828347 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −39.1849 | −1.55013 | ||||||||
\(640\) | 11.2546 | 0.444878 | ||||||||
\(641\) | −45.7358 | −1.80646 | −0.903228 | − | 0.429162i | \(-0.858809\pi\) | ||||
−0.903228 | + | 0.429162i | \(0.858809\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | −11.4658 | −0.452166 | −0.226083 | − | 0.974108i | \(-0.572592\pi\) | ||||
−0.226083 | + | 0.974108i | \(0.572592\pi\) | |||||||
\(644\) | 1.48133 | 0.0583726 | ||||||||
\(645\) | 7.16261 | 0.282027 | ||||||||
\(646\) | −6.66314 | −0.262158 | ||||||||
\(647\) | −31.5824 | −1.24163 | −0.620816 | − | 0.783956i | \(-0.713199\pi\) | ||||
−0.620816 | + | 0.783956i | \(0.713199\pi\) | |||||||
\(648\) | −15.7431 | −0.618449 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.33358 | 0.0523071 | ||||||||
\(651\) | −1.92491 | −0.0754431 | ||||||||
\(652\) | −29.0072 | −1.13601 | ||||||||
\(653\) | 3.60724 | 0.141162 | 0.0705811 | − | 0.997506i | \(-0.477515\pi\) | ||||
0.0705811 | + | 0.997506i | \(0.477515\pi\) | |||||||
\(654\) | 27.7724 | 1.08599 | ||||||||
\(655\) | 15.7193 | 0.614205 | ||||||||
\(656\) | 17.9953 | 0.702597 | ||||||||
\(657\) | −13.9926 | −0.545903 | ||||||||
\(658\) | 0.257538 | 0.0100399 | ||||||||
\(659\) | −19.0672 | −0.742753 | −0.371377 | − | 0.928482i | \(-0.621114\pi\) | ||||
−0.371377 | + | 0.928482i | \(0.621114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.139279 | 0.00541732 | 0.00270866 | − | 0.999996i | \(-0.499138\pi\) | ||||
0.00270866 | + | 0.999996i | \(0.499138\pi\) | |||||||
\(662\) | 12.1868 | 0.473652 | ||||||||
\(663\) | 34.7761 | 1.35059 | ||||||||
\(664\) | −40.4609 | −1.57019 | ||||||||
\(665\) | −1.61246 | −0.0625287 | ||||||||
\(666\) | −3.46944 | −0.134438 | ||||||||
\(667\) | −2.24198 | −0.0868096 | ||||||||
\(668\) | 8.85034 | 0.342430 | ||||||||
\(669\) | 32.1236 | 1.24197 | ||||||||
\(670\) | 0.503599 | 0.0194557 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −14.5943 | −0.562986 | ||||||||
\(673\) | 30.8673 | 1.18985 | 0.594923 | − | 0.803783i | \(-0.297183\pi\) | ||||
0.594923 | + | 0.803783i | \(0.297183\pi\) | |||||||
\(674\) | 8.45278 | 0.325589 | ||||||||
\(675\) | −1.52295 | −0.0586183 | ||||||||
\(676\) | 13.7473 | 0.528741 | ||||||||
\(677\) | 20.0624 | 0.771061 | 0.385530 | − | 0.922695i | \(-0.374018\pi\) | ||||
0.385530 | + | 0.922695i | \(0.374018\pi\) | |||||||
\(678\) | −10.7305 | −0.412104 | ||||||||
\(679\) | 16.6584 | 0.639289 | ||||||||
\(680\) | 14.8477 | 0.569385 | ||||||||
\(681\) | −62.4347 | −2.39250 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.1013 | −1.49617 | −0.748085 | − | 0.663603i | \(-0.769026\pi\) | ||||
−0.748085 | + | 0.663603i | \(0.769026\pi\) | |||||||
\(684\) | −9.23015 | −0.352924 | ||||||||
\(685\) | 14.7184 | 0.562360 | ||||||||
\(686\) | 0.637875 | 0.0243542 | ||||||||
\(687\) | 50.9996 | 1.94576 | ||||||||
\(688\) | −4.80979 | −0.183372 | ||||||||
\(689\) | −12.1141 | −0.461511 | ||||||||
\(690\) | 1.52295 | 0.0579776 | ||||||||
\(691\) | −47.0562 | −1.79010 | −0.895052 | − | 0.445962i | \(-0.852862\pi\) | ||||
−0.895052 | + | 0.445962i | \(0.852862\pi\) | |||||||
\(692\) | −0.985383 | −0.0374587 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.8522 | 0.563782 | ||||||||
\(695\) | −2.58391 | −0.0980135 | ||||||||
\(696\) | 14.1899 | 0.537865 | ||||||||
\(697\) | 67.6101 | 2.56091 | ||||||||
\(698\) | −16.3592 | −0.619205 | ||||||||
\(699\) | 5.97637 | 0.226047 | ||||||||
\(700\) | 1.59312 | 0.0602141 | ||||||||
\(701\) | 12.7715 | 0.482373 | 0.241187 | − | 0.970479i | \(-0.422463\pi\) | ||||
0.241187 | + | 0.970479i | \(0.422463\pi\) | |||||||
\(702\) | −2.03097 | −0.0766539 | ||||||||
\(703\) | 2.44086 | 0.0920589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.03669 | −0.0390442 | ||||||||
\(706\) | 5.85338 | 0.220295 | ||||||||
\(707\) | −8.52609 | −0.320657 | ||||||||
\(708\) | 36.5335 | 1.37301 | ||||||||
\(709\) | −14.2137 | −0.533808 | −0.266904 | − | 0.963723i | \(-0.586001\pi\) | ||||
−0.266904 | + | 0.963723i | \(0.586001\pi\) | |||||||
\(710\) | 6.95638 | 0.261068 | ||||||||
\(711\) | −21.0875 | −0.790844 | ||||||||
\(712\) | 30.2764 | 1.13466 | ||||||||
\(713\) | −0.697058 | −0.0261050 | ||||||||
\(714\) | −10.6105 | −0.397087 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.99015 | −0.373350 | ||||||||
\(717\) | −11.0967 | −0.414414 | ||||||||
\(718\) | −19.0216 | −0.709881 | ||||||||
\(719\) | −6.32971 | −0.236058 | −0.118029 | − | 0.993010i | \(-0.537658\pi\) | ||||
−0.118029 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(720\) | 6.19543 | 0.230890 | ||||||||
\(721\) | 20.1975 | 0.752195 | ||||||||
\(722\) | 10.4611 | 0.389322 | ||||||||
\(723\) | −75.9069 | −2.82301 | ||||||||
\(724\) | 29.7249 | 1.10472 | ||||||||
\(725\) | −2.41116 | −0.0895483 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.5329 | 1.02114 | 0.510569 | − | 0.859837i | \(-0.329435\pi\) | ||||
0.510569 | + | 0.859837i | \(0.329435\pi\) | |||||||
\(728\) | 4.79169 | 0.177592 | ||||||||
\(729\) | −36.4121 | −1.34860 | ||||||||
\(730\) | 2.48406 | 0.0919391 | ||||||||
\(731\) | −18.0709 | −0.668376 | ||||||||
\(732\) | −33.2663 | −1.22956 | ||||||||
\(733\) | −23.4494 | −0.866124 | −0.433062 | − | 0.901364i | \(-0.642567\pi\) | ||||
−0.433062 | + | 0.901364i | \(0.642567\pi\) | |||||||
\(734\) | 4.15508 | 0.153367 | ||||||||
\(735\) | −2.56771 | −0.0947113 | ||||||||
\(736\) | −5.28495 | −0.194806 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −23.9202 | −0.880514 | ||||||||
\(739\) | 5.55014 | 0.204165 | 0.102083 | − | 0.994776i | \(-0.467449\pi\) | ||||
0.102083 | + | 0.994776i | \(0.467449\pi\) | |||||||
\(740\) | −2.41157 | −0.0886512 | ||||||||
\(741\) | 8.65601 | 0.317987 | ||||||||
\(742\) | 3.69611 | 0.135689 | ||||||||
\(743\) | −46.9974 | −1.72417 | −0.862083 | − | 0.506767i | \(-0.830840\pi\) | ||||
−0.862083 | + | 0.506767i | \(0.830840\pi\) | |||||||
\(744\) | 4.41181 | 0.161745 | ||||||||
\(745\) | 6.05082 | 0.221685 | ||||||||
\(746\) | −12.1644 | −0.445369 | ||||||||
\(747\) | −63.4308 | −2.32081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.32657 | 0.267707 | ||||||||
\(750\) | 1.63787 | 0.0598067 | ||||||||
\(751\) | 47.1787 | 1.72157 | 0.860787 | − | 0.508966i | \(-0.169972\pi\) | ||||
0.860787 | + | 0.508966i | \(0.169972\pi\) | |||||||
\(752\) | 0.696155 | 0.0253862 | ||||||||
\(753\) | −19.2128 | −0.700153 | ||||||||
\(754\) | −3.21547 | −0.117100 | ||||||||
\(755\) | 12.8252 | 0.466758 | ||||||||
\(756\) | −2.42623 | −0.0882412 | ||||||||
\(757\) | 48.2852 | 1.75496 | 0.877478 | − | 0.479617i | \(-0.159224\pi\) | ||||
0.877478 | + | 0.479617i | \(0.159224\pi\) | |||||||
\(758\) | −9.01348 | −0.327384 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.69570 | 0.134057 | ||||||||
\(761\) | 42.2057 | 1.52995 | 0.764977 | − | 0.644058i | \(-0.222750\pi\) | ||||
0.764977 | + | 0.644058i | \(0.222750\pi\) | |||||||
\(762\) | 17.1885 | 0.622674 | ||||||||
\(763\) | −16.9564 | −0.613862 | ||||||||
\(764\) | 3.13459 | 0.113405 | ||||||||
\(765\) | 23.2769 | 0.841578 | ||||||||
\(766\) | 0.242467 | 0.00876068 | ||||||||
\(767\) | −18.6716 | −0.674191 | ||||||||
\(768\) | 19.3428 | 0.697972 | ||||||||
\(769\) | −24.6277 | −0.888099 | −0.444049 | − | 0.896002i | \(-0.646458\pi\) | ||||
−0.444049 | + | 0.896002i | \(0.646458\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 58.2020 | 2.09609 | ||||||||
\(772\) | 32.0609 | 1.15390 | ||||||||
\(773\) | −44.9737 | −1.61759 | −0.808796 | − | 0.588089i | \(-0.799880\pi\) | ||||
−0.808796 | + | 0.588089i | \(0.799880\pi\) | |||||||
\(774\) | 6.39340 | 0.229806 | ||||||||
\(775\) | −0.749661 | −0.0269286 | ||||||||
\(776\) | −38.1803 | −1.37059 | ||||||||
\(777\) | 3.88686 | 0.139440 | ||||||||
\(778\) | −10.9604 | −0.392949 | ||||||||
\(779\) | 16.8286 | 0.602947 | ||||||||
\(780\) | −8.55214 | −0.306216 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.84232 | −0.137401 | ||||||||
\(783\) | 3.67207 | 0.131229 | ||||||||
\(784\) | 1.72425 | 0.0615804 | ||||||||
\(785\) | −8.65836 | −0.309030 | ||||||||
\(786\) | 25.7463 | 0.918340 | ||||||||
\(787\) | 1.51416 | 0.0539739 | 0.0269870 | − | 0.999636i | \(-0.491409\pi\) | ||||
0.0269870 | + | 0.999636i | \(0.491409\pi\) | |||||||
\(788\) | −33.1337 | −1.18034 | ||||||||
\(789\) | 14.0121 | 0.498845 | ||||||||
\(790\) | 3.74360 | 0.133191 | ||||||||
\(791\) | 6.55150 | 0.232944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0018 | 0.603751 | ||||||||
\(794\) | −6.50947 | −0.231012 | ||||||||
\(795\) | −14.8784 | −0.527681 | ||||||||
\(796\) | −0.301693 | −0.0106932 | ||||||||
\(797\) | 31.3462 | 1.11034 | 0.555169 | − | 0.831737i | \(-0.312653\pi\) | ||||
0.555169 | + | 0.831737i | \(0.312653\pi\) | |||||||
\(798\) | −2.64102 | −0.0934909 | ||||||||
\(799\) | 2.61553 | 0.0925306 | ||||||||
\(800\) | −5.68377 | −0.200952 | ||||||||
\(801\) | 47.4646 | 1.67708 | ||||||||
\(802\) | −10.6293 | −0.375333 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.22955 | −0.113898 | ||||||||
\(805\) | −0.929832 | −0.0327723 | ||||||||
\(806\) | −0.999729 | −0.0352139 | ||||||||
\(807\) | −44.1957 | −1.55576 | ||||||||
\(808\) | 19.5414 | 0.687465 | ||||||||
\(809\) | −9.70948 | −0.341367 | −0.170684 | − | 0.985326i | \(-0.554598\pi\) | ||||
−0.170684 | + | 0.985326i | \(0.554598\pi\) | |||||||
\(810\) | 4.38147 | 0.153949 | ||||||||
\(811\) | 23.3079 | 0.818452 | 0.409226 | − | 0.912433i | \(-0.365799\pi\) | ||||
0.409226 | + | 0.912433i | \(0.365799\pi\) | |||||||
\(812\) | −3.84126 | −0.134802 | ||||||||
\(813\) | 31.5390 | 1.10612 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.2079 | 0.637793 | ||||||||
\(816\) | −28.6813 | −1.00405 | ||||||||
\(817\) | −4.49796 | −0.157364 | ||||||||
\(818\) | −16.0645 | −0.561683 | ||||||||
\(819\) | 7.51196 | 0.262489 | ||||||||
\(820\) | −16.6267 | −0.580628 | ||||||||
\(821\) | 3.74985 | 0.130871 | 0.0654354 | − | 0.997857i | \(-0.479156\pi\) | ||||
0.0654354 | + | 0.997857i | \(0.479156\pi\) | |||||||
\(822\) | 24.1069 | 0.840823 | ||||||||
\(823\) | −31.1092 | −1.08440 | −0.542200 | − | 0.840249i | \(-0.682409\pi\) | ||||
−0.542200 | + | 0.840249i | \(0.682409\pi\) | |||||||
\(824\) | −46.2918 | −1.61265 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.69684 | 0.198218 | ||||||||
\(827\) | −15.3613 | −0.534164 | −0.267082 | − | 0.963674i | \(-0.586060\pi\) | ||||
−0.267082 | + | 0.963674i | \(0.586060\pi\) | |||||||
\(828\) | −5.32259 | −0.184973 | ||||||||
\(829\) | −5.22493 | −0.181469 | −0.0907347 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907347 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(830\) | 11.2607 | 0.390864 | ||||||||
\(831\) | −46.7052 | −1.62018 | ||||||||
\(832\) | −0.370110 | −0.0128313 | ||||||||
\(833\) | 6.47819 | 0.224456 | ||||||||
\(834\) | −4.23213 | −0.146547 | ||||||||
\(835\) | −5.55536 | −0.192251 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14169 | 0.0394627 | ||||||||
\(838\) | 23.0857 | 0.797483 | ||||||||
\(839\) | −52.4526 | −1.81087 | −0.905433 | − | 0.424489i | \(-0.860454\pi\) | ||||
−0.905433 | + | 0.424489i | \(0.860454\pi\) | |||||||
\(840\) | 5.88507 | 0.203054 | ||||||||
\(841\) | −23.1863 | −0.799528 | ||||||||
\(842\) | 9.97172 | 0.343648 | ||||||||
\(843\) | −20.6410 | −0.710914 | ||||||||
\(844\) | −17.2929 | −0.595245 | ||||||||
\(845\) | −8.62916 | −0.296852 | ||||||||
\(846\) | −0.925362 | −0.0318146 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.99103 | 0.343093 | ||||||||
\(849\) | 34.3239 | 1.17799 | ||||||||
\(850\) | −4.13227 | −0.141736 | ||||||||
\(851\) | 1.40753 | 0.0482495 | ||||||||
\(852\) | −44.6109 | −1.52834 | ||||||||
\(853\) | 35.1937 | 1.20501 | 0.602504 | − | 0.798116i | \(-0.294170\pi\) | ||||
0.602504 | + | 0.798116i | \(0.294170\pi\) | |||||||
\(854\) | −5.18737 | −0.177508 | ||||||||
\(855\) | 5.79377 | 0.198143 | ||||||||
\(856\) | −16.7922 | −0.573945 | ||||||||
\(857\) | −54.5011 | −1.86172 | −0.930862 | − | 0.365372i | \(-0.880942\pi\) | ||||
−0.930862 | + | 0.365372i | \(0.880942\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.5923 | 0.395523 | 0.197762 | − | 0.980250i | \(-0.436633\pi\) | ||||
0.197762 | + | 0.980250i | \(0.436633\pi\) | |||||||
\(860\) | 4.44399 | 0.151539 | ||||||||
\(861\) | 26.7981 | 0.913275 | ||||||||
\(862\) | 13.1737 | 0.448698 | ||||||||
\(863\) | 26.6514 | 0.907225 | 0.453613 | − | 0.891199i | \(-0.350135\pi\) | ||||
0.453613 | + | 0.891199i | \(0.350135\pi\) | |||||||
\(864\) | 8.65609 | 0.294486 | ||||||||
\(865\) | 0.618526 | 0.0210305 | ||||||||
\(866\) | 13.4054 | 0.455535 | ||||||||
\(867\) | −64.1078 | −2.17721 | ||||||||
\(868\) | −1.19430 | −0.0405371 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.94918 | −0.133890 | ||||||||
\(871\) | 1.65056 | 0.0559272 | ||||||||
\(872\) | 38.8633 | 1.31608 | ||||||||
\(873\) | −59.8554 | −2.02580 | ||||||||
\(874\) | −0.956379 | −0.0323500 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −15.9301 | −0.538229 | ||||||||
\(877\) | 12.0449 | 0.406729 | 0.203365 | − | 0.979103i | \(-0.434812\pi\) | ||||
0.203365 | + | 0.979103i | \(0.434812\pi\) | |||||||
\(878\) | −4.82005 | −0.162669 | ||||||||
\(879\) | −76.0610 | −2.56547 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.11314 | −0.205957 | −0.102979 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102979 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(882\) | −2.29196 | −0.0771742 | ||||||||
\(883\) | 11.5321 | 0.388088 | 0.194044 | − | 0.980993i | \(-0.437840\pi\) | ||||
0.194044 | + | 0.980993i | \(0.437840\pi\) | |||||||
\(884\) | 21.5766 | 0.725700 | ||||||||
\(885\) | −22.9321 | −0.770854 | ||||||||
\(886\) | −18.4266 | −0.619055 | ||||||||
\(887\) | 19.6325 | 0.659196 | 0.329598 | − | 0.944121i | \(-0.393087\pi\) | ||||
0.329598 | + | 0.944121i | \(0.393087\pi\) | |||||||
\(888\) | −8.90851 | −0.298950 | ||||||||
\(889\) | −10.4944 | −0.351971 | ||||||||
\(890\) | −8.42623 | −0.282448 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.9308 | 0.667334 | ||||||||
\(893\) | 0.651022 | 0.0217856 | ||||||||
\(894\) | 9.91048 | 0.331456 | ||||||||
\(895\) | 6.27083 | 0.209611 | ||||||||
\(896\) | −11.2546 | −0.375990 | ||||||||
\(897\) | 4.99151 | 0.166662 | ||||||||
\(898\) | −19.4931 | −0.650492 | ||||||||
\(899\) | 1.80755 | 0.0602853 | ||||||||
\(900\) | −5.72425 | −0.190808 | ||||||||
\(901\) | 37.5373 | 1.25055 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.16261 | −0.238357 | ||||||||
\(904\) | −15.0158 | −0.499417 | ||||||||
\(905\) | −18.6584 | −0.620225 | ||||||||
\(906\) | 21.0061 | 0.697882 | ||||||||
\(907\) | −30.3586 | −1.00804 | −0.504021 | − | 0.863691i | \(-0.668147\pi\) | ||||
−0.504021 | + | 0.863691i | \(0.668147\pi\) | |||||||
\(908\) | −38.7372 | −1.28554 | ||||||||
\(909\) | 30.6352 | 1.01611 | ||||||||
\(910\) | −1.33358 | −0.0442076 | ||||||||
\(911\) | 14.7391 | 0.488328 | 0.244164 | − | 0.969734i | \(-0.421487\pi\) | ||||
0.244164 | + | 0.969734i | \(0.421487\pi\) | |||||||
\(912\) | −7.13898 | −0.236395 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.06911 | 0.299980 | ||||||||
\(915\) | 20.8813 | 0.690314 | ||||||||
\(916\) | 31.6424 | 1.04549 | ||||||||
\(917\) | −15.7193 | −0.519098 | ||||||||
\(918\) | 6.29324 | 0.207708 | ||||||||
\(919\) | −4.78135 | −0.157722 | −0.0788611 | − | 0.996886i | \(-0.525128\pi\) | ||||
−0.0788611 | + | 0.996886i | \(0.525128\pi\) | |||||||
\(920\) | 2.13113 | 0.0702614 | ||||||||
\(921\) | −85.1485 | −2.80574 | ||||||||
\(922\) | −15.2982 | −0.503821 | ||||||||
\(923\) | 22.7998 | 0.750463 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.51375 | 0.0497717 | ||||||||
\(926\) | −21.2846 | −0.699454 | ||||||||
\(927\) | −72.5720 | −2.38358 | ||||||||
\(928\) | 13.7045 | 0.449872 | ||||||||
\(929\) | 1.68714 | 0.0553534 | 0.0276767 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276767 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(930\) | −1.22785 | −0.0402628 | ||||||||
\(931\) | 1.61246 | 0.0528464 | ||||||||
\(932\) | 3.70800 | 0.121460 | ||||||||
\(933\) | −46.8102 | −1.53250 | ||||||||
\(934\) | 22.4175 | 0.733523 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −17.2171 | −0.562758 | ||||||||
\(937\) | 22.1923 | 0.724991 | 0.362495 | − | 0.931986i | \(-0.381925\pi\) | ||||
0.362495 | + | 0.931986i | \(0.381925\pi\) | |||||||
\(938\) | −0.503599 | −0.0164431 | ||||||||
\(939\) | 4.28424 | 0.139811 | ||||||||
\(940\) | −0.643210 | −0.0209792 | ||||||||
\(941\) | 15.0418 | 0.490350 | 0.245175 | − | 0.969479i | \(-0.421155\pi\) | ||||
0.245175 | + | 0.969479i | \(0.421155\pi\) | |||||||
\(942\) | −14.1813 | −0.462052 | ||||||||
\(943\) | 9.70426 | 0.316014 | ||||||||
\(944\) | 15.3992 | 0.501202 | ||||||||
\(945\) | 1.52295 | 0.0495415 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7171 | 0.348259 | 0.174129 | − | 0.984723i | \(-0.444289\pi\) | ||||
0.174129 | + | 0.984723i | \(0.444289\pi\) | |||||||
\(948\) | −24.0075 | −0.779727 | ||||||||
\(949\) | 8.14158 | 0.264287 | ||||||||
\(950\) | −1.02855 | −0.0333706 | ||||||||
\(951\) | −66.6830 | −2.16234 | ||||||||
\(952\) | −14.8477 | −0.481218 | ||||||||
\(953\) | −31.2924 | −1.01366 | −0.506831 | − | 0.862045i | \(-0.669183\pi\) | ||||
−0.506831 | + | 0.862045i | \(0.669183\pi\) | |||||||
\(954\) | −13.2806 | −0.429974 | ||||||||
\(955\) | −1.96758 | −0.0636695 | ||||||||
\(956\) | −6.88488 | −0.222673 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.97198 | −0.257563 | ||||||||
\(959\) | −14.7184 | −0.475281 | ||||||||
\(960\) | −0.454563 | −0.0146709 | ||||||||
\(961\) | −30.4380 | −0.981871 | ||||||||
\(962\) | 2.01869 | 0.0650853 | ||||||||
\(963\) | −26.3252 | −0.848318 | ||||||||
\(964\) | −47.0959 | −1.51686 | ||||||||
\(965\) | −20.1246 | −0.647834 | ||||||||
\(966\) | −1.52295 | −0.0490000 | ||||||||
\(967\) | 30.8263 | 0.991307 | 0.495654 | − | 0.868520i | \(-0.334929\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.8219 | −0.861643 | ||||||||
\(970\) | 10.6259 | 0.341179 | ||||||||
\(971\) | −27.1359 | −0.870833 | −0.435416 | − | 0.900229i | \(-0.643399\pi\) | ||||
−0.435416 | + | 0.900229i | \(0.643399\pi\) | |||||||
\(972\) | −35.3769 | −1.13471 | ||||||||
\(973\) | 2.58391 | 0.0828365 | ||||||||
\(974\) | −14.4528 | −0.463097 | ||||||||
\(975\) | 5.36819 | 0.171920 | ||||||||
\(976\) | −14.0221 | −0.448836 | ||||||||
\(977\) | 42.5686 | 1.36189 | 0.680945 | − | 0.732334i | \(-0.261569\pi\) | ||||
0.680945 | + | 0.732334i | \(0.261569\pi\) | |||||||
\(978\) | 29.8222 | 0.953608 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.59312 | −0.0508902 | ||||||||
\(981\) | 60.9262 | 1.94523 | ||||||||
\(982\) | 5.55017 | 0.177113 | ||||||||
\(983\) | 42.1199 | 1.34342 | 0.671708 | − | 0.740816i | \(-0.265561\pi\) | ||||
0.671708 | + | 0.740816i | \(0.265561\pi\) | |||||||
\(984\) | −61.4200 | −1.95800 | ||||||||
\(985\) | 20.7981 | 0.662681 | ||||||||
\(986\) | 9.96358 | 0.317305 | ||||||||
\(987\) | 1.03669 | 0.0329983 | ||||||||
\(988\) | 5.37056 | 0.170860 | ||||||||
\(989\) | −2.59376 | −0.0824768 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.5439 | −1.16086 | −0.580428 | − | 0.814312i | \(-0.697115\pi\) | ||||
−0.580428 | + | 0.814312i | \(0.697115\pi\) | |||||||
\(992\) | 4.26090 | 0.135284 | ||||||||
\(993\) | 49.0567 | 1.55677 | ||||||||
\(994\) | −6.95638 | −0.220643 | ||||||||
\(995\) | 0.189373 | 0.00600352 | ||||||||
\(996\) | −72.2141 | −2.28819 | ||||||||
\(997\) | −15.0094 | −0.475352 | −0.237676 | − | 0.971344i | \(-0.576386\pi\) | ||||
−0.237676 | + | 0.971344i | \(0.576386\pi\) | |||||||
\(998\) | −9.78189 | −0.309640 | ||||||||
\(999\) | −2.30536 | −0.0729383 |
(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 | 4235.2.a.v.1.2 | yes | 4 | |
11.10 | odd | 2 | 4235.2.a.u.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.u.1.3 | ✓ | 4 | 11.10 | odd | 2 | ||
4235.2.a.v.1.2 | yes | 4 | 1.1 | even | 1 | trivial |