Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.20087896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.39144\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.944775 | −0.357091 | −0.178546 | − | 0.983932i | \(-0.557139\pi\) | ||||
−0.178546 | + | 0.983932i | \(0.557139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.62816 | 1.69696 | 0.848478 | − | 0.529231i | \(-0.177520\pi\) | ||||
0.848478 | + | 0.529231i | \(0.177520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.42401 | 1.22700 | 0.613500 | − | 0.789695i | \(-0.289761\pi\) | ||||
0.613500 | + | 0.789695i | \(0.289761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.41410 | 0.828041 | 0.414021 | − | 0.910267i | \(-0.364124\pi\) | ||||
0.414021 | + | 0.910267i | \(0.364124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.35888 | −0.541164 | −0.270582 | − | 0.962697i | \(-0.587216\pi\) | ||||
−0.270582 | + | 0.962697i | \(0.587216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.944775 | 0.206167 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.57294 | 1.59195 | 0.795977 | − | 0.605326i | \(-0.206957\pi\) | ||||
0.795977 | + | 0.605326i | \(0.206957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.99695 | −1.61590 | −0.807950 | − | 0.589251i | \(-0.799423\pi\) | ||||
−0.807950 | + | 0.589251i | \(0.799423\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.62816 | −0.979738 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.944775 | −0.159696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.05522 | 0.173478 | 0.0867389 | − | 0.996231i | \(-0.472355\pi\) | ||||
0.0867389 | + | 0.996231i | \(0.472355\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.42401 | −0.708409 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.35583 | −1.46113 | −0.730567 | − | 0.682841i | \(-0.760744\pi\) | ||||
−0.730567 | + | 0.682841i | \(0.760744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78289 | 0.729384 | 0.364692 | − | 0.931128i | \(-0.381174\pi\) | ||||
0.364692 | + | 0.931128i | \(0.381174\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.35888 | 0.344078 | 0.172039 | − | 0.985090i | \(-0.444965\pi\) | ||||
0.172039 | + | 0.985090i | \(0.444965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.10740 | −0.872486 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.41410 | −0.478070 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4663 | −1.57501 | −0.787507 | − | 0.616306i | \(-0.788629\pi\) | ||||
−0.787507 | + | 0.616306i | \(0.788629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.62816 | 0.758901 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.35888 | 0.312441 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2454 | 1.72440 | 0.862201 | − | 0.506567i | \(-0.169086\pi\) | ||||
0.862201 | + | 0.506567i | \(0.169086\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6933 | 1.49717 | 0.748587 | − | 0.663037i | \(-0.230733\pi\) | ||||
0.748587 | + | 0.663037i | \(0.230733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.944775 | −0.119030 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.42401 | 0.548731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.93182 | −1.09119 | −0.545597 | − | 0.838047i | \(-0.683697\pi\) | ||||
−0.545597 | + | 0.838047i | \(0.683697\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.68339 | −0.555816 | −0.277908 | − | 0.960608i | \(-0.589641\pi\) | ||||
−0.277908 | + | 0.960608i | \(0.589641\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.53067 | 0.179152 | 0.0895759 | − | 0.995980i | \(-0.471449\pi\) | ||||
0.0895759 | + | 0.995980i | \(0.471449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.31735 | −0.605968 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.7699 | 1.88676 | 0.943382 | − | 0.331708i | \(-0.107625\pi\) | ||||
0.943382 | + | 0.331708i | \(0.107625\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.41410 | −0.594275 | −0.297137 | − | 0.954835i | \(-0.596032\pi\) | ||||
−0.297137 | + | 0.954835i | \(0.596032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.41410 | 0.370311 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.57294 | −0.919116 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.8351 | 1.99651 | 0.998256 | − | 0.0590273i | \(-0.0187999\pi\) | ||||
0.998256 | + | 0.0590273i | \(0.0187999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.17970 | −0.438151 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.99695 | 0.932940 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.35888 | −0.242016 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.47344 | 0.860347 | 0.430174 | − | 0.902746i | \(-0.358452\pi\) | ||||
0.430174 | + | 0.902746i | \(0.358452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.62816 | 0.565652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4011 | 1.13446 | 0.567228 | − | 0.823561i | \(-0.308016\pi\) | ||||
0.567228 | + | 0.823561i | \(0.308016\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.94173 | −0.979587 | −0.489794 | − | 0.871838i | \(-0.662928\pi\) | ||||
−0.489794 | + | 0.871838i | \(0.662928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.944775 | 0.0922006 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5600 | −1.02087 | −0.510436 | − | 0.859916i | \(-0.670516\pi\) | ||||
−0.510436 | + | 0.859916i | \(0.670516\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.73483 | 0.836645 | 0.418322 | − | 0.908299i | \(-0.362618\pi\) | ||||
0.418322 | + | 0.908299i | \(0.362618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.05522 | −0.100158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4495 | −1.35930 | −0.679649 | − | 0.733538i | \(-0.737868\pi\) | ||||
−0.679649 | + | 0.733538i | \(0.737868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.42401 | 0.409000 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.22556 | −0.295686 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.6762 | 1.87966 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.35583 | 0.843587 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6803 | 1.56888 | 0.784438 | − | 0.620207i | \(-0.212951\pi\) | ||||
0.784438 | + | 0.620207i | \(0.212951\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.78289 | −0.421110 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.22861 | 0.193245 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.16262 | 0.697380 | 0.348690 | − | 0.937238i | \(-0.386627\pi\) | ||||
0.348690 | + | 0.937238i | \(0.386627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.71470 | −0.823990 | −0.411995 | − | 0.911186i | \(-0.635168\pi\) | ||||
−0.411995 | + | 0.911186i | \(0.635168\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.35888 | −0.198653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.8991 | 2.08216 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.57294 | 0.711944 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.10740 | 0.503730 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.7870 | 1.37524 | 0.687622 | − | 0.726069i | \(-0.258655\pi\) | ||||
0.687622 | + | 0.726069i | \(0.258655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.67623 | −0.624682 | −0.312341 | − | 0.949970i | \(-0.601113\pi\) | ||||
−0.312341 | + | 0.949970i | \(0.601113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.41410 | 0.276014 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.99695 | −0.722652 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.77298 | 0.460734 | 0.230367 | − | 0.973104i | \(-0.426007\pi\) | ||||
0.230367 | + | 0.973104i | \(0.426007\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.4663 | 0.909335 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.944775 | 0.0744587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0845 | −1.41649 | −0.708245 | − | 0.705967i | \(-0.750513\pi\) | ||||
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.62816 | −0.438152 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9860 | 1.46918 | 0.734590 | − | 0.678511i | \(-0.237374\pi\) | ||||
0.734590 | + | 0.678511i | \(0.237374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.57188 | 0.505529 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.35888 | −0.180388 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.88955 | −0.599831 | −0.299916 | − | 0.953966i | \(-0.596959\pi\) | ||||
−0.299916 | + | 0.953966i | \(0.596959\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.944775 | −0.0714183 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.2454 | −0.995584 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.42812 | −0.629948 | −0.314974 | − | 0.949100i | \(-0.601996\pi\) | ||||
−0.314974 | + | 0.949100i | \(0.601996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.37595 | 0.473921 | 0.236960 | − | 0.971519i | \(-0.423849\pi\) | ||||
0.236960 | + | 0.971519i | \(0.423849\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6933 | −0.864393 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.05522 | 0.0775817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.2151 | 1.40515 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.944775 | 0.0687223 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.20690 | −0.521473 | −0.260736 | − | 0.965410i | \(-0.583965\pi\) | ||||
−0.260736 | + | 0.965410i | \(0.583965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.39270 | 0.244212 | 0.122106 | − | 0.992517i | \(-0.461035\pi\) | ||||
0.122106 | + | 0.992517i | \(0.461035\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.42401 | −0.316810 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.2304 | −1.79759 | −0.898796 | − | 0.438367i | \(-0.855557\pi\) | ||||
−0.898796 | + | 0.438367i | \(0.855557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.05827 | 0.145907 | 0.0729536 | − | 0.997335i | \(-0.476757\pi\) | ||||
0.0729536 | + | 0.997335i | \(0.476757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.93182 | 0.630002 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.09950 | −0.568473 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.35583 | −0.653439 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.2761 | −0.918330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7147 | 1.21953 | 0.609765 | − | 0.792582i | \(-0.291264\pi\) | ||||
0.609765 | + | 0.792582i | \(0.291264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.68339 | 0.320900 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.78289 | 0.326190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.50010 | 0.577024 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.53067 | −0.103433 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.1040 | 1.01601 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.32146 | 0.490281 | 0.245141 | − | 0.969488i | \(-0.421166\pi\) | ||||
0.245141 | + | 0.969488i | \(0.421166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.11352 | −0.206652 | −0.103326 | − | 0.994648i | \(-0.532948\pi\) | ||||
−0.103326 | + | 0.994648i | \(0.532948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.57093 | −0.434219 | −0.217110 | − | 0.976147i | \(-0.569663\pi\) | ||||
−0.217110 | + | 0.976147i | \(0.569663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.31735 | 0.349856 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.67623 | 0.371862 | 0.185931 | − | 0.982563i | \(-0.440470\pi\) | ||||
0.185931 | + | 0.982563i | \(0.440470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.35888 | 0.153876 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.7699 | −1.08932 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3950 | −1.25456 | −0.627281 | − | 0.778793i | \(-0.715832\pi\) | ||||
−0.627281 | + | 0.778793i | \(0.715832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7870 | 1.33901 | 0.669504 | − | 0.742808i | \(-0.266507\pi\) | ||||
0.669504 | + | 0.742808i | \(0.266507\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.10740 | −0.390187 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4357 | −0.664008 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.41410 | 0.343105 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.20794 | 0.265603 | 0.132801 | − | 0.991143i | \(-0.457603\pi\) | ||||
0.132801 | + | 0.991143i | \(0.457603\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.62816 | −0.353840 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.41410 | −0.213799 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.30977 | 0.0817015 | 0.0408507 | − | 0.999165i | \(-0.486993\pi\) | ||||
0.0408507 | + | 0.999165i | \(0.486993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.996950 | −0.0619475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.57294 | 0.530652 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.3143 | −1.86926 | −0.934630 | − | 0.355622i | \(-0.884269\pi\) | ||||
−0.934630 | + | 0.355622i | \(0.884269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.4663 | −0.704368 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.8351 | −1.15269 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2492 | 0.990729 | 0.495365 | − | 0.868685i | \(-0.335034\pi\) | ||||
0.495365 | + | 0.868685i | \(0.335034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1074 | 0.917709 | 0.458855 | − | 0.888511i | \(-0.348260\pi\) | ||||
0.458855 | + | 0.888511i | \(0.348260\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.17970 | 0.252967 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.62816 | 0.339391 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4591 | 0.868764 | 0.434382 | − | 0.900729i | \(-0.356967\pi\) | ||||
0.434382 | + | 0.900729i | \(0.356967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.99695 | −0.538633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0835 | −1.61567 | −0.807833 | − | 0.589412i | \(-0.799360\pi\) | ||||
−0.807833 | + | 0.589412i | \(0.799360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.53912 | 0.448154 | 0.224077 | − | 0.974571i | \(-0.428063\pi\) | ||||
0.224077 | + | 0.974571i | \(0.428063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.35888 | 0.139728 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.83915 | 0.521759 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.34391 | −0.314348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.47344 | −0.496722 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.4819 | 1.19656 | 0.598282 | − | 0.801285i | \(-0.295850\pi\) | ||||
0.598282 | + | 0.801285i | \(0.295850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.2454 | 0.771176 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.62816 | −0.326579 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.42401 | −0.255847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.51875 | −0.260457 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4011 | −0.654979 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6933 | 0.669556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2069 | 0.639612 | 0.319806 | − | 0.947483i | \(-0.396382\pi\) | ||||
0.319806 | + | 0.947483i | \(0.396382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.94173 | 0.565565 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.80271 | 0.385746 | 0.192873 | − | 0.981224i | \(-0.438219\pi\) | ||||
0.192873 | + | 0.981224i | \(0.438219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.06208 | −0.399173 | −0.199586 | − | 0.979880i | \(-0.563960\pi\) | ||||
−0.199586 | + | 0.979880i | \(0.563960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.944775 | −0.0532321 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.69023 | −0.151098 | −0.0755491 | − | 0.997142i | \(-0.524071\pi\) | ||||
−0.0755491 | + | 0.997142i | \(0.524071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.2499 | 2.70148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5600 | 0.589401 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.05345 | −0.448106 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.42401 | 0.245400 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.73483 | −0.483037 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.22861 | −0.122867 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2731 | 1.44410 | 0.722050 | − | 0.691841i | \(-0.243200\pi\) | ||||
0.722050 | + | 0.691841i | \(0.243200\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.05522 | 0.0578260 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.93182 | −0.487997 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.8674 | 1.57251 | 0.786254 | − | 0.617903i | \(-0.212018\pi\) | ||||
0.786254 | + | 0.617903i | \(0.212018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.4495 | 0.784791 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −50.6363 | −2.74211 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.3835 | 0.668649 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.6012 | 1.53539 | 0.767697 | − | 0.640814i | \(-0.221403\pi\) | ||||
0.767697 | + | 0.640814i | \(0.221403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0324 | 1.17937 | 0.589683 | − | 0.807635i | \(-0.299253\pi\) | ||||
0.589683 | + | 0.807635i | \(0.299253\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.42401 | −0.236136 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.4830 | −1.62245 | −0.811224 | − | 0.584735i | \(-0.801199\pi\) | ||||
−0.811224 | + | 0.584735i | \(0.801199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.68339 | −0.248568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.22556 | 0.170715 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.9860 | 0.579819 | 0.289909 | − | 0.957054i | \(-0.406375\pi\) | ||||
0.289909 | + | 0.957054i | \(0.406375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4357 | −0.707142 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.6762 | −1.08522 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.53067 | 0.0801191 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.7669 | −1.13622 | −0.568111 | − | 0.822952i | \(-0.692326\pi\) | ||||
−0.568111 | + | 0.822952i | \(0.692326\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.35583 | −0.487045 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.8331 | 0.562424 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6595 | −0.655483 | −0.327742 | − | 0.944767i | \(-0.606288\pi\) | ||||
−0.327742 | + | 0.944767i | \(0.606288\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.9268 | 1.95333 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4751 | −0.692172 | −0.346086 | − | 0.938203i | \(-0.612489\pi\) | ||||
−0.346086 | + | 0.938203i | \(0.612489\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6803 | −0.905791 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6122 | −1.15543 | −0.577714 | − | 0.816240i | \(-0.696055\pi\) | ||||
−0.577714 | + | 0.816240i | \(0.696055\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.31735 | −0.270997 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.78289 | 0.243128 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6646 | 0.794228 | 0.397114 | − | 0.917769i | \(-0.370012\pi\) | ||||
0.397114 | + | 0.917769i | \(0.370012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.41410 | −0.172659 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.7699 | 0.843787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.5164 | −1.48139 | −0.740694 | − | 0.671843i | \(-0.765503\pi\) | ||||
−0.740694 | + | 0.671843i | \(0.765503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.22861 | −0.111570 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4778 | 1.22236 | 0.611181 | − | 0.791491i | \(-0.290695\pi\) | ||||
0.611181 | + | 0.791491i | \(0.290695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −39.8026 | −1.98271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.93898 | 0.294384 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.82387 | 0.139631 | 0.0698157 | − | 0.997560i | \(-0.477759\pi\) | ||||
0.0698157 | + | 0.997560i | \(0.477759\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.16262 | −0.402633 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.5139 | −0.615769 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.41410 | −0.265768 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.71470 | 0.475731 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.4148 | −1.33930 | −0.669651 | − | 0.742676i | \(-0.733556\pi\) | ||||
−0.669651 | + | 0.742676i | \(0.733556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.3619 | −0.651222 | −0.325611 | − | 0.945504i | \(-0.605570\pi\) | ||||
−0.325611 | + | 0.945504i | \(0.605570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.35888 | 0.114693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.41410 | 0.165608 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.0475 | −0.534628 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.8991 | −1.20214 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1261 | −0.535923 | −0.267962 | − | 0.963430i | \(-0.586350\pi\) | ||||
−0.267962 | + | 0.963430i | \(0.586350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.2986 | 1.35994 | 0.679972 | − | 0.733238i | \(-0.261992\pi\) | ||||
0.679972 | + | 0.733238i | \(0.261992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.57294 | −0.411041 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.35888 | 0.112840 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.8419 | 1.85382 | 0.926912 | − | 0.375279i | \(-0.122453\pi\) | ||||
0.926912 | + | 0.375279i | \(0.122453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.10740 | −0.290829 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.44951 | −0.116380 | −0.0581898 | − | 0.998306i | \(-0.518533\pi\) | ||||
−0.0581898 | + | 0.998306i | \(0.518533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.8351 | 0.892868 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.7870 | −0.793998 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.8590 | −1.55071 | −0.775355 | − | 0.631525i | \(-0.782429\pi\) | ||||
−0.775355 | + | 0.631525i | \(0.782429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −52.6561 | −2.47948 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.67623 | 0.360661 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.17970 | −0.195947 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3798 | −0.812991 | −0.406495 | − | 0.913653i | \(-0.633249\pi\) | ||||
−0.406495 | + | 0.913653i | \(0.633249\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.41410 | −0.159357 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.2996 | −1.36462 | −0.682308 | − | 0.731065i | \(-0.739024\pi\) | ||||
−0.682308 | + | 0.731065i | \(0.739024\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8521 | −1.06203 | −0.531014 | − | 0.847363i | \(-0.678189\pi\) | ||||
−0.531014 | + | 0.847363i | \(0.678189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.99695 | 0.417224 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.2703 | 1.03055 | 0.515274 | − | 0.857025i | \(-0.327690\pi\) | ||||
0.515274 | + | 0.857025i | \(0.327690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.43856 | 0.389656 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.77298 | −0.266005 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.9189 | 1.23773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.35888 | −0.108233 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.4663 | −0.525005 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.6582 | 1.76634 | 0.883169 | − | 0.469054i | \(-0.155405\pi\) | ||||
0.883169 | + | 0.469054i | \(0.155405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.66833 | 0.212857 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.944775 | −0.0429888 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.47344 | 0.384759 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.6544 | 1.16251 | 0.581256 | − | 0.813720i | \(-0.302561\pi\) | ||||
0.581256 | + | 0.813720i | \(0.302561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0845 | 0.817811 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.2038 | −1.09230 | −0.546152 | − | 0.837686i | \(-0.683908\pi\) | ||||
−0.546152 | + | 0.837686i | \(0.683908\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.2689 | 1.31820 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.62816 | 0.252967 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.42475 | 0.198477 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.9295 | −1.42936 | −0.714680 | − | 0.699451i | \(-0.753428\pi\) | ||||
−0.714680 | + | 0.699451i | \(0.753428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9860 | −0.848232 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.09950 | −0.361139 | −0.180569 | − | 0.983562i | \(-0.557794\pi\) | ||||
−0.180569 | + | 0.983562i | \(0.557794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4011 | 0.507344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.57188 | −0.291867 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.1436 | −1.69068 | −0.845342 | − | 0.534226i | \(-0.820603\pi\) | ||||
−0.845342 | + | 0.534226i | \(0.820603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.44614 | −0.0639736 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.35888 | 0.104147 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.94173 | −0.438085 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2761 | 0.583884 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.88955 | 0.346313 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.7740 | −1.26061 | −0.630307 | − | 0.776346i | \(-0.717071\pi\) | ||||
−0.630307 | + | 0.776346i | \(0.717071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.3426 | 1.41424 | 0.707121 | − | 0.707093i | \(-0.249994\pi\) | ||||
0.707121 | + | 0.707093i | \(0.249994\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.944775 | 0.0412334 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.7165 | −1.33803 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.2454 | 0.574800 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.3903 | −1.79281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.5600 | −0.456548 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.42812 | 0.363700 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.3734 | −1.48057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.7376 | −1.40750 | −0.703749 | − | 0.710449i | \(-0.748492\pi\) | ||||
−0.703749 | + | 0.710449i | \(0.748492\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.37595 | −0.273618 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.73483 | 0.374159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.5127 | −1.47565 | −0.737827 | − | 0.674990i | \(-0.764148\pi\) | ||||
−0.737827 | + | 0.674990i | \(0.764148\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6933 | 0.499058 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.2225 | −0.861508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.8438 | −0.673747 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.05522 | −0.0447918 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.2257 | −1.28071 | −0.640353 | − | 0.768081i | \(-0.721212\pi\) | ||||
−0.640353 | + | 0.768081i | \(0.721212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.1596 | 0.894954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.2151 | −0.811263 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.2703 | −1.61290 | −0.806451 | − | 0.591300i | \(-0.798615\pi\) | ||||
−0.806451 | + | 0.591300i | \(0.798615\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.4495 | −0.607896 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.944775 | −0.0396768 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.00894 | 0.0842192 | 0.0421096 | − | 0.999113i | \(-0.486592\pi\) | ||||
0.0421096 | + | 0.999113i | \(0.486592\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.84220 | −0.328186 | −0.164093 | − | 0.986445i | \(-0.552470\pi\) | ||||
−0.164093 | + | 0.986445i | \(0.552470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.20690 | 0.301073 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0470 | −0.792938 | −0.396469 | − | 0.918048i | \(-0.629765\pi\) | ||||
−0.396469 | + | 0.918048i | \(0.629765\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.39270 | −0.140996 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.11511 | 0.212210 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −64.5341 | −2.67273 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.42401 | 0.182910 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.6231 | −0.686109 | −0.343054 | − | 0.939316i | \(-0.611462\pi\) | ||||
−0.343054 | + | 0.939316i | \(0.611462\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.2227 | 0.874466 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.2304 | 1.03784 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.16537 | 0.335312 | 0.167656 | − | 0.985846i | \(-0.446380\pi\) | ||||
0.167656 | + | 0.985846i | \(0.446380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.22556 | −0.132235 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.05827 | −0.0842396 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3902 | 0.465391 | 0.232695 | − | 0.972550i | \(-0.425246\pi\) | ||||
0.232695 | + | 0.972550i | \(0.425246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7836 | −0.847782 | −0.423891 | − | 0.905713i | \(-0.639336\pi\) | ||||
−0.423891 | + | 0.905713i | \(0.639336\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.93182 | −0.363732 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.6762 | 0.840608 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.6114 | 0.674237 | 0.337118 | − | 0.941462i | \(-0.390548\pi\) | ||||
0.337118 | + | 0.941462i | \(0.390548\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.09950 | 0.328208 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4357 | 0.422183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.3085 | 1.18376 | 0.591880 | − | 0.806026i | \(-0.298386\pi\) | ||||
0.591880 | + | 0.806026i | \(0.298386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.35583 | 0.377263 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8838 | −0.840748 | −0.420374 | − | 0.907351i | \(-0.638101\pi\) | ||||
−0.420374 | + | 0.907351i | \(0.638101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.94688 | 0.198832 | 0.0994159 | − | 0.995046i | \(-0.468303\pi\) | ||||
0.0994159 | + | 0.995046i | \(0.468303\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.7949 | −0.712938 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.2761 | 0.530198 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.60265 | 0.143647 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.23168 | 0.287889 | 0.143944 | − | 0.989586i | \(-0.454021\pi\) | ||||
0.143944 | + | 0.989586i | \(0.454021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.7147 | −0.704096 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.6803 | 0.701623 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.0192 | −1.07054 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.68339 | −0.185272 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.40116 | 0.371324 | 0.185662 | − | 0.982614i | \(-0.440557\pi\) | ||||
0.185662 | + | 0.982614i | \(0.440557\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.0007 | −1.34086 | −0.670429 | − | 0.741974i | \(-0.733890\pi\) | ||||
−0.670429 | + | 0.741974i | \(0.733890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.78289 | −0.188326 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.77878 | 0.266501 | 0.133251 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133251 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 74.5472 | 2.92623 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.50010 | −0.333145 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.3372 | 0.991520 | 0.495760 | − | 0.868460i | \(-0.334890\pi\) | ||||
0.495760 | + | 0.868460i | \(0.334890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.53067 | 0.0597173 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8428 | 0.422374 | 0.211187 | − | 0.977446i | \(-0.432267\pi\) | ||||
0.211187 | + | 0.977446i | \(0.432267\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.61667 | 0.179568 | 0.0897838 | − | 0.995961i | \(-0.471382\pi\) | ||||
0.0897838 | + | 0.995961i | \(0.471382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.1040 | −0.586592 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.22861 | 0.0864217 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.57294 | −0.331946 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.32146 | −0.283064 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65.8118 | 2.54064 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.64112 | 0.294544 | 0.147272 | − | 0.989096i | \(-0.452951\pi\) | ||||
0.147272 | + | 0.989096i | \(0.452951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.4956 | −1.71011 | −0.855053 | − | 0.518541i | \(-0.826475\pi\) | ||||
−0.855053 | + | 0.518541i | \(0.826475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.00549 | −0.307223 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.11352 | 0.119310 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3726 | 0.396896 | 0.198448 | − | 0.980111i | \(-0.436410\pi\) | ||||
0.198448 | + | 0.980111i | \(0.436410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.16262 | 0.311878 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.57093 | 0.250697 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −50.7269 | −1.93254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8623 | −0.717557 | −0.358779 | − | 0.933423i | \(-0.616807\pi\) | ||||
−0.358779 | + | 0.933423i | \(0.616807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.31735 | −0.201989 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.71470 | −0.368500 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.9417 | −1.20988 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.67623 | −0.214695 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.9820 | −1.85002 | −0.925012 | − | 0.379938i | \(-0.875945\pi\) | ||||
−0.925012 | + | 0.379938i | \(0.875945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.48915 | −0.0938799 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.35888 | −0.0888405 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.7715 | −0.405105 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2039 | −1.05922 | −0.529609 | − | 0.848242i | \(-0.677661\pi\) | ||||
−0.529609 | + | 0.848242i | \(0.677661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7699 | 0.628921 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.99695 | 0.336938 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.8991 | 0.931172 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.3950 | 0.724321 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.0426 | 1.34416 | 0.672081 | − | 0.740478i | \(-0.265401\pi\) | ||||
0.672081 | + | 0.740478i | \(0.265401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.39270 | 0.349802 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.7870 | −0.773077 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.57294 | 0.318391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8971 | 0.515417 | 0.257708 | − | 0.966223i | \(-0.417033\pi\) | ||||
0.257708 | + | 0.966223i | \(0.417033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3293 | 0.603960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4629 | −1.08824 | −0.544119 | − | 0.839008i | \(-0.683136\pi\) | ||||
−0.544119 | + | 0.839008i | \(0.683136\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.10740 | 0.225275 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.2697 | −1.85171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1504 | 1.32981 | 0.664907 | − | 0.746926i | \(-0.268471\pi\) | ||||
0.664907 | + | 0.746926i | \(0.268471\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.4357 | 0.383365 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.7608 | 1.38531 | 0.692654 | − | 0.721270i | \(-0.256441\pi\) | ||||
0.692654 | + | 0.721270i | \(0.256441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.7870 | 0.615028 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.41410 | −0.198092 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.97681 | 0.364545 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.7015 | 1.37575 | 0.687874 | − | 0.725830i | \(-0.258544\pi\) | ||||
0.687874 | + | 0.725830i | \(0.258544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.20794 | −0.153346 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.67623 | −0.279366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.5481 | −0.928560 | −0.464280 | − | 0.885688i | \(-0.653687\pi\) | ||||
−0.464280 | + | 0.885688i | \(0.653687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.62816 | 0.204289 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5352 | −0.889400 | −0.444700 | − | 0.895680i | \(-0.646690\pi\) | ||||
−0.444700 | + | 0.895680i | \(0.646690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.25245 | −0.298759 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.41410 | 0.123437 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.5977 | 2.11584 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.7550 | 1.68603 | 0.843014 | − | 0.537892i | \(-0.180779\pi\) | ||||
0.843014 | + | 0.537892i | \(0.180779\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.30977 | −0.0471704 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.3879 | −1.74039 | −0.870196 | − | 0.492706i | \(-0.836008\pi\) | ||||
−0.870196 | + | 0.492706i | \(0.836008\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.99695 | −0.323180 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.996950 | 0.0357654 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.0692 | 0.790713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.3589 | −0.943195 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.57294 | −0.306372 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.77298 | 0.206046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.2216 | −1.07729 | −0.538643 | − | 0.842534i | \(-0.681063\pi\) | ||||
−0.538643 | + | 0.842534i | \(0.681063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.3143 | 1.07922 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6516 | 0.485394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.7313 | 1.83703 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.4663 | 0.406667 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.7443 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.05345 | 0.284910 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.8351 | 0.665504 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.61488 | 0.304013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.944775 | 0.0332989 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.2492 | −0.571998 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.1705 | −1.86938 | −0.934688 | − | 0.355468i | \(-0.884321\pi\) | ||||
−0.934688 | + | 0.355468i | \(0.884321\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0522 | −0.774357 | −0.387179 | − | 0.922005i | \(-0.626550\pi\) | ||||
−0.387179 | + | 0.922005i | \(0.626550\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.1074 | −0.529840 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0845 | −0.633473 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.2822 | −0.394716 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.17970 | −0.146050 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.1708 | 1.57647 | 0.788235 | − | 0.615374i | \(-0.210995\pi\) | ||||
0.788235 | + | 0.615374i | \(0.210995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.8299 | −0.760943 | −0.380471 | − | 0.924793i | \(-0.624238\pi\) | ||||
−0.380471 | + | 0.924793i | \(0.624238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.62816 | −0.195948 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.7904 | 1.59229 | 0.796144 | − | 0.605107i | \(-0.206870\pi\) | ||||
0.796144 | + | 0.605107i | \(0.206870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.77813 | 0.165951 | 0.0829757 | − | 0.996552i | \(-0.473558\pi\) | ||||
0.0829757 | + | 0.996552i | \(0.473558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.4591 | −0.501581 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.8513 | −0.722454 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.9860 | 0.657038 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.99695 | 0.310980 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2344 | 0.525951 | 0.262975 | − | 0.964803i | \(-0.415296\pi\) | ||||
0.262975 | + | 0.964803i | \(0.415296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.4953 | 1.53432 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0835 | 0.932805 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.57188 | 0.226079 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.5344 | −0.671209 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.53912 | −0.258742 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.05522 | −0.0361726 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.2724 | 1.03651 | 0.518253 | − | 0.855227i | \(-0.326583\pi\) | ||||
0.518253 | + | 0.855227i | \(0.326583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.35888 | −0.0806719 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.408305 | −0.0139474 | −0.00697371 | − | 0.999976i | \(-0.502220\pi\) | ||||
−0.00697371 | + | 0.999976i | \(0.502220\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.6772 | 0.569019 | 0.284509 | − | 0.958673i | \(-0.408169\pi\) | ||||
0.284509 | + | 0.958673i | \(0.408169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.83915 | −0.301238 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.6210 | 0.633867 | 0.316934 | − | 0.948448i | \(-0.397347\pi\) | ||||
0.316934 | + | 0.948448i | \(0.397347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.88955 | −0.268253 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.34391 | 0.181489 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 94.3839 | 3.20175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.5145 | −1.33890 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.47344 | 0.286782 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.944775 | −0.0319392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.51918 | −0.220137 | −0.110068 | − | 0.993924i | \(-0.535107\pi\) | ||||
−0.110068 | + | 0.993924i | \(0.535107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.4819 | −0.690837 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.3358 | −1.42633 | −0.713165 | − | 0.700997i | \(-0.752739\pi\) | ||||
−0.713165 | + | 0.700997i | \(0.752739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5123 | −0.723948 | −0.361974 | − | 0.932188i | \(-0.617897\pi\) | ||||
−0.361974 | + | 0.932188i | \(0.617897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.2454 | −0.445238 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.8023 | 1.70577 | 0.852887 | − | 0.522096i | \(-0.174850\pi\) | ||||
0.852887 | + | 0.522096i | \(0.174850\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.7039 | −0.560232 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.62816 | 0.188551 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.56430 | −0.186202 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.42812 | −0.281721 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.42401 | 0.147713 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −77.1303 | −2.57244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.1470 | −1.30418 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.51875 | 0.150375 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.37595 | 0.211944 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1255 | −0.601848 | −0.300924 | − | 0.953648i | \(-0.597295\pi\) | ||||
−0.300924 | + | 0.953648i | \(0.597295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4011 | 0.378152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.67013 | −0.320386 | −0.160193 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160193 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.4715 | −1.00846 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6933 | −0.386569 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.7324 | 0.782860 | 0.391430 | − | 0.920208i | \(-0.371980\pi\) | ||||
0.391430 | + | 0.920208i | \(0.371980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2069 | −0.369280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7194 | −0.681986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.05522 | 0.0346956 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.94173 | −0.326529 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.0519 | −1.15001 | −0.575007 | − | 0.818148i | \(-0.695001\pi\) | ||||
−0.575007 | + | 0.818148i | \(0.695001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.4066 | 0.472157 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.80271 | −0.222711 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.2151 | 0.628402 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.0767 | −0.753884 | −0.376942 | − | 0.926237i | \(-0.623024\pi\) | ||||
−0.376942 | + | 0.926237i | \(0.623024\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.06208 | 0.230462 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.9466 | 0.715437 | 0.357719 | − | 0.933829i | \(-0.383555\pi\) | ||||
0.357719 | + | 0.933829i | \(0.383555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.35583 | 0.304668 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.944775 | 0.0307335 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.5494 | −1.18769 | −0.593847 | − | 0.804578i | \(-0.702392\pi\) | ||||
−0.593847 | + | 0.804578i | \(0.702392\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.77172 | 0.219819 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.69023 | 0.0872366 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.0180 | −0.583661 | −0.291831 | − | 0.956470i | \(-0.594264\pi\) | ||||
−0.291831 | + | 0.956470i | \(0.594264\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.20690 | −0.233210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −48.2499 | −1.55970 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.71185 | −0.249028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.9451 | 1.61113 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.5600 | −0.340291 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.39270 | 0.109215 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.6837 | −1.50125 | −0.750623 | − | 0.660730i | \(-0.770247\pi\) | ||||
−0.750623 | + | 0.660730i | \(0.770247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.05345 | 0.258714 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.5747 | −0.949098 | −0.474549 | − | 0.880229i | \(-0.657389\pi\) | ||||
−0.474549 | + | 0.880229i | \(0.657389\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.17821 | 0.294240 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.42401 | −0.141682 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.3195 | 0.874027 | 0.437013 | − | 0.899455i | \(-0.356036\pi\) | ||||
0.437013 | + | 0.899455i | \(0.356036\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 106.007 | 3.38799 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.73483 | 0.278882 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.5133 | 0.973223 | 0.486612 | − | 0.873618i | \(-0.338233\pi\) | ||||
0.486612 | + | 0.873618i | \(0.338233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.2304 | −0.803908 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.22861 | 0.0709374 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.78289 | −0.152087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3637 | −0.329215 | −0.164607 | − | 0.986359i | \(-0.552636\pi\) | ||||
−0.164607 | + | 0.986359i | \(0.552636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.2731 | −0.833752 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.05827 | 0.0652517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.0726 | 1.49080 | 0.745402 | − | 0.666616i | \(-0.232258\pi\) | ||||
0.745402 | + | 0.666616i | \(0.232258\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.05522 | −0.0333858 |
(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 | 2760.2.a.w.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 8280.2.a.br.1.3 | 5 | |||
4.3 | odd | 2 | 5520.2.a.cc.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.w.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5520.2.a.cc.1.3 | 5 | 4.3 | odd | 2 | |||
8280.2.a.br.1.3 | 5 | 3.2 | odd | 2 |