Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(73.4623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.521397.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 9x^{3} - 3x^{2} + 18x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.61696\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 2.61696 | 1.51090 | 0.755452 | − | 0.655204i | \(-0.227417\pi\) | ||||
0.755452 | + | 0.655204i | \(0.227417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.83744 | 1.45041 | 0.725207 | − | 0.688531i | \(-0.241744\pi\) | ||||
0.725207 | + | 0.688531i | \(0.241744\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.84849 | 1.28283 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.508005 | 0.153169 | 0.0765847 | − | 0.997063i | \(-0.475598\pi\) | ||||
0.0765847 | + | 0.997063i | \(0.475598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.01106 | −0.280417 | −0.140208 | − | 0.990122i | \(-0.544777\pi\) | ||||
−0.140208 | + | 0.990122i | \(0.544777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44705 | −0.350961 | −0.175481 | − | 0.984483i | \(-0.556148\pi\) | ||||
−0.175481 | + | 0.984483i | \(0.556148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.508005 | 0.116544 | 0.0582722 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582722 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.0424 | 2.19144 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.22047 | 0.427330 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.51040 | 1.39465 | 0.697323 | − | 0.716757i | \(-0.254374\pi\) | ||||
0.697323 | + | 0.716757i | \(0.254374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.439038 | 0.0788536 | 0.0394268 | − | 0.999222i | \(-0.487447\pi\) | ||||
0.0394268 | + | 0.999222i | \(0.487447\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.32943 | 0.231424 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.02642 | 1.15514 | 0.577568 | − | 0.816343i | \(-0.304002\pi\) | ||||
0.577568 | + | 0.816343i | \(0.304002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.64590 | −0.423683 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.47041 | 0.854335 | 0.427167 | − | 0.904173i | \(-0.359512\pi\) | ||||
0.427167 | + | 0.904173i | \(0.359512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.72592 | 1.02569 | 0.512847 | − | 0.858480i | \(-0.328591\pi\) | ||||
0.512847 | + | 0.858480i | \(0.328591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.64098 | −0.385227 | −0.192614 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192614 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.72592 | 1.10370 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.78688 | −0.530269 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.77648 | −0.656100 | −0.328050 | − | 0.944660i | \(-0.606391\pi\) | ||||
−0.328050 | + | 0.944660i | \(0.606391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.32943 | 0.176087 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.85345 | −0.501676 | −0.250838 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250838 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.05844 | −1.15981 | −0.579907 | − | 0.814683i | \(-0.696911\pi\) | ||||
−0.579907 | + | 0.814683i | \(0.696911\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.7683 | 1.86064 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.45696 | 0.422335 | 0.211167 | − | 0.977450i | \(-0.432273\pi\) | ||||
0.211167 | + | 0.977450i | \(0.432273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.61696 | −0.315045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.73649 | 0.324762 | 0.162381 | − | 0.986728i | \(-0.448083\pi\) | ||||
0.162381 | + | 0.986728i | \(0.448083\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.21300 | 1.07830 | 0.539150 | − | 0.842210i | \(-0.318746\pi\) | ||||
0.539150 | + | 0.842210i | \(0.318746\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.94944 | 0.222159 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.5504 | −1.18702 | −0.593508 | − | 0.804828i | \(-0.702258\pi\) | ||||
−0.593508 | + | 0.804828i | \(0.702258\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.73458 | −0.637176 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.40211 | −0.153901 | −0.0769505 | − | 0.997035i | \(-0.524518\pi\) | ||||
−0.0769505 | + | 0.997035i | \(0.524518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.6544 | 2.10718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.77086 | 0.717710 | 0.358855 | − | 0.933393i | \(-0.383167\pi\) | ||||
0.358855 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.87986 | −0.406720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.14895 | 0.119140 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.313420 | 0.0318230 | 0.0159115 | − | 0.999873i | \(-0.494935\pi\) | ||||
0.0159115 | + | 0.999873i | \(0.494935\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95506 | 0.196490 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.83182 | −0.480784 | −0.240392 | − | 0.970676i | \(-0.577276\pi\) | ||||
−0.240392 | + | 0.970676i | \(0.577276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.07746 | 0.795896 | 0.397948 | − | 0.917408i | \(-0.369722\pi\) | ||||
0.397948 | + | 0.917408i | \(0.369722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.1587 | −1.07876 | −0.539378 | − | 0.842064i | \(-0.681341\pi\) | ||||
−0.539378 | + | 0.842064i | \(0.681341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6015 | 1.68592 | 0.842958 | − | 0.537979i | \(-0.180812\pi\) | ||||
0.842958 | + | 0.537979i | \(0.180812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.3879 | 1.74530 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.06454 | 0.382360 | 0.191180 | − | 0.981555i | \(-0.438769\pi\) | ||||
0.191180 | + | 0.981555i | \(0.438769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.89104 | −0.359727 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.55296 | −0.509039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7419 | −0.976539 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.3159 | 1.29082 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.75246 | 0.421713 | 0.210856 | − | 0.977517i | \(-0.432375\pi\) | ||||
0.210856 | + | 0.977517i | \(0.432375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.6015 | 1.54972 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.96851 | −0.171989 | −0.0859946 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859946 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.94944 | 0.169038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.64285 | 0.482101 | 0.241051 | − | 0.970513i | \(-0.422508\pi\) | ||||
0.241051 | + | 0.970513i | \(0.422508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.59724 | 0.644390 | 0.322195 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322195 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.91136 | −0.582041 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.513622 | −0.0429512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.2184 | 1.66759 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.7709 | 0.882384 | 0.441192 | − | 0.897413i | \(-0.354556\pi\) | ||||
0.441192 | + | 0.897413i | \(0.354556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.5333 | 1.34546 | 0.672729 | − | 0.739889i | \(-0.265122\pi\) | ||||
0.672729 | + | 0.739889i | \(0.265122\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.56896 | −0.450224 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.5436 | 0.921281 | 0.460640 | − | 0.887587i | \(-0.347620\pi\) | ||||
0.460640 | + | 0.887587i | \(0.347620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4999 | −0.991304 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.83744 | −0.302432 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.32143 | 0.260155 | 0.130077 | − | 0.991504i | \(-0.458477\pi\) | ||||
0.130077 | + | 0.991504i | \(0.458477\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.6742 | 0.980755 | 0.490378 | − | 0.871510i | \(-0.336859\pi\) | ||||
0.490378 | + | 0.871510i | \(0.336859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9778 | −0.921367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.95506 | 0.149507 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.5733 | −1.33607 | −0.668035 | − | 0.744130i | \(-0.732864\pi\) | ||||
−0.668035 | + | 0.744130i | \(0.732864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0843 | −0.757984 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8952 | 1.11332 | 0.556659 | − | 0.830741i | \(-0.312083\pi\) | ||||
0.556659 | + | 0.830741i | \(0.312083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.2868 | −1.73089 | −0.865446 | − | 0.501003i | \(-0.832965\pi\) | ||||
−0.865446 | + | 0.501003i | \(0.832965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.7056 | −1.75237 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.735109 | −0.0537565 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.52093 | 0.619806 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.92360 | −0.500974 | −0.250487 | − | 0.968120i | \(-0.580591\pi\) | ||||
−0.250487 | + | 0.968120i | \(0.580591\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.74318 | 0.557366 | 0.278683 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278683 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8908 | 1.70215 | 0.851074 | − | 0.525045i | \(-0.175952\pi\) | ||||
0.851074 | + | 0.525045i | \(0.175952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9444 | 1.69737 | 0.848687 | − | 0.528896i | \(-0.177394\pi\) | ||||
0.848687 | + | 0.528896i | \(0.177394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.04673 | 0.638107 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.8207 | 2.02282 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.84849 | −0.267489 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.258070 | 0.0178510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.4709 | −0.996220 | −0.498110 | − | 0.867114i | \(-0.665973\pi\) | ||||
−0.498110 | + | 0.867114i | \(0.665973\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.16129 | 0.490684 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.68478 | 0.114370 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.1101 | 1.62921 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46305 | 0.0984153 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.74755 | −0.317919 | −0.158960 | − | 0.987285i | \(-0.550814\pi\) | ||||
−0.158960 | + | 0.987285i | \(0.550814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.98399 | 0.596288 | 0.298144 | − | 0.954521i | \(-0.403632\pi\) | ||||
0.298144 | + | 0.954521i | \(0.403632\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.7290 | 1.36981 | 0.684906 | − | 0.728631i | \(-0.259843\pi\) | ||||
0.684906 | + | 0.728631i | \(0.259843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.10161 | 0.335661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0634 | −1.70747 | −0.853735 | − | 0.520707i | \(-0.825668\pi\) | ||||
−0.853735 | + | 0.520707i | \(0.825668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.6101 | −1.79347 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.94209 | 0.190308 | 0.0951540 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951540 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9413 | −1.60661 | −0.803306 | − | 0.595567i | \(-0.796927\pi\) | ||||
−0.803306 | + | 0.595567i | \(0.796927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6686 | −1.39004 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.513622 | −0.0326810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.66926 | −0.232530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.1908 | −1.33755 | −0.668774 | − | 0.743465i | \(-0.733181\pi\) | ||||
−0.668774 | + | 0.743465i | \(0.733181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.508005 | −0.0319380 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.2110 | −1.63500 | −0.817500 | − | 0.575929i | \(-0.804640\pi\) | ||||
−0.817500 | + | 0.575929i | \(0.804640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.9634 | 1.67543 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.9037 | 1.78910 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.65276 | −0.348564 | −0.174282 | − | 0.984696i | \(-0.555760\pi\) | ||||
−0.174282 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7191 | 1.08439 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.65772 | 0.588841 | 0.294421 | − | 0.955676i | \(-0.404873\pi\) | ||||
0.294421 | + | 0.955676i | \(0.404873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.39040 | −0.509680 | −0.254840 | − | 0.966983i | \(-0.582023\pi\) | ||||
−0.254840 | + | 0.966983i | \(0.582023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.1535 | −0.614515 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.3317 | −1.82246 | −0.911229 | − | 0.411900i | \(-0.864865\pi\) | ||||
−0.911229 | + | 0.411900i | \(0.864865\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.68964 | 0.101156 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3132 | −1.51006 | −0.755028 | − | 0.655692i | \(-0.772377\pi\) | ||||
−0.755028 | + | 0.655692i | \(0.772377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9629 | −0.770566 | −0.385283 | − | 0.922798i | \(-0.625896\pi\) | ||||
−0.385283 | + | 0.922798i | \(0.625896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.9924 | 1.23914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9060 | −0.876826 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.820209 | 0.0480815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.9469 | −1.51584 | −0.757918 | − | 0.652350i | \(-0.773783\pi\) | ||||
−0.757918 | + | 0.652350i | \(0.773783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.12801 | 0.0654539 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.01106 | 0.0584709 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.8103 | 1.48768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.6447 | −0.726419 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0640 | 0.688531 | 0.344266 | − | 0.938872i | \(-0.388128\pi\) | ||||
0.344266 | + | 0.938872i | \(0.388128\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.1384 | 1.20252 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.8125 | 1.80392 | 0.901959 | − | 0.431821i | \(-0.142129\pi\) | ||||
0.901959 | + | 0.431821i | \(0.142129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.30122 | 0.243119 | 0.121560 | − | 0.992584i | \(-0.461210\pi\) | ||||
0.121560 | + | 0.992584i | \(0.461210\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.28317 | 0.352898 | 0.176449 | − | 0.984310i | \(-0.443539\pi\) | ||||
0.176449 | + | 0.984310i | \(0.443539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.81532 | 0.213617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.2020 | −1.62990 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.735109 | −0.0409026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.0624 | 2.54726 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.1346 | −0.558739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00053 | 0.439749 | 0.219874 | − | 0.975528i | \(-0.429435\pi\) | ||||
0.219874 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.0411 | 1.48184 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1436 | −0.552554 | −0.276277 | − | 0.961078i | \(-0.589101\pi\) | ||||
−0.276277 | + | 0.961078i | \(0.589101\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6367 | 0.577709 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.223034 | 0.0120780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.78567 | 0.150412 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.8747 | −1.01325 | −0.506625 | − | 0.862167i | \(-0.669107\pi\) | ||||
−0.506625 | + | 0.862167i | \(0.669107\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.26611 | 0.496004 | 0.248002 | − | 0.968760i | \(-0.420226\pi\) | ||||
0.248002 | + | 0.968760i | \(0.420226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.24502 | −0.119831 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.04442 | −0.428161 | −0.214081 | − | 0.976816i | \(-0.568676\pi\) | ||||
−0.214081 | + | 0.976816i | \(0.568676\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.5319 | −0.769109 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5443 | −1.08429 | −0.542144 | − | 0.840285i | \(-0.682387\pi\) | ||||
−0.542144 | + | 0.840285i | \(0.682387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7419 | −0.986417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.1112 | −1.47546 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.64032 | −0.451021 | −0.225511 | − | 0.974241i | \(-0.572405\pi\) | ||||
−0.225511 | + | 0.974241i | \(0.572405\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.0528 | 1.09597 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.3294 | −0.951617 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0442 | 0.986073 | 0.493037 | − | 0.870009i | \(-0.335887\pi\) | ||||
0.493037 | + | 0.870009i | \(0.335887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.59344 | −0.391082 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.926121 | −0.0475717 | −0.0237858 | − | 0.999717i | \(-0.507572\pi\) | ||||
−0.0237858 | + | 0.999717i | \(0.507572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4370 | 0.637167 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.38526 | −0.479564 | −0.239782 | − | 0.970827i | \(-0.577076\pi\) | ||||
−0.239782 | + | 0.970827i | \(0.577076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.8847 | 1.31579 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.22865 | 0.112997 | 0.0564985 | − | 0.998403i | \(-0.482006\pi\) | ||||
0.0564985 | + | 0.998403i | \(0.482006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.44705 | 0.0731805 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.15151 | −0.259859 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0448 | −0.654701 | −0.327350 | − | 0.944903i | \(-0.606156\pi\) | ||||
−0.327350 | + | 0.944903i | \(0.606156\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.10161 | 0.255400 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.22221 | −0.110972 | −0.0554859 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554859 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.443893 | −0.0221119 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.56946 | 0.176931 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.5232 | −0.965362 | −0.482681 | − | 0.875796i | \(-0.660337\pi\) | ||||
−0.482681 | + | 0.875796i | \(0.660337\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.7671 | 0.728409 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.7874 | −0.727638 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.8817 | 0.973611 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.9180 | 1.21732 | 0.608662 | − | 0.793430i | \(-0.291707\pi\) | ||||
0.608662 | + | 0.793430i | \(0.291707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.10721 | 0.297647 | 0.148824 | − | 0.988864i | \(-0.452451\pi\) | ||||
0.148824 | + | 0.988864i | \(0.452451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.1638 | −0.494181 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.7612 | −1.68221 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.34413 | −0.0648952 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.44095 | −0.213913 | −0.106956 | − | 0.994264i | \(-0.534111\pi\) | ||||
−0.106956 | + | 0.994264i | \(0.534111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.25554 | −0.156451 | −0.0782257 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782257 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.508005 | −0.0243012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9611 | 1.28678 | 0.643392 | − | 0.765537i | \(-0.277527\pi\) | ||||
0.643392 | + | 0.765537i | \(0.277527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.7331 | 1.41586 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0072 | −0.760526 | −0.380263 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380263 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.1869 | 1.33320 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4278 | −1.76633 | −0.883163 | − | 0.469066i | \(-0.844591\pi\) | ||||
−0.883163 | + | 0.469066i | \(0.844591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.77900 | 0.130858 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.2670 | 2.03286 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.75949 | 0.409752 | 0.204876 | − | 0.978788i | \(-0.434321\pi\) | ||||
0.204876 | + | 0.978788i | \(0.434321\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.21314 | −0.149976 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4459 | 0.533089 | 0.266545 | − | 0.963823i | \(-0.414118\pi\) | ||||
0.266545 | + | 0.963823i | \(0.414118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.23570 | 0.382745 | 0.191373 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191373 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9436 | −1.33935 | −0.669675 | − | 0.742654i | \(-0.733567\pi\) | ||||
−0.669675 | + | 0.742654i | \(0.733567\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2659 | 0.612561 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.2092 | 1.39197 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.41680 | 0.157105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.3823 | −0.841666 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.1031 | −1.42114 | −0.710569 | − | 0.703627i | \(-0.751563\pi\) | ||||
−0.710569 | + | 0.703627i | \(0.751563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.10410 | −0.323919 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.0424 | −0.456946 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.90588 | 0.0863635 | 0.0431817 | − | 0.999067i | \(-0.486251\pi\) | ||||
0.0431817 | + | 0.999067i | \(0.486251\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.69206 | 0.393069 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.2222 | 1.22852 | 0.614259 | − | 0.789104i | \(-0.289455\pi\) | ||||
0.614259 | + | 0.789104i | \(0.289455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8679 | −0.489467 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.5011 | 0.471039 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.38913 | 0.420315 | 0.210158 | − | 0.977668i | \(-0.432602\pi\) | ||||
0.210158 | + | 0.977668i | \(0.432602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.1678 | 1.48183 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.5613 | 1.31807 | 0.659037 | − | 0.752110i | \(-0.270964\pi\) | ||||
0.659037 | + | 0.752110i | \(0.270964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.3454 | −1.39210 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.448890 | 0.0198967 | 0.00994835 | − | 0.999951i | \(-0.496833\pi\) | ||||
0.00994835 | + | 0.999951i | \(0.496833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.3543 | 1.56398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.12801 | 0.0498030 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.34163 | −0.0590050 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −45.9886 | −2.01867 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8712 | 1.17725 | 0.588623 | − | 0.808407i | \(-0.299670\pi\) | ||||
0.588623 | + | 0.808407i | \(0.299670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.90473 | 0.127015 | 0.0635075 | − | 0.997981i | \(-0.479771\pi\) | ||||
0.0635075 | + | 0.997981i | \(0.479771\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.635311 | −0.0276746 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8300 | −0.643566 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.53089 | −0.239570 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.9801 | 1.68212 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.92481 | 0.169053 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.0386 | 1.46343 | 0.731716 | − | 0.681610i | \(-0.238720\pi\) | ||||
0.731716 | + | 0.681610i | \(0.238720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −60.9406 | −2.61521 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.8364 | −1.01917 | −0.509586 | − | 0.860420i | \(-0.670202\pi\) | ||||
−0.509586 | + | 0.860420i | \(0.670202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.8613 | −1.48785 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.81532 | 0.162538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.4866 | −1.72167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.4201 | −1.71265 | −0.856326 | − | 0.516435i | \(-0.827259\pi\) | ||||
−0.856326 | + | 0.516435i | \(0.827259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.80028 | −0.287621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.92375 | −0.0812209 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.54758 | −0.275948 | −0.137974 | − | 0.990436i | \(-0.544059\pi\) | ||||
−0.137974 | + | 0.990436i | \(0.544059\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0061 | −0.924169 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.4590 | 0.857686 | 0.428843 | − | 0.903379i | \(-0.358921\pi\) | ||||
0.428843 | + | 0.903379i | \(0.358921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.71300 | −0.197233 | −0.0986164 | − | 0.995126i | \(-0.531442\pi\) | ||||
−0.0986164 | + | 0.995126i | \(0.531442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1188 | −0.756924 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.9331 | 1.07961 | 0.539805 | − | 0.841790i | \(-0.318498\pi\) | ||||
0.539805 | + | 0.841790i | \(0.318498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.2636 | 0.842127 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.38049 | −0.223220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.42648 | −0.100494 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.4711 | 0.432189 | 0.216095 | − | 0.976372i | \(-0.430668\pi\) | ||||
0.216095 | + | 0.976372i | \(0.430668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.223034 | 0.00918995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 62.5213 | 2.57178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.8158 | −0.854803 | −0.427401 | − | 0.904062i | \(-0.640571\pi\) | ||||
−0.427401 | + | 0.904062i | \(0.640571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 62.6616 | 2.56457 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7951 | 0.604511 | 0.302256 | − | 0.953227i | \(-0.402260\pi\) | ||||
0.302256 | + | 0.953227i | \(0.402260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.8995 | −1.38279 | −0.691394 | − | 0.722477i | \(-0.743003\pi\) | ||||
−0.691394 | + | 0.722477i | \(0.743003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3041 | 0.541784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9350 | 1.33679 | 0.668394 | − | 0.743807i | \(-0.266982\pi\) | ||||
0.668394 | + | 0.743807i | \(0.266982\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 75.4227 | 3.05628 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.67018 | 0.108024 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.8664 | 1.00434 | 0.502172 | − | 0.864768i | \(-0.332535\pi\) | ||||
0.502172 | + | 0.864768i | \(0.332535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1280 | 0.810324 | 0.405162 | − | 0.914245i | \(-0.367215\pi\) | ||||
0.405162 | + | 0.914245i | \(0.367215\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.3719 | 0.617847 | 0.308924 | − | 0.951087i | \(-0.400031\pi\) | ||||
0.308924 | + | 0.951087i | \(0.400031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.22047 | −0.0891046 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.9828 | 1.04098 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.675358 | 0.0269712 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1676 | −0.405408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7115 | 1.02356 | 0.511779 | − | 0.859117i | \(-0.328987\pi\) | ||||
0.511779 | + | 0.859117i | \(0.328987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −37.8699 | −1.50519 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.81134 | −0.309497 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.5314 | 0.416614 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.95684 | 0.116788 | 0.0583941 | − | 0.998294i | \(-0.481402\pi\) | ||||
0.0583941 | + | 0.998294i | \(0.481402\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.7764 | −0.661596 | −0.330798 | − | 0.943702i | \(-0.607318\pi\) | ||||
−0.330798 | + | 0.943702i | \(0.607318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.99247 | −0.0783322 | −0.0391661 | − | 0.999233i | \(-0.512470\pi\) | ||||
−0.0391661 | + | 0.999233i | \(0.512470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.95757 | −0.0768414 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.40901 | 0.172803 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.4989 | −1.81964 | −0.909822 | − | 0.414999i | \(-0.863782\pi\) | ||||
−0.909822 | + | 0.414999i | \(0.863782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.4562 | 1.38328 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1468 | 1.44703 | 0.723517 | − | 0.690307i | \(-0.242524\pi\) | ||||
0.723517 | + | 0.690307i | \(0.242524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.01756 | −0.272952 | −0.136476 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136476 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.82874 | 0.148696 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.51040 | −0.290804 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.4242 | −0.480346 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.60174 | −0.177648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.81155 | 0.262566 | 0.131283 | − | 0.991345i | \(-0.458090\pi\) | ||||
0.131283 | + | 0.991345i | \(0.458090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.522812 | −0.0200933 | −0.0100466 | − | 0.999950i | \(-0.503198\pi\) | ||||
−0.0100466 | + | 0.999950i | \(0.503198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.20273 | 0.0461566 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5108 | 0.900934 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.93412 | 0.112271 | 0.0561355 | − | 0.998423i | \(-0.482122\pi\) | ||||
0.0561355 | + | 0.998423i | \(0.482122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.2471 | 2.06965 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.82929 | 0.183981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8456 | 1.21146 | 0.605731 | − | 0.795669i | \(-0.292881\pi\) | ||||
0.605731 | + | 0.795669i | \(0.292881\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50240 | 0.284993 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.91596 | −0.299838 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −68.2070 | −2.57982 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2070 | 0.423283 | 0.211642 | − | 0.977347i | \(-0.432119\pi\) | ||||
0.211642 | + | 0.977347i | \(0.432119\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.56946 | 0.134625 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.5418 | −0.697336 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7300 | 0.891198 | 0.445599 | − | 0.895233i | \(-0.352991\pi\) | ||||
0.445599 | + | 0.895233i | \(0.352991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.6033 | −1.52274 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.439038 | −0.0164421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.69934 | 0.287537 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8687 | 1.03933 | 0.519664 | − | 0.854371i | \(-0.326057\pi\) | ||||
0.519664 | + | 0.854371i | \(0.326057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.9968 | 1.15438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −65.2705 | −2.42744 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.5773 | −1.76455 | −0.882273 | − | 0.470739i | \(-0.843987\pi\) | ||||
−0.882273 | + | 0.470739i | \(0.843987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5022 | −1.46304 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.73274 | −0.359978 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4086 | −0.569129 | −0.284565 | − | 0.958657i | \(-0.591849\pi\) | ||||
−0.284565 | + | 0.958657i | \(0.591849\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.75615 | 0.0646888 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.0212 | −1.95042 | −0.975208 | − | 0.221292i | \(-0.928973\pi\) | ||||
−0.975208 | + | 0.221292i | \(0.928973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.34413 | −0.0493778 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6611 | 0.574551 | 0.287275 | − | 0.957848i | \(-0.407250\pi\) | ||||
0.287275 | + | 0.957848i | \(0.407250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.39599 | −0.197429 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.8209 | −1.56464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.6216 | −1.26336 | −0.631679 | − | 0.775230i | \(-0.717634\pi\) | ||||
−0.631679 | + | 0.775230i | \(0.717634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −55.4554 | −2.02091 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.4389 | 1.39709 | 0.698543 | − | 0.715568i | \(-0.253832\pi\) | ||||
0.698543 | + | 0.715568i | \(0.253832\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.32943 | −0.0482553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.0932 | 1.52588 | 0.762939 | − | 0.646470i | \(-0.223755\pi\) | ||||
0.762939 | + | 0.646470i | \(0.223755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.5446 | 2.44528 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.89605 | 0.140678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.2859 | 1.23638 | 0.618191 | − | 0.786028i | \(-0.287866\pi\) | ||||
0.618191 | + | 0.786028i | \(0.287866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −68.5933 | −2.47033 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7422 | 0.458304 | 0.229152 | − | 0.973391i | \(-0.426405\pi\) | ||||
0.229152 | + | 0.973391i | \(0.426405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 70.5623 | 2.53141 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.77900 | 0.0995679 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.39015 | 0.0497436 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.6766 | 0.595975 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.5534 | 1.01782 | 0.508910 | − | 0.860820i | \(-0.330049\pi\) | ||||
0.508910 | + | 0.860820i | \(0.330049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.7931 | −0.526647 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.5974 | 0.554580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.15859 | 0.325231 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.39925 | 0.297517 | 0.148758 | − | 0.988874i | \(-0.452472\pi\) | ||||
0.148758 | + | 0.988874i | \(0.452472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.82164 | 0.135200 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.0576 | 0.920701 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.68026 | 0.165163 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2739 | 0.889683 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.8816 | −1.01542 | −0.507712 | − | 0.861527i | \(-0.669509\pi\) | ||||
−0.507712 | + | 0.861527i | \(0.669509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.5292 | 1.63386 | 0.816931 | − | 0.576736i | \(-0.195674\pi\) | ||||
0.816931 | + | 0.576736i | \(0.195674\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.9574 | −0.770078 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.41680 | 0.119539 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.9316 | −0.521753 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.99065 | −0.104374 | −0.0521872 | − | 0.998637i | \(-0.516619\pi\) | ||||
−0.0521872 | + | 0.998637i | \(0.516619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.14357 | 0.179294 | 0.0896468 | − | 0.995974i | \(-0.471426\pi\) | ||||
0.0896468 | + | 0.995974i | \(0.471426\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.4288 | −1.85790 | −0.928950 | − | 0.370205i | \(-0.879287\pi\) | ||||
−0.928950 | + | 0.370205i | \(0.879287\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5290 | 0.400420 | 0.200210 | − | 0.979753i | \(-0.435838\pi\) | ||||
0.200210 | + | 0.979753i | \(0.435838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −79.3770 | −2.75356 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.1798 | −0.387357 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.974874 | 0.0336966 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0983 | −0.417678 | −0.208839 | − | 0.977950i | \(-0.566968\pi\) | ||||
−0.208839 | + | 0.977950i | \(0.566968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4061 | 0.945038 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −66.2436 | −2.28155 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41.2215 | −1.41639 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −33.9235 | −1.16425 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.02642 | −0.240862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.10103 | −0.106177 | −0.0530886 | − | 0.998590i | \(-0.516907\pi\) | ||||
−0.0530886 | + | 0.998590i | \(0.516907\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.39457 | −0.150116 | −0.0750578 | − | 0.997179i | \(-0.523914\pi\) | ||||
−0.0750578 | + | 0.997179i | \(0.523914\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0453 | 0.991014 | 0.495507 | − | 0.868604i | \(-0.334982\pi\) | ||||
0.495507 | + | 0.868604i | \(0.334982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 54.9362 | 1.87222 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.1020 | −1.36509 | −0.682543 | − | 0.730845i | \(-0.739126\pi\) | ||||
−0.682543 | + | 0.730845i | \(0.739126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.0086 | −1.32480 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.35968 | −0.181815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.49518 | −0.118430 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.20620 | 0.0408235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.7503 | −1.27474 | −0.637368 | − | 0.770559i | \(-0.719977\pi\) | ||||
−0.637368 | + | 0.770559i | \(0.719977\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −67.9021 | −2.29028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.1541 | −0.982227 | −0.491113 | − | 0.871096i | \(-0.663410\pi\) | ||||
−0.491113 | + | 0.871096i | \(0.663410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.3971 | −1.46043 | −0.730214 | − | 0.683218i | \(-0.760580\pi\) | ||||
−0.730214 | + | 0.683218i | \(0.760580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.4091 | −0.853155 | −0.426578 | − | 0.904451i | \(-0.640281\pi\) | ||||
−0.426578 | + | 0.904451i | \(0.640281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.2373 | 0.611658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.91320 | −0.0975958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.34163 | −0.0448961 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.64590 | 0.0883439 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.29735 | 0.109973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.91181 | 0.230266 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.5446 | 2.24774 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.00778 | 0.0666672 | 0.0333336 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333336 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.5952 | −0.616765 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.45792 | 0.280223 | 0.140112 | − | 0.990136i | \(-0.455254\pi\) | ||||
0.140112 | + | 0.990136i | \(0.455254\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.712277 | −0.0235729 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.55402 | −0.249456 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.840028 | −0.0277100 | −0.0138550 | − | 0.999904i | \(-0.504410\pi\) | ||||
−0.0138550 | + | 0.999904i | \(0.504410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5711 | 1.04030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.76675 | −0.0910686 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.0861 | 1.02100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.7877 | 0.517979 | 0.258989 | − | 0.965880i | \(-0.416611\pi\) | ||||
0.258989 | + | 0.965880i | \(0.416611\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.92481 | 0.128630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 83.2520 | 2.72555 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.6568 | −1.03418 | −0.517091 | − | 0.855930i | \(-0.672985\pi\) | ||||
−0.517091 | + | 0.855930i | \(0.672985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2561 | 0.367330 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.3932 | −1.25158 | −0.625792 | − | 0.779990i | \(-0.715224\pi\) | ||||
−0.625792 | + | 0.779990i | \(0.715224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.47041 | −0.178141 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.3783 | −1.11714 | −0.558572 | − | 0.829456i | \(-0.688651\pi\) | ||||
−0.558572 | + | 0.829456i | \(0.688651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.31486 | −0.302373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.4428 | 0.533195 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.3782 | −1.56712 | −0.783562 | − | 0.621314i | \(-0.786599\pi\) | ||||
−0.783562 | + | 0.621314i | \(0.786599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.98456 | 0.322755 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.6541 | 0.699247 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8072 | −0.993782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.9443 | −1.38386 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.3705 | −1.65196 | −0.825982 | − | 0.563697i | \(-0.809379\pi\) | ||||
−0.825982 | + | 0.563697i | \(0.809379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.92375 | −0.0617999 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.4587 | −1.61930 | −0.809649 | − | 0.586914i | \(-0.800343\pi\) | ||||
−0.809649 | + | 0.586914i | \(0.800343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1539 | 0.934633 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.1406 | −1.02827 | −0.514134 | − | 0.857710i | \(-0.671887\pi\) | ||||
−0.514134 | + | 0.857710i | \(0.671887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.43964 | 0.109931 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 67.7392 | 2.16275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.1306 | 0.769647 | 0.384824 | − | 0.922990i | \(-0.374262\pi\) | ||||
0.384824 | + | 0.922990i | \(0.374262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.5219 | −0.844201 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.72592 | −0.213872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.1267 | −1.27467 | −0.637333 | − | 0.770588i | \(-0.719962\pi\) | ||||
−0.637333 | + | 0.770588i | \(0.719962\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.9371 | 0.664418 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.9890 | 1.55150 | 0.775749 | − | 0.631042i | \(-0.217372\pi\) | ||||
0.775749 | + | 0.631042i | \(0.217372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.6020 | 0.493625 |
(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 | 9200.2.a.cv.1.5 | 5 | ||
4.3 | odd | 2 | 4600.2.a.bd.1.1 | ✓ | 5 | ||
5.4 | even | 2 | 9200.2.a.ct.1.1 | 5 | |||
20.3 | even | 4 | 4600.2.e.w.4049.1 | 10 | |||
20.7 | even | 4 | 4600.2.e.w.4049.10 | 10 | |||
20.19 | odd | 2 | 4600.2.a.bf.1.5 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bd.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
4600.2.a.bf.1.5 | yes | 5 | 20.19 | odd | 2 | ||
4600.2.e.w.4049.1 | 10 | 20.3 | even | 4 | |||
4600.2.e.w.4049.10 | 10 | 20.7 | even | 4 | |||
9200.2.a.ct.1.1 | 5 | 5.4 | even | 2 | |||
9200.2.a.cv.1.5 | 5 | 1.1 | even | 1 | trivial |