Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, 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("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.47214 | −1.34840 | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23607 | −0.784862 | −0.392431 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392431 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.47214 | −1.76656 | −0.883281 | − | 0.468844i | \(-0.844671\pi\) | ||||
−0.883281 | + | 0.468844i | \(0.844671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.76393 | −0.513249 | −0.256625 | − | 0.966511i | \(-0.582610\pi\) | ||||
−0.256625 | + | 0.966511i | \(0.582610\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47214 | −0.444009 | −0.222004 | − | 0.975046i | \(-0.571260\pi\) | ||||
−0.222004 | + | 0.975046i | \(0.571260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.23607 | −0.546995 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214 | 0.735215 | 0.367607 | − | 0.929981i | \(-0.380177\pi\) | ||||
0.367607 | + | 0.929981i | \(0.380177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.23607 | −0.180299 | −0.0901495 | − | 0.995928i | \(-0.528734\pi\) | ||||
−0.0901495 | + | 0.995928i | \(0.528734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.23607 | −0.169787 | −0.0848935 | − | 0.996390i | \(-0.527055\pi\) | ||||
−0.0848935 | + | 0.996390i | \(0.527055\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4721 | −1.95142 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4721 | 1.79505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4721 | −1.27938 | −0.639688 | − | 0.768635i | \(-0.720936\pi\) | ||||
−0.639688 | + | 0.768635i | \(0.720936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.763932 | −0.0906621 | −0.0453310 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453310 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.47214 | −0.523424 | −0.261712 | − | 0.965146i | \(-0.584287\pi\) | ||||
−0.261712 | + | 0.965146i | \(0.584287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214 | 0.509647 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.70820 | −0.846085 | −0.423043 | − | 0.906110i | \(-0.639038\pi\) | ||||
−0.423043 | + | 0.906110i | \(0.639038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4721 | −1.13586 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.94427 | 0.736091 | 0.368046 | − | 0.929808i | \(-0.380027\pi\) | ||||
0.368046 | + | 0.929808i | \(0.380027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47214 | −0.468807 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.23607 | 0.332014 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4721 | 1.26635 | 0.633177 | − | 0.774007i | \(-0.281751\pi\) | ||||
0.633177 | + | 0.774007i | \(0.281751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.18034 | 0.415959 | 0.207980 | − | 0.978133i | \(-0.433311\pi\) | ||||
0.207980 | + | 0.978133i | \(0.433311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.94427 | 0.881305 | 0.440653 | − | 0.897678i | \(-0.354747\pi\) | ||||
0.440653 | + | 0.897678i | \(0.354747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.70820 | −0.551833 | −0.275916 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275916 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94427 | −0.282010 | −0.141005 | − | 0.990009i | \(-0.545033\pi\) | ||||
−0.141005 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.7639 | −1.01259 | −0.506293 | − | 0.862362i | \(-0.668984\pi\) | ||||
−0.506293 | + | 0.862362i | \(0.668984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.4164 | −2.55659 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.23607 | 0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.52786 | −0.135576 | −0.0677880 | − | 0.997700i | \(-0.521594\pi\) | ||||
−0.0677880 | + | 0.997700i | \(0.521594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2361 | −1.15644 | −0.578220 | − | 0.815881i | \(-0.696253\pi\) | ||||
−0.578220 | + | 0.815881i | \(0.696253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9443 | −1.44765 | −0.723823 | − | 0.689985i | \(-0.757617\pi\) | ||||
−0.723823 | + | 0.689985i | \(0.757617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4721 | −0.888235 | −0.444117 | − | 0.895969i | \(-0.646483\pi\) | ||||
−0.444117 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.0000 | −1.67248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.94427 | −0.742781 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.52786 | −0.125167 | −0.0625837 | − | 0.998040i | \(-0.519934\pi\) | ||||
−0.0625837 | + | 0.998040i | \(0.519934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3607 | −1.78458 | −0.892288 | − | 0.451466i | \(-0.850901\pi\) | ||||
−0.892288 | + | 0.451466i | \(0.850901\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.47214 | 0.667698 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.47214 | −0.500829 | −0.250414 | − | 0.968139i | \(-0.580567\pi\) | ||||
−0.250414 | + | 0.968139i | \(0.580567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9443 | 0.832078 | 0.416039 | − | 0.909347i | \(-0.363418\pi\) | ||||
0.416039 | + | 0.909347i | \(0.363418\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.47214 | −0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.70820 | 0.426651 | 0.213326 | − | 0.976981i | \(-0.431570\pi\) | ||||
0.213326 | + | 0.976981i | \(0.431570\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.47214 | −0.332411 | −0.166206 | − | 0.986091i | \(-0.553152\pi\) | ||||
−0.166206 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.4721 | 1.06401 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.4721 | 1.05831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5279 | −1.12356 | −0.561778 | − | 0.827288i | \(-0.689883\pi\) | ||||
−0.561778 | + | 0.827288i | \(0.689883\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.47214 | 0.609838 | 0.304919 | − | 0.952378i | \(-0.401371\pi\) | ||||
0.304919 | + | 0.952378i | \(0.401371\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9443 | −0.917595 | −0.458798 | − | 0.888541i | \(-0.651720\pi\) | ||||
−0.458798 | + | 0.888541i | \(0.651720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.76393 | 0.193990 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47214 | 0.452034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.47214 | 0.170189 | 0.0850944 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850944 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.8885 | 1.76558 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.47214 | 0.167820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4721 | −0.973501 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.41641 | 0.228780 | 0.114390 | − | 0.993436i | \(-0.463509\pi\) | ||||
0.114390 | + | 0.993436i | \(0.463509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.4164 | −0.757734 | −0.378867 | − | 0.925451i | \(-0.623686\pi\) | ||||
−0.378867 | + | 0.925451i | \(0.623686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.05573 | 0.334092 | 0.167046 | − | 0.985949i | \(-0.446577\pi\) | ||||
0.167046 | + | 0.985949i | \(0.446577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.47214 | −0.424004 | −0.212002 | − | 0.977269i | \(-0.567998\pi\) | ||||
−0.212002 | + | 0.977269i | \(0.567998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | −0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9443 | 1.48414 | 0.742071 | − | 0.670322i | \(-0.233844\pi\) | ||||
0.742071 | + | 0.670322i | \(0.233844\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.47214 | −0.545738 | −0.272869 | − | 0.962051i | \(-0.587973\pi\) | ||||
−0.272869 | + | 0.962051i | \(0.587973\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.23607 | 0.206745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.47214 | 0.284555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1803 | −1.40001 | −0.700005 | − | 0.714138i | \(-0.746819\pi\) | ||||
−0.700005 | + | 0.714138i | \(0.746819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.8885 | 2.38203 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.52786 | −0.220062 | −0.110031 | − | 0.993928i | \(-0.535095\pi\) | ||||
−0.110031 | + | 0.993928i | \(0.535095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.47214 | −0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.9443 | 0.921503 | 0.460752 | − | 0.887529i | \(-0.347580\pi\) | ||||
0.460752 | + | 0.887529i | \(0.347580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.4721 | −1.49209 | −0.746046 | − | 0.665894i | \(-0.768050\pi\) | ||||
−0.746046 | + | 0.665894i | \(0.768050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4721 | −0.879120 | −0.439560 | − | 0.898213i | \(-0.644866\pi\) | ||||
−0.439560 | + | 0.898213i | \(0.644866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.4721 | −1.47573 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.47214 | 0.268705 | 0.134352 | − | 0.990934i | \(-0.457105\pi\) | ||||
0.134352 | + | 0.990934i | \(0.457105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1803 | 0.845928 | 0.422964 | − | 0.906146i | \(-0.360990\pi\) | ||||
0.422964 | + | 0.906146i | \(0.360990\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9443 | −1.48278 | −0.741392 | − | 0.671073i | \(-0.765834\pi\) | ||||
−0.741392 | + | 0.671073i | \(0.765834\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.52786 | −0.383992 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.0000 | −1.51894 | −0.759468 | − | 0.650545i | \(-0.774541\pi\) | ||||
−0.759468 | + | 0.650545i | \(0.774541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9443 | 0.753645 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.8885 | −2.19115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.3607 | −2.31105 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4721 | 1.51084 | 0.755422 | − | 0.655238i | \(-0.227432\pi\) | ||||
0.755422 | + | 0.655238i | \(0.227432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.18034 | −0.350455 | −0.175227 | − | 0.984528i | \(-0.556066\pi\) | ||||
−0.175227 | + | 0.984528i | \(0.556066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4721 | 0.704967 | 0.352483 | − | 0.935818i | \(-0.385337\pi\) | ||||
0.352483 | + | 0.935818i | \(0.385337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.1246 | 1.52347 | 0.761735 | − | 0.647889i | \(-0.224348\pi\) | ||||
0.761735 | + | 0.647889i | \(0.224348\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.3607 | 0.692065 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.23607 | −0.180060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.4721 | 1.35747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.23607 | 0.0681466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8885 | 1.42296 | 0.711482 | − | 0.702705i | \(-0.248025\pi\) | ||||
0.711482 | + | 0.702705i | \(0.248025\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.8885 | −1.85153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9443 | −0.814066 | −0.407033 | − | 0.913413i | \(-0.633437\pi\) | ||||
−0.407033 | + | 0.913413i | \(0.633437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.0557 | 0.598701 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.0000 | −1.61048 | −0.805242 | − | 0.592946i | \(-0.797965\pi\) | ||||
−0.805242 | + | 0.592946i | \(0.797965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.8328 | 1.54339 | 0.771693 | − | 0.635996i | \(-0.219410\pi\) | ||||
0.771693 | + | 0.635996i | \(0.219410\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.2918 | −0.760676 | −0.380338 | − | 0.924848i | \(-0.624192\pi\) | ||||
−0.380338 | + | 0.924848i | \(0.624192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.47214 | −0.131207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.4164 | 1.55254 | 0.776269 | − | 0.630401i | \(-0.217110\pi\) | ||||
0.776269 | + | 0.630401i | \(0.217110\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4721 | −0.757506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.9443 | −0.675685 | −0.337843 | − | 0.941203i | \(-0.609697\pi\) | ||||
−0.337843 | + | 0.941203i | \(0.609697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23607 | 0.0641735 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.94427 | 0.152449 | 0.0762243 | − | 0.997091i | \(-0.475713\pi\) | ||||
0.0762243 | + | 0.997091i | \(0.475713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.3607 | −0.636607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.05573 | −0.156962 | −0.0784811 | − | 0.996916i | \(-0.525007\pi\) | ||||
−0.0784811 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4721 | 0.535101 | 0.267551 | − | 0.963544i | \(-0.413786\pi\) | ||||
0.267551 | + | 0.963544i | \(0.413786\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4721 | 0.737568 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.4164 | 1.59288 | 0.796438 | − | 0.604721i | \(-0.206715\pi\) | ||||
0.796438 | + | 0.604721i | \(0.206715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.4164 | 1.38651 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.8328 | −1.95389 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.8885 | −0.596669 | −0.298334 | − | 0.954461i | \(-0.596431\pi\) | ||||
−0.298334 | + | 0.954461i | \(0.596431\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.1803 | −1.50713 | −0.753567 | − | 0.657371i | \(-0.771668\pi\) | ||||
−0.753567 | + | 0.657371i | \(0.771668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0557 | −0.550725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.3607 | −1.10566 | −0.552832 | − | 0.833293i | \(-0.686453\pi\) | ||||
−0.552832 | + | 0.833293i | \(0.686453\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.9443 | −1.22447 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.1246 | 0.934298 | 0.467149 | − | 0.884178i | \(-0.345281\pi\) | ||||
0.467149 | + | 0.884178i | \(0.345281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.3050 | 1.13581 | 0.567907 | − | 0.823093i | \(-0.307753\pi\) | ||||
0.567907 | + | 0.823093i | \(0.307753\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.7082 | −0.858974 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4721 | 0.603569 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.0689 | 1.06302 | 0.531510 | − | 0.847052i | \(-0.321625\pi\) | ||||
0.531510 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.47214 | 0.407145 | 0.203572 | − | 0.979060i | \(-0.434745\pi\) | ||||
0.203572 | + | 0.979060i | \(0.434745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.47214 | −0.405277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5836 | −0.600582 | −0.300291 | − | 0.953848i | \(-0.597084\pi\) | ||||
−0.300291 | + | 0.953848i | \(0.597084\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.8885 | 0.944933 | 0.472467 | − | 0.881349i | \(-0.343364\pi\) | ||||
0.472467 | + | 0.881349i | \(0.343364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.4721 | 1.06528 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7639 | 0.507981 | 0.253991 | − | 0.967207i | \(-0.418257\pi\) | ||||
0.253991 | + | 0.967207i | \(0.418257\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.94427 | −0.421169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.4721 | −0.678464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.41641 | −0.253369 | −0.126684 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.763932 | −0.0355799 | −0.0177899 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177899 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.88854 | 0.459560 | 0.229780 | − | 0.973243i | \(-0.426199\pi\) | ||||
0.229780 | + | 0.973243i | \(0.426199\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.81966 | 0.0842038 | 0.0421019 | − | 0.999113i | \(-0.486595\pi\) | ||||
0.0421019 | + | 0.999113i | \(0.486595\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4721 | 0.483558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.7771 | −1.64503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.47214 | 0.251079 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1246 | 0.873826 | 0.436913 | − | 0.899504i | \(-0.356072\pi\) | ||||
0.436913 | + | 0.899504i | \(0.356072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | 0.911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 40.3607 | 1.83268 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.41641 | −0.154812 | −0.0774061 | − | 0.997000i | \(-0.524664\pi\) | ||||
−0.0774061 | + | 0.997000i | \(0.524664\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.94427 | 0.402830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.763932 | 0.0342670 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.11146 | 0.0945218 | 0.0472609 | − | 0.998883i | \(-0.484951\pi\) | ||||
0.0472609 | + | 0.998883i | \(0.484951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.81966 | 0.259486 | 0.129743 | − | 0.991548i | \(-0.458585\pi\) | ||||
0.129743 | + | 0.991548i | \(0.458585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5279 | 0.601982 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −40.4721 | −1.79390 | −0.896948 | − | 0.442136i | \(-0.854221\pi\) | ||||
−0.896948 | + | 0.442136i | \(0.854221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.47214 | 0.197836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.9443 | 1.27544 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.52786 | 0.243115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.4164 | −1.11351 | −0.556757 | − | 0.830676i | \(-0.687954\pi\) | ||||
−0.556757 | + | 0.830676i | \(0.687954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.4721 | −1.33245 | −0.666227 | − | 0.745749i | \(-0.732092\pi\) | ||||
−0.666227 | + | 0.745749i | \(0.732092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.7771 | 2.12074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.4721 | −0.798620 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.47214 | −0.192629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.111456 | −0.00479188 | −0.00239594 | − | 0.999997i | \(-0.500763\pi\) | ||||
−0.00239594 | + | 0.999997i | \(0.500763\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.52786 | −0.408129 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.8328 | 1.66037 | 0.830186 | − | 0.557487i | \(-0.188234\pi\) | ||||
0.830186 | + | 0.557487i | \(0.188234\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.76393 | −0.117747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | 0.510292 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.4164 | −1.16167 | −0.580835 | − | 0.814021i | \(-0.697274\pi\) | ||||
−0.580835 | + | 0.814021i | \(0.697274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.7771 | 1.51321 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.41641 | 0.143984 | 0.0719922 | − | 0.997405i | \(-0.477064\pi\) | ||||
0.0719922 | + | 0.997405i | \(0.477064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.8328 | −1.46543 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.2918 | 0.515299 | 0.257649 | − | 0.966238i | \(-0.417052\pi\) | ||||
0.257649 | + | 0.966238i | \(0.417052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8885 | −1.25080 | −0.625398 | − | 0.780306i | \(-0.715063\pi\) | ||||
−0.625398 | + | 0.780306i | \(0.715063\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.3607 | −1.93337 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.41641 | 0.0589658 | 0.0294829 | − | 0.999565i | \(-0.490614\pi\) | ||||
0.0294829 | + | 0.999565i | \(0.490614\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.70820 | 0.319790 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.52786 | 0.228941 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7082 | 1.47384 | 0.736918 | − | 0.675983i | \(-0.236281\pi\) | ||||
0.736918 | + | 0.675983i | \(0.236281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.47214 | −0.101863 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.2918 | 1.07967 | 0.539837 | − | 0.841769i | \(-0.318486\pi\) | ||||
0.539837 | + | 0.841769i | \(0.318486\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.4721 | 0.429316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5967 | 1.12757 | 0.563786 | − | 0.825921i | \(-0.309344\pi\) | ||||
0.563786 | + | 0.825921i | \(0.309344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.4164 | 1.85257 | 0.926287 | − | 0.376819i | \(-0.122982\pi\) | ||||
0.926287 | + | 0.376819i | \(0.122982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.1246 | 1.18408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.52786 | −0.223633 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.3607 | −1.38781 | −0.693907 | − | 0.720064i | \(-0.744112\pi\) | ||||
−0.693907 | + | 0.720064i | \(0.744112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.0557 | −1.25026 | −0.625128 | − | 0.780522i | \(-0.714953\pi\) | ||||
−0.625128 | + | 0.780522i | \(0.714953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4164 | 1.26273 | 0.631366 | − | 0.775485i | \(-0.282495\pi\) | ||||
0.631366 | + | 0.775485i | \(0.282495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.94427 | −0.278216 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.4721 | −0.577042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.944272 | 0.0375909 | 0.0187954 | − | 0.999823i | \(-0.494017\pi\) | ||||
0.0187954 | + | 0.999823i | \(0.494017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.94427 | −0.196207 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.47214 | 0.177192 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2918 | −0.801478 | −0.400739 | − | 0.916192i | \(-0.631247\pi\) | ||||
−0.400739 | + | 0.916192i | \(0.631247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9443 | 1.29920 | 0.649598 | − | 0.760278i | \(-0.274937\pi\) | ||||
0.649598 | + | 0.760278i | \(0.274937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6525 | 0.969189 | 0.484594 | − | 0.874739i | \(-0.338967\pi\) | ||||
0.484594 | + | 0.874739i | \(0.338967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8885 | −0.702187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.8885 | −1.63923 | −0.819613 | − | 0.572918i | \(-0.805811\pi\) | ||||
−0.819613 | + | 0.572918i | \(0.805811\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −42.8328 | −1.67362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.2918 | −1.18000 | −0.590000 | − | 0.807403i | \(-0.700872\pi\) | ||||
−0.590000 | + | 0.807403i | \(0.700872\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41641 | −0.0550919 | −0.0275459 | − | 0.999621i | \(-0.508769\pi\) | ||||
−0.0275459 | + | 0.999621i | \(0.508769\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.23607 | −0.125489 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.4164 | 0.906687 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 55.7771 | 2.15325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.2492 | 1.70568 | 0.852841 | − | 0.522171i | \(-0.174878\pi\) | ||||
0.852841 | + | 0.522171i | \(0.174878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.4164 | −0.669367 | −0.334683 | − | 0.942331i | \(-0.608629\pi\) | ||||
−0.334683 | + | 0.942331i | \(0.608629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.4721 | −0.478637 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.2361 | −0.889103 | −0.444552 | − | 0.895753i | \(-0.646637\pi\) | ||||
−0.444552 | + | 0.895753i | \(0.646637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −54.8328 | −2.09505 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.52786 | −0.210595 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5279 | 0.514624 | 0.257312 | − | 0.966328i | \(-0.417163\pi\) | ||||
0.257312 | + | 0.966328i | \(0.417163\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.8885 | −1.28547 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.47214 | −0.245150 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.8328 | −1.46670 | −0.733348 | − | 0.679854i | \(-0.762043\pi\) | ||||
−0.733348 | + | 0.679854i | \(0.762043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.47214 | 0.168670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.18034 | −0.157218 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.2492 | 1.66181 | 0.830907 | − | 0.556411i | \(-0.187822\pi\) | ||||
0.830907 | + | 0.556411i | \(0.187822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.9443 | 0.784369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −64.7214 | −2.42044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.875388 | −0.0326465 | −0.0163232 | − | 0.999867i | \(-0.505196\pi\) | ||||
−0.0163232 | + | 0.999867i | \(0.505196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.94427 | −0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.1246 | −0.561714 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.3607 | −1.49689 | −0.748447 | − | 0.663194i | \(-0.769200\pi\) | ||||
−0.748447 | + | 0.663194i | \(0.769200\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4721 | 0.756156 | 0.378078 | − | 0.925774i | \(-0.376585\pi\) | ||||
0.378078 | + | 0.925774i | \(0.376585\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46.8328 | 1.72511 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.8885 | −0.658041 | −0.329020 | − | 0.944323i | \(-0.606718\pi\) | ||||
−0.329020 | + | 0.944323i | \(0.606718\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.6525 | −0.977785 | −0.488892 | − | 0.872344i | \(-0.662599\pi\) | ||||
−0.488892 | + | 0.872344i | \(0.662599\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.94427 | −0.181144 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.70820 | 0.208573 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.8328 | −1.27107 | −0.635534 | − | 0.772073i | \(-0.719220\pi\) | ||||
−0.635534 | + | 0.772073i | \(0.719220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 64.7214 | 2.35545 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.8885 | −0.577479 | −0.288739 | − | 0.957408i | \(-0.593236\pi\) | ||||
−0.288739 | + | 0.957408i | \(0.593236\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.2361 | 1.56731 | 0.783653 | − | 0.621199i | \(-0.213354\pi\) | ||||
0.783653 | + | 0.621199i | \(0.213354\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.94427 | 0.106590 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.8885 | 0.645918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.3607 | 1.09483 | 0.547417 | − | 0.836860i | \(-0.315611\pi\) | ||||
0.547417 | + | 0.836860i | \(0.315611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.88854 | −0.139861 | −0.0699306 | − | 0.997552i | \(-0.522278\pi\) | ||||
−0.0699306 | + | 0.997552i | \(0.522278\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.5279 | −0.485935 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.00000 | 0.0716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.41641 | 0.122249 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −72.3607 | −2.58266 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.4164 | −1.54763 | −0.773814 | − | 0.633413i | \(-0.781653\pi\) | ||||
−0.773814 | + | 0.633413i | \(0.781653\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7639 | 0.382721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.7771 | −1.98070 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.9443 | 1.52116 | 0.760582 | − | 0.649242i | \(-0.224914\pi\) | ||||
0.760582 | + | 0.649242i | \(0.224914\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.0000 | 0.705785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.4164 | 0.966301 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.8328 | −1.64452 | −0.822261 | − | 0.569110i | \(-0.807288\pi\) | ||||
−0.822261 | + | 0.569110i | \(0.807288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | 0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3607 | 0.570992 | 0.285496 | − | 0.958380i | \(-0.407842\pi\) | ||||
0.285496 | + | 0.958380i | \(0.407842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8328 | 0.377608 | 0.188804 | − | 0.982015i | \(-0.439539\pi\) | ||||
0.188804 | + | 0.982015i | \(0.439539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.2361 | 1.08618 | 0.543092 | − | 0.839673i | \(-0.317253\pi\) | ||||
0.543092 | + | 0.839673i | \(0.317253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.52786 | −0.261454 | −0.130727 | − | 0.991418i | \(-0.541731\pi\) | ||||
−0.130727 | + | 0.991418i | \(0.541731\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.23607 | −0.112123 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.9443 | −0.724806 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3607 | −0.736575 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.6525 | 0.779269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.00000 | −0.309244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.8885 | −1.29880 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.7771 | −1.29346 | −0.646731 | − | 0.762718i | \(-0.723865\pi\) | ||||
−0.646731 | + | 0.762718i | \(0.723865\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.8328 | 0.848273 | 0.424136 | − | 0.905598i | \(-0.360578\pi\) | ||||
0.424136 | + | 0.905598i | \(0.360578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9443 | −0.578131 | −0.289066 | − | 0.957309i | \(-0.593345\pi\) | ||||
−0.289066 | + | 0.957309i | \(0.593345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.8197 | 0.402346 | 0.201173 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201173 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.4164 | 1.20419 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.6656 | 1.82048 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.8328 | −1.58687 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.52786 | −0.0516512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.11146 | 0.138834 | 0.0694170 | − | 0.997588i | \(-0.477886\pi\) | ||||
0.0694170 | + | 0.997588i | \(0.477886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.70820 | 0.0575509 | 0.0287754 | − | 0.999586i | \(-0.490839\pi\) | ||||
0.0287754 | + | 0.999586i | \(0.490839\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.8885 | 1.81349 | 0.906747 | − | 0.421675i | \(-0.138558\pi\) | ||||
0.906747 | + | 0.421675i | \(0.138558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.3607 | 1.62379 | 0.811896 | − | 0.583802i | \(-0.198435\pi\) | ||||
0.811896 | + | 0.583802i | \(0.198435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.52786 | 0.0512429 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.23607 | −0.0413634 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4721 | 0.617455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.83282 | 0.227887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.4721 | −0.481070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.4164 | 1.30880 | 0.654400 | − | 0.756148i | \(-0.272921\pi\) | ||||
0.654400 | + | 0.756148i | \(0.272921\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.12461 | −0.169786 | −0.0848930 | − | 0.996390i | \(-0.527055\pi\) | ||||
−0.0848930 | + | 0.996390i | \(0.527055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.4721 | 1.14086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.2361 | 0.437093 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.88854 | −0.326193 | −0.163096 | − | 0.986610i | \(-0.552148\pi\) | ||||
−0.163096 | + | 0.986610i | \(0.552148\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.41641 | −0.112452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.4721 | 0.804639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.0132 | −1.41122 | −0.705608 | − | 0.708602i | \(-0.749326\pi\) | ||||
−0.705608 | + | 0.708602i | \(0.749326\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.8328 | 1.53160 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.3050 | −1.54210 | −0.771049 | − | 0.636776i | \(-0.780268\pi\) | ||||
−0.771049 | + | 0.636776i | \(0.780268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.9443 | −0.551781 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.5279 | 0.634570 | 0.317285 | − | 0.948330i | \(-0.397229\pi\) | ||||
0.317285 | + | 0.948330i | \(0.397229\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.0000 | −0.649227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.5410 | 0.471030 | 0.235515 | − | 0.971871i | \(-0.424322\pi\) | ||||
0.235515 | + | 0.971871i | \(0.424322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.2492 | −1.62603 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9443 | 0.547159 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.4164 | 0.882565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8328 | −0.605623 | −0.302811 | − | 0.953051i | \(-0.597925\pi\) | ||||
−0.302811 | + | 0.953051i | \(0.597925\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.8328 | −1.24620 | −0.623102 | − | 0.782140i | \(-0.714128\pi\) | ||||
−0.623102 | + | 0.782140i | \(0.714128\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4721 | 0.335721 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1246 | −1.12374 | −0.561868 | − | 0.827227i | \(-0.689917\pi\) | ||||
−0.561868 | + | 0.827227i | \(0.689917\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.0557 | −0.992545 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.9443 | −1.17834 | −0.589170 | − | 0.808009i | \(-0.700545\pi\) | ||||
−0.589170 | + | 0.808009i | \(0.700545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9443 | −0.412439 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.7771 | −2.15519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.4164 | −0.870911 | −0.435455 | − | 0.900210i | \(-0.643413\pi\) | ||||
−0.435455 | + | 0.900210i | \(0.643413\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.8885 | −1.32796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.3607 | 1.08821 | 0.544107 | − | 0.839016i | \(-0.316869\pi\) | ||||
0.544107 | + | 0.839016i | \(0.316869\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 9576.2.a.bq.1.2 | yes | 2 | |
3.2 | odd | 2 | 9576.2.a.be.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9576.2.a.be.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
9576.2.a.bq.1.2 | yes | 2 | 1.1 | even | 1 | trivial |