Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7872,2,Mod(1,7872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7872, 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("7872.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7872 = 2^{6} \cdot 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7872.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: | \(62.8582364712\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 123) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7872.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.853635 | −0.381757 | −0.190878 | − | 0.981614i | \(-0.561134\pi\) | ||||
−0.190878 | + | 0.981614i | \(0.561134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83221 | −1.44844 | −0.724220 | − | 0.689569i | \(-0.757800\pi\) | ||||
−0.724220 | + | 0.689569i | \(0.757800\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.34292 | 1.00793 | 0.503965 | − | 0.863724i | \(-0.331874\pi\) | ||||
0.503965 | + | 0.863724i | \(0.331874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.14637 | −0.872645 | −0.436322 | − | 0.899790i | \(-0.643719\pi\) | ||||
−0.436322 | + | 0.899790i | \(0.643719\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.853635 | −0.220407 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.63565 | 0.881776 | 0.440888 | − | 0.897562i | \(-0.354664\pi\) | ||||
0.440888 | + | 0.897562i | \(0.354664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.14637 | −0.262994 | −0.131497 | − | 0.991317i | \(-0.541978\pi\) | ||||
−0.131497 | + | 0.991317i | \(0.541978\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.83221 | −0.836257 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.85363 | −0.595024 | −0.297512 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297512 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.27131 | −0.854262 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.02877 | 1.49091 | 0.745453 | − | 0.666559i | \(-0.232233\pi\) | ||||
0.745453 | + | 0.666559i | \(0.232233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.86098 | 1.77108 | 0.885542 | − | 0.464559i | \(-0.153787\pi\) | ||||
0.885542 | + | 0.464559i | \(0.153787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.34292 | 0.581928 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.27131 | 0.552952 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.19656 | −1.34751 | −0.673753 | − | 0.738957i | \(-0.735319\pi\) | ||||
−0.673753 | + | 0.738957i | \(0.735319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.14637 | −0.503822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7606 | −1.79347 | −0.896737 | − | 0.442564i | \(-0.854069\pi\) | ||||
−0.896737 | + | 0.442564i | \(0.854069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.853635 | −0.127252 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.32150 | 1.21382 | 0.606908 | − | 0.794772i | \(-0.292410\pi\) | ||||
0.606908 | + | 0.794772i | \(0.292410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.68585 | 1.09798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.63565 | 0.509093 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.60688 | −0.220723 | −0.110361 | − | 0.993892i | \(-0.535201\pi\) | ||||
−0.110361 | + | 0.993892i | \(0.535201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.85363 | −0.384784 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.14637 | −0.151840 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6644 | 1.51858 | 0.759289 | − | 0.650753i | \(-0.225547\pi\) | ||||
0.759289 | + | 0.650753i | \(0.225547\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.19656 | 0.537314 | 0.268657 | − | 0.963236i | \(-0.413420\pi\) | ||||
0.268657 | + | 0.963236i | \(0.413420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.83221 | −0.482813 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.68585 | 0.333138 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.10038 | −0.745281 | −0.372640 | − | 0.927976i | \(-0.621547\pi\) | ||||
−0.372640 | + | 0.927976i | \(0.621547\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.85363 | −0.343537 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.65708 | −1.02741 | −0.513703 | − | 0.857968i | \(-0.671727\pi\) | ||||
−0.513703 | + | 0.857968i | \(0.671727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.1537 | −1.18840 | −0.594201 | − | 0.804317i | \(-0.702532\pi\) | ||||
−0.594201 | + | 0.804317i | \(0.702532\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.27131 | −0.493208 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.8108 | −1.45992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.60688 | −0.405806 | −0.202903 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202903 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.1249 | 1.11136 | 0.555678 | − | 0.831397i | \(-0.312459\pi\) | ||||
0.555678 | + | 0.831397i | \(0.312459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.10352 | −0.336624 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.02877 | 0.860774 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.37169 | −0.357399 | −0.178699 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178699 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0575 | 1.26397 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.86098 | 1.02254 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.978577 | 0.100400 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.53948 | −0.765518 | −0.382759 | − | 0.923848i | \(-0.625026\pi\) | ||||
−0.382759 | + | 0.923848i | \(0.625026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.34292 | 0.335976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00735 | −0.498250 | −0.249125 | − | 0.968471i | \(-0.580143\pi\) | ||||
−0.249125 | + | 0.968471i | \(0.580143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21798 | 0.120011 | 0.0600056 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600056 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.27131 | 0.319247 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7648 | −1.33069 | −0.665347 | − | 0.746534i | \(-0.731716\pi\) | ||||
−0.665347 | + | 0.746534i | \(0.731716\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.14637 | −0.301367 | −0.150684 | − | 0.988582i | \(-0.548147\pi\) | ||||
−0.150684 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.19656 | −0.777983 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.73183 | −0.727349 | −0.363675 | − | 0.931526i | \(-0.618478\pi\) | ||||
−0.363675 | + | 0.931526i | \(0.618478\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.43596 | 0.227155 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.14637 | −0.290882 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.9326 | −1.27720 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.175135 | 0.0159213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.91431 | 0.707877 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0575 | −1.06993 | −0.534967 | − | 0.844873i | \(-0.679676\pi\) | ||||
−0.534967 | + | 0.844873i | \(0.679676\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7606 | −1.03546 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2253 | −1.06813 | −0.534066 | − | 0.845443i | \(-0.679337\pi\) | ||||
−0.534066 | + | 0.845443i | \(0.679337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.39312 | 0.380931 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.853635 | −0.0734692 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.69319 | 0.657274 | 0.328637 | − | 0.944456i | \(-0.393411\pi\) | ||||
0.328637 | + | 0.944456i | \(0.393411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.0147 | 1.52799 | 0.763993 | − | 0.645224i | \(-0.223236\pi\) | ||||
0.763993 | + | 0.645224i | \(0.223236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.32150 | 0.700797 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5181 | −0.879564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.85363 | −0.569163 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.68585 | 0.633918 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.5426 | −1.02753 | −0.513766 | − | 0.857931i | \(-0.671750\pi\) | ||||
−0.513766 | + | 0.857931i | \(0.671750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.62831 | 0.213889 | 0.106944 | − | 0.994265i | \(-0.465893\pi\) | ||||
0.106944 | + | 0.994265i | \(0.465893\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.63565 | 0.293925 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.41767 | −0.676124 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1579 | −1.60878 | −0.804389 | − | 0.594103i | \(-0.797507\pi\) | ||||
−0.804389 | + | 0.594103i | \(0.797507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.60688 | −0.127434 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9357 | 0.861856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.2541 | −1.42977 | −0.714886 | − | 0.699241i | \(-0.753521\pi\) | ||||
−0.714886 | + | 0.699241i | \(0.753521\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.85363 | −0.222155 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.31415 | 0.101692 | 0.0508461 | − | 0.998706i | \(-0.483808\pi\) | ||||
0.0508461 | + | 0.998706i | \(0.483808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.10038 | −0.238491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.14637 | −0.0876648 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.18921 | −0.0904141 | −0.0452070 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452070 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.3686 | 1.23735 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6644 | 0.876752 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0073 | 1.42068 | 0.710338 | − | 0.703861i | \(-0.248542\pi\) | ||||
0.710338 | + | 0.703861i | \(0.248542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3931 | −0.772514 | −0.386257 | − | 0.922391i | \(-0.626232\pi\) | ||||
−0.386257 | + | 0.922391i | \(0.626232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.19656 | 0.310218 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.99686 | 0.514420 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.1537 | 0.888767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.83221 | −0.278752 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.87819 | −0.497689 | −0.248844 | − | 0.968544i | \(-0.580051\pi\) | ||||
−0.248844 | + | 0.968544i | \(0.580051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.5970 | −1.41062 | −0.705312 | − | 0.708897i | \(-0.749193\pi\) | ||||
−0.705312 | + | 0.708897i | \(0.749193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.68585 | 0.192337 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7679 | 1.76464 | 0.882321 | − | 0.470647i | \(-0.155980\pi\) | ||||
0.882321 | + | 0.470647i | \(0.155980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.8108 | 0.908133 | 0.454066 | − | 0.890968i | \(-0.349973\pi\) | ||||
0.454066 | + | 0.890968i | \(0.349973\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.10038 | −0.430288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.7679 | −2.15949 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.853635 | −0.0596204 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.85363 | −0.198341 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.83221 | −0.265080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.66442 | −0.252269 | −0.126135 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126135 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.65708 | −0.593173 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0393 | 0.684671 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.7894 | −2.56531 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.1537 | −0.686124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4391 | −0.769477 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.17092 | 0.614130 | 0.307065 | − | 0.951688i | \(-0.400653\pi\) | ||||
0.307065 | + | 0.951688i | \(0.400653\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.27131 | −0.284754 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.263962 | −0.0175198 | −0.00875988 | − | 0.999962i | \(-0.502788\pi\) | ||||
−0.00875988 | + | 0.999962i | \(0.502788\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.20390 | −0.476047 | −0.238024 | − | 0.971259i | \(-0.576500\pi\) | ||||
−0.238024 | + | 0.971259i | \(0.576500\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.8108 | −0.842888 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1579 | 1.05854 | 0.529270 | − | 0.848453i | \(-0.322466\pi\) | ||||
0.529270 | + | 0.848453i | \(0.322466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.10352 | −0.463383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.60688 | −0.234292 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6644 | −1.01325 | −0.506624 | − | 0.862167i | \(-0.669107\pi\) | ||||
−0.506624 | + | 0.862167i | \(0.669107\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5468 | 0.679381 | 0.339690 | − | 0.940537i | \(-0.389678\pi\) | ||||
0.339690 | + | 0.940537i | \(0.389678\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.56090 | −0.419161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.60688 | 0.229501 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.1249 | 0.641642 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.4292 | −1.35260 | −0.676301 | − | 0.736626i | \(-0.736418\pi\) | ||||
−0.676301 | + | 0.736626i | \(0.736418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.53948 | −0.599742 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.10352 | −0.194350 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.10773 | −0.443368 | −0.221684 | − | 0.975119i | \(-0.571155\pi\) | ||||
−0.221684 | + | 0.975119i | \(0.571155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.4109 | 1.95178 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.02877 | 0.496968 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.97123 | −0.614852 | −0.307426 | − | 0.951572i | \(-0.599468\pi\) | ||||
−0.307426 | + | 0.951572i | \(0.599468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37169 | 0.0842624 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.37169 | −0.206344 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.685846 | 0.0418168 | 0.0209084 | − | 0.999781i | \(-0.493344\pi\) | ||||
0.0209084 | + | 0.999781i | \(0.493344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8034 | 0.838499 | 0.419250 | − | 0.907871i | \(-0.362293\pi\) | ||||
0.419250 | + | 0.907871i | \(0.362293\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0575 | 0.729755 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.2787 | −0.861035 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.2113 | −1.33454 | −0.667272 | − | 0.744814i | \(-0.732538\pi\) | ||||
−0.667272 | + | 0.744814i | \(0.732538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.86098 | 0.590361 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.61423 | 0.275262 | 0.137631 | − | 0.990484i | \(-0.456051\pi\) | ||||
0.137631 | + | 0.990484i | \(0.456051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.13229 | −0.542858 | −0.271429 | − | 0.962458i | \(-0.587496\pi\) | ||||
−0.271429 | + | 0.962458i | \(0.587496\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.978577 | 0.0579659 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.83221 | −0.226208 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.78202 | −0.222472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.53948 | −0.441972 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.4433 | −1.36957 | −0.684786 | − | 0.728744i | \(-0.740104\pi\) | ||||
−0.684786 | + | 0.728744i | \(0.740104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.95715 | −0.579728 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.34292 | 0.193976 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.97858 | 0.519245 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45.0691 | 2.59774 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00735 | −0.287665 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.58233 | −0.205123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.2541 | −1.04182 | −0.520908 | − | 0.853613i | \(-0.674407\pi\) | ||||
−0.520908 | + | 0.853613i | \(0.674407\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.21798 | 0.0692885 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8782 | 0.843665 | 0.421832 | − | 0.906674i | \(-0.361387\pi\) | ||||
0.421832 | + | 0.906674i | \(0.361387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.4752 | −1.49647 | −0.748234 | − | 0.663435i | \(-0.769098\pi\) | ||||
−0.748234 | + | 0.663435i | \(0.769098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.27131 | 0.184317 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.6503 | −1.66533 | −0.832665 | − | 0.553777i | \(-0.813186\pi\) | ||||
−0.832665 | + | 0.553777i | \(0.813186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.8396 | 1.50273 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7648 | −0.768277 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.16779 | −0.231902 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.4391 | 0.745467 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.14637 | −0.173994 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.8898 | −1.75814 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.60375 | −0.143115 | −0.0715575 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715575 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.19656 | −0.449169 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.20750 | 0.284516 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.51071 | −0.0822937 | −0.0411468 | − | 0.999153i | \(-0.513101\pi\) | ||||
−0.0411468 | + | 0.999153i | \(0.513101\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.73183 | −0.419935 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.9645 | 1.78513 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.62831 | −0.141915 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.43596 | 0.131148 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2787 | 0.766518 | 0.383259 | − | 0.923641i | \(-0.374802\pi\) | ||||
0.383259 | + | 0.923641i | \(0.374802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.2541 | 0.870062 | 0.435031 | − | 0.900416i | \(-0.356737\pi\) | ||||
0.435031 | + | 0.900416i | \(0.356737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.14637 | −0.167941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1709 | 0.594568 | 0.297284 | − | 0.954789i | \(-0.403919\pi\) | ||||
0.297284 | + | 0.954789i | \(0.403919\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.38998 | 0.392219 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.9326 | −0.737391 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.2253 | −0.856340 | −0.428170 | − | 0.903698i | \(-0.640842\pi\) | ||||
−0.428170 | + | 0.903698i | \(0.640842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6858 | −0.930834 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.175135 | 0.00919219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.66756 | 0.453681 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.431750 | 0.0225372 | 0.0112686 | − | 0.999937i | \(-0.496413\pi\) | ||||
0.0112686 | + | 0.999937i | \(0.496413\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.15792 | 0.319703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.66863 | 0.189955 | 0.0949773 | − | 0.995479i | \(-0.469722\pi\) | ||||
0.0949773 | + | 0.995479i | \(0.469722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.91431 | 0.408693 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.2614 | −1.30103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.89962 | 0.508509 | 0.254255 | − | 0.967137i | \(-0.418170\pi\) | ||||
0.254255 | + | 0.967137i | \(0.418170\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0575 | −0.617726 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.3148 | −1.60011 | −0.800055 | − | 0.599927i | \(-0.795196\pi\) | ||||
−0.800055 | + | 0.599927i | \(0.795196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.9357 | 0.557336 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.7606 | −0.597825 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.39625 | −0.375005 | −0.187502 | − | 0.982264i | \(-0.560039\pi\) | ||||
−0.187502 | + | 0.982264i | \(0.560039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3748 | −0.524678 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.2253 | −0.616686 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.07896 | 0.154919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9326 | −0.598880 | −0.299440 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299440 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.39312 | 0.219931 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.7648 | −0.787257 | −0.393628 | − | 0.919270i | \(-0.628780\pi\) | ||||
−0.393628 | + | 0.919270i | \(0.628780\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.0263 | −1.54553 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.853635 | −0.0424174 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.4005 | −1.35819 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.55356 | −0.373499 | −0.186750 | − | 0.982408i | \(-0.559795\pi\) | ||||
−0.186750 | + | 0.982408i | \(0.559795\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.69319 | 0.379477 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −44.7005 | −2.19957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.64300 | −0.424268 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.0147 | 0.882183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.59702 | −0.468845 | −0.234423 | − | 0.972135i | \(-0.575320\pi\) | ||||
−0.234423 | + | 0.972135i | \(0.575320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.3503 | −0.601915 | −0.300958 | − | 0.953638i | \(-0.597306\pi\) | ||||
−0.300958 | + | 0.953638i | \(0.597306\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.32150 | 0.404605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.5290 | −0.753267 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.0821 | −0.778267 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5181 | −0.507817 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.14637 | 0.247892 | 0.123946 | − | 0.992289i | \(-0.460445\pi\) | ||||
0.123946 | + | 0.992289i | \(0.460445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0894 | 0.821266 | 0.410633 | − | 0.911801i | \(-0.365308\pi\) | ||||
0.410633 | + | 0.911801i | \(0.365308\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.85363 | −0.328607 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.27131 | 0.156488 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.3503 | −1.06672 | −0.533360 | − | 0.845888i | \(-0.679071\pi\) | ||||
−0.533360 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.68585 | 0.365993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.4145 | −1.11246 | −0.556229 | − | 0.831029i | \(-0.687752\pi\) | ||||
−0.556229 | + | 0.831029i | \(0.687752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.87819 | 0.136439 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.5426 | −0.593245 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2713 | −1.57017 | −0.785085 | − | 0.619388i | \(-0.787381\pi\) | ||||
−0.785085 | + | 0.619388i | \(0.787381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.34292 | 0.157412 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.62831 | 0.123489 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.2927 | −0.482531 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3931 | −1.23462 | −0.617309 | − | 0.786721i | \(-0.711777\pi\) | ||||
−0.617309 | + | 0.786721i | \(0.711777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.63565 | 0.169698 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.20077 | −0.102500 | −0.0512500 | − | 0.998686i | \(-0.516321\pi\) | ||||
−0.0512500 | + | 0.998686i | \(0.516321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5328 | 1.14013 | 0.570067 | − | 0.821598i | \(-0.306917\pi\) | ||||
0.570067 | + | 0.821598i | \(0.306917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.41767 | −0.390360 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.9357 | 1.06134 | 0.530670 | − | 0.847579i | \(-0.321941\pi\) | ||||
0.530670 | + | 0.847579i | \(0.321941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.3780 | 1.07949 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.1579 | −0.928828 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.3148 | −1.80770 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89648 | 0.224666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60688 | −0.0735742 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 41.6075 | 1.90110 | 0.950548 | − | 0.310579i | \(-0.100523\pi\) | ||||
0.950548 | + | 0.310579i | \(0.100523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.7894 | 1.17589 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.9357 | 0.497593 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.43596 | 0.292242 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.4036 | 1.83086 | 0.915431 | − | 0.402475i | \(-0.131850\pi\) | ||||
0.915431 | + | 0.402475i | \(0.131850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.2541 | −0.825479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6184 | 0.749980 | 0.374990 | − | 0.927029i | \(-0.377646\pi\) | ||||
0.374990 | + | 0.927029i | \(0.377646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.1898 | 1.31464 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.85363 | −0.128261 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.1758 | 1.48814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.921039 | 0.0412314 | 0.0206157 | − | 0.999787i | \(-0.493437\pi\) | ||||
0.0206157 | + | 0.999787i | \(0.493437\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31415 | 0.0587121 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9217 | 0.843675 | 0.421837 | − | 0.906671i | \(-0.361385\pi\) | ||||
0.421837 | + | 0.906671i | \(0.361385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.27444 | 0.190210 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.10038 | −0.137693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.8855 | −1.23600 | −0.618002 | − | 0.786176i | \(-0.712058\pi\) | ||||
−0.618002 | + | 0.786176i | \(0.712058\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.9112 | 1.72133 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.14637 | −0.0506133 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.03971 | −0.0458151 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.8181 | 1.22344 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.18921 | −0.0522006 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.93681 | 0.435339 | 0.217670 | − | 0.976022i | \(-0.430154\pi\) | ||||
0.217670 | + | 0.976022i | \(0.430154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.9718 | 1.57294 | 0.786470 | − | 0.617629i | \(-0.211907\pi\) | ||||
0.786470 | + | 0.617629i | \(0.211907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.3686 | 0.714382 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.8511 | 1.56170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8568 | −0.645947 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6644 | 0.506193 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.14637 | −0.136284 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.7501 | 0.508002 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.0073 | 0.820228 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.6932 | 1.10668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.79923 | −0.421302 | −0.210651 | − | 0.977561i | \(-0.567558\pi\) | ||||
−0.210651 | + | 0.977561i | \(0.567558\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.3931 | −0.446011 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.68585 | 0.115049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.8223 | 1.44614 | 0.723070 | − | 0.690775i | \(-0.242731\pi\) | ||||
0.723070 | + | 0.690775i | \(0.242731\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.19656 | 0.179105 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.20390 | −0.392099 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8223 | 0.587786 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.99686 | 0.297000 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9217 | 0.886479 | 0.443239 | − | 0.896403i | \(-0.353829\pi\) | ||||
0.443239 | + | 0.896403i | \(0.353829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.0031 | 1.56507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1537 | 0.513130 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.6289 | 1.20657 | 0.603283 | − | 0.797527i | \(-0.293859\pi\) | ||||
0.603283 | + | 0.797527i | \(0.293859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.60015 | 0.277671 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.83221 | −0.160938 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.9603 | −0.878701 | −0.439351 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439351 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2860 | 0.556002 | 0.278001 | − | 0.960581i | \(-0.410328\pi\) | ||||
0.278001 | + | 0.960581i | \(0.410328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.87819 | −0.287341 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.1888 | 0.508306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.35700 | 0.0564926 | 0.0282463 | − | 0.999601i | \(-0.491008\pi\) | ||||
0.0282463 | + | 0.999601i | \(0.491008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5970 | −0.814424 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.8009 | −1.60973 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.37169 | −0.222473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.68585 | 0.111046 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.9431 | −1.23588 | −0.617942 | − | 0.786224i | \(-0.712033\pi\) | ||||
−0.617942 | + | 0.786224i | \(0.712033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.3043 | −0.465785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.7679 | 1.01882 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.01408 | −0.246969 | −0.123484 | − | 0.992347i | \(-0.539407\pi\) | ||||
−0.123484 | + | 0.992347i | \(0.539407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.8933 | 0.487580 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8108 | 0.524311 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0477 | 1.22771 | 0.613857 | − | 0.789417i | \(-0.289617\pi\) | ||||
0.613857 | + | 0.789417i | \(0.289617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.1642 | −1.55675 | −0.778375 | − | 0.627800i | \(-0.783956\pi\) | ||||
−0.778375 | + | 0.627800i | \(0.783956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.10038 | −0.248427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.149501 | −0.00607808 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7220 | 1.44991 | 0.724955 | − | 0.688796i | \(-0.241861\pi\) | ||||
0.724955 | + | 0.688796i | \(0.241861\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.7679 | −1.24678 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1825 | −1.05923 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.68585 | 0.350818 | 0.175409 | − | 0.984496i | \(-0.443875\pi\) | ||||
0.175409 | + | 0.984496i | \(0.443875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.853635 | −0.0344219 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.4391 | 1.02414 | 0.512070 | − | 0.858944i | \(-0.328879\pi\) | ||||
0.512070 | + | 0.858944i | \(0.328879\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.28852 | −0.172370 | −0.0861851 | − | 0.996279i | \(-0.527468\pi\) | ||||
−0.0861851 | + | 0.996279i | \(0.527468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.85363 | −0.114512 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9210 | 0.517670 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6006 | 0.584025 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.83221 | −0.153044 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.7998 | −1.18820 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.17513 | −0.126400 | −0.0632001 | − | 0.998001i | \(-0.520131\pi\) | ||||
−0.0632001 | + | 0.998001i | \(0.520131\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.66442 | −0.145648 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2927 | 0.408455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1825 | −0.958145 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.65708 | −0.342469 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0565 | −0.831680 | −0.415840 | − | 0.909438i | \(-0.636512\pi\) | ||||
−0.415840 | + | 0.909438i | \(0.636512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2070 | 0.718016 | 0.359008 | − | 0.933335i | \(-0.383115\pi\) | ||||
0.359008 | + | 0.933335i | \(0.383115\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0393 | 0.395295 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.6890 | −0.774054 | −0.387027 | − | 0.922068i | \(-0.626498\pi\) | ||||
−0.387027 | + | 0.922068i | \(0.626498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.9933 | 1.53062 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.7894 | −1.48108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.80031 | 0.109584 | 0.0547922 | − | 0.998498i | \(-0.482550\pi\) | ||||
0.0547922 | + | 0.998498i | \(0.482550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4360 | 0.407767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.1537 | −0.396134 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.07896 | 0.275757 | 0.137879 | − | 0.990449i | \(-0.455972\pi\) | ||||
0.137879 | + | 0.990449i | \(0.455972\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6791 | 0.609847 | 0.304923 | − | 0.952377i | \(-0.401369\pi\) | ||||
0.304923 | + | 0.952377i | \(0.401369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.4391 | −0.444258 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.75011 | −0.145423 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.9112 | −0.887124 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.17092 | 0.354568 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0288 | 0.541575 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2070 | −0.470547 | −0.235273 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235273 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.27131 | −0.164403 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.7121 | 1.52626 | 0.763130 | − | 0.646245i | \(-0.223662\pi\) | ||||
0.763130 | + | 0.646245i | \(0.223662\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.8929 | 1.10881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.263962 | −0.0101150 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.22846 | −0.353117 | −0.176559 | − | 0.984290i | \(-0.556497\pi\) | ||||
−0.176559 | + | 0.984290i | \(0.556497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.56717 | −0.250919 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.20390 | −0.274846 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.05585 | 0.192612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.75325 | 0.180822 | 0.0904111 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904111 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.8108 | −0.486642 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.3780 | −0.583319 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.63565 | 0.137710 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.1579 | 0.611149 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0790 | 0.796141 | 0.398071 | − | 0.917355i | \(-0.369680\pi\) | ||||
0.398071 | + | 0.917355i | \(0.369680\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.39625 | 0.354386 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.10352 | −0.267534 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.1892 | 0.721685 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.7497 | −1.60550 | −0.802749 | − | 0.596318i | \(-0.796630\pi\) | ||||
−0.802749 | + | 0.596318i | \(0.796630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.60688 | −0.135269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.1396 | −1.05384 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.97858 | 0.335780 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.6644 | −0.584999 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.00735 | −0.261330 | −0.130665 | − | 0.991427i | \(-0.541711\pi\) | ||||
−0.130665 | + | 0.991427i | \(0.541711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.66756 | −0.173829 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.5468 | 0.392241 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.2933 | −1.27362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.3963 | −1.23860 | −0.619299 | − | 0.785155i | \(-0.712583\pi\) | ||||
−0.619299 | + | 0.785155i | \(0.712583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.7575 | −1.58144 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1176 | −0.484509 | −0.242255 | − | 0.970213i | \(-0.577887\pi\) | ||||
−0.242255 | + | 0.970213i | \(0.577887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.56090 | −0.242003 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.3931 | −0.751190 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.2902 | 1.73960 | 0.869799 | − | 0.493406i | \(-0.164248\pi\) | ||||
0.869799 | + | 0.493406i | \(0.164248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.60688 | 0.132502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5510 | −0.680572 | −0.340286 | − | 0.940322i | \(-0.610524\pi\) | ||||
−0.340286 | + | 0.940322i | \(0.610524\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7068 | 0.392267 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.1249 | 0.370452 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.7497 | 1.92743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6791 | −0.499158 | −0.249579 | − | 0.968354i | \(-0.580292\pi\) | ||||
−0.249579 | + | 0.968354i | \(0.580292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.4292 | −0.780925 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.24361 | −0.0816535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0031 | 0.836063 | 0.418032 | − | 0.908432i | \(-0.362720\pi\) | ||||
0.418032 | + | 0.908432i | \(0.362720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.53948 | −0.346261 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4851 | 0.742583 | 0.371292 | − | 0.928516i | \(-0.378915\pi\) | ||||
0.371292 | + | 0.928516i | \(0.378915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0575 | 0.436512 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.10352 | −0.112208 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.7005 | −1.32518 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.5107 | −0.631452 | −0.315726 | − | 0.948850i | \(-0.602248\pi\) | ||||
−0.315726 | + | 0.948850i | \(0.602248\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.10773 | −0.255979 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.8083 | 1.14406 | 0.572032 | − | 0.820231i | \(-0.306155\pi\) | ||||
0.572032 | + | 0.820231i | \(0.306155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.1193 | −1.51297 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.4109 | 1.12686 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.14637 | −0.0410728 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.9399 | −1.03555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.02877 | 0.286925 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.2075 | 0.614162 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.5040 | −0.517011 | −0.258506 | − | 0.966010i | \(-0.583230\pi\) | ||||
−0.258506 | + | 0.966010i | \(0.583230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.97123 | −0.354985 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.6300 | 1.05352 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2039 | −0.468884 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.37169 | 0.0486489 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.3650 | −1.78402 | −0.892009 | − | 0.452017i | \(-0.850705\pi\) | ||||
−0.892009 | + | 0.452017i | \(0.850705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.2541 | 1.07031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.37169 | −0.119133 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.9431 | −1.19783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.33512 | −0.329020 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.685846 | 0.0241429 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.2369 | 1.23886 | 0.619431 | − | 0.785051i | \(-0.287363\pi\) | ||||
0.619431 | + | 0.785051i | \(0.287363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8610 | 0.486725 | 0.243362 | − | 0.969935i | \(-0.421750\pi\) | ||||
0.243362 | + | 0.969935i | \(0.421750\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8034 | 0.484108 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.5823 | 0.545825 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4819 | 0.471673 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0575 | 0.421324 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.20390 | −0.251418 | −0.125709 | − | 0.992067i | \(-0.540121\pi\) | ||||
−0.125709 | + | 0.992067i | \(0.540121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.81392 | −0.342092 | −0.171046 | − | 0.985263i | \(-0.554715\pi\) | ||||
−0.171046 | + | 0.985263i | \(0.554715\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.2787 | −0.497119 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.8788 | −0.865121 | −0.432560 | − | 0.901605i | \(-0.642390\pi\) | ||||
−0.432560 | + | 0.901605i | \(0.642390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.3759 | −0.464564 | −0.232282 | − | 0.972648i | \(-0.574619\pi\) | ||||
−0.232282 | + | 0.972648i | \(0.574619\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.2113 | −0.770500 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.9431 | 0.968170 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.12181 | −0.0388217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.86098 | 0.340845 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9210 | −0.446084 | −0.223042 | − | 0.974809i | \(-0.571599\pi\) | ||||
−0.223042 | + | 0.974809i | \(0.571599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.4611 | 1.22280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.61423 | 0.158923 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.64659 | 0.0910456 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.671153 | −0.0230611 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.13229 | −0.313419 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.3900 | 0.801798 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4851 | −0.564438 | −0.282219 | − | 0.959350i | \(-0.591071\pi\) | ||||
−0.282219 | + | 0.959350i | \(0.591071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.978577 | 0.0334666 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.5149 | −0.393342 | −0.196671 | − | 0.980470i | \(-0.563013\pi\) | ||||
−0.196671 | + | 0.980470i | \(0.563013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7392 | 0.980568 | 0.490284 | − | 0.871563i | \(-0.336893\pi\) | ||||
0.490284 | + | 0.871563i | \(0.336893\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.83221 | −0.130601 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.1611 | 1.74154 | 0.870771 | − | 0.491688i | \(-0.163620\pi\) | ||||
0.870771 | + | 0.491688i | \(0.163620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.01515 | 0.0345162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.78202 | −0.128444 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0575 | −0.409024 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.1940 | 0.650365 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.53948 | −0.255173 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.3293 | −1.02532 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.3179 | −1.15883 | −0.579417 | − | 0.815031i | \(-0.696720\pi\) | ||||
−0.579417 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4433 | −0.790723 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.9786 | −1.31322 | −0.656611 | − | 0.754230i | \(-0.728011\pi\) | ||||
−0.656611 | + | 0.754230i | \(0.728011\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2253 | 0.949858 | 0.474929 | − | 0.880024i | \(-0.342474\pi\) | ||||
0.474929 | + | 0.880024i | \(0.342474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.95715 | −0.334706 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.1438 | −1.01213 | −0.506066 | − | 0.862495i | \(-0.668901\pi\) | ||||
−0.506066 | + | 0.862495i | \(0.668901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.2070 | 1.54973 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.34292 | 0.111992 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.53948 | −0.319227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.2253 | −0.542353 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.97858 | 0.299786 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 79.1715 | 2.64052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.84208 | −0.194628 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 45.0691 | 1.49981 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.87192 | 0.294913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.3435 | −1.37279 | −0.686395 | − | 0.727229i | \(-0.740808\pi\) | ||||
−0.686395 | + | 0.727229i | \(0.740808\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.00735 | −0.166083 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.23206 | −0.0408199 | −0.0204099 | − | 0.999792i | \(-0.506497\pi\) | ||||
−0.0204099 | + | 0.999792i | \(0.506497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8469 | 1.12017 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.58233 | −0.118428 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.8500 | 1.54712 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.4047 | −0.706075 | −0.353037 | − | 0.935609i | \(-0.614851\pi\) | ||||
−0.353037 | + | 0.935609i | \(0.614851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.2541 | −0.601493 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.2383 | 0.896560 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.0100 | 1.15112 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21798 | 0.0400037 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.8150 | 1.07663 | 0.538313 | − | 0.842745i | \(-0.319062\pi\) | ||||
0.538313 | + | 0.842745i | \(0.319062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.81079 | −0.288762 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.8782 | 0.487090 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3748 | −0.339293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.4783 | 0.897678 | 0.448839 | − | 0.893613i | \(-0.351838\pi\) | ||||
0.448839 | + | 0.893613i | \(0.351838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.4752 | −0.863986 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.1151 | −1.24252 | −0.621258 | − | 0.783606i | \(-0.713378\pi\) | ||||
−0.621258 | + | 0.783606i | \(0.713378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.85363 | −0.0929271 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.27131 | 0.106416 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.85050 | 0.320098 | 0.160049 | − | 0.987109i | \(-0.448835\pi\) | ||||
0.160049 | + | 0.987109i | \(0.448835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9473 | 1.03705 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.6503 | −0.961478 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.92417 | 0.127116 | 0.0635582 | − | 0.997978i | \(-0.479755\pi\) | ||||
0.0635582 | + | 0.997978i | \(0.479755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.87146 | 0.189996 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.8396 | 0.867600 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.4819 | −0.952022 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.2389 | 2.13674 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.7648 | −0.443565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.7287 | 0.538516 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.3074 | −1.29620 | −0.648100 | − | 0.761556i | \(-0.724436\pi\) | ||||
−0.648100 | + | 0.761556i | \(0.724436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.16779 | −0.133889 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.8280 | −1.21396 | −0.606979 | − | 0.794718i | \(-0.707619\pi\) | ||||
−0.606979 | + | 0.794718i | \(0.707619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.0361 | −2.21320 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.4391 | 0.430396 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.89227 | 0.284489 | 0.142244 | − | 0.989832i | \(-0.454568\pi\) | ||||
0.142244 | + | 0.989832i | \(0.454568\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.2713 | −0.360233 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.14637 | −0.100456 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.6247 | −0.976777 | −0.488388 | − | 0.872626i | \(-0.662415\pi\) | ||||
−0.488388 | + | 0.872626i | \(0.662415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.1428 | −0.673665 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.8898 | −1.01506 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.5604 | 1.06716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.1512 | −1.68840 | −0.844202 | − | 0.536026i | \(-0.819925\pi\) | ||||
−0.844202 | + | 0.536026i | \(0.819925\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.60375 | −0.0826275 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.9357 | −0.346686 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.5181 | 1.40990 | 0.704951 | − | 0.709256i | \(-0.250969\pi\) | ||||
0.704951 | + | 0.709256i | \(0.250969\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.19656 | −0.259328 |
(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 | 7872.2.a.bx.1.2 | 3 | ||
4.3 | odd | 2 | 7872.2.a.bs.1.2 | 3 | |||
8.3 | odd | 2 | 1968.2.a.w.1.2 | 3 | |||
8.5 | even | 2 | 123.2.a.d.1.3 | ✓ | 3 | ||
24.5 | odd | 2 | 369.2.a.e.1.1 | 3 | |||
24.11 | even | 2 | 5904.2.a.bd.1.2 | 3 | |||
40.29 | even | 2 | 3075.2.a.t.1.1 | 3 | |||
56.13 | odd | 2 | 6027.2.a.s.1.3 | 3 | |||
120.29 | odd | 2 | 9225.2.a.bx.1.3 | 3 | |||
328.245 | even | 2 | 5043.2.a.n.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
123.2.a.d.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
369.2.a.e.1.1 | 3 | 24.5 | odd | 2 | |||
1968.2.a.w.1.2 | 3 | 8.3 | odd | 2 | |||
3075.2.a.t.1.1 | 3 | 40.29 | even | 2 | |||
5043.2.a.n.1.3 | 3 | 328.245 | even | 2 | |||
5904.2.a.bd.1.2 | 3 | 24.11 | even | 2 | |||
6027.2.a.s.1.3 | 3 | 56.13 | odd | 2 | |||
7872.2.a.bs.1.2 | 3 | 4.3 | odd | 2 | |||
7872.2.a.bx.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9225.2.a.bx.1.3 | 3 | 120.29 | odd | 2 |