Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 2x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | 0.554958 | 0.320405 | 0.160203 | − | 0.987084i | \(-0.448785\pi\) | ||||
0.160203 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.04892 | −1.15238 | −0.576191 | − | 0.817315i | \(-0.695462\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.69202 | −0.897340 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93900 | 0.886142 | 0.443071 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443071 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24698 | −0.900550 | −0.450275 | − | 0.892890i | \(-0.648674\pi\) | ||||
−0.450275 | + | 0.892890i | \(0.648674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.15883 | 0.523594 | 0.261797 | − | 0.965123i | \(-0.415685\pi\) | ||||
0.261797 | + | 0.965123i | \(0.415685\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69202 | −0.369229 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.19806 | 0.249813 | 0.124907 | − | 0.992169i | \(-0.460137\pi\) | ||||
0.124907 | + | 0.992169i | \(0.460137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.15883 | −0.607918 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.77479 | −0.329570 | −0.164785 | − | 0.986329i | \(-0.552693\pi\) | ||||
−0.164785 | + | 0.986329i | \(0.552693\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.34481 | 1.67838 | 0.839189 | − | 0.543840i | \(-0.183030\pi\) | ||||
0.839189 | + | 0.543840i | \(0.183030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.63102 | 0.283925 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.15883 | 0.190511 | 0.0952555 | − | 0.995453i | \(-0.469633\pi\) | ||||
0.0952555 | + | 0.995453i | \(0.469633\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.80194 | −0.288541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.57002 | 1.33841 | 0.669206 | − | 0.743077i | \(-0.266634\pi\) | ||||
0.669206 | + | 0.743077i | \(0.266634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.27413 | 0.804297 | 0.402148 | − | 0.915575i | \(-0.368264\pi\) | ||||
0.402148 | + | 0.915575i | \(0.368264\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.35690 | 0.343789 | 0.171894 | − | 0.985115i | \(-0.445011\pi\) | ||||
0.171894 | + | 0.985115i | \(0.445011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.29590 | 0.327985 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.19806 | 0.167762 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.82371 | −1.21203 | −0.606015 | − | 0.795453i | \(-0.707233\pi\) | ||||
−0.606015 | + | 0.795453i | \(0.707233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.554958 | 0.0735060 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.70171 | 0.742299 | 0.371150 | − | 0.928573i | \(-0.378964\pi\) | ||||
0.371150 | + | 0.928573i | \(0.378964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.96077 | −1.27535 | −0.637673 | − | 0.770307i | \(-0.720103\pi\) | ||||
−0.637673 | + | 0.770307i | \(0.720103\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.20775 | 1.03408 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.98254 | 0.608714 | 0.304357 | − | 0.952558i | \(-0.401558\pi\) | ||||
0.304357 | + | 0.952558i | \(0.401558\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.664874 | 0.0800415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.70171 | −0.320634 | −0.160317 | − | 0.987066i | \(-0.551252\pi\) | ||||
−0.160317 | + | 0.987066i | \(0.551252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.7778 | −1.61257 | −0.806283 | − | 0.591530i | \(-0.798524\pi\) | ||||
−0.806283 | + | 0.591530i | \(0.798524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.96077 | −1.02117 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.66487 | −0.637348 | −0.318674 | − | 0.947864i | \(-0.603238\pi\) | ||||
−0.318674 | + | 0.947864i | \(0.603238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.32304 | 0.702560 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.00969 | −0.330356 | −0.165178 | − | 0.986264i | \(-0.552820\pi\) | ||||
−0.165178 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.984935 | −0.105596 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.2838 | −1.09008 | −0.545041 | − | 0.838409i | \(-0.683486\pi\) | ||||
−0.545041 | + | 0.838409i | \(0.683486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.89977 | 1.03778 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.18598 | 0.537761 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.24698 | −0.329681 | −0.164840 | − | 0.986320i | \(-0.552711\pi\) | ||||
−0.164840 | + | 0.986320i | \(0.552711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.91185 | −0.795171 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.09246 | 0.506718 | 0.253359 | − | 0.967372i | \(-0.418465\pi\) | ||||
0.253359 | + | 0.967372i | \(0.418465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3110 | −1.41010 | −0.705051 | − | 0.709157i | \(-0.749076\pi\) | ||||
−0.705051 | + | 0.709157i | \(0.749076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.18598 | −0.791369 | −0.395684 | − | 0.918387i | \(-0.629493\pi\) | ||||
−0.395684 | + | 0.918387i | \(0.629493\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3274 | −1.08496 | −0.542482 | − | 0.840067i | \(-0.682515\pi\) | ||||
−0.542482 | + | 0.840067i | \(0.682515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.643104 | 0.0610407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.43535 | −0.323171 | −0.161585 | − | 0.986859i | \(-0.551661\pi\) | ||||
−0.161585 | + | 0.986859i | \(0.551661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.74094 | 0.808100 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.58211 | −0.603381 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.36227 | −0.214752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.75600 | 0.428834 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.46144 | 0.129681 | 0.0648407 | − | 0.997896i | \(-0.479346\pi\) | ||||
0.0648407 | + | 0.997896i | \(0.479346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.92692 | 0.257701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.2295 | 1.15587 | 0.577934 | − | 0.816083i | \(-0.303859\pi\) | ||||
0.577934 | + | 0.816083i | \(0.303859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.04892 | −0.264375 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1739 | −1.38183 | −0.690915 | − | 0.722936i | \(-0.742792\pi\) | ||||
−0.690915 | + | 0.722936i | \(0.742792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0978 | −1.11094 | −0.555472 | − | 0.831535i | \(-0.687462\pi\) | ||||
−0.555472 | + | 0.831535i | \(0.687462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.30798 | 0.110152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.54288 | −0.798015 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.27413 | 0.105088 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0640 | 0.906397 | 0.453198 | − | 0.891410i | \(-0.350283\pi\) | ||||
0.453198 | + | 0.891410i | \(0.350283\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4426 | −0.849811 | −0.424905 | − | 0.905238i | \(-0.639693\pi\) | ||||
−0.424905 | + | 0.905238i | \(0.639693\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.81163 | −0.469842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.48427 | −0.198266 | −0.0991332 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991332 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.89679 | −0.388341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.65279 | −0.287880 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.16852 | 0.248178 | 0.124089 | − | 0.992271i | \(-0.460399\pi\) | ||||
0.124089 | + | 0.992271i | \(0.460399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.74632 | 0.367281 | 0.183640 | − | 0.982993i | \(-0.441212\pi\) | ||||
0.183640 | + | 0.982993i | \(0.441212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.45712 | −0.189009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.69202 | −0.205864 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.96316 | −0.301314 | −0.150657 | − | 0.988586i | \(-0.548139\pi\) | ||||
−0.150657 | + | 0.988586i | \(0.548139\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.16421 | 0.237837 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0858 | 1.05282 | 0.526409 | − | 0.850231i | \(-0.323538\pi\) | ||||
0.526409 | + | 0.850231i | \(0.323538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2513 | −0.910631 | −0.455316 | − | 0.890330i | \(-0.650474\pi\) | ||||
−0.455316 | + | 0.890330i | \(0.650474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.52781 | −0.408628 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.34481 | 0.463979 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.63102 | 0.700554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.1468 | −1.45777 | −0.728884 | − | 0.684637i | \(-0.759961\pi\) | ||||
−0.728884 | + | 0.684637i | \(0.759961\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.52781 | 0.685827 | 0.342913 | − | 0.939367i | \(-0.388586\pi\) | ||||
0.342913 | + | 0.939367i | \(0.388586\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.96316 | −0.353611 | −0.176805 | − | 0.984246i | \(-0.556576\pi\) | ||||
−0.176805 | + | 0.984246i | \(0.556576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.42221 | −0.384370 | −0.192185 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192185 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.76510 | 0.195035 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.41119 | 0.379791 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.22521 | −0.224168 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.93900 | 0.203295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9638 | −1.09899 | −0.549495 | − | 0.835497i | \(-0.685180\pi\) | ||||
−0.549495 | + | 0.835497i | \(0.685180\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.49934 | −0.102733 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.4916 | −1.93413 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.64609 | −0.516675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.00969 | −0.471523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.2150 | −1.55459 | −0.777297 | − | 0.629134i | \(-0.783410\pi\) | ||||
−0.777297 | + | 0.629134i | \(0.783410\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4795 | −1.16015 | −0.580077 | − | 0.814562i | \(-0.696978\pi\) | ||||
−0.580077 | + | 0.814562i | \(0.696978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.32544 | −0.153669 | −0.0768346 | − | 0.997044i | \(-0.524481\pi\) | ||||
−0.0768346 | + | 0.997044i | \(0.524481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.97285 | −0.327190 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9342 | 1.24042 | 0.620211 | − | 0.784435i | \(-0.287047\pi\) | ||||
0.620211 | + | 0.784435i | \(0.287047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.14377 | −0.204210 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1685 | −0.722432 | −0.361216 | − | 0.932482i | \(-0.617638\pi\) | ||||
−0.361216 | + | 0.932482i | \(0.617638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.42998 | 0.478607 | 0.239303 | − | 0.970945i | \(-0.423081\pi\) | ||||
0.239303 | + | 0.970945i | \(0.423081\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.9855 | 0.833022 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.24698 | −0.206600 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.67025 | −0.105848 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7409 | 0.930440 | 0.465220 | − | 0.885195i | \(-0.345975\pi\) | ||||
0.465220 | + | 0.885195i | \(0.345975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.52111 | 0.221370 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.34721 | −0.208793 | −0.104397 | − | 0.994536i | \(-0.533291\pi\) | ||||
−0.104397 | + | 0.994536i | \(0.533291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.53319 | −0.219542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.77777 | 0.295737 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.6853 | −1.02886 | −0.514430 | − | 0.857532i | \(-0.671997\pi\) | ||||
−0.514430 | + | 0.857532i | \(0.671997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.70709 | −0.349268 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.5961 | 0.950911 | 0.475456 | − | 0.879740i | \(-0.342283\pi\) | ||||
0.475456 | + | 0.879740i | \(0.342283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2131 | 0.802640 | 0.401320 | − | 0.915938i | \(-0.368551\pi\) | ||||
0.401320 | + | 0.915938i | \(0.368551\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.49396 | 0.332510 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.9758 | −0.779642 | −0.389821 | − | 0.920891i | \(-0.627463\pi\) | ||||
−0.389821 | + | 0.920891i | \(0.627463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.1564 | −1.50608 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8901 | 1.48482 | 0.742409 | − | 0.669947i | \(-0.233683\pi\) | ||||
0.742409 | + | 0.669947i | \(0.233683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5821 | −0.807372 | −0.403686 | − | 0.914898i | \(-0.632271\pi\) | ||||
−0.403686 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.1293 | −1.54236 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3394 | −0.725849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.80194 | −0.105631 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.27652 | −0.0745751 | −0.0372875 | − | 0.999305i | \(-0.511872\pi\) | ||||
−0.0372875 | + | 0.999305i | \(0.511872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.28382 | −0.538702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.89008 | −0.224969 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0804 | −0.926857 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.82610 | 0.162355 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.2295 | −1.83944 | −0.919718 | − | 0.392580i | \(-0.871583\pi\) | ||||
−0.919718 | + | 0.392580i | \(0.871583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.94198 | −0.451804 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.4983 | −0.708712 | −0.354356 | − | 0.935111i | \(-0.615300\pi\) | ||||
−0.354356 | + | 0.935111i | \(0.615300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9390 | 1.18354 | 0.591771 | − | 0.806106i | \(-0.298429\pi\) | ||||
0.591771 | + | 0.806106i | \(0.298429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.8562 | −0.890575 | −0.445287 | − | 0.895388i | \(-0.646898\pi\) | ||||
−0.445287 | + | 0.895388i | \(0.646898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.21611 | −0.292046 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.54288 | −0.253559 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.15883 | 0.120121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.28621 | −0.347628 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.18598 | −0.396176 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.2349 | 0.727456 | 0.363728 | − | 0.931505i | \(-0.381504\pi\) | ||||
0.363728 | + | 0.931505i | \(0.381504\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.11960 | −0.170953 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.0780 | 1.42056 | 0.710279 | − | 0.703920i | \(-0.248569\pi\) | ||||
0.710279 | + | 0.703920i | \(0.248569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.90648 | −0.103546 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.4644 | 1.48728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.3424 | 0.774418 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.98254 | 0.482208 | 0.241104 | − | 0.970499i | \(-0.422490\pi\) | ||||
0.241104 | + | 0.970499i | \(0.422490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.599564 | 0.0320939 | 0.0160470 | − | 0.999871i | \(-0.494892\pi\) | ||||
0.0160470 | + | 0.999871i | \(0.494892\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.2567 | 0.547460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.8896 | −1.69731 | −0.848656 | − | 0.528945i | \(-0.822588\pi\) | ||||
−0.848656 | + | 0.528945i | \(0.822588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.65279 | −0.193326 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3763 | 0.969863 | 0.484931 | − | 0.874552i | \(-0.338845\pi\) | ||||
0.484931 | + | 0.874552i | \(0.338845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.31096 | −0.0688077 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6377 | −0.764083 | −0.382042 | − | 0.924145i | \(-0.624779\pi\) | ||||
−0.382042 | + | 0.924145i | \(0.624779\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.0707 | −1.20101 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.9028 | 1.39672 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.02715 | 0.0531837 | 0.0265918 | − | 0.999646i | \(-0.491535\pi\) | ||||
0.0265918 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.76271 | 0.296795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.5284 | 1.15721 | 0.578603 | − | 0.815609i | \(-0.303598\pi\) | ||||
0.578603 | + | 0.815609i | \(0.303598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.811035 | 0.0415506 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.6698 | 1.66935 | 0.834674 | − | 0.550745i | \(-0.185656\pi\) | ||||
0.834674 | + | 0.550745i | \(0.185656\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.1981 | −0.721728 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.16421 | −0.413942 | −0.206971 | − | 0.978347i | \(-0.566361\pi\) | ||||
−0.206971 | + | 0.978347i | \(0.566361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58642 | 0.130801 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.34183 | 0.370346 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.5478 | −1.88447 | −0.942235 | − | 0.334954i | \(-0.891279\pi\) | ||||
−0.942235 | + | 0.334954i | \(0.891279\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.69202 | −0.0847070 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.2519 | 1.61058 | 0.805291 | − | 0.592880i | \(-0.202009\pi\) | ||||
0.805291 | + | 0.592880i | \(0.202009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.3424 | −1.51146 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.40581 | 0.168820 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.5459 | −1.55984 | −0.779921 | − | 0.625878i | \(-0.784741\pi\) | ||||
−0.779921 | + | 0.625878i | \(0.784741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.97584 | −0.442745 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.3840 | −0.855413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.26875 | −0.355952 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6866 | 0.717490 | 0.358745 | − | 0.933436i | \(-0.383205\pi\) | ||||
0.358745 | + | 0.933436i | \(0.383205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1142 | 0.736622 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.34481 | −0.308495 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.3696 | 1.46969 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.29590 | −0.255688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.67696 | −0.0807761 | −0.0403881 | − | 0.999184i | \(-0.512859\pi\) | ||||
−0.0403881 | + | 0.999184i | \(0.512859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1545 | 0.632166 | 0.316083 | − | 0.948732i | \(-0.397632\pi\) | ||||
0.316083 | + | 0.948732i | \(0.397632\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.19806 | 0.0573111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.45580 | −0.308118 | −0.154059 | − | 0.988062i | \(-0.549235\pi\) | ||||
−0.154059 | + | 0.988062i | \(0.549235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.18060 | −0.294314 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.3709 | −1.20541 | −0.602704 | − | 0.797965i | \(-0.705910\pi\) | ||||
−0.602704 | + | 0.797965i | \(0.705910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.14005 | 0.290414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.59956 | −0.169874 | −0.0849370 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849370 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.1873 | 1.18602 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.79523 | −0.272284 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2784 | 0.574361 | 0.287181 | − | 0.957876i | \(-0.407282\pi\) | ||||
0.287181 | + | 0.957876i | \(0.407282\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.81940 | −0.318302 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.4935 | 1.83939 | 0.919697 | − | 0.392628i | \(-0.128434\pi\) | ||||
0.919697 | + | 0.392628i | \(0.128434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.3991 | 0.855079 | 0.427540 | − | 0.903997i | \(-0.359380\pi\) | ||||
0.427540 | + | 0.903997i | \(0.359380\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.2282 | −1.67644 | −0.838220 | − | 0.545332i | \(-0.816404\pi\) | ||||
−0.838220 | + | 0.545332i | \(0.816404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1914 | −0.701472 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.37867 | −0.0635256 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5007 | 0.712721 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.7536 | 1.08760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.3129 | 1.56780 | 0.783898 | − | 0.620890i | \(-0.213229\pi\) | ||||
0.783898 | + | 0.620890i | \(0.213229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.76271 | −0.171565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.02715 | −0.0922384 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.4722 | −1.10894 | −0.554470 | − | 0.832203i | \(-0.687079\pi\) | ||||
−0.554470 | + | 0.832203i | \(0.687079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.75840 | 0.0795175 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.3067 | −0.826168 | −0.413084 | − | 0.910693i | \(-0.635548\pi\) | ||||
−0.413084 | + | 0.910693i | \(0.635548\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.83148 | −0.172561 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.23729 | 0.369493 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3424 | 1.13448 | 0.567241 | − | 0.823552i | \(-0.308011\pi\) | ||||
0.567241 | + | 0.823552i | \(0.308011\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63401 | 0.117679 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.1105 | 0.629156 | 0.314578 | − | 0.949232i | \(-0.398137\pi\) | ||||
0.314578 | + | 0.949232i | \(0.398137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.36360 | −0.0605596 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.8019 | −0.789057 | −0.394529 | − | 0.918884i | \(-0.629092\pi\) | ||||
−0.394529 | + | 0.918884i | \(0.629092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 42.0073 | 1.85829 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.15883 | −0.139466 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.92692 | 0.304646 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.19939 | −0.0965425 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3948 | 0.586837 | 0.293418 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293418 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.46921 | −0.0642439 | −0.0321219 | − | 0.999484i | \(-0.510226\pi\) | ||||
−0.0321219 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1739 | 0.878789 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5646 | −0.937593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.3491 | −0.666095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.8267 | −1.20531 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.81700 | 0.337329 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.74764 | 0.290642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.7144 | −1.83643 | −0.918217 | − | 0.396077i | \(-0.870371\pi\) | ||||
−0.918217 | + | 0.396077i | \(0.870371\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.79895 | −0.291771 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6866 | 0.456928 | 0.228464 | − | 0.973552i | \(-0.426630\pi\) | ||||
0.228464 | + | 0.973552i | \(0.426630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.8146 | 1.14442 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.77479 | −0.0756086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.2717 | 0.734469 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.2083 | 1.44945 | 0.724727 | − | 0.689036i | \(-0.241966\pi\) | ||||
0.724727 | + | 0.689036i | \(0.241966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.1250 | −0.724310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.52111 | 0.148661 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.46788 | −0.230444 | −0.115222 | − | 0.993340i | \(-0.536758\pi\) | ||||
−0.115222 | + | 0.993340i | \(0.536758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.2784 | −0.809618 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.4819 | −0.732878 | −0.366439 | − | 0.930442i | \(-0.619423\pi\) | ||||
−0.366439 | + | 0.930442i | \(0.619423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.21877 | 0.302096 | 0.151048 | − | 0.988526i | \(-0.451735\pi\) | ||||
0.151048 | + | 0.988526i | \(0.451735\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.1806 | −0.467076 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.80625 | −0.0751952 | −0.0375976 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0375976 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.28754 | 0.219743 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.17629 | 0.380697 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.9329 | −1.07403 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.39075 | 0.0986767 | 0.0493384 | − | 0.998782i | \(-0.484289\pi\) | ||||
0.0493384 | + | 0.998782i | \(0.484289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.34481 | 0.385046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.75435 | −0.113299 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.2650 | 1.73562 | 0.867808 | − | 0.496899i | \(-0.165528\pi\) | ||||
0.867808 | + | 0.496899i | \(0.165528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.00910 | −0.123154 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.95838 | −0.366029 | −0.183015 | − | 0.983110i | \(-0.558586\pi\) | ||||
−0.183015 | + | 0.983110i | \(0.558586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8998 | −0.811729 | −0.405864 | − | 0.913933i | \(-0.633029\pi\) | ||||
−0.405864 | + | 0.913933i | \(0.633029\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.4131 | −0.546224 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0084 | 1.05565 | 0.527823 | − | 0.849354i | \(-0.323008\pi\) | ||||
0.527823 | + | 0.849354i | \(0.323008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.00298 | 0.121687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.65279 | −0.309599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.3763 | −1.67117 | −0.835586 | − | 0.549360i | \(-0.814872\pi\) | ||||
−0.835586 | + | 0.549360i | \(0.814872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.9845 | −1.77075 | −0.885374 | − | 0.464880i | \(-0.846098\pi\) | ||||
−0.885374 | + | 0.464880i | \(0.846098\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.4553 | −0.942749 | −0.471374 | − | 0.881933i | \(-0.656242\pi\) | ||||
−0.471374 | + | 0.881933i | \(0.656242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.78448 | −0.151866 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.3545 | 1.25619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.63102 | 0.0651368 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.50173 | 0.0997505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8877 | 1.38886 | 0.694429 | − | 0.719562i | \(-0.255657\pi\) | ||||
0.694429 | + | 0.719562i | \(0.255657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.85922 | −0.352122 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.45473 | −0.295367 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.27306 | 0.287718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.5314 | −1.52190 | −0.760949 | − | 0.648812i | \(-0.775266\pi\) | ||||
−0.760949 | + | 0.648812i | \(0.775266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6353 | −0.734906 | −0.367453 | − | 0.930042i | \(-0.619770\pi\) | ||||
−0.367453 | + | 0.930042i | \(0.619770\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.2282 | 0.755938 | 0.377969 | − | 0.925818i | \(-0.376623\pi\) | ||||
0.377969 | + | 0.925818i | \(0.376623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7573 | 0.657783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.8116 | −0.619706 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.98553 | 0.155966 | 0.0779828 | − | 0.996955i | \(-0.475152\pi\) | ||||
0.0779828 | + | 0.996955i | \(0.475152\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.0901 | 1.44702 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.5719 | −1.30778 | −0.653889 | − | 0.756591i | \(-0.726864\pi\) | ||||
−0.653889 | + | 0.756591i | \(0.726864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.9909 | 1.43878 | 0.719390 | − | 0.694607i | \(-0.244422\pi\) | ||||
0.719390 | + | 0.694607i | \(0.244422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.89008 | −0.151078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.12631 | −0.0823310 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8834 | −0.498100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.2747 | −1.13014 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0747 | −0.465447 | −0.232723 | − | 0.972543i | \(-0.574764\pi\) | ||||
−0.232723 | + | 0.972543i | \(0.574764\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.9135 | −1.61087 | −0.805434 | − | 0.592686i | \(-0.798067\pi\) | ||||
−0.805434 | + | 0.592686i | \(0.798067\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.89977 | 0.379918 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.70038 | −0.371719 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.17092 | 0.350915 | 0.175458 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175458 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.29052 | −0.0492364 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.6504 | 1.09149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.111244 | 0.00423193 | 0.00211596 | − | 0.999998i | \(-0.499326\pi\) | ||||
0.00211596 | + | 0.999998i | \(0.499326\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.1226 | 0.916341 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5013 | 0.700785 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.5077 | 0.397438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7832 | −1.04936 | −0.524678 | − | 0.851301i | \(-0.675814\pi\) | ||||
−0.524678 | + | 0.851301i | \(0.675814\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.15883 | 0.0437062 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.5265 | −0.583933 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.4668 | 1.40710 | 0.703548 | − | 0.710648i | \(-0.251598\pi\) | ||||
0.703548 | + | 0.710648i | \(0.251598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.2500 | 0.571918 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.1957 | 0.419281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.19806 | −0.231471 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0513 | 0.785081 | 0.392541 | − | 0.919735i | \(-0.371596\pi\) | ||||
0.392541 | + | 0.919735i | \(0.371596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.6329 | 1.62498 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.12333 | 0.153348 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.7023 | −1.65792 | −0.828958 | − | 0.559310i | \(-0.811066\pi\) | ||||
−0.828958 | + | 0.559310i | \(0.811066\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.7627 | −0.435656 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3860 | 0.421125 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0301 | −0.924509 | −0.462254 | − | 0.886747i | \(-0.652959\pi\) | ||||
−0.462254 | + | 0.886747i | \(0.652959\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.6437 | 0.539407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.9982 | 0.882788 | 0.441394 | − | 0.897313i | \(-0.354484\pi\) | ||||
0.441394 | + | 0.897313i | \(0.354484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.80194 | −0.0661958 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.4601 | 0.383744 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.10215 | 0.296442 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.9584 | 0.911959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.9420 | 1.09260 | 0.546299 | − | 0.837590i | \(-0.316036\pi\) | ||||
0.546299 | + | 0.837590i | \(0.316036\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.18060 | 0.298118 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2174 | −0.989235 | −0.494617 | − | 0.869111i | \(-0.664692\pi\) | ||||
−0.494617 | + | 0.869111i | \(0.664692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.95407 | 0.0709281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.6813 | 0.677195 | 0.338598 | − | 0.940931i | \(-0.390047\pi\) | ||||
0.338598 | + | 0.940931i | \(0.390047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.5362 | 1.25029 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.5133 | −0.668478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.34780 | 0.228907 | 0.114454 | − | 0.993429i | \(-0.463488\pi\) | ||||
0.114454 | + | 0.993429i | \(0.463488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.85756 | −0.0668984 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.7851 | −1.79064 | −0.895322 | − | 0.445419i | \(-0.853055\pi\) | ||||
−0.895322 | + | 0.445419i | \(0.853055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.96077 | −0.0703423 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.57002 | 0.307053 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.94033 | −0.284127 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.60627 | 0.200352 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.19865 | −0.327897 | −0.163948 | − | 0.986469i | \(-0.552423\pi\) | ||||
−0.163948 | + | 0.986469i | \(0.552423\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.25965 | −0.329652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.4741 | 0.372416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.3424 | 1.14851 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.5084 | −0.478493 | −0.239247 | − | 0.970959i | \(-0.576900\pi\) | ||||
−0.239247 | + | 0.970959i | \(0.576900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.08815 | 0.180006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.6843 | 0.978175 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.4929 | −1.42896 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.65519 | 0.304677 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.9560 | 1.12351 | 0.561756 | − | 0.827303i | \(-0.310126\pi\) | ||||
0.561756 | + | 0.827303i | \(0.310126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7012 | −1.42921 | −0.714607 | − | 0.699526i | \(-0.753394\pi\) | ||||
−0.714607 | + | 0.699526i | \(0.753394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.33273 | 0.257170 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.27413 | 0.184518 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.6504 | −0.931240 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4300 | −0.468709 | −0.234355 | − | 0.972151i | \(-0.575298\pi\) | ||||
−0.234355 | + | 0.972151i | \(0.575298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.7275 | −0.931663 | −0.465832 | − | 0.884873i | \(-0.654245\pi\) | ||||
−0.465832 | + | 0.884873i | \(0.654245\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.3435 | 1.15947 | 0.579733 | − | 0.814806i | \(-0.303157\pi\) | ||||
0.579733 | + | 0.814806i | \(0.303157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2849 | 0.426672 | 0.213336 | − | 0.976979i | \(-0.431567\pi\) | ||||
0.213336 | + | 0.976979i | \(0.431567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.20105 | −0.249802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.95646 | 0.171731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.5187 | −1.02032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.9922 | −1.27711 | −0.638557 | − | 0.769575i | \(-0.720468\pi\) | ||||
−0.638557 | + | 0.769575i | \(0.720468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8501 | −0.891383 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.8130 | 0.475743 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.20237 | 0.247477 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.53750 | −0.258686 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.38835 | 0.0475922 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.16959 | −0.245482 | −0.122741 | − | 0.992439i | \(-0.539168\pi\) | ||||
−0.122741 | + | 0.992439i | \(0.539168\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.55124 | −0.0871486 | −0.0435743 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435743 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.9493 | −1.84073 | −0.920363 | − | 0.391065i | \(-0.872107\pi\) | ||||
−0.920363 | + | 0.391065i | \(0.872107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5007 | −0.494181 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.4698 | 0.730840 | 0.365420 | − | 0.930843i | \(-0.380925\pi\) | ||||
0.365420 | + | 0.930843i | \(0.380925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.84787 | −0.232566 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.6491 | −0.564781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1782 | −0.548178 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.74094 | 0.295836 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.9638 | 1.31571 | 0.657856 | − | 0.753144i | \(-0.271463\pi\) | ||||
0.657856 | + | 0.753144i | \(0.271463\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.708415 | −0.0238942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.4373 | −0.452713 | −0.226357 | − | 0.974045i | \(-0.572681\pi\) | ||||
−0.226357 | + | 0.974045i | \(0.572681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.8799 | −0.938234 | −0.469117 | − | 0.883136i | \(-0.655428\pi\) | ||||
−0.469117 | + | 0.883136i | \(0.655428\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.9135 | −0.970821 | −0.485410 | − | 0.874286i | \(-0.661330\pi\) | ||||
−0.485410 | + | 0.874286i | \(0.661330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.45580 | −0.149443 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.5834 | 0.622568 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.35690 | 0.0788705 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.15883 | −0.0720814 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.5851 | −0.553144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.0489 | −0.634611 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.92394 | −0.296970 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.7127 | 1.01980 | 0.509900 | − | 0.860234i | \(-0.329683\pi\) | ||||
0.509900 | + | 0.860234i | \(0.329683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7090 | −0.454699 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.3690 | −1.30435 | −0.652176 | − | 0.758067i | \(-0.726144\pi\) | ||||
−0.652176 | + | 0.758067i | \(0.726144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.84548 | −0.292743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.3357 | −1.33200 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.87023 | 0.259615 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.8860 | −0.589365 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.77240 | 0.288747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.5254 | 1.26534 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.2924 | 1.28914 | 0.644572 | − | 0.764544i | \(-0.277036\pi\) | ||||
0.644572 | + | 0.764544i | \(0.277036\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29590 | 0.0752450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.93602 | −0.227075 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7554 | 0.874061 | 0.437031 | − | 0.899447i | \(-0.356030\pi\) | ||||
0.437031 | + | 0.899447i | \(0.356030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6203 | 0.379213 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.9191 | −1.36653 | −0.683263 | − | 0.730173i | \(-0.739440\pi\) | ||||
−0.683263 | + | 0.730173i | \(0.739440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2674 | 0.334353 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.4868 | 1.80308 | 0.901539 | − | 0.432698i | \(-0.142438\pi\) | ||||
0.901539 | + | 0.432698i | \(0.142438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.7362 | 1.45220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.79954 | −0.285345 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.48081 | −0.274720 | −0.137360 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137360 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.89472 | −0.0935731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.3129 | 1.59240 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.3256 | 1.81695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.0368 | 0.710127 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.63102 | −0.245397 | −0.122699 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122699 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.19806 | 0.0384873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.3599 | 0.621288 | 0.310644 | − | 0.950526i | \(-0.399455\pi\) | ||||
0.310644 | + | 0.950526i | \(0.399455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.9342 | 1.28023 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −55.8883 | −1.78802 | −0.894012 | − | 0.448042i | \(-0.852121\pi\) | ||||
−0.894012 | + | 0.448042i | \(0.852121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.2241 | −0.965968 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30.4935 | 0.973582 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.58450 | −0.146223 | −0.0731114 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731114 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.98792 | −0.126937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.31873 | 0.200924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5666 | −0.875681 | −0.437840 | − | 0.899053i | \(-0.644257\pi\) | ||||
−0.437840 | + | 0.899053i | \(0.644257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.34481 | 0.233081 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.9119 | −0.503933 | −0.251967 | − | 0.967736i | \(-0.581077\pi\) | ||||
−0.251967 | + | 0.967736i | \(0.581077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.66056 | −0.115815 |
(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 | 7600.2.a.bw.1.2 | 3 | ||
4.3 | odd | 2 | 475.2.a.d.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bn.1.2 | 3 | |||
12.11 | even | 2 | 4275.2.a.bn.1.3 | 3 | |||
20.3 | even | 4 | 475.2.b.c.324.6 | 6 | |||
20.7 | even | 4 | 475.2.b.c.324.1 | 6 | |||
20.19 | odd | 2 | 475.2.a.h.1.3 | yes | 3 | ||
60.59 | even | 2 | 4275.2.a.z.1.1 | 3 | |||
76.75 | even | 2 | 9025.2.a.be.1.3 | 3 | |||
380.379 | even | 2 | 9025.2.a.w.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.d.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
475.2.a.h.1.3 | yes | 3 | 20.19 | odd | 2 | ||
475.2.b.c.324.1 | 6 | 20.7 | even | 4 | |||
475.2.b.c.324.6 | 6 | 20.3 | even | 4 | |||
4275.2.a.z.1.1 | 3 | 60.59 | even | 2 | |||
4275.2.a.bn.1.3 | 3 | 12.11 | even | 2 | |||
7600.2.a.bn.1.2 | 3 | 5.4 | even | 2 | |||
7600.2.a.bw.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.w.1.1 | 3 | 380.379 | even | 2 | |||
9025.2.a.be.1.3 | 3 | 76.75 | even | 2 |