Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 16 x^{13} + 123 x^{12} - 76 x^{11} - 630 x^{10} + 937 x^{9} + 1083 x^{8} - 2602 x^{7} - 249 x^{6} + 2736 x^{5} - 801 x^{4} - 900 x^{3} + 429 x^{2} - 36 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-0.829690\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-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 | ||||||||
\(3\) | 1.84628 | 1.06595 | 0.532974 | − | 0.846132i | \(-0.321074\pi\) | ||||
0.532974 | + | 0.846132i | \(0.321074\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.98774 | −1.33616 | −0.668078 | − | 0.744091i | \(-0.732883\pi\) | ||||
−0.668078 | + | 0.744091i | \(0.732883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.920155 | −0.347786 | −0.173893 | − | 0.984765i | \(-0.555635\pi\) | ||||
−0.173893 | + | 0.984765i | \(0.555635\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.408737 | 0.136246 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.28823 | −0.388415 | −0.194208 | − | 0.980960i | \(-0.562214\pi\) | ||||
−0.194208 | + | 0.980960i | \(0.562214\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44378 | 0.677783 | 0.338891 | − | 0.940825i | \(-0.389948\pi\) | ||||
0.338891 | + | 0.940825i | \(0.389948\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.51619 | −1.42427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.97874 | 1.37162 | 0.685809 | − | 0.727782i | \(-0.259449\pi\) | ||||
0.685809 | + | 0.727782i | \(0.259449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.69886 | −0.370722 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.336054 | 0.0700722 | 0.0350361 | − | 0.999386i | \(-0.488845\pi\) | ||||
0.0350361 | + | 0.999386i | \(0.488845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.92657 | 0.785313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.78419 | −0.920717 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.998551 | 0.185426 | 0.0927131 | − | 0.995693i | \(-0.470446\pi\) | ||||
0.0927131 | + | 0.995693i | \(0.470446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.84063 | 0.510192 | 0.255096 | − | 0.966916i | \(-0.417893\pi\) | ||||
0.255096 | + | 0.966916i | \(0.417893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.37843 | −0.414031 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.74918 | 0.464696 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.24001 | −1.35465 | −0.677325 | − | 0.735684i | \(-0.736861\pi\) | ||||
−0.677325 | + | 0.735684i | \(0.736861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.51190 | 0.722481 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.60887 | 0.407437 | 0.203718 | − | 0.979030i | \(-0.434697\pi\) | ||||
0.203718 | + | 0.979030i | \(0.434697\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5002 | −1.60126 | −0.800632 | − | 0.599156i | \(-0.795503\pi\) | ||||
−0.800632 | + | 0.599156i | \(0.795503\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.22120 | −0.182046 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.00237639 | −0.000346633 0 | −0.000173316 | − | 1.00000i | \(-0.500055\pi\) | ||||
−0.000173316 | 1.00000i | \(0.500055\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.15331 | −0.879045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.84628 | 0.258530 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.66109 | −0.777610 | −0.388805 | − | 0.921320i | \(-0.627112\pi\) | ||||
−0.388805 | + | 0.921320i | \(0.627112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.84889 | 0.518984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0384 | 1.46207 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4554 | 1.46671 | 0.733356 | − | 0.679845i | \(-0.237953\pi\) | ||||
0.733356 | + | 0.679845i | \(0.237953\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.376102 | −0.0473844 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.30137 | −0.905624 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2645 | −1.49835 | −0.749174 | − | 0.662373i | \(-0.769549\pi\) | ||||
−0.749174 | + | 0.662373i | \(0.769549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.620449 | 0.0746933 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.33343 | 0.158249 | 0.0791244 | − | 0.996865i | \(-0.474788\pi\) | ||||
0.0791244 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.50879 | −0.995878 | −0.497939 | − | 0.867212i | \(-0.665910\pi\) | ||||
−0.497939 | + | 0.867212i | \(0.665910\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.24953 | 0.837103 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.18537 | 0.135085 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.03414 | −1.01642 | −0.508210 | − | 0.861233i | \(-0.669693\pi\) | ||||
−0.508210 | + | 0.861233i | \(0.669693\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0591 | −1.11768 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.93365 | −0.651302 | −0.325651 | − | 0.945490i | \(-0.605584\pi\) | ||||
−0.325651 | + | 0.945490i | \(0.605584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.98774 | −0.324065 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.84360 | 0.197655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.5190 | −1.32701 | −0.663506 | − | 0.748171i | \(-0.730932\pi\) | ||||
−0.663506 | + | 0.748171i | \(0.730932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.24866 | −0.235723 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.24459 | 0.543838 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.8629 | −1.83270 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.539984 | −0.0548271 | −0.0274135 | − | 0.999624i | \(-0.508727\pi\) | ||||
−0.0274135 | + | 0.999624i | \(0.508727\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.526547 | −0.0529200 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.27122 | −0.225994 | −0.112997 | − | 0.993595i | \(-0.536045\pi\) | ||||
−0.112997 | + | 0.993595i | \(0.536045\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.08582 | 0.106989 | 0.0534943 | − | 0.998568i | \(-0.482964\pi\) | ||||
0.0534943 | + | 0.998568i | \(0.482964\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.07575 | 0.495342 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.95470 | −0.962357 | −0.481179 | − | 0.876623i | \(-0.659791\pi\) | ||||
−0.481179 | + | 0.876623i | \(0.659791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7596 | 1.41371 | 0.706856 | − | 0.707358i | \(-0.250113\pi\) | ||||
0.706856 | + | 0.707358i | \(0.250113\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.2133 | −1.44399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4972 | −1.74007 | −0.870035 | − | 0.492991i | \(-0.835904\pi\) | ||||
−0.870035 | + | 0.492991i | \(0.835904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00404 | −0.0936273 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.998864 | 0.0923450 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.920155 | −0.0843505 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.34047 | −0.849133 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.81669 | 0.434306 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.20714 | 0.286855 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.39775 | 0.212766 | 0.106383 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106383 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −19.3863 | −1.70687 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.39946 | −0.646494 | −0.323247 | − | 0.946315i | \(-0.604774\pi\) | ||||
−0.323247 | + | 0.946315i | \(0.604774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50137 | −0.477029 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.2939 | 1.23022 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.23075 | 0.276022 | 0.138011 | − | 0.990431i | \(-0.455929\pi\) | ||||
0.138011 | + | 0.990431i | \(0.455929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.1902 | 1.88215 | 0.941076 | − | 0.338196i | \(-0.109817\pi\) | ||||
0.941076 | + | 0.338196i | \(0.109817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.00438748 | −0.000369493 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.14815 | −0.263261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.98341 | −0.247758 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.3607 | −0.937016 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.187452 | 0.0153567 | 0.00767833 | − | 0.999971i | \(-0.497556\pi\) | ||||
0.00767833 | + | 0.999971i | \(0.497556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8102 | 1.36800 | 0.683999 | − | 0.729483i | \(-0.260239\pi\) | ||||
0.683999 | + | 0.729483i | \(0.260239\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.408737 | 0.0330444 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.48705 | −0.681696 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.69664 | −0.534450 | −0.267225 | − | 0.963634i | \(-0.586107\pi\) | ||||
−0.267225 | + | 0.963634i | \(0.586107\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4519 | −0.828892 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.309222 | −0.0243701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7340 | 1.54568 | 0.772841 | − | 0.634599i | \(-0.218835\pi\) | ||||
0.772841 | + | 0.634599i | \(0.218835\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.10611 | 0.553210 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.9146 | −1.54104 | −0.770519 | − | 0.637416i | \(-0.780003\pi\) | ||||
−0.770519 | + | 0.637416i | \(0.780003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.02794 | −0.540610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.44373 | 0.186877 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.0069 | −1.90124 | −0.950618 | − | 0.310363i | \(-0.899549\pi\) | ||||
−0.950618 | + | 0.310363i | \(0.899549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.61305 | −0.273121 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84628 | −0.138775 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.80769 | −0.658318 | −0.329159 | − | 0.944275i | \(-0.606765\pi\) | ||||
−0.329159 | + | 0.944275i | \(0.606765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1467 | 1.20017 | 0.600087 | − | 0.799935i | \(-0.295133\pi\) | ||||
0.600087 | + | 0.799935i | \(0.295133\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.1498 | 1.56344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.6190 | 1.81002 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.28823 | −0.0942046 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.40219 | 0.320213 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.35701 | −0.242905 | −0.121453 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121453 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.5565 | −1.69563 | −0.847815 | − | 0.530292i | \(-0.822082\pi\) | ||||
−0.847815 | + | 0.530292i | \(0.822082\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.4804 | −0.965348 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.9599 | −1.70707 | −0.853536 | − | 0.521033i | \(-0.825547\pi\) | ||||
−0.853536 | + | 0.521033i | \(0.825547\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.03038 | 0.498370 | 0.249185 | − | 0.968456i | \(-0.419837\pi\) | ||||
0.249185 | + | 0.968456i | \(0.419837\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.6437 | −1.59716 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.918821 | −0.0644886 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.79461 | −0.544399 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.137358 | 0.00954703 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.70198 | −0.532757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8192 | −0.744823 | −0.372411 | − | 0.928068i | \(-0.621469\pi\) | ||||
−0.372411 | + | 0.928068i | \(0.621469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.46188 | 0.168685 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.3718 | 2.13954 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.61382 | −0.177438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.7096 | −1.06155 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.44378 | 0.164386 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7214 | 1.38761 | 0.693804 | − | 0.720164i | \(-0.255934\pi\) | ||||
0.693804 | + | 0.720164i | \(0.255934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.60493 | 0.106996 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.8150 | −1.44791 | −0.723956 | − | 0.689846i | \(-0.757678\pi\) | ||||
−0.723956 | + | 0.689846i | \(0.757678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.7000 | 1.96263 | 0.981316 | − | 0.192403i | \(-0.0616282\pi\) | ||||
0.981316 | + | 0.192403i | \(0.0616282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.18852 | 0.143994 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.7710 | −1.16422 | −0.582108 | − | 0.813112i | \(-0.697772\pi\) | ||||
−0.582108 | + | 0.813112i | \(0.697772\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.00710004 | 0.000463155 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.6795 | −1.08345 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.78169 | −0.244617 | −0.122309 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122309 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7821 | −0.758952 | −0.379476 | − | 0.925202i | \(-0.623896\pi\) | ||||
−0.379476 | + | 0.925202i | \(0.623896\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.21940 | −0.270675 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.3845 | 1.17454 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.6107 | 0.929659 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.9552 | −0.694255 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.6042 | 1.30052 | 0.650261 | − | 0.759710i | \(-0.274659\pi\) | ||||
0.650261 | + | 0.759710i | \(0.274659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.432915 | −0.0272171 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.51619 | −0.345437 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9272 | 1.05589 | 0.527945 | − | 0.849278i | \(-0.322963\pi\) | ||||
0.527945 | + | 0.849278i | \(0.322963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.58208 | 0.471128 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.408145 | 0.0252635 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5433 | 0.835118 | 0.417559 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417559 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.9138 | 1.03901 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.1136 | −1.41453 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.4540 | 1.49099 | 0.745493 | − | 0.666514i | \(-0.232214\pi\) | ||||
0.745493 | + | 0.666514i | \(0.232214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.620782 | 0.0377098 | 0.0188549 | − | 0.999822i | \(-0.493998\pi\) | ||||
0.0188549 | + | 0.999822i | \(0.493998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.15164 | −0.251269 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.05831 | −0.305028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.4470 | −1.58904 | −0.794522 | − | 0.607236i | \(-0.792278\pi\) | ||||
−0.794522 | + | 0.607236i | \(0.792278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.16107 | 0.0695115 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6953 | 0.936306 | 0.468153 | − | 0.883647i | \(-0.344920\pi\) | ||||
0.468153 | + | 0.883647i | \(0.344920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0161 | 0.952059 | 0.476030 | − | 0.879429i | \(-0.342075\pi\) | ||||
0.476030 | + | 0.879429i | \(0.342075\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −32.9799 | −1.95356 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.40056 | −0.141701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.996960 | −0.0584428 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2126 | 1.00557 | 0.502785 | − | 0.864411i | \(-0.332309\pi\) | ||||
0.502785 | + | 0.864411i | \(0.332309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.98774 | 0.173953 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.16313 | 0.357621 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.821243 | 0.0474937 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.66181 | 0.556897 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.19329 | −0.240898 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.2256 | −1.95975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.07638 | −0.289724 | −0.144862 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144862 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00472 | 0.114044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.58385 | −0.486745 | −0.243373 | − | 0.969933i | \(-0.578254\pi\) | ||||
−0.243373 | + | 0.969933i | \(0.578254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5346 | 1.83897 | 0.919483 | − | 0.393130i | \(-0.128608\pi\) | ||||
0.919483 | + | 0.393130i | \(0.128608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.12369 | 0.0633129 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −35.2574 | −1.98025 | −0.990126 | − | 0.140182i | \(-0.955231\pi\) | ||||
−0.990126 | + | 0.140182i | \(0.955231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.28636 | −0.0720224 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3791 | −1.02582 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.97874 | 0.332666 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.59567 | 0.532272 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.2503 | 1.50694 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.00218665 | 0.000120554 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.876073 | −0.0481533 | −0.0240767 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240767 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.36800 | −0.184565 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.6431 | 2.00203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6057 | 0.686674 | 0.343337 | − | 0.939212i | \(-0.388443\pi\) | ||||
0.343337 | + | 0.939212i | \(0.388443\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.1509 | −1.85482 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.65938 | −0.198167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.1031 | 0.653505 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.85374 | −0.0998019 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.0255483 | −0.00137150 | −0.000685751 | − | 1.00000i | \(-0.500218\pi\) | ||||
−0.000685751 | 1.00000i | \(0.500218\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7755 | −0.951503 | −0.475751 | − | 0.879580i | \(-0.657824\pi\) | ||||
−0.475751 | + | 0.879580i | \(0.657824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6915 | −0.624046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4502 | 0.822332 | 0.411166 | − | 0.911560i | \(-0.365122\pi\) | ||||
0.411166 | + | 0.911560i | \(0.365122\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.98393 | −0.211445 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.69886 | −0.0899132 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6396 | 1.30043 | 0.650214 | − | 0.759751i | \(-0.274679\pi\) | ||||
0.650214 | + | 0.759751i | \(0.274679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.7454 | 0.881335 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.2451 | −0.905132 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.4220 | 1.33065 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.9405 | 0.832087 | 0.416043 | − | 0.909345i | \(-0.363416\pi\) | ||||
0.416043 | + | 0.909345i | \(0.363416\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.06634 | 0.0555115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.20908 | 0.270442 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4515 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.92126 | 0.305773 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.44024 | 0.125679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.6820 | −0.908263 | −0.454131 | − | 0.890935i | \(-0.650050\pi\) | ||||
−0.454131 | + | 0.890935i | \(0.650050\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.42691 | 0.226798 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5516 | −0.743554 | −0.371777 | − | 0.928322i | \(-0.621251\pi\) | ||||
−0.371777 | + | 0.928322i | \(0.621251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.54157 | −0.180495 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.29182 | −0.218166 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.1547 | −0.514864 | −0.257432 | − | 0.966296i | \(-0.582876\pi\) | ||||
−0.257432 | + | 0.966296i | \(0.582876\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.336054 | 0.0169950 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.6615 | −0.689129 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.9916 | 1.35810 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4963 | −1.32981 | −0.664906 | − | 0.746927i | \(-0.731528\pi\) | ||||
−0.664906 | + | 0.746927i | \(0.731528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.1571 | −0.508489 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.20993 | −0.409984 | −0.204992 | − | 0.978764i | \(-0.565717\pi\) | ||||
−0.204992 | + | 0.978764i | \(0.565717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.94188 | 0.345799 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.0541 | 1.49340 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6150 | 0.526167 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9582 | −0.690187 | −0.345093 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345093 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.96486 | 0.294225 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.920155 | 0.0452779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7282 | 0.870242 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.9693 | 2.00628 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.23425 | 0.255710 | 0.127855 | − | 0.991793i | \(-0.459191\pi\) | ||||
0.127855 | + | 0.991793i | \(0.459191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5396 | 0.562406 | 0.281203 | − | 0.959648i | \(-0.409267\pi\) | ||||
0.281203 | + | 0.959648i | \(0.409267\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.000971321 0 | −4.72272e−5 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.92657 | 0.190466 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.5407 | −0.510101 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.81235 | −0.280623 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6113 | −0.655631 | −0.327816 | − | 0.944742i | \(-0.606312\pi\) | ||||
−0.327816 | + | 0.944742i | \(0.606312\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0180 | 1.15423 | 0.577116 | − | 0.816662i | \(-0.304178\pi\) | ||||
0.577116 | + | 0.816662i | \(0.304178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.50819 | −0.264098 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00918 | 0.0961122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6067 | −0.983503 | −0.491752 | − | 0.870735i | \(-0.663643\pi\) | ||||
−0.491752 | + | 0.870735i | \(0.663643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.51509 | −0.119766 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.90401 | 0.232997 | 0.116498 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116498 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.4035 | 1.77310 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.346088 | 0.0163694 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.7661 | 1.78229 | 0.891147 | − | 0.453716i | \(-0.149902\pi\) | ||||
0.891147 | + | 0.453716i | \(0.149902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.36082 | −0.158255 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 31.0363 | 1.45821 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.71839 | 0.314963 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1073 | 0.800246 | 0.400123 | − | 0.916461i | \(-0.368967\pi\) | ||||
0.400123 | + | 0.916461i | \(0.368967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.78419 | −0.223307 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.11911 | 0.191846 | 0.0959230 | − | 0.995389i | \(-0.469420\pi\) | ||||
0.0959230 | + | 0.995389i | \(0.469420\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.2807 | 0.524257 | 0.262129 | − | 0.965033i | \(-0.415576\pi\) | ||||
0.262129 | + | 0.965033i | \(0.415576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.6694 | −0.726653 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.57635 | 0.211768 | 0.105884 | − | 0.994378i | \(-0.466233\pi\) | ||||
0.105884 | + | 0.994378i | \(0.466233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2853 | 0.521105 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.3639 | −0.569696 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.5266 | 0.621956 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.4759 | 1.07715 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.31390 | −0.105946 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.7294 | −0.718694 | −0.359347 | − | 0.933204i | \(-0.617001\pi\) | ||||
−0.359347 | + | 0.933204i | \(0.617001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.1368 | −0.918158 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.570909 | −0.0259773 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.61333 | 0.0732575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.3417 | −1.78274 | −0.891370 | − | 0.453276i | \(-0.850255\pi\) | ||||
−0.891370 | + | 0.453276i | \(0.850255\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.4343 | 1.64762 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6586 | −0.796919 | −0.398460 | − | 0.917186i | \(-0.630455\pi\) | ||||
−0.398460 | + | 0.917186i | \(0.630455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.998551 | 0.0449725 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.57318 | 0.0707093 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.22696 | −0.0550367 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.4805 | −1.45403 | −0.727013 | − | 0.686623i | \(-0.759092\pi\) | ||||
−0.727013 | + | 0.686623i | \(0.759092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.7679 | −1.64267 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5928 | −0.650659 | −0.325330 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325330 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.78579 | 0.301964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9755 | −0.576263 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.1907 | 0.850612 | 0.425306 | − | 0.905050i | \(-0.360167\pi\) | ||||
0.425306 | + | 0.905050i | \(0.360167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.82940 | 0.346352 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.6034 | −1.26287 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.24413 | −0.142953 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.00306134 | 0.000134638 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.1696 | −2.02662 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0003 | 1.57720 | 0.788600 | − | 0.614906i | \(-0.210806\pi\) | ||||
0.788600 | + | 0.614906i | \(0.210806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.105819 | 0.00462716 | 0.00231358 | − | 0.999997i | \(-0.499264\pi\) | ||||
0.00231358 | + | 0.999997i | \(0.499264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.67069 | −0.291133 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.84063 | 0.123740 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8871 | −0.995090 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.408737 | −0.0177377 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.37550 | 0.276154 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.7420 | 1.28586 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.2614 | −0.701733 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.92687 | 0.341435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.64850 | −0.199854 | −0.0999272 | − | 0.994995i | \(-0.531861\pi\) | ||||
−0.0999272 | + | 0.994995i | \(0.531861\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.8112 | 1.27932 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.0977 | −1.88894 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9851 | 1.41034 | 0.705170 | − | 0.709038i | \(-0.250870\pi\) | ||||
0.705170 | + | 0.709038i | \(0.250870\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.68224 | 0.199833 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.97008 | 0.254334 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.31281 | 0.353497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 45.4534 | 1.92939 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.4474 | −1.71381 | −0.856905 | − | 0.515474i | \(-0.827616\pi\) | ||||
−0.856905 | + | 0.515474i | \(0.827616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.6602 | −1.08531 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.37843 | −0.100417 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0428 | 0.549687 | 0.274844 | − | 0.961489i | \(-0.411374\pi\) | ||||
0.274844 | + | 0.961489i | \(0.411374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.2647 | 2.32500 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.25597 | 0.388714 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.5410 | −1.78341 | −0.891705 | − | 0.452618i | \(-0.850490\pi\) | ||||
−0.891705 | + | 0.452618i | \(0.850490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.8720 | −1.62674 | −0.813371 | − | 0.581746i | \(-0.802370\pi\) | ||||
−0.813371 | + | 0.581746i | \(0.802370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.19798 | −0.258924 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.31954 | 0.0550286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8267 | −0.575615 | −0.287808 | − | 0.957688i | \(-0.592926\pi\) | ||||
−0.287808 | + | 0.957688i | \(0.592926\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.4917 | −1.80745 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.45988 | 0.226514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.29277 | 0.302036 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.98434 | −0.123387 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5809 | −0.560542 | −0.280271 | − | 0.959921i | \(-0.590424\pi\) | ||||
−0.280271 | + | 0.959921i | \(0.590424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9834 | 0.699789 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.2366 | −1.81965 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.64504 | −0.190749 | −0.0953744 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953744 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.74918 | 0.112705 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.9800 | 0.531237 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.78858 | 0.399950 | 0.199975 | − | 0.979801i | \(-0.435914\pi\) | ||||
0.199975 | + | 0.979801i | \(0.435914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.02445 | 0.245742 | 0.122871 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122871 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.01296 | −0.204144 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.9069 | 1.13457 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2650 | −0.863121 | −0.431561 | − | 0.902084i | \(-0.642037\pi\) | ||||
−0.431561 | + | 0.902084i | \(0.642037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.69640 | −0.0687415 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.00580739 | −0.000234942 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.7254 | 0.958258 | 0.479129 | − | 0.877744i | \(-0.340953\pi\) | ||||
0.479129 | + | 0.877744i | \(0.340953\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.3910 | −0.580301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.4226 | 0.741666 | 0.370833 | − | 0.928700i | \(-0.379072\pi\) | ||||
0.370833 | + | 0.928700i | \(0.379072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0814 | 0.646365 | 0.323183 | − | 0.946337i | \(-0.395247\pi\) | ||||
0.323183 | + | 0.946337i | \(0.395247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.60775 | −0.0645166 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5194 | 0.461516 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.2149 | −1.16860 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.2200 | −0.567892 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.24001 | −0.328551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5260 | 1.29484 | 0.647419 | − | 0.762134i | \(-0.275848\pi\) | ||||
0.647419 | + | 0.762134i | \(0.275848\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.9752 | −0.793943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.16385 | −0.284289 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0374 | −0.595802 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.545022 | 0.0215607 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9288 | −0.787139 | −0.393570 | − | 0.919295i | \(-0.628760\pi\) | ||||
−0.393570 | + | 0.919295i | \(0.628760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.39349 | 0.0549538 | 0.0274769 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274769 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 57.9210 | 2.28064 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.8709 | −1.05641 | −0.528203 | − | 0.849118i | \(-0.677134\pi\) | ||||
−0.528203 | + | 0.849118i | \(0.677134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.28823 | 0.0505674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.82583 | −0.189139 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.64819 | 0.0644985 | 0.0322492 | − | 0.999480i | \(-0.489733\pi\) | ||||
0.0322492 | + | 0.999480i | \(0.489733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.1076 | 0.863817 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.47786 | −0.135684 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.5279 | 1.77352 | 0.886758 | − | 0.462234i | \(-0.152952\pi\) | ||||
0.886758 | + | 0.462234i | \(0.152952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6899 | −0.649163 | −0.324582 | − | 0.945858i | \(-0.605223\pi\) | ||||
−0.324582 | + | 0.945858i | \(0.605223\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.51190 | 0.175227 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.4366 | 0.637386 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.335567 | 0.0129932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.2574 | 1.47912 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7571 | −0.569693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.3277 | 0.513747 | 0.256873 | − | 0.966445i | \(-0.417308\pi\) | ||||
0.256873 | + | 0.966445i | \(0.417308\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.7854 | −0.723051 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.1095 | 1.08034 | 0.540168 | − | 0.841557i | \(-0.318361\pi\) | ||||
0.540168 | + | 0.841557i | \(0.318361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.496869 | 0.0190681 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.2765 | −1.54340 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.4010 | −1.73722 | −0.868610 | − | 0.495496i | \(-0.834986\pi\) | ||||
−0.868610 | + | 0.495496i | \(0.834986\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.65263 | −0.368808 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 54.8344 | 2.09206 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.8345 | −0.527051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.4877 | −0.475056 | −0.237528 | − | 0.971381i | \(-0.576337\pi\) | ||||
−0.237528 | + | 0.971381i | \(0.576337\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.484505 | 0.0184048 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −66.2986 | −2.51485 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.60887 | 0.0988179 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.8101 | −1.24099 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.6614 | 1.15807 | 0.579033 | − | 0.815304i | \(-0.303430\pi\) | ||||
0.579033 | + | 0.815304i | \(0.303430\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.2649 | −1.85806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0131086 | 0.000493700 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.08987 | 0.0785977 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9981 | −0.863712 | −0.431856 | − | 0.901942i | \(-0.642141\pi\) | ||||
−0.431856 | + | 0.901942i | \(0.642141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.69259 | −0.138483 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.954606 | 0.0357503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.40583 | 0.351758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.98205 | −0.260749 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.4124 | −0.873135 | −0.436568 | − | 0.899671i | \(-0.643806\pi\) | ||||
−0.436568 | + | 0.899671i | \(0.643806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.999119 | −0.0372091 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.7530 | −0.809004 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.92088 | 0.145618 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3768 | 0.459031 | 0.229515 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229515 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3873 | 0.829158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5002 | −0.388364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.1601 | −0.523015 | −0.261508 | − | 0.965201i | \(-0.584220\pi\) | ||||
−0.261508 | + | 0.965201i | \(0.584220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.9428 | 1.25200 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.7995 | 0.581982 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.7321 | −1.20407 | −0.602036 | − | 0.798469i | \(-0.705644\pi\) | ||||
−0.602036 | + | 0.798469i | \(0.705644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.9755 | 0.990968 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.2542 | −1.62353 | −0.811765 | − | 0.583984i | \(-0.801493\pi\) | ||||
−0.811765 | + | 0.583984i | \(0.801493\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.560057 | −0.0205189 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.42530 | −0.0887372 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.15987 | 0.334694 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7398 | −1.08522 | −0.542611 | − | 0.839984i | \(-0.682564\pi\) | ||||
−0.542611 | + | 0.839984i | \(0.682564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.0410 | 1.38629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50.2245 | −1.82786 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.9286 | 1.01508 | 0.507541 | − | 0.861628i | \(-0.330555\pi\) | ||||
0.507541 | + | 0.861628i | \(0.330555\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.799280 | −0.0290120 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.86737 | −0.248942 | −0.124471 | − | 0.992223i | \(-0.539723\pi\) | ||||
−0.124471 | + | 0.992223i | \(0.539723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5811 | −0.491669 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.22120 | −0.0441525 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.44378 | −0.0882398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.8947 | 1.40258 | 0.701290 | − | 0.712876i | \(-0.252608\pi\) | ||||
0.701290 | + | 0.712876i | \(0.252608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2523 | 1.12552 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.4472 | 1.02317 | 0.511587 | − | 0.859232i | \(-0.329058\pi\) | ||||
0.511587 | + | 0.859232i | \(0.329058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.1539 | 0.400661 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.9986 | 0.502198 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.5977 | 0.558847 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.71776 | −0.0614663 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.77725 | −0.170725 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0078 | 0.714109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0141 | 0.642134 | 0.321067 | − | 0.947056i | \(-0.395958\pi\) | ||||
0.321067 | + | 0.947056i | \(0.395958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.0048 | 0.890193 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.0203 | 0.605172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.9944 | 0.994112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.2276 | 1.10753 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.01310 | −0.0713077 | −0.0356538 | − | 0.999364i | \(-0.511351\pi\) | ||||
−0.0356538 | + | 0.999364i | \(0.511351\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.00237639 | −8.40708e−5 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.11699 | −0.180800 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.9613 | 0.386814 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.923874 | 0.0325623 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 45.1488 | 1.58931 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.6206 | 0.760139 | 0.380070 | − | 0.924958i | \(-0.375900\pi\) | ||||
0.380070 | + | 0.924958i | \(0.375900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.9880 | −0.420956 | −0.210478 | − | 0.977599i | \(-0.567502\pi\) | ||||
−0.210478 | + | 0.977599i | \(0.567502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.14613 | 0.0401967 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −58.9599 | −2.06527 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.7780 | −2.19632 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.919110 | −0.0321163 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.8778 | −1.04274 | −0.521372 | − | 0.853330i | \(-0.674579\pi\) | ||||
−0.521372 | + | 0.853330i | \(0.674579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2418 | −0.949591 | −0.474795 | − | 0.880096i | \(-0.657478\pi\) | ||||
−0.474795 | + | 0.880096i | \(0.657478\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.33905 | −0.325144 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.7153 | −1.90264 | −0.951318 | − | 0.308210i | \(-0.900270\pi\) | ||||
−0.951318 | + | 0.308210i | \(0.900270\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1651 | 1.29080 | 0.645399 | − | 0.763845i | \(-0.276691\pi\) | ||||
0.645399 | + | 0.763845i | \(0.276691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −48.8284 | −1.69384 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.15331 | −0.213200 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 59.4996 | 2.05907 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5901 | −0.469743 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.6254 | −1.54064 | −0.770320 | − | 0.637658i | \(-0.779903\pi\) | ||||
−0.770320 | + | 0.637658i | \(0.779903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0029 | −0.965617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.9780 | 0.998054 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20.9976 | 0.722340 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.59468 | 0.295317 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.5702 | 1.01485 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.76909 | −0.0949232 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.0605 | 0.378705 | 0.189352 | − | 0.981909i | \(-0.439361\pi\) | ||||
0.189352 | + | 0.981909i | \(0.439361\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.30123 | −0.249697 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.6770 | 1.76525 | 0.882626 | − | 0.470076i | \(-0.155773\pi\) | ||||
0.882626 | + | 0.470076i | \(0.155773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.4190 | 1.68616 | 0.843078 | − | 0.537791i | \(-0.180741\pi\) | ||||
0.843078 | + | 0.537791i | \(0.180741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.43210 | −0.151046 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.90264 | 0.269009 | 0.134505 | − | 0.990913i | \(-0.457056\pi\) | ||||
0.134505 | + | 0.990913i | \(0.457056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 74.7139 | 2.54035 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.84628 | 0.0627028 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6380 | 0.394793 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.9718 | −1.01555 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.220712 | −0.00746996 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.95106 | −0.0997642 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.6026 | 1.40482 | 0.702410 | − | 0.711773i | \(-0.252107\pi\) | ||||
0.702410 | + | 0.711773i | \(0.252107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.7792 | 1.07189 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.40995 | −0.283339 | −0.141669 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141669 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.86398 | −0.230991 | −0.115496 | − | 0.993308i | \(-0.536846\pi\) | ||||
−0.115496 | + | 0.993308i | \(0.536846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.51619 | 0.185425 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9773 | −0.670772 | −0.335386 | − | 0.942081i | \(-0.608867\pi\) | ||||
−0.335386 | + | 0.942081i | \(0.608867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.20630 | −0.0739970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.9585 | 0.434125 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0142079 | −0.000475448 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.3151 | 0.879615 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.51624 | 0.0506258 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.83651 | 0.0946030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.66109 | −0.188598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.8384 | 0.593624 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.2420 | −1.60362 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.4888 | 0.979161 | 0.489580 | − | 0.871958i | \(-0.337150\pi\) | ||||
0.489580 | + | 0.871958i | \(0.337150\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.928330 | −0.0307908 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.1170 | 0.533981 | 0.266991 | − | 0.963699i | \(-0.413971\pi\) | ||||
0.266991 | + | 0.963699i | \(0.413971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.64389 | 0.252976 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −63.1900 | −2.08900 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.80865 | 0.224841 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.6310 | 0.779515 | 0.389757 | − | 0.920918i | \(-0.372559\pi\) | ||||
0.389757 | + | 0.920918i | \(0.372559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.37240 | −0.308831 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.25861 | 0.107258 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.3549 | −1.06382 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.443813 | 0.0145767 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.3474 | −1.45499 | −0.727495 | − | 0.686113i | \(-0.759315\pi\) | ||||
−0.727495 | + | 0.686113i | \(0.759315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.7891 | −1.20571 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.8482 | −0.518845 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.84889 | 0.125872 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.6166 | 0.608179 | 0.304090 | − | 0.952643i | \(-0.401648\pi\) | ||||
0.304090 | + | 0.952643i | \(0.401648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.0679 | 1.96024 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.7179 | 1.35997 | 0.679983 | − | 0.733228i | \(-0.261987\pi\) | ||||
0.679983 | + | 0.733228i | \(0.261987\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.876721 | 0.0285500 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.1526 | −0.427854 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.6862 | −0.704705 | −0.352353 | − | 0.935867i | \(-0.614618\pi\) | ||||
−0.352353 | + | 0.935867i | \(0.614618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.7936 | −0.674989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.0949 | −2.11085 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.0043 | −0.745183 | −0.372591 | − | 0.927996i | \(-0.621531\pi\) | ||||
−0.372591 | + | 0.927996i | \(0.621531\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.0299 | 0.324559 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.37498 | −0.0767722 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.97279 | −0.0959964 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.9308 | −0.739704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.06886 | −0.131117 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70.3805 | 2.26563 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2831 | −0.427155 | −0.213578 | − | 0.976926i | \(-0.568512\pi\) | ||||
−0.213578 | + | 0.976926i | \(0.568512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.0384 | 0.354605 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.2995 | 0.811901 | 0.405950 | − | 0.913895i | \(-0.366941\pi\) | ||||
0.405950 | + | 0.913895i | \(0.366941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.4185 | −0.654586 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.7163 | 0.567374 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.7028 | −1.43017 | −0.715085 | − | 0.699037i | \(-0.753612\pi\) | ||||
−0.715085 | + | 0.699037i | \(0.753612\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.1273 | 0.515432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.03279 | 0.192612 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.1552 | −1.31265 | −0.656324 | − | 0.754479i | \(-0.727889\pi\) | ||||
−0.656324 | + | 0.754479i | \(0.727889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71.5859 | 2.28092 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.00403716 | 0.000128504 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.52864 | −0.112204 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.5372 | −1.73243 | −0.866215 | − | 0.499671i | \(-0.833454\pi\) | ||||
−0.866215 | + | 0.499671i | \(0.833454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.61747 | −0.0513289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0049 | −0.665900 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.5922 | 1.34891 | 0.674454 | − | 0.738317i | \(-0.264379\pi\) | ||||
0.674454 | + | 0.738317i | \(0.264379\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.4217 | 1.24725 |
(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 | 4012.2.a.h.1.12 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.h.1.12 | ✓ | 15 | 1.1 | even | 1 | trivial |