Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4840,2,Mod(1,4840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4840, 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("4840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4840.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: | \(38.6475945783\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.22733568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 8x^{4} - 2x^{3} + 16x^{2} + 8x - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.821728\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.32476 | −1.34220 | −0.671101 | − | 0.741366i | \(-0.734178\pi\) | ||||
−0.671101 | + | 0.741366i | \(0.734178\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.78768 | −1.80957 | −0.904786 | − | 0.425867i | \(-0.859969\pi\) | ||||
−0.904786 | + | 0.425867i | \(0.859969\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.40452 | 0.801508 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.601547 | 0.166839 | 0.0834195 | − | 0.996515i | \(-0.473416\pi\) | ||||
0.0834195 | + | 0.996515i | \(0.473416\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.32476 | −0.600251 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.64953 | 0.642605 | 0.321302 | − | 0.946977i | \(-0.395879\pi\) | ||||
0.321302 | + | 0.946977i | \(0.395879\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.60155 | −0.596836 | −0.298418 | − | 0.954435i | \(-0.596459\pi\) | ||||
−0.298418 | + | 0.954435i | \(0.596459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1302 | 2.42881 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.17083 | 1.07819 | 0.539096 | − | 0.842244i | \(-0.318766\pi\) | ||||
0.539096 | + | 0.842244i | \(0.318766\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.38434 | 0.266417 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.44643 | −1.01138 | −0.505689 | − | 0.862716i | \(-0.668762\pi\) | ||||
−0.505689 | + | 0.862716i | \(0.668762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4577 | −1.87827 | −0.939133 | − | 0.343554i | \(-0.888369\pi\) | ||||
−0.939133 | + | 0.343554i | \(0.888369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.78768 | −0.809265 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.39816 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.39845 | −0.223932 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54633 | 0.710018 | 0.355009 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355009 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.48547 | 0.531530 | 0.265765 | − | 0.964038i | \(-0.414376\pi\) | ||||
0.265765 | + | 0.964038i | \(0.414376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.40452 | 0.358445 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.07340 | 0.740031 | 0.370016 | − | 0.929026i | \(-0.379352\pi\) | ||||
0.370016 | + | 0.929026i | \(0.379352\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.9218 | 2.27455 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.15952 | −0.862506 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.76714 | 0.517456 | 0.258728 | − | 0.965950i | \(-0.416697\pi\) | ||||
0.258728 | + | 0.965950i | \(0.416697\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.04798 | 0.801074 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7599 | 1.53101 | 0.765507 | − | 0.643428i | \(-0.222488\pi\) | ||||
0.765507 | + | 0.643428i | \(0.222488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6454 | −1.61908 | −0.809542 | − | 0.587063i | \(-0.800284\pi\) | ||||
−0.809542 | + | 0.587063i | \(0.800284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.5121 | −1.45039 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.601547 | 0.0746127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.0452 | −1.83806 | −0.919030 | − | 0.394187i | \(-0.871026\pi\) | ||||
−0.919030 | + | 0.394187i | \(0.871026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.0210 | −1.44715 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.346489 | 0.0411207 | 0.0205604 | − | 0.999789i | \(-0.493455\pi\) | ||||
0.0205604 | + | 0.999789i | \(0.493455\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.68096 | −0.430823 | −0.215412 | − | 0.976523i | \(-0.569109\pi\) | ||||
−0.215412 | + | 0.976523i | \(0.569109\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.32476 | −0.268441 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.05322 | 0.906058 | 0.453029 | − | 0.891496i | \(-0.350343\pi\) | ||||
0.453029 | + | 0.891496i | \(0.350343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4318 | −1.15909 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0094 | 1.42796 | 0.713981 | − | 0.700165i | \(-0.246890\pi\) | ||||
0.713981 | + | 0.700165i | \(0.246890\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.64953 | 0.287381 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6617 | 1.35747 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.462692 | 0.0490453 | 0.0245226 | − | 0.999699i | \(-0.492193\pi\) | ||||
0.0245226 | + | 0.999699i | \(0.492193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.88001 | −0.301907 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24.3118 | 2.52101 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.60155 | −0.266913 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.97011 | 0.809242 | 0.404621 | − | 0.914484i | \(-0.367403\pi\) | ||||
0.404621 | + | 0.914484i | \(0.367403\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9134 | 1.08592 | 0.542960 | − | 0.839759i | \(-0.317304\pi\) | ||||
0.542960 | + | 0.839759i | \(0.317304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9081 | −1.66600 | −0.833001 | − | 0.553271i | \(-0.813379\pi\) | ||||
−0.833001 | + | 0.553271i | \(0.813379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.1302 | 1.08620 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.94029 | −0.864291 | −0.432145 | − | 0.901804i | \(-0.642243\pi\) | ||||
−0.432145 | + | 0.901804i | \(0.642243\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.76627 | −0.839656 | −0.419828 | − | 0.907604i | \(-0.637910\pi\) | ||||
−0.419828 | + | 0.907604i | \(0.637910\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.8485 | −2.07377 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.49000 | −0.234240 | −0.117120 | − | 0.993118i | \(-0.537366\pi\) | ||||
−0.117120 | + | 0.993118i | \(0.537366\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.17083 | 0.482182 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.44643 | 0.133723 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.6851 | −1.16284 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.5692 | −0.952988 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.22655 | 0.818724 | 0.409362 | − | 0.912372i | \(-0.365751\pi\) | ||||
0.409362 | + | 0.912372i | \(0.365751\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.10290 | −0.713421 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.09882 | −0.707597 | −0.353799 | − | 0.935322i | \(-0.615110\pi\) | ||||
−0.353799 | + | 0.935322i | \(0.615110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4554 | 1.08002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.38434 | 0.119145 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.57195 | 0.561480 | 0.280740 | − | 0.959784i | \(-0.409420\pi\) | ||||
0.280740 | + | 0.959784i | \(0.409420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.61119 | 0.306297 | 0.153149 | − | 0.988203i | \(-0.451059\pi\) | ||||
0.153149 | + | 0.988203i | \(0.451059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.7945 | −0.993272 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.44643 | −0.452302 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −37.0145 | −3.05291 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1685 | −0.996886 | −0.498443 | − | 0.866922i | \(-0.666095\pi\) | ||||
−0.498443 | + | 0.866922i | \(0.666095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5830 | −1.75640 | −0.878198 | − | 0.478296i | \(-0.841254\pi\) | ||||
−0.878198 | + | 0.478296i | \(0.841254\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.37085 | 0.515053 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4577 | −0.839986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.68096 | 0.613007 | 0.306504 | − | 0.951870i | \(-0.400841\pi\) | ||||
0.306504 | + | 0.951870i | \(0.400841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.75771 | −0.694531 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.7562 | −1.95107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.21691 | −0.408620 | −0.204310 | − | 0.978906i | \(-0.565495\pi\) | ||||
−0.204310 | + | 0.978906i | \(0.565495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.2767 | 1.49168 | 0.745838 | − | 0.666127i | \(-0.232049\pi\) | ||||
0.745838 | + | 0.666127i | \(0.232049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6381 | −0.972165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.25548 | −0.478369 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.6210 | −1.49175 | −0.745877 | − | 0.666084i | \(-0.767969\pi\) | ||||
−0.745877 | + | 0.666084i | \(0.767969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.78768 | −0.361914 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.3391 | −2.05493 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.26184 | −0.542775 | −0.271388 | − | 0.962470i | \(-0.587483\pi\) | ||||
−0.271388 | + | 0.962470i | \(0.587483\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.78809 | −0.653214 | −0.326607 | − | 0.945160i | \(-0.605905\pi\) | ||||
−0.326607 | + | 0.945160i | \(0.605905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.3977 | 2.17314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.39816 | 0.690967 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.62778 | −0.482100 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.9236 | 1.80341 | 0.901703 | − | 0.432355i | \(-0.142317\pi\) | ||||
0.901703 | + | 0.432355i | \(0.142317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.66623 | 0.479845 | 0.239923 | − | 0.970792i | \(-0.422878\pi\) | ||||
0.239923 | + | 0.970792i | \(0.422878\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.39845 | −0.100145 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.66329 | 0.118504 | 0.0592522 | − | 0.998243i | \(-0.481128\pi\) | ||||
0.0592522 | + | 0.998243i | \(0.481128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.0008 | −1.48870 | −0.744352 | − | 0.667787i | \(-0.767242\pi\) | ||||
−0.744352 | + | 0.667787i | \(0.767242\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.9765 | 2.46705 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.0758 | 1.83016 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.54633 | 0.317530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4334 | 0.864180 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3170 | −0.779095 | −0.389548 | − | 0.921006i | \(-0.627369\pi\) | ||||
−0.389548 | + | 0.921006i | \(0.627369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.805506 | −0.0551924 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.48547 | 0.237707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 50.0683 | 3.39886 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.55735 | 0.578252 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.59381 | 0.107212 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.746956 | 0.0500198 | 0.0250099 | − | 0.999687i | \(-0.492038\pi\) | ||||
0.0250099 | + | 0.999687i | \(0.492038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40452 | 0.160302 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.5057 | 0.896405 | 0.448203 | − | 0.893932i | \(-0.352064\pi\) | ||||
0.448203 | + | 0.893932i | \(0.352064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.36737 | 0.156440 | 0.0782201 | − | 0.996936i | \(-0.475076\pi\) | ||||
0.0782201 | + | 0.996936i | \(0.475076\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.15499 | 0.141178 | 0.0705892 | − | 0.997505i | \(-0.477512\pi\) | ||||
0.0705892 | + | 0.997505i | \(0.477512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.07340 | 0.330952 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.7218 | −1.21611 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.5539 | −1.84700 | −0.923500 | − | 0.383600i | \(-0.874684\pi\) | ||||
−0.923500 | + | 0.383600i | \(0.874684\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.62289 | −0.362202 | −0.181101 | − | 0.983465i | \(-0.557966\pi\) | ||||
−0.181101 | + | 0.983465i | \(0.557966\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.0985 | 1.28932 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.9218 | 1.01721 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56495 | −0.0995755 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.2437 | −1.91661 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.5337 | 1.29607 | 0.648036 | − | 0.761609i | \(-0.275590\pi\) | ||||
0.648036 | + | 0.761609i | \(0.275590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.15952 | −0.385724 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.7592 | −0.983030 | −0.491515 | − | 0.870869i | \(-0.663557\pi\) | ||||
−0.491515 | + | 0.870869i | \(0.663557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.9954 | −2.79588 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0961 | −0.810627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.8194 | −0.975464 | −0.487732 | − | 0.872993i | \(-0.662176\pi\) | ||||
−0.487732 | + | 0.872993i | \(0.662176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.76714 | 0.231413 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.07565 | −0.0658287 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1701 | 1.10785 | 0.553924 | − | 0.832567i | \(-0.313130\pi\) | ||||
0.553924 | + | 0.832567i | \(0.313130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.8599 | −1.51013 | −0.755065 | − | 0.655650i | \(-0.772395\pi\) | ||||
−0.755065 | + | 0.655650i | \(0.772395\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.69534 | 0.405221 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.6352 | −1.42010 | −0.710050 | − | 0.704151i | \(-0.751328\pi\) | ||||
−0.710050 | + | 0.704151i | \(0.751328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.1459 | −1.50544 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.70036 | 0.399710 | 0.199855 | − | 0.979825i | \(-0.435953\pi\) | ||||
0.199855 | + | 0.979825i | \(0.435953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.11292 | −0.422819 | −0.211410 | − | 0.977398i | \(-0.567805\pi\) | ||||
−0.211410 | + | 0.977398i | \(0.567805\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.04798 | 0.358251 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.7664 | −1.28483 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.98001 | −0.587059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.5286 | −1.08617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.4950 | −1.60628 | −0.803138 | − | 0.595793i | \(-0.796838\pi\) | ||||
−0.803138 | + | 0.595793i | \(0.796838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.7599 | 0.684690 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.11049 | 0.179885 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.6873 | −0.961841 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.3710 | −1.45752 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.6454 | −0.724076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0888 | 1.31775 | 0.658875 | − | 0.752253i | \(-0.271033\pi\) | ||||
0.658875 | + | 0.752253i | \(0.271033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 39.3073 | 2.23611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.07508 | −0.401191 | −0.200595 | − | 0.979674i | \(-0.564288\pi\) | ||||
−0.200595 | + | 0.979674i | \(0.564288\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.1646 | −1.59196 | −0.795979 | − | 0.605325i | \(-0.793043\pi\) | ||||
−0.795979 | + | 0.605325i | \(0.793043\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.5121 | −0.648632 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.4408 | 1.31657 | 0.658284 | − | 0.752770i | \(-0.271283\pi\) | ||||
0.658284 | + | 0.752770i | \(0.271283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.7841 | 1.16005 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.89287 | −0.383529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.601547 | 0.0333678 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.3795 | 1.12699 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.2898 | −1.33914 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.08798 | 0.279661 | 0.139830 | − | 0.990175i | \(-0.455344\pi\) | ||||
0.139830 | + | 0.990175i | \(0.455344\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.5981 | 1.23837 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0452 | −0.822006 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4172 | −1.38456 | −0.692280 | − | 0.721629i | \(-0.743394\pi\) | ||||
−0.692280 | + | 0.721629i | \(0.743394\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.78867 | 0.314398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.7149 | −2.30639 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0210 | −0.647186 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.8827 | 0.959995 | 0.479997 | − | 0.877270i | \(-0.340638\pi\) | ||||
0.479997 | + | 0.877270i | \(0.340638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.29515 | −0.336971 | −0.168486 | − | 0.985704i | \(-0.553888\pi\) | ||||
−0.168486 | + | 0.985704i | \(0.553888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.832746 | 0.0444487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.17636 | 0.169060 | 0.0845302 | − | 0.996421i | \(-0.473061\pi\) | ||||
0.0845302 | + | 0.996421i | \(0.473061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.346489 | 0.0183898 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.4898 | 1.56077 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.12020 | 0.270234 | 0.135117 | − | 0.990830i | \(-0.456859\pi\) | ||||
0.135117 | + | 0.990830i | \(0.456859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2320 | −0.643787 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.68096 | −0.192670 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.8346 | −0.565564 | −0.282782 | − | 0.959184i | \(-0.591257\pi\) | ||||
−0.282782 | + | 0.959184i | \(0.591257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9318 | 0.569085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0358 | −0.936374 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.5605 | −1.89303 | −0.946516 | − | 0.322656i | \(-0.895424\pi\) | ||||
−0.946516 | + | 0.322656i | \(0.895424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.32476 | −0.120050 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.27628 | −0.168737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.681538 | 0.0350083 | 0.0175041 | − | 0.999847i | \(-0.494428\pi\) | ||||
0.0175041 | + | 0.999847i | \(0.494428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.4495 | −1.09889 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.6876 | 1.87465 | 0.937323 | − | 0.348461i | \(-0.113295\pi\) | ||||
0.937323 | + | 0.348461i | \(0.113295\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.38090 | 0.426025 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.9171 | 1.87177 | 0.935887 | − | 0.352301i | \(-0.114601\pi\) | ||||
0.935887 | + | 0.352301i | \(0.114601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7002 | 0.692851 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.8278 | 0.949739 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.05322 | 0.405201 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6085 | −1.48601 | −0.743003 | − | 0.669288i | \(-0.766599\pi\) | ||||
−0.743003 | + | 0.669288i | \(0.766599\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.9558 | −1.44960 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.1919 | −0.858523 | −0.429262 | − | 0.903180i | \(-0.641226\pi\) | ||||
−0.429262 | + | 0.903180i | \(0.641226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.29082 | −0.313368 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.4318 | −0.518362 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.36760 | −0.364304 | −0.182152 | − | 0.983270i | \(-0.558306\pi\) | ||||
−0.182152 | + | 0.983270i | \(0.558306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.2782 | −0.753619 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −56.3028 | −2.77048 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0094 | 0.638604 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.39516 | −0.411113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.3728 | 0.946425 | 0.473212 | − | 0.880948i | \(-0.343094\pi\) | ||||
0.473212 | + | 0.880948i | \(0.343094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2101 | 0.838769 | 0.419384 | − | 0.907809i | \(-0.362246\pi\) | ||||
0.419384 | + | 0.907809i | \(0.362246\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.1991 | 0.593141 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.64953 | 0.128521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 60.5423 | 2.92985 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.8744 | −1.48717 | −0.743584 | − | 0.668643i | \(-0.766876\pi\) | ||||
−0.743584 | + | 0.668643i | \(0.766876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.48737 | 0.119536 | 0.0597678 | − | 0.998212i | \(-0.480964\pi\) | ||||
0.0597678 | + | 0.998212i | \(0.480964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.6617 | 0.607080 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.4522 | −0.643504 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.6203 | 0.697790 | 0.348895 | − | 0.937162i | \(-0.386557\pi\) | ||||
0.348895 | + | 0.937162i | \(0.386557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.2844 | 1.82307 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.0885 | −1.52457 | −0.762285 | − | 0.647241i | \(-0.775923\pi\) | ||||
−0.762285 | + | 0.647241i | \(0.775923\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.462692 | 0.0219337 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.2890 | 1.33802 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2208 | 0.529544 | 0.264772 | − | 0.964311i | \(-0.414703\pi\) | ||||
0.264772 | + | 0.964311i | \(0.414703\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 50.1753 | 2.35744 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.88001 | −0.135017 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.28861 | −0.340947 | −0.170473 | − | 0.985362i | \(-0.554530\pi\) | ||||
−0.170473 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.66785 | 0.171200 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.56686 | 0.398999 | 0.199499 | − | 0.979898i | \(-0.436068\pi\) | ||||
0.199499 | + | 0.979898i | \(0.436068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.6373 | −1.05204 | −0.526022 | − | 0.850471i | \(-0.676317\pi\) | ||||
−0.526022 | + | 0.850471i | \(0.676317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.3118 | 1.12743 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.1970 | −1.44363 | −0.721813 | − | 0.692089i | \(-0.756691\pi\) | ||||
−0.721813 | + | 0.692089i | \(0.756691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 72.0314 | 3.32610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8564 | −0.822780 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.60155 | −0.119367 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.05817 | 0.414745 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.1292 | −1.51371 | −0.756856 | − | 0.653582i | \(-0.773265\pi\) | ||||
−0.756856 | + | 0.653582i | \(0.773265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65343 | 0.257774 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 57.5524 | 2.61873 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.97011 | 0.361904 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.89985 | −0.312662 | −0.156331 | − | 0.987705i | \(-0.549967\pi\) | ||||
−0.156331 | + | 0.987705i | \(0.549967\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.1281 | 0.548451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.53178 | −0.159387 | −0.0796935 | − | 0.996819i | \(-0.525394\pi\) | ||||
−0.0796935 | + | 0.996819i | \(0.525394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.4305 | −0.649916 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.65888 | −0.0744109 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.67978 | −0.209496 | −0.104748 | − | 0.994499i | \(-0.533404\pi\) | ||||
−0.104748 | + | 0.994499i | \(0.533404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −44.8138 | −2.00213 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.5622 | −1.58564 | −0.792821 | − | 0.609455i | \(-0.791388\pi\) | ||||
−0.792821 | + | 0.609455i | \(0.791388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9134 | 0.485638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.3807 | 1.30484 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.7168 | −0.475012 | −0.237506 | − | 0.971386i | \(-0.576330\pi\) | ||||
−0.237506 | + | 0.971386i | \(0.576330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6232 | 0.779606 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.60143 | −0.159007 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.9081 | −0.745059 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.6141 | 2.00224 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.19519 | −0.0961729 | −0.0480865 | − | 0.998843i | \(-0.515312\pi\) | ||||
−0.0480865 | + | 0.998843i | \(0.515312\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.21848 | −0.0970075 | −0.0485038 | − | 0.998823i | \(-0.515445\pi\) | ||||
−0.0485038 | + | 0.998823i | \(0.515445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.1302 | 0.485762 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.7081 | −1.20698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.73746 | 0.162498 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.2771 | 1.22712 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.73483 | 0.118459 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.94029 | −0.386523 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.8821 | 0.728514 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.8481 | −1.67021 | −0.835106 | − | 0.550089i | \(-0.814594\pi\) | ||||
−0.835106 | + | 0.550089i | \(0.814594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.4302 | 0.876745 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.76627 | −0.375506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4573 | 0.532637 | 0.266319 | − | 0.963885i | \(-0.414193\pi\) | ||||
0.266319 | + | 0.963885i | \(0.414193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −30.4063 | −1.29771 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.1691 | 0.603626 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.5562 | −1.63958 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.8485 | −0.927417 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.9789 | 1.43973 | 0.719867 | − | 0.694112i | \(-0.244203\pi\) | ||||
0.719867 | + | 0.694112i | \(0.244203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.09667 | 0.0886799 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.9594 | 1.00977 | 0.504884 | − | 0.863187i | \(-0.331535\pi\) | ||||
0.504884 | + | 0.863187i | \(0.331535\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.49000 | −0.104755 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 49.9443 | 2.09746 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.52879 | −0.315623 | −0.157812 | − | 0.987469i | \(-0.550444\pi\) | ||||
−0.157812 | + | 0.987469i | \(0.550444\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5353 | −0.566433 | −0.283216 | − | 0.959056i | \(-0.591401\pi\) | ||||
−0.283216 | + | 0.959056i | \(0.591401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −57.9414 | −2.42054 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.17083 | 0.215638 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.3683 | 1.13936 | 0.569678 | − | 0.821868i | \(-0.307068\pi\) | ||||
0.569678 | + | 0.821868i | \(0.307068\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.4974 | −0.644050 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62.2846 | −2.58400 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.44643 | 0.0598027 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.1927 | 0.709618 | 0.354809 | − | 0.934939i | \(-0.384546\pi\) | ||||
0.354809 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.2063 | 1.12102 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.86675 | −0.159057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.4574 | −1.57925 | −0.789627 | − | 0.613587i | \(-0.789726\pi\) | ||||
−0.789627 | + | 0.613587i | \(0.789726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.6851 | −0.520037 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 48.8218 | 1.99814 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.63410 | −0.393639 | −0.196819 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0426 | 0.817555 | 0.408777 | − | 0.912634i | \(-0.365955\pi\) | ||||
0.408777 | + | 0.912634i | \(0.365955\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.1765 | −1.47322 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.4596 | 0.708662 | 0.354331 | − | 0.935120i | \(-0.384709\pi\) | ||||
0.354331 | + | 0.935120i | \(0.384709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −60.6200 | −2.45644 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.05189 | 0.123466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9105 | 0.844569 | 0.422284 | − | 0.906463i | \(-0.361228\pi\) | ||||
0.422284 | + | 0.906463i | \(0.361228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.5692 | −0.426189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.2590 | −1.66103 | −0.830513 | − | 0.557000i | \(-0.811952\pi\) | ||||
−0.830513 | + | 0.557000i | \(0.811952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.151406 | 0.00608551 | 0.00304276 | − | 0.999995i | \(-0.499031\pi\) | ||||
0.00304276 | + | 0.999995i | \(0.499031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.15819 | 0.287248 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.21522 | −0.0887510 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.9007 | 0.992855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.21832 | 0.366976 | 0.183488 | − | 0.983022i | \(-0.441261\pi\) | ||||
0.183488 | + | 0.983022i | \(0.441261\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.3094 | 1.04570 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.22655 | 0.366145 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.57773 | 0.379483 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.833142 | 0.0329586 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.8665 | −0.784678 | −0.392339 | − | 0.919821i | \(-0.628334\pi\) | ||||
−0.392339 | + | 0.919821i | \(0.628334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.8982 | −0.705838 | −0.352919 | − | 0.935654i | \(-0.614811\pi\) | ||||
−0.352919 | + | 0.935654i | \(0.614811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.10290 | −0.319051 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6373 | −0.889964 | −0.444982 | − | 0.895539i | \(-0.646790\pi\) | ||||
−0.444982 | + | 0.895539i | \(0.646790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −116.397 | −4.56195 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1498 | 0.436325 | 0.218163 | − | 0.975912i | \(-0.429994\pi\) | ||||
0.218163 | + | 0.975912i | \(0.429994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.09882 | −0.316447 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.85095 | −0.345308 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0304 | 0.702366 | 0.351183 | − | 0.936307i | \(-0.385779\pi\) | ||||
0.351183 | + | 0.936307i | \(0.385779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1373 | −0.627668 | −0.313834 | − | 0.949478i | \(-0.601613\pi\) | ||||
−0.313834 | + | 0.949478i | \(0.601613\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.70524 | −0.143900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4554 | 0.482998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.1626 | −1.09046 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.73649 | −0.0671368 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5210 | 1.36923 | 0.684617 | − | 0.728903i | \(-0.259969\pi\) | ||||
0.684617 | + | 0.728903i | \(0.259969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.38434 | 0.0532833 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.4138 | 1.24576 | 0.622882 | − | 0.782315i | \(-0.285961\pi\) | ||||
0.622882 | + | 0.782315i | \(0.285961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −38.1583 | −1.46438 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.3976 | −1.20316 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.36687 | 0.281885 | 0.140943 | − | 0.990018i | \(-0.454987\pi\) | ||||
0.140943 | + | 0.990018i | \(0.454987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.57195 | 0.251101 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.50357 | −0.209974 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.26611 | 0.0863319 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.768429 | −0.0292324 | −0.0146162 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146162 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.61119 | 0.136980 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0456 | 0.456261 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.00985 | −0.189490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.95905 | 0.300609 | 0.150305 | − | 0.988640i | \(-0.451975\pi\) | ||||
0.150305 | + | 0.988640i | \(0.451975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4498 | −0.922140 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.7945 | −0.444205 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −52.2496 | −1.96505 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3307 | 0.575755 | 0.287877 | − | 0.957667i | \(-0.407050\pi\) | ||||
0.287877 | + | 0.957667i | \(0.407050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.3642 | 0.726212 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54.0752 | −2.02513 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 66.3811 | 2.47905 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.2627 | 1.72531 | 0.862654 | − | 0.505794i | \(-0.168800\pi\) | ||||
0.862654 | + | 0.505794i | \(0.168800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 80.9504 | 3.01475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.0719 | 0.486148 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.44643 | −0.202275 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0817 | 0.893140 | 0.446570 | − | 0.894749i | \(-0.352645\pi\) | ||||
0.446570 | + | 0.894749i | \(0.352645\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.4288 | −0.571437 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.23485 | 0.341563 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0668 | 0.482632 | 0.241316 | − | 0.970447i | \(-0.422421\pi\) | ||||
0.241316 | + | 0.970447i | \(0.422421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −37.0145 | −1.36530 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.5963 | 1.23586 | 0.617930 | − | 0.786233i | \(-0.287972\pi\) | ||||
0.617930 | + | 0.786233i | \(0.287972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.63814 | 0.133650 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.1661 | 0.996626 | 0.498313 | − | 0.866997i | \(-0.333953\pi\) | ||||
0.498313 | + | 0.866997i | \(0.333953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1685 | −0.445821 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.2813 | 1.14452 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 42.8032 | 1.56400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5581 | 0.494742 | 0.247371 | − | 0.968921i | \(-0.420433\pi\) | ||||
0.247371 | + | 0.968921i | \(0.420433\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.7359 | −1.73959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5830 | −0.785485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1498 | 1.16850 | 0.584252 | − | 0.811572i | \(-0.301388\pi\) | ||||
0.584252 | + | 0.811572i | \(0.301388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.70988 | −0.351983 | −0.175991 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175991 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.9701 | 1.51942 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.37085 | 0.230339 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.07415 | 0.255433 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.6081 | −0.562841 | −0.281421 | − | 0.959584i | \(-0.590806\pi\) | ||||
−0.281421 | + | 0.959584i | \(0.590806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.6363 | 1.31943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.4874 | −0.772849 | −0.386425 | − | 0.922321i | \(-0.626290\pi\) | ||||
−0.386425 | + | 0.922321i | \(0.626290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.4577 | −0.375653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 104.604 | 3.75263 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.8275 | −0.423764 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.53972 | −0.269448 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.68096 | 0.274145 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.04684 | −0.215547 | −0.107773 | − | 0.994175i | \(-0.534372\pi\) | ||||
−0.107773 | + | 0.994175i | \(0.534372\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.7763 | 1.30927 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9213 | 0.423874 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60682 | −0.270126 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.75771 | −0.310604 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.0918 | 1.13675 | 0.568376 | − | 0.822769i | \(-0.307572\pi\) | ||||
0.568376 | + | 0.822769i | \(0.307572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4421 | 0.475547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.11255 | 0.0393102 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.7562 | −0.872543 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.2411 | −1.48696 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.20394 | 0.0774865 | 0.0387432 | − | 0.999249i | \(-0.487665\pi\) | ||||
0.0387432 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.59190 | 0.336817 | 0.168409 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168409 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57.7933 | 2.02690 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.21691 | −0.182741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.06762 | −0.317236 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.92505 | −0.241981 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.2376 | −0.496894 | −0.248447 | − | 0.968645i | \(-0.579920\pi\) | ||||
−0.248447 | + | 0.968645i | \(0.579920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.430172 | −0.0149949 | −0.00749743 | − | 0.999972i | \(-0.502387\pi\) | ||||
−0.00749743 | + | 0.999972i | \(0.502387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6560 | −1.23988 | −0.619940 | − | 0.784649i | \(-0.712843\pi\) | ||||
−0.619940 | + | 0.784649i | \(0.712843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.9221 | 0.379339 | 0.189669 | − | 0.981848i | \(-0.439258\pi\) | ||||
0.189669 | + | 0.981848i | \(0.439258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 54.9462 | 1.90606 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.1853 | 1.46164 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.2767 | 0.667098 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.4771 | −0.500401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.0181 | 1.03634 | 0.518169 | − | 0.855278i | \(-0.326614\pi\) | ||||
0.518169 | + | 0.855278i | \(0.326614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.663634 | 0.0228839 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.5768 | −0.536492 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6381 | −0.434765 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.5359 | 0.567509 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.5963 | 1.66586 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.5878 | −0.704912 | −0.352456 | − | 0.935828i | \(-0.614653\pi\) | ||||
−0.352456 | + | 0.935828i | \(0.614653\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.25548 | −0.213933 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.44802 | 0.254419 | 0.127210 | − | 0.991876i | \(-0.459398\pi\) | ||||
0.127210 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.0056 | −1.80853 | −0.904263 | − | 0.426975i | \(-0.859579\pi\) | ||||
−0.904263 | + | 0.426975i | \(0.859579\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50.6017 | 1.72450 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.1040 | −0.990713 | −0.495356 | − | 0.868690i | \(-0.664963\pi\) | ||||
−0.495356 | + | 0.868690i | \(0.664963\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.6210 | −0.667132 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.2012 | 0.787953 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.05037 | −0.306660 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.1643 | 0.648614 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.78768 | −0.161853 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.1013 | 0.948912 | 0.474456 | − | 0.880279i | \(-0.342645\pi\) | ||||
0.474456 | + | 0.880279i | \(0.342645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 63.9194 | 2.15595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.5508 | 0.995591 | 0.497796 | − | 0.867294i | \(-0.334143\pi\) | ||||
0.497796 | + | 0.867294i | \(0.334143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.9274 | 1.31001 | 0.655005 | − | 0.755624i | \(-0.272666\pi\) | ||||
0.655005 | + | 0.755624i | \(0.272666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.3391 | −0.918993 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.2960 | 0.882933 | 0.441467 | − | 0.897278i | \(-0.354458\pi\) | ||||
0.441467 | + | 0.897278i | \(0.354458\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.1737 | −1.48154 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.1987 | −0.441677 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.26184 | −0.242736 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.23116 | −0.241441 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56.9574 | 1.89964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.98113 | 0.332520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.7941 | 1.29099 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.78809 | −0.292126 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5540 | 0.848505 | 0.424253 | − | 0.905544i | \(-0.360537\pi\) | ||||
0.424253 | + | 0.905544i | \(0.360537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.2414 | 0.870373 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0753 | −1.59281 | −0.796403 | − | 0.604766i | \(-0.793267\pi\) | ||||
−0.796403 | + | 0.604766i | \(0.793267\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.3977 | 0.971857 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.7745 | 1.28045 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.02354 | −0.264672 | −0.132336 | − | 0.991205i | \(-0.542248\pi\) | ||||
−0.132336 | + | 0.991205i | \(0.542248\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.6761 | −1.76869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.208430 | 0.00686054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.39816 | 0.309010 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −40.6559 | −1.33531 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.7554 | 1.56680 | 0.783402 | − | 0.621516i | \(-0.213483\pi\) | ||||
0.783402 | + | 0.621516i | \(0.213483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.4214 | −1.35753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.4479 | 0.538480 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.5515 | 0.442709 | 0.221354 | − | 0.975193i | \(-0.428952\pi\) | ||||
0.221354 | + | 0.975193i | \(0.428952\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.4760 | 2.13673 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7661 | 0.383564 | 0.191782 | − | 0.981438i | \(-0.438573\pi\) | ||||
0.191782 | + | 0.981438i | \(0.438573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.5083 | 0.765536 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.62778 | −0.215602 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.85540 | 0.255266 | 0.127633 | − | 0.991821i | \(-0.459262\pi\) | ||||
0.127633 | + | 0.991821i | \(0.459262\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.21427 | −0.0718782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.4944 | −1.76710 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7034 | −1.15655 | −0.578274 | − | 0.815843i | \(-0.696274\pi\) | ||||
−0.578274 | + | 0.815843i | \(0.696274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.9236 | 0.806508 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.4644 | −1.01604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.3643 | 2.52788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.4971 | −0.692736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.66623 | 0.214593 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5681 | 0.404162 | 0.202081 | − | 0.979369i | \(-0.435230\pi\) | ||||
0.202081 | + | 0.979369i | \(0.435230\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0243 | 0.514774 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.33283 | 0.0427724 | 0.0213862 | − | 0.999771i | \(-0.493192\pi\) | ||||
0.0213862 | + | 0.999771i | \(0.493192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.2892 | −0.554267 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.39845 | −0.0447864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.0415 | −1.40901 | −0.704506 | − | 0.709698i | \(-0.748831\pi\) | ||||
−0.704506 | + | 0.709698i | \(0.748831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.0787 | −0.672991 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.3425 | −0.425560 | −0.212780 | − | 0.977100i | \(-0.568252\pi\) | ||||
−0.212780 | + | 0.977100i | \(0.568252\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.66329 | 0.0529968 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.4680 | 1.79740 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.0228 | 0.573091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.69302 | 0.276143 | 0.138071 | − | 0.990422i | \(-0.455910\pi\) | ||||
0.138071 | + | 0.990422i | \(0.455910\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.8283 | −0.375361 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.0008 | −0.665769 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.1952 | 0.607918 | 0.303959 | − | 0.952685i | \(-0.401691\pi\) | ||||
0.303959 | + | 0.952685i | \(0.401691\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.0103 | 0.411626 |
(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 | 4840.2.a.bc.1.2 | ✓ | 6 | |
4.3 | odd | 2 | 9680.2.a.db.1.5 | 6 | |||
11.10 | odd | 2 | 4840.2.a.bd.1.2 | yes | 6 | ||
44.43 | even | 2 | 9680.2.a.da.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4840.2.a.bc.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4840.2.a.bd.1.2 | yes | 6 | 11.10 | odd | 2 | ||
9680.2.a.da.1.5 | 6 | 44.43 | even | 2 | |||
9680.2.a.db.1.5 | 6 | 4.3 | odd | 2 |