Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 12x^{3} - 14x^{2} - 6x + 3 \) |
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 | \(1.47270\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.01562 | −1.34862 | −0.674312 | − | 0.738446i | \(-0.735560\pi\) | ||||
−0.674312 | + | 0.738446i | \(0.735560\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.84677 | −0.698012 | −0.349006 | − | 0.937120i | \(-0.613481\pi\) | ||||
−0.349006 | + | 0.937120i | \(0.613481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0702134 | −0.0211701 | −0.0105851 | − | 0.999944i | \(-0.503369\pi\) | ||||
−0.0105851 | + | 0.999944i | \(0.503369\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.68809 | 0.468191 | 0.234096 | − | 0.972214i | \(-0.424787\pi\) | ||||
0.234096 | + | 0.972214i | \(0.424787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.01562 | 0.778629 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.17362 | −0.527179 | −0.263590 | − | 0.964635i | \(-0.584907\pi\) | ||||
−0.263590 | + | 0.964635i | \(0.584907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.90752 | −0.667030 | −0.333515 | − | 0.942745i | \(-0.608235\pi\) | ||||
−0.333515 | + | 0.942745i | \(0.608235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.84677 | 0.402998 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.67315 | 0.348876 | 0.174438 | − | 0.984668i | \(-0.444189\pi\) | ||||
0.174438 | + | 0.984668i | \(0.444189\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.09394 | 0.818788 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24297 | −0.787899 | −0.393950 | − | 0.919132i | \(-0.628892\pi\) | ||||
−0.393950 | + | 0.919132i | \(0.628892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.28787 | −0.770124 | −0.385062 | − | 0.922891i | \(-0.625820\pi\) | ||||
−0.385062 | + | 0.922891i | \(0.625820\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0702134 | 0.0122226 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.56914 | 0.941356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8489 | −1.78355 | −0.891776 | − | 0.452477i | \(-0.850540\pi\) | ||||
−0.891776 | + | 0.452477i | \(0.850540\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.68809 | −0.270310 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.20331 | −1.12497 | −0.562484 | − | 0.826808i | \(-0.690154\pi\) | ||||
−0.562484 | + | 0.826808i | \(0.690154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.33921 | −0.661724 | −0.330862 | − | 0.943679i | \(-0.607339\pi\) | ||||
−0.330862 | + | 0.943679i | \(0.607339\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.01562 | −0.449541 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5944 | 1.69122 | 0.845609 | − | 0.533803i | \(-0.179238\pi\) | ||||
0.845609 | + | 0.533803i | \(0.179238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.58945 | −0.512779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.17362 | 0.304367 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.88527 | 0.533683 | 0.266841 | − | 0.963740i | \(-0.414020\pi\) | ||||
0.266841 | + | 0.963740i | \(0.414020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.211737 | 0.0285505 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.90752 | 0.385110 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.40850 | 0.704127 | 0.352063 | − | 0.935976i | \(-0.385480\pi\) | ||||
0.352063 | + | 0.935976i | \(0.385480\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.01512 | 0.258010 | 0.129005 | − | 0.991644i | \(-0.458822\pi\) | ||||
0.129005 | + | 0.991644i | \(0.458822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.84677 | −0.232671 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.09062 | −0.631414 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.98849 | −0.853780 | −0.426890 | − | 0.904304i | \(-0.640391\pi\) | ||||
−0.426890 | + | 0.904304i | \(0.640391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.67315 | −0.201424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.15920 | 0.256250 | 0.128125 | − | 0.991758i | \(-0.459104\pi\) | ||||
0.128125 | + | 0.991758i | \(0.459104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.46808 | −0.991114 | −0.495557 | − | 0.868575i | \(-0.665036\pi\) | ||||
−0.495557 | + | 0.868575i | \(0.665036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.09394 | −0.472727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.129668 | 0.0147770 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8442 | −1.22007 | −0.610035 | − | 0.792374i | \(-0.708845\pi\) | ||||
−0.610035 | + | 0.792374i | \(0.708845\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.35160 | −1.02647 | −0.513236 | − | 0.858248i | \(-0.671553\pi\) | ||||
−0.513236 | + | 0.858248i | \(0.671553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.55479 | 0.710967 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.24297 | 0.454894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2378 | 1.72120 | 0.860601 | − | 0.509279i | \(-0.170088\pi\) | ||||
0.860601 | + | 0.509279i | \(0.170088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.11750 | −0.326803 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.28787 | 0.444631 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.76795 | 0.899573 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2480 | 1.34513 | 0.672563 | − | 0.740040i | \(-0.265193\pi\) | ||||
0.672563 | + | 0.740040i | \(0.265193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0702134 | −0.00705671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.67392 | −0.564577 | −0.282288 | − | 0.959330i | \(-0.591093\pi\) | ||||
−0.282288 | + | 0.959330i | \(0.591093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.5307 | 1.72735 | 0.863677 | − | 0.504046i | \(-0.168156\pi\) | ||||
0.863677 | + | 0.504046i | \(0.168156\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.56914 | −0.543492 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.56293 | 0.247768 | 0.123884 | − | 0.992297i | \(-0.460465\pi\) | ||||
0.123884 | + | 0.992297i | \(0.460465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.3817 | 1.76065 | 0.880325 | − | 0.474370i | \(-0.157324\pi\) | ||||
0.880325 | + | 0.474370i | \(0.157324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.8489 | 1.02973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.64947 | 0.813674 | 0.406837 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406837 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.04558 | −0.470503 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.68809 | 0.156064 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.01416 | 0.367978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9951 | −0.999552 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.20331 | 0.649500 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.73233 | 0.244387 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.114006 | −0.0101164 | −0.00505819 | − | 0.999987i | \(-0.501610\pi\) | ||||
−0.00505819 | + | 0.999987i | \(0.501610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.33921 | 0.382046 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5617 | 1.09752 | 0.548759 | − | 0.835981i | \(-0.315101\pi\) | ||||
0.548759 | + | 0.835981i | \(0.315101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.36950 | 0.465595 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.01562 | 0.259543 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.59365 | −0.563333 | −0.281667 | − | 0.959512i | \(-0.590887\pi\) | ||||
−0.281667 | + | 0.959512i | \(0.590887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.80181 | 0.492103 | 0.246051 | − | 0.969257i | \(-0.420867\pi\) | ||||
0.246051 | + | 0.969257i | \(0.420867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5944 | −0.976425 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.118526 | −0.00991167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.7952 | 1.06258 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.58945 | 0.296053 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.34532 | 0.355983 | 0.177991 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177991 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8907 | 1.45592 | 0.727961 | − | 0.685619i | \(-0.240468\pi\) | ||||
0.727961 | + | 0.685619i | \(0.240468\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.17362 | −0.175726 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.9306 | 1.03861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9620 | −1.43352 | −0.716760 | − | 0.697320i | \(-0.754376\pi\) | ||||
−0.716760 | + | 0.697320i | \(0.754376\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.88527 | −0.308122 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.08992 | −0.243520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.95764 | −0.623291 | −0.311645 | − | 0.950198i | \(-0.600880\pi\) | ||||
−0.311645 | + | 0.950198i | \(0.600880\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.211737 | −0.0164837 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1504 | −0.780797 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.90752 | −0.222343 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0823 | −0.994632 | −0.497316 | − | 0.867570i | \(-0.665681\pi\) | ||||
−0.497316 | + | 0.867570i | \(0.665681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.56055 | −0.571524 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.40850 | −0.406528 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4300 | 0.779575 | 0.389788 | − | 0.920905i | \(-0.372548\pi\) | ||||
0.389788 | + | 0.920905i | \(0.372548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.31004 | −0.320362 | −0.160181 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160181 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.01512 | −0.148962 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 32.7162 | 2.40534 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.152617 | 0.0111605 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.84677 | 0.134333 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.7287 | 1.35516 | 0.677581 | − | 0.735448i | \(-0.263028\pi\) | ||||
0.677581 | + | 0.735448i | \(0.263028\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3962 | 1.10824 | 0.554121 | − | 0.832436i | \(-0.313054\pi\) | ||||
0.554121 | + | 0.832436i | \(0.313054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.09062 | 0.364547 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.0789986 | 0.00562842 | 0.00281421 | − | 0.999996i | \(-0.499104\pi\) | ||||
0.00281421 | + | 0.999996i | \(0.499104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4542 | 0.811967 | 0.405983 | − | 0.913880i | \(-0.366929\pi\) | ||||
0.405983 | + | 0.913880i | \(0.366929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.98849 | 0.492930 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.83577 | 0.549963 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.7224 | 1.51716 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.67315 | 0.116292 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.204146 | 0.0141211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3500 | 1.05674 | 0.528370 | − | 0.849014i | \(-0.322803\pi\) | ||||
0.528370 | + | 0.849014i | \(0.322803\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.15920 | −0.147946 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.0854 | 0.892417 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.91869 | 0.537556 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.46808 | 0.572220 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.66926 | −0.246821 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.6893 | 1.65332 | 0.826658 | − | 0.562705i | \(-0.190239\pi\) | ||||
0.826658 | + | 0.562705i | \(0.190239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.09394 | 0.272929 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.5728 | 1.63096 | 0.815478 | − | 0.578788i | \(-0.196474\pi\) | ||||
0.815478 | + | 0.578788i | \(0.196474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.98726 | −0.593895 | −0.296947 | − | 0.954894i | \(-0.595969\pi\) | ||||
−0.296947 | + | 0.954894i | \(0.595969\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.129668 | −0.00853151 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.6629 | −1.48470 | −0.742348 | − | 0.670014i | \(-0.766288\pi\) | ||||
−0.742348 | + | 0.670014i | \(0.766288\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.9643 | −2.28082 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8442 | 0.704408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.63603 | 0.493934 | 0.246967 | − | 0.969024i | \(-0.420566\pi\) | ||||
0.246967 | + | 0.969024i | \(0.420566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3487 | −1.05311 | −0.526555 | − | 0.850141i | \(-0.676516\pi\) | ||||
−0.526555 | + | 0.850141i | \(0.676516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.8244 | 0.691546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.90814 | −0.312298 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.35160 | 0.592633 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.3237 | −1.59842 | −0.799209 | − | 0.601053i | \(-0.794748\pi\) | ||||
−0.799209 | + | 0.601053i | \(0.794748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.117478 | −0.00738575 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.55479 | −0.410477 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.8241 | 0.987082 | 0.493541 | − | 0.869723i | \(-0.335702\pi\) | ||||
0.493541 | + | 0.869723i | \(0.335702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0354 | 1.24494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24297 | −0.262633 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1324 | 1.17975 | 0.589877 | − | 0.807493i | \(-0.299176\pi\) | ||||
0.589877 | + | 0.807493i | \(0.299176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7165 | −0.719738 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.2378 | −0.993737 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.78513 | 0.474668 | 0.237334 | − | 0.971428i | \(-0.423726\pi\) | ||||
0.237334 | + | 0.971428i | \(0.423726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7908 | −0.716237 | −0.358119 | − | 0.933676i | \(-0.616582\pi\) | ||||
−0.358119 | + | 0.933676i | \(0.616582\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.11750 | 0.188680 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.287449 | −0.0173338 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.54189 | 0.152728 | 0.0763638 | − | 0.997080i | \(-0.475669\pi\) | ||||
0.0763638 | + | 0.997080i | \(0.475669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.28787 | −0.256708 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.37140 | −0.439741 | −0.219870 | − | 0.975529i | \(-0.570563\pi\) | ||||
−0.219870 | + | 0.975529i | \(0.570563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.42659 | 0.500909 | 0.250455 | − | 0.968128i | \(-0.419420\pi\) | ||||
0.250455 | + | 0.968128i | \(0.419420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.76795 | −0.519369 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3028 | 0.785241 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2754 | −0.722082 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.2480 | −0.776609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.3212 | 1.01192 | 0.505958 | − | 0.862558i | \(-0.331139\pi\) | ||||
0.505958 | + | 0.862558i | \(0.331139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.3100 | −0.949603 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0702134 | 0.00407419 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.82442 | 0.163341 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.01351 | 0.461891 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.67392 | 0.325958 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.07684 | −0.347959 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.40036 | 0.365288 | 0.182644 | − | 0.983179i | \(-0.441534\pi\) | ||||
0.182644 | + | 0.983179i | \(0.441534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.5307 | −0.997288 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9862 | 1.01991 | 0.509953 | − | 0.860202i | \(-0.329663\pi\) | ||||
0.509953 | + | 0.860202i | \(0.329663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.4712 | −1.21363 | −0.606813 | − | 0.794844i | \(-0.707552\pi\) | ||||
−0.606813 | + | 0.794844i | \(0.707552\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.56914 | 0.313785 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.8128 | −1.28130 | −0.640648 | − | 0.767834i | \(-0.721334\pi\) | ||||
−0.640648 | + | 0.767834i | \(0.721334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.297913 | 0.0166799 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.56293 | −0.143049 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.31982 | 0.351644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.91093 | 0.383349 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.3817 | −1.01651 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.4122 | −1.18049 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1607 | −1.21806 | −0.609031 | − | 0.793147i | \(-0.708441\pi\) | ||||
−0.609031 | + | 0.793147i | \(0.708441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.8489 | −0.594517 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.0746 | 1.15143 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.6497 | 1.77854 | 0.889271 | − | 0.457380i | \(-0.151212\pi\) | ||||
0.889271 | + | 0.457380i | \(0.151212\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.64947 | −0.469775 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.301066 | 0.0163036 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5562 | 1.05594 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.04558 | 0.271645 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.5493 | −1.15683 | −0.578414 | − | 0.815744i | \(-0.696328\pi\) | ||||
−0.578414 | + | 0.815744i | \(0.696328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.96612 | −0.105244 | −0.0526219 | − | 0.998615i | \(-0.516758\pi\) | ||||
−0.0526219 | + | 0.998615i | \(0.516758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.68809 | −0.0901035 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.411409 | 0.0218971 | 0.0109485 | − | 0.999940i | \(-0.496515\pi\) | ||||
0.0109485 | + | 0.999940i | \(0.496515\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.51131 | −0.345585 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.01416 | −0.212452 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.1536 | 0.905334 | 0.452667 | − | 0.891680i | \(-0.350473\pi\) | ||||
0.452667 | + | 0.891680i | \(0.350473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5464 | −0.555071 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9951 | 0.577092 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.5365 | 1.33664 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.3616 | −1.21947 | −0.609733 | − | 0.792607i | \(-0.708723\pi\) | ||||
−0.609733 | + | 0.792607i | \(0.708723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.20331 | −0.374989 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.17519 | −0.372517 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3568 | 0.536257 | 0.268129 | − | 0.963383i | \(-0.413595\pi\) | ||||
0.268129 | + | 0.963383i | \(0.413595\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.73233 | −0.141097 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.16250 | −0.368888 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.75887 | 0.0903471 | 0.0451735 | − | 0.998979i | \(-0.485616\pi\) | ||||
0.0451735 | + | 0.998979i | \(0.485616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.114006 | 0.00584069 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.23977 | 0.114447 | 0.0572233 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572233 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.391028 | −0.0199286 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.33921 | −0.220575 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.8084 | 0.548008 | 0.274004 | − | 0.961729i | \(-0.411652\pi\) | ||||
0.274004 | + | 0.961729i | \(0.411652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.63679 | −0.183920 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.5617 | −0.633652 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.7020 | 1.64542 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3168 | −0.567975 | −0.283987 | − | 0.958828i | \(-0.591657\pi\) | ||||
−0.283987 | + | 0.958828i | \(0.591657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.36950 | −0.268811 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5327 | −0.775667 | −0.387834 | − | 0.921729i | \(-0.626776\pi\) | ||||
−0.387834 | + | 0.921729i | \(0.626776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.23830 | −0.360565 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.01562 | −0.149847 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.761739 | 0.0377580 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0150 | −0.791890 | −0.395945 | − | 0.918274i | \(-0.629583\pi\) | ||||
−0.395945 | + | 0.918274i | \(0.629583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.59365 | 0.325241 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.98824 | −0.491489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.2008 | 1.38432 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.80181 | −0.284116 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.60543 | −0.224990 | −0.112495 | − | 0.993652i | \(-0.535884\pi\) | ||||
−0.112495 | + | 0.993652i | \(0.535884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.7515 | −1.15758 | −0.578789 | − | 0.815478i | \(-0.696474\pi\) | ||||
−0.578789 | + | 0.815478i | \(0.696474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5944 | 0.563739 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.89865 | −0.431648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.72146 | −0.180094 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.118526 | 0.00572250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.50119 | −0.409488 | −0.204744 | − | 0.978816i | \(-0.565636\pi\) | ||||
−0.204744 | + | 0.978816i | \(0.565636\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.1642 | 1.30543 | 0.652715 | − | 0.757604i | \(-0.273630\pi\) | ||||
0.652715 | + | 0.757604i | \(0.273630\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.7952 | −0.613481 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.86471 | −0.232711 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9205 | 1.52348 | 0.761740 | − | 0.647882i | \(-0.224345\pi\) | ||||
0.761740 | + | 0.647882i | \(0.224345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.58945 | −0.170926 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.34160 | 0.206276 | 0.103138 | − | 0.994667i | \(-0.467112\pi\) | ||||
0.103138 | + | 0.994667i | \(0.467112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.9669 | −2.32126 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.34532 | −0.205527 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9358 | −0.516093 | −0.258046 | − | 0.966133i | \(-0.583079\pi\) | ||||
−0.258046 | + | 0.966133i | \(0.583079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.505768 | 0.0238157 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.8907 | −0.840577 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.40120 | 0.440735 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.9782 | 1.12165 | 0.560826 | − | 0.827933i | \(-0.310484\pi\) | ||||
0.560826 | + | 0.827933i | \(0.310484\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.17362 | 0.101456 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.39210 | 0.297710 | 0.148855 | − | 0.988859i | \(-0.452441\pi\) | ||||
0.148855 | + | 0.988859i | \(0.452441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8982 | 0.924748 | 0.462374 | − | 0.886685i | \(-0.346998\pi\) | ||||
0.462374 | + | 0.886685i | \(0.346998\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.9306 | −0.599640 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.50454 | 0.300994 | 0.150497 | − | 0.988610i | \(-0.451913\pi\) | ||||
0.150497 | + | 0.988610i | \(0.451913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9061 | 0.595949 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.9620 | 0.827643 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.304671 | 0.0140088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.9032 | −0.546156 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.88527 | 0.177894 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.93092 | 0.0882259 | 0.0441130 | − | 0.999027i | \(-0.485954\pi\) | ||||
0.0441130 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3139 | −0.835044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.08992 | 0.140596 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.9508 | −1.81407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3754 | 1.01392 | 0.506962 | − | 0.861968i | \(-0.330768\pi\) | ||||
0.506962 | + | 0.861968i | \(0.330768\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.95764 | 0.359857 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.000619001 0 | 2.79351e−5 0 | 1.39676e−5 | − | 1.00000i | \(-0.499996\pi\) | ||||
1.39676e−5 | 1.00000i | \(0.499996\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.22259 | 0.415364 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.211737 | 0.00951685 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.98754 | −0.178865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.6573 | −1.73054 | −0.865269 | − | 0.501309i | \(-0.832852\pi\) | ||||
−0.865269 | + | 0.501309i | \(0.832852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2786 | 1.03794 | 0.518971 | − | 0.854792i | \(-0.326315\pi\) | ||||
0.518971 | + | 0.854792i | \(0.326315\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.1104 | 0.761402 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1504 | 0.450793 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8713 | 0.659157 | 0.329578 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329578 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.6386 | 0.691810 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.90752 | 0.128370 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −52.8659 | −2.32955 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.814082 | −0.0358033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0823 | 0.574251 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4692 | 0.458663 | 0.229331 | − | 0.973348i | \(-0.426346\pi\) | ||||
0.229331 | + | 0.973348i | \(0.426346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.32882 | −0.276740 | −0.138370 | − | 0.990381i | \(-0.544186\pi\) | ||||
−0.138370 | + | 0.990381i | \(0.544186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.56055 | 0.329969 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.32018 | 0.405993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2006 | −0.878286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.40850 | 0.234709 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1598 | −0.526700 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.72882 | −0.334146 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.4300 | −0.450088 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.252027 | 0.0108556 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5446 | 0.496340 | 0.248170 | − | 0.968716i | \(-0.420171\pi\) | ||||
0.248170 | + | 0.968716i | \(0.420171\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.31004 | 0.184961 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.4322 | −2.37446 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.7041 | −0.885243 | −0.442622 | − | 0.896708i | \(-0.645952\pi\) | ||||
−0.442622 | + | 0.896708i | \(0.645952\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.01512 | 0.0860034 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3365 | 0.525552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0268 | 0.851625 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.7162 | −1.38872 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.1956 | 1.44891 | 0.724457 | − | 0.689320i | \(-0.242091\pi\) | ||||
0.724457 | + | 0.689320i | \(0.242091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.32497 | −0.309813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.152617 | −0.00644349 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.4440 | 0.566598 | 0.283299 | − | 0.959032i | \(-0.408571\pi\) | ||||
0.283299 | + | 0.959032i | \(0.408571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.0835 | −1.09734 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.84677 | −0.0775569 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.42022 | 0.0595386 | 0.0297693 | − | 0.999557i | \(-0.490523\pi\) | ||||
0.0297693 | + | 0.999557i | \(0.490523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.0276 | −0.796280 | −0.398140 | − | 0.917325i | \(-0.630344\pi\) | ||||
−0.398140 | + | 0.917325i | \(0.630344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.7287 | −0.782404 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.84977 | 0.285655 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.5919 | 1.27356 | 0.636778 | − | 0.771047i | \(-0.280267\pi\) | ||||
0.636778 | + | 0.771047i | \(0.280267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.3962 | −0.639844 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.2702 | 0.716490 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.272798 | −0.0112981 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.09062 | −0.210471 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.6169 | 1.34624 | 0.673121 | − | 0.739532i | \(-0.264953\pi\) | ||||
0.673121 | + | 0.739532i | \(0.264953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4670 | 0.513696 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0789986 | −0.00324957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.2145 | 0.665849 | 0.332924 | − | 0.942953i | \(-0.391965\pi\) | ||||
0.332924 | + | 0.942953i | \(0.391965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.1052 | −0.496264 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.4542 | −0.468789 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.5160 | 0.838263 | 0.419131 | − | 0.907926i | \(-0.362335\pi\) | ||||
0.419131 | + | 0.907926i | \(0.362335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.1781 | 0.863874 | 0.431937 | − | 0.901904i | \(-0.357830\pi\) | ||||
0.431937 | + | 0.901904i | \(0.357830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.98849 | −0.284593 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.1569 | 1.34802 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.963530 | −0.0391085 | −0.0195542 | − | 0.999809i | \(-0.506225\pi\) | ||||
−0.0195542 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.83577 | −0.317522 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.5724 | 0.791813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.3703 | −1.50937 | −0.754685 | − | 0.656087i | \(-0.772210\pi\) | ||||
−0.754685 | + | 0.656087i | \(0.772210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.7224 | −0.875932 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.9204 | −0.721448 | −0.360724 | − | 0.932673i | \(-0.617470\pi\) | ||||
−0.360724 | + | 0.932673i | \(0.617470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.709375 | 0.0285122 | 0.0142561 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142561 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.67315 | −0.0671412 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.9874 | −1.20142 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.7094 | −1.14837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.204146 | −0.00815282 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.5814 | 0.940252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.1195 | 0.482472 | 0.241236 | − | 0.970467i | \(-0.422447\pi\) | ||||
0.241236 | + | 0.970467i | \(0.422447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3500 | −0.610109 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.343798 | 0.0136432 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.05931 | −0.240079 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.15920 | 0.0854166 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.8998 | 0.628003 | 0.314002 | − | 0.949422i | \(-0.398330\pi\) | ||||
0.314002 | + | 0.949422i | \(0.398330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.8562 | −0.940798 | −0.470399 | − | 0.882454i | \(-0.655890\pi\) | ||||
−0.470399 | + | 0.882454i | \(0.655890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.0854 | −0.515237 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.97952 | 0.117137 | 0.0585685 | − | 0.998283i | \(-0.481346\pi\) | ||||
0.0585685 | + | 0.998283i | \(0.481346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.379749 | −0.0149065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.91869 | −0.310358 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.97720 | 0.312172 | 0.156086 | − | 0.987743i | \(-0.450112\pi\) | ||||
0.156086 | + | 0.987743i | \(0.450112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.8811 | −1.48014 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.46808 | −0.330371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.9289 | −1.16586 | −0.582931 | − | 0.812521i | \(-0.698094\pi\) | ||||
−0.582931 | + | 0.812521i | \(0.698094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.2290 | 0.592339 | 0.296170 | − | 0.955135i | \(-0.404291\pi\) | ||||
0.296170 | + | 0.955135i | \(0.404291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.66926 | 0.142502 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.1924 | −0.627913 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.09912 | −0.274879 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.6893 | −0.954542 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.141489 | −0.00546211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.3603 | 1.13176 | 0.565878 | − | 0.824489i | \(-0.308537\pi\) | ||||
0.565878 | + | 0.824489i | \(0.308537\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.09394 | −0.157576 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.142354 | 0.00547111 | 0.00273556 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273556 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.4659 | −0.938915 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.5728 | −0.941633 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.2505 | −1.42535 | −0.712676 | − | 0.701494i | \(-0.752517\pi\) | ||||
−0.712676 | + | 0.701494i | \(0.752517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.8839 | 0.759725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.98726 | 0.342885 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.55868 | 0.249866 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.4586 | 1.38695 | 0.693475 | − | 0.720481i | \(-0.256079\pi\) | ||||
0.693475 | + | 0.720481i | \(0.256079\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.129668 | 0.00492567 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.4960 | −0.663662 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6572 | 0.593060 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.6629 | 0.857190 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.2147 | −1.33004 | −0.665020 | − | 0.746826i | \(-0.731577\pi\) | ||||
−0.665020 | + | 0.746826i | \(0.731577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.5434 | 1.18968 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.9643 | 1.31683 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.4784 | 0.394081 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.7522 | −1.45537 | −0.727684 | − | 0.685912i | \(-0.759403\pi\) | ||||
−0.727684 | + | 0.685912i | \(0.759403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.8442 | −0.406690 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.17425 | −0.268678 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.357430 | 0.0133671 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.63603 | −0.285173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.2855 | −1.05487 | −0.527435 | − | 0.849596i | \(-0.676846\pi\) | ||||
−0.527435 | + | 0.849596i | \(0.676846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.3752 | −1.20571 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.3487 | 0.608013 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.3705 | −0.645122 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0460 | 0.817642 | 0.408821 | − | 0.912615i | \(-0.365940\pi\) | ||||
0.408821 | + | 0.912615i | \(0.365940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.43179 | 0.348847 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1625 | 0.486167 | 0.243084 | − | 0.970005i | \(-0.421841\pi\) | ||||
0.243084 | + | 0.970005i | \(0.421841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.8244 | −0.399264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.490685 | 0.0180746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.86634 | −0.362939 | −0.181470 | − | 0.983397i | \(-0.558085\pi\) | ||||
−0.181470 | + | 0.983397i | \(0.558085\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.90814 | 0.180305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.70369 | 0.209248 | 0.104624 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104624 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.1038 | −0.480087 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.35160 | −0.342157 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.73314 | −0.172945 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.2515 | −0.921439 | −0.460719 | − | 0.887546i | \(-0.652409\pi\) | ||||
−0.460719 | + | 0.887546i | \(0.652409\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.3237 | 0.922847 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −53.9514 | −1.96349 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6032 | 0.966910 | 0.483455 | − | 0.875369i | \(-0.339382\pi\) | ||||
0.483455 | + | 0.875369i | \(0.339382\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.117478 | 0.00426416 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.0804 | −1.38041 | −0.690207 | − | 0.723612i | \(-0.742481\pi\) | ||||
−0.690207 | + | 0.723612i | \(0.742481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.9468 | −1.22896 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.55479 | 0.236989 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.13003 | 0.329666 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50542 | 0.198531 | 0.0992653 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992653 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8241 | −0.569892 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.0250 | −0.612345 | −0.306173 | − | 0.951976i | \(-0.599048\pi\) | ||||
−0.306173 | + | 0.951976i | \(0.599048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5543 | −0.630568 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.0354 | −0.718767 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.9437 | 0.750387 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.151605 | −0.00542484 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.24297 | 0.151631 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54.1664 | 1.93328 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.9181 | 1.56551 | 0.782756 | − | 0.622329i | \(-0.213813\pi\) | ||||
0.782756 | + | 0.622329i | \(0.213813\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.1324 | −0.681131 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.9736 | −0.567955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.40170 | 0.120798 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.7165 | 0.415541 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.5931 | 1.96921 | 0.984605 | − | 0.174795i | \(-0.0559264\pi\) | ||||
0.984605 | + | 0.174795i | \(0.0559264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.2018 | −0.891575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.2378 | 0.573734 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.594572 | 0.0209820 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.31801 | 0.328417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.78513 | −0.274050 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9154 | 1.40335 | 0.701675 | − | 0.712497i | \(-0.252436\pi\) | ||||
0.701675 | + | 0.712497i | \(0.252436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.6843 | −1.42862 | −0.714309 | − | 0.699830i | \(-0.753259\pi\) | ||||
−0.714309 | + | 0.699830i | \(0.753259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.7908 | 0.413520 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.9972 | 0.840585 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6163 | 0.441390 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.11750 | −0.108934 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4731 | −0.819217 | −0.409608 | − | 0.912261i | \(-0.634335\pi\) | ||||
−0.409608 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.51601 | −0.227134 | −0.113567 | − | 0.993530i | \(-0.536228\pi\) | ||||
−0.113567 | + | 0.993530i | \(0.536228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.287449 | 0.0100077 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.4145 | 1.57922 | 0.789609 | − | 0.613611i | \(-0.210283\pi\) | ||||
0.789609 | + | 0.613611i | \(0.210283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9723 | 1.14518 | 0.572588 | − | 0.819843i | \(-0.305939\pi\) | ||||
0.572588 | + | 0.819843i | \(0.305939\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.54189 | −0.0881773 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.80209 | 0.270326 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.01562 | 0.104360 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.28787 | 0.148210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.4949 | −0.949230 | −0.474615 | − | 0.880193i | \(-0.657413\pi\) | ||||
−0.474615 | + | 0.880193i | \(0.657413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.9972 | −0.379215 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.37140 | 0.253884 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.6096 | 1.05300 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.3053 | 0.697699 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.42659 | −0.289200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.1519 | −0.622238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.91679 | 0.0656298 | 0.0328149 | − | 0.999461i | \(-0.489553\pi\) | ||||
0.0328149 | + | 0.999461i | \(0.489553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.76795 | 0.299858 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.386484 | −0.0132021 | −0.00660103 | − | 0.999978i | \(-0.502101\pi\) | ||||
−0.00660103 | + | 0.999978i | \(0.502101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.7433 | −0.741873 | −0.370937 | − | 0.928658i | \(-0.620963\pi\) | ||||
−0.370937 | + | 0.928658i | \(0.620963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.3028 | −0.453359 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.4063 | −1.37545 | −0.687723 | − | 0.725973i | \(-0.741390\pi\) | ||||
−0.687723 | + | 0.725973i | \(0.741390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.4513 | 1.34138 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.2754 | 0.416894 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.761410 | 0.0258291 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.7972 | −0.399732 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2480 | 0.448376 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.04598 | −0.170585 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.3266 | −1.59811 | −0.799053 | − | 0.601261i | \(-0.794665\pi\) | ||||
−0.799053 | + | 0.601261i | \(0.794665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.3212 | −0.584229 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0078 | 1.34790 | 0.673949 | − | 0.738778i | \(-0.264597\pi\) | ||||
0.673949 | + | 0.738778i | \(0.264597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.2412 | 0.479255 | 0.239627 | − | 0.970865i | \(-0.422975\pi\) | ||||
0.239627 | + | 0.970865i | \(0.422975\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.3100 | 0.548253 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.2299 | 0.544948 | 0.272474 | − | 0.962163i | \(-0.412158\pi\) | ||||
0.272474 | + | 0.962163i | \(0.412158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.210542 | 0.00706136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0702134 | −0.00235224 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.7109 | −1.12809 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.4529 | −1.05135 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.82442 | −0.0943048 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.1933 | 0.606780 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.44509 | −0.281347 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.01351 | −0.266673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.9974 | 0.432049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.4413 | 0.479516 | 0.239758 | − | 0.970833i | \(-0.422932\pi\) | ||||
0.239758 | + | 0.970833i | \(0.422932\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.67392 | −0.188192 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.7207 | −1.77984 | −0.889922 | − | 0.456112i | \(-0.849242\pi\) | ||||
−0.889922 | + | 0.456112i | \(0.849242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.656607 | 0.0217305 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.07684 | 0.200894 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.1985 | −0.766081 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.4559 | 0.971661 | 0.485831 | − | 0.874053i | \(-0.338517\pi\) | ||||
0.485831 | + | 0.874053i | \(0.338517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.40036 | −0.210899 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.64492 | 0.119974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.4148 | −1.46035 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.5307 | 0.575785 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.9105 | −1.14538 | −0.572688 | − | 0.819773i | \(-0.694100\pi\) | ||||
−0.572688 | + | 0.819773i | \(0.694100\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.4364 | 0.342039 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.9862 | −0.588843 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.460234 | −0.0150513 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0982 | 1.37529 | 0.687644 | − | 0.726048i | \(-0.258645\pi\) | ||||
0.687644 | + | 0.726048i | \(0.258645\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.4712 | 0.700688 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.7714 | 0.546732 | 0.273366 | − | 0.961910i | \(-0.411863\pi\) | ||||
0.273366 | + | 0.961910i | \(0.411863\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0522 | −0.392474 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.56914 | −0.181164 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.4958 | −1.05597 | −0.527985 | − | 0.849254i | \(-0.677052\pi\) | ||||
−0.527985 | + | 0.849254i | \(0.677052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.2949 | −0.464031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.8128 | 0.739757 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.5661 | 1.21689 | 0.608443 | − | 0.793597i | \(-0.291794\pi\) | ||||
0.608443 | + | 0.793597i | \(0.291794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56.4786 | −1.82761 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.297913 | −0.00963016 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.1769 | 0.393214 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6142 | −0.406909 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.56293 | 0.0825894 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.4290 | −1.49460 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.46025 | −0.175590 | −0.0877949 | − | 0.996139i | \(-0.527982\pi\) | ||||
−0.0877949 | + | 0.996139i | \(0.527982\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.31982 | −0.203022 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.4319 | −1.10497 | −0.552487 | − | 0.833522i | \(-0.686321\pi\) | ||||
−0.552487 | + | 0.833522i | \(0.686321\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7146 | −0.343494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.91093 | −0.221327 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.1807 | 0.421689 | 0.210844 | − | 0.977520i | \(-0.432379\pi\) | ||||
0.210844 | + | 0.977520i | \(0.432379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.14011 | −0.0364381 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.3817 | 0.586884 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.2408 | 0.326632 | 0.163316 | − | 0.986574i | \(-0.447781\pi\) | ||||
0.163316 | + | 0.986574i | \(0.447781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.238229 | −0.00759062 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.4122 | 0.681557 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.26015 | −0.230859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.8098 | 0.883409 | 0.441704 | − | 0.897161i | \(-0.354374\pi\) | ||||
0.441704 | + | 0.897161i | \(0.354374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.1607 | 0.703248 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.5415 | −1.09504 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4323 | 0.362065 | 0.181033 | − | 0.983477i | \(-0.442056\pi\) | ||||
0.181033 | + | 0.983477i | \(0.442056\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.8489 | 0.343245 |
(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 | 4008.2.a.g.1.2 | ✓ | 7 | |
4.3 | odd | 2 | 8016.2.a.w.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.g.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
8016.2.a.w.1.2 | 7 | 4.3 | odd | 2 |