Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 1.49100 | 0.860831 | 0.430415 | − | 0.902631i | \(-0.358367\pi\) | ||||
0.430415 | + | 0.902631i | \(0.358367\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.09730 | −0.490728 | −0.245364 | − | 0.969431i | \(-0.578907\pi\) | ||||
−0.245364 | + | 0.969431i | \(0.578907\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.799854 | −0.302316 | −0.151158 | − | 0.988510i | \(-0.548300\pi\) | ||||
−0.151158 | + | 0.988510i | \(0.548300\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.776913 | −0.258971 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.838888 | −0.252934 | −0.126467 | − | 0.991971i | \(-0.540364\pi\) | ||||
−0.126467 | + | 0.991971i | \(0.540364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.03223 | 0.563640 | 0.281820 | − | 0.959467i | \(-0.409062\pi\) | ||||
0.281820 | + | 0.959467i | \(0.409062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.63608 | −0.422433 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.82317 | −0.442183 | −0.221091 | − | 0.975253i | \(-0.570962\pi\) | ||||
−0.221091 | + | 0.975253i | \(0.570962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.30282 | 0.987134 | 0.493567 | − | 0.869708i | \(-0.335693\pi\) | ||||
0.493567 | + | 0.869708i | \(0.335693\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.19258 | −0.260243 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.747572 | −0.155880 | −0.0779398 | − | 0.996958i | \(-0.524834\pi\) | ||||
−0.0779398 | + | 0.996958i | \(0.524834\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.79593 | −0.759186 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63138 | −1.08376 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.79315 | 0.518675 | 0.259337 | − | 0.965787i | \(-0.416496\pi\) | ||||
0.259337 | + | 0.965787i | \(0.416496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0226322 | −0.00406487 | −0.00203243 | − | 0.999998i | \(-0.500647\pi\) | ||||
−0.00203243 | + | 0.999998i | \(0.500647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.25078 | −0.217733 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.877680 | 0.148355 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.80488 | 0.296721 | 0.148360 | − | 0.988933i | \(-0.452600\pi\) | ||||
0.148360 | + | 0.988933i | \(0.452600\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.03006 | 0.485198 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.90939 | 1.07907 | 0.539533 | − | 0.841965i | \(-0.318601\pi\) | ||||
0.539533 | + | 0.841965i | \(0.318601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.84694 | −1.34914 | −0.674572 | − | 0.738209i | \(-0.735672\pi\) | ||||
−0.674572 | + | 0.738209i | \(0.735672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.852507 | 0.127084 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.50163 | −0.948360 | −0.474180 | − | 0.880428i | \(-0.657255\pi\) | ||||
−0.474180 | + | 0.880428i | \(0.657255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.36023 | −0.908605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.71835 | −0.380645 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.42159 | −1.15679 | −0.578397 | − | 0.815755i | \(-0.696321\pi\) | ||||
−0.578397 | + | 0.815755i | \(0.696321\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.920512 | 0.124122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.41551 | 0.849755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.81714 | −0.236572 | −0.118286 | − | 0.992980i | \(-0.537740\pi\) | ||||
−0.118286 | + | 0.992980i | \(0.537740\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.08359 | −1.03500 | −0.517499 | − | 0.855684i | \(-0.673137\pi\) | ||||
−0.517499 | + | 0.855684i | \(0.673137\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.621417 | 0.0782911 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.22997 | −0.276594 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6490 | 1.42315 | 0.711577 | − | 0.702608i | \(-0.247981\pi\) | ||||
0.711577 | + | 0.702608i | \(0.247981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.11463 | −0.134186 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.18928 | −0.141142 | −0.0705709 | − | 0.997507i | \(-0.522482\pi\) | ||||
−0.0705709 | + | 0.997507i | \(0.522482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.90124 | 0.456605 | 0.228303 | − | 0.973590i | \(-0.426682\pi\) | ||||
0.228303 | + | 0.973590i | \(0.426682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.65974 | −0.653531 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.670988 | 0.0764661 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.22799 | −0.925721 | −0.462861 | − | 0.886431i | \(-0.653177\pi\) | ||||
−0.462861 | + | 0.886431i | \(0.653177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.06567 | −0.673963 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.12022 | −0.562017 | −0.281009 | − | 0.959705i | \(-0.590669\pi\) | ||||
−0.281009 | + | 0.959705i | \(0.590669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00056 | 0.216991 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.16459 | 0.446491 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.57753 | −1.01522 | −0.507608 | − | 0.861588i | \(-0.669470\pi\) | ||||
−0.507608 | + | 0.861588i | \(0.669470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62549 | −0.170398 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0337447 | −0.00349916 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.72149 | −0.484414 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.843274 | −0.0856215 | −0.0428108 | − | 0.999083i | \(-0.513631\pi\) | ||||
−0.0428108 | + | 0.999083i | \(0.513631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.651742 | 0.0655026 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.2484 | −1.41777 | −0.708885 | − | 0.705324i | \(-0.750802\pi\) | ||||
−0.708885 | + | 0.705324i | \(0.750802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.0465 | −1.67964 | −0.839822 | − | 0.542862i | \(-0.817340\pi\) | ||||
−0.839822 | + | 0.542862i | \(0.817340\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30862 | 0.127709 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.481214 | 0.0465207 | 0.0232604 | − | 0.999729i | \(-0.492595\pi\) | ||||
0.0232604 | + | 0.999729i | \(0.492595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2858 | 1.65568 | 0.827840 | − | 0.560964i | \(-0.189569\pi\) | ||||
0.827840 | + | 0.560964i | \(0.189569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.69108 | 0.255426 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.97071 | −0.561677 | −0.280839 | − | 0.959755i | \(-0.590613\pi\) | ||||
−0.280839 | + | 0.959755i | \(0.590613\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.820311 | 0.0764944 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.57887 | −0.145966 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.45827 | 0.133679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2963 | −0.936024 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3019 | 0.928892 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.65178 | 0.863282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.211759 | 0.0187906 | 0.00939528 | − | 0.999956i | \(-0.497009\pi\) | ||||
0.00939528 | + | 0.999956i | \(0.497009\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1908 | −1.16139 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.0638 | 1.14139 | 0.570696 | − | 0.821161i | \(-0.306673\pi\) | ||||
0.570696 | + | 0.821161i | \(0.306673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.44163 | −0.298427 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.17932 | 0.531831 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.99672 | −0.341463 | −0.170731 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170731 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0245475 | −0.00208209 | −0.00104104 | − | 0.999999i | \(-0.500331\pi\) | ||||
−0.00104104 | + | 0.999999i | \(0.500331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.69394 | −0.816377 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.70481 | −0.142564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.06493 | −0.254528 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.48312 | −0.782155 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.5192 | −1.84485 | −0.922423 | − | 0.386181i | \(-0.873794\pi\) | ||||
−0.922423 | + | 0.386181i | \(0.873794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9657 | −1.54341 | −0.771703 | − | 0.635983i | \(-0.780595\pi\) | ||||
−0.771703 | + | 0.635983i | \(0.780595\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.41644 | 0.114512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0248343 | 0.00199474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2221 | 1.61390 | 0.806951 | − | 0.590619i | \(-0.201116\pi\) | ||||
0.806951 | + | 0.590619i | \(0.201116\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.5566 | −0.995803 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.597949 | 0.0471249 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.22151 | 0.174002 | 0.0870011 | − | 0.996208i | \(-0.472272\pi\) | ||||
0.0870011 | + | 0.996208i | \(0.472272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.37249 | 0.106848 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3196 | −1.34023 | −0.670117 | − | 0.742256i | \(-0.733756\pi\) | ||||
−0.670117 | + | 0.742256i | \(0.733756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.87003 | −0.682310 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.34291 | −0.255639 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.64302 | 0.276974 | 0.138487 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138487 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.03619 | 0.229514 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.70936 | −0.203648 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8085 | −1.03210 | −0.516050 | − | 0.856559i | \(-0.672598\pi\) | ||||
−0.516050 | + | 0.856559i | \(0.672598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.95829 | −0.591535 | −0.295768 | − | 0.955260i | \(-0.595575\pi\) | ||||
−0.295768 | + | 0.955260i | \(0.595575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0527 | −0.890958 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.98050 | −0.145609 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.52943 | 0.111843 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.50429 | 0.327639 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.49411 | −0.325182 | −0.162591 | − | 0.986694i | \(-0.551985\pi\) | ||||
−0.162591 | + | 0.986694i | \(0.551985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.8118 | 1.92996 | 0.964979 | − | 0.262328i | \(-0.0844903\pi\) | ||||
0.964979 | + | 0.262328i | \(0.0844903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.32489 | −0.238100 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.67895 | −0.547103 | −0.273551 | − | 0.961857i | \(-0.588198\pi\) | ||||
−0.273551 | + | 0.961857i | \(0.588198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.27465 | −0.0903578 | −0.0451789 | − | 0.998979i | \(-0.514386\pi\) | ||||
−0.0451789 | + | 0.998979i | \(0.514386\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.3687 | 1.22509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.23411 | −0.156804 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.58168 | −0.529527 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.580798 | 0.0403683 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.60958 | −0.249680 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0159 | 1.10258 | 0.551291 | − | 0.834313i | \(-0.314135\pi\) | ||||
0.551291 | + | 0.834313i | \(0.314135\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.77322 | −0.121499 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.70775 | 0.662063 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0181025 | 0.00122888 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.81675 | 0.393060 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.70510 | −0.249232 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.3323 | 1.36155 | 0.680775 | − | 0.732492i | \(-0.261643\pi\) | ||||
0.680775 | + | 0.732492i | \(0.261643\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.94911 | 0.196607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.56302 | 0.170113 | 0.0850567 | − | 0.996376i | \(-0.472893\pi\) | ||||
0.0850567 | + | 0.996376i | \(0.472893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5606 | −0.697865 | −0.348932 | − | 0.937148i | \(-0.613456\pi\) | ||||
−0.348932 | + | 0.937148i | \(0.613456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00044 | 0.0658244 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.1168 | 1.25238 | 0.626192 | − | 0.779669i | \(-0.284613\pi\) | ||||
0.626192 | + | 0.779669i | \(0.284613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.13424 | 0.465387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.2680 | −0.796889 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.24459 | −0.533298 | −0.266649 | − | 0.963794i | \(-0.585916\pi\) | ||||
−0.266649 | + | 0.963794i | \(0.585916\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.11563 | 0.522774 | 0.261387 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261387 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.85023 | 0.503592 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.97909 | 0.445878 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.74433 | 0.556388 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.63426 | −0.483802 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.53539 | 0.223152 | 0.111576 | − | 0.993756i | \(-0.464410\pi\) | ||||
0.111576 | + | 0.993756i | \(0.464410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.627129 | 0.0394273 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.98284 | 0.186793 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.3707 | −1.33307 | −0.666535 | − | 0.745474i | \(-0.732223\pi\) | ||||
−0.666535 | + | 0.745474i | \(0.732223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.44364 | −0.0897036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17003 | −0.134322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.15569 | 0.132925 | 0.0664627 | − | 0.997789i | \(-0.478829\pi\) | ||||
0.0664627 | + | 0.997789i | \(0.478829\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.24101 | 0.567671 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.2801 | −0.873929 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.55734 | −0.338837 | −0.169419 | − | 0.985544i | \(-0.554189\pi\) | ||||
−0.169419 | + | 0.985544i | \(0.554189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2990 | 1.23307 | 0.616537 | − | 0.787326i | \(-0.288535\pi\) | ||||
0.616537 | + | 0.787326i | \(0.288535\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.42361 | −0.146683 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.18436 | 0.192024 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2147 | −1.45492 | −0.727461 | − | 0.686149i | \(-0.759300\pi\) | ||||
−0.727461 | + | 0.686149i | \(0.759300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0175833 | 0.00105268 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.0352 | 1.91106 | 0.955530 | − | 0.294894i | \(-0.0952842\pi\) | ||||
0.955530 | + | 0.294894i | \(0.0952842\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0778 | 1.43128 | 0.715638 | − | 0.698472i | \(-0.246136\pi\) | ||||
0.715638 | + | 0.698472i | \(0.246136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.03975 | −0.416999 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.52650 | −0.326219 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6761 | −0.804474 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.25732 | −0.0737056 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.373309 | −0.0218089 | −0.0109045 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109045 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.99395 | 0.116092 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.72410 | 0.274120 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.51924 | −0.0878599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.07626 | 0.407869 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.2444 | −1.22046 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.87013 | 0.507902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.5239 | 1.62795 | 0.813974 | − | 0.580901i | \(-0.197300\pi\) | ||||
0.813974 | + | 0.580901i | \(0.197300\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4164 | −1.44589 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.2504 | −1.20500 | −0.602500 | − | 0.798119i | \(-0.705829\pi\) | ||||
−0.602500 | + | 0.798119i | \(0.705829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0831 | −0.796022 | −0.398011 | − | 0.917381i | \(-0.630299\pi\) | ||||
−0.398011 | + | 0.917381i | \(0.630299\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.681881 | −0.0384196 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.0436 | −1.51892 | −0.759459 | − | 0.650555i | \(-0.774536\pi\) | ||||
−0.759459 | + | 0.650555i | \(0.774536\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.34314 | −0.131191 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.717491 | 0.0400464 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.84476 | −0.436494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.71421 | −0.427908 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.7732 | 1.42526 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.20035 | 0.286705 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.83232 | 0.485468 | 0.242734 | − | 0.970093i | \(-0.421956\pi\) | ||||
0.242734 | + | 0.970093i | \(0.421956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.40224 | −0.0768421 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.7825 | −0.698381 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.01026 | 0.272926 | 0.136463 | − | 0.990645i | \(-0.456426\pi\) | ||||
0.136463 | + | 0.990645i | \(0.456426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.90234 | −0.483509 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0189859 | 0.00102814 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.6862 | 0.577003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.22309 | 0.0658487 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.1935 | 0.976679 | 0.488339 | − | 0.872654i | \(-0.337603\pi\) | ||||
0.488339 | + | 0.872654i | \(0.337603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.8229 | −1.06109 | −0.530547 | − | 0.847656i | \(-0.678013\pi\) | ||||
−0.530547 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.4443 | −0.610851 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.7268 | −1.36930 | −0.684650 | − | 0.728872i | \(-0.740045\pi\) | ||||
−0.684650 | + | 0.728872i | \(0.740045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.30500 | 0.0692622 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.17428 | 0.115075 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.6690 | 1.72421 | 0.862103 | − | 0.506733i | \(-0.169147\pi\) | ||||
0.862103 | + | 0.506733i | \(0.169147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.485748 | −0.0255657 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3518 | −0.805758 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.28083 | −0.224069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.33622 | 0.330748 | 0.165374 | − | 0.986231i | \(-0.447117\pi\) | ||||
0.165374 | + | 0.986231i | \(0.447117\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.36799 | −0.279446 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.73604 | 0.349718 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.77574 | 0.143722 | 0.0718612 | − | 0.997415i | \(-0.477106\pi\) | ||||
0.0718612 | + | 0.997415i | \(0.477106\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3908 | 0.743139 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.67633 | 0.292346 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.36981 | 0.0703624 | 0.0351812 | − | 0.999381i | \(-0.488799\pi\) | ||||
0.0351812 | + | 0.999381i | \(0.488799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.315733 | 0.0161755 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9702 | 1.12262 | 0.561312 | − | 0.827604i | \(-0.310297\pi\) | ||||
0.561312 | + | 0.827604i | \(0.310297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.736275 | −0.0375241 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.87329 | 0.349389 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.99985 | 0.456310 | 0.228155 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228155 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.36295 | 0.0689273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.4782 | 0.982545 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.02858 | 0.454277 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.02280 | −0.302276 | −0.151138 | − | 0.988513i | \(-0.548294\pi\) | ||||
−0.151138 | + | 0.988513i | \(0.548294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.13147 | −0.256895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.1265 | 1.05501 | 0.527503 | − | 0.849553i | \(-0.323128\pi\) | ||||
0.527503 | + | 0.849553i | \(0.323128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0459939 | −0.00229112 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.65586 | 0.330733 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.51409 | −0.0750508 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.2674 | −1.54607 | −0.773036 | − | 0.634363i | \(-0.781263\pi\) | ||||
−0.773036 | + | 0.634363i | \(0.781263\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.95911 | −0.293941 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.45345 | 0.0715195 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.61842 | 0.275798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0366003 | −0.00179233 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.24693 | −0.158623 | −0.0793115 | − | 0.996850i | \(-0.525272\pi\) | ||||
−0.0793115 | + | 0.996850i | \(0.525272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2288 | 0.839680 | 0.419840 | − | 0.907598i | \(-0.362086\pi\) | ||||
0.419840 | + | 0.907598i | \(0.362086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.05120 | 0.245598 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.92062 | 0.335699 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.46569 | 0.312897 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.54188 | −0.122723 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4443 | 0.792095 | 0.396047 | − | 0.918230i | \(-0.370382\pi\) | ||||
0.396047 | + | 0.918230i | \(0.370382\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2198 | −0.635305 | −0.317652 | − | 0.948207i | \(-0.602895\pi\) | ||||
−0.317652 | + | 0.948207i | \(0.602895\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.56981 | −0.219106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.21667 | −0.153874 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5145 | 0.979106 | 0.489553 | − | 0.871974i | \(-0.337160\pi\) | ||||
0.489553 | + | 0.871974i | \(0.337160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.94135 | 0.235302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5081 | 1.63953 | 0.819764 | − | 0.572702i | \(-0.194105\pi\) | ||||
0.819764 | + | 0.572702i | \(0.194105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.5094 | 0.498195 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.5762 | −1.58810 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1657 | 1.28203 | 0.641014 | − | 0.767529i | \(-0.278514\pi\) | ||||
0.641014 | + | 0.767529i | \(0.278514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.79620 | −0.272932 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.2779 | −1.32861 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.78365 | 0.0836188 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.1314 | −0.848153 | −0.424077 | − | 0.905626i | \(-0.639401\pi\) | ||||
−0.424077 | + | 0.905626i | \(0.639401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.2670 | 0.479220 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.1606 | −1.12527 | −0.562636 | − | 0.826705i | \(-0.690213\pi\) | ||||
−0.562636 | + | 0.826705i | \(0.690213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8126 | −1.19961 | −0.599806 | − | 0.800146i | \(-0.704755\pi\) | ||||
−0.599806 | + | 0.800146i | \(0.704755\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0370281 | 0.00171714 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.9669 | −1.10906 | −0.554528 | − | 0.832165i | \(-0.687101\pi\) | ||||
−0.554528 | + | 0.832165i | \(0.687101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.31751 | −0.430243 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.1512 | 1.38930 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.42158 | 0.341245 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.3332 | −0.749419 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.54284 | 0.299576 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.97853 | −0.136092 | −0.0680462 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680462 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.66794 | 0.167244 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.891543 | 0.0405666 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.925325 | 0.0420169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0404 | 1.40657 | 0.703287 | − | 0.710906i | \(-0.251715\pi\) | ||||
0.703287 | + | 0.710906i | \(0.251715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.31228 | 0.149786 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.52070 | −0.294275 | −0.147138 | − | 0.989116i | \(-0.547006\pi\) | ||||
−0.147138 | + | 0.989116i | \(0.547006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.09238 | −0.229349 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.715157 | −0.0321439 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.951252 | 0.0426695 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.8087 | 1.55825 | 0.779125 | − | 0.626869i | \(-0.215664\pi\) | ||||
0.779125 | + | 0.626869i | \(0.215664\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.8236 | −1.15371 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.6348 | 0.695739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.2252 | −0.587353 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.27277 | 0.366684 | 0.183342 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183342 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.12042 | −0.138039 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.2308 | −1.06982 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.7052 | 0.824248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.45413 | 0.239873 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.43175 | 0.238427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.4742 | 0.765559 | 0.382779 | − | 0.923840i | \(-0.374967\pi\) | ||||
0.382779 | + | 0.923840i | \(0.374967\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.26300 | 0.142681 | 0.0713404 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713404 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.52697 | 0.197573 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0412623 | 0.00179741 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4411 | −0.975702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41176 | 0.0612651 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.0415 | 0.608204 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.528036 | −0.0228290 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.5886 | −0.888462 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.33552 | 0.229817 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.8792 | −1.58556 | −0.792781 | − | 0.609507i | \(-0.791367\pi\) | ||||
−0.792781 | + | 0.609507i | \(0.791367\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.8658 | −0.509212 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.9677 | −0.812489 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.57057 | 0.152667 | 0.0763334 | − | 0.997082i | \(-0.475679\pi\) | ||||
0.0763334 | + | 0.997082i | \(0.475679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.28024 | 0.268034 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0184 | 0.512002 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.58119 | 0.279861 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.95293 | −0.125345 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.2578 | −1.28206 | −0.641032 | − | 0.767514i | \(-0.721494\pi\) | ||||
−0.641032 | + | 0.767514i | \(0.721494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.9790 | −0.760432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.28039 | 0.0962780 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.4953 | −0.948062 | −0.474031 | − | 0.880508i | \(-0.657202\pi\) | ||||
−0.474031 | + | 0.880508i | \(0.657202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.55166 | 0.275631 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.85165 | 0.203750 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.4374 | −1.52753 | −0.763767 | − | 0.645492i | \(-0.776652\pi\) | ||||
−0.763767 | + | 0.645492i | \(0.776652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.2768 | 0.974104 | 0.487052 | − | 0.873373i | \(-0.338072\pi\) | ||||
0.487052 | + | 0.873373i | \(0.338072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.70072 | −0.279927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.83773 | 0.118342 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7394 | 0.655241 | 0.327621 | − | 0.944809i | \(-0.393753\pi\) | ||||
0.327621 | + | 0.944809i | \(0.393753\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.9765 | 1.66137 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.09543 | 0.169907 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.06476 | 0.292593 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.73249 | 0.0716297 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7718 | 0.816068 | 0.408034 | − | 0.912967i | \(-0.366214\pi\) | ||||
0.408034 | + | 0.912967i | \(0.366214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0973823 | −0.00401257 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.4493 | −0.470963 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9384 | 1.10623 | 0.553114 | − | 0.833106i | \(-0.313439\pi\) | ||||
0.553114 | + | 0.833106i | \(0.313439\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.60016 | −0.0656001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.90051 | −0.0777827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.4760 | −1.73552 | −0.867761 | − | 0.496982i | \(-0.834442\pi\) | ||||
−0.867761 | + | 0.496982i | \(0.834442\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.6101 | 1.37099 | 0.685493 | − | 0.728080i | \(-0.259587\pi\) | ||||
0.685493 | + | 0.728080i | \(0.259587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.05027 | −0.368555 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2981 | 0.459333 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3897 | 0.462295 | 0.231147 | − | 0.972919i | \(-0.425752\pi\) | ||||
0.231147 | + | 0.972919i | \(0.425752\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.33107 | −0.134982 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.2128 | −0.534533 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.30427 | 0.0526789 | 0.0263395 | − | 0.999653i | \(-0.491615\pi\) | ||||
0.0263395 | + | 0.999653i | \(0.491615\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.3043 | −0.455833 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.4802 | −0.743985 | −0.371992 | − | 0.928236i | \(-0.621325\pi\) | ||||
−0.371992 | + | 0.928236i | \(0.621325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.5751 | −1.26911 | −0.634554 | − | 0.772878i | \(-0.718816\pi\) | ||||
−0.634554 | + | 0.772878i | \(0.718816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.20987 | 0.168936 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.66063 | 0.306917 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.38875 | 0.335550 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.38189 | −0.214932 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.29060 | −0.131205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9916 | 1.71147 | 0.855734 | − | 0.517416i | \(-0.173106\pi\) | ||||
0.855734 | + | 0.517416i | \(0.173106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.8798 | 0.949137 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.232363 | −0.00922105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.9255 | −0.512126 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.923968 | 0.0365516 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.0209 | −0.790779 | −0.395390 | − | 0.918513i | \(-0.629390\pi\) | ||||
−0.395390 | + | 0.918513i | \(0.629390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.3527 | −1.11812 | −0.559060 | − | 0.829127i | \(-0.688838\pi\) | ||||
−0.559060 | + | 0.829127i | \(0.688838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4743 | 0.569924 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.7284 | −1.01149 | −0.505744 | − | 0.862683i | \(-0.668782\pi\) | ||||
−0.505744 | + | 0.862683i | \(0.668782\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.52438 | 0.0598370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0269908 | 0.00105785 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.4989 | 1.46744 | 0.733722 | − | 0.679449i | \(-0.237781\pi\) | ||||
0.733722 | + | 0.679449i | \(0.237781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3349 | −0.560113 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.03092 | −0.118247 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.3066 | −0.829988 | −0.414994 | − | 0.909824i | \(-0.636216\pi\) | ||||
−0.414994 | + | 0.909824i | \(0.636216\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.3872 | −0.909656 | −0.454828 | − | 0.890579i | \(-0.650299\pi\) | ||||
−0.454828 | + | 0.890579i | \(0.650299\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.52431 | −0.214546 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.77650 | 0.146446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.08808 | −0.0808508 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.3155 | 1.17206 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.78123 | 0.261786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6684 | 0.796706 | 0.398353 | − | 0.917232i | \(-0.369582\pi\) | ||||
0.398353 | + | 0.917232i | \(0.369582\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 21.3763 | 0.822776 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.0320 | 1.00049 | 0.500246 | − | 0.865883i | \(-0.333243\pi\) | ||||
0.500246 | + | 0.865883i | \(0.333243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.674496 | 0.0258848 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.82147 | 0.146439 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.3035 | −0.509043 | −0.254522 | − | 0.967067i | \(-0.581918\pi\) | ||||
−0.254522 | + | 0.967067i | \(0.581918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.38560 | 0.167565 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7459 | −0.600743 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.1146 | −0.652015 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2943 | −0.429657 | −0.214828 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214828 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.521299 | −0.0198025 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0269359 | 0.00102174 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5970 | −0.477144 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.5032 | 1.07809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.64761 | −0.251077 | −0.125538 | − | 0.992089i | \(-0.540066\pi\) | ||||
−0.125538 | + | 0.992089i | \(0.540066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.76608 | 0.292903 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.6372 | 0.400619 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3966 | 0.428615 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.8987 | −0.972648 | −0.486324 | − | 0.873779i | \(-0.661662\pi\) | ||||
−0.486324 | + | 0.873779i | \(0.661662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.39243 | 0.239735 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0169192 | 0.000633630 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.87069 | 0.0699600 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.2927 | −0.459079 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.3355 | −0.609210 | −0.304605 | − | 0.952479i | \(-0.598525\pi\) | ||||
−0.304605 | + | 0.952479i | \(0.598525\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.6347 | 0.507784 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.1004 | 0.450020 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.6026 | −0.393771 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.6052 | −0.727117 | −0.363559 | − | 0.931571i | \(-0.618438\pi\) | ||||
−0.363559 | + | 0.931571i | \(0.618438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9017 | 1.10747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.1294 | 0.596569 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.6268 | −1.27897 | −0.639484 | − | 0.768804i | \(-0.720852\pi\) | ||||
−0.639484 | + | 0.768804i | \(0.720852\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.4058 | 0.383825 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.77221 | −0.359964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.1192 | 1.88045 | 0.940225 | − | 0.340554i | \(-0.110615\pi\) | ||||
0.940225 | + | 0.340554i | \(0.110615\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0378 | 0.478956 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3318 | 0.672530 | 0.336265 | − | 0.941767i | \(-0.390836\pi\) | ||||
0.336265 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.7104 | 0.905317 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.97797 | 0.145546 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.384901 | −0.0140640 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.2142 | 0.701136 | 0.350568 | − | 0.936537i | \(-0.385989\pi\) | ||||
0.350568 | + | 0.936537i | \(0.385989\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.27127 | 0.192096 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.8111 | 0.757392 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.5974 | −0.930352 | −0.465176 | − | 0.885218i | \(-0.654009\pi\) | ||||
−0.465176 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.935051 | 0.0339402 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0281 | 1.01602 | 0.508009 | − | 0.861352i | \(-0.330382\pi\) | ||||
0.508009 | + | 0.861352i | \(0.330382\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8261 | −0.500539 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.55426 | −0.0561945 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.69285 | −0.133341 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.7564 | 1.83032 | 0.915162 | − | 0.403087i | \(-0.132063\pi\) | ||||
0.915162 | + | 0.403087i | \(0.132063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.8638 | −1.14755 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −55.0059 | −1.97842 | −0.989212 | − | 0.146494i | \(-0.953201\pi\) | ||||
−0.989212 | + | 0.146494i | \(0.953201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0859103 | 0.00308599 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.15247 | −0.0772196 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.7299 | 1.06518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.997674 | 0.0356996 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.7293 | −0.562119 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.1898 | −0.791986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.78536 | 0.241872 | 0.120936 | − | 0.992660i | \(-0.461410\pi\) | ||||
0.120936 | + | 0.992660i | \(0.461410\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.21414 | 0.114426 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.77570 | 0.169804 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.4277 | −0.583366 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.7784 | 0.488668 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.3449 | −1.49993 | −0.749967 | − | 0.661475i | \(-0.769931\pi\) | ||||
−0.749967 | + | 0.661475i | \(0.769931\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8536 | 0.419349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.44091 | 0.262911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.27270 | −0.115491 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.656129 | −0.0231255 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.28601 | −0.291681 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.3991 | −0.892984 | −0.446492 | − | 0.894788i | \(-0.647327\pi\) | ||||
−0.446492 | + | 0.894788i | \(0.647327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0288 | 0.703306 | 0.351653 | − | 0.936130i | \(-0.385620\pi\) | ||||
0.351653 | + | 0.936130i | \(0.385620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.2658 | 1.06147 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.43767 | −0.0853877 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.0668 | −1.33179 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.26286 | 0.0441280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1634 | 0.424506 | 0.212253 | − | 0.977215i | \(-0.431920\pi\) | ||||
0.212253 | + | 0.977215i | \(0.431920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.1250 | −1.39867 | −0.699335 | − | 0.714794i | \(-0.746520\pi\) | ||||
−0.699335 | + | 0.714794i | \(0.746520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.74789 | 0.165300 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.2441 | −1.29510 | −0.647552 | − | 0.762022i | \(-0.724207\pi\) | ||||
−0.647552 | + | 0.762022i | \(0.724207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.9066 | 0.899774 | 0.449887 | − | 0.893086i | \(-0.351464\pi\) | ||||
0.449887 | + | 0.893086i | \(0.351464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.1042 | −1.25244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.5958 | 0.401770 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.0048 | 0.657690 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.127451 | 0.00440534 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.02724 | 0.173560 | 0.0867798 | − | 0.996228i | \(-0.472342\pi\) | ||||
0.0867798 | + | 0.996228i | \(0.472342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1983 | −0.730976 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.7646 | 1.64510 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.73309 | 0.334829 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.23551 | 0.282976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.9000 | 1.23209 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.34928 | −0.0462527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7681 | 0.916524 | 0.458262 | − | 0.888817i | \(-0.348472\pi\) | ||||
0.458262 | + | 0.888817i | \(0.348472\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.66818 | 0.125449 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.8760 | 1.66957 | 0.834787 | − | 0.550574i | \(-0.185591\pi\) | ||||
0.834787 | + | 0.550574i | \(0.185591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.54729 | 0.0527928 | 0.0263964 | − | 0.999652i | \(-0.491597\pi\) | ||||
0.0263964 | + | 0.999652i | \(0.491597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.24003 | −0.280819 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.76724 | −0.128238 | −0.0641192 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641192 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.99749 | −0.135919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.3910 | −0.692516 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.90236 | 0.234146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.6735 | 0.802146 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.655150 | 0.0221735 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.72002 | −0.260984 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.29648 | −0.145082 | −0.0725410 | − | 0.997365i | \(-0.523111\pi\) | ||||
−0.0725410 | + | 0.997365i | \(0.523111\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.556604 | −0.0187738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.7084 | −0.933519 | −0.466760 | − | 0.884384i | \(-0.654579\pi\) | ||||
−0.466760 | + | 0.884384i | \(0.654579\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.4492 | 1.26027 | 0.630134 | − | 0.776487i | \(-0.283000\pi\) | ||||
0.630134 | + | 0.776487i | \(0.283000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.97298 | 0.0999357 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.219360 | 0.00736539 | 0.00368270 | − | 0.999993i | \(-0.498828\pi\) | ||||
0.00368270 | + | 0.999993i | \(0.498828\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.169376 | −0.00568070 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.08841 | 0.170468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.9753 | −0.936159 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.1521 | 0.506480 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.26519 | −0.0756325 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0632152 | −0.00210834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3540 | 0.511515 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.5507 | 0.351106 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.73264 | 0.290283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.0680 | 1.72889 | 0.864444 | − | 0.502729i | \(-0.167670\pi\) | ||||
0.864444 | + | 0.502729i | \(0.167670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0698 | 0.367161 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.6078 | 1.37853 | 0.689263 | − | 0.724511i | \(-0.257934\pi\) | ||||
0.689263 | + | 0.724511i | \(0.257934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.29529 | 0.142153 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.2254 | 0.437218 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.4492 | −0.345062 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.3382 | 1.79245 | 0.896226 | − | 0.443597i | \(-0.146298\pi\) | ||||
0.896226 | + | 0.443597i | \(0.146298\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.5293 | 1.40139 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.41690 | −0.0795532 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.85121 | −0.225266 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.2437 | 0.434979 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.9579 | 1.04851 | 0.524253 | − | 0.851563i | \(-0.324345\pi\) | ||||
0.524253 | + | 0.851563i | \(0.324345\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.3669 | −0.896915 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.6844 | −1.03730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67825 | −0.0548845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.6379 | −1.71960 | −0.859802 | − | 0.510627i | \(-0.829413\pi\) | ||||
−0.859802 | + | 0.510627i | \(0.829413\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.9979 | −0.685240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.74283 | 0.252409 | 0.126205 | − | 0.992004i | \(-0.459720\pi\) | ||||
0.126205 | + | 0.992004i | \(0.459720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.16527 | −0.168204 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.94256 | −0.160781 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.5052 | −1.77118 | −0.885591 | − | 0.464467i | \(-0.846246\pi\) | ||||
−0.885591 | + | 0.464467i | \(0.846246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.92822 | 0.257361 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.3220 | −1.30753 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8770 | 0.643880 | 0.321940 | − | 0.946760i | \(-0.395665\pi\) | ||||
0.321940 | + | 0.946760i | \(0.395665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.93139 | 0.159576 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.49362 | −0.112933 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.19679 | 0.103230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9995 | −0.999983 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.373861 | −0.0120475 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.4206 | −0.947084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0432 | 0.580230 | 0.290115 | − | 0.956992i | \(-0.406306\pi\) | ||||
0.290115 | + | 0.956992i | \(0.406306\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.6966 | −0.375747 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.4956 | −0.978649 | −0.489324 | − | 0.872102i | \(-0.662757\pi\) | ||||
−0.489324 | + | 0.872102i | \(0.662757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0196344 | 0.000629450 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.5019 | −0.368356 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.3960 | 1.19640 | 0.598201 | − | 0.801346i | \(-0.295882\pi\) | ||||
0.598201 | + | 0.801346i | \(0.295882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.03447 | 0.256783 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.4296 | −0.428773 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.8473 | −0.569239 | −0.284620 | − | 0.958641i | \(-0.591867\pi\) | ||||
−0.284620 | + | 0.958641i | \(0.591867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.42612 | 0.268479 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.75374 | 0.246804 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.61372 | 0.210304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.9819 | −0.698277 | −0.349138 | − | 0.937071i | \(-0.613526\pi\) | ||||
−0.349138 | + | 0.937071i | \(0.613526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.1690 | 0.417906 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.39868 | 0.0443411 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.0250 | 0.982571 | 0.491286 | − | 0.870999i | \(-0.336527\pi\) | ||||
0.491286 | + | 0.870999i | \(0.336527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.1640 | −0.321574 |
(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 | 4024.2.a.d.1.19 | ✓ | 28 | |
4.3 | odd | 2 | 8048.2.a.v.1.10 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.19 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8048.2.a.v.1.10 | 28 | 4.3 | odd | 2 |