Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.80686 | 1.62054 | 0.810271 | − | 0.586055i | \(-0.199320\pi\) | ||||
0.810271 | + | 0.586055i | \(0.199320\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.33080 | −1.48958 | −0.744789 | − | 0.667300i | \(-0.767450\pi\) | ||||
−0.744789 | + | 0.667300i | \(0.767450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85725 | 1.07994 | 0.539970 | − | 0.841684i | \(-0.318435\pi\) | ||||
0.539970 | + | 0.841684i | \(0.318435\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.87847 | 1.62616 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.16199 | 1.85791 | 0.928955 | − | 0.370192i | \(-0.120708\pi\) | ||||
0.928955 | + | 0.370192i | \(0.120708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18285 | −0.882763 | −0.441381 | − | 0.897320i | \(-0.645511\pi\) | ||||
−0.441381 | + | 0.897320i | \(0.645511\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.34908 | −2.41392 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.44720 | −0.836069 | −0.418035 | − | 0.908431i | \(-0.637281\pi\) | ||||
−0.418035 | + | 0.908431i | \(0.637281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.59579 | −1.51318 | −0.756589 | − | 0.653890i | \(-0.773136\pi\) | ||||
−0.756589 | + | 0.653890i | \(0.773136\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.01992 | 1.75009 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.22071 | −1.92265 | −0.961326 | − | 0.275414i | \(-0.911185\pi\) | ||||
−0.961326 | + | 0.275414i | \(0.911185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.09421 | 1.21884 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.27260 | 1.01471 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.40217 | 0.260377 | 0.130188 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130188 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.702160 | −0.126112 | −0.0630558 | − | 0.998010i | \(-0.520085\pi\) | ||||
−0.0630558 | + | 0.998010i | \(0.520085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.2959 | 3.01082 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.51693 | −1.60866 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.54930 | −1.56989 | −0.784947 | − | 0.619562i | \(-0.787310\pi\) | ||||
−0.784947 | + | 0.619562i | \(0.787310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.93381 | −1.43055 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.82571 | −0.441301 | −0.220651 | − | 0.975353i | \(-0.570818\pi\) | ||||
−0.220651 | + | 0.975353i | \(0.570818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.28009 | −1.26270 | −0.631351 | − | 0.775497i | \(-0.717499\pi\) | ||||
−0.631351 | + | 0.775497i | \(0.717499\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −16.2492 | −2.42229 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2543 | −1.49574 | −0.747872 | − | 0.663842i | \(-0.768925\pi\) | ||||
−0.747872 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.16390 | 0.166272 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.67581 | −1.35488 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.03097 | −0.691057 | −0.345529 | − | 0.938408i | \(-0.612300\pi\) | ||||
−0.345529 | + | 0.938408i | \(0.612300\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.5243 | −2.76750 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.5135 | −2.45217 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.57284 | 0.465145 | 0.232572 | − | 0.972579i | \(-0.425286\pi\) | ||||
0.232572 | + | 0.972579i | \(0.425286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46580 | 0.315713 | 0.157856 | − | 0.987462i | \(-0.449542\pi\) | ||||
0.157856 | + | 0.987462i | \(0.449542\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.9390 | 1.75615 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.6014 | 1.31494 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.271159 | −0.0331273 | −0.0165636 | − | 0.999863i | \(-0.505273\pi\) | ||||
−0.0165636 | + | 0.999863i | \(0.505273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −25.8813 | −3.11574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.18072 | 0.733517 | 0.366759 | − | 0.930316i | \(-0.380468\pi\) | ||||
0.366759 | + | 0.930316i | \(0.380468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2210 | 1.54740 | 0.773699 | − | 0.633553i | \(-0.218404\pi\) | ||||
0.773699 | + | 0.633553i | \(0.218404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.1056 | 1.97518 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.6064 | 2.00643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.67343 | 0.863329 | 0.431664 | − | 0.902034i | \(-0.357926\pi\) | ||||
0.431664 | + | 0.902034i | \(0.357926\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.164052 | 0.0182280 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.85568 | −0.203688 | −0.101844 | − | 0.994800i | \(-0.532474\pi\) | ||||
−0.101844 | + | 0.994800i | \(0.532474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4819 | 1.24539 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.93570 | 0.421952 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.46966 | −0.155784 | −0.0778920 | − | 0.996962i | \(-0.524819\pi\) | ||||
−0.0778920 | + | 0.996962i | \(0.524819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.09420 | −0.953331 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.97087 | −0.204369 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.9692 | 2.25400 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.763796 | −0.0775518 | −0.0387759 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387759 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30.0611 | 3.02125 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.20829 | 0.418741 | 0.209370 | − | 0.977836i | \(-0.432859\pi\) | ||||
0.209370 | + | 0.977836i | \(0.432859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.5406 | −1.53126 | −0.765632 | − | 0.643279i | \(-0.777573\pi\) | ||||
−0.765632 | + | 0.643279i | \(0.777573\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −26.7127 | −2.60689 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.77861 | −0.848660 | −0.424330 | − | 0.905508i | \(-0.639490\pi\) | ||||
−0.424330 | + | 0.905508i | \(0.639490\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4923 | −1.00498 | −0.502492 | − | 0.864582i | \(-0.667583\pi\) | ||||
−0.502492 | + | 0.864582i | \(0.667583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26.8036 | −2.54408 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.15796 | −0.861509 | −0.430754 | − | 0.902469i | \(-0.641752\pi\) | ||||
−0.430754 | + | 0.902469i | \(0.641752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.7123 | 2.86394 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.5274 | −1.43551 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.84953 | −0.902905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.9701 | 2.45183 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.93137 | −0.715147 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.64458 | −0.325981 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.14813 | −0.811765 | −0.405883 | − | 0.913925i | \(-0.633036\pi\) | ||||
−0.405883 | + | 0.913925i | \(0.633036\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.2411 | −2.04626 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.38571 | 0.732662 | 0.366331 | − | 0.930485i | \(-0.380614\pi\) | ||||
0.366331 | + | 0.930485i | \(0.380614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.8459 | −1.63414 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.5620 | −1.51149 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.8496 | 1.61043 | 0.805216 | − | 0.592981i | \(-0.202049\pi\) | ||||
0.805216 | + | 0.592981i | \(0.202049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0650 | 0.853706 | 0.426853 | − | 0.904321i | \(-0.359622\pi\) | ||||
0.426853 | + | 0.904321i | \(0.359622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.7824 | −2.42392 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.6127 | −1.64009 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.67035 | −0.387852 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.26692 | 0.269451 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.5789 | −1.52205 | −0.761023 | − | 0.648725i | \(-0.775303\pi\) | ||||
−0.761023 | + | 0.648725i | \(0.775303\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.78604 | 0.552240 | 0.276120 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276120 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.8171 | −1.35958 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.33875 | 0.187853 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.7470 | 1.57598 | 0.787990 | − | 0.615688i | \(-0.211122\pi\) | ||||
0.787990 | + | 0.615688i | \(0.211122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1212 | −1.11989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.3459 | −2.07635 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4905 | −0.900005 | −0.450002 | − | 0.893027i | \(-0.648577\pi\) | ||||
−0.450002 | + | 0.893027i | \(0.648577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −57.6090 | −4.48485 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.914891 | 0.0707964 | 0.0353982 | − | 0.999373i | \(-0.488730\pi\) | ||||
0.0353982 | + | 0.999373i | \(0.488730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.86949 | −0.220730 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −32.1774 | −2.46067 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.8348 | 1.88815 | 0.944076 | − | 0.329727i | \(-0.106957\pi\) | ||||
0.944076 | + | 0.329727i | \(0.106957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.4127 | 1.31628 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0285 | 0.753787 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6568 | 0.871274 | 0.435637 | − | 0.900123i | \(-0.356523\pi\) | ||||
0.435637 | + | 0.900123i | \(0.356523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2535 | 1.28244 | 0.641221 | − | 0.767356i | \(-0.278428\pi\) | ||||
0.641221 | + | 0.767356i | \(0.278428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.92115 | 0.511626 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.8068 | 2.33848 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.2416 | −1.55334 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.0652 | 1.09583 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.5481 | 1.77624 | 0.888119 | − | 0.459614i | \(-0.152012\pi\) | ||||
0.888119 | + | 0.459614i | \(0.152012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1606 | −1.30723 | −0.653616 | − | 0.756826i | \(-0.726749\pi\) | ||||
−0.653616 | + | 0.756826i | \(0.726749\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 29.7567 | 2.13092 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.6761 | −1.11688 | −0.558439 | − | 0.829546i | \(-0.688600\pi\) | ||||
−0.558439 | + | 0.829546i | \(0.688600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.24717 | −0.655514 | −0.327757 | − | 0.944762i | \(-0.606293\pi\) | ||||
−0.327757 | + | 0.944762i | \(0.606293\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.761104 | −0.0536842 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00636 | 0.281192 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.41185 | 0.657352 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −44.9830 | −3.12653 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.6432 | −2.81135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9897 | −0.825403 | −0.412702 | − | 0.910866i | \(-0.635415\pi\) | ||||
−0.412702 | + | 0.910866i | \(0.635415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.3484 | 1.18870 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.5793 | 1.88089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00625 | −0.136193 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.1094 | 2.50762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9719 | 0.738051 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.80822 | 0.589842 | 0.294921 | − | 0.955522i | \(-0.404707\pi\) | ||||
0.294921 | + | 0.955522i | \(0.404707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.7304 | 1.98203 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.3011 | 0.816454 | 0.408227 | − | 0.912881i | \(-0.366147\pi\) | ||||
0.408227 | + | 0.912881i | \(0.366147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.49454 | 0.230926 | 0.115463 | − | 0.993312i | \(-0.463165\pi\) | ||||
0.115463 | + | 0.993312i | \(0.463165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 49.4187 | 3.25151 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.16901 | −0.535170 | −0.267585 | − | 0.963534i | \(-0.586226\pi\) | ||||
−0.267585 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.1550 | 2.22803 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.5383 | 1.39906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.2842 | 1.05334 | 0.526668 | − | 0.850071i | \(-0.323441\pi\) | ||||
0.526668 | + | 0.850071i | \(0.323441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.2260 | 1.10963 | 0.554813 | − | 0.831975i | \(-0.312790\pi\) | ||||
0.554813 | + | 0.831975i | \(0.312790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3573 | −0.985173 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.87673 | −0.247675 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.9934 | 1.33578 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.20864 | −0.330084 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.70328 | 0.423107 | 0.211553 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −56.8180 | −3.57211 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.2282 | 2.01821 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3504 | 1.39418 | 0.697091 | − | 0.716983i | \(-0.254477\pi\) | ||||
0.697091 | + | 0.716983i | \(0.254477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.2848 | −1.69539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.84045 | 0.423414 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2208 | 0.815229 | 0.407614 | − | 0.913154i | \(-0.366361\pi\) | ||||
0.407614 | + | 0.913154i | \(0.366361\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.7572 | 1.02938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.12514 | −0.252455 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.2269 | −1.72102 | −0.860511 | − | 0.509431i | \(-0.829856\pi\) | ||||
−0.860511 | + | 0.509431i | \(0.829856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3618 | −1.29764 | −0.648818 | − | 0.760944i | \(-0.724736\pi\) | ||||
−0.648818 | + | 0.760944i | \(0.724736\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.5262 | −1.54491 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 37.5524 | 2.26450 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.8538 | −1.61349 | −0.806744 | − | 0.590902i | \(-0.798772\pi\) | ||||
−0.806744 | + | 0.590902i | \(0.798772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.42547 | −0.205077 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1142 | 1.49819 | 0.749093 | − | 0.662465i | \(-0.230490\pi\) | ||||
0.749093 | + | 0.662465i | \(0.230490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.7681 | −1.53175 | −0.765877 | − | 0.642987i | \(-0.777695\pi\) | ||||
−0.765877 | + | 0.642987i | \(0.777695\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 61.6646 | 3.65270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.07376 | −0.476579 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.11681 | −0.300989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.14387 | −0.125676 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.2273 | 1.06485 | 0.532424 | − | 0.846478i | \(-0.321281\pi\) | ||||
0.532424 | + | 0.846478i | \(0.321281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9004 | −0.692869 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32.4897 | 1.88524 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.3481 | 1.69724 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.6583 | −1.36364 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8121 | 0.678587 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.21306 | −0.470279 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.85756 | 0.277236 | 0.138618 | − | 0.990346i | \(-0.455734\pi\) | ||||
0.138618 | + | 0.990346i | \(0.455734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −43.6204 | −2.48148 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.1372 | 0.971763 | 0.485882 | − | 0.874025i | \(-0.338499\pi\) | ||||
0.485882 | + | 0.874025i | \(0.338499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.12125 | 0.402517 | 0.201258 | − | 0.979538i | \(-0.435497\pi\) | ||||
0.201258 | + | 0.979538i | \(0.435497\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −46.4281 | −2.61593 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5055 | −1.71336 | −0.856680 | − | 0.515848i | \(-0.827477\pi\) | ||||
−0.856680 | + | 0.515848i | \(0.827477\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.64017 | 0.483757 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.6403 | −1.37529 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.7370 | 1.26512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.3969 | −1.07595 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.4505 | −1.62862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.2992 | −1.61532 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.25577 | 0.398813 | 0.199407 | − | 0.979917i | \(-0.436099\pi\) | ||||
0.199407 | + | 0.979917i | \(0.436099\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −46.5860 | −2.55289 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.903174 | 0.0493457 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.67495 | 0.0912405 | 0.0456203 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456203 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.7051 | −1.39611 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.32670 | −0.234304 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.6752 | −0.900377 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 86.2052 | 4.64113 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.7470 | −0.737979 | −0.368989 | − | 0.929434i | \(-0.620296\pi\) | ||||
−0.368989 | + | 0.929434i | \(0.620296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1465 | −0.971360 | −0.485680 | − | 0.874137i | \(-0.661428\pi\) | ||||
−0.485680 | + | 0.874137i | \(0.661428\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.7819 | −0.895750 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2901 | −1.18638 | −0.593191 | − | 0.805061i | \(-0.702132\pi\) | ||||
−0.593191 | + | 0.805061i | \(0.702132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.5867 | −1.09263 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.6463 | −1.46320 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1349 | −0.957125 | −0.478563 | − | 0.878053i | \(-0.658842\pi\) | ||||
−0.478563 | + | 0.878053i | \(0.658842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.5045 | 1.28971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 75.7014 | 3.97329 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −44.0364 | −2.30497 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.0147 | 1.61896 | 0.809478 | − | 0.587150i | \(-0.199750\pi\) | ||||
0.809478 | + | 0.587150i | \(0.199750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.7851 | −0.717625 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.3748 | −0.746301 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7975 | 1.33574 | 0.667871 | − | 0.744277i | \(-0.267206\pi\) | ||||
0.667871 | + | 0.744277i | \(0.267206\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.2298 | −0.528265 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.46290 | −0.229851 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.02969 | −0.361091 | −0.180545 | − | 0.983567i | \(-0.557786\pi\) | ||||
−0.180545 | + | 0.983567i | \(0.557786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.6775 | −1.31550 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.24162 | −0.216737 | −0.108368 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108368 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58.6433 | −2.98874 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −40.3942 | −2.05335 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.56789 | 0.180899 | 0.0904497 | − | 0.995901i | \(-0.471170\pi\) | ||||
0.0904497 | + | 0.995901i | \(0.471170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.7856 | 1.60747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.5375 | 1.18731 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.5586 | −1.28599 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3759 | −0.821883 | −0.410941 | − | 0.911662i | \(-0.634800\pi\) | ||||
−0.410941 | + | 0.911662i | \(0.634800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −52.8977 | −2.64820 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.06998 | 0.303120 | 0.151560 | − | 0.988448i | \(-0.451570\pi\) | ||||
0.151560 | + | 0.988448i | \(0.451570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.23487 | 0.111327 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.546425 | −0.0271521 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −58.8427 | −2.91672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.2379 | 1.49517 | 0.747584 | − | 0.664167i | \(-0.231214\pi\) | ||||
0.747584 | + | 0.664167i | \(0.231214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 52.9083 | 2.60977 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.2085 | 0.502329 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.18090 | 0.303408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 28.2512 | 1.38347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.93225 | −0.143250 | −0.0716249 | − | 0.997432i | \(-0.522818\pi\) | ||||
−0.0716249 | + | 0.997432i | \(0.522818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.43693 | 0.313717 | 0.156858 | − | 0.987621i | \(-0.449863\pi\) | ||||
0.156858 | + | 0.987621i | \(0.449863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −50.0253 | −2.43231 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0080 | −1.01904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.04541 | 0.340951 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −55.0500 | −2.65784 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4701 | −1.66037 | −0.830184 | − | 0.557490i | \(-0.811765\pi\) | ||||
−0.830184 | + | 0.557490i | \(0.811765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.07058 | 0.195620 | 0.0978098 | − | 0.995205i | \(-0.468816\pi\) | ||||
0.0978098 | + | 0.995205i | \(0.468816\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.1090 | −0.628530 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 60.8179 | 2.90932 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.95459 | −0.475107 | −0.237553 | − | 0.971374i | \(-0.576345\pi\) | ||||
−0.237553 | + | 0.971374i | \(0.576345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.67807 | 0.270384 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5544 | −0.834036 | −0.417018 | − | 0.908898i | \(-0.636925\pi\) | ||||
−0.417018 | + | 0.908898i | \(0.636925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89515 | 0.232052 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −52.1485 | −2.46654 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8811 | 1.31579 | 0.657896 | − | 0.753109i | \(-0.271447\pi\) | ||||
0.657896 | + | 0.753109i | \(0.271447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.4120 | −0.819898 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.0475 | 0.894928 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.2909 | 1.42006 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1029 | −0.987152 | −0.493576 | − | 0.869703i | \(-0.664311\pi\) | ||||
−0.493576 | + | 0.869703i | \(0.664311\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.1757 | −0.848370 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.4681 | −1.41904 | −0.709520 | − | 0.704685i | \(-0.751088\pi\) | ||||
−0.709520 | + | 0.704685i | \(0.751088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.6310 | −1.47002 | −0.735008 | − | 0.678058i | \(-0.762822\pi\) | ||||
−0.735008 | + | 0.678058i | \(0.762822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.56455 | 0.304424 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.78847 | 0.129035 | 0.0645174 | − | 0.997917i | \(-0.479449\pi\) | ||||
0.0645174 | + | 0.997917i | \(0.479449\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.774769 | −0.0357755 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55.4270 | 2.55394 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −51.0219 | −2.34599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.1961 | −1.84432 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.5435 | −1.12377 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.186867 | 0.00853819 | 0.00426910 | − | 0.999991i | \(-0.498641\pi\) | ||||
0.00426910 | + | 0.999991i | \(0.498641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.3939 | 1.38584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −73.9493 | −3.36481 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.54405 | 0.115519 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6009 | 0.706943 | 0.353472 | − | 0.935445i | \(-0.385001\pi\) | ||||
0.353472 | + | 0.935445i | \(0.385001\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.2522 | −1.45850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.6367 | −1.60826 | −0.804130 | − | 0.594453i | \(-0.797369\pi\) | ||||
−0.804130 | + | 0.594453i | \(0.797369\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.83357 | −0.217693 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −100.127 | −4.50039 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.6599 | 0.792155 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9141 | −1.16007 | −0.580037 | − | 0.814590i | \(-0.696962\pi\) | ||||
−0.580037 | + | 0.814590i | \(0.696962\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.56797 | 0.114728 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0170 | −0.623747 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.05426 | −0.357702 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.1469 | 1.91245 | 0.956227 | − | 0.292627i | \(-0.0945293\pi\) | ||||
0.956227 | + | 0.292627i | \(0.0945293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.7757 | 1.67110 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −34.7770 | −1.53544 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 51.7627 | 2.28094 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −63.1870 | −2.77896 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 69.7078 | 3.05983 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9789 | −1.00673 | −0.503363 | − | 0.864075i | \(-0.667904\pi\) | ||||
−0.503363 | + | 0.864075i | \(0.667904\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.68716 | 0.117501 | 0.0587506 | − | 0.998273i | \(-0.481288\pi\) | ||||
0.0587506 | + | 0.998273i | \(0.481288\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 48.8750 | 2.13308 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.42049 | 0.105438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.0215 | 2.69659 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.4300 | 0.756398 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.99379 | 0.389564 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.2398 | 1.26415 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.7192 | 1.41194 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.17197 | 0.308919 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7406 | 0.590754 | 0.295377 | − | 0.955381i | \(-0.404555\pi\) | ||||
0.295377 | + | 0.955381i | \(0.404555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 48.4281 | 2.07825 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 34.9478 | 1.49700 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.1975 | −1.63321 | −0.816604 | − | 0.577199i | \(-0.804146\pi\) | ||||
−0.816604 | + | 0.577199i | \(0.804146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.0293 | 0.513398 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.24844 | −0.393997 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.9250 | 0.932344 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 89.2772 | 3.78961 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.0835 | −1.44416 | −0.722082 | − | 0.691807i | \(-0.756815\pi\) | ||||
−0.722082 | + | 0.691807i | \(0.756815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.3543 | 1.11467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −59.6223 | −2.51725 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5491 | −0.823896 | −0.411948 | − | 0.911207i | \(-0.635151\pi\) | ||||
−0.411948 | + | 0.911207i | \(0.635151\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.5033 | 1.28328 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.468739 | 0.0196852 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.6019 | 0.695987 | 0.347994 | − | 0.937497i | \(-0.386863\pi\) | ||||
0.347994 | + | 0.937497i | \(0.386863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2433 | −0.554213 | −0.277107 | − | 0.960839i | \(-0.589376\pi\) | ||||
−0.277107 | + | 0.960839i | \(0.589376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 68.9031 | 2.87847 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −56.1929 | −2.34341 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.5290 | −1.02116 | −0.510578 | − | 0.859831i | \(-0.670569\pi\) | ||||
−0.510578 | + | 0.859831i | \(0.670569\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −50.9744 | −2.11842 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.30216 | −0.219971 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.0008 | −1.28392 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 51.7187 | 2.13830 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.2759 | 1.16707 | 0.583535 | − | 0.812088i | \(-0.301669\pi\) | ||||
0.583535 | + | 0.812088i | \(0.301669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.63130 | 0.190829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.0007 | −1.80995 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.9323 | −0.654260 | −0.327130 | − | 0.944979i | \(-0.606082\pi\) | ||||
−0.327130 | + | 0.944979i | \(0.606082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.8068 | 1.34495 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.9555 | −1.06229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.9491 | 1.67313 | 0.836567 | − | 0.547865i | \(-0.184559\pi\) | ||||
0.836567 | + | 0.547865i | \(0.184559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.2764 | −1.60212 | −0.801058 | − | 0.598587i | \(-0.795729\pi\) | ||||
−0.801058 | + | 0.598587i | \(0.795729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.32284 | −0.0538701 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −89.8320 | −3.65219 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.80079 | 0.194858 | 0.0974290 | − | 0.995242i | \(-0.468938\pi\) | ||||
0.0974290 | + | 0.995242i | \(0.468938\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.2453 | 0.455683 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.6379 | 1.32039 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.56017 | 0.345742 | 0.172871 | − | 0.984944i | \(-0.444696\pi\) | ||||
0.172871 | + | 0.984944i | \(0.444696\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.4178 | 1.06527 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.4421 | −0.863228 | −0.431614 | − | 0.902058i | \(-0.642056\pi\) | ||||
−0.431614 | + | 0.902058i | \(0.642056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.7723 | −0.473167 | −0.236584 | − | 0.971611i | \(-0.576028\pi\) | ||||
−0.236584 | + | 0.971611i | \(0.576028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.6171 | −1.95094 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.19920 | −0.168238 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.3317 | −0.733268 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −114.080 | −4.55591 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.9184 | 1.31254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.7998 | 1.46498 | 0.732489 | − | 0.680779i | \(-0.238359\pi\) | ||||
0.732489 | + | 0.680779i | \(0.238359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.6534 | −1.33760 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.4706 | 1.20919 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.70453 | −0.146779 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.1525 | 1.19281 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.1857 | 1.38975 | 0.694877 | − | 0.719129i | \(-0.255459\pi\) | ||||
0.694877 | + | 0.719129i | \(0.255459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3621 | −0.881874 | −0.440937 | − | 0.897538i | \(-0.645354\pi\) | ||||
−0.440937 | + | 0.897538i | \(0.645354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 77.4113 | 3.04807 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3698 | 0.486308 | 0.243154 | − | 0.969988i | \(-0.421818\pi\) | ||||
0.243154 | + | 0.969988i | \(0.421818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0158 | 0.864197 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.63126 | −0.220707 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.19397 | 0.164123 | 0.0820613 | − | 0.996627i | \(-0.473850\pi\) | ||||
0.0820613 | + | 0.996627i | \(0.473850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.9311 | −1.09136 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 64.4981 | 2.51631 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2209 | 0.709784 | 0.354892 | − | 0.934907i | \(-0.384518\pi\) | ||||
0.354892 | + | 0.934907i | \(0.384518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2704 | −0.827324 | −0.413662 | − | 0.910430i | \(-0.635751\pi\) | ||||
−0.413662 | + | 0.910430i | \(0.635751\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.7966 | 1.19604 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 62.7717 | 2.43418 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9290 | −0.500614 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.7235 | 0.955864 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.1942 | 0.586566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5656 | −0.600011 | −0.300005 | − | 0.953938i | \(-0.596988\pi\) | ||||
−0.300005 | + | 0.953938i | \(0.596988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 32.1323 | 1.23677 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.63298 | −0.216493 | −0.108247 | − | 0.994124i | \(-0.534524\pi\) | ||||
−0.108247 | + | 0.994124i | \(0.534524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.18236 | −0.0837513 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.5275 | 1.32310 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.67984 | 0.140805 | 0.0704026 | − | 0.997519i | \(-0.477572\pi\) | ||||
0.0704026 | + | 0.997519i | \(0.477572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62.7843 | −2.39886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.80868 | 0.374225 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.0128 | 0.610040 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.37801 | 0.242631 | 0.121316 | − | 0.992614i | \(-0.461289\pi\) | ||||
0.121316 | + | 0.992614i | \(0.461289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 85.8922 | 3.26277 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.5246 | −1.27166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.74078 | 0.368958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.9293 | −0.867265 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.3301 | 0.918936 | 0.459468 | − | 0.888194i | \(-0.348040\pi\) | ||||
0.459468 | + | 0.888194i | \(0.348040\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 62.9852 | 2.37553 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 95.8684 | 3.61061 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0242 | 0.452215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8738 | −0.708822 | −0.354411 | − | 0.935090i | \(-0.615319\pi\) | ||||
−0.354411 | + | 0.935090i | \(0.615319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.4346 | 1.40391 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.47441 | 0.242469 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 65.3258 | 2.44305 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.7074 | 1.70697 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.6619 | −1.70290 | −0.851450 | − | 0.524435i | \(-0.824276\pi\) | ||||
−0.851450 | + | 0.524435i | \(0.824276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.4035 | −1.65367 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.3511 | 1.79820 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.54513 | 0.317358 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.1174 | −1.41370 | −0.706849 | − | 0.707365i | \(-0.749884\pi\) | ||||
−0.706849 | + | 0.707365i | \(0.749884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.5981 | −1.61474 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.5431 | 1.05571 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.54071 | −0.130779 | −0.0653895 | − | 0.997860i | \(-0.520829\pi\) | ||||
−0.0653895 | + | 0.997860i | \(0.520829\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.8814 | −0.401368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.67088 | −0.0615475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2057 | 0.706495 | 0.353247 | − | 0.935530i | \(-0.385077\pi\) | ||||
0.353247 | + | 0.935530i | \(0.385077\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 58.9255 | 2.16468 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.96467 | 0.255509 | 0.127755 | − | 0.991806i | \(-0.459223\pi\) | ||||
0.127755 | + | 0.991806i | \(0.459223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 61.8827 | 2.26721 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.05289 | −0.331228 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.0827 | −0.916503 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2850 | 0.448288 | 0.224144 | − | 0.974556i | \(-0.428041\pi\) | ||||
0.224144 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8152 | 0.685663 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.6029 | −0.822604 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5894 | −0.493915 | −0.246958 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246958 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −159.480 | −5.78876 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.8241 | −1.44362 | −0.721811 | − | 0.692090i | \(-0.756690\pi\) | ||||
−0.721811 | + | 0.692090i | \(0.756690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.9793 | −1.08532 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56.0142 | 2.02520 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3718 | −0.410612 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0475 | −0.975358 | −0.487679 | − | 0.873023i | \(-0.662156\pi\) | ||||
−0.487679 | + | 0.873023i | \(0.662156\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 62.7346 | 2.25933 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.0712 | −0.542073 | −0.271036 | − | 0.962569i | \(-0.587366\pi\) | ||||
−0.271036 | + | 0.962569i | \(0.587366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.27911 | −0.153710 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −76.5846 | −2.74746 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.6378 | 0.667768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.0856 | 1.36281 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.39310 | 0.264208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −65.7732 | −2.34755 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.1114 | 1.00206 | 0.501032 | − | 0.865429i | \(-0.332954\pi\) | ||||
0.501032 | + | 0.865429i | \(0.332954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.1089 | 1.32111 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.1666 | −0.930378 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.84825 | −0.278699 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.0350 | 1.66816 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8844 | −0.491810 | −0.245905 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245905 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.3487 | 1.25055 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.16971 | −0.253329 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 81.4675 | 2.87493 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 87.7529 | 3.09288 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −79.2289 | −2.78899 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.5748 | 1.25074 | 0.625371 | − | 0.780327i | \(-0.284948\pi\) | ||||
0.625371 | + | 0.780327i | \(0.284948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.0995 | −0.811133 | −0.405567 | − | 0.914065i | \(-0.632926\pi\) | ||||
−0.405567 | + | 0.914065i | \(0.632926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −59.9595 | −2.10287 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.2725 | 1.34063 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.6138 | 1.91069 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −44.3658 | −1.55027 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.0963 | −0.736265 | −0.368132 | − | 0.929773i | \(-0.620003\pi\) | ||||
−0.368132 | + | 0.929773i | \(0.620003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7224 | −1.00120 | −0.500599 | − | 0.865679i | \(-0.666887\pi\) | ||||
−0.500599 | + | 0.865679i | \(0.666887\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 105.404 | 3.66971 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4860 | 0.955782 | 0.477891 | − | 0.878419i | \(-0.341401\pi\) | ||||
0.477891 | + | 0.878419i | \(0.341401\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.5174 | 0.886255 | 0.443127 | − | 0.896459i | \(-0.353869\pi\) | ||||
0.443127 | + | 0.896459i | \(0.353869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −75.3748 | −2.61472 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.01221 | −0.139015 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.04731 | −0.105457 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.70221 | −0.127967 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1427 | 0.522784 | 0.261392 | − | 0.965233i | \(-0.415819\pi\) | ||||
0.261392 | + | 0.965233i | \(0.415819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0339 | −0.932204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 70.4920 | 2.42787 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.55769 | 0.328795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 77.0605 | 2.64783 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −72.3275 | −2.48227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 88.0513 | 3.01836 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9554 | 0.409346 | 0.204673 | − | 0.978830i | \(-0.434387\pi\) | ||||
0.204673 | + | 0.978830i | \(0.434387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 107.176 | 3.66535 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.53741 | 0.325792 | 0.162896 | − | 0.986643i | \(-0.447917\pi\) | ||||
0.162896 | + | 0.986643i | \(0.447917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9007 | −0.747243 | −0.373621 | − | 0.927581i | \(-0.621884\pi\) | ||||
−0.373621 | + | 0.927581i | \(0.621884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.6619 | −0.772317 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.82525 | 0.266375 | 0.133187 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133187 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −82.7196 | −2.81255 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.3622 | −0.487765 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.2836 | 1.60399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.863056 | 0.0292435 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.72616 | −0.126111 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.4135 | −0.352040 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.9618 | 0.775365 | 0.387682 | − | 0.921793i | \(-0.373276\pi\) | ||||
0.387682 | + | 0.921793i | \(0.373276\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.1614 | 1.72563 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0701 | 0.440343 | 0.220171 | − | 0.975461i | \(-0.429338\pi\) | ||||
0.220171 | + | 0.975461i | \(0.429338\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.64794 | −0.190068 | −0.0950341 | − | 0.995474i | \(-0.530296\pi\) | ||||
−0.0950341 | + | 0.995474i | \(0.530296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −33.4028 | −1.12282 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.03708 | −0.0683985 | −0.0341992 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341992 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.1385 | −0.876658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.01089 | 0.0338661 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 67.6353 | 2.26333 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.8266 | −1.29783 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 82.3761 | 2.75046 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.984549 | −0.0328366 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.3428 | 0.577772 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −66.4057 | −2.20984 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −57.4679 | −1.91030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.0974 | −1.63025 | −0.815127 | − | 0.579282i | \(-0.803333\pi\) | ||||
−0.815127 | + | 0.579282i | \(0.803333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.5300 | 0.680938 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9150 | 0.792340 | 0.396170 | − | 0.918177i | \(-0.370339\pi\) | ||||
0.396170 | + | 0.918177i | \(0.370339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.4347 | −0.378433 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.0529 | −0.762106 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.9601 | 0.791232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0185 | 0.891260 | 0.445630 | − | 0.895217i | \(-0.352980\pi\) | ||||
0.445630 | + | 0.895217i | \(0.352980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.6345 | 0.449272 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.6723 | −0.647522 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.1954 | −1.91345 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −75.8145 | −2.49007 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.8916 | 0.587003 | 0.293501 | − | 0.955959i | \(-0.405179\pi\) | ||||
0.293501 | + | 0.955959i | \(0.405179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.67687 | −0.251599 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 48.1018 | 1.57478 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 70.7515 | 2.31382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2903 | −0.597519 | −0.298760 | − | 0.954328i | \(-0.596573\pi\) | ||||
−0.298760 | + | 0.954328i | \(0.596573\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.9884 | 0.652295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2134 | 0.528543 | 0.264272 | − | 0.964448i | \(-0.414869\pi\) | ||||
0.264272 | + | 0.964448i | \(0.414869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.0550 | 0.848469 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.1790 | −1.63232 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.25401 | 0.203228 | 0.101614 | − | 0.994824i | \(-0.467599\pi\) | ||||
0.101614 | + | 0.994824i | \(0.467599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.0803 | −1.36599 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −85.6247 | −2.77657 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.2420 | −0.590916 | −0.295458 | − | 0.955356i | \(-0.595472\pi\) | ||||
−0.295458 | + | 0.955356i | \(0.595472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −81.7647 | −2.64584 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.2518 | 0.783948 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.8582 | 1.73917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5070 | −0.984096 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.8262 | −1.38005 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.4894 | 1.94722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.35525 | 0.204371 | 0.102186 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102186 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.8197 | 2.05018 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 56.2895 | 1.80642 | 0.903208 | − | 0.429204i | \(-0.141206\pi\) | ||||
0.903208 | + | 0.429204i | \(0.141206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.7584 | 0.921952 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.4445 | −1.74362 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.3434 | 1.64262 | 0.821310 | − | 0.570482i | \(-0.193243\pi\) | ||||
0.821310 | + | 0.570482i | \(0.193243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.05606 | −0.289433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.1865 | −1.63426 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8340 | 0.441235 | 0.220617 | − | 0.975360i | \(-0.429193\pi\) | ||||
0.220617 | + | 0.975360i | \(0.429193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.2140 | 1.66368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −82.2387 | −2.61769 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 76.3484 | 2.42774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.41841 | −0.235653 | −0.117827 | − | 0.993034i | \(-0.537593\pi\) | ||||
−0.117827 | + | 0.993034i | \(0.537593\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.3659 | 0.646293 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.8004 | 0.976439 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.9777 | −1.07608 | −0.538042 | − | 0.842918i | \(-0.680836\pi\) | ||||
−0.538042 | + | 0.842918i | \(0.680836\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.3496 | −1.59299 |
(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 | 8048.2.a.v.1.26 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.3 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.3 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.26 | 28 | 1.1 | even | 1 | trivial |