Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 | ||||||||
\(3\) | 0.453475 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.43721 | 1.08995 | 0.544977 | − | 0.838451i | \(-0.316538\pi\) | ||||
0.544977 | + | 0.838451i | \(0.316538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.57711 | 0.596090 | 0.298045 | − | 0.954552i | \(-0.403665\pi\) | ||||
0.298045 | + | 0.954552i | \(0.403665\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79436 | −0.931453 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43482 | −0.432615 | −0.216307 | − | 0.976325i | \(-0.569401\pi\) | ||||
−0.216307 | + | 0.976325i | \(0.569401\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.06317 | −0.849569 | −0.424785 | − | 0.905294i | \(-0.639650\pi\) | ||||
−0.424785 | + | 0.905294i | \(0.639650\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.10521 | 0.285365 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.99994 | 0.917648 | 0.458824 | − | 0.888527i | \(-0.348271\pi\) | ||||
0.458824 | + | 0.888527i | \(0.348271\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.715178 | 0.156065 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.82452 | −1.42301 | −0.711505 | − | 0.702681i | \(-0.751986\pi\) | ||||
−0.711505 | + | 0.702681i | \(0.751986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.939999 | 0.188000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.62760 | −0.505682 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.52783 | −0.655101 | −0.327550 | − | 0.944834i | \(-0.606223\pi\) | ||||
−0.327550 | + | 0.944834i | \(0.606223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.83929 | 1.40798 | 0.703989 | − | 0.710211i | \(-0.251400\pi\) | ||||
0.703989 | + | 0.710211i | \(0.251400\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.650656 | −0.113265 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.84374 | 0.649711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.03921 | −0.992839 | −0.496420 | − | 0.868083i | \(-0.665352\pi\) | ||||
−0.496420 | + | 0.868083i | \(0.665352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.38907 | −0.222429 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.39294 | 0.217540 | 0.108770 | − | 0.994067i | \(-0.465309\pi\) | ||||
0.108770 | + | 0.994067i | \(0.465309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.98117 | 1.21712 | 0.608559 | − | 0.793509i | \(-0.291748\pi\) | ||||
0.608559 | + | 0.793509i | \(0.291748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.81045 | −1.01524 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.67044 | −1.26471 | −0.632357 | − | 0.774677i | \(-0.717912\pi\) | ||||
−0.632357 | + | 0.774677i | \(0.717912\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.51274 | −0.644677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.453475 | −0.0634992 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.22706 | 0.168550 | 0.0842750 | − | 0.996443i | \(-0.473143\pi\) | ||||
0.0842750 | + | 0.996443i | \(0.473143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.49696 | −0.471530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.81387 | 0.240253 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68615 | 0.728036 | 0.364018 | − | 0.931392i | \(-0.381405\pi\) | ||||
0.364018 | + | 0.931392i | \(0.381405\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.40700 | −0.555230 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.46558 | −0.925992 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.05183 | −0.617179 | −0.308589 | − | 0.951195i | \(-0.599857\pi\) | ||||
−0.308589 | + | 0.951195i | \(0.599857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.09475 | −0.372564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.31175 | 0.393033 | 0.196516 | − | 0.980501i | \(-0.437037\pi\) | ||||
0.196516 | + | 0.980501i | \(0.437037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.07942 | 0.360419 | 0.180209 | − | 0.983628i | \(-0.442322\pi\) | ||||
0.180209 | + | 0.983628i | \(0.442322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.426266 | 0.0492210 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.26286 | −0.257877 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.6823 | −1.65189 | −0.825946 | − | 0.563749i | \(-0.809359\pi\) | ||||
−0.825946 | + | 0.563749i | \(0.809359\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.19153 | 0.799059 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.49480 | −0.273840 | −0.136920 | − | 0.990582i | \(-0.543720\pi\) | ||||
−0.136920 | + | 0.990582i | \(0.543720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.43721 | −0.264353 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.59978 | −0.171515 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.8134 | 1.57022 | 0.785109 | − | 0.619357i | \(-0.212607\pi\) | ||||
0.785109 | + | 0.619357i | \(0.212607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.83094 | −0.506420 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.55492 | 0.368628 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.74869 | 1.00019 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.8517 | −1.60949 | −0.804746 | − | 0.593620i | \(-0.797698\pi\) | ||||
−0.804746 | + | 0.593620i | \(0.797698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00941 | 0.402961 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4735 | −1.14166 | −0.570828 | − | 0.821070i | \(-0.693378\pi\) | ||||
−0.570828 | + | 0.821070i | \(0.693378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.2243 | −1.50010 | −0.750049 | − | 0.661383i | \(-0.769970\pi\) | ||||
−0.750049 | + | 0.661383i | \(0.769970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.74304 | 0.170103 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0961 | 1.55607 | 0.778035 | − | 0.628221i | \(-0.216217\pi\) | ||||
0.778035 | + | 0.628221i | \(0.216217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.86840 | −0.657873 | −0.328937 | − | 0.944352i | \(-0.606690\pi\) | ||||
−0.328937 | + | 0.944352i | \(0.606690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.73863 | −0.259939 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.61190 | 0.904211 | 0.452106 | − | 0.891964i | \(-0.350673\pi\) | ||||
0.452106 | + | 0.891964i | \(0.350673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.6328 | −1.55102 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.55959 | 0.791334 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.57711 | −0.144573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.94129 | −0.812844 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.631662 | 0.0569551 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.89508 | −0.885043 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6578 | −1.65561 | −0.827807 | − | 0.561013i | \(-0.810412\pi\) | ||||
−0.827807 | + | 0.561013i | \(0.810412\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.61926 | 0.318658 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6672 | −0.931994 | −0.465997 | − | 0.884786i | \(-0.654304\pi\) | ||||
−0.465997 | + | 0.884786i | \(0.654304\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.30832 | 0.547001 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.40401 | −0.551170 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8766 | −1.27099 | −0.635497 | − | 0.772103i | \(-0.719205\pi\) | ||||
−0.635497 | + | 0.772103i | \(0.719205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.9484 | −1.69200 | −0.845999 | − | 0.533184i | \(-0.820995\pi\) | ||||
−0.845999 | + | 0.533184i | \(0.820995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.93183 | −0.331120 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.39509 | 0.367536 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.59806 | −0.714030 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.04641 | −0.168785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.4861 | 0.940976 | 0.470488 | − | 0.882406i | \(-0.344078\pi\) | ||||
0.470488 | + | 0.882406i | \(0.344078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0206329 | −0.00167908 | −0.000839542 | − | 1.00000i | \(-0.500267\pi\) | ||||
−0.000839542 | 1.00000i | \(0.500267\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.79436 | 0.225911 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.1060 | 1.53463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.61670 | 0.208835 | 0.104418 | − | 0.994534i | \(-0.466702\pi\) | ||||
0.104418 | + | 0.994534i | \(0.466702\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.556442 | 0.0441288 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.7630 | −0.848242 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.5424 | −1.37403 | −0.687013 | − | 0.726645i | \(-0.741079\pi\) | ||||
−0.687013 | + | 0.726645i | \(0.741079\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.58579 | −0.123453 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6026 | 1.43951 | 0.719756 | − | 0.694227i | \(-0.244254\pi\) | ||||
0.719756 | + | 0.694227i | \(0.244254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.61701 | −0.278232 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1773 | −0.854747 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.9698 | 1.82239 | 0.911193 | − | 0.411979i | \(-0.135162\pi\) | ||||
0.911193 | + | 0.411979i | \(0.135162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.48248 | 0.112065 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.453475 | −0.0340853 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.49846 | −0.485718 | −0.242859 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242859 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6417 | −0.790989 | −0.395494 | − | 0.918468i | \(-0.629427\pi\) | ||||
−0.395494 | + | 0.918468i | \(0.629427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.57853 | 0.190610 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.7188 | −1.08215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.43482 | 0.104924 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.14400 | −0.301432 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.36528 | −0.460576 | −0.230288 | − | 0.973123i | \(-0.573967\pi\) | ||||
−0.230288 | + | 0.973123i | \(0.573967\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9200 | 1.28991 | 0.644956 | − | 0.764220i | \(-0.276876\pi\) | ||||
0.644956 | + | 0.764220i | \(0.276876\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.38546 | −0.242438 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9517 | −0.851522 | −0.425761 | − | 0.904836i | \(-0.639993\pi\) | ||||
−0.425761 | + | 0.904836i | \(0.639993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.46122 | −0.670688 | −0.335344 | − | 0.942096i | \(-0.608853\pi\) | ||||
−0.335344 | + | 0.942096i | \(0.608853\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.29088 | −0.161586 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.56375 | −0.390499 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.39488 | 0.237109 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.0702 | 1.32547 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.73919 | −0.396988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2497 | −0.912149 | −0.456074 | − | 0.889942i | \(-0.650745\pi\) | ||||
−0.456074 | + | 0.889942i | \(0.650745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.50180 | 0.102901 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.4518 | 1.32660 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3634 | 0.839281 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.39644 | 0.0943627 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.06317 | 0.206051 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8774 | 1.53199 | 0.765993 | − | 0.642849i | \(-0.222248\pi\) | ||||
0.765993 | + | 0.642849i | \(0.222248\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.62670 | −0.175113 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.94528 | −0.527347 | −0.263673 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263673 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4559 | 0.955271 | 0.477635 | − | 0.878558i | \(-0.341494\pi\) | ||||
0.477635 | + | 0.878558i | \(0.341494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02615 | −0.0675159 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.71087 | −0.243107 | −0.121554 | − | 0.992585i | \(-0.538788\pi\) | ||||
−0.121554 | + | 0.992585i | \(0.538788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1317 | −1.37848 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.65808 | −0.432489 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5117 | −1.00337 | −0.501685 | − | 0.865050i | \(-0.667286\pi\) | ||||
−0.501685 | + | 0.865050i | \(0.667286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.60096 | −0.360790 | −0.180395 | − | 0.983594i | \(-0.557738\pi\) | ||||
−0.180395 | + | 0.983594i | \(0.557738\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.1440 | 0.714886 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.9985 | −0.702668 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.2525 | −0.779606 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.13133 | −0.0716951 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.03446 | −0.128414 | −0.0642069 | − | 0.997937i | \(-0.520452\pi\) | ||||
−0.0642069 | + | 0.997937i | \(0.520452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.79196 | 0.615615 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.10521 | −0.0692112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7256 | −0.856177 | −0.428088 | − | 0.903737i | \(-0.640813\pi\) | ||||
−0.428088 | + | 0.903737i | \(0.640813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.52447 | −0.591822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.85802 | 0.610196 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.8680 | 1.22511 | 0.612557 | − | 0.790427i | \(-0.290141\pi\) | ||||
0.612557 | + | 0.790427i | \(0.290141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.99061 | 0.183712 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.71751 | 0.411105 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.6357 | −0.709441 | −0.354721 | − | 0.934972i | \(-0.615424\pi\) | ||||
−0.354721 | + | 0.934972i | \(0.615424\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5163 | −1.18553 | −0.592765 | − | 0.805376i | \(-0.701964\pi\) | ||||
−0.592765 | + | 0.805376i | \(0.701964\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.19071 | −0.132588 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.34873 | −0.0813315 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3188 | 0.680079 | 0.340040 | − | 0.940411i | \(-0.389560\pi\) | ||||
0.340040 | + | 0.940411i | \(0.389560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.9058 | −1.31147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4310 | −0.980193 | −0.490096 | − | 0.871668i | \(-0.663038\pi\) | ||||
−0.490096 | + | 0.871668i | \(0.663038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.8720 | 1.06238 | 0.531190 | − | 0.847253i | \(-0.321745\pi\) | ||||
0.531190 | + | 0.847253i | \(0.321745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.42079 | 0.261865 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19681 | 0.129674 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.18833 | −0.421387 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.884128 | −0.0516513 | −0.0258257 | − | 0.999666i | \(-0.508221\pi\) | ||||
−0.0258257 | + | 0.999666i | \(0.508221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.43721 | −0.141900 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.77013 | 0.218765 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.9046 | 1.20895 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5872 | 0.725511 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.20295 | −0.298902 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.8583 | 0.793526 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.0731 | 1.37392 | 0.686961 | − | 0.726694i | \(-0.258944\pi\) | ||||
0.686961 | + | 0.726694i | \(0.258944\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.90385 | −0.392746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7987 | −1.23609 | −0.618046 | − | 0.786142i | \(-0.712075\pi\) | ||||
−0.618046 | + | 0.786142i | \(0.712075\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5090 | 1.83752 | 0.918758 | − | 0.394820i | \(-0.129193\pi\) | ||||
0.918758 | + | 0.394820i | \(0.129193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.7408 | −0.605175 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6868 | 0.768728 | 0.384364 | − | 0.923182i | \(-0.374421\pi\) | ||||
0.384364 | + | 0.923182i | \(0.374421\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.06180 | 0.283406 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.29919 | 0.407401 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.99994 | −0.222562 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.87937 | −0.159719 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.11465 | −0.172240 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6742 | −0.753883 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.58772 | −0.197199 | −0.0985994 | − | 0.995127i | \(-0.531436\pi\) | ||||
−0.0985994 | + | 0.995127i | \(0.531436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.8757 | 0.924784 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.3124 | −0.672697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1021 | 1.63977 | 0.819884 | − | 0.572529i | \(-0.194038\pi\) | ||||
0.819884 | + | 0.572529i | \(0.194038\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.35876 | 0.236735 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2480 | −0.609112 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1568 | −0.980375 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.54256 | −0.406078 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.0184 | −1.77252 | −0.886260 | − | 0.463187i | \(-0.846706\pi\) | ||||
−0.886260 | + | 0.463187i | \(0.846706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4164 | 1.30698 | 0.653490 | − | 0.756936i | \(-0.273304\pi\) | ||||
0.653490 | + | 0.756936i | \(0.273304\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.04877 | 0.429612 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.87403 | −0.0997445 | −0.0498722 | − | 0.998756i | \(-0.515881\pi\) | ||||
−0.0498722 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.07144 | 0.428388 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.715178 | −0.0378512 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.04466 | 0.107913 | 0.0539565 | − | 0.998543i | \(-0.482817\pi\) | ||||
0.0539565 | + | 0.998543i | \(0.482817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00051 | −0.157922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.05465 | −0.212814 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.50519 | 0.392840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.1148 | −1.25878 | −0.629390 | − | 0.777089i | \(-0.716695\pi\) | ||||
−0.629390 | + | 0.777089i | \(0.716695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.89237 | −0.202629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.93521 | 0.100471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.3010 | −1.10292 | −0.551462 | − | 0.834200i | \(-0.685930\pi\) | ||||
−0.551462 | + | 0.834200i | \(0.685930\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.48717 | −0.231717 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8063 | 0.556554 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9252 | 0.715292 | 0.357646 | − | 0.933857i | \(-0.383580\pi\) | ||||
0.357646 | + | 0.933857i | \(0.383580\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.46086 | −0.433463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.48053 | −0.126749 | −0.0633745 | − | 0.997990i | \(-0.520186\pi\) | ||||
−0.0633745 | + | 0.997990i | \(0.520186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.51508 | −0.281074 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.3023 | −1.13369 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.4212 | 1.39031 | 0.695154 | − | 0.718861i | \(-0.255336\pi\) | ||||
0.695154 | + | 0.718861i | \(0.255336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82452 | 0.345131 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.83729 | −0.244009 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.7840 | −1.80049 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.07589 | 0.254751 | 0.127376 | − | 0.991855i | \(-0.459345\pi\) | ||||
0.127376 | + | 0.991855i | \(0.459345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.86067 | 0.143212 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6730 | 0.882546 | 0.441273 | − | 0.897373i | \(-0.354527\pi\) | ||||
0.441273 | + | 0.897373i | \(0.354527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0130 | −1.19617 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.5273 | 0.870938 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.66518 | 0.429517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5746 | 1.11624 | 0.558121 | − | 0.829760i | \(-0.311523\pi\) | ||||
0.558121 | + | 0.829760i | \(0.311523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.74617 | −0.332764 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.57711 | −0.0776043 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.08035 | −0.298473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.04609 | −0.442989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.3638 | 0.506304 | 0.253152 | − | 0.967427i | \(-0.418533\pi\) | ||||
0.253152 | + | 0.967427i | \(0.418533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.64460 | −0.177627 | −0.0888136 | − | 0.996048i | \(-0.528308\pi\) | ||||
−0.0888136 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.2283 | 1.17802 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.939999 | −0.0455967 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.96765 | 0.433975 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.99307 | 0.0962261 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.3289 | 0.931043 | 0.465521 | − | 0.885037i | \(-0.345867\pi\) | ||||
0.465521 | + | 0.885037i | \(0.345867\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8067 | −1.43242 | −0.716209 | − | 0.697885i | \(-0.754124\pi\) | ||||
−0.716209 | + | 0.697885i | \(0.754124\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.89901 | −0.186943 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.2976 | −1.30582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0908 | 1.34070 | 0.670350 | − | 0.742045i | \(-0.266144\pi\) | ||||
0.670350 | + | 0.742045i | \(0.266144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.6102 | 0.600487 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.28491 | 0.108559 | 0.0542797 | − | 0.998526i | \(-0.482714\pi\) | ||||
0.0542797 | + | 0.998526i | \(0.482714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.1034 | 1.71147 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.20865 | 0.246361 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.1490 | 0.809312 | 0.404656 | − | 0.914469i | \(-0.367391\pi\) | ||||
0.404656 | + | 0.914469i | \(0.367391\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.99862 | −0.0941111 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.00935652 | −0.000439608 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.7740 | −0.551974 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.30477 | 0.388481 | 0.194240 | − | 0.980954i | \(-0.437776\pi\) | ||||
0.194240 | + | 0.980954i | \(0.437776\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.62760 | 0.122646 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.1785 | 1.40555 | 0.702776 | − | 0.711411i | \(-0.251944\pi\) | ||||
0.702776 | + | 0.711411i | \(0.251944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.36001 | 0.388523 | 0.194261 | − | 0.980950i | \(-0.437769\pi\) | ||||
0.194261 | + | 0.980950i | \(0.437769\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.66410 | 0.401788 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.57523 | 0.0728929 | 0.0364464 | − | 0.999336i | \(-0.488396\pi\) | ||||
0.0364464 | + | 0.999336i | \(0.488396\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.96726 | −0.367894 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.18661 | 0.0546760 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4516 | −0.526543 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.75994 | 0.172518 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.42885 | −0.156996 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.8890 | −0.908754 | −0.454377 | − | 0.890810i | \(-0.650138\pi\) | ||||
−0.454377 | + | 0.890810i | \(0.650138\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.4991 | 0.843486 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.88075 | −0.222082 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −38.6338 | −1.75427 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.1816 | −1.36766 | −0.683830 | − | 0.729642i | \(-0.739687\pi\) | ||||
−0.683830 | + | 0.729642i | \(0.739687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.95504 | −0.359739 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9373 | 0.628981 | 0.314491 | − | 0.949261i | \(-0.398166\pi\) | ||||
0.314491 | + | 0.949261i | \(0.398166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.52783 | 0.158885 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.77177 | 0.439208 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.22298 | 0.234283 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7489 | −0.749784 | −0.374892 | − | 0.927068i | \(-0.622320\pi\) | ||||
−0.374892 | + | 0.927068i | \(0.622320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.43582 | 0.376885 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.9450 | 1.78106 | 0.890530 | − | 0.454925i | \(-0.150334\pi\) | ||||
0.890530 | + | 0.454925i | \(0.150334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.9634 | −1.24435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.64023 | −0.0728450 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.8624 | 0.658764 | 0.329382 | − | 0.944197i | \(-0.393160\pi\) | ||||
0.329382 | + | 0.944197i | \(0.393160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.85657 | 0.214842 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.5102 | −0.464038 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.1049 | −1.63504 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4405 | 0.547134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.8697 | 0.477126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.2768 | −1.32645 | −0.663226 | − | 0.748419i | \(-0.730813\pi\) | ||||
−0.663226 | + | 0.748419i | \(0.730813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.87499 | 0.388076 | 0.194038 | − | 0.980994i | \(-0.437841\pi\) | ||||
0.194038 | + | 0.980994i | \(0.437841\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.672267 | 0.0293401 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.83929 | −0.341485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.5740 | 1.02496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.79436 | 0.121265 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.26680 | −0.184816 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.2296 | 1.69605 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.94689 | −0.127168 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.47497 | 0.278897 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.49305 | 0.193171 | 0.0965857 | − | 0.995325i | \(-0.469208\pi\) | ||||
0.0965857 | + | 0.995325i | \(0.469208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.82573 | −0.207092 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.7397 | −0.717052 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0040 | −1.53942 | −0.769710 | − | 0.638394i | \(-0.779599\pi\) | ||||
−0.769710 | + | 0.638394i | \(0.779599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.8891 | −0.678132 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1111 | −0.601152 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.1556 | −0.984676 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.67462 | −0.283322 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0897 | −0.512259 | −0.256129 | − | 0.966643i | \(-0.582447\pi\) | ||||
−0.256129 | + | 0.966643i | \(0.582447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.4477 | −1.03403 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.650656 | 0.0274707 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.8784 | 1.04850 | 0.524250 | − | 0.851565i | \(-0.324346\pi\) | ||||
0.524250 | + | 0.851565i | \(0.324346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.4262 | 0.985549 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.3418 | 0.476311 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.46486 | −0.187177 | −0.0935884 | − | 0.995611i | \(-0.529834\pi\) | ||||
−0.0935884 | + | 0.995611i | \(0.529834\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.29575 | −0.389015 | −0.194508 | − | 0.980901i | \(-0.562311\pi\) | ||||
−0.194508 | + | 0.980901i | \(0.562311\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.88650 | −0.120585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.41504 | −0.267526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7856 | 0.906948 | 0.453474 | − | 0.891269i | \(-0.350184\pi\) | ||||
0.453474 | + | 0.891269i | \(0.350184\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.12629 | 0.337717 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.93456 | −0.163233 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.76061 | −0.0729172 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.8615 | 0.862518 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.8082 | 0.817574 | 0.408787 | − | 0.912630i | \(-0.365952\pi\) | ||||
0.408787 | + | 0.912630i | \(0.365952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3567 | 1.29203 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.41979 | −0.222940 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.36921 | 0.179422 | 0.0897111 | − | 0.995968i | \(-0.471406\pi\) | ||||
0.0897111 | + | 0.995968i | \(0.471406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.84374 | −0.157578 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.29043 | −0.175596 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.4978 | −0.674082 | −0.337041 | − | 0.941490i | \(-0.609426\pi\) | ||||
−0.337041 | + | 0.941490i | \(0.609426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6233 | −0.678080 | −0.339040 | − | 0.940772i | \(-0.610102\pi\) | ||||
−0.339040 | + | 0.940772i | \(0.610102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.1166 | 0.574873 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.7918 | −0.885963 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3661 | −0.583100 | −0.291550 | − | 0.956556i | \(-0.594171\pi\) | ||||
−0.291550 | + | 0.956556i | \(0.594171\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.52302 | −0.102238 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.5590 | 1.07446 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.3099 | −1.70888 | −0.854440 | − | 0.519551i | \(-0.826099\pi\) | ||||
−0.854440 | + | 0.519551i | \(0.826099\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.53949 | 0.0620784 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.74462 | −0.0702356 | −0.0351178 | − | 0.999383i | \(-0.511181\pi\) | ||||
−0.0351178 | + | 0.999383i | \(0.511181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.61399 | −0.386419 | −0.193209 | − | 0.981158i | \(-0.561890\pi\) | ||||
−0.193209 | + | 0.981158i | \(0.561890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.9321 | 0.719590 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.3623 | 0.935991 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8164 | −1.15266 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.60258 | −0.103937 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.03921 | 0.240799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.1841 | −1.00256 | −0.501282 | − | 0.865284i | \(-0.667138\pi\) | ||||
−0.501282 | + | 0.865284i | \(0.667138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00842 | −0.238813 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −45.4731 | −1.80454 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8233 | 0.547698 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.25423 | −0.366092 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.0536 | −1.85851 | −0.929253 | − | 0.369445i | \(-0.879548\pi\) | ||||
−0.929253 | + | 0.369445i | \(0.879548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.71605 | −0.0676746 | −0.0338373 | − | 0.999427i | \(-0.510773\pi\) | ||||
−0.0338373 | + | 0.999427i | \(0.510773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.82091 | 0.347323 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.87748 | 0.231068 | 0.115534 | − | 0.993304i | \(-0.463142\pi\) | ||||
0.115534 | + | 0.993304i | \(0.463142\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.43482 | 0.0563216 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.60649 | 0.219736 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.6602 | 0.612832 | 0.306416 | − | 0.951898i | \(-0.400870\pi\) | ||||
0.306416 | + | 0.951898i | \(0.400870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.9981 | −1.01583 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.60501 | −0.335713 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3607 | 0.442549 | 0.221274 | − | 0.975212i | \(-0.428978\pi\) | ||||
0.221274 | + | 0.975212i | \(0.428978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.2976 | −1.60629 | −0.803146 | − | 0.595782i | \(-0.796842\pi\) | ||||
−0.803146 | + | 0.595782i | \(0.796842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.38907 | 0.0539470 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.3747 | 0.596206 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0757 | 0.932215 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3743 | 0.401095 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.15860 | −0.314959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.5471 | −1.02331 | −0.511657 | − | 0.859190i | \(-0.670968\pi\) | ||||
−0.511657 | + | 0.859190i | \(0.670968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.46994 | −0.0950681 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.4424 | 1.47746 | 0.738731 | − | 0.674000i | \(-0.235425\pi\) | ||||
0.738731 | + | 0.674000i | \(0.235425\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9997 | −0.959401 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.60299 | −0.138067 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.1923 | −1.15528 | −0.577638 | − | 0.816293i | \(-0.696026\pi\) | ||||
−0.577638 | + | 0.816293i | \(0.696026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.2574 | −1.38532 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.55538 | 0.250103 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.75870 | −0.143195 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.49880 | 0.323309 | 0.161655 | − | 0.986847i | \(-0.448317\pi\) | ||||
0.161655 | + | 0.986847i | \(0.448317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.32326 | 0.240201 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −48.6184 | −1.84420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.39294 | −0.0527613 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.68279 | −0.0636489 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6404 | −1.15727 | −0.578637 | − | 0.815585i | \(-0.696415\pi\) | ||||
−0.578637 | + | 0.815585i | \(0.696415\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.1564 | −0.911077 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.58270 | −0.360905 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.0949 | −0.680530 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.0445 | −1.09079 | −0.545395 | − | 0.838179i | \(-0.683620\pi\) | ||||
−0.545395 | + | 0.838179i | \(0.683620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.0278 | 1.53866 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.4994 | −2.00357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7118 | 0.400598 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.03418 | −0.262696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.2759 | −1.91227 | −0.956134 | − | 0.292930i | \(-0.905370\pi\) | ||||
−0.956134 | + | 0.292930i | \(0.905370\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0104 | −0.894193 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.53990 | −0.0944598 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.31615 | −0.123159 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.4988 | 1.65037 | 0.825185 | − | 0.564862i | \(-0.191071\pi\) | ||||
0.825185 | + | 0.564862i | \(0.191071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.5211 | −0.611892 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.98117 | −0.295194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.7666 | −1.13639 | −0.568195 | − | 0.822894i | \(-0.692358\pi\) | ||||
−0.568195 | + | 0.822894i | \(0.692358\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.98755 | −0.183968 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.24847 | 0.267001 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.24740 | −0.119458 | −0.0597288 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597288 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.55619 | −0.204112 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0248 | 1.39500 | 0.697498 | − | 0.716587i | \(-0.254297\pi\) | ||||
0.697498 | + | 0.716587i | \(0.254297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.9940 | 1.02562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.97137 | 0.255069 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.3853 | 0.927558 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.1695 | −0.735996 | −0.367998 | − | 0.929827i | \(-0.619957\pi\) | ||||
−0.367998 | + | 0.929827i | \(0.619957\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.922576 | −0.0336206 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0502868 | −0.00183012 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1157 | 0.658425 | 0.329213 | − | 0.944256i | \(-0.393217\pi\) | ||||
0.329213 | + | 0.944256i | \(0.393217\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.44041 | 0.161177 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.8732 | 1.62665 | 0.813327 | − | 0.581807i | \(-0.197654\pi\) | ||||
0.813327 | + | 0.581807i | \(0.197654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8322 | −0.392152 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.81045 | 0.246232 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.06317 | 0.110605 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.9293 | −0.790790 | −0.395395 | − | 0.918511i | \(-0.629392\pi\) | ||||
−0.395395 | + | 0.918511i | \(0.629392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.22420 | −0.224159 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.1495 | 0.580858 | 0.290429 | − | 0.956897i | \(-0.406202\pi\) | ||||
0.290429 | + | 0.956897i | \(0.406202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.36893 | 0.264700 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.31911 | −0.154947 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.57166 | 0.199625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.75177 | −0.170032 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.26971 | 0.331272 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.37745 | 0.227621 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.3748 | 1.61744 | 0.808718 | − | 0.588196i | \(-0.200162\pi\) | ||||
0.808718 | + | 0.588196i | \(0.200162\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.00965 | 0.320752 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1590 | 0.538991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.4176 | −0.618517 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.35617 | 0.0480983 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.6951 | −1.58318 | −0.791592 | − | 0.611050i | \(-0.790747\pi\) | ||||
−0.791592 | + | 0.611050i | \(0.790747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.67044 | 0.306738 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −41.3940 | −1.46259 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.41841 | −0.155922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.2317 | −0.924545 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.27650 | −0.185742 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.56691 | 0.301197 | 0.150598 | − | 0.988595i | \(-0.451880\pi\) | ||||
0.150598 | + | 0.988595i | \(0.451880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.1858 | −1.48134 | −0.740671 | − | 0.671868i | \(-0.765492\pi\) | ||||
−0.740671 | + | 0.671868i | \(0.765492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.85015 | −0.310388 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.7545 | −1.49763 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.9242 | 1.11689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.4994 | 0.471706 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.6151 | −0.789273 | −0.394636 | − | 0.918837i | \(-0.629129\pi\) | ||||
−0.394636 | + | 0.918837i | \(0.629129\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.32448 | 0.325031 | 0.162515 | − | 0.986706i | \(-0.448039\pi\) | ||||
0.162515 | + | 0.986706i | \(0.448039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.611616 | −0.0212937 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.4618 | −1.02449 | −0.512244 | − | 0.858840i | \(-0.671186\pi\) | ||||
−0.512244 | + | 0.858840i | \(0.671186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7991 | 0.722381 | 0.361191 | − | 0.932492i | \(-0.382370\pi\) | ||||
0.361191 | + | 0.932492i | \(0.382370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.13278 | 0.178054 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.51274 | 0.156357 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.3385 | 1.56900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.5985 | −0.711988 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.3721 | 1.22118 | 0.610590 | − | 0.791947i | \(-0.290932\pi\) | ||||
0.610590 | + | 0.791947i | \(0.290932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5544 | −0.570843 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.45106 | −0.256628 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.81543 | −0.303260 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1014 | −0.484528 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.10451 | 0.278146 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.2147 | 1.41282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.3840 | 0.492498 | 0.246249 | − | 0.969207i | \(-0.420802\pi\) | ||||
0.246249 | + | 0.969207i | \(0.420802\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.2414 | −0.931635 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.6732 | 1.42353 | 0.711765 | − | 0.702418i | \(-0.247896\pi\) | ||||
0.711765 | + | 0.702418i | \(0.247896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.4605 | 1.51697 | 0.758487 | − | 0.651688i | \(-0.225939\pi\) | ||||
0.758487 | + | 0.651688i | \(0.225939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.996198 | 0.0339503 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.1056 | −0.446121 | −0.223061 | − | 0.974805i | \(-0.571605\pi\) | ||||
−0.223061 | + | 0.974805i | \(0.571605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.4194 | 1.98632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.453475 | 0.0154008 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0665 | 0.714633 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4746 | 0.524336 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 44.2952 | 1.49917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6056 | −0.527565 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.6575 | 1.37291 | 0.686454 | − | 0.727174i | \(-0.259166\pi\) | ||||
0.686454 | + | 0.727174i | \(0.259166\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.400930 | −0.0135230 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.7742 | 0.632518 | 0.316259 | − | 0.948673i | \(-0.397573\pi\) | ||||
0.316259 | + | 0.948673i | \(0.397573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.0066 | −1.78381 | −0.891907 | − | 0.452219i | \(-0.850632\pi\) | ||||
−0.891907 | + | 0.452219i | \(0.850632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.10521 | −0.0371514 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.8268 | −1.00148 | −0.500742 | − | 0.865596i | \(-0.666940\pi\) | ||||
−0.500742 | + | 0.865596i | \(0.666940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.4254 | −0.986895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.3186 | −0.345685 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.6812 | −1.16056 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.8381 | −0.529410 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.47973 | 0.316519 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.6556 | −0.922367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.22706 | −0.0408794 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.70796 | 0.189949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.9360 | −0.862142 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.9145 | −0.462025 | −0.231012 | − | 0.972951i | \(-0.574204\pi\) | ||||
−0.231012 | + | 0.972951i | \(0.574204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.0611 | 1.06340 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.0797 | −1.12911 | −0.564556 | − | 0.825395i | \(-0.690953\pi\) | ||||
−0.564556 | + | 0.825395i | \(0.690953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.57959 | 0.118467 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.28441 | 0.207756 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.8232 | −0.555552 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.3312 | 1.00054 | 0.500268 | − | 0.865871i | \(-0.333235\pi\) | ||||
0.500268 | + | 0.865871i | \(0.333235\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9165 | 0.359712 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.1445 | −0.333909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.67685 | −0.186654 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 42.5422 | 1.39727 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.9229 | 1.70354 | 0.851768 | − | 0.523919i | \(-0.175531\pi\) | ||||
0.851768 | + | 0.523919i | \(0.175531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0507 | −0.591587 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.88517 | −0.323626 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.49696 | 0.114363 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.2471 | 1.44549 | 0.722745 | − | 0.691115i | \(-0.242880\pi\) | ||||
0.722745 | + | 0.691115i | \(0.242880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.7420 | 0.481088 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.5218 | 1.45137 | 0.725684 | − | 0.688028i | \(-0.241524\pi\) | ||||
0.725684 | + | 0.688028i | \(0.241524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.50612 | −0.309562 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.0998 | −0.328547 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.36074 | −0.141705 | −0.0708524 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708524 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.43277 | −0.306201 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.20663 | 0.201264 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.1795 | 1.33393 | 0.666967 | − | 0.745087i | \(-0.267592\pi\) | ||||
0.666967 | + | 0.745087i | \(0.267592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5135 | −0.502006 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.29540 | 0.0741997 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.4620 | −0.757626 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.4545 | 0.982402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.9783 | −1.44941 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.6749 | 1.40594 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.1059 | −0.903826 | −0.451913 | − | 0.892062i | \(-0.649258\pi\) | ||||
−0.451913 | + | 0.892062i | \(0.649258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.81387 | −0.0582700 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.54825 | 0.0496857 | 0.0248428 | − | 0.999691i | \(-0.492091\pi\) | ||||
0.0248428 | + | 0.999691i | \(0.492091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.4607 | −1.00858 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.30572 | −0.0418167 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.7224 | 1.20685 | 0.603423 | − | 0.797421i | \(-0.293803\pi\) | ||||
0.603423 | + | 0.797421i | \(0.293803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.2546 | −0.679300 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.1928 | 0.612778 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.83845 | 0.154323 | 0.0771614 | − | 0.997019i | \(-0.475414\pi\) | ||||
0.0771614 | + | 0.997019i | \(0.475414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.1288 | −0.928119 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.20091 | −0.197377 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54.4676 | −1.73197 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.16037 | 0.195691 | 0.0978454 | − | 0.995202i | \(-0.468805\pi\) | ||||
0.0978454 | + | 0.995202i | \(0.468805\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.62694 | −0.0516294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.0590 | −0.731020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.3698 | −0.993491 | −0.496745 | − | 0.867896i | \(-0.665472\pi\) | ||||
−0.496745 | + | 0.867896i | \(0.665472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.8686 | 0.502061 |
(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 | 8024.2.a.y.1.14 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.y.1.14 | ✓ | 23 | 1.1 | even | 1 | trivial |