Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.942656 | 0.666558 | 0.333279 | − | 0.942828i | \(-0.391845\pi\) | ||||
0.333279 | + | 0.942828i | \(0.391845\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.11140 | −0.555700 | ||||||||
\(5\) | 2.02754 | 0.906745 | 0.453372 | − | 0.891321i | \(-0.350221\pi\) | ||||
0.453372 | + | 0.891321i | \(0.350221\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.93298 | −1.03696 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.91127 | 0.604398 | ||||||||
\(11\) | 0.393608 | 0.118677 | 0.0593387 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593387 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52460 | −0.422847 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(14\) | −0.942656 | −0.251935 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.541991 | −0.135498 | ||||||||
\(17\) | −7.22498 | −1.75232 | −0.876158 | − | 0.482025i | \(-0.839902\pi\) | ||||
−0.876158 | + | 0.482025i | \(0.839902\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.33043 | 1.22288 | 0.611442 | − | 0.791289i | \(-0.290590\pi\) | ||||
0.611442 | + | 0.791289i | \(0.290590\pi\) | |||||||
\(20\) | −2.25341 | −0.503878 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.371037 | 0.0791054 | ||||||||
\(23\) | 6.14596 | 1.28152 | 0.640760 | − | 0.767741i | \(-0.278619\pi\) | ||||
0.640760 | + | 0.767741i | \(0.278619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.889072 | −0.177814 | ||||||||
\(26\) | −1.43717 | −0.281852 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.11140 | 0.210035 | ||||||||
\(29\) | 10.3543 | 1.92275 | 0.961376 | − | 0.275239i | \(-0.0887570\pi\) | ||||
0.961376 | + | 0.275239i | \(0.0887570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.51081 | −0.989771 | −0.494885 | − | 0.868958i | \(-0.664790\pi\) | ||||
−0.494885 | + | 0.868958i | \(0.664790\pi\) | |||||||
\(32\) | 5.35505 | 0.946648 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.81067 | −1.16802 | ||||||||
\(35\) | −2.02754 | −0.342717 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.11637 | 0.183529 | 0.0917647 | − | 0.995781i | \(-0.470749\pi\) | ||||
0.0917647 | + | 0.995781i | \(0.470749\pi\) | |||||||
\(38\) | 5.02476 | 0.815124 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.94674 | −0.940262 | ||||||||
\(41\) | −12.0128 | −1.87609 | −0.938043 | − | 0.346519i | \(-0.887364\pi\) | ||||
−0.938043 | + | 0.346519i | \(0.887364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.215108 | −0.0328036 | −0.0164018 | − | 0.999865i | \(-0.505221\pi\) | ||||
−0.0164018 | + | 0.999865i | \(0.505221\pi\) | |||||||
\(44\) | −0.437456 | −0.0659490 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.79352 | 0.854208 | ||||||||
\(47\) | −4.05988 | −0.592194 | −0.296097 | − | 0.955158i | \(-0.595685\pi\) | ||||
−0.296097 | + | 0.955158i | \(0.595685\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.838089 | −0.118524 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.69443 | 0.234976 | ||||||||
\(53\) | 6.05109 | 0.831181 | 0.415591 | − | 0.909552i | \(-0.363575\pi\) | ||||
0.415591 | + | 0.909552i | \(0.363575\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.798057 | 0.107610 | ||||||||
\(56\) | 2.93298 | 0.391936 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.76057 | 1.28163 | ||||||||
\(59\) | 3.92402 | 0.510864 | 0.255432 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255432 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.48704 | −0.446469 | −0.223235 | − | 0.974765i | \(-0.571662\pi\) | ||||
−0.223235 | + | 0.974765i | \(0.571662\pi\) | |||||||
\(62\) | −5.19480 | −0.659740 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.13195 | 0.766494 | ||||||||
\(65\) | −3.09118 | −0.383414 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.31796 | 1.13837 | 0.569185 | − | 0.822209i | \(-0.307259\pi\) | ||||
0.569185 | + | 0.822209i | \(0.307259\pi\) | |||||||
\(68\) | 8.02984 | 0.973761 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.91127 | −0.228441 | ||||||||
\(71\) | −6.78717 | −0.805489 | −0.402744 | − | 0.915313i | \(-0.631944\pi\) | ||||
−0.402744 | + | 0.915313i | \(0.631944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.2119 | −1.31225 | −0.656125 | − | 0.754652i | \(-0.727806\pi\) | ||||
−0.656125 | + | 0.754652i | \(0.727806\pi\) | |||||||
\(74\) | 1.05235 | 0.122333 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.92424 | −0.679557 | ||||||||
\(77\) | −0.393608 | −0.0448558 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.16136 | −0.580698 | −0.290349 | − | 0.956921i | \(-0.593771\pi\) | ||||
−0.290349 | + | 0.956921i | \(0.593771\pi\) | |||||||
\(80\) | −1.09891 | −0.122862 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.3239 | −1.25052 | ||||||||
\(83\) | −6.24052 | −0.684986 | −0.342493 | − | 0.939520i | \(-0.611271\pi\) | ||||
−0.342493 | + | 0.939520i | \(0.611271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.6490 | −1.58890 | ||||||||
\(86\) | −0.202772 | −0.0218655 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.15444 | −0.123064 | ||||||||
\(89\) | −13.9448 | −1.47815 | −0.739074 | − | 0.673624i | \(-0.764737\pi\) | ||||
−0.739074 | + | 0.673624i | \(0.764737\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.52460 | 0.159821 | ||||||||
\(92\) | −6.83062 | −0.712141 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.82707 | −0.394732 | ||||||||
\(95\) | 10.8077 | 1.10884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5474 | 1.07093 | 0.535465 | − | 0.844557i | \(-0.320136\pi\) | ||||
0.535465 | + | 0.844557i | \(0.320136\pi\) | |||||||
\(98\) | 0.942656 | 0.0952226 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.988114 | 0.0988114 | ||||||||
\(101\) | −15.7128 | −1.56348 | −0.781739 | − | 0.623605i | \(-0.785667\pi\) | ||||
−0.781739 | + | 0.623605i | \(0.785667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.27528 | 0.421256 | 0.210628 | − | 0.977566i | \(-0.432449\pi\) | ||||
0.210628 | + | 0.977566i | \(0.432449\pi\) | |||||||
\(104\) | 4.47161 | 0.438477 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.70410 | 0.554031 | ||||||||
\(107\) | −8.30037 | −0.802427 | −0.401214 | − | 0.915985i | \(-0.631412\pi\) | ||||
−0.401214 | + | 0.915985i | \(0.631412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.24166 | 0.502060 | 0.251030 | − | 0.967979i | \(-0.419231\pi\) | ||||
0.251030 | + | 0.967979i | \(0.419231\pi\) | |||||||
\(110\) | 0.752293 | 0.0717284 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.541991 | 0.0512133 | ||||||||
\(113\) | −1.08075 | −0.101669 | −0.0508344 | − | 0.998707i | \(-0.516188\pi\) | ||||
−0.0508344 | + | 0.998707i | \(0.516188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.4612 | 1.16201 | ||||||||
\(116\) | −11.5078 | −1.06847 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.69900 | 0.340521 | ||||||||
\(119\) | 7.22498 | 0.662313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8451 | −0.985916 | ||||||||
\(122\) | −3.28708 | −0.297598 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.12472 | 0.550016 | ||||||||
\(125\) | −11.9403 | −1.06798 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −4.92978 | −0.435735 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.91392 | −0.255568 | ||||||||
\(131\) | −7.36931 | −0.643860 | −0.321930 | − | 0.946764i | \(-0.604332\pi\) | ||||
−0.321930 | + | 0.946764i | \(0.604332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.33043 | −0.462207 | ||||||||
\(134\) | 8.78363 | 0.758790 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.1907 | 1.81709 | ||||||||
\(137\) | −2.37680 | −0.203063 | −0.101532 | − | 0.994832i | \(-0.532374\pi\) | ||||
−0.101532 | + | 0.994832i | \(0.532374\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1222 | −1.19783 | −0.598916 | − | 0.800812i | \(-0.704402\pi\) | ||||
−0.598916 | + | 0.800812i | \(0.704402\pi\) | |||||||
\(140\) | 2.25341 | 0.190448 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.39796 | −0.536905 | ||||||||
\(143\) | −0.600093 | −0.0501823 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.9939 | 1.74344 | ||||||||
\(146\) | −10.5689 | −0.874691 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.24073 | −0.101987 | ||||||||
\(149\) | 13.5063 | 1.10648 | 0.553240 | − | 0.833022i | \(-0.313391\pi\) | ||||
0.553240 | + | 0.833022i | \(0.313391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6796 | 1.76426 | 0.882129 | − | 0.471007i | \(-0.156109\pi\) | ||||
0.882129 | + | 0.471007i | \(0.156109\pi\) | |||||||
\(152\) | −15.6340 | −1.26809 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.371037 | −0.0298990 | ||||||||
\(155\) | −11.1734 | −0.897469 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2097 | −0.974438 | −0.487219 | − | 0.873280i | \(-0.661989\pi\) | ||||
−0.487219 | + | 0.873280i | \(0.661989\pi\) | |||||||
\(158\) | −4.86538 | −0.387069 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.8576 | 0.858368 | ||||||||
\(161\) | −6.14596 | −0.484369 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4746 | −0.898759 | −0.449379 | − | 0.893341i | \(-0.648355\pi\) | ||||
−0.449379 | + | 0.893341i | \(0.648355\pi\) | |||||||
\(164\) | 13.3510 | 1.04254 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.88266 | −0.456583 | ||||||||
\(167\) | −9.48483 | −0.733958 | −0.366979 | − | 0.930229i | \(-0.619608\pi\) | ||||
−0.366979 | + | 0.930229i | \(0.619608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6756 | −0.821201 | ||||||||
\(170\) | −13.8089 | −1.05910 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.239071 | 0.0182290 | ||||||||
\(173\) | −21.7904 | −1.65669 | −0.828346 | − | 0.560216i | \(-0.810718\pi\) | ||||
−0.828346 | + | 0.560216i | \(0.810718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.889072 | 0.0672075 | ||||||||
\(176\) | −0.213332 | −0.0160805 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.1452 | −0.985272 | ||||||||
\(179\) | 4.32122 | 0.322983 | 0.161492 | − | 0.986874i | \(-0.448370\pi\) | ||||
0.161492 | + | 0.986874i | \(0.448370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.17405 | 0.681902 | 0.340951 | − | 0.940081i | \(-0.389251\pi\) | ||||
0.340951 | + | 0.940081i | \(0.389251\pi\) | |||||||
\(182\) | 1.43717 | 0.106530 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.0260 | −1.32889 | ||||||||
\(185\) | 2.26348 | 0.166414 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.84381 | −0.207960 | ||||||||
\(188\) | 4.51215 | 0.329082 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.1879 | 0.739109 | ||||||||
\(191\) | −14.7115 | −1.06449 | −0.532244 | − | 0.846591i | \(-0.678651\pi\) | ||||
−0.532244 | + | 0.846591i | \(0.678651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2579 | −0.882345 | −0.441173 | − | 0.897422i | \(-0.645437\pi\) | ||||
−0.441173 | + | 0.897422i | \(0.645437\pi\) | |||||||
\(194\) | 9.94261 | 0.713838 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.11140 | −0.0793857 | ||||||||
\(197\) | −3.36875 | −0.240013 | −0.120007 | − | 0.992773i | \(-0.538292\pi\) | ||||
−0.120007 | + | 0.992773i | \(0.538292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0623 | −1.42218 | −0.711089 | − | 0.703102i | \(-0.751798\pi\) | ||||
−0.711089 | + | 0.703102i | \(0.751798\pi\) | |||||||
\(200\) | 2.60763 | 0.184387 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.8117 | −1.04215 | ||||||||
\(203\) | −10.3543 | −0.726732 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.3565 | −1.70113 | ||||||||
\(206\) | 4.03012 | 0.280792 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.826316 | 0.0572947 | ||||||||
\(209\) | 2.09810 | 0.145129 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.1999 | −1.80368 | −0.901839 | − | 0.432071i | \(-0.857783\pi\) | ||||
−0.901839 | + | 0.432071i | \(0.857783\pi\) | |||||||
\(212\) | −6.72518 | −0.461887 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.82440 | −0.534865 | ||||||||
\(215\) | −0.436140 | −0.0297445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.51081 | 0.374098 | ||||||||
\(218\) | 4.94108 | 0.334652 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.886961 | −0.0597989 | ||||||||
\(221\) | 11.0152 | 0.740961 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.28885 | −0.488098 | −0.244049 | − | 0.969763i | \(-0.578476\pi\) | ||||
−0.244049 | + | 0.969763i | \(0.578476\pi\) | |||||||
\(224\) | −5.35505 | −0.357799 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.01878 | −0.0677681 | ||||||||
\(227\) | 25.9000 | 1.71904 | 0.859522 | − | 0.511098i | \(-0.170761\pi\) | ||||
0.859522 | + | 0.511098i | \(0.170761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.9555 | 1.97951 | 0.989757 | − | 0.142764i | \(-0.0455990\pi\) | ||||
0.989757 | + | 0.142764i | \(0.0455990\pi\) | |||||||
\(230\) | 11.7466 | 0.774549 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −30.3691 | −1.99383 | ||||||||
\(233\) | 12.2443 | 0.802152 | 0.401076 | − | 0.916045i | \(-0.368636\pi\) | ||||
0.401076 | + | 0.916045i | \(0.368636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.23157 | −0.536969 | ||||||||
\(236\) | −4.36116 | −0.283887 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.81067 | 0.441470 | ||||||||
\(239\) | −0.293187 | −0.0189647 | −0.00948234 | − | 0.999955i | \(-0.503018\pi\) | ||||
−0.00948234 | + | 0.999955i | \(0.503018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4415 | −1.12351 | −0.561753 | − | 0.827305i | \(-0.689873\pi\) | ||||
−0.561753 | + | 0.827305i | \(0.689873\pi\) | |||||||
\(242\) | −10.2232 | −0.657170 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.87549 | 0.248103 | ||||||||
\(245\) | 2.02754 | 0.129535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.12675 | −0.517093 | ||||||||
\(248\) | 16.1631 | 1.02636 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.2556 | −0.711869 | ||||||||
\(251\) | −0.315392 | −0.0199074 | −0.00995368 | − | 0.999950i | \(-0.503168\pi\) | ||||
−0.00995368 | + | 0.999950i | \(0.503168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.41910 | 0.152087 | ||||||||
\(254\) | −0.942656 | −0.0591475 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9110 | −1.05694 | ||||||||
\(257\) | 6.88363 | 0.429389 | 0.214695 | − | 0.976681i | \(-0.431124\pi\) | ||||
0.214695 | + | 0.976681i | \(0.431124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.11637 | −0.0693676 | ||||||||
\(260\) | 3.43554 | 0.213063 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.94672 | −0.429170 | ||||||||
\(263\) | 17.9942 | 1.10957 | 0.554784 | − | 0.831994i | \(-0.312801\pi\) | ||||
0.554784 | + | 0.831994i | \(0.312801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.2688 | 0.753669 | ||||||||
\(266\) | −5.02476 | −0.308088 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.3560 | −0.632592 | ||||||||
\(269\) | 6.25866 | 0.381597 | 0.190799 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190799 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0536 | −0.914443 | −0.457222 | − | 0.889353i | \(-0.651155\pi\) | ||||
−0.457222 | + | 0.889353i | \(0.651155\pi\) | |||||||
\(272\) | 3.91587 | 0.237435 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.24050 | −0.135354 | ||||||||
\(275\) | −0.349946 | −0.0211025 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9805 | −0.900090 | −0.450045 | − | 0.893006i | \(-0.648592\pi\) | ||||
−0.450045 | + | 0.893006i | \(0.648592\pi\) | |||||||
\(278\) | −13.3124 | −0.798425 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.94674 | 0.355386 | ||||||||
\(281\) | 28.4947 | 1.69985 | 0.849925 | − | 0.526903i | \(-0.176647\pi\) | ||||
0.849925 | + | 0.526903i | \(0.176647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.7506 | 1.88737 | 0.943687 | − | 0.330839i | \(-0.107332\pi\) | ||||
0.943687 | + | 0.330839i | \(0.107332\pi\) | |||||||
\(284\) | 7.54326 | 0.447610 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.565681 | −0.0334494 | ||||||||
\(287\) | 12.0128 | 0.709094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.2003 | 2.07061 | ||||||||
\(290\) | 19.7900 | 1.16211 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.4609 | 0.729217 | ||||||||
\(293\) | −26.7569 | −1.56316 | −0.781578 | − | 0.623807i | \(-0.785585\pi\) | ||||
−0.781578 | + | 0.623807i | \(0.785585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.95613 | 0.463224 | ||||||||
\(296\) | −3.27428 | −0.190314 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.7318 | 0.737533 | ||||||||
\(299\) | −9.37010 | −0.541887 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.215108 | 0.0123986 | ||||||||
\(302\) | 20.4364 | 1.17598 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.88904 | −0.165698 | ||||||||
\(305\) | −7.07011 | −0.404834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9334 | 0.738147 | 0.369073 | − | 0.929400i | \(-0.379675\pi\) | ||||
0.369073 | + | 0.929400i | \(0.379675\pi\) | |||||||
\(308\) | 0.437456 | 0.0249264 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.5327 | −0.598216 | ||||||||
\(311\) | 33.8815 | 1.92124 | 0.960620 | − | 0.277864i | \(-0.0896264\pi\) | ||||
0.960620 | + | 0.277864i | \(0.0896264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.8784 | −1.68883 | −0.844413 | − | 0.535692i | \(-0.820051\pi\) | ||||
−0.844413 | + | 0.535692i | \(0.820051\pi\) | |||||||
\(314\) | −11.5095 | −0.649520 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.73633 | 0.322694 | ||||||||
\(317\) | 12.1570 | 0.682804 | 0.341402 | − | 0.939917i | \(-0.389098\pi\) | ||||
0.341402 | + | 0.939917i | \(0.389098\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.07555 | 0.228187 | ||||||||
\(320\) | 12.4328 | 0.695014 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.79352 | −0.322860 | ||||||||
\(323\) | −38.5123 | −2.14288 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.35547 | 0.0751882 | ||||||||
\(326\) | −10.8166 | −0.599075 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 35.2333 | 1.94544 | ||||||||
\(329\) | 4.05988 | 0.223828 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.00611 | −0.165231 | −0.0826155 | − | 0.996581i | \(-0.526327\pi\) | ||||
−0.0826155 | + | 0.996581i | \(0.526327\pi\) | |||||||
\(332\) | 6.93571 | 0.380647 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.94093 | −0.489226 | ||||||||
\(335\) | 18.8926 | 1.03221 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.6283 | −0.905799 | −0.452899 | − | 0.891562i | \(-0.649610\pi\) | ||||
−0.452899 | + | 0.891562i | \(0.649610\pi\) | |||||||
\(338\) | −10.0634 | −0.547378 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.2808 | 0.882953 | ||||||||
\(341\) | −2.16910 | −0.117463 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.630906 | 0.0340162 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.5408 | −1.10428 | ||||||||
\(347\) | −22.0246 | −1.18234 | −0.591172 | − | 0.806546i | \(-0.701334\pi\) | ||||
−0.591172 | + | 0.806546i | \(0.701334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.78704 | 0.309773 | 0.154887 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154887 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(350\) | 0.838089 | 0.0447977 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.10779 | 0.112346 | ||||||||
\(353\) | 19.2731 | 1.02580 | 0.512902 | − | 0.858447i | \(-0.328571\pi\) | ||||
0.512902 | + | 0.858447i | \(0.328571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7613 | −0.730372 | ||||||||
\(356\) | 15.4983 | 0.821407 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.07343 | 0.215287 | ||||||||
\(359\) | −6.30280 | −0.332649 | −0.166325 | − | 0.986071i | \(-0.553190\pi\) | ||||
−0.166325 | + | 0.986071i | \(0.553190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.41349 | 0.495447 | ||||||||
\(362\) | 8.64798 | 0.454528 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.69443 | −0.0888125 | ||||||||
\(365\) | −22.7325 | −1.18988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.8154 | −0.825559 | −0.412780 | − | 0.910831i | \(-0.635442\pi\) | ||||
−0.412780 | + | 0.910831i | \(0.635442\pi\) | |||||||
\(368\) | −3.33105 | −0.173643 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.13368 | 0.110925 | ||||||||
\(371\) | −6.05109 | −0.314157 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5380 | −1.47764 | −0.738821 | − | 0.673902i | \(-0.764617\pi\) | ||||
−0.738821 | + | 0.673902i | \(0.764617\pi\) | |||||||
\(374\) | −2.68074 | −0.138618 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.9075 | 0.614084 | ||||||||
\(377\) | −15.7862 | −0.813029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.4675 | −1.71911 | −0.859554 | − | 0.511045i | \(-0.829258\pi\) | ||||
−0.859554 | + | 0.511045i | \(0.829258\pi\) | |||||||
\(380\) | −12.0116 | −0.616185 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.8679 | −0.709543 | ||||||||
\(383\) | 22.2341 | 1.13611 | 0.568055 | − | 0.822990i | \(-0.307696\pi\) | ||||
0.568055 | + | 0.822990i | \(0.307696\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.798057 | −0.0406728 | ||||||||
\(386\) | −11.5550 | −0.588135 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.7224 | −0.595116 | ||||||||
\(389\) | −19.0317 | −0.964943 | −0.482472 | − | 0.875912i | \(-0.660261\pi\) | ||||
−0.482472 | + | 0.875912i | \(0.660261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.4044 | −2.24563 | ||||||||
\(392\) | −2.93298 | −0.148138 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.17557 | −0.159983 | ||||||||
\(395\) | −10.4649 | −0.526545 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.12683 | −0.307497 | −0.153748 | − | 0.988110i | \(-0.549135\pi\) | ||||
−0.153748 | + | 0.988110i | \(0.549135\pi\) | |||||||
\(398\) | −18.9118 | −0.947964 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.481868 | 0.0240934 | ||||||||
\(401\) | 7.88878 | 0.393947 | 0.196974 | − | 0.980409i | \(-0.436889\pi\) | ||||
0.196974 | + | 0.980409i | \(0.436889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.40176 | 0.418521 | ||||||||
\(404\) | 17.4632 | 0.868825 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.76057 | −0.484409 | ||||||||
\(407\) | 0.439411 | 0.0217808 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4698 | 1.70442 | 0.852211 | − | 0.523198i | \(-0.175261\pi\) | ||||
0.852211 | + | 0.523198i | \(0.175261\pi\) | |||||||
\(410\) | −22.9598 | −1.13390 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.75155 | −0.234092 | ||||||||
\(413\) | −3.92402 | −0.193089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.6529 | −0.621107 | ||||||||
\(416\) | −8.16428 | −0.400287 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.97779 | 0.0967367 | ||||||||
\(419\) | −24.4461 | −1.19427 | −0.597135 | − | 0.802141i | \(-0.703694\pi\) | ||||
−0.597135 | + | 0.802141i | \(0.703694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1674 | 1.42153 | 0.710767 | − | 0.703428i | \(-0.248348\pi\) | ||||
0.710767 | + | 0.703428i | \(0.248348\pi\) | |||||||
\(422\) | −24.6975 | −1.20226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.7477 | −0.861906 | ||||||||
\(425\) | 6.42353 | 0.311587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.48704 | 0.168750 | ||||||||
\(428\) | 9.22503 | 0.445909 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.411130 | −0.0198264 | ||||||||
\(431\) | 8.12744 | 0.391485 | 0.195742 | − | 0.980655i | \(-0.437288\pi\) | ||||
0.195742 | + | 0.980655i | \(0.437288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8060 | −0.615419 | −0.307709 | − | 0.951480i | \(-0.599562\pi\) | ||||
−0.307709 | + | 0.951480i | \(0.599562\pi\) | |||||||
\(434\) | 5.19480 | 0.249358 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.82558 | −0.278995 | ||||||||
\(437\) | 32.7606 | 1.56715 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2637 | −0.871679 | −0.435840 | − | 0.900024i | \(-0.643549\pi\) | ||||
−0.435840 | + | 0.900024i | \(0.643549\pi\) | |||||||
\(440\) | −2.34069 | −0.111588 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.3835 | 0.493893 | ||||||||
\(443\) | −6.35839 | −0.302096 | −0.151048 | − | 0.988526i | \(-0.548265\pi\) | ||||
−0.151048 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.2737 | −1.34030 | ||||||||
\(446\) | −6.87088 | −0.325346 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.13195 | −0.289707 | ||||||||
\(449\) | −37.4797 | −1.76878 | −0.884388 | − | 0.466753i | \(-0.845424\pi\) | ||||
−0.884388 | + | 0.466753i | \(0.845424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.72834 | −0.222649 | ||||||||
\(452\) | 1.20115 | 0.0564973 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.4148 | 1.14584 | ||||||||
\(455\) | 3.09118 | 0.144917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.1237 | 1.78335 | 0.891677 | − | 0.452673i | \(-0.149529\pi\) | ||||
0.891677 | + | 0.452673i | \(0.149529\pi\) | |||||||
\(458\) | 28.2377 | 1.31946 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.8494 | −0.645730 | ||||||||
\(461\) | 4.34534 | 0.202382 | 0.101191 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101191 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.5836 | 1.51429 | 0.757144 | − | 0.653248i | \(-0.226594\pi\) | ||||
0.757144 | + | 0.653248i | \(0.226594\pi\) | |||||||
\(464\) | −5.61195 | −0.260528 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.5422 | 0.534681 | ||||||||
\(467\) | −7.91842 | −0.366421 | −0.183210 | − | 0.983074i | \(-0.558649\pi\) | ||||
−0.183210 | + | 0.983074i | \(0.558649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.31796 | −0.430263 | ||||||||
\(470\) | −7.75954 | −0.357921 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.5091 | −0.529748 | ||||||||
\(473\) | −0.0846681 | −0.00389304 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.73914 | −0.217446 | ||||||||
\(476\) | −8.02984 | −0.368047 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.276374 | −0.0126411 | ||||||||
\(479\) | 28.9770 | 1.32399 | 0.661996 | − | 0.749508i | \(-0.269710\pi\) | ||||
0.661996 | + | 0.749508i | \(0.269710\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.70201 | −0.0776048 | ||||||||
\(482\) | −16.4413 | −0.748883 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.0532 | 0.547873 | ||||||||
\(485\) | 21.3854 | 0.971061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.20818 | −0.417262 | −0.208631 | − | 0.977994i | \(-0.566901\pi\) | ||||
−0.208631 | + | 0.977994i | \(0.566901\pi\) | |||||||
\(488\) | 10.2274 | 0.462973 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.91127 | 0.0863426 | ||||||||
\(491\) | −36.3971 | −1.64258 | −0.821288 | − | 0.570513i | \(-0.806744\pi\) | ||||
−0.821288 | + | 0.570513i | \(0.806744\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −74.8099 | −3.36927 | ||||||||
\(494\) | −7.66073 | −0.344672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.98681 | 0.134112 | ||||||||
\(497\) | 6.78717 | 0.304446 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.80459 | 0.394148 | 0.197074 | − | 0.980389i | \(-0.436856\pi\) | ||||
0.197074 | + | 0.980389i | \(0.436856\pi\) | |||||||
\(500\) | 13.2705 | 0.593475 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.297306 | −0.0132694 | ||||||||
\(503\) | 30.0843 | 1.34139 | 0.670696 | − | 0.741732i | \(-0.265996\pi\) | ||||
0.670696 | + | 0.741732i | \(0.265996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8583 | −1.41768 | ||||||||
\(506\) | 2.28038 | 0.101375 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.11140 | 0.0493104 | ||||||||
\(509\) | 14.6613 | 0.649849 | 0.324924 | − | 0.945740i | \(-0.394661\pi\) | ||||
0.324924 | + | 0.945740i | \(0.394661\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2119 | 0.495984 | ||||||||
\(512\) | −6.08168 | −0.268775 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.48890 | 0.286213 | ||||||||
\(515\) | 8.66831 | 0.381972 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.59800 | −0.0702800 | ||||||||
\(518\) | −1.05235 | −0.0462376 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.06637 | 0.397587 | ||||||||
\(521\) | −23.4040 | −1.02535 | −0.512674 | − | 0.858583i | \(-0.671345\pi\) | ||||
−0.512674 | + | 0.858583i | \(0.671345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.58294 | −0.0692173 | −0.0346087 | − | 0.999401i | \(-0.511018\pi\) | ||||
−0.0346087 | + | 0.999401i | \(0.511018\pi\) | |||||||
\(524\) | 8.19025 | 0.357793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.9623 | 0.739592 | ||||||||
\(527\) | 39.8155 | 1.73439 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.7728 | 0.642296 | ||||||||
\(530\) | 11.5653 | 0.502364 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.92424 | 0.256848 | ||||||||
\(533\) | 18.3147 | 0.793297 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.8294 | −0.727597 | ||||||||
\(536\) | −27.3294 | −1.18045 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.89976 | 0.254357 | ||||||||
\(539\) | 0.393608 | 0.0169539 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8950 | −0.726372 | −0.363186 | − | 0.931717i | \(-0.618311\pi\) | ||||
−0.363186 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(542\) | −14.1904 | −0.609530 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −38.6901 | −1.65883 | ||||||||
\(545\) | 10.6277 | 0.455240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0686 | −1.20013 | −0.600064 | − | 0.799952i | \(-0.704858\pi\) | ||||
−0.600064 | + | 0.799952i | \(0.704858\pi\) | |||||||
\(548\) | 2.64157 | 0.112842 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.329879 | −0.0140661 | ||||||||
\(551\) | 55.1931 | 2.35130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.16136 | 0.219483 | ||||||||
\(554\) | −14.1214 | −0.599963 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6954 | 0.665635 | ||||||||
\(557\) | 30.4192 | 1.28890 | 0.644452 | − | 0.764645i | \(-0.277086\pi\) | ||||
0.644452 | + | 0.764645i | \(0.277086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.327952 | 0.0138709 | ||||||||
\(560\) | 1.09891 | 0.0464374 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.8607 | 1.13305 | ||||||||
\(563\) | −38.0568 | −1.60390 | −0.801952 | − | 0.597388i | \(-0.796205\pi\) | ||||
−0.801952 | + | 0.597388i | \(0.796205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.19127 | −0.0921876 | ||||||||
\(566\) | 29.9298 | 1.25805 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.9066 | 0.835263 | ||||||||
\(569\) | −8.39927 | −0.352116 | −0.176058 | − | 0.984380i | \(-0.556335\pi\) | ||||
−0.176058 | + | 0.984380i | \(0.556335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.2531 | −1.39160 | −0.695799 | − | 0.718236i | \(-0.744950\pi\) | ||||
−0.695799 | + | 0.718236i | \(0.744950\pi\) | |||||||
\(572\) | 0.666943 | 0.0278863 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.3239 | 0.472652 | ||||||||
\(575\) | −5.46420 | −0.227873 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8513 | −0.784790 | −0.392395 | − | 0.919797i | \(-0.628353\pi\) | ||||
−0.392395 | + | 0.919797i | \(0.628353\pi\) | |||||||
\(578\) | 33.1818 | 1.38018 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −23.3326 | −0.968832 | ||||||||
\(581\) | 6.24052 | 0.258900 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.38176 | 0.0986423 | ||||||||
\(584\) | 32.8842 | 1.36076 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25.2226 | −1.04194 | ||||||||
\(587\) | −28.6206 | −1.18130 | −0.590648 | − | 0.806929i | \(-0.701128\pi\) | ||||
−0.590648 | + | 0.806929i | \(0.701128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.3750 | −1.21038 | ||||||||
\(590\) | 7.49989 | 0.308766 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.605060 | −0.0248678 | ||||||||
\(593\) | −13.7191 | −0.563377 | −0.281689 | − | 0.959506i | \(-0.590895\pi\) | ||||
−0.281689 | + | 0.959506i | \(0.590895\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.6490 | 0.600549 | ||||||||
\(596\) | −15.0109 | −0.614870 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.83278 | −0.361199 | ||||||||
\(599\) | 40.0016 | 1.63442 | 0.817211 | − | 0.576338i | \(-0.195519\pi\) | ||||
0.817211 | + | 0.576338i | \(0.195519\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8800 | −0.443806 | −0.221903 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221903 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(602\) | 0.202772 | 0.00826439 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.0947 | −0.980398 | ||||||||
\(605\) | −21.9888 | −0.893974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.1563 | −0.818119 | −0.409060 | − | 0.912508i | \(-0.634143\pi\) | ||||
−0.409060 | + | 0.912508i | \(0.634143\pi\) | |||||||
\(608\) | 28.5447 | 1.15764 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.66468 | −0.269845 | ||||||||
\(611\) | 6.18967 | 0.250407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4960 | 0.989382 | 0.494691 | − | 0.869069i | \(-0.335281\pi\) | ||||
0.494691 | + | 0.869069i | \(0.335281\pi\) | |||||||
\(614\) | 12.1917 | 0.492018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15444 | 0.0465139 | ||||||||
\(617\) | −33.8571 | −1.36304 | −0.681518 | − | 0.731801i | \(-0.738680\pi\) | ||||
−0.681518 | + | 0.731801i | \(0.738680\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.1828 | −1.89644 | −0.948219 | − | 0.317619i | \(-0.897117\pi\) | ||||
−0.948219 | + | 0.317619i | \(0.897117\pi\) | |||||||
\(620\) | 12.4181 | 0.498724 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.9386 | 1.28062 | ||||||||
\(623\) | 13.9448 | 0.558688 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.7642 | −0.790568 | ||||||||
\(626\) | −28.1650 | −1.12570 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5698 | 0.541495 | ||||||||
\(629\) | −8.06572 | −0.321601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.13033 | −0.244045 | −0.122022 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122022 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(632\) | 15.1381 | 0.602163 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.4599 | 0.455129 | ||||||||
\(635\) | −2.02754 | −0.0804606 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.52460 | −0.0604067 | ||||||||
\(638\) | 3.84184 | 0.152100 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.99534 | −0.395100 | ||||||||
\(641\) | −15.4511 | −0.610281 | −0.305140 | − | 0.952307i | \(-0.598703\pi\) | ||||
−0.305140 | + | 0.952307i | \(0.598703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.9559 | 1.14191 | 0.570955 | − | 0.820982i | \(-0.306573\pi\) | ||||
0.570955 | + | 0.820982i | \(0.306573\pi\) | |||||||
\(644\) | 6.83062 | 0.269164 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36.3038 | −1.42835 | ||||||||
\(647\) | 17.7543 | 0.697993 | 0.348996 | − | 0.937124i | \(-0.386523\pi\) | ||||
0.348996 | + | 0.937124i | \(0.386523\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.54453 | 0.0606280 | ||||||||
\(650\) | 1.27775 | 0.0501173 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.7529 | 0.499440 | ||||||||
\(653\) | 47.4601 | 1.85726 | 0.928628 | − | 0.371013i | \(-0.120989\pi\) | ||||
0.928628 | + | 0.371013i | \(0.120989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9416 | −0.583816 | ||||||||
\(656\) | 6.51083 | 0.254205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.82707 | 0.149195 | ||||||||
\(659\) | −4.97190 | −0.193678 | −0.0968388 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968388 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.29780 | −0.206060 | −0.103030 | − | 0.994678i | \(-0.532854\pi\) | ||||
−0.103030 | + | 0.994678i | \(0.532854\pi\) | |||||||
\(662\) | −2.83373 | −0.110136 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.3033 | 0.710306 | ||||||||
\(665\) | −10.8077 | −0.419104 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 63.6373 | 2.46405 | ||||||||
\(668\) | 10.5414 | 0.407860 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.8092 | 0.688029 | ||||||||
\(671\) | −1.37253 | −0.0529858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4834 | −1.17505 | −0.587524 | − | 0.809206i | \(-0.699897\pi\) | ||||
−0.587524 | + | 0.809206i | \(0.699897\pi\) | |||||||
\(674\) | −15.6747 | −0.603768 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8649 | 0.456341 | ||||||||
\(677\) | −1.37014 | −0.0526588 | −0.0263294 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263294 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5474 | −0.404774 | ||||||||
\(680\) | 42.9651 | 1.64764 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.04472 | −0.0782962 | ||||||||
\(683\) | 39.0704 | 1.49499 | 0.747494 | − | 0.664268i | \(-0.231257\pi\) | ||||
0.747494 | + | 0.664268i | \(0.231257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.81905 | −0.184127 | ||||||||
\(686\) | −0.942656 | −0.0359908 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.116586 | 0.00444481 | ||||||||
\(689\) | −9.22546 | −0.351462 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0221 | 1.48447 | 0.742235 | − | 0.670140i | \(-0.233766\pi\) | ||||
0.742235 | + | 0.670140i | \(0.233766\pi\) | |||||||
\(692\) | 24.2178 | 0.920624 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.7616 | −0.788101 | ||||||||
\(695\) | −28.6334 | −1.08613 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 86.7923 | 3.28749 | ||||||||
\(698\) | 5.45519 | 0.206482 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.988114 | −0.0373472 | ||||||||
\(701\) | −5.33026 | −0.201321 | −0.100661 | − | 0.994921i | \(-0.532096\pi\) | ||||
−0.100661 | + | 0.994921i | \(0.532096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.95071 | 0.224435 | ||||||||
\(704\) | 2.41359 | 0.0909654 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.1679 | 0.683758 | ||||||||
\(707\) | 15.7128 | 0.590939 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.31243 | 0.312180 | 0.156090 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156090 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(710\) | −12.9721 | −0.486836 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40.8999 | 1.53279 | ||||||||
\(713\) | −33.8692 | −1.26841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.21671 | −0.0455025 | ||||||||
\(716\) | −4.80261 | −0.179482 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.94137 | −0.221730 | ||||||||
\(719\) | −15.6948 | −0.585319 | −0.292659 | − | 0.956217i | \(-0.594540\pi\) | ||||
−0.292659 | + | 0.956217i | \(0.594540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.27528 | −0.159220 | ||||||||
\(722\) | 8.87368 | 0.330244 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.1960 | −0.378933 | ||||||||
\(725\) | −9.20575 | −0.341893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.8055 | 0.919985 | 0.459993 | − | 0.887923i | \(-0.347852\pi\) | ||||
0.459993 | + | 0.887923i | \(0.347852\pi\) | |||||||
\(728\) | −4.47161 | −0.165729 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −21.4290 | −0.793121 | ||||||||
\(731\) | 1.55415 | 0.0574822 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.1964 | −1.48469 | −0.742344 | − | 0.670018i | \(-0.766286\pi\) | ||||
−0.742344 | + | 0.670018i | \(0.766286\pi\) | |||||||
\(734\) | −14.9085 | −0.550283 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 32.9119 | 1.21315 | ||||||||
\(737\) | 3.66763 | 0.135099 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.54978 | −0.314509 | −0.157254 | − | 0.987558i | \(-0.550264\pi\) | ||||
−0.157254 | + | 0.987558i | \(0.550264\pi\) | |||||||
\(740\) | −2.51563 | −0.0924764 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.70410 | −0.209404 | ||||||||
\(743\) | −16.6201 | −0.609732 | −0.304866 | − | 0.952395i | \(-0.598612\pi\) | ||||
−0.304866 | + | 0.952395i | \(0.598612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.3846 | 1.00329 | ||||||||
\(746\) | −26.9015 | −0.984934 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.16061 | 0.115563 | ||||||||
\(749\) | 8.30037 | 0.303289 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.5495 | −0.895825 | −0.447912 | − | 0.894077i | \(-0.647832\pi\) | ||||
−0.447912 | + | 0.894077i | \(0.647832\pi\) | |||||||
\(752\) | 2.20041 | 0.0802409 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.8809 | −0.541931 | ||||||||
\(755\) | 43.9563 | 1.59973 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.8571 | −0.430952 | −0.215476 | − | 0.976509i | \(-0.569130\pi\) | ||||
−0.215476 | + | 0.976509i | \(0.569130\pi\) | |||||||
\(758\) | −31.5483 | −1.14589 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −31.6987 | −1.14983 | ||||||||
\(761\) | 48.1062 | 1.74385 | 0.871924 | − | 0.489641i | \(-0.162872\pi\) | ||||
0.871924 | + | 0.489641i | \(0.162872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.24166 | −0.189761 | ||||||||
\(764\) | 16.3504 | 0.591536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.9591 | 0.757284 | ||||||||
\(767\) | −5.98255 | −0.216017 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.7773 | −1.21804 | −0.609021 | − | 0.793154i | \(-0.708437\pi\) | ||||
−0.609021 | + | 0.793154i | \(0.708437\pi\) | |||||||
\(770\) | −0.752293 | −0.0271108 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.6235 | 0.490319 | ||||||||
\(773\) | 22.2790 | 0.801321 | 0.400661 | − | 0.916227i | \(-0.368781\pi\) | ||||
0.400661 | + | 0.916227i | \(0.368781\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.89951 | 0.175995 | ||||||||
\(776\) | −30.9354 | −1.11052 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.9403 | −0.643191 | ||||||||
\(779\) | −64.0335 | −2.29424 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.67148 | −0.0955932 | ||||||||
\(782\) | −41.8581 | −1.49684 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.541991 | −0.0193568 | ||||||||
\(785\) | −24.7556 | −0.883566 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1520 | −0.789634 | −0.394817 | − | 0.918760i | \(-0.629192\pi\) | ||||
−0.394817 | + | 0.918760i | \(0.629192\pi\) | |||||||
\(788\) | 3.74403 | 0.133375 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.86477 | −0.350973 | ||||||||
\(791\) | 1.08075 | 0.0384272 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.31632 | 0.188788 | ||||||||
\(794\) | −5.77549 | −0.204965 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.2972 | 0.790304 | ||||||||
\(797\) | −6.03663 | −0.213828 | −0.106914 | − | 0.994268i | \(-0.534097\pi\) | ||||
−0.106914 | + | 0.994268i | \(0.534097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.3325 | 1.03771 | ||||||||
\(800\) | −4.76102 | −0.168328 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.43641 | 0.262589 | ||||||||
\(803\) | −4.41308 | −0.155734 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.4612 | −0.439199 | ||||||||
\(806\) | 7.91997 | 0.278969 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 46.0852 | 1.62127 | ||||||||
\(809\) | 1.64082 | 0.0576880 | 0.0288440 | − | 0.999584i | \(-0.490817\pi\) | ||||
0.0288440 | + | 0.999584i | \(0.490817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1361 | 0.847532 | 0.423766 | − | 0.905772i | \(-0.360708\pi\) | ||||
0.423766 | + | 0.905772i | \(0.360708\pi\) | |||||||
\(812\) | 11.5078 | 0.403845 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.414213 | 0.0145182 | ||||||||
\(815\) | −23.2652 | −0.814945 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.14662 | −0.0401150 | ||||||||
\(818\) | 32.4932 | 1.13610 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.0698 | 0.945318 | ||||||||
\(821\) | 8.59622 | 0.300010 | 0.150005 | − | 0.988685i | \(-0.452071\pi\) | ||||
0.150005 | + | 0.988685i | \(0.452071\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4797 | 0.400156 | 0.200078 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200078 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(824\) | −12.5393 | −0.436828 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.69900 | −0.128705 | ||||||||
\(827\) | −12.1662 | −0.423061 | −0.211531 | − | 0.977371i | \(-0.567845\pi\) | ||||
−0.211531 | + | 0.977371i | \(0.567845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.9606 | −0.658530 | −0.329265 | − | 0.944237i | \(-0.606801\pi\) | ||||
−0.329265 | + | 0.944237i | \(0.606801\pi\) | |||||||
\(830\) | −11.9273 | −0.414004 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.34874 | −0.324109 | ||||||||
\(833\) | −7.22498 | −0.250331 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.2309 | −0.665512 | ||||||||
\(836\) | −2.33183 | −0.0806480 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.0443 | −0.796051 | ||||||||
\(839\) | −37.6366 | −1.29936 | −0.649680 | − | 0.760208i | \(-0.725097\pi\) | ||||
−0.649680 | + | 0.760208i | \(0.725097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78.2122 | 2.69697 | ||||||||
\(842\) | 27.4949 | 0.947535 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.1186 | 1.00230 | ||||||||
\(845\) | −21.6453 | −0.744619 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.8451 | 0.372641 | ||||||||
\(848\) | −3.27963 | −0.112623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.05517 | 0.207691 | ||||||||
\(851\) | 6.86114 | 0.235197 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5742 | 0.807165 | 0.403583 | − | 0.914943i | \(-0.367765\pi\) | ||||
0.403583 | + | 0.914943i | \(0.367765\pi\) | |||||||
\(854\) | 3.28708 | 0.112481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.3448 | 0.832089 | ||||||||
\(857\) | 46.2533 | 1.57998 | 0.789991 | − | 0.613118i | \(-0.210085\pi\) | ||||
0.789991 | + | 0.613118i | \(0.210085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.4044 | −1.31034 | −0.655171 | − | 0.755480i | \(-0.727404\pi\) | ||||
−0.655171 | + | 0.755480i | \(0.727404\pi\) | |||||||
\(860\) | 0.484726 | 0.0165290 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.66138 | 0.260948 | ||||||||
\(863\) | 40.9841 | 1.39511 | 0.697557 | − | 0.716529i | \(-0.254270\pi\) | ||||
0.697557 | + | 0.716529i | \(0.254270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.1809 | −1.50220 | ||||||||
\(866\) | −12.0717 | −0.410212 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.12472 | −0.207886 | ||||||||
\(869\) | −2.03155 | −0.0689157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.2061 | −0.481356 | ||||||||
\(872\) | −15.3737 | −0.520618 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.8820 | 1.04460 | ||||||||
\(875\) | 11.9403 | 0.403657 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1446 | 0.376325 | 0.188163 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188163 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(878\) | −17.2164 | −0.581025 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.432539 | −0.0145809 | ||||||||
\(881\) | 50.5138 | 1.70185 | 0.850926 | − | 0.525285i | \(-0.176041\pi\) | ||||
0.850926 | + | 0.525285i | \(0.176041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0412 | 0.876357 | 0.438179 | − | 0.898888i | \(-0.355624\pi\) | ||||
0.438179 | + | 0.898888i | \(0.355624\pi\) | |||||||
\(884\) | −12.2423 | −0.411752 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.99378 | −0.201365 | ||||||||
\(887\) | 31.8404 | 1.06910 | 0.534548 | − | 0.845138i | \(-0.320482\pi\) | ||||
0.534548 | + | 0.845138i | \(0.320482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −26.6524 | −0.893390 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.10083 | 0.271236 | ||||||||
\(893\) | −21.6409 | −0.724185 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.76146 | 0.292863 | ||||||||
\(896\) | 4.92978 | 0.164692 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −35.3304 | −1.17899 | ||||||||
\(899\) | −57.0608 | −1.90308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.7190 | −1.45649 | ||||||||
\(902\) | −4.45720 | −0.148408 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.16983 | 0.105427 | ||||||||
\(905\) | 18.6008 | 0.618311 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.2737 | −1.07163 | −0.535815 | − | 0.844335i | \(-0.679996\pi\) | ||||
−0.535815 | + | 0.844335i | \(0.679996\pi\) | |||||||
\(908\) | −28.7853 | −0.955273 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.91392 | 0.0965955 | ||||||||
\(911\) | 34.4345 | 1.14087 | 0.570433 | − | 0.821344i | \(-0.306776\pi\) | ||||
0.570433 | + | 0.821344i | \(0.306776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.45632 | −0.0812923 | ||||||||
\(914\) | 35.9376 | 1.18871 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.2925 | −1.10002 | ||||||||
\(917\) | 7.36931 | 0.243356 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.27192 | 0.173904 | 0.0869522 | − | 0.996212i | \(-0.472287\pi\) | ||||
0.0869522 | + | 0.996212i | \(0.472287\pi\) | |||||||
\(920\) | −36.5484 | −1.20497 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.09616 | 0.134900 | ||||||||
\(923\) | 10.3477 | 0.340598 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.992530 | −0.0326342 | ||||||||
\(926\) | 30.7151 | 1.00936 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 55.4480 | 1.82017 | ||||||||
\(929\) | −7.44226 | −0.244173 | −0.122086 | − | 0.992519i | \(-0.538958\pi\) | ||||
−0.122086 | + | 0.992519i | \(0.538958\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.33043 | 0.174698 | ||||||||
\(932\) | −13.6083 | −0.445756 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.46435 | −0.244241 | ||||||||
\(935\) | −5.76595 | −0.188567 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.8635 | 1.56363 | 0.781816 | − | 0.623510i | \(-0.214294\pi\) | ||||
0.781816 | + | 0.623510i | \(0.214294\pi\) | |||||||
\(938\) | −8.78363 | −0.286796 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.14857 | 0.298393 | ||||||||
\(941\) | −34.0814 | −1.11102 | −0.555511 | − | 0.831509i | \(-0.687477\pi\) | ||||
−0.555511 | + | 0.831509i | \(0.687477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.8302 | −2.40424 | ||||||||
\(944\) | −2.12678 | −0.0692209 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0798129 | −0.00259494 | ||||||||
\(947\) | 2.35915 | 0.0766620 | 0.0383310 | − | 0.999265i | \(-0.487796\pi\) | ||||
0.0383310 | + | 0.999265i | \(0.487796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.0936 | 0.554880 | ||||||||
\(950\) | −4.46737 | −0.144941 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.1907 | −0.686795 | ||||||||
\(953\) | 38.2987 | 1.24062 | 0.620308 | − | 0.784358i | \(-0.287007\pi\) | ||||
0.620308 | + | 0.784358i | \(0.287007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.8282 | −0.965218 | ||||||||
\(956\) | 0.325848 | 0.0105387 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.3153 | 0.882517 | ||||||||
\(959\) | 2.37680 | 0.0767507 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.630958 | −0.0203535 | ||||||||
\(962\) | −1.60441 | −0.0517281 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.3845 | 0.624333 | ||||||||
\(965\) | −24.8535 | −0.800062 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3209 | 0.846423 | 0.423211 | − | 0.906031i | \(-0.360903\pi\) | ||||
0.423211 | + | 0.906031i | \(0.360903\pi\) | |||||||
\(968\) | 31.8084 | 1.02236 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 20.1591 | 0.647269 | ||||||||
\(971\) | 28.2912 | 0.907908 | 0.453954 | − | 0.891025i | \(-0.350013\pi\) | ||||
0.453954 | + | 0.891025i | \(0.350013\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1222 | 0.452738 | ||||||||
\(974\) | −8.68014 | −0.278130 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.88994 | 0.0604955 | ||||||||
\(977\) | 12.7823 | 0.408943 | 0.204471 | − | 0.978873i | \(-0.434452\pi\) | ||||
0.204471 | + | 0.978873i | \(0.434452\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.48880 | −0.175423 | ||||||||
\(980\) | −2.25341 | −0.0719826 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.3099 | −1.09487 | ||||||||
\(983\) | −23.7874 | −0.758701 | −0.379350 | − | 0.925253i | \(-0.623852\pi\) | ||||
−0.379350 | + | 0.925253i | \(0.623852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.83028 | −0.217631 | ||||||||
\(986\) | −70.5200 | −2.24581 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.03207 | 0.287348 | ||||||||
\(989\) | −1.32204 | −0.0420385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9078 | −0.441794 | −0.220897 | − | 0.975297i | \(-0.570899\pi\) | ||||
−0.220897 | + | 0.975297i | \(0.570899\pi\) | |||||||
\(992\) | −29.5107 | −0.936964 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.39796 | 0.202931 | ||||||||
\(995\) | −40.6771 | −1.28955 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.1698 | −0.923816 | −0.461908 | − | 0.886928i | \(-0.652835\pi\) | ||||
−0.461908 | + | 0.886928i | \(0.652835\pi\) | |||||||
\(998\) | 8.29970 | 0.262722 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.z.1.21 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.12 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.12 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.21 | yes | 32 | 1.1 | even | 1 | trivial |