Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-3.32949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.49704 | 0.565827 | 0.282913 | − | 0.959145i | \(-0.408699\pi\) | ||||
0.282913 | + | 0.959145i | \(0.408699\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.73349 | 1.42720 | 0.713600 | − | 0.700553i | \(-0.247063\pi\) | ||||
0.713600 | + | 0.700553i | \(0.247063\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.92548 | −0.534033 | −0.267017 | − | 0.963692i | \(-0.586038\pi\) | ||||
−0.267017 | + | 0.963692i | \(0.586038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.33757 | 1.53709 | 0.768543 | − | 0.639798i | \(-0.220982\pi\) | ||||
0.768543 | + | 0.639798i | \(0.220982\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73349 | 1.54477 | 0.772384 | − | 0.635156i | \(-0.219064\pi\) | ||||
0.772384 | + | 0.635156i | \(0.219064\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.74063 | −0.323226 | −0.161613 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161613 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.26306 | 1.12488 | 0.562439 | − | 0.826839i | \(-0.309863\pi\) | ||||
0.562439 | + | 0.826839i | \(0.309863\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.49704 | 0.253045 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.53082 | 1.56686 | 0.783429 | − | 0.621481i | \(-0.213469\pi\) | ||||
0.783429 | + | 0.621481i | \(0.213469\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.07573 | 0.324174 | 0.162087 | − | 0.986776i | \(-0.448177\pi\) | ||||
0.162087 | + | 0.986776i | \(0.448177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.65897 | 1.32048 | 0.660241 | − | 0.751054i | \(-0.270454\pi\) | ||||
0.660241 | + | 0.751054i | \(0.270454\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.29437 | −0.918128 | −0.459064 | − | 0.888403i | \(-0.651815\pi\) | ||||
−0.459064 | + | 0.888403i | \(0.651815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.75888 | −0.679840 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.00247 | −1.09922 | −0.549612 | − | 0.835420i | \(-0.685224\pi\) | ||||
−0.549612 | + | 0.835420i | \(0.685224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.73349 | 0.638264 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.428447 | 0.0557791 | 0.0278895 | − | 0.999611i | \(-0.491121\pi\) | ||||
0.0278895 | + | 0.999611i | \(0.491121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.42966 | −0.567160 | −0.283580 | − | 0.958949i | \(-0.591522\pi\) | ||||
−0.283580 | + | 0.958949i | \(0.591522\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.92548 | −0.238827 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5249 | −1.53016 | −0.765080 | − | 0.643935i | \(-0.777301\pi\) | ||||
−0.765080 | + | 0.643935i | \(0.777301\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.08742 | −0.841122 | −0.420561 | − | 0.907264i | \(-0.638167\pi\) | ||||
−0.420561 | + | 0.907264i | \(0.638167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.43748 | −0.402326 | −0.201163 | − | 0.979558i | \(-0.564472\pi\) | ||||
−0.201163 | + | 0.979558i | \(0.564472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.08621 | 0.807548 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.1631 | −1.48097 | −0.740485 | − | 0.672073i | \(-0.765404\pi\) | ||||
−0.740485 | + | 0.672073i | \(0.765404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1802 | 1.22719 | 0.613593 | − | 0.789623i | \(-0.289724\pi\) | ||||
0.613593 | + | 0.789623i | \(0.289724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.33757 | 0.687406 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.52369 | −0.903509 | −0.451754 | − | 0.892142i | \(-0.649202\pi\) | ||||
−0.451754 | + | 0.892142i | \(0.649202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.88252 | −0.302170 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.73349 | 0.690841 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.71568 | −0.174201 | −0.0871005 | − | 0.996200i | \(-0.527760\pi\) | ||||
−0.0871005 | + | 0.996200i | \(0.527760\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1466 | 1.60664 | 0.803321 | − | 0.595546i | \(-0.203064\pi\) | ||||
0.803321 | + | 0.595546i | \(0.203064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7181 | 1.35169 | 0.675843 | − | 0.737046i | \(-0.263780\pi\) | ||||
0.675843 | + | 0.737046i | \(0.263780\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.839322 | −0.0811403 | −0.0405702 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405702 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9474 | −1.52749 | −0.763743 | − | 0.645521i | \(-0.776640\pi\) | ||||
−0.763743 | + | 0.645521i | \(0.776640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.89845 | 0.931168 | 0.465584 | − | 0.885004i | \(-0.345844\pi\) | ||||
0.465584 | + | 0.885004i | \(0.345844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.48758 | 0.869725 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.4059 | 1.03690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0735 | −1.69250 | −0.846251 | − | 0.532784i | \(-0.821146\pi\) | ||||
−0.846251 | + | 0.532784i | \(0.821146\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.1480 | 1.84771 | 0.923857 | − | 0.382738i | \(-0.125019\pi\) | ||||
0.923857 | + | 0.382738i | \(0.125019\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0803 | 0.874071 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.9828 | 1.79269 | 0.896343 | − | 0.443362i | \(-0.146214\pi\) | ||||
0.896343 | + | 0.443362i | \(0.146214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.90791 | 0.161827 | 0.0809135 | − | 0.996721i | \(-0.474216\pi\) | ||||
0.0809135 | + | 0.996721i | \(0.474216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.11426 | −0.762173 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.74063 | −0.144551 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2596 | −1.08627 | −0.543134 | − | 0.839646i | \(-0.682763\pi\) | ||||
−0.543134 | + | 0.839646i | \(0.682763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0338 | −1.14205 | −0.571027 | − | 0.820931i | \(-0.693455\pi\) | ||||
−0.571027 | + | 0.820931i | \(0.693455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.26306 | 0.503061 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.57395 | 0.125615 | 0.0628073 | − | 0.998026i | \(-0.479995\pi\) | ||||
0.0628073 | + | 0.998026i | \(0.479995\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49704 | 0.117983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.3771 | −1.59606 | −0.798028 | − | 0.602620i | \(-0.794123\pi\) | ||||
−0.798028 | + | 0.602620i | \(0.794123\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.22931 | 0.482039 | 0.241019 | − | 0.970520i | \(-0.422518\pi\) | ||||
0.241019 | + | 0.970520i | \(0.422518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.29251 | −0.714808 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9126 | −1.28584 | −0.642921 | − | 0.765932i | \(-0.722278\pi\) | ||||
−0.642921 | + | 0.765932i | \(0.722278\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.49704 | 0.113165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.8162 | −1.70536 | −0.852681 | − | 0.522431i | \(-0.825025\pi\) | ||||
−0.852681 | + | 0.522431i | \(0.825025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.84179 | −0.359888 | −0.179944 | − | 0.983677i | \(-0.557592\pi\) | ||||
−0.179944 | + | 0.983677i | \(0.557592\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.53082 | 0.700720 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.9988 | 2.19373 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.11748 | 0.659718 | 0.329859 | − | 0.944030i | \(-0.392999\pi\) | ||||
0.329859 | + | 0.944030i | \(0.392999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8476 | 1.50064 | 0.750320 | − | 0.661075i | \(-0.229899\pi\) | ||||
0.750320 | + | 0.661075i | \(0.229899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.05320 | −0.288779 | −0.144389 | − | 0.989521i | \(-0.546122\pi\) | ||||
−0.144389 | + | 0.989521i | \(0.546122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37131 | 0.309874 | 0.154937 | − | 0.987924i | \(-0.450483\pi\) | ||||
0.154937 | + | 0.987924i | \(0.450483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.60578 | −0.182890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.07573 | 0.144975 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.8729 | 2.20469 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9396 | −1.44154 | −0.720772 | − | 0.693172i | \(-0.756213\pi\) | ||||
−0.720772 | + | 0.693172i | \(0.756213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.65897 | 0.590537 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.37603 | 0.636486 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.2029 | −0.820855 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6336 | −1.18084 | −0.590418 | − | 0.807098i | \(-0.701037\pi\) | ||||
−0.590418 | + | 0.807098i | \(0.701037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7708 | 0.914001 | 0.457000 | − | 0.889467i | \(-0.348924\pi\) | ||||
0.457000 | + | 0.889467i | \(0.348924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.6726 | −1.69649 | −0.848245 | − | 0.529604i | \(-0.822341\pi\) | ||||
−0.848245 | + | 0.529604i | \(0.822341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0049 | 1.17954 | 0.589771 | − | 0.807570i | \(-0.299218\pi\) | ||||
0.589771 | + | 0.807570i | \(0.299218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.29437 | −0.410600 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.391410 | 0.0253182 | 0.0126591 | − | 0.999920i | \(-0.495970\pi\) | ||||
0.0126591 | + | 0.999920i | \(0.495970\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6709 | 0.816202 | 0.408101 | − | 0.912937i | \(-0.366191\pi\) | ||||
0.408101 | + | 0.912937i | \(0.366191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.75888 | −0.304034 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9652 | −0.824958 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.14903 | 0.388123 | 0.194062 | − | 0.980989i | \(-0.437834\pi\) | ||||
0.194062 | + | 0.980989i | \(0.437834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73349 | 0.297592 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.6064 | −0.786365 | −0.393183 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393183 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.2680 | 0.886570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.4492 | −1.26095 | −0.630477 | − | 0.776208i | \(-0.717141\pi\) | ||||
−0.630477 | + | 0.776208i | \(0.717141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00247 | −0.491588 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.2100 | 1.65902 | 0.829512 | − | 0.558488i | \(-0.188618\pi\) | ||||
0.829512 | + | 0.558488i | \(0.188618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.0142 | 1.15503 | 0.577515 | − | 0.816380i | \(-0.304022\pi\) | ||||
0.577515 | + | 0.816380i | \(0.304022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.73349 | 0.285440 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7200 | 0.944525 | 0.472262 | − | 0.881458i | \(-0.343437\pi\) | ||||
0.472262 | + | 0.881458i | \(0.343437\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.3247 | −1.39143 | −0.695716 | − | 0.718317i | \(-0.744913\pi\) | ||||
−0.695716 | + | 0.718317i | \(0.744913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.96500 | −0.116807 | −0.0584036 | − | 0.998293i | \(-0.518601\pi\) | ||||
−0.0584036 | + | 0.998293i | \(0.518601\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.10744 | 0.183426 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.1648 | 1.36264 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.6463 | 1.79038 | 0.895189 | − | 0.445686i | \(-0.147040\pi\) | ||||
0.895189 | + | 0.445686i | \(0.147040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.428447 | 0.0249452 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.92548 | −0.111354 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9628 | 0.747164 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.42966 | −0.253642 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9845 | −1.14057 | −0.570287 | − | 0.821446i | \(-0.693168\pi\) | ||||
−0.570287 | + | 0.821446i | \(0.693168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8985 | 1.01493 | 0.507465 | − | 0.861672i | \(-0.330583\pi\) | ||||
0.507465 | + | 0.861672i | \(0.330583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4765 | 0.705216 | 0.352608 | − | 0.935771i | \(-0.385295\pi\) | ||||
0.352608 | + | 0.935771i | \(0.385295\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.9455 | 1.00792 | 0.503961 | − | 0.863727i | \(-0.331876\pi\) | ||||
0.503961 | + | 0.863727i | \(0.331876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.23924 | −0.461309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.6740 | 2.37444 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.92548 | −0.106807 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.42291 | −0.519502 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.47122 | 0.0808654 | 0.0404327 | − | 0.999182i | \(-0.487126\pi\) | ||||
0.0404327 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.5249 | −0.684308 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2139 | 1.37349 | 0.686745 | − | 0.726898i | \(-0.259039\pi\) | ||||
0.686745 | + | 0.726898i | \(0.259039\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.6461 | 1.60543 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6035 | −0.950499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.31795 | −0.500214 | −0.250107 | − | 0.968218i | \(-0.580466\pi\) | ||||
−0.250107 | + | 0.968218i | \(0.580466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.52733 | −0.135285 | −0.0676425 | − | 0.997710i | \(-0.521548\pi\) | ||||
−0.0676425 | + | 0.997710i | \(0.521548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.2875 | −1.82494 | −0.912469 | − | 0.409146i | \(-0.865827\pi\) | ||||
−0.912469 | + | 0.409146i | \(0.865827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.08742 | −0.376161 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.5751 | −1.50814 | −0.754069 | − | 0.656796i | \(-0.771911\pi\) | ||||
−0.754069 | + | 0.656796i | \(0.771911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3399 | 1.38631 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.43748 | −0.179926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.85218 | −0.514280 | −0.257140 | − | 0.966374i | \(-0.582780\pi\) | ||||
−0.257140 | + | 0.966374i | \(0.582780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9800 | −0.621970 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.06102 | 0.469162 | 0.234581 | − | 0.972097i | \(-0.424628\pi\) | ||||
0.234581 | + | 0.972097i | \(0.424628\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.35155 | 0.172614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3721 | −0.635514 | −0.317757 | − | 0.948172i | \(-0.602930\pi\) | ||||
−0.317757 | + | 0.948172i | \(0.602930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2724 | −0.575990 | −0.287995 | − | 0.957632i | \(-0.592989\pi\) | ||||
−0.287995 | + | 0.957632i | \(0.592989\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.08621 | 0.361147 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.8750 | 0.855594 | 0.427797 | − | 0.903875i | \(-0.359290\pi\) | ||||
0.427797 | + | 0.903875i | \(0.359290\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.33757 | 0.320505 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1631 | −0.662310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.759942 | 0.0381404 | 0.0190702 | − | 0.999818i | \(-0.493929\pi\) | ||||
0.0190702 | + | 0.999818i | \(0.493929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.37806 | 0.0688172 | 0.0344086 | − | 0.999408i | \(-0.489045\pi\) | ||||
0.0344086 | + | 0.999408i | \(0.489045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0594 | −0.600722 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.1141 | 2.23622 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0619 | −0.596422 | −0.298211 | − | 0.954500i | \(-0.596390\pi\) | ||||
−0.298211 | + | 0.954500i | \(0.596390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.641401 | 0.0315613 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.1802 | 0.548814 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.75748 | −0.183565 | −0.0917823 | − | 0.995779i | \(-0.529256\pi\) | ||||
−0.0917823 | + | 0.995779i | \(0.529256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.1073 | −1.80850 | −0.904250 | − | 0.427003i | \(-0.859569\pi\) | ||||
−0.904250 | + | 0.427003i | \(0.859569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.33757 | 0.307417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.63136 | −0.320914 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7368 | −1.33603 | −0.668017 | − | 0.744146i | \(-0.732857\pi\) | ||||
−0.668017 | + | 0.744146i | \(0.732857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.8473 | −0.905744 | −0.452872 | − | 0.891575i | \(-0.649601\pi\) | ||||
−0.452872 | + | 0.891575i | \(0.649601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.73349 | 0.322106 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8271 | 1.42357 | 0.711784 | − | 0.702398i | \(-0.247887\pi\) | ||||
0.711784 | + | 0.702398i | \(0.247887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.4514 | 1.96942 | 0.984709 | − | 0.174210i | \(-0.0557371\pi\) | ||||
0.984709 | + | 0.174210i | \(0.0557371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.52369 | −0.404061 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6805 | 1.40071 | 0.700354 | − | 0.713795i | \(-0.253025\pi\) | ||||
0.700354 | + | 0.713795i | \(0.253025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.82544 | 0.462662 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.88252 | −0.135135 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6148 | 0.917542 | 0.458771 | − | 0.888555i | \(-0.348290\pi\) | ||||
0.458771 | + | 0.888555i | \(0.348290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.76237 | 0.128656 | 0.0643281 | − | 0.997929i | \(-0.479510\pi\) | ||||
0.0643281 | + | 0.997929i | \(0.479510\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4516 | −0.950466 | −0.475233 | − | 0.879860i | \(-0.657636\pi\) | ||||
−0.475233 | + | 0.879860i | \(0.657636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.6917 | −1.09632 | −0.548161 | − | 0.836373i | \(-0.684672\pi\) | ||||
−0.548161 | + | 0.836373i | \(0.684672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.7502 | −0.865805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 40.9872 | 1.88459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.73349 | 0.308954 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.781847 | 0.0357235 | 0.0178617 | − | 0.999840i | \(-0.494314\pi\) | ||||
0.0178617 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3515 | −0.836754 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.71568 | −0.0779051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2992 | 1.78081 | 0.890407 | − | 0.455165i | \(-0.150420\pi\) | ||||
0.890407 | + | 0.455165i | \(0.150420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.27204 | −0.237924 | −0.118962 | − | 0.992899i | \(-0.537957\pi\) | ||||
−0.118962 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0314 | −0.496827 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6101 | −0.475929 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.1074 | −0.989664 | −0.494832 | − | 0.868989i | \(-0.664770\pi\) | ||||
−0.494832 | + | 0.868989i | \(0.664770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.62248 | −0.384458 | −0.192229 | − | 0.981350i | \(-0.561572\pi\) | ||||
−0.192229 | + | 0.981350i | \(0.561572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1466 | 0.718512 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.1176 | −0.492779 | −0.246390 | − | 0.969171i | \(-0.579244\pi\) | ||||
−0.246390 | + | 0.969171i | \(0.579244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.14603 | −0.227647 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.7181 | 0.604492 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.7943 | −1.31035 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7301 | −1.30250 | −0.651249 | − | 0.758864i | \(-0.725755\pi\) | ||||
−0.651249 | + | 0.758864i | \(0.725755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.3418 | −1.72030 | −0.860148 | − | 0.510045i | \(-0.829629\pi\) | ||||
−0.860148 | + | 0.510045i | \(0.829629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.6926 | 1.72903 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.99678 | −0.173120 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.839322 | −0.0362871 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.5261 | −0.970268 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.4938 | 1.86994 | 0.934971 | − | 0.354723i | \(-0.115425\pi\) | ||||
0.934971 | + | 0.354723i | \(0.115425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.9474 | −0.683112 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6776 | 1.05514 | 0.527568 | − | 0.849513i | \(-0.323104\pi\) | ||||
0.527568 | + | 0.849513i | \(0.323104\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.7205 | −0.499310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.7057 | −0.837972 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.2698 | 0.943600 | 0.471800 | − | 0.881706i | \(-0.343604\pi\) | ||||
0.471800 | + | 0.881706i | \(0.343604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.6727 | −0.705181 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.8156 | 1.04585 | 0.522927 | − | 0.852378i | \(-0.324840\pi\) | ||||
0.522927 | + | 0.852378i | \(0.324840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.89845 | 0.416431 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.7790 | 1.08071 | 0.540356 | − | 0.841437i | \(-0.318290\pi\) | ||||
0.540356 | + | 0.841437i | \(0.318290\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4651 | −0.479800 | −0.239900 | − | 0.970798i | \(-0.577115\pi\) | ||||
−0.239900 | + | 0.970798i | \(0.577115\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.3005 | 0.761859 | 0.380930 | − | 0.924604i | \(-0.375604\pi\) | ||||
0.380930 | + | 0.924604i | \(0.375604\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.7372 | 0.694374 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.8796 | −1.56881 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.8559 | 1.14974 | 0.574868 | − | 0.818246i | \(-0.305053\pi\) | ||||
0.574868 | + | 0.818246i | \(0.305053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.1722 | 1.73768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.97885 | −0.122327 | −0.0611633 | − | 0.998128i | \(-0.519481\pi\) | ||||
−0.0611633 | + | 0.998128i | \(0.519481\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.48758 | 0.388953 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.5143 | 1.16506 | 0.582531 | − | 0.812808i | \(-0.302062\pi\) | ||||
0.582531 | + | 0.812808i | \(0.302062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.0058 | 1.83582 | 0.917912 | − | 0.396784i | \(-0.129874\pi\) | ||||
0.917912 | + | 0.396784i | \(0.129874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.4059 | 0.463717 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.2267 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1197 | 0.490311 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0817 | −1.01304 | −0.506520 | − | 0.862228i | \(-0.669068\pi\) | ||||
−0.506520 | + | 0.862228i | \(0.669068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.26659 | −0.0509909 | −0.0254955 | − | 0.999675i | \(-0.508116\pi\) | ||||
−0.0254955 | + | 0.999675i | \(0.508116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.3545 | −1.50140 | −0.750701 | − | 0.660642i | \(-0.770284\pi\) | ||||
−0.750701 | + | 0.660642i | \(0.770284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.7603 | −0.511230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.4023 | 2.40840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.82336 | −0.391062 | −0.195531 | − | 0.980698i | \(-0.562643\pi\) | ||||
−0.195531 | + | 0.980698i | \(0.562643\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.0735 | −0.756910 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.16315 | 0.363057 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8077 | 0.584867 | 0.292434 | − | 0.956286i | \(-0.405535\pi\) | ||||
0.292434 | + | 0.956286i | \(0.405535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.05527 | −0.159924 | −0.0799622 | − | 0.996798i | \(-0.525480\pi\) | ||||
−0.0799622 | + | 0.996798i | \(0.525480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.7763 | 0.974057 | 0.487028 | − | 0.873386i | \(-0.338081\pi\) | ||||
0.487028 | + | 0.873386i | \(0.338081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.02805 | 0.0796079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.5591 | −0.608875 | −0.304438 | − | 0.952532i | \(-0.598469\pi\) | ||||
−0.304438 | + | 0.952532i | \(0.598469\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.1480 | 0.826323 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.2777 | 1.37422 | 0.687111 | − | 0.726552i | \(-0.258878\pi\) | ||||
0.687111 | + | 0.726552i | \(0.258878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1647 | 1.79560 | 0.897799 | − | 0.440405i | \(-0.145165\pi\) | ||||
0.897799 | + | 0.440405i | \(0.145165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0803 | 0.390897 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.74063 | −0.0673974 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9677 | −0.809451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1114 | −0.775236 | −0.387618 | − | 0.921820i | \(-0.626702\pi\) | ||||
−0.387618 | + | 0.921820i | \(0.626702\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.9433 | −0.497453 | −0.248726 | − | 0.968574i | \(-0.580012\pi\) | ||||
−0.248726 | + | 0.968574i | \(0.580012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.56844 | −0.0985676 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.80047 | 0.260213 | 0.130106 | − | 0.991500i | \(-0.458468\pi\) | ||||
0.130106 | + | 0.991500i | \(0.458468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.9828 | 0.801713 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.4086 | 0.587022 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.7072 | −0.825780 | −0.412890 | − | 0.910781i | \(-0.635481\pi\) | ||||
−0.412890 | + | 0.910781i | \(0.635481\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.90791 | 0.0723712 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.1551 | 0.498284 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.3077 | −0.767013 | −0.383506 | − | 0.923538i | \(-0.625284\pi\) | ||||
−0.383506 | + | 0.923538i | \(0.625284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 64.1757 | 2.42043 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.1720 | 0.909081 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.9415 | −1.01181 | −0.505905 | − | 0.862589i | \(-0.668841\pi\) | ||||
−0.505905 | + | 0.862589i | \(0.668841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.26306 | 0.234553 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.11426 | −0.340854 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.58226 | 0.208183 | 0.104092 | − | 0.994568i | \(-0.466806\pi\) | ||||
0.104092 | + | 0.994568i | \(0.466806\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5365 | 0.764820 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.74063 | −0.0646453 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.5285 | −0.909711 | −0.454856 | − | 0.890565i | \(-0.650309\pi\) | ||||
−0.454856 | + | 0.890565i | \(0.650309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.8769 | 2.02969 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.6383 | 0.836165 | 0.418083 | − | 0.908409i | \(-0.362702\pi\) | ||||
0.418083 | + | 0.908409i | \(0.362702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −59.2865 | −2.18385 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6000 | −0.684214 | −0.342107 | − | 0.939661i | \(-0.611140\pi\) | ||||
−0.342107 | + | 0.939661i | \(0.611140\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.3333 | 0.452465 | 0.226232 | − | 0.974073i | \(-0.427359\pi\) | ||||
0.226232 | + | 0.974073i | \(0.427359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.2596 | −0.485794 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.25650 | −0.0459114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.9642 | −0.874467 | −0.437233 | − | 0.899348i | \(-0.644042\pi\) | ||||
−0.437233 | + | 0.899348i | \(0.644042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.0338 | −0.510742 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4936 | 0.817545 | 0.408772 | − | 0.912636i | \(-0.365957\pi\) | ||||
0.408772 | + | 0.912636i | \(0.365957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.0079 | 1.19653 | 0.598267 | − | 0.801297i | \(-0.295856\pi\) | ||||
0.598267 | + | 0.801297i | \(0.295856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.8739 | −0.864292 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.824968 | −0.0297879 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.42291 | −0.123433 | −0.0617166 | − | 0.998094i | \(-0.519657\pi\) | ||||
−0.0617166 | + | 0.998094i | \(0.519657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.866323 | −0.0311595 | −0.0155797 | − | 0.999879i | \(-0.504959\pi\) | ||||
−0.0155797 | + | 0.999879i | \(0.504959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.26306 | 0.224976 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.9769 | 0.500774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.5482 | −1.20045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.57395 | 0.0561765 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.8550 | 1.52762 | 0.763808 | − | 0.645444i | \(-0.223328\pi\) | ||||
0.763808 | + | 0.645444i | \(0.223328\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.8184 | 0.526880 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.52924 | 0.302882 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.0736 | −1.31321 | −0.656607 | − | 0.754233i | \(-0.728009\pi\) | ||||
−0.656607 | + | 0.754233i | \(0.728009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.8910 | −1.41124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.2713 | −0.574200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.49704 | 0.0527636 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.89436 | 0.207235 | 0.103617 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103617 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.8029 | −0.590031 | −0.295016 | − | 0.955492i | \(-0.595325\pi\) | ||||
−0.295016 | + | 0.955492i | \(0.595325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.3771 | −0.713778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.3051 | 2.03984 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.7218 | 1.35140 | 0.675699 | − | 0.737177i | \(-0.263842\pi\) | ||||
0.675699 | + | 0.737177i | \(0.263842\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1457 | −0.493088 | −0.246544 | − | 0.969132i | \(-0.579295\pi\) | ||||
−0.246544 | + | 0.969132i | \(0.579295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.9508 | −1.42400 | −0.711999 | − | 0.702181i | \(-0.752210\pi\) | ||||
−0.711999 | + | 0.702181i | \(0.752210\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.4522 | −0.849259 | −0.424630 | − | 0.905367i | \(-0.639596\pi\) | ||||
−0.424630 | + | 0.905367i | \(0.639596\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.1597 | −1.04497 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.22931 | 0.215574 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.7425 | 0.612539 | 0.306269 | − | 0.951945i | \(-0.400919\pi\) | ||||
0.306269 | + | 0.951945i | \(0.400919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9702 | −0.895525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.29251 | −0.319672 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.0751 | 0.586707 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.53082 | 0.326712 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.9338 | 1.16187 | 0.580936 | − | 0.813950i | \(-0.302687\pi\) | ||||
0.580936 | + | 0.813950i | \(0.302687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.9241 | −1.53458 | −0.767288 | − | 0.641302i | \(-0.778394\pi\) | ||||
−0.767288 | + | 0.641302i | \(0.778394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.0733 | 0.753132 | 0.376566 | − | 0.926390i | \(-0.377105\pi\) | ||||
0.376566 | + | 0.926390i | \(0.377105\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.1613 | 1.50327 | 0.751635 | − | 0.659580i | \(-0.229266\pi\) | ||||
0.751635 | + | 0.659580i | \(0.229266\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.9126 | −0.575046 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −62.3076 | −2.11364 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.1165 | 0.817156 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.49704 | 0.0506091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.09723 | −0.104586 | −0.0522931 | − | 0.998632i | \(-0.516653\pi\) | ||||
−0.0522931 | + | 0.998632i | \(0.516653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.5068 | −1.70162 | −0.850808 | − | 0.525476i | \(-0.823887\pi\) | ||||
−0.850808 | + | 0.525476i | \(0.823887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.9737 | −0.773126 | −0.386563 | − | 0.922263i | \(-0.626338\pi\) | ||||
−0.386563 | + | 0.922263i | \(0.626338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.4277 | −0.786626 | −0.393313 | − | 0.919405i | \(-0.628671\pi\) | ||||
−0.393313 | + | 0.919405i | \(0.628671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.5538 | −0.957663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.3831 | −1.41830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.8162 | −0.762661 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.9016 | −0.363590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.7162 | −1.68960 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.84179 | −0.160947 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.9870 | 0.464432 | 0.232216 | − | 0.972664i | \(-0.425402\pi\) | ||||
0.232216 | + | 0.972664i | \(0.425402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.25544 | −0.273515 | −0.136757 | − | 0.990605i | \(-0.543668\pi\) | ||||
−0.136757 | + | 0.990605i | \(0.543668\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.9213 | 1.75144 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.6594 | 1.04549 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.68684 | 0.0556436 | 0.0278218 | − | 0.999613i | \(-0.491143\pi\) | ||||
0.0278218 | + | 0.999613i | \(0.491143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.6467 | 0.449187 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.53082 | 0.313372 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.41408 | 0.144821 | 0.0724106 | − | 0.997375i | \(-0.476931\pi\) | ||||
0.0724106 | + | 0.997375i | \(0.476931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0439 | −1.05020 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9988 | 0.981067 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0221 | 1.01345 | 0.506724 | − | 0.862108i | \(-0.330856\pi\) | ||||
0.506724 | + | 0.862108i | \(0.330856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.5490 | −1.38706 | −0.693529 | − | 0.720429i | \(-0.743945\pi\) | ||||
−0.693529 | + | 0.720429i | \(0.743945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.07573 | 0.0675950 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.1679 | −1.30528 | −0.652641 | − | 0.757667i | \(-0.726339\pi\) | ||||
−0.652641 | + | 0.757667i | \(0.726339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.61881 | 0.214856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.8233 | −1.12804 | −0.564019 | − | 0.825762i | \(-0.690746\pi\) | ||||
−0.564019 | + | 0.825762i | \(0.690746\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.11748 | 0.295035 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.4121 | 1.01435 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.22586 | 0.265350 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.8476 | 0.671107 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.3241 | 0.750053 | 0.375027 | − | 0.927014i | \(-0.377634\pi\) | ||||
0.375027 | + | 0.927014i | \(0.377634\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.52104 | −0.241362 | −0.120681 | − | 0.992691i | \(-0.538508\pi\) | ||||
−0.120681 | + | 0.992691i | \(0.538508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.85621 | 0.0915660 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0158 | −0.960291 | −0.480145 | − | 0.877189i | \(-0.659416\pi\) | ||||
−0.480145 | + | 0.877189i | \(0.659416\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.3468 | −1.28949 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6034 | 0.944203 | 0.472102 | − | 0.881544i | \(-0.343496\pi\) | ||||
0.472102 | + | 0.881544i | \(0.343496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.05320 | −0.129146 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.65897 | 0.275339 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.8686 | −0.631146 | −0.315573 | − | 0.948901i | \(-0.602197\pi\) | ||||
−0.315573 | + | 0.948901i | \(0.602197\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.37131 | 0.138580 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.60419 | −0.177487 | −0.0887433 | − | 0.996055i | \(-0.528285\pi\) | ||||
−0.0887433 | + | 0.996055i | \(0.528285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8280.2.a.bu.1.4 | yes | 6 | |
3.2 | odd | 2 | 8280.2.a.bt.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.4 | ✓ | 6 | 3.2 | odd | 2 | ||
8280.2.a.bu.1.4 | yes | 6 | 1.1 | even | 1 | trivial |