Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8496,2,Mod(1,8496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8496.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8496 = 2^{4} \cdot 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8496.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: | \(67.8409015573\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.22896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2124) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.398683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8496.1 |
$q$-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 | ||||||||
\(5\) | 0.852003 | 0.381028 | 0.190514 | − | 0.981685i | \(-0.438985\pi\) | ||||
0.190514 | + | 0.981685i | \(0.438985\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.13705 | −1.18569 | −0.592846 | − | 0.805316i | \(-0.701996\pi\) | ||||
−0.592846 | + | 0.805316i | \(0.701996\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.38773 | 1.92597 | 0.962987 | − | 0.269549i | \(-0.0868745\pi\) | ||||
0.962987 | + | 0.269549i | \(0.0868745\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53573 | 0.703284 | 0.351642 | − | 0.936134i | \(-0.385623\pi\) | ||||
0.351642 | + | 0.936134i | \(0.385623\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.72741 | −1.63164 | −0.815818 | − | 0.578308i | \(-0.803713\pi\) | ||||
−0.815818 | + | 0.578308i | \(0.803713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.84105 | 1.34003 | 0.670015 | − | 0.742348i | \(-0.266288\pi\) | ||||
0.670015 | + | 0.742348i | \(0.266288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.39868 | 0.708674 | 0.354337 | − | 0.935118i | \(-0.384707\pi\) | ||||
0.354337 | + | 0.935118i | \(0.384707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.27409 | −0.854818 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.60132 | −0.297357 | −0.148679 | − | 0.988886i | \(-0.547502\pi\) | ||||
−0.148679 | + | 0.988886i | \(0.547502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 11.0261 | 1.98035 | 0.990177 | − | 0.139817i | \(-0.0446513\pi\) | ||||
0.990177 | + | 0.139817i | \(0.0446513\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.67277 | −0.451781 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.19168 | −0.195911 | −0.0979557 | − | 0.995191i | \(-0.531230\pi\) | ||||
−0.0979557 | + | 0.995191i | \(0.531230\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.65087 | 1.35104 | 0.675519 | − | 0.737342i | \(-0.263919\pi\) | ||||
0.675519 | + | 0.737342i | \(0.263919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.71646 | −1.17675 | −0.588374 | − | 0.808589i | \(-0.700232\pi\) | ||||
−0.588374 | + | 0.808589i | \(0.700232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.213586 | 0.0311547 | 0.0155773 | − | 0.999879i | \(-0.495041\pi\) | ||||
0.0155773 | + | 0.999879i | \(0.495041\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.84105 | 0.405865 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.72083 | −1.19790 | −0.598949 | − | 0.800787i | \(-0.704415\pi\) | ||||
−0.598949 | + | 0.800787i | \(0.704415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.44237 | 0.733849 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.43142 | 0.951496 | 0.475748 | − | 0.879582i | \(-0.342178\pi\) | ||||
0.475748 | + | 0.879582i | \(0.342178\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.16045 | 0.267971 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.261638 | −0.0319641 | −0.0159821 | − | 0.999872i | \(-0.505087\pi\) | ||||
−0.0159821 | + | 0.999872i | \(0.505087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.35063 | 0.278969 | 0.139484 | − | 0.990224i | \(-0.455456\pi\) | ||||
0.139484 | + | 0.990224i | \(0.455456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.93004 | 0.577018 | 0.288509 | − | 0.957477i | \(-0.406840\pi\) | ||||
0.288509 | + | 0.957477i | \(0.406840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20.0386 | −2.28361 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.29874 | −0.708663 | −0.354332 | − | 0.935120i | \(-0.615292\pi\) | ||||
−0.354332 | + | 0.935120i | \(0.615292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.08241 | 0.887159 | 0.443580 | − | 0.896235i | \(-0.353708\pi\) | ||||
0.443580 | + | 0.896235i | \(0.353708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.73178 | −0.621698 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.28504 | −0.136214 | −0.0681071 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681071 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.95469 | −0.833878 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.97660 | 0.510588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.64775 | 0.979580 | 0.489790 | − | 0.871840i | \(-0.337073\pi\) | ||||
0.489790 | + | 0.871840i | \(0.337073\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2768 | 1.12209 | 0.561044 | − | 0.827786i | \(-0.310400\pi\) | ||||
0.561044 | + | 0.827786i | \(0.310400\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7755 | 1.25880 | 0.629402 | − | 0.777080i | \(-0.283300\pi\) | ||||
0.629402 | + | 0.777080i | \(0.283300\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.20413 | −0.406429 | −0.203215 | − | 0.979134i | \(-0.565139\pi\) | ||||
−0.203215 | + | 0.979134i | \(0.565139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.66841 | −0.638718 | −0.319359 | − | 0.947634i | \(-0.603468\pi\) | ||||
−0.319359 | + | 0.947634i | \(0.603468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.69964 | −0.724321 | −0.362161 | − | 0.932116i | \(-0.617961\pi\) | ||||
−0.362161 | + | 0.932116i | \(0.617961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.89569 | 0.270024 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.1042 | 1.93462 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.8031 | 2.70937 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90156 | −0.706737 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.3236 | −1.44849 | −0.724245 | − | 0.689543i | \(-0.757811\pi\) | ||||
−0.724245 | + | 0.689543i | \(0.757811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0277 | −1.13823 | −0.569116 | − | 0.822258i | \(-0.692714\pi\) | ||||
−0.569116 | + | 0.822258i | \(0.692714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.3236 | −1.58886 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1975 | −1.38385 | −0.691925 | − | 0.721969i | \(-0.743237\pi\) | ||||
−0.691925 | + | 0.721969i | \(0.743237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.77546 | 0.320231 | 0.160115 | − | 0.987098i | \(-0.448813\pi\) | ||||
0.160115 | + | 0.987098i | \(0.448813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.1975 | 1.35451 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.36433 | −0.113301 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.9250 | 1.46847 | 0.734235 | − | 0.678895i | \(-0.237541\pi\) | ||||
0.734235 | + | 0.678895i | \(0.237541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.09486 | 0.414614 | 0.207307 | − | 0.978276i | \(-0.433530\pi\) | ||||
0.207307 | + | 0.978276i | \(0.433530\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.39432 | 0.754570 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1959 | −1.61181 | −0.805905 | − | 0.592044i | \(-0.798321\pi\) | ||||
−0.805905 | + | 0.592044i | \(0.798321\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6618 | −0.840269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.63842 | 0.598287 | 0.299144 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299144 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6509 | 1.44325 | 0.721624 | − | 0.692285i | \(-0.243396\pi\) | ||||
0.721624 | + | 0.692285i | \(0.243396\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.57008 | −0.505391 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.4190 | 0.792139 | 0.396070 | − | 0.918220i | \(-0.370374\pi\) | ||||
0.396070 | + | 0.918220i | \(0.370374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.4080 | 1.01355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.6180 | −1.69055 | −0.845275 | − | 0.534332i | \(-0.820563\pi\) | ||||
−0.845275 | + | 0.534332i | \(0.820563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.06833 | −0.525385 | −0.262693 | − | 0.964880i | \(-0.584611\pi\) | ||||
−0.262693 | + | 0.964880i | \(0.584611\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.01532 | −0.0746476 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −42.9729 | −3.14249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.6153 | 1.85346 | 0.926728 | − | 0.375733i | \(-0.122609\pi\) | ||||
0.926728 | + | 0.375733i | \(0.122609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.523276 | −0.0376662 | −0.0188331 | − | 0.999823i | \(-0.505995\pi\) | ||||
−0.0188331 | + | 0.999823i | \(0.505995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.9781 | 1.13839 | 0.569196 | − | 0.822202i | \(-0.307255\pi\) | ||||
0.569196 | + | 0.822202i | \(0.307255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5072 | 0.815727 | 0.407863 | − | 0.913043i | \(-0.366274\pi\) | ||||
0.407863 | + | 0.913043i | \(0.366274\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.02340 | 0.352574 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.37057 | 0.514783 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.3111 | 2.58086 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4526 | −0.926115 | −0.463058 | − | 0.886328i | \(-0.653248\pi\) | ||||
−0.463058 | + | 0.886328i | \(0.653248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.57445 | −0.448374 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.5895 | −2.34809 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.0589 | −1.14750 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.109275 | −0.00731760 | −0.00365880 | − | 0.999993i | \(-0.501165\pi\) | ||||
−0.00365880 | + | 0.999993i | \(0.501165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.8562 | 1.58339 | 0.791697 | − | 0.610913i | \(-0.209198\pi\) | ||||
0.791697 | + | 0.610913i | \(0.209198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.74931 | 0.247762 | 0.123881 | − | 0.992297i | \(-0.460466\pi\) | ||||
0.123881 | + | 0.992297i | \(0.460466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.32064 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.181976 | 0.0118708 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4495 | 1.38745 | 0.693726 | − | 0.720239i | \(-0.255968\pi\) | ||||
0.693726 | + | 0.720239i | \(0.255968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.67936 | −0.430255 | −0.215128 | − | 0.976586i | \(-0.569017\pi\) | ||||
−0.215128 | + | 0.976586i | \(0.569017\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.42059 | 0.154646 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.8113 | 0.942422 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9889 | 1.38793 | 0.693964 | − | 0.720009i | \(-0.255862\pi\) | ||||
0.693964 | + | 0.720009i | \(0.255862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.7099 | 1.36489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8223 | 0.799831 | 0.399916 | − | 0.916552i | \(-0.369039\pi\) | ||||
0.399916 | + | 0.916552i | \(0.369039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.73836 | 0.232291 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.41460 | −0.0872279 | −0.0436140 | − | 0.999048i | \(-0.513887\pi\) | ||||
−0.0436140 | + | 0.999048i | \(0.513887\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.43017 | −0.456432 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.9737 | 1.33976 | 0.669881 | − | 0.742468i | \(-0.266345\pi\) | ||||
0.669881 | + | 0.742468i | \(0.266345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.6196 | −1.00957 | −0.504786 | − | 0.863245i | \(-0.668428\pi\) | ||||
−0.504786 | + | 0.863245i | \(0.668428\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.3017 | −1.64636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.6821 | −1.00233 | −0.501165 | − | 0.865352i | \(-0.667095\pi\) | ||||
−0.501165 | + | 0.865352i | \(0.667095\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.02739 | −0.478874 | −0.239437 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239437 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.87104 | 0.586772 | 0.293386 | − | 0.955994i | \(-0.405218\pi\) | ||||
0.293386 | + | 0.955994i | \(0.405218\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.1382 | −1.60192 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.2581 | 1.66224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.8922 | 1.33738 | 0.668689 | − | 0.743542i | \(-0.266856\pi\) | ||||
0.668689 | + | 0.743542i | \(0.266856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.852003 | −0.0496056 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.61814 | 0.498400 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2069 | 1.39526 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.33159 | 0.362546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.8656 | −1.59037 | −0.795186 | − | 0.606365i | \(-0.792627\pi\) | ||||
−0.795186 | + | 0.606365i | \(0.792627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1168 | 0.573669 | 0.286834 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286834 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6333 | −1.16626 | −0.583132 | − | 0.812377i | \(-0.698173\pi\) | ||||
−0.583132 | + | 0.812377i | \(0.698173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.46540 | −0.250802 | −0.125401 | − | 0.992106i | \(-0.540022\pi\) | ||||
−0.125401 | + | 0.992106i | \(0.540022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2288 | −0.572702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.2952 | −2.18644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8379 | −0.601180 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.670028 | −0.0369398 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.46081 | 0.135258 | 0.0676291 | − | 0.997711i | \(-0.478457\pi\) | ||||
0.0676291 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.222916 | −0.0121792 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.0050 | 0.926319 | 0.463160 | − | 0.886275i | \(-0.346716\pi\) | ||||
0.463160 | + | 0.886275i | \(0.346716\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 70.4321 | 3.81411 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0468 | 0.704461 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.7152 | 0.736271 | 0.368136 | − | 0.929772i | \(-0.379996\pi\) | ||||
0.368136 | + | 0.929772i | \(0.379996\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.01245 | 0.107724 | 0.0538621 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538621 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.9934 | 0.904468 | 0.452234 | − | 0.891899i | \(-0.350627\pi\) | ||||
0.452234 | + | 0.891899i | \(0.350627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.00275 | 0.106295 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1183 | −1.11458 | −0.557290 | − | 0.830318i | \(-0.688159\pi\) | ||||
−0.557290 | + | 0.830318i | \(0.688159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.1179 | 0.795678 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.20041 | 0.219860 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.69181 | −0.244911 | −0.122455 | − | 0.992474i | \(-0.539077\pi\) | ||||
−0.122455 | + | 0.992474i | \(0.539077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.3576 | 1.42034 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.84105 | −0.302438 | −0.151219 | − | 0.988500i | \(-0.548320\pi\) | ||||
−0.151219 | + | 0.988500i | \(0.548320\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.06050 | −0.209127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.5818 | 1.51952 | 0.759758 | − | 0.650206i | \(-0.225317\pi\) | ||||
0.759758 | + | 0.650206i | \(0.225317\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.9979 | 1.78831 | 0.894155 | − | 0.447758i | \(-0.147777\pi\) | ||||
0.894155 | + | 0.447758i | \(0.147777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.0730 | −0.870118 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8661 | 1.05795 | 0.528976 | − | 0.848637i | \(-0.322576\pi\) | ||||
0.528976 | + | 0.848637i | \(0.322576\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8643 | −1.15630 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.36655 | −0.270020 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.7282 | 1.29126 | 0.645631 | − | 0.763650i | \(-0.276595\pi\) | ||||
0.645631 | + | 0.763650i | \(0.276595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.9469 | −0.596598 | −0.298299 | − | 0.954472i | \(-0.596419\pi\) | ||||
−0.298299 | + | 0.954472i | \(0.596419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.9593 | 1.39275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.61215 | −0.377320 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.72591 | −0.382022 | −0.191011 | − | 0.981588i | \(-0.561177\pi\) | ||||
−0.191011 | + | 0.981588i | \(0.561177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.13705 | 0.154364 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.88624 | 0.338032 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.8656 | 1.16591 | 0.582955 | − | 0.812504i | \(-0.301896\pi\) | ||||
0.582955 | + | 0.812504i | \(0.301896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8038 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321694\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.7536 | 1.39475 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3127 | −1.12818 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.8051 | 0.953977 | 0.476988 | − | 0.878910i | \(-0.341728\pi\) | ||||
0.476988 | + | 0.878910i | \(0.341728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8191 | 0.567992 | 0.283996 | − | 0.958825i | \(-0.408340\pi\) | ||||
0.283996 | + | 0.958825i | \(0.408340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.8519 | 0.949644 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6168 | 1.41353 | 0.706766 | − | 0.707448i | \(-0.250154\pi\) | ||||
0.706766 | + | 0.707448i | \(0.250154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.0370 | −1.56963 | −0.784817 | − | 0.619727i | \(-0.787243\pi\) | ||||
−0.784817 | + | 0.619727i | \(0.787243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.09486 | −0.0519013 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9043 | −0.703377 | −0.351689 | − | 0.936117i | \(-0.614392\pi\) | ||||
−0.351689 | + | 0.936117i | \(0.614392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 55.2594 | 2.60207 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.77743 | −0.317731 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.5059 | −1.70767 | −0.853836 | − | 0.520541i | \(-0.825730\pi\) | ||||
−0.853836 | + | 0.520541i | \(0.825730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.89223 | −0.134704 | −0.0673522 | − | 0.997729i | \(-0.521455\pi\) | ||||
−0.0673522 | + | 0.997729i | \(0.521455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.80832 | 0.409357 | 0.204679 | − | 0.978829i | \(-0.434385\pi\) | ||||
0.204679 | + | 0.978829i | \(0.434385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.2607 | 1.67794 | 0.838972 | − | 0.544174i | \(-0.183157\pi\) | ||||
0.838972 | + | 0.544174i | \(0.183157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.820770 | 0.0378996 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −49.2907 | −2.26639 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.9652 | −1.14548 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.4081 | −1.75491 | −0.877455 | − | 0.479659i | \(-0.840760\pi\) | ||||
−0.877455 | + | 0.479659i | \(0.840760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.02178 | −0.137781 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.21991 | 0.373247 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9093 | −0.675603 | −0.337802 | − | 0.941217i | \(-0.609683\pi\) | ||||
−0.337802 | + | 0.941217i | \(0.609683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.3987 | 0.830321 | 0.415160 | − | 0.909748i | \(-0.363725\pi\) | ||||
0.415160 | + | 0.909748i | \(0.363725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.7727 | 0.485179 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.37403 | −0.330771 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8250 | −1.20085 | −0.600426 | − | 0.799680i | \(-0.705002\pi\) | ||||
−0.600426 | + | 0.799680i | \(0.705002\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.2136 | −0.901279 | −0.450640 | − | 0.892706i | \(-0.648804\pi\) | ||||
−0.450640 | + | 0.892706i | \(0.648804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.60790 | 0.427546 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.40605 | −0.416916 | −0.208458 | − | 0.978031i | \(-0.566844\pi\) | ||||
−0.208458 | + | 0.978031i | \(0.566844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.4658 | −0.684166 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8847 | 0.479639 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36433 | 0.0600031 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.0835 | 1.01131 | 0.505654 | − | 0.862736i | \(-0.331251\pi\) | ||||
0.505654 | + | 0.862736i | \(0.331251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.1925 | 1.58259 | 0.791293 | − | 0.611437i | \(-0.209408\pi\) | ||||
0.791293 | + | 0.611437i | \(0.209408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −74.1774 | −3.23122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4490 | −0.497781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.9363 | 0.950165 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.58194 | −0.154861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.1479 | 0.781684 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.9495 | −0.814702 | −0.407351 | − | 0.913272i | \(-0.633547\pi\) | ||||
−0.407351 | + | 0.913272i | \(0.633547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.68151 | −0.243369 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.7315 | 1.86983 | 0.934913 | − | 0.354878i | \(-0.115477\pi\) | ||||
0.934913 | + | 0.354878i | \(0.115477\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.35338 | −0.398467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.7594 | 0.840256 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.8688 | 1.18084 | 0.590420 | − | 0.807096i | \(-0.298962\pi\) | ||||
0.590420 | + | 0.807096i | \(0.298962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.5668 | −0.827589 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.0479 | −1.26637 | −0.633185 | − | 0.774001i | \(-0.718253\pi\) | ||||
−0.633185 | + | 0.774001i | \(0.718253\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.56012 | −0.275986 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0792 | −0.590229 | −0.295115 | − | 0.955462i | \(-0.595358\pi\) | ||||
−0.295115 | + | 0.955462i | \(0.595358\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8750 | −0.580652 | −0.290326 | − | 0.956928i | \(-0.593764\pi\) | ||||
−0.290326 | + | 0.956928i | \(0.593764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.5263 | −0.605788 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.7653 | 1.57219 | 0.786095 | − | 0.618106i | \(-0.212100\pi\) | ||||
0.786095 | + | 0.618106i | \(0.212100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.3549 | −1.05190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −55.7063 | −2.30712 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.61252 | −0.355477 | −0.177738 | − | 0.984078i | \(-0.556878\pi\) | ||||
−0.177738 | + | 0.984078i | \(0.556878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 64.4043 | 2.65373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.03473 | 0.329947 | 0.164973 | − | 0.986298i | \(-0.447246\pi\) | ||||
0.164973 | + | 0.986298i | \(0.447246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.9808 | 0.737143 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.40827 | −0.343553 | −0.171776 | − | 0.985136i | \(-0.554951\pi\) | ||||
−0.171776 | + | 0.985136i | \(0.554951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.39706 | −0.220151 | −0.110075 | − | 0.993923i | \(-0.535109\pi\) | ||||
−0.110075 | + | 0.993923i | \(0.535109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.3924 | 1.03235 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8773 | 1.17209 | 0.586047 | − | 0.810277i | \(-0.300683\pi\) | ||||
0.586047 | + | 0.810277i | \(0.300683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.541595 | 0.0219106 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.2084 | −0.896988 | −0.448494 | − | 0.893786i | \(-0.648039\pi\) | ||||
−0.448494 | + | 0.893786i | \(0.648039\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.7583 | −1.35906 | −0.679529 | − | 0.733649i | \(-0.737816\pi\) | ||||
−0.679529 | + | 0.733649i | \(0.737816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.3368 | −0.576245 | −0.288123 | − | 0.957594i | \(-0.593031\pi\) | ||||
−0.288123 | + | 0.957594i | \(0.593031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.03123 | 0.161508 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.6383 | 0.585532 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.01694 | 0.319656 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.4989 | 0.696620 | 0.348310 | − | 0.937379i | \(-0.386756\pi\) | ||||
0.348310 | + | 0.937379i | \(0.386756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.9078 | −0.551914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.20413 | 0.285438 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.3840 | 1.75306 | 0.876532 | − | 0.481344i | \(-0.159851\pi\) | ||||
0.876532 | + | 0.481344i | \(0.159851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.3618 | −0.566376 | −0.283188 | − | 0.959064i | \(-0.591392\pi\) | ||||
−0.283188 | + | 0.959064i | \(0.591392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.04331 | 0.0410167 | 0.0205084 | − | 0.999790i | \(-0.493472\pi\) | ||||
0.0205084 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.38773 | −0.250740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.5881 | 0.610011 | 0.305006 | − | 0.952351i | \(-0.401342\pi\) | ||||
0.305006 | + | 0.952351i | \(0.401342\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.0996 | −0.433697 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.8740 | −0.968952 | −0.484476 | − | 0.874804i | \(-0.660990\pi\) | ||||
−0.484476 | + | 0.874804i | \(0.660990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.3482 | −1.88053 | −0.940263 | − | 0.340449i | \(-0.889421\pi\) | ||||
−0.940263 | + | 0.340449i | \(0.889421\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.6118 | −0.605400 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.44237 | −0.210729 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.4699 | 1.83256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.21411 | 0.316631 | 0.158315 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158315 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2798 | −0.894717 | −0.447358 | − | 0.894355i | \(-0.647635\pi\) | ||||
−0.447358 | + | 0.894355i | \(0.647635\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.2654 | −1.16148 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.1600 | −1.34536 | −0.672679 | − | 0.739934i | \(-0.734857\pi\) | ||||
−0.672679 | + | 0.739934i | \(0.734857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8004 | −0.527285 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.1136 | −0.842463 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.72267 | 0.141617 | 0.0708085 | − | 0.997490i | \(-0.477442\pi\) | ||||
0.0708085 | + | 0.997490i | \(0.477442\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.21671 | 0.122017 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.1980 | −2.20440 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.6273 | 1.23232 | 0.616159 | − | 0.787622i | \(-0.288688\pi\) | ||||
0.616159 | + | 0.787622i | \(0.288688\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.96068 | −0.262527 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.3759 | −1.33045 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.9781 | 0.524958 | 0.262479 | − | 0.964938i | \(-0.415460\pi\) | ||||
0.262479 | + | 0.964938i | \(0.415460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.4744 | 1.40343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.8004 | 0.516104 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.6076 | −0.470183 | −0.235091 | − | 0.971973i | \(-0.575539\pi\) | ||||
−0.235091 | + | 0.971973i | \(0.575539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0772 | −1.49255 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.84417 | 0.254186 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.47921 | −0.129037 | −0.0645184 | − | 0.997917i | \(-0.520551\pi\) | ||||
−0.0645184 | + | 0.997917i | \(0.520551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.9118 | 1.92003 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.4830 | −0.682684 | −0.341342 | − | 0.939939i | \(-0.610881\pi\) | ||||
−0.341342 | + | 0.939939i | \(0.610881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.67127 | −0.0615621 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.4469 | −1.00965 | −0.504825 | − | 0.863222i | \(-0.668443\pi\) | ||||
−0.504825 | + | 0.863222i | \(0.668443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.2778 | 1.66108 | 0.830541 | − | 0.556957i | \(-0.188031\pi\) | ||||
0.830541 | + | 0.556957i | \(0.188031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.2721 | 0.559527 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.1886 | 0.481900 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.5567 | 1.69888 | 0.849439 | − | 0.527688i | \(-0.176941\pi\) | ||||
0.849439 | + | 0.527688i | \(0.176941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.34084 | 0.157979 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.3427 | −1.50263 | −0.751313 | − | 0.659946i | \(-0.770579\pi\) | ||||
−0.751313 | + | 0.659946i | \(0.770579\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1699 | −0.839908 | −0.419954 | − | 0.907545i | \(-0.637954\pi\) | ||||
−0.419954 | + | 0.907545i | \(0.637954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.9191 | 0.757322 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.53573 | −0.0915598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.7297 | −1.21632 | −0.608162 | − | 0.793813i | \(-0.708093\pi\) | ||||
−0.608162 | + | 0.793813i | \(0.708093\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.3697 | −0.696680 | −0.348340 | − | 0.937368i | \(-0.613254\pi\) | ||||
−0.348340 | + | 0.937368i | \(0.613254\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.1268 | −1.69284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.5302 | 1.81043 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0152 | 0.537286 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.2070 | −0.614144 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.7810 | 1.09722 | 0.548611 | − | 0.836078i | \(-0.315157\pi\) | ||||
0.548611 | + | 0.836078i | \(0.315157\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.1541 | 0.858822 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.8441 | 0.669172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.70950 | 0.202241 | 0.101120 | − | 0.994874i | \(-0.467757\pi\) | ||||
0.101120 | + | 0.994874i | \(0.467757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.43688 | −0.0508331 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.4918 | 1.11132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.08391 | −0.320166 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.2013 | 1.83530 | 0.917650 | − | 0.397390i | \(-0.130084\pi\) | ||||
0.917650 | + | 0.397390i | \(0.130084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.84966 | −0.240524 | −0.120262 | − | 0.992742i | \(-0.538374\pi\) | ||||
−0.120262 | + | 0.992742i | \(0.538374\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.50796 | 0.227964 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.0722 | −1.57688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.9734 | 0.522575 | 0.261287 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261287 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.0224 | −0.976799 | −0.488399 | − | 0.872620i | \(-0.662419\pi\) | ||||
−0.488399 | + | 0.872620i | \(0.662419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.4527 | −1.33713 | −0.668566 | − | 0.743652i | \(-0.733092\pi\) | ||||
−0.668566 | + | 0.743652i | \(0.733092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.8364 | −1.90455 | −0.952273 | − | 0.305248i | \(-0.901261\pi\) | ||||
−0.952273 | + | 0.305248i | \(0.901261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.1129 | −0.662224 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.8906 | 0.549917 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.3598 | −0.392185 | −0.196093 | − | 0.980585i | \(-0.562825\pi\) | ||||
−0.196093 | + | 0.980585i | \(0.562825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4358 | −0.911579 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.59773 | −0.192568 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −93.4937 | −3.21248 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.05015 | −0.138837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.73152 | 0.0935255 | 0.0467627 | − | 0.998906i | \(-0.485110\pi\) | ||||
0.0467627 | + | 0.998906i | \(0.485110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.0728 | −1.91541 | −0.957706 | − | 0.287749i | \(-0.907093\pi\) | ||||
−0.957706 | + | 0.287749i | \(0.907093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.13991 | −0.209491 | −0.104746 | − | 0.994499i | \(-0.533403\pi\) | ||||
−0.104746 | + | 0.994499i | \(0.533403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7746 | 1.31990 | 0.659952 | − | 0.751308i | \(-0.270577\pi\) | ||||
0.659952 | + | 0.751308i | \(0.270577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.87699 | 0.301827 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.2347 | −1.36487 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.663442 | −0.0224799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.7875 | 0.837972 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.4025 | −0.452571 | −0.226286 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226286 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.4389 | −0.688604 | −0.344302 | − | 0.938859i | \(-0.611884\pi\) | ||||
−0.344302 | + | 0.938859i | \(0.611884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8059 | −0.363646 | −0.181823 | − | 0.983331i | \(-0.558200\pi\) | ||||
−0.181823 | + | 0.983331i | \(0.558200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.1139 | 0.574628 | 0.287314 | − | 0.957836i | \(-0.407238\pi\) | ||||
0.287314 | + | 0.957836i | \(0.407238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 51.2080 | 1.71746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.24756 | 0.0417482 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.2706 | −0.644146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.6564 | −0.588873 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.6686 | 1.95453 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.02225 | −0.200186 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.04930 | −0.234068 | −0.117034 | − | 0.993128i | \(-0.537339\pi\) | ||||
−0.117034 | + | 0.993128i | \(0.537339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.05039 | 0.200458 | 0.100229 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100229 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.6282 | 1.70865 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.8683 | 1.34959 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.04655 | 0.232444 | 0.116222 | − | 0.993223i | \(-0.462922\pi\) | ||||
0.116222 | + | 0.993223i | \(0.462922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.96056 | 0.196194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.09336 | 0.167469 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7183 | −0.581319 | −0.290659 | − | 0.956827i | \(-0.593875\pi\) | ||||
−0.290659 | + | 0.956827i | \(0.593875\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5947 | 0.543870 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.6131 | −1.19737 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1685 | 0.724214 | 0.362107 | − | 0.932136i | \(-0.382057\pi\) | ||||
0.362107 | + | 0.932136i | \(0.382057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.75662 | −0.0572641 | −0.0286320 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286320 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.4016 | 0.957447 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.3738 | 1.79941 | 0.899703 | − | 0.436502i | \(-0.143783\pi\) | ||||
0.899703 | + | 0.436502i | \(0.143783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5013 | 0.405808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.1588 | −0.814974 | −0.407487 | − | 0.913211i | \(-0.633595\pi\) | ||||
−0.407487 | + | 0.913211i | \(0.633595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.8243 | 0.706218 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.8124 | 1.64082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 90.5760 | 2.92181 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.445833 | −0.0143519 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.0734189 | −0.00236099 | −0.00118050 | − | 0.999999i | \(-0.500376\pi\) | ||||
−0.00118050 | + | 0.999999i | \(0.500376\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.97610 | −0.255965 | −0.127983 | − | 0.991776i | \(-0.540850\pi\) | ||||
−0.127983 | + | 0.991776i | \(0.540850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8438 | −0.379695 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.94166 | 0.126105 | 0.0630524 | − | 0.998010i | \(-0.479916\pi\) | ||||
0.0630524 | + | 0.998010i | \(0.479916\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.20850 | −0.262345 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.1049 | −0.449877 | −0.224938 | − | 0.974373i | \(-0.572218\pi\) | ||||
−0.224938 | + | 0.974373i | \(0.572218\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6134 | 0.433759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26.2258 | −0.833932 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.0752 | 1.81305 | 0.906527 | − | 0.422147i | \(-0.138723\pi\) | ||||
0.906527 | + | 0.422147i | \(0.138723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.80421 | 0.310814 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2175 | 0.988668 | 0.494334 | − | 0.869272i | \(-0.335412\pi\) | ||||
0.494334 | + | 0.869272i | \(0.335412\pi\) | |||||||
\(998\) | 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 | 8496.2.a.bs.1.3 | 4 | ||
3.2 | odd | 2 | 8496.2.a.bp.1.2 | 4 | |||
4.3 | odd | 2 | 2124.2.a.i.1.3 | ✓ | 4 | ||
12.11 | even | 2 | 2124.2.a.j.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2124.2.a.i.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
2124.2.a.j.1.2 | yes | 4 | 12.11 | even | 2 | ||
8496.2.a.bp.1.2 | 4 | 3.2 | odd | 2 | |||
8496.2.a.bs.1.3 | 4 | 1.1 | even | 1 | trivial |