Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4840,2,Mod(1,4840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4840, 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("4840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4840.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: | \(38.6475945783\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 21x^{6} + 15x^{5} + 140x^{4} - 60x^{3} - 295x^{2} + 50x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.21195\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4840.1 |
$q$-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 | ||||||||
\(3\) | 3.21195 | 1.85442 | 0.927210 | − | 0.374542i | \(-0.122200\pi\) | ||||
0.927210 | + | 0.374542i | \(0.122200\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.90937 | 1.85557 | 0.927783 | − | 0.373120i | \(-0.121712\pi\) | ||||
0.927783 | + | 0.373120i | \(0.121712\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.31662 | 2.43887 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.804699 | 0.223183 | 0.111592 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.21195 | 0.829322 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.84749 | −0.448082 | −0.224041 | − | 0.974580i | \(-0.571925\pi\) | ||||
−0.224041 | + | 0.974580i | \(0.571925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.61737 | −1.28871 | −0.644357 | − | 0.764725i | \(-0.722875\pi\) | ||||
−0.644357 | + | 0.764725i | \(0.722875\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 15.7686 | 3.44100 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.60313 | −0.334275 | −0.167138 | − | 0.985934i | \(-0.553452\pi\) | ||||
−0.167138 | + | 0.985934i | \(0.553452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.8648 | 2.66827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.86486 | −1.46047 | −0.730234 | − | 0.683197i | \(-0.760589\pi\) | ||||
−0.730234 | + | 0.683197i | \(0.760589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.86973 | 0.695024 | 0.347512 | − | 0.937676i | \(-0.387027\pi\) | ||||
0.347512 | + | 0.937676i | \(0.387027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.90937 | 0.829834 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.67764 | −1.09780 | −0.548899 | − | 0.835889i | \(-0.684953\pi\) | ||||
−0.548899 | + | 0.835889i | \(0.684953\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.58465 | 0.413876 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.23795 | 0.818031 | 0.409015 | − | 0.912527i | \(-0.365872\pi\) | ||||
0.409015 | + | 0.912527i | \(0.365872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.05407 | −0.160744 | −0.0803718 | − | 0.996765i | \(-0.525611\pi\) | ||||
−0.0803718 | + | 0.996765i | \(0.525611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.31662 | 1.09070 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.65181 | 1.26200 | 0.630998 | − | 0.775784i | \(-0.282645\pi\) | ||||
0.630998 | + | 0.775784i | \(0.282645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.1019 | 2.44313 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.93404 | −0.830932 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.82577 | 1.07495 | 0.537476 | − | 0.843279i | \(-0.319378\pi\) | ||||
0.537476 | + | 0.843279i | \(0.319378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.0427 | −2.38982 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.89313 | 0.506842 | 0.253421 | − | 0.967356i | \(-0.418444\pi\) | ||||
0.253421 | + | 0.967356i | \(0.418444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.62282 | −0.847965 | −0.423983 | − | 0.905670i | \(-0.639368\pi\) | ||||
−0.423983 | + | 0.905670i | \(0.639368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 35.9200 | 4.52549 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.804699 | 0.0998107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.52774 | −0.675321 | −0.337661 | − | 0.941268i | \(-0.609636\pi\) | ||||
−0.337661 | + | 0.941268i | \(0.609636\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.14916 | −0.619887 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9694 | −1.30183 | −0.650915 | − | 0.759150i | \(-0.725615\pi\) | ||||
−0.650915 | + | 0.759150i | \(0.725615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.79991 | −0.327705 | −0.163853 | − | 0.986485i | \(-0.552392\pi\) | ||||
−0.163853 | + | 0.986485i | \(0.552392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.21195 | 0.370884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.91983 | 0.328506 | 0.164253 | − | 0.986418i | \(-0.447479\pi\) | ||||
0.164253 | + | 0.986418i | \(0.447479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 22.5830 | 2.50923 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.93633 | −0.212540 | −0.106270 | − | 0.994337i | \(-0.533891\pi\) | ||||
−0.106270 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.84749 | −0.200388 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −25.2615 | −2.70832 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.32421 | 0.776365 | 0.388183 | − | 0.921583i | \(-0.373103\pi\) | ||||
0.388183 | + | 0.921583i | \(0.373103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.95056 | 0.414132 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4294 | 1.28887 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.61737 | −0.576330 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.15740 | 0.828258 | 0.414129 | − | 0.910218i | \(-0.364086\pi\) | ||||
0.414129 | + | 0.910218i | \(0.364086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.38078 | 0.634912 | 0.317456 | − | 0.948273i | \(-0.397171\pi\) | ||||
0.317456 | + | 0.948273i | \(0.397171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0414 | −1.48208 | −0.741038 | − | 0.671463i | \(-0.765666\pi\) | ||||
−0.741038 | + | 0.671463i | \(0.765666\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.7686 | 1.53886 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.61756 | 0.543070 | 0.271535 | − | 0.962429i | \(-0.412469\pi\) | ||||
0.271535 | + | 0.962429i | \(0.412469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2032 | −1.36042 | −0.680208 | − | 0.733019i | \(-0.738110\pi\) | ||||
−0.680208 | + | 0.733019i | \(0.738110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.4482 | −2.03578 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.01592 | 0.565930 | 0.282965 | − | 0.959130i | \(-0.408682\pi\) | ||||
0.282965 | + | 0.959130i | \(0.408682\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.60313 | −0.149492 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.88768 | 0.544316 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.07001 | −0.831446 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8240 | 1.51697 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.26040 | 0.111842 | 0.0559211 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559211 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.38561 | −0.298086 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0760 | −1.05509 | −0.527543 | − | 0.849528i | \(-0.676887\pi\) | ||||
−0.527543 | + | 0.849528i | \(0.676887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.5777 | −2.39129 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.8648 | 1.19329 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.04007 | −0.772345 | −0.386173 | − | 0.922426i | \(-0.626203\pi\) | ||||
−0.386173 | + | 0.922426i | \(0.626203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.6951 | −1.84015 | −0.920076 | − | 0.391740i | \(-0.871873\pi\) | ||||
−0.920076 | + | 0.391740i | \(0.871873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.7892 | 2.34027 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.86486 | −0.653141 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.9304 | 4.53058 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.62139 | 0.542445 | 0.271223 | − | 0.962517i | \(-0.412572\pi\) | ||||
0.271223 | + | 0.962517i | \(0.412572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.12497 | −0.0915489 | −0.0457745 | − | 0.998952i | \(-0.514576\pi\) | ||||
−0.0457745 | + | 0.998952i | \(0.514576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5174 | −1.09282 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.86973 | 0.310824 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.84097 | −0.466160 | −0.233080 | − | 0.972458i | \(-0.574880\pi\) | ||||
−0.233080 | + | 0.972458i | \(0.574880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.1360 | 1.99341 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.87034 | −0.620270 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6105 | −1.14438 | −0.572190 | − | 0.820121i | \(-0.693906\pi\) | ||||
−0.572190 | + | 0.820121i | \(0.693906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.73740 | 0.521356 | 0.260678 | − | 0.965426i | \(-0.416054\pi\) | ||||
0.260678 | + | 0.965426i | \(0.416054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3525 | −0.950189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −41.1002 | −3.14301 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.48506 | −0.188936 | −0.0944678 | − | 0.995528i | \(-0.530115\pi\) | ||||
−0.0944678 | + | 0.995528i | \(0.530115\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.90937 | 0.371113 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.5045 | 0.939898 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.8751 | −1.93400 | −0.966999 | − | 0.254782i | \(-0.917996\pi\) | ||||
−0.966999 | + | 0.254782i | \(0.917996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2925 | 1.06235 | 0.531177 | − | 0.847261i | \(-0.321750\pi\) | ||||
0.531177 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.2722 | −1.57248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.67764 | −0.490950 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 68.0671 | 4.95116 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.92551 | 0.284040 | 0.142020 | − | 0.989864i | \(-0.454640\pi\) | ||||
0.142020 | + | 0.989864i | \(0.454640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5814 | −0.761669 | −0.380835 | − | 0.924643i | \(-0.624363\pi\) | ||||
−0.380835 | + | 0.924643i | \(0.624363\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.58465 | 0.185091 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.89648 | 0.135119 | 0.0675594 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675594 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9966 | 0.992189 | 0.496095 | − | 0.868268i | \(-0.334767\pi\) | ||||
0.496095 | + | 0.868268i | \(0.334767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.7548 | −1.25233 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −38.6115 | −2.70999 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.23795 | 0.365834 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.7295 | −0.815255 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.2000 | −1.87252 | −0.936262 | − | 0.351302i | \(-0.885739\pi\) | ||||
−0.936262 | + | 0.351302i | \(0.885739\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −35.2332 | −2.41414 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.05407 | −0.0718867 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9979 | 1.28966 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.99318 | −0.607703 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.48667 | −0.100005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1911 | 0.816378 | 0.408189 | − | 0.912897i | \(-0.366160\pi\) | ||||
0.408189 | + | 0.912897i | \(0.366160\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.31662 | 0.487774 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3556 | 1.15193 | 0.575966 | − | 0.817474i | \(-0.304626\pi\) | ||||
0.575966 | + | 0.817474i | \(0.304626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.676698 | 0.0447175 | 0.0223587 | − | 0.999750i | \(-0.492882\pi\) | ||||
0.0223587 | + | 0.999750i | \(0.492882\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.38766 | −0.156421 | −0.0782105 | − | 0.996937i | \(-0.524921\pi\) | ||||
−0.0782105 | + | 0.996937i | \(0.524921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.65181 | 0.564382 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.37834 | 0.609189 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.18939 | 0.529727 | 0.264864 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264864 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.43609 | −0.607832 | −0.303916 | − | 0.952699i | \(-0.598294\pi\) | ||||
−0.303916 | + | 0.952699i | \(0.598294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 30.9413 | 1.98488 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.1019 | 1.09260 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.52030 | −0.287619 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.21940 | −0.394138 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5177 | 1.16882 | 0.584412 | − | 0.811457i | \(-0.301325\pi\) | ||||
0.584412 | + | 0.811457i | \(0.301325\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.93404 | −0.371604 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0138 | 1.68507 | 0.842536 | − | 0.538640i | \(-0.181062\pi\) | ||||
0.842536 | + | 0.538640i | \(0.181062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.7830 | −2.03704 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −57.5442 | −3.56189 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.4169 | 1.07397 | 0.536985 | − | 0.843592i | \(-0.319563\pi\) | ||||
0.536985 | + | 0.843592i | \(0.319563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.82577 | 0.480734 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.5250 | 1.43971 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4185 | −0.635226 | −0.317613 | − | 0.948220i | \(-0.602881\pi\) | ||||
−0.317613 | + | 0.948220i | \(0.602881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.2995 | 1.84056 | 0.920282 | − | 0.391255i | \(-0.127959\pi\) | ||||
0.920282 | + | 0.391255i | \(0.127959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6890 | 0.767974 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.13844 | 0.188571 | 0.0942854 | − | 0.995545i | \(-0.469943\pi\) | ||||
0.0942854 | + | 0.995545i | \(0.469943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.3133 | 1.69507 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6302 | −0.693801 | −0.346901 | − | 0.937902i | \(-0.612766\pi\) | ||||
−0.346901 | + | 0.937902i | \(0.612766\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.14782 | 0.127675 | 0.0638374 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638374 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.0427 | −1.06876 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.7150 | 1.51791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5868 | −0.799222 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.2011 | 1.53594 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.1399 | 1.52711 | 0.763553 | − | 0.645745i | \(-0.223453\pi\) | ||||
0.763553 | + | 0.645745i | \(0.223453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.89313 | 0.226667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.29004 | −0.0746047 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.17480 | −0.298270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.4947 | 1.17739 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.62282 | −0.379222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.59232 | 0.319171 | 0.159585 | − | 0.987184i | \(-0.448984\pi\) | ||||
0.159585 | + | 0.987184i | \(0.448984\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.3123 | −2.74839 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71451 | 0.0972211 | 0.0486106 | − | 0.998818i | \(-0.484521\pi\) | ||||
0.0486106 | + | 0.998818i | \(0.484521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.29655 | −0.299379 | −0.149689 | − | 0.988733i | \(-0.547827\pi\) | ||||
−0.149689 | + | 0.988733i | \(0.547827\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 35.9200 | 2.02386 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.73781 | 0.434599 | 0.217299 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217299 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0433 | 1.00708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3780 | 0.577450 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.804699 | 0.0446367 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −45.6198 | −2.52278 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.4749 | 2.34172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7346 | −1.02975 | −0.514874 | − | 0.857266i | \(-0.672161\pi\) | ||||
−0.514874 | + | 0.857266i | \(0.672161\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −48.8577 | −2.67739 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.52774 | −0.302013 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8034 | 0.588499 | 0.294250 | − | 0.955729i | \(-0.404930\pi\) | ||||
0.294250 | + | 0.955729i | \(0.404930\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.3228 | 1.04947 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 49.5938 | 2.67782 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.14916 | −0.277222 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.4530 | 0.829560 | 0.414780 | − | 0.909922i | \(-0.363859\pi\) | ||||
0.414780 | + | 0.909922i | \(0.363859\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.4964 | 1.52538 | 0.762690 | − | 0.646765i | \(-0.223878\pi\) | ||||
0.762690 | + | 0.646765i | \(0.223878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1570 | 0.595514 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.7619 | −0.892148 | −0.446074 | − | 0.894996i | \(-0.647178\pi\) | ||||
−0.446074 | + | 0.894996i | \(0.647178\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.9694 | −0.582196 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.1324 | −1.54185 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0160 | 0.792514 | 0.396257 | − | 0.918140i | \(-0.370309\pi\) | ||||
0.396257 | + | 0.918140i | \(0.370309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.5549 | 0.660783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.79991 | −0.146554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.4306 | −1.06647 | −0.533236 | − | 0.845967i | \(-0.679024\pi\) | ||||
−0.533236 | + | 0.845967i | \(0.679024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.3241 | 1.99507 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38.4196 | 1.99465 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.8624 | −0.873101 | −0.436550 | − | 0.899680i | \(-0.643800\pi\) | ||||
−0.436550 | + | 0.899680i | \(0.643800\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.21195 | 0.165864 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.32885 | −0.325952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3238 | −1.24943 | −0.624715 | − | 0.780853i | \(-0.714785\pi\) | ||||
−0.624715 | + | 0.780853i | \(0.714785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.04833 | 0.207402 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5978 | 0.643716 | 0.321858 | − | 0.946788i | \(-0.395693\pi\) | ||||
0.321858 | + | 0.946788i | \(0.395693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.71220 | −0.392033 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.7471 | −1.05192 | −0.525961 | − | 0.850509i | \(-0.676294\pi\) | ||||
−0.525961 | + | 0.850509i | \(0.676294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.96176 | 0.149783 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −38.7876 | −1.95657 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.91983 | 0.146913 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.76055 | −0.188737 | −0.0943683 | − | 0.995537i | \(-0.530083\pi\) | ||||
−0.0943683 | + | 0.995537i | \(0.530083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −88.5783 | −4.43446 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8516 | −0.841530 | −0.420765 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420765 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.11397 | 0.155118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.5830 | 1.12216 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.7119 | −1.07358 | −0.536792 | − | 0.843715i | \(-0.680364\pi\) | ||||
−0.536792 | + | 0.843715i | \(0.680364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.0362 | −1.43225 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.1128 | 0.940479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.93633 | −0.0950507 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −69.6835 | −3.41241 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.1675 | −1.91346 | −0.956729 | − | 0.290981i | \(-0.906018\pi\) | ||||
−0.956729 | + | 0.290981i | \(0.906018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.44175 | −0.411426 | −0.205713 | − | 0.978612i | \(-0.565951\pi\) | ||||
−0.205713 | + | 0.978612i | \(0.565951\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 63.3020 | 3.07785 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.84749 | −0.0896164 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.5138 | −1.57346 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.69401 | −0.0815977 | −0.0407988 | − | 0.999167i | \(-0.512990\pi\) | ||||
−0.0407988 | + | 0.999167i | \(0.512990\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.8944 | 1.91720 | 0.958601 | − | 0.284754i | \(-0.0919118\pi\) | ||||
0.958601 | + | 0.284754i | \(0.0919118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.2615 | −1.21120 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.00536 | 0.430785 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.598520 | 0.0285658 | 0.0142829 | − | 0.999898i | \(-0.495453\pi\) | ||||
0.0142829 | + | 0.999898i | \(0.495453\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 125.128 | 5.95847 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.5608 | −1.73706 | −0.868529 | − | 0.495639i | \(-0.834934\pi\) | ||||
−0.868529 | + | 0.495639i | \(0.834934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.32421 | 0.347201 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.2676 | 1.00592 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.0092 | −1.69938 | −0.849689 | − | 0.527284i | \(-0.823210\pi\) | ||||
−0.849689 | + | 0.527284i | \(0.823210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.61335 | −0.169770 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.95056 | 0.185205 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.8344 | 0.506812 | 0.253406 | − | 0.967360i | \(-0.418449\pi\) | ||||
0.253406 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.6150 | −1.19561 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.70020 | −0.265485 | −0.132742 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132742 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.28911 | −0.292280 | −0.146140 | − | 0.989264i | \(-0.546685\pi\) | ||||
−0.146140 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.4294 | 0.576398 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.785087 | 0.0363295 | 0.0181647 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181647 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.1377 | −1.25310 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7609 | −0.864456 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.61737 | −0.257743 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 57.2582 | 2.62167 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.5558 | −1.76166 | −0.880829 | − | 0.473435i | \(-0.843014\pi\) | ||||
−0.880829 | + | 0.473435i | \(0.843014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.37349 | −0.245010 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.2791 | −1.15024 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.15740 | 0.370408 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9940 | 0.724759 | 0.362379 | − | 0.932031i | \(-0.381965\pi\) | ||||
0.362379 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.9280 | −2.12216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.2541 | 1.13970 | 0.569850 | − | 0.821749i | \(-0.307001\pi\) | ||||
0.569850 | + | 0.821749i | \(0.307001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5302 | 0.654409 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −53.8529 | −2.41563 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.96527 | −0.222276 | −0.111138 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111138 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6402 | 0.966812 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.1890 | 0.900185 | 0.450093 | − | 0.892982i | \(-0.351391\pi\) | ||||
0.450093 | + | 0.892982i | \(0.351391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.38078 | 0.283941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.6755 | −1.76205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.2638 | 1.60736 | 0.803682 | − | 0.595059i | \(-0.202871\pi\) | ||||
0.803682 | + | 0.595059i | \(0.202871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7458 | −0.608079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −77.8835 | −3.43864 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.0414 | −0.662805 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.98188 | −0.350366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0780 | −0.485337 | −0.242668 | − | 0.970109i | \(-0.578023\pi\) | ||||
−0.242668 | + | 0.970109i | \(0.578023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.5405 | 1.02935 | 0.514676 | − | 0.857385i | \(-0.327912\pi\) | ||||
0.514676 | + | 0.857385i | \(0.327912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.7686 | 0.688200 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.14928 | −0.311428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4300 | −0.888260 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.4845 | 1.23612 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.21498 | 0.182571 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.61756 | 0.242868 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −83.1096 | −3.58644 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.6020 | 1.10072 | 0.550358 | − | 0.834929i | \(-0.314491\pi\) | ||||
0.550358 | + | 0.834929i | \(0.314491\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.9069 | 1.97005 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.2032 | −0.608396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7459 | 1.18633 | 0.593164 | − | 0.805081i | \(-0.297878\pi\) | ||||
0.593164 | + | 0.805081i | \(0.297878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −48.4566 | −2.06808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.1798 | 1.88212 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3345 | 0.609565 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.4482 | −0.910427 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.80957 | −0.330902 | −0.165451 | − | 0.986218i | \(-0.552908\pi\) | ||||
−0.165451 | + | 0.986218i | \(0.552908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.848206 | −0.0358753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.3975 | 1.28110 | 0.640551 | − | 0.767916i | \(-0.278706\pi\) | ||||
0.640551 | + | 0.767916i | \(0.278706\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.01592 | 0.253092 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 110.868 | 4.65603 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.98020 | 0.0830141 | 0.0415071 | − | 0.999138i | \(-0.486784\pi\) | ||||
0.0415071 | + | 0.999138i | \(0.486784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.2773 | 1.39261 | 0.696307 | − | 0.717744i | \(-0.254825\pi\) | ||||
0.696307 | + | 0.717744i | \(0.254825\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6085 | 0.526729 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.60313 | −0.0668550 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.9736 | 1.49760 | 0.748800 | − | 0.662796i | \(-0.230630\pi\) | ||||
0.748800 | + | 0.662796i | \(0.230630\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.9871 | −1.41245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.50616 | −0.394382 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.88768 | 0.243425 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.4760 | 0.886411 | 0.443205 | − | 0.896420i | \(-0.353841\pi\) | ||||
0.443205 | + | 0.896420i | \(0.353841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.7377 | −0.895686 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.09140 | 0.250567 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.2405 | −0.584787 | −0.292393 | − | 0.956298i | \(-0.594452\pi\) | ||||
−0.292393 | + | 0.956298i | \(0.594452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.07001 | −0.371834 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.9562 | 1.83994 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.8230 | 1.74970 | 0.874851 | − | 0.484393i | \(-0.160959\pi\) | ||||
0.874851 | + | 0.484393i | \(0.160959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8267 | −0.645584 | −0.322792 | − | 0.946470i | \(-0.604621\pi\) | ||||
−0.322792 | + | 0.946470i | \(0.604621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −40.4444 | −1.64702 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.2675 | −1.47205 | −0.736025 | − | 0.676954i | \(-0.763300\pi\) | ||||
−0.736025 | + | 0.676954i | \(0.763300\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −124.018 | −5.02547 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.96211 | 0.281657 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.9422 | −1.57286 | −0.786430 | − | 0.617679i | \(-0.788073\pi\) | ||||
−0.786430 | + | 0.617679i | \(0.788073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.8240 | 0.678411 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2869 | −1.21931 | −0.609653 | − | 0.792669i | \(-0.708691\pi\) | ||||
−0.609653 | + | 0.792669i | \(0.708691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0538 | 0.806032 | 0.403016 | − | 0.915193i | \(-0.367962\pi\) | ||||
0.403016 | + | 0.915193i | \(0.367962\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.2270 | −0.891937 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.9572 | 1.44060 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.3369 | 0.491903 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1601 | −0.484085 | −0.242043 | − | 0.970266i | \(-0.577817\pi\) | ||||
−0.242043 | + | 0.970266i | \(0.577817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −87.3650 | −3.47245 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.26040 | 0.0500174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.7619 | 0.545265 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −80.2590 | −3.17500 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.1883 | 0.678897 | 0.339449 | − | 0.940625i | \(-0.389760\pi\) | ||||
0.339449 | + | 0.940625i | \(0.389760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3045 | −0.445807 | −0.222904 | − | 0.974840i | \(-0.571554\pi\) | ||||
−0.222904 | + | 0.974840i | \(0.571554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.38561 | −0.133308 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.1833 | 0.832801 | 0.416400 | − | 0.909181i | \(-0.363291\pi\) | ||||
0.416400 | + | 0.909181i | \(0.363291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 61.0203 | 2.39158 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.4832 | 0.488507 | 0.244253 | − | 0.969711i | \(-0.421457\pi\) | ||||
0.244253 | + | 0.969711i | \(0.421457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.0760 | −0.471849 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.4859 | −0.799231 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.2784 | 0.400391 | 0.200195 | − | 0.979756i | \(-0.435842\pi\) | ||||
0.200195 | + | 0.979756i | \(0.435842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.9264 | −1.55296 | −0.776478 | − | 0.630145i | \(-0.782996\pi\) | ||||
−0.776478 | + | 0.630145i | \(0.782996\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.77512 | −0.185450 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.5777 | −1.06942 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.6084 | 0.488198 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.1573 | 1.51391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.9293 | −0.806765 | −0.403382 | − | 0.915031i | \(-0.632166\pi\) | ||||
−0.403382 | + | 0.915031i | \(0.632166\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.8648 | 0.533655 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.8878 | −0.725917 | −0.362958 | − | 0.931805i | \(-0.618233\pi\) | ||||
−0.362958 | + | 0.931805i | \(0.618233\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.0477 | 1.53689 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 55.7453 | 2.13616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.5145 | 0.440590 | 0.220295 | − | 0.975433i | \(-0.429298\pi\) | ||||
0.220295 | + | 0.975433i | \(0.429298\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.04007 | −0.345403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.17352 | 0.0829249 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.29740 | 0.239912 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7689 | 0.866170 | 0.433085 | − | 0.901353i | \(-0.357425\pi\) | ||||
0.433085 | + | 0.901353i | \(0.357425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.6951 | −0.822941 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.67707 | −0.366545 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.66905 | −0.290070 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.63323 | 0.250534 | 0.125267 | − | 0.992123i | \(-0.460021\pi\) | ||||
0.125267 | + | 0.992123i | \(0.460021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.5108 | 1.41475 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.7892 | 1.04660 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.3256 | 1.17812 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.3101 | −1.40121 | −0.700604 | − | 0.713550i | \(-0.747086\pi\) | ||||
−0.700604 | + | 0.713550i | \(0.747086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.3633 | 0.801185 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.20367 | −0.232329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.3039 | 0.982337 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.6334 | 0.918670 | 0.459335 | − | 0.888263i | \(-0.348088\pi\) | ||||
0.459335 | + | 0.888263i | \(0.348088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −73.8439 | −2.75009 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.3082 | −1.12717 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.86486 | −0.292094 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.1865 | −1.15664 | −0.578321 | − | 0.815809i | \(-0.696292\pi\) | ||||
−0.578321 | + | 0.815809i | \(0.696292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 31.6327 | 1.17158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.94738 | 0.0720263 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2957 | 0.454152 | 0.227076 | − | 0.973877i | \(-0.427083\pi\) | ||||
0.227076 | + | 0.973877i | \(0.427083\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 54.9304 | 2.02614 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.49260 | −0.0549063 | −0.0274532 | − | 0.999623i | \(-0.508740\pi\) | ||||
−0.0274532 | + | 0.999623i | \(0.508740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.5190 | −0.533367 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.96694 | −0.365652 | −0.182826 | − | 0.983145i | \(-0.558524\pi\) | ||||
−0.182826 | + | 0.983145i | \(0.558524\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.62139 | 0.242589 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1674 | −0.518358 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.5786 | 1.00770 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1885 | 0.408275 | 0.204137 | − | 0.978942i | \(-0.434561\pi\) | ||||
0.204137 | + | 0.978942i | \(0.434561\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 59.4778 | 2.16749 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.12497 | −0.0409419 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.7830 | 1.59132 | 0.795661 | − | 0.605742i | \(-0.207124\pi\) | ||||
0.795661 | + | 0.605742i | \(0.207124\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.41151 | 0.0511670 | 0.0255835 | − | 0.999673i | \(-0.491856\pi\) | ||||
0.0255835 | + | 0.999673i | \(0.491856\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −69.7285 | −2.52434 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.5174 | −0.488722 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.13280 | 0.113119 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.9335 | −1.54822 | −0.774111 | − | 0.633049i | \(-0.781803\pi\) | ||||
−0.774111 | + | 0.633049i | \(0.781803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 86.7668 | 3.12483 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.09741 | 0.255276 | 0.127638 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127638 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.86973 | 0.139005 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −105.297 | −3.77752 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.4235 | −1.05421 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −109.044 | −3.89693 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.84097 | −0.208473 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2598 | 1.54205 | 0.771023 | − | 0.636807i | \(-0.219745\pi\) | ||||
0.771023 | + | 0.636807i | \(0.219745\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 55.9421 | 1.99159 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.5343 | 1.05012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.32938 | −0.189252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.1360 | 0.891482 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.3172 | −1.25100 | −0.625500 | − | 0.780224i | \(-0.715105\pi\) | ||||
−0.625500 | + | 0.780224i | \(0.715105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9841 | −0.565478 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 53.5885 | 1.89346 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.87034 | −0.277393 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.4636 | −1.17798 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.08007 | −0.143448 | −0.0717238 | − | 0.997425i | \(-0.522850\pi\) | ||||
−0.0717238 | + | 0.997425i | \(0.522850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.1960 | 1.27102 | 0.635508 | − | 0.772095i | \(-0.280791\pi\) | ||||
0.635508 | + | 0.772095i | \(0.280791\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 97.3205 | 3.41318 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.6105 | −0.511782 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.92108 | 0.207152 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.9048 | 1.01001 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.0761 | 0.561060 | 0.280530 | − | 0.959845i | \(-0.409490\pi\) | ||||
0.280530 | + | 0.959845i | \(0.409490\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.0538 | −1.04761 | −0.523805 | − | 0.851838i | \(-0.675488\pi\) | ||||
−0.523805 | + | 0.851838i | \(0.675488\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.628773 | 0.0218646 | 0.0109323 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109323 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.92727 | 0.171131 | 0.0855655 | − | 0.996333i | \(-0.472730\pi\) | ||||
0.0855655 | + | 0.996333i | \(0.472730\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0805 | 0.349689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.5956 | −1.09472 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.73740 | 0.233157 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.6528 | 1.85451 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.09432 | 0.210399 | 0.105200 | − | 0.994451i | \(-0.466452\pi\) | ||||
0.105200 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8560 | 1.13297 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.3557 | −1.28660 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.3525 | −0.424938 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.89870 | 0.236763 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.7051 | 0.366966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2383 | −0.555990 | −0.277995 | − | 0.960582i | \(-0.589670\pi\) | ||||
−0.277995 | + | 0.960582i | \(0.589670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41.1002 | −1.40560 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.8315 | −1.46310 | −0.731548 | − | 0.681790i | \(-0.761202\pi\) | ||||
−0.731548 | + | 0.681790i | \(0.761202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.2561 | 0.861725 | 0.430863 | − | 0.902417i | \(-0.358209\pi\) | ||||
0.430863 | + | 0.902417i | \(0.358209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 82.5954 | 2.81484 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.1766 | 0.754901 | 0.377451 | − | 0.926030i | \(-0.376801\pi\) | ||||
0.377451 | + | 0.926030i | \(0.376801\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.48506 | −0.0844946 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.6400 | −1.48209 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.44817 | −0.150720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 59.6846 | 2.02002 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.90937 | 0.165967 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3555 | −0.653589 | −0.326794 | − | 0.945095i | \(-0.605968\pi\) | ||||
−0.326794 | + | 0.945095i | \(0.605968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 83.9599 | 2.83190 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.6226 | −1.16646 | −0.583232 | − | 0.812306i | \(-0.698212\pi\) | ||||
−0.583232 | + | 0.812306i | \(0.698212\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.68596 | −0.124042 | −0.0620211 | − | 0.998075i | \(-0.519755\pi\) | ||||
−0.0620211 | + | 0.998075i | \(0.519755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.5045 | 0.420335 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.06129 | −0.304248 | −0.152124 | − | 0.988361i | \(-0.548611\pi\) | ||||
−0.152124 | + | 0.988361i | \(0.548611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.18775 | 0.207531 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.6005 | −1.62635 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.8751 | −0.864910 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.14353 | −0.138348 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.4349 | −1.01506 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4580 | −0.481667 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.6212 | −0.553118 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.2925 | 0.475100 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4654 | 1.07799 | 0.538997 | − | 0.842308i | \(-0.318803\pi\) | ||||
0.538997 | + | 0.842308i | \(0.318803\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.6857 | 1.54847 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2941 | 1.69945 | 0.849724 | − | 0.527227i | \(-0.176768\pi\) | ||||
0.849724 | + | 0.527227i | \(0.176768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.2722 | −0.703236 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −59.2856 | −1.95778 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.3040 | −0.405870 | −0.202935 | − | 0.979192i | \(-0.565048\pi\) | ||||
−0.202935 | + | 0.979192i | \(0.565048\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.9623 | 0.591877 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.82708 | −0.290547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.67764 | −0.219559 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −110.052 | −3.61460 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3854 | 0.603207 | 0.301603 | − | 0.953434i | \(-0.402478\pi\) | ||||
0.301603 | + | 0.953434i | \(0.402478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −96.0676 | −3.14849 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.50693 | 0.180289 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.8251 | −0.418979 | −0.209489 | − | 0.977811i | \(-0.567180\pi\) | ||||
−0.209489 | + | 0.977811i | \(0.567180\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0123 | −0.555174 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.62568 | 0.281189 | 0.140595 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140595 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.39711 | −0.273447 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 68.0671 | 2.21422 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.1259 | 0.718996 | 0.359498 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359498 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.25309 | −0.0731384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.8535 | 0.805929 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.4842 | 0.987481 | 0.493741 | − | 0.869609i | \(-0.335629\pi\) | ||||
0.493741 | + | 0.869609i | \(0.335629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.92551 | 0.127027 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.3810 | −1.43314 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0252 | −0.516942 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.1015 | 1.32448 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.5814 | −0.340629 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.7942 | 1.47264 | 0.736321 | − | 0.676632i | \(-0.236561\pi\) | ||||
0.736321 | + | 0.676632i | \(0.236561\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.3337 | 1.07083 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 58.7275 | 1.88465 | 0.942327 | − | 0.334694i | \(-0.108633\pi\) | ||||
0.942327 | + | 0.334694i | \(0.108633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −106.509 | −3.41452 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.58465 | 0.0827751 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.7484 | −0.727786 | −0.363893 | − | 0.931441i | \(-0.618553\pi\) | ||||
−0.363893 | + | 0.931441i | \(0.618553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −103.919 | −3.31788 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.1105 | −1.05606 | −0.528030 | − | 0.849226i | \(-0.677069\pi\) | ||||
−0.528030 | + | 0.849226i | \(0.677069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.89648 | 0.0604270 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 136.427 | 4.34253 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.68980 | 0.0537326 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.6263 | 0.401088 | 0.200544 | − | 0.979685i | \(-0.435729\pi\) | ||||
0.200544 | + | 0.979685i | \(0.435729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −60.1747 | −1.90959 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.9966 | 0.443721 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0865 | 0.604477 | 0.302238 | − | 0.953232i | \(-0.402266\pi\) | ||||
0.302238 | + | 0.953232i | \(0.402266\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −92.5838 | −2.92922 |
(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 | 4840.2.a.bh.1.8 | 8 | ||
4.3 | odd | 2 | 9680.2.a.de.1.1 | 8 | |||
11.7 | odd | 10 | 440.2.y.d.401.1 | yes | 16 | ||
11.8 | odd | 10 | 440.2.y.d.361.1 | ✓ | 16 | ||
11.10 | odd | 2 | 4840.2.a.bg.1.8 | 8 | |||
44.7 | even | 10 | 880.2.bo.k.401.4 | 16 | |||
44.19 | even | 10 | 880.2.bo.k.801.4 | 16 | |||
44.43 | even | 2 | 9680.2.a.df.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.d.361.1 | ✓ | 16 | 11.8 | odd | 10 | ||
440.2.y.d.401.1 | yes | 16 | 11.7 | odd | 10 | ||
880.2.bo.k.401.4 | 16 | 44.7 | even | 10 | |||
880.2.bo.k.801.4 | 16 | 44.19 | even | 10 | |||
4840.2.a.bg.1.8 | 8 | 11.10 | odd | 2 | |||
4840.2.a.bh.1.8 | 8 | 1.1 | even | 1 | trivial | ||
9680.2.a.de.1.1 | 8 | 4.3 | odd | 2 | |||
9680.2.a.df.1.1 | 8 | 44.43 | even | 2 |