Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), degree \(4\), not minimal) |
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: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.228765625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 444.2 | ||
Root | \(1.37924 - 1.04771i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.444 |
Dual form | 605.2.j.b.124.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(3\) | 3.15430 | + | 1.02489i | 1.82113 | + | 0.591722i | 0.999773 | + | 0.0213149i | \(0.00678525\pi\) |
0.821362 | + | 0.570408i | \(0.193215\pi\) | |||||||
\(4\) | 0.618034 | + | 1.90211i | 0.309017 | + | 0.951057i | ||||
\(5\) | −2.18826 | − | 0.459925i | −0.978618 | − | 0.205685i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.47214 | + | 4.70228i | 2.15738 | + | 1.56743i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.63325i | 1.91485i | ||||||||
\(13\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.43104 | − | 3.69347i | −1.66049 | − | 0.953650i | ||||
\(16\) | −3.23607 | + | 2.35114i | −0.809017 | + | 0.587785i | ||||
\(17\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −0.477588 | − | 4.44656i | −0.106792 | − | 0.994281i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.31662i | − | 0.691564i | −0.938315 | − | 0.345782i | \(-0.887614\pi\) | ||
0.938315 | − | 0.345782i | \(-0.112386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.57694 | + | 2.01287i | 0.915388 | + | 0.402574i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.74732 | + | 13.4160i | 1.87587 | + | 2.58192i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.04508 | − | 2.93893i | −0.726519 | − | 0.527847i | 0.161942 | − | 0.986800i | \(-0.448224\pi\) |
−0.888460 | + | 0.458954i | \(0.848224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.94427 | + | 15.2169i | −0.824045 | + | 2.53615i | ||||
\(37\) | 9.46289 | − | 3.07468i | 1.55569 | − | 0.505474i | 0.600038 | − | 0.799972i | \(-0.295152\pi\) |
0.955652 | + | 0.294497i | \(0.0951522\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.0000 | − | 13.2665i | −1.78885 | − | 1.97765i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.30860 | − | 2.04979i | −0.920203 | − | 0.298992i | −0.189653 | − | 0.981851i | \(-0.560736\pi\) |
−0.730550 | + | 0.682859i | \(0.760736\pi\) | |||||||
\(48\) | −12.6172 | + | 4.09957i | −1.82113 | + | 0.591722i | ||||
\(49\) | −5.66312 | + | 4.11450i | −0.809017 | + | 0.587785i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.79785 | − | 10.7328i | 1.07112 | − | 1.47427i | 0.202178 | − | 0.979349i | \(-0.435198\pi\) |
0.868940 | − | 0.494918i | \(-0.164802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.63525 | − | 14.2658i | −0.603459 | − | 1.85726i | −0.507057 | − | 0.861913i | \(-0.669267\pi\) |
−0.0964021 | − | 0.995342i | \(-0.530733\pi\) | |||||||
\(60\) | 3.05080 | − | 14.5153i | 0.393856 | − | 1.87391i | ||||
\(61\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.47214 | − | 4.70228i | −0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.94987i | 1.21557i | 0.794101 | + | 0.607785i | \(0.207942\pi\) | ||||
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.39919 | − | 10.4616i | 0.409214 | − | 1.25943i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.42705 | − | 1.76336i | 0.288038 | − | 0.209272i | −0.434378 | − | 0.900731i | \(-0.643032\pi\) |
0.722416 | + | 0.691459i | \(0.243032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.3740 | + | 11.0401i | 1.42883 | + | 1.27480i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 8.16270 | − | 3.65655i | 0.912617 | − | 0.408815i | ||||
\(81\) | 9.57953 | + | 29.4828i | 1.06439 | + | 3.27586i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.30860 | − | 2.04979i | 0.657717 | − | 0.213705i | ||||
\(93\) | −9.74732 | − | 13.4160i | −1.01075 | − | 1.39118i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.84839 | + | 8.04962i | −0.593814 | + | 0.817315i | −0.995124 | − | 0.0986273i | \(-0.968555\pi\) |
0.401310 | + | 0.915942i | \(0.368555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | + | 9.94987i | −0.100000 | + | 0.994987i | ||||
\(101\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.9258 | − | 6.14936i | 1.86481 | − | 0.605914i | 0.871510 | − | 0.490378i | \(-0.163141\pi\) |
0.993303 | − | 0.115536i | \(-0.0368587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(108\) | −19.4946 | + | 26.8321i | −1.87587 | + | 2.58192i | ||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 33.0000 | 3.13222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.15430 | − | 1.02489i | −0.296731 | − | 0.0964139i | 0.156868 | − | 0.987620i | \(-0.449860\pi\) |
−0.453599 | + | 0.891206i | \(0.649860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.52540 | + | 7.25763i | −0.142244 | + | 0.676777i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.09017 | − | 9.51057i | 0.277505 | − | 0.854074i | ||||
\(125\) | −9.08975 | − | 6.50972i | −0.813012 | − | 0.582247i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.1593 | − | 33.8408i | −1.30470 | − | 2.91255i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6462 | − | 18.7824i | −1.16588 | − | 1.60469i | −0.686617 | − | 0.727019i | \(-0.740905\pi\) |
−0.479260 | − | 0.877673i | \(-0.659095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.7984 | − | 12.9313i | −1.49889 | − | 1.08901i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −32.0000 | −2.66667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −22.0801 | + | 7.17425i | −1.82113 | + | 0.591722i | ||||
\(148\) | 11.6968 | + | 16.0992i | 0.961469 | + | 1.32335i | ||||
\(149\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.50000 | + | 8.29156i | 0.602414 | + | 0.665994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.46289 | − | 3.07468i | −0.755221 | − | 0.245386i | −0.0939948 | − | 0.995573i | \(-0.529964\pi\) |
−0.661226 | + | 0.750186i | \(0.729964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 35.5967 | − | 25.8626i | 2.82301 | − | 2.05103i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6968 | − | 16.0992i | 0.916162 | − | 1.26099i | −0.0488556 | − | 0.998806i | \(-0.515557\pi\) |
0.965018 | − | 0.262184i | \(-0.0844426\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01722 | + | 12.3637i | 0.309017 | + | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 49.7494i | − | 3.73939i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.48936 | + | 19.9722i | −0.485037 | + | 1.49279i | 0.346890 | + | 0.937906i | \(0.387238\pi\) |
−0.831927 | + | 0.554885i | \(0.812762\pi\) | |||||||
\(180\) | 17.8180 | − | 31.0245i | 1.32807 | − | 2.31243i | ||||
\(181\) | −20.2254 | + | 14.6946i | −1.50334 | + | 1.09224i | −0.534318 | + | 0.845283i | \(0.679432\pi\) |
−0.969026 | + | 0.246960i | \(0.920568\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.1214 | + | 2.37597i | −1.62640 | + | 0.174685i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 13.2665i | − | 0.967559i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.63525 | + | 14.2658i | 0.335395 | + | 1.03224i | 0.966527 | + | 0.256565i | \(0.0825907\pi\) |
−0.631132 | + | 0.775676i | \(0.717409\pi\) | |||||||
\(192\) | −15.5957 | − | 21.4656i | −1.12552 | − | 1.54915i | ||||
\(193\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.3262 | − | 8.22899i | −0.809017 | − | 0.587785i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.1976 | + | 31.3849i | −0.719280 | + | 2.21372i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.5957 | − | 21.4656i | 1.08398 | − | 1.49197i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(212\) | 25.2344 | + | 8.19915i | 1.73310 | + | 0.563120i | ||||
\(213\) | 9.46289 | − | 3.07468i | 0.648387 | − | 0.210674i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.3887 | − | 9.22404i | −1.90105 | − | 0.617687i | −0.960870 | − | 0.277000i | \(-0.910660\pi\) |
−0.940177 | − | 0.340687i | \(-0.889340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.1575 | + | 34.5496i | 1.34383 | + | 2.30331i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.04508 | + | 2.93893i | 0.267307 | + | 0.194210i | 0.713362 | − | 0.700796i | \(-0.247172\pi\) |
−0.446055 | + | 0.895005i | \(0.647172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8621 | + | 7.38694i | 0.839030 | + | 0.481871i | ||||
\(236\) | 24.2705 | − | 17.6336i | 1.57988 | − | 1.14785i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | 29.4952 | − | 3.16796i | 1.90390 | − | 0.204491i | ||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 53.0660i | 3.40419i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.2847 | − | 6.39897i | 0.912617 | − | 0.408815i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8435 | + | 15.8702i | 1.37875 | + | 1.00172i | 0.996996 | + | 0.0774530i | \(0.0246788\pi\) |
0.381751 | + | 0.924265i | \(0.375321\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | − | 15.2169i | 0.309017 | − | 0.951057i | ||||
\(257\) | −25.2344 | + | 8.19915i | −1.57408 | + | 0.511449i | −0.960522 | − | 0.278203i | \(-0.910261\pi\) |
−0.613555 | + | 0.789652i | \(0.710261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.0000 | + | 19.8997i | −1.35145 | + | 1.22243i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.3887 | + | 9.22404i | 1.73736 | + | 0.564502i | ||||
\(268\) | −18.9258 | + | 6.14936i | −1.15608 | + | 0.375632i | ||||
\(269\) | −24.2705 | + | 17.6336i | −1.47980 | + | 1.07514i | −0.502178 | + | 0.864764i | \(0.667468\pi\) |
−0.977621 | + | 0.210373i | \(0.932532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 22.0000 | 1.32424 | ||||||||
\(277\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.3607 | − | 38.0423i | −0.740015 | − | 2.27753i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(284\) | 4.85410 | + | 3.52671i | 0.288038 | + | 0.209272i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.25329 | − | 16.1680i | 0.309017 | − | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.6976 | + | 19.3969i | −1.56504 | + | 1.13707i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58191 | + | 33.3492i | 0.208547 | + | 1.94167i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.3519 | + | 30.3600i | −0.770870 | + | 1.75283i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 66.0000 | 3.75461 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70820 | + | 11.4127i | −0.210273 | + | 0.647154i | 0.789183 | + | 0.614159i | \(0.210505\pi\) |
−0.999456 | + | 0.0329949i | \(0.989495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5452 | + | 24.1489i | 0.991712 | + | 1.36497i | 0.930275 | + | 0.366863i | \(0.119568\pi\) |
0.0614365 | + | 0.998111i | \(0.480432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.6462 | + | 18.7824i | −0.766449 | + | 1.05493i | 0.230201 | + | 0.973143i | \(0.426062\pi\) |
−0.996650 | + | 0.0817838i | \(0.973938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.0000 | + | 13.2665i | 0.670820 | + | 0.741620i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −50.1591 | + | 36.4427i | −2.78661 | + | 2.02459i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.0000 | −1.92377 | −0.961887 | − | 0.273447i | \(-0.911836\pi\) | ||||
−0.961887 | + | 0.273447i | \(0.911836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 75.7031 | + | 24.5974i | 4.14851 | + | 1.34793i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.57620 | − | 21.7729i | 0.250024 | − | 1.18958i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.89919 | − | 6.46564i | −0.483337 | − | 0.351165i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.2499 | + | 21.3293i | −0.659510 | + | 1.14833i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 36.4829i | − | 1.94179i | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||
0.239511 | − | 0.970894i | \(-0.423013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.12202 | + | 2.74241i | −0.324923 | + | 0.145552i | ||||
\(356\) | 5.56231 | + | 17.1190i | 0.294802 | + | 0.907306i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.46289 | + | 3.07468i | −0.493959 | + | 0.160497i | −0.545395 | − | 0.838179i | \(-0.683620\pi\) |
0.0514358 | + | 0.998676i | \(0.483620\pi\) | |||||||
\(368\) | 7.79785 | + | 10.7328i | 0.406491 | + | 0.559487i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 19.4946 | − | 26.8321i | 1.01075 | − | 1.39118i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.0000 | − | 29.8496i | −1.13608 | − | 1.54143i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.2254 | − | 14.6946i | 1.03891 | − | 0.754813i | 0.0688378 | − | 0.997628i | \(-0.478071\pi\) |
0.970073 | + | 0.242815i | \(0.0780709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.94946 | − | 2.68321i | 0.0996129 | − | 0.137105i | −0.756301 | − | 0.654224i | \(-0.772995\pi\) |
0.855914 | + | 0.517119i | \(0.172995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9258 | − | 6.14936i | −0.960811 | − | 0.312186i | ||||
\(389\) | −4.63525 | − | 14.2658i | −0.235017 | − | 0.723307i | −0.997119 | − | 0.0758507i | \(-0.975833\pi\) |
0.762102 | − | 0.647456i | \(-0.224167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.7995i | 1.99748i | 0.0501886 | + | 0.998740i | \(0.484018\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.5438 | + | 4.24725i | −0.977191 | + | 0.212362i | ||||
\(401\) | 24.2705 | − | 17.6336i | 1.21201 | − | 0.880578i | 0.216600 | − | 0.976261i | \(-0.430503\pi\) |
0.995412 | + | 0.0956827i | \(0.0305034\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.40261 | − | 68.9217i | −0.367839 | − | 3.42475i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.7943 | − | 73.2314i | −1.17369 | − | 3.61224i | ||||
\(412\) | 23.3936 | + | 32.1985i | 1.15252 | + | 1.58630i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09017 | + | 9.51057i | −0.150606 | + | 0.463517i | −0.997689 | − | 0.0679432i | \(-0.978356\pi\) |
0.847084 | + | 0.531460i | \(0.178356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.1914 | − | 42.9313i | −1.51658 | − | 2.08739i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(432\) | −63.0860 | − | 20.4979i | −3.03522 | − | 0.986204i | ||||
\(433\) | 28.3887 | − | 9.22404i | 1.36427 | − | 0.443279i | 0.466805 | − | 0.884360i | \(-0.345405\pi\) |
0.897467 | + | 0.441081i | \(0.145405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56.0000 | −2.66667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.6973 | − | 11.2738i | −1.64852 | − | 0.535636i | −0.670099 | − | 0.742271i | \(-0.733748\pi\) |
−0.978418 | + | 0.206636i | \(0.933748\pi\) | |||||||
\(444\) | 20.3951 | + | 62.7697i | 0.967910 | + | 2.97892i | ||||
\(445\) | −19.6943 | − | 4.13933i | −0.933600 | − | 0.196223i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.5517 | + | 22.9236i | 1.48902 | + | 1.08183i | 0.974510 | + | 0.224346i | \(0.0720244\pi\) |
0.514505 | + | 0.857487i | \(0.327976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.63325i | − | 0.312002i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.7476 | + | 1.58398i | −0.687609 | + | 0.0738534i | ||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 29.8496i | − | 1.38723i | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||
0.720346 | − | 0.693615i | \(-0.243983\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.1593 | + | 33.8408i | 0.702994 | + | 1.56933i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.3430 | + | 34.8817i | 1.17274 | + | 1.61413i | 0.642523 | + | 0.766267i | \(0.277888\pi\) |
0.530212 | + | 0.847865i | \(0.322112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.6976 | − | 19.3969i | −1.23016 | − | 0.893763i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 100.938 | − | 32.7966i | 4.62161 | − | 1.50165i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5000 | − | 14.9248i | 0.749226 | − | 0.677701i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.46289 | + | 3.07468i | 0.428805 | + | 0.139327i | 0.515465 | − | 0.856911i | \(-0.327619\pi\) |
−0.0866600 | + | 0.996238i | \(0.527619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 53.3951 | − | 38.7938i | 2.41461 | − | 1.75432i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | 0.898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3607 | + | 38.0423i | 0.553340 | + | 1.70301i | 0.700287 | + | 0.713861i | \(0.253055\pi\) |
−0.146947 | + | 0.989144i | \(0.546945\pi\) | |||||||
\(500\) | 6.76445 | − | 21.3130i | 0.302516 | − | 0.953144i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 43.1161i | 1.91485i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9058 | + | 42.7975i | −0.616362 | + | 1.89697i | −0.238275 | + | 0.971198i | \(0.576582\pi\) |
−0.378087 | + | 0.925770i | \(0.623418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −44.2427 | + | 4.75194i | −1.94957 | + | 0.209395i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.63525 | + | 14.2658i | 0.203074 | + | 0.624998i | 0.999787 | + | 0.0206400i | \(0.00657038\pi\) |
−0.796713 | + | 0.604358i | \(0.793430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0000 | 0.521739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.0820 | − | 114.127i | 1.60922 | − | 4.95268i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.9387 | + | 56.3473i | −1.76664 | + | 2.43157i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 55.0000 | − | 49.7494i | 2.36682 | − | 2.14087i | ||||
\(541\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −78.8574 | + | 25.6223i | −3.38410 | + | 1.09956i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(548\) | 27.2925 | − | 37.5649i | 1.16588 | − | 1.60469i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −72.2125 | − | 15.1775i | −3.06525 | − | 0.644250i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | 13.5967 | − | 41.8465i | 0.572526 | − | 1.76205i | ||||
\(565\) | 6.43104 | + | 3.69347i | 0.270556 | + | 0.155385i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.7494i | 2.07831i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.67593 | − | 15.1800i | 0.278405 | − | 0.633049i | ||||
\(576\) | −19.7771 | − | 60.8676i | −0.824045 | − | 2.53615i | ||||
\(577\) | −5.84839 | − | 8.04962i | −0.243472 | − | 0.335110i | 0.669740 | − | 0.742596i | \(-0.266406\pi\) |
−0.913212 | + | 0.407486i | \(0.866406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.30860 | + | 2.04979i | −0.260384 | + | 0.0846038i | −0.436300 | − | 0.899801i | \(-0.643711\pi\) |
0.175916 | + | 0.984405i | \(0.443711\pi\) | |||||||
\(588\) | −27.2925 | − | 37.5649i | −1.12552 | − | 1.54915i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.3936 | + | 32.1985i | −0.961469 | + | 1.32335i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −63.0860 | − | 20.4979i | −2.58194 | − | 0.838922i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.1246 | + | 21.1603i | −1.19000 | + | 0.864585i | −0.993264 | − | 0.115872i | \(-0.963034\pi\) |
−0.196735 | + | 0.980457i | \(0.563034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.7871 | + | 64.3969i | −1.90532 | + | 2.62245i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5330i | 1.06818i | 0.845428 | + | 0.534089i | \(0.179345\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.309017 | − | 0.951057i | 0.0124204 | − | 0.0382262i | −0.944654 | − | 0.328068i | \(-0.893603\pi\) |
0.957075 | + | 0.289841i | \(0.0936026\pi\) | |||||||
\(620\) | −11.1362 | + | 19.3903i | −0.447242 | + | 0.778734i | ||||
\(621\) | 44.4959 | − | 32.3282i | 1.78556 | − | 1.29729i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.8967 | + | 18.4255i | 0.675869 | + | 0.737022i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 19.8997i | − | 0.794086i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.16312 | + | 6.65740i | 0.0861124 | + | 0.265027i | 0.984836 | − | 0.173489i | \(-0.0555042\pi\) |
−0.898723 | + | 0.438516i | \(0.855504\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 71.1935 | + | 51.7251i | 2.82301 | + | 2.05103i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9058 | − | 42.7975i | 0.549245 | − | 1.69040i | −0.161433 | − | 0.986884i | \(-0.551612\pi\) |
0.710678 | − | 0.703518i | \(-0.248388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5452 | − | 24.1489i | −0.691914 | − | 0.952338i | −1.00000 | 0.000979141i | \(-0.999688\pi\) | |
0.308086 | − | 0.951359i | \(-0.400312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.3430 | − | 34.8817i | 0.996337 | − | 1.37134i | 0.0687910 | − | 0.997631i | \(-0.478086\pi\) |
0.927546 | − | 0.373709i | \(-0.121914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37.8516 | + | 12.2987i | 1.48238 | + | 0.481655i | ||||
\(653\) | 3.15430 | − | 1.02489i | 0.123437 | − | 0.0401072i | −0.246647 | − | 0.969105i | \(-0.579329\pi\) |
0.370084 | + | 0.928998i | \(0.379329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0000 | 0.505641 | 0.252821 | − | 0.967513i | \(-0.418642\pi\) | ||||
0.252821 | + | 0.967513i | \(0.418642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −80.0927 | − | 58.1907i | −3.09656 | − | 2.24978i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.6082 | + | 81.0244i | 0.677738 | + | 3.11863i | ||||
\(676\) | −21.0344 | + | 15.2824i | −0.809017 | + | 0.587785i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 46.4327i | − | 1.77670i | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||
0.459167 | − | 0.888350i | \(-0.348148\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.2230 | + | 47.3771i | 0.810888 | + | 1.81018i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.74732 | + | 13.4160i | 0.371883 | + | 0.511853i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7533 | − | 9.99235i | −0.523200 | − | 0.380127i | 0.294608 | − | 0.955618i | \(-0.404811\pi\) |
−0.817808 | + | 0.575491i | \(0.804811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.0000 | + | 36.4829i | 1.24285 | + | 1.37402i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 94.6289 | − | 30.7468i | 3.55637 | − | 1.15554i | ||||
\(709\) | 15.3713 | − | 11.1679i | 0.577282 | − | 0.419420i | −0.260461 | − | 0.965484i | \(-0.583875\pi\) |
0.837743 | + | 0.546064i | \(0.183875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.74732 | + | 13.4160i | −0.365040 | + | 0.502434i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −42.0000 | −1.56961 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.7599 | − | 48.5039i | −0.587744 | − | 1.80889i | −0.587961 | − | 0.808890i | \(-0.700069\pi\) |
0.000216702 | − | 1.00000i | \(-0.499931\pi\) | |||||||
\(720\) | 70.0242 | + | 14.7176i | 2.60965 | + | 0.548493i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.4508 | − | 29.3893i | −1.50334 | − | 1.09224i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.94987i | − | 0.369020i | −0.982831 | − | 0.184510i | \(-0.940930\pi\) | ||
0.982831 | − | 0.184510i | \(-0.0590699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.6484 | + | 78.9377i | −0.949941 | + | 2.92362i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 51.6165 | − | 5.54393i | 1.90390 | − | 0.204491i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(740\) | −18.1911 | − | 40.6089i | −0.668719 | − | 1.49281i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.10739 | + | 21.8743i | −0.259352 | + | 0.798205i | 0.733588 | + | 0.679594i | \(0.237844\pi\) |
−0.992941 | + | 0.118611i | \(0.962156\pi\) | |||||||
\(752\) | 25.2344 | − | 8.19915i | 0.920203 | − | 0.298992i | ||||
\(753\) | 52.6355 | + | 72.4466i | 1.91814 | + | 2.64010i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3936 | − | 32.1985i | 0.850253 | − | 1.17027i | −0.133554 | − | 0.991042i | \(-0.542639\pi\) |
0.983807 | − | 0.179232i | \(-0.0573612\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.2705 | + | 17.6336i | −0.878076 | + | 0.637960i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 31.1914 | − | 42.9313i | 1.12552 | − | 1.54915i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −88.0000 | −3.16924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.6172 | − | 4.09957i | −0.453809 | − | 0.147451i | 0.0731890 | − | 0.997318i | \(-0.476682\pi\) |
−0.526998 | + | 0.849867i | \(0.676682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.5984 | − | 21.5935i | −0.452549 | − | 0.775662i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.65248 | − | 26.6296i | 0.309017 | − | 0.951057i | ||||
\(785\) | 19.2931 | + | 11.0804i | 0.688601 | + | 0.395477i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −89.7897 | + | 40.2221i | −3.18451 | + | 1.42653i | ||||
\(796\) | −12.3607 | − | 38.0423i | −0.438113 | − | 1.34837i | ||||
\(797\) | −33.1409 | − | 45.6145i | −1.17391 | − | 1.61575i | −0.629940 | − | 0.776644i | \(-0.716921\pi\) |
−0.543970 | − | 0.839105i | \(-0.683079\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 58.2492 | + | 42.3205i | 2.05814 | + | 1.49532i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −66.0000 | −2.32764 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −94.6289 | + | 30.7468i | −3.33110 | + | 1.08234i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.0000 | + | 29.8496i | −1.15594 | + | 1.04559i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5452 | − | 24.1489i | 0.611586 | − | 0.841776i | −0.385121 | − | 0.922866i | \(-0.625840\pi\) |
0.996707 | + | 0.0810902i | \(0.0258402\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(828\) | 50.4688 | + | 16.3983i | 1.75391 | + | 0.569880i | ||||
\(829\) | −8.96149 | − | 27.5806i | −0.311246 | − | 0.957915i | −0.977272 | − | 0.211987i | \(-0.932006\pi\) |
0.666027 | − | 0.745928i | \(-0.267994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 82.9156i | − | 2.86598i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.9058 | + | 42.7975i | −0.480080 | + | 1.47754i | 0.358901 | + | 0.933376i | \(0.383151\pi\) |
−0.838982 | + | 0.544160i | \(0.816849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.10432 | − | 28.9027i | −0.106792 | − | 0.994281i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 53.0660i | 1.82229i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1976 | − | 31.3849i | −0.349568 | − | 1.07586i | ||||
\(852\) | 11.6968 | + | 16.0992i | 0.400725 | + | 0.551551i | ||||
\(853\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0000 | 1.05771 | 0.528853 | − | 0.848713i | \(-0.322622\pi\) | ||||
0.528853 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.2925 | + | 37.5649i | 0.929047 | + | 1.27872i | 0.960230 | + | 0.279210i | \(0.0900725\pi\) |
−0.0311832 | + | 0.999514i | \(0.509928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.1409 | − | 45.6145i | 1.12552 | − | 1.54915i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −75.7031 | + | 24.5974i | −2.56216 | + | 0.832497i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.0000 | 1.92038 | 0.960189 | − | 0.279350i | \(-0.0901189\pi\) | ||||
0.960189 | + | 0.279350i | \(0.0901189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9258 | + | 6.14936i | 0.636903 | + | 0.206942i | 0.609631 | − | 0.792686i | \(-0.291318\pi\) |
0.0272727 | + | 0.999628i | \(0.491318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.8810 | + | 108.864i | −0.769136 | + | 3.65944i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 59.6992i | − | 1.99888i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3861 | − | 40.7197i | 0.781711 | − | 1.36111i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −53.2593 | + | 59.6947i | −1.77531 | + | 1.98982i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.0169 | − | 22.8535i | 1.69586 | − | 0.759674i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0903 | − | 48.2977i | −1.16516 | − | 1.60370i | −0.690030 | − | 0.723781i | \(-0.742403\pi\) |
−0.475126 | − | 0.879918i | \(-0.657597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.5410 | − | 35.2671i | −1.60824 | − | 1.16845i | −0.868706 | − | 0.495327i | \(-0.835048\pi\) |
−0.739529 | − | 0.673124i | \(-0.764952\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.09017 | + | 9.51057i | −0.102102 | + | 0.314238i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 49.5000 | + | 4.97494i | 1.62755 | + | 0.163575i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 151.406 | + | 49.1949i | 4.97283 | + | 1.61577i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.2705 | + | 17.6336i | −0.796290 | + | 0.578538i | −0.909823 | − | 0.414996i | \(-0.863783\pi\) |
0.113534 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.3936 | + | 32.1985i | −0.765871 | + | 1.05413i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.5927 | + | 94.1546i | 0.998354 | + | 3.07262i | ||||
\(940\) | −6.10160 | + | 29.0305i | −0.199012 | + | 0.946871i | ||||
\(941\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 48.5410 | + | 35.2671i | 1.57988 | + | 1.14785i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.2164i | 0.754431i | 0.926126 | + | 0.377215i | \(0.123118\pi\) | ||||
−0.926126 | + | 0.377215i | \(0.876882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −62.2943 | + | 45.2595i | −2.02003 | + | 1.46764i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.58191 | − | 33.3492i | −0.115908 | − | 1.07916i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 24.2548 | + | 54.1452i | 0.782821 | + | 1.74753i | ||||
\(961\) | −1.85410 | − | 5.70634i | −0.0598097 | − | 0.184075i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.9058 | − | 42.7975i | 0.446257 | − | 1.37344i | −0.434842 | − | 0.900507i | \(-0.643196\pi\) |
0.881099 | − | 0.472932i | \(-0.156804\pi\) | |||||||
\(972\) | −100.938 | + | 32.7966i | −3.23757 | + | 1.05195i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.1409 | + | 45.6145i | −1.06027 | + | 1.45934i | −0.180718 | + | 0.983535i | \(0.557842\pi\) |
−0.879552 | + | 0.475802i | \(0.842158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 21.0000 | + | 23.2164i | 0.670820 | + | 0.741620i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.6973 | − | 11.2738i | 1.10667 | − | 0.359579i | 0.302005 | − | 0.953306i | \(-0.402344\pi\) |
0.804666 | + | 0.593727i | \(0.202344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −110.400 | − | 35.8713i | −3.50345 | − | 1.13834i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.7651 | + | 9.19850i | 1.38745 | + | 0.291612i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 133.488 | + | 96.9846i | 4.22337 | + | 3.06846i |
(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 | 605.2.j.b.444.2 | 8 | ||
5.4 | even | 2 | inner | 605.2.j.b.444.1 | 8 | ||
11.2 | odd | 10 | inner | 605.2.j.b.269.2 | 8 | ||
11.3 | even | 5 | inner | 605.2.j.b.124.1 | 8 | ||
11.4 | even | 5 | inner | 605.2.j.b.9.1 | 8 | ||
11.5 | even | 5 | 605.2.b.a.364.2 | yes | 2 | ||
11.6 | odd | 10 | 605.2.b.a.364.2 | yes | 2 | ||
11.7 | odd | 10 | inner | 605.2.j.b.9.1 | 8 | ||
11.8 | odd | 10 | inner | 605.2.j.b.124.1 | 8 | ||
11.9 | even | 5 | inner | 605.2.j.b.269.2 | 8 | ||
11.10 | odd | 2 | CM | 605.2.j.b.444.2 | 8 | ||
55.4 | even | 10 | inner | 605.2.j.b.9.2 | 8 | ||
55.9 | even | 10 | inner | 605.2.j.b.269.1 | 8 | ||
55.14 | even | 10 | inner | 605.2.j.b.124.2 | 8 | ||
55.17 | even | 20 | 3025.2.a.k.1.2 | 2 | |||
55.19 | odd | 10 | inner | 605.2.j.b.124.2 | 8 | ||
55.24 | odd | 10 | inner | 605.2.j.b.269.1 | 8 | ||
55.27 | odd | 20 | 3025.2.a.k.1.2 | 2 | |||
55.28 | even | 20 | 3025.2.a.k.1.1 | 2 | |||
55.29 | odd | 10 | inner | 605.2.j.b.9.2 | 8 | ||
55.38 | odd | 20 | 3025.2.a.k.1.1 | 2 | |||
55.39 | odd | 10 | 605.2.b.a.364.1 | ✓ | 2 | ||
55.49 | even | 10 | 605.2.b.a.364.1 | ✓ | 2 | ||
55.54 | odd | 2 | inner | 605.2.j.b.444.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.a.364.1 | ✓ | 2 | 55.39 | odd | 10 | ||
605.2.b.a.364.1 | ✓ | 2 | 55.49 | even | 10 | ||
605.2.b.a.364.2 | yes | 2 | 11.5 | even | 5 | ||
605.2.b.a.364.2 | yes | 2 | 11.6 | odd | 10 | ||
605.2.j.b.9.1 | 8 | 11.4 | even | 5 | inner | ||
605.2.j.b.9.1 | 8 | 11.7 | odd | 10 | inner | ||
605.2.j.b.9.2 | 8 | 55.4 | even | 10 | inner | ||
605.2.j.b.9.2 | 8 | 55.29 | odd | 10 | inner | ||
605.2.j.b.124.1 | 8 | 11.3 | even | 5 | inner | ||
605.2.j.b.124.1 | 8 | 11.8 | odd | 10 | inner | ||
605.2.j.b.124.2 | 8 | 55.14 | even | 10 | inner | ||
605.2.j.b.124.2 | 8 | 55.19 | odd | 10 | inner | ||
605.2.j.b.269.1 | 8 | 55.9 | even | 10 | inner | ||
605.2.j.b.269.1 | 8 | 55.24 | odd | 10 | inner | ||
605.2.j.b.269.2 | 8 | 11.2 | odd | 10 | inner | ||
605.2.j.b.269.2 | 8 | 11.9 | even | 5 | inner | ||
605.2.j.b.444.1 | 8 | 5.4 | even | 2 | inner | ||
605.2.j.b.444.1 | 8 | 55.54 | odd | 2 | inner | ||
605.2.j.b.444.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.j.b.444.2 | 8 | 11.10 | odd | 2 | CM | ||
3025.2.a.k.1.1 | 2 | 55.28 | even | 20 | |||
3025.2.a.k.1.1 | 2 | 55.38 | odd | 20 | |||
3025.2.a.k.1.2 | 2 | 55.17 | even | 20 | |||
3025.2.a.k.1.2 | 2 | 55.27 | odd | 20 |