Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.15785648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 12x^{3} + 22x^{2} + 24x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-3.08104\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-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 | ||||||||
\(3\) | 3.08104 | 1.77884 | 0.889419 | − | 0.457092i | \(-0.151109\pi\) | ||||
0.889419 | + | 0.457092i | \(0.151109\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.49280 | 2.16427 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.59262 | 1.55111 | 0.775557 | − | 0.631278i | \(-0.217469\pi\) | ||||
0.775557 | + | 0.631278i | \(0.217469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.08104 | 0.795521 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.59262 | 0.871339 | 0.435669 | − | 0.900107i | \(-0.356512\pi\) | ||||
0.435669 | + | 0.900107i | \(0.356512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.08779 | −1.39663 | −0.698317 | − | 0.715788i | \(-0.746068\pi\) | ||||
−0.698317 | + | 0.715788i | \(0.746068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.08104 | −0.672338 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.98122 | −1.03866 | −0.519328 | − | 0.854575i | \(-0.673818\pi\) | ||||
−0.519328 | + | 0.854575i | \(0.673818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.7614 | 2.07104 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.511583 | 0.0949985 | 0.0474993 | − | 0.998871i | \(-0.484875\pi\) | ||||
0.0474993 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.08542 | 1.27258 | 0.636290 | − | 0.771450i | \(-0.280468\pi\) | ||||
0.636290 | + | 0.771450i | \(0.280468\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.08104 | −0.536340 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.00438163 | −0.000720336 0 | −0.000360168 | − | 1.00000i | \(-0.500115\pi\) | ||||
−0.000360168 | 1.00000i | \(0.500115\pi\) | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.2311 | 2.75918 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.97447 | 0.620707 | 0.310354 | − | 0.950621i | \(-0.399553\pi\) | ||||
0.310354 | + | 0.950621i | \(0.399553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.893428 | 0.136246 | 0.0681232 | − | 0.997677i | \(-0.478299\pi\) | ||||
0.0681232 | + | 0.997677i | \(0.478299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.49280 | 0.967889 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.99235 | −1.45753 | −0.728767 | − | 0.684762i | \(-0.759906\pi\) | ||||
−0.728767 | + | 0.684762i | \(0.759906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.0690 | 1.54997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.98122 | 0.958944 | 0.479472 | − | 0.877557i | \(-0.340828\pi\) | ||||
0.479472 | + | 0.877557i | \(0.340828\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.7567 | −2.48439 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6616 | 1.64840 | 0.824202 | − | 0.566296i | \(-0.191624\pi\) | ||||
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.08542 | −0.907195 | −0.453598 | − | 0.891207i | \(-0.649860\pi\) | ||||
−0.453598 | + | 0.891207i | \(0.649860\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.49280 | −0.818016 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.59262 | 0.693679 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.65488 | 1.17953 | 0.589765 | − | 0.807575i | \(-0.299220\pi\) | ||||
0.589765 | + | 0.807575i | \(0.299220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.3473 | −1.84760 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9624 | 1.65704 | 0.828518 | − | 0.559963i | \(-0.189184\pi\) | ||||
0.828518 | + | 0.559963i | \(0.189184\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7315 | 1.49011 | 0.745057 | − | 0.667001i | \(-0.232422\pi\) | ||||
0.745057 | + | 0.667001i | \(0.232422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.08104 | 0.355768 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.58059 | −0.627865 | −0.313933 | − | 0.949445i | \(-0.601647\pi\) | ||||
−0.313933 | + | 0.949445i | \(0.601647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.6780 | 1.51978 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.58587 | 0.722893 | 0.361447 | − | 0.932393i | \(-0.382283\pi\) | ||||
0.361447 | + | 0.932393i | \(0.382283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.59262 | 0.389674 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.57621 | 0.168987 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.78461 | −0.613168 | −0.306584 | − | 0.951844i | \(-0.599186\pi\) | ||||
−0.306584 | + | 0.951844i | \(0.599186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.59262 | −0.586266 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 21.8305 | 2.26371 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.08779 | −0.624594 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2962 | 1.24849 | 0.624245 | − | 0.781229i | \(-0.285407\pi\) | ||||
0.624245 | + | 0.781229i | \(0.285407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.49280 | −0.652551 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8613 | 1.08074 | 0.540368 | − | 0.841429i | \(-0.318285\pi\) | ||||
0.540368 | + | 0.841429i | \(0.318285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.194234 | −0.0191385 | −0.00956923 | − | 0.999954i | \(-0.503046\pi\) | ||||
−0.00956923 | + | 0.999954i | \(0.503046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.08104 | −0.300679 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.77585 | −0.171678 | −0.0858390 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858390 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6129 | −1.49545 | −0.747724 | − | 0.664010i | \(-0.768853\pi\) | ||||
−0.747724 | + | 0.664010i | \(0.768853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0135000 | −0.00128136 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9991 | −1.03471 | −0.517354 | − | 0.855771i | \(-0.673083\pi\) | ||||
−0.517354 | + | 0.855771i | \(0.673083\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.98122 | −0.464501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36.3118 | 3.35702 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.59262 | −0.329335 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2455 | 1.10414 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.98650 | −0.531216 | −0.265608 | − | 0.964081i | \(-0.585573\pi\) | ||||
−0.265608 | + | 0.964081i | \(0.585573\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.75269 | 0.242360 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.85014 | −0.336388 | −0.168194 | − | 0.985754i | \(-0.553794\pi\) | ||||
−0.168194 | + | 0.985754i | \(0.553794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.08779 | 0.527878 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.7614 | 0.926198 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.5016 | −1.15352 | −0.576758 | − | 0.816915i | \(-0.695683\pi\) | ||||
−0.576758 | + | 0.816915i | \(0.695683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6824 | −1.41498 | −0.707492 | − | 0.706721i | \(-0.750174\pi\) | ||||
−0.707492 | + | 0.706721i | \(0.750174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.7868 | −2.59272 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.59262 | −0.467678 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.511583 | 0.0424846 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.08104 | 0.254120 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.6361 | −1.03519 | −0.517595 | − | 0.855626i | \(-0.673172\pi\) | ||||
−0.517595 | + | 0.855626i | \(0.673172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.7427 | −1.93215 | −0.966075 | − | 0.258260i | \(-0.916851\pi\) | ||||
−0.966075 | + | 0.258260i | \(0.916851\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 23.3262 | 1.88581 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.08542 | 0.569115 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.58497 | −0.764964 | −0.382482 | − | 0.923963i | \(-0.624931\pi\) | ||||
−0.382482 | + | 0.923963i | \(0.624931\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.5094 | 1.70581 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.98122 | 0.392575 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.456134 | −0.0357271 | −0.0178636 | − | 0.999840i | \(-0.505686\pi\) | ||||
−0.0178636 | + | 0.999840i | \(0.505686\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.08104 | −0.239859 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.36306 | −0.724535 | −0.362268 | − | 0.932074i | \(-0.617997\pi\) | ||||
−0.362268 | + | 0.932074i | \(0.617997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.2774 | 1.40595 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −39.5268 | −3.02269 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.76910 | 0.210531 | 0.105265 | − | 0.994444i | \(-0.466431\pi\) | ||||
0.105265 | + | 0.994444i | \(0.466431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 39.0110 | 2.93224 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.1000 | 1.65183 | 0.825916 | − | 0.563793i | \(-0.190659\pi\) | ||||
0.825916 | + | 0.563793i | \(0.190659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.36306 | 0.249974 | 0.124987 | − | 0.992158i | \(-0.460111\pi\) | ||||
0.124987 | + | 0.992158i | \(0.460111\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.8305 | −1.61375 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.00438163 | −0.000322144 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.59262 | −0.262718 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.7614 | −0.782780 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.4950 | −1.91711 | −0.958555 | − | 0.284907i | \(-0.908037\pi\) | ||||
−0.958555 | + | 0.284907i | \(0.908037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.20882 | 0.230976 | 0.115488 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115488 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.2311 | 1.23394 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0310 | −0.785926 | −0.392963 | − | 0.919554i | \(-0.628550\pi\) | ||||
−0.392963 | + | 0.919554i | \(0.628550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.07102 | −0.572139 | −0.286070 | − | 0.958209i | \(-0.592349\pi\) | ||||
−0.286070 | + | 0.958209i | \(0.592349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 29.7470 | 2.09819 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.511583 | −0.0359061 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.97447 | 0.277589 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −32.3420 | −2.24793 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.08779 | 0.421101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13891 | −0.0784059 | −0.0392030 | − | 0.999231i | \(-0.512482\pi\) | ||||
−0.0392030 | + | 0.999231i | \(0.512482\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 43.0188 | 2.94760 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.893428 | 0.0609313 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.08542 | −0.480990 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.2263 | 2.65067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0922 | 1.35155 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8560 | 1.53055 | 0.765277 | − | 0.643701i | \(-0.222602\pi\) | ||||
0.765277 | + | 0.643701i | \(0.222602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.49280 | 0.432853 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.2778 | −1.21314 | −0.606571 | − | 0.795029i | \(-0.707455\pi\) | ||||
−0.606571 | + | 0.795029i | \(0.707455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9091 | −1.05130 | −0.525652 | − | 0.850700i | \(-0.676179\pi\) | ||||
−0.525652 | + | 0.850700i | \(0.676179\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.08104 | 0.202717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.6270 | 0.827221 | 0.413610 | − | 0.910454i | \(-0.364268\pi\) | ||||
0.413610 | + | 0.910454i | \(0.364268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.99235 | −0.651829 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.1940 | −1.11687 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6593 | 1.27165 | 0.635826 | − | 0.771833i | \(-0.280660\pi\) | ||||
0.635826 | + | 0.771833i | \(0.280660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.16445 | 0.590334 | 0.295167 | − | 0.955446i | \(-0.404625\pi\) | ||||
0.295167 | + | 0.955446i | \(0.404625\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.85823 | 0.632406 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.0467 | −2.16634 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.2913 | 1.28591 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4620 | 1.03907 | 0.519536 | − | 0.854449i | \(-0.326105\pi\) | ||||
0.519536 | + | 0.854449i | \(0.326105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.98122 | 0.313166 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.0690 | 0.693168 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.4263 | 1.58605 | 0.793026 | − | 0.609188i | \(-0.208504\pi\) | ||||
0.793026 | + | 0.609188i | \(0.208504\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.00438163 | 0.000272261 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.32160 | 0.205602 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.5557 | 1.57583 | 0.787917 | − | 0.615782i | \(-0.211160\pi\) | ||||
0.787917 | + | 0.615782i | \(0.211160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.98122 | 0.428853 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.8226 | −1.09073 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.208408 | 0.0127069 | 0.00635343 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635343 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.28749 | −0.564175 | −0.282087 | − | 0.959389i | \(-0.591027\pi\) | ||||
−0.282087 | + | 0.959389i | \(0.591027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.2311 | −1.04287 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9009 | 0.835221 | 0.417611 | − | 0.908626i | \(-0.362868\pi\) | ||||
0.417611 | + | 0.908626i | \(0.362868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46.0042 | 2.75420 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.93050 | −0.174819 | −0.0874096 | − | 0.996172i | \(-0.527859\pi\) | ||||
−0.0874096 | + | 0.996172i | \(0.527859\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.6627 | −1.52549 | −0.762745 | − | 0.646699i | \(-0.776149\pi\) | ||||
−0.762745 | + | 0.646699i | \(0.776149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.7567 | −1.11105 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.97447 | −0.234605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.09307 | −0.240769 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.8851 | 2.22086 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5672 | 0.617343 | 0.308672 | − | 0.951169i | \(-0.400116\pi\) | ||||
0.308672 | + | 0.951169i | \(0.400116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6616 | 0.737188 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.7614 | −0.624443 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.8581 | −1.61107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.893428 | −0.0514963 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.4640 | 1.92246 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.08542 | −0.405710 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.7248 | 0.897461 | 0.448730 | − | 0.893667i | \(-0.351876\pi\) | ||||
0.448730 | + | 0.893667i | \(0.351876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.598443 | −0.0340442 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.6337 | −1.56696 | −0.783482 | − | 0.621414i | \(-0.786559\pi\) | ||||
−0.783482 | + | 0.621414i | \(0.786559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0345 | 1.69765 | 0.848825 | − | 0.528675i | \(-0.177311\pi\) | ||||
0.848825 | + | 0.528675i | \(0.177311\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.49280 | −0.365828 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.9699 | −1.34628 | −0.673142 | − | 0.739513i | \(-0.735056\pi\) | ||||
−0.673142 | + | 0.739513i | \(0.735056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.511583 | −0.0286431 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.47146 | −0.305387 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.8711 | −1.21694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.59262 | 0.310223 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −48.1040 | −2.66016 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.99235 | 0.550896 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.8213 | 1.14444 | 0.572221 | − | 0.820100i | \(-0.306082\pi\) | ||||
0.572221 | + | 0.820100i | \(0.306082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0284490 | −0.00155900 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.65488 | 0.527502 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.1778 | −1.15363 | −0.576813 | − | 0.816876i | \(-0.695704\pi\) | ||||
−0.576813 | + | 0.816876i | \(0.695704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.8886 | −1.84058 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.08542 | −0.383697 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.3473 | −0.826272 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.4019 | −1.57838 | −0.789189 | − | 0.614150i | \(-0.789499\pi\) | ||||
−0.789189 | + | 0.614150i | \(0.789499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.27540 | −0.442972 | −0.221486 | − | 0.975164i | \(-0.571091\pi\) | ||||
−0.221486 | + | 0.975164i | \(0.571091\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 60.1847 | 3.21242 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.36301 | −0.232219 | −0.116110 | − | 0.993236i | \(-0.537042\pi\) | ||||
−0.116110 | + | 0.993236i | \(0.537042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.9624 | 0.741049 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.0690 | −0.585834 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.4783 | 0.816916 | 0.408458 | − | 0.912777i | \(-0.366067\pi\) | ||||
0.408458 | + | 0.912777i | \(0.366067\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0612 | 0.950588 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.08104 | 0.161713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.7315 | 0.666399 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9413 | 0.727729 | 0.363864 | − | 0.931452i | \(-0.381457\pi\) | ||||
0.363864 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.8054 | 1.34338 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.98122 | −0.362447 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0166 | −1.13998 | −0.569988 | − | 0.821653i | \(-0.693052\pi\) | ||||
−0.569988 | + | 0.821653i | \(0.693052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.08104 | 0.159104 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.86109 | 0.147354 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6802 | 1.52457 | 0.762286 | − | 0.647241i | \(-0.224077\pi\) | ||||
0.762286 | + | 0.647241i | \(0.224077\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.4446 | −0.944947 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.420879 | −0.0215059 | −0.0107529 | − | 0.999942i | \(-0.503423\pi\) | ||||
−0.0107529 | + | 0.999942i | \(0.503423\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.80085 | 0.294874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.74571 | −0.443425 | −0.221712 | − | 0.975112i | \(-0.571165\pi\) | ||||
−0.221712 | + | 0.975112i | \(0.571165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8956 | −0.905021 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.8624 | −0.598380 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.58059 | −0.280790 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.40063 | 0.471804 | 0.235902 | − | 0.971777i | \(-0.424196\pi\) | ||||
0.235902 | + | 0.971777i | \(0.424196\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.7567 | 0.939010 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.46046 | −0.172807 | −0.0864035 | − | 0.996260i | \(-0.527537\pi\) | ||||
−0.0864035 | + | 0.996260i | \(0.527537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.6261 | 1.97392 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.6780 | 0.679667 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.00438163 | 0.000217189 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.30951 | −0.213092 | −0.106546 | − | 0.994308i | \(-0.533979\pi\) | ||||
−0.106546 | + | 0.994308i | \(0.533979\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.5988 | −2.05192 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6616 | −0.623038 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.58587 | 0.323288 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −51.3992 | −2.51703 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.4568 | 1.29250 | 0.646250 | − | 0.763126i | \(-0.276336\pi\) | ||||
0.646250 | + | 0.763126i | \(0.276336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3430 | −0.796509 | −0.398254 | − | 0.917275i | \(-0.630384\pi\) | ||||
−0.398254 | + | 0.917275i | \(0.630384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −64.8783 | −3.15449 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.59262 | 0.174268 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.08542 | 0.342888 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.2311 | −0.831924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9742 | −0.624947 | −0.312474 | − | 0.949926i | \(-0.601158\pi\) | ||||
−0.312474 | + | 0.949926i | \(0.601158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.56660 | 0.459741 | 0.229871 | − | 0.973221i | \(-0.426170\pi\) | ||||
0.229871 | + | 0.973221i | \(0.426170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.57621 | 0.0755733 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.3246 | 1.45062 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.3194 | −0.683429 | −0.341714 | − | 0.939804i | \(-0.611008\pi\) | ||||
−0.341714 | + | 0.939804i | \(0.611008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.49280 | 0.309181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2102 | 0.675145 | 0.337572 | − | 0.941300i | \(-0.390394\pi\) | ||||
0.337572 | + | 0.941300i | \(0.390394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.78461 | −0.274217 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −38.9323 | −1.84143 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.52070 | 0.307731 | 0.153865 | − | 0.988092i | \(-0.450828\pi\) | ||||
0.153865 | + | 0.988092i | \(0.450828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.97447 | −0.187150 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −73.1521 | −3.43698 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.59262 | −0.262186 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.3783 | −1.51459 | −0.757297 | − | 0.653071i | \(-0.773480\pi\) | ||||
−0.757297 | + | 0.653071i | \(0.773480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 38.6618 | 1.80458 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.7001 | −0.544928 | −0.272464 | − | 0.962166i | \(-0.587839\pi\) | ||||
−0.272464 | + | 0.962166i | \(0.587839\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8611 | −1.62013 | −0.810066 | − | 0.586338i | \(-0.800569\pi\) | ||||
−0.810066 | + | 0.586338i | \(0.800569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.8305 | 1.01236 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.09454 | 0.235747 | 0.117874 | − | 0.993029i | \(-0.462392\pi\) | ||||
0.117874 | + | 0.993029i | \(0.462392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.65488 | −0.445821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.5317 | −1.36075 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.893428 | −0.0410798 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.08779 | −0.279327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 45.3276 | 2.07541 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.450794 | −0.0205973 | −0.0102987 | − | 0.999947i | \(-0.503278\pi\) | ||||
−0.0102987 | + | 0.999947i | \(0.503278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0245048 | −0.00111732 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.3473 | 0.698327 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2962 | 0.558342 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.63390 | −0.345925 | −0.172962 | − | 0.984928i | \(-0.555334\pi\) | ||||
−0.172962 | + | 0.984928i | \(0.555334\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.40537 | −0.0635528 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.2158 | −1.13797 | −0.568986 | − | 0.822347i | \(-0.692664\pi\) | ||||
−0.568986 | + | 0.822347i | \(0.692664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.83792 | 0.0827759 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.49280 | −0.291830 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.9624 | −0.626301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.2555 | −1.80209 | −0.901043 | − | 0.433730i | \(-0.857197\pi\) | ||||
−0.901043 | + | 0.433730i | \(0.857197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.8480 | −1.28883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.2843 | 1.61784 | 0.808920 | − | 0.587919i | \(-0.200053\pi\) | ||||
0.808920 | + | 0.587919i | \(0.200053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8613 | 0.483320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 56.3134 | 2.50097 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.4631 | −1.21728 | −0.608640 | − | 0.793447i | \(-0.708284\pi\) | ||||
−0.608640 | + | 0.793447i | \(0.708284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7315 | −0.563210 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −65.5134 | −2.89249 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.194234 | −0.00855898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.99235 | 0.439463 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.53171 | 0.374500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.1079 | −1.53810 | −0.769052 | − | 0.639186i | \(-0.779271\pi\) | ||||
−0.769052 | + | 0.639186i | \(0.779271\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.998661 | 0.0436684 | 0.0218342 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218342 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.08104 | −0.134468 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4552 | 1.10885 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.81252 | 0.0788050 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 82.2094 | 3.56758 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2277 | 0.962788 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.77585 | −0.0767767 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 68.0910 | 2.93834 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0066 | 0.989130 | 0.494565 | − | 0.869141i | \(-0.335327\pi\) | ||||
0.494565 | + | 0.869141i | \(0.335327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3617 | 0.444664 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.6129 | −0.668784 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9433 | −1.15201 | −0.576006 | − | 0.817445i | \(-0.695390\pi\) | ||||
−0.576006 | + | 0.817445i | \(0.695390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.0042 | −1.96341 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.11441 | −0.132678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.58059 | 0.237311 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0135000 | −0.000573042 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.4033 | −1.20348 | −0.601742 | − | 0.798690i | \(-0.705527\pi\) | ||||
−0.601742 | + | 0.798690i | \(0.705527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.99660 | 0.211334 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0690 | −0.467334 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.4950 | −1.11663 | −0.558315 | − | 0.829629i | \(-0.688552\pi\) | ||||
−0.558315 | + | 0.829629i | \(0.688552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9991 | −0.462736 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.6780 | −0.574424 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.01350 | −0.168255 | −0.0841273 | − | 0.996455i | \(-0.526810\pi\) | ||||
−0.0841273 | + | 0.996455i | \(0.526810\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.68371 | −0.363402 | −0.181701 | − | 0.983354i | \(-0.558160\pi\) | ||||
−0.181701 | + | 0.983354i | \(0.558160\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −81.6321 | −3.41023 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.98122 | −0.207731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.2123 | 1.50754 | 0.753769 | − | 0.657140i | \(-0.228234\pi\) | ||||
0.753769 | + | 0.657140i | \(0.228234\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.88649 | 0.410869 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.58587 | −0.273228 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.98122 | −0.289132 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 36.3118 | 1.50131 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.6318 | 1.47068 | 0.735342 | − | 0.677697i | \(-0.237022\pi\) | ||||
0.735342 | + | 0.677697i | \(0.237022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.1345 | −1.77733 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.9869 | −1.39804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.3253 | 0.998919 | 0.499459 | − | 0.866337i | \(-0.333532\pi\) | ||||
0.499459 | + | 0.866337i | \(0.333532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.59262 | −0.147283 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.8671 | −1.01774 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.6239 | 0.679233 | 0.339617 | − | 0.940564i | \(-0.389703\pi\) | ||||
0.339617 | + | 0.940564i | \(0.389703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1086 | 0.453131 | 0.226565 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226565 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62.6872 | 2.55282 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48.0642 | 1.95087 | 0.975433 | − | 0.220295i | \(-0.0707020\pi\) | ||||
0.975433 | + | 0.220295i | \(0.0707020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.57621 | −0.0638711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.8834 | −2.26080 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.64521 | −0.349177 | −0.174588 | − | 0.984642i | \(-0.555859\pi\) | ||||
−0.174588 | + | 0.984642i | \(0.555859\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.2455 | 0.493786 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −49.0997 | −1.97668 | −0.988340 | − | 0.152264i | \(-0.951344\pi\) | ||||
−0.988340 | + | 0.152264i | \(0.951344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.9932 | 1.20553 | 0.602764 | − | 0.797919i | \(-0.294066\pi\) | ||||
0.602764 | + | 0.797919i | \(0.294066\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −53.6051 | −2.15110 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.78461 | 0.231756 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.7567 | 0.749071 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.0157415 | −0.000627656 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0175 | 0.796885 | 0.398443 | − | 0.917193i | \(-0.369551\pi\) | ||||
0.398443 | + | 0.917193i | \(0.369551\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.50903 | −0.139471 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.98650 | −0.237567 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.59262 | 0.221588 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 90.6553 | 3.58627 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.85969 | −0.231444 | −0.115722 | − | 0.993282i | \(-0.536918\pi\) | ||||
−0.115722 | + | 0.993282i | \(0.536918\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.3362 | −1.15691 | −0.578454 | − | 0.815715i | \(-0.696344\pi\) | ||||
−0.578454 | + | 0.815715i | \(0.696344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.75269 | 0.108387 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7736 | 0.895321 | 0.447661 | − | 0.894204i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894204i | \(0.352257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.6616 | −0.497012 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.8305 | −0.855603 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0673 | 0.393964 | 0.196982 | − | 0.980407i | \(-0.436886\pi\) | ||||
0.196982 | + | 0.980407i | \(0.436886\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.85014 | −0.150437 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 82.6633 | 3.22500 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.3684 | −1.68939 | −0.844696 | − | 0.535246i | \(-0.820219\pi\) | ||||
−0.844696 | + | 0.535246i | \(0.820219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.7470 | 0.768071 | 0.384036 | − | 0.923318i | \(-0.374534\pi\) | ||||
0.384036 | + | 0.923318i | \(0.374534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 61.9048 | 2.40418 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.08779 | 0.236074 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.54830 | −0.0986707 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 70.4204 | 2.72261 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.08542 | 0.273530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6117 | 0.794521 | 0.397261 | − | 0.917706i | \(-0.369961\pi\) | ||||
0.397261 | + | 0.917706i | \(0.369961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.7614 | 0.414208 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0193 | 0.461941 | 0.230971 | − | 0.972961i | \(-0.425810\pi\) | ||||
0.230971 | + | 0.972961i | \(0.425810\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2962 | −0.471885 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.3147 | −2.15798 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.6461 | 0.675210 | 0.337605 | − | 0.941288i | \(-0.390383\pi\) | ||||
0.337605 | + | 0.941288i | \(0.390383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.5016 | −0.515868 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −49.0166 | −1.87010 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.0433 | 1.48743 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.96967 | 0.341222 | 0.170611 | − | 0.985338i | \(-0.445426\pi\) | ||||
0.170611 | + | 0.985338i | \(0.445426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.49280 | 0.246641 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.6824 | −0.632800 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.2788 | 0.540846 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.9042 | 1.47149 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7741 | 1.46448 | 0.732239 | − | 0.681048i | \(-0.238475\pi\) | ||||
0.732239 | + | 0.681048i | \(0.238475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0266744 | 0.00100605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.7868 | −1.15950 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8613 | −0.408480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.8990 | 0.559544 | 0.279772 | − | 0.960066i | \(-0.409741\pi\) | ||||
0.279772 | + | 0.960066i | \(0.409741\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.2336 | −1.35887 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.2940 | −1.32177 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.59262 | −0.209152 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 60.5709 | 2.26206 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.2666 | 0.681231 | 0.340615 | − | 0.940203i | \(-0.389365\pi\) | ||||
0.340615 | + | 0.940203i | \(0.389365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.194234 | 0.00723366 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.2360 | 1.05011 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.511583 | 0.0189997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0678 | −1.56021 | −0.780105 | − | 0.625649i | \(-0.784834\pi\) | ||||
−0.780105 | + | 0.625649i | \(0.784834\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.6605 | −0.394835 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.20975 | 0.118717 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −54.0964 | −1.99810 | −0.999048 | − | 0.0436317i | \(-0.986107\pi\) | ||||
−0.999048 | + | 0.0436317i | \(0.986107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.08104 | 0.113646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.65488 | −0.355642 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.1712 | −1.40415 | −0.702075 | − | 0.712103i | \(-0.747743\pi\) | ||||
−0.702075 | + | 0.712103i | \(0.747743\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −104.899 | −3.85357 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.4352 | −0.823066 | −0.411533 | − | 0.911395i | \(-0.635007\pi\) | ||||
−0.411533 | + | 0.911395i | \(0.635007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.6361 | −0.462951 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.7607 | 1.56453 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.77585 | 0.0648882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.78979 | −0.211272 | −0.105636 | − | 0.994405i | \(-0.533688\pi\) | ||||
−0.105636 | + | 0.994405i | \(0.533688\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50.7200 | 1.84834 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.7427 | −0.864084 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.53565 | 0.310233 | 0.155117 | − | 0.987896i | \(-0.450425\pi\) | ||||
0.155117 | + | 0.987896i | \(0.450425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.3473 | 0.557072 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.0688 | −1.41624 | −0.708122 | − | 0.706090i | \(-0.750457\pi\) | ||||
−0.708122 | + | 0.706090i | \(0.750457\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.6129 | 0.565226 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.3262 | 0.843359 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 70.8117 | 2.55686 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.23778 | −0.116757 | −0.0583786 | − | 0.998295i | \(-0.518593\pi\) | ||||
−0.0583786 | + | 0.998295i | \(0.518593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 78.3396 | 2.82133 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2223 | −0.727347 | −0.363674 | − | 0.931526i | \(-0.618478\pi\) | ||||
−0.363674 | + | 0.931526i | \(0.618478\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.08542 | 0.254516 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0135000 | 0.000484309 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.1957 | −0.866901 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.9624 | −0.499615 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.50537 | 0.196746 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.58497 | −0.342102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.6955 | −0.915947 | −0.457974 | − | 0.888966i | \(-0.651425\pi\) | ||||
−0.457974 | + | 0.888966i | \(0.651425\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 78.7382 | 2.80315 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9991 | 0.391083 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.6261 | −1.40716 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.5094 | 0.762860 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.4596 | −0.370497 | −0.185248 | − | 0.982692i | \(-0.559309\pi\) | ||||
−0.185248 | + | 0.982692i | \(0.559309\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.8987 | −1.27001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.5583 | −1.32706 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.7315 | −0.449286 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.98122 | 0.175565 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.642113 | 0.0226034 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.1612 | 1.02525 | 0.512626 | − | 0.858612i | \(-0.328673\pi\) | ||||
0.512626 | + | 0.858612i | \(0.328673\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.9633 | −0.630776 | −0.315388 | − | 0.948963i | \(-0.602135\pi\) | ||||
−0.315388 | + | 0.948963i | \(0.602135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.6151 | −1.00358 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.456134 | −0.0159777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.43900 | −0.190286 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −36.3118 | −1.26884 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.3207 | −0.988399 | −0.494200 | − | 0.869348i | \(-0.664539\pi\) | ||||
−0.494200 | + | 0.869348i | \(0.664539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.5313 | −1.86598 | −0.932992 | − | 0.359897i | \(-0.882812\pi\) | ||||
−0.932992 | + | 0.359897i | \(0.882812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.08104 | −0.107268 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.2700 | 1.33078 | 0.665389 | − | 0.746497i | \(-0.268266\pi\) | ||||
0.665389 | + | 0.746497i | \(0.268266\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.3268 | −1.36588 | −0.682939 | − | 0.730476i | \(-0.739298\pi\) | ||||
−0.682939 | + | 0.730476i | \(0.739298\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.8291 | 1.48572 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.59262 | 0.124477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.36306 | −0.324022 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 76.2494 | 2.63556 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.47548 | −0.154511 | −0.0772554 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772554 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7383 | −0.990975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.02900 | −0.310975 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.2774 | 0.628762 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −79.0678 | −2.71360 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0218259 | 0.000748181 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.85253 | 0.268866 | 0.134433 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134433 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −39.5268 | −1.35179 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.4105 | 0.799688 | 0.399844 | − | 0.916583i | \(-0.369064\pi\) | ||||
0.399844 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.1104 | −1.02735 | −0.513676 | − | 0.857984i | \(-0.671717\pi\) | ||||
−0.513676 | + | 0.857984i | \(0.671717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2455 | −0.417325 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.5174 | −1.03882 | −0.519412 | − | 0.854524i | \(-0.673849\pi\) | ||||
−0.519412 | + | 0.854524i | \(0.673849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.76910 | 0.0941522 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.6109 | −0.428289 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.58059 | 0.189308 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53.9961 | 1.82959 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 79.8367 | 2.70206 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.2288 | 1.52727 | 0.763635 | − | 0.645649i | \(-0.223413\pi\) | ||||
0.763635 | + | 0.645649i | \(0.223413\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.5580 | 1.09815 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.31278 | −0.145301 | −0.0726507 | − | 0.997357i | \(-0.523146\pi\) | ||||
−0.0726507 | + | 0.997357i | \(0.523146\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.0939 | −1.85406 | −0.927028 | − | 0.374991i | \(-0.877646\pi\) | ||||
−0.927028 | + | 0.374991i | \(0.877646\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 39.0110 | 1.31134 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.0611 | −1.31154 | −0.655772 | − | 0.754959i | \(-0.727657\pi\) | ||||
−0.655772 | + | 0.754959i | \(0.727657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.98650 | 0.200781 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.6780 | −0.458232 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60.8313 | 2.03564 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.1000 | 0.738722 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −85.8317 | −2.86584 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.62478 | 0.120893 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.0809 | 0.835565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.75269 | −0.0916036 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.36306 | 0.111792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.70594 | −0.0566449 | −0.0283225 | − | 0.999599i | \(-0.509017\pi\) | ||||
−0.0283225 | + | 0.999599i | \(0.509017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 70.5200 | 2.33900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.96243 | −0.197544 | −0.0987721 | − | 0.995110i | \(-0.531491\pi\) | ||||
−0.0987721 | + | 0.995110i | \(0.531491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.58587 | −0.217961 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.8305 | −0.721693 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.85014 | 0.127143 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.0839 | −1.71809 | −0.859044 | − | 0.511902i | \(-0.828941\pi\) | ||||
−0.859044 | + | 0.511902i | \(0.828941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.4487 | 1.59644 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 78.0866 | 2.57025 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.00438163 | −0.000144067 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.26112 | −0.0414207 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.16815 | 0.169562 | 0.0847808 | − | 0.996400i | \(-0.472981\pi\) | ||||
0.0847808 | + | 0.996400i | \(0.472981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.08779 | −0.199519 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −85.1406 | −2.78738 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.59262 | −0.117491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.4410 | −1.45182 | −0.725912 | − | 0.687787i | \(-0.758582\pi\) | ||||
−0.725912 | + | 0.687787i | \(0.758582\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 92.5374 | 3.01984 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.6371 | −0.607553 | −0.303776 | − | 0.952743i | \(-0.598248\pi\) | ||||
−0.303776 | + | 0.952743i | \(0.598248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7977 | −0.644701 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.7614 | −0.350070 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3254 | −0.920453 | −0.460227 | − | 0.887801i | \(-0.652232\pi\) | ||||
−0.460227 | + | 0.887801i | \(0.652232\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.2026 | 2.31134 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −73.8522 | −2.39482 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.5352 | 1.28067 | 0.640335 | − | 0.768095i | \(-0.278795\pi\) | ||||
0.640335 | + | 0.768095i | \(0.278795\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.4950 | −0.857358 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.57621 | −0.0509515 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.5016 | 0.435988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.2032 | 0.619457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.5302 | −0.371557 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.20882 | 0.103296 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.0995 | −1.41814 | −0.709072 | − | 0.705136i | \(-0.750886\pi\) | ||||
−0.709072 | + | 0.705136i | \(0.750886\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −67.3858 | −2.16474 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.1124 | 0.805896 | 0.402948 | − | 0.915223i | \(-0.367986\pi\) | ||||
0.402948 | + | 0.915223i | \(0.367986\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6824 | 0.534814 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.2311 | 0.551836 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.0179 | −1.08833 | −0.544164 | − | 0.838979i | \(-0.683153\pi\) | ||||
−0.544164 | + | 0.838979i | \(0.683153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.78461 | 0.184877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −101.372 | −3.23655 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.45158 | 0.269564 | 0.134782 | − | 0.990875i | \(-0.456967\pi\) | ||||
0.134782 | + | 0.990875i | \(0.456967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0310 | −0.351477 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.7868 | 0.979955 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.45036 | −0.141513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9433 | −0.601754 | −0.300877 | − | 0.953663i | \(-0.597279\pi\) | ||||
−0.300877 | + | 0.953663i | \(0.597279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 64.1512 | 2.03578 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.07102 | −0.255868 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.8783 | 1.23129 | 0.615644 | − | 0.788024i | \(-0.288896\pi\) | ||||
0.615644 | + | 0.788024i | \(0.288896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0471527 | −0.00149185 |
(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 | 6160.2.a.bx.1.5 | 5 | ||
4.3 | odd | 2 | 3080.2.a.u.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.u.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
6160.2.a.bx.1.5 | 5 | 1.1 | even | 1 | trivial |