Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | 1.24698 | 0.719944 | 0.359972 | − | 0.932963i | \(-0.382786\pi\) | ||||
0.359972 | + | 0.932963i | \(0.382786\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.24698 | 0.471314 | 0.235657 | − | 0.971836i | \(-0.424276\pi\) | ||||
0.235657 | + | 0.971836i | \(0.424276\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.44504 | −0.481681 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.198062 | 0.0597180 | 0.0298590 | − | 0.999554i | \(-0.490494\pi\) | ||||
0.0298590 | + | 0.999554i | \(0.490494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.24698 | −0.321969 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.85086 | −1.17651 | −0.588253 | − | 0.808677i | \(-0.700184\pi\) | ||||
−0.588253 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35690 | 0.311293 | 0.155647 | − | 0.987813i | \(-0.450254\pi\) | ||||
0.155647 | + | 0.987813i | \(0.450254\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.55496 | 0.339320 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.44504 | −0.301312 | −0.150656 | − | 0.988586i | \(-0.548139\pi\) | ||||
−0.150656 | + | 0.988586i | \(0.548139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.54288 | −1.06673 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.13706 | 0.211147 | 0.105574 | − | 0.994411i | \(-0.466332\pi\) | ||||
0.105574 | + | 0.994411i | \(0.466332\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.85086 | −1.23045 | −0.615225 | − | 0.788352i | \(-0.710935\pi\) | ||||
−0.615225 | + | 0.788352i | \(0.710935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.246980 | 0.0429936 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.24698 | −0.210778 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54288 | −0.553304 | −0.276652 | − | 0.960970i | \(-0.589225\pi\) | ||||
−0.276652 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.89977 | −1.20470 | −0.602352 | − | 0.798231i | \(-0.705770\pi\) | ||||
−0.602352 | + | 0.798231i | \(0.705770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.44504 | 0.215414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.87263 | 1.29421 | 0.647103 | − | 0.762403i | \(-0.275980\pi\) | ||||
0.647103 | + | 0.762403i | \(0.275980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.44504 | −0.777863 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.04892 | −0.847018 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.86831 | −0.256633 | −0.128316 | − | 0.991733i | \(-0.540957\pi\) | ||||
−0.128316 | + | 0.991733i | \(0.540957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.198062 | −0.0267067 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69202 | 0.224114 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.878002 | 0.114306 | 0.0571531 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571531 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.19806 | −1.04965 | −0.524827 | − | 0.851209i | \(-0.675870\pi\) | ||||
−0.524827 | + | 0.851209i | \(0.675870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.80194 | −0.227023 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.207751 | −0.0253808 | −0.0126904 | − | 0.999919i | \(-0.504040\pi\) | ||||
−0.0126904 | + | 0.999919i | \(0.504040\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.80194 | −0.216928 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.664874 | −0.0789061 | −0.0394530 | − | 0.999221i | \(-0.512562\pi\) | ||||
−0.0394530 | + | 0.999221i | \(0.512562\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.72587 | 0.201998 | 0.100999 | − | 0.994887i | \(-0.467796\pi\) | ||||
0.100999 | + | 0.994887i | \(0.467796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.24698 | 0.143989 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.246980 | 0.0281459 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5700 | −1.41424 | −0.707119 | − | 0.707094i | \(-0.750006\pi\) | ||||
−0.707119 | + | 0.707094i | \(0.750006\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.57673 | −0.286303 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3230 | −1.35263 | −0.676315 | − | 0.736613i | \(-0.736424\pi\) | ||||
−0.676315 | + | 0.736613i | \(0.736424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.85086 | 0.526149 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.41789 | 0.152014 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.8659 | 1.68178 | 0.840892 | − | 0.541203i | \(-0.182031\pi\) | ||||
0.840892 | + | 0.541203i | \(0.182031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.54288 | −0.885855 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.35690 | −0.139215 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.31336 | 0.133351 | 0.0666755 | − | 0.997775i | \(-0.478761\pi\) | ||||
0.0666755 | + | 0.997775i | \(0.478761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.286208 | −0.0287650 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7506 | 1.36824 | 0.684119 | − | 0.729370i | \(-0.260187\pi\) | ||||
0.684119 | + | 0.729370i | \(0.260187\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9608 | −1.17853 | −0.589265 | − | 0.807940i | \(-0.700583\pi\) | ||||
−0.589265 | + | 0.807940i | \(0.700583\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.55496 | −0.151748 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.47219 | −0.529016 | −0.264508 | − | 0.964383i | \(-0.585210\pi\) | ||||
−0.264508 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.8116 | −1.80183 | −0.900914 | − | 0.433999i | \(-0.857102\pi\) | ||||
−0.900914 | + | 0.433999i | \(0.857102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.74094 | 0.355074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.72886 | 0.350781 | 0.175391 | − | 0.984499i | \(-0.443881\pi\) | ||||
0.175391 | + | 0.984499i | \(0.443881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.44504 | 0.134751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.04892 | −0.554503 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9608 | −0.996434 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.41789 | −0.398348 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.66786 | 0.680412 | 0.340206 | − | 0.940351i | \(-0.389503\pi\) | ||||
0.340206 | + | 0.940351i | \(0.389503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.85086 | −0.867319 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.32304 | −0.814558 | −0.407279 | − | 0.913304i | \(-0.633522\pi\) | ||||
−0.407279 | + | 0.913304i | \(0.633522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.69202 | 0.146717 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.54288 | 0.477055 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.72348 | 0.403554 | 0.201777 | − | 0.979431i | \(-0.435328\pi\) | ||||
0.201777 | + | 0.979431i | \(0.435328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.818331 | 0.0694099 | 0.0347050 | − | 0.999398i | \(-0.488951\pi\) | ||||
0.0347050 | + | 0.999398i | \(0.488951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0640 | 0.931755 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.13706 | −0.0944280 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.78986 | −0.560018 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.6233 | 1.93529 | 0.967646 | − | 0.252311i | \(-0.0811907\pi\) | ||||
0.967646 | + | 0.252311i | \(0.0811907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.78448 | 0.552113 | 0.276057 | − | 0.961141i | \(-0.410972\pi\) | ||||
0.276057 | + | 0.961141i | \(0.410972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.00969 | 0.566700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.85086 | 0.550274 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4276 | −1.31106 | −0.655532 | − | 0.755167i | \(-0.727556\pi\) | ||||
−0.655532 | + | 0.755167i | \(0.727556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.32975 | −0.184761 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.80194 | −0.142013 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7463 | −0.998368 | −0.499184 | − | 0.866496i | \(-0.666367\pi\) | ||||
−0.499184 | + | 0.866496i | \(0.666367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.246980 | −0.0192273 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.2054 | −1.17663 | −0.588313 | − | 0.808633i | \(-0.700208\pi\) | ||||
−0.588313 | + | 0.808633i | \(0.700208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.96077 | −0.149944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.7845 | −1.04801 | −0.524007 | − | 0.851714i | \(-0.675564\pi\) | ||||
−0.524007 | + | 0.851714i | \(0.675564\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.24698 | 0.0942628 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.09485 | 0.0822940 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.51035 | −0.486607 | −0.243303 | − | 0.969950i | \(-0.578231\pi\) | ||||
−0.243303 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.45712 | −0.331295 | −0.165648 | − | 0.986185i | \(-0.552971\pi\) | ||||
−0.165648 | + | 0.986185i | \(0.552971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.2228 | −0.755692 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.960771 | −0.0702586 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.91185 | −0.502763 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.1564 | 1.67554 | 0.837771 | − | 0.546022i | \(-0.183859\pi\) | ||||
0.837771 | + | 0.546022i | \(0.183859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.692021 | 0.0498128 | 0.0249064 | − | 0.999690i | \(-0.492071\pi\) | ||||
0.0249064 | + | 0.999690i | \(0.492071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.98792 | −0.497869 | −0.248934 | − | 0.968520i | \(-0.580080\pi\) | ||||
−0.248934 | + | 0.968520i | \(0.580080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1400 | 1.28591 | 0.642957 | − | 0.765902i | \(-0.277707\pi\) | ||||
0.642957 | + | 0.765902i | \(0.277707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.259061 | −0.0182728 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41789 | 0.0995167 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.54288 | 0.247445 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.08815 | 0.145136 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.268750 | 0.0185898 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9095 | 1.16410 | 0.582048 | − | 0.813155i | \(-0.302252\pi\) | ||||
0.582048 | + | 0.813155i | \(0.302252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.829085 | −0.0568080 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.89977 | 0.538760 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.54288 | −0.579928 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.15213 | 0.145427 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0532 | −0.807144 | −0.403572 | − | 0.914948i | \(-0.632231\pi\) | ||||
−0.403572 | + | 0.914948i | \(0.632231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.44504 | −0.0963361 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1642 | 1.00648 | 0.503242 | − | 0.864146i | \(-0.332140\pi\) | ||||
0.503242 | + | 0.864146i | \(0.332140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5375 | −1.35716 | −0.678578 | − | 0.734528i | \(-0.737403\pi\) | ||||
−0.678578 | + | 0.734528i | \(0.737403\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.307979 | 0.0202635 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.2198 | −1.12811 | −0.564054 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564054 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.87263 | −0.578786 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.6746 | −1.01817 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4112 | −0.996867 | −0.498434 | − | 0.866928i | \(-0.666091\pi\) | ||||
−0.498434 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2892 | −0.662785 | −0.331393 | − | 0.943493i | \(-0.607518\pi\) | ||||
−0.331393 | + | 0.943493i | \(0.607518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.4155 | 0.860605 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.44504 | 0.347871 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.3666 | −0.973818 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.09246 | −0.510791 | −0.255396 | − | 0.966837i | \(-0.582206\pi\) | ||||
−0.255396 | + | 0.966837i | \(0.582206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.286208 | −0.0179938 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.04892 | 0.378798 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.4228 | 1.96010 | 0.980050 | − | 0.198750i | \(-0.0636883\pi\) | ||||
0.980050 | + | 0.198750i | \(0.0636883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74094 | 0.232451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.64310 | −0.101706 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.84117 | 0.421844 | 0.210922 | − | 0.977503i | \(-0.432353\pi\) | ||||
0.210922 | + | 0.977503i | \(0.432353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.86831 | 0.114770 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.7845 | 1.21079 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.735562 | 0.0448480 | 0.0224240 | − | 0.999749i | \(-0.492862\pi\) | ||||
0.0224240 | + | 0.999749i | \(0.492862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.994623 | 0.0604191 | 0.0302095 | − | 0.999544i | \(-0.490383\pi\) | ||||
0.0302095 | + | 0.999544i | \(0.490383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.198062 | 0.0119436 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.3110 | −1.64096 | −0.820478 | − | 0.571678i | \(-0.806293\pi\) | ||||
−0.820478 | + | 0.571678i | \(0.806293\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.89977 | 0.592684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.3327 | −0.795364 | −0.397682 | − | 0.917523i | \(-0.630185\pi\) | ||||
−0.397682 | + | 0.917523i | \(0.630185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.907542 | 0.0539478 | 0.0269739 | − | 0.999636i | \(-0.491413\pi\) | ||||
0.0269739 | + | 0.999636i | \(0.491413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.69202 | −0.100227 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.41789 | −0.260780 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.53079 | 0.384164 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.63773 | 0.0960053 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.68425 | −0.390498 | −0.195249 | − | 0.980754i | \(-0.562552\pi\) | ||||
−0.195249 | + | 0.980754i | \(0.562552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.878002 | −0.0511193 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.09783 | −0.0637028 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.85086 | −0.567794 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.1468 | 0.985055 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.19806 | 0.469420 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.9269 | 1.76509 | 0.882546 | − | 0.470226i | \(-0.155827\pi\) | ||||
0.882546 | + | 0.470226i | \(0.155827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.9148 | −0.848475 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9095 | −1.12896 | −0.564481 | − | 0.825446i | \(-0.690924\pi\) | ||||
−0.564481 | + | 0.825446i | \(0.690924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.9681 | 1.52433 | 0.762163 | − | 0.647386i | \(-0.224138\pi\) | ||||
0.762163 | + | 0.647386i | \(0.224138\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.80194 | 0.101528 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 33.6829 | 1.89182 | 0.945911 | − | 0.324427i | \(-0.105171\pi\) | ||||
0.945911 | + | 0.324427i | \(0.105171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.225209 | 0.0126093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.82371 | −0.380862 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.58211 | −0.366238 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.4577 | −1.29721 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0640 | 0.609977 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.115293 | 0.00633708 | 0.00316854 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00316854 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.33513 | −0.237563 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.207751 | 0.0113506 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0006 | 1.36187 | 0.680934 | − | 0.732344i | \(-0.261574\pi\) | ||||
0.680934 | + | 0.732344i | \(0.261574\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.64981 | 0.252543 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.35690 | −0.0734800 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5187 | −0.837932 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.80194 | 0.0970131 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.92931 | 0.318302 | 0.159151 | − | 0.987254i | \(-0.449124\pi\) | ||||
0.159151 | + | 0.987254i | \(0.449124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0441 | 1.50117 | 0.750584 | − | 0.660775i | \(-0.229772\pi\) | ||||
0.750584 | + | 0.660775i | \(0.229772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.1957 | 1.18136 | 0.590678 | − | 0.806907i | \(-0.298860\pi\) | ||||
0.590678 | + | 0.806907i | \(0.298860\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.664874 | 0.0352879 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.54288 | −0.399211 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.31037 | −0.280271 | −0.140135 | − | 0.990132i | \(-0.544754\pi\) | ||||
−0.140135 | + | 0.990132i | \(0.544754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1588 | −0.903097 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.6679 | −0.717377 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.72587 | −0.0903363 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.29696 | −0.172100 | −0.0860500 | − | 0.996291i | \(-0.527424\pi\) | ||||
−0.0860500 | + | 0.996291i | \(0.527424\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.11960 | 0.266516 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.32975 | −0.120955 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.70410 | −0.450681 | −0.225341 | − | 0.974280i | \(-0.572350\pi\) | ||||
−0.225341 | + | 0.974280i | \(0.572350\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.24698 | −0.0643937 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9269 | 0.818111 | 0.409055 | − | 0.912510i | \(-0.365858\pi\) | ||||
0.409055 | + | 0.912510i | \(0.365858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.56166 | 0.489859 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.13169 | −0.211119 | −0.105560 | − | 0.994413i | \(-0.533663\pi\) | ||||
−0.105560 | + | 0.994413i | \(0.533663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.246980 | −0.0125872 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4155 | 0.580283 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.1347 | −0.767358 | −0.383679 | − | 0.923466i | \(-0.625343\pi\) | ||||
−0.383679 | + | 0.923466i | \(0.625343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.00969 | 0.354495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.6256 | −0.586436 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.5700 | 0.632467 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5080 | 0.979076 | 0.489538 | − | 0.871982i | \(-0.337165\pi\) | ||||
0.489538 | + | 0.871982i | \(0.337165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.10992 | 0.105628 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.8974 | −1.39313 | −0.696564 | − | 0.717494i | \(-0.745289\pi\) | ||||
−0.696564 | + | 0.717494i | \(0.745289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57673 | 0.128039 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.594187 | 0.0294527 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.46788 | −0.319816 | −0.159908 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159908 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.89008 | 0.290536 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.09485 | 0.0538741 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.3230 | 0.604914 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.02044 | 0.0499713 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9541 | 1.02367 | 0.511837 | − | 0.859083i | \(-0.328965\pi\) | ||||
0.511837 | + | 0.859083i | \(0.328965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.5211 | −0.561504 | −0.280752 | − | 0.959780i | \(-0.590584\pi\) | ||||
−0.280752 | + | 0.959780i | \(0.590584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.8213 | −0.623394 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.85086 | −0.235301 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2228 | −0.494717 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.33273 | 0.305037 | 0.152519 | − | 0.988301i | \(-0.451262\pi\) | ||||
0.152519 | + | 0.988301i | \(0.451262\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.5332 | −0.554250 | −0.277125 | − | 0.960834i | \(-0.589382\pi\) | ||||
−0.277125 | + | 0.960834i | \(0.589382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41789 | −0.0679829 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.96077 | −0.0937964 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.7036 | −1.32222 | −0.661111 | − | 0.750288i | \(-0.729915\pi\) | ||||
−0.661111 | + | 0.750288i | \(0.729915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.86831 | 0.374682 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.2814 | −0.583508 | −0.291754 | − | 0.956493i | \(-0.594239\pi\) | ||||
−0.291754 | + | 0.956493i | \(0.594239\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.8659 | −0.752117 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.4577 | 1.39330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2556 | −1.19189 | −0.595943 | − | 0.803027i | \(-0.703222\pi\) | ||||
−0.595943 | + | 0.803027i | \(0.703222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.701710 | −0.0330422 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.46011 | 0.397491 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.1608 | 1.45764 | 0.728819 | − | 0.684706i | \(-0.240069\pi\) | ||||
0.728819 | + | 0.684706i | \(0.240069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.8877 | 1.25501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.605203 | 0.0281871 | 0.0140936 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140936 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.3575 | 0.992567 | 0.496283 | − | 0.868161i | \(-0.334698\pi\) | ||||
0.496283 | + | 0.868161i | \(0.334698\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.54288 | 0.396166 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.4886 | 1.22575 | 0.612873 | − | 0.790182i | \(-0.290014\pi\) | ||||
0.612873 | + | 0.790182i | \(0.290014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.259061 | −0.0119623 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.4849 | −0.943893 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.56465 | −0.0719425 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.35690 | 0.0622587 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.69979 | 0.123615 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.08038 | 0.232128 | 0.116064 | − | 0.993242i | \(-0.462972\pi\) | ||||
0.116064 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.24698 | −0.102241 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.31336 | −0.0596364 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.7646 | −1.07688 | −0.538439 | − | 0.842664i | \(-0.680986\pi\) | ||||
−0.538439 | + | 0.842664i | \(0.680986\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.8944 | −0.718769 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.9071 | −0.582488 | −0.291244 | − | 0.956649i | \(-0.594069\pi\) | ||||
−0.291244 | + | 0.956649i | \(0.594069\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.51573 | −0.248416 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.286208 | 0.0128641 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.829085 | −0.0371895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.3749 | −1.80743 | −0.903715 | − | 0.428134i | \(-0.859171\pi\) | ||||
−0.903715 | + | 0.428134i | \(0.859171\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.9608 | −0.847105 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.2634 | −0.457621 | −0.228811 | − | 0.973471i | \(-0.573484\pi\) | ||||
−0.228811 | + | 0.973471i | \(0.573484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7506 | −0.611895 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.40342 | 0.106530 | 0.0532649 | − | 0.998580i | \(-0.483037\pi\) | ||||
0.0532649 | + | 0.998580i | \(0.483037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.15213 | 0.0952046 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.52111 | −0.332065 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9608 | 0.527055 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.75733 | 0.0772874 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.1890 | −0.754512 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.1806 | 1.01556 | 0.507780 | − | 0.861487i | \(-0.330466\pi\) | ||||
0.507780 | + | 0.861487i | \(0.330466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.0073 | 1.74940 | 0.874698 | − | 0.484668i | \(-0.161059\pi\) | ||||
0.874698 | + | 0.484668i | \(0.161059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.55496 | 0.0678639 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.2325 | 1.44763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9119 | −0.909211 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.26875 | −0.0550591 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.47219 | 0.236583 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.11828 | −0.350330 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.07846 | −0.0464524 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.13813 | 0.134919 | 0.0674593 | − | 0.997722i | \(-0.478511\pi\) | ||||
0.0674593 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.55794 | −0.238514 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.8116 | 0.805802 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9280 | 0.467247 | 0.233623 | − | 0.972327i | \(-0.424942\pi\) | ||||
0.233623 | + | 0.972327i | \(0.424942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.8465 | 0.505598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.54288 | 0.0657288 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6746 | −0.666550 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.74094 | −0.158794 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.19508 | 0.262494 | 0.131247 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131247 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19806 | −0.0505822 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.0411 | 1.39252 | 0.696259 | − | 0.717790i | \(-0.254846\pi\) | ||||
0.696259 | + | 0.717790i | \(0.254846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.72886 | −0.156874 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.21313 | −0.134939 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4577 | −0.606099 | −0.303049 | − | 0.952975i | \(-0.598005\pi\) | ||||
−0.303049 | + | 0.952975i | \(0.598005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.6765 | 1.45117 | 0.725583 | − | 0.688135i | \(-0.241570\pi\) | ||||
0.725583 | + | 0.688135i | \(0.241570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.8756 | 1.20630 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.44504 | −0.0602624 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9842 | 1.53967 | 0.769836 | − | 0.638242i | \(-0.220338\pi\) | ||||
0.769836 | + | 0.638242i | \(0.220338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.862937 | 0.0358624 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.3666 | −0.637513 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.370042 | −0.0153256 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0043 | 1.48606 | 0.743028 | − | 0.669260i | \(-0.233389\pi\) | ||||
0.743028 | + | 0.669260i | \(0.233389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.29590 | −0.383031 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.71379 | −0.358437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.4161 | −1.78289 | −0.891443 | − | 0.453134i | \(-0.850306\pi\) | ||||
−0.891443 | + | 0.453134i | \(0.850306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.04892 | 0.247981 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.6203 | 0.925786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.7549 | 1.58348 | 0.791742 | − | 0.610856i | \(-0.209174\pi\) | ||||
0.791742 | + | 0.610856i | \(0.209174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1293 | −0.739509 | −0.369755 | − | 0.929129i | \(-0.620558\pi\) | ||||
−0.369755 | + | 0.929129i | \(0.620558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.300209 | 0.0122254 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9608 | 0.445619 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.1094 | −1.22210 | −0.611052 | − | 0.791590i | \(-0.709253\pi\) | ||||
−0.611052 | + | 0.791590i | \(0.709253\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.76809 | 0.0716465 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.9197 | 1.65273 | 0.826366 | − | 0.563133i | \(-0.190404\pi\) | ||||
0.826366 | + | 0.563133i | \(0.190404\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.41789 | 0.178147 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7308 | −1.15666 | −0.578329 | − | 0.815804i | \(-0.696295\pi\) | ||||
−0.578329 | + | 0.815804i | \(0.696295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.1118 | −1.29068 | −0.645342 | − | 0.763894i | \(-0.723285\pi\) | ||||
−0.645342 | + | 0.763894i | \(0.723285\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00969 | 0.321418 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.7845 | 0.792648 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.335126 | 0.0133836 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.5526 | −0.580249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.2010 | 1.36152 | 0.680761 | − | 0.732506i | \(-0.261649\pi\) | ||||
0.680761 | + | 0.732506i | \(0.261649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0858 | 0.838083 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.66786 | −0.304290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.960771 | 0.0380075 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.39506 | 0.173594 | 0.0867972 | − | 0.996226i | \(-0.472337\pi\) | ||||
0.0867972 | + | 0.996226i | \(0.472337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.3773 | −1.43458 | −0.717291 | − | 0.696774i | \(-0.754618\pi\) | ||||
−0.717291 | + | 0.696774i | \(0.754618\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.85086 | 0.387877 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.1129 | 0.712092 | 0.356046 | − | 0.934469i | \(-0.384125\pi\) | ||||
0.356046 | + | 0.934469i | \(0.384125\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.173899 | 0.00682614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6528 | −0.417516 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.6601 | −0.651960 | −0.325980 | − | 0.945377i | \(-0.605694\pi\) | ||||
−0.325980 | + | 0.945377i | \(0.605694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.32304 | 0.364281 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.49396 | −0.0972986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.8471 | 1.20163 | 0.600817 | − | 0.799387i | \(-0.294842\pi\) | ||||
0.600817 | + | 0.799387i | \(0.294842\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4896 | −0.874746 | −0.437373 | − | 0.899280i | \(-0.644091\pi\) | ||||
−0.437373 | + | 0.899280i | \(0.644091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.69202 | −0.0656138 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64310 | −0.0636212 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0301 | −0.581098 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.62373 | −0.0626833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.7405 | −1.87881 | −0.939403 | − | 0.342814i | \(-0.888620\pi\) | ||||
−0.939403 | + | 0.342814i | \(0.888620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.54288 | −0.213345 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.81295 | −0.108111 | −0.0540553 | − | 0.998538i | \(-0.517215\pi\) | ||||
−0.0540553 | + | 0.998538i | \(0.517215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.63773 | 0.0628502 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.9095 | 0.724612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.701710 | −0.0268502 | −0.0134251 | − | 0.999910i | \(-0.504273\pi\) | ||||
−0.0134251 | + | 0.999910i | \(0.504273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.72348 | −0.180475 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.6098 | −0.977076 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1377 | 1.33670 | 0.668350 | − | 0.743847i | \(-0.267001\pi\) | ||||
0.668350 | + | 0.743847i | \(0.267001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.356896 | −0.0135574 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.818331 | −0.0310411 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.1860 | 0.650965 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.4728 | −0.812175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.23968 | 0.311209 | 0.155604 | − | 0.987819i | \(-0.450268\pi\) | ||||
0.155604 | + | 0.987819i | \(0.450268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.07069 | 0.153529 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0640 | −0.416694 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.1468 | 0.644870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.6359 | −1.33834 | −0.669168 | − | 0.743111i | \(-0.733349\pi\) | ||||
−0.669168 | + | 0.743111i | \(0.733349\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.1642 | 0.681211 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.89977 | 0.370749 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.2174 | −0.717688 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.3497 | 1.69126 | 0.845630 | − | 0.533770i | \(-0.179225\pi\) | ||||
0.845630 | + | 0.533770i | \(0.179225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.9148 | −0.555458 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.8304 | −0.477168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.13706 | 0.0422295 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.2664 | 1.30796 | 0.653978 | − | 0.756513i | \(-0.273099\pi\) | ||||
0.653978 | + | 0.756513i | \(0.273099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4590 | 0.905890 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.3207 | 1.41734 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.6722 | −0.578865 | −0.289432 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289432 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.78986 | 0.250448 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0411476 | −0.00151569 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.80433 | −0.323873 | −0.161936 | − | 0.986801i | \(-0.551774\pi\) | ||||
−0.161936 | + | 0.986801i | \(0.551774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.8974 | −0.986769 | −0.493385 | − | 0.869811i | \(-0.664240\pi\) | ||||
−0.493385 | + | 0.869811i | \(0.664240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.6233 | −0.865489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.8073 | 0.651536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.82371 | −0.249333 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.0200 | −1.35088 | −0.675439 | − | 0.737416i | \(-0.736046\pi\) | ||||
−0.675439 | + | 0.737416i | \(0.736046\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.0911 | −0.367741 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.78448 | −0.246912 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3730 | −0.740470 | −0.370235 | − | 0.928938i | \(-0.620723\pi\) | ||||
−0.370235 | + | 0.928938i | \(0.620723\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.356896 | −0.0129545 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.7362 | −1.44043 | −0.720217 | − | 0.693749i | \(-0.755958\pi\) | ||||
−0.720217 | + | 0.693749i | \(0.755958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.4577 | −0.849226 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.00969 | −0.253436 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.6171 | 1.50075 | 0.750376 | − | 0.661011i | \(-0.229872\pi\) | ||||
0.750376 | + | 0.661011i | \(0.229872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.1836 | 1.41116 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.2948 | 1.37737 | 0.688685 | − | 0.725061i | \(-0.258188\pi\) | ||||
0.688685 | + | 0.725061i | \(0.258188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.85086 | −0.246090 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.66487 | 0.167351 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.80731 | −0.172240 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.131687 | −0.00471211 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.30260 | −0.225237 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4276 | 0.586326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.0847 | 1.85662 | 0.928309 | − | 0.371809i | \(-0.121262\pi\) | ||||
0.928309 | + | 0.371809i | \(0.121262\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.53079 | 0.303704 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.64981 | 0.165328 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.32975 | 0.0826277 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.8278 | −0.702335 | −0.351168 | − | 0.936313i | \(-0.614215\pi\) | ||||
−0.351168 | + | 0.936313i | \(0.614215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.0398 | −1.52264 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.9269 | −0.810083 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.341830 | 0.0120629 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.80194 | 0.0635100 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.917231 | 0.0322881 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.59073 | −0.0910852 | −0.0455426 | − | 0.998962i | \(-0.514502\pi\) | ||||
−0.0455426 | + | 0.998962i | \(0.514502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.946297 | −0.0332290 | −0.0166145 | − | 0.999862i | \(-0.505289\pi\) | ||||
−0.0166145 | + | 0.999862i | \(0.505289\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.24027 | 0.0434983 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7463 | 0.446484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7192 | −0.375016 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.83148 | −0.203520 | −0.101760 | − | 0.994809i | \(-0.532447\pi\) | ||||
−0.101760 | + | 0.994809i | \(0.532447\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2083 | 0.878708 | 0.439354 | − | 0.898314i | \(-0.355207\pi\) | ||||
0.439354 | + | 0.898314i | \(0.355207\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.246980 | 0.00859873 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.0127 | 0.939323 | 0.469661 | − | 0.882847i | \(-0.344376\pi\) | ||||
0.469661 | + | 0.882847i | \(0.344376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.4064 | −0.708744 | −0.354372 | − | 0.935105i | \(-0.615305\pi\) | ||||
−0.354372 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.0562 | −1.18140 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.4131 | 0.915160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.2054 | 0.526203 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.9734 | 1.31255 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.1463 | −1.35148 | −0.675740 | − | 0.737140i | \(-0.736176\pi\) | ||||
−0.675740 | + | 0.737140i | \(0.736176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7071 | −0.955417 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6256 | −0.572618 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6679 | −0.469633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.13169 | 0.0388394 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.33513 | −0.148606 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.51009 | 0.154423 | 0.0772113 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772113 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.96077 | 0.0670570 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.3948 | 0.662514 | 0.331257 | − | 0.943541i | \(-0.392527\pi\) | ||||
0.331257 | + | 0.943541i | \(0.392527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7429 | 1.35601 | 0.678004 | − | 0.735058i | \(-0.262845\pi\) | ||||
0.678004 | + | 0.735058i | \(0.262845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.50902 | −0.187747 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7827 | 0.911693 | 0.455846 | − | 0.890058i | \(-0.349337\pi\) | ||||
0.455846 | + | 0.890058i | \(0.349337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7845 | 0.468686 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.14377 | 0.276577 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.48965 | −0.0844555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.89785 | −0.0642326 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.24698 | −0.0421556 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.2185 | 0.412590 | 0.206295 | − | 0.978490i | \(-0.433859\pi\) | ||||
0.206295 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.33513 | −0.281137 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.72827 | −0.0582268 | −0.0291134 | − | 0.999576i | \(-0.509268\pi\) | ||||
−0.0291134 | + | 0.999576i | \(0.509268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.6340 | 1.30014 | 0.650069 | − | 0.759875i | \(-0.274740\pi\) | ||||
0.650069 | + | 0.759875i | \(0.274740\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.09485 | −0.0368030 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.6055 | −1.22909 | −0.614547 | − | 0.788880i | \(-0.710661\pi\) | ||||
−0.614547 | + | 0.788880i | \(0.710661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.56166 | 0.320688 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.510353 | −0.0170975 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0392 | 0.402877 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.51035 | 0.217617 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.78986 | −0.259806 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.06292 | 0.301930 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.2838 | −0.408780 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.45712 | 0.148160 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.5881 | 1.64654 | 0.823272 | − | 0.567646i | \(-0.192146\pi\) | ||||
0.823272 | + | 0.567646i | \(0.192146\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.8702 | −0.659054 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.7982 | 1.08665 | 0.543327 | − | 0.839521i | \(-0.317164\pi\) | ||||
0.543327 | + | 0.839521i | \(0.317164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.44073 | −0.0807764 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.2228 | 0.337956 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.6256 | −0.383913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.6944 | −0.484724 | −0.242362 | − | 0.970186i | \(-0.577922\pi\) | ||||
−0.242362 | + | 0.970186i | \(0.577922\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.5652 | 1.27077 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | 0.0986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.2838 | 0.567675 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.53127 | −0.0830482 | −0.0415241 | − | 0.999138i | \(-0.513221\pi\) | ||||
−0.0415241 | + | 0.999138i | \(0.513221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.38835 | −0.242144 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.8267 | −0.812789 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.960771 | 0.0314206 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.3951 | −0.470266 | −0.235133 | − | 0.971963i | \(-0.575553\pi\) | ||||
−0.235133 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.6286 | 1.09743 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.7885 | 0.612489 | 0.306244 | − | 0.951953i | \(-0.400928\pi\) | ||||
0.306244 | + | 0.951953i | \(0.400928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.11960 | 0.166717 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.91185 | 0.224843 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.4543 | −1.63954 | −0.819772 | − | 0.572691i | \(-0.805900\pi\) | ||||
−0.819772 | + | 0.572691i | \(0.805900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.0019 | 1.36201 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.6708 | 1.83575 | 0.917874 | − | 0.396871i | \(-0.129904\pi\) | ||||
0.917874 | + | 0.396871i | \(0.129904\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.1564 | −0.749325 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.280831 | 0.00907799 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.89008 | 0.190201 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.9342 | 0.514007 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.90754 | 0.254817 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.692021 | −0.0222770 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.4421 | 0.432267 | 0.216134 | − | 0.976364i | \(-0.430655\pi\) | ||||
0.216134 | + | 0.976364i | \(0.430655\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.20775 | −0.263671 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6963 | 1.33810 | 0.669050 | − | 0.743218i | \(-0.266701\pi\) | ||||
0.669050 | + | 0.743218i | \(0.266701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.02044 | 0.0327139 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.2228 | 0.487021 | 0.243511 | − | 0.969898i | \(-0.421701\pi\) | ||||
0.243511 | + | 0.969898i | \(0.421701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.14244 | 0.100433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1836 | 0.867905 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.7888 | −1.36475 | −0.682375 | − | 0.731002i | \(-0.739053\pi\) | ||||
−0.682375 | + | 0.731002i | \(0.739053\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.98792 | 0.222654 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.7966 | 0.439149 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4155 | 0.362992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2857 | 0.580865 | 0.290433 | − | 0.956895i | \(-0.406201\pi\) | ||||
0.290433 | + | 0.956895i | \(0.406201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.143768 | 0.00456234 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.1400 | −0.575078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.7415 | −0.941924 | −0.470962 | − | 0.882154i | \(-0.656093\pi\) | ||||
−0.470962 | + | 0.882154i | \(0.656093\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.6286 | −0.526107 |
(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 | 3380.2.a.k.1.3 | ✓ | 3 | |
13.5 | odd | 4 | 3380.2.f.g.3041.6 | 6 | |||
13.8 | odd | 4 | 3380.2.f.g.3041.5 | 6 | |||
13.12 | even | 2 | 3380.2.a.l.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.k.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3380.2.a.l.1.3 | yes | 3 | 13.12 | even | 2 | ||
3380.2.f.g.3041.5 | 6 | 13.8 | odd | 4 | |||
3380.2.f.g.3041.6 | 6 | 13.5 | odd | 4 |