Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(1,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, 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("1425.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.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: | \(11.3786822880\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.36147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36147 | −1.66981 | −0.834905 | − | 0.550394i | \(-0.814478\pi\) | ||||
−0.834905 | + | 0.550394i | \(0.814478\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.57653 | 1.78827 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.36147 | 0.964066 | ||||||||
\(7\) | −0.784934 | −0.296677 | −0.148339 | − | 0.988937i | \(-0.547393\pi\) | ||||
−0.148339 | + | 0.988937i | \(0.547393\pi\) | |||||||
\(8\) | −3.72294 | −1.31626 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93800 | 0.885841 | 0.442921 | − | 0.896561i | \(-0.353942\pi\) | ||||
0.442921 | + | 0.896561i | \(0.353942\pi\) | |||||||
\(12\) | −3.57653 | −1.03246 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 1.85360 | 0.495395 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.63853 | 0.409633 | ||||||||
\(17\) | 5.15307 | 1.24980 | 0.624901 | − | 0.780704i | \(-0.285139\pi\) | ||||
0.624901 | + | 0.780704i | \(0.285139\pi\) | |||||||
\(18\) | −2.36147 | −0.556604 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.784934 | 0.171287 | ||||||||
\(22\) | −6.93800 | −1.47919 | ||||||||
\(23\) | 3.78493 | 0.789213 | 0.394607 | − | 0.918850i | \(-0.370881\pi\) | ||||
0.394607 | + | 0.918850i | \(0.370881\pi\) | |||||||
\(24\) | 3.72294 | 0.759941 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.44588 | 1.85249 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.80734 | −0.530538 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06200 | 0.190740 | 0.0953701 | − | 0.995442i | \(-0.469597\pi\) | ||||
0.0953701 | + | 0.995442i | \(0.469597\pi\) | |||||||
\(32\) | 3.57653 | 0.632248 | ||||||||
\(33\) | −2.93800 | −0.511441 | ||||||||
\(34\) | −12.1688 | −2.08693 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.57653 | 0.596089 | ||||||||
\(37\) | 0.722938 | 0.118850 | 0.0594251 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594251 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(38\) | 2.36147 | 0.383081 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.93800 | 1.23971 | 0.619854 | − | 0.784717i | \(-0.287192\pi\) | ||||
0.619854 | + | 0.784717i | \(0.287192\pi\) | |||||||
\(42\) | −1.85360 | −0.286016 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 10.5079 | 1.58412 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.93800 | −1.31784 | ||||||||
\(47\) | 3.87601 | 0.565374 | 0.282687 | − | 0.959212i | \(-0.408774\pi\) | ||||
0.282687 | + | 0.959212i | \(0.408774\pi\) | |||||||
\(48\) | −1.63853 | −0.236502 | ||||||||
\(49\) | −6.38388 | −0.911983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.15307 | −0.721574 | ||||||||
\(52\) | −14.3061 | −1.98390 | ||||||||
\(53\) | −6.44588 | −0.885409 | −0.442705 | − | 0.896668i | \(-0.645981\pi\) | ||||
−0.442705 | + | 0.896668i | \(0.645981\pi\) | |||||||
\(54\) | 2.36147 | 0.321355 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.92226 | 0.390503 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 11.8073 | 1.55038 | ||||||||
\(59\) | −4.66094 | −0.606803 | −0.303401 | − | 0.952863i | \(-0.598122\pi\) | ||||
−0.303401 | + | 0.952863i | \(0.598122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.87601 | 1.13646 | 0.568228 | − | 0.822871i | \(-0.307629\pi\) | ||||
0.568228 | + | 0.822871i | \(0.307629\pi\) | |||||||
\(62\) | −2.50787 | −0.318500 | ||||||||
\(63\) | −0.784934 | −0.0988924 | ||||||||
\(64\) | −11.7229 | −1.46537 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.93800 | 0.854009 | ||||||||
\(67\) | −8.93800 | −1.09195 | −0.545975 | − | 0.837801i | \(-0.683841\pi\) | ||||
−0.545975 | + | 0.837801i | \(0.683841\pi\) | |||||||
\(68\) | 18.4301 | 2.23498 | ||||||||
\(69\) | −3.78493 | −0.455653 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.66094 | −0.315796 | −0.157898 | − | 0.987455i | \(-0.550472\pi\) | ||||
−0.157898 | + | 0.987455i | \(0.550472\pi\) | |||||||
\(72\) | −3.72294 | −0.438752 | ||||||||
\(73\) | 8.44588 | 0.988515 | 0.494257 | − | 0.869316i | \(-0.335440\pi\) | ||||
0.494257 | + | 0.869316i | \(0.335440\pi\) | |||||||
\(74\) | −1.70719 | −0.198457 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.57653 | −0.410257 | ||||||||
\(77\) | −2.30614 | −0.262809 | ||||||||
\(78\) | −9.44588 | −1.06953 | ||||||||
\(79\) | 3.35480 | 0.377445 | 0.188722 | − | 0.982030i | \(-0.439565\pi\) | ||||
0.188722 | + | 0.982030i | \(0.439565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −18.7453 | −2.07008 | ||||||||
\(83\) | −4.93800 | −0.542016 | −0.271008 | − | 0.962577i | \(-0.587357\pi\) | ||||
−0.271008 | + | 0.962577i | \(0.587357\pi\) | |||||||
\(84\) | 2.80734 | 0.306306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.44588 | 1.01857 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | −10.9380 | −1.16600 | ||||||||
\(89\) | 0.569868 | 0.0604059 | 0.0302029 | − | 0.999544i | \(-0.490385\pi\) | ||||
0.0302029 | + | 0.999544i | \(0.490385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.13974 | 0.329134 | ||||||||
\(92\) | 13.5369 | 1.41132 | ||||||||
\(93\) | −1.06200 | −0.110124 | ||||||||
\(94\) | −9.15307 | −0.944067 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.57653 | −0.365029 | ||||||||
\(97\) | −8.59894 | −0.873091 | −0.436545 | − | 0.899682i | \(-0.643798\pi\) | ||||
−0.436545 | + | 0.899682i | \(0.643798\pi\) | |||||||
\(98\) | 15.0753 | 1.52284 | ||||||||
\(99\) | 2.93800 | 0.295280 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.15307 | −0.114735 | −0.0573674 | − | 0.998353i | \(-0.518271\pi\) | ||||
−0.0573674 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(102\) | 12.1688 | 1.20489 | ||||||||
\(103\) | 19.9537 | 1.96610 | 0.983051 | − | 0.183335i | \(-0.0586892\pi\) | ||||
0.983051 | + | 0.183335i | \(0.0586892\pi\) | |||||||
\(104\) | 14.8918 | 1.46026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.2217 | 1.47847 | ||||||||
\(107\) | 12.2308 | 1.18240 | 0.591198 | − | 0.806526i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806526i | \(0.298655\pi\) | |||||||
\(108\) | −3.57653 | −0.344152 | ||||||||
\(109\) | −2.41680 | −0.231487 | −0.115744 | − | 0.993279i | \(-0.536925\pi\) | ||||
−0.115744 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.722938 | −0.0686182 | ||||||||
\(112\) | −1.28614 | −0.121529 | ||||||||
\(113\) | 20.6900 | 1.94635 | 0.973177 | − | 0.230060i | \(-0.0738921\pi\) | ||||
0.973177 | + | 0.230060i | \(0.0738921\pi\) | |||||||
\(114\) | −2.36147 | −0.221172 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.8827 | −1.66036 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | 11.0067 | 1.01325 | ||||||||
\(119\) | −4.04482 | −0.370788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.36814 | −0.215285 | ||||||||
\(122\) | −20.9604 | −1.89767 | ||||||||
\(123\) | −7.93800 | −0.715746 | ||||||||
\(124\) | 3.79827 | 0.341094 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.85360 | 0.165132 | ||||||||
\(127\) | 13.5369 | 1.20121 | 0.600605 | − | 0.799546i | \(-0.294926\pi\) | ||||
0.600605 | + | 0.799546i | \(0.294926\pi\) | |||||||
\(128\) | 20.5303 | 1.81464 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.50787 | −0.393855 | −0.196927 | − | 0.980418i | \(-0.563096\pi\) | ||||
−0.196927 | + | 0.980418i | \(0.563096\pi\) | |||||||
\(132\) | −10.5079 | −0.914593 | ||||||||
\(133\) | 0.784934 | 0.0680624 | ||||||||
\(134\) | 21.1068 | 1.82335 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19.1846 | −1.64506 | ||||||||
\(137\) | 16.2928 | 1.39199 | 0.695994 | − | 0.718047i | \(-0.254964\pi\) | ||||
0.695994 | + | 0.718047i | \(0.254964\pi\) | |||||||
\(138\) | 8.93800 | 0.760853 | ||||||||
\(139\) | −2.78493 | −0.236215 | −0.118108 | − | 0.993001i | \(-0.537683\pi\) | ||||
−0.118108 | + | 0.993001i | \(0.537683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.87601 | −0.326419 | ||||||||
\(142\) | 6.28373 | 0.527319 | ||||||||
\(143\) | −11.7520 | −0.982753 | ||||||||
\(144\) | 1.63853 | 0.136544 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.9447 | −1.65063 | ||||||||
\(147\) | 6.38388 | 0.526533 | ||||||||
\(148\) | 2.58561 | 0.212536 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5989 | 1.83908 | 0.919538 | − | 0.393001i | \(-0.128563\pi\) | ||||
0.919538 | + | 0.393001i | \(0.128563\pi\) | |||||||
\(152\) | 3.72294 | 0.301970 | ||||||||
\(153\) | 5.15307 | 0.416601 | ||||||||
\(154\) | 5.44588 | 0.438841 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.3061 | 1.14541 | ||||||||
\(157\) | 14.2441 | 1.13681 | 0.568403 | − | 0.822750i | \(-0.307561\pi\) | ||||
0.568403 | + | 0.822750i | \(0.307561\pi\) | |||||||
\(158\) | −7.92226 | −0.630261 | ||||||||
\(159\) | 6.44588 | 0.511191 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.97092 | −0.234142 | ||||||||
\(162\) | −2.36147 | −0.185535 | ||||||||
\(163\) | 19.9828 | 1.56518 | 0.782588 | − | 0.622540i | \(-0.213899\pi\) | ||||
0.782588 | + | 0.622540i | \(0.213899\pi\) | |||||||
\(164\) | 28.3905 | 2.21693 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.6609 | 0.905065 | ||||||||
\(167\) | 14.7849 | 1.14409 | 0.572046 | − | 0.820221i | \(-0.306150\pi\) | ||||
0.572046 | + | 0.820221i | \(0.306150\pi\) | |||||||
\(168\) | −2.92226 | −0.225457 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −14.3061 | −1.09083 | ||||||||
\(173\) | −22.7520 | −1.72980 | −0.864902 | − | 0.501941i | \(-0.832619\pi\) | ||||
−0.864902 | + | 0.501941i | \(0.832619\pi\) | |||||||
\(174\) | −11.8073 | −0.895112 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.81401 | 0.362870 | ||||||||
\(177\) | 4.66094 | 0.350338 | ||||||||
\(178\) | −1.34573 | −0.100866 | ||||||||
\(179\) | 22.1068 | 1.65234 | 0.826171 | − | 0.563420i | \(-0.190515\pi\) | ||||
0.826171 | + | 0.563420i | \(0.190515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1979 | 0.980991 | 0.490496 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490496 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(182\) | −7.41439 | −0.549591 | ||||||||
\(183\) | −8.87601 | −0.656133 | ||||||||
\(184\) | −14.0911 | −1.03881 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.50787 | 0.183886 | ||||||||
\(187\) | 15.1397 | 1.10713 | ||||||||
\(188\) | 13.8627 | 1.01104 | ||||||||
\(189\) | 0.784934 | 0.0570955 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6743 | 0.989436 | 0.494718 | − | 0.869054i | \(-0.335271\pi\) | ||||
0.494718 | + | 0.869054i | \(0.335271\pi\) | |||||||
\(192\) | 11.7229 | 0.846030 | ||||||||
\(193\) | −24.5989 | −1.77067 | −0.885335 | − | 0.464953i | \(-0.846071\pi\) | ||||
−0.885335 | + | 0.464953i | \(0.846071\pi\) | |||||||
\(194\) | 20.3061 | 1.45790 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.8322 | −1.63087 | ||||||||
\(197\) | 25.6147 | 1.82497 | 0.912485 | − | 0.409109i | \(-0.134160\pi\) | ||||
0.912485 | + | 0.409109i | \(0.134160\pi\) | |||||||
\(198\) | −6.93800 | −0.493062 | ||||||||
\(199\) | −0.230809 | −0.0163616 | −0.00818081 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818081 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.93800 | 0.630438 | ||||||||
\(202\) | 2.72294 | 0.191585 | ||||||||
\(203\) | 3.92467 | 0.275458 | ||||||||
\(204\) | −18.4301 | −1.29037 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −47.1201 | −3.28302 | ||||||||
\(207\) | 3.78493 | 0.263071 | ||||||||
\(208\) | −6.55412 | −0.454447 | ||||||||
\(209\) | −2.93800 | −0.203226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.35480 | 0.368640 | 0.184320 | − | 0.982866i | \(-0.440992\pi\) | ||||
0.184320 | + | 0.982866i | \(0.440992\pi\) | |||||||
\(212\) | −23.0539 | −1.58335 | ||||||||
\(213\) | 2.66094 | 0.182325 | ||||||||
\(214\) | −28.8827 | −1.97438 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.72294 | 0.253314 | ||||||||
\(217\) | −0.833597 | −0.0565883 | ||||||||
\(218\) | 5.70719 | 0.386540 | ||||||||
\(219\) | −8.44588 | −0.570719 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.6123 | −1.38653 | ||||||||
\(222\) | 1.70719 | 0.114579 | ||||||||
\(223\) | −1.78493 | −0.119528 | −0.0597640 | − | 0.998213i | \(-0.519035\pi\) | ||||
−0.0597640 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(224\) | −2.80734 | −0.187574 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −48.8588 | −3.25004 | ||||||||
\(227\) | −8.96708 | −0.595166 | −0.297583 | − | 0.954696i | \(-0.596181\pi\) | ||||
−0.297583 | + | 0.954696i | \(0.596181\pi\) | |||||||
\(228\) | 3.57653 | 0.236862 | ||||||||
\(229\) | 26.5660 | 1.75553 | 0.877766 | − | 0.479089i | \(-0.159033\pi\) | ||||
0.877766 | + | 0.479089i | \(0.159033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.30614 | 0.151733 | ||||||||
\(232\) | 18.6147 | 1.22211 | ||||||||
\(233\) | −9.56987 | −0.626943 | −0.313471 | − | 0.949598i | \(-0.601492\pi\) | ||||
−0.313471 | + | 0.949598i | \(0.601492\pi\) | |||||||
\(234\) | 9.44588 | 0.617496 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.6700 | −1.08513 | ||||||||
\(237\) | −3.35480 | −0.217918 | ||||||||
\(238\) | 9.55172 | 0.619146 | ||||||||
\(239\) | 16.9051 | 1.09350 | 0.546749 | − | 0.837296i | \(-0.315865\pi\) | ||||
0.546749 | + | 0.837296i | \(0.315865\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.27706 | −0.597588 | −0.298794 | − | 0.954318i | \(-0.596584\pi\) | ||||
−0.298794 | + | 0.954318i | \(0.596584\pi\) | |||||||
\(242\) | 5.59228 | 0.359485 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 31.7453 | 2.03229 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.7453 | 1.19516 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | −3.95375 | −0.251063 | ||||||||
\(249\) | 4.93800 | 0.312933 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1531 | 1.58765 | 0.793824 | − | 0.608148i | \(-0.208087\pi\) | ||||
0.793824 | + | 0.608148i | \(0.208087\pi\) | |||||||
\(252\) | −2.80734 | −0.176846 | ||||||||
\(253\) | 11.1201 | 0.699118 | ||||||||
\(254\) | −31.9671 | −2.00579 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −25.0357 | −1.56473 | ||||||||
\(257\) | −21.1821 | −1.32131 | −0.660653 | − | 0.750691i | \(-0.729721\pi\) | ||||
−0.660653 | + | 0.750691i | \(0.729721\pi\) | |||||||
\(258\) | −9.44588 | −0.588074 | ||||||||
\(259\) | −0.567458 | −0.0352601 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | 10.6452 | 0.657663 | ||||||||
\(263\) | 3.78493 | 0.233389 | 0.116695 | − | 0.993168i | \(-0.462770\pi\) | ||||
0.116695 | + | 0.993168i | \(0.462770\pi\) | |||||||
\(264\) | 10.9380 | 0.673188 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.85360 | −0.113651 | ||||||||
\(267\) | −0.569868 | −0.0348754 | ||||||||
\(268\) | −31.9671 | −1.95270 | ||||||||
\(269\) | 16.3061 | 0.994203 | 0.497101 | − | 0.867692i | \(-0.334398\pi\) | ||||
0.497101 | + | 0.867692i | \(0.334398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.66094 | −0.161641 | −0.0808203 | − | 0.996729i | \(-0.525754\pi\) | ||||
−0.0808203 | + | 0.996729i | \(0.525754\pi\) | |||||||
\(272\) | 8.44347 | 0.511960 | ||||||||
\(273\) | −3.13974 | −0.190025 | ||||||||
\(274\) | −38.4750 | −2.32436 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.5369 | −0.814829 | ||||||||
\(277\) | −21.1821 | −1.27271 | −0.636356 | − | 0.771396i | \(-0.719559\pi\) | ||||
−0.636356 | + | 0.771396i | \(0.719559\pi\) | |||||||
\(278\) | 6.57653 | 0.394434 | ||||||||
\(279\) | 1.06200 | 0.0635801 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.3839 | −1.57393 | −0.786965 | − | 0.616997i | \(-0.788349\pi\) | ||||
−0.786965 | + | 0.616997i | \(0.788349\pi\) | |||||||
\(282\) | 9.15307 | 0.545057 | ||||||||
\(283\) | −18.8918 | −1.12300 | −0.561499 | − | 0.827477i | \(-0.689775\pi\) | ||||
−0.561499 | + | 0.827477i | \(0.689775\pi\) | |||||||
\(284\) | −9.51695 | −0.564727 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.7520 | 1.64101 | ||||||||
\(287\) | −6.23081 | −0.367793 | ||||||||
\(288\) | 3.57653 | 0.210749 | ||||||||
\(289\) | 9.55412 | 0.562007 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.59894 | 0.504079 | ||||||||
\(292\) | 30.2070 | 1.76773 | ||||||||
\(293\) | −7.49213 | −0.437695 | −0.218847 | − | 0.975759i | \(-0.570230\pi\) | ||||
−0.218847 | + | 0.975759i | \(0.570230\pi\) | |||||||
\(294\) | −15.0753 | −0.879211 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.69145 | −0.156437 | ||||||||
\(297\) | −2.93800 | −0.170480 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.1397 | −0.875554 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.13974 | 0.180971 | ||||||||
\(302\) | −53.3667 | −3.07091 | ||||||||
\(303\) | 1.15307 | 0.0662421 | ||||||||
\(304\) | −1.63853 | −0.0939762 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12.1688 | −0.695645 | ||||||||
\(307\) | −20.8140 | −1.18792 | −0.593959 | − | 0.804495i | \(-0.702436\pi\) | ||||
−0.593959 | + | 0.804495i | \(0.702436\pi\) | |||||||
\(308\) | −8.24799 | −0.469973 | ||||||||
\(309\) | −19.9537 | −1.13513 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.8918 | 1.52489 | 0.762446 | − | 0.647052i | \(-0.223998\pi\) | ||||
0.762446 | + | 0.647052i | \(0.223998\pi\) | |||||||
\(312\) | −14.8918 | −0.843079 | ||||||||
\(313\) | −24.2599 | −1.37125 | −0.685625 | − | 0.727955i | \(-0.740471\pi\) | ||||
−0.685625 | + | 0.727955i | \(0.740471\pi\) | |||||||
\(314\) | −33.6371 | −1.89825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.9986 | 0.674972 | ||||||||
\(317\) | 23.3061 | 1.30900 | 0.654502 | − | 0.756061i | \(-0.272879\pi\) | ||||
0.654502 | + | 0.756061i | \(0.272879\pi\) | |||||||
\(318\) | −15.2217 | −0.853592 | ||||||||
\(319\) | −14.6900 | −0.822483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2308 | −0.682657 | ||||||||
\(322\) | 7.01574 | 0.390972 | ||||||||
\(323\) | −5.15307 | −0.286724 | ||||||||
\(324\) | 3.57653 | 0.198696 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −47.1888 | −2.61355 | ||||||||
\(327\) | 2.41680 | 0.133649 | ||||||||
\(328\) | −29.5527 | −1.63177 | ||||||||
\(329\) | −3.04241 | −0.167733 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.8298 | −1.30980 | −0.654901 | − | 0.755715i | \(-0.727290\pi\) | ||||
−0.654901 | + | 0.755715i | \(0.727290\pi\) | |||||||
\(332\) | −17.6609 | −0.969270 | ||||||||
\(333\) | 0.722938 | 0.0396167 | ||||||||
\(334\) | −34.9142 | −1.91042 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.28614 | 0.0701646 | ||||||||
\(337\) | 6.43013 | 0.350272 | 0.175136 | − | 0.984544i | \(-0.443964\pi\) | ||||
0.175136 | + | 0.984544i | \(0.443964\pi\) | |||||||
\(338\) | −7.08441 | −0.385341 | ||||||||
\(339\) | −20.6900 | −1.12373 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.12015 | 0.168966 | ||||||||
\(342\) | 2.36147 | 0.127694 | ||||||||
\(343\) | 10.5055 | 0.567242 | ||||||||
\(344\) | 14.8918 | 0.802909 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 53.7282 | 2.88844 | ||||||||
\(347\) | −9.27706 | −0.498019 | −0.249009 | − | 0.968501i | \(-0.580105\pi\) | ||||
−0.249009 | + | 0.968501i | \(0.580105\pi\) | |||||||
\(348\) | 17.8827 | 0.958612 | ||||||||
\(349\) | −8.01574 | −0.429073 | −0.214536 | − | 0.976716i | \(-0.568824\pi\) | ||||
−0.214536 | + | 0.976716i | \(0.568824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 10.5079 | 0.560071 | ||||||||
\(353\) | 22.3061 | 1.18724 | 0.593618 | − | 0.804747i | \(-0.297699\pi\) | ||||
0.593618 | + | 0.804747i | \(0.297699\pi\) | |||||||
\(354\) | −11.0067 | −0.584998 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.03815 | 0.108022 | ||||||||
\(357\) | 4.04482 | 0.214075 | ||||||||
\(358\) | −52.2046 | −2.75910 | ||||||||
\(359\) | −9.40106 | −0.496169 | −0.248084 | − | 0.968738i | \(-0.579801\pi\) | ||||
−0.248084 | + | 0.968738i | \(0.579801\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −31.1664 | −1.63807 | ||||||||
\(363\) | 2.36814 | 0.124295 | ||||||||
\(364\) | 11.2294 | 0.588579 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 20.9604 | 1.09562 | ||||||||
\(367\) | −7.32188 | −0.382199 | −0.191100 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191100 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(368\) | 6.20173 | 0.323288 | ||||||||
\(369\) | 7.93800 | 0.413236 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.05959 | 0.262681 | ||||||||
\(372\) | −3.79827 | −0.196931 | ||||||||
\(373\) | −9.02908 | −0.467508 | −0.233754 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233754 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(374\) | −35.7520 | −1.84869 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.4301 | −0.744177 | ||||||||
\(377\) | 20.0000 | 1.03005 | ||||||||
\(378\) | −1.85360 | −0.0953388 | ||||||||
\(379\) | 28.0448 | 1.44057 | 0.720283 | − | 0.693681i | \(-0.244012\pi\) | ||||
0.720283 | + | 0.693681i | \(0.244012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5369 | −0.693519 | ||||||||
\(382\) | −32.2914 | −1.65217 | ||||||||
\(383\) | 33.6767 | 1.72080 | 0.860399 | − | 0.509621i | \(-0.170214\pi\) | ||||
0.860399 | + | 0.509621i | \(0.170214\pi\) | |||||||
\(384\) | −20.5303 | −1.04768 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 58.0896 | 2.95668 | ||||||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | −30.7544 | −1.56132 | ||||||||
\(389\) | 0.678118 | 0.0343819 | 0.0171910 | − | 0.999852i | \(-0.494528\pi\) | ||||
0.0171910 | + | 0.999852i | \(0.494528\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5040 | 0.986361 | ||||||||
\(392\) | 23.7668 | 1.20040 | ||||||||
\(393\) | 4.50787 | 0.227392 | ||||||||
\(394\) | −60.4883 | −3.04736 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.5079 | 0.528040 | ||||||||
\(397\) | −10.8140 | −0.542740 | −0.271370 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271370 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(398\) | 0.545048 | 0.0273208 | ||||||||
\(399\) | −0.784934 | −0.0392959 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2599 | −1.41123 | −0.705616 | − | 0.708595i | \(-0.749329\pi\) | ||||
−0.705616 | + | 0.708595i | \(0.749329\pi\) | |||||||
\(402\) | −21.1068 | −1.05271 | ||||||||
\(403\) | −4.24799 | −0.211607 | ||||||||
\(404\) | −4.12399 | −0.205176 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.26799 | −0.459962 | ||||||||
\(407\) | 2.12399 | 0.105282 | ||||||||
\(408\) | 19.1846 | 0.949777 | ||||||||
\(409\) | 29.1846 | 1.44308 | 0.721542 | − | 0.692371i | \(-0.243434\pi\) | ||||
0.721542 | + | 0.692371i | \(0.243434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2928 | −0.803665 | ||||||||
\(412\) | 71.3653 | 3.51591 | ||||||||
\(413\) | 3.65853 | 0.180025 | ||||||||
\(414\) | −8.93800 | −0.439279 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.3061 | −0.701416 | ||||||||
\(417\) | 2.78493 | 0.136379 | ||||||||
\(418\) | 6.93800 | 0.339349 | ||||||||
\(419\) | −26.7678 | −1.30769 | −0.653845 | − | 0.756628i | \(-0.726845\pi\) | ||||
−0.653845 | + | 0.756628i | \(0.726845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5040 | 1.43794 | 0.718969 | − | 0.695042i | \(-0.244614\pi\) | ||||
0.718969 | + | 0.695042i | \(0.244614\pi\) | |||||||
\(422\) | −12.6452 | −0.615559 | ||||||||
\(423\) | 3.87601 | 0.188458 | ||||||||
\(424\) | 23.9976 | 1.16543 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.28373 | −0.304448 | ||||||||
\(427\) | −6.96708 | −0.337161 | ||||||||
\(428\) | 43.7439 | 2.11444 | ||||||||
\(429\) | 11.7520 | 0.567393 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.90893 | 0.140118 | 0.0700590 | − | 0.997543i | \(-0.477681\pi\) | ||||
0.0700590 | + | 0.997543i | \(0.477681\pi\) | |||||||
\(432\) | −1.63853 | −0.0788339 | ||||||||
\(433\) | 6.00000 | 0.288342 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(434\) | 1.96851 | 0.0944917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.64376 | −0.413961 | ||||||||
\(437\) | −3.78493 | −0.181058 | ||||||||
\(438\) | 19.9447 | 0.952993 | ||||||||
\(439\) | 33.4130 | 1.59471 | 0.797357 | − | 0.603508i | \(-0.206231\pi\) | ||||
0.797357 | + | 0.603508i | \(0.206231\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.38388 | −0.303994 | ||||||||
\(442\) | 48.6753 | 2.31525 | ||||||||
\(443\) | −23.5818 | −1.12040 | −0.560202 | − | 0.828356i | \(-0.689276\pi\) | ||||
−0.560202 | + | 0.828356i | \(0.689276\pi\) | |||||||
\(444\) | −2.58561 | −0.122708 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.21507 | 0.199589 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.20173 | 0.434741 | ||||||||
\(449\) | −6.87601 | −0.324499 | −0.162249 | − | 0.986750i | \(-0.551875\pi\) | ||||
−0.162249 | + | 0.986750i | \(0.551875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.3219 | 1.09818 | ||||||||
\(452\) | 73.9986 | 3.48060 | ||||||||
\(453\) | −22.5989 | −1.06179 | ||||||||
\(454\) | 21.1755 | 0.993814 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.72294 | −0.174343 | ||||||||
\(457\) | −33.2599 | −1.55583 | −0.777916 | − | 0.628368i | \(-0.783723\pi\) | ||||
−0.777916 | + | 0.628368i | \(0.783723\pi\) | |||||||
\(458\) | −62.7348 | −2.93141 | ||||||||
\(459\) | −5.15307 | −0.240525 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.2928 | 0.758832 | 0.379416 | − | 0.925226i | \(-0.376125\pi\) | ||||
0.379416 | + | 0.925226i | \(0.376125\pi\) | |||||||
\(462\) | −5.44588 | −0.253365 | ||||||||
\(463\) | 33.4459 | 1.55436 | 0.777181 | − | 0.629277i | \(-0.216649\pi\) | ||||
0.777181 | + | 0.629277i | \(0.216649\pi\) | |||||||
\(464\) | −8.19266 | −0.380335 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.5989 | 1.04688 | ||||||||
\(467\) | 20.5212 | 0.949608 | 0.474804 | − | 0.880092i | \(-0.342519\pi\) | ||||
0.474804 | + | 0.880092i | \(0.342519\pi\) | |||||||
\(468\) | −14.3061 | −0.661302 | ||||||||
\(469\) | 7.01574 | 0.323957 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2441 | −0.656335 | ||||||||
\(472\) | 17.3524 | 0.798709 | ||||||||
\(473\) | −11.7520 | −0.540358 | ||||||||
\(474\) | 7.92226 | 0.363881 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.4664 | −0.663068 | ||||||||
\(477\) | −6.44588 | −0.295136 | ||||||||
\(478\) | −39.9208 | −1.82594 | ||||||||
\(479\) | −7.84309 | −0.358360 | −0.179180 | − | 0.983816i | \(-0.557344\pi\) | ||||
−0.179180 | + | 0.983816i | \(0.557344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.89175 | −0.131852 | ||||||||
\(482\) | 21.9075 | 0.997859 | ||||||||
\(483\) | 2.97092 | 0.135182 | ||||||||
\(484\) | −8.46972 | −0.384987 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.36147 | 0.107118 | ||||||||
\(487\) | 7.16640 | 0.324741 | 0.162370 | − | 0.986730i | \(-0.448086\pi\) | ||||
0.162370 | + | 0.986730i | \(0.448086\pi\) | |||||||
\(488\) | −33.0448 | −1.49587 | ||||||||
\(489\) | −19.9828 | −0.903654 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2928 | 0.735284 | 0.367642 | − | 0.929967i | \(-0.380165\pi\) | ||||
0.367642 | + | 0.929967i | \(0.380165\pi\) | |||||||
\(492\) | −28.3905 | −1.27994 | ||||||||
\(493\) | −25.7653 | −1.16041 | ||||||||
\(494\) | −9.44588 | −0.424990 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.74011 | 0.0781334 | ||||||||
\(497\) | 2.08866 | 0.0936893 | ||||||||
\(498\) | −11.6609 | −0.522539 | ||||||||
\(499\) | 40.2890 | 1.80358 | 0.901791 | − | 0.432173i | \(-0.142253\pi\) | ||||
0.901791 | + | 0.432173i | \(0.142253\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.7849 | −0.660542 | ||||||||
\(502\) | −59.3982 | −2.65107 | ||||||||
\(503\) | −15.1397 | −0.675047 | −0.337524 | − | 0.941317i | \(-0.609589\pi\) | ||||
−0.337524 | + | 0.941317i | \(0.609589\pi\) | |||||||
\(504\) | 2.92226 | 0.130168 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −26.2599 | −1.16739 | ||||||||
\(507\) | −3.00000 | −0.133235 | ||||||||
\(508\) | 48.4154 | 2.14808 | ||||||||
\(509\) | 7.55412 | 0.334831 | 0.167415 | − | 0.985886i | \(-0.446458\pi\) | ||||
0.167415 | + | 0.985886i | \(0.446458\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.62945 | −0.293270 | ||||||||
\(512\) | 18.0606 | 0.798172 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 50.0210 | 2.20633 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 14.3061 | 0.629793 | ||||||||
\(517\) | 11.3877 | 0.500831 | ||||||||
\(518\) | 1.34003 | 0.0588778 | ||||||||
\(519\) | 22.7520 | 0.998703 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.4616 | −1.46598 | −0.732990 | − | 0.680239i | \(-0.761876\pi\) | ||||
−0.732990 | + | 0.680239i | \(0.761876\pi\) | |||||||
\(522\) | 11.8073 | 0.516793 | ||||||||
\(523\) | 35.9208 | 1.57071 | 0.785354 | − | 0.619047i | \(-0.212481\pi\) | ||||
0.785354 | + | 0.619047i | \(0.212481\pi\) | |||||||
\(524\) | −16.1226 | −0.704317 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.93800 | −0.389715 | ||||||||
\(527\) | 5.47254 | 0.238388 | ||||||||
\(528\) | −4.81401 | −0.209503 | ||||||||
\(529\) | −8.67427 | −0.377142 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.66094 | −0.202268 | ||||||||
\(532\) | 2.80734 | 0.121714 | ||||||||
\(533\) | −31.7520 | −1.37533 | ||||||||
\(534\) | 1.34573 | 0.0582352 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 33.2756 | 1.43729 | ||||||||
\(537\) | −22.1068 | −0.953980 | ||||||||
\(538\) | −38.5064 | −1.66013 | ||||||||
\(539\) | −18.7559 | −0.807872 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1516 | −1.85523 | −0.927617 | − | 0.373533i | \(-0.878146\pi\) | ||||
−0.927617 | + | 0.373533i | \(0.878146\pi\) | |||||||
\(542\) | 6.28373 | 0.269909 | ||||||||
\(543\) | −13.1979 | −0.566376 | ||||||||
\(544\) | 18.4301 | 0.790185 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.41439 | 0.317307 | ||||||||
\(547\) | −23.2308 | −0.993278 | −0.496639 | − | 0.867957i | \(-0.665433\pi\) | ||||
−0.496639 | + | 0.867957i | \(0.665433\pi\) | |||||||
\(548\) | 58.2718 | 2.48925 | ||||||||
\(549\) | 8.87601 | 0.378819 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00000 | 0.213007 | ||||||||
\(552\) | 14.0911 | 0.599756 | ||||||||
\(553\) | −2.63330 | −0.111979 | ||||||||
\(554\) | 50.0210 | 2.12519 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.96041 | −0.422416 | ||||||||
\(557\) | 8.24799 | 0.349478 | 0.174739 | − | 0.984615i | \(-0.444092\pi\) | ||||
0.174739 | + | 0.984615i | \(0.444092\pi\) | |||||||
\(558\) | −2.50787 | −0.106167 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.1397 | −0.639200 | ||||||||
\(562\) | 62.3047 | 2.62817 | ||||||||
\(563\) | 25.8273 | 1.08849 | 0.544246 | − | 0.838925i | \(-0.316816\pi\) | ||||
0.544246 | + | 0.838925i | \(0.316816\pi\) | |||||||
\(564\) | −13.8627 | −0.583724 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 44.6123 | 1.87519 | ||||||||
\(567\) | −0.784934 | −0.0329641 | ||||||||
\(568\) | 9.90652 | 0.415668 | ||||||||
\(569\) | −12.1860 | −0.510863 | −0.255432 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255432 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2308 | 0.511843 | 0.255922 | − | 0.966698i | \(-0.417621\pi\) | ||||
0.255922 | + | 0.966698i | \(0.417621\pi\) | |||||||
\(572\) | −42.0315 | −1.75742 | ||||||||
\(573\) | −13.6743 | −0.571251 | ||||||||
\(574\) | 14.7139 | 0.614145 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.7229 | −0.488456 | ||||||||
\(577\) | −21.9537 | −0.913946 | −0.456973 | − | 0.889480i | \(-0.651066\pi\) | ||||
−0.456973 | + | 0.889480i | \(0.651066\pi\) | |||||||
\(578\) | −22.5618 | −0.938446 | ||||||||
\(579\) | 24.5989 | 1.02230 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.87601 | 0.160804 | ||||||||
\(582\) | −20.3061 | −0.841717 | ||||||||
\(583\) | −18.9380 | −0.784332 | ||||||||
\(584\) | −31.4435 | −1.30114 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.6924 | 0.730867 | ||||||||
\(587\) | −22.5527 | −0.930849 | −0.465425 | − | 0.885088i | \(-0.654098\pi\) | ||||
−0.465425 | + | 0.885088i | \(0.654098\pi\) | |||||||
\(588\) | 22.8322 | 0.941583 | ||||||||
\(589\) | −1.06200 | −0.0437588 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.6147 | −1.05365 | ||||||||
\(592\) | 1.18456 | 0.0486849 | ||||||||
\(593\) | 28.3376 | 1.16369 | 0.581843 | − | 0.813301i | \(-0.302332\pi\) | ||||
0.581843 | + | 0.813301i | \(0.302332\pi\) | |||||||
\(594\) | 6.93800 | 0.284670 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.230809 | 0.00944639 | ||||||||
\(598\) | 35.7520 | 1.46201 | ||||||||
\(599\) | 2.27947 | 0.0931367 | 0.0465684 | − | 0.998915i | \(-0.485171\pi\) | ||||
0.0465684 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.56987 | −0.145618 | −0.0728090 | − | 0.997346i | \(-0.523196\pi\) | ||||
−0.0728090 | + | 0.997346i | \(0.523196\pi\) | |||||||
\(602\) | −7.41439 | −0.302188 | ||||||||
\(603\) | −8.93800 | −0.363984 | ||||||||
\(604\) | 80.8259 | 3.28876 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.72294 | −0.110612 | ||||||||
\(607\) | −27.6609 | −1.12272 | −0.561361 | − | 0.827571i | \(-0.689722\pi\) | ||||
−0.561361 | + | 0.827571i | \(0.689722\pi\) | |||||||
\(608\) | −3.57653 | −0.145048 | ||||||||
\(609\) | −3.92467 | −0.159036 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.5040 | −0.627226 | ||||||||
\(612\) | 18.4301 | 0.744994 | ||||||||
\(613\) | −5.50787 | −0.222461 | −0.111230 | − | 0.993795i | \(-0.535479\pi\) | ||||
−0.111230 | + | 0.993795i | \(0.535479\pi\) | |||||||
\(614\) | 49.1516 | 1.98360 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.58561 | 0.345924 | ||||||||
\(617\) | 19.4459 | 0.782861 | 0.391431 | − | 0.920208i | \(-0.371980\pi\) | ||||
0.391431 | + | 0.920208i | \(0.371980\pi\) | |||||||
\(618\) | 47.1201 | 1.89545 | ||||||||
\(619\) | 16.5369 | 0.664676 | 0.332338 | − | 0.943160i | \(-0.392163\pi\) | ||||
0.332338 | + | 0.943160i | \(0.392163\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.78493 | −0.151884 | ||||||||
\(622\) | −63.5040 | −2.54628 | ||||||||
\(623\) | −0.447309 | −0.0179211 | ||||||||
\(624\) | 6.55412 | 0.262375 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 57.2890 | 2.28973 | ||||||||
\(627\) | 2.93800 | 0.117333 | ||||||||
\(628\) | 50.9447 | 2.03291 | ||||||||
\(629\) | 3.72535 | 0.148539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.41439 | 0.135925 | 0.0679623 | − | 0.997688i | \(-0.478350\pi\) | ||||
0.0679623 | + | 0.997688i | \(0.478350\pi\) | |||||||
\(632\) | −12.4897 | −0.496814 | ||||||||
\(633\) | −5.35480 | −0.212834 | ||||||||
\(634\) | −55.0367 | −2.18579 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 23.0539 | 0.914146 | ||||||||
\(637\) | 25.5355 | 1.01175 | ||||||||
\(638\) | 34.6900 | 1.37339 | ||||||||
\(639\) | −2.66094 | −0.105265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.6123 | −1.20911 | −0.604556 | − | 0.796563i | \(-0.706649\pi\) | ||||
−0.604556 | + | 0.796563i | \(0.706649\pi\) | |||||||
\(642\) | 28.8827 | 1.13991 | ||||||||
\(643\) | −10.5369 | −0.415537 | −0.207768 | − | 0.978178i | \(-0.566620\pi\) | ||||
−0.207768 | + | 0.978178i | \(0.566620\pi\) | |||||||
\(644\) | −10.6256 | −0.418708 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.1688 | 0.478776 | ||||||||
\(647\) | −23.0935 | −0.907898 | −0.453949 | − | 0.891028i | \(-0.649985\pi\) | ||||
−0.453949 | + | 0.891028i | \(0.649985\pi\) | |||||||
\(648\) | −3.72294 | −0.146251 | ||||||||
\(649\) | −13.6939 | −0.537531 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.833597 | 0.0326712 | ||||||||
\(652\) | 71.4693 | 2.79895 | ||||||||
\(653\) | 0.833597 | 0.0326212 | 0.0163106 | − | 0.999867i | \(-0.494808\pi\) | ||||
0.0163106 | + | 0.999867i | \(0.494808\pi\) | |||||||
\(654\) | −5.70719 | −0.223169 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.0067 | 0.507825 | ||||||||
\(657\) | 8.44588 | 0.329505 | ||||||||
\(658\) | 7.18456 | 0.280083 | ||||||||
\(659\) | −37.1712 | −1.44799 | −0.723993 | − | 0.689808i | \(-0.757695\pi\) | ||||
−0.723993 | + | 0.689808i | \(0.757695\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.98667 | 0.388436 | 0.194218 | − | 0.980958i | \(-0.437783\pi\) | ||||
0.194218 | + | 0.980958i | \(0.437783\pi\) | |||||||
\(662\) | 56.2732 | 2.18712 | ||||||||
\(663\) | 20.6123 | 0.800515 | ||||||||
\(664\) | 18.3839 | 0.713433 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.70719 | −0.0661524 | ||||||||
\(667\) | −18.9247 | −0.732766 | ||||||||
\(668\) | 52.8788 | 2.04594 | ||||||||
\(669\) | 1.78493 | 0.0690095 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26.0777 | 1.00672 | ||||||||
\(672\) | 2.80734 | 0.108296 | ||||||||
\(673\) | 7.13974 | 0.275217 | 0.137608 | − | 0.990487i | \(-0.456058\pi\) | ||||
0.137608 | + | 0.990487i | \(0.456058\pi\) | |||||||
\(674\) | −15.1846 | −0.584887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.7296 | 0.412677 | ||||||||
\(677\) | 15.5856 | 0.599004 | 0.299502 | − | 0.954096i | \(-0.403180\pi\) | ||||
0.299502 | + | 0.954096i | \(0.403180\pi\) | |||||||
\(678\) | 48.8588 | 1.87641 | ||||||||
\(679\) | 6.74960 | 0.259026 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.96708 | 0.343619 | ||||||||
\(682\) | −7.36814 | −0.282140 | ||||||||
\(683\) | −3.49454 | −0.133715 | −0.0668574 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668574 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(684\) | −3.57653 | −0.136752 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.8083 | −0.947186 | ||||||||
\(687\) | −26.5660 | −1.01356 | ||||||||
\(688\) | −6.55412 | −0.249874 | ||||||||
\(689\) | 25.7835 | 0.982273 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.6280 | 1.43144 | 0.715719 | − | 0.698389i | \(-0.246099\pi\) | ||||
0.715719 | + | 0.698389i | \(0.246099\pi\) | |||||||
\(692\) | −81.3734 | −3.09335 | ||||||||
\(693\) | −2.30614 | −0.0876030 | ||||||||
\(694\) | 21.9075 | 0.831597 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.6147 | −0.705588 | ||||||||
\(697\) | 40.9051 | 1.54939 | ||||||||
\(698\) | 18.9289 | 0.716470 | ||||||||
\(699\) | 9.56987 | 0.361966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.92083 | −0.299165 | −0.149583 | − | 0.988749i | \(-0.547793\pi\) | ||||
−0.149583 | + | 0.988749i | \(0.547793\pi\) | |||||||
\(702\) | −9.44588 | −0.356512 | ||||||||
\(703\) | −0.722938 | −0.0272661 | ||||||||
\(704\) | −34.4420 | −1.29808 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.6753 | −1.98246 | ||||||||
\(707\) | 0.905083 | 0.0340392 | ||||||||
\(708\) | 16.6700 | 0.626498 | ||||||||
\(709\) | −28.0739 | −1.05434 | −0.527169 | − | 0.849761i | \(-0.676746\pi\) | ||||
−0.527169 | + | 0.849761i | \(0.676746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.35480 | 0.125815 | ||||||||
\(712\) | −2.12158 | −0.0795097 | ||||||||
\(713\) | 4.01959 | 0.150535 | ||||||||
\(714\) | −9.55172 | −0.357464 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 79.0658 | 2.95483 | ||||||||
\(717\) | −16.9051 | −0.631332 | ||||||||
\(718\) | 22.2003 | 0.828508 | ||||||||
\(719\) | 20.2017 | 0.753397 | 0.376699 | − | 0.926336i | \(-0.377059\pi\) | ||||
0.376699 | + | 0.926336i | \(0.377059\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6624 | −0.583297 | ||||||||
\(722\) | −2.36147 | −0.0878848 | ||||||||
\(723\) | 9.27706 | 0.345018 | ||||||||
\(724\) | 47.2027 | 1.75427 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.59228 | −0.207549 | ||||||||
\(727\) | 17.0644 | 0.632884 | 0.316442 | − | 0.948612i | \(-0.397512\pi\) | ||||
0.316442 | + | 0.948612i | \(0.397512\pi\) | |||||||
\(728\) | −11.6890 | −0.433225 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.6123 | −0.762373 | ||||||||
\(732\) | −31.7453 | −1.17334 | ||||||||
\(733\) | 46.3534 | 1.71210 | 0.856050 | − | 0.516892i | \(-0.172911\pi\) | ||||
0.856050 | + | 0.516892i | \(0.172911\pi\) | |||||||
\(734\) | 17.2904 | 0.638200 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.5369 | 0.498979 | ||||||||
\(737\) | −26.2599 | −0.967295 | ||||||||
\(738\) | −18.7453 | −0.690026 | ||||||||
\(739\) | 3.46305 | 0.127390 | 0.0636952 | − | 0.997969i | \(-0.479711\pi\) | ||||
0.0636952 | + | 0.997969i | \(0.479711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | −11.9481 | −0.438627 | ||||||||
\(743\) | 21.3972 | 0.784988 | 0.392494 | − | 0.919755i | \(-0.371612\pi\) | ||||
0.392494 | + | 0.919755i | \(0.371612\pi\) | |||||||
\(744\) | 3.95375 | 0.144951 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.3219 | 0.780650 | ||||||||
\(747\) | −4.93800 | −0.180672 | ||||||||
\(748\) | 54.1478 | 1.97984 | ||||||||
\(749\) | −9.60038 | −0.350790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.5198 | −1.40561 | −0.702803 | − | 0.711384i | \(-0.748069\pi\) | ||||
−0.702803 | + | 0.711384i | \(0.748069\pi\) | |||||||
\(752\) | 6.35096 | 0.231596 | ||||||||
\(753\) | −25.1531 | −0.916629 | ||||||||
\(754\) | −47.2294 | −1.71999 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.80734 | 0.102102 | ||||||||
\(757\) | −44.8760 | −1.63105 | −0.815523 | − | 0.578725i | \(-0.803551\pi\) | ||||
−0.815523 | + | 0.578725i | \(0.803551\pi\) | |||||||
\(758\) | −66.2270 | −2.40547 | ||||||||
\(759\) | −11.1201 | −0.403636 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.2427 | 1.85755 | 0.928773 | − | 0.370648i | \(-0.120864\pi\) | ||||
0.928773 | + | 0.370648i | \(0.120864\pi\) | |||||||
\(762\) | 31.9671 | 1.15805 | ||||||||
\(763\) | 1.89703 | 0.0686770 | ||||||||
\(764\) | 48.9065 | 1.76938 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −79.5264 | −2.87341 | ||||||||
\(767\) | 18.6438 | 0.673187 | ||||||||
\(768\) | 25.0357 | 0.903400 | ||||||||
\(769\) | −31.3061 | −1.12893 | −0.564464 | − | 0.825458i | \(-0.690917\pi\) | ||||
−0.564464 | + | 0.825458i | \(0.690917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.1821 | 0.762856 | ||||||||
\(772\) | −87.9790 | −3.16643 | ||||||||
\(773\) | 37.9695 | 1.36567 | 0.682834 | − | 0.730574i | \(-0.260747\pi\) | ||||
0.682834 | + | 0.730574i | \(0.260747\pi\) | |||||||
\(774\) | 9.44588 | 0.339525 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 32.0133 | 1.14921 | ||||||||
\(777\) | 0.567458 | 0.0203575 | ||||||||
\(778\) | −1.60135 | −0.0574113 | ||||||||
\(779\) | −7.93800 | −0.284408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.81785 | −0.279745 | ||||||||
\(782\) | −46.0582 | −1.64704 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | −10.4602 | −0.373578 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.6452 | −0.379702 | ||||||||
\(787\) | −29.5369 | −1.05288 | −0.526439 | − | 0.850213i | \(-0.676473\pi\) | ||||
−0.526439 | + | 0.850213i | \(0.676473\pi\) | |||||||
\(788\) | 91.6118 | 3.26354 | ||||||||
\(789\) | −3.78493 | −0.134747 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2403 | −0.577439 | ||||||||
\(792\) | −10.9380 | −0.388665 | ||||||||
\(793\) | −35.5040 | −1.26079 | ||||||||
\(794\) | 25.5369 | 0.906272 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.825497 | −0.0292590 | ||||||||
\(797\) | 12.7716 | 0.452393 | 0.226197 | − | 0.974082i | \(-0.427371\pi\) | ||||
0.226197 | + | 0.974082i | \(0.427371\pi\) | |||||||
\(798\) | 1.85360 | 0.0656166 | ||||||||
\(799\) | 19.9733 | 0.706606 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.569868 | 0.0201353 | ||||||||
\(802\) | 66.7348 | 2.35649 | ||||||||
\(803\) | 24.8140 | 0.875667 | ||||||||
\(804\) | 31.9671 | 1.12739 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0315 | 0.353344 | ||||||||
\(807\) | −16.3061 | −0.574003 | ||||||||
\(808\) | 4.29281 | 0.151020 | ||||||||
\(809\) | 5.56987 | 0.195826 | 0.0979131 | − | 0.995195i | \(-0.468783\pi\) | ||||
0.0979131 | + | 0.995195i | \(0.468783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.55028 | −0.0544377 | −0.0272189 | − | 0.999629i | \(-0.508665\pi\) | ||||
−0.0272189 | + | 0.999629i | \(0.508665\pi\) | |||||||
\(812\) | 14.0367 | 0.492592 | ||||||||
\(813\) | 2.66094 | 0.0933233 | ||||||||
\(814\) | −5.01574 | −0.175802 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.44347 | −0.295580 | ||||||||
\(817\) | 4.00000 | 0.139942 | ||||||||
\(818\) | −68.9184 | −2.40968 | ||||||||
\(819\) | 3.13974 | 0.109711 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −49.7968 | −1.73792 | −0.868961 | − | 0.494881i | \(-0.835212\pi\) | ||||
−0.868961 | + | 0.494881i | \(0.835212\pi\) | |||||||
\(822\) | 38.4750 | 1.34197 | ||||||||
\(823\) | −6.78493 | −0.236508 | −0.118254 | − | 0.992983i | \(-0.537730\pi\) | ||||
−0.118254 | + | 0.992983i | \(0.537730\pi\) | |||||||
\(824\) | −74.2866 | −2.58789 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.63951 | −0.300607 | ||||||||
\(827\) | 26.8918 | 0.935118 | 0.467559 | − | 0.883962i | \(-0.345134\pi\) | ||||
0.467559 | + | 0.883962i | \(0.345134\pi\) | |||||||
\(828\) | 13.5369 | 0.470441 | ||||||||
\(829\) | 33.4774 | 1.16272 | 0.581358 | − | 0.813648i | \(-0.302521\pi\) | ||||
0.581358 | + | 0.813648i | \(0.302521\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1821 | 0.734801 | ||||||||
\(832\) | 46.8918 | 1.62568 | ||||||||
\(833\) | −32.8966 | −1.13980 | ||||||||
\(834\) | −6.57653 | −0.227727 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.5079 | −0.363422 | ||||||||
\(837\) | −1.06200 | −0.0367080 | ||||||||
\(838\) | 63.2112 | 2.18360 | ||||||||
\(839\) | 26.1335 | 0.902228 | 0.451114 | − | 0.892466i | \(-0.351027\pi\) | ||||
0.451114 | + | 0.892466i | \(0.351027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | −69.6728 | −2.40108 | ||||||||
\(843\) | 26.3839 | 0.908709 | ||||||||
\(844\) | 19.1516 | 0.659226 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.15307 | −0.314689 | ||||||||
\(847\) | 1.85883 | 0.0638702 | ||||||||
\(848\) | −10.5618 | −0.362693 | ||||||||
\(849\) | 18.8918 | 0.648363 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.73627 | 0.0937982 | ||||||||
\(852\) | 9.51695 | 0.326045 | ||||||||
\(853\) | −4.77160 | −0.163376 | −0.0816882 | − | 0.996658i | \(-0.526031\pi\) | ||||
−0.0816882 | + | 0.996658i | \(0.526031\pi\) | |||||||
\(854\) | 16.4525 | 0.562994 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −45.5345 | −1.55634 | ||||||||
\(857\) | −26.9537 | −0.920722 | −0.460361 | − | 0.887732i | \(-0.652280\pi\) | ||||
−0.460361 | + | 0.887732i | \(0.652280\pi\) | |||||||
\(858\) | −27.7520 | −0.947438 | ||||||||
\(859\) | −41.7034 | −1.42290 | −0.711450 | − | 0.702737i | \(-0.751961\pi\) | ||||
−0.711450 | + | 0.702737i | \(0.751961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.23081 | 0.212345 | ||||||||
\(862\) | −6.86934 | −0.233971 | ||||||||
\(863\) | −33.1492 | −1.12841 | −0.564206 | − | 0.825634i | \(-0.690818\pi\) | ||||
−0.564206 | + | 0.825634i | \(0.690818\pi\) | |||||||
\(864\) | −3.57653 | −0.121676 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.1688 | −0.481476 | ||||||||
\(867\) | −9.55412 | −0.324475 | ||||||||
\(868\) | −2.98139 | −0.101195 | ||||||||
\(869\) | 9.85642 | 0.334356 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.7520 | 1.21141 | ||||||||
\(872\) | 8.99759 | 0.304697 | ||||||||
\(873\) | −8.59894 | −0.291030 | ||||||||
\(874\) | 8.93800 | 0.302332 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.2070 | −1.02060 | ||||||||
\(877\) | −31.0739 | −1.04929 | −0.524645 | − | 0.851321i | \(-0.675802\pi\) | ||||
−0.524645 | + | 0.851321i | \(0.675802\pi\) | |||||||
\(878\) | −78.9036 | −2.66287 | ||||||||
\(879\) | 7.49213 | 0.252703 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.44588 | −0.183476 | −0.0917381 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917381 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(882\) | 15.0753 | 0.507613 | ||||||||
\(883\) | −23.1492 | −0.779033 | −0.389517 | − | 0.921019i | \(-0.627358\pi\) | ||||
−0.389517 | + | 0.921019i | \(0.627358\pi\) | |||||||
\(884\) | −73.7205 | −2.47949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 55.6876 | 1.87086 | ||||||||
\(887\) | −44.3643 | −1.48961 | −0.744804 | − | 0.667284i | \(-0.767457\pi\) | ||||
−0.744804 | + | 0.667284i | \(0.767457\pi\) | |||||||
\(888\) | 2.69145 | 0.0903192 | ||||||||
\(889\) | −10.6256 | −0.356372 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.93800 | 0.0984268 | ||||||||
\(892\) | −6.38388 | −0.213748 | ||||||||
\(893\) | −3.87601 | −0.129706 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.1149 | −0.538362 | ||||||||
\(897\) | 15.1397 | 0.505501 | ||||||||
\(898\) | 16.2375 | 0.541852 | ||||||||
\(899\) | −5.30998 | −0.177098 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.2160 | −1.10659 | ||||||||
\(902\) | −55.0739 | −1.83376 | ||||||||
\(903\) | −3.13974 | −0.104484 | ||||||||
\(904\) | −77.0276 | −2.56190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 53.3667 | 1.77299 | ||||||||
\(907\) | 0.319472 | 0.0106079 | 0.00530395 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530395 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(908\) | −32.0711 | −1.06432 | ||||||||
\(909\) | −1.15307 | −0.0382449 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0487 | 0.465453 | 0.232726 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232726 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(912\) | 1.63853 | 0.0542572 | ||||||||
\(913\) | −14.5079 | −0.480140 | ||||||||
\(914\) | 78.5422 | 2.59794 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 95.0143 | 3.13936 | ||||||||
\(917\) | 3.53838 | 0.116848 | ||||||||
\(918\) | 12.1688 | 0.401631 | ||||||||
\(919\) | −25.8007 | −0.851086 | −0.425543 | − | 0.904938i | \(-0.639917\pi\) | ||||
−0.425543 | + | 0.904938i | \(0.639917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8140 | 0.685845 | ||||||||
\(922\) | −38.4750 | −1.26711 | ||||||||
\(923\) | 10.6438 | 0.350344 | ||||||||
\(924\) | 8.24799 | 0.271339 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −78.9814 | −2.59549 | ||||||||
\(927\) | 19.9537 | 0.655367 | ||||||||
\(928\) | −17.8827 | −0.587028 | ||||||||
\(929\) | −9.86267 | −0.323584 | −0.161792 | − | 0.986825i | \(-0.551727\pi\) | ||||
−0.161792 | + | 0.986825i | \(0.551727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.38388 | 0.209223 | ||||||||
\(932\) | −34.2270 | −1.12114 | ||||||||
\(933\) | −26.8918 | −0.880396 | ||||||||
\(934\) | −48.4602 | −1.58567 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.8918 | 0.486752 | ||||||||
\(937\) | 30.4921 | 0.996134 | 0.498067 | − | 0.867138i | \(-0.334043\pi\) | ||||
0.498067 | + | 0.867138i | \(0.334043\pi\) | |||||||
\(938\) | −16.5675 | −0.540947 | ||||||||
\(939\) | 24.2599 | 0.791691 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.20173 | 0.0717744 | 0.0358872 | − | 0.999356i | \(-0.488574\pi\) | ||||
0.0358872 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(942\) | 33.6371 | 1.09596 | ||||||||
\(943\) | 30.0448 | 0.978394 | ||||||||
\(944\) | −7.63710 | −0.248566 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.7520 | 0.902296 | ||||||||
\(947\) | −11.7520 | −0.381889 | −0.190945 | − | 0.981601i | \(-0.561155\pi\) | ||||
−0.190945 | + | 0.981601i | \(0.561155\pi\) | |||||||
\(948\) | −11.9986 | −0.389695 | ||||||||
\(949\) | −33.7835 | −1.09666 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.3061 | −0.755753 | ||||||||
\(952\) | 15.0586 | 0.488052 | ||||||||
\(953\) | 21.7363 | 0.704107 | 0.352053 | − | 0.935980i | \(-0.385484\pi\) | ||||
0.352053 | + | 0.935980i | \(0.385484\pi\) | |||||||
\(954\) | 15.2217 | 0.492822 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 60.4616 | 1.95547 | ||||||||
\(957\) | 14.6900 | 0.474861 | ||||||||
\(958\) | 18.5212 | 0.598393 | ||||||||
\(959\) | −12.7888 | −0.412971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.8722 | −0.963618 | ||||||||
\(962\) | 6.82878 | 0.220169 | ||||||||
\(963\) | 12.2308 | 0.394132 | ||||||||
\(964\) | −33.1797 | −1.06865 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.01574 | −0.225728 | ||||||||
\(967\) | 15.2466 | 0.490296 | 0.245148 | − | 0.969486i | \(-0.421163\pi\) | ||||
0.245148 | + | 0.969486i | \(0.421163\pi\) | |||||||
\(968\) | 8.81642 | 0.283370 | ||||||||
\(969\) | 5.15307 | 0.165540 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.5951 | 1.23858 | 0.619288 | − | 0.785164i | \(-0.287421\pi\) | ||||
0.619288 | + | 0.785164i | \(0.287421\pi\) | |||||||
\(972\) | −3.57653 | −0.114717 | ||||||||
\(973\) | 2.18599 | 0.0700796 | ||||||||
\(974\) | −16.9232 | −0.542255 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.5436 | 0.465530 | ||||||||
\(977\) | −3.10825 | −0.0994417 | −0.0497209 | − | 0.998763i | \(-0.515833\pi\) | ||||
−0.0497209 | + | 0.998763i | \(0.515833\pi\) | |||||||
\(978\) | 47.1888 | 1.50893 | ||||||||
\(979\) | 1.67427 | 0.0535100 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.41680 | −0.0771624 | ||||||||
\(982\) | −38.4750 | −1.22779 | ||||||||
\(983\) | −14.4616 | −0.461254 | −0.230627 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230627 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(984\) | 29.5527 | 0.942105 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 60.8441 | 1.93767 | ||||||||
\(987\) | 3.04241 | 0.0968410 | ||||||||
\(988\) | 14.3061 | 0.455139 | ||||||||
\(989\) | −15.1397 | −0.481416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8298 | −0.756977 | −0.378489 | − | 0.925606i | \(-0.623556\pi\) | ||||
−0.378489 | + | 0.925606i | \(0.623556\pi\) | |||||||
\(992\) | 3.79827 | 0.120595 | ||||||||
\(993\) | 23.8298 | 0.756214 | ||||||||
\(994\) | −4.93231 | −0.156443 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.6609 | 0.559608 | ||||||||
\(997\) | 1.79827 | 0.0569517 | 0.0284758 | − | 0.999594i | \(-0.490935\pi\) | ||||
0.0284758 | + | 0.999594i | \(0.490935\pi\) | |||||||
\(998\) | −95.1411 | −3.01164 | ||||||||
\(999\) | −0.722938 | −0.0228727 |
(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 | 1425.2.a.t.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 4275.2.a.bf.1.3 | 3 | |||
5.2 | odd | 4 | 1425.2.c.o.799.2 | 6 | |||
5.3 | odd | 4 | 1425.2.c.o.799.5 | 6 | |||
5.4 | even | 2 | 1425.2.a.w.1.3 | yes | 3 | ||
15.14 | odd | 2 | 4275.2.a.bg.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1425.2.a.t.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1425.2.a.w.1.3 | yes | 3 | 5.4 | even | 2 | ||
1425.2.c.o.799.2 | 6 | 5.2 | odd | 4 | |||
1425.2.c.o.799.5 | 6 | 5.3 | odd | 4 | |||
4275.2.a.bf.1.3 | 3 | 3.2 | odd | 2 | |||
4275.2.a.bg.1.1 | 3 | 15.14 | odd | 2 |