Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8044,2,Mod(1,8044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8044 = 2^{2} \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8044.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: | \(64.2316633859\) |
Analytic rank: | \(1\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8044.1 |
$q$-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 | ||||||||
\(3\) | −2.41417 | −1.39382 | −0.696910 | − | 0.717159i | \(-0.745442\pi\) | ||||
−0.696910 | + | 0.717159i | \(0.745442\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.367373 | −0.164294 | −0.0821470 | − | 0.996620i | \(-0.526178\pi\) | ||||
−0.0821470 | + | 0.996620i | \(0.526178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85158 | 1.07780 | 0.538899 | − | 0.842371i | \(-0.318841\pi\) | ||||
0.538899 | + | 0.842371i | \(0.318841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82820 | 0.942733 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.63133 | 1.09489 | 0.547443 | − | 0.836843i | \(-0.315601\pi\) | ||||
0.547443 | + | 0.836843i | \(0.315601\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.28112 | 1.18737 | 0.593684 | − | 0.804698i | \(-0.297673\pi\) | ||||
0.593684 | + | 0.804698i | \(0.297673\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.886899 | 0.228996 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.777112 | −0.188477 | −0.0942387 | − | 0.995550i | \(-0.530042\pi\) | ||||
−0.0942387 | + | 0.995550i | \(0.530042\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65314 | 0.838088 | 0.419044 | − | 0.907966i | \(-0.362365\pi\) | ||||
0.419044 | + | 0.907966i | \(0.362365\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.88420 | −1.50225 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.929268 | 0.193766 | 0.0968829 | − | 0.995296i | \(-0.469113\pi\) | ||||
0.0968829 | + | 0.995296i | \(0.469113\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86504 | −0.973007 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414759 | 0.0798204 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.53312 | −1.77026 | −0.885128 | − | 0.465348i | \(-0.845929\pi\) | ||||
−0.885128 | + | 0.465348i | \(0.845929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.17630 | −0.929691 | −0.464845 | − | 0.885392i | \(-0.653890\pi\) | ||||
−0.464845 | + | 0.885392i | \(0.653890\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.76663 | −1.52607 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.04759 | −0.177076 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.24185 | −0.697355 | −0.348678 | − | 0.937243i | \(-0.613369\pi\) | ||||
−0.348678 | + | 0.937243i | \(0.613369\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.3353 | −1.65498 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.10567 | 0.485024 | 0.242512 | − | 0.970148i | \(-0.422029\pi\) | ||||
0.242512 | + | 0.970148i | \(0.422029\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.09145 | 0.623941 | 0.311970 | − | 0.950092i | \(-0.399011\pi\) | ||||
0.311970 | + | 0.950092i | \(0.399011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.03900 | −0.154885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.6131 | −1.69394 | −0.846970 | − | 0.531641i | \(-0.821575\pi\) | ||||
−0.846970 | + | 0.531641i | \(0.821575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.13153 | 0.161647 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.87608 | 0.262704 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.14880 | −1.25668 | −0.628342 | − | 0.777937i | \(-0.716266\pi\) | ||||
−0.628342 | + | 0.777937i | \(0.716266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.33405 | −0.179883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.81929 | −1.16814 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.67604 | −1.25971 | −0.629857 | − | 0.776711i | \(-0.716886\pi\) | ||||
−0.629857 | + | 0.776711i | \(0.716886\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5770 | −1.35425 | −0.677125 | − | 0.735868i | \(-0.736774\pi\) | ||||
−0.677125 | + | 0.735868i | \(0.736774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.06484 | 1.01607 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.57277 | −0.195078 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.44331 | −0.665006 | −0.332503 | − | 0.943102i | \(-0.607893\pi\) | ||||
−0.332503 | + | 0.943102i | \(0.607893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.24341 | −0.270075 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.68267 | 0.318375 | 0.159187 | − | 0.987248i | \(-0.449113\pi\) | ||||
0.159187 | + | 0.987248i | \(0.449113\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0473 | 1.29299 | 0.646496 | − | 0.762917i | \(-0.276234\pi\) | ||||
0.646496 | + | 0.762917i | \(0.276234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.7450 | 1.35620 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3550 | 1.18007 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.12019 | 0.688575 | 0.344287 | − | 0.938864i | \(-0.388121\pi\) | ||||
0.344287 | + | 0.938864i | \(0.388121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48589 | −1.05399 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8266 | −1.73720 | −0.868598 | − | 0.495518i | \(-0.834978\pi\) | ||||
−0.868598 | + | 0.495518i | \(0.834978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.285490 | 0.0309657 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.0145 | 2.46742 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.77794 | 1.03646 | 0.518230 | − | 0.855241i | \(-0.326591\pi\) | ||||
0.518230 | + | 0.855241i | \(0.326591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2080 | 1.27974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4964 | 1.29582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.34206 | −0.137693 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.42721 | −0.144911 | −0.0724555 | − | 0.997372i | \(-0.523084\pi\) | ||||
−0.0724555 | + | 0.997372i | \(0.523084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.2701 | 1.03219 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.34347 | 0.631199 | 0.315599 | − | 0.948893i | \(-0.397794\pi\) | ||||
0.315599 | + | 0.948893i | \(0.397794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00942 | −0.296527 | −0.148264 | − | 0.988948i | \(-0.547368\pi\) | ||||
−0.148264 | + | 0.988948i | \(0.547368\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.52907 | 0.246812 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.51267 | 0.339582 | 0.169791 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169791 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.24429 | 0.885442 | 0.442721 | − | 0.896659i | \(-0.354013\pi\) | ||||
0.442721 | + | 0.896659i | \(0.354013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2405 | 0.971987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.547548 | −0.0515090 | −0.0257545 | − | 0.999668i | \(-0.508199\pi\) | ||||
−0.0257545 | + | 0.999668i | \(0.508199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.341388 | −0.0318346 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1079 | 1.11937 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.21600 | −0.203140 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.18655 | 0.198777 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.49760 | −0.676036 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.62415 | 0.324153 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.6989 | −1.83673 | −0.918367 | − | 0.395730i | \(-0.870492\pi\) | ||||
−0.918367 | + | 0.395730i | \(0.870492\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.87745 | −0.869661 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.0504 | −1.14022 | −0.570109 | − | 0.821569i | \(-0.693099\pi\) | ||||
−0.570109 | + | 0.821569i | \(0.693099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.4172 | 0.903289 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.152371 | −0.0131140 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9610 | −1.44908 | −0.724539 | − | 0.689234i | \(-0.757947\pi\) | ||||
−0.724539 | + | 0.689234i | \(0.757947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6667 | −1.49847 | −0.749236 | − | 0.662303i | \(-0.769579\pi\) | ||||
−0.749236 | + | 0.662303i | \(0.769579\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.0359 | 2.36105 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5462 | 1.30003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.50221 | 0.290842 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.73170 | −0.225307 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.8664 | −1.29983 | −0.649914 | − | 0.760007i | \(-0.725195\pi\) | ||||
−0.649914 | + | 0.760007i | \(0.725195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29820 | −0.187025 | −0.0935123 | − | 0.995618i | \(-0.529809\pi\) | ||||
−0.0935123 | + | 0.995618i | \(0.529809\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.19783 | −0.177684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.90163 | 0.152743 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.69403 | −0.374624 | −0.187312 | − | 0.982300i | \(-0.559978\pi\) | ||||
−0.187312 | + | 0.982300i | \(0.559978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.0867 | 1.75159 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.64989 | 0.208840 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.2952 | 1.90295 | 0.951473 | − | 0.307731i | \(-0.0995697\pi\) | ||||
0.951473 | + | 0.307731i | \(0.0995697\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.22062 | 0.250725 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.62550 | 0.125785 | 0.0628926 | − | 0.998020i | \(-0.479967\pi\) | ||||
0.0628926 | + | 0.998020i | \(0.479967\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.32798 | 0.409844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3318 | 0.790093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0184491 | 0.00140266 | 0.000701330 | − | 1.00000i | \(-0.499777\pi\) | ||||
0.000701330 | 1.00000i | \(0.499777\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8731 | −1.04870 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.3596 | 1.75581 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.99441 | 0.373300 | 0.186650 | − | 0.982426i | \(-0.440237\pi\) | ||||
0.186650 | + | 0.982426i | \(0.440237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6284 | 1.68195 | 0.840977 | − | 0.541071i | \(-0.181981\pi\) | ||||
0.840977 | + | 0.541071i | \(0.181981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.5347 | 1.88758 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.55834 | 0.114571 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.82195 | −0.206361 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.18272 | 0.0860302 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.09224 | 0.657891 | 0.328946 | − | 0.944349i | \(-0.393307\pi\) | ||||
0.328946 | + | 0.944349i | \(0.393307\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.77854 | −0.343967 | −0.171984 | − | 0.985100i | \(-0.555018\pi\) | ||||
−0.171984 | + | 0.985100i | \(0.555018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.79692 | 0.271903 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.32913 | 0.664673 | 0.332337 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332337 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.2474 | 1.57708 | 0.788540 | − | 0.614984i | \(-0.210837\pi\) | ||||
0.788540 | + | 0.614984i | \(0.210837\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1411 | 0.926898 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −27.1845 | −1.90798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.14094 | −0.0796866 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.62815 | 0.182669 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2658 | 0.917611 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.2416 | −1.66886 | −0.834430 | − | 0.551114i | \(-0.814203\pi\) | ||||
−0.834430 | + | 0.551114i | \(0.814203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.47642 | −0.443757 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.50309 | −0.102510 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7607 | −1.00202 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.6701 | −1.80220 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.32691 | −0.223792 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.7858 | −1.65978 | −0.829890 | − | 0.557927i | \(-0.811597\pi\) | ||||
−0.829890 | + | 0.557927i | \(0.811597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.7593 | −0.917286 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.82621 | −0.386699 | −0.193350 | − | 0.981130i | \(-0.561935\pi\) | ||||
−0.193350 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.3234 | 1.60733 | 0.803666 | − | 0.595080i | \(-0.202880\pi\) | ||||
0.803666 | + | 0.595080i | \(0.202880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.9988 | −1.64480 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.4156 | −0.878883 | −0.439442 | − | 0.898271i | \(-0.644824\pi\) | ||||
−0.439442 | + | 0.898271i | \(0.644824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.26632 | 0.278304 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7752 | −0.959749 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2470 | −0.727507 | −0.363754 | − | 0.931495i | \(-0.618505\pi\) | ||||
−0.363754 | + | 0.931495i | \(0.618505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.55764 | 0.164752 | 0.0823760 | − | 0.996601i | \(-0.473749\pi\) | ||||
0.0823760 | + | 0.996601i | \(0.473749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.6562 | 1.38925 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.415693 | −0.0265576 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.6395 | 0.995119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 38.2080 | 2.42134 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.4374 | −1.54248 | −0.771238 | − | 0.636547i | \(-0.780362\pi\) | ||||
−0.771238 | + | 0.636547i | \(0.780362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.37448 | 0.212152 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.689220 | −0.0431606 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.49352 | −0.342677 | −0.171338 | − | 0.985212i | \(-0.554809\pi\) | ||||
−0.171338 | + | 0.985212i | \(0.554809\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0960 | −0.751607 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.9615 | −1.66888 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0407 | 1.60574 | 0.802868 | − | 0.596157i | \(-0.203306\pi\) | ||||
0.802868 | + | 0.596157i | \(0.203306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.36102 | 0.206466 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.6056 | −1.44464 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0104 | 1.46394 | 0.731969 | − | 0.681338i | \(-0.238601\pi\) | ||||
0.731969 | + | 0.681338i | \(0.238601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.4310 | −1.78780 | −0.893902 | − | 0.448262i | \(-0.852043\pi\) | ||||
−0.893902 | + | 0.448262i | \(0.852043\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −29.4721 | −1.78373 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.6666 | −1.06533 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.76518 | −0.166143 | −0.0830716 | − | 0.996544i | \(-0.526473\pi\) | ||||
−0.0830716 | + | 0.996544i | \(0.526473\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.6396 | −0.876450 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.9931 | −1.19269 | −0.596343 | − | 0.802730i | \(-0.703380\pi\) | ||||
−0.596343 | + | 0.802730i | \(0.703380\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1579 | 1.43604 | 0.718018 | − | 0.696024i | \(-0.245049\pi\) | ||||
0.718018 | + | 0.696024i | \(0.245049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.23997 | 0.191919 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.85607 | 0.522758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3961 | −0.964476 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.44552 | 0.201980 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.03723 | −0.177437 | −0.0887185 | − | 0.996057i | \(-0.528277\pi\) | ||||
−0.0887185 | + | 0.996057i | \(0.528277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.55471 | 0.206963 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.50613 | 0.0873943 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.97831 | 0.230072 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6671 | 0.672482 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.3142 | −0.879777 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.88571 | 0.222495 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.60560 | 0.262856 | 0.131428 | − | 0.991326i | \(-0.458044\pi\) | ||||
0.131428 | + | 0.991326i | \(0.458044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.26524 | 0.413305 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.97411 | 0.338761 | 0.169380 | − | 0.985551i | \(-0.445823\pi\) | ||||
0.169380 | + | 0.985551i | \(0.445823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6450 | −0.714736 | −0.357368 | − | 0.933964i | \(-0.616326\pi\) | ||||
−0.357368 | + | 0.933964i | \(0.616326\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.96280 | −0.166935 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3654 | 0.919174 | 0.459587 | − | 0.888133i | \(-0.347997\pi\) | ||||
0.459587 | + | 0.888133i | \(0.347997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.6179 | −1.93823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.48016 | −0.473317 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.83890 | −0.157961 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.8278 | −1.15532 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.3173 | −1.23415 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.1156 | −1.82572 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7402 | 0.810194 | 0.405097 | − | 0.914274i | \(-0.367238\pi\) | ||||
0.405097 | + | 0.914274i | \(0.367238\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.9968 | −0.657419 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.99972 | 0.109257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.2279 | 1.26530 | 0.632652 | − | 0.774436i | \(-0.281966\pi\) | ||||
0.632652 | + | 0.774436i | \(0.281966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.32187 | 0.0717942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.7968 | −1.01791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.7344 | −0.903575 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.824167 | 0.0443717 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.4020 | −1.20260 | −0.601301 | − | 0.799022i | \(-0.705351\pi\) | ||||
−0.601301 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.940983 | 0.0503697 | 0.0251848 | − | 0.999683i | \(-0.491983\pi\) | ||||
0.0251848 | + | 0.999683i | \(0.491983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.77563 | 0.0947763 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.07233 | 0.376422 | 0.188211 | − | 0.982129i | \(-0.439731\pi\) | ||||
0.188211 | + | 0.982129i | \(0.439731\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.985541 | −0.0523071 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.34979 | 0.283141 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.7926 | 0.833502 | 0.416751 | − | 0.909021i | \(-0.363169\pi\) | ||||
0.416751 | + | 0.909021i | \(0.363169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.65457 | −0.297609 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.27870 | −0.277060 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.05849 | −0.212431 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.5186 | −1.54086 | −0.770430 | − | 0.637525i | \(-0.779958\pi\) | ||||
−0.770430 | + | 0.637525i | \(0.779958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.78345 | 0.457248 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.0886 | −1.35445 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.15659 | −0.111664 | −0.0558321 | − | 0.998440i | \(-0.517781\pi\) | ||||
−0.0558321 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.74929 | −0.451811 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.8124 | −2.10195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.56186 | −0.234327 | −0.117164 | − | 0.993113i | \(-0.537380\pi\) | ||||
−0.117164 | + | 0.993113i | \(0.537380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.9707 | 2.56008 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.7538 | −1.21376 | −0.606880 | − | 0.794793i | \(-0.707579\pi\) | ||||
−0.606880 | + | 0.794793i | \(0.707579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.80416 | −0.193878 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.5714 | 0.588209 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.7427 | 1.45731 | 0.728657 | − | 0.684879i | \(-0.240145\pi\) | ||||
0.728657 | + | 0.684879i | \(0.240145\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.722146 | −0.0365205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.5058 | 1.58926 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.24839 | −0.113129 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.4648 | 1.88030 | 0.940152 | − | 0.340756i | \(-0.110683\pi\) | ||||
0.940152 | + | 0.340756i | \(0.110683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.1489 | −1.25902 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.8520 | 1.64055 | 0.820274 | − | 0.571970i | \(-0.193821\pi\) | ||||
0.820274 | + | 0.571970i | \(0.193821\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.1604 | −1.10389 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.48486 | 0.173164 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.4035 | −0.763525 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.16645 | 0.156571 | 0.0782854 | − | 0.996931i | \(-0.475055\pi\) | ||||
0.0782854 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.9467 | 2.01975 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.5920 | −1.35772 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.81426 | 0.285411 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.6504 | 2.08860 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.1456 | −1.13074 | −0.565368 | − | 0.824838i | \(-0.691266\pi\) | ||||
−0.565368 | + | 0.824838i | \(0.691266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2102 | 0.984987 | 0.492493 | − | 0.870316i | \(-0.336086\pi\) | ||||
0.492493 | + | 0.870316i | \(0.336086\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.8440 | −1.59693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.78068 | 0.183390 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.1613 | −1.45961 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −37.5310 | −1.81201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6640 | −1.38070 | −0.690348 | − | 0.723478i | \(-0.742543\pi\) | ||||
−0.690348 | + | 0.723478i | \(0.742543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.7452 | −0.852778 | −0.426389 | − | 0.904540i | \(-0.640215\pi\) | ||||
−0.426389 | + | 0.904540i | \(0.640215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.45491 | −0.405382 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.39475 | 0.162393 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5014 | −0.835295 | −0.417648 | − | 0.908609i | \(-0.637145\pi\) | ||||
−0.417648 | + | 0.908609i | \(0.637145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.20019 | 0.152390 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.7660 | −0.606533 | −0.303266 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303266 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.59215 | −0.170284 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 38.3042 | 1.81173 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.2187 | 0.576635 | 0.288317 | − | 0.957535i | \(-0.406904\pi\) | ||||
0.288317 | + | 0.957535i | \(0.406904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2777 | 0.531046 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.54823 | 0.260679 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.48487 | −0.210254 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.6417 | 0.778464 | 0.389232 | − | 0.921140i | \(-0.372740\pi\) | ||||
0.389232 | + | 0.921140i | \(0.372740\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.322314 | −0.0150444 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.4364 | −1.55729 | −0.778643 | − | 0.627467i | \(-0.784092\pi\) | ||||
−0.778643 | + | 0.627467i | \(0.784092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.3663 | −1.27182 | −0.635910 | − | 0.771763i | \(-0.719375\pi\) | ||||
−0.635910 | + | 0.771763i | \(0.719375\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.59085 | −0.212896 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.52445 | 0.394464 | 0.197232 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197232 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5221 | −0.716742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.3322 | 0.522158 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.8574 | 0.683144 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.7727 | −0.815466 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.8746 | −1.18472 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.34014 | 0.106924 | 0.0534618 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534618 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.1598 | −0.828018 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.39727 | −0.291086 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.524317 | 0.0238080 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1539 | 0.732005 | 0.366003 | − | 0.930614i | \(-0.380726\pi\) | ||||
0.366003 | + | 0.930614i | \(0.380726\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −58.6526 | −2.65236 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5042 | −0.609436 | −0.304718 | − | 0.952443i | \(-0.598562\pi\) | ||||
−0.304718 | + | 0.952443i | \(0.598562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.40830 | 0.333653 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.77296 | −0.169582 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.64986 | 0.343143 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.99308 | 0.133989 | 0.0669944 | − | 0.997753i | \(-0.478659\pi\) | ||||
0.0669944 | + | 0.997753i | \(0.478659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.92424 | −0.175322 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.8606 | 0.484250 | 0.242125 | − | 0.970245i | \(-0.422156\pi\) | ||||
0.242125 | + | 0.970245i | \(0.422156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.33042 | −0.103702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8626 | −0.571249 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.27449 | −0.189463 | −0.0947316 | − | 0.995503i | \(-0.530199\pi\) | ||||
−0.0947316 | + | 0.995503i | \(0.530199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5024 | 1.39358 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.51517 | 0.0668965 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.10558 | 0.0487176 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.1709 | −1.85467 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0445392 | −0.00195505 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.66847 | −0.379773 | −0.189886 | − | 0.981806i | \(-0.560812\pi\) | ||||
−0.189886 | + | 0.981806i | \(0.560812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.6824 | 1.51656 | 0.758279 | − | 0.651930i | \(-0.226041\pi\) | ||||
0.758279 | + | 0.651930i | \(0.226041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.4919 | 1.46171 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.02257 | 0.175226 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1365 | −0.962455 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.3658 | −1.18757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.2957 | 0.575902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.29046 | −0.0557914 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0573 | −0.520313 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.10895 | 0.176985 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2221 | 0.654448 | 0.327224 | − | 0.944947i | \(-0.393887\pi\) | ||||
0.327224 | + | 0.944947i | \(0.393887\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −54.6287 | −2.34434 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.39610 | −0.145473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.6742 | 0.499152 | 0.249576 | − | 0.968355i | \(-0.419709\pi\) | ||||
0.249576 | + | 0.968355i | \(0.419709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.9139 | −1.27670 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.8258 | −1.48363 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.4522 | 0.742144 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.76209 | −0.159692 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.6636 | −1.21452 | −0.607258 | − | 0.794505i | \(-0.707731\pi\) | ||||
−0.607258 | + | 0.794505i | \(0.707731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5160 | 0.740848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.81266 | 0.287631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.5163 | −1.32826 | −0.664128 | − | 0.747619i | \(-0.731197\pi\) | ||||
−0.664128 | + | 0.747619i | \(0.731197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.201154 | 0.00846262 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.0498 | −1.13599 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.96701 | −0.417839 | −0.208920 | − | 0.977933i | \(-0.566995\pi\) | ||||
−0.208920 | + | 0.977933i | \(0.566995\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.32818 | −0.139280 | −0.0696401 | − | 0.997572i | \(-0.522185\pi\) | ||||
−0.0696401 | + | 0.997572i | \(0.522185\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.9502 | −0.916982 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.52093 | −0.188536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9601 | 0.789318 | 0.394659 | − | 0.918828i | \(-0.370863\pi\) | ||||
0.394659 | + | 0.918828i | \(0.370863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.5362 | 0.479428 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.1309 | −1.87234 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.2223 | −1.37593 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.44809 | −0.183906 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.3196 | 1.82927 | 0.914633 | − | 0.404286i | \(-0.132480\pi\) | ||||
0.914633 | + | 0.404286i | \(0.132480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9097 | −0.779163 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.5221 | −0.926434 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.7045 | −0.685971 | −0.342986 | − | 0.939341i | \(-0.611438\pi\) | ||||
−0.342986 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.814098 | 0.0333748 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −53.7090 | −2.19816 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.51457 | 0.266178 | 0.133089 | − | 0.991104i | \(-0.457510\pi\) | ||||
0.133089 | + | 0.991104i | \(0.457510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.7093 | −1.61978 | −0.809888 | − | 0.586585i | \(-0.800472\pi\) | ||||
−0.809888 | + | 0.586585i | \(0.800472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.3948 | −0.626923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.803279 | −0.0326579 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.7313 | 1.65323 | 0.826616 | − | 0.562767i | \(-0.190263\pi\) | ||||
0.826616 | + | 0.562767i | \(0.190263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 65.6278 | 2.65937 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.7169 | −2.01133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7368 | 0.554824 | 0.277412 | − | 0.960751i | \(-0.410523\pi\) | ||||
0.277412 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.75441 | 0.111069 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.06795 | 0.284545 | 0.142273 | − | 0.989828i | \(-0.454559\pi\) | ||||
0.142273 | + | 0.989828i | \(0.454559\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.29328 | −0.252948 | −0.126474 | − | 0.991970i | \(-0.540366\pi\) | ||||
−0.126474 | + | 0.991970i | \(0.540366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.385423 | 0.0154665 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.8826 | 1.11709 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.9938 | 0.919751 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.0257 | −1.27898 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.29639 | 0.131436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.0056 | 1.71202 | 0.856012 | − | 0.516956i | \(-0.172935\pi\) | ||||
0.856012 | + | 0.516956i | \(0.172935\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.5232 | 2.32609 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.60423 | 0.301765 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.84421 | 0.191934 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.58713 | 0.300142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1266 | −0.399977 | −0.199988 | − | 0.979798i | \(-0.564090\pi\) | ||||
−0.199988 | + | 0.979798i | \(0.564090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.2279 | 0.639964 | 0.319982 | − | 0.947424i | \(-0.396323\pi\) | ||||
0.319982 | + | 0.947424i | \(0.396323\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.62870 | 0.142880 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.6203 | −0.928611 | −0.464305 | − | 0.885675i | \(-0.653696\pi\) | ||||
−0.464305 | + | 0.885675i | \(0.653696\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.1369 | −1.37924 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.6347 | 1.39663 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2350 | −0.517925 | −0.258962 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258962 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.79436 | 0.187331 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.2440 | 1.21895 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.9188 | 1.74979 | 0.874894 | − | 0.484315i | \(-0.160931\pi\) | ||||
0.874894 | + | 0.484315i | \(0.160931\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.7701 | −1.23572 | −0.617858 | − | 0.786290i | \(-0.711999\pi\) | ||||
−0.617858 | + | 0.786290i | \(0.711999\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.03171 | 0.311926 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.82701 | −0.148405 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.85882 | −0.343015 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 59.8370 | 2.31343 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.4087 | −1.48275 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.43016 | −0.324959 | −0.162479 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162479 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.01782 | −0.0776659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.57365 | 0.291079 | 0.145540 | − | 0.989352i | \(-0.453508\pi\) | ||||
0.145540 | + | 0.989352i | \(0.453508\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.06980 | −0.156185 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0654 | 0.538989 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3196 | 1.23668 | 0.618338 | − | 0.785912i | \(-0.287806\pi\) | ||||
0.618338 | + | 0.785912i | \(0.287806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.23102 | 0.238075 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.7206 | −2.24033 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.1671 | −1.49215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.3266 | 0.963468 | 0.481734 | − | 0.876318i | \(-0.340007\pi\) | ||||
0.481734 | + | 0.876318i | \(0.340007\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.2861 | 1.11249 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.49028 | 0.246190 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.41345 | −0.0914161 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.3874 | 1.22500 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.65906 | −0.138201 | −0.0691003 | − | 0.997610i | \(-0.522013\pi\) | ||||
−0.0691003 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4961 | −0.584445 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2996 | −0.387906 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0889 | 0.680304 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.9484 | −0.636510 | −0.318255 | − | 0.948005i | \(-0.603097\pi\) | ||||
−0.318255 | + | 0.948005i | \(0.603097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.3091 | 0.649142 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.81017 | −0.180142 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.71123 | −0.213588 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.1521 | 1.01401 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.41889 | 0.0902094 | 0.0451047 | − | 0.998982i | \(-0.485638\pi\) | ||||
0.0451047 | + | 0.998982i | \(0.485638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.58161 | −0.319596 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.17456 | −0.229634 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46.3790 | 1.72247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.06509 | −0.113678 | −0.0568389 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568389 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8241 | −0.882373 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.17952 | −0.117599 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.06199 | −0.260841 | −0.130420 | − | 0.991459i | \(-0.541633\pi\) | ||||
−0.130420 | + | 0.991459i | \(0.541633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00355 | 0.0370165 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.7664 | −0.728106 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5968 | 1.01517 | 0.507583 | − | 0.861603i | \(-0.330539\pi\) | ||||
0.507583 | + | 0.861603i | \(0.330539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.7564 | −1.38702 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.9671 | −1.20945 | −0.604723 | − | 0.796436i | \(-0.706716\pi\) | ||||
−0.604723 | + | 0.796436i | \(0.706716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.82889 | 0.213554 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.7608 | −1.63771 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0167 | 0.366001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4940 | −1.51414 | −0.757069 | − | 0.653334i | \(-0.773370\pi\) | ||||
−0.757069 | + | 0.653334i | \(0.773370\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.9960 | 2.14993 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.844295 | 0.0307271 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.79135 | −0.246836 | −0.123418 | − | 0.992355i | \(-0.539386\pi\) | ||||
−0.123418 | + | 0.992355i | \(0.539386\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.14655 | −0.295701 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.1721 | −1.38374 | −0.691870 | − | 0.722023i | \(-0.743213\pi\) | ||||
−0.691870 | + | 0.722023i | \(0.743213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.3609 | 0.954327 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.807422 | 0.0291924 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.4243 | −1.49574 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.54758 | 0.344295 | 0.172147 | − | 0.985071i | \(-0.444930\pi\) | ||||
0.172147 | + | 0.985071i | \(0.444930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.2623 | 0.477629 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0303 | 0.468667 | 0.234333 | − | 0.972156i | \(-0.424709\pi\) | ||||
0.234333 | + | 0.972156i | \(0.424709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.1829 | 0.904596 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.2017 | 1.04761 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.3454 | 0.406493 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.74167 | 0.348584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.95395 | −0.141303 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.72446 | 0.0615485 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5859 | 0.377346 | 0.188673 | − | 0.982040i | \(-0.439581\pi\) | ||||
0.188673 | + | 0.982040i | \(0.439581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −62.8665 | −2.23811 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.56138 | −0.0555162 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.2815 | −1.60799 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.11406 | −0.287776 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.3773 | 0.969754 | 0.484877 | − | 0.874582i | \(-0.338864\pi\) | ||||
0.484877 | + | 0.874582i | \(0.338864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.02465 | 0.319269 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.6540 | 0.977104 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.1165 | 1.41568 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.973496 | −0.0343112 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −57.9650 | −2.04047 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.77858 | 0.308638 | 0.154319 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154319 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3590 | −1.62788 | −0.813942 | − | 0.580946i | \(-0.802683\pi\) | ||||
−0.813942 | + | 0.580946i | \(0.802683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.0513 | 2.49188 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.92539 | −0.312643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.9466 | 0.522917 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 34.5265 | 1.20646 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6208 | 0.580070 | 0.290035 | − | 0.957016i | \(-0.406333\pi\) | ||||
0.290035 | + | 0.957016i | \(0.406333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.7490 | 1.07184 | 0.535922 | − | 0.844268i | \(-0.319964\pi\) | ||||
0.535922 | + | 0.844268i | \(0.319964\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.6500 | 1.48488 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.8130 | −1.87126 | −0.935630 | − | 0.352982i | \(-0.885168\pi\) | ||||
−0.935630 | + | 0.352982i | \(0.885168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.9817 | −1.63174 | −0.815870 | − | 0.578235i | \(-0.803742\pi\) | ||||
−0.815870 | + | 0.578235i | \(0.803742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.67559 | 0.231574 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.879325 | −0.0304668 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.597166 | −0.0206658 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.14692 | −0.0742083 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.36976 | −0.0472894 | −0.0236447 | − | 0.999720i | \(-0.507527\pi\) | ||||
−0.0236447 | + | 0.999720i | \(0.507527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.8803 | 2.13380 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.2666 | 1.66239 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.95735 | −0.0673350 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.23513 | 0.214242 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −58.3211 | −2.00158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.94181 | −0.135124 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.8613 | 1.43330 | 0.716652 | − | 0.697431i | \(-0.245674\pi\) | ||||
0.716652 | + | 0.697431i | \(0.245674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.79562 | −0.129808 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5582 | 0.975529 | 0.487765 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487765 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.0371 | −1.26369 | −0.631845 | − | 0.775095i | \(-0.717702\pi\) | ||||
−0.631845 | + | 0.775095i | \(0.717702\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.3800 | −0.728630 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.2897 | −1.88208 | −0.941042 | − | 0.338290i | \(-0.890152\pi\) | ||||
−0.941042 | + | 0.338290i | \(0.890152\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.00677770 | −0.000230449 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.5829 | 1.34431 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.2244 | 0.753912 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.3035 | −0.789607 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.03643 | −0.136612 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.3346 | 0.349372 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.4835 | 0.759215 | 0.379607 | − | 0.925148i | \(-0.376059\pi\) | ||||
0.379607 | + | 0.925148i | \(0.376059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.33238 | 0.247315 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.0250 | −1.31479 | −0.657393 | − | 0.753548i | \(-0.728341\pi\) | ||||
−0.657393 | + | 0.753548i | \(0.728341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0904 | −0.844358 | −0.422179 | − | 0.906513i | \(-0.638735\pi\) | ||||
−0.422179 | + | 0.906513i | \(0.638735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.58167 | −0.288470 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.896277 | 0.0300940 | 0.0150470 | − | 0.999887i | \(-0.495210\pi\) | ||||
0.0150470 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.0248 | −1.97963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.4464 | −1.15400 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −42.4241 | −1.41967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.83481 | −0.0613310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.60430 | −0.320678 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.3463 | 1.64579 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.10964 | 0.236857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −28.1664 | −0.937318 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.31305 | −0.276335 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.5332 | 1.77754 | 0.888771 | − | 0.458352i | \(-0.151560\pi\) | ||||
0.888771 | + | 0.458352i | \(0.151560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.9406 | 0.595052 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8448 | −1.25385 | −0.626926 | − | 0.779079i | \(-0.715687\pi\) | ||||
−0.626926 | + | 0.779079i | \(0.715687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57.4716 | −1.90203 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.38075 | −0.310118 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.2143 | −1.22892 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.6564 | 0.978275 | 0.489138 | − | 0.872207i | \(-0.337312\pi\) | ||||
0.489138 | + | 0.872207i | \(0.337312\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1187 | −0.366373 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.4848 | 0.378028 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.6367 | 0.678532 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.51124 | −0.279546 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.56393 | 0.116929 | 0.0584644 | − | 0.998289i | \(-0.481380\pi\) | ||||
0.0584644 | + | 0.998289i | \(0.481380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.13363 | 0.135474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.4225 | −0.472171 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.03671 | 0.0339040 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9586 | 0.390672 | 0.195336 | − | 0.980736i | \(-0.437420\pi\) | ||||
0.195336 | + | 0.980736i | \(0.437420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.5271 | 0.996213 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.7537 | 0.546156 | 0.273078 | − | 0.961992i | \(-0.411958\pi\) | ||||
0.273078 | + | 0.961992i | \(0.411958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.88600 | 0.0939811 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.434499 | −0.0141343 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.1667 | −1.33774 | −0.668870 | − | 0.743380i | \(-0.733222\pi\) | ||||
−0.668870 | + | 0.743380i | \(0.733222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.2950 | 1.53526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.5089 | −1.28116 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.4059 | 0.790585 | 0.395292 | − | 0.918555i | \(-0.370643\pi\) | ||||
0.395292 | + | 0.918555i | \(0.370643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.34024 | −0.108088 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 83.5733 | 2.70154 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.3658 | −1.56181 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.20592 | −0.135675 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.93452 | 0.320135 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.75551 | 0.0565118 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.0370 | 1.89850 | 0.949251 | − | 0.314519i | \(-0.101843\pi\) | ||||
0.949251 | + | 0.314519i | \(0.101843\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.85358 | 0.220169 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.0766 | 1.63913 | 0.819563 | − | 0.572990i | \(-0.194216\pi\) | ||||
0.819563 | + | 0.572990i | \(0.194216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.3782 | −1.61505 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 50.2818 | 1.61031 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.27766 | −0.136854 | −0.0684272 | − | 0.997656i | \(-0.521798\pi\) | ||||
−0.0684272 | + | 0.997656i | \(0.521798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5069 | 1.13481 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.1447 | 0.834735 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.4130 | −1.57603 | −0.788014 | − | 0.615657i | \(-0.788891\pi\) | ||||
−0.788014 | + | 0.615657i | \(0.788891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.42727 | −0.109202 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 79.9466 | 2.54473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.80206 | 0.120898 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.37601 | −0.139009 | −0.0695043 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695043 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.5853 | −1.12926 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.17311 | −0.259105 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0002 | 0.633412 | 0.316706 | − | 0.948524i | \(-0.397423\pi\) | ||||
0.316706 | + | 0.948524i | \(0.397423\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.75934 | −0.0556632 |
(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 | 8044.2.a.a.1.15 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8044.2.a.a.1.15 | ✓ | 80 | 1.1 | even | 1 | trivial |