Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33095 | −1.64823 | −0.824114 | − | 0.566425i | \(-0.808326\pi\) | ||||
−0.824114 | + | 0.566425i | \(0.808326\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.43331 | 1.71665 | ||||||||
\(5\) | 2.03702 | 0.910981 | 0.455491 | − | 0.890241i | \(-0.349464\pi\) | ||||
0.455491 | + | 0.890241i | \(0.349464\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.28183 | 1.61838 | 0.809189 | − | 0.587548i | \(-0.199907\pi\) | ||||
0.809189 | + | 0.587548i | \(0.199907\pi\) | |||||||
\(8\) | −3.34096 | −1.18121 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.74817 | −1.50150 | ||||||||
\(11\) | 3.57655 | 1.07837 | 0.539186 | − | 0.842187i | \(-0.318732\pi\) | ||||
0.539186 | + | 0.842187i | \(0.318732\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.73812 | −1.59147 | −0.795734 | − | 0.605646i | \(-0.792915\pi\) | ||||
−0.795734 | + | 0.605646i | \(0.792915\pi\) | |||||||
\(14\) | −9.98070 | −2.66746 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.920976 | 0.230244 | ||||||||
\(17\) | −4.13707 | −1.00339 | −0.501693 | − | 0.865046i | \(-0.667289\pi\) | ||||
−0.501693 | + | 0.865046i | \(0.667289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.31788 | −1.90825 | −0.954126 | − | 0.299406i | \(-0.903212\pi\) | ||||
−0.954126 | + | 0.299406i | \(0.903212\pi\) | |||||||
\(20\) | 6.99370 | 1.56384 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.33675 | −1.77740 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.850567 | −0.170113 | ||||||||
\(26\) | 13.3752 | 2.62310 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.7008 | 2.77819 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.54582 | 0.816454 | 0.408227 | − | 0.912880i | \(-0.366147\pi\) | ||||
0.408227 | + | 0.912880i | \(0.366147\pi\) | |||||||
\(32\) | 4.53517 | 0.801712 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.64327 | 1.65381 | ||||||||
\(35\) | 8.72215 | 1.47431 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.15659 | −1.50533 | −0.752667 | − | 0.658401i | \(-0.771233\pi\) | ||||
−0.752667 | + | 0.658401i | \(0.771233\pi\) | |||||||
\(38\) | 19.3885 | 3.14523 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.80558 | −1.07606 | ||||||||
\(41\) | 3.77238 | 0.589146 | 0.294573 | − | 0.955629i | \(-0.404823\pi\) | ||||
0.294573 | + | 0.955629i | \(0.404823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.11401 | −0.627380 | −0.313690 | − | 0.949525i | \(-0.601565\pi\) | ||||
−0.313690 | + | 0.949525i | \(0.601565\pi\) | |||||||
\(44\) | 12.2794 | 1.85119 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.33095 | −0.343679 | ||||||||
\(47\) | −6.22762 | −0.908392 | −0.454196 | − | 0.890902i | \(-0.650073\pi\) | ||||
−0.454196 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3340 | 1.61915 | ||||||||
\(50\) | 1.98263 | 0.280386 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.7007 | −2.73200 | ||||||||
\(53\) | −1.32969 | −0.182647 | −0.0913237 | − | 0.995821i | \(-0.529110\pi\) | ||||
−0.0913237 | + | 0.995821i | \(0.529110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.28549 | 0.982376 | ||||||||
\(56\) | −14.3054 | −1.91164 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.33095 | −0.306068 | ||||||||
\(59\) | 12.0838 | 1.57318 | 0.786591 | − | 0.617475i | \(-0.211844\pi\) | ||||
0.786591 | + | 0.617475i | \(0.211844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.42239 | 0.566229 | 0.283115 | − | 0.959086i | \(-0.408632\pi\) | ||||
0.283115 | + | 0.959086i | \(0.408632\pi\) | |||||||
\(62\) | −10.5961 | −1.34570 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4132 | −1.55165 | ||||||||
\(65\) | −11.6886 | −1.44980 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.73198 | −0.700273 | −0.350136 | − | 0.936699i | \(-0.613865\pi\) | ||||
−0.350136 | + | 0.936699i | \(0.613865\pi\) | |||||||
\(68\) | −14.2038 | −1.72246 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20.3309 | −2.43000 | ||||||||
\(71\) | −9.12802 | −1.08330 | −0.541648 | − | 0.840605i | \(-0.682199\pi\) | ||||
−0.541648 | + | 0.840605i | \(0.682199\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8581 | −1.38788 | −0.693940 | − | 0.720033i | \(-0.744127\pi\) | ||||
−0.693940 | + | 0.720033i | \(0.744127\pi\) | |||||||
\(74\) | 21.3435 | 2.48113 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.5578 | −3.27581 | ||||||||
\(77\) | 15.3142 | 1.74521 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.03687 | 0.229166 | 0.114583 | − | 0.993414i | \(-0.463447\pi\) | ||||
0.114583 | + | 0.993414i | \(0.463447\pi\) | |||||||
\(80\) | 1.87604 | 0.209748 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.79321 | −0.971047 | ||||||||
\(83\) | −2.51017 | −0.275527 | −0.137764 | − | 0.990465i | \(-0.543991\pi\) | ||||
−0.137764 | + | 0.990465i | \(0.543991\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.42727 | −0.914065 | ||||||||
\(86\) | 9.58952 | 1.03406 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.9491 | −1.27378 | ||||||||
\(89\) | −10.0168 | −1.06178 | −0.530889 | − | 0.847441i | \(-0.678142\pi\) | ||||
−0.530889 | + | 0.847441i | \(0.678142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.5696 | −2.57560 | ||||||||
\(92\) | 3.43331 | 0.357947 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.5163 | 1.49724 | ||||||||
\(95\) | −16.9436 | −1.73838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.738955 | 0.0750295 | 0.0375147 | − | 0.999296i | \(-0.488056\pi\) | ||||
0.0375147 | + | 0.999296i | \(0.488056\pi\) | |||||||
\(98\) | −26.4190 | −2.66873 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.92026 | −0.292026 | ||||||||
\(101\) | −14.1605 | −1.40902 | −0.704509 | − | 0.709695i | \(-0.748833\pi\) | ||||
−0.704509 | + | 0.709695i | \(0.748833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3578 | −1.51325 | −0.756626 | − | 0.653848i | \(-0.773154\pi\) | ||||
−0.756626 | + | 0.653848i | \(0.773154\pi\) | |||||||
\(104\) | 19.1708 | 1.87985 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.09944 | 0.301044 | ||||||||
\(107\) | −13.1005 | −1.26647 | −0.633237 | − | 0.773958i | \(-0.718274\pi\) | ||||
−0.633237 | + | 0.773958i | \(0.718274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4120 | 1.66777 | 0.833883 | − | 0.551941i | \(-0.186113\pi\) | ||||
0.833883 | + | 0.551941i | \(0.186113\pi\) | |||||||
\(110\) | −16.9821 | −1.61918 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.94346 | 0.372622 | ||||||||
\(113\) | 13.9526 | 1.31255 | 0.656276 | − | 0.754521i | \(-0.272131\pi\) | ||||
0.656276 | + | 0.754521i | \(0.272131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.03702 | 0.189953 | ||||||||
\(116\) | 3.43331 | 0.318774 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −28.1668 | −2.59296 | ||||||||
\(119\) | −17.7142 | −1.62386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.79173 | 0.162884 | ||||||||
\(122\) | −10.3084 | −0.933275 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.6072 | 1.40157 | ||||||||
\(125\) | −11.9177 | −1.06595 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.48833 | 0.841953 | 0.420976 | − | 0.907072i | \(-0.361687\pi\) | ||||
0.420976 | + | 0.907072i | \(0.361687\pi\) | |||||||
\(128\) | 19.8641 | 1.75576 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27.2456 | 2.38959 | ||||||||
\(131\) | −8.07820 | −0.705795 | −0.352898 | − | 0.935662i | \(-0.614804\pi\) | ||||
−0.352898 | + | 0.935662i | \(0.614804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −35.6157 | −3.08827 | ||||||||
\(134\) | 13.3609 | 1.15421 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.8218 | 1.18521 | ||||||||
\(137\) | 14.5574 | 1.24372 | 0.621861 | − | 0.783128i | \(-0.286377\pi\) | ||||
0.621861 | + | 0.783128i | \(0.286377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1942 | −1.37358 | −0.686788 | − | 0.726858i | \(-0.740980\pi\) | ||||
−0.686788 | + | 0.726858i | \(0.740980\pi\) | |||||||
\(140\) | 29.9458 | 2.53088 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.2769 | 1.78552 | ||||||||
\(143\) | −20.5227 | −1.71619 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.03702 | 0.169165 | ||||||||
\(146\) | 27.6405 | 2.28754 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −31.4374 | −2.58414 | ||||||||
\(149\) | 8.75292 | 0.717067 | 0.358533 | − | 0.933517i | \(-0.383277\pi\) | ||||
0.358533 | + | 0.933517i | \(0.383277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0492 | 1.63158 | 0.815791 | − | 0.578347i | \(-0.196302\pi\) | ||||
0.815791 | + | 0.578347i | \(0.196302\pi\) | |||||||
\(152\) | 27.7897 | 2.25404 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −35.6965 | −2.87651 | ||||||||
\(155\) | 9.25991 | 0.743774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.08819 | −0.725316 | −0.362658 | − | 0.931922i | \(-0.618131\pi\) | ||||
−0.362658 | + | 0.931922i | \(0.618131\pi\) | |||||||
\(158\) | −4.74783 | −0.377717 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.23821 | 0.730345 | ||||||||
\(161\) | 4.28183 | 0.337455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1959 | −0.876933 | −0.438467 | − | 0.898747i | \(-0.644478\pi\) | ||||
−0.438467 | + | 0.898747i | \(0.644478\pi\) | |||||||
\(164\) | 12.9517 | 1.01136 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.85107 | 0.454131 | ||||||||
\(167\) | 11.7353 | 0.908102 | 0.454051 | − | 0.890976i | \(-0.349978\pi\) | ||||
0.454051 | + | 0.890976i | \(0.349978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.9260 | 1.53277 | ||||||||
\(170\) | 19.6435 | 1.50659 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.1246 | −1.07699 | ||||||||
\(173\) | 20.2443 | 1.53915 | 0.769573 | − | 0.638558i | \(-0.220469\pi\) | ||||
0.769573 | + | 0.638558i | \(0.220469\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.64198 | −0.275308 | ||||||||
\(176\) | 3.29392 | 0.248288 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23.3486 | 1.75005 | ||||||||
\(179\) | −8.16709 | −0.610437 | −0.305219 | − | 0.952282i | \(-0.598730\pi\) | ||||
−0.305219 | + | 0.952282i | \(0.598730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.1168 | 1.86692 | 0.933459 | − | 0.358684i | \(-0.116774\pi\) | ||||
0.933459 | + | 0.358684i | \(0.116774\pi\) | |||||||
\(182\) | 57.2705 | 4.24517 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.34096 | −0.246299 | ||||||||
\(185\) | −18.6521 | −1.37133 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7964 | −1.08202 | ||||||||
\(188\) | −21.3813 | −1.55939 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 39.4947 | 2.86525 | ||||||||
\(191\) | −24.6470 | −1.78340 | −0.891699 | − | 0.452629i | \(-0.850486\pi\) | ||||
−0.891699 | + | 0.452629i | \(0.850486\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.35264 | 0.0973648 | 0.0486824 | − | 0.998814i | \(-0.484498\pi\) | ||||
0.0486824 | + | 0.998814i | \(0.484498\pi\) | |||||||
\(194\) | −1.72246 | −0.123666 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38.9132 | 2.77952 | ||||||||
\(197\) | −6.03899 | −0.430260 | −0.215130 | − | 0.976585i | \(-0.569018\pi\) | ||||
−0.215130 | + | 0.976585i | \(0.569018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.5865 | −1.53023 | −0.765114 | − | 0.643895i | \(-0.777317\pi\) | ||||
−0.765114 | + | 0.643895i | \(0.777317\pi\) | |||||||
\(200\) | 2.84171 | 0.200939 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 33.0072 | 2.32238 | ||||||||
\(203\) | 4.28183 | 0.300525 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.68439 | 0.536701 | ||||||||
\(206\) | 35.7983 | 2.49418 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.28467 | −0.366426 | ||||||||
\(209\) | −29.7493 | −2.05780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2713 | −1.12016 | −0.560081 | − | 0.828438i | \(-0.689230\pi\) | ||||
−0.560081 | + | 0.828438i | \(0.689230\pi\) | |||||||
\(212\) | −4.56524 | −0.313542 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 30.5366 | 2.08744 | ||||||||
\(215\) | −8.38029 | −0.571531 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.4644 | 1.32133 | ||||||||
\(218\) | −40.5864 | −2.74886 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.0133 | 1.68640 | ||||||||
\(221\) | 23.7390 | 1.59686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7544 | −0.720165 | −0.360083 | − | 0.932920i | \(-0.617252\pi\) | ||||
−0.360083 | + | 0.932920i | \(0.617252\pi\) | |||||||
\(224\) | 19.4188 | 1.29747 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.5228 | −2.16338 | ||||||||
\(227\) | 8.21789 | 0.545441 | 0.272720 | − | 0.962093i | \(-0.412077\pi\) | ||||
0.272720 | + | 0.962093i | \(0.412077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.0859 | −1.85597 | −0.927984 | − | 0.372620i | \(-0.878460\pi\) | ||||
−0.927984 | + | 0.372620i | \(0.878460\pi\) | |||||||
\(230\) | −4.74817 | −0.313085 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.34096 | −0.219345 | ||||||||
\(233\) | 3.17124 | 0.207755 | 0.103878 | − | 0.994590i | \(-0.466875\pi\) | ||||
0.103878 | + | 0.994590i | \(0.466875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.6858 | −0.827528 | ||||||||
\(236\) | 41.4875 | 2.70061 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 41.2908 | 2.67649 | ||||||||
\(239\) | −17.8380 | −1.15384 | −0.576921 | − | 0.816800i | \(-0.695746\pi\) | ||||
−0.576921 | + | 0.816800i | \(0.695746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.9855 | −1.54504 | −0.772522 | − | 0.634988i | \(-0.781005\pi\) | ||||
−0.772522 | + | 0.634988i | \(0.781005\pi\) | |||||||
\(242\) | −4.17642 | −0.268470 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.1834 | 0.972019 | ||||||||
\(245\) | 23.0876 | 1.47501 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 47.7290 | 3.03692 | ||||||||
\(248\) | −15.1874 | −0.964401 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.7795 | 1.75693 | ||||||||
\(251\) | −10.0692 | −0.635564 | −0.317782 | − | 0.948164i | \(-0.602938\pi\) | ||||
−0.317782 | + | 0.948164i | \(0.602938\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.57655 | 0.224856 | ||||||||
\(254\) | −22.1168 | −1.38773 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.4758 | −1.34224 | ||||||||
\(257\) | −7.58949 | −0.473419 | −0.236710 | − | 0.971580i | \(-0.576069\pi\) | ||||
−0.236710 | + | 0.971580i | \(0.576069\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.2069 | −2.43620 | ||||||||
\(260\) | −40.1307 | −2.48880 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.8298 | 1.16331 | ||||||||
\(263\) | 12.8724 | 0.793746 | 0.396873 | − | 0.917874i | \(-0.370095\pi\) | ||||
0.396873 | + | 0.917874i | \(0.370095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.70861 | −0.166388 | ||||||||
\(266\) | 83.0183 | 5.09018 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −19.6796 | −1.20213 | ||||||||
\(269\) | −16.0869 | −0.980835 | −0.490417 | − | 0.871488i | \(-0.663156\pi\) | ||||
−0.490417 | + | 0.871488i | \(0.663156\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.79337 | −0.351922 | −0.175961 | − | 0.984397i | \(-0.556303\pi\) | ||||
−0.175961 | + | 0.984397i | \(0.556303\pi\) | |||||||
\(272\) | −3.81014 | −0.231023 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.9325 | −2.04993 | ||||||||
\(275\) | −3.04210 | −0.183445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.05254 | 0.243494 | 0.121747 | − | 0.992561i | \(-0.461150\pi\) | ||||
0.121747 | + | 0.992561i | \(0.461150\pi\) | |||||||
\(278\) | 37.7478 | 2.26396 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −29.1403 | −1.74147 | ||||||||
\(281\) | 30.6926 | 1.83096 | 0.915482 | − | 0.402359i | \(-0.131810\pi\) | ||||
0.915482 | + | 0.402359i | \(0.131810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6797 | 1.52650 | 0.763250 | − | 0.646103i | \(-0.223602\pi\) | ||||
0.763250 | + | 0.646103i | \(0.223602\pi\) | |||||||
\(284\) | −31.3393 | −1.85964 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 47.8372 | 2.82868 | ||||||||
\(287\) | 16.1527 | 0.953462 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.115308 | 0.00678284 | ||||||||
\(290\) | −4.74817 | −0.278822 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −40.7123 | −2.38251 | ||||||||
\(293\) | −16.9783 | −0.991886 | −0.495943 | − | 0.868355i | \(-0.665177\pi\) | ||||
−0.495943 | + | 0.868355i | \(0.665177\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.6150 | 1.43314 | ||||||||
\(296\) | 30.5918 | 1.77811 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.4026 | −1.18189 | ||||||||
\(299\) | −5.73812 | −0.331844 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.6155 | −1.01534 | ||||||||
\(302\) | −46.7336 | −2.68922 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.66056 | −0.439363 | ||||||||
\(305\) | 9.00848 | 0.515824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.04995 | 0.288216 | 0.144108 | − | 0.989562i | \(-0.453969\pi\) | ||||
0.144108 | + | 0.989562i | \(0.453969\pi\) | |||||||
\(308\) | 52.5783 | 2.99592 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.5843 | −1.22591 | ||||||||
\(311\) | 11.5885 | 0.657124 | 0.328562 | − | 0.944482i | \(-0.393436\pi\) | ||||
0.328562 | + | 0.944482i | \(0.393436\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4835 | −0.988226 | −0.494113 | − | 0.869398i | \(-0.664507\pi\) | ||||
−0.494113 | + | 0.869398i | \(0.664507\pi\) | |||||||
\(314\) | 21.1841 | 1.19549 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.99320 | 0.393398 | ||||||||
\(317\) | −17.8893 | −1.00476 | −0.502382 | − | 0.864646i | \(-0.667543\pi\) | ||||
−0.502382 | + | 0.864646i | \(0.667543\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.57655 | 0.200248 | ||||||||
\(320\) | −25.2858 | −1.41352 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.98070 | −0.556203 | ||||||||
\(323\) | 34.4116 | 1.91471 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.88066 | 0.270730 | ||||||||
\(326\) | 26.0971 | 1.44539 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.6034 | −0.695904 | ||||||||
\(329\) | −26.6656 | −1.47012 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.66032 | −0.256154 | −0.128077 | − | 0.991764i | \(-0.540880\pi\) | ||||
−0.128077 | + | 0.991764i | \(0.540880\pi\) | |||||||
\(332\) | −8.61819 | −0.472985 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −27.3543 | −1.49676 | ||||||||
\(335\) | −11.6761 | −0.637935 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.31254 | −0.398339 | −0.199170 | − | 0.979965i | \(-0.563824\pi\) | ||||
−0.199170 | + | 0.979965i | \(0.563824\pi\) | |||||||
\(338\) | −46.4464 | −2.52635 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −28.9334 | −1.56913 | ||||||||
\(341\) | 16.2584 | 0.880440 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5576 | 1.00202 | ||||||||
\(344\) | 13.7447 | 0.741065 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −47.1884 | −2.53686 | ||||||||
\(347\) | 27.3907 | 1.47041 | 0.735204 | − | 0.677846i | \(-0.237086\pi\) | ||||
0.735204 | + | 0.677846i | \(0.237086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2650 | 1.08476 | 0.542379 | − | 0.840134i | \(-0.317524\pi\) | ||||
0.542379 | + | 0.840134i | \(0.317524\pi\) | |||||||
\(350\) | 8.48926 | 0.453770 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2203 | 0.864543 | ||||||||
\(353\) | −9.51815 | −0.506600 | −0.253300 | − | 0.967388i | \(-0.581516\pi\) | ||||
−0.253300 | + | 0.967388i | \(0.581516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.5939 | −0.986863 | ||||||||
\(356\) | −34.3907 | −1.82271 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0370 | 1.00614 | ||||||||
\(359\) | −8.98273 | −0.474090 | −0.237045 | − | 0.971499i | \(-0.576179\pi\) | ||||
−0.237045 | + | 0.971499i | \(0.576179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.1871 | 2.64142 | ||||||||
\(362\) | −58.5459 | −3.07711 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −84.3550 | −4.42141 | ||||||||
\(365\) | −24.1550 | −1.26433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2777 | −1.31949 | −0.659744 | − | 0.751491i | \(-0.729335\pi\) | ||||
−0.659744 | + | 0.751491i | \(0.729335\pi\) | |||||||
\(368\) | 0.920976 | 0.0480092 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.4771 | 2.26027 | ||||||||
\(371\) | −5.69352 | −0.295593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.48700 | 0.128772 | 0.0643859 | − | 0.997925i | \(-0.479491\pi\) | ||||
0.0643859 | + | 0.997925i | \(0.479491\pi\) | |||||||
\(374\) | 34.4897 | 1.78342 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.8062 | 1.07300 | ||||||||
\(377\) | −5.73812 | −0.295528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.0311 | 1.64533 | 0.822664 | − | 0.568528i | \(-0.192487\pi\) | ||||
0.822664 | + | 0.568528i | \(0.192487\pi\) | |||||||
\(380\) | −58.1727 | −2.98420 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 57.4509 | 2.93944 | ||||||||
\(383\) | 0.611138 | 0.0312277 | 0.0156139 | − | 0.999878i | \(-0.495030\pi\) | ||||
0.0156139 | + | 0.999878i | \(0.495030\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.1952 | 1.58986 | ||||||||
\(386\) | −3.15292 | −0.160479 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.53706 | 0.128800 | ||||||||
\(389\) | −20.0636 | −1.01727 | −0.508633 | − | 0.860984i | \(-0.669849\pi\) | ||||
−0.508633 | + | 0.860984i | \(0.669849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.13707 | −0.209220 | ||||||||
\(392\) | −37.8665 | −1.91255 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.0765 | 0.709166 | ||||||||
\(395\) | 4.14914 | 0.208766 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.630252 | 0.0316314 | 0.0158157 | − | 0.999875i | \(-0.494965\pi\) | ||||
0.0158157 | + | 0.999875i | \(0.494965\pi\) | |||||||
\(398\) | 50.3170 | 2.52216 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.783352 | −0.0391676 | ||||||||
\(401\) | 23.2037 | 1.15874 | 0.579368 | − | 0.815066i | \(-0.303299\pi\) | ||||
0.579368 | + | 0.815066i | \(0.303299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.0845 | −1.29936 | ||||||||
\(404\) | −48.6172 | −2.41879 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.98070 | −0.495334 | ||||||||
\(407\) | −32.7490 | −1.62331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6159 | 0.673265 | 0.336632 | − | 0.941636i | \(-0.390712\pi\) | ||||
0.336632 | + | 0.941636i | \(0.390712\pi\) | |||||||
\(410\) | −17.9119 | −0.884606 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −52.7281 | −2.59773 | ||||||||
\(413\) | 51.7409 | 2.54600 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.11326 | −0.251000 | ||||||||
\(416\) | −26.0233 | −1.27590 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 69.3440 | 3.39173 | ||||||||
\(419\) | 29.5393 | 1.44309 | 0.721543 | − | 0.692369i | \(-0.243433\pi\) | ||||
0.721543 | + | 0.692369i | \(0.243433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1117 | 0.492816 | 0.246408 | − | 0.969166i | \(-0.420750\pi\) | ||||
0.246408 | + | 0.969166i | \(0.420750\pi\) | |||||||
\(422\) | 37.9275 | 1.84628 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.44245 | 0.215744 | ||||||||
\(425\) | 3.51885 | 0.170689 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.9359 | 0.916374 | ||||||||
\(428\) | −44.9780 | −2.17410 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.5340 | 0.942013 | ||||||||
\(431\) | 0.288442 | 0.0138937 | 0.00694687 | − | 0.999976i | \(-0.497789\pi\) | ||||
0.00694687 | + | 0.999976i | \(0.497789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.5475 | −0.602993 | −0.301496 | − | 0.953467i | \(-0.597486\pi\) | ||||
−0.301496 | + | 0.953467i | \(0.597486\pi\) | |||||||
\(434\) | −45.3705 | −2.17785 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 59.7807 | 2.86298 | ||||||||
\(437\) | −8.31788 | −0.397898 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.33735 | 0.254738 | 0.127369 | − | 0.991855i | \(-0.459347\pi\) | ||||
0.127369 | + | 0.991855i | \(0.459347\pi\) | |||||||
\(440\) | −24.3405 | −1.16039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −55.3342 | −2.63198 | ||||||||
\(443\) | −22.8067 | −1.08358 | −0.541790 | − | 0.840514i | \(-0.682253\pi\) | ||||
−0.541790 | + | 0.840514i | \(0.682253\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.4044 | −0.967260 | ||||||||
\(446\) | 25.0678 | 1.18700 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −53.1511 | −2.51115 | ||||||||
\(449\) | −23.8512 | −1.12561 | −0.562805 | − | 0.826590i | \(-0.690278\pi\) | ||||
−0.562805 | + | 0.826590i | \(0.690278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.4921 | 0.635319 | ||||||||
\(452\) | 47.9036 | 2.25320 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.1555 | −0.899010 | ||||||||
\(455\) | −50.0487 | −2.34632 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1886 | 1.03794 | 0.518969 | − | 0.854793i | \(-0.326316\pi\) | ||||
0.518969 | + | 0.854793i | \(0.326316\pi\) | |||||||
\(458\) | 65.4667 | 3.05906 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.99370 | 0.326083 | ||||||||
\(461\) | 18.8126 | 0.876192 | 0.438096 | − | 0.898928i | \(-0.355653\pi\) | ||||
0.438096 | + | 0.898928i | \(0.355653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.42370 | −0.252061 | −0.126030 | − | 0.992026i | \(-0.540224\pi\) | ||||
−0.126030 | + | 0.992026i | \(0.540224\pi\) | |||||||
\(464\) | 0.920976 | 0.0427552 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.39200 | −0.342428 | ||||||||
\(467\) | 16.8183 | 0.778257 | 0.389129 | − | 0.921183i | \(-0.372776\pi\) | ||||
0.389129 | + | 0.921183i | \(0.372776\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.5434 | −1.13331 | ||||||||
\(470\) | 29.5698 | 1.36395 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −40.3716 | −1.85825 | ||||||||
\(473\) | −14.7140 | −0.676548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.07491 | 0.324619 | ||||||||
\(476\) | −60.8183 | −2.78760 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 41.5793 | 1.90179 | ||||||||
\(479\) | 32.8574 | 1.50129 | 0.750647 | − | 0.660704i | \(-0.229742\pi\) | ||||
0.750647 | + | 0.660704i | \(0.229742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.5416 | 2.39569 | ||||||||
\(482\) | 55.9090 | 2.54658 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.15155 | 0.279616 | ||||||||
\(485\) | 1.50526 | 0.0683504 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.35263 | 0.106608 | 0.0533039 | − | 0.998578i | \(-0.483025\pi\) | ||||
0.0533039 | + | 0.998578i | \(0.483025\pi\) | |||||||
\(488\) | −14.7750 | −0.668834 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −53.8160 | −2.43116 | ||||||||
\(491\) | 14.0933 | 0.636023 | 0.318011 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318011 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.13707 | −0.186324 | ||||||||
\(494\) | −111.254 | −5.00554 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.18659 | 0.187984 | ||||||||
\(497\) | −39.0846 | −1.75318 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.21406 | −0.322946 | −0.161473 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161473 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(500\) | −40.9171 | −1.82987 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.4708 | 1.04755 | ||||||||
\(503\) | 35.3702 | 1.57708 | 0.788541 | − | 0.614983i | \(-0.210837\pi\) | ||||
0.788541 | + | 0.614983i | \(0.210837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.8451 | −1.28359 | ||||||||
\(506\) | −8.33675 | −0.370614 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.5763 | 1.44534 | ||||||||
\(509\) | −7.23766 | −0.320803 | −0.160402 | − | 0.987052i | \(-0.551279\pi\) | ||||
−0.160402 | + | 0.987052i | \(0.551279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −50.7741 | −2.24612 | ||||||||
\(512\) | 10.3307 | 0.456555 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.6907 | 0.780303 | ||||||||
\(515\) | −31.2841 | −1.37854 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.2734 | −0.979584 | ||||||||
\(518\) | 91.3892 | 4.01541 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 39.0512 | 1.71251 | ||||||||
\(521\) | 41.0518 | 1.79851 | 0.899256 | − | 0.437422i | \(-0.144108\pi\) | ||||
0.899256 | + | 0.437422i | \(0.144108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1248 | −1.27354 | −0.636770 | − | 0.771054i | \(-0.719730\pi\) | ||||
−0.636770 | + | 0.771054i | \(0.719730\pi\) | |||||||
\(524\) | −27.7349 | −1.21161 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0048 | −1.30827 | ||||||||
\(527\) | −18.8064 | −0.819218 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.31361 | 0.274246 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −122.280 | −5.30149 | ||||||||
\(533\) | −21.6464 | −0.937608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6859 | −1.15373 | ||||||||
\(536\) | 19.1503 | 0.827167 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.4976 | 1.61664 | ||||||||
\(539\) | 40.5368 | 1.74604 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.1303 | 1.12343 | 0.561715 | − | 0.827331i | \(-0.310142\pi\) | ||||
0.561715 | + | 0.827331i | \(0.310142\pi\) | |||||||
\(542\) | 13.5040 | 0.580048 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.7623 | −0.804427 | ||||||||
\(545\) | 35.4685 | 1.51930 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.3917 | −1.08567 | −0.542835 | − | 0.839839i | \(-0.682649\pi\) | ||||
−0.542835 | + | 0.839839i | \(0.682649\pi\) | |||||||
\(548\) | 49.9799 | 2.13504 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.09097 | 0.302360 | ||||||||
\(551\) | −8.31788 | −0.354353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.72153 | 0.370877 | ||||||||
\(554\) | −9.44626 | −0.401333 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −55.5997 | −2.35795 | ||||||||
\(557\) | −29.2515 | −1.23943 | −0.619714 | − | 0.784828i | \(-0.712751\pi\) | ||||
−0.619714 | + | 0.784828i | \(0.712751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.6067 | 0.998455 | ||||||||
\(560\) | 8.03289 | 0.339451 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −71.5427 | −3.01784 | ||||||||
\(563\) | −28.7525 | −1.21177 | −0.605886 | − | 0.795551i | \(-0.707181\pi\) | ||||
−0.605886 | + | 0.795551i | \(0.707181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.4217 | 1.19571 | ||||||||
\(566\) | −59.8580 | −2.51602 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.4963 | 1.27960 | ||||||||
\(569\) | −13.9221 | −0.583647 | −0.291823 | − | 0.956472i | \(-0.594262\pi\) | ||||
−0.291823 | + | 0.956472i | \(0.594262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.66013 | 0.320566 | 0.160283 | − | 0.987071i | \(-0.448759\pi\) | ||||
0.160283 | + | 0.987071i | \(0.448759\pi\) | |||||||
\(572\) | −70.4606 | −2.94611 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −37.6510 | −1.57152 | ||||||||
\(575\) | −0.850567 | −0.0354711 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.4816 | −1.18570 | −0.592851 | − | 0.805312i | \(-0.701998\pi\) | ||||
−0.592851 | + | 0.805312i | \(0.701998\pi\) | |||||||
\(578\) | −0.268777 | −0.0111797 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.99370 | 0.290397 | ||||||||
\(581\) | −10.7481 | −0.445907 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.75572 | −0.196962 | ||||||||
\(584\) | 39.6172 | 1.63937 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.5756 | 1.63485 | ||||||||
\(587\) | −28.0018 | −1.15576 | −0.577879 | − | 0.816122i | \(-0.696120\pi\) | ||||
−0.577879 | + | 0.816122i | \(0.696120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.8116 | −1.55800 | ||||||||
\(590\) | −57.3761 | −2.36214 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.43300 | −0.346594 | ||||||||
\(593\) | −37.7603 | −1.55063 | −0.775315 | − | 0.631575i | \(-0.782409\pi\) | ||||
−0.775315 | + | 0.631575i | \(0.782409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0841 | −1.47930 | ||||||||
\(596\) | 30.0514 | 1.23095 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.3752 | 0.546954 | ||||||||
\(599\) | 15.7412 | 0.643168 | 0.321584 | − | 0.946881i | \(-0.395785\pi\) | ||||
0.321584 | + | 0.946881i | \(0.395785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.6070 | −0.718204 | −0.359102 | − | 0.933298i | \(-0.616917\pi\) | ||||
−0.359102 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(602\) | 41.0607 | 1.67351 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 68.8351 | 2.80086 | ||||||||
\(605\) | 3.64978 | 0.148385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.3243 | 1.35259 | 0.676297 | − | 0.736629i | \(-0.263584\pi\) | ||||
0.676297 | + | 0.736629i | \(0.263584\pi\) | |||||||
\(608\) | −37.7230 | −1.52987 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.9983 | −0.850196 | ||||||||
\(611\) | 35.7348 | 1.44568 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.6103 | −0.792053 | −0.396027 | − | 0.918239i | \(-0.629611\pi\) | ||||
−0.396027 | + | 0.918239i | \(0.629611\pi\) | |||||||
\(614\) | −11.7712 | −0.475046 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −51.1640 | −2.06146 | ||||||||
\(617\) | −1.16373 | −0.0468500 | −0.0234250 | − | 0.999726i | \(-0.507457\pi\) | ||||
−0.0234250 | + | 0.999726i | \(0.507457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.1267 | −0.849154 | −0.424577 | − | 0.905392i | \(-0.639577\pi\) | ||||
−0.424577 | + | 0.905392i | \(0.639577\pi\) | |||||||
\(620\) | 31.7921 | 1.27680 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −27.0122 | −1.08309 | ||||||||
\(623\) | −42.8902 | −1.71836 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.0237 | −0.800948 | ||||||||
\(626\) | 40.7531 | 1.62882 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.2025 | −1.24512 | ||||||||
\(629\) | 37.8814 | 1.51043 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5717 | 0.898565 | 0.449282 | − | 0.893390i | \(-0.351680\pi\) | ||||
0.449282 | + | 0.893390i | \(0.351680\pi\) | |||||||
\(632\) | −6.80510 | −0.270692 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41.6990 | 1.65608 | ||||||||
\(635\) | 19.3279 | 0.767003 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −65.0361 | −2.57682 | ||||||||
\(638\) | −8.33675 | −0.330055 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.4635 | 1.59946 | ||||||||
\(641\) | 1.63884 | 0.0647303 | 0.0323651 | − | 0.999476i | \(-0.489696\pi\) | ||||
0.0323651 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0563 | −0.672634 | −0.336317 | − | 0.941749i | \(-0.609181\pi\) | ||||
−0.336317 | + | 0.941749i | \(0.609181\pi\) | |||||||
\(644\) | 14.7008 | 0.579293 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −80.2115 | −3.15588 | ||||||||
\(647\) | 42.8199 | 1.68342 | 0.841712 | − | 0.539926i | \(-0.181548\pi\) | ||||
0.841712 | + | 0.539926i | \(0.181548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.2185 | 1.69647 | ||||||||
\(650\) | −11.3765 | −0.446225 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −38.4391 | −1.50539 | ||||||||
\(653\) | −13.5203 | −0.529091 | −0.264545 | − | 0.964373i | \(-0.585222\pi\) | ||||
−0.264545 | + | 0.964373i | \(0.585222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4554 | −0.642966 | ||||||||
\(656\) | 3.47427 | 0.135647 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 62.1561 | 2.42310 | ||||||||
\(659\) | −3.50630 | −0.136586 | −0.0682929 | − | 0.997665i | \(-0.521755\pi\) | ||||
−0.0682929 | + | 0.997665i | \(0.521755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3043 | −0.945328 | −0.472664 | − | 0.881243i | \(-0.656708\pi\) | ||||
−0.472664 | + | 0.881243i | \(0.656708\pi\) | |||||||
\(662\) | 10.8629 | 0.422200 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.38638 | 0.325455 | ||||||||
\(665\) | −72.5498 | −2.81336 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 40.2907 | 1.55890 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.2164 | 1.05146 | ||||||||
\(671\) | 15.8169 | 0.610606 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.49381 | −0.327412 | −0.163706 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163706 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(674\) | 17.0451 | 0.656553 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 68.4120 | 2.63123 | ||||||||
\(677\) | −6.22294 | −0.239167 | −0.119584 | − | 0.992824i | \(-0.538156\pi\) | ||||
−0.119584 | + | 0.992824i | \(0.538156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.16408 | 0.121426 | ||||||||
\(680\) | 28.1551 | 1.07970 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −37.8974 | −1.45117 | ||||||||
\(683\) | −24.5440 | −0.939152 | −0.469576 | − | 0.882892i | \(-0.655593\pi\) | ||||
−0.469576 | + | 0.882892i | \(0.655593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 29.6536 | 1.13301 | ||||||||
\(686\) | −43.2568 | −1.65155 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.78890 | −0.144450 | ||||||||
\(689\) | 7.62994 | 0.290678 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7582 | −0.523386 | −0.261693 | − | 0.965151i | \(-0.584281\pi\) | ||||
−0.261693 | + | 0.965151i | \(0.584281\pi\) | |||||||
\(692\) | 69.5049 | 2.64218 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −63.8462 | −2.42357 | ||||||||
\(695\) | −32.9879 | −1.25130 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.6066 | −0.591141 | ||||||||
\(698\) | −47.2365 | −1.78793 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.5040 | −0.472608 | ||||||||
\(701\) | 38.9004 | 1.46925 | 0.734625 | − | 0.678474i | \(-0.237358\pi\) | ||||
0.734625 | + | 0.678474i | \(0.237358\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 76.1634 | 2.87256 | ||||||||
\(704\) | −44.3964 | −1.67325 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.1863 | 0.834991 | ||||||||
\(707\) | −60.6326 | −2.28032 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.1600 | 1.84624 | 0.923121 | − | 0.384510i | \(-0.125629\pi\) | ||||
0.923121 | + | 0.384510i | \(0.125629\pi\) | |||||||
\(710\) | 43.3414 | 1.62657 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 33.4657 | 1.25418 | ||||||||
\(713\) | 4.54582 | 0.170242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41.8050 | −1.56342 | ||||||||
\(716\) | −28.0401 | −1.04791 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.9382 | 0.781408 | ||||||||
\(719\) | −26.3301 | −0.981947 | −0.490973 | − | 0.871175i | \(-0.663359\pi\) | ||||
−0.490973 | + | 0.871175i | \(0.663359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −65.7596 | −2.44901 | ||||||||
\(722\) | −116.983 | −4.35367 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 86.2337 | 3.20485 | ||||||||
\(725\) | −0.850567 | −0.0315893 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.5986 | 1.13484 | 0.567420 | − | 0.823428i | \(-0.307942\pi\) | ||||
0.567420 | + | 0.823428i | \(0.307942\pi\) | |||||||
\(728\) | 82.0861 | 3.04231 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 56.3041 | 2.08391 | ||||||||
\(731\) | 17.0199 | 0.629504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.0714 | −1.73862 | −0.869311 | − | 0.494266i | \(-0.835437\pi\) | ||||
−0.869311 | + | 0.494266i | \(0.835437\pi\) | |||||||
\(734\) | 58.9210 | 2.17482 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.53517 | 0.167169 | ||||||||
\(737\) | −20.5007 | −0.755154 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.4173 | −1.30285 | −0.651424 | − | 0.758714i | \(-0.725828\pi\) | ||||
−0.651424 | + | 0.758714i | \(0.725828\pi\) | |||||||
\(740\) | −64.0384 | −2.35410 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.2713 | 0.487204 | ||||||||
\(743\) | −11.1959 | −0.410738 | −0.205369 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205369 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.8298 | 0.653234 | ||||||||
\(746\) | −5.79706 | −0.212245 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.8007 | −1.85746 | ||||||||
\(749\) | −56.0941 | −2.04963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.4942 | −0.711352 | −0.355676 | − | 0.934609i | \(-0.615749\pi\) | ||||
−0.355676 | + | 0.934609i | \(0.615749\pi\) | |||||||
\(752\) | −5.73549 | −0.209152 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.3752 | 0.487097 | ||||||||
\(755\) | 40.8406 | 1.48634 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4467 | 1.25199 | 0.625993 | − | 0.779829i | \(-0.284694\pi\) | ||||
0.625993 | + | 0.779829i | \(0.284694\pi\) | |||||||
\(758\) | −74.6628 | −2.71187 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 56.6080 | 2.05339 | ||||||||
\(761\) | −26.7158 | −0.968447 | −0.484223 | − | 0.874944i | \(-0.660898\pi\) | ||||
−0.484223 | + | 0.874944i | \(0.660898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 74.5551 | 2.69908 | ||||||||
\(764\) | −84.6208 | −3.06147 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.42453 | −0.0514704 | ||||||||
\(767\) | −69.3385 | −2.50367 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.6647 | 0.853372 | 0.426686 | − | 0.904400i | \(-0.359681\pi\) | ||||
0.426686 | + | 0.904400i | \(0.359681\pi\) | |||||||
\(770\) | −72.7144 | −2.62044 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.64401 | 0.167142 | ||||||||
\(773\) | −49.9240 | −1.79564 | −0.897822 | − | 0.440359i | \(-0.854851\pi\) | ||||
−0.897822 | + | 0.440359i | \(0.854851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.86653 | −0.138890 | ||||||||
\(776\) | −2.46882 | −0.0886253 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.7672 | 1.67668 | ||||||||
\(779\) | −31.3782 | −1.12424 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.6468 | −1.16820 | ||||||||
\(782\) | 9.64327 | 0.344843 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.4384 | 0.372799 | ||||||||
\(785\) | −18.5128 | −0.660749 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.48300 | −0.266740 | −0.133370 | − | 0.991066i | \(-0.542580\pi\) | ||||
−0.133370 | + | 0.991066i | \(0.542580\pi\) | |||||||
\(788\) | −20.7337 | −0.738607 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.67141 | −0.344093 | ||||||||
\(791\) | 59.7427 | 2.12421 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.3762 | −0.901136 | ||||||||
\(794\) | −1.46908 | −0.0521358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −74.1131 | −2.62687 | ||||||||
\(797\) | 36.0709 | 1.27770 | 0.638849 | − | 0.769332i | \(-0.279411\pi\) | ||||
0.638849 | + | 0.769332i | \(0.279411\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.7641 | 0.911468 | ||||||||
\(800\) | −3.85747 | −0.136382 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −54.0865 | −1.90986 | ||||||||
\(803\) | −42.4110 | −1.49665 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.72215 | 0.307415 | ||||||||
\(806\) | 60.8015 | 2.14164 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 47.3095 | 1.66434 | ||||||||
\(809\) | −15.9545 | −0.560929 | −0.280465 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280465 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.2089 | 1.27147 | 0.635733 | − | 0.771909i | \(-0.280698\pi\) | ||||
0.635733 | + | 0.771909i | \(0.280698\pi\) | |||||||
\(812\) | 14.7008 | 0.515898 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 76.3362 | 2.67558 | ||||||||
\(815\) | −22.8063 | −0.798870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.2198 | 1.19720 | ||||||||
\(818\) | −31.7380 | −1.10969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.3829 | 0.921330 | ||||||||
\(821\) | 5.97804 | 0.208635 | 0.104317 | − | 0.994544i | \(-0.466734\pi\) | ||||
0.104317 | + | 0.994544i | \(0.466734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.2654 | 0.741264 | 0.370632 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370632 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(824\) | 51.3098 | 1.78746 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −120.605 | −4.19639 | ||||||||
\(827\) | 35.3932 | 1.23074 | 0.615371 | − | 0.788237i | \(-0.289006\pi\) | ||||
0.615371 | + | 0.788237i | \(0.289006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3204 | 0.358444 | 0.179222 | − | 0.983809i | \(-0.442642\pi\) | ||||
0.179222 | + | 0.983809i | \(0.442642\pi\) | |||||||
\(830\) | 11.9187 | 0.413705 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 71.2283 | 2.46940 | ||||||||
\(833\) | −46.8897 | −1.62463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.9049 | 0.827264 | ||||||||
\(836\) | −102.139 | −3.53253 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −68.8544 | −2.37853 | ||||||||
\(839\) | −23.4456 | −0.809433 | −0.404717 | − | 0.914442i | \(-0.632630\pi\) | ||||
−0.404717 | + | 0.914442i | \(0.632630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −23.5699 | −0.812272 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −55.8643 | −1.92293 | ||||||||
\(845\) | 40.5896 | 1.39632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.67187 | 0.263608 | ||||||||
\(848\) | −1.22462 | −0.0420535 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.20225 | −0.281335 | ||||||||
\(851\) | −9.15659 | −0.313884 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.9444 | 0.819842 | 0.409921 | − | 0.912121i | \(-0.365556\pi\) | ||||
0.409921 | + | 0.912121i | \(0.365556\pi\) | |||||||
\(854\) | −44.1386 | −1.51039 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 43.7682 | 1.49597 | ||||||||
\(857\) | 13.0836 | 0.446927 | 0.223464 | − | 0.974712i | \(-0.428264\pi\) | ||||
0.223464 | + | 0.974712i | \(0.428264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.8025 | 1.42628 | 0.713141 | − | 0.701020i | \(-0.247272\pi\) | ||||
0.713141 | + | 0.701020i | \(0.247272\pi\) | |||||||
\(860\) | −28.7721 | −0.981121 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.672342 | −0.0229000 | ||||||||
\(863\) | −10.4612 | −0.356105 | −0.178052 | − | 0.984021i | \(-0.556980\pi\) | ||||
−0.178052 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.2380 | 1.40213 | ||||||||
\(866\) | 29.2474 | 0.993869 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 66.8273 | 2.26827 | ||||||||
\(869\) | 7.28498 | 0.247126 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.8908 | 1.11446 | ||||||||
\(872\) | −58.1727 | −1.96998 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.3885 | 0.655826 | ||||||||
\(875\) | −51.0295 | −1.72511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.4848 | 0.961862 | 0.480931 | − | 0.876758i | \(-0.340299\pi\) | ||||
0.480931 | + | 0.876758i | \(0.340299\pi\) | |||||||
\(878\) | −12.4411 | −0.419866 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.70976 | 0.226186 | ||||||||
\(881\) | 38.9665 | 1.31281 | 0.656407 | − | 0.754407i | \(-0.272075\pi\) | ||||
0.656407 | + | 0.754407i | \(0.272075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6192 | 0.357365 | 0.178683 | − | 0.983907i | \(-0.442816\pi\) | ||||
0.178683 | + | 0.983907i | \(0.442816\pi\) | |||||||
\(884\) | 81.5031 | 2.74125 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 53.1612 | 1.78599 | ||||||||
\(887\) | 0.468182 | 0.0157200 | 0.00786000 | − | 0.999969i | \(-0.497498\pi\) | ||||
0.00786000 | + | 0.999969i | \(0.497498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.6274 | 1.36260 | ||||||||
\(890\) | 47.5615 | 1.59426 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.9230 | −1.23627 | ||||||||
\(893\) | 51.8006 | 1.73344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.6365 | −0.556097 | ||||||||
\(896\) | 85.0547 | 2.84148 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 55.5959 | 1.85526 | ||||||||
\(899\) | 4.54582 | 0.151612 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.50103 | 0.183266 | ||||||||
\(902\) | −31.4494 | −1.04715 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.6151 | −1.55040 | ||||||||
\(905\) | 51.1633 | 1.70073 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.6922 | 0.388233 | 0.194117 | − | 0.980978i | \(-0.437816\pi\) | ||||
0.194117 | + | 0.980978i | \(0.437816\pi\) | |||||||
\(908\) | 28.2145 | 0.936332 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 116.661 | 3.86727 | ||||||||
\(911\) | 29.7390 | 0.985298 | 0.492649 | − | 0.870228i | \(-0.336029\pi\) | ||||
0.492649 | + | 0.870228i | \(0.336029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.97776 | −0.297121 | ||||||||
\(914\) | −51.7203 | −1.71076 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −96.4275 | −3.18605 | ||||||||
\(917\) | −34.5894 | −1.14224 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8566 | −0.556048 | −0.278024 | − | 0.960574i | \(-0.589679\pi\) | ||||
−0.278024 | + | 0.960574i | \(0.589679\pi\) | |||||||
\(920\) | −6.80558 | −0.224373 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.8512 | −1.44416 | ||||||||
\(923\) | 52.3776 | 1.72403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.78830 | 0.256078 | ||||||||
\(926\) | 12.6423 | 0.415453 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.53517 | 0.148874 | ||||||||
\(929\) | −24.0401 | −0.788730 | −0.394365 | − | 0.918954i | \(-0.629035\pi\) | ||||
−0.394365 | + | 0.918954i | \(0.629035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −94.2752 | −3.08974 | ||||||||
\(932\) | 10.8878 | 0.356643 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.2025 | −1.28275 | ||||||||
\(935\) | −30.1406 | −0.985702 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.39247 | 0.176164 | 0.0880821 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880821 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(938\) | 57.2092 | 1.86795 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −43.5541 | −1.42058 | ||||||||
\(941\) | 8.82008 | 0.287527 | 0.143763 | − | 0.989612i | \(-0.454080\pi\) | ||||
0.143763 | + | 0.989612i | \(0.454080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.77238 | 0.122846 | ||||||||
\(944\) | 11.1289 | 0.362215 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.2974 | 1.11511 | ||||||||
\(947\) | −9.44632 | −0.306964 | −0.153482 | − | 0.988151i | \(-0.549049\pi\) | ||||
−0.153482 | + | 0.988151i | \(0.549049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.0429 | 2.20877 | ||||||||
\(950\) | −16.4912 | −0.535046 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 59.1824 | 1.91811 | ||||||||
\(953\) | 52.6988 | 1.70708 | 0.853541 | − | 0.521025i | \(-0.174450\pi\) | ||||
0.853541 | + | 0.521025i | \(0.174450\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.2064 | −1.62464 | ||||||||
\(956\) | −61.2432 | −1.98075 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −76.5888 | −2.47447 | ||||||||
\(959\) | 62.3322 | 2.01281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3355 | −0.333403 | ||||||||
\(962\) | −122.472 | −3.94864 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −82.3497 | −2.65230 | ||||||||
\(965\) | 2.75534 | 0.0886975 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.7635 | −1.21439 | −0.607197 | − | 0.794552i | \(-0.707706\pi\) | ||||
−0.607197 | + | 0.794552i | \(0.707706\pi\) | |||||||
\(968\) | −5.98608 | −0.192400 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.50868 | −0.112657 | ||||||||
\(971\) | −10.8940 | −0.349605 | −0.174803 | − | 0.984604i | \(-0.555929\pi\) | ||||
−0.174803 | + | 0.984604i | \(0.555929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −69.3408 | −2.22297 | ||||||||
\(974\) | −5.48385 | −0.175714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.07292 | 0.130371 | ||||||||
\(977\) | −57.4977 | −1.83951 | −0.919756 | − | 0.392489i | \(-0.871614\pi\) | ||||
−0.919756 | + | 0.392489i | \(0.871614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.8256 | −1.14499 | ||||||||
\(980\) | 79.2669 | 2.53209 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32.8508 | −1.04831 | ||||||||
\(983\) | 48.8762 | 1.55891 | 0.779454 | − | 0.626459i | \(-0.215496\pi\) | ||||
0.779454 | + | 0.626459i | \(0.215496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3015 | −0.391959 | ||||||||
\(986\) | 9.64327 | 0.307104 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 163.868 | 5.21334 | ||||||||
\(989\) | −4.11401 | −0.130818 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.1297 | 1.24300 | 0.621498 | − | 0.783416i | \(-0.286524\pi\) | ||||
0.621498 | + | 0.783416i | \(0.286524\pi\) | |||||||
\(992\) | 20.6161 | 0.654561 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 91.1040 | 2.88964 | ||||||||
\(995\) | −43.9721 | −1.39401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.04245 | 0.0646851 | 0.0323425 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323425 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(998\) | 16.8156 | 0.532288 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.t.1.2 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.21 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.21 | yes | 22 | 3.2 | odd | 2 |