Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8012,2,Mod(1,8012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8012, 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("8012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8012 = 2^{2} \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8012.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: | \(63.9761420994\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.17871 | −1.83523 | −0.917614 | − | 0.397473i | \(-0.869887\pi\) | ||||
−0.917614 | + | 0.397473i | \(0.869887\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.27908 | −0.572022 | −0.286011 | − | 0.958226i | \(-0.592329\pi\) | ||||
−0.286011 | + | 0.958226i | \(0.592329\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.10162 | 0.794339 | 0.397170 | − | 0.917745i | \(-0.369992\pi\) | ||||
0.397170 | + | 0.917745i | \(0.369992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.10419 | 2.36806 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.72848 | −1.12418 | −0.562090 | − | 0.827076i | \(-0.690003\pi\) | ||||
−0.562090 | + | 0.827076i | \(0.690003\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.44031 | 1.50887 | 0.754435 | − | 0.656375i | \(-0.227911\pi\) | ||||
0.754435 | + | 0.656375i | \(0.227911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.06583 | 1.04979 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.20119 | 1.26147 | 0.630737 | − | 0.775997i | \(-0.282753\pi\) | ||||
0.630737 | + | 0.775997i | \(0.282753\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.34715 | 0.538474 | 0.269237 | − | 0.963074i | \(-0.413229\pi\) | ||||
0.269237 | + | 0.963074i | \(0.413229\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.68045 | −1.45779 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.59231 | −1.16608 | −0.583039 | − | 0.812444i | \(-0.698137\pi\) | ||||
−0.583039 | + | 0.812444i | \(0.698137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.36395 | −0.672790 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.0460 | −2.51071 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.67788 | 1.42575 | 0.712874 | − | 0.701292i | \(-0.247393\pi\) | ||||
0.712874 | + | 0.701292i | \(0.247393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.93668 | −1.24587 | −0.622933 | − | 0.782276i | \(-0.714059\pi\) | ||||
−0.622933 | + | 0.782276i | \(0.714059\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.8518 | 2.06313 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.68815 | −0.454380 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.90921 | −0.971468 | −0.485734 | − | 0.874107i | \(-0.661448\pi\) | ||||
−0.485734 | + | 0.874107i | \(0.661448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.2932 | −2.76912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29198 | −0.357947 | −0.178973 | − | 0.983854i | \(-0.557278\pi\) | ||||
−0.178973 | + | 0.983854i | \(0.557278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7154 | −1.63409 | −0.817044 | − | 0.576575i | \(-0.804389\pi\) | ||||
−0.817044 | + | 0.576575i | \(0.804389\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.08683 | −1.35458 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.18881 | −0.756866 | −0.378433 | − | 0.925629i | \(-0.623537\pi\) | ||||
−0.378433 | + | 0.925629i | \(0.623537\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.58318 | −0.369025 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.5331 | −2.31509 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.40890 | 1.29241 | 0.646206 | − | 0.763163i | \(-0.276355\pi\) | ||||
0.646206 | + | 0.763163i | \(0.276355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.76903 | 0.643056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.46092 | −0.988223 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3119 | 1.86325 | 0.931627 | − | 0.363415i | \(-0.118389\pi\) | ||||
0.931627 | + | 0.363415i | \(0.118389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8624 | 1.39078 | 0.695391 | − | 0.718631i | \(-0.255231\pi\) | ||||
0.695391 | + | 0.718631i | \(0.255231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.9303 | 1.88104 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.95860 | −0.863108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.890134 | −0.108747 | −0.0543736 | − | 0.998521i | \(-0.517316\pi\) | ||||
−0.0543736 | + | 0.998521i | \(0.517316\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.7763 | 2.14002 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1973 | −1.68491 | −0.842456 | − | 0.538764i | \(-0.818891\pi\) | ||||
−0.842456 | + | 0.538764i | \(0.818891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.46780 | −0.991081 | −0.495540 | − | 0.868585i | \(-0.665030\pi\) | ||||
−0.495540 | + | 0.868585i | \(0.665030\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6930 | 1.23472 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.83587 | −0.892980 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.25307 | −0.365999 | −0.183000 | − | 0.983113i | \(-0.558581\pi\) | ||||
−0.183000 | + | 0.983113i | \(0.558581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20.1569 | 2.23966 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1541 | 1.55361 | 0.776805 | − | 0.629741i | \(-0.216839\pi\) | ||||
0.776805 | + | 0.629741i | \(0.216839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.65274 | −0.721591 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.4058 | −2.61657 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.98160 | 0.740048 | 0.370024 | − | 0.929022i | \(-0.379349\pi\) | ||||
0.370024 | + | 0.929022i | \(0.379349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4335 | 1.19855 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.0497 | 2.28645 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00220 | −0.308019 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.14684 | −0.725652 | −0.362826 | − | 0.931857i | \(-0.618188\pi\) | ||||
−0.362826 | + | 0.931857i | \(0.618188\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26.4879 | −2.66213 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.99616 | −0.298129 | −0.149065 | − | 0.988827i | \(-0.547626\pi\) | ||||
−0.149065 | + | 0.988827i | \(0.547626\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0645 | 1.28728 | 0.643642 | − | 0.765327i | \(-0.277423\pi\) | ||||
0.643642 | + | 0.765327i | \(0.277423\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.54484 | 0.833891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5063 | −1.01568 | −0.507840 | − | 0.861451i | \(-0.669556\pi\) | ||||
−0.507840 | + | 0.861451i | \(0.669556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.88964 | −0.947256 | −0.473628 | − | 0.880725i | \(-0.657056\pi\) | ||||
−0.473628 | + | 0.880725i | \(0.657056\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.7836 | 1.78286 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.21987 | −0.585116 | −0.292558 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292558 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.15302 | 0.667023 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38.6490 | 3.57310 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.9309 | 1.00204 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.90160 | 0.263782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.28553 | 0.656914 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6982 | 0.956874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.8050 | 1.84614 | 0.923072 | − | 0.384626i | \(-0.125670\pi\) | ||||
0.923072 | + | 0.384626i | \(0.125670\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 34.0612 | 2.99892 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.14247 | −0.274559 | −0.137279 | − | 0.990532i | \(-0.543836\pi\) | ||||
−0.137279 | + | 0.990532i | \(0.543836\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.93283 | 0.427731 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.6869 | 1.43618 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.61305 | 0.308684 | 0.154342 | − | 0.988018i | \(-0.450674\pi\) | ||||
0.154342 | + | 0.988018i | \(0.450674\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.95234 | 0.589690 | 0.294845 | − | 0.955545i | \(-0.404732\pi\) | ||||
0.294845 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4937 | 1.38902 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2841 | −1.69624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.82064 | −0.815559 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.21117 | 0.677246 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9782 | −1.14514 | −0.572568 | − | 0.819857i | \(-0.694053\pi\) | ||||
−0.572568 | + | 0.819857i | \(0.694053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.90853 | −0.399451 | −0.199725 | − | 0.979852i | \(-0.564005\pi\) | ||||
−0.199725 | + | 0.979852i | \(0.564005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.9502 | 2.98725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.87258 | 0.712663 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.52372 | −0.121606 | −0.0608029 | − | 0.998150i | \(-0.519366\pi\) | ||||
−0.0608029 | + | 0.998150i | \(0.519366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −29.9082 | −2.37187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7529 | −0.926261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.13735 | 0.402388 | 0.201194 | − | 0.979551i | \(-0.435518\pi\) | ||||
0.201194 | + | 0.979551i | \(0.435518\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.1594 | −1.18016 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.78075 | 0.369945 | 0.184973 | − | 0.982744i | \(-0.440780\pi\) | ||||
0.184973 | + | 0.982744i | \(0.440780\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.5970 | 1.27669 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.6746 | 1.27514 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4275 | −1.02088 | −0.510438 | − | 0.859915i | \(-0.670517\pi\) | ||||
−0.510438 | + | 0.859915i | \(0.670517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.06976 | −0.534424 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −45.4935 | −3.41950 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.34796 | 0.324982 | 0.162491 | − | 0.986710i | \(-0.448047\pi\) | ||||
0.162491 | + | 0.986710i | \(0.448047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.74834 | −0.427271 | −0.213635 | − | 0.976913i | \(-0.568530\pi\) | ||||
−0.213635 | + | 0.976913i | \(0.568530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −34.5283 | −2.55240 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.55836 | 0.555701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.3926 | −1.41812 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.4178 | −1.99435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.61082 | 0.188913 | 0.0944563 | − | 0.995529i | \(-0.469889\pi\) | ||||
0.0944563 | + | 0.995529i | \(0.469889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.78415 | −0.704278 | −0.352139 | − | 0.935948i | \(-0.614546\pi\) | ||||
−0.352139 | + | 0.935948i | \(0.614546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 22.1193 | 1.58400 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1065 | 0.791307 | 0.395653 | − | 0.918400i | \(-0.370518\pi\) | ||||
0.395653 | + | 0.918400i | \(0.370518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.8972 | −1.83580 | −0.917901 | − | 0.396810i | \(-0.870117\pi\) | ||||
−0.917901 | + | 0.396810i | \(0.870117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.82948 | 0.199576 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1360 | 1.13253 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.93162 | 0.204754 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39.7288 | −2.76135 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.75133 | −0.605342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.67120 | 0.321579 | 0.160789 | − | 0.986989i | \(-0.448596\pi\) | ||||
0.160789 | + | 0.986989i | \(0.448596\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 45.1292 | 3.09220 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.7059 | 0.934735 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.5783 | −0.989639 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.9167 | 1.81886 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.2961 | 1.90340 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0194 | 1.13970 | 0.569851 | − | 0.821748i | \(-0.307001\pi\) | ||||
0.569851 | + | 0.821748i | \(0.307001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.8981 | −1.59321 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.00692156 | 0.000459400 0 | 0.000229700 | − | 1.00000i | \(-0.499927\pi\) | ||||
0.000229700 | 1.00000i | \(0.499927\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8935 | −1.31460 | −0.657299 | − | 0.753630i | \(-0.728301\pi\) | ||||
−0.657299 | + | 0.753630i | \(0.728301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 24.9080 | 1.63882 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9958 | 1.70304 | 0.851521 | − | 0.524320i | \(-0.175681\pi\) | ||||
0.851521 | + | 0.524320i | \(0.175681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.63691 | 0.432944 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3406 | 0.671692 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.1381 | 1.43199 | 0.715997 | − | 0.698103i | \(-0.245972\pi\) | ||||
0.715997 | + | 0.698103i | \(0.245972\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2920 | −0.662969 | −0.331484 | − | 0.943461i | \(-0.607549\pi\) | ||||
−0.331484 | + | 0.943461i | \(0.607549\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −24.9349 | −1.59957 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.30409 | 0.211091 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.7692 | 0.812487 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44.9916 | −2.85123 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.6564 | −1.36694 | −0.683470 | − | 0.729978i | \(-0.739530\pi\) | ||||
−0.683470 | + | 0.729978i | \(0.739530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.8509 | 1.31088 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.1471 | 1.32428 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.4986 | −1.09154 | −0.545768 | − | 0.837936i | \(-0.683762\pi\) | ||||
−0.545768 | + | 0.837936i | \(0.683762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4189 | −0.771675 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.5451 | 3.37626 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7109 | 0.660463 | 0.330231 | − | 0.943900i | \(-0.392873\pi\) | ||||
0.330231 | + | 0.943900i | \(0.392873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0347 | −0.739289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.1925 | −1.35816 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.48215 | 0.273281 | 0.136641 | − | 0.990621i | \(-0.456369\pi\) | ||||
0.136641 | + | 0.990621i | \(0.456369\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.1009 | −0.917316 | −0.458658 | − | 0.888613i | \(-0.651670\pi\) | ||||
−0.458658 | + | 0.888613i | \(0.651670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −36.3437 | −2.19962 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.5424 | 0.756338 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.9920 | −1.50162 | −0.750811 | − | 0.660517i | \(-0.770337\pi\) | ||||
−0.750811 | + | 0.660517i | \(0.770337\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −49.2795 | −2.95029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9284 | 1.12917 | 0.564586 | − | 0.825374i | \(-0.309036\pi\) | ||||
0.564586 | + | 0.825374i | \(0.309036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.0710 | 1.66865 | 0.834325 | − | 0.551274i | \(-0.185858\pi\) | ||||
0.834325 | + | 0.551274i | \(0.185858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.54312 | 0.565286 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.81687 | −0.284331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.0524 | 0.591317 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.7177 | 1.33174 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.30729 | −0.426896 | −0.213448 | − | 0.976954i | \(-0.568469\pi\) | ||||
−0.213448 | + | 0.976954i | \(0.568469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.3061 | −1.06582 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 48.6419 | 2.82249 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −30.4239 | −1.75946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5198 | −1.29802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.52392 | 0.547135 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8938 | −0.795559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.3771 | −1.22006 | −0.610029 | − | 0.792379i | \(-0.708842\pi\) | ||||
−0.610029 | + | 0.792379i | \(0.708842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −41.5283 | −2.36246 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6329 | 0.886458 | 0.443229 | − | 0.896408i | \(-0.353833\pi\) | ||||
0.443229 | + | 0.896408i | \(0.353833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7482 | −1.17276 | −0.586378 | − | 0.810038i | \(-0.699447\pi\) | ||||
−0.586378 | + | 0.810038i | \(0.699447\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.0971 | −1.07600 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.88566 | −0.105909 | −0.0529545 | − | 0.998597i | \(-0.516864\pi\) | ||||
−0.0529545 | + | 0.998597i | \(0.516864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.6269 | −1.60280 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.3964 | 1.86401 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2080 | 0.679271 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3009 | −1.01515 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.4363 | 1.73843 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.9049 | −0.601208 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.64651 | −0.145465 | −0.0727327 | − | 0.997351i | \(-0.523172\pi\) | ||||
−0.0727327 | + | 0.997351i | \(0.523172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −41.9801 | −2.30050 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.13855 | 0.0622059 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3187 | −0.616571 | −0.308286 | − | 0.951294i | \(-0.599755\pi\) | ||||
−0.308286 | + | 0.951294i | \(0.599755\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.7711 | 1.07382 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.8633 | 1.40058 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1402 | −1.08747 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.7374 | −1.22414 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.4058 | −1.52490 | −0.762451 | − | 0.647045i | \(-0.776004\pi\) | ||||
−0.762451 | + | 0.647045i | \(0.776004\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1102 | 0.541189 | 0.270594 | − | 0.962693i | \(-0.412780\pi\) | ||||
0.270594 | + | 0.962693i | \(0.412780\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −70.9743 | −3.78833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.77887 | 0.254354 | 0.127177 | − | 0.991880i | \(-0.459408\pi\) | ||||
0.127177 | + | 0.991880i | \(0.459408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.1595 | 0.963808 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.7463 | −1.83897 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.26001 | 0.435947 | 0.217973 | − | 0.975955i | \(-0.430055\pi\) | ||||
0.217973 | + | 0.975955i | \(0.430055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4909 | −0.710046 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.22333 | −0.484100 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8310 | 0.566920 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.69811 | −0.0886408 | −0.0443204 | − | 0.999017i | \(-0.514112\pi\) | ||||
−0.0443204 | + | 0.999017i | \(0.514112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.2826 | −0.847640 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7740 | 1.02661 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.4445 | 0.799688 | 0.399844 | − | 0.916583i | \(-0.369064\pi\) | ||||
0.399844 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.0064 | −1.75608 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.7701 | 2.15127 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.25410 | 0.167152 | 0.0835759 | − | 0.996501i | \(-0.473366\pi\) | ||||
0.0835759 | + | 0.996501i | \(0.473366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −66.1330 | −3.38810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.7738 | −1.87905 | −0.939525 | − | 0.342479i | \(-0.888733\pi\) | ||||
−0.939525 | + | 0.342479i | \(0.888733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0227 | 0.510805 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −76.1244 | −3.86962 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9193 | 1.61837 | 0.809187 | − | 0.587551i | \(-0.199908\pi\) | ||||
0.809187 | + | 0.587551i | \(0.199908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.0867 | −1.47098 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.98899 | 0.503878 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.16094 | 0.209360 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.1598 | 1.71443 | 0.857215 | − | 0.514959i | \(-0.172193\pi\) | ||||
0.857215 | + | 0.514959i | \(0.172193\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.6800 | −0.784984 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6354 | 0.581045 | 0.290523 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290523 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.7377 | −1.87985 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.7823 | −1.28113 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.0324 | 1.09211 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0899 | −0.795593 | −0.397796 | − | 0.917474i | \(-0.630225\pi\) | ||||
−0.397796 | + | 0.917474i | \(0.630225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4848 | −0.566505 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.0783 | 1.48006 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.1042 | −0.888700 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.0995 | −1.08222 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.1402 | 1.76556 | 0.882782 | − | 0.469783i | \(-0.155668\pi\) | ||||
0.882782 | + | 0.469783i | \(0.155668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.6735 | −1.59241 | −0.796205 | − | 0.605027i | \(-0.793162\pi\) | ||||
−0.796205 | + | 0.605027i | \(0.793162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.8623 | −1.79231 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.4966 | −0.848707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8286 | 1.10475 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 64.4773 | 3.11299 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.50339 | −0.0724160 | −0.0362080 | − | 0.999344i | \(-0.511528\pi\) | ||||
−0.0362080 | + | 0.999344i | \(0.511528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.9950 | 0.672555 | 0.336277 | − | 0.941763i | \(-0.390832\pi\) | ||||
0.336277 | + | 0.941763i | \(0.390832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.2169 | 1.49674 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1260 | −0.627903 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.35894 | −0.208041 | −0.104020 | − | 0.994575i | \(-0.533171\pi\) | ||||
−0.104020 | + | 0.994575i | \(0.533171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.3514 | −0.873875 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0318 | −1.14178 | −0.570892 | − | 0.821025i | \(-0.693403\pi\) | ||||
−0.570892 | + | 0.821025i | \(0.693403\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.93003 | −0.423324 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.4325 | 2.10158 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.6604 | −1.11660 | −0.558302 | − | 0.829638i | \(-0.688547\pi\) | ||||
−0.558302 | + | 0.829638i | \(0.688547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.54560 | 0.402397 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6028 | 0.733083 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6243 | −0.685600 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.7010 | −1.48291 | −0.741455 | − | 0.671003i | \(-0.765864\pi\) | ||||
−0.741455 | + | 0.671003i | \(0.765864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −67.8548 | −3.16719 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.6680 | 1.56808 | 0.784038 | − | 0.620712i | \(-0.213157\pi\) | ||||
0.784038 | + | 0.620712i | \(0.213157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7432 | −0.592228 | −0.296114 | − | 0.955153i | \(-0.595691\pi\) | ||||
−0.296114 | + | 0.955153i | \(0.595691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.2033 | −1.30790 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0257 | −0.556485 | −0.278242 | − | 0.960511i | \(-0.589752\pi\) | ||||
−0.278242 | + | 0.960511i | \(0.589752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.87073 | −0.0863822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.84345 | 0.223174 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 39.9523 | 1.83701 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.89571 | −0.362280 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66.8426 | 3.06051 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2215 | −1.47224 | −0.736118 | − | 0.676853i | \(-0.763343\pi\) | ||||
−0.736118 | + | 0.676853i | \(0.763343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.1479 | −1.46582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.3592 | 1.69990 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.14139 | 0.415089 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.6158 | −0.526361 | −0.263181 | − | 0.964747i | \(-0.584772\pi\) | ||||
−0.263181 | + | 0.964747i | \(0.584772\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.3301 | −0.738474 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.50475 | −0.203297 | −0.101648 | − | 0.994820i | \(-0.532412\pi\) | ||||
−0.101648 | + | 0.994820i | \(0.532412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.9341 | 1.79854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.8801 | 1.52280 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.8374 | −1.33839 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.7092 | 0.792774 | 0.396387 | − | 0.918084i | \(-0.370264\pi\) | ||||
0.396387 | + | 0.918084i | \(0.370264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1966 | −0.678934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.3299 | −1.48611 | −0.743053 | − | 0.669232i | \(-0.766623\pi\) | ||||
−0.743053 | + | 0.669232i | \(0.766623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.83233 | 0.170537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −52.7569 | −2.34302 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.96218 | 0.175620 | 0.0878102 | − | 0.996137i | \(-0.472013\pi\) | ||||
0.0878102 | + | 0.996137i | \(0.472013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7961 | −0.787254 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.6210 | −1.35195 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.7106 | −0.736356 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3464 | 0.850854 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 42.6822 | 1.87354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.8476 | −1.30765 | −0.653824 | − | 0.756647i | \(-0.726836\pi\) | ||||
−0.653824 | + | 0.756647i | \(0.726836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.37508 | −0.191309 | −0.0956544 | − | 0.995415i | \(-0.530494\pi\) | ||||
−0.0956544 | + | 0.995415i | \(0.530494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.4727 | 0.980789 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.0790 | −1.57163 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.27397 | 0.359738 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 101.675 | 4.41230 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.4691 | −0.540095 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4384 | 0.580992 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.8209 | −0.596416 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.63134 | 0.414851 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6271 | 0.671862 | 0.335931 | − | 0.941887i | \(-0.390949\pi\) | ||||
0.335931 | + | 0.941887i | \(0.390949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.2723 | 0.784139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.6497 | 0.541852 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.3422 | −1.16907 | −0.584534 | − | 0.811369i | \(-0.698723\pi\) | ||||
−0.584534 | + | 0.811369i | \(0.698723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 77.1682 | 3.29346 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.0212 | 0.767728 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.83674 | −0.290728 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.0258 | −1.01984 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.75092 | −0.243674 | −0.121837 | − | 0.992550i | \(-0.538879\pi\) | ||||
−0.121837 | + | 0.992550i | \(0.538879\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −58.2953 | −2.46563 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 61.6433 | 2.60258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.20075 | 0.0927507 | 0.0463753 | − | 0.998924i | \(-0.485233\pi\) | ||||
0.0463753 | + | 0.998924i | \(0.485233\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.95572 | 0.334699 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.3622 | 1.77905 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.99283 | −0.167388 | −0.0836942 | − | 0.996491i | \(-0.526672\pi\) | ||||
−0.0836942 | + | 0.996491i | \(0.526672\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.73008 | 0.197948 | 0.0989738 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989738 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.29905 | −0.346698 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.8123 | 0.784526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0254 | 1.58302 | 0.791508 | − | 0.611158i | \(-0.209296\pi\) | ||||
0.791508 | + | 0.611158i | \(0.209296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.1010 | 1.29251 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.7465 | 1.23409 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.0809 | −1.45290 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.4352 | −2.04389 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.0470 | 0.662329 | 0.331164 | − | 0.943573i | \(-0.392559\pi\) | ||||
0.331164 | + | 0.943573i | \(0.392559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2815 | −0.670866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.3044 | −1.45223 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.3836 | −0.754924 | −0.377462 | − | 0.926025i | \(-0.623203\pi\) | ||||
−0.377462 | + | 0.926025i | \(0.623203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9816 | −0.573188 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 82.3195 | 3.36911 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5833 | −0.881868 | −0.440934 | − | 0.897539i | \(-0.645353\pi\) | ||||
−0.440934 | + | 0.897539i | \(0.645353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.04840 | 0.328301 | 0.164150 | − | 0.986435i | \(-0.447512\pi\) | ||||
0.164150 | + | 0.986435i | \(0.447512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.32368 | −0.257520 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.71138 | −0.150889 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.6486 | −1.44693 | −0.723466 | − | 0.690360i | \(-0.757452\pi\) | ||||
−0.723466 | + | 0.690360i | \(0.757452\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −51.2917 | −2.07845 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.2287 | −1.14201 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.7657 | −0.555992 | −0.277996 | − | 0.960582i | \(-0.589670\pi\) | ||||
−0.277996 | + | 0.960582i | \(0.589670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.31878 | −0.375769 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7078 | 0.431078 | 0.215539 | − | 0.976495i | \(-0.430849\pi\) | ||||
0.215539 | + | 0.976495i | \(0.430849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.38688 | 0.296904 | 0.148452 | − | 0.988920i | \(-0.452571\pi\) | ||||
0.148452 | + | 0.988920i | \(0.452571\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 72.9574 | 2.92768 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6727 | 0.587849 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.13593 | 0.125437 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.8179 | 1.11094 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30.7349 | −1.22548 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7947 | 0.628779 | 0.314390 | − | 0.949294i | \(-0.398200\pi\) | ||||
0.314390 | + | 0.949294i | \(0.398200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.8484 | −0.590171 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.6113 | −1.05604 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.0533 | −0.556811 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −100.860 | −3.98998 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.387491 | 0.0153050 | 0.00765249 | − | 0.999971i | \(-0.497564\pi\) | ||||
0.00765249 | + | 0.999971i | \(0.497564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2249 | 0.560977 | 0.280488 | − | 0.959857i | \(-0.409504\pi\) | ||||
0.280488 | + | 0.959857i | \(0.409504\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.5671 | −1.71545 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.91597 | −0.114639 | −0.0573193 | − | 0.998356i | \(-0.518255\pi\) | ||||
−0.0573193 | + | 0.998356i | \(0.518255\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −53.3618 | −2.09463 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.3402 | 1.81621 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.13227 | 0.239974 | 0.119987 | − | 0.992775i | \(-0.461715\pi\) | ||||
0.119987 | + | 0.992775i | \(0.461715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.01947 | 0.157054 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −60.1568 | −2.34694 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.28241 | 0.0889102 | 0.0444551 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444551 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.2139 | −1.33077 | −0.665384 | − | 0.746502i | \(-0.731732\pi\) | ||||
−0.665384 | + | 0.746502i | \(0.731732\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −89.9450 | −3.49317 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.30949 | −0.244672 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.9371 | −1.66253 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −54.0996 | −2.09161 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.5001 | −1.56349 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4778 | −1.17483 | −0.587416 | − | 0.809285i | \(-0.699855\pi\) | ||||
−0.587416 | + | 0.809285i | \(0.699855\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 43.8862 | 1.68918 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.1054 | −1.38764 | −0.693821 | − | 0.720147i | \(-0.744074\pi\) | ||||
−0.693821 | + | 0.720147i | \(0.744074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0200 | −0.576413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0220016 | −0.000843104 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.14902 | 0.0439659 | 0.0219830 | − | 0.999758i | \(-0.493002\pi\) | ||||
0.0219830 | + | 0.999758i | \(0.493002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.62138 | −0.176574 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 63.2355 | 2.41259 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 51.1873 | 1.95008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.2295 | 0.997817 | 0.498909 | − | 0.866655i | \(-0.333734\pi\) | ||||
0.498909 | + | 0.866655i | \(0.333734\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −55.6675 | −2.11463 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.89261 | −0.337316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.9210 | −0.451540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −82.6331 | −3.12547 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0227 | 1.13394 | 0.566972 | − | 0.823737i | \(-0.308115\pi\) | ||||
0.566972 | + | 0.823737i | \(0.308115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8698 | −0.523110 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.0968 | −0.794551 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.29680 | −0.236816 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4762 | −0.618777 | −0.309388 | − | 0.950936i | \(-0.600124\pi\) | ||||
−0.309388 | + | 0.950936i | \(0.600124\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.1104 | −0.866709 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.7921 | 1.45278 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.9450 | 0.970289 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −70.3705 | −2.62804 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.7056 | 1.70453 | 0.852265 | − | 0.523110i | \(-0.175228\pi\) | ||||
0.852265 | + | 0.523110i | \(0.175228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4567 | 1.02254 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.7154 | 1.21670 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.8280 | −0.959229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.8430 | −1.44061 | −0.720303 | − | 0.693659i | \(-0.755997\pi\) | ||||
−0.720303 | + | 0.693659i | \(0.755997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.7901 | 0.695928 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −55.7330 | −2.06136 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.8160 | −1.61838 | −0.809191 | − | 0.587546i | \(-0.800094\pi\) | ||||
−0.809191 | + | 0.587546i | \(0.800094\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.5028 | −0.387400 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.31885 | 0.122252 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2001 | −0.448789 | −0.224394 | − | 0.974498i | \(-0.572040\pi\) | ||||
−0.224394 | + | 0.974498i | \(0.572040\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −40.5897 | −1.49110 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.02770 | 0.111075 | 0.0555377 | − | 0.998457i | \(-0.482313\pi\) | ||||
0.0555377 | + | 0.998457i | \(0.482313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.8792 | 0.655043 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 100.553 | 3.67904 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.0802 | −0.806795 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5312 | −0.384287 | −0.192144 | − | 0.981367i | \(-0.561544\pi\) | ||||
−0.192144 | + | 0.981367i | \(0.561544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 68.8394 | 2.50865 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.27841 | 0.228495 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0982 | −1.38470 | −0.692351 | − | 0.721561i | \(-0.743425\pi\) | ||||
−0.692351 | + | 0.721561i | \(0.743425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −66.2788 | −2.40577 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.8117 | −1.22567 | −0.612837 | − | 0.790210i | \(-0.709972\pi\) | ||||
−0.612837 | + | 0.790210i | \(0.709972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7843 | −0.752442 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −47.2623 | −1.70877 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 77.8613 | 2.81141 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.4037 | −1.16851 | −0.584254 | − | 0.811571i | \(-0.698613\pi\) | ||||
−0.584254 | + | 0.811571i | \(0.698613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.6231 | 2.00322 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.2161 | 1.08680 | 0.543399 | − | 0.839475i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839475i | \(0.317137\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.3347 | 0.838206 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.4762 | 1.41620 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.37962 | −0.192745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.9345 | 1.89415 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −100.166 | −3.57963 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.94896 | 0.0695612 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2739 | −0.437516 | −0.218758 | − | 0.975779i | \(-0.570201\pi\) | ||||
−0.218758 | + | 0.975779i | \(0.570201\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.0468 | −1.21210 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.0718 | −0.464781 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.0946 | 2.09851 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38.2549 | 1.35676 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.132785 | −0.00470349 | −0.00235174 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235174 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.9880 | −0.954767 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.5986 | 1.75248 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.5721 | 1.11415 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.0330 | 0.529842 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2474 | −0.501534 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.141139 | 0.00496218 | 0.00248109 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248109 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.2468 | 0.851419 | 0.425709 | − | 0.904860i | \(-0.360025\pi\) | ||||
0.425709 | + | 0.904860i | \(0.360025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 48.0015 | 1.68348 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.57108 | −0.230175 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.1508 | −0.879914 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 81.2256 | 2.83825 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.3285 | −1.16317 | −0.581587 | − | 0.813484i | \(-0.697568\pi\) | ||||
−0.581587 | + | 0.813484i | \(0.697568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.20364 | 0.111672 | 0.0558359 | − | 0.998440i | \(-0.482218\pi\) | ||||
0.0558359 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.8688 | −1.38805 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.1257 | 0.734612 | 0.367306 | − | 0.930100i | \(-0.380280\pi\) | ||||
0.367306 | + | 0.930100i | \(0.380280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8570 | −1.59268 | −0.796340 | − | 0.604850i | \(-0.793233\pi\) | ||||
−0.796340 | + | 0.604850i | \(0.793233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 79.4422 | 2.75582 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.4356 | −0.465516 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.11496 | −0.211617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 90.4961 | 3.12800 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.8162 | 1.44366 | 0.721829 | − | 0.692072i | \(-0.243302\pi\) | ||||
0.721829 | + | 0.692072i | \(0.243302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.9499 | 1.03276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −60.1677 | −2.07229 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.2288 | −0.730295 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.09807 | 0.209532 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −89.2296 | −3.06235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.0461 | 1.13281 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.8933 | −0.886568 | −0.443284 | − | 0.896381i | \(-0.646187\pi\) | ||||
−0.443284 | + | 0.896381i | \(0.646187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.3282 | −0.729409 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.23515 | 0.178829 | 0.0894147 | − | 0.995994i | \(-0.471500\pi\) | ||||
0.0894147 | + | 0.995994i | \(0.471500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.0132 | 0.546363 | 0.273182 | − | 0.961962i | \(-0.411924\pi\) | ||||
0.273182 | + | 0.961962i | \(0.411924\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.3114 | 0.521812 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.1259 | 0.617014 | 0.308507 | − | 0.951222i | \(-0.400171\pi\) | ||||
0.308507 | + | 0.951222i | \(0.400171\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1749 | 0.583964 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.9536 | −1.08520 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.1290 | 0.411449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.84261 | −0.164085 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −50.7725 | −1.71839 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.4835 | 0.760082 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5933 | −0.661620 | −0.330810 | − | 0.943697i | \(-0.607322\pi\) | ||||
−0.330810 | + | 0.943697i | \(0.607322\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.2277 | 0.783452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.23899 | −0.0417428 | −0.0208714 | − | 0.999782i | \(-0.506644\pi\) | ||||
−0.0208714 | + | 0.999782i | \(0.506644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.4579 | 0.856727 | 0.428364 | − | 0.903606i | \(-0.359090\pi\) | ||||
0.428364 | + | 0.903606i | \(0.359090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 58.1898 | 1.95603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.1798 | −1.41626 | −0.708130 | − | 0.706083i | \(-0.750461\pi\) | ||||
−0.708130 | + | 0.706083i | \(0.750461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.7243 | 1.46646 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −75.1547 | −2.51778 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.1789 | −0.407553 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.56139 | −0.185897 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 96.7087 | 3.22901 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −53.2591 | −1.77629 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.9375 | 1.63034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 71.5839 | 2.38216 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.35259 | 0.244408 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.3862 | −0.743322 | −0.371661 | − | 0.928369i | \(-0.621212\pi\) | ||||
−0.371661 | + | 0.928369i | \(0.621212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.2853 | −0.705989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.8677 | −0.823904 | −0.411952 | − | 0.911206i | \(-0.635153\pi\) | ||||
−0.411952 | + | 0.911206i | \(0.635153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.7732 | −1.74654 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.1645 | 1.46003 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.60429 | −0.218093 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.7609 | 1.93834 | 0.969172 | − | 0.246386i | \(-0.0792432\pi\) | ||||
0.969172 | + | 0.246386i | \(0.0792432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.9517 | 2.23909 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −77.2378 | −2.54231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.8783 | 0.653594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 92.8127 | 3.04837 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.5440 | 1.42863 | 0.714317 | − | 0.699822i | \(-0.246738\pi\) | ||||
0.714317 | + | 0.699822i | \(0.246738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.06312 | −0.198711 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.6923 | −1.62685 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.8047 | 0.811199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.25779 | −0.0410903 | −0.0205451 | − | 0.999789i | \(-0.506540\pi\) | ||||
−0.0205451 | + | 0.999789i | \(0.506540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.9524 | 2.15227 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.1912 | −1.37539 | −0.687697 | − | 0.725998i | \(-0.741378\pi\) | ||||
−0.687697 | + | 0.725998i | \(0.741378\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.8175 | 0.417394 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35.0696 | 1.14081 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.4161 | 0.955894 | 0.477947 | − | 0.878389i | \(-0.341381\pi\) | ||||
0.477947 | + | 0.878389i | \(0.341381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.0674 | −1.49541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.99396 | 0.194367 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.24426 | −0.299451 | −0.149726 | − | 0.988728i | \(-0.547839\pi\) | ||||
−0.149726 | + | 0.988728i | \(0.547839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.33946 | −0.108062 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 90.9965 | 2.94150 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.59327 | 0.245199 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.1176 | 0.552180 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −74.6386 | −2.40519 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.5147 | 0.402863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5302 | 0.338627 | 0.169313 | − | 0.985562i | \(-0.445845\pi\) | ||||
0.169313 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.8057 | −1.24662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.1256 | −1.48024 | −0.740120 | − | 0.672475i | \(-0.765231\pi\) | ||||
−0.740120 | + | 0.672475i | \(0.765231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.6112 | 0.468414 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 58.1733 | 1.86304 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.5947 | −0.850841 | −0.425420 | − | 0.904996i | \(-0.639874\pi\) | ||||
−0.425420 | + | 0.904996i | \(0.639874\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.0308 | −0.831947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −70.2579 | −2.24316 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.9146 | −0.730861 | −0.365430 | − | 0.930839i | \(-0.619078\pi\) | ||||
−0.365430 | + | 0.930839i | \(0.619078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.2061 | −0.452645 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.6636 | 1.10335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 59.9241 | 1.90547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8112 | 1.29641 | 0.648205 | − | 0.761466i | \(-0.275520\pi\) | ||||
0.648205 | + | 0.761466i | \(0.275520\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.41249 | 0.266962 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.1246 | 1.05012 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.4399 | −0.330636 | −0.165318 | − | 0.986240i | \(-0.552865\pi\) | ||||
−0.165318 | + | 0.986240i | \(0.552865\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 77.0916 | 2.43907 |
(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 | 8012.2.a.a.1.6 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8012.2.a.a.1.6 | ✓ | 79 | 1.1 | even | 1 | trivial |