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: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.24285\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24285 | −1.58594 | −0.792968 | − | 0.609263i | \(-0.791465\pi\) | ||||
−0.792968 | + | 0.609263i | \(0.791465\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.03039 | 1.51519 | ||||||||
\(5\) | −3.33222 | −1.49021 | −0.745107 | − | 0.666945i | \(-0.767602\pi\) | ||||
−0.745107 | + | 0.666945i | \(0.767602\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.336371 | 0.127136 | 0.0635682 | − | 0.997977i | \(-0.479752\pi\) | ||||
0.0635682 | + | 0.997977i | \(0.479752\pi\) | |||||||
\(8\) | −2.31101 | −0.817066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.47368 | 2.36338 | ||||||||
\(11\) | −5.35570 | −1.61480 | −0.807402 | − | 0.590001i | \(-0.799127\pi\) | ||||
−0.807402 | + | 0.590001i | \(0.799127\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.46960 | −0.684944 | −0.342472 | − | 0.939528i | \(-0.611264\pi\) | ||||
−0.342472 | + | 0.939528i | \(0.611264\pi\) | |||||||
\(14\) | −0.754431 | −0.201630 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.877521 | −0.219380 | ||||||||
\(17\) | −3.61233 | −0.876118 | −0.438059 | − | 0.898946i | \(-0.644334\pi\) | ||||
−0.438059 | + | 0.898946i | \(0.644334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.53686 | −1.27024 | −0.635121 | − | 0.772413i | \(-0.719050\pi\) | ||||
−0.635121 | + | 0.772413i | \(0.719050\pi\) | |||||||
\(20\) | −10.0979 | −2.25796 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.0120 | 2.56098 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.10369 | 1.22074 | ||||||||
\(26\) | 5.53895 | 1.08628 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.01934 | 0.192636 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.47832 | 1.52275 | 0.761376 | − | 0.648311i | \(-0.224524\pi\) | ||||
0.761376 | + | 0.648311i | \(0.224524\pi\) | |||||||
\(32\) | 6.59017 | 1.16499 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.10192 | 1.38947 | ||||||||
\(35\) | −1.12086 | −0.189460 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.55887 | 1.57147 | 0.785734 | − | 0.618565i | \(-0.212285\pi\) | ||||
0.785734 | + | 0.618565i | \(0.212285\pi\) | |||||||
\(38\) | 12.4184 | 2.01452 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.70079 | 1.21760 | ||||||||
\(41\) | 11.0317 | 1.72287 | 0.861434 | − | 0.507870i | \(-0.169567\pi\) | ||||
0.861434 | + | 0.507870i | \(0.169567\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.41828 | 0.521282 | 0.260641 | − | 0.965436i | \(-0.416066\pi\) | ||||
0.260641 | + | 0.965436i | \(0.416066\pi\) | |||||||
\(44\) | −16.2299 | −2.44674 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.24285 | 0.330691 | ||||||||
\(47\) | 9.57079 | 1.39604 | 0.698022 | − | 0.716077i | \(-0.254064\pi\) | ||||
0.698022 | + | 0.716077i | \(0.254064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.88685 | −0.983836 | ||||||||
\(50\) | −13.6897 | −1.93601 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.48385 | −1.03782 | ||||||||
\(53\) | 6.66459 | 0.915452 | 0.457726 | − | 0.889093i | \(-0.348664\pi\) | ||||
0.457726 | + | 0.889093i | \(0.348664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.8464 | 2.40640 | ||||||||
\(56\) | −0.777358 | −0.103879 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.24285 | −0.294501 | ||||||||
\(59\) | 1.21308 | 0.157930 | 0.0789650 | − | 0.996877i | \(-0.474838\pi\) | ||||
0.0789650 | + | 0.996877i | \(0.474838\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.12445 | 0.912193 | 0.456096 | − | 0.889930i | \(-0.349247\pi\) | ||||
0.456096 | + | 0.889930i | \(0.349247\pi\) | |||||||
\(62\) | −19.0156 | −2.41499 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0257 | −1.62822 | ||||||||
\(65\) | 8.22926 | 1.02071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.16723 | 0.631278 | 0.315639 | − | 0.948879i | \(-0.397781\pi\) | ||||
0.315639 | + | 0.948879i | \(0.397781\pi\) | |||||||
\(68\) | −10.9468 | −1.32749 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.51393 | 0.300472 | ||||||||
\(71\) | −2.09303 | −0.248397 | −0.124199 | − | 0.992257i | \(-0.539636\pi\) | ||||
−0.124199 | + | 0.992257i | \(0.539636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2973 | −1.20520 | −0.602602 | − | 0.798042i | \(-0.705869\pi\) | ||||
−0.602602 | + | 0.798042i | \(0.705869\pi\) | |||||||
\(74\) | −21.4391 | −2.49225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.7788 | −1.92466 | ||||||||
\(77\) | −1.80150 | −0.205300 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.62841 | −0.408229 | −0.204114 | − | 0.978947i | \(-0.565431\pi\) | ||||
−0.204114 | + | 0.978947i | \(0.565431\pi\) | |||||||
\(80\) | 2.92409 | 0.326924 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24.7426 | −2.73236 | ||||||||
\(83\) | −12.6742 | −1.39117 | −0.695587 | − | 0.718442i | \(-0.744856\pi\) | ||||
−0.695587 | + | 0.718442i | \(0.744856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0371 | 1.30560 | ||||||||
\(86\) | −7.66669 | −0.826721 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.3771 | 1.31940 | ||||||||
\(89\) | −11.8040 | −1.25122 | −0.625611 | − | 0.780135i | \(-0.715150\pi\) | ||||
−0.625611 | + | 0.780135i | \(0.715150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.830703 | −0.0870814 | ||||||||
\(92\) | −3.03039 | −0.315940 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.4659 | −2.21404 | ||||||||
\(95\) | 18.4500 | 1.89293 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.01739 | −0.306369 | −0.153185 | − | 0.988198i | \(-0.548953\pi\) | ||||
−0.153185 | + | 0.988198i | \(0.548953\pi\) | |||||||
\(98\) | 15.4462 | 1.56030 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.4966 | 1.84966 | ||||||||
\(101\) | 16.5824 | 1.65001 | 0.825007 | − | 0.565122i | \(-0.191171\pi\) | ||||
0.825007 | + | 0.565122i | \(0.191171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.41290 | 0.631882 | 0.315941 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315941 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(104\) | 5.70728 | 0.559644 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.9477 | −1.45185 | ||||||||
\(107\) | −13.1923 | −1.27535 | −0.637673 | − | 0.770307i | \(-0.720103\pi\) | ||||
−0.637673 | + | 0.770307i | \(0.720103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5087 | −1.00655 | −0.503274 | − | 0.864127i | \(-0.667871\pi\) | ||||
−0.503274 | + | 0.864127i | \(0.667871\pi\) | |||||||
\(110\) | −40.0268 | −3.81640 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.295173 | −0.0278912 | ||||||||
\(113\) | −3.10892 | −0.292462 | −0.146231 | − | 0.989250i | \(-0.546714\pi\) | ||||
−0.146231 | + | 0.989250i | \(0.546714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.33222 | 0.310731 | ||||||||
\(116\) | 3.03039 | 0.281365 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.72077 | −0.250467 | ||||||||
\(119\) | −1.21508 | −0.111387 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6835 | 1.60759 | ||||||||
\(122\) | −15.9791 | −1.44668 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.6926 | 2.30726 | ||||||||
\(125\) | −3.67774 | −0.328947 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.8180 | 1.31489 | 0.657443 | − | 0.753504i | \(-0.271638\pi\) | ||||
0.657443 | + | 0.753504i | \(0.271638\pi\) | |||||||
\(128\) | 16.0345 | 1.41726 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.4570 | −1.61879 | ||||||||
\(131\) | −2.63363 | −0.230102 | −0.115051 | − | 0.993360i | \(-0.536703\pi\) | ||||
−0.115051 | + | 0.993360i | \(0.536703\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.86244 | −0.161494 | ||||||||
\(134\) | −11.5893 | −1.00117 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.34813 | 0.715846 | ||||||||
\(137\) | 11.2822 | 0.963901 | 0.481951 | − | 0.876198i | \(-0.339928\pi\) | ||||
0.481951 | + | 0.876198i | \(0.339928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.55731 | 0.301727 | 0.150863 | − | 0.988555i | \(-0.451795\pi\) | ||||
0.150863 | + | 0.988555i | \(0.451795\pi\) | |||||||
\(140\) | −3.39665 | −0.287069 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.69437 | 0.393942 | ||||||||
\(143\) | 13.2264 | 1.10605 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.33222 | −0.276726 | ||||||||
\(146\) | 23.0952 | 1.91138 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.9671 | 2.38108 | ||||||||
\(149\) | −14.5948 | −1.19565 | −0.597827 | − | 0.801625i | \(-0.703969\pi\) | ||||
−0.597827 | + | 0.801625i | \(0.703969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5847 | 1.51240 | 0.756202 | − | 0.654338i | \(-0.227053\pi\) | ||||
0.756202 | + | 0.654338i | \(0.227053\pi\) | |||||||
\(152\) | 12.7957 | 1.03787 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.04051 | 0.325593 | ||||||||
\(155\) | −28.2516 | −2.26923 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.26130 | −0.739132 | −0.369566 | − | 0.929204i | \(-0.620494\pi\) | ||||
−0.369566 | + | 0.929204i | \(0.620494\pi\) | |||||||
\(158\) | 8.13800 | 0.647425 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.9599 | −1.73608 | ||||||||
\(161\) | −0.336371 | −0.0265098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2102 | −1.66131 | −0.830655 | − | 0.556788i | \(-0.812034\pi\) | ||||
−0.830655 | + | 0.556788i | \(0.812034\pi\) | |||||||
\(164\) | 33.4304 | 2.61048 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.4264 | 2.20631 | ||||||||
\(167\) | 21.3627 | 1.65310 | 0.826549 | − | 0.562865i | \(-0.190301\pi\) | ||||
0.826549 | + | 0.562865i | \(0.190301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.90107 | −0.530851 | ||||||||
\(170\) | −26.9974 | −2.07060 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.3587 | 0.789844 | ||||||||
\(173\) | 10.6746 | 0.811578 | 0.405789 | − | 0.913967i | \(-0.366997\pi\) | ||||
0.405789 | + | 0.913967i | \(0.366997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.05311 | 0.155200 | ||||||||
\(176\) | 4.69974 | 0.354256 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.4746 | 1.98436 | ||||||||
\(179\) | 2.48471 | 0.185716 | 0.0928579 | − | 0.995679i | \(-0.470400\pi\) | ||||
0.0928579 | + | 0.995679i | \(0.470400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3160 | −0.766784 | −0.383392 | − | 0.923586i | \(-0.625244\pi\) | ||||
−0.383392 | + | 0.923586i | \(0.625244\pi\) | |||||||
\(182\) | 1.86315 | 0.138106 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.31101 | 0.170370 | ||||||||
\(185\) | −31.8522 | −2.34182 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.3466 | 1.41476 | ||||||||
\(188\) | 29.0032 | 2.11528 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −41.3807 | −3.00207 | ||||||||
\(191\) | 21.4183 | 1.54977 | 0.774886 | − | 0.632101i | \(-0.217807\pi\) | ||||
0.774886 | + | 0.632101i | \(0.217807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.7870 | −0.992409 | −0.496204 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496204 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(194\) | 6.76756 | 0.485882 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.8698 | −1.49070 | ||||||||
\(197\) | 15.4879 | 1.10347 | 0.551735 | − | 0.834019i | \(-0.313966\pi\) | ||||
0.551735 | + | 0.834019i | \(0.313966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.97074 | 0.352367 | 0.176183 | − | 0.984357i | \(-0.443625\pi\) | ||||
0.176183 | + | 0.984357i | \(0.443625\pi\) | |||||||
\(200\) | −14.1057 | −0.997423 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −37.1920 | −2.61682 | ||||||||
\(203\) | 0.336371 | 0.0236086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −36.7602 | −2.56744 | ||||||||
\(206\) | −14.3832 | −1.00212 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.16713 | 0.150263 | ||||||||
\(209\) | 29.6537 | 2.05119 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.1099 | −1.79748 | −0.898739 | − | 0.438484i | \(-0.855516\pi\) | ||||
−0.898739 | + | 0.438484i | \(0.855516\pi\) | |||||||
\(212\) | 20.1963 | 1.38709 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 29.5883 | 2.02262 | ||||||||
\(215\) | −11.3905 | −0.776823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.85186 | 0.193597 | ||||||||
\(218\) | 23.5694 | 1.59632 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 54.0814 | 3.64617 | ||||||||
\(221\) | 8.92101 | 0.600092 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.28206 | −0.554608 | −0.277304 | − | 0.960782i | \(-0.589441\pi\) | ||||
−0.277304 | + | 0.960782i | \(0.589441\pi\) | |||||||
\(224\) | 2.21675 | 0.148113 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.97284 | 0.463826 | ||||||||
\(227\) | 15.0362 | 0.997985 | 0.498992 | − | 0.866606i | \(-0.333704\pi\) | ||||
0.498992 | + | 0.866606i | \(0.333704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.35622 | −0.618277 | −0.309138 | − | 0.951017i | \(-0.600041\pi\) | ||||
−0.309138 | + | 0.951017i | \(0.600041\pi\) | |||||||
\(230\) | −7.47368 | −0.492800 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.31101 | −0.151725 | ||||||||
\(233\) | −1.51916 | −0.0995233 | −0.0497616 | − | 0.998761i | \(-0.515846\pi\) | ||||
−0.0497616 | + | 0.998761i | \(0.515846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.8920 | −2.08040 | ||||||||
\(236\) | 3.67612 | 0.239295 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.72525 | 0.176652 | ||||||||
\(239\) | 13.1287 | 0.849225 | 0.424612 | − | 0.905375i | \(-0.360410\pi\) | ||||
0.424612 | + | 0.905375i | \(0.360410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0253 | 1.67644 | 0.838218 | − | 0.545335i | \(-0.183598\pi\) | ||||
0.838218 | + | 0.545335i | \(0.183598\pi\) | |||||||
\(242\) | −39.6616 | −2.54954 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.5899 | 1.38215 | ||||||||
\(245\) | 22.9485 | 1.46613 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6738 | 0.870045 | ||||||||
\(248\) | −19.5935 | −1.24419 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.24863 | 0.521689 | ||||||||
\(251\) | −24.1425 | −1.52386 | −0.761932 | − | 0.647657i | \(-0.775749\pi\) | ||||
−0.761932 | + | 0.647657i | \(0.775749\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.35570 | 0.336710 | ||||||||
\(254\) | −33.2346 | −2.08533 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.91149 | −0.619468 | ||||||||
\(257\) | −23.1679 | −1.44518 | −0.722588 | − | 0.691279i | \(-0.757048\pi\) | ||||
−0.722588 | + | 0.691279i | \(0.757048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.21533 | 0.199791 | ||||||||
\(260\) | 24.9378 | 1.54658 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.90685 | 0.364927 | ||||||||
\(263\) | −11.8107 | −0.728277 | −0.364138 | − | 0.931345i | \(-0.618636\pi\) | ||||
−0.364138 | + | 0.931345i | \(0.618636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.2079 | −1.36422 | ||||||||
\(266\) | 4.17718 | 0.256119 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.6587 | 0.956508 | ||||||||
\(269\) | 8.58123 | 0.523207 | 0.261603 | − | 0.965175i | \(-0.415749\pi\) | ||||
0.261603 | + | 0.965175i | \(0.415749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0288 | −0.669952 | −0.334976 | − | 0.942227i | \(-0.608728\pi\) | ||||
−0.334976 | + | 0.942227i | \(0.608728\pi\) | |||||||
\(272\) | 3.16990 | 0.192203 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.3043 | −1.52869 | ||||||||
\(275\) | −32.6895 | −1.97125 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.78001 | 0.587624 | 0.293812 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293812 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(278\) | −7.97851 | −0.478520 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.59033 | 0.154802 | ||||||||
\(281\) | 2.79284 | 0.166607 | 0.0833034 | − | 0.996524i | \(-0.473453\pi\) | ||||
0.0833034 | + | 0.996524i | \(0.473453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.6337 | −1.34544 | −0.672718 | − | 0.739899i | \(-0.734873\pi\) | ||||
−0.672718 | + | 0.739899i | \(0.734873\pi\) | |||||||
\(284\) | −6.34270 | −0.376370 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.6650 | −1.75413 | ||||||||
\(287\) | 3.71076 | 0.219039 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.95108 | −0.232417 | ||||||||
\(290\) | 7.47368 | 0.438870 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −31.2047 | −1.82612 | ||||||||
\(293\) | −26.9534 | −1.57463 | −0.787316 | − | 0.616550i | \(-0.788530\pi\) | ||||
−0.787316 | + | 0.616550i | \(0.788530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.04226 | −0.235350 | ||||||||
\(296\) | −22.0906 | −1.28399 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 32.7340 | 1.89623 | ||||||||
\(299\) | 2.46960 | 0.142821 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14981 | 0.0662740 | ||||||||
\(302\) | −41.6828 | −2.39858 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.85871 | 0.278666 | ||||||||
\(305\) | −23.7402 | −1.35936 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5081 | 0.599727 | 0.299863 | − | 0.953982i | \(-0.403059\pi\) | ||||
0.299863 | + | 0.953982i | \(0.403059\pi\) | |||||||
\(308\) | −5.45926 | −0.311070 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 63.3643 | 3.59885 | ||||||||
\(311\) | −31.8702 | −1.80719 | −0.903596 | − | 0.428385i | \(-0.859083\pi\) | ||||
−0.903596 | + | 0.428385i | \(0.859083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3092 | −1.20446 | −0.602232 | − | 0.798321i | \(-0.705722\pi\) | ||||
−0.602232 | + | 0.798321i | \(0.705722\pi\) | |||||||
\(314\) | 20.7717 | 1.17222 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.9955 | −0.618546 | ||||||||
\(317\) | −13.6193 | −0.764935 | −0.382467 | − | 0.923969i | \(-0.624926\pi\) | ||||
−0.382467 | + | 0.923969i | \(0.624926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.35570 | −0.299862 | ||||||||
\(320\) | 43.4046 | 2.42639 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.754431 | 0.0420428 | ||||||||
\(323\) | 20.0009 | 1.11288 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0737 | −0.836138 | ||||||||
\(326\) | 47.5713 | 2.63473 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −25.4945 | −1.40770 | ||||||||
\(329\) | 3.21934 | 0.177488 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.92149 | −0.490370 | −0.245185 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245185 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(332\) | −38.4078 | −2.10790 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −47.9135 | −2.62171 | ||||||||
\(335\) | −17.2183 | −0.940739 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.68953 | 0.364402 | 0.182201 | − | 0.983261i | \(-0.441678\pi\) | ||||
0.182201 | + | 0.983261i | \(0.441678\pi\) | |||||||
\(338\) | 15.4781 | 0.841896 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36.4770 | 1.97824 | ||||||||
\(341\) | −45.4074 | −2.45895 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.67114 | −0.252218 | ||||||||
\(344\) | −7.89968 | −0.425922 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.9416 | −1.28711 | ||||||||
\(347\) | 10.4807 | 0.562635 | 0.281317 | − | 0.959615i | \(-0.409229\pi\) | ||||
0.281317 | + | 0.959615i | \(0.409229\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7281 | −1.16308 | −0.581538 | − | 0.813519i | \(-0.697549\pi\) | ||||
−0.581538 | + | 0.813519i | \(0.697549\pi\) | |||||||
\(350\) | −4.60482 | −0.246138 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35.2950 | −1.88123 | ||||||||
\(353\) | 24.6326 | 1.31106 | 0.655530 | − | 0.755169i | \(-0.272445\pi\) | ||||
0.655530 | + | 0.755169i | \(0.272445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.97445 | 0.370165 | ||||||||
\(356\) | −35.7707 | −1.89584 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.57284 | −0.294534 | ||||||||
\(359\) | 5.00818 | 0.264322 | 0.132161 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132161 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6568 | 0.613515 | ||||||||
\(362\) | 23.1373 | 1.21607 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.51735 | −0.131945 | ||||||||
\(365\) | 34.3127 | 1.79601 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.98074 | −0.312192 | −0.156096 | − | 0.987742i | \(-0.549891\pi\) | ||||
−0.156096 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(368\) | 0.877521 | 0.0457440 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 71.4399 | 3.71398 | ||||||||
\(371\) | 2.24178 | 0.116387 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.9060 | 1.34136 | 0.670680 | − | 0.741747i | \(-0.266002\pi\) | ||||
0.670680 | + | 0.741747i | \(0.266002\pi\) | |||||||
\(374\) | −43.3915 | −2.24372 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.1182 | −1.14066 | ||||||||
\(377\) | −2.46960 | −0.127191 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.7368 | 1.78431 | 0.892155 | − | 0.451729i | \(-0.149193\pi\) | ||||
0.892155 | + | 0.451729i | \(0.149193\pi\) | |||||||
\(380\) | 55.9107 | 2.86816 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −48.0380 | −2.45784 | ||||||||
\(383\) | 22.0435 | 1.12637 | 0.563184 | − | 0.826331i | \(-0.309576\pi\) | ||||
0.563184 | + | 0.826331i | \(0.309576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00301 | 0.305942 | ||||||||
\(386\) | 30.9222 | 1.57390 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.14386 | −0.464209 | ||||||||
\(389\) | 10.7238 | 0.543716 | 0.271858 | − | 0.962337i | \(-0.412362\pi\) | ||||
0.271858 | + | 0.962337i | \(0.412362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.61233 | 0.182683 | ||||||||
\(392\) | 15.9156 | 0.803859 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.7372 | −1.75003 | ||||||||
\(395\) | 12.0907 | 0.608348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.85754 | −0.394358 | −0.197179 | − | 0.980367i | \(-0.563178\pi\) | ||||
−0.197179 | + | 0.980367i | \(0.563178\pi\) | |||||||
\(398\) | −11.1486 | −0.558831 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.35612 | −0.267806 | ||||||||
\(401\) | −15.0606 | −0.752089 | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.9381 | −1.04300 | ||||||||
\(404\) | 50.2512 | 2.50009 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.754431 | −0.0374418 | ||||||||
\(407\) | −51.1944 | −2.53761 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.3347 | 1.45051 | 0.725253 | − | 0.688483i | \(-0.241723\pi\) | ||||
0.725253 | + | 0.688483i | \(0.241723\pi\) | |||||||
\(410\) | 82.4476 | 4.07180 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.4336 | 0.957424 | ||||||||
\(413\) | 0.408047 | 0.0200787 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.2332 | 2.07315 | ||||||||
\(416\) | −16.2751 | −0.797952 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −66.5090 | −3.25306 | ||||||||
\(419\) | 28.4982 | 1.39223 | 0.696114 | − | 0.717931i | \(-0.254911\pi\) | ||||
0.696114 | + | 0.717931i | \(0.254911\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1838 | 0.642540 | 0.321270 | − | 0.946988i | \(-0.395890\pi\) | ||||
0.321270 | + | 0.946988i | \(0.395890\pi\) | |||||||
\(422\) | 58.5606 | 2.85069 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.4019 | −0.747984 | ||||||||
\(425\) | −22.0485 | −1.06951 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.39646 | 0.115973 | ||||||||
\(428\) | −39.9777 | −1.93240 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.5471 | 1.23199 | ||||||||
\(431\) | −21.0595 | −1.01440 | −0.507200 | − | 0.861829i | \(-0.669319\pi\) | ||||
−0.507200 | + | 0.861829i | \(0.669319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.6426 | −1.42453 | −0.712267 | − | 0.701909i | \(-0.752331\pi\) | ||||
−0.712267 | + | 0.701909i | \(0.752331\pi\) | |||||||
\(434\) | −6.39631 | −0.307033 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.8454 | −1.52512 | ||||||||
\(437\) | 5.53686 | 0.264864 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1064 | 0.864171 | 0.432086 | − | 0.901833i | \(-0.357778\pi\) | ||||
0.432086 | + | 0.901833i | \(0.357778\pi\) | |||||||
\(440\) | −41.2432 | −1.96619 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.0085 | −0.951708 | ||||||||
\(443\) | −20.7008 | −0.983527 | −0.491763 | − | 0.870729i | \(-0.663647\pi\) | ||||
−0.491763 | + | 0.870729i | \(0.663647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.3335 | 1.86459 | ||||||||
\(446\) | 18.5754 | 0.879573 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.38149 | −0.207006 | ||||||||
\(449\) | 13.6101 | 0.642301 | 0.321150 | − | 0.947028i | \(-0.395931\pi\) | ||||
0.321150 | + | 0.947028i | \(0.395931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −59.0827 | −2.78209 | ||||||||
\(452\) | −9.42122 | −0.443137 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −33.7239 | −1.58274 | ||||||||
\(455\) | 2.76809 | 0.129770 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.36067 | 0.203984 | 0.101992 | − | 0.994785i | \(-0.467478\pi\) | ||||
0.101992 | + | 0.994785i | \(0.467478\pi\) | |||||||
\(458\) | 20.9846 | 0.980548 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.0979 | 0.470818 | ||||||||
\(461\) | −1.61989 | −0.0754459 | −0.0377230 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377230 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.152373 | −0.00708136 | −0.00354068 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354068 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(464\) | −0.877521 | −0.0407379 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.40725 | 0.157838 | ||||||||
\(467\) | −25.7057 | −1.18952 | −0.594758 | − | 0.803904i | \(-0.702752\pi\) | ||||
−0.594758 | + | 0.803904i | \(0.702752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.73811 | 0.0802584 | ||||||||
\(470\) | 71.5290 | 3.29939 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.80345 | −0.129039 | ||||||||
\(473\) | −18.3073 | −0.841769 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.7953 | −1.55063 | ||||||||
\(476\) | −3.68218 | −0.168772 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.4457 | −1.34682 | ||||||||
\(479\) | −5.89195 | −0.269210 | −0.134605 | − | 0.990899i | \(-0.542977\pi\) | ||||
−0.134605 | + | 0.990899i | \(0.542977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.6066 | −1.07637 | ||||||||
\(482\) | −58.3709 | −2.65872 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 53.5880 | 2.43582 | ||||||||
\(485\) | 10.0546 | 0.456556 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.3733 | −1.42166 | −0.710831 | − | 0.703363i | \(-0.751681\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(488\) | −16.4647 | −0.745321 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −51.4701 | −2.32518 | ||||||||
\(491\) | −2.87963 | −0.129956 | −0.0649778 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649778 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.61233 | −0.162691 | ||||||||
\(494\) | −30.6684 | −1.37984 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.43991 | −0.334062 | ||||||||
\(497\) | −0.704036 | −0.0315804 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.8494 | 1.96297 | 0.981484 | − | 0.191542i | \(-0.0613489\pi\) | ||||
0.981484 | + | 0.191542i | \(0.0613489\pi\) | |||||||
\(500\) | −11.1450 | −0.498419 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 54.1482 | 2.41675 | ||||||||
\(503\) | 41.9172 | 1.86900 | 0.934498 | − | 0.355969i | \(-0.115849\pi\) | ||||
0.934498 | + | 0.355969i | \(0.115849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.2563 | −2.45887 | ||||||||
\(506\) | −12.0120 | −0.534001 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 44.9044 | 1.99231 | ||||||||
\(509\) | 15.4761 | 0.685966 | 0.342983 | − | 0.939342i | \(-0.388563\pi\) | ||||
0.342983 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.46370 | −0.153225 | ||||||||
\(512\) | −9.83894 | −0.434824 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 51.9623 | 2.29196 | ||||||||
\(515\) | −21.3692 | −0.941640 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.2583 | −2.25434 | ||||||||
\(518\) | −7.21151 | −0.316856 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.0179 | −0.833990 | ||||||||
\(521\) | −1.20679 | −0.0528705 | −0.0264352 | − | 0.999651i | \(-0.508416\pi\) | ||||
−0.0264352 | + | 0.999651i | \(0.508416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.84819 | −0.386905 | −0.193452 | − | 0.981110i | \(-0.561968\pi\) | ||||
−0.193452 | + | 0.981110i | \(0.561968\pi\) | |||||||
\(524\) | −7.98094 | −0.348649 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.4896 | 1.15500 | ||||||||
\(527\) | −30.6265 | −1.33411 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 49.8090 | 2.16357 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.64392 | −0.244695 | ||||||||
\(533\) | −27.2440 | −1.18007 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.9596 | 1.90054 | ||||||||
\(536\) | −11.9415 | −0.515795 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.2464 | −0.829772 | ||||||||
\(539\) | 36.8839 | 1.58870 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.1794 | 0.953567 | 0.476783 | − | 0.879021i | \(-0.341803\pi\) | ||||
0.476783 | + | 0.879021i | \(0.341803\pi\) | |||||||
\(542\) | 24.7360 | 1.06250 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.8059 | −1.02067 | ||||||||
\(545\) | 35.0172 | 1.49997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7728 | 0.973697 | 0.486848 | − | 0.873486i | \(-0.338146\pi\) | ||||
0.486848 | + | 0.873486i | \(0.338146\pi\) | |||||||
\(548\) | 34.1894 | 1.46050 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 73.3178 | 3.12628 | ||||||||
\(551\) | −5.53686 | −0.235878 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.22049 | −0.0519007 | ||||||||
\(554\) | −21.9351 | −0.931934 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.7800 | 0.457175 | ||||||||
\(557\) | −0.846399 | −0.0358631 | −0.0179315 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179315 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.44179 | −0.357049 | ||||||||
\(560\) | 0.983582 | 0.0415639 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.26393 | −0.264228 | ||||||||
\(563\) | 40.0831 | 1.68930 | 0.844650 | − | 0.535318i | \(-0.179808\pi\) | ||||
0.844650 | + | 0.535318i | \(0.179808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3596 | 0.435831 | ||||||||
\(566\) | 50.7641 | 2.13378 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.83702 | 0.202957 | ||||||||
\(569\) | −23.3038 | −0.976945 | −0.488472 | − | 0.872579i | \(-0.662446\pi\) | ||||
−0.488472 | + | 0.872579i | \(0.662446\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.411433 | −0.0172179 | −0.00860896 | − | 0.999963i | \(-0.502740\pi\) | ||||
−0.00860896 | + | 0.999963i | \(0.502740\pi\) | |||||||
\(572\) | 40.0813 | 1.67588 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.32269 | −0.347382 | ||||||||
\(575\) | −6.10369 | −0.254541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5456 | −0.563910 | −0.281955 | − | 0.959428i | \(-0.590983\pi\) | ||||
−0.281955 | + | 0.959428i | \(0.590983\pi\) | |||||||
\(578\) | 8.86169 | 0.368598 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.0979 | −0.419293 | ||||||||
\(581\) | −4.26324 | −0.176869 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.6936 | −1.47828 | ||||||||
\(584\) | 23.7971 | 0.984730 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 60.4524 | 2.49727 | ||||||||
\(587\) | −33.9417 | −1.40092 | −0.700461 | − | 0.713690i | \(-0.747022\pi\) | ||||
−0.700461 | + | 0.713690i | \(0.747022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −46.9433 | −1.93426 | ||||||||
\(590\) | 9.06620 | 0.373250 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.38811 | −0.344749 | ||||||||
\(593\) | 35.4814 | 1.45705 | 0.728524 | − | 0.685021i | \(-0.240207\pi\) | ||||
0.728524 | + | 0.685021i | \(0.240207\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.04893 | 0.165990 | ||||||||
\(596\) | −44.2280 | −1.81165 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.53895 | −0.226505 | ||||||||
\(599\) | −39.5554 | −1.61619 | −0.808094 | − | 0.589054i | \(-0.799501\pi\) | ||||
−0.808094 | + | 0.589054i | \(0.799501\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7875 | 0.643984 | 0.321992 | − | 0.946742i | \(-0.395648\pi\) | ||||
0.321992 | + | 0.946742i | \(0.395648\pi\) | |||||||
\(602\) | −2.57886 | −0.105106 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 56.3190 | 2.29159 | ||||||||
\(605\) | −58.9254 | −2.39566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.3376 | 0.947244 | 0.473622 | − | 0.880728i | \(-0.342946\pi\) | ||||
0.473622 | + | 0.880728i | \(0.342946\pi\) | |||||||
\(608\) | −36.4888 | −1.47982 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 53.2459 | 2.15586 | ||||||||
\(611\) | −23.6360 | −0.956212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.7636 | −1.52526 | −0.762628 | − | 0.646837i | \(-0.776091\pi\) | ||||
−0.762628 | + | 0.646837i | \(0.776091\pi\) | |||||||
\(614\) | −23.5680 | −0.951129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.16329 | 0.167744 | ||||||||
\(617\) | 19.3263 | 0.778046 | 0.389023 | − | 0.921228i | \(-0.372813\pi\) | ||||
0.389023 | + | 0.921228i | \(0.372813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.2999 | 1.61979 | 0.809894 | − | 0.586576i | \(-0.199524\pi\) | ||||
0.809894 | + | 0.586576i | \(0.199524\pi\) | |||||||
\(620\) | −85.6134 | −3.43832 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 71.4801 | 2.86609 | ||||||||
\(623\) | −3.97053 | −0.159076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.2634 | −0.730537 | ||||||||
\(626\) | 47.7933 | 1.91020 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.0653 | −1.11993 | ||||||||
\(629\) | −34.5298 | −1.37679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.24160 | −0.168855 | −0.0844276 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844276 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(632\) | 8.38530 | 0.333549 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.5460 | 1.21314 | ||||||||
\(635\) | −49.3769 | −1.95946 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0078 | 0.673873 | ||||||||
\(638\) | 12.0120 | 0.475562 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −53.4304 | −2.11202 | ||||||||
\(641\) | −14.6358 | −0.578080 | −0.289040 | − | 0.957317i | \(-0.593336\pi\) | ||||
−0.289040 | + | 0.957317i | \(0.593336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.97033 | −0.314319 | −0.157159 | − | 0.987573i | \(-0.550234\pi\) | ||||
−0.157159 | + | 0.987573i | \(0.550234\pi\) | |||||||
\(644\) | −1.01934 | −0.0401675 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −44.8592 | −1.76496 | ||||||||
\(647\) | 0.258751 | 0.0101726 | 0.00508628 | − | 0.999987i | \(-0.498381\pi\) | ||||
0.00508628 | + | 0.999987i | \(0.498381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.49691 | −0.255026 | ||||||||
\(650\) | 33.8081 | 1.32606 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −64.2751 | −2.51721 | ||||||||
\(653\) | −25.8829 | −1.01288 | −0.506438 | − | 0.862276i | \(-0.669038\pi\) | ||||
−0.506438 | + | 0.862276i | \(0.669038\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.77585 | 0.342901 | ||||||||
\(656\) | −9.68058 | −0.377963 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.22051 | −0.281485 | ||||||||
\(659\) | 2.80499 | 0.109267 | 0.0546335 | − | 0.998506i | \(-0.482601\pi\) | ||||
0.0546335 | + | 0.998506i | \(0.482601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.3102 | 1.29562 | 0.647809 | − | 0.761803i | \(-0.275685\pi\) | ||||
0.647809 | + | 0.761803i | \(0.275685\pi\) | |||||||
\(662\) | 20.0096 | 0.777695 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.2902 | 1.13668 | ||||||||
\(665\) | 6.20606 | 0.240661 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 64.7374 | 2.50476 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38.6182 | 1.49195 | ||||||||
\(671\) | −38.1564 | −1.47301 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.265368 | −0.0102292 | −0.00511459 | − | 0.999987i | \(-0.501628\pi\) | ||||
−0.00511459 | + | 0.999987i | \(0.501628\pi\) | |||||||
\(674\) | −15.0036 | −0.577918 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.9129 | −0.804343 | ||||||||
\(677\) | −16.0535 | −0.616987 | −0.308494 | − | 0.951226i | \(-0.599825\pi\) | ||||
−0.308494 | + | 0.951226i | \(0.599825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.01496 | −0.0389507 | ||||||||
\(680\) | −27.8178 | −1.06676 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 101.842 | 3.89973 | ||||||||
\(683\) | −32.7737 | −1.25405 | −0.627025 | − | 0.778999i | \(-0.715728\pi\) | ||||
−0.627025 | + | 0.778999i | \(0.715728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.5947 | −1.43642 | ||||||||
\(686\) | 10.4767 | 0.400001 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.99961 | −0.114359 | ||||||||
\(689\) | −16.4589 | −0.627034 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.9477 | 1.74793 | 0.873966 | − | 0.485986i | \(-0.161540\pi\) | ||||
0.873966 | + | 0.485986i | \(0.161540\pi\) | |||||||
\(692\) | 32.3483 | 1.22970 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.5067 | −0.892303 | ||||||||
\(695\) | −11.8537 | −0.449638 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.8503 | −1.50944 | ||||||||
\(698\) | 48.7328 | 1.84457 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.22171 | 0.235159 | ||||||||
\(701\) | 11.1726 | 0.421984 | 0.210992 | − | 0.977488i | \(-0.432331\pi\) | ||||
0.210992 | + | 0.977488i | \(0.432331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −52.9261 | −1.99614 | ||||||||
\(704\) | 69.7620 | 2.62925 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −55.2473 | −2.07926 | ||||||||
\(707\) | 5.57786 | 0.209777 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.376876 | −0.0141539 | −0.00707693 | − | 0.999975i | \(-0.502253\pi\) | ||||
−0.00707693 | + | 0.999975i | \(0.502253\pi\) | |||||||
\(710\) | −15.6427 | −0.587059 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.2792 | 1.02233 | ||||||||
\(713\) | −8.47832 | −0.317516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.0734 | −1.64825 | ||||||||
\(716\) | 7.52963 | 0.281396 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.2326 | −0.419198 | ||||||||
\(719\) | −33.2548 | −1.24020 | −0.620098 | − | 0.784525i | \(-0.712907\pi\) | ||||
−0.620098 | + | 0.784525i | \(0.712907\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.15712 | 0.0803352 | ||||||||
\(722\) | −26.1444 | −0.972995 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −31.2616 | −1.16183 | ||||||||
\(725\) | 6.10369 | 0.226685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5234 | −0.390293 | −0.195146 | − | 0.980774i | \(-0.562518\pi\) | ||||
−0.195146 | + | 0.980774i | \(0.562518\pi\) | |||||||
\(728\) | 1.91976 | 0.0711512 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −76.9584 | −2.84836 | ||||||||
\(731\) | −12.3479 | −0.456705 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.1253 | −0.632536 | −0.316268 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316268 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(734\) | 13.4139 | 0.495117 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.59017 | −0.242917 | ||||||||
\(737\) | −27.6741 | −1.01939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.9535 | 0.770788 | 0.385394 | − | 0.922752i | \(-0.374065\pi\) | ||||
0.385394 | + | 0.922752i | \(0.374065\pi\) | |||||||
\(740\) | −96.5247 | −3.54832 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.02798 | −0.184583 | ||||||||
\(743\) | −15.7655 | −0.578381 | −0.289190 | − | 0.957272i | \(-0.593386\pi\) | ||||
−0.289190 | + | 0.957272i | \(0.593386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.6332 | 1.78178 | ||||||||
\(746\) | −58.1033 | −2.12731 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 58.6276 | 2.14364 | ||||||||
\(749\) | −4.43750 | −0.162143 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8709 | 1.49140 | 0.745700 | − | 0.666282i | \(-0.232115\pi\) | ||||
0.745700 | + | 0.666282i | \(0.232115\pi\) | |||||||
\(752\) | −8.39858 | −0.306265 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.53895 | 0.201717 | ||||||||
\(755\) | −61.9284 | −2.25381 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.3932 | 1.35908 | 0.679539 | − | 0.733639i | \(-0.262180\pi\) | ||||
0.679539 | + | 0.733639i | \(0.262180\pi\) | |||||||
\(758\) | −77.9096 | −2.82980 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −42.6382 | −1.54665 | ||||||||
\(761\) | 12.0596 | 0.437161 | 0.218581 | − | 0.975819i | \(-0.429857\pi\) | ||||
0.218581 | + | 0.975819i | \(0.429857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.53482 | −0.127969 | ||||||||
\(764\) | 64.9057 | 2.34820 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −49.4402 | −1.78635 | ||||||||
\(767\) | −2.99583 | −0.108173 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8157 | 1.00306 | 0.501531 | − | 0.865140i | \(-0.332770\pi\) | ||||
0.501531 | + | 0.865140i | \(0.332770\pi\) | |||||||
\(770\) | −13.4639 | −0.485204 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41.7799 | −1.50369 | ||||||||
\(773\) | 12.1443 | 0.436801 | 0.218401 | − | 0.975859i | \(-0.429916\pi\) | ||||
0.218401 | + | 0.975859i | \(0.429916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.7491 | 1.85888 | ||||||||
\(776\) | 6.97321 | 0.250324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0518 | −0.862299 | ||||||||
\(779\) | −61.0811 | −2.18846 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2097 | 0.401113 | ||||||||
\(782\) | −8.10192 | −0.289724 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.04336 | 0.215834 | ||||||||
\(785\) | 30.8607 | 1.10147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.7378 | −0.667929 | −0.333964 | − | 0.942586i | \(-0.608387\pi\) | ||||
−0.333964 | + | 0.942586i | \(0.608387\pi\) | |||||||
\(788\) | 46.9345 | 1.67197 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.1176 | −0.964801 | ||||||||
\(791\) | −1.04575 | −0.0371826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5946 | −0.624801 | ||||||||
\(794\) | 17.6233 | 0.625427 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.0633 | 0.533904 | ||||||||
\(797\) | −26.9033 | −0.952964 | −0.476482 | − | 0.879184i | \(-0.658088\pi\) | ||||
−0.476482 | + | 0.879184i | \(0.658088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.5728 | −1.22310 | ||||||||
\(800\) | 40.2244 | 1.42215 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.7786 | 1.19277 | ||||||||
\(803\) | 55.1490 | 1.94617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.12086 | 0.0395052 | ||||||||
\(806\) | 46.9610 | 1.65413 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −38.3222 | −1.34817 | ||||||||
\(809\) | 25.3753 | 0.892147 | 0.446073 | − | 0.894996i | \(-0.352822\pi\) | ||||
0.446073 | + | 0.894996i | \(0.352822\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.9252 | −0.945471 | −0.472736 | − | 0.881204i | \(-0.656733\pi\) | ||||
−0.472736 | + | 0.881204i | \(0.656733\pi\) | |||||||
\(812\) | 1.01934 | 0.0357717 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 114.822 | 4.02449 | ||||||||
\(815\) | 70.6770 | 2.47571 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.9265 | −0.662155 | ||||||||
\(818\) | −65.7933 | −2.30041 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.398 | −3.89017 | ||||||||
\(821\) | 24.9489 | 0.870722 | 0.435361 | − | 0.900256i | \(-0.356621\pi\) | ||||
0.435361 | + | 0.900256i | \(0.356621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.2224 | 0.739765 | 0.369882 | − | 0.929079i | \(-0.379398\pi\) | ||||
0.369882 | + | 0.929079i | \(0.379398\pi\) | |||||||
\(824\) | −14.8203 | −0.516289 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.915189 | −0.0318435 | ||||||||
\(827\) | −13.9717 | −0.485844 | −0.242922 | − | 0.970046i | \(-0.578106\pi\) | ||||
−0.242922 | + | 0.970046i | \(0.578106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.62458 | 0.195350 | 0.0976748 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976748 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(830\) | −94.7229 | −3.28788 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.1684 | 1.11524 | ||||||||
\(833\) | 24.8776 | 0.861957 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −71.1853 | −2.46347 | ||||||||
\(836\) | 89.8624 | 3.10796 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −63.9173 | −2.20799 | ||||||||
\(839\) | −47.4932 | −1.63965 | −0.819824 | − | 0.572616i | \(-0.805929\pi\) | ||||
−0.819824 | + | 0.572616i | \(0.805929\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −29.5693 | −1.01903 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −79.1231 | −2.72353 | ||||||||
\(845\) | 22.9959 | 0.791082 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.94823 | 0.204384 | ||||||||
\(848\) | −5.84832 | −0.200832 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 49.4516 | 1.69618 | ||||||||
\(851\) | −9.55887 | −0.327674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5035 | −0.359634 | −0.179817 | − | 0.983700i | \(-0.557550\pi\) | ||||
−0.179817 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(854\) | −5.37491 | −0.183926 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.4875 | 1.04204 | ||||||||
\(857\) | 21.3106 | 0.727956 | 0.363978 | − | 0.931407i | \(-0.381418\pi\) | ||||
0.363978 | + | 0.931407i | \(0.381418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.9655 | −0.749452 | −0.374726 | − | 0.927136i | \(-0.622263\pi\) | ||||
−0.374726 | + | 0.927136i | \(0.622263\pi\) | |||||||
\(860\) | −34.5175 | −1.17704 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.2333 | 1.60877 | ||||||||
\(863\) | −50.0442 | −1.70353 | −0.851763 | − | 0.523928i | \(-0.824466\pi\) | ||||
−0.851763 | + | 0.523928i | \(0.824466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.5702 | −1.20942 | ||||||||
\(866\) | 66.4841 | 2.25922 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.64226 | 0.293337 | ||||||||
\(869\) | 19.4327 | 0.659209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.7610 | −0.432390 | ||||||||
\(872\) | 24.2857 | 0.822416 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.4184 | −0.420057 | ||||||||
\(875\) | −1.23709 | −0.0418211 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.3344 | −0.889248 | −0.444624 | − | 0.895717i | \(-0.646663\pi\) | ||||
−0.444624 | + | 0.895717i | \(0.646663\pi\) | |||||||
\(878\) | −40.6100 | −1.37052 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15.6606 | −0.527918 | ||||||||
\(881\) | −53.3563 | −1.79762 | −0.898809 | − | 0.438340i | \(-0.855567\pi\) | ||||
−0.898809 | + | 0.438340i | \(0.855567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.46924 | 0.0830966 | 0.0415483 | − | 0.999136i | \(-0.486771\pi\) | ||||
0.0415483 | + | 0.999136i | \(0.486771\pi\) | |||||||
\(884\) | 27.0341 | 0.909256 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.4289 | 1.55981 | ||||||||
\(887\) | −53.9526 | −1.81155 | −0.905776 | − | 0.423757i | \(-0.860711\pi\) | ||||
−0.905776 | + | 0.423757i | \(0.860711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.98436 | 0.167170 | ||||||||
\(890\) | −88.2193 | −2.95712 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.0979 | −0.840339 | ||||||||
\(893\) | −52.9921 | −1.77331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.27960 | −0.276756 | ||||||||
\(896\) | 5.39354 | 0.180186 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.5255 | −1.01865 | ||||||||
\(899\) | 8.47832 | 0.282768 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0747 | −0.802044 | ||||||||
\(902\) | 132.514 | 4.41222 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.18474 | 0.238961 | ||||||||
\(905\) | 34.3753 | 1.14267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.54378 | 0.150874 | 0.0754368 | − | 0.997151i | \(-0.475965\pi\) | ||||
0.0754368 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(908\) | 45.5654 | 1.51214 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.20841 | −0.205807 | ||||||||
\(911\) | 14.6485 | 0.485327 | 0.242664 | − | 0.970110i | \(-0.421979\pi\) | ||||
0.242664 | + | 0.970110i | \(0.421979\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 67.8792 | 2.24647 | ||||||||
\(914\) | −9.78035 | −0.323505 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.3530 | −0.936809 | ||||||||
\(917\) | −0.885879 | −0.0292543 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7669 | 0.487114 | 0.243557 | − | 0.969887i | \(-0.421686\pi\) | ||||
0.243557 | + | 0.969887i | \(0.421686\pi\) | |||||||
\(920\) | −7.70079 | −0.253888 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.63318 | 0.119652 | ||||||||
\(923\) | 5.16896 | 0.170138 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 58.3444 | 1.91835 | ||||||||
\(926\) | 0.341750 | 0.0112306 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.59017 | 0.216333 | ||||||||
\(929\) | 27.7957 | 0.911947 | 0.455973 | − | 0.889993i | \(-0.349291\pi\) | ||||
0.455973 | + | 0.889993i | \(0.349291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.1315 | 1.24971 | ||||||||
\(932\) | −4.60364 | −0.150797 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 57.6541 | 1.88650 | ||||||||
\(935\) | −64.4670 | −2.10830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.42265 | 0.242487 | 0.121244 | − | 0.992623i | \(-0.461312\pi\) | ||||
0.121244 | + | 0.992623i | \(0.461312\pi\) | |||||||
\(938\) | −3.89832 | −0.127285 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −96.6451 | −3.15222 | ||||||||
\(941\) | −42.6205 | −1.38939 | −0.694695 | − | 0.719305i | \(-0.744461\pi\) | ||||
−0.694695 | + | 0.719305i | \(0.744461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0317 | −0.359243 | ||||||||
\(944\) | −1.06451 | −0.0346468 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.0605 | 1.33499 | ||||||||
\(947\) | −18.8970 | −0.614069 | −0.307035 | − | 0.951698i | \(-0.599337\pi\) | ||||
−0.307035 | + | 0.951698i | \(0.599337\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.4301 | 0.825497 | ||||||||
\(950\) | 75.7978 | 2.45920 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.80807 | 0.0910101 | ||||||||
\(953\) | 4.93984 | 0.160017 | 0.0800086 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800086 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −71.3704 | −2.30949 | ||||||||
\(956\) | 39.7851 | 1.28674 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.2148 | 0.426950 | ||||||||
\(959\) | 3.79500 | 0.122547 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.8820 | 1.31877 | ||||||||
\(962\) | 52.9461 | 1.70705 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 78.8667 | 2.54013 | ||||||||
\(965\) | 45.9413 | 1.47890 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.7015 | 1.14808 | 0.574041 | − | 0.818827i | \(-0.305375\pi\) | ||||
0.574041 | + | 0.818827i | \(0.305375\pi\) | |||||||
\(968\) | −40.8668 | −1.31351 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.5510 | −0.724069 | ||||||||
\(971\) | −57.8911 | −1.85781 | −0.928906 | − | 0.370315i | \(-0.879250\pi\) | ||||
−0.928906 | + | 0.370315i | \(0.879250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.19658 | 0.0383605 | ||||||||
\(974\) | 70.3658 | 2.25467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.25186 | −0.200117 | ||||||||
\(977\) | 24.1856 | 0.773766 | 0.386883 | − | 0.922129i | \(-0.373552\pi\) | ||||
0.386883 | + | 0.922129i | \(0.373552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.2187 | 2.02048 | ||||||||
\(980\) | 69.5429 | 2.22147 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.45858 | 0.206101 | ||||||||
\(983\) | 30.1771 | 0.962500 | 0.481250 | − | 0.876583i | \(-0.340183\pi\) | ||||
0.481250 | + | 0.876583i | \(0.340183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.6092 | −1.64441 | ||||||||
\(986\) | 8.10192 | 0.258018 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 41.4370 | 1.31829 | ||||||||
\(989\) | −3.41828 | −0.108695 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1655 | 0.767642 | 0.383821 | − | 0.923407i | \(-0.374608\pi\) | ||||
0.383821 | + | 0.923407i | \(0.374608\pi\) | |||||||
\(992\) | 55.8736 | 1.77399 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.57905 | 0.0500844 | ||||||||
\(995\) | −16.5636 | −0.525102 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.3183 | −1.05520 | −0.527600 | − | 0.849493i | \(-0.676908\pi\) | ||||
−0.527600 | + | 0.849493i | \(0.676908\pi\) | |||||||
\(998\) | −98.3478 | −3.11314 | ||||||||
\(999\) | 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.m.1.3 | 11 | ||
3.2 | odd | 2 | 2001.2.a.l.1.9 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.9 | ✓ | 11 | 3.2 | odd | 2 | ||
6003.2.a.m.1.3 | 11 | 1.1 | even | 1 | trivial |