Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93234 | 1.36637 | 0.683184 | − | 0.730246i | \(-0.260595\pi\) | ||||
0.683184 | + | 0.730246i | \(0.260595\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73393 | 0.866963 | ||||||||
\(5\) | 2.82056 | 1.26139 | 0.630696 | − | 0.776030i | \(-0.282770\pi\) | ||||
0.630696 | + | 0.776030i | \(0.282770\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.97268 | −1.50153 | −0.750766 | − | 0.660568i | \(-0.770316\pi\) | ||||
−0.750766 | + | 0.660568i | \(0.770316\pi\) | |||||||
\(8\) | −0.514145 | −0.181778 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.45026 | 1.72352 | ||||||||
\(11\) | 4.70087 | 1.41737 | 0.708683 | − | 0.705527i | \(-0.249290\pi\) | ||||
0.708683 | + | 0.705527i | \(0.249290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.71953 | −1.58631 | −0.793156 | − | 0.609018i | \(-0.791564\pi\) | ||||
−0.793156 | + | 0.609018i | \(0.791564\pi\) | |||||||
\(14\) | −7.67656 | −2.05165 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.46135 | −1.11534 | ||||||||
\(17\) | −5.11092 | −1.23958 | −0.619790 | − | 0.784768i | \(-0.712782\pi\) | ||||
−0.619790 | + | 0.784768i | \(0.712782\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.224637 | 0.0515353 | 0.0257676 | − | 0.999668i | \(-0.491797\pi\) | ||||
0.0257676 | + | 0.999668i | \(0.491797\pi\) | |||||||
\(20\) | 4.89063 | 1.09358 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.08366 | 1.93664 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.95554 | 0.591107 | ||||||||
\(26\) | −11.0521 | −2.16749 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.88834 | −1.30177 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.16107 | 0.926956 | 0.463478 | − | 0.886108i | \(-0.346601\pi\) | ||||
0.463478 | + | 0.886108i | \(0.346601\pi\) | |||||||
\(32\) | −7.59255 | −1.34219 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.87602 | −1.69372 | ||||||||
\(35\) | −11.2052 | −1.89402 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.77440 | −0.949305 | −0.474652 | − | 0.880173i | \(-0.657426\pi\) | ||||
−0.474652 | + | 0.880173i | \(0.657426\pi\) | |||||||
\(38\) | 0.434074 | 0.0704162 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.45017 | −0.229293 | ||||||||
\(41\) | 0.469446 | 0.0733152 | 0.0366576 | − | 0.999328i | \(-0.488329\pi\) | ||||
0.0366576 | + | 0.999328i | \(0.488329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.68640 | 0.409672 | 0.204836 | − | 0.978796i | \(-0.434334\pi\) | ||||
0.204836 | + | 0.978796i | \(0.434334\pi\) | |||||||
\(44\) | 8.15096 | 1.22880 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.93234 | 0.284908 | ||||||||
\(47\) | −12.2820 | −1.79152 | −0.895759 | − | 0.444540i | \(-0.853367\pi\) | ||||
−0.895759 | + | 0.444540i | \(0.853367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.78220 | 1.25460 | ||||||||
\(50\) | 5.71109 | 0.807670 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.91724 | −1.37527 | ||||||||
\(53\) | 3.63780 | 0.499690 | 0.249845 | − | 0.968286i | \(-0.419620\pi\) | ||||
0.249845 | + | 0.968286i | \(0.419620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.2591 | 1.78785 | ||||||||
\(56\) | 2.04253 | 0.272945 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.93234 | 0.253728 | ||||||||
\(59\) | −8.78187 | −1.14330 | −0.571651 | − | 0.820497i | \(-0.693697\pi\) | ||||
−0.571651 | + | 0.820497i | \(0.693697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.68255 | 0.599539 | 0.299770 | − | 0.954012i | \(-0.403090\pi\) | ||||
0.299770 | + | 0.954012i | \(0.403090\pi\) | |||||||
\(62\) | 9.97293 | 1.26656 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.74865 | −0.718582 | ||||||||
\(65\) | −16.1323 | −2.00096 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.9642 | −1.95034 | −0.975170 | − | 0.221457i | \(-0.928919\pi\) | ||||
−0.975170 | + | 0.221457i | \(0.928919\pi\) | |||||||
\(68\) | −8.86195 | −1.07467 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −21.6522 | −2.58793 | ||||||||
\(71\) | −10.0253 | −1.18979 | −0.594894 | − | 0.803804i | \(-0.702806\pi\) | ||||
−0.594894 | + | 0.803804i | \(0.702806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.41059 | 0.984385 | 0.492193 | − | 0.870486i | \(-0.336196\pi\) | ||||
0.492193 | + | 0.870486i | \(0.336196\pi\) | |||||||
\(74\) | −11.1581 | −1.29710 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.389504 | 0.0446792 | ||||||||
\(77\) | −18.6751 | −2.12822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9991 | −1.46251 | −0.731254 | − | 0.682105i | \(-0.761065\pi\) | ||||
−0.731254 | + | 0.682105i | \(0.761065\pi\) | |||||||
\(80\) | −12.5835 | −1.40688 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.907129 | 0.100176 | ||||||||
\(83\) | −11.6167 | −1.27509 | −0.637547 | − | 0.770412i | \(-0.720051\pi\) | ||||
−0.637547 | + | 0.770412i | \(0.720051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.4156 | −1.56360 | ||||||||
\(86\) | 5.19102 | 0.559762 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.41693 | −0.257645 | ||||||||
\(89\) | −10.7508 | −1.13958 | −0.569790 | − | 0.821790i | \(-0.692975\pi\) | ||||
−0.569790 | + | 0.821790i | \(0.692975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.7219 | 2.38190 | ||||||||
\(92\) | 1.73393 | 0.180774 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −23.7330 | −2.44787 | ||||||||
\(95\) | 0.633601 | 0.0650061 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.53357 | −0.561849 | −0.280924 | − | 0.959730i | \(-0.590641\pi\) | ||||
−0.280924 | + | 0.959730i | \(0.590641\pi\) | |||||||
\(98\) | 16.9702 | 1.71425 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.12468 | 0.512468 | ||||||||
\(101\) | 0.789577 | 0.0785659 | 0.0392829 | − | 0.999228i | \(-0.487493\pi\) | ||||
0.0392829 | + | 0.999228i | \(0.487493\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.12240 | −0.110593 | −0.0552967 | − | 0.998470i | \(-0.517610\pi\) | ||||
−0.0552967 | + | 0.998470i | \(0.517610\pi\) | |||||||
\(104\) | 2.94067 | 0.288356 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.02945 | 0.682761 | ||||||||
\(107\) | 9.39437 | 0.908188 | 0.454094 | − | 0.890954i | \(-0.349963\pi\) | ||||
0.454094 | + | 0.890954i | \(0.349963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.34828 | 0.799620 | 0.399810 | − | 0.916598i | \(-0.369076\pi\) | ||||
0.399810 | + | 0.916598i | \(0.369076\pi\) | |||||||
\(110\) | 25.6210 | 2.44286 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17.7235 | 1.67472 | ||||||||
\(113\) | −0.894306 | −0.0841292 | −0.0420646 | − | 0.999115i | \(-0.513394\pi\) | ||||
−0.0420646 | + | 0.999115i | \(0.513394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82056 | 0.263018 | ||||||||
\(116\) | 1.73393 | 0.160991 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.9695 | −1.56217 | ||||||||
\(119\) | 20.3041 | 1.86127 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0982 | 1.00893 | ||||||||
\(122\) | 9.04827 | 0.819192 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.94892 | 0.803637 | ||||||||
\(125\) | −5.76652 | −0.515774 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1089 | −0.897018 | −0.448509 | − | 0.893778i | \(-0.648045\pi\) | ||||
−0.448509 | + | 0.893778i | \(0.648045\pi\) | |||||||
\(128\) | 4.07676 | 0.360338 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31.1730 | −2.73405 | ||||||||
\(131\) | 14.7583 | 1.28944 | 0.644718 | − | 0.764420i | \(-0.276975\pi\) | ||||
0.644718 | + | 0.764420i | \(0.276975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.892411 | −0.0773819 | ||||||||
\(134\) | −30.8483 | −2.66488 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.62775 | 0.225328 | ||||||||
\(137\) | 9.23341 | 0.788864 | 0.394432 | − | 0.918925i | \(-0.370941\pi\) | ||||
0.394432 | + | 0.918925i | \(0.370941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4024 | 0.882319 | 0.441160 | − | 0.897429i | \(-0.354567\pi\) | ||||
0.441160 | + | 0.897429i | \(0.354567\pi\) | |||||||
\(140\) | −19.4289 | −1.64204 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −19.3723 | −1.62569 | ||||||||
\(143\) | −26.8868 | −2.24838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.82056 | 0.234234 | ||||||||
\(146\) | 16.2521 | 1.34503 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0124 | −0.823012 | ||||||||
\(149\) | −13.6004 | −1.11419 | −0.557093 | − | 0.830450i | \(-0.688083\pi\) | ||||
−0.557093 | + | 0.830450i | \(0.688083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.89036 | −0.235214 | −0.117607 | − | 0.993060i | \(-0.537522\pi\) | ||||
−0.117607 | + | 0.993060i | \(0.537522\pi\) | |||||||
\(152\) | −0.115496 | −0.00936796 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −36.0865 | −2.90793 | ||||||||
\(155\) | 14.5571 | 1.16925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9053 | 0.950150 | 0.475075 | − | 0.879945i | \(-0.342421\pi\) | ||||
0.475075 | + | 0.879945i | \(0.342421\pi\) | |||||||
\(158\) | −25.1186 | −1.99833 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −21.4152 | −1.69302 | ||||||||
\(161\) | −3.97268 | −0.313091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.05697 | 0.552745 | 0.276372 | − | 0.961051i | \(-0.410868\pi\) | ||||
0.276372 | + | 0.961051i | \(0.410868\pi\) | |||||||
\(164\) | 0.813985 | 0.0635616 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.4473 | −1.74225 | ||||||||
\(167\) | −12.2598 | −0.948689 | −0.474344 | − | 0.880339i | \(-0.657315\pi\) | ||||
−0.474344 | + | 0.880339i | \(0.657315\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.7130 | 1.51639 | ||||||||
\(170\) | −27.8559 | −2.13645 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.65801 | 0.355170 | ||||||||
\(173\) | 2.41040 | 0.183259 | 0.0916296 | − | 0.995793i | \(-0.470792\pi\) | ||||
0.0916296 | + | 0.995793i | \(0.470792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.7414 | −0.887567 | ||||||||
\(176\) | −20.9722 | −1.58084 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.7741 | −1.55709 | ||||||||
\(179\) | 5.21330 | 0.389661 | 0.194830 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194830 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.8370 | −1.17715 | −0.588576 | − | 0.808442i | \(-0.700311\pi\) | ||||
−0.588576 | + | 0.808442i | \(0.700311\pi\) | |||||||
\(182\) | 43.9063 | 3.25455 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.514145 | −0.0379033 | ||||||||
\(185\) | −16.2870 | −1.19744 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.0258 | −1.75694 | ||||||||
\(188\) | −21.2961 | −1.55318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.22433 | 0.0888223 | ||||||||
\(191\) | 25.5745 | 1.85051 | 0.925254 | − | 0.379349i | \(-0.123852\pi\) | ||||
0.925254 | + | 0.379349i | \(0.123852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.38745 | 0.675723 | 0.337862 | − | 0.941196i | \(-0.390296\pi\) | ||||
0.337862 | + | 0.941196i | \(0.390296\pi\) | |||||||
\(194\) | −10.6927 | −0.767692 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.2277 | 1.08769 | ||||||||
\(197\) | −10.9347 | −0.779066 | −0.389533 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389533 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.0802 | 1.35256 | 0.676281 | − | 0.736644i | \(-0.263590\pi\) | ||||
0.676281 | + | 0.736644i | \(0.263590\pi\) | |||||||
\(200\) | −1.51957 | −0.107450 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.52573 | 0.107350 | ||||||||
\(203\) | −3.97268 | −0.278828 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.32410 | 0.0924792 | ||||||||
\(206\) | −2.16886 | −0.151111 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 25.5168 | 1.76927 | ||||||||
\(209\) | 1.05599 | 0.0730443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.96719 | −0.686170 | −0.343085 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343085 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(212\) | 6.30767 | 0.433213 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.1531 | 1.24092 | ||||||||
\(215\) | 7.57713 | 0.516756 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.5033 | −1.39185 | ||||||||
\(218\) | 16.1317 | 1.09258 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.9902 | 1.55000 | ||||||||
\(221\) | 29.2321 | 1.96636 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5991 | 0.843695 | 0.421847 | − | 0.906667i | \(-0.361382\pi\) | ||||
0.421847 | + | 0.906667i | \(0.361382\pi\) | |||||||
\(224\) | 30.1628 | 2.01534 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.72810 | −0.114952 | ||||||||
\(227\) | 8.62488 | 0.572453 | 0.286227 | − | 0.958162i | \(-0.407599\pi\) | ||||
0.286227 | + | 0.958162i | \(0.407599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6654 | −1.76210 | −0.881050 | − | 0.473022i | \(-0.843163\pi\) | ||||
−0.881050 | + | 0.473022i | \(0.843163\pi\) | |||||||
\(230\) | 5.45026 | 0.359380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.514145 | −0.0337553 | ||||||||
\(233\) | 3.28507 | 0.215212 | 0.107606 | − | 0.994194i | \(-0.465681\pi\) | ||||
0.107606 | + | 0.994194i | \(0.465681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.6421 | −2.25980 | ||||||||
\(236\) | −15.2271 | −0.991200 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 39.2343 | 2.54318 | ||||||||
\(239\) | 13.3297 | 0.862224 | 0.431112 | − | 0.902298i | \(-0.358121\pi\) | ||||
0.431112 | + | 0.902298i | \(0.358121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.39449 | 0.411906 | 0.205953 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205953 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(242\) | 21.4454 | 1.37856 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.11920 | 0.519778 | ||||||||
\(245\) | 24.7707 | 1.58254 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.28482 | −0.0817510 | ||||||||
\(248\) | −2.65354 | −0.168500 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1429 | −0.704737 | ||||||||
\(251\) | −15.6412 | −0.987262 | −0.493631 | − | 0.869671i | \(-0.664331\pi\) | ||||
−0.493631 | + | 0.869671i | \(0.664331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.70087 | 0.295541 | ||||||||
\(254\) | −19.5338 | −1.22566 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.3750 | 1.21094 | ||||||||
\(257\) | 9.59553 | 0.598552 | 0.299276 | − | 0.954167i | \(-0.403255\pi\) | ||||
0.299276 | + | 0.954167i | \(0.403255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.9398 | 1.42541 | ||||||||
\(260\) | −27.9721 | −1.73476 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 28.5180 | 1.76185 | ||||||||
\(263\) | −8.20978 | −0.506237 | −0.253118 | − | 0.967435i | \(-0.581456\pi\) | ||||
−0.253118 | + | 0.967435i | \(0.581456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2606 | 0.630305 | ||||||||
\(266\) | −1.72444 | −0.105732 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.6808 | −1.69087 | ||||||||
\(269\) | −2.60278 | −0.158694 | −0.0793471 | − | 0.996847i | \(-0.525284\pi\) | ||||
−0.0793471 | + | 0.996847i | \(0.525284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9550 | 0.908452 | 0.454226 | − | 0.890887i | \(-0.349916\pi\) | ||||
0.454226 | + | 0.890887i | \(0.349916\pi\) | |||||||
\(272\) | 22.8016 | 1.38255 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.8421 | 1.07788 | ||||||||
\(275\) | 13.8936 | 0.837815 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0554 | −1.08484 | −0.542422 | − | 0.840106i | \(-0.682493\pi\) | ||||
−0.542422 | + | 0.840106i | \(0.682493\pi\) | |||||||
\(278\) | 20.1009 | 1.20557 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.76108 | 0.344291 | ||||||||
\(281\) | −6.43104 | −0.383644 | −0.191822 | − | 0.981430i | \(-0.561440\pi\) | ||||
−0.191822 | + | 0.981430i | \(0.561440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.16593 | −0.366526 | −0.183263 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183263 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(284\) | −17.3832 | −1.03150 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −51.9543 | −3.07212 | ||||||||
\(287\) | −1.86496 | −0.110085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.12150 | 0.536559 | ||||||||
\(290\) | 5.45026 | 0.320051 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.5833 | 0.853425 | ||||||||
\(293\) | −6.44220 | −0.376357 | −0.188179 | − | 0.982135i | \(-0.560258\pi\) | ||||
−0.188179 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.7697 | −1.44215 | ||||||||
\(296\) | 2.96888 | 0.172562 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −26.2805 | −1.52239 | ||||||||
\(299\) | −5.71953 | −0.330769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6722 | −0.615135 | ||||||||
\(302\) | −5.58514 | −0.321389 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00218 | −0.0574792 | ||||||||
\(305\) | 13.2074 | 0.756253 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0115 | 0.856749 | 0.428374 | − | 0.903601i | \(-0.359086\pi\) | ||||
0.428374 | + | 0.903601i | \(0.359086\pi\) | |||||||
\(308\) | −32.3812 | −1.84509 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 28.1292 | 1.59763 | ||||||||
\(311\) | −22.3886 | −1.26954 | −0.634771 | − | 0.772700i | \(-0.718906\pi\) | ||||
−0.634771 | + | 0.772700i | \(0.718906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3858 | −0.756613 | −0.378306 | − | 0.925680i | \(-0.623493\pi\) | ||||
−0.378306 | + | 0.925680i | \(0.623493\pi\) | |||||||
\(314\) | 23.0051 | 1.29825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.5394 | −1.26794 | ||||||||
\(317\) | 20.2458 | 1.13712 | 0.568559 | − | 0.822642i | \(-0.307501\pi\) | ||||
0.568559 | + | 0.822642i | \(0.307501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.70087 | 0.263198 | ||||||||
\(320\) | −16.2144 | −0.906412 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.67656 | −0.427798 | ||||||||
\(323\) | −1.14810 | −0.0638821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.9043 | −0.937681 | ||||||||
\(326\) | 13.6364 | 0.755253 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.241364 | −0.0133271 | ||||||||
\(329\) | 48.7926 | 2.69002 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.2462 | 1.55255 | 0.776275 | − | 0.630394i | \(-0.217107\pi\) | ||||
0.776275 | + | 0.630394i | \(0.217107\pi\) | |||||||
\(332\) | −20.1424 | −1.10546 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.6900 | −1.29626 | ||||||||
\(335\) | −45.0280 | −2.46014 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9484 | 0.759818 | 0.379909 | − | 0.925024i | \(-0.375955\pi\) | ||||
0.379909 | + | 0.925024i | \(0.375955\pi\) | |||||||
\(338\) | 38.0922 | 2.07194 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.9956 | −1.35558 | ||||||||
\(341\) | 24.2615 | 1.31384 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.08012 | −0.382291 | ||||||||
\(344\) | −1.38120 | −0.0744692 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.65770 | 0.250400 | ||||||||
\(347\) | −13.0430 | −0.700186 | −0.350093 | − | 0.936715i | \(-0.613850\pi\) | ||||
−0.350093 | + | 0.936715i | \(0.613850\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.9323 | −1.38813 | −0.694063 | − | 0.719914i | \(-0.744181\pi\) | ||||
−0.694063 | + | 0.719914i | \(0.744181\pi\) | |||||||
\(350\) | −22.6884 | −1.21274 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −35.6916 | −1.90237 | ||||||||
\(353\) | −19.7060 | −1.04884 | −0.524422 | − | 0.851459i | \(-0.675718\pi\) | ||||
−0.524422 | + | 0.851459i | \(0.675718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.2770 | −1.50079 | ||||||||
\(356\) | −18.6410 | −0.987973 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0739 | 0.532420 | ||||||||
\(359\) | 35.4959 | 1.87340 | 0.936701 | − | 0.350129i | \(-0.113862\pi\) | ||||
0.936701 | + | 0.350129i | \(0.113862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9495 | −0.997344 | ||||||||
\(362\) | −30.6023 | −1.60842 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 39.3980 | 2.06502 | ||||||||
\(365\) | 23.7225 | 1.24169 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.8149 | −0.721134 | −0.360567 | − | 0.932733i | \(-0.617417\pi\) | ||||
−0.360567 | + | 0.932733i | \(0.617417\pi\) | |||||||
\(368\) | −4.46135 | −0.232564 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −31.4720 | −1.63615 | ||||||||
\(371\) | −14.4518 | −0.750301 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9343 | 1.39460 | 0.697301 | − | 0.716778i | \(-0.254384\pi\) | ||||
0.697301 | + | 0.716778i | \(0.254384\pi\) | |||||||
\(374\) | −46.4259 | −2.40062 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.31474 | 0.325658 | ||||||||
\(377\) | −5.71953 | −0.294571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.3899 | 1.66376 | 0.831880 | − | 0.554956i | \(-0.187265\pi\) | ||||
0.831880 | + | 0.554956i | \(0.187265\pi\) | |||||||
\(380\) | 1.09862 | 0.0563579 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 49.4186 | 2.52848 | ||||||||
\(383\) | 36.9727 | 1.88922 | 0.944608 | − | 0.328200i | \(-0.106442\pi\) | ||||
0.944608 | + | 0.328200i | \(0.106442\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −52.6741 | −2.68452 | ||||||||
\(386\) | 18.1397 | 0.923287 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.59479 | −0.487102 | ||||||||
\(389\) | −4.21678 | −0.213799 | −0.106900 | − | 0.994270i | \(-0.534092\pi\) | ||||
−0.106900 | + | 0.994270i | \(0.534092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.11092 | −0.258470 | ||||||||
\(392\) | −4.51533 | −0.228058 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.1296 | −1.06449 | ||||||||
\(395\) | −36.6646 | −1.84480 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.67840 | −0.0842364 | −0.0421182 | − | 0.999113i | \(-0.513411\pi\) | ||||
−0.0421182 | + | 0.999113i | \(0.513411\pi\) | |||||||
\(398\) | 36.8694 | 1.84810 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.1857 | −0.659285 | ||||||||
\(401\) | −35.0056 | −1.74810 | −0.874048 | − | 0.485839i | \(-0.838514\pi\) | ||||
−0.874048 | + | 0.485839i | \(0.838514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.5189 | −1.47044 | ||||||||
\(404\) | 1.36907 | 0.0681137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.67656 | −0.380981 | ||||||||
\(407\) | −27.1447 | −1.34551 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.76285 | 0.383848 | 0.191924 | − | 0.981410i | \(-0.438527\pi\) | ||||
0.191924 | + | 0.981410i | \(0.438527\pi\) | |||||||
\(410\) | 2.55861 | 0.126361 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.94616 | −0.0958804 | ||||||||
\(413\) | 34.8876 | 1.71670 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.7654 | −1.60839 | ||||||||
\(416\) | 43.4258 | 2.12913 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.04053 | 0.0998054 | ||||||||
\(419\) | −4.61054 | −0.225240 | −0.112620 | − | 0.993638i | \(-0.535924\pi\) | ||||
−0.112620 | + | 0.993638i | \(0.535924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.4865 | −1.58329 | −0.791647 | − | 0.610979i | \(-0.790776\pi\) | ||||
−0.791647 | + | 0.610979i | \(0.790776\pi\) | |||||||
\(422\) | −19.2600 | −0.937560 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.87036 | −0.0908325 | ||||||||
\(425\) | −15.1055 | −0.732725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.6023 | −0.900228 | ||||||||
\(428\) | 16.2891 | 0.787365 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.6416 | 0.706079 | ||||||||
\(431\) | 0.775560 | 0.0373574 | 0.0186787 | − | 0.999826i | \(-0.494054\pi\) | ||||
0.0186787 | + | 0.999826i | \(0.494054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.57931 | −0.316181 | −0.158091 | − | 0.987425i | \(-0.550534\pi\) | ||||
−0.158091 | + | 0.987425i | \(0.550534\pi\) | |||||||
\(434\) | −39.6193 | −1.90179 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.4753 | 0.693241 | ||||||||
\(437\) | 0.224637 | 0.0107458 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.1830 | 1.67919 | 0.839595 | − | 0.543212i | \(-0.182792\pi\) | ||||
0.839595 | + | 0.543212i | \(0.182792\pi\) | |||||||
\(440\) | −6.81708 | −0.324992 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 56.4862 | 2.68677 | ||||||||
\(443\) | 24.4074 | 1.15963 | 0.579815 | − | 0.814748i | \(-0.303125\pi\) | ||||
0.579815 | + | 0.814748i | \(0.303125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.3232 | −1.43746 | ||||||||
\(446\) | 24.3456 | 1.15280 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22.8376 | 1.07897 | ||||||||
\(449\) | 5.62450 | 0.265437 | 0.132718 | − | 0.991154i | \(-0.457629\pi\) | ||||
0.132718 | + | 0.991154i | \(0.457629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.20681 | 0.103914 | ||||||||
\(452\) | −1.55066 | −0.0729369 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.6662 | 0.782182 | ||||||||
\(455\) | 64.0883 | 3.00451 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.51862 | 0.304928 | 0.152464 | − | 0.988309i | \(-0.451279\pi\) | ||||
0.152464 | + | 0.988309i | \(0.451279\pi\) | |||||||
\(458\) | −51.5266 | −2.40768 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.89063 | 0.228027 | ||||||||
\(461\) | −4.33185 | −0.201754 | −0.100877 | − | 0.994899i | \(-0.532165\pi\) | ||||
−0.100877 | + | 0.994899i | \(0.532165\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.2599 | −1.03451 | −0.517254 | − | 0.855832i | \(-0.673046\pi\) | ||||
−0.517254 | + | 0.855832i | \(0.673046\pi\) | |||||||
\(464\) | −4.46135 | −0.207113 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.34786 | 0.294059 | ||||||||
\(467\) | −4.41272 | −0.204196 | −0.102098 | − | 0.994774i | \(-0.532556\pi\) | ||||
−0.102098 | + | 0.994774i | \(0.532556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.4208 | 2.92850 | ||||||||
\(470\) | −66.9403 | −3.08773 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.51515 | 0.207827 | ||||||||
\(473\) | 12.6284 | 0.580654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.663923 | 0.0304629 | ||||||||
\(476\) | 35.2057 | 1.61365 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.7574 | 1.17812 | ||||||||
\(479\) | −9.33238 | −0.426407 | −0.213204 | − | 0.977008i | \(-0.568390\pi\) | ||||
−0.213204 | + | 0.977008i | \(0.568390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.0268 | 1.50589 | ||||||||
\(482\) | 12.3563 | 0.562815 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.2434 | 0.874701 | ||||||||
\(485\) | −15.6077 | −0.708711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00747 | 0.272225 | 0.136112 | − | 0.990693i | \(-0.456539\pi\) | ||||
0.136112 | + | 0.990693i | \(0.456539\pi\) | |||||||
\(488\) | −2.40751 | −0.108983 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 47.8653 | 2.16233 | ||||||||
\(491\) | 16.0494 | 0.724299 | 0.362149 | − | 0.932120i | \(-0.382043\pi\) | ||||
0.362149 | + | 0.932120i | \(0.382043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.11092 | −0.230184 | ||||||||
\(494\) | −2.48270 | −0.111702 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.0254 | −1.03387 | ||||||||
\(497\) | 39.8275 | 1.78651 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7809 | −1.10935 | −0.554674 | − | 0.832068i | \(-0.687157\pi\) | ||||
−0.554674 | + | 0.832068i | \(0.687157\pi\) | |||||||
\(500\) | −9.99872 | −0.447157 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.2240 | −1.34896 | ||||||||
\(503\) | −38.0583 | −1.69694 | −0.848469 | − | 0.529245i | \(-0.822475\pi\) | ||||
−0.848469 | + | 0.529245i | \(0.822475\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.22705 | 0.0991023 | ||||||||
\(506\) | 9.08366 | 0.403818 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.5281 | −0.777682 | ||||||||
\(509\) | −19.2146 | −0.851671 | −0.425836 | − | 0.904800i | \(-0.640020\pi\) | ||||
−0.425836 | + | 0.904800i | \(0.640020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.4126 | −1.47809 | ||||||||
\(512\) | 29.2855 | 1.29425 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.5418 | 0.817843 | ||||||||
\(515\) | −3.16579 | −0.139502 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.7362 | −2.53924 | ||||||||
\(518\) | 44.3275 | 1.94764 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.29432 | 0.363730 | ||||||||
\(521\) | −19.4926 | −0.853988 | −0.426994 | − | 0.904254i | \(-0.640427\pi\) | ||||
−0.426994 | + | 0.904254i | \(0.640427\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.4432 | 1.24373 | 0.621866 | − | 0.783124i | \(-0.286375\pi\) | ||||
0.621866 | + | 0.783124i | \(0.286375\pi\) | |||||||
\(524\) | 25.5898 | 1.11789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.8641 | −0.691706 | ||||||||
\(527\) | −26.3778 | −1.14904 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 19.8270 | 0.861228 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.54737 | −0.0670872 | ||||||||
\(533\) | −2.68501 | −0.116301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.4973 | 1.14558 | ||||||||
\(536\) | 8.20793 | 0.354528 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.02945 | −0.216835 | ||||||||
\(539\) | 41.2840 | 1.77823 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.26466 | −0.269339 | −0.134669 | − | 0.990891i | \(-0.542997\pi\) | ||||
−0.134669 | + | 0.990891i | \(0.542997\pi\) | |||||||
\(542\) | 28.8981 | 1.24128 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 38.8049 | 1.66375 | ||||||||
\(545\) | 23.5468 | 1.00863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.9269 | −1.40785 | −0.703927 | − | 0.710272i | \(-0.748572\pi\) | ||||
−0.703927 | + | 0.710272i | \(0.748572\pi\) | |||||||
\(548\) | 16.0101 | 0.683916 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26.8471 | 1.14476 | ||||||||
\(551\) | 0.224637 | 0.00956986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.6411 | 2.19600 | ||||||||
\(554\) | −34.8891 | −1.48230 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.0370 | 0.764938 | ||||||||
\(557\) | 36.0931 | 1.52931 | 0.764657 | − | 0.644438i | \(-0.222908\pi\) | ||||
0.764657 | + | 0.644438i | \(0.222908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.3649 | −0.649867 | ||||||||
\(560\) | 49.9902 | 2.11247 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.4269 | −0.524199 | ||||||||
\(563\) | 24.8551 | 1.04752 | 0.523758 | − | 0.851867i | \(-0.324529\pi\) | ||||
0.523758 | + | 0.851867i | \(0.324529\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.52244 | −0.106120 | ||||||||
\(566\) | −11.9147 | −0.500810 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.15448 | 0.216277 | ||||||||
\(569\) | −24.2965 | −1.01856 | −0.509281 | − | 0.860600i | \(-0.670089\pi\) | ||||
−0.509281 | + | 0.860600i | \(0.670089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.3348 | 1.52056 | 0.760282 | − | 0.649593i | \(-0.225061\pi\) | ||||
0.760282 | + | 0.649593i | \(0.225061\pi\) | |||||||
\(572\) | −46.6197 | −1.94927 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.60373 | −0.150417 | ||||||||
\(575\) | 2.95554 | 0.123254 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.50544 | 0.270825 | 0.135412 | − | 0.990789i | \(-0.456764\pi\) | ||||
0.135412 | + | 0.990789i | \(0.456764\pi\) | |||||||
\(578\) | 17.6258 | 0.733137 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.89063 | 0.203073 | ||||||||
\(581\) | 46.1493 | 1.91459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.1008 | 0.708243 | ||||||||
\(584\) | −4.32426 | −0.178939 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.4485 | −0.514242 | ||||||||
\(587\) | −44.9379 | −1.85479 | −0.927394 | − | 0.374087i | \(-0.877956\pi\) | ||||
−0.927394 | + | 0.374087i | \(0.877956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15937 | 0.0477709 | ||||||||
\(590\) | −47.8635 | −1.97051 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.7616 | 1.05880 | ||||||||
\(593\) | 48.0280 | 1.97227 | 0.986136 | − | 0.165939i | \(-0.0530656\pi\) | ||||
0.986136 | + | 0.165939i | \(0.0530656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 57.2687 | 2.34779 | ||||||||
\(596\) | −23.5821 | −0.965958 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.0521 | −0.451952 | ||||||||
\(599\) | −8.51888 | −0.348072 | −0.174036 | − | 0.984739i | \(-0.555681\pi\) | ||||
−0.174036 | + | 0.984739i | \(0.555681\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.6288 | −0.882257 | −0.441129 | − | 0.897444i | \(-0.645422\pi\) | ||||
−0.441129 | + | 0.897444i | \(0.645422\pi\) | |||||||
\(602\) | −20.6223 | −0.840501 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.01166 | −0.203922 | ||||||||
\(605\) | 31.3030 | 1.27265 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.96277 | −0.120255 | −0.0601275 | − | 0.998191i | \(-0.519151\pi\) | ||||
−0.0601275 | + | 0.998191i | \(0.519151\pi\) | |||||||
\(608\) | −1.70557 | −0.0691699 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5211 | 1.03332 | ||||||||
\(611\) | 70.2474 | 2.84191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7840 | −1.36452 | −0.682262 | − | 0.731108i | \(-0.739004\pi\) | ||||
−0.682262 | + | 0.731108i | \(0.739004\pi\) | |||||||
\(614\) | 29.0072 | 1.17063 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.60169 | 0.386863 | ||||||||
\(617\) | 16.0811 | 0.647400 | 0.323700 | − | 0.946160i | \(-0.395073\pi\) | ||||
0.323700 | + | 0.946160i | \(0.395073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.1296 | 1.13062 | 0.565312 | − | 0.824877i | \(-0.308756\pi\) | ||||
0.565312 | + | 0.824877i | \(0.308756\pi\) | |||||||
\(620\) | 25.2409 | 1.01370 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −43.2624 | −1.73466 | ||||||||
\(623\) | 42.7094 | 1.71112 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0425 | −1.24170 | ||||||||
\(626\) | −25.8660 | −1.03381 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.6430 | 0.823745 | ||||||||
\(629\) | 29.5125 | 1.17674 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6943 | 1.06268 | 0.531341 | − | 0.847158i | \(-0.321688\pi\) | ||||
0.531341 | + | 0.847158i | \(0.321688\pi\) | |||||||
\(632\) | 6.68340 | 0.265851 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.1218 | 1.55372 | ||||||||
\(635\) | −28.5127 | −1.13149 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −50.2301 | −1.99019 | ||||||||
\(638\) | 9.08366 | 0.359626 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.4987 | 0.454527 | ||||||||
\(641\) | 15.2742 | 0.603296 | 0.301648 | − | 0.953419i | \(-0.402463\pi\) | ||||
0.301648 | + | 0.953419i | \(0.402463\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.1583 | −1.46538 | −0.732690 | − | 0.680562i | \(-0.761736\pi\) | ||||
−0.732690 | + | 0.680562i | \(0.761736\pi\) | |||||||
\(644\) | −6.88834 | −0.271438 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.21852 | −0.0872865 | ||||||||
\(647\) | −4.05766 | −0.159523 | −0.0797615 | − | 0.996814i | \(-0.525416\pi\) | ||||
−0.0797615 | + | 0.996814i | \(0.525416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.2824 | −1.62048 | ||||||||
\(650\) | −32.6648 | −1.28122 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.2363 | 0.479209 | ||||||||
\(653\) | 39.9199 | 1.56219 | 0.781093 | − | 0.624415i | \(-0.214663\pi\) | ||||
0.781093 | + | 0.624415i | \(0.214663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.6265 | 1.62648 | ||||||||
\(656\) | −2.09437 | −0.0817713 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 94.2837 | 3.67556 | ||||||||
\(659\) | 8.93986 | 0.348248 | 0.174124 | − | 0.984724i | \(-0.444291\pi\) | ||||
0.174124 | + | 0.984724i | \(0.444291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.2868 | −0.750171 | −0.375086 | − | 0.926990i | \(-0.622387\pi\) | ||||
−0.375086 | + | 0.926990i | \(0.622387\pi\) | |||||||
\(662\) | 54.5811 | 2.12136 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.97265 | 0.231784 | ||||||||
\(665\) | −2.51710 | −0.0976088 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −21.2575 | −0.822478 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −87.0092 | −3.36146 | ||||||||
\(671\) | 22.0121 | 0.849766 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.74414 | 0.259967 | 0.129984 | − | 0.991516i | \(-0.458507\pi\) | ||||
0.129984 | + | 0.991516i | \(0.458507\pi\) | |||||||
\(674\) | 26.9530 | 1.03819 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.1809 | 1.31465 | ||||||||
\(677\) | −30.5313 | −1.17341 | −0.586706 | − | 0.809800i | \(-0.699575\pi\) | ||||
−0.586706 | + | 0.809800i | \(0.699575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.9831 | 0.843634 | ||||||||
\(680\) | 7.41173 | 0.284227 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46.8815 | 1.79518 | ||||||||
\(683\) | −50.6678 | −1.93875 | −0.969376 | − | 0.245583i | \(-0.921021\pi\) | ||||
−0.969376 | + | 0.245583i | \(0.921021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.0434 | 0.995066 | ||||||||
\(686\) | −13.6812 | −0.522350 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.9850 | −0.456922 | ||||||||
\(689\) | −20.8065 | −0.792664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.90345 | 0.224578 | 0.112289 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112289 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(692\) | 4.17945 | 0.158879 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.2035 | −0.956713 | ||||||||
\(695\) | 29.3405 | 1.11295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.39930 | −0.0908801 | ||||||||
\(698\) | −50.1100 | −1.89669 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −20.3587 | −0.769488 | ||||||||
\(701\) | 41.5271 | 1.56846 | 0.784228 | − | 0.620473i | \(-0.213059\pi\) | ||||
0.784228 | + | 0.620473i | \(0.213059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.29714 | −0.0489227 | ||||||||
\(704\) | −27.0237 | −1.01849 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38.0786 | −1.43311 | ||||||||
\(707\) | −3.13674 | −0.117969 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6554 | 1.33907 | 0.669534 | − | 0.742781i | \(-0.266494\pi\) | ||||
0.669534 | + | 0.742781i | \(0.266494\pi\) | |||||||
\(710\) | −54.6407 | −2.05063 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.52746 | 0.207150 | ||||||||
\(713\) | 5.16107 | 0.193284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −75.8356 | −2.83609 | ||||||||
\(716\) | 9.03948 | 0.337821 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 68.5901 | 2.55976 | ||||||||
\(719\) | 8.21784 | 0.306474 | 0.153237 | − | 0.988189i | \(-0.451030\pi\) | ||||
0.153237 | + | 0.988189i | \(0.451030\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.45894 | 0.166060 | ||||||||
\(722\) | −36.6169 | −1.36274 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.4601 | −1.02055 | ||||||||
\(725\) | 2.95554 | 0.109766 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.0160 | −1.52120 | −0.760599 | − | 0.649222i | \(-0.775095\pi\) | ||||
−0.760599 | + | 0.649222i | \(0.775095\pi\) | |||||||
\(728\) | −11.6823 | −0.432976 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 45.8399 | 1.69661 | ||||||||
\(731\) | −13.7300 | −0.507821 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0254 | −0.518040 | −0.259020 | − | 0.965872i | \(-0.583400\pi\) | ||||
−0.259020 | + | 0.965872i | \(0.583400\pi\) | |||||||
\(734\) | −26.6951 | −0.985334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.59255 | −0.279865 | ||||||||
\(737\) | −75.0457 | −2.76434 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.3370 | −1.04239 | −0.521197 | − | 0.853437i | \(-0.674514\pi\) | ||||
−0.521197 | + | 0.853437i | \(0.674514\pi\) | |||||||
\(740\) | −28.2405 | −1.03814 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.9258 | −1.02519 | ||||||||
\(743\) | 13.0956 | 0.480433 | 0.240216 | − | 0.970719i | \(-0.422782\pi\) | ||||
0.240216 | + | 0.970719i | \(0.422782\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.3606 | −1.40543 | ||||||||
\(746\) | 52.0460 | 1.90554 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −41.6589 | −1.52320 | ||||||||
\(749\) | −37.3208 | −1.36367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.4975 | −1.47778 | −0.738888 | − | 0.673828i | \(-0.764649\pi\) | ||||
−0.738888 | + | 0.673828i | \(0.764649\pi\) | |||||||
\(752\) | 54.7945 | 1.99815 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.0521 | −0.402492 | ||||||||
\(755\) | −8.15241 | −0.296697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3831 | −1.57679 | −0.788394 | − | 0.615171i | \(-0.789087\pi\) | ||||
−0.788394 | + | 0.615171i | \(0.789087\pi\) | |||||||
\(758\) | 62.5883 | 2.27331 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.325763 | −0.0118167 | ||||||||
\(761\) | −33.3792 | −1.21000 | −0.604998 | − | 0.796227i | \(-0.706826\pi\) | ||||
−0.604998 | + | 0.796227i | \(0.706826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.1650 | −1.20066 | ||||||||
\(764\) | 44.3443 | 1.60432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 71.4437 | 2.58137 | ||||||||
\(767\) | 50.2281 | 1.81363 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9543 | 0.575327 | 0.287663 | − | 0.957732i | \(-0.407122\pi\) | ||||
0.287663 | + | 0.957732i | \(0.407122\pi\) | |||||||
\(770\) | −101.784 | −3.66804 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.2771 | 0.585827 | ||||||||
\(773\) | 36.1871 | 1.30156 | 0.650780 | − | 0.759266i | \(-0.274442\pi\) | ||||
0.650780 | + | 0.759266i | \(0.274442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.2537 | 0.547931 | ||||||||
\(776\) | 2.84506 | 0.102132 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.14824 | −0.292129 | ||||||||
\(779\) | 0.105455 | 0.00377832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.1278 | −1.68637 | ||||||||
\(782\) | −9.87602 | −0.353166 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39.1805 | −1.39930 | ||||||||
\(785\) | 33.5797 | 1.19851 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.4245 | 1.15581 | 0.577905 | − | 0.816104i | \(-0.303870\pi\) | ||||
0.577905 | + | 0.816104i | \(0.303870\pi\) | |||||||
\(788\) | −18.9600 | −0.675421 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −70.8483 | −2.52067 | ||||||||
\(791\) | 3.55279 | 0.126323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.7820 | −0.951056 | ||||||||
\(794\) | −3.24323 | −0.115098 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.0837 | 1.17262 | ||||||||
\(797\) | 43.9980 | 1.55849 | 0.779245 | − | 0.626720i | \(-0.215603\pi\) | ||||
0.779245 | + | 0.626720i | \(0.215603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.7724 | 2.22073 | ||||||||
\(800\) | −22.4401 | −0.793376 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −67.6426 | −2.38854 | ||||||||
\(803\) | 39.5371 | 1.39523 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.2052 | −0.394930 | ||||||||
\(806\) | −57.0405 | −2.00917 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.405957 | −0.0142815 | ||||||||
\(809\) | 0.740559 | 0.0260367 | 0.0130183 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130183 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.6291 | −1.70760 | −0.853800 | − | 0.520602i | \(-0.825708\pi\) | ||||
−0.853800 | + | 0.520602i | \(0.825708\pi\) | |||||||
\(812\) | −6.88834 | −0.241733 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −52.4527 | −1.83847 | ||||||||
\(815\) | 19.9046 | 0.697227 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.603464 | 0.0211125 | ||||||||
\(818\) | 15.0004 | 0.524478 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.29589 | 0.0801760 | ||||||||
\(821\) | −3.00633 | −0.104922 | −0.0524608 | − | 0.998623i | \(-0.516706\pi\) | ||||
−0.0524608 | + | 0.998623i | \(0.516706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4507 | 0.399146 | 0.199573 | − | 0.979883i | \(-0.436045\pi\) | ||||
0.199573 | + | 0.979883i | \(0.436045\pi\) | |||||||
\(824\) | 0.577077 | 0.0201034 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 67.4145 | 2.34565 | ||||||||
\(827\) | 24.1302 | 0.839089 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.02376 | −0.278677 | −0.139338 | − | 0.990245i | \(-0.544498\pi\) | ||||
−0.139338 | + | 0.990245i | \(0.544498\pi\) | |||||||
\(830\) | −63.3138 | −2.19766 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.8796 | 1.13989 | ||||||||
\(833\) | −44.8851 | −1.55518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.5793 | −1.19667 | ||||||||
\(836\) | 1.83101 | 0.0633267 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.90912 | −0.307760 | ||||||||
\(839\) | −29.8644 | −1.03103 | −0.515516 | − | 0.856880i | \(-0.672400\pi\) | ||||
−0.515516 | + | 0.856880i | \(0.672400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −62.7748 | −2.16336 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.2824 | −0.594884 | ||||||||
\(845\) | 55.6017 | 1.91276 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −44.0895 | −1.51493 | ||||||||
\(848\) | −16.2295 | −0.557323 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −29.1889 | −1.00117 | ||||||||
\(851\) | −5.77440 | −0.197944 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.1122 | −1.75005 | −0.875023 | − | 0.484081i | \(-0.839154\pi\) | ||||
−0.875023 | + | 0.484081i | \(0.839154\pi\) | |||||||
\(854\) | −35.9459 | −1.23004 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.83007 | −0.165088 | ||||||||
\(857\) | −13.5277 | −0.462096 | −0.231048 | − | 0.972942i | \(-0.574215\pi\) | ||||
−0.231048 | + | 0.972942i | \(0.574215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.5821 | 1.45288 | 0.726440 | − | 0.687229i | \(-0.241173\pi\) | ||||
0.726440 | + | 0.687229i | \(0.241173\pi\) | |||||||
\(860\) | 13.1382 | 0.448008 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.49864 | 0.0510440 | ||||||||
\(863\) | 40.9531 | 1.39406 | 0.697031 | − | 0.717041i | \(-0.254504\pi\) | ||||
0.697031 | + | 0.717041i | \(0.254504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.79867 | 0.231162 | ||||||||
\(866\) | −12.7134 | −0.432020 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −35.5512 | −1.20669 | ||||||||
\(869\) | −61.1069 | −2.07291 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 91.3078 | 3.09385 | ||||||||
\(872\) | −4.29222 | −0.145353 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.434074 | 0.0146828 | ||||||||
\(875\) | 22.9086 | 0.774451 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.6726 | 0.833136 | 0.416568 | − | 0.909105i | \(-0.363233\pi\) | ||||
0.416568 | + | 0.909105i | \(0.363233\pi\) | |||||||
\(878\) | 67.9853 | 2.29439 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −59.1534 | −1.99406 | ||||||||
\(881\) | −44.4515 | −1.49761 | −0.748804 | − | 0.662791i | \(-0.769372\pi\) | ||||
−0.748804 | + | 0.662791i | \(0.769372\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.759374 | −0.0255550 | −0.0127775 | − | 0.999918i | \(-0.504067\pi\) | ||||
−0.0127775 | + | 0.999918i | \(0.504067\pi\) | |||||||
\(884\) | 50.6862 | 1.70476 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 47.1633 | 1.58448 | ||||||||
\(887\) | 39.0346 | 1.31065 | 0.655326 | − | 0.755346i | \(-0.272531\pi\) | ||||
0.655326 | + | 0.755346i | \(0.272531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.1594 | 1.34690 | ||||||||
\(890\) | −58.5946 | −1.96409 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.8458 | 0.731452 | ||||||||
\(893\) | −2.75900 | −0.0923263 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.7044 | 0.491514 | ||||||||
\(896\) | −16.1957 | −0.541060 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8684 | 0.362684 | ||||||||
\(899\) | 5.16107 | 0.172131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.5925 | −0.619406 | ||||||||
\(902\) | 4.26429 | 0.141985 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.459803 | 0.0152928 | ||||||||
\(905\) | −44.6690 | −1.48485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.394908 | 0.0131127 | 0.00655636 | − | 0.999979i | \(-0.497913\pi\) | ||||
0.00655636 | + | 0.999979i | \(0.497913\pi\) | |||||||
\(908\) | 14.9549 | 0.496296 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 123.840 | 4.10526 | ||||||||
\(911\) | −24.8847 | −0.824468 | −0.412234 | − | 0.911078i | \(-0.635251\pi\) | ||||
−0.412234 | + | 0.911078i | \(0.635251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.6084 | −1.80727 | ||||||||
\(914\) | 12.5962 | 0.416644 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.2359 | −1.52768 | ||||||||
\(917\) | −58.6299 | −1.93613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.2769 | −1.59251 | −0.796254 | − | 0.604963i | \(-0.793188\pi\) | ||||
−0.796254 | + | 0.604963i | \(0.793188\pi\) | |||||||
\(920\) | −1.45017 | −0.0478108 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.37060 | −0.275671 | ||||||||
\(923\) | 57.3402 | 1.88738 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0664 | −0.561141 | ||||||||
\(926\) | −43.0137 | −1.41352 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.59255 | −0.249238 | ||||||||
\(929\) | −15.2969 | −0.501874 | −0.250937 | − | 0.968003i | \(-0.580739\pi\) | ||||
−0.250937 | + | 0.968003i | \(0.580739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.97281 | 0.0646562 | ||||||||
\(932\) | 5.69607 | 0.186581 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.52686 | −0.279007 | ||||||||
\(935\) | −67.7660 | −2.21619 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.1270 | −1.27822 | −0.639111 | − | 0.769114i | \(-0.720698\pi\) | ||||
−0.639111 | + | 0.769114i | \(0.720698\pi\) | |||||||
\(938\) | 122.550 | 4.00141 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −60.0669 | −1.95917 | ||||||||
\(941\) | −0.719765 | −0.0234637 | −0.0117318 | − | 0.999931i | \(-0.503734\pi\) | ||||
−0.0117318 | + | 0.999931i | \(0.503734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.469446 | 0.0152873 | ||||||||
\(944\) | 39.1790 | 1.27517 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.4023 | 0.793388 | ||||||||
\(947\) | −29.9337 | −0.972714 | −0.486357 | − | 0.873760i | \(-0.661675\pi\) | ||||
−0.486357 | + | 0.873760i | \(0.661675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.1046 | −1.56154 | ||||||||
\(950\) | 1.28292 | 0.0416235 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.4392 | −0.338337 | ||||||||
\(953\) | −46.7453 | −1.51423 | −0.757114 | − | 0.653282i | \(-0.773391\pi\) | ||||
−0.757114 | + | 0.653282i | \(0.773391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 72.1344 | 2.33421 | ||||||||
\(956\) | 23.1126 | 0.747516 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.0333 | −0.582629 | ||||||||
\(959\) | −36.6814 | −1.18450 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.36332 | −0.140752 | ||||||||
\(962\) | 63.8190 | 2.05761 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.0876 | 0.357107 | ||||||||
\(965\) | 26.4778 | 0.852351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.9325 | 1.18767 | 0.593834 | − | 0.804587i | \(-0.297613\pi\) | ||||
0.593834 | + | 0.804587i | \(0.297613\pi\) | |||||||
\(968\) | −5.70607 | −0.183400 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −30.1594 | −0.968360 | ||||||||
\(971\) | −10.7651 | −0.345469 | −0.172735 | − | 0.984968i | \(-0.555260\pi\) | ||||
−0.172735 | + | 0.984968i | \(0.555260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.3254 | −1.32483 | ||||||||
\(974\) | 11.6085 | 0.371959 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.8905 | −0.668689 | ||||||||
\(977\) | 8.98778 | 0.287545 | 0.143772 | − | 0.989611i | \(-0.454077\pi\) | ||||
0.143772 | + | 0.989611i | \(0.454077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.5380 | −1.61520 | ||||||||
\(980\) | 42.9505 | 1.37200 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31.0128 | 0.989659 | ||||||||
\(983\) | 41.4053 | 1.32062 | 0.660312 | − | 0.750991i | \(-0.270424\pi\) | ||||
0.660312 | + | 0.750991i | \(0.270424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.8420 | −0.982707 | ||||||||
\(986\) | −9.87602 | −0.314516 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.22778 | −0.0708751 | ||||||||
\(989\) | 2.68640 | 0.0854224 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0411 | 1.27195 | 0.635974 | − | 0.771710i | \(-0.280598\pi\) | ||||
0.635974 | + | 0.771710i | \(0.280598\pi\) | |||||||
\(992\) | −39.1857 | −1.24415 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 76.9601 | 2.44103 | ||||||||
\(995\) | 53.8169 | 1.70611 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.3402 | −0.359149 | −0.179575 | − | 0.983744i | \(-0.557472\pi\) | ||||
−0.179575 | + | 0.983744i | \(0.557472\pi\) | |||||||
\(998\) | −47.8851 | −1.51578 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.t.1.19 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.4 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.19 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.4 | yes | 22 | 3.2 | odd | 2 |