Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53120 | −1.78983 | −0.894915 | − | 0.446237i | \(-0.852764\pi\) | ||||
−0.894915 | + | 0.446237i | \(0.852764\pi\) | |||||||
\(3\) | −2.76336 | −1.59543 | −0.797714 | − | 0.603037i | \(-0.793957\pi\) | ||||
−0.797714 | + | 0.603037i | \(0.793957\pi\) | |||||||
\(4\) | 4.40698 | 2.20349 | ||||||||
\(5\) | 3.58460 | 1.60308 | 0.801541 | − | 0.597940i | \(-0.204014\pi\) | ||||
0.801541 | + | 0.597940i | \(0.204014\pi\) | |||||||
\(6\) | 6.99462 | 2.85554 | ||||||||
\(7\) | −0.727911 | −0.275125 | −0.137562 | − | 0.990493i | \(-0.543927\pi\) | ||||
−0.137562 | + | 0.990493i | \(0.543927\pi\) | |||||||
\(8\) | −6.09254 | −2.15404 | ||||||||
\(9\) | 4.63616 | 1.54539 | ||||||||
\(10\) | −9.07334 | −2.86924 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −12.1781 | −3.51551 | ||||||||
\(13\) | −1.11146 | −0.308263 | −0.154132 | − | 0.988050i | \(-0.549258\pi\) | ||||
−0.154132 | + | 0.988050i | \(0.549258\pi\) | |||||||
\(14\) | 1.84249 | 0.492426 | ||||||||
\(15\) | −9.90554 | −2.55760 | ||||||||
\(16\) | 6.60750 | 1.65187 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −11.7351 | −2.76598 | ||||||||
\(19\) | 3.30470 | 0.758151 | 0.379075 | − | 0.925366i | \(-0.376242\pi\) | ||||
0.379075 | + | 0.925366i | \(0.376242\pi\) | |||||||
\(20\) | 15.7973 | 3.53237 | ||||||||
\(21\) | 2.01148 | 0.438941 | ||||||||
\(22\) | −2.53120 | −0.539654 | ||||||||
\(23\) | −5.19699 | −1.08365 | −0.541824 | − | 0.840492i | \(-0.682266\pi\) | ||||
−0.541824 | + | 0.840492i | \(0.682266\pi\) | |||||||
\(24\) | 16.8359 | 3.43661 | ||||||||
\(25\) | 7.84935 | 1.56987 | ||||||||
\(26\) | 2.81333 | 0.551739 | ||||||||
\(27\) | −4.52131 | −0.870126 | ||||||||
\(28\) | −3.20789 | −0.606234 | ||||||||
\(29\) | −1.68648 | −0.313172 | −0.156586 | − | 0.987664i | \(-0.550049\pi\) | ||||
−0.156586 | + | 0.987664i | \(0.550049\pi\) | |||||||
\(30\) | 25.0729 | 4.57767 | ||||||||
\(31\) | 3.36917 | 0.605120 | 0.302560 | − | 0.953130i | \(-0.402159\pi\) | ||||
0.302560 | + | 0.953130i | \(0.402159\pi\) | |||||||
\(32\) | −4.53982 | −0.802534 | ||||||||
\(33\) | −2.76336 | −0.481039 | ||||||||
\(34\) | 2.53120 | 0.434097 | ||||||||
\(35\) | −2.60927 | −0.441047 | ||||||||
\(36\) | 20.4315 | 3.40524 | ||||||||
\(37\) | −8.94366 | −1.47033 | −0.735164 | − | 0.677889i | \(-0.762895\pi\) | ||||
−0.735164 | + | 0.677889i | \(0.762895\pi\) | |||||||
\(38\) | −8.36487 | −1.35696 | ||||||||
\(39\) | 3.07136 | 0.491812 | ||||||||
\(40\) | −21.8393 | −3.45310 | ||||||||
\(41\) | −5.08833 | −0.794663 | −0.397331 | − | 0.917675i | \(-0.630064\pi\) | ||||
−0.397331 | + | 0.917675i | \(0.630064\pi\) | |||||||
\(42\) | −5.09146 | −0.785630 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 4.40698 | 0.664377 | ||||||||
\(45\) | 16.6188 | 2.47738 | ||||||||
\(46\) | 13.1546 | 1.93954 | ||||||||
\(47\) | 2.08535 | 0.304180 | 0.152090 | − | 0.988367i | \(-0.451400\pi\) | ||||
0.152090 | + | 0.988367i | \(0.451400\pi\) | |||||||
\(48\) | −18.2589 | −2.63545 | ||||||||
\(49\) | −6.47015 | −0.924306 | ||||||||
\(50\) | −19.8683 | −2.80980 | ||||||||
\(51\) | 2.76336 | 0.386948 | ||||||||
\(52\) | −4.89818 | −0.679255 | ||||||||
\(53\) | −0.317816 | −0.0436554 | −0.0218277 | − | 0.999762i | \(-0.506949\pi\) | ||||
−0.0218277 | + | 0.999762i | \(0.506949\pi\) | |||||||
\(54\) | 11.4443 | 1.55738 | ||||||||
\(55\) | 3.58460 | 0.483347 | ||||||||
\(56\) | 4.43483 | 0.592629 | ||||||||
\(57\) | −9.13209 | −1.20957 | ||||||||
\(58\) | 4.26882 | 0.560524 | ||||||||
\(59\) | 5.62610 | 0.732455 | 0.366228 | − | 0.930525i | \(-0.380649\pi\) | ||||
0.366228 | + | 0.930525i | \(0.380649\pi\) | |||||||
\(60\) | −43.6535 | −5.63564 | ||||||||
\(61\) | −11.2332 | −1.43826 | −0.719130 | − | 0.694875i | \(-0.755459\pi\) | ||||
−0.719130 | + | 0.694875i | \(0.755459\pi\) | |||||||
\(62\) | −8.52804 | −1.08306 | ||||||||
\(63\) | −3.37471 | −0.425174 | ||||||||
\(64\) | −1.72381 | −0.215476 | ||||||||
\(65\) | −3.98414 | −0.494171 | ||||||||
\(66\) | 6.99462 | 0.860978 | ||||||||
\(67\) | −7.90842 | −0.966167 | −0.483084 | − | 0.875574i | \(-0.660483\pi\) | ||||
−0.483084 | + | 0.875574i | \(0.660483\pi\) | |||||||
\(68\) | −4.40698 | −0.534425 | ||||||||
\(69\) | 14.3612 | 1.72888 | ||||||||
\(70\) | 6.60459 | 0.789399 | ||||||||
\(71\) | 9.16197 | 1.08733 | 0.543663 | − | 0.839304i | \(-0.317037\pi\) | ||||
0.543663 | + | 0.839304i | \(0.317037\pi\) | |||||||
\(72\) | −28.2460 | −3.32883 | ||||||||
\(73\) | −10.6186 | −1.24282 | −0.621408 | − | 0.783488i | \(-0.713439\pi\) | ||||
−0.621408 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(74\) | 22.6382 | 2.63164 | ||||||||
\(75\) | −21.6906 | −2.50461 | ||||||||
\(76\) | 14.5638 | 1.67058 | ||||||||
\(77\) | −0.727911 | −0.0829532 | ||||||||
\(78\) | −7.77424 | −0.880259 | ||||||||
\(79\) | 13.4281 | 1.51078 | 0.755389 | − | 0.655277i | \(-0.227448\pi\) | ||||
0.755389 | + | 0.655277i | \(0.227448\pi\) | |||||||
\(80\) | 23.6852 | 2.64809 | ||||||||
\(81\) | −1.41449 | −0.157165 | ||||||||
\(82\) | 12.8796 | 1.42231 | ||||||||
\(83\) | −8.85038 | −0.971455 | −0.485728 | − | 0.874110i | \(-0.661445\pi\) | ||||
−0.485728 | + | 0.874110i | \(0.661445\pi\) | |||||||
\(84\) | 8.86455 | 0.967202 | ||||||||
\(85\) | −3.58460 | −0.388804 | ||||||||
\(86\) | 2.53120 | 0.272946 | ||||||||
\(87\) | 4.66035 | 0.499642 | ||||||||
\(88\) | −6.09254 | −0.649467 | ||||||||
\(89\) | 7.04878 | 0.747169 | 0.373584 | − | 0.927596i | \(-0.378129\pi\) | ||||
0.373584 | + | 0.927596i | \(0.378129\pi\) | |||||||
\(90\) | −42.0655 | −4.43409 | ||||||||
\(91\) | 0.809044 | 0.0848109 | ||||||||
\(92\) | −22.9030 | −2.38781 | ||||||||
\(93\) | −9.31022 | −0.965425 | ||||||||
\(94\) | −5.27845 | −0.544431 | ||||||||
\(95\) | 11.8460 | 1.21538 | ||||||||
\(96\) | 12.5452 | 1.28038 | ||||||||
\(97\) | 12.3075 | 1.24964 | 0.624819 | − | 0.780769i | \(-0.285173\pi\) | ||||
0.624819 | + | 0.780769i | \(0.285173\pi\) | |||||||
\(98\) | 16.3772 | 1.65435 | ||||||||
\(99\) | 4.63616 | 0.465952 | ||||||||
\(100\) | 34.5919 | 3.45919 | ||||||||
\(101\) | −15.5117 | −1.54347 | −0.771736 | − | 0.635943i | \(-0.780611\pi\) | ||||
−0.771736 | + | 0.635943i | \(0.780611\pi\) | |||||||
\(102\) | −6.99462 | −0.692571 | ||||||||
\(103\) | 1.85325 | 0.182606 | 0.0913032 | − | 0.995823i | \(-0.470897\pi\) | ||||
0.0913032 | + | 0.995823i | \(0.470897\pi\) | |||||||
\(104\) | 6.77162 | 0.664012 | ||||||||
\(105\) | 7.21035 | 0.703659 | ||||||||
\(106\) | 0.804456 | 0.0781357 | ||||||||
\(107\) | −9.02054 | −0.872049 | −0.436024 | − | 0.899935i | \(-0.643614\pi\) | ||||
−0.436024 | + | 0.899935i | \(0.643614\pi\) | |||||||
\(108\) | −19.9253 | −1.91731 | ||||||||
\(109\) | 17.7576 | 1.70087 | 0.850435 | − | 0.526080i | \(-0.176339\pi\) | ||||
0.850435 | + | 0.526080i | \(0.176339\pi\) | |||||||
\(110\) | −9.07334 | −0.865109 | ||||||||
\(111\) | 24.7146 | 2.34580 | ||||||||
\(112\) | −4.80967 | −0.454471 | ||||||||
\(113\) | −2.02453 | −0.190452 | −0.0952259 | − | 0.995456i | \(-0.530357\pi\) | ||||
−0.0952259 | + | 0.995456i | \(0.530357\pi\) | |||||||
\(114\) | 23.1151 | 2.16493 | ||||||||
\(115\) | −18.6291 | −1.73718 | ||||||||
\(116\) | −7.43228 | −0.690070 | ||||||||
\(117\) | −5.15291 | −0.476386 | ||||||||
\(118\) | −14.2408 | −1.31097 | ||||||||
\(119\) | 0.727911 | 0.0667275 | ||||||||
\(120\) | 60.3500 | 5.50917 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 28.4334 | 2.57424 | ||||||||
\(123\) | 14.0609 | 1.26783 | ||||||||
\(124\) | 14.8478 | 1.33338 | ||||||||
\(125\) | 10.2138 | 0.913549 | ||||||||
\(126\) | 8.54208 | 0.760989 | ||||||||
\(127\) | 13.3695 | 1.18635 | 0.593174 | − | 0.805074i | \(-0.297875\pi\) | ||||
0.593174 | + | 0.805074i | \(0.297875\pi\) | |||||||
\(128\) | 13.4429 | 1.18820 | ||||||||
\(129\) | 2.76336 | 0.243300 | ||||||||
\(130\) | 10.0847 | 0.884483 | ||||||||
\(131\) | 6.46156 | 0.564549 | 0.282275 | − | 0.959334i | \(-0.408911\pi\) | ||||
0.282275 | + | 0.959334i | \(0.408911\pi\) | |||||||
\(132\) | −12.1781 | −1.05996 | ||||||||
\(133\) | −2.40553 | −0.208586 | ||||||||
\(134\) | 20.0178 | 1.72927 | ||||||||
\(135\) | −16.2071 | −1.39488 | ||||||||
\(136\) | 6.09254 | 0.522431 | ||||||||
\(137\) | 19.0000 | 1.62328 | 0.811639 | − | 0.584160i | \(-0.198576\pi\) | ||||
0.811639 | + | 0.584160i | \(0.198576\pi\) | |||||||
\(138\) | −36.3510 | −3.09440 | ||||||||
\(139\) | 7.35355 | 0.623720 | 0.311860 | − | 0.950128i | \(-0.399048\pi\) | ||||
0.311860 | + | 0.950128i | \(0.399048\pi\) | |||||||
\(140\) | −11.4990 | −0.971843 | ||||||||
\(141\) | −5.76259 | −0.485297 | ||||||||
\(142\) | −23.1908 | −1.94613 | ||||||||
\(143\) | −1.11146 | −0.0929449 | ||||||||
\(144\) | 30.6334 | 2.55279 | ||||||||
\(145\) | −6.04536 | −0.502040 | ||||||||
\(146\) | 26.8779 | 2.22443 | ||||||||
\(147\) | 17.8793 | 1.47466 | ||||||||
\(148\) | −39.4145 | −3.23985 | ||||||||
\(149\) | 0.0875898 | 0.00717564 | 0.00358782 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358782 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(150\) | 54.9033 | 4.48283 | ||||||||
\(151\) | −0.931349 | −0.0757921 | −0.0378961 | − | 0.999282i | \(-0.512066\pi\) | ||||
−0.0378961 | + | 0.999282i | \(0.512066\pi\) | |||||||
\(152\) | −20.1340 | −1.63309 | ||||||||
\(153\) | −4.63616 | −0.374811 | ||||||||
\(154\) | 1.84249 | 0.148472 | ||||||||
\(155\) | 12.0771 | 0.970057 | ||||||||
\(156\) | 13.5354 | 1.08370 | ||||||||
\(157\) | 12.4048 | 0.990009 | 0.495005 | − | 0.868890i | \(-0.335166\pi\) | ||||
0.495005 | + | 0.868890i | \(0.335166\pi\) | |||||||
\(158\) | −33.9892 | −2.70403 | ||||||||
\(159\) | 0.878240 | 0.0696490 | ||||||||
\(160\) | −16.2734 | −1.28653 | ||||||||
\(161\) | 3.78295 | 0.298138 | ||||||||
\(162\) | 3.58035 | 0.281299 | ||||||||
\(163\) | 13.3465 | 1.04538 | 0.522688 | − | 0.852524i | \(-0.324929\pi\) | ||||
0.522688 | + | 0.852524i | \(0.324929\pi\) | |||||||
\(164\) | −22.4241 | −1.75103 | ||||||||
\(165\) | −9.90554 | −0.771145 | ||||||||
\(166\) | 22.4021 | 1.73874 | ||||||||
\(167\) | 6.43560 | 0.498002 | 0.249001 | − | 0.968503i | \(-0.419898\pi\) | ||||
0.249001 | + | 0.968503i | \(0.419898\pi\) | |||||||
\(168\) | −12.2550 | −0.945497 | ||||||||
\(169\) | −11.7647 | −0.904974 | ||||||||
\(170\) | 9.07334 | 0.695894 | ||||||||
\(171\) | 15.3211 | 1.17164 | ||||||||
\(172\) | −4.40698 | −0.336029 | ||||||||
\(173\) | −1.68221 | −0.127896 | −0.0639479 | − | 0.997953i | \(-0.520369\pi\) | ||||
−0.0639479 | + | 0.997953i | \(0.520369\pi\) | |||||||
\(174\) | −11.7963 | −0.894275 | ||||||||
\(175\) | −5.71363 | −0.431910 | ||||||||
\(176\) | 6.60750 | 0.498059 | ||||||||
\(177\) | −15.5469 | −1.16858 | ||||||||
\(178\) | −17.8419 | −1.33730 | ||||||||
\(179\) | 9.36711 | 0.700131 | 0.350065 | − | 0.936725i | \(-0.386159\pi\) | ||||
0.350065 | + | 0.936725i | \(0.386159\pi\) | |||||||
\(180\) | 73.2386 | 5.45888 | ||||||||
\(181\) | 10.7297 | 0.797533 | 0.398766 | − | 0.917053i | \(-0.369438\pi\) | ||||
0.398766 | + | 0.917053i | \(0.369438\pi\) | |||||||
\(182\) | −2.04785 | −0.151797 | ||||||||
\(183\) | 31.0413 | 2.29464 | ||||||||
\(184\) | 31.6629 | 2.33422 | ||||||||
\(185\) | −32.0594 | −2.35706 | ||||||||
\(186\) | 23.5660 | 1.72795 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 9.19011 | 0.670258 | ||||||||
\(189\) | 3.29111 | 0.239393 | ||||||||
\(190\) | −29.9847 | −2.17532 | ||||||||
\(191\) | 13.4288 | 0.971674 | 0.485837 | − | 0.874049i | \(-0.338515\pi\) | ||||
0.485837 | + | 0.874049i | \(0.338515\pi\) | |||||||
\(192\) | 4.76351 | 0.343776 | ||||||||
\(193\) | 10.6725 | 0.768225 | 0.384112 | − | 0.923286i | \(-0.374508\pi\) | ||||
0.384112 | + | 0.923286i | \(0.374508\pi\) | |||||||
\(194\) | −31.1528 | −2.23664 | ||||||||
\(195\) | 11.0096 | 0.788415 | ||||||||
\(196\) | −28.5138 | −2.03670 | ||||||||
\(197\) | 15.7843 | 1.12458 | 0.562292 | − | 0.826938i | \(-0.309920\pi\) | ||||
0.562292 | + | 0.826938i | \(0.309920\pi\) | |||||||
\(198\) | −11.7351 | −0.833974 | ||||||||
\(199\) | 8.05060 | 0.570692 | 0.285346 | − | 0.958425i | \(-0.407892\pi\) | ||||
0.285346 | + | 0.958425i | \(0.407892\pi\) | |||||||
\(200\) | −47.8225 | −3.38156 | ||||||||
\(201\) | 21.8538 | 1.54145 | ||||||||
\(202\) | 39.2632 | 2.76255 | ||||||||
\(203\) | 1.22761 | 0.0861612 | ||||||||
\(204\) | 12.1781 | 0.852635 | ||||||||
\(205\) | −18.2396 | −1.27391 | ||||||||
\(206\) | −4.69096 | −0.326834 | ||||||||
\(207\) | −24.0941 | −1.67466 | ||||||||
\(208\) | −7.34397 | −0.509213 | ||||||||
\(209\) | 3.30470 | 0.228591 | ||||||||
\(210\) | −18.2509 | −1.25943 | ||||||||
\(211\) | 9.21320 | 0.634263 | 0.317131 | − | 0.948382i | \(-0.397280\pi\) | ||||
0.317131 | + | 0.948382i | \(0.397280\pi\) | |||||||
\(212\) | −1.40061 | −0.0961941 | ||||||||
\(213\) | −25.3178 | −1.73475 | ||||||||
\(214\) | 22.8328 | 1.56082 | ||||||||
\(215\) | −3.58460 | −0.244468 | ||||||||
\(216\) | 27.5463 | 1.87429 | ||||||||
\(217\) | −2.45245 | −0.166483 | ||||||||
\(218\) | −44.9481 | −3.04427 | ||||||||
\(219\) | 29.3431 | 1.98282 | ||||||||
\(220\) | 15.7973 | 1.06505 | ||||||||
\(221\) | 1.11146 | 0.0747649 | ||||||||
\(222\) | −62.5575 | −4.19859 | ||||||||
\(223\) | 11.3001 | 0.756710 | 0.378355 | − | 0.925661i | \(-0.376490\pi\) | ||||
0.378355 | + | 0.925661i | \(0.376490\pi\) | |||||||
\(224\) | 3.30458 | 0.220797 | ||||||||
\(225\) | 36.3909 | 2.42606 | ||||||||
\(226\) | 5.12449 | 0.340876 | ||||||||
\(227\) | −12.4027 | −0.823198 | −0.411599 | − | 0.911365i | \(-0.635030\pi\) | ||||
−0.411599 | + | 0.911365i | \(0.635030\pi\) | |||||||
\(228\) | −40.2449 | −2.66528 | ||||||||
\(229\) | −16.7062 | −1.10397 | −0.551987 | − | 0.833853i | \(-0.686130\pi\) | ||||
−0.551987 | + | 0.833853i | \(0.686130\pi\) | |||||||
\(230\) | 47.1541 | 3.10925 | ||||||||
\(231\) | 2.01148 | 0.132346 | ||||||||
\(232\) | 10.2750 | 0.674584 | ||||||||
\(233\) | 0.928042 | 0.0607981 | 0.0303990 | − | 0.999538i | \(-0.490322\pi\) | ||||
0.0303990 | + | 0.999538i | \(0.490322\pi\) | |||||||
\(234\) | 13.0430 | 0.852650 | ||||||||
\(235\) | 7.47516 | 0.487626 | ||||||||
\(236\) | 24.7941 | 1.61396 | ||||||||
\(237\) | −37.1066 | −2.41033 | ||||||||
\(238\) | −1.84249 | −0.119431 | ||||||||
\(239\) | −10.7737 | −0.696891 | −0.348445 | − | 0.937329i | \(-0.613290\pi\) | ||||
−0.348445 | + | 0.937329i | \(0.613290\pi\) | |||||||
\(240\) | −65.4508 | −4.22483 | ||||||||
\(241\) | −16.2593 | −1.04735 | −0.523675 | − | 0.851918i | \(-0.675439\pi\) | ||||
−0.523675 | + | 0.851918i | \(0.675439\pi\) | |||||||
\(242\) | −2.53120 | −0.162712 | ||||||||
\(243\) | 17.4727 | 1.12087 | ||||||||
\(244\) | −49.5043 | −3.16919 | ||||||||
\(245\) | −23.1929 | −1.48174 | ||||||||
\(246\) | −35.5909 | −2.26919 | ||||||||
\(247\) | −3.67304 | −0.233710 | ||||||||
\(248\) | −20.5268 | −1.30345 | ||||||||
\(249\) | 24.4568 | 1.54989 | ||||||||
\(250\) | −25.8532 | −1.63510 | ||||||||
\(251\) | −4.98582 | −0.314702 | −0.157351 | − | 0.987543i | \(-0.550295\pi\) | ||||
−0.157351 | + | 0.987543i | \(0.550295\pi\) | |||||||
\(252\) | −14.8723 | −0.936866 | ||||||||
\(253\) | −5.19699 | −0.326732 | ||||||||
\(254\) | −33.8408 | −2.12336 | ||||||||
\(255\) | 9.90554 | 0.620309 | ||||||||
\(256\) | −30.5792 | −1.91120 | ||||||||
\(257\) | 16.3442 | 1.01953 | 0.509763 | − | 0.860315i | \(-0.329733\pi\) | ||||
0.509763 | + | 0.860315i | \(0.329733\pi\) | |||||||
\(258\) | −6.99462 | −0.435466 | ||||||||
\(259\) | 6.51019 | 0.404524 | ||||||||
\(260\) | −17.5580 | −1.08890 | ||||||||
\(261\) | −7.81880 | −0.483971 | ||||||||
\(262\) | −16.3555 | −1.01045 | ||||||||
\(263\) | 9.81069 | 0.604953 | 0.302476 | − | 0.953157i | \(-0.402187\pi\) | ||||
0.302476 | + | 0.953157i | \(0.402187\pi\) | |||||||
\(264\) | 16.8359 | 1.03618 | ||||||||
\(265\) | −1.13924 | −0.0699831 | ||||||||
\(266\) | 6.08888 | 0.373333 | ||||||||
\(267\) | −19.4783 | −1.19205 | ||||||||
\(268\) | −34.8522 | −2.12894 | ||||||||
\(269\) | 1.48875 | 0.0907706 | 0.0453853 | − | 0.998970i | \(-0.485548\pi\) | ||||
0.0453853 | + | 0.998970i | \(0.485548\pi\) | |||||||
\(270\) | 41.0234 | 2.49660 | ||||||||
\(271\) | −27.7376 | −1.68494 | −0.842468 | − | 0.538746i | \(-0.818898\pi\) | ||||
−0.842468 | + | 0.538746i | \(0.818898\pi\) | |||||||
\(272\) | −6.60750 | −0.400638 | ||||||||
\(273\) | −2.23568 | −0.135310 | ||||||||
\(274\) | −48.0928 | −2.90539 | ||||||||
\(275\) | 7.84935 | 0.473334 | ||||||||
\(276\) | 63.2893 | 3.80957 | ||||||||
\(277\) | −24.6505 | −1.48110 | −0.740552 | − | 0.671999i | \(-0.765436\pi\) | ||||
−0.740552 | + | 0.671999i | \(0.765436\pi\) | |||||||
\(278\) | −18.6133 | −1.11635 | ||||||||
\(279\) | 15.6200 | 0.935145 | ||||||||
\(280\) | 15.8971 | 0.950033 | ||||||||
\(281\) | 2.76881 | 0.165173 | 0.0825867 | − | 0.996584i | \(-0.473682\pi\) | ||||
0.0825867 | + | 0.996584i | \(0.473682\pi\) | |||||||
\(282\) | 14.5863 | 0.868599 | ||||||||
\(283\) | −14.7986 | −0.879685 | −0.439843 | − | 0.898075i | \(-0.644966\pi\) | ||||
−0.439843 | + | 0.898075i | \(0.644966\pi\) | |||||||
\(284\) | 40.3766 | 2.39591 | ||||||||
\(285\) | −32.7349 | −1.93905 | ||||||||
\(286\) | 2.81333 | 0.166356 | ||||||||
\(287\) | 3.70385 | 0.218631 | ||||||||
\(288\) | −21.0473 | −1.24023 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 15.3020 | 0.898565 | ||||||||
\(291\) | −34.0101 | −1.99371 | ||||||||
\(292\) | −46.7960 | −2.73853 | ||||||||
\(293\) | 28.3688 | 1.65732 | 0.828662 | − | 0.559749i | \(-0.189103\pi\) | ||||
0.828662 | + | 0.559749i | \(0.189103\pi\) | |||||||
\(294\) | −45.2562 | −2.63940 | ||||||||
\(295\) | 20.1673 | 1.17419 | ||||||||
\(296\) | 54.4897 | 3.16715 | ||||||||
\(297\) | −4.52131 | −0.262353 | ||||||||
\(298\) | −0.221707 | −0.0128432 | ||||||||
\(299\) | 5.77625 | 0.334049 | ||||||||
\(300\) | −95.5900 | −5.51889 | ||||||||
\(301\) | 0.727911 | 0.0419561 | ||||||||
\(302\) | 2.35743 | 0.135655 | ||||||||
\(303\) | 42.8644 | 2.46250 | ||||||||
\(304\) | 21.8358 | 1.25237 | ||||||||
\(305\) | −40.2664 | −2.30565 | ||||||||
\(306\) | 11.7351 | 0.670849 | ||||||||
\(307\) | −9.77116 | −0.557670 | −0.278835 | − | 0.960339i | \(-0.589948\pi\) | ||||
−0.278835 | + | 0.960339i | \(0.589948\pi\) | |||||||
\(308\) | −3.20789 | −0.182786 | ||||||||
\(309\) | −5.12121 | −0.291335 | ||||||||
\(310\) | −30.5696 | −1.73624 | ||||||||
\(311\) | −9.98449 | −0.566168 | −0.283084 | − | 0.959095i | \(-0.591358\pi\) | ||||
−0.283084 | + | 0.959095i | \(0.591358\pi\) | |||||||
\(312\) | −18.7124 | −1.05938 | ||||||||
\(313\) | 31.9647 | 1.80675 | 0.903376 | − | 0.428849i | \(-0.141081\pi\) | ||||
0.903376 | + | 0.428849i | \(0.141081\pi\) | |||||||
\(314\) | −31.3990 | −1.77195 | ||||||||
\(315\) | −12.0970 | −0.681589 | ||||||||
\(316\) | 59.1773 | 3.32898 | ||||||||
\(317\) | −17.1474 | −0.963092 | −0.481546 | − | 0.876421i | \(-0.659925\pi\) | ||||
−0.481546 | + | 0.876421i | \(0.659925\pi\) | |||||||
\(318\) | −2.22300 | −0.124660 | ||||||||
\(319\) | −1.68648 | −0.0944248 | ||||||||
\(320\) | −6.17916 | −0.345426 | ||||||||
\(321\) | 24.9270 | 1.39129 | ||||||||
\(322\) | −9.57541 | −0.533616 | ||||||||
\(323\) | −3.30470 | −0.183879 | ||||||||
\(324\) | −6.23362 | −0.346312 | ||||||||
\(325\) | −8.72424 | −0.483934 | ||||||||
\(326\) | −33.7826 | −1.87105 | ||||||||
\(327\) | −49.0707 | −2.71361 | ||||||||
\(328\) | 31.0009 | 1.71174 | ||||||||
\(329\) | −1.51795 | −0.0836874 | ||||||||
\(330\) | 25.0729 | 1.38022 | ||||||||
\(331\) | 10.9993 | 0.604578 | 0.302289 | − | 0.953216i | \(-0.402249\pi\) | ||||
0.302289 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(332\) | −39.0034 | −2.14059 | ||||||||
\(333\) | −41.4643 | −2.27223 | ||||||||
\(334\) | −16.2898 | −0.891338 | ||||||||
\(335\) | −28.3485 | −1.54884 | ||||||||
\(336\) | 13.2909 | 0.725076 | ||||||||
\(337\) | −8.51147 | −0.463649 | −0.231825 | − | 0.972758i | \(-0.574470\pi\) | ||||
−0.231825 | + | 0.972758i | \(0.574470\pi\) | |||||||
\(338\) | 29.7787 | 1.61975 | ||||||||
\(339\) | 5.59451 | 0.303852 | ||||||||
\(340\) | −15.7973 | −0.856726 | ||||||||
\(341\) | 3.36917 | 0.182451 | ||||||||
\(342\) | −38.7809 | −2.09703 | ||||||||
\(343\) | 9.80507 | 0.529424 | ||||||||
\(344\) | 6.09254 | 0.328488 | ||||||||
\(345\) | 51.4790 | 2.77154 | ||||||||
\(346\) | 4.25800 | 0.228912 | ||||||||
\(347\) | 16.1557 | 0.867282 | 0.433641 | − | 0.901086i | \(-0.357229\pi\) | ||||
0.433641 | + | 0.901086i | \(0.357229\pi\) | |||||||
\(348\) | 20.5381 | 1.10096 | ||||||||
\(349\) | 17.5613 | 0.940034 | 0.470017 | − | 0.882657i | \(-0.344248\pi\) | ||||
0.470017 | + | 0.882657i | \(0.344248\pi\) | |||||||
\(350\) | 14.4624 | 0.773045 | ||||||||
\(351\) | 5.02525 | 0.268228 | ||||||||
\(352\) | −4.53982 | −0.241973 | ||||||||
\(353\) | 8.61383 | 0.458468 | 0.229234 | − | 0.973371i | \(-0.426378\pi\) | ||||
0.229234 | + | 0.973371i | \(0.426378\pi\) | |||||||
\(354\) | 39.3524 | 2.09156 | ||||||||
\(355\) | 32.8420 | 1.74307 | ||||||||
\(356\) | 31.0638 | 1.64638 | ||||||||
\(357\) | −2.01148 | −0.106459 | ||||||||
\(358\) | −23.7100 | −1.25311 | ||||||||
\(359\) | 8.45971 | 0.446486 | 0.223243 | − | 0.974763i | \(-0.428336\pi\) | ||||
0.223243 | + | 0.974763i | \(0.428336\pi\) | |||||||
\(360\) | −101.251 | −5.33638 | ||||||||
\(361\) | −8.07894 | −0.425207 | ||||||||
\(362\) | −27.1590 | −1.42745 | ||||||||
\(363\) | −2.76336 | −0.145039 | ||||||||
\(364\) | 3.56544 | 0.186880 | ||||||||
\(365\) | −38.0635 | −1.99233 | ||||||||
\(366\) | −78.5718 | −4.10701 | ||||||||
\(367\) | −17.2297 | −0.899385 | −0.449692 | − | 0.893184i | \(-0.648466\pi\) | ||||
−0.449692 | + | 0.893184i | \(0.648466\pi\) | |||||||
\(368\) | −34.3391 | −1.79005 | ||||||||
\(369\) | −23.5903 | −1.22806 | ||||||||
\(370\) | 81.1489 | 4.21873 | ||||||||
\(371\) | 0.231342 | 0.0120107 | ||||||||
\(372\) | −41.0299 | −2.12730 | ||||||||
\(373\) | −32.2724 | −1.67100 | −0.835500 | − | 0.549490i | \(-0.814822\pi\) | ||||
−0.835500 | + | 0.549490i | \(0.814822\pi\) | |||||||
\(374\) | 2.53120 | 0.130885 | ||||||||
\(375\) | −28.2244 | −1.45750 | ||||||||
\(376\) | −12.7051 | −0.655216 | ||||||||
\(377\) | 1.87446 | 0.0965393 | ||||||||
\(378\) | −8.33046 | −0.428473 | ||||||||
\(379\) | −8.33140 | −0.427955 | −0.213978 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213978 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(380\) | 52.2052 | 2.67807 | ||||||||
\(381\) | −36.9446 | −1.89273 | ||||||||
\(382\) | −33.9910 | −1.73913 | ||||||||
\(383\) | −19.9560 | −1.01970 | −0.509852 | − | 0.860262i | \(-0.670300\pi\) | ||||
−0.509852 | + | 0.860262i | \(0.670300\pi\) | |||||||
\(384\) | −37.1477 | −1.89569 | ||||||||
\(385\) | −2.60927 | −0.132981 | ||||||||
\(386\) | −27.0143 | −1.37499 | ||||||||
\(387\) | −4.63616 | −0.235669 | ||||||||
\(388\) | 54.2389 | 2.75356 | ||||||||
\(389\) | 12.2884 | 0.623048 | 0.311524 | − | 0.950238i | \(-0.399161\pi\) | ||||
0.311524 | + | 0.950238i | \(0.399161\pi\) | |||||||
\(390\) | −27.8675 | −1.41113 | ||||||||
\(391\) | 5.19699 | 0.262823 | ||||||||
\(392\) | 39.4196 | 1.99099 | ||||||||
\(393\) | −17.8556 | −0.900697 | ||||||||
\(394\) | −39.9532 | −2.01282 | ||||||||
\(395\) | 48.1343 | 2.42190 | ||||||||
\(396\) | 20.4315 | 1.02672 | ||||||||
\(397\) | 30.2991 | 1.52067 | 0.760334 | − | 0.649532i | \(-0.225035\pi\) | ||||
0.760334 | + | 0.649532i | \(0.225035\pi\) | |||||||
\(398\) | −20.3777 | −1.02144 | ||||||||
\(399\) | 6.64735 | 0.332784 | ||||||||
\(400\) | 51.8646 | 2.59323 | ||||||||
\(401\) | 26.1087 | 1.30381 | 0.651903 | − | 0.758302i | \(-0.273971\pi\) | ||||
0.651903 | + | 0.758302i | \(0.273971\pi\) | |||||||
\(402\) | −55.3164 | −2.75893 | ||||||||
\(403\) | −3.74469 | −0.186536 | ||||||||
\(404\) | −68.3597 | −3.40102 | ||||||||
\(405\) | −5.07037 | −0.251949 | ||||||||
\(406\) | −3.10732 | −0.154214 | ||||||||
\(407\) | −8.94366 | −0.443321 | ||||||||
\(408\) | −16.8359 | −0.833501 | ||||||||
\(409\) | −19.0915 | −0.944014 | −0.472007 | − | 0.881595i | \(-0.656470\pi\) | ||||
−0.472007 | + | 0.881595i | \(0.656470\pi\) | |||||||
\(410\) | 46.1681 | 2.28008 | ||||||||
\(411\) | −52.5038 | −2.58982 | ||||||||
\(412\) | 8.16724 | 0.402371 | ||||||||
\(413\) | −4.09530 | −0.201516 | ||||||||
\(414\) | 60.9870 | 2.99735 | ||||||||
\(415\) | −31.7251 | −1.55732 | ||||||||
\(416\) | 5.04582 | 0.247392 | ||||||||
\(417\) | −20.3205 | −0.995100 | ||||||||
\(418\) | −8.36487 | −0.409139 | ||||||||
\(419\) | 25.7764 | 1.25926 | 0.629631 | − | 0.776894i | \(-0.283206\pi\) | ||||
0.629631 | + | 0.776894i | \(0.283206\pi\) | |||||||
\(420\) | 31.7759 | 1.55050 | ||||||||
\(421\) | 16.7687 | 0.817256 | 0.408628 | − | 0.912701i | \(-0.366007\pi\) | ||||
0.408628 | + | 0.912701i | \(0.366007\pi\) | |||||||
\(422\) | −23.3205 | −1.13522 | ||||||||
\(423\) | 9.66804 | 0.470076 | ||||||||
\(424\) | 1.93631 | 0.0940354 | ||||||||
\(425\) | −7.84935 | −0.380750 | ||||||||
\(426\) | 64.0845 | 3.10490 | ||||||||
\(427\) | 8.17675 | 0.395701 | ||||||||
\(428\) | −39.7533 | −1.92155 | ||||||||
\(429\) | 3.07136 | 0.148287 | ||||||||
\(430\) | 9.07334 | 0.437555 | ||||||||
\(431\) | 17.0944 | 0.823410 | 0.411705 | − | 0.911317i | \(-0.364933\pi\) | ||||
0.411705 | + | 0.911317i | \(0.364933\pi\) | |||||||
\(432\) | −29.8745 | −1.43734 | ||||||||
\(433\) | −8.46890 | −0.406989 | −0.203495 | − | 0.979076i | \(-0.565230\pi\) | ||||
−0.203495 | + | 0.979076i | \(0.565230\pi\) | |||||||
\(434\) | 6.20765 | 0.297977 | ||||||||
\(435\) | 16.7055 | 0.800968 | ||||||||
\(436\) | 78.2574 | 3.74785 | ||||||||
\(437\) | −17.1745 | −0.821569 | ||||||||
\(438\) | −74.2732 | −3.54891 | ||||||||
\(439\) | −2.76905 | −0.132159 | −0.0660797 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660797 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(440\) | −21.8393 | −1.04115 | ||||||||
\(441\) | −29.9966 | −1.42841 | ||||||||
\(442\) | −2.81333 | −0.133816 | ||||||||
\(443\) | 29.2479 | 1.38961 | 0.694804 | − | 0.719199i | \(-0.255491\pi\) | ||||
0.694804 | + | 0.719199i | \(0.255491\pi\) | |||||||
\(444\) | 108.917 | 5.16895 | ||||||||
\(445\) | 25.2670 | 1.19777 | ||||||||
\(446\) | −28.6028 | −1.35438 | ||||||||
\(447\) | −0.242042 | −0.0114482 | ||||||||
\(448\) | 1.25478 | 0.0592828 | ||||||||
\(449\) | −4.22147 | −0.199224 | −0.0996118 | − | 0.995026i | \(-0.531760\pi\) | ||||
−0.0996118 | + | 0.995026i | \(0.531760\pi\) | |||||||
\(450\) | −92.1126 | −4.34223 | ||||||||
\(451\) | −5.08833 | −0.239600 | ||||||||
\(452\) | −8.92206 | −0.419658 | ||||||||
\(453\) | 2.57365 | 0.120921 | ||||||||
\(454\) | 31.3938 | 1.47338 | ||||||||
\(455\) | 2.90010 | 0.135959 | ||||||||
\(456\) | 55.6376 | 2.60547 | ||||||||
\(457\) | 5.45810 | 0.255319 | 0.127659 | − | 0.991818i | \(-0.459254\pi\) | ||||
0.127659 | + | 0.991818i | \(0.459254\pi\) | |||||||
\(458\) | 42.2867 | 1.97593 | ||||||||
\(459\) | 4.52131 | 0.211036 | ||||||||
\(460\) | −82.0982 | −3.82785 | ||||||||
\(461\) | −23.6125 | −1.09974 | −0.549872 | − | 0.835249i | \(-0.685324\pi\) | ||||
−0.549872 | + | 0.835249i | \(0.685324\pi\) | |||||||
\(462\) | −5.09146 | −0.236876 | ||||||||
\(463\) | −9.62190 | −0.447168 | −0.223584 | − | 0.974685i | \(-0.571776\pi\) | ||||
−0.223584 | + | 0.974685i | \(0.571776\pi\) | |||||||
\(464\) | −11.1434 | −0.517320 | ||||||||
\(465\) | −33.3734 | −1.54766 | ||||||||
\(466\) | −2.34906 | −0.108818 | ||||||||
\(467\) | 28.5389 | 1.32062 | 0.660312 | − | 0.750992i | \(-0.270424\pi\) | ||||
0.660312 | + | 0.750992i | \(0.270424\pi\) | |||||||
\(468\) | −22.7087 | −1.04971 | ||||||||
\(469\) | 5.75663 | 0.265816 | ||||||||
\(470\) | −18.9211 | −0.872767 | ||||||||
\(471\) | −34.2789 | −1.57949 | ||||||||
\(472\) | −34.2772 | −1.57774 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 93.9243 | 4.31409 | ||||||||
\(475\) | 25.9398 | 1.19020 | ||||||||
\(476\) | 3.20789 | 0.147033 | ||||||||
\(477\) | −1.47345 | −0.0674645 | ||||||||
\(478\) | 27.2703 | 1.24732 | ||||||||
\(479\) | 38.0948 | 1.74060 | 0.870298 | − | 0.492525i | \(-0.163926\pi\) | ||||
0.870298 | + | 0.492525i | \(0.163926\pi\) | |||||||
\(480\) | 44.9693 | 2.05256 | ||||||||
\(481\) | 9.94052 | 0.453249 | ||||||||
\(482\) | 41.1554 | 1.87458 | ||||||||
\(483\) | −10.4537 | −0.475658 | ||||||||
\(484\) | 4.40698 | 0.200317 | ||||||||
\(485\) | 44.1175 | 2.00327 | ||||||||
\(486\) | −44.2268 | −2.00617 | ||||||||
\(487\) | 21.4050 | 0.969955 | 0.484978 | − | 0.874527i | \(-0.338828\pi\) | ||||
0.484978 | + | 0.874527i | \(0.338828\pi\) | |||||||
\(488\) | 68.4386 | 3.09807 | ||||||||
\(489\) | −36.8811 | −1.66782 | ||||||||
\(490\) | 58.7058 | 2.65206 | ||||||||
\(491\) | 7.63187 | 0.344421 | 0.172211 | − | 0.985060i | \(-0.444909\pi\) | ||||
0.172211 | + | 0.985060i | \(0.444909\pi\) | |||||||
\(492\) | 61.9660 | 2.79364 | ||||||||
\(493\) | 1.68648 | 0.0759553 | ||||||||
\(494\) | 9.29721 | 0.418301 | ||||||||
\(495\) | 16.6188 | 0.746959 | ||||||||
\(496\) | 22.2618 | 0.999583 | ||||||||
\(497\) | −6.66910 | −0.299150 | ||||||||
\(498\) | −61.9050 | −2.77403 | ||||||||
\(499\) | −1.11221 | −0.0497895 | −0.0248948 | − | 0.999690i | \(-0.507925\pi\) | ||||
−0.0248948 | + | 0.999690i | \(0.507925\pi\) | |||||||
\(500\) | 45.0119 | 2.01300 | ||||||||
\(501\) | −17.7839 | −0.794526 | ||||||||
\(502\) | 12.6201 | 0.563263 | ||||||||
\(503\) | −13.8676 | −0.618325 | −0.309163 | − | 0.951009i | \(-0.600049\pi\) | ||||
−0.309163 | + | 0.951009i | \(0.600049\pi\) | |||||||
\(504\) | 20.5606 | 0.915842 | ||||||||
\(505\) | −55.6033 | −2.47431 | ||||||||
\(506\) | 13.1546 | 0.584795 | ||||||||
\(507\) | 32.5100 | 1.44382 | ||||||||
\(508\) | 58.9189 | 2.61410 | ||||||||
\(509\) | −15.0736 | −0.668125 | −0.334063 | − | 0.942551i | \(-0.608420\pi\) | ||||
−0.334063 | + | 0.942551i | \(0.608420\pi\) | |||||||
\(510\) | −25.0729 | −1.11025 | ||||||||
\(511\) | 7.72941 | 0.341929 | ||||||||
\(512\) | 50.5161 | 2.23252 | ||||||||
\(513\) | −14.9416 | −0.659687 | ||||||||
\(514\) | −41.3706 | −1.82478 | ||||||||
\(515\) | 6.64317 | 0.292733 | ||||||||
\(516\) | 12.1781 | 0.536110 | ||||||||
\(517\) | 2.08535 | 0.0917138 | ||||||||
\(518\) | −16.4786 | −0.724028 | ||||||||
\(519\) | 4.64854 | 0.204048 | ||||||||
\(520\) | 24.2735 | 1.06447 | ||||||||
\(521\) | 36.0203 | 1.57808 | 0.789040 | − | 0.614342i | \(-0.210579\pi\) | ||||
0.789040 | + | 0.614342i | \(0.210579\pi\) | |||||||
\(522\) | 19.7909 | 0.866226 | ||||||||
\(523\) | 3.39338 | 0.148382 | 0.0741910 | − | 0.997244i | \(-0.476363\pi\) | ||||
0.0741910 | + | 0.997244i | \(0.476363\pi\) | |||||||
\(524\) | 28.4760 | 1.24398 | ||||||||
\(525\) | 15.7888 | 0.689081 | ||||||||
\(526\) | −24.8328 | −1.08276 | ||||||||
\(527\) | −3.36917 | −0.146763 | ||||||||
\(528\) | −18.2589 | −0.794617 | ||||||||
\(529\) | 4.00874 | 0.174293 | ||||||||
\(530\) | 2.88365 | 0.125258 | ||||||||
\(531\) | 26.0835 | 1.13193 | ||||||||
\(532\) | −10.6011 | −0.459617 | ||||||||
\(533\) | 5.65547 | 0.244966 | ||||||||
\(534\) | 49.3035 | 2.13357 | ||||||||
\(535\) | −32.3350 | −1.39797 | ||||||||
\(536\) | 48.1824 | 2.08116 | ||||||||
\(537\) | −25.8847 | −1.11701 | ||||||||
\(538\) | −3.76832 | −0.162464 | ||||||||
\(539\) | −6.47015 | −0.278689 | ||||||||
\(540\) | −71.4242 | −3.07361 | ||||||||
\(541\) | 28.0282 | 1.20502 | 0.602512 | − | 0.798110i | \(-0.294166\pi\) | ||||
0.602512 | + | 0.798110i | \(0.294166\pi\) | |||||||
\(542\) | 70.2093 | 3.01575 | ||||||||
\(543\) | −29.6500 | −1.27240 | ||||||||
\(544\) | 4.53982 | 0.194643 | ||||||||
\(545\) | 63.6539 | 2.72663 | ||||||||
\(546\) | 5.65896 | 0.242181 | ||||||||
\(547\) | −1.08127 | −0.0462317 | −0.0231159 | − | 0.999733i | \(-0.507359\pi\) | ||||
−0.0231159 | + | 0.999733i | \(0.507359\pi\) | |||||||
\(548\) | 83.7325 | 3.57687 | ||||||||
\(549\) | −52.0788 | −2.22267 | ||||||||
\(550\) | −19.8683 | −0.847187 | ||||||||
\(551\) | −5.57332 | −0.237431 | ||||||||
\(552\) | −87.4960 | −3.72408 | ||||||||
\(553\) | −9.77445 | −0.415652 | ||||||||
\(554\) | 62.3953 | 2.65092 | ||||||||
\(555\) | 88.5918 | 3.76051 | ||||||||
\(556\) | 32.4070 | 1.37436 | ||||||||
\(557\) | −28.3971 | −1.20322 | −0.601612 | − | 0.798788i | \(-0.705475\pi\) | ||||
−0.601612 | + | 0.798788i | \(0.705475\pi\) | |||||||
\(558\) | −39.5374 | −1.67375 | ||||||||
\(559\) | 1.11146 | 0.0470097 | ||||||||
\(560\) | −17.2407 | −0.728555 | ||||||||
\(561\) | 2.76336 | 0.116669 | ||||||||
\(562\) | −7.00841 | −0.295632 | ||||||||
\(563\) | 23.4617 | 0.988793 | 0.494396 | − | 0.869237i | \(-0.335389\pi\) | ||||
0.494396 | + | 0.869237i | \(0.335389\pi\) | |||||||
\(564\) | −25.3956 | −1.06935 | ||||||||
\(565\) | −7.25713 | −0.305310 | ||||||||
\(566\) | 37.4582 | 1.57449 | ||||||||
\(567\) | 1.02962 | 0.0432400 | ||||||||
\(568\) | −55.8197 | −2.34214 | ||||||||
\(569\) | −28.0592 | −1.17630 | −0.588152 | − | 0.808750i | \(-0.700144\pi\) | ||||
−0.588152 | + | 0.808750i | \(0.700144\pi\) | |||||||
\(570\) | 82.8585 | 3.47056 | ||||||||
\(571\) | 29.8020 | 1.24718 | 0.623588 | − | 0.781753i | \(-0.285674\pi\) | ||||
0.623588 | + | 0.781753i | \(0.285674\pi\) | |||||||
\(572\) | −4.89818 | −0.204803 | ||||||||
\(573\) | −37.1086 | −1.55024 | ||||||||
\(574\) | −9.37519 | −0.391313 | ||||||||
\(575\) | −40.7930 | −1.70119 | ||||||||
\(576\) | −7.99186 | −0.332994 | ||||||||
\(577\) | −36.2189 | −1.50781 | −0.753906 | − | 0.656982i | \(-0.771833\pi\) | ||||
−0.753906 | + | 0.656982i | \(0.771833\pi\) | |||||||
\(578\) | −2.53120 | −0.105284 | ||||||||
\(579\) | −29.4920 | −1.22565 | ||||||||
\(580\) | −26.6418 | −1.10624 | ||||||||
\(581\) | 6.44229 | 0.267271 | ||||||||
\(582\) | 86.0864 | 3.56840 | ||||||||
\(583\) | −0.317816 | −0.0131626 | ||||||||
\(584\) | 64.6944 | 2.67707 | ||||||||
\(585\) | −18.4711 | −0.763686 | ||||||||
\(586\) | −71.8072 | −2.96633 | ||||||||
\(587\) | 10.5470 | 0.435321 | 0.217660 | − | 0.976025i | \(-0.430157\pi\) | ||||
0.217660 | + | 0.976025i | \(0.430157\pi\) | |||||||
\(588\) | 78.7939 | 3.24940 | ||||||||
\(589\) | 11.1341 | 0.458772 | ||||||||
\(590\) | −51.0475 | −2.10159 | ||||||||
\(591\) | −43.6177 | −1.79419 | ||||||||
\(592\) | −59.0952 | −2.42880 | ||||||||
\(593\) | −17.3195 | −0.711228 | −0.355614 | − | 0.934633i | \(-0.615728\pi\) | ||||
−0.355614 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(594\) | 11.4443 | 0.469567 | ||||||||
\(595\) | 2.60927 | 0.106970 | ||||||||
\(596\) | 0.386006 | 0.0158114 | ||||||||
\(597\) | −22.2467 | −0.910497 | ||||||||
\(598\) | −14.6208 | −0.597891 | ||||||||
\(599\) | 14.3361 | 0.585756 | 0.292878 | − | 0.956150i | \(-0.405387\pi\) | ||||
0.292878 | + | 0.956150i | \(0.405387\pi\) | |||||||
\(600\) | 132.151 | 5.39504 | ||||||||
\(601\) | −25.2401 | −1.02957 | −0.514783 | − | 0.857320i | \(-0.672128\pi\) | ||||
−0.514783 | + | 0.857320i | \(0.672128\pi\) | |||||||
\(602\) | −1.84249 | −0.0750943 | ||||||||
\(603\) | −36.6647 | −1.49310 | ||||||||
\(604\) | −4.10443 | −0.167007 | ||||||||
\(605\) | 3.58460 | 0.145735 | ||||||||
\(606\) | −108.499 | −4.40745 | ||||||||
\(607\) | 31.2892 | 1.26999 | 0.634994 | − | 0.772517i | \(-0.281003\pi\) | ||||
0.634994 | + | 0.772517i | \(0.281003\pi\) | |||||||
\(608\) | −15.0027 | −0.608442 | ||||||||
\(609\) | −3.39232 | −0.137464 | ||||||||
\(610\) | 101.922 | 4.12672 | ||||||||
\(611\) | −2.31779 | −0.0937676 | ||||||||
\(612\) | −20.4315 | −0.825893 | ||||||||
\(613\) | −37.0168 | −1.49509 | −0.747547 | − | 0.664209i | \(-0.768768\pi\) | ||||
−0.747547 | + | 0.664209i | \(0.768768\pi\) | |||||||
\(614\) | 24.7328 | 0.998134 | ||||||||
\(615\) | 50.4026 | 2.03243 | ||||||||
\(616\) | 4.43483 | 0.178684 | ||||||||
\(617\) | 5.36868 | 0.216135 | 0.108067 | − | 0.994144i | \(-0.465534\pi\) | ||||
0.108067 | + | 0.994144i | \(0.465534\pi\) | |||||||
\(618\) | 12.9628 | 0.521440 | ||||||||
\(619\) | 24.3846 | 0.980100 | 0.490050 | − | 0.871694i | \(-0.336979\pi\) | ||||
0.490050 | + | 0.871694i | \(0.336979\pi\) | |||||||
\(620\) | 53.2236 | 2.13751 | ||||||||
\(621\) | 23.4972 | 0.942910 | ||||||||
\(622\) | 25.2727 | 1.01334 | ||||||||
\(623\) | −5.13088 | −0.205564 | ||||||||
\(624\) | 20.2940 | 0.812412 | ||||||||
\(625\) | −2.63442 | −0.105377 | ||||||||
\(626\) | −80.9091 | −3.23378 | ||||||||
\(627\) | −9.13209 | −0.364700 | ||||||||
\(628\) | 54.6676 | 2.18147 | ||||||||
\(629\) | 8.94366 | 0.356607 | ||||||||
\(630\) | 30.6199 | 1.21993 | ||||||||
\(631\) | −21.7848 | −0.867239 | −0.433620 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433620 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(632\) | −81.8112 | −3.25427 | ||||||||
\(633\) | −25.4594 | −1.01192 | ||||||||
\(634\) | 43.4034 | 1.72377 | ||||||||
\(635\) | 47.9242 | 1.90181 | ||||||||
\(636\) | 3.87038 | 0.153471 | ||||||||
\(637\) | 7.19131 | 0.284930 | ||||||||
\(638\) | 4.26882 | 0.169004 | ||||||||
\(639\) | 42.4764 | 1.68034 | ||||||||
\(640\) | 48.1876 | 1.90478 | ||||||||
\(641\) | 28.1880 | 1.11336 | 0.556680 | − | 0.830727i | \(-0.312075\pi\) | ||||
0.556680 | + | 0.830727i | \(0.312075\pi\) | |||||||
\(642\) | −63.0953 | −2.49017 | ||||||||
\(643\) | −0.986771 | −0.0389144 | −0.0194572 | − | 0.999811i | \(-0.506194\pi\) | ||||
−0.0194572 | + | 0.999811i | \(0.506194\pi\) | |||||||
\(644\) | 16.6714 | 0.656944 | ||||||||
\(645\) | 9.90554 | 0.390030 | ||||||||
\(646\) | 8.36487 | 0.329111 | ||||||||
\(647\) | 12.6065 | 0.495614 | 0.247807 | − | 0.968809i | \(-0.420290\pi\) | ||||
0.247807 | + | 0.968809i | \(0.420290\pi\) | |||||||
\(648\) | 8.61783 | 0.338540 | ||||||||
\(649\) | 5.62610 | 0.220844 | ||||||||
\(650\) | 22.0828 | 0.866159 | ||||||||
\(651\) | 6.77702 | 0.265612 | ||||||||
\(652\) | 58.8176 | 2.30348 | ||||||||
\(653\) | 39.5312 | 1.54698 | 0.773488 | − | 0.633811i | \(-0.218510\pi\) | ||||
0.773488 | + | 0.633811i | \(0.218510\pi\) | |||||||
\(654\) | 124.208 | 4.85691 | ||||||||
\(655\) | 23.1621 | 0.905019 | ||||||||
\(656\) | −33.6211 | −1.31268 | ||||||||
\(657\) | −49.2296 | −1.92063 | ||||||||
\(658\) | 3.84224 | 0.149786 | ||||||||
\(659\) | 4.72138 | 0.183919 | 0.0919594 | − | 0.995763i | \(-0.470687\pi\) | ||||
0.0919594 | + | 0.995763i | \(0.470687\pi\) | |||||||
\(660\) | −43.6535 | −1.69921 | ||||||||
\(661\) | −13.5522 | −0.527121 | −0.263561 | − | 0.964643i | \(-0.584897\pi\) | ||||
−0.263561 | + | 0.964643i | \(0.584897\pi\) | |||||||
\(662\) | −27.8415 | −1.08209 | ||||||||
\(663\) | −3.07136 | −0.119282 | ||||||||
\(664\) | 53.9213 | 2.09255 | ||||||||
\(665\) | −8.62286 | −0.334380 | ||||||||
\(666\) | 104.954 | 4.06690 | ||||||||
\(667\) | 8.76463 | 0.339368 | ||||||||
\(668\) | 28.3616 | 1.09734 | ||||||||
\(669\) | −31.2262 | −1.20728 | ||||||||
\(670\) | 71.7558 | 2.77217 | ||||||||
\(671\) | −11.2332 | −0.433652 | ||||||||
\(672\) | −9.13176 | −0.352265 | ||||||||
\(673\) | −43.0031 | −1.65765 | −0.828823 | − | 0.559511i | \(-0.810989\pi\) | ||||
−0.828823 | + | 0.559511i | \(0.810989\pi\) | |||||||
\(674\) | 21.5442 | 0.829853 | ||||||||
\(675\) | −35.4893 | −1.36598 | ||||||||
\(676\) | −51.8466 | −1.99410 | ||||||||
\(677\) | −5.30738 | −0.203979 | −0.101990 | − | 0.994785i | \(-0.532521\pi\) | ||||
−0.101990 | + | 0.994785i | \(0.532521\pi\) | |||||||
\(678\) | −14.1608 | −0.543843 | ||||||||
\(679\) | −8.95878 | −0.343806 | ||||||||
\(680\) | 21.8393 | 0.837500 | ||||||||
\(681\) | 34.2732 | 1.31335 | ||||||||
\(682\) | −8.52804 | −0.326555 | ||||||||
\(683\) | −19.4323 | −0.743555 | −0.371777 | − | 0.928322i | \(-0.621252\pi\) | ||||
−0.371777 | + | 0.928322i | \(0.621252\pi\) | |||||||
\(684\) | 67.5199 | 2.58169 | ||||||||
\(685\) | 68.1073 | 2.60225 | ||||||||
\(686\) | −24.8186 | −0.947579 | ||||||||
\(687\) | 46.1652 | 1.76131 | ||||||||
\(688\) | −6.60750 | −0.251909 | ||||||||
\(689\) | 0.353240 | 0.0134574 | ||||||||
\(690\) | −130.304 | −4.96058 | ||||||||
\(691\) | −19.1445 | −0.728290 | −0.364145 | − | 0.931342i | \(-0.618639\pi\) | ||||
−0.364145 | + | 0.931342i | \(0.618639\pi\) | |||||||
\(692\) | −7.41344 | −0.281817 | ||||||||
\(693\) | −3.37471 | −0.128195 | ||||||||
\(694\) | −40.8933 | −1.55229 | ||||||||
\(695\) | 26.3595 | 0.999875 | ||||||||
\(696\) | −28.3934 | −1.07625 | ||||||||
\(697\) | 5.08833 | 0.192734 | ||||||||
\(698\) | −44.4511 | −1.68250 | ||||||||
\(699\) | −2.56452 | −0.0969989 | ||||||||
\(700\) | −25.1799 | −0.951709 | ||||||||
\(701\) | −17.8388 | −0.673764 | −0.336882 | − | 0.941547i | \(-0.609372\pi\) | ||||
−0.336882 | + | 0.941547i | \(0.609372\pi\) | |||||||
\(702\) | −12.7199 | −0.480082 | ||||||||
\(703\) | −29.5561 | −1.11473 | ||||||||
\(704\) | −1.72381 | −0.0649685 | ||||||||
\(705\) | −20.6566 | −0.777971 | ||||||||
\(706\) | −21.8033 | −0.820579 | ||||||||
\(707\) | 11.2911 | 0.424647 | ||||||||
\(708\) | −68.5150 | −2.57495 | ||||||||
\(709\) | −43.9451 | −1.65039 | −0.825196 | − | 0.564847i | \(-0.808935\pi\) | ||||
−0.825196 | + | 0.564847i | \(0.808935\pi\) | |||||||
\(710\) | −83.1297 | −3.11980 | ||||||||
\(711\) | 62.2548 | 2.33474 | ||||||||
\(712\) | −42.9450 | −1.60943 | ||||||||
\(713\) | −17.5095 | −0.655737 | ||||||||
\(714\) | 5.09146 | 0.190543 | ||||||||
\(715\) | −3.98414 | −0.148998 | ||||||||
\(716\) | 41.2806 | 1.54273 | ||||||||
\(717\) | 29.7715 | 1.11184 | ||||||||
\(718\) | −21.4132 | −0.799135 | ||||||||
\(719\) | −21.3436 | −0.795983 | −0.397991 | − | 0.917389i | \(-0.630293\pi\) | ||||
−0.397991 | + | 0.917389i | \(0.630293\pi\) | |||||||
\(720\) | 109.809 | 4.09232 | ||||||||
\(721\) | −1.34900 | −0.0502395 | ||||||||
\(722\) | 20.4494 | 0.761049 | ||||||||
\(723\) | 44.9302 | 1.67097 | ||||||||
\(724\) | 47.2856 | 1.75735 | ||||||||
\(725\) | −13.2378 | −0.491639 | ||||||||
\(726\) | 6.99462 | 0.259595 | ||||||||
\(727\) | 22.3115 | 0.827487 | 0.413743 | − | 0.910394i | \(-0.364221\pi\) | ||||
0.413743 | + | 0.910394i | \(0.364221\pi\) | |||||||
\(728\) | −4.92914 | −0.182686 | ||||||||
\(729\) | −44.0398 | −1.63110 | ||||||||
\(730\) | 96.3463 | 3.56594 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 136.798 | 5.05621 | ||||||||
\(733\) | 13.4155 | 0.495512 | 0.247756 | − | 0.968823i | \(-0.420307\pi\) | ||||
0.247756 | + | 0.968823i | \(0.420307\pi\) | |||||||
\(734\) | 43.6119 | 1.60974 | ||||||||
\(735\) | 64.0903 | 2.36401 | ||||||||
\(736\) | 23.5934 | 0.869664 | ||||||||
\(737\) | −7.90842 | −0.291310 | ||||||||
\(738\) | 59.7118 | 2.19802 | ||||||||
\(739\) | 26.7037 | 0.982310 | 0.491155 | − | 0.871072i | \(-0.336575\pi\) | ||||
0.491155 | + | 0.871072i | \(0.336575\pi\) | |||||||
\(740\) | −141.285 | −5.19375 | ||||||||
\(741\) | 10.1499 | 0.372868 | ||||||||
\(742\) | −0.585572 | −0.0214970 | ||||||||
\(743\) | −46.4708 | −1.70485 | −0.852425 | − | 0.522849i | \(-0.824869\pi\) | ||||
−0.852425 | + | 0.522849i | \(0.824869\pi\) | |||||||
\(744\) | 56.7229 | 2.07956 | ||||||||
\(745\) | 0.313974 | 0.0115031 | ||||||||
\(746\) | 81.6879 | 2.99081 | ||||||||
\(747\) | −41.0318 | −1.50127 | ||||||||
\(748\) | −4.40698 | −0.161135 | ||||||||
\(749\) | 6.56615 | 0.239922 | ||||||||
\(750\) | 71.4416 | 2.60868 | ||||||||
\(751\) | 29.2481 | 1.06728 | 0.533639 | − | 0.845712i | \(-0.320824\pi\) | ||||
0.533639 | + | 0.845712i | \(0.320824\pi\) | |||||||
\(752\) | 13.7790 | 0.502467 | ||||||||
\(753\) | 13.7776 | 0.502084 | ||||||||
\(754\) | −4.74462 | −0.172789 | ||||||||
\(755\) | −3.33851 | −0.121501 | ||||||||
\(756\) | 14.5038 | 0.527500 | ||||||||
\(757\) | −47.5353 | −1.72770 | −0.863850 | − | 0.503748i | \(-0.831954\pi\) | ||||
−0.863850 | + | 0.503748i | \(0.831954\pi\) | |||||||
\(758\) | 21.0885 | 0.765967 | ||||||||
\(759\) | 14.3612 | 0.521277 | ||||||||
\(760\) | −72.1725 | −2.61797 | ||||||||
\(761\) | 8.45911 | 0.306642 | 0.153321 | − | 0.988176i | \(-0.451003\pi\) | ||||
0.153321 | + | 0.988176i | \(0.451003\pi\) | |||||||
\(762\) | 93.5143 | 3.38767 | ||||||||
\(763\) | −12.9260 | −0.467951 | ||||||||
\(764\) | 59.1804 | 2.14107 | ||||||||
\(765\) | −16.6188 | −0.600853 | ||||||||
\(766\) | 50.5127 | 1.82510 | ||||||||
\(767\) | −6.25318 | −0.225789 | ||||||||
\(768\) | 84.5013 | 3.04918 | ||||||||
\(769\) | 27.4662 | 0.990458 | 0.495229 | − | 0.868763i | \(-0.335084\pi\) | ||||
0.495229 | + | 0.868763i | \(0.335084\pi\) | |||||||
\(770\) | 6.60459 | 0.238013 | ||||||||
\(771\) | −45.1650 | −1.62658 | ||||||||
\(772\) | 47.0336 | 1.69277 | ||||||||
\(773\) | 33.8368 | 1.21702 | 0.608512 | − | 0.793544i | \(-0.291767\pi\) | ||||
0.608512 | + | 0.793544i | \(0.291767\pi\) | |||||||
\(774\) | 11.7351 | 0.421808 | ||||||||
\(775\) | 26.4458 | 0.949960 | ||||||||
\(776\) | −74.9841 | −2.69177 | ||||||||
\(777\) | −17.9900 | −0.645388 | ||||||||
\(778\) | −31.1045 | −1.11515 | ||||||||
\(779\) | −16.8154 | −0.602474 | ||||||||
\(780\) | 48.5191 | 1.73726 | ||||||||
\(781\) | 9.16197 | 0.327841 | ||||||||
\(782\) | −13.1546 | −0.470409 | ||||||||
\(783\) | 7.62509 | 0.272499 | ||||||||
\(784\) | −42.7515 | −1.52684 | ||||||||
\(785\) | 44.4662 | 1.58707 | ||||||||
\(786\) | 45.1962 | 1.61209 | ||||||||
\(787\) | 7.45921 | 0.265892 | 0.132946 | − | 0.991123i | \(-0.457556\pi\) | ||||
0.132946 | + | 0.991123i | \(0.457556\pi\) | |||||||
\(788\) | 69.5611 | 2.47801 | ||||||||
\(789\) | −27.1105 | −0.965158 | ||||||||
\(790\) | −121.838 | −4.33479 | ||||||||
\(791\) | 1.47368 | 0.0523980 | ||||||||
\(792\) | −28.2460 | −1.00368 | ||||||||
\(793\) | 12.4852 | 0.443363 | ||||||||
\(794\) | −76.6931 | −2.72174 | ||||||||
\(795\) | 3.14814 | 0.111653 | ||||||||
\(796\) | 35.4788 | 1.25751 | ||||||||
\(797\) | 49.1949 | 1.74257 | 0.871286 | − | 0.490775i | \(-0.163286\pi\) | ||||
0.871286 | + | 0.490775i | \(0.163286\pi\) | |||||||
\(798\) | −16.8258 | −0.595626 | ||||||||
\(799\) | −2.08535 | −0.0737745 | ||||||||
\(800\) | −35.6346 | −1.25987 | ||||||||
\(801\) | 32.6793 | 1.15467 | ||||||||
\(802\) | −66.0863 | −2.33359 | ||||||||
\(803\) | −10.6186 | −0.374723 | ||||||||
\(804\) | 96.3093 | 3.39657 | ||||||||
\(805\) | 13.5604 | 0.477940 | ||||||||
\(806\) | 9.47857 | 0.333868 | ||||||||
\(807\) | −4.11395 | −0.144818 | ||||||||
\(808\) | 94.5058 | 3.32470 | ||||||||
\(809\) | −24.9932 | −0.878713 | −0.439356 | − | 0.898313i | \(-0.644793\pi\) | ||||
−0.439356 | + | 0.898313i | \(0.644793\pi\) | |||||||
\(810\) | 12.8341 | 0.450945 | ||||||||
\(811\) | 16.9689 | 0.595859 | 0.297929 | − | 0.954588i | \(-0.403704\pi\) | ||||
0.297929 | + | 0.954588i | \(0.403704\pi\) | |||||||
\(812\) | 5.41004 | 0.189855 | ||||||||
\(813\) | 76.6489 | 2.68819 | ||||||||
\(814\) | 22.6382 | 0.793469 | ||||||||
\(815\) | 47.8418 | 1.67582 | ||||||||
\(816\) | 18.2589 | 0.639189 | ||||||||
\(817\) | −3.30470 | −0.115617 | ||||||||
\(818\) | 48.3244 | 1.68962 | ||||||||
\(819\) | 3.75086 | 0.131066 | ||||||||
\(820\) | −80.3816 | −2.80705 | ||||||||
\(821\) | 21.2283 | 0.740874 | 0.370437 | − | 0.928858i | \(-0.379208\pi\) | ||||
0.370437 | + | 0.928858i | \(0.379208\pi\) | |||||||
\(822\) | 132.898 | 4.63534 | ||||||||
\(823\) | −21.6128 | −0.753375 | −0.376687 | − | 0.926340i | \(-0.622937\pi\) | ||||
−0.376687 | + | 0.926340i | \(0.622937\pi\) | |||||||
\(824\) | −11.2910 | −0.393342 | ||||||||
\(825\) | −21.6906 | −0.755170 | ||||||||
\(826\) | 10.3660 | 0.360680 | ||||||||
\(827\) | −34.6050 | −1.20333 | −0.601666 | − | 0.798747i | \(-0.705496\pi\) | ||||
−0.601666 | + | 0.798747i | \(0.705496\pi\) | |||||||
\(828\) | −106.182 | −3.69009 | ||||||||
\(829\) | −16.8068 | −0.583726 | −0.291863 | − | 0.956460i | \(-0.594275\pi\) | ||||
−0.291863 | + | 0.956460i | \(0.594275\pi\) | |||||||
\(830\) | 80.3025 | 2.78734 | ||||||||
\(831\) | 68.1181 | 2.36299 | ||||||||
\(832\) | 1.91594 | 0.0664234 | ||||||||
\(833\) | 6.47015 | 0.224177 | ||||||||
\(834\) | 51.4353 | 1.78106 | ||||||||
\(835\) | 23.0691 | 0.798338 | ||||||||
\(836\) | 14.5638 | 0.503698 | ||||||||
\(837\) | −15.2330 | −0.526531 | ||||||||
\(838\) | −65.2454 | −2.25386 | ||||||||
\(839\) | 46.9449 | 1.62072 | 0.810358 | − | 0.585935i | \(-0.199273\pi\) | ||||
0.810358 | + | 0.585935i | \(0.199273\pi\) | |||||||
\(840\) | −43.9294 | −1.51571 | ||||||||
\(841\) | −26.1558 | −0.901924 | ||||||||
\(842\) | −42.4449 | −1.46275 | ||||||||
\(843\) | −7.65122 | −0.263522 | ||||||||
\(844\) | 40.6024 | 1.39759 | ||||||||
\(845\) | −42.1716 | −1.45075 | ||||||||
\(846\) | −24.4717 | −0.841356 | ||||||||
\(847\) | −0.727911 | −0.0250113 | ||||||||
\(848\) | −2.09997 | −0.0721132 | ||||||||
\(849\) | 40.8939 | 1.40347 | ||||||||
\(850\) | 19.8683 | 0.681477 | ||||||||
\(851\) | 46.4801 | 1.59332 | ||||||||
\(852\) | −111.575 | −3.82250 | ||||||||
\(853\) | 22.0380 | 0.754566 | 0.377283 | − | 0.926098i | \(-0.376858\pi\) | ||||
0.377283 | + | 0.926098i | \(0.376858\pi\) | |||||||
\(854\) | −20.6970 | −0.708237 | ||||||||
\(855\) | 54.9201 | 1.87823 | ||||||||
\(856\) | 54.9581 | 1.87843 | ||||||||
\(857\) | 49.2367 | 1.68189 | 0.840946 | − | 0.541119i | \(-0.181999\pi\) | ||||
0.840946 | + | 0.541119i | \(0.181999\pi\) | |||||||
\(858\) | −7.77424 | −0.265408 | ||||||||
\(859\) | 11.4770 | 0.391590 | 0.195795 | − | 0.980645i | \(-0.437271\pi\) | ||||
0.195795 | + | 0.980645i | \(0.437271\pi\) | |||||||
\(860\) | −15.7973 | −0.538682 | ||||||||
\(861\) | −10.2351 | −0.348810 | ||||||||
\(862\) | −43.2695 | −1.47376 | ||||||||
\(863\) | −25.2768 | −0.860434 | −0.430217 | − | 0.902726i | \(-0.641563\pi\) | ||||
−0.430217 | + | 0.902726i | \(0.641563\pi\) | |||||||
\(864\) | 20.5259 | 0.698305 | ||||||||
\(865\) | −6.03003 | −0.205027 | ||||||||
\(866\) | 21.4365 | 0.728441 | ||||||||
\(867\) | −2.76336 | −0.0938486 | ||||||||
\(868\) | −10.8079 | −0.366844 | ||||||||
\(869\) | 13.4281 | 0.455516 | ||||||||
\(870\) | −42.2850 | −1.43360 | ||||||||
\(871\) | 8.78989 | 0.297834 | ||||||||
\(872\) | −108.189 | −3.66374 | ||||||||
\(873\) | 57.0596 | 1.93118 | ||||||||
\(874\) | 43.4722 | 1.47047 | ||||||||
\(875\) | −7.43473 | −0.251340 | ||||||||
\(876\) | 129.314 | 4.36912 | ||||||||
\(877\) | −16.0833 | −0.543093 | −0.271546 | − | 0.962425i | \(-0.587535\pi\) | ||||
−0.271546 | + | 0.962425i | \(0.587535\pi\) | |||||||
\(878\) | 7.00902 | 0.236543 | ||||||||
\(879\) | −78.3933 | −2.64414 | ||||||||
\(880\) | 23.6852 | 0.798429 | ||||||||
\(881\) | −39.9404 | −1.34563 | −0.672813 | − | 0.739812i | \(-0.734914\pi\) | ||||
−0.672813 | + | 0.739812i | \(0.734914\pi\) | |||||||
\(882\) | 75.9275 | 2.55661 | ||||||||
\(883\) | −23.3355 | −0.785303 | −0.392651 | − | 0.919687i | \(-0.628442\pi\) | ||||
−0.392651 | + | 0.919687i | \(0.628442\pi\) | |||||||
\(884\) | 4.89818 | 0.164744 | ||||||||
\(885\) | −55.7295 | −1.87333 | ||||||||
\(886\) | −74.0322 | −2.48716 | ||||||||
\(887\) | 19.0914 | 0.641028 | 0.320514 | − | 0.947244i | \(-0.396144\pi\) | ||||
0.320514 | + | 0.947244i | \(0.396144\pi\) | |||||||
\(888\) | −150.575 | −5.05295 | ||||||||
\(889\) | −9.73178 | −0.326393 | ||||||||
\(890\) | −63.9559 | −2.14381 | ||||||||
\(891\) | −1.41449 | −0.0473871 | ||||||||
\(892\) | 49.7992 | 1.66740 | ||||||||
\(893\) | 6.89148 | 0.230614 | ||||||||
\(894\) | 0.612658 | 0.0204903 | ||||||||
\(895\) | 33.5773 | 1.12237 | ||||||||
\(896\) | −9.78527 | −0.326903 | ||||||||
\(897\) | −15.9619 | −0.532951 | ||||||||
\(898\) | 10.6854 | 0.356576 | ||||||||
\(899\) | −5.68203 | −0.189506 | ||||||||
\(900\) | 160.374 | 5.34579 | ||||||||
\(901\) | 0.317816 | 0.0105880 | ||||||||
\(902\) | 12.8796 | 0.428843 | ||||||||
\(903\) | −2.01148 | −0.0669379 | ||||||||
\(904\) | 12.3345 | 0.410241 | ||||||||
\(905\) | 38.4617 | 1.27851 | ||||||||
\(906\) | −6.51443 | −0.216428 | ||||||||
\(907\) | 6.32800 | 0.210118 | 0.105059 | − | 0.994466i | \(-0.466497\pi\) | ||||
0.105059 | + | 0.994466i | \(0.466497\pi\) | |||||||
\(908\) | −54.6585 | −1.81391 | ||||||||
\(909\) | −71.9148 | −2.38526 | ||||||||
\(910\) | −7.34073 | −0.243343 | ||||||||
\(911\) | 39.9389 | 1.32324 | 0.661618 | − | 0.749841i | \(-0.269870\pi\) | ||||
0.661618 | + | 0.749841i | \(0.269870\pi\) | |||||||
\(912\) | −60.3402 | −1.99807 | ||||||||
\(913\) | −8.85038 | −0.292905 | ||||||||
\(914\) | −13.8155 | −0.456977 | ||||||||
\(915\) | 111.271 | 3.67849 | ||||||||
\(916\) | −73.6237 | −2.43260 | ||||||||
\(917\) | −4.70344 | −0.155321 | ||||||||
\(918\) | −11.4443 | −0.377719 | ||||||||
\(919\) | −11.2318 | −0.370503 | −0.185252 | − | 0.982691i | \(-0.559310\pi\) | ||||
−0.185252 | + | 0.982691i | \(0.559310\pi\) | |||||||
\(920\) | 113.499 | 3.74195 | ||||||||
\(921\) | 27.0013 | 0.889721 | ||||||||
\(922\) | 59.7680 | 1.96835 | ||||||||
\(923\) | −10.1832 | −0.335183 | ||||||||
\(924\) | 8.86455 | 0.291622 | ||||||||
\(925\) | −70.2020 | −2.30823 | ||||||||
\(926\) | 24.3550 | 0.800354 | ||||||||
\(927\) | 8.59198 | 0.282198 | ||||||||
\(928\) | 7.65631 | 0.251331 | ||||||||
\(929\) | 56.6387 | 1.85826 | 0.929128 | − | 0.369759i | \(-0.120560\pi\) | ||||
0.929128 | + | 0.369759i | \(0.120560\pi\) | |||||||
\(930\) | 84.4748 | 2.77004 | ||||||||
\(931\) | −21.3819 | −0.700764 | ||||||||
\(932\) | 4.08986 | 0.133968 | ||||||||
\(933\) | 27.5907 | 0.903280 | ||||||||
\(934\) | −72.2377 | −2.36369 | ||||||||
\(935\) | −3.58460 | −0.117229 | ||||||||
\(936\) | 31.3943 | 1.02616 | ||||||||
\(937\) | −30.9539 | −1.01122 | −0.505610 | − | 0.862762i | \(-0.668732\pi\) | ||||
−0.505610 | + | 0.862762i | \(0.668732\pi\) | |||||||
\(938\) | −14.5712 | −0.475766 | ||||||||
\(939\) | −88.3300 | −2.88254 | ||||||||
\(940\) | 32.9429 | 1.07448 | ||||||||
\(941\) | −9.45627 | −0.308266 | −0.154133 | − | 0.988050i | \(-0.549258\pi\) | ||||
−0.154133 | + | 0.988050i | \(0.549258\pi\) | |||||||
\(942\) | 86.7667 | 2.82701 | ||||||||
\(943\) | 26.4440 | 0.861135 | ||||||||
\(944\) | 37.1744 | 1.20992 | ||||||||
\(945\) | 11.7973 | 0.383766 | ||||||||
\(946\) | 2.53120 | 0.0822964 | ||||||||
\(947\) | 22.4456 | 0.729383 | 0.364692 | − | 0.931128i | \(-0.381174\pi\) | ||||
0.364692 | + | 0.931128i | \(0.381174\pi\) | |||||||
\(948\) | −163.528 | −5.31115 | ||||||||
\(949\) | 11.8022 | 0.383114 | ||||||||
\(950\) | −65.6588 | −2.13025 | ||||||||
\(951\) | 47.3844 | 1.53654 | ||||||||
\(952\) | −4.43483 | −0.143734 | ||||||||
\(953\) | 53.3749 | 1.72898 | 0.864492 | − | 0.502647i | \(-0.167640\pi\) | ||||
0.864492 | + | 0.502647i | \(0.167640\pi\) | |||||||
\(954\) | 3.72959 | 0.120750 | ||||||||
\(955\) | 48.1369 | 1.55767 | ||||||||
\(956\) | −47.4793 | −1.53559 | ||||||||
\(957\) | 4.66035 | 0.150648 | ||||||||
\(958\) | −96.4256 | −3.11537 | ||||||||
\(959\) | −13.8303 | −0.446604 | ||||||||
\(960\) | 17.0753 | 0.551102 | ||||||||
\(961\) | −19.6487 | −0.633830 | ||||||||
\(962\) | −25.1615 | −0.811238 | ||||||||
\(963\) | −41.8207 | −1.34765 | ||||||||
\(964\) | −71.6542 | −2.30783 | ||||||||
\(965\) | 38.2567 | 1.23153 | ||||||||
\(966\) | 26.4603 | 0.851346 | ||||||||
\(967\) | 46.7318 | 1.50279 | 0.751397 | − | 0.659851i | \(-0.229381\pi\) | ||||
0.751397 | + | 0.659851i | \(0.229381\pi\) | |||||||
\(968\) | −6.09254 | −0.195822 | ||||||||
\(969\) | 9.13209 | 0.293365 | ||||||||
\(970\) | −111.670 | −3.58552 | ||||||||
\(971\) | 18.9699 | 0.608775 | 0.304387 | − | 0.952548i | \(-0.401548\pi\) | ||||
0.304387 | + | 0.952548i | \(0.401548\pi\) | |||||||
\(972\) | 77.0016 | 2.46983 | ||||||||
\(973\) | −5.35274 | −0.171601 | ||||||||
\(974\) | −54.1805 | −1.73605 | ||||||||
\(975\) | 24.1082 | 0.772081 | ||||||||
\(976\) | −74.2232 | −2.37583 | ||||||||
\(977\) | −12.6718 | −0.405407 | −0.202703 | − | 0.979240i | \(-0.564973\pi\) | ||||
−0.202703 | + | 0.979240i | \(0.564973\pi\) | |||||||
\(978\) | 93.3535 | 2.98512 | ||||||||
\(979\) | 7.04878 | 0.225280 | ||||||||
\(980\) | −102.211 | −3.26499 | ||||||||
\(981\) | 82.3271 | 2.62850 | ||||||||
\(982\) | −19.3178 | −0.616456 | ||||||||
\(983\) | −42.1953 | −1.34582 | −0.672911 | − | 0.739723i | \(-0.734956\pi\) | ||||
−0.672911 | + | 0.739723i | \(0.734956\pi\) | |||||||
\(984\) | −85.6665 | −2.73095 | ||||||||
\(985\) | 56.5804 | 1.80280 | ||||||||
\(986\) | −4.26882 | −0.135947 | ||||||||
\(987\) | 4.19465 | 0.133517 | ||||||||
\(988\) | −16.1870 | −0.514978 | ||||||||
\(989\) | 5.19699 | 0.165255 | ||||||||
\(990\) | −42.0655 | −1.33693 | ||||||||
\(991\) | −46.4445 | −1.47536 | −0.737679 | − | 0.675151i | \(-0.764078\pi\) | ||||
−0.737679 | + | 0.675151i | \(0.764078\pi\) | |||||||
\(992\) | −15.2954 | −0.485629 | ||||||||
\(993\) | −30.3951 | −0.964560 | ||||||||
\(994\) | 16.8808 | 0.535427 | ||||||||
\(995\) | 28.8582 | 0.914865 | ||||||||
\(996\) | 107.781 | 3.41516 | ||||||||
\(997\) | 0.465258 | 0.0147349 | 0.00736743 | − | 0.999973i | \(-0.497655\pi\) | ||||
0.00736743 | + | 0.999973i | \(0.497655\pi\) | |||||||
\(998\) | 2.81524 | 0.0891147 | ||||||||
\(999\) | 40.4370 | 1.27937 |
(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 | 8041.2.a.i.1.6 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.6 | ✓ | 78 | 1.1 | even | 1 | trivial |