Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.67736 | −1.54578 | −0.772888 | − | 0.634542i | \(-0.781189\pi\) | ||||
−0.772888 | + | 0.634542i | \(0.781189\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.29688 | 1.92162 | 0.960812 | − | 0.277200i | \(-0.0894063\pi\) | ||||
0.960812 | + | 0.277200i | \(0.0894063\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.01755 | 1.51849 | 0.759246 | − | 0.650804i | \(-0.225568\pi\) | ||||
0.759246 | + | 0.650804i | \(0.225568\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.16827 | 1.38942 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.88107 | −1.47170 | −0.735849 | − | 0.677146i | \(-0.763217\pi\) | ||||
−0.735849 | + | 0.677146i | \(0.763217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.92210 | −1.08780 | −0.543898 | − | 0.839151i | \(-0.683052\pi\) | ||||
−0.543898 | + | 0.839151i | \(0.683052\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.5043 | −2.97040 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.345632 | 0.0838280 | 0.0419140 | − | 0.999121i | \(-0.486654\pi\) | ||||
0.0419140 | + | 0.999121i | \(0.486654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26874 | −0.749900 | −0.374950 | − | 0.927045i | \(-0.622340\pi\) | ||||
−0.374950 | + | 0.927045i | \(0.622340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.7564 | −2.34725 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.48325 | −1.56037 | −0.780183 | − | 0.625551i | \(-0.784874\pi\) | ||||
−0.780183 | + | 0.625551i | \(0.784874\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.4632 | 2.69264 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.12789 | −0.601962 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.5555 | −1.96011 | −0.980053 | − | 0.198735i | \(-0.936317\pi\) | ||||
−0.980053 | + | 0.198735i | \(0.936317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.70877 | 1.74375 | 0.871873 | − | 0.489731i | \(-0.162905\pi\) | ||||
0.871873 | + | 0.489731i | \(0.162905\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.0684 | 2.27492 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.2630 | 2.91797 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.92845 | 0.810232 | 0.405116 | − | 0.914265i | \(-0.367231\pi\) | ||||
0.405116 | + | 0.914265i | \(0.367231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.5009 | 1.68149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.39986 | 1.15566 | 0.577832 | − | 0.816156i | \(-0.303899\pi\) | ||||
0.577832 | + | 0.816156i | \(0.303899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.90581 | 0.748129 | 0.374064 | − | 0.927403i | \(-0.377964\pi\) | ||||
0.374064 | + | 0.927403i | \(0.377964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 17.9106 | 2.66995 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.34062 | −0.195550 | −0.0977750 | − | 0.995209i | \(-0.531173\pi\) | ||||
−0.0977750 | + | 0.995209i | \(0.531173\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.14073 | 1.30582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.925381 | −0.129579 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.36208 | 0.187096 | 0.0935479 | − | 0.995615i | \(-0.470179\pi\) | ||||
0.0935479 | + | 0.995615i | \(0.470179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.9734 | −2.82805 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.75160 | 1.15918 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.330955 | 0.0430867 | 0.0215434 | − | 0.999768i | \(-0.493142\pi\) | ||||
0.0215434 | + | 0.999768i | \(0.493142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.87403 | 1.26424 | 0.632120 | − | 0.774871i | \(-0.282185\pi\) | ||||
0.632120 | + | 0.774871i | \(0.282185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.7463 | 2.10983 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.8528 | −2.09034 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.0820 | 1.35389 | 0.676943 | − | 0.736035i | \(-0.263304\pi\) | ||||
0.676943 | + | 0.736035i | \(0.263304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.0354 | 2.41198 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1094 | 1.19977 | 0.599884 | − | 0.800087i | \(-0.295213\pi\) | ||||
0.599884 | + | 0.800087i | \(0.295213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6687 | 1.59980 | 0.799900 | − | 0.600133i | \(-0.204886\pi\) | ||||
0.799900 | + | 0.600133i | \(0.204886\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −36.0459 | −4.16222 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.6100 | −2.23476 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.91873 | 1.00344 | 0.501718 | − | 0.865031i | \(-0.332702\pi\) | ||||
0.501718 | + | 0.865031i | \(0.332702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.13032 | −0.458925 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.12340 | −0.342838 | −0.171419 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171419 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.48514 | 0.161086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.2609 | 3.02989 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.28030 | −0.771710 | −0.385855 | − | 0.922559i | \(-0.626094\pi\) | ||||
−0.385855 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7573 | −1.65181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.9939 | −2.69544 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.0454 | −1.44103 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.84471 | 0.288837 | 0.144418 | − | 0.989517i | \(-0.453869\pi\) | ||||
0.144418 | + | 0.989517i | \(0.453869\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.3456 | −2.04481 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.85666 | 0.284248 | 0.142124 | − | 0.989849i | \(-0.454607\pi\) | ||||
0.142124 | + | 0.989849i | \(0.454607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.89586 | 0.285338 | 0.142669 | − | 0.989770i | \(-0.454432\pi\) | ||||
0.142669 | + | 0.989770i | \(0.454432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46.2192 | −4.51053 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3609 | 1.19498 | 0.597488 | − | 0.801878i | \(-0.296166\pi\) | ||||
0.597488 | + | 0.801878i | \(0.296166\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.64043 | 0.252908 | 0.126454 | − | 0.991973i | \(-0.459640\pi\) | ||||
0.126454 | + | 0.991973i | \(0.459640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.1953 | −1.25244 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.02036 | −0.190060 | −0.0950299 | − | 0.995474i | \(-0.530295\pi\) | ||||
−0.0950299 | + | 0.995474i | \(0.530295\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.1547 | −2.99844 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3484 | −1.51141 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.38859 | 0.127292 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.8248 | 1.16589 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.8121 | −1.78640 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 36.3654 | 3.25262 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.08326 | 0.0961240 | 0.0480620 | − | 0.998844i | \(-0.484695\pi\) | ||||
0.0480620 | + | 0.998844i | \(0.484695\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.1346 | −1.15644 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8410 | 0.947181 | 0.473590 | − | 0.880745i | \(-0.342958\pi\) | ||||
0.473590 | + | 0.880745i | \(0.342958\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.1323 | −1.13872 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.4402 | −1.15675 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.67905 | −0.399758 | −0.199879 | − | 0.979821i | \(-0.564055\pi\) | ||||
−0.199879 | + | 0.979821i | \(0.564055\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.19070 | 0.694726 | 0.347363 | − | 0.937731i | \(-0.387077\pi\) | ||||
0.347363 | + | 0.937731i | \(0.387077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.58933 | 0.302276 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.1441 | 1.60091 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −45.3557 | −3.76659 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −24.4730 | −2.01850 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.2822 | −0.924273 | −0.462136 | − | 0.886809i | \(-0.652917\pi\) | ||||
−0.462136 | + | 0.886809i | \(0.652917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.55491 | 0.207916 | 0.103958 | − | 0.994582i | \(-0.466849\pi\) | ||||
0.103958 | + | 0.994582i | \(0.466849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.44069 | 0.116473 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 41.7175 | 3.35083 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5622 | 1.00257 | 0.501286 | − | 0.865281i | \(-0.332860\pi\) | ||||
0.501286 | + | 0.865281i | \(0.332860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.64678 | −0.289208 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.0644 | −2.36940 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.55995 | 0.513815 | 0.256908 | − | 0.966436i | \(-0.417296\pi\) | ||||
0.256908 | + | 0.966436i | \(0.417296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 56.1534 | 4.37153 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.9818 | 1.70100 | 0.850502 | − | 0.525972i | \(-0.176298\pi\) | ||||
0.850502 | + | 0.525972i | \(0.176298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.38290 | 0.183300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.6250 | −1.04193 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5338 | 0.876900 | 0.438450 | − | 0.898756i | \(-0.355528\pi\) | ||||
0.438450 | + | 0.898756i | \(0.355528\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 54.0891 | 4.08875 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.886087 | −0.0666024 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1386 | 0.907278 | 0.453639 | − | 0.891185i | \(-0.350126\pi\) | ||||
0.453639 | + | 0.891185i | \(0.350126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.83347 | 0.433598 | 0.216799 | − | 0.976216i | \(-0.430438\pi\) | ||||
0.216799 | + | 0.976216i | \(0.430438\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.4364 | −1.95423 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.1770 | 1.55696 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.68705 | −0.123369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5665 | −0.914075 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.2293 | −0.884879 | −0.442440 | − | 0.896798i | \(-0.645887\pi\) | ||||
−0.442440 | + | 0.896798i | \(0.645887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50148 | −0.396005 | −0.198003 | − | 0.980201i | \(-0.563445\pi\) | ||||
−0.198003 | + | 0.980201i | \(0.563445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 45.1211 | 3.23119 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.94394 | −0.708477 | −0.354238 | − | 0.935155i | \(-0.615260\pi\) | ||||
−0.354238 | + | 0.935155i | \(0.615260\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.1814 | −1.21796 | −0.608979 | − | 0.793187i | \(-0.708421\pi\) | ||||
−0.608979 | + | 0.793187i | \(0.708421\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.6706 | −2.09281 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −42.4073 | −2.97641 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.7963 | 2.22075 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −31.1922 | −2.16801 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9549 | 1.10363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.36612 | 0.231733 | 0.115867 | − | 0.993265i | \(-0.463035\pi\) | ||||
0.115867 | + | 0.993265i | \(0.463035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.0666 | −1.85457 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.0797 | 1.43762 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 39.0055 | 2.64787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36.5961 | −2.47293 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.35560 | −0.0911877 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.42756 | −0.430421 | −0.215210 | − | 0.976568i | \(-0.569044\pi\) | ||||
−0.215210 | + | 0.976568i | \(0.569044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 56.1183 | 3.74122 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.11613 | −0.405942 | −0.202971 | − | 0.979185i | \(-0.565060\pi\) | ||||
−0.202971 | + | 0.979185i | \(0.565060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.0264 | −1.19122 | −0.595608 | − | 0.803275i | \(-0.703089\pi\) | ||||
−0.595608 | + | 0.803275i | \(0.703089\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 52.5030 | 3.45444 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.2752 | −0.869689 | −0.434845 | − | 0.900506i | \(-0.643197\pi\) | ||||
−0.434845 | + | 0.900506i | \(0.643197\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.76050 | −0.375774 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.8787 | −1.55109 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.87379 | 0.315259 | 0.157630 | − | 0.987498i | \(-0.449615\pi\) | ||||
0.157630 | + | 0.987498i | \(0.449615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7989 | 0.953280 | 0.476640 | − | 0.879099i | \(-0.341854\pi\) | ||||
0.476640 | + | 0.879099i | \(0.341854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.4420 | 1.31136 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.2766 | 2.50929 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8203 | 0.815739 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.36248 | 0.529950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.5263 | 2.29639 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.97626 | −0.249003 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.551631 | −0.0344098 | −0.0172049 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172049 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.8003 | 1.23033 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −43.9982 | −2.72342 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.8398 | −1.59335 | −0.796676 | − | 0.604407i | \(-0.793410\pi\) | ||||
−0.796676 | + | 0.604407i | \(0.793410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.85269 | 0.359528 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.4920 | 1.19289 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6689 | 1.07729 | 0.538647 | − | 0.842532i | \(-0.318936\pi\) | ||||
0.538647 | + | 0.842532i | \(0.318936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.60636 | 0.462053 | 0.231027 | − | 0.972947i | \(-0.425792\pi\) | ||||
0.231027 | + | 0.972947i | \(0.425792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 42.1879 | 2.55333 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −65.7148 | −3.96275 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6033 | −1.29802 | −0.649009 | − | 0.760781i | \(-0.724816\pi\) | ||||
−0.649009 | + | 0.760781i | \(0.724816\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 40.4688 | 2.42280 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.6953 | −1.35389 | −0.676943 | − | 0.736035i | \(-0.736696\pi\) | ||||
−0.676943 | + | 0.736035i | \(0.736696\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.1542 | −1.37638 | −0.688188 | − | 0.725533i | \(-0.741593\pi\) | ||||
−0.688188 | + | 0.725533i | \(0.741593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 37.6046 | 2.22751 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.7293 | 1.75487 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8805 | −0.992973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.61633 | −0.446477 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7530 | 1.15398 | 0.576991 | − | 0.816751i | \(-0.304227\pi\) | ||||
0.576991 | + | 0.816751i | \(0.304227\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.42208 | 0.0827965 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.2674 | 0.885907 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.3501 | 1.69736 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.7093 | 1.13603 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.64831 | −0.439384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 42.4275 | 2.42939 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.29451 | 0.245101 | 0.122550 | − | 0.992462i | \(-0.460893\pi\) | ||||
0.122550 | + | 0.992462i | \(0.460893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.75327 | −0.441068 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9165 | 0.902540 | 0.451270 | − | 0.892387i | \(-0.350971\pi\) | ||||
0.451270 | + | 0.892387i | \(0.350971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1655 | 1.19635 | 0.598173 | − | 0.801367i | \(-0.295893\pi\) | ||||
0.598173 | + | 0.801367i | \(0.295893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 71.9567 | 4.05430 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6269 | 0.821530 | 0.410765 | − | 0.911741i | \(-0.365262\pi\) | ||||
0.410765 | + | 0.911741i | \(0.365262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 51.5221 | 2.88468 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.0947 | −1.84716 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.12978 | −0.0628626 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −52.8041 | −2.92904 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.06939 | −0.390938 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.38602 | −0.296941 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2268 | −0.562114 | −0.281057 | − | 0.959691i | \(-0.590685\pi\) | ||||
−0.281057 | + | 0.959691i | \(0.590685\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.5431 | 1.12576 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 47.6182 | 2.60166 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9429 | 1.08636 | 0.543181 | − | 0.839616i | \(-0.317220\pi\) | ||||
0.543181 | + | 0.839616i | \(0.317220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.40925 | 0.293790 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −47.3892 | −2.56627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.60049 | 0.464383 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 86.0897 | 4.63491 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.2758 | −1.94739 | −0.973693 | − | 0.227864i | \(-0.926826\pi\) | ||||
−0.973693 | + | 0.227864i | \(0.926826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.9190 | −1.76211 | −0.881056 | − | 0.473011i | \(-0.843167\pi\) | ||||
−0.881056 | + | 0.473011i | \(0.843167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.2679 | 0.654812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.34949 | −0.444398 | −0.222199 | − | 0.975001i | \(-0.571324\pi\) | ||||
−0.222199 | + | 0.975001i | \(0.571324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 43.4390 | 2.30550 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.71777 | −0.196765 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.3855 | −1.23424 | −0.617119 | − | 0.786870i | \(-0.711700\pi\) | ||||
−0.617119 | + | 0.786870i | \(0.711700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.31534 | −0.437649 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −34.3367 | −1.80221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.7328 | 3.07422 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.95074 | −0.519424 | −0.259712 | − | 0.965686i | \(-0.583628\pi\) | ||||
−0.259712 | + | 0.965686i | \(0.583628\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.8446 | 1.60571 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.47222 | 0.284103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1591 | −0.836688 | −0.418344 | − | 0.908289i | \(-0.637389\pi\) | ||||
−0.418344 | + | 0.908289i | \(0.637389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −97.3634 | −5.02782 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.3997 | 2.13220 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0285 | −0.771962 | −0.385981 | − | 0.922507i | \(-0.626137\pi\) | ||||
−0.385981 | + | 0.922507i | \(0.626137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.90029 | −0.148586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.6944 | −0.801944 | −0.400972 | − | 0.916090i | \(-0.631328\pi\) | ||||
−0.400972 | + | 0.916090i | \(0.631328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −84.2617 | −4.29437 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.4487 | 1.03947 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.70628 | 0.187916 | 0.0939580 | − | 0.995576i | \(-0.470048\pi\) | ||||
0.0939580 | + | 0.995576i | \(0.470048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58645 | −0.130802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.0252 | −1.46413 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.3227 | 1.92823 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.520696 | 0.0261330 | 0.0130665 | − | 0.999915i | \(-0.495841\pi\) | ||||
0.0130665 | + | 0.999915i | \(0.495841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 35.1600 | 1.76020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.47427 | −0.0736217 | −0.0368109 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368109 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.0788 | −1.89684 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.7475 | −0.881882 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0561 | −1.19242 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.3081 | 1.15251 | 0.576256 | − | 0.817269i | \(-0.304513\pi\) | ||||
0.576256 | + | 0.817269i | \(0.304513\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5275 | 0.617937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.32963 | 0.0654268 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4209 | −0.658806 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.9295 | −1.07389 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5740 | 0.809691 | 0.404846 | − | 0.914385i | \(-0.367325\pi\) | ||||
0.404846 | + | 0.914385i | \(0.367325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7926 | −0.769686 | −0.384843 | − | 0.922982i | \(-0.625744\pi\) | ||||
−0.384843 | + | 0.922982i | \(0.625744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.58808 | −0.271702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.65331 | 0.225719 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.6694 | 1.91974 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −51.2556 | −2.47464 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.47799 | 0.456539 | 0.228269 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228269 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.5164 | −1.51458 | −0.757291 | − | 0.653078i | \(-0.773477\pi\) | ||||
−0.757291 | + | 0.653078i | \(0.773477\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 121.434 | 5.82230 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.4608 | 1.17012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.6164 | 1.50897 | 0.754485 | − | 0.656318i | \(-0.227887\pi\) | ||||
0.754485 | + | 0.656318i | \(0.227887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 38.1010 | 1.81434 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.80425 | −0.323279 | −0.161640 | − | 0.986850i | \(-0.551678\pi\) | ||||
−0.161640 | + | 0.986850i | \(0.551678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.2826 | −1.48294 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 30.2065 | 1.42872 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.7833 | 1.54714 | 0.773571 | − | 0.633710i | \(-0.218469\pi\) | ||||
0.773571 | + | 0.633710i | \(0.218469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.1192 | −1.70079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.84043 | −0.321391 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −67.7071 | −3.17416 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4517 | −0.769578 | −0.384789 | − | 0.923004i | \(-0.625726\pi\) | ||||
−0.384789 | + | 0.923004i | \(0.625726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.08110 | −0.0504613 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.4167 | 0.764602 | 0.382301 | − | 0.924038i | \(-0.375132\pi\) | ||||
0.382301 | + | 0.924038i | \(0.375132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.17134 | 0.193859 | 0.0969293 | − | 0.995291i | \(-0.469098\pi\) | ||||
0.0969293 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −111.693 | −5.17963 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.6901 | 0.633501 | 0.316751 | − | 0.948509i | \(-0.397408\pi\) | ||||
0.316751 | + | 0.948509i | \(0.397408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.5227 | 2.05587 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.6336 | −1.54975 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.9456 | −1.10102 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −44.0077 | −2.01921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.67751 | 0.259955 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.4423 | 0.705578 | 0.352789 | − | 0.935703i | \(-0.385233\pi\) | ||||
0.352789 | + | 0.935703i | \(0.385233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.3299 | −0.881367 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 80.4932 | 3.66257 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2234 | 0.555036 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7327 | 1.25669 | 0.628343 | − | 0.777936i | \(-0.283733\pi\) | ||||
0.628343 | + | 0.777936i | \(0.283733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.5634 | −0.794243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.8181 | 1.57132 | 0.785660 | − | 0.618658i | \(-0.212323\pi\) | ||||
0.785660 | + | 0.618658i | \(0.212323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.64831 | −0.164312 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −87.4228 | −3.92936 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.6152 | 1.82184 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.95889 | −0.356289 | −0.178144 | − | 0.984004i | \(-0.557009\pi\) | ||||
−0.178144 | + | 0.984004i | \(0.557009\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −58.8533 | −2.62937 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.50633 | 0.156339 | 0.0781697 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781697 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2747 | 0.546218 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.37988 | −0.283340 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.4551 | −1.17260 | −0.586300 | − | 0.810094i | \(-0.699416\pi\) | ||||
−0.586300 | + | 0.810094i | \(0.699416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.9147 | 2.42928 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.2243 | 0.451412 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.4432 | 0.548312 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.54367 | 0.287790 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.8802 | −1.35549 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.3080 | −1.41544 | −0.707720 | − | 0.706493i | \(-0.750276\pi\) | ||||
−0.707720 | + | 0.706493i | \(0.750276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.08738 | 0.0475479 | 0.0237739 | − | 0.999717i | \(-0.492432\pi\) | ||||
0.0237739 | + | 0.999717i | \(0.492432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −144.816 | −6.32030 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.35566 | 0.146175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.9991 | 1.43474 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.37951 | 0.0598657 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.0230 | −1.25713 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53.1134 | 2.29629 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −32.4993 | −1.40245 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −44.6165 | −1.92177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5224 | −0.624369 | −0.312184 | − | 0.950022i | \(-0.601061\pi\) | ||||
−0.312184 | + | 0.950022i | \(0.601061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.6183 | −0.670246 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3456 | 0.485993 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7522 | 1.14384 | 0.571920 | − | 0.820309i | \(-0.306199\pi\) | ||||
0.571920 | + | 0.820309i | \(0.306199\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.1576 | 1.75657 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.5032 | 1.46988 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.8315 | 1.52371 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −56.6985 | −2.40672 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5837 | 0.745047 | 0.372523 | − | 0.928023i | \(-0.378493\pi\) | ||||
0.372523 | + | 0.928023i | \(0.378493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.2411 | −0.813811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.51685 | 0.190702 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.8164 | −1.42519 | −0.712595 | − | 0.701575i | \(-0.752480\pi\) | ||||
−0.712595 | + | 0.701575i | \(0.752480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.68127 | −0.365224 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.5938 | −0.696874 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.5754 | 0.694877 | 0.347439 | − | 0.937703i | \(-0.387051\pi\) | ||||
0.347439 | + | 0.937703i | \(0.387051\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8103 | −0.829034 | −0.414517 | − | 0.910041i | \(-0.636050\pi\) | ||||
−0.414517 | + | 0.910041i | \(0.636050\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.7422 | 1.36783 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −100.749 | −4.20151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.26144 | −0.177406 | −0.0887031 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887031 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.7295 | 0.612135 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5484 | −0.520596 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.64840 | −0.275348 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −70.2471 | −2.90436 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.7936 | −0.858244 | −0.429122 | − | 0.903247i | \(-0.641177\pi\) | ||||
−0.429122 | + | 0.903247i | \(0.641177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.7355 | −1.30764 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.6235 | 1.09515 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.8668 | −1.43181 | −0.715904 | − | 0.698199i | \(-0.753985\pi\) | ||||
−0.715904 | + | 0.698199i | \(0.753985\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.96662 | 0.244608 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.0009 | 1.88269 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5394 | −0.594064 | −0.297032 | − | 0.954868i | \(-0.595997\pi\) | ||||
−0.297032 | + | 0.954868i | \(0.595997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.9360 | 0.935579 | 0.467790 | − | 0.883840i | \(-0.345051\pi\) | ||||
0.467790 | + | 0.883840i | \(0.345051\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.1929 | 1.88112 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 55.1068 | 2.24041 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.8454 | −1.57669 | −0.788343 | − | 0.615235i | \(-0.789061\pi\) | ||||
−0.788343 | + | 0.615235i | \(0.789061\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 113.540 | 4.60086 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.25806 | 0.212718 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.80742 | −0.153780 | −0.0768901 | − | 0.997040i | \(-0.524499\pi\) | ||||
−0.0768901 | + | 0.997040i | \(0.524499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −85.1303 | −3.43279 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.05826 | 0.163380 | 0.0816898 | − | 0.996658i | \(-0.473968\pi\) | ||||
0.0816898 | + | 0.996658i | \(0.473968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.6601 | −0.750014 | −0.375007 | − | 0.927022i | \(-0.622360\pi\) | ||||
−0.375007 | + | 0.927022i | \(0.622360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.4068 | 0.939282 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.2490 | −1.17184 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 88.9419 | 3.55768 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −42.7172 | −1.70596 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.70343 | 0.0679202 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.64043 | 0.0653045 | 0.0326523 | − | 0.999467i | \(-0.489605\pi\) | ||||
0.0326523 | + | 0.999467i | \(0.489605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.01233 | −0.358208 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.65465 | 0.184714 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.8509 | −1.42046 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 42.1388 | 1.66699 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0740 | −0.595386 | −0.297693 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297693 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.7735 | −1.37133 | −0.685666 | − | 0.727916i | \(-0.740489\pi\) | ||||
−0.685666 | + | 0.727916i | \(0.740489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −56.4380 | −2.22224 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.2866 | 1.19069 | 0.595344 | − | 0.803471i | \(-0.297016\pi\) | ||||
0.595344 | + | 0.803471i | \(0.297016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.61542 | −0.0634106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −104.432 | −4.09301 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.7825 | 0.617618 | 0.308809 | − | 0.951124i | \(-0.400070\pi\) | ||||
0.308809 | + | 0.951124i | \(0.400070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.5824 | 1.82013 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 56.9749 | 2.22280 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.44667 | 0.212172 | 0.106086 | − | 0.994357i | \(-0.466168\pi\) | ||||
0.106086 | + | 0.994357i | \(0.466168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6197 | 0.490851 | 0.245425 | − | 0.969416i | \(-0.421072\pi\) | ||||
0.245425 | + | 0.969416i | \(0.421072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.62944 | 0.140956 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −56.4281 | −2.18819 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 78.9894 | 3.05848 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.2089 | 0.665334 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −48.1958 | −1.86058 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.25268 | −0.0868345 | −0.0434172 | − | 0.999057i | \(-0.513824\pi\) | ||||
−0.0434172 | + | 0.999057i | \(0.513824\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.1114 | −1.62087 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.09785 | −0.119060 | −0.0595299 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595299 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4288 | 0.438596 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3751 | 0.627495 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1587 | −0.465239 | −0.232620 | − | 0.972568i | \(-0.574730\pi\) | ||||
−0.232620 | + | 0.972568i | \(0.574730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.1053 | −0.768185 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.2632 | 1.84135 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.34221 | −0.203522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.64379 | −0.252742 | −0.126371 | − | 0.991983i | \(-0.540333\pi\) | ||||
−0.126371 | + | 0.991983i | \(0.540333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −81.7396 | −3.10503 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.1945 | 1.33500 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.55763 | 0.0968770 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.5426 | 1.34434 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.3048 | −0.426976 | −0.213488 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213488 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1098 | −0.607594 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.4229 | 0.580862 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4768 | 0.431629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.9207 | 1.01103 | 0.505514 | − | 0.862818i | \(-0.331303\pi\) | ||||
0.505514 | + | 0.862818i | \(0.331303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.1757 | 1.39420 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −72.6532 | −2.72088 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 82.2598 | 3.07634 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.0489 | −0.487320 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.7292 | 1.07142 | 0.535709 | − | 0.844403i | \(-0.320045\pi\) | ||||
0.535709 | + | 0.844403i | \(0.320045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6343 | 0.433283 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.6220 | −1.47356 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −142.111 | −5.27786 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.9674 | −1.25978 | −0.629891 | − | 0.776684i | \(-0.716900\pi\) | ||||
−0.629891 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.3398 | −1.56814 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.69560 | 0.0627141 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.35368 | 0.345486 | 0.172743 | − | 0.984967i | \(-0.444737\pi\) | ||||
0.172743 | + | 0.984967i | \(0.444737\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −105.158 | −3.87880 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.0922 | −1.99251 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.87995 | 0.142726 | 0.0713632 | − | 0.997450i | \(-0.477265\pi\) | ||||
0.0713632 | + | 0.997450i | \(0.477265\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34.3247 | −1.26095 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.00715 | 0.0369487 | 0.0184744 | − | 0.999829i | \(-0.494119\pi\) | ||||
0.0184744 | + | 0.999829i | \(0.494119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.4782 | −1.77611 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.0192 | −0.476347 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.6607 | 1.81456 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.10756 | 0.259359 | 0.129679 | − | 0.991556i | \(-0.458605\pi\) | ||||
0.129679 | + | 0.991556i | \(0.458605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.67736 | −0.0975685 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.9782 | 0.399536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.48536 | −0.344751 | −0.172376 | − | 0.985031i | \(-0.555144\pi\) | ||||
−0.172376 | + | 0.985031i | \(0.555144\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −97.7941 | −3.54970 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.9039 | −0.504017 | −0.252008 | − | 0.967725i | \(-0.581091\pi\) | ||||
−0.252008 | + | 0.967725i | \(0.581091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.6081 | 0.384038 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.19046 | 0.223817 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.29804 | −0.0468695 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.6544 | 1.42997 | 0.714987 | − | 0.699138i | \(-0.246433\pi\) | ||||
0.714987 | + | 0.699138i | \(0.246433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.47692 | 0.0531898 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.2169 | 1.51844 | 0.759218 | − | 0.650836i | \(-0.225582\pi\) | ||||
0.759218 | + | 0.650836i | \(0.225582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 130.711 | 4.69529 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −53.0126 | −1.90182 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.1882 | −0.866633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.3448 | −1.76570 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.0164 | 1.17991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.9783 | 1.92657 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.7090 | −0.880782 | −0.440391 | − | 0.897806i | \(-0.645160\pi\) | ||||
−0.440391 | + | 0.897806i | \(0.645160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 69.1826 | 2.46296 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.11692 | −0.288604 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.7270 | −1.37523 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.6698 | −0.555750 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.7654 | 0.487595 | 0.243798 | − | 0.969826i | \(-0.421607\pi\) | ||||
0.243798 | + | 0.969826i | \(0.421607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.463362 | −0.0163926 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.3463 | −1.07223 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −66.7179 | −2.35442 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −129.183 | −4.55310 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.3061 | −1.66526 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.0960 | 0.776854 | 0.388427 | − | 0.921479i | \(-0.373019\pi\) | ||||
0.388427 | + | 0.921479i | \(0.373019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1728 | 0.497676 | 0.248838 | − | 0.968545i | \(-0.419951\pi\) | ||||
0.248838 | + | 0.968545i | \(0.419951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.3650 | −0.714231 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.1874 | 0.987360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0358 | −0.561022 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −65.6805 | −2.29506 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.8108 | 1.11020 | 0.555102 | − | 0.831782i | \(-0.312679\pi\) | ||||
0.555102 | + | 0.831782i | \(0.312679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.4343 | −1.58374 | −0.791870 | − | 0.610690i | \(-0.790892\pi\) | ||||
−0.791870 | + | 0.610690i | \(0.790892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 175.942 | 6.12553 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.6944 | 1.17167 | 0.585835 | − | 0.810430i | \(-0.300767\pi\) | ||||
0.585835 | + | 0.810430i | \(0.300767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.1188 | −1.04607 | −0.523035 | − | 0.852311i | \(-0.675200\pi\) | ||||
−0.523035 | + | 0.852311i | \(0.675200\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 57.8399 | 2.00644 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.15932 | 0.109464 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 94.4533 | 3.26869 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.3680 | −1.04967 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.3559 | −1.04800 | −0.524001 | − | 0.851718i | \(-0.675561\pi\) | ||||
−0.524001 | + | 0.851718i | \(0.675561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.4185 | 2.84202 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60.7635 | 2.09281 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.2390 | 0.352233 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.5245 | 1.77040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 61.9922 | 2.12757 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.8809 | −1.26426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.6812 | −0.913546 | −0.456773 | − | 0.889583i | \(-0.650995\pi\) | ||||
−0.456773 | + | 0.889583i | \(0.650995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −58.5450 | −2.00220 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.6142 | 0.806646 | 0.403323 | − | 0.915058i | \(-0.367855\pi\) | ||||
0.403323 | + | 0.915058i | \(0.367855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0244 | 0.990301 | 0.495151 | − | 0.868807i | \(-0.335113\pi\) | ||||
0.495151 | + | 0.868807i | \(0.335113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −79.5962 | −2.71263 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.4293 | −1.64855 | −0.824275 | − | 0.566189i | \(-0.808417\pi\) | ||||
−0.824275 | + | 0.566189i | \(0.808417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.5595 | 1.68507 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.1953 | 1.53491 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.5329 | −1.47675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.4649 | −1.47275 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.8575 | 0.401317 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 146.100 | 4.93908 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.3861 | −1.16114 | −0.580569 | − | 0.814211i | \(-0.697170\pi\) | ||||
−0.580569 | + | 0.814211i | \(0.697170\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −52.8859 | −1.78380 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.7982 | −1.91358 | −0.956790 | − | 0.290780i | \(-0.906085\pi\) | ||||
−0.956790 | + | 0.290780i | \(0.906085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.65446 | 0.0556770 | 0.0278385 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278385 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.80741 | −0.127985 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.2107 | 1.45087 | 0.725436 | − | 0.688289i | \(-0.241638\pi\) | ||||
0.725436 | + | 0.688289i | \(0.241638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.35207 | 0.145964 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.1604 | 0.675399 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.38215 | 0.146643 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.1580 | 1.74345 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −78.5809 | −2.62374 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −102.481 | −3.41793 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.470777 | 0.0156839 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −52.7691 | −1.75604 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.0657 | 0.833213 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.0162 | −1.49474 | −0.747369 | − | 0.664409i | \(-0.768683\pi\) | ||||
−0.747369 | + | 0.664409i | \(0.768683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.9073 | 0.394941 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9780 | 0.595638 | 0.297819 | − | 0.954622i | \(-0.403741\pi\) | ||||
0.297819 | + | 0.954622i | \(0.403741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.2455 | 0.504554 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −113.594 | −3.75530 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.5542 | 1.43829 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.36987 | −0.111162 | −0.0555809 | − | 0.998454i | \(-0.517701\pi\) | ||||
−0.0555809 | + | 0.998454i | \(0.517701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4980 | −0.378871 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39.6502 | −1.30510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66.3528 | 2.18167 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0707 | 0.396455 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.8213 | 1.40492 | 0.702460 | − | 0.711723i | \(-0.252085\pi\) | ||||
0.702460 | + | 0.711723i | \(0.252085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.8787 | −0.979234 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.6142 | −1.39513 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.24907 | −0.237070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.08754 | −0.198871 | −0.0994356 | − | 0.995044i | \(-0.531704\pi\) | ||||
−0.0994356 | + | 0.995044i | \(0.531704\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −56.6678 | −1.84928 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.2223 | 1.60460 | 0.802300 | − | 0.596921i | \(-0.203609\pi\) | ||||
0.802300 | + | 0.596921i | \(0.203609\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.3750 | −1.80326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −53.9966 | −1.75651 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.53886 | −0.0500062 | −0.0250031 | − | 0.999687i | \(-0.507960\pi\) | ||||
−0.0250031 | + | 0.999687i | \(0.507960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.6100 | −1.74026 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.1616 | −1.26990 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0563 | 1.16798 | 0.583989 | − | 0.811761i | \(-0.301491\pi\) | ||||
0.583989 | + | 0.811761i | \(0.301491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.5478 | −1.70041 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −137.943 | −4.45908 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7983 | −0.607030 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.2603 | 2.04065 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.5237 | 1.66033 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.6392 | −0.760973 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9184 | 1.05858 | 0.529292 | − | 0.848440i | \(-0.322458\pi\) | ||||
0.529292 | + | 0.848440i | \(0.322458\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.02483 | 0.0971716 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3151 | −0.972858 | −0.486429 | − | 0.873720i | \(-0.661701\pi\) | ||||
−0.486429 | + | 0.873720i | \(0.661701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.9066 | 1.05494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 141.376 | 4.52765 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.0269 | −1.28057 | −0.640287 | − | 0.768136i | \(-0.721185\pi\) | ||||
−0.640287 | + | 0.768136i | \(0.721185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5356 | 1.13572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.0060 | 0.351396 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.34084 | −0.170346 | −0.0851732 | − | 0.996366i | \(-0.527144\pi\) | ||||
−0.0851732 | + | 0.996366i | \(0.527144\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42.7280 | −1.36143 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.4203 | 0.459004 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.7114 | −1.16735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.3871 | 1.02881 | 0.514405 | − | 0.857547i | \(-0.328013\pi\) | ||||
0.514405 | + | 0.857547i | \(0.328013\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.3808 | 0.868902 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.8265 | −2.34046 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.0628 | 0.825416 | 0.412708 | − | 0.910863i | \(-0.364583\pi\) | ||||
0.412708 | + | 0.910863i | \(0.364583\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.4156 | −0.487729 |
(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 | 4016.2.a.m.1.4 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.20 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.20 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.4 | 23 | 1.1 | even | 1 | trivial |