Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 15 x^{10} + 100 x^{9} + 36 x^{8} - 641 x^{7} + 129 x^{6} + 1804 x^{5} - 433 x^{4} - 2399 x^{3} + 148 x^{2} + 1224 x + 224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.31023\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.31023 | −1.91116 | −0.955582 | − | 0.294726i | \(-0.904772\pi\) | ||||
−0.955582 | + | 0.294726i | \(0.904772\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.56191 | −1.14572 | −0.572861 | − | 0.819653i | \(-0.694166\pi\) | ||||
−0.572861 | + | 0.819653i | \(0.694166\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.56163 | 0.590240 | 0.295120 | − | 0.955460i | \(-0.404640\pi\) | ||||
0.295120 | + | 0.955460i | \(0.404640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.95764 | 2.65255 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12161 | 0.639688 | 0.319844 | − | 0.947470i | \(-0.396369\pi\) | ||||
0.319844 | + | 0.947470i | \(0.396369\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.14247 | −1.70361 | −0.851807 | − | 0.523856i | \(-0.824493\pi\) | ||||
−0.851807 | + | 0.523856i | \(0.824493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.48052 | 2.18966 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.33456 | −1.77889 | −0.889446 | − | 0.457041i | \(-0.848909\pi\) | ||||
−0.889446 | + | 0.457041i | \(0.848909\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.28452 | −0.753520 | −0.376760 | − | 0.926311i | \(-0.622962\pi\) | ||||
−0.376760 | + | 0.926311i | \(0.622962\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.16935 | −1.12805 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.25065 | −0.469294 | −0.234647 | − | 0.972081i | \(-0.575393\pi\) | ||||
−0.234647 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56338 | 0.312677 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −16.4109 | −3.15829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.64505 | 0.676870 | 0.338435 | − | 0.940990i | \(-0.390103\pi\) | ||||
0.338435 | + | 0.940990i | \(0.390103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04298 | 0.546535 | 0.273268 | − | 0.961938i | \(-0.411896\pi\) | ||||
0.273268 | + | 0.961938i | \(0.411896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.02301 | −1.22255 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.00075 | −0.676251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.09544 | −1.16648 | −0.583242 | − | 0.812299i | \(-0.698216\pi\) | ||||
−0.583242 | + | 0.812299i | \(0.698216\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.3330 | 3.25588 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.18380 | 1.27810 | 0.639048 | − | 0.769167i | \(-0.279329\pi\) | ||||
0.639048 | + | 0.769167i | \(0.279329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.642462 | 0.0979745 | 0.0489872 | − | 0.998799i | \(-0.484401\pi\) | ||||
0.0489872 | + | 0.998799i | \(0.484401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.3868 | −3.03908 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1274 | 1.62310 | 0.811552 | − | 0.584281i | \(-0.198623\pi\) | ||||
0.811552 | + | 0.584281i | \(0.198623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.56132 | −0.651617 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24.2791 | 3.39975 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.50174 | −0.893083 | −0.446541 | − | 0.894763i | \(-0.647344\pi\) | ||||
−0.446541 | + | 0.894763i | \(0.647344\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.43536 | −0.732904 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.8725 | 1.44010 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7360 | 1.52790 | 0.763948 | − | 0.645278i | \(-0.223259\pi\) | ||||
0.763948 | + | 0.645278i | \(0.223259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.63676 | 0.721713 | 0.360857 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360857 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.4269 | 1.56564 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.7364 | 1.95187 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4572 | 1.76623 | 0.883113 | − | 0.469161i | \(-0.155443\pi\) | ||||
0.883113 | + | 0.469161i | \(0.155443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.45019 | 0.896897 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.48926 | −0.888812 | −0.444406 | − | 0.895825i | \(-0.646585\pi\) | ||||
−0.444406 | + | 0.895825i | \(0.646585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.35719 | −1.09518 | −0.547588 | − | 0.836748i | \(-0.684454\pi\) | ||||
−0.547588 | + | 0.836748i | \(0.684454\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.17517 | −0.597577 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.31316 | 0.377570 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.89017 | −0.212661 | −0.106330 | − | 0.994331i | \(-0.533910\pi\) | ||||
−0.106330 | + | 0.994331i | \(0.533910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.4511 | 3.38346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.97961 | 0.327055 | 0.163527 | − | 0.986539i | \(-0.447713\pi\) | ||||
0.163527 | + | 0.986539i | \(0.447713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.7905 | 2.03811 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.0660 | −1.29361 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.79360 | −0.720120 | −0.360060 | − | 0.932929i | \(-0.617244\pi\) | ||||
−0.360060 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.59225 | −1.00554 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.0730 | −1.04452 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.41464 | 0.863323 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9868 | 1.42015 | 0.710073 | − | 0.704128i | \(-0.248662\pi\) | ||||
0.710073 | + | 0.704128i | \(0.248662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.8830 | 1.69680 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2281 | 1.31624 | 0.658122 | − | 0.752911i | \(-0.271351\pi\) | ||||
0.658122 | + | 0.752911i | \(0.271351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.28957 | −0.915329 | −0.457664 | − | 0.889125i | \(-0.651314\pi\) | ||||
−0.457664 | + | 0.889125i | \(0.651314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.2434 | 1.29243 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.51451 | 0.629781 | 0.314891 | − | 0.949128i | \(-0.398032\pi\) | ||||
0.314891 | + | 0.949128i | \(0.398032\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.88317 | −0.755071 | −0.377536 | − | 0.925995i | \(-0.623228\pi\) | ||||
−0.377536 | + | 0.925995i | \(0.623228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 23.4876 | 2.22934 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.06423 | 0.758619 | 0.379309 | − | 0.925270i | \(-0.376162\pi\) | ||||
0.379309 | + | 0.925270i | \(0.376162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.76597 | 0.537680 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −48.8795 | −4.51891 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.4539 | −1.04997 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.49879 | −0.590799 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.0903 | −2.44265 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.80430 | 0.787481 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.06236 | 0.715418 | 0.357709 | − | 0.933833i | \(-0.383558\pi\) | ||||
0.357709 | + | 0.933833i | \(0.383558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.12670 | −0.187245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2829 | −1.42264 | −0.711320 | − | 0.702868i | \(-0.751902\pi\) | ||||
−0.711320 | + | 0.702868i | \(0.751902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.12919 | −0.444758 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 42.0434 | 3.61852 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.7692 | 1.51813 | 0.759064 | − | 0.651016i | \(-0.225657\pi\) | ||||
0.759064 | + | 0.651016i | \(0.225657\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.92501 | −0.417734 | −0.208867 | − | 0.977944i | \(-0.566978\pi\) | ||||
−0.208867 | + | 0.977944i | \(0.566978\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −36.8344 | −3.10202 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.0319 | −1.08978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.33830 | −0.775504 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.0990 | 1.24535 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.90152 | −0.401548 | −0.200774 | − | 0.979638i | \(-0.564346\pi\) | ||||
−0.200774 | + | 0.979638i | \(0.564346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.20868 | 0.179739 | 0.0898697 | − | 0.995954i | \(-0.471355\pi\) | ||||
0.0898697 | + | 0.995954i | \(0.471355\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −58.3658 | −4.71859 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.79584 | −0.626177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8311 | −1.26346 | −0.631731 | − | 0.775188i | \(-0.717655\pi\) | ||||
−0.631731 | + | 0.775188i | \(0.717655\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.5223 | 1.70683 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.51469 | −0.276996 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1837 | 1.18928 | 0.594640 | − | 0.803992i | \(-0.297295\pi\) | ||||
0.594640 | + | 0.803992i | \(0.297295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.9923 | 1.40070 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.7299 | 1.90230 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.1370 | −1.99875 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.5401 | 1.78972 | 0.894859 | − | 0.446350i | \(-0.147276\pi\) | ||||
0.894859 | + | 0.446350i | \(0.147276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.44143 | 0.184554 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −38.8488 | −2.92006 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.61437 | 0.643868 | 0.321934 | − | 0.946762i | \(-0.395667\pi\) | ||||
0.321934 | + | 0.946762i | \(0.395667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.10168 | 0.602193 | 0.301096 | − | 0.953594i | \(-0.402647\pi\) | ||||
0.301096 | + | 0.953594i | \(0.402647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.6590 | −1.37931 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.1779 | 1.33646 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.5610 | −1.13794 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −25.6278 | −1.86415 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.41971 | 0.609229 | 0.304615 | − | 0.952476i | \(-0.401472\pi\) | ||||
0.304615 | + | 0.952476i | \(0.401472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2603 | 1.09846 | 0.549228 | − | 0.835672i | \(-0.314922\pi\) | ||||
0.549228 | + | 0.835672i | \(0.314922\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −52.0913 | −3.73034 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.2933 | 1.30335 | 0.651673 | − | 0.758500i | \(-0.274067\pi\) | ||||
0.651673 | + | 0.758500i | \(0.274067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.83014 | 0.555064 | 0.277532 | − | 0.960716i | \(-0.410484\pi\) | ||||
0.277532 | + | 0.960716i | \(0.410484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −47.8566 | −3.37555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.69222 | 0.399516 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.9662 | −1.46434 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.9099 | −1.24482 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.96845 | −0.482018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5183 | −1.34369 | −0.671847 | − | 0.740690i | \(-0.734499\pi\) | ||||
−0.671847 | + | 0.740690i | \(0.734499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.7912 | 1.69867 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.64593 | −0.112251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.75200 | 0.322587 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.9745 | 2.09306 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 45.0523 | 3.03054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.92970 | 0.196187 | 0.0980935 | − | 0.995177i | \(-0.468726\pi\) | ||||
0.0980935 | + | 0.995177i | \(0.468726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.4408 | 0.829390 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.1969 | 1.73875 | 0.869375 | − | 0.494153i | \(-0.164522\pi\) | ||||
0.869375 | + | 0.494153i | \(0.164522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.16248 | 0.605474 | 0.302737 | − | 0.953074i | \(-0.402100\pi\) | ||||
0.302737 | + | 0.953074i | \(0.402100\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.9673 | −0.721597 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.32880 | −0.218077 | −0.109038 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109038 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.5075 | −1.85962 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.25691 | 0.406430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.84311 | 0.572013 | 0.286007 | − | 0.958228i | \(-0.407672\pi\) | ||||
0.286007 | + | 0.958228i | \(0.407672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.90434 | −0.187085 | −0.0935424 | − | 0.995615i | \(-0.529819\pi\) | ||||
−0.0935424 | + | 0.995615i | \(0.529819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −51.5674 | −3.30805 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.6857 | 0.746571 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.1750 | 1.28371 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.86320 | −0.625055 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3817 | −0.655286 | −0.327643 | − | 0.944802i | \(-0.606254\pi\) | ||||
−0.327643 | + | 0.944802i | \(0.606254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.77500 | −0.300202 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −62.2009 | −3.89517 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.74771 | 0.483289 | 0.241645 | − | 0.970365i | \(-0.422313\pi\) | ||||
0.241645 | + | 0.970365i | \(0.422313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0804 | −0.688505 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.0060 | 1.79543 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.69311 | 0.289389 | 0.144695 | − | 0.989476i | \(-0.453780\pi\) | ||||
0.144695 | + | 0.989476i | \(0.453780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.6569 | 1.02322 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.4884 | 1.37627 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.50641 | −0.579616 | −0.289808 | − | 0.957085i | \(-0.593591\pi\) | ||||
−0.289808 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3745 | −1.35915 | −0.679576 | − | 0.733605i | \(-0.737836\pi\) | ||||
−0.679576 | + | 0.733605i | \(0.737836\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 31.7526 | 1.92175 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.31689 | 0.200016 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5847 | −1.53724 | −0.768618 | − | 0.639708i | \(-0.779055\pi\) | ||||
−0.768618 | + | 0.639708i | \(0.779055\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.2149 | 1.44971 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.21507 | 0.311105 | 0.155553 | − | 0.987828i | \(-0.450284\pi\) | ||||
0.155553 | + | 0.987828i | \(0.450284\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.2065 | 1.14171 | 0.570855 | − | 0.821051i | \(-0.306612\pi\) | ||||
0.570855 | + | 0.821051i | \(0.306612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.8544 | −1.64995 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.7801 | 0.754383 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.7957 | 2.16446 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −46.2996 | −2.71413 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.26658 | 0.132415 | 0.0662074 | − | 0.997806i | \(-0.478910\pi\) | ||||
0.0662074 | + | 0.997806i | \(0.478910\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.0665 | −1.75054 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.8175 | −2.02032 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.8246 | 0.799495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00329 | 0.0578285 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.7880 | −2.51556 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4409 | −0.826882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.8192 | 1.24529 | 0.622644 | − | 0.782505i | \(-0.286058\pi\) | ||||
0.622644 | + | 0.782505i | \(0.286058\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.7506 | 1.74934 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.6351 | −1.96398 | −0.981988 | − | 0.188944i | \(-0.939494\pi\) | ||||
−0.981988 | + | 0.188944i | \(0.939494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.39255 | −0.191758 | −0.0958792 | − | 0.995393i | \(-0.530566\pi\) | ||||
−0.0958792 | + | 0.995393i | \(0.530566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −31.8365 | −1.79379 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.5365 | −0.647956 | −0.323978 | − | 0.946065i | \(-0.605020\pi\) | ||||
−0.323978 | + | 0.946065i | \(0.605020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.73337 | 0.432986 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.5645 | −1.20361 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0905 | 1.34043 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.60303 | −0.532681 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.0951 | 1.44306 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.3769 | 0.958021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9843 | −0.713684 | −0.356842 | − | 0.934165i | \(-0.616147\pi\) | ||||
−0.356842 | + | 0.934165i | \(0.616147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −56.4630 | −3.09415 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −37.0380 | −2.02360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0996 | −1.14937 | −0.574685 | − | 0.818375i | \(-0.694876\pi\) | ||||
−0.574685 | + | 0.818375i | \(0.694876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.6945 | −1.44984 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.45600 | 0.349612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0545 | −0.974850 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.0867 | −1.02759 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.0371 | 0.646184 | 0.323092 | − | 0.946368i | \(-0.395278\pi\) | ||||
0.323092 | + | 0.946368i | \(0.395278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.01866 | −0.215114 | −0.107557 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107557 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 100.804 | 5.38050 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.2203 | −1.76814 | −0.884070 | − | 0.467354i | \(-0.845207\pi\) | ||||
−0.884070 | + | 0.467354i | \(0.845207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1868 | 1.01833 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 37.9149 | 2.00667 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.9262 | −0.682219 | −0.341109 | − | 0.940024i | \(-0.610803\pi\) | ||||
−0.341109 | + | 0.940024i | \(0.610803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.21195 | −0.432208 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.5125 | 1.12911 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.9723 | 1.25477 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7877 | 0.615314 | 0.307657 | − | 0.951497i | \(-0.400455\pi\) | ||||
0.307657 | + | 0.951497i | \(0.400455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 65.1238 | 3.39021 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.1533 | −0.527133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5556 | −0.857218 | −0.428609 | − | 0.903490i | \(-0.640996\pi\) | ||||
−0.428609 | + | 0.903490i | \(0.640996\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.1443 | −1.50500 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.3896 | −1.15312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.6357 | 0.546320 | 0.273160 | − | 0.961969i | \(-0.411931\pi\) | ||||
0.273160 | + | 0.961969i | \(0.411931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.6883 | −1.36728 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.6397 | −1.05464 | −0.527320 | − | 0.849667i | \(-0.676803\pi\) | ||||
−0.527320 | + | 0.849667i | \(0.676803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.48802 | −0.432590 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.11248 | 0.259882 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5991 | −0.588099 | −0.294050 | − | 0.955790i | \(-0.595003\pi\) | ||||
−0.294050 | + | 0.955790i | \(0.595003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5076 | 0.834823 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 53.9001 | 2.71890 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.84245 | 0.243650 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.23583 | −0.112213 | −0.0561066 | − | 0.998425i | \(-0.517869\pi\) | ||||
−0.0561066 | + | 0.998425i | \(0.517869\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.9788 | 0.850004 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.98943 | 0.199223 | 0.0996114 | − | 0.995026i | \(-0.468240\pi\) | ||||
0.0996114 | + | 0.995026i | \(0.468240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6914 | −0.931085 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −78.0130 | −3.87650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.0537 | −0.746186 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8308 | 0.634441 | 0.317221 | − | 0.948352i | \(-0.397250\pi\) | ||||
0.317221 | + | 0.948352i | \(0.397250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −58.8203 | −2.90139 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3273 | 0.901825 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.63349 | −0.374714 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3029 | 0.798358 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9249 | −0.582571 | −0.291286 | − | 0.956636i | \(-0.594083\pi\) | ||||
−0.291286 | + | 0.956636i | \(0.594083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9454 | −0.630919 | −0.315459 | − | 0.948939i | \(-0.602159\pi\) | ||||
−0.315459 | + | 0.948939i | \(0.602159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 88.5481 | 4.30536 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4667 | −0.556218 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.80253 | 0.425984 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.1386 | 2.08275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.8474 | 1.48587 | 0.742934 | − | 0.669365i | \(-0.233434\pi\) | ||||
0.742934 | + | 0.669365i | \(0.233434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.65891 | −0.0797223 | −0.0398612 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398612 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.9120 | 1.48211 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.39231 | 0.353622 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.8794 | 1.33061 | 0.665307 | − | 0.746570i | \(-0.268301\pi\) | ||||
0.665307 | + | 0.746570i | \(0.268301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.2973 | −1.72844 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25652 | −0.249745 | −0.124872 | − | 0.992173i | \(-0.539852\pi\) | ||||
−0.124872 | + | 0.992173i | \(0.539852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4046 | 0.825057 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.2252 | 0.767424 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0192 | 0.661609 | 0.330804 | − | 0.943699i | \(-0.392680\pi\) | ||||
0.330804 | + | 0.943699i | \(0.392680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3628 | 0.817583 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.31123 | −0.343512 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.5745 | 1.15207 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6088 | −0.636591 | −0.318296 | − | 0.947991i | \(-0.603110\pi\) | ||||
−0.318296 | + | 0.947991i | \(0.603110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 120.367 | 5.61825 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.1444 | 0.938217 | 0.469108 | − | 0.883141i | \(-0.344575\pi\) | ||||
0.469108 | + | 0.883141i | \(0.344575\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.2893 | 1.40766 | 0.703831 | − | 0.710367i | \(-0.251471\pi\) | ||||
0.703831 | + | 0.710367i | \(0.251471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.8060 | 1.19673 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.9528 | 0.599383 | 0.299692 | − | 0.954036i | \(-0.403116\pi\) | ||||
0.299692 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.5767 | 1.04250 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 52.4047 | 2.41468 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.36305 | 0.0626731 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.13496 | −0.235608 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −51.7385 | −2.36894 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.5271 | −1.30343 | −0.651717 | − | 0.758462i | \(-0.725951\pi\) | ||||
−0.651717 | + | 0.758462i | \(0.725951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.5835 | 1.98724 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.6344 | 0.529385 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.8330 | −1.62709 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.0787 | −1.31768 | −0.658842 | − | 0.752282i | \(-0.728953\pi\) | ||||
−0.658842 | + | 0.752282i | \(0.728953\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −50.2616 | −2.27291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9855 | 0.766545 | 0.383272 | − | 0.923635i | \(-0.374797\pi\) | ||||
0.383272 | + | 0.923635i | \(0.374797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.7349 | −1.20408 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −43.2527 | −1.94406 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.6954 | −0.524613 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.4814 | 1.36454 | 0.682268 | − | 0.731102i | \(-0.260994\pi\) | ||||
0.682268 | + | 0.731102i | \(0.260994\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.31023 | −0.147890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.93185 | −0.175313 | −0.0876564 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876564 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.8892 | −1.50805 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −81.8617 | −3.63561 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4779 | 0.686045 | 0.343023 | − | 0.939327i | \(-0.388549\pi\) | ||||
0.343023 | + | 0.939327i | \(0.388549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6124 | −0.646417 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 53.9020 | 2.37983 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.7990 | 1.04871 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.6080 | 1.03828 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −77.9231 | −3.42044 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0406 | −0.658939 | −0.329469 | − | 0.944166i | \(-0.606870\pi\) | ||||
−0.329469 | + | 0.944166i | \(0.606870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.2973 | −1.01872 | −0.509359 | − | 0.860554i | \(-0.670117\pi\) | ||||
−0.509359 | + | 0.860554i | \(0.670117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.08169 | −0.352714 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.3189 | −0.972227 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9346 | −0.779763 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 93.3907 | 4.05281 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −50.2687 | −2.17738 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6896 | −0.721553 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.5156 | −1.23054 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.67731 | −0.416831 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0397 | 1.20552 | 0.602760 | − | 0.797922i | \(-0.294068\pi\) | ||||
0.602760 | + | 0.797922i | \(0.294068\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.8184 | −1.15089 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.1960 | 0.865101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.99565 | 0.299112 | 0.149556 | − | 0.988753i | \(-0.452215\pi\) | ||||
0.149556 | + | 0.988753i | \(0.452215\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 44.8553 | 1.91438 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.9722 | −0.510035 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.95175 | −0.125521 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −60.1730 | −2.55420 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.213626 | −0.00905163 | −0.00452582 | − | 0.999990i | \(-0.501441\pi\) | ||||
−0.00452582 | + | 0.999990i | \(0.501441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.94630 | −0.166911 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.5107 | 2.17478 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.8050 | −0.750393 | −0.375197 | − | 0.926945i | \(-0.622425\pi\) | ||||
−0.375197 | + | 0.926945i | \(0.622425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.6598 | −0.869166 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 47.5533 | 1.99705 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.3874 | −1.56736 | −0.783681 | − | 0.621164i | \(-0.786660\pi\) | ||||
−0.783681 | + | 0.621164i | \(0.786660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.7937 | −0.995737 | −0.497869 | − | 0.867252i | \(-0.665884\pi\) | ||||
−0.497869 | + | 0.867252i | \(0.665884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.8712 | −1.16434 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.51864 | −0.146737 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6525 | 0.485100 | 0.242550 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242550 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −50.5150 | −2.09933 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.65305 | 0.193041 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.7941 | −0.571294 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 125.225 | 5.17742 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0583 | 1.19937 | 0.599683 | − | 0.800237i | \(-0.295293\pi\) | ||||
0.599683 | + | 0.800237i | \(0.295293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.99471 | −0.411825 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −60.5552 | −2.49091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.6140 | 1.21610 | 0.608051 | − | 0.793898i | \(-0.291952\pi\) | ||||
0.608051 | + | 0.793898i | \(0.291952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.3438 | 1.20298 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.9196 | −1.06082 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.97837 | −0.407705 | −0.203853 | − | 0.979002i | \(-0.565346\pi\) | ||||
−0.203853 | + | 0.979002i | \(0.565346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.4179 | 0.628910 | 0.314455 | − | 0.949272i | \(-0.398178\pi\) | ||||
0.314455 | + | 0.949272i | \(0.398178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 115.045 | 4.68500 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.6493 | 0.676891 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9572 | −0.688271 | −0.344136 | − | 0.938920i | \(-0.611828\pi\) | ||||
−0.344136 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.8426 | −0.763540 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −68.3499 | −2.76514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.20743 | 0.291105 | 0.145553 | − | 0.989351i | \(-0.453504\pi\) | ||||
0.145553 | + | 0.989351i | \(0.453504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 69.4029 | 2.79860 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.4731 | 1.66964 | 0.834822 | − | 0.550520i | \(-0.185570\pi\) | ||||
0.834822 | + | 0.550520i | \(0.185570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.9537 | 1.72645 | 0.863226 | − | 0.504817i | \(-0.168440\pi\) | ||||
0.863226 | + | 0.504817i | \(0.168440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.9353 | 1.48216 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.6091 | −0.425044 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3728 | −1.21491 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.0672 | 0.921215 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.0419 | 2.07505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.2821 | 1.20551 | 0.602756 | − | 0.797926i | \(-0.294069\pi\) | ||||
0.602756 | + | 0.797926i | \(0.294069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 64.6101 | 2.56802 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.6550 | −0.819670 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0177 | 1.11010 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −59.5969 | −2.35762 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.0327 | 1.54170 | 0.770849 | − | 0.637018i | \(-0.219832\pi\) | ||||
0.770849 | + | 0.637018i | \(0.219832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.4273 | −1.67317 | −0.836585 | − | 0.547837i | \(-0.815451\pi\) | ||||
−0.836585 | + | 0.547837i | \(0.815451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.44841 | 0.214531 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.2379 | −1.42466 | −0.712330 | − | 0.701845i | \(-0.752360\pi\) | ||||
−0.712330 | + | 0.701845i | \(0.752360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.8991 | 0.977377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.7302 | −0.616516 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.0559 | −1.76317 | −0.881587 | − | 0.472022i | \(-0.843524\pi\) | ||||
−0.881587 | + | 0.472022i | \(0.843524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.7152 | 1.62995 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −74.4611 | −2.90500 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.3965 | 0.833487 | 0.416744 | − | 0.909024i | \(-0.363171\pi\) | ||||
0.416744 | + | 0.909024i | \(0.363171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2681 | −1.37177 | −0.685885 | − | 0.727710i | \(-0.740585\pi\) | ||||
−0.685885 | + | 0.727710i | \(0.740585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −149.134 | −5.79187 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.1405 | 0.509568 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.20376 | −0.317651 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.69798 | −0.374945 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9590 | 0.461671 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.7417 | 1.45484 | 0.727418 | − | 0.686195i | \(-0.240720\pi\) | ||||
0.727418 | + | 0.686195i | \(0.240720\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6566 | −0.987523 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.3028 | 1.20307 | 0.601533 | − | 0.798848i | \(-0.294557\pi\) | ||||
0.601533 | + | 0.798848i | \(0.294557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.8422 | 0.838227 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −86.7178 | −3.32303 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.4903 | 1.35800 | 0.679000 | − | 0.734138i | \(-0.262414\pi\) | ||||
0.679000 | + | 0.734138i | \(0.262414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −45.5232 | −1.73935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.3299 | −1.15716 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.9367 | 1.52147 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.36456 | 0.242119 | 0.121060 | − | 0.992645i | \(-0.461371\pi\) | ||||
0.121060 | + | 0.992645i | \(0.461371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.3649 | 1.00152 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.6174 | 0.478607 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.0246 | −2.27359 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.0191 | 0.416780 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.2577 | −0.916200 | −0.458100 | − | 0.888901i | \(-0.651470\pi\) | ||||
−0.458100 | + | 0.888901i | \(0.651470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.3051 | 0.878968 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 94.3664 | 3.55404 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.6574 | 0.776900 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4415 | −1.33103 | −0.665517 | − | 0.746383i | \(-0.731789\pi\) | ||||
−0.665517 | + | 0.746383i | \(0.731789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0413 | −0.564093 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.84869 | −0.256486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.3865 | 1.24859 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.2727 | −1.09321 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.95811 | −0.296787 | −0.148394 | − | 0.988928i | \(-0.547410\pi\) | ||||
−0.148394 | + | 0.988928i | \(0.547410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5069 | −0.540264 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.61404 | 0.357550 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.69862 | 0.211641 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.7441 | 1.28859 | 0.644293 | − | 0.764778i | \(-0.277152\pi\) | ||||
0.644293 | + | 0.764778i | \(0.277152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 79.3469 | 2.93877 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.71217 | −0.174286 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.93098 | 0.0713226 | 0.0356613 | − | 0.999364i | \(-0.488646\pi\) | ||||
0.0356613 | + | 0.999364i | \(0.488646\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −38.6823 | −1.42682 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.6724 | 1.12983 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.7931 | −0.728102 | −0.364051 | − | 0.931379i | \(-0.618607\pi\) | ||||
−0.364051 | + | 0.931379i | \(0.618607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −66.7840 | −2.45337 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3838 | 1.22473 | 0.612366 | − | 0.790575i | \(-0.290218\pi\) | ||||
0.612366 | + | 0.790575i | \(0.290218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.5572 | 0.460062 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.7107 | 0.867528 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1732 | 0.371722 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.85107 | 0.249999 | 0.125000 | − | 0.992157i | \(-0.460107\pi\) | ||||
0.125000 | + | 0.992157i | \(0.460107\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.3658 | 1.25236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.65843 | −0.205931 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.6656 | −0.860141 | −0.430070 | − | 0.902795i | \(-0.641511\pi\) | ||||
−0.430070 | + | 0.902795i | \(0.641511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.8064 | 0.573735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.41790 | −0.0876488 | −0.0438244 | − | 0.999039i | \(-0.513954\pi\) | ||||
−0.0438244 | + | 0.999039i | \(0.513954\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.3106 | −0.445673 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 149.528 | 5.40619 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −72.0879 | −2.60294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.0804 | −0.651995 | −0.325997 | − | 0.945371i | \(-0.605700\pi\) | ||||
−0.325997 | + | 0.945371i | \(0.605700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.6467 | −0.923645 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.0927 | 0.398976 | 0.199488 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199488 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.75734 | 0.170889 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.6789 | 1.31585 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.8798 | −0.963070 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.8893 | −0.568563 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −59.8188 | −2.13775 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.5579 | 1.44757 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.8184 | 0.991620 | 0.495810 | − | 0.868431i | \(-0.334871\pi\) | ||||
0.495810 | + | 0.868431i | \(0.334871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.5353 | −0.553070 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.5933 | 0.447767 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.6236 | −1.22952 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55.1381 | −1.95555 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3973 | −0.757931 | −0.378966 | − | 0.925411i | \(-0.623720\pi\) | ||||
−0.378966 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −81.6148 | −2.88732 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.0610 | −1.91015 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.8523 | −0.700571 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.00431 | 0.317360 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.4684 | 1.10774 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.5325 | −1.63600 | −0.817998 | − | 0.575220i | \(-0.804916\pi\) | ||||
−0.817998 | + | 0.575220i | \(0.804916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1372 | 1.90101 | 0.950506 | − | 0.310705i | \(-0.100565\pi\) | ||||
0.950506 | + | 0.310705i | \(0.100565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 74.0647 | 2.59756 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.8993 | −1.36258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.11018 | −0.0738257 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −76.3317 | −2.66724 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6157 | −0.684592 | −0.342296 | − | 0.939592i | \(-0.611205\pi\) | ||||
−0.342296 | + | 0.939592i | \(0.611205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4516 | 0.991759 | 0.495879 | − | 0.868391i | \(-0.334846\pi\) | ||||
0.495879 | + | 0.868391i | \(0.334846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.9797 | −0.382263 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.1268 | 1.11716 | 0.558579 | − | 0.829451i | \(-0.311347\pi\) | ||||
0.558579 | + | 0.829451i | \(0.311347\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.8622 | −1.03716 | −0.518579 | − | 0.855030i | \(-0.673539\pi\) | ||||
−0.518579 | + | 0.855030i | \(0.673539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 84.6913 | 2.93791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.4552 | 1.15916 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.56191 | −0.0886586 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −49.9381 | −1.72611 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.8590 | 1.85942 | 0.929710 | − | 0.368292i | \(-0.120057\pi\) | ||||
0.929710 | + | 0.368292i | \(0.120057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7136 | −0.541848 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.2631 | −0.594573 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −63.3558 | −2.17950 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.1487 | −0.348713 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −63.5781 | −2.18199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.9694 | 0.547424 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.78694 | 0.198141 | 0.0990705 | − | 0.995080i | \(-0.468413\pi\) | ||||
0.0990705 | + | 0.995080i | \(0.468413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 66.9606 | 2.29001 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3296 | 1.54843 | 0.774215 | − | 0.632923i | \(-0.218145\pi\) | ||||
0.774215 | + | 0.632923i | \(0.218145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2246 | 0.417097 | 0.208548 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208548 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −42.3050 | −1.44175 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.466464 | 0.0158786 | 0.00793931 | − | 0.999968i | \(-0.497473\pi\) | ||||
0.00793931 | + | 0.999968i | \(0.497473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.3075 | −2.05052 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −121.802 | −4.13663 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.01020 | −0.136037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −88.8027 | −3.00897 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 111.302 | 3.76700 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.7490 | 0.464803 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.3905 | 1.56649 | 0.783247 | − | 0.621710i | \(-0.213562\pi\) | ||||
0.783247 | + | 0.621710i | \(0.213562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.50289 | −0.253066 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.2865 | 1.82896 | 0.914480 | − | 0.404632i | \(-0.132600\pi\) | ||||
0.914480 | + | 0.404632i | \(0.132600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3626 | 0.617952 | 0.308976 | − | 0.951070i | \(-0.400014\pi\) | ||||
0.308976 | + | 0.951070i | \(0.400014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 99.5272 | 3.34557 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.35576 | −0.112675 | −0.0563377 | − | 0.998412i | \(-0.517942\pi\) | ||||
−0.0563377 | + | 0.998412i | \(0.517942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.5904 | 0.422269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 64.6052 | 2.16436 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.5482 | −1.22304 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.0692 | −0.737693 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −45.7625 | −1.52797 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0918 | 0.369933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.6874 | 1.58870 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.32111 | −0.110520 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.7558 | −0.689945 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.01069 | 0.0999684 | 0.0499842 | − | 0.998750i | \(-0.484083\pi\) | ||||
0.0499842 | + | 0.998750i | \(0.484083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 105.264 | 3.49140 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.18018 | 0.105364 | 0.0526820 | − | 0.998611i | \(-0.483223\pi\) | ||||
0.0526820 | + | 0.998611i | \(0.483223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.32156 | 0.209213 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 47.8027 | 1.58031 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.4278 | −0.839700 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3109 | 1.19779 | 0.598893 | − | 0.800829i | \(-0.295608\pi\) | ||||
0.598893 | + | 0.800829i | \(0.295608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −72.2267 | −2.37995 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.0026 | 1.51419 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0929 | −0.364732 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −73.9231 | −2.42795 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.21107 | 0.170970 | 0.0854849 | − | 0.996339i | \(-0.472756\pi\) | ||||
0.0854849 | + | 0.996339i | \(0.472756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.9817 | 0.491006 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 114.650 | 3.75348 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.8660 | 1.30376 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.0899 | 0.786984 | 0.393492 | − | 0.919328i | \(-0.371267\pi\) | ||||
0.393492 | + | 0.919328i | \(0.371267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2301 | 0.366482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.5653 | 1.48539 | 0.742694 | − | 0.669631i | \(-0.233548\pi\) | ||||
0.742694 | + | 0.669631i | \(0.233548\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.4189 | −0.599802 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 65.6561 | 2.13579 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.5248 | −0.601974 | −0.300987 | − | 0.953628i | \(-0.597316\pi\) | ||||
−0.300987 | + | 0.953628i | \(0.597316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.4762 | 1.86576 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.1886 | 1.23835 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1796 | 0.459323 | 0.229662 | − | 0.973271i | \(-0.426238\pi\) | ||||
0.229662 | + | 0.973271i | \(0.426238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.5705 | −0.698007 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.5992 | −0.827506 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.7489 | 0.896060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7403 | −0.701299 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.8401 | 1.67052 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.0954 | −1.25853 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4050 | −0.784811 | −0.392405 | − | 0.919792i | \(-0.628357\pi\) | ||||
−0.392405 | + | 0.919792i | \(0.628357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −79.7451 | −2.56178 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0560 | 0.771994 | 0.385997 | − | 0.922500i | \(-0.373857\pi\) | ||||
0.385997 | + | 0.922500i | \(0.373857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.69104 | −0.246564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.7883 | 1.01804 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.8248 | −1.21012 | −0.605062 | − | 0.796179i | \(-0.706852\pi\) | ||||
−0.605062 | + | 0.796179i | \(0.706852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4133 | −0.460653 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −62.7315 | −2.00286 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.8078 | 0.567980 | 0.283990 | − | 0.958827i | \(-0.408342\pi\) | ||||
0.283990 | + | 0.958827i | \(0.408342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.8659 | −1.49327 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57.5217 | −1.83093 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.44596 | −0.0459788 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.2086 | −1.43610 | −0.718050 | − | 0.695992i | \(-0.754965\pi\) | ||||
−0.718050 | + | 0.695992i | \(0.754965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42.9812 | 1.36397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0601 | −0.635948 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.8763 | −0.534477 | −0.267239 | − | 0.963630i | \(-0.586111\pi\) | ||||
−0.267239 | + | 0.963630i | \(0.586111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 116.443 | 3.68409 |
(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 | 1336.2.a.e.1.1 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.n.1.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.e.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.n.1.12 | 12 | 4.3 | odd | 2 |