Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4332,2,Mod(1,4332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4332, 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("4332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4332.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: | \(34.5911941556\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4332.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.34730 | 0.602529 | 0.301265 | − | 0.953541i | \(-0.402591\pi\) | ||||
0.301265 | + | 0.953541i | \(0.402591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41147 | 0.911452 | 0.455726 | − | 0.890120i | \(-0.349380\pi\) | ||||
0.455726 | + | 0.890120i | \(0.349380\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.94356 | −1.79205 | −0.896026 | − | 0.444002i | \(-0.853558\pi\) | ||||
−0.896026 | + | 0.444002i | \(0.853558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.69459 | −1.02470 | −0.512348 | − | 0.858778i | \(-0.671224\pi\) | ||||
−0.512348 | + | 0.858778i | \(0.671224\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.34730 | 0.347870 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.162504 | −0.0394130 | −0.0197065 | − | 0.999806i | \(-0.506273\pi\) | ||||
−0.0197065 | + | 0.999806i | \(0.506273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.41147 | 0.526227 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.57398 | −1.37077 | −0.685385 | − | 0.728181i | \(-0.740366\pi\) | ||||
−0.685385 | + | 0.728181i | \(0.740366\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.18479 | −0.636959 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38919 | 0.443661 | 0.221830 | − | 0.975085i | \(-0.428797\pi\) | ||||
0.221830 | + | 0.975085i | \(0.428797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59627 | −0.466303 | −0.233152 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233152 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.94356 | −1.03464 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.24897 | 0.549176 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.94356 | −1.14151 | −0.570757 | − | 0.821119i | \(-0.693350\pi\) | ||||
−0.570757 | + | 0.821119i | \(0.693350\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.69459 | −0.591608 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.361844 | −0.0565106 | −0.0282553 | − | 0.999601i | \(-0.508995\pi\) | ||||
−0.0282553 | + | 0.999601i | \(0.508995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4534 | −1.74662 | −0.873311 | − | 0.487164i | \(-0.838032\pi\) | ||||
−0.873311 | + | 0.487164i | \(0.838032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.34730 | 0.200843 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.87939 | −1.00346 | −0.501731 | − | 0.865024i | \(-0.667303\pi\) | ||||
−0.501731 | + | 0.865024i | \(0.667303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.18479 | −0.169256 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.162504 | −0.0227551 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.02229 | 0.552504 | 0.276252 | − | 0.961085i | \(-0.410908\pi\) | ||||
0.276252 | + | 0.961085i | \(0.410908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00774 | −1.07976 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0496 | 1.56873 | 0.784364 | − | 0.620301i | \(-0.212989\pi\) | ||||
0.784364 | + | 0.620301i | \(0.212989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.18479 | 0.791882 | 0.395941 | − | 0.918276i | \(-0.370419\pi\) | ||||
0.395941 | + | 0.918276i | \(0.370419\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.41147 | 0.303817 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.97771 | −0.617409 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.75877 | −0.703546 | −0.351773 | − | 0.936085i | \(-0.614421\pi\) | ||||
−0.351773 | + | 0.936085i | \(0.614421\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.57398 | −0.791414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1925 | 1.44699 | 0.723494 | − | 0.690331i | \(-0.242535\pi\) | ||||
0.723494 | + | 0.690331i | \(0.242535\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.17024 | −1.07330 | −0.536648 | − | 0.843806i | \(-0.680310\pi\) | ||||
−0.536648 | + | 0.843806i | \(0.680310\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.18479 | −0.367748 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.3327 | −1.63337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.69459 | −1.09073 | −0.545363 | − | 0.838200i | \(-0.683608\pi\) | ||||
−0.545363 | + | 0.838200i | \(0.683608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.02734 | 0.222530 | 0.111265 | − | 0.993791i | \(-0.464510\pi\) | ||||
0.111265 | + | 0.993791i | \(0.464510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.218941 | −0.0237475 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.38919 | 0.256148 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.44831 | 0.365520 | 0.182760 | − | 0.983158i | \(-0.441497\pi\) | ||||
0.182760 | + | 0.983158i | \(0.441497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.90941 | −0.933960 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.59627 | −0.269220 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0915 | 1.22771 | 0.613854 | − | 0.789420i | \(-0.289618\pi\) | ||||
0.613854 | + | 0.789420i | \(0.289618\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.94356 | −0.597351 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.93582 | −0.391629 | −0.195814 | − | 0.980641i | \(-0.562735\pi\) | ||||
−0.195814 | + | 0.980641i | \(0.562735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3131 | −1.21325 | −0.606625 | − | 0.794988i | \(-0.707477\pi\) | ||||
−0.606625 | + | 0.794988i | \(0.707477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.24897 | 0.317067 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4338 | −1.29869 | −0.649345 | − | 0.760494i | \(-0.724957\pi\) | ||||
−0.649345 | + | 0.760494i | \(0.724957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.26857 | 0.217290 | 0.108645 | − | 0.994081i | \(-0.465349\pi\) | ||||
0.108645 | + | 0.994081i | \(0.465349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.94356 | −0.659054 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7101 | −1.19566 | −0.597832 | − | 0.801622i | \(-0.703971\pi\) | ||||
−0.597832 | + | 0.801622i | \(0.703971\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.85710 | −0.825929 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.69459 | −0.341565 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.391874 | −0.0359230 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.3259 | 2.21145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.361844 | −0.0326264 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0273 | −0.986315 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.73143 | 0.686053 | 0.343027 | − | 0.939326i | \(-0.388548\pi\) | ||||
0.343027 | + | 0.939326i | \(0.388548\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.4534 | −1.00841 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.5672 | 1.09800 | 0.548999 | − | 0.835823i | \(-0.315009\pi\) | ||||
0.548999 | + | 0.835823i | \(0.315009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.34730 | 0.115957 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.7101 | 1.34220 | 0.671101 | − | 0.741366i | \(-0.265822\pi\) | ||||
0.671101 | + | 0.741366i | \(0.265822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23442 | 0.274340 | 0.137170 | − | 0.990548i | \(-0.456199\pi\) | ||||
0.137170 | + | 0.990548i | \(0.456199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.87939 | −0.579349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.9590 | 1.83631 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.21894 | 0.267318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.18479 | −0.0977200 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.46017 | 0.365391 | 0.182696 | − | 0.983170i | \(-0.441518\pi\) | ||||
0.182696 | + | 0.983170i | \(0.441518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94862 | 0.728228 | 0.364114 | − | 0.931354i | \(-0.381372\pi\) | ||||
0.364114 | + | 0.931354i | \(0.381372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.162504 | −0.0131377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.49794 | −0.280961 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5202 | −0.919414 | −0.459707 | − | 0.888071i | \(-0.652046\pi\) | ||||
−0.459707 | + | 0.888071i | \(0.652046\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.02229 | 0.318988 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.8530 | −1.24939 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5243 | −0.824331 | −0.412165 | − | 0.911109i | \(-0.635227\pi\) | ||||
−0.412165 | + | 0.911109i | \(0.635227\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00774 | −0.623402 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7392 | 0.831022 | 0.415511 | − | 0.909588i | \(-0.363603\pi\) | ||||
0.415511 | + | 0.909588i | \(0.363603\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.650015 | 0.0500012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.53983 | −0.573243 | −0.286621 | − | 0.958044i | \(-0.592532\pi\) | ||||
−0.286621 | + | 0.958044i | \(0.592532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.68004 | −0.580557 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0496 | 0.905706 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.3628 | 1.97045 | 0.985223 | − | 0.171275i | \(-0.0547886\pi\) | ||||
0.985223 | + | 0.171275i | \(0.0547886\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.0915 | 1.56772 | 0.783860 | − | 0.620937i | \(-0.213248\pi\) | ||||
0.783860 | + | 0.620937i | \(0.213248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.18479 | 0.457193 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.35504 | −0.687796 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.965852 | 0.0706301 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.41147 | 0.175409 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.255777 | −0.0185074 | −0.00925370 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925370 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3482 | 1.03281 | 0.516404 | − | 0.856345i | \(-0.327270\pi\) | ||||
0.516404 | + | 0.856345i | \(0.327270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.97771 | −0.356461 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6810 | 1.68720 | 0.843600 | − | 0.536972i | \(-0.180432\pi\) | ||||
0.843600 | + | 0.536972i | \(0.180432\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7956 | −0.836168 | −0.418084 | − | 0.908408i | \(-0.637298\pi\) | ||||
−0.418084 | + | 0.908408i | \(0.637298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.75877 | −0.406192 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.76146 | 0.404375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.487511 | −0.0340493 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.57398 | −0.456923 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.8580 | 1.91783 | 0.958913 | − | 0.283700i | \(-0.0915621\pi\) | ||||
0.958913 | + | 0.283700i | \(0.0915621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.1925 | 0.835419 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.4311 | −1.05239 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.26083 | −0.425013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.17024 | −0.619668 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.600385 | 0.0403863 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.7374 | −1.65654 | −0.828270 | − | 0.560329i | \(-0.810675\pi\) | ||||
−0.828270 | + | 0.560329i | \(0.810675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.18479 | −0.212320 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0155 | −1.46122 | −0.730609 | − | 0.682796i | \(-0.760764\pi\) | ||||
−0.730609 | + | 0.682796i | \(0.760764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.29591 | −0.614291 | −0.307146 | − | 0.951663i | \(-0.599374\pi\) | ||||
−0.307146 | + | 0.951663i | \(0.599374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.3327 | −0.943026 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.98814 | −0.523320 | −0.261660 | − | 0.965160i | \(-0.584270\pi\) | ||||
−0.261660 | + | 0.965160i | \(0.584270\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.26857 | −0.604615 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.69459 | −0.629731 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.4492 | −1.71086 | −0.855430 | − | 0.517919i | \(-0.826707\pi\) | ||||
−0.855430 | + | 0.517919i | \(0.826707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.73917 | −0.176445 | −0.0882227 | − | 0.996101i | \(-0.528119\pi\) | ||||
−0.0882227 | + | 0.996101i | \(0.528119\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.59627 | −0.101982 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.02734 | 0.128478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.2294 | 0.961269 | 0.480635 | − | 0.876921i | \(-0.340406\pi\) | ||||
0.480635 | + | 0.876921i | \(0.340406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.0729 | 2.45649 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.218941 | −0.0137106 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.0351 | 0.813106 | 0.406553 | − | 0.913627i | \(-0.366731\pi\) | ||||
0.406553 | + | 0.913627i | \(0.366731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.7442 | −1.04044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.38919 | 0.147887 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.9263 | −0.735409 | −0.367704 | − | 0.929943i | \(-0.619856\pi\) | ||||
−0.367704 | + | 0.929943i | \(0.619856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.41921 | 0.332900 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.44831 | 0.211033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8580 | 1.57659 | 0.788296 | − | 0.615296i | \(-0.210964\pi\) | ||||
0.788296 | + | 0.615296i | \(0.210964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8726 | 0.721208 | 0.360604 | − | 0.932719i | \(-0.382571\pi\) | ||||
0.360604 | + | 0.932719i | \(0.382571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.90941 | −0.539222 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.9290 | 1.14146 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4115 | 0.865902 | 0.432951 | − | 0.901418i | \(-0.357472\pi\) | ||||
0.432951 | + | 0.901418i | \(0.357472\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.59627 | −0.155434 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.63135 | −0.156973 | −0.0784865 | − | 0.996915i | \(-0.525009\pi\) | ||||
−0.0784865 | + | 0.996915i | \(0.525009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.09152 | 0.362103 | 0.181052 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181052 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.872578 | −0.0515067 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9736 | −0.998447 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0915 | 0.708817 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.7306 | −1.91214 | −0.956071 | − | 0.293134i | \(-0.905302\pi\) | ||||
−0.956071 | + | 0.293134i | \(0.905302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.2344 | 0.945205 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.94356 | −0.344881 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.2882 | 1.40462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.6195 | −1.59196 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.93582 | −0.226107 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.33275 | 0.477132 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.20945 | −0.354392 | −0.177196 | − | 0.984176i | \(-0.556703\pi\) | ||||
−0.177196 | + | 0.984176i | \(0.556703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.3131 | −0.700471 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.10607 | 0.176129 | 0.0880644 | − | 0.996115i | \(-0.471932\pi\) | ||||
0.0880644 | + | 0.996115i | \(0.471932\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8726 | −0.953695 | −0.476847 | − | 0.878986i | \(-0.658221\pi\) | ||||
−0.476847 | + | 0.878986i | \(0.658221\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.24897 | 0.183059 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.4260 | 0.810246 | 0.405123 | − | 0.914262i | \(-0.367229\pi\) | ||||
0.405123 | + | 0.914262i | \(0.367229\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.2003 | −0.795063 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.4338 | −0.749800 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.7665 | 0.652689 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.26857 | 0.125452 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5895 | −0.914607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.99731 | −0.494537 | −0.247268 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247268 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.94356 | −0.380505 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.75877 | −0.423907 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.27807 | −0.124094 | −0.0620471 | − | 0.998073i | \(-0.519763\pi\) | ||||
−0.0620471 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.7101 | −0.690316 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4311 | 0.835640 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7374 | −1.06572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.85710 | −0.476850 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.50299 | 0.402782 | 0.201391 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201391 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.0351 | −1.55421 | −0.777106 | − | 0.629370i | \(-0.783313\pi\) | ||||
−0.777106 | + | 0.629370i | \(0.783313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.69459 | −0.197203 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4192 | −1.24648 | −0.623240 | − | 0.782031i | \(-0.714184\pi\) | ||||
−0.623240 | + | 0.782031i | \(0.714184\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.4270 | 0.871852 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.391874 | −0.0207402 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.7178 | −1.88511 | −0.942557 | − | 0.334045i | \(-0.891586\pi\) | ||||
−0.942557 | + | 0.334045i | \(0.891586\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.3259 | 1.27678 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.3550 | −0.646692 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.9317 | −1.09263 | −0.546313 | − | 0.837581i | \(-0.683969\pi\) | ||||
−0.546313 | + | 0.837581i | \(0.683969\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.361844 | −0.0188369 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.69965 | 0.503580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.89124 | −0.149703 | −0.0748515 | − | 0.997195i | \(-0.523848\pi\) | ||||
−0.0748515 | + | 0.997195i | \(0.523848\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.0273 | −0.569449 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.82707 | −0.454617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7374 | −1.27068 | −0.635338 | − | 0.772234i | \(-0.719139\pi\) | ||||
−0.635338 | + | 0.772234i | \(0.719139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.73143 | 0.396093 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8571 | 0.759162 | 0.379581 | − | 0.925158i | \(-0.376068\pi\) | ||||
0.379581 | + | 0.925158i | \(0.376068\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.3105 | −0.984152 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4534 | −0.582207 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.7588 | 1.61023 | 0.805117 | − | 0.593116i | \(-0.202103\pi\) | ||||
0.805117 | + | 0.593116i | \(0.202103\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06830 | 0.0540261 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.5672 | 0.633930 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.0615 | −0.657195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7716 | −0.891929 | −0.445965 | − | 0.895051i | \(-0.647139\pi\) | ||||
−0.445965 | + | 0.895051i | \(0.647139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.0333 | −1.74948 | −0.874740 | − | 0.484592i | \(-0.838968\pi\) | ||||
−0.874740 | + | 0.484592i | \(0.838968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.59215 | 0.477819 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.34730 | 0.0669477 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.2695 | 2.04565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5294 | −0.570092 | −0.285046 | − | 0.958514i | \(-0.592009\pi\) | ||||
−0.285046 | + | 0.958514i | \(0.592009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.7101 | 0.774921 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.0574 | 1.42982 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.73143 | 0.134081 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.23442 | 0.158390 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.7692 | −1.69859 | −0.849293 | − | 0.527921i | \(-0.822972\pi\) | ||||
−0.849293 | + | 0.527921i | \(0.822972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7050 | −0.765416 | −0.382708 | − | 0.923869i | \(-0.625008\pi\) | ||||
−0.382708 | + | 0.923869i | \(0.625008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.87939 | −0.334487 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.517541 | 0.0251044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.9145 | 0.721762 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.9590 | 1.06019 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.4730 | −0.648970 | −0.324485 | − | 0.945891i | \(-0.605191\pi\) | ||||
−0.324485 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7733 | 0.565790 | 0.282895 | − | 0.959151i | \(-0.408705\pi\) | ||||
0.282895 | + | 0.959151i | \(0.408705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.21894 | 0.154336 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7151 | 0.750042 | 0.375021 | − | 0.927016i | \(-0.377635\pi\) | ||||
0.375021 | + | 0.927016i | \(0.377635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18479 | −0.0564187 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6432 | −0.743231 | −0.371616 | − | 0.928387i | \(-0.621196\pi\) | ||||
−0.371616 | + | 0.928387i | \(0.621196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.64590 | 0.220237 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.46017 | 0.210959 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1857 | −0.858237 | −0.429119 | − | 0.903248i | \(-0.641176\pi\) | ||||
−0.429119 | + | 0.903248i | \(0.641176\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.15064 | 0.101270 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.94862 | 0.420443 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0036 | −0.562738 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.8111 | 0.786390 | 0.393195 | − | 0.919455i | \(-0.371370\pi\) | ||||
0.393195 | + | 0.919455i | \(0.371370\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.162504 | −0.00758503 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6364 | −0.588536 | −0.294268 | − | 0.955723i | \(-0.595076\pi\) | ||||
−0.294268 | + | 0.955723i | \(0.595076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.89487 | −0.273958 | −0.136979 | − | 0.990574i | \(-0.543739\pi\) | ||||
−0.136979 | + | 0.990574i | \(0.543739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.49794 | −0.162213 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.36959 | −0.248475 | −0.124237 | − | 0.992253i | \(-0.539648\pi\) | ||||
−0.124237 | + | 0.992253i | \(0.539648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.8871 | −0.641248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5202 | −0.530824 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 68.0738 | 3.13004 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.02229 | 0.184168 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.8476 | −0.906860 | −0.453430 | − | 0.891292i | \(-0.649800\pi\) | ||||
−0.453430 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.6536 | 1.16971 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.8530 | −0.721335 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.2909 | 0.739730 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0077 | 0.589437 | 0.294718 | − | 0.955584i | \(-0.404774\pi\) | ||||
0.294718 | + | 0.955584i | \(0.404774\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.5243 | −0.475927 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.7478 | 1.34250 | 0.671251 | − | 0.741230i | \(-0.265757\pi\) | ||||
0.671251 | + | 0.741230i | \(0.265757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.388252 | −0.0174860 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00774 | −0.359921 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.4020 | 1.31886 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9855 | 0.670841 | 0.335420 | − | 0.942069i | \(-0.391122\pi\) | ||||
0.335420 | + | 0.942069i | \(0.391122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7392 | 0.479791 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.7074 | −0.789533 | −0.394767 | − | 0.918781i | \(-0.629175\pi\) | ||||
−0.394767 | + | 0.918781i | \(0.629175\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.30272 | −0.235968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.650015 | 0.0288682 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.2226 | 1.20662 | 0.603309 | − | 0.797507i | \(-0.293848\pi\) | ||||
0.603309 | + | 0.797507i | \(0.293848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.1138 | −0.978257 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.5895 | −0.731019 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.8881 | 1.79825 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.53983 | −0.330962 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4260 | 0.894880 | 0.447440 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447440 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.1147 | −1.79782 | −0.898911 | − | 0.438131i | \(-0.855641\pi\) | ||||
−0.898911 | + | 0.438131i | \(0.855641\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.68004 | −0.335185 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.421903 | 0.0183784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2172 | 0.879008 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0496 | 0.522909 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.33687 | 0.0579061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0993 | −0.782499 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.3628 | 1.13764 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.04189 | 0.303316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.07098 | −0.261012 | −0.130506 | − | 0.991448i | \(-0.541660\pi\) | ||||
−0.130506 | + | 0.991448i | \(0.541660\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.0915 | 0.905124 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.05644 | 0.130923 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.8152 | −1.01826 | −0.509132 | − | 0.860688i | \(-0.670034\pi\) | ||||
−0.509132 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.18479 | 0.263961 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.3783 | −0.994145 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.35504 | −0.397099 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.3155 | −0.987910 | −0.493955 | − | 0.869487i | \(-0.664449\pi\) | ||||
−0.493955 | + | 0.869487i | \(0.664449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.3155 | 1.78976 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.965852 | 0.0407783 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.7074 | 0.619842 | 0.309921 | − | 0.950762i | \(-0.399697\pi\) | ||||
0.309921 | + | 0.950762i | \(0.399697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.1242 | −0.720422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.41147 | 0.101272 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.6750 | 1.36981 | 0.684903 | − | 0.728634i | \(-0.259844\pi\) | ||||
0.684903 | + | 0.728634i | \(0.259844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3901 | 1.27179 | 0.635893 | − | 0.771777i | \(-0.280632\pi\) | ||||
0.635893 | + | 0.771777i | \(0.280632\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.255777 | −0.0106853 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.9368 | 0.873123 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.8648 | 1.28492 | 0.642460 | − | 0.766319i | \(-0.277914\pi\) | ||||
0.642460 | + | 0.766319i | \(0.277914\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.3482 | 0.596292 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.88888 | 0.202825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.9067 | −0.990115 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.97771 | −0.205803 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.1712 | 1.16275 | 0.581374 | − | 0.813636i | \(-0.302515\pi\) | ||||
0.581374 | + | 0.813636i | \(0.302515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6810 | 0.974105 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.82058 | −0.280088 | −0.140044 | − | 0.990145i | \(-0.544724\pi\) | ||||
−0.140044 | + | 0.990145i | \(0.544724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.527970 | −0.0216447 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.7956 | −0.482762 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.7110 | −1.45911 | −0.729556 | − | 0.683921i | \(-0.760273\pi\) | ||||
−0.729556 | + | 0.683921i | \(0.760273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.52797 | 0.225491 | 0.112745 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112745 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.75877 | −0.234515 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.7743 | 1.33246 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.4953 | 0.791288 | 0.395644 | − | 0.918404i | \(-0.370521\pi\) | ||||
0.395644 | + | 0.918404i | \(0.370521\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.76146 | 0.233466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.4165 | 1.02824 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.5202 | 1.59621 | 0.798104 | − | 0.602520i | \(-0.205837\pi\) | ||||
0.798104 | + | 0.602520i | \(0.205837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.487511 | −0.0196584 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.24359 | −0.0500652 | −0.0250326 | − | 0.999687i | \(-0.507969\pi\) | ||||
−0.0250326 | + | 0.999687i | \(0.507969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.40373 | −0.337775 | −0.168887 | − | 0.985635i | \(-0.554017\pi\) | ||||
−0.168887 | + | 0.985635i | \(0.554017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.57398 | −0.263805 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.31551 | 0.333154 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.06687 | 0.0426746 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.12836 | 0.0449905 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.28075 | −0.369461 | −0.184731 | − | 0.982789i | \(-0.559141\pi\) | ||||
−0.184731 | + | 0.982789i | \(0.559141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.8580 | 1.10726 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.4165 | 0.413367 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.37733 | 0.173436 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.1925 | 0.482329 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.71419 | −0.344190 | −0.172095 | − | 0.985080i | \(-0.555054\pi\) | ||||
−0.172095 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.1310 | −0.596710 | −0.298355 | − | 0.954455i | \(-0.596438\pi\) | ||||
−0.298355 | + | 0.954455i | \(0.596438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.4311 | −0.607598 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.31282 | 0.287497 | 0.143748 | − | 0.989614i | \(-0.454084\pi\) | ||||
0.143748 | + | 0.989614i | \(0.454084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −71.6177 | −2.81124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.26083 | −0.245381 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.5381 | 0.686318 | 0.343159 | − | 0.939277i | \(-0.388503\pi\) | ||||
0.343159 | + | 0.939277i | \(0.388503\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9317 | 0.661576 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.17024 | −0.357765 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.87164 | −0.306636 | −0.153318 | − | 0.988177i | \(-0.548996\pi\) | ||||
−0.153318 | + | 0.988177i | \(0.548996\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.964097 | 0.0374990 | 0.0187495 | − | 0.999824i | \(-0.494031\pi\) | ||||
0.0187495 | + | 0.999824i | \(0.494031\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.600385 | 0.0233170 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.7065 | −0.608156 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.7374 | −0.956404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.7597 | −1.41909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8530 | −0.996559 | −0.498280 | − | 0.867016i | \(-0.666035\pi\) | ||||
−0.498280 | + | 0.867016i | \(0.666035\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.18479 | −0.122583 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.9956 | 1.15282 | 0.576411 | − | 0.817160i | \(-0.304453\pi\) | ||||
0.576411 | + | 0.817160i | \(0.304453\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.1584 | 1.11900 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.0155 | −0.843635 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.5084 | 1.28216 | 0.641081 | − | 0.767473i | \(-0.278486\pi\) | ||||
0.641081 | + | 0.767473i | \(0.278486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.1661 | 0.808716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.29591 | −0.354661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.8607 | −0.566148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.8135 | −0.487447 | −0.243723 | − | 0.969845i | \(-0.578369\pi\) | ||||
−0.243723 | + | 0.969845i | \(0.578369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.3327 | −0.544456 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.35773 | 0.165298 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0588011 | 0.00222725 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.98814 | −0.302139 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.97266 | 0.150045 | 0.0750226 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750226 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.26857 | −0.349075 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.49113 | −0.356951 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.3054 | 1.21326 | 0.606628 | − | 0.794986i | \(-0.292522\pi\) | ||||
0.606628 | + | 0.794986i | \(0.292522\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.69459 | −0.363576 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.0678 | 0.639194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.5853 | 1.10643 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.4492 | −0.987765 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.2686 | 1.68823 | 0.844116 | − | 0.536160i | \(-0.180126\pi\) | ||||
0.844116 | + | 0.536160i | \(0.180126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.6928 | −1.10582 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.73917 | −0.101871 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.60906 | −0.282593 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.1821 | −0.822689 | −0.411344 | − | 0.911480i | \(-0.634941\pi\) | ||||
−0.411344 | + | 0.911480i | \(0.634941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.86122 | 0.0688395 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8212 | 1.69244 | 0.846222 | − | 0.532830i | \(-0.178872\pi\) | ||||
0.846222 | + | 0.532830i | \(0.178872\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.59627 | −0.0588792 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.2276 | 1.26079 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.77425 | −0.138838 | −0.0694191 | − | 0.997588i | \(-0.522115\pi\) | ||||
−0.0694191 | + | 0.997588i | \(0.522115\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.4858 | −0.824922 | −0.412461 | − | 0.910975i | \(-0.635331\pi\) | ||||
−0.412461 | + | 0.910975i | \(0.635331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00917 | 0.220159 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.02734 | 0.0741765 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32.3952 | −1.18369 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4962 | −1.51422 | −0.757109 | − | 0.653289i | \(-0.773389\pi\) | ||||
−0.757109 | + | 0.653289i | \(0.773389\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.2294 | 0.554989 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0564 | 0.438779 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8821 | −0.649935 | −0.324968 | − | 0.945725i | \(-0.605353\pi\) | ||||
−0.324968 | + | 0.945725i | \(0.605353\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 39.0729 | 1.41825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0806 | 1.38042 | 0.690210 | − | 0.723609i | \(-0.257518\pi\) | ||||
0.690210 | + | 0.723609i | \(0.257518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.47060 | 0.198049 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.218941 | −0.00791582 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.5185 | −1.60747 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.6245 | −0.455253 | −0.227626 | − | 0.973749i | \(-0.573096\pi\) | ||||
−0.227626 | + | 0.973749i | \(0.573096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.0351 | 0.469447 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.7989 | 1.21566 | 0.607831 | − | 0.794066i | \(-0.292040\pi\) | ||||
0.607831 | + | 0.794066i | \(0.292040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.26857 | 0.297016 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.7442 | −0.600696 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −72.4671 | −2.59308 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.38919 | 0.0853825 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.5212 | −0.553974 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6117 | −1.19813 | −0.599065 | − | 0.800701i | \(-0.704461\pi\) | ||||
−0.599065 | + | 0.800701i | \(0.704461\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.9263 | −0.424588 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.6500 | −1.08979 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8503 | −0.811438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.41921 | 0.192200 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.0547 | −1.63134 | −0.815670 | − | 0.578517i | \(-0.803632\pi\) | ||||
−0.815670 | + | 0.578517i | \(0.803632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.11793 | 0.0395494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.44831 | 0.121840 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.5039 | 1.92340 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.3587 | −0.752794 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.8580 | 0.910246 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.3705 | 1.41935 | 0.709676 | − | 0.704528i | \(-0.248841\pi\) | ||||
0.709676 | + | 0.704528i | \(0.248841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.5853 | −1.81141 | −0.905703 | − | 0.423912i | \(-0.860656\pi\) | ||||
−0.905703 | + | 0.423912i | \(0.860656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.8726 | 0.416389 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.1794 | −0.496683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.90941 | −0.311320 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8289 | 1.39004 | 0.695020 | − | 0.718991i | \(-0.255396\pi\) | ||||
0.695020 | + | 0.718991i | \(0.255396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9736 | −0.661378 | −0.330689 | − | 0.943740i | \(-0.607281\pi\) | ||||
−0.330689 | + | 0.943740i | \(0.607281\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.9290 | 0.659024 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.91891 | −0.171047 | −0.0855236 | − | 0.996336i | \(-0.527256\pi\) | ||||
−0.0855236 | + | 0.996336i | \(0.527256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.2799 | −1.15586 | −0.577930 | − | 0.816086i | \(-0.696139\pi\) | ||||
−0.577930 | + | 0.816086i | \(0.696139\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.4115 | 0.499928 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.192533 | 0.00667088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.4688 | 0.500715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.59627 | −0.0897401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5003 | 0.638701 | 0.319351 | − | 0.947637i | \(-0.396535\pi\) | ||||
0.319351 | + | 0.947637i | \(0.396535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2918 | −0.803165 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.63135 | −0.0906285 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.875763 | 0.0301272 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.6614 | 2.01563 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.09152 | 0.209060 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.6468 | 1.56475 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.67768 | 0.297118 | 0.148559 | − | 0.988904i | \(-0.452536\pi\) | ||||
0.148559 | + | 0.988904i | \(0.452536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.0164 | −0.922863 | −0.461432 | − | 0.887176i | \(-0.652664\pi\) | ||||
−0.461432 | + | 0.887176i | \(0.652664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.1995 | −1.74690 | −0.873451 | − | 0.486911i | \(-0.838123\pi\) | ||||
−0.873451 | + | 0.486911i | \(0.838123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.872578 | −0.0297374 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.1607 | 0.652239 | 0.326120 | − | 0.945328i | \(-0.394259\pi\) | ||||
0.326120 | + | 0.945328i | \(0.394259\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1584 | −0.345395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9736 | −0.576453 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.6204 | 1.95464 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.2763 | 0.720920 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0915 | 0.409236 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.5921 | −0.898979 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.3218 | 1.80055 | 0.900275 | − | 0.435322i | \(-0.143365\pi\) | ||||
0.900275 | + | 0.435322i | \(0.143365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.7306 | −1.10398 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.673238 | −0.0226820 | −0.0113410 | − | 0.999936i | \(-0.503610\pi\) | ||||
−0.0113410 | + | 0.999936i | \(0.503610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.79116 | 0.329499 | 0.164749 | − | 0.986335i | \(-0.447318\pi\) | ||||
0.164749 | + | 0.986335i | \(0.447318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.2344 | 0.545714 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.79467 | −0.295296 | −0.147648 | − | 0.989040i | \(-0.547170\pi\) | ||||
−0.147648 | + | 0.989040i | \(0.547170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6441 | 0.625304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.94356 | −0.199117 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.5185 | 1.18725 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.2882 | 0.810958 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.20296 | −0.206880 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.653637 | −0.0217758 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6195 | −0.919119 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.4165 | 0.944597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.79797 | −0.192518 | −0.0962592 | − | 0.995356i | \(-0.530688\pi\) | ||||
−0.0962592 | + | 0.995356i | \(0.530688\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.93582 | −0.130543 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9145 | −0.560401 | −0.280201 | − | 0.959941i | \(-0.590401\pi\) | ||||
−0.280201 | + | 0.959941i | \(0.590401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0496 | −0.398785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.33275 | 0.275472 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.3054 | 1.00077 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8759 | −1.21642 | −0.608211 | − | 0.793775i | \(-0.708113\pi\) | ||||
−0.608211 | + | 0.793775i | \(0.708113\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.20945 | −0.204608 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.0464 | −1.48272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.1138 | 0.727098 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.3131 | −0.404417 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0368 | 0.985477 | 0.492738 | − | 0.870178i | \(-0.335996\pi\) | ||||
0.492738 | + | 0.870178i | \(0.335996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.10607 | 0.101688 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.30129 | 0.0425567 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.20615 | −0.137409 | −0.0687044 | − | 0.997637i | \(-0.521887\pi\) | ||||
−0.0687044 | + | 0.997637i | \(0.521887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8726 | −0.550616 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.8111 | −1.16741 | −0.583704 | − | 0.811966i | \(-0.698397\pi\) | ||||
−0.583704 | + | 0.811966i | \(0.698397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.37876 | 0.0774630 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.24897 | 0.105689 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.4510 | −0.339612 | −0.169806 | − | 0.985478i | \(-0.554314\pi\) | ||||
−0.169806 | + | 0.985478i | \(0.554314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33.8803 | 1.09980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.4260 | 0.467796 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.6132 | 0.700120 | 0.350060 | − | 0.936727i | \(-0.386161\pi\) | ||||
0.350060 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.344608 | −0.0111513 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.2003 | −0.459030 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.8844 | 1.22335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.2594 | −0.782561 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.4338 | −0.432897 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3313 | 0.622297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.12155 | 0.293329 | 0.146665 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146665 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.8221 | −1.56678 | −0.783388 | − | 0.621533i | \(-0.786510\pi\) | ||||
−0.783388 | + | 0.621533i | \(0.786510\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.79973 | 0.250048 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.7665 | 0.376830 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.62536 | 0.0839928 | 0.0419964 | − | 0.999118i | \(-0.486628\pi\) | ||||
0.0419964 | + | 0.999118i | \(0.486628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.4953 | −0.655031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.26857 | 0.0724299 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.7264 | 0.342118 | 0.171059 | − | 0.985261i | \(-0.445281\pi\) | ||||
0.171059 | + | 0.985261i | \(0.445281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.9053 | 1.01659 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5895 | −0.528048 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75.2942 | 2.39421 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.5776 | 1.79725 | 0.898623 | − | 0.438721i | \(-0.144568\pi\) | ||||
0.898623 | + | 0.438721i | \(0.144568\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.99731 | −0.285521 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.8922 | −0.503816 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0541 | 0.350086 | 0.175043 | − | 0.984561i | \(-0.443994\pi\) | ||||
0.175043 | + | 0.984561i | \(0.443994\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.94356 | −0.219685 |
(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 | 4332.2.a.o.1.2 | 3 | ||
19.4 | even | 9 | 228.2.q.a.73.1 | yes | 6 | ||
19.5 | even | 9 | 228.2.q.a.25.1 | ✓ | 6 | ||
19.18 | odd | 2 | 4332.2.a.n.1.2 | 3 | |||
57.5 | odd | 18 | 684.2.bo.a.253.1 | 6 | |||
57.23 | odd | 18 | 684.2.bo.a.73.1 | 6 | |||
76.23 | odd | 18 | 912.2.bo.e.529.1 | 6 | |||
76.43 | odd | 18 | 912.2.bo.e.481.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.a.25.1 | ✓ | 6 | 19.5 | even | 9 | ||
228.2.q.a.73.1 | yes | 6 | 19.4 | even | 9 | ||
684.2.bo.a.73.1 | 6 | 57.23 | odd | 18 | |||
684.2.bo.a.253.1 | 6 | 57.5 | odd | 18 | |||
912.2.bo.e.481.1 | 6 | 76.43 | odd | 18 | |||
912.2.bo.e.529.1 | 6 | 76.23 | odd | 18 | |||
4332.2.a.n.1.2 | 3 | 19.18 | odd | 2 | |||
4332.2.a.o.1.2 | 3 | 1.1 | even | 1 | trivial |