Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3087,2,Mod(3086,3087)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3087, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3087.3086");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3087 = 3^{2} \cdot 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3087.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(24.6498191040\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3086.10 | ||
Character | \(\chi\) | \(=\) | 3087.3086 |
Dual form | 3087.2.c.c.3086.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3087\mathbb{Z}\right)^\times\).
\(n\) | \(344\) | \(2404\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.223929i | 0.158342i | 0.996861 | + | 0.0791708i | \(0.0252273\pi\) | ||||
−0.996861 | + | 0.0791708i | \(0.974773\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.94986 | 0.974928 | ||||||||
\(5\) | −3.02565 | −1.35311 | −0.676556 | − | 0.736392i | \(-0.736528\pi\) | ||||
−0.676556 | + | 0.736392i | \(0.736528\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.884487i | 0.312713i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.677530i | − 0.214254i | ||||||||
\(11\) | 2.32440i | 0.700832i | 0.936594 | + | 0.350416i | \(0.113960\pi\) | ||||
−0.936594 | + | 0.350416i | \(0.886040\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.38925i | − 1.77206i | −0.463629 | − | 0.886029i | \(-0.653453\pi\) | ||||
0.463629 | − | 0.886029i | \(-0.346547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.70165 | 0.925412 | ||||||||
\(17\) | −1.14736 | −0.278276 | −0.139138 | − | 0.990273i | \(-0.544433\pi\) | ||||
−0.139138 | + | 0.990273i | \(0.544433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16976i | 0.727194i | 0.931556 | + | 0.363597i | \(0.118451\pi\) | ||||
−0.931556 | + | 0.363597i | \(0.881549\pi\) | |||||||
\(20\) | −5.89958 | −1.31919 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.520500 | −0.110971 | ||||||||
\(23\) | 4.24909i | 0.885996i | 0.896523 | + | 0.442998i | \(0.146085\pi\) | ||||
−0.896523 | + | 0.442998i | \(0.853915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.15455 | 0.830910 | ||||||||
\(26\) | 1.43074 | 0.280591 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.88568i | − 0.535858i | −0.963439 | − | 0.267929i | \(-0.913661\pi\) | ||||
0.963439 | − | 0.267929i | \(-0.0863392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.49978i | 0.987790i | 0.869522 | + | 0.493895i | \(0.164427\pi\) | ||||
−0.869522 | + | 0.493895i | \(0.835573\pi\) | |||||||
\(32\) | 2.59788i | 0.459245i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 0.256928i | − 0.0440627i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.09447 | 0.837526 | 0.418763 | − | 0.908096i | \(-0.362464\pi\) | ||||
0.418763 | + | 0.908096i | \(0.362464\pi\) | |||||||
\(38\) | −0.709802 | −0.115145 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 2.67615i | − 0.423136i | ||||||||
\(41\) | −3.05199 | −0.476640 | −0.238320 | − | 0.971187i | \(-0.576597\pi\) | ||||
−0.238320 | + | 0.971187i | \(0.576597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.57547 | −0.392756 | −0.196378 | − | 0.980528i | \(-0.562918\pi\) | ||||
−0.196378 | + | 0.980528i | \(0.562918\pi\) | |||||||
\(44\) | 4.53224i | 0.683260i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.951493 | −0.140290 | ||||||||
\(47\) | 11.9772 | 1.74706 | 0.873528 | − | 0.486774i | \(-0.161826\pi\) | ||||
0.873528 | + | 0.486774i | \(0.161826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.930324i | 0.131568i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 12.4581i | − 1.72763i | ||||||||
\(53\) | 10.8964i | 1.49673i | 0.663285 | + | 0.748367i | \(0.269162\pi\) | ||||
−0.663285 | + | 0.748367i | \(0.730838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.03280i | − 0.948303i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.646188 | 0.0848486 | ||||||||
\(59\) | 10.5715 | 1.37629 | 0.688146 | − | 0.725573i | \(-0.258425\pi\) | ||||
0.688146 | + | 0.725573i | \(0.258425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.99201i | − 1.02327i | −0.859202 | − | 0.511636i | \(-0.829040\pi\) | ||||
0.859202 | − | 0.511636i | \(-0.170960\pi\) | |||||||
\(62\) | −1.23156 | −0.156408 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.82156 | 0.852695 | ||||||||
\(65\) | 19.3316i | 2.39779i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.22716 | 0.149922 | 0.0749610 | − | 0.997186i | \(-0.476117\pi\) | ||||
0.0749610 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(68\) | −2.23719 | −0.271299 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 9.56431i | − 1.13508i | −0.823347 | − | 0.567538i | \(-0.807896\pi\) | ||||
0.823347 | − | 0.567538i | \(-0.192104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2895i | 1.20430i | 0.798383 | + | 0.602150i | \(0.205689\pi\) | ||||
−0.798383 | + | 0.602150i | \(0.794311\pi\) | |||||||
\(74\) | 1.14080i | 0.132615i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.18058i | 0.708962i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.12059 | 1.02615 | 0.513073 | − | 0.858345i | \(-0.328507\pi\) | ||||
0.513073 | + | 0.858345i | \(0.328507\pi\) | |||||||
\(80\) | −11.1999 | −1.25219 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 0.683428i | − 0.0754720i | ||||||||
\(83\) | 12.9254 | 1.41875 | 0.709373 | − | 0.704833i | \(-0.248978\pi\) | ||||
0.709373 | + | 0.704833i | \(0.248978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.47152 | 0.376539 | ||||||||
\(86\) | − 0.576723i | − 0.0621897i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.05590 | −0.219159 | ||||||||
\(89\) | −13.9772 | −1.48158 | −0.740788 | − | 0.671738i | \(-0.765548\pi\) | ||||
−0.740788 | + | 0.671738i | \(0.765548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.28511i | 0.863782i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.68204i | 0.276632i | ||||||||
\(95\) | − 9.59059i | − 0.983974i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0998i | 1.12701i | 0.826112 | + | 0.563506i | \(0.190548\pi\) | ||||
−0.826112 | + | 0.563506i | \(0.809452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.10077 | 0.810077 | ||||||||
\(101\) | −3.01393 | −0.299897 | −0.149948 | − | 0.988694i | \(-0.547911\pi\) | ||||
−0.149948 | + | 0.988694i | \(0.547911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.05076i | 0.497667i | 0.968546 | + | 0.248833i | \(0.0800471\pi\) | ||||
−0.968546 | + | 0.248833i | \(0.919953\pi\) | |||||||
\(104\) | 5.65121 | 0.554147 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.44002 | −0.236995 | ||||||||
\(107\) | 16.3005i | 1.57583i | 0.615784 | + | 0.787915i | \(0.288840\pi\) | ||||
−0.615784 | + | 0.787915i | \(0.711160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.91055 | −0.661911 | −0.330955 | − | 0.943646i | \(-0.607371\pi\) | ||||
−0.330955 | + | 0.943646i | \(0.607371\pi\) | |||||||
\(110\) | 1.57485 | 0.150156 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.54328i | 0.897756i | 0.893593 | + | 0.448878i | \(0.148176\pi\) | ||||
−0.893593 | + | 0.448878i | \(0.851824\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 12.8562i | − 1.19885i | ||||||||
\(116\) | − 5.62666i | − 0.522423i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.36726i | 0.217924i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.59718 | 0.508835 | ||||||||
\(122\) | 1.78964 | 0.162027 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.7238i | 0.963024i | ||||||||
\(125\) | 2.55804 | 0.228798 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0393502 | 0.00349176 | 0.00174588 | − | 0.999998i | \(-0.499444\pi\) | ||||
0.00174588 | + | 0.999998i | \(0.499444\pi\) | |||||||
\(128\) | 6.72331i | 0.594262i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.32891 | −0.379670 | ||||||||
\(131\) | −7.66082 | −0.669329 | −0.334665 | − | 0.942337i | \(-0.608623\pi\) | ||||
−0.334665 | + | 0.942337i | \(0.608623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.274798i | 0.0237389i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 1.01483i | − 0.0870207i | ||||||||
\(137\) | − 18.8659i | − 1.61182i | −0.592038 | − | 0.805910i | \(-0.701677\pi\) | ||||
0.592038 | − | 0.805910i | \(-0.298323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.9952i | 1.69597i | 0.530019 | + | 0.847986i | \(0.322185\pi\) | ||||
−0.530019 | + | 0.847986i | \(0.677815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.14173 | 0.179730 | ||||||||
\(143\) | 14.8511 | 1.24191 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.73106i | 0.725075i | ||||||||
\(146\) | −2.30413 | −0.190691 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.93349 | 0.816528 | ||||||||
\(149\) | 22.1466i | 1.81432i | 0.420783 | + | 0.907161i | \(0.361755\pi\) | ||||
−0.420783 | + | 0.907161i | \(0.638245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.53160 | 0.694291 | 0.347146 | − | 0.937811i | \(-0.387151\pi\) | ||||
0.347146 | + | 0.937811i | \(0.387151\pi\) | |||||||
\(152\) | −2.80362 | −0.227403 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 16.6404i | − 1.33659i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5709i | 1.40231i | 0.713010 | + | 0.701154i | \(0.247332\pi\) | ||||
−0.713010 | + | 0.701154i | \(0.752668\pi\) | |||||||
\(158\) | 2.04236i | 0.162482i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 7.86027i | − 0.621409i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.0627 | 1.72809 | 0.864043 | − | 0.503418i | \(-0.167924\pi\) | ||||
0.864043 | + | 0.503418i | \(0.167924\pi\) | |||||||
\(164\) | −5.95093 | −0.464690 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.89437i | 0.224647i | ||||||||
\(167\) | −2.91067 | −0.225234 | −0.112617 | − | 0.993638i | \(-0.535923\pi\) | ||||
−0.112617 | + | 0.993638i | \(0.535923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.8225 | −2.14019 | ||||||||
\(170\) | 0.777373i | 0.0596218i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.02180 | −0.382909 | ||||||||
\(173\) | 16.6720 | 1.26755 | 0.633774 | − | 0.773519i | \(-0.281505\pi\) | ||||
0.633774 | + | 0.773519i | \(0.281505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.60410i | 0.648558i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3.12989i | − 0.234595i | ||||||||
\(179\) | − 16.0778i | − 1.20171i | −0.799357 | − | 0.600856i | \(-0.794827\pi\) | ||||
0.799357 | − | 0.600856i | \(-0.205173\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0644i | 1.41705i | 0.705687 | + | 0.708524i | \(0.250638\pi\) | ||||
−0.705687 | + | 0.708524i | \(0.749362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.75826 | −0.277063 | ||||||||
\(185\) | −15.4141 | −1.13327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.66692i | − 0.195025i | ||||||||
\(188\) | 23.3538 | 1.70325 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.14761 | 0.155804 | ||||||||
\(191\) | − 5.45997i | − 0.395070i | −0.980296 | − | 0.197535i | \(-0.936706\pi\) | ||||
0.980296 | − | 0.197535i | \(-0.0632935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.198662 | 0.0143000 | 0.00715001 | − | 0.999974i | \(-0.497724\pi\) | ||||
0.00715001 | + | 0.999974i | \(0.497724\pi\) | |||||||
\(194\) | −2.48556 | −0.178453 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 15.0110i | − 1.06949i | −0.845014 | − | 0.534743i | \(-0.820408\pi\) | ||||
0.845014 | − | 0.534743i | \(-0.179592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0497196i | 0.00352453i | 0.999998 | + | 0.00176226i | \(0.000560946\pi\) | ||||
−0.999998 | + | 0.00176226i | \(0.999439\pi\) | |||||||
\(200\) | 3.67464i | 0.259837i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 0.674906i | − 0.0474862i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.23424 | 0.644947 | ||||||||
\(206\) | −1.13101 | −0.0788014 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 23.6508i | − 1.63989i | ||||||||
\(209\) | −7.36779 | −0.509641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.8681 | 1.36777 | 0.683887 | − | 0.729588i | \(-0.260288\pi\) | ||||
0.683887 | + | 0.729588i | \(0.260288\pi\) | |||||||
\(212\) | 21.2464i | 1.45921i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.65016 | −0.249520 | ||||||||
\(215\) | 7.79248 | 0.531443 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 1.54747i | − 0.104808i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 13.7130i | − 0.924527i | ||||||||
\(221\) | 7.33078i | 0.493122i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 11.1172i | − 0.744461i | −0.928140 | − | 0.372231i | \(-0.878593\pi\) | ||||
0.928140 | − | 0.372231i | \(-0.121407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.13702 | −0.142152 | ||||||||
\(227\) | 17.0090 | 1.12893 | 0.564463 | − | 0.825458i | \(-0.309083\pi\) | ||||
0.564463 | + | 0.825458i | \(0.309083\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 28.1557i | − 1.86058i | −0.366821 | − | 0.930292i | \(-0.619554\pi\) | ||||
0.366821 | − | 0.930292i | \(-0.380446\pi\) | |||||||
\(230\) | 2.87888 | 0.189828 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.55235 | 0.167570 | ||||||||
\(233\) | − 6.83120i | − 0.447527i | −0.974643 | − | 0.223763i | \(-0.928166\pi\) | ||||
0.974643 | − | 0.223763i | \(-0.0718343\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.2388 | −2.36396 | ||||||||
\(236\) | 20.6129 | 1.34178 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 7.63188i | − 0.493666i | −0.969058 | − | 0.246833i | \(-0.920610\pi\) | ||||
0.969058 | − | 0.246833i | \(-0.0793898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0422i | 0.968954i | 0.874804 | + | 0.484477i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484477i | \(0.839010\pi\) | |||||||
\(242\) | 1.25337i | 0.0805698i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 15.5833i | − 0.997617i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.2524 | 1.28863 | ||||||||
\(248\) | −4.86448 | −0.308895 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.572819i | 0.0362282i | ||||||||
\(251\) | −30.6693 | −1.93583 | −0.967915 | − | 0.251279i | \(-0.919149\pi\) | ||||
−0.967915 | + | 0.251279i | \(0.919149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.87656 | −0.620934 | ||||||||
\(254\) | 0.00881165i | 0 0.000552892i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.1376 | 0.758598 | ||||||||
\(257\) | −24.3456 | −1.51864 | −0.759318 | − | 0.650720i | \(-0.774467\pi\) | ||||
−0.759318 | + | 0.650720i | \(0.774467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 37.6939i | 2.33767i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 1.71548i | − 0.105983i | ||||||||
\(263\) | 1.00517i | 0.0619814i | 0.999520 | + | 0.0309907i | \(0.00986623\pi\) | ||||
−0.999520 | + | 0.0309907i | \(0.990134\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 32.9686i | − 2.02525i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.39279 | 0.146163 | ||||||||
\(269\) | −0.0217090 | −0.00132362 | −0.000661811 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000661811 | 1.00000i | \(0.500211\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5128i | 0.881592i | 0.897607 | + | 0.440796i | \(0.145304\pi\) | ||||
−0.897607 | + | 0.440796i | \(0.854696\pi\) | |||||||
\(272\) | −4.24713 | −0.257520 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.22461 | 0.255218 | ||||||||
\(275\) | 9.65682i | 0.582328i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0680 | 0.905346 | 0.452673 | − | 0.891677i | \(-0.350470\pi\) | ||||
0.452673 | + | 0.891677i | \(0.350470\pi\) | |||||||
\(278\) | −4.47751 | −0.268543 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.94171i | 0.593073i | 0.955022 | + | 0.296536i | \(0.0958316\pi\) | ||||
−0.955022 | + | 0.296536i | \(0.904168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 13.5621i | − 0.806186i | −0.915159 | − | 0.403093i | \(-0.867935\pi\) | ||||
0.915159 | − | 0.403093i | \(-0.132065\pi\) | |||||||
\(284\) | − 18.6490i | − 1.10662i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.32560i | 0.196647i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6836 | −0.922562 | ||||||||
\(290\) | −1.95514 | −0.114810 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.0631i | 1.17410i | ||||||||
\(293\) | 8.24489 | 0.481671 | 0.240836 | − | 0.970566i | \(-0.422578\pi\) | ||||
0.240836 | + | 0.970566i | \(0.422578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.9856 | −1.86227 | ||||||||
\(296\) | 4.50600i | 0.261906i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.95927 | −0.287283 | ||||||||
\(299\) | 27.1485 | 1.57004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.91047i | 0.109935i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.7334i | 0.672954i | ||||||||
\(305\) | 24.1810i | 1.38460i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.21948i | − 0.183746i | −0.995771 | − | 0.0918728i | \(-0.970715\pi\) | ||||
0.995771 | − | 0.0918728i | \(-0.0292853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.72627 | 0.211638 | ||||||||
\(311\) | −8.35230 | −0.473615 | −0.236808 | − | 0.971557i | \(-0.576101\pi\) | ||||
−0.236808 | + | 0.971557i | \(0.576101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.60985i | 0.147517i | 0.997276 | + | 0.0737587i | \(0.0234995\pi\) | ||||
−0.997276 | + | 0.0737587i | \(0.976501\pi\) | |||||||
\(314\) | −3.93463 | −0.222044 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.7838 | 1.00042 | ||||||||
\(317\) | − 6.43056i | − 0.361176i | −0.983559 | − | 0.180588i | \(-0.942200\pi\) | ||||
0.983559 | − | 0.180588i | \(-0.0578001\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.70747 | 0.375546 | ||||||||
\(320\) | −20.6396 | −1.15379 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.63687i | − 0.202361i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 26.5444i | − 1.47242i | ||||||||
\(326\) | 4.94048i | 0.273628i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 2.69944i | − 0.149052i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6831 | −1.35671 | −0.678353 | − | 0.734736i | \(-0.737306\pi\) | ||||
−0.678353 | + | 0.734736i | \(0.737306\pi\) | |||||||
\(332\) | 25.2027 | 1.38318 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 0.651783i | − 0.0356640i | ||||||||
\(335\) | −3.71297 | −0.202861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.66492 | 0.0906942 | 0.0453471 | − | 0.998971i | \(-0.485561\pi\) | ||||
0.0453471 | + | 0.998971i | \(0.485561\pi\) | |||||||
\(338\) | − 6.23026i | − 0.338882i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.76896 | 0.367098 | ||||||||
\(341\) | −12.7837 | −0.692274 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 2.27797i | − 0.122820i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.73334i | 0.200706i | ||||||||
\(347\) | 24.7331i | 1.32774i | 0.747848 | + | 0.663870i | \(0.231087\pi\) | ||||
−0.747848 | + | 0.663870i | \(0.768913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.05909i | − 0.431393i | −0.976460 | − | 0.215697i | \(-0.930798\pi\) | ||||
0.976460 | − | 0.215697i | \(-0.0692022\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.03850 | −0.321853 | ||||||||
\(353\) | −2.70943 | −0.144208 | −0.0721042 | − | 0.997397i | \(-0.522971\pi\) | ||||
−0.0721042 | + | 0.997397i | \(0.522971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.9383i | 1.53588i | ||||||||
\(356\) | −27.2535 | −1.44443 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.60029 | 0.190281 | ||||||||
\(359\) | 18.0536i | 0.952833i | 0.879220 | + | 0.476416i | \(0.158064\pi\) | ||||
−0.879220 | + | 0.476416i | \(0.841936\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.95259 | 0.471189 | ||||||||
\(362\) | −4.26908 | −0.224378 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 31.1325i | − 1.62955i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8669i | 1.03704i | 0.855064 | + | 0.518522i | \(0.173518\pi\) | ||||
−0.855064 | + | 0.518522i | \(0.826482\pi\) | |||||||
\(368\) | 15.7286i | 0.819911i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 3.45166i | − 0.179443i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3014 | 0.947612 | 0.473806 | − | 0.880629i | \(-0.342880\pi\) | ||||
0.473806 | + | 0.880629i | \(0.342880\pi\) | |||||||
\(374\) | 0.597202 | 0.0308806 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5937i | 0.546328i | ||||||||
\(377\) | −18.4373 | −0.949571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.26172 | −0.116177 | −0.0580883 | − | 0.998311i | \(-0.518500\pi\) | ||||
−0.0580883 | + | 0.998311i | \(0.518500\pi\) | |||||||
\(380\) | − 18.7003i | − 0.959304i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.22265 | 0.0625560 | ||||||||
\(383\) | −9.19920 | −0.470057 | −0.235029 | − | 0.971988i | \(-0.575518\pi\) | ||||
−0.235029 | + | 0.971988i | \(0.575518\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0444863i | 0.00226429i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.6430i | 1.09876i | ||||||||
\(389\) | 6.06660i | 0.307589i | 0.988103 | + | 0.153794i | \(0.0491493\pi\) | ||||
−0.988103 | + | 0.153794i | \(0.950851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4.87524i | − 0.246552i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.36139 | 0.169344 | ||||||||
\(395\) | −27.5957 | −1.38849 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.6875i | − 0.737146i | −0.929599 | − | 0.368573i | \(-0.879847\pi\) | ||||
0.929599 | − | 0.368573i | \(-0.120153\pi\) | |||||||
\(398\) | −0.0111336 | −0.000558079 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.3787 | 0.768934 | ||||||||
\(401\) | − 35.9779i | − 1.79665i | −0.439330 | − | 0.898326i | \(-0.644784\pi\) | ||||
0.439330 | − | 0.898326i | \(-0.355216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.1395 | 1.75042 | ||||||||
\(404\) | −5.87672 | −0.292378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.8416i | 0.586965i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 17.0212i | − 0.841642i | −0.907144 | − | 0.420821i | \(-0.861742\pi\) | ||||
0.907144 | − | 0.420821i | \(-0.138258\pi\) | |||||||
\(410\) | 2.06781i | 0.102122i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.84826i | 0.485189i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.1077 | −1.91972 | ||||||||
\(416\) | 16.5985 | 0.813809 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 1.64986i | − 0.0806973i | ||||||||
\(419\) | 9.93475 | 0.485345 | 0.242672 | − | 0.970108i | \(-0.421976\pi\) | ||||
0.242672 | + | 0.970108i | \(0.421976\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7851 | −1.45164 | −0.725819 | − | 0.687886i | \(-0.758539\pi\) | ||||
−0.725819 | + | 0.687886i | \(0.758539\pi\) | |||||||
\(422\) | 4.44904i | 0.216576i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.63771 | −0.468049 | ||||||||
\(425\) | −4.76677 | −0.231222 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 31.7837i | 1.53632i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.74496i | 0.0841495i | ||||||||
\(431\) | − 23.3144i | − 1.12301i | −0.827472 | − | 0.561507i | \(-0.810222\pi\) | ||||
0.827472 | − | 0.561507i | \(-0.189778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 23.4403i | − 1.12647i | −0.826297 | − | 0.563234i | \(-0.809557\pi\) | ||||
0.826297 | − | 0.563234i | \(-0.190443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4746 | −0.645315 | ||||||||
\(437\) | −13.4686 | −0.644291 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 4.21244i | − 0.201049i | −0.994935 | − | 0.100524i | \(-0.967948\pi\) | ||||
0.994935 | − | 0.100524i | \(-0.0320521\pi\) | |||||||
\(440\) | 6.22042 | 0.296547 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.64157 | −0.0780818 | ||||||||
\(443\) | − 2.38333i | − 0.113235i | −0.998396 | − | 0.0566177i | \(-0.981968\pi\) | ||||
0.998396 | − | 0.0566177i | \(-0.0180316\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.2900 | 2.00474 | ||||||||
\(446\) | 2.48946 | 0.117879 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 29.8102i | − 1.40683i | −0.710778 | − | 0.703416i | \(-0.751657\pi\) | ||||
0.710778 | − | 0.703416i | \(-0.248343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.09402i | − 0.334045i | ||||||||
\(452\) | 18.6080i | 0.875248i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.80881i | 0.178756i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.1343 | 0.520842 | 0.260421 | − | 0.965495i | \(-0.416139\pi\) | ||||
0.260421 | + | 0.965495i | \(0.416139\pi\) | |||||||
\(458\) | 6.30488 | 0.294608 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 25.0678i | − 1.16879i | ||||||||
\(461\) | 34.6787 | 1.61515 | 0.807574 | − | 0.589766i | \(-0.200780\pi\) | ||||
0.807574 | + | 0.589766i | \(0.200780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8060 | −0.548673 | −0.274337 | − | 0.961634i | \(-0.588458\pi\) | ||||
−0.274337 | + | 0.961634i | \(0.588458\pi\) | |||||||
\(464\) | − 10.6818i | − 0.495889i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.52970 | 0.0708622 | ||||||||
\(467\) | 15.5098 | 0.717707 | 0.358853 | − | 0.933394i | \(-0.383168\pi\) | ||||
0.358853 | + | 0.933394i | \(0.383168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 8.11492i | − 0.374314i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.35035i | 0.430385i | ||||||||
\(473\) | − 5.98642i | − 0.275256i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1689i | 0.604232i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.70900 | 0.0781678 | ||||||||
\(479\) | −7.36161 | −0.336360 | −0.168180 | − | 0.985756i | \(-0.553789\pi\) | ||||
−0.168180 | + | 0.985756i | \(0.553789\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 32.5499i | − 1.48415i | ||||||||
\(482\) | −3.36839 | −0.153426 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9137 | 0.496077 | ||||||||
\(485\) | − 33.5840i | − 1.52497i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.3340 | −1.87302 | −0.936510 | − | 0.350640i | \(-0.885964\pi\) | ||||
−0.936510 | + | 0.350640i | \(0.885964\pi\) | |||||||
\(488\) | 7.06883 | 0.319991 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 22.2997i | − 1.00637i | −0.864179 | − | 0.503185i | \(-0.832162\pi\) | ||||
0.864179 | − | 0.503185i | \(-0.167838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.31092i | 0.149117i | ||||||||
\(494\) | 4.53510i | 0.204044i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.3583i | 0.914113i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5901 | −0.697907 | −0.348953 | − | 0.937140i | \(-0.613463\pi\) | ||||
−0.348953 | + | 0.937140i | \(0.613463\pi\) | |||||||
\(500\) | 4.98781 | 0.223061 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 6.86775i | − 0.306523i | ||||||||
\(503\) | 28.0258 | 1.24961 | 0.624803 | − | 0.780782i | \(-0.285179\pi\) | ||||
0.624803 | + | 0.780782i | \(0.285179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.11908 | 0.405794 | ||||||||
\(506\) | − 2.21165i | − 0.0983197i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.0767272 | 0.00340422 | ||||||||
\(509\) | 23.4522 | 1.03950 | 0.519751 | − | 0.854318i | \(-0.326025\pi\) | ||||
0.519751 | + | 0.854318i | \(0.326025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.1646i | 0.714380i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 5.45168i | − 0.240463i | ||||||||
\(515\) | − 15.2818i | − 0.673398i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.8398i | 1.22439i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.0986 | −0.749822 | ||||||||
\(521\) | 19.6897 | 0.862622 | 0.431311 | − | 0.902203i | \(-0.358051\pi\) | ||||
0.431311 | + | 0.902203i | \(0.358051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.3345i | 1.28271i | 0.767246 | + | 0.641353i | \(0.221627\pi\) | ||||
−0.767246 | + | 0.641353i | \(0.778373\pi\) | |||||||
\(524\) | −14.9375 | −0.652548 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.225087 | −0.00981424 | ||||||||
\(527\) | − 6.31024i | − 0.274878i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.94526 | 0.215012 | ||||||||
\(530\) | 7.38263 | 0.320681 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4999i | 0.844634i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 49.3196i | − 2.13227i | ||||||||
\(536\) | 1.08541i | 0.0468826i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 0.00486128i | 0 0.000209584i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.1811 | −0.609693 | −0.304847 | − | 0.952401i | \(-0.598605\pi\) | ||||
−0.304847 | + | 0.952401i | \(0.598605\pi\) | |||||||
\(542\) | −3.24984 | −0.139593 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 2.98071i | − 0.127797i | ||||||||
\(545\) | 20.9089 | 0.895639 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.29433 | −0.0980983 | −0.0490492 | − | 0.998796i | \(-0.515619\pi\) | ||||
−0.0490492 | + | 0.998796i | \(0.515619\pi\) | |||||||
\(548\) | − 36.7857i | − 1.57141i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.16244 | −0.0922068 | ||||||||
\(551\) | 9.14693 | 0.389672 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.37415i | 0.143354i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.9878i | 1.65345i | ||||||||
\(557\) | 29.7218i | 1.25935i | 0.776858 | + | 0.629676i | \(0.216812\pi\) | ||||
−0.776858 | + | 0.629676i | \(0.783188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4553i | 0.695987i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.22624 | −0.0939081 | ||||||||
\(563\) | 4.47480 | 0.188590 | 0.0942951 | − | 0.995544i | \(-0.469940\pi\) | ||||
0.0942951 | + | 0.995544i | \(0.469940\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 28.8746i | − 1.21476i | ||||||||
\(566\) | 3.03696 | 0.127653 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.45951 | 0.354953 | ||||||||
\(569\) | − 1.12610i | − 0.0472086i | −0.999721 | − | 0.0236043i | \(-0.992486\pi\) | ||||
0.999721 | − | 0.0236043i | \(-0.00751418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.6881 | −1.11686 | −0.558431 | − | 0.829551i | \(-0.688596\pi\) | ||||
−0.558431 | + | 0.829551i | \(0.688596\pi\) | |||||||
\(572\) | 28.9576 | 1.21078 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.6530i | 0.736183i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 2.17852i | − 0.0906930i | −0.998971 | − | 0.0453465i | \(-0.985561\pi\) | ||||
0.998971 | − | 0.0453465i | \(-0.0144392\pi\) | |||||||
\(578\) | − 3.51200i | − 0.146080i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.0243i | 0.706896i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3275 | −1.04896 | ||||||||
\(584\) | −9.10096 | −0.376600 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.84627i | 0.0762687i | ||||||||
\(587\) | 5.94259 | 0.245277 | 0.122639 | − | 0.992451i | \(-0.460864\pi\) | ||||
0.122639 | + | 0.992451i | \(0.460864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.4330 | −0.718315 | ||||||||
\(590\) | − 7.16251i | − 0.294876i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.8580 | 0.775057 | ||||||||
\(593\) | −33.7933 | −1.38773 | −0.693863 | − | 0.720107i | \(-0.744093\pi\) | ||||
−0.693863 | + | 0.720107i | \(0.744093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43.1827i | 1.76883i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.07933i | 0.248602i | ||||||||
\(599\) | − 0.576506i | − 0.0235554i | −0.999931 | − | 0.0117777i | \(-0.996251\pi\) | ||||
0.999931 | − | 0.0117777i | \(-0.00374905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.20844i | 0.375620i | 0.982205 | + | 0.187810i | \(0.0601389\pi\) | ||||
−0.982205 | + | 0.187810i | \(0.939861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.6354 | 0.676884 | ||||||||
\(605\) | −16.9351 | −0.688510 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.9707i | 1.01353i | 0.862085 | + | 0.506764i | \(0.169159\pi\) | ||||
−0.862085 | + | 0.506764i | \(0.830841\pi\) | |||||||
\(608\) | −8.23467 | −0.333960 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.41483 | −0.219240 | ||||||||
\(611\) | − 76.5254i | − 3.09589i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.2739 | −1.30353 | −0.651765 | − | 0.758421i | \(-0.725971\pi\) | ||||
−0.651765 | + | 0.758421i | \(0.725971\pi\) | |||||||
\(614\) | 0.720936 | 0.0290946 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 38.0815i | − 1.53310i | −0.642183 | − | 0.766551i | \(-0.721971\pi\) | ||||
0.642183 | − | 0.766551i | \(-0.278029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.4687i | 1.22464i | 0.790610 | + | 0.612319i | \(0.209763\pi\) | ||||
−0.790610 | + | 0.612319i | \(0.790237\pi\) | |||||||
\(620\) | − 32.4464i | − 1.30308i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 1.87032i | − 0.0749931i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5125 | −1.14050 | ||||||||
\(626\) | −0.584421 | −0.0233582 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.2607i | 1.36715i | ||||||||
\(629\) | −5.84521 | −0.233064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9820 | 0.636232 | 0.318116 | − | 0.948052i | \(-0.396950\pi\) | ||||
0.318116 | + | 0.948052i | \(0.396950\pi\) | |||||||
\(632\) | 8.06704i | 0.320890i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.43999 | 0.0571893 | ||||||||
\(635\) | −0.119060 | −0.00472475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.50200i | 0.0594646i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 20.3424i | − 0.804102i | ||||||||
\(641\) | 22.0916i | 0.872565i | 0.899810 | + | 0.436283i | \(0.143705\pi\) | ||||
−0.899810 | + | 0.436283i | \(0.856295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.61541i | 0.103142i | 0.998669 | + | 0.0515709i | \(0.0164228\pi\) | ||||
−0.998669 | + | 0.0515709i | \(0.983577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.814400 | 0.0320422 | ||||||||
\(647\) | −31.5745 | −1.24132 | −0.620660 | − | 0.784079i | \(-0.713135\pi\) | ||||
−0.620660 | + | 0.784079i | \(0.713135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.5723i | 0.964548i | ||||||||
\(650\) | 5.94407 | 0.233146 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.0191 | 1.68476 | ||||||||
\(653\) | 18.8178i | 0.736397i | 0.929747 | + | 0.368199i | \(0.120025\pi\) | ||||
−0.929747 | + | 0.368199i | \(0.879975\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1790 | 0.905677 | ||||||||
\(656\) | −11.2974 | −0.441089 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 47.7090i | − 1.85848i | −0.369480 | − | 0.929239i | \(-0.620464\pi\) | ||||
0.369480 | − | 0.929239i | \(-0.379536\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 24.3935i | − 0.948799i | −0.880310 | − | 0.474399i | \(-0.842665\pi\) | ||||
0.880310 | − | 0.474399i | \(-0.157335\pi\) | |||||||
\(662\) | − 5.52727i | − 0.214823i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.4323i | 0.443661i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.2615 | 0.474768 | ||||||||
\(668\) | −5.67538 | −0.219587 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 0.831441i | − 0.0321214i | ||||||||
\(671\) | 18.5766 | 0.717142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.5844 | 1.21749 | 0.608745 | − | 0.793366i | \(-0.291673\pi\) | ||||
0.608745 | + | 0.793366i | \(0.291673\pi\) | |||||||
\(674\) | 0.372825i | 0.0143607i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −54.2499 | −2.08653 | ||||||||
\(677\) | −17.7436 | −0.681941 | −0.340971 | − | 0.940074i | \(-0.610756\pi\) | ||||
−0.340971 | + | 0.940074i | \(0.610756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.07051i | 0.117749i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 2.86263i | − 0.109616i | ||||||||
\(683\) | − 51.3592i | − 1.96521i | −0.185720 | − | 0.982603i | \(-0.559462\pi\) | ||||
0.185720 | − | 0.982603i | \(-0.440538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 57.0815i | 2.18097i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.53350 | −0.363461 | ||||||||
\(689\) | 69.6197 | 2.65230 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.59175i | 0.326846i | 0.986556 | + | 0.163423i | \(0.0522535\pi\) | ||||
−0.986556 | + | 0.163423i | \(0.947747\pi\) | |||||||
\(692\) | 32.5080 | 1.23577 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.53845 | −0.210237 | ||||||||
\(695\) | − 60.4985i | − 2.29484i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.50173 | 0.132638 | ||||||||
\(698\) | 1.80466 | 0.0683075 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.97794i | 0.0747059i | 0.999302 | + | 0.0373529i | \(0.0118926\pi\) | ||||
−0.999302 | + | 0.0373529i | \(0.988107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1483i | 0.609044i | ||||||||
\(704\) | 15.8560i | 0.597596i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 0.606720i | − 0.0228342i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.8892 | −1.49807 | −0.749035 | − | 0.662530i | \(-0.769483\pi\) | ||||
−0.749035 | + | 0.662530i | \(0.769483\pi\) | |||||||
\(710\) | −6.48011 | −0.243194 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 12.3626i | − 0.463309i | ||||||||
\(713\) | −23.3690 | −0.875178 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.9343 | −1.68045 | ||||||||
\(716\) | − 31.3494i | − 1.17158i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.04272 | −0.150873 | ||||||||
\(719\) | −14.8851 | −0.555122 | −0.277561 | − | 0.960708i | \(-0.589526\pi\) | ||||
−0.277561 | + | 0.960708i | \(0.589526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.00474i | 0.0746089i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37.1729i | 1.38152i | ||||||||
\(725\) | − 11.9887i | − 0.445249i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 38.0550i | − 1.41138i | −0.708521 | − | 0.705690i | \(-0.750637\pi\) | ||||
0.708521 | − | 0.705690i | \(-0.249363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.97147 | 0.258026 | ||||||||
\(731\) | 2.95500 | 0.109295 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 36.2727i | − 1.33976i | −0.742468 | − | 0.669882i | \(-0.766345\pi\) | ||||
0.742468 | − | 0.669882i | \(-0.233655\pi\) | |||||||
\(734\) | −4.44878 | −0.164207 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.0386 | −0.406889 | ||||||||
\(737\) | 2.85242i | 0.105070i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.6658 | −1.56949 | −0.784744 | − | 0.619820i | \(-0.787206\pi\) | ||||
−0.784744 | + | 0.619820i | \(0.787206\pi\) | |||||||
\(740\) | −30.0552 | −1.10485 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.00817i | − 0.0369862i | −0.999829 | − | 0.0184931i | \(-0.994113\pi\) | ||||
0.999829 | − | 0.0184931i | \(-0.00588688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 67.0079i | − 2.45498i | ||||||||
\(746\) | 4.09822i | 0.150046i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 5.20012i | − 0.190135i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.2217 | −1.17579 | −0.587893 | − | 0.808938i | \(-0.700043\pi\) | ||||
−0.587893 | + | 0.808938i | \(0.700043\pi\) | |||||||
\(752\) | 44.3354 | 1.61675 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 4.12865i | − 0.150357i | ||||||||
\(755\) | −25.8136 | −0.939454 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.4357 | −0.670057 | −0.335028 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335028 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(758\) | − 0.506464i | − 0.0183956i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.48276 | 0.307702 | ||||||||
\(761\) | −32.2294 | −1.16832 | −0.584158 | − | 0.811640i | \(-0.698575\pi\) | ||||
−0.584158 | + | 0.811640i | \(0.698575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − 10.6462i | − 0.385164i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 2.05997i | − 0.0744297i | ||||||||
\(767\) | − 67.5439i | − 2.43887i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 43.1786i | − 1.55706i | −0.627608 | − | 0.778530i | \(-0.715966\pi\) | ||||
0.627608 | − | 0.778530i | \(-0.284034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.387363 | 0.0139415 | ||||||||
\(773\) | 0.0127856 | 0.000459867 0 | 0.000229934 | − | 1.00000i | \(-0.499927\pi\) | ||||
0.000229934 | 1.00000i | \(0.499927\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.8491i | 0.820764i | ||||||||
\(776\) | −9.81761 | −0.352432 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.35849 | −0.0487041 | ||||||||
\(779\) | − 9.67408i | − 0.346610i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.2313 | 0.795497 | ||||||||
\(782\) | 1.09171 | 0.0390394 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 53.1633i | − 1.89748i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.8954i | 1.24389i | 0.783062 | + | 0.621943i | \(0.213657\pi\) | ||||
−0.783062 | + | 0.621943i | \(0.786343\pi\) | |||||||
\(788\) | − 29.2692i | − 1.04267i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 6.17947i | − 0.219856i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.0630 | −1.81330 | ||||||||
\(794\) | 3.28896 | 0.116721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.0969460i | 0.00343616i | ||||||||
\(797\) | −2.12544 | −0.0752869 | −0.0376434 | − | 0.999291i | \(-0.511985\pi\) | ||||
−0.0376434 | + | 0.999291i | \(0.511985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.7422 | −0.486164 | ||||||||
\(800\) | 10.7930i | 0.381591i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.05650 | 0.284485 | ||||||||
\(803\) | −23.9170 | −0.844011 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.86874i | 0.277165i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 2.66578i | − 0.0937818i | ||||||||
\(809\) | 5.67156i | 0.199401i | 0.995017 | + | 0.0997007i | \(0.0317885\pi\) | ||||
−0.995017 | + | 0.0997007i | \(0.968211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 47.7024i | − 1.67506i | −0.546394 | − | 0.837528i | \(-0.684000\pi\) | ||||
0.546394 | − | 0.837528i | \(-0.316000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.65167 | −0.0929410 | ||||||||
\(815\) | −66.7541 | −2.33829 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 8.16365i | − 0.285610i | ||||||||
\(818\) | 3.81153 | 0.133267 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.0054 | 0.628777 | ||||||||
\(821\) | − 18.4310i | − 0.643247i | −0.946868 | − | 0.321624i | \(-0.895771\pi\) | ||||
0.946868 | − | 0.321624i | \(-0.104229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5774 | 0.473278 | 0.236639 | − | 0.971598i | \(-0.423954\pi\) | ||||
0.236639 | + | 0.971598i | \(0.423954\pi\) | |||||||
\(824\) | −4.46734 | −0.155627 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9807i | 0.694799i | 0.937717 | + | 0.347399i | \(0.112935\pi\) | ||||
−0.937717 | + | 0.347399i | \(0.887065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.53405i | 0.331131i | 0.986199 | + | 0.165566i | \(0.0529449\pi\) | ||||
−0.986199 | + | 0.165566i | \(0.947055\pi\) | |||||||
\(830\) | − 8.75735i | − 0.303972i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 43.5846i | − 1.51103i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.80666 | 0.304767 | ||||||||
\(836\) | −14.3661 | −0.496863 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.22468i | 0.0768503i | ||||||||
\(839\) | 1.12969 | 0.0390013 | 0.0195006 | − | 0.999810i | \(-0.493792\pi\) | ||||
0.0195006 | + | 0.999810i | \(0.493792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6728 | 0.712856 | ||||||||
\(842\) | − 6.66975i | − 0.229855i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 38.7399 | 1.33348 | ||||||||
\(845\) | 84.1811 | 2.89592 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.3346i | 1.38510i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 1.06742i | − 0.0366122i | ||||||||
\(851\) | 21.6469i | 0.742045i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.2466i | 1.30954i | 0.755828 | + | 0.654770i | \(0.227234\pi\) | ||||
−0.755828 | + | 0.654770i | \(0.772766\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.4176 | −0.492783 | ||||||||
\(857\) | −39.8391 | −1.36088 | −0.680439 | − | 0.732805i | \(-0.738211\pi\) | ||||
−0.680439 | + | 0.732805i | \(0.738211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 10.5008i | − 0.358283i | −0.983823 | − | 0.179141i | \(-0.942668\pi\) | ||||
0.983823 | − | 0.179141i | \(-0.0573320\pi\) | |||||||
\(860\) | 15.1942 | 0.518118 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.22076 | 0.177820 | ||||||||
\(863\) | 18.1541i | 0.617971i | 0.951067 | + | 0.308986i | \(0.0999895\pi\) | ||||
−0.951067 | + | 0.308986i | \(0.900010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.4436 | −1.71513 | ||||||||
\(866\) | 5.24896 | 0.178367 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.1999i | 0.719156i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 7.84066i | − 0.265671i | ||||||||
\(872\) | − 6.11229i | − 0.206988i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 3.01601i | − 0.102018i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.4339 | 0.858843 | 0.429421 | − | 0.903104i | \(-0.358718\pi\) | ||||
0.429421 | + | 0.903104i | \(0.358718\pi\) | |||||||
\(878\) | 0.943288 | 0.0318344 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 26.0330i | − 0.877571i | ||||||||
\(881\) | −41.4113 | −1.39518 | −0.697591 | − | 0.716496i | \(-0.745745\pi\) | ||||
−0.697591 | + | 0.716496i | \(0.745745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.807894 | −0.0271878 | −0.0135939 | − | 0.999908i | \(-0.504327\pi\) | ||||
−0.0135939 | + | 0.999908i | \(0.504327\pi\) | |||||||
\(884\) | 14.2940i | 0.480758i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.533697 | 0.0179299 | ||||||||
\(887\) | 42.6601 | 1.43239 | 0.716193 | − | 0.697902i | \(-0.245883\pi\) | ||||
0.716193 | + | 0.697902i | \(0.245883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.46995i | 0.317434i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 21.6769i | − 0.725796i | ||||||||
\(893\) | 37.9649i | 1.27045i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 48.6458i | 1.62605i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.67537 | 0.222760 | ||||||||
\(899\) | 15.8706 | 0.529315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 12.5021i | − 0.416506i | ||||||||
\(902\) | 1.58856 | 0.0528932 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.44091 | −0.280740 | ||||||||
\(905\) | − 57.6822i | − 1.91742i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8200 | −0.890545 | −0.445272 | − | 0.895395i | \(-0.646893\pi\) | ||||
−0.445272 | + | 0.895395i | \(0.646893\pi\) | |||||||
\(908\) | 33.1651 | 1.10062 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 28.3322i | − 0.938689i | −0.883015 | − | 0.469345i | \(-0.844490\pi\) | ||||
0.883015 | − | 0.469345i | \(-0.155510\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.0437i | 0.994303i | ||||||||
\(914\) | 2.49330i | 0.0824709i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 54.8996i | − 1.81393i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2895 | 1.09812 | 0.549060 | − | 0.835783i | \(-0.314986\pi\) | ||||
0.549060 | + | 0.835783i | \(0.314986\pi\) | |||||||
\(920\) | 11.3712 | 0.374897 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.76556i | 0.255745i | ||||||||
\(923\) | −61.1088 | −2.01142 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.1652 | 0.695909 | ||||||||
\(926\) | − 2.64371i | − 0.0868778i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.49666 | 0.246090 | ||||||||
\(929\) | −15.3510 | −0.503650 | −0.251825 | − | 0.967773i | \(-0.581031\pi\) | ||||
−0.251825 | + | 0.967773i | \(0.581031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 13.3199i | − 0.436307i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.47309i | 0.113643i | ||||||||
\(935\) | 8.06918i | 0.263890i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 19.4414i | − 0.635124i | −0.948238 | − | 0.317562i | \(-0.897136\pi\) | ||||
0.948238 | − | 0.317562i | \(-0.102864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −70.6605 | −2.30469 | ||||||||
\(941\) | 40.5112 | 1.32063 | 0.660314 | − | 0.750989i | \(-0.270423\pi\) | ||||
0.660314 | + | 0.750989i | \(0.270423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 12.9682i | − 0.422301i | ||||||||
\(944\) | 39.1320 | 1.27364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.34053 | 0.0435845 | ||||||||
\(947\) | 7.07798i | 0.230004i | 0.993365 | + | 0.115002i | \(0.0366874\pi\) | ||||
−0.993365 | + | 0.115002i | \(0.963313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.7424 | 2.13409 | ||||||||
\(950\) | −2.94891 | −0.0956752 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9587i | 0.678919i | 0.940621 | + | 0.339459i | \(0.110244\pi\) | ||||
−0.940621 | + | 0.339459i | \(0.889756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.5199i | 0.534573i | ||||||||
\(956\) | − 14.8811i | − 0.481288i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 1.64848i | − 0.0532599i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.752414 | 0.0242714 | ||||||||
\(962\) | 7.28885 | 0.235002 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.3302i | 0.944661i | ||||||||
\(965\) | −0.601082 | −0.0193495 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.53992 | 0.242468 | 0.121234 | − | 0.992624i | \(-0.461315\pi\) | ||||
0.121234 | + | 0.992624i | \(0.461315\pi\) | |||||||
\(968\) | 4.95064i | 0.159119i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.52044 | 0.241467 | ||||||||
\(971\) | 33.6134 | 1.07871 | 0.539353 | − | 0.842080i | \(-0.318669\pi\) | ||||
0.539353 | + | 0.842080i | \(0.318669\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 9.25587i | − 0.296577i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 29.5836i | − 0.946949i | ||||||||
\(977\) | 19.7436i | 0.631655i | 0.948817 | + | 0.315827i | \(0.102282\pi\) | ||||
−0.948817 | + | 0.315827i | \(0.897718\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 32.4885i | − 1.03834i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.99354 | 0.159350 | ||||||||
\(983\) | 42.1779 | 1.34526 | 0.672632 | − | 0.739977i | \(-0.265164\pi\) | ||||
0.672632 | + | 0.739977i | \(0.265164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.4179i | 1.44713i | ||||||||
\(986\) | −0.741412 | −0.0236114 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 39.4893 | 1.25632 | ||||||||
\(989\) | − 10.9434i | − 0.347980i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6276 | −0.687023 | −0.343511 | − | 0.939149i | \(-0.611616\pi\) | ||||
−0.343511 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(992\) | −14.2878 | −0.453637 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 0.150434i | − 0.00476907i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 10.6195i | − 0.336322i | −0.985760 | − | 0.168161i | \(-0.946217\pi\) | ||||
0.985760 | − | 0.168161i | \(-0.0537828\pi\) | |||||||
\(998\) | − 3.49107i | − 0.110508i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3087.2.c.c.3086.10 | yes | 24 | |
3.2 | odd | 2 | inner | 3087.2.c.c.3086.15 | yes | 24 | |
7.6 | odd | 2 | inner | 3087.2.c.c.3086.16 | yes | 24 | |
21.20 | even | 2 | inner | 3087.2.c.c.3086.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3087.2.c.c.3086.9 | ✓ | 24 | 21.20 | even | 2 | inner | |
3087.2.c.c.3086.10 | yes | 24 | 1.1 | even | 1 | trivial | |
3087.2.c.c.3086.15 | yes | 24 | 3.2 | odd | 2 | inner | |
3087.2.c.c.3086.16 | yes | 24 | 7.6 | odd | 2 | inner |