Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), degree \(2\), not 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(1.73018 + 0.0805675i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.2.bc.f.257.5 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −0.0805675 | + | 1.73018i | −0.0465156 | + | 0.998918i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.90017 | + | 3.29119i | 0.849781 | + | 1.47186i | 0.881404 | + | 0.472364i | \(0.156599\pi\) |
−0.0316229 | + | 0.999500i | \(0.510068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23495 | + | 1.41598i | −0.844732 | + | 0.535190i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98702 | − | 0.278792i | −0.995673 | − | 0.0929306i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.309539 | − | 0.178712i | −0.0933294 | − | 0.0538838i | 0.452609 | − | 0.891709i | \(-0.350493\pi\) |
−0.545938 | + | 0.837825i | \(0.683827\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.04570i | − | 1.12207i | −0.827791 | − | 0.561037i | \(-0.810403\pi\) | ||
0.827791 | − | 0.561037i | \(-0.189597\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.84742 | + | 3.02246i | −1.50980 | + | 0.780396i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0519689 | − | 0.0900129i | 0.0126043 | − | 0.0218313i | −0.859654 | − | 0.510876i | \(-0.829321\pi\) |
0.872259 | + | 0.489045i | \(0.162654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.12615 | − | 1.22753i | 0.487772 | − | 0.281615i | −0.235878 | − | 0.971783i | \(-0.575796\pi\) |
0.723650 | + | 0.690167i | \(0.242463\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.26983 | − | 3.98094i | −0.495318 | − | 0.868712i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.15188 | − | 0.665037i | 0.240183 | − | 0.138670i | −0.375078 | − | 0.926993i | \(-0.622384\pi\) |
0.615261 | + | 0.788323i | \(0.289051\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72127 | + | 8.17749i | −0.944255 | + | 1.63550i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.723015 | − | 5.14560i | 0.139144 | − | 0.990272i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.97265i | 0.923398i | 0.887037 | + | 0.461699i | \(0.152760\pi\) | ||||
−0.887037 | + | 0.461699i | \(0.847240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.83007 | + | 3.94335i | 1.22672 | + | 0.708246i | 0.966342 | − | 0.257262i | \(-0.0828202\pi\) |
0.260376 | + | 0.965507i | \(0.416154\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.334142 | − | 0.521158i | 0.0581667 | − | 0.0907220i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.90704 | − | 4.66504i | −1.50556 | − | 0.788535i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.45622 | + | 9.45046i | 0.896998 | + | 1.55365i | 0.831312 | + | 0.555805i | \(0.187590\pi\) |
0.0656853 | + | 0.997840i | \(0.479077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.99976 | + | 0.325951i | 1.12086 | + | 0.0521940i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.15464 | −0.961193 | −0.480597 | − | 0.876942i | \(-0.659580\pi\) | ||||
−0.480597 | + | 0.876942i | \(0.659580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.502751 | −0.0766688 | −0.0383344 | − | 0.999265i | \(-0.512205\pi\) | ||||
−0.0383344 | + | 0.999265i | \(0.512205\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.75828 | − | 10.3606i | −0.709322 | − | 1.54446i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.72578 | + | 9.91734i | 0.835190 | + | 1.44659i | 0.893875 | + | 0.448316i | \(0.147976\pi\) |
−0.0586849 | + | 0.998277i | \(0.518691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.99000 | − | 6.32929i | 0.427143 | − | 0.904184i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.151551 | + | 0.0971675i | 0.0212214 | + | 0.0136062i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.08143 | − | 2.93376i | −0.697988 | − | 0.402983i | 0.108610 | − | 0.994084i | \(-0.465360\pi\) |
−0.806597 | + | 0.591101i | \(0.798693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.35833i | − | 0.183158i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.95255 | + | 3.77751i | 0.258622 | + | 0.500344i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.77364 | − | 6.53614i | 0.491286 | − | 0.850933i | −0.508664 | − | 0.860965i | \(-0.669860\pi\) |
0.999950 | + | 0.0100329i | \(0.00319361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.20485 | − | 4.73707i | 1.05052 | − | 0.606520i | 0.127727 | − | 0.991809i | \(-0.459232\pi\) |
0.922796 | + | 0.385289i | \(0.125898\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.07060 | − | 3.60647i | 0.890812 | − | 0.454373i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.3151 | − | 7.68750i | 1.65154 | − | 0.953517i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34375 | − | 2.32744i | 0.164165 | − | 0.284342i | −0.772193 | − | 0.635388i | \(-0.780840\pi\) |
0.936358 | + | 0.351045i | \(0.114174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.05783 | + | 2.04653i | 0.127348 | + | 0.246374i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.78975i | − | 0.687117i | −0.939131 | − | 0.343558i | \(-0.888368\pi\) | ||
0.939131 | − | 0.343558i | \(-0.111632\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.203925 | − | 0.117736i | −0.0238676 | − | 0.0137800i | 0.488019 | − | 0.872833i | \(-0.337720\pi\) |
−0.511886 | + | 0.859053i | \(0.671053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.7681 | − | 8.82748i | −1.58980 | − | 1.01931i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.944856 | − | 0.0388878i | 0.107676 | − | 0.00443168i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61247 | + | 2.79289i | 0.181418 | + | 0.314224i | 0.942364 | − | 0.334591i | \(-0.108598\pi\) |
−0.760946 | + | 0.648815i | \(0.775265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.84455 | + | 1.66551i | 0.982728 | + | 0.185057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.07747 | −0.996382 | −0.498191 | − | 0.867067i | \(-0.666002\pi\) | ||||
−0.498191 | + | 0.867067i | \(0.666002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.394999 | 0.0428436 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.60356 | − | 0.400634i | −0.922398 | − | 0.0429525i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.41213 | − | 5.90999i | −0.361685 | − | 0.626457i | 0.626553 | − | 0.779379i | \(-0.284465\pi\) |
−0.988238 | + | 0.152921i | \(0.951132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.72862 | + | 9.04192i | 0.600523 | + | 0.947851i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.37296 | + | 11.4995i | −0.764541 | + | 1.19245i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.08008 | + | 4.66504i | 0.828999 | + | 0.478623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.14243i | 0.522134i | 0.965321 | + | 0.261067i | \(0.0840744\pi\) | ||||
−0.965321 | + | 0.261067i | \(0.915926\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.874774 | + | 0.620114i | 0.0879181 | + | 0.0623238i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.43891 | − | 11.1525i | 0.640695 | − | 1.10972i | −0.344583 | − | 0.938756i | \(-0.611980\pi\) |
0.985278 | − | 0.170960i | \(-0.0546870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.88120 | + | 2.81816i | −0.480959 | + | 0.277682i | −0.720816 | − | 0.693126i | \(-0.756233\pi\) |
0.239857 | + | 0.970808i | \(0.422899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.78895 | − | 15.0349i | 0.857714 | − | 1.46725i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.62737 | − | 4.40366i | 0.737365 | − | 0.425718i | −0.0837453 | − | 0.996487i | \(-0.526688\pi\) |
0.821111 | + | 0.570769i | \(0.193355\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.23862 | − | 3.87741i | 0.214421 | − | 0.371389i | −0.738672 | − | 0.674065i | \(-0.764547\pi\) |
0.953093 | + | 0.302676i | \(0.0978801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7905 | + | 8.67883i | −1.59369 | + | 0.823758i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.37753 | + | 2.52737i | 0.408206 | + | 0.235678i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12791 | + | 12.0846i | −0.104275 | + | 1.11722i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0113084 | + | 0.274761i | 0.00103664 | + | 0.0251873i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.43612 | − | 9.41564i | −0.494193 | − | 0.855968i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.495864 | − | 10.6486i | 0.0447105 | − | 0.960153i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16.8832 | −1.51008 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9198 | −1.14645 | −0.573223 | − | 0.819399i | \(-0.694307\pi\) | ||||
−0.573223 | + | 0.819399i | \(0.694307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0405054 | − | 0.869848i | 0.00356630 | − | 0.0765858i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.66384 | + | 4.61391i | 0.232741 | + | 0.403119i | 0.958614 | − | 0.284710i | \(-0.0918972\pi\) |
−0.725873 | + | 0.687829i | \(0.758564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.01367 | + | 5.75406i | −0.261319 | + | 0.498940i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.3090 | − | 7.39793i | 1.57579 | − | 0.636713i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.37380 | + | 2.52521i | 0.373679 | + | 0.215744i | 0.675064 | − | 0.737759i | \(-0.264116\pi\) |
−0.301386 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.2651i | − | 1.80368i | −0.432067 | − | 0.901841i | \(-0.642216\pi\) | ||
0.432067 | − | 0.901841i | \(-0.357784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.6200 | + | 9.10759i | −1.48388 | + | 0.766997i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.723015 | + | 1.25230i | −0.0604616 | + | 0.104723i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3659 | + | 9.44887i | −1.35912 | + | 0.784686i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7099 | + | 5.68316i | 0.883337 | + | 0.468739i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5482 | − | 6.09001i | 0.864143 | − | 0.498913i | −0.00125437 | − | 0.999999i | \(-0.500399\pi\) |
0.865398 | + | 0.501086i | \(0.167066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.10880 | + | 7.11665i | −0.334369 | + | 0.579145i | −0.983363 | − | 0.181649i | \(-0.941857\pi\) |
0.648994 | + | 0.760793i | \(0.275190\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.180327 | + | 0.254381i | −0.0145786 | + | 0.0205655i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.9721i | 2.40741i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2104 | + | 6.47230i | 0.894683 | + | 0.516546i | 0.875472 | − | 0.483270i | \(-0.160551\pi\) |
0.0192119 | + | 0.999815i | \(0.493884\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.48532 | − | 8.55539i | 0.435014 | − | 0.678487i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.63271 | + | 3.11736i | −0.128676 | + | 0.245683i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.09237 | − | 1.89205i | −0.0855613 | − | 0.148197i | 0.820069 | − | 0.572265i | \(-0.193935\pi\) |
−0.905630 | + | 0.424068i | \(0.860602\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.35016 | + | 0.109437i | 0.182959 | + | 0.00851969i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.464592 | 0.0359512 | 0.0179756 | − | 0.999838i | \(-0.494278\pi\) | ||||
0.0179756 | + | 0.999838i | \(0.494278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.36765 | −0.259050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69307 | + | 3.07391i | −0.511832 | + | 0.235068i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.62587 | − | 8.01224i | −0.351698 | − | 0.609159i | 0.634849 | − | 0.772636i | \(-0.281062\pi\) |
−0.986547 | + | 0.163477i | \(0.947729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.02735 | − | 24.9615i | −0.0776603 | − | 1.88691i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0046 | + | 7.05566i | 0.827159 | + | 0.530336i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.77096 | + | 1.02246i | 0.132367 | + | 0.0764224i | 0.564722 | − | 0.825282i | \(-0.308984\pi\) |
−0.432354 | + | 0.901704i | \(0.642317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.6193i | − | 1.30963i | −0.755790 | − | 0.654815i | \(-0.772747\pi\) | ||
0.755790 | − | 0.654815i | \(-0.227253\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.53492 | + | 14.5775i | 0.556998 | + | 1.07760i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.7355 | + | 35.9149i | −1.52450 | + | 2.64052i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0321728 | + | 0.0185750i | −0.00235271 | + | 0.00135834i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.67017 | + | 12.5239i | 0.412444 | + | 0.910983i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4811 | + | 11.2474i | −1.40960 | + | 0.813834i | −0.995350 | − | 0.0963279i | \(-0.969290\pi\) |
−0.414252 | + | 0.910162i | \(0.635957\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.81985 | + | 8.34823i | −0.346940 | + | 0.600918i | −0.985704 | − | 0.168484i | \(-0.946113\pi\) |
0.638764 | + | 0.769403i | \(0.279446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.2280 | + | 23.6569i | 0.875662 | + | 1.69411i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3750i | 1.09542i | 0.836667 | + | 0.547712i | \(0.184501\pi\) | ||||
−0.836667 | + | 0.547712i | \(0.815499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.96967 | + | 2.29189i | 0.281403 | + | 0.162468i | 0.634058 | − | 0.773285i | \(-0.281388\pi\) |
−0.352656 | + | 0.935753i | \(0.614721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.91862 | + | 2.51244i | 0.276398 | + | 0.177214i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.04117 | − | 11.1136i | −0.494194 | − | 0.780023i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6948 | − | 20.2561i | −0.816804 | − | 1.41475i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.62609 | + | 1.66534i | −0.252031 | + | 0.115749i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.877501 | −0.0606980 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.870400 | 0.0599208 | 0.0299604 | − | 0.999551i | \(-0.490462\pi\) | ||||
0.0299604 | + | 0.999551i | \(0.490462\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.0173 | + | 0.466465i | 0.686373 | + | 0.0319617i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.955311 | − | 1.65465i | −0.0651517 | − | 0.112846i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.8486 | + | 0.858072i | −1.41529 | + | 0.0582497i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.220134 | − | 0.343341i | 0.0148753 | − | 0.0232008i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.364165 | − | 0.210251i | −0.0244964 | − | 0.0141430i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.21373i | 0.0812777i | 0.999174 | + | 0.0406388i | \(0.0129393\pi\) | ||||
−0.999174 | + | 0.0406388i | \(0.987061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 16.3823 | − | 23.1100i | 1.09216 | − | 1.54067i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.67205 | − | 11.5563i | 0.442840 | − | 0.767021i | −0.555059 | − | 0.831811i | \(-0.687304\pi\) |
0.997899 | + | 0.0647898i | \(0.0206377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.60627 | − | 5.54618i | 0.634800 | − | 0.366502i | −0.147808 | − | 0.989016i | \(-0.547222\pi\) |
0.782609 | + | 0.622514i | \(0.213889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.00884196 | + | 1.63790i | −0.000581758 | + | 0.107766i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.08411 | − | 4.09001i | 0.464095 | − | 0.267946i | −0.249669 | − | 0.968331i | \(-0.580322\pi\) |
0.713765 | + | 0.700386i | \(0.246989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.7599 | + | 37.6892i | −1.41946 | + | 2.45857i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.96210 | + | 2.56485i | −0.322323 | + | 0.166605i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.5944i | − | 1.46151i | −0.682638 | − | 0.730757i | \(-0.739167\pi\) | ||
0.682638 | − | 0.730757i | \(-0.260833\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24127 | + | 2.44870i | 0.273205 | + | 0.157735i | 0.630343 | − | 0.776317i | \(-0.282914\pi\) |
−0.357138 | + | 0.934051i | \(0.616248\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.59421 | + | 15.1684i | −0.230569 | + | 0.973056i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.5124 | − | 2.18606i | 1.69381 | − | 0.139662i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.96622 | − | 8.60175i | −0.315993 | − | 0.547316i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.731349 | − | 15.7056i | 0.0463474 | − | 0.995304i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.17857 | 0.579346 | 0.289673 | − | 0.957126i | \(-0.406453\pi\) | ||||
0.289673 | + | 0.957126i | \(0.406453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.475401 | −0.0298882 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0318241 | + | 0.683418i | −0.00199290 | + | 0.0427973i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.31055 | − | 10.9302i | −0.393641 | − | 0.681806i | 0.599286 | − | 0.800535i | \(-0.295451\pi\) |
−0.992927 | + | 0.118729i | \(0.962118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.5760 | − | 13.3954i | −1.58922 | − | 0.832349i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.38633 | − | 14.8534i | 0.0858119 | − | 0.919402i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.2489 | − | 14.5775i | −1.55692 | − | 0.898886i | −0.997549 | − | 0.0699665i | \(-0.977711\pi\) |
−0.559367 | − | 0.828920i | \(-0.688956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 22.2986i | − | 1.36979i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5002 | − | 5.42744i | 0.642603 | − | 0.332154i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.23640 | + | 3.87356i | −0.136356 | + | 0.236175i | −0.926115 | − | 0.377242i | \(-0.876872\pi\) |
0.789759 | + | 0.613418i | \(0.210206\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.4985 | − | 8.37071i | 0.880721 | − | 0.508485i | 0.00982495 | − | 0.999952i | \(-0.496873\pi\) |
0.870896 | + | 0.491467i | \(0.163539\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.1057 | + | 9.18304i | −0.974759 | + | 0.555783i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.92283 | − | 1.68750i | 0.176254 | − | 0.101760i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.510924 | + | 0.884946i | −0.0306984 | + | 0.0531713i | −0.880966 | − | 0.473179i | \(-0.843106\pi\) |
0.850268 | + | 0.526350i | \(0.176440\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.3022 | − | 13.6830i | −1.15559 | − | 0.819181i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.9453i | − | 0.831907i | −0.909386 | − | 0.415953i | \(-0.863448\pi\) | ||
0.909386 | − | 0.415953i | \(-0.136552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0386 | − | 8.10519i | −0.834508 | − | 0.481803i | 0.0208856 | − | 0.999782i | \(-0.493351\pi\) |
−0.855394 | + | 0.517978i | \(0.826685\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.72233 | + | 13.6041i | −0.516666 | + | 0.805838i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.7553 | − | 8.71485i | 0.811950 | − | 0.514421i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.49460 | + | 14.7131i | 0.499682 | + | 0.865475i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.89731 | − | 0.414312i | −0.521569 | − | 0.0242874i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2067 | 1.12207 | 0.561034 | − | 0.827793i | \(-0.310404\pi\) | ||||
0.561034 | + | 0.827793i | \(0.310404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.6822 | 1.66994 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.14338 | + | 1.46355i | −0.0663459 | + | 0.0849239i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.69054 | − | 4.66015i | −0.155598 | − | 0.269503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.12362 | − | 0.711886i | 0.0647646 | − | 0.0410324i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.7770 | + | 12.0390i | 1.07871 | + | 0.691621i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.1812 | + | 18.0025i | 1.78543 | + | 1.03082i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.480498i | 0.0274235i | 0.999906 | + | 0.0137117i | \(0.00436472\pi\) | ||||
−0.999906 | + | 0.0137117i | \(0.995635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.48265 | − | 8.67239i | −0.255009 | − | 0.493355i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.66653 | − | 8.08266i | 0.264615 | − | 0.458326i | −0.702848 | − | 0.711340i | \(-0.748089\pi\) |
0.967463 | + | 0.253014i | \(0.0814220\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5147 | − | 8.95742i | 0.876943 | − | 0.506303i | 0.00729351 | − | 0.999973i | \(-0.497678\pi\) |
0.869649 | + | 0.493670i | \(0.164345\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.3049 | + | 16.4178i | 1.42577 | + | 0.925036i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.3275 | + | 11.1587i | −1.08554 | + | 0.626736i | −0.932385 | − | 0.361467i | \(-0.882276\pi\) |
−0.153153 | + | 0.988202i | \(0.548943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.888674 | − | 1.53923i | 0.0497562 | − | 0.0861802i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.00459 | + | 13.5515i | 0.390958 | + | 0.756370i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.255174i | − | 0.0141983i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.0836 | + | 19.1008i | 1.83515 | + | 1.05952i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.52824 | + | 4.18561i | 0.361013 | + | 0.231465i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.8396 | − | 14.0572i | −1.47971 | − | 0.774996i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.05860 | + | 12.2259i | 0.387976 | + | 0.671994i | 0.992177 | − | 0.124838i | \(-0.0398411\pi\) |
−0.604201 | + | 0.796832i | \(0.706508\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.6631 | − | 29.7498i | −0.748735 | − | 1.63028i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.2134 | 0.558018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4042 | −1.00254 | −0.501270 | − | 0.865291i | \(-0.667134\pi\) | ||||
−0.501270 | + | 0.865291i | \(0.667134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.92070 | − | 0.322270i | −0.375881 | − | 0.0175033i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.40945 | − | 2.44124i | −0.0763259 | − | 0.132200i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.27965 | + | 18.3794i | 0.123089 | + | 0.992396i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.72547 | + | 7.37027i | −0.254411 | + | 0.396802i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.6474 | + | 15.9623i | 1.48419 | + | 0.856899i | 0.999838 | − | 0.0179729i | \(-0.00572127\pi\) |
0.484354 | + | 0.874872i | \(0.339055\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7367i | 0.788840i | 0.918930 | + | 0.394420i | \(0.129055\pi\) | ||||
−0.918930 | + | 0.394420i | \(0.870945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.8175 | − | 2.92510i | −1.11116 | − | 0.156130i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.5686 | − | 23.5016i | 0.722185 | − | 1.25086i | −0.237937 | − | 0.971281i | \(-0.576471\pi\) |
0.960122 | − | 0.279581i | \(-0.0901956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.0551 | − | 11.0015i | 1.01134 | − | 0.583899i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.476296 | − | 0.00257121i | −0.0252083 | − | 0.000136083i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.9479 | + | 9.78486i | −0.894475 | + | 0.516425i | −0.875404 | − | 0.483393i | \(-0.839404\pi\) |
−0.0190713 | + | 0.999818i | \(0.506071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.48633 | + | 11.2346i | −0.341386 | + | 0.591297i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.7287 | − | 8.64686i | 0.878029 | − | 0.453842i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.894875i | − | 0.0468399i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.16258 | + | 0.671213i | 0.0606860 | + | 0.0350371i | 0.530036 | − | 0.847975i | \(-0.322178\pi\) |
−0.469350 | + | 0.883012i | \(0.655512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.3840 | + | 1.71586i | 0.957034 | + | 0.0893243i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.5109 | − | 0.638387i | 0.805285 | − | 0.0331434i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.52378 | − | 11.2995i | −0.337788 | − | 0.585066i | 0.646228 | − | 0.763144i | \(-0.276345\pi\) |
−0.984016 | + | 0.178078i | \(0.943012\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.36023 | − | 29.2109i | 0.0702422 | − | 1.50844i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.1178 | 1.03612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0822 | 1.03156 | 0.515778 | − | 0.856722i | \(-0.327503\pi\) | ||||
0.515778 | + | 0.856722i | \(0.327503\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.04092 | − | 22.3535i | 0.0533277 | − | 1.14521i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.2613 | − | 19.5052i | −0.575428 | − | 0.996670i | −0.995995 | − | 0.0894085i | \(-0.971502\pi\) |
0.420567 | − | 0.907261i | \(-0.361831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.92337 | + | 3.03581i | 0.0980242 | + | 0.154719i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.50173 | + | 0.140163i | 0.0763370 | + | 0.00712488i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.1899 | − | 18.5848i | −1.63209 | − | 0.942289i | −0.983447 | − | 0.181197i | \(-0.942003\pi\) |
−0.648645 | − | 0.761091i | \(-0.724664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.138245i | − | 0.00699136i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.19750 | + | 4.23719i | −0.413509 | + | 0.213738i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.12795 | + | 10.6139i | −0.308330 | + | 0.534044i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0288 | + | 13.8730i | −1.20597 | + | 0.696268i | −0.961877 | − | 0.273483i | \(-0.911824\pi\) |
−0.244095 | + | 0.969751i | \(0.578491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.71273 | − | 5.67778i | −0.486245 | − | 0.284244i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.7233 | + | 11.3872i | −0.984933 | + | 0.568651i | −0.903756 | − | 0.428048i | \(-0.859201\pi\) |
−0.0811773 | + | 0.996700i | \(0.525868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.9536 | − | 27.6324i | 0.794704 | − | 1.37647i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.3246 | + | 32.2738i | 0.562725 | + | 1.60370i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.90038i | − | 0.193334i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6849 | − | 13.0972i | −1.12170 | − | 0.647613i | −0.179865 | − | 0.983691i | \(-0.557566\pi\) |
−0.941834 | + | 0.336078i | \(0.890899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.72145 | + | 7.36399i | −0.232892 | + | 0.363239i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.821144 | + | 19.9513i | 0.0404059 | + | 0.981741i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.2487 | − | 29.8757i | −0.846707 | − | 1.46654i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.7924 | + | 1.71328i | 1.80173 | + | 0.0838995i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.93992 | −0.436744 | −0.218372 | − | 0.975866i | \(-0.570075\pi\) | ||||
−0.218372 | + | 0.975866i | \(0.570075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00735 | −0.244043 | −0.122022 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122022 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.3381 | − | 31.2196i | −0.697144 | − | 1.51795i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.490719 | + | 0.849951i | 0.0238034 | + | 0.0412287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.6298 | + | 22.2050i | −0.562807 | + | 1.07458i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.10845 | − | 1.35184i | −0.101797 | − | 0.0652674i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.62468 | + | 3.24741i | 0.270931 | + | 0.156422i | 0.629311 | − | 0.777154i | \(-0.283337\pi\) |
−0.358379 | + | 0.933576i | \(0.616671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.05254i | 0.0505818i | 0.999680 | + | 0.0252909i | \(0.00805120\pi\) | ||||
−0.999680 | + | 0.0252909i | \(0.991949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.0296 | − | 29.0772i | −0.720616 | − | 1.39414i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.63271 | − | 2.82794i | 0.0781032 | − | 0.135279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.8990 | + | 14.9528i | −1.23609 | + | 0.713658i | −0.968293 | − | 0.249817i | \(-0.919630\pi\) |
−0.267799 | + | 0.963475i | \(0.586296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6957 | + | 18.0721i | −0.509321 | + | 0.860577i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.7104 | + | 15.4212i | −1.26905 | + | 0.732685i | −0.974808 | − | 0.223047i | \(-0.928400\pi\) |
−0.294240 | + | 0.955732i | \(0.595066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9672 | − | 22.4599i | 0.614707 | − | 1.06470i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.68695 | + | 18.7409i | 0.458177 | + | 0.886415i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.6953i | − | 1.73176i | −0.500253 | − | 0.865879i | \(-0.666760\pi\) | ||
0.500253 | − | 0.865879i | \(-0.333240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.90510 | + | 1.09991i | 0.0897076 | + | 0.0517927i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.9820 | − | 7.68232i | −0.562964 | − | 0.360947i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.8733 | + | 36.0351i | −0.884795 | + | 1.68935i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8750 | + | 20.5681i | 0.555489 | + | 0.962135i | 0.997865 | + | 0.0653057i | \(0.0208022\pi\) |
−0.442376 | + | 0.896830i | \(0.645864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.425596 | − | 0.332492i | −0.0198651 | − | 0.0155194i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5938 | −0.493404 | −0.246702 | − | 0.969091i | \(-0.579347\pi\) | ||||
−0.246702 | + | 0.969091i | \(0.579347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.367649 | 0.0170861 | 0.00854305 | − | 0.999964i | \(-0.497281\pi\) | ||||
0.00854305 | + | 0.999964i | \(0.497281\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.8570 | − | 2.41477i | −2.40481 | − | 0.111982i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.7847 | + | 27.3399i | 0.730428 | + | 1.26514i | 0.956700 | + | 0.291075i | \(0.0940129\pi\) |
−0.226272 | + | 0.974064i | \(0.572654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.292400 | + | 7.10444i | 0.0135018 | + | 0.328053i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1014 | + | 18.8744i | −0.557603 | + | 0.869688i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.155621 | + | 0.0898478i | 0.00715546 | + | 0.00413120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.1821i | 1.06367i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.3604 | + | 10.1799i | 0.657518 | + | 0.466104i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.01497 | + | 10.4182i | −0.274831 | + | 0.476022i | −0.970093 | − | 0.242735i | \(-0.921955\pi\) |
0.695261 | + | 0.718757i | \(0.255289\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.2337 | − | 22.0742i | 1.74331 | − | 1.00650i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.26204 | − | 3.07604i | −0.239431 | − | 0.139964i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.9247 | + | 9.77148i | −0.768511 | + | 0.443700i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.47737 | + | 16.4153i | −0.429461 | + | 0.743848i | −0.996825 | − | 0.0796188i | \(-0.974630\pi\) |
0.567365 | + | 0.823467i | \(0.307963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.36159 | − | 1.73756i | 0.152016 | − | 0.0785753i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.8373i | − | 0.714727i | −0.933965 | − | 0.357364i | \(-0.883676\pi\) | ||
0.933965 | − | 0.357364i | \(-0.116324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.447602 | + | 0.258423i | 0.0201590 | + | 0.0116388i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.378692 | + | 4.05736i | −0.0170209 | + | 0.182365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.19817 | + | 12.9398i | 0.367738 | + | 0.580429i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0988 | + | 17.4916i | 0.452084 | + | 0.783033i | 0.998515 | − | 0.0544710i | \(-0.0173473\pi\) |
−0.546431 | + | 0.837504i | \(0.684014\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0374310 | + | 0.803826i | −0.00167229 | + | 0.0359123i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.8663 | 1.64379 | 0.821893 | − | 0.569641i | \(-0.192918\pi\) | ||||
0.821893 | + | 0.569641i | \(0.192918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.9400 | 2.17780 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.271323 | − | 5.82663i | 0.0120499 | − | 0.258770i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.13197 | + | 8.88884i | 0.227471 | + | 0.393991i | 0.957058 | − | 0.289897i | \(-0.0936211\pi\) |
−0.729587 | + | 0.683888i | \(0.760288\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.622475 | − | 0.0256194i | 0.0275367 | − | 0.00113334i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.77916 | − | 11.8279i | −0.211005 | − | 0.522212i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.5502 | − | 10.7100i | −0.817419 | − | 0.471937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.09307i | − | 0.180013i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.2353 | − | 7.35804i | 0.624859 | − | 0.322982i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.98887 | + | 13.8371i | −0.349999 | + | 0.606216i | −0.986249 | − | 0.165267i | \(-0.947151\pi\) |
0.636250 | + | 0.771483i | \(0.280485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.676700 | + | 0.390693i | −0.0295900 | + | 0.0170838i | −0.514722 | − | 0.857357i | \(-0.672105\pi\) |
0.485132 | + | 0.874441i | \(0.338772\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 43.2706 | + | 0.233590i | 1.88848 | + | 0.0101947i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.709904 | − | 0.409863i | 0.0309239 | − | 0.0178539i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6155 | + | 18.3865i | −0.461541 | + | 0.799413i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.0942 | + | 18.4715i | −0.568238 | + | 0.801595i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.8998i | 1.07853i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.9865 | + | 16.7354i | 1.25320 | + | 0.723534i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.91172 | + | 2.98169i | −0.0824968 | + | 0.128669i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.05664 | + | 1.42481i | −0.0885859 | + | 0.0613709i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.63362 | + | 6.29362i | 0.156222 | + | 0.270584i | 0.933503 | − | 0.358569i | \(-0.116735\pi\) |
−0.777282 | + | 0.629153i | \(0.783402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.4844 | + | 1.41954i | 1.30821 | + | 0.0609182i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.0150 | 0.728845 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.2546 | −1.76392 | −0.881960 | − | 0.471325i | \(-0.843776\pi\) | ||||
−0.881960 | + | 0.471325i | \(0.843776\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.8287 | + | 11.8623i | −1.10234 | + | 0.506269i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.10409 | + | 10.5726i | 0.260043 | + | 0.450408i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.55847 | − | 3.95873i | −0.321419 | − | 0.168342i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −60.4685 | − | 38.7696i | −2.56675 | − | 1.64568i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.48798 | + | 3.16849i | 0.232533 | + | 0.134253i | 0.611740 | − | 0.791059i | \(-0.290470\pi\) |
−0.379207 | + | 0.925312i | \(0.623803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.03398i | 0.0860281i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0295459 | − | 0.0571611i | −0.00124743 | − | 0.00241335i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.73130 | + | 13.3910i | −0.325836 | + | 0.564364i | −0.981681 | − | 0.190531i | \(-0.938979\pi\) |
0.655846 | + | 0.754895i | \(0.272312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1647 | + | 7.60067i | −0.553845 | + | 0.319763i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.1255 | + | 8.80137i | −0.929182 | + | 0.369623i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.2364 | + | 5.90999i | −0.429132 | + | 0.247760i | −0.698977 | − | 0.715144i | \(-0.746361\pi\) |
0.269845 | + | 0.962904i | \(0.413028\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0386 | − | 31.2438i | 0.754892 | − | 1.30751i | −0.190536 | − | 0.981680i | \(-0.561023\pi\) |
0.945428 | − | 0.325831i | \(-0.105644\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.8905 | − | 34.6119i | −0.747385 | − | 1.44593i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.5593i | 0.523759i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.4253 | − | 11.7926i | −0.850316 | − | 0.490930i | 0.0104412 | − | 0.999945i | \(-0.496676\pi\) |
−0.860758 | + | 0.509015i | \(0.830010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.0556 | − | 9.01178i | −0.584130 | − | 0.374517i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.2877 | − | 12.8535i | 0.841676 | − | 0.533254i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.04860 | + | 1.81623i | 0.0434285 | + | 0.0752204i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −41.9158 | + | 19.2505i | −1.73300 | + | 0.795912i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.287490 | 0.0118660 | 0.00593298 | − | 0.999982i | \(-0.498111\pi\) | ||||
0.00593298 | + | 0.999982i | \(0.498111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.3623 | 0.797812 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.6015 | − | 1.23872i | −1.09424 | − | 0.0509543i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.71589 | + | 9.90021i | 0.234723 | + | 0.406553i | 0.959192 | − | 0.282755i | \(-0.0912482\pi\) |
−0.724469 | + | 0.689308i | \(0.757915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.882803 | + | 0.559311i | −0.0361914 | + | 0.0229295i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.28520 | + | 6.68358i | −0.175382 | + | 0.273541i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7842 | + | 10.8451i | 0.767502 | + | 0.443117i | 0.831983 | − | 0.554802i | \(-0.187206\pi\) |
−0.0644810 | + | 0.997919i | \(0.520539\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7036i | 0.966889i | 0.875375 | + | 0.483445i | \(0.160615\pi\) | ||||
−0.875375 | + | 0.483445i | \(0.839385\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.66268 | + | 6.57749i | −0.189879 | + | 0.267856i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.6591 | − | 35.7826i | 0.839912 | − | 1.45477i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5031 | − | 10.6828i | 0.751017 | − | 0.433600i | −0.0750445 | − | 0.997180i | \(-0.523910\pi\) |
0.826061 | + | 0.563580i | \(0.190577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.7958 | − | 11.2871i | 0.802167 | − | 0.457375i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.1225 | − | 23.1647i | 1.62318 | − | 0.937145i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8248 | + | 34.3376i | −0.800716 | + | 1.38688i | 0.118429 | + | 0.992962i | \(0.462214\pi\) |
−0.919145 | + | 0.393918i | \(0.871119\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.9888 | − | 18.6022i | 1.45121 | − | 0.750112i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.6296i | − | 1.15258i | −0.817244 | − | 0.576292i | \(-0.804499\pi\) | ||
0.817244 | − | 0.576292i | \(-0.195501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9529 | + | 19.0254i | 1.32449 | + | 0.764694i | 0.984441 | − | 0.175714i | \(-0.0562235\pi\) |
0.340047 | + | 0.940408i | \(0.389557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.58919 | − | 6.40794i | −0.103901 | − | 0.257142i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.9944 | + | 8.37701i | 0.640801 | + | 0.335618i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.47450 | − | 14.6783i | −0.338980 | − | 0.587130i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0706980 | − | 1.51823i | 0.00282341 | − | 0.0606323i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.13422 | 0.0452242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.65235 | 0.145398 | 0.0726989 | − | 0.997354i | \(-0.476839\pi\) | ||||
0.0726989 | + | 0.997354i | \(0.476839\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0701259 | + | 1.50595i | −0.00278726 | + | 0.0598560i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.5498 | − | 42.5215i | −0.974228 | − | 1.68741i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.6064 | − | 12.0966i | −1.01456 | − | 0.479286i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.61413 | + | 17.2941i | −0.0638542 | + | 0.684143i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.2563 | − | 12.2723i | −0.839574 | − | 0.484728i | 0.0175456 | − | 0.999846i | \(-0.494415\pi\) |
−0.857119 | + | 0.515118i | \(0.827748\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 27.3936i | − | 1.08030i | −0.841569 | − | 0.540149i | \(-0.818368\pi\) | ||
0.841569 | − | 0.540149i | \(-0.181632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.93980 | − | 1.51955i | 0.115754 | − | 0.0598321i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.1181 | + | 27.9173i | −0.633667 | + | 1.09754i | 0.353129 | + | 0.935575i | \(0.385118\pi\) |
−0.986796 | + | 0.161969i | \(0.948216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.33618 | + | 1.34879i | −0.0917029 | + | 0.0529447i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.195101 | − | 36.1408i | 0.00764660 | − | 1.41647i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5027 | − | 7.79579i | 0.528401 | − | 0.305073i | −0.211964 | − | 0.977278i | \(-0.567986\pi\) |
0.740365 | + | 0.672205i | \(0.234653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.1235 | + | 17.5344i | −0.395558 | + | 0.685126i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.576304 | + | 0.408533i | 0.0224838 | + | 0.0159384i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 35.1100i | − | 1.36769i | −0.729626 | − | 0.683847i | \(-0.760306\pi\) | ||
0.729626 | − | 0.683847i | \(-0.239694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.96082 | + | 4.01883i | 0.270745 | + | 0.156314i | 0.629226 | − | 0.777222i | \(-0.283372\pi\) |
−0.358481 | + | 0.933537i | \(0.616705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.393110 | − | 0.613129i | 0.0152671 | − | 0.0238120i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.6642 | + | 1.01511i | −0.956436 | + | 0.0393644i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.30700 | + | 5.72789i | 0.128047 | + | 0.221785i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.09997 | − | 0.0977875i | −0.0811897 | − | 0.00378068i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.38629 | −0.130726 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.1744 | 1.08604 | 0.543022 | − | 0.839719i | \(-0.317280\pi\) | ||||
0.543022 | + | 0.839719i | \(0.317280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38.6646 | + | 30.2063i | 1.48820 | + | 1.16264i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3844 | + | 30.1106i | 0.668135 | + | 1.15724i | 0.978425 | + | 0.206602i | \(0.0662405\pi\) |
−0.310290 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.28158 | − | 11.4931i | −0.279441 | − | 0.441063i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4569 | + | 12.4749i | 0.745592 | + | 0.478039i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7393 | − | 23.5209i | −1.55885 | − | 0.900001i | −0.997368 | − | 0.0725098i | \(-0.976899\pi\) |
−0.561479 | − | 0.827491i | \(-0.689768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1933i | 0.733339i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.82192 | + | 17.0674i | 0.336577 | + | 0.651161i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.8691 | + | 20.5579i | −0.452177 | + | 0.783194i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1758 | − | 15.6900i | 1.03382 | − | 0.596874i | 0.115740 | − | 0.993279i | \(-0.463076\pi\) |
0.918076 | + | 0.396406i | \(0.129743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.83314 | − | 0.147260i | −0.107622 | − | 0.00559393i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 69.9874 | − | 40.4073i | 2.65478 | − | 1.53274i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.319850 | + | 0.553997i | −0.0121152 | + | 0.0209841i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.50569 | + | 12.5863i | 0.246068 | + | 0.476057i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 29.9818i | − | 1.13240i | −0.824268 | − | 0.566199i | \(-0.808413\pi\) | ||
0.824268 | − | 0.566199i | \(-0.191587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.2015 | + | 13.3954i | 0.875061 | + | 0.505217i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −63.4558 | − | 40.6849i | −2.38988 | − | 1.53228i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.40111 | + | 34.0427i | 0.0526940 | + | 1.28031i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5451 | − | 19.9968i | −0.433587 | − | 0.750995i | 0.563592 | − | 0.826053i | \(-0.309419\pi\) |
−0.997179 | + | 0.0750583i | \(0.976086\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.03786 | − | 8.79195i | −0.151431 | − | 0.329724i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.4899 | 0.392849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.49540 | −0.205516 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.0924 | + | 1.82038i | 1.45993 | + | 0.0679832i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.5340 | − | 39.0300i | −0.840376 | − | 1.45557i | −0.889577 | − | 0.456785i | \(-0.849001\pi\) |
0.0492012 | − | 0.998789i | \(-0.484332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.91877 | − | 13.2101i | 0.257669 | − | 0.491971i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.57839 | + | 7.14087i | −0.170272 | + | 0.265572i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.6638 | − | 23.4772i | −1.51022 | − | 0.871923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.14662i | − | 0.116702i | −0.998296 | − | 0.0583508i | \(-0.981416\pi\) | ||
0.998296 | − | 0.0583508i | \(-0.0185842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9545 | − | 7.44070i | −0.961278 | − | 0.275582i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0261274 | + | 0.0452541i | −0.000966358 | + | 0.00167378i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.9590 | − | 8.63657i | 0.552522 | − | 0.318999i | −0.197616 | − | 0.980279i | \(-0.563320\pi\) |
0.750139 | + | 0.661281i | \(0.229987\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.64624 | + | 46.0472i | 0.0607224 | + | 1.69848i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.831885 | + | 0.480289i | −0.0306429 | + | 0.0176917i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.996550 | − | 1.72607i | 0.0366587 | − | 0.0634947i | −0.847114 | − | 0.531411i | \(-0.821662\pi\) |
0.883773 | + | 0.467917i | \(0.154995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.2827 | − | 7.89942i | 0.561423 | − | 0.290192i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.54435i | 0.203402i | 0.994815 | + | 0.101701i | \(0.0324286\pi\) | ||||
−0.994815 | + | 0.101701i | \(0.967571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.0867 | + | 23.1441i | 1.46866 | + | 0.847934i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.1146 | + | 2.53073i | 0.992071 | + | 0.0925944i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8113 | + | 20.6422i | −0.395036 | + | 0.754248i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0897 | − | 38.2605i | −0.806065 | − | 1.39615i | −0.915569 | − | 0.402160i | \(-0.868260\pi\) |
0.109504 | − | 0.993986i | \(-0.465074\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.739494 | + | 15.8805i | −0.0269487 | + | 0.578719i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.2296 | −1.13656 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.6250 | 0.386172 | 0.193086 | − | 0.981182i | \(-0.438150\pi\) | ||||
0.193086 | + | 0.981182i | \(0.438150\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0383019 | − | 0.822528i | 0.00139027 | − | 0.0298559i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.9084 | + | 24.0900i | 0.504178 | + | 0.873262i | 0.999988 | + | 0.00483132i | \(0.00153786\pi\) |
−0.495810 | + | 0.868431i | \(0.665129\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.487125 | + | 11.8357i | 0.0176351 | + | 0.428480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.17987 | − | 0.110122i | −0.0426582 | − | 0.00398149i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.4432 | − | 15.2670i | −0.954809 | − | 0.551259i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2707i | 0.370369i | 0.982704 | + | 0.185185i | \(0.0592883\pi\) | ||||
−0.982704 | + | 0.185185i | \(0.940712\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.4196 | − | 10.0377i | 0.699379 | − | 0.361500i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.2953 | − | 35.1525i | 0.729972 | − | 1.26435i | −0.226923 | − | 0.973913i | \(-0.572867\pi\) |
0.956895 | − | 0.290435i | \(-0.0938001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −64.4933 | + | 37.2352i | −2.31667 | + | 1.33753i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.2370 | − | 43.1718i | 0.905372 | − | 1.54878i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.0857 | + | 7.55502i | −0.468843 | + | 0.270687i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.03470 | + | 1.79215i | −0.0370244 | + | 0.0641282i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.5873 | + | 3.59530i | 0.914415 | + | 0.128486i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 49.1938i | 1.75580i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.6225 | − | 13.0611i | −0.806404 | − | 0.465578i | 0.0393014 | − | 0.999227i | \(-0.487487\pi\) |
−0.845706 | + | 0.533650i | \(0.820820\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.2559 | − | 42.5107i | 0.970334 | − | 1.51342i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.66392 | − | 8.93980i | −0.201386 | − | 0.317863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1647 | − | 33.1943i | −0.680560 | − | 1.17876i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38.5804 | + | 1.79654i | 1.36831 | + | 0.0637167i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0284 | 1.34704 | 0.673518 | − | 0.739171i | \(-0.264782\pi\) | ||||
0.673518 | + | 0.739171i | \(0.264782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19025 | 0.0421080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.54444 | + | 18.6045i | 0.301903 | + | 0.657358i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0420818 | + | 0.0728879i | 0.00148504 | + | 0.00257216i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.3622 | + | 0.549955i | −0.470957 | + | 0.0193834i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.52176 | − | 4.18145i | −0.229577 | − | 0.147194i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8553 | + | 14.9276i | 0.909024 | + | 0.524825i | 0.880117 | − | 0.474757i | \(-0.157464\pi\) |
0.0289068 | + | 0.999582i | \(0.490797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.4099i | − | 0.541114i | −0.962704 | − | 0.270557i | \(-0.912792\pi\) | ||
0.962704 | − | 0.270557i | \(-0.0872079\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.3147 | + | 25.7594i | 0.466967 | + | 0.903420i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.15139 | − | 7.19042i | 0.145417 | − | 0.251869i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.06892 | + | 0.617144i | −0.0373969 | + | 0.0215911i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.5907 | − | 28.6055i | −0.509840 | − | 0.999557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.0908 | + | 14.4862i | −0.875674 | + | 0.505570i | −0.869230 | − | 0.494409i | \(-0.835385\pi\) |
−0.00644422 | + | 0.999979i | \(0.502051\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.58962 | + | 6.21741i | −0.125126 | + | 0.216725i | −0.921782 | − | 0.387708i | \(-0.873267\pi\) |
0.796656 | + | 0.604433i | \(0.206600\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.68419 | + | 5.19298i | 0.0934513 | + | 0.180796i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37.6512i | − | 1.30926i | −0.755949 | − | 0.654630i | \(-0.772824\pi\) | ||
0.755949 | − | 0.654630i | \(-0.227176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.4385 | − | 25.0792i | −1.50868 | − | 0.871038i | −0.999949 | − | 0.0101139i | \(-0.996781\pi\) |
−0.508733 | − | 0.860924i | \(-0.669886\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.48995 | − | 0.955286i | −0.0516857 | − | 0.0331385i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.414330 | − | 0.598065i | −0.0143557 | − | 0.0207217i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.882803 | + | 1.52906i | 0.0305506 | + | 0.0529153i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.2291 | − | 32.2938i | 0.872047 | − | 1.11624i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2849 | −0.355073 | −0.177536 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177536 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.27275 | 0.147336 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1278 | + | 1.12354i | 0.831006 | + | 0.0386967i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.39910 | − | 11.0836i | −0.220136 | − | 0.381286i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.4818 | + | 13.3460i | 0.875566 | + | 0.458575i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1545 | − | 23.6362i | 0.520100 | − | 0.811193i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.5698 | + | 7.25719i | 0.430888 | + | 0.248773i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.0278i | − | 0.993891i | −0.867782 | − | 0.496946i | \(-0.834455\pi\) | ||
0.867782 | − | 0.496946i | \(-0.165545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.8348 | − | 16.1872i | −0.780933 | − | 0.553591i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.98887 | + | 13.8371i | −0.272895 | + | 0.472668i | −0.969602 | − | 0.244688i | \(-0.921314\pi\) |
0.696707 | + | 0.717356i | \(0.254648\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.98253 | − | 2.87666i | 0.170002 | − | 0.0981505i | −0.412585 | − | 0.910919i | \(-0.635374\pi\) |
0.582587 | + | 0.812769i | \(0.302041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.9700 | + | 24.5012i | 0.476096 | + | 0.835000i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.7735 | + | 6.22006i | −0.366733 | + | 0.211733i | −0.672030 | − | 0.740524i | \(-0.734578\pi\) |
0.305297 | + | 0.952257i | \(0.401244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.5798 | − | 30.4492i | 0.597733 | − | 1.03530i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.1406 | + | 13.5118i | −0.887781 | + | 0.458883i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.15268i | − | 0.0391019i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.41612 | − | 5.43640i | −0.319053 | − | 0.184205i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.43367 | − | 15.3605i | 0.0485223 | − | 0.519875i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 37.7331 | − | 23.9062i | 1.27561 | − | 0.808179i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.9672 | + | 38.0484i | 0.741781 | + | 1.28480i | 0.951684 | + | 0.307080i | \(0.0993521\pi\) |
−0.209902 | + | 0.977722i | \(0.567315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.54744 | + | 33.2310i | −0.0521937 | + | 1.12085i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.0805 | −1.72095 | −0.860473 | − | 0.509496i | \(-0.829832\pi\) | ||||
−0.860473 | + | 0.509496i | \(0.829832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3823 | 1.15706 | 0.578529 | − | 0.815662i | \(-0.303627\pi\) | ||||
0.578529 | + | 0.815662i | \(0.303627\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.31085 | + | 49.6253i | −0.0776784 | + | 1.66813i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8829 | + | 36.1703i | 0.701180 | + | 1.21448i | 0.968053 | + | 0.250748i | \(0.0806764\pi\) |
−0.266873 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.8751 | − | 18.2942i | 0.968440 | − | 0.613567i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.44008 | − | 2.09617i | −0.0817459 | − | 0.0702243i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3477 | + | 14.0572i | 0.814765 | + | 0.470405i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.77140i | 0.259769i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.27965 | − | 4.27965i | 0.276449 | − | 0.142893i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.6089 | + | 33.9636i | −0.653993 | + | 1.13275i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.528153 | + | 0.304929i | −0.0175953 | + | 0.0101587i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.14116 | + | 2.00142i | 0.0379754 | + | 0.0666031i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 57.9883 | − | 33.4795i | 1.92760 | − | 1.11290i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9839 | + | 32.8811i | −0.630350 | + | 1.09180i | 0.357130 | + | 0.934055i | \(0.383755\pi\) |
−0.987480 | + | 0.157744i | \(0.949578\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.3424 | + | 31.5176i | −0.741049 | + | 1.04537i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.0007i | 1.82225i | 0.412127 | + | 0.911126i | \(0.364786\pi\) | ||||
−0.412127 | + | 0.911126i | \(0.635214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.80983 | + | 1.62226i | 0.0929918 | + | 0.0536888i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −33.6596 | + | 52.4985i | −1.11275 | + | 1.73555i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4868 | − | 6.53991i | −0.412349 | − | 0.215967i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.5889 | + | 23.5367i | 0.448256 | + | 0.776403i | 0.998273 | − | 0.0587510i | \(-0.0187118\pi\) |
−0.550016 | + | 0.835154i | \(0.685378\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.831347 | − | 0.0387125i | −0.0273938 | − | 0.00127562i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.4236 | −0.770996 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −103.041 | −3.38798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.3659 | − | 7.05706i | 0.504683 | − | 0.231784i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.982860 | + | 1.70236i | 0.0322466 | + | 0.0558527i | 0.881698 | − | 0.471814i | \(-0.156400\pi\) |
−0.849452 | + | 0.527666i | \(0.823067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.41222 | − | 17.1273i | −0.0462838 | − | 0.561326i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.6085 | + | 8.72511i | 0.445521 | + | 0.285647i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.122267 | − | 0.0705911i | −0.00399857 | − | 0.00230858i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 31.0157i | − | 1.01324i | −0.862170 | − | 0.506620i | \(-0.830895\pi\) | ||
0.862170 | − | 0.506620i | \(-0.169105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2479 | + | 27.5648i | 0.464963 | + | 0.899544i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7914 | + | 29.0836i | −0.547384 | + | 0.948097i | 0.451069 | + | 0.892489i | \(0.351043\pi\) |
−0.998453 | + | 0.0556078i | \(0.982290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.08940 | + | 4.09307i | −0.230863 | + | 0.133289i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30.4444 | + | 42.4592i | −0.990355 | + | 1.38120i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.89077 | − | 5.13309i | 0.288911 | − | 0.166803i | −0.348539 | − | 0.937294i | \(-0.613322\pi\) |
0.637451 | + | 0.770491i | \(0.279989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.476325 | + | 0.825019i | −0.0154622 | + | 0.0267813i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.7494 | − | 34.3389i | −0.575563 | − | 1.11352i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.00920i | − | 0.0326911i | −0.999866 | − | 0.0163455i | \(-0.994797\pi\) | ||
0.999866 | − | 0.0163455i | \(-0.00520318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −74.0347 | − | 42.7439i | −2.39571 | − | 1.38316i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.59154 | + | 1.66157i | 0.0837725 | + | 0.0537110i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.3509 | + | 0.549486i | −0.431122 | + | 0.0177438i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5999 | + | 27.0199i | 0.503224 | + | 0.871610i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0108 | + | 11.0274i | −0.773737 | + | 0.355352i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.6341 | −1.17929 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.83020 | −0.0588552 | −0.0294276 | − | 0.999567i | \(-0.509368\pi\) | ||||
−0.0294276 | + | 0.999567i | \(0.509368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.441497 | + | 0.0205588i | 0.0141829 | + | 0.000660442i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.28478 | + | 12.6176i | 0.233780 | + | 0.404918i | 0.958917 | − | 0.283686i | \(-0.0915572\pi\) |
−0.725138 | + | 0.688604i | \(0.758224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.1110 | + | 47.5264i | 0.965313 | + | 1.52363i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.7133 | + | 55.7016i | −1.14374 | + | 1.78388i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.93615 | − | 3.42724i | −0.189914 | − | 0.109647i | 0.402028 | − | 0.915627i | \(-0.368305\pi\) |
−0.591942 | + | 0.805980i | \(0.701639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.43916i | 0.0779559i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.76780 | + | 10.9578i | −0.248007 | + | 0.349855i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.5934 | − | 51.2573i | 0.943883 | − | 1.63485i | 0.185910 | − | 0.982567i | \(-0.440477\pi\) |
0.757973 | − | 0.652286i | \(-0.226190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.6020 | + | 29.2151i | −1.61231 | + | 0.930870i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.4838 | − | 45.3046i | 0.842987 | − | 1.44206i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.579108 | + | 0.334348i | −0.0184146 | + | 0.0106317i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.2143 | − | 48.8686i | 0.896256 | − | 1.55236i | 0.0640132 | − | 0.997949i | \(-0.479610\pi\) |
0.832243 | − | 0.554412i | \(-0.187057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.7216 | + | 11.2276i | −0.689313 | + | 0.356297i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4199i | 0.552249i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.5831 | − | 26.3174i | −1.44363 | − | 0.833480i | −0.445541 | − | 0.895262i | \(-0.646988\pi\) |
−0.998090 | + | 0.0617814i | \(0.980322\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 52.5733 | − | 21.2427i | 1.66334 | − | 0.672091i |
(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 | 336.2.bc.f.17.5 | 16 | ||
3.2 | odd | 2 | inner | 336.2.bc.f.17.7 | 16 | ||
4.3 | odd | 2 | 168.2.u.a.17.4 | yes | 16 | ||
7.3 | odd | 6 | 2352.2.k.i.881.2 | 16 | |||
7.4 | even | 3 | 2352.2.k.i.881.15 | 16 | |||
7.5 | odd | 6 | inner | 336.2.bc.f.257.7 | 16 | ||
12.11 | even | 2 | 168.2.u.a.17.2 | ✓ | 16 | ||
21.5 | even | 6 | inner | 336.2.bc.f.257.5 | 16 | ||
21.11 | odd | 6 | 2352.2.k.i.881.1 | 16 | |||
21.17 | even | 6 | 2352.2.k.i.881.16 | 16 | |||
28.3 | even | 6 | 1176.2.k.a.881.15 | 16 | |||
28.11 | odd | 6 | 1176.2.k.a.881.2 | 16 | |||
28.19 | even | 6 | 168.2.u.a.89.2 | yes | 16 | ||
28.23 | odd | 6 | 1176.2.u.b.1097.7 | 16 | |||
28.27 | even | 2 | 1176.2.u.b.521.5 | 16 | |||
84.11 | even | 6 | 1176.2.k.a.881.16 | 16 | |||
84.23 | even | 6 | 1176.2.u.b.1097.5 | 16 | |||
84.47 | odd | 6 | 168.2.u.a.89.4 | yes | 16 | ||
84.59 | odd | 6 | 1176.2.k.a.881.1 | 16 | |||
84.83 | odd | 2 | 1176.2.u.b.521.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.2 | ✓ | 16 | 12.11 | even | 2 | ||
168.2.u.a.17.4 | yes | 16 | 4.3 | odd | 2 | ||
168.2.u.a.89.2 | yes | 16 | 28.19 | even | 6 | ||
168.2.u.a.89.4 | yes | 16 | 84.47 | odd | 6 | ||
336.2.bc.f.17.5 | 16 | 1.1 | even | 1 | trivial | ||
336.2.bc.f.17.7 | 16 | 3.2 | odd | 2 | inner | ||
336.2.bc.f.257.5 | 16 | 21.5 | even | 6 | inner | ||
336.2.bc.f.257.7 | 16 | 7.5 | odd | 6 | inner | ||
1176.2.k.a.881.1 | 16 | 84.59 | odd | 6 | |||
1176.2.k.a.881.2 | 16 | 28.11 | odd | 6 | |||
1176.2.k.a.881.15 | 16 | 28.3 | even | 6 | |||
1176.2.k.a.881.16 | 16 | 84.11 | even | 6 | |||
1176.2.u.b.521.5 | 16 | 28.27 | even | 2 | |||
1176.2.u.b.521.7 | 16 | 84.83 | odd | 2 | |||
1176.2.u.b.1097.5 | 16 | 84.23 | even | 6 | |||
1176.2.u.b.1097.7 | 16 | 28.23 | odd | 6 | |||
2352.2.k.i.881.1 | 16 | 21.11 | odd | 6 | |||
2352.2.k.i.881.2 | 16 | 7.3 | odd | 6 | |||
2352.2.k.i.881.15 | 16 | 7.4 | even | 3 | |||
2352.2.k.i.881.16 | 16 | 21.17 | even | 6 |