Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [297,2,Mod(82,297)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(297, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("297.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.f (of order \(5\), degree \(4\), 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: | \(2.37155694003\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 35x^{12} + 108x^{10} + 589x^{8} + 792x^{6} + 465x^{4} + 22x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 190.4 | ||
Root | \(0.723396 - 2.22638i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 297.190 |
Dual form | 297.2.f.c.136.4 |
$q$-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 \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(244\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89387 | − | 1.37598i | 1.33917 | − | 0.972965i | 0.339697 | − | 0.940535i | \(-0.389675\pi\) |
0.999474 | − | 0.0324303i | \(-0.0103247\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.07540 | − | 3.30976i | 0.537702 | − | 1.65488i | ||||
\(5\) | −2.90288 | − | 2.10907i | −1.29821 | − | 0.943204i | −0.298273 | − | 0.954481i | \(-0.596411\pi\) |
−0.999936 | + | 0.0112765i | \(0.996411\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.355620 | − | 1.09448i | 0.134412 | − | 0.413676i | −0.861086 | − | 0.508459i | \(-0.830215\pi\) |
0.995498 | + | 0.0947823i | \(0.0302155\pi\) | |||||||
\(8\) | −1.07069 | − | 3.29523i | −0.378544 | − | 1.16504i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.39974 | −2.65623 | ||||||||
\(11\) | −1.63261 | + | 2.88697i | −0.492251 | + | 0.870453i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.13089 | − | 3.72781i | 1.42305 | − | 1.03391i | 0.431795 | − | 0.901972i | \(-0.357880\pi\) |
0.991258 | − | 0.131937i | \(-0.0421197\pi\) | |||||||
\(14\) | −0.832490 | − | 2.56214i | −0.222492 | − | 0.684761i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.931024 | − | 0.676429i | −0.232756 | − | 0.169107i | ||||
\(17\) | 3.16415 | + | 2.29889i | 0.767418 | + | 0.557562i | 0.901177 | − | 0.433452i | \(-0.142705\pi\) |
−0.133758 | + | 0.991014i | \(0.542705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.457371 | + | 1.40764i | 0.104928 | + | 0.322935i | 0.989714 | − | 0.143063i | \(-0.0456952\pi\) |
−0.884786 | + | 0.465998i | \(0.845695\pi\) | |||||||
\(20\) | −10.1023 | + | 7.33973i | −2.25894 | + | 1.64121i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.880448 | + | 7.71399i | 0.187712 | + | 1.64463i | ||||
\(23\) | −1.24720 | −0.260060 | −0.130030 | − | 0.991510i | \(-0.541507\pi\) | ||||
−0.130030 | + | 0.991510i | \(0.541507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.43348 | + | 7.48948i | 0.486696 | + | 1.49790i | ||||
\(26\) | 4.58787 | − | 14.1200i | 0.899755 | − | 2.76916i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.24004 | − | 2.35403i | −0.612310 | − | 0.444869i | ||||
\(29\) | 1.74091 | − | 5.35798i | 0.323280 | − | 0.994952i | −0.648932 | − | 0.760847i | \(-0.724784\pi\) |
0.972211 | − | 0.234105i | \(-0.0752161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.60209 | − | 1.89053i | 0.467349 | − | 0.339549i | −0.329058 | − | 0.944310i | \(-0.606731\pi\) |
0.796407 | + | 0.604761i | \(0.206731\pi\) | |||||||
\(32\) | 4.23563 | 0.748760 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.15572 | 1.57019 | ||||||||
\(35\) | −3.34067 | + | 2.42714i | −0.564676 | + | 0.410261i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09812 | + | 9.53502i | −0.509327 | + | 1.56755i | 0.284045 | + | 0.958811i | \(0.408324\pi\) |
−0.793372 | + | 0.608737i | \(0.791676\pi\) | |||||||
\(38\) | 2.80309 | + | 2.03656i | 0.454721 | + | 0.330374i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.84179 | + | 11.8238i | −0.607441 | + | 1.86951i | ||||
\(41\) | −0.600044 | − | 1.84675i | −0.0937111 | − | 0.288413i | 0.893205 | − | 0.449651i | \(-0.148452\pi\) |
−0.986916 | + | 0.161237i | \(0.948452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.18338 | −1.40045 | −0.700226 | − | 0.713921i | \(-0.746917\pi\) | ||||
−0.700226 | + | 0.713921i | \(0.746917\pi\) | |||||||
\(44\) | 7.79944 | + | 8.50820i | 1.17581 | + | 1.28266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.36205 | + | 1.71613i | −0.348265 | + | 0.253029i | ||||
\(47\) | 0.0767256 | + | 0.236137i | 0.0111916 | + | 0.0344441i | 0.956496 | − | 0.291744i | \(-0.0942356\pi\) |
−0.945305 | + | 0.326188i | \(0.894236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.59169 | + | 3.33606i | 0.655955 | + | 0.476579i | ||||
\(50\) | 14.9141 | + | 10.8357i | 2.10917 | + | 1.53240i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.82036 | − | 20.9909i | −0.945813 | − | 2.91091i | ||||
\(53\) | −4.71073 | + | 3.42255i | −0.647069 | + | 0.470123i | −0.862271 | − | 0.506446i | \(-0.830959\pi\) |
0.215203 | + | 0.976569i | \(0.430959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8281 | − | 4.93724i | 1.46006 | − | 0.665737i | ||||
\(56\) | −3.98734 | −0.532830 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.07540 | − | 12.5428i | −0.535127 | − | 1.64695i | ||||
\(59\) | −2.04158 | + | 6.28333i | −0.265791 | + | 0.818020i | 0.725719 | + | 0.687991i | \(0.241507\pi\) |
−0.991510 | + | 0.130029i | \(0.958493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.66709 | + | 1.93776i | 0.341486 | + | 0.248104i | 0.745289 | − | 0.666742i | \(-0.232312\pi\) |
−0.403802 | + | 0.914846i | \(0.632312\pi\) | |||||||
\(62\) | 2.32670 | − | 7.16085i | 0.295491 | − | 0.909429i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.88379 | − | 7.18099i | 1.23547 | − | 0.897624i | ||||
\(65\) | −22.7566 | −2.82261 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0761 | −1.71966 | −0.859832 | − | 0.510578i | \(-0.829432\pi\) | ||||
−0.859832 | + | 0.510578i | \(0.829432\pi\) | |||||||
\(68\) | 11.0115 | − | 8.00032i | 1.33534 | − | 0.970181i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.98711 | + | 9.19338i | −0.357028 | + | 1.09882i | ||||
\(71\) | −4.25711 | − | 3.09297i | −0.505226 | − | 0.367068i | 0.305784 | − | 0.952101i | \(-0.401082\pi\) |
−0.811009 | + | 0.585033i | \(0.801082\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.683585 | − | 2.10386i | 0.0800075 | − | 0.246238i | −0.903050 | − | 0.429536i | \(-0.858677\pi\) |
0.983057 | + | 0.183298i | \(0.0586773\pi\) | |||||||
\(74\) | 7.25256 | + | 22.3211i | 0.843093 | + | 2.59477i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.15081 | 0.590838 | ||||||||
\(77\) | 2.57915 | + | 2.81353i | 0.293922 | + | 0.320632i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.40070 | − | 1.74421i | 0.270100 | − | 0.196239i | −0.444488 | − | 0.895785i | \(-0.646614\pi\) |
0.714588 | + | 0.699546i | \(0.246614\pi\) | |||||||
\(80\) | 1.27602 | + | 3.92719i | 0.142663 | + | 0.439073i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.67749 | − | 2.67186i | −0.406111 | − | 0.295057i | ||||
\(83\) | 9.46937 | + | 6.87990i | 1.03940 | + | 0.755167i | 0.970168 | − | 0.242433i | \(-0.0779456\pi\) |
0.0692306 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.33664 | − | 13.3468i | −0.470375 | − | 1.44766i | ||||
\(86\) | −17.3922 | + | 12.6361i | −1.87544 | + | 1.36259i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11.2612 | + | 2.28880i | 1.20045 | + | 0.243987i | ||||
\(89\) | 8.93456 | 0.947061 | 0.473531 | − | 0.880777i | \(-0.342979\pi\) | ||||
0.473531 | + | 0.880777i | \(0.342979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.25539 | − | 6.94137i | −0.236429 | − | 0.727653i | ||||
\(92\) | −1.34125 | + | 4.12794i | −0.139835 | + | 0.430368i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.470228 | + | 0.341641i | 0.0485004 | + | 0.0352376i | ||||
\(95\) | 1.64112 | − | 5.05085i | 0.168375 | − | 0.518206i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.99937 | + | 5.81188i | −0.812213 | + | 0.590107i | −0.914471 | − | 0.404651i | \(-0.867393\pi\) |
0.102258 | + | 0.994758i | \(0.467393\pi\) | |||||||
\(98\) | 13.2864 | 1.34213 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 27.4053 | 2.74053 | ||||||||
\(101\) | 6.41432 | − | 4.66028i | 0.638249 | − | 0.463715i | −0.220999 | − | 0.975274i | \(-0.570932\pi\) |
0.859248 | + | 0.511559i | \(0.170932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.99754 | − | 6.14781i | 0.196824 | − | 0.605762i | −0.803127 | − | 0.595808i | \(-0.796832\pi\) |
0.999950 | − | 0.00995321i | \(-0.00316826\pi\) | |||||||
\(104\) | −17.7776 | − | 12.9162i | −1.74323 | − | 1.26653i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.21218 | + | 12.9637i | −0.409123 | + | 1.25915i | ||||
\(107\) | 1.91774 | + | 5.90218i | 0.185394 | + | 0.570586i | 0.999955 | − | 0.00949312i | \(-0.00302180\pi\) |
−0.814560 | + | 0.580079i | \(0.803022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.74313 | −0.166961 | −0.0834807 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834807 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(110\) | 13.7135 | − | 24.2498i | 1.30753 | − | 2.31212i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.07143 | + | 0.778440i | −0.101241 | + | 0.0735557i | ||||
\(113\) | −5.19116 | − | 15.9768i | −0.488344 | − | 1.50297i | −0.827079 | − | 0.562086i | \(-0.809999\pi\) |
0.338735 | − | 0.940882i | \(-0.390001\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.62049 | + | 2.63044i | 0.337612 | + | 0.245290i | ||||
\(116\) | −15.8614 | − | 11.5240i | −1.47270 | − | 1.06998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.77925 | + | 14.7090i | 0.439965 | + | 1.35407i | ||||
\(119\) | 3.64133 | − | 2.64558i | 0.333800 | − | 0.242520i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.66916 | − | 9.42659i | −0.515378 | − | 0.856963i | ||||
\(122\) | 7.71745 | 0.698705 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.45889 | − | 10.6454i | −0.310617 | − | 0.955982i | ||||
\(125\) | 3.18770 | − | 9.81075i | 0.285117 | − | 0.877500i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.79273 | − | 1.30250i | −0.159079 | − | 0.115578i | 0.505398 | − | 0.862886i | \(-0.331346\pi\) |
−0.664477 | + | 0.747308i | \(0.731346\pi\) | |||||||
\(128\) | 6.21999 | − | 19.1432i | 0.549775 | − | 1.69203i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −43.0981 | + | 31.3126i | −3.77996 | + | 2.74630i | ||||
\(131\) | −11.8297 | −1.03357 | −0.516784 | − | 0.856116i | \(-0.672871\pi\) | ||||
−0.516784 | + | 0.856116i | \(0.672871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70329 | 0.147694 | ||||||||
\(134\) | −26.6583 | + | 19.3684i | −2.30292 | + | 1.67317i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.18756 | − | 12.8880i | 0.359080 | − | 1.10513i | ||||
\(137\) | 13.7646 | + | 10.0006i | 1.17599 | + | 0.854406i | 0.991714 | − | 0.128469i | \(-0.0410062\pi\) |
0.184275 | + | 0.982875i | \(0.441006\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.16582 | + | 6.66569i | −0.183702 | + | 0.565377i | −0.999924 | − | 0.0123622i | \(-0.996065\pi\) |
0.816222 | + | 0.577739i | \(0.196065\pi\) | |||||||
\(140\) | 4.44066 | + | 13.6669i | 0.375304 | + | 1.15507i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.3183 | −1.03373 | ||||||||
\(143\) | 2.38531 | + | 20.8988i | 0.199470 | + | 1.74764i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.3540 | + | 11.8819i | −1.35813 | + | 0.986737i | ||||
\(146\) | −1.60024 | − | 4.92504i | −0.132437 | − | 0.407599i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.2269 | + | 20.5080i | 2.32023 | + | 1.68575i | ||||
\(149\) | −6.84488 | − | 4.97309i | −0.560754 | − | 0.407412i | 0.270981 | − | 0.962585i | \(-0.412652\pi\) |
−0.831735 | + | 0.555173i | \(0.812652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.74304 | + | 20.7530i | 0.548741 | + | 1.68885i | 0.711924 | + | 0.702256i | \(0.247824\pi\) |
−0.163183 | + | 0.986596i | \(0.552176\pi\) | |||||||
\(152\) | 4.14881 | − | 3.01428i | 0.336513 | − | 0.244491i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.75595 | + | 1.77961i | 0.705575 | + | 0.143405i | ||||
\(155\) | −11.5408 | −0.926981 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.60632 | − | 8.02144i | −0.208007 | − | 0.640181i | −0.999576 | − | 0.0291010i | \(-0.990736\pi\) |
0.791569 | − | 0.611080i | \(-0.209264\pi\) | |||||||
\(158\) | 2.14663 | − | 6.60664i | 0.170777 | − | 0.525596i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.2955 | − | 8.93322i | −0.972047 | − | 0.706233i | ||||
\(161\) | −0.443530 | + | 1.36505i | −0.0349551 | + | 0.107581i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.69987 | − | 3.41465i | 0.368122 | − | 0.267456i | −0.388310 | − | 0.921529i | \(-0.626941\pi\) |
0.756432 | + | 0.654073i | \(0.226941\pi\) | |||||||
\(164\) | −6.75757 | −0.527677 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.4004 | 2.12668 | ||||||||
\(167\) | −13.0668 | + | 9.49361i | −1.01114 | + | 0.734638i | −0.964448 | − | 0.264272i | \(-0.914868\pi\) |
−0.0466938 | + | 0.998909i | \(0.514868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.41225 | − | 25.8903i | 0.647096 | − | 1.99156i | ||||
\(170\) | −26.5780 | − | 19.3100i | −2.03844 | − | 1.48101i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.87584 | + | 30.3947i | −0.753026 | + | 2.31758i | ||||
\(173\) | −4.45601 | − | 13.7142i | −0.338784 | − | 1.04267i | −0.964828 | − | 0.262883i | \(-0.915327\pi\) |
0.626044 | − | 0.779788i | \(-0.284673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.06252 | 0.685062 | ||||||||
\(176\) | 3.47283 | − | 1.58349i | 0.261774 | − | 0.119360i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.9209 | − | 12.2938i | 1.26828 | − | 0.921457i | ||||
\(179\) | 1.34424 | + | 4.13714i | 0.100473 | + | 0.309224i | 0.988641 | − | 0.150294i | \(-0.0480220\pi\) |
−0.888168 | + | 0.459518i | \(0.848022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1278 | − | 8.81137i | −0.901453 | − | 0.654944i | 0.0373860 | − | 0.999301i | \(-0.488097\pi\) |
−0.938839 | + | 0.344357i | \(0.888097\pi\) | |||||||
\(182\) | −13.8226 | − | 10.0427i | −1.02460 | − | 0.744415i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.33536 | + | 4.10983i | 0.0984443 | + | 0.302980i | ||||
\(185\) | 29.1035 | − | 21.1449i | 2.13973 | − | 1.55461i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8026 | + | 5.38160i | −0.863094 | + | 0.393541i | ||||
\(188\) | 0.864067 | 0.0630185 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.84179 | − | 11.8238i | −0.278713 | − | 0.857790i | ||||
\(191\) | −3.83437 | + | 11.8010i | −0.277446 | + | 0.853890i | 0.711116 | + | 0.703074i | \(0.248190\pi\) |
−0.988562 | + | 0.150815i | \(0.951810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.36053 | + | 6.07428i | 0.601804 | + | 0.437236i | 0.846519 | − | 0.532359i | \(-0.178694\pi\) |
−0.244715 | + | 0.969595i | \(0.578694\pi\) | |||||||
\(194\) | −7.15277 | + | 22.0139i | −0.513539 | + | 1.58051i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.9795 | − | 11.6098i | 1.14139 | − | 0.829268i | ||||
\(197\) | −0.770815 | −0.0549183 | −0.0274591 | − | 0.999623i | \(-0.508742\pi\) | ||||
−0.0274591 | + | 0.999623i | \(0.508742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.63580 | −0.257735 | −0.128868 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128868 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(200\) | 22.0741 | − | 16.0378i | 1.56087 | − | 1.13404i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.73547 | − | 17.6520i | 0.403546 | − | 1.24199i | ||||
\(203\) | −5.24512 | − | 3.81081i | −0.368136 | − | 0.267466i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.15306 | + | 6.62642i | −0.150376 | + | 0.462809i | ||||
\(206\) | −4.67617 | − | 14.3918i | −0.325804 | − | 1.00272i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.29858 | −0.506066 | ||||||||
\(209\) | −4.81053 | − | 0.977719i | −0.332751 | − | 0.0676302i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8992 | + | 9.37181i | −0.888017 | + | 0.645182i | −0.935360 | − | 0.353697i | \(-0.884924\pi\) |
0.0473435 | + | 0.998879i | \(0.484924\pi\) | |||||||
\(212\) | 6.26185 | + | 19.2720i | 0.430066 | + | 1.32361i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.7532 | + | 8.53923i | 0.803435 | + | 0.583730i | ||||
\(215\) | 26.6583 | + | 19.3684i | 1.81808 | + | 1.32091i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.14380 | − | 3.52026i | −0.0776462 | − | 0.238971i | ||||
\(218\) | −3.30127 | + | 2.39851i | −0.223590 | + | 0.162448i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.69647 | − | 41.1479i | −0.316636 | − | 2.77419i | ||||
\(221\) | 24.8047 | 1.66855 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.77548 | − | 5.46437i | −0.118895 | − | 0.365921i | 0.873844 | − | 0.486206i | \(-0.161619\pi\) |
−0.992739 | + | 0.120284i | \(0.961619\pi\) | |||||||
\(224\) | 1.50627 | − | 4.63583i | 0.100642 | − | 0.309744i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.8151 | − | 23.1150i | −2.11631 | − | 1.53759i | ||||
\(227\) | 5.76936 | − | 17.7563i | 0.382926 | − | 1.17852i | −0.555048 | − | 0.831818i | \(-0.687300\pi\) |
0.937974 | − | 0.346706i | \(-0.112700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.38776 | − | 1.00827i | 0.0917060 | − | 0.0666283i | −0.540987 | − | 0.841031i | \(-0.681949\pi\) |
0.632693 | + | 0.774402i | \(0.281949\pi\) | |||||||
\(230\) | 10.4762 | 0.690779 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.5198 | −1.28153 | ||||||||
\(233\) | −5.81874 | + | 4.22756i | −0.381198 | + | 0.276957i | −0.761839 | − | 0.647766i | \(-0.775703\pi\) |
0.380641 | + | 0.924723i | \(0.375703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.275304 | − | 0.847298i | 0.0179588 | − | 0.0552716i | ||||
\(236\) | 18.6008 | + | 13.5142i | 1.21081 | + | 0.879702i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.25595 | − | 10.0208i | 0.211052 | − | 0.649552i | ||||
\(239\) | 2.97991 | + | 9.17123i | 0.192755 | + | 0.593237i | 0.999995 | + | 0.00301535i | \(0.000959817\pi\) |
−0.807241 | + | 0.590222i | \(0.799040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.97674 | 0.191748 | 0.0958742 | − | 0.995393i | \(-0.469435\pi\) | ||||
0.0958742 | + | 0.995393i | \(0.469435\pi\) | |||||||
\(242\) | −23.7075 | − | 10.0521i | −1.52397 | − | 0.646176i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.28170 | − | 6.74355i | 0.594200 | − | 0.431712i | ||||
\(245\) | −6.29316 | − | 19.3684i | −0.402056 | − | 1.23740i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.59414 | + | 5.51747i | 0.483204 | + | 0.351068i | ||||
\(248\) | −9.01575 | − | 6.55032i | −0.572501 | − | 0.415946i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.46228 | − | 22.9665i | −0.471956 | − | 1.45253i | ||||
\(251\) | 13.0518 | − | 9.48268i | 0.823821 | − | 0.598541i | −0.0939831 | − | 0.995574i | \(-0.529960\pi\) |
0.917805 | + | 0.397032i | \(0.129960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.03620 | − | 3.60064i | 0.128015 | − | 0.226370i | ||||
\(254\) | −5.18742 | −0.325488 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.01019 | − | 21.5752i | −0.438137 | − | 1.34845i | ||||
\(257\) | 1.32222 | − | 4.06939i | 0.0824781 | − | 0.253841i | −0.901310 | − | 0.433174i | \(-0.857394\pi\) |
0.983789 | + | 0.179332i | \(0.0573937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.33418 | + | 6.78168i | 0.579998 | + | 0.421393i | ||||
\(260\) | −24.4725 | + | 75.3188i | −1.51772 | + | 4.67107i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.4040 | + | 16.2775i | −1.38412 | + | 1.00563i | ||||
\(263\) | 26.8429 | 1.65521 | 0.827603 | − | 0.561314i | \(-0.189704\pi\) | ||||
0.827603 | + | 0.561314i | \(0.189704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.8931 | 1.28345 | ||||||||
\(266\) | 3.22582 | − | 2.34370i | 0.197788 | − | 0.143701i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.1375 | + | 46.5883i | −0.924667 | + | 2.84583i | ||||
\(269\) | −1.43046 | − | 1.03929i | −0.0872166 | − | 0.0633666i | 0.543322 | − | 0.839524i | \(-0.317166\pi\) |
−0.630539 | + | 0.776158i | \(0.717166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.99637 | + | 18.4549i | −0.364253 | + | 1.12106i | 0.586194 | + | 0.810171i | \(0.300626\pi\) |
−0.950447 | + | 0.310886i | \(0.899374\pi\) | |||||||
\(272\) | −1.39086 | − | 4.28064i | −0.0843335 | − | 0.259552i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.8290 | 2.40616 | ||||||||
\(275\) | −25.5948 | − | 5.20204i | −1.54343 | − | 0.313695i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.79710 | − | 2.03221i | 0.168061 | − | 0.122104i | −0.500575 | − | 0.865693i | \(-0.666878\pi\) |
0.668637 | + | 0.743589i | \(0.266878\pi\) | |||||||
\(278\) | 5.07008 | + | 15.6041i | 0.304083 | + | 0.935872i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.5748 | + | 8.40957i | 0.691725 | + | 0.502568i | ||||
\(281\) | 0.948127 | + | 0.688854i | 0.0565605 | + | 0.0410936i | 0.615706 | − | 0.787976i | \(-0.288871\pi\) |
−0.559146 | + | 0.829069i | \(0.688871\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.26884 | − | 3.90510i | −0.0754249 | − | 0.232134i | 0.906235 | − | 0.422774i | \(-0.138944\pi\) |
−0.981660 | + | 0.190640i | \(0.938944\pi\) | |||||||
\(284\) | −14.8151 | + | 10.7638i | −0.879113 | + | 0.638713i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 33.2738 | + | 36.2975i | 1.96752 | + | 2.14632i | ||||
\(287\) | −2.23462 | −0.131906 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.526346 | − | 1.61993i | −0.0309616 | − | 0.0952899i | ||||
\(290\) | −14.6232 | + | 45.0056i | −0.858705 | + | 2.64282i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.22812 | − | 4.52500i | −0.364473 | − | 0.264805i | ||||
\(293\) | −1.84922 | + | 5.69130i | −0.108032 | + | 0.332489i | −0.990430 | − | 0.138015i | \(-0.955928\pi\) |
0.882398 | + | 0.470504i | \(0.155928\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1784 | − | 13.9339i | 1.11661 | − | 0.811266i | ||||
\(296\) | 34.7372 | 2.01906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.8062 | −1.14734 | ||||||||
\(299\) | −6.39927 | + | 4.64934i | −0.370079 | + | 0.268878i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.26579 | + | 10.0511i | −0.188237 | + | 0.579334i | ||||
\(302\) | 41.3261 | + | 30.0252i | 2.37805 | + | 1.72776i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.526346 | − | 1.61993i | 0.0301880 | − | 0.0929092i | ||||
\(305\) | −3.65540 | − | 11.2502i | −0.209308 | − | 0.644182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.70930 | 0.268774 | 0.134387 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134387 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(308\) | 12.0857 | − | 5.51068i | 0.688648 | − | 0.314000i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.8569 | + | 15.8799i | −1.24139 | + | 0.901920i | ||||
\(311\) | 6.54171 | + | 20.1333i | 0.370947 | + | 1.14166i | 0.946173 | + | 0.323662i | \(0.104914\pi\) |
−0.575226 | + | 0.817994i | \(0.695086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.3590 | − | 12.6121i | −0.981189 | − | 0.712876i | −0.0232153 | − | 0.999730i | \(-0.507390\pi\) |
−0.957974 | + | 0.286855i | \(0.907390\pi\) | |||||||
\(314\) | −15.9734 | − | 11.6053i | −0.901431 | − | 0.654928i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.19119 | − | 9.82148i | −0.179519 | − | 0.552501i | ||||
\(317\) | 0.897839 | − | 0.652318i | 0.0504276 | − | 0.0366378i | −0.562286 | − | 0.826943i | \(-0.690078\pi\) |
0.612714 | + | 0.790305i | \(0.290078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.6261 | + | 13.7735i | 0.706925 | + | 0.771166i | ||||
\(320\) | −43.8367 | −2.45055 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.03829 | + | 3.19551i | 0.0578614 | + | 0.178079i | ||||
\(323\) | −1.78882 | + | 5.50543i | −0.0995328 | + | 0.306330i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.4053 | + | 29.3562i | 2.24128 | + | 1.62839i | ||||
\(326\) | 4.20246 | − | 12.9339i | 0.232753 | − | 0.716340i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.44300 | + | 3.95457i | −0.300539 | + | 0.218354i | ||||
\(329\) | 0.285733 | 0.0157530 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.93868 | −0.326420 | −0.163210 | − | 0.986591i | \(-0.552185\pi\) | ||||
−0.163210 | + | 0.986591i | \(0.552185\pi\) | |||||||
\(332\) | 32.9542 | − | 23.9426i | 1.80860 | − | 1.31402i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.6839 | + | 35.9594i | −0.639316 | + | 1.96761i | ||||
\(335\) | 40.8611 | + | 29.6874i | 2.23248 | + | 1.62199i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.58204 | + | 29.4905i | −0.521967 | + | 1.60645i | 0.248269 | + | 0.968691i | \(0.420138\pi\) |
−0.770236 | + | 0.637759i | \(0.779862\pi\) | |||||||
\(338\) | −19.6927 | − | 60.6080i | −1.07114 | − | 3.29664i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −48.8383 | −2.64863 | ||||||||
\(341\) | 1.20969 | + | 10.5986i | 0.0655085 | + | 0.573949i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.8013 | − | 8.57417i | 0.637212 | − | 0.462961i | ||||
\(344\) | 9.83250 | + | 30.2613i | 0.530133 | + | 1.63158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.3096 | − | 19.8416i | −1.46817 | − | 1.06669i | ||||
\(347\) | −20.0950 | − | 14.5998i | −1.07875 | − | 0.783761i | −0.101289 | − | 0.994857i | \(-0.532297\pi\) |
−0.977465 | + | 0.211096i | \(0.932297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.73395 | − | 11.4919i | −0.199874 | − | 0.615148i | −0.999885 | − | 0.0151633i | \(-0.995173\pi\) |
0.800011 | − | 0.599985i | \(-0.204827\pi\) | |||||||
\(350\) | 17.1633 | − | 12.4698i | 0.917415 | − | 0.666541i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.91513 | + | 12.2281i | −0.368578 | + | 0.651760i | ||||
\(353\) | −8.73656 | −0.465000 | −0.232500 | − | 0.972596i | \(-0.574691\pi\) | ||||
−0.232500 | + | 0.972596i | \(0.574691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.83460 | + | 17.9571i | 0.309669 | + | 0.953062i | ||||
\(356\) | 9.60826 | − | 29.5712i | 0.509237 | − | 1.56727i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.23844 | + | 5.98558i | 0.435415 | + | 0.316348i | ||||
\(359\) | 4.65359 | − | 14.3223i | 0.245607 | − | 0.755901i | −0.749929 | − | 0.661518i | \(-0.769912\pi\) |
0.995536 | − | 0.0943824i | \(-0.0300876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.5991 | − | 9.88029i | 0.715740 | − | 0.520015i | ||||
\(362\) | −35.0928 | −1.84444 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −25.3997 | −1.33130 | ||||||||
\(365\) | −6.42155 | + | 4.66553i | −0.336119 | + | 0.244205i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.40104 | − | 19.7004i | 0.334132 | − | 1.02835i | −0.633016 | − | 0.774138i | \(-0.718183\pi\) |
0.967148 | − | 0.254213i | \(-0.0818166\pi\) | |||||||
\(368\) | 1.16118 | + | 0.843645i | 0.0605306 | + | 0.0439780i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.0234 | − | 80.0917i | 1.35289 | − | 4.16377i | ||||
\(371\) | 2.07070 | + | 6.37295i | 0.107505 | + | 0.330867i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0439 | −0.623610 | −0.311805 | − | 0.950146i | \(-0.600934\pi\) | ||||
−0.311805 | + | 0.950146i | \(0.600934\pi\) | |||||||
\(374\) | −14.9477 | + | 26.4323i | −0.772929 | + | 1.36678i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.695977 | − | 0.505657i | 0.0358923 | − | 0.0260773i | ||||
\(377\) | −11.0411 | − | 33.9810i | −0.568646 | − | 1.75011i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.75138 | + | 6.35825i | 0.449528 | + | 0.326601i | 0.789409 | − | 0.613867i | \(-0.210387\pi\) |
−0.339881 | + | 0.940468i | \(0.610387\pi\) | |||||||
\(380\) | −14.9522 | − | 10.8634i | −0.767032 | − | 0.557281i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.97611 | + | 27.6256i | 0.459258 | + | 1.41345i | ||||
\(383\) | 24.8994 | − | 18.0905i | 1.27230 | − | 0.924381i | 0.273010 | − | 0.962011i | \(-0.411981\pi\) |
0.999292 | + | 0.0376296i | \(0.0119807\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.55305 | − | 13.6070i | −0.0791508 | − | 0.693475i | ||||
\(386\) | 24.1919 | 1.23133 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.6333 | + | 32.7261i | 0.539826 | + | 1.66141i | ||||
\(389\) | −0.416722 | + | 1.28254i | −0.0211287 | + | 0.0650273i | −0.961065 | − | 0.276323i | \(-0.910884\pi\) |
0.939936 | + | 0.341350i | \(0.110884\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.94634 | − | 2.86718i | −0.199575 | − | 0.145000i | ||||
\(392\) | 6.07682 | − | 18.7025i | 0.306926 | − | 0.944621i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.45983 | + | 1.06063i | −0.0735450 | + | 0.0534336i | ||||
\(395\) | −10.6476 | −0.535741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.13262 | −0.0568446 | −0.0284223 | − | 0.999596i | \(-0.509048\pi\) | ||||
−0.0284223 | + | 0.999596i | \(0.509048\pi\) | |||||||
\(398\) | −6.88575 | + | 5.00279i | −0.345152 | + | 0.250767i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.80047 | − | 8.61896i | 0.140024 | − | 0.430948i | ||||
\(401\) | 26.7475 | + | 19.4332i | 1.33571 | + | 0.970447i | 0.999590 | + | 0.0286260i | \(0.00911319\pi\) |
0.336115 | + | 0.941821i | \(0.390887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.30351 | − | 19.4002i | 0.314000 | − | 0.966393i | ||||
\(404\) | −8.52638 | − | 26.2415i | −0.424203 | − | 1.30556i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.1772 | −0.753232 | ||||||||
\(407\) | −22.4693 | − | 24.5111i | −1.11376 | − | 1.21497i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.28288 | − | 0.932067i | 0.0634343 | − | 0.0460877i | −0.555616 | − | 0.831439i | \(-0.687518\pi\) |
0.619051 | + | 0.785351i | \(0.287518\pi\) | |||||||
\(410\) | 5.04021 | + | 15.5122i | 0.248918 | + | 0.766092i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.1996 | − | 13.2228i | −0.896629 | − | 0.651439i | ||||
\(413\) | 6.15098 | + | 4.46895i | 0.302670 | + | 0.219903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.9783 | − | 39.9431i | −0.637080 | − | 1.96073i | ||||
\(416\) | 21.7325 | − | 15.7896i | 1.06553 | − | 0.774149i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.4559 | + | 4.76751i | −0.511412 | + | 0.233187i | ||||
\(419\) | −3.23928 | −0.158249 | −0.0791245 | − | 0.996865i | \(-0.525212\pi\) | ||||
−0.0791245 | + | 0.996865i | \(0.525212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3884 | + | 35.0499i | 0.555036 | + | 1.70823i | 0.695847 | + | 0.718190i | \(0.255029\pi\) |
−0.140811 | + | 0.990037i | \(0.544971\pi\) | |||||||
\(422\) | −11.5340 | + | 35.4981i | −0.561467 | + | 1.72802i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.3218 | + | 11.8585i | 0.792656 | + | 0.575899i | ||||
\(425\) | −9.51758 | + | 29.2921i | −0.461671 | + | 1.42088i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.06931 | − | 2.22999i | 0.148535 | − | 0.107917i | ||||
\(428\) | 21.5971 | 1.04394 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 77.1379 | 3.71992 | ||||||||
\(431\) | 4.37531 | − | 3.17885i | 0.210751 | − | 0.153120i | −0.477402 | − | 0.878685i | \(-0.658422\pi\) |
0.688154 | + | 0.725565i | \(0.258422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.71285 | − | 29.8931i | 0.466770 | − | 1.43657i | −0.389973 | − | 0.920826i | \(-0.627516\pi\) |
0.856743 | − | 0.515744i | \(-0.172484\pi\) | |||||||
\(434\) | −7.01002 | − | 5.09308i | −0.336492 | − | 0.244476i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.87457 | + | 5.76933i | −0.0897755 | + | 0.276301i | ||||
\(437\) | −0.570435 | − | 1.75562i | −0.0272876 | − | 0.0839826i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8081 | −1.27948 | −0.639740 | − | 0.768591i | \(-0.720958\pi\) | ||||
−0.639740 | + | 0.768591i | \(0.720958\pi\) | |||||||
\(440\) | −27.8628 | − | 30.3948i | −1.32831 | − | 1.44902i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 46.9770 | − | 34.1308i | 2.23447 | − | 1.62344i | ||||
\(443\) | −5.89130 | − | 18.1316i | −0.279904 | − | 0.861457i | −0.987880 | − | 0.155220i | \(-0.950391\pi\) |
0.707976 | − | 0.706237i | \(-0.249609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.9360 | − | 18.8436i | −1.22948 | − | 0.893272i | ||||
\(446\) | −10.8814 | − | 7.90580i | −0.515249 | − | 0.374351i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.34462 | − | 13.3714i | −0.205264 | − | 0.631737i | ||||
\(449\) | −22.4771 | + | 16.3306i | −1.06076 | + | 0.770687i | −0.974229 | − | 0.225562i | \(-0.927578\pi\) |
−0.0865311 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.31113 | + | 1.28271i | 0.297180 | + | 0.0604005i | ||||
\(452\) | −58.4618 | −2.74981 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.5058 | − | 41.5666i | −0.633859 | − | 1.95082i | ||||
\(455\) | −8.09269 | + | 24.9067i | −0.379391 | + | 1.16765i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.1643 | − | 11.0175i | −0.709354 | − | 0.515376i | 0.173611 | − | 0.984814i | \(-0.444456\pi\) |
−0.882965 | + | 0.469438i | \(0.844456\pi\) | |||||||
\(458\) | 1.24089 | − | 3.81907i | 0.0579831 | − | 0.178454i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.5996 | − | 9.15415i | 0.587459 | − | 0.426814i | ||||
\(461\) | −18.1064 | −0.843297 | −0.421649 | − | 0.906759i | \(-0.638548\pi\) | ||||
−0.421649 | + | 0.906759i | \(0.638548\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.5770 | −1.14219 | −0.571096 | − | 0.820883i | \(-0.693482\pi\) | ||||
−0.571096 | + | 0.820883i | \(0.693482\pi\) | |||||||
\(464\) | −5.24512 | + | 3.81081i | −0.243499 | + | 0.176912i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.20292 | + | 16.0129i | −0.241021 | + | 0.741786i | ||||
\(467\) | −12.5464 | − | 9.11548i | −0.580578 | − | 0.421814i | 0.258355 | − | 0.966050i | \(-0.416820\pi\) |
−0.838932 | + | 0.544236i | \(0.816820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00572 | + | 15.4060i | −0.231143 | + | 0.711384i | ||||
\(470\) | −0.644474 | − | 1.98349i | −0.0297274 | − | 0.0914915i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.8909 | 1.05364 | ||||||||
\(473\) | 14.9929 | − | 26.5121i | 0.689374 | − | 1.21903i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.42951 | + | 6.85094i | −0.432655 | + | 0.314343i | ||||
\(476\) | −4.84032 | − | 14.8970i | −0.221856 | − | 0.682802i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.2630 | + | 13.2689i | 0.835331 | + | 0.606903i | ||||
\(479\) | 7.79546 | + | 5.66373i | 0.356184 | + | 0.258783i | 0.751459 | − | 0.659780i | \(-0.229351\pi\) |
−0.395275 | + | 0.918563i | \(0.629351\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.6487 | + | 60.4724i | 0.895902 | + | 2.75730i | ||||
\(482\) | 5.63756 | − | 4.09593i | 0.256784 | − | 0.186564i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.2964 | + | 8.62612i | −1.69529 | + | 0.392097i | ||||
\(485\) | 35.4789 | 1.61101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6077 | + | 32.6472i | 0.480681 | + | 1.47938i | 0.838140 | + | 0.545456i | \(0.183643\pi\) |
−0.357458 | + | 0.933929i | \(0.616357\pi\) | |||||||
\(488\) | 3.52974 | − | 10.8634i | 0.159784 | − | 0.491763i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −38.5690 | − | 28.0220i | −1.74237 | − | 1.26590i | ||||
\(491\) | −5.41835 | + | 16.6760i | −0.244527 | + | 0.752576i | 0.751187 | + | 0.660089i | \(0.229482\pi\) |
−0.995714 | + | 0.0924868i | \(0.970518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8259 | − | 12.9513i | 0.802838 | − | 0.583296i | ||||
\(494\) | 21.9743 | 0.988670 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.70142 | −0.166199 | ||||||||
\(497\) | −4.89912 | + | 3.55942i | −0.219755 | + | 0.159662i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.45891 | − | 22.9562i | 0.333907 | − | 1.02766i | −0.633352 | − | 0.773864i | \(-0.718321\pi\) |
0.967258 | − | 0.253795i | \(-0.0816787\pi\) | |||||||
\(500\) | −29.0431 | − | 21.1010i | −1.29885 | − | 0.943667i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.6705 | − | 35.9180i | 0.520878 | − | 1.60310i | ||||
\(503\) | 6.51381 | + | 20.0474i | 0.290436 | + | 0.893872i | 0.984716 | + | 0.174166i | \(0.0557230\pi\) |
−0.694280 | + | 0.719705i | \(0.744277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.4489 | −1.26596 | ||||||||
\(506\) | −1.09810 | − | 9.62093i | −0.0488165 | − | 0.427702i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.23886 | + | 4.53280i | −0.276805 | + | 0.201110i | ||||
\(509\) | −10.1551 | − | 31.2543i | −0.450119 | − | 1.38532i | −0.876771 | − | 0.480907i | \(-0.840307\pi\) |
0.426653 | − | 0.904416i | \(-0.359693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.05954 | − | 1.49635i | −0.0911088 | − | 0.0661944i | ||||
\(512\) | −10.3951 | − | 7.55249i | −0.459404 | − | 0.333776i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.09527 | − | 9.52626i | −0.136527 | − | 0.420186i | ||||
\(515\) | −18.7648 | + | 13.6334i | −0.826876 | + | 0.600760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.806983 | − | 0.164016i | −0.0354911 | − | 0.00721341i | ||||
\(518\) | 27.0092 | 1.18672 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.3652 | + | 74.9882i | 1.06848 | + | 3.28845i | ||||
\(521\) | 7.10565 | − | 21.8689i | 0.311304 | − | 0.958096i | −0.665945 | − | 0.746001i | \(-0.731971\pi\) |
0.977249 | − | 0.212095i | \(-0.0680286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.7327 | − | 16.5163i | −0.994031 | − | 0.722206i | −0.0332309 | − | 0.999448i | \(-0.510580\pi\) |
−0.960800 | + | 0.277242i | \(0.910580\pi\) | |||||||
\(524\) | −12.7217 | + | 39.1535i | −0.555752 | + | 1.71043i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 50.8371 | − | 36.9353i | 2.21660 | − | 1.61046i | ||||
\(527\) | 12.5795 | 0.547972 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4445 | −0.932369 | ||||||||
\(530\) | 39.5689 | − | 28.7485i | 1.71876 | − | 1.24875i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.83173 | − | 5.63748i | 0.0794155 | − | 0.244416i | ||||
\(533\) | −9.96308 | − | 7.23860i | −0.431549 | − | 0.313539i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.88115 | − | 21.1780i | 0.297498 | − | 0.915604i | ||||
\(536\) | 15.0710 | + | 46.3838i | 0.650969 | + | 2.00348i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.13915 | −0.178451 | ||||||||
\(539\) | −17.1275 | + | 7.80957i | −0.737735 | + | 0.336382i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2202 | − | 7.42539i | 0.439400 | − | 0.319243i | −0.345997 | − | 0.938236i | \(-0.612459\pi\) |
0.785396 | + | 0.618993i | \(0.212459\pi\) | |||||||
\(542\) | 14.0372 | + | 43.2022i | 0.602951 | + | 1.85569i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.4021 | + | 9.73722i | 0.574612 | + | 0.417480i | ||||
\(545\) | 5.06010 | + | 3.67638i | 0.216751 | + | 0.157479i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.91799 | − | 21.2914i | −0.295792 | − | 0.910353i | −0.982954 | − | 0.183850i | \(-0.941144\pi\) |
0.687163 | − | 0.726504i | \(-0.258856\pi\) | |||||||
\(548\) | 47.9019 | − | 34.8028i | 2.04627 | − | 1.48670i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −55.6313 | + | 25.3660i | −2.37213 | + | 1.08161i | ||||
\(551\) | 8.33836 | 0.355226 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.05528 | − | 3.24781i | −0.0448750 | − | 0.138111i | ||||
\(554\) | 2.50107 | − | 7.69750i | 0.106260 | − | 0.327036i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.7327 | + | 14.3366i | 0.836852 | + | 0.608009i | ||||
\(557\) | −1.64815 | + | 5.07249i | −0.0698344 | + | 0.214928i | −0.979883 | − | 0.199574i | \(-0.936044\pi\) |
0.910048 | + | 0.414502i | \(0.136044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.1189 | + | 34.2339i | −1.99292 | + | 1.44794i | ||||
\(560\) | 4.75203 | 0.200810 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.74348 | 0.115727 | ||||||||
\(563\) | −36.8747 | + | 26.7910i | −1.55408 | + | 1.12911i | −0.613425 | + | 0.789753i | \(0.710209\pi\) |
−0.940658 | + | 0.339355i | \(0.889791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.6267 | + | 57.3272i | −0.783633 | + | 2.41177i | ||||
\(566\) | −7.77637 | − | 5.64986i | −0.326865 | − | 0.237481i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.63402 | + | 17.3397i | −0.236398 | + | 0.727560i | ||||
\(569\) | −7.98042 | − | 24.5612i | −0.334557 | − | 1.02966i | −0.966940 | − | 0.255004i | \(-0.917923\pi\) |
0.632383 | − | 0.774656i | \(-0.282077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7759 | −0.911295 | −0.455648 | − | 0.890160i | \(-0.650592\pi\) | ||||
−0.455648 | + | 0.890160i | \(0.650592\pi\) | |||||||
\(572\) | 71.7350 | + | 14.5798i | 2.99939 | + | 0.609614i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.23209 | + | 3.07480i | −0.176644 | + | 0.128340i | ||||
\(575\) | −3.03505 | − | 9.34091i | −0.126570 | − | 0.389543i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6324 | + | 20.0761i | 1.15035 | + | 0.835780i | 0.988528 | − | 0.151039i | \(-0.0482620\pi\) |
0.161825 | + | 0.986819i | \(0.448262\pi\) | |||||||
\(578\) | −3.22582 | − | 2.34370i | −0.134177 | − | 0.0974850i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.7390 | + | 66.9056i | 0.902661 | + | 2.77811i | ||||
\(581\) | 10.8974 | − | 7.91745i | 0.452102 | − | 0.328471i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.18998 | − | 19.1874i | −0.0906999 | − | 0.794662i | ||||
\(584\) | −7.66460 | −0.317163 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.32893 | + | 13.3231i | 0.178827 | + | 0.550372i | ||||
\(587\) | 9.03764 | − | 27.8150i | 0.373023 | − | 1.14805i | −0.571779 | − | 0.820408i | \(-0.693747\pi\) |
0.944803 | − | 0.327640i | \(-0.106253\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.85131 | + | 2.79814i | 0.158690 | + | 0.115295i | ||||
\(590\) | 17.1487 | − | 52.7783i | 0.706001 | − | 2.17285i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.33418 | − | 6.78168i | 0.383633 | − | 0.278725i | ||||
\(593\) | −6.12062 | −0.251344 | −0.125672 | − | 0.992072i | \(-0.540109\pi\) | ||||
−0.125672 | + | 0.992072i | \(0.540109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1501 | −0.662088 | ||||||||
\(596\) | −23.8207 | + | 17.3068i | −0.975735 | + | 0.708913i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.72201 | + | 17.6105i | −0.233990 | + | 0.720149i | ||||
\(599\) | −15.8456 | − | 11.5125i | −0.647433 | − | 0.470387i | 0.214963 | − | 0.976622i | \(-0.431037\pi\) |
−0.862396 | + | 0.506235i | \(0.831037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.62705 | − | 11.1629i | 0.147950 | − | 0.455345i | −0.849428 | − | 0.527704i | \(-0.823053\pi\) |
0.997379 | + | 0.0723596i | \(0.0230529\pi\) | |||||||
\(602\) | 7.64507 | + | 23.5291i | 0.311590 | + | 0.958975i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 75.9387 | 3.08990 | ||||||||
\(605\) | −3.42442 | + | 39.3209i | −0.139223 | + | 1.59862i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.59025 | + | 4.06156i | −0.226901 | + | 0.164853i | −0.695428 | − | 0.718596i | \(-0.744785\pi\) |
0.468526 | + | 0.883449i | \(0.344785\pi\) | |||||||
\(608\) | 1.93725 | + | 5.96224i | 0.0785659 | + | 0.241801i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.4029 | − | 16.2766i | −0.907066 | − | 0.659022i | ||||
\(611\) | 1.27394 | + | 0.925575i | 0.0515383 | + | 0.0374448i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.52119 | − | 13.9148i | −0.182609 | − | 0.562014i | 0.817290 | − | 0.576227i | \(-0.195476\pi\) |
−0.999899 | + | 0.0142134i | \(0.995476\pi\) | |||||||
\(614\) | 8.91882 | − | 6.47990i | 0.359934 | − | 0.261508i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.50977 | − | 11.5113i | 0.262286 | − | 0.463804i | ||||
\(617\) | −19.6654 | −0.791699 | −0.395850 | − | 0.918315i | \(-0.629550\pi\) | ||||
−0.395850 | + | 0.918315i | \(0.629550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.88924 | + | 5.81447i | 0.0759348 | + | 0.233703i | 0.981818 | − | 0.189824i | \(-0.0607918\pi\) |
−0.905883 | + | 0.423527i | \(0.860792\pi\) | |||||||
\(620\) | −12.4111 | + | 38.1973i | −0.498440 | + | 1.53404i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.0923 | + | 29.1287i | 1.60755 | + | 1.16796i | ||||
\(623\) | 3.17730 | − | 9.77874i | 0.127296 | − | 0.391777i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.90959 | − | 1.38740i | 0.0763836 | − | 0.0554959i | ||||
\(626\) | −50.2297 | −2.00758 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −29.3519 | −1.17127 | ||||||||
\(629\) | −31.7228 | + | 23.0480i | −1.26487 | + | 0.918984i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.27739 | − | 10.0868i | 0.130471 | − | 0.401548i | −0.864387 | − | 0.502827i | \(-0.832293\pi\) |
0.994858 | + | 0.101279i | \(0.0322934\pi\) | |||||||
\(632\) | −8.31799 | − | 6.04337i | −0.330872 | − | 0.240392i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.802817 | − | 2.47082i | 0.0318839 | − | 0.0981287i | ||||
\(635\) | 2.45704 | + | 7.56200i | 0.0975047 | + | 0.300089i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.9956 | 1.42620 | ||||||||
\(638\) | 42.8642 | + | 8.71197i | 1.69701 | + | 0.344910i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.4302 | + | 42.4520i | −2.30966 | + | 1.67806i | ||||
\(641\) | 11.6981 | + | 36.0029i | 0.462045 | + | 1.42203i | 0.862661 | + | 0.505783i | \(0.168796\pi\) |
−0.400615 | + | 0.916246i | \(0.631204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.26221 | + | 3.82322i | 0.207521 | + | 0.150773i | 0.686691 | − | 0.726949i | \(-0.259062\pi\) |
−0.479170 | + | 0.877722i | \(0.659062\pi\) | |||||||
\(644\) | 4.04099 | + | 2.93595i | 0.159237 | + | 0.115693i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.18756 | + | 12.8880i | 0.164757 | + | 0.507071i | ||||
\(647\) | −19.9715 | + | 14.5101i | −0.785161 | + | 0.570453i | −0.906523 | − | 0.422155i | \(-0.861274\pi\) |
0.121363 | + | 0.992608i | \(0.461274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.8067 | − | 16.1522i | −0.581212 | − | 0.634029i | ||||
\(650\) | 116.916 | 4.58583 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.24741 | − | 19.2275i | −0.244667 | − | 0.753009i | ||||
\(653\) | −8.58310 | + | 26.4161i | −0.335883 | + | 1.03374i | 0.630403 | + | 0.776268i | \(0.282890\pi\) |
−0.966286 | + | 0.257473i | \(0.917110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.3403 | + | 24.9497i | 1.34179 | + | 0.974866i | ||||
\(656\) | −0.690536 | + | 2.12525i | −0.0269609 | + | 0.0829772i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.541143 | − | 0.393164i | 0.0210960 | − | 0.0153271i | ||||
\(659\) | 35.1489 | 1.36921 | 0.684603 | − | 0.728917i | \(-0.259976\pi\) | ||||
0.684603 | + | 0.728917i | \(0.259976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.1379 | −0.977751 | −0.488875 | − | 0.872354i | \(-0.662593\pi\) | ||||
−0.488875 | + | 0.872354i | \(0.662593\pi\) | |||||||
\(662\) | −11.2471 | + | 8.17151i | −0.437132 | + | 0.317595i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.5321 | − | 38.5700i | 0.486342 | − | 1.49681i | ||||
\(665\) | −4.94446 | − | 3.59236i | −0.191738 | − | 0.139306i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.17127 | + | 6.68250i | −0.0840721 | + | 0.258747i | ||||
\(668\) | 17.3694 | + | 53.4575i | 0.672042 | + | 2.06833i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 118.235 | 4.56782 | ||||||||
\(671\) | −9.94856 | + | 4.53620i | −0.384060 | + | 0.175118i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.3692 | − | 14.7991i | 0.785175 | − | 0.570463i | −0.121353 | − | 0.992609i | \(-0.538723\pi\) |
0.906528 | + | 0.422146i | \(0.138723\pi\) | |||||||
\(674\) | 22.4312 | + | 69.0360i | 0.864016 | + | 2.65917i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −76.6438 | − | 55.6850i | −2.94784 | − | 2.14173i | ||||
\(677\) | −22.6873 | − | 16.4833i | −0.871943 | − | 0.633503i | 0.0591649 | − | 0.998248i | \(-0.481156\pi\) |
−0.931108 | + | 0.364745i | \(0.881156\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.51628 | + | 10.8220i | 0.134943 | + | 0.415310i | ||||
\(680\) | −39.3376 | + | 28.5805i | −1.50853 | + | 1.09601i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.8745 | + | 18.4080i | 0.646159 | + | 0.704879i | ||||
\(683\) | −48.2755 | −1.84721 | −0.923605 | − | 0.383346i | \(-0.874772\pi\) | ||||
−0.923605 | + | 0.383346i | \(0.874772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.8652 | − | 58.0610i | −0.720800 | − | 2.21840i | ||||
\(686\) | 10.5523 | − | 32.4768i | 0.402891 | − | 1.23997i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.54995 | + | 6.21190i | 0.325964 | + | 0.236826i | ||||
\(689\) | −11.4116 | + | 35.1214i | −0.434749 | + | 1.33802i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6840 | − | 7.76238i | 0.406439 | − | 0.295295i | −0.365720 | − | 0.930725i | \(-0.619177\pi\) |
0.772158 | + | 0.635430i | \(0.219177\pi\) | |||||||
\(692\) | −50.1826 | −1.90766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −58.1464 | −2.20721 | ||||||||
\(695\) | 20.3455 | − | 14.7819i | 0.771750 | − | 0.560709i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.34683 | − | 7.22281i | 0.0888926 | − | 0.273583i | ||||
\(698\) | −22.8843 | − | 16.6264i | −0.866183 | − | 0.629319i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.74587 | − | 29.9947i | 0.368359 | − | 1.13369i | ||||
\(701\) | 10.0560 | + | 30.9490i | 0.379808 | + | 1.16893i | 0.940177 | + | 0.340686i | \(0.110659\pi\) |
−0.560369 | + | 0.828243i | \(0.689341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.8389 | −0.559659 | ||||||||
\(704\) | 4.59490 | + | 40.2580i | 0.173177 | + | 1.51728i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.5459 | + | 12.0213i | −0.622715 | + | 0.452429i | ||||
\(707\) | −2.81954 | − | 8.67766i | −0.106040 | − | 0.326357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.61618 | − | 1.17422i | −0.0606968 | − | 0.0440988i | 0.557023 | − | 0.830497i | \(-0.311943\pi\) |
−0.617720 | + | 0.786398i | \(0.711943\pi\) | |||||||
\(710\) | 35.7586 | + | 25.9801i | 1.34200 | + | 0.975017i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.56610 | − | 29.4414i | −0.358505 | − | 1.10336i | ||||
\(713\) | −3.24534 | + | 2.35788i | −0.121539 | + | 0.0883031i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.1527 | − | 65.6975i | 1.38943 | − | 2.45695i | ||||
\(716\) | 15.1385 | 0.565753 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.8939 | − | 33.5278i | −0.406555 | − | 1.25125i | ||||
\(719\) | 14.0695 | − | 43.3014i | 0.524703 | − | 1.61487i | −0.240198 | − | 0.970724i | \(-0.577212\pi\) |
0.764901 | − | 0.644147i | \(-0.222788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.01832 | − | 4.37256i | −0.224134 | − | 0.162843i | ||||
\(722\) | 12.1598 | − | 37.4241i | 0.452541 | − | 1.39278i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42.2058 | + | 30.6643i | −1.56856 | + | 1.13963i | ||||
\(725\) | 44.3650 | 1.64767 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.5005 | −1.27955 | −0.639776 | − | 0.768562i | \(-0.720973\pi\) | ||||
−0.639776 | + | 0.768562i | \(0.720973\pi\) | |||||||
\(728\) | −20.4586 | + | 14.8640i | −0.758246 | + | 0.550898i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.74193 | + | 17.6718i | −0.212518 | + | 0.654064i | ||||
\(731\) | −29.0575 | − | 21.1115i | −1.07473 | − | 0.780839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.49867 | − | 10.7678i | 0.129226 | − | 0.397718i | −0.865421 | − | 0.501045i | \(-0.832949\pi\) |
0.994647 | + | 0.103327i | \(0.0329490\pi\) | |||||||
\(734\) | −14.9846 | − | 46.1178i | −0.553091 | − | 1.70224i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.28269 | −0.194723 | ||||||||
\(737\) | 22.9807 | − | 40.6371i | 0.846506 | − | 1.49689i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.54111 | + | 4.02585i | −0.203833 | + | 0.148093i | −0.685019 | − | 0.728525i | \(-0.740206\pi\) |
0.481186 | + | 0.876619i | \(0.340206\pi\) | |||||||
\(740\) | −38.6865 | − | 119.065i | −1.42214 | − | 4.37691i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.6907 | + | 9.22033i | 0.465890 | + | 0.338489i | ||||
\(743\) | 14.6994 | + | 10.6798i | 0.539270 | + | 0.391803i | 0.823814 | − | 0.566860i | \(-0.191842\pi\) |
−0.284544 | + | 0.958663i | \(0.591842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.38129 | + | 28.8726i | 0.343704 | + | 1.05781i | ||||
\(746\) | −22.8096 | + | 16.5722i | −0.835120 | + | 0.606750i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.11916 | + | 44.8512i | 0.187175 | + | 1.63992i | ||||
\(749\) | 7.14183 | 0.260957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.44189 | − | 16.7484i | −0.198578 | − | 0.611159i | −0.999916 | − | 0.0129479i | \(-0.995878\pi\) |
0.801339 | − | 0.598211i | \(-0.204122\pi\) | |||||||
\(752\) | 0.0882965 | − | 0.271749i | 0.00321984 | − | 0.00990965i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −67.6677 | − | 49.1634i | −2.46431 | − | 1.79043i | ||||
\(755\) | 24.1951 | − | 74.4650i | 0.880551 | − | 2.71006i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.69987 | − | 1.23503i | 0.0617827 | − | 0.0448878i | −0.556465 | − | 0.830871i | \(-0.687843\pi\) |
0.618248 | + | 0.785983i | \(0.287843\pi\) | |||||||
\(758\) | 25.3228 | 0.919767 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.4008 | −0.667468 | ||||||||
\(761\) | 12.8668 | − | 9.34825i | 0.466420 | − | 0.338874i | −0.329625 | − | 0.944112i | \(-0.606922\pi\) |
0.796044 | + | 0.605238i | \(0.206922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.619890 | + | 1.90783i | −0.0224415 | + | 0.0690680i | ||||
\(764\) | 34.9349 | + | 25.3817i | 1.26390 | + | 0.918277i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.2642 | − | 68.5223i | 0.804440 | − | 2.47581i | ||||
\(767\) | 12.9479 | + | 39.8497i | 0.467523 | + | 1.43889i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.44506 | −0.232415 | −0.116207 | − | 0.993225i | \(-0.537074\pi\) | ||||
−0.116207 | + | 0.993225i | \(0.537074\pi\) | |||||||
\(770\) | −21.6642 | − | 23.6329i | −0.780723 | − | 0.851671i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29.0953 | − | 21.1390i | 1.04716 | − | 0.760809i | ||||
\(773\) | −14.0473 | − | 43.2331i | −0.505246 | − | 1.55499i | −0.800357 | − | 0.599524i | \(-0.795357\pi\) |
0.295111 | − | 0.955463i | \(-0.404643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.4912 | + | 14.8877i | 0.736066 | + | 0.534783i | ||||
\(776\) | 27.7163 | + | 20.1371i | 0.994957 | + | 0.722879i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.975530 | + | 3.00237i | 0.0349744 | + | 0.107640i | ||||
\(779\) | 2.32511 | − | 1.68929i | 0.0833059 | − | 0.0605253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8795 | − | 7.24051i | 0.568213 | − | 0.259086i | ||||
\(782\) | −11.4191 | −0.408345 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.01837 | − | 6.21190i | −0.0720846 | − | 0.221854i | ||||
\(785\) | −9.35191 | + | 28.7822i | −0.333784 | + | 1.02728i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.7262 | + | 29.5893i | 1.45173 | + | 1.05475i | 0.985422 | + | 0.170125i | \(0.0544172\pi\) |
0.466311 | + | 0.884621i | \(0.345583\pi\) | |||||||
\(788\) | −0.828938 | + | 2.55121i | −0.0295297 | + | 0.0908830i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20.1653 | + | 14.6509i | −0.717449 | + | 0.521257i | ||||
\(791\) | −19.3324 | −0.687381 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.9081 | 0.742470 | ||||||||
\(794\) | −2.14504 | + | 1.55846i | −0.0761247 | + | 0.0553079i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.90996 | + | 12.0336i | −0.138585 | + | 0.426520i | ||||
\(797\) | 36.1986 | + | 26.2998i | 1.28222 | + | 0.931588i | 0.999618 | − | 0.0276488i | \(-0.00880200\pi\) |
0.282603 | + | 0.959237i | \(0.408802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.300081 | + | 0.923556i | −0.0106161 | + | 0.0326730i | ||||
\(800\) | 10.3073 | + | 31.7226i | 0.364418 | + | 1.12156i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 77.3961 | 2.73295 | ||||||||
\(803\) | 4.95774 | + | 5.40827i | 0.174955 | + | 0.190854i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.16649 | − | 3.02713i | 0.146850 | − | 0.106692i | ||||
\(806\) | −14.7562 | − | 45.4150i | −0.519766 | − | 1.59968i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22.2244 | − | 16.1470i | −0.781852 | − | 0.568049i | ||||
\(809\) | 21.6493 | + | 15.7291i | 0.761148 | + | 0.553006i | 0.899262 | − | 0.437410i | \(-0.144104\pi\) |
−0.138114 | + | 0.990416i | \(0.544104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8989 | + | 48.9318i | 0.558286 | + | 1.71823i | 0.687105 | + | 0.726559i | \(0.258881\pi\) |
−0.128819 | + | 0.991668i | \(0.541119\pi\) | |||||||
\(812\) | −18.2535 | + | 13.2619i | −0.640571 | + | 0.465402i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −76.2808 | − | 15.5038i | −2.67364 | − | 0.543407i | ||||
\(815\) | −20.8449 | −0.730165 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.20021 | − | 12.9269i | −0.146947 | − | 0.452255i | ||||
\(818\) | 1.14711 | − | 3.53044i | 0.0401077 | − | 0.123439i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.6164 | + | 14.2522i | 0.685036 | + | 0.497707i | ||||
\(821\) | 0.166002 | − | 0.510902i | 0.00579352 | − | 0.0178306i | −0.948118 | − | 0.317919i | \(-0.897016\pi\) |
0.953911 | + | 0.300088i | \(0.0970161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.85190 | + | 5.70474i | −0.273700 | + | 0.198855i | −0.716165 | − | 0.697931i | \(-0.754104\pi\) |
0.442465 | + | 0.896786i | \(0.354104\pi\) | |||||||
\(824\) | −22.3972 | −0.780243 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.7984 | 0.619285 | ||||||||
\(827\) | 32.2959 | − | 23.4643i | 1.12304 | − | 0.815934i | 0.138370 | − | 0.990381i | \(-0.455814\pi\) |
0.984667 | + | 0.174447i | \(0.0558136\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.01231 | − | 18.5040i | 0.208816 | − | 0.642670i | −0.790719 | − | 0.612179i | \(-0.790293\pi\) |
0.999535 | − | 0.0304906i | \(-0.00970697\pi\) | |||||||
\(830\) | −79.5402 | − | 57.7894i | −2.76088 | − | 2.00590i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23.9433 | − | 73.6898i | 0.830084 | − | 2.55473i | ||||
\(833\) | 6.85956 | + | 21.1115i | 0.237670 | + | 0.731472i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 57.9542 | 2.00559 | ||||||||
\(836\) | −8.40927 | + | 14.8702i | −0.290841 | + | 0.514297i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.13478 | + | 4.45718i | −0.211923 | + | 0.153971i | ||||
\(839\) | 3.05596 | + | 9.40529i | 0.105504 | + | 0.324707i | 0.989848 | − | 0.142128i | \(-0.0453944\pi\) |
−0.884345 | + | 0.466834i | \(0.845394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.21569 | − | 1.60979i | −0.0764029 | − | 0.0555100i | ||||
\(842\) | 69.7961 | + | 50.7099i | 2.40533 | + | 1.74758i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.1465 | + | 52.7716i | 0.590208 | + | 1.81647i | ||||
\(845\) | −79.0241 | + | 57.4144i | −2.71851 | + | 1.97512i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.3333 | + | 2.85253i | −0.423778 | + | 0.0980139i | ||||
\(848\) | 6.70091 | 0.230110 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.2803 | + | 68.5716i | 0.764207 | + | 2.35199i | ||||
\(851\) | 3.86398 | − | 11.8921i | 0.132456 | − | 0.407657i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5819 | + | 24.3987i | 1.14982 | + | 0.835396i | 0.988457 | − | 0.151499i | \(-0.0484100\pi\) |
0.161366 | + | 0.986895i | \(0.448410\pi\) | |||||||
\(854\) | 2.74448 | − | 8.44663i | 0.0939141 | − | 0.289038i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3958 | − | 12.6388i | 0.594575 | − | 0.431984i | ||||
\(857\) | −37.8305 | −1.29227 | −0.646133 | − | 0.763225i | \(-0.723615\pi\) | ||||
−0.646133 | + | 0.763225i | \(0.723615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.5423 | 1.51976 | 0.759882 | − | 0.650061i | \(-0.225257\pi\) | ||||
0.759882 | + | 0.650061i | \(0.225257\pi\) | |||||||
\(860\) | 92.7730 | − | 67.4035i | 3.16353 | − | 2.29844i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.91225 | − | 12.0407i | 0.133252 | − | 0.410107i | ||||
\(863\) | −15.9320 | − | 11.5753i | −0.542332 | − | 0.394028i | 0.282618 | − | 0.959233i | \(-0.408797\pi\) |
−0.824951 | + | 0.565205i | \(0.808797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9889 | + | 49.2087i | −0.543638 | + | 1.67315i | ||||
\(866\) | −22.7374 | − | 69.9785i | −0.772648 | − | 2.37796i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.8812 | −0.437218 | ||||||||
\(869\) | 1.11607 | + | 9.77838i | 0.0378601 | + | 0.331709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.2227 | + | 52.4729i | −2.44717 | + | 1.77797i | ||||
\(872\) | 1.86634 | + | 5.74401i | 0.0632023 | + | 0.194517i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.49603 | − | 2.54001i | −0.118255 | − | 0.0859172i | ||||
\(875\) | −9.60410 | − | 6.97779i | −0.324678 | − | 0.235892i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.6113 | − | 38.8136i | −0.425854 | − | 1.31064i | −0.902174 | − | 0.431372i | \(-0.858030\pi\) |
0.476321 | − | 0.879272i | \(-0.341970\pi\) | |||||||
\(878\) | −50.7712 | + | 36.8874i | −1.71344 | + | 1.24489i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.4209 | − | 2.72774i | −0.452419 | − | 0.0919522i | ||||
\(881\) | −37.0974 | −1.24984 | −0.624921 | − | 0.780688i | \(-0.714869\pi\) | ||||
−0.624921 | + | 0.780688i | \(0.714869\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8664 | + | 39.5986i | 0.432988 | + | 1.33260i | 0.895134 | + | 0.445797i | \(0.147080\pi\) |
−0.462146 | + | 0.886804i | \(0.652920\pi\) | |||||||
\(884\) | 26.6751 | − | 82.0975i | 0.897181 | − | 2.76124i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.1061 | − | 26.2326i | −1.21301 | − | 0.881301i | ||||
\(887\) | 3.65713 | − | 11.2555i | 0.122794 | − | 0.377922i | −0.870698 | − | 0.491817i | \(-0.836333\pi\) |
0.993493 | + | 0.113895i | \(0.0363328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.06309 | + | 1.49893i | −0.0691940 | + | 0.0502724i | ||||
\(890\) | −75.0479 | −2.51561 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.9951 | −0.669485 | ||||||||
\(893\) | −0.297304 | + | 0.216004i | −0.00994891 | + | 0.00722831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.82334 | − | 14.8447i | 0.161227 | − | 0.496204i | ||||
\(896\) | −18.7400 | − | 13.6154i | −0.626058 | − | 0.454858i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.0983 | + | 61.8561i | −0.670688 | + | 2.06416i | ||||
\(899\) | −5.59940 | − | 17.2332i | −0.186751 | − | 0.574759i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7735 | −0.758695 | ||||||||
\(902\) | 13.7175 | − | 6.25470i | 0.456742 | − | 0.208259i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.0890 | + | 34.2122i | −1.56616 | + | 1.13788i | ||||
\(905\) | 16.6218 | + | 51.1567i | 0.552529 | + | 1.70051i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.6443 | + | 25.8971i | 1.18355 | + | 0.859899i | 0.992568 | − | 0.121694i | \(-0.0388327\pi\) |
0.190982 | + | 0.981593i | \(0.438833\pi\) | |||||||
\(908\) | −52.5645 | − | 38.1903i | −1.74441 | − | 1.26739i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.9446 | + | 58.3056i | 0.628009 | + | 1.93281i | ||||
\(911\) | 21.3540 | − | 15.5146i | 0.707491 | − | 0.514022i | −0.174872 | − | 0.984591i | \(-0.555951\pi\) |
0.882363 | + | 0.470569i | \(0.155951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.3219 | + | 16.1056i | −1.16898 | + | 0.533016i | ||||
\(914\) | −43.8790 | −1.45139 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.84472 | − | 5.67746i | −0.0609512 | − | 0.187588i | ||||
\(917\) | −4.20688 | + | 12.9475i | −0.138924 | + | 0.427563i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.55803 | − | 1.13197i | −0.0513945 | − | 0.0373403i | 0.561791 | − | 0.827279i | \(-0.310112\pi\) |
−0.613186 | + | 0.789939i | \(0.710112\pi\) | |||||||
\(920\) | 4.79150 | − | 14.7467i | 0.157971 | − | 0.486185i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −34.2912 | + | 24.9140i | −1.12932 | + | 0.820499i | ||||
\(923\) | −33.3728 | −1.09848 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −78.9516 | −2.59591 | ||||||||
\(926\) | −46.5458 | + | 33.8175i | −1.52959 | + | 1.11131i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.37386 | − | 22.6944i | 0.242059 | − | 0.744980i | ||||
\(929\) | −19.9286 | − | 14.4789i | −0.653835 | − | 0.475039i | 0.210741 | − | 0.977542i | \(-0.432412\pi\) |
−0.864575 | + | 0.502503i | \(0.832412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.59587 | + | 7.98927i | −0.0850762 | + | 0.261838i | ||||
\(932\) | 7.73470 | + | 23.8050i | 0.253358 | + | 0.779757i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.3040 | −1.18790 | ||||||||
\(935\) | 45.6118 | + | 9.27041i | 1.49167 | + | 0.303175i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.1168 | − | 32.0527i | 1.44123 | − | 1.04712i | 0.453450 | − | 0.891282i | \(-0.350193\pi\) |
0.987783 | − | 0.155835i | \(-0.0498068\pi\) | |||||||
\(938\) | 11.7182 | + | 36.0648i | 0.382612 | + | 1.17756i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.50829 | − | 1.82238i | −0.0818112 | − | 0.0594393i | ||||
\(941\) | −22.2658 | − | 16.1771i | −0.725846 | − | 0.527358i | 0.162401 | − | 0.986725i | \(-0.448076\pi\) |
−0.888246 | + | 0.459367i | \(0.848076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.748378 | + | 2.30327i | 0.0243705 | + | 0.0750048i | ||||
\(944\) | 6.15098 | − | 4.46895i | 0.200197 | − | 0.145452i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.08549 | − | 70.8405i | −0.262882 | − | 2.30322i | ||||
\(947\) | 19.2088 | 0.624203 | 0.312102 | − | 0.950049i | \(-0.398967\pi\) | ||||
0.312102 | + | 0.950049i | \(0.398967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.33538 | − | 13.3429i | −0.140732 | − | 0.433130i | ||||
\(950\) | −8.43155 | + | 25.9496i | −0.273555 | + | 0.841917i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.6165 | − | 9.16644i | −0.408904 | − | 0.297086i | ||||
\(953\) | 8.93933 | − | 27.5124i | 0.289573 | − | 0.891215i | −0.695417 | − | 0.718606i | \(-0.744780\pi\) |
0.984991 | − | 0.172608i | \(-0.0552195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0198 | − | 26.1700i | 1.16557 | − | 0.846840i | ||||
\(956\) | 33.5591 | 1.08538 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22.5568 | 0.728777 | ||||||||
\(959\) | 15.8404 | − | 11.5087i | 0.511514 | − | 0.371637i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.38276 | + | 19.6441i | −0.205895 | + | 0.633681i | ||||
\(962\) | 120.421 | + | 87.4909i | 3.88252 | + | 2.82082i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.20120 | − | 9.85227i | 0.103104 | − | 0.317320i | ||||
\(965\) | −11.4586 | − | 35.2659i | −0.368865 | − | 1.13525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.8862 | −0.446552 | −0.223276 | − | 0.974755i | \(-0.571675\pi\) | ||||
−0.223276 | + | 0.974755i | \(0.571675\pi\) | |||||||
\(968\) | −24.9929 | + | 28.7741i | −0.803303 | + | 0.924834i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 67.1926 | − | 48.8183i | 2.15742 | − | 1.56746i | ||||
\(971\) | 9.80736 | + | 30.1840i | 0.314733 | + | 0.968649i | 0.975864 | + | 0.218379i | \(0.0700768\pi\) |
−0.661131 | + | 0.750271i | \(0.729923\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.52529 | + | 4.74090i | 0.209191 | + | 0.151986i | ||||
\(974\) | 65.0115 | + | 47.2337i | 2.08310 | + | 1.51346i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.17237 | − | 3.60820i | −0.0375268 | − | 0.115496i | ||||
\(977\) | −5.26888 | + | 3.82806i | −0.168566 | + | 0.122471i | −0.668870 | − | 0.743379i | \(-0.733222\pi\) |
0.500304 | + | 0.865850i | \(0.333222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5867 | + | 25.7938i | −0.466192 | + | 0.824373i | ||||
\(980\) | −70.8723 | −2.26393 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.6841 | + | 39.0377i | 0.404767 | + | 1.24574i | ||||
\(983\) | 18.1369 | − | 55.8197i | 0.578478 | − | 1.78037i | −0.0455410 | − | 0.998962i | \(-0.514501\pi\) |
0.624019 | − | 0.781409i | \(-0.285499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.23759 | + | 1.62570i | 0.0712954 | + | 0.0517991i | ||||
\(986\) | 15.9393 | − | 49.0562i | 0.507611 | − | 1.56227i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.4282 | − | 19.2012i | 0.840794 | − | 0.610873i | ||||
\(989\) | 11.4535 | 0.364202 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.1267 | 1.71939 | 0.859696 | − | 0.510806i | \(-0.170653\pi\) | ||||
0.859696 | + | 0.510806i | \(0.170653\pi\) | |||||||
\(992\) | 11.0215 | − | 8.00757i | 0.349932 | − | 0.254241i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.38063 | + | 13.4822i | −0.138945 | + | 0.427629i | ||||
\(995\) | 10.5543 | + | 7.66816i | 0.334594 | + | 0.243097i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.23734 | + | 13.0412i | −0.134198 | + | 0.413019i | −0.995464 | − | 0.0951346i | \(-0.969672\pi\) |
0.861266 | + | 0.508154i | \(0.169672\pi\) | |||||||
\(998\) | −17.4610 | − | 53.7394i | −0.552718 | − | 1.70109i | ||||
\(999\) | 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 | 297.2.f.c.190.4 | yes | 16 | |
3.2 | odd | 2 | inner | 297.2.f.c.190.1 | yes | 16 | |
9.2 | odd | 6 | 891.2.n.g.190.4 | 32 | |||
9.4 | even | 3 | 891.2.n.g.784.4 | 32 | |||
9.5 | odd | 6 | 891.2.n.g.784.1 | 32 | |||
9.7 | even | 3 | 891.2.n.g.190.1 | 32 | |||
11.2 | odd | 10 | 3267.2.a.bh.1.8 | 8 | |||
11.4 | even | 5 | inner | 297.2.f.c.136.4 | yes | 16 | |
11.9 | even | 5 | 3267.2.a.bg.1.1 | 8 | |||
33.2 | even | 10 | 3267.2.a.bh.1.1 | 8 | |||
33.20 | odd | 10 | 3267.2.a.bg.1.8 | 8 | |||
33.26 | odd | 10 | inner | 297.2.f.c.136.1 | ✓ | 16 | |
99.4 | even | 15 | 891.2.n.g.136.1 | 32 | |||
99.59 | odd | 30 | 891.2.n.g.136.4 | 32 | |||
99.70 | even | 15 | 891.2.n.g.433.4 | 32 | |||
99.92 | odd | 30 | 891.2.n.g.433.1 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
297.2.f.c.136.1 | ✓ | 16 | 33.26 | odd | 10 | inner | |
297.2.f.c.136.4 | yes | 16 | 11.4 | even | 5 | inner | |
297.2.f.c.190.1 | yes | 16 | 3.2 | odd | 2 | inner | |
297.2.f.c.190.4 | yes | 16 | 1.1 | even | 1 | trivial | |
891.2.n.g.136.1 | 32 | 99.4 | even | 15 | |||
891.2.n.g.136.4 | 32 | 99.59 | odd | 30 | |||
891.2.n.g.190.1 | 32 | 9.7 | even | 3 | |||
891.2.n.g.190.4 | 32 | 9.2 | odd | 6 | |||
891.2.n.g.433.1 | 32 | 99.92 | odd | 30 | |||
891.2.n.g.433.4 | 32 | 99.70 | even | 15 | |||
891.2.n.g.784.1 | 32 | 9.5 | odd | 6 | |||
891.2.n.g.784.4 | 32 | 9.4 | even | 3 | |||
3267.2.a.bg.1.1 | 8 | 11.9 | even | 5 | |||
3267.2.a.bg.1.8 | 8 | 33.20 | odd | 10 | |||
3267.2.a.bh.1.1 | 8 | 33.2 | even | 10 | |||
3267.2.a.bh.1.8 | 8 | 11.2 | odd | 10 |