Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(61,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.u (of order \(9\), degree \(6\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 3 x^{17} + 3 x^{15} + 36 x^{14} + 72 x^{13} - 134 x^{12} - 741 x^{11} + 486 x^{10} + 5700 x^{9} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 61.2 | ||
Root | \(-0.344606 - 0.289159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.61 |
Dual form | 380.2.u.a.81.2 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0781159 | − | 0.443017i | −0.0451002 | − | 0.255776i | 0.953919 | − | 0.300066i | \(-0.0970086\pi\) |
−0.999019 | + | 0.0442897i | \(0.985898\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.766044 | + | 0.642788i | −0.342585 | + | 0.287463i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.06981 | + | 1.85297i | −0.404352 | + | 0.700357i | −0.994246 | − | 0.107123i | \(-0.965836\pi\) |
0.589894 | + | 0.807481i | \(0.299169\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.62892 | − | 0.956847i | 0.876305 | − | 0.318949i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.25634 | + | 3.90810i | 0.680313 | + | 1.17834i | 0.974885 | + | 0.222707i | \(0.0714894\pi\) |
−0.294573 | + | 0.955629i | \(0.595177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.155380 | + | 0.881206i | −0.0430947 | + | 0.244402i | −0.998744 | − | 0.0501049i | \(-0.984044\pi\) |
0.955649 | + | 0.294507i | \(0.0951555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.344606 | + | 0.289159i | 0.0889769 | + | 0.0746605i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.00854515 | − | 0.00311018i | −0.00207250 | − | 0.000754330i | 0.340984 | − | 0.940069i | \(-0.389240\pi\) |
−0.343056 | + | 0.939315i | \(0.611462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.31164 | + | 0.640134i | 0.989158 | + | 0.146857i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.904468 | + | 0.329199i | 0.197371 | + | 0.0718372i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.94633 | + | 4.15046i | 1.03138 | + | 0.865431i | 0.991015 | − | 0.133754i | \(-0.0427032\pi\) |
0.0403658 | + | 0.999185i | \(0.487148\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.173648 | − | 0.984808i | 0.0347296 | − | 0.196962i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.30404 | − | 2.25866i | −0.250962 | − | 0.434679i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.381463 | + | 0.138841i | −0.0708359 | + | 0.0257822i | −0.377195 | − | 0.926134i | \(-0.623111\pi\) |
0.306359 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.920071 | + | 1.59361i | −0.165250 | + | 0.286221i | −0.936744 | − | 0.350016i | \(-0.886176\pi\) |
0.771494 | + | 0.636236i | \(0.219510\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.55510 | − | 1.30488i | 0.270708 | − | 0.227151i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.371542 | − | 2.10712i | −0.0628021 | − | 0.356169i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.75663 | −1.11078 | −0.555392 | − | 0.831589i | \(-0.687432\pi\) | ||||
−0.555392 | + | 0.831589i | \(0.687432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.402527 | 0.0644559 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.24280 | − | 7.04829i | −0.194093 | − | 1.10076i | −0.913704 | − | 0.406380i | \(-0.866791\pi\) |
0.719611 | − | 0.694378i | \(-0.244320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.04904 | − | 0.880252i | 0.159978 | − | 0.134237i | −0.559285 | − | 0.828975i | \(-0.688924\pi\) |
0.719263 | + | 0.694738i | \(0.244480\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.39882 | + | 2.42282i | −0.208523 | + | 0.361173i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.13486 | − | 0.413057i | 0.165537 | − | 0.0602505i | −0.257922 | − | 0.966166i | \(-0.583038\pi\) |
0.423459 | + | 0.905915i | \(0.360816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.21100 | + | 2.09751i | 0.173000 | + | 0.299644i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.000710351 | 0.00402860i | −9.94691e−5 | 0.000564117i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.90313 | + | 1.59691i | 0.261415 | + | 0.219353i | 0.764069 | − | 0.645135i | \(-0.223199\pi\) |
−0.502654 | + | 0.864487i | \(0.667643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.24054 | − | 1.54343i | −0.571794 | − | 0.208116i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0532169 | − | 1.96013i | −0.00704875 | − | 0.259626i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.35638 | + | 3.04147i | 1.08791 | + | 0.395966i | 0.822845 | − | 0.568265i | \(-0.192385\pi\) |
0.265062 | + | 0.964231i | \(0.414607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.44422 | − | 3.72914i | −0.569024 | − | 0.477468i | 0.312298 | − | 0.949984i | \(-0.398901\pi\) |
−0.881322 | + | 0.472517i | \(0.843346\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.03944 | + | 5.89495i | −0.130957 | + | 0.742694i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.447400 | − | 0.774919i | −0.0554931 | − | 0.0961169i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.6860 | + | 5.34527i | −1.79418 | + | 0.653029i | −0.795276 | + | 0.606247i | \(0.792674\pi\) |
−0.998905 | + | 0.0467817i | \(0.985103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.45234 | − | 2.51552i | 0.174841 | − | 0.302834i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.71938 | + | 4.79913i | −0.678766 | + | 0.569552i | −0.915646 | − | 0.401987i | \(-0.868320\pi\) |
0.236879 | + | 0.971539i | \(0.423875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.93685 | − | 10.9844i | −0.226691 | − | 1.28563i | −0.859426 | − | 0.511260i | \(-0.829179\pi\) |
0.632735 | − | 0.774369i | \(-0.281932\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.449851 | −0.0519444 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.65546 | −1.10034 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.27942 | − | 7.25594i | −0.143946 | − | 0.816357i | −0.968208 | − | 0.250148i | \(-0.919521\pi\) |
0.824262 | − | 0.566209i | \(-0.191590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.53058 | − | 4.64071i | 0.614509 | − | 0.515634i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.0758467 | + | 0.131370i | −0.00832526 | + | 0.0144198i | −0.870158 | − | 0.492773i | \(-0.835983\pi\) |
0.861833 | + | 0.507193i | \(0.169317\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.00854515 | − | 0.00311018i | 0.000926852 | − | 0.000337346i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0913074 | + | 0.158149i | 0.00978918 | + | 0.0169554i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.98885 | − | 11.2793i | 0.210817 | − | 1.19560i | −0.677202 | − | 0.735797i | \(-0.736808\pi\) |
0.888019 | − | 0.459807i | \(-0.152081\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46662 | − | 1.23064i | −0.153744 | − | 0.129006i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.777868 | + | 0.283121i | 0.0806612 | + | 0.0293583i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.71438 | + | 2.28110i | −0.381087 | + | 0.234036i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.85592 | − | 2.85932i | −0.797648 | − | 0.290320i | −0.0891365 | − | 0.996019i | \(-0.528411\pi\) |
−0.708511 | + | 0.705699i | \(0.750633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.67119 | + | 8.11509i | 0.971991 | + | 0.815597i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.53748 | − | 8.71948i | 0.152985 | − | 0.867621i | −0.807620 | − | 0.589703i | \(-0.799245\pi\) |
0.960605 | − | 0.277918i | \(-0.0896442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.48725 | − | 14.7003i | −0.836273 | − | 1.44847i | −0.892989 | − | 0.450078i | \(-0.851396\pi\) |
0.0567161 | − | 0.998390i | \(-0.481937\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.904468 | + | 0.329199i | −0.0882670 | + | 0.0321266i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.73769 | + | 6.47387i | −0.361336 | + | 0.625853i | −0.988181 | − | 0.153291i | \(-0.951013\pi\) |
0.626845 | + | 0.779144i | \(0.284346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.821088 | + | 0.688975i | −0.0786460 | + | 0.0659918i | −0.681263 | − | 0.732039i | \(-0.738569\pi\) |
0.602617 | + | 0.798030i | \(0.294125\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.527800 | + | 2.99330i | 0.0500966 | + | 0.284112i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.3614 | 1.72729 | 0.863647 | − | 0.504097i | \(-0.168175\pi\) | ||||
0.863647 | + | 0.504097i | \(0.168175\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.45697 | −0.602116 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.434697 | + | 2.46529i | 0.0401878 | + | 0.227916i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0149048 | − | 0.0125066i | 0.00136632 | − | 0.00114648i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68216 | + | 8.10974i | −0.425651 | + | 0.737249i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.02543 | + | 1.10117i | −0.272794 | + | 0.0992889i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.500000 | + | 0.866025i | 0.0447214 | + | 0.0774597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.45854 | − | 8.27177i | 0.129424 | − | 0.734001i | −0.849157 | − | 0.528140i | \(-0.822889\pi\) |
0.978581 | − | 0.205861i | \(-0.0659994\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.471913 | − | 0.395982i | −0.0415497 | − | 0.0348643i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0821 | + | 6.21737i | 1.49247 | + | 0.543214i | 0.954098 | − | 0.299495i | \(-0.0968181\pi\) |
0.538370 | + | 0.842709i | \(0.319040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.79880 | + | 7.30452i | −0.502820 | + | 0.633382i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.45079 | + | 0.892014i | 0.210930 | + | 0.0767723i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.1065 | − | 10.1585i | −1.03432 | − | 0.867901i | −0.0429651 | − | 0.999077i | \(-0.513680\pi\) |
−0.991359 | + | 0.131175i | \(0.958125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.06326 | + | 6.03005i | −0.0901845 | + | 0.511462i | 0.905932 | + | 0.423422i | \(0.139171\pi\) |
−0.996117 | + | 0.0880396i | \(0.971940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.271642 | − | 0.470498i | −0.0228764 | − | 0.0396231i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.79443 | + | 1.38106i | −0.317306 | + | 0.115490i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.202972 | − | 0.351558i | 0.0168559 | − | 0.0291953i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.834634 | − | 0.700341i | 0.0688395 | − | 0.0577632i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.54257 | + | 8.74835i | 0.126372 | + | 0.716693i | 0.980483 | + | 0.196602i | \(0.0629908\pi\) |
−0.854111 | + | 0.520091i | \(0.825898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4216 | 1.17362 | 0.586808 | − | 0.809726i | \(-0.300384\pi\) | ||||
0.586808 | + | 0.809726i | \(0.300384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0254405 | −0.00205674 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.319537 | − | 1.81219i | −0.0256658 | − | 0.145558i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.18908 | − | 7.71055i | 0.733368 | − | 0.615369i | −0.197679 | − | 0.980267i | \(-0.563340\pi\) |
0.931048 | + | 0.364898i | \(0.118896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.558796 | − | 0.967862i | 0.0443154 | − | 0.0767565i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.9823 | + | 4.72518i | −1.02315 | + | 0.372397i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.03640 | − | 5.25920i | −0.237829 | − | 0.411932i | 0.722262 | − | 0.691620i | \(-0.243102\pi\) |
−0.960091 | + | 0.279687i | \(0.909769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.352512 | + | 1.99920i | −0.0274430 | + | 0.155637i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.34194 | + | 5.32152i | 0.490754 | + | 0.411792i | 0.854296 | − | 0.519786i | \(-0.173988\pi\) |
−0.363542 | + | 0.931578i | \(0.618433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4636 | + | 4.17242i | 0.881817 | + | 0.320955i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9474 | − | 2.44272i | 0.913644 | − | 0.186799i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.7600 | + | 7.19207i | 1.50233 | + | 0.546803i | 0.956662 | − | 0.291200i | \(-0.0940545\pi\) |
0.545666 | + | 0.838003i | \(0.316277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63905 | + | 1.37533i | 0.123901 | + | 0.103965i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.694659 | − | 3.93961i | 0.0522138 | − | 0.296119i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.30897 | − | 9.19540i | −0.396811 | − | 0.687296i | 0.596520 | − | 0.802598i | \(-0.296550\pi\) |
−0.993330 | + | 0.115302i | \(0.963216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7436 | + | 4.27432i | −0.872895 | + | 0.317708i | −0.739339 | − | 0.673333i | \(-0.764862\pi\) |
−0.133556 | + | 0.991041i | \(0.542640\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.30491 | + | 2.26017i | −0.0964617 | + | 0.167077i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.17588 | − | 4.34308i | 0.380538 | − | 0.319310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.00712589 | − | 0.0404129i | −0.000521097 | − | 0.00295529i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.58031 | 0.405908 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.16539 | −0.373755 | −0.186877 | − | 0.982383i | \(-0.559837\pi\) | ||||
−0.186877 | + | 0.982383i | \(0.559837\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.30453 | + | 18.7409i | 0.237866 | + | 1.34900i | 0.836494 | + | 0.547976i | \(0.184601\pi\) |
−0.598629 | + | 0.801027i | \(0.704287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.308353 | + | 0.258739i | −0.0220817 | + | 0.0185287i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.2779 | + | 19.5339i | −0.803516 | + | 1.39173i | 0.113773 | + | 0.993507i | \(0.463706\pi\) |
−0.917288 | + | 0.398223i | \(0.869627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.01263 | + | 1.09651i | −0.213559 | + | 0.0777293i | −0.446585 | − | 0.894741i | \(-0.647360\pi\) |
0.233025 | + | 0.972471i | \(0.425138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.51526 | + | 6.08860i | 0.247947 | + | 0.429457i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.150826 | − | 0.855375i | 0.0105859 | − | 0.0600355i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.48260 | + | 4.60044i | 0.382921 | + | 0.321309i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.9748 | + | 6.17833i | 1.17983 | + | 0.429424i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.22682 | + | 18.2947i | 0.499890 | + | 1.26547i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.1660 | − | 4.42808i | −0.837545 | − | 0.304841i | −0.112593 | − | 0.993641i | \(-0.535916\pi\) |
−0.724952 | + | 0.688800i | \(0.758138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.57287 | + | 2.15890i | 0.176290 | + | 0.147925i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.237799 | + | 1.34862i | −0.0162177 | + | 0.0919754i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.96861 | − | 3.40973i | −0.133638 | − | 0.231468i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.71499 | + | 1.71611i | −0.318609 | + | 0.115964i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.00406846 | − | 0.00704677i | 0.000273674 | − | 0.000474017i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.59373 | − | 5.53280i | 0.441549 | − | 0.370504i | −0.394740 | − | 0.918793i | \(-0.629165\pi\) |
0.836289 | + | 0.548289i | \(0.184721\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.485804 | − | 2.75513i | −0.0323869 | − | 0.183675i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.99196 | 0.530445 | 0.265223 | − | 0.964187i | \(-0.414555\pi\) | ||||
0.265223 | + | 0.964187i | \(0.414555\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9777 | −0.791510 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.754245 | + | 4.27754i | 0.0496257 | + | 0.281441i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.4257 | − | 15.4610i | 1.20711 | − | 1.01288i | 0.207709 | − | 0.978191i | \(-0.433399\pi\) |
0.999398 | − | 0.0346928i | \(-0.0110453\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.603849 | + | 1.04590i | −0.0393907 | + | 0.0682268i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.11456 | + | 1.13361i | −0.202313 | + | 0.0736357i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.44437 | + | 7.69788i | 0.287483 | + | 0.497935i | 0.973208 | − | 0.229926i | \(-0.0738483\pi\) |
−0.685726 | + | 0.727860i | \(0.740515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.14103 | − | 23.4850i | 0.266747 | − | 1.51280i | −0.497266 | − | 0.867598i | \(-0.665663\pi\) |
0.764013 | − | 0.645201i | \(-0.223226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.48164 | − | 7.11694i | −0.544097 | − | 0.456552i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.27593 | − | 0.828371i | −0.145404 | − | 0.0529227i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23403 | + | 3.69998i | −0.0785197 | + | 0.235424i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0641241 | + | 0.0233393i | 0.00406370 | + | 0.00147907i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.90062 | + | 2.43391i | 0.183086 | + | 0.153627i | 0.729724 | − | 0.683741i | \(-0.239648\pi\) |
−0.546639 | + | 0.837369i | \(0.684093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.05981 | + | 28.6956i | −0.318107 | + | 1.80408i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.00204538 | − | 0.00354269i | −0.000128086 | − | 0.000221852i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.30524 | − | 2.29492i | 0.393310 | − | 0.143153i | −0.137792 | − | 0.990461i | \(-0.544000\pi\) |
0.531102 | + | 0.847308i | \(0.321778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.22834 | − | 12.5198i | 0.449147 | − | 0.777946i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.869985 | + | 0.730004i | −0.0538507 | + | 0.0451861i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.90776 | − | 22.1620i | −0.240963 | − | 1.36657i | −0.829684 | − | 0.558233i | \(-0.811479\pi\) |
0.588721 | − | 0.808336i | \(-0.299632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.48436 | −0.152613 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.15229 | −0.315315 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.97959 | − | 28.2406i | −0.303611 | − | 1.72186i | −0.629973 | − | 0.776617i | \(-0.716934\pi\) |
0.326362 | − | 0.945245i | \(-0.394177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.15115 | − | 7.67872i | 0.555892 | − | 0.466449i | −0.321038 | − | 0.947066i | \(-0.604032\pi\) |
0.876931 | + | 0.480617i | \(0.159587\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.430629 | + | 0.745871i | −0.0260628 | + | 0.0451422i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.24054 | − | 1.54343i | 0.255714 | − | 0.0930723i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.6617 | + | 23.6628i | 0.820852 | + | 1.42176i | 0.905049 | + | 0.425308i | \(0.139834\pi\) |
−0.0841968 | + | 0.996449i | \(0.526832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.893948 | + | 5.06983i | −0.0535193 | + | 0.303523i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.31699 | − | 1.94419i | −0.138220 | − | 0.115980i | 0.571056 | − | 0.820911i | \(-0.306534\pi\) |
−0.709276 | + | 0.704930i | \(0.750978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.3558 | − | 4.86113i | −0.793923 | − | 0.288964i | −0.0869569 | − | 0.996212i | \(-0.527714\pi\) |
−0.706966 | + | 0.707248i | \(0.749936\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.30072 | + | 1.46734i | 0.0770478 | + | 0.0869179i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3898 | + | 5.23748i | 0.849406 | + | 0.309158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0227 | − | 10.9273i | −0.766041 | − | 0.642784i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.653056 | + | 3.70367i | −0.0382828 | + | 0.217113i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0582602 | − | 0.100910i | −0.00340360 | − | 0.00589520i | 0.864319 | − | 0.502945i | \(-0.167750\pi\) |
−0.867722 | + | 0.497050i | \(0.834417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.35638 | + | 3.04147i | −0.486527 | + | 0.177081i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.88471 | − | 10.1926i | 0.341465 | − | 0.591435i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.42597 | + | 3.71383i | −0.255961 | + | 0.214776i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.508801 | + | 2.88555i | 0.0293268 | + | 0.166320i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.98298 | −0.228816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.80151 | 0.332194 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0503112 | − | 0.285329i | −0.00287141 | − | 0.0162846i | 0.983338 | − | 0.181785i | \(-0.0581873\pi\) |
−0.986210 | + | 0.165500i | \(0.947076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.84952 | + | 4.90833i | −0.332767 | + | 0.279225i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.4600 | + | 18.1173i | −0.593133 | + | 1.02734i | 0.400674 | + | 0.916221i | \(0.368776\pi\) |
−0.993807 | + | 0.111116i | \(0.964557\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0335 | + | 11.2953i | −1.75412 | + | 0.638446i | −0.999836 | − | 0.0181073i | \(-0.994236\pi\) |
−0.754280 | + | 0.656553i | \(0.772014\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.99295 | − | 5.18394i | −0.168633 | − | 0.292082i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.452529 | − | 2.56642i | 0.0254165 | − | 0.144144i | −0.969459 | − | 0.245255i | \(-0.921128\pi\) |
0.994875 | + | 0.101110i | \(0.0322395\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.40332 | − | 1.17752i | −0.0785706 | − | 0.0659286i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.16001 | + | 1.15015i | 0.176375 | + | 0.0641951i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0348527 | − | 0.0188800i | −0.00193925 | − | 0.00105051i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.840837 | + | 0.306040i | 0.0466412 | + | 0.0169760i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.369368 | + | 0.309936i | 0.0204261 | + | 0.0171395i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.448711 | + | 2.54477i | −0.0247382 | + | 0.140297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.50939 | − | 16.4708i | −0.522684 | − | 0.905314i | −0.999652 | − | 0.0263938i | \(-0.991598\pi\) |
0.476968 | − | 0.878921i | \(-0.341736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.7626 | + | 6.46506i | −0.973385 | + | 0.354283i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.81426 | − | 13.5347i | 0.426939 | − | 0.739480i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5519 | − | 13.8887i | 0.901642 | − | 0.756568i | −0.0688686 | − | 0.997626i | \(-0.521939\pi\) |
0.970511 | + | 0.241058i | \(0.0774945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.43432 | − | 8.13441i | −0.0779014 | − | 0.441801i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.30398 | −0.449686 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1596 | −1.08851 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.504392 | + | 2.86055i | 0.0271555 | + | 0.154007i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7429 | − | 9.01436i | 0.576709 | − | 0.483916i | −0.307155 | − | 0.951659i | \(-0.599377\pi\) |
0.883865 | + | 0.467743i | \(0.154933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0053 | + | 17.3296i | −0.535570 | + | 0.927634i | 0.463566 | + | 0.886062i | \(0.346570\pi\) |
−0.999136 | + | 0.0415713i | \(0.986764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.19296 | − | 0.798174i | 0.117052 | − | 0.0426034i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.53402 | + | 11.3173i | 0.347771 | + | 0.602357i | 0.985853 | − | 0.167611i | \(-0.0536053\pi\) |
−0.638082 | + | 0.769968i | \(0.720272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.29648 | − | 7.35270i | 0.0688100 | − | 0.390241i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.00670494 | − | 0.00562612i | −0.000354863 | − | 0.000297766i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.9748 | − | 7.27025i | −1.05423 | − | 0.383709i | −0.243973 | − | 0.969782i | \(-0.578451\pi\) |
−0.810258 | + | 0.586073i | \(0.800673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1805 | + | 5.52006i | 0.956866 | + | 0.290529i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.95851 | + | 1.44078i | 0.207768 | + | 0.0756212i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.54436 | + | 7.16957i | 0.447232 | + | 0.375272i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.75221 | − | 21.2799i | 0.195864 | − | 1.11080i | −0.715319 | − | 0.698798i | \(-0.753719\pi\) |
0.911183 | − | 0.412002i | \(-0.135170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0114 | − | 17.3402i | −0.521171 | − | 0.902694i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.99503 | + | 1.81804i | −0.259329 | + | 0.0943880i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.22242 | − | 15.9737i | 0.477519 | − | 0.827086i | −0.522149 | − | 0.852854i | \(-0.674870\pi\) |
0.999668 | + | 0.0257676i | \(0.00820299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.344606 | − | 0.289159i | 0.0177954 | − | 0.0149321i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0630758 | − | 0.357721i | −0.00324857 | − | 0.0184235i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0324 | −1.43993 | −0.719964 | − | 0.694012i | \(-0.755842\pi\) | ||||
−0.719964 | + | 0.694012i | \(0.755842\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.77847 | −0.193577 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.29445 | − | 24.3550i | −0.219436 | − | 1.24448i | −0.873040 | − | 0.487648i | \(-0.837855\pi\) |
0.653604 | − | 0.756836i | \(-0.273256\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.39651 | − | 6.20641i | 0.376961 | − | 0.316308i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.91558 | − | 3.31788i | 0.0973744 | − | 0.168657i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0959 | + | 4.40256i | −0.613289 | + | 0.223219i | −0.629942 | − | 0.776642i | \(-0.716921\pi\) |
0.0166528 | + | 0.999861i | \(0.494699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0293584 | − | 0.0508503i | −0.00148472 | − | 0.00257161i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.42002 | − | 8.05333i | 0.0716305 | − | 0.406237i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.64412 | + | 4.73598i | 0.283986 | + | 0.238293i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.54281 | − | 1.65345i | −0.227997 | − | 0.0829842i | 0.225495 | − | 0.974244i | \(-0.427600\pi\) |
−0.453493 | + | 0.891260i | \(0.649822\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.68901 | + | 1.99837i | 0.184681 | + | 0.100044i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.8719 | − | 9.05262i | −1.24204 | − | 0.452066i | −0.364336 | − | 0.931267i | \(-0.618704\pi\) |
−0.877705 | + | 0.479201i | \(0.840926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.26134 | − | 1.05839i | −0.0628316 | − | 0.0527220i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.25368 | + | 7.10997i | −0.0622959 | + | 0.353297i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.2453 | − | 26.4056i | −0.755680 | − | 1.30888i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.15328 | + | 3.33152i | −0.452601 | + | 0.164733i | −0.558254 | − | 0.829670i | \(-0.688529\pi\) |
0.105654 | + | 0.994403i | \(0.466306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.55469 | + | 6.15691i | −0.175340 | + | 0.303698i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.5755 | + | 12.2303i | −0.717215 | + | 0.601815i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0263413 | − | 0.149389i | −0.00129304 | − | 0.00733321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.75447 | 0.134887 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.5930 | −0.615211 | −0.307605 | − | 0.951514i | \(-0.599528\pi\) | ||||
−0.307605 | + | 0.951514i | \(0.599528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.389772 | − | 2.21051i | −0.0189963 | − | 0.107734i | 0.973835 | − | 0.227255i | \(-0.0729751\pi\) |
−0.992832 | + | 0.119521i | \(0.961864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.58823 | − | 2.17178i | 0.125844 | − | 0.105596i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.00454678 | + | 0.00787525i | −0.000220551 | + | 0.000382006i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.6645 | − | 4.24552i | 0.564484 | − | 0.205455i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.908238 | + | 1.57312i | 0.0438502 | + | 0.0759507i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.94744 | + | 11.0445i | −0.0938051 | + | 0.531995i | 0.901302 | + | 0.433192i | \(0.142613\pi\) |
−0.995107 | + | 0.0988036i | \(0.968498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.4565 | + | 17.1651i | 0.983078 | + | 0.824900i | 0.984551 | − | 0.175099i | \(-0.0560244\pi\) |
−0.00147297 | + | 0.999999i | \(0.500469\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.171602 | − | 0.0624579i | −0.00822767 | − | 0.00299463i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.6699 | + | 21.0616i | 0.893103 | + | 1.00751i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.65088 | + | 0.964842i | 0.126520 | + | 0.0460494i | 0.404504 | − | 0.914536i | \(-0.367444\pi\) |
−0.277984 | + | 0.960586i | \(0.589666\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.19061 | + | 4.35544i | 0.247172 | + | 0.207402i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.321970 | − | 1.82598i | 0.0152973 | − | 0.0867551i | −0.976203 | − | 0.216857i | \(-0.930419\pi\) |
0.991501 | + | 0.130102i | \(0.0415305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.72665 | + | 9.91886i | 0.271469 | + | 0.470199i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.75517 | − | 1.36677i | 0.177614 | − | 0.0646460i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.89875 | + | 17.1451i | −0.467151 | + | 0.809129i | −0.999296 | − | 0.0375242i | \(-0.988053\pi\) |
0.532145 | + | 0.846653i | \(0.321386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.7412 | − | 20.7604i | 1.16502 | − | 0.977567i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.12656 | − | 6.38903i | −0.0529303 | − | 0.300183i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.91454 | 0.0897549 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.6117 | 1.29162 | 0.645811 | − | 0.763497i | \(-0.276519\pi\) | ||||
0.645811 | + | 0.763497i | \(0.276519\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.00411836 | + | 0.0233564i | 0.000192228 | + | 0.00109018i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.3590 | + | 22.9569i | −1.27424 | + | 1.06921i | −0.280226 | + | 0.959934i | \(0.590409\pi\) |
−0.994011 | + | 0.109278i | \(0.965146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24784 | + | 7.35747i | −0.197414 | + | 0.341931i | −0.947689 | − | 0.319195i | \(-0.896588\pi\) |
0.750275 | + | 0.661126i | \(0.229921\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.777868 | + | 0.283121i | −0.0360728 | + | 0.0131294i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.09252 | + | 14.0167i | 0.374477 | + | 0.648613i | 0.990249 | − | 0.139311i | \(-0.0444889\pi\) |
−0.615772 | + | 0.787925i | \(0.711156\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.80666 | − | 32.9312i | 0.268127 | − | 1.52062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.13372 | − | 3.46860i | −0.190472 | − | 0.159825i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.80711 | + | 2.11362i | 0.267011 | + | 0.0971841i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.37912 | − | 4.13498i | 0.0632783 | − | 0.189726i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.53116 | + | 2.37715i | 0.299041 | + | 0.108842i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.14947 | + | 5.99912i | 0.326668 | + | 0.274107i | 0.791340 | − | 0.611376i | \(-0.209384\pi\) |
−0.464673 | + | 0.885482i | \(0.653828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04985 | − | 5.95398i | 0.0478689 | − | 0.271478i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.10746 | + | 5.38228i | 0.141394 | + | 0.244902i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.85592 | − | 2.85932i | 0.356719 | − | 0.129835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.1310 | + | 29.6718i | −0.776281 | + | 1.34456i | 0.157790 | + | 0.987473i | \(0.449563\pi\) |
−0.934071 | + | 0.357086i | \(0.883770\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.09272 | + | 1.75600i | −0.0946362 | + | 0.0794092i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00626 | + | 17.0493i | 0.135670 | + | 0.769425i | 0.974391 | + | 0.224862i | \(0.0721932\pi\) |
−0.838720 | + | 0.544563i | \(0.816696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.00369148 | 0.000166256 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.6248 | −0.567444 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.77398 | − | 15.7320i | −0.124430 | − | 0.705678i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.3552 | − | 9.52812i | 0.508327 | − | 0.426537i | −0.352213 | − | 0.935920i | \(-0.614571\pi\) |
0.860540 | + | 0.509383i | \(0.170126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.86212 | − | 3.22528i | 0.0831933 | − | 0.144095i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.934331 | + | 0.340069i | −0.0416598 | + | 0.0151629i | −0.362766 | − | 0.931880i | \(-0.618168\pi\) |
0.321106 | + | 0.947043i | \(0.395945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.42700 | + | 7.66778i | 0.196999 | + | 0.341212i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.952962 | − | 5.40451i | 0.0423225 | − | 0.240023i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.66391 | + | 7.26988i | 0.384021 | + | 0.322232i | 0.814279 | − | 0.580474i | \(-0.197133\pi\) |
−0.430258 | + | 0.902706i | \(0.641577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4259 | + | 8.16235i | 0.992063 | + | 0.361081i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.17669 | − | 10.5733i | −0.184405 | − | 0.466822i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.9508 | + | 5.80562i | 0.702877 | + | 0.255826i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.17491 | + | 3.50316i | 0.183612 | + | 0.154069i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.64264 | − | 9.31585i | 0.0721037 | − | 0.408921i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2138 | − | 35.0113i | −0.885582 | − | 1.53387i | −0.845045 | − | 0.534695i | \(-0.820427\pi\) |
−0.0405365 | − | 0.999178i | \(-0.512907\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2979 | + | 9.57167i | −1.14993 | + | 0.418540i | −0.845490 | − | 0.533992i | \(-0.820691\pi\) |
−0.304439 | + | 0.952532i | \(0.598469\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.481257 | − | 0.833562i | 0.0210038 | − | 0.0363796i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0128186 | − | 0.0107560i | 0.000558385 | − | 0.000468541i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24591 | + | 18.4085i | 0.141127 | + | 0.800369i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.8784 | 1.07963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.40410 | 0.277392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.29809 | − | 7.36182i | −0.0561212 | − | 0.318279i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.65900 | + | 3.07027i | −0.157898 | + | 0.132492i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.46485 | + | 9.46540i | −0.235388 | + | 0.407703i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0543 | − | 3.65946i | 0.432268 | − | 0.157333i | −0.116717 | − | 0.993165i | \(-0.537237\pi\) |
0.548984 | + | 0.835833i | \(0.315015\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.81096 | + | 4.86872i | 0.120630 | + | 0.208937i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.186126 | − | 1.05557i | 0.00797274 | − | 0.0452157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6218 | + | 18.1429i | 0.924483 | + | 0.775734i | 0.974819 | − | 0.222999i | \(-0.0715846\pi\) |
−0.0503355 | + | 0.998732i | \(0.516029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.2517 | − | 5.55116i | −0.650926 | − | 0.236918i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.73361 | + | 0.354445i | −0.0738542 | + | 0.0150999i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8138 | + | 5.39178i | 0.629946 | + | 0.229282i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.32838 | − | 1.95374i | −0.0988341 | − | 0.0829317i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.01173 | + | 22.7517i | −0.169983 | + | 0.964019i | 0.773795 | + | 0.633436i | \(0.218356\pi\) |
−0.943777 | + | 0.330582i | \(0.892755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.612682 | + | 1.06120i | 0.0259137 | + | 0.0448838i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0173470 | + | 0.00631378i | −0.000732390 | + | 0.000266568i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.5328 | − | 30.3677i | 0.738918 | − | 1.27984i | −0.214064 | − | 0.976820i | \(-0.568670\pi\) |
0.952983 | − | 0.303025i | \(-0.0979965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0656 | + | 11.8025i | −0.591746 | + | 0.496534i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.68241 | + | 15.2127i | 0.112651 | + | 0.638873i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.9610 | 0.836811 | 0.418405 | − | 0.908260i | \(-0.362589\pi\) | ||||
0.418405 | + | 0.908260i | \(0.362589\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.1675 | −0.551044 | −0.275522 | − | 0.961295i | \(-0.588851\pi\) | ||||
−0.275522 | + | 0.961295i | \(0.588851\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.403499 | + | 2.28836i | 0.0168564 | + | 0.0955975i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.94633 | − | 4.15046i | 0.206276 | − | 0.173086i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.96695 | − | 17.2633i | 0.414930 | − | 0.718679i | −0.580491 | − | 0.814266i | \(-0.697140\pi\) |
0.995421 | + | 0.0955871i | \(0.0304729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.04442 | − | 2.92793i | 0.334315 | − | 0.121681i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.162284 | − | 0.281084i | −0.00673266 | − | 0.0116613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.94679 | + | 11.0408i | −0.0806278 | + | 0.457263i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.91766 | − | 1.60910i | −0.0792853 | − | 0.0665283i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0954 | + | 6.22220i | 0.705601 | + | 0.256818i | 0.669800 | − | 0.742541i | \(-0.266380\pi\) |
0.0358006 | + | 0.999359i | \(0.488602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.98714 | + | 6.28210i | −0.205491 | + | 0.258849i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.53482 | + | 3.47039i | 0.392210 | + | 0.142753i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.42900 | − | 2.87727i | −0.140812 | − | 0.118155i | 0.569661 | − | 0.821880i | \(-0.307075\pi\) |
−0.710473 | + | 0.703724i | \(0.751519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.00337864 | + | 0.0191612i | −0.000138511 | + | 0.000785534i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.721105 | + | 1.24899i | 0.0295129 | + | 0.0511178i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0414 | + | 4.74670i | −0.532859 | + | 0.193945i | −0.594414 | − | 0.804159i | \(-0.702616\pi\) |
0.0615555 | + | 0.998104i | \(0.480394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7807 | + | 20.4048i | −0.480545 | + | 0.832328i | −0.999751 | − | 0.0223210i | \(-0.992894\pi\) |
0.519206 | + | 0.854649i | \(0.326228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.4937 | + | 28.1045i | −1.36397 | + | 1.14450i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.62610 | − | 9.22206i | −0.0661103 | − | 0.374930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.7548 | 1.61360 | 0.806799 | − | 0.590826i | \(-0.201198\pi\) | ||||
0.806799 | + | 0.590826i | \(0.201198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.390727 | −0.0158331 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.187652 | + | 1.06423i | 0.00759160 | + | 0.0430541i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.8058 | − | 25.8492i | 1.24424 | − | 1.04404i | 0.247055 | − | 0.969001i | \(-0.420537\pi\) |
0.997181 | − | 0.0750365i | \(-0.0239073\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.60980 | − | 2.78825i | 0.0649133 | − | 0.112433i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.58432 | + | 0.576645i | −0.0637823 | + | 0.0232149i | −0.373714 | − | 0.927544i | \(-0.621916\pi\) |
0.309932 | + | 0.950759i | \(0.399694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.54040 | + | 7.86421i | 0.182494 | + | 0.316089i | 0.942729 | − | 0.333559i | \(-0.108250\pi\) |
−0.760235 | + | 0.649648i | \(0.774916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.92428 | − | 16.5844i | 0.117347 | − | 0.665510i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.7725 | + | 15.7520i | 0.752106 | + | 0.631092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.939693 | − | 0.342020i | −0.0375877 | − | 0.0136808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.54033 | − | 4.63071i | 0.301132 | − | 0.184933i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0577364 | + | 0.0210143i | 0.00230210 | + | 0.000837897i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.65759 | + | 4.74728i | 0.225225 | + | 0.188986i | 0.748417 | − | 0.663229i | \(-0.230814\pi\) |
−0.523192 | + | 0.852215i | \(0.675259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.01135 | + | 5.73567i | −0.0401977 | + | 0.227972i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.19969 | + | 7.27407i | 0.166660 | + | 0.288663i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.03650 | + | 0.741226i | −0.0806891 | + | 0.0293684i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.4437 | + | 18.0891i | −0.413148 | + | 0.715594i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.25431 | + | 1.05249i | −0.0495424 | + | 0.0415710i | −0.667223 | − | 0.744858i | \(-0.732517\pi\) |
0.617680 | + | 0.786429i | \(0.288073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.84236 | − | 10.4486i | −0.0726557 | − | 0.412051i | −0.999344 | − | 0.0362197i | \(-0.988468\pi\) |
0.926688 | − | 0.375831i | \(-0.122643\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.616039 | 0.0242565 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.6557 | −1.24451 | −0.622257 | − | 0.782813i | \(-0.713784\pi\) | ||||
−0.622257 | + | 0.782813i | \(0.713784\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.96847 | + | 39.5202i | 0.273536 | + | 1.55130i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.35679 | + | 1.13848i | −0.0531768 | + | 0.0446206i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3857 | − | 37.0410i | 0.836885 | − | 1.44953i | −0.0556007 | − | 0.998453i | \(-0.517707\pi\) |
0.892486 | − | 0.451075i | \(-0.148959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.0821 | + | 6.21737i | −0.667452 | + | 0.242933i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.6022 | − | 27.0238i | −0.608701 | − | 1.05430i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.87136 | + | 27.6269i | −0.189761 | + | 1.07619i | 0.729922 | + | 0.683530i | \(0.239556\pi\) |
−0.919684 | + | 0.392660i | \(0.871555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.0335 | + | 23.5229i | 1.09038 | + | 0.914935i | 0.996741 | − | 0.0806714i | \(-0.0257064\pi\) |
0.0936364 | + | 0.995606i | \(0.470151\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.00343965 | − | 0.00125193i | −0.000133585 | − | 4.86210e-5i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.253115 | − | 9.32298i | −0.00981539 | − | 0.361530i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.46310 | − | 0.896494i | −0.0953715 | − | 0.0347124i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.96620 | − | 2.48894i | −0.114680 | − | 0.0962279i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.54618 | − | 25.7827i | 0.175503 | − | 0.995329i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4796 | + | 32.0075i | 0.712335 | + | 1.23380i | 0.963979 | + | 0.265980i | \(0.0856954\pi\) |
−0.251644 | + | 0.967820i | \(0.580971\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.45079 | + | 0.892014i | −0.0943309 | + | 0.0343336i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.75900 | − | 8.24282i | 0.182903 | − | 0.316797i | −0.759965 | − | 0.649964i | \(-0.774784\pi\) |
0.942868 | + | 0.333167i | \(0.108117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.7026 | − | 11.4979i | 0.525858 | − | 0.441247i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.624299 | − | 3.54058i | −0.0239232 | − | 0.135675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.2832 | −1.80924 | −0.904620 | − | 0.426218i | \(-0.859846\pi\) | ||||
−0.904620 | + | 0.426218i | \(0.859846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8039 | 0.603834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.935650 | + | 5.30634i | 0.0356973 | + | 0.202449i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.70292 | + | 1.42892i | −0.0648760 | + | 0.0544374i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.4880 | + | 38.9504i | −0.855485 | + | 1.48174i | 0.0207098 | + | 0.999786i | \(0.493407\pi\) |
−0.876195 | + | 0.481958i | \(0.839926\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.3834 | + | 9.23880i | −0.964236 | + | 0.350953i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.06153 | − | 5.30273i | −0.116131 | − | 0.201144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0113015 | + | 0.0640940i | −0.000428075 | + | 0.00242773i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.28882 | − | 6.95515i | −0.313512 | − | 0.263068i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.2174 | − | 13.5460i | −1.40568 | − | 0.511626i | −0.475821 | − | 0.879542i | \(-0.657849\pi\) |
−0.929859 | + | 0.367916i | \(0.880071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.1322 | − | 4.32515i | −1.09874 | − | 0.163126i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.510520 | + | 0.185814i | 0.0192273 | + | 0.00699817i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5121 | + | 12.1771i | 0.545785 | + | 0.457968i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.81747 | − | 15.9787i | 0.105812 | − | 0.600092i | −0.885080 | − | 0.465438i | \(-0.845897\pi\) |
0.990893 | − | 0.134654i | \(-0.0429922\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.3063 | − | 17.8510i | −0.386516 | − | 0.669466i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.1652 | + | 4.06379i | −0.418139 | + | 0.152190i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.01897 | − | 3.49697i | 0.0755054 | − | 0.130779i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.06312 | − | 2.57026i | 0.114394 | − | 0.0959881i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00667 | − | 17.0517i | −0.112130 | − | 0.635920i | −0.988131 | − | 0.153612i | \(-0.950909\pi\) |
0.876001 | − | 0.482309i | \(-0.160202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.3191 | 1.35259 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.7277 | −0.398968 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0704915 | + | 0.399777i | 0.00261799 | + | 0.0148474i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.4738 | + | 10.4668i | −0.462628 | + | 0.388191i | −0.844097 | − | 0.536191i | \(-0.819863\pi\) |
0.381469 | + | 0.924382i | \(0.375418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.33911 | − | 14.4438i | 0.308856 | − | 0.534954i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0117020 | + | 0.00425917i | −0.000432813 | + | 0.000157531i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.13699 | − | 5.43342i | −0.115867 | − | 0.200688i | 0.802259 | − | 0.596976i | \(-0.203631\pi\) |
−0.918126 | + | 0.396288i | \(0.870298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.189196 | + | 1.07299i | −0.00697861 | + | 0.0395777i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.0265 | − | 45.3336i | −1.99009 | − | 1.66989i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.7952 | + | 14.8482i | 1.50068 | + | 0.546201i | 0.956235 | − | 0.292598i | \(-0.0945199\pi\) |
0.544440 | + | 0.838800i | \(0.316742\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.73555 | + | 0.257671i | 0.0637570 | + | 0.00946579i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.4446 | + | 18.3603i | 1.85063 | + | 0.673575i | 0.984914 | + | 0.173043i | \(0.0553599\pi\) |
0.865718 | + | 0.500532i | \(0.166862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.80501 | − | 5.71008i | −0.249316 | − | 0.209201i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0736932 | + | 0.417935i | −0.00269629 | + | 0.0152914i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.99727 | − | 13.8517i | −0.292214 | − | 0.506129i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.2594 | − | 17.9290i | 1.79750 | − | 0.654237i | 0.798896 | − | 0.601470i | \(-0.205418\pi\) |
0.998607 | − | 0.0527677i | \(-0.0168043\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.851680 | − | 1.47515i | 0.0310369 | − | 0.0537576i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0476 | + | 9.27005i | −0.402064 | + | 0.337372i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.15681 | + | 6.56062i | 0.0420451 | + | 0.238450i | 0.998587 | − | 0.0531460i | \(-0.0169249\pi\) |
−0.956542 | + | 0.291596i | \(0.905814\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.1079 | 0.475786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7342 | 0.425364 | 0.212682 | − | 0.977121i | \(-0.431780\pi\) | ||||
0.212682 | + | 0.977121i | \(0.431780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.398239 | − | 2.25853i | −0.0144172 | − | 0.0817642i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0194885 | − | 0.0163528i | 0.000704609 | − | 0.000591237i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.97858 | + | 6.89110i | −0.143658 | + | 0.248823i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.95903 | − | 0.713030i | 0.0706446 | − | 0.0257125i | −0.306456 | − | 0.951885i | \(-0.599143\pi\) |
0.377101 | + | 0.926172i | \(0.376921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.50923 | − | 2.61406i | −0.0543535 | − | 0.0941431i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.65027 | − | 32.0443i | 0.203226 | − | 1.15255i | −0.696980 | − | 0.717090i | \(-0.745474\pi\) |
0.900207 | − | 0.435463i | \(-0.143415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.40963 | + | 1.18282i | 0.0506354 | + | 0.0424882i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.11116 | − | 2.22428i | −0.219236 | − | 0.0797956i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.846667 | − | 31.1852i | −0.0303350 | − | 1.11733i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.6604 | − | 11.5234i | −1.13290 | − | 0.412341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.811037 | + | 0.680541i | 0.0289841 | + | 0.0243205i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.08300 | + | 11.8133i | −0.0743453 | + | 0.421633i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.4871 | − | 35.4846i | −0.730285 | − | 1.26489i | −0.956761 | − | 0.290874i | \(-0.906054\pi\) |
0.226476 | − | 0.974017i | \(-0.427279\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.51290 | + | 3.46241i | −0.338668 | + | 0.123265i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.6433 | + | 34.0231i | −0.698434 | + | 1.20972i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.97668 | − | 3.33683i | 0.141216 | − | 0.118494i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.194068 | + | 1.10061i | 0.00688287 | + | 0.0390347i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.7920 | −1.19697 | −0.598487 | − | 0.801132i | \(-0.704231\pi\) | ||||
−0.598487 | + | 0.801132i | \(0.704231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0109823 | −0.000388525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.56406 | − | 31.5554i | −0.196597 | − | 1.11495i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.5580 | − | 32.3540i | 1.36068 | − | 1.14175i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.90776 | − | 11.9646i | 0.243466 | − | 0.421696i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.1221 | + | 4.41208i | −0.426718 | + | 0.155313i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.46472 | − | 12.9293i | −0.262445 | − | 0.454569i | 0.704446 | − | 0.709758i | \(-0.251196\pi\) |
−0.966891 | + | 0.255189i | \(0.917862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.28041 | + | 35.6180i | −0.220535 | + | 1.25072i | 0.650504 | + | 0.759503i | \(0.274558\pi\) |
−0.871039 | + | 0.491214i | \(0.836553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.11666 | − | 3.45428i | −0.144377 | − | 0.121147i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.70656 | + | 2.07702i | 0.199892 | + | 0.0727548i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.08657 | − | 3.12380i | 0.177957 | − | 0.109288i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.03316 | − | 1.83192i | −0.175873 | − | 0.0640125i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.21404 | − | 5.21420i | −0.216872 | − | 0.181977i | 0.527879 | − | 0.849319i | \(-0.322987\pi\) |
−0.744751 | + | 0.667342i | \(0.767432\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.27345 | + | 7.22211i | −0.0443898 | + | 0.251747i | −0.998925 | − | 0.0463504i | \(-0.985241\pi\) |
0.954535 | + | 0.298097i | \(0.0963520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.01502 | − | 1.75806i | −0.0353384 | − | 0.0612079i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.0689 | + | 8.03243i | −0.767412 | + | 0.279315i | −0.695913 | − | 0.718126i | \(-0.745000\pi\) |
−0.0714983 | + | 0.997441i | \(0.522778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.3729 | − | 23.1625i | 0.464459 | − | 0.804467i | −0.534718 | − | 0.845031i | \(-0.679582\pi\) |
0.999177 | + | 0.0405640i | \(0.0129155\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.41581 | − | 7.90080i | 0.326631 | − | 0.274076i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.00382452 | − | 0.0216900i | −0.000132512 | − | 0.000751512i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.27882 | −0.286500 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.79922 | 0.165885 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.51241 | + | 14.2486i | 0.0867380 | + | 0.491916i | 0.996968 | + | 0.0778127i | \(0.0247936\pi\) |
−0.910230 | + | 0.414103i | \(0.864095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0891 | + | 18.5349i | −0.761691 | + | 0.639135i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.680314 | + | 1.17834i | −0.0234313 | + | 0.0405841i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.4636 | + | 4.17242i | −0.394361 | + | 0.143536i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0181 | − | 17.3518i | −0.344225 | − | 0.596216i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.11026 | + | 6.29660i | −0.0381040 | + | 0.216099i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.4205 | − | 28.0431i | −1.14564 | − | 0.961306i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2436 | − | 7.00411i | −0.658889 | − | 0.239816i | −0.00913255 | − | 0.999958i | \(-0.502907\pi\) |
−0.649757 | + | 0.760142i | \(0.725129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.58212 | + | 9.55090i | −0.259303 | + | 0.326634i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.3628 | − | 18.3305i | −1.72036 | − | 0.626159i | −0.722488 | − | 0.691383i | \(-0.757002\pi\) |
−0.997871 | + | 0.0652238i | \(0.979224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.7374 | − | 18.2399i | −0.741672 | − | 0.622337i | 0.191614 | − | 0.981470i | \(-0.438628\pi\) |
−0.933286 | + | 0.359134i | \(0.883072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.19622 | − | 6.78408i | 0.0407669 | − | 0.231201i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6593 | + | 44.4432i | 0.873452 | + | 1.51286i | 0.858403 | + | 0.512976i | \(0.171457\pi\) |
0.0150485 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.7600 | + | 7.19207i | −0.671862 | + | 0.244538i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.82372 | + | 6.62287i | −0.129860 | + | 0.224925i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.4701 | − | 21.3720i | 0.864014 | − | 0.724994i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.42837 | − | 13.7719i | −0.0822820 | − | 0.466645i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.3885 | −0.791580 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.13963 | −0.0723326 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.28817 | + | 24.3194i | 0.144801 | + | 0.821209i | 0.967526 | + | 0.252770i | \(0.0813415\pi\) |
−0.822725 | + | 0.568439i | \(0.807547\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0401536 | + | 0.0336929i | −0.00135435 | + | 0.00113643i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.1551 | + | 17.5891i | −0.342133 | + | 0.592592i | −0.984829 | − | 0.173530i | \(-0.944483\pi\) |
0.642696 | + | 0.766122i | \(0.277816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.6680 | − | 15.5299i | 1.43589 | − | 0.522622i | 0.497278 | − | 0.867591i | \(-0.334333\pi\) |
0.938614 | + | 0.344969i | \(0.112111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00019 | + | 3.46443i | 0.0672357 | + | 0.116456i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.06102 | + | 17.3599i | −0.102779 | + | 0.582889i | 0.889305 | + | 0.457315i | \(0.151189\pi\) |
−0.992084 | + | 0.125575i | \(0.959922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7670 | + | 11.5519i | 0.461730 | + | 0.387438i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.6152 | + | 11.1430i | 1.02565 | + | 0.373305i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.15754 | − | 1.05449i | 0.172590 | − | 0.0352870i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.97759 | + | 3.63155i | 0.333514 | + | 0.121389i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.99103 | + | 1.67067i | 0.0664785 | + | 0.0557821i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.129714 | − | 0.735647i | 0.00432622 | − | 0.0245352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0112958 | − | 0.0195649i | −0.000376318 | − | 0.000651803i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.23860 | − | 0.450815i | 0.0412182 | − | 0.0150022i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.24864 | − | 10.8230i | 0.207712 | − | 0.359767i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0126 | + | 22.6663i | −0.896940 | + | 0.752622i | −0.969590 | − | 0.244736i | \(-0.921299\pi\) |
0.0726501 | + | 0.997357i | \(0.476854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.30131 | − | 24.3939i | −0.142665 | − | 0.809095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.09159 | 0.0361660 | 0.0180830 | − | 0.999836i | \(-0.494244\pi\) | ||||
0.0180830 | + | 0.999836i | \(0.494244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.684544 | −0.0226551 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.453190 | − | 2.57017i | −0.0149820 | − | 0.0849672i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.7952 | + | 25.0012i | −0.983926 | + | 0.825612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.43232 | + | 4.21291i | −0.0802350 | + | 0.138971i | −0.903351 | − | 0.428902i | \(-0.858900\pi\) |
0.823116 | + | 0.567874i | \(0.192234\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.122476 | + | 0.0445775i | −0.00403571 | + | 0.00146888i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.34034 | − | 5.78565i | −0.109949 | − | 0.190437i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.17328 | + | 6.65398i | −0.0385771 | + | 0.218782i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.3782 | − | 30.5250i | −1.19482 | − | 1.00257i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.7981 | + | 9.02577i | 0.813599 | + | 0.296126i | 0.715110 | − | 0.699012i | \(-0.246377\pi\) |
0.0984895 | + | 0.995138i | \(0.468599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.87870 | + | 9.81890i | 0.127119 | + | 0.321802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.84336 | + | 3.21872i | 0.289519 | + | 0.105376i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0314357 | + | 0.0263777i | 0.00102806 | + | 0.000862642i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.495573 | − | 2.81053i | 0.0161897 | − | 0.0918162i | −0.975642 | − | 0.219367i | \(-0.929601\pi\) |
0.991832 | + | 0.127551i | \(0.0407118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.42820 | + | 12.8660i | 0.242410 | + | 0.419867i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.2216 | − | 14.2755i | 1.27859 | − | 0.465368i | 0.388624 | − | 0.921397i | \(-0.372951\pi\) |
0.889965 | + | 0.456028i | \(0.150728\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1063 | − | 40.0213i | 0.752446 | − | 1.30327i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.27476 | + | 3.58695i | −0.139058 | + | 0.116684i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.05892 | + | 17.3480i | 0.0994016 | + | 0.563734i | 0.993309 | + | 0.115483i | \(0.0368417\pi\) |
−0.893908 | + | 0.448251i | \(0.852047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.98048 | 0.323980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.17232 | −0.0380150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.46296 | + | 19.6394i | 0.112176 | + | 0.636183i | 0.988110 | + | 0.153751i | \(0.0491353\pi\) |
−0.875934 | + | 0.482432i | \(0.839754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.95692 | − | 3.32025i | 0.128043 | − | 0.107441i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.412041 | + | 0.713677i | −0.0133194 | + | 0.0230699i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.7751 | − | 11.5652i | 1.02607 | − | 0.373460i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8069 | + | 23.9143i | 0.445385 | + | 0.771430i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.63157 | + | 20.5957i | −0.117026 | + | 0.663686i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.5779 | − | 12.2323i | −0.469278 | − | 0.393771i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.9538 | − | 7.62656i | −0.673829 | − | 0.245254i | −0.0176332 | − | 0.999845i | \(-0.505613\pi\) |
−0.656196 | + | 0.754591i | \(0.727835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.00564163 | + | 0.0169152i | −0.000181235 | + | 0.000543393i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.7102 | − | 11.5416i | −1.01763 | − | 0.370387i | −0.221271 | − | 0.975212i | \(-0.571021\pi\) |
−0.796358 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.0360 | − | 8.42122i | −0.321740 | − | 0.269972i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0698981 | − | 0.396412i | 0.00223853 | − | 0.0126953i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.47596 | − | 4.28849i | −0.0792129 | − | 0.137201i | 0.823698 | − | 0.567029i | \(-0.191907\pi\) |
−0.902911 | + | 0.429828i | \(0.858574\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.5682 | − | 17.6774i | 1.55225 | − | 0.564971i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.49933 | + | 2.59691i | −0.0478698 | + | 0.0829130i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.9610 | + | 11.7147i | −0.445288 | + | 0.373641i | −0.837684 | − | 0.546155i | \(-0.816091\pi\) |
0.392396 | + | 0.919796i | \(0.371646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.91677 | − | 22.2131i | −0.124799 | − | 0.707768i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.16243 | 0.0370004 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.84236 | 0.281171 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.16408 | + | 6.60185i | 0.0369784 | + | 0.209715i | 0.997699 | − | 0.0678037i | \(-0.0215992\pi\) |
−0.960720 | + | 0.277518i | \(0.910488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.55399 | + | 5.49945i | −0.207985 | + | 0.174520i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.60299 | − | 2.77645i | 0.0508181 | − | 0.0880195i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2083 | − | 6.99126i | 0.608334 | − | 0.221415i | −0.0194403 | − | 0.999811i | \(-0.506188\pi\) |
0.627774 | + | 0.778396i | \(0.283966\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.81090 | + | 15.2609i | 0.278764 | + | 0.482834i |
(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 | 380.2.u.a.61.2 | ✓ | 18 | |
19.5 | even | 9 | inner | 380.2.u.a.81.2 | yes | 18 | |
19.9 | even | 9 | 7220.2.a.v.1.5 | 9 | |||
19.10 | odd | 18 | 7220.2.a.x.1.5 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.u.a.61.2 | ✓ | 18 | 1.1 | even | 1 | trivial | |
380.2.u.a.81.2 | yes | 18 | 19.5 | even | 9 | inner | |
7220.2.a.v.1.5 | 9 | 19.9 | even | 9 | |||
7220.2.a.x.1.5 | 9 | 19.10 | odd | 18 |