Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(101,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.l (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: | \(7.58578819202\) |
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: | \( x^{18} + 24 x^{16} - 12 x^{15} + 393 x^{14} - 222 x^{13} + 3518 x^{12} - 2478 x^{11} + 22809 x^{10} - 12862 x^{9} + 77397 x^{8} - 24822 x^{7} + 178501 x^{6} - 39408 x^{5} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 651.3 | ||
Root | \(1.60792 - 2.78500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.651 |
Dual form | 950.2.l.i.251.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.939693 | + | 0.342020i | −0.664463 | + | 0.241845i | ||||
\(3\) | 0.558424 | − | 3.16698i | 0.322406 | − | 1.82846i | −0.204901 | − | 0.978783i | \(-0.565687\pi\) |
0.527307 | − | 0.849675i | \(-0.323202\pi\) | |||||||
\(4\) | 0.766044 | − | 0.642788i | 0.383022 | − | 0.321394i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.558424 | + | 3.16698i | 0.227976 | + | 1.29291i | ||||
\(7\) | −0.0116976 | − | 0.0202608i | −0.00442126 | − | 0.00765785i | 0.863806 | − | 0.503824i | \(-0.168074\pi\) |
−0.868228 | + | 0.496166i | \(0.834741\pi\) | |||||||
\(8\) | −0.500000 | + | 0.866025i | −0.176777 | + | 0.306186i | ||||
\(9\) | −6.89886 | − | 2.51098i | −2.29962 | − | 0.836993i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.08041 | + | 1.87132i | −0.325755 | + | 0.564225i | −0.981665 | − | 0.190615i | \(-0.938952\pi\) |
0.655910 | + | 0.754839i | \(0.272285\pi\) | |||||||
\(12\) | −1.60792 | − | 2.78500i | −0.464166 | − | 0.803959i | ||||
\(13\) | 0.276152 | + | 1.56613i | 0.0765907 | + | 0.434368i | 0.998856 | + | 0.0478110i | \(0.0152245\pi\) |
−0.922266 | + | 0.386557i | \(0.873664\pi\) | |||||||
\(14\) | 0.0179217 | + | 0.0150381i | 0.00478977 | + | 0.00401910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.173648 | − | 0.984808i | 0.0434120 | − | 0.246202i | ||||
\(17\) | −7.49847 | + | 2.72922i | −1.81865 | + | 0.661933i | −0.823073 | + | 0.567936i | \(0.807742\pi\) |
−0.995573 | + | 0.0939966i | \(0.970036\pi\) | |||||||
\(18\) | 7.34161 | 1.73043 | ||||||||
\(19\) | 1.06458 | + | 4.22690i | 0.244232 | + | 0.969717i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0706976 | + | 0.0257318i | −0.0154275 | + | 0.00561515i | ||||
\(22\) | 0.375222 | − | 2.12799i | 0.0799976 | − | 0.453689i | ||||
\(23\) | −3.43239 | + | 2.88011i | −0.715702 | + | 0.600545i | −0.926193 | − | 0.377050i | \(-0.876938\pi\) |
0.210491 | + | 0.977596i | \(0.432494\pi\) | |||||||
\(24\) | 2.46347 | + | 2.06710i | 0.502855 | + | 0.421945i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.795147 | − | 1.37724i | −0.155941 | − | 0.270098i | ||||
\(27\) | −6.98095 | + | 12.0914i | −1.34348 | + | 2.32698i | ||||
\(28\) | −0.0219842 | − | 0.00800160i | −0.00415463 | − | 0.00151216i | ||||
\(29\) | −7.09702 | − | 2.58310i | −1.31788 | − | 0.479670i | −0.415104 | − | 0.909774i | \(-0.636255\pi\) |
−0.902780 | + | 0.430104i | \(0.858477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.22993 | − | 3.86236i | −0.400508 | − | 0.693700i | 0.593279 | − | 0.804997i | \(-0.297833\pi\) |
−0.993787 | + | 0.111297i | \(0.964500\pi\) | |||||||
\(32\) | 0.173648 | + | 0.984808i | 0.0306970 | + | 0.174091i | ||||
\(33\) | 5.32312 | + | 4.46663i | 0.926636 | + | 0.777540i | ||||
\(34\) | 6.11281 | − | 5.12925i | 1.04834 | − | 0.879660i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.89886 | + | 2.51098i | −1.14981 | + | 0.418496i | ||||
\(37\) | 0.389132 | 0.0639729 | 0.0319864 | − | 0.999488i | \(-0.489817\pi\) | ||||
0.0319864 | + | 0.999488i | \(0.489817\pi\) | |||||||
\(38\) | −2.44606 | − | 3.60788i | −0.396804 | − | 0.585275i | ||||
\(39\) | 5.11413 | 0.818916 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.972920 | − | 5.51771i | 0.151945 | − | 0.861721i | −0.809582 | − | 0.587007i | \(-0.800306\pi\) |
0.961526 | − | 0.274713i | \(-0.0885830\pi\) | |||||||
\(42\) | 0.0576332 | − | 0.0483600i | 0.00889300 | − | 0.00746212i | ||||
\(43\) | −7.43337 | − | 6.23734i | −1.13358 | − | 0.951185i | −0.134369 | − | 0.990931i | \(-0.542901\pi\) |
−0.999210 | + | 0.0397459i | \(0.987345\pi\) | |||||||
\(44\) | 0.375222 | + | 2.12799i | 0.0565668 | + | 0.320806i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.24033 | − | 3.88037i | 0.330319 | − | 0.572129i | ||||
\(47\) | 4.01711 | + | 1.46211i | 0.585956 | + | 0.213271i | 0.617950 | − | 0.786218i | \(-0.287963\pi\) |
−0.0319938 | + | 0.999488i | \(0.510186\pi\) | |||||||
\(48\) | −3.02190 | − | 1.09988i | −0.436173 | − | 0.158754i | ||||
\(49\) | 3.49973 | − | 6.06170i | 0.499961 | − | 0.865958i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.45606 | + | 25.2716i | 0.623973 | + | 3.53873i | ||||
\(52\) | 1.21824 | + | 1.02222i | 0.168939 | + | 0.141757i | ||||
\(53\) | 2.89731 | − | 2.43113i | 0.397976 | − | 0.333941i | −0.421735 | − | 0.906719i | \(-0.638579\pi\) |
0.819711 | + | 0.572778i | \(0.194134\pi\) | |||||||
\(54\) | 2.42446 | − | 13.7498i | 0.329927 | − | 1.87111i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0233951 | 0.00312630 | ||||||||
\(57\) | 13.9810 | − | 1.01111i | 1.85183 | − | 0.133925i | ||||
\(58\) | 7.55249 | 0.991691 | ||||||||
\(59\) | 3.41426 | − | 1.24269i | 0.444499 | − | 0.161784i | −0.110067 | − | 0.993924i | \(-0.535107\pi\) |
0.554566 | + | 0.832140i | \(0.312884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.84152 | + | 7.41891i | −1.13204 | + | 0.949894i | −0.999149 | − | 0.0412364i | \(-0.986870\pi\) |
−0.132891 | + | 0.991131i | \(0.542426\pi\) | |||||||
\(62\) | 3.41646 | + | 2.86675i | 0.433890 | + | 0.364077i | ||||
\(63\) | 0.0298254 | + | 0.169148i | 0.00375765 | + | 0.0213107i | ||||
\(64\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.52977 | − | 2.37664i | −0.803759 | − | 0.292544i | ||||
\(67\) | 3.62429 | + | 1.31913i | 0.442778 | + | 0.161158i | 0.553781 | − | 0.832662i | \(-0.313184\pi\) |
−0.111004 | + | 0.993820i | \(0.535407\pi\) | |||||||
\(68\) | −3.98985 | + | 6.91062i | −0.483840 | + | 0.838036i | ||||
\(69\) | 7.20454 | + | 12.4786i | 0.867325 | + | 1.50225i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.85813 | − | 8.27195i | −1.16994 | − | 0.981700i | −0.169952 | − | 0.985452i | \(-0.554361\pi\) |
−0.999993 | + | 0.00375214i | \(0.998806\pi\) | |||||||
\(72\) | 5.62400 | − | 4.71909i | 0.662795 | − | 0.556151i | ||||
\(73\) | 0.330206 | − | 1.87269i | 0.0386477 | − | 0.219182i | −0.959367 | − | 0.282161i | \(-0.908949\pi\) |
0.998015 | + | 0.0629785i | \(0.0200600\pi\) | |||||||
\(74\) | −0.365664 | + | 0.133091i | −0.0425076 | + | 0.0154715i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.53251 | + | 2.55369i | 0.405207 | + | 0.292928i | ||||
\(77\) | 0.0505526 | 0.00576100 | ||||||||
\(78\) | −4.80571 | + | 1.74914i | −0.544139 | + | 0.198051i | ||||
\(79\) | −1.65165 | + | 9.36698i | −0.185825 | + | 1.05387i | 0.739065 | + | 0.673634i | \(0.235267\pi\) |
−0.924891 | + | 0.380233i | \(0.875844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 17.5228 | + | 14.7034i | 1.94698 | + | 1.63371i | ||||
\(82\) | 0.972920 | + | 5.51771i | 0.107441 | + | 0.609329i | ||||
\(83\) | −1.31417 | − | 2.27622i | −0.144249 | − | 0.249847i | 0.784843 | − | 0.619694i | \(-0.212743\pi\) |
−0.929093 | + | 0.369847i | \(0.879410\pi\) | |||||||
\(84\) | −0.0376174 | + | 0.0651553i | −0.00410440 | + | 0.00710903i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.11838 | + | 3.31882i | 0.983260 | + | 0.357877i | ||||
\(87\) | −12.1438 | + | 21.0337i | −1.30195 | + | 2.25505i | ||||
\(88\) | −1.08041 | − | 1.87132i | −0.115172 | − | 0.199484i | ||||
\(89\) | 1.54115 | + | 8.74032i | 0.163362 | + | 0.926472i | 0.950737 | + | 0.309998i | \(0.100328\pi\) |
−0.787375 | + | 0.616474i | \(0.788561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0285008 | − | 0.0239150i | 0.00298769 | − | 0.00250697i | ||||
\(92\) | −0.778059 | + | 4.41259i | −0.0811183 | + | 0.460045i | ||||
\(93\) | −13.4773 | + | 4.90532i | −1.39753 | + | 0.508658i | ||||
\(94\) | −4.27492 | −0.440924 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.21584 | 0.328215 | ||||||||
\(97\) | 10.4812 | − | 3.81486i | 1.06421 | − | 0.387340i | 0.250201 | − | 0.968194i | \(-0.419503\pi\) |
0.814008 | + | 0.580854i | \(0.197281\pi\) | |||||||
\(98\) | −1.21544 | + | 6.89312i | −0.122778 | + | 0.696310i | ||||
\(99\) | 12.1524 | − | 10.1971i | 1.22137 | − | 1.02485i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.23809 | − | 18.3641i | −0.322202 | − | 1.82730i | −0.528651 | − | 0.848840i | \(-0.677302\pi\) |
0.206449 | − | 0.978457i | \(-0.433809\pi\) | |||||||
\(102\) | −12.8307 | − | 22.2234i | −1.27043 | − | 2.20045i | ||||
\(103\) | 1.76795 | − | 3.06218i | 0.174201 | − | 0.301726i | −0.765683 | − | 0.643218i | \(-0.777599\pi\) |
0.939885 | + | 0.341492i | \(0.110932\pi\) | |||||||
\(104\) | −1.49439 | − | 0.543913i | −0.146537 | − | 0.0533350i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.89108 | + | 3.27545i | −0.183678 | + | 0.318140i | ||||
\(107\) | 2.79632 | + | 4.84336i | 0.270330 | + | 0.468226i | 0.968946 | − | 0.247271i | \(-0.0795338\pi\) |
−0.698616 | + | 0.715497i | \(0.746200\pi\) | |||||||
\(108\) | 2.42446 | + | 13.7498i | 0.233294 | + | 1.32307i | ||||
\(109\) | 7.21936 | + | 6.05777i | 0.691490 | + | 0.580229i | 0.919338 | − | 0.393468i | \(-0.128725\pi\) |
−0.227849 | + | 0.973697i | \(0.573169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.217301 | − | 1.23237i | 0.0206253 | − | 0.116972i | ||||
\(112\) | −0.0219842 | + | 0.00800160i | −0.00207731 | + | 0.000756080i | ||||
\(113\) | 5.69339 | 0.535589 | 0.267795 | − | 0.963476i | \(-0.413705\pi\) | ||||
0.267795 | + | 0.963476i | \(0.413705\pi\) | |||||||
\(114\) | −12.7920 | + | 5.73191i | −1.19808 | + | 0.536843i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.09702 | + | 2.58310i | −0.658942 | + | 0.239835i | ||||
\(117\) | 2.02740 | − | 11.4979i | 0.187433 | − | 1.06299i | ||||
\(118\) | −2.78333 | + | 2.33549i | −0.256226 | + | 0.214999i | ||||
\(119\) | 0.143010 | + | 0.119999i | 0.0131097 | + | 0.0110003i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.16544 | + | 5.48269i | 0.287767 | + | 0.498427i | ||||
\(122\) | 5.77089 | − | 9.99547i | 0.522472 | − | 0.904948i | ||||
\(123\) | −16.9312 | − | 6.16244i | −1.52663 | − | 0.555649i | ||||
\(124\) | −4.19091 | − | 1.52536i | −0.376354 | − | 0.136982i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0858789 | − | 0.148747i | −0.00765070 | − | 0.0132514i | ||||
\(127\) | −1.50642 | − | 8.54334i | −0.133673 | − | 0.758099i | −0.975774 | − | 0.218779i | \(-0.929793\pi\) |
0.842101 | − | 0.539320i | \(-0.181319\pi\) | |||||||
\(128\) | 0.766044 | + | 0.642788i | 0.0677094 | + | 0.0568149i | ||||
\(129\) | −23.9045 | + | 20.0583i | −2.10468 | + | 1.76603i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4945 | + | 7.09542i | −1.70324 | + | 0.619930i | −0.996188 | − | 0.0872292i | \(-0.972199\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(132\) | 6.94884 | 0.604818 | ||||||||
\(133\) | 0.0731872 | − | 0.0710136i | 0.00634613 | − | 0.00615766i | ||||
\(134\) | −3.85689 | −0.333185 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.38566 | − | 7.85847i | 0.118819 | − | 0.673858i | ||||
\(137\) | −4.57200 | + | 3.83636i | −0.390612 | + | 0.327762i | −0.816852 | − | 0.576848i | \(-0.804283\pi\) |
0.426240 | + | 0.904610i | \(0.359838\pi\) | |||||||
\(138\) | −11.0380 | − | 9.26198i | −0.939617 | − | 0.788432i | ||||
\(139\) | −2.44517 | − | 13.8672i | −0.207397 | − | 1.17620i | −0.893624 | − | 0.448817i | \(-0.851845\pi\) |
0.686227 | − | 0.727387i | \(-0.259266\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.87373 | − | 11.9056i | 0.578872 | − | 1.00264i | ||||
\(142\) | 12.0928 | + | 4.40141i | 1.01480 | + | 0.369358i | ||||
\(143\) | −3.22910 | − | 1.17530i | −0.270031 | − | 0.0982832i | ||||
\(144\) | −3.67080 | + | 6.35802i | −0.305900 | + | 0.529835i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.330206 | + | 1.87269i | 0.0273281 | + | 0.154985i | ||||
\(147\) | −17.2430 | − | 14.4686i | −1.42218 | − | 1.19335i | ||||
\(148\) | 0.298092 | − | 0.250129i | 0.0245030 | − | 0.0205605i | ||||
\(149\) | 1.22145 | − | 6.92721i | 0.100065 | − | 0.567499i | −0.893012 | − | 0.450034i | \(-0.851412\pi\) |
0.993077 | − | 0.117465i | \(-0.0374769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0840 | −1.14614 | −0.573070 | − | 0.819507i | \(-0.694248\pi\) | ||||
−0.573070 | + | 0.819507i | \(0.694248\pi\) | |||||||
\(152\) | −4.19289 | − | 1.19149i | −0.340088 | − | 0.0966429i | ||||
\(153\) | 58.5838 | 4.73622 | ||||||||
\(154\) | −0.0475039 | + | 0.0172900i | −0.00382797 | + | 0.00139327i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.91765 | − | 3.28730i | 0.313663 | − | 0.263195i | ||||
\(157\) | −2.07466 | − | 1.74085i | −0.165576 | − | 0.138935i | 0.556235 | − | 0.831025i | \(-0.312245\pi\) |
−0.721811 | + | 0.692090i | \(0.756690\pi\) | |||||||
\(158\) | −1.65165 | − | 9.36698i | −0.131398 | − | 0.745197i | ||||
\(159\) | −6.08141 | − | 10.5333i | −0.482288 | − | 0.835346i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0985039 | + | 0.0358525i | 0.00776319 | + | 0.00282557i | ||||
\(162\) | −21.4949 | − | 7.82350i | −1.68880 | − | 0.614672i | ||||
\(163\) | 6.89810 | − | 11.9479i | 0.540301 | − | 0.935829i | −0.458585 | − | 0.888650i | \(-0.651644\pi\) |
0.998886 | − | 0.0471785i | \(-0.0150229\pi\) | |||||||
\(164\) | −2.80141 | − | 4.85219i | −0.218754 | − | 0.378892i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.01343 | + | 1.68947i | 0.156273 | + | 0.131128i | ||||
\(167\) | −18.5877 | + | 15.5969i | −1.43836 | + | 1.20692i | −0.497798 | + | 0.867293i | \(0.665858\pi\) |
−0.940558 | + | 0.339632i | \(0.889698\pi\) | |||||||
\(168\) | 0.0130644 | − | 0.0740919i | 0.00100794 | − | 0.00571631i | ||||
\(169\) | 9.83949 | − | 3.58128i | 0.756884 | − | 0.275483i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.26925 | − | 31.8339i | 0.250006 | − | 2.43440i | ||||
\(172\) | −9.70358 | −0.739891 | ||||||||
\(173\) | −18.1956 | + | 6.62267i | −1.38339 | + | 0.503512i | −0.923204 | − | 0.384311i | \(-0.874439\pi\) |
−0.460184 | + | 0.887823i | \(0.652217\pi\) | |||||||
\(174\) | 4.21749 | − | 23.9186i | 0.319727 | − | 1.81326i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.65528 | + | 1.38895i | 0.124772 | + | 0.104696i | ||||
\(177\) | −2.02897 | − | 11.5068i | −0.152506 | − | 0.864907i | ||||
\(178\) | −4.43758 | − | 7.68611i | −0.332610 | − | 0.576098i | ||||
\(179\) | −4.29621 | + | 7.44125i | −0.321114 | + | 0.556185i | −0.980718 | − | 0.195428i | \(-0.937391\pi\) |
0.659604 | + | 0.751613i | \(0.270724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.94197 | + | 1.43476i | 0.293005 | + | 0.106645i | 0.484340 | − | 0.874880i | \(-0.339060\pi\) |
−0.191336 | + | 0.981525i | \(0.561282\pi\) | |||||||
\(182\) | −0.0186026 | + | 0.0322206i | −0.00137891 | + | 0.00238835i | ||||
\(183\) | 18.5582 | + | 32.1438i | 1.37186 | + | 2.37614i | ||||
\(184\) | −0.778059 | − | 4.41259i | −0.0573593 | − | 0.325301i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.9868 | − | 9.21899i | 0.805589 | − | 0.675969i | ||||
\(187\) | 2.99416 | − | 16.9807i | 0.218955 | − | 1.24175i | ||||
\(188\) | 4.01711 | − | 1.46211i | 0.292978 | − | 0.106635i | ||||
\(189\) | 0.326640 | 0.0237596 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8620 | 1.36481 | 0.682403 | − | 0.730976i | \(-0.260935\pi\) | ||||
0.682403 | + | 0.730976i | \(0.260935\pi\) | |||||||
\(192\) | −3.02190 | + | 1.09988i | −0.218087 | + | 0.0793771i | ||||
\(193\) | 3.08999 | − | 17.5242i | 0.222422 | − | 1.26142i | −0.645130 | − | 0.764073i | \(-0.723197\pi\) |
0.867552 | − | 0.497346i | \(-0.165692\pi\) | |||||||
\(194\) | −8.54438 | + | 7.16959i | −0.613451 | + | 0.514747i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.21544 | − | 6.89312i | −0.0868173 | − | 0.492365i | ||||
\(197\) | 6.75642 | + | 11.7025i | 0.481375 | + | 0.833766i | 0.999772 | − | 0.0213742i | \(-0.00680412\pi\) |
−0.518396 | + | 0.855140i | \(0.673471\pi\) | |||||||
\(198\) | −7.93194 | + | 13.7385i | −0.563698 | + | 0.976354i | ||||
\(199\) | −6.59301 | − | 2.39966i | −0.467366 | − | 0.170107i | 0.0975926 | − | 0.995226i | \(-0.468886\pi\) |
−0.564959 | + | 0.825119i | \(0.691108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.20156 | − | 10.7414i | 0.437425 | − | 0.757642i | ||||
\(202\) | 9.32370 | + | 16.1491i | 0.656013 | + | 1.13625i | ||||
\(203\) | 0.0306821 | + | 0.174007i | 0.00215346 | + | 0.0122129i | ||||
\(204\) | 19.6578 | + | 16.4948i | 1.37632 | + | 1.15487i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.614003 | + | 3.48218i | −0.0427796 | + | 0.242615i | ||||
\(207\) | 30.9114 | − | 11.2508i | 2.14849 | − | 0.781988i | ||||
\(208\) | 1.59029 | 0.110267 | ||||||||
\(209\) | −9.06007 | − | 2.57460i | −0.626698 | − | 0.178089i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.68827 | + | 2.43433i | −0.460440 | + | 0.167586i | −0.561817 | − | 0.827262i | \(-0.689897\pi\) |
0.101377 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(212\) | 0.656766 | − | 3.72471i | 0.0451069 | − | 0.255814i | ||||
\(213\) | −31.7021 | + | 26.6013i | −2.17219 | + | 1.82269i | ||||
\(214\) | −4.28421 | − | 3.59488i | −0.292862 | − | 0.245741i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.98095 | − | 12.0914i | −0.474994 | − | 0.822713i | ||||
\(217\) | −0.0521696 | + | 0.0903603i | −0.00354150 | + | 0.00613406i | ||||
\(218\) | −8.85586 | − | 3.22327i | −0.599795 | − | 0.218307i | ||||
\(219\) | −5.74639 | − | 2.09151i | −0.388305 | − | 0.141331i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.34504 | − | 10.9899i | −0.426813 | − | 0.739263i | ||||
\(222\) | 0.217301 | + | 1.23237i | 0.0145843 | + | 0.0827115i | ||||
\(223\) | 3.34000 | + | 2.80259i | 0.223663 | + | 0.187675i | 0.747733 | − | 0.664000i | \(-0.231142\pi\) |
−0.524070 | + | 0.851675i | \(0.675587\pi\) | |||||||
\(224\) | 0.0179217 | − | 0.0150381i | 0.00119744 | − | 0.00100477i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.35004 | + | 1.94725i | −0.355879 | + | 0.129529i | ||||
\(227\) | −9.44623 | −0.626969 | −0.313484 | − | 0.949593i | \(-0.601496\pi\) | ||||
−0.313484 | + | 0.949593i | \(0.601496\pi\) | |||||||
\(228\) | 10.0601 | − | 9.76136i | 0.666249 | − | 0.646462i | ||||
\(229\) | 22.8675 | 1.51112 | 0.755562 | − | 0.655077i | \(-0.227364\pi\) | ||||
0.755562 | + | 0.655077i | \(0.227364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0282298 | − | 0.160099i | 0.00185738 | − | 0.0105337i | ||||
\(232\) | 5.78554 | − | 4.85465i | 0.379840 | − | 0.318723i | ||||
\(233\) | 8.10215 | + | 6.79851i | 0.530790 | + | 0.445385i | 0.868374 | − | 0.495910i | \(-0.165165\pi\) |
−0.337584 | + | 0.941295i | \(0.609610\pi\) | |||||||
\(234\) | 2.02740 | + | 11.4979i | 0.132535 | + | 0.751644i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.81669 | − | 3.14660i | 0.118256 | − | 0.204826i | ||||
\(237\) | 28.7427 | + | 10.4615i | 1.86704 | + | 0.679547i | ||||
\(238\) | −0.175427 | − | 0.0638504i | −0.0113713 | − | 0.00413880i | ||||
\(239\) | −8.67636 | + | 15.0279i | −0.561227 | + | 0.972074i | 0.436163 | + | 0.899868i | \(0.356337\pi\) |
−0.997390 | + | 0.0722058i | \(0.976996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0833347 | − | 0.472614i | −0.00536806 | − | 0.0304438i | 0.982006 | − | 0.188849i | \(-0.0604758\pi\) |
−0.987374 | + | 0.158406i | \(0.949365\pi\) | |||||||
\(242\) | −4.84973 | − | 4.06940i | −0.311752 | − | 0.261591i | ||||
\(243\) | 24.2641 | − | 20.3600i | 1.55655 | − | 1.30610i | ||||
\(244\) | −2.00421 | + | 11.3664i | −0.128306 | + | 0.727661i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.0178 | 1.14877 | ||||||||
\(247\) | −6.32590 | + | 2.83454i | −0.402508 | + | 0.180358i | ||||
\(248\) | 4.45987 | 0.283202 | ||||||||
\(249\) | −7.94260 | + | 2.89087i | −0.503342 | + | 0.183202i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.56913 | − | 3.83396i | 0.288401 | − | 0.241997i | −0.487096 | − | 0.873348i | \(-0.661944\pi\) |
0.775497 | + | 0.631351i | \(0.217499\pi\) | |||||||
\(252\) | 0.131574 | + | 0.110404i | 0.00828839 | + | 0.00695478i | ||||
\(253\) | −1.68124 | − | 9.53480i | −0.105699 | − | 0.599448i | ||||
\(254\) | 4.33757 | + | 7.51289i | 0.272163 | + | 0.471400i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.939693 | − | 0.342020i | −0.0587308 | − | 0.0213763i | ||||
\(257\) | −12.7121 | − | 4.62683i | −0.792959 | − | 0.288614i | −0.0863936 | − | 0.996261i | \(-0.527534\pi\) |
−0.706566 | + | 0.707648i | \(0.749756\pi\) | |||||||
\(258\) | 15.6026 | − | 27.0244i | 0.971373 | − | 1.68247i | ||||
\(259\) | −0.00455189 | − | 0.00788411i | −0.000282841 | − | 0.000489895i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 42.4752 | + | 35.6409i | 2.62915 | + | 2.20612i | ||||
\(262\) | 15.8921 | − | 13.3350i | 0.981815 | − | 0.823841i | ||||
\(263\) | 3.05915 | − | 17.3493i | 0.188635 | − | 1.06980i | −0.732560 | − | 0.680703i | \(-0.761674\pi\) |
0.921195 | − | 0.389101i | \(-0.127214\pi\) | |||||||
\(264\) | −6.52977 | + | 2.37664i | −0.401880 | + | 0.146272i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0444853 | + | 0.0917624i | −0.00272757 | + | 0.00562632i | ||||
\(267\) | 28.5410 | 1.74668 | ||||||||
\(268\) | 3.62429 | − | 1.31913i | 0.221389 | − | 0.0805789i | ||||
\(269\) | −0.447725 | + | 2.53918i | −0.0272983 | + | 0.154816i | −0.995410 | − | 0.0957028i | \(-0.969490\pi\) |
0.968112 | + | 0.250519i | \(0.0806013\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.49966 | − | 7.13206i | −0.516318 | − | 0.433242i | 0.347028 | − | 0.937855i | \(-0.387191\pi\) |
−0.863346 | + | 0.504613i | \(0.831635\pi\) | |||||||
\(272\) | 1.38566 | + | 7.85847i | 0.0840180 | + | 0.476490i | ||||
\(273\) | −0.0598228 | − | 0.103616i | −0.00362064 | − | 0.00627113i | ||||
\(274\) | 2.98416 | − | 5.16871i | 0.180280 | − | 0.312253i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.5401 | + | 4.92820i | 0.815019 | + | 0.296643i | ||||
\(277\) | −1.47762 | + | 2.55932i | −0.0887817 | + | 0.153774i | −0.906996 | − | 0.421138i | \(-0.861631\pi\) |
0.818215 | + | 0.574913i | \(0.194964\pi\) | |||||||
\(278\) | 7.04059 | + | 12.1947i | 0.422266 | + | 0.731387i | ||||
\(279\) | 5.68569 | + | 32.2452i | 0.340394 | + | 1.93047i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6181 | − | 8.90966i | 0.633424 | − | 0.531506i | −0.268567 | − | 0.963261i | \(-0.586550\pi\) |
0.901991 | + | 0.431755i | \(0.142106\pi\) | |||||||
\(282\) | −2.38722 | + | 13.5386i | −0.142157 | + | 0.806212i | ||||
\(283\) | −4.36045 | + | 1.58707i | −0.259202 | + | 0.0943418i | −0.468353 | − | 0.883542i | \(-0.655152\pi\) |
0.209151 | + | 0.977883i | \(0.432930\pi\) | |||||||
\(284\) | −12.8689 | −0.763627 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.43634 | 0.203195 | ||||||||
\(287\) | −0.123174 | + | 0.0448316i | −0.00727071 | + | 0.00264632i | ||||
\(288\) | 1.27486 | − | 7.23007i | 0.0751217 | − | 0.426036i | ||||
\(289\) | 35.7556 | − | 30.0025i | 2.10327 | − | 1.76485i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.22861 | − | 35.3242i | −0.365128 | − | 2.07074i | ||||
\(292\) | −0.950791 | − | 1.64682i | −0.0556409 | − | 0.0963728i | ||||
\(293\) | 5.93313 | − | 10.2765i | 0.346617 | − | 0.600358i | −0.639029 | − | 0.769182i | \(-0.720664\pi\) |
0.985646 | + | 0.168824i | \(0.0539971\pi\) | |||||||
\(294\) | 21.1516 | + | 7.69857i | 1.23359 | + | 0.448989i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.194566 | + | 0.336998i | −0.0113089 | + | 0.0195876i | ||||
\(297\) | −15.0846 | − | 26.1272i | −0.875295 | − | 1.51606i | ||||
\(298\) | 1.22145 | + | 6.92721i | 0.0707569 | + | 0.401282i | ||||
\(299\) | −5.45851 | − | 4.58023i | −0.315674 | − | 0.264882i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0394210 | + | 0.223567i | −0.00227219 | + | 0.0128862i | ||||
\(302\) | 13.2346 | − | 4.81701i | 0.761567 | − | 0.277188i | ||||
\(303\) | −59.9670 | −3.44501 | ||||||||
\(304\) | 4.34754 | − | 0.314416i | 0.249349 | − | 0.0180330i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −55.0508 | + | 20.0369i | −3.14704 | + | 1.14543i | ||||
\(307\) | −1.81328 | + | 10.2836i | −0.103489 | + | 0.586918i | 0.888323 | + | 0.459218i | \(0.151870\pi\) |
−0.991813 | + | 0.127699i | \(0.959241\pi\) | |||||||
\(308\) | 0.0387255 | − | 0.0324946i | 0.00220659 | − | 0.00185155i | ||||
\(309\) | −8.71060 | − | 7.30906i | −0.495529 | − | 0.415798i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.33307 | + | 12.7012i | 0.415820 | + | 0.720222i | 0.995514 | − | 0.0946125i | \(-0.0301612\pi\) |
−0.579694 | + | 0.814834i | \(0.696828\pi\) | |||||||
\(312\) | −2.55706 | + | 4.42897i | −0.144765 | + | 0.250741i | ||||
\(313\) | −20.1826 | − | 7.34588i | −1.14079 | − | 0.415214i | −0.298592 | − | 0.954381i | \(-0.596517\pi\) |
−0.842199 | + | 0.539167i | \(0.818739\pi\) | |||||||
\(314\) | 2.54495 | + | 0.926285i | 0.143620 | + | 0.0522733i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.75574 | + | 8.23718i | 0.267531 | + | 0.463378i | ||||
\(317\) | −2.05192 | − | 11.6370i | −0.115247 | − | 0.653599i | −0.986628 | − | 0.162991i | \(-0.947886\pi\) |
0.871381 | − | 0.490608i | \(-0.163225\pi\) | |||||||
\(318\) | 9.31727 | + | 7.81812i | 0.522486 | + | 0.438418i | ||||
\(319\) | 12.5015 | − | 10.4900i | 0.699950 | − | 0.587327i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9004 | − | 6.15123i | 0.943287 | − | 0.343328i | ||||
\(322\) | −0.104826 | −0.00584170 | ||||||||
\(323\) | −19.5189 | − | 28.7898i | −1.08606 | − | 1.60191i | ||||
\(324\) | 22.8744 | 1.27080 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.39569 | + | 13.5866i | −0.132685 | + | 0.752493i | ||||
\(327\) | 23.2163 | − | 19.4808i | 1.28386 | − | 1.07729i | ||||
\(328\) | 4.29201 | + | 3.60143i | 0.236987 | + | 0.198856i | ||||
\(329\) | −0.0173669 | − | 0.0984928i | −0.000957471 | − | 0.00543009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.88073 | + | 15.3819i | −0.488129 | + | 0.845464i | −0.999907 | − | 0.0136535i | \(-0.995654\pi\) |
0.511778 | + | 0.859118i | \(0.328987\pi\) | |||||||
\(332\) | −2.46984 | − | 0.898948i | −0.135550 | − | 0.0493362i | ||||
\(333\) | −2.68456 | − | 0.977102i | −0.147113 | − | 0.0535448i | ||||
\(334\) | 12.1322 | − | 21.0137i | 0.663847 | − | 1.14982i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0130644 | + | 0.0740919i | 0.000712721 | + | 0.00404204i | ||||
\(337\) | −1.82756 | − | 1.53351i | −0.0995537 | − | 0.0835354i | 0.591652 | − | 0.806193i | \(-0.298476\pi\) |
−0.691206 | + | 0.722658i | \(0.742920\pi\) | |||||||
\(338\) | −8.02122 | + | 6.73060i | −0.436297 | + | 0.366097i | ||||
\(339\) | 3.17933 | − | 18.0309i | 0.172677 | − | 0.979302i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.63696 | 0.521871 | ||||||||
\(342\) | 7.81574 | + | 31.0322i | 0.422627 | + | 1.67803i | ||||
\(343\) | −0.327519 | −0.0176843 | ||||||||
\(344\) | 9.11838 | − | 3.31882i | 0.491630 | − | 0.178939i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.8332 | − | 12.4465i | 0.797438 | − | 0.669130i | ||||
\(347\) | −11.7982 | − | 9.89984i | −0.633359 | − | 0.531451i | 0.268612 | − | 0.963249i | \(-0.413435\pi\) |
−0.901971 | + | 0.431797i | \(0.857880\pi\) | |||||||
\(348\) | 4.21749 | + | 23.9186i | 0.226081 | + | 1.28217i | ||||
\(349\) | −4.92259 | − | 8.52618i | −0.263500 | − | 0.456396i | 0.703669 | − | 0.710528i | \(-0.251544\pi\) |
−0.967170 | + | 0.254132i | \(0.918210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.8645 | − | 7.59406i | −1.11366 | − | 0.405341i | ||||
\(352\) | −2.03050 | − | 0.739043i | −0.108226 | − | 0.0393911i | ||||
\(353\) | −4.25682 | + | 7.37302i | −0.226567 | + | 0.392426i | −0.956789 | − | 0.290785i | \(-0.906084\pi\) |
0.730221 | + | 0.683211i | \(0.239417\pi\) | |||||||
\(354\) | 5.84218 | + | 10.1189i | 0.310508 | + | 0.537816i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.79876 | + | 5.70484i | 0.360334 | + | 0.302356i | ||||
\(357\) | 0.459896 | − | 0.385899i | 0.0243403 | − | 0.0204239i | ||||
\(358\) | 1.49206 | − | 8.46188i | 0.0788577 | − | 0.447224i | ||||
\(359\) | −29.6177 | + | 10.7800i | −1.56317 | + | 0.568946i | −0.971459 | − | 0.237208i | \(-0.923768\pi\) |
−0.591706 | + | 0.806154i | \(0.701545\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7333 | + | 8.99976i | −0.880702 | + | 0.473672i | ||||
\(362\) | −4.19496 | −0.220482 | ||||||||
\(363\) | 19.1312 | − | 6.96320i | 1.00413 | − | 0.365473i | ||||
\(364\) | 0.00646060 | − | 0.0366399i | 0.000338628 | − | 0.00192045i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −28.4329 | − | 23.8580i | −1.48621 | − | 1.24708i | ||||
\(367\) | −1.21117 | − | 6.86889i | −0.0632226 | − | 0.358553i | −0.999964 | − | 0.00853004i | \(-0.997285\pi\) |
0.936741 | − | 0.350023i | \(-0.113826\pi\) | |||||||
\(368\) | 2.24033 | + | 3.88037i | 0.116785 | + | 0.202278i | ||||
\(369\) | −20.5669 | + | 35.6229i | −1.07067 | + | 1.85445i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0831479 | − | 0.0302634i | −0.00431683 | − | 0.00157120i | ||||
\(372\) | −7.17110 | + | 12.4207i | −0.371804 | + | 0.643984i | ||||
\(373\) | 6.02737 | + | 10.4397i | 0.312085 | + | 0.540548i | 0.978814 | − | 0.204753i | \(-0.0656392\pi\) |
−0.666728 | + | 0.745301i | \(0.732306\pi\) | |||||||
\(374\) | 2.99416 | + | 16.9807i | 0.154824 | + | 0.878052i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.27478 | + | 2.74787i | −0.168884 | + | 0.141710i | ||||
\(377\) | 2.08563 | − | 11.8282i | 0.107416 | − | 0.609184i | ||||
\(378\) | −0.306941 | + | 0.111718i | −0.0157874 | + | 0.00574613i | ||||
\(379\) | −6.82285 | −0.350466 | −0.175233 | − | 0.984527i | \(-0.556068\pi\) | ||||
−0.175233 | + | 0.984527i | \(0.556068\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.8978 | −1.42925 | ||||||||
\(382\) | −17.7245 | + | 6.45118i | −0.906863 | + | 0.330071i | ||||
\(383\) | −1.88011 | + | 10.6626i | −0.0960690 | + | 0.544834i | 0.898346 | + | 0.439290i | \(0.144770\pi\) |
−0.994415 | + | 0.105545i | \(0.966341\pi\) | |||||||
\(384\) | 2.46347 | − | 2.06710i | 0.125714 | − | 0.105486i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.08999 | + | 17.5242i | 0.157276 | + | 0.891958i | ||||
\(387\) | 35.6199 | + | 61.6955i | 1.81066 | + | 3.13616i | ||||
\(388\) | 5.57695 | − | 9.65956i | 0.283127 | − | 0.490390i | ||||
\(389\) | 7.07236 | + | 2.57413i | 0.358583 | + | 0.130513i | 0.515028 | − | 0.857173i | \(-0.327781\pi\) |
−0.156446 | + | 0.987687i | \(0.550004\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.8772 | − | 30.9642i | 0.904088 | − | 1.56593i | ||||
\(392\) | 3.49973 | + | 6.06170i | 0.176763 | + | 0.306162i | ||||
\(393\) | 11.5849 | + | 65.7010i | 0.584379 | + | 3.31418i | ||||
\(394\) | −10.3514 | − | 8.68589i | −0.521498 | − | 0.437589i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.75473 | − | 15.6229i | 0.138431 | − | 0.785078i | ||||
\(397\) | −4.65031 | + | 1.69258i | −0.233393 | + | 0.0849479i | −0.456069 | − | 0.889944i | \(-0.650743\pi\) |
0.222676 | + | 0.974892i | \(0.428521\pi\) | |||||||
\(398\) | 7.01614 | 0.351687 | ||||||||
\(399\) | −0.184029 | − | 0.271438i | −0.00921299 | − | 0.0135889i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6833 | + | 6.80015i | −0.932998 | + | 0.339583i | −0.763397 | − | 0.645929i | \(-0.776470\pi\) |
−0.169601 | + | 0.985513i | \(0.554248\pi\) | |||||||
\(402\) | −2.15378 | + | 12.2147i | −0.107421 | + | 0.609214i | ||||
\(403\) | 5.43317 | − | 4.55897i | 0.270646 | − | 0.227099i | ||||
\(404\) | −14.2847 | − | 11.9863i | −0.710692 | − | 0.596342i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0883457 | − | 0.153019i | −0.00438452 | − | 0.00759422i | ||||
\(407\) | −0.420421 | + | 0.728191i | −0.0208395 | + | 0.0360951i | ||||
\(408\) | −24.1138 | − | 8.77672i | −1.19381 | − | 0.434512i | ||||
\(409\) | −12.1132 | − | 4.40884i | −0.598958 | − | 0.218003i | 0.0247068 | − | 0.999695i | \(-0.492135\pi\) |
−0.623665 | + | 0.781692i | \(0.714357\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.59657 | + | 16.6217i | 0.473364 | + | 0.819890i | ||||
\(412\) | −0.614003 | − | 3.48218i | −0.0302497 | − | 0.171555i | ||||
\(413\) | −0.0651163 | − | 0.0546391i | −0.00320416 | − | 0.00268861i | ||||
\(414\) | −25.1992 | + | 21.1447i | −1.23848 | + | 1.03920i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.49439 | + | 0.543913i | −0.0732684 | + | 0.0266675i | ||||
\(417\) | −45.2828 | −2.21751 | ||||||||
\(418\) | 9.39425 | − | 0.679394i | 0.459488 | − | 0.0332303i | ||||
\(419\) | 4.48425 | 0.219070 | 0.109535 | − | 0.993983i | \(-0.465064\pi\) | ||||
0.109535 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.74698 | + | 21.2502i | −0.182616 | + | 1.03567i | 0.746363 | + | 0.665539i | \(0.231798\pi\) |
−0.928980 | + | 0.370131i | \(0.879313\pi\) | |||||||
\(422\) | 5.45233 | − | 4.57505i | 0.265415 | − | 0.222710i | ||||
\(423\) | −24.0421 | − | 20.1738i | −1.16897 | − | 0.980882i | ||||
\(424\) | 0.656766 | + | 3.72471i | 0.0318954 | + | 0.180888i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.6921 | − | 35.8398i | 1.00254 | − | 1.73644i | ||||
\(427\) | 0.253737 | + | 0.0923527i | 0.0122792 | + | 0.00446926i | ||||
\(428\) | 5.25536 | + | 1.91279i | 0.254027 | + | 0.0924584i | ||||
\(429\) | −5.52535 | + | 9.57018i | −0.266766 | + | 0.462053i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.06827 | + | 11.7298i | 0.0996252 | + | 0.565003i | 0.993232 | + | 0.116151i | \(0.0370557\pi\) |
−0.893606 | + | 0.448852i | \(0.851833\pi\) | |||||||
\(432\) | 10.6954 | + | 8.97454i | 0.514585 | + | 0.431788i | ||||
\(433\) | −16.9528 | + | 14.2251i | −0.814701 | + | 0.683615i | −0.951725 | − | 0.306952i | \(-0.900691\pi\) |
0.137024 | + | 0.990568i | \(0.456246\pi\) | |||||||
\(434\) | 0.0181183 | − | 0.102754i | 0.000869706 | − | 0.00493235i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.42421 | 0.451338 | ||||||||
\(437\) | −15.8280 | − | 11.4422i | −0.757156 | − | 0.547356i | ||||
\(438\) | 6.11518 | 0.292195 | ||||||||
\(439\) | 6.47904 | − | 2.35818i | 0.309228 | − | 0.112550i | −0.182745 | − | 0.983160i | \(-0.558498\pi\) |
0.491973 | + | 0.870611i | \(0.336276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.3649 | + | 33.0311i | −1.87452 | + | 1.57291i | ||||
\(442\) | 9.72116 | + | 8.15702i | 0.462389 | + | 0.387990i | ||||
\(443\) | 0.268390 | + | 1.52212i | 0.0127516 | + | 0.0723180i | 0.990520 | − | 0.137372i | \(-0.0438656\pi\) |
−0.977768 | + | 0.209690i | \(0.932754\pi\) | |||||||
\(444\) | −0.625692 | − | 1.08373i | −0.0296940 | − | 0.0514316i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.09711 | − | 1.49123i | −0.194004 | − | 0.0706117i | ||||
\(447\) | −21.2562 | − | 7.73664i | −1.00539 | − | 0.365931i | ||||
\(448\) | −0.0116976 | + | 0.0202608i | −0.000552658 | + | 0.000957231i | ||||
\(449\) | −2.95993 | − | 5.12674i | −0.139688 | − | 0.241946i | 0.787691 | − | 0.616071i | \(-0.211276\pi\) |
−0.927378 | + | 0.374125i | \(0.877943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.27425 | + | 7.78202i | 0.436708 | + | 0.366441i | ||||
\(452\) | 4.36139 | − | 3.65964i | 0.205143 | − | 0.172135i | ||||
\(453\) | −7.86485 | + | 44.6038i | −0.369523 | + | 2.09567i | ||||
\(454\) | 8.87656 | − | 3.23080i | 0.416597 | − | 0.151629i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.11485 | + | 12.6135i | −0.286354 | + | 0.590679i | ||||
\(457\) | −29.5382 | −1.38174 | −0.690870 | − | 0.722979i | \(-0.742772\pi\) | ||||
−0.690870 | + | 0.722979i | \(0.742772\pi\) | |||||||
\(458\) | −21.4884 | + | 7.82113i | −1.00409 | + | 0.365458i | ||||
\(459\) | 19.3465 | − | 109.719i | 0.903015 | − | 5.12125i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.3287 | + | 19.5751i | 1.08652 | + | 0.911702i | 0.996446 | − | 0.0842331i | \(-0.0268440\pi\) |
0.0900776 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(462\) | 0.0282298 | + | 0.160099i | 0.00131337 | + | 0.00744848i | ||||
\(463\) | 19.4309 | + | 33.6554i | 0.903033 | + | 1.56410i | 0.823536 | + | 0.567263i | \(0.191998\pi\) |
0.0794963 | + | 0.996835i | \(0.474669\pi\) | |||||||
\(464\) | −3.77625 | + | 6.54065i | −0.175308 | + | 0.303642i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.93876 | − | 3.61741i | −0.460404 | − | 0.167573i | ||||
\(467\) | 14.3141 | − | 24.7927i | 0.662377 | − | 1.14727i | −0.317612 | − | 0.948221i | \(-0.602881\pi\) |
0.979989 | − | 0.199050i | \(-0.0637857\pi\) | |||||||
\(468\) | −5.83766 | − | 10.1111i | −0.269846 | − | 0.467387i | ||||
\(469\) | −0.0156687 | − | 0.0888615i | −0.000723513 | − | 0.00410324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.67177 | + | 5.59828i | −0.307419 | + | 0.257955i | ||||
\(472\) | −0.630930 | + | 3.57818i | −0.0290409 | + | 0.164699i | ||||
\(473\) | 19.7032 | − | 7.17136i | 0.905952 | − | 0.329740i | ||||
\(474\) | −30.5874 | −1.40492 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.186686 | 0.00855674 | ||||||||
\(477\) | −26.0926 | + | 9.49693i | −1.19470 | + | 0.434835i | ||||
\(478\) | 3.01327 | − | 17.0891i | 0.137824 | − | 0.781637i | ||||
\(479\) | −12.7889 | + | 10.7312i | −0.584340 | + | 0.490320i | −0.886369 | − | 0.462979i | \(-0.846781\pi\) |
0.302029 | + | 0.953299i | \(0.402336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.107459 | + | 0.609433i | 0.00489973 | + | 0.0277877i | ||||
\(482\) | 0.239953 | + | 0.415610i | 0.0109295 | + | 0.0189305i | ||||
\(483\) | 0.168551 | − | 0.291939i | 0.00766934 | − | 0.0132837i | ||||
\(484\) | 5.94907 | + | 2.16529i | 0.270412 | + | 0.0984221i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −15.8373 | + | 27.4310i | −0.718394 | + | 1.24430i | ||||
\(487\) | 9.69165 | + | 16.7864i | 0.439171 | + | 0.760666i | 0.997626 | − | 0.0688690i | \(-0.0219390\pi\) |
−0.558455 | + | 0.829535i | \(0.688606\pi\) | |||||||
\(488\) | −2.00421 | − | 11.3664i | −0.0907263 | − | 0.514534i | ||||
\(489\) | −33.9866 | − | 28.5181i | −1.53693 | − | 1.28963i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.30923 | − | 35.7814i | 0.284731 | − | 1.61479i | −0.421511 | − | 0.906823i | \(-0.638500\pi\) |
0.706243 | − | 0.707970i | \(-0.250389\pi\) | |||||||
\(492\) | −16.9312 | + | 6.16244i | −0.763316 | + | 0.277824i | ||||
\(493\) | 60.2666 | 2.71427 | ||||||||
\(494\) | 4.97493 | − | 4.82719i | 0.223833 | − | 0.217185i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.19091 | + | 1.52536i | −0.188177 | + | 0.0684909i | ||||
\(497\) | −0.0522800 | + | 0.296495i | −0.00234508 | + | 0.0132996i | ||||
\(498\) | 6.47487 | − | 5.43306i | 0.290146 | − | 0.243461i | ||||
\(499\) | −5.94585 | − | 4.98916i | −0.266173 | − | 0.223346i | 0.499926 | − | 0.866068i | \(-0.333360\pi\) |
−0.766099 | + | 0.642722i | \(0.777805\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 39.0153 | + | 67.5765i | 1.74308 | + | 3.01909i | ||||
\(502\) | −2.98229 | + | 5.16548i | −0.133106 | + | 0.230546i | ||||
\(503\) | 0.597098 | + | 0.217326i | 0.0266233 | + | 0.00969008i | 0.355297 | − | 0.934753i | \(-0.384380\pi\) |
−0.328674 | + | 0.944443i | \(0.606602\pi\) | |||||||
\(504\) | −0.161399 | − | 0.0587446i | −0.00718930 | − | 0.00261669i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.84095 | + | 8.38477i | 0.215206 | + | 0.372748i | ||||
\(507\) | −5.84724 | − | 33.1613i | −0.259685 | − | 1.47275i | ||||
\(508\) | −6.64554 | − | 5.57627i | −0.294848 | − | 0.247407i | ||||
\(509\) | 20.1192 | − | 16.8820i | 0.891767 | − | 0.748282i | −0.0767966 | − | 0.997047i | \(-0.524469\pi\) |
0.968564 | + | 0.248765i | \(0.0800248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0418048 | + | 0.0152157i | −0.00184934 | + | 0.000673103i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −58.5408 | − | 16.6355i | −2.58464 | − | 0.734476i | ||||
\(514\) | 13.5279 | 0.596692 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.41871 | + | 30.7311i | −0.238546 | + | 1.35286i | ||||
\(517\) | −7.07620 | + | 5.93764i | −0.311211 | + | 0.261137i | ||||
\(518\) | 0.00697390 | + | 0.00585180i | 0.000306416 | + | 0.000257113i | ||||
\(519\) | 10.8130 | + | 61.3235i | 0.474637 | + | 2.69180i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.1453 | + | 34.8927i | −0.882583 | + | 1.52868i | −0.0341245 | + | 0.999418i | \(0.510864\pi\) |
−0.848459 | + | 0.529262i | \(0.822469\pi\) | |||||||
\(522\) | −52.1035 | − | 18.9641i | −2.28051 | − | 0.830038i | ||||
\(523\) | 15.7402 | + | 5.72897i | 0.688271 | + | 0.250510i | 0.662395 | − | 0.749155i | \(-0.269540\pi\) |
0.0258764 | + | 0.999665i | \(0.491762\pi\) | |||||||
\(524\) | −10.3728 | + | 17.9662i | −0.453138 | + | 0.784859i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.05915 | + | 17.3493i | 0.133385 | + | 0.756466i | ||||
\(527\) | 27.2623 | + | 22.8758i | 1.18756 | + | 0.996485i | ||||
\(528\) | 5.32312 | − | 4.46663i | 0.231659 | − | 0.194385i | ||||
\(529\) | −0.507688 | + | 2.87924i | −0.0220734 | + | 0.125184i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.6748 | −1.15759 | ||||||||
\(532\) | 0.0104179 | − | 0.101443i | 0.000451675 | − | 0.00439813i | ||||
\(533\) | 8.91014 | 0.385941 | ||||||||
\(534\) | −26.8198 | + | 9.76161i | −1.16061 | + | 0.422426i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.95455 | + | 2.47916i | −0.127617 | + | 0.107083i | ||||
\(537\) | 21.1672 | + | 17.7614i | 0.913432 | + | 0.766461i | ||||
\(538\) | −0.447725 | − | 2.53918i | −0.0193028 | − | 0.109472i | ||||
\(539\) | 7.56227 | + | 13.0982i | 0.325730 | + | 0.564181i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7784 | − | 10.4745i | −1.23728 | − | 0.450334i | −0.361196 | − | 0.932490i | \(-0.617632\pi\) |
−0.876085 | + | 0.482156i | \(0.839854\pi\) | |||||||
\(542\) | 10.4264 | + | 3.79489i | 0.447851 | + | 0.163005i | ||||
\(543\) | 6.74515 | − | 11.6830i | 0.289462 | − | 0.501363i | ||||
\(544\) | −3.98985 | − | 6.91062i | −0.171063 | − | 0.296291i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.0916539 | + | 0.0769067i | 0.00392242 | + | 0.00329130i | ||||
\(547\) | 0.00614318 | − | 0.00515474i | 0.000262663 | − | 0.000220401i | −0.642656 | − | 0.766155i | \(-0.722168\pi\) |
0.642919 | + | 0.765934i | \(0.277723\pi\) | |||||||
\(548\) | −1.03639 | + | 5.87764i | −0.0442723 | + | 0.251081i | ||||
\(549\) | 79.6251 | − | 28.9812i | 3.39831 | − | 1.23689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.36316 | − | 32.7483i | 0.143275 | − | 1.39512i | ||||
\(552\) | −14.4091 | −0.613291 | ||||||||
\(553\) | 0.209102 | − | 0.0761070i | 0.00889194 | − | 0.00323640i | ||||
\(554\) | 0.513173 | − | 2.91035i | 0.0218026 | − | 0.123649i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.7868 | − | 9.05120i | −0.457462 | − | 0.383856i | ||||
\(557\) | −1.16220 | − | 6.59116i | −0.0492440 | − | 0.279276i | 0.950236 | − | 0.311532i | \(-0.100842\pi\) |
−0.999480 | + | 0.0322555i | \(0.989731\pi\) | |||||||
\(558\) | −16.3713 | − | 28.3559i | −0.693052 | − | 1.20040i | ||||
\(559\) | 7.71578 | − | 13.3641i | 0.326343 | − | 0.565242i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −52.1056 | − | 18.9649i | −2.19990 | − | 0.800698i | ||||
\(562\) | −6.93049 | + | 12.0040i | −0.292345 | + | 0.506356i | ||||
\(563\) | 3.30354 | + | 5.72191i | 0.139228 | + | 0.241150i | 0.927205 | − | 0.374555i | \(-0.122205\pi\) |
−0.787977 | + | 0.615705i | \(0.788871\pi\) | |||||||
\(564\) | −2.38722 | − | 13.5386i | −0.100520 | − | 0.570078i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.55467 | − | 2.98272i | 0.149414 | − | 0.125373i | ||||
\(567\) | 0.0929276 | − | 0.527019i | 0.00390259 | − | 0.0221327i | ||||
\(568\) | 12.0928 | − | 4.40141i | 0.507402 | − | 0.184679i | ||||
\(569\) | −18.2452 | −0.764879 | −0.382440 | − | 0.923980i | \(-0.624916\pi\) | ||||
−0.382440 | + | 0.923980i | \(0.624916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.61851 | −0.193279 | −0.0966393 | − | 0.995319i | \(-0.530809\pi\) | ||||
−0.0966393 | + | 0.995319i | \(0.530809\pi\) | |||||||
\(572\) | −3.22910 | + | 1.17530i | −0.135015 | + | 0.0491416i | ||||
\(573\) | 10.5330 | − | 59.7356i | 0.440022 | − | 2.49549i | ||||
\(574\) | 0.100412 | − | 0.0842558i | 0.00419112 | − | 0.00351677i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.27486 | + | 7.23007i | 0.0531190 | + | 0.301253i | ||||
\(577\) | −20.1637 | − | 34.9245i | −0.839424 | − | 1.45393i | −0.890377 | − | 0.455224i | \(-0.849559\pi\) |
0.0509529 | − | 0.998701i | \(-0.483774\pi\) | |||||||
\(578\) | −23.3378 | + | 40.4223i | −0.970725 | + | 1.68135i | ||||
\(579\) | −53.7733 | − | 19.5719i | −2.23474 | − | 0.813379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0307453 | + | 0.0532524i | −0.00127553 | + | 0.00220928i | ||||
\(582\) | 17.9346 | + | 31.0636i | 0.743412 | + | 1.28763i | ||||
\(583\) | 1.41915 | + | 8.04841i | 0.0587752 | + | 0.333331i | ||||
\(584\) | 1.45670 | + | 1.22231i | 0.0602785 | + | 0.0505797i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.06055 | + | 11.6860i | −0.0851207 | + | 0.482743i | ||||
\(587\) | 14.3315 | − | 5.21623i | 0.591523 | − | 0.215297i | −0.0288761 | − | 0.999583i | \(-0.509193\pi\) |
0.620399 | + | 0.784286i | \(0.286971\pi\) | |||||||
\(588\) | −22.5091 | −0.928260 | ||||||||
\(589\) | 13.9518 | − | 13.5375i | 0.574876 | − | 0.557803i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.8344 | − | 14.8625i | 1.67970 | − | 0.611363i | ||||
\(592\) | 0.0675720 | − | 0.383220i | 0.00277719 | − | 0.0157502i | ||||
\(593\) | 30.6860 | − | 25.7487i | 1.26012 | − | 1.05737i | 0.264456 | − | 0.964398i | \(-0.414808\pi\) |
0.995669 | − | 0.0929726i | \(-0.0296369\pi\) | |||||||
\(594\) | 23.1109 | + | 19.3923i | 0.948251 | + | 0.795677i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.51704 | − | 6.09168i | −0.144063 | − | 0.249525i | ||||
\(597\) | −11.2814 | + | 19.5399i | −0.461716 | + | 0.799716i | ||||
\(598\) | 6.69585 | + | 2.43709i | 0.273814 | + | 0.0996600i | ||||
\(599\) | 25.5138 | + | 9.28628i | 1.04247 | + | 0.379427i | 0.805815 | − | 0.592167i | \(-0.201728\pi\) |
0.236652 | + | 0.971594i | \(0.423950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9663 | + | 22.4583i | 0.528907 | + | 0.916094i | 0.999432 | + | 0.0337070i | \(0.0107313\pi\) |
−0.470525 | + | 0.882387i | \(0.655935\pi\) | |||||||
\(602\) | −0.0394210 | − | 0.223567i | −0.00160668 | − | 0.00911193i | ||||
\(603\) | −21.6911 | − | 18.2010i | −0.883332 | − | 0.741203i | ||||
\(604\) | −10.7890 | + | 9.05302i | −0.438997 | + | 0.368362i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 56.3506 | − | 20.5099i | 2.28908 | − | 0.833159i | ||||
\(607\) | 15.2583 | 0.619316 | 0.309658 | − | 0.950848i | \(-0.399785\pi\) | ||||
0.309658 | + | 0.950848i | \(0.399785\pi\) | |||||||
\(608\) | −3.97782 | + | 1.78240i | −0.161322 | + | 0.0722859i | ||||
\(609\) | 0.568211 | 0.0230251 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.18053 | + | 6.69510i | −0.0477590 | + | 0.270855i | ||||
\(612\) | 44.8778 | − | 37.6570i | 1.81408 | − | 1.52219i | ||||
\(613\) | 3.61626 | + | 3.03440i | 0.146059 | + | 0.122558i | 0.712890 | − | 0.701276i | \(-0.247386\pi\) |
−0.566830 | + | 0.823835i | \(0.691831\pi\) | |||||||
\(614\) | −1.81328 | − | 10.2836i | −0.0731781 | − | 0.415013i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0252763 | + | 0.0437798i | −0.00101841 | + | 0.00176394i | ||||
\(617\) | 28.4553 | + | 10.3569i | 1.14557 | + | 0.416953i | 0.843922 | − | 0.536467i | \(-0.180241\pi\) |
0.301647 | + | 0.953420i | \(0.402463\pi\) | |||||||
\(618\) | 10.6851 | + | 3.88907i | 0.429819 | + | 0.156441i | ||||
\(619\) | 2.84795 | − | 4.93279i | 0.114469 | − | 0.198266i | −0.803099 | − | 0.595846i | \(-0.796817\pi\) |
0.917567 | + | 0.397581i | \(0.130150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.8632 | − | 61.6082i | −0.435925 | − | 2.47225i | ||||
\(622\) | −11.2349 | − | 9.42721i | −0.450479 | − | 0.377997i | ||||
\(623\) | 0.159058 | − | 0.133465i | 0.00637252 | − | 0.00534718i | ||||
\(624\) | 0.888059 | − | 5.03643i | 0.0355508 | − | 0.201619i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.4779 | 0.858430 | ||||||||
\(627\) | −13.2131 | + | 27.2554i | −0.527679 | + | 1.08847i | ||||
\(628\) | −2.70828 | −0.108072 | ||||||||
\(629\) | −2.91789 | + | 1.06203i | −0.116344 | + | 0.0423457i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.4485 | + | 27.2275i | −1.29175 | + | 1.08391i | −0.300246 | + | 0.953862i | \(0.597069\pi\) |
−0.991508 | + | 0.130048i | \(0.958487\pi\) | |||||||
\(632\) | −7.28621 | − | 6.11386i | −0.289830 | − | 0.243196i | ||||
\(633\) | 3.97459 | + | 22.5410i | 0.157976 | + | 0.895925i | ||||
\(634\) | 5.90826 | + | 10.2334i | 0.234647 | + | 0.406420i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.4293 | − | 4.15993i | −0.453202 | − | 0.164952i | ||||
\(637\) | 10.4599 | + | 3.80709i | 0.414436 | + | 0.150842i | ||||
\(638\) | −8.15977 | + | 14.1331i | −0.323049 | + | 0.559537i | ||||
\(639\) | 47.2391 | + | 81.8206i | 1.86875 | + | 3.23677i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8636 | − | 17.5066i | −0.824062 | − | 0.691470i | 0.129858 | − | 0.991533i | \(-0.458548\pi\) |
−0.953920 | + | 0.300063i | \(0.902992\pi\) | |||||||
\(642\) | −13.7773 | + | 11.5605i | −0.543747 | + | 0.456258i | ||||
\(643\) | 0.608700 | − | 3.45211i | 0.0240048 | − | 0.136138i | −0.970450 | − | 0.241302i | \(-0.922426\pi\) |
0.994455 | + | 0.105164i | \(0.0335367\pi\) | |||||||
\(644\) | 0.0985039 | − | 0.0358525i | 0.00388160 | − | 0.00141279i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.1884 | + | 20.3777i | 1.10906 | + | 0.801750i | ||||
\(647\) | −44.9855 | −1.76856 | −0.884280 | − | 0.466956i | \(-0.845351\pi\) | ||||
−0.884280 | + | 0.466956i | \(0.845351\pi\) | |||||||
\(648\) | −21.4949 | + | 7.82350i | −0.844399 | + | 0.307336i | ||||
\(649\) | −1.36332 | + | 7.73179i | −0.0535151 | + | 0.303499i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.257037 | + | 0.215679i | 0.0100741 | + | 0.00845314i | ||||
\(652\) | −2.39569 | − | 13.5866i | −0.0938223 | − | 0.532093i | ||||
\(653\) | 7.96033 | + | 13.7877i | 0.311512 | + | 0.539555i | 0.978690 | − | 0.205344i | \(-0.0658313\pi\) |
−0.667178 | + | 0.744898i | \(0.732498\pi\) | |||||||
\(654\) | −15.1534 | + | 26.2464i | −0.592543 | + | 1.02632i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.26493 | − | 1.91628i | −0.205561 | − | 0.0748181i | ||||
\(657\) | −6.98034 | + | 12.0903i | −0.272329 | + | 0.471687i | ||||
\(658\) | 0.0500061 | + | 0.0866132i | 0.00194944 | + | 0.00337653i | ||||
\(659\) | 3.30453 | + | 18.7409i | 0.128726 | + | 0.730042i | 0.979025 | + | 0.203741i | \(0.0653102\pi\) |
−0.850299 | + | 0.526301i | \(0.823579\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6520 | − | 14.8118i | 0.686583 | − | 0.576111i | −0.231339 | − | 0.972873i | \(-0.574311\pi\) |
0.917922 | + | 0.396762i | \(0.129866\pi\) | |||||||
\(662\) | 3.08425 | − | 17.4916i | 0.119873 | − | 0.679831i | ||||
\(663\) | −38.3481 | + | 13.9576i | −1.48932 | + | 0.542067i | ||||
\(664\) | 2.62835 | 0.102000 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.85685 | 0.110701 | ||||||||
\(667\) | 31.7994 | − | 11.5740i | 1.23128 | − | 0.448148i | ||||
\(668\) | −4.21348 | + | 23.8958i | −0.163025 | + | 0.924558i | ||||
\(669\) | 10.7409 | − | 9.01268i | 0.415267 | − | 0.348450i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.33073 | − | 24.5608i | −0.167186 | − | 0.948158i | ||||
\(672\) | −0.0376174 | − | 0.0651553i | −0.00145112 | − | 0.00251342i | ||||
\(673\) | 5.68840 | − | 9.85260i | 0.219272 | − | 0.379790i | −0.735314 | − | 0.677727i | \(-0.762965\pi\) |
0.954586 | + | 0.297937i | \(0.0962985\pi\) | |||||||
\(674\) | 2.24184 | + | 0.815962i | 0.0863523 | + | 0.0314297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.23548 | − | 9.06812i | 0.201365 | − | 0.348774i | ||||
\(677\) | 20.8875 | + | 36.1782i | 0.802771 | + | 1.39044i | 0.917786 | + | 0.397076i | \(0.129975\pi\) |
−0.115015 | + | 0.993364i | \(0.536692\pi\) | |||||||
\(678\) | 3.17933 | + | 18.0309i | 0.122101 | + | 0.692471i | ||||
\(679\) | −0.199897 | − | 0.167733i | −0.00767134 | − | 0.00643701i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.27501 | + | 29.9160i | −0.202139 | + | 1.14639i | ||||
\(682\) | −9.05578 | + | 3.29603i | −0.346764 | + | 0.126212i | ||||
\(683\) | −9.65205 | −0.369325 | −0.184663 | − | 0.982802i | \(-0.559119\pi\) | ||||
−0.184663 | + | 0.982802i | \(0.559119\pi\) | |||||||
\(684\) | −17.9580 | − | 26.4876i | −0.686643 | − | 1.01278i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.307767 | − | 0.112018i | 0.0117506 | − | 0.00427687i | ||||
\(687\) | 12.7697 | − | 72.4208i | 0.487196 | − | 2.76303i | ||||
\(688\) | −7.43337 | + | 6.23734i | −0.283395 | + | 0.237796i | ||||
\(689\) | 4.60757 | + | 3.86621i | 0.175535 | + | 0.147291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.58223 | + | 6.20461i | 0.136275 | + | 0.236034i | 0.926084 | − | 0.377318i | \(-0.123154\pi\) |
−0.789809 | + | 0.613353i | \(0.789820\pi\) | |||||||
\(692\) | −9.68169 | + | 16.7692i | −0.368043 | + | 0.637469i | ||||
\(693\) | −0.348755 | − | 0.126936i | −0.0132481 | − | 0.00482191i | ||||
\(694\) | 14.4726 | + | 5.26759i | 0.549372 | + | 0.199955i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.1438 | − | 21.0337i | −0.460309 | − | 0.797279i | ||||
\(697\) | 7.76361 | + | 44.0296i | 0.294068 | + | 1.66774i | ||||
\(698\) | 7.54185 | + | 6.32836i | 0.285463 | + | 0.239532i | ||||
\(699\) | 26.0552 | − | 21.8629i | 0.985498 | − | 0.826931i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.58820 | + | 2.03394i | −0.211063 | + | 0.0768208i | −0.445388 | − | 0.895338i | \(-0.646934\pi\) |
0.234325 | + | 0.972158i | \(0.424712\pi\) | |||||||
\(702\) | 22.2035 | 0.838019 | ||||||||
\(703\) | 0.414263 | + | 1.64482i | 0.0156242 | + | 0.0620356i | ||||
\(704\) | 2.16082 | 0.0814389 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.47838 | − | 8.38429i | 0.0556394 | − | 0.315547i | ||||
\(707\) | −0.334193 | + | 0.280421i | −0.0125686 | + | 0.0105463i | ||||
\(708\) | −8.95073 | − | 7.51056i | −0.336389 | − | 0.282264i | ||||
\(709\) | 6.60131 | + | 37.4379i | 0.247918 | + | 1.40601i | 0.813618 | + | 0.581400i | \(0.197495\pi\) |
−0.565701 | + | 0.824611i | \(0.691394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.9148 | − | 60.4742i | 1.30941 | − | 2.26796i | ||||
\(712\) | −8.33992 | − | 3.03548i | −0.312552 | − | 0.113759i | ||||
\(713\) | 18.7780 | + | 6.83465i | 0.703243 | + | 0.255959i | ||||
\(714\) | −0.300176 | + | 0.519920i | −0.0112338 | + | 0.0194575i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.49206 | + | 8.46188i | 0.0557608 | + | 0.316235i | ||||
\(717\) | 42.7480 | + | 35.8698i | 1.59645 | + | 1.33958i | ||||
\(718\) | 24.1446 | − | 20.2597i | 0.901069 | − | 0.756087i | ||||
\(719\) | 1.48425 | − | 8.41760i | 0.0553532 | − | 0.313923i | −0.944542 | − | 0.328390i | \(-0.893494\pi\) |
0.999895 | + | 0.0144667i | \(0.00460506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0827228 | −0.00308076 | ||||||||
\(722\) | 12.6461 | − | 14.1801i | 0.470639 | − | 0.527730i | ||||
\(723\) | −1.54330 | −0.0573958 | ||||||||
\(724\) | 3.94197 | − | 1.43476i | 0.146502 | − | 0.0533225i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.5959 | + | 13.0865i | −0.578819 | + | 0.485687i | ||||
\(727\) | −6.42127 | − | 5.38809i | −0.238152 | − | 0.199833i | 0.515899 | − | 0.856650i | \(-0.327458\pi\) |
−0.754050 | + | 0.656817i | \(0.771903\pi\) | |||||||
\(728\) | 0.00646060 | + | 0.0366399i | 0.000239446 | + | 0.00135796i | ||||
\(729\) | −16.6186 | − | 28.7842i | −0.615503 | − | 1.06608i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72.7620 | + | 26.4832i | 2.69120 | + | 0.979516i | ||||
\(732\) | 34.8781 | + | 12.6946i | 1.28913 | + | 0.469205i | ||||
\(733\) | −5.96195 | + | 10.3264i | −0.220210 | + | 0.381414i | −0.954872 | − | 0.297019i | \(-0.904007\pi\) |
0.734662 | + | 0.678433i | \(0.237341\pi\) | |||||||
\(734\) | 3.48743 | + | 6.04040i | 0.128723 | + | 0.222955i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.43239 | − | 2.88011i | −0.126519 | − | 0.106162i | ||||
\(737\) | −6.38424 | + | 5.35701i | −0.235166 | + | 0.197328i | ||||
\(738\) | 7.14280 | − | 40.5088i | 0.262930 | − | 1.49115i | ||||
\(739\) | −23.9241 | + | 8.70767i | −0.880063 | + | 0.320317i | −0.742235 | − | 0.670140i | \(-0.766234\pi\) |
−0.137828 | + | 0.990456i | \(0.544012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.44441 | + | 21.6169i | 0.200005 | + | 0.794117i | ||||
\(742\) | 0.0884842 | 0.00324836 | ||||||||
\(743\) | 14.9949 | − | 5.45769i | 0.550109 | − | 0.200223i | −0.0519860 | − | 0.998648i | \(-0.516555\pi\) |
0.602095 | + | 0.798425i | \(0.294333\pi\) | |||||||
\(744\) | 2.49050 | − | 14.1243i | 0.0913061 | − | 0.517823i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.23447 | − | 7.74864i | −0.338098 | − | 0.283698i | ||||
\(747\) | 3.35077 | + | 19.0032i | 0.122598 | + | 0.695289i | ||||
\(748\) | −8.62134 | − | 14.9326i | −0.315227 | − | 0.545990i | ||||
\(749\) | 0.0654201 | − | 0.113311i | 0.00239040 | − | 0.00414029i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.48505 | + | 0.540514i | 0.0541903 | + | 0.0197237i | 0.368973 | − | 0.929440i | \(-0.379709\pi\) |
−0.314783 | + | 0.949164i | \(0.601932\pi\) | |||||||
\(752\) | 2.13746 | − | 3.70219i | 0.0779452 | − | 0.135005i | ||||
\(753\) | −9.59055 | − | 16.6113i | −0.349499 | − | 0.605350i | ||||
\(754\) | 2.08563 | + | 11.8282i | 0.0759543 | + | 0.430758i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.250221 | − | 0.209960i | 0.00910045 | − | 0.00763618i | ||||
\(757\) | 3.33882 | − | 18.9354i | 0.121351 | − | 0.688217i | −0.862057 | − | 0.506811i | \(-0.830824\pi\) |
0.983408 | − | 0.181406i | \(-0.0580648\pi\) | |||||||
\(758\) | 6.41138 | − | 2.33355i | 0.232872 | − | 0.0847584i | ||||
\(759\) | −31.1354 | −1.13014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.6228 | 0.457576 | 0.228788 | − | 0.973476i | \(-0.426524\pi\) | ||||
0.228788 | + | 0.973476i | \(0.426524\pi\) | |||||||
\(762\) | 26.2154 | − | 9.54161i | 0.949683 | − | 0.345656i | ||||
\(763\) | 0.0382860 | − | 0.217131i | 0.00138605 | − | 0.00786067i | ||||
\(764\) | 14.4491 | − | 12.1243i | 0.522751 | − | 0.438640i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.88011 | − | 10.6626i | −0.0679310 | − | 0.385256i | ||||
\(767\) | 2.88907 | + | 5.00402i | 0.104318 | + | 0.180685i | ||||
\(768\) | −1.60792 | + | 2.78500i | −0.0580208 | + | 0.100495i | ||||
\(769\) | 37.7534 | + | 13.7411i | 1.36142 | + | 0.495518i | 0.916494 | − | 0.400048i | \(-0.131007\pi\) |
0.444929 | + | 0.895566i | \(0.353229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7518 | + | 37.6753i | −0.783373 | + | 1.35684i | ||||
\(772\) | −8.89727 | − | 15.4105i | −0.320220 | − | 0.554637i | ||||
\(773\) | −4.48376 | − | 25.4287i | −0.161270 | − | 0.914606i | −0.952828 | − | 0.303512i | \(-0.901841\pi\) |
0.791558 | − | 0.611094i | \(-0.209270\pi\) | |||||||
\(774\) | −54.5729 | − | 45.7921i | −1.96158 | − | 1.64596i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.93685 | + | 10.9844i | −0.0695290 | + | 0.394319i | ||||
\(777\) | −0.0275107 | + | 0.0100131i | −0.000986941 | + | 0.000359217i | ||||
\(778\) | −7.52625 | −0.269829 | ||||||||
\(779\) | 24.3585 | − | 1.76162i | 0.872735 | − | 0.0631164i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.1303 | − | 9.51065i | 0.935016 | − | 0.340318i | ||||
\(782\) | −6.20868 | + | 35.2112i | −0.222022 | + | 1.25915i | ||||
\(783\) | 80.7772 | − | 67.7801i | 2.88674 | − | 2.42226i | ||||
\(784\) | −5.36189 | − | 4.49916i | −0.191496 | − | 0.160684i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.3573 | − | 57.7765i | −1.18981 | − | 2.06082i | ||||
\(787\) | −12.3413 | + | 21.3757i | −0.439919 | + | 0.761963i | −0.997683 | − | 0.0680373i | \(-0.978326\pi\) |
0.557763 | + | 0.830000i | \(0.311660\pi\) | |||||||
\(788\) | 12.6979 | + | 4.62167i | 0.452345 | + | 0.164640i | ||||
\(789\) | −53.2366 | − | 19.3766i | −1.89527 | − | 0.689823i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0665987 | − | 0.115352i | −0.00236798 | − | 0.00410146i | ||||
\(792\) | 2.75473 | + | 15.6229i | 0.0978852 | + | 0.555134i | ||||
\(793\) | −14.0606 | − | 11.7983i | −0.499307 | − | 0.418968i | ||||
\(794\) | 3.79097 | − | 3.18100i | 0.134537 | − | 0.112890i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.59301 | + | 2.39966i | −0.233683 | + | 0.0850537i | ||||
\(797\) | −20.6723 | −0.732249 | −0.366124 | − | 0.930566i | \(-0.619316\pi\) | ||||
−0.366124 | + | 0.930566i | \(0.619316\pi\) | |||||||
\(798\) | 0.265768 | + | 0.192127i | 0.00940809 | + | 0.00680121i | ||||
\(799\) | −34.1126 | −1.20682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.3145 | − | 64.1680i | 0.399780 | − | 2.26726i | ||||
\(802\) | 15.2307 | − | 12.7801i | 0.537816 | − | 0.451281i | ||||
\(803\) | 3.14766 | + | 2.64120i | 0.111078 | + | 0.0932058i | ||||
\(804\) | −2.15378 | − | 12.2147i | −0.0759580 | − | 0.430779i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.54625 | + | 6.14229i | −0.124911 | + | 0.216353i | ||||
\(807\) | 7.79150 | + | 2.83587i | 0.274274 | + | 0.0998275i | ||||
\(808\) | 17.5228 | + | 6.37779i | 0.616451 | + | 0.224370i | ||||
\(809\) | 14.2987 | − | 24.7661i | 0.502716 | − | 0.870729i | −0.497279 | − | 0.867590i | \(-0.665668\pi\) |
0.999995 | − | 0.00313869i | \(-0.000999078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.71497 | − | 15.3973i | −0.0953353 | − | 0.540674i | −0.994644 | − | 0.103359i | \(-0.967041\pi\) |
0.899309 | − | 0.437314i | \(-0.144070\pi\) | |||||||
\(812\) | 0.135353 | + | 0.113575i | 0.00474997 | + | 0.00398570i | ||||
\(813\) | −27.3335 | + | 22.9355i | −0.958628 | + | 0.804385i | ||||
\(814\) | 0.146011 | − | 0.828068i | 0.00511768 | − | 0.0290238i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 25.6614 | 0.898329 | ||||||||
\(817\) | 18.4512 | − | 38.0603i | 0.645525 | − | 1.33156i | ||||
\(818\) | 12.8906 | 0.450708 | ||||||||
\(819\) | −0.256673 | + | 0.0934212i | −0.00896887 | + | 0.00326440i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.8911 | − | 16.6906i | 0.694204 | − | 0.582506i | −0.225914 | − | 0.974147i | \(-0.572537\pi\) |
0.920118 | + | 0.391641i | \(0.128092\pi\) | |||||||
\(822\) | −14.7028 | − | 12.3371i | −0.512819 | − | 0.430306i | ||||
\(823\) | 6.29176 | + | 35.6823i | 0.219317 | + | 1.24381i | 0.873256 | + | 0.487261i | \(0.162004\pi\) |
−0.653939 | + | 0.756547i | \(0.726885\pi\) | |||||||
\(824\) | 1.76795 | + | 3.06218i | 0.0615895 | + | 0.106676i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0798770 | + | 0.0290728i | 0.00277928 | + | 0.00101157i | ||||
\(827\) | −16.9142 | − | 6.15626i | −0.588164 | − | 0.214074i | 0.0307580 | − | 0.999527i | \(-0.490208\pi\) |
−0.618921 | + | 0.785453i | \(0.712430\pi\) | |||||||
\(828\) | 16.4476 | − | 28.4881i | 0.571595 | − | 0.990031i | ||||
\(829\) | 13.0982 | + | 22.6867i | 0.454919 | + | 0.787943i | 0.998684 | − | 0.0512947i | \(-0.0163348\pi\) |
−0.543764 | + | 0.839238i | \(0.683001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.28016 | + | 6.10878i | 0.252546 | + | 0.211911i | ||||
\(832\) | 1.21824 | − | 1.02222i | 0.0422348 | − | 0.0354392i | ||||
\(833\) | −9.69887 | + | 55.0050i | −0.336046 | + | 1.90581i | ||||
\(834\) | 42.5519 | − | 15.4876i | 1.47345 | − | 0.536292i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.59534 | + | 3.85144i | −0.297276 | + | 0.133205i | ||||
\(837\) | 62.2683 | 2.15231 | ||||||||
\(838\) | −4.21382 | + | 1.53371i | −0.145564 | + | 0.0529810i | ||||
\(839\) | 0.609122 | − | 3.45450i | 0.0210292 | − | 0.119263i | −0.972486 | − | 0.232961i | \(-0.925159\pi\) |
0.993515 | + | 0.113698i | \(0.0362697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4800 | + | 18.0238i | 0.740689 | + | 0.621512i | ||||
\(842\) | −3.74698 | − | 21.2502i | −0.129129 | − | 0.732329i | ||||
\(843\) | −22.2873 | − | 38.6028i | −0.767616 | − | 1.32955i | ||||
\(844\) | −3.55876 | + | 6.16395i | −0.122497 | + | 0.212172i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.4921 | + | 10.7342i | 1.01396 | + | 0.369051i | ||||
\(847\) | 0.0740557 | − | 0.128268i | 0.00254458 | − | 0.00440735i | ||||
\(848\) | −1.89108 | − | 3.27545i | −0.0649400 | − | 0.112479i | ||||
\(849\) | 2.59125 | + | 14.6957i | 0.0889316 | + | 0.504356i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.33565 | + | 1.12074i | −0.0457855 | + | 0.0384186i | ||||
\(852\) | −7.18629 | + | 40.7555i | −0.246198 | + | 1.39626i | ||||
\(853\) | 37.9556 | − | 13.8147i | 1.29958 | − | 0.473007i | 0.402717 | − | 0.915325i | \(-0.368066\pi\) |
0.896858 | + | 0.442318i | \(0.145844\pi\) | |||||||
\(854\) | −0.270021 | −0.00923993 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.59263 | −0.191152 | ||||||||
\(857\) | −15.9081 | + | 5.79009i | −0.543412 | + | 0.197786i | −0.599117 | − | 0.800662i | \(-0.704482\pi\) |
0.0557051 | + | 0.998447i | \(0.482259\pi\) | |||||||
\(858\) | 1.91893 | − | 10.8828i | 0.0655113 | − | 0.371533i | ||||
\(859\) | 8.61145 | − | 7.22586i | 0.293819 | − | 0.246543i | −0.483947 | − | 0.875097i | \(-0.660797\pi\) |
0.777766 | + | 0.628554i | \(0.216353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0731975 | + | 0.415124i | 0.00249457 | + | 0.0141474i | ||||
\(862\) | −5.95535 | − | 10.3150i | −0.202840 | − | 0.351329i | ||||
\(863\) | −27.5361 | + | 47.6939i | −0.937340 | + | 1.62352i | −0.166932 | + | 0.985968i | \(0.553386\pi\) |
−0.770407 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(864\) | −13.1199 | − | 4.77525i | −0.446348 | − | 0.162457i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.0652 | − | 19.1654i | 0.376010 | − | 0.651268i | ||||
\(867\) | −75.0506 | − | 129.991i | −2.54885 | − | 4.41474i | ||||
\(868\) | 0.0181183 | + | 0.102754i | 0.000614975 | + | 0.00348770i | ||||
\(869\) | −15.7442 | − | 13.2109i | −0.534085 | − | 0.448150i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06509 | + | 6.04041i | −0.0360891 | + | 0.204671i | ||||
\(872\) | −8.85586 | + | 3.22327i | −0.299897 | + | 0.109154i | ||||
\(873\) | −81.8876 | −2.77147 | ||||||||
\(874\) | 18.7869 | + | 5.33868i | 0.635478 | + | 0.180584i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.74639 | + | 2.09151i | −0.194153 | + | 0.0706657i | ||||
\(877\) | 3.25617 | − | 18.4667i | 0.109953 | − | 0.623575i | −0.879173 | − | 0.476503i | \(-0.841904\pi\) |
0.989126 | − | 0.147072i | \(-0.0469848\pi\) | |||||||
\(878\) | −5.28176 | + | 4.43192i | −0.178251 | + | 0.149570i | ||||
\(879\) | −29.2322 | − | 24.5287i | −0.985978 | − | 0.827334i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.3287 | − | 43.8706i | −0.853345 | − | 1.47804i | −0.878172 | − | 0.478345i | \(-0.841237\pi\) |
0.0248271 | − | 0.999692i | \(-0.492096\pi\) | |||||||
\(882\) | 25.6936 | − | 44.5027i | 0.865149 | − | 1.49848i | ||||
\(883\) | −32.0818 | − | 11.6768i | −1.07964 | − | 0.392956i | −0.259866 | − | 0.965645i | \(-0.583678\pi\) |
−0.819773 | + | 0.572688i | \(0.805901\pi\) | |||||||
\(884\) | −11.9248 | − | 4.34026i | −0.401073 | − | 0.145979i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.772800 | − | 1.33853i | −0.0259627 | − | 0.0449687i | ||||
\(887\) | 6.11812 | + | 34.6976i | 0.205426 | + | 1.16503i | 0.896767 | + | 0.442502i | \(0.145909\pi\) |
−0.691341 | + | 0.722529i | \(0.742980\pi\) | |||||||
\(888\) | 0.958616 | + | 0.804375i | 0.0321691 | + | 0.0269930i | ||||
\(889\) | −0.155473 | + | 0.130457i | −0.00521440 | + | 0.00437540i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46.4465 | + | 16.9052i | −1.55602 | + | 0.566344i | ||||
\(892\) | 4.36006 | 0.145986 | ||||||||
\(893\) | −1.90364 | + | 18.5365i | −0.0637029 | + | 0.620299i | ||||
\(894\) | 22.6204 | 0.756540 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.00406252 | − | 0.0230397i | 0.000135719 | − | 0.000769702i | ||||
\(897\) | −17.5537 | + | 14.7293i | −0.586100 | + | 0.491796i | ||||
\(898\) | 4.53487 | + | 3.80521i | 0.151331 | + | 0.126981i | ||||
\(899\) | 5.84901 | + | 33.1714i | 0.195075 | + | 1.10633i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0903 | + | 26.1371i | −0.502730 | + | 0.870754i | ||||
\(902\) | −11.3766 | − | 4.14073i | −0.378798 | − | 0.137871i | ||||
\(903\) | 0.686020 | + | 0.249691i | 0.0228293 | + | 0.00830919i | ||||
\(904\) | −2.84670 | + | 4.93062i | −0.0946797 | + | 0.163990i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7.86485 | − | 44.6038i | −0.261292 | − | 1.48186i | ||||
\(907\) | −14.6698 | − | 12.3094i | −0.487103 | − | 0.408728i | 0.365883 | − | 0.930661i | \(-0.380767\pi\) |
−0.852987 | + | 0.521932i | \(0.825211\pi\) | |||||||
\(908\) | −7.23624 | + | 6.07192i | −0.240143 | + | 0.201504i | ||||
\(909\) | −23.7728 | + | 134.822i | −0.788493 | + | 4.47177i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5134 | 0.812164 | 0.406082 | − | 0.913837i | \(-0.366895\pi\) | ||||
0.406082 | + | 0.913837i | \(0.366895\pi\) | |||||||
\(912\) | 1.43203 | − | 13.9442i | 0.0474191 | − | 0.461738i | ||||
\(913\) | 5.67938 | 0.187960 | ||||||||
\(914\) | 27.7569 | − | 10.1027i | 0.918115 | − | 0.334167i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.5175 | − | 14.6989i | 0.578794 | − | 0.485666i | ||||
\(917\) | 0.371797 | + | 0.311974i | 0.0122778 | + | 0.0103023i | ||||
\(918\) | 19.3465 | + | 109.719i | 0.638528 | + | 3.62127i | ||||
\(919\) | −14.3060 | − | 24.7787i | −0.471911 | − | 0.817374i | 0.527573 | − | 0.849510i | \(-0.323102\pi\) |
−0.999483 | + | 0.0321362i | \(0.989769\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5555 | + | 11.4853i | 1.03979 | + | 0.378452i | ||||
\(922\) | −28.6168 | − | 10.4157i | −0.942445 | − | 0.343022i | ||||
\(923\) | 10.2327 | − | 17.7235i | 0.336812 | − | 0.583375i | ||||
\(924\) | −0.0812844 | − | 0.140789i | −0.00267406 | − | 0.00463161i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −29.7699 | − | 24.9799i | −0.978301 | − | 0.820892i | ||||
\(927\) | −19.8859 | + | 16.6862i | −0.653139 | + | 0.548048i | ||||
\(928\) | 1.31148 | − | 7.43775i | 0.0430513 | − | 0.244156i | ||||
\(929\) | −3.68171 | + | 1.34003i | −0.120793 | + | 0.0439650i | −0.401709 | − | 0.915767i | \(-0.631584\pi\) |
0.280917 | + | 0.959732i | \(0.409362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.3479 | + | 8.33980i | 0.961840 | + | 0.273326i | ||||
\(932\) | 10.5766 | 0.346448 | ||||||||
\(933\) | 44.3196 | − | 16.1310i | 1.45096 | − | 0.528106i | ||||
\(934\) | −4.97123 | + | 28.1933i | −0.162664 | + | 0.922512i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.94382 | + | 7.50475i | 0.292338 | + | 0.245300i | ||||
\(937\) | 7.63564 | + | 43.3039i | 0.249446 | + | 1.41468i | 0.809937 | + | 0.586516i | \(0.199501\pi\) |
−0.560492 | + | 0.828160i | \(0.689388\pi\) | |||||||
\(938\) | 0.0451162 | + | 0.0781435i | 0.00147310 | + | 0.00255148i | ||||
\(939\) | −34.5347 | + | 59.8159i | −1.12700 | + | 1.95202i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.71790 | + | 2.08115i | 0.186398 | + | 0.0678434i | 0.433533 | − | 0.901138i | \(-0.357267\pi\) |
−0.247135 | + | 0.968981i | \(0.579489\pi\) | |||||||
\(942\) | 4.35469 | − | 7.54254i | 0.141883 | − | 0.245749i | ||||
\(943\) | 12.5522 | + | 21.7410i | 0.408755 | + | 0.707985i | ||||
\(944\) | −0.630930 | − | 3.57818i | −0.0205350 | − | 0.116460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0622 | + | 13.4778i | −0.522226 | + | 0.438199i | ||||
\(947\) | 1.60281 | − | 9.09001i | 0.0520845 | − | 0.295386i | −0.947628 | − | 0.319377i | \(-0.896526\pi\) |
0.999712 | + | 0.0239914i | \(0.00763743\pi\) | |||||||
\(948\) | 28.7427 | − | 10.4615i | 0.933520 | − | 0.339774i | ||||
\(949\) | 3.02408 | 0.0981657 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.0000 | −1.23223 | ||||||||
\(952\) | −0.175427 | + | 0.0638504i | −0.00568564 | + | 0.00206940i | ||||
\(953\) | 5.36804 | − | 30.4437i | 0.173888 | − | 0.986167i | −0.765532 | − | 0.643398i | \(-0.777524\pi\) |
0.939420 | − | 0.342769i | \(-0.111365\pi\) | |||||||
\(954\) | 21.2709 | − | 17.8484i | 0.688671 | − | 0.577863i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.01327 | + | 17.0891i | 0.0974560 | + | 0.552701i | ||||
\(957\) | −26.2405 | − | 45.4499i | −0.848235 | − | 1.46919i | ||||
\(958\) | 8.34737 | − | 14.4581i | 0.269691 | − | 0.467119i | ||||
\(959\) | 0.131209 | + | 0.0477561i | 0.00423695 | + | 0.00154212i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.55479 | − | 9.62118i | 0.179187 | − | 0.310360i | ||||
\(962\) | −0.309417 | − | 0.535926i | −0.00997601 | − | 0.0172790i | ||||
\(963\) | −7.12981 | − | 40.4352i | −0.229755 | − | 1.30300i | ||||
\(964\) | −0.367629 | − | 0.308477i | −0.0118405 | − | 0.00993538i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.0585372 | + | 0.331981i | −0.00188340 | + | 0.0106813i | ||||
\(967\) | −23.8796 | + | 8.69145i | −0.767915 | + | 0.279498i | −0.696124 | − | 0.717922i | \(-0.745094\pi\) |
−0.0717907 | + | 0.997420i | \(0.522871\pi\) | |||||||
\(968\) | −6.33087 | −0.203482 | ||||||||
\(969\) | −102.076 | + | 45.7390i | −3.27917 | + | 1.46935i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9775 | − | 18.5543i | 1.63595 | − | 0.595436i | 0.649623 | − | 0.760256i | \(-0.274927\pi\) |
0.986324 | + | 0.164820i | \(0.0527044\pi\) | |||||||
\(972\) | 5.50023 | − | 31.1934i | 0.176420 | − | 1.00053i | ||||
\(973\) | −0.252358 | + | 0.211754i | −0.00809024 | + | 0.00678852i | ||||
\(974\) | −14.8485 | − | 12.4593i | −0.475776 | − | 0.399223i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.77089 | + | 9.99547i | 0.184722 | + | 0.319947i | ||||
\(977\) | 19.6132 | − | 33.9710i | 0.627481 | − | 1.08683i | −0.360574 | − | 0.932731i | \(-0.617419\pi\) |
0.988055 | − | 0.154099i | \(-0.0492475\pi\) | |||||||
\(978\) | 41.6907 | + | 15.1742i | 1.33312 | + | 0.485217i | ||||
\(979\) | −18.0210 | − | 6.55912i | −0.575955 | − | 0.209630i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.5944 | − | 59.9193i | −1.10452 | − | 1.91308i | ||||
\(982\) | 6.30923 | + | 35.7814i | 0.201336 | + | 1.14183i | ||||
\(983\) | 3.62947 | + | 3.04549i | 0.115762 | + | 0.0971359i | 0.698831 | − | 0.715287i | \(-0.253704\pi\) |
−0.583069 | + | 0.812423i | \(0.698148\pi\) | |||||||
\(984\) | 13.8024 | − | 11.5816i | 0.440005 | − | 0.369208i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −56.6321 | + | 20.6124i | −1.80353 | + | 0.656432i | ||||
\(987\) | −0.321623 | −0.0102374 | ||||||||
\(988\) | −3.02391 | + | 6.23760i | −0.0962035 | + | 0.198444i | ||||
\(989\) | 43.4785 | 1.38253 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.17962 | + | 23.7038i | −0.132770 | + | 0.752976i | 0.843617 | + | 0.536946i | \(0.180422\pi\) |
−0.976387 | + | 0.216030i | \(0.930689\pi\) | |||||||
\(992\) | 3.41646 | − | 2.86675i | 0.108473 | − | 0.0910193i | ||||
\(993\) | 43.7549 | + | 36.7147i | 1.38852 | + | 1.16511i | ||||
\(994\) | −0.0522800 | − | 0.296495i | −0.00165822 | − | 0.00940425i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.22617 | + | 7.31994i | −0.133911 | + | 0.231941i | ||||
\(997\) | 13.3716 | + | 4.86686i | 0.423483 | + | 0.154135i | 0.544966 | − | 0.838458i | \(-0.316543\pi\) |
−0.121483 | + | 0.992594i | \(0.538765\pi\) | |||||||
\(998\) | 7.29367 | + | 2.65468i | 0.230877 | + | 0.0840323i | ||||
\(999\) | −2.71651 | + | 4.70514i | −0.0859466 | + | 0.148864i |
(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 | 950.2.l.i.651.3 | 18 | ||
5.2 | odd | 4 | 950.2.u.g.499.1 | 36 | |||
5.3 | odd | 4 | 950.2.u.g.499.6 | 36 | |||
5.4 | even | 2 | 190.2.k.d.81.1 | yes | 18 | ||
19.4 | even | 9 | inner | 950.2.l.i.251.3 | 18 | ||
95.4 | even | 18 | 190.2.k.d.61.1 | ✓ | 18 | ||
95.23 | odd | 36 | 950.2.u.g.99.1 | 36 | |||
95.42 | odd | 36 | 950.2.u.g.99.6 | 36 | |||
95.59 | odd | 18 | 3610.2.a.bj.1.9 | 9 | |||
95.74 | even | 18 | 3610.2.a.bi.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.d.61.1 | ✓ | 18 | 95.4 | even | 18 | ||
190.2.k.d.81.1 | yes | 18 | 5.4 | even | 2 | ||
950.2.l.i.251.3 | 18 | 19.4 | even | 9 | inner | ||
950.2.l.i.651.3 | 18 | 1.1 | even | 1 | trivial | ||
950.2.u.g.99.1 | 36 | 95.23 | odd | 36 | |||
950.2.u.g.99.6 | 36 | 95.42 | odd | 36 | |||
950.2.u.g.499.1 | 36 | 5.2 | odd | 4 | |||
950.2.u.g.499.6 | 36 | 5.3 | odd | 4 | |||
3610.2.a.bi.1.1 | 9 | 95.74 | even | 18 | |||
3610.2.a.bj.1.9 | 9 | 95.59 | odd | 18 |