Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(751,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.bc (of order \(6\), degree \(2\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.5 | ||
Root | \(-2.39378 + 0.0429626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.901 |
Dual form | 1950.2.bc.j.751.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −1.42559 | + | 0.823063i | −0.538821 | + | 0.311088i | −0.744601 | − | 0.667510i | \(-0.767360\pi\) |
0.205780 | + | 0.978598i | \(0.434027\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.08305 | + | 1.20265i | 0.628063 | + | 0.362612i | 0.780001 | − | 0.625778i | \(-0.215218\pi\) |
−0.151939 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0.256262 | + | 3.59643i | 0.0710744 | + | 0.997471i | ||||
\(14\) | −1.64613 | −0.439946 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.121649 | + | 0.210702i | 0.0295041 | + | 0.0511027i | 0.880400 | − | 0.474231i | \(-0.157274\pi\) |
−0.850896 | + | 0.525334i | \(0.823941\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.82681 | + | 2.20941i | −0.877930 | + | 0.506873i | −0.869975 | − | 0.493095i | \(-0.835865\pi\) |
−0.00795483 | + | 0.999968i | \(0.502532\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.64613i | 0.359214i | ||||||||
\(22\) | 1.20265 | + | 2.08305i | 0.256405 | + | 0.444107i | ||||
\(23\) | −4.31141 | + | 7.46758i | −0.898991 | + | 1.55710i | −0.0702038 | + | 0.997533i | \(0.522365\pi\) |
−0.828787 | + | 0.559565i | \(0.810968\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.57629 | + | 3.24273i | −0.309135 | + | 0.635952i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.42559 | − | 0.823063i | −0.269411 | − | 0.155544i | ||||
\(29\) | −0.0221633 | + | 0.0383880i | −0.00411562 | + | 0.00712846i | −0.868076 | − | 0.496432i | \(-0.834643\pi\) |
0.863960 | + | 0.503560i | \(0.167977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.24458i | − | 0.762348i | −0.924503 | − | 0.381174i | \(-0.875520\pi\) | ||
0.924503 | − | 0.381174i | \(-0.124480\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 2.08305 | − | 1.20265i | 0.362612 | − | 0.209354i | ||||
\(34\) | 0.243297i | 0.0417251i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | − | 0.866025i | 0.0833333 | − | 0.144338i | ||||
\(37\) | 7.74945 | + | 4.47415i | 1.27400 | + | 0.735545i | 0.975739 | − | 0.218939i | \(-0.0702595\pi\) |
0.298263 | + | 0.954484i | \(0.403593\pi\) | |||||||
\(38\) | −4.41882 | −0.716827 | ||||||||
\(39\) | 3.24273 | + | 1.57629i | 0.519253 | + | 0.252408i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.210702 | + | 0.121649i | 0.0329061 | + | 0.0189983i | 0.516363 | − | 0.856370i | \(-0.327286\pi\) |
−0.483457 | + | 0.875368i | \(0.660619\pi\) | |||||||
\(42\) | −0.823063 | + | 1.42559i | −0.127001 | + | 0.219973i | ||||
\(43\) | 3.36438 | + | 5.82728i | 0.513063 | + | 0.888652i | 0.999885 | + | 0.0151507i | \(0.00482279\pi\) |
−0.486822 | + | 0.873501i | \(0.661844\pi\) | |||||||
\(44\) | 2.40530i | 0.362612i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.46758 | + | 4.31141i | −1.10103 | + | 0.635682i | ||||
\(47\) | − | 7.29560i | − | 1.06417i | −0.846690 | − | 0.532086i | \(-0.821408\pi\) | ||
0.846690 | − | 0.532086i | \(-0.178592\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −2.14514 | + | 3.71548i | −0.306448 | + | 0.530783i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.243297 | 0.0340684 | ||||||||
\(52\) | −2.98647 | + | 2.02015i | −0.414149 | + | 0.280144i | ||||
\(53\) | 2.44613 | 0.336002 | 0.168001 | − | 0.985787i | \(-0.446269\pi\) | ||||
0.168001 | + | 0.985787i | \(0.446269\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.823063 | − | 1.42559i | −0.109986 | − | 0.190502i | ||||
\(57\) | 4.41882i | 0.585287i | ||||||||
\(58\) | −0.0383880 | + | 0.0221633i | −0.00504059 | + | 0.00291018i | ||||
\(59\) | 8.35669 | − | 4.82474i | 1.08795 | − | 0.628127i | 0.154919 | − | 0.987927i | \(-0.450488\pi\) |
0.933029 | + | 0.359800i | \(0.117155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31630 | + | 2.27990i | 0.168535 | + | 0.291911i | 0.937905 | − | 0.346892i | \(-0.112763\pi\) |
−0.769370 | + | 0.638804i | \(0.779430\pi\) | |||||||
\(62\) | 2.12229 | − | 3.67591i | 0.269531 | − | 0.466841i | ||||
\(63\) | 1.42559 | + | 0.823063i | 0.179607 | + | 0.103696i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.40530 | 0.296072 | ||||||||
\(67\) | 1.62310 | + | 0.937098i | 0.198293 | + | 0.114485i | 0.595859 | − | 0.803089i | \(-0.296812\pi\) |
−0.397566 | + | 0.917574i | \(0.630145\pi\) | |||||||
\(68\) | −0.121649 | + | 0.210702i | −0.0147521 | + | 0.0255513i | ||||
\(69\) | 4.31141 | + | 7.46758i | 0.519032 | + | 0.898991i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.53035 | + | 3.77030i | −0.775010 | + | 0.447452i | −0.834659 | − | 0.550767i | \(-0.814335\pi\) |
0.0596488 | + | 0.998219i | \(0.481002\pi\) | |||||||
\(72\) | 0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | ||||
\(73\) | − | 1.70370i | − | 0.199403i | −0.995017 | − | 0.0997015i | \(-0.968211\pi\) | ||
0.995017 | − | 0.0997015i | \(-0.0317888\pi\) | |||||||
\(74\) | 4.47415 | + | 7.74945i | 0.520109 | + | 0.900855i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.82681 | − | 2.20941i | −0.438965 | − | 0.253437i | ||||
\(77\) | −3.95942 | −0.451218 | ||||||||
\(78\) | 2.02015 | + | 2.98647i | 0.228737 | + | 0.338151i | ||||
\(79\) | −6.79707 | −0.764730 | −0.382365 | − | 0.924011i | \(-0.624890\pi\) | ||||
−0.382365 | + | 0.924011i | \(0.624890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.121649 | + | 0.210702i | 0.0134338 | + | 0.0232681i | ||||
\(83\) | 17.4986i | 1.92073i | 0.278754 | + | 0.960363i | \(0.410079\pi\) | ||||
−0.278754 | + | 0.960363i | \(0.589921\pi\) | |||||||
\(84\) | −1.42559 | + | 0.823063i | −0.155544 | + | 0.0898035i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.72876i | 0.725581i | ||||||||
\(87\) | 0.0221633 | + | 0.0383880i | 0.00237615 | + | 0.00411562i | ||||
\(88\) | −1.20265 | + | 2.08305i | −0.128203 | + | 0.222054i | ||||
\(89\) | 8.69772 | + | 5.02163i | 0.921956 | + | 0.532292i | 0.884259 | − | 0.466997i | \(-0.154664\pi\) |
0.0376977 | + | 0.999289i | \(0.487998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.32541 | − | 4.91611i | −0.348598 | − | 0.515348i | ||||
\(92\) | −8.62281 | −0.898991 | ||||||||
\(93\) | −3.67591 | − | 2.12229i | −0.381174 | − | 0.220071i | ||||
\(94\) | 3.64780 | − | 6.31817i | 0.376242 | − | 0.651670i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −14.3006 | + | 8.25647i | −1.45201 | + | 0.838317i | −0.998595 | − | 0.0529831i | \(-0.983127\pi\) |
−0.453413 | + | 0.891301i | \(0.649794\pi\) | |||||||
\(98\) | −3.71548 | + | 2.14514i | −0.375321 | + | 0.216691i | ||||
\(99\) | − | 2.40530i | − | 0.241741i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.66777 | − | 9.81687i | 0.563964 | − | 0.976815i | −0.433181 | − | 0.901307i | \(-0.642609\pi\) |
0.997145 | − | 0.0755077i | \(-0.0240577\pi\) | |||||||
\(102\) | 0.210702 | + | 0.121649i | 0.0208626 | + | 0.0120450i | ||||
\(103\) | 5.98168 | 0.589392 | 0.294696 | − | 0.955591i | \(-0.404782\pi\) | ||||
0.294696 | + | 0.955591i | \(0.404782\pi\) | |||||||
\(104\) | −3.59643 | + | 0.256262i | −0.352659 | + | 0.0251286i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.11841 | + | 1.22307i | 0.205758 | + | 0.118795i | ||||
\(107\) | −5.33795 | + | 9.24559i | −0.516039 | + | 0.893805i | 0.483788 | + | 0.875185i | \(0.339261\pi\) |
−0.999827 | + | 0.0186200i | \(0.994073\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 9.50683i | − | 0.910589i | −0.890341 | − | 0.455295i | \(-0.849534\pi\) | ||
0.890341 | − | 0.455295i | \(-0.150466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.74945 | − | 4.47415i | 0.735545 | − | 0.424667i | ||||
\(112\) | − | 1.64613i | − | 0.155544i | ||||||
\(113\) | 1.79806 | + | 3.11433i | 0.169147 | + | 0.292972i | 0.938120 | − | 0.346310i | \(-0.112565\pi\) |
−0.768973 | + | 0.639281i | \(0.779232\pi\) | |||||||
\(114\) | −2.20941 | + | 3.82681i | −0.206930 | + | 0.358414i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0443266 | −0.00411562 | ||||||||
\(117\) | 2.98647 | − | 2.02015i | 0.276099 | − | 0.186763i | ||||
\(118\) | 9.64947 | 0.888306 | ||||||||
\(119\) | −0.346841 | − | 0.200249i | −0.0317949 | − | 0.0183568i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.60727 | − | 4.51593i | −0.237025 | − | 0.410539i | ||||
\(122\) | 2.63260i | 0.238345i | ||||||||
\(123\) | 0.210702 | − | 0.121649i | 0.0189983 | − | 0.0109687i | ||||
\(124\) | 3.67591 | − | 2.12229i | 0.330106 | − | 0.190587i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.823063 | + | 1.42559i | 0.0733243 | + | 0.127001i | ||||
\(127\) | 8.67351 | − | 15.0230i | 0.769650 | − | 1.33307i | −0.168103 | − | 0.985769i | \(-0.553764\pi\) |
0.937753 | − | 0.347303i | \(-0.112902\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.72876 | 0.592435 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1654 | 1.23764 | 0.618818 | − | 0.785534i | \(-0.287612\pi\) | ||||
0.618818 | + | 0.785534i | \(0.287612\pi\) | |||||||
\(132\) | 2.08305 | + | 1.20265i | 0.181306 | + | 0.104677i | ||||
\(133\) | 3.63697 | − | 6.29941i | 0.315365 | − | 0.546228i | ||||
\(134\) | 0.937098 | + | 1.62310i | 0.0809530 | + | 0.140215i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.210702 | + | 0.121649i | −0.0180675 | + | 0.0104313i | ||||
\(137\) | −6.35158 | + | 3.66709i | −0.542652 | + | 0.313300i | −0.746153 | − | 0.665774i | \(-0.768101\pi\) |
0.203501 | + | 0.979075i | \(0.434768\pi\) | |||||||
\(138\) | 8.62281i | 0.734023i | ||||||||
\(139\) | −7.10185 | − | 12.3008i | −0.602371 | − | 1.04334i | −0.992461 | − | 0.122561i | \(-0.960889\pi\) |
0.390090 | − | 0.920777i | \(-0.372444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.31817 | − | 3.64780i | −0.532086 | − | 0.307200i | ||||
\(142\) | −7.54060 | −0.632793 | ||||||||
\(143\) | −3.79144 | + | 7.79974i | −0.317056 | + | 0.652247i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.851850 | − | 1.47545i | 0.0704996 | − | 0.122109i | ||||
\(147\) | 2.14514 | + | 3.71548i | 0.176928 | + | 0.306448i | ||||
\(148\) | 8.94829i | 0.735545i | ||||||||
\(149\) | 9.61623 | − | 5.55193i | 0.787792 | − | 0.454832i | −0.0513926 | − | 0.998679i | \(-0.516366\pi\) |
0.839185 | + | 0.543847i | \(0.183033\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.874663i | 0.0711791i | 0.999366 | + | 0.0355895i | \(0.0113309\pi\) | ||||
−0.999366 | + | 0.0355895i | \(0.988669\pi\) | |||||||
\(152\) | −2.20941 | − | 3.82681i | −0.179207 | − | 0.310395i | ||||
\(153\) | 0.121649 | − | 0.210702i | 0.00983471 | − | 0.0170342i | ||||
\(154\) | −3.42896 | − | 1.97971i | −0.276313 | − | 0.159530i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.256262 | + | 3.59643i | 0.0205174 | + | 0.287945i | ||||
\(157\) | 15.5085 | 1.23771 | 0.618856 | − | 0.785504i | \(-0.287596\pi\) | ||||
0.618856 | + | 0.785504i | \(0.287596\pi\) | |||||||
\(158\) | −5.88644 | − | 3.39854i | −0.468300 | − | 0.270373i | ||||
\(159\) | 1.22307 | − | 2.11841i | 0.0969954 | − | 0.168001i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 14.1942i | − | 1.11866i | ||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −18.9597 | + | 10.9464i | −1.48504 | + | 0.857388i | −0.999855 | − | 0.0170229i | \(-0.994581\pi\) |
−0.485185 | + | 0.874411i | \(0.661248\pi\) | |||||||
\(164\) | 0.243297i | 0.0189983i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.74932 | + | 15.1543i | −0.679079 | + | 1.17620i | ||||
\(167\) | 4.58673 | + | 2.64815i | 0.354932 | + | 0.204920i | 0.666855 | − | 0.745187i | \(-0.267640\pi\) |
−0.311923 | + | 0.950107i | \(0.600973\pi\) | |||||||
\(168\) | −1.64613 | −0.127001 | ||||||||
\(169\) | −12.8687 | + | 1.84326i | −0.989897 | + | 0.141789i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.82681 | + | 2.20941i | 0.292643 | + | 0.168958i | ||||
\(172\) | −3.36438 | + | 5.82728i | −0.256532 | + | 0.444326i | ||||
\(173\) | −8.62958 | − | 14.9469i | −0.656095 | − | 1.13639i | −0.981618 | − | 0.190856i | \(-0.938874\pi\) |
0.325523 | − | 0.945534i | \(-0.394460\pi\) | |||||||
\(174\) | 0.0443266i | 0.00336039i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.08305 | + | 1.20265i | −0.157016 | + | 0.0906530i | ||||
\(177\) | − | 9.64947i | − | 0.725299i | ||||||
\(178\) | 5.02163 | + | 8.69772i | 0.376387 | + | 0.651922i | ||||
\(179\) | 4.17781 | − | 7.23617i | 0.312264 | − | 0.540857i | −0.666588 | − | 0.745426i | \(-0.732246\pi\) |
0.978852 | + | 0.204569i | \(0.0655794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.7335 | 0.946476 | 0.473238 | − | 0.880935i | \(-0.343085\pi\) | ||||
0.473238 | + | 0.880935i | \(0.343085\pi\) | |||||||
\(182\) | −0.421840 | − | 5.92018i | −0.0312689 | − | 0.438833i | ||||
\(183\) | 2.63260 | 0.194608 | ||||||||
\(184\) | −7.46758 | − | 4.31141i | −0.550517 | − | 0.317841i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.12229 | − | 3.67591i | −0.155614 | − | 0.269531i | ||||
\(187\) | 0.585202i | 0.0427942i | ||||||||
\(188\) | 6.31817 | − | 3.64780i | 0.460800 | − | 0.266043i | ||||
\(189\) | 1.42559 | − | 0.823063i | 0.103696 | − | 0.0598690i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.207632 | − | 0.359629i | −0.0150237 | − | 0.0260219i | 0.858416 | − | 0.512955i | \(-0.171449\pi\) |
−0.873440 | + | 0.486933i | \(0.838116\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −22.5025 | − | 12.9918i | −1.61977 | − | 0.935173i | −0.986979 | − | 0.160849i | \(-0.948577\pi\) |
−0.632789 | − | 0.774324i | \(-0.718090\pi\) | |||||||
\(194\) | −16.5129 | −1.18556 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.29027 | −0.306448 | ||||||||
\(197\) | 13.3735 | + | 7.72121i | 0.952824 | + | 0.550113i | 0.893957 | − | 0.448152i | \(-0.147918\pi\) |
0.0588672 | + | 0.998266i | \(0.481251\pi\) | |||||||
\(198\) | 1.20265 | − | 2.08305i | 0.0854685 | − | 0.148036i | ||||
\(199\) | −6.85286 | − | 11.8695i | −0.485787 | − | 0.841407i | 0.514080 | − | 0.857742i | \(-0.328133\pi\) |
−0.999867 | + | 0.0163352i | \(0.994800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.62310 | − | 0.937098i | 0.114485 | − | 0.0660978i | ||||
\(202\) | 9.81687 | − | 5.66777i | 0.690712 | − | 0.398783i | ||||
\(203\) | − | 0.0729671i | − | 0.00512129i | ||||||
\(204\) | 0.121649 | + | 0.210702i | 0.00851711 | + | 0.0147521i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.18029 | + | 2.99084i | 0.360928 | + | 0.208382i | ||||
\(207\) | 8.62281 | 0.599327 | ||||||||
\(208\) | −3.24273 | − | 1.57629i | −0.224843 | − | 0.109296i | ||||
\(209\) | −10.6286 | −0.735193 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.05616 | − | 13.9537i | 0.554609 | − | 0.960611i | −0.443325 | − | 0.896361i | \(-0.646201\pi\) |
0.997934 | − | 0.0642497i | \(-0.0204654\pi\) | |||||||
\(212\) | 1.22307 | + | 2.11841i | 0.0840005 | + | 0.145493i | ||||
\(213\) | 7.54060i | 0.516673i | ||||||||
\(214\) | −9.24559 | + | 5.33795i | −0.632016 | + | 0.364894i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 3.49355 | + | 6.05101i | 0.237158 | + | 0.410769i | ||||
\(218\) | 4.75342 | − | 8.23316i | 0.321942 | − | 0.557620i | ||||
\(219\) | −1.47545 | − | 0.851850i | −0.0997015 | − | 0.0575627i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.726600 | + | 0.491496i | −0.0488764 | + | 0.0330616i | ||||
\(222\) | 8.94829 | 0.600570 | ||||||||
\(223\) | 9.62823 | + | 5.55886i | 0.644754 | + | 0.372249i | 0.786443 | − | 0.617662i | \(-0.211920\pi\) |
−0.141690 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(224\) | 0.823063 | − | 1.42559i | 0.0549932 | − | 0.0952510i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.59612i | 0.239210i | ||||||||
\(227\) | −19.1217 | + | 11.0399i | −1.26915 | + | 0.732747i | −0.974828 | − | 0.222958i | \(-0.928429\pi\) |
−0.294327 | + | 0.955705i | \(0.595095\pi\) | |||||||
\(228\) | −3.82681 | + | 2.20941i | −0.253437 | + | 0.146322i | ||||
\(229\) | − | 10.3397i | − | 0.683266i | −0.939834 | − | 0.341633i | \(-0.889020\pi\) | ||
0.939834 | − | 0.341633i | \(-0.110980\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.97971 | + | 3.42896i | −0.130255 | + | 0.225609i | ||||
\(232\) | −0.0383880 | − | 0.0221633i | −0.00252029 | − | 0.00145509i | ||||
\(233\) | 21.8928 | 1.43425 | 0.717123 | − | 0.696947i | \(-0.245459\pi\) | ||||
0.717123 | + | 0.696947i | \(0.245459\pi\) | |||||||
\(234\) | 3.59643 | − | 0.256262i | 0.235106 | − | 0.0167524i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.35669 | + | 4.82474i | 0.543974 | + | 0.314064i | ||||
\(237\) | −3.39854 | + | 5.88644i | −0.220759 | + | 0.382365i | ||||
\(238\) | −0.200249 | − | 0.346841i | −0.0129802 | − | 0.0224824i | ||||
\(239\) | 26.2510i | 1.69804i | 0.528362 | + | 0.849019i | \(0.322806\pi\) | ||||
−0.528362 | + | 0.849019i | \(0.677194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5952 | − | 13.0454i | 1.45549 | − | 0.840326i | 0.456703 | − | 0.889619i | \(-0.349030\pi\) |
0.998784 | + | 0.0492931i | \(0.0156968\pi\) | |||||||
\(242\) | − | 5.21455i | − | 0.335204i | ||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −1.31630 | + | 2.27990i | −0.0842676 | + | 0.145956i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.243297 | 0.0155121 | ||||||||
\(247\) | −8.92666 | − | 13.1967i | −0.567990 | − | 0.839684i | ||||
\(248\) | 4.24458 | 0.269531 | ||||||||
\(249\) | 15.1543 | + | 8.74932i | 0.960363 | + | 0.554466i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.312397 | − | 0.541088i | −0.0197183 | − | 0.0341532i | 0.855998 | − | 0.516979i | \(-0.172944\pi\) |
−0.875716 | + | 0.482826i | \(0.839610\pi\) | |||||||
\(252\) | 1.64613i | 0.103696i | ||||||||
\(253\) | −17.9617 | + | 10.3702i | −1.12924 | + | 0.651970i | ||||
\(254\) | 15.0230 | − | 8.67351i | 0.942624 | − | 0.544224i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.97195 | + | 12.0758i | −0.434898 | + | 0.753266i | −0.997287 | − | 0.0736066i | \(-0.976549\pi\) |
0.562389 | + | 0.826873i | \(0.309882\pi\) | |||||||
\(258\) | 5.82728 | + | 3.36438i | 0.362791 | + | 0.209457i | ||||
\(259\) | −14.7300 | −0.915278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0443266 | 0.00274375 | ||||||||
\(262\) | 12.2676 | + | 7.08270i | 0.757894 | + | 0.437571i | ||||
\(263\) | 9.71828 | − | 16.8325i | 0.599255 | − | 1.03794i | −0.393677 | − | 0.919249i | \(-0.628797\pi\) |
0.992931 | − | 0.118690i | \(-0.0378696\pi\) | |||||||
\(264\) | 1.20265 | + | 2.08305i | 0.0740179 | + | 0.128203i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.29941 | − | 3.63697i | 0.386242 | − | 0.222997i | ||||
\(267\) | 8.69772 | − | 5.02163i | 0.532292 | − | 0.307319i | ||||
\(268\) | 1.87420i | 0.114485i | ||||||||
\(269\) | 1.50069 | + | 2.59928i | 0.0914989 | + | 0.158481i | 0.908142 | − | 0.418662i | \(-0.137501\pi\) |
−0.816643 | + | 0.577143i | \(0.804168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.6538 | − | 14.2339i | −1.49761 | − | 0.864645i | −0.497613 | − | 0.867399i | \(-0.665790\pi\) |
−0.999996 | + | 0.00275396i | \(0.999123\pi\) | |||||||
\(272\) | −0.243297 | −0.0147521 | ||||||||
\(273\) | −5.92018 | + | 0.421840i | −0.358306 | + | 0.0255309i | ||||
\(274\) | −7.33417 | −0.443074 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.31141 | + | 7.46758i | −0.259516 | + | 0.449495i | ||||
\(277\) | 0.426329 | + | 0.738423i | 0.0256156 | + | 0.0443676i | 0.878549 | − | 0.477652i | \(-0.158512\pi\) |
−0.852933 | + | 0.522020i | \(0.825179\pi\) | |||||||
\(278\) | − | 14.2037i | − | 0.851882i | ||||||
\(279\) | −3.67591 | + | 2.12229i | −0.220071 | + | 0.127058i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6851i | 0.935697i | 0.883809 | + | 0.467848i | \(0.154971\pi\) | ||||
−0.883809 | + | 0.467848i | \(0.845029\pi\) | |||||||
\(282\) | −3.64780 | − | 6.31817i | −0.217223 | − | 0.376242i | ||||
\(283\) | 4.04370 | − | 7.00390i | 0.240373 | − | 0.416339i | −0.720447 | − | 0.693510i | \(-0.756063\pi\) |
0.960821 | + | 0.277171i | \(0.0893968\pi\) | |||||||
\(284\) | −6.53035 | − | 3.77030i | −0.387505 | − | 0.223726i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.18335 | + | 4.85905i | −0.424760 | + | 0.287322i | ||||
\(287\) | −0.400498 | −0.0236406 | ||||||||
\(288\) | 0.866025 | + | 0.500000i | 0.0510310 | + | 0.0294628i | ||||
\(289\) | 8.47040 | − | 14.6712i | 0.498259 | − | 0.863010i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.5129i | 0.968006i | ||||||||
\(292\) | 1.47545 | − | 0.851850i | 0.0863440 | − | 0.0498508i | ||||
\(293\) | −1.67523 | + | 0.967192i | −0.0978677 | + | 0.0565040i | −0.548135 | − | 0.836390i | \(-0.684662\pi\) |
0.450267 | + | 0.892894i | \(0.351329\pi\) | |||||||
\(294\) | 4.29027i | 0.250214i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.47415 | + | 7.74945i | −0.260054 | + | 0.450427i | ||||
\(297\) | −2.08305 | − | 1.20265i | −0.120871 | − | 0.0697847i | ||||
\(298\) | 11.1039 | 0.643229 | ||||||||
\(299\) | −27.9615 | − | 13.5920i | −1.61705 | − | 0.786047i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.59244 | − | 5.53820i | −0.552899 | − | 0.319216i | ||||
\(302\) | −0.437332 | + | 0.757480i | −0.0251656 | + | 0.0435881i | ||||
\(303\) | −5.66777 | − | 9.81687i | −0.325605 | − | 0.563964i | ||||
\(304\) | − | 4.41882i | − | 0.253437i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.210702 | − | 0.121649i | 0.0120450 | − | 0.00695419i | ||||
\(307\) | − | 12.4384i | − | 0.709894i | −0.934886 | − | 0.354947i | \(-0.884499\pi\) | ||
0.934886 | − | 0.354947i | \(-0.115501\pi\) | |||||||
\(308\) | −1.97971 | − | 3.42896i | −0.112804 | − | 0.195383i | ||||
\(309\) | 2.99084 | − | 5.18029i | 0.170143 | − | 0.294696i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.3700 | −1.04167 | −0.520835 | − | 0.853657i | \(-0.674379\pi\) | ||||
−0.520835 | + | 0.853657i | \(0.674379\pi\) | |||||||
\(312\) | −1.57629 | + | 3.24273i | −0.0892397 | + | 0.183584i | ||||
\(313\) | 31.9445 | 1.80561 | 0.902804 | − | 0.430051i | \(-0.141504\pi\) | ||||
0.902804 | + | 0.430051i | \(0.141504\pi\) | |||||||
\(314\) | 13.4307 | + | 7.75425i | 0.757941 | + | 0.437597i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.39854 | − | 5.88644i | −0.191183 | − | 0.331138i | ||||
\(317\) | − | 23.3625i | − | 1.31217i | −0.754689 | − | 0.656083i | \(-0.772212\pi\) | ||
0.754689 | − | 0.656083i | \(-0.227788\pi\) | |||||||
\(318\) | 2.11841 | − | 1.22307i | 0.118795 | − | 0.0685861i | ||||
\(319\) | −0.0923344 | + | 0.0533093i | −0.00516973 | + | 0.00298475i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.33795 | + | 9.24559i | 0.297935 | + | 0.516039i | ||||
\(322\) | 7.09712 | − | 12.2926i | 0.395507 | − | 0.685038i | ||||
\(323\) | −0.931052 | − | 0.537543i | −0.0518051 | − | 0.0299097i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.8928 | −1.21253 | ||||||||
\(327\) | −8.23316 | − | 4.75342i | −0.455295 | − | 0.262865i | ||||
\(328\) | −0.121649 | + | 0.210702i | −0.00671692 | + | 0.0116341i | ||||
\(329\) | 6.00474 | + | 10.4005i | 0.331052 | + | 0.573399i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.5879 | + | 10.7317i | −1.02168 | + | 0.589868i | −0.914590 | − | 0.404382i | \(-0.867487\pi\) |
−0.107090 | + | 0.994249i | \(0.534153\pi\) | |||||||
\(332\) | −15.1543 | + | 8.74932i | −0.831698 | + | 0.480181i | ||||
\(333\) | − | 8.94829i | − | 0.490363i | ||||||
\(334\) | 2.64815 | + | 4.58673i | 0.144900 | + | 0.250975i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.42559 | − | 0.823063i | −0.0777721 | − | 0.0449018i | ||||
\(337\) | −14.3561 | −0.782026 | −0.391013 | − | 0.920385i | \(-0.627875\pi\) | ||||
−0.391013 | + | 0.920385i | \(0.627875\pi\) | |||||||
\(338\) | −12.0662 | − | 4.83802i | −0.656316 | − | 0.263154i | ||||
\(339\) | 3.59612 | 0.195314 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.10473 | − | 8.84165i | 0.276437 | − | 0.478802i | ||||
\(342\) | 2.20941 | + | 3.82681i | 0.119471 | + | 0.206930i | ||||
\(343\) | − | 18.5852i | − | 1.00351i | ||||||
\(344\) | −5.82728 | + | 3.36438i | −0.314186 | + | 0.181395i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 17.2592i | − | 0.927858i | ||||||
\(347\) | −0.332557 | − | 0.576005i | −0.0178526 | − | 0.0309216i | 0.856961 | − | 0.515381i | \(-0.172350\pi\) |
−0.874814 | + | 0.484460i | \(0.839016\pi\) | |||||||
\(348\) | −0.0221633 | + | 0.0383880i | −0.00118808 | + | 0.00205781i | ||||
\(349\) | −3.25007 | − | 1.87643i | −0.173972 | − | 0.100443i | 0.410485 | − | 0.911867i | \(-0.365359\pi\) |
−0.584458 | + | 0.811424i | \(0.698693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.256262 | − | 3.59643i | −0.0136783 | − | 0.191963i | ||||
\(352\) | −2.40530 | −0.128203 | ||||||||
\(353\) | 3.95219 | + | 2.28180i | 0.210354 | + | 0.121448i | 0.601476 | − | 0.798891i | \(-0.294580\pi\) |
−0.391122 | + | 0.920339i | \(0.627913\pi\) | |||||||
\(354\) | 4.82474 | − | 8.35669i | 0.256432 | − | 0.444153i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0433i | 0.532292i | ||||||||
\(357\) | −0.346841 | + | 0.200249i | −0.0183568 | + | 0.0105983i | ||||
\(358\) | 7.23617 | − | 4.17781i | 0.382444 | − | 0.220804i | ||||
\(359\) | 4.75785i | 0.251110i | 0.992087 | + | 0.125555i | \(0.0400711\pi\) | ||||
−0.992087 | + | 0.125555i | \(0.959929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.262979 | − | 0.455494i | 0.0138410 | − | 0.0239733i | ||||
\(362\) | 11.0276 | + | 6.36677i | 0.579596 | + | 0.334630i | ||||
\(363\) | −5.21455 | −0.273693 | ||||||||
\(364\) | 2.59477 | − | 5.33795i | 0.136003 | − | 0.279784i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.27990 | + | 1.31630i | 0.119172 | + | 0.0688042i | ||||
\(367\) | −0.747277 | + | 1.29432i | −0.0390075 | + | 0.0675630i | −0.884870 | − | 0.465838i | \(-0.845753\pi\) |
0.845863 | + | 0.533401i | \(0.179086\pi\) | |||||||
\(368\) | −4.31141 | − | 7.46758i | −0.224748 | − | 0.389274i | ||||
\(369\) | − | 0.243297i | − | 0.0126656i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.48717 | + | 2.01332i | −0.181045 | + | 0.104526i | ||||
\(372\) | − | 4.24458i | − | 0.220071i | ||||||
\(373\) | −10.2955 | − | 17.8323i | −0.533081 | − | 0.923323i | −0.999254 | − | 0.0386291i | \(-0.987701\pi\) |
0.466173 | − | 0.884694i | \(-0.345632\pi\) | |||||||
\(374\) | −0.292601 | + | 0.506800i | −0.0151300 | + | 0.0262060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.29560 | 0.376242 | ||||||||
\(377\) | −0.143739 | − | 0.0698714i | −0.00740295 | − | 0.00359856i | ||||
\(378\) | 1.64613 | 0.0846676 | ||||||||
\(379\) | 18.4173 | + | 10.6332i | 0.946032 | + | 0.546192i | 0.891846 | − | 0.452339i | \(-0.149410\pi\) |
0.0541858 | + | 0.998531i | \(0.482744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.67351 | − | 15.0230i | −0.444357 | − | 0.769650i | ||||
\(382\) | − | 0.415264i | − | 0.0212468i | ||||||
\(383\) | 9.19884 | − | 5.31095i | 0.470039 | − | 0.271377i | −0.246217 | − | 0.969215i | \(-0.579188\pi\) |
0.716256 | + | 0.697838i | \(0.245854\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9918 | − | 22.5025i | −0.661267 | − | 1.14535i | ||||
\(387\) | 3.36438 | − | 5.82728i | 0.171021 | − | 0.296217i | ||||
\(388\) | −14.3006 | − | 8.25647i | −0.726004 | − | 0.419159i | ||||
\(389\) | 37.0443 | 1.87822 | 0.939111 | − | 0.343613i | \(-0.111651\pi\) | ||||
0.939111 | + | 0.343613i | \(0.111651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.09791 | −0.106096 | ||||||||
\(392\) | −3.71548 | − | 2.14514i | −0.187660 | − | 0.108346i | ||||
\(393\) | 7.08270 | − | 12.2676i | 0.357275 | − | 0.618818i | ||||
\(394\) | 7.72121 | + | 13.3735i | 0.388989 | + | 0.673749i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.08305 | − | 1.20265i | 0.104677 | − | 0.0604353i | ||||
\(397\) | 1.46115 | − | 0.843593i | 0.0733328 | − | 0.0423387i | −0.462885 | − | 0.886418i | \(-0.653186\pi\) |
0.536218 | + | 0.844079i | \(0.319852\pi\) | |||||||
\(398\) | − | 13.7057i | − | 0.687006i | ||||||
\(399\) | −3.63697 | − | 6.29941i | −0.182076 | − | 0.315365i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2949 | + | 9.98524i | 0.863668 | + | 0.498639i | 0.865239 | − | 0.501360i | \(-0.167167\pi\) |
−0.00157101 | + | 0.999999i | \(0.500500\pi\) | |||||||
\(402\) | 1.87420 | 0.0934764 | ||||||||
\(403\) | 15.2653 | − | 1.08772i | 0.760420 | − | 0.0541834i | ||||
\(404\) | 11.3355 | 0.563964 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0364836 | − | 0.0631914i | 0.00181065 | − | 0.00313614i | ||||
\(407\) | 10.7616 | + | 18.6397i | 0.533435 | + | 0.923936i | ||||
\(408\) | 0.243297i | 0.0120450i | ||||||||
\(409\) | −10.6603 | + | 6.15471i | −0.527117 | + | 0.304331i | −0.739842 | − | 0.672781i | \(-0.765100\pi\) |
0.212725 | + | 0.977112i | \(0.431766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.33417i | 0.361768i | ||||||||
\(412\) | 2.99084 | + | 5.18029i | 0.147348 | + | 0.255214i | ||||
\(413\) | −7.94212 | + | 13.7562i | −0.390806 | + | 0.676896i | ||||
\(414\) | 7.46758 | + | 4.31141i | 0.367011 | + | 0.211894i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.02015 | − | 2.98647i | −0.0990458 | − | 0.146424i | ||||
\(417\) | −14.2037 | −0.695559 | ||||||||
\(418\) | −9.20461 | − | 5.31428i | −0.450212 | − | 0.259930i | ||||
\(419\) | −11.0411 | + | 19.1238i | −0.539393 | + | 0.934256i | 0.459544 | + | 0.888155i | \(0.348013\pi\) |
−0.998937 | + | 0.0461011i | \(0.985320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.98036i | 0.437676i | 0.975761 | + | 0.218838i | \(0.0702266\pi\) | ||||
−0.975761 | + | 0.218838i | \(0.929773\pi\) | |||||||
\(422\) | 13.9537 | − | 8.05616i | 0.679254 | − | 0.392168i | ||||
\(423\) | −6.31817 | + | 3.64780i | −0.307200 | + | 0.177362i | ||||
\(424\) | 2.44613i | 0.118795i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.77030 | + | 6.53035i | −0.182672 | + | 0.316397i | ||||
\(427\) | −3.75300 | − | 2.16680i | −0.181621 | − | 0.104859i | ||||
\(428\) | −10.6759 | −0.516039 | ||||||||
\(429\) | 4.85905 | + | 7.18335i | 0.234597 | + | 0.346815i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.16090 | + | 4.13435i | 0.344928 | + | 0.199145i | 0.662449 | − | 0.749107i | \(-0.269517\pi\) |
−0.317521 | + | 0.948251i | \(0.602850\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −9.92035 | − | 17.1825i | −0.476741 | − | 0.825740i | 0.522903 | − | 0.852392i | \(-0.324849\pi\) |
−0.999645 | + | 0.0266515i | \(0.991516\pi\) | |||||||
\(434\) | 6.98710i | 0.335392i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.23316 | − | 4.75342i | 0.394297 | − | 0.227647i | ||||
\(437\) | − | 38.1027i | − | 1.82270i | ||||||
\(438\) | −0.851850 | − | 1.47545i | −0.0407030 | − | 0.0704996i | ||||
\(439\) | 14.4415 | − | 25.0134i | 0.689255 | − | 1.19382i | −0.282824 | − | 0.959172i | \(-0.591271\pi\) |
0.972079 | − | 0.234653i | \(-0.0753953\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.29027 | 0.204299 | ||||||||
\(442\) | −0.875002 | + | 0.0623479i | −0.0416196 | + | 0.00296559i | ||||
\(443\) | 5.76986 | 0.274134 | 0.137067 | − | 0.990562i | \(-0.456232\pi\) | ||||
0.137067 | + | 0.990562i | \(0.456232\pi\) | |||||||
\(444\) | 7.74945 | + | 4.47415i | 0.367772 | + | 0.212334i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.55886 | + | 9.62823i | 0.263220 | + | 0.455910i | ||||
\(447\) | − | 11.1039i | − | 0.525195i | ||||||
\(448\) | 1.42559 | − | 0.823063i | 0.0673526 | − | 0.0388861i | ||||
\(449\) | 33.9034 | − | 19.5741i | 1.60000 | − | 0.923760i | 0.608514 | − | 0.793543i | \(-0.291766\pi\) |
0.991486 | − | 0.130217i | \(-0.0415674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.292601 | + | 0.506800i | 0.0137780 | + | 0.0238643i | ||||
\(452\) | −1.79806 | + | 3.11433i | −0.0845736 | + | 0.146486i | ||||
\(453\) | 0.757480 | + | 0.437332i | 0.0355895 | + | 0.0205476i | ||||
\(454\) | −22.0799 | −1.03626 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.41882 | −0.206930 | ||||||||
\(457\) | −21.2008 | − | 12.2403i | −0.991730 | − | 0.572575i | −0.0859387 | − | 0.996300i | \(-0.527389\pi\) |
−0.905791 | + | 0.423725i | \(0.860722\pi\) | |||||||
\(458\) | 5.16984 | − | 8.95443i | 0.241571 | − | 0.418413i | ||||
\(459\) | −0.121649 | − | 0.210702i | −0.00567807 | − | 0.00983471i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.02923 | − | 1.74893i | 0.141085 | − | 0.0814557i | −0.427796 | − | 0.903875i | \(-0.640710\pi\) |
0.568881 | + | 0.822420i | \(0.307376\pi\) | |||||||
\(462\) | −3.42896 | + | 1.97971i | −0.159530 | + | 0.0921044i | ||||
\(463\) | − | 18.3063i | − | 0.850767i | −0.905013 | − | 0.425384i | \(-0.860139\pi\) | ||
0.905013 | − | 0.425384i | \(-0.139861\pi\) | |||||||
\(464\) | −0.0221633 | − | 0.0383880i | −0.00102891 | − | 0.00178212i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.9597 | + | 10.9464i | 0.878292 | + | 0.507082i | ||||
\(467\) | −6.46019 | −0.298942 | −0.149471 | − | 0.988766i | \(-0.547757\pi\) | ||||
−0.149471 | + | 0.988766i | \(0.547757\pi\) | |||||||
\(468\) | 3.24273 | + | 1.57629i | 0.149895 | + | 0.0728639i | ||||
\(469\) | −3.08516 | −0.142460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.75425 | − | 13.4307i | 0.357297 | − | 0.618856i | ||||
\(472\) | 4.82474 | + | 8.35669i | 0.222077 | + | 0.384648i | ||||
\(473\) | 16.1847i | 0.744172i | ||||||||
\(474\) | −5.88644 | + | 3.39854i | −0.270373 | + | 0.156100i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 0.400498i | − | 0.0183568i | ||||||
\(477\) | −1.22307 | − | 2.11841i | −0.0560003 | − | 0.0969954i | ||||
\(478\) | −13.1255 | + | 22.7341i | −0.600347 | + | 1.03983i | ||||
\(479\) | −26.5980 | − | 15.3564i | −1.21529 | − | 0.701651i | −0.251387 | − | 0.967887i | \(-0.580887\pi\) |
−0.963908 | + | 0.266236i | \(0.914220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.1051 | + | 29.0169i | −0.643136 | + | 1.32306i | ||||
\(482\) | 26.0907 | 1.18840 | ||||||||
\(483\) | −12.2926 | − | 7.09712i | −0.559331 | − | 0.322930i | ||||
\(484\) | 2.60727 | − | 4.51593i | 0.118512 | − | 0.205270i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −10.7965 | + | 6.23335i | −0.489235 | + | 0.282460i | −0.724257 | − | 0.689530i | \(-0.757817\pi\) |
0.235022 | + | 0.971990i | \(0.424484\pi\) | |||||||
\(488\) | −2.27990 | + | 1.31630i | −0.103206 | + | 0.0595862i | ||||
\(489\) | 21.8928i | 0.990027i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.29120 | − | 2.23642i | 0.0582710 | − | 0.100928i | −0.835418 | − | 0.549615i | \(-0.814775\pi\) |
0.893689 | + | 0.448686i | \(0.148108\pi\) | |||||||
\(492\) | 0.210702 | + | 0.121649i | 0.00949916 | + | 0.00548434i | ||||
\(493\) | −0.0107845 | −0.000485711 | ||||||||
\(494\) | −1.13238 | − | 15.8920i | −0.0509480 | − | 0.715014i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.67591 | + | 2.12229i | 0.165053 | + | 0.0952935i | ||||
\(497\) | 6.20639 | − | 10.7498i | 0.278395 | − | 0.482194i | ||||
\(498\) | 8.74932 | + | 15.1543i | 0.392066 | + | 0.679079i | ||||
\(499\) | 20.2443i | 0.906261i | 0.891444 | + | 0.453130i | \(0.149693\pi\) | ||||
−0.891444 | + | 0.453130i | \(0.850307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.58673 | − | 2.64815i | 0.204920 | − | 0.118311i | ||||
\(502\) | − | 0.624794i | − | 0.0278859i | ||||||
\(503\) | 4.23283 | + | 7.33148i | 0.188733 | + | 0.326894i | 0.944828 | − | 0.327567i | \(-0.106229\pi\) |
−0.756095 | + | 0.654461i | \(0.772895\pi\) | |||||||
\(504\) | −0.823063 | + | 1.42559i | −0.0366621 | + | 0.0635007i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.7404 | −0.922024 | ||||||||
\(507\) | −4.83802 | + | 12.0662i | −0.214864 | + | 0.535879i | ||||
\(508\) | 17.3470 | 0.769650 | ||||||||
\(509\) | 33.4172 | + | 19.2935i | 1.48119 | + | 0.855167i | 0.999773 | − | 0.0213225i | \(-0.00678766\pi\) |
0.481421 | + | 0.876490i | \(0.340121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40225 | + | 2.42877i | 0.0620320 | + | 0.107443i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 3.82681 | − | 2.20941i | 0.168958 | − | 0.0975478i | ||||
\(514\) | −12.0758 | + | 6.97195i | −0.532640 | + | 0.307520i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.36438 | + | 5.82728i | 0.148109 | + | 0.256532i | ||||
\(517\) | 8.77404 | − | 15.1971i | 0.385882 | − | 0.668367i | ||||
\(518\) | −12.7566 | − | 7.36500i | −0.560491 | − | 0.323600i | ||||
\(519\) | −17.2592 | −0.757593 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5345 | 0.549148 | 0.274574 | − | 0.961566i | \(-0.411463\pi\) | ||||
0.274574 | + | 0.961566i | \(0.411463\pi\) | |||||||
\(522\) | 0.0383880 | + | 0.0221633i | 0.00168020 | + | 0.000970061i | ||||
\(523\) | 6.39970 | − | 11.0846i | 0.279839 | − | 0.484696i | −0.691505 | − | 0.722371i | \(-0.743052\pi\) |
0.971345 | + | 0.237676i | \(0.0763855\pi\) | |||||||
\(524\) | 7.08270 | + | 12.2676i | 0.309409 | + | 0.535912i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8325 | − | 9.71828i | 0.733934 | − | 0.423737i | ||||
\(527\) | 0.894339 | − | 0.516347i | 0.0389580 | − | 0.0224924i | ||||
\(528\) | 2.40530i | 0.104677i | ||||||||
\(529\) | −25.6765 | − | 44.4729i | −1.11637 | − | 1.93361i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.35669 | − | 4.82474i | −0.362649 | − | 0.209376i | ||||
\(532\) | 7.27393 | 0.315365 | ||||||||
\(533\) | −0.383506 | + | 0.788948i | −0.0166115 | + | 0.0341731i | ||||
\(534\) | 10.0433 | 0.434614 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.937098 | + | 1.62310i | −0.0404765 | + | 0.0701073i | ||||
\(537\) | −4.17781 | − | 7.23617i | −0.180286 | − | 0.312264i | ||||
\(538\) | 3.00139i | 0.129399i | ||||||||
\(539\) | −8.93684 | + | 5.15969i | −0.384937 | + | 0.222243i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.9605i | 1.07314i | 0.843857 | + | 0.536568i | \(0.180280\pi\) | ||||
−0.843857 | + | 0.536568i | \(0.819720\pi\) | |||||||
\(542\) | −14.2339 | − | 24.6538i | −0.611396 | − | 1.05897i | ||||
\(543\) | 6.36677 | − | 11.0276i | 0.273224 | − | 0.473238i | ||||
\(544\) | −0.210702 | − | 0.121649i | −0.00903376 | − | 0.00521564i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.33795 | − | 2.59477i | −0.228443 | − | 0.111046i | ||||
\(547\) | 10.4152 | 0.445321 | 0.222660 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222660 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(548\) | −6.35158 | − | 3.66709i | −0.271326 | − | 0.156650i | ||||
\(549\) | 1.31630 | − | 2.27990i | 0.0561784 | − | 0.0973038i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.195871i | − | 0.00834439i | ||||||
\(552\) | −7.46758 | + | 4.31141i | −0.317841 | + | 0.183506i | ||||
\(553\) | 9.68981 | − | 5.59442i | 0.412053 | − | 0.237899i | ||||
\(554\) | 0.852658i | 0.0362260i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.10185 | − | 12.3008i | 0.301186 | − | 0.521669i | ||||
\(557\) | 1.20792 | + | 0.697392i | 0.0511812 | + | 0.0295495i | 0.525372 | − | 0.850872i | \(-0.323926\pi\) |
−0.474191 | + | 0.880422i | \(0.657259\pi\) | |||||||
\(558\) | −4.24458 | −0.179687 | ||||||||
\(559\) | −20.0953 | + | 13.5931i | −0.849939 | + | 0.574926i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.506800 | + | 0.292601i | 0.0213971 | + | 0.0123536i | ||||
\(562\) | −7.84257 | + | 13.5837i | −0.330819 | + | 0.572995i | ||||
\(563\) | 8.10624 | + | 14.0404i | 0.341637 | + | 0.591733i | 0.984737 | − | 0.174049i | \(-0.0556853\pi\) |
−0.643100 | + | 0.765782i | \(0.722352\pi\) | |||||||
\(564\) | − | 7.29560i | − | 0.307200i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.00390 | − | 4.04370i | 0.294396 | − | 0.169970i | ||||
\(567\) | − | 1.64613i | − | 0.0691308i | ||||||
\(568\) | −3.77030 | − | 6.53035i | −0.158198 | − | 0.274007i | ||||
\(569\) | −19.6198 | + | 33.9825i | −0.822505 | + | 1.42462i | 0.0813055 | + | 0.996689i | \(0.474091\pi\) |
−0.903811 | + | 0.427932i | \(0.859242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0498 | −0.671662 | −0.335831 | − | 0.941922i | \(-0.609017\pi\) | ||||
−0.335831 | + | 0.941922i | \(0.609017\pi\) | |||||||
\(572\) | −8.65049 | + | 0.616387i | −0.361695 | + | 0.0257724i | ||||
\(573\) | −0.415264 | −0.0173479 | ||||||||
\(574\) | −0.346841 | − | 0.200249i | −0.0144769 | − | 0.00835823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 28.5363i | 1.18798i | 0.804471 | + | 0.593992i | \(0.202449\pi\) | ||||
−0.804471 | + | 0.593992i | \(0.797551\pi\) | |||||||
\(578\) | 14.6712 | − | 8.47040i | 0.610240 | − | 0.352322i | ||||
\(579\) | −22.5025 | + | 12.9918i | −0.935173 | + | 0.539923i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4025 | − | 24.9458i | −0.597515 | − | 1.03493i | ||||
\(582\) | −8.25647 | + | 14.3006i | −0.342242 | + | 0.592780i | ||||
\(583\) | 5.09541 | + | 2.94183i | 0.211030 | + | 0.121838i | ||||
\(584\) | 1.70370 | 0.0704996 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.93438 | −0.0799087 | ||||||||
\(587\) | 39.0171 | + | 22.5265i | 1.61041 | + | 0.929770i | 0.989275 | + | 0.146066i | \(0.0466610\pi\) |
0.621134 | + | 0.783704i | \(0.286672\pi\) | |||||||
\(588\) | −2.14514 | + | 3.71548i | −0.0884639 | + | 0.153224i | ||||
\(589\) | 9.37800 | + | 16.2432i | 0.386414 | + | 0.669289i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.3735 | − | 7.72121i | 0.550113 | − | 0.317608i | ||||
\(592\) | −7.74945 | + | 4.47415i | −0.318500 | + | 0.183886i | ||||
\(593\) | − | 37.0634i | − | 1.52201i | −0.648746 | − | 0.761005i | \(-0.724706\pi\) | ||
0.648746 | − | 0.761005i | \(-0.275294\pi\) | |||||||
\(594\) | −1.20265 | − | 2.08305i | −0.0493453 | − | 0.0854685i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.61623 | + | 5.55193i | 0.393896 | + | 0.227416i | ||||
\(597\) | −13.7057 | −0.560938 | ||||||||
\(598\) | −17.4193 | − | 25.7518i | −0.712330 | − | 1.05307i | ||||
\(599\) | −18.6309 | −0.761238 | −0.380619 | − | 0.924732i | \(-0.624289\pi\) | ||||
−0.380619 | + | 0.924732i | \(0.624289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.69008 | − | 16.7837i | 0.395266 | − | 0.684622i | −0.597869 | − | 0.801594i | \(-0.703986\pi\) |
0.993135 | + | 0.116972i | \(0.0373189\pi\) | |||||||
\(602\) | −5.53820 | − | 9.59244i | −0.225720 | − | 0.390958i | ||||
\(603\) | − | 1.87420i | − | 0.0763232i | ||||||
\(604\) | −0.757480 | + | 0.437332i | −0.0308214 | + | 0.0177948i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 11.3355i | − | 0.460475i | ||||||
\(607\) | 17.4398 | + | 30.2066i | 0.707858 | + | 1.22605i | 0.965650 | + | 0.259846i | \(0.0836717\pi\) |
−0.257792 | + | 0.966200i | \(0.582995\pi\) | |||||||
\(608\) | 2.20941 | − | 3.82681i | 0.0896034 | − | 0.155198i | ||||
\(609\) | −0.0631914 | − | 0.0364836i | −0.00256064 | − | 0.00147839i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2381 | − | 1.86959i | 1.06148 | − | 0.0756354i | ||||
\(612\) | 0.243297 | 0.00983471 | ||||||||
\(613\) | 7.05254 | + | 4.07179i | 0.284849 | + | 0.164458i | 0.635617 | − | 0.772005i | \(-0.280746\pi\) |
−0.350767 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(614\) | 6.21918 | − | 10.7719i | 0.250986 | − | 0.434720i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 3.95942i | − | 0.159530i | ||||||
\(617\) | 28.9752 | − | 16.7288i | 1.16650 | − | 0.673477i | 0.213644 | − | 0.976912i | \(-0.431467\pi\) |
0.952852 | + | 0.303435i | \(0.0981334\pi\) | |||||||
\(618\) | 5.18029 | − | 2.99084i | 0.208382 | − | 0.120309i | ||||
\(619\) | 41.1780i | 1.65508i | 0.561404 | + | 0.827542i | \(0.310261\pi\) | ||||
−0.561404 | + | 0.827542i | \(0.689739\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.31141 | − | 7.46758i | 0.173011 | − | 0.299664i | ||||
\(622\) | −15.9089 | − | 9.18502i | −0.637890 | − | 0.368286i | ||||
\(623\) | −16.5325 | −0.662359 | ||||||||
\(624\) | −2.98647 | + | 2.02015i | −0.119555 | + | 0.0808706i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.6647 | + | 15.9722i | 1.10571 | + | 0.638379i | ||||
\(627\) | −5.31428 | + | 9.20461i | −0.212232 | + | 0.367597i | ||||
\(628\) | 7.75425 | + | 13.4307i | 0.309428 | + | 0.535945i | ||||
\(629\) | 2.17709i | 0.0868065i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6839 | − | 7.32307i | 0.504939 | − | 0.291527i | −0.225812 | − | 0.974171i | \(-0.572503\pi\) |
0.730751 | + | 0.682644i | \(0.239170\pi\) | |||||||
\(632\) | − | 6.79707i | − | 0.270373i | ||||||
\(633\) | −8.05616 | − | 13.9537i | −0.320204 | − | 0.554609i | ||||
\(634\) | 11.6812 | − | 20.2325i | 0.463921 | − | 0.803535i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.44613 | 0.0969954 | ||||||||
\(637\) | −13.9122 | − | 6.76270i | −0.551222 | − | 0.267948i | ||||
\(638\) | −0.106619 | −0.00422107 | ||||||||
\(639\) | 6.53035 | + | 3.77030i | 0.258337 | + | 0.149151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.9793 | + | 41.5334i | 0.947125 | + | 1.64047i | 0.751439 | + | 0.659803i | \(0.229360\pi\) |
0.195686 | + | 0.980667i | \(0.437307\pi\) | |||||||
\(642\) | 10.6759i | 0.421344i | ||||||||
\(643\) | −3.46209 | + | 1.99884i | −0.136531 | + | 0.0788265i | −0.566710 | − | 0.823917i | \(-0.691784\pi\) |
0.430178 | + | 0.902744i | \(0.358451\pi\) | |||||||
\(644\) | 12.2926 | − | 7.09712i | 0.484395 | − | 0.279666i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.537543 | − | 0.931052i | −0.0211494 | − | 0.0366318i | ||||
\(647\) | 11.8080 | − | 20.4521i | 0.464220 | − | 0.804053i | −0.534946 | − | 0.844886i | \(-0.679668\pi\) |
0.999166 | + | 0.0408333i | \(0.0130013\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 23.2098 | 0.911066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.98710 | 0.273846 | ||||||||
\(652\) | −18.9597 | − | 10.9464i | −0.742520 | − | 0.428694i | ||||
\(653\) | −17.6329 | + | 30.5411i | −0.690029 | + | 1.19516i | 0.281799 | + | 0.959473i | \(0.409069\pi\) |
−0.971828 | + | 0.235692i | \(0.924265\pi\) | |||||||
\(654\) | −4.75342 | − | 8.23316i | −0.185873 | − | 0.321942i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.210702 | + | 0.121649i | −0.00822652 | + | 0.00474958i | ||||
\(657\) | −1.47545 | + | 0.851850i | −0.0575627 | + | 0.0332338i | ||||
\(658\) | 12.0095i | 0.468178i | ||||||||
\(659\) | −12.6686 | − | 21.9427i | −0.493499 | − | 0.854765i | 0.506473 | − | 0.862256i | \(-0.330949\pi\) |
−0.999972 | + | 0.00749088i | \(0.997616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.21373 | + | 2.43280i | 0.163895 | + | 0.0946248i | 0.579704 | − | 0.814827i | \(-0.303168\pi\) |
−0.415809 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(662\) | −21.4634 | −0.834199 | ||||||||
\(663\) | 0.0623479 | + | 0.875002i | 0.00242139 | + | 0.0339823i | ||||
\(664\) | −17.4986 | −0.679079 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.47415 | − | 7.74945i | 0.173370 | − | 0.300285i | ||||
\(667\) | −0.191110 | − | 0.331012i | −0.00739981 | − | 0.0128168i | ||||
\(668\) | 5.29630i | 0.204920i | ||||||||
\(669\) | 9.62823 | − | 5.55886i | 0.372249 | − | 0.214918i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.33219i | 0.244452i | ||||||||
\(672\) | −0.823063 | − | 1.42559i | −0.0317503 | − | 0.0549932i | ||||
\(673\) | 3.74408 | − | 6.48493i | 0.144324 | − | 0.249976i | −0.784797 | − | 0.619753i | \(-0.787233\pi\) |
0.929120 | + | 0.369777i | \(0.120566\pi\) | |||||||
\(674\) | −12.4327 | − | 7.17805i | −0.478891 | − | 0.276488i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.03064 | − | 10.2230i | −0.308871 | − | 0.393191i | ||||
\(677\) | 37.4181 | 1.43810 | 0.719048 | − | 0.694961i | \(-0.244578\pi\) | ||||
0.719048 | + | 0.694961i | \(0.244578\pi\) | |||||||
\(678\) | 3.11433 | + | 1.79806i | 0.119605 | + | 0.0690541i | ||||
\(679\) | 13.5912 | − | 23.5406i | 0.521582 | − | 0.903406i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.0799i | 0.846103i | ||||||||
\(682\) | 8.84165 | − | 5.10473i | 0.338564 | − | 0.195470i | ||||
\(683\) | −5.43761 | + | 3.13940i | −0.208064 | + | 0.120126i | −0.600411 | − | 0.799691i | \(-0.704997\pi\) |
0.392347 | + | 0.919817i | \(0.371663\pi\) | |||||||
\(684\) | 4.41882i | 0.168958i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.29260 | − | 16.0953i | 0.354793 | − | 0.614520i | ||||
\(687\) | −8.95443 | − | 5.16984i | −0.341633 | − | 0.197242i | ||||
\(688\) | −6.72876 | −0.256532 | ||||||||
\(689\) | 0.626851 | + | 8.79735i | 0.0238811 | + | 0.335152i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.17461 | − | 5.29696i | −0.349019 | − | 0.201506i | 0.315234 | − | 0.949014i | \(-0.397917\pi\) |
−0.664253 | + | 0.747508i | \(0.731250\pi\) | |||||||
\(692\) | 8.62958 | − | 14.9469i | 0.328047 | − | 0.568195i | ||||
\(693\) | 1.97971 | + | 3.42896i | 0.0752030 | + | 0.130255i | ||||
\(694\) | − | 0.665114i | − | 0.0252474i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.0383880 | + | 0.0221633i | −0.00145509 | + | 0.000840098i | ||||
\(697\) | 0.0591936i | 0.00224212i | ||||||||
\(698\) | −1.87643 | − | 3.25007i | −0.0710239 | − | 0.123017i | ||||
\(699\) | 10.9464 | − | 18.9597i | 0.414031 | − | 0.717123i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6773 | −1.12090 | −0.560449 | − | 0.828189i | \(-0.689371\pi\) | ||||
−0.560449 | + | 0.828189i | \(0.689371\pi\) | |||||||
\(702\) | 1.57629 | − | 3.24273i | 0.0594931 | − | 0.122389i | ||||
\(703\) | −39.5409 | −1.49131 | ||||||||
\(704\) | −2.08305 | − | 1.20265i | −0.0785078 | − | 0.0453265i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.28180 | + | 3.95219i | 0.0858766 | + | 0.148743i | ||||
\(707\) | 18.6597i | 0.701771i | ||||||||
\(708\) | 8.35669 | − | 4.82474i | 0.314064 | − | 0.181325i | ||||
\(709\) | −0.563901 | + | 0.325568i | −0.0211777 | + | 0.0122270i | −0.510551 | − | 0.859847i | \(-0.670559\pi\) |
0.489374 | + | 0.872074i | \(0.337225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.39854 | + | 5.88644i | 0.127455 | + | 0.220759i | ||||
\(712\) | −5.02163 | + | 8.69772i | −0.188194 | + | 0.325961i | ||||
\(713\) | 31.6967 | + | 18.3001i | 1.18705 | + | 0.685344i | ||||
\(714\) | −0.400498 | −0.0149883 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.35561 | 0.312264 | ||||||||
\(717\) | 22.7341 | + | 13.1255i | 0.849019 | + | 0.490181i | ||||
\(718\) | −2.37892 | + | 4.12042i | −0.0887807 | + | 0.153773i | ||||
\(719\) | 3.21203 | + | 5.56340i | 0.119789 | + | 0.207480i | 0.919684 | − | 0.392660i | \(-0.128445\pi\) |
−0.799895 | + | 0.600140i | \(0.795112\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.52740 | + | 4.92330i | −0.317577 | + | 0.183353i | ||||
\(722\) | 0.455494 | − | 0.262979i | 0.0169517 | − | 0.00978708i | ||||
\(723\) | − | 26.0907i | − | 0.970325i | ||||||
\(724\) | 6.36677 | + | 11.0276i | 0.236619 | + | 0.409836i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.51593 | − | 2.60727i | −0.167602 | − | 0.0967650i | ||||
\(727\) | −16.3170 | −0.605165 | −0.302583 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302583 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(728\) | 4.91611 | − | 3.32541i | 0.182203 | − | 0.123248i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.818545 | + | 1.41776i | −0.0302750 | + | 0.0524378i | ||||
\(732\) | 1.31630 | + | 2.27990i | 0.0486519 | + | 0.0842676i | ||||
\(733\) | − | 24.4136i | − | 0.901735i | −0.892591 | − | 0.450868i | \(-0.851115\pi\) | ||
0.892591 | − | 0.450868i | \(-0.148885\pi\) | |||||||
\(734\) | −1.29432 | + | 0.747277i | −0.0477743 | + | 0.0275825i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.62281i | − | 0.317841i | ||||||
\(737\) | 2.25400 | + | 3.90404i | 0.0830271 | + | 0.143807i | ||||
\(738\) | 0.121649 | − | 0.210702i | 0.00447795 | − | 0.00775603i | ||||
\(739\) | −4.75775 | − | 2.74689i | −0.175017 | − | 0.101046i | 0.409932 | − | 0.912116i | \(-0.365552\pi\) |
−0.584949 | + | 0.811070i | \(0.698886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8920 | + | 1.13238i | −0.583807 | + | 0.0415989i | ||||
\(742\) | −4.02664 | −0.147823 | ||||||||
\(743\) | 18.4484 | + | 10.6512i | 0.676804 | + | 0.390753i | 0.798650 | − | 0.601796i | \(-0.205548\pi\) |
−0.121845 | + | 0.992549i | \(0.538881\pi\) | |||||||
\(744\) | 2.12229 | − | 3.67591i | 0.0778068 | − | 0.134765i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 20.5910i | − | 0.753890i | ||||||
\(747\) | 15.1543 | − | 8.74932i | 0.554466 | − | 0.320121i | ||||
\(748\) | −0.506800 | + | 0.292601i | −0.0185304 | + | 0.0106986i | ||||
\(749\) | − | 17.5739i | − | 0.642135i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.4023 | + | 26.6776i | −0.562040 | + | 0.973481i | 0.435279 | + | 0.900296i | \(0.356650\pi\) |
−0.997318 | + | 0.0731853i | \(0.976684\pi\) | |||||||
\(752\) | 6.31817 | + | 3.64780i | 0.230400 | + | 0.133022i | ||||
\(753\) | −0.624794 | −0.0227688 | ||||||||
\(754\) | −0.0895462 | − | 0.132380i | −0.00326108 | − | 0.00482100i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.42559 | + | 0.823063i | 0.0518481 | + | 0.0299345i | ||||
\(757\) | 17.5618 | − | 30.4180i | 0.638296 | − | 1.10556i | −0.347511 | − | 0.937676i | \(-0.612973\pi\) |
0.985807 | − | 0.167885i | \(-0.0536936\pi\) | |||||||
\(758\) | 10.6332 | + | 18.4173i | 0.386216 | + | 0.668946i | ||||
\(759\) | 20.7404i | 0.752830i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.0686 | + | 14.4734i | −0.908737 | + | 0.524659i | −0.880024 | − | 0.474928i | \(-0.842474\pi\) |
−0.0287122 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(762\) | − | 17.3470i | − | 0.628416i | ||||||
\(763\) | 7.82472 | + | 13.5528i | 0.283274 | + | 0.490645i | ||||
\(764\) | 0.207632 | − | 0.359629i | 0.00751187 | − | 0.0130109i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.6219 | 0.383785 | ||||||||
\(767\) | 19.4933 | + | 28.8179i | 0.703864 | + | 1.04055i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 34.3740 | + | 19.8459i | 1.23956 | + | 0.715660i | 0.969004 | − | 0.247045i | \(-0.0794594\pi\) |
0.270555 | + | 0.962704i | \(0.412793\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.97195 | + | 12.0758i | 0.251089 | + | 0.434898i | ||||
\(772\) | − | 25.9837i | − | 0.935173i | ||||||
\(773\) | −12.4177 | + | 7.16938i | −0.446635 | + | 0.257865i | −0.706408 | − | 0.707805i | \(-0.749686\pi\) |
0.259773 | + | 0.965670i | \(0.416352\pi\) | |||||||
\(774\) | 5.82728 | − | 3.36438i | 0.209457 | − | 0.120930i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.25647 | − | 14.3006i | −0.296390 | − | 0.513363i | ||||
\(777\) | −7.36500 | + | 12.7566i | −0.264218 | + | 0.457639i | ||||
\(778\) | 32.0813 | + | 18.5222i | 1.15017 | + | 0.664052i | ||||
\(779\) | −1.07509 | −0.0385190 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.1374 | −0.649007 | ||||||||
\(782\) | −1.81684 | − | 1.04895i | −0.0649701 | − | 0.0375105i | ||||
\(783\) | 0.0221633 | − | 0.0383880i | 0.000792052 | − | 0.00137187i | ||||
\(784\) | −2.14514 | − | 3.71548i | −0.0766120 | − | 0.132696i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.2676 | − | 7.08270i | 0.437571 | − | 0.252631i | ||||
\(787\) | −9.57437 | + | 5.52776i | −0.341289 | + | 0.197043i | −0.660842 | − | 0.750525i | \(-0.729801\pi\) |
0.319553 | + | 0.947568i | \(0.396467\pi\) | |||||||
\(788\) | 15.4424i | 0.550113i | ||||||||
\(789\) | −9.71828 | − | 16.8325i | −0.345980 | − | 0.599255i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.12658 | − | 2.95983i | −0.182280 | − | 0.105240i | ||||
\(792\) | 2.40530 | 0.0854685 | ||||||||
\(793\) | −7.86219 | + | 5.31824i | −0.279195 | + | 0.188856i | ||||
\(794\) | 1.68719 | 0.0598760 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.85286 | − | 11.8695i | 0.242893 | − | 0.420704i | ||||
\(797\) | 0.261666 | + | 0.453218i | 0.00926867 | + | 0.0160538i | 0.870623 | − | 0.491952i | \(-0.163716\pi\) |
−0.861354 | + | 0.508005i | \(0.830383\pi\) | |||||||
\(798\) | − | 7.27393i | − | 0.257494i | ||||||
\(799\) | 1.53719 | − | 0.887500i | 0.0543820 | − | 0.0313975i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.0433i | − | 0.354861i | ||||||
\(802\) | 9.98524 | + | 17.2949i | 0.352591 | + | 0.610705i | ||||
\(803\) | 2.04895 | − | 3.54889i | 0.0723059 | − | 0.125238i | ||||
\(804\) | 1.62310 | + | 0.937098i | 0.0572424 | + | 0.0330489i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.7640 | + | 6.69067i | 0.484817 | + | 0.235669i | ||||
\(807\) | 3.00139 | 0.105654 | ||||||||
\(808\) | 9.81687 | + | 5.66777i | 0.345356 | + | 0.199391i | ||||
\(809\) | 24.5608 | − | 42.5405i | 0.863511 | − | 1.49564i | −0.00500771 | − | 0.999987i | \(-0.501594\pi\) |
0.868518 | − | 0.495657i | \(-0.165073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.5157i | − | 1.10667i | −0.832960 | − | 0.553333i | \(-0.813356\pi\) | ||
0.832960 | − | 0.553333i | \(-0.186644\pi\) | |||||||
\(812\) | 0.0631914 | − | 0.0364836i | 0.00221758 | − | 0.00128032i | ||||
\(813\) | −24.6538 | + | 14.2339i | −0.864645 | + | 0.499203i | ||||
\(814\) | 21.5233i | 0.754391i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.121649 | + | 0.210702i | −0.00425855 | + | 0.00737603i | ||||
\(817\) | −25.7497 | − | 14.8666i | −0.900868 | − | 0.520116i | ||||
\(818\) | −12.3094 | −0.430389 | ||||||||
\(819\) | −2.59477 | + | 5.33795i | −0.0906685 | + | 0.186523i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8449 | − | 7.99335i | −0.483190 | − | 0.278970i | 0.238555 | − | 0.971129i | \(-0.423326\pi\) |
−0.721745 | + | 0.692159i | \(0.756660\pi\) | |||||||
\(822\) | −3.66709 | + | 6.35158i | −0.127904 | + | 0.221537i | ||||
\(823\) | −12.6028 | − | 21.8287i | −0.439306 | − | 0.760900i | 0.558330 | − | 0.829619i | \(-0.311442\pi\) |
−0.997636 | + | 0.0687187i | \(0.978109\pi\) | |||||||
\(824\) | 5.98168i | 0.208382i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.7562 | + | 7.94212i | −0.478638 | + | 0.276342i | ||||
\(827\) | 22.0889i | 0.768106i | 0.923311 | + | 0.384053i | \(0.125472\pi\) | ||||
−0.923311 | + | 0.384053i | \(0.874528\pi\) | |||||||
\(828\) | 4.31141 | + | 7.46758i | 0.149832 | + | 0.259516i | ||||
\(829\) | 4.72499 | − | 8.18393i | 0.164106 | − | 0.284240i | −0.772232 | − | 0.635341i | \(-0.780859\pi\) |
0.936337 | + | 0.351102i | \(0.114193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.852658 | 0.0295784 | ||||||||
\(832\) | −0.256262 | − | 3.59643i | −0.00888430 | − | 0.124684i | ||||
\(833\) | −1.04381 | −0.0361659 | ||||||||
\(834\) | −12.3008 | − | 7.10185i | −0.425941 | − | 0.245917i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.31428 | − | 9.20461i | −0.183798 | − | 0.318348i | ||||
\(837\) | 4.24458i | 0.146714i | ||||||||
\(838\) | −19.1238 | + | 11.0411i | −0.660619 | + | 0.381409i | ||||
\(839\) | 10.8542 | − | 6.26667i | 0.374728 | − | 0.216350i | −0.300794 | − | 0.953689i | \(-0.597252\pi\) |
0.675522 | + | 0.737340i | \(0.263918\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4990 | + | 25.1130i | 0.499966 | + | 0.865967i | ||||
\(842\) | −4.49018 | + | 7.77722i | −0.154742 | + | 0.268021i | ||||
\(843\) | 13.5837 | + | 7.84257i | 0.467848 | + | 0.270112i | ||||
\(844\) | 16.1123 | 0.554609 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.29560 | −0.250828 | ||||||||
\(847\) | 7.43379 | + | 4.29190i | 0.255428 | + | 0.147471i | ||||
\(848\) | −1.22307 | + | 2.11841i | −0.0420002 | + | 0.0727465i | ||||
\(849\) | −4.04370 | − | 7.00390i | −0.138780 | − | 0.240373i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −66.8220 | + | 38.5797i | −2.29063 | + | 1.32250i | ||||
\(852\) | −6.53035 | + | 3.77030i | −0.223726 | + | 0.129168i | ||||
\(853\) | 54.5472i | 1.86766i | 0.357718 | + | 0.933830i | \(0.383555\pi\) | ||||
−0.357718 | + | 0.933830i | \(0.616445\pi\) | |||||||
\(854\) | −2.16680 | − | 3.75300i | −0.0741463 | − | 0.128425i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.24559 | − | 5.33795i | −0.316008 | − | 0.182447i | ||||
\(857\) | 16.1596 | 0.552000 | 0.276000 | − | 0.961158i | \(-0.410991\pi\) | ||||
0.276000 | + | 0.961158i | \(0.410991\pi\) | |||||||
\(858\) | 0.616387 | + | 8.65049i | 0.0210431 | + | 0.295323i | ||||
\(859\) | −8.02338 | −0.273754 | −0.136877 | − | 0.990588i | \(-0.543707\pi\) | ||||
−0.136877 | + | 0.990588i | \(0.543707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.200249 | + | 0.346841i | −0.00682447 | + | 0.0118203i | ||||
\(862\) | 4.13435 | + | 7.16090i | 0.140816 | + | 0.243901i | ||||
\(863\) | 28.2909i | 0.963033i | 0.876437 | + | 0.481517i | \(0.159914\pi\) | ||||
−0.876437 | + | 0.481517i | \(0.840086\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 19.8407i | − | 0.674214i | ||||||
\(867\) | −8.47040 | − | 14.6712i | −0.287670 | − | 0.498259i | ||||
\(868\) | −3.49355 | + | 6.05101i | −0.118579 | + | 0.205385i | ||||
\(869\) | −14.1586 | − | 8.17449i | −0.480298 | − | 0.277300i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.95427 | + | 6.07752i | −0.100102 | + | 0.205929i | ||||
\(872\) | 9.50683 | 0.321942 | ||||||||
\(873\) | 14.3006 | + | 8.25647i | 0.484003 | + | 0.279439i | ||||
\(874\) | 19.0513 | − | 32.9979i | 0.644421 | − | 1.11617i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.70370i | − | 0.0575627i | ||||||
\(877\) | −19.5775 | + | 11.3031i | −0.661085 | + | 0.381678i | −0.792690 | − | 0.609625i | \(-0.791320\pi\) |
0.131605 | + | 0.991302i | \(0.457987\pi\) | |||||||
\(878\) | 25.0134 | − | 14.4415i | 0.844161 | − | 0.487377i | ||||
\(879\) | 1.93438i | 0.0652451i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1679 | − | 38.3959i | 0.746854 | − | 1.29359i | −0.202470 | − | 0.979289i | \(-0.564897\pi\) |
0.949324 | − | 0.314301i | \(-0.101770\pi\) | |||||||
\(882\) | 3.71548 | + | 2.14514i | 0.125107 | + | 0.0722305i | ||||
\(883\) | 3.93200 | 0.132322 | 0.0661612 | − | 0.997809i | \(-0.478925\pi\) | ||||
0.0661612 | + | 0.997809i | \(0.478925\pi\) | |||||||
\(884\) | −0.788948 | − | 0.383506i | −0.0265352 | − | 0.0128987i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.99684 | + | 2.88493i | 0.167872 | + | 0.0969211i | ||||
\(887\) | −14.5713 | + | 25.2382i | −0.489256 | + | 0.847416i | −0.999924 | − | 0.0123622i | \(-0.996065\pi\) |
0.510668 | + | 0.859778i | \(0.329398\pi\) | |||||||
\(888\) | 4.47415 | + | 7.74945i | 0.150142 | + | 0.260054i | ||||
\(889\) | 28.5554i | 0.957717i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.08305 | + | 1.20265i | −0.0697847 | + | 0.0402902i | ||||
\(892\) | 11.1177i | 0.372249i | ||||||||
\(893\) | 16.1190 | + | 27.9189i | 0.539401 | + | 0.934269i | ||||
\(894\) | 5.55193 | − | 9.61623i | 0.185684 | − | 0.321615i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.64613 | 0.0549932 | ||||||||
\(897\) | −25.7518 | + | 17.4193i | −0.859827 | + | 0.581615i | ||||
\(898\) | 39.1483 | 1.30639 | ||||||||
\(899\) | 0.162941 | + | 0.0940738i | 0.00543437 | + | 0.00313754i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.297569 | + | 0.515404i | 0.00991344 | + | 0.0171706i | ||||
\(902\) | 0.585202i | 0.0194851i | ||||||||
\(903\) | −9.59244 | + | 5.53820i | −0.319216 | + | 0.184300i | ||||
\(904\) | −3.11433 | + | 1.79806i | −0.103581 | + | 0.0598026i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.437332 | + | 0.757480i | 0.0145294 | + | 0.0251656i | ||||
\(907\) | −18.0592 | + | 31.2795i | −0.599647 | + | 1.03862i | 0.393226 | + | 0.919442i | \(0.371359\pi\) |
−0.992873 | + | 0.119177i | \(0.961974\pi\) | |||||||
\(908\) | −19.1217 | − | 11.0399i | −0.634577 | − | 0.366373i | ||||
\(909\) | −11.3355 | −0.375976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.1738 | −0.535863 | −0.267931 | − | 0.963438i | \(-0.586340\pi\) | ||||
−0.267931 | + | 0.963438i | \(0.586340\pi\) | |||||||
\(912\) | −3.82681 | − | 2.20941i | −0.126718 | − | 0.0731609i | ||||
\(913\) | −21.0447 | + | 36.4505i | −0.696478 | + | 1.20634i | ||||
\(914\) | −12.2403 | − | 21.2008i | −0.404872 | − | 0.701259i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.95443 | − | 5.16984i | 0.295863 | − | 0.170816i | ||||
\(917\) | −20.1940 | + | 11.6590i | −0.666865 | + | 0.385014i | ||||
\(918\) | − | 0.243297i | − | 0.00803001i | ||||||
\(919\) | 1.12534 | + | 1.94914i | 0.0371214 | + | 0.0642962i | 0.883989 | − | 0.467507i | \(-0.154848\pi\) |
−0.846868 | + | 0.531803i | \(0.821514\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.7719 | − | 6.21918i | −0.354947 | − | 0.204929i | ||||
\(922\) | 3.49785 | 0.115196 | ||||||||
\(923\) | −15.2331 | − | 22.5198i | −0.501404 | − | 0.741248i | ||||
\(924\) | −3.95942 | −0.130255 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.15317 | − | 15.8537i | 0.300792 | − | 0.520987i | ||||
\(927\) | −2.99084 | − | 5.18029i | −0.0982321 | − | 0.170143i | ||||
\(928\) | − | 0.0443266i | − | 0.00145509i | ||||||
\(929\) | −23.2193 | + | 13.4057i | −0.761801 | + | 0.439826i | −0.829942 | − | 0.557850i | \(-0.811626\pi\) |
0.0681412 | + | 0.997676i | \(0.478293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 18.9579i | − | 0.621321i | ||||||
\(932\) | 10.9464 | + | 18.9597i | 0.358561 | + | 0.621046i | ||||
\(933\) | −9.18502 | + | 15.9089i | −0.300704 | + | 0.520835i | ||||
\(934\) | −5.59469 | − | 3.23010i | −0.183064 | − | 0.105692i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.02015 | + | 2.98647i | 0.0660305 | + | 0.0976159i | ||||
\(937\) | 44.1333 | 1.44177 | 0.720887 | − | 0.693053i | \(-0.243735\pi\) | ||||
0.720887 | + | 0.693053i | \(0.243735\pi\) | |||||||
\(938\) | −2.67183 | − | 1.54258i | −0.0872383 | − | 0.0503671i | ||||
\(939\) | 15.9722 | − | 27.6647i | 0.521234 | − | 0.902804i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.3857i | 0.925348i | 0.886528 | + | 0.462674i | \(0.153110\pi\) | ||||
−0.886528 | + | 0.462674i | \(0.846890\pi\) | |||||||
\(942\) | 13.4307 | − | 7.75425i | 0.437597 | − | 0.252647i | ||||
\(943\) | −1.81684 | + | 1.04895i | −0.0591645 | + | 0.0341586i | ||||
\(944\) | 9.64947i | 0.314064i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.09234 | + | 14.0163i | −0.263105 | + | 0.455710i | ||||
\(947\) | −42.7256 | − | 24.6676i | −1.38839 | − | 0.801590i | −0.395260 | − | 0.918569i | \(-0.629346\pi\) |
−0.993134 | + | 0.116979i | \(0.962679\pi\) | |||||||
\(948\) | −6.79707 | −0.220759 | ||||||||
\(949\) | 6.12724 | − | 0.436594i | 0.198899 | − | 0.0141724i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2325 | − | 11.6812i | −0.656083 | − | 0.378790i | ||||
\(952\) | 0.200249 | − | 0.346841i | 0.00649011 | − | 0.0112412i | ||||
\(953\) | 5.55933 | + | 9.62904i | 0.180084 | + | 0.311915i | 0.941909 | − | 0.335868i | \(-0.109030\pi\) |
−0.761825 | + | 0.647783i | \(0.775696\pi\) | |||||||
\(954\) | − | 2.44613i | − | 0.0791964i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.7341 | + | 13.1255i | −0.735272 | + | 0.424510i | ||||
\(957\) | 0.106619i | 0.00344649i | ||||||||
\(958\) | −15.3564 | − | 26.5980i | −0.496142 | − | 0.859343i | ||||
\(959\) | 6.03648 | − | 10.4555i | 0.194928 | − | 0.337626i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.9836 | 0.418825 | ||||||||
\(962\) | −26.7238 | + | 18.0769i | −0.861610 | + | 0.582821i | ||||
\(963\) | 10.6759 | 0.344026 | ||||||||
\(964\) | 22.5952 | + | 13.0454i | 0.727744 | + | 0.420163i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.09712 | − | 12.2926i | −0.228346 | − | 0.395507i | ||||
\(967\) | − | 55.3514i | − | 1.77998i | −0.455980 | − | 0.889990i | \(-0.650711\pi\) | ||
0.455980 | − | 0.889990i | \(-0.349289\pi\) | |||||||
\(968\) | 4.51593 | − | 2.60727i | 0.145148 | − | 0.0838010i | ||||
\(969\) | −0.931052 | + | 0.537543i | −0.0299097 | + | 0.0172684i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.8248 | − | 46.4619i | −0.860848 | − | 1.49103i | −0.871112 | − | 0.491085i | \(-0.836601\pi\) |
0.0102641 | − | 0.999947i | \(-0.496733\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 20.2486 | + | 11.6905i | 0.649141 | + | 0.374782i | ||||
\(974\) | −12.4667 | −0.399459 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.63260 | −0.0842676 | ||||||||
\(977\) | −10.7978 | − | 6.23411i | −0.345452 | − | 0.199447i | 0.317228 | − | 0.948349i | \(-0.397248\pi\) |
−0.662680 | + | 0.748902i | \(0.730581\pi\) | |||||||
\(978\) | −10.9464 | + | 18.9597i | −0.350027 | + | 0.606265i | ||||
\(979\) | 12.0785 | + | 20.9206i | 0.386031 | + | 0.668625i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.23316 | + | 4.75342i | −0.262865 | + | 0.151765i | ||||
\(982\) | 2.23642 | − | 1.29120i | 0.0713671 | − | 0.0412038i | ||||
\(983\) | − | 19.1972i | − | 0.612296i | −0.951984 | − | 0.306148i | \(-0.900960\pi\) | ||
0.951984 | − | 0.306148i | \(-0.0990403\pi\) | |||||||
\(984\) | 0.121649 | + | 0.210702i | 0.00387802 | + | 0.00671692i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.00933969 | − | 0.00539227i | −0.000297436 | − | 0.000171725i | ||||
\(987\) | 12.0095 | 0.382266 | ||||||||
\(988\) | 6.96533 | − | 14.3291i | 0.221597 | − | 0.455868i | ||||
\(989\) | −58.0209 | −1.84496 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.4152 | + | 47.4845i | −0.870872 | + | 1.50840i | −0.00977694 | + | 0.999952i | \(0.503112\pi\) |
−0.861096 | + | 0.508443i | \(0.830221\pi\) | |||||||
\(992\) | 2.12229 | + | 3.67591i | 0.0673827 | + | 0.116710i | ||||
\(993\) | 21.4634i | 0.681120i | ||||||||
\(994\) | 10.7498 | − | 6.20639i | 0.340962 | − | 0.196855i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.4986i | 0.554466i | ||||||||
\(997\) | 20.4513 | + | 35.4227i | 0.647700 | + | 1.12185i | 0.983671 | + | 0.179977i | \(0.0576022\pi\) |
−0.335971 | + | 0.941872i | \(0.609064\pi\) | |||||||
\(998\) | −10.1222 | + | 17.5321i | −0.320412 | + | 0.554969i | ||||
\(999\) | −7.74945 | − | 4.47415i | −0.245182 | − | 0.141556i |
(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 | 1950.2.bc.j.901.5 | 12 | ||
5.2 | odd | 4 | 390.2.x.a.199.1 | yes | 12 | ||
5.3 | odd | 4 | 390.2.x.b.199.6 | yes | 12 | ||
5.4 | even | 2 | 1950.2.bc.i.901.2 | 12 | |||
13.10 | even | 6 | inner | 1950.2.bc.j.751.5 | 12 | ||
15.2 | even | 4 | 1170.2.bj.d.199.6 | 12 | |||
15.8 | even | 4 | 1170.2.bj.c.199.1 | 12 | |||
65.23 | odd | 12 | 390.2.x.a.49.1 | ✓ | 12 | ||
65.49 | even | 6 | 1950.2.bc.i.751.2 | 12 | |||
65.62 | odd | 12 | 390.2.x.b.49.6 | yes | 12 | ||
195.23 | even | 12 | 1170.2.bj.d.829.6 | 12 | |||
195.62 | even | 12 | 1170.2.bj.c.829.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.x.a.49.1 | ✓ | 12 | 65.23 | odd | 12 | ||
390.2.x.a.199.1 | yes | 12 | 5.2 | odd | 4 | ||
390.2.x.b.49.6 | yes | 12 | 65.62 | odd | 12 | ||
390.2.x.b.199.6 | yes | 12 | 5.3 | odd | 4 | ||
1170.2.bj.c.199.1 | 12 | 15.8 | even | 4 | |||
1170.2.bj.c.829.1 | 12 | 195.62 | even | 12 | |||
1170.2.bj.d.199.6 | 12 | 15.2 | even | 4 | |||
1170.2.bj.d.829.6 | 12 | 195.23 | even | 12 | |||
1950.2.bc.i.751.2 | 12 | 65.49 | even | 6 | |||
1950.2.bc.i.901.2 | 12 | 5.4 | even | 2 | |||
1950.2.bc.j.751.5 | 12 | 13.10 | even | 6 | inner | ||
1950.2.bc.j.901.5 | 12 | 1.1 | even | 1 | trivial |