Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.3 | ||
Root | \(-0.114009 - 0.197470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.373 |
Dual form | 546.2.k.e.445.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.114009 | − | 0.197470i | 0.0509865 | − | 0.0883113i | −0.839406 | − | 0.543505i | \(-0.817097\pi\) |
0.890392 | + | 0.455194i | \(0.150430\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 0.848534 | − | 2.50599i | 0.320716 | − | 0.947176i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.228019 | 0.0721058 | ||||||||
\(11\) | 3.41122 | 1.02852 | 0.514260 | − | 0.857634i | \(-0.328067\pi\) | ||||
0.514260 | + | 0.857634i | \(0.328067\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −1.62906 | + | 3.21655i | −0.451819 | + | 0.892110i | ||||
\(14\) | 2.59452 | − | 0.518144i | 0.693414 | − | 0.138480i | ||||
\(15\) | −0.114009 | + | 0.197470i | −0.0294371 | + | 0.0509865i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.70561 | − | 4.68625i | 0.656206 | − | 1.13658i | −0.325384 | − | 0.945582i | \(-0.605493\pi\) |
0.981590 | − | 0.191001i | \(-0.0611733\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 6.34214 | 1.45499 | 0.727494 | − | 0.686115i | \(-0.240685\pi\) | ||||
0.727494 | + | 0.686115i | \(0.240685\pi\) | |||||||
\(20\) | 0.114009 | + | 0.197470i | 0.0254933 | + | 0.0441556i | ||||
\(21\) | −0.848534 | + | 2.50599i | −0.185165 | + | 0.546852i | ||||
\(22\) | 1.70561 | + | 2.95420i | 0.363637 | + | 0.629838i | ||||
\(23\) | 0.959623 | + | 1.66212i | 0.200095 | + | 0.346575i | 0.948559 | − | 0.316601i | \(-0.102542\pi\) |
−0.748464 | + | 0.663176i | \(0.769208\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 2.47400 | + | 4.28510i | 0.494801 | + | 0.857020i | ||||
\(26\) | −3.60014 | + | 0.197470i | −0.706045 | + | 0.0387270i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.74599 | + | 1.98785i | 0.329960 | + | 0.375668i | ||||
\(29\) | 0.851453 | − | 1.47476i | 0.158111 | − | 0.273856i | −0.776077 | − | 0.630639i | \(-0.782793\pi\) |
0.934187 | + | 0.356783i | \(0.116126\pi\) | |||||||
\(30\) | −0.228019 | −0.0416303 | ||||||||
\(31\) | −1.78052 | − | 3.08395i | −0.319791 | − | 0.553895i | 0.660653 | − | 0.750691i | \(-0.270279\pi\) |
−0.980444 | + | 0.196797i | \(0.936946\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.41122 | −0.593817 | ||||||||
\(34\) | 5.41122 | 0.928016 | ||||||||
\(35\) | −0.398117 | − | 0.453266i | −0.0672941 | − | 0.0766160i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 2.09160 | + | 3.62276i | 0.343857 | + | 0.595577i | 0.985145 | − | 0.171722i | \(-0.0549332\pi\) |
−0.641289 | + | 0.767300i | \(0.721600\pi\) | |||||||
\(38\) | 3.17107 | + | 5.49246i | 0.514416 | + | 0.890994i | ||||
\(39\) | 1.62906 | − | 3.21655i | 0.260858 | − | 0.515060i | ||||
\(40\) | −0.114009 | + | 0.197470i | −0.0180265 | + | 0.0312227i | ||||
\(41\) | 1.59160 | − | 2.75673i | 0.248566 | − | 0.430529i | −0.714562 | − | 0.699572i | \(-0.753374\pi\) |
0.963128 | + | 0.269043i | \(0.0867074\pi\) | |||||||
\(42\) | −2.59452 | + | 0.518144i | −0.400343 | + | 0.0799513i | ||||
\(43\) | 5.17961 | + | 8.97135i | 0.789883 | + | 1.36812i | 0.926038 | + | 0.377431i | \(0.123192\pi\) |
−0.136154 | + | 0.990688i | \(0.543474\pi\) | |||||||
\(44\) | −1.70561 | + | 2.95420i | −0.257130 | + | 0.445362i | ||||
\(45\) | 0.114009 | − | 0.197470i | 0.0169955 | − | 0.0294371i | ||||
\(46\) | −0.959623 | + | 1.66212i | −0.141489 | + | 0.245066i | ||||
\(47\) | −5.57211 | + | 9.65117i | −0.812775 | + | 1.40777i | 0.0981388 | + | 0.995173i | \(0.468711\pi\) |
−0.910914 | + | 0.412596i | \(0.864622\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −5.55998 | − | 4.25284i | −0.794283 | − | 0.607548i | ||||
\(50\) | −2.47400 | + | 4.28510i | −0.349877 | + | 0.606005i | ||||
\(51\) | −2.70561 | + | 4.68625i | −0.378861 | + | 0.656206i | ||||
\(52\) | −1.97108 | − | 3.01908i | −0.273340 | − | 0.418671i | ||||
\(53\) | −3.31400 | − | 5.74001i | −0.455212 | − | 0.788451i | 0.543488 | − | 0.839417i | \(-0.317103\pi\) |
−0.998700 | + | 0.0509659i | \(0.983770\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0.388911 | − | 0.673613i | 0.0524407 | − | 0.0908299i | ||||
\(56\) | −0.848534 | + | 2.50599i | −0.113390 | + | 0.334877i | ||||
\(57\) | −6.34214 | −0.840037 | ||||||||
\(58\) | 1.70291 | 0.223603 | ||||||||
\(59\) | 7.38522 | − | 12.7916i | 0.961474 | − | 1.66532i | 0.242669 | − | 0.970109i | \(-0.421977\pi\) |
0.718804 | − | 0.695212i | \(-0.244690\pi\) | |||||||
\(60\) | −0.114009 | − | 0.197470i | −0.0147185 | − | 0.0254933i | ||||
\(61\) | −6.71999 | −0.860406 | −0.430203 | − | 0.902732i | \(-0.641558\pi\) | ||||
−0.430203 | + | 0.902732i | \(0.641558\pi\) | |||||||
\(62\) | 1.78052 | − | 3.08395i | 0.226127 | − | 0.391663i | ||||
\(63\) | 0.848534 | − | 2.50599i | 0.106905 | − | 0.315725i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.449444 | + | 0.688406i | 0.0557467 | + | 0.0853863i | ||||
\(66\) | −1.70561 | − | 2.95420i | −0.209946 | − | 0.363637i | ||||
\(67\) | 11.1613 | 1.36357 | 0.681785 | − | 0.731553i | \(-0.261204\pi\) | ||||
0.681785 | + | 0.731553i | \(0.261204\pi\) | |||||||
\(68\) | 2.70561 | + | 4.68625i | 0.328103 | + | 0.568291i | ||||
\(69\) | −0.959623 | − | 1.66212i | −0.115525 | − | 0.200095i | ||||
\(70\) | 0.193482 | − | 0.571413i | 0.0231255 | − | 0.0682969i | ||||
\(71\) | −0.0390952 | − | 0.0677149i | −0.00463975 | − | 0.00803628i | 0.863696 | − | 0.504013i | \(-0.168144\pi\) |
−0.868336 | + | 0.495976i | \(0.834810\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.31721 | − | 10.9417i | −0.739373 | − | 1.28063i | −0.952778 | − | 0.303668i | \(-0.901789\pi\) |
0.213404 | − | 0.976964i | \(-0.431545\pi\) | |||||||
\(74\) | −2.09160 | + | 3.62276i | −0.243143 | + | 0.421137i | ||||
\(75\) | −2.47400 | − | 4.28510i | −0.285673 | − | 0.494801i | ||||
\(76\) | −3.17107 | + | 5.49246i | −0.363747 | + | 0.630028i | ||||
\(77\) | 2.89453 | − | 8.54848i | 0.329862 | − | 0.974189i | ||||
\(78\) | 3.60014 | − | 0.197470i | 0.407636 | − | 0.0223591i | ||||
\(79\) | 0.811077 | − | 1.40483i | 0.0912532 | − | 0.158055i | −0.816785 | − | 0.576941i | \(-0.804246\pi\) |
0.908039 | + | 0.418886i | \(0.137579\pi\) | |||||||
\(80\) | −0.228019 | −0.0254933 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.18320 | 0.351525 | ||||||||
\(83\) | −1.70291 | −0.186918 | −0.0934592 | − | 0.995623i | \(-0.529792\pi\) | ||||
−0.0934592 | + | 0.995623i | \(0.529792\pi\) | |||||||
\(84\) | −1.74599 | − | 1.98785i | −0.190503 | − | 0.216892i | ||||
\(85\) | −0.616929 | − | 1.06855i | −0.0669154 | − | 0.115901i | ||||
\(86\) | −5.17961 | + | 8.97135i | −0.558532 | + | 0.967406i | ||||
\(87\) | −0.851453 | + | 1.47476i | −0.0912854 | + | 0.158111i | ||||
\(88\) | −3.41122 | −0.363637 | ||||||||
\(89\) | −8.77285 | − | 15.1950i | −0.929920 | − | 1.61067i | −0.783451 | − | 0.621454i | \(-0.786542\pi\) |
−0.146469 | − | 0.989215i | \(-0.546791\pi\) | |||||||
\(90\) | 0.228019 | 0.0240353 | ||||||||
\(91\) | 6.67833 | + | 6.81175i | 0.700079 | + | 0.714065i | ||||
\(92\) | −1.91925 | −0.200095 | ||||||||
\(93\) | 1.78052 | + | 3.08395i | 0.184632 | + | 0.319791i | ||||
\(94\) | −11.1442 | −1.14944 | ||||||||
\(95\) | 0.723063 | − | 1.25238i | 0.0741847 | − | 0.128492i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 6.82663 | + | 11.8241i | 0.693140 | + | 1.20055i | 0.970804 | + | 0.239875i | \(0.0771064\pi\) |
−0.277664 | + | 0.960678i | \(0.589560\pi\) | |||||||
\(98\) | 0.903072 | − | 6.94150i | 0.0912241 | − | 0.701198i | ||||
\(99\) | 3.41122 | 0.342840 | ||||||||
\(100\) | −4.94801 | −0.494801 | ||||||||
\(101\) | −16.5165 | −1.64345 | −0.821724 | − | 0.569885i | \(-0.806988\pi\) | ||||
−0.821724 | + | 0.569885i | \(0.806988\pi\) | |||||||
\(102\) | −5.41122 | −0.535790 | ||||||||
\(103\) | −3.17961 | + | 5.50725i | −0.313296 | + | 0.542645i | −0.979074 | − | 0.203505i | \(-0.934767\pi\) |
0.665777 | + | 0.746150i | \(0.268100\pi\) | |||||||
\(104\) | 1.62906 | − | 3.21655i | 0.159742 | − | 0.315408i | ||||
\(105\) | 0.398117 | + | 0.453266i | 0.0388523 | + | 0.0442343i | ||||
\(106\) | 3.31400 | − | 5.74001i | 0.321884 | − | 0.557519i | ||||
\(107\) | −3.27362 | − | 5.67008i | −0.316473 | − | 0.548147i | 0.663277 | − | 0.748374i | \(-0.269165\pi\) |
−0.979749 | + | 0.200227i | \(0.935832\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 0.797093 | + | 1.38061i | 0.0763477 | + | 0.132238i | 0.901672 | − | 0.432422i | \(-0.142341\pi\) |
−0.825324 | + | 0.564660i | \(0.809007\pi\) | |||||||
\(110\) | 0.777821 | 0.0741623 | ||||||||
\(111\) | −2.09160 | − | 3.62276i | −0.198526 | − | 0.343857i | ||||
\(112\) | −2.59452 | + | 0.518144i | −0.245159 | + | 0.0489600i | ||||
\(113\) | −4.12255 | − | 7.14047i | −0.387817 | − | 0.671719i | 0.604339 | − | 0.796728i | \(-0.293437\pi\) |
−0.992156 | + | 0.125009i | \(0.960104\pi\) | |||||||
\(114\) | −3.17107 | − | 5.49246i | −0.296998 | − | 0.514416i | ||||
\(115\) | 0.437624 | 0.0408086 | ||||||||
\(116\) | 0.851453 | + | 1.47476i | 0.0790555 | + | 0.136928i | ||||
\(117\) | −1.62906 | + | 3.21655i | −0.150606 | + | 0.297370i | ||||
\(118\) | 14.7704 | 1.35973 | ||||||||
\(119\) | −9.44790 | − | 10.7567i | −0.866088 | − | 0.986062i | ||||
\(120\) | 0.114009 | − | 0.197470i | 0.0104076 | − | 0.0180265i | ||||
\(121\) | 0.636396 | 0.0578542 | ||||||||
\(122\) | −3.35999 | − | 5.81968i | −0.304200 | − | 0.526889i | ||||
\(123\) | −1.59160 | + | 2.75673i | −0.143510 | + | 0.248566i | ||||
\(124\) | 3.56104 | 0.319791 | ||||||||
\(125\) | 2.26833 | 0.202886 | ||||||||
\(126\) | 2.59452 | − | 0.518144i | 0.231138 | − | 0.0461599i | ||||
\(127\) | −6.40560 | + | 11.0948i | −0.568405 | + | 0.984506i | 0.428319 | + | 0.903627i | \(0.359106\pi\) |
−0.996724 | + | 0.0808783i | \(0.974227\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −5.17961 | − | 8.97135i | −0.456039 | − | 0.789883i | ||||
\(130\) | −0.371455 | + | 0.733433i | −0.0325788 | + | 0.0643263i | ||||
\(131\) | −1.75964 | + | 3.04778i | −0.153740 | + | 0.266286i | −0.932600 | − | 0.360913i | \(-0.882465\pi\) |
0.778859 | + | 0.627199i | \(0.215799\pi\) | |||||||
\(132\) | 1.70561 | − | 2.95420i | 0.148454 | − | 0.257130i | ||||
\(133\) | 5.38152 | − | 15.8934i | 0.466637 | − | 1.37813i | ||||
\(134\) | 5.58065 | + | 9.66597i | 0.482095 | + | 0.835012i | ||||
\(135\) | −0.114009 | + | 0.197470i | −0.00981236 | + | 0.0169955i | ||||
\(136\) | −2.70561 | + | 4.68625i | −0.232004 | + | 0.401843i | ||||
\(137\) | −8.84776 | + | 15.3248i | −0.755915 | + | 1.30928i | 0.189003 | + | 0.981977i | \(0.439475\pi\) |
−0.944918 | + | 0.327307i | \(0.893859\pi\) | |||||||
\(138\) | 0.959623 | − | 1.66212i | 0.0816885 | − | 0.141489i | ||||
\(139\) | 3.98321 | + | 6.89912i | 0.337851 | + | 0.585176i | 0.984028 | − | 0.178012i | \(-0.0569665\pi\) |
−0.646177 | + | 0.763188i | \(0.723633\pi\) | |||||||
\(140\) | 0.591599 | − | 0.118146i | 0.0499992 | − | 0.00998520i | ||||
\(141\) | 5.57211 | − | 9.65117i | 0.469256 | − | 0.812775i | ||||
\(142\) | 0.0390952 | − | 0.0677149i | 0.00328080 | − | 0.00568251i | ||||
\(143\) | −5.55706 | + | 10.9723i | −0.464705 | + | 0.917553i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −0.194147 | − | 0.336273i | −0.0161231 | − | 0.0279260i | ||||
\(146\) | 6.31721 | − | 10.9417i | 0.522816 | − | 0.905544i | ||||
\(147\) | 5.55998 | + | 4.25284i | 0.458580 | + | 0.350768i | ||||
\(148\) | −4.18320 | −0.343857 | ||||||||
\(149\) | 2.69358 | 0.220667 | 0.110333 | − | 0.993895i | \(-0.464808\pi\) | ||||
0.110333 | + | 0.993895i | \(0.464808\pi\) | |||||||
\(150\) | 2.47400 | − | 4.28510i | 0.202002 | − | 0.349877i | ||||
\(151\) | 6.56432 | + | 11.3697i | 0.534197 | + | 0.925256i | 0.999202 | + | 0.0399480i | \(0.0127192\pi\) |
−0.465005 | + | 0.885308i | \(0.653947\pi\) | |||||||
\(152\) | −6.34214 | −0.514416 | ||||||||
\(153\) | 2.70561 | − | 4.68625i | 0.218735 | − | 0.378861i | ||||
\(154\) | 8.85046 | − | 1.76750i | 0.713191 | − | 0.142429i | ||||
\(155\) | −0.811985 | −0.0652202 | ||||||||
\(156\) | 1.97108 | + | 3.01908i | 0.157813 | + | 0.241720i | ||||
\(157\) | −1.59071 | − | 2.75520i | −0.126953 | − | 0.219889i | 0.795542 | − | 0.605899i | \(-0.207186\pi\) |
−0.922495 | + | 0.386010i | \(0.873853\pi\) | |||||||
\(158\) | 1.62215 | 0.129052 | ||||||||
\(159\) | 3.31400 | + | 5.74001i | 0.262817 | + | 0.455212i | ||||
\(160\) | −0.114009 | − | 0.197470i | −0.00901323 | − | 0.0156114i | ||||
\(161\) | 4.97952 | − | 0.994446i | 0.392441 | − | 0.0783733i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −16.2940 | −1.27625 | −0.638124 | − | 0.769934i | \(-0.720289\pi\) | ||||
−0.638124 | + | 0.769934i | \(0.720289\pi\) | |||||||
\(164\) | 1.59160 | + | 2.75673i | 0.124283 | + | 0.215264i | ||||
\(165\) | −0.388911 | + | 0.673613i | −0.0302766 | + | 0.0524407i | ||||
\(166\) | −0.851453 | − | 1.47476i | −0.0660856 | − | 0.114464i | ||||
\(167\) | 0.826739 | − | 1.43195i | 0.0639750 | − | 0.110808i | −0.832264 | − | 0.554380i | \(-0.812956\pi\) |
0.896239 | + | 0.443572i | \(0.146289\pi\) | |||||||
\(168\) | 0.848534 | − | 2.50599i | 0.0654658 | − | 0.193341i | ||||
\(169\) | −7.69235 | − | 10.4799i | −0.591720 | − | 0.806144i | ||||
\(170\) | 0.616929 | − | 1.06855i | 0.0473163 | − | 0.0819543i | ||||
\(171\) | 6.34214 | 0.484996 | ||||||||
\(172\) | −10.3592 | −0.789883 | ||||||||
\(173\) | 14.0420 | 1.06759 | 0.533797 | − | 0.845613i | \(-0.320765\pi\) | ||||
0.533797 | + | 0.845613i | \(0.320765\pi\) | |||||||
\(174\) | −1.70291 | −0.129097 | ||||||||
\(175\) | 12.8377 | − | 2.56378i | 0.970439 | − | 0.193804i | ||||
\(176\) | −1.70561 | − | 2.95420i | −0.128565 | − | 0.222681i | ||||
\(177\) | −7.38522 | + | 12.7916i | −0.555107 | + | 0.961474i | ||||
\(178\) | 8.77285 | − | 15.1950i | 0.657553 | − | 1.13891i | ||||
\(179\) | −9.33325 | −0.697600 | −0.348800 | − | 0.937197i | \(-0.613411\pi\) | ||||
−0.348800 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(180\) | 0.114009 | + | 0.197470i | 0.00849776 | + | 0.0147185i | ||||
\(181\) | 1.13838 | 0.0846148 | 0.0423074 | − | 0.999105i | \(-0.486529\pi\) | ||||
0.0423074 | + | 0.999105i | \(0.486529\pi\) | |||||||
\(182\) | −2.55998 | + | 9.18948i | −0.189758 | + | 0.681169i | ||||
\(183\) | 6.71999 | 0.496756 | ||||||||
\(184\) | −0.959623 | − | 1.66212i | −0.0707444 | − | 0.122533i | ||||
\(185\) | 0.953847 | 0.0701282 | ||||||||
\(186\) | −1.78052 | + | 3.08395i | −0.130554 | + | 0.226127i | ||||
\(187\) | 9.22941 | − | 15.9858i | 0.674922 | − | 1.16900i | ||||
\(188\) | −5.57211 | − | 9.65117i | −0.406388 | − | 0.703884i | ||||
\(189\) | −0.848534 | + | 2.50599i | −0.0617217 | + | 0.182284i | ||||
\(190\) | 1.44613 | 0.104913 | ||||||||
\(191\) | 18.0851 | 1.30859 | 0.654294 | − | 0.756240i | \(-0.272966\pi\) | ||||
0.654294 | + | 0.756240i | \(0.272966\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −5.82592 | −0.419359 | −0.209679 | − | 0.977770i | \(-0.567242\pi\) | ||||
−0.209679 | + | 0.977770i | \(0.567242\pi\) | |||||||
\(194\) | −6.82663 | + | 11.8241i | −0.490124 | + | 0.848919i | ||||
\(195\) | −0.449444 | − | 0.688406i | −0.0321854 | − | 0.0492978i | ||||
\(196\) | 6.46305 | − | 2.68867i | 0.461647 | − | 0.192048i | ||||
\(197\) | −10.3527 | + | 17.9315i | −0.737602 | + | 1.27756i | 0.215970 | + | 0.976400i | \(0.430709\pi\) |
−0.953572 | + | 0.301165i | \(0.902625\pi\) | |||||||
\(198\) | 1.70561 | + | 2.95420i | 0.121212 | + | 0.209946i | ||||
\(199\) | 8.19922 | − | 14.2015i | 0.581227 | − | 1.00671i | −0.414107 | − | 0.910228i | \(-0.635906\pi\) |
0.995334 | − | 0.0964867i | \(-0.0307605\pi\) | |||||||
\(200\) | −2.47400 | − | 4.28510i | −0.174938 | − | 0.303002i | ||||
\(201\) | −11.1613 | −0.787257 | ||||||||
\(202\) | −8.25823 | − | 14.3037i | −0.581047 | − | 1.00640i | ||||
\(203\) | −2.97325 | − | 3.38512i | −0.208681 | − | 0.237589i | ||||
\(204\) | −2.70561 | − | 4.68625i | −0.189430 | − | 0.328103i | ||||
\(205\) | −0.362914 | − | 0.628586i | −0.0253470 | − | 0.0439023i | ||||
\(206\) | −6.35922 | −0.443068 | ||||||||
\(207\) | 0.959623 | + | 1.66212i | 0.0666984 | + | 0.115525i | ||||
\(208\) | 3.60014 | − | 0.197470i | 0.249625 | − | 0.0136921i | ||||
\(209\) | 21.6344 | 1.49648 | ||||||||
\(210\) | −0.193482 | + | 0.571413i | −0.0133515 | + | 0.0394312i | ||||
\(211\) | 3.74446 | − | 6.48560i | 0.257779 | − | 0.446487i | −0.707867 | − | 0.706345i | \(-0.750343\pi\) |
0.965647 | + | 0.259858i | \(0.0836759\pi\) | |||||||
\(212\) | 6.62799 | 0.455212 | ||||||||
\(213\) | 0.0390952 | + | 0.0677149i | 0.00267876 | + | 0.00463975i | ||||
\(214\) | 3.27362 | − | 5.67008i | 0.223780 | − | 0.387598i | ||||
\(215\) | 2.36210 | 0.161094 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −9.23920 | + | 1.84513i | −0.627198 | + | 0.125256i | ||||
\(218\) | −0.797093 | + | 1.38061i | −0.0539860 | + | 0.0935064i | ||||
\(219\) | 6.31721 | + | 10.9417i | 0.426877 | + | 0.739373i | ||||
\(220\) | 0.388911 | + | 0.673613i | 0.0262203 | + | 0.0454150i | ||||
\(221\) | 10.6660 | + | 16.3369i | 0.717470 | + | 1.09894i | ||||
\(222\) | 2.09160 | − | 3.62276i | 0.140379 | − | 0.243143i | ||||
\(223\) | −8.41325 | + | 14.5722i | −0.563393 | + | 0.975825i | 0.433804 | + | 0.901007i | \(0.357171\pi\) |
−0.997197 | + | 0.0748181i | \(0.976162\pi\) | |||||||
\(224\) | −1.74599 | − | 1.98785i | −0.116659 | − | 0.132819i | ||||
\(225\) | 2.47400 | + | 4.28510i | 0.164934 | + | 0.285673i | ||||
\(226\) | 4.12255 | − | 7.14047i | 0.274228 | − | 0.474977i | ||||
\(227\) | 2.11607 | − | 3.66514i | 0.140449 | − | 0.243264i | −0.787217 | − | 0.616676i | \(-0.788479\pi\) |
0.927666 | + | 0.373412i | \(0.121812\pi\) | |||||||
\(228\) | 3.17107 | − | 5.49246i | 0.210009 | − | 0.363747i | ||||
\(229\) | −6.86498 | + | 11.8905i | −0.453650 | + | 0.785745i | −0.998609 | − | 0.0527171i | \(-0.983212\pi\) |
0.544959 | + | 0.838463i | \(0.316545\pi\) | |||||||
\(230\) | 0.218812 | + | 0.378993i | 0.0144280 | + | 0.0249901i | ||||
\(231\) | −2.89453 | + | 8.54848i | −0.190446 | + | 0.562448i | ||||
\(232\) | −0.851453 | + | 1.47476i | −0.0559007 | + | 0.0968228i | ||||
\(233\) | −3.85349 | + | 6.67444i | −0.252450 | + | 0.437257i | −0.964200 | − | 0.265176i | \(-0.914570\pi\) |
0.711749 | + | 0.702433i | \(0.247903\pi\) | |||||||
\(234\) | −3.60014 | + | 0.197470i | −0.235348 | + | 0.0129090i | ||||
\(235\) | 1.27054 | + | 2.20065i | 0.0828812 | + | 0.143554i | ||||
\(236\) | 7.38522 | + | 12.7916i | 0.480737 | + | 0.832661i | ||||
\(237\) | −0.811077 | + | 1.40483i | −0.0526851 | + | 0.0912532i | ||||
\(238\) | 4.59160 | − | 13.5605i | 0.297629 | − | 0.878994i | ||||
\(239\) | −25.2189 | −1.63128 | −0.815638 | − | 0.578562i | \(-0.803614\pi\) | ||||
−0.815638 | + | 0.578562i | \(0.803614\pi\) | |||||||
\(240\) | 0.228019 | 0.0147185 | ||||||||
\(241\) | −13.9183 | + | 24.1073i | −0.896560 | + | 1.55289i | −0.0646969 | + | 0.997905i | \(0.520608\pi\) |
−0.831863 | + | 0.554982i | \(0.812725\pi\) | |||||||
\(242\) | 0.318198 | + | 0.551135i | 0.0204545 | + | 0.0354283i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.35999 | − | 5.81968i | 0.215102 | − | 0.372567i | ||||
\(245\) | −1.47370 | + | 0.613066i | −0.0941511 | + | 0.0391674i | ||||
\(246\) | −3.18320 | −0.202953 | ||||||||
\(247\) | −10.3317 | + | 20.3998i | −0.657391 | + | 1.29801i | ||||
\(248\) | 1.78052 | + | 3.08395i | 0.113063 | + | 0.195831i | ||||
\(249\) | 1.70291 | 0.107917 | ||||||||
\(250\) | 1.13417 | + | 1.96443i | 0.0717309 | + | 0.124242i | ||||
\(251\) | 2.12395 | + | 3.67878i | 0.134062 | + | 0.232203i | 0.925239 | − | 0.379385i | \(-0.123864\pi\) |
−0.791177 | + | 0.611588i | \(0.790531\pi\) | |||||||
\(252\) | 1.74599 | + | 1.98785i | 0.109987 | + | 0.125223i | ||||
\(253\) | 3.27348 | + | 5.66984i | 0.205802 | + | 0.356460i | ||||
\(254\) | −12.8112 | −0.803846 | ||||||||
\(255\) | 0.616929 | + | 1.06855i | 0.0386336 | + | 0.0669154i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.35836 | − | 12.7450i | −0.459002 | − | 0.795014i | 0.539907 | − | 0.841725i | \(-0.318459\pi\) |
−0.998908 | + | 0.0467106i | \(0.985126\pi\) | |||||||
\(258\) | 5.17961 | − | 8.97135i | 0.322469 | − | 0.558532i | ||||
\(259\) | 10.8534 | − | 2.16750i | 0.674396 | − | 0.134682i | ||||
\(260\) | −0.820899 | + | 0.0450268i | −0.0509100 | + | 0.00279245i | ||||
\(261\) | 0.851453 | − | 1.47476i | 0.0527036 | − | 0.0912854i | ||||
\(262\) | −3.51927 | −0.217421 | ||||||||
\(263\) | 23.4105 | 1.44355 | 0.721777 | − | 0.692125i | \(-0.243325\pi\) | ||||
0.721777 | + | 0.692125i | \(0.243325\pi\) | |||||||
\(264\) | 3.41122 | 0.209946 | ||||||||
\(265\) | −1.51131 | −0.0928388 | ||||||||
\(266\) | 16.4548 | − | 3.28614i | 1.00891 | − | 0.201486i | ||||
\(267\) | 8.77285 | + | 15.1950i | 0.536890 | + | 0.929920i | ||||
\(268\) | −5.58065 | + | 9.66597i | −0.340892 | + | 0.590443i | ||||
\(269\) | 4.67886 | − | 8.10402i | 0.285275 | − | 0.494111i | −0.687401 | − | 0.726278i | \(-0.741248\pi\) |
0.972676 | + | 0.232167i | \(0.0745817\pi\) | |||||||
\(270\) | −0.228019 | −0.0138768 | ||||||||
\(271\) | 7.57375 | + | 13.1181i | 0.460072 | + | 0.796869i | 0.998964 | − | 0.0455064i | \(-0.0144901\pi\) |
−0.538892 | + | 0.842375i | \(0.681157\pi\) | |||||||
\(272\) | −5.41122 | −0.328103 | ||||||||
\(273\) | −6.67833 | − | 6.81175i | −0.404191 | − | 0.412266i | ||||
\(274\) | −17.6955 | −1.06903 | ||||||||
\(275\) | 8.43936 | + | 14.6174i | 0.508913 | + | 0.881463i | ||||
\(276\) | 1.91925 | 0.115525 | ||||||||
\(277\) | 16.4391 | − | 28.4734i | 0.987731 | − | 1.71080i | 0.358622 | − | 0.933483i | \(-0.383247\pi\) |
0.629109 | − | 0.777317i | \(-0.283420\pi\) | |||||||
\(278\) | −3.98321 | + | 6.89912i | −0.238897 | + | 0.413782i | ||||
\(279\) | −1.78052 | − | 3.08395i | −0.106597 | − | 0.184632i | ||||
\(280\) | 0.398117 | + | 0.453266i | 0.0237921 | + | 0.0270878i | ||||
\(281\) | −16.8072 | −1.00263 | −0.501316 | − | 0.865264i | \(-0.667150\pi\) | ||||
−0.501316 | + | 0.865264i | \(0.667150\pi\) | |||||||
\(282\) | 11.1442 | 0.663628 | ||||||||
\(283\) | −12.1600 | −0.722835 | −0.361417 | − | 0.932404i | \(-0.617707\pi\) | ||||
−0.361417 | + | 0.932404i | \(0.617707\pi\) | |||||||
\(284\) | 0.0781905 | 0.00463975 | ||||||||
\(285\) | −0.723063 | + | 1.25238i | −0.0428306 | + | 0.0741847i | ||||
\(286\) | −12.2809 | + | 0.673613i | −0.726182 | + | 0.0398316i | ||||
\(287\) | −5.55782 | − | 6.32771i | −0.328067 | − | 0.373513i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −6.14063 | − | 10.6359i | −0.361214 | − | 0.625640i | ||||
\(290\) | 0.194147 | − | 0.336273i | 0.0114007 | − | 0.0197466i | ||||
\(291\) | −6.82663 | − | 11.8241i | −0.400184 | − | 0.693140i | ||||
\(292\) | 12.6344 | 0.739373 | ||||||||
\(293\) | 13.8954 | + | 24.0675i | 0.811778 | + | 1.40604i | 0.911619 | + | 0.411037i | \(0.134833\pi\) |
−0.0998407 | + | 0.995003i | \(0.531833\pi\) | |||||||
\(294\) | −0.903072 | + | 6.94150i | −0.0526683 | + | 0.404837i | ||||
\(295\) | −1.68397 | − | 2.91672i | −0.0980444 | − | 0.169818i | ||||
\(296\) | −2.09160 | − | 3.62276i | −0.121572 | − | 0.210568i | ||||
\(297\) | −3.41122 | −0.197939 | ||||||||
\(298\) | 1.34679 | + | 2.33271i | 0.0780175 | + | 0.135130i | ||||
\(299\) | −6.90955 | + | 0.378993i | −0.399590 | + | 0.0219178i | ||||
\(300\) | 4.94801 | 0.285673 | ||||||||
\(301\) | 26.8772 | − | 5.36757i | 1.54918 | − | 0.309381i | ||||
\(302\) | −6.56432 | + | 11.3697i | −0.377734 | + | 0.654255i | ||||
\(303\) | 16.5165 | 0.948845 | ||||||||
\(304\) | −3.17107 | − | 5.49246i | −0.181873 | − | 0.315014i | ||||
\(305\) | −0.766142 | + | 1.32700i | −0.0438691 | + | 0.0759836i | ||||
\(306\) | 5.41122 | 0.309339 | ||||||||
\(307\) | −14.6849 | −0.838110 | −0.419055 | − | 0.907961i | \(-0.637639\pi\) | ||||
−0.419055 | + | 0.907961i | \(0.637639\pi\) | |||||||
\(308\) | 5.95593 | + | 6.78098i | 0.339371 | + | 0.386382i | ||||
\(309\) | 3.17961 | − | 5.50725i | 0.180882 | − | 0.313296i | ||||
\(310\) | −0.405992 | − | 0.703199i | −0.0230588 | − | 0.0399390i | ||||
\(311\) | 3.86348 | + | 6.69174i | 0.219078 | + | 0.379453i | 0.954526 | − | 0.298127i | \(-0.0963619\pi\) |
−0.735449 | + | 0.677580i | \(0.763029\pi\) | |||||||
\(312\) | −1.62906 | + | 3.21655i | −0.0922271 | + | 0.182101i | ||||
\(313\) | −10.0982 | + | 17.4906i | −0.570784 | + | 0.988626i | 0.425702 | + | 0.904863i | \(0.360027\pi\) |
−0.996486 | + | 0.0837628i | \(0.973306\pi\) | |||||||
\(314\) | 1.59071 | − | 2.75520i | 0.0897692 | − | 0.155485i | ||||
\(315\) | −0.398117 | − | 0.453266i | −0.0224314 | − | 0.0255387i | ||||
\(316\) | 0.811077 | + | 1.40483i | 0.0456266 | + | 0.0790276i | ||||
\(317\) | 7.36088 | − | 12.7494i | 0.413428 | − | 0.716079i | −0.581834 | − | 0.813308i | \(-0.697665\pi\) |
0.995262 | + | 0.0972291i | \(0.0309980\pi\) | |||||||
\(318\) | −3.31400 | + | 5.74001i | −0.185840 | + | 0.321884i | ||||
\(319\) | 2.90449 | − | 5.03073i | 0.162620 | − | 0.281667i | ||||
\(320\) | 0.114009 | − | 0.197470i | 0.00637332 | − | 0.0110389i | ||||
\(321\) | 3.27362 | + | 5.67008i | 0.182716 | + | 0.316473i | ||||
\(322\) | 3.35098 | + | 3.81517i | 0.186743 | + | 0.212611i | ||||
\(323\) | 17.1594 | − | 29.7209i | 0.954772 | − | 1.65371i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −17.8135 | + | 0.977083i | −0.988116 | + | 0.0541988i | ||||
\(326\) | −8.14702 | − | 14.1111i | −0.451222 | − | 0.781539i | ||||
\(327\) | −0.797093 | − | 1.38061i | −0.0440793 | − | 0.0763477i | ||||
\(328\) | −1.59160 | + | 2.75673i | −0.0878813 | + | 0.152215i | ||||
\(329\) | 19.4576 | + | 22.1530i | 1.07273 | + | 1.22133i | ||||
\(330\) | −0.777821 | −0.0428176 | ||||||||
\(331\) | 4.10872 | 0.225836 | 0.112918 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112918 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(332\) | 0.851453 | − | 1.47476i | 0.0467296 | − | 0.0809380i | ||||
\(333\) | 2.09160 | + | 3.62276i | 0.114619 | + | 0.198526i | ||||
\(334\) | 1.65348 | 0.0904743 | ||||||||
\(335\) | 1.27249 | − | 2.20402i | 0.0695237 | − | 0.120419i | ||||
\(336\) | 2.59452 | − | 0.518144i | 0.141543 | − | 0.0282671i | ||||
\(337\) | −7.44592 | −0.405605 | −0.202802 | − | 0.979220i | \(-0.565005\pi\) | ||||
−0.202802 | + | 0.979220i | \(0.565005\pi\) | |||||||
\(338\) | 5.22966 | − | 11.9017i | 0.284456 | − | 0.647368i | ||||
\(339\) | 4.12255 | + | 7.14047i | 0.223906 | + | 0.387817i | ||||
\(340\) | 1.23386 | 0.0669154 | ||||||||
\(341\) | −6.07375 | − | 10.5200i | −0.328912 | − | 0.569692i | ||||
\(342\) | 3.17107 | + | 5.49246i | 0.171472 | + | 0.296998i | ||||
\(343\) | −15.3754 | + | 10.3246i | −0.830193 | + | 0.557475i | ||||
\(344\) | −5.17961 | − | 8.97135i | −0.279266 | − | 0.483703i | ||||
\(345\) | −0.437624 | −0.0235609 | ||||||||
\(346\) | 7.02100 | + | 12.1607i | 0.377451 | + | 0.653765i | ||||
\(347\) | 5.26407 | − | 9.11763i | 0.282590 | − | 0.489460i | −0.689432 | − | 0.724350i | \(-0.742140\pi\) |
0.972022 | + | 0.234890i | \(0.0754731\pi\) | |||||||
\(348\) | −0.851453 | − | 1.47476i | −0.0456427 | − | 0.0790555i | ||||
\(349\) | −4.74127 | + | 8.21212i | −0.253794 | + | 0.439585i | −0.964567 | − | 0.263837i | \(-0.915012\pi\) |
0.710773 | + | 0.703422i | \(0.248345\pi\) | |||||||
\(350\) | 8.63915 | + | 9.83588i | 0.461782 | + | 0.525750i | ||||
\(351\) | 1.62906 | − | 3.21655i | 0.0869526 | − | 0.171687i | ||||
\(352\) | 1.70561 | − | 2.95420i | 0.0909092 | − | 0.157459i | ||||
\(353\) | 5.44223 | 0.289661 | 0.144830 | − | 0.989456i | \(-0.453736\pi\) | ||||
0.144830 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(354\) | −14.7704 | −0.785040 | ||||||||
\(355\) | −0.0178289 | −0.000946259 | ||||||||
\(356\) | 17.5457 | 0.929920 | ||||||||
\(357\) | 9.44790 | + | 10.7567i | 0.500036 | + | 0.569303i | ||||
\(358\) | −4.66663 | − | 8.08283i | −0.246639 | − | 0.427191i | ||||
\(359\) | −5.29579 | + | 9.17257i | −0.279501 | + | 0.484110i | −0.971261 | − | 0.238018i | \(-0.923502\pi\) |
0.691760 | + | 0.722128i | \(0.256836\pi\) | |||||||
\(360\) | −0.114009 | + | 0.197470i | −0.00600882 | + | 0.0104076i | ||||
\(361\) | 21.2228 | 1.11699 | ||||||||
\(362\) | 0.569188 | + | 0.985863i | 0.0299159 | + | 0.0518158i | ||||
\(363\) | −0.636396 | −0.0334021 | ||||||||
\(364\) | −9.23831 | + | 2.37773i | −0.484219 | + | 0.124627i | ||||
\(365\) | −2.88088 | −0.150792 | ||||||||
\(366\) | 3.35999 | + | 5.81968i | 0.175630 | + | 0.304200i | ||||
\(367\) | −7.19793 | −0.375729 | −0.187864 | − | 0.982195i | \(-0.560157\pi\) | ||||
−0.187864 | + | 0.982195i | \(0.560157\pi\) | |||||||
\(368\) | 0.959623 | − | 1.66212i | 0.0500238 | − | 0.0866438i | ||||
\(369\) | 1.59160 | − | 2.75673i | 0.0828553 | − | 0.143510i | ||||
\(370\) | 0.476924 | + | 0.826056i | 0.0247941 | + | 0.0429446i | ||||
\(371\) | −17.1965 | + | 3.43425i | −0.892795 | + | 0.178298i | ||||
\(372\) | −3.56104 | −0.184632 | ||||||||
\(373\) | −28.5523 | −1.47838 | −0.739192 | − | 0.673494i | \(-0.764793\pi\) | ||||
−0.739192 | + | 0.673494i | \(0.764793\pi\) | |||||||
\(374\) | 18.4588 | 0.954483 | ||||||||
\(375\) | −2.26833 | −0.117136 | ||||||||
\(376\) | 5.57211 | − | 9.65117i | 0.287360 | − | 0.497721i | ||||
\(377\) | 3.35657 | + | 5.14121i | 0.172872 | + | 0.264786i | ||||
\(378\) | −2.59452 | + | 0.518144i | −0.133448 | + | 0.0266504i | ||||
\(379\) | 15.5638 | − | 26.9572i | 0.799457 | − | 1.38470i | −0.120513 | − | 0.992712i | \(-0.538454\pi\) |
0.919970 | − | 0.391989i | \(-0.128213\pi\) | |||||||
\(380\) | 0.723063 | + | 1.25238i | 0.0370924 | + | 0.0642459i | ||||
\(381\) | 6.40560 | − | 11.0948i | 0.328169 | − | 0.568405i | ||||
\(382\) | 9.04253 | + | 15.6621i | 0.462656 | + | 0.801343i | ||||
\(383\) | 21.9521 | 1.12170 | 0.560849 | − | 0.827918i | \(-0.310475\pi\) | ||||
0.560849 | + | 0.827918i | \(0.310475\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −1.35806 | − | 1.54619i | −0.0692133 | − | 0.0788011i | ||||
\(386\) | −2.91296 | − | 5.04539i | −0.148266 | − | 0.256804i | ||||
\(387\) | 5.17961 | + | 8.97135i | 0.263294 | + | 0.456039i | ||||
\(388\) | −13.6533 | −0.693140 | ||||||||
\(389\) | 1.87365 | + | 3.24525i | 0.0949976 | + | 0.164541i | 0.909608 | − | 0.415468i | \(-0.136382\pi\) |
−0.814610 | + | 0.580009i | \(0.803049\pi\) | |||||||
\(390\) | 0.371455 | − | 0.733433i | 0.0188094 | − | 0.0371388i | ||||
\(391\) | 10.3855 | 0.525215 | ||||||||
\(392\) | 5.55998 | + | 4.25284i | 0.280821 | + | 0.214801i | ||||
\(393\) | 1.75964 | − | 3.04778i | 0.0887619 | − | 0.153740i | ||||
\(394\) | −20.7055 | −1.04313 | ||||||||
\(395\) | −0.184941 | − | 0.320327i | −0.00930537 | − | 0.0161174i | ||||
\(396\) | −1.70561 | + | 2.95420i | −0.0857100 | + | 0.148454i | ||||
\(397\) | −3.91005 | −0.196240 | −0.0981198 | − | 0.995175i | \(-0.531283\pi\) | ||||
−0.0981198 | + | 0.995175i | \(0.531283\pi\) | |||||||
\(398\) | 16.3984 | 0.821979 | ||||||||
\(399\) | −5.38152 | + | 15.8934i | −0.269413 | + | 0.795663i | ||||
\(400\) | 2.47400 | − | 4.28510i | 0.123700 | − | 0.214255i | ||||
\(401\) | 13.1130 | + | 22.7124i | 0.654833 | + | 1.13420i | 0.981936 | + | 0.189215i | \(0.0605944\pi\) |
−0.327103 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(402\) | −5.58065 | − | 9.66597i | −0.278337 | − | 0.482095i | ||||
\(403\) | 12.8203 | − | 0.703199i | 0.638623 | − | 0.0350289i | ||||
\(404\) | 8.25823 | − | 14.3037i | 0.410862 | − | 0.711634i | ||||
\(405\) | 0.114009 | − | 0.197470i | 0.00566517 | − | 0.00981236i | ||||
\(406\) | 1.44497 | − | 4.26747i | 0.0717128 | − | 0.211791i | ||||
\(407\) | 7.13490 | + | 12.3580i | 0.353664 | + | 0.612563i | ||||
\(408\) | 2.70561 | − | 4.68625i | 0.133948 | − | 0.232004i | ||||
\(409\) | −2.01759 | + | 3.49457i | −0.0997635 | + | 0.172796i | −0.911587 | − | 0.411108i | \(-0.865142\pi\) |
0.811823 | + | 0.583903i | \(0.198475\pi\) | |||||||
\(410\) | 0.362914 | − | 0.628586i | 0.0179231 | − | 0.0310436i | ||||
\(411\) | 8.84776 | − | 15.3248i | 0.436428 | − | 0.755915i | ||||
\(412\) | −3.17961 | − | 5.50725i | −0.156648 | − | 0.271323i | ||||
\(413\) | −25.7890 | − | 29.3614i | −1.26899 | − | 1.44478i | ||||
\(414\) | −0.959623 | + | 1.66212i | −0.0471629 | + | 0.0816885i | ||||
\(415\) | −0.194147 | + | 0.336273i | −0.00953032 | + | 0.0165070i | ||||
\(416\) | 1.97108 | + | 3.01908i | 0.0966403 | + | 0.148022i | ||||
\(417\) | −3.98321 | − | 6.89912i | −0.195059 | − | 0.337851i | ||||
\(418\) | 10.8172 | + | 18.7360i | 0.529087 | + | 0.916406i | ||||
\(419\) | 1.74139 | − | 3.01617i | 0.0850723 | − | 0.147350i | −0.820350 | − | 0.571862i | \(-0.806221\pi\) |
0.905422 | + | 0.424513i | \(0.139555\pi\) | |||||||
\(420\) | −0.591599 | + | 0.118146i | −0.0288671 | + | 0.00576496i | ||||
\(421\) | 18.6028 | 0.906647 | 0.453323 | − | 0.891346i | \(-0.350238\pi\) | ||||
0.453323 | + | 0.891346i | \(0.350238\pi\) | |||||||
\(422\) | 7.48892 | 0.364555 | ||||||||
\(423\) | −5.57211 | + | 9.65117i | −0.270925 | + | 0.469256i | ||||
\(424\) | 3.31400 | + | 5.74001i | 0.160942 | + | 0.278760i | ||||
\(425\) | 26.7747 | 1.29877 | ||||||||
\(426\) | −0.0390952 | + | 0.0677149i | −0.00189417 | + | 0.00328080i | ||||
\(427\) | −5.70214 | + | 16.8402i | −0.275946 | + | 0.814956i | ||||
\(428\) | 6.54724 | 0.316473 | ||||||||
\(429\) | 5.55706 | − | 10.9723i | 0.268297 | − | 0.529750i | ||||
\(430\) | 1.18105 | + | 2.04564i | 0.0569552 | + | 0.0986493i | ||||
\(431\) | −19.0532 | −0.917762 | −0.458881 | − | 0.888498i | \(-0.651750\pi\) | ||||
−0.458881 | + | 0.888498i | \(0.651750\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −16.7336 | − | 28.9834i | −0.804164 | − | 1.39285i | −0.916854 | − | 0.399223i | \(-0.869280\pi\) |
0.112689 | − | 0.993630i | \(-0.464053\pi\) | |||||||
\(434\) | −6.21753 | − | 7.07881i | −0.298451 | − | 0.339794i | ||||
\(435\) | 0.194147 | + | 0.336273i | 0.00930865 | + | 0.0161231i | ||||
\(436\) | −1.59419 | −0.0763477 | ||||||||
\(437\) | 6.08607 | + | 10.5414i | 0.291136 | + | 0.504262i | ||||
\(438\) | −6.31721 | + | 10.9417i | −0.301848 | + | 0.522816i | ||||
\(439\) | −19.0229 | − | 32.9487i | −0.907915 | − | 1.57255i | −0.816956 | − | 0.576700i | \(-0.804340\pi\) |
−0.0909591 | − | 0.995855i | \(-0.528993\pi\) | |||||||
\(440\) | −0.388911 | + | 0.673613i | −0.0185406 | + | 0.0321132i | ||||
\(441\) | −5.55998 | − | 4.25284i | −0.264761 | − | 0.202516i | ||||
\(442\) | −8.81517 | + | 17.4054i | −0.419295 | + | 0.827892i | ||||
\(443\) | 4.35467 | − | 7.54250i | 0.206896 | − | 0.358355i | −0.743839 | − | 0.668359i | \(-0.766997\pi\) |
0.950735 | + | 0.310004i | \(0.100330\pi\) | |||||||
\(444\) | 4.18320 | 0.198526 | ||||||||
\(445\) | −4.00075 | −0.189654 | ||||||||
\(446\) | −16.8265 | −0.796758 | ||||||||
\(447\) | −2.69358 | −0.127402 | ||||||||
\(448\) | 0.848534 | − | 2.50599i | 0.0400894 | − | 0.118397i | ||||
\(449\) | −11.4930 | − | 19.9065i | −0.542389 | − | 0.939445i | −0.998766 | − | 0.0496589i | \(-0.984187\pi\) |
0.456377 | − | 0.889786i | \(-0.349147\pi\) | |||||||
\(450\) | −2.47400 | + | 4.28510i | −0.116626 | + | 0.202002i | ||||
\(451\) | 5.42929 | − | 9.40380i | 0.255655 | − | 0.442808i | ||||
\(452\) | 8.24510 | 0.387817 | ||||||||
\(453\) | −6.56432 | − | 11.3697i | −0.308419 | − | 0.534197i | ||||
\(454\) | 4.23214 | 0.198624 | ||||||||
\(455\) | 2.10651 | − | 0.542167i | 0.0987546 | − | 0.0254172i | ||||
\(456\) | 6.34214 | 0.296998 | ||||||||
\(457\) | −5.79493 | − | 10.0371i | −0.271075 | − | 0.469516i | 0.698062 | − | 0.716037i | \(-0.254046\pi\) |
−0.969137 | + | 0.246521i | \(0.920713\pi\) | |||||||
\(458\) | −13.7300 | −0.641558 | ||||||||
\(459\) | −2.70561 | + | 4.68625i | −0.126287 | + | 0.218735i | ||||
\(460\) | −0.218812 | + | 0.378993i | −0.0102022 | + | 0.0176707i | ||||
\(461\) | −17.4236 | − | 30.1785i | −0.811496 | − | 1.40555i | −0.911817 | − | 0.410597i | \(-0.865320\pi\) |
0.100321 | − | 0.994955i | \(-0.468013\pi\) | |||||||
\(462\) | −8.85046 | + | 1.76750i | −0.411761 | + | 0.0822316i | ||||
\(463\) | −39.5334 | −1.83727 | −0.918635 | − | 0.395106i | \(-0.870708\pi\) | ||||
−0.918635 | + | 0.395106i | \(0.870708\pi\) | |||||||
\(464\) | −1.70291 | −0.0790555 | ||||||||
\(465\) | 0.811985 | 0.0376549 | ||||||||
\(466\) | −7.70698 | −0.357019 | ||||||||
\(467\) | −0.425191 | + | 0.736452i | −0.0196755 | + | 0.0340789i | −0.875695 | − | 0.482864i | \(-0.839597\pi\) |
0.856020 | + | 0.516943i | \(0.172930\pi\) | |||||||
\(468\) | −1.97108 | − | 3.01908i | −0.0911134 | − | 0.139557i | ||||
\(469\) | 9.47074 | − | 27.9701i | 0.437318 | − | 1.29154i | ||||
\(470\) | −1.27054 | + | 2.20065i | −0.0586059 | + | 0.101508i | ||||
\(471\) | 1.59071 | + | 2.75520i | 0.0732962 | + | 0.126953i | ||||
\(472\) | −7.38522 | + | 12.7916i | −0.339932 | + | 0.588780i | ||||
\(473\) | 17.6688 | + | 30.6032i | 0.812411 | + | 1.40714i | ||||
\(474\) | −1.62215 | −0.0745080 | ||||||||
\(475\) | 15.6905 | + | 27.1767i | 0.719929 | + | 1.24695i | ||||
\(476\) | 14.0395 | − | 2.80379i | 0.643499 | − | 0.128511i | ||||
\(477\) | −3.31400 | − | 5.74001i | −0.151737 | − | 0.262817i | ||||
\(478\) | −12.6095 | − | 21.8402i | −0.576743 | − | 0.998949i | ||||
\(479\) | 11.5746 | 0.528859 | 0.264429 | − | 0.964405i | \(-0.414816\pi\) | ||||
0.264429 | + | 0.964405i | \(0.414816\pi\) | |||||||
\(480\) | 0.114009 | + | 0.197470i | 0.00520379 | + | 0.00901323i | ||||
\(481\) | −15.0601 | + | 0.826056i | −0.686681 | + | 0.0376649i | ||||
\(482\) | −27.8367 | −1.26793 | ||||||||
\(483\) | −4.97952 | + | 0.994446i | −0.226576 | + | 0.0452488i | ||||
\(484\) | −0.318198 | + | 0.551135i | −0.0144635 | + | 0.0250516i | ||||
\(485\) | 3.11320 | 0.141363 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 6.96602 | − | 12.0655i | 0.315661 | − | 0.546740i | −0.663917 | − | 0.747806i | \(-0.731107\pi\) |
0.979578 | + | 0.201066i | \(0.0644405\pi\) | |||||||
\(488\) | 6.71999 | 0.304200 | ||||||||
\(489\) | 16.2940 | 0.736842 | ||||||||
\(490\) | −1.26778 | − | 0.969726i | −0.0572724 | − | 0.0438078i | ||||
\(491\) | 4.76716 | − | 8.25697i | 0.215139 | − | 0.372632i | −0.738177 | − | 0.674608i | \(-0.764313\pi\) |
0.953316 | + | 0.301976i | \(0.0976462\pi\) | |||||||
\(492\) | −1.59160 | − | 2.75673i | −0.0717548 | − | 0.124283i | ||||
\(493\) | −4.60740 | − | 7.98025i | −0.207507 | − | 0.359412i | ||||
\(494\) | −22.8326 | + | 1.25238i | −1.02729 | + | 0.0563474i | ||||
\(495\) | 0.388911 | − | 0.673613i | 0.0174802 | − | 0.0302766i | ||||
\(496\) | −1.78052 | + | 3.08395i | −0.0799478 | + | 0.138474i | ||||
\(497\) | −0.202867 | + | 0.0405139i | −0.00909981 | + | 0.00181730i | ||||
\(498\) | 0.851453 | + | 1.47476i | 0.0381545 | + | 0.0660856i | ||||
\(499\) | 21.9135 | − | 37.9553i | 0.980982 | − | 1.69911i | 0.322397 | − | 0.946605i | \(-0.395511\pi\) |
0.658585 | − | 0.752506i | \(-0.271155\pi\) | |||||||
\(500\) | −1.13417 | + | 1.96443i | −0.0507214 | + | 0.0878521i | ||||
\(501\) | −0.826739 | + | 1.43195i | −0.0369360 | + | 0.0639750i | ||||
\(502\) | −2.12395 | + | 3.67878i | −0.0947963 | + | 0.164192i | ||||
\(503\) | −7.35181 | − | 12.7337i | −0.327801 | − | 0.567768i | 0.654274 | − | 0.756257i | \(-0.272974\pi\) |
−0.982075 | + | 0.188489i | \(0.939641\pi\) | |||||||
\(504\) | −0.848534 | + | 2.50599i | −0.0377967 | + | 0.111626i | ||||
\(505\) | −1.88303 | + | 3.26150i | −0.0837937 | + | 0.145135i | ||||
\(506\) | −3.27348 | + | 5.66984i | −0.145524 | + | 0.252055i | ||||
\(507\) | 7.69235 | + | 10.4799i | 0.341629 | + | 0.465427i | ||||
\(508\) | −6.40560 | − | 11.0948i | −0.284202 | − | 0.492253i | ||||
\(509\) | 7.23975 | + | 12.5396i | 0.320896 | + | 0.555809i | 0.980673 | − | 0.195653i | \(-0.0626826\pi\) |
−0.659777 | + | 0.751461i | \(0.729349\pi\) | |||||||
\(510\) | −0.616929 | + | 1.06855i | −0.0273181 | + | 0.0473163i | ||||
\(511\) | −32.7802 | + | 6.54645i | −1.45011 | + | 0.289598i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.34214 | −0.280012 | ||||||||
\(514\) | 7.35836 | − | 12.7450i | 0.324563 | − | 0.562160i | ||||
\(515\) | 0.725011 | + | 1.25576i | 0.0319478 | + | 0.0553352i | ||||
\(516\) | 10.3592 | 0.456039 | ||||||||
\(517\) | −19.0077 | + | 32.9222i | −0.835956 | + | 1.44792i | ||||
\(518\) | 7.30380 | + | 8.31556i | 0.320911 | + | 0.365365i | ||||
\(519\) | −14.0420 | −0.616375 | ||||||||
\(520\) | −0.449444 | − | 0.688406i | −0.0197094 | − | 0.0301886i | ||||
\(521\) | 7.18959 | + | 12.4527i | 0.314982 | + | 0.545564i | 0.979434 | − | 0.201767i | \(-0.0646683\pi\) |
−0.664452 | + | 0.747331i | \(0.731335\pi\) | |||||||
\(522\) | 1.70291 | 0.0745342 | ||||||||
\(523\) | 0.511770 | + | 0.886412i | 0.0223781 | + | 0.0387601i | 0.876998 | − | 0.480495i | \(-0.159543\pi\) |
−0.854619 | + | 0.519255i | \(0.826210\pi\) | |||||||
\(524\) | −1.75964 | − | 3.04778i | −0.0768701 | − | 0.133143i | ||||
\(525\) | −12.8377 | + | 2.56378i | −0.560283 | + | 0.111893i | ||||
\(526\) | 11.7053 | + | 20.2741i | 0.510374 | + | 0.883993i | ||||
\(527\) | −19.2696 | −0.839396 | ||||||||
\(528\) | 1.70561 | + | 2.95420i | 0.0742271 | + | 0.128565i | ||||
\(529\) | 9.65825 | − | 16.7286i | 0.419924 | − | 0.727329i | ||||
\(530\) | −0.755653 | − | 1.30883i | −0.0328235 | − | 0.0568519i | ||||
\(531\) | 7.38522 | − | 12.7916i | 0.320491 | − | 0.555107i | ||||
\(532\) | 11.0733 | + | 12.6072i | 0.480088 | + | 0.546592i | ||||
\(533\) | 6.27435 | + | 9.61032i | 0.271772 | + | 0.416269i | ||||
\(534\) | −8.77285 | + | 15.1950i | −0.379638 | + | 0.657553i | ||||
\(535\) | −1.49289 | −0.0645434 | ||||||||
\(536\) | −11.1613 | −0.482095 | ||||||||
\(537\) | 9.33325 | 0.402760 | ||||||||
\(538\) | 9.35772 | 0.403440 | ||||||||
\(539\) | −18.9663 | − | 14.5073i | −0.816936 | − | 0.624875i | ||||
\(540\) | −0.114009 | − | 0.197470i | −0.00490618 | − | 0.00849776i | ||||
\(541\) | 0.804352 | − | 1.39318i | 0.0345818 | − | 0.0598974i | −0.848217 | − | 0.529650i | \(-0.822323\pi\) |
0.882798 | + | 0.469752i | \(0.155657\pi\) | |||||||
\(542\) | −7.57375 | + | 13.1181i | −0.325320 | + | 0.563471i | ||||
\(543\) | −1.13838 | −0.0488524 | ||||||||
\(544\) | −2.70561 | − | 4.68625i | −0.116002 | − | 0.200921i | ||||
\(545\) | 0.363504 | 0.0155708 | ||||||||
\(546\) | 2.55998 | − | 9.18948i | 0.109557 | − | 0.393273i | ||||
\(547\) | 26.9289 | 1.15140 | 0.575699 | − | 0.817661i | \(-0.304730\pi\) | ||||
0.575699 | + | 0.817661i | \(0.304730\pi\) | |||||||
\(548\) | −8.84776 | − | 15.3248i | −0.377958 | − | 0.654642i | ||||
\(549\) | −6.71999 | −0.286802 | ||||||||
\(550\) | −8.43936 | + | 14.6174i | −0.359856 | + | 0.623288i | ||||
\(551\) | 5.40004 | − | 9.35314i | 0.230049 | − | 0.398457i | ||||
\(552\) | 0.959623 | + | 1.66212i | 0.0408443 | + | 0.0707444i | ||||
\(553\) | −2.83226 | − | 3.22459i | −0.120440 | − | 0.137124i | ||||
\(554\) | 32.8782 | 1.39686 | ||||||||
\(555\) | −0.953847 | −0.0404886 | ||||||||
\(556\) | −7.96642 | −0.337851 | ||||||||
\(557\) | −36.3681 | −1.54097 | −0.770484 | − | 0.637460i | \(-0.779985\pi\) | ||||
−0.770484 | + | 0.637460i | \(0.779985\pi\) | |||||||
\(558\) | 1.78052 | − | 3.08395i | 0.0753755 | − | 0.130554i | ||||
\(559\) | −37.2947 | + | 2.04564i | −1.57740 | + | 0.0865212i | ||||
\(560\) | −0.193482 | + | 0.571413i | −0.00817609 | + | 0.0241466i | ||||
\(561\) | −9.22941 | + | 15.9858i | −0.389666 | + | 0.674922i | ||||
\(562\) | −8.40358 | − | 14.5554i | −0.354484 | − | 0.613984i | ||||
\(563\) | 1.86510 | − | 3.23046i | 0.0786048 | − | 0.136147i | −0.824043 | − | 0.566527i | \(-0.808287\pi\) |
0.902648 | + | 0.430379i | \(0.141620\pi\) | |||||||
\(564\) | 5.57211 | + | 9.65117i | 0.234628 | + | 0.406388i | ||||
\(565\) | −1.88004 | −0.0790938 | ||||||||
\(566\) | −6.07998 | − | 10.5308i | −0.255561 | − | 0.442644i | ||||
\(567\) | 0.848534 | − | 2.50599i | 0.0356351 | − | 0.105242i | ||||
\(568\) | 0.0390952 | + | 0.0677149i | 0.00164040 | + | 0.00284126i | ||||
\(569\) | 7.69596 | + | 13.3298i | 0.322632 | + | 0.558814i | 0.981030 | − | 0.193855i | \(-0.0620992\pi\) |
−0.658399 | + | 0.752669i | \(0.728766\pi\) | |||||||
\(570\) | −1.44613 | −0.0605716 | ||||||||
\(571\) | −10.1994 | − | 17.6659i | −0.426832 | − | 0.739296i | 0.569757 | − | 0.821813i | \(-0.307037\pi\) |
−0.996590 | + | 0.0825176i | \(0.973704\pi\) | |||||||
\(572\) | −6.72379 | − | 10.2987i | −0.281136 | − | 0.430611i | ||||
\(573\) | −18.0851 | −0.755514 | ||||||||
\(574\) | 2.70105 | − | 7.97706i | 0.112740 | − | 0.332956i | ||||
\(575\) | −4.74822 | + | 8.22416i | −0.198015 | + | 0.342971i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.90380 | − | 10.2257i | −0.245779 | − | 0.425701i | 0.716572 | − | 0.697513i | \(-0.245710\pi\) |
−0.962350 | + | 0.271813i | \(0.912377\pi\) | |||||||
\(578\) | 6.14063 | − | 10.6359i | 0.255417 | − | 0.442394i | ||||
\(579\) | 5.82592 | 0.242117 | ||||||||
\(580\) | 0.388295 | 0.0161231 | ||||||||
\(581\) | −1.44497 | + | 4.26747i | −0.0599476 | + | 0.177044i | ||||
\(582\) | 6.82663 | − | 11.8241i | 0.282973 | − | 0.490124i | ||||
\(583\) | −11.3048 | − | 19.5804i | −0.468195 | − | 0.810938i | ||||
\(584\) | 6.31721 | + | 10.9417i | 0.261408 | + | 0.452772i | ||||
\(585\) | 0.449444 | + | 0.688406i | 0.0185822 | + | 0.0284621i | ||||
\(586\) | −13.8954 | + | 24.0675i | −0.574014 | + | 0.994221i | ||||
\(587\) | −21.9241 | + | 37.9736i | −0.904903 | + | 1.56734i | −0.0838564 | + | 0.996478i | \(0.526724\pi\) |
−0.821047 | + | 0.570861i | \(0.806610\pi\) | |||||||
\(588\) | −6.46305 | + | 2.68867i | −0.266532 | + | 0.110879i | ||||
\(589\) | −11.2923 | − | 19.5589i | −0.465292 | − | 0.805910i | ||||
\(590\) | 1.68397 | − | 2.91672i | 0.0693279 | − | 0.120079i | ||||
\(591\) | 10.3527 | − | 17.9315i | 0.425855 | − | 0.737602i | ||||
\(592\) | 2.09160 | − | 3.62276i | 0.0859642 | − | 0.148894i | ||||
\(593\) | −5.18125 | + | 8.97419i | −0.212768 | + | 0.368526i | −0.952580 | − | 0.304288i | \(-0.901581\pi\) |
0.739812 | + | 0.672814i | \(0.234915\pi\) | |||||||
\(594\) | −1.70561 | − | 2.95420i | −0.0699819 | − | 0.121212i | ||||
\(595\) | −3.20127 | + | 0.639316i | −0.131239 | + | 0.0262094i | ||||
\(596\) | −1.34679 | + | 2.33271i | −0.0551667 | + | 0.0955515i | ||||
\(597\) | −8.19922 | + | 14.2015i | −0.335572 | + | 0.581227i | ||||
\(598\) | −3.78300 | − | 5.79435i | −0.154698 | − | 0.236949i | ||||
\(599\) | −19.7135 | − | 34.1448i | −0.805471 | − | 1.39512i | −0.915973 | − | 0.401241i | \(-0.868579\pi\) |
0.110501 | − | 0.993876i | \(-0.464754\pi\) | |||||||
\(600\) | 2.47400 | + | 4.28510i | 0.101001 | + | 0.174938i | ||||
\(601\) | −1.03443 | + | 1.79169i | −0.0421954 | + | 0.0730845i | −0.886352 | − | 0.463012i | \(-0.846769\pi\) |
0.844156 | + | 0.536097i | \(0.180102\pi\) | |||||||
\(602\) | 18.0870 | + | 20.5926i | 0.737173 | + | 0.839290i | ||||
\(603\) | 11.1613 | 0.454523 | ||||||||
\(604\) | −13.1286 | −0.534197 | ||||||||
\(605\) | 0.0725551 | − | 0.125669i | 0.00294978 | − | 0.00510918i | ||||
\(606\) | 8.25823 | + | 14.3037i | 0.335467 | + | 0.581047i | ||||
\(607\) | 5.77956 | 0.234585 | 0.117292 | − | 0.993097i | \(-0.462579\pi\) | ||||
0.117292 | + | 0.993097i | \(0.462579\pi\) | |||||||
\(608\) | 3.17107 | − | 5.49246i | 0.128604 | − | 0.222749i | ||||
\(609\) | 2.97325 | + | 3.38512i | 0.120482 | + | 0.137172i | ||||
\(610\) | −1.53228 | −0.0620403 | ||||||||
\(611\) | −21.9662 | − | 33.6453i | −0.888657 | − | 1.36114i | ||||
\(612\) | 2.70561 | + | 4.68625i | 0.109368 | + | 0.189430i | ||||
\(613\) | 14.9090 | 0.602170 | 0.301085 | − | 0.953597i | \(-0.402651\pi\) | ||||
0.301085 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(614\) | −7.34243 | − | 12.7175i | −0.296317 | − | 0.513235i | ||||
\(615\) | 0.362914 | + | 0.628586i | 0.0146341 | + | 0.0253470i | ||||
\(616\) | −2.89453 | + | 8.54848i | −0.116624 | + | 0.344428i | ||||
\(617\) | −1.29988 | − | 2.25147i | −0.0523314 | − | 0.0906406i | 0.838673 | − | 0.544635i | \(-0.183332\pi\) |
−0.891004 | + | 0.453995i | \(0.849999\pi\) | |||||||
\(618\) | 6.35922 | 0.255805 | ||||||||
\(619\) | 24.4693 | + | 42.3821i | 0.983505 | + | 1.70348i | 0.648399 | + | 0.761300i | \(0.275439\pi\) |
0.335106 | + | 0.942180i | \(0.391228\pi\) | |||||||
\(620\) | 0.405992 | − | 0.703199i | 0.0163050 | − | 0.0282412i | ||||
\(621\) | −0.959623 | − | 1.66212i | −0.0385083 | − | 0.0666984i | ||||
\(622\) | −3.86348 | + | 6.69174i | −0.154911 | + | 0.268314i | ||||
\(623\) | −45.5226 | + | 9.09119i | −1.82383 | + | 0.364231i | ||||
\(624\) | −3.60014 | + | 0.197470i | −0.144121 | + | 0.00790513i | ||||
\(625\) | −12.1114 | + | 20.9776i | −0.484456 | + | 0.839103i | ||||
\(626\) | −20.1964 | −0.807210 | ||||||||
\(627\) | −21.6344 | −0.863995 | ||||||||
\(628\) | 3.18143 | 0.126953 | ||||||||
\(629\) | 22.6362 | 0.902564 | ||||||||
\(630\) | 0.193482 | − | 0.571413i | 0.00770849 | − | 0.0227656i | ||||
\(631\) | 14.0099 | + | 24.2659i | 0.557726 | + | 0.966010i | 0.997686 | + | 0.0679924i | \(0.0216594\pi\) |
−0.439960 | + | 0.898017i | \(0.645007\pi\) | |||||||
\(632\) | −0.811077 | + | 1.40483i | −0.0322629 | + | 0.0558810i | ||||
\(633\) | −3.74446 | + | 6.48560i | −0.148829 | + | 0.257779i | ||||
\(634\) | 14.7218 | 0.584676 | ||||||||
\(635\) | 1.46060 | + | 2.52983i | 0.0579620 | + | 0.100393i | ||||
\(636\) | −6.62799 | −0.262817 | ||||||||
\(637\) | 22.7370 | − | 10.9558i | 0.900871 | − | 0.434086i | ||||
\(638\) | 5.80898 | 0.229980 | ||||||||
\(639\) | −0.0390952 | − | 0.0677149i | −0.00154658 | − | 0.00267876i | ||||
\(640\) | 0.228019 | 0.00901323 | ||||||||
\(641\) | 17.9656 | − | 31.1173i | 0.709598 | − | 1.22906i | −0.255409 | − | 0.966833i | \(-0.582210\pi\) |
0.965006 | − | 0.262226i | \(-0.0844566\pi\) | |||||||
\(642\) | −3.27362 | + | 5.67008i | −0.129199 | + | 0.223780i | ||||
\(643\) | 10.6007 | + | 18.3609i | 0.418050 | + | 0.724084i | 0.995743 | − | 0.0921702i | \(-0.0293804\pi\) |
−0.577693 | + | 0.816254i | \(0.696047\pi\) | |||||||
\(644\) | −1.62854 | + | 4.80961i | −0.0641737 | + | 0.189525i | ||||
\(645\) | −2.36210 | −0.0930075 | ||||||||
\(646\) | 34.3187 | 1.35025 | ||||||||
\(647\) | 4.12288 | 0.162087 | 0.0810436 | − | 0.996711i | \(-0.474175\pi\) | ||||
0.0810436 | + | 0.996711i | \(0.474175\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 25.1926 | − | 43.6348i | 0.988895 | − | 1.71282i | ||||
\(650\) | −9.75294 | − | 14.9384i | −0.382542 | − | 0.585933i | ||||
\(651\) | 9.23920 | − | 1.84513i | 0.362113 | − | 0.0723165i | ||||
\(652\) | 8.14702 | − | 14.1111i | 0.319062 | − | 0.552632i | ||||
\(653\) | 23.7186 | + | 41.0818i | 0.928179 | + | 1.60765i | 0.786367 | + | 0.617760i | \(0.211960\pi\) |
0.141812 | + | 0.989894i | \(0.454707\pi\) | |||||||
\(654\) | 0.797093 | − | 1.38061i | 0.0311688 | − | 0.0539860i | ||||
\(655\) | 0.401230 | + | 0.694951i | 0.0156773 | + | 0.0271540i | ||||
\(656\) | −3.18320 | −0.124283 | ||||||||
\(657\) | −6.31721 | − | 10.9417i | −0.246458 | − | 0.426877i | ||||
\(658\) | −9.45624 | + | 27.9273i | −0.368643 | + | 1.08872i | ||||
\(659\) | −12.4744 | − | 21.6062i | −0.485932 | − | 0.841659i | 0.513937 | − | 0.857828i | \(-0.328186\pi\) |
−0.999869 | + | 0.0161688i | \(0.994853\pi\) | |||||||
\(660\) | −0.388911 | − | 0.673613i | −0.0151383 | − | 0.0262203i | ||||
\(661\) | −8.61529 | −0.335096 | −0.167548 | − | 0.985864i | \(-0.553585\pi\) | ||||
−0.167548 | + | 0.985864i | \(0.553585\pi\) | |||||||
\(662\) | 2.05436 | + | 3.55826i | 0.0798450 | + | 0.138296i | ||||
\(663\) | −10.6660 | − | 16.3369i | −0.414232 | − | 0.634472i | ||||
\(664\) | 1.70291 | 0.0660856 | ||||||||
\(665\) | −2.52492 | − | 2.87468i | −0.0979120 | − | 0.111475i | ||||
\(666\) | −2.09160 | + | 3.62276i | −0.0810478 | + | 0.140379i | ||||
\(667\) | 3.26830 | 0.126549 | ||||||||
\(668\) | 0.826739 | + | 1.43195i | 0.0319875 | + | 0.0554040i | ||||
\(669\) | 8.41325 | − | 14.5722i | 0.325275 | − | 0.563393i | ||||
\(670\) | 2.54498 | 0.0983213 | ||||||||
\(671\) | −22.9233 | −0.884946 | ||||||||
\(672\) | 1.74599 | + | 1.98785i | 0.0673528 | + | 0.0766829i | ||||
\(673\) | 3.15527 | − | 5.46509i | 0.121627 | − | 0.210664i | −0.798783 | − | 0.601620i | \(-0.794522\pi\) |
0.920409 | + | 0.390956i | \(0.127856\pi\) | |||||||
\(674\) | −3.72296 | − | 6.44835i | −0.143403 | − | 0.248381i | ||||
\(675\) | −2.47400 | − | 4.28510i | −0.0952244 | − | 0.164934i | ||||
\(676\) | 12.9220 | − | 1.42184i | 0.497000 | − | 0.0546861i | ||||
\(677\) | −3.67011 | + | 6.35682i | −0.141054 | + | 0.244313i | −0.927894 | − | 0.372845i | \(-0.878382\pi\) |
0.786840 | + | 0.617157i | \(0.211716\pi\) | |||||||
\(678\) | −4.12255 | + | 7.14047i | −0.158326 | + | 0.274228i | ||||
\(679\) | 35.4237 | − | 7.07436i | 1.35944 | − | 0.271489i | ||||
\(680\) | 0.616929 | + | 1.06855i | 0.0236582 | + | 0.0409771i | ||||
\(681\) | −2.11607 | + | 3.66514i | −0.0810880 | + | 0.140449i | ||||
\(682\) | 6.07375 | − | 10.5200i | 0.232576 | − | 0.402833i | ||||
\(683\) | −9.95558 | + | 17.2436i | −0.380940 | + | 0.659807i | −0.991197 | − | 0.132396i | \(-0.957733\pi\) |
0.610257 | + | 0.792204i | \(0.291066\pi\) | |||||||
\(684\) | −3.17107 | + | 5.49246i | −0.121249 | + | 0.210009i | ||||
\(685\) | 2.01746 | + | 3.49434i | 0.0770830 | + | 0.133512i | ||||
\(686\) | −16.6291 | − | 8.15319i | −0.634900 | − | 0.311290i | ||||
\(687\) | 6.86498 | − | 11.8905i | 0.261915 | − | 0.453650i | ||||
\(688\) | 5.17961 | − | 8.97135i | 0.197471 | − | 0.342030i | ||||
\(689\) | 23.8617 | − | 1.30883i | 0.909058 | − | 0.0498624i | ||||
\(690\) | −0.218812 | − | 0.378993i | −0.00833003 | − | 0.0144280i | ||||
\(691\) | 9.53454 | + | 16.5143i | 0.362711 | + | 0.628234i | 0.988406 | − | 0.151834i | \(-0.0485179\pi\) |
−0.625695 | + | 0.780068i | \(0.715185\pi\) | |||||||
\(692\) | −7.02100 | + | 12.1607i | −0.266898 | + | 0.462282i | ||||
\(693\) | 2.89453 | − | 8.54848i | 0.109954 | − | 0.324730i | ||||
\(694\) | 10.5281 | 0.399642 | ||||||||
\(695\) | 1.81649 | 0.0689035 | ||||||||
\(696\) | 0.851453 | − | 1.47476i | 0.0322743 | − | 0.0559007i | ||||
\(697\) | −8.61248 | − | 14.9173i | −0.326221 | − | 0.565032i | ||||
\(698\) | −9.48254 | −0.358920 | ||||||||
\(699\) | 3.85349 | − | 6.67444i | 0.145752 | − | 0.252450i | ||||
\(700\) | −4.19855 | + | 12.3997i | −0.158690 | + | 0.468663i | ||||
\(701\) | 21.2816 | 0.803796 | 0.401898 | − | 0.915685i | \(-0.368351\pi\) | ||||
0.401898 | + | 0.915685i | \(0.368351\pi\) | |||||||
\(702\) | 3.60014 | − | 0.197470i | 0.135879 | − | 0.00745302i | ||||
\(703\) | 13.2652 | + | 22.9760i | 0.500307 | + | 0.866557i | ||||
\(704\) | 3.41122 | 0.128565 | ||||||||
\(705\) | −1.27054 | − | 2.20065i | −0.0478515 | − | 0.0828812i | ||||
\(706\) | 2.72112 | + | 4.71311i | 0.102411 | + | 0.177380i | ||||
\(707\) | −14.0148 | + | 41.3901i | −0.527079 | + | 1.55663i | ||||
\(708\) | −7.38522 | − | 12.7916i | −0.277554 | − | 0.480737i | ||||
\(709\) | −26.8217 | −1.00731 | −0.503655 | − | 0.863905i | \(-0.668012\pi\) | ||||
−0.503655 | + | 0.863905i | \(0.668012\pi\) | |||||||
\(710\) | −0.00891445 | − | 0.0154403i | −0.000334553 | − | 0.000579463i | ||||
\(711\) | 0.811077 | − | 1.40483i | 0.0304177 | − | 0.0526851i | ||||
\(712\) | 8.77285 | + | 15.1950i | 0.328776 | + | 0.569457i | ||||
\(713\) | 3.41726 | − | 5.91887i | 0.127977 | − | 0.221663i | ||||
\(714\) | −4.59160 | + | 13.5605i | −0.171836 | + | 0.507487i | ||||
\(715\) | 1.53315 | + | 2.34830i | 0.0573366 | + | 0.0878215i | ||||
\(716\) | 4.66663 | − | 8.08283i | 0.174400 | − | 0.302070i | ||||
\(717\) | 25.2189 | 0.941818 | ||||||||
\(718\) | −10.5916 | −0.395274 | ||||||||
\(719\) | −43.1706 | −1.60999 | −0.804997 | − | 0.593279i | \(-0.797833\pi\) | ||||
−0.804997 | + | 0.593279i | \(0.797833\pi\) | |||||||
\(720\) | −0.228019 | −0.00849776 | ||||||||
\(721\) | 11.1031 | + | 12.6412i | 0.413501 | + | 0.470782i | ||||
\(722\) | 10.6114 | + | 18.3795i | 0.394915 | + | 0.684012i | ||||
\(723\) | 13.9183 | − | 24.1073i | 0.517629 | − | 0.896560i | ||||
\(724\) | −0.569188 | + | 0.985863i | −0.0211537 | + | 0.0366393i | ||||
\(725\) | 8.42600 | 0.312934 | ||||||||
\(726\) | −0.318198 | − | 0.551135i | −0.0118094 | − | 0.0204545i | ||||
\(727\) | −16.1609 | −0.599373 | −0.299687 | − | 0.954038i | \(-0.596882\pi\) | ||||
−0.299687 | + | 0.954038i | \(0.596882\pi\) | |||||||
\(728\) | −6.67833 | − | 6.81175i | −0.247515 | − | 0.252460i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.44044 | − | 2.49492i | −0.0533131 | − | 0.0923411i | ||||
\(731\) | 56.0560 | 2.07331 | ||||||||
\(732\) | −3.35999 | + | 5.81968i | −0.124189 | + | 0.215102i | ||||
\(733\) | 6.79983 | − | 11.7777i | 0.251158 | − | 0.435018i | −0.712687 | − | 0.701482i | \(-0.752522\pi\) |
0.963845 | + | 0.266464i | \(0.0858554\pi\) | |||||||
\(734\) | −3.59896 | − | 6.23359i | −0.132840 | − | 0.230086i | ||||
\(735\) | 1.47370 | − | 0.613066i | 0.0543581 | − | 0.0226133i | ||||
\(736\) | 1.91925 | 0.0707444 | ||||||||
\(737\) | 38.0736 | 1.40246 | ||||||||
\(738\) | 3.18320 | 0.117175 | ||||||||
\(739\) | 0.383605 | 0.0141111 | 0.00705557 | − | 0.999975i | \(-0.497754\pi\) | ||||
0.00705557 | + | 0.999975i | \(0.497754\pi\) | |||||||
\(740\) | −0.476924 | + | 0.826056i | −0.0175321 | + | 0.0303664i | ||||
\(741\) | 10.3317 | − | 20.3998i | 0.379545 | − | 0.749405i | ||||
\(742\) | −11.5724 | − | 13.1754i | −0.424835 | − | 0.483685i | ||||
\(743\) | 10.4715 | − | 18.1372i | 0.384162 | − | 0.665388i | −0.607491 | − | 0.794327i | \(-0.707824\pi\) |
0.991653 | + | 0.128939i | \(0.0411572\pi\) | |||||||
\(744\) | −1.78052 | − | 3.08395i | −0.0652771 | − | 0.113063i | ||||
\(745\) | 0.307093 | − | 0.531901i | 0.0112510 | − | 0.0194874i | ||||
\(746\) | −14.2762 | − | 24.7271i | −0.522688 | − | 0.905322i | ||||
\(747\) | −1.70291 | −0.0623061 | ||||||||
\(748\) | 9.22941 | + | 15.9858i | 0.337461 | + | 0.584499i | ||||
\(749\) | −16.9869 | + | 3.39241i | −0.620689 | + | 0.123956i | ||||
\(750\) | −1.13417 | − | 1.96443i | −0.0414139 | − | 0.0717309i | ||||
\(751\) | −7.90695 | − | 13.6952i | −0.288529 | − | 0.499746i | 0.684930 | − | 0.728609i | \(-0.259833\pi\) |
−0.973459 | + | 0.228862i | \(0.926499\pi\) | |||||||
\(752\) | 11.1442 | 0.406388 | ||||||||
\(753\) | −2.12395 | − | 3.67878i | −0.0774009 | − | 0.134062i | ||||
\(754\) | −2.77413 | + | 5.47748i | −0.101028 | + | 0.199478i | ||||
\(755\) | 2.99358 | 0.108947 | ||||||||
\(756\) | −1.74599 | − | 1.98785i | −0.0635009 | − | 0.0722973i | ||||
\(757\) | −4.41633 | + | 7.64930i | −0.160514 | + | 0.278019i | −0.935053 | − | 0.354507i | \(-0.884649\pi\) |
0.774539 | + | 0.632526i | \(0.217982\pi\) | |||||||
\(758\) | 31.1275 | 1.13060 | ||||||||
\(759\) | −3.27348 | − | 5.66984i | −0.118820 | − | 0.205802i | ||||
\(760\) | −0.723063 | + | 1.25238i | −0.0262283 | + | 0.0454287i | ||||
\(761\) | 38.7406 | 1.40434 | 0.702172 | − | 0.712007i | \(-0.252214\pi\) | ||||
0.702172 | + | 0.712007i | \(0.252214\pi\) | |||||||
\(762\) | 12.8112 | 0.464100 | ||||||||
\(763\) | 4.13615 | − | 0.826018i | 0.149739 | − | 0.0299038i | ||||
\(764\) | −9.04253 | + | 15.6621i | −0.327147 | + | 0.566635i | ||||
\(765\) | −0.616929 | − | 1.06855i | −0.0223051 | − | 0.0386336i | ||||
\(766\) | 10.9760 | + | 19.0111i | 0.396580 | + | 0.686897i | ||||
\(767\) | 29.1138 | + | 44.5931i | 1.05124 | + | 1.61016i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −9.17950 | + | 15.8994i | −0.331021 | + | 0.573345i | −0.982712 | − | 0.185139i | \(-0.940726\pi\) |
0.651691 | + | 0.758484i | \(0.274060\pi\) | |||||||
\(770\) | 0.660007 | − | 1.94921i | 0.0237850 | − | 0.0702447i | ||||
\(771\) | 7.35836 | + | 12.7450i | 0.265005 | + | 0.459002i | ||||
\(772\) | 2.91296 | − | 5.04539i | 0.104840 | − | 0.181588i | ||||
\(773\) | −6.42407 | + | 11.1268i | −0.231058 | + | 0.400204i | −0.958120 | − | 0.286368i | \(-0.907552\pi\) |
0.727062 | + | 0.686572i | \(0.240885\pi\) | |||||||
\(774\) | −5.17961 | + | 8.97135i | −0.186177 | + | 0.322469i | ||||
\(775\) | 8.81004 | − | 15.2594i | 0.316466 | − | 0.548135i | ||||
\(776\) | −6.82663 | − | 11.8241i | −0.245062 | − | 0.424460i | ||||
\(777\) | −10.8534 | + | 2.16750i | −0.389363 | + | 0.0777586i | ||||
\(778\) | −1.87365 | + | 3.24525i | −0.0671734 | + | 0.116348i | ||||
\(779\) | 10.0941 | − | 17.4836i | 0.361660 | − | 0.626414i | ||||
\(780\) | 0.820899 | − | 0.0450268i | 0.0293929 | − | 0.00161222i | ||||
\(781\) | −0.133362 | − | 0.230990i | −0.00477208 | − | 0.00826548i | ||||
\(782\) | 5.19273 | + | 8.99407i | 0.185692 | + | 0.321627i | ||||
\(783\) | −0.851453 | + | 1.47476i | −0.0304285 | + | 0.0527036i | ||||
\(784\) | −0.903072 | + | 6.94150i | −0.0322526 | + | 0.247911i | ||||
\(785\) | −0.725425 | −0.0258915 | ||||||||
\(786\) | 3.51927 | 0.125528 | ||||||||
\(787\) | 1.69729 | − | 2.93979i | 0.0605017 | − | 0.104792i | −0.834188 | − | 0.551480i | \(-0.814063\pi\) |
0.894690 | + | 0.446688i | \(0.147397\pi\) | |||||||
\(788\) | −10.3527 | − | 17.9315i | −0.368801 | − | 0.638782i | ||||
\(789\) | −23.4105 | −0.833437 | ||||||||
\(790\) | 0.184941 | − | 0.320327i | 0.00657989 | − | 0.0113967i | ||||
\(791\) | −21.3921 | + | 4.27215i | −0.760614 | + | 0.151900i | ||||
\(792\) | −3.41122 | −0.121212 | ||||||||
\(793\) | 10.9472 | − | 21.6152i | 0.388748 | − | 0.767577i | ||||
\(794\) | −1.95502 | − | 3.38620i | −0.0693812 | − | 0.120172i | ||||
\(795\) | 1.51131 | 0.0536005 | ||||||||
\(796\) | 8.19922 | + | 14.2015i | 0.290614 | + | 0.503357i | ||||
\(797\) | 1.71983 | + | 2.97884i | 0.0609197 | + | 0.105516i | 0.894877 | − | 0.446313i | \(-0.147263\pi\) |
−0.833957 | + | 0.551829i | \(0.813930\pi\) | |||||||
\(798\) | −16.4548 | + | 3.28614i | −0.582494 | + | 0.116328i | ||||
\(799\) | 30.1519 | + | 52.2246i | 1.06670 | + | 1.84757i | ||||
\(800\) | 4.94801 | 0.174938 | ||||||||
\(801\) | −8.77285 | − | 15.1950i | −0.309973 | − | 0.536890i | ||||
\(802\) | −13.1130 | + | 22.7124i | −0.463037 | + | 0.802003i | ||||
\(803\) | −21.5494 | − | 37.3246i | −0.760461 | − | 1.31716i | ||||
\(804\) | 5.58065 | − | 9.66597i | 0.196814 | − | 0.340892i | ||||
\(805\) | 0.371339 | − | 1.09668i | 0.0130880 | − | 0.0386530i | ||||
\(806\) | 7.01912 | + | 10.7511i | 0.247238 | + | 0.378690i | ||||
\(807\) | −4.67886 | + | 8.10402i | −0.164704 | + | 0.285275i | ||||
\(808\) | 16.5165 | 0.581047 | ||||||||
\(809\) | −27.9826 | −0.983815 | −0.491908 | − | 0.870647i | \(-0.663700\pi\) | ||||
−0.491908 | + | 0.870647i | \(0.663700\pi\) | |||||||
\(810\) | 0.228019 | 0.00801176 | ||||||||
\(811\) | 26.2105 | 0.920377 | 0.460188 | − | 0.887821i | \(-0.347782\pi\) | ||||
0.460188 | + | 0.887821i | \(0.347782\pi\) | |||||||
\(812\) | 4.41822 | − | 0.882351i | 0.155049 | − | 0.0309644i | ||||
\(813\) | −7.57375 | − | 13.1181i | −0.265623 | − | 0.460072i | ||||
\(814\) | −7.13490 | + | 12.3580i | −0.250078 | + | 0.433148i | ||||
\(815\) | −1.85767 | + | 3.21758i | −0.0650715 | + | 0.112707i | ||||
\(816\) | 5.41122 | 0.189430 | ||||||||
\(817\) | 32.8498 | + | 56.8976i | 1.14927 | + | 1.99059i | ||||
\(818\) | −4.03519 | −0.141087 | ||||||||
\(819\) | 6.67833 | + | 6.81175i | 0.233360 | + | 0.238022i | ||||
\(820\) | 0.725829 | 0.0253470 | ||||||||
\(821\) | 7.77317 | + | 13.4635i | 0.271285 | + | 0.469880i | 0.969191 | − | 0.246309i | \(-0.0792179\pi\) |
−0.697906 | + | 0.716190i | \(0.745885\pi\) | |||||||
\(822\) | 17.6955 | 0.617202 | ||||||||
\(823\) | 23.9106 | − | 41.4144i | 0.833471 | − | 1.44361i | −0.0617981 | − | 0.998089i | \(-0.519683\pi\) |
0.895269 | − | 0.445526i | \(-0.146983\pi\) | |||||||
\(824\) | 3.17961 | − | 5.50725i | 0.110767 | − | 0.191854i | ||||
\(825\) | −8.43936 | − | 14.6174i | −0.293821 | − | 0.508913i | ||||
\(826\) | 12.5332 | − | 37.0146i | 0.436086 | − | 1.28790i | ||||
\(827\) | 28.2671 | 0.982944 | 0.491472 | − | 0.870893i | \(-0.336459\pi\) | ||||
0.491472 | + | 0.870893i | \(0.336459\pi\) | |||||||
\(828\) | −1.91925 | −0.0666984 | ||||||||
\(829\) | 39.6825 | 1.37823 | 0.689116 | − | 0.724651i | \(-0.257999\pi\) | ||||
0.689116 | + | 0.724651i | \(0.257999\pi\) | |||||||
\(830\) | −0.388295 | −0.0134779 | ||||||||
\(831\) | −16.4391 | + | 28.4734i | −0.570267 | + | 0.987731i | ||||
\(832\) | −1.62906 | + | 3.21655i | −0.0564773 | + | 0.111514i | ||||
\(833\) | −34.9730 | + | 14.5490i | −1.21174 | + | 0.504092i | ||||
\(834\) | 3.98321 | − | 6.89912i | 0.137927 | − | 0.238897i | ||||
\(835\) | −0.188512 | − | 0.326512i | −0.00652372 | − | 0.0112994i | ||||
\(836\) | −10.8172 | + | 18.7360i | −0.374121 | + | 0.647997i | ||||
\(837\) | 1.78052 | + | 3.08395i | 0.0615439 | + | 0.106597i | ||||
\(838\) | 3.48277 | 0.120310 | ||||||||
\(839\) | 2.60142 | + | 4.50579i | 0.0898110 | + | 0.155557i | 0.907431 | − | 0.420201i | \(-0.138040\pi\) |
−0.817620 | + | 0.575758i | \(0.804707\pi\) | |||||||
\(840\) | −0.398117 | − | 0.453266i | −0.0137363 | − | 0.0156392i | ||||
\(841\) | 13.0501 | + | 22.6034i | 0.450002 | + | 0.779426i | ||||
\(842\) | 9.30142 | + | 16.1105i | 0.320548 | + | 0.555205i | ||||
\(843\) | 16.8072 | 0.578870 | ||||||||
\(844\) | 3.74446 | + | 6.48560i | 0.128890 | + | 0.223243i | ||||
\(845\) | −2.94646 | + | 0.324206i | −0.101361 | + | 0.0111530i | ||||
\(846\) | −11.1442 | −0.383146 | ||||||||
\(847\) | 0.540003 | − | 1.59480i | 0.0185547 | − | 0.0547981i | ||||
\(848\) | −3.31400 | + | 5.74001i | −0.113803 | + | 0.197113i | ||||
\(849\) | 12.1600 | 0.417329 | ||||||||
\(850\) | 13.3874 | + | 23.1876i | 0.459183 | + | 0.795328i | ||||
\(851\) | −4.01429 | + | 6.95296i | −0.137608 | + | 0.238344i | ||||
\(852\) | −0.0781905 | −0.00267876 | ||||||||
\(853\) | 21.5926 | 0.739318 | 0.369659 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369659 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(854\) | −17.4351 | + | 3.48192i | −0.596618 | + | 0.119149i | ||||
\(855\) | 0.723063 | − | 1.25238i | 0.0247282 | − | 0.0428306i | ||||
\(856\) | 3.27362 | + | 5.67008i | 0.111890 | + | 0.193799i | ||||
\(857\) | −6.31723 | − | 10.9418i | −0.215792 | − | 0.373763i | 0.737725 | − | 0.675101i | \(-0.235900\pi\) |
−0.953517 | + | 0.301338i | \(0.902567\pi\) | |||||||
\(858\) | 12.2809 | − | 0.673613i | 0.419261 | − | 0.0229968i | ||||
\(859\) | 4.17670 | − | 7.23426i | 0.142507 | − | 0.246830i | −0.785933 | − | 0.618312i | \(-0.787817\pi\) |
0.928440 | + | 0.371482i | \(0.121150\pi\) | |||||||
\(860\) | −1.18105 | + | 2.04564i | −0.0402734 | + | 0.0697556i | ||||
\(861\) | 5.55782 | + | 6.32771i | 0.189410 | + | 0.215648i | ||||
\(862\) | −9.52662 | − | 16.5006i | −0.324478 | − | 0.562012i | ||||
\(863\) | −6.28858 | + | 10.8921i | −0.214066 | + | 0.370772i | −0.952983 | − | 0.303023i | \(-0.902004\pi\) |
0.738918 | + | 0.673796i | \(0.235337\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 1.60092 | − | 2.77287i | 0.0544329 | − | 0.0942805i | ||||
\(866\) | 16.7336 | − | 28.9834i | 0.568630 | − | 0.984896i | ||||
\(867\) | 6.14063 | + | 10.6359i | 0.208547 | + | 0.361214i | ||||
\(868\) | 3.02167 | − | 8.92395i | 0.102562 | − | 0.302898i | ||||
\(869\) | 2.76676 | − | 4.79216i | 0.0938558 | − | 0.162563i | ||||
\(870\) | −0.194147 | + | 0.336273i | −0.00658221 | + | 0.0114007i | ||||
\(871\) | −18.1824 | + | 35.9008i | −0.616086 | + | 1.21645i | ||||
\(872\) | −0.797093 | − | 1.38061i | −0.0269930 | − | 0.0467532i | ||||
\(873\) | 6.82663 | + | 11.8241i | 0.231047 | + | 0.400184i | ||||
\(874\) | −6.08607 | + | 10.5414i | −0.205864 | + | 0.356567i | ||||
\(875\) | 1.92476 | − | 5.68442i | 0.0650686 | − | 0.192168i | ||||
\(876\) | −12.6344 | −0.426877 | ||||||||
\(877\) | 6.49901 | 0.219456 | 0.109728 | − | 0.993962i | \(-0.465002\pi\) | ||||
0.109728 | + | 0.993962i | \(0.465002\pi\) | |||||||
\(878\) | 19.0229 | − | 32.9487i | 0.641993 | − | 1.11196i | ||||
\(879\) | −13.8954 | − | 24.0675i | −0.468680 | − | 0.811778i | ||||
\(880\) | −0.777821 | −0.0262203 | ||||||||
\(881\) | 6.17234 | − | 10.6908i | 0.207951 | − | 0.360182i | −0.743118 | − | 0.669161i | \(-0.766654\pi\) |
0.951069 | + | 0.308979i | \(0.0999871\pi\) | |||||||
\(882\) | 0.903072 | − | 6.94150i | 0.0304080 | − | 0.233733i | ||||
\(883\) | 42.2001 | 1.42015 | 0.710073 | − | 0.704128i | \(-0.248662\pi\) | ||||
0.710073 | + | 0.704128i | \(0.248662\pi\) | |||||||
\(884\) | −19.4811 | + | 1.06855i | −0.655221 | + | 0.0359393i | ||||
\(885\) | 1.68397 | + | 2.91672i | 0.0566060 | + | 0.0980444i | ||||
\(886\) | 8.70933 | 0.292596 | ||||||||
\(887\) | 17.1690 | + | 29.7376i | 0.576478 | + | 0.998490i | 0.995879 | + | 0.0906888i | \(0.0289068\pi\) |
−0.419401 | + | 0.907801i | \(0.637760\pi\) | |||||||
\(888\) | 2.09160 | + | 3.62276i | 0.0701895 | + | 0.121572i | ||||
\(889\) | 22.3681 | + | 25.4667i | 0.750204 | + | 0.854125i | ||||
\(890\) | −2.00037 | − | 3.46475i | −0.0670527 | − | 0.116139i | ||||
\(891\) | 3.41122 | 0.114280 | ||||||||
\(892\) | −8.41325 | − | 14.5722i | −0.281696 | − | 0.487913i | ||||
\(893\) | −35.3391 | + | 61.2091i | −1.18258 | + | 2.04828i | ||||
\(894\) | −1.34679 | − | 2.33271i | −0.0450434 | − | 0.0780175i | ||||
\(895\) | −1.06408 | + | 1.84304i | −0.0355682 | + | 0.0616059i | ||||
\(896\) | 2.59452 | − | 0.518144i | 0.0866768 | − | 0.0173100i | ||||
\(897\) | 6.90955 | − | 0.378993i | 0.230703 | − | 0.0126542i | ||||
\(898\) | 11.4930 | − | 19.9065i | 0.383527 | − | 0.664288i | ||||
\(899\) | −6.06413 | −0.202250 | ||||||||
\(900\) | −4.94801 | −0.164934 | ||||||||
\(901\) | −35.8655 | −1.19485 | ||||||||
\(902\) | 10.8586 | 0.361551 | ||||||||
\(903\) | −26.8772 | + | 5.36757i | −0.894417 | + | 0.178621i | ||||
\(904\) | 4.12255 | + | 7.14047i | 0.137114 | + | 0.237488i | ||||
\(905\) | 0.129786 | − | 0.224795i | 0.00431422 | − | 0.00747244i | ||||
\(906\) | 6.56432 | − | 11.3697i | 0.218085 | − | 0.377734i | ||||
\(907\) | −18.7208 | −0.621614 | −0.310807 | − | 0.950473i | \(-0.600599\pi\) | ||||
−0.310807 | + | 0.950473i | \(0.600599\pi\) | |||||||
\(908\) | 2.11607 | + | 3.66514i | 0.0702243 | + | 0.121632i | ||||
\(909\) | −16.5165 | −0.547816 | ||||||||
\(910\) | 1.52278 | + | 1.55321i | 0.0504798 | + | 0.0514883i | ||||
\(911\) | −30.3513 | −1.00558 | −0.502791 | − | 0.864408i | \(-0.667694\pi\) | ||||
−0.502791 | + | 0.864408i | \(0.667694\pi\) | |||||||
\(912\) | 3.17107 | + | 5.49246i | 0.105005 | + | 0.181873i | ||||
\(913\) | −5.80898 | −0.192249 | ||||||||
\(914\) | 5.79493 | − | 10.0371i | 0.191679 | − | 0.331998i | ||||
\(915\) | 0.766142 | − | 1.32700i | 0.0253279 | − | 0.0438691i | ||||
\(916\) | −6.86498 | − | 11.8905i | −0.226825 | − | 0.392873i | ||||
\(917\) | 6.14460 | + | 6.99577i | 0.202912 | + | 0.231021i | ||||
\(918\) | −5.41122 | −0.178597 | ||||||||
\(919\) | 40.7516 | 1.34427 | 0.672135 | − | 0.740428i | \(-0.265377\pi\) | ||||
0.672135 | + | 0.740428i | \(0.265377\pi\) | |||||||
\(920\) | −0.437624 | −0.0144280 | ||||||||
\(921\) | 14.6849 | 0.483883 | ||||||||
\(922\) | 17.4236 | − | 30.1785i | 0.573814 | − | 0.993876i | ||||
\(923\) | 0.281497 | − | 0.0154403i | 0.00926557 | − | 0.000508223i | ||||
\(924\) | −5.95593 | − | 6.78098i | −0.195936 | − | 0.223078i | ||||
\(925\) | −10.3492 | + | 17.9254i | −0.340281 | + | 0.589384i | ||||
\(926\) | −19.7667 | − | 34.2369i | −0.649573 | − | 1.12509i | ||||
\(927\) | −3.17961 | + | 5.50725i | −0.104432 | + | 0.180882i | ||||
\(928\) | −0.851453 | − | 1.47476i | −0.0279503 | − | 0.0484114i | ||||
\(929\) | 5.21956 | 0.171248 | 0.0856242 | − | 0.996328i | \(-0.472712\pi\) | ||||
0.0856242 | + | 0.996328i | \(0.472712\pi\) | |||||||
\(930\) | 0.405992 | + | 0.703199i | 0.0133130 | + | 0.0230588i | ||||
\(931\) | −35.2622 | − | 26.9721i | −1.15567 | − | 0.883974i | ||||
\(932\) | −3.85349 | − | 6.67444i | −0.126225 | − | 0.218629i | ||||
\(933\) | −3.86348 | − | 6.69174i | −0.126484 | − | 0.219078i | ||||
\(934\) | −0.850382 | −0.0278253 | ||||||||
\(935\) | −2.10448 | − | 3.64506i | −0.0688238 | − | 0.119206i | ||||
\(936\) | 1.62906 | − | 3.21655i | 0.0532474 | − | 0.105136i | ||||
\(937\) | −31.2199 | −1.01991 | −0.509956 | − | 0.860201i | \(-0.670338\pi\) | ||||
−0.509956 | + | 0.860201i | \(0.670338\pi\) | |||||||
\(938\) | 28.9582 | − | 5.78316i | 0.945519 | − | 0.188827i | ||||
\(939\) | 10.0982 | − | 17.4906i | 0.329542 | − | 0.570784i | ||||
\(940\) | −2.54109 | −0.0828812 | ||||||||
\(941\) | −25.3480 | − | 43.9041i | −0.826322 | − | 1.43123i | −0.900904 | − | 0.434018i | \(-0.857096\pi\) |
0.0745820 | − | 0.997215i | \(-0.476238\pi\) | |||||||
\(942\) | −1.59071 | + | 2.75520i | −0.0518283 | + | 0.0897692i | ||||
\(943\) | 6.10934 | 0.198947 | ||||||||
\(944\) | −14.7704 | −0.480737 | ||||||||
\(945\) | 0.398117 | + | 0.453266i | 0.0129508 | + | 0.0147448i | ||||
\(946\) | −17.6688 | + | 30.6032i | −0.574461 | + | 0.994996i | ||||
\(947\) | −24.1704 | − | 41.8643i | −0.785431 | − | 1.36041i | −0.928741 | − | 0.370729i | \(-0.879108\pi\) |
0.143310 | − | 0.989678i | \(-0.454225\pi\) | |||||||
\(948\) | −0.811077 | − | 1.40483i | −0.0263425 | − | 0.0456266i | ||||
\(949\) | 45.4857 | − | 2.49492i | 1.47653 | − | 0.0809885i | ||||
\(950\) | −15.6905 | + | 27.1767i | −0.509066 | + | 0.881729i | ||||
\(951\) | −7.36088 | + | 12.7494i | −0.238693 | + | 0.413428i | ||||
\(952\) | 9.44790 | + | 10.7567i | 0.306208 | + | 0.348626i | ||||
\(953\) | 0.444682 | + | 0.770211i | 0.0144046 | + | 0.0249496i | 0.873138 | − | 0.487473i | \(-0.162081\pi\) |
−0.858733 | + | 0.512423i | \(0.828748\pi\) | |||||||
\(954\) | 3.31400 | − | 5.74001i | 0.107295 | − | 0.185840i | ||||
\(955\) | 2.06187 | − | 3.57125i | 0.0667204 | − | 0.115563i | ||||
\(956\) | 12.6095 | − | 21.8402i | 0.407819 | − | 0.706363i | ||||
\(957\) | −2.90449 | + | 5.03073i | −0.0938889 | + | 0.162620i | ||||
\(958\) | 5.78732 | + | 10.0239i | 0.186980 | + | 0.323859i | ||||
\(959\) | 30.8961 | + | 35.1760i | 0.997688 | + | 1.13589i | ||||
\(960\) | −0.114009 | + | 0.197470i | −0.00367964 | + | 0.00637332i | ||||
\(961\) | 9.15948 | − | 15.8647i | 0.295467 | − | 0.511764i | ||||
\(962\) | −8.24543 | − | 12.6294i | −0.265843 | − | 0.407188i | ||||
\(963\) | −3.27362 | − | 5.67008i | −0.105491 | − | 0.182716i | ||||
\(964\) | −13.9183 | − | 24.1073i | −0.448280 | − | 0.776443i | ||||
\(965\) | −0.664209 | + | 1.15044i | −0.0213817 | + | 0.0370341i | ||||
\(966\) | −3.35098 | − | 3.81517i | −0.107816 | − | 0.122751i | ||||
\(967\) | 4.75544 | 0.152925 | 0.0764623 | − | 0.997072i | \(-0.475638\pi\) | ||||
0.0764623 | + | 0.997072i | \(0.475638\pi\) | |||||||
\(968\) | −0.636396 | −0.0204545 | ||||||||
\(969\) | −17.1594 | + | 29.7209i | −0.551238 | + | 0.954772i | ||||
\(970\) | 1.55660 | + | 2.69611i | 0.0499794 | + | 0.0865669i | ||||
\(971\) | 1.55188 | 0.0498022 | 0.0249011 | − | 0.999690i | \(-0.492073\pi\) | ||||
0.0249011 | + | 0.999690i | \(0.492073\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 20.6690 | − | 4.12775i | 0.662619 | − | 0.132330i | ||||
\(974\) | 13.9320 | 0.446412 | ||||||||
\(975\) | 17.8135 | − | 0.977083i | 0.570489 | − | 0.0312917i | ||||
\(976\) | 3.35999 | + | 5.81968i | 0.107551 | + | 0.186283i | ||||
\(977\) | −31.5419 | −1.00911 | −0.504557 | − | 0.863378i | \(-0.668344\pi\) | ||||
−0.504557 | + | 0.863378i | \(0.668344\pi\) | |||||||
\(978\) | 8.14702 | + | 14.1111i | 0.260513 | + | 0.451222i | ||||
\(979\) | −29.9261 | − | 51.8335i | −0.956442 | − | 1.65661i | ||||
\(980\) | 0.205917 | − | 1.58279i | 0.00657779 | − | 0.0505604i | ||||
\(981\) | 0.797093 | + | 1.38061i | 0.0254492 | + | 0.0440793i | ||||
\(982\) | 9.53433 | 0.304253 | ||||||||
\(983\) | −15.7150 | − | 27.2192i | −0.501230 | − | 0.868157i | −0.999999 | − | 0.00142135i | \(-0.999548\pi\) |
0.498769 | − | 0.866735i | \(-0.333786\pi\) | |||||||
\(984\) | 1.59160 | − | 2.75673i | 0.0507383 | − | 0.0878813i | ||||
\(985\) | 2.36062 | + | 4.08871i | 0.0752156 | + | 0.130277i | ||||
\(986\) | 4.60740 | − | 7.98025i | 0.146729 | − | 0.254143i | ||||
\(987\) | −19.4576 | − | 22.1530i | −0.619343 | − | 0.705138i | ||||
\(988\) | −12.5009 | − | 19.1474i | −0.397706 | − | 0.609160i | ||||
\(989\) | −9.94095 | + | 17.2182i | −0.316104 | + | 0.547508i | ||||
\(990\) | 0.777821 | 0.0247208 | ||||||||
\(991\) | 0.605608 | 0.0192378 | 0.00961888 | − | 0.999954i | \(-0.496938\pi\) | ||||
0.00961888 | + | 0.999954i | \(0.496938\pi\) | |||||||
\(992\) | −3.56104 | −0.113063 | ||||||||
\(993\) | −4.10872 | −0.130386 | ||||||||
\(994\) | −0.136519 | − | 0.155431i | −0.00433013 | − | 0.00492996i | ||||
\(995\) | −1.86957 | − | 3.23820i | −0.0592695 | − | 0.102658i | ||||
\(996\) | −0.851453 | + | 1.47476i | −0.0269793 | + | 0.0467296i | ||||
\(997\) | −0.184170 | + | 0.318992i | −0.00583272 | + | 0.0101026i | −0.868927 | − | 0.494940i | \(-0.835190\pi\) |
0.863094 | + | 0.505043i | \(0.168523\pi\) | |||||||
\(998\) | 43.8270 | 1.38732 | ||||||||
\(999\) | −2.09160 | − | 3.62276i | −0.0661753 | − | 0.114619i |
(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 | 546.2.k.e.373.3 | yes | 10 | |
3.2 | odd | 2 | 1638.2.p.j.919.3 | 10 | |||
7.4 | even | 3 | 546.2.j.e.529.3 | yes | 10 | ||
13.3 | even | 3 | 546.2.j.e.289.3 | ✓ | 10 | ||
21.11 | odd | 6 | 1638.2.m.k.1621.3 | 10 | |||
39.29 | odd | 6 | 1638.2.m.k.289.3 | 10 | |||
91.81 | even | 3 | inner | 546.2.k.e.445.3 | yes | 10 | |
273.263 | odd | 6 | 1638.2.p.j.991.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.3 | ✓ | 10 | 13.3 | even | 3 | ||
546.2.j.e.529.3 | yes | 10 | 7.4 | even | 3 | ||
546.2.k.e.373.3 | yes | 10 | 1.1 | even | 1 | trivial | |
546.2.k.e.445.3 | yes | 10 | 91.81 | even | 3 | inner | |
1638.2.m.k.289.3 | 10 | 39.29 | odd | 6 | |||
1638.2.m.k.1621.3 | 10 | 21.11 | odd | 6 | |||
1638.2.p.j.919.3 | 10 | 3.2 | odd | 2 | |||
1638.2.p.j.991.3 | 10 | 273.263 | odd | 6 |