Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
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, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (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 | 289.3 | ||
Root | \(-0.114009 + 0.197470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.289 |
Dual form | 546.2.j.e.529.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 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 | ||||
\(7\) | −2.59452 | + | 0.518144i | −0.980636 | + | 0.195840i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.114009 | + | 0.197470i | −0.0360529 | + | 0.0624455i | ||||
\(11\) | −1.70561 | + | 2.95420i | −0.514260 | + | 0.890725i | 0.485603 | + | 0.874180i | \(0.338600\pi\) |
−0.999863 | + | 0.0165453i | \(0.994733\pi\) | |||||||
\(12\) | 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 | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.41122 | −1.31241 | −0.656206 | − | 0.754581i | \(-0.727840\pi\) | ||||
−0.656206 | + | 0.754581i | \(0.727840\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −3.17107 | − | 5.49246i | −0.727494 | − | 1.26006i | −0.957939 | − | 0.286971i | \(-0.907352\pi\) |
0.230446 | − | 0.973085i | \(-0.425982\pi\) | |||||||
\(20\) | 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 | ||||
\(23\) | −1.91925 | −0.400190 | −0.200095 | − | 0.979776i | \(-0.564125\pi\) | ||||
−0.200095 | + | 0.979776i | \(0.564125\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 2.47400 | + | 4.28510i | 0.494801 | + | 0.857020i | ||||
\(26\) | 1.62906 | + | 3.21655i | 0.319484 | + | 0.630817i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.59452 | + | 0.518144i | −0.490318 | + | 0.0979200i | ||||
\(29\) | 0.851453 | + | 1.47476i | 0.158111 | + | 0.273856i | 0.934187 | − | 0.356783i | \(-0.116126\pi\) |
−0.776077 | + | 0.630639i | \(0.782793\pi\) | |||||||
\(30\) | 0.114009 | + | 0.197470i | 0.0208152 | + | 0.0360529i | ||||
\(31\) | −1.78052 | − | 3.08395i | −0.319791 | − | 0.553895i | 0.660653 | − | 0.750691i | \(-0.270279\pi\) |
−0.980444 | + | 0.196797i | \(0.936946\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.70561 | + | 2.95420i | 0.296908 | + | 0.514260i | ||||
\(34\) | 5.41122 | 0.928016 | ||||||||
\(35\) | −0.193482 | + | 0.571413i | −0.0327043 | + | 0.0965864i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −4.18320 | −0.687713 | −0.343857 | − | 0.939022i | \(-0.611733\pi\) | ||||
−0.343857 | + | 0.939022i | \(0.611733\pi\) | |||||||
\(38\) | 3.17107 | + | 5.49246i | 0.514416 | + | 0.890994i | ||||
\(39\) | −3.60014 | − | 0.197470i | −0.576484 | − | 0.0316205i | ||||
\(40\) | −0.114009 | + | 0.197470i | −0.0180265 | + | 0.0312227i | ||||
\(41\) | 1.59160 | + | 2.75673i | 0.248566 | + | 0.430529i | 0.963128 | − | 0.269043i | \(-0.0867074\pi\) |
−0.714562 | + | 0.699572i | \(0.753374\pi\) | |||||||
\(42\) | 0.848534 | − | 2.50599i | 0.130932 | − | 0.386683i | ||||
\(43\) | 5.17961 | − | 8.97135i | 0.789883 | − | 1.36812i | −0.136154 | − | 0.990688i | \(-0.543474\pi\) |
0.926038 | − | 0.377431i | \(-0.123192\pi\) | |||||||
\(44\) | −1.70561 | + | 2.95420i | −0.257130 | + | 0.445362i | ||||
\(45\) | −0.228019 | −0.0339910 | ||||||||
\(46\) | 1.91925 | 0.282977 | ||||||||
\(47\) | −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 | ||||
\(49\) | 6.46305 | − | 2.68867i | 0.923293 | − | 0.384095i | ||||
\(50\) | −2.47400 | − | 4.28510i | −0.349877 | − | 0.606005i | ||||
\(51\) | −2.70561 | + | 4.68625i | −0.378861 | + | 0.656206i | ||||
\(52\) | −1.62906 | − | 3.21655i | −0.225909 | − | 0.446055i | ||||
\(53\) | −3.31400 | − | 5.74001i | −0.455212 | − | 0.788451i | 0.543488 | − | 0.839417i | \(-0.317103\pi\) |
−0.998700 | + | 0.0509659i | \(0.983770\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.388911 | + | 0.673613i | 0.0524407 | + | 0.0908299i | ||||
\(56\) | 2.59452 | − | 0.518144i | 0.346707 | − | 0.0692399i | ||||
\(57\) | −6.34214 | −0.840037 | ||||||||
\(58\) | −0.851453 | − | 1.47476i | −0.111801 | − | 0.193646i | ||||
\(59\) | −14.7704 | −1.92295 | −0.961474 | − | 0.274897i | \(-0.911356\pi\) | ||||
−0.961474 | + | 0.274897i | \(0.911356\pi\) | |||||||
\(60\) | −0.114009 | − | 0.197470i | −0.0147185 | − | 0.0254933i | ||||
\(61\) | 3.35999 | + | 5.81968i | 0.430203 | + | 0.745134i | 0.996891 | − | 0.0787991i | \(-0.0251086\pi\) |
−0.566687 | + | 0.823933i | \(0.691775\pi\) | |||||||
\(62\) | 1.78052 | + | 3.08395i | 0.226127 | + | 0.391663i | ||||
\(63\) | 1.74599 | + | 1.98785i | 0.219973 | + | 0.250445i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.820899 | − | 0.0450268i | −0.101820 | − | 0.00558489i | ||||
\(66\) | −1.70561 | − | 2.95420i | −0.209946 | − | 0.363637i | ||||
\(67\) | −5.58065 | + | 9.66597i | −0.681785 | + | 1.18089i | 0.292651 | + | 0.956219i | \(0.405463\pi\) |
−0.974436 | + | 0.224667i | \(0.927871\pi\) | |||||||
\(68\) | −5.41122 | −0.656206 | ||||||||
\(69\) | −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 | −0.868336 | − | 0.495976i | \(-0.834810\pi\) |
0.863696 | + | 0.504013i | \(0.168144\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −6.31721 | − | 10.9417i | −0.739373 | − | 1.28063i | −0.952778 | − | 0.303668i | \(-0.901789\pi\) |
0.213404 | − | 0.976964i | \(-0.431545\pi\) | |||||||
\(74\) | 4.18320 | 0.486287 | ||||||||
\(75\) | 4.94801 | 0.571347 | ||||||||
\(76\) | −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 | \(0.137579\pi\) | |||||||
\(80\) | 0.114009 | − | 0.197470i | 0.0127466 | − | 0.0220778i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.59160 | − | 2.75673i | −0.175763 | − | 0.304430i | ||||
\(83\) | −1.70291 | −0.186918 | −0.0934592 | − | 0.995623i | \(-0.529792\pi\) | ||||
−0.0934592 | + | 0.995623i | \(0.529792\pi\) | |||||||
\(84\) | −0.848534 | + | 2.50599i | −0.0925826 | + | 0.273426i | ||||
\(85\) | −0.616929 | + | 1.06855i | −0.0669154 | + | 0.115901i | ||||
\(86\) | −5.17961 | + | 8.97135i | −0.558532 | + | 0.967406i | ||||
\(87\) | 1.70291 | 0.182571 | ||||||||
\(88\) | 1.70561 | − | 2.95420i | 0.181818 | − | 0.314919i | ||||
\(89\) | 17.5457 | 1.85984 | 0.929920 | − | 0.367762i | \(-0.119876\pi\) | ||||
0.929920 | + | 0.367762i | \(0.119876\pi\) | |||||||
\(90\) | 0.228019 | 0.0240353 | ||||||||
\(91\) | 5.89325 | + | 7.50131i | 0.617780 | + | 0.786351i | ||||
\(92\) | −1.91925 | −0.200095 | ||||||||
\(93\) | −3.56104 | −0.369263 | ||||||||
\(94\) | 5.57211 | − | 9.65117i | 0.574719 | − | 0.995443i | ||||
\(95\) | −1.44613 | −0.148369 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 6.82663 | − | 11.8241i | 0.693140 | − | 1.20055i | −0.277664 | − | 0.960678i | \(-0.589560\pi\) |
0.970804 | − | 0.239875i | \(-0.0771064\pi\) | |||||||
\(98\) | −6.46305 | + | 2.68867i | −0.652867 | + | 0.271596i | ||||
\(99\) | 3.41122 | 0.342840 | ||||||||
\(100\) | 2.47400 | + | 4.28510i | 0.247400 | + | 0.428510i | ||||
\(101\) | 8.25823 | − | 14.3037i | 0.821724 | − | 1.42327i | −0.0826732 | − | 0.996577i | \(-0.526346\pi\) |
0.904397 | − | 0.426691i | \(-0.140321\pi\) | |||||||
\(102\) | 2.70561 | − | 4.68625i | 0.267895 | − | 0.464008i | ||||
\(103\) | −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 | ||||
\(107\) | 6.54724 | 0.632945 | 0.316473 | − | 0.948602i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948602i | \(0.397501\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 0.797093 | + | 1.38061i | 0.0763477 | + | 0.132238i | 0.901672 | − | 0.432422i | \(-0.142341\pi\) |
−0.825324 | + | 0.564660i | \(0.809007\pi\) | |||||||
\(110\) | −0.388911 | − | 0.673613i | −0.0370812 | − | 0.0642265i | ||||
\(111\) | −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 | −0.992156 | − | 0.125009i | \(-0.960104\pi\) |
0.604339 | + | 0.796728i | \(0.293437\pi\) | |||||||
\(114\) | 6.34214 | 0.593996 | ||||||||
\(115\) | −0.218812 | + | 0.378993i | −0.0204043 | + | 0.0353413i | ||||
\(116\) | 0.851453 | + | 1.47476i | 0.0790555 | + | 0.136928i | ||||
\(117\) | −1.97108 | + | 3.01908i | −0.182227 | + | 0.279114i | ||||
\(118\) | 14.7704 | 1.35973 | ||||||||
\(119\) | 14.0395 | − | 2.80379i | 1.28700 | − | 0.257023i | ||||
\(120\) | 0.114009 | + | 0.197470i | 0.0104076 | + | 0.0180265i | ||||
\(121\) | −0.318198 | − | 0.551135i | −0.0289271 | − | 0.0501032i | ||||
\(122\) | −3.35999 | − | 5.81968i | −0.304200 | − | 0.526889i | ||||
\(123\) | 3.18320 | 0.287019 | ||||||||
\(124\) | −1.78052 | − | 3.08395i | −0.159896 | − | 0.276947i | ||||
\(125\) | 2.26833 | 0.202886 | ||||||||
\(126\) | −1.74599 | − | 1.98785i | −0.155545 | − | 0.177091i | ||||
\(127\) | −6.40560 | − | 11.0948i | −0.568405 | − | 0.984506i | −0.996724 | − | 0.0808783i | \(-0.974227\pi\) |
0.428319 | − | 0.903627i | \(-0.359106\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.17961 | − | 8.97135i | −0.456039 | − | 0.789883i | ||||
\(130\) | 0.820899 | + | 0.0450268i | 0.0719976 | + | 0.00394912i | ||||
\(131\) | −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 | ||||
\(133\) | 11.0733 | + | 12.6072i | 0.960176 | + | 1.09318i | ||||
\(134\) | 5.58065 | − | 9.66597i | 0.482095 | − | 0.835012i | ||||
\(135\) | −0.114009 | + | 0.197470i | −0.00981236 | + | 0.0169955i | ||||
\(136\) | 5.41122 | 0.464008 | ||||||||
\(137\) | 17.6955 | 1.51183 | 0.755915 | − | 0.654669i | \(-0.227192\pi\) | ||||
0.755915 | + | 0.654669i | \(0.227192\pi\) | |||||||
\(138\) | 0.959623 | − | 1.66212i | 0.0816885 | − | 0.141489i | ||||
\(139\) | 3.98321 | − | 6.89912i | 0.337851 | − | 0.585176i | −0.646177 | − | 0.763188i | \(-0.723633\pi\) |
0.984028 | + | 0.178012i | \(0.0569665\pi\) | |||||||
\(140\) | −0.193482 | + | 0.571413i | −0.0163522 | + | 0.0482932i | ||||
\(141\) | 5.57211 | + | 9.65117i | 0.469256 | + | 0.812775i | ||||
\(142\) | 0.0390952 | − | 0.0677149i | 0.00328080 | − | 0.00568251i | ||||
\(143\) | 12.2809 | + | 0.673613i | 1.02698 | + | 0.0563303i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.388295 | 0.0322461 | ||||||||
\(146\) | 6.31721 | + | 10.9417i | 0.522816 | + | 0.905544i | ||||
\(147\) | 0.903072 | − | 6.94150i | 0.0744842 | − | 0.572525i | ||||
\(148\) | −4.18320 | −0.343857 | ||||||||
\(149\) | −1.34679 | − | 2.33271i | −0.110333 | − | 0.191103i | 0.805571 | − | 0.592499i | \(-0.201859\pi\) |
−0.915905 | + | 0.401396i | \(0.868525\pi\) | |||||||
\(150\) | −4.94801 | −0.404003 | ||||||||
\(151\) | 6.56432 | + | 11.3697i | 0.534197 | + | 0.925256i | 0.999202 | + | 0.0399480i | \(0.0127192\pi\) |
−0.465005 | + | 0.885308i | \(0.653947\pi\) | |||||||
\(152\) | 3.17107 | + | 5.49246i | 0.257208 | + | 0.445497i | ||||
\(153\) | 2.70561 | + | 4.68625i | 0.218735 | + | 0.378861i | ||||
\(154\) | −2.89453 | + | 8.54848i | −0.233248 | + | 0.688856i | ||||
\(155\) | −0.811985 | −0.0652202 | ||||||||
\(156\) | −3.60014 | − | 0.197470i | −0.288242 | − | 0.0158103i | ||||
\(157\) | −1.59071 | − | 2.75520i | −0.126953 | − | 0.219889i | 0.795542 | − | 0.605899i | \(-0.207186\pi\) |
−0.922495 | + | 0.386010i | \(0.873853\pi\) | |||||||
\(158\) | −0.811077 | + | 1.40483i | −0.0645258 | + | 0.111762i | ||||
\(159\) | −6.62799 | −0.525634 | ||||||||
\(160\) | −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 | ||||
\(163\) | 8.14702 | + | 14.1111i | 0.638124 | + | 1.10526i | 0.985844 | + | 0.167665i | \(0.0536226\pi\) |
−0.347720 | + | 0.937598i | \(0.613044\pi\) | |||||||
\(164\) | 1.59160 | + | 2.75673i | 0.124283 | + | 0.215264i | ||||
\(165\) | 0.777821 | 0.0605533 | ||||||||
\(166\) | 1.70291 | 0.132171 | ||||||||
\(167\) | 0.826739 | + | 1.43195i | 0.0639750 | + | 0.110808i | 0.896239 | − | 0.443572i | \(-0.146289\pi\) |
−0.832264 | + | 0.554380i | \(0.812956\pi\) | |||||||
\(168\) | 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 | ||||
\(171\) | −3.17107 | + | 5.49246i | −0.242498 | + | 0.420019i | ||||
\(172\) | 5.17961 | − | 8.97135i | 0.394942 | − | 0.684059i | ||||
\(173\) | −7.02100 | − | 12.1607i | −0.533797 | − | 0.924563i | −0.999221 | − | 0.0394751i | \(-0.987431\pi\) |
0.465424 | − | 0.885088i | \(-0.345902\pi\) | |||||||
\(174\) | −1.70291 | −0.129097 | ||||||||
\(175\) | −8.63915 | − | 9.83588i | −0.653058 | − | 0.743523i | ||||
\(176\) | −1.70561 | + | 2.95420i | −0.128565 | + | 0.222681i | ||||
\(177\) | −7.38522 | + | 12.7916i | −0.555107 | + | 0.961474i | ||||
\(178\) | −17.5457 | −1.31511 | ||||||||
\(179\) | 4.66663 | − | 8.08283i | 0.348800 | − | 0.604139i | −0.637237 | − | 0.770668i | \(-0.719923\pi\) |
0.986037 | + | 0.166529i | \(0.0532559\pi\) | |||||||
\(180\) | −0.228019 | −0.0169955 | ||||||||
\(181\) | 1.13838 | 0.0846148 | 0.0423074 | − | 0.999105i | \(-0.486529\pi\) | ||||
0.0423074 | + | 0.999105i | \(0.486529\pi\) | |||||||
\(182\) | −5.89325 | − | 7.50131i | −0.436837 | − | 0.556034i | ||||
\(183\) | 6.71999 | 0.496756 | ||||||||
\(184\) | 1.91925 | 0.141489 | ||||||||
\(185\) | −0.476924 | + | 0.826056i | −0.0350641 | + | 0.0607328i | ||||
\(186\) | 3.56104 | 0.261108 | ||||||||
\(187\) | 9.22941 | − | 15.9858i | 0.674922 | − | 1.16900i | ||||
\(188\) | −5.57211 | + | 9.65117i | −0.406388 | + | 0.703884i | ||||
\(189\) | 2.59452 | − | 0.518144i | 0.188723 | − | 0.0376894i | ||||
\(190\) | 1.44613 | 0.104913 | ||||||||
\(191\) | −9.04253 | − | 15.6621i | −0.654294 | − | 1.13327i | −0.982070 | − | 0.188515i | \(-0.939632\pi\) |
0.327776 | − | 0.944755i | \(-0.393701\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2.91296 | − | 5.04539i | 0.209679 | − | 0.363175i | −0.741934 | − | 0.670473i | \(-0.766091\pi\) |
0.951614 | + | 0.307297i | \(0.0994246\pi\) | |||||||
\(194\) | −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 | −0.953572 | − | 0.301165i | \(-0.902625\pi\) |
0.215970 | − | 0.976400i | \(-0.430709\pi\) | |||||||
\(198\) | −3.41122 | −0.242425 | ||||||||
\(199\) | −16.3984 | −1.16245 | −0.581227 | − | 0.813741i | \(-0.697427\pi\) | ||||
−0.581227 | + | 0.813741i | \(0.697427\pi\) | |||||||
\(200\) | −2.47400 | − | 4.28510i | −0.174938 | − | 0.303002i | ||||
\(201\) | 5.58065 | + | 9.66597i | 0.393629 | + | 0.681785i | ||||
\(202\) | −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 | ||||
\(205\) | 0.725829 | 0.0506941 | ||||||||
\(206\) | 3.17961 | − | 5.50725i | 0.221534 | − | 0.383708i | ||||
\(207\) | 0.959623 | + | 1.66212i | 0.0666984 | + | 0.115525i | ||||
\(208\) | −1.62906 | − | 3.21655i | −0.112955 | − | 0.223027i | ||||
\(209\) | 21.6344 | 1.49648 | ||||||||
\(210\) | −0.398117 | − | 0.453266i | −0.0274727 | − | 0.0312783i | ||||
\(211\) | 3.74446 | + | 6.48560i | 0.257779 | + | 0.446487i | 0.965647 | − | 0.259858i | \(-0.0836759\pi\) |
−0.707867 | + | 0.706345i | \(0.750343\pi\) | |||||||
\(212\) | −3.31400 | − | 5.74001i | −0.227606 | − | 0.394226i | ||||
\(213\) | 0.0390952 | + | 0.0677149i | 0.00267876 | + | 0.00463975i | ||||
\(214\) | −6.54724 | −0.447560 | ||||||||
\(215\) | −1.18105 | − | 2.04564i | −0.0805468 | − | 0.139511i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.21753 | + | 7.07881i | 0.422073 | + | 0.480541i | ||||
\(218\) | −0.797093 | − | 1.38061i | −0.0539860 | − | 0.0935064i | ||||
\(219\) | −12.6344 | −0.853755 | ||||||||
\(220\) | 0.388911 | + | 0.673613i | 0.0262203 | + | 0.0454150i | ||||
\(221\) | 8.81517 | + | 17.4054i | 0.592973 | + | 1.17082i | ||||
\(222\) | 2.09160 | − | 3.62276i | 0.140379 | − | 0.243143i | ||||
\(223\) | −8.41325 | − | 14.5722i | −0.563393 | − | 0.975825i | −0.997197 | − | 0.0748181i | \(-0.976162\pi\) |
0.433804 | − | 0.901007i | \(-0.357171\pi\) | |||||||
\(224\) | 2.59452 | − | 0.518144i | 0.173354 | − | 0.0346199i | ||||
\(225\) | 2.47400 | − | 4.28510i | 0.164934 | − | 0.285673i | ||||
\(226\) | 4.12255 | − | 7.14047i | 0.274228 | − | 0.474977i | ||||
\(227\) | −4.23214 | −0.280897 | −0.140449 | − | 0.990088i | \(-0.544854\pi\) | ||||
−0.140449 | + | 0.990088i | \(0.544854\pi\) | |||||||
\(228\) | −6.34214 | −0.420019 | ||||||||
\(229\) | −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 | ||||
\(231\) | −5.95593 | − | 6.78098i | −0.391872 | − | 0.446155i | ||||
\(232\) | −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 | \(0.247903\pi\) | |||||||
\(234\) | 1.97108 | − | 3.01908i | 0.128854 | − | 0.197363i | ||||
\(235\) | 1.27054 | + | 2.20065i | 0.0828812 | + | 0.143554i | ||||
\(236\) | −14.7704 | −0.961474 | ||||||||
\(237\) | −0.811077 | − | 1.40483i | −0.0526851 | − | 0.0912532i | ||||
\(238\) | −14.0395 | + | 2.80379i | −0.910046 | + | 0.181743i | ||||
\(239\) | −25.2189 | −1.63128 | −0.815638 | − | 0.578562i | \(-0.803614\pi\) | ||||
−0.815638 | + | 0.578562i | \(0.803614\pi\) | |||||||
\(240\) | −0.114009 | − | 0.197470i | −0.00735927 | − | 0.0127466i | ||||
\(241\) | 27.8367 | 1.79312 | 0.896560 | − | 0.442923i | \(-0.146059\pi\) | ||||
0.896560 | + | 0.442923i | \(0.146059\pi\) | |||||||
\(242\) | 0.318198 | + | 0.551135i | 0.0204545 | + | 0.0354283i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.35999 | + | 5.81968i | 0.215102 | + | 0.372567i | ||||
\(245\) | 0.205917 | − | 1.58279i | 0.0131556 | − | 0.101121i | ||||
\(246\) | −3.18320 | −0.202953 | ||||||||
\(247\) | −12.5009 | + | 19.1474i | −0.795413 | + | 1.21832i | ||||
\(248\) | 1.78052 | + | 3.08395i | 0.113063 | + | 0.195831i | ||||
\(249\) | −0.851453 | + | 1.47476i | −0.0539587 | + | 0.0934592i | ||||
\(250\) | −2.26833 | −0.143462 | ||||||||
\(251\) | 2.12395 | − | 3.67878i | 0.134062 | − | 0.232203i | −0.791177 | − | 0.611588i | \(-0.790531\pi\) |
0.925239 | + | 0.379385i | \(0.123864\pi\) | |||||||
\(252\) | 1.74599 | + | 1.98785i | 0.109987 | + | 0.125223i | ||||
\(253\) | 3.27348 | − | 5.66984i | 0.205802 | − | 0.356460i | ||||
\(254\) | 6.40560 | + | 11.0948i | 0.401923 | + | 0.696151i | ||||
\(255\) | 0.616929 | + | 1.06855i | 0.0386336 | + | 0.0669154i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7167 | 0.918003 | 0.459002 | − | 0.888435i | \(-0.348207\pi\) | ||||
0.459002 | + | 0.888435i | \(0.348207\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 1.75964 | − | 3.04778i | 0.108711 | − | 0.188292i | ||||
\(263\) | −11.7053 | + | 20.2741i | −0.721777 | + | 1.25015i | 0.238510 | + | 0.971140i | \(0.423341\pi\) |
−0.960287 | + | 0.279015i | \(0.909992\pi\) | |||||||
\(264\) | −1.70561 | − | 2.95420i | −0.104973 | − | 0.181818i | ||||
\(265\) | −1.51131 | −0.0928388 | ||||||||
\(266\) | −11.0733 | − | 12.6072i | −0.678947 | − | 0.772998i | ||||
\(267\) | 8.77285 | − | 15.1950i | 0.536890 | − | 0.929920i | ||||
\(268\) | −5.58065 | + | 9.66597i | −0.340892 | + | 0.590443i | ||||
\(269\) | −9.35772 | −0.570550 | −0.285275 | − | 0.958446i | \(-0.592085\pi\) | ||||
−0.285275 | + | 0.958446i | \(0.592085\pi\) | |||||||
\(270\) | 0.114009 | − | 0.197470i | 0.00693839 | − | 0.0120176i | ||||
\(271\) | −15.1475 | −0.920145 | −0.460072 | − | 0.887881i | \(-0.652177\pi\) | ||||
−0.460072 | + | 0.887881i | \(0.652177\pi\) | |||||||
\(272\) | −5.41122 | −0.328103 | ||||||||
\(273\) | 9.44295 | − | 1.35305i | 0.571513 | − | 0.0818903i | ||||
\(274\) | −17.6955 | −1.06903 | ||||||||
\(275\) | −16.8787 | −1.01783 | ||||||||
\(276\) | −0.959623 | + | 1.66212i | −0.0577625 | + | 0.100048i | ||||
\(277\) | −32.8782 | −1.97546 | −0.987731 | − | 0.156165i | \(-0.950087\pi\) | ||||
−0.987731 | + | 0.156165i | \(0.950087\pi\) | |||||||
\(278\) | −3.98321 | + | 6.89912i | −0.238897 | + | 0.413782i | ||||
\(279\) | −1.78052 | + | 3.08395i | −0.106597 | + | 0.184632i | ||||
\(280\) | 0.193482 | − | 0.571413i | 0.0115627 | − | 0.0341484i | ||||
\(281\) | −16.8072 | −1.00263 | −0.501316 | − | 0.865264i | \(-0.667150\pi\) | ||||
−0.501316 | + | 0.865264i | \(0.667150\pi\) | |||||||
\(282\) | −5.57211 | − | 9.65117i | −0.331814 | − | 0.574719i | ||||
\(283\) | 6.07998 | − | 10.5308i | 0.361417 | − | 0.625993i | −0.626777 | − | 0.779199i | \(-0.715626\pi\) |
0.988194 | + | 0.153205i | \(0.0489596\pi\) | |||||||
\(284\) | −0.0390952 | + | 0.0677149i | −0.00231988 | + | 0.00401814i | ||||
\(285\) | −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 | ||||
\(289\) | 12.2813 | 0.722427 | ||||||||
\(290\) | −0.388295 | −0.0228014 | ||||||||
\(291\) | −6.82663 | − | 11.8241i | −0.400184 | − | 0.693140i | ||||
\(292\) | −6.31721 | − | 10.9417i | −0.369687 | − | 0.640316i | ||||
\(293\) | 13.8954 | − | 24.0675i | 0.811778 | − | 1.40604i | −0.0998407 | − | 0.995003i | \(-0.531833\pi\) |
0.911619 | − | 0.411037i | \(-0.134833\pi\) | |||||||
\(294\) | −0.903072 | + | 6.94150i | −0.0526683 | + | 0.404837i | ||||
\(295\) | −1.68397 | + | 2.91672i | −0.0980444 | + | 0.169818i | ||||
\(296\) | 4.18320 | 0.243143 | ||||||||
\(297\) | 1.70561 | − | 2.95420i | 0.0989694 | − | 0.171420i | ||||
\(298\) | 1.34679 | + | 2.33271i | 0.0780175 | + | 0.135130i | ||||
\(299\) | 3.12656 | + | 6.17335i | 0.180814 | + | 0.357014i | ||||
\(300\) | 4.94801 | 0.285673 | ||||||||
\(301\) | −8.79015 | + | 25.9601i | −0.506656 | + | 1.49632i | ||||
\(302\) | −6.56432 | − | 11.3697i | −0.377734 | − | 0.654255i | ||||
\(303\) | −8.25823 | − | 14.3037i | −0.474423 | − | 0.821724i | ||||
\(304\) | −3.17107 | − | 5.49246i | −0.181873 | − | 0.315014i | ||||
\(305\) | 1.53228 | 0.0877383 | ||||||||
\(306\) | −2.70561 | − | 4.68625i | −0.154669 | − | 0.267895i | ||||
\(307\) | −14.6849 | −0.838110 | −0.419055 | − | 0.907961i | \(-0.637639\pi\) | ||||
−0.419055 | + | 0.907961i | \(0.637639\pi\) | |||||||
\(308\) | 2.89453 | − | 8.54848i | 0.164931 | − | 0.487095i | ||||
\(309\) | 3.17961 | + | 5.50725i | 0.180882 | + | 0.313296i | ||||
\(310\) | 0.811985 | 0.0461176 | ||||||||
\(311\) | 3.86348 | + | 6.69174i | 0.219078 | + | 0.379453i | 0.954526 | − | 0.298127i | \(-0.0963619\pi\) |
−0.735449 | + | 0.677580i | \(0.763029\pi\) | |||||||
\(312\) | 3.60014 | + | 0.197470i | 0.203818 | + | 0.0111795i | ||||
\(313\) | −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 | ||||
\(315\) | 0.591599 | − | 0.118146i | 0.0333328 | − | 0.00665680i | ||||
\(316\) | 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 | \(0.0309980\pi\) | |||||||
\(318\) | 6.62799 | 0.371679 | ||||||||
\(319\) | −5.80898 | −0.325241 | ||||||||
\(320\) | 0.114009 | − | 0.197470i | 0.00637332 | − | 0.0110389i | ||||
\(321\) | 3.27362 | − | 5.67008i | 0.182716 | − | 0.316473i | ||||
\(322\) | −4.97952 | + | 0.994446i | −0.277498 | + | 0.0554183i | ||||
\(323\) | 17.1594 | + | 29.7209i | 0.954772 | + | 1.65371i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 9.75294 | − | 14.9384i | 0.540996 | − | 0.828634i | ||||
\(326\) | −8.14702 | − | 14.1111i | −0.451222 | − | 0.781539i | ||||
\(327\) | 1.59419 | 0.0881587 | ||||||||
\(328\) | −1.59160 | − | 2.75673i | −0.0878813 | − | 0.152215i | ||||
\(329\) | 9.45624 | − | 27.9273i | 0.521339 | − | 1.53968i | ||||
\(330\) | −0.777821 | −0.0428176 | ||||||||
\(331\) | −2.05436 | − | 3.55826i | −0.112918 | − | 0.195579i | 0.804028 | − | 0.594592i | \(-0.202686\pi\) |
−0.916946 | + | 0.399012i | \(0.869353\pi\) | |||||||
\(332\) | −1.70291 | −0.0934592 | ||||||||
\(333\) | 2.09160 | + | 3.62276i | 0.114619 | + | 0.198526i | ||||
\(334\) | −0.826739 | − | 1.43195i | −0.0452371 | − | 0.0783530i | ||||
\(335\) | 1.27249 | + | 2.20402i | 0.0695237 | + | 0.120419i | ||||
\(336\) | −0.848534 | + | 2.50599i | −0.0462913 | + | 0.136713i | ||||
\(337\) | −7.44592 | −0.405605 | −0.202802 | − | 0.979220i | \(-0.565005\pi\) | ||||
−0.202802 | + | 0.979220i | \(0.565005\pi\) | |||||||
\(338\) | 7.69235 | − | 10.4799i | 0.418409 | − | 0.570030i | ||||
\(339\) | 4.12255 | + | 7.14047i | 0.223906 | + | 0.387817i | ||||
\(340\) | −0.616929 | + | 1.06855i | −0.0334577 | + | 0.0579504i | ||||
\(341\) | 12.1475 | 0.657824 | ||||||||
\(342\) | 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 | ||||
\(345\) | 0.218812 | + | 0.378993i | 0.0117804 | + | 0.0204043i | ||||
\(346\) | 7.02100 | + | 12.1607i | 0.377451 | + | 0.653765i | ||||
\(347\) | −10.5281 | −0.565180 | −0.282590 | − | 0.959241i | \(-0.591194\pi\) | ||||
−0.282590 | + | 0.959241i | \(0.591194\pi\) | |||||||
\(348\) | 1.70291 | 0.0912854 | ||||||||
\(349\) | −4.74127 | − | 8.21212i | −0.253794 | − | 0.439585i | 0.710773 | − | 0.703422i | \(-0.248345\pi\) |
−0.964567 | + | 0.263837i | \(0.915012\pi\) | |||||||
\(350\) | 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 | ||||
\(353\) | −2.72112 | + | 4.71311i | −0.144830 | + | 0.250854i | −0.929310 | − | 0.369301i | \(-0.879597\pi\) |
0.784479 | + | 0.620155i | \(0.212930\pi\) | |||||||
\(354\) | 7.38522 | − | 12.7916i | 0.392520 | − | 0.679865i | ||||
\(355\) | 0.00891445 | + | 0.0154403i | 0.000473130 | + | 0.000819485i | ||||
\(356\) | 17.5457 | 0.929920 | ||||||||
\(357\) | 4.59160 | − | 13.5605i | 0.243013 | − | 0.717696i | ||||
\(358\) | −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 | \(0.256836\pi\) | |||||||
\(360\) | 0.228019 | 0.0120176 | ||||||||
\(361\) | −10.6114 | + | 18.3795i | −0.558494 | + | 0.967340i | ||||
\(362\) | −1.13838 | −0.0598317 | ||||||||
\(363\) | −0.636396 | −0.0334021 | ||||||||
\(364\) | 5.89325 | + | 7.50131i | 0.308890 | + | 0.393175i | ||||
\(365\) | −2.88088 | −0.150792 | ||||||||
\(366\) | −6.71999 | −0.351259 | ||||||||
\(367\) | 3.59896 | − | 6.23359i | 0.187864 | − | 0.325391i | −0.756674 | − | 0.653793i | \(-0.773177\pi\) |
0.944538 | + | 0.328402i | \(0.106510\pi\) | |||||||
\(368\) | −1.91925 | −0.100048 | ||||||||
\(369\) | 1.59160 | − | 2.75673i | 0.0828553 | − | 0.143510i | ||||
\(370\) | 0.476924 | − | 0.826056i | 0.0247941 | − | 0.0429446i | ||||
\(371\) | 11.5724 | + | 13.1754i | 0.600808 | + | 0.684035i | ||||
\(372\) | −3.56104 | −0.184632 | ||||||||
\(373\) | 14.2762 | + | 24.7271i | 0.739192 | + | 1.28032i | 0.952859 | + | 0.303412i | \(0.0981259\pi\) |
−0.213667 | + | 0.976907i | \(0.568541\pi\) | |||||||
\(374\) | −9.22941 | + | 15.9858i | −0.477242 | + | 0.826607i | ||||
\(375\) | 1.13417 | − | 1.96443i | 0.0585681 | − | 0.101443i | ||||
\(376\) | 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 | 0.919970 | + | 0.391989i | \(0.128213\pi\) |
−0.120513 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(380\) | −1.44613 | −0.0741847 | ||||||||
\(381\) | −12.8112 | −0.656337 | ||||||||
\(382\) | 9.04253 | + | 15.6621i | 0.462656 | + | 0.801343i | ||||
\(383\) | −10.9760 | − | 19.0111i | −0.560849 | − | 0.971420i | −0.997423 | − | 0.0717509i | \(-0.977141\pi\) |
0.436573 | − | 0.899669i | \(-0.356192\pi\) | |||||||
\(384\) | −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 | ||||
\(387\) | −10.3592 | −0.526589 | ||||||||
\(388\) | 6.82663 | − | 11.8241i | 0.346570 | − | 0.600277i | ||||
\(389\) | 1.87365 | + | 3.24525i | 0.0949976 | + | 0.164541i | 0.909608 | − | 0.415468i | \(-0.136382\pi\) |
−0.814610 | + | 0.580009i | \(0.803049\pi\) | |||||||
\(390\) | 0.449444 | − | 0.688406i | 0.0227585 | − | 0.0348588i | ||||
\(391\) | 10.3855 | 0.525215 | ||||||||
\(392\) | −6.46305 | + | 2.68867i | −0.326434 | + | 0.135798i | ||||
\(393\) | 1.75964 | + | 3.04778i | 0.0887619 | + | 0.153740i | ||||
\(394\) | 10.3527 | + | 17.9315i | 0.521564 | + | 0.903375i | ||||
\(395\) | −0.184941 | − | 0.320327i | −0.00930537 | − | 0.0161174i | ||||
\(396\) | 3.41122 | 0.171420 | ||||||||
\(397\) | 1.95502 | + | 3.38620i | 0.0981198 | + | 0.169949i | 0.910906 | − | 0.412613i | \(-0.135384\pi\) |
−0.812787 | + | 0.582562i | \(0.802050\pi\) | |||||||
\(398\) | 16.3984 | 0.821979 | ||||||||
\(399\) | 16.4548 | − | 3.28614i | 0.823771 | − | 0.164513i | ||||
\(400\) | 2.47400 | + | 4.28510i | 0.123700 | + | 0.214255i | ||||
\(401\) | −26.2260 | −1.30967 | −0.654833 | − | 0.755774i | \(-0.727261\pi\) | ||||
−0.654833 | + | 0.755774i | \(0.727261\pi\) | |||||||
\(402\) | −5.58065 | − | 9.66597i | −0.278337 | − | 0.482095i | ||||
\(403\) | −7.01912 | + | 10.7511i | −0.349647 | + | 0.535549i | ||||
\(404\) | 8.25823 | − | 14.3037i | 0.410862 | − | 0.711634i | ||||
\(405\) | 0.114009 | + | 0.197470i | 0.00566517 | + | 0.00981236i | ||||
\(406\) | 2.97325 | + | 3.38512i | 0.147560 | + | 0.168001i | ||||
\(407\) | 7.13490 | − | 12.3580i | 0.353664 | − | 0.612563i | ||||
\(408\) | 2.70561 | − | 4.68625i | 0.133948 | − | 0.232004i | ||||
\(409\) | 4.03519 | 0.199527 | 0.0997635 | − | 0.995011i | \(-0.468191\pi\) | ||||
0.0997635 | + | 0.995011i | \(0.468191\pi\) | |||||||
\(410\) | −0.725829 | −0.0358461 | ||||||||
\(411\) | 8.84776 | − | 15.3248i | 0.436428 | − | 0.755915i | ||||
\(412\) | −3.17961 | + | 5.50725i | −0.156648 | + | 0.271323i | ||||
\(413\) | 38.3222 | − | 7.65321i | 1.88571 | − | 0.376590i | ||||
\(414\) | −0.959623 | − | 1.66212i | −0.0471629 | − | 0.0816885i | ||||
\(415\) | −0.194147 | + | 0.336273i | −0.00953032 | + | 0.0165070i | ||||
\(416\) | 1.62906 | + | 3.21655i | 0.0798710 | + | 0.157704i | ||||
\(417\) | −3.98321 | − | 6.89912i | −0.195059 | − | 0.337851i | ||||
\(418\) | −21.6344 | −1.05817 | ||||||||
\(419\) | 1.74139 | + | 3.01617i | 0.0850723 | + | 0.147350i | 0.905422 | − | 0.424513i | \(-0.139555\pi\) |
−0.820350 | + | 0.571862i | \(0.806221\pi\) | |||||||
\(420\) | 0.398117 | + | 0.453266i | 0.0194261 | + | 0.0221171i | ||||
\(421\) | 18.6028 | 0.906647 | 0.453323 | − | 0.891346i | \(-0.350238\pi\) | ||||
0.453323 | + | 0.891346i | \(0.350238\pi\) | |||||||
\(422\) | −3.74446 | − | 6.48560i | −0.182277 | − | 0.315714i | ||||
\(423\) | 11.1442 | 0.541850 | ||||||||
\(424\) | 3.31400 | + | 5.74001i | 0.160942 | + | 0.278760i | ||||
\(425\) | −13.3874 | − | 23.1876i | −0.649383 | − | 1.12476i | ||||
\(426\) | −0.0390952 | − | 0.0677149i | −0.00189417 | − | 0.00328080i | ||||
\(427\) | −11.7330 | − | 13.3583i | −0.567800 | − | 0.646454i | ||||
\(428\) | 6.54724 | 0.316473 | ||||||||
\(429\) | 6.72379 | − | 10.2987i | 0.324628 | − | 0.497227i | ||||
\(430\) | 1.18105 | + | 2.04564i | 0.0569552 | + | 0.0986493i | ||||
\(431\) | 9.52662 | − | 16.5006i | 0.458881 | − | 0.794806i | −0.540021 | − | 0.841652i | \(-0.681584\pi\) |
0.998902 | + | 0.0468461i | \(0.0149170\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −16.7336 | + | 28.9834i | −0.804164 | + | 1.39285i | 0.112689 | + | 0.993630i | \(0.464053\pi\) |
−0.916854 | + | 0.399223i | \(0.869280\pi\) | |||||||
\(434\) | −6.21753 | − | 7.07881i | −0.298451 | − | 0.339794i | ||||
\(435\) | 0.194147 | − | 0.336273i | 0.00930865 | − | 0.0161231i | ||||
\(436\) | 0.797093 | + | 1.38061i | 0.0381738 | + | 0.0661190i | ||||
\(437\) | 6.08607 | + | 10.5414i | 0.291136 | + | 0.504262i | ||||
\(438\) | 12.6344 | 0.603696 | ||||||||
\(439\) | 38.0459 | 1.81583 | 0.907915 | − | 0.419154i | \(-0.137673\pi\) | ||||
0.907915 | + | 0.419154i | \(0.137673\pi\) | |||||||
\(440\) | −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 | \(0.100330\pi\) | |||||||
\(444\) | −2.09160 | + | 3.62276i | −0.0992629 | + | 0.171928i | ||||
\(445\) | 2.00037 | − | 3.46475i | 0.0948268 | − | 0.164245i | ||||
\(446\) | 8.41325 | + | 14.5722i | 0.398379 | + | 0.690013i | ||||
\(447\) | −2.69358 | −0.127402 | ||||||||
\(448\) | −2.59452 | + | 0.518144i | −0.122579 | + | 0.0244800i | ||||
\(449\) | −11.4930 | + | 19.9065i | −0.542389 | + | 0.939445i | 0.456377 | + | 0.889786i | \(0.349147\pi\) |
−0.998766 | + | 0.0496589i | \(0.984187\pi\) | |||||||
\(450\) | −2.47400 | + | 4.28510i | −0.116626 | + | 0.202002i | ||||
\(451\) | −10.8586 | −0.511310 | ||||||||
\(452\) | −4.12255 | + | 7.14047i | −0.193908 | + | 0.335859i | ||||
\(453\) | 13.1286 | 0.616837 | ||||||||
\(454\) | 4.23214 | 0.198624 | ||||||||
\(455\) | 2.15317 | − | 0.308521i | 0.100942 | − | 0.0144637i | ||||
\(456\) | 6.34214 | 0.296998 | ||||||||
\(457\) | 11.5899 | 0.542150 | 0.271075 | − | 0.962558i | \(-0.412621\pi\) | ||||
0.271075 | + | 0.962558i | \(0.412621\pi\) | |||||||
\(458\) | 6.86498 | − | 11.8905i | 0.320779 | − | 0.555606i | ||||
\(459\) | 5.41122 | 0.252574 | ||||||||
\(460\) | −0.218812 | + | 0.378993i | −0.0102022 | + | 0.0176707i | ||||
\(461\) | −17.4236 | + | 30.1785i | −0.811496 | + | 1.40555i | 0.100321 | + | 0.994955i | \(0.468013\pi\) |
−0.911817 | + | 0.410597i | \(0.865320\pi\) | |||||||
\(462\) | 5.95593 | + | 6.78098i | 0.277095 | + | 0.315480i | ||||
\(463\) | −39.5334 | −1.83727 | −0.918635 | − | 0.395106i | \(-0.870708\pi\) | ||||
−0.918635 | + | 0.395106i | \(0.870708\pi\) | |||||||
\(464\) | 0.851453 | + | 1.47476i | 0.0395277 | + | 0.0684640i | ||||
\(465\) | −0.405992 | + | 0.703199i | −0.0188274 | + | 0.0326101i | ||||
\(466\) | 3.85349 | − | 6.67444i | 0.178509 | − | 0.309187i | ||||
\(467\) | −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 | ||||
\(471\) | −3.18143 | −0.146592 | ||||||||
\(472\) | 14.7704 | 0.679865 | ||||||||
\(473\) | 17.6688 | + | 30.6032i | 0.812411 | + | 1.40714i | ||||
\(474\) | 0.811077 | + | 1.40483i | 0.0372540 | + | 0.0645258i | ||||
\(475\) | 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 | ||||
\(478\) | 25.2189 | 1.15349 | ||||||||
\(479\) | −5.78732 | + | 10.0239i | −0.264429 | + | 0.458005i | −0.967414 | − | 0.253200i | \(-0.918517\pi\) |
0.702985 | + | 0.711205i | \(0.251850\pi\) | |||||||
\(480\) | 0.114009 | + | 0.197470i | 0.00520379 | + | 0.00901323i | ||||
\(481\) | 6.81466 | + | 13.4555i | 0.310722 | + | 0.613516i | ||||
\(482\) | −27.8367 | −1.26793 | ||||||||
\(483\) | 1.62854 | − | 4.80961i | 0.0741014 | − | 0.218845i | ||||
\(484\) | −0.318198 | − | 0.551135i | −0.0144635 | − | 0.0250516i | ||||
\(485\) | −1.55660 | − | 2.69611i | −0.0706816 | − | 0.122424i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −13.9320 | −0.631321 | −0.315661 | − | 0.948872i | \(-0.602226\pi\) | ||||
−0.315661 | + | 0.948872i | \(0.602226\pi\) | |||||||
\(488\) | −3.35999 | − | 5.81968i | −0.152100 | − | 0.263445i | ||||
\(489\) | 16.2940 | 0.736842 | ||||||||
\(490\) | −0.205917 | + | 1.58279i | −0.00930240 | + | 0.0715033i | ||||
\(491\) | 4.76716 | + | 8.25697i | 0.215139 | + | 0.372632i | 0.953316 | − | 0.301976i | \(-0.0976462\pi\) |
−0.738177 | + | 0.674608i | \(0.764313\pi\) | |||||||
\(492\) | 3.18320 | 0.143510 | ||||||||
\(493\) | −4.60740 | − | 7.98025i | −0.207507 | − | 0.359412i | ||||
\(494\) | 12.5009 | − | 19.1474i | 0.562442 | − | 0.861483i | ||||
\(495\) | 0.388911 | − | 0.673613i | 0.0174802 | − | 0.0302766i | ||||
\(496\) | −1.78052 | − | 3.08395i | −0.0799478 | − | 0.138474i | ||||
\(497\) | 0.0663472 | − | 0.195945i | 0.00297608 | − | 0.00878932i | ||||
\(498\) | 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 | \(-0.271155\pi\) | |||||||
\(500\) | 2.26833 | 0.101443 | ||||||||
\(501\) | 1.65348 | 0.0738719 | ||||||||
\(502\) | −2.12395 | + | 3.67878i | −0.0947963 | + | 0.164192i | ||||
\(503\) | −7.35181 | + | 12.7337i | −0.327801 | + | 0.567768i | −0.982075 | − | 0.188489i | \(-0.939641\pi\) |
0.654274 | + | 0.756257i | \(0.272974\pi\) | |||||||
\(504\) | −1.74599 | − | 1.98785i | −0.0777724 | − | 0.0885457i | ||||
\(505\) | −1.88303 | − | 3.26150i | −0.0837937 | − | 0.145135i | ||||
\(506\) | −3.27348 | + | 5.66984i | −0.145524 | + | 0.252055i | ||||
\(507\) | 5.22966 | + | 11.9017i | 0.232257 | + | 0.528573i | ||||
\(508\) | −6.40560 | − | 11.0948i | −0.284202 | − | 0.492253i | ||||
\(509\) | −14.4795 | −0.641792 | −0.320896 | − | 0.947114i | \(-0.603984\pi\) | ||||
−0.320896 | + | 0.947114i | \(0.603984\pi\) | |||||||
\(510\) | −0.616929 | − | 1.06855i | −0.0273181 | − | 0.0473163i | ||||
\(511\) | 22.0595 | + | 25.1153i | 0.975855 | + | 1.11104i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.17107 | + | 5.49246i | 0.140006 | + | 0.242498i | ||||
\(514\) | −14.7167 | −0.649126 | ||||||||
\(515\) | 0.725011 | + | 1.25576i | 0.0319478 | + | 0.0553352i | ||||
\(516\) | −5.17961 | − | 8.97135i | −0.228020 | − | 0.394942i | ||||
\(517\) | −19.0077 | − | 32.9222i | −0.835956 | − | 1.44792i | ||||
\(518\) | −10.8534 | + | 2.16750i | −0.476870 | + | 0.0952344i | ||||
\(519\) | −14.0420 | −0.616375 | ||||||||
\(520\) | 0.820899 | + | 0.0450268i | 0.0359988 | + | 0.00197456i | ||||
\(521\) | 7.18959 | + | 12.4527i | 0.314982 | + | 0.545564i | 0.979434 | − | 0.201767i | \(-0.0646683\pi\) |
−0.664452 | + | 0.747331i | \(0.731335\pi\) | |||||||
\(522\) | −0.851453 | + | 1.47476i | −0.0372671 | + | 0.0645485i | ||||
\(523\) | −1.02354 | −0.0447563 | −0.0223781 | − | 0.999750i | \(-0.507124\pi\) | ||||
−0.0223781 | + | 0.999750i | \(0.507124\pi\) | |||||||
\(524\) | −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 | ||||
\(527\) | 9.63479 | + | 16.6879i | 0.419698 | + | 0.726938i | ||||
\(528\) | 1.70561 | + | 2.95420i | 0.0742271 | + | 0.128565i | ||||
\(529\) | −19.3165 | −0.839848 | ||||||||
\(530\) | 1.51131 | 0.0656470 | ||||||||
\(531\) | 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 | ||||
\(535\) | 0.746446 | − | 1.29288i | 0.0322717 | − | 0.0558962i | ||||
\(536\) | 5.58065 | − | 9.66597i | 0.241047 | − | 0.417506i | ||||
\(537\) | −4.66663 | − | 8.08283i | −0.201380 | − | 0.348800i | ||||
\(538\) | 9.35772 | 0.403440 | ||||||||
\(539\) | −3.08058 | + | 23.6790i | −0.132690 | + | 1.01993i | ||||
\(540\) | −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 | \(0.155657\pi\) | |||||||
\(542\) | 15.1475 | 0.650641 | ||||||||
\(543\) | 0.569188 | − | 0.985863i | 0.0244262 | − | 0.0423074i | ||||
\(544\) | 5.41122 | 0.232004 | ||||||||
\(545\) | 0.363504 | 0.0155708 | ||||||||
\(546\) | −9.44295 | + | 1.35305i | −0.404121 | + | 0.0579052i | ||||
\(547\) | 26.9289 | 1.15140 | 0.575699 | − | 0.817661i | \(-0.304730\pi\) | ||||
0.575699 | + | 0.817661i | \(0.304730\pi\) | |||||||
\(548\) | 17.6955 | 0.755915 | ||||||||
\(549\) | 3.35999 | − | 5.81968i | 0.143401 | − | 0.248378i | ||||
\(550\) | 16.8787 | 0.719711 | ||||||||
\(551\) | 5.40004 | − | 9.35314i | 0.230049 | − | 0.398457i | ||||
\(552\) | 0.959623 | − | 1.66212i | 0.0408443 | − | 0.0707444i | ||||
\(553\) | −1.37645 | + | 4.06510i | −0.0585327 | + | 0.172866i | ||||
\(554\) | 32.8782 | 1.39686 | ||||||||
\(555\) | 0.476924 | + | 0.826056i | 0.0202443 | + | 0.0350641i | ||||
\(556\) | 3.98321 | − | 6.89912i | 0.168926 | − | 0.292588i | ||||
\(557\) | 18.1841 | − | 31.4957i | 0.770484 | − | 1.33452i | −0.166815 | − | 0.985988i | \(-0.553348\pi\) |
0.937298 | − | 0.348528i | \(-0.113319\pi\) | |||||||
\(558\) | 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 | ||||
\(562\) | 16.8072 | 0.708968 | ||||||||
\(563\) | −3.73021 | −0.157210 | −0.0786048 | − | 0.996906i | \(-0.525047\pi\) | ||||
−0.0786048 | + | 0.996906i | \(0.525047\pi\) | |||||||
\(564\) | 5.57211 | + | 9.65117i | 0.234628 | + | 0.406388i | ||||
\(565\) | 0.940019 | + | 1.62816i | 0.0395469 | + | 0.0684972i | ||||
\(566\) | −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 | ||||
\(569\) | −15.3919 | −0.645263 | −0.322632 | − | 0.946525i | \(-0.604567\pi\) | ||||
−0.322632 | + | 0.946525i | \(0.604567\pi\) | |||||||
\(570\) | 0.723063 | − | 1.25238i | 0.0302858 | − | 0.0524565i | ||||
\(571\) | −10.1994 | − | 17.6659i | −0.426832 | − | 0.739296i | 0.569757 | − | 0.821813i | \(-0.307037\pi\) |
−0.996590 | + | 0.0825176i | \(0.973704\pi\) | |||||||
\(572\) | 12.2809 | + | 0.673613i | 0.513488 | + | 0.0281652i | ||||
\(573\) | −18.0851 | −0.755514 | ||||||||
\(574\) | 5.55782 | + | 6.32771i | 0.231979 | + | 0.264114i | ||||
\(575\) | −4.74822 | − | 8.22416i | −0.198015 | − | 0.342971i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −5.90380 | − | 10.2257i | −0.245779 | − | 0.425701i | 0.716572 | − | 0.697513i | \(-0.245710\pi\) |
−0.962350 | + | 0.271813i | \(0.912377\pi\) | |||||||
\(578\) | −12.2813 | −0.510833 | ||||||||
\(579\) | −2.91296 | − | 5.04539i | −0.121058 | − | 0.209679i | ||||
\(580\) | 0.388295 | 0.0161231 | ||||||||
\(581\) | 4.41822 | − | 0.882351i | 0.183299 | − | 0.0366061i | ||||
\(582\) | 6.82663 | + | 11.8241i | 0.282973 | + | 0.490124i | ||||
\(583\) | 22.6095 | 0.936391 | ||||||||
\(584\) | 6.31721 | + | 10.9417i | 0.261408 | + | 0.452772i | ||||
\(585\) | 0.371455 | + | 0.733433i | 0.0153578 | + | 0.0303237i | ||||
\(586\) | −13.8954 | + | 24.0675i | −0.574014 | + | 0.994221i | ||||
\(587\) | −21.9241 | − | 37.9736i | −0.904903 | − | 1.56734i | −0.821047 | − | 0.570861i | \(-0.806610\pi\) |
−0.0838564 | − | 0.996478i | \(-0.526724\pi\) | |||||||
\(588\) | 0.903072 | − | 6.94150i | 0.0372421 | − | 0.286263i | ||||
\(589\) | −11.2923 | + | 19.5589i | −0.465292 | + | 0.805910i | ||||
\(590\) | 1.68397 | − | 2.91672i | 0.0693279 | − | 0.120079i | ||||
\(591\) | −20.7055 | −0.851710 | ||||||||
\(592\) | −4.18320 | −0.171928 | ||||||||
\(593\) | −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 | ||||
\(595\) | 1.04697 | − | 3.09204i | 0.0429216 | − | 0.126761i | ||||
\(596\) | −1.34679 | − | 2.33271i | −0.0551667 | − | 0.0955515i | ||||
\(597\) | −8.19922 | + | 14.2015i | −0.335572 | + | 0.581227i | ||||
\(598\) | −3.12656 | − | 6.17335i | −0.127855 | − | 0.252447i | ||||
\(599\) | −19.7135 | − | 34.1448i | −0.805471 | − | 1.39512i | −0.915973 | − | 0.401241i | \(-0.868579\pi\) |
0.110501 | − | 0.993876i | \(-0.464754\pi\) | |||||||
\(600\) | −4.94801 | −0.202002 | ||||||||
\(601\) | −1.03443 | − | 1.79169i | −0.0421954 | − | 0.0730845i | 0.844156 | − | 0.536097i | \(-0.180102\pi\) |
−0.886352 | + | 0.463012i | \(0.846769\pi\) | |||||||
\(602\) | 8.79015 | − | 25.9601i | 0.358260 | − | 1.05806i | ||||
\(603\) | 11.1613 | 0.454523 | ||||||||
\(604\) | 6.56432 | + | 11.3697i | 0.267098 | + | 0.462628i | ||||
\(605\) | −0.145110 | −0.00589957 | ||||||||
\(606\) | 8.25823 | + | 14.3037i | 0.335467 | + | 0.581047i | ||||
\(607\) | −2.88978 | − | 5.00524i | −0.117292 | − | 0.203157i | 0.801401 | − | 0.598127i | \(-0.204088\pi\) |
−0.918694 | + | 0.394970i | \(0.870755\pi\) | |||||||
\(608\) | 3.17107 | + | 5.49246i | 0.128604 | + | 0.222749i | ||||
\(609\) | −4.41822 | + | 0.882351i | −0.179035 | + | 0.0357547i | ||||
\(610\) | −1.53228 | −0.0620403 | ||||||||
\(611\) | 40.1207 | + | 2.20065i | 1.62311 | + | 0.0890287i | ||||
\(612\) | 2.70561 | + | 4.68625i | 0.109368 | + | 0.189430i | ||||
\(613\) | −7.45451 | + | 12.9116i | −0.301085 | + | 0.521494i | −0.976382 | − | 0.216051i | \(-0.930682\pi\) |
0.675297 | + | 0.737546i | \(0.264015\pi\) | |||||||
\(614\) | 14.6849 | 0.592633 | ||||||||
\(615\) | 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 | −0.891004 | − | 0.453995i | \(-0.849999\pi\) |
0.838673 | + | 0.544635i | \(0.183332\pi\) | |||||||
\(618\) | −3.17961 | − | 5.50725i | −0.127903 | − | 0.221534i | ||||
\(619\) | 24.4693 | + | 42.3821i | 0.983505 | + | 1.70348i | 0.648399 | + | 0.761300i | \(0.275439\pi\) |
0.335106 | + | 0.942180i | \(0.391228\pi\) | |||||||
\(620\) | −0.811985 | −0.0326101 | ||||||||
\(621\) | 1.91925 | 0.0770167 | ||||||||
\(622\) | −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 | ||||
\(626\) | 10.0982 | − | 17.4906i | 0.403605 | − | 0.699064i | ||||
\(627\) | 10.8172 | − | 18.7360i | 0.431998 | − | 0.748242i | ||||
\(628\) | −1.59071 | − | 2.75520i | −0.0634764 | − | 0.109944i | ||||
\(629\) | 22.6362 | 0.902564 | ||||||||
\(630\) | −0.591599 | + | 0.118146i | −0.0235699 | + | 0.00470707i | ||||
\(631\) | 14.0099 | − | 24.2659i | 0.557726 | − | 0.966010i | −0.439960 | − | 0.898017i | \(-0.645007\pi\) |
0.997686 | − | 0.0679924i | \(-0.0216594\pi\) | |||||||
\(632\) | −0.811077 | + | 1.40483i | −0.0322629 | + | 0.0558810i | ||||
\(633\) | 7.48892 | 0.297658 | ||||||||
\(634\) | −7.36088 | + | 12.7494i | −0.292338 | + | 0.506344i | ||||
\(635\) | −2.92119 | −0.115924 | ||||||||
\(636\) | −6.62799 | −0.262817 | ||||||||
\(637\) | −19.1769 | − | 16.4087i | −0.759817 | − | 0.650138i | ||||
\(638\) | 5.80898 | 0.229980 | ||||||||
\(639\) | 0.0781905 | 0.00309317 | ||||||||
\(640\) | −0.114009 | + | 0.197470i | −0.00450662 | + | 0.00780569i | ||||
\(641\) | −35.9312 | −1.41920 | −0.709598 | − | 0.704607i | \(-0.751123\pi\) | ||||
−0.709598 | + | 0.704607i | \(0.751123\pi\) | |||||||
\(642\) | −3.27362 | + | 5.67008i | −0.129199 | + | 0.223780i | ||||
\(643\) | 10.6007 | − | 18.3609i | 0.418050 | − | 0.724084i | −0.577693 | − | 0.816254i | \(-0.696047\pi\) |
0.995743 | + | 0.0921702i | \(0.0293804\pi\) | |||||||
\(644\) | 4.97952 | − | 0.994446i | 0.196221 | − | 0.0391866i | ||||
\(645\) | −2.36210 | −0.0930075 | ||||||||
\(646\) | −17.1594 | − | 29.7209i | −0.675126 | − | 1.16935i | ||||
\(647\) | −2.06144 | + | 3.57052i | −0.0810436 | + | 0.140372i | −0.903698 | − | 0.428169i | \(-0.859159\pi\) |
0.822655 | + | 0.568541i | \(0.192492\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 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 | ||||
\(653\) | −47.4371 | −1.85636 | −0.928179 | − | 0.372134i | \(-0.878626\pi\) | ||||
−0.928179 | + | 0.372134i | \(0.878626\pi\) | |||||||
\(654\) | −1.59419 | −0.0623376 | ||||||||
\(655\) | 0.401230 | + | 0.694951i | 0.0156773 | + | 0.0271540i | ||||
\(656\) | 1.59160 | + | 2.75673i | 0.0621415 | + | 0.107632i | ||||
\(657\) | −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 | −0.999869 | − | 0.0161688i | \(-0.994853\pi\) |
0.513937 | + | 0.857828i | \(0.328186\pi\) | |||||||
\(660\) | 0.777821 | 0.0302766 | ||||||||
\(661\) | 4.30765 | − | 7.46106i | 0.167548 | − | 0.290202i | −0.770009 | − | 0.638033i | \(-0.779748\pi\) |
0.937557 | + | 0.347831i | \(0.113082\pi\) | |||||||
\(662\) | 2.05436 | + | 3.55826i | 0.0798450 | + | 0.138296i | ||||
\(663\) | 19.4811 | + | 1.06855i | 0.756585 | + | 0.0414992i | ||||
\(664\) | 1.70291 | 0.0660856 | ||||||||
\(665\) | 3.75200 | − | 0.749302i | 0.145496 | − | 0.0290567i | ||||
\(666\) | −2.09160 | − | 3.62276i | −0.0810478 | − | 0.140379i | ||||
\(667\) | −1.63415 | − | 2.83043i | −0.0632745 | − | 0.109595i | ||||
\(668\) | 0.826739 | + | 1.43195i | 0.0319875 | + | 0.0554040i | ||||
\(669\) | −16.8265 | −0.650550 | ||||||||
\(670\) | −1.27249 | − | 2.20402i | −0.0491607 | − | 0.0851488i | ||||
\(671\) | −22.9233 | −0.884946 | ||||||||
\(672\) | 0.848534 | − | 2.50599i | 0.0327329 | − | 0.0966707i | ||||
\(673\) | 3.15527 | + | 5.46509i | 0.121627 | + | 0.210664i | 0.920409 | − | 0.390956i | \(-0.127856\pi\) |
−0.798783 | + | 0.601620i | \(0.794522\pi\) | |||||||
\(674\) | 7.44592 | 0.286806 | ||||||||
\(675\) | −2.47400 | − | 4.28510i | −0.0952244 | − | 0.164934i | ||||
\(676\) | −7.69235 | + | 10.4799i | −0.295860 | + | 0.403072i | ||||
\(677\) | −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 | ||||
\(679\) | −11.5853 | + | 34.2150i | −0.444601 | + | 1.31305i | ||||
\(680\) | 0.616929 | − | 1.06855i | 0.0236582 | − | 0.0409771i | ||||
\(681\) | −2.11607 | + | 3.66514i | −0.0810880 | + | 0.140449i | ||||
\(682\) | −12.1475 | −0.465152 | ||||||||
\(683\) | 19.9112 | 0.761880 | 0.380940 | − | 0.924600i | \(-0.375600\pi\) | ||||
0.380940 | + | 0.924600i | \(0.375600\pi\) | |||||||
\(684\) | −3.17107 | + | 5.49246i | −0.121249 | + | 0.210009i | ||||
\(685\) | 2.01746 | − | 3.49434i | 0.0770830 | − | 0.133512i | ||||
\(686\) | 15.3754 | − | 10.3246i | 0.587035 | − | 0.394195i | ||||
\(687\) | 6.86498 | + | 11.8905i | 0.261915 | + | 0.453650i | ||||
\(688\) | 5.17961 | − | 8.97135i | 0.197471 | − | 0.342030i | ||||
\(689\) | −13.0643 | + | 20.0104i | −0.497711 | + | 0.762336i | ||||
\(690\) | −0.218812 | − | 0.378993i | −0.00833003 | − | 0.0144280i | ||||
\(691\) | −19.0691 | −0.725422 | −0.362711 | − | 0.931902i | \(-0.618149\pi\) | ||||
−0.362711 | + | 0.931902i | \(0.618149\pi\) | |||||||
\(692\) | −7.02100 | − | 12.1607i | −0.266898 | − | 0.462282i | ||||
\(693\) | −8.85046 | + | 1.76750i | −0.336201 | + | 0.0671418i | ||||
\(694\) | 10.5281 | 0.399642 | ||||||||
\(695\) | −0.908246 | − | 1.57313i | −0.0344518 | − | 0.0596722i | ||||
\(696\) | −1.70291 | −0.0645485 | ||||||||
\(697\) | −8.61248 | − | 14.9173i | −0.326221 | − | 0.565032i | ||||
\(698\) | 4.74127 | + | 8.21212i | 0.179460 | + | 0.310833i | ||||
\(699\) | 3.85349 | + | 6.67444i | 0.145752 | + | 0.252450i | ||||
\(700\) | −8.63915 | − | 9.83588i | −0.326529 | − | 0.371761i | ||||
\(701\) | 21.2816 | 0.803796 | 0.401898 | − | 0.915685i | \(-0.368351\pi\) | ||||
0.401898 | + | 0.915685i | \(0.368351\pi\) | |||||||
\(702\) | −1.62906 | − | 3.21655i | −0.0614847 | − | 0.121401i | ||||
\(703\) | 13.2652 | + | 22.9760i | 0.500307 | + | 0.866557i | ||||
\(704\) | −1.70561 | + | 2.95420i | −0.0642825 | + | 0.111341i | ||||
\(705\) | 2.54109 | 0.0957030 | ||||||||
\(706\) | 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 | ||||
\(709\) | 13.4109 | + | 23.2283i | 0.503655 | + | 0.872357i | 0.999991 | + | 0.00422606i | \(0.00134520\pi\) |
−0.496336 | + | 0.868131i | \(0.665321\pi\) | |||||||
\(710\) | −0.00891445 | − | 0.0154403i | −0.000334553 | − | 0.000579463i | ||||
\(711\) | −1.62215 | −0.0608355 | ||||||||
\(712\) | −17.5457 | −0.657553 | ||||||||
\(713\) | 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 | ||||
\(717\) | −12.6095 | + | 21.8402i | −0.470909 | + | 0.815638i | ||||
\(718\) | 5.29579 | − | 9.17257i | 0.197637 | − | 0.342317i | ||||
\(719\) | 21.5853 | + | 37.3869i | 0.804997 | + | 1.39430i | 0.916293 | + | 0.400508i | \(0.131166\pi\) |
−0.111297 | + | 0.993787i | \(0.535500\pi\) | |||||||
\(720\) | −0.228019 | −0.00849776 | ||||||||
\(721\) | 5.39601 | − | 15.9362i | 0.200958 | − | 0.593494i | ||||
\(722\) | 10.6114 | − | 18.3795i | 0.394915 | − | 0.684012i | ||||
\(723\) | 13.9183 | − | 24.1073i | 0.517629 | − | 0.896560i | ||||
\(724\) | 1.13838 | 0.0423074 | ||||||||
\(725\) | −4.21300 | + | 7.29713i | −0.156467 | + | 0.271008i | ||||
\(726\) | 0.636396 | 0.0236189 | ||||||||
\(727\) | −16.1609 | −0.599373 | −0.299687 | − | 0.954038i | \(-0.596882\pi\) | ||||
−0.299687 | + | 0.954038i | \(0.596882\pi\) | |||||||
\(728\) | −5.89325 | − | 7.50131i | −0.218418 | − | 0.278017i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.88088 | 0.106626 | ||||||||
\(731\) | −28.0280 | + | 48.5459i | −1.03665 | + | 1.79554i | ||||
\(732\) | 6.71999 | 0.248378 | ||||||||
\(733\) | 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 | ||||
\(735\) | −1.26778 | − | 0.969726i | −0.0467628 | − | 0.0357689i | ||||
\(736\) | 1.91925 | 0.0707444 | ||||||||
\(737\) | −19.0368 | − | 32.9727i | −0.701230 | − | 1.21457i | ||||
\(738\) | −1.59160 | + | 2.75673i | −0.0585876 | + | 0.101477i | ||||
\(739\) | −0.191803 | + | 0.332212i | −0.00705557 | + | 0.0122206i | −0.869532 | − | 0.493877i | \(-0.835579\pi\) |
0.862476 | + | 0.506098i | \(0.168913\pi\) | |||||||
\(740\) | −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 | 0.991653 | − | 0.128939i | \(-0.0411572\pi\) |
−0.607491 | + | 0.794327i | \(0.707824\pi\) | |||||||
\(744\) | 3.56104 | 0.130554 | ||||||||
\(745\) | −0.614187 | −0.0225021 | ||||||||
\(746\) | −14.2762 | − | 24.7271i | −0.522688 | − | 0.905322i | ||||
\(747\) | 0.851453 | + | 1.47476i | 0.0311531 | + | 0.0539587i | ||||
\(748\) | 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 | ||||
\(751\) | 15.8139 | 0.577057 | 0.288529 | − | 0.957471i | \(-0.406834\pi\) | ||||
0.288529 | + | 0.957471i | \(0.406834\pi\) | |||||||
\(752\) | −5.57211 | + | 9.65117i | −0.203194 | + | 0.351942i | ||||
\(753\) | −2.12395 | − | 3.67878i | −0.0774009 | − | 0.134062i | ||||
\(754\) | −3.35657 | + | 5.14121i | −0.122239 | + | 0.187232i | ||||
\(755\) | 2.99358 | 0.108947 | ||||||||
\(756\) | 2.59452 | − | 0.518144i | 0.0943617 | − | 0.0188447i | ||||
\(757\) | −4.41633 | − | 7.64930i | −0.160514 | − | 0.278019i | 0.774539 | − | 0.632526i | \(-0.217982\pi\) |
−0.935053 | + | 0.354507i | \(0.884649\pi\) | |||||||
\(758\) | −15.5638 | − | 26.9572i | −0.565302 | − | 0.979131i | ||||
\(759\) | −3.27348 | − | 5.66984i | −0.118820 | − | 0.205802i | ||||
\(760\) | 1.44613 | 0.0524565 | ||||||||
\(761\) | −19.3703 | − | 33.5503i | −0.702172 | − | 1.21620i | −0.967702 | − | 0.252096i | \(-0.918880\pi\) |
0.265530 | − | 0.964103i | \(-0.414453\pi\) | |||||||
\(762\) | 12.8112 | 0.464100 | ||||||||
\(763\) | −2.78343 | − | 3.16900i | −0.100767 | − | 0.114725i | ||||
\(764\) | −9.04253 | − | 15.6621i | −0.327147 | − | 0.566635i | ||||
\(765\) | 1.23386 | 0.0446102 | ||||||||
\(766\) | 10.9760 | + | 19.0111i | 0.396580 | + | 0.686897i | ||||
\(767\) | 24.0619 | + | 47.5098i | 0.868824 | + | 1.71548i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | −9.17950 | − | 15.8994i | −0.331021 | − | 0.573345i | 0.651691 | − | 0.758484i | \(-0.274060\pi\) |
−0.982712 | + | 0.185139i | \(0.940726\pi\) | |||||||
\(770\) | 1.35806 | + | 1.54619i | 0.0489412 | + | 0.0557208i | ||||
\(771\) | 7.35836 | − | 12.7450i | 0.265005 | − | 0.459002i | ||||
\(772\) | 2.91296 | − | 5.04539i | 0.104840 | − | 0.181588i | ||||
\(773\) | 12.8481 | 0.462116 | 0.231058 | − | 0.972940i | \(-0.425781\pi\) | ||||
0.231058 | + | 0.972940i | \(0.425781\pi\) | |||||||
\(774\) | 10.3592 | 0.372355 | ||||||||
\(775\) | 8.81004 | − | 15.2594i | 0.316466 | − | 0.548135i | ||||
\(776\) | −6.82663 | + | 11.8241i | −0.245062 | + | 0.424460i | ||||
\(777\) | 3.54958 | − | 10.4831i | 0.127341 | − | 0.376078i | ||||
\(778\) | −1.87365 | − | 3.24525i | −0.0671734 | − | 0.116348i | ||||
\(779\) | 10.0941 | − | 17.4836i | 0.361660 | − | 0.626414i | ||||
\(780\) | −0.449444 | + | 0.688406i | −0.0160927 | + | 0.0246489i | ||||
\(781\) | −0.133362 | − | 0.230990i | −0.00477208 | − | 0.00826548i | ||||
\(782\) | −10.3855 | −0.371383 | ||||||||
\(783\) | −0.851453 | − | 1.47476i | −0.0304285 | − | 0.0527036i | ||||
\(784\) | 6.46305 | − | 2.68867i | 0.230823 | − | 0.0960238i | ||||
\(785\) | −0.725425 | −0.0258915 | ||||||||
\(786\) | −1.75964 | − | 3.04778i | −0.0627641 | − | 0.108711i | ||||
\(787\) | −3.39457 | −0.121003 | −0.0605017 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605017 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(788\) | −10.3527 | − | 17.9315i | −0.368801 | − | 0.638782i | ||||
\(789\) | 11.7053 | + | 20.2741i | 0.416718 | + | 0.721777i | ||||
\(790\) | 0.184941 | + | 0.320327i | 0.00657989 | + | 0.0113967i | ||||
\(791\) | 6.99624 | − | 20.6621i | 0.248758 | − | 0.734661i | ||||
\(792\) | −3.41122 | −0.121212 | ||||||||
\(793\) | 13.2457 | − | 20.2882i | 0.470367 | − | 0.720454i | ||||
\(794\) | −1.95502 | − | 3.38620i | −0.0693812 | − | 0.120172i | ||||
\(795\) | −0.755653 | + | 1.30883i | −0.0268003 | + | 0.0464194i | ||||
\(796\) | −16.3984 | −0.581227 | ||||||||
\(797\) | 1.71983 | − | 2.97884i | 0.0609197 | − | 0.105516i | −0.833957 | − | 0.551829i | \(-0.813930\pi\) |
0.894877 | + | 0.446313i | \(0.147263\pi\) | |||||||
\(798\) | −16.4548 | + | 3.28614i | −0.582494 | + | 0.116328i | ||||
\(799\) | 30.1519 | − | 52.2246i | 1.06670 | − | 1.84757i | ||||
\(800\) | −2.47400 | − | 4.28510i | −0.0874692 | − | 0.151501i | ||||
\(801\) | −8.77285 | − | 15.1950i | −0.309973 | − | 0.536890i | ||||
\(802\) | 26.2260 | 0.926074 | ||||||||
\(803\) | 43.0987 | 1.52092 | ||||||||
\(804\) | 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 | ||||
\(808\) | −8.25823 | + | 14.3037i | −0.290523 | + | 0.503201i | ||||
\(809\) | 13.9913 | − | 24.2336i | 0.491908 | − | 0.852009i | −0.508049 | − | 0.861328i | \(-0.669633\pi\) |
0.999957 | + | 0.00931928i | \(0.00296646\pi\) | |||||||
\(810\) | −0.114009 | − | 0.197470i | −0.00400588 | − | 0.00693839i | ||||
\(811\) | 26.2105 | 0.920377 | 0.460188 | − | 0.887821i | \(-0.347782\pi\) | ||||
0.460188 | + | 0.887821i | \(0.347782\pi\) | |||||||
\(812\) | −2.97325 | − | 3.38512i | −0.104341 | − | 0.118794i | ||||
\(813\) | −7.57375 | + | 13.1181i | −0.265623 | + | 0.460072i | ||||
\(814\) | −7.13490 | + | 12.3580i | −0.250078 | + | 0.433148i | ||||
\(815\) | 3.71535 | 0.130143 | ||||||||
\(816\) | −2.70561 | + | 4.68625i | −0.0947152 | + | 0.164052i | ||||
\(817\) | −65.6997 | −2.29854 | ||||||||
\(818\) | −4.03519 | −0.141087 | ||||||||
\(819\) | 3.54970 | − | 8.85436i | 0.124036 | − | 0.309396i | ||||
\(820\) | 0.725829 | 0.0253470 | ||||||||
\(821\) | −15.5463 | −0.542571 | −0.271285 | − | 0.962499i | \(-0.587449\pi\) | ||||
−0.271285 | + | 0.962499i | \(0.587449\pi\) | |||||||
\(822\) | −8.84776 | + | 15.3248i | −0.308601 | + | 0.534513i | ||||
\(823\) | −47.8212 | −1.66694 | −0.833471 | − | 0.552563i | \(-0.813650\pi\) | ||||
−0.833471 | + | 0.552563i | \(0.813650\pi\) | |||||||
\(824\) | 3.17961 | − | 5.50725i | 0.110767 | − | 0.191854i | ||||
\(825\) | −8.43936 | + | 14.6174i | −0.293821 | + | 0.508913i | ||||
\(826\) | −38.3222 | + | 7.65321i | −1.33340 | + | 0.266289i | ||||
\(827\) | 28.2671 | 0.982944 | 0.491472 | − | 0.870893i | \(-0.336459\pi\) | ||||
0.491472 | + | 0.870893i | \(0.336459\pi\) | |||||||
\(828\) | 0.959623 | + | 1.66212i | 0.0333492 | + | 0.0577625i | ||||
\(829\) | −19.8413 | + | 34.3661i | −0.689116 | + | 1.19358i | 0.283009 | + | 0.959117i | \(0.408667\pi\) |
−0.972124 | + | 0.234466i | \(0.924666\pi\) | |||||||
\(830\) | 0.194147 | − | 0.336273i | 0.00673895 | − | 0.0116722i | ||||
\(831\) | −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 | ||||
\(835\) | 0.377024 | 0.0130474 | ||||||||
\(836\) | 21.6344 | 0.748242 | ||||||||
\(837\) | 1.78052 | + | 3.08395i | 0.0615439 | + | 0.106597i | ||||
\(838\) | −1.74139 | − | 3.01617i | −0.0601552 | − | 0.104192i | ||||
\(839\) | 2.60142 | − | 4.50579i | 0.0898110 | − | 0.155557i | −0.817620 | − | 0.575758i | \(-0.804707\pi\) |
0.907431 | + | 0.420201i | \(0.138040\pi\) | |||||||
\(840\) | −0.398117 | − | 0.453266i | −0.0137363 | − | 0.0156392i | ||||
\(841\) | 13.0501 | − | 22.6034i | 0.450002 | − | 0.779426i | ||||
\(842\) | −18.6028 | −0.641096 | ||||||||
\(843\) | −8.40358 | + | 14.5554i | −0.289435 | + | 0.501316i | ||||
\(844\) | 3.74446 | + | 6.48560i | 0.128890 | + | 0.223243i | ||||
\(845\) | 1.19246 | + | 2.71381i | 0.0410219 | + | 0.0933580i | ||||
\(846\) | −11.1442 | −0.383146 | ||||||||
\(847\) | 1.11114 | + | 1.26506i | 0.0381792 | + | 0.0434679i | ||||
\(848\) | −3.31400 | − | 5.74001i | −0.113803 | − | 0.197113i | ||||
\(849\) | −6.07998 | − | 10.5308i | −0.208664 | − | 0.361417i | ||||
\(850\) | 13.3874 | + | 23.1876i | 0.459183 | + | 0.795328i | ||||
\(851\) | 8.02859 | 0.275216 | ||||||||
\(852\) | 0.0390952 | + | 0.0677149i | 0.00133938 | + | 0.00231988i | ||||
\(853\) | 21.5926 | 0.739318 | 0.369659 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369659 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(854\) | 11.7330 | + | 13.3583i | 0.401495 | + | 0.457112i | ||||
\(855\) | 0.723063 | + | 1.25238i | 0.0247282 | + | 0.0428306i | ||||
\(856\) | −6.54724 | −0.223780 | ||||||||
\(857\) | −6.31723 | − | 10.9418i | −0.215792 | − | 0.373763i | 0.737725 | − | 0.675101i | \(-0.235900\pi\) |
−0.953517 | + | 0.301338i | \(0.902567\pi\) | |||||||
\(858\) | −6.72379 | + | 10.2987i | −0.229547 | + | 0.351593i | ||||
\(859\) | 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 | ||||
\(861\) | −8.25887 | + | 1.64935i | −0.281461 | + | 0.0562098i | ||||
\(862\) | −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 | \(0.235337\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −3.20184 | −0.108866 | ||||||||
\(866\) | 16.7336 | − | 28.9834i | 0.568630 | − | 0.984896i | ||||
\(867\) | 6.14063 | − | 10.6359i | 0.208547 | − | 0.361214i | ||||
\(868\) | 6.21753 | + | 7.07881i | 0.211037 | + | 0.240271i | ||||
\(869\) | 2.76676 | + | 4.79216i | 0.0938558 | + | 0.162563i | ||||
\(870\) | −0.194147 | + | 0.336273i | −0.00658221 | + | 0.0114007i | ||||
\(871\) | 40.1822 | + | 2.20402i | 1.36152 | + | 0.0746804i | ||||
\(872\) | −0.797093 | − | 1.38061i | −0.0269930 | − | 0.0467532i | ||||
\(873\) | −13.6533 | −0.462093 | ||||||||
\(874\) | −6.08607 | − | 10.5414i | −0.205864 | − | 0.356567i | ||||
\(875\) | −5.88523 | + | 1.17532i | −0.198957 | + | 0.0397331i | ||||
\(876\) | −12.6344 | −0.426877 | ||||||||
\(877\) | −3.24950 | − | 5.62831i | −0.109728 | − | 0.190054i | 0.805932 | − | 0.592008i | \(-0.201665\pi\) |
−0.915660 | + | 0.401954i | \(0.868331\pi\) | |||||||
\(878\) | −38.0459 | −1.28399 | ||||||||
\(879\) | −13.8954 | − | 24.0675i | −0.468680 | − | 0.811778i | ||||
\(880\) | 0.388911 | + | 0.673613i | 0.0131102 | + | 0.0227075i | ||||
\(881\) | 6.17234 | + | 10.6908i | 0.207951 | + | 0.360182i | 0.951069 | − | 0.308979i | \(-0.0999871\pi\) |
−0.743118 | + | 0.669161i | \(0.766654\pi\) | |||||||
\(882\) | 5.55998 | + | 4.25284i | 0.187214 | + | 0.143200i | ||||
\(883\) | 42.2001 | 1.42015 | 0.710073 | − | 0.704128i | \(-0.248662\pi\) | ||||
0.710073 | + | 0.704128i | \(0.248662\pi\) | |||||||
\(884\) | 8.81517 | + | 17.4054i | 0.296486 | + | 0.585408i | ||||
\(885\) | 1.68397 | + | 2.91672i | 0.0566060 | + | 0.0980444i | ||||
\(886\) | −4.35467 | + | 7.54250i | −0.146298 | + | 0.253395i | ||||
\(887\) | −34.3380 | −1.15296 | −0.576478 | − | 0.817112i | \(-0.695574\pi\) | ||||
−0.576478 | + | 0.817112i | \(0.695574\pi\) | |||||||
\(888\) | 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 | ||||
\(891\) | −1.70561 | − | 2.95420i | −0.0571400 | − | 0.0989694i | ||||
\(892\) | −8.41325 | − | 14.5722i | −0.281696 | − | 0.487913i | ||||
\(893\) | 70.6782 | 2.36516 | ||||||||
\(894\) | 2.69358 | 0.0900868 | ||||||||
\(895\) | −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 | ||||
\(899\) | 3.03206 | − | 5.25169i | 0.101125 | − | 0.175154i | ||||
\(900\) | 2.47400 | − | 4.28510i | 0.0824668 | − | 0.142837i | ||||
\(901\) | 17.9328 | + | 31.0604i | 0.597427 | + | 1.03477i | ||||
\(902\) | 10.8586 | 0.361551 | ||||||||
\(903\) | 18.0870 | + | 20.5926i | 0.601899 | + | 0.685277i | ||||
\(904\) | 4.12255 | − | 7.14047i | 0.137114 | − | 0.237488i | ||||
\(905\) | 0.129786 | − | 0.224795i | 0.00431422 | − | 0.00747244i | ||||
\(906\) | −13.1286 | −0.436170 | ||||||||
\(907\) | 9.36040 | − | 16.2127i | 0.310807 | − | 0.538334i | −0.667730 | − | 0.744403i | \(-0.732734\pi\) |
0.978537 | + | 0.206070i | \(0.0660674\pi\) | |||||||
\(908\) | −4.23214 | −0.140449 | ||||||||
\(909\) | −16.5165 | −0.547816 | ||||||||
\(910\) | −2.15317 | + | 0.308521i | −0.0713768 | + | 0.0102274i | ||||
\(911\) | −30.3513 | −1.00558 | −0.502791 | − | 0.864408i | \(-0.667694\pi\) | ||||
−0.502791 | + | 0.864408i | \(0.667694\pi\) | |||||||
\(912\) | −6.34214 | −0.210009 | ||||||||
\(913\) | 2.90449 | − | 5.03073i | 0.0961247 | − | 0.166493i | ||||
\(914\) | −11.5899 | −0.383358 | ||||||||
\(915\) | 0.766142 | − | 1.32700i | 0.0253279 | − | 0.0438691i | ||||
\(916\) | −6.86498 | + | 11.8905i | −0.226825 | + | 0.392873i | ||||
\(917\) | 2.98622 | − | 8.81926i | 0.0986137 | − | 0.291238i | ||||
\(918\) | −5.41122 | −0.178597 | ||||||||
\(919\) | −20.3758 | − | 35.2919i | −0.672135 | − | 1.16417i | −0.977297 | − | 0.211872i | \(-0.932044\pi\) |
0.305162 | − | 0.952300i | \(-0.401289\pi\) | |||||||
\(920\) | 0.218812 | − | 0.378993i | 0.00721402 | − | 0.0124950i | ||||
\(921\) | −7.34243 | + | 12.7175i | −0.241941 | + | 0.419055i | ||||
\(922\) | 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 | ||||
\(926\) | 39.5334 | 1.29915 | ||||||||
\(927\) | 6.35922 | 0.208864 | ||||||||
\(928\) | −0.851453 | − | 1.47476i | −0.0279503 | − | 0.0484114i | ||||
\(929\) | −2.60978 | − | 4.52027i | −0.0856242 | − | 0.148305i | 0.820033 | − | 0.572316i | \(-0.193955\pi\) |
−0.905657 | + | 0.424011i | \(0.860622\pi\) | |||||||
\(930\) | 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 | ||||
\(933\) | 7.72695 | 0.252969 | ||||||||
\(934\) | 0.425191 | − | 0.736452i | 0.0139127 | − | 0.0240974i | ||||
\(935\) | −2.10448 | − | 3.64506i | −0.0688238 | − | 0.119206i | ||||
\(936\) | 1.97108 | − | 3.01908i | 0.0644269 | − | 0.0986816i | ||||
\(937\) | −31.2199 | −1.01991 | −0.509956 | − | 0.860201i | \(-0.670338\pi\) | ||||
−0.509956 | + | 0.860201i | \(0.670338\pi\) | |||||||
\(938\) | −9.47074 | + | 27.9701i | −0.309231 | + | 0.913257i | ||||
\(939\) | 10.0982 | + | 17.4906i | 0.329542 | + | 0.570784i | ||||
\(940\) | 1.27054 | + | 2.20065i | 0.0414406 | + | 0.0717772i | ||||
\(941\) | −25.3480 | − | 43.9041i | −0.826322 | − | 1.43123i | −0.900904 | − | 0.434018i | \(-0.857096\pi\) |
0.0745820 | − | 0.997215i | \(-0.476238\pi\) | |||||||
\(942\) | 3.18143 | 0.103657 | ||||||||
\(943\) | −3.05467 | − | 5.29084i | −0.0994737 | − | 0.172294i | ||||
\(944\) | −14.7704 | −0.480737 | ||||||||
\(945\) | 0.193482 | − | 0.571413i | 0.00629395 | − | 0.0185881i | ||||
\(946\) | −17.6688 | − | 30.6032i | −0.574461 | − | 0.994996i | ||||
\(947\) | 48.3407 | 1.57086 | 0.785431 | − | 0.618949i | \(-0.212441\pi\) | ||||
0.785431 | + | 0.618949i | \(0.212441\pi\) | |||||||
\(948\) | −0.811077 | − | 1.40483i | −0.0263425 | − | 0.0456266i | ||||
\(949\) | −24.9035 | + | 38.1443i | −0.808402 | + | 1.23822i | ||||
\(950\) | −15.6905 | + | 27.1767i | −0.509066 | + | 0.881729i | ||||
\(951\) | −7.36088 | − | 12.7494i | −0.238693 | − | 0.413428i | ||||
\(952\) | −14.0395 | + | 2.80379i | −0.455023 | + | 0.0908713i | ||||
\(953\) | 0.444682 | − | 0.770211i | 0.0144046 | − | 0.0249496i | −0.858733 | − | 0.512423i | \(-0.828748\pi\) |
0.873138 | + | 0.487473i | \(0.162081\pi\) | |||||||
\(954\) | 3.31400 | − | 5.74001i | 0.107295 | − | 0.185840i | ||||
\(955\) | −4.12373 | −0.133441 | ||||||||
\(956\) | −25.2189 | −0.815638 | ||||||||
\(957\) | −2.90449 | + | 5.03073i | −0.0938889 | + | 0.162620i | ||||
\(958\) | 5.78732 | − | 10.0239i | 0.186980 | − | 0.323859i | ||||
\(959\) | −45.9114 | + | 9.16883i | −1.48256 | + | 0.296077i | ||||
\(960\) | −0.114009 | − | 0.197470i | −0.00367964 | − | 0.00637332i | ||||
\(961\) | 9.15948 | − | 15.8647i | 0.295467 | − | 0.511764i | ||||
\(962\) | −6.81466 | − | 13.4555i | −0.219714 | − | 0.433821i | ||||
\(963\) | −3.27362 | − | 5.67008i | −0.105491 | − | 0.182716i | ||||
\(964\) | 27.8367 | 0.896560 | ||||||||
\(965\) | −0.664209 | − | 1.15044i | −0.0213817 | − | 0.0370341i | ||||
\(966\) | −1.62854 | + | 4.80961i | −0.0523976 | + | 0.154747i | ||||
\(967\) | 4.75544 | 0.152925 | 0.0764623 | − | 0.997072i | \(-0.475638\pi\) | ||||
0.0764623 | + | 0.997072i | \(0.475638\pi\) | |||||||
\(968\) | 0.318198 | + | 0.551135i | 0.0102273 | + | 0.0177142i | ||||
\(969\) | 34.3187 | 1.10248 | ||||||||
\(970\) | 1.55660 | + | 2.69611i | 0.0499794 | + | 0.0865669i | ||||
\(971\) | −0.775940 | − | 1.34397i | −0.0249011 | − | 0.0431300i | 0.853306 | − | 0.521410i | \(-0.174594\pi\) |
−0.878207 | + | 0.478280i | \(0.841260\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −6.75978 | + | 19.9638i | −0.216708 | + | 0.640009i | ||||
\(974\) | 13.9320 | 0.446412 | ||||||||
\(975\) | −8.06058 | − | 15.9155i | −0.258145 | − | 0.509704i | ||||
\(976\) | 3.35999 | + | 5.81968i | 0.107551 | + | 0.186283i | ||||
\(977\) | 15.7709 | − | 27.3161i | 0.504557 | − | 0.873919i | −0.495429 | − | 0.868648i | \(-0.664989\pi\) |
0.999986 | − | 0.00527014i | \(-0.00167755\pi\) | |||||||
\(978\) | −16.2940 | −0.521026 | ||||||||
\(979\) | −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 | ||||
\(982\) | −4.76716 | − | 8.25697i | −0.152126 | − | 0.263490i | ||||
\(983\) | −15.7150 | − | 27.2192i | −0.501230 | − | 0.868157i | −0.999999 | − | 0.00142135i | \(-0.999548\pi\) |
0.498769 | − | 0.866735i | \(-0.333786\pi\) | |||||||
\(984\) | −3.18320 | −0.101477 | ||||||||
\(985\) | −4.72124 | −0.150431 | ||||||||
\(986\) | 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 | ||||
\(990\) | −0.388911 | + | 0.673613i | −0.0123604 | + | 0.0214088i | ||||
\(991\) | −0.302804 | + | 0.524472i | −0.00961888 | + | 0.0166604i | −0.870795 | − | 0.491647i | \(-0.836395\pi\) |
0.861176 | + | 0.508307i | \(0.169729\pi\) | |||||||
\(992\) | 1.78052 | + | 3.08395i | 0.0565316 | + | 0.0979157i | ||||
\(993\) | −4.10872 | −0.130386 | ||||||||
\(994\) | −0.0663472 | + | 0.195945i | −0.00210441 | + | 0.00621499i | ||||
\(995\) | −1.86957 | + | 3.23820i | −0.0592695 | + | 0.102658i | ||||
\(996\) | −0.851453 | + | 1.47476i | −0.0269793 | + | 0.0467296i | ||||
\(997\) | 0.368340 | 0.0116654 | 0.00583272 | − | 0.999983i | \(-0.498143\pi\) | ||||
0.00583272 | + | 0.999983i | \(0.498143\pi\) | |||||||
\(998\) | −21.9135 | + | 37.9553i | −0.693659 | + | 1.20145i | ||||
\(999\) | 4.18320 | 0.132351 |
(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.j.e.289.3 | ✓ | 10 | |
3.2 | odd | 2 | 1638.2.m.k.289.3 | 10 | |||
7.4 | even | 3 | 546.2.k.e.445.3 | yes | 10 | ||
13.9 | even | 3 | 546.2.k.e.373.3 | yes | 10 | ||
21.11 | odd | 6 | 1638.2.p.j.991.3 | 10 | |||
39.35 | odd | 6 | 1638.2.p.j.919.3 | 10 | |||
91.74 | even | 3 | inner | 546.2.j.e.529.3 | yes | 10 | |
273.74 | odd | 6 | 1638.2.m.k.1621.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
546.2.j.e.529.3 | yes | 10 | 91.74 | even | 3 | inner | |
546.2.k.e.373.3 | yes | 10 | 13.9 | even | 3 | ||
546.2.k.e.445.3 | yes | 10 | 7.4 | even | 3 | ||
1638.2.m.k.289.3 | 10 | 3.2 | odd | 2 | |||
1638.2.m.k.1621.3 | 10 | 273.74 | odd | 6 | |||
1638.2.p.j.919.3 | 10 | 39.35 | odd | 6 | |||
1638.2.p.j.991.3 | 10 | 21.11 | odd | 6 |