Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(93,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.93");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.e (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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.6498455769.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.2 | ||
Root | \(0.271028 - 0.469434i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.277 |
Dual form | 322.2.e.d.93.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.271028 | + | 0.469434i | −0.156478 | + | 0.271028i | −0.933596 | − | 0.358327i | \(-0.883347\pi\) |
0.777118 | + | 0.629355i | \(0.216681\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.298300 | + | 0.516670i | 0.133404 | + | 0.231062i | 0.924987 | − | 0.380000i | \(-0.124076\pi\) |
−0.791583 | + | 0.611062i | \(0.790743\pi\) | |||||||
\(6\) | −0.542055 | −0.221293 | ||||||||
\(7\) | −2.61586 | − | 0.396592i | −0.988702 | − | 0.149898i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.35309 | + | 2.34362i | 0.451029 | + | 0.781206i | ||||
\(10\) | −0.298300 | + | 0.516670i | −0.0943306 | + | 0.163385i | ||||
\(11\) | −2.92689 | + | 5.06952i | −0.882491 | + | 1.52852i | −0.0339283 | + | 0.999424i | \(0.510802\pi\) |
−0.848563 | + | 0.529095i | \(0.822532\pi\) | |||||||
\(12\) | −0.271028 | − | 0.469434i | −0.0782389 | − | 0.135514i | ||||
\(13\) | 0.239279 | 0.0663642 | 0.0331821 | − | 0.999449i | \(-0.489436\pi\) | ||||
0.0331821 | + | 0.999449i | \(0.489436\pi\) | |||||||
\(14\) | −0.964471 | − | 2.46370i | −0.257766 | − | 0.658450i | ||||
\(15\) | −0.323390 | −0.0834989 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.20170 | − | 2.08141i | 0.291455 | − | 0.504815i | −0.682699 | − | 0.730700i | \(-0.739194\pi\) |
0.974154 | + | 0.225885i | \(0.0725273\pi\) | |||||||
\(18\) | −1.35309 | + | 2.34362i | −0.318926 | + | 0.552396i | ||||
\(19\) | 2.54653 | + | 4.41072i | 0.584214 | + | 1.01189i | 0.994973 | + | 0.100145i | \(0.0319306\pi\) |
−0.410759 | + | 0.911744i | \(0.634736\pi\) | |||||||
\(20\) | −0.596599 | −0.133404 | ||||||||
\(21\) | 0.895143 | − | 1.12048i | 0.195336 | − | 0.244510i | ||||
\(22\) | −5.85378 | −1.24803 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 0.271028 | − | 0.469434i | 0.0553233 | − | 0.0958227i | ||||
\(25\) | 2.32203 | − | 4.02188i | 0.464407 | − | 0.804376i | ||||
\(26\) | 0.119640 | + | 0.207222i | 0.0234633 | + | 0.0406396i | ||||
\(27\) | −3.09306 | −0.595260 | ||||||||
\(28\) | 1.65139 | − | 2.06710i | 0.312083 | − | 0.390646i | ||||
\(29\) | −5.19369 | −0.964443 | −0.482222 | − | 0.876049i | \(-0.660170\pi\) | ||||
−0.482222 | + | 0.876049i | \(0.660170\pi\) | |||||||
\(30\) | −0.161695 | − | 0.280064i | −0.0295213 | − | 0.0511324i | ||||
\(31\) | 1.22072 | − | 2.11434i | 0.219247 | − | 0.379747i | −0.735331 | − | 0.677708i | \(-0.762973\pi\) |
0.954578 | + | 0.297961i | \(0.0963066\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.58654 | − | 2.74796i | −0.276181 | − | 0.478359i | ||||
\(34\) | 2.40340 | 0.412180 | ||||||||
\(35\) | −0.575403 | − | 1.46984i | −0.0972608 | − | 0.248448i | ||||
\(36\) | −2.70618 | −0.451029 | ||||||||
\(37\) | −1.33005 | − | 2.30371i | −0.218659 | − | 0.378728i | 0.735740 | − | 0.677265i | \(-0.236835\pi\) |
−0.954398 | + | 0.298537i | \(0.903501\pi\) | |||||||
\(38\) | −2.54653 | + | 4.41072i | −0.413102 | + | 0.715513i | ||||
\(39\) | −0.0648513 | + | 0.112326i | −0.0103845 | + | 0.0179865i | ||||
\(40\) | −0.298300 | − | 0.516670i | −0.0471653 | − | 0.0816927i | ||||
\(41\) | 11.6365 | 1.81732 | 0.908658 | − | 0.417540i | \(-0.137108\pi\) | ||||
0.908658 | + | 0.417540i | \(0.137108\pi\) | |||||||
\(42\) | 1.41794 | + | 0.214975i | 0.218793 | + | 0.0331713i | ||||
\(43\) | 3.93789 | 0.600523 | 0.300262 | − | 0.953857i | \(-0.402926\pi\) | ||||
0.300262 | + | 0.953857i | \(0.402926\pi\) | |||||||
\(44\) | −2.92689 | − | 5.06952i | −0.441245 | − | 0.764260i | ||||
\(45\) | −0.807252 | + | 1.39820i | −0.120338 | + | 0.208431i | ||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | 3.86787 | + | 6.69935i | 0.564187 | + | 0.977201i | 0.997125 | + | 0.0757767i | \(0.0241436\pi\) |
−0.432938 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(48\) | 0.542055 | 0.0782389 | ||||||||
\(49\) | 6.68543 | + | 2.07486i | 0.955061 | + | 0.296408i | ||||
\(50\) | 4.64407 | 0.656771 | ||||||||
\(51\) | 0.651388 | + | 1.12824i | 0.0912125 | + | 0.157985i | ||||
\(52\) | −0.119640 | + | 0.207222i | −0.0165910 | + | 0.0287365i | ||||
\(53\) | −2.18692 | + | 3.78785i | −0.300396 | + | 0.520301i | −0.976226 | − | 0.216757i | \(-0.930452\pi\) |
0.675830 | + | 0.737058i | \(0.263786\pi\) | |||||||
\(54\) | −1.54653 | − | 2.67867i | −0.210456 | − | 0.364521i | ||||
\(55\) | −3.49236 | −0.470910 | ||||||||
\(56\) | 2.61586 | + | 0.396592i | 0.349559 | + | 0.0529968i | ||||
\(57\) | −2.76072 | −0.365666 | ||||||||
\(58\) | −2.59684 | − | 4.49786i | −0.340982 | − | 0.590599i | ||||
\(59\) | 5.08206 | − | 8.80239i | 0.661628 | − | 1.14597i | −0.318560 | − | 0.947903i | \(-0.603199\pi\) |
0.980188 | − | 0.198070i | \(-0.0634675\pi\) | |||||||
\(60\) | 0.161695 | − | 0.280064i | 0.0208747 | − | 0.0361561i | ||||
\(61\) | 0.340355 | + | 0.589512i | 0.0435780 | + | 0.0754793i | 0.886992 | − | 0.461785i | \(-0.152791\pi\) |
−0.843414 | + | 0.537265i | \(0.819458\pi\) | |||||||
\(62\) | 2.44143 | 0.310062 | ||||||||
\(63\) | −2.61003 | − | 6.66719i | −0.328833 | − | 0.839988i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0713770 | + | 0.123629i | 0.00885323 | + | 0.0153342i | ||||
\(66\) | 1.58654 | − | 2.74796i | 0.195289 | − | 0.338251i | ||||
\(67\) | 1.56131 | − | 2.70428i | 0.190745 | − | 0.330380i | −0.754752 | − | 0.656010i | \(-0.772243\pi\) |
0.945497 | + | 0.325630i | \(0.105576\pi\) | |||||||
\(68\) | 1.20170 | + | 2.08141i | 0.145728 | + | 0.252408i | ||||
\(69\) | −0.542055 | −0.0652558 | ||||||||
\(70\) | 0.985217 | − | 1.23323i | 0.117756 | − | 0.147400i | ||||
\(71\) | −5.55947 | −0.659788 | −0.329894 | − | 0.944018i | \(-0.607013\pi\) | ||||
−0.329894 | + | 0.944018i | \(0.607013\pi\) | |||||||
\(72\) | −1.35309 | − | 2.34362i | −0.159463 | − | 0.276198i | ||||
\(73\) | 3.30483 | − | 5.72413i | 0.386801 | − | 0.669958i | −0.605217 | − | 0.796061i | \(-0.706914\pi\) |
0.992017 | + | 0.126103i | \(0.0402469\pi\) | |||||||
\(74\) | 1.33005 | − | 2.30371i | 0.154615 | − | 0.267801i | ||||
\(75\) | 1.25867 | + | 2.18008i | 0.145339 | + | 0.251734i | ||||
\(76\) | −5.09306 | −0.584214 | ||||||||
\(77\) | 9.66687 | − | 12.1004i | 1.10164 | − | 1.37897i | ||||
\(78\) | −0.129703 | −0.0146859 | ||||||||
\(79\) | 2.99199 | + | 5.18227i | 0.336625 | + | 0.583051i | 0.983796 | − | 0.179294i | \(-0.0573813\pi\) |
−0.647171 | + | 0.762345i | \(0.724048\pi\) | |||||||
\(80\) | 0.298300 | − | 0.516670i | 0.0333509 | − | 0.0577655i | ||||
\(81\) | −3.22096 | + | 5.57887i | −0.357884 | + | 0.619874i | ||||
\(82\) | 5.81825 | + | 10.0775i | 0.642519 | + | 1.11287i | ||||
\(83\) | −0.386886 | −0.0424662 | −0.0212331 | − | 0.999775i | \(-0.506759\pi\) | ||||
−0.0212331 | + | 0.999775i | \(0.506759\pi\) | |||||||
\(84\) | 0.522796 | + | 1.33546i | 0.0570417 | + | 0.145711i | ||||
\(85\) | 1.43387 | 0.155525 | ||||||||
\(86\) | 1.96895 | + | 3.41032i | 0.212317 | + | 0.367744i | ||||
\(87\) | 1.40763 | − | 2.43809i | 0.150914 | − | 0.261391i | ||||
\(88\) | 2.92689 | − | 5.06952i | 0.312008 | − | 0.540413i | ||||
\(89\) | 6.54653 | + | 11.3389i | 0.693931 | + | 1.20192i | 0.970540 | + | 0.240941i | \(0.0774560\pi\) |
−0.276609 | + | 0.960983i | \(0.589211\pi\) | |||||||
\(90\) | −1.61450 | −0.170184 | ||||||||
\(91\) | −0.625921 | − | 0.0948963i | −0.0656144 | − | 0.00994784i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0.661695 | + | 1.14609i | 0.0686146 | + | 0.118844i | ||||
\(94\) | −3.86787 | + | 6.69935i | −0.398940 | + | 0.690985i | ||||
\(95\) | −1.51926 | + | 2.63143i | −0.155873 | + | 0.269979i | ||||
\(96\) | 0.271028 | + | 0.469434i | 0.0276616 | + | 0.0479114i | ||||
\(97\) | −0.0666948 | −0.00677183 | −0.00338592 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338592 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(98\) | 1.54584 | + | 6.82718i | 0.156153 | + | 0.689649i | ||||
\(99\) | −15.8414 | −1.59212 | ||||||||
\(100\) | 2.32203 | + | 4.02188i | 0.232203 | + | 0.402188i | ||||
\(101\) | 8.17935 | − | 14.1671i | 0.813876 | − | 1.40967i | −0.0962559 | − | 0.995357i | \(-0.530687\pi\) |
0.910132 | − | 0.414318i | \(-0.135980\pi\) | |||||||
\(102\) | −0.651388 | + | 1.12824i | −0.0644970 | + | 0.111712i | ||||
\(103\) | −9.90684 | − | 17.1591i | −0.976150 | − | 1.69074i | −0.676087 | − | 0.736822i | \(-0.736326\pi\) |
−0.300063 | − | 0.953919i | \(-0.597008\pi\) | |||||||
\(104\) | −0.239279 | −0.0234633 | ||||||||
\(105\) | 0.845942 | + | 0.128254i | 0.0825555 | + | 0.0125163i | ||||
\(106\) | −4.37383 | −0.424824 | ||||||||
\(107\) | 7.69837 | + | 13.3340i | 0.744229 | + | 1.28904i | 0.950554 | + | 0.310560i | \(0.100516\pi\) |
−0.206324 | + | 0.978484i | \(0.566150\pi\) | |||||||
\(108\) | 1.54653 | − | 2.67867i | 0.148815 | − | 0.257755i | ||||
\(109\) | −8.14407 | + | 14.1059i | −0.780060 | + | 1.35110i | 0.151846 | + | 0.988404i | \(0.451478\pi\) |
−0.931906 | + | 0.362700i | \(0.881855\pi\) | |||||||
\(110\) | −1.74618 | − | 3.02448i | −0.166492 | − | 0.288372i | ||||
\(111\) | 1.44192 | 0.136861 | ||||||||
\(112\) | 0.964471 | + | 2.46370i | 0.0911339 | + | 0.232797i | ||||
\(113\) | −2.86135 | −0.269173 | −0.134586 | − | 0.990902i | \(-0.542971\pi\) | ||||
−0.134586 | + | 0.990902i | \(0.542971\pi\) | |||||||
\(114\) | −1.38036 | − | 2.39085i | −0.129283 | − | 0.223924i | ||||
\(115\) | −0.298300 | + | 0.516670i | −0.0278166 | + | 0.0481797i | ||||
\(116\) | 2.59684 | − | 4.49786i | 0.241111 | − | 0.417616i | ||||
\(117\) | 0.323766 | + | 0.560780i | 0.0299322 | + | 0.0518441i | ||||
\(118\) | 10.1641 | 0.935683 | ||||||||
\(119\) | −3.96895 | + | 4.96808i | −0.363833 | + | 0.455423i | ||||
\(120\) | 0.323390 | 0.0295213 | ||||||||
\(121\) | −11.6334 | − | 20.1496i | −1.05758 | − | 1.83178i | ||||
\(122\) | −0.340355 | + | 0.589512i | −0.0308143 | + | 0.0533719i | ||||
\(123\) | −3.15381 | + | 5.46257i | −0.284370 | + | 0.492543i | ||||
\(124\) | 1.22072 | + | 2.11434i | 0.109623 | + | 0.189873i | ||||
\(125\) | 5.75365 | 0.514622 | ||||||||
\(126\) | 4.46895 | − | 5.59395i | 0.398125 | − | 0.498348i | ||||
\(127\) | −1.66420 | −0.147673 | −0.0738367 | − | 0.997270i | \(-0.523524\pi\) | ||||
−0.0738367 | + | 0.997270i | \(0.523524\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.06728 | + | 1.84858i | −0.0939685 | + | 0.162758i | ||||
\(130\) | −0.0713770 | + | 0.123629i | −0.00626018 | + | 0.0108429i | ||||
\(131\) | 7.44820 | + | 12.9007i | 0.650752 | + | 1.12714i | 0.982941 | + | 0.183923i | \(0.0588797\pi\) |
−0.332188 | + | 0.943213i | \(0.607787\pi\) | |||||||
\(132\) | 3.17307 | 0.276181 | ||||||||
\(133\) | −4.91211 | − | 12.5478i | −0.425934 | − | 1.08803i | ||||
\(134\) | 3.12263 | 0.269754 | ||||||||
\(135\) | −0.922660 | − | 1.59809i | −0.0794099 | − | 0.137542i | ||||
\(136\) | −1.20170 | + | 2.08141i | −0.103045 | + | 0.178479i | ||||
\(137\) | −1.13442 | + | 1.96488i | −0.0969203 | + | 0.167871i | −0.910408 | − | 0.413711i | \(-0.864233\pi\) |
0.813488 | + | 0.581581i | \(0.197566\pi\) | |||||||
\(138\) | −0.271028 | − | 0.469434i | −0.0230714 | − | 0.0399608i | ||||
\(139\) | −18.1536 | −1.53977 | −0.769883 | − | 0.638185i | \(-0.779686\pi\) | ||||
−0.769883 | + | 0.638185i | \(0.779686\pi\) | |||||||
\(140\) | 1.56062 | + | 0.236606i | 0.131896 | + | 0.0199969i | ||||
\(141\) | −4.19320 | −0.353131 | ||||||||
\(142\) | −2.77974 | − | 4.81464i | −0.233270 | − | 0.404036i | ||||
\(143\) | −0.700345 | + | 1.21303i | −0.0585658 | + | 0.101439i | ||||
\(144\) | 1.35309 | − | 2.34362i | 0.112757 | − | 0.195301i | ||||
\(145\) | −1.54928 | − | 2.68342i | −0.128660 | − | 0.222846i | ||||
\(146\) | 6.60965 | 0.547019 | ||||||||
\(147\) | −2.78594 | + | 2.57602i | −0.229781 | + | 0.212467i | ||||
\(148\) | 2.66010 | 0.218659 | ||||||||
\(149\) | 2.67661 | + | 4.63602i | 0.219276 | + | 0.379798i | 0.954587 | − | 0.297932i | \(-0.0962970\pi\) |
−0.735311 | + | 0.677730i | \(0.762964\pi\) | |||||||
\(150\) | −1.25867 | + | 2.18008i | −0.102770 | + | 0.178003i | ||||
\(151\) | 3.49244 | − | 6.04908i | 0.284211 | − | 0.492267i | −0.688207 | − | 0.725514i | \(-0.741602\pi\) |
0.972417 | + | 0.233247i | \(0.0749352\pi\) | |||||||
\(152\) | −2.54653 | − | 4.41072i | −0.206551 | − | 0.357757i | ||||
\(153\) | 6.50403 | 0.525819 | ||||||||
\(154\) | 15.3127 | + | 2.32156i | 1.23393 | + | 0.187077i | ||||
\(155\) | 1.45656 | 0.116993 | ||||||||
\(156\) | −0.0648513 | − | 0.112326i | −0.00519226 | − | 0.00899326i | ||||
\(157\) | 3.96471 | − | 6.86709i | 0.316419 | − | 0.548053i | −0.663319 | − | 0.748336i | \(-0.730853\pi\) |
0.979738 | + | 0.200283i | \(0.0641862\pi\) | |||||||
\(158\) | −2.99199 | + | 5.18227i | −0.238030 | + | 0.412280i | ||||
\(159\) | −1.18543 | − | 2.05322i | −0.0940107 | − | 0.162831i | ||||
\(160\) | 0.596599 | 0.0471653 | ||||||||
\(161\) | −0.964471 | − | 2.46370i | −0.0760109 | − | 0.194166i | ||||
\(162\) | −6.44192 | −0.506125 | ||||||||
\(163\) | −7.07232 | − | 12.2496i | −0.553947 | − | 0.959464i | −0.997985 | − | 0.0634556i | \(-0.979788\pi\) |
0.444038 | − | 0.896008i | \(-0.353545\pi\) | |||||||
\(164\) | −5.81825 | + | 10.0775i | −0.454329 | + | 0.786921i | ||||
\(165\) | 0.946527 | − | 1.63943i | 0.0736870 | − | 0.127630i | ||||
\(166\) | −0.193443 | − | 0.335053i | −0.0150141 | − | 0.0260052i | ||||
\(167\) | −17.8346 | −1.38008 | −0.690040 | − | 0.723771i | \(-0.742407\pi\) | ||||
−0.690040 | + | 0.723771i | \(0.742407\pi\) | |||||||
\(168\) | −0.895143 | + | 1.12048i | −0.0690618 | + | 0.0864472i | ||||
\(169\) | −12.9427 | −0.995596 | ||||||||
\(170\) | 0.716934 | + | 1.24177i | 0.0549863 | + | 0.0952391i | ||||
\(171\) | −6.89136 | + | 11.9362i | −0.526996 | + | 0.912783i | ||||
\(172\) | −1.96895 | + | 3.41032i | −0.150131 | + | 0.260034i | ||||
\(173\) | 3.34060 | + | 5.78609i | 0.253981 | + | 0.439908i | 0.964618 | − | 0.263651i | \(-0.0849266\pi\) |
−0.710637 | + | 0.703559i | \(0.751593\pi\) | |||||||
\(174\) | 2.81526 | 0.213425 | ||||||||
\(175\) | −7.66916 | + | 9.59977i | −0.579734 | + | 0.725675i | ||||
\(176\) | 5.85378 | 0.441245 | ||||||||
\(177\) | 2.75476 | + | 4.77138i | 0.207060 | + | 0.358639i | ||||
\(178\) | −6.54653 | + | 11.3389i | −0.490683 | + | 0.849888i | ||||
\(179\) | −6.68140 | + | 11.5725i | −0.499392 | + | 0.864972i | −1.00000 | 0.000702380i | \(-0.999776\pi\) | |
0.500608 | + | 0.865674i | \(0.333110\pi\) | |||||||
\(180\) | −0.807252 | − | 1.39820i | −0.0601690 | − | 0.104216i | ||||
\(181\) | −23.6069 | −1.75469 | −0.877345 | − | 0.479860i | \(-0.840687\pi\) | ||||
−0.877345 | + | 0.479860i | \(0.840687\pi\) | |||||||
\(182\) | −0.230778 | − | 0.589512i | −0.0171064 | − | 0.0436975i | ||||
\(183\) | −0.368982 | −0.0272759 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 0.793506 | − | 1.37439i | 0.0583397 | − | 0.101047i | ||||
\(186\) | −0.661695 | + | 1.14609i | −0.0485178 | + | 0.0840353i | ||||
\(187\) | 7.03449 | + | 12.1841i | 0.514413 | + | 0.890989i | ||||
\(188\) | −7.73574 | −0.564187 | ||||||||
\(189\) | 8.09101 | + | 1.22668i | 0.588535 | + | 0.0892281i | ||||
\(190\) | −3.03852 | −0.220437 | ||||||||
\(191\) | −3.45243 | − | 5.97979i | −0.249809 | − | 0.432682i | 0.713664 | − | 0.700489i | \(-0.247035\pi\) |
−0.963473 | + | 0.267806i | \(0.913701\pi\) | |||||||
\(192\) | −0.271028 | + | 0.469434i | −0.0195597 | + | 0.0338784i | ||||
\(193\) | 9.74650 | − | 16.8814i | 0.701568 | − | 1.21515i | −0.266347 | − | 0.963877i | \(-0.585817\pi\) |
0.967916 | − | 0.251275i | \(-0.0808498\pi\) | |||||||
\(194\) | −0.0333474 | − | 0.0577594i | −0.00239420 | − | 0.00414688i | ||||
\(195\) | −0.0773805 | −0.00554134 | ||||||||
\(196\) | −5.13959 | + | 4.75232i | −0.367114 | + | 0.339452i | ||||
\(197\) | 15.5739 | 1.10960 | 0.554798 | − | 0.831985i | \(-0.312796\pi\) | ||||
0.554798 | + | 0.831985i | \(0.312796\pi\) | |||||||
\(198\) | −7.92068 | − | 13.7190i | −0.562898 | − | 0.974969i | ||||
\(199\) | −1.68897 | + | 2.92538i | −0.119728 | + | 0.207374i | −0.919660 | − | 0.392716i | \(-0.871535\pi\) |
0.799932 | + | 0.600091i | \(0.204869\pi\) | |||||||
\(200\) | −2.32203 | + | 4.02188i | −0.164193 | + | 0.284390i | ||||
\(201\) | 0.846318 | + | 1.46587i | 0.0596947 | + | 0.103394i | ||||
\(202\) | 16.3587 | 1.15099 | ||||||||
\(203\) | 13.5859 | + | 2.05977i | 0.953547 | + | 0.144568i | ||||
\(204\) | −1.30278 | −0.0912125 | ||||||||
\(205\) | 3.47117 | + | 6.01224i | 0.242437 | + | 0.419913i | ||||
\(206\) | 9.90684 | − | 17.1591i | 0.690242 | − | 1.19553i | ||||
\(207\) | −1.35309 | + | 2.34362i | −0.0940461 | + | 0.162893i | ||||
\(208\) | −0.119640 | − | 0.207222i | −0.00829552 | − | 0.0143683i | ||||
\(209\) | −29.8137 | −2.06226 | ||||||||
\(210\) | 0.311900 | + | 0.796734i | 0.0215231 | + | 0.0549799i | ||||
\(211\) | 4.02818 | 0.277311 | 0.138656 | − | 0.990341i | \(-0.455722\pi\) | ||||
0.138656 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(212\) | −2.18692 | − | 3.78785i | −0.150198 | − | 0.260151i | ||||
\(213\) | 1.50677 | − | 2.60980i | 0.103242 | − | 0.178821i | ||||
\(214\) | −7.69837 | + | 13.3340i | −0.526250 | + | 0.911491i | ||||
\(215\) | 1.17467 | + | 2.03459i | 0.0801120 | + | 0.138758i | ||||
\(216\) | 3.09306 | 0.210456 | ||||||||
\(217\) | −4.03175 | + | 5.04669i | −0.273693 | + | 0.342592i | ||||
\(218\) | −16.2881 | −1.10317 | ||||||||
\(219\) | 1.79140 | + | 3.10279i | 0.121051 | + | 0.209667i | ||||
\(220\) | 1.74618 | − | 3.02448i | 0.117728 | − | 0.203910i | ||||
\(221\) | 0.287542 | − | 0.498038i | 0.0193422 | − | 0.0335016i | ||||
\(222\) | 0.720959 | + | 1.24874i | 0.0483876 | + | 0.0838098i | ||||
\(223\) | 28.2386 | 1.89100 | 0.945498 | − | 0.325628i | \(-0.105576\pi\) | ||||
0.945498 | + | 0.325628i | \(0.105576\pi\) | |||||||
\(224\) | −1.65139 | + | 2.06710i | −0.110338 | + | 0.138114i | ||||
\(225\) | 12.5677 | 0.837845 | ||||||||
\(226\) | −1.43067 | − | 2.47800i | −0.0951669 | − | 0.164834i | ||||
\(227\) | 5.11176 | − | 8.85383i | 0.339279 | − | 0.587649i | −0.645018 | − | 0.764167i | \(-0.723150\pi\) |
0.984297 | + | 0.176518i | \(0.0564835\pi\) | |||||||
\(228\) | 1.38036 | − | 2.39085i | 0.0914166 | − | 0.158338i | ||||
\(229\) | 1.25041 | + | 2.16578i | 0.0826296 | + | 0.143119i | 0.904379 | − | 0.426731i | \(-0.140335\pi\) |
−0.821749 | + | 0.569850i | \(0.807001\pi\) | |||||||
\(230\) | −0.596599 | −0.0393386 | ||||||||
\(231\) | 3.06034 | + | 7.81749i | 0.201355 | + | 0.514353i | ||||
\(232\) | 5.19369 | 0.340982 | ||||||||
\(233\) | −2.23300 | − | 3.86767i | −0.146289 | − | 0.253379i | 0.783564 | − | 0.621311i | \(-0.213399\pi\) |
−0.929853 | + | 0.367931i | \(0.880066\pi\) | |||||||
\(234\) | −0.323766 | + | 0.560780i | −0.0211653 | + | 0.0366593i | ||||
\(235\) | −2.30757 | + | 3.99683i | −0.150529 | + | 0.260724i | ||||
\(236\) | 5.08206 | + | 8.80239i | 0.330814 | + | 0.572987i | ||||
\(237\) | −3.24364 | −0.210697 | ||||||||
\(238\) | −6.28696 | − | 0.953169i | −0.407523 | − | 0.0617848i | ||||
\(239\) | 20.8462 | 1.34843 | 0.674215 | − | 0.738535i | \(-0.264482\pi\) | ||||
0.674215 | + | 0.738535i | \(0.264482\pi\) | |||||||
\(240\) | 0.161695 | + | 0.280064i | 0.0104374 | + | 0.0180780i | ||||
\(241\) | −2.03244 | + | 3.52029i | −0.130921 | + | 0.226762i | −0.924032 | − | 0.382315i | \(-0.875127\pi\) |
0.793111 | + | 0.609077i | \(0.208460\pi\) | |||||||
\(242\) | 11.6334 | − | 20.1496i | 0.747822 | − | 1.29527i | ||||
\(243\) | −6.38553 | − | 11.0601i | −0.409632 | − | 0.709503i | ||||
\(244\) | −0.680710 | −0.0435780 | ||||||||
\(245\) | 0.922245 | + | 4.07309i | 0.0589201 | + | 0.260220i | ||||
\(246\) | −6.30763 | −0.402160 | ||||||||
\(247\) | 0.609333 | + | 1.05540i | 0.0387709 | + | 0.0671532i | ||||
\(248\) | −1.22072 | + | 2.11434i | −0.0775155 | + | 0.134261i | ||||
\(249\) | 0.104857 | − | 0.181617i | 0.00664503 | − | 0.0115095i | ||||
\(250\) | 2.87682 | + | 4.98280i | 0.181946 | + | 0.315140i | ||||
\(251\) | −27.8969 | −1.76084 | −0.880418 | − | 0.474198i | \(-0.842738\pi\) | ||||
−0.880418 | + | 0.474198i | \(0.842738\pi\) | |||||||
\(252\) | 7.07897 | + | 1.07325i | 0.445933 | + | 0.0676082i | ||||
\(253\) | −5.85378 | −0.368024 | ||||||||
\(254\) | −0.832098 | − | 1.44124i | −0.0522104 | − | 0.0904311i | ||||
\(255\) | −0.388618 | + | 0.673105i | −0.0243362 | + | 0.0421515i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 13.9929 | + | 24.2364i | 0.872852 | + | 1.51182i | 0.859033 | + | 0.511920i | \(0.171066\pi\) |
0.0138193 | + | 0.999905i | \(0.495601\pi\) | |||||||
\(258\) | −2.13456 | −0.132892 | ||||||||
\(259\) | 2.56558 | + | 6.55367i | 0.159418 | + | 0.407225i | ||||
\(260\) | −0.142754 | −0.00885323 | ||||||||
\(261\) | −7.02752 | − | 12.1720i | −0.434992 | − | 0.753429i | ||||
\(262\) | −7.44820 | + | 12.9007i | −0.460151 | + | 0.797005i | ||||
\(263\) | 14.4661 | − | 25.0560i | 0.892018 | − | 1.54502i | 0.0545660 | − | 0.998510i | \(-0.482622\pi\) |
0.837452 | − | 0.546511i | \(-0.184044\pi\) | |||||||
\(264\) | 1.58654 | + | 2.74796i | 0.0976446 | + | 0.169125i | ||||
\(265\) | −2.60943 | −0.160296 | ||||||||
\(266\) | 8.41062 | − | 10.5279i | 0.515688 | − | 0.645506i | ||||
\(267\) | −7.09716 | −0.434339 | ||||||||
\(268\) | 1.56131 | + | 2.70428i | 0.0953724 | + | 0.165190i | ||||
\(269\) | 7.95590 | − | 13.7800i | 0.485079 | − | 0.840182i | −0.514774 | − | 0.857326i | \(-0.672124\pi\) |
0.999853 | + | 0.0171439i | \(0.00545733\pi\) | |||||||
\(270\) | 0.922660 | − | 1.59809i | 0.0561513 | − | 0.0972569i | ||||
\(271\) | −3.08379 | − | 5.34128i | −0.187327 | − | 0.324460i | 0.757031 | − | 0.653379i | \(-0.226649\pi\) |
−0.944358 | + | 0.328919i | \(0.893316\pi\) | |||||||
\(272\) | −2.40340 | −0.145728 | ||||||||
\(273\) | 0.214189 | − | 0.268109i | 0.0129633 | − | 0.0162267i | ||||
\(274\) | −2.26885 | −0.137066 | ||||||||
\(275\) | 13.5927 | + | 23.5432i | 0.819670 | + | 1.41971i | ||||
\(276\) | 0.271028 | − | 0.469434i | 0.0163139 | − | 0.0282566i | ||||
\(277\) | −2.61828 | + | 4.53500i | −0.157317 | + | 0.272482i | −0.933900 | − | 0.357533i | \(-0.883618\pi\) |
0.776583 | + | 0.630015i | \(0.216951\pi\) | |||||||
\(278\) | −9.07679 | − | 15.7215i | −0.544390 | − | 0.942911i | ||||
\(279\) | 6.60694 | 0.395547 | ||||||||
\(280\) | 0.575403 | + | 1.46984i | 0.0343869 | + | 0.0878397i | ||||
\(281\) | 12.4295 | 0.741482 | 0.370741 | − | 0.928736i | \(-0.379104\pi\) | ||||
0.370741 | + | 0.928736i | \(0.379104\pi\) | |||||||
\(282\) | −2.09660 | − | 3.63142i | −0.124851 | − | 0.216248i | ||||
\(283\) | 1.16798 | − | 2.02299i | 0.0694290 | − | 0.120255i | −0.829221 | − | 0.558921i | \(-0.811216\pi\) |
0.898650 | + | 0.438666i | \(0.144549\pi\) | |||||||
\(284\) | 2.77974 | − | 4.81464i | 0.164947 | − | 0.285696i | ||||
\(285\) | −0.823522 | − | 1.42638i | −0.0487812 | − | 0.0844916i | ||||
\(286\) | −1.40069 | −0.0828245 | ||||||||
\(287\) | −30.4395 | − | 4.61494i | −1.79678 | − | 0.272412i | ||||
\(288\) | 2.70618 | 0.159463 | ||||||||
\(289\) | 5.61183 | + | 9.71998i | 0.330108 | + | 0.571764i | ||||
\(290\) | 1.54928 | − | 2.68342i | 0.0909766 | − | 0.157576i | ||||
\(291\) | 0.0180761 | − | 0.0313088i | 0.00105964 | − | 0.00183535i | ||||
\(292\) | 3.30483 | + | 5.72413i | 0.193400 | + | 0.334979i | ||||
\(293\) | 2.87120 | 0.167737 | 0.0838686 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838686 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(294\) | −3.62387 | − | 1.12469i | −0.211348 | − | 0.0655931i | ||||
\(295\) | 6.06391 | 0.353054 | ||||||||
\(296\) | 1.33005 | + | 2.30371i | 0.0773075 | + | 0.133900i | ||||
\(297\) | 9.05306 | − | 15.6804i | 0.525312 | − | 0.909866i | ||||
\(298\) | −2.67661 | + | 4.63602i | −0.155052 | + | 0.268558i | ||||
\(299\) | 0.119640 | + | 0.207222i | 0.00691895 | + | 0.0119840i | ||||
\(300\) | −2.51734 | −0.145339 | ||||||||
\(301\) | −10.3010 | − | 1.56174i | −0.593738 | − | 0.0900170i | ||||
\(302\) | 6.98487 | 0.401934 | ||||||||
\(303\) | 4.43366 | + | 7.67933i | 0.254707 | + | 0.441166i | ||||
\(304\) | 2.54653 | − | 4.41072i | 0.146054 | − | 0.252972i | ||||
\(305\) | −0.203055 | + | 0.351702i | −0.0116269 | + | 0.0201384i | ||||
\(306\) | 3.25201 | + | 5.63265i | 0.185905 | + | 0.321997i | ||||
\(307\) | 25.5863 | 1.46029 | 0.730144 | − | 0.683293i | \(-0.239453\pi\) | ||||
0.730144 | + | 0.683293i | \(0.239453\pi\) | |||||||
\(308\) | 5.64580 | + | 14.4219i | 0.321699 | + | 0.821766i | ||||
\(309\) | 10.7401 | 0.610983 | ||||||||
\(310\) | 0.728278 | + | 1.26141i | 0.0413634 | + | 0.0716435i | ||||
\(311\) | 6.46093 | − | 11.1907i | 0.366366 | − | 0.634564i | −0.622628 | − | 0.782518i | \(-0.713935\pi\) |
0.988994 | + | 0.147953i | \(0.0472685\pi\) | |||||||
\(312\) | 0.0648513 | − | 0.112326i | 0.00367148 | − | 0.00635920i | ||||
\(313\) | −12.9010 | − | 22.3452i | −0.729208 | − | 1.26303i | −0.957218 | − | 0.289367i | \(-0.906555\pi\) |
0.228010 | − | 0.973659i | \(-0.426778\pi\) | |||||||
\(314\) | 7.92943 | 0.447484 | ||||||||
\(315\) | 2.66617 | − | 3.33735i | 0.150222 | − | 0.188038i | ||||
\(316\) | −5.98397 | −0.336625 | ||||||||
\(317\) | 12.5012 | + | 21.6527i | 0.702136 | + | 1.21614i | 0.967715 | + | 0.252047i | \(0.0811037\pi\) |
−0.265579 | + | 0.964089i | \(0.585563\pi\) | |||||||
\(318\) | 1.18543 | − | 2.05322i | 0.0664756 | − | 0.115139i | ||||
\(319\) | 15.2014 | − | 26.3295i | 0.851113 | − | 1.47417i | ||||
\(320\) | 0.298300 | + | 0.516670i | 0.0166755 | + | 0.0288827i | ||||
\(321\) | −8.34588 | −0.465822 | ||||||||
\(322\) | 1.65139 | − | 2.06710i | 0.0920282 | − | 0.115195i | ||||
\(323\) | 12.2407 | 0.681089 | ||||||||
\(324\) | −3.22096 | − | 5.57887i | −0.178942 | − | 0.309937i | ||||
\(325\) | 0.555615 | − | 0.962354i | 0.0308200 | − | 0.0533818i | ||||
\(326\) | 7.07232 | − | 12.2496i | 0.391699 | − | 0.678443i | ||||
\(327\) | −4.41453 | − | 7.64620i | −0.244124 | − | 0.422836i | ||||
\(328\) | −11.6365 | −0.642519 | ||||||||
\(329\) | −7.46090 | − | 19.0585i | −0.411332 | − | 1.05073i | ||||
\(330\) | 1.89305 | 0.104209 | ||||||||
\(331\) | −5.20868 | − | 9.02169i | −0.286295 | − | 0.495877i | 0.686628 | − | 0.727009i | \(-0.259090\pi\) |
−0.972922 | + | 0.231132i | \(0.925757\pi\) | |||||||
\(332\) | 0.193443 | − | 0.335053i | 0.0106166 | − | 0.0183884i | ||||
\(333\) | 3.59934 | − | 6.23425i | 0.197243 | − | 0.341635i | ||||
\(334\) | −8.91728 | − | 15.4452i | −0.487932 | − | 0.845123i | ||||
\(335\) | 1.86296 | 0.101784 | ||||||||
\(336\) | −1.41794 | − | 0.214975i | −0.0773549 | − | 0.0117278i | ||||
\(337\) | 22.8133 | 1.24272 | 0.621359 | − | 0.783526i | \(-0.286581\pi\) | ||||
0.621359 | + | 0.783526i | \(0.286581\pi\) | |||||||
\(338\) | −6.47137 | − | 11.2087i | −0.351996 | − | 0.609675i | ||||
\(339\) | 0.775504 | − | 1.34321i | 0.0421196 | − | 0.0729532i | ||||
\(340\) | −0.716934 | + | 1.24177i | −0.0388812 | + | 0.0673442i | ||||
\(341\) | 7.14580 | + | 12.3769i | 0.386967 | + | 0.670246i | ||||
\(342\) | −13.7827 | −0.745284 | ||||||||
\(343\) | −16.6653 | − | 8.07892i | −0.899840 | − | 0.436221i | ||||
\(344\) | −3.93789 | −0.212317 | ||||||||
\(345\) | −0.161695 | − | 0.280064i | −0.00870536 | − | 0.0150781i | ||||
\(346\) | −3.34060 | + | 5.78609i | −0.179592 | + | 0.311062i | ||||
\(347\) | −6.26544 | + | 10.8521i | −0.336346 | + | 0.582569i | −0.983743 | − | 0.179585i | \(-0.942525\pi\) |
0.647396 | + | 0.762154i | \(0.275858\pi\) | |||||||
\(348\) | 1.40763 | + | 2.43809i | 0.0754570 | + | 0.130695i | ||||
\(349\) | 13.8292 | 0.740261 | 0.370131 | − | 0.928980i | \(-0.379313\pi\) | ||||
0.370131 | + | 0.928980i | \(0.379313\pi\) | |||||||
\(350\) | −12.1482 | − | 1.84180i | −0.649350 | − | 0.0984484i | ||||
\(351\) | −0.740106 | −0.0395040 | ||||||||
\(352\) | 2.92689 | + | 5.06952i | 0.156004 | + | 0.270207i | ||||
\(353\) | 0.360064 | − | 0.623649i | 0.0191643 | − | 0.0331935i | −0.856284 | − | 0.516505i | \(-0.827233\pi\) |
0.875448 | + | 0.483311i | \(0.160566\pi\) | |||||||
\(354\) | −2.75476 | + | 4.77138i | −0.146414 | + | 0.253596i | ||||
\(355\) | −1.65839 | − | 2.87241i | −0.0880181 | − | 0.152452i | ||||
\(356\) | −13.0931 | −0.693931 | ||||||||
\(357\) | −1.25649 | − | 3.20964i | −0.0665004 | − | 0.169872i | ||||
\(358\) | −13.3628 | −0.706246 | ||||||||
\(359\) | −6.49851 | − | 11.2558i | −0.342978 | − | 0.594056i | 0.642006 | − | 0.766700i | \(-0.278102\pi\) |
−0.984984 | + | 0.172644i | \(0.944769\pi\) | |||||||
\(360\) | 0.807252 | − | 1.39820i | 0.0425459 | − | 0.0736916i | ||||
\(361\) | −3.46964 | + | 6.00959i | −0.182613 | + | 0.316294i | ||||
\(362\) | −11.8035 | − | 20.4442i | −0.620377 | − | 1.07452i | ||||
\(363\) | 12.6119 | 0.661952 | ||||||||
\(364\) | 0.395143 | − | 0.494616i | 0.0207111 | − | 0.0259249i | ||||
\(365\) | 3.94331 | 0.206402 | ||||||||
\(366\) | −0.184491 | − | 0.319548i | −0.00964350 | − | 0.0167030i | ||||
\(367\) | −2.10933 | + | 3.65347i | −0.110106 | + | 0.190710i | −0.915813 | − | 0.401605i | \(-0.868452\pi\) |
0.805707 | + | 0.592315i | \(0.201786\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | 15.7452 | + | 27.2715i | 0.819663 | + | 1.41970i | ||||
\(370\) | 1.58701 | 0.0825048 | ||||||||
\(371\) | 7.22290 | − | 9.04117i | 0.374994 | − | 0.469394i | ||||
\(372\) | −1.32339 | −0.0686146 | ||||||||
\(373\) | 9.76371 | + | 16.9112i | 0.505546 | + | 0.875631i | 0.999979 | + | 0.00641549i | \(0.00204213\pi\) |
−0.494434 | + | 0.869215i | \(0.664625\pi\) | |||||||
\(374\) | −7.03449 | + | 12.1841i | −0.363745 | + | 0.630025i | ||||
\(375\) | −1.55940 | + | 2.70095i | −0.0805269 | + | 0.139477i | ||||
\(376\) | −3.86787 | − | 6.69935i | −0.199470 | − | 0.345493i | ||||
\(377\) | −1.24274 | −0.0640045 | ||||||||
\(378\) | 2.98317 | + | 7.62036i | 0.153438 | + | 0.391949i | ||||
\(379\) | 21.8162 | 1.12063 | 0.560313 | − | 0.828281i | \(-0.310681\pi\) | ||||
0.560313 | + | 0.828281i | \(0.310681\pi\) | |||||||
\(380\) | −1.51926 | − | 2.63143i | −0.0779363 | − | 0.134990i | ||||
\(381\) | 0.451043 | − | 0.781229i | 0.0231076 | − | 0.0400236i | ||||
\(382\) | 3.45243 | − | 5.97979i | 0.176642 | − | 0.305953i | ||||
\(383\) | −12.8533 | − | 22.2626i | −0.656775 | − | 1.13757i | −0.981446 | − | 0.191740i | \(-0.938587\pi\) |
0.324671 | − | 0.945827i | \(-0.394746\pi\) | |||||||
\(384\) | −0.542055 | −0.0276616 | ||||||||
\(385\) | 9.13553 | + | 1.38504i | 0.465590 | + | 0.0705883i | ||||
\(386\) | 19.4930 | 0.992168 | ||||||||
\(387\) | 5.32832 | + | 9.22891i | 0.270854 | + | 0.469132i | ||||
\(388\) | 0.0333474 | − | 0.0577594i | 0.00169296 | − | 0.00293229i | ||||
\(389\) | −10.3222 | + | 17.8786i | −0.523358 | + | 0.906483i | 0.476272 | + | 0.879298i | \(0.341988\pi\) |
−0.999630 | + | 0.0271853i | \(0.991346\pi\) | |||||||
\(390\) | −0.0386903 | − | 0.0670135i | −0.00195916 | − | 0.00339336i | ||||
\(391\) | 2.40340 | 0.121545 | ||||||||
\(392\) | −6.68543 | − | 2.07486i | −0.337665 | − | 0.104796i | ||||
\(393\) | −8.07467 | −0.407313 | ||||||||
\(394\) | 7.78696 | + | 13.4874i | 0.392301 | + | 0.679486i | ||||
\(395\) | −1.78502 | + | 3.09174i | −0.0898140 | + | 0.155562i | ||||
\(396\) | 7.92068 | − | 13.7190i | 0.398029 | − | 0.689407i | ||||
\(397\) | −7.88241 | − | 13.6527i | −0.395607 | − | 0.685211i | 0.597572 | − | 0.801816i | \(-0.296132\pi\) |
−0.993178 | + | 0.116604i | \(0.962799\pi\) | |||||||
\(398\) | −3.37793 | −0.169321 | ||||||||
\(399\) | 7.22165 | + | 1.09488i | 0.361535 | + | 0.0548125i | ||||
\(400\) | −4.64407 | −0.232203 | ||||||||
\(401\) | −5.33817 | − | 9.24599i | −0.266576 | − | 0.461723i | 0.701400 | − | 0.712768i | \(-0.252559\pi\) |
−0.967975 | + | 0.251046i | \(0.919226\pi\) | |||||||
\(402\) | −0.846318 | + | 1.46587i | −0.0422105 | + | 0.0731108i | ||||
\(403\) | 0.292092 | − | 0.505918i | 0.0145501 | − | 0.0252016i | ||||
\(404\) | 8.17935 | + | 14.1671i | 0.406938 | + | 0.704837i | ||||
\(405\) | −3.84324 | −0.190972 | ||||||||
\(406\) | 5.00916 | + | 12.7957i | 0.248600 | + | 0.635038i | ||||
\(407\) | 15.5716 | 0.771857 | ||||||||
\(408\) | −0.651388 | − | 1.12824i | −0.0322485 | − | 0.0558560i | ||||
\(409\) | −6.03231 | + | 10.4483i | −0.298279 | + | 0.516634i | −0.975742 | − | 0.218923i | \(-0.929746\pi\) |
0.677464 | + | 0.735556i | \(0.263079\pi\) | |||||||
\(410\) | −3.47117 | + | 6.01224i | −0.171429 | + | 0.296923i | ||||
\(411\) | −0.614920 | − | 1.06507i | −0.0303318 | − | 0.0525361i | ||||
\(412\) | 19.8137 | 0.976150 | ||||||||
\(413\) | −16.7849 | + | 21.0103i | −0.825931 | + | 1.03385i | ||||
\(414\) | −2.70618 | −0.133001 | ||||||||
\(415\) | −0.115408 | − | 0.199892i | −0.00566515 | − | 0.00981233i | ||||
\(416\) | 0.119640 | − | 0.207222i | 0.00586582 | − | 0.0101599i | ||||
\(417\) | 4.92012 | − | 8.52190i | 0.240939 | − | 0.417319i | ||||
\(418\) | −14.9068 | − | 25.8194i | −0.729117 | − | 1.26287i | ||||
\(419\) | 10.9183 | 0.533392 | 0.266696 | − | 0.963781i | \(-0.414068\pi\) | ||||
0.266696 | + | 0.963781i | \(0.414068\pi\) | |||||||
\(420\) | −0.534042 | + | 0.668480i | −0.0260586 | + | 0.0326185i | ||||
\(421\) | −35.8943 | −1.74938 | −0.874691 | − | 0.484681i | \(-0.838936\pi\) | ||||
−0.874691 | + | 0.484681i | \(0.838936\pi\) | |||||||
\(422\) | 2.01409 | + | 3.48850i | 0.0980443 | + | 0.169818i | ||||
\(423\) | −10.4671 | + | 18.1296i | −0.508930 | + | 0.881492i | ||||
\(424\) | 2.18692 | − | 3.78785i | 0.106206 | − | 0.183954i | ||||
\(425\) | −5.58078 | − | 9.66619i | −0.270708 | − | 0.468879i | ||||
\(426\) | 3.01354 | 0.146006 | ||||||||
\(427\) | −0.656524 | − | 1.67706i | −0.0317714 | − | 0.0811587i | ||||
\(428\) | −15.3967 | −0.744229 | ||||||||
\(429\) | −0.379626 | − | 0.657531i | −0.0183285 | − | 0.0317459i | ||||
\(430\) | −1.17467 | + | 2.03459i | −0.0566477 | + | 0.0981167i | ||||
\(431\) | 12.5390 | − | 21.7181i | 0.603981 | − | 1.04613i | −0.388231 | − | 0.921562i | \(-0.626914\pi\) |
0.992212 | − | 0.124563i | \(-0.0397530\pi\) | |||||||
\(432\) | 1.54653 | + | 2.67867i | 0.0744075 | + | 0.128878i | ||||
\(433\) | −4.76433 | −0.228959 | −0.114480 | − | 0.993426i | \(-0.536520\pi\) | ||||
−0.114480 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(434\) | −6.38644 | − | 0.968251i | −0.306559 | − | 0.0464776i | ||||
\(435\) | 1.67959 | 0.0805300 | ||||||||
\(436\) | −8.14407 | − | 14.1059i | −0.390030 | − | 0.675552i | ||||
\(437\) | −2.54653 | + | 4.41072i | −0.121817 | + | 0.210993i | ||||
\(438\) | −1.79140 | + | 3.10279i | −0.0855963 | + | 0.148257i | ||||
\(439\) | −8.68289 | − | 15.0392i | −0.414412 | − | 0.717782i | 0.580955 | − | 0.813936i | \(-0.302679\pi\) |
−0.995367 | + | 0.0961536i | \(0.969346\pi\) | |||||||
\(440\) | 3.49236 | 0.166492 | ||||||||
\(441\) | 4.18331 | + | 18.4756i | 0.199205 | + | 0.879788i | ||||
\(442\) | 0.575084 | 0.0273540 | ||||||||
\(443\) | −3.10128 | − | 5.37158i | −0.147346 | − | 0.255211i | 0.782900 | − | 0.622148i | \(-0.213740\pi\) |
−0.930246 | + | 0.366937i | \(0.880407\pi\) | |||||||
\(444\) | −0.720959 | + | 1.24874i | −0.0342152 | + | 0.0592625i | ||||
\(445\) | −3.90566 | + | 6.76480i | −0.185146 | + | 0.320682i | ||||
\(446\) | 14.1193 | + | 24.4553i | 0.668568 | + | 1.15799i | ||||
\(447\) | −2.90174 | −0.137248 | ||||||||
\(448\) | −2.61586 | − | 0.396592i | −0.123588 | − | 0.0187372i | ||||
\(449\) | −16.2709 | −0.767870 | −0.383935 | − | 0.923360i | \(-0.625431\pi\) | ||||
−0.383935 | + | 0.923360i | \(0.625431\pi\) | |||||||
\(450\) | 6.28383 | + | 10.8839i | 0.296223 | + | 0.513073i | ||||
\(451\) | −34.0588 | + | 58.9916i | −1.60377 | + | 2.77780i | ||||
\(452\) | 1.43067 | − | 2.47800i | 0.0672932 | − | 0.116555i | ||||
\(453\) | 1.89309 | + | 3.27893i | 0.0889453 | + | 0.154058i | ||||
\(454\) | 10.2235 | 0.479813 | ||||||||
\(455\) | −0.137682 | − | 0.351702i | −0.00645463 | − | 0.0164881i | ||||
\(456\) | 2.76072 | 0.129283 | ||||||||
\(457\) | −8.18259 | − | 14.1727i | −0.382765 | − | 0.662969i | 0.608691 | − | 0.793407i | \(-0.291695\pi\) |
−0.991456 | + | 0.130438i | \(0.958362\pi\) | |||||||
\(458\) | −1.25041 | + | 2.16578i | −0.0584280 | + | 0.101200i | ||||
\(459\) | −3.71693 | + | 6.43792i | −0.173492 | + | 0.300496i | ||||
\(460\) | −0.298300 | − | 0.516670i | −0.0139083 | − | 0.0240899i | ||||
\(461\) | 18.1965 | 0.847494 | 0.423747 | − | 0.905781i | \(-0.360715\pi\) | ||||
0.423747 | + | 0.905781i | \(0.360715\pi\) | |||||||
\(462\) | −5.23997 | + | 6.55907i | −0.243786 | + | 0.305156i | ||||
\(463\) | 0.424651 | 0.0197352 | 0.00986760 | − | 0.999951i | \(-0.496859\pi\) | ||||
0.00986760 | + | 0.999951i | \(0.496859\pi\) | |||||||
\(464\) | 2.59684 | + | 4.49786i | 0.120555 | + | 0.208808i | ||||
\(465\) | −0.394767 | + | 0.683756i | −0.0183069 | + | 0.0317084i | ||||
\(466\) | 2.23300 | − | 3.86767i | 0.103442 | − | 0.179166i | ||||
\(467\) | −14.0860 | − | 24.3976i | −0.651822 | − | 1.12899i | −0.982680 | − | 0.185308i | \(-0.940672\pi\) |
0.330859 | − | 0.943680i | \(-0.392662\pi\) | |||||||
\(468\) | −0.647532 | −0.0299322 | ||||||||
\(469\) | −5.15667 | + | 6.45480i | −0.238113 | + | 0.298055i | ||||
\(470\) | −4.61514 | −0.212880 | ||||||||
\(471\) | 2.14909 | + | 3.72234i | 0.0990250 | + | 0.171516i | ||||
\(472\) | −5.08206 | + | 8.80239i | −0.233921 | + | 0.405163i | ||||
\(473\) | −11.5258 | + | 19.9632i | −0.529956 | + | 0.917911i | ||||
\(474\) | −1.62182 | − | 2.80908i | −0.0744927 | − | 0.129025i | ||||
\(475\) | 23.6525 | 1.08525 | ||||||||
\(476\) | −2.31801 | − | 5.92125i | −0.106246 | − | 0.271400i | ||||
\(477\) | −11.8364 | −0.541950 | ||||||||
\(478\) | 10.4231 | + | 18.0534i | 0.476742 | + | 0.825741i | ||||
\(479\) | −4.88310 | + | 8.45779i | −0.223115 | + | 0.386446i | −0.955752 | − | 0.294173i | \(-0.904956\pi\) |
0.732637 | + | 0.680619i | \(0.238289\pi\) | |||||||
\(480\) | −0.161695 | + | 0.280064i | −0.00738033 | + | 0.0127831i | ||||
\(481\) | −0.318253 | − | 0.551231i | −0.0145111 | − | 0.0251340i | ||||
\(482\) | −4.06489 | −0.185150 | ||||||||
\(483\) | 1.41794 | + | 0.214975i | 0.0645185 | + | 0.00978169i | ||||
\(484\) | 23.2668 | 1.05758 | ||||||||
\(485\) | −0.0198950 | − | 0.0344592i | −0.000903387 | − | 0.00156471i | ||||
\(486\) | 6.38553 | − | 11.0601i | 0.289654 | − | 0.501695i | ||||
\(487\) | −10.3765 | + | 17.9726i | −0.470203 | + | 0.814416i | −0.999419 | − | 0.0340712i | \(-0.989153\pi\) |
0.529216 | + | 0.848487i | \(0.322486\pi\) | |||||||
\(488\) | −0.340355 | − | 0.589512i | −0.0154071 | − | 0.0266859i | ||||
\(489\) | 7.66717 | 0.346721 | ||||||||
\(490\) | −3.06628 | + | 2.83523i | −0.138520 | + | 0.128083i | ||||
\(491\) | −25.9031 | −1.16899 | −0.584496 | − | 0.811397i | \(-0.698708\pi\) | ||||
−0.584496 | + | 0.811397i | \(0.698708\pi\) | |||||||
\(492\) | −3.15381 | − | 5.46257i | −0.142185 | − | 0.246271i | ||||
\(493\) | −6.24126 | + | 10.8102i | −0.281092 | + | 0.486866i | ||||
\(494\) | −0.609333 | + | 1.05540i | −0.0274152 | + | 0.0474845i | ||||
\(495\) | −4.72548 | − | 8.18476i | −0.212394 | − | 0.367878i | ||||
\(496\) | −2.44143 | −0.109623 | ||||||||
\(497\) | 14.5428 | + | 2.20484i | 0.652333 | + | 0.0989006i | ||||
\(498\) | 0.209713 | 0.00939749 | ||||||||
\(499\) | 16.8329 | + | 29.1555i | 0.753546 | + | 1.30518i | 0.946094 | + | 0.323892i | \(0.104991\pi\) |
−0.192548 | + | 0.981288i | \(0.561675\pi\) | |||||||
\(500\) | −2.87682 | + | 4.98280i | −0.128655 | + | 0.222838i | ||||
\(501\) | 4.83366 | − | 8.37214i | 0.215952 | − | 0.374040i | ||||
\(502\) | −13.9484 | − | 24.1594i | −0.622550 | − | 1.07829i | ||||
\(503\) | 7.77016 | 0.346454 | 0.173227 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173227 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(504\) | 2.61003 | + | 6.66719i | 0.116260 | + | 0.296980i | ||||
\(505\) | 9.75960 | 0.434296 | ||||||||
\(506\) | −2.92689 | − | 5.06952i | −0.130116 | − | 0.225368i | ||||
\(507\) | 3.50784 | − | 6.07576i | 0.155789 | − | 0.269834i | ||||
\(508\) | 0.832098 | − | 1.44124i | 0.0369184 | − | 0.0639445i | ||||
\(509\) | 4.29785 | + | 7.44409i | 0.190499 | + | 0.329954i | 0.945416 | − | 0.325867i | \(-0.105656\pi\) |
−0.754917 | + | 0.655821i | \(0.772323\pi\) | |||||||
\(510\) | −0.777235 | −0.0344166 | ||||||||
\(511\) | −10.9151 | + | 13.6628i | −0.482855 | + | 0.604408i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.87658 | − | 13.6426i | −0.347759 | − | 0.602337i | ||||
\(514\) | −13.9929 | + | 24.2364i | −0.617200 | + | 1.06902i | ||||
\(515\) | 5.91041 | − | 10.2371i | 0.260444 | − | 0.451102i | ||||
\(516\) | −1.06728 | − | 1.84858i | −0.0469843 | − | 0.0813791i | ||||
\(517\) | −45.2834 | −1.99156 | ||||||||
\(518\) | −4.39285 | + | 5.49869i | −0.193011 | + | 0.241599i | ||||
\(519\) | −3.62158 | −0.158970 | ||||||||
\(520\) | −0.0713770 | − | 0.123629i | −0.00313009 | − | 0.00542147i | ||||
\(521\) | −6.17501 | + | 10.6954i | −0.270532 | + | 0.468575i | −0.968998 | − | 0.247068i | \(-0.920533\pi\) |
0.698466 | + | 0.715643i | \(0.253866\pi\) | |||||||
\(522\) | 7.02752 | − | 12.1720i | 0.307586 | − | 0.532755i | ||||
\(523\) | 12.1520 | + | 21.0479i | 0.531369 | + | 0.920358i | 0.999330 | + | 0.0366090i | \(0.0116556\pi\) |
−0.467961 | + | 0.883749i | \(0.655011\pi\) | |||||||
\(524\) | −14.8964 | −0.650752 | ||||||||
\(525\) | −2.42790 | − | 6.20196i | −0.105962 | − | 0.270676i | ||||
\(526\) | 28.9322 | 1.26150 | ||||||||
\(527\) | −2.93387 | − | 5.08161i | −0.127801 | − | 0.221358i | ||||
\(528\) | −1.58654 | + | 2.74796i | −0.0690451 | + | 0.119590i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −1.30471 | − | 2.25983i | −0.0566731 | − | 0.0981608i | ||||
\(531\) | 27.5059 | 1.19365 | ||||||||
\(532\) | 13.3227 | + | 2.01987i | 0.577614 | + | 0.0875723i | ||||
\(533\) | 2.78438 | 0.120605 | ||||||||
\(534\) | −3.54858 | − | 6.14632i | −0.153562 | − | 0.265977i | ||||
\(535\) | −4.59284 | + | 7.95504i | −0.198566 | + | 0.343926i | ||||
\(536\) | −1.56131 | + | 2.70428i | −0.0674385 | + | 0.116807i | ||||
\(537\) | −3.62169 | − | 6.27295i | −0.156287 | − | 0.270698i | ||||
\(538\) | 15.9118 | 0.686006 | ||||||||
\(539\) | −30.0861 | + | 27.8191i | −1.29590 | + | 1.19825i | ||||
\(540\) | 1.84532 | 0.0794099 | ||||||||
\(541\) | 11.2091 | + | 19.4148i | 0.481918 | + | 0.834706i | 0.999785 | − | 0.0207549i | \(-0.00660697\pi\) |
−0.517867 | + | 0.855461i | \(0.673274\pi\) | |||||||
\(542\) | 3.08379 | − | 5.34128i | 0.132460 | − | 0.229428i | ||||
\(543\) | 6.39813 | − | 11.0819i | 0.274570 | − | 0.475569i | ||||
\(544\) | −1.20170 | − | 2.08141i | −0.0515225 | − | 0.0892395i | ||||
\(545\) | −9.71749 | −0.416252 | ||||||||
\(546\) | 0.339284 | + | 0.0514390i | 0.0145200 | + | 0.00220139i | ||||
\(547\) | 31.1827 | 1.33327 | 0.666637 | − | 0.745382i | \(-0.267733\pi\) | ||||
0.666637 | + | 0.745382i | \(0.267733\pi\) | |||||||
\(548\) | −1.13442 | − | 1.96488i | −0.0484601 | − | 0.0839354i | ||||
\(549\) | −0.921060 | + | 1.59532i | −0.0393099 | + | 0.0680867i | ||||
\(550\) | −13.5927 | + | 23.5432i | −0.579594 | + | 1.00389i | ||||
\(551\) | −13.2259 | − | 22.9079i | −0.563442 | − | 0.975910i | ||||
\(552\) | 0.542055 | 0.0230714 | ||||||||
\(553\) | −5.77137 | − | 14.7427i | −0.245423 | − | 0.626923i | ||||
\(554\) | −5.23657 | −0.222481 | ||||||||
\(555\) | 0.430124 | + | 0.744996i | 0.0182577 | + | 0.0316233i | ||||
\(556\) | 9.07679 | − | 15.7215i | 0.384942 | − | 0.666739i | ||||
\(557\) | −13.6725 | + | 23.6814i | −0.579320 | + | 1.00341i | 0.416237 | + | 0.909256i | \(0.363349\pi\) |
−0.995557 | + | 0.0941562i | \(0.969985\pi\) | |||||||
\(558\) | 3.30347 | + | 5.72178i | 0.139847 | + | 0.242222i | ||||
\(559\) | 0.942257 | 0.0398532 | ||||||||
\(560\) | −0.985217 | + | 1.23323i | −0.0416330 | + | 0.0521136i | ||||
\(561\) | −7.62617 | −0.321977 | ||||||||
\(562\) | 6.21475 | + | 10.7643i | 0.262153 | + | 0.454063i | ||||
\(563\) | 8.62780 | − | 14.9438i | 0.363618 | − | 0.629805i | −0.624935 | − | 0.780677i | \(-0.714875\pi\) |
0.988553 | + | 0.150871i | \(0.0482079\pi\) | |||||||
\(564\) | 2.09660 | − | 3.63142i | 0.0882828 | − | 0.152910i | ||||
\(565\) | −0.853539 | − | 1.47837i | −0.0359086 | − | 0.0621956i | ||||
\(566\) | 2.33595 | 0.0981874 | ||||||||
\(567\) | 10.6381 | − | 13.3161i | 0.446758 | − | 0.559224i | ||||
\(568\) | 5.55947 | 0.233270 | ||||||||
\(569\) | 7.75028 | + | 13.4239i | 0.324909 | + | 0.562758i | 0.981494 | − | 0.191494i | \(-0.0613331\pi\) |
−0.656585 | + | 0.754252i | \(0.728000\pi\) | |||||||
\(570\) | 0.823522 | − | 1.42638i | 0.0344935 | − | 0.0597446i | ||||
\(571\) | 13.0127 | − | 22.5387i | 0.544566 | − | 0.943216i | −0.454068 | − | 0.890967i | \(-0.650028\pi\) |
0.998634 | − | 0.0522489i | \(-0.0166389\pi\) | |||||||
\(572\) | −0.700345 | − | 1.21303i | −0.0292829 | − | 0.0507195i | ||||
\(573\) | 3.74282 | 0.156358 | ||||||||
\(574\) | −11.2231 | − | 28.6688i | −0.468442 | − | 1.19661i | ||||
\(575\) | 4.64407 | 0.193671 | ||||||||
\(576\) | 1.35309 | + | 2.34362i | 0.0563787 | + | 0.0976507i | ||||
\(577\) | 9.17204 | − | 15.8864i | 0.381837 | − | 0.661361i | −0.609488 | − | 0.792795i | \(-0.708625\pi\) |
0.991325 | + | 0.131434i | \(0.0419583\pi\) | |||||||
\(578\) | −5.61183 | + | 9.71998i | −0.233421 | + | 0.404298i | ||||
\(579\) | 5.28314 | + | 9.15067i | 0.219560 | + | 0.380289i | ||||
\(580\) | 3.09855 | 0.128660 | ||||||||
\(581\) | 1.01204 | + | 0.153436i | 0.0419864 | + | 0.00636559i | ||||
\(582\) | 0.0361523 | 0.00149856 | ||||||||
\(583\) | −12.8017 | − | 22.1733i | −0.530194 | − | 0.918323i | ||||
\(584\) | −3.30483 | + | 5.72413i | −0.136755 | + | 0.236866i | ||||
\(585\) | −0.193159 | + | 0.334561i | −0.00798613 | + | 0.0138324i | ||||
\(586\) | 1.43560 | + | 2.48653i | 0.0593041 | + | 0.102718i | ||||
\(587\) | −40.3997 | −1.66748 | −0.833738 | − | 0.552160i | \(-0.813804\pi\) | ||||
−0.833738 | + | 0.552160i | \(0.813804\pi\) | |||||||
\(588\) | −0.837929 | − | 3.70071i | −0.0345556 | − | 0.152615i | ||||
\(589\) | 12.4344 | 0.512349 | ||||||||
\(590\) | 3.03195 | + | 5.25150i | 0.124824 | + | 0.216201i | ||||
\(591\) | −4.22096 | + | 7.31092i | −0.173627 | + | 0.300731i | ||||
\(592\) | −1.33005 | + | 2.30371i | −0.0546646 | + | 0.0946819i | ||||
\(593\) | −11.1406 | − | 19.2961i | −0.457491 | − | 0.792397i | 0.541337 | − | 0.840806i | \(-0.317918\pi\) |
−0.998828 | + | 0.0484085i | \(0.984585\pi\) | |||||||
\(594\) | 18.1061 | 0.742903 | ||||||||
\(595\) | −3.75079 | − | 0.568660i | −0.153768 | − | 0.0233128i | ||||
\(596\) | −5.35322 | −0.219276 | ||||||||
\(597\) | −0.915513 | − | 1.58572i | −0.0374695 | − | 0.0648990i | ||||
\(598\) | −0.119640 | + | 0.207222i | −0.00489243 | + | 0.00847394i | ||||
\(599\) | 4.92939 | − | 8.53796i | 0.201409 | − | 0.348851i | −0.747573 | − | 0.664179i | \(-0.768781\pi\) |
0.948983 | + | 0.315328i | \(0.102114\pi\) | |||||||
\(600\) | −1.25867 | − | 2.18008i | −0.0513850 | − | 0.0890015i | ||||
\(601\) | −3.48778 | −0.142269 | −0.0711347 | − | 0.997467i | \(-0.522662\pi\) | ||||
−0.0711347 | + | 0.997467i | \(0.522662\pi\) | |||||||
\(602\) | −3.79798 | − | 9.70177i | −0.154794 | − | 0.395415i | ||||
\(603\) | 8.45038 | 0.344126 | ||||||||
\(604\) | 3.49244 | + | 6.04908i | 0.142105 | + | 0.246134i | ||||
\(605\) | 6.94047 | − | 12.0212i | 0.282170 | − | 0.488733i | ||||
\(606\) | −4.43366 | + | 7.67933i | −0.180105 | + | 0.311951i | ||||
\(607\) | −19.1003 | − | 33.0827i | −0.775257 | − | 1.34278i | −0.934650 | − | 0.355569i | \(-0.884287\pi\) |
0.159394 | − | 0.987215i | \(-0.449046\pi\) | |||||||
\(608\) | 5.09306 | 0.206551 | ||||||||
\(609\) | −4.64909 | + | 5.81944i | −0.188391 | + | 0.235816i | ||||
\(610\) | −0.406111 | −0.0164430 | ||||||||
\(611\) | 0.925502 | + | 1.60302i | 0.0374418 | + | 0.0648511i | ||||
\(612\) | −3.25201 | + | 5.63265i | −0.131455 | + | 0.227686i | ||||
\(613\) | 10.3547 | − | 17.9348i | 0.418222 | − | 0.724381i | −0.577539 | − | 0.816363i | \(-0.695987\pi\) |
0.995761 | + | 0.0919818i | \(0.0293202\pi\) | |||||||
\(614\) | 12.7932 | + | 22.1584i | 0.516290 | + | 0.894241i | ||||
\(615\) | −3.76313 | −0.151744 | ||||||||
\(616\) | −9.66687 | + | 12.1004i | −0.389489 | + | 0.487538i | ||||
\(617\) | −40.1980 | −1.61831 | −0.809155 | − | 0.587595i | \(-0.800075\pi\) | ||||
−0.809155 | + | 0.587595i | \(0.800075\pi\) | |||||||
\(618\) | 5.37005 | + | 9.30120i | 0.216015 | + | 0.374149i | ||||
\(619\) | 10.8528 | − | 18.7977i | 0.436213 | − | 0.755542i | −0.561181 | − | 0.827693i | \(-0.689653\pi\) |
0.997394 | + | 0.0721506i | \(0.0229862\pi\) | |||||||
\(620\) | −0.728278 | + | 1.26141i | −0.0292483 | + | 0.0506596i | ||||
\(621\) | −1.54653 | − | 2.67867i | −0.0620602 | − | 0.107491i | ||||
\(622\) | 12.9219 | 0.518120 | ||||||||
\(623\) | −12.6279 | − | 32.2573i | −0.505925 | − | 1.29236i | ||||
\(624\) | 0.129703 | 0.00519226 | ||||||||
\(625\) | −9.89386 | − | 17.1367i | −0.395754 | − | 0.685467i | ||||
\(626\) | 12.9010 | − | 22.3452i | 0.515628 | − | 0.893094i | ||||
\(627\) | 8.08033 | − | 13.9955i | 0.322697 | − | 0.558928i | ||||
\(628\) | 3.96471 | + | 6.86709i | 0.158209 | + | 0.274027i | ||||
\(629\) | −6.39328 | −0.254917 | ||||||||
\(630\) | 4.22331 | + | 0.640299i | 0.168261 | + | 0.0255101i | ||||
\(631\) | 46.8061 | 1.86332 | 0.931661 | − | 0.363329i | \(-0.118360\pi\) | ||||
0.931661 | + | 0.363329i | \(0.118360\pi\) | |||||||
\(632\) | −2.99199 | − | 5.18227i | −0.119015 | − | 0.206140i | ||||
\(633\) | −1.09175 | + | 1.89096i | −0.0433930 | + | 0.0751590i | ||||
\(634\) | −12.5012 | + | 21.6527i | −0.496485 | + | 0.859938i | ||||
\(635\) | −0.496429 | − | 0.859840i | −0.0197002 | − | 0.0341217i | ||||
\(636\) | 2.37086 | 0.0940107 | ||||||||
\(637\) | 1.59969 | + | 0.496471i | 0.0633819 | + | 0.0196709i | ||||
\(638\) | 30.4027 | 1.20366 | ||||||||
\(639\) | −7.52245 | − | 13.0293i | −0.297584 | − | 0.515430i | ||||
\(640\) | −0.298300 | + | 0.516670i | −0.0117913 | + | 0.0204232i | ||||
\(641\) | −10.8628 | + | 18.8150i | −0.429057 | + | 0.743148i | −0.996790 | − | 0.0800649i | \(-0.974487\pi\) |
0.567733 | + | 0.823213i | \(0.307821\pi\) | |||||||
\(642\) | −4.17294 | − | 7.22775i | −0.164693 | − | 0.285256i | ||||
\(643\) | 27.3018 | 1.07668 | 0.538339 | − | 0.842728i | \(-0.319052\pi\) | ||||
0.538339 | + | 0.842728i | \(0.319052\pi\) | |||||||
\(644\) | 2.61586 | + | 0.396592i | 0.103079 | + | 0.0156279i | ||||
\(645\) | −1.27347 | −0.0501430 | ||||||||
\(646\) | 6.12033 | + | 10.6007i | 0.240801 | + | 0.417080i | ||||
\(647\) | −3.56568 | + | 6.17594i | −0.140181 | + | 0.242801i | −0.927565 | − | 0.373662i | \(-0.878102\pi\) |
0.787384 | + | 0.616463i | \(0.211435\pi\) | |||||||
\(648\) | 3.22096 | − | 5.57887i | 0.126531 | − | 0.219159i | ||||
\(649\) | 29.7493 | + | 51.5273i | 1.16776 | + | 2.02262i | ||||
\(650\) | 1.11123 | 0.0435860 | ||||||||
\(651\) | −1.27637 | − | 3.26043i | −0.0500249 | − | 0.127786i | ||||
\(652\) | 14.1446 | 0.553947 | ||||||||
\(653\) | −8.12425 | − | 14.0716i | −0.317926 | − | 0.550665i | 0.662129 | − | 0.749390i | \(-0.269653\pi\) |
−0.980055 | + | 0.198725i | \(0.936320\pi\) | |||||||
\(654\) | 4.41453 | − | 7.64620i | 0.172622 | − | 0.298990i | ||||
\(655\) | −4.44359 | + | 7.69653i | −0.173625 | + | 0.300728i | ||||
\(656\) | −5.81825 | − | 10.0775i | −0.227165 | − | 0.393461i | ||||
\(657\) | 17.8869 | 0.697834 | ||||||||
\(658\) | 12.7747 | − | 15.9906i | 0.498010 | − | 0.623378i | ||||
\(659\) | −0.0321286 | −0.00125155 | −0.000625776 | − | 1.00000i | \(-0.500199\pi\) | ||||
−0.000625776 | 1.00000i | \(0.500199\pi\) | ||||||||
\(660\) | 0.946527 | + | 1.63943i | 0.0368435 | + | 0.0638148i | ||||
\(661\) | 5.33283 | − | 9.23673i | 0.207423 | − | 0.359267i | −0.743479 | − | 0.668759i | \(-0.766826\pi\) |
0.950902 | + | 0.309492i | \(0.100159\pi\) | |||||||
\(662\) | 5.20868 | − | 9.02169i | 0.202441 | − | 0.350638i | ||||
\(663\) | 0.155864 | + | 0.269964i | 0.00605325 | + | 0.0104845i | ||||
\(664\) | 0.386886 | 0.0150141 | ||||||||
\(665\) | 5.01777 | − | 6.28093i | 0.194581 | − | 0.243564i | ||||
\(666\) | 7.19869 | 0.278943 | ||||||||
\(667\) | −2.59684 | − | 4.49786i | −0.100550 | − | 0.174158i | ||||
\(668\) | 8.91728 | − | 15.4452i | 0.345020 | − | 0.597592i | ||||
\(669\) | −7.65344 | + | 13.2561i | −0.295899 | + | 0.512512i | ||||
\(670\) | 0.931479 | + | 1.61337i | 0.0359862 | + | 0.0623299i | ||||
\(671\) | −3.98473 | −0.153829 | ||||||||
\(672\) | −0.522796 | − | 1.33546i | −0.0201673 | − | 0.0515164i | ||||
\(673\) | −25.7353 | −0.992021 | −0.496011 | − | 0.868316i | \(-0.665202\pi\) | ||||
−0.496011 | + | 0.868316i | \(0.665202\pi\) | |||||||
\(674\) | 11.4066 | + | 19.7569i | 0.439367 | + | 0.761006i | ||||
\(675\) | −7.18220 | + | 12.4399i | −0.276443 | + | 0.478813i | ||||
\(676\) | 6.47137 | − | 11.2087i | 0.248899 | − | 0.431106i | ||||
\(677\) | −17.9812 | − | 31.1444i | −0.691074 | − | 1.19698i | −0.971486 | − | 0.237095i | \(-0.923805\pi\) |
0.280413 | − | 0.959880i | \(-0.409529\pi\) | |||||||
\(678\) | 1.55101 | 0.0595661 | ||||||||
\(679\) | 0.174464 | + | 0.0264506i | 0.00669532 | + | 0.00101508i | ||||
\(680\) | −1.43387 | −0.0549863 | ||||||||
\(681\) | 2.77086 | + | 4.79926i | 0.106179 | + | 0.183908i | ||||
\(682\) | −7.14580 | + | 12.3769i | −0.273627 | + | 0.473936i | ||||
\(683\) | −2.86052 | + | 4.95456i | −0.109455 | + | 0.189581i | −0.915549 | − | 0.402205i | \(-0.868244\pi\) |
0.806095 | + | 0.591786i | \(0.201577\pi\) | |||||||
\(684\) | −6.89136 | − | 11.9362i | −0.263498 | − | 0.456392i | ||||
\(685\) | −1.35359 | −0.0517181 | ||||||||
\(686\) | −1.33609 | − | 18.4720i | −0.0510120 | − | 0.705264i | ||||
\(687\) | −1.35559 | −0.0517188 | ||||||||
\(688\) | −1.96895 | − | 3.41032i | −0.0750654 | − | 0.130017i | ||||
\(689\) | −0.523284 | + | 0.906355i | −0.0199356 | + | 0.0345294i | ||||
\(690\) | 0.161695 | − | 0.280064i | 0.00615562 | − | 0.0106618i | ||||
\(691\) | −8.45465 | − | 14.6439i | −0.321630 | − | 0.557080i | 0.659194 | − | 0.751973i | \(-0.270897\pi\) |
−0.980825 | + | 0.194893i | \(0.937564\pi\) | |||||||
\(692\) | −6.68120 | −0.253981 | ||||||||
\(693\) | 41.4388 | + | 6.28256i | 1.57413 | + | 0.238655i | ||||
\(694\) | −12.5309 | −0.475666 | ||||||||
\(695\) | −5.41521 | − | 9.37942i | −0.205411 | − | 0.355782i | ||||
\(696\) | −1.40763 | + | 2.43809i | −0.0533562 | + | 0.0924156i | ||||
\(697\) | 13.9836 | − | 24.2203i | 0.529666 | − | 0.917409i | ||||
\(698\) | 6.91461 | + | 11.9765i | 0.261722 | + | 0.453315i | ||||
\(699\) | 2.42082 | 0.0915637 | ||||||||
\(700\) | −4.47907 | − | 11.4416i | −0.169293 | − | 0.432451i | ||||
\(701\) | 24.3619 | 0.920137 | 0.460068 | − | 0.887884i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887884i | \(0.347825\pi\) | |||||||
\(702\) | −0.370053 | − | 0.640951i | −0.0139668 | − | 0.0241911i | ||||
\(703\) | 6.77402 | − | 11.7329i | 0.255487 | − | 0.442516i | ||||
\(704\) | −2.92689 | + | 5.06952i | −0.110311 | + | 0.191065i | ||||
\(705\) | −1.25083 | − | 2.16650i | −0.0471090 | − | 0.0815952i | ||||
\(706\) | 0.720128 | 0.0271024 | ||||||||
\(707\) | −27.0146 | + | 33.8152i | −1.01599 | + | 1.27175i | ||||
\(708\) | −5.50951 | −0.207060 | ||||||||
\(709\) | −6.86513 | − | 11.8907i | −0.257825 | − | 0.446566i | 0.707834 | − | 0.706379i | \(-0.249673\pi\) |
−0.965659 | + | 0.259813i | \(0.916339\pi\) | |||||||
\(710\) | 1.65839 | − | 2.87241i | 0.0622382 | − | 0.107800i | ||||
\(711\) | −8.09684 | + | 14.0241i | −0.303655 | + | 0.525947i | ||||
\(712\) | −6.54653 | − | 11.3389i | −0.245342 | − | 0.424944i | ||||
\(713\) | 2.44143 | 0.0914323 | ||||||||
\(714\) | 2.15139 | − | 2.69297i | 0.0805137 | − | 0.100782i | ||||
\(715\) | −0.835651 | −0.0312516 | ||||||||
\(716\) | −6.68140 | − | 11.5725i | −0.249696 | − | 0.432486i | ||||
\(717\) | −5.64990 | + | 9.78591i | −0.210999 | + | 0.365462i | ||||
\(718\) | 6.49851 | − | 11.2558i | 0.242522 | − | 0.420061i | ||||
\(719\) | −24.3899 | − | 42.2446i | −0.909590 | − | 1.57546i | −0.814634 | − | 0.579975i | \(-0.803062\pi\) |
−0.0949556 | − | 0.995482i | \(-0.530271\pi\) | |||||||
\(720\) | 1.61450 | 0.0601690 | ||||||||
\(721\) | 19.1097 | + | 48.8149i | 0.711683 | + | 1.81796i | ||||
\(722\) | −6.93928 | −0.258253 | ||||||||
\(723\) | −1.10170 | − | 1.90819i | −0.0409725 | − | 0.0709665i | ||||
\(724\) | 11.8035 | − | 20.4442i | 0.438673 | − | 0.759803i | ||||
\(725\) | −12.0599 | + | 20.8884i | −0.447894 | + | 0.775776i | ||||
\(726\) | 6.30594 | + | 10.9222i | 0.234035 | + | 0.405361i | ||||
\(727\) | 13.3162 | 0.493869 | 0.246935 | − | 0.969032i | \(-0.420577\pi\) | ||||
0.246935 | + | 0.969032i | \(0.420577\pi\) | |||||||
\(728\) | 0.625921 | + | 0.0948963i | 0.0231982 | + | 0.00351709i | ||||
\(729\) | −12.4031 | −0.459375 | ||||||||
\(730\) | 1.97166 | + | 3.41501i | 0.0729743 | + | 0.126395i | ||||
\(731\) | 4.73217 | − | 8.19635i | 0.175026 | − | 0.303153i | ||||
\(732\) | 0.184491 | − | 0.319548i | 0.00681899 | − | 0.0118108i | ||||
\(733\) | −12.6501 | − | 21.9106i | −0.467242 | − | 0.809287i | 0.532057 | − | 0.846708i | \(-0.321419\pi\) |
−0.999300 | + | 0.0374209i | \(0.988086\pi\) | |||||||
\(734\) | −4.21867 | −0.155714 | ||||||||
\(735\) | −2.16200 | − | 0.670987i | −0.0797466 | − | 0.0247497i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 9.13959 | + | 15.8302i | 0.336661 | + | 0.583114i | ||||
\(738\) | −15.7452 | + | 27.2715i | −0.579589 | + | 1.00388i | ||||
\(739\) | 16.4401 | − | 28.4750i | 0.604758 | − | 1.04747i | −0.387332 | − | 0.921940i | \(-0.626603\pi\) |
0.992090 | − | 0.125531i | \(-0.0400635\pi\) | |||||||
\(740\) | 0.793506 | + | 1.37439i | 0.0291699 | + | 0.0505237i | ||||
\(741\) | −0.660584 | −0.0242672 | ||||||||
\(742\) | 11.4413 | + | 1.73463i | 0.420025 | + | 0.0636802i | ||||
\(743\) | 11.9697 | 0.439127 | 0.219564 | − | 0.975598i | \(-0.429537\pi\) | ||||
0.219564 | + | 0.975598i | \(0.429537\pi\) | |||||||
\(744\) | −0.661695 | − | 1.14609i | −0.0242589 | − | 0.0420177i | ||||
\(745\) | −1.59686 | + | 2.76585i | −0.0585046 | + | 0.101333i | ||||
\(746\) | −9.76371 | + | 16.9112i | −0.357475 | + | 0.619164i | ||||
\(747\) | −0.523491 | − | 0.906713i | −0.0191535 | − | 0.0331749i | ||||
\(748\) | −14.0690 | −0.514413 | ||||||||
\(749\) | −14.8497 | − | 37.9329i | −0.542596 | − | 1.38604i | ||||
\(750\) | −3.11879 | −0.113882 | ||||||||
\(751\) | −5.56933 | − | 9.64636i | −0.203228 | − | 0.352001i | 0.746339 | − | 0.665566i | \(-0.231810\pi\) |
−0.949567 | + | 0.313565i | \(0.898476\pi\) | |||||||
\(752\) | 3.86787 | − | 6.69935i | 0.141047 | − | 0.244300i | ||||
\(753\) | 7.56083 | − | 13.0957i | 0.275532 | − | 0.477235i | ||||
\(754\) | −0.621371 | − | 1.07625i | −0.0226290 | − | 0.0391946i | ||||
\(755\) | 4.16717 | 0.151659 | ||||||||
\(756\) | −5.10785 | + | 6.39368i | −0.185771 | + | 0.232536i | ||||
\(757\) | −14.5258 | −0.527949 | −0.263975 | − | 0.964530i | \(-0.585034\pi\) | ||||
−0.263975 | + | 0.964530i | \(0.585034\pi\) | |||||||
\(758\) | 10.9081 | + | 18.8934i | 0.396201 | + | 0.686240i | ||||
\(759\) | 1.58654 | − | 2.74796i | 0.0575876 | − | 0.0997447i | ||||
\(760\) | 1.51926 | − | 2.63143i | 0.0551093 | − | 0.0954521i | ||||
\(761\) | 2.77880 | + | 4.81302i | 0.100731 | + | 0.174472i | 0.911986 | − | 0.410221i | \(-0.134548\pi\) |
−0.811255 | + | 0.584693i | \(0.801215\pi\) | |||||||
\(762\) | 0.902085 | 0.0326791 | ||||||||
\(763\) | 26.8980 | − | 33.6693i | 0.973774 | − | 1.21891i | ||||
\(764\) | 6.90486 | 0.249809 | ||||||||
\(765\) | 1.94015 | + | 3.36044i | 0.0701462 | + | 0.121497i | ||||
\(766\) | 12.8533 | − | 22.2626i | 0.464410 | − | 0.804381i | ||||
\(767\) | 1.21603 | − | 2.10623i | 0.0439084 | − | 0.0760516i | ||||
\(768\) | −0.271028 | − | 0.469434i | −0.00977986 | − | 0.0169392i | ||||
\(769\) | 21.4784 | 0.774530 | 0.387265 | − | 0.921969i | \(-0.373420\pi\) | ||||
0.387265 | + | 0.921969i | \(0.373420\pi\) | |||||||
\(770\) | 3.36828 | + | 8.60412i | 0.121384 | + | 0.310071i | ||||
\(771\) | −15.1698 | −0.546328 | ||||||||
\(772\) | 9.74650 | + | 16.8814i | 0.350784 | + | 0.607576i | ||||
\(773\) | −14.2853 | + | 24.7428i | −0.513805 | + | 0.889937i | 0.486067 | + | 0.873922i | \(0.338431\pi\) |
−0.999872 | + | 0.0160149i | \(0.994902\pi\) | |||||||
\(774\) | −5.32832 | + | 9.22891i | −0.191522 | + | 0.331726i | ||||
\(775\) | −5.66909 | − | 9.81914i | −0.203640 | − | 0.352714i | ||||
\(776\) | 0.0666948 | 0.00239420 | ||||||||
\(777\) | −3.77185 | − | 0.571853i | −0.135315 | − | 0.0205151i | ||||
\(778\) | −20.6445 | −0.740141 | ||||||||
\(779\) | 29.6327 | + | 51.3254i | 1.06170 | + | 1.83892i | ||||
\(780\) | 0.0386903 | − | 0.0670135i | 0.00138533 | − | 0.00239947i | ||||
\(781\) | 16.2720 | − | 28.1839i | 0.582257 | − | 1.00850i | ||||
\(782\) | 1.20170 | + | 2.08141i | 0.0429727 | + | 0.0744309i | ||||
\(783\) | 16.0644 | 0.574095 | ||||||||
\(784\) | −1.54584 | − | 6.82718i | −0.0552084 | − | 0.243828i | ||||
\(785\) | 4.73069 | 0.168846 | ||||||||
\(786\) | −4.03734 | − | 6.99287i | −0.144007 | − | 0.249427i | ||||
\(787\) | −20.9575 | + | 36.2994i | −0.747053 | + | 1.29393i | 0.202176 | + | 0.979349i | \(0.435199\pi\) |
−0.949229 | + | 0.314585i | \(0.898135\pi\) | |||||||
\(788\) | −7.78696 | + | 13.4874i | −0.277399 | + | 0.480469i | ||||
\(789\) | 7.84143 | + | 13.5817i | 0.279162 | + | 0.483523i | ||||
\(790\) | −3.57004 | −0.127016 | ||||||||
\(791\) | 7.48487 | + | 1.13479i | 0.266131 | + | 0.0403484i | ||||
\(792\) | 15.8414 | 0.562898 | ||||||||
\(793\) | 0.0814399 | + | 0.141058i | 0.00289202 | + | 0.00500912i | ||||
\(794\) | 7.88241 | − | 13.6527i | 0.279736 | − | 0.484517i | ||||
\(795\) | 0.707227 | − | 1.22495i | 0.0250827 | − | 0.0434446i | ||||
\(796\) | −1.68897 | − | 2.92538i | −0.0598638 | − | 0.103687i | ||||
\(797\) | 47.4495 | 1.68075 | 0.840375 | − | 0.542006i | \(-0.182335\pi\) | ||||
0.840375 | + | 0.542006i | \(0.182335\pi\) | |||||||
\(798\) | 2.66263 | + | 6.80158i | 0.0942562 | + | 0.240773i | ||||
\(799\) | 18.5921 | 0.657741 | ||||||||
\(800\) | −2.32203 | − | 4.02188i | −0.0820963 | − | 0.142195i | ||||
\(801\) | −17.7161 | + | 30.6851i | −0.625966 | + | 1.08421i | ||||
\(802\) | 5.33817 | − | 9.24599i | 0.188497 | − | 0.326487i | ||||
\(803\) | 19.3457 | + | 33.5078i | 0.682696 | + | 1.18246i | ||||
\(804\) | −1.69264 | −0.0596947 | ||||||||
\(805\) | 0.985217 | − | 1.23323i | 0.0347243 | − | 0.0434657i | ||||
\(806\) | 0.584184 | 0.0205770 | ||||||||
\(807\) | 4.31253 | + | 7.46953i | 0.151808 | + | 0.262940i | ||||
\(808\) | −8.17935 | + | 14.1671i | −0.287749 | + | 0.498395i | ||||
\(809\) | −12.0705 | + | 20.9067i | −0.424375 | + | 0.735039i | −0.996362 | − | 0.0852235i | \(-0.972840\pi\) |
0.571987 | + | 0.820263i | \(0.306173\pi\) | |||||||
\(810\) | −1.92162 | − | 3.32835i | −0.0675189 | − | 0.116946i | ||||
\(811\) | 36.4282 | 1.27917 | 0.639583 | − | 0.768722i | \(-0.279107\pi\) | ||||
0.639583 | + | 0.768722i | \(0.279107\pi\) | |||||||
\(812\) | −8.57679 | + | 10.7359i | −0.300986 | + | 0.376756i | ||||
\(813\) | 3.34317 | 0.117250 | ||||||||
\(814\) | 7.78581 | + | 13.4854i | 0.272893 | + | 0.472664i | ||||
\(815\) | 4.21934 | − | 7.30811i | 0.147797 | − | 0.255992i | ||||
\(816\) | 0.651388 | − | 1.12824i | 0.0228031 | − | 0.0394962i | ||||
\(817\) | 10.0280 | + | 17.3689i | 0.350834 | + | 0.607663i | ||||
\(818\) | −12.0646 | −0.421830 | ||||||||
\(819\) | −0.624526 | − | 1.59532i | −0.0218227 | − | 0.0557451i | ||||
\(820\) | −6.94233 | −0.242437 | ||||||||
\(821\) | −18.7800 | − | 32.5278i | −0.655425 | − | 1.13523i | −0.981787 | − | 0.189984i | \(-0.939156\pi\) |
0.326362 | − | 0.945245i | \(-0.394177\pi\) | |||||||
\(822\) | 0.614920 | − | 1.06507i | 0.0214478 | − | 0.0371487i | ||||
\(823\) | −4.21270 | + | 7.29661i | −0.146846 | + | 0.254344i | −0.930060 | − | 0.367408i | \(-0.880245\pi\) |
0.783214 | + | 0.621752i | \(0.213579\pi\) | |||||||
\(824\) | 9.90684 | + | 17.1591i | 0.345121 | + | 0.597767i | ||||
\(825\) | −14.7360 | −0.513041 | ||||||||
\(826\) | −26.5879 | − | 4.03101i | −0.925111 | − | 0.140257i | ||||
\(827\) | 36.8035 | 1.27978 | 0.639891 | − | 0.768466i | \(-0.278980\pi\) | ||||
0.639891 | + | 0.768466i | \(0.278980\pi\) | |||||||
\(828\) | −1.35309 | − | 2.34362i | −0.0470231 | − | 0.0814463i | ||||
\(829\) | 6.21592 | − | 10.7663i | 0.215888 | − | 0.373929i | −0.737659 | − | 0.675173i | \(-0.764069\pi\) |
0.953547 | + | 0.301245i | \(0.0974021\pi\) | |||||||
\(830\) | 0.115408 | − | 0.199892i | 0.00400587 | − | 0.00693837i | ||||
\(831\) | −1.41925 | − | 2.45822i | −0.0492334 | − | 0.0852747i | ||||
\(832\) | 0.239279 | 0.00829552 | ||||||||
\(833\) | 12.3525 | − | 11.4217i | 0.427989 | − | 0.395740i | ||||
\(834\) | 9.84024 | 0.340740 | ||||||||
\(835\) | −5.32004 | − | 9.21459i | −0.184108 | − | 0.318884i | ||||
\(836\) | 14.9068 | − | 25.8194i | 0.515564 | − | 0.892983i | ||||
\(837\) | −3.77575 | + | 6.53979i | −0.130509 | + | 0.226048i | ||||
\(838\) | 5.45913 | + | 9.45549i | 0.188582 | + | 0.326634i | ||||
\(839\) | −21.8483 | −0.754287 | −0.377143 | − | 0.926155i | \(-0.623094\pi\) | ||||
−0.377143 | + | 0.926155i | \(0.623094\pi\) | |||||||
\(840\) | −0.845942 | − | 0.128254i | −0.0291878 | − | 0.00442518i | ||||
\(841\) | −2.02561 | −0.0698488 | ||||||||
\(842\) | −17.9472 | − | 31.0854i | −0.618500 | − | 1.07127i | ||||
\(843\) | −3.36874 | + | 5.83483i | −0.116026 | + | 0.200962i | ||||
\(844\) | −2.01409 | + | 3.48850i | −0.0693278 | + | 0.120079i | ||||
\(845\) | −3.86082 | − | 6.68713i | −0.132816 | − | 0.230044i | ||||
\(846\) | −20.9343 | −0.719735 | ||||||||
\(847\) | 22.4401 | + | 57.3222i | 0.771051 | + | 1.96962i | ||||
\(848\) | 4.37383 | 0.150198 | ||||||||
\(849\) | 0.633108 | + | 1.09657i | 0.0217282 | + | 0.0376343i | ||||
\(850\) | 5.58078 | − | 9.66619i | 0.191419 | − | 0.331548i | ||||
\(851\) | 1.33005 | − | 2.30371i | 0.0455935 | − | 0.0789702i | ||||
\(852\) | 1.50677 | + | 2.60980i | 0.0516211 | + | 0.0894103i | ||||
\(853\) | −0.543709 | −0.0186162 | −0.00930812 | − | 0.999957i | \(-0.502963\pi\) | ||||
−0.00930812 | + | 0.999957i | \(0.502963\pi\) | |||||||
\(854\) | 1.12412 | − | 1.40710i | 0.0384664 | − | 0.0481499i | ||||
\(855\) | −8.22276 | −0.281213 | ||||||||
\(856\) | −7.69837 | − | 13.3340i | −0.263125 | − | 0.455746i | ||||
\(857\) | −14.4504 | + | 25.0289i | −0.493617 | + | 0.854970i | −0.999973 | − | 0.00735490i | \(-0.997659\pi\) |
0.506356 | + | 0.862325i | \(0.330992\pi\) | |||||||
\(858\) | 0.379626 | − | 0.657531i | 0.0129602 | − | 0.0224477i | ||||
\(859\) | −10.0895 | − | 17.4756i | −0.344250 | − | 0.596259i | 0.640967 | − | 0.767568i | \(-0.278533\pi\) |
−0.985217 | + | 0.171310i | \(0.945200\pi\) | |||||||
\(860\) | −2.34934 | −0.0801120 | ||||||||
\(861\) | 10.4163 | − | 13.0385i | 0.354988 | − | 0.444352i | ||||
\(862\) | 25.0779 | 0.854158 | ||||||||
\(863\) | 25.1190 | + | 43.5073i | 0.855060 | + | 1.48101i | 0.876589 | + | 0.481239i | \(0.159813\pi\) |
−0.0215294 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(864\) | −1.54653 | + | 2.67867i | −0.0526141 | + | 0.0911302i | ||||
\(865\) | −1.99300 | + | 3.45198i | −0.0677640 | + | 0.117371i | ||||
\(866\) | −2.38217 | − | 4.12603i | −0.0809493 | − | 0.140208i | ||||
\(867\) | −6.08385 | −0.206618 | ||||||||
\(868\) | −2.35469 | − | 6.01494i | −0.0799233 | − | 0.204160i | ||||
\(869\) | −35.0289 | −1.18827 | ||||||||
\(870\) | 0.839793 | + | 1.45456i | 0.0284716 | + | 0.0493143i | ||||
\(871\) | 0.373590 | − | 0.647078i | 0.0126586 | − | 0.0219254i | ||||
\(872\) | 8.14407 | − | 14.1059i | 0.275793 | − | 0.477687i | ||||
\(873\) | −0.0902440 | − | 0.156307i | −0.00305430 | − | 0.00529019i | ||||
\(874\) | −5.09306 | −0.172275 | ||||||||
\(875\) | −15.0507 | − | 2.28185i | −0.508807 | − | 0.0771406i | ||||
\(876\) | −3.58280 | −0.121051 | ||||||||
\(877\) | −23.4201 | − | 40.5647i | −0.790839 | − | 1.36977i | −0.925448 | − | 0.378875i | \(-0.876311\pi\) |
0.134609 | − | 0.990899i | \(-0.457022\pi\) | |||||||
\(878\) | 8.68289 | − | 15.0392i | 0.293033 | − | 0.507549i | ||||
\(879\) | −0.778174 | + | 1.34784i | −0.0262472 | + | 0.0454614i | ||||
\(880\) | 1.74618 | + | 3.02448i | 0.0588638 | + | 0.101955i | ||||
\(881\) | −39.8060 | −1.34110 | −0.670549 | − | 0.741866i | \(-0.733941\pi\) | ||||
−0.670549 | + | 0.741866i | \(0.733941\pi\) | |||||||
\(882\) | −13.9086 | + | 12.8606i | −0.468328 | + | 0.433040i | ||||
\(883\) | −20.8918 | −0.703065 | −0.351533 | − | 0.936176i | \(-0.614339\pi\) | ||||
−0.351533 | + | 0.936176i | \(0.614339\pi\) | |||||||
\(884\) | 0.287542 | + | 0.498038i | 0.00967109 | + | 0.0167508i | ||||
\(885\) | −1.64349 | + | 2.84660i | −0.0552452 | + | 0.0956875i | ||||
\(886\) | 3.10128 | − | 5.37158i | 0.104190 | − | 0.180462i | ||||
\(887\) | 23.4100 | + | 40.5473i | 0.786031 | + | 1.36145i | 0.928381 | + | 0.371629i | \(0.121201\pi\) |
−0.142351 | + | 0.989816i | \(0.545466\pi\) | |||||||
\(888\) | −1.44192 | −0.0483876 | ||||||||
\(889\) | 4.35330 | + | 0.660006i | 0.146005 | + | 0.0221359i | ||||
\(890\) | −7.81131 | −0.261836 | ||||||||
\(891\) | −18.8548 | − | 32.6575i | −0.631659 | − | 1.09407i | ||||
\(892\) | −14.1193 | + | 24.4553i | −0.472749 | + | 0.818825i | ||||
\(893\) | −19.6993 | + | 34.1202i | −0.659212 | + | 1.14179i | ||||
\(894\) | −1.45087 | − | 2.51298i | −0.0485244 | − | 0.0840467i | ||||
\(895\) | −7.97224 | −0.266483 | ||||||||
\(896\) | −0.964471 | − | 2.46370i | −0.0322207 | − | 0.0823063i | ||||
\(897\) | −0.129703 | −0.00433065 | ||||||||
\(898\) | −8.13544 | − | 14.0910i | −0.271483 | − | 0.470222i | ||||
\(899\) | −6.34001 | + | 10.9812i | −0.211451 | + | 0.366244i | ||||
\(900\) | −6.28383 | + | 10.8839i | −0.209461 | + | 0.362797i | ||||
\(901\) | 5.25604 | + | 9.10373i | 0.175104 | + | 0.303289i | ||||
\(902\) | −68.1176 | −2.26807 | ||||||||
\(903\) | 3.52498 | − | 4.41235i | 0.117304 | − | 0.146834i | ||||
\(904\) | 2.86135 | 0.0951669 | ||||||||
\(905\) | −7.04194 | − | 12.1970i | −0.234082 | − | 0.405442i | ||||
\(906\) | −1.89309 | + | 3.27893i | −0.0628938 | + | 0.108935i | ||||
\(907\) | 7.78036 | − | 13.4760i | 0.258342 | − | 0.447462i | −0.707456 | − | 0.706758i | \(-0.750157\pi\) |
0.965798 | + | 0.259296i | \(0.0834904\pi\) | |||||||
\(908\) | 5.11176 | + | 8.85383i | 0.169640 | + | 0.293825i | ||||
\(909\) | 44.2695 | 1.46833 | ||||||||
\(910\) | 0.235742 | − | 0.295087i | 0.00781478 | − | 0.00978205i | ||||
\(911\) | −5.19715 | −0.172189 | −0.0860946 | − | 0.996287i | \(-0.527439\pi\) | ||||
−0.0860946 | + | 0.996287i | \(0.527439\pi\) | |||||||
\(912\) | 1.38036 | + | 2.39085i | 0.0457083 | + | 0.0791691i | ||||
\(913\) | 1.13237 | − | 1.96133i | 0.0374761 | − | 0.0649105i | ||||
\(914\) | 8.18259 | − | 14.1727i | 0.270656 | − | 0.468790i | ||||
\(915\) | −0.110067 | − | 0.190642i | −0.00363871 | − | 0.00630243i | ||||
\(916\) | −2.50083 | −0.0826296 | ||||||||
\(917\) | −14.3671 | − | 36.7002i | −0.474445 | − | 1.21195i | ||||
\(918\) | −7.43387 | −0.245354 | ||||||||
\(919\) | 19.7906 | + | 34.2784i | 0.652833 | + | 1.13074i | 0.982432 | + | 0.186619i | \(0.0597530\pi\) |
−0.329599 | + | 0.944121i | \(0.606914\pi\) | |||||||
\(920\) | 0.298300 | − | 0.516670i | 0.00983465 | − | 0.0170341i | ||||
\(921\) | −6.93460 | + | 12.0111i | −0.228503 | + | 0.395779i | ||||
\(922\) | 9.09823 | + | 15.7586i | 0.299634 | + | 0.518982i | ||||
\(923\) | −1.33027 | −0.0437863 | ||||||||
\(924\) | −8.30031 | − | 1.25841i | −0.273060 | − | 0.0413988i | ||||
\(925\) | −12.3537 | −0.406186 | ||||||||
\(926\) | 0.212325 | + | 0.367758i | 0.00697745 | + | 0.0120853i | ||||
\(927\) | 26.8097 | − | 46.4357i | 0.880545 | − | 1.52515i | ||||
\(928\) | −2.59684 | + | 4.49786i | −0.0852456 | + | 0.147650i | ||||
\(929\) | 16.0130 | + | 27.7353i | 0.525369 | + | 0.909965i | 0.999563 | + | 0.0295454i | \(0.00940595\pi\) |
−0.474195 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(930\) | −0.789534 | −0.0258898 | ||||||||
\(931\) | 7.87304 | + | 34.7713i | 0.258029 | + | 1.13958i | ||||
\(932\) | 4.46600 | 0.146289 | ||||||||
\(933\) | 3.50218 | + | 6.06596i | 0.114656 | + | 0.198591i | ||||
\(934\) | 14.0860 | − | 24.3976i | 0.460908 | − | 0.798315i | ||||
\(935\) | −4.19677 | + | 7.26903i | −0.137249 | + | 0.237723i | ||||
\(936\) | −0.323766 | − | 0.560780i | −0.0105826 | − | 0.0183297i | ||||
\(937\) | −39.9634 | −1.30555 | −0.652773 | − | 0.757554i | \(-0.726394\pi\) | ||||
−0.652773 | + | 0.757554i | \(0.726394\pi\) | |||||||
\(938\) | −8.16835 | − | 1.23841i | −0.266706 | − | 0.0404355i | ||||
\(939\) | 13.9861 | 0.456420 | ||||||||
\(940\) | −2.30757 | − | 3.99683i | −0.0752646 | − | 0.130362i | ||||
\(941\) | 22.0476 | − | 38.1876i | 0.718731 | − | 1.24488i | −0.242771 | − | 0.970084i | \(-0.578056\pi\) |
0.961503 | − | 0.274796i | \(-0.0886102\pi\) | |||||||
\(942\) | −2.14909 | + | 3.72234i | −0.0700213 | + | 0.121280i | ||||
\(943\) | 5.81825 | + | 10.0775i | 0.189468 | + | 0.328169i | ||||
\(944\) | −10.1641 | −0.330814 | ||||||||
\(945\) | 1.77976 | + | 4.54630i | 0.0578955 | + | 0.147891i | ||||
\(946\) | −23.0516 | −0.749471 | ||||||||
\(947\) | 14.4016 | + | 24.9443i | 0.467989 | + | 0.810580i | 0.999331 | − | 0.0365770i | \(-0.0116454\pi\) |
−0.531342 | + | 0.847157i | \(0.678312\pi\) | |||||||
\(948\) | 1.62182 | − | 2.80908i | 0.0526743 | − | 0.0912346i | ||||
\(949\) | 0.790777 | − | 1.36967i | 0.0256697 | − | 0.0444612i | ||||
\(950\) | 11.8263 | + | 20.4837i | 0.383695 | + | 0.664579i | ||||
\(951\) | −13.5527 | −0.439475 | ||||||||
\(952\) | 3.96895 | − | 4.96808i | 0.128634 | − | 0.161016i | ||||
\(953\) | −52.0903 | −1.68737 | −0.843685 | − | 0.536838i | \(-0.819619\pi\) | ||||
−0.843685 | + | 0.536838i | \(0.819619\pi\) | |||||||
\(954\) | −5.91818 | − | 10.2506i | −0.191608 | − | 0.331875i | ||||
\(955\) | 2.05972 | − | 3.56754i | 0.0666509 | − | 0.115443i | ||||
\(956\) | −10.4231 | + | 18.0534i | −0.337107 | + | 0.583887i | ||||
\(957\) | 8.23997 | + | 14.2721i | 0.266361 | + | 0.461350i | ||||
\(958\) | −9.76621 | −0.315532 | ||||||||
\(959\) | 3.74674 | − | 4.68994i | 0.120989 | − | 0.151446i | ||||
\(960\) | −0.323390 | −0.0104374 | ||||||||
\(961\) | 12.5197 | + | 21.6848i | 0.403862 | + | 0.699509i | ||||
\(962\) | 0.318253 | − | 0.551231i | 0.0102609 | − | 0.0177724i | ||||
\(963\) | −20.8331 | + | 36.0841i | −0.671339 | + | 1.16279i | ||||
\(964\) | −2.03244 | − | 3.52029i | −0.0654606 | − | 0.113381i | ||||
\(965\) | 11.6295 | 0.374367 | ||||||||
\(966\) | 0.522796 | + | 1.33546i | 0.0168207 | + | 0.0429677i | ||||
\(967\) | −8.53400 | −0.274435 | −0.137218 | − | 0.990541i | \(-0.543816\pi\) | ||||
−0.137218 | + | 0.990541i | \(0.543816\pi\) | |||||||
\(968\) | 11.6334 | + | 20.1496i | 0.373911 | + | 0.647633i | ||||
\(969\) | −3.31756 | + | 5.74618i | −0.106575 | + | 0.184594i | ||||
\(970\) | 0.0198950 | − | 0.0344592i | 0.000638791 | − | 0.00110642i | ||||
\(971\) | −12.2179 | − | 21.1621i | −0.392093 | − | 0.679124i | 0.600633 | − | 0.799525i | \(-0.294915\pi\) |
−0.992725 | + | 0.120401i | \(0.961582\pi\) | |||||||
\(972\) | 12.7711 | 0.409632 | ||||||||
\(973\) | 47.4872 | + | 7.19956i | 1.52237 | + | 0.230807i | ||||
\(974\) | −20.7530 | −0.664968 | ||||||||
\(975\) | 0.301174 | + | 0.521649i | 0.00964529 | + | 0.0167061i | ||||
\(976\) | 0.340355 | − | 0.589512i | 0.0108945 | − | 0.0188698i | ||||
\(977\) | 31.1750 | − | 53.9967i | 0.997377 | − | 1.72751i | 0.436009 | − | 0.899942i | \(-0.356392\pi\) |
0.561369 | − | 0.827566i | \(-0.310275\pi\) | |||||||
\(978\) | 3.83359 | + | 6.63996i | 0.122585 | + | 0.212323i | ||||
\(979\) | −76.6439 | −2.44955 | ||||||||
\(980\) | −3.98852 | − | 1.23786i | −0.127409 | − | 0.0395419i | ||||
\(981\) | −44.0786 | −1.40732 | ||||||||
\(982\) | −12.9516 | − | 22.4328i | −0.413301 | − | 0.715858i | ||||
\(983\) | 19.9111 | − | 34.4870i | 0.635065 | − | 1.09996i | −0.351437 | − | 0.936212i | \(-0.614307\pi\) |
0.986501 | − | 0.163752i | \(-0.0523598\pi\) | |||||||
\(984\) | 3.15381 | − | 5.46257i | 0.100540 | − | 0.174140i | ||||
\(985\) | 4.64569 | + | 8.04658i | 0.148024 | + | 0.256385i | ||||
\(986\) | −12.4825 | −0.397524 | ||||||||
\(987\) | 10.9688 | + | 1.66299i | 0.349141 | + | 0.0529335i | ||||
\(988\) | −1.21867 | −0.0387709 | ||||||||
\(989\) | 1.96895 | + | 3.41032i | 0.0626089 | + | 0.108442i | ||||
\(990\) | 4.72548 | − | 8.18476i | 0.150185 | − | 0.260129i | ||||
\(991\) | −3.02762 | + | 5.24400i | −0.0961756 | + | 0.166581i | −0.910099 | − | 0.414392i | \(-0.863994\pi\) |
0.813923 | + | 0.580973i | \(0.197328\pi\) | |||||||
\(992\) | −1.22072 | − | 2.11434i | −0.0387577 | − | 0.0671304i | ||||
\(993\) | 5.64678 | 0.179195 | ||||||||
\(994\) | 5.36195 | + | 13.6968i | 0.170071 | + | 0.434438i | ||||
\(995\) | −2.01527 | −0.0638885 | ||||||||
\(996\) | 0.104857 | + | 0.181617i | 0.00332251 | + | 0.00575476i | ||||
\(997\) | −27.1119 | + | 46.9592i | −0.858643 | + | 1.48721i | 0.0145814 | + | 0.999894i | \(0.495358\pi\) |
−0.873224 | + | 0.487319i | \(0.837975\pi\) | |||||||
\(998\) | −16.8329 | + | 29.1555i | −0.532837 | + | 0.922901i | ||||
\(999\) | 4.11392 | + | 7.12552i | 0.130159 | + | 0.225441i |
(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 | 322.2.e.d.277.2 | yes | 8 | |
7.2 | even | 3 | inner | 322.2.e.d.93.2 | ✓ | 8 | |
7.3 | odd | 6 | 2254.2.a.r.1.2 | 4 | |||
7.4 | even | 3 | 2254.2.a.u.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.e.d.93.2 | ✓ | 8 | 7.2 | even | 3 | inner | |
322.2.e.d.277.2 | yes | 8 | 1.1 | even | 1 | trivial | |
2254.2.a.r.1.2 | 4 | 7.3 | odd | 6 | |||
2254.2.a.u.1.3 | 4 | 7.4 | even | 3 |