Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not 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: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 5^{6} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(-0.705457 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.151 |
Dual form | 750.2.g.f.601.2 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | −0.329315 | −0.124469 | −0.0622347 | − | 0.998062i | \(-0.519823\pi\) | ||||
−0.0622347 | + | 0.998062i | \(0.519823\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.55540 | − | 4.78704i | −0.468972 | − | 1.44335i | −0.853918 | − | 0.520408i | \(-0.825780\pi\) |
0.384946 | − | 0.922939i | \(-0.374220\pi\) | |||||||
\(12\) | 0.309017 | − | 0.951057i | 0.0892055 | − | 0.274546i | ||||
\(13\) | −0.148993 | + | 0.458554i | −0.0413233 | + | 0.127180i | −0.969590 | − | 0.244735i | \(-0.921299\pi\) |
0.928267 | + | 0.371915i | \(0.121299\pi\) | |||||||
\(14\) | −0.101764 | − | 0.313197i | −0.0271975 | − | 0.0837054i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −5.49007 | − | 3.98877i | −1.33154 | − | 0.967418i | −0.999710 | − | 0.0240779i | \(-0.992335\pi\) |
−0.331827 | − | 0.943340i | \(-0.607665\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.40115 | − | 3.19762i | −1.00969 | − | 0.733585i | −0.0455487 | − | 0.998962i | \(-0.514504\pi\) |
−0.964145 | + | 0.265377i | \(0.914504\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.266421 | − | 0.193566i | 0.0581379 | − | 0.0422397i | ||||
\(22\) | 4.07210 | − | 2.95855i | 0.868175 | − | 0.630766i | ||||
\(23\) | 2.00878 | + | 6.18239i | 0.418860 | + | 1.28912i | 0.908753 | + | 0.417335i | \(0.137036\pi\) |
−0.489893 | + | 0.871783i | \(0.662964\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.482152 | −0.0945578 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 0.266421 | − | 0.193566i | 0.0503489 | − | 0.0365806i | ||||
\(29\) | 4.87203 | − | 3.53974i | 0.904714 | − | 0.657313i | −0.0349585 | − | 0.999389i | \(-0.511130\pi\) |
0.939672 | + | 0.342076i | \(0.111130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.06685 | − | 0.775108i | −0.191611 | − | 0.139214i | 0.487844 | − | 0.872931i | \(-0.337784\pi\) |
−0.679455 | + | 0.733717i | \(0.737784\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.07210 | + | 2.95855i | 0.708862 | + | 0.515018i | ||||
\(34\) | 2.09702 | − | 6.45396i | 0.359636 | − | 1.10685i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | 0.241076 | − | 0.741956i | 0.0396327 | − | 0.121977i | −0.929283 | − | 0.369369i | \(-0.879574\pi\) |
0.968915 | + | 0.247393i | \(0.0795737\pi\) | |||||||
\(38\) | 1.68109 | − | 5.17386i | 0.272709 | − | 0.839312i | ||||
\(39\) | −0.148993 | − | 0.458554i | −0.0238580 | − | 0.0734274i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.86905 | − | 11.9077i | 0.604245 | − | 1.85967i | 0.102344 | − | 0.994749i | \(-0.467366\pi\) |
0.501901 | − | 0.864925i | \(-0.332634\pi\) | |||||||
\(42\) | 0.266421 | + | 0.193566i | 0.0411097 | + | 0.0298680i | ||||
\(43\) | −2.47582 | −0.377559 | −0.188779 | − | 0.982020i | \(-0.560453\pi\) | ||||
−0.188779 | + | 0.982020i | \(0.560453\pi\) | |||||||
\(44\) | 4.07210 | + | 2.95855i | 0.613892 | + | 0.446019i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.25906 | + | 3.82093i | −0.775405 | + | 0.563365i | ||||
\(47\) | 3.54381 | − | 2.57473i | 0.516918 | − | 0.375563i | −0.298523 | − | 0.954402i | \(-0.596494\pi\) |
0.815442 | + | 0.578839i | \(0.196494\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −6.89155 | −0.984507 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.78610 | 0.950244 | ||||||||
\(52\) | −0.148993 | − | 0.458554i | −0.0206616 | − | 0.0635900i | ||||
\(53\) | 1.36393 | − | 0.990953i | 0.187350 | − | 0.136118i | −0.490157 | − | 0.871634i | \(-0.663060\pi\) |
0.677507 | + | 0.735516i | \(0.263060\pi\) | |||||||
\(54\) | −0.809017 | + | 0.587785i | −0.110093 | + | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.266421 | + | 0.193566i | 0.0356021 | + | 0.0258664i | ||||
\(57\) | 5.44012 | 0.720562 | ||||||||
\(58\) | 4.87203 | + | 3.53974i | 0.639729 | + | 0.464791i | ||||
\(59\) | 0.313909 | − | 0.966113i | 0.0408675 | − | 0.125777i | −0.928541 | − | 0.371229i | \(-0.878936\pi\) |
0.969409 | + | 0.245452i | \(0.0789364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29419 | + | 3.98310i | 0.165704 | + | 0.509984i | 0.999087 | − | 0.0427111i | \(-0.0135995\pi\) |
−0.833384 | + | 0.552695i | \(0.813599\pi\) | |||||||
\(62\) | 0.407499 | − | 1.25415i | 0.0517524 | − | 0.159277i | ||||
\(63\) | −0.101764 | + | 0.313197i | −0.0128210 | + | 0.0394591i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.55540 | + | 4.78704i | −0.191457 | + | 0.589244i | ||||
\(67\) | −2.54381 | − | 1.84819i | −0.310776 | − | 0.225792i | 0.421453 | − | 0.906850i | \(-0.361520\pi\) |
−0.732230 | + | 0.681058i | \(0.761520\pi\) | |||||||
\(68\) | 6.78610 | 0.822935 | ||||||||
\(69\) | −5.25906 | − | 3.82093i | −0.633116 | − | 0.459986i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.62101 | + | 3.35736i | −0.548413 | + | 0.398446i | −0.827200 | − | 0.561907i | \(-0.810068\pi\) |
0.278787 | + | 0.960353i | \(0.410068\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | 0.909340 | + | 2.79866i | 0.106430 | + | 0.327558i | 0.990063 | − | 0.140621i | \(-0.0449100\pi\) |
−0.883633 | + | 0.468180i | \(0.844910\pi\) | |||||||
\(74\) | 0.780139 | 0.0906893 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.44012 | 0.624025 | ||||||||
\(77\) | 0.512218 | + | 1.57644i | 0.0583726 | + | 0.179652i | ||||
\(78\) | 0.390069 | − | 0.283402i | 0.0441667 | − | 0.0320890i | ||||
\(79\) | −6.86459 | + | 4.98742i | −0.772327 | + | 0.561128i | −0.902666 | − | 0.430341i | \(-0.858393\pi\) |
0.130339 | + | 0.991469i | \(0.458393\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 12.5205 | 1.38266 | ||||||||
\(83\) | −13.9114 | − | 10.1073i | −1.52698 | − | 1.10942i | −0.957888 | − | 0.287142i | \(-0.907295\pi\) |
−0.569092 | − | 0.822274i | \(-0.692705\pi\) | |||||||
\(84\) | −0.101764 | + | 0.313197i | −0.0111034 | + | 0.0341726i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.765070 | − | 2.35464i | −0.0824996 | − | 0.253908i | ||||
\(87\) | −1.86095 | + | 5.72742i | −0.199515 | + | 0.614044i | ||||
\(88\) | −1.55540 | + | 4.78704i | −0.165807 | + | 0.510300i | ||||
\(89\) | 1.06683 | + | 3.28336i | 0.113084 | + | 0.348036i | 0.991543 | − | 0.129782i | \(-0.0414279\pi\) |
−0.878459 | + | 0.477818i | \(0.841428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0490657 | − | 0.151009i | 0.00514348 | − | 0.0158300i | ||||
\(92\) | −5.25906 | − | 3.82093i | −0.548294 | − | 0.398359i | ||||
\(93\) | 1.31869 | 0.136742 | ||||||||
\(94\) | 3.54381 | + | 2.57473i | 0.365517 | + | 0.265563i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.809017 | + | 0.587785i | −0.0825700 | + | 0.0599906i | ||||
\(97\) | 7.69378 | − | 5.58986i | 0.781185 | − | 0.567564i | −0.124149 | − | 0.992264i | \(-0.539620\pi\) |
0.905334 | + | 0.424699i | \(0.139620\pi\) | |||||||
\(98\) | −2.12961 | − | 6.55426i | −0.215123 | − | 0.662080i | ||||
\(99\) | −5.03339 | −0.505875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.2435 | 1.91480 | 0.957400 | − | 0.288765i | \(-0.0932447\pi\) | ||||
0.957400 | + | 0.288765i | \(0.0932447\pi\) | |||||||
\(102\) | 2.09702 | + | 6.45396i | 0.207636 | + | 0.639037i | ||||
\(103\) | −4.13156 | + | 3.00175i | −0.407095 | + | 0.295771i | −0.772424 | − | 0.635107i | \(-0.780956\pi\) |
0.365330 | + | 0.930878i | \(0.380956\pi\) | |||||||
\(104\) | 0.390069 | − | 0.283402i | 0.0382494 | − | 0.0277898i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.36393 | + | 0.990953i | 0.132477 | + | 0.0962499i | ||||
\(107\) | −15.3340 | −1.48239 | −0.741194 | − | 0.671290i | \(-0.765740\pi\) | ||||
−0.741194 | + | 0.671290i | \(0.765740\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | −3.01609 | + | 9.28257i | −0.288889 | + | 0.889109i | 0.696317 | + | 0.717735i | \(0.254821\pi\) |
−0.985206 | + | 0.171375i | \(0.945179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.241076 | + | 0.741956i | 0.0228819 | + | 0.0704233i | ||||
\(112\) | −0.101764 | + | 0.313197i | −0.00961579 | + | 0.0295943i | ||||
\(113\) | 0.468364 | − | 1.44148i | 0.0440599 | − | 0.135603i | −0.926607 | − | 0.376032i | \(-0.877288\pi\) |
0.970667 | + | 0.240429i | \(0.0772883\pi\) | |||||||
\(114\) | 1.68109 | + | 5.17386i | 0.157449 | + | 0.484577i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.86095 | + | 5.72742i | −0.172785 | + | 0.531778i | ||||
\(117\) | 0.390069 | + | 0.283402i | 0.0360619 | + | 0.0262005i | ||||
\(118\) | 1.01583 | 0.0935149 | ||||||||
\(119\) | 1.80796 | + | 1.31356i | 0.165736 | + | 0.120414i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.5973 | + | 8.42593i | −1.05430 | + | 0.765993i | ||||
\(122\) | −3.38823 | + | 2.46169i | −0.306756 | + | 0.222871i | ||||
\(123\) | 3.86905 | + | 11.9077i | 0.348861 | + | 1.07368i | ||||
\(124\) | 1.31869 | 0.118422 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.329315 | −0.0293377 | ||||||||
\(127\) | 3.89534 | + | 11.9886i | 0.345656 | + | 1.06382i | 0.961232 | + | 0.275741i | \(0.0889233\pi\) |
−0.615576 | + | 0.788077i | \(0.711077\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | 2.00298 | − | 1.45525i | 0.176352 | − | 0.128128i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3715 | − | 8.26187i | −0.993532 | − | 0.721843i | −0.0328399 | − | 0.999461i | \(-0.510455\pi\) |
−0.960692 | + | 0.277618i | \(0.910455\pi\) | |||||||
\(132\) | −5.03339 | −0.438101 | ||||||||
\(133\) | 1.44936 | + | 1.05303i | 0.125676 | + | 0.0913089i | ||||
\(134\) | 0.971651 | − | 2.99043i | 0.0839378 | − | 0.258334i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.09702 | + | 6.45396i | 0.179818 | + | 0.553423i | ||||
\(137\) | −2.06690 | + | 6.36127i | −0.176587 | + | 0.543480i | −0.999702 | − | 0.0243949i | \(-0.992234\pi\) |
0.823115 | + | 0.567874i | \(0.192234\pi\) | |||||||
\(138\) | 2.00878 | − | 6.18239i | 0.170999 | − | 0.526280i | ||||
\(139\) | −0.951151 | − | 2.92734i | −0.0806755 | − | 0.248294i | 0.902581 | − | 0.430520i | \(-0.141670\pi\) |
−0.983257 | + | 0.182226i | \(0.941670\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.35362 | + | 4.16600i | −0.113995 | + | 0.350841i | ||||
\(142\) | −4.62101 | − | 3.35736i | −0.387787 | − | 0.281744i | ||||
\(143\) | 2.42686 | 0.202944 | ||||||||
\(144\) | −0.809017 | − | 0.587785i | −0.0674181 | − | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.38068 | + | 1.72967i | −0.197027 | + | 0.143148i | ||||
\(147\) | 5.57538 | − | 4.05075i | 0.459850 | − | 0.334100i | ||||
\(148\) | 0.241076 | + | 0.741956i | 0.0198163 | + | 0.0609884i | ||||
\(149\) | 5.06465 | 0.414912 | 0.207456 | − | 0.978244i | \(-0.433482\pi\) | ||||
0.207456 | + | 0.978244i | \(0.433482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9581 | −1.38003 | −0.690015 | − | 0.723795i | \(-0.742396\pi\) | ||||
−0.690015 | + | 0.723795i | \(0.742396\pi\) | |||||||
\(152\) | 1.68109 | + | 5.17386i | 0.136354 | + | 0.419656i | ||||
\(153\) | −5.49007 | + | 3.98877i | −0.443846 | + | 0.322473i | ||||
\(154\) | −1.34100 | + | 0.974296i | −0.108061 | + | 0.0785110i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.390069 | + | 0.283402i | 0.0312305 | + | 0.0226903i | ||||
\(157\) | −22.8284 | −1.82190 | −0.910952 | − | 0.412513i | \(-0.864651\pi\) | ||||
−0.910952 | + | 0.412513i | \(0.864651\pi\) | |||||||
\(158\) | −6.86459 | − | 4.98742i | −0.546118 | − | 0.396778i | ||||
\(159\) | −0.520975 | + | 1.60340i | −0.0413160 | + | 0.127158i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.661521 | − | 2.03595i | −0.0521352 | − | 0.160456i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | 2.45923 | − | 7.56873i | 0.192622 | − | 0.592829i | −0.807374 | − | 0.590039i | \(-0.799112\pi\) |
0.999996 | − | 0.00278919i | \(-0.000887829\pi\) | |||||||
\(164\) | 3.86905 | + | 11.9077i | 0.302122 | + | 0.929837i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.31370 | − | 16.3539i | 0.412423 | − | 1.26931i | ||||
\(167\) | −11.2860 | − | 8.19979i | −0.873340 | − | 0.634519i | 0.0581411 | − | 0.998308i | \(-0.481483\pi\) |
−0.931481 | + | 0.363790i | \(0.881483\pi\) | |||||||
\(168\) | −0.329315 | −0.0254072 | ||||||||
\(169\) | 10.3291 | + | 7.50457i | 0.794550 | + | 0.577274i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.40115 | + | 3.19762i | −0.336564 | + | 0.244528i | ||||
\(172\) | 2.00298 | − | 1.45525i | 0.152726 | − | 0.110962i | ||||
\(173\) | −6.02610 | − | 18.5464i | −0.458156 | − | 1.41006i | −0.867390 | − | 0.497629i | \(-0.834204\pi\) |
0.409234 | − | 0.912430i | \(-0.365796\pi\) | |||||||
\(174\) | −6.02216 | −0.456539 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.03339 | −0.379406 | ||||||||
\(177\) | 0.313909 | + | 0.966113i | 0.0235949 | + | 0.0726175i | ||||
\(178\) | −2.79299 | + | 2.02923i | −0.209344 | + | 0.152097i | ||||
\(179\) | 15.3641 | − | 11.1627i | 1.14837 | − | 0.834338i | 0.160105 | − | 0.987100i | \(-0.448817\pi\) |
0.988263 | + | 0.152761i | \(0.0488166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3296 | + | 11.1376i | 1.13944 | + | 0.827850i | 0.987041 | − | 0.160470i | \(-0.0513008\pi\) |
0.152397 | + | 0.988319i | \(0.451301\pi\) | |||||||
\(182\) | 0.158780 | 0.0117695 | ||||||||
\(183\) | −3.38823 | − | 2.46169i | −0.250465 | − | 0.181973i | ||||
\(184\) | 2.00878 | − | 6.18239i | 0.148089 | − | 0.455772i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.407499 | + | 1.25415i | 0.0298793 | + | 0.0919589i | ||||
\(187\) | −10.5551 | + | 32.4853i | −0.771867 | + | 2.37556i | ||||
\(188\) | −1.35362 | + | 4.16600i | −0.0987226 | + | 0.303837i | ||||
\(189\) | −0.101764 | − | 0.313197i | −0.00740223 | − | 0.0227817i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.73703 | + | 11.5014i | −0.270402 | + | 0.832212i | 0.719997 | + | 0.693977i | \(0.244143\pi\) |
−0.990399 | + | 0.138235i | \(0.955857\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | −11.0357 | −0.794368 | −0.397184 | − | 0.917739i | \(-0.630013\pi\) | ||||
−0.397184 | + | 0.917739i | \(0.630013\pi\) | |||||||
\(194\) | 7.69378 | + | 5.58986i | 0.552381 | + | 0.401329i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.57538 | − | 4.05075i | 0.398242 | − | 0.289339i | ||||
\(197\) | 16.6829 | − | 12.1208i | 1.18861 | − | 0.863573i | 0.195490 | − | 0.980706i | \(-0.437370\pi\) |
0.993116 | + | 0.117133i | \(0.0373704\pi\) | |||||||
\(198\) | −1.55540 | − | 4.78704i | −0.110538 | − | 0.340200i | ||||
\(199\) | 18.5313 | 1.31365 | 0.656826 | − | 0.754042i | \(-0.271899\pi\) | ||||
0.656826 | + | 0.754042i | \(0.271899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.14433 | 0.221784 | ||||||||
\(202\) | 5.94657 | + | 18.3017i | 0.418399 | + | 1.28770i | ||||
\(203\) | −1.60443 | + | 1.16569i | −0.112609 | + | 0.0818153i | ||||
\(204\) | −5.49007 | + | 3.98877i | −0.384382 | + | 0.279270i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.13156 | − | 3.00175i | −0.287859 | − | 0.209142i | ||||
\(207\) | 6.50055 | 0.451819 | ||||||||
\(208\) | 0.390069 | + | 0.283402i | 0.0270464 | + | 0.0196504i | ||||
\(209\) | −8.46159 | + | 26.0421i | −0.585300 | + | 1.80137i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.87129 | + | 14.9923i | 0.335353 | + | 1.03211i | 0.966548 | + | 0.256487i | \(0.0825650\pi\) |
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(212\) | −0.520975 | + | 1.60340i | −0.0357807 | + | 0.110122i | ||||
\(213\) | 1.76507 | − | 5.43233i | 0.120941 | − | 0.372217i | ||||
\(214\) | −4.73845 | − | 14.5835i | −0.323914 | − | 0.996904i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.309017 | − | 0.951057i | 0.0210259 | − | 0.0647112i | ||||
\(217\) | 0.351328 | + | 0.255255i | 0.0238497 | + | 0.0173278i | ||||
\(218\) | −9.76027 | −0.661049 | ||||||||
\(219\) | −2.38068 | − | 1.72967i | −0.160872 | − | 0.116880i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.64705 | − | 1.92319i | 0.178060 | − | 0.129368i | ||||
\(222\) | −0.631145 | + | 0.458554i | −0.0423597 | + | 0.0307761i | ||||
\(223\) | −6.85345 | − | 21.0928i | −0.458941 | − | 1.41248i | −0.866445 | − | 0.499272i | \(-0.833601\pi\) |
0.407504 | − | 0.913203i | \(-0.366399\pi\) | |||||||
\(224\) | −0.329315 | −0.0220033 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51566 | 0.100820 | ||||||||
\(227\) | 3.42913 | + | 10.5538i | 0.227600 | + | 0.700480i | 0.998017 | + | 0.0629401i | \(0.0200477\pi\) |
−0.770418 | + | 0.637539i | \(0.779952\pi\) | |||||||
\(228\) | −4.40115 | + | 3.19762i | −0.291473 | + | 0.211768i | ||||
\(229\) | −1.45525 | + | 1.05730i | −0.0961658 | + | 0.0698685i | −0.634829 | − | 0.772653i | \(-0.718929\pi\) |
0.538663 | + | 0.842521i | \(0.318929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.34100 | − | 0.974296i | −0.0882315 | − | 0.0641040i | ||||
\(232\) | −6.02216 | −0.395374 | ||||||||
\(233\) | −2.99805 | − | 2.17821i | −0.196409 | − | 0.142699i | 0.485234 | − | 0.874384i | \(-0.338734\pi\) |
−0.681643 | + | 0.731685i | \(0.738734\pi\) | |||||||
\(234\) | −0.148993 | + | 0.458554i | −0.00973999 | + | 0.0299766i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.313909 | + | 0.966113i | 0.0204338 | + | 0.0628886i | ||||
\(237\) | 2.62204 | − | 8.06981i | 0.170320 | − | 0.524191i | ||||
\(238\) | −0.690580 | + | 2.12539i | −0.0447636 | + | 0.137768i | ||||
\(239\) | −5.21415 | − | 16.0475i | −0.337275 | − | 1.03803i | −0.965590 | − | 0.260068i | \(-0.916255\pi\) |
0.628315 | − | 0.777959i | \(-0.283745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.37366 | − | 19.6161i | 0.410564 | − | 1.26359i | −0.505595 | − | 0.862771i | \(-0.668727\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | −11.5973 | − | 8.42593i | −0.745502 | − | 0.541639i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.38823 | − | 2.46169i | −0.216909 | − | 0.157594i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.1293 | + | 7.35938i | −0.645822 | + | 0.469217i | ||||
\(247\) | 2.12202 | − | 1.54174i | 0.135021 | − | 0.0980986i | ||||
\(248\) | 0.407499 | + | 1.25415i | 0.0258762 | + | 0.0796387i | ||||
\(249\) | 17.1955 | 1.08972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.69615 | 0.548896 | 0.274448 | − | 0.961602i | \(-0.411505\pi\) | ||||
0.274448 | + | 0.961602i | \(0.411505\pi\) | |||||||
\(252\) | −0.101764 | − | 0.313197i | −0.00641052 | − | 0.0197296i | ||||
\(253\) | 26.4709 | − | 19.2322i | 1.66421 | − | 1.20912i | ||||
\(254\) | −10.1981 | + | 7.40938i | −0.639888 | + | 0.464906i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 7.10714 | 0.443331 | 0.221666 | − | 0.975123i | \(-0.428851\pi\) | ||||
0.221666 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(258\) | 2.00298 | + | 1.45525i | 0.124700 | + | 0.0905999i | ||||
\(259\) | −0.0793900 | + | 0.244337i | −0.00493305 | + | 0.0151824i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.86095 | − | 5.72742i | −0.115190 | − | 0.354518i | ||||
\(262\) | 4.34352 | − | 13.3680i | 0.268344 | − | 0.825877i | ||||
\(263\) | −4.90130 | + | 15.0847i | −0.302227 | + | 0.930160i | 0.678470 | + | 0.734628i | \(0.262643\pi\) |
−0.980697 | + | 0.195532i | \(0.937357\pi\) | |||||||
\(264\) | −1.55540 | − | 4.78704i | −0.0957285 | − | 0.294622i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.553608 | + | 1.70383i | −0.0339439 | + | 0.104469i | ||||
\(267\) | −2.79299 | − | 2.02923i | −0.170928 | − | 0.124187i | ||||
\(268\) | 3.14433 | 0.192070 | ||||||||
\(269\) | −3.65623 | − | 2.65641i | −0.222925 | − | 0.161964i | 0.470718 | − | 0.882284i | \(-0.343995\pi\) |
−0.693642 | + | 0.720320i | \(0.743995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.00551 | + | 6.54289i | −0.547046 | + | 0.397452i | −0.826695 | − | 0.562650i | \(-0.809782\pi\) |
0.279649 | + | 0.960102i | \(0.409782\pi\) | |||||||
\(272\) | −5.49007 | + | 3.98877i | −0.332884 | + | 0.241855i | ||||
\(273\) | 0.0490657 | + | 0.151009i | 0.00296959 | + | 0.00913946i | ||||
\(274\) | −6.68863 | −0.404075 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.50055 | 0.391287 | ||||||||
\(277\) | −7.05603 | − | 21.7162i | −0.423956 | − | 1.30480i | −0.903991 | − | 0.427552i | \(-0.859376\pi\) |
0.480035 | − | 0.877249i | \(-0.340624\pi\) | |||||||
\(278\) | 2.49014 | − | 1.80920i | 0.149349 | − | 0.108508i | ||||
\(279\) | −1.06685 | + | 0.775108i | −0.0638704 | + | 0.0464045i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.2631 | − | 16.9016i | −1.38776 | − | 1.00827i | −0.996107 | − | 0.0881540i | \(-0.971903\pi\) |
−0.391653 | − | 0.920113i | \(-0.628097\pi\) | |||||||
\(282\) | −4.38040 | −0.260849 | ||||||||
\(283\) | 15.6522 | + | 11.3720i | 0.930424 | + | 0.675992i | 0.946097 | − | 0.323885i | \(-0.104989\pi\) |
−0.0156727 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(284\) | 1.76507 | − | 5.43233i | 0.104738 | − | 0.322349i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.749941 | + | 2.30808i | 0.0443450 | + | 0.136480i | ||||
\(287\) | −1.27414 | + | 3.92139i | −0.0752100 | + | 0.231472i | ||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | 8.97729 | + | 27.6292i | 0.528076 | + | 1.62525i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.93876 | + | 9.04458i | −0.172273 | + | 0.530203i | ||||
\(292\) | −2.38068 | − | 1.72967i | −0.139319 | − | 0.101221i | ||||
\(293\) | 15.0301 | 0.878069 | 0.439035 | − | 0.898470i | \(-0.355321\pi\) | ||||
0.439035 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(294\) | 5.57538 | + | 4.05075i | 0.325163 | + | 0.236245i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.631145 | + | 0.458554i | −0.0366846 | + | 0.0266529i | ||||
\(297\) | 4.07210 | − | 2.95855i | 0.236287 | − | 0.171673i | ||||
\(298\) | 1.56506 | + | 4.81677i | 0.0906617 | + | 0.279028i | ||||
\(299\) | −3.13425 | −0.181259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.815324 | 0.0469945 | ||||||||
\(302\) | −5.24034 | − | 16.1281i | −0.301548 | − | 0.928069i | ||||
\(303\) | −15.5683 | + | 11.3110i | −0.894377 | + | 0.649803i | ||||
\(304\) | −4.40115 | + | 3.19762i | −0.252423 | + | 0.183396i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.49007 | − | 3.98877i | −0.313846 | − | 0.228023i | ||||
\(307\) | 19.7061 | 1.12468 | 0.562342 | − | 0.826905i | \(-0.309900\pi\) | ||||
0.562342 | + | 0.826905i | \(0.309900\pi\) | |||||||
\(308\) | −1.34100 | − | 0.974296i | −0.0764108 | − | 0.0555157i | ||||
\(309\) | 1.57811 | − | 4.85694i | 0.0897758 | − | 0.276302i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.72642 | + | 26.8572i | 0.494830 | + | 1.52293i | 0.817222 | + | 0.576323i | \(0.195513\pi\) |
−0.322392 | + | 0.946606i | \(0.604487\pi\) | |||||||
\(312\) | −0.148993 | + | 0.458554i | −0.00843508 | + | 0.0259605i | ||||
\(313\) | −3.47577 | + | 10.6973i | −0.196462 | + | 0.604648i | 0.803494 | + | 0.595312i | \(0.202972\pi\) |
−0.999956 | + | 0.00933550i | \(0.997028\pi\) | |||||||
\(314\) | −7.05436 | − | 21.7111i | −0.398101 | − | 1.22523i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.62204 | − | 8.06981i | 0.147501 | − | 0.453962i | ||||
\(317\) | 18.8433 | + | 13.6905i | 1.05835 | + | 0.768935i | 0.973782 | − | 0.227483i | \(-0.0730497\pi\) |
0.0845658 | + | 0.996418i | \(0.473050\pi\) | |||||||
\(318\) | −1.68591 | −0.0945412 | ||||||||
\(319\) | −24.5229 | − | 17.8169i | −1.37302 | − | 0.997555i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4054 | − | 9.01307i | 0.692403 | − | 0.503060i | ||||
\(322\) | 1.73189 | − | 1.25829i | 0.0965142 | − | 0.0701217i | ||||
\(323\) | 11.4080 | + | 35.1103i | 0.634760 | + | 1.95359i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.95823 | 0.440766 | ||||||||
\(327\) | −3.01609 | − | 9.28257i | −0.166790 | − | 0.513327i | ||||
\(328\) | −10.1293 | + | 7.35938i | −0.559298 | + | 0.406354i | ||||
\(329\) | −1.16703 | + | 0.847898i | −0.0643405 | + | 0.0467461i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.104633 | − | 0.0760205i | −0.00575116 | − | 0.00417847i | 0.584906 | − | 0.811101i | \(-0.301131\pi\) |
−0.590657 | + | 0.806923i | \(0.701131\pi\) | |||||||
\(332\) | 17.1955 | 0.943725 | ||||||||
\(333\) | −0.631145 | − | 0.458554i | −0.0345866 | − | 0.0251286i | ||||
\(334\) | 4.31088 | − | 13.2675i | 0.235881 | − | 0.725967i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.101764 | − | 0.313197i | −0.00555168 | − | 0.0170863i | ||||
\(337\) | 0.166272 | − | 0.511734i | 0.00905743 | − | 0.0278759i | −0.946426 | − | 0.322922i | \(-0.895335\pi\) |
0.955483 | + | 0.295046i | \(0.0953349\pi\) | |||||||
\(338\) | −3.94538 | + | 12.1426i | −0.214601 | + | 0.660473i | ||||
\(339\) | 0.468364 | + | 1.44148i | 0.0254380 | + | 0.0782902i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.05110 | + | 6.31264i | −0.111073 | + | 0.341849i | ||||
\(342\) | −4.40115 | − | 3.19762i | −0.237987 | − | 0.172908i | ||||
\(343\) | 4.57470 | 0.247010 | ||||||||
\(344\) | 2.00298 | + | 1.45525i | 0.107993 | + | 0.0784618i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.7765 | − | 11.4623i | 0.848152 | − | 0.616218i | ||||
\(347\) | 18.3773 | − | 13.3519i | 0.986546 | − | 0.716767i | 0.0273838 | − | 0.999625i | \(-0.491282\pi\) |
0.959162 | + | 0.282858i | \(0.0912824\pi\) | |||||||
\(348\) | −1.86095 | − | 5.72742i | −0.0997575 | − | 0.307022i | ||||
\(349\) | 6.84350 | 0.366324 | 0.183162 | − | 0.983083i | \(-0.441367\pi\) | ||||
0.183162 | + | 0.983083i | \(0.441367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.482152 | −0.0257354 | ||||||||
\(352\) | −1.55540 | − | 4.78704i | −0.0829033 | − | 0.255150i | ||||
\(353\) | 13.5744 | − | 9.86237i | 0.722492 | − | 0.524921i | −0.164688 | − | 0.986346i | \(-0.552662\pi\) |
0.887179 | + | 0.461425i | \(0.152662\pi\) | |||||||
\(354\) | −0.821825 | + | 0.597091i | −0.0436795 | + | 0.0317350i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.79299 | − | 2.02923i | −0.148028 | − | 0.107549i | ||||
\(357\) | −2.23476 | −0.118276 | ||||||||
\(358\) | 15.3641 | + | 11.1627i | 0.812019 | + | 0.589966i | ||||
\(359\) | −2.30639 | + | 7.09834i | −0.121727 | + | 0.374636i | −0.993291 | − | 0.115646i | \(-0.963106\pi\) |
0.871564 | + | 0.490282i | \(0.163106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.27401 | + | 10.0764i | 0.172317 | + | 0.530336i | ||||
\(362\) | −5.85537 | + | 18.0210i | −0.307752 | + | 0.947162i | ||||
\(363\) | 4.42977 | − | 13.6334i | 0.232503 | − | 0.715570i | ||||
\(364\) | 0.0490657 | + | 0.151009i | 0.00257174 | + | 0.00791500i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.29419 | − | 3.98310i | 0.0676483 | − | 0.208200i | ||||
\(367\) | −4.97929 | − | 3.61766i | −0.259917 | − | 0.188841i | 0.450194 | − | 0.892931i | \(-0.351355\pi\) |
−0.710110 | + | 0.704090i | \(0.751355\pi\) | |||||||
\(368\) | 6.50055 | 0.338865 | ||||||||
\(369\) | −10.1293 | − | 7.35938i | −0.527311 | − | 0.383114i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.449163 | + | 0.326336i | −0.0233194 | + | 0.0169425i | ||||
\(372\) | −1.06685 | + | 0.775108i | −0.0553134 | + | 0.0401875i | ||||
\(373\) | −2.83346 | − | 8.72051i | −0.146711 | − | 0.451531i | 0.850516 | − | 0.525949i | \(-0.176290\pi\) |
−0.997227 | + | 0.0744187i | \(0.976290\pi\) | |||||||
\(374\) | −34.1571 | −1.76622 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.38040 | −0.225902 | ||||||||
\(377\) | 0.897262 | + | 2.76149i | 0.0462113 | + | 0.142224i | ||||
\(378\) | 0.266421 | − | 0.193566i | 0.0137032 | − | 0.00995598i | ||||
\(379\) | 28.0179 | − | 20.3562i | 1.43918 | − | 1.04563i | 0.450972 | − | 0.892538i | \(-0.351077\pi\) |
0.988212 | − | 0.153090i | \(-0.0489226\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.1981 | − | 7.40938i | −0.522466 | − | 0.379594i | ||||
\(382\) | −12.0933 | −0.618746 | ||||||||
\(383\) | 7.70220 | + | 5.59597i | 0.393564 | + | 0.285941i | 0.766914 | − | 0.641749i | \(-0.221791\pi\) |
−0.373350 | + | 0.927690i | \(0.621791\pi\) | |||||||
\(384\) | 0.309017 | − | 0.951057i | 0.0157695 | − | 0.0485334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.41022 | − | 10.4956i | −0.173576 | − | 0.534211i | ||||
\(387\) | −0.765070 | + | 2.35464i | −0.0388907 | + | 0.119693i | ||||
\(388\) | −2.93876 | + | 9.04458i | −0.149193 | + | 0.459169i | ||||
\(389\) | −5.39091 | − | 16.5915i | −0.273330 | − | 0.841224i | −0.989656 | − | 0.143458i | \(-0.954178\pi\) |
0.716326 | − | 0.697766i | \(-0.245822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6318 | − | 41.9543i | 0.689389 | − | 2.12172i | ||||
\(392\) | 5.57538 | + | 4.05075i | 0.281599 | + | 0.204594i | ||||
\(393\) | 14.0559 | 0.709028 | ||||||||
\(394\) | 16.6829 | + | 12.1208i | 0.840471 | + | 0.610638i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.07210 | − | 2.95855i | 0.204631 | − | 0.148673i | ||||
\(397\) | 10.9663 | − | 7.96751i | 0.550385 | − | 0.399878i | −0.277542 | − | 0.960713i | \(-0.589520\pi\) |
0.827927 | + | 0.560835i | \(0.189520\pi\) | |||||||
\(398\) | 5.72650 | + | 17.6244i | 0.287044 | + | 0.883429i | ||||
\(399\) | −1.79151 | −0.0896879 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1105 | 0.704642 | 0.352321 | − | 0.935879i | \(-0.385392\pi\) | ||||
0.352321 | + | 0.935879i | \(0.385392\pi\) | |||||||
\(402\) | 0.971651 | + | 2.99043i | 0.0484615 | + | 0.149149i | ||||
\(403\) | 0.514382 | − | 0.373720i | 0.0256232 | − | 0.0186163i | ||||
\(404\) | −15.5683 | + | 11.3110i | −0.774553 | + | 0.562746i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.60443 | − | 1.16569i | −0.0796267 | − | 0.0578522i | ||||
\(407\) | −3.92674 | −0.194641 | ||||||||
\(408\) | −5.49007 | − | 3.98877i | −0.271799 | − | 0.197473i | ||||
\(409\) | −5.11848 | + | 15.7531i | −0.253092 | + | 0.778938i | 0.741107 | + | 0.671387i | \(0.234301\pi\) |
−0.994200 | + | 0.107552i | \(0.965699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.06690 | − | 6.36127i | −0.101953 | − | 0.313778i | ||||
\(412\) | 1.57811 | − | 4.85694i | 0.0777481 | − | 0.239284i | ||||
\(413\) | −0.103375 | + | 0.318156i | −0.00508675 | + | 0.0156554i | ||||
\(414\) | 2.00878 | + | 6.18239i | 0.0987262 | + | 0.303848i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.148993 | + | 0.458554i | −0.00730499 | + | 0.0224825i | ||||
\(417\) | 2.49014 | + | 1.80920i | 0.121943 | + | 0.0885967i | ||||
\(418\) | −27.3823 | −1.33931 | ||||||||
\(419\) | −13.7294 | − | 9.97500i | −0.670725 | − | 0.487310i | 0.199543 | − | 0.979889i | \(-0.436054\pi\) |
−0.870268 | + | 0.492579i | \(0.836054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.71360 | − | 4.15118i | 0.278464 | − | 0.202316i | −0.439783 | − | 0.898104i | \(-0.644945\pi\) |
0.718247 | + | 0.695788i | \(0.244945\pi\) | |||||||
\(422\) | −12.7532 | + | 9.26574i | −0.620816 | + | 0.451049i | ||||
\(423\) | −1.35362 | − | 4.16600i | −0.0658151 | − | 0.202558i | ||||
\(424\) | −1.68591 | −0.0818751 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.71189 | 0.276742 | ||||||||
\(427\) | −0.426195 | − | 1.31169i | −0.0206250 | − | 0.0634773i | ||||
\(428\) | 12.4054 | − | 9.01307i | 0.599639 | − | 0.435663i | ||||
\(429\) | −1.96337 | + | 1.42647i | −0.0947925 | + | 0.0688708i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.4476 | + | 10.4968i | 0.695915 | + | 0.505612i | 0.878599 | − | 0.477560i | \(-0.158479\pi\) |
−0.182684 | + | 0.983172i | \(0.558479\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.5618 | + | 14.2125i | 0.940078 | + | 0.683007i | 0.948440 | − | 0.316958i | \(-0.102661\pi\) |
−0.00836116 | + | 0.999965i | \(0.502661\pi\) | |||||||
\(434\) | −0.134195 | + | 0.413011i | −0.00644158 | + | 0.0198252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.01609 | − | 9.28257i | −0.144445 | − | 0.444555i | ||||
\(437\) | 10.9280 | − | 33.6330i | 0.522758 | − | 1.60888i | ||||
\(438\) | 0.909340 | − | 2.79866i | 0.0434499 | − | 0.133725i | ||||
\(439\) | −5.84359 | − | 17.9847i | −0.278899 | − | 0.858364i | −0.988161 | − | 0.153419i | \(-0.950972\pi\) |
0.709262 | − | 0.704945i | \(-0.249028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.12961 | + | 6.55426i | −0.101410 | + | 0.312107i | ||||
\(442\) | 2.64705 | + | 1.92319i | 0.125907 | + | 0.0914770i | ||||
\(443\) | 4.05769 | 0.192787 | 0.0963933 | − | 0.995343i | \(-0.469269\pi\) | ||||
0.0963933 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(444\) | −0.631145 | − | 0.458554i | −0.0299528 | − | 0.0217620i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.9426 | − | 13.0360i | 0.849605 | − | 0.617274i | ||||
\(447\) | −4.09739 | + | 2.97693i | −0.193800 | + | 0.140804i | ||||
\(448\) | −0.101764 | − | 0.313197i | −0.00480789 | − | 0.0147972i | ||||
\(449\) | −6.26150 | −0.295498 | −0.147749 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147749 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −63.0207 | −2.96753 | ||||||||
\(452\) | 0.468364 | + | 1.44148i | 0.0220300 | + | 0.0678013i | ||||
\(453\) | 13.7194 | − | 9.96772i | 0.644593 | − | 0.468325i | ||||
\(454\) | −8.97759 | + | 6.52260i | −0.421339 | + | 0.306121i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.40115 | − | 3.19762i | −0.206103 | − | 0.149742i | ||||
\(457\) | 1.94229 | 0.0908564 | 0.0454282 | − | 0.998968i | \(-0.485535\pi\) | ||||
0.0454282 | + | 0.998968i | \(0.485535\pi\) | |||||||
\(458\) | −1.45525 | − | 1.05730i | −0.0679995 | − | 0.0494045i | ||||
\(459\) | 2.09702 | − | 6.45396i | 0.0978805 | − | 0.301245i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.965342 | + | 2.97102i | 0.0449605 | + | 0.138374i | 0.971017 | − | 0.239011i | \(-0.0768233\pi\) |
−0.926056 | + | 0.377385i | \(0.876823\pi\) | |||||||
\(462\) | 0.512218 | − | 1.57644i | 0.0238305 | − | 0.0733428i | ||||
\(463\) | −2.55446 | + | 7.86182i | −0.118716 | + | 0.365370i | −0.992704 | − | 0.120578i | \(-0.961525\pi\) |
0.873988 | + | 0.485947i | \(0.161525\pi\) | |||||||
\(464\) | −1.86095 | − | 5.72742i | −0.0863925 | − | 0.265889i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.14515 | − | 3.52442i | 0.0530482 | − | 0.163265i | ||||
\(467\) | 24.7715 | + | 17.9975i | 1.14629 | + | 0.832827i | 0.987983 | − | 0.154563i | \(-0.0493971\pi\) |
0.158305 | + | 0.987390i | \(0.449397\pi\) | |||||||
\(468\) | −0.482152 | −0.0222875 | ||||||||
\(469\) | 0.837716 | + | 0.608636i | 0.0386821 | + | 0.0281042i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4686 | − | 13.4182i | 0.850986 | − | 0.618278i | ||||
\(472\) | −0.821825 | + | 0.597091i | −0.0378276 | + | 0.0274833i | ||||
\(473\) | 3.85090 | + | 11.8518i | 0.177064 | + | 0.544948i | ||||
\(474\) | 8.48510 | 0.389734 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.23476 | −0.102430 | ||||||||
\(477\) | −0.520975 | − | 1.60340i | −0.0238538 | − | 0.0734145i | ||||
\(478\) | 13.6508 | − | 9.91790i | 0.624374 | − | 0.453634i | ||||
\(479\) | 0.948887 | − | 0.689407i | 0.0433558 | − | 0.0314998i | −0.565896 | − | 0.824476i | \(-0.691470\pi\) |
0.609252 | + | 0.792977i | \(0.291470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.304308 | + | 0.221093i | 0.0138753 | + | 0.0100810i | ||||
\(482\) | 20.6256 | 0.939471 | ||||||||
\(483\) | 1.73189 | + | 1.25829i | 0.0788035 | + | 0.0572541i | ||||
\(484\) | 4.42977 | − | 13.6334i | 0.201353 | − | 0.619702i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | 3.63267 | − | 11.1802i | 0.164612 | − | 0.506623i | −0.834396 | − | 0.551166i | \(-0.814183\pi\) |
0.999007 | + | 0.0445428i | \(0.0141831\pi\) | |||||||
\(488\) | 1.29419 | − | 3.98310i | 0.0585851 | − | 0.180307i | ||||
\(489\) | 2.45923 | + | 7.56873i | 0.111210 | + | 0.342270i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.27640 | − | 3.92836i | 0.0576031 | − | 0.177284i | −0.918115 | − | 0.396314i | \(-0.870289\pi\) |
0.975718 | + | 0.219030i | \(0.0702892\pi\) | |||||||
\(492\) | −10.1293 | − | 7.35938i | −0.456665 | − | 0.331786i | ||||
\(493\) | −40.8670 | −1.84056 | ||||||||
\(494\) | 2.12202 | + | 1.54174i | 0.0954744 | + | 0.0693662i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.06685 | + | 0.775108i | −0.0479028 | + | 0.0348034i | ||||
\(497\) | 1.52177 | − | 1.10563i | 0.0682606 | − | 0.0495943i | ||||
\(498\) | 5.31370 | + | 16.3539i | 0.238113 | + | 0.732835i | ||||
\(499\) | 9.59154 | 0.429376 | 0.214688 | − | 0.976683i | \(-0.431127\pi\) | ||||
0.214688 | + | 0.976683i | \(0.431127\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9503 | 0.623254 | ||||||||
\(502\) | 2.68726 | + | 8.27053i | 0.119938 | + | 0.369132i | ||||
\(503\) | −13.7091 | + | 9.96021i | −0.611257 | + | 0.444104i | −0.849857 | − | 0.527014i | \(-0.823312\pi\) |
0.238600 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(504\) | 0.266421 | − | 0.193566i | 0.0118674 | − | 0.00862213i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.4709 | + | 19.2322i | 1.17677 | + | 0.854977i | ||||
\(507\) | −12.7675 | −0.567026 | ||||||||
\(508\) | −10.1981 | − | 7.40938i | −0.452469 | − | 0.328738i | ||||
\(509\) | 10.5993 | − | 32.6213i | 0.469805 | − | 1.44591i | −0.383032 | − | 0.923735i | \(-0.625120\pi\) |
0.852837 | − | 0.522177i | \(-0.174880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.299459 | − | 0.921641i | −0.0132473 | − | 0.0407710i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | 1.68109 | − | 5.17386i | 0.0742220 | − | 0.228432i | ||||
\(514\) | 2.19623 | + | 6.75929i | 0.0968714 | + | 0.298140i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.765070 | + | 2.35464i | −0.0336803 | + | 0.103657i | ||||
\(517\) | −17.8374 | − | 12.9596i | −0.784488 | − | 0.569964i | ||||
\(518\) | −0.256911 | −0.0112880 | ||||||||
\(519\) | 15.7765 | + | 11.4623i | 0.692513 | + | 0.503140i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2185 | + | 12.5100i | −0.754356 | + | 0.548072i | −0.897174 | − | 0.441677i | \(-0.854384\pi\) |
0.142818 | + | 0.989749i | \(0.454384\pi\) | |||||||
\(522\) | 4.87203 | − | 3.53974i | 0.213243 | − | 0.154930i | ||||
\(523\) | −12.7776 | − | 39.3254i | −0.558726 | − | 1.71958i | −0.685896 | − | 0.727700i | \(-0.740589\pi\) |
0.127170 | − | 0.991881i | \(-0.459411\pi\) | |||||||
\(524\) | 14.0559 | 0.614036 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.8609 | −0.691570 | ||||||||
\(527\) | 2.76533 | + | 8.51080i | 0.120459 | + | 0.370736i | ||||
\(528\) | 4.07210 | − | 2.95855i | 0.177215 | − | 0.128755i | ||||
\(529\) | −15.5794 | + | 11.3191i | −0.677364 | + | 0.492133i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.821825 | − | 0.597091i | −0.0356642 | − | 0.0259115i | ||||
\(532\) | −1.79151 | −0.0776720 | ||||||||
\(533\) | 4.88387 | + | 3.54834i | 0.211544 | + | 0.153696i | ||||
\(534\) | 1.06683 | − | 3.28336i | 0.0461662 | − | 0.142085i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.971651 | + | 2.99043i | 0.0419689 | + | 0.129167i | ||||
\(537\) | −5.86857 | + | 18.0616i | −0.253248 | + | 0.779416i | ||||
\(538\) | 1.39656 | − | 4.29816i | 0.0602099 | − | 0.185307i | ||||
\(539\) | 10.7191 | + | 32.9901i | 0.461706 | + | 1.42099i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0695 | + | 34.0685i | −0.475916 | + | 1.46472i | 0.368803 | + | 0.929507i | \(0.379768\pi\) |
−0.844719 | + | 0.535210i | \(0.820232\pi\) | |||||||
\(542\) | −9.00551 | − | 6.54289i | −0.386820 | − | 0.281041i | ||||
\(543\) | −18.9484 | −0.813153 | ||||||||
\(544\) | −5.49007 | − | 3.98877i | −0.235385 | − | 0.171017i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.128456 | + | 0.0933285i | −0.00549739 | + | 0.00399409i | ||||
\(547\) | −6.76543 | + | 4.91537i | −0.289269 | + | 0.210166i | −0.722950 | − | 0.690900i | \(-0.757214\pi\) |
0.433681 | + | 0.901066i | \(0.357214\pi\) | |||||||
\(548\) | −2.06690 | − | 6.36127i | −0.0882936 | − | 0.271740i | ||||
\(549\) | 4.18808 | 0.178743 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.7613 | −1.39568 | ||||||||
\(552\) | 2.00878 | + | 6.18239i | 0.0854994 | + | 0.263140i | ||||
\(553\) | 2.26061 | − | 1.64243i | 0.0961310 | − | 0.0698433i | ||||
\(554\) | 18.4729 | − | 13.4214i | 0.784840 | − | 0.570219i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.49014 | + | 1.80920i | 0.105606 | + | 0.0767270i | ||||
\(557\) | −28.1467 | −1.19262 | −0.596308 | − | 0.802756i | \(-0.703366\pi\) | ||||
−0.596308 | + | 0.802756i | \(0.703366\pi\) | |||||||
\(558\) | −1.06685 | − | 0.775108i | −0.0451632 | − | 0.0328130i | ||||
\(559\) | 0.368880 | − | 1.13530i | 0.0156020 | − | 0.0480179i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.5551 | − | 32.4853i | −0.445638 | − | 1.37153i | ||||
\(562\) | 8.88571 | − | 27.3474i | 0.374821 | − | 1.15358i | ||||
\(563\) | −1.06633 | + | 3.28183i | −0.0449406 | + | 0.138313i | −0.971009 | − | 0.239043i | \(-0.923166\pi\) |
0.926069 | + | 0.377355i | \(0.123166\pi\) | |||||||
\(564\) | −1.35362 | − | 4.16600i | −0.0569975 | − | 0.175420i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.97859 | + | 18.4002i | −0.251299 | + | 0.773418i | ||||
\(567\) | 0.266421 | + | 0.193566i | 0.0111886 | + | 0.00812903i | ||||
\(568\) | 5.71189 | 0.239665 | ||||||||
\(569\) | −14.0801 | − | 10.2298i | −0.590270 | − | 0.428856i | 0.252142 | − | 0.967690i | \(-0.418865\pi\) |
−0.842412 | + | 0.538834i | \(0.818865\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1126 | − | 21.8781i | 1.26017 | − | 0.915570i | 0.261408 | − | 0.965228i | \(-0.415813\pi\) |
0.998766 | + | 0.0496580i | \(0.0158131\pi\) | |||||||
\(572\) | −1.96337 | + | 1.42647i | −0.0820927 | + | 0.0596438i | ||||
\(573\) | −3.73703 | − | 11.5014i | −0.156117 | − | 0.480478i | ||||
\(574\) | −4.12320 | −0.172099 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.21250 | − | 19.1201i | −0.258630 | − | 0.795980i | −0.993093 | − | 0.117332i | \(-0.962566\pi\) |
0.734463 | − | 0.678649i | \(-0.237434\pi\) | |||||||
\(578\) | −23.5028 | + | 17.0758i | −0.977589 | + | 0.710260i | ||||
\(579\) | 8.92808 | − | 6.48663i | 0.371038 | − | 0.269575i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.58125 | + | 3.32847i | 0.190062 | + | 0.138088i | ||||
\(582\) | −9.51004 | −0.394204 | ||||||||
\(583\) | −6.86520 | − | 4.98786i | −0.284327 | − | 0.206576i | ||||
\(584\) | 0.909340 | − | 2.79866i | 0.0376287 | − | 0.115809i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.64456 | + | 14.2945i | 0.191865 | + | 0.590500i | ||||
\(587\) | −1.89068 | + | 5.81892i | −0.0780368 | + | 0.240173i | −0.982463 | − | 0.186457i | \(-0.940299\pi\) |
0.904426 | + | 0.426630i | \(0.140299\pi\) | |||||||
\(588\) | −2.12961 | + | 6.55426i | −0.0878235 | + | 0.270293i | ||||
\(589\) | 2.21684 | + | 6.82274i | 0.0913434 | + | 0.281126i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.37229 | + | 19.6119i | −0.262121 | + | 0.806726i | ||||
\(592\) | −0.631145 | − | 0.458554i | −0.0259399 | − | 0.0188465i | ||||
\(593\) | 24.9458 | 1.02440 | 0.512201 | − | 0.858866i | \(-0.328830\pi\) | ||||
0.512201 | + | 0.858866i | \(0.328830\pi\) | |||||||
\(594\) | 4.07210 | + | 2.95855i | 0.167080 | + | 0.121391i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.09739 | + | 2.97693i | −0.167836 | + | 0.121940i | ||||
\(597\) | −14.9922 | + | 10.8925i | −0.613589 | + | 0.445798i | ||||
\(598\) | −0.968538 | − | 2.98085i | −0.0396065 | − | 0.121896i | ||||
\(599\) | −0.941228 | −0.0384575 | −0.0192288 | − | 0.999815i | \(-0.506121\pi\) | ||||
−0.0192288 | + | 0.999815i | \(0.506121\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2333 | 0.417426 | 0.208713 | − | 0.977977i | \(-0.433073\pi\) | ||||
0.208713 | + | 0.977977i | \(0.433073\pi\) | |||||||
\(602\) | 0.251949 | + | 0.775419i | 0.0102687 | + | 0.0316037i | ||||
\(603\) | −2.54381 | + | 1.84819i | −0.103592 | + | 0.0752641i | ||||
\(604\) | 13.7194 | − | 9.96772i | 0.558234 | − | 0.405581i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.5683 | − | 11.3110i | −0.632420 | − | 0.459480i | ||||
\(607\) | 6.80623 | 0.276256 | 0.138128 | − | 0.990414i | \(-0.455891\pi\) | ||||
0.138128 | + | 0.990414i | \(0.455891\pi\) | |||||||
\(608\) | −4.40115 | − | 3.19762i | −0.178490 | − | 0.129681i | ||||
\(609\) | 0.612839 | − | 1.88612i | 0.0248335 | − | 0.0764296i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.652649 | + | 2.00865i | 0.0264034 | + | 0.0812612i | ||||
\(612\) | 2.09702 | − | 6.45396i | 0.0847670 | − | 0.260886i | ||||
\(613\) | −0.352106 | + | 1.08367i | −0.0142214 | + | 0.0437690i | −0.957915 | − | 0.287051i | \(-0.907325\pi\) |
0.943694 | + | 0.330820i | \(0.107325\pi\) | |||||||
\(614\) | 6.08951 | + | 18.7416i | 0.245753 | + | 0.756349i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.512218 | − | 1.57644i | 0.0206378 | − | 0.0635167i | ||||
\(617\) | 11.6156 | + | 8.43925i | 0.467628 | + | 0.339752i | 0.796516 | − | 0.604617i | \(-0.206674\pi\) |
−0.328888 | + | 0.944369i | \(0.606674\pi\) | |||||||
\(618\) | 5.10689 | 0.205429 | ||||||||
\(619\) | −0.385511 | − | 0.280090i | −0.0154950 | − | 0.0112578i | 0.580011 | − | 0.814609i | \(-0.303048\pi\) |
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.25906 | + | 3.82093i | −0.211039 | + | 0.153329i | ||||
\(622\) | −22.8461 | + | 16.5986i | −0.916044 | + | 0.665545i | ||||
\(623\) | −0.351323 | − | 1.08126i | −0.0140754 | − | 0.0433198i | ||||
\(624\) | −0.482152 | −0.0193015 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.2478 | −0.449553 | ||||||||
\(627\) | −8.46159 | − | 26.0421i | −0.337923 | − | 1.04002i | ||||
\(628\) | 18.4686 | − | 13.4182i | 0.736976 | − | 0.535444i | ||||
\(629\) | −4.28301 | + | 3.11179i | −0.170775 | + | 0.124075i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.7958 | + | 10.0232i | 0.549201 | + | 0.399018i | 0.827491 | − | 0.561479i | \(-0.189768\pi\) |
−0.278290 | + | 0.960497i | \(0.589768\pi\) | |||||||
\(632\) | 8.48510 | 0.337519 | ||||||||
\(633\) | −12.7532 | − | 9.26574i | −0.506894 | − | 0.368280i | ||||
\(634\) | −7.19752 | + | 22.1517i | −0.285850 | + | 0.879756i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.520975 | − | 1.60340i | −0.0206580 | − | 0.0635788i | ||||
\(637\) | 1.02679 | − | 3.16015i | 0.0406831 | − | 0.125210i | ||||
\(638\) | 9.36690 | − | 28.8283i | 0.370839 | − | 1.14133i | ||||
\(639\) | 1.76507 | + | 5.43233i | 0.0698251 | + | 0.214900i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1127 | + | 31.1237i | −0.399428 | + | 1.22931i | 0.526031 | + | 0.850465i | \(0.323680\pi\) |
−0.925459 | + | 0.378848i | \(0.876320\pi\) | |||||||
\(642\) | 12.4054 | + | 9.01307i | 0.489603 | + | 0.355717i | ||||
\(643\) | −12.5844 | −0.496281 | −0.248141 | − | 0.968724i | \(-0.579820\pi\) | ||||
−0.248141 | + | 0.968724i | \(0.579820\pi\) | |||||||
\(644\) | 1.73189 | + | 1.25829i | 0.0682458 | + | 0.0495835i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.8666 | + | 21.6994i | −1.17509 | + | 0.853751i | ||||
\(647\) | −20.7430 | + | 15.0706i | −0.815490 | + | 0.592488i | −0.915417 | − | 0.402507i | \(-0.868139\pi\) |
0.0999273 | + | 0.994995i | \(0.468139\pi\) | |||||||
\(648\) | 0.309017 | + | 0.951057i | 0.0121393 | + | 0.0373610i | ||||
\(649\) | −5.11308 | −0.200706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.434265 | −0.0170202 | ||||||||
\(652\) | 2.45923 | + | 7.56873i | 0.0963109 | + | 0.296414i | ||||
\(653\) | −24.3165 | + | 17.6669i | −0.951577 | + | 0.691361i | −0.951179 | − | 0.308639i | \(-0.900127\pi\) |
−0.000397632 | 1.00000i | \(0.500127\pi\) | ||||||||
\(654\) | 7.89623 | − | 5.73695i | 0.308767 | − | 0.224332i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.1293 | − | 7.35938i | −0.395483 | − | 0.287335i | ||||
\(657\) | 2.94269 | 0.114805 | ||||||||
\(658\) | −1.16703 | − | 0.847898i | −0.0454956 | − | 0.0330545i | ||||
\(659\) | −2.48706 | + | 7.65438i | −0.0968821 | + | 0.298172i | −0.987740 | − | 0.156110i | \(-0.950104\pi\) |
0.890858 | + | 0.454283i | \(0.150104\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.225140 | − | 0.692909i | −0.00875692 | − | 0.0269510i | 0.946583 | − | 0.322461i | \(-0.104510\pi\) |
−0.955340 | + | 0.295510i | \(0.904510\pi\) | |||||||
\(662\) | 0.0399663 | − | 0.123004i | 0.00155334 | − | 0.00478068i | ||||
\(663\) | −1.01108 | + | 3.11179i | −0.0392672 | + | 0.120852i | ||||
\(664\) | 5.31370 | + | 16.3539i | 0.206212 | + | 0.634654i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.241076 | − | 0.741956i | 0.00934151 | − | 0.0287502i | ||||
\(667\) | 31.6709 | + | 23.0103i | 1.22630 | + | 0.890961i | ||||
\(668\) | 13.9503 | 0.539754 | ||||||||
\(669\) | 17.9426 | + | 13.0360i | 0.693700 | + | 0.504002i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.0543 | − | 12.3907i | 0.658373 | − | 0.478336i | ||||
\(672\) | 0.266421 | − | 0.193566i | 0.0102774 | − | 0.00746699i | ||||
\(673\) | 2.28926 | + | 7.04563i | 0.0882446 | + | 0.271589i | 0.985434 | − | 0.170056i | \(-0.0543950\pi\) |
−0.897190 | + | 0.441645i | \(0.854395\pi\) | |||||||
\(674\) | 0.538069 | 0.0207256 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7675 | −0.491059 | ||||||||
\(677\) | 3.02683 | + | 9.31563i | 0.116331 | + | 0.358029i | 0.992222 | − | 0.124479i | \(-0.0397260\pi\) |
−0.875892 | + | 0.482508i | \(0.839726\pi\) | |||||||
\(678\) | −1.22619 | + | 0.890881i | −0.0470916 | + | 0.0342141i | ||||
\(679\) | −2.53368 | + | 1.84082i | −0.0972336 | + | 0.0706444i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.97759 | − | 6.52260i | −0.344022 | − | 0.249947i | ||||
\(682\) | −6.63750 | −0.254163 | ||||||||
\(683\) | −27.1706 | − | 19.7406i | −1.03966 | − | 0.755354i | −0.0694369 | − | 0.997586i | \(-0.522120\pi\) |
−0.970218 | + | 0.242233i | \(0.922120\pi\) | |||||||
\(684\) | 1.68109 | − | 5.17386i | 0.0642781 | − | 0.197828i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.41366 | + | 4.35079i | 0.0539737 | + | 0.166114i | ||||
\(687\) | 0.555857 | − | 1.71075i | 0.0212073 | − | 0.0652692i | ||||
\(688\) | −0.765070 | + | 2.35464i | −0.0291680 | + | 0.0897699i | ||||
\(689\) | 0.251189 | + | 0.773081i | 0.00956955 | + | 0.0294520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.06874 | − | 24.8330i | 0.306950 | − | 0.944693i | −0.671993 | − | 0.740557i | \(-0.734562\pi\) |
0.978943 | − | 0.204136i | \(-0.0654385\pi\) | |||||||
\(692\) | 15.7765 | + | 11.4623i | 0.599734 | + | 0.435732i | ||||
\(693\) | 1.65757 | 0.0629659 | ||||||||
\(694\) | 18.3773 | + | 13.3519i | 0.697593 | + | 0.506831i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.87203 | − | 3.53974i | 0.184674 | − | 0.134173i | ||||
\(697\) | −68.7385 | + | 49.9415i | −2.60366 | + | 1.89167i | ||||
\(698\) | 2.11476 | + | 6.50855i | 0.0800447 | + | 0.246352i | ||||
\(699\) | 3.70579 | 0.140166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.8212 | 1.57956 | 0.789782 | − | 0.613388i | \(-0.210194\pi\) | ||||
0.789782 | + | 0.613388i | \(0.210194\pi\) | |||||||
\(702\) | −0.148993 | − | 0.458554i | −0.00562339 | − | 0.0173070i | ||||
\(703\) | −3.43351 | + | 2.49459i | −0.129497 | + | 0.0940852i | ||||
\(704\) | 4.07210 | − | 2.95855i | 0.153473 | − | 0.111505i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.5744 | + | 9.86237i | 0.510879 | + | 0.371175i | ||||
\(707\) | −6.33717 | −0.238334 | ||||||||
\(708\) | −0.821825 | − | 0.597091i | −0.0308861 | − | 0.0224401i | ||||
\(709\) | −2.74068 | + | 8.43495i | −0.102928 | + | 0.316781i | −0.989239 | − | 0.146311i | \(-0.953260\pi\) |
0.886310 | + | 0.463092i | \(0.153260\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.62204 | + | 8.06981i | 0.0983342 | + | 0.302642i | ||||
\(712\) | 1.06683 | − | 3.28336i | 0.0399811 | − | 0.123049i | ||||
\(713\) | 2.64897 | − | 8.15268i | 0.0992045 | − | 0.305320i | ||||
\(714\) | −0.690580 | − | 2.12539i | −0.0258443 | − | 0.0795406i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.86857 | + | 18.0616i | −0.219319 | + | 0.674994i | ||||
\(717\) | 13.6508 | + | 9.91790i | 0.509799 | + | 0.370391i | ||||
\(718\) | −7.46364 | −0.278541 | ||||||||
\(719\) | 2.14802 | + | 1.56062i | 0.0801074 | + | 0.0582015i | 0.627118 | − | 0.778924i | \(-0.284234\pi\) |
−0.547011 | + | 0.837126i | \(0.684234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.36058 | − | 0.988522i | 0.0506708 | − | 0.0368145i | ||||
\(722\) | −8.57148 | + | 6.22755i | −0.318998 | + | 0.231765i | ||||
\(723\) | 6.37366 | + | 19.6161i | 0.237039 | + | 0.729531i | ||||
\(724\) | −18.9484 | −0.704211 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.3350 | 0.532023 | ||||||||
\(727\) | −2.17449 | − | 6.69240i | −0.0806475 | − | 0.248207i | 0.902601 | − | 0.430479i | \(-0.141655\pi\) |
−0.983248 | + | 0.182271i | \(0.941655\pi\) | |||||||
\(728\) | −0.128456 | + | 0.0933285i | −0.00476088 | + | 0.00345898i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5924 | + | 9.87546i | 0.502733 | + | 0.365257i | ||||
\(732\) | 4.18808 | 0.154796 | ||||||||
\(733\) | −16.3908 | − | 11.9086i | −0.605407 | − | 0.439854i | 0.242387 | − | 0.970180i | \(-0.422070\pi\) |
−0.847794 | + | 0.530326i | \(0.822070\pi\) | |||||||
\(734\) | 1.90192 | − | 5.85350i | 0.0702011 | − | 0.216057i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00878 | + | 6.18239i | 0.0740446 | + | 0.227886i | ||||
\(737\) | −4.89070 | + | 15.0520i | −0.180151 | + | 0.554448i | ||||
\(738\) | 3.86905 | − | 11.9077i | 0.142422 | − | 0.438329i | ||||
\(739\) | 5.30003 | + | 16.3118i | 0.194965 | + | 0.600039i | 0.999977 | + | 0.00678134i | \(0.00215858\pi\) |
−0.805012 | + | 0.593258i | \(0.797841\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.810541 | + | 2.49459i | −0.0297760 | + | 0.0916410i | ||||
\(742\) | −0.449163 | − | 0.326336i | −0.0164893 | − | 0.0119802i | ||||
\(743\) | −9.94252 | −0.364756 | −0.182378 | − | 0.983229i | \(-0.558379\pi\) | ||||
−0.182378 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(744\) | −1.06685 | − | 0.775108i | −0.0391124 | − | 0.0284169i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.41811 | − | 5.38957i | 0.271596 | − | 0.197326i | ||||
\(747\) | −13.9114 | + | 10.1073i | −0.508993 | + | 0.369805i | ||||
\(748\) | −10.5551 | − | 32.4853i | −0.385933 | − | 1.18778i | ||||
\(749\) | 5.04970 | 0.184512 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6941 | −0.645667 | −0.322833 | − | 0.946456i | \(-0.604635\pi\) | ||||
−0.322833 | + | 0.946456i | \(0.604635\pi\) | |||||||
\(752\) | −1.35362 | − | 4.16600i | −0.0493613 | − | 0.151919i | ||||
\(753\) | −7.03533 | + | 5.11147i | −0.256382 | + | 0.186272i | ||||
\(754\) | −2.34906 | + | 1.70669i | −0.0855478 | + | 0.0621541i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.266421 | + | 0.193566i | 0.00968965 | + | 0.00703994i | ||||
\(757\) | 37.1272 | 1.34941 | 0.674706 | − | 0.738087i | \(-0.264271\pi\) | ||||
0.674706 | + | 0.738087i | \(0.264271\pi\) | |||||||
\(758\) | 28.0179 | + | 20.3562i | 1.01766 | + | 0.739371i | ||||
\(759\) | −10.1110 | + | 31.1184i | −0.367005 | + | 1.12953i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.3161 | − | 47.1381i | −0.555208 | − | 1.70876i | −0.695393 | − | 0.718630i | \(-0.744770\pi\) |
0.140184 | − | 0.990125i | \(-0.455230\pi\) | |||||||
\(762\) | 3.89534 | − | 11.9886i | 0.141113 | − | 0.434302i | ||||
\(763\) | 0.993244 | − | 3.05689i | 0.0359578 | − | 0.110667i | ||||
\(764\) | −3.73703 | − | 11.5014i | −0.135201 | − | 0.416106i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.94198 | + | 9.05448i | −0.106298 | + | 0.327152i | ||||
\(767\) | 0.396245 | + | 0.287889i | 0.0143076 | + | 0.0103951i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −27.8015 | − | 20.1990i | −1.00255 | − | 0.728393i | −0.0399144 | − | 0.999203i | \(-0.512709\pi\) |
−0.962633 | + | 0.270810i | \(0.912709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.74980 | + | 4.17747i | −0.207074 | + | 0.150448i | ||||
\(772\) | 8.92808 | − | 6.48663i | 0.321329 | − | 0.233459i | ||||
\(773\) | −7.10509 | − | 21.8672i | −0.255552 | − | 0.786510i | −0.993720 | − | 0.111893i | \(-0.964309\pi\) |
0.738168 | − | 0.674617i | \(-0.235691\pi\) | |||||||
\(774\) | −2.47582 | −0.0889915 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.51004 | −0.341390 | ||||||||
\(777\) | −0.0793900 | − | 0.244337i | −0.00284810 | − | 0.00876555i | ||||
\(778\) | 14.1136 | − | 10.2541i | 0.505997 | − | 0.367628i | ||||
\(779\) | −55.1047 | + | 40.0359i | −1.97433 | + | 1.43444i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.2594 | + | 16.8989i | 0.832286 | + | 0.604691i | ||||
\(782\) | 44.1134 | 1.57749 | ||||||||
\(783\) | 4.87203 | + | 3.53974i | 0.174112 | + | 0.126500i | ||||
\(784\) | −2.12961 | + | 6.55426i | −0.0760574 | + | 0.234081i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.34352 | + | 13.3680i | 0.154928 | + | 0.476820i | ||||
\(787\) | −2.59940 | + | 8.00012i | −0.0926585 | + | 0.285174i | −0.986636 | − | 0.162938i | \(-0.947903\pi\) |
0.893978 | + | 0.448111i | \(0.147903\pi\) | |||||||
\(788\) | −6.37229 | + | 19.6119i | −0.227004 | + | 0.698645i | ||||
\(789\) | −4.90130 | − | 15.0847i | −0.174491 | − | 0.537028i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.154239 | + | 0.474699i | −0.00548411 | + | 0.0168784i | ||||
\(792\) | 4.07210 | + | 2.95855i | 0.144696 | + | 0.105128i | ||||
\(793\) | −2.01929 | −0.0717072 | ||||||||
\(794\) | 10.9663 | + | 7.96751i | 0.389181 | + | 0.282757i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.9922 | + | 10.8925i | −0.531383 | + | 0.386073i | ||||
\(797\) | −30.9647 | + | 22.4972i | −1.09683 | + | 0.796890i | −0.980539 | − | 0.196325i | \(-0.937099\pi\) |
−0.116287 | + | 0.993216i | \(0.537099\pi\) | |||||||
\(798\) | −0.553608 | − | 1.70383i | −0.0195975 | − | 0.0603149i | ||||
\(799\) | −29.7258 | −1.05162 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.45233 | 0.121982 | ||||||||
\(802\) | 4.36037 | + | 13.4198i | 0.153970 | + | 0.473871i | ||||
\(803\) | 11.9829 | − | 8.70609i | 0.422868 | − | 0.307231i | ||||
\(804\) | −2.54381 | + | 1.84819i | −0.0897134 | + | 0.0651806i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.514382 | + | 0.373720i | 0.0181183 | + | 0.0131637i | ||||
\(807\) | 4.51935 | 0.159089 | ||||||||
\(808\) | −15.5683 | − | 11.3110i | −0.547692 | − | 0.397921i | ||||
\(809\) | −9.51817 | + | 29.2939i | −0.334641 | + | 1.02992i | 0.632258 | + | 0.774758i | \(0.282128\pi\) |
−0.966899 | + | 0.255161i | \(0.917872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.243268 | − | 0.748703i | −0.00854230 | − | 0.0262905i | 0.946695 | − | 0.322133i | \(-0.104400\pi\) |
−0.955237 | + | 0.295842i | \(0.904400\pi\) | |||||||
\(812\) | 0.612839 | − | 1.88612i | 0.0215064 | − | 0.0661900i | ||||
\(813\) | 3.43980 | − | 10.5866i | 0.120639 | − | 0.371289i | ||||
\(814\) | −1.21343 | − | 3.73456i | −0.0425307 | − | 0.130896i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.09702 | − | 6.45396i | 0.0734104 | − | 0.225934i | ||||
\(817\) | 10.8965 | + | 7.91674i | 0.381219 | + | 0.276972i | ||||
\(818\) | −16.5637 | −0.579138 | ||||||||
\(819\) | −0.128456 | − | 0.0933285i | −0.00448860 | − | 0.00326116i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.1344 | + | 10.2692i | −0.493293 | + | 0.358398i | −0.806449 | − | 0.591303i | \(-0.798614\pi\) |
0.313157 | + | 0.949702i | \(0.398614\pi\) | |||||||
\(822\) | 5.41122 | − | 3.93148i | 0.188738 | − | 0.137126i | ||||
\(823\) | 11.5655 | + | 35.5950i | 0.403149 | + | 1.24077i | 0.922431 | + | 0.386162i | \(0.126199\pi\) |
−0.519282 | + | 0.854603i | \(0.673801\pi\) | |||||||
\(824\) | 5.10689 | 0.177907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.334529 | −0.0116397 | ||||||||
\(827\) | −3.64386 | − | 11.2147i | −0.126710 | − | 0.389972i | 0.867499 | − | 0.497439i | \(-0.165726\pi\) |
−0.994209 | + | 0.107467i | \(0.965726\pi\) | |||||||
\(828\) | −5.25906 | + | 3.82093i | −0.182765 | + | 0.132786i | ||||
\(829\) | 28.3388 | − | 20.5893i | 0.984247 | − | 0.715098i | 0.0255936 | − | 0.999672i | \(-0.491852\pi\) |
0.958654 | + | 0.284575i | \(0.0918524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.4729 | + | 13.4214i | 0.640819 | + | 0.465582i | ||||
\(832\) | −0.482152 | −0.0167156 | ||||||||
\(833\) | 37.8351 | + | 27.4888i | 1.31091 | + | 0.952430i | ||||
\(834\) | −0.951151 | + | 2.92734i | −0.0329357 | + | 0.101366i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.46159 | − | 26.0421i | −0.292650 | − | 0.900684i | ||||
\(837\) | 0.407499 | − | 1.25415i | 0.0140852 | − | 0.0433498i | ||||
\(838\) | 5.24417 | − | 16.1399i | 0.181157 | − | 0.557543i | ||||
\(839\) | 0.154094 | + | 0.474252i | 0.00531991 | + | 0.0163730i | 0.953681 | − | 0.300819i | \(-0.0972600\pi\) |
−0.948361 | + | 0.317192i | \(0.897260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.24546 | − | 6.91082i | 0.0774297 | − | 0.238304i | ||||
\(842\) | 5.71360 | + | 4.15118i | 0.196904 | + | 0.143059i | ||||
\(843\) | 28.7548 | 0.990367 | ||||||||
\(844\) | −12.7532 | − | 9.26574i | −0.438983 | − | 0.318940i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.54381 | − | 2.57473i | 0.121839 | − | 0.0885211i | ||||
\(847\) | 3.81916 | − | 2.77478i | 0.131228 | − | 0.0953427i | ||||
\(848\) | −0.520975 | − | 1.60340i | −0.0178904 | − | 0.0550609i | ||||
\(849\) | −19.3471 | −0.663992 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.07133 | 0.173843 | ||||||||
\(852\) | 1.76507 | + | 5.43233i | 0.0604703 | + | 0.186108i | ||||
\(853\) | −17.2793 | + | 12.5542i | −0.591633 | + | 0.429846i | −0.842899 | − | 0.538072i | \(-0.819153\pi\) |
0.251266 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(854\) | 1.11579 | − | 0.810672i | 0.0381817 | − | 0.0277406i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4054 | + | 9.01307i | 0.424009 | + | 0.308060i | ||||
\(857\) | −33.4831 | −1.14376 | −0.571880 | − | 0.820337i | \(-0.693786\pi\) | ||||
−0.571880 | + | 0.820337i | \(0.693786\pi\) | |||||||
\(858\) | −1.96337 | − | 1.42647i | −0.0670284 | − | 0.0486990i | ||||
\(859\) | 14.0563 | − | 43.2610i | 0.479596 | − | 1.47605i | −0.360061 | − | 0.932929i | \(-0.617244\pi\) |
0.839657 | − | 0.543117i | \(-0.182756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.27414 | − | 3.92139i | −0.0434225 | − | 0.133641i | ||||
\(862\) | −5.51848 | + | 16.9841i | −0.187960 | + | 0.578482i | ||||
\(863\) | 4.47115 | − | 13.7608i | 0.152200 | − | 0.468423i | −0.845667 | − | 0.533711i | \(-0.820797\pi\) |
0.997866 | + | 0.0652888i | \(0.0207969\pi\) | |||||||
\(864\) | 0.309017 | + | 0.951057i | 0.0105130 | + | 0.0323556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.47193 | + | 22.9962i | −0.253906 | + | 0.781444i | ||||
\(867\) | −23.5028 | − | 17.0758i | −0.798198 | − | 0.579925i | ||||
\(868\) | −0.434265 | −0.0147399 | ||||||||
\(869\) | 34.5522 | + | 25.1036i | 1.17210 | + | 0.851582i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22651 | − | 0.891108i | 0.0415586 | − | 0.0301941i | ||||
\(872\) | 7.89623 | − | 5.73695i | 0.267400 | − | 0.194277i | ||||
\(873\) | −2.93876 | − | 9.04458i | −0.0994621 | − | 0.306113i | ||||
\(874\) | 35.3638 | 1.19620 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.94269 | 0.0994241 | ||||||||
\(877\) | −13.9673 | − | 42.9869i | −0.471641 | − | 1.45156i | −0.850434 | − | 0.526082i | \(-0.823661\pi\) |
0.378793 | − | 0.925482i | \(-0.376339\pi\) | |||||||
\(878\) | 15.2987 | − | 11.1152i | 0.516307 | − | 0.375119i | ||||
\(879\) | −12.1596 | + | 8.83449i | −0.410134 | + | 0.297980i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3062 | − | 8.21440i | −0.380914 | − | 0.276750i | 0.380808 | − | 0.924654i | \(-0.375646\pi\) |
−0.761722 | + | 0.647904i | \(0.775646\pi\) | |||||||
\(882\) | −6.89155 | −0.232051 | ||||||||
\(883\) | 9.49373 | + | 6.89760i | 0.319490 | + | 0.232123i | 0.735958 | − | 0.677028i | \(-0.236732\pi\) |
−0.416468 | + | 0.909150i | \(0.636732\pi\) | |||||||
\(884\) | −1.01108 | + | 3.11179i | −0.0340064 | + | 0.104661i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.25389 | + | 3.85909i | 0.0421254 | + | 0.129649i | ||||
\(887\) | 6.10346 | − | 18.7845i | 0.204934 | − | 0.630722i | −0.794782 | − | 0.606895i | \(-0.792415\pi\) |
0.999716 | − | 0.0238271i | \(-0.00758513\pi\) | |||||||
\(888\) | 0.241076 | − | 0.741956i | 0.00808998 | − | 0.0248984i | ||||
\(889\) | −1.28279 | − | 3.94803i | −0.0430235 | − | 0.132413i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.55540 | + | 4.78704i | −0.0521080 | + | 0.160372i | ||||
\(892\) | 17.9426 | + | 13.0360i | 0.600762 | + | 0.436479i | ||||
\(893\) | −23.8299 | −0.797437 | ||||||||
\(894\) | −4.09739 | − | 2.97693i | −0.137037 | − | 0.0995634i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.266421 | − | 0.193566i | 0.00890051 | − | 0.00646660i | ||||
\(897\) | 2.53566 | − | 1.84227i | 0.0846634 | − | 0.0615116i | ||||
\(898\) | −1.93491 | − | 5.95504i | −0.0645688 | − | 0.198722i | ||||
\(899\) | −7.94139 | −0.264860 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4408 | −0.381147 | ||||||||
\(902\) | −19.4745 | − | 59.9363i | −0.648429 | − | 1.99566i | ||||
\(903\) | −0.659611 | + | 0.479235i | −0.0219505 | + | 0.0159480i | ||||
\(904\) | −1.22619 | + | 0.890881i | −0.0407825 | + | 0.0296302i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.7194 | + | 9.96772i | 0.455796 | + | 0.331155i | ||||
\(907\) | −21.0111 | −0.697661 | −0.348831 | − | 0.937186i | \(-0.613421\pi\) | ||||
−0.348831 | + | 0.937186i | \(0.613421\pi\) | |||||||
\(908\) | −8.97759 | − | 6.52260i | −0.297932 | − | 0.216460i | ||||
\(909\) | 5.94657 | − | 18.3017i | 0.197235 | − | 0.607028i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.67252 | + | 23.6136i | 0.254202 | + | 0.782353i | 0.993986 | + | 0.109508i | \(0.0349277\pi\) |
−0.739784 | + | 0.672844i | \(0.765072\pi\) | |||||||
\(912\) | 1.68109 | − | 5.17386i | 0.0556665 | − | 0.171324i | ||||
\(913\) | −26.7459 | + | 82.3155i | −0.885161 | + | 2.72425i | ||||
\(914\) | 0.600200 | + | 1.84723i | 0.0198528 | + | 0.0611008i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.555857 | − | 1.71075i | 0.0183660 | − | 0.0565248i | ||||
\(917\) | 3.74480 | + | 2.72076i | 0.123664 | + | 0.0898473i | ||||
\(918\) | 6.78610 | 0.223975 | ||||||||
\(919\) | 29.1482 | + | 21.1774i | 0.961511 | + | 0.698579i | 0.953501 | − | 0.301389i | \(-0.0974503\pi\) |
0.00801012 | + | 0.999968i | \(0.497450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.9425 | + | 11.5829i | −0.525325 | + | 0.381671i | ||||
\(922\) | −2.52730 | + | 1.83619i | −0.0832321 | + | 0.0604717i | ||||
\(923\) | −0.851032 | − | 2.61921i | −0.0280121 | − | 0.0862123i | ||||
\(924\) | 1.65757 | 0.0545301 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.26641 | −0.271651 | ||||||||
\(927\) | 1.57811 | + | 4.85694i | 0.0518321 | + | 0.159523i | ||||
\(928\) | 4.87203 | − | 3.53974i | 0.159932 | − | 0.116198i | ||||
\(929\) | 46.0844 | − | 33.4822i | 1.51198 | − | 1.09852i | 0.546689 | − | 0.837336i | \(-0.315888\pi\) |
0.965290 | − | 0.261181i | \(-0.0841119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.3308 | + | 22.0366i | 0.994051 | + | 0.722220i | ||||
\(932\) | 3.70579 | 0.121387 | ||||||||
\(933\) | −22.8461 | − | 16.5986i | −0.747946 | − | 0.543415i | ||||
\(934\) | −9.46187 | + | 29.1206i | −0.309602 | + | 0.952856i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.148993 | − | 0.458554i | −0.00487000 | − | 0.0149883i | ||||
\(937\) | 12.9036 | − | 39.7133i | 0.421543 | − | 1.29738i | −0.484723 | − | 0.874668i | \(-0.661080\pi\) |
0.906266 | − | 0.422708i | \(-0.138920\pi\) | |||||||
\(938\) | −0.319979 | + | 0.984794i | −0.0104477 | + | 0.0321547i | ||||
\(939\) | −3.47577 | − | 10.6973i | −0.113427 | − | 0.349094i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.05275 | + | 21.7061i | −0.229913 | + | 0.707599i | 0.767843 | + | 0.640638i | \(0.221330\pi\) |
−0.997756 | + | 0.0669608i | \(0.978670\pi\) | |||||||
\(942\) | 18.4686 | + | 13.4182i | 0.601738 | + | 0.437188i | ||||
\(943\) | 81.3903 | 2.65043 | ||||||||
\(944\) | −0.821825 | − | 0.597091i | −0.0267481 | − | 0.0194337i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0818 | + | 7.32484i | −0.327787 | + | 0.238151i | ||||
\(947\) | 6.85030 | − | 4.97703i | 0.222605 | − | 0.161732i | −0.470894 | − | 0.882190i | \(-0.656068\pi\) |
0.693498 | + | 0.720458i | \(0.256068\pi\) | |||||||
\(948\) | 2.62204 | + | 8.06981i | 0.0851599 | + | 0.262095i | ||||
\(949\) | −1.41882 | −0.0460569 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.2917 | −0.755284 | ||||||||
\(952\) | −0.690580 | − | 2.12539i | −0.0223818 | − | 0.0688841i | ||||
\(953\) | −20.1346 | + | 14.6287i | −0.652225 | + | 0.473869i | −0.864028 | − | 0.503443i | \(-0.832066\pi\) |
0.211803 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(954\) | 1.36393 | − | 0.990953i | 0.0441589 | − | 0.0320833i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.6508 | + | 9.91790i | 0.441499 | + | 0.320768i | ||||
\(957\) | 30.3119 | 0.979845 | ||||||||
\(958\) | 0.948887 | + | 0.689407i | 0.0306571 | + | 0.0222737i | ||||
\(959\) | 0.680661 | − | 2.09486i | 0.0219797 | − | 0.0676465i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.04216 | − | 27.8289i | −0.291683 | − | 0.897707i | ||||
\(962\) | −0.116235 | + | 0.357736i | −0.00374758 | + | 0.0115339i | ||||
\(963\) | −4.73845 | + | 14.5835i | −0.152694 | + | 0.469945i | ||||
\(964\) | 6.37366 | + | 19.6161i | 0.205282 | + | 0.631793i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.661521 | + | 2.03595i | −0.0212841 | + | 0.0655057i | ||||
\(967\) | 17.8993 | + | 13.0046i | 0.575602 | + | 0.418199i | 0.837136 | − | 0.546995i | \(-0.184228\pi\) |
−0.261534 | + | 0.965194i | \(0.584228\pi\) | |||||||
\(968\) | 14.3350 | 0.460746 | ||||||||
\(969\) | −29.8666 | − | 21.6994i | −0.959455 | − | 0.697085i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.7573 | − | 9.99529i | 0.441494 | − | 0.320764i | −0.344734 | − | 0.938700i | \(-0.612031\pi\) |
0.786228 | + | 0.617936i | \(0.212031\pi\) | |||||||
\(972\) | −0.809017 | + | 0.587785i | −0.0259492 | + | 0.0188532i | ||||
\(973\) | 0.313228 | + | 0.964017i | 0.0100416 | + | 0.0309050i | ||||
\(974\) | 11.7556 | 0.376672 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.18808 | 0.134057 | ||||||||
\(977\) | 12.7633 | + | 39.2815i | 0.408335 | + | 1.25673i | 0.918078 | + | 0.396400i | \(0.129741\pi\) |
−0.509742 | + | 0.860327i | \(0.670259\pi\) | |||||||
\(978\) | −6.43835 | + | 4.67773i | −0.205876 | + | 0.149577i | ||||
\(979\) | 14.0582 | − | 10.2139i | 0.449303 | − | 0.326438i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.89623 | + | 5.73695i | 0.252107 | + | 0.183167i | ||||
\(982\) | 4.13052 | 0.131810 | ||||||||
\(983\) | −50.0911 | − | 36.3933i | −1.59766 | − | 1.16077i | −0.891816 | − | 0.452398i | \(-0.850569\pi\) |
−0.705842 | − | 0.708369i | \(-0.749431\pi\) | |||||||
\(984\) | 3.86905 | − | 11.9077i | 0.123341 | − | 0.379604i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.6286 | − | 38.8668i | −0.402176 | − | 1.23777i | ||||
\(987\) | 0.445766 | − | 1.37193i | 0.0141889 | − | 0.0436689i | ||||
\(988\) | −0.810541 | + | 2.49459i | −0.0257868 | + | 0.0793635i | ||||
\(989\) | −4.97338 | − | 15.3065i | −0.158144 | − | 0.486718i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.52376 | − | 4.68964i | 0.0484037 | − | 0.148971i | −0.923933 | − | 0.382553i | \(-0.875045\pi\) |
0.972337 | + | 0.233582i | \(0.0750448\pi\) | |||||||
\(992\) | −1.06685 | − | 0.775108i | −0.0338724 | − | 0.0246097i | ||||
\(993\) | 0.129334 | 0.00410428 | ||||||||
\(994\) | 1.52177 | + | 1.10563i | 0.0482676 | + | 0.0350684i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.9114 | + | 10.1073i | −0.440801 | + | 0.320261i | ||||
\(997\) | 40.0946 | − | 29.1304i | 1.26981 | − | 0.922569i | 0.270612 | − | 0.962688i | \(-0.412774\pi\) |
0.999195 | + | 0.0401195i | \(0.0127739\pi\) | |||||||
\(998\) | 2.96395 | + | 9.12209i | 0.0938221 | + | 0.288755i | ||||
\(999\) | 0.780139 | 0.0246825 |
(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 | 750.2.g.f.151.2 | 16 | ||
5.2 | odd | 4 | 750.2.h.d.349.1 | 16 | |||
5.3 | odd | 4 | 150.2.h.b.19.4 | ✓ | 16 | ||
5.4 | even | 2 | 750.2.g.g.151.3 | 16 | |||
15.8 | even | 4 | 450.2.l.c.19.1 | 16 | |||
25.2 | odd | 20 | 3750.2.c.k.1249.12 | 16 | |||
25.3 | odd | 20 | 750.2.h.d.649.2 | 16 | |||
25.4 | even | 10 | 750.2.g.g.601.3 | 16 | |||
25.11 | even | 5 | 3750.2.a.v.1.4 | 8 | |||
25.14 | even | 10 | 3750.2.a.u.1.5 | 8 | |||
25.21 | even | 5 | inner | 750.2.g.f.601.2 | 16 | ||
25.22 | odd | 20 | 150.2.h.b.79.4 | yes | 16 | ||
25.23 | odd | 20 | 3750.2.c.k.1249.5 | 16 | |||
75.47 | even | 20 | 450.2.l.c.379.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.19.4 | ✓ | 16 | 5.3 | odd | 4 | ||
150.2.h.b.79.4 | yes | 16 | 25.22 | odd | 20 | ||
450.2.l.c.19.1 | 16 | 15.8 | even | 4 | |||
450.2.l.c.379.1 | 16 | 75.47 | even | 20 | |||
750.2.g.f.151.2 | 16 | 1.1 | even | 1 | trivial | ||
750.2.g.f.601.2 | 16 | 25.21 | even | 5 | inner | ||
750.2.g.g.151.3 | 16 | 5.4 | even | 2 | |||
750.2.g.g.601.3 | 16 | 25.4 | even | 10 | |||
750.2.h.d.349.1 | 16 | 5.2 | odd | 4 | |||
750.2.h.d.649.2 | 16 | 25.3 | odd | 20 | |||
3750.2.a.u.1.5 | 8 | 25.14 | even | 10 | |||
3750.2.a.v.1.4 | 8 | 25.11 | even | 5 | |||
3750.2.c.k.1249.5 | 16 | 25.23 | odd | 20 | |||
3750.2.c.k.1249.12 | 16 | 25.2 | odd | 20 |