Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(239,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 239.9 | ||
Character | \(\chi\) | \(=\) | 507.239 |
Dual form | 507.2.f.g.437.10 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.540287 | − | 0.540287i | −0.382040 | − | 0.382040i | 0.489796 | − | 0.871837i | \(-0.337071\pi\) |
−0.871837 | + | 0.489796i | \(0.837071\pi\) | |||||||
\(3\) | 0.0858391 | − | 1.72992i | 0.0495592 | − | 0.998771i | ||||
\(4\) | − | 1.41618i | − | 0.708090i | ||||||
\(5\) | 0.996141 | + | 0.996141i | 0.445488 | + | 0.445488i | 0.893851 | − | 0.448363i | \(-0.147993\pi\) |
−0.448363 | + | 0.893851i | \(0.647993\pi\) | |||||||
\(6\) | −0.981032 | + | 0.888277i | −0.400505 | + | 0.362637i | ||||
\(7\) | −1.80254 | − | 1.80254i | −0.681296 | − | 0.681296i | 0.278996 | − | 0.960292i | \(-0.409998\pi\) |
−0.960292 | + | 0.278996i | \(0.909998\pi\) | |||||||
\(8\) | −1.84572 | + | 1.84572i | −0.652560 | + | 0.652560i | ||||
\(9\) | −2.98526 | − | 0.296990i | −0.995088 | − | 0.0989967i | ||||
\(10\) | − | 1.07640i | − | 0.340389i | ||||||
\(11\) | −3.35957 | + | 3.35957i | −1.01295 | + | 1.01295i | −0.0130325 | + | 0.999915i | \(0.504148\pi\) |
−0.999915 | + | 0.0130325i | \(0.995852\pi\) | |||||||
\(12\) | −2.44988 | − | 0.121564i | −0.707220 | − | 0.0350924i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.94778i | 0.520565i | ||||||||
\(15\) | 1.80876 | − | 1.63774i | 0.467019 | − | 0.422862i | ||||
\(16\) | −0.837927 | −0.209482 | ||||||||
\(17\) | −5.80420 | −1.40773 | −0.703863 | − | 0.710336i | \(-0.748543\pi\) | ||||
−0.703863 | + | 0.710336i | \(0.748543\pi\) | |||||||
\(18\) | 1.45244 | + | 1.77336i | 0.342343 | + | 0.417985i | ||||
\(19\) | 2.39843 | − | 2.39843i | 0.550239 | − | 0.550239i | −0.376271 | − | 0.926510i | \(-0.622794\pi\) |
0.926510 | + | 0.376271i | \(0.122794\pi\) | |||||||
\(20\) | 1.41072 | − | 1.41072i | 0.315446 | − | 0.315446i | ||||
\(21\) | −3.27298 | + | 2.96353i | −0.714223 | + | 0.646694i | ||||
\(22\) | 3.63026 | 0.773974 | ||||||||
\(23\) | 3.39759 | 0.708446 | 0.354223 | − | 0.935161i | \(-0.384745\pi\) | ||||
0.354223 | + | 0.935161i | \(0.384745\pi\) | |||||||
\(24\) | 3.03451 | + | 3.35138i | 0.619417 | + | 0.684098i | ||||
\(25\) | − | 3.01541i | − | 0.603081i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.770022 | + | 5.13878i | −0.148191 | + | 0.988959i | ||||
\(28\) | −2.55272 | + | 2.55272i | −0.482419 | + | 0.482419i | ||||
\(29\) | − | 6.57944i | − | 1.22177i | −0.791719 | − | 0.610885i | \(-0.790814\pi\) | ||
0.791719 | − | 0.610885i | \(-0.209186\pi\) | |||||||
\(30\) | −1.86210 | − | 0.0923975i | −0.339971 | − | 0.0168694i | ||||
\(31\) | 0.386730 | − | 0.386730i | 0.0694587 | − | 0.0694587i | −0.671524 | − | 0.740983i | \(-0.734360\pi\) |
0.740983 | + | 0.671524i | \(0.234360\pi\) | |||||||
\(32\) | 4.14416 | + | 4.14416i | 0.732590 | + | 0.732590i | ||||
\(33\) | 5.52341 | + | 6.10017i | 0.961502 | + | 1.06190i | ||||
\(34\) | 3.13593 | + | 3.13593i | 0.537808 | + | 0.537808i | ||||
\(35\) | − | 3.59117i | − | 0.607018i | ||||||
\(36\) | −0.420591 | + | 4.22767i | −0.0700986 | + | 0.704612i | ||||
\(37\) | −5.93729 | − | 5.93729i | −0.976084 | − | 0.976084i | 0.0236364 | − | 0.999721i | \(-0.492476\pi\) |
−0.999721 | + | 0.0236364i | \(0.992476\pi\) | |||||||
\(38\) | −2.59169 | −0.420427 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.67719 | −0.581415 | ||||||||
\(41\) | −0.734507 | − | 0.734507i | −0.114711 | − | 0.114711i | 0.647421 | − | 0.762132i | \(-0.275847\pi\) |
−0.762132 | + | 0.647421i | \(0.775847\pi\) | |||||||
\(42\) | 3.36950 | + | 0.167195i | 0.519926 | + | 0.0257988i | ||||
\(43\) | 7.56816i | 1.15413i | 0.816697 | + | 0.577067i | \(0.195803\pi\) | ||||
−0.816697 | + | 0.577067i | \(0.804197\pi\) | |||||||
\(44\) | 4.75775 | + | 4.75775i | 0.717258 | + | 0.717258i | ||||
\(45\) | −2.67790 | − | 3.26959i | −0.399198 | − | 0.487401i | ||||
\(46\) | −1.83567 | − | 1.83567i | −0.270655 | − | 0.270655i | ||||
\(47\) | 0.243559 | − | 0.243559i | 0.0355267 | − | 0.0355267i | −0.689120 | − | 0.724647i | \(-0.742003\pi\) |
0.724647 | + | 0.689120i | \(0.242003\pi\) | |||||||
\(48\) | −0.0719269 | + | 1.44955i | −0.0103818 | + | 0.209224i | ||||
\(49\) | − | 0.501699i | − | 0.0716713i | ||||||
\(50\) | −1.62918 | + | 1.62918i | −0.230401 | + | 0.230401i | ||||
\(51\) | −0.498228 | + | 10.0408i | −0.0697658 | + | 1.40600i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.07223i | − | 0.284642i | −0.989821 | − | 0.142321i | \(-0.954543\pi\) | ||
0.989821 | − | 0.142321i | \(-0.0454566\pi\) | |||||||
\(54\) | 3.19245 | − | 2.36038i | 0.434437 | − | 0.321207i | ||||
\(55\) | −6.69321 | −0.902512 | ||||||||
\(56\) | 6.65396 | 0.889173 | ||||||||
\(57\) | −3.94323 | − | 4.35499i | −0.522293 | − | 0.576832i | ||||
\(58\) | −3.55478 | + | 3.55478i | −0.466766 | + | 0.466766i | ||||
\(59\) | −3.56074 | + | 3.56074i | −0.463569 | + | 0.463569i | −0.899823 | − | 0.436254i | \(-0.856305\pi\) |
0.436254 | + | 0.899823i | \(0.356305\pi\) | |||||||
\(60\) | −2.31933 | − | 2.56152i | −0.299425 | − | 0.330691i | ||||
\(61\) | 7.04831 | 0.902443 | 0.451222 | − | 0.892412i | \(-0.350988\pi\) | ||||
0.451222 | + | 0.892412i | \(0.350988\pi\) | |||||||
\(62\) | −0.417890 | −0.0530721 | ||||||||
\(63\) | 4.84572 | + | 5.91639i | 0.610503 | + | 0.745395i | ||||
\(64\) | − | 2.80221i | − | 0.350276i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.311618 | − | 6.28007i | 0.0383575 | − | 0.773023i | ||||
\(67\) | −4.54045 | + | 4.54045i | −0.554704 | + | 0.554704i | −0.927795 | − | 0.373091i | \(-0.878298\pi\) |
0.373091 | + | 0.927795i | \(0.378298\pi\) | |||||||
\(68\) | 8.21980i | 0.996797i | ||||||||
\(69\) | 0.291646 | − | 5.87756i | 0.0351100 | − | 0.707575i | ||||
\(70\) | −1.94026 | + | 1.94026i | −0.231906 | + | 0.231906i | ||||
\(71\) | −6.79242 | − | 6.79242i | −0.806112 | − | 0.806112i | 0.177931 | − | 0.984043i | \(-0.443060\pi\) |
−0.984043 | + | 0.177931i | \(0.943060\pi\) | |||||||
\(72\) | 6.05811 | − | 4.96179i | 0.713955 | − | 0.584753i | ||||
\(73\) | −6.04700 | − | 6.04700i | −0.707748 | − | 0.707748i | 0.258313 | − | 0.966061i | \(-0.416833\pi\) |
−0.966061 | + | 0.258313i | \(0.916833\pi\) | |||||||
\(74\) | 6.41568i | 0.745807i | ||||||||
\(75\) | −5.21642 | − | 0.258840i | −0.602340 | − | 0.0298882i | ||||
\(76\) | −3.39662 | − | 3.39662i | −0.389619 | − | 0.389619i | ||||
\(77\) | 12.1115 | 1.38023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.77426 | 0.987182 | 0.493591 | − | 0.869694i | \(-0.335684\pi\) | ||||
0.493591 | + | 0.869694i | \(0.335684\pi\) | |||||||
\(80\) | −0.834694 | − | 0.834694i | −0.0933216 | − | 0.0933216i | ||||
\(81\) | 8.82359 | + | 1.77319i | 0.980399 | + | 0.197021i | ||||
\(82\) | 0.793689i | 0.0876483i | ||||||||
\(83\) | −8.31849 | − | 8.31849i | −0.913073 | − | 0.913073i | 0.0834395 | − | 0.996513i | \(-0.473409\pi\) |
−0.996513 | + | 0.0834395i | \(0.973409\pi\) | |||||||
\(84\) | 4.19689 | + | 4.63513i | 0.457918 | + | 0.505735i | ||||
\(85\) | −5.78181 | − | 5.78181i | −0.627125 | − | 0.627125i | ||||
\(86\) | 4.08898 | − | 4.08898i | 0.440926 | − | 0.440926i | ||||
\(87\) | −11.3819 | − | 0.564773i | −1.22027 | − | 0.0605500i | ||||
\(88\) | − | 12.4016i | − | 1.32202i | ||||||
\(89\) | 9.62559 | − | 9.62559i | 1.02031 | − | 1.02031i | 0.0205215 | − | 0.999789i | \(-0.493467\pi\) |
0.999789 | − | 0.0205215i | \(-0.00653265\pi\) | |||||||
\(90\) | −0.319681 | + | 3.21335i | −0.0336974 | + | 0.338717i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 4.81159i | − | 0.501643i | ||||||
\(93\) | −0.635816 | − | 0.702209i | −0.0659311 | − | 0.0728157i | ||||
\(94\) | −0.263183 | −0.0271453 | ||||||||
\(95\) | 4.77836 | 0.490249 | ||||||||
\(96\) | 7.52480 | − | 6.81334i | 0.767996 | − | 0.695383i | ||||
\(97\) | −1.34200 | + | 1.34200i | −0.136260 | + | 0.136260i | −0.771947 | − | 0.635687i | \(-0.780717\pi\) |
0.635687 | + | 0.771947i | \(0.280717\pi\) | |||||||
\(98\) | −0.271062 | + | 0.271062i | −0.0273813 | + | 0.0273813i | ||||
\(99\) | 11.0270 | − | 9.03143i | 1.10825 | − | 0.907693i | ||||
\(100\) | −4.27036 | −0.427036 | ||||||||
\(101\) | −2.06768 | −0.205742 | −0.102871 | − | 0.994695i | \(-0.532803\pi\) | ||||
−0.102871 | + | 0.994695i | \(0.532803\pi\) | |||||||
\(102\) | 5.69411 | − | 5.15574i | 0.563801 | − | 0.510494i | ||||
\(103\) | − | 13.3818i | − | 1.31854i | −0.751905 | − | 0.659272i | \(-0.770865\pi\) | ||
0.751905 | − | 0.659272i | \(-0.229135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.21244 | − | 0.308263i | −0.606272 | − | 0.0300834i | ||||
\(106\) | −1.11960 | + | 1.11960i | −0.108745 | + | 0.108745i | ||||
\(107\) | 7.52219i | 0.727197i | 0.931556 | + | 0.363599i | \(0.118452\pi\) | ||||
−0.931556 | + | 0.363599i | \(0.881548\pi\) | |||||||
\(108\) | 7.27744 | + | 1.09049i | 0.700272 | + | 0.104932i | ||||
\(109\) | −2.10533 | + | 2.10533i | −0.201654 | + | 0.201654i | −0.800709 | − | 0.599054i | \(-0.795543\pi\) |
0.599054 | + | 0.800709i | \(0.295543\pi\) | |||||||
\(110\) | 3.61625 | + | 3.61625i | 0.344796 | + | 0.344796i | ||||
\(111\) | −10.7807 | + | 9.76140i | −1.02326 | + | 0.926511i | ||||
\(112\) | 1.51040 | + | 1.51040i | 0.142719 | + | 0.142719i | ||||
\(113\) | − | 1.89573i | − | 0.178335i | −0.996017 | − | 0.0891677i | \(-0.971579\pi\) | ||
0.996017 | − | 0.0891677i | \(-0.0284207\pi\) | |||||||
\(114\) | −0.222468 | + | 4.48341i | −0.0208360 | + | 0.419910i | ||||
\(115\) | 3.38448 | + | 3.38448i | 0.315604 | + | 0.315604i | ||||
\(116\) | −9.31767 | −0.865124 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.84764 | 0.354204 | ||||||||
\(119\) | 10.4623 | + | 10.4623i | 0.959078 | + | 0.959078i | ||||
\(120\) | −0.315647 | + | 6.36125i | −0.0288145 | + | 0.580700i | ||||
\(121\) | − | 11.5734i | − | 1.05213i | ||||||
\(122\) | −3.80811 | − | 3.80811i | −0.344770 | − | 0.344770i | ||||
\(123\) | −1.33369 | + | 1.20759i | −0.120255 | + | 0.108885i | ||||
\(124\) | −0.547679 | − | 0.547679i | −0.0491831 | − | 0.0491831i | ||||
\(125\) | 7.98448 | − | 7.98448i | 0.714153 | − | 0.714153i | ||||
\(126\) | 0.578470 | − | 5.81463i | 0.0515342 | − | 0.518008i | ||||
\(127\) | 7.11474i | 0.631331i | 0.948871 | + | 0.315665i | \(0.102228\pi\) | ||||
−0.948871 | + | 0.315665i | \(0.897772\pi\) | |||||||
\(128\) | 6.77431 | − | 6.77431i | 0.598770 | − | 0.598770i | ||||
\(129\) | 13.0923 | + | 0.649644i | 1.15272 | + | 0.0571980i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 5.36072i | − | 0.468368i | −0.972192 | − | 0.234184i | \(-0.924758\pi\) | ||
0.972192 | − | 0.234184i | \(-0.0752419\pi\) | |||||||
\(132\) | 8.63894 | − | 7.82214i | 0.751924 | − | 0.680830i | ||||
\(133\) | −8.64655 | −0.749751 | ||||||||
\(134\) | 4.90629 | 0.423839 | ||||||||
\(135\) | −5.88600 | + | 4.35190i | −0.506586 | + | 0.374552i | ||||
\(136\) | 10.7129 | − | 10.7129i | 0.918625 | − | 0.918625i | ||||
\(137\) | 3.42266 | − | 3.42266i | 0.292417 | − | 0.292417i | −0.545617 | − | 0.838035i | \(-0.683705\pi\) |
0.838035 | + | 0.545617i | \(0.183705\pi\) | |||||||
\(138\) | −3.33314 | + | 3.01800i | −0.283736 | + | 0.256909i | ||||
\(139\) | 11.7881 | 0.999851 | 0.499926 | − | 0.866068i | \(-0.333361\pi\) | ||||
0.499926 | + | 0.866068i | \(0.333361\pi\) | |||||||
\(140\) | −5.08574 | −0.429824 | ||||||||
\(141\) | −0.400431 | − | 0.442245i | −0.0337224 | − | 0.0372437i | ||||
\(142\) | 7.33971i | 0.615935i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.50143 | + | 0.248856i | 0.208453 | + | 0.0207380i | ||||
\(145\) | 6.55405 | − | 6.55405i | 0.544284 | − | 0.544284i | ||||
\(146\) | 6.53423i | 0.540777i | ||||||||
\(147\) | −0.867901 | − | 0.0430654i | −0.0715833 | − | 0.00355198i | ||||
\(148\) | −8.40827 | + | 8.40827i | −0.691156 | + | 0.691156i | ||||
\(149\) | −4.87047 | − | 4.87047i | −0.399004 | − | 0.399004i | 0.478877 | − | 0.877882i | \(-0.341044\pi\) |
−0.877882 | + | 0.478877i | \(0.841044\pi\) | |||||||
\(150\) | 2.67851 | + | 2.95821i | 0.218700 | + | 0.241537i | ||||
\(151\) | 12.2053 | + | 12.2053i | 0.993251 | + | 0.993251i | 0.999977 | − | 0.00672628i | \(-0.00214106\pi\) |
−0.00672628 | + | 0.999977i | \(0.502141\pi\) | |||||||
\(152\) | 8.85366i | 0.718127i | ||||||||
\(153\) | 17.3271 | + | 1.72379i | 1.40081 | + | 0.139360i | ||||
\(154\) | −6.54369 | − | 6.54369i | −0.527305 | − | 0.527305i | ||||
\(155\) | 0.770475 | 0.0618861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.4410 | −1.07271 | −0.536355 | − | 0.843993i | \(-0.680199\pi\) | ||||
−0.536355 | + | 0.843993i | \(0.680199\pi\) | |||||||
\(158\) | −4.74062 | − | 4.74062i | −0.377143 | − | 0.377143i | ||||
\(159\) | −3.58479 | − | 0.177878i | −0.284293 | − | 0.0141067i | ||||
\(160\) | 8.25633i | 0.652720i | ||||||||
\(161\) | −6.12428 | − | 6.12428i | −0.482661 | − | 0.482661i | ||||
\(162\) | −3.80924 | − | 5.72530i | −0.299282 | − | 0.449822i | ||||
\(163\) | 4.50040 | + | 4.50040i | 0.352498 | + | 0.352498i | 0.861038 | − | 0.508540i | \(-0.169815\pi\) |
−0.508540 | + | 0.861038i | \(0.669815\pi\) | |||||||
\(164\) | −1.04019 | + | 1.04019i | −0.0812256 | + | 0.0812256i | ||||
\(165\) | −0.574539 | + | 11.5787i | −0.0447278 | + | 0.901403i | ||||
\(166\) | 8.98875i | 0.697662i | ||||||||
\(167\) | −3.09828 | + | 3.09828i | −0.239752 | + | 0.239752i | −0.816747 | − | 0.576995i | \(-0.804225\pi\) |
0.576995 | + | 0.816747i | \(0.304225\pi\) | |||||||
\(168\) | 0.571170 | − | 11.5108i | 0.0440667 | − | 0.888080i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.24767i | 0.479174i | ||||||||
\(171\) | −7.87227 | + | 6.44765i | −0.602008 | + | 0.493064i | ||||
\(172\) | 10.7179 | 0.817230 | ||||||||
\(173\) | −4.33355 | −0.329474 | −0.164737 | − | 0.986338i | \(-0.552677\pi\) | ||||
−0.164737 | + | 0.986338i | \(0.552677\pi\) | |||||||
\(174\) | 5.84436 | + | 6.45464i | 0.443060 | + | 0.489325i | ||||
\(175\) | −5.43539 | + | 5.43539i | −0.410877 | + | 0.410877i | ||||
\(176\) | 2.81507 | − | 2.81507i | 0.212194 | − | 0.212194i | ||||
\(177\) | 5.85416 | + | 6.46546i | 0.440025 | + | 0.485974i | ||||
\(178\) | −10.4012 | −0.779600 | ||||||||
\(179\) | −13.9923 | −1.04583 | −0.522916 | − | 0.852384i | \(-0.675156\pi\) | ||||
−0.522916 | + | 0.852384i | \(0.675156\pi\) | |||||||
\(180\) | −4.63033 | + | 3.79239i | −0.345124 | + | 0.282668i | ||||
\(181\) | 0.976007i | 0.0725460i | 0.999342 | + | 0.0362730i | \(0.0115486\pi\) | ||||
−0.999342 | + | 0.0362730i | \(0.988451\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.605020 | − | 12.1930i | 0.0447244 | − | 0.901334i | ||||
\(184\) | −6.27098 | + | 6.27098i | −0.462303 | + | 0.462303i | ||||
\(185\) | − | 11.8288i | − | 0.869667i | ||||||
\(186\) | −0.0358713 | + | 0.722918i | −0.00263021 | + | 0.0530069i | ||||
\(187\) | 19.4996 | − | 19.4996i | 1.42595 | − | 1.42595i | ||||
\(188\) | −0.344923 | − | 0.344923i | −0.0251561 | − | 0.0251561i | ||||
\(189\) | 10.6509 | − | 7.87486i | 0.774736 | − | 0.572812i | ||||
\(190\) | −2.58168 | − | 2.58168i | −0.187295 | − | 0.187295i | ||||
\(191\) | − | 17.1073i | − | 1.23784i | −0.785454 | − | 0.618920i | \(-0.787571\pi\) | ||
0.785454 | − | 0.618920i | \(-0.212429\pi\) | |||||||
\(192\) | −4.84761 | − | 0.240539i | −0.349846 | − | 0.0173594i | ||||
\(193\) | 1.79543 | + | 1.79543i | 0.129238 | + | 0.129238i | 0.768767 | − | 0.639529i | \(-0.220871\pi\) |
−0.639529 | + | 0.768767i | \(0.720871\pi\) | |||||||
\(194\) | 1.45013 | 0.104114 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.710497 | −0.0507498 | ||||||||
\(197\) | −12.6256 | − | 12.6256i | −0.899536 | − | 0.899536i | 0.0958594 | − | 0.995395i | \(-0.469440\pi\) |
−0.995395 | + | 0.0958594i | \(0.969440\pi\) | |||||||
\(198\) | −10.8373 | − | 1.07815i | −0.770172 | − | 0.0766208i | ||||
\(199\) | 2.60975i | 0.185000i | 0.995713 | + | 0.0925001i | \(0.0294859\pi\) | ||||
−0.995713 | + | 0.0925001i | \(0.970514\pi\) | |||||||
\(200\) | 5.56558 | + | 5.56558i | 0.393546 | + | 0.393546i | ||||
\(201\) | 7.46487 | + | 8.24437i | 0.526532 | + | 0.581513i | ||||
\(202\) | 1.11714 | + | 1.11714i | 0.0786018 | + | 0.0786018i | ||||
\(203\) | −11.8597 | + | 11.8597i | −0.832387 | + | 0.832387i | ||||
\(204\) | 14.2196 | + | 0.705580i | 0.995572 | + | 0.0494005i | ||||
\(205\) | − | 1.46335i | − | 0.102205i | ||||||
\(206\) | −7.22998 | + | 7.22998i | −0.503737 | + | 0.503737i | ||||
\(207\) | −10.1427 | − | 1.00905i | −0.704965 | − | 0.0701337i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.1154i | 1.11473i | ||||||||
\(210\) | 3.18995 | + | 3.52305i | 0.220128 | + | 0.243114i | ||||
\(211\) | 13.5443 | 0.932426 | 0.466213 | − | 0.884673i | \(-0.345618\pi\) | ||||
0.466213 | + | 0.884673i | \(0.345618\pi\) | |||||||
\(212\) | −2.93465 | −0.201552 | ||||||||
\(213\) | −12.3334 | + | 11.1673i | −0.845072 | + | 0.765171i | ||||
\(214\) | 4.06414 | − | 4.06414i | 0.277819 | − | 0.277819i | ||||
\(215\) | −7.53895 | + | 7.53895i | −0.514152 | + | 0.514152i | ||||
\(216\) | −8.06349 | − | 10.9060i | −0.548651 | − | 0.742058i | ||||
\(217\) | −1.39419 | −0.0946439 | ||||||||
\(218\) | 2.27497 | 0.154080 | ||||||||
\(219\) | −10.9799 | + | 9.94178i | −0.741954 | + | 0.671803i | ||||
\(220\) | 9.47879i | 0.639060i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 11.0986 | + | 0.550716i | 0.744891 | + | 0.0369616i | ||||
\(223\) | 7.32302 | − | 7.32302i | 0.490386 | − | 0.490386i | −0.418042 | − | 0.908428i | \(-0.637284\pi\) |
0.908428 | + | 0.418042i | \(0.137284\pi\) | |||||||
\(224\) | − | 14.9400i | − | 0.998222i | ||||||
\(225\) | −0.895545 | + | 9.00178i | −0.0597030 | + | 0.600119i | ||||
\(226\) | −1.02424 | + | 1.02424i | −0.0681314 | + | 0.0681314i | ||||
\(227\) | 0.0467074 | + | 0.0467074i | 0.00310008 | + | 0.00310008i | 0.708655 | − | 0.705555i | \(-0.249302\pi\) |
−0.705555 | + | 0.708655i | \(0.749302\pi\) | |||||||
\(228\) | −6.16744 | + | 5.58432i | −0.408449 | + | 0.369831i | ||||
\(229\) | −19.2246 | − | 19.2246i | −1.27040 | − | 1.27040i | −0.945880 | − | 0.324517i | \(-0.894798\pi\) |
−0.324517 | − | 0.945880i | \(-0.605202\pi\) | |||||||
\(230\) | − | 3.65717i | − | 0.241147i | ||||||
\(231\) | 1.03964 | − | 20.9520i | 0.0684033 | − | 1.37854i | ||||
\(232\) | 12.1438 | + | 12.1438i | 0.797278 | + | 0.797278i | ||||
\(233\) | −16.5148 | −1.08192 | −0.540961 | − | 0.841047i | \(-0.681939\pi\) | ||||
−0.540961 | + | 0.841047i | \(0.681939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.485238 | 0.0316534 | ||||||||
\(236\) | 5.04265 | + | 5.04265i | 0.328249 | + | 0.328249i | ||||
\(237\) | 0.753175 | − | 15.1788i | 0.0489240 | − | 0.985969i | ||||
\(238\) | − | 11.3053i | − | 0.732813i | ||||||
\(239\) | 18.7548 | + | 18.7548i | 1.21315 | + | 1.21315i | 0.969985 | + | 0.243165i | \(0.0781856\pi\) |
0.243165 | + | 0.969985i | \(0.421814\pi\) | |||||||
\(240\) | −1.51561 | + | 1.37231i | −0.0978319 | + | 0.0885820i | ||||
\(241\) | −3.33327 | − | 3.33327i | −0.214715 | − | 0.214715i | 0.591552 | − | 0.806267i | \(-0.298515\pi\) |
−0.806267 | + | 0.591552i | \(0.798515\pi\) | |||||||
\(242\) | −6.25295 | + | 6.25295i | −0.401955 | + | 0.401955i | ||||
\(243\) | 3.82488 | − | 15.1119i | 0.245366 | − | 0.969430i | ||||
\(244\) | − | 9.98167i | − | 0.639011i | ||||||
\(245\) | 0.499763 | − | 0.499763i | 0.0319287 | − | 0.0319287i | ||||
\(246\) | 1.37302 | + | 0.0681296i | 0.0875406 | + | 0.00434378i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.42759i | 0.0906519i | ||||||||
\(249\) | −15.1044 | + | 13.6763i | −0.957203 | + | 0.866700i | ||||
\(250\) | −8.62781 | −0.545671 | ||||||||
\(251\) | −14.0462 | −0.886586 | −0.443293 | − | 0.896377i | \(-0.646190\pi\) | ||||
−0.443293 | + | 0.896377i | \(0.646190\pi\) | |||||||
\(252\) | 8.37868 | − | 6.86241i | 0.527807 | − | 0.432291i | ||||
\(253\) | −11.4144 | + | 11.4144i | −0.717618 | + | 0.717618i | ||||
\(254\) | 3.84400 | − | 3.84400i | 0.241194 | − | 0.241194i | ||||
\(255\) | −10.4984 | + | 9.50577i | −0.657434 | + | 0.595275i | ||||
\(256\) | −12.9246 | −0.807785 | ||||||||
\(257\) | 19.5348 | 1.21855 | 0.609274 | − | 0.792960i | \(-0.291461\pi\) | ||||
0.609274 | + | 0.792960i | \(0.291461\pi\) | |||||||
\(258\) | −6.72262 | − | 7.42461i | −0.418532 | − | 0.462236i | ||||
\(259\) | 21.4044i | 1.33000i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.95403 | + | 19.6413i | −0.120951 | + | 1.21577i | ||||
\(262\) | −2.89633 | + | 2.89633i | −0.178936 | + | 0.178936i | ||||
\(263\) | 1.30868i | 0.0806967i | 0.999186 | + | 0.0403484i | \(0.0128468\pi\) | ||||
−0.999186 | + | 0.0403484i | \(0.987153\pi\) | |||||||
\(264\) | −21.4538 | − | 1.06454i | −1.32039 | − | 0.0655182i | ||||
\(265\) | 2.06423 | − | 2.06423i | 0.126805 | − | 0.126805i | ||||
\(266\) | 4.67162 | + | 4.67162i | 0.286435 | + | 0.286435i | ||||
\(267\) | −15.8253 | − | 17.4778i | −0.968491 | − | 1.06962i | ||||
\(268\) | 6.43009 | + | 6.43009i | 0.392780 | + | 0.392780i | ||||
\(269\) | 28.2787i | 1.72419i | 0.506750 | + | 0.862093i | \(0.330847\pi\) | ||||
−0.506750 | + | 0.862093i | \(0.669153\pi\) | |||||||
\(270\) | 5.53140 | + | 0.828855i | 0.336631 | + | 0.0504425i | ||||
\(271\) | 5.02990 | + | 5.02990i | 0.305545 | + | 0.305545i | 0.843178 | − | 0.537634i | \(-0.180682\pi\) |
−0.537634 | + | 0.843178i | \(0.680682\pi\) | |||||||
\(272\) | 4.86350 | 0.294893 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.69843 | −0.223431 | ||||||||
\(275\) | 10.1305 | + | 10.1305i | 0.610889 | + | 0.610889i | ||||
\(276\) | −8.32368 | − | 0.413023i | −0.501027 | − | 0.0248611i | ||||
\(277\) | 12.2519i | 0.736143i | 0.929798 | + | 0.368071i | \(0.119982\pi\) | ||||
−0.929798 | + | 0.368071i | \(0.880018\pi\) | |||||||
\(278\) | −6.36894 | − | 6.36894i | −0.381984 | − | 0.381984i | ||||
\(279\) | −1.26935 | + | 1.03964i | −0.0759937 | + | 0.0622414i | ||||
\(280\) | 6.62828 | + | 6.62828i | 0.396116 | + | 0.396116i | ||||
\(281\) | −17.0443 | + | 17.0443i | −1.01678 | + | 1.01678i | −0.0169217 | + | 0.999857i | \(0.505387\pi\) |
−0.999857 | + | 0.0169217i | \(0.994613\pi\) | |||||||
\(282\) | −0.0225914 | + | 0.455286i | −0.00134530 | + | 0.0271119i | ||||
\(283\) | 12.3279i | 0.732817i | 0.930454 | + | 0.366408i | \(0.119413\pi\) | ||||
−0.930454 | + | 0.366408i | \(0.880587\pi\) | |||||||
\(284\) | −9.61929 | + | 9.61929i | −0.570800 | + | 0.570800i | ||||
\(285\) | 0.410170 | − | 8.26619i | 0.0242964 | − | 0.489647i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.64796i | 0.156304i | ||||||||
\(288\) | −11.1406 | − | 13.6022i | −0.656467 | − | 0.801515i | ||||
\(289\) | 16.6888 | 0.981693 | ||||||||
\(290\) | −7.08213 | −0.415877 | ||||||||
\(291\) | 2.20637 | + | 2.43676i | 0.129339 | + | 0.142845i | ||||
\(292\) | −8.56365 | + | 8.56365i | −0.501150 | + | 0.501150i | ||||
\(293\) | 11.1173 | − | 11.1173i | 0.649482 | − | 0.649482i | −0.303386 | − | 0.952868i | \(-0.598117\pi\) |
0.952868 | + | 0.303386i | \(0.0981170\pi\) | |||||||
\(294\) | 0.445648 | + | 0.492183i | 0.0259907 | + | 0.0287047i | ||||
\(295\) | −7.09400 | −0.413029 | ||||||||
\(296\) | 21.9171 | 1.27391 | ||||||||
\(297\) | −14.6771 | − | 19.8510i | −0.851654 | − | 1.15187i | ||||
\(298\) | 5.26290i | 0.304872i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.366564 | + | 7.38739i | −0.0211636 | + | 0.426511i | ||||
\(301\) | 13.6419 | − | 13.6419i | 0.786306 | − | 0.786306i | ||||
\(302\) | − | 13.1887i | − | 0.758924i | ||||||
\(303\) | −0.177488 | + | 3.57693i | −0.0101964 | + | 0.205489i | ||||
\(304\) | −2.00971 | + | 2.00971i | −0.115265 | + | 0.115265i | ||||
\(305\) | 7.02111 | + | 7.02111i | 0.402027 | + | 0.402027i | ||||
\(306\) | −8.43025 | − | 10.2929i | −0.481925 | − | 0.588408i | ||||
\(307\) | −1.83038 | − | 1.83038i | −0.104465 | − | 0.104465i | 0.652942 | − | 0.757408i | \(-0.273534\pi\) |
−0.757408 | + | 0.652942i | \(0.773534\pi\) | |||||||
\(308\) | − | 17.1521i | − | 0.977330i | ||||||
\(309\) | −23.1494 | − | 1.14868i | −1.31692 | − | 0.0653460i | ||||
\(310\) | −0.416278 | − | 0.416278i | −0.0236430 | − | 0.0236430i | ||||
\(311\) | −15.2844 | −0.866701 | −0.433350 | − | 0.901226i | \(-0.642669\pi\) | ||||
−0.433350 | + | 0.901226i | \(0.642669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.4063 | 1.77519 | 0.887593 | − | 0.460628i | \(-0.152376\pi\) | ||||
0.887593 | + | 0.460628i | \(0.152376\pi\) | |||||||
\(314\) | 7.26200 | + | 7.26200i | 0.409819 | + | 0.409819i | ||||
\(315\) | −1.06654 | + | 10.7206i | −0.0600928 | + | 0.604037i | ||||
\(316\) | − | 12.4259i | − | 0.699014i | ||||||
\(317\) | 11.8144 | + | 11.8144i | 0.663565 | + | 0.663565i | 0.956219 | − | 0.292654i | \(-0.0945383\pi\) |
−0.292654 | + | 0.956219i | \(0.594538\pi\) | |||||||
\(318\) | 1.84071 | + | 2.03292i | 0.103222 | + | 0.114001i | ||||
\(319\) | 22.1041 | + | 22.1041i | 1.23759 | + | 1.23759i | ||||
\(320\) | 2.79140 | − | 2.79140i | 0.156044 | − | 0.156044i | ||||
\(321\) | 13.0128 | + | 0.645698i | 0.726304 | + | 0.0360393i | ||||
\(322\) | 6.61774i | 0.368792i | ||||||||
\(323\) | −13.9210 | + | 13.9210i | −0.774585 | + | 0.774585i | ||||
\(324\) | 2.51115 | − | 12.4958i | 0.139508 | − | 0.694211i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 4.86301i | − | 0.269337i | ||||||
\(327\) | 3.46135 | + | 3.82279i | 0.191413 | + | 0.211401i | ||||
\(328\) | 2.71139 | 0.149711 | ||||||||
\(329\) | −0.878049 | −0.0484084 | ||||||||
\(330\) | 6.56625 | − | 5.94542i | 0.361460 | − | 0.327285i | ||||
\(331\) | 15.8890 | − | 15.8890i | 0.873340 | − | 0.873340i | −0.119495 | − | 0.992835i | \(-0.538127\pi\) |
0.992835 | + | 0.119495i | \(0.0381274\pi\) | |||||||
\(332\) | −11.7805 | + | 11.7805i | −0.646538 | + | 0.646538i | ||||
\(333\) | 15.9611 | + | 19.4877i | 0.874660 | + | 1.06792i | ||||
\(334\) | 3.34792 | 0.183190 | ||||||||
\(335\) | −9.04585 | −0.494228 | ||||||||
\(336\) | 2.74252 | − | 2.48322i | 0.149617 | − | 0.135471i | ||||
\(337\) | − | 9.19516i | − | 0.500892i | −0.968131 | − | 0.250446i | \(-0.919423\pi\) | ||
0.968131 | − | 0.250446i | \(-0.0805773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.27947 | − | 0.162728i | −0.178116 | − | 0.00883817i | ||||
\(340\) | −8.18808 | + | 8.18808i | −0.444061 | + | 0.444061i | ||||
\(341\) | 2.59849i | 0.140716i | ||||||||
\(342\) | 7.73686 | + | 0.769704i | 0.418362 | + | 0.0416209i | ||||
\(343\) | −13.5221 | + | 13.5221i | −0.730125 | + | 0.730125i | ||||
\(344\) | −13.9687 | − | 13.9687i | −0.753141 | − | 0.753141i | ||||
\(345\) | 6.14540 | − | 5.56436i | 0.330857 | − | 0.299575i | ||||
\(346\) | 2.34136 | + | 2.34136i | 0.125872 | + | 0.125872i | ||||
\(347\) | − | 11.2350i | − | 0.603128i | −0.953446 | − | 0.301564i | \(-0.902491\pi\) | ||
0.953446 | − | 0.301564i | \(-0.0975087\pi\) | |||||||
\(348\) | −0.799820 | + | 16.1188i | −0.0428749 | + | 0.864061i | ||||
\(349\) | 24.6546 | + | 24.6546i | 1.31973 | + | 1.31973i | 0.913985 | + | 0.405748i | \(0.132989\pi\) |
0.405748 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(350\) | 5.87334 | 0.313943 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.8451 | −1.48415 | ||||||||
\(353\) | −22.7730 | − | 22.7730i | −1.21209 | − | 1.21209i | −0.970340 | − | 0.241746i | \(-0.922280\pi\) |
−0.241746 | − | 0.970340i | \(-0.577720\pi\) | |||||||
\(354\) | 0.330278 | − | 6.65612i | 0.0175541 | − | 0.353769i | ||||
\(355\) | − | 13.5324i | − | 0.718226i | ||||||
\(356\) | −13.6316 | − | 13.6316i | −0.722472 | − | 0.722472i | ||||
\(357\) | 18.9971 | − | 17.2009i | 1.00543 | − | 0.910369i | ||||
\(358\) | 7.55984 | + | 7.55984i | 0.399550 | + | 0.399550i | ||||
\(359\) | 20.8500 | − | 20.8500i | 1.10042 | − | 1.10042i | 0.106064 | − | 0.994359i | \(-0.466175\pi\) |
0.994359 | − | 0.106064i | \(-0.0338248\pi\) | |||||||
\(360\) | 10.9774 | + | 1.09209i | 0.578559 | + | 0.0575581i | ||||
\(361\) | 7.49502i | 0.394475i | ||||||||
\(362\) | 0.527324 | − | 0.527324i | 0.0277155 | − | 0.0277155i | ||||
\(363\) | −20.0211 | − | 0.993449i | −1.05083 | − | 0.0521425i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12.0473i | − | 0.630587i | ||||||
\(366\) | −6.91461 | + | 6.26084i | −0.361433 | + | 0.327260i | ||||
\(367\) | −21.3180 | −1.11279 | −0.556395 | − | 0.830918i | \(-0.687816\pi\) | ||||
−0.556395 | + | 0.830918i | \(0.687816\pi\) | |||||||
\(368\) | −2.84693 | −0.148406 | ||||||||
\(369\) | 1.97456 | + | 2.41084i | 0.102791 | + | 0.125503i | ||||
\(370\) | −6.39092 | + | 6.39092i | −0.332248 | + | 0.332248i | ||||
\(371\) | −3.73527 | + | 3.73527i | −0.193926 | + | 0.193926i | ||||
\(372\) | −0.994455 | + | 0.900431i | −0.0515601 | + | 0.0466851i | ||||
\(373\) | −13.9035 | −0.719898 | −0.359949 | − | 0.932972i | \(-0.617206\pi\) | ||||
−0.359949 | + | 0.932972i | \(0.617206\pi\) | |||||||
\(374\) | −21.0708 | −1.08954 | ||||||||
\(375\) | −13.1271 | − | 14.4979i | −0.677883 | − | 0.748669i | ||||
\(376\) | 0.899081i | 0.0463666i | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −10.0092 | − | 1.49983i | −0.514818 | − | 0.0771430i | ||||
\(379\) | 24.5826 | − | 24.5826i | 1.26272 | − | 1.26272i | 0.312957 | − | 0.949767i | \(-0.398680\pi\) |
0.949767 | − | 0.312957i | \(-0.101320\pi\) | |||||||
\(380\) | − | 6.76702i | − | 0.347141i | ||||||
\(381\) | 12.3079 | + | 0.610722i | 0.630555 | + | 0.0312883i | ||||
\(382\) | −9.24284 | + | 9.24284i | −0.472905 | + | 0.472905i | ||||
\(383\) | 11.9301 | + | 11.9301i | 0.609600 | + | 0.609600i | 0.942841 | − | 0.333242i | \(-0.108142\pi\) |
−0.333242 | + | 0.942841i | \(0.608142\pi\) | |||||||
\(384\) | −11.1375 | − | 12.3005i | −0.568360 | − | 0.627709i | ||||
\(385\) | 12.0648 | + | 12.0648i | 0.614878 | + | 0.614878i | ||||
\(386\) | − | 1.94009i | − | 0.0987480i | ||||||
\(387\) | 2.24767 | − | 22.5929i | 0.114255 | − | 1.14846i | ||||
\(388\) | 1.90052 | + | 1.90052i | 0.0964842 | + | 0.0964842i | ||||
\(389\) | 35.0012 | 1.77463 | 0.887315 | − | 0.461164i | \(-0.152568\pi\) | ||||
0.887315 | + | 0.461164i | \(0.152568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7203 | −0.997297 | ||||||||
\(392\) | 0.925995 | + | 0.925995i | 0.0467698 | + | 0.0467698i | ||||
\(393\) | −9.27363 | − | 0.460160i | −0.467793 | − | 0.0232120i | ||||
\(394\) | 13.6429i | 0.687318i | ||||||||
\(395\) | 8.74040 | + | 8.74040i | 0.439777 | + | 0.439777i | ||||
\(396\) | −12.7901 | − | 15.6162i | −0.642729 | − | 0.784741i | ||||
\(397\) | −0.937607 | − | 0.937607i | −0.0470571 | − | 0.0470571i | 0.683187 | − | 0.730244i | \(-0.260594\pi\) |
−0.730244 | + | 0.683187i | \(0.760594\pi\) | |||||||
\(398\) | 1.41001 | − | 1.41001i | 0.0706776 | − | 0.0706776i | ||||
\(399\) | −0.742212 | + | 14.9579i | −0.0371571 | + | 0.748830i | ||||
\(400\) | 2.52669i | 0.126335i | ||||||||
\(401\) | 18.7960 | − | 18.7960i | 0.938629 | − | 0.938629i | −0.0595935 | − | 0.998223i | \(-0.518980\pi\) |
0.998223 | + | 0.0595935i | \(0.0189804\pi\) | |||||||
\(402\) | 0.421151 | − | 8.48750i | 0.0210051 | − | 0.423318i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.92821i | 0.145684i | ||||||||
\(405\) | 7.02320 | + | 10.5559i | 0.348986 | + | 0.524526i | ||||
\(406\) | 12.8153 | 0.636011 | ||||||||
\(407\) | 39.8934 | 1.97744 | ||||||||
\(408\) | −17.6129 | − | 19.4521i | −0.871970 | − | 0.963023i | ||||
\(409\) | 6.64641 | − | 6.64641i | 0.328644 | − | 0.328644i | −0.523427 | − | 0.852071i | \(-0.675347\pi\) |
0.852071 | + | 0.523427i | \(0.175347\pi\) | |||||||
\(410\) | −0.790627 | + | 0.790627i | −0.0390463 | + | 0.0390463i | ||||
\(411\) | −5.62713 | − | 6.21473i | −0.277566 | − | 0.306550i | ||||
\(412\) | −18.9510 | −0.933648 | ||||||||
\(413\) | 12.8368 | 0.631656 | ||||||||
\(414\) | 4.93478 | + | 6.02514i | 0.242531 | + | 0.296119i | ||||
\(415\) | − | 16.5728i | − | 0.813526i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.01188 | − | 20.3925i | 0.0495519 | − | 0.998623i | ||||
\(418\) | 8.70694 | − | 8.70694i | 0.425870 | − | 0.425870i | ||||
\(419\) | 31.8789i | 1.55738i | 0.627406 | + | 0.778692i | \(0.284117\pi\) | ||||
−0.627406 | + | 0.778692i | \(0.715883\pi\) | |||||||
\(420\) | −0.436556 | + | 8.79794i | −0.0213017 | + | 0.429296i | ||||
\(421\) | 19.6414 | − | 19.6414i | 0.957263 | − | 0.957263i | −0.0418609 | − | 0.999123i | \(-0.513329\pi\) |
0.999123 | + | 0.0418609i | \(0.0133286\pi\) | |||||||
\(422\) | −7.31779 | − | 7.31779i | −0.356224 | − | 0.356224i | ||||
\(423\) | −0.799421 | + | 0.654752i | −0.0388692 | + | 0.0318351i | ||||
\(424\) | 3.82475 | + | 3.82475i | 0.185746 | + | 0.185746i | ||||
\(425\) | 17.5020i | 0.848973i | ||||||||
\(426\) | 12.6971 | + | 0.630034i | 0.615178 | + | 0.0305252i | ||||
\(427\) | −12.7049 | − | 12.7049i | −0.614831 | − | 0.614831i | ||||
\(428\) | 10.6528 | 0.514921 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.14640 | 0.392854 | ||||||||
\(431\) | −3.36047 | − | 3.36047i | −0.161868 | − | 0.161868i | 0.621526 | − | 0.783394i | \(-0.286513\pi\) |
−0.783394 | + | 0.621526i | \(0.786513\pi\) | |||||||
\(432\) | 0.645222 | − | 4.30593i | 0.0310433 | − | 0.207169i | ||||
\(433\) | − | 2.05935i | − | 0.0989662i | −0.998775 | − | 0.0494831i | \(-0.984243\pi\) | ||
0.998775 | − | 0.0494831i | \(-0.0157574\pi\) | |||||||
\(434\) | 0.753264 | + | 0.753264i | 0.0361578 | + | 0.0361578i | ||||
\(435\) | −10.7754 | − | 11.9006i | −0.516641 | − | 0.570590i | ||||
\(436\) | 2.98153 | + | 2.98153i | 0.142790 | + | 0.142790i | ||||
\(437\) | 8.14889 | − | 8.14889i | 0.389814 | − | 0.389814i | ||||
\(438\) | 11.3037 | + | 0.560893i | 0.540113 | + | 0.0268005i | ||||
\(439\) | 12.8652i | 0.614023i | 0.951706 | + | 0.307011i | \(0.0993290\pi\) | ||||
−0.951706 | + | 0.307011i | \(0.900671\pi\) | |||||||
\(440\) | 12.3538 | − | 12.3538i | 0.588943 | − | 0.588943i | ||||
\(441\) | −0.149000 | + | 1.49770i | −0.00709522 | + | 0.0713193i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.4060i | − | 0.684449i | −0.939618 | − | 0.342224i | \(-0.888820\pi\) | ||
0.939618 | − | 0.342224i | \(-0.111180\pi\) | |||||||
\(444\) | 13.8239 | + | 15.2674i | 0.656053 | + | 0.724559i | ||||
\(445\) | 19.1769 | 0.909072 | ||||||||
\(446\) | −7.91306 | −0.374694 | ||||||||
\(447\) | −8.84361 | + | 8.00746i | −0.418288 | + | 0.378740i | ||||
\(448\) | −5.05110 | + | 5.05110i | −0.238642 | + | 0.238642i | ||||
\(449\) | 11.6046 | − | 11.6046i | 0.547657 | − | 0.547657i | −0.378105 | − | 0.925763i | \(-0.623424\pi\) |
0.925763 | + | 0.378105i | \(0.123424\pi\) | |||||||
\(450\) | 5.34739 | − | 4.37969i | 0.252079 | − | 0.206461i | ||||
\(451\) | 4.93525 | 0.232392 | ||||||||
\(452\) | −2.68470 | −0.126278 | ||||||||
\(453\) | 22.1619 | − | 20.0665i | 1.04126 | − | 0.942806i | ||||
\(454\) | − | 0.0504707i | − | 0.00236871i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.3162 | + | 0.759991i | 0.717245 | + | 0.0355898i | ||||
\(457\) | −16.1290 | + | 16.1290i | −0.754481 | + | 0.754481i | −0.975312 | − | 0.220831i | \(-0.929123\pi\) |
0.220831 | + | 0.975312i | \(0.429123\pi\) | |||||||
\(458\) | 20.7736i | 0.970686i | ||||||||
\(459\) | 4.46936 | − | 29.8265i | 0.208612 | − | 1.39218i | ||||
\(460\) | 4.79303 | − | 4.79303i | 0.223476 | − | 0.223476i | ||||
\(461\) | 20.8758 | + | 20.8758i | 0.972282 | + | 0.972282i | 0.999626 | − | 0.0273439i | \(-0.00870493\pi\) |
−0.0273439 | + | 0.999626i | \(0.508705\pi\) | |||||||
\(462\) | −11.8818 | + | 10.7584i | −0.552790 | + | 0.500525i | ||||
\(463\) | −25.6118 | − | 25.6118i | −1.19028 | − | 1.19028i | −0.976988 | − | 0.213295i | \(-0.931580\pi\) |
−0.213295 | − | 0.976988i | \(-0.568420\pi\) | |||||||
\(464\) | 5.51309i | 0.255939i | ||||||||
\(465\) | 0.0661369 | − | 1.33286i | 0.00306703 | − | 0.0618100i | ||||
\(466\) | 8.92275 | + | 8.92275i | 0.413338 | + | 0.413338i | ||||
\(467\) | −14.0544 | −0.650361 | −0.325180 | − | 0.945652i | \(-0.605425\pi\) | ||||
−0.325180 | + | 0.945652i | \(0.605425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3687 | 0.755835 | ||||||||
\(470\) | −0.262168 | − | 0.262168i | −0.0120929 | − | 0.0120929i | ||||
\(471\) | −1.15376 | + | 23.2519i | −0.0531627 | + | 1.07139i | ||||
\(472\) | − | 13.1442i | − | 0.605013i | ||||||
\(473\) | −25.4257 | − | 25.4257i | −1.16908 | − | 1.16908i | ||||
\(474\) | −8.60783 | + | 7.79397i | −0.395371 | + | 0.357989i | ||||
\(475\) | −7.23225 | − | 7.23225i | −0.331838 | − | 0.331838i | ||||
\(476\) | 14.8165 | − | 14.8165i | 0.679114 | − | 0.679114i | ||||
\(477\) | −0.615431 | + | 6.18614i | −0.0281786 | + | 0.283244i | ||||
\(478\) | − | 20.2660i | − | 0.926945i | ||||||
\(479\) | −9.09054 | + | 9.09054i | −0.415357 | + | 0.415357i | −0.883600 | − | 0.468243i | \(-0.844887\pi\) |
0.468243 | + | 0.883600i | \(0.344887\pi\) | |||||||
\(480\) | 14.2828 | + | 0.708716i | 0.651918 | + | 0.0323483i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.60185i | 0.164060i | ||||||||
\(483\) | −11.1202 | + | 10.0688i | −0.505988 | + | 0.458148i | ||||
\(484\) | −16.3900 | −0.745000 | ||||||||
\(485\) | −2.67365 | −0.121404 | ||||||||
\(486\) | −10.2313 | + | 6.09824i | −0.464102 | + | 0.276622i | ||||
\(487\) | −19.1664 | + | 19.1664i | −0.868515 | + | 0.868515i | −0.992308 | − | 0.123793i | \(-0.960494\pi\) |
0.123793 | + | 0.992308i | \(0.460494\pi\) | |||||||
\(488\) | −13.0092 | + | 13.0092i | −0.588898 | + | 0.588898i | ||||
\(489\) | 8.17165 | − | 7.39903i | 0.369535 | − | 0.334596i | ||||
\(490\) | −0.540031 | −0.0243961 | ||||||||
\(491\) | −12.5414 | −0.565983 | −0.282992 | − | 0.959122i | \(-0.591327\pi\) | ||||
−0.282992 | + | 0.959122i | \(0.591327\pi\) | |||||||
\(492\) | 1.71017 | + | 1.88875i | 0.0771003 | + | 0.0851512i | ||||
\(493\) | 38.1884i | 1.71992i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.9810 | + | 1.98782i | 0.898079 | + | 0.0893457i | ||||
\(496\) | −0.324052 | + | 0.324052i | −0.0145503 | + | 0.0145503i | ||||
\(497\) | 24.4872i | 1.09840i | ||||||||
\(498\) | 15.5498 | + | 0.771586i | 0.696805 | + | 0.0345756i | ||||
\(499\) | −5.98039 | + | 5.98039i | −0.267719 | + | 0.267719i | −0.828180 | − | 0.560461i | \(-0.810624\pi\) |
0.560461 | + | 0.828180i | \(0.310624\pi\) | |||||||
\(500\) | −11.3075 | − | 11.3075i | −0.505685 | − | 0.505685i | ||||
\(501\) | 5.09383 | + | 5.62573i | 0.227575 | + | 0.251339i | ||||
\(502\) | 7.58896 | + | 7.58896i | 0.338712 | + | 0.338712i | ||||
\(503\) | − | 18.5579i | − | 0.827458i | −0.910400 | − | 0.413729i | \(-0.864226\pi\) | ||
0.910400 | − | 0.413729i | \(-0.135774\pi\) | |||||||
\(504\) | −19.8638 | − | 1.97616i | −0.884805 | − | 0.0880251i | ||||
\(505\) | −2.05970 | − | 2.05970i | −0.0916556 | − | 0.0916556i | ||||
\(506\) | 12.3341 | 0.548318 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0757 | 0.447039 | ||||||||
\(509\) | 25.8788 | + | 25.8788i | 1.14706 | + | 1.14706i | 0.987129 | + | 0.159928i | \(0.0511261\pi\) |
0.159928 | + | 0.987129i | \(0.448874\pi\) | |||||||
\(510\) | 10.8080 | + | 0.536294i | 0.478585 | + | 0.0237475i | ||||
\(511\) | 21.7999i | 0.964372i | ||||||||
\(512\) | −6.56566 | − | 6.56566i | −0.290164 | − | 0.290164i | ||||
\(513\) | 10.4782 | + | 14.1719i | 0.462623 | + | 0.625704i | ||||
\(514\) | −10.5544 | − | 10.5544i | −0.465534 | − | 0.465534i | ||||
\(515\) | 13.3301 | − | 13.3301i | 0.587395 | − | 0.587395i | ||||
\(516\) | 0.920013 | − | 18.5411i | 0.0405013 | − | 0.816226i | ||||
\(517\) | 1.63650i | 0.0719733i | ||||||||
\(518\) | 11.5645 | − | 11.5645i | 0.508116 | − | 0.508116i | ||||
\(519\) | −0.371988 | + | 7.49670i | −0.0163285 | + | 0.329069i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 32.0270i | − | 1.40313i | −0.712605 | − | 0.701565i | \(-0.752485\pi\) | ||
0.712605 | − | 0.701565i | \(-0.247515\pi\) | |||||||
\(522\) | 11.6677 | − | 9.55623i | 0.510681 | − | 0.418265i | ||||
\(523\) | 16.4059 | 0.717380 | 0.358690 | − | 0.933457i | \(-0.383224\pi\) | ||||
0.358690 | + | 0.933457i | \(0.383224\pi\) | |||||||
\(524\) | −7.59175 | −0.331647 | ||||||||
\(525\) | 8.93623 | + | 9.86937i | 0.390009 | + | 0.430735i | ||||
\(526\) | 0.707063 | − | 0.707063i | 0.0308294 | − | 0.0308294i | ||||
\(527\) | −2.24466 | + | 2.24466i | −0.0977789 | + | 0.0977789i | ||||
\(528\) | −4.62822 | − | 5.11150i | −0.201417 | − | 0.222450i | ||||
\(529\) | −11.4564 | −0.498105 | ||||||||
\(530\) | −2.23055 | −0.0968891 | ||||||||
\(531\) | 11.6873 | − | 9.57225i | 0.507184 | − | 0.415400i | ||||
\(532\) | 12.2451i | 0.530891i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.892826 | + | 17.9932i | −0.0386364 | + | 0.778642i | ||||
\(535\) | −7.49316 | + | 7.49316i | −0.323958 | + | 0.323958i | ||||
\(536\) | − | 16.7608i | − | 0.723955i | ||||||
\(537\) | −1.20108 | + | 24.2055i | −0.0518306 | + | 1.04455i | ||||
\(538\) | 15.2786 | − | 15.2786i | 0.658709 | − | 0.658709i | ||||
\(539\) | 1.68549 | + | 1.68549i | 0.0725993 | + | 0.0725993i | ||||
\(540\) | 6.16308 | + | 8.33564i | 0.265217 | + | 0.358709i | ||||
\(541\) | −10.4088 | − | 10.4088i | −0.447508 | − | 0.447508i | 0.447017 | − | 0.894525i | \(-0.352486\pi\) |
−0.894525 | + | 0.447017i | \(0.852486\pi\) | |||||||
\(542\) | − | 5.43518i | − | 0.233461i | ||||||
\(543\) | 1.68842 | + | 0.0837796i | 0.0724569 | + | 0.00359532i | ||||
\(544\) | −24.0535 | − | 24.0535i | −1.03129 | − | 1.03129i | ||||
\(545\) | −4.19442 | −0.179669 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.0787 | −0.772988 | −0.386494 | − | 0.922292i | \(-0.626314\pi\) | ||||
−0.386494 | + | 0.922292i | \(0.626314\pi\) | |||||||
\(548\) | −4.84710 | − | 4.84710i | −0.207058 | − | 0.207058i | ||||
\(549\) | −21.0410 | − | 2.09328i | −0.898010 | − | 0.0893388i | ||||
\(550\) | − | 10.9467i | − | 0.466769i | ||||||
\(551\) | −15.7803 | − | 15.7803i | −0.672265 | − | 0.672265i | ||||
\(552\) | 10.3100 | + | 11.3866i | 0.438823 | + | 0.484646i | ||||
\(553\) | −15.8160 | − | 15.8160i | −0.672563 | − | 0.672563i | ||||
\(554\) | 6.61952 | − | 6.61952i | 0.281236 | − | 0.281236i | ||||
\(555\) | −20.4628 | − | 1.01537i | −0.868599 | − | 0.0431000i | ||||
\(556\) | − | 16.6940i | − | 0.707985i | ||||||
\(557\) | 9.10043 | − | 9.10043i | 0.385597 | − | 0.385597i | −0.487516 | − | 0.873114i | \(-0.662097\pi\) |
0.873114 | + | 0.487516i | \(0.162097\pi\) | |||||||
\(558\) | 1.24751 | + | 0.124109i | 0.0528114 | + | 0.00525396i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.00914i | 0.127159i | ||||||||
\(561\) | −32.0590 | − | 35.4066i | −1.35353 | − | 1.49487i | ||||
\(562\) | 18.4176 | 0.776901 | ||||||||
\(563\) | 27.8875 | 1.17532 | 0.587659 | − | 0.809109i | \(-0.300050\pi\) | ||||
0.587659 | + | 0.809109i | \(0.300050\pi\) | |||||||
\(564\) | −0.626298 | + | 0.567082i | −0.0263719 | + | 0.0238785i | ||||
\(565\) | 1.88842 | − | 1.88842i | 0.0794463 | − | 0.0794463i | ||||
\(566\) | 6.66059 | − | 6.66059i | 0.279966 | − | 0.279966i | ||||
\(567\) | −12.7086 | − | 19.1011i | −0.533713 | − | 0.802172i | ||||
\(568\) | 25.0738 | 1.05207 | ||||||||
\(569\) | −1.75416 | −0.0735383 | −0.0367692 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367692 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(570\) | −4.68772 | + | 4.24450i | −0.196347 | + | 0.177783i | ||||
\(571\) | − | 13.1497i | − | 0.550300i | −0.961401 | − | 0.275150i | \(-0.911273\pi\) | ||
0.961401 | − | 0.275150i | \(-0.0887275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.5943 | − | 1.46847i | −1.23632 | − | 0.0613464i | ||||
\(574\) | 1.43066 | − | 1.43066i | 0.0597145 | − | 0.0597145i | ||||
\(575\) | − | 10.2451i | − | 0.427250i | ||||||
\(576\) | −0.832228 | + | 8.36533i | −0.0346762 | + | 0.348556i | ||||
\(577\) | 2.17547 | − | 2.17547i | 0.0905662 | − | 0.0905662i | −0.660372 | − | 0.750938i | \(-0.729601\pi\) |
0.750938 | + | 0.660372i | \(0.229601\pi\) | |||||||
\(578\) | −9.01673 | − | 9.01673i | −0.375046 | − | 0.375046i | ||||
\(579\) | 3.26007 | − | 2.95183i | 0.135484 | − | 0.122674i | ||||
\(580\) | −9.28171 | − | 9.28171i | −0.385402 | − | 0.385402i | ||||
\(581\) | 29.9888i | 1.24415i | ||||||||
\(582\) | 0.124478 | − | 2.50862i | 0.00515979 | − | 0.103986i | ||||
\(583\) | 6.96179 | + | 6.96179i | 0.288328 | + | 0.288328i | ||||
\(584\) | 22.3221 | 0.923696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.0131 | −0.496257 | ||||||||
\(587\) | 10.6501 | + | 10.6501i | 0.439576 | + | 0.439576i | 0.891869 | − | 0.452294i | \(-0.149394\pi\) |
−0.452294 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(588\) | −0.0609884 | + | 1.22910i | −0.00251512 | + | 0.0506874i | ||||
\(589\) | − | 1.85509i | − | 0.0764378i | ||||||
\(590\) | 3.83280 | + | 3.83280i | 0.157794 | + | 0.157794i | ||||
\(591\) | −22.9250 | + | 20.7575i | −0.943010 | + | 0.853850i | ||||
\(592\) | 4.97502 | + | 4.97502i | 0.204472 | + | 0.204472i | ||||
\(593\) | −18.1461 | + | 18.1461i | −0.745171 | + | 0.745171i | −0.973568 | − | 0.228397i | \(-0.926652\pi\) |
0.228397 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(594\) | −2.79538 | + | 18.6551i | −0.114696 | + | 0.765428i | ||||
\(595\) | 20.8439i | 0.854516i | ||||||||
\(596\) | −6.89746 | + | 6.89746i | −0.282531 | + | 0.282531i | ||||
\(597\) | 4.51467 | + | 0.224019i | 0.184773 | + | 0.00916847i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.9578i | 0.815455i | 0.913104 | + | 0.407728i | \(0.133679\pi\) | ||||
−0.913104 | + | 0.407728i | \(0.866321\pi\) | |||||||
\(600\) | 10.1058 | − | 9.15029i | 0.412567 | − | 0.373559i | ||||
\(601\) | −46.9281 | −1.91424 | −0.957118 | − | 0.289697i | \(-0.906445\pi\) | ||||
−0.957118 | + | 0.289697i | \(0.906445\pi\) | |||||||
\(602\) | −14.7411 | −0.600802 | ||||||||
\(603\) | 14.9029 | − | 12.2060i | 0.606893 | − | 0.497065i | ||||
\(604\) | 17.2849 | − | 17.2849i | 0.703311 | − | 0.703311i | ||||
\(605\) | 11.5287 | − | 11.5287i | 0.468709 | − | 0.468709i | ||||
\(606\) | 2.02846 | − | 1.83667i | 0.0824006 | − | 0.0746097i | ||||
\(607\) | 33.5601 | 1.36216 | 0.681081 | − | 0.732208i | \(-0.261510\pi\) | ||||
0.681081 | + | 0.732208i | \(0.261510\pi\) | |||||||
\(608\) | 19.8790 | 0.806199 | ||||||||
\(609\) | 19.4983 | + | 21.5344i | 0.790112 | + | 0.872617i | ||||
\(610\) | − | 7.58682i | − | 0.307182i | ||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.44120 | − | 24.5383i | 0.0986796 | − | 0.991901i | ||||
\(613\) | −21.7869 | + | 21.7869i | −0.879966 | + | 0.879966i | −0.993531 | − | 0.113565i | \(-0.963773\pi\) |
0.113565 | + | 0.993531i | \(0.463773\pi\) | |||||||
\(614\) | 1.97786i | 0.0798199i | ||||||||
\(615\) | −2.53148 | − | 0.125612i | −0.102079 | − | 0.00506518i | ||||
\(616\) | −22.3544 | + | 22.3544i | −0.900685 | + | 0.900685i | ||||
\(617\) | −20.5242 | − | 20.5242i | −0.826274 | − | 0.826274i | 0.160725 | − | 0.986999i | \(-0.448617\pi\) |
−0.986999 | + | 0.160725i | \(0.948617\pi\) | |||||||
\(618\) | 11.8867 | + | 13.1279i | 0.478153 | + | 0.528083i | ||||
\(619\) | 28.5202 | + | 28.5202i | 1.14633 | + | 1.14633i | 0.987270 | + | 0.159056i | \(0.0508449\pi\) |
0.159056 | + | 0.987270i | \(0.449155\pi\) | |||||||
\(620\) | − | 1.09113i | − | 0.0438209i | ||||||
\(621\) | −2.61622 | + | 17.4594i | −0.104985 | + | 0.700623i | ||||
\(622\) | 8.25798 | + | 8.25798i | 0.331115 | + | 0.331115i | ||||
\(623\) | −34.7010 | −1.39027 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.830307 | 0.0332123 | ||||||||
\(626\) | −16.9684 | − | 16.9684i | −0.678193 | − | 0.678193i | ||||
\(627\) | 27.8784 | + | 1.38333i | 1.11336 | + | 0.0552449i | ||||
\(628\) | 19.0349i | 0.759575i | ||||||||
\(629\) | 34.4612 | + | 34.4612i | 1.37406 | + | 1.37406i | ||||
\(630\) | 6.36843 | − | 5.21595i | 0.253724 | − | 0.207809i | ||||
\(631\) | 17.1705 | + | 17.1705i | 0.683545 | + | 0.683545i | 0.960797 | − | 0.277252i | \(-0.0894238\pi\) |
−0.277252 | + | 0.960797i | \(0.589424\pi\) | |||||||
\(632\) | −16.1948 | + | 16.1948i | −0.644195 | + | 0.644195i | ||||
\(633\) | 1.16263 | − | 23.4305i | 0.0462103 | − | 0.931280i | ||||
\(634\) | − | 12.7664i | − | 0.507017i | ||||||
\(635\) | −7.08728 | + | 7.08728i | −0.281250 | + | 0.281250i | ||||
\(636\) | −0.251907 | + | 5.07671i | −0.00998878 | + | 0.201305i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 23.8851i | − | 0.945619i | ||||||
\(639\) | 18.2599 | + | 22.2944i | 0.722350 | + | 0.881955i | ||||
\(640\) | 13.4963 | 0.533490 | ||||||||
\(641\) | 9.40735 | 0.371568 | 0.185784 | − | 0.982591i | \(-0.440518\pi\) | ||||
0.185784 | + | 0.982591i | \(0.440518\pi\) | |||||||
\(642\) | −6.68178 | − | 7.37951i | −0.263709 | − | 0.291246i | ||||
\(643\) | 32.3448 | − | 32.3448i | 1.27555 | − | 1.27555i | 0.332424 | − | 0.943130i | \(-0.392134\pi\) |
0.943130 | − | 0.332424i | \(-0.107866\pi\) | |||||||
\(644\) | −8.67309 | + | 8.67309i | −0.341768 | + | 0.341768i | ||||
\(645\) | 12.3947 | + | 13.6889i | 0.488040 | + | 0.539002i | ||||
\(646\) | 15.0427 | 0.591846 | ||||||||
\(647\) | −8.80759 | −0.346262 | −0.173131 | − | 0.984899i | \(-0.555388\pi\) | ||||
−0.173131 | + | 0.984899i | \(0.555388\pi\) | |||||||
\(648\) | −19.5587 | + | 13.0131i | −0.768337 | + | 0.511201i | ||||
\(649\) | − | 23.9251i | − | 0.939142i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.119676 | + | 2.41184i | −0.00469048 | + | 0.0945276i | ||||
\(652\) | 6.37337 | − | 6.37337i | 0.249601 | − | 0.249601i | ||||
\(653\) | − | 16.2320i | − | 0.635207i | −0.948224 | − | 0.317603i | \(-0.897122\pi\) | ||
0.948224 | − | 0.317603i | \(-0.102878\pi\) | |||||||
\(654\) | 0.195281 | − | 3.93552i | 0.00763610 | − | 0.153891i | ||||
\(655\) | 5.34004 | − | 5.34004i | 0.208653 | − | 0.208653i | ||||
\(656\) | 0.615464 | + | 0.615464i | 0.0240298 | + | 0.0240298i | ||||
\(657\) | 16.2560 | + | 19.8478i | 0.634207 | + | 0.774336i | ||||
\(658\) | 0.474398 | + | 0.474398i | 0.0184940 | + | 0.0184940i | ||||
\(659\) | 18.6480i | 0.726422i | 0.931707 | + | 0.363211i | \(0.118320\pi\) | ||||
−0.931707 | + | 0.363211i | \(0.881680\pi\) | |||||||
\(660\) | 16.3976 | + | 0.813651i | 0.638274 | + | 0.0316713i | ||||
\(661\) | −19.9989 | − | 19.9989i | −0.777867 | − | 0.777867i | 0.201601 | − | 0.979468i | \(-0.435386\pi\) |
−0.979468 | + | 0.201601i | \(0.935386\pi\) | |||||||
\(662\) | −17.1693 | −0.667303 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 30.7072 | 1.19167 | ||||||||
\(665\) | −8.61318 | − | 8.61318i | −0.334005 | − | 0.334005i | ||||
\(666\) | 1.90539 | − | 19.1525i | 0.0738324 | − | 0.742144i | ||||
\(667\) | − | 22.3542i | − | 0.865558i | ||||||
\(668\) | 4.38772 | + | 4.38772i | 0.169766 | + | 0.169766i | ||||
\(669\) | −12.0397 | − | 13.2969i | −0.465480 | − | 0.514086i | ||||
\(670\) | 4.88736 | + | 4.88736i | 0.188815 | + | 0.188815i | ||||
\(671\) | −23.6793 | + | 23.6793i | −0.914128 | + | 0.914128i | ||||
\(672\) | −25.8451 | − | 1.28244i | −0.996995 | − | 0.0494711i | ||||
\(673\) | − | 24.6690i | − | 0.950918i | −0.879738 | − | 0.475459i | \(-0.842282\pi\) | ||
0.879738 | − | 0.475459i | \(-0.157718\pi\) | |||||||
\(674\) | −4.96802 | + | 4.96802i | −0.191361 | + | 0.191361i | ||||
\(675\) | 15.4955 | + | 2.32193i | 0.596422 | + | 0.0893710i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.4537i | 1.86223i | 0.364727 | + | 0.931114i | \(0.381162\pi\) | ||||
−0.364727 | + | 0.931114i | \(0.618838\pi\) | |||||||
\(678\) | 1.68393 | + | 1.85977i | 0.0646711 | + | 0.0714242i | ||||
\(679\) | 4.83803 | 0.185667 | ||||||||
\(680\) | 21.3432 | 0.818473 | ||||||||
\(681\) | 0.0848094 | − | 0.0767908i | 0.00324990 | − | 0.00294263i | ||||
\(682\) | 1.40393 | − | 1.40393i | 0.0537593 | − | 0.0537593i | ||||
\(683\) | −12.9552 | + | 12.9552i | −0.495716 | + | 0.495716i | −0.910101 | − | 0.414385i | \(-0.863997\pi\) |
0.414385 | + | 0.910101i | \(0.363997\pi\) | |||||||
\(684\) | 9.13103 | + | 11.1486i | 0.349134 | + | 0.426276i | ||||
\(685\) | 6.81890 | 0.260537 | ||||||||
\(686\) | 14.6116 | 0.557875 | ||||||||
\(687\) | −34.9073 | + | 31.6068i | −1.33180 | + | 1.20588i | ||||
\(688\) | − | 6.34157i | − | 0.241770i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.32663 | − | 0.313929i | −0.240851 | − | 0.0119511i | ||||
\(691\) | −7.31417 | + | 7.31417i | −0.278244 | + | 0.278244i | −0.832408 | − | 0.554164i | \(-0.813038\pi\) |
0.554164 | + | 0.832408i | \(0.313038\pi\) | |||||||
\(692\) | 6.13708i | 0.233297i | ||||||||
\(693\) | −36.1560 | − | 3.59700i | −1.37345 | − | 0.136639i | ||||
\(694\) | −6.07014 | + | 6.07014i | −0.230419 | + | 0.230419i | ||||
\(695\) | 11.7426 | + | 11.7426i | 0.445422 | + | 0.445422i | ||||
\(696\) | 22.0502 | − | 19.9654i | 0.835811 | − | 0.756786i | ||||
\(697\) | 4.26323 | + | 4.26323i | 0.161481 | + | 0.161481i | ||||
\(698\) | − | 26.6412i | − | 1.00838i | ||||||
\(699\) | −1.41762 | + | 28.5694i | −0.0536193 | + | 1.08059i | ||||
\(700\) | 7.69749 | + | 7.69749i | 0.290938 | + | 0.290938i | ||||
\(701\) | −1.23945 | −0.0468132 | −0.0234066 | − | 0.999726i | \(-0.507451\pi\) | ||||
−0.0234066 | + | 0.999726i | \(0.507451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.4804 | −1.07416 | ||||||||
\(704\) | 9.41421 | + | 9.41421i | 0.354811 | + | 0.354811i | ||||
\(705\) | 0.0416524 | − | 0.839424i | 0.00156872 | − | 0.0316145i | ||||
\(706\) | 24.6079i | 0.926131i | ||||||||
\(707\) | 3.72708 | + | 3.72708i | 0.140171 | + | 0.140171i | ||||
\(708\) | 9.15625 | − | 8.29054i | 0.344113 | − | 0.311578i | ||||
\(709\) | −19.1156 | − | 19.1156i | −0.717900 | − | 0.717900i | 0.250275 | − | 0.968175i | \(-0.419479\pi\) |
−0.968175 | + | 0.250275i | \(0.919479\pi\) | |||||||
\(710\) | −7.31139 | + | 7.31139i | −0.274392 | + | 0.274392i | ||||
\(711\) | −26.1935 | − | 2.60587i | −0.982332 | − | 0.0977277i | ||||
\(712\) | 35.5322i | 1.33163i | ||||||||
\(713\) | 1.31395 | − | 1.31395i | 0.0492077 | − | 0.0492077i | ||||
\(714\) | −19.5573 | − | 0.970436i | −0.731913 | − | 0.0363177i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.8156i | 0.740543i | ||||||||
\(717\) | 34.0543 | − | 30.8345i | 1.27178 | − | 1.15154i | ||||
\(718\) | −22.5300 | −0.840812 | ||||||||
\(719\) | −38.1356 | −1.42222 | −0.711109 | − | 0.703082i | \(-0.751807\pi\) | ||||
−0.711109 | + | 0.703082i | \(0.751807\pi\) | |||||||
\(720\) | 2.24389 | + | 2.73968i | 0.0836247 | + | 0.102102i | ||||
\(721\) | −24.1211 | + | 24.1211i | −0.898318 | + | 0.898318i | ||||
\(722\) | 4.04946 | − | 4.04946i | 0.150705 | − | 0.150705i | ||||
\(723\) | −6.05243 | + | 5.48018i | −0.225092 | + | 0.203810i | ||||
\(724\) | 1.38220 | 0.0513691 | ||||||||
\(725\) | −19.8397 | −0.736827 | ||||||||
\(726\) | 10.2804 | + | 11.3539i | 0.381540 | + | 0.421381i | ||||
\(727\) | − | 15.5870i | − | 0.578091i | −0.957315 | − | 0.289046i | \(-0.906662\pi\) | ||
0.957315 | − | 0.289046i | \(-0.0933379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.8141 | − | 7.91395i | −0.956079 | − | 0.293109i | ||||
\(730\) | −6.50902 | + | 6.50902i | −0.240910 | + | 0.240910i | ||||
\(731\) | − | 43.9271i | − | 1.62470i | ||||||
\(732\) | −17.2675 | − | 0.856818i | −0.638226 | − | 0.0316689i | ||||
\(733\) | 0.240557 | − | 0.240557i | 0.00888518 | − | 0.00888518i | −0.702650 | − | 0.711535i | \(-0.748000\pi\) |
0.711535 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(734\) | 11.5178 | + | 11.5178i | 0.425131 | + | 0.425131i | ||||
\(735\) | −0.821653 | − | 0.907451i | −0.0303071 | − | 0.0334718i | ||||
\(736\) | 14.0801 | + | 14.0801i | 0.519000 | + | 0.519000i | ||||
\(737\) | − | 30.5079i | − | 1.12377i | ||||||
\(738\) | 0.235718 | − | 2.36937i | 0.00867689 | − | 0.0872178i | ||||
\(739\) | −23.9551 | − | 23.9551i | −0.881204 | − | 0.881204i | 0.112453 | − | 0.993657i | \(-0.464129\pi\) |
−0.993657 | + | 0.112453i | \(0.964129\pi\) | |||||||
\(740\) | −16.7517 | −0.615803 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.03624 | 0.148175 | ||||||||
\(743\) | −23.3974 | − | 23.3974i | −0.858367 | − | 0.858367i | 0.132779 | − | 0.991146i | \(-0.457610\pi\) |
−0.991146 | + | 0.132779i | \(0.957610\pi\) | |||||||
\(744\) | 2.46962 | + | 0.122543i | 0.0905405 | + | 0.00449264i | ||||
\(745\) | − | 9.70335i | − | 0.355503i | ||||||
\(746\) | 7.51190 | + | 7.51190i | 0.275030 | + | 0.275030i | ||||
\(747\) | 22.3624 | + | 27.3034i | 0.818197 | + | 0.998979i | ||||
\(748\) | −27.6150 | − | 27.6150i | −1.00970 | − | 1.00970i | ||||
\(749\) | 13.5590 | − | 13.5590i | 0.495437 | − | 0.495437i | ||||
\(750\) | −0.740604 | + | 14.9254i | −0.0270430 | + | 0.545000i | ||||
\(751\) | − | 5.37402i | − | 0.196101i | −0.995181 | − | 0.0980503i | \(-0.968739\pi\) | ||
0.995181 | − | 0.0980503i | \(-0.0312606\pi\) | |||||||
\(752\) | −0.204085 | + | 0.204085i | −0.00744220 | + | 0.00744220i | ||||
\(753\) | −1.20571 | + | 24.2988i | −0.0439385 | + | 0.885497i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.3164i | 0.884963i | ||||||||
\(756\) | −11.1522 | − | 15.0835i | −0.405603 | − | 0.548583i | ||||
\(757\) | −41.6670 | −1.51441 | −0.757207 | − | 0.653175i | \(-0.773437\pi\) | ||||
−0.757207 | + | 0.653175i | \(0.773437\pi\) | |||||||
\(758\) | −26.5633 | −0.964824 | ||||||||
\(759\) | 18.7663 | + | 20.7259i | 0.681172 | + | 0.752301i | ||||
\(760\) | −8.81950 | + | 8.81950i | −0.319917 | + | 0.319917i | ||||
\(761\) | 4.81729 | − | 4.81729i | 0.174626 | − | 0.174626i | −0.614382 | − | 0.789009i | \(-0.710595\pi\) |
0.789009 | + | 0.614382i | \(0.210595\pi\) | |||||||
\(762\) | −6.31985 | − | 6.97978i | −0.228944 | − | 0.252851i | ||||
\(763\) | 7.58990 | 0.274773 | ||||||||
\(764\) | −24.2270 | −0.876502 | ||||||||
\(765\) | 15.5431 | + | 18.9774i | 0.561961 | + | 0.686128i | ||||
\(766\) | − | 12.8914i | − | 0.465784i | ||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.10943 | + | 22.3585i | −0.0400332 | + | 0.806793i | ||||
\(769\) | 15.2356 | − | 15.2356i | 0.549410 | − | 0.549410i | −0.376860 | − | 0.926270i | \(-0.622996\pi\) |
0.926270 | + | 0.376860i | \(0.122996\pi\) | |||||||
\(770\) | − | 13.0369i | − | 0.469816i | ||||||
\(771\) | 1.67685 | − | 33.7937i | 0.0603903 | − | 1.21705i | ||||
\(772\) | 2.54265 | − | 2.54265i | 0.0915119 | − | 0.0915119i | ||||
\(773\) | −1.99339 | − | 1.99339i | −0.0716973 | − | 0.0716973i | 0.670349 | − | 0.742046i | \(-0.266144\pi\) |
−0.742046 | + | 0.670349i | \(0.766144\pi\) | |||||||
\(774\) | −13.4211 | + | 10.9923i | −0.482410 | + | 0.395110i | ||||
\(775\) | −1.16615 | − | 1.16615i | −0.0418893 | − | 0.0418893i | ||||
\(776\) | − | 4.95392i | − | 0.177835i | ||||||
\(777\) | 37.0280 | + | 1.83733i | 1.32837 | + | 0.0659140i | ||||
\(778\) | −18.9107 | − | 18.9107i | −0.677980 | − | 0.677980i | ||||
\(779\) | −3.52334 | −0.126237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.6392 | 1.63310 | ||||||||
\(782\) | 10.6546 | + | 10.6546i | 0.381008 | + | 0.381008i | ||||
\(783\) | 33.8103 | + | 5.06631i | 1.20828 | + | 0.181055i | ||||
\(784\) | 0.420388i | 0.0150138i | ||||||||
\(785\) | −13.3892 | − | 13.3892i | −0.477879 | − | 0.477879i | ||||
\(786\) | 4.76180 | + | 5.25904i | 0.169848 | + | 0.187584i | ||||
\(787\) | −15.2212 | − | 15.2212i | −0.542576 | − | 0.542576i | 0.381707 | − | 0.924283i | \(-0.375336\pi\) |
−0.924283 | + | 0.381707i | \(0.875336\pi\) | |||||||
\(788\) | −17.8801 | + | 17.8801i | −0.636952 | + | 0.636952i | ||||
\(789\) | 2.26392 | + | 0.112336i | 0.0805976 | + | 0.00399927i | ||||
\(790\) | − | 9.44465i | − | 0.336026i | ||||||
\(791\) | −3.41713 | + | 3.41713i | −0.121499 | + | 0.121499i | ||||
\(792\) | −3.68316 | + | 37.0221i | −0.130875 | + | 1.31552i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.01315i | 0.0359555i | ||||||||
\(795\) | −3.39377 | − | 3.74815i | −0.120365 | − | 0.132933i | ||||
\(796\) | 3.69588 | 0.130997 | ||||||||
\(797\) | −37.5528 | −1.33019 | −0.665095 | − | 0.746759i | \(-0.731609\pi\) | ||||
−0.665095 | + | 0.746759i | \(0.731609\pi\) | |||||||
\(798\) | 8.48254 | − | 7.68053i | 0.300279 | − | 0.271888i | ||||
\(799\) | −1.41366 | + | 1.41366i | −0.0500118 | + | 0.0500118i | ||||
\(800\) | 12.4963 | − | 12.4963i | 0.441811 | − | 0.441811i | ||||
\(801\) | −31.5936 | + | 25.8762i | −1.11631 | + | 0.914292i | ||||
\(802\) | −20.3105 | −0.717189 | ||||||||
\(803\) | 40.6306 | 1.43382 | ||||||||
\(804\) | 11.6755 | − | 10.5716i | 0.411764 | − | 0.372832i | ||||
\(805\) | − | 12.2013i | − | 0.430039i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.9200 | + | 2.42742i | 1.72207 | + | 0.0854493i | ||||
\(808\) | 3.81636 | − | 3.81636i | 0.134259 | − | 0.134259i | ||||
\(809\) | − | 32.4453i | − | 1.14072i | −0.821396 | − | 0.570358i | \(-0.806804\pi\) | ||
0.821396 | − | 0.570358i | \(-0.193196\pi\) | |||||||
\(810\) | 1.90866 | − | 9.49775i | 0.0670636 | − | 0.333717i | ||||
\(811\) | −26.3972 | + | 26.3972i | −0.926930 | + | 0.926930i | −0.997506 | − | 0.0705768i | \(-0.977516\pi\) |
0.0705768 | + | 0.997506i | \(0.477516\pi\) | |||||||
\(812\) | 16.7955 | + | 16.7955i | 0.589405 | + | 0.589405i | ||||
\(813\) | 9.13310 | − | 8.26957i | 0.320312 | − | 0.290027i | ||||
\(814\) | −21.5539 | − | 21.5539i | −0.755464 | − | 0.755464i | ||||
\(815\) | 8.96606i | 0.314067i | ||||||||
\(816\) | 0.417479 | − | 8.41348i | 0.0146147 | − | 0.294531i | ||||
\(817\) | 18.1517 | + | 18.1517i | 0.635049 | + | 0.635049i | ||||
\(818\) | −7.18193 | −0.251110 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.07236 | −0.0723700 | ||||||||
\(821\) | 13.9802 | + | 13.9802i | 0.487911 | + | 0.487911i | 0.907646 | − | 0.419736i | \(-0.137877\pi\) |
−0.419736 | + | 0.907646i | \(0.637877\pi\) | |||||||
\(822\) | −0.317470 | + | 6.39800i | −0.0110730 | + | 0.223156i | ||||
\(823\) | 2.45399i | 0.0855409i | 0.999085 | + | 0.0427704i | \(0.0136184\pi\) | ||||
−0.999085 | + | 0.0427704i | \(0.986382\pi\) | |||||||
\(824\) | 24.6989 | + | 24.6989i | 0.860428 | + | 0.860428i | ||||
\(825\) | 18.3945 | − | 16.6553i | 0.640414 | − | 0.579864i | ||||
\(826\) | −6.93553 | − | 6.93553i | −0.241318 | − | 0.241318i | ||||
\(827\) | −12.7904 | + | 12.7904i | −0.444765 | + | 0.444765i | −0.893610 | − | 0.448845i | \(-0.851836\pi\) |
0.448845 | + | 0.893610i | \(0.351836\pi\) | |||||||
\(828\) | −1.42899 | + | 14.3639i | −0.0496610 | + | 0.499179i | ||||
\(829\) | − | 47.1067i | − | 1.63608i | −0.575159 | − | 0.818042i | \(-0.695060\pi\) | ||
0.575159 | − | 0.818042i | \(-0.304940\pi\) | |||||||
\(830\) | −8.95406 | + | 8.95406i | −0.310800 | + | 0.310800i | ||||
\(831\) | 21.1948 | + | 1.05169i | 0.735238 | + | 0.0364827i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.91196i | 0.100894i | ||||||||
\(834\) | −11.5645 | + | 10.4711i | −0.400445 | + | 0.362583i | ||||
\(835\) | −6.17264 | −0.213613 | ||||||||
\(836\) | 22.8223 | 0.789326 | ||||||||
\(837\) | 1.68953 | + | 2.28511i | 0.0583987 | + | 0.0789850i | ||||
\(838\) | 17.2237 | − | 17.2237i | 0.594984 | − | 0.594984i | ||||
\(839\) | −4.27577 | + | 4.27577i | −0.147616 | + | 0.147616i | −0.777052 | − | 0.629436i | \(-0.783286\pi\) |
0.629436 | + | 0.777052i | \(0.283286\pi\) | |||||||
\(840\) | 12.0354 | − | 10.8974i | 0.415260 | − | 0.375998i | ||||
\(841\) | −14.2890 | −0.492723 | ||||||||
\(842\) | −21.2240 | −0.731426 | ||||||||
\(843\) | 28.0223 | + | 30.9484i | 0.965138 | + | 1.06592i | ||||
\(844\) | − | 19.1811i | − | 0.660242i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.785671 | + | 0.0781627i | 0.0270119 | + | 0.00268729i | ||||
\(847\) | −20.8615 | + | 20.8615i | −0.716809 | + | 0.716809i | ||||
\(848\) | 1.73638i | 0.0596274i | ||||||||
\(849\) | 21.3263 | + | 1.05821i | 0.731916 | + | 0.0363178i | ||||
\(850\) | 9.45611 | − | 9.45611i | 0.324342 | − | 0.324342i | ||||
\(851\) | −20.1724 | − | 20.1724i | −0.691503 | − | 0.691503i | ||||
\(852\) | 15.8149 | + | 17.4663i | 0.541810 | + | 0.598387i | ||||
\(853\) | 13.7031 | + | 13.7031i | 0.469185 | + | 0.469185i | 0.901650 | − | 0.432466i | \(-0.142356\pi\) |
−0.432466 | + | 0.901650i | \(0.642356\pi\) | |||||||
\(854\) | 13.7285i | 0.469781i | ||||||||
\(855\) | −14.2647 | − | 1.41912i | −0.487841 | − | 0.0485330i | ||||
\(856\) | −13.8838 | − | 13.8838i | −0.474539 | − | 0.474539i | ||||
\(857\) | −15.1228 | −0.516585 | −0.258292 | − | 0.966067i | \(-0.583160\pi\) | ||||
−0.258292 | + | 0.966067i | \(0.583160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.35366 | −0.182665 | −0.0913323 | − | 0.995820i | \(-0.529113\pi\) | ||||
−0.0913323 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(860\) | 10.6765 | + | 10.6765i | 0.364066 | + | 0.364066i | ||||
\(861\) | 4.58076 | + | 0.227298i | 0.156112 | + | 0.00774631i | ||||
\(862\) | 3.63124i | 0.123680i | ||||||||
\(863\) | −18.3335 | − | 18.3335i | −0.624080 | − | 0.624080i | 0.322492 | − | 0.946572i | \(-0.395479\pi\) |
−0.946572 | + | 0.322492i | \(0.895479\pi\) | |||||||
\(864\) | −24.4870 | + | 18.1048i | −0.833065 | + | 0.615938i | ||||
\(865\) | −4.31683 | − | 4.31683i | −0.146776 | − | 0.146776i | ||||
\(866\) | −1.11264 | + | 1.11264i | −0.0378091 | + | 0.0378091i | ||||
\(867\) | 1.43255 | − | 28.8703i | 0.0486519 | − | 0.980487i | ||||
\(868\) | 1.97443i | 0.0670164i | ||||||||
\(869\) | −29.4777 | + | 29.4777i | −0.999963 | + | 0.999963i | ||||
\(870\) | −0.607924 | + | 12.2515i | −0.0206105 | + | 0.415366i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 7.77170i | − | 0.263183i | ||||||
\(873\) | 4.40480 | − | 3.60767i | 0.149080 | − | 0.122101i | ||||
\(874\) | −8.80547 | −0.297850 | ||||||||
\(875\) | −28.7847 | −0.973100 | ||||||||
\(876\) | 14.0794 | + | 15.5495i | 0.475697 | + | 0.525370i | ||||
\(877\) | −19.7646 | + | 19.7646i | −0.667402 | + | 0.667402i | −0.957114 | − | 0.289712i | \(-0.906440\pi\) |
0.289712 | + | 0.957114i | \(0.406440\pi\) | |||||||
\(878\) | 6.95090 | − | 6.95090i | 0.234582 | − | 0.234582i | ||||
\(879\) | −18.2778 | − | 20.1865i | −0.616496 | − | 0.680872i | ||||
\(880\) | 5.60842 | 0.189060 | ||||||||
\(881\) | 21.9951 | 0.741035 | 0.370517 | − | 0.928826i | \(-0.379180\pi\) | ||||
0.370517 | + | 0.928826i | \(0.379180\pi\) | |||||||
\(882\) | 0.889693 | − | 0.728687i | 0.0299575 | − | 0.0245362i | ||||
\(883\) | − | 11.7640i | − | 0.395889i | −0.980213 | − | 0.197945i | \(-0.936573\pi\) | ||
0.980213 | − | 0.197945i | \(-0.0634266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.608943 | + | 12.2721i | −0.0204694 | + | 0.412521i | ||||
\(886\) | −7.78336 | + | 7.78336i | −0.261487 | + | 0.261487i | ||||
\(887\) | 30.5005i | 1.02411i | 0.858953 | + | 0.512054i | \(0.171115\pi\) | ||||
−0.858953 | + | 0.512054i | \(0.828885\pi\) | |||||||
\(888\) | 1.88134 | − | 37.9149i | 0.0631338 | − | 1.27234i | ||||
\(889\) | 12.8246 | − | 12.8246i | 0.430123 | − | 0.430123i | ||||
\(890\) | −10.3610 | − | 10.3610i | −0.347302 | − | 0.347302i | ||||
\(891\) | −35.6006 | + | 23.6863i | −1.19266 | + | 0.793521i | ||||
\(892\) | −10.3707 | − | 10.3707i | −0.347237 | − | 0.347237i | ||||
\(893\) | − | 1.16832i | − | 0.0390963i | ||||||
\(894\) | 9.10441 | + | 0.451763i | 0.304497 | + | 0.0151092i | ||||
\(895\) | −13.9383 | − | 13.9383i | −0.465905 | − | 0.465905i | ||||
\(896\) | −24.4219 | −0.815880 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.5397 | −0.418454 | ||||||||
\(899\) | −2.54446 | − | 2.54446i | −0.0848627 | − | 0.0848627i | ||||
\(900\) | 12.7481 | + | 1.26825i | 0.424938 | + | 0.0422751i | ||||
\(901\) | 12.0276i | 0.400698i | ||||||||
\(902\) | −2.66645 | − | 2.66645i | −0.0887832 | − | 0.0887832i | ||||
\(903\) | −22.4284 | − | 24.7705i | −0.746372 | − | 0.824309i | ||||
\(904\) | 3.49898 | + | 3.49898i | 0.116375 | + | 0.116375i | ||||
\(905\) | −0.972241 | + | 0.972241i | −0.0323184 | + | 0.0323184i | ||||
\(906\) | −22.8154 | − | 1.13211i | −0.757992 | − | 0.0376117i | ||||
\(907\) | − | 18.8219i | − | 0.624971i | −0.949923 | − | 0.312485i | \(-0.898838\pi\) | ||
0.949923 | − | 0.312485i | \(-0.101162\pi\) | |||||||
\(908\) | 0.0661461 | − | 0.0661461i | 0.00219513 | − | 0.00219513i | ||||
\(909\) | 6.17257 | + | 0.614081i | 0.204731 | + | 0.0203678i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52.2340i | − | 1.73059i | −0.501262 | − | 0.865296i | \(-0.667131\pi\) | ||
0.501262 | − | 0.865296i | \(-0.332869\pi\) | |||||||
\(912\) | 3.30414 | + | 3.64916i | 0.109411 | + | 0.120836i | ||||
\(913\) | 55.8931 | 1.84979 | ||||||||
\(914\) | 17.4285 | 0.576485 | ||||||||
\(915\) | 12.7487 | − | 11.5433i | 0.421458 | − | 0.381609i | ||||
\(916\) | −27.2255 | + | 27.2255i | −0.899556 | + | 0.899556i | ||||
\(917\) | −9.66292 | + | 9.66292i | −0.319098 | + | 0.319098i | ||||
\(918\) | −18.5296 | + | 13.7001i | −0.611569 | + | 0.452172i | ||||
\(919\) | 2.88054 | 0.0950204 | 0.0475102 | − | 0.998871i | \(-0.484871\pi\) | ||||
0.0475102 | + | 0.998871i | \(0.484871\pi\) | |||||||
\(920\) | −12.4936 | −0.411901 | ||||||||
\(921\) | −3.32353 | + | 3.00930i | −0.109514 | + | 0.0991596i | ||||
\(922\) | − | 22.5578i | − | 0.742902i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −29.6718 | − | 1.47232i | −0.976129 | − | 0.0484357i | ||||
\(925\) | −17.9033 | + | 17.9033i | −0.588658 | + | 0.588658i | ||||
\(926\) | 27.6755i | 0.909473i | ||||||||
\(927\) | −3.97425 | + | 39.9481i | −0.130531 | + | 1.31207i | ||||
\(928\) | 27.2662 | − | 27.2662i | 0.895057 | − | 0.895057i | ||||
\(929\) | −5.13978 | − | 5.13978i | −0.168631 | − | 0.168631i | 0.617747 | − | 0.786377i | \(-0.288046\pi\) |
−0.786377 | + | 0.617747i | \(0.788046\pi\) | |||||||
\(930\) | −0.755861 | + | 0.684395i | −0.0247857 | + | 0.0224422i | ||||
\(931\) | −1.20329 | − | 1.20329i | −0.0394363 | − | 0.0394363i | ||||
\(932\) | 23.3880i | 0.766099i | ||||||||
\(933\) | −1.31200 | + | 26.4409i | −0.0429530 | + | 0.865636i | ||||
\(934\) | 7.59341 | + | 7.59341i | 0.248464 | + | 0.248464i | ||||
\(935\) | 38.8487 | 1.27049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76482 | 0.122991 | 0.0614957 | − | 0.998107i | \(-0.480413\pi\) | ||||
0.0614957 | + | 0.998107i | \(0.480413\pi\) | |||||||
\(938\) | −8.84378 | − | 8.84378i | −0.288760 | − | 0.288760i | ||||
\(939\) | 2.69588 | − | 54.3304i | 0.0879769 | − | 1.77300i | ||||
\(940\) | − | 0.687184i | − | 0.0224135i | ||||||
\(941\) | −10.0291 | − | 10.0291i | −0.326941 | − | 0.326941i | 0.524481 | − | 0.851422i | \(-0.324259\pi\) |
−0.851422 | + | 0.524481i | \(0.824259\pi\) | |||||||
\(942\) | 13.1861 | − | 11.9393i | 0.429625 | − | 0.389005i | ||||
\(943\) | −2.49555 | − | 2.49555i | −0.0812663 | − | 0.0812663i | ||||
\(944\) | 2.98364 | − | 2.98364i | 0.0971093 | − | 0.0971093i | ||||
\(945\) | 18.4542 | + | 2.76528i | 0.600316 | + | 0.0899545i | ||||
\(946\) | 27.4744i | 0.893269i | ||||||||
\(947\) | 12.7618 | − | 12.7618i | 0.414703 | − | 0.414703i | −0.468671 | − | 0.883373i | \(-0.655267\pi\) |
0.883373 | + | 0.468671i | \(0.155267\pi\) | |||||||
\(948\) | −21.4959 | − | 1.06663i | −0.698155 | − | 0.0346426i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.81498i | 0.253551i | ||||||||
\(951\) | 21.4522 | − | 19.4239i | 0.695635 | − | 0.629864i | ||||
\(952\) | −38.6209 | −1.25171 | ||||||||
\(953\) | 56.2122 | 1.82089 | 0.910445 | − | 0.413630i | \(-0.135739\pi\) | ||||
0.910445 | + | 0.413630i | \(0.135739\pi\) | |||||||
\(954\) | 3.67480 | − | 3.00978i | 0.118976 | − | 0.0974453i | ||||
\(955\) | 17.0413 | − | 17.0413i | 0.551443 | − | 0.551443i | ||||
\(956\) | 26.5602 | − | 26.5602i | 0.859019 | − | 0.859019i | ||||
\(957\) | 40.1357 | − | 36.3409i | 1.29740 | − | 1.17473i | ||||
\(958\) | 9.82300 | 0.317367 | ||||||||
\(959\) | −12.3390 | −0.398446 | ||||||||
\(960\) | −4.58929 | − | 5.06851i | −0.148119 | − | 0.163586i | ||||
\(961\) | 30.7009i | 0.990351i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.23401 | − | 22.4557i | 0.0719901 | − | 0.723625i | ||||
\(964\) | −4.72051 | + | 4.72051i | −0.152038 | + | 0.152038i | ||||
\(965\) | 3.57700i | 0.115148i | ||||||||
\(966\) | 11.4482 | + | 0.568061i | 0.368339 | + | 0.0182771i | ||||
\(967\) | −29.9079 | + | 29.9079i | −0.961772 | + | 0.961772i | −0.999296 | − | 0.0375237i | \(-0.988053\pi\) |
0.0375237 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(968\) | 21.3612 | + | 21.3612i | 0.686575 | + | 0.686575i | ||||
\(969\) | 22.8873 | + | 25.2772i | 0.735246 | + | 0.812021i | ||||
\(970\) | 1.44454 | + | 1.44454i | 0.0463813 | + | 0.0463813i | ||||
\(971\) | 3.11267i | 0.0998905i | 0.998752 | + | 0.0499452i | \(0.0159047\pi\) | ||||
−0.998752 | + | 0.0499452i | \(0.984095\pi\) | |||||||
\(972\) | −21.4012 | − | 5.41673i | −0.686444 | − | 0.173742i | ||||
\(973\) | −21.2485 | − | 21.2485i | −0.681195 | − | 0.681195i | ||||
\(974\) | 20.7108 | 0.663616 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.90597 | −0.189045 | ||||||||
\(977\) | −22.3521 | − | 22.3521i | −0.715108 | − | 0.715108i | 0.252491 | − | 0.967599i | \(-0.418750\pi\) |
−0.967599 | + | 0.252491i | \(0.918750\pi\) | |||||||
\(978\) | −8.41263 | − | 0.417436i | −0.269006 | − | 0.0133481i | ||||
\(979\) | 64.6757i | 2.06704i | ||||||||
\(980\) | −0.707755 | − | 0.707755i | −0.0226084 | − | 0.0226084i | ||||
\(981\) | 6.91024 | − | 5.65971i | 0.220627 | − | 0.180701i | ||||
\(982\) | 6.77593 | + | 6.77593i | 0.216229 | + | 0.216229i | ||||
\(983\) | 19.2933 | − | 19.2933i | 0.615360 | − | 0.615360i | −0.328978 | − | 0.944338i | \(-0.606704\pi\) |
0.944338 | + | 0.328978i | \(0.106704\pi\) | |||||||
\(984\) | 0.232743 | − | 4.69049i | 0.00741957 | − | 0.149527i | ||||
\(985\) | − | 25.1537i | − | 0.801464i | ||||||
\(986\) | 20.6327 | − | 20.6327i | 0.657078 | − | 0.657078i | ||||
\(987\) | −0.0753709 | + | 1.51896i | −0.00239908 | + | 0.0483489i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.7135i | 0.817641i | ||||||||
\(990\) | −9.72147 | − | 11.8695i | −0.308969 | − | 0.377236i | ||||
\(991\) | −30.3951 | −0.965533 | −0.482767 | − | 0.875749i | \(-0.660368\pi\) | ||||
−0.482767 | + | 0.875749i | \(0.660368\pi\) | |||||||
\(992\) | 3.20534 | 0.101770 | ||||||||
\(993\) | −26.1229 | − | 28.8507i | −0.828985 | − | 0.915549i | ||||
\(994\) | 13.2301 | − | 13.2301i | 0.419634 | − | 0.419634i | ||||
\(995\) | −2.59968 | + | 2.59968i | −0.0824154 | + | 0.0824154i | ||||
\(996\) | 19.3681 | + | 21.3906i | 0.613702 | + | 0.677786i | ||||
\(997\) | 39.2462 | 1.24294 | 0.621470 | − | 0.783438i | \(-0.286536\pi\) | ||||
0.621470 | + | 0.783438i | \(0.286536\pi\) | |||||||
\(998\) | 6.46225 | 0.204559 | ||||||||
\(999\) | 35.0823 | − | 25.9386i | 1.10995 | − | 0.820660i |
(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 | 507.2.f.g.239.9 | ✓ | 48 | |
3.2 | odd | 2 | inner | 507.2.f.g.239.16 | yes | 48 | |
13.2 | odd | 12 | 507.2.k.k.488.10 | 96 | |||
13.3 | even | 3 | 507.2.k.k.188.16 | 96 | |||
13.4 | even | 6 | 507.2.k.k.80.15 | 96 | |||
13.5 | odd | 4 | inner | 507.2.f.g.437.9 | yes | 48 | |
13.6 | odd | 12 | 507.2.k.k.89.15 | 96 | |||
13.7 | odd | 12 | 507.2.k.k.89.9 | 96 | |||
13.8 | odd | 4 | inner | 507.2.f.g.437.15 | yes | 48 | |
13.9 | even | 3 | 507.2.k.k.80.9 | 96 | |||
13.10 | even | 6 | 507.2.k.k.188.10 | 96 | |||
13.11 | odd | 12 | 507.2.k.k.488.16 | 96 | |||
13.12 | even | 2 | inner | 507.2.f.g.239.15 | yes | 48 | |
39.2 | even | 12 | 507.2.k.k.488.15 | 96 | |||
39.5 | even | 4 | inner | 507.2.f.g.437.16 | yes | 48 | |
39.8 | even | 4 | inner | 507.2.f.g.437.10 | yes | 48 | |
39.11 | even | 12 | 507.2.k.k.488.9 | 96 | |||
39.17 | odd | 6 | 507.2.k.k.80.10 | 96 | |||
39.20 | even | 12 | 507.2.k.k.89.16 | 96 | |||
39.23 | odd | 6 | 507.2.k.k.188.15 | 96 | |||
39.29 | odd | 6 | 507.2.k.k.188.9 | 96 | |||
39.32 | even | 12 | 507.2.k.k.89.10 | 96 | |||
39.35 | odd | 6 | 507.2.k.k.80.16 | 96 | |||
39.38 | odd | 2 | inner | 507.2.f.g.239.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.f.g.239.9 | ✓ | 48 | 1.1 | even | 1 | trivial | |
507.2.f.g.239.10 | yes | 48 | 39.38 | odd | 2 | inner | |
507.2.f.g.239.15 | yes | 48 | 13.12 | even | 2 | inner | |
507.2.f.g.239.16 | yes | 48 | 3.2 | odd | 2 | inner | |
507.2.f.g.437.9 | yes | 48 | 13.5 | odd | 4 | inner | |
507.2.f.g.437.10 | yes | 48 | 39.8 | even | 4 | inner | |
507.2.f.g.437.15 | yes | 48 | 13.8 | odd | 4 | inner | |
507.2.f.g.437.16 | yes | 48 | 39.5 | even | 4 | inner | |
507.2.k.k.80.9 | 96 | 13.9 | even | 3 | |||
507.2.k.k.80.10 | 96 | 39.17 | odd | 6 | |||
507.2.k.k.80.15 | 96 | 13.4 | even | 6 | |||
507.2.k.k.80.16 | 96 | 39.35 | odd | 6 | |||
507.2.k.k.89.9 | 96 | 13.7 | odd | 12 | |||
507.2.k.k.89.10 | 96 | 39.32 | even | 12 | |||
507.2.k.k.89.15 | 96 | 13.6 | odd | 12 | |||
507.2.k.k.89.16 | 96 | 39.20 | even | 12 | |||
507.2.k.k.188.9 | 96 | 39.29 | odd | 6 | |||
507.2.k.k.188.10 | 96 | 13.10 | even | 6 | |||
507.2.k.k.188.15 | 96 | 39.23 | odd | 6 | |||
507.2.k.k.188.16 | 96 | 13.3 | even | 3 | |||
507.2.k.k.488.9 | 96 | 39.11 | even | 12 | |||
507.2.k.k.488.10 | 96 | 13.2 | odd | 12 | |||
507.2.k.k.488.15 | 96 | 39.2 | even | 12 | |||
507.2.k.k.488.16 | 96 | 13.11 | odd | 12 |