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 | 239.15 | ||
Character | \(\chi\) | \(=\) | 507.239 |
Dual form | 507.2.f.g.437.16 |
$q$-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 | 0.871837 | − | 0.489796i | \(-0.162929\pi\) |
−0.489796 | + | 0.871837i | \(0.662929\pi\) | |||||||
\(3\) | 0.0858391 | − | 1.72992i | 0.0495592 | − | 0.998771i | ||||
\(4\) | − | 1.41618i | − | 0.708090i | ||||||
\(5\) | −0.996141 | − | 0.996141i | −0.445488 | − | 0.445488i | 0.448363 | − | 0.893851i | \(-0.352007\pi\) |
−0.893851 | + | 0.448363i | \(0.852007\pi\) | |||||||
\(6\) | 0.981032 | − | 0.888277i | 0.400505 | − | 0.362637i | ||||
\(7\) | 1.80254 | + | 1.80254i | 0.681296 | + | 0.681296i | 0.960292 | − | 0.278996i | \(-0.0900017\pi\) |
−0.278996 | + | 0.960292i | \(0.590002\pi\) | |||||||
\(8\) | 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 | \(-0.495852\pi\) |
0.999915 | − | 0.0130325i | \(-0.00414850\pi\) | |||||||
\(12\) | −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 | −0.926510 | − | 0.376271i | \(-0.877206\pi\) |
0.376271 | + | 0.926510i | \(0.377206\pi\) | |||||||
\(20\) | −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 | −0.740983 | − | 0.671524i | \(-0.765640\pi\) |
0.671524 | + | 0.740983i | \(0.265640\pi\) | |||||||
\(32\) | −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 | 0.999721 | − | 0.0236364i | \(-0.00752440\pi\) |
−0.0236364 | + | 0.999721i | \(0.507524\pi\) | |||||||
\(38\) | −2.59169 | −0.420427 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.67719 | −0.581415 | ||||||||
\(41\) | 0.734507 | + | 0.734507i | 0.114711 | + | 0.114711i | 0.762132 | − | 0.647421i | \(-0.224153\pi\) |
−0.647421 | + | 0.762132i | \(0.724153\pi\) | |||||||
\(42\) | 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 | −0.724647 | − | 0.689120i | \(-0.757997\pi\) |
0.689120 | + | 0.724647i | \(0.257997\pi\) | |||||||
\(48\) | −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 | −0.436254 | − | 0.899823i | \(-0.643695\pi\) |
0.899823 | + | 0.436254i | \(0.143695\pi\) | |||||||
\(60\) | 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 | −0.373091 | − | 0.927795i | \(-0.621702\pi\) |
0.927795 | + | 0.373091i | \(0.121702\pi\) | |||||||
\(68\) | 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 | 0.984043 | − | 0.177931i | \(-0.0569404\pi\) |
−0.177931 | + | 0.984043i | \(0.556940\pi\) | |||||||
\(72\) | −6.05811 | + | 4.96179i | −0.713955 | + | 0.584753i | ||||
\(73\) | 6.04700 | + | 6.04700i | 0.707748 | + | 0.707748i | 0.966061 | − | 0.258313i | \(-0.0831666\pi\) |
−0.258313 | + | 0.966061i | \(0.583167\pi\) | |||||||
\(74\) | 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 | 0.996513 | − | 0.0834395i | \(-0.0265905\pi\) |
−0.0834395 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(84\) | −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 | \(0.506533\pi\) |
−0.999789 | + | 0.0205215i | \(0.993467\pi\) | |||||||
\(90\) | −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 | −0.635687 | − | 0.771947i | \(-0.719283\pi\) |
0.771947 | + | 0.635687i | \(0.219283\pi\) | |||||||
\(98\) | 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 | −0.599054 | − | 0.800709i | \(-0.704457\pi\) |
0.800709 | + | 0.599054i | \(0.204457\pi\) | |||||||
\(110\) | −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 | −0.838035 | − | 0.545617i | \(-0.816295\pi\) |
0.545617 | + | 0.838035i | \(0.316295\pi\) | |||||||
\(138\) | 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 | 0.877882 | − | 0.478877i | \(-0.158956\pi\) |
−0.478877 | + | 0.877882i | \(0.658956\pi\) | |||||||
\(150\) | −2.67851 | − | 2.95821i | −0.218700 | − | 0.241537i | ||||
\(151\) | −12.2053 | − | 12.2053i | −0.993251 | − | 0.993251i | 0.00672628 | − | 0.999977i | \(-0.497859\pi\) |
−0.999977 | + | 0.00672628i | \(0.997859\pi\) | |||||||
\(152\) | 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 | 0.508540 | − | 0.861038i | \(-0.330185\pi\) |
−0.861038 | + | 0.508540i | \(0.830185\pi\) | |||||||
\(164\) | 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 | −0.576995 | − | 0.816747i | \(-0.695775\pi\) |
0.816747 | + | 0.576995i | \(0.195775\pi\) | |||||||
\(168\) | 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 | 0.639529 | − | 0.768767i | \(-0.279129\pi\) |
−0.768767 | + | 0.639529i | \(0.779129\pi\) | |||||||
\(194\) | 1.45013 | 0.104114 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.710497 | −0.0507498 | ||||||||
\(197\) | 12.6256 | + | 12.6256i | 0.899536 | + | 0.899536i | 0.995395 | − | 0.0958594i | \(-0.0305599\pi\) |
−0.0958594 | + | 0.995395i | \(0.530560\pi\) | |||||||
\(198\) | −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 | −0.908428 | − | 0.418042i | \(-0.862716\pi\) |
0.418042 | + | 0.908428i | \(0.362716\pi\) | |||||||
\(224\) | − | 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 | 0.705555 | − | 0.708655i | \(-0.250698\pi\) |
−0.708655 | + | 0.705555i | \(0.750698\pi\) | |||||||
\(228\) | 6.16744 | − | 5.58432i | 0.408449 | − | 0.369831i | ||||
\(229\) | 19.2246 | + | 19.2246i | 1.27040 | + | 1.27040i | 0.945880 | + | 0.324517i | \(0.105202\pi\) |
0.324517 | + | 0.945880i | \(0.394798\pi\) | |||||||
\(230\) | − | 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 | \(-0.921814\pi\) |
−0.243165 | − | 0.969985i | \(-0.578186\pi\) | |||||||
\(240\) | 1.51561 | − | 1.37231i | 0.0978319 | − | 0.0885820i | ||||
\(241\) | 3.33327 | + | 3.33327i | 0.214715 | + | 0.214715i | 0.806267 | − | 0.591552i | \(-0.201485\pi\) |
−0.591552 | + | 0.806267i | \(0.701485\pi\) | |||||||
\(242\) | 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 | 0.537634 | − | 0.843178i | \(-0.319318\pi\) |
−0.843178 | + | 0.537634i | \(0.819318\pi\) | |||||||
\(272\) | 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 | \(-0.494613\pi\) |
0.999857 | − | 0.0169217i | \(-0.00538659\pi\) | |||||||
\(282\) | −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 | −0.952868 | − | 0.303386i | \(-0.901883\pi\) |
0.303386 | + | 0.952868i | \(0.401883\pi\) | |||||||
\(294\) | −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 | 0.757408 | − | 0.652942i | \(-0.226466\pi\) |
−0.652942 | + | 0.757408i | \(0.726466\pi\) | |||||||
\(308\) | − | 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 | 0.292654 | − | 0.956219i | \(-0.405462\pi\) |
−0.956219 | + | 0.292654i | \(0.905462\pi\) | |||||||
\(318\) | −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 | −0.992835 | − | 0.119495i | \(-0.961873\pi\) |
0.119495 | + | 0.992835i | \(0.461873\pi\) | |||||||
\(332\) | 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 | \(-0.867011\pi\) |
−0.405748 | − | 0.913985i | \(-0.632989\pi\) | |||||||
\(350\) | 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 | \(0.0777199\pi\) |
0.241746 | + | 0.970340i | \(0.422280\pi\) | |||||||
\(354\) | 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 | \(0.533825\pi\) |
−0.994359 | + | 0.106064i | \(0.966175\pi\) | |||||||
\(360\) | 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 | \(0.601320\pi\) |
−0.949767 | + | 0.312957i | \(0.898680\pi\) | |||||||
\(380\) | − | 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 | 0.333242 | − | 0.942841i | \(-0.391858\pi\) |
−0.942841 | + | 0.333242i | \(0.891858\pi\) | |||||||
\(384\) | 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 | 0.730244 | − | 0.683187i | \(-0.239406\pi\) |
−0.683187 | + | 0.730244i | \(0.739406\pi\) | |||||||
\(398\) | −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 | −0.998223 | − | 0.0595935i | \(-0.981020\pi\) |
0.0595935 | + | 0.998223i | \(0.481020\pi\) | |||||||
\(402\) | 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 | −0.852071 | − | 0.523427i | \(-0.824653\pi\) |
0.523427 | + | 0.852071i | \(0.324653\pi\) | |||||||
\(410\) | 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 | −0.999123 | − | 0.0418609i | \(-0.986671\pi\) |
0.0418609 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(422\) | 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 | 0.783394 | − | 0.621526i | \(-0.213487\pi\) |
−0.621526 | + | 0.783394i | \(0.713487\pi\) | |||||||
\(432\) | 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 | −0.925763 | − | 0.378105i | \(-0.876576\pi\) |
0.378105 | + | 0.925763i | \(0.376576\pi\) | |||||||
\(450\) | −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 | −0.220831 | − | 0.975312i | \(-0.570877\pi\) |
0.975312 | + | 0.220831i | \(0.0708769\pi\) | |||||||
\(458\) | 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 | 0.0273439 | − | 0.999626i | \(-0.491295\pi\) |
−0.999626 | + | 0.0273439i | \(0.991295\pi\) | |||||||
\(462\) | 11.8818 | − | 10.7584i | 0.552790 | − | 0.500525i | ||||
\(463\) | 25.6118 | + | 25.6118i | 1.19028 | + | 1.19028i | 0.976988 | + | 0.213295i | \(0.0684197\pi\) |
0.213295 | + | 0.976988i | \(0.431580\pi\) | |||||||
\(464\) | 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 | −0.468243 | − | 0.883600i | \(-0.655113\pi\) |
0.883600 | + | 0.468243i | \(0.155113\pi\) | |||||||
\(480\) | 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 | −0.123793 | − | 0.992308i | \(-0.539506\pi\) |
0.992308 | + | 0.123793i | \(0.0395060\pi\) | |||||||
\(488\) | 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 | −0.560461 | − | 0.828180i | \(-0.689376\pi\) |
0.828180 | + | 0.560461i | \(0.189376\pi\) | |||||||
\(500\) | 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 | \(-0.948874\pi\) |
−0.159928 | − | 0.987129i | \(-0.551126\pi\) | |||||||
\(510\) | 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 | 0.894525 | − | 0.447017i | \(-0.147514\pi\) |
−0.447017 | + | 0.894525i | \(0.647514\pi\) | |||||||
\(542\) | − | 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 | −0.873114 | − | 0.487516i | \(-0.837903\pi\) |
0.487516 | + | 0.873114i | \(0.337903\pi\) | |||||||
\(558\) | 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 | −0.750938 | − | 0.660372i | \(-0.770399\pi\) |
0.660372 | + | 0.750938i | \(0.270399\pi\) | |||||||
\(578\) | 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 | 0.452294 | − | 0.891869i | \(-0.350606\pi\) |
−0.891869 | + | 0.452294i | \(0.850606\pi\) | |||||||
\(588\) | −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 | −0.228397 | − | 0.973568i | \(-0.573348\pi\) |
0.973568 | + | 0.228397i | \(0.0733483\pi\) | |||||||
\(594\) | −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 | −0.113565 | − | 0.993531i | \(-0.536227\pi\) |
0.993531 | + | 0.113565i | \(0.0362270\pi\) | |||||||
\(614\) | 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 | 0.986999 | − | 0.160725i | \(-0.0513832\pi\) |
−0.160725 | + | 0.986999i | \(0.551383\pi\) | |||||||
\(618\) | −11.8867 | − | 13.1279i | −0.478153 | − | 0.528083i | ||||
\(619\) | −28.5202 | − | 28.5202i | −1.14633 | − | 1.14633i | −0.987270 | − | 0.159056i | \(-0.949155\pi\) |
−0.159056 | − | 0.987270i | \(-0.550845\pi\) | |||||||
\(620\) | − | 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 | 0.277252 | − | 0.960797i | \(-0.410576\pi\) |
−0.960797 | + | 0.277252i | \(0.910576\pi\) | |||||||
\(632\) | 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 | \(0.607866\pi\) |
−0.943130 | + | 0.332424i | \(0.892134\pi\) | |||||||
\(644\) | 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 | 0.979468 | − | 0.201601i | \(-0.0646143\pi\) |
−0.201601 | + | 0.979468i | \(0.564614\pi\) | |||||||
\(662\) | −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 | −0.414385 | − | 0.910101i | \(-0.636003\pi\) |
0.910101 | + | 0.414385i | \(0.136003\pi\) | |||||||
\(684\) | −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 | −0.554164 | − | 0.832408i | \(-0.686962\pi\) |
0.832408 | + | 0.554164i | \(0.186962\pi\) | |||||||
\(692\) | 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 | 0.968175 | − | 0.250275i | \(-0.0805209\pi\) |
−0.250275 | + | 0.968175i | \(0.580521\pi\) | |||||||
\(710\) | 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 | −0.711535 | − | 0.702650i | \(-0.752000\pi\) |
0.702650 | + | 0.711535i | \(0.252000\pi\) | |||||||
\(734\) | −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 | 0.993657 | − | 0.112453i | \(-0.0358709\pi\) |
−0.112453 | + | 0.993657i | \(0.535871\pi\) | |||||||
\(740\) | −16.7517 | −0.615803 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.03624 | 0.148175 | ||||||||
\(743\) | 23.3974 | + | 23.3974i | 0.858367 | + | 0.858367i | 0.991146 | − | 0.132779i | \(-0.0423900\pi\) |
−0.132779 | + | 0.991146i | \(0.542390\pi\) | |||||||
\(744\) | 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 | −0.789009 | − | 0.614382i | \(-0.789405\pi\) |
0.614382 | + | 0.789009i | \(0.289405\pi\) | |||||||
\(762\) | 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 | −0.926270 | − | 0.376860i | \(-0.877004\pi\) |
0.376860 | + | 0.926270i | \(0.377004\pi\) | |||||||
\(770\) | − | 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 | 0.742046 | − | 0.670349i | \(-0.233856\pi\) |
−0.670349 | + | 0.742046i | \(0.733856\pi\) | |||||||
\(774\) | 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 | 0.924283 | − | 0.381707i | \(-0.124664\pi\) |
−0.381707 | + | 0.924283i | \(0.624664\pi\) | |||||||
\(788\) | 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 | −0.0705768 | − | 0.997506i | \(-0.522484\pi\) |
0.997506 | + | 0.0705768i | \(0.0224840\pi\) | |||||||
\(812\) | −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 | 0.419736 | − | 0.907646i | \(-0.362123\pi\) |
−0.907646 | + | 0.419736i | \(0.862123\pi\) | |||||||
\(822\) | −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 | −0.448845 | − | 0.893610i | \(-0.648164\pi\) |
0.893610 | + | 0.448845i | \(0.148164\pi\) | |||||||
\(828\) | −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 | −0.629436 | − | 0.777052i | \(-0.716714\pi\) |
0.777052 | + | 0.629436i | \(0.216714\pi\) | |||||||
\(840\) | −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 | 0.432466 | − | 0.901650i | \(-0.357644\pi\) |
−0.901650 | + | 0.432466i | \(0.857644\pi\) | |||||||
\(854\) | 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 | 0.946572 | − | 0.322492i | \(-0.104521\pi\) |
−0.322492 | + | 0.946572i | \(0.604521\pi\) | |||||||
\(864\) | 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 | −0.289712 | − | 0.957114i | \(-0.593560\pi\) |
0.957114 | + | 0.289712i | \(0.0935595\pi\) | |||||||
\(878\) | −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 | 0.786377 | − | 0.617747i | \(-0.211954\pi\) |
−0.617747 | + | 0.786377i | \(0.711954\pi\) | |||||||
\(930\) | 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 | 0.851422 | − | 0.524481i | \(-0.175741\pi\) |
−0.524481 | + | 0.851422i | \(0.675741\pi\) | |||||||
\(942\) | −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 | −0.883373 | − | 0.468671i | \(-0.844733\pi\) |
0.468671 | + | 0.883373i | \(0.344733\pi\) | |||||||
\(948\) | −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 | −0.0375237 | − | 0.999296i | \(-0.511947\pi\) |
0.999296 | + | 0.0375237i | \(0.0119470\pi\) | |||||||
\(968\) | −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 | 0.967599 | − | 0.252491i | \(-0.0812498\pi\) |
−0.252491 | + | 0.967599i | \(0.581250\pi\) | |||||||
\(978\) | −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 | −0.944338 | − | 0.328978i | \(-0.893296\pi\) |
0.328978 | + | 0.944338i | \(0.393296\pi\) | |||||||
\(984\) | 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.239.15 | yes | 48 | |
3.2 | odd | 2 | inner | 507.2.f.g.239.10 | yes | 48 | |
13.2 | odd | 12 | 507.2.k.k.488.16 | 96 | |||
13.3 | even | 3 | 507.2.k.k.188.10 | 96 | |||
13.4 | even | 6 | 507.2.k.k.80.9 | 96 | |||
13.5 | odd | 4 | inner | 507.2.f.g.437.15 | yes | 48 | |
13.6 | odd | 12 | 507.2.k.k.89.9 | 96 | |||
13.7 | odd | 12 | 507.2.k.k.89.15 | 96 | |||
13.8 | odd | 4 | inner | 507.2.f.g.437.9 | yes | 48 | |
13.9 | even | 3 | 507.2.k.k.80.15 | 96 | |||
13.10 | even | 6 | 507.2.k.k.188.16 | 96 | |||
13.11 | odd | 12 | 507.2.k.k.488.10 | 96 | |||
13.12 | even | 2 | inner | 507.2.f.g.239.9 | ✓ | 48 | |
39.2 | even | 12 | 507.2.k.k.488.9 | 96 | |||
39.5 | even | 4 | inner | 507.2.f.g.437.10 | yes | 48 | |
39.8 | even | 4 | inner | 507.2.f.g.437.16 | yes | 48 | |
39.11 | even | 12 | 507.2.k.k.488.15 | 96 | |||
39.17 | odd | 6 | 507.2.k.k.80.16 | 96 | |||
39.20 | even | 12 | 507.2.k.k.89.10 | 96 | |||
39.23 | odd | 6 | 507.2.k.k.188.9 | 96 | |||
39.29 | odd | 6 | 507.2.k.k.188.15 | 96 | |||
39.32 | even | 12 | 507.2.k.k.89.16 | 96 | |||
39.35 | odd | 6 | 507.2.k.k.80.10 | 96 | |||
39.38 | odd | 2 | inner | 507.2.f.g.239.16 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.f.g.239.9 | ✓ | 48 | 13.12 | even | 2 | inner | |
507.2.f.g.239.10 | yes | 48 | 3.2 | odd | 2 | inner | |
507.2.f.g.239.15 | yes | 48 | 1.1 | even | 1 | trivial | |
507.2.f.g.239.16 | yes | 48 | 39.38 | odd | 2 | inner | |
507.2.f.g.437.9 | yes | 48 | 13.8 | odd | 4 | inner | |
507.2.f.g.437.10 | yes | 48 | 39.5 | even | 4 | inner | |
507.2.f.g.437.15 | yes | 48 | 13.5 | odd | 4 | inner | |
507.2.f.g.437.16 | yes | 48 | 39.8 | even | 4 | inner | |
507.2.k.k.80.9 | 96 | 13.4 | even | 6 | |||
507.2.k.k.80.10 | 96 | 39.35 | odd | 6 | |||
507.2.k.k.80.15 | 96 | 13.9 | even | 3 | |||
507.2.k.k.80.16 | 96 | 39.17 | odd | 6 | |||
507.2.k.k.89.9 | 96 | 13.6 | odd | 12 | |||
507.2.k.k.89.10 | 96 | 39.20 | even | 12 | |||
507.2.k.k.89.15 | 96 | 13.7 | odd | 12 | |||
507.2.k.k.89.16 | 96 | 39.32 | even | 12 | |||
507.2.k.k.188.9 | 96 | 39.23 | odd | 6 | |||
507.2.k.k.188.10 | 96 | 13.3 | even | 3 | |||
507.2.k.k.188.15 | 96 | 39.29 | odd | 6 | |||
507.2.k.k.188.16 | 96 | 13.10 | even | 6 | |||
507.2.k.k.488.9 | 96 | 39.2 | even | 12 | |||
507.2.k.k.488.10 | 96 | 13.11 | odd | 12 | |||
507.2.k.k.488.15 | 96 | 39.11 | even | 12 | |||
507.2.k.k.488.16 | 96 | 13.2 | odd | 12 |