Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(49,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.bx (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 80x^{12} - 529x^{10} + 3359x^{8} - 10729x^{6} + 15420x^{4} + 1089x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 724.3 | ||
Root | \(-0.548716 + 0.755243i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.724 |
Dual form | 825.2.bx.g.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.887841 | + | 0.288477i | 0.627798 | + | 0.203984i | 0.605600 | − | 0.795770i | \(-0.292933\pi\) |
0.0221988 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(3\) | 0.587785 | + | 0.809017i | 0.339358 | + | 0.467086i | ||||
\(4\) | −0.912991 | − | 0.663327i | −0.456496 | − | 0.331664i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.288477 | + | 0.887841i | 0.117770 | + | 0.362460i | ||||
\(7\) | 1.19972 | − | 1.65127i | 0.453450 | − | 0.624121i | −0.519684 | − | 0.854358i | \(-0.673950\pi\) |
0.973134 | + | 0.230238i | \(0.0739504\pi\) | |||||||
\(8\) | −1.71667 | − | 2.36279i | −0.606934 | − | 0.835373i | ||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.85274 | − | 2.75088i | 0.558621 | − | 0.829423i | ||||
\(12\) | − | 1.12852i | − | 0.325775i | ||||||
\(13\) | −1.37754 | − | 0.447591i | −0.382062 | − | 0.124139i | 0.111688 | − | 0.993743i | \(-0.464374\pi\) |
−0.493750 | + | 0.869604i | \(0.664374\pi\) | |||||||
\(14\) | 1.54151 | − | 1.11997i | 0.411986 | − | 0.299325i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.145054 | − | 0.446431i | −0.0362636 | − | 0.111608i | ||||
\(17\) | 0.824626 | − | 0.267937i | 0.200001 | − | 0.0649843i | −0.207303 | − | 0.978277i | \(-0.566469\pi\) |
0.407305 | + | 0.913292i | \(0.366469\pi\) | |||||||
\(18\) | −0.548716 | + | 0.755243i | −0.129334 | + | 0.178012i | ||||
\(19\) | 2.53103 | − | 1.83890i | 0.580657 | − | 0.421872i | −0.258304 | − | 0.966064i | \(-0.583164\pi\) |
0.838961 | + | 0.544192i | \(0.183164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.04108 | 0.445400 | ||||||||
\(22\) | 2.43850 | − | 1.90788i | 0.519891 | − | 0.406761i | ||||
\(23\) | − | 4.70547i | − | 0.981159i | −0.871396 | − | 0.490580i | \(-0.836785\pi\) | ||
0.871396 | − | 0.490580i | \(-0.163215\pi\) | |||||||
\(24\) | 0.902506 | − | 2.77763i | 0.184223 | − | 0.566981i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.09392 | − | 0.794779i | −0.214535 | − | 0.155869i | ||||
\(27\) | −0.951057 | + | 0.309017i | −0.183031 | + | 0.0594703i | ||||
\(28\) | −2.19066 | + | 0.711789i | −0.413996 | + | 0.134516i | ||||
\(29\) | 1.64906 | + | 1.19811i | 0.306223 | + | 0.222484i | 0.730274 | − | 0.683154i | \(-0.239392\pi\) |
−0.424051 | + | 0.905638i | \(0.639392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.27979 | − | 10.0941i | 0.589067 | − | 1.81296i | 0.00678348 | − | 0.999977i | \(-0.497841\pi\) |
0.582284 | − | 0.812986i | \(-0.302159\pi\) | |||||||
\(32\) | 5.40294i | 0.955113i | ||||||||
\(33\) | 3.31452 | − | 0.118034i | 0.576985 | − | 0.0205471i | ||||
\(34\) | 0.809430 | 0.138816 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.912991 | − | 0.663327i | 0.152165 | − | 0.110555i | ||||
\(37\) | −2.44321 | + | 3.36279i | −0.401661 | + | 0.552839i | −0.961160 | − | 0.275992i | \(-0.910994\pi\) |
0.559499 | + | 0.828831i | \(0.310994\pi\) | |||||||
\(38\) | 2.77763 | − | 0.902506i | 0.450591 | − | 0.146406i | ||||
\(39\) | −0.447591 | − | 1.37754i | −0.0716719 | − | 0.220583i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.651268 | − | 0.473174i | 0.101711 | − | 0.0738974i | −0.535767 | − | 0.844366i | \(-0.679978\pi\) |
0.637478 | + | 0.770468i | \(0.279978\pi\) | |||||||
\(42\) | 1.81215 | + | 0.588805i | 0.279622 | + | 0.0908545i | ||||
\(43\) | − | 2.34089i | − | 0.356982i | −0.983942 | − | 0.178491i | \(-0.942878\pi\) | ||
0.983942 | − | 0.178491i | \(-0.0571215\pi\) | |||||||
\(44\) | −3.51627 | + | 1.28256i | −0.530097 | + | 0.193354i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.35742 | − | 4.17771i | 0.200141 | − | 0.615970i | ||||
\(47\) | 6.10137 | + | 8.39782i | 0.889977 | + | 1.22495i | 0.973556 | + | 0.228447i | \(0.0733648\pi\) |
−0.0835794 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(48\) | 0.275910 | − | 0.379757i | 0.0398241 | − | 0.0548132i | ||||
\(49\) | 0.875752 | + | 2.69529i | 0.125107 | + | 0.385041i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.701468 | + | 0.509647i | 0.0982252 | + | 0.0713648i | ||||
\(52\) | 0.960786 | + | 1.32241i | 0.133237 | + | 0.183385i | ||||
\(53\) | 6.86278 | + | 2.22985i | 0.942676 | + | 0.306294i | 0.739736 | − | 0.672897i | \(-0.234950\pi\) |
0.202940 | + | 0.979191i | \(0.434950\pi\) | |||||||
\(54\) | −0.933531 | −0.127038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.96112 | −0.796588 | ||||||||
\(57\) | 2.97540 | + | 0.966766i | 0.394101 | + | 0.128051i | ||||
\(58\) | 1.11847 | + | 1.53945i | 0.146863 | + | 0.202139i | ||||
\(59\) | −6.73386 | − | 4.89243i | −0.876674 | − | 0.636941i | 0.0556956 | − | 0.998448i | \(-0.482262\pi\) |
−0.932369 | + | 0.361507i | \(0.882262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.70931 | − | 8.33841i | −0.346892 | − | 1.06762i | −0.960563 | − | 0.278062i | \(-0.910308\pi\) |
0.613671 | − | 0.789562i | \(-0.289692\pi\) | |||||||
\(62\) | 5.82386 | − | 8.01586i | 0.739631 | − | 1.01801i | ||||
\(63\) | 1.19972 | + | 1.65127i | 0.151150 | + | 0.208040i | ||||
\(64\) | −1.84873 | + | 5.68981i | −0.231091 | + | 0.711226i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.97682 | + | 0.851369i | 0.366421 | + | 0.104796i | ||||
\(67\) | 3.15664i | 0.385645i | 0.981234 | + | 0.192822i | \(0.0617641\pi\) | ||||
−0.981234 | + | 0.192822i | \(0.938236\pi\) | |||||||
\(68\) | −0.930606 | − | 0.302372i | −0.112853 | − | 0.0366680i | ||||
\(69\) | 3.80681 | − | 2.76581i | 0.458286 | − | 0.332964i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.97725 | + | 12.2407i | 0.472013 | + | 1.45271i | 0.849944 | + | 0.526873i | \(0.176636\pi\) |
−0.377931 | + | 0.925834i | \(0.623364\pi\) | |||||||
\(72\) | 2.77763 | − | 0.902506i | 0.327347 | − | 0.106361i | ||||
\(73\) | −8.65128 | + | 11.9075i | −1.01256 | + | 1.39366i | −0.0952617 | + | 0.995452i | \(0.530369\pi\) |
−0.917294 | + | 0.398211i | \(0.869631\pi\) | |||||||
\(74\) | −3.13927 | + | 2.28081i | −0.364933 | + | 0.265139i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.53059 | −0.404987 | ||||||||
\(77\) | −2.31969 | − | 6.35965i | −0.264353 | − | 0.724749i | ||||
\(78\) | − | 1.35216i | − | 0.153102i | ||||||
\(79\) | 5.25303 | − | 16.1672i | 0.591012 | − | 1.81895i | 0.0173618 | − | 0.999849i | \(-0.494473\pi\) |
0.573651 | − | 0.819100i | \(-0.305527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0.714723 | − | 0.232227i | 0.0789279 | − | 0.0256452i | ||||
\(83\) | −5.84089 | + | 1.89782i | −0.641121 | + | 0.208313i | −0.611495 | − | 0.791248i | \(-0.709432\pi\) |
−0.0296262 | + | 0.999561i | \(0.509432\pi\) | |||||||
\(84\) | −1.86349 | − | 1.35390i | −0.203323 | − | 0.147723i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.675292 | − | 2.07833i | 0.0728186 | − | 0.224113i | ||||
\(87\) | 2.03835i | 0.218534i | ||||||||
\(88\) | −9.68030 | + | 0.344727i | −1.03192 | + | 0.0367480i | ||||
\(89\) | −3.77194 | −0.399825 | −0.199913 | − | 0.979814i | \(-0.564066\pi\) | ||||
−0.199913 | + | 0.979814i | \(0.564066\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39175 | + | 1.73771i | −0.250724 | + | 0.182162i | ||||
\(92\) | −3.12127 | + | 4.29606i | −0.325415 | + | 0.447895i | ||||
\(93\) | 10.0941 | − | 3.27979i | 1.04671 | − | 0.340098i | ||||
\(94\) | 2.99447 | + | 9.21604i | 0.308856 | + | 0.950562i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.37107 | + | 3.17577i | −0.446120 | + | 0.324125i | ||||
\(97\) | 1.84310 | + | 0.598859i | 0.187138 | + | 0.0608049i | 0.401087 | − | 0.916040i | \(-0.368633\pi\) |
−0.213949 | + | 0.976845i | \(0.568633\pi\) | |||||||
\(98\) | 2.64562i | 0.267248i | ||||||||
\(99\) | 2.04372 | + | 2.61213i | 0.205402 | + | 0.262529i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.62288 | + | 4.99472i | −0.161483 | + | 0.496993i | −0.998760 | − | 0.0497857i | \(-0.984146\pi\) |
0.837277 | + | 0.546779i | \(0.184146\pi\) | |||||||
\(102\) | 0.475771 | + | 0.654843i | 0.0471084 | + | 0.0648391i | ||||
\(103\) | −7.99426 | + | 11.0032i | −0.787698 | + | 1.08417i | 0.206693 | + | 0.978406i | \(0.433730\pi\) |
−0.994391 | + | 0.105768i | \(0.966270\pi\) | |||||||
\(104\) | 1.30722 | + | 4.02321i | 0.128184 | + | 0.394508i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.44980 | + | 3.95951i | 0.529331 | + | 0.384582i | ||||
\(107\) | −5.87235 | − | 8.08259i | −0.567701 | − | 0.781374i | 0.424579 | − | 0.905391i | \(-0.360422\pi\) |
−0.992280 | + | 0.124017i | \(0.960422\pi\) | |||||||
\(108\) | 1.07329 | + | 0.348732i | 0.103277 | + | 0.0335567i | ||||
\(109\) | 6.75183 | 0.646708 | 0.323354 | − | 0.946278i | \(-0.395189\pi\) | ||||
0.323354 | + | 0.946278i | \(0.395189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.15664 | −0.394531 | ||||||||
\(112\) | −0.911202 | − | 0.296067i | −0.0861005 | − | 0.0279757i | ||||
\(113\) | 3.08270 | + | 4.24298i | 0.289996 | + | 0.399146i | 0.929013 | − | 0.370047i | \(-0.120658\pi\) |
−0.639017 | + | 0.769193i | \(0.720658\pi\) | |||||||
\(114\) | 2.36279 | + | 1.71667i | 0.221296 | + | 0.160781i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.710837 | − | 2.18773i | −0.0659996 | − | 0.203126i | ||||
\(117\) | 0.851369 | − | 1.17181i | 0.0787091 | − | 0.108334i | ||||
\(118\) | −4.56724 | − | 6.28627i | −0.420449 | − | 0.578698i | ||||
\(119\) | 0.546881 | − | 1.68313i | 0.0501325 | − | 0.154292i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.13473 | − | 10.1933i | −0.375885 | − | 0.926666i | ||||
\(122\) | − | 8.18476i | − | 0.741013i | ||||||
\(123\) | 0.765612 | + | 0.248762i | 0.0690329 | + | 0.0224301i | ||||
\(124\) | −9.69014 | + | 7.04030i | −0.870200 | + | 0.632237i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.588805 | + | 1.81215i | 0.0524549 | + | 0.161440i | ||||
\(127\) | −19.6632 | + | 6.38897i | −1.74483 | + | 0.566929i | −0.995456 | − | 0.0952195i | \(-0.969645\pi\) |
−0.749372 | + | 0.662149i | \(0.769645\pi\) | |||||||
\(128\) | 3.06877 | − | 4.22380i | 0.271244 | − | 0.373335i | ||||
\(129\) | 1.89382 | − | 1.37594i | 0.166741 | − | 0.121145i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3089 | 1.77439 | 0.887197 | − | 0.461392i | \(-0.152650\pi\) | ||||
0.887197 | + | 0.461392i | \(0.152650\pi\) | |||||||
\(132\) | −3.10443 | − | 2.09085i | −0.270206 | − | 0.181985i | ||||
\(133\) | − | 6.38556i | − | 0.553698i | ||||||
\(134\) | −0.910618 | + | 2.80259i | −0.0786654 | + | 0.242107i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.04869 | − | 1.48846i | −0.175674 | − | 0.127634i | ||||
\(137\) | −3.30950 | + | 1.07532i | −0.282750 | + | 0.0918710i | −0.446959 | − | 0.894555i | \(-0.647493\pi\) |
0.164209 | + | 0.986426i | \(0.447493\pi\) | |||||||
\(138\) | 4.17771 | − | 1.35742i | 0.355630 | − | 0.115551i | ||||
\(139\) | 2.20931 | + | 1.60516i | 0.187392 | + | 0.136148i | 0.677526 | − | 0.735499i | \(-0.263052\pi\) |
−0.490134 | + | 0.871647i | \(0.663052\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.20768 | + | 9.87223i | −0.270136 | + | 0.831392i | ||||
\(142\) | 12.0152i | 1.00829i | ||||||||
\(143\) | −3.78350 | + | 2.96019i | −0.316392 | + | 0.247544i | ||||
\(144\) | 0.469405 | 0.0391171 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.1160 | + | 8.07624i | −0.919966 | + | 0.668394i | ||||
\(147\) | −1.66578 | + | 2.29275i | −0.137391 | + | 0.189103i | ||||
\(148\) | 4.46126 | − | 1.44955i | 0.366713 | − | 0.119152i | ||||
\(149\) | 2.81465 | + | 8.66261i | 0.230585 | + | 0.709669i | 0.997676 | + | 0.0681306i | \(0.0217035\pi\) |
−0.767091 | + | 0.641538i | \(0.778297\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.4541 | + | 12.6811i | −1.42039 | + | 1.03198i | −0.428687 | + | 0.903453i | \(0.641024\pi\) |
−0.991706 | + | 0.128523i | \(0.958976\pi\) | |||||||
\(152\) | −8.68986 | − | 2.82351i | −0.704841 | − | 0.229017i | ||||
\(153\) | 0.867063i | 0.0700979i | ||||||||
\(154\) | −0.224903 | − | 6.31553i | −0.0181232 | − | 0.508920i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.505115 | + | 1.55458i | −0.0404416 | + | 0.124466i | ||||
\(157\) | −13.9857 | − | 19.2497i | −1.11618 | − | 1.53629i | −0.811978 | − | 0.583688i | \(-0.801609\pi\) |
−0.304205 | − | 0.952607i | \(-0.598391\pi\) | |||||||
\(158\) | 9.32772 | − | 12.8385i | 0.742073 | − | 1.02138i | ||||
\(159\) | 2.22985 | + | 6.86278i | 0.176839 | + | 0.544254i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.77000 | − | 5.64523i | −0.612362 | − | 0.444907i | ||||
\(162\) | −0.548716 | − | 0.755243i | −0.0431112 | − | 0.0593375i | ||||
\(163\) | −1.71506 | − | 0.557258i | −0.134334 | − | 0.0436478i | 0.241078 | − | 0.970506i | \(-0.422499\pi\) |
−0.375412 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(164\) | −0.908472 | −0.0709397 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.73326 | −0.444988 | ||||||||
\(167\) | 23.3840 | + | 7.59792i | 1.80951 | + | 0.587945i | 1.00000 | 0.000837897i | \(0.000266711\pi\) | |
0.809509 | + | 0.587107i | \(0.199733\pi\) | |||||||
\(168\) | −3.50386 | − | 4.82265i | −0.270328 | − | 0.372075i | ||||
\(169\) | −8.81993 | − | 6.40806i | −0.678456 | − | 0.492927i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.966766 | + | 2.97540i | 0.0739304 | + | 0.227534i | ||||
\(172\) | −1.55277 | + | 2.13721i | −0.118398 | + | 0.162961i | ||||
\(173\) | 9.52890 | + | 13.1154i | 0.724469 | + | 0.997146i | 0.999364 | + | 0.0356719i | \(0.0113571\pi\) |
−0.274894 | + | 0.961474i | \(0.588643\pi\) | |||||||
\(174\) | −0.588017 | + | 1.80973i | −0.0445775 | + | 0.137195i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.49683 | − | 0.428092i | −0.112828 | − | 0.0322686i | ||||
\(177\) | − | 8.32351i | − | 0.625633i | ||||||
\(178\) | −3.34888 | − | 1.08812i | −0.251010 | − | 0.0815579i | ||||
\(179\) | 13.7287 | − | 9.97452i | 1.02613 | − | 0.745530i | 0.0586031 | − | 0.998281i | \(-0.481335\pi\) |
0.967531 | + | 0.252751i | \(0.0813353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.67071 | + | 17.4526i | 0.421500 | + | 1.29725i | 0.906306 | + | 0.422623i | \(0.138891\pi\) |
−0.484805 | + | 0.874622i | \(0.661109\pi\) | |||||||
\(182\) | −2.62479 | + | 0.852845i | −0.194562 | + | 0.0632171i | ||||
\(183\) | 5.15342 | − | 7.09308i | 0.380952 | − | 0.524335i | ||||
\(184\) | −11.1181 | + | 8.07774i | −0.819634 | + | 0.595499i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.90814 | 0.726500 | ||||||||
\(187\) | 0.790750 | − | 2.76487i | 0.0578254 | − | 0.202187i | ||||
\(188\) | − | 11.7143i | − | 0.854356i | ||||||
\(189\) | −0.630728 | + | 1.94118i | −0.0458787 | + | 0.141200i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4577 | + | 9.05102i | 0.901405 | + | 0.654909i | 0.938826 | − | 0.344391i | \(-0.111914\pi\) |
−0.0374216 | + | 0.999300i | \(0.511914\pi\) | |||||||
\(192\) | −5.68981 | + | 1.84873i | −0.410627 | + | 0.133421i | ||||
\(193\) | 7.01824 | − | 2.28037i | 0.505184 | − | 0.164144i | −0.0453268 | − | 0.998972i | \(-0.514433\pi\) |
0.550511 | + | 0.834828i | \(0.314433\pi\) | |||||||
\(194\) | 1.46362 | + | 1.06338i | 0.105082 | + | 0.0763465i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.988303 | − | 3.04168i | 0.0705931 | − | 0.217263i | ||||
\(197\) | − | 3.14676i | − | 0.224197i | −0.993697 | − | 0.112099i | \(-0.964243\pi\) | ||
0.993697 | − | 0.112099i | \(-0.0357573\pi\) | |||||||
\(198\) | 1.06096 | + | 2.90872i | 0.0753991 | + | 0.206714i | ||||
\(199\) | 3.25757 | 0.230923 | 0.115462 | − | 0.993312i | \(-0.463165\pi\) | ||||
0.115462 | + | 0.993312i | \(0.463165\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.55377 | + | 1.85543i | −0.180129 | + | 0.130872i | ||||
\(202\) | −2.88172 | + | 3.96635i | −0.202757 | + | 0.279072i | ||||
\(203\) | 3.95681 | − | 1.28564i | 0.277713 | − | 0.0902346i | ||||
\(204\) | −0.302372 | − | 0.930606i | −0.0211703 | − | 0.0651554i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.2718 | + | 7.46290i | −0.715670 | + | 0.519965i | ||||
\(207\) | 4.47517 | + | 1.45407i | 0.311046 | + | 0.101065i | ||||
\(208\) | 0.679903i | 0.0471428i | ||||||||
\(209\) | −0.369272 | − | 10.3696i | −0.0255431 | − | 0.717277i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.15690 | − | 18.9490i | 0.423859 | − | 1.30450i | −0.480224 | − | 0.877146i | \(-0.659445\pi\) |
0.904083 | − | 0.427357i | \(-0.140555\pi\) | |||||||
\(212\) | −4.78654 | − | 6.58811i | −0.328741 | − | 0.452473i | ||||
\(213\) | −7.56518 | + | 10.4126i | −0.518358 | + | 0.713458i | ||||
\(214\) | −2.88207 | − | 8.87009i | −0.197014 | − | 0.606347i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.36279 | + | 1.71667i | 0.160768 | + | 0.116804i | ||||
\(217\) | −12.7333 | − | 17.5259i | −0.864395 | − | 1.18974i | ||||
\(218\) | 5.99455 | + | 1.94775i | 0.406002 | + | 0.131918i | ||||
\(219\) | −14.7184 | −0.994580 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.25588 | −0.0844799 | ||||||||
\(222\) | −3.69043 | − | 1.19909i | −0.247686 | − | 0.0804780i | ||||
\(223\) | −6.16008 | − | 8.47862i | −0.412509 | − | 0.567770i | 0.551319 | − | 0.834295i | \(-0.314125\pi\) |
−0.963828 | + | 0.266524i | \(0.914125\pi\) | |||||||
\(224\) | 8.92170 | + | 6.48199i | 0.596106 | + | 0.433096i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.51295 | + | 4.65638i | 0.100640 | + | 0.309738i | ||||
\(227\) | −10.3880 | + | 14.2979i | −0.689476 | + | 0.948982i | −0.999999 | − | 0.00158404i | \(-0.999496\pi\) |
0.310523 | + | 0.950566i | \(0.399496\pi\) | |||||||
\(228\) | −2.07523 | − | 2.85631i | −0.137436 | − | 0.189164i | ||||
\(229\) | −1.27614 | + | 3.92755i | −0.0843297 | + | 0.259540i | −0.984326 | − | 0.176357i | \(-0.943569\pi\) |
0.899997 | + | 0.435897i | \(0.143569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.78158 | − | 5.61478i | 0.248810 | − | 0.369425i | ||||
\(232\) | − | 5.95314i | − | 0.390843i | ||||||
\(233\) | 12.9334 | + | 4.20231i | 0.847294 | + | 0.275303i | 0.700312 | − | 0.713837i | \(-0.253044\pi\) |
0.146982 | + | 0.989139i | \(0.453044\pi\) | |||||||
\(234\) | 1.09392 | − | 0.794779i | 0.0715118 | − | 0.0519563i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.90267 | + | 8.93350i | 0.188948 | + | 0.581521i | ||||
\(237\) | 16.1672 | − | 5.25303i | 1.05017 | − | 0.341221i | ||||
\(238\) | 0.971087 | − | 1.33659i | 0.0629462 | − | 0.0866380i | ||||
\(239\) | 6.47725 | − | 4.70600i | 0.418979 | − | 0.304406i | −0.358248 | − | 0.933626i | \(-0.616626\pi\) |
0.777227 | + | 0.629221i | \(0.216626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.501943 | −0.0323330 | −0.0161665 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161665 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(242\) | −0.730444 | − | 10.2428i | −0.0469547 | − | 0.658434i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −3.05751 | + | 9.41006i | −0.195737 | + | 0.602417i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.607979 | + | 0.441723i | 0.0387633 | + | 0.0281632i | ||||
\(247\) | −4.30967 | + | 1.40030i | −0.274218 | + | 0.0890988i | ||||
\(248\) | −29.4807 | + | 9.57885i | −1.87202 | + | 0.608258i | ||||
\(249\) | −4.96856 | − | 3.60987i | −0.314870 | − | 0.228766i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.72933 | + | 17.6331i | −0.361632 | + | 1.11299i | 0.590431 | + | 0.807088i | \(0.298958\pi\) |
−0.952063 | + | 0.305901i | \(0.901042\pi\) | |||||||
\(252\) | − | 2.30340i | − | 0.145100i | ||||||
\(253\) | −12.9442 | − | 8.71800i | −0.813796 | − | 0.548096i | ||||
\(254\) | −19.3009 | −1.21105 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.6231 | − | 9.89779i | 0.851446 | − | 0.618612i | ||||
\(257\) | −4.33791 | + | 5.97062i | −0.270592 | + | 0.372437i | −0.922589 | − | 0.385784i | \(-0.873931\pi\) |
0.651998 | + | 0.758221i | \(0.273931\pi\) | |||||||
\(258\) | 2.07833 | − | 0.675292i | 0.129391 | − | 0.0420418i | ||||
\(259\) | 2.62171 | + | 8.06879i | 0.162905 | + | 0.501370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.64906 | + | 1.19811i | −0.102074 | + | 0.0741613i | ||||
\(262\) | 18.0310 | + | 5.85864i | 1.11396 | + | 0.361948i | ||||
\(263\) | − | 3.05950i | − | 0.188657i | −0.995541 | − | 0.0943285i | \(-0.969930\pi\) | ||
0.995541 | − | 0.0943285i | \(-0.0300704\pi\) | |||||||
\(264\) | −5.96883 | − | 7.62890i | −0.367356 | − | 0.469527i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.84209 | − | 5.66936i | 0.112946 | − | 0.347611i | ||||
\(267\) | −2.21709 | − | 3.05157i | −0.135684 | − | 0.186753i | ||||
\(268\) | 2.09388 | − | 2.88198i | 0.127904 | − | 0.176045i | ||||
\(269\) | 5.46345 | + | 16.8148i | 0.333112 | + | 1.02521i | 0.967644 | + | 0.252318i | \(0.0811928\pi\) |
−0.634532 | + | 0.772896i | \(0.718807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3773 | + | 8.99262i | 0.751866 | + | 0.546263i | 0.896405 | − | 0.443236i | \(-0.146170\pi\) |
−0.144538 | + | 0.989499i | \(0.546170\pi\) | |||||||
\(272\) | −0.239231 | − | 0.329273i | −0.0145055 | − | 0.0199651i | ||||
\(273\) | −2.81168 | − | 0.913569i | −0.170170 | − | 0.0552917i | ||||
\(274\) | −3.24852 | −0.196250 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.31022 | −0.319638 | ||||||||
\(277\) | 16.9514 | + | 5.50785i | 1.01851 | + | 0.330934i | 0.770239 | − | 0.637756i | \(-0.220137\pi\) |
0.248273 | + | 0.968690i | \(0.420137\pi\) | |||||||
\(278\) | 1.49847 | + | 2.06246i | 0.0898721 | + | 0.123698i | ||||
\(279\) | 8.58660 | + | 6.23853i | 0.514066 | + | 0.373491i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.34568 | − | 16.4523i | −0.318896 | − | 0.981462i | −0.974121 | − | 0.226028i | \(-0.927426\pi\) |
0.655224 | − | 0.755434i | \(-0.272574\pi\) | |||||||
\(282\) | −5.69582 | + | 7.83963i | −0.339181 | + | 0.466843i | ||||
\(283\) | 15.1510 | + | 20.8535i | 0.900633 | + | 1.23961i | 0.970266 | + | 0.242042i | \(0.0778171\pi\) |
−0.0696333 | + | 0.997573i | \(0.522183\pi\) | |||||||
\(284\) | 4.48840 | − | 13.8139i | 0.266338 | − | 0.819704i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.21309 | + | 1.53673i | −0.249125 | + | 0.0908688i | ||||
\(287\) | − | 1.64309i | − | 0.0969888i | ||||||
\(288\) | −5.13850 | − | 1.66960i | −0.302789 | − | 0.0983821i | ||||
\(289\) | −13.1451 | + | 9.55045i | −0.773240 | + | 0.561791i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.598859 | + | 1.84310i | 0.0351058 | + | 0.108044i | ||||
\(292\) | 15.7971 | − | 5.13278i | 0.924454 | − | 0.300373i | ||||
\(293\) | 7.95310 | − | 10.9465i | 0.464625 | − | 0.639502i | −0.510835 | − | 0.859679i | \(-0.670664\pi\) |
0.975460 | + | 0.220177i | \(0.0706635\pi\) | |||||||
\(294\) | −2.14035 | + | 1.55506i | −0.124828 | + | 0.0906928i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.1398 | 0.705609 | ||||||||
\(297\) | −0.911987 | + | 3.18877i | −0.0529189 | + | 0.185031i | ||||
\(298\) | 8.50299i | 0.492565i | ||||||||
\(299\) | −2.10613 | + | 6.48199i | −0.121800 | + | 0.374863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.86543 | − | 2.80840i | −0.222800 | − | 0.161873i | ||||
\(302\) | −19.1547 | + | 6.22373i | −1.10223 | + | 0.358135i | ||||
\(303\) | −4.99472 | + | 1.62288i | −0.286939 | + | 0.0932322i | ||||
\(304\) | −1.18808 | − | 0.863188i | −0.0681409 | − | 0.0495073i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.250128 | + | 0.769814i | −0.0142988 | + | 0.0440073i | ||||
\(307\) | 13.0268i | 0.743478i | 0.928337 | + | 0.371739i | \(0.121238\pi\) | ||||
−0.928337 | + | 0.371739i | \(0.878762\pi\) | |||||||
\(308\) | −2.10067 | + | 7.34502i | −0.119697 | + | 0.418521i | ||||
\(309\) | −13.6007 | −0.773714 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.53971 | + | 1.11867i | −0.0873092 | + | 0.0634339i | −0.630584 | − | 0.776121i | \(-0.717184\pi\) |
0.543274 | + | 0.839555i | \(0.317184\pi\) | |||||||
\(312\) | −2.48648 | + | 3.42235i | −0.140769 | + | 0.193752i | ||||
\(313\) | −10.3973 | + | 3.37829i | −0.587691 | + | 0.190952i | −0.587743 | − | 0.809048i | \(-0.699983\pi\) |
5.23383e−5 | 1.00000i | \(0.499983\pi\) | ||||||||
\(314\) | −6.86401 | − | 21.1252i | −0.387358 | − | 1.19217i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5201 | + | 11.2760i | −0.873074 | + | 0.634325i | ||||
\(317\) | 15.2856 | + | 4.96660i | 0.858526 | + | 0.278952i | 0.705013 | − | 0.709194i | \(-0.250941\pi\) |
0.153513 | + | 0.988147i | \(0.450941\pi\) | |||||||
\(318\) | 6.73632i | 0.377754i | ||||||||
\(319\) | 6.35114 | − | 2.31659i | 0.355596 | − | 0.129704i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.08727 | − | 9.50166i | 0.172315 | − | 0.530331i | ||||
\(322\) | −5.27000 | − | 7.25354i | −0.293686 | − | 0.404224i | ||||
\(323\) | 1.59444 | − | 2.19456i | 0.0887170 | − | 0.122108i | ||||
\(324\) | 0.348732 | + | 1.07329i | 0.0193740 | + | 0.0596270i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.36195 | − | 0.989513i | −0.0754313 | − | 0.0548040i | ||||
\(327\) | 3.96863 | + | 5.46235i | 0.219466 | + | 0.302069i | ||||
\(328\) | −2.23602 | − | 0.726528i | −0.123464 | − | 0.0401158i | ||||
\(329\) | 21.1870 | 1.16808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.39579 | 0.0767195 | 0.0383597 | − | 0.999264i | \(-0.487787\pi\) | ||||
0.0383597 | + | 0.999264i | \(0.487787\pi\) | |||||||
\(332\) | 6.59156 | + | 2.14173i | 0.361759 | + | 0.117543i | ||||
\(333\) | −2.44321 | − | 3.36279i | −0.133887 | − | 0.184280i | ||||
\(334\) | 18.5695 | + | 13.4915i | 1.01608 | + | 0.738222i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.296067 | − | 0.911202i | −0.0161518 | − | 0.0497101i | ||||
\(337\) | 1.62429 | − | 2.23564i | 0.0884805 | − | 0.121783i | −0.762482 | − | 0.647009i | \(-0.776019\pi\) |
0.850962 | + | 0.525227i | \(0.176019\pi\) | |||||||
\(338\) | −5.98212 | − | 8.23368i | −0.325384 | − | 0.447853i | ||||
\(339\) | −1.62067 | + | 4.98792i | −0.0880229 | + | 0.270907i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.6913 | − | 27.7241i | −1.17465 | − | 1.50135i | ||||
\(342\) | 2.92057i | 0.157926i | ||||||||
\(343\) | 19.0896 | + | 6.20258i | 1.03074 | + | 0.334908i | ||||
\(344\) | −5.53103 | + | 4.01853i | −0.298213 | + | 0.216664i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.67666 | + | 14.3933i | 0.251419 | + | 0.773787i | ||||
\(347\) | −2.97379 | + | 0.966244i | −0.159642 | + | 0.0518707i | −0.387748 | − | 0.921766i | \(-0.626747\pi\) |
0.228106 | + | 0.973636i | \(0.426747\pi\) | |||||||
\(348\) | 1.35209 | − | 1.86100i | 0.0724798 | − | 0.0997598i | ||||
\(349\) | 10.6205 | − | 7.71626i | 0.568504 | − | 0.413042i | −0.266058 | − | 0.963957i | \(-0.585721\pi\) |
0.834561 | + | 0.550915i | \(0.185721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.44843 | 0.0773117 | ||||||||
\(352\) | 14.8629 | + | 10.0102i | 0.792193 | + | 0.533546i | ||||
\(353\) | 10.7984i | 0.574739i | 0.957820 | + | 0.287370i | \(0.0927808\pi\) | ||||
−0.957820 | + | 0.287370i | \(0.907219\pi\) | |||||||
\(354\) | 2.40114 | − | 7.38995i | 0.127619 | − | 0.392771i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.44375 | + | 2.50203i | 0.182518 | + | 0.132607i | ||||
\(357\) | 1.68313 | − | 0.546881i | 0.0890805 | − | 0.0289440i | ||||
\(358\) | 15.0664 | − | 4.89536i | 0.796282 | − | 0.258728i | ||||
\(359\) | 19.3934 | + | 14.0901i | 1.02354 | + | 0.743649i | 0.967007 | − | 0.254752i | \(-0.0819937\pi\) |
0.0565382 | + | 0.998400i | \(0.481994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.84678 | + | 8.76148i | −0.149830 | + | 0.461131i | ||||
\(362\) | 17.1310i | 0.900388i | ||||||||
\(363\) | 5.81624 | − | 9.33656i | 0.305274 | − | 0.490042i | ||||
\(364\) | 3.33632 | 0.174871 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.62161 | − | 4.81088i | 0.346117 | − | 0.251469i | ||||
\(367\) | −5.21534 | + | 7.17831i | −0.272239 | + | 0.374705i | −0.923144 | − | 0.384455i | \(-0.874390\pi\) |
0.650905 | + | 0.759159i | \(0.274390\pi\) | |||||||
\(368\) | −2.10067 | + | 0.682549i | −0.109505 | + | 0.0355803i | ||||
\(369\) | 0.248762 | + | 0.765612i | 0.0129501 | + | 0.0398562i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.9155 | − | 8.65711i | 0.618621 | − | 0.449455i | ||||
\(372\) | −11.3914 | − | 3.70130i | −0.590619 | − | 0.191904i | ||||
\(373\) | − | 26.3389i | − | 1.36378i | −0.731456 | − | 0.681888i | \(-0.761159\pi\) | ||
0.731456 | − | 0.681888i | \(-0.238841\pi\) | |||||||
\(374\) | 1.49966 | − | 2.22665i | 0.0775456 | − | 0.115137i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.36826 | − | 28.8325i | 0.483131 | − | 1.48693i | ||||
\(377\) | −1.73539 | − | 2.38855i | −0.0893770 | − | 0.123017i | ||||
\(378\) | −1.11997 | + | 1.54151i | −0.0576052 | + | 0.0792868i | ||||
\(379\) | −1.45118 | − | 4.46626i | −0.0745419 | − | 0.229416i | 0.906843 | − | 0.421469i | \(-0.138485\pi\) |
−0.981385 | + | 0.192053i | \(0.938485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7265 | − | 12.1525i | −0.856926 | − | 0.622593i | ||||
\(382\) | 8.44941 | + | 11.6296i | 0.432310 | + | 0.595023i | ||||
\(383\) | −6.56163 | − | 2.13200i | −0.335284 | − | 0.108940i | 0.136537 | − | 0.990635i | \(-0.456403\pi\) |
−0.471820 | + | 0.881695i | \(0.656403\pi\) | |||||||
\(384\) | 5.22091 | 0.266428 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.88892 | 0.350637 | ||||||||
\(387\) | 2.22631 | + | 0.723374i | 0.113170 | + | 0.0367711i | ||||
\(388\) | −1.28549 | − | 1.76933i | −0.0652611 | − | 0.0898242i | ||||
\(389\) | 1.94538 | + | 1.41340i | 0.0986348 | + | 0.0716624i | 0.636009 | − | 0.771681i | \(-0.280584\pi\) |
−0.537375 | + | 0.843344i | \(0.680584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.26077 | − | 3.88025i | −0.0637599 | − | 0.196233i | ||||
\(392\) | 4.86503 | − | 6.69613i | 0.245721 | − | 0.338206i | ||||
\(393\) | 11.9372 | + | 16.4302i | 0.602155 | + | 0.828795i | ||||
\(394\) | 0.907768 | − | 2.79382i | 0.0457327 | − | 0.140751i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.133204 | − | 3.74050i | −0.00669373 | − | 0.187967i | ||||
\(397\) | − | 37.6715i | − | 1.89068i | −0.326091 | − | 0.945338i | \(-0.605732\pi\) | ||
0.326091 | − | 0.945338i | \(-0.394268\pi\) | |||||||
\(398\) | 2.89221 | + | 0.939734i | 0.144973 | + | 0.0471046i | ||||
\(399\) | 5.16602 | − | 3.75334i | 0.258625 | − | 0.187902i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.86791 | − | 11.9042i | −0.193154 | − | 0.594467i | −0.999993 | − | 0.00369578i | \(-0.998824\pi\) |
0.806839 | − | 0.590771i | \(-0.201176\pi\) | |||||||
\(402\) | −2.80259 | + | 0.910618i | −0.139781 | + | 0.0454175i | ||||
\(403\) | −9.03610 | + | 12.4371i | −0.450120 | + | 0.619537i | ||||
\(404\) | 4.79481 | − | 3.48363i | 0.238551 | − | 0.173317i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.88390 | 0.192754 | ||||||||
\(407\) | 4.72402 | + | 12.9514i | 0.234161 | + | 0.641975i | ||||
\(408\) | − | 2.53232i | − | 0.125368i | ||||||
\(409\) | 8.17728 | − | 25.1671i | 0.404340 | − | 1.24443i | −0.517104 | − | 0.855922i | \(-0.672990\pi\) |
0.921445 | − | 0.388510i | \(-0.127010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.81523 | − | 2.04539i | −0.138865 | − | 0.100891i | ||||
\(412\) | 14.5974 | − | 4.74298i | 0.719162 | − | 0.233670i | ||||
\(413\) | −16.1574 | + | 5.24987i | −0.795056 | + | 0.258329i | ||||
\(414\) | 3.55377 | + | 2.58197i | 0.174658 | + | 0.126897i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.41831 | − | 7.44278i | 0.118567 | − | 0.364912i | ||||
\(417\) | 2.73086i | 0.133731i | ||||||||
\(418\) | 2.66352 | − | 9.31304i | 0.130277 | − | 0.455516i | ||||
\(419\) | −30.9711 | −1.51304 | −0.756518 | − | 0.653973i | \(-0.773101\pi\) | ||||
−0.756518 | + | 0.653973i | \(0.773101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7593 | + | 10.7232i | −0.719323 | + | 0.522618i | −0.886168 | − | 0.463365i | \(-0.846642\pi\) |
0.166845 | + | 0.985983i | \(0.446642\pi\) | |||||||
\(422\) | 10.9327 | − | 15.0476i | 0.532196 | − | 0.732505i | ||||
\(423\) | −9.87223 | + | 3.20768i | −0.480004 | + | 0.155963i | ||||
\(424\) | −6.51245 | − | 20.0432i | −0.316272 | − | 0.973386i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.72047 | + | 7.06233i | −0.470958 | + | 0.342171i | ||||
\(427\) | −17.0194 | − | 5.52993i | −0.823625 | − | 0.267612i | ||||
\(428\) | 11.2746i | 0.544979i | ||||||||
\(429\) | −4.61873 | − | 1.32095i | −0.222994 | − | 0.0637763i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.37829 | − | 28.8634i | 0.451736 | − | 1.39030i | −0.423188 | − | 0.906042i | \(-0.639089\pi\) |
0.874924 | − | 0.484260i | \(-0.160911\pi\) | |||||||
\(432\) | 0.275910 | + | 0.379757i | 0.0132747 | + | 0.0182711i | ||||
\(433\) | 7.46560 | − | 10.2755i | 0.358774 | − | 0.493810i | −0.591033 | − | 0.806648i | \(-0.701280\pi\) |
0.949807 | + | 0.312838i | \(0.101280\pi\) | |||||||
\(434\) | −6.24935 | − | 19.2335i | −0.299978 | − | 0.923238i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.16436 | − | 4.47867i | −0.295220 | − | 0.214490i | ||||
\(437\) | −8.65288 | − | 11.9097i | −0.413924 | − | 0.569717i | ||||
\(438\) | −13.0676 | − | 4.24593i | −0.624395 | − | 0.202878i | ||||
\(439\) | 25.6564 | 1.22451 | 0.612257 | − | 0.790659i | \(-0.290262\pi\) | ||||
0.612257 | + | 0.790659i | \(0.290262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83399 | −0.134952 | ||||||||
\(442\) | −1.11502 | − | 0.362294i | −0.0530363 | − | 0.0172325i | ||||
\(443\) | 15.4087 | + | 21.2082i | 0.732088 | + | 1.00763i | 0.999035 | + | 0.0439211i | \(0.0139850\pi\) |
−0.266947 | + | 0.963711i | \(0.586015\pi\) | |||||||
\(444\) | 3.79498 | + | 2.75721i | 0.180102 | + | 0.130851i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.02328 | − | 9.30470i | −0.143157 | − | 0.440590i | ||||
\(447\) | −5.35379 | + | 7.36886i | −0.253226 | + | 0.348535i | ||||
\(448\) | 7.17745 | + | 9.87891i | 0.339103 | + | 0.466735i | ||||
\(449\) | 3.71010 | − | 11.4185i | 0.175091 | − | 0.538873i | −0.824547 | − | 0.565793i | \(-0.808570\pi\) |
0.999638 | + | 0.0269202i | \(0.00856999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0950188 | − | 2.66823i | −0.00447426 | − | 0.125642i | ||||
\(452\) | − | 5.91864i | − | 0.278390i | ||||||
\(453\) | −20.5185 | − | 6.66687i | −0.964044 | − | 0.313237i | ||||
\(454\) | −13.3475 | + | 9.69752i | −0.626429 | + | 0.455127i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.82351 | − | 8.68986i | −0.132223 | − | 0.406940i | ||||
\(457\) | 13.1141 | − | 4.26104i | 0.613453 | − | 0.199323i | 0.0142215 | − | 0.999899i | \(-0.495473\pi\) |
0.599231 | + | 0.800576i | \(0.295473\pi\) | |||||||
\(458\) | −2.26602 | + | 3.11891i | −0.105884 | + | 0.145737i | ||||
\(459\) | −0.701468 | + | 0.509647i | −0.0327417 | + | 0.0237883i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3262 | 0.527515 | 0.263758 | − | 0.964589i | \(-0.415038\pi\) | ||||
0.263758 | + | 0.964589i | \(0.415038\pi\) | |||||||
\(462\) | 4.97718 | − | 3.89413i | 0.231559 | − | 0.181171i | ||||
\(463\) | 6.18784i | 0.287573i | 0.989609 | + | 0.143787i | \(0.0459279\pi\) | ||||
−0.989609 | + | 0.143787i | \(0.954072\pi\) | |||||||
\(464\) | 0.295671 | − | 0.909983i | 0.0137262 | − | 0.0422449i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2705 | + | 7.46197i | 0.475773 | + | 0.345669i | ||||
\(467\) | 8.06770 | − | 2.62135i | 0.373328 | − | 0.121302i | −0.116342 | − | 0.993209i | \(-0.537117\pi\) |
0.489671 | + | 0.871907i | \(0.337117\pi\) | |||||||
\(468\) | −1.55458 | + | 0.505115i | −0.0718607 | + | 0.0233490i | ||||
\(469\) | 5.21246 | + | 3.78707i | 0.240689 | + | 0.174871i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.35274 | − | 22.6294i | 0.338796 | − | 1.04271i | ||||
\(472\) | 24.3094i | 1.11893i | ||||||||
\(473\) | −6.43951 | − | 4.33705i | −0.296089 | − | 0.199418i | ||||
\(474\) | 15.8693 | 0.728899 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.61576 | + | 1.17392i | −0.0740583 | + | 0.0538065i | ||||
\(477\) | −4.24143 | + | 5.83783i | −0.194202 | + | 0.267296i | ||||
\(478\) | 7.10834 | − | 2.30964i | 0.325128 | − | 0.105640i | ||||
\(479\) | −2.85394 | − | 8.78352i | −0.130400 | − | 0.401329i | 0.864446 | − | 0.502725i | \(-0.167669\pi\) |
−0.994846 | + | 0.101396i | \(0.967669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.87078 | − | 3.53883i | 0.222089 | − | 0.161357i | ||||
\(482\) | −0.445645 | − | 0.144799i | −0.0202986 | − | 0.00659541i | ||||
\(483\) | − | 9.60425i | − | 0.437008i | ||||||
\(484\) | −2.98654 | + | 12.0491i | −0.135752 | + | 0.547686i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.288477 | − | 0.887841i | 0.0130856 | − | 0.0402733i | ||||
\(487\) | 11.8561 | + | 16.3185i | 0.537250 | + | 0.739461i | 0.988214 | − | 0.153081i | \(-0.0489196\pi\) |
−0.450964 | + | 0.892542i | \(0.648920\pi\) | |||||||
\(488\) | −15.0509 | + | 20.7158i | −0.681324 | + | 0.937762i | ||||
\(489\) | −0.557258 | − | 1.71506i | −0.0252001 | − | 0.0775578i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.31686 | + | 3.13638i | 0.194817 | + | 0.141543i | 0.680918 | − | 0.732360i | \(-0.261581\pi\) |
−0.486100 | + | 0.873903i | \(0.661581\pi\) | |||||||
\(492\) | −0.533986 | − | 0.734969i | −0.0240740 | − | 0.0331350i | ||||
\(493\) | 1.68087 | + | 0.546149i | 0.0757028 | + | 0.0245973i | ||||
\(494\) | −4.23026 | −0.190328 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.98209 | −0.223702 | ||||||||
\(497\) | 24.9843 | + | 8.11789i | 1.12070 | + | 0.364137i | ||||
\(498\) | −3.36993 | − | 4.63831i | −0.151010 | − | 0.207848i | ||||
\(499\) | −31.7795 | − | 23.0891i | −1.42265 | − | 1.03361i | −0.991328 | − | 0.131412i | \(-0.958049\pi\) |
−0.431317 | − | 0.902200i | \(-0.641951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.59792 | + | 23.3840i | 0.339450 | + | 1.04472i | ||||
\(502\) | −10.1735 | + | 14.0026i | −0.454064 | + | 0.624966i | ||||
\(503\) | −19.0549 | − | 26.2268i | −0.849616 | − | 1.16940i | −0.983947 | − | 0.178460i | \(-0.942889\pi\) |
0.134331 | − | 0.990936i | \(-0.457111\pi\) | |||||||
\(504\) | 1.84209 | − | 5.66936i | 0.0820531 | − | 0.252533i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.97746 | − | 11.4743i | −0.399097 | − | 0.510095i | ||||
\(507\) | − | 10.9020i | − | 0.484176i | ||||||
\(508\) | 22.1903 | + | 7.21007i | 0.984536 | + | 0.319895i | ||||
\(509\) | −13.8064 | + | 10.0309i | −0.611958 | + | 0.444613i | −0.850103 | − | 0.526616i | \(-0.823461\pi\) |
0.238145 | + | 0.971229i | \(0.423461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.28333 | + | 28.5712i | 0.410671 | + | 1.26391i | ||||
\(512\) | 5.01971 | − | 1.63100i | 0.221842 | − | 0.0720808i | ||||
\(513\) | −1.83890 | + | 2.53103i | −0.0811893 | + | 0.111747i | ||||
\(514\) | −5.57376 | + | 4.04958i | −0.245848 | + | 0.178619i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.64174 | −0.116296 | ||||||||
\(517\) | 34.4057 | − | 1.22523i | 1.51316 | − | 0.0538854i | ||||
\(518\) | 7.92011i | 0.347990i | ||||||||
\(519\) | −5.00964 | + | 15.4181i | −0.219899 | + | 0.676779i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.1733 | + | 8.84445i | 0.533324 | + | 0.387482i | 0.821600 | − | 0.570065i | \(-0.193082\pi\) |
−0.288276 | + | 0.957547i | \(0.593082\pi\) | |||||||
\(522\) | −1.80973 | + | 0.588017i | −0.0792097 | + | 0.0257368i | ||||
\(523\) | 35.2287 | − | 11.4465i | 1.54044 | − | 0.500520i | 0.588945 | − | 0.808173i | \(-0.299544\pi\) |
0.951499 | + | 0.307653i | \(0.0995435\pi\) | |||||||
\(524\) | −18.5418 | − | 13.4714i | −0.810003 | − | 0.588502i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.882596 | − | 2.71635i | 0.0384830 | − | 0.118439i | ||||
\(527\) | − | 9.20267i | − | 0.400875i | ||||||
\(528\) | −0.533480 | − | 1.46259i | −0.0232167 | − | 0.0636508i | ||||
\(529\) | 0.858520 | 0.0373270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.73386 | − | 4.89243i | 0.292225 | − | 0.212314i | ||||
\(532\) | −4.23571 | + | 5.82996i | −0.183641 | + | 0.252761i | ||||
\(533\) | −1.10894 | + | 0.360316i | −0.0480335 | + | 0.0156070i | ||||
\(534\) | −1.08812 | − | 3.34888i | −0.0470875 | − | 0.144920i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.45848 | − | 5.41890i | 0.322157 | − | 0.234061i | ||||
\(537\) | 16.1391 | + | 5.24391i | 0.696454 | + | 0.226292i | ||||
\(538\) | 16.5049i | 0.711577i | ||||||||
\(539\) | 9.03696 | + | 2.58457i | 0.389250 | + | 0.111325i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0547265 | − | 0.168431i | 0.00235288 | − | 0.00724141i | −0.949873 | − | 0.312635i | \(-0.898788\pi\) |
0.952226 | + | 0.305394i | \(0.0987882\pi\) | |||||||
\(542\) | 8.39489 | + | 11.5546i | 0.360592 | + | 0.496312i | ||||
\(543\) | −10.7863 | + | 14.8461i | −0.462886 | + | 0.637108i | ||||
\(544\) | 1.44765 | + | 4.45540i | 0.0620674 | + | 0.191024i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.23278 | − | 1.62221i | −0.0955541 | − | 0.0694241i | ||||
\(547\) | 0.712805 | + | 0.981092i | 0.0304773 | + | 0.0419484i | 0.823984 | − | 0.566613i | \(-0.191747\pi\) |
−0.793506 | + | 0.608562i | \(0.791747\pi\) | |||||||
\(548\) | 3.73484 | + | 1.21352i | 0.159544 | + | 0.0518391i | ||||
\(549\) | 8.76752 | 0.374189 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.37702 | 0.271670 | ||||||||
\(552\) | −13.0701 | − | 4.24672i | −0.556298 | − | 0.180752i | ||||
\(553\) | −20.3942 | − | 28.0702i | −0.867249 | − | 1.19367i | ||||
\(554\) | 13.4613 | + | 9.78018i | 0.571914 | + | 0.415520i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.952338 | − | 2.93100i | −0.0403881 | − | 0.124302i | ||||
\(557\) | −1.13940 | + | 1.56825i | −0.0482778 | + | 0.0664488i | −0.832473 | − | 0.554065i | \(-0.813076\pi\) |
0.784196 | + | 0.620514i | \(0.213076\pi\) | |||||||
\(558\) | 5.82386 | + | 8.01586i | 0.246544 | + | 0.339338i | ||||
\(559\) | −1.04776 | + | 3.22467i | −0.0443155 | + | 0.136389i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.70162 | − | 0.985418i | 0.114062 | − | 0.0416044i | ||||
\(562\) | − | 16.1491i | − | 0.681210i | ||||||
\(563\) | −19.9682 | − | 6.48805i | −0.841558 | − | 0.273439i | −0.143652 | − | 0.989628i | \(-0.545885\pi\) |
−0.697906 | + | 0.716190i | \(0.745885\pi\) | |||||||
\(564\) | 9.47710 | − | 6.88552i | 0.399058 | − | 0.289933i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.43590 | + | 22.8853i | 0.312554 | + | 0.961943i | ||||
\(567\) | −1.94118 | + | 0.630728i | −0.0815220 | + | 0.0264881i | ||||
\(568\) | 22.0946 | − | 30.4107i | 0.927071 | − | 1.27600i | ||||
\(569\) | −31.8556 | + | 23.1444i | −1.33546 | + | 0.970265i | −0.335857 | + | 0.941913i | \(0.609026\pi\) |
−0.999598 | + | 0.0283521i | \(0.990974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6796 | 1.28390 | 0.641950 | − | 0.766746i | \(-0.278126\pi\) | ||||
0.641950 | + | 0.766746i | \(0.278126\pi\) | |||||||
\(572\) | 5.41788 | − | 0.192937i | 0.226533 | − | 0.00806709i | ||||
\(573\) | 15.3985i | 0.643282i | ||||||||
\(574\) | 0.473995 | − | 1.45881i | 0.0197842 | − | 0.0608894i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.84004 | − | 3.51650i | −0.201668 | − | 0.146521i | ||||
\(577\) | −33.0053 | + | 10.7241i | −1.37403 | + | 0.446448i | −0.900701 | − | 0.434439i | \(-0.856947\pi\) |
−0.473326 | + | 0.880887i | \(0.656947\pi\) | |||||||
\(578\) | −14.4258 | + | 4.68723i | −0.600035 | + | 0.194963i | ||||
\(579\) | 5.97007 | + | 4.33751i | 0.248108 | + | 0.180261i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.87361 | + | 11.9217i | −0.160704 | + | 0.494597i | ||||
\(582\) | 1.80914i | 0.0749911i | ||||||||
\(583\) | 18.8490 | − | 14.7474i | 0.780646 | − | 0.610775i | ||||
\(584\) | 42.9862 | 1.77878 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2189 | − | 7.42447i | 0.422139 | − | 0.306702i | ||||
\(587\) | −4.73584 | + | 6.51833i | −0.195469 | + | 0.269040i | −0.895489 | − | 0.445083i | \(-0.853174\pi\) |
0.700020 | + | 0.714123i | \(0.253174\pi\) | |||||||
\(588\) | 3.04168 | − | 0.988303i | 0.125437 | − | 0.0407569i | ||||
\(589\) | −10.2609 | − | 31.5797i | −0.422792 | − | 1.30122i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.54578 | − | 1.84962i | 0.104719 | − | 0.0760832i | ||||
\(592\) | 1.85565 | + | 0.602938i | 0.0762669 | + | 0.0247806i | ||||
\(593\) | − | 28.1409i | − | 1.15561i | −0.816175 | − | 0.577805i | \(-0.803909\pi\) | ||
0.816175 | − | 0.577805i | \(-0.196091\pi\) | |||||||
\(594\) | −1.72959 | + | 2.56804i | −0.0709658 | + | 0.105368i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.17639 | − | 9.77593i | 0.130110 | − | 0.400438i | ||||
\(597\) | 1.91475 | + | 2.63543i | 0.0783656 | + | 0.107861i | ||||
\(598\) | −3.73981 | + | 5.14741i | −0.152932 | + | 0.210493i | ||||
\(599\) | 8.83751 | + | 27.1991i | 0.361091 | + | 1.11132i | 0.952393 | + | 0.304873i | \(0.0986141\pi\) |
−0.591302 | + | 0.806450i | \(0.701386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.88649 | + | 4.27679i | 0.240115 | + | 0.174454i | 0.701335 | − | 0.712832i | \(-0.252588\pi\) |
−0.461219 | + | 0.887286i | \(0.652588\pi\) | |||||||
\(602\) | −2.62173 | − | 3.60850i | −0.106854 | − | 0.147072i | ||||
\(603\) | −3.00214 | − | 0.975455i | −0.122257 | − | 0.0397236i | ||||
\(604\) | 24.3472 | 0.990672 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.90268 | −0.199158 | ||||||||
\(607\) | 5.08611 | + | 1.65258i | 0.206439 | + | 0.0670761i | 0.410411 | − | 0.911901i | \(-0.365385\pi\) |
−0.203972 | + | 0.978977i | \(0.565385\pi\) | |||||||
\(608\) | 9.93545 | + | 13.6750i | 0.402936 | + | 0.554593i | ||||
\(609\) | 3.36586 | + | 2.44544i | 0.136392 | + | 0.0990943i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.64612 | − | 14.2993i | −0.187962 | − | 0.578487i | ||||
\(612\) | 0.575146 | − | 0.791621i | 0.0232489 | − | 0.0319994i | ||||
\(613\) | 2.72790 | + | 3.75464i | 0.110179 | + | 0.151648i | 0.860545 | − | 0.509374i | \(-0.170123\pi\) |
−0.750366 | + | 0.661022i | \(0.770123\pi\) | |||||||
\(614\) | −3.75793 | + | 11.5657i | −0.151658 | + | 0.466754i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0444 | + | 16.3983i | −0.444991 | + | 0.660708i | ||||
\(617\) | − | 24.5843i | − | 0.989727i | −0.868971 | − | 0.494864i | \(-0.835218\pi\) | ||
0.868971 | − | 0.494864i | \(-0.164782\pi\) | |||||||
\(618\) | −12.0752 | − | 3.92348i | −0.485737 | − | 0.157825i | ||||
\(619\) | −4.96566 | + | 3.60776i | −0.199587 | + | 0.145008i | −0.683090 | − | 0.730335i | \(-0.739364\pi\) |
0.483503 | + | 0.875343i | \(0.339364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.45407 | + | 4.47517i | 0.0583499 | + | 0.179582i | ||||
\(622\) | −1.68973 | + | 0.549027i | −0.0677521 | + | 0.0220140i | ||||
\(623\) | −4.52526 | + | 6.22849i | −0.181301 | + | 0.249539i | ||||
\(624\) | −0.550053 | + | 0.399637i | −0.0220197 | + | 0.0159983i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.2057 | −0.407902 | ||||||||
\(627\) | 8.17209 | − | 6.39382i | 0.326362 | − | 0.255344i | ||||
\(628\) | 26.8519i | 1.07151i | ||||||||
\(629\) | −1.11372 | + | 3.42767i | −0.0444068 | + | 0.136670i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3265 | + | 10.4088i | 0.570329 | + | 0.414368i | 0.835225 | − | 0.549909i | \(-0.185338\pi\) |
−0.264896 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(632\) | −47.2174 | + | 15.3419i | −1.87821 | + | 0.610266i | ||||
\(633\) | 18.9490 | − | 6.15690i | 0.753155 | − | 0.244715i | ||||
\(634\) | 12.1385 | + | 8.81910i | 0.482080 | + | 0.350251i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.51643 | − | 7.74479i | 0.0997831 | − | 0.307101i | ||||
\(637\) | − | 4.10485i | − | 0.162640i | ||||||
\(638\) | 6.30708 | − | 0.224603i | 0.249700 | − | 0.00889210i | ||||
\(639\) | −12.8707 | −0.509155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.2492 | + | 23.4304i | −1.27377 | + | 0.925444i | −0.999346 | − | 0.0361657i | \(-0.988486\pi\) |
−0.274419 | + | 0.961610i | \(0.588486\pi\) | |||||||
\(642\) | 5.48202 | − | 7.54535i | 0.216358 | − | 0.297791i | ||||
\(643\) | 16.9918 | − | 5.52097i | 0.670091 | − | 0.217726i | 0.0458392 | − | 0.998949i | \(-0.485404\pi\) |
0.624252 | + | 0.781223i | \(0.285404\pi\) | |||||||
\(644\) | 3.34931 | + | 10.3081i | 0.131981 | + | 0.406196i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.04869 | − | 1.48846i | 0.0806045 | − | 0.0585626i | ||||
\(647\) | −4.79404 | − | 1.55768i | −0.188473 | − | 0.0612386i | 0.213260 | − | 0.976996i | \(-0.431592\pi\) |
−0.401733 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(648\) | 2.92057i | 0.114731i | ||||||||
\(649\) | −25.9346 | + | 9.45968i | −1.01802 | + | 0.371325i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.69431 | − | 20.6030i | 0.262371 | − | 0.807494i | ||||
\(652\) | 1.19619 | + | 1.64642i | 0.0468466 | + | 0.0644788i | ||||
\(653\) | 23.9353 | − | 32.9441i | 0.936661 | − | 1.28920i | −0.0205434 | − | 0.999789i | \(-0.506540\pi\) |
0.957204 | − | 0.289414i | \(-0.0934604\pi\) | |||||||
\(654\) | 1.94775 | + | 5.99455i | 0.0761630 | + | 0.234406i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.305709 | − | 0.222111i | −0.0119359 | − | 0.00867196i | ||||
\(657\) | −8.65128 | − | 11.9075i | −0.337519 | − | 0.464554i | ||||
\(658\) | 18.8107 | + | 6.11196i | 0.733316 | + | 0.238269i | ||||
\(659\) | −48.7556 | −1.89925 | −0.949624 | − | 0.313390i | \(-0.898535\pi\) | ||||
−0.949624 | + | 0.313390i | \(0.898535\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0061 | −1.59495 | −0.797477 | − | 0.603350i | \(-0.793832\pi\) | ||||
−0.797477 | + | 0.603350i | \(0.793832\pi\) | |||||||
\(662\) | 1.23924 | + | 0.402653i | 0.0481643 | + | 0.0156495i | ||||
\(663\) | −0.738190 | − | 1.01603i | −0.0286689 | − | 0.0394594i | ||||
\(664\) | 14.5110 | + | 10.5429i | 0.563137 | + | 0.409143i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.19909 | − | 3.69043i | −0.0464640 | − | 0.143001i | ||||
\(667\) | 5.63768 | − | 7.75960i | 0.218292 | − | 0.300453i | ||||
\(668\) | −16.3095 | − | 22.4481i | −0.631033 | − | 0.868542i | ||||
\(669\) | 3.23854 | − | 9.96721i | 0.125209 | − | 0.385355i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.9577 | − | 7.99587i | −1.07929 | − | 0.308677i | ||||
\(672\) | 11.0278i | 0.425408i | ||||||||
\(673\) | −29.0012 | − | 9.42305i | −1.11791 | − | 0.363232i | −0.308942 | − | 0.951081i | \(-0.599975\pi\) |
−0.808971 | + | 0.587849i | \(0.799975\pi\) | |||||||
\(674\) | 2.08704 | − | 1.51632i | 0.0803897 | − | 0.0584065i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.80189 | + | 11.7010i | 0.146226 | + | 0.450038i | ||||
\(677\) | −41.3161 | + | 13.4244i | −1.58791 | + | 0.515943i | −0.964079 | − | 0.265617i | \(-0.914424\pi\) |
−0.623830 | + | 0.781560i | \(0.714424\pi\) | |||||||
\(678\) | −2.87780 | + | 3.96095i | −0.110521 | + | 0.152120i | ||||
\(679\) | 3.20007 | − | 2.32499i | 0.122808 | − | 0.0892249i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.6731 | −0.677235 | ||||||||
\(682\) | −11.2606 | − | 30.8720i | −0.431191 | − | 1.18215i | ||||
\(683\) | − | 43.5970i | − | 1.66819i | −0.551619 | − | 0.834096i | \(-0.685990\pi\) | ||
0.551619 | − | 0.834096i | \(-0.314010\pi\) | |||||||
\(684\) | 1.09101 | − | 3.35779i | 0.0417160 | − | 0.128388i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.1592 | + | 11.0138i | 0.578781 | + | 0.420509i | ||||
\(687\) | −3.92755 | + | 1.27614i | −0.149846 | + | 0.0486878i | ||||
\(688\) | −1.04504 | + | 0.339555i | −0.0398419 | + | 0.0129454i | ||||
\(689\) | −8.45572 | − | 6.14344i | −0.322137 | − | 0.234046i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.56761 | + | 7.90230i | −0.0976766 | + | 0.300618i | −0.987942 | − | 0.154824i | \(-0.950519\pi\) |
0.890265 | + | 0.455442i | \(0.150519\pi\) | |||||||
\(692\) | − | 18.2950i | − | 0.695473i | ||||||
\(693\) | 6.76521 | − | 0.240917i | 0.256989 | − | 0.00915167i | ||||
\(694\) | −2.91900 | −0.110804 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.81619 | − | 3.49917i | 0.182557 | − | 0.132636i | ||||
\(697\) | 0.410272 | − | 0.564690i | 0.0155401 | − | 0.0213892i | ||||
\(698\) | 11.6553 | − | 3.78704i | 0.441160 | − | 0.143342i | ||||
\(699\) | 4.20231 | + | 12.9334i | 0.158946 | + | 0.489186i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.35189 | + | 5.34146i | −0.277677 | + | 0.201744i | −0.717904 | − | 0.696143i | \(-0.754898\pi\) |
0.440226 | + | 0.897887i | \(0.354898\pi\) | |||||||
\(702\) | 1.28598 | + | 0.417840i | 0.0485362 | + | 0.0157704i | ||||
\(703\) | 13.0041i | 0.490460i | ||||||||
\(704\) | 12.2268 | + | 15.6274i | 0.460815 | + | 0.588979i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.11508 | + | 9.58724i | −0.117238 | + | 0.360821i | ||||
\(707\) | 6.30062 | + | 8.67206i | 0.236959 | + | 0.326147i | ||||
\(708\) | −5.52121 | + | 7.59929i | −0.207500 | + | 0.285599i | ||||
\(709\) | 1.50049 | + | 4.61802i | 0.0563520 | + | 0.173434i | 0.975271 | − | 0.221013i | \(-0.0709363\pi\) |
−0.918919 | + | 0.394447i | \(0.870936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.7526 | + | 9.99186i | 0.515764 | + | 0.374724i | ||||
\(712\) | 6.47517 | + | 8.91231i | 0.242667 | + | 0.334003i | ||||
\(713\) | −47.4977 | − | 15.4330i | −1.77880 | − | 0.577969i | ||||
\(714\) | 1.65211 | 0.0618287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.1506 | −0.715691 | ||||||||
\(717\) | 7.61447 | + | 2.47409i | 0.284367 | + | 0.0923966i | ||||
\(718\) | 13.1536 | + | 18.1043i | 0.490887 | + | 0.675648i | ||||
\(719\) | 19.3383 | + | 14.0501i | 0.721196 | + | 0.523980i | 0.886766 | − | 0.462218i | \(-0.152946\pi\) |
−0.165570 | + | 0.986198i | \(0.552946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.57832 | + | 26.4014i | 0.319473 | + | 0.983238i | ||||
\(722\) | −5.05497 | + | 6.95757i | −0.188127 | + | 0.258934i | ||||
\(723\) | −0.295035 | − | 0.406080i | −0.0109725 | − | 0.0151023i | ||||
\(724\) | 6.39951 | − | 19.6957i | 0.237836 | − | 0.731983i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.85728 | − | 6.61153i | 0.291611 | − | 0.245377i | ||||
\(727\) | 11.3674i | 0.421592i | 0.977530 | + | 0.210796i | \(0.0676055\pi\) | ||||
−0.977530 | + | 0.210796i | \(0.932394\pi\) | |||||||
\(728\) | 8.21170 | + | 2.66814i | 0.304346 | + | 0.0988879i | ||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.627210 | − | 1.93035i | −0.0231982 | − | 0.0713967i | ||||
\(732\) | −9.41006 | + | 3.05751i | −0.347806 | + | 0.113009i | ||||
\(733\) | −20.0539 | + | 27.6019i | −0.740709 | + | 1.01950i | 0.257869 | + | 0.966180i | \(0.416980\pi\) |
−0.998578 | + | 0.0533185i | \(0.983020\pi\) | |||||||
\(734\) | −6.70117 | + | 4.86869i | −0.247345 | + | 0.179707i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.4234 | 0.937118 | ||||||||
\(737\) | 8.68355 | + | 5.84842i | 0.319863 | + | 0.215429i | ||||
\(738\) | 0.751504i | 0.0276632i | ||||||||
\(739\) | −0.722631 | + | 2.22403i | −0.0265824 | + | 0.0818123i | −0.963468 | − | 0.267825i | \(-0.913695\pi\) |
0.936885 | + | 0.349637i | \(0.113695\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.66602 | − | 2.66352i | −0.134675 | − | 0.0978470i | ||||
\(742\) | 13.0764 | − | 4.24879i | 0.480051 | − | 0.155978i | ||||
\(743\) | −13.7794 | + | 4.47721i | −0.505518 | + | 0.164253i | −0.550663 | − | 0.834728i | \(-0.685625\pi\) |
0.0451450 | + | 0.998980i | \(0.485625\pi\) | |||||||
\(744\) | −25.0778 | − | 18.2201i | −0.919395 | − | 0.667980i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.59817 | − | 23.3848i | 0.278189 | − | 0.856177i | ||||
\(747\) | − | 6.14148i | − | 0.224705i | ||||||
\(748\) | −2.55596 | + | 1.99977i | −0.0934551 | + | 0.0731190i | ||||
\(749\) | −20.3917 | −0.745096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.9567 | + | 19.5852i | −0.983663 | + | 0.714673i | −0.958524 | − | 0.285011i | \(-0.908003\pi\) |
−0.0251387 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(752\) | 2.86402 | − | 3.94198i | 0.104440 | − | 0.143749i | ||||
\(753\) | −17.6331 | + | 5.72933i | −0.642585 | + | 0.208788i | ||||
\(754\) | −0.851704 | − | 2.62128i | −0.0310172 | − | 0.0954612i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.86349 | − | 1.35390i | 0.0677744 | − | 0.0492410i | ||||
\(757\) | −38.4015 | − | 12.4774i | −1.39573 | − | 0.453499i | −0.487921 | − | 0.872888i | \(-0.662244\pi\) |
−0.907807 | + | 0.419389i | \(0.862244\pi\) | |||||||
\(758\) | − | 4.38396i | − | 0.159233i | ||||||
\(759\) | −0.555406 | − | 15.5964i | −0.0201600 | − | 0.566114i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.4190 | + | 47.4549i | −0.558940 | + | 1.72024i | 0.126364 | + | 0.991984i | \(0.459669\pi\) |
−0.685304 | + | 0.728257i | \(0.740331\pi\) | |||||||
\(762\) | −11.3448 | − | 15.6147i | −0.410978 | − | 0.565662i | ||||
\(763\) | 8.10029 | − | 11.1491i | 0.293250 | − | 0.403624i | ||||
\(764\) | −5.36995 | − | 16.5270i | −0.194278 | − | 0.597926i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.21065 | − | 3.78576i | −0.188268 | − | 0.136785i | ||||
\(767\) | 7.08637 | + | 9.75356i | 0.255874 | + | 0.352180i | ||||
\(768\) | 16.0150 | + | 5.20358i | 0.577890 | + | 0.187768i | ||||
\(769\) | −4.93932 | −0.178116 | −0.0890582 | − | 0.996026i | \(-0.528386\pi\) | ||||
−0.0890582 | + | 0.996026i | \(0.528386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.38010 | −0.265788 | ||||||||
\(772\) | −7.92022 | − | 2.57344i | −0.285055 | − | 0.0926200i | ||||
\(773\) | 19.6738 | + | 27.0786i | 0.707616 | + | 0.973950i | 0.999845 | + | 0.0176019i | \(0.00560313\pi\) |
−0.292229 | + | 0.956348i | \(0.594397\pi\) | |||||||
\(774\) | 1.76794 | + | 1.28448i | 0.0635472 | + | 0.0461697i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.74901 | − | 5.38290i | −0.0627858 | − | 0.193235i | ||||
\(777\) | −4.98679 | + | 6.86373i | −0.178900 | + | 0.246235i | ||||
\(778\) | 1.31946 | + | 1.81607i | 0.0473048 | + | 0.0651094i | ||||
\(779\) | 0.778258 | − | 2.39523i | 0.0278840 | − | 0.0858181i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.0416 | + | 11.7379i | 1.46858 | + | 0.420014i | ||||
\(782\) | − | 3.80875i | − | 0.136201i | ||||||
\(783\) | −1.93859 | − | 0.629885i | −0.0692794 | − | 0.0225102i | ||||
\(784\) | 1.07623 | − | 0.781926i | 0.0384367 | − | 0.0279259i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.85864 | + | 18.0310i | 0.208971 | + | 0.643146i | ||||
\(787\) | 24.6704 | − | 8.01590i | 0.879405 | − | 0.285736i | 0.165695 | − | 0.986177i | \(-0.447013\pi\) |
0.713710 | + | 0.700441i | \(0.247013\pi\) | |||||||
\(788\) | −2.08733 | + | 2.87296i | −0.0743581 | + | 0.102345i | ||||
\(789\) | 2.47519 | − | 1.79833i | 0.0881191 | − | 0.0640222i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7047 | 0.380614 | ||||||||
\(792\) | 2.66352 | − | 9.31304i | 0.0946442 | − | 0.330924i | ||||
\(793\) | 12.6992i | 0.450961i | ||||||||
\(794\) | 10.8674 | − | 33.4463i | 0.385668 | − | 1.18696i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.97413 | − | 2.16083i | −0.105415 | − | 0.0765888i | ||||
\(797\) | 9.37993 | − | 3.04772i | 0.332254 | − | 0.107956i | −0.138139 | − | 0.990413i | \(-0.544112\pi\) |
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(798\) | 5.66936 | − | 1.84209i | 0.200693 | − | 0.0652092i | ||||
\(799\) | 7.28144 | + | 5.29027i | 0.257599 | + | 0.187156i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.16559 | − | 3.58733i | 0.0411842 | − | 0.126752i | ||||
\(802\) | − | 11.6848i | − | 0.412606i | ||||||
\(803\) | 16.7275 | + | 45.8601i | 0.590301 | + | 1.61837i | ||||
\(804\) | 3.56233 | 0.125634 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.6104 | + | 8.43548i | −0.408960 | + | 0.297127i | ||||
\(807\) | −10.3921 | + | 14.3035i | −0.365819 | + | 0.503507i | ||||
\(808\) | 14.5874 | − | 4.73974i | 0.513184 | − | 0.166744i | ||||
\(809\) | 10.2158 | + | 31.4410i | 0.359168 | + | 1.10541i | 0.953553 | + | 0.301225i | \(0.0973956\pi\) |
−0.594385 | + | 0.804181i | \(0.702604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.21750 | + | 3.06419i | −0.148096 | + | 0.107598i | −0.659366 | − | 0.751822i | \(-0.729175\pi\) |
0.511270 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(812\) | −4.46533 | − | 1.45088i | −0.156703 | − | 0.0509157i | ||||
\(813\) | 15.2992i | 0.536565i | ||||||||
\(814\) | 0.458013 | + | 12.8615i | 0.0160534 | + | 0.450796i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.125771 | − | 0.387084i | 0.00440287 | − | 0.0135506i | ||||
\(817\) | −4.30465 | − | 5.92484i | −0.150601 | − | 0.207284i | ||||
\(818\) | 14.5202 | − | 19.9854i | 0.507689 | − | 0.698773i | ||||
\(819\) | −0.913569 | − | 2.81168i | −0.0319227 | − | 0.0982479i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.32625 | + | 0.963576i | 0.0462864 | + | 0.0336290i | 0.610688 | − | 0.791871i | \(-0.290893\pi\) |
−0.564401 | + | 0.825500i | \(0.690893\pi\) | |||||||
\(822\) | −1.90943 | − | 2.62811i | −0.0665991 | − | 0.0916657i | ||||
\(823\) | −17.0139 | − | 5.52814i | −0.593066 | − | 0.192699i | −0.00292037 | − | 0.999996i | \(-0.500930\pi\) |
−0.590145 | + | 0.807297i | \(0.700930\pi\) | |||||||
\(824\) | 39.7217 | 1.38377 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.8597 | −0.551830 | ||||||||
\(827\) | −33.8052 | − | 10.9840i | −1.17552 | − | 0.381951i | −0.344821 | − | 0.938668i | \(-0.612061\pi\) |
−0.830702 | + | 0.556718i | \(0.812061\pi\) | |||||||
\(828\) | −3.12127 | − | 4.29606i | −0.108472 | − | 0.149298i | ||||
\(829\) | −21.8039 | − | 15.8415i | −0.757282 | − | 0.550198i | 0.140793 | − | 0.990039i | \(-0.455035\pi\) |
−0.898076 | + | 0.439841i | \(0.855035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.50785 | + | 16.9514i | 0.191065 | + | 0.588038i | ||||
\(832\) | 5.09342 | − | 7.01049i | 0.176582 | − | 0.243045i | ||||
\(833\) | 1.44433 | + | 1.98796i | 0.0500432 | + | 0.0688786i | ||||
\(834\) | −0.787791 | + | 2.42457i | −0.0272790 | + | 0.0839560i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.54126 | + | 9.71226i | −0.226234 | + | 0.335905i | ||||
\(837\) | 10.6136i | 0.366860i | ||||||||
\(838\) | −27.4974 | − | 8.93444i | −0.949881 | − | 0.308635i | ||||
\(839\) | −9.57654 | + | 6.95776i | −0.330619 | + | 0.240209i | −0.740693 | − | 0.671843i | \(-0.765503\pi\) |
0.410074 | + | 0.912052i | \(0.365503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.67757 | − | 23.6291i | −0.264744 | − | 0.814797i | ||||
\(842\) | −16.1973 | + | 5.26282i | −0.558195 | + | 0.181369i | ||||
\(843\) | 10.1681 | − | 13.9952i | 0.350207 | − | 0.482019i | ||||
\(844\) | −18.1906 | + | 13.2162i | −0.626146 | + | 0.454922i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.69031 | −0.333160 | ||||||||
\(847\) | −21.7924 | − | 5.40155i | −0.748797 | − | 0.185600i | ||||
\(848\) | − | 3.38721i | − | 0.116317i | ||||||
\(849\) | −7.96534 | + | 24.5148i | −0.273370 | + | 0.841346i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8235 | + | 11.4965i | 0.542423 | + | 0.394094i | ||||
\(852\) | 13.8139 | − | 4.48840i | 0.473256 | − | 0.153770i | ||||
\(853\) | 28.8211 | − | 9.36453i | 0.986814 | − | 0.320635i | 0.229230 | − | 0.973372i | \(-0.426379\pi\) |
0.757585 | + | 0.652737i | \(0.226379\pi\) | |||||||
\(854\) | −13.5152 | − | 9.81939i | −0.462482 | − | 0.336013i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.01660 | + | 27.7503i | −0.308181 | + | 0.948484i | ||||
\(857\) | 29.2318i | 0.998540i | 0.866446 | + | 0.499270i | \(0.166398\pi\) | ||||
−0.866446 | + | 0.499270i | \(0.833602\pi\) | |||||||
\(858\) | −3.71963 | − | 2.50519i | −0.126986 | − | 0.0855259i | ||||
\(859\) | 36.7151 | 1.25270 | 0.626351 | − | 0.779541i | \(-0.284548\pi\) | ||||
0.626351 | + | 0.779541i | \(0.284548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.32929 | − | 0.965786i | 0.0453021 | − | 0.0329139i | ||||
\(862\) | 16.6529 | − | 22.9207i | 0.567199 | − | 0.780682i | ||||
\(863\) | −41.4431 | + | 13.4657i | −1.41074 | + | 0.458377i | −0.912647 | − | 0.408748i | \(-0.865966\pi\) |
−0.498091 | + | 0.867125i | \(0.665966\pi\) | |||||||
\(864\) | −1.66960 | − | 5.13850i | −0.0568009 | − | 0.174815i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.59252 | − | 6.96937i | 0.325967 | − | 0.236829i | ||||
\(867\) | −15.4530 | − | 5.02097i | −0.524810 | − | 0.170521i | ||||
\(868\) | 24.4474i | 0.829798i | ||||||||
\(869\) | −34.7415 | − | 44.4040i | −1.17853 | − | 1.50630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.41288 | − | 4.34841i | 0.0478737 | − | 0.147340i | ||||
\(872\) | −11.5907 | − | 15.9532i | −0.392509 | − | 0.540243i | ||||
\(873\) | −1.13910 | + | 1.56783i | −0.0385526 | + | 0.0530631i | ||||
\(874\) | −4.24672 | − | 13.0701i | −0.143647 | − | 0.442101i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.4378 | + | 9.76314i | 0.454021 | + | 0.329866i | ||||
\(877\) | −6.53457 | − | 8.99407i | −0.220657 | − | 0.303708i | 0.684309 | − | 0.729192i | \(-0.260104\pi\) |
−0.904966 | + | 0.425484i | \(0.860104\pi\) | |||||||
\(878\) | 22.7788 | + | 7.40129i | 0.768748 | + | 0.249781i | ||||
\(879\) | 13.5306 | 0.456377 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.1155 | −1.31783 | −0.658917 | − | 0.752216i | \(-0.728985\pi\) | ||||
−0.658917 | + | 0.752216i | \(0.728985\pi\) | |||||||
\(882\) | −2.51613 | − | 0.817542i | −0.0847227 | − | 0.0275281i | ||||
\(883\) | −11.4728 | − | 15.7910i | −0.386091 | − | 0.531408i | 0.571094 | − | 0.820884i | \(-0.306519\pi\) |
−0.957185 | + | 0.289476i | \(0.906519\pi\) | |||||||
\(884\) | 1.14661 | + | 0.833061i | 0.0385647 | + | 0.0280189i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.56236 | + | 23.2746i | 0.254063 | + | 0.781924i | ||||
\(887\) | 3.05124 | − | 4.19967i | 0.102451 | − | 0.141011i | −0.754714 | − | 0.656054i | \(-0.772224\pi\) |
0.857164 | + | 0.515043i | \(0.172224\pi\) | |||||||
\(888\) | 7.13557 | + | 9.82127i | 0.239454 | + | 0.329580i | ||||
\(889\) | −13.0404 | + | 40.1342i | −0.437361 | + | 1.34606i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.11582 | + | 1.13650i | −0.104384 | + | 0.0380742i | ||||
\(892\) | 11.8270i | 0.395999i | ||||||||
\(893\) | 30.8855 | + | 10.0353i | 1.03354 | + | 0.335818i | ||||
\(894\) | −6.87906 | + | 4.99793i | −0.230070 | + | 0.167156i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.29298 | − | 10.1347i | −0.110011 | − | 0.338578i | ||||
\(897\) | −6.48199 | + | 2.10613i | −0.216427 | + | 0.0703215i | ||||
\(898\) | 6.58796 | − | 9.06755i | 0.219843 | − | 0.302588i | ||||
\(899\) | 17.5025 | − | 12.7163i | 0.583740 | − | 0.424112i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.25669 | 0.208440 | ||||||||
\(902\) | 0.685362 | − | 2.39638i | 0.0228201 | − | 0.0797906i | ||||
\(903\) | − | 4.77794i | − | 0.159000i | ||||||
\(904\) | 4.73329 | − | 14.5676i | 0.157427 | − | 0.484510i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.2939 | − | 11.8382i | −0.541330 | − | 0.393299i | ||||
\(907\) | −40.3608 | + | 13.1140i | −1.34016 | + | 0.435444i | −0.889371 | − | 0.457187i | \(-0.848857\pi\) |
−0.450789 | + | 0.892631i | \(0.648857\pi\) | |||||||
\(908\) | 18.9683 | − | 6.16318i | 0.629485 | − | 0.204532i | ||||
\(909\) | −4.24876 | − | 3.08691i | −0.140923 | − | 0.102386i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.10306 | + | 18.7833i | −0.202203 | + | 0.622318i | 0.797613 | + | 0.603169i | \(0.206096\pi\) |
−0.999817 | + | 0.0191487i | \(0.993904\pi\) | |||||||
\(912\) | − | 1.46854i | − | 0.0486283i | ||||||
\(913\) | −5.60095 | + | 19.5838i | −0.185364 | + | 0.648129i | ||||
\(914\) | 12.8725 | 0.425783 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.77036 | − | 2.73932i | 0.124576 | − | 0.0905098i | ||||
\(917\) | 24.3649 | − | 33.5354i | 0.804599 | − | 1.10744i | ||||
\(918\) | −0.769814 | + | 0.250128i | −0.0254076 | + | 0.00825544i | ||||
\(919\) | 7.56638 | + | 23.2869i | 0.249592 | + | 0.768165i | 0.994847 | + | 0.101385i | \(0.0323275\pi\) |
−0.745255 | + | 0.666779i | \(0.767672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5389 | + | 7.65695i | −0.347268 | + | 0.252305i | ||||
\(922\) | 10.0559 | + | 3.26736i | 0.331173 | + | 0.107605i | ||||
\(923\) | − | 18.6423i | − | 0.613619i | ||||||
\(924\) | −7.17699 | + | 2.61781i | −0.236105 | + | 0.0861198i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.78505 | + | 5.49382i | −0.0586604 | + | 0.180538i | ||||
\(927\) | −7.99426 | − | 11.0032i | −0.262566 | − | 0.361391i | ||||
\(928\) | −6.47332 | + | 8.90976i | −0.212497 | + | 0.292477i | ||||
\(929\) | 1.87044 | + | 5.75664i | 0.0613673 | + | 0.188869i | 0.977040 | − | 0.213055i | \(-0.0683415\pi\) |
−0.915673 | + | 0.401924i | \(0.868341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.17291 | + | 5.21142i | 0.235083 | + | 0.170797i | ||||
\(932\) | −9.02056 | − | 12.4157i | −0.295478 | − | 0.406691i | ||||
\(933\) | −1.81004 | − | 0.588119i | −0.0592582 | − | 0.0192541i | ||||
\(934\) | 7.91903 | 0.259119 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.23026 | −0.138270 | ||||||||
\(937\) | −6.50394 | − | 2.11326i | −0.212475 | − | 0.0690372i | 0.200846 | − | 0.979623i | \(-0.435631\pi\) |
−0.413320 | + | 0.910586i | \(0.635631\pi\) | |||||||
\(938\) | 3.53535 | + | 4.86599i | 0.115433 | + | 0.158880i | ||||
\(939\) | −8.84448 | − | 6.42589i | −0.288629 | − | 0.209701i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.22191 | − | 3.76064i | −0.0398330 | − | 0.122593i | 0.929163 | − | 0.369671i | \(-0.120530\pi\) |
−0.968996 | + | 0.247078i | \(0.920530\pi\) | |||||||
\(942\) | 13.0561 | − | 17.9702i | 0.425391 | − | 0.585501i | ||||
\(943\) | −2.22651 | − | 3.06453i | −0.0725051 | − | 0.0997947i | ||||
\(944\) | −1.20736 | + | 3.71587i | −0.0392962 | + | 0.120941i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.46612 | − | 5.70826i | −0.145206 | − | 0.185591i | ||||
\(947\) | 40.1742i | 1.30549i | 0.757579 | + | 0.652743i | \(0.226382\pi\) | ||||
−0.757579 | + | 0.652743i | \(0.773618\pi\) | |||||||
\(948\) | −18.2450 | − | 5.92815i | −0.592569 | − | 0.192537i | ||||
\(949\) | 17.2472 | − | 12.5308i | 0.559867 | − | 0.406767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.96660 | + | 15.2856i | 0.161053 | + | 0.495670i | ||||
\(952\) | −4.91569 | + | 1.59720i | −0.159318 | + | 0.0517657i | ||||
\(953\) | −24.2444 | + | 33.3696i | −0.785353 | + | 1.08095i | 0.209318 | + | 0.977848i | \(0.432876\pi\) |
−0.994671 | + | 0.103098i | \(0.967124\pi\) | |||||||
\(954\) | −5.44980 | + | 3.95951i | −0.176444 | + | 0.128194i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.03529 | −0.292222 | ||||||||
\(957\) | 5.60726 | + | 3.77652i | 0.181257 | + | 0.122078i | ||||
\(958\) | − | 8.62166i | − | 0.278553i | ||||||
\(959\) | −2.19482 | + | 6.75496i | −0.0708744 | + | 0.218129i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −66.0553 | − | 47.9920i | −2.13082 | − | 1.54813i | ||||
\(962\) | 5.34535 | − | 1.73681i | 0.172341 | − | 0.0559970i | ||||
\(963\) | 9.50166 | − | 3.08727i | 0.306187 | − | 0.0994860i | ||||
\(964\) | 0.458269 | + | 0.332952i | 0.0147599 | + | 0.0107237i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.77060 | − | 8.52704i | 0.0891427 | − | 0.274353i | ||||
\(967\) | − | 9.16826i | − | 0.294831i | −0.989075 | − | 0.147416i | \(-0.952904\pi\) | ||
0.989075 | − | 0.147416i | \(-0.0470955\pi\) | |||||||
\(968\) | −16.9867 | + | 27.2681i | −0.545975 | + | 0.876429i | ||||
\(969\) | 2.71262 | 0.0871420 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.00359 | − | 2.18224i | 0.0963899 | − | 0.0700313i | −0.538546 | − | 0.842596i | \(-0.681026\pi\) |
0.634936 | + | 0.772565i | \(0.281026\pi\) | |||||||
\(972\) | −0.663327 | + | 0.912991i | −0.0212762 | + | 0.0292842i | ||||
\(973\) | 5.30110 | − | 1.72243i | 0.169946 | − | 0.0552186i | ||||
\(974\) | 5.81880 | + | 17.9084i | 0.186446 | + | 0.573823i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.32953 | + | 2.41904i | −0.106576 | + | 0.0774317i | ||||
\(977\) | −11.7867 | − | 3.82972i | −0.377089 | − | 0.122524i | 0.114339 | − | 0.993442i | \(-0.463525\pi\) |
−0.491428 | + | 0.870918i | \(0.663525\pi\) | |||||||
\(978\) | − | 1.68346i | − | 0.0538311i | ||||||
\(979\) | −6.98842 | + | 10.3762i | −0.223351 | + | 0.331624i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.08643 | + | 6.42137i | −0.0666146 | + | 0.205019i | ||||
\(982\) | 2.92791 | + | 4.02993i | 0.0934335 | + | 0.128600i | ||||
\(983\) | 13.6924 | − | 18.8460i | 0.436720 | − | 0.601093i | −0.532760 | − | 0.846267i | \(-0.678845\pi\) |
0.969479 | + | 0.245174i | \(0.0788450\pi\) | |||||||
\(984\) | −0.726528 | − | 2.23602i | −0.0231609 | − | 0.0712818i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.33480 | + | 0.969788i | 0.0425086 | + | 0.0308843i | ||||
\(987\) | 12.4534 | + | 17.1406i | 0.396396 | + | 0.545592i | ||||
\(988\) | 4.86355 | + | 1.58026i | 0.154730 | + | 0.0502748i | ||||
\(989\) | −11.0150 | −0.350256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7826 | −1.20020 | −0.600101 | − | 0.799924i | \(-0.704873\pi\) | ||||
−0.600101 | + | 0.799924i | \(0.704873\pi\) | |||||||
\(992\) | 54.5380 | + | 17.7205i | 1.73158 | + | 0.562626i | ||||
\(993\) | 0.820424 | + | 1.12922i | 0.0260354 | + | 0.0358346i | ||||
\(994\) | 19.8403 | + | 14.4148i | 0.629295 | + | 0.457209i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.14173 | + | 6.59156i | 0.0678633 | + | 0.208862i | ||||
\(997\) | −4.62934 | + | 6.37174i | −0.146613 | + | 0.201795i | −0.876007 | − | 0.482299i | \(-0.839802\pi\) |
0.729394 | + | 0.684094i | \(0.239802\pi\) | |||||||
\(998\) | −21.5544 | − | 29.6671i | −0.682294 | − | 0.939097i | ||||
\(999\) | 1.28447 | − | 3.95320i | 0.0406389 | − | 0.125074i |
(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 | 825.2.bx.g.724.3 | 16 | ||
5.2 | odd | 4 | 165.2.m.b.31.1 | yes | 8 | ||
5.3 | odd | 4 | 825.2.n.i.526.2 | 8 | |||
5.4 | even | 2 | inner | 825.2.bx.g.724.2 | 16 | ||
11.5 | even | 5 | inner | 825.2.bx.g.49.2 | 16 | ||
15.2 | even | 4 | 495.2.n.b.361.2 | 8 | |||
55.7 | even | 20 | 1815.2.a.r.1.3 | 4 | |||
55.18 | even | 20 | 9075.2.a.dg.1.2 | 4 | |||
55.27 | odd | 20 | 165.2.m.b.16.1 | ✓ | 8 | ||
55.37 | odd | 20 | 1815.2.a.v.1.2 | 4 | |||
55.38 | odd | 20 | 825.2.n.i.676.2 | 8 | |||
55.48 | odd | 20 | 9075.2.a.cq.1.3 | 4 | |||
55.49 | even | 10 | inner | 825.2.bx.g.49.3 | 16 | ||
165.62 | odd | 20 | 5445.2.a.br.1.2 | 4 | |||
165.92 | even | 20 | 5445.2.a.bk.1.3 | 4 | |||
165.137 | even | 20 | 495.2.n.b.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.b.16.1 | ✓ | 8 | 55.27 | odd | 20 | ||
165.2.m.b.31.1 | yes | 8 | 5.2 | odd | 4 | ||
495.2.n.b.181.2 | 8 | 165.137 | even | 20 | |||
495.2.n.b.361.2 | 8 | 15.2 | even | 4 | |||
825.2.n.i.526.2 | 8 | 5.3 | odd | 4 | |||
825.2.n.i.676.2 | 8 | 55.38 | odd | 20 | |||
825.2.bx.g.49.2 | 16 | 11.5 | even | 5 | inner | ||
825.2.bx.g.49.3 | 16 | 55.49 | even | 10 | inner | ||
825.2.bx.g.724.2 | 16 | 5.4 | even | 2 | inner | ||
825.2.bx.g.724.3 | 16 | 1.1 | even | 1 | trivial | ||
1815.2.a.r.1.3 | 4 | 55.7 | even | 20 | |||
1815.2.a.v.1.2 | 4 | 55.37 | odd | 20 | |||
5445.2.a.bk.1.3 | 4 | 165.92 | even | 20 | |||
5445.2.a.br.1.2 | 4 | 165.62 | odd | 20 | |||
9075.2.a.cq.1.3 | 4 | 55.48 | odd | 20 | |||
9075.2.a.dg.1.2 | 4 | 55.18 | even | 20 |