Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (of order \(6\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.10 | ||
Character | \(\chi\) | \(=\) | 1110.529 |
Dual form | 1110.2.ba.b.619.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.02746 | + | 0.943089i | 0.906706 | + | 0.421762i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 3.31268 | + | 1.91258i | 1.25208 | + | 0.722886i | 0.971521 | − | 0.236952i | \(-0.0761485\pi\) |
0.280554 | + | 0.959838i | \(0.409482\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0.196990 | + | 2.22737i | 0.0622936 | + | 0.704358i | ||||
\(11\) | 1.67653 | 0.505494 | 0.252747 | − | 0.967532i | \(-0.418666\pi\) | ||||
0.252747 | + | 0.967532i | \(0.418666\pi\) | |||||||
\(12\) | −0.866025 | + | 0.500000i | −0.250000 | + | 0.144338i | ||||
\(13\) | −1.56010 | + | 2.70218i | −0.432694 | + | 0.749449i | −0.997104 | − | 0.0760461i | \(-0.975770\pi\) |
0.564410 | + | 0.825495i | \(0.309104\pi\) | |||||||
\(14\) | 3.82515i | 1.02232i | ||||||||
\(15\) | 1.28429 | + | 1.83047i | 0.331601 | + | 0.472625i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.75979 | − | 4.78010i | −0.669348 | − | 1.15935i | −0.978087 | − | 0.208199i | \(-0.933240\pi\) |
0.308738 | − | 0.951147i | \(-0.400093\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | −1.27752 | − | 0.737577i | −0.293083 | − | 0.169212i | 0.346248 | − | 0.938143i | \(-0.387455\pi\) |
−0.639331 | + | 0.768931i | \(0.720789\pi\) | |||||||
\(20\) | −1.83047 | + | 1.28429i | −0.409305 | + | 0.287175i | ||||
\(21\) | 1.91258 | + | 3.31268i | 0.417358 | + | 0.722886i | ||||
\(22\) | 0.838266 | + | 1.45192i | 0.178719 | + | 0.309550i | ||||
\(23\) | 1.21394 | 0.253124 | 0.126562 | − | 0.991959i | \(-0.459606\pi\) | ||||
0.126562 | + | 0.991959i | \(0.459606\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 3.22117 | + | 3.82415i | 0.644233 | + | 0.764829i | ||||
\(26\) | −3.12020 | −0.611922 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −3.31268 | + | 1.91258i | −0.626038 | + | 0.361443i | ||||
\(29\) | − | 2.97019i | − | 0.551551i | −0.961222 | − | 0.275775i | \(-0.911065\pi\) | ||
0.961222 | − | 0.275775i | \(-0.0889346\pi\) | |||||||
\(30\) | −0.943089 | + | 2.02746i | −0.172184 | + | 0.370161i | ||||
\(31\) | − | 5.65752i | − | 1.01612i | −0.861322 | − | 0.508060i | \(-0.830363\pi\) | ||
0.861322 | − | 0.508060i | \(-0.169637\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.45192 | + | 0.838266i | 0.252747 | + | 0.145923i | ||||
\(34\) | 2.75979 | − | 4.78010i | 0.473301 | − | 0.819781i | ||||
\(35\) | 4.91259 | + | 7.00182i | 0.830379 | + | 1.18352i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.06142 | − | 5.98944i | 0.174497 | − | 0.984658i | ||||
\(38\) | − | 1.47515i | − | 0.239301i | ||||||
\(39\) | −2.70218 | + | 1.56010i | −0.432694 | + | 0.249816i | ||||
\(40\) | −2.02746 | − | 0.943089i | −0.320569 | − | 0.149115i | ||||
\(41\) | 4.89193 | − | 8.47308i | 0.763992 | − | 1.32327i | −0.176786 | − | 0.984249i | \(-0.556570\pi\) |
0.940778 | − | 0.339023i | \(-0.110096\pi\) | |||||||
\(42\) | −1.91258 | + | 3.31268i | −0.295117 | + | 0.511158i | ||||
\(43\) | −11.7908 | −1.79808 | −0.899040 | − | 0.437866i | \(-0.855734\pi\) | ||||
−0.899040 | + | 0.437866i | \(0.855734\pi\) | |||||||
\(44\) | −0.838266 | + | 1.45192i | −0.126373 | + | 0.218885i | ||||
\(45\) | 0.196990 | + | 2.22737i | 0.0293655 | + | 0.332037i | ||||
\(46\) | 0.606969 | + | 1.05130i | 0.0894927 | + | 0.155006i | ||||
\(47\) | 11.2816i | 1.64559i | 0.568336 | + | 0.822796i | \(0.307587\pi\) | ||||
−0.568336 | + | 0.822796i | \(0.692413\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 3.81590 | + | 6.60933i | 0.545128 | + | 0.944190i | ||||
\(50\) | −1.70122 | + | 4.70168i | −0.240589 | + | 0.664919i | ||||
\(51\) | − | 5.51959i | − | 0.772897i | ||||||
\(52\) | −1.56010 | − | 2.70218i | −0.216347 | − | 0.374724i | ||||
\(53\) | −2.49973 | + | 1.44322i | −0.343365 | + | 0.198242i | −0.661759 | − | 0.749717i | \(-0.730190\pi\) |
0.318394 | + | 0.947958i | \(0.396856\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 3.39910 | + | 1.58112i | 0.458334 | + | 0.213198i | ||||
\(56\) | −3.31268 | − | 1.91258i | −0.442675 | − | 0.255579i | ||||
\(57\) | −0.737577 | − | 1.27752i | −0.0976944 | − | 0.169212i | ||||
\(58\) | 2.57226 | − | 1.48510i | 0.337755 | − | 0.195003i | ||||
\(59\) | 5.20788 | − | 3.00677i | 0.678009 | − | 0.391448i | −0.121096 | − | 0.992641i | \(-0.538641\pi\) |
0.799104 | + | 0.601192i | \(0.205307\pi\) | |||||||
\(60\) | −2.22737 | + | 0.196990i | −0.287553 | + | 0.0254313i | ||||
\(61\) | −5.55247 | − | 3.20572i | −0.710921 | − | 0.410451i | 0.100481 | − | 0.994939i | \(-0.467962\pi\) |
−0.811402 | + | 0.584488i | \(0.801295\pi\) | |||||||
\(62\) | 4.89955 | − | 2.82876i | 0.622244 | − | 0.359253i | ||||
\(63\) | 3.82515i | 0.481924i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.71143 | + | 4.00723i | −0.708416 | + | 0.497036i | ||||
\(66\) | 1.67653i | 0.206367i | ||||||||
\(67\) | −0.933703 | − | 0.539074i | −0.114070 | − | 0.0658583i | 0.441879 | − | 0.897074i | \(-0.354312\pi\) |
−0.555949 | + | 0.831216i | \(0.687645\pi\) | |||||||
\(68\) | 5.51959 | 0.669348 | ||||||||
\(69\) | 1.05130 | + | 0.606969i | 0.126562 | + | 0.0730705i | ||||
\(70\) | −3.60746 | + | 7.75534i | −0.431174 | + | 0.926940i | ||||
\(71\) | 0.807805 | − | 1.39916i | 0.0958689 | − | 0.166050i | −0.814102 | − | 0.580722i | \(-0.802770\pi\) |
0.909971 | + | 0.414672i | \(0.136104\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 12.7659i | 1.49414i | 0.664747 | + | 0.747069i | \(0.268539\pi\) | ||||
−0.664747 | + | 0.747069i | \(0.731461\pi\) | |||||||
\(74\) | 5.71772 | − | 2.07550i | 0.664671 | − | 0.241272i | ||||
\(75\) | 0.877540 | + | 4.92239i | 0.101330 | + | 0.568389i | ||||
\(76\) | 1.27752 | − | 0.737577i | 0.146542 | − | 0.0846058i | ||||
\(77\) | 5.55382 | + | 3.20650i | 0.632916 | + | 0.365414i | ||||
\(78\) | −2.70218 | − | 1.56010i | −0.305961 | − | 0.176647i | ||||
\(79\) | −1.38034 | − | 0.796940i | −0.155301 | − | 0.0896628i | 0.420336 | − | 0.907369i | \(-0.361912\pi\) |
−0.575636 | + | 0.817706i | \(0.695246\pi\) | |||||||
\(80\) | −0.196990 | − | 2.22737i | −0.0220241 | − | 0.249028i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 9.78387 | 1.08045 | ||||||||
\(83\) | −3.79462 | + | 2.19082i | −0.416513 | + | 0.240474i | −0.693584 | − | 0.720375i | \(-0.743970\pi\) |
0.277071 | + | 0.960849i | \(0.410636\pi\) | |||||||
\(84\) | −3.82515 | −0.417358 | ||||||||
\(85\) | −1.08730 | − | 12.2942i | −0.117934 | − | 1.33349i | ||||
\(86\) | −5.89540 | − | 10.2111i | −0.635717 | − | 1.10109i | ||||
\(87\) | 1.48510 | − | 2.57226i | 0.159219 | − | 0.275775i | ||||
\(88\) | −1.67653 | −0.178719 | ||||||||
\(89\) | −7.36049 | + | 4.24958i | −0.780210 | + | 0.450454i | −0.836505 | − | 0.547960i | \(-0.815405\pi\) |
0.0562948 | + | 0.998414i | \(0.482071\pi\) | |||||||
\(90\) | −1.83047 | + | 1.28429i | −0.192948 | + | 0.135376i | ||||
\(91\) | −10.3362 | + | 5.96763i | −1.08353 | + | 0.625577i | ||||
\(92\) | −0.606969 | + | 1.05130i | −0.0632809 | + | 0.109606i | ||||
\(93\) | 2.82876 | − | 4.89955i | 0.293329 | − | 0.508060i | ||||
\(94\) | −9.77017 | + | 5.64081i | −1.00772 | + | 0.581805i | ||||
\(95\) | −1.89452 | − | 2.70022i | −0.194373 | − | 0.277037i | ||||
\(96\) | 0.866025 | − | 0.500000i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | −16.8340 | −1.70923 | −0.854617 | − | 0.519259i | \(-0.826208\pi\) | ||||
−0.854617 | + | 0.519259i | \(0.826208\pi\) | |||||||
\(98\) | −3.81590 | + | 6.60933i | −0.385464 | + | 0.667643i | ||||
\(99\) | 0.838266 | + | 1.45192i | 0.0842489 | + | 0.145923i | ||||
\(100\) | −4.92239 | + | 0.877540i | −0.492239 | + | 0.0877540i | ||||
\(101\) | 2.23855 | 0.222744 | 0.111372 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(102\) | 4.78010 | − | 2.75979i | 0.473301 | − | 0.273260i | ||||
\(103\) | 4.22889 | 0.416684 | 0.208342 | − | 0.978056i | \(-0.433193\pi\) | ||||
0.208342 | + | 0.978056i | \(0.433193\pi\) | |||||||
\(104\) | 1.56010 | − | 2.70218i | 0.152981 | − | 0.264970i | ||||
\(105\) | 0.753516 | + | 8.52005i | 0.0735356 | + | 0.831471i | ||||
\(106\) | −2.49973 | − | 1.44322i | −0.242795 | − | 0.140178i | ||||
\(107\) | 2.24493 | + | 1.29611i | 0.217026 | + | 0.125300i | 0.604572 | − | 0.796550i | \(-0.293344\pi\) |
−0.387547 | + | 0.921850i | \(0.626677\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 12.2762 | − | 7.08769i | 1.17585 | − | 0.678877i | 0.220799 | − | 0.975319i | \(-0.429133\pi\) |
0.955051 | + | 0.296442i | \(0.0958001\pi\) | |||||||
\(110\) | 0.330260 | + | 3.73427i | 0.0314890 | + | 0.356048i | ||||
\(111\) | 3.91394 | − | 4.65629i | 0.371495 | − | 0.441956i | ||||
\(112\) | − | 3.82515i | − | 0.361443i | ||||||
\(113\) | 8.59155 | + | 14.8810i | 0.808225 | + | 1.39989i | 0.914092 | + | 0.405506i | \(0.132905\pi\) |
−0.105868 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(114\) | 0.737577 | − | 1.27752i | 0.0690804 | − | 0.119651i | ||||
\(115\) | 2.46121 | + | 1.14485i | 0.229509 | + | 0.106758i | ||||
\(116\) | 2.57226 | + | 1.48510i | 0.238829 | + | 0.137888i | ||||
\(117\) | −3.12020 | −0.288463 | ||||||||
\(118\) | 5.20788 | + | 3.00677i | 0.479424 | + | 0.276796i | ||||
\(119\) | − | 21.1133i | − | 1.93545i | ||||||
\(120\) | −1.28429 | − | 1.83047i | −0.117239 | − | 0.167098i | ||||
\(121\) | −8.18924 | −0.744476 | ||||||||
\(122\) | − | 6.41144i | − | 0.580465i | ||||||
\(123\) | 8.47308 | − | 4.89193i | 0.763992 | − | 0.441091i | ||||
\(124\) | 4.89955 | + | 2.82876i | 0.439993 | + | 0.254030i | ||||
\(125\) | 2.92427 | + | 10.7911i | 0.261555 | + | 0.965189i | ||||
\(126\) | −3.31268 | + | 1.91258i | −0.295117 | + | 0.170386i | ||||
\(127\) | 14.0316 | − | 8.10117i | 1.24511 | − | 0.718862i | 0.274977 | − | 0.961451i | \(-0.411330\pi\) |
0.970129 | + | 0.242589i | \(0.0779966\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −10.2111 | − | 5.89540i | −0.899040 | − | 0.519061i | ||||
\(130\) | −6.32608 | − | 2.94263i | −0.554834 | − | 0.258086i | ||||
\(131\) | 15.8066 | − | 9.12596i | 1.38103 | − | 0.797339i | 0.388750 | − | 0.921343i | \(-0.372907\pi\) |
0.992282 | + | 0.124004i | \(0.0395736\pi\) | |||||||
\(132\) | −1.45192 | + | 0.838266i | −0.126373 | + | 0.0729617i | ||||
\(133\) | −2.82134 | − | 4.88671i | −0.244642 | − | 0.423732i | ||||
\(134\) | − | 1.07815i | − | 0.0931378i | ||||||
\(135\) | −0.943089 | + | 2.02746i | −0.0811682 | + | 0.174496i | ||||
\(136\) | 2.75979 | + | 4.78010i | 0.236650 | + | 0.409891i | ||||
\(137\) | − | 2.97364i | − | 0.254055i | −0.991899 | − | 0.127028i | \(-0.959456\pi\) | ||
0.991899 | − | 0.127028i | \(-0.0405437\pi\) | |||||||
\(138\) | 1.21394i | 0.103337i | ||||||||
\(139\) | −5.43980 | − | 9.42200i | −0.461397 | − | 0.799164i | 0.537633 | − | 0.843179i | \(-0.319318\pi\) |
−0.999031 | + | 0.0440148i | \(0.985985\pi\) | |||||||
\(140\) | −8.52005 | + | 0.753516i | −0.720075 | + | 0.0636837i | ||||
\(141\) | −5.64081 | + | 9.77017i | −0.475042 | + | 0.822796i | ||||
\(142\) | 1.61561 | 0.135579 | ||||||||
\(143\) | −2.61556 | + | 4.53028i | −0.218724 | + | 0.378841i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 2.80116 | − | 6.02194i | 0.232623 | − | 0.500095i | ||||
\(146\) | −11.0556 | + | 6.38296i | −0.914969 | + | 0.528257i | ||||
\(147\) | 7.63180i | 0.629460i | ||||||||
\(148\) | 4.65629 | + | 3.91394i | 0.382745 | + | 0.321724i | ||||
\(149\) | 8.97575 | 0.735322 | 0.367661 | − | 0.929960i | \(-0.380159\pi\) | ||||
0.367661 | + | 0.929960i | \(0.380159\pi\) | |||||||
\(150\) | −3.82415 | + | 3.22117i | −0.312240 | + | 0.263007i | ||||
\(151\) | −5.87683 | + | 10.1790i | −0.478250 | + | 0.828353i | −0.999689 | − | 0.0249354i | \(-0.992062\pi\) |
0.521439 | + | 0.853288i | \(0.325395\pi\) | |||||||
\(152\) | 1.27752 | + | 0.737577i | 0.103621 | + | 0.0598254i | ||||
\(153\) | 2.75979 | − | 4.78010i | 0.223116 | − | 0.386449i | ||||
\(154\) | 6.41299i | 0.516774i | ||||||||
\(155\) | 5.33554 | − | 11.4704i | 0.428561 | − | 0.921322i | ||||
\(156\) | − | 3.12020i | − | 0.249816i | ||||||
\(157\) | 0.108243 | − | 0.0624939i | 0.00863870 | − | 0.00498755i | −0.495674 | − | 0.868508i | \(-0.665079\pi\) |
0.504313 | + | 0.863521i | \(0.331746\pi\) | |||||||
\(158\) | − | 1.59388i | − | 0.126802i | ||||||
\(159\) | −2.88644 | −0.228910 | ||||||||
\(160\) | 1.83047 | − | 1.28429i | 0.144711 | − | 0.101532i | ||||
\(161\) | 4.02139 | + | 2.32175i | 0.316930 | + | 0.182980i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.41453 | − | 14.5744i | −0.659077 | − | 1.14155i | −0.980855 | − | 0.194740i | \(-0.937614\pi\) |
0.321778 | − | 0.946815i | \(-0.395720\pi\) | |||||||
\(164\) | 4.89193 | + | 8.47308i | 0.381996 | + | 0.661636i | ||||
\(165\) | 2.15315 | + | 3.06884i | 0.167622 | + | 0.238909i | ||||
\(166\) | −3.79462 | − | 2.19082i | −0.294519 | − | 0.170041i | ||||
\(167\) | 10.0346 | − | 17.3805i | 0.776503 | − | 1.34494i | −0.157443 | − | 0.987528i | \(-0.550325\pi\) |
0.933946 | − | 0.357415i | \(-0.116342\pi\) | |||||||
\(168\) | −1.91258 | − | 3.31268i | −0.147558 | − | 0.255579i | ||||
\(169\) | 1.63217 | + | 2.82700i | 0.125551 | + | 0.217461i | ||||
\(170\) | 10.1034 | − | 7.08873i | 0.774898 | − | 0.543680i | ||||
\(171\) | − | 1.47515i | − | 0.112808i | ||||||
\(172\) | 5.89540 | − | 10.2111i | 0.449520 | − | 0.778592i | ||||
\(173\) | −11.9639 | + | 6.90737i | −0.909599 | + | 0.525157i | −0.880302 | − | 0.474414i | \(-0.842660\pi\) |
−0.0292969 | + | 0.999571i | \(0.509327\pi\) | |||||||
\(174\) | 2.97019 | 0.225170 | ||||||||
\(175\) | 3.35672 | + | 18.8289i | 0.253744 | + | 1.42333i | ||||
\(176\) | −0.838266 | − | 1.45192i | −0.0631867 | − | 0.109443i | ||||
\(177\) | 6.01354 | 0.452006 | ||||||||
\(178\) | −7.36049 | − | 4.24958i | −0.551692 | − | 0.318519i | ||||
\(179\) | − | 12.8111i | − | 0.957545i | −0.877939 | − | 0.478773i | \(-0.841082\pi\) | ||
0.877939 | − | 0.478773i | \(-0.158918\pi\) | |||||||
\(180\) | −2.02746 | − | 0.943089i | −0.151118 | − | 0.0702937i | ||||
\(181\) | −7.43016 | + | 12.8694i | −0.552280 | + | 0.956576i | 0.445830 | + | 0.895118i | \(0.352909\pi\) |
−0.998110 | + | 0.0614588i | \(0.980425\pi\) | |||||||
\(182\) | −10.3362 | − | 5.96763i | −0.766173 | − | 0.442350i | ||||
\(183\) | −3.20572 | − | 5.55247i | −0.236974 | − | 0.410451i | ||||
\(184\) | −1.21394 | −0.0894927 | ||||||||
\(185\) | 7.80057 | − | 11.1423i | 0.573509 | − | 0.819199i | ||||
\(186\) | 5.65752 | 0.414829 | ||||||||
\(187\) | −4.62689 | − | 8.01400i | −0.338351 | − | 0.586042i | ||||
\(188\) | −9.77017 | − | 5.64081i | −0.712563 | − | 0.411398i | ||||
\(189\) | −1.91258 | + | 3.31268i | −0.139119 | + | 0.240962i | ||||
\(190\) | 1.39120 | − | 2.99081i | 0.100928 | − | 0.216976i | ||||
\(191\) | − | 12.5432i | − | 0.907597i | −0.891104 | − | 0.453798i | \(-0.850069\pi\) | ||
0.891104 | − | 0.453798i | \(-0.149931\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | −26.1467 | −1.88208 | −0.941041 | − | 0.338292i | \(-0.890151\pi\) | ||||
−0.941041 | + | 0.338292i | \(0.890151\pi\) | |||||||
\(194\) | −8.41700 | − | 14.5787i | −0.604306 | − | 1.04669i | ||||
\(195\) | −6.94986 | + | 0.614648i | −0.497690 | + | 0.0440159i | ||||
\(196\) | −7.63180 | −0.545128 | ||||||||
\(197\) | 20.8765 | − | 12.0530i | 1.48739 | − | 0.858744i | 0.487492 | − | 0.873128i | \(-0.337912\pi\) |
0.999897 | + | 0.0143835i | \(0.00457858\pi\) | |||||||
\(198\) | −0.838266 | + | 1.45192i | −0.0595730 | + | 0.103183i | ||||
\(199\) | 21.4951i | 1.52374i | 0.647727 | + | 0.761872i | \(0.275720\pi\) | ||||
−0.647727 | + | 0.761872i | \(0.724280\pi\) | |||||||
\(200\) | −3.22117 | − | 3.82415i | −0.227771 | − | 0.270408i | ||||
\(201\) | −0.539074 | − | 0.933703i | −0.0380233 | − | 0.0658583i | ||||
\(202\) | 1.11927 | + | 1.93864i | 0.0787519 | + | 0.136402i | ||||
\(203\) | 5.68072 | − | 9.83930i | 0.398708 | − | 0.690583i | ||||
\(204\) | 4.78010 | + | 2.75979i | 0.334674 | + | 0.193224i | ||||
\(205\) | 17.9091 | − | 12.5653i | 1.25082 | − | 0.877597i | ||||
\(206\) | 2.11444 | + | 3.66232i | 0.147320 | + | 0.255166i | ||||
\(207\) | 0.606969 | + | 1.05130i | 0.0421873 | + | 0.0730705i | ||||
\(208\) | 3.12020 | 0.216347 | ||||||||
\(209\) | −2.14180 | − | 1.23657i | −0.148152 | − | 0.0855354i | ||||
\(210\) | −7.00182 | + | 4.91259i | −0.483171 | + | 0.339001i | ||||
\(211\) | 7.62398 | 0.524856 | 0.262428 | − | 0.964952i | \(-0.415477\pi\) | ||||
0.262428 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(212\) | − | 2.88644i | − | 0.198242i | ||||||
\(213\) | 1.39916 | − | 0.807805i | 0.0958689 | − | 0.0553499i | ||||
\(214\) | 2.59222i | 0.177201i | ||||||||
\(215\) | −23.9053 | − | 11.1198i | −1.63033 | − | 0.758362i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 10.8204 | − | 18.7415i | 0.734539 | − | 1.27226i | ||||
\(218\) | 12.2762 | + | 7.08769i | 0.831452 | + | 0.480039i | ||||
\(219\) | −6.38296 | + | 11.0556i | −0.431320 | + | 0.747069i | ||||
\(220\) | −3.06884 | + | 2.15315i | −0.206901 | + | 0.145165i | ||||
\(221\) | 17.2222 | 1.15849 | ||||||||
\(222\) | 5.98944 | + | 1.06142i | 0.401985 | + | 0.0712382i | ||||
\(223\) | − | 4.00109i | − | 0.267933i | −0.990986 | − | 0.133966i | \(-0.957229\pi\) | ||
0.990986 | − | 0.133966i | \(-0.0427714\pi\) | |||||||
\(224\) | 3.31268 | − | 1.91258i | 0.221338 | − | 0.127789i | ||||
\(225\) | −1.70122 | + | 4.70168i | −0.113415 | + | 0.313446i | ||||
\(226\) | −8.59155 | + | 14.8810i | −0.571501 | + | 0.989869i | ||||
\(227\) | 6.44101 | − | 11.1562i | 0.427505 | − | 0.740460i | −0.569146 | − | 0.822237i | \(-0.692726\pi\) |
0.996651 | + | 0.0817765i | \(0.0260594\pi\) | |||||||
\(228\) | 1.47515 | 0.0976944 | ||||||||
\(229\) | −7.81590 | + | 13.5375i | −0.516489 | + | 0.894586i | 0.483327 | + | 0.875440i | \(0.339428\pi\) |
−0.999817 | + | 0.0191460i | \(0.993905\pi\) | |||||||
\(230\) | 0.239133 | + | 2.70389i | 0.0157680 | + | 0.178290i | ||||
\(231\) | 3.20650 | + | 5.55382i | 0.210972 | + | 0.365414i | ||||
\(232\) | 2.97019i | 0.195003i | ||||||||
\(233\) | − | 2.50962i | − | 0.164410i | −0.996615 | − | 0.0822052i | \(-0.973804\pi\) | ||
0.996615 | − | 0.0822052i | \(-0.0261963\pi\) | |||||||
\(234\) | −1.56010 | − | 2.70218i | −0.101987 | − | 0.176647i | ||||
\(235\) | −10.6396 | + | 22.8730i | −0.694049 | + | 1.49207i | ||||
\(236\) | 6.01354i | 0.391448i | ||||||||
\(237\) | −0.796940 | − | 1.38034i | −0.0517668 | − | 0.0896628i | ||||
\(238\) | 18.2846 | − | 10.5566i | 1.18522 | − | 0.684285i | ||||
\(239\) | 3.69433 | − | 2.13292i | 0.238966 | − | 0.137967i | −0.375735 | − | 0.926727i | \(-0.622610\pi\) |
0.614702 | + | 0.788760i | \(0.289276\pi\) | |||||||
\(240\) | 0.943089 | − | 2.02746i | 0.0608761 | − | 0.130872i | ||||
\(241\) | 25.2255 | + | 14.5640i | 1.62492 | + | 0.938147i | 0.985578 | + | 0.169223i | \(0.0541259\pi\) |
0.639341 | + | 0.768924i | \(0.279207\pi\) | |||||||
\(242\) | −4.09462 | − | 7.09209i | −0.263212 | − | 0.455897i | ||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 5.55247 | − | 3.20572i | 0.355461 | − | 0.205225i | ||||
\(245\) | 1.50339 | + | 16.9989i | 0.0960478 | + | 1.08602i | ||||
\(246\) | 8.47308 | + | 4.89193i | 0.540224 | + | 0.311898i | ||||
\(247\) | 3.98612 | − | 2.30139i | 0.253631 | − | 0.146434i | ||||
\(248\) | 5.65752i | 0.359253i | ||||||||
\(249\) | −4.38165 | −0.277676 | ||||||||
\(250\) | −7.88326 | + | 7.92806i | −0.498581 | + | 0.501415i | ||||
\(251\) | 13.7583i | 0.868414i | 0.900813 | + | 0.434207i | \(0.142971\pi\) | ||||
−0.900813 | + | 0.434207i | \(0.857029\pi\) | |||||||
\(252\) | −3.31268 | − | 1.91258i | −0.208679 | − | 0.120481i | ||||
\(253\) | 2.03521 | 0.127952 | ||||||||
\(254\) | 14.0316 | + | 8.10117i | 0.880423 | + | 0.508312i | ||||
\(255\) | 5.20546 | − | 11.1907i | 0.325979 | − | 0.700791i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.17314 | − | 5.49604i | −0.197935 | − | 0.342833i | 0.749924 | − | 0.661524i | \(-0.230090\pi\) |
−0.947859 | + | 0.318691i | \(0.896757\pi\) | |||||||
\(258\) | − | 11.7908i | − | 0.734063i | ||||||
\(259\) | 14.9714 | − | 17.8110i | 0.930279 | − | 1.10672i | ||||
\(260\) | −0.614648 | − | 6.94986i | −0.0381188 | − | 0.431012i | ||||
\(261\) | 2.57226 | − | 1.48510i | 0.159219 | − | 0.0919252i | ||||
\(262\) | 15.8066 | + | 9.12596i | 0.976537 | + | 0.563804i | ||||
\(263\) | 0.942492 | + | 0.544148i | 0.0581165 | + | 0.0335536i | 0.528777 | − | 0.848761i | \(-0.322651\pi\) |
−0.470660 | + | 0.882315i | \(0.655984\pi\) | |||||||
\(264\) | −1.45192 | − | 0.838266i | −0.0893595 | − | 0.0515917i | ||||
\(265\) | −6.42919 | + | 0.568599i | −0.394942 | + | 0.0349288i | ||||
\(266\) | 2.82134 | − | 4.88671i | 0.172988 | − | 0.299623i | ||||
\(267\) | −8.49916 | −0.520140 | ||||||||
\(268\) | 0.933703 | − | 0.539074i | 0.0570350 | − | 0.0329292i | ||||
\(269\) | −3.18400 | −0.194132 | −0.0970658 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970658 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(270\) | −2.22737 | + | 0.196990i | −0.135554 | + | 0.0119884i | ||||
\(271\) | −8.94307 | − | 15.4898i | −0.543253 | − | 0.940941i | −0.998715 | − | 0.0506859i | \(-0.983859\pi\) |
0.455462 | − | 0.890255i | \(-0.349474\pi\) | |||||||
\(272\) | −2.75979 | + | 4.78010i | −0.167337 | + | 0.289836i | ||||
\(273\) | −11.9353 | −0.722354 | ||||||||
\(274\) | 2.57525 | − | 1.48682i | 0.155576 | − | 0.0898221i | ||||
\(275\) | 5.40039 | + | 6.41130i | 0.325656 | + | 0.386616i | ||||
\(276\) | −1.05130 | + | 0.606969i | −0.0632809 | + | 0.0365353i | ||||
\(277\) | −9.81717 | + | 17.0038i | −0.589857 | + | 1.02166i | 0.404394 | + | 0.914585i | \(0.367482\pi\) |
−0.994251 | + | 0.107077i | \(0.965851\pi\) | |||||||
\(278\) | 5.43980 | − | 9.42200i | 0.326257 | − | 0.565094i | ||||
\(279\) | 4.89955 | − | 2.82876i | 0.293329 | − | 0.169353i | ||||
\(280\) | −4.91259 | − | 7.00182i | −0.293583 | − | 0.418439i | ||||
\(281\) | 10.2198 | − | 5.90041i | 0.609662 | − | 0.351989i | −0.163171 | − | 0.986598i | \(-0.552172\pi\) |
0.772833 | + | 0.634609i | \(0.218839\pi\) | |||||||
\(282\) | −11.2816 | −0.671810 | ||||||||
\(283\) | 1.07987 | − | 1.87039i | 0.0641916 | − | 0.111183i | −0.832144 | − | 0.554560i | \(-0.812886\pi\) |
0.896335 | + | 0.443377i | \(0.146220\pi\) | |||||||
\(284\) | 0.807805 | + | 1.39916i | 0.0479344 | + | 0.0830249i | ||||
\(285\) | −0.290590 | − | 3.28572i | −0.0172131 | − | 0.194629i | ||||
\(286\) | −5.23112 | −0.309323 | ||||||||
\(287\) | 32.4108 | − | 18.7124i | 1.91315 | − | 1.10456i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −6.73293 | + | 11.6618i | −0.396055 | + | 0.685987i | ||||
\(290\) | 6.61573 | − | 0.585097i | 0.388489 | − | 0.0343581i | ||||
\(291\) | −14.5787 | − | 8.41700i | −0.854617 | − | 0.493413i | ||||
\(292\) | −11.0556 | − | 6.38296i | −0.646981 | − | 0.373534i | ||||
\(293\) | −3.09718 | − | 1.78816i | −0.180939 | − | 0.104465i | 0.406795 | − | 0.913520i | \(-0.366646\pi\) |
−0.587734 | + | 0.809054i | \(0.699980\pi\) | |||||||
\(294\) | −6.60933 | + | 3.81590i | −0.385464 | + | 0.222548i | ||||
\(295\) | 13.3944 | − | 1.18461i | 0.779853 | − | 0.0689705i | ||||
\(296\) | −1.06142 | + | 5.98944i | −0.0616941 | + | 0.348129i | ||||
\(297\) | 1.67653i | 0.0972823i | ||||||||
\(298\) | 4.48787 | + | 7.77322i | 0.259975 | + | 0.450291i | ||||
\(299\) | −1.89387 | + | 3.28027i | −0.109525 | + | 0.189703i | ||||
\(300\) | −4.70168 | − | 1.70122i | −0.271452 | − | 0.0982202i | ||||
\(301\) | −39.0591 | − | 22.5508i | −2.25133 | − | 1.29981i | ||||
\(302\) | −11.7537 | −0.676347 | ||||||||
\(303\) | 1.93864 | + | 1.11927i | 0.111372 | + | 0.0643006i | ||||
\(304\) | 1.47515i | 0.0846058i | ||||||||
\(305\) | −8.23412 | − | 11.7359i | −0.471484 | − | 0.671998i | ||||
\(306\) | 5.51959 | 0.315534 | ||||||||
\(307\) | − | 11.3779i | − | 0.649371i | −0.945822 | − | 0.324685i | \(-0.894742\pi\) | ||
0.945822 | − | 0.324685i | \(-0.105258\pi\) | |||||||
\(308\) | −5.55382 | + | 3.20650i | −0.316458 | + | 0.182707i | ||||
\(309\) | 3.66232 | + | 2.11444i | 0.208342 | + | 0.120286i | ||||
\(310\) | 12.6014 | − | 1.11447i | 0.715712 | − | 0.0632978i | ||||
\(311\) | 25.0523 | − | 14.4639i | 1.42058 | − | 0.820174i | 0.424234 | − | 0.905552i | \(-0.360543\pi\) |
0.996349 | + | 0.0853784i | \(0.0272099\pi\) | |||||||
\(312\) | 2.70218 | − | 1.56010i | 0.152981 | − | 0.0883234i | ||||
\(313\) | 6.77595 | + | 11.7363i | 0.382999 | + | 0.663374i | 0.991489 | − | 0.130187i | \(-0.0415579\pi\) |
−0.608490 | + | 0.793561i | \(0.708225\pi\) | |||||||
\(314\) | 0.108243 | + | 0.0624939i | 0.00610848 | + | 0.00352673i | ||||
\(315\) | −3.60746 | + | 7.75534i | −0.203257 | + | 0.436964i | ||||
\(316\) | 1.38034 | − | 0.796940i | 0.0776503 | − | 0.0448314i | ||||
\(317\) | 0.669018 | − | 0.386258i | 0.0375758 | − | 0.0216944i | −0.481094 | − | 0.876669i | \(-0.659761\pi\) |
0.518670 | + | 0.854974i | \(0.326427\pi\) | |||||||
\(318\) | −1.44322 | − | 2.49973i | −0.0809318 | − | 0.140178i | ||||
\(319\) | − | 4.97962i | − | 0.278805i | ||||||
\(320\) | 2.02746 | + | 0.943089i | 0.113338 | + | 0.0527203i | ||||
\(321\) | 1.29611 | + | 2.24493i | 0.0723419 | + | 0.125300i | ||||
\(322\) | 4.64350i | 0.258772i | ||||||||
\(323\) | 8.14224i | 0.453046i | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −15.3589 | + | 2.73810i | −0.851956 | + | 0.151883i | ||||
\(326\) | 8.41453 | − | 14.5744i | 0.466038 | − | 0.807201i | ||||
\(327\) | 14.1754 | 0.783900 | ||||||||
\(328\) | −4.89193 | + | 8.47308i | −0.270112 | + | 0.467847i | ||||
\(329\) | −21.5770 | + | 37.3724i | −1.18958 | + | 2.06041i | ||||
\(330\) | −1.58112 | + | 3.39910i | −0.0870377 | + | 0.187114i | ||||
\(331\) | −6.34735 | + | 3.66465i | −0.348882 | + | 0.201427i | −0.664193 | − | 0.747561i | \(-0.731225\pi\) |
0.315311 | + | 0.948988i | \(0.397891\pi\) | |||||||
\(332\) | − | 4.38165i | − | 0.240474i | ||||||
\(333\) | 5.71772 | − | 2.07550i | 0.313329 | − | 0.113737i | ||||
\(334\) | 20.0693 | 1.09814 | ||||||||
\(335\) | −1.38465 | − | 1.97351i | −0.0756514 | − | 0.107825i | ||||
\(336\) | 1.91258 | − | 3.31268i | 0.104340 | − | 0.180722i | ||||
\(337\) | 10.2237 | + | 5.90267i | 0.556922 | + | 0.321539i | 0.751909 | − | 0.659267i | \(-0.229133\pi\) |
−0.194987 | + | 0.980806i | \(0.562467\pi\) | |||||||
\(338\) | −1.63217 | + | 2.82700i | −0.0887782 | + | 0.153768i | ||||
\(339\) | 17.1831i | 0.933257i | ||||||||
\(340\) | 11.1907 | + | 5.20546i | 0.606903 | + | 0.282306i | ||||
\(341\) | − | 9.48501i | − | 0.513642i | ||||||
\(342\) | 1.27752 | − | 0.737577i | 0.0690804 | − | 0.0398836i | ||||
\(343\) | 2.41672i | 0.130491i | ||||||||
\(344\) | 11.7908 | 0.635717 | ||||||||
\(345\) | 1.55904 | + | 2.22208i | 0.0839361 | + | 0.119632i | ||||
\(346\) | −11.9639 | − | 6.90737i | −0.643184 | − | 0.371342i | ||||
\(347\) | −10.5172 | −0.564593 | −0.282297 | − | 0.959327i | \(-0.591096\pi\) | ||||
−0.282297 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(348\) | 1.48510 | + | 2.57226i | 0.0796095 | + | 0.137888i | ||||
\(349\) | −10.6455 | − | 18.4385i | −0.569840 | − | 0.986991i | −0.996581 | − | 0.0826177i | \(-0.973672\pi\) |
0.426742 | − | 0.904374i | \(-0.359661\pi\) | |||||||
\(350\) | −14.6279 | + | 12.3215i | −0.781896 | + | 0.658610i | ||||
\(351\) | −2.70218 | − | 1.56010i | −0.144231 | − | 0.0832721i | ||||
\(352\) | 0.838266 | − | 1.45192i | 0.0446797 | − | 0.0773876i | ||||
\(353\) | 1.38917 | + | 2.40612i | 0.0739383 | + | 0.128065i | 0.900624 | − | 0.434599i | \(-0.143110\pi\) |
−0.826686 | + | 0.562664i | \(0.809777\pi\) | |||||||
\(354\) | 3.00677 | + | 5.20788i | 0.159808 | + | 0.276796i | ||||
\(355\) | 2.95732 | − | 2.07491i | 0.156958 | − | 0.110125i | ||||
\(356\) | − | 8.49916i | − | 0.450454i | ||||||
\(357\) | 10.5566 | − | 18.2846i | 0.558716 | − | 0.967725i | ||||
\(358\) | 11.0947 | − | 6.40554i | 0.586374 | − | 0.338543i | ||||
\(359\) | −27.0841 | −1.42945 | −0.714723 | − | 0.699408i | \(-0.753447\pi\) | ||||
−0.714723 | + | 0.699408i | \(0.753447\pi\) | |||||||
\(360\) | −0.196990 | − | 2.22737i | −0.0103823 | − | 0.117393i | ||||
\(361\) | −8.41196 | − | 14.5699i | −0.442735 | − | 0.766839i | ||||
\(362\) | −14.8603 | −0.781041 | ||||||||
\(363\) | −7.09209 | − | 4.09462i | −0.372238 | − | 0.214912i | ||||
\(364\) | − | 11.9353i | − | 0.625577i | ||||||
\(365\) | −12.0394 | + | 25.8824i | −0.630171 | + | 1.35474i | ||||
\(366\) | 3.20572 | − | 5.55247i | 0.167566 | − | 0.290232i | ||||
\(367\) | −0.553552 | − | 0.319593i | −0.0288952 | − | 0.0166826i | 0.485483 | − | 0.874246i | \(-0.338644\pi\) |
−0.514378 | + | 0.857564i | \(0.671977\pi\) | |||||||
\(368\) | −0.606969 | − | 1.05130i | −0.0316405 | − | 0.0548029i | ||||
\(369\) | 9.78387 | 0.509328 | ||||||||
\(370\) | 13.5498 | + | 1.18433i | 0.704421 | + | 0.0615705i | ||||
\(371\) | −11.0411 | −0.573224 | ||||||||
\(372\) | 2.82876 | + | 4.89955i | 0.146664 | + | 0.254030i | ||||
\(373\) | 8.09384 | + | 4.67298i | 0.419083 | + | 0.241958i | 0.694685 | − | 0.719314i | \(-0.255544\pi\) |
−0.275602 | + | 0.961272i | \(0.588877\pi\) | |||||||
\(374\) | 4.62689 | − | 8.01400i | 0.239251 | − | 0.414394i | ||||
\(375\) | −2.86308 | + | 10.8075i | −0.147849 | + | 0.558099i | ||||
\(376\) | − | 11.2816i | − | 0.581805i | ||||||
\(377\) | 8.02598 | + | 4.63380i | 0.413359 | + | 0.238653i | ||||
\(378\) | −3.82515 | −0.196745 | ||||||||
\(379\) | 14.4675 | + | 25.0584i | 0.743144 | + | 1.28716i | 0.951057 | + | 0.309015i | \(0.0999995\pi\) |
−0.207913 | + | 0.978147i | \(0.566667\pi\) | |||||||
\(380\) | 3.28572 | − | 0.290590i | 0.168554 | − | 0.0149070i | ||||
\(381\) | 16.2023 | 0.830071 | ||||||||
\(382\) | 10.8628 | − | 6.27162i | 0.555787 | − | 0.320884i | ||||
\(383\) | −5.13077 | + | 8.88675i | −0.262170 | + | 0.454092i | −0.966818 | − | 0.255465i | \(-0.917771\pi\) |
0.704648 | + | 0.709557i | \(0.251105\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 8.23611 | + | 11.7388i | 0.419751 | + | 0.598264i | ||||
\(386\) | −13.0734 | − | 22.6437i | −0.665417 | − | 1.15254i | ||||
\(387\) | −5.89540 | − | 10.2111i | −0.299680 | − | 0.519061i | ||||
\(388\) | 8.41700 | − | 14.5787i | 0.427309 | − | 0.740120i | ||||
\(389\) | −24.1044 | − | 13.9167i | −1.22214 | − | 0.705605i | −0.256769 | − | 0.966473i | \(-0.582658\pi\) |
−0.965374 | + | 0.260868i | \(0.915991\pi\) | |||||||
\(390\) | −4.00723 | − | 5.71143i | −0.202914 | − | 0.289210i | ||||
\(391\) | −3.35022 | − | 5.80275i | −0.169428 | − | 0.293458i | ||||
\(392\) | −3.81590 | − | 6.60933i | −0.192732 | − | 0.333822i | ||||
\(393\) | 18.2519 | 0.920688 | ||||||||
\(394\) | 20.8765 | + | 12.0530i | 1.05174 | + | 0.607224i | ||||
\(395\) | −2.04700 | − | 2.91755i | −0.102996 | − | 0.146798i | ||||
\(396\) | −1.67653 | −0.0842489 | ||||||||
\(397\) | − | 12.4253i | − | 0.623610i | −0.950146 | − | 0.311805i | \(-0.899066\pi\) | ||
0.950146 | − | 0.311805i | \(-0.100934\pi\) | |||||||
\(398\) | −18.6153 | + | 10.7475i | −0.933099 | + | 0.538725i | ||||
\(399\) | − | 5.64269i | − | 0.282488i | ||||||
\(400\) | 1.70122 | − | 4.70168i | 0.0850612 | − | 0.235084i | ||||
\(401\) | 34.4549i | 1.72060i | 0.509790 | + | 0.860299i | \(0.329723\pi\) | ||||
−0.509790 | + | 0.860299i | \(0.670277\pi\) | |||||||
\(402\) | 0.539074 | − | 0.933703i | 0.0268866 | − | 0.0465689i | ||||
\(403\) | 15.2876 | + | 8.82630i | 0.761530 | + | 0.439669i | ||||
\(404\) | −1.11927 | + | 1.93864i | −0.0556860 | + | 0.0964509i | ||||
\(405\) | −1.83047 | + | 1.28429i | −0.0909567 | + | 0.0638166i | ||||
\(406\) | 11.3614 | 0.563859 | ||||||||
\(407\) | 1.77951 | − | 10.0415i | 0.0882072 | − | 0.497738i | ||||
\(408\) | 5.51959i | 0.273260i | ||||||||
\(409\) | −9.78149 | + | 5.64735i | −0.483664 | + | 0.279243i | −0.721942 | − | 0.691954i | \(-0.756750\pi\) |
0.238278 | + | 0.971197i | \(0.423417\pi\) | |||||||
\(410\) | 19.8364 | + | 9.22706i | 0.979649 | + | 0.455692i | ||||
\(411\) | 1.48682 | − | 2.57525i | 0.0733394 | − | 0.127028i | ||||
\(412\) | −2.11444 | + | 3.66232i | −0.104171 | + | 0.180430i | ||||
\(413\) | 23.0027 | 1.13189 | ||||||||
\(414\) | −0.606969 | + | 1.05130i | −0.0298309 | + | 0.0516687i | ||||
\(415\) | −9.75957 | + | 0.863139i | −0.479078 | + | 0.0423698i | ||||
\(416\) | 1.56010 | + | 2.70218i | 0.0764903 | + | 0.132485i | ||||
\(417\) | − | 10.8796i | − | 0.532776i | ||||||
\(418\) | − | 2.47314i | − | 0.120965i | ||||||
\(419\) | 1.76879 | + | 3.06364i | 0.0864111 | + | 0.149668i | 0.905992 | − | 0.423296i | \(-0.139127\pi\) |
−0.819581 | + | 0.572964i | \(0.805793\pi\) | |||||||
\(420\) | −7.75534 | − | 3.60746i | −0.378422 | − | 0.176026i | ||||
\(421\) | 0.321990i | 0.0156928i | 0.999969 | + | 0.00784642i | \(0.00249762\pi\) | ||||
−0.999969 | + | 0.00784642i | \(0.997502\pi\) | |||||||
\(422\) | 3.81199 | + | 6.60256i | 0.185565 | + | 0.321407i | ||||
\(423\) | −9.77017 | + | 5.64081i | −0.475042 | + | 0.274265i | ||||
\(424\) | 2.49973 | − | 1.44322i | 0.121398 | − | 0.0700890i | ||||
\(425\) | 9.39005 | − | 25.9514i | 0.455485 | − | 1.25883i | ||||
\(426\) | 1.39916 | + | 0.807805i | 0.0677895 | + | 0.0391383i | ||||
\(427\) | −12.2624 | − | 21.2391i | −0.593418 | − | 1.02783i | ||||
\(428\) | −2.24493 | + | 1.29611i | −0.108513 | + | 0.0626499i | ||||
\(429\) | −4.53028 | + | 2.61556i | −0.218724 | + | 0.126280i | ||||
\(430\) | −2.32267 | − | 26.2625i | −0.112009 | − | 1.26649i | ||||
\(431\) | 21.4026 | + | 12.3568i | 1.03093 | + | 0.595206i | 0.917250 | − | 0.398312i | \(-0.130404\pi\) |
0.113676 | + | 0.993518i | \(0.463737\pi\) | |||||||
\(432\) | 0.866025 | − | 0.500000i | 0.0416667 | − | 0.0240563i | ||||
\(433\) | 2.86272i | 0.137574i | 0.997631 | + | 0.0687868i | \(0.0219128\pi\) | ||||
−0.997631 | + | 0.0687868i | \(0.978087\pi\) | |||||||
\(434\) | 21.6409 | 1.03879 | ||||||||
\(435\) | 5.43684 | − | 3.81457i | 0.260677 | − | 0.182895i | ||||
\(436\) | 14.1754i | 0.678877i | ||||||||
\(437\) | −1.55083 | − | 0.895373i | −0.0741863 | − | 0.0428315i | ||||
\(438\) | −12.7659 | −0.609979 | ||||||||
\(439\) | −1.68156 | − | 0.970851i | −0.0802566 | − | 0.0463362i | 0.459335 | − | 0.888263i | \(-0.348088\pi\) |
−0.539591 | + | 0.841927i | \(0.681421\pi\) | |||||||
\(440\) | −3.39910 | − | 1.58112i | −0.162046 | − | 0.0753769i | ||||
\(441\) | −3.81590 | + | 6.60933i | −0.181709 | + | 0.314730i | ||||
\(442\) | 8.61112 | + | 14.9149i | 0.409589 | + | 0.709429i | ||||
\(443\) | 19.3246i | 0.918141i | 0.888400 | + | 0.459070i | \(0.151817\pi\) | ||||
−0.888400 | + | 0.459070i | \(0.848183\pi\) | |||||||
\(444\) | 2.07550 | + | 5.71772i | 0.0984988 | + | 0.271351i | ||||
\(445\) | −18.9308 | + | 1.67425i | −0.897406 | + | 0.0793669i | ||||
\(446\) | 3.46504 | − | 2.00054i | 0.164075 | − | 0.0947285i | ||||
\(447\) | 7.77322 | + | 4.48787i | 0.367661 | + | 0.212269i | ||||
\(448\) | 3.31268 | + | 1.91258i | 0.156509 | + | 0.0903608i | ||||
\(449\) | −19.4648 | − | 11.2380i | −0.918600 | − | 0.530354i | −0.0354115 | − | 0.999373i | \(-0.511274\pi\) |
−0.883188 | + | 0.469019i | \(0.844608\pi\) | |||||||
\(450\) | −4.92239 | + | 0.877540i | −0.232044 | + | 0.0413676i | ||||
\(451\) | 8.20149 | − | 14.2054i | 0.386193 | − | 0.668906i | ||||
\(452\) | −17.1831 | −0.808225 | ||||||||
\(453\) | −10.1790 | + | 5.87683i | −0.478250 | + | 0.276118i | ||||
\(454\) | 12.8820 | 0.604583 | ||||||||
\(455\) | −26.5843 | + | 2.35112i | −1.24629 | + | 0.110222i | ||||
\(456\) | 0.737577 | + | 1.27752i | 0.0345402 | + | 0.0598254i | ||||
\(457\) | 5.93888 | − | 10.2864i | 0.277809 | − | 0.481179i | −0.693031 | − | 0.720908i | \(-0.743725\pi\) |
0.970840 | + | 0.239729i | \(0.0770584\pi\) | |||||||
\(458\) | −15.6318 | −0.730426 | ||||||||
\(459\) | 4.78010 | − | 2.75979i | 0.223116 | − | 0.128816i | ||||
\(460\) | −2.22208 | + | 1.55904i | −0.103605 | + | 0.0726908i | ||||
\(461\) | 7.12646 | − | 4.11446i | 0.331912 | − | 0.191630i | −0.324777 | − | 0.945790i | \(-0.605289\pi\) |
0.656690 | + | 0.754161i | \(0.271956\pi\) | |||||||
\(462\) | −3.20650 | + | 5.55382i | −0.149180 | + | 0.258387i | ||||
\(463\) | 12.3478 | − | 21.3871i | 0.573853 | − | 0.993942i | −0.422313 | − | 0.906450i | \(-0.638782\pi\) |
0.996165 | − | 0.0874916i | \(-0.0278851\pi\) | |||||||
\(464\) | −2.57226 | + | 1.48510i | −0.119414 | + | 0.0689439i | ||||
\(465\) | 10.3559 | − | 7.26586i | 0.480243 | − | 0.336946i | ||||
\(466\) | 2.17339 | − | 1.25481i | 0.100680 | − | 0.0581279i | ||||
\(467\) | 14.7594 | 0.682984 | 0.341492 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341492 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(468\) | 1.56010 | − | 2.70218i | 0.0721157 | − | 0.124908i | ||||
\(469\) | −2.06204 | − | 3.57156i | −0.0952161 | − | 0.164919i | ||||
\(470\) | −25.1284 | + | 2.22236i | −1.15909 | + | 0.102510i | ||||
\(471\) | 0.124988 | 0.00575913 | ||||||||
\(472\) | −5.20788 | + | 3.00677i | −0.239712 | + | 0.138398i | ||||
\(473\) | −19.7677 | −0.908918 | ||||||||
\(474\) | 0.796940 | − | 1.38034i | 0.0366047 | − | 0.0634012i | ||||
\(475\) | −1.29451 | − | 7.26128i | −0.0593960 | − | 0.333170i | ||||
\(476\) | 18.2846 | + | 10.5566i | 0.838075 | + | 0.483863i | ||||
\(477\) | −2.49973 | − | 1.44322i | −0.114455 | − | 0.0660805i | ||||
\(478\) | 3.69433 | + | 2.13292i | 0.168975 | + | 0.0975577i | ||||
\(479\) | −25.0708 | + | 14.4746i | −1.14551 | + | 0.661363i | −0.947790 | − | 0.318895i | \(-0.896688\pi\) |
−0.197724 | + | 0.980258i | \(0.563355\pi\) | |||||||
\(480\) | 2.22737 | − | 0.196990i | 0.101665 | − | 0.00899131i | ||||
\(481\) | 14.5286 | + | 12.2123i | 0.662446 | + | 0.556832i | ||||
\(482\) | 29.1279i | 1.32674i | ||||||||
\(483\) | 2.32175 | + | 4.02139i | 0.105643 | + | 0.182980i | ||||
\(484\) | 4.09462 | − | 7.09209i | 0.186119 | − | 0.322368i | ||||
\(485\) | −34.1302 | − | 15.8760i | −1.54977 | − | 0.720890i | ||||
\(486\) | −0.866025 | − | 0.500000i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −42.1560 | −1.91027 | −0.955135 | − | 0.296171i | \(-0.904290\pi\) | ||||
−0.955135 | + | 0.296171i | \(0.904290\pi\) | |||||||
\(488\) | 5.55247 | + | 3.20572i | 0.251349 | + | 0.145116i | ||||
\(489\) | − | 16.8291i | − | 0.761037i | ||||||
\(490\) | −13.9698 | + | 9.80140i | −0.631089 | + | 0.442782i | ||||
\(491\) | −26.3161 | −1.18763 | −0.593814 | − | 0.804602i | \(-0.702379\pi\) | ||||
−0.593814 | + | 0.804602i | \(0.702379\pi\) | |||||||
\(492\) | 9.78387i | 0.441091i | ||||||||
\(493\) | −14.1978 | + | 8.19712i | −0.639438 | + | 0.369180i | ||||
\(494\) | 3.98612 | + | 2.30139i | 0.179344 | + | 0.103544i | ||||
\(495\) | 0.330260 | + | 3.73427i | 0.0148441 | + | 0.167843i | ||||
\(496\) | −4.89955 | + | 2.82876i | −0.219996 | + | 0.127015i | ||||
\(497\) | 5.35200 | − | 3.08998i | 0.240070 | − | 0.138605i | ||||
\(498\) | −2.19082 | − | 3.79462i | −0.0981731 | − | 0.170041i | ||||
\(499\) | −17.0790 | − | 9.86057i | −0.764561 | − | 0.441420i | 0.0663697 | − | 0.997795i | \(-0.478858\pi\) |
−0.830931 | + | 0.556375i | \(0.812192\pi\) | |||||||
\(500\) | −10.8075 | − | 2.86308i | −0.483328 | − | 0.128041i | ||||
\(501\) | 17.3805 | − | 10.0346i | 0.776503 | − | 0.448314i | ||||
\(502\) | −11.9150 | + | 6.87914i | −0.531793 | + | 0.307031i | ||||
\(503\) | −9.47499 | − | 16.4112i | −0.422469 | − | 0.731738i | 0.573711 | − | 0.819058i | \(-0.305503\pi\) |
−0.996180 | + | 0.0873197i | \(0.972170\pi\) | |||||||
\(504\) | − | 3.82515i | − | 0.170386i | ||||||
\(505\) | 4.53856 | + | 2.11115i | 0.201963 | + | 0.0939449i | ||||
\(506\) | 1.01760 | + | 1.76254i | 0.0452380 | + | 0.0783545i | ||||
\(507\) | 3.26433i | 0.144974i | ||||||||
\(508\) | 16.2023i | 0.718862i | ||||||||
\(509\) | 12.3220 | + | 21.3424i | 0.546164 | + | 0.945984i | 0.998533 | + | 0.0541528i | \(0.0172458\pi\) |
−0.452369 | + | 0.891831i | \(0.649421\pi\) | |||||||
\(510\) | 12.2942 | − | 1.08730i | 0.544396 | − | 0.0481466i | ||||
\(511\) | −24.4158 | + | 42.2894i | −1.08009 | + | 1.87077i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.737577 | − | 1.27752i | 0.0325648 | − | 0.0564039i | ||||
\(514\) | 3.17314 | − | 5.49604i | 0.139961 | − | 0.242420i | ||||
\(515\) | 8.57389 | + | 3.98822i | 0.377811 | + | 0.175742i | ||||
\(516\) | 10.2111 | − | 5.89540i | 0.449520 | − | 0.259531i | ||||
\(517\) | 18.9140i | 0.831837i | ||||||||
\(518\) | 22.9105 | + | 4.06011i | 1.00663 | + | 0.178391i | ||||
\(519\) | −13.8147 | −0.606399 | ||||||||
\(520\) | 5.71143 | − | 4.00723i | 0.250463 | − | 0.175729i | ||||
\(521\) | 0.538526 | − | 0.932754i | 0.0235933 | − | 0.0408647i | −0.853988 | − | 0.520293i | \(-0.825823\pi\) |
0.877581 | + | 0.479428i | \(0.159156\pi\) | |||||||
\(522\) | 2.57226 | + | 1.48510i | 0.112585 | + | 0.0650009i | ||||
\(523\) | 13.2793 | − | 23.0004i | 0.580662 | − | 1.00574i | −0.414739 | − | 0.909940i | \(-0.636127\pi\) |
0.995401 | − | 0.0957956i | \(-0.0305395\pi\) | |||||||
\(524\) | 18.2519i | 0.797339i | ||||||||
\(525\) | −6.50744 | + | 17.9847i | −0.284008 | + | 0.784915i | ||||
\(526\) | 1.08830i | 0.0474519i | ||||||||
\(527\) | −27.0435 | + | 15.6136i | −1.17803 | + | 0.680138i | ||||
\(528\) | − | 1.67653i | − | 0.0729617i | ||||||
\(529\) | −21.5264 | −0.935928 | ||||||||
\(530\) | −3.70701 | − | 5.28354i | −0.161022 | − | 0.229502i | ||||
\(531\) | 5.20788 | + | 3.00677i | 0.226003 | + | 0.130483i | ||||
\(532\) | 5.64269 | 0.244642 | ||||||||
\(533\) | 15.2638 | + | 26.4377i | 0.661150 | + | 1.14514i | ||||
\(534\) | −4.24958 | − | 7.36049i | −0.183897 | − | 0.318519i | ||||
\(535\) | 3.32915 | + | 4.74498i | 0.143932 | + | 0.205143i | ||||
\(536\) | 0.933703 | + | 0.539074i | 0.0403298 | + | 0.0232844i | ||||
\(537\) | 6.40554 | − | 11.0947i | 0.276419 | − | 0.478773i | ||||
\(538\) | −1.59200 | − | 2.75742i | −0.0686359 | − | 0.118881i | ||||
\(539\) | 6.39748 | + | 11.0808i | 0.275559 | + | 0.477282i | ||||
\(540\) | −1.28429 | − | 1.83047i | −0.0552668 | − | 0.0787708i | ||||
\(541\) | 32.7874i | 1.40964i | 0.709386 | + | 0.704821i | \(0.248973\pi\) | ||||
−0.709386 | + | 0.704821i | \(0.751027\pi\) | |||||||
\(542\) | 8.94307 | − | 15.4898i | 0.384138 | − | 0.665346i | ||||
\(543\) | −12.8694 | + | 7.43016i | −0.552280 | + | 0.318859i | ||||
\(544\) | −5.51959 | −0.236650 | ||||||||
\(545\) | 31.5739 | − | 2.79240i | 1.35248 | − | 0.119613i | ||||
\(546\) | −5.96763 | − | 10.3362i | −0.255391 | − | 0.442350i | ||||
\(547\) | 15.9573 | 0.682284 | 0.341142 | − | 0.940012i | \(-0.389186\pi\) | ||||
0.341142 | + | 0.940012i | \(0.389186\pi\) | |||||||
\(548\) | 2.57525 | + | 1.48682i | 0.110009 | + | 0.0635138i | ||||
\(549\) | − | 6.41144i | − | 0.273634i | ||||||
\(550\) | −2.85216 | + | 7.88253i | −0.121616 | + | 0.336112i | ||||
\(551\) | −2.19074 | + | 3.79448i | −0.0933289 | + | 0.161650i | ||||
\(552\) | −1.05130 | − | 0.606969i | −0.0447464 | − | 0.0258343i | ||||
\(553\) | −3.04842 | − | 5.28002i | −0.129632 | − | 0.224529i | ||||
\(554\) | −19.6343 | −0.834183 | ||||||||
\(555\) | 12.3266 | − | 5.74924i | 0.523237 | − | 0.244042i | ||||
\(556\) | 10.8796 | 0.461397 | ||||||||
\(557\) | 14.2933 | + | 24.7567i | 0.605626 | + | 1.04898i | 0.991952 | + | 0.126613i | \(0.0404106\pi\) |
−0.386326 | + | 0.922362i | \(0.626256\pi\) | |||||||
\(558\) | 4.89955 | + | 2.82876i | 0.207415 | + | 0.119751i | ||||
\(559\) | 18.3948 | − | 31.8608i | 0.778019 | − | 1.34757i | ||||
\(560\) | 3.60746 | − | 7.75534i | 0.152443 | − | 0.327723i | ||||
\(561\) | − | 9.25377i | − | 0.390695i | ||||||
\(562\) | 10.2198 | + | 5.90041i | 0.431096 | + | 0.248894i | ||||
\(563\) | −10.1756 | −0.428850 | −0.214425 | − | 0.976740i | \(-0.568788\pi\) | ||||
−0.214425 | + | 0.976740i | \(0.568788\pi\) | |||||||
\(564\) | −5.64081 | − | 9.77017i | −0.237521 | − | 0.411398i | ||||
\(565\) | 3.38489 | + | 38.2732i | 0.142403 | + | 1.61016i | ||||
\(566\) | 2.15974 | 0.0907806 | ||||||||
\(567\) | −3.31268 | + | 1.91258i | −0.139119 | + | 0.0803207i | ||||
\(568\) | −0.807805 | + | 1.39916i | −0.0338948 | + | 0.0587075i | ||||
\(569\) | 41.4725i | 1.73862i | 0.494270 | + | 0.869308i | \(0.335435\pi\) | ||||
−0.494270 | + | 0.869308i | \(0.664565\pi\) | |||||||
\(570\) | 2.70022 | − | 1.89452i | 0.113100 | − | 0.0793526i | ||||
\(571\) | −3.26000 | − | 5.64649i | −0.136427 | − | 0.236298i | 0.789715 | − | 0.613474i | \(-0.210229\pi\) |
−0.926142 | + | 0.377176i | \(0.876895\pi\) | |||||||
\(572\) | −2.61556 | − | 4.53028i | −0.109362 | − | 0.189421i | ||||
\(573\) | 6.27162 | − | 10.8628i | 0.262001 | − | 0.453798i | ||||
\(574\) | 32.4108 | + | 18.7124i | 1.35280 | + | 0.781040i | ||||
\(575\) | 3.91030 | + | 4.64228i | 0.163071 | + | 0.193596i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 17.6741 | + | 30.6124i | 0.735781 | + | 1.27441i | 0.954380 | + | 0.298596i | \(0.0965182\pi\) |
−0.218599 | + | 0.975815i | \(0.570149\pi\) | |||||||
\(578\) | −13.4659 | −0.560106 | ||||||||
\(579\) | −22.6437 | − | 13.0734i | −0.941041 | − | 0.543310i | ||||
\(580\) | 3.81457 | + | 5.43684i | 0.158392 | + | 0.225753i | ||||
\(581\) | −16.7605 | −0.695341 | ||||||||
\(582\) | − | 16.8340i | − | 0.697792i | ||||||
\(583\) | −4.19088 | + | 2.41961i | −0.173569 | + | 0.100210i | ||||
\(584\) | − | 12.7659i | − | 0.528257i | ||||||
\(585\) | −6.32608 | − | 2.94263i | −0.261551 | − | 0.121663i | ||||
\(586\) | − | 3.57631i | − | 0.147736i | ||||||
\(587\) | −4.39397 | + | 7.61058i | −0.181359 | + | 0.314122i | −0.942343 | − | 0.334647i | \(-0.891383\pi\) |
0.760985 | + | 0.648770i | \(0.224716\pi\) | |||||||
\(588\) | −6.60933 | − | 3.81590i | −0.272564 | − | 0.157365i | ||||
\(589\) | −4.17285 | + | 7.22759i | −0.171939 | + | 0.297808i | ||||
\(590\) | 7.72311 | + | 11.0076i | 0.317955 | + | 0.453176i | ||||
\(591\) | 24.1061 | 0.991592 | ||||||||
\(592\) | −5.71772 | + | 2.07550i | −0.234997 | + | 0.0853025i | ||||
\(593\) | 25.1637i | 1.03335i | 0.856182 | + | 0.516675i | \(0.172830\pi\) | ||||
−0.856182 | + | 0.516675i | \(0.827170\pi\) | |||||||
\(594\) | −1.45192 | + | 0.838266i | −0.0595730 | + | 0.0343945i | ||||
\(595\) | 19.9117 | − | 42.8063i | 0.816300 | − | 1.75489i | ||||
\(596\) | −4.48787 | + | 7.77322i | −0.183830 | + | 0.318404i | ||||
\(597\) | −10.7475 | + | 18.6153i | −0.439867 | + | 0.761872i | ||||
\(598\) | −3.78773 | −0.154892 | ||||||||
\(599\) | 14.2456 | − | 24.6741i | 0.582060 | − | 1.00816i | −0.413175 | − | 0.910652i | \(-0.635580\pi\) |
0.995235 | − | 0.0975062i | \(-0.0310866\pi\) | |||||||
\(600\) | −0.877540 | − | 4.92239i | −0.0358254 | − | 0.200956i | ||||
\(601\) | 11.6102 | + | 20.1095i | 0.473591 | + | 0.820284i | 0.999543 | − | 0.0302304i | \(-0.00962411\pi\) |
−0.525952 | + | 0.850514i | \(0.676291\pi\) | |||||||
\(602\) | − | 45.1016i | − | 1.83820i | ||||||
\(603\) | − | 1.07815i | − | 0.0439056i | ||||||
\(604\) | −5.87683 | − | 10.1790i | −0.239125 | − | 0.414177i | ||||
\(605\) | −16.6033 | − | 7.72318i | −0.675021 | − | 0.313992i | ||||
\(606\) | 2.23855i | 0.0909348i | ||||||||
\(607\) | 23.1472 | + | 40.0921i | 0.939515 | + | 1.62729i | 0.766377 | + | 0.642391i | \(0.222057\pi\) |
0.173138 | + | 0.984898i | \(0.444609\pi\) | |||||||
\(608\) | −1.27752 | + | 0.737577i | −0.0518103 | + | 0.0299127i | ||||
\(609\) | 9.83930 | − | 5.68072i | 0.398708 | − | 0.230194i | ||||
\(610\) | 6.04656 | − | 12.9989i | 0.244818 | − | 0.526311i | ||||
\(611\) | −30.4849 | − | 17.6005i | −1.23329 | − | 0.712039i | ||||
\(612\) | 2.75979 | + | 4.78010i | 0.111558 | + | 0.193224i | ||||
\(613\) | −23.1733 | + | 13.3791i | −0.935963 | + | 0.540378i | −0.888692 | − | 0.458504i | \(-0.848386\pi\) |
−0.0472702 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(614\) | 9.85354 | − | 5.68895i | 0.397657 | − | 0.229587i | ||||
\(615\) | 21.7923 | − | 1.92732i | 0.878752 | − | 0.0777171i | ||||
\(616\) | −5.55382 | − | 3.20650i | −0.223770 | − | 0.129193i | ||||
\(617\) | −4.78348 | + | 2.76174i | −0.192576 | + | 0.111184i | −0.593188 | − | 0.805064i | \(-0.702131\pi\) |
0.400612 | + | 0.916248i | \(0.368797\pi\) | |||||||
\(618\) | 4.22889i | 0.170111i | ||||||||
\(619\) | −22.2474 | −0.894200 | −0.447100 | − | 0.894484i | \(-0.647543\pi\) | ||||
−0.447100 | + | 0.894484i | \(0.647543\pi\) | |||||||
\(620\) | 7.26586 | + | 10.3559i | 0.291804 | + | 0.415903i | ||||
\(621\) | 1.21394i | 0.0487137i | ||||||||
\(622\) | 25.0523 | + | 14.4639i | 1.00450 | + | 0.579951i | ||||
\(623\) | −32.5106 | −1.30251 | ||||||||
\(624\) | 2.70218 | + | 1.56010i | 0.108174 | + | 0.0624540i | ||||
\(625\) | −4.24817 | + | 24.6364i | −0.169927 | + | 0.985457i | ||||
\(626\) | −6.77595 | + | 11.7363i | −0.270821 | + | 0.469076i | ||||
\(627\) | −1.23657 | − | 2.14180i | −0.0493839 | − | 0.0855354i | ||||
\(628\) | 0.124988i | 0.00498755i | ||||||||
\(629\) | −31.5595 | + | 11.4559i | −1.25836 | + | 0.456777i | ||||
\(630\) | −8.52005 | + | 0.753516i | −0.339447 | + | 0.0300208i | ||||
\(631\) | −27.6705 | + | 15.9756i | −1.10154 | + | 0.635977i | −0.936626 | − | 0.350330i | \(-0.886069\pi\) |
−0.164918 | + | 0.986307i | \(0.552736\pi\) | |||||||
\(632\) | 1.38034 | + | 0.796940i | 0.0549070 | + | 0.0317006i | ||||
\(633\) | 6.60256 | + | 3.81199i | 0.262428 | + | 0.151513i | ||||
\(634\) | 0.669018 | + | 0.386258i | 0.0265701 | + | 0.0153403i | ||||
\(635\) | 36.0887 | − | 3.19169i | 1.43213 | − | 0.126658i | ||||
\(636\) | 1.44322 | − | 2.49973i | 0.0572274 | − | 0.0991208i | ||||
\(637\) | −23.8128 | −0.943496 | ||||||||
\(638\) | 4.31248 | − | 2.48981i | 0.170733 | − | 0.0985726i | ||||
\(639\) | 1.61561 | 0.0639126 | ||||||||
\(640\) | 0.196990 | + | 2.22737i | 0.00778670 | + | 0.0880447i | ||||
\(641\) | −7.48229 | − | 12.9597i | −0.295533 | − | 0.511878i | 0.679576 | − | 0.733605i | \(-0.262164\pi\) |
−0.975109 | + | 0.221727i | \(0.928830\pi\) | |||||||
\(642\) | −1.29611 | + | 2.24493i | −0.0511534 | + | 0.0886004i | ||||
\(643\) | 11.0905 | 0.437365 | 0.218683 | − | 0.975796i | \(-0.429824\pi\) | ||||
0.218683 | + | 0.975796i | \(0.429824\pi\) | |||||||
\(644\) | −4.02139 | + | 2.32175i | −0.158465 | + | 0.0914898i | ||||
\(645\) | −15.1427 | − | 21.5827i | −0.596245 | − | 0.849817i | ||||
\(646\) | −7.05139 | + | 4.07112i | −0.277433 | + | 0.160176i | ||||
\(647\) | −10.1375 | + | 17.5587i | −0.398547 | + | 0.690304i | −0.993547 | − | 0.113422i | \(-0.963819\pi\) |
0.595000 | + | 0.803726i | \(0.297152\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 8.73118 | − | 5.04095i | 0.342729 | − | 0.197875i | ||||
\(650\) | −10.0507 | − | 11.9321i | −0.394221 | − | 0.468016i | ||||
\(651\) | 18.7415 | − | 10.8204i | 0.734539 | − | 0.424086i | ||||
\(652\) | 16.8291 | 0.659077 | ||||||||
\(653\) | 16.6048 | − | 28.7604i | 0.649797 | − | 1.12548i | −0.333375 | − | 0.942794i | \(-0.608187\pi\) |
0.983171 | − | 0.182686i | \(-0.0584793\pi\) | |||||||
\(654\) | 7.08769 | + | 12.2762i | 0.277151 | + | 0.480039i | ||||
\(655\) | 40.6539 | − | 3.59544i | 1.58848 | − | 0.140486i | ||||
\(656\) | −9.78387 | −0.381996 | ||||||||
\(657\) | −11.0556 | + | 6.38296i | −0.431320 | + | 0.249023i | ||||
\(658\) | −43.1539 | −1.68231 | ||||||||
\(659\) | 14.0393 | − | 24.3168i | 0.546894 | − | 0.947249i | −0.451591 | − | 0.892225i | \(-0.649143\pi\) |
0.998485 | − | 0.0550236i | \(-0.0175234\pi\) | |||||||
\(660\) | −3.73427 | + | 0.330260i | −0.145356 | + | 0.0128553i | ||||
\(661\) | −15.3660 | − | 8.87157i | −0.597669 | − | 0.345064i | 0.170455 | − | 0.985365i | \(-0.445476\pi\) |
−0.768124 | + | 0.640301i | \(0.778810\pi\) | |||||||
\(662\) | −6.34735 | − | 3.66465i | −0.246697 | − | 0.142430i | ||||
\(663\) | 14.9149 | + | 8.61112i | 0.579247 | + | 0.334428i | ||||
\(664\) | 3.79462 | − | 2.19082i | 0.147260 | − | 0.0850204i | ||||
\(665\) | −1.11155 | − | 12.5684i | −0.0431041 | − | 0.487381i | ||||
\(666\) | 4.65629 | + | 3.91394i | 0.180428 | + | 0.151662i | ||||
\(667\) | − | 3.60563i | − | 0.139611i | ||||||
\(668\) | 10.0346 | + | 17.3805i | 0.388252 | + | 0.672471i | ||||
\(669\) | 2.00054 | − | 3.46504i | 0.0773455 | − | 0.133966i | ||||
\(670\) | 1.01679 | − | 2.18590i | 0.0392820 | − | 0.0844486i | ||||
\(671\) | −9.30890 | − | 5.37450i | −0.359366 | − | 0.207480i | ||||
\(672\) | 3.82515 | 0.147558 | ||||||||
\(673\) | −21.5251 | − | 12.4275i | −0.829730 | − | 0.479045i | 0.0240303 | − | 0.999711i | \(-0.492350\pi\) |
−0.853760 | + | 0.520666i | \(0.825684\pi\) | |||||||
\(674\) | 11.8053i | 0.454725i | ||||||||
\(675\) | −3.82415 | + | 3.22117i | −0.147191 | + | 0.123983i | ||||
\(676\) | −3.26433 | −0.125551 | ||||||||
\(677\) | 31.6990i | 1.21829i | 0.793059 | + | 0.609145i | \(0.208487\pi\) | ||||
−0.793059 | + | 0.609145i | \(0.791513\pi\) | |||||||
\(678\) | −14.8810 | + | 8.59155i | −0.571501 | + | 0.329956i | ||||
\(679\) | −55.7657 | − | 32.1963i | −2.14009 | − | 1.23558i | ||||
\(680\) | 1.08730 | + | 12.2942i | 0.0416961 | + | 0.471461i | ||||
\(681\) | 11.1562 | − | 6.44101i | 0.427505 | − | 0.246820i | ||||
\(682\) | 8.21426 | − | 4.74250i | 0.314540 | − | 0.181600i | ||||
\(683\) | 23.4462 | + | 40.6100i | 0.897144 | + | 1.55390i | 0.831129 | + | 0.556080i | \(0.187695\pi\) |
0.0660151 | + | 0.997819i | \(0.478971\pi\) | |||||||
\(684\) | 1.27752 | + | 0.737577i | 0.0488472 | + | 0.0282019i | ||||
\(685\) | 2.80441 | − | 6.02893i | 0.107151 | − | 0.230354i | ||||
\(686\) | −2.09294 | + | 1.20836i | −0.0799089 | + | 0.0461354i | ||||
\(687\) | −13.5375 | + | 7.81590i | −0.516489 | + | 0.298195i | ||||
\(688\) | 5.89540 | + | 10.2111i | 0.224760 | + | 0.389296i | ||||
\(689\) | − | 9.00628i | − | 0.343112i | ||||||
\(690\) | −1.14485 | + | 2.46121i | −0.0435838 | + | 0.0936966i | ||||
\(691\) | 4.24583 | + | 7.35399i | 0.161519 | + | 0.279759i | 0.935414 | − | 0.353555i | \(-0.115027\pi\) |
−0.773895 | + | 0.633314i | \(0.781694\pi\) | |||||||
\(692\) | − | 13.8147i | − | 0.525157i | ||||||
\(693\) | 6.41299i | 0.243609i | ||||||||
\(694\) | −5.25860 | − | 9.10817i | −0.199614 | − | 0.345741i | ||||
\(695\) | −2.14317 | − | 24.2329i | −0.0812950 | − | 0.919207i | ||||
\(696\) | −1.48510 | + | 2.57226i | −0.0562924 | + | 0.0975014i | ||||
\(697\) | −54.0029 | −2.04551 | ||||||||
\(698\) | 10.6455 | − | 18.4385i | 0.402938 | − | 0.697908i | ||||
\(699\) | 1.25481 | − | 2.17339i | 0.0474612 | − | 0.0822052i | ||||
\(700\) | −17.9847 | − | 6.50744i | −0.679756 | − | 0.245958i | ||||
\(701\) | 10.6232 | − | 6.13333i | 0.401234 | − | 0.231653i | −0.285782 | − | 0.958295i | \(-0.592253\pi\) |
0.687016 | + | 0.726642i | \(0.258920\pi\) | |||||||
\(702\) | − | 3.12020i | − | 0.117764i | ||||||
\(703\) | −5.77366 | + | 6.86875i | −0.217758 | + | 0.259060i | ||||
\(704\) | 1.67653 | 0.0631867 | ||||||||
\(705\) | −20.6506 | + | 14.4888i | −0.777748 | + | 0.545680i | ||||
\(706\) | −1.38917 | + | 2.40612i | −0.0522823 | + | 0.0905555i | ||||
\(707\) | 7.41559 | + | 4.28140i | 0.278892 | + | 0.161018i | ||||
\(708\) | −3.00677 | + | 5.20788i | −0.113001 | + | 0.195724i | ||||
\(709\) | − | 11.8142i | − | 0.443692i | −0.975082 | − | 0.221846i | \(-0.928792\pi\) | ||
0.975082 | − | 0.221846i | \(-0.0712083\pi\) | |||||||
\(710\) | 3.27558 | + | 1.52366i | 0.122930 | + | 0.0571821i | ||||
\(711\) | − | 1.59388i | − | 0.0597752i | ||||||
\(712\) | 7.36049 | − | 4.24958i | 0.275846 | − | 0.159260i | ||||
\(713\) | − | 6.86788i | − | 0.257204i | ||||||
\(714\) | 21.1133 | 0.790144 | ||||||||
\(715\) | −9.57540 | + | 6.71825i | −0.358100 | + | 0.251248i | ||||
\(716\) | 11.0947 | + | 6.40554i | 0.414629 | + | 0.239386i | ||||
\(717\) | 4.26585 | 0.159311 | ||||||||
\(718\) | −13.5421 | − | 23.4555i | −0.505385 | − | 0.875353i | ||||
\(719\) | 7.22948 | + | 12.5218i | 0.269614 | + | 0.466985i | 0.968762 | − | 0.247992i | \(-0.0797705\pi\) |
−0.699148 | + | 0.714977i | \(0.746437\pi\) | |||||||
\(720\) | 1.83047 | − | 1.28429i | 0.0682175 | − | 0.0478625i | ||||
\(721\) | 14.0089 | + | 8.08807i | 0.521720 | + | 0.301215i | ||||
\(722\) | 8.41196 | − | 14.5699i | 0.313061 | − | 0.542237i | ||||
\(723\) | 14.5640 | + | 25.2255i | 0.541639 | + | 0.938147i | ||||
\(724\) | −7.43016 | − | 12.8694i | −0.276140 | − | 0.478288i | ||||
\(725\) | 11.3584 | − | 9.56749i | 0.421842 | − | 0.355327i | ||||
\(726\) | − | 8.18924i | − | 0.303931i | ||||||
\(727\) | −15.6966 | + | 27.1874i | −0.582156 | + | 1.00832i | 0.413068 | + | 0.910700i | \(0.364457\pi\) |
−0.995223 | + | 0.0976231i | \(0.968876\pi\) | |||||||
\(728\) | 10.3362 | − | 5.96763i | 0.383086 | − | 0.221175i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −28.4345 | + | 2.51475i | −1.05241 | + | 0.0930752i | ||||
\(731\) | 32.5402 | + | 56.3613i | 1.20354 | + | 2.08460i | ||||
\(732\) | 6.41144 | 0.236974 | ||||||||
\(733\) | −17.0623 | − | 9.85091i | −0.630210 | − | 0.363852i | 0.150624 | − | 0.988591i | \(-0.451872\pi\) |
−0.780833 | + | 0.624739i | \(0.785205\pi\) | |||||||
\(734\) | − | 0.639187i | − | 0.0235928i | ||||||
\(735\) | −7.19746 | + | 15.4731i | −0.265482 | + | 0.570735i | ||||
\(736\) | 0.606969 | − | 1.05130i | 0.0223732 | − | 0.0387515i | ||||
\(737\) | −1.56538 | − | 0.903775i | −0.0576616 | − | 0.0332910i | ||||
\(738\) | 4.89193 | + | 8.47308i | 0.180075 | + | 0.311898i | ||||
\(739\) | 20.8046 | 0.765309 | 0.382654 | − | 0.923892i | \(-0.375010\pi\) | ||||
0.382654 | + | 0.923892i | \(0.375010\pi\) | |||||||
\(740\) | 5.74924 | + | 12.3266i | 0.211346 | + | 0.453137i | ||||
\(741\) | 4.60278 | 0.169087 | ||||||||
\(742\) | −5.52054 | − | 9.56186i | −0.202665 | − | 0.351027i | ||||
\(743\) | −32.1117 | − | 18.5397i | −1.17807 | − | 0.680156i | −0.222499 | − | 0.974933i | \(-0.571421\pi\) |
−0.955566 | + | 0.294776i | \(0.904755\pi\) | |||||||
\(744\) | −2.82876 | + | 4.89955i | −0.103707 | + | 0.179626i | ||||
\(745\) | 18.1979 | + | 8.46493i | 0.666721 | + | 0.310131i | ||||
\(746\) | 9.34596i | 0.342180i | ||||||||
\(747\) | −3.79462 | − | 2.19082i | −0.138838 | − | 0.0801580i | ||||
\(748\) | 9.25377 | 0.338351 | ||||||||
\(749\) | 4.95783 | + | 8.58721i | 0.181155 | + | 0.313770i | ||||
\(750\) | −10.7911 | + | 2.92427i | −0.394037 | + | 0.106779i | ||||
\(751\) | −8.36573 | −0.305270 | −0.152635 | − | 0.988283i | \(-0.548776\pi\) | ||||
−0.152635 | + | 0.988283i | \(0.548776\pi\) | |||||||
\(752\) | 9.77017 | − | 5.64081i | 0.356281 | − | 0.205699i | ||||
\(753\) | −6.87914 | + | 11.9150i | −0.250690 | + | 0.434207i | ||||
\(754\) | 9.26760i | 0.337506i | ||||||||
\(755\) | −21.5147 | + | 15.0951i | −0.783000 | + | 0.549365i | ||||
\(756\) | −1.91258 | − | 3.31268i | −0.0695597 | − | 0.120481i | ||||
\(757\) | 7.05341 | + | 12.2169i | 0.256361 | + | 0.444030i | 0.965264 | − | 0.261276i | \(-0.0841432\pi\) |
−0.708904 | + | 0.705305i | \(0.750810\pi\) | |||||||
\(758\) | −14.4675 | + | 25.0584i | −0.525482 | + | 0.910161i | ||||
\(759\) | 1.76254 | + | 1.01760i | 0.0639762 | + | 0.0369367i | ||||
\(760\) | 1.89452 | + | 2.70022i | 0.0687214 | + | 0.0979473i | ||||
\(761\) | 8.89832 | + | 15.4123i | 0.322564 | + | 0.558697i | 0.981016 | − | 0.193926i | \(-0.0621220\pi\) |
−0.658453 | + | 0.752622i | \(0.728789\pi\) | |||||||
\(762\) | 8.10117 | + | 14.0316i | 0.293474 | + | 0.508312i | ||||
\(763\) | 54.2230 | 1.96300 | ||||||||
\(764\) | 10.8628 | + | 6.27162i | 0.393001 | + | 0.226899i | ||||
\(765\) | 10.1034 | − | 7.08873i | 0.365290 | − | 0.256293i | ||||
\(766\) | −10.2615 | −0.370764 | ||||||||
\(767\) | 18.7635i | 0.677510i | ||||||||
\(768\) | −0.866025 | + | 0.500000i | −0.0312500 | + | 0.0180422i | ||||
\(769\) | 21.3406i | 0.769563i | 0.923008 | + | 0.384782i | \(0.125723\pi\) | ||||
−0.923008 | + | 0.384782i | \(0.874277\pi\) | |||||||
\(770\) | −6.04802 | + | 13.0021i | −0.217956 | + | 0.468562i | ||||
\(771\) | − | 6.34628i | − | 0.228556i | ||||||
\(772\) | 13.0734 | − | 22.6437i | 0.470521 | − | 0.814966i | ||||
\(773\) | −39.3866 | − | 22.7399i | −1.41664 | − | 0.817896i | −0.420636 | − | 0.907229i | \(-0.638193\pi\) |
−0.996002 | + | 0.0893331i | \(0.971526\pi\) | |||||||
\(774\) | 5.89540 | − | 10.2111i | 0.211906 | − | 0.367032i | ||||
\(775\) | 21.6352 | − | 18.2238i | 0.777158 | − | 0.654618i | ||||
\(776\) | 16.8340 | 0.604306 | ||||||||
\(777\) | 21.8711 | − | 7.93910i | 0.784623 | − | 0.284814i | ||||
\(778\) | − | 27.8334i | − | 0.997876i | ||||||
\(779\) | −12.4991 | + | 7.21635i | −0.447826 | + | 0.258553i | ||||
\(780\) | 2.94263 | − | 6.32608i | 0.105363 | − | 0.226510i | ||||
\(781\) | 1.35431 | − | 2.34574i | 0.0484611 | − | 0.0839371i | ||||
\(782\) | 3.35022 | − | 5.80275i | 0.119804 | − | 0.207506i | ||||
\(783\) | 2.97019 | 0.106146 | ||||||||
\(784\) | 3.81590 | − | 6.60933i | 0.136282 | − | 0.236048i | ||||
\(785\) | 0.278394 | − | 0.0246213i | 0.00993632 | − | 0.000878772i | ||||
\(786\) | 9.12596 | + | 15.8066i | 0.325512 | + | 0.563804i | ||||
\(787\) | − | 50.6502i | − | 1.80549i | −0.430181 | − | 0.902743i | \(-0.641550\pi\) | ||
0.430181 | − | 0.902743i | \(-0.358450\pi\) | |||||||
\(788\) | 24.1061i | 0.858744i | ||||||||
\(789\) | 0.544148 | + | 0.942492i | 0.0193722 | + | 0.0335536i | ||||
\(790\) | 1.50317 | − | 3.23152i | 0.0534804 | − | 0.114972i | ||||
\(791\) | 65.7280i | 2.33702i | ||||||||
\(792\) | −0.838266 | − | 1.45192i | −0.0297865 | − | 0.0515917i | ||||
\(793\) | 17.3248 | − | 10.0025i | 0.615223 | − | 0.355199i | ||||
\(794\) | 10.7607 | − | 6.21267i | 0.381881 | − | 0.220479i | ||||
\(795\) | −5.85214 | − | 2.72217i | −0.207554 | − | 0.0965455i | ||||
\(796\) | −18.6153 | − | 10.7475i | −0.659801 | − | 0.380936i | ||||
\(797\) | −14.5683 | − | 25.2330i | −0.516034 | − | 0.893797i | −0.999827 | − | 0.0186145i | \(-0.994074\pi\) |
0.483793 | − | 0.875183i | \(-0.339259\pi\) | |||||||
\(798\) | 4.88671 | − | 2.82134i | 0.172988 | − | 0.0998745i | ||||
\(799\) | 53.9273 | − | 31.1349i | 1.90781 | − | 1.10147i | ||||
\(800\) | 4.92239 | − | 0.877540i | 0.174033 | − | 0.0310257i | ||||
\(801\) | −7.36049 | − | 4.24958i | −0.260070 | − | 0.150151i | ||||
\(802\) | −29.8389 | + | 17.2275i | −1.05365 | + | 0.608323i | ||||
\(803\) | 21.4025i | 0.755277i | ||||||||
\(804\) | 1.07815 | 0.0380233 | ||||||||
\(805\) | 5.96358 | + | 8.49978i | 0.210189 | + | 0.299578i | ||||
\(806\) | 17.6526i | 0.621786i | ||||||||
\(807\) | −2.75742 | − | 1.59200i | −0.0970658 | − | 0.0560410i | ||||
\(808\) | −2.23855 | −0.0787519 | ||||||||
\(809\) | 11.6111 | + | 6.70365i | 0.408223 | + | 0.235688i | 0.690026 | − | 0.723785i | \(-0.257599\pi\) |
−0.281803 | + | 0.959472i | \(0.590932\pi\) | |||||||
\(810\) | −2.02746 | − | 0.943089i | −0.0712376 | − | 0.0331368i | ||||
\(811\) | −10.3926 | + | 18.0005i | −0.364933 | + | 0.632082i | −0.988765 | − | 0.149476i | \(-0.952241\pi\) |
0.623833 | + | 0.781558i | \(0.285575\pi\) | |||||||
\(812\) | 5.68072 | + | 9.83930i | 0.199354 | + | 0.345292i | ||||
\(813\) | − | 17.8861i | − | 0.627294i | ||||||
\(814\) | 9.58594 | − | 3.47964i | 0.335987 | − | 0.121961i | ||||
\(815\) | −3.31515 | − | 37.4846i | −0.116125 | − | 1.31303i | ||||
\(816\) | −4.78010 | + | 2.75979i | −0.167337 | + | 0.0966121i | ||||
\(817\) | 15.0630 | + | 8.69662i | 0.526987 | + | 0.304256i | ||||
\(818\) | −9.78149 | − | 5.64735i | −0.342002 | − | 0.197455i | ||||
\(819\) | −10.3362 | − | 5.96763i | −0.361177 | − | 0.208526i | ||||
\(820\) | 1.92732 | + | 21.7923i | 0.0673050 | + | 0.761021i | ||||
\(821\) | −16.4776 | + | 28.5400i | −0.575072 | + | 0.996053i | 0.420962 | + | 0.907078i | \(0.361693\pi\) |
−0.996034 | + | 0.0889752i | \(0.971641\pi\) | |||||||
\(822\) | 2.97364 | 0.103718 | ||||||||
\(823\) | 42.3090 | − | 24.4271i | 1.47480 | − | 0.851476i | 0.475203 | − | 0.879876i | \(-0.342374\pi\) |
0.999597 | + | 0.0283998i | \(0.00904115\pi\) | |||||||
\(824\) | −4.22889 | −0.147320 | ||||||||
\(825\) | 1.47122 | + | 8.25255i | 0.0512214 | + | 0.287317i | ||||
\(826\) | 11.5014 | + | 19.9209i | 0.400184 | + | 0.693138i | ||||
\(827\) | 4.83019 | − | 8.36614i | 0.167962 | − | 0.290919i | −0.769741 | − | 0.638356i | \(-0.779615\pi\) |
0.937703 | + | 0.347437i | \(0.112948\pi\) | |||||||
\(828\) | −1.21394 | −0.0421873 | ||||||||
\(829\) | −6.94733 | + | 4.01104i | −0.241291 | + | 0.139309i | −0.615770 | − | 0.787926i | \(-0.711155\pi\) |
0.374479 | + | 0.927235i | \(0.377822\pi\) | |||||||
\(830\) | −5.62728 | − | 8.02046i | −0.195326 | − | 0.278394i | ||||
\(831\) | −17.0038 | + | 9.81717i | −0.589857 | + | 0.340554i | ||||
\(832\) | −1.56010 | + | 2.70218i | −0.0540868 | + | 0.0936811i | ||||
\(833\) | 21.0622 | − | 36.4808i | 0.729762 | − | 1.26398i | ||||
\(834\) | 9.42200 | − | 5.43980i | 0.326257 | − | 0.188365i | ||||
\(835\) | 36.7361 | − | 25.7747i | 1.27131 | − | 0.891969i | ||||
\(836\) | 2.14180 | − | 1.23657i | 0.0740758 | − | 0.0427677i | ||||
\(837\) | 5.65752 | 0.195552 | ||||||||
\(838\) | −1.76879 | + | 3.06364i | −0.0611019 | + | 0.105832i | ||||
\(839\) | −6.52889 | − | 11.3084i | −0.225402 | − | 0.390408i | 0.731038 | − | 0.682337i | \(-0.239036\pi\) |
−0.956440 | + | 0.291929i | \(0.905703\pi\) | |||||||
\(840\) | −0.753516 | − | 8.52005i | −0.0259988 | − | 0.293970i | ||||
\(841\) | 20.1780 | 0.695792 | ||||||||
\(842\) | −0.278852 | + | 0.160995i | −0.00960986 | + | 0.00554825i | ||||
\(843\) | 11.8008 | 0.406442 | ||||||||
\(844\) | −3.81199 | + | 6.60256i | −0.131214 | + | 0.227269i | ||||
\(845\) | 0.643040 | + | 7.27089i | 0.0221213 | + | 0.250126i | ||||
\(846\) | −9.77017 | − | 5.64081i | −0.335905 | − | 0.193935i | ||||
\(847\) | −27.1283 | − | 15.6625i | −0.932140 | − | 0.538171i | ||||
\(848\) | 2.49973 | + | 1.44322i | 0.0858411 | + | 0.0495604i | ||||
\(849\) | 1.87039 | − | 1.07987i | 0.0641916 | − | 0.0370610i | ||||
\(850\) | 27.1696 | − | 4.84366i | 0.931909 | − | 0.166136i | ||||
\(851\) | 1.28850 | − | 7.27081i | 0.0441694 | − | 0.249240i | ||||
\(852\) | 1.61561i | 0.0553499i | ||||||||
\(853\) | −2.75064 | − | 4.76425i | −0.0941802 | − | 0.163125i | 0.815086 | − | 0.579340i | \(-0.196690\pi\) |
−0.909266 | + | 0.416215i | \(0.863356\pi\) | |||||||
\(854\) | 12.2624 | − | 21.2391i | 0.419610 | − | 0.726786i | ||||
\(855\) | 1.39120 | − | 2.99081i | 0.0475781 | − | 0.102284i | ||||
\(856\) | −2.24493 | − | 1.29611i | −0.0767302 | − | 0.0443002i | ||||
\(857\) | −41.3989 | −1.41416 | −0.707080 | − | 0.707133i | \(-0.749988\pi\) | ||||
−0.707080 | + | 0.707133i | \(0.749988\pi\) | |||||||
\(858\) | −4.53028 | − | 2.61556i | −0.154661 | − | 0.0892938i | ||||
\(859\) | − | 53.2983i | − | 1.81851i | −0.416234 | − | 0.909257i | \(-0.636650\pi\) | ||
0.416234 | − | 0.909257i | \(-0.363350\pi\) | |||||||
\(860\) | 21.5827 | − | 15.1427i | 0.735963 | − | 0.516363i | ||||
\(861\) | 37.4248 | 1.27543 | ||||||||
\(862\) | 24.7136i | 0.841748i | ||||||||
\(863\) | −2.65162 | + | 1.53092i | −0.0902623 | + | 0.0521130i | −0.544452 | − | 0.838792i | \(-0.683262\pi\) |
0.454189 | + | 0.890905i | \(0.349929\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −30.7706 | + | 2.72136i | −1.04623 | + | 0.0925290i | ||||
\(866\) | −2.47919 | + | 1.43136i | −0.0842463 | + | 0.0486396i | ||||
\(867\) | −11.6618 | + | 6.73293i | −0.396055 | + | 0.228662i | ||||
\(868\) | 10.8204 | + | 18.7415i | 0.367269 | + | 0.636129i | ||||
\(869\) | −2.31419 | − | 1.33610i | −0.0785034 | − | 0.0453240i | ||||
\(870\) | 6.02194 | + | 2.80116i | 0.204163 | + | 0.0949681i | ||||
\(871\) | 2.91334 | − | 1.68202i | 0.0987149 | − | 0.0569931i | ||||
\(872\) | −12.2762 | + | 7.08769i | −0.415726 | + | 0.240019i | ||||
\(873\) | −8.41700 | − | 14.5787i | −0.284872 | − | 0.493413i | ||||
\(874\) | − | 1.79075i | − | 0.0605729i | ||||||
\(875\) | −10.9517 | + | 41.3405i | −0.370235 | + | 1.39756i | ||||
\(876\) | −6.38296 | − | 11.0556i | −0.215660 | − | 0.373534i | ||||
\(877\) | − | 6.30833i | − | 0.213017i | −0.994312 | − | 0.106509i | \(-0.966033\pi\) | ||
0.994312 | − | 0.106509i | \(-0.0339672\pi\) | |||||||
\(878\) | − | 1.94170i | − | 0.0655292i | ||||||
\(879\) | −1.78816 | − | 3.09718i | −0.0603130 | − | 0.104465i | ||||
\(880\) | −0.330260 | − | 3.73427i | −0.0111331 | − | 0.125882i | ||||
\(881\) | 28.6385 | − | 49.6034i | 0.964857 | − | 1.67118i | 0.254858 | − | 0.966978i | \(-0.417971\pi\) |
0.709999 | − | 0.704203i | \(-0.248696\pi\) | |||||||
\(882\) | −7.63180 | −0.256976 | ||||||||
\(883\) | −9.87025 | + | 17.0958i | −0.332160 | + | 0.575319i | −0.982935 | − | 0.183952i | \(-0.941111\pi\) |
0.650775 | + | 0.759271i | \(0.274444\pi\) | |||||||
\(884\) | −8.61112 | + | 14.9149i | −0.289623 | + | 0.501642i | ||||
\(885\) | 12.1922 | + | 5.67131i | 0.409836 | + | 0.190639i | ||||
\(886\) | −16.7356 | + | 9.66231i | −0.562244 | + | 0.324612i | ||||
\(887\) | − | 1.06021i | − | 0.0355983i | −0.999842 | − | 0.0177992i | \(-0.994334\pi\) | ||
0.999842 | − | 0.0177992i | \(-0.00566595\pi\) | |||||||
\(888\) | −3.91394 | + | 4.65629i | −0.131343 | + | 0.156255i | ||||
\(889\) | 61.9764 | 2.07862 | ||||||||
\(890\) | −10.9153 | − | 15.5574i | −0.365883 | − | 0.521486i | ||||
\(891\) | −0.838266 | + | 1.45192i | −0.0280830 | + | 0.0486411i | ||||
\(892\) | 3.46504 | + | 2.00054i | 0.116018 | + | 0.0669831i | ||||
\(893\) | 8.32106 | − | 14.4125i | 0.278453 | − | 0.482296i | ||||
\(894\) | 8.97575i | 0.300194i | ||||||||
\(895\) | 12.0820 | − | 25.9739i | 0.403856 | − | 0.868212i | ||||
\(896\) | 3.82515i | 0.127789i | ||||||||
\(897\) | −3.28027 | + | 1.89387i | −0.109525 | + | 0.0632344i | ||||
\(898\) | − | 22.4760i | − | 0.750033i | ||||||
\(899\) | −16.8039 | −0.560442 | ||||||||
\(900\) | −3.22117 | − | 3.82415i | −0.107372 | − | 0.127472i | ||||
\(901\) | 13.7975 | + | 7.96599i | 0.459661 | + | 0.265385i | ||||
\(902\) | 16.4030 | 0.546159 | ||||||||
\(903\) | −22.5508 | − | 39.0591i | −0.750444 | − | 1.29981i | ||||
\(904\) | −8.59155 | − | 14.8810i | −0.285751 | − | 0.494934i | ||||
\(905\) | −27.2013 | + | 19.0849i | −0.904203 | + | 0.634403i | ||||
\(906\) | −10.1790 | − | 5.87683i | −0.338174 | − | 0.195245i | ||||
\(907\) | 19.2578 | − | 33.3555i | 0.639445 | − | 1.10755i | −0.346110 | − | 0.938194i | \(-0.612497\pi\) |
0.985555 | − | 0.169357i | \(-0.0541692\pi\) | |||||||
\(908\) | 6.44101 | + | 11.1562i | 0.213752 | + | 0.370230i | ||||
\(909\) | 1.11927 | + | 1.93864i | 0.0371240 | + | 0.0643006i | ||||
\(910\) | −15.3283 | − | 21.8471i | −0.508127 | − | 0.724224i | ||||
\(911\) | 10.9579i | 0.363052i | 0.983386 | + | 0.181526i | \(0.0581037\pi\) | ||||
−0.983386 | + | 0.181526i | \(0.941896\pi\) | |||||||
\(912\) | −0.737577 | + | 1.27752i | −0.0244236 | + | 0.0423029i | ||||
\(913\) | −6.36180 | + | 3.67299i | −0.210545 | + | 0.121558i | ||||
\(914\) | 11.8778 | 0.392881 | ||||||||
\(915\) | −1.26299 | − | 14.2807i | −0.0417531 | − | 0.472105i | ||||
\(916\) | −7.81590 | − | 13.5375i | −0.258245 | − | 0.447293i | ||||
\(917\) | 69.8164 | 2.30554 | ||||||||
\(918\) | 4.78010 | + | 2.75979i | 0.157767 | + | 0.0910868i | ||||
\(919\) | 31.2290i | 1.03015i | 0.857145 | + | 0.515076i | \(0.172236\pi\) | ||||
−0.857145 | + | 0.515076i | \(0.827764\pi\) | |||||||
\(920\) | −2.46121 | − | 1.14485i | −0.0811436 | − | 0.0377446i | ||||
\(921\) | 5.68895 | − | 9.85354i | 0.187457 | − | 0.324685i | ||||
\(922\) | 7.12646 | + | 4.11446i | 0.234698 | + | 0.135503i | ||||
\(923\) | 2.52052 | + | 4.36566i | 0.0829638 | + | 0.143698i | ||||
\(924\) | −6.41299 | −0.210972 | ||||||||
\(925\) | 26.3235 | − | 15.2339i | 0.865512 | − | 0.500889i | ||||
\(926\) | 24.6957 | 0.811550 | ||||||||
\(927\) | 2.11444 | + | 3.66232i | 0.0694474 | + | 0.120286i | ||||
\(928\) | −2.57226 | − | 1.48510i | −0.0844386 | − | 0.0487507i | ||||
\(929\) | −24.0026 | + | 41.5738i | −0.787501 | + | 1.36399i | 0.139992 | + | 0.990153i | \(0.455292\pi\) |
−0.927493 | + | 0.373840i | \(0.878041\pi\) | |||||||
\(930\) | 11.4704 | + | 5.33554i | 0.376128 | + | 0.174959i | ||||
\(931\) | − | 11.2581i | − | 0.368968i | ||||||
\(932\) | 2.17339 | + | 1.25481i | 0.0711918 | + | 0.0411026i | ||||
\(933\) | 28.9279 | 0.947055 | ||||||||
\(934\) | 7.37971 | + | 12.7820i | 0.241471 | + | 0.418241i | ||||
\(935\) | −1.82290 | − | 20.6116i | −0.0596151 | − | 0.674072i | ||||
\(936\) | 3.12020 | 0.101987 | ||||||||
\(937\) | −30.9441 | + | 17.8656i | −1.01090 | + | 0.583643i | −0.911455 | − | 0.411400i | \(-0.865040\pi\) |
−0.0994447 | + | 0.995043i | \(0.531707\pi\) | |||||||
\(938\) | 2.06204 | − | 3.57156i | 0.0673280 | − | 0.116615i | ||||
\(939\) | 13.5519i | 0.442249i | ||||||||
\(940\) | −14.4888 | − | 20.6506i | −0.472573 | − | 0.673549i | ||||
\(941\) | −23.9541 | − | 41.4898i | −0.780883 | − | 1.35253i | −0.931428 | − | 0.363926i | \(-0.881436\pi\) |
0.150545 | − | 0.988603i | \(-0.451897\pi\) | |||||||
\(942\) | 0.0624939 | + | 0.108243i | 0.00203616 | + | 0.00352673i | ||||
\(943\) | 5.93851 | − | 10.2858i | 0.193384 | − | 0.334952i | ||||
\(944\) | −5.20788 | − | 3.00677i | −0.169502 | − | 0.0978621i | ||||
\(945\) | −7.00182 | + | 4.91259i | −0.227769 | + | 0.159806i | ||||
\(946\) | −9.88383 | − | 17.1193i | −0.321351 | − | 0.556596i | ||||
\(947\) | 0.223569 | + | 0.387232i | 0.00726501 | + | 0.0125834i | 0.869635 | − | 0.493695i | \(-0.164354\pi\) |
−0.862370 | + | 0.506278i | \(0.831021\pi\) | |||||||
\(948\) | 1.59388 | 0.0517668 | ||||||||
\(949\) | −34.4957 | − | 19.9161i | −1.11978 | − | 0.646505i | ||||
\(950\) | 5.64120 | − | 4.75171i | 0.183025 | − | 0.154166i | ||||
\(951\) | 0.772516 | 0.0250505 | ||||||||
\(952\) | 21.1133i | 0.684285i | ||||||||
\(953\) | 22.5991 | − | 13.0476i | 0.732056 | − | 0.422653i | −0.0871180 | − | 0.996198i | \(-0.527766\pi\) |
0.819174 | + | 0.573545i | \(0.194432\pi\) | |||||||
\(954\) | − | 2.88644i | − | 0.0934520i | ||||||
\(955\) | 11.8294 | − | 25.4309i | 0.382790 | − | 0.822924i | ||||
\(956\) | 4.26585i | 0.137967i | ||||||||
\(957\) | 2.48981 | − | 4.31248i | 0.0804842 | − | 0.139403i | ||||
\(958\) | −25.0708 | − | 14.4746i | −0.810001 | − | 0.467654i | ||||
\(959\) | 5.68732 | − | 9.85072i | 0.183653 | − | 0.318096i | ||||
\(960\) | 1.28429 | + | 1.83047i | 0.0414501 | + | 0.0590781i | ||||
\(961\) | −1.00749 | −0.0324995 | ||||||||
\(962\) | −3.31186 | + | 18.6883i | −0.106779 | + | 0.602534i | ||||
\(963\) | 2.59222i | 0.0835332i | ||||||||
\(964\) | −25.2255 | + | 14.5640i | −0.812459 | + | 0.469074i | ||||
\(965\) | −53.0114 | − | 24.6587i | −1.70650 | − | 0.793791i | ||||
\(966\) | −2.32175 | + | 4.02139i | −0.0747011 | + | 0.129386i | ||||
\(967\) | 18.8285 | − | 32.6119i | 0.605483 | − | 1.04873i | −0.386492 | − | 0.922293i | \(-0.626313\pi\) |
0.991975 | − | 0.126435i | \(-0.0403535\pi\) | |||||||
\(968\) | 8.18924 | 0.263212 | ||||||||
\(969\) | −4.07112 | + | 7.05139i | −0.130783 | + | 0.226523i | ||||
\(970\) | −3.31613 | − | 37.4956i | −0.106474 | − | 1.20391i | ||||
\(971\) | −3.15080 | − | 5.45735i | −0.101114 | − | 0.175135i | 0.811030 | − | 0.585005i | \(-0.198907\pi\) |
−0.912144 | + | 0.409870i | \(0.865574\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | − | 41.6161i | − | 1.33415i | ||||||
\(974\) | −21.0780 | − | 36.5082i | −0.675382 | − | 1.16980i | ||||
\(975\) | −14.6702 | − | 5.30816i | −0.469823 | − | 0.169997i | ||||
\(976\) | 6.41144i | 0.205225i | ||||||||
\(977\) | 12.1860 | + | 21.1068i | 0.389865 | + | 0.675267i | 0.992431 | − | 0.122803i | \(-0.0391882\pi\) |
−0.602566 | + | 0.798069i | \(0.705855\pi\) | |||||||
\(978\) | 14.5744 | − | 8.41453i | 0.466038 | − | 0.269067i | ||||
\(979\) | −12.3401 | + | 7.12456i | −0.394391 | + | 0.227702i | ||||
\(980\) | −15.4731 | − | 7.19746i | −0.494271 | − | 0.229915i | ||||
\(981\) | 12.2762 | + | 7.08769i | 0.391950 | + | 0.226292i | ||||
\(982\) | −13.1580 | − | 22.7904i | −0.419890 | − | 0.727271i | ||||
\(983\) | −21.8424 | + | 12.6107i | −0.696664 | + | 0.402219i | −0.806104 | − | 0.591774i | \(-0.798428\pi\) |
0.109440 | + | 0.993993i | \(0.465094\pi\) | |||||||
\(984\) | −8.47308 | + | 4.89193i | −0.270112 | + | 0.155949i | ||||
\(985\) | 53.6933 | − | 4.74865i | 1.71081 | − | 0.151305i | ||||
\(986\) | −14.1978 | − | 8.19712i | −0.452151 | − | 0.261050i | ||||
\(987\) | −37.3724 | + | 21.5770i | −1.18958 | + | 0.686802i | ||||
\(988\) | 4.60278i | 0.146434i | ||||||||
\(989\) | −14.3133 | −0.455137 | ||||||||
\(990\) | −3.06884 | + | 2.15315i | −0.0975341 | + | 0.0684315i | ||||
\(991\) | − | 29.9420i | − | 0.951138i | −0.879678 | − | 0.475569i | \(-0.842242\pi\) | ||
0.879678 | − | 0.475569i | \(-0.157758\pi\) | |||||||
\(992\) | −4.89955 | − | 2.82876i | −0.155561 | − | 0.0898132i | ||||
\(993\) | −7.32929 | −0.232588 | ||||||||
\(994\) | 5.35200 | + | 3.08998i | 0.169755 | + | 0.0980082i | ||||
\(995\) | −20.2718 | + | 43.5803i | −0.642658 | + | 1.38159i | ||||
\(996\) | 2.19082 | − | 3.79462i | 0.0694189 | − | 0.120237i | ||||
\(997\) | 1.46033 | + | 2.52937i | 0.0462492 | + | 0.0801059i | 0.888223 | − | 0.459412i | \(-0.151940\pi\) |
−0.841974 | + | 0.539518i | \(0.818607\pi\) | |||||||
\(998\) | − | 19.7211i | − | 0.624262i | ||||||
\(999\) | 5.98944 | + | 1.06142i | 0.189497 | + | 0.0335820i |
(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 | 1110.2.ba.b.529.10 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.a.529.9 | ✓ | 36 | ||
37.27 | even | 6 | 1110.2.ba.a.619.9 | yes | 36 | ||
185.64 | even | 6 | inner | 1110.2.ba.b.619.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.9 | ✓ | 36 | 5.4 | even | 2 | ||
1110.2.ba.a.619.9 | yes | 36 | 37.27 | even | 6 | ||
1110.2.ba.b.529.10 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.619.10 | yes | 36 | 185.64 | even | 6 | inner |