Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.7 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.f.401.7 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.70946 | + | 0.278802i | 0.986960 | + | 0.160966i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −1.01163 | − | 1.40592i | −0.412997 | − | 0.573963i | ||||
\(7\) | −0.348034 | −0.131544 | −0.0657722 | − | 0.997835i | \(-0.520951\pi\) | ||||
−0.0657722 | + | 0.997835i | \(0.520951\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.84454 | + | 0.953204i | 0.948180 | + | 0.317735i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −3.72020 | −1.12168 | −0.560841 | − | 0.827923i | \(-0.689522\pi\) | ||||
−0.560841 | + | 0.827923i | \(0.689522\pi\) | |||||||
\(12\) | −0.278802 | + | 1.70946i | −0.0804832 | + | 0.493480i | ||||
\(13\) | 0.586358 | + | 0.586358i | 0.162626 | + | 0.162626i | 0.783729 | − | 0.621103i | \(-0.213315\pi\) |
−0.621103 | + | 0.783729i | \(0.713315\pi\) | |||||||
\(14\) | 0.246097 | + | 0.246097i | 0.0657722 | + | 0.0657722i | ||||
\(15\) | 1.40592 | − | 1.01163i | 0.363006 | − | 0.261202i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.90814 | − | 2.90814i | 0.705327 | − | 0.705327i | −0.260222 | − | 0.965549i | \(-0.583796\pi\) |
0.965549 | + | 0.260222i | \(0.0837957\pi\) | |||||||
\(18\) | −1.33738 | − | 2.68541i | −0.315223 | − | 0.632957i | ||||
\(19\) | 3.00391 | + | 3.00391i | 0.689143 | + | 0.689143i | 0.962043 | − | 0.272899i | \(-0.0879826\pi\) |
−0.272899 | + | 0.962043i | \(0.587983\pi\) | |||||||
\(20\) | 0.707107 | + | 0.707107i | 0.158114 | + | 0.158114i | ||||
\(21\) | −0.594951 | − | 0.0970324i | −0.129829 | − | 0.0211742i | ||||
\(22\) | 2.63058 | + | 2.63058i | 0.560841 | + | 0.560841i | ||||
\(23\) | 6.48575 | − | 6.48575i | 1.35237 | − | 1.35237i | 0.469372 | − | 0.883000i | \(-0.344480\pi\) |
0.883000 | − | 0.469372i | \(-0.155520\pi\) | |||||||
\(24\) | 1.40592 | − | 1.01163i | 0.286982 | − | 0.206498i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | − | 0.829235i | − | 0.162626i | ||||||
\(27\) | 4.59688 | + | 2.42253i | 0.884671 | + | 0.466216i | ||||
\(28\) | − | 0.348034i | − | 0.0657722i | ||||||
\(29\) | −0.289070 | − | 0.289070i | −0.0536789 | − | 0.0536789i | 0.679758 | − | 0.733437i | \(-0.262085\pi\) |
−0.733437 | + | 0.679758i | \(0.762085\pi\) | |||||||
\(30\) | −1.70946 | − | 0.278802i | −0.312104 | − | 0.0509020i | ||||
\(31\) | 4.18795 | − | 4.18795i | 0.752178 | − | 0.752178i | −0.222707 | − | 0.974885i | \(-0.571489\pi\) |
0.974885 | + | 0.222707i | \(0.0714894\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −6.35955 | − | 1.03720i | −1.10706 | − | 0.180553i | ||||
\(34\) | −4.11273 | −0.705327 | ||||||||
\(35\) | −0.246097 | + | 0.246097i | −0.0415980 | + | 0.0415980i | ||||
\(36\) | −0.953204 | + | 2.84454i | −0.158867 | + | 0.474090i | ||||
\(37\) | 2.18867 | + | 5.67536i | 0.359815 | + | 0.933024i | ||||
\(38\) | − | 4.24816i | − | 0.689143i | ||||||
\(39\) | 0.838880 | + | 1.16584i | 0.134328 | + | 0.186683i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 9.94709 | 1.55347 | 0.776737 | − | 0.629825i | \(-0.216873\pi\) | ||||
0.776737 | + | 0.629825i | \(0.216873\pi\) | |||||||
\(42\) | 0.352082 | + | 0.489306i | 0.0543274 | + | 0.0755016i | ||||
\(43\) | −4.12802 | − | 4.12802i | −0.629517 | − | 0.629517i | 0.318430 | − | 0.947946i | \(-0.396844\pi\) |
−0.947946 | + | 0.318430i | \(0.896844\pi\) | |||||||
\(44\) | − | 3.72020i | − | 0.560841i | ||||||
\(45\) | 2.68541 | − | 1.33738i | 0.400317 | − | 0.199364i | ||||
\(46\) | −9.17224 | −1.35237 | ||||||||
\(47\) | 7.55524i | 1.10205i | 0.834490 | + | 0.551023i | \(0.185762\pi\) | ||||
−0.834490 | + | 0.551023i | \(0.814238\pi\) | |||||||
\(48\) | −1.70946 | − | 0.278802i | −0.246740 | − | 0.0402416i | ||||
\(49\) | −6.87887 | −0.982696 | ||||||||
\(50\) | −0.707107 | + | 0.707107i | −0.100000 | + | 0.100000i | ||||
\(51\) | 5.78215 | − | 4.16056i | 0.809663 | − | 0.582596i | ||||
\(52\) | −0.586358 | + | 0.586358i | −0.0813132 | + | 0.0813132i | ||||
\(53\) | 0.164161i | 0.0225492i | 0.999936 | + | 0.0112746i | \(0.00358889\pi\) | ||||
−0.999936 | + | 0.0112746i | \(0.996411\pi\) | |||||||
\(54\) | −1.53750 | − | 4.96348i | −0.209227 | − | 0.675444i | ||||
\(55\) | −2.63058 | + | 2.63058i | −0.354707 | + | 0.354707i | ||||
\(56\) | −0.246097 | + | 0.246097i | −0.0328861 | + | 0.0328861i | ||||
\(57\) | 4.29758 | + | 5.97257i | 0.569228 | + | 0.791086i | ||||
\(58\) | 0.408806i | 0.0536789i | ||||||||
\(59\) | 6.51580 | − | 6.51580i | 0.848285 | − | 0.848285i | −0.141634 | − | 0.989919i | \(-0.545236\pi\) |
0.989919 | + | 0.141634i | \(0.0452355\pi\) | |||||||
\(60\) | 1.01163 | + | 1.40592i | 0.130601 | + | 0.181503i | ||||
\(61\) | −8.60550 | + | 8.60550i | −1.10182 | + | 1.10182i | −0.107630 | + | 0.994191i | \(0.534326\pi\) |
−0.994191 | + | 0.107630i | \(0.965674\pi\) | |||||||
\(62\) | −5.92266 | −0.752178 | ||||||||
\(63\) | −0.989995 | − | 0.331747i | −0.124728 | − | 0.0417962i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.829235 | 0.102854 | ||||||||
\(66\) | 3.76347 | + | 5.23029i | 0.463251 | + | 0.643804i | ||||
\(67\) | − | 14.1406i | − | 1.72755i | −0.503879 | − | 0.863774i | \(-0.668094\pi\) | ||
0.503879 | − | 0.863774i | \(-0.331906\pi\) | |||||||
\(68\) | 2.90814 | + | 2.90814i | 0.352664 | + | 0.352664i | ||||
\(69\) | 12.8954 | − | 9.27892i | 1.55242 | − | 1.11705i | ||||
\(70\) | 0.348034 | 0.0415980 | ||||||||
\(71\) | − | 0.738626i | − | 0.0876587i | −0.999039 | − | 0.0438294i | \(-0.986044\pi\) | ||
0.999039 | − | 0.0438294i | \(-0.0139558\pi\) | |||||||
\(72\) | 2.68541 | − | 1.33738i | 0.316479 | − | 0.157611i | ||||
\(73\) | 15.9210i | 1.86341i | 0.363210 | + | 0.931707i | \(0.381681\pi\) | ||||
−0.363210 | + | 0.931707i | \(0.618319\pi\) | |||||||
\(74\) | 2.46547 | − | 5.56071i | 0.286605 | − | 0.646419i | ||||
\(75\) | 0.278802 | − | 1.70946i | 0.0321933 | − | 0.197392i | ||||
\(76\) | −3.00391 | + | 3.00391i | −0.344572 | + | 0.344572i | ||||
\(77\) | 1.29475 | 0.147551 | ||||||||
\(78\) | 0.231192 | − | 1.41755i | 0.0261774 | − | 0.160506i | ||||
\(79\) | 6.84427 | + | 6.84427i | 0.770041 | + | 0.770041i | 0.978113 | − | 0.208073i | \(-0.0667191\pi\) |
−0.208073 | + | 0.978113i | \(0.566719\pi\) | |||||||
\(80\) | −0.707107 | + | 0.707107i | −0.0790569 | + | 0.0790569i | ||||
\(81\) | 7.18281 | + | 5.42285i | 0.798089 | + | 0.602539i | ||||
\(82\) | −7.03365 | − | 7.03365i | −0.776737 | − | 0.776737i | ||||
\(83\) | − | 9.66311i | − | 1.06066i | −0.847790 | − | 0.530332i | \(-0.822067\pi\) | ||
0.847790 | − | 0.530332i | \(-0.177933\pi\) | |||||||
\(84\) | 0.0970324 | − | 0.594951i | 0.0105871 | − | 0.0649145i | ||||
\(85\) | − | 4.11273i | − | 0.446088i | ||||||
\(86\) | 5.83790i | 0.629517i | ||||||||
\(87\) | −0.413561 | − | 0.574747i | −0.0443384 | − | 0.0616194i | ||||
\(88\) | −2.63058 | + | 2.63058i | −0.280421 | + | 0.280421i | ||||
\(89\) | −5.63114 | − | 5.63114i | −0.596900 | − | 0.596900i | 0.342586 | − | 0.939486i | \(-0.388697\pi\) |
−0.939486 | + | 0.342586i | \(0.888697\pi\) | |||||||
\(90\) | −2.84454 | − | 0.953204i | −0.299841 | − | 0.100476i | ||||
\(91\) | −0.204072 | − | 0.204072i | −0.0213926 | − | 0.0213926i | ||||
\(92\) | 6.48575 | + | 6.48575i | 0.676186 | + | 0.676186i | ||||
\(93\) | 8.32676 | − | 5.99154i | 0.863445 | − | 0.621294i | ||||
\(94\) | 5.34236 | − | 5.34236i | 0.551023 | − | 0.551023i | ||||
\(95\) | 4.24816 | 0.435852 | ||||||||
\(96\) | 1.01163 | + | 1.40592i | 0.103249 | + | 0.143491i | ||||
\(97\) | 11.0221 | + | 11.0221i | 1.11913 | + | 1.11913i | 0.991870 | + | 0.127257i | \(0.0406171\pi\) |
0.127257 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(98\) | 4.86410 | + | 4.86410i | 0.491348 | + | 0.491348i | ||||
\(99\) | −10.5823 | − | 3.54611i | −1.06356 | − | 0.356397i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.0733 | −1.59936 | −0.799678 | − | 0.600429i | \(-0.794997\pi\) | ||||
−0.799678 | + | 0.600429i | \(0.794997\pi\) | |||||||
\(102\) | −7.03056 | − | 1.14664i | −0.696129 | − | 0.113534i | ||||
\(103\) | −6.58533 | + | 6.58533i | −0.648872 | + | 0.648872i | −0.952720 | − | 0.303848i | \(-0.901728\pi\) |
0.303848 | + | 0.952720i | \(0.401728\pi\) | |||||||
\(104\) | 0.829235 | 0.0813132 | ||||||||
\(105\) | −0.489306 | + | 0.352082i | −0.0477514 | + | 0.0343597i | ||||
\(106\) | 0.116079 | − | 0.116079i | 0.0112746 | − | 0.0112746i | ||||
\(107\) | 9.53842i | 0.922114i | 0.887371 | + | 0.461057i | \(0.152530\pi\) | ||||
−0.887371 | + | 0.461057i | \(0.847470\pi\) | |||||||
\(108\) | −2.42253 | + | 4.59688i | −0.233108 | + | 0.442335i | ||||
\(109\) | −9.32002 | − | 9.32002i | −0.892696 | − | 0.892696i | 0.102080 | − | 0.994776i | \(-0.467450\pi\) |
−0.994776 | + | 0.102080i | \(0.967450\pi\) | |||||||
\(110\) | 3.72020 | 0.354707 | ||||||||
\(111\) | 2.15915 | + | 10.3120i | 0.204937 | + | 0.978775i | ||||
\(112\) | 0.348034 | 0.0328861 | ||||||||
\(113\) | −5.27517 | − | 5.27517i | −0.496247 | − | 0.496247i | 0.414021 | − | 0.910267i | \(-0.364124\pi\) |
−0.910267 | + | 0.414021i | \(0.864124\pi\) | |||||||
\(114\) | 1.18440 | − | 7.26209i | 0.110929 | − | 0.680157i | ||||
\(115\) | − | 9.17224i | − | 0.855316i | ||||||
\(116\) | 0.289070 | − | 0.289070i | 0.0268394 | − | 0.0268394i | ||||
\(117\) | 1.10900 | + | 2.22684i | 0.102527 | + | 0.205871i | ||||
\(118\) | −9.21474 | −0.848285 | ||||||||
\(119\) | −1.01213 | + | 1.01213i | −0.0927818 | + | 0.0927818i | ||||
\(120\) | 0.278802 | − | 1.70946i | 0.0254510 | − | 0.156052i | ||||
\(121\) | 2.83989 | 0.258172 | ||||||||
\(122\) | 12.1700 | 1.10182 | ||||||||
\(123\) | 17.0042 | + | 2.77327i | 1.53322 | + | 0.250057i | ||||
\(124\) | 4.18795 | + | 4.18795i | 0.376089 | + | 0.376089i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 0.465452 | + | 0.934613i | 0.0414657 | + | 0.0832619i | ||||
\(127\) | 6.85581 | 0.608355 | 0.304178 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304178 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −5.90580 | − | 8.20760i | −0.519977 | − | 0.722639i | ||||
\(130\) | −0.586358 | − | 0.586358i | −0.0514270 | − | 0.0514270i | ||||
\(131\) | −3.32864 | − | 3.32864i | −0.290824 | − | 0.290824i | 0.546582 | − | 0.837406i | \(-0.315929\pi\) |
−0.837406 | + | 0.546582i | \(0.815929\pi\) | |||||||
\(132\) | 1.03720 | − | 6.35955i | 0.0902766 | − | 0.553528i | ||||
\(133\) | −1.04546 | − | 1.04546i | −0.0906529 | − | 0.0906529i | ||||
\(134\) | −9.99891 | + | 9.99891i | −0.863774 | + | 0.863774i | ||||
\(135\) | 4.96348 | − | 1.53750i | 0.427188 | − | 0.132327i | ||||
\(136\) | − | 4.11273i | − | 0.352664i | ||||||
\(137\) | − | 2.18171i | − | 0.186396i | −0.995648 | − | 0.0931980i | \(-0.970291\pi\) | ||
0.995648 | − | 0.0931980i | \(-0.0297089\pi\) | |||||||
\(138\) | −15.6796 | − | 2.55724i | −1.33474 | − | 0.217686i | ||||
\(139\) | − | 3.77025i | − | 0.319788i | −0.987134 | − | 0.159894i | \(-0.948885\pi\) | ||
0.987134 | − | 0.159894i | \(-0.0511153\pi\) | |||||||
\(140\) | −0.246097 | − | 0.246097i | −0.0207990 | − | 0.0207990i | ||||
\(141\) | −2.10642 | + | 12.9154i | −0.177392 | + | 1.08767i | ||||
\(142\) | −0.522287 | + | 0.522287i | −0.0438294 | + | 0.0438294i | ||||
\(143\) | −2.18137 | − | 2.18137i | −0.182415 | − | 0.182415i | ||||
\(144\) | −2.84454 | − | 0.953204i | −0.237045 | − | 0.0794336i | ||||
\(145\) | −0.408806 | −0.0339495 | ||||||||
\(146\) | 11.2579 | − | 11.2579i | 0.931707 | − | 0.931707i | ||||
\(147\) | −11.7592 | − | 1.91784i | −0.969882 | − | 0.158181i | ||||
\(148\) | −5.67536 | + | 2.18867i | −0.466512 | + | 0.179907i | ||||
\(149\) | − | 14.7936i | − | 1.21194i | −0.795489 | − | 0.605968i | \(-0.792786\pi\) | ||
0.795489 | − | 0.605968i | \(-0.207214\pi\) | |||||||
\(150\) | −1.40592 | + | 1.01163i | −0.114793 | + | 0.0825994i | ||||
\(151\) | − | 2.35718i | − | 0.191825i | −0.995390 | − | 0.0959124i | \(-0.969423\pi\) | ||
0.995390 | − | 0.0959124i | \(-0.0305769\pi\) | |||||||
\(152\) | 4.24816 | 0.344572 | ||||||||
\(153\) | 11.0444 | − | 5.50026i | 0.892884 | − | 0.444670i | ||||
\(154\) | −0.915530 | − | 0.915530i | −0.0737755 | − | 0.0737755i | ||||
\(155\) | − | 5.92266i | − | 0.475719i | ||||||
\(156\) | −1.16584 | + | 0.838880i | −0.0933415 | + | 0.0671642i | ||||
\(157\) | −17.5824 | −1.40323 | −0.701616 | − | 0.712555i | \(-0.747538\pi\) | ||||
−0.701616 | + | 0.712555i | \(0.747538\pi\) | |||||||
\(158\) | − | 9.67926i | − | 0.770041i | ||||||
\(159\) | −0.0457683 | + | 0.280627i | −0.00362966 | + | 0.0222552i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.25726 | + | 2.25726i | −0.177897 | + | 0.177897i | ||||
\(162\) | −1.24448 | − | 8.91354i | −0.0977753 | − | 0.700314i | ||||
\(163\) | 2.83898 | − | 2.83898i | 0.222366 | − | 0.222366i | −0.587128 | − | 0.809494i | \(-0.699742\pi\) |
0.809494 | + | 0.587128i | \(0.199742\pi\) | |||||||
\(164\) | 9.94709i | 0.776737i | ||||||||
\(165\) | −5.23029 | + | 3.76347i | −0.407178 | + | 0.292986i | ||||
\(166\) | −6.83285 | + | 6.83285i | −0.530332 | + | 0.530332i | ||||
\(167\) | −8.73935 | + | 8.73935i | −0.676272 | + | 0.676272i | −0.959154 | − | 0.282883i | \(-0.908709\pi\) |
0.282883 | + | 0.959154i | \(0.408709\pi\) | |||||||
\(168\) | −0.489306 | + | 0.352082i | −0.0377508 | + | 0.0271637i | ||||
\(169\) | − | 12.3124i | − | 0.947105i | ||||||
\(170\) | −2.90814 | + | 2.90814i | −0.223044 | + | 0.223044i | ||||
\(171\) | 5.68139 | + | 11.4081i | 0.434467 | + | 0.872396i | ||||
\(172\) | 4.12802 | − | 4.12802i | 0.314758 | − | 0.314758i | ||||
\(173\) | 19.5438 | 1.48588 | 0.742942 | − | 0.669356i | \(-0.233430\pi\) | ||||
0.742942 | + | 0.669356i | \(0.233430\pi\) | |||||||
\(174\) | −0.113976 | + | 0.698840i | −0.00864049 | + | 0.0529789i | ||||
\(175\) | 0.348034i | 0.0263089i | ||||||||
\(176\) | 3.72020 | 0.280421 | ||||||||
\(177\) | 12.9552 | − | 9.32192i | 0.973769 | − | 0.700678i | ||||
\(178\) | 7.96364i | 0.596900i | ||||||||
\(179\) | −4.09892 | − | 4.09892i | −0.306368 | − | 0.306368i | 0.537131 | − | 0.843499i | \(-0.319508\pi\) |
−0.843499 | + | 0.537131i | \(0.819508\pi\) | |||||||
\(180\) | 1.33738 | + | 2.68541i | 0.0996821 | + | 0.200159i | ||||
\(181\) | −10.8868 | −0.809211 | −0.404605 | − | 0.914491i | \(-0.632591\pi\) | ||||
−0.404605 | + | 0.914491i | \(0.632591\pi\) | |||||||
\(182\) | 0.288602i | 0.0213926i | ||||||||
\(183\) | −17.1100 | + | 12.3116i | −1.26481 | + | 0.910097i | ||||
\(184\) | − | 9.17224i | − | 0.676186i | ||||||
\(185\) | 5.56071 | + | 2.46547i | 0.408831 | + | 0.181265i | ||||
\(186\) | −10.1246 | − | 1.65125i | −0.742370 | − | 0.121075i | ||||
\(187\) | −10.8189 | + | 10.8189i | −0.791153 | + | 0.791153i | ||||
\(188\) | −7.55524 | −0.551023 | ||||||||
\(189\) | −1.59987 | − | 0.843122i | −0.116373 | − | 0.0613281i | ||||
\(190\) | −3.00391 | − | 3.00391i | −0.217926 | − | 0.217926i | ||||
\(191\) | −14.0022 | + | 14.0022i | −1.01316 | + | 1.01316i | −0.0132497 | + | 0.999912i | \(0.504218\pi\) |
−0.999912 | + | 0.0132497i | \(0.995782\pi\) | |||||||
\(192\) | 0.278802 | − | 1.70946i | 0.0201208 | − | 0.123370i | ||||
\(193\) | 11.7248 | + | 11.7248i | 0.843971 | + | 0.843971i | 0.989373 | − | 0.145401i | \(-0.0464473\pi\) |
−0.145401 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(194\) | − | 15.5876i | − | 1.11913i | ||||||
\(195\) | 1.41755 | + | 0.231192i | 0.101513 | + | 0.0165560i | ||||
\(196\) | − | 6.87887i | − | 0.491348i | ||||||
\(197\) | 1.38691i | 0.0988132i | 0.998779 | + | 0.0494066i | \(0.0157330\pi\) | ||||
−0.998779 | + | 0.0494066i | \(0.984267\pi\) | |||||||
\(198\) | 4.97531 | + | 9.99026i | 0.353580 | + | 0.709977i | ||||
\(199\) | 12.9450 | − | 12.9450i | 0.917647 | − | 0.917647i | −0.0792111 | − | 0.996858i | \(-0.525240\pi\) |
0.996858 | + | 0.0792111i | \(0.0252401\pi\) | |||||||
\(200\) | −0.707107 | − | 0.707107i | −0.0500000 | − | 0.0500000i | ||||
\(201\) | 3.94242 | − | 24.1728i | 0.278077 | − | 1.70502i | ||||
\(202\) | 11.3656 | + | 11.3656i | 0.799678 | + | 0.799678i | ||||
\(203\) | 0.100606 | + | 0.100606i | 0.00706115 | + | 0.00706115i | ||||
\(204\) | 4.16056 | + | 5.78215i | 0.291298 | + | 0.404832i | ||||
\(205\) | 7.03365 | − | 7.03365i | 0.491252 | − | 0.491252i | ||||
\(206\) | 9.31307 | 0.648872 | ||||||||
\(207\) | 24.6312 | − | 12.2667i | 1.71199 | − | 0.852597i | ||||
\(208\) | −0.586358 | − | 0.586358i | −0.0406566 | − | 0.0406566i | ||||
\(209\) | −11.1751 | − | 11.1751i | −0.773000 | − | 0.773000i | ||||
\(210\) | 0.594951 | + | 0.0970324i | 0.0410555 | + | 0.00669587i | ||||
\(211\) | 16.2108 | 1.11600 | 0.557999 | − | 0.829841i | \(-0.311569\pi\) | ||||
0.557999 | + | 0.829841i | \(0.311569\pi\) | |||||||
\(212\) | −0.164161 | −0.0112746 | ||||||||
\(213\) | 0.205930 | − | 1.26265i | 0.0141101 | − | 0.0865157i | ||||
\(214\) | 6.74468 | − | 6.74468i | 0.461057 | − | 0.461057i | ||||
\(215\) | −5.83790 | −0.398141 | ||||||||
\(216\) | 4.96348 | − | 1.53750i | 0.337722 | − | 0.104614i | ||||
\(217\) | −1.45755 | + | 1.45755i | −0.0989448 | + | 0.0989448i | ||||
\(218\) | 13.1805i | 0.892696i | ||||||||
\(219\) | −4.43881 | + | 27.2164i | −0.299947 | + | 1.83912i | ||||
\(220\) | −2.63058 | − | 2.63058i | −0.177354 | − | 0.177354i | ||||
\(221\) | 3.41042 | 0.229410 | ||||||||
\(222\) | 5.76496 | − | 8.81846i | 0.386919 | − | 0.591856i | ||||
\(223\) | −5.18177 | −0.346997 | −0.173498 | − | 0.984834i | \(-0.555507\pi\) | ||||
−0.173498 | + | 0.984834i | \(0.555507\pi\) | |||||||
\(224\) | −0.246097 | − | 0.246097i | −0.0164430 | − | 0.0164430i | ||||
\(225\) | 0.953204 | − | 2.84454i | 0.0635469 | − | 0.189636i | ||||
\(226\) | 7.46022i | 0.496247i | ||||||||
\(227\) | −14.9028 | + | 14.9028i | −0.989133 | + | 0.989133i | −0.999942 | − | 0.0108088i | \(-0.996559\pi\) |
0.0108088 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(228\) | −5.97257 | + | 4.29758i | −0.395543 | + | 0.284614i | ||||
\(229\) | −15.8227 | −1.04559 | −0.522796 | − | 0.852458i | \(-0.675111\pi\) | ||||
−0.522796 | + | 0.852458i | \(0.675111\pi\) | |||||||
\(230\) | −6.48575 | + | 6.48575i | −0.427658 | + | 0.427658i | ||||
\(231\) | 2.21334 | + | 0.360980i | 0.145627 | + | 0.0237507i | ||||
\(232\) | −0.408806 | −0.0268394 | ||||||||
\(233\) | −17.2520 | −1.13022 | −0.565109 | − | 0.825016i | \(-0.691166\pi\) | ||||
−0.565109 | + | 0.825016i | \(0.691166\pi\) | |||||||
\(234\) | 0.790430 | − | 2.35879i | 0.0516720 | − | 0.154199i | ||||
\(235\) | 5.34236 | + | 5.34236i | 0.348497 | + | 0.348497i | ||||
\(236\) | 6.51580 | + | 6.51580i | 0.424143 | + | 0.424143i | ||||
\(237\) | 9.79184 | + | 13.6082i | 0.636049 | + | 0.883950i | ||||
\(238\) | 1.43137 | 0.0927818 | ||||||||
\(239\) | −8.68104 | + | 8.68104i | −0.561530 | + | 0.561530i | −0.929742 | − | 0.368212i | \(-0.879970\pi\) |
0.368212 | + | 0.929742i | \(0.379970\pi\) | |||||||
\(240\) | −1.40592 | + | 1.01163i | −0.0907515 | + | 0.0653005i | ||||
\(241\) | 11.6905 | + | 11.6905i | 0.753050 | + | 0.753050i | 0.975047 | − | 0.221997i | \(-0.0712576\pi\) |
−0.221997 | + | 0.975047i | \(0.571258\pi\) | |||||||
\(242\) | −2.00811 | − | 2.00811i | −0.129086 | − | 0.129086i | ||||
\(243\) | 10.7669 | + | 11.2728i | 0.690694 | + | 0.723147i | ||||
\(244\) | −8.60550 | − | 8.60550i | −0.550911 | − | 0.550911i | ||||
\(245\) | −4.86410 | + | 4.86410i | −0.310756 | + | 0.310756i | ||||
\(246\) | −10.0628 | − | 13.9848i | −0.641580 | − | 0.891637i | ||||
\(247\) | 3.52273i | 0.224146i | ||||||||
\(248\) | − | 5.92266i | − | 0.376089i | ||||||
\(249\) | 2.69409 | − | 16.5187i | 0.170731 | − | 1.04683i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −5.17135 | − | 5.17135i | −0.326413 | − | 0.326413i | 0.524808 | − | 0.851221i | \(-0.324137\pi\) |
−0.851221 | + | 0.524808i | \(0.824137\pi\) | |||||||
\(252\) | 0.331747 | − | 0.989995i | 0.0208981 | − | 0.0623638i | ||||
\(253\) | −24.1283 | + | 24.1283i | −1.51693 | + | 1.51693i | ||||
\(254\) | −4.84779 | − | 4.84779i | −0.304178 | − | 0.304178i | ||||
\(255\) | 1.14664 | − | 7.03056i | 0.0718051 | − | 0.440271i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.9443 | + | 20.9443i | −1.30647 | + | 1.30647i | −0.382520 | + | 0.923947i | \(0.624944\pi\) |
−0.923947 | + | 0.382520i | \(0.875056\pi\) | |||||||
\(258\) | −1.62762 | + | 9.97968i | −0.101331 | + | 0.621308i | ||||
\(259\) | −0.761730 | − | 1.97522i | −0.0473316 | − | 0.122734i | ||||
\(260\) | 0.829235i | 0.0514270i | ||||||||
\(261\) | −0.546728 | − | 1.09781i | −0.0338416 | − | 0.0679529i | ||||
\(262\) | 4.70740i | 0.290824i | ||||||||
\(263\) | −0.826816 | −0.0509837 | −0.0254918 | − | 0.999675i | \(-0.508115\pi\) | ||||
−0.0254918 | + | 0.999675i | \(0.508115\pi\) | |||||||
\(264\) | −5.23029 | + | 3.76347i | −0.321902 | + | 0.231626i | ||||
\(265\) | 0.116079 | + | 0.116079i | 0.00713068 | + | 0.00713068i | ||||
\(266\) | 1.47850i | 0.0906529i | ||||||||
\(267\) | −8.05627 | − | 11.1962i | −0.493035 | − | 0.685197i | ||||
\(268\) | 14.1406 | 0.863774 | ||||||||
\(269\) | 22.9891i | 1.40167i | 0.713323 | + | 0.700835i | \(0.247189\pi\) | ||||
−0.713323 | + | 0.700835i | \(0.752811\pi\) | |||||||
\(270\) | −4.59688 | − | 2.42253i | −0.279757 | − | 0.147431i | ||||
\(271\) | −8.57848 | −0.521105 | −0.260553 | − | 0.965460i | \(-0.583905\pi\) | ||||
−0.260553 | + | 0.965460i | \(0.583905\pi\) | |||||||
\(272\) | −2.90814 | + | 2.90814i | −0.176332 | + | 0.176332i | ||||
\(273\) | −0.291959 | − | 0.405750i | −0.0176701 | − | 0.0245571i | ||||
\(274\) | −1.54270 | + | 1.54270i | −0.0931980 | + | 0.0931980i | ||||
\(275\) | 3.72020i | 0.224337i | ||||||||
\(276\) | 9.27892 | + | 12.8954i | 0.558526 | + | 0.776212i | ||||
\(277\) | −12.4445 | + | 12.4445i | −0.747719 | + | 0.747719i | −0.974050 | − | 0.226332i | \(-0.927327\pi\) |
0.226332 | + | 0.974050i | \(0.427327\pi\) | |||||||
\(278\) | −2.66597 | + | 2.66597i | −0.159894 | + | 0.159894i | ||||
\(279\) | 15.9048 | − | 7.92082i | 0.952193 | − | 0.474207i | ||||
\(280\) | 0.348034i | 0.0207990i | ||||||||
\(281\) | 0.971269 | − | 0.971269i | 0.0579410 | − | 0.0579410i | −0.677543 | − | 0.735484i | \(-0.736955\pi\) |
0.735484 | + | 0.677543i | \(0.236955\pi\) | |||||||
\(282\) | 10.6220 | − | 7.64312i | 0.632533 | − | 0.455141i | ||||
\(283\) | −1.46923 | + | 1.46923i | −0.0873364 | + | 0.0873364i | −0.749425 | − | 0.662089i | \(-0.769670\pi\) |
0.662089 | + | 0.749425i | \(0.269670\pi\) | |||||||
\(284\) | 0.738626 | 0.0438294 | ||||||||
\(285\) | 7.26209 | + | 1.18440i | 0.430169 | + | 0.0701576i | ||||
\(286\) | 3.08492i | 0.182415i | ||||||||
\(287\) | −3.46192 | −0.204351 | ||||||||
\(288\) | 1.33738 | + | 2.68541i | 0.0788056 | + | 0.158239i | ||||
\(289\) | 0.0854698i | 0.00502764i | ||||||||
\(290\) | 0.289070 | + | 0.289070i | 0.0169748 | + | 0.0169748i | ||||
\(291\) | 15.7689 | + | 21.9149i | 0.924391 | + | 1.28467i | ||||
\(292\) | −15.9210 | −0.931707 | ||||||||
\(293\) | − | 1.74107i | − | 0.101715i | −0.998706 | − | 0.0508573i | \(-0.983805\pi\) | ||
0.998706 | − | 0.0508573i | \(-0.0161954\pi\) | |||||||
\(294\) | 6.95888 | + | 9.67112i | 0.405850 | + | 0.564031i | ||||
\(295\) | − | 9.21474i | − | 0.536503i | ||||||
\(296\) | 5.56071 | + | 2.46547i | 0.323210 | + | 0.143302i | ||||
\(297\) | −17.1013 | − | 9.01230i | −0.992320 | − | 0.522947i | ||||
\(298\) | −10.4606 | + | 10.4606i | −0.605968 | + | 0.605968i | ||||
\(299\) | 7.60594 | 0.439863 | ||||||||
\(300\) | 1.70946 | + | 0.278802i | 0.0986960 | + | 0.0160966i | ||||
\(301\) | 1.43669 | + | 1.43669i | 0.0828093 | + | 0.0828093i | ||||
\(302\) | −1.66678 | + | 1.66678i | −0.0959124 | + | 0.0959124i | ||||
\(303\) | −27.4768 | − | 4.48127i | −1.57850 | − | 0.257442i | ||||
\(304\) | −3.00391 | − | 3.00391i | −0.172286 | − | 0.172286i | ||||
\(305\) | 12.1700i | 0.696853i | ||||||||
\(306\) | −11.6988 | − | 3.92027i | −0.668777 | − | 0.224107i | ||||
\(307\) | 9.43400i | 0.538427i | 0.963081 | + | 0.269213i | \(0.0867637\pi\) | ||||
−0.963081 | + | 0.269213i | \(0.913236\pi\) | |||||||
\(308\) | 1.29475i | 0.0737755i | ||||||||
\(309\) | −13.0934 | + | 9.42139i | −0.744857 | + | 0.535964i | ||||
\(310\) | −4.18795 | + | 4.18795i | −0.237860 | + | 0.237860i | ||||
\(311\) | −17.4484 | − | 17.4484i | −0.989408 | − | 0.989408i | 0.0105370 | − | 0.999944i | \(-0.496646\pi\) |
−0.999944 | + | 0.0105370i | \(0.996646\pi\) | |||||||
\(312\) | 1.41755 | + | 0.231192i | 0.0802529 | + | 0.0130887i | ||||
\(313\) | 7.61657 | + | 7.61657i | 0.430514 | + | 0.430514i | 0.888803 | − | 0.458289i | \(-0.151538\pi\) |
−0.458289 | + | 0.888803i | \(0.651538\pi\) | |||||||
\(314\) | 12.4327 | + | 12.4327i | 0.701616 | + | 0.701616i | ||||
\(315\) | −0.934613 | + | 0.465452i | −0.0526595 | + | 0.0262252i | ||||
\(316\) | −6.84427 | + | 6.84427i | −0.385020 | + | 0.385020i | ||||
\(317\) | −20.5090 | −1.15190 | −0.575951 | − | 0.817485i | \(-0.695368\pi\) | ||||
−0.575951 | + | 0.817485i | \(0.695368\pi\) | |||||||
\(318\) | 0.230796 | − | 0.166070i | 0.0129424 | − | 0.00931275i | ||||
\(319\) | 1.07540 | + | 1.07540i | 0.0602107 | + | 0.0602107i | ||||
\(320\) | −0.707107 | − | 0.707107i | −0.0395285 | − | 0.0395285i | ||||
\(321\) | −2.65933 | + | 16.3056i | −0.148429 | + | 0.910089i | ||||
\(322\) | 3.19225 | 0.177897 | ||||||||
\(323\) | 17.4715 | 0.972143 | ||||||||
\(324\) | −5.42285 | + | 7.18281i | −0.301269 | + | 0.399045i | ||||
\(325\) | 0.586358 | − | 0.586358i | 0.0325253 | − | 0.0325253i | ||||
\(326\) | −4.01492 | −0.222366 | ||||||||
\(327\) | −13.3338 | − | 18.5307i | −0.737362 | − | 1.02475i | ||||
\(328\) | 7.03365 | − | 7.03365i | 0.388369 | − | 0.388369i | ||||
\(329\) | − | 2.62948i | − | 0.144968i | ||||||
\(330\) | 6.35955 | + | 1.03720i | 0.350082 | + | 0.0570959i | ||||
\(331\) | −1.37048 | − | 1.37048i | −0.0753283 | − | 0.0753283i | 0.668439 | − | 0.743767i | \(-0.266963\pi\) |
−0.743767 | + | 0.668439i | \(0.766963\pi\) | |||||||
\(332\) | 9.66311 | 0.530332 | ||||||||
\(333\) | 0.815972 | + | 18.2300i | 0.0447150 | + | 0.999000i | ||||
\(334\) | 12.3593 | 0.676272 | ||||||||
\(335\) | −9.99891 | − | 9.99891i | −0.546299 | − | 0.546299i | ||||
\(336\) | 0.594951 | + | 0.0970324i | 0.0324572 | + | 0.00529355i | ||||
\(337\) | 33.5414i | 1.82711i | 0.406711 | + | 0.913557i | \(0.366676\pi\) | ||||
−0.406711 | + | 0.913557i | \(0.633324\pi\) | |||||||
\(338\) | −8.70616 | + | 8.70616i | −0.473553 | + | 0.473553i | ||||
\(339\) | −7.54699 | − | 10.4884i | −0.409896 | − | 0.569654i | ||||
\(340\) | 4.11273 | 0.223044 | ||||||||
\(341\) | −15.5800 | + | 15.5800i | −0.843705 | + | 0.843705i | ||||
\(342\) | 4.04937 | − | 12.0841i | 0.218965 | − | 0.653432i | ||||
\(343\) | 4.83031 | 0.260812 | ||||||||
\(344\) | −5.83790 | −0.314758 | ||||||||
\(345\) | 2.55724 | − | 15.6796i | 0.137677 | − | 0.844162i | ||||
\(346\) | −13.8195 | − | 13.8195i | −0.742942 | − | 0.742942i | ||||
\(347\) | 14.2780 | + | 14.2780i | 0.766484 | + | 0.766484i | 0.977486 | − | 0.211002i | \(-0.0676727\pi\) |
−0.211002 | + | 0.977486i | \(0.567673\pi\) | |||||||
\(348\) | 0.574747 | − | 0.413561i | 0.0308097 | − | 0.0221692i | ||||
\(349\) | 6.56028 | 0.351164 | 0.175582 | − | 0.984465i | \(-0.443819\pi\) | ||||
0.175582 | + | 0.984465i | \(0.443819\pi\) | |||||||
\(350\) | 0.246097 | − | 0.246097i | 0.0131544 | − | 0.0131544i | ||||
\(351\) | 1.27495 | + | 4.11589i | 0.0680517 | + | 0.219690i | ||||
\(352\) | −2.63058 | − | 2.63058i | −0.140210 | − | 0.140210i | ||||
\(353\) | 25.6324 | + | 25.6324i | 1.36427 | + | 1.36427i | 0.868386 | + | 0.495889i | \(0.165158\pi\) |
0.495889 | + | 0.868386i | \(0.334842\pi\) | |||||||
\(354\) | −15.7523 | − | 2.56909i | −0.837224 | − | 0.136545i | ||||
\(355\) | −0.522287 | − | 0.522287i | −0.0277201 | − | 0.0277201i | ||||
\(356\) | 5.63114 | − | 5.63114i | 0.298450 | − | 0.298450i | ||||
\(357\) | −2.01238 | + | 1.44802i | −0.106507 | + | 0.0766372i | ||||
\(358\) | 5.79675i | 0.306368i | ||||||||
\(359\) | − | 18.5723i | − | 0.980209i | −0.871664 | − | 0.490104i | \(-0.836959\pi\) | ||
0.871664 | − | 0.490104i | \(-0.163041\pi\) | |||||||
\(360\) | 0.953204 | − | 2.84454i | 0.0502382 | − | 0.149920i | ||||
\(361\) | − | 0.953098i | − | 0.0501631i | ||||||
\(362\) | 7.69814 | + | 7.69814i | 0.404605 | + | 0.404605i | ||||
\(363\) | 4.85470 | + | 0.791767i | 0.254805 | + | 0.0415570i | ||||
\(364\) | 0.204072 | − | 0.204072i | 0.0106963 | − | 0.0106963i | ||||
\(365\) | 11.2579 | + | 11.2579i | 0.589263 | + | 0.589263i | ||||
\(366\) | 20.8042 | + | 3.39302i | 1.08745 | + | 0.177356i | ||||
\(367\) | −10.8985 | −0.568898 | −0.284449 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284449 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(368\) | −6.48575 | + | 6.48575i | −0.338093 | + | 0.338093i | ||||
\(369\) | 28.2949 | + | 9.48160i | 1.47297 | + | 0.493592i | ||||
\(370\) | −2.18867 | − | 5.67536i | −0.113783 | − | 0.295048i | ||||
\(371\) | − | 0.0571334i | − | 0.00296622i | ||||||
\(372\) | 5.99154 | + | 8.32676i | 0.310647 | + | 0.431722i | ||||
\(373\) | − | 27.5555i | − | 1.42677i | −0.700772 | − | 0.713385i | \(-0.747161\pi\) | ||
0.700772 | − | 0.713385i | \(-0.252839\pi\) | |||||||
\(374\) | 15.3002 | 0.791153 | ||||||||
\(375\) | −1.01163 | − | 1.40592i | −0.0522404 | − | 0.0726012i | ||||
\(376\) | 5.34236 | + | 5.34236i | 0.275511 | + | 0.275511i | ||||
\(377\) | − | 0.338996i | − | 0.0174592i | ||||||
\(378\) | 0.535102 | + | 1.72746i | 0.0275227 | + | 0.0888508i | ||||
\(379\) | 5.24130 | 0.269228 | 0.134614 | − | 0.990898i | \(-0.457021\pi\) | ||||
0.134614 | + | 0.990898i | \(0.457021\pi\) | |||||||
\(380\) | 4.24816i | 0.217926i | ||||||||
\(381\) | 11.7198 | + | 1.91141i | 0.600422 | + | 0.0979247i | ||||
\(382\) | 19.8021 | 1.01316 | ||||||||
\(383\) | 20.0864 | − | 20.0864i | 1.02637 | − | 1.02637i | 0.0267254 | − | 0.999643i | \(-0.491492\pi\) |
0.999643 | − | 0.0267254i | \(-0.00850796\pi\) | |||||||
\(384\) | −1.40592 | + | 1.01163i | −0.0717454 | + | 0.0516246i | ||||
\(385\) | 0.915530 | − | 0.915530i | 0.0466597 | − | 0.0466597i | ||||
\(386\) | − | 16.5814i | − | 0.843971i | ||||||
\(387\) | −7.80746 | − | 15.6771i | −0.396876 | − | 0.796914i | ||||
\(388\) | −11.0221 | + | 11.0221i | −0.559563 | + | 0.559563i | ||||
\(389\) | 5.94620 | − | 5.94620i | 0.301484 | − | 0.301484i | −0.540110 | − | 0.841594i | \(-0.681617\pi\) |
0.841594 | + | 0.540110i | \(0.181617\pi\) | |||||||
\(390\) | −0.838880 | − | 1.16584i | −0.0424784 | − | 0.0590344i | ||||
\(391\) | − | 37.7229i | − | 1.90773i | ||||||
\(392\) | −4.86410 | + | 4.86410i | −0.245674 | + | 0.245674i | ||||
\(393\) | −4.76216 | − | 6.61822i | −0.240219 | − | 0.333845i | ||||
\(394\) | 0.980693 | − | 0.980693i | 0.0494066 | − | 0.0494066i | ||||
\(395\) | 9.67926 | 0.487016 | ||||||||
\(396\) | 3.54611 | − | 10.5823i | 0.178199 | − | 0.531778i | ||||
\(397\) | − | 12.6809i | − | 0.636435i | −0.948018 | − | 0.318218i | \(-0.896916\pi\) | ||
0.948018 | − | 0.318218i | \(-0.103084\pi\) | |||||||
\(398\) | −18.3070 | −0.917647 | ||||||||
\(399\) | −1.49570 | − | 2.07865i | −0.0748787 | − | 0.104063i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | −21.8657 | − | 21.8657i | −1.09192 | − | 1.09192i | −0.995324 | − | 0.0965961i | \(-0.969204\pi\) |
−0.0965961 | − | 0.995324i | \(-0.530796\pi\) | |||||||
\(402\) | −19.8805 | + | 14.3051i | −0.991549 | + | 0.713472i | ||||
\(403\) | 4.91127 | 0.244648 | ||||||||
\(404\) | − | 16.0733i | − | 0.799678i | ||||||
\(405\) | 8.91354 | − | 1.24448i | 0.442918 | − | 0.0618385i | ||||
\(406\) | − | 0.142278i | − | 0.00706115i | ||||||
\(407\) | −8.14228 | − | 21.1135i | −0.403598 | − | 1.04656i | ||||
\(408\) | 1.14664 | − | 7.03056i | 0.0567669 | − | 0.348065i | ||||
\(409\) | −19.3828 | + | 19.3828i | −0.958419 | + | 0.958419i | −0.999169 | − | 0.0407505i | \(-0.987025\pi\) |
0.0407505 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(410\) | −9.94709 | −0.491252 | ||||||||
\(411\) | 0.608264 | − | 3.72955i | 0.0300035 | − | 0.183965i | ||||
\(412\) | −6.58533 | − | 6.58533i | −0.324436 | − | 0.324436i | ||||
\(413\) | −2.26772 | + | 2.26772i | −0.111587 | + | 0.111587i | ||||
\(414\) | −26.0908 | − | 8.74301i | −1.28229 | − | 0.429696i | ||||
\(415\) | −6.83285 | − | 6.83285i | −0.335411 | − | 0.335411i | ||||
\(416\) | 0.829235i | 0.0406566i | ||||||||
\(417\) | 1.05115 | − | 6.44510i | 0.0514751 | − | 0.315618i | ||||
\(418\) | 15.8040i | 0.773000i | ||||||||
\(419\) | − | 24.4184i | − | 1.19292i | −0.802643 | − | 0.596459i | \(-0.796574\pi\) | ||
0.802643 | − | 0.596459i | \(-0.203426\pi\) | |||||||
\(420\) | −0.352082 | − | 0.489306i | −0.0171798 | − | 0.0238757i | ||||
\(421\) | 1.06044 | − | 1.06044i | 0.0516825 | − | 0.0516825i | −0.680793 | − | 0.732476i | \(-0.738365\pi\) |
0.732476 | + | 0.680793i | \(0.238365\pi\) | |||||||
\(422\) | −11.4628 | − | 11.4628i | −0.557999 | − | 0.557999i | ||||
\(423\) | −7.20169 | + | 21.4912i | −0.350158 | + | 1.04494i | ||||
\(424\) | 0.116079 | + | 0.116079i | 0.00563730 | + | 0.00563730i | ||||
\(425\) | −2.90814 | − | 2.90814i | −0.141065 | − | 0.141065i | ||||
\(426\) | −1.03845 | + | 0.747217i | −0.0503129 | + | 0.0362028i | ||||
\(427\) | 2.99500 | − | 2.99500i | 0.144938 | − | 0.144938i | ||||
\(428\) | −9.53842 | −0.461057 | ||||||||
\(429\) | −3.12080 | − | 4.33714i | −0.150674 | − | 0.209399i | ||||
\(430\) | 4.12802 | + | 4.12802i | 0.199071 | + | 0.199071i | ||||
\(431\) | 10.7838 | + | 10.7838i | 0.519437 | + | 0.519437i | 0.917401 | − | 0.397964i | \(-0.130283\pi\) |
−0.397964 | + | 0.917401i | \(0.630283\pi\) | |||||||
\(432\) | −4.59688 | − | 2.42253i | −0.221168 | − | 0.116554i | ||||
\(433\) | 15.8953 | 0.763879 | 0.381940 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381940 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(434\) | 2.06128 | 0.0989448 | ||||||||
\(435\) | −0.698840 | − | 0.113976i | −0.0335068 | − | 0.00546473i | ||||
\(436\) | 9.32002 | − | 9.32002i | 0.446348 | − | 0.446348i | ||||
\(437\) | 38.9652 | 1.86396 | ||||||||
\(438\) | 22.3836 | − | 16.1062i | 1.06953 | − | 0.769584i | ||||
\(439\) | −9.33981 | + | 9.33981i | −0.445765 | + | 0.445765i | −0.893944 | − | 0.448179i | \(-0.852073\pi\) |
0.448179 | + | 0.893944i | \(0.352073\pi\) | |||||||
\(440\) | 3.72020i | 0.177354i | ||||||||
\(441\) | −19.5672 | − | 6.55697i | −0.931772 | − | 0.312237i | ||||
\(442\) | −2.41153 | − | 2.41153i | −0.114705 | − | 0.114705i | ||||
\(443\) | −9.89122 | −0.469946 | −0.234973 | − | 0.972002i | \(-0.575500\pi\) | ||||
−0.234973 | + | 0.972002i | \(0.575500\pi\) | |||||||
\(444\) | −10.3120 | + | 2.15915i | −0.489388 | + | 0.102469i | ||||
\(445\) | −7.96364 | −0.377513 | ||||||||
\(446\) | 3.66406 | + | 3.66406i | 0.173498 | + | 0.173498i | ||||
\(447\) | 4.12447 | − | 25.2891i | 0.195081 | − | 1.19613i | ||||
\(448\) | 0.348034i | 0.0164430i | ||||||||
\(449\) | −6.81279 | + | 6.81279i | −0.321516 | + | 0.321516i | −0.849348 | − | 0.527833i | \(-0.823005\pi\) |
0.527833 | + | 0.849348i | \(0.323005\pi\) | |||||||
\(450\) | −2.68541 | + | 1.33738i | −0.126591 | + | 0.0630445i | ||||
\(451\) | −37.0052 | −1.74251 | ||||||||
\(452\) | 5.27517 | − | 5.27517i | 0.248123 | − | 0.248123i | ||||
\(453\) | 0.657187 | − | 4.02952i | 0.0308773 | − | 0.189323i | ||||
\(454\) | 21.0757 | 0.989133 | ||||||||
\(455\) | −0.288602 | −0.0135299 | ||||||||
\(456\) | 7.26209 | + | 1.18440i | 0.340078 | + | 0.0554644i | ||||
\(457\) | 17.0996 | + | 17.0996i | 0.799888 | + | 0.799888i | 0.983078 | − | 0.183190i | \(-0.0586423\pi\) |
−0.183190 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(458\) | 11.1883 | + | 11.1883i | 0.522796 | + | 0.522796i | ||||
\(459\) | 20.4134 | − | 6.32332i | 0.952817 | − | 0.295147i | ||||
\(460\) | 9.17224 | 0.427658 | ||||||||
\(461\) | −0.729355 | + | 0.729355i | −0.0339694 | + | 0.0339694i | −0.723887 | − | 0.689918i | \(-0.757647\pi\) |
0.689918 | + | 0.723887i | \(0.257647\pi\) | |||||||
\(462\) | −1.30981 | − | 1.82032i | −0.0609381 | − | 0.0846888i | ||||
\(463\) | 6.28322 | + | 6.28322i | 0.292006 | + | 0.292006i | 0.837872 | − | 0.545866i | \(-0.183799\pi\) |
−0.545866 | + | 0.837872i | \(0.683799\pi\) | |||||||
\(464\) | 0.289070 | + | 0.289070i | 0.0134197 | + | 0.0134197i | ||||
\(465\) | 1.65125 | − | 10.1246i | 0.0765748 | − | 0.469516i | ||||
\(466\) | 12.1990 | + | 12.1990i | 0.565109 | + | 0.565109i | ||||
\(467\) | −8.64673 | + | 8.64673i | −0.400123 | + | 0.400123i | −0.878276 | − | 0.478153i | \(-0.841306\pi\) |
0.478153 | + | 0.878276i | \(0.341306\pi\) | |||||||
\(468\) | −2.22684 | + | 1.10900i | −0.102936 | + | 0.0512635i | ||||
\(469\) | 4.92140i | 0.227249i | ||||||||
\(470\) | − | 7.55524i | − | 0.348497i | ||||||
\(471\) | −30.0566 | − | 4.90202i | −1.38493 | − | 0.225873i | ||||
\(472\) | − | 9.21474i | − | 0.424143i | ||||||
\(473\) | 15.3570 | + | 15.3570i | 0.706118 | + | 0.706118i | ||||
\(474\) | 2.69860 | − | 16.5464i | 0.123951 | − | 0.759999i | ||||
\(475\) | 3.00391 | − | 3.00391i | 0.137829 | − | 0.137829i | ||||
\(476\) | −1.01213 | − | 1.01213i | −0.0463909 | − | 0.0463909i | ||||
\(477\) | −0.156479 | + | 0.466961i | −0.00716466 | + | 0.0213807i | ||||
\(478\) | 12.2768 | 0.561530 | ||||||||
\(479\) | −4.52948 | + | 4.52948i | −0.206957 | + | 0.206957i | −0.802973 | − | 0.596016i | \(-0.796750\pi\) |
0.596016 | + | 0.802973i | \(0.296750\pi\) | |||||||
\(480\) | 1.70946 | + | 0.278802i | 0.0780260 | + | 0.0127255i | ||||
\(481\) | −2.04445 | + | 4.61113i | −0.0932189 | + | 0.210250i | ||||
\(482\) | − | 16.5328i | − | 0.753050i | ||||||
\(483\) | −4.48803 | + | 3.22938i | −0.204213 | + | 0.146942i | ||||
\(484\) | 2.83989i | 0.129086i | ||||||||
\(485\) | 15.5876 | 0.707798 | ||||||||
\(486\) | 0.357725 | − | 15.5844i | 0.0162267 | − | 0.706921i | ||||
\(487\) | 3.72320 | + | 3.72320i | 0.168714 | + | 0.168714i | 0.786414 | − | 0.617700i | \(-0.211935\pi\) |
−0.617700 | + | 0.786414i | \(0.711935\pi\) | |||||||
\(488\) | 12.1700i | 0.550911i | ||||||||
\(489\) | 5.64465 | − | 4.06162i | 0.255260 | − | 0.183673i | ||||
\(490\) | 6.87887 | 0.310756 | ||||||||
\(491\) | − | 4.21252i | − | 0.190108i | −0.995472 | − | 0.0950542i | \(-0.969698\pi\) | ||
0.995472 | − | 0.0950542i | \(-0.0303024\pi\) | |||||||
\(492\) | −2.77327 | + | 17.0042i | −0.125028 | + | 0.766608i | ||||
\(493\) | −1.68131 | −0.0757223 | ||||||||
\(494\) | 2.49094 | − | 2.49094i | 0.112073 | − | 0.112073i | ||||
\(495\) | −9.99026 | + | 4.97531i | −0.449029 | + | 0.223623i | ||||
\(496\) | −4.18795 | + | 4.18795i | −0.188045 | + | 0.188045i | ||||
\(497\) | 0.257067i | 0.0115310i | ||||||||
\(498\) | −13.5855 | + | 9.77550i | −0.608782 | + | 0.438051i | ||||
\(499\) | 14.6597 | − | 14.6597i | 0.656259 | − | 0.656259i | −0.298234 | − | 0.954493i | \(-0.596398\pi\) |
0.954493 | + | 0.298234i | \(0.0963975\pi\) | |||||||
\(500\) | 0.707107 | − | 0.707107i | 0.0316228 | − | 0.0316228i | ||||
\(501\) | −17.3762 | + | 12.5031i | −0.776310 | + | 0.558596i | ||||
\(502\) | 7.31340i | 0.326413i | ||||||||
\(503\) | −17.8082 | + | 17.8082i | −0.794028 | + | 0.794028i | −0.982146 | − | 0.188118i | \(-0.939761\pi\) |
0.188118 | + | 0.982146i | \(0.439761\pi\) | |||||||
\(504\) | −0.934613 | + | 0.465452i | −0.0416310 | + | 0.0207329i | ||||
\(505\) | −11.3656 | + | 11.3656i | −0.505761 | + | 0.505761i | ||||
\(506\) | 34.1226 | 1.51693 | ||||||||
\(507\) | 3.43271 | − | 21.0476i | 0.152452 | − | 0.934755i | ||||
\(508\) | 6.85581i | 0.304178i | ||||||||
\(509\) | −29.2452 | −1.29627 | −0.648136 | − | 0.761525i | \(-0.724451\pi\) | ||||
−0.648136 | + | 0.761525i | \(0.724451\pi\) | |||||||
\(510\) | −5.78215 | + | 4.16056i | −0.256038 | + | 0.184233i | ||||
\(511\) | − | 5.54105i | − | 0.245122i | ||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 6.53155 | + | 21.0857i | 0.288375 | + | 0.930955i | ||||
\(514\) | 29.6197 | 1.30647 | ||||||||
\(515\) | 9.31307i | 0.410383i | ||||||||
\(516\) | 8.20760 | − | 5.90580i | 0.361319 | − | 0.259988i | ||||
\(517\) | − | 28.1070i | − | 1.23615i | ||||||
\(518\) | −0.858065 | + | 1.93531i | −0.0377012 | + | 0.0850328i | ||||
\(519\) | 33.4094 | + | 5.44883i | 1.46651 | + | 0.239177i | ||||
\(520\) | 0.586358 | − | 0.586358i | 0.0257135 | − | 0.0257135i | ||||
\(521\) | 43.3318 | 1.89840 | 0.949201 | − | 0.314670i | \(-0.101894\pi\) | ||||
0.949201 | + | 0.314670i | \(0.101894\pi\) | |||||||
\(522\) | −0.389676 | + | 1.16287i | −0.0170556 | + | 0.0508972i | ||||
\(523\) | −28.8478 | − | 28.8478i | −1.26143 | − | 1.26143i | −0.950402 | − | 0.311025i | \(-0.899328\pi\) |
−0.311025 | − | 0.950402i | \(-0.600672\pi\) | |||||||
\(524\) | 3.32864 | − | 3.32864i | 0.145412 | − | 0.145412i | ||||
\(525\) | −0.0970324 | + | 0.594951i | −0.00423484 | + | 0.0259658i | ||||
\(526\) | 0.584647 | + | 0.584647i | 0.0254918 | + | 0.0254918i | ||||
\(527\) | − | 24.3583i | − | 1.06106i | ||||||
\(528\) | 6.35955 | + | 1.03720i | 0.276764 | + | 0.0451383i | ||||
\(529\) | − | 61.1299i | − | 2.65782i | ||||||
\(530\) | − | 0.164161i | − | 0.00713068i | ||||||
\(531\) | 24.7453 | − | 12.3236i | 1.07386 | − | 0.534797i | ||||
\(532\) | 1.04546 | − | 1.04546i | 0.0453265 | − | 0.0453265i | ||||
\(533\) | 5.83255 | + | 5.83255i | 0.252636 | + | 0.252636i | ||||
\(534\) | −2.22028 | + | 13.6136i | −0.0960808 | + | 0.589116i | ||||
\(535\) | 6.74468 | + | 6.74468i | 0.291598 | + | 0.291598i | ||||
\(536\) | −9.99891 | − | 9.99891i | −0.431887 | − | 0.431887i | ||||
\(537\) | −5.86418 | − | 8.14975i | −0.253058 | − | 0.351688i | ||||
\(538\) | 16.2557 | − | 16.2557i | 0.700835 | − | 0.700835i | ||||
\(539\) | 25.5908 | 1.10227 | ||||||||
\(540\) | 1.53750 | + | 4.96348i | 0.0661635 | + | 0.213594i | ||||
\(541\) | −8.31534 | − | 8.31534i | −0.357504 | − | 0.357504i | 0.505388 | − | 0.862892i | \(-0.331349\pi\) |
−0.862892 | + | 0.505388i | \(0.831349\pi\) | |||||||
\(542\) | 6.06590 | + | 6.06590i | 0.260553 | + | 0.260553i | ||||
\(543\) | −18.6106 | − | 3.03526i | −0.798658 | − | 0.130256i | ||||
\(544\) | 4.11273 | 0.176332 | ||||||||
\(545\) | −13.1805 | −0.564591 | ||||||||
\(546\) | −0.0804627 | + | 0.493354i | −0.00344348 | + | 0.0211136i | ||||
\(547\) | 23.2358 | − | 23.2358i | 0.993489 | − | 0.993489i | −0.00648976 | − | 0.999979i | \(-0.502066\pi\) |
0.999979 | + | 0.00648976i | \(0.00206577\pi\) | |||||||
\(548\) | 2.18171 | 0.0931980 | ||||||||
\(549\) | −32.6815 | + | 16.2759i | −1.39481 | + | 0.694638i | ||||
\(550\) | 2.63058 | − | 2.63058i | 0.112168 | − | 0.112168i | ||||
\(551\) | − | 1.73668i | − | 0.0739849i | ||||||
\(552\) | 2.55724 | − | 15.6796i | 0.108843 | − | 0.667369i | ||||
\(553\) | −2.38204 | − | 2.38204i | −0.101294 | − | 0.101294i | ||||
\(554\) | 17.5992 | 0.747719 | ||||||||
\(555\) | 8.81846 | + | 5.76496i | 0.374323 | + | 0.244709i | ||||
\(556\) | 3.77025 | 0.159894 | ||||||||
\(557\) | 12.9487 | + | 12.9487i | 0.548653 | + | 0.548653i | 0.926051 | − | 0.377398i | \(-0.123181\pi\) |
−0.377398 | + | 0.926051i | \(0.623181\pi\) | |||||||
\(558\) | −16.8472 | − | 5.64550i | −0.713200 | − | 0.238993i | ||||
\(559\) | − | 4.84099i | − | 0.204752i | ||||||
\(560\) | 0.246097 | − | 0.246097i | 0.0103995 | − | 0.0103995i | ||||
\(561\) | −21.5108 | + | 15.4781i | −0.908185 | + | 0.653487i | ||||
\(562\) | −1.37358 | −0.0579410 | ||||||||
\(563\) | −13.8676 | + | 13.8676i | −0.584452 | + | 0.584452i | −0.936123 | − | 0.351672i | \(-0.885613\pi\) |
0.351672 | + | 0.936123i | \(0.385613\pi\) | |||||||
\(564\) | −12.9154 | − | 2.10642i | −0.543837 | − | 0.0886961i | ||||
\(565\) | −7.46022 | −0.313854 | ||||||||
\(566\) | 2.07780 | 0.0873364 | ||||||||
\(567\) | −2.49986 | − | 1.88733i | −0.104984 | − | 0.0792606i | ||||
\(568\) | −0.522287 | − | 0.522287i | −0.0219147 | − | 0.0219147i | ||||
\(569\) | −4.33445 | − | 4.33445i | −0.181710 | − | 0.181710i | 0.610391 | − | 0.792100i | \(-0.291012\pi\) |
−0.792100 | + | 0.610391i | \(0.791012\pi\) | |||||||
\(570\) | −4.29758 | − | 5.97257i | −0.180006 | − | 0.250163i | ||||
\(571\) | −2.93311 | −0.122747 | −0.0613734 | − | 0.998115i | \(-0.519548\pi\) | ||||
−0.0613734 | + | 0.998115i | \(0.519548\pi\) | |||||||
\(572\) | 2.18137 | − | 2.18137i | 0.0912076 | − | 0.0912076i | ||||
\(573\) | −27.8401 | + | 20.0324i | −1.16304 | + | 0.836865i | ||||
\(574\) | 2.44795 | + | 2.44795i | 0.102175 | + | 0.102175i | ||||
\(575\) | −6.48575 | − | 6.48575i | −0.270475 | − | 0.270475i | ||||
\(576\) | 0.953204 | − | 2.84454i | 0.0397168 | − | 0.118522i | ||||
\(577\) | 9.36579 | + | 9.36579i | 0.389903 | + | 0.389903i | 0.874653 | − | 0.484750i | \(-0.161089\pi\) |
−0.484750 | + | 0.874653i | \(0.661089\pi\) | |||||||
\(578\) | 0.0604363 | − | 0.0604363i | 0.00251382 | − | 0.00251382i | ||||
\(579\) | 16.7743 | + | 23.3121i | 0.697115 | + | 0.968817i | ||||
\(580\) | − | 0.408806i | − | 0.0169748i | ||||||
\(581\) | 3.36309i | 0.139524i | ||||||||
\(582\) | 4.34586 | − | 26.6465i | 0.180142 | − | 1.10453i | ||||
\(583\) | − | 0.610710i | − | 0.0252930i | ||||||
\(584\) | 11.2579 | + | 11.2579i | 0.465854 | + | 0.465854i | ||||
\(585\) | 2.35879 | + | 0.790430i | 0.0975240 | + | 0.0326803i | ||||
\(586\) | −1.23113 | + | 1.23113i | −0.0508573 | + | 0.0508573i | ||||
\(587\) | −18.1736 | − | 18.1736i | −0.750105 | − | 0.750105i | 0.224394 | − | 0.974499i | \(-0.427960\pi\) |
−0.974499 | + | 0.224394i | \(0.927960\pi\) | |||||||
\(588\) | 1.91784 | − | 11.7592i | 0.0790905 | − | 0.484941i | ||||
\(589\) | 25.1604 | 1.03672 | ||||||||
\(590\) | −6.51580 | + | 6.51580i | −0.268251 | + | 0.268251i | ||||
\(591\) | −0.386673 | + | 2.37087i | −0.0159056 | + | 0.0975247i | ||||
\(592\) | −2.18867 | − | 5.67536i | −0.0899537 | − | 0.233256i | ||||
\(593\) | − | 43.6579i | − | 1.79282i | −0.443229 | − | 0.896408i | \(-0.646167\pi\) | ||
0.443229 | − | 0.896408i | \(-0.353833\pi\) | |||||||
\(594\) | 5.71981 | + | 18.4651i | 0.234687 | + | 0.757633i | ||||
\(595\) | 1.43137i | 0.0586803i | ||||||||
\(596\) | 14.7936 | 0.605968 | ||||||||
\(597\) | 25.7381 | − | 18.5199i | 1.05339 | − | 0.757970i | ||||
\(598\) | −5.37821 | − | 5.37821i | −0.219931 | − | 0.219931i | ||||
\(599\) | − | 10.4813i | − | 0.428254i | −0.976806 | − | 0.214127i | \(-0.931309\pi\) | ||
0.976806 | − | 0.214127i | \(-0.0686907\pi\) | |||||||
\(600\) | −1.01163 | − | 1.40592i | −0.0412997 | − | 0.0573963i | ||||
\(601\) | 31.5992 | 1.28896 | 0.644480 | − | 0.764621i | \(-0.277074\pi\) | ||||
0.644480 | + | 0.764621i | \(0.277074\pi\) | |||||||
\(602\) | − | 2.03178i | − | 0.0828093i | ||||||
\(603\) | 13.4789 | − | 40.2235i | 0.548902 | − | 1.63803i | ||||
\(604\) | 2.35718 | 0.0959124 | ||||||||
\(605\) | 2.00811 | − | 2.00811i | 0.0816412 | − | 0.0816412i | ||||
\(606\) | 16.2603 | + | 22.5978i | 0.660529 | + | 0.917972i | ||||
\(607\) | 14.2922 | − | 14.2922i | 0.580101 | − | 0.580101i | −0.354830 | − | 0.934931i | \(-0.615461\pi\) |
0.934931 | + | 0.354830i | \(0.115461\pi\) | |||||||
\(608\) | 4.24816i | 0.172286i | ||||||||
\(609\) | 0.143933 | + | 0.200031i | 0.00583247 | + | 0.00810568i | ||||
\(610\) | 8.60550 | − | 8.60550i | 0.348426 | − | 0.348426i | ||||
\(611\) | −4.43008 | + | 4.43008i | −0.179222 | + | 0.179222i | ||||
\(612\) | 5.50026 | + | 11.0444i | 0.222335 | + | 0.446442i | ||||
\(613\) | 0.137392i | 0.00554922i | 0.999996 | + | 0.00277461i | \(0.000883187\pi\) | ||||
−0.999996 | + | 0.00277461i | \(0.999117\pi\) | |||||||
\(614\) | 6.67084 | − | 6.67084i | 0.269213 | − | 0.269213i | ||||
\(615\) | 13.9848 | − | 10.0628i | 0.563921 | − | 0.405771i | ||||
\(616\) | 0.915530 | − | 0.915530i | 0.0368878 | − | 0.0368878i | ||||
\(617\) | −28.1830 | −1.13461 | −0.567303 | − | 0.823509i | \(-0.692013\pi\) | ||||
−0.567303 | + | 0.823509i | \(0.692013\pi\) | |||||||
\(618\) | 15.9204 | + | 2.59650i | 0.640411 | + | 0.104447i | ||||
\(619\) | − | 19.2838i | − | 0.775080i | −0.921853 | − | 0.387540i | \(-0.873325\pi\) | ||
0.921853 | − | 0.387540i | \(-0.126675\pi\) | |||||||
\(620\) | 5.92266 | 0.237860 | ||||||||
\(621\) | 45.5262 | − | 14.1023i | 1.82690 | − | 0.565906i | ||||
\(622\) | 24.6758i | 0.989408i | ||||||||
\(623\) | 1.95983 | + | 1.95983i | 0.0785188 | + | 0.0785188i | ||||
\(624\) | −0.838880 | − | 1.16584i | −0.0335821 | − | 0.0466708i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | − | 10.7714i | − | 0.430514i | ||||||
\(627\) | −15.9878 | − | 22.2191i | −0.638493 | − | 0.887347i | ||||
\(628\) | − | 17.5824i | − | 0.701616i | ||||||
\(629\) | 22.8697 | + | 10.1398i | 0.911874 | + | 0.404300i | ||||
\(630\) | 0.989995 | + | 0.331747i | 0.0394424 | + | 0.0132171i | ||||
\(631\) | −1.01625 | + | 1.01625i | −0.0404564 | + | 0.0404564i | −0.727046 | − | 0.686589i | \(-0.759107\pi\) |
0.686589 | + | 0.727046i | \(0.259107\pi\) | |||||||
\(632\) | 9.67926 | 0.385020 | ||||||||
\(633\) | 27.7118 | + | 4.51961i | 1.10145 | + | 0.179638i | ||||
\(634\) | 14.5021 | + | 14.5021i | 0.575951 | + | 0.575951i | ||||
\(635\) | 4.84779 | − | 4.84779i | 0.192379 | − | 0.192379i | ||||
\(636\) | −0.280627 | − | 0.0457683i | −0.0111276 | − | 0.00181483i | ||||
\(637\) | −4.03348 | − | 4.03348i | −0.159812 | − | 0.159812i | ||||
\(638\) | − | 1.52084i | − | 0.0602107i | ||||||
\(639\) | 0.704061 | − | 2.10105i | 0.0278522 | − | 0.0831162i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 15.8819i | 0.627297i | 0.949539 | + | 0.313648i | \(0.101551\pi\) | ||||
−0.949539 | + | 0.313648i | \(0.898449\pi\) | |||||||
\(642\) | 13.4102 | − | 9.64937i | 0.529259 | − | 0.380830i | ||||
\(643\) | 29.9979 | − | 29.9979i | 1.18300 | − | 1.18300i | 0.204037 | − | 0.978963i | \(-0.434594\pi\) |
0.978963 | − | 0.204037i | \(-0.0654064\pi\) | |||||||
\(644\) | −2.25726 | − | 2.25726i | −0.0889485 | − | 0.0889485i | ||||
\(645\) | −9.97968 | − | 1.62762i | −0.392949 | − | 0.0640873i | ||||
\(646\) | −12.3542 | − | 12.3542i | −0.486071 | − | 0.486071i | ||||
\(647\) | −2.08271 | − | 2.08271i | −0.0818800 | − | 0.0818800i | 0.664981 | − | 0.746861i | \(-0.268440\pi\) |
−0.746861 | + | 0.664981i | \(0.768440\pi\) | |||||||
\(648\) | 8.91354 | − | 1.24448i | 0.350157 | − | 0.0488876i | ||||
\(649\) | −24.2401 | + | 24.2401i | −0.951507 | + | 0.951507i | ||||
\(650\) | −0.829235 | −0.0325253 | ||||||||
\(651\) | −2.89799 | + | 2.08526i | −0.113581 | + | 0.0817277i | ||||
\(652\) | 2.83898 | + | 2.83898i | 0.111183 | + | 0.111183i | ||||
\(653\) | 18.6146 | + | 18.6146i | 0.728447 | + | 0.728447i | 0.970310 | − | 0.241863i | \(-0.0777586\pi\) |
−0.241863 | + | 0.970310i | \(0.577759\pi\) | |||||||
\(654\) | −3.67475 | + | 22.5316i | −0.143694 | + | 0.881056i | ||||
\(655\) | −4.70740 | −0.183933 | ||||||||
\(656\) | −9.94709 | −0.388369 | ||||||||
\(657\) | −15.1760 | + | 45.2880i | −0.592071 | + | 1.76685i | ||||
\(658\) | −1.85932 | + | 1.85932i | −0.0724839 | + | 0.0724839i | ||||
\(659\) | 6.86347 | 0.267363 | 0.133681 | − | 0.991024i | \(-0.457320\pi\) | ||||
0.133681 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(660\) | −3.76347 | − | 5.23029i | −0.146493 | − | 0.203589i | ||||
\(661\) | −20.0138 | + | 20.0138i | −0.778446 | + | 0.778446i | −0.979566 | − | 0.201121i | \(-0.935542\pi\) |
0.201121 | + | 0.979566i | \(0.435542\pi\) | |||||||
\(662\) | 1.93815i | 0.0753283i | ||||||||
\(663\) | 5.82999 | + | 0.950831i | 0.226418 | + | 0.0369272i | ||||
\(664\) | −6.83285 | − | 6.83285i | −0.265166 | − | 0.265166i | ||||
\(665\) | −1.47850 | −0.0573339 | ||||||||
\(666\) | 12.3136 | − | 13.4676i | 0.477142 | − | 0.521857i | ||||
\(667\) | −3.74967 | −0.145188 | ||||||||
\(668\) | −8.73935 | − | 8.73935i | −0.338136 | − | 0.338136i | ||||
\(669\) | −8.85804 | − | 1.44469i | −0.342472 | − | 0.0558548i | ||||
\(670\) | 14.1406i | 0.546299i | ||||||||
\(671\) | 32.0142 | − | 32.0142i | 1.23589 | − | 1.23589i | ||||
\(672\) | −0.352082 | − | 0.489306i | −0.0135818 | − | 0.0188754i | ||||
\(673\) | 37.7218 | 1.45407 | 0.727034 | − | 0.686601i | \(-0.240898\pi\) | ||||
0.727034 | + | 0.686601i | \(0.240898\pi\) | |||||||
\(674\) | 23.7173 | − | 23.7173i | 0.913557 | − | 0.913557i | ||||
\(675\) | 2.42253 | − | 4.59688i | 0.0932433 | − | 0.176934i | ||||
\(676\) | 12.3124 | 0.473553 | ||||||||
\(677\) | −26.3889 | −1.01421 | −0.507104 | − | 0.861885i | \(-0.669284\pi\) | ||||
−0.507104 | + | 0.861885i | \(0.669284\pi\) | |||||||
\(678\) | −2.07992 | + | 12.7530i | −0.0798790 | + | 0.489775i | ||||
\(679\) | −3.83607 | − | 3.83607i | −0.147215 | − | 0.147215i | ||||
\(680\) | −2.90814 | − | 2.90814i | −0.111522 | − | 0.111522i | ||||
\(681\) | −29.6307 | + | 21.3209i | −1.13545 | + | 0.817017i | ||||
\(682\) | 22.0335 | 0.843705 | ||||||||
\(683\) | 30.4848 | − | 30.4848i | 1.16647 | − | 1.16647i | 0.183435 | − | 0.983032i | \(-0.441278\pi\) |
0.983032 | − | 0.183435i | \(-0.0587218\pi\) | |||||||
\(684\) | −11.4081 | + | 5.68139i | −0.436198 | + | 0.217234i | ||||
\(685\) | −1.54270 | − | 1.54270i | −0.0589436 | − | 0.0589436i | ||||
\(686\) | −3.41555 | − | 3.41555i | −0.130406 | − | 0.130406i | ||||
\(687\) | −27.0483 | − | 4.41140i | −1.03196 | − | 0.168305i | ||||
\(688\) | 4.12802 | + | 4.12802i | 0.157379 | + | 0.157379i | ||||
\(689\) | −0.0962569 | + | 0.0962569i | −0.00366709 | + | 0.00366709i | ||||
\(690\) | −12.8954 | + | 9.27892i | −0.490920 | + | 0.353243i | ||||
\(691\) | 14.1593i | 0.538646i | 0.963050 | + | 0.269323i | \(0.0867998\pi\) | ||||
−0.963050 | + | 0.269323i | \(0.913200\pi\) | |||||||
\(692\) | 19.5438i | 0.742942i | ||||||||
\(693\) | 3.68298 | + | 1.23417i | 0.139905 | + | 0.0468821i | ||||
\(694\) | − | 20.1922i | − | 0.766484i | ||||||
\(695\) | −2.66597 | − | 2.66597i | −0.101126 | − | 0.101126i | ||||
\(696\) | −0.698840 | − | 0.113976i | −0.0264895 | − | 0.00432025i | ||||
\(697\) | 28.9275 | − | 28.9275i | 1.09571 | − | 1.09571i | ||||
\(698\) | −4.63882 | − | 4.63882i | −0.175582 | − | 0.175582i | ||||
\(699\) | −29.4917 | − | 4.80990i | −1.11548 | − | 0.181927i | ||||
\(700\) | −0.348034 | −0.0131544 | ||||||||
\(701\) | −18.6242 | + | 18.6242i | −0.703428 | + | 0.703428i | −0.965145 | − | 0.261717i | \(-0.915711\pi\) |
0.261717 | + | 0.965145i | \(0.415711\pi\) | |||||||
\(702\) | 2.00885 | − | 3.81190i | 0.0758191 | − | 0.143871i | ||||
\(703\) | −10.4737 | + | 23.6228i | −0.395023 | + | 0.890951i | ||||
\(704\) | 3.72020i | 0.140210i | ||||||||
\(705\) | 7.64312 | + | 10.6220i | 0.287857 | + | 0.400049i | ||||
\(706\) | − | 36.2497i | − | 1.36427i | ||||||
\(707\) | 5.59406 | 0.210386 | ||||||||
\(708\) | 9.32192 | + | 12.9552i | 0.350339 | + | 0.486885i | ||||
\(709\) | 16.5635 | + | 16.5635i | 0.622054 | + | 0.622054i | 0.946056 | − | 0.324002i | \(-0.105029\pi\) |
−0.324002 | + | 0.946056i | \(0.605029\pi\) | |||||||
\(710\) | 0.738626i | 0.0277201i | ||||||||
\(711\) | 12.9448 | + | 25.9928i | 0.485468 | + | 0.974805i | ||||
\(712\) | −7.96364 | −0.298450 | ||||||||
\(713\) | − | 54.3240i | − | 2.03445i | ||||||
\(714\) | 2.44687 | + | 0.399068i | 0.0915719 | + | 0.0149347i | ||||
\(715\) | −3.08492 | −0.115370 | ||||||||
\(716\) | 4.09892 | − | 4.09892i | 0.153184 | − | 0.153184i | ||||
\(717\) | −17.2602 | + | 12.4196i | −0.644595 | + | 0.463820i | ||||
\(718\) | −13.1326 | + | 13.1326i | −0.490104 | + | 0.490104i | ||||
\(719\) | 12.6073i | 0.470174i | 0.971974 | + | 0.235087i | \(0.0755376\pi\) | ||||
−0.971974 | + | 0.235087i | \(0.924462\pi\) | |||||||
\(720\) | −2.68541 | + | 1.33738i | −0.100079 | + | 0.0498411i | ||||
\(721\) | 2.29192 | − | 2.29192i | 0.0853555 | − | 0.0853555i | ||||
\(722\) | −0.673942 | + | 0.673942i | −0.0250815 | + | 0.0250815i | ||||
\(723\) | 16.7251 | + | 23.2438i | 0.622014 | + | 0.864446i | ||||
\(724\) | − | 10.8868i | − | 0.404605i | ||||||
\(725\) | −0.289070 | + | 0.289070i | −0.0107358 | + | 0.0107358i | ||||
\(726\) | −2.87292 | − | 3.99265i | −0.106624 | − | 0.148181i | ||||
\(727\) | −16.6603 | + | 16.6603i | −0.617895 | + | 0.617895i | −0.944991 | − | 0.327096i | \(-0.893930\pi\) |
0.327096 | + | 0.944991i | \(0.393930\pi\) | |||||||
\(728\) | −0.288602 | −0.0106963 | ||||||||
\(729\) | 15.2627 | + | 22.2722i | 0.565285 | + | 0.824896i | ||||
\(730\) | − | 15.9210i | − | 0.589263i | ||||||
\(731\) | −24.0097 | −0.888030 | ||||||||
\(732\) | −12.3116 | − | 17.1100i | −0.455049 | − | 0.632405i | ||||
\(733\) | 19.0725i | 0.704460i | 0.935913 | + | 0.352230i | \(0.114577\pi\) | ||||
−0.935913 | + | 0.352230i | \(0.885423\pi\) | |||||||
\(734\) | 7.70642 | + | 7.70642i | 0.284449 | + | 0.284449i | ||||
\(735\) | −9.67112 | + | 6.95888i | −0.356725 | + | 0.256682i | ||||
\(736\) | 9.17224 | 0.338093 | ||||||||
\(737\) | 52.6058i | 1.93776i | ||||||||
\(738\) | −13.3030 | − | 26.7120i | −0.489690 | − | 0.983283i | ||||
\(739\) | 39.6325i | 1.45791i | 0.684563 | + | 0.728953i | \(0.259993\pi\) | ||||
−0.684563 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(740\) | −2.46547 | + | 5.56071i | −0.0906323 | + | 0.204416i | ||||
\(741\) | −0.982143 | + | 6.02198i | −0.0360799 | + | 0.221223i | ||||
\(742\) | −0.0403994 | + | 0.0403994i | −0.00148311 | + | 0.00148311i | ||||
\(743\) | 4.80447 | 0.176259 | 0.0881295 | − | 0.996109i | \(-0.471911\pi\) | ||||
0.0881295 | + | 0.996109i | \(0.471911\pi\) | |||||||
\(744\) | 1.65125 | − | 10.1246i | 0.0605377 | − | 0.371185i | ||||
\(745\) | −10.4606 | − | 10.4606i | −0.383248 | − | 0.383248i | ||||
\(746\) | −19.4847 | + | 19.4847i | −0.713385 | + | 0.713385i | ||||
\(747\) | 9.21091 | − | 27.4871i | 0.337010 | − | 1.00570i | ||||
\(748\) | −10.8189 | − | 10.8189i | −0.395577 | − | 0.395577i | ||||
\(749\) | − | 3.31969i | − | 0.121299i | ||||||
\(750\) | −0.278802 | + | 1.70946i | −0.0101804 | + | 0.0624208i | ||||
\(751\) | − | 4.63856i | − | 0.169264i | −0.996412 | − | 0.0846318i | \(-0.973029\pi\) | ||
0.996412 | − | 0.0846318i | \(-0.0269714\pi\) | |||||||
\(752\) | − | 7.55524i | − | 0.275511i | ||||||
\(753\) | −7.39847 | − | 10.2820i | −0.269615 | − | 0.374698i | ||||
\(754\) | −0.239707 | + | 0.239707i | −0.00872960 | + | 0.00872960i | ||||
\(755\) | −1.66678 | − | 1.66678i | −0.0606603 | − | 0.0606603i | ||||
\(756\) | 0.843122 | − | 1.59987i | 0.0306641 | − | 0.0581867i | ||||
\(757\) | −24.2357 | − | 24.2357i | −0.880861 | − | 0.880861i | 0.112761 | − | 0.993622i | \(-0.464030\pi\) |
−0.993622 | + | 0.112761i | \(0.964030\pi\) | |||||||
\(758\) | −3.70616 | − | 3.70616i | −0.134614 | − | 0.134614i | ||||
\(759\) | −47.9735 | + | 34.5195i | −1.74133 | + | 1.25298i | ||||
\(760\) | 3.00391 | − | 3.00391i | 0.108963 | − | 0.108963i | ||||
\(761\) | 1.10162 | 0.0399339 | 0.0199669 | − | 0.999801i | \(-0.493644\pi\) | ||||
0.0199669 | + | 0.999801i | \(0.493644\pi\) | |||||||
\(762\) | −6.93556 | − | 9.63870i | −0.251249 | − | 0.349173i | ||||
\(763\) | 3.24368 | + | 3.24368i | 0.117429 | + | 0.117429i | ||||
\(764\) | −14.0022 | − | 14.0022i | −0.506581 | − | 0.506581i | ||||
\(765\) | 3.92027 | − | 11.6988i | 0.141738 | − | 0.422972i | ||||
\(766\) | −28.4065 | −1.02637 | ||||||||
\(767\) | 7.64119 | 0.275907 | ||||||||
\(768\) | 1.70946 | + | 0.278802i | 0.0616850 | + | 0.0100604i | ||||
\(769\) | −4.38921 | + | 4.38921i | −0.158279 | + | 0.158279i | −0.781804 | − | 0.623525i | \(-0.785700\pi\) |
0.623525 | + | 0.781804i | \(0.285700\pi\) | |||||||
\(770\) | −1.29475 | −0.0466597 | ||||||||
\(771\) | −41.6428 | + | 29.9642i | −1.49973 | + | 1.07913i | ||||
\(772\) | −11.7248 | + | 11.7248i | −0.421986 | + | 0.421986i | ||||
\(773\) | − | 36.7986i | − | 1.32355i | −0.749701 | − | 0.661777i | \(-0.769803\pi\) | ||
0.749701 | − | 0.661777i | \(-0.230197\pi\) | |||||||
\(774\) | −5.56470 | + | 16.6061i | −0.200019 | + | 0.596895i | ||||
\(775\) | −4.18795 | − | 4.18795i | −0.150436 | − | 0.150436i | ||||
\(776\) | 15.5876 | 0.559563 | ||||||||
\(777\) | −0.751456 | − | 3.58894i | −0.0269583 | − | 0.128752i | ||||
\(778\) | −8.40919 | −0.301484 | ||||||||
\(779\) | 29.8801 | + | 29.8801i | 1.07057 | + | 1.07057i | ||||
\(780\) | −0.231192 | + | 1.41755i | −0.00827801 | + | 0.0507564i | ||||
\(781\) | 2.74784i | 0.0983253i | ||||||||
\(782\) | −26.6741 | + | 26.6741i | −0.953865 | + | 0.953865i | ||||
\(783\) | −0.628540 | − | 2.02910i | −0.0224622 | − | 0.0725141i | ||||
\(784\) | 6.87887 | 0.245674 | ||||||||
\(785\) | −12.4327 | + | 12.4327i | −0.443741 | + | 0.443741i | ||||
\(786\) | −1.31243 | + | 8.04714i | −0.0468129 | + | 0.287032i | ||||
\(787\) | 2.73413 | 0.0974614 | 0.0487307 | − | 0.998812i | \(-0.484482\pi\) | ||||
0.0487307 | + | 0.998812i | \(0.484482\pi\) | |||||||
\(788\) | −1.38691 | −0.0494066 | ||||||||
\(789\) | −1.41341 | − | 0.230518i | −0.0503188 | − | 0.00820665i | ||||
\(790\) | −6.84427 | − | 6.84427i | −0.243508 | − | 0.243508i | ||||
\(791\) | 1.83594 | + | 1.83594i | 0.0652784 | + | 0.0652784i | ||||
\(792\) | −9.99026 | + | 4.97531i | −0.354989 | + | 0.176790i | ||||
\(793\) | −10.0918 | −0.358370 | ||||||||
\(794\) | −8.96674 | + | 8.96674i | −0.318218 | + | 0.318218i | ||||
\(795\) | 0.166070 | + | 0.230796i | 0.00588990 | + | 0.00818550i | ||||
\(796\) | 12.9450 | + | 12.9450i | 0.458823 | + | 0.458823i | ||||
\(797\) | 9.60816 | + | 9.60816i | 0.340338 | + | 0.340338i | 0.856495 | − | 0.516156i | \(-0.172638\pi\) |
−0.516156 | + | 0.856495i | \(0.672638\pi\) | |||||||
\(798\) | −0.412210 | + | 2.52745i | −0.0145921 | + | 0.0894708i | ||||
\(799\) | 21.9717 | + | 21.9717i | 0.777302 | + | 0.777302i | ||||
\(800\) | 0.707107 | − | 0.707107i | 0.0250000 | − | 0.0250000i | ||||
\(801\) | −10.6504 | − | 21.3856i | −0.376313 | − | 0.755624i | ||||
\(802\) | 30.9227i | 1.09192i | ||||||||
\(803\) | − | 59.2294i | − | 2.09016i | ||||||
\(804\) | 24.1728 | + | 3.94242i | 0.852511 | + | 0.139039i | ||||
\(805\) | 3.19225i | 0.112512i | ||||||||
\(806\) | −3.47280 | − | 3.47280i | −0.122324 | − | 0.122324i | ||||
\(807\) | −6.40940 | + | 39.2991i | −0.225622 | + | 1.38339i | ||||
\(808\) | −11.3656 | + | 11.3656i | −0.399839 | + | 0.399839i | ||||
\(809\) | −15.3138 | − | 15.3138i | −0.538405 | − | 0.538405i | 0.384656 | − | 0.923060i | \(-0.374320\pi\) |
−0.923060 | + | 0.384656i | \(0.874320\pi\) | |||||||
\(810\) | −7.18281 | − | 5.42285i | −0.252378 | − | 0.190540i | ||||
\(811\) | −8.02200 | −0.281690 | −0.140845 | − | 0.990032i | \(-0.544982\pi\) | ||||
−0.140845 | + | 0.990032i | \(0.544982\pi\) | |||||||
\(812\) | −0.100606 | + | 0.100606i | −0.00353058 | + | 0.00353058i | ||||
\(813\) | −14.6646 | − | 2.39169i | −0.514310 | − | 0.0838804i | ||||
\(814\) | −9.17203 | + | 20.6870i | −0.321479 | + | 0.725077i | ||||
\(815\) | − | 4.01492i | − | 0.140637i | ||||||
\(816\) | −5.78215 | + | 4.16056i | −0.202416 | + | 0.145649i | ||||
\(817\) | − | 24.8003i | − | 0.867654i | ||||||
\(818\) | 27.4114 | 0.958419 | ||||||||
\(819\) | −0.385969 | − | 0.775014i | −0.0134868 | − | 0.0270812i | ||||
\(820\) | 7.03365 | + | 7.03365i | 0.245626 | + | 0.245626i | ||||
\(821\) | 17.6701i | 0.616691i | 0.951274 | + | 0.308346i | \(0.0997753\pi\) | ||||
−0.951274 | + | 0.308346i | \(0.900225\pi\) | |||||||
\(822\) | −3.06730 | + | 2.20708i | −0.106984 | + | 0.0769809i | ||||
\(823\) | −47.3923 | −1.65199 | −0.825996 | − | 0.563676i | \(-0.809387\pi\) | ||||
−0.825996 | + | 0.563676i | \(0.809387\pi\) | |||||||
\(824\) | 9.31307i | 0.324436i | ||||||||
\(825\) | −1.03720 | + | 6.35955i | −0.0361106 | + | 0.221411i | ||||
\(826\) | 3.20704 | 0.111587 | ||||||||
\(827\) | 23.8439 | − | 23.8439i | 0.829133 | − | 0.829133i | −0.158264 | − | 0.987397i | \(-0.550590\pi\) |
0.987397 | + | 0.158264i | \(0.0505896\pi\) | |||||||
\(828\) | 12.2667 | + | 24.6312i | 0.426298 | + | 0.855994i | ||||
\(829\) | −18.4809 | + | 18.4809i | −0.641867 | + | 0.641867i | −0.951014 | − | 0.309147i | \(-0.899956\pi\) |
0.309147 | + | 0.951014i | \(0.399956\pi\) | |||||||
\(830\) | 9.66311i | 0.335411i | ||||||||
\(831\) | −24.7430 | + | 17.8039i | −0.858326 | + | 0.617611i | ||||
\(832\) | 0.586358 | − | 0.586358i | 0.0203283 | − | 0.0203283i | ||||
\(833\) | −20.0047 | + | 20.0047i | −0.693122 | + | 0.693122i | ||||
\(834\) | −5.30065 | + | 3.81410i | −0.183547 | + | 0.132072i | ||||
\(835\) | 12.3593i | 0.427712i | ||||||||
\(836\) | 11.1751 | − | 11.1751i | 0.386500 | − | 0.386500i | ||||
\(837\) | 29.3970 | − | 9.10608i | 1.01611 | − | 0.314752i | ||||
\(838\) | −17.2664 | + | 17.2664i | −0.596459 | + | 0.596459i | ||||
\(839\) | 33.1366 | 1.14400 | 0.572000 | − | 0.820253i | \(-0.306168\pi\) | ||||
0.572000 | + | 0.820253i | \(0.306168\pi\) | |||||||
\(840\) | −0.0970324 | + | 0.594951i | −0.00334794 | + | 0.0205278i | ||||
\(841\) | − | 28.8329i | − | 0.994237i | ||||||
\(842\) | −1.49968 | −0.0516825 | ||||||||
\(843\) | 1.93114 | − | 1.38956i | 0.0665120 | − | 0.0478589i | ||||
\(844\) | 16.2108i | 0.557999i | ||||||||
\(845\) | −8.70616 | − | 8.70616i | −0.299501 | − | 0.299501i | ||||
\(846\) | 20.2889 | − | 10.1042i | 0.697548 | − | 0.347390i | ||||
\(847\) | −0.988378 | −0.0339611 | ||||||||
\(848\) | − | 0.164161i | − | 0.00563730i | ||||||
\(849\) | −2.92121 | + | 2.10197i | −0.100256 | + | 0.0721393i | ||||
\(850\) | 4.11273i | 0.141065i | ||||||||
\(851\) | 51.0041 | + | 22.6138i | 1.74840 | + | 0.775192i | ||||
\(852\) | 1.26265 | + | 0.205930i | 0.0432578 | + | 0.00705505i | ||||
\(853\) | −3.14167 | + | 3.14167i | −0.107569 | + | 0.107569i | −0.758843 | − | 0.651274i | \(-0.774235\pi\) |
0.651274 | + | 0.758843i | \(0.274235\pi\) | |||||||
\(854\) | −4.23557 | −0.144938 | ||||||||
\(855\) | 12.0841 | + | 4.04937i | 0.413266 | + | 0.138485i | ||||
\(856\) | 6.74468 | + | 6.74468i | 0.230528 | + | 0.230528i | ||||
\(857\) | −6.44238 | + | 6.44238i | −0.220067 | + | 0.220067i | −0.808527 | − | 0.588459i | \(-0.799735\pi\) |
0.588459 | + | 0.808527i | \(0.299735\pi\) | |||||||
\(858\) | −0.860082 | + | 5.27356i | −0.0293627 | + | 0.180036i | ||||
\(859\) | 7.97483 | + | 7.97483i | 0.272098 | + | 0.272098i | 0.829944 | − | 0.557846i | \(-0.188372\pi\) |
−0.557846 | + | 0.829944i | \(0.688372\pi\) | |||||||
\(860\) | − | 5.83790i | − | 0.199071i | ||||||
\(861\) | −5.91803 | − | 0.965190i | −0.201686 | − | 0.0328936i | ||||
\(862\) | − | 15.2506i | − | 0.519437i | ||||||
\(863\) | − | 13.3993i | − | 0.456119i | −0.973647 | − | 0.228060i | \(-0.926762\pi\) | ||
0.973647 | − | 0.228060i | \(-0.0732381\pi\) | |||||||
\(864\) | 1.53750 | + | 4.96348i | 0.0523068 | + | 0.168861i | ||||
\(865\) | 13.8195 | − | 13.8195i | 0.469878 | − | 0.469878i | ||||
\(866\) | −11.2397 | − | 11.2397i | −0.381940 | − | 0.381940i | ||||
\(867\) | −0.0238291 | + | 0.146108i | −0.000809280 | + | 0.00496207i | ||||
\(868\) | −1.45755 | − | 1.45755i | −0.0494724 | − | 0.0494724i | ||||
\(869\) | −25.4621 | − | 25.4621i | −0.863741 | − | 0.863741i | ||||
\(870\) | 0.413561 | + | 0.574747i | 0.0140210 | + | 0.0194858i | ||||
\(871\) | 8.29145 | − | 8.29145i | 0.280945 | − | 0.280945i | ||||
\(872\) | −13.1805 | −0.446348 | ||||||||
\(873\) | 20.8465 | + | 41.8592i | 0.705548 | + | 1.41672i | ||||
\(874\) | −27.5525 | − | 27.5525i | −0.931979 | − | 0.931979i | ||||
\(875\) | 0.246097 | + | 0.246097i | 0.00831959 | + | 0.00831959i | ||||
\(876\) | −27.2164 | − | 4.43881i | −0.919558 | − | 0.149973i | ||||
\(877\) | 26.2075 | 0.884965 | 0.442483 | − | 0.896777i | \(-0.354098\pi\) | ||||
0.442483 | + | 0.896777i | \(0.354098\pi\) | |||||||
\(878\) | 13.2085 | 0.445765 | ||||||||
\(879\) | 0.485415 | − | 2.97630i | 0.0163726 | − | 0.100388i | ||||
\(880\) | 2.63058 | − | 2.63058i | 0.0886768 | − | 0.0886768i | ||||
\(881\) | −16.8777 | −0.568623 | −0.284312 | − | 0.958732i | \(-0.591765\pi\) | ||||
−0.284312 | + | 0.958732i | \(0.591765\pi\) | |||||||
\(882\) | 9.19964 | + | 18.4726i | 0.309768 | + | 0.622004i | ||||
\(883\) | 38.5237 | − | 38.5237i | 1.29643 | − | 1.29643i | 0.365690 | − | 0.930737i | \(-0.380833\pi\) |
0.930737 | − | 0.365690i | \(-0.119167\pi\) | |||||||
\(884\) | 3.41042i | 0.114705i | ||||||||
\(885\) | 2.56909 | − | 15.7523i | 0.0863589 | − | 0.529507i | ||||
\(886\) | 6.99415 | + | 6.99415i | 0.234973 | + | 0.234973i | ||||
\(887\) | −30.2782 | −1.01664 | −0.508321 | − | 0.861168i | \(-0.669734\pi\) | ||||
−0.508321 | + | 0.861168i | \(0.669734\pi\) | |||||||
\(888\) | 8.81846 | + | 5.76496i | 0.295928 | + | 0.193459i | ||||
\(889\) | −2.38605 | −0.0800257 | ||||||||
\(890\) | 5.63114 | + | 5.63114i | 0.188756 | + | 0.188756i | ||||
\(891\) | −26.7215 | − | 20.1741i | −0.895203 | − | 0.675857i | ||||
\(892\) | − | 5.18177i | − | 0.173498i | ||||||
\(893\) | −22.6952 | + | 22.6952i | −0.759467 | + | 0.759467i | ||||
\(894\) | −20.7985 | + | 14.9656i | −0.695606 | + | 0.500525i | ||||
\(895\) | −5.79675 | −0.193764 | ||||||||
\(896\) | 0.246097 | − | 0.246097i | 0.00822152 | − | 0.00822152i | ||||
\(897\) | 13.0021 | + | 2.12055i | 0.434127 | + | 0.0708031i | ||||
\(898\) | 9.63475 | 0.321516 | ||||||||
\(899\) | −2.42122 | −0.0807522 | ||||||||
\(900\) | 2.84454 | + | 0.953204i | 0.0948180 | + | 0.0317735i | ||||
\(901\) | 0.477402 | + | 0.477402i | 0.0159046 | + | 0.0159046i | ||||
\(902\) | 26.1666 | + | 26.1666i | 0.871253 | + | 0.871253i | ||||
\(903\) | 2.05542 | + | 2.85652i | 0.0684000 | + | 0.0950590i | ||||
\(904\) | −7.46022 | −0.248123 | ||||||||
\(905\) | −7.69814 | + | 7.69814i | −0.255895 | + | 0.255895i | ||||
\(906\) | −3.31400 | + | 2.38460i | −0.110100 | + | 0.0792230i | ||||
\(907\) | 32.4218 | + | 32.4218i | 1.07655 | + | 1.07655i | 0.996816 | + | 0.0797310i | \(0.0254061\pi\) |
0.0797310 | + | 0.996816i | \(0.474594\pi\) | |||||||
\(908\) | −14.9028 | − | 14.9028i | −0.494566 | − | 0.494566i | ||||
\(909\) | −45.7212 | − | 15.3212i | −1.51648 | − | 0.508171i | ||||
\(910\) | 0.204072 | + | 0.204072i | 0.00676493 | + | 0.00676493i | ||||
\(911\) | −4.77098 | + | 4.77098i | −0.158069 | + | 0.158069i | −0.781711 | − | 0.623641i | \(-0.785653\pi\) |
0.623641 | + | 0.781711i | \(0.285653\pi\) | |||||||
\(912\) | −4.29758 | − | 5.97257i | −0.142307 | − | 0.197771i | ||||
\(913\) | 35.9487i | 1.18973i | ||||||||
\(914\) | − | 24.1826i | − | 0.799888i | ||||||
\(915\) | −3.39302 | + | 20.8042i | −0.112170 | + | 0.687766i | ||||
\(916\) | − | 15.8227i | − | 0.522796i | ||||||
\(917\) | 1.15848 | + | 1.15848i | 0.0382563 | + | 0.0382563i | ||||
\(918\) | −18.9057 | − | 9.96321i | −0.623982 | − | 0.328835i | ||||
\(919\) | −41.5937 | + | 41.5937i | −1.37205 | + | 1.37205i | −0.514651 | + | 0.857400i | \(0.672078\pi\) |
−0.857400 | + | 0.514651i | \(0.827922\pi\) | |||||||
\(920\) | −6.48575 | − | 6.48575i | −0.213829 | − | 0.213829i | ||||
\(921\) | −2.63022 | + | 16.1271i | −0.0866685 | + | 0.531406i | ||||
\(922\) | 1.03146 | 0.0339694 | ||||||||
\(923\) | 0.433099 | − | 0.433099i | 0.0142556 | − | 0.0142556i | ||||
\(924\) | −0.360980 | + | 2.21334i | −0.0118754 | + | 0.0728135i | ||||
\(925\) | 5.67536 | − | 2.18867i | 0.186605 | − | 0.0719629i | ||||
\(926\) | − | 8.88581i | − | 0.292006i | ||||||
\(927\) | −25.0094 | + | 12.4551i | −0.821417 | + | 0.409078i | ||||
\(928\) | − | 0.408806i | − | 0.0134197i | ||||||
\(929\) | 26.8594 | 0.881228 | 0.440614 | − | 0.897697i | \(-0.354761\pi\) | ||||
0.440614 | + | 0.897697i | \(0.354761\pi\) | |||||||
\(930\) | −8.32676 | + | 5.99154i | −0.273045 | + | 0.196470i | ||||
\(931\) | −20.6635 | − | 20.6635i | −0.677218 | − | 0.677218i | ||||
\(932\) | − | 17.2520i | − | 0.565109i | ||||||
\(933\) | −24.9628 | − | 34.6921i | −0.817244 | − | 1.13577i | ||||
\(934\) | 12.2283 | 0.400123 | ||||||||
\(935\) | 15.3002i | 0.500369i | ||||||||
\(936\) | 2.35879 | + | 0.790430i | 0.0770995 | + | 0.0258360i | ||||
\(937\) | −2.71379 | −0.0886557 | −0.0443278 | − | 0.999017i | \(-0.514115\pi\) | ||||
−0.0443278 | + | 0.999017i | \(0.514115\pi\) | |||||||
\(938\) | 3.47996 | − | 3.47996i | 0.113625 | − | 0.113625i | ||||
\(939\) | 10.8967 | + | 15.1438i | 0.355602 | + | 0.494198i | ||||
\(940\) | −5.34236 | + | 5.34236i | −0.174249 | + | 0.174249i | ||||
\(941\) | 5.22310i | 0.170268i | 0.996369 | + | 0.0851342i | \(0.0271319\pi\) | ||||
−0.996369 | + | 0.0851342i | \(0.972868\pi\) | |||||||
\(942\) | 17.7870 | + | 24.7195i | 0.579530 | + | 0.805403i | ||||
\(943\) | 64.5143 | − | 64.5143i | 2.10088 | − | 2.10088i | ||||
\(944\) | −6.51580 | + | 6.51580i | −0.212071 | + | 0.212071i | ||||
\(945\) | −1.72746 | + | 0.535102i | −0.0561942 | + | 0.0174069i | ||||
\(946\) | − | 21.7181i | − | 0.706118i | ||||||
\(947\) | 3.68356 | − | 3.68356i | 0.119700 | − | 0.119700i | −0.644720 | − | 0.764419i | \(-0.723026\pi\) |
0.764419 | + | 0.644720i | \(0.223026\pi\) | |||||||
\(948\) | −13.6082 | + | 9.79184i | −0.441975 | + | 0.318024i | ||||
\(949\) | −9.33542 | + | 9.33542i | −0.303040 | + | 0.303040i | ||||
\(950\) | −4.24816 | −0.137829 | ||||||||
\(951\) | −35.0594 | − | 5.71795i | −1.13688 | − | 0.185417i | ||||
\(952\) | 1.43137i | 0.0463909i | ||||||||
\(953\) | −9.01908 | −0.292157 | −0.146078 | − | 0.989273i | \(-0.546665\pi\) | ||||
−0.146078 | + | 0.989273i | \(0.546665\pi\) | |||||||
\(954\) | 0.440839 | − | 0.219544i | 0.0142727 | − | 0.00710802i | ||||
\(955\) | 19.8021i | 0.640780i | ||||||||
\(956\) | −8.68104 | − | 8.68104i | −0.280765 | − | 0.280765i | ||||
\(957\) | 1.53853 | + | 2.13818i | 0.0497336 | + | 0.0691174i | ||||
\(958\) | 6.40565 | 0.206957 | ||||||||
\(959\) | 0.759308i | 0.0245193i | ||||||||
\(960\) | −1.01163 | − | 1.40592i | −0.0326503 | − | 0.0453758i | ||||
\(961\) | − | 4.07785i | − | 0.131544i | ||||||
\(962\) | 4.70621 | − | 1.81492i | 0.151734 | − | 0.0585153i | ||||
\(963\) | −9.09206 | + | 27.1324i | −0.292987 | + | 0.874330i | ||||
\(964\) | −11.6905 | + | 11.6905i | −0.376525 | + | 0.376525i | ||||
\(965\) | 16.5814 | 0.533774 | ||||||||
\(966\) | 5.45703 | + | 0.890004i | 0.175577 | + | 0.0286354i | ||||
\(967\) | −8.75126 | − | 8.75126i | −0.281422 | − | 0.281422i | 0.552254 | − | 0.833676i | \(-0.313768\pi\) |
−0.833676 | + | 0.552254i | \(0.813768\pi\) | |||||||
\(968\) | 2.00811 | − | 2.00811i | 0.0645430 | − | 0.0645430i | ||||
\(969\) | 29.8670 | + | 4.87110i | 0.959466 | + | 0.156482i | ||||
\(970\) | −11.0221 | − | 11.0221i | −0.353899 | − | 0.353899i | ||||
\(971\) | 35.3826i | 1.13548i | 0.823208 | + | 0.567740i | \(0.192182\pi\) | ||||
−0.823208 | + | 0.567740i | \(0.807818\pi\) | |||||||
\(972\) | −11.2728 | + | 10.7669i | −0.361574 | + | 0.345347i | ||||
\(973\) | 1.31217i | 0.0420663i | ||||||||
\(974\) | − | 5.26540i | − | 0.168714i | ||||||
\(975\) | 1.16584 | − | 0.838880i | 0.0373366 | − | 0.0268657i | ||||
\(976\) | 8.60550 | − | 8.60550i | 0.275455 | − | 0.275455i | ||||
\(977\) | 25.2942 | + | 25.2942i | 0.809232 | + | 0.809232i | 0.984518 | − | 0.175286i | \(-0.0560850\pi\) |
−0.175286 | + | 0.984518i | \(0.556085\pi\) | |||||||
\(978\) | −6.86337 | − | 1.11937i | −0.219466 | − | 0.0357934i | ||||
\(979\) | 20.9490 | + | 20.9490i | 0.669532 | + | 0.669532i | ||||
\(980\) | −4.86410 | − | 4.86410i | −0.155378 | − | 0.155378i | ||||
\(981\) | −17.6273 | − | 35.3951i | −0.562796 | − | 1.13008i | ||||
\(982\) | −2.97870 | + | 2.97870i | −0.0950542 | + | 0.0950542i | ||||
\(983\) | 6.06207 | 0.193350 | 0.0966750 | − | 0.995316i | \(-0.469179\pi\) | ||||
0.0966750 | + | 0.995316i | \(0.469179\pi\) | |||||||
\(984\) | 13.9848 | − | 10.0628i | 0.445818 | − | 0.320790i | ||||
\(985\) | 0.980693 | + | 0.980693i | 0.0312475 | + | 0.0312475i | ||||
\(986\) | 1.18886 | + | 1.18886i | 0.0378612 | + | 0.0378612i | ||||
\(987\) | 0.733103 | − | 4.49500i | 0.0233349 | − | 0.143077i | ||||
\(988\) | −3.52273 | −0.112073 | ||||||||
\(989\) | −53.5466 | −1.70268 | ||||||||
\(990\) | 10.5823 | + | 3.54611i | 0.336326 | + | 0.112703i | ||||
\(991\) | 21.7632 | − | 21.7632i | 0.691331 | − | 0.691331i | −0.271194 | − | 0.962525i | \(-0.587418\pi\) |
0.962525 | + | 0.271194i | \(0.0874184\pi\) | |||||||
\(992\) | 5.92266 | 0.188045 | ||||||||
\(993\) | −1.96069 | − | 2.72487i | −0.0622207 | − | 0.0864713i | ||||
\(994\) | 0.181774 | − | 0.181774i | 0.00576551 | − | 0.00576551i | ||||
\(995\) | − | 18.3070i | − | 0.580371i | ||||||
\(996\) | 16.5187 | + | 2.69409i | 0.523416 | + | 0.0853656i | ||||
\(997\) | 27.2352 | + | 27.2352i | 0.862546 | + | 0.862546i | 0.991633 | − | 0.129087i | \(-0.0412048\pi\) |
−0.129087 | + | 0.991633i | \(0.541205\pi\) | |||||||
\(998\) | −20.7320 | −0.656259 | ||||||||
\(999\) | −3.68769 | + | 31.3911i | −0.116673 | + | 0.993170i |
(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.u.f.191.7 | ✓ | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.f.191.13 | yes | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.f.401.13 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.f.401.7 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.f.191.7 | ✓ | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.f.191.13 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.f.401.7 | yes | 40 | 111.68 | even | 4 | inner | |
1110.2.u.f.401.13 | yes | 40 | 37.31 | odd | 4 | inner |