Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(671,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.20 | ||
Character | \(\chi\) | \(=\) | 804.671 |
Dual form | 804.2.c.b.671.19 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27439 | + | 0.613127i | −0.901131 | + | 0.433546i | ||||
\(3\) | −1.63926 | + | 0.559297i | −0.946430 | + | 0.322910i | ||||
\(4\) | 1.24815 | − | 1.56273i | 0.624076 | − | 0.781364i | ||||
\(5\) | 0.350980i | 0.156963i | 0.996916 | + | 0.0784815i | \(0.0250072\pi\) | ||||
−0.996916 | + | 0.0784815i | \(0.974993\pi\) | |||||||
\(6\) | 1.74615 | − | 1.71784i | 0.712861 | − | 0.701305i | ||||
\(7\) | − | 2.98214i | − | 1.12714i | −0.826068 | − | 0.563571i | \(-0.809427\pi\) | ||
0.826068 | − | 0.563571i | \(-0.190573\pi\) | |||||||
\(8\) | −0.632485 | + | 2.75680i | −0.223617 | + | 0.974677i | ||||
\(9\) | 2.37437 | − | 1.83367i | 0.791458 | − | 0.611224i | ||||
\(10\) | −0.215195 | − | 0.447286i | −0.0680507 | − | 0.141444i | ||||
\(11\) | −1.69575 | −0.511288 | −0.255644 | − | 0.966771i | \(-0.582287\pi\) | ||||
−0.255644 | + | 0.966771i | \(0.582287\pi\) | |||||||
\(12\) | −1.17202 | + | 3.25981i | −0.338333 | + | 0.941026i | ||||
\(13\) | −4.42815 | −1.22815 | −0.614073 | − | 0.789249i | \(-0.710470\pi\) | ||||
−0.614073 | + | 0.789249i | \(0.710470\pi\) | |||||||
\(14\) | 1.82843 | + | 3.80041i | 0.488668 | + | 1.01570i | ||||
\(15\) | −0.196302 | − | 0.575349i | −0.0506850 | − | 0.148554i | ||||
\(16\) | −0.884236 | − | 3.90104i | −0.221059 | − | 0.975260i | ||||
\(17\) | − | 2.00327i | − | 0.485863i | −0.970043 | − | 0.242932i | \(-0.921891\pi\) | ||
0.970043 | − | 0.242932i | \(-0.0781091\pi\) | |||||||
\(18\) | −1.90161 | + | 3.79261i | −0.448214 | + | 0.893926i | ||||
\(19\) | 1.45165i | 0.333032i | 0.986039 | + | 0.166516i | \(0.0532517\pi\) | ||||
−0.986039 | + | 0.166516i | \(0.946748\pi\) | |||||||
\(20\) | 0.548486 | + | 0.438076i | 0.122645 | + | 0.0979568i | ||||
\(21\) | 1.66790 | + | 4.88851i | 0.363966 | + | 1.06676i | ||||
\(22\) | 2.16105 | − | 1.03971i | 0.460737 | − | 0.221667i | ||||
\(23\) | 3.48501 | 0.726675 | 0.363338 | − | 0.931658i | \(-0.381637\pi\) | ||||
0.363338 | + | 0.931658i | \(0.381637\pi\) | |||||||
\(24\) | −0.505063 | − | 4.87288i | −0.103096 | − | 0.994671i | ||||
\(25\) | 4.87681 | 0.975363 | ||||||||
\(26\) | 5.64319 | − | 2.71501i | 1.10672 | − | 0.532458i | ||||
\(27\) | −2.86666 | + | 4.33385i | −0.551689 | + | 0.834050i | ||||
\(28\) | −4.66027 | − | 3.72216i | −0.880708 | − | 0.703422i | ||||
\(29\) | 3.03917i | 0.564359i | 0.959362 | + | 0.282180i | \(0.0910574\pi\) | ||||
−0.959362 | + | 0.282180i | \(0.908943\pi\) | |||||||
\(30\) | 0.602928 | + | 0.612862i | 0.110079 | + | 0.111893i | ||||
\(31\) | 10.5902i | 1.90206i | 0.309104 | + | 0.951028i | \(0.399971\pi\) | ||||
−0.309104 | + | 0.951028i | \(0.600029\pi\) | |||||||
\(32\) | 3.51870 | + | 4.42931i | 0.622023 | + | 0.782999i | ||||
\(33\) | 2.77978 | − | 0.948428i | 0.483898 | − | 0.165100i | ||||
\(34\) | 1.22826 | + | 2.55295i | 0.210644 | + | 0.437827i | ||||
\(35\) | 1.04667 | 0.176920 | ||||||||
\(36\) | 0.0980481 | − | 5.99920i | 0.0163414 | − | 0.999866i | ||||
\(37\) | −6.83128 | −1.12305 | −0.561527 | − | 0.827458i | \(-0.689786\pi\) | ||||
−0.561527 | + | 0.827458i | \(0.689786\pi\) | |||||||
\(38\) | −0.890047 | − | 1.84997i | −0.144385 | − | 0.300105i | ||||
\(39\) | 7.25890 | − | 2.47665i | 1.16235 | − | 0.396581i | ||||
\(40\) | −0.967583 | − | 0.221989i | −0.152988 | − | 0.0350996i | ||||
\(41\) | 0.934816i | 0.145994i | 0.997332 | + | 0.0729968i | \(0.0232563\pi\) | ||||
−0.997332 | + | 0.0729968i | \(0.976744\pi\) | |||||||
\(42\) | −5.12284 | − | 5.20725i | −0.790471 | − | 0.803496i | ||||
\(43\) | 2.28333i | 0.348205i | 0.984728 | + | 0.174103i | \(0.0557024\pi\) | ||||
−0.984728 | + | 0.174103i | \(0.944298\pi\) | |||||||
\(44\) | −2.11655 | + | 2.65000i | −0.319082 | + | 0.399502i | ||||
\(45\) | 0.643582 | + | 0.833358i | 0.0959396 | + | 0.124230i | ||||
\(46\) | −4.44127 | + | 2.13675i | −0.654830 | + | 0.315047i | ||||
\(47\) | −11.7382 | −1.71220 | −0.856099 | − | 0.516813i | \(-0.827118\pi\) | ||||
−0.856099 | + | 0.516813i | \(0.827118\pi\) | |||||||
\(48\) | 3.63134 | + | 5.90029i | 0.524138 | + | 0.851633i | ||||
\(49\) | −1.89315 | −0.270450 | ||||||||
\(50\) | −6.21497 | + | 2.99010i | −0.878930 | + | 0.422865i | ||||
\(51\) | 1.12042 | + | 3.28388i | 0.156890 | + | 0.459836i | ||||
\(52\) | −5.52700 | + | 6.91999i | −0.766456 | + | 0.959629i | ||||
\(53\) | − | 1.53931i | − | 0.211441i | −0.994396 | − | 0.105720i | \(-0.966285\pi\) | ||
0.994396 | − | 0.105720i | \(-0.0337149\pi\) | |||||||
\(54\) | 0.996046 | − | 7.28065i | 0.135545 | − | 0.990771i | ||||
\(55\) | − | 0.595174i | − | 0.0802533i | ||||||
\(56\) | 8.22117 | + | 1.88616i | 1.09860 | + | 0.252048i | ||||
\(57\) | −0.811905 | − | 2.37964i | −0.107539 | − | 0.315191i | ||||
\(58\) | −1.86339 | − | 3.87309i | −0.244676 | − | 0.508562i | ||||
\(59\) | −14.8437 | −1.93248 | −0.966241 | − | 0.257641i | \(-0.917055\pi\) | ||||
−0.966241 | + | 0.257641i | \(0.917055\pi\) | |||||||
\(60\) | −1.14413 | − | 0.411356i | −0.147706 | − | 0.0531058i | ||||
\(61\) | −3.43726 | −0.440096 | −0.220048 | − | 0.975489i | \(-0.570621\pi\) | ||||
−0.220048 | + | 0.975489i | \(0.570621\pi\) | |||||||
\(62\) | −6.49314 | − | 13.4961i | −0.824629 | − | 1.71400i | ||||
\(63\) | −5.46826 | − | 7.08071i | −0.688936 | − | 0.892086i | ||||
\(64\) | −7.19993 | − | 3.48727i | −0.899991 | − | 0.435909i | ||||
\(65\) | − | 1.55419i | − | 0.192774i | ||||||
\(66\) | −2.96103 | + | 2.91303i | −0.364477 | + | 0.358569i | ||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | −3.13056 | − | 2.50038i | −0.379636 | − | 0.303216i | ||||
\(69\) | −5.71286 | + | 1.94916i | −0.687747 | + | 0.234651i | ||||
\(70\) | −1.33387 | + | 0.641742i | −0.159428 | + | 0.0767028i | ||||
\(71\) | 14.0214 | 1.66403 | 0.832017 | − | 0.554750i | \(-0.187186\pi\) | ||||
0.832017 | + | 0.554750i | \(0.187186\pi\) | |||||||
\(72\) | 3.55332 | + | 7.70545i | 0.418762 | + | 0.908096i | ||||
\(73\) | −5.28996 | −0.619143 | −0.309572 | − | 0.950876i | \(-0.600186\pi\) | ||||
−0.309572 | + | 0.950876i | \(0.600186\pi\) | |||||||
\(74\) | 8.70573 | − | 4.18844i | 1.01202 | − | 0.486896i | ||||
\(75\) | −7.99438 | + | 2.72759i | −0.923112 | + | 0.314955i | ||||
\(76\) | 2.26854 | + | 1.81188i | 0.260219 | + | 0.207837i | ||||
\(77\) | 5.05696i | 0.576294i | ||||||||
\(78\) | −7.73219 | + | 7.60685i | −0.875498 | + | 0.861306i | ||||
\(79\) | 16.7488i | 1.88439i | 0.335062 | + | 0.942196i | \(0.391243\pi\) | ||||
−0.335062 | + | 0.942196i | \(0.608757\pi\) | |||||||
\(80\) | 1.36919 | − | 0.310349i | 0.153080 | − | 0.0346981i | ||||
\(81\) | 2.27530 | − | 8.70764i | 0.252811 | − | 0.967516i | ||||
\(82\) | −0.573160 | − | 1.19132i | −0.0632950 | − | 0.131559i | ||||
\(83\) | −6.63054 | −0.727797 | −0.363898 | − | 0.931439i | \(-0.618554\pi\) | ||||
−0.363898 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(84\) | 9.72121 | + | 3.49513i | 1.06067 | + | 0.381350i | ||||
\(85\) | 0.703107 | 0.0762626 | ||||||||
\(86\) | −1.39997 | − | 2.90986i | −0.150963 | − | 0.313779i | ||||
\(87\) | −1.69980 | − | 4.98200i | −0.182237 | − | 0.534126i | ||||
\(88\) | 1.07254 | − | 4.67485i | 0.114333 | − | 0.498340i | ||||
\(89\) | − | 5.60971i | − | 0.594628i | −0.954780 | − | 0.297314i | \(-0.903909\pi\) | ||
0.954780 | − | 0.297314i | \(-0.0960908\pi\) | |||||||
\(90\) | −1.33113 | − | 0.667427i | −0.140313 | − | 0.0703530i | ||||
\(91\) | 13.2053i | 1.38430i | ||||||||
\(92\) | 4.34982 | − | 5.44613i | 0.453500 | − | 0.567798i | ||||
\(93\) | −5.92307 | − | 17.3601i | −0.614194 | − | 1.80016i | ||||
\(94\) | 14.9591 | − | 7.19702i | 1.54291 | − | 0.742316i | ||||
\(95\) | −0.509501 | −0.0522737 | ||||||||
\(96\) | −8.24537 | − | 5.29281i | −0.841540 | − | 0.540195i | ||||
\(97\) | −9.69599 | −0.984479 | −0.492239 | − | 0.870460i | \(-0.663822\pi\) | ||||
−0.492239 | + | 0.870460i | \(0.663822\pi\) | |||||||
\(98\) | 2.41261 | − | 1.16074i | 0.243711 | − | 0.117252i | ||||
\(99\) | −4.02634 | + | 3.10945i | −0.404663 | + | 0.312511i | ||||
\(100\) | 6.08700 | − | 7.62113i | 0.608700 | − | 0.762113i | ||||
\(101\) | 12.5232i | 1.24610i | 0.782180 | + | 0.623052i | \(0.214108\pi\) | ||||
−0.782180 | + | 0.623052i | \(0.785892\pi\) | |||||||
\(102\) | −3.44129 | − | 3.49799i | −0.340739 | − | 0.346353i | ||||
\(103\) | 3.32384i | 0.327508i | 0.986501 | + | 0.163754i | \(0.0523603\pi\) | ||||
−0.986501 | + | 0.163754i | \(0.947640\pi\) | |||||||
\(104\) | 2.80073 | − | 12.2075i | 0.274635 | − | 1.19705i | ||||
\(105\) | −1.71577 | + | 0.585400i | −0.167442 | + | 0.0571292i | ||||
\(106\) | 0.943794 | + | 1.96169i | 0.0916694 | + | 0.190536i | ||||
\(107\) | −0.522441 | −0.0505063 | −0.0252531 | − | 0.999681i | \(-0.508039\pi\) | ||||
−0.0252531 | + | 0.999681i | \(0.508039\pi\) | |||||||
\(108\) | 3.19461 | + | 9.88911i | 0.307401 | + | 0.951580i | ||||
\(109\) | −10.6357 | −1.01872 | −0.509358 | − | 0.860554i | \(-0.670117\pi\) | ||||
−0.509358 | + | 0.860554i | \(0.670117\pi\) | |||||||
\(110\) | 0.364917 | + | 0.758486i | 0.0347935 | + | 0.0723188i | ||||
\(111\) | 11.1983 | − | 3.82071i | 1.06289 | − | 0.362646i | ||||
\(112\) | −11.6334 | + | 2.63691i | −1.09926 | + | 0.249165i | ||||
\(113\) | 15.8801i | 1.49387i | 0.664895 | + | 0.746937i | \(0.268476\pi\) | ||||
−0.664895 | + | 0.746937i | \(0.731524\pi\) | |||||||
\(114\) | 2.49371 | + | 2.53480i | 0.233557 | + | 0.237405i | ||||
\(115\) | 1.22317i | 0.114061i | ||||||||
\(116\) | 4.74939 | + | 3.79334i | 0.440970 | + | 0.352203i | ||||
\(117\) | −10.5141 | + | 8.11976i | −0.972026 | + | 0.750672i | ||||
\(118\) | 18.9167 | − | 9.10105i | 1.74142 | − | 0.837820i | ||||
\(119\) | −5.97402 | −0.547637 | ||||||||
\(120\) | 1.71028 | − | 0.177267i | 0.156127 | − | 0.0161822i | ||||
\(121\) | −8.12443 | −0.738585 | ||||||||
\(122\) | 4.38041 | − | 2.10747i | 0.396584 | − | 0.190802i | ||||
\(123\) | −0.522840 | − | 1.53241i | −0.0471429 | − | 0.138173i | ||||
\(124\) | 16.5496 | + | 13.2182i | 1.48620 | + | 1.18703i | ||||
\(125\) | 3.46656i | 0.310059i | ||||||||
\(126\) | 11.3101 | + | 5.67086i | 1.00758 | + | 0.505201i | ||||
\(127\) | − | 5.42211i | − | 0.481135i | −0.970632 | − | 0.240567i | \(-0.922666\pi\) | ||
0.970632 | − | 0.240567i | \(-0.0773335\pi\) | |||||||
\(128\) | 11.3137 | + | 0.0296842i | 0.999997 | + | 0.00262374i | ||||
\(129\) | −1.27706 | − | 3.74299i | −0.112439 | − | 0.329552i | ||||
\(130\) | 0.952916 | + | 1.98065i | 0.0835762 | + | 0.173714i | ||||
\(131\) | 9.82550 | 0.858458 | 0.429229 | − | 0.903196i | \(-0.358785\pi\) | ||||
0.429229 | + | 0.903196i | \(0.358785\pi\) | |||||||
\(132\) | 1.98745 | − | 5.52782i | 0.172986 | − | 0.481135i | ||||
\(133\) | 4.32903 | 0.375374 | ||||||||
\(134\) | 0.613127 | + | 1.27439i | 0.0529661 | + | 0.110091i | ||||
\(135\) | −1.52110 | − | 1.00614i | −0.130915 | − | 0.0865947i | ||||
\(136\) | 5.52261 | + | 1.26704i | 0.473560 | + | 0.108647i | ||||
\(137\) | 0.602999i | 0.0515177i | 0.999668 | + | 0.0257589i | \(0.00820021\pi\) | ||||
−0.999668 | + | 0.0257589i | \(0.991800\pi\) | |||||||
\(138\) | 6.08534 | − | 5.98670i | 0.518018 | − | 0.509621i | ||||
\(139\) | − | 16.3980i | − | 1.39086i | −0.718595 | − | 0.695429i | \(-0.755214\pi\) | ||
0.718595 | − | 0.695429i | \(-0.244786\pi\) | |||||||
\(140\) | 1.30640 | − | 1.63566i | 0.110411 | − | 0.138239i | ||||
\(141\) | 19.2421 | − | 6.56516i | 1.62047 | − | 0.552886i | ||||
\(142\) | −17.8688 | + | 8.59690i | −1.49951 | + | 0.721436i | ||||
\(143\) | 7.50903 | 0.627936 | ||||||||
\(144\) | −9.25274 | − | 7.64113i | −0.771061 | − | 0.636761i | ||||
\(145\) | −1.06669 | −0.0885836 | ||||||||
\(146\) | 6.74148 | − | 3.24342i | 0.557929 | − | 0.268427i | ||||
\(147\) | 3.10337 | − | 1.05883i | 0.255962 | − | 0.0873311i | ||||
\(148\) | −8.52647 | + | 10.6754i | −0.700871 | + | 0.877515i | ||||
\(149\) | − | 1.22296i | − | 0.100189i | −0.998744 | − | 0.0500945i | \(-0.984048\pi\) | ||
0.998744 | − | 0.0500945i | \(-0.0159523\pi\) | |||||||
\(150\) | 8.51562 | − | 8.37759i | 0.695298 | − | 0.684027i | ||||
\(151\) | 13.9947i | 1.13887i | 0.822037 | + | 0.569435i | \(0.192838\pi\) | ||||
−0.822037 | + | 0.569435i | \(0.807162\pi\) | |||||||
\(152\) | −4.00192 | − | 0.918147i | −0.324598 | − | 0.0744716i | ||||
\(153\) | −3.67333 | − | 4.75650i | −0.296971 | − | 0.384540i | ||||
\(154\) | −3.10056 | − | 6.44455i | −0.249850 | − | 0.519317i | ||||
\(155\) | −3.71695 | −0.298553 | ||||||||
\(156\) | 5.18988 | − | 14.4349i | 0.415523 | − | 1.15572i | ||||
\(157\) | 3.91727 | 0.312632 | 0.156316 | − | 0.987707i | \(-0.450038\pi\) | ||||
0.156316 | + | 0.987707i | \(0.450038\pi\) | |||||||
\(158\) | −10.2692 | − | 21.3446i | −0.816971 | − | 1.69809i | ||||
\(159\) | 0.860934 | + | 2.52334i | 0.0682765 | + | 0.200114i | ||||
\(160\) | −1.55460 | + | 1.23499i | −0.122902 | + | 0.0976347i | ||||
\(161\) | − | 10.3928i | − | 0.819067i | ||||||
\(162\) | 2.43927 | + | 12.4920i | 0.191647 | + | 0.981464i | ||||
\(163\) | − | 1.06905i | − | 0.0837345i | −0.999123 | − | 0.0418673i | \(-0.986669\pi\) | ||
0.999123 | − | 0.0418673i | \(-0.0133307\pi\) | |||||||
\(164\) | 1.46086 | + | 1.16679i | 0.114074 | + | 0.0911111i | ||||
\(165\) | 0.332879 | + | 0.975648i | 0.0259146 | + | 0.0759541i | ||||
\(166\) | 8.44991 | − | 4.06536i | 0.655841 | − | 0.315533i | ||||
\(167\) | 5.77658 | 0.447005 | 0.223503 | − | 0.974703i | \(-0.428251\pi\) | ||||
0.223503 | + | 0.974703i | \(0.428251\pi\) | |||||||
\(168\) | −14.5316 | + | 1.50617i | −1.12114 | + | 0.116203i | ||||
\(169\) | 6.60847 | 0.508344 | ||||||||
\(170\) | −0.896034 | + | 0.431093i | −0.0687226 | + | 0.0330634i | ||||
\(171\) | 2.66185 | + | 3.44676i | 0.203557 | + | 0.263581i | ||||
\(172\) | 3.56823 | + | 2.84995i | 0.272075 | + | 0.217306i | ||||
\(173\) | 11.3842i | 0.865521i | 0.901509 | + | 0.432761i | \(0.142460\pi\) | ||||
−0.901509 | + | 0.432761i | \(0.857540\pi\) | |||||||
\(174\) | 5.22080 | + | 5.30683i | 0.395788 | + | 0.402310i | ||||
\(175\) | − | 14.5433i | − | 1.09937i | ||||||
\(176\) | 1.49944 | + | 6.61519i | 0.113025 | + | 0.498639i | ||||
\(177\) | 24.3327 | − | 8.30202i | 1.82896 | − | 0.624018i | ||||
\(178\) | 3.43946 | + | 7.14897i | 0.257799 | + | 0.535838i | ||||
\(179\) | 6.51691 | 0.487097 | 0.243548 | − | 0.969889i | \(-0.421689\pi\) | ||||
0.243548 | + | 0.969889i | \(0.421689\pi\) | |||||||
\(180\) | 2.10560 | + | 0.0344129i | 0.156942 | + | 0.00256499i | ||||
\(181\) | 16.6921 | 1.24071 | 0.620357 | − | 0.784320i | \(-0.286988\pi\) | ||||
0.620357 | + | 0.784320i | \(0.286988\pi\) | |||||||
\(182\) | −8.09655 | − | 16.8288i | −0.600156 | − | 1.24743i | ||||
\(183\) | 5.63457 | − | 1.92245i | 0.416520 | − | 0.142111i | ||||
\(184\) | −2.20422 | + | 9.60749i | −0.162497 | + | 0.708274i | ||||
\(185\) | − | 2.39764i | − | 0.176278i | ||||||
\(186\) | 18.1923 | + | 18.4920i | 1.33392 | + | 1.35590i | ||||
\(187\) | 3.39704i | 0.248416i | ||||||||
\(188\) | −14.6511 | + | 18.3437i | −1.06854 | + | 1.33785i | ||||
\(189\) | 12.9241 | + | 8.54877i | 0.940093 | + | 0.621831i | ||||
\(190\) | 0.649304 | − | 0.312389i | 0.0471055 | − | 0.0226631i | ||||
\(191\) | 11.6575 | 0.843505 | 0.421752 | − | 0.906711i | \(-0.361415\pi\) | ||||
0.421752 | + | 0.906711i | \(0.361415\pi\) | |||||||
\(192\) | 13.7530 | + | 1.68966i | 0.992537 | + | 0.121941i | ||||
\(193\) | −18.5012 | −1.33174 | −0.665872 | − | 0.746066i | \(-0.731940\pi\) | ||||
−0.665872 | + | 0.746066i | \(0.731940\pi\) | |||||||
\(194\) | 12.3565 | − | 5.94487i | 0.887145 | − | 0.426817i | ||||
\(195\) | 0.869254 | + | 2.54773i | 0.0622486 | + | 0.182447i | ||||
\(196\) | −2.36294 | + | 2.95848i | −0.168781 | + | 0.211320i | ||||
\(197\) | − | 7.06882i | − | 0.503632i | −0.967775 | − | 0.251816i | \(-0.918972\pi\) | ||
0.967775 | − | 0.251816i | \(-0.0810278\pi\) | |||||||
\(198\) | 3.22465 | − | 6.43131i | 0.229166 | − | 0.457054i | ||||
\(199\) | 13.5499i | 0.960530i | 0.877124 | + | 0.480265i | \(0.159459\pi\) | ||||
−0.877124 | + | 0.480265i | \(0.840541\pi\) | |||||||
\(200\) | −3.08451 | + | 13.4444i | −0.218108 | + | 0.950664i | ||||
\(201\) | 0.559297 | + | 1.63926i | 0.0394498 | + | 0.115625i | ||||
\(202\) | −7.67830 | − | 15.9595i | −0.540243 | − | 1.12290i | ||||
\(203\) | 9.06322 | 0.636113 | ||||||||
\(204\) | 6.53027 | + | 2.34787i | 0.457210 | + | 0.164384i | ||||
\(205\) | −0.328102 | −0.0229156 | ||||||||
\(206\) | −2.03793 | − | 4.23588i | −0.141990 | − | 0.295127i | ||||
\(207\) | 8.27472 | − | 6.39037i | 0.575133 | − | 0.444161i | ||||
\(208\) | 3.91553 | + | 17.2744i | 0.271493 | + | 1.19776i | ||||
\(209\) | − | 2.46164i | − | 0.170275i | ||||||
\(210\) | 1.82764 | − | 1.79801i | 0.126119 | − | 0.124075i | ||||
\(211\) | 6.42279i | 0.442163i | 0.975255 | + | 0.221082i | \(0.0709587\pi\) | ||||
−0.975255 | + | 0.221082i | \(0.929041\pi\) | |||||||
\(212\) | −2.40553 | − | 1.92130i | −0.165212 | − | 0.131955i | ||||
\(213\) | −22.9848 | + | 7.84213i | −1.57489 | + | 0.537334i | ||||
\(214\) | 0.665794 | − | 0.320322i | 0.0455128 | − | 0.0218968i | ||||
\(215\) | −0.801405 | −0.0546553 | ||||||||
\(216\) | −10.1345 | − | 10.6439i | −0.689563 | − | 0.724226i | ||||
\(217\) | 31.5814 | 2.14389 | ||||||||
\(218\) | 13.5541 | − | 6.52104i | 0.917998 | − | 0.441661i | ||||
\(219\) | 8.67164 | − | 2.95866i | 0.585975 | − | 0.199928i | ||||
\(220\) | −0.930095 | − | 0.742868i | −0.0627070 | − | 0.0500841i | ||||
\(221\) | 8.87075i | 0.596712i | ||||||||
\(222\) | −11.9284 | + | 11.7350i | −0.800582 | + | 0.787605i | ||||
\(223\) | − | 28.1790i | − | 1.88701i | −0.331362 | − | 0.943504i | \(-0.607508\pi\) | ||
0.331362 | − | 0.943504i | \(-0.392492\pi\) | |||||||
\(224\) | 13.2088 | − | 10.4932i | 0.882551 | − | 0.701109i | ||||
\(225\) | 11.5794 | − | 8.94247i | 0.771958 | − | 0.596165i | ||||
\(226\) | −9.73651 | − | 20.2375i | −0.647663 | − | 1.34618i | ||||
\(227\) | 4.26297 | 0.282943 | 0.141472 | − | 0.989942i | \(-0.454817\pi\) | ||||
0.141472 | + | 0.989942i | \(0.454817\pi\) | |||||||
\(228\) | −4.73211 | − | 1.70137i | −0.313392 | − | 0.112676i | ||||
\(229\) | 18.4957 | 1.22223 | 0.611114 | − | 0.791543i | \(-0.290722\pi\) | ||||
0.611114 | + | 0.791543i | \(0.290722\pi\) | |||||||
\(230\) | −0.749958 | − | 1.55880i | −0.0494508 | − | 0.102784i | ||||
\(231\) | −2.82834 | − | 8.28969i | −0.186091 | − | 0.545422i | ||||
\(232\) | −8.37839 | − | 1.92223i | −0.550068 | − | 0.126200i | ||||
\(233\) | 23.5352i | 1.54184i | 0.636932 | + | 0.770920i | \(0.280203\pi\) | ||||
−0.636932 | + | 0.770920i | \(0.719797\pi\) | |||||||
\(234\) | 8.42061 | − | 16.7942i | 0.550472 | − | 1.09787i | ||||
\(235\) | − | 4.11989i | − | 0.268752i | ||||||
\(236\) | −18.5272 | + | 23.1966i | −1.20601 | + | 1.50997i | ||||
\(237\) | −9.36758 | − | 27.4558i | −0.608490 | − | 1.78344i | ||||
\(238\) | 7.61324 | − | 3.66283i | 0.493493 | − | 0.237426i | ||||
\(239\) | −9.29173 | −0.601032 | −0.300516 | − | 0.953777i | \(-0.597159\pi\) | ||||
−0.300516 | + | 0.953777i | \(0.597159\pi\) | |||||||
\(240\) | −2.07088 | + | 1.27453i | −0.133675 | + | 0.0822704i | ||||
\(241\) | −17.3434 | −1.11719 | −0.558593 | − | 0.829442i | \(-0.688659\pi\) | ||||
−0.558593 | + | 0.829442i | \(0.688659\pi\) | |||||||
\(242\) | 10.3537 | − | 4.98131i | 0.665562 | − | 0.320211i | ||||
\(243\) | 1.14035 | + | 15.5467i | 0.0731532 | + | 0.997321i | ||||
\(244\) | −4.29022 | + | 5.37150i | −0.274653 | + | 0.343875i | ||||
\(245\) | − | 0.664458i | − | 0.0424506i | ||||||
\(246\) | 1.60586 | + | 1.63232i | 0.102386 | + | 0.104073i | ||||
\(247\) | − | 6.42813i | − | 0.409012i | ||||||
\(248\) | −29.1951 | − | 6.69814i | −1.85389 | − | 0.425332i | ||||
\(249\) | 10.8692 | − | 3.70844i | 0.688808 | − | 0.235013i | ||||
\(250\) | −2.12544 | − | 4.41776i | −0.134425 | − | 0.279404i | ||||
\(251\) | −12.0936 | −0.763344 | −0.381672 | − | 0.924298i | \(-0.624652\pi\) | ||||
−0.381672 | + | 0.924298i | \(0.624652\pi\) | |||||||
\(252\) | −17.8904 | − | 0.292393i | −1.12699 | − | 0.0184190i | ||||
\(253\) | −5.90971 | −0.371540 | ||||||||
\(254\) | 3.32444 | + | 6.90990i | 0.208594 | + | 0.433566i | ||||
\(255\) | −1.15258 | + | 0.393246i | −0.0721772 | + | 0.0246260i | ||||
\(256\) | −14.4363 | + | 6.89888i | −0.902266 | + | 0.431180i | ||||
\(257\) | − | 3.87147i | − | 0.241496i | −0.992683 | − | 0.120748i | \(-0.961471\pi\) | ||
0.992683 | − | 0.120748i | \(-0.0385293\pi\) | |||||||
\(258\) | 3.92240 | + | 3.98703i | 0.244198 | + | 0.248222i | ||||
\(259\) | 20.3718i | 1.26584i | ||||||||
\(260\) | −2.42878 | − | 1.93987i | −0.150626 | − | 0.120305i | ||||
\(261\) | 5.57283 | + | 7.21612i | 0.344950 | + | 0.446667i | ||||
\(262\) | −12.5215 | + | 6.02428i | −0.773584 | + | 0.372181i | ||||
\(263\) | −20.9768 | −1.29349 | −0.646743 | − | 0.762708i | \(-0.723869\pi\) | ||||
−0.646743 | + | 0.762708i | \(0.723869\pi\) | |||||||
\(264\) | 0.856460 | + | 8.26318i | 0.0527115 | + | 0.508563i | ||||
\(265\) | 0.540268 | 0.0331884 | ||||||||
\(266\) | −5.51688 | + | 2.65424i | −0.338262 | + | 0.162742i | ||||
\(267\) | 3.13749 | + | 9.19579i | 0.192012 | + | 0.562773i | ||||
\(268\) | −1.56273 | − | 1.24815i | −0.0954588 | − | 0.0762430i | ||||
\(269\) | − | 25.9623i | − | 1.58295i | −0.611203 | − | 0.791474i | \(-0.709314\pi\) | ||
0.611203 | − | 0.791474i | \(-0.290686\pi\) | |||||||
\(270\) | 2.55536 | + | 0.349592i | 0.155514 | + | 0.0212755i | ||||
\(271\) | − | 3.87398i | − | 0.235328i | −0.993053 | − | 0.117664i | \(-0.962459\pi\) | ||
0.993053 | − | 0.117664i | \(-0.0375405\pi\) | |||||||
\(272\) | −7.81483 | + | 1.77136i | −0.473843 | + | 0.107404i | ||||
\(273\) | −7.38571 | − | 21.6470i | −0.447004 | − | 1.31014i | ||||
\(274\) | −0.369715 | − | 0.768458i | −0.0223353 | − | 0.0464242i | ||||
\(275\) | −8.26985 | −0.498691 | ||||||||
\(276\) | −4.08451 | + | 11.3605i | −0.245858 | + | 0.683821i | ||||
\(277\) | 10.4518 | 0.627988 | 0.313994 | − | 0.949425i | \(-0.398333\pi\) | ||||
0.313994 | + | 0.949425i | \(0.398333\pi\) | |||||||
\(278\) | 10.0540 | + | 20.8974i | 0.603001 | + | 1.25335i | ||||
\(279\) | 19.4190 | + | 25.1451i | 1.16258 | + | 1.50540i | ||||
\(280\) | −0.662003 | + | 2.88547i | −0.0395623 | + | 0.172440i | ||||
\(281\) | − | 10.0426i | − | 0.599093i | −0.954082 | − | 0.299547i | \(-0.903165\pi\) | ||
0.954082 | − | 0.299547i | \(-0.0968354\pi\) | |||||||
\(282\) | −20.4967 | + | 20.1644i | −1.22056 | + | 1.20077i | ||||
\(283\) | 13.7073i | 0.814814i | 0.913247 | + | 0.407407i | \(0.133567\pi\) | ||||
−0.913247 | + | 0.407407i | \(0.866433\pi\) | |||||||
\(284\) | 17.5008 | − | 21.9116i | 1.03848 | − | 1.30022i | ||||
\(285\) | 0.835207 | − | 0.284962i | 0.0494734 | − | 0.0168797i | ||||
\(286\) | −9.56944 | + | 4.60398i | −0.565853 | + | 0.272239i | ||||
\(287\) | 2.78775 | 0.164556 | ||||||||
\(288\) | 16.4766 | + | 4.06470i | 0.970893 | + | 0.239515i | ||||
\(289\) | 12.9869 | 0.763937 | ||||||||
\(290\) | 1.35938 | − | 0.654014i | 0.0798254 | − | 0.0384050i | ||||
\(291\) | 15.8943 | − | 5.42294i | 0.931740 | − | 0.317898i | ||||
\(292\) | −6.60267 | + | 8.26677i | −0.386392 | + | 0.483776i | ||||
\(293\) | 27.3566i | 1.59819i | 0.601207 | + | 0.799094i | \(0.294687\pi\) | ||||
−0.601207 | + | 0.799094i | \(0.705313\pi\) | |||||||
\(294\) | −3.30571 | + | 3.25213i | −0.192793 | + | 0.189668i | ||||
\(295\) | − | 5.20983i | − | 0.303328i | ||||||
\(296\) | 4.32068 | − | 18.8325i | 0.251134 | − | 1.09462i | ||||
\(297\) | 4.86113 | − | 7.34913i | 0.282072 | − | 0.426440i | ||||
\(298\) | 0.749832 | + | 1.55854i | 0.0434366 | + | 0.0902835i | ||||
\(299\) | −15.4321 | −0.892464 | ||||||||
\(300\) | −5.71573 | + | 15.8975i | −0.329998 | + | 0.917842i | ||||
\(301\) | 6.80922 | 0.392477 | ||||||||
\(302\) | −8.58050 | − | 17.8347i | −0.493752 | − | 1.02627i | ||||
\(303\) | −7.00419 | − | 20.5288i | −0.402380 | − | 1.17935i | ||||
\(304\) | 5.66296 | − | 1.28360i | 0.324793 | − | 0.0736197i | ||||
\(305\) | − | 1.20641i | − | 0.0690788i | ||||||
\(306\) | 7.59761 | + | 3.80943i | 0.434326 | + | 0.217771i | ||||
\(307\) | − | 19.8275i | − | 1.13161i | −0.824538 | − | 0.565806i | \(-0.808565\pi\) | ||
0.824538 | − | 0.565806i | \(-0.191435\pi\) | |||||||
\(308\) | 7.90265 | + | 6.31185i | 0.450295 | + | 0.359651i | ||||
\(309\) | −1.85901 | − | 5.44865i | −0.105756 | − | 0.309963i | ||||
\(310\) | 4.73685 | − | 2.27896i | 0.269035 | − | 0.129436i | ||||
\(311\) | −27.4539 | −1.55677 | −0.778383 | − | 0.627789i | \(-0.783960\pi\) | ||||
−0.778383 | + | 0.627789i | \(0.783960\pi\) | |||||||
\(312\) | 2.23649 | + | 21.5778i | 0.126616 | + | 1.22160i | ||||
\(313\) | −8.09384 | −0.457491 | −0.228745 | − | 0.973486i | \(-0.573462\pi\) | ||||
−0.228745 | + | 0.973486i | \(0.573462\pi\) | |||||||
\(314\) | −4.99214 | + | 2.40178i | −0.281723 | + | 0.135540i | ||||
\(315\) | 2.48519 | − | 1.91925i | 0.140024 | − | 0.108138i | ||||
\(316\) | 26.1739 | + | 20.9051i | 1.47240 | + | 1.17600i | ||||
\(317\) | − | 0.987602i | − | 0.0554692i | −0.999615 | − | 0.0277346i | \(-0.991171\pi\) | ||
0.999615 | − | 0.0277346i | \(-0.00882934\pi\) | |||||||
\(318\) | −2.64429 | − | 2.68786i | −0.148285 | − | 0.150728i | ||||
\(319\) | − | 5.15367i | − | 0.288550i | ||||||
\(320\) | 1.22396 | − | 2.52703i | 0.0684216 | − | 0.141265i | ||||
\(321\) | 0.856418 | − | 0.292200i | 0.0478006 | − | 0.0163090i | ||||
\(322\) | 6.37210 | + | 13.2445i | 0.355103 | + | 0.738087i | ||||
\(323\) | 2.90805 | 0.161808 | ||||||||
\(324\) | −10.7678 | − | 14.4241i | −0.598209 | − | 0.801340i | ||||
\(325\) | −21.5952 | −1.19789 | ||||||||
\(326\) | 0.655463 | + | 1.36239i | 0.0363028 | + | 0.0754558i | ||||
\(327\) | 17.4347 | − | 5.94853i | 0.964144 | − | 0.328954i | ||||
\(328\) | −2.57710 | − | 0.591256i | −0.142297 | − | 0.0326467i | ||||
\(329\) | 35.0050i | 1.92989i | ||||||||
\(330\) | −1.02241 | − | 1.03926i | −0.0562821 | − | 0.0572094i | ||||
\(331\) | − | 12.4813i | − | 0.686036i | −0.939329 | − | 0.343018i | \(-0.888551\pi\) | ||
0.939329 | − | 0.343018i | \(-0.111449\pi\) | |||||||
\(332\) | −8.27592 | + | 10.3617i | −0.454200 | + | 0.568674i | ||||
\(333\) | −16.2200 | + | 12.5263i | −0.888851 | + | 0.686438i | ||||
\(334\) | −7.36163 | + | 3.54177i | −0.402810 | + | 0.193797i | ||||
\(335\) | 0.350980 | 0.0191761 | ||||||||
\(336\) | 17.5955 | − | 10.8292i | 0.959912 | − | 0.590779i | ||||
\(337\) | −8.52881 | −0.464594 | −0.232297 | − | 0.972645i | \(-0.574624\pi\) | ||||
−0.232297 | + | 0.972645i | \(0.574624\pi\) | |||||||
\(338\) | −8.42178 | + | 4.05183i | −0.458085 | + | 0.220390i | ||||
\(339\) | −8.88170 | − | 26.0317i | −0.482388 | − | 1.41385i | ||||
\(340\) | 0.877583 | − | 1.09876i | 0.0475936 | − | 0.0595889i | ||||
\(341\) | − | 17.9583i | − | 0.972498i | ||||||
\(342\) | −5.50555 | − | 2.76048i | −0.297706 | − | 0.149269i | ||||
\(343\) | − | 15.2293i | − | 0.822307i | ||||||
\(344\) | −6.29470 | − | 1.44417i | −0.339388 | − | 0.0778646i | ||||
\(345\) | −0.684116 | − | 2.00510i | −0.0368315 | − | 0.107951i | ||||
\(346\) | −6.97993 | − | 14.5079i | −0.375243 | − | 0.779948i | ||||
\(347\) | −16.6008 | −0.891179 | −0.445589 | − | 0.895237i | \(-0.647006\pi\) | ||||
−0.445589 | + | 0.895237i | \(0.647006\pi\) | |||||||
\(348\) | −9.90711 | − | 3.56197i | −0.531077 | − | 0.190941i | ||||
\(349\) | 2.10653 | 0.112760 | 0.0563799 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563799 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(350\) | 8.91690 | + | 18.5339i | 0.476629 | + | 0.990679i | ||||
\(351\) | 12.6940 | − | 19.1909i | 0.677554 | − | 1.02434i | ||||
\(352\) | −5.96683 | − | 7.51100i | −0.318033 | − | 0.400338i | ||||
\(353\) | − | 11.1806i | − | 0.595081i | −0.954709 | − | 0.297541i | \(-0.903834\pi\) | ||
0.954709 | − | 0.297541i | \(-0.0961663\pi\) | |||||||
\(354\) | −25.9192 | + | 25.4991i | −1.37759 | + | 1.35526i | ||||
\(355\) | 4.92123i | 0.261192i | ||||||||
\(356\) | −8.76645 | − | 7.00177i | −0.464621 | − | 0.371093i | ||||
\(357\) | 9.79299 | − | 3.34125i | 0.518300 | − | 0.176838i | ||||
\(358\) | −8.30510 | + | 3.99569i | −0.438938 | + | 0.211179i | ||||
\(359\) | 13.3649 | 0.705375 | 0.352688 | − | 0.935741i | \(-0.385268\pi\) | ||||
0.352688 | + | 0.935741i | \(0.385268\pi\) | |||||||
\(360\) | −2.70446 | + | 1.24714i | −0.142538 | + | 0.0657302i | ||||
\(361\) | 16.8927 | 0.889090 | ||||||||
\(362\) | −21.2723 | + | 10.2344i | −1.11805 | + | 0.537907i | ||||
\(363\) | 13.3181 | − | 4.54397i | 0.699019 | − | 0.238497i | ||||
\(364\) | 20.6364 | + | 16.4823i | 1.08164 | + | 0.863905i | ||||
\(365\) | − | 1.85667i | − | 0.0971826i | ||||||
\(366\) | −6.00195 | + | 5.90466i | −0.313727 | + | 0.308641i | ||||
\(367\) | 15.4682i | 0.807435i | 0.914884 | + | 0.403717i | \(0.132282\pi\) | ||||
−0.914884 | + | 0.403717i | \(0.867718\pi\) | |||||||
\(368\) | −3.08157 | − | 13.5952i | −0.160638 | − | 0.708698i | ||||
\(369\) | 1.71414 | + | 2.21960i | 0.0892348 | + | 0.115548i | ||||
\(370\) | 1.47006 | + | 3.05554i | 0.0764247 | + | 0.158850i | ||||
\(371\) | −4.59044 | −0.238324 | ||||||||
\(372\) | −34.5221 | − | 12.4119i | −1.78989 | − | 0.643529i | ||||
\(373\) | −3.08450 | −0.159709 | −0.0798546 | − | 0.996807i | \(-0.525446\pi\) | ||||
−0.0798546 | + | 0.996807i | \(0.525446\pi\) | |||||||
\(374\) | −2.08281 | − | 4.32916i | −0.107700 | − | 0.223856i | ||||
\(375\) | −1.93884 | − | 5.68261i | −0.100121 | − | 0.293449i | ||||
\(376\) | 7.42425 | − | 32.3600i | 0.382876 | − | 1.66884i | ||||
\(377\) | − | 13.4579i | − | 0.693116i | ||||||
\(378\) | −21.7119 | − | 2.97035i | −1.11674 | − | 0.152778i | ||||
\(379\) | − | 26.8870i | − | 1.38109i | −0.723288 | − | 0.690547i | \(-0.757370\pi\) | ||
0.723288 | − | 0.690547i | \(-0.242630\pi\) | |||||||
\(380\) | −0.635934 | + | 0.796211i | −0.0326227 | + | 0.0408448i | ||||
\(381\) | 3.03257 | + | 8.88828i | 0.155363 | + | 0.455360i | ||||
\(382\) | −14.8562 | + | 7.14750i | −0.760109 | + | 0.365698i | ||||
\(383\) | 6.19252 | 0.316423 | 0.158211 | − | 0.987405i | \(-0.449427\pi\) | ||||
0.158211 | + | 0.987405i | \(0.449427\pi\) | |||||||
\(384\) | −18.5627 | + | 6.27904i | −0.947274 | + | 0.320426i | ||||
\(385\) | −1.77489 | −0.0904569 | ||||||||
\(386\) | 23.5778 | − | 11.3436i | 1.20008 | − | 0.577372i | ||||
\(387\) | 4.18688 | + | 5.42149i | 0.212831 | + | 0.275590i | ||||
\(388\) | −12.1021 | + | 15.1522i | −0.614389 | + | 0.769236i | ||||
\(389\) | 29.3150i | 1.48633i | 0.669107 | + | 0.743166i | \(0.266677\pi\) | ||||
−0.669107 | + | 0.743166i | \(0.733323\pi\) | |||||||
\(390\) | −2.66985 | − | 2.71384i | −0.135193 | − | 0.137421i | ||||
\(391\) | − | 6.98141i | − | 0.353065i | ||||||
\(392\) | 1.19739 | − | 5.21904i | 0.0604772 | − | 0.263601i | ||||
\(393\) | −16.1066 | + | 5.49538i | −0.812470 | + | 0.277205i | ||||
\(394\) | 4.33408 | + | 9.00844i | 0.218348 | + | 0.453839i | ||||
\(395\) | −5.87851 | −0.295780 | ||||||||
\(396\) | −0.166265 | + | 10.1731i | −0.00835513 | + | 0.511219i | ||||
\(397\) | 27.2186 | 1.36606 | 0.683030 | − | 0.730390i | \(-0.260662\pi\) | ||||
0.683030 | + | 0.730390i | \(0.260662\pi\) | |||||||
\(398\) | −8.30783 | − | 17.2679i | −0.416434 | − | 0.865563i | ||||
\(399\) | −7.09642 | + | 2.42121i | −0.355265 | + | 0.121212i | ||||
\(400\) | −4.31225 | − | 19.0247i | −0.215613 | − | 0.951233i | ||||
\(401\) | − | 11.7112i | − | 0.584827i | −0.956292 | − | 0.292413i | \(-0.905542\pi\) | ||
0.956292 | − | 0.292413i | \(-0.0944583\pi\) | |||||||
\(402\) | −1.71784 | − | 1.74615i | −0.0856781 | − | 0.0870898i | ||||
\(403\) | − | 46.8950i | − | 2.33600i | ||||||
\(404\) | 19.5703 | + | 15.6308i | 0.973661 | + | 0.777663i | ||||
\(405\) | 3.05621 | + | 0.798584i | 0.151864 | + | 0.0396820i | ||||
\(406\) | −11.5501 | + | 5.55690i | −0.573222 | + | 0.275784i | ||||
\(407\) | 11.5841 | 0.574204 | ||||||||
\(408\) | −9.76167 | + | 1.01178i | −0.483275 | + | 0.0500904i | ||||
\(409\) | −32.9181 | −1.62770 | −0.813848 | − | 0.581078i | \(-0.802631\pi\) | ||||
−0.813848 | + | 0.581078i | \(0.802631\pi\) | |||||||
\(410\) | 0.418130 | − | 0.201168i | 0.0206500 | − | 0.00993497i | ||||
\(411\) | −0.337256 | − | 0.988475i | −0.0166356 | − | 0.0487579i | ||||
\(412\) | 5.19426 | + | 4.14866i | 0.255903 | + | 0.204390i | ||||
\(413\) | 44.2659i | 2.17818i | ||||||||
\(414\) | −6.62714 | + | 13.2173i | −0.325706 | + | 0.649594i | ||||
\(415\) | − | 2.32719i | − | 0.114237i | ||||||
\(416\) | −15.5813 | − | 19.6136i | −0.763936 | − | 0.961637i | ||||
\(417\) | 9.17134 | + | 26.8806i | 0.449122 | + | 1.31635i | ||||
\(418\) | 1.50930 | + | 3.13709i | 0.0738221 | + | 0.153440i | ||||
\(419\) | 16.4243 | 0.802382 | 0.401191 | − | 0.915994i | \(-0.368596\pi\) | ||||
0.401191 | + | 0.915994i | \(0.368596\pi\) | |||||||
\(420\) | −1.22672 | + | 3.41195i | −0.0598578 | + | 0.166486i | ||||
\(421\) | −16.4637 | −0.802391 | −0.401196 | − | 0.915992i | \(-0.631405\pi\) | ||||
−0.401196 | + | 0.915992i | \(0.631405\pi\) | |||||||
\(422\) | −3.93798 | − | 8.18516i | −0.191698 | − | 0.398447i | ||||
\(423\) | −27.8709 | + | 21.5241i | −1.35513 | + | 1.04654i | ||||
\(424\) | 4.24358 | + | 0.973592i | 0.206087 | + | 0.0472818i | ||||
\(425\) | − | 9.76956i | − | 0.473893i | ||||||
\(426\) | 24.4834 | − | 24.0865i | 1.18623 | − | 1.16700i | ||||
\(427\) | 10.2504i | 0.496050i | ||||||||
\(428\) | −0.652085 | + | 0.816433i | −0.0315197 | + | 0.0394638i | ||||
\(429\) | −12.3093 | + | 4.19978i | −0.594297 | + | 0.202767i | ||||
\(430\) | 1.02130 | − | 0.491362i | 0.0492516 | − | 0.0236956i | ||||
\(431\) | 9.67349 | 0.465956 | 0.232978 | − | 0.972482i | \(-0.425153\pi\) | ||||
0.232978 | + | 0.972482i | \(0.425153\pi\) | |||||||
\(432\) | 19.4413 | + | 7.35080i | 0.935372 | + | 0.353666i | ||||
\(433\) | 10.5507 | 0.507034 | 0.253517 | − | 0.967331i | \(-0.418413\pi\) | ||||
0.253517 | + | 0.967331i | \(0.418413\pi\) | |||||||
\(434\) | −40.2472 | + | 19.3634i | −1.93193 | + | 0.929474i | ||||
\(435\) | 1.74858 | − | 0.596595i | 0.0838381 | − | 0.0286045i | ||||
\(436\) | −13.2750 | + | 16.6207i | −0.635757 | + | 0.795989i | ||||
\(437\) | 5.05903i | 0.242006i | ||||||||
\(438\) | −9.23704 | + | 9.08731i | −0.441363 | + | 0.434208i | ||||
\(439\) | − | 23.5551i | − | 1.12422i | −0.827061 | − | 0.562112i | \(-0.809989\pi\) | ||
0.827061 | − | 0.562112i | \(-0.190011\pi\) | |||||||
\(440\) | 1.64078 | + | 0.376439i | 0.0782210 | + | 0.0179460i | ||||
\(441\) | −4.49504 | + | 3.47141i | −0.214050 | + | 0.165305i | ||||
\(442\) | −5.43890 | − | 11.3048i | −0.258702 | − | 0.537716i | ||||
\(443\) | 2.64159 | 0.125506 | 0.0627530 | − | 0.998029i | \(-0.480012\pi\) | ||||
0.0627530 | + | 0.998029i | \(0.480012\pi\) | |||||||
\(444\) | 8.00640 | − | 22.2687i | 0.379967 | − | 1.05682i | ||||
\(445\) | 1.96890 | 0.0933346 | ||||||||
\(446\) | 17.2773 | + | 35.9111i | 0.818105 | + | 1.70044i | ||||
\(447\) | 0.684000 | + | 2.00476i | 0.0323521 | + | 0.0948219i | ||||
\(448\) | −10.3995 | + | 21.4712i | −0.491331 | + | 1.01442i | ||||
\(449\) | 23.9282i | 1.12924i | 0.825350 | + | 0.564621i | \(0.190978\pi\) | ||||
−0.825350 | + | 0.564621i | \(0.809022\pi\) | |||||||
\(450\) | −9.27380 | + | 18.4958i | −0.437171 | + | 0.871902i | ||||
\(451\) | − | 1.58521i | − | 0.0746448i | ||||||
\(452\) | 24.8163 | + | 19.8208i | 1.16726 | + | 0.932291i | ||||
\(453\) | −7.82717 | − | 22.9409i | −0.367753 | − | 1.07786i | ||||
\(454\) | −5.43269 | + | 2.61374i | −0.254969 | + | 0.122669i | ||||
\(455\) | −4.63481 | −0.217283 | ||||||||
\(456\) | 7.07372 | − | 0.733176i | 0.331257 | − | 0.0343341i | ||||
\(457\) | 0.231675 | 0.0108373 | 0.00541864 | − | 0.999985i | \(-0.498275\pi\) | ||||
0.00541864 | + | 0.999985i | \(0.498275\pi\) | |||||||
\(458\) | −23.5707 | + | 11.3402i | −1.10139 | + | 0.529892i | ||||
\(459\) | 8.68186 | + | 5.74268i | 0.405235 | + | 0.268045i | ||||
\(460\) | 1.91148 | + | 1.52670i | 0.0891233 | + | 0.0711828i | ||||
\(461\) | 23.3656i | 1.08824i | 0.839007 | + | 0.544121i | \(0.183137\pi\) | ||||
−0.839007 | + | 0.544121i | \(0.816863\pi\) | |||||||
\(462\) | 8.68705 | + | 8.83019i | 0.404158 | + | 0.410818i | ||||
\(463\) | 11.3756i | 0.528667i | 0.964431 | + | 0.264334i | \(0.0851520\pi\) | ||||
−0.964431 | + | 0.264334i | \(0.914848\pi\) | |||||||
\(464\) | 11.8559 | − | 2.68734i | 0.550397 | − | 0.124757i | ||||
\(465\) | 6.09306 | − | 2.07888i | 0.282559 | − | 0.0964057i | ||||
\(466\) | −14.4300 | − | 29.9930i | −0.668458 | − | 1.38940i | ||||
\(467\) | 18.8649 | 0.872962 | 0.436481 | − | 0.899713i | \(-0.356225\pi\) | ||||
0.436481 | + | 0.899713i | \(0.356225\pi\) | |||||||
\(468\) | −0.434171 | + | 26.5653i | −0.0200696 | + | 1.22798i | ||||
\(469\) | −2.98214 | −0.137702 | ||||||||
\(470\) | 2.52601 | + | 5.25035i | 0.116516 | + | 0.242181i | ||||
\(471\) | −6.42144 | + | 2.19092i | −0.295884 | + | 0.100952i | ||||
\(472\) | 9.38839 | − | 40.9211i | 0.432136 | − | 1.88355i | ||||
\(473\) | − | 3.87196i | − | 0.178033i | ||||||
\(474\) | 28.7718 | + | 29.2459i | 1.32153 | + | 1.34331i | ||||
\(475\) | 7.07944i | 0.324827i | ||||||||
\(476\) | −7.45648 | + | 9.33576i | −0.341767 | + | 0.427904i | ||||
\(477\) | −2.82259 | − | 3.65490i | −0.129238 | − | 0.167347i | ||||
\(478\) | 11.8413 | − | 5.69701i | 0.541609 | − | 0.260575i | ||||
\(479\) | −42.4876 | −1.94131 | −0.970655 | − | 0.240476i | \(-0.922697\pi\) | ||||
−0.970655 | + | 0.240476i | \(0.922697\pi\) | |||||||
\(480\) | 1.85767 | − | 2.89396i | 0.0847907 | − | 0.132091i | ||||
\(481\) | 30.2499 | 1.37928 | ||||||||
\(482\) | 22.1023 | − | 10.6337i | 1.00673 | − | 0.484352i | ||||
\(483\) | 5.81266 | + | 17.0365i | 0.264485 | + | 0.775189i | ||||
\(484\) | −10.1405 | + | 12.6963i | −0.460933 | + | 0.577103i | ||||
\(485\) | − | 3.40310i | − | 0.154527i | ||||||
\(486\) | −10.9853 | − | 19.1134i | −0.498305 | − | 0.867002i | ||||
\(487\) | 2.38057i | 0.107874i | 0.998544 | + | 0.0539369i | \(0.0171770\pi\) | ||||
−0.998544 | + | 0.0539369i | \(0.982823\pi\) | |||||||
\(488\) | 2.17401 | − | 9.47584i | 0.0984129 | − | 0.428951i | ||||
\(489\) | 0.597917 | + | 1.75246i | 0.0270387 | + | 0.0792488i | ||||
\(490\) | 0.407397 | + | 0.846780i | 0.0184043 | + | 0.0382536i | ||||
\(491\) | −4.74100 | −0.213958 | −0.106979 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106979 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(492\) | −3.04732 | − | 1.09562i | −0.137384 | − | 0.0493945i | ||||
\(493\) | 6.08826 | 0.274202 | ||||||||
\(494\) | 3.94126 | + | 8.19195i | 0.177325 | + | 0.368573i | ||||
\(495\) | −1.09135 | − | 1.41317i | −0.0490527 | − | 0.0635171i | ||||
\(496\) | 41.3128 | − | 9.36424i | 1.85500 | − | 0.420467i | ||||
\(497\) | − | 41.8138i | − | 1.87560i | ||||||
\(498\) | −11.5779 | + | 11.3902i | −0.518818 | + | 0.510408i | ||||
\(499\) | − | 24.6933i | − | 1.10542i | −0.833373 | − | 0.552711i | \(-0.813593\pi\) | ||
0.833373 | − | 0.552711i | \(-0.186407\pi\) | |||||||
\(500\) | 5.41730 | + | 4.32680i | 0.242269 | + | 0.193500i | ||||
\(501\) | −9.46934 | + | 3.23082i | −0.423059 | + | 0.144343i | ||||
\(502\) | 15.4120 | − | 7.41494i | 0.687873 | − | 0.330945i | ||||
\(503\) | −7.15017 | −0.318810 | −0.159405 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159405 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(504\) | 22.9787 | − | 10.5965i | 1.02355 | − | 0.472005i | ||||
\(505\) | −4.39539 | −0.195592 | ||||||||
\(506\) | 7.53129 | − | 3.62340i | 0.334807 | − | 0.161080i | ||||
\(507\) | −10.8330 | + | 3.69610i | −0.481112 | + | 0.164150i | ||||
\(508\) | −8.47329 | − | 6.76762i | −0.375941 | − | 0.300265i | ||||
\(509\) | 39.5239i | 1.75187i | 0.482432 | + | 0.875934i | \(0.339754\pi\) | ||||
−0.482432 | + | 0.875934i | \(0.660246\pi\) | |||||||
\(510\) | 1.22773 | − | 1.20782i | 0.0543646 | − | 0.0534834i | ||||
\(511\) | 15.7754i | 0.697862i | ||||||||
\(512\) | 14.1676 | − | 17.6431i | 0.626124 | − | 0.779724i | ||||
\(513\) | −6.29125 | − | 4.16139i | −0.277765 | − | 0.183730i | ||||
\(514\) | 2.37370 | + | 4.93378i | 0.104700 | + | 0.217619i | ||||
\(515\) | −1.16660 | −0.0514066 | ||||||||
\(516\) | −7.44324 | − | 2.67611i | −0.327670 | − | 0.117809i | ||||
\(517\) | 19.9051 | 0.875425 | ||||||||
\(518\) | −12.4905 | − | 25.9617i | −0.548801 | − | 1.14069i | ||||
\(519\) | −6.36713 | − | 18.6616i | −0.279486 | − | 0.819155i | ||||
\(520\) | 4.28460 | + | 0.983002i | 0.187892 | + | 0.0431075i | ||||
\(521\) | 0.206774i | 0.00905892i | 0.999990 | + | 0.00452946i | \(0.00144178\pi\) | ||||
−0.999990 | + | 0.00452946i | \(0.998558\pi\) | |||||||
\(522\) | −11.5264 | − | 5.77931i | −0.504496 | − | 0.252954i | ||||
\(523\) | 26.7093i | 1.16792i | 0.811784 | + | 0.583958i | \(0.198497\pi\) | ||||
−0.811784 | + | 0.583958i | \(0.801503\pi\) | |||||||
\(524\) | 12.2637 | − | 15.3546i | 0.535743 | − | 0.670768i | ||||
\(525\) | 8.13404 | + | 23.8404i | 0.354999 | + | 1.04048i | ||||
\(526\) | 26.7327 | − | 12.8614i | 1.16560 | − | 0.560786i | ||||
\(527\) | 21.2150 | 0.924140 | ||||||||
\(528\) | −6.15784 | − | 10.0054i | −0.267986 | − | 0.435430i | ||||
\(529\) | −10.8547 | −0.471943 | ||||||||
\(530\) | −0.688514 | + | 0.331253i | −0.0299071 | + | 0.0143887i | ||||
\(531\) | −35.2444 | + | 27.2184i | −1.52948 | + | 1.18118i | ||||
\(532\) | 5.40328 | − | 6.76509i | 0.234262 | − | 0.293304i | ||||
\(533\) | − | 4.13950i | − | 0.179302i | ||||||
\(534\) | −9.63658 | − | 9.79537i | −0.417016 | − | 0.423887i | ||||
\(535\) | − | 0.183366i | − | 0.00792762i | ||||||
\(536\) | 2.75680 | + | 0.632485i | 0.119076 | + | 0.0273192i | ||||
\(537\) | −10.6829 | + | 3.64489i | −0.461003 | + | 0.157289i | ||||
\(538\) | 15.9182 | + | 33.0861i | 0.686281 | + | 1.42644i | ||||
\(539\) | 3.21031 | 0.138278 | ||||||||
\(540\) | −3.47088 | + | 1.12124i | −0.149363 | + | 0.0482507i | ||||
\(541\) | −6.64574 | −0.285723 | −0.142861 | − | 0.989743i | \(-0.545630\pi\) | ||||
−0.142861 | + | 0.989743i | \(0.545630\pi\) | |||||||
\(542\) | 2.37524 | + | 4.93697i | 0.102025 | + | 0.212061i | ||||
\(543\) | −27.3628 | + | 9.33584i | −1.17425 | + | 0.400639i | ||||
\(544\) | 8.87309 | − | 7.04889i | 0.380430 | − | 0.302218i | ||||
\(545\) | − | 3.73292i | − | 0.159901i | ||||||
\(546\) | 22.6847 | + | 23.0584i | 0.970814 | + | 0.986810i | ||||
\(547\) | 22.0801i | 0.944077i | 0.881578 | + | 0.472038i | \(0.156482\pi\) | ||||
−0.881578 | + | 0.472038i | \(0.843518\pi\) | |||||||
\(548\) | 0.942324 | + | 0.752634i | 0.0402541 | + | 0.0321510i | ||||
\(549\) | −8.16133 | + | 6.30280i | −0.348317 | + | 0.268997i | ||||
\(550\) | 10.5390 | − | 5.07047i | 0.449386 | − | 0.216205i | ||||
\(551\) | −4.41181 | −0.187950 | ||||||||
\(552\) | −1.76015 | − | 16.9820i | −0.0749170 | − | 0.722803i | ||||
\(553\) | 49.9474 | 2.12398 | ||||||||
\(554\) | −13.3197 | + | 6.40828i | −0.565899 | + | 0.272262i | ||||
\(555\) | 1.34099 | + | 3.93037i | 0.0569220 | + | 0.166835i | ||||
\(556\) | −25.6256 | − | 20.4671i | −1.08677 | − | 0.868000i | ||||
\(557\) | 40.4670i | 1.71464i | 0.514783 | + | 0.857321i | \(0.327873\pi\) | ||||
−0.514783 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(558\) | −40.1645 | − | 20.1384i | −1.70030 | − | 0.852528i | ||||
\(559\) | − | 10.1109i | − | 0.427647i | ||||||
\(560\) | −0.925504 | − | 4.08311i | −0.0391097 | − | 0.172543i | ||||
\(561\) | −1.89995 | − | 5.56864i | −0.0802161 | − | 0.235108i | ||||
\(562\) | 6.15740 | + | 12.7983i | 0.259734 | + | 0.539862i | ||||
\(563\) | −16.7710 | −0.706814 | −0.353407 | − | 0.935470i | \(-0.614977\pi\) | ||||
−0.353407 | + | 0.935470i | \(0.614977\pi\) | |||||||
\(564\) | 13.7574 | − | 38.2644i | 0.579293 | − | 1.61122i | ||||
\(565\) | −5.57360 | −0.234483 | ||||||||
\(566\) | −8.40430 | − | 17.4685i | −0.353259 | − | 0.734254i | ||||
\(567\) | −25.9674 | − | 6.78525i | −1.09053 | − | 0.284954i | ||||
\(568\) | −8.86832 | + | 38.6543i | −0.372107 | + | 1.62190i | ||||
\(569\) | − | 29.1776i | − | 1.22319i | −0.791172 | − | 0.611594i | \(-0.790529\pi\) | ||
0.791172 | − | 0.611594i | \(-0.209471\pi\) | |||||||
\(570\) | −0.889663 | + | 0.875241i | −0.0372639 | + | 0.0366598i | ||||
\(571\) | − | 29.1656i | − | 1.22054i | −0.792193 | − | 0.610270i | \(-0.791061\pi\) | ||
0.792193 | − | 0.610270i | \(-0.208939\pi\) | |||||||
\(572\) | 9.37240 | − | 11.7346i | 0.391880 | − | 0.490647i | ||||
\(573\) | −19.1097 | + | 6.51999i | −0.798318 | + | 0.272376i | ||||
\(574\) | −3.55269 | + | 1.70924i | −0.148286 | + | 0.0713424i | ||||
\(575\) | 16.9958 | 0.708772 | ||||||||
\(576\) | −23.4898 | + | 4.92222i | −0.978743 | + | 0.205092i | ||||
\(577\) | 3.09196 | 0.128720 | 0.0643601 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643601 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(578\) | −16.5504 | + | 7.96263i | −0.688407 | + | 0.331202i | ||||
\(579\) | 30.3283 | − | 10.3477i | 1.26040 | − | 0.430034i | ||||
\(580\) | −1.33139 | + | 1.66694i | −0.0552828 | + | 0.0692160i | ||||
\(581\) | 19.7732i | 0.820330i | ||||||||
\(582\) | −16.9306 | + | 16.6562i | −0.701796 | + | 0.690420i | ||||
\(583\) | 2.61029i | 0.108107i | ||||||||
\(584\) | 3.34582 | − | 14.5834i | 0.138451 | − | 0.603465i | ||||
\(585\) | −2.84988 | − | 3.69023i | −0.117828 | − | 0.152572i | ||||
\(586\) | −16.7730 | − | 34.8630i | −0.692888 | − | 1.44018i | ||||
\(587\) | −3.55145 | −0.146584 | −0.0732921 | − | 0.997311i | \(-0.523351\pi\) | ||||
−0.0732921 | + | 0.997311i | \(0.523351\pi\) | |||||||
\(588\) | 2.21881 | − | 6.17131i | 0.0915022 | − | 0.254500i | ||||
\(589\) | −15.3733 | −0.633445 | ||||||||
\(590\) | 3.19429 | + | 6.63937i | 0.131507 | + | 0.273339i | ||||
\(591\) | 3.95357 | + | 11.5877i | 0.162628 | + | 0.476652i | ||||
\(592\) | 6.04046 | + | 26.6491i | 0.248261 | + | 1.09527i | ||||
\(593\) | − | 36.4122i | − | 1.49527i | −0.664110 | − | 0.747635i | \(-0.731190\pi\) | ||
0.664110 | − | 0.747635i | \(-0.268810\pi\) | |||||||
\(594\) | −1.68904 | + | 12.3462i | −0.0693023 | + | 0.506569i | ||||
\(595\) | − | 2.09676i | − | 0.0859588i | ||||||
\(596\) | −1.91116 | − | 1.52644i | −0.0782841 | − | 0.0625256i | ||||
\(597\) | −7.57844 | − | 22.2119i | −0.310165 | − | 0.909074i | ||||
\(598\) | 19.6666 | − | 9.46186i | 0.804227 | − | 0.386924i | ||||
\(599\) | 2.90754 | 0.118799 | 0.0593994 | − | 0.998234i | \(-0.481081\pi\) | ||||
0.0593994 | + | 0.998234i | \(0.481081\pi\) | |||||||
\(600\) | −2.46310 | − | 23.7641i | −0.100556 | − | 0.970165i | ||||
\(601\) | 0.0252815 | 0.00103125 | 0.000515627 | − | 1.00000i | \(-0.499836\pi\) | ||||
0.000515627 | 1.00000i | \(0.499836\pi\) | ||||||||
\(602\) | −8.67761 | + | 4.17491i | −0.353673 | + | 0.170157i | ||||
\(603\) | −1.83367 | − | 2.37437i | −0.0746729 | − | 0.0966920i | ||||
\(604\) | 21.8698 | + | 17.4675i | 0.889871 | + | 0.710741i | ||||
\(605\) | − | 2.85151i | − | 0.115931i | ||||||
\(606\) | 21.5128 | + | 21.8673i | 0.873900 | + | 0.888299i | ||||
\(607\) | − | 32.3617i | − | 1.31352i | −0.754099 | − | 0.656761i | \(-0.771926\pi\) | ||
0.754099 | − | 0.656761i | \(-0.228074\pi\) | |||||||
\(608\) | −6.42982 | + | 5.10792i | −0.260763 | + | 0.207154i | ||||
\(609\) | −14.8570 | + | 5.06903i | −0.602036 | + | 0.205408i | ||||
\(610\) | 0.739681 | + | 1.53744i | 0.0299488 | + | 0.0622490i | ||||
\(611\) | 51.9786 | 2.10283 | ||||||||
\(612\) | −12.0180 | − | 0.196417i | −0.485799 | − | 0.00793967i | ||||
\(613\) | 25.0972 | 1.01367 | 0.506834 | − | 0.862044i | \(-0.330816\pi\) | ||||
0.506834 | + | 0.862044i | \(0.330816\pi\) | |||||||
\(614\) | 12.1567 | + | 25.2680i | 0.490606 | + | 1.01973i | ||||
\(615\) | 0.537845 | − | 0.183506i | 0.0216880 | − | 0.00739969i | ||||
\(616\) | −13.9410 | − | 3.19845i | −0.561701 | − | 0.128869i | ||||
\(617\) | − | 36.3347i | − | 1.46278i | −0.681958 | − | 0.731391i | \(-0.738872\pi\) | ||
0.681958 | − | 0.731391i | \(-0.261128\pi\) | |||||||
\(618\) | 5.70983 | + | 5.80391i | 0.229683 | + | 0.233467i | ||||
\(619\) | 15.1003i | 0.606934i | 0.952842 | + | 0.303467i | \(0.0981442\pi\) | ||||
−0.952842 | + | 0.303467i | \(0.901856\pi\) | |||||||
\(620\) | −4.63932 | + | 5.80858i | −0.186319 | + | 0.233278i | ||||
\(621\) | −9.99034 | + | 15.1035i | −0.400898 | + | 0.606084i | ||||
\(622\) | 34.9870 | − | 16.8327i | 1.40285 | − | 0.674930i | ||||
\(623\) | −16.7289 | −0.670230 | ||||||||
\(624\) | −16.0801 | − | 26.1273i | −0.643719 | − | 1.04593i | ||||
\(625\) | 23.1674 | 0.926695 | ||||||||
\(626\) | 10.3147 | − | 4.96255i | 0.412259 | − | 0.198343i | ||||
\(627\) | 1.37679 | + | 4.03528i | 0.0549836 | + | 0.161153i | ||||
\(628\) | 4.88934 | − | 6.12162i | 0.195106 | − | 0.244279i | ||||
\(629\) | 13.6849i | 0.545651i | ||||||||
\(630\) | −1.99036 | + | 3.96961i | −0.0792979 | + | 0.158153i | ||||
\(631\) | 11.8772i | 0.472822i | 0.971653 | + | 0.236411i | \(0.0759712\pi\) | ||||
−0.971653 | + | 0.236411i | \(0.924029\pi\) | |||||||
\(632\) | −46.1733 | − | 10.5934i | −1.83667 | − | 0.421382i | ||||
\(633\) | −3.59225 | − | 10.5287i | −0.142779 | − | 0.418476i | ||||
\(634\) | 0.605525 | + | 1.25859i | 0.0240485 | + | 0.0499851i | ||||
\(635\) | 1.90305 | 0.0755204 | ||||||||
\(636\) | 5.01787 | + | 1.80411i | 0.198971 | + | 0.0715375i | ||||
\(637\) | 8.38314 | 0.332152 | ||||||||
\(638\) | 3.15985 | + | 6.56779i | 0.125100 | + | 0.260021i | ||||
\(639\) | 33.2921 | − | 25.7107i | 1.31701 | − | 1.01710i | ||||
\(640\) | −0.0104186 | + | 3.97087i | −0.000411830 | + | 0.156963i | ||||
\(641\) | − | 36.4801i | − | 1.44088i | −0.693520 | − | 0.720438i | \(-0.743941\pi\) | ||
0.693520 | − | 0.720438i | \(-0.256059\pi\) | |||||||
\(642\) | −0.912258 | + | 0.897470i | −0.0360039 | + | 0.0354203i | ||||
\(643\) | − | 32.3140i | − | 1.27434i | −0.770724 | − | 0.637170i | \(-0.780105\pi\) | ||
0.770724 | − | 0.637170i | \(-0.219895\pi\) | |||||||
\(644\) | −16.2411 | − | 12.9718i | −0.639989 | − | 0.511160i | ||||
\(645\) | 1.31371 | − | 0.448223i | 0.0517274 | − | 0.0176488i | ||||
\(646\) | −3.70599 | + | 1.78300i | −0.145810 | + | 0.0701512i | ||||
\(647\) | −17.8380 | −0.701285 | −0.350642 | − | 0.936509i | \(-0.614037\pi\) | ||||
−0.350642 | + | 0.936509i | \(0.614037\pi\) | |||||||
\(648\) | 22.5662 | + | 11.7800i | 0.886483 | + | 0.462762i | ||||
\(649\) | 25.1712 | 0.988054 | ||||||||
\(650\) | 27.5208 | − | 13.2406i | 1.07945 | − | 0.519340i | ||||
\(651\) | −51.7703 | + | 17.6634i | −2.02904 | + | 0.692284i | ||||
\(652\) | −1.67064 | − | 1.33434i | −0.0654271 | − | 0.0522567i | ||||
\(653\) | − | 19.6414i | − | 0.768627i | −0.923203 | − | 0.384314i | \(-0.874438\pi\) | ||
0.923203 | − | 0.384314i | \(-0.125562\pi\) | |||||||
\(654\) | −18.5715 | + | 18.2705i | −0.726203 | + | 0.714432i | ||||
\(655\) | 3.44856i | 0.134746i | ||||||||
\(656\) | 3.64675 | − | 0.826598i | 0.142382 | − | 0.0322732i | ||||
\(657\) | −12.5603 | + | 9.70005i | −0.490026 | + | 0.378435i | ||||
\(658\) | −21.4625 | − | 44.6101i | −0.836696 | − | 1.73908i | ||||
\(659\) | −12.1305 | −0.472536 | −0.236268 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236268 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(660\) | 1.94016 | + | 0.697557i | 0.0755205 | + | 0.0271524i | ||||
\(661\) | −46.6603 | −1.81488 | −0.907439 | − | 0.420185i | \(-0.861965\pi\) | ||||
−0.907439 | + | 0.420185i | \(0.861965\pi\) | |||||||
\(662\) | 7.65263 | + | 15.9061i | 0.297428 | + | 0.618208i | ||||
\(663\) | −4.96139 | − | 14.5415i | −0.192684 | − | 0.564745i | ||||
\(664\) | 4.19372 | − | 18.2791i | 0.162748 | − | 0.709367i | ||||
\(665\) | 1.51940i | 0.0589199i | ||||||||
\(666\) | 12.9904 | − | 25.9084i | 0.503369 | − | 1.00393i | ||||
\(667\) | 10.5915i | 0.410106i | ||||||||
\(668\) | 7.21004 | − | 9.02722i | 0.278965 | − | 0.349274i | ||||
\(669\) | 15.7605 | + | 46.1929i | 0.609334 | + | 1.78592i | ||||
\(670\) | −0.447286 | + | 0.215195i | −0.0172802 | + | 0.00831372i | ||||
\(671\) | 5.82873 | 0.225016 | ||||||||
\(672\) | −15.7839 | + | 24.5888i | −0.608877 | + | 0.948535i | ||||
\(673\) | −46.2504 | −1.78282 | −0.891411 | − | 0.453196i | \(-0.850284\pi\) | ||||
−0.891411 | + | 0.453196i | \(0.850284\pi\) | |||||||
\(674\) | 10.8690 | − | 5.22924i | 0.418660 | − | 0.201423i | ||||
\(675\) | −13.9802 | + | 21.1354i | −0.538096 | + | 0.813501i | ||||
\(676\) | 8.24837 | − | 10.3272i | 0.317245 | − | 0.397202i | ||||
\(677\) | − | 45.5607i | − | 1.75104i | −0.483183 | − | 0.875519i | \(-0.660519\pi\) | ||
0.483183 | − | 0.875519i | \(-0.339481\pi\) | |||||||
\(678\) | 27.2795 | + | 27.7290i | 1.04766 | + | 1.06492i | ||||
\(679\) | 28.9148i | 1.10965i | ||||||||
\(680\) | −0.444704 | + | 1.93833i | −0.0170536 | + | 0.0743314i | ||||
\(681\) | −6.98813 | + | 2.38427i | −0.267786 | + | 0.0913653i | ||||
\(682\) | 11.0107 | + | 22.8860i | 0.421623 | + | 0.876349i | ||||
\(683\) | 42.0262 | 1.60809 | 0.804043 | − | 0.594571i | \(-0.202678\pi\) | ||||
0.804043 | + | 0.594571i | \(0.202678\pi\) | |||||||
\(684\) | 8.70875 | + | 0.142332i | 0.332987 | + | 0.00544219i | ||||
\(685\) | −0.211641 | −0.00808638 | ||||||||
\(686\) | 9.33751 | + | 19.4081i | 0.356508 | + | 0.741007i | ||||
\(687\) | −30.3193 | + | 10.3446i | −1.15675 | + | 0.394670i | ||||
\(688\) | 8.90738 | − | 2.01901i | 0.339591 | − | 0.0769739i | ||||
\(689\) | 6.81630i | 0.259680i | ||||||||
\(690\) | 2.10121 | + | 2.13583i | 0.0799917 | + | 0.0813098i | ||||
\(691\) | 12.4465i | 0.473489i | 0.971572 | + | 0.236744i | \(0.0760804\pi\) | ||||
−0.971572 | + | 0.236744i | \(0.923920\pi\) | |||||||
\(692\) | 17.7903 | + | 14.2091i | 0.676287 | + | 0.540151i | ||||
\(693\) | 9.27280 | + | 12.0071i | 0.352245 | + | 0.456112i | ||||
\(694\) | 21.1560 | − | 10.1784i | 0.803069 | − | 0.386367i | ||||
\(695\) | 5.75536 | 0.218313 | ||||||||
\(696\) | 14.8095 | − | 1.53497i | 0.561352 | − | 0.0581829i | ||||
\(697\) | 1.87268 | 0.0709330 | ||||||||
\(698\) | −2.68454 | + | 1.29157i | −0.101611 | + | 0.0488865i | ||||
\(699\) | −13.1631 | − | 38.5803i | −0.497876 | − | 1.45924i | ||||
\(700\) | −22.7273 | − | 18.1523i | −0.859010 | − | 0.686092i | ||||
\(701\) | − | 38.1395i | − | 1.44051i | −0.693710 | − | 0.720255i | \(-0.744025\pi\) | ||
0.693710 | − | 0.720255i | \(-0.255975\pi\) | |||||||
\(702\) | −4.41064 | + | 32.2398i | −0.166469 | + | 1.21681i | ||||
\(703\) | − | 9.91664i | − | 0.374013i | ||||||
\(704\) | 12.2093 | + | 5.91354i | 0.460154 | + | 0.222875i | ||||
\(705\) | 2.30424 | + | 6.75358i | 0.0867827 | + | 0.254355i | ||||
\(706\) | 6.85510 | + | 14.2484i | 0.257995 | + | 0.536246i | ||||
\(707\) | 37.3459 | 1.40454 | ||||||||
\(708\) | 17.3971 | − | 48.3876i | 0.653823 | − | 1.81852i | ||||
\(709\) | 33.0619 | 1.24166 | 0.620832 | − | 0.783943i | \(-0.286795\pi\) | ||||
0.620832 | + | 0.783943i | \(0.286795\pi\) | |||||||
\(710\) | −3.01734 | − | 6.27158i | −0.113239 | − | 0.235368i | ||||
\(711\) | 30.7119 | + | 39.7680i | 1.15179 | + | 1.49142i | ||||
\(712\) | 15.4649 | + | 3.54805i | 0.579570 | + | 0.132969i | ||||
\(713\) | 36.9070i | 1.38218i | ||||||||
\(714\) | −10.4315 | + | 10.2624i | −0.390389 | + | 0.384061i | ||||
\(715\) | 2.63552i | 0.0985628i | ||||||||
\(716\) | 8.13409 | − | 10.1842i | 0.303985 | − | 0.380600i | ||||
\(717\) | 15.2316 | − | 5.19684i | 0.568835 | − | 0.194080i | ||||
\(718\) | −17.0322 | + | 8.19441i | −0.635636 | + | 0.305813i | ||||
\(719\) | 2.64623 | 0.0986878 | 0.0493439 | − | 0.998782i | \(-0.484287\pi\) | ||||
0.0493439 | + | 0.998782i | \(0.484287\pi\) | |||||||
\(720\) | 2.68188 | − | 3.24753i | 0.0999479 | − | 0.121028i | ||||
\(721\) | 9.91215 | 0.369148 | ||||||||
\(722\) | −21.5279 | + | 10.3574i | −0.801187 | + | 0.385461i | ||||
\(723\) | 28.4304 | − | 9.70011i | 1.05734 | − | 0.360751i | ||||
\(724\) | 20.8343 | − | 26.0852i | 0.774299 | − | 0.969449i | ||||
\(725\) | 14.8215i | 0.550455i | ||||||||
\(726\) | −14.1864 | + | 13.9565i | −0.526508 | + | 0.517974i | ||||
\(727\) | 48.0337i | 1.78147i | 0.454522 | + | 0.890736i | \(0.349810\pi\) | ||||
−0.454522 | + | 0.890736i | \(0.650190\pi\) | |||||||
\(728\) | −36.4045 | − | 8.35217i | −1.34924 | − | 0.309552i | ||||
\(729\) | −10.5645 | − | 24.8473i | −0.391280 | − | 0.920272i | ||||
\(730\) | 1.13837 | + | 2.36613i | 0.0421331 | + | 0.0875743i | ||||
\(731\) | 4.57413 | 0.169180 | ||||||||
\(732\) | 4.02854 | − | 11.2048i | 0.148899 | − | 0.414142i | ||||
\(733\) | −26.9253 | −0.994510 | −0.497255 | − | 0.867605i | \(-0.665659\pi\) | ||||
−0.497255 | + | 0.867605i | \(0.665659\pi\) | |||||||
\(734\) | −9.48398 | − | 19.7126i | −0.350060 | − | 0.727605i | ||||
\(735\) | 0.371629 | + | 1.08922i | 0.0137078 | + | 0.0401765i | ||||
\(736\) | 12.2627 | + | 15.4362i | 0.452009 | + | 0.568986i | ||||
\(737\) | 1.69575i | 0.0624637i | ||||||||
\(738\) | −3.54539 | − | 1.77765i | −0.130508 | − | 0.0654364i | ||||
\(739\) | − | 35.8090i | − | 1.31725i | −0.752470 | − | 0.658627i | \(-0.771138\pi\) | ||
0.752470 | − | 0.658627i | \(-0.228862\pi\) | |||||||
\(740\) | −3.74686 | − | 2.99262i | −0.137737 | − | 0.110011i | ||||
\(741\) | 3.59523 | + | 10.5374i | 0.132074 | + | 0.387101i | ||||
\(742\) | 5.85003 | − | 2.81452i | 0.214761 | − | 0.103324i | ||||
\(743\) | −22.9337 | −0.841357 | −0.420679 | − | 0.907210i | \(-0.638208\pi\) | ||||
−0.420679 | + | 0.907210i | \(0.638208\pi\) | |||||||
\(744\) | 51.6047 | − | 5.34872i | 1.89192 | − | 0.196094i | ||||
\(745\) | 0.429236 | 0.0157260 | ||||||||
\(746\) | 3.93086 | − | 1.89119i | 0.143919 | − | 0.0692413i | ||||
\(747\) | −15.7434 | + | 12.1582i | −0.576020 | + | 0.444847i | ||||
\(748\) | 5.30865 | + | 4.24002i | 0.194103 | + | 0.155030i | ||||
\(749\) | 1.55799i | 0.0569277i | ||||||||
\(750\) | 5.95500 | + | 6.05313i | 0.217446 | + | 0.221029i | ||||
\(751\) | 0.147527i | 0.00538332i | 0.999996 | + | 0.00269166i | \(0.000856783\pi\) | ||||
−0.999996 | + | 0.00269166i | \(0.999143\pi\) | |||||||
\(752\) | 10.3794 | + | 45.7913i | 0.378497 | + | 1.66984i | ||||
\(753\) | 19.8247 | − | 6.76394i | 0.722451 | − | 0.246492i | ||||
\(754\) | 8.25138 | + | 17.1506i | 0.300498 | + | 0.624588i | ||||
\(755\) | −4.91185 | −0.178760 | ||||||||
\(756\) | 29.4907 | − | 9.52676i | 1.07257 | − | 0.346485i | ||||
\(757\) | −30.6339 | −1.11341 | −0.556703 | − | 0.830711i | \(-0.687934\pi\) | ||||
−0.556703 | + | 0.830711i | \(0.687934\pi\) | |||||||
\(758\) | 16.4851 | + | 34.2646i | 0.598767 | + | 1.24455i | ||||
\(759\) | 9.68757 | − | 3.30528i | 0.351637 | − | 0.119974i | ||||
\(760\) | 0.322251 | − | 1.40459i | 0.0116893 | − | 0.0509500i | ||||
\(761\) | − | 19.4924i | − | 0.706599i | −0.935510 | − | 0.353299i | \(-0.885060\pi\) | ||
0.935510 | − | 0.353299i | \(-0.114940\pi\) | |||||||
\(762\) | −9.31433 | − | 9.46780i | −0.337423 | − | 0.342982i | ||||
\(763\) | 31.7172i | 1.14824i | ||||||||
\(764\) | 14.5503 | − | 18.2174i | 0.526411 | − | 0.659084i | ||||
\(765\) | 1.66944 | − | 1.28927i | 0.0603586 | − | 0.0466135i | ||||
\(766\) | −7.89170 | + | 3.79680i | −0.285139 | + | 0.137184i | ||||
\(767\) | 65.7299 | 2.37337 | ||||||||
\(768\) | 19.8063 | − | 19.3832i | 0.714698 | − | 0.699433i | ||||
\(769\) | 51.5761 | 1.85988 | 0.929940 | − | 0.367711i | \(-0.119858\pi\) | ||||
0.929940 | + | 0.367711i | \(0.119858\pi\) | |||||||
\(770\) | 2.26191 | − | 1.08823i | 0.0815135 | − | 0.0392172i | ||||
\(771\) | 2.16530 | + | 6.34637i | 0.0779815 | + | 0.228559i | ||||
\(772\) | −23.0923 | + | 28.9123i | −0.831109 | + | 1.04058i | ||||
\(773\) | − | 32.5670i | − | 1.17135i | −0.810544 | − | 0.585677i | \(-0.800829\pi\) | ||
0.810544 | − | 0.585677i | \(-0.199171\pi\) | |||||||
\(774\) | −8.65979 | − | 4.34201i | −0.311270 | − | 0.156070i | ||||
\(775\) | 51.6464i | 1.85519i | ||||||||
\(776\) | 6.13257 | − | 26.7299i | 0.220146 | − | 0.959549i | ||||
\(777\) | −11.3939 | − | 33.3948i | −0.408754 | − | 1.19803i | ||||
\(778\) | −17.9738 | − | 37.3589i | −0.644393 | − | 1.33938i | ||||
\(779\) | −1.35703 | −0.0486205 | ||||||||
\(780\) | 5.06637 | + | 1.82154i | 0.181405 | + | 0.0652217i | ||||
\(781\) | −23.7768 | −0.850801 | ||||||||
\(782\) | 4.28049 | + | 8.89705i | 0.153070 | + | 0.318158i | ||||
\(783\) | −13.1713 | − | 8.71225i | −0.470704 | − | 0.311351i | ||||
\(784\) | 1.67399 | + | 7.38525i | 0.0597854 | + | 0.263759i | ||||
\(785\) | 1.37488i | 0.0490717i | ||||||||
\(786\) | 17.1568 | − | 16.8786i | 0.611961 | − | 0.602041i | ||||
\(787\) | − | 28.3287i | − | 1.00981i | −0.863175 | − | 0.504904i | \(-0.831528\pi\) | ||
0.863175 | − | 0.504904i | \(-0.168472\pi\) | |||||||
\(788\) | −11.0466 | − | 8.82295i | −0.393520 | − | 0.314305i | ||||
\(789\) | 34.3866 | − | 11.7323i | 1.22419 | − | 0.417680i | ||||
\(790\) | 7.49153 | − | 3.60427i | 0.266537 | − | 0.128234i | ||||
\(791\) | 47.3567 | 1.68381 | ||||||||
\(792\) | −6.02554 | − | 13.0665i | −0.214108 | − | 0.464298i | ||||
\(793\) | 15.2207 | 0.540502 | ||||||||
\(794\) | −34.6871 | + | 16.6884i | −1.23100 | + | 0.592250i | ||||
\(795\) | −0.885642 | + | 0.302171i | −0.0314105 | + | 0.0107169i | ||||
\(796\) | 21.1749 | + | 16.9124i | 0.750523 | + | 0.599443i | ||||
\(797\) | 36.5770i | 1.29562i | 0.761801 | + | 0.647811i | \(0.224315\pi\) | ||||
−0.761801 | + | 0.647811i | \(0.775685\pi\) | |||||||
\(798\) | 7.55911 | − | 7.43658i | 0.267590 | − | 0.263252i | ||||
\(799\) | 23.5148i | 0.831894i | ||||||||
\(800\) | 17.1600 | + | 21.6009i | 0.606698 | + | 0.763708i | ||||
\(801\) | −10.2864 | − | 13.3195i | −0.363451 | − | 0.470623i | ||||
\(802\) | 7.18042 | + | 14.9246i | 0.253549 | + | 0.527006i | ||||
\(803\) | 8.97045 | 0.316560 | ||||||||
\(804\) | 3.25981 | + | 1.17202i | 0.114965 | + | 0.0413340i | ||||
\(805\) | 3.64766 | 0.128563 | ||||||||
\(806\) | 28.7525 | + | 59.7626i | 1.01277 | + | 2.10505i | ||||
\(807\) | 14.5206 | + | 42.5590i | 0.511150 | + | 1.49815i | ||||
\(808\) | −34.5240 | − | 7.92072i | −1.21455 | − | 0.278650i | ||||
\(809\) | − | 12.6520i | − | 0.444822i | −0.974953 | − | 0.222411i | \(-0.928607\pi\) | ||
0.974953 | − | 0.222411i | \(-0.0713927\pi\) | |||||||
\(810\) | −4.38444 | + | 0.856134i | −0.154054 | + | 0.0300815i | ||||
\(811\) | 33.9464i | 1.19202i | 0.802977 | + | 0.596010i | \(0.203248\pi\) | ||||
−0.802977 | + | 0.596010i | \(0.796752\pi\) | |||||||
\(812\) | 11.3123 | − | 14.1633i | 0.396983 | − | 0.497036i | ||||
\(813\) | 2.16671 | + | 6.35048i | 0.0759897 | + | 0.222721i | ||||
\(814\) | −14.7627 | + | 7.10254i | −0.517434 | + | 0.248944i | ||||
\(815\) | 0.375215 | 0.0131432 | ||||||||
\(816\) | 11.8198 | − | 7.27454i | 0.413777 | − | 0.254660i | ||||
\(817\) | −3.31461 | −0.115963 | ||||||||
\(818\) | 41.9506 | − | 20.1830i | 1.46677 | − | 0.705681i | ||||
\(819\) | 24.2143 | + | 31.3544i | 0.846115 | + | 1.09561i | ||||
\(820\) | −0.409521 | + | 0.512734i | −0.0143011 | + | 0.0179054i | ||||
\(821\) | − | 9.29308i | − | 0.324331i | −0.986764 | − | 0.162165i | \(-0.948152\pi\) | ||
0.986764 | − | 0.162165i | \(-0.0518478\pi\) | |||||||
\(822\) | 1.03586 | + | 1.05292i | 0.0361296 | + | 0.0367250i | ||||
\(823\) | − | 0.0285875i | − | 0.000996496i | −1.00000 | 0.000498248i | \(-0.999841\pi\) | |||
1.00000 | 0.000498248i | \(-0.000158597\pi\) | ||||||||
\(824\) | −9.16317 | − | 2.10228i | −0.319214 | − | 0.0732363i | ||||
\(825\) | 13.5565 | − | 4.62531i | 0.471976 | − | 0.161032i | ||||
\(826\) | −27.1406 | − | 56.4121i | −0.944342 | − | 1.96283i | ||||
\(827\) | 34.0218 | 1.18306 | 0.591528 | − | 0.806285i | \(-0.298525\pi\) | ||||
0.591528 | + | 0.806285i | \(0.298525\pi\) | |||||||
\(828\) | 0.341699 | − | 20.9073i | 0.0118749 | − | 0.726578i | ||||
\(829\) | −38.6899 | −1.34376 | −0.671878 | − | 0.740662i | \(-0.734512\pi\) | ||||
−0.671878 | + | 0.740662i | \(0.734512\pi\) | |||||||
\(830\) | 1.42686 | + | 2.96575i | 0.0495271 | + | 0.102943i | ||||
\(831\) | −17.1333 | + | 5.84566i | −0.594346 | + | 0.202784i | ||||
\(832\) | 31.8823 | + | 15.4421i | 1.10532 | + | 0.535360i | ||||
\(833\) | 3.79248i | 0.131402i | ||||||||
\(834\) | −28.1691 | − | 28.6332i | −0.975416 | − | 0.991488i | ||||
\(835\) | 2.02746i | 0.0701633i | ||||||||
\(836\) | −3.84687 | − | 3.07250i | −0.133047 | − | 0.106265i | ||||
\(837\) | −45.8964 | − | 30.3585i | −1.58641 | − | 1.04934i | ||||
\(838\) | −20.9311 | + | 10.0702i | −0.723052 | + | 0.347869i | ||||
\(839\) | 34.4929 | 1.19083 | 0.595414 | − | 0.803419i | \(-0.296988\pi\) | ||||
0.595414 | + | 0.803419i | \(0.296988\pi\) | |||||||
\(840\) | −0.528635 | − | 5.10030i | −0.0182396 | − | 0.175977i | ||||
\(841\) | 19.7635 | 0.681499 | ||||||||
\(842\) | 20.9812 | − | 10.0943i | 0.723060 | − | 0.347874i | ||||
\(843\) | 5.61682 | + | 16.4625i | 0.193453 | + | 0.566999i | ||||
\(844\) | 10.0371 | + | 8.01662i | 0.345490 | + | 0.275943i | ||||
\(845\) | 2.31944i | 0.0797912i | ||||||||
\(846\) | 22.3215 | − | 44.5185i | 0.767430 | − | 1.53058i | ||||
\(847\) | 24.2282i | 0.832490i | ||||||||
\(848\) | −6.00492 | + | 1.36112i | −0.206210 | + | 0.0467409i | ||||
\(849\) | −7.66645 | − | 22.4699i | −0.263112 | − | 0.771164i | ||||
\(850\) | 5.98997 | + | 12.4502i | 0.205454 | + | 0.427040i | ||||
\(851\) | −23.8071 | −0.816096 | ||||||||
\(852\) | −16.4334 | + | 45.7071i | −0.562998 | + | 1.56590i | ||||
\(853\) | 1.74939 | 0.0598981 | 0.0299490 | − | 0.999551i | \(-0.490465\pi\) | ||||
0.0299490 | + | 0.999551i | \(0.490465\pi\) | |||||||
\(854\) | −6.28478 | − | 13.0630i | −0.215061 | − | 0.447007i | ||||
\(855\) | −1.20975 | + | 0.934257i | −0.0413724 | + | 0.0319509i | ||||
\(856\) | 0.330436 | − | 1.44027i | 0.0112941 | − | 0.0492273i | ||||
\(857\) | 8.72576i | 0.298066i | 0.988832 | + | 0.149033i | \(0.0476161\pi\) | ||||
−0.988832 | + | 0.149033i | \(0.952384\pi\) | |||||||
\(858\) | 13.1119 | − | 12.8993i | 0.447631 | − | 0.440375i | ||||
\(859\) | 21.0392i | 0.717847i | 0.933367 | + | 0.358924i | \(0.116856\pi\) | ||||
−0.933367 | + | 0.358924i | \(0.883144\pi\) | |||||||
\(860\) | −1.00027 | + | 1.25238i | −0.0341091 | + | 0.0427057i | ||||
\(861\) | −4.56986 | + | 1.55918i | −0.155740 | + | 0.0531367i | ||||
\(862\) | −12.3278 | + | 5.93107i | −0.419887 | + | 0.202013i | ||||
\(863\) | −50.8751 | −1.73181 | −0.865904 | − | 0.500210i | \(-0.833256\pi\) | ||||
−0.865904 | + | 0.500210i | \(0.833256\pi\) | |||||||
\(864\) | −29.2829 | + | 2.55220i | −0.996223 | + | 0.0868275i | ||||
\(865\) | −3.99561 | −0.135855 | ||||||||
\(866\) | −13.4457 | + | 6.46892i | −0.456905 | + | 0.219823i | ||||
\(867\) | −21.2890 | + | 7.26355i | −0.723012 | + | 0.246683i | ||||
\(868\) | 39.4184 | − | 49.3532i | 1.33795 | − | 1.67516i | ||||
\(869\) | − | 28.4019i | − | 0.963467i | ||||||
\(870\) | −1.86259 | + | 1.83240i | −0.0631478 | + | 0.0621241i | ||||
\(871\) | 4.42815i | 0.150042i | ||||||||
\(872\) | 6.72693 | − | 29.3206i | 0.227802 | − | 0.992920i | ||||
\(873\) | −23.0219 | + | 17.7793i | −0.779173 | + | 0.601737i | ||||
\(874\) | −3.10182 | − | 6.44718i | −0.104921 | − | 0.218079i | ||||
\(875\) | 10.3378 | 0.349481 | ||||||||
\(876\) | 6.19994 | − | 17.2443i | 0.209477 | − | 0.582630i | ||||
\(877\) | 25.6253 | 0.865306 | 0.432653 | − | 0.901561i | \(-0.357578\pi\) | ||||
0.432653 | + | 0.901561i | \(0.357578\pi\) | |||||||
\(878\) | 14.4423 | + | 30.0184i | 0.487403 | + | 1.01307i | ||||
\(879\) | −15.3004 | − | 44.8446i | −0.516071 | − | 1.51257i | ||||
\(880\) | −2.32180 | + | 0.526275i | −0.0782679 | + | 0.0177407i | ||||
\(881\) | − | 54.1226i | − | 1.82344i | −0.410816 | − | 0.911718i | \(-0.634756\pi\) | ||
0.410816 | − | 0.911718i | \(-0.365244\pi\) | |||||||
\(882\) | 3.60003 | − | 7.17997i | 0.121219 | − | 0.241762i | ||||
\(883\) | − | 24.3636i | − | 0.819900i | −0.912108 | − | 0.409950i | \(-0.865546\pi\) | ||
0.912108 | − | 0.409950i | \(-0.134454\pi\) | |||||||
\(884\) | 13.8626 | + | 11.0720i | 0.466249 | + | 0.372393i | ||||
\(885\) | 2.91385 | + | 8.54029i | 0.0979478 | + | 0.287079i | ||||
\(886\) | −3.36643 | + | 1.61963i | −0.113097 | + | 0.0544126i | ||||
\(887\) | 12.3265 | 0.413883 | 0.206941 | − | 0.978353i | \(-0.433649\pi\) | ||||
0.206941 | + | 0.978353i | \(0.433649\pi\) | |||||||
\(888\) | 3.45022 | + | 33.2880i | 0.115782 | + | 1.11707i | ||||
\(889\) | −16.1695 | −0.542307 | ||||||||
\(890\) | −2.50915 | + | 1.20718i | −0.0841068 | + | 0.0404649i | ||||
\(891\) | −3.85833 | + | 14.7660i | −0.129259 | + | 0.494679i | ||||
\(892\) | −44.0362 | − | 35.1717i | −1.47444 | − | 1.17764i | ||||
\(893\) | − | 17.0398i | − | 0.570216i | ||||||
\(894\) | −2.10086 | − | 2.13547i | −0.0702631 | − | 0.0714209i | ||||
\(895\) | 2.28731i | 0.0764562i | ||||||||
\(896\) | 0.0885224 | − | 33.7389i | 0.00295733 | − | 1.12714i | ||||
\(897\) | 25.2974 | − | 8.63115i | 0.844654 | − | 0.288186i | ||||
\(898\) | −14.6710 | − | 30.4939i | −0.489579 | − | 1.01760i | ||||
\(899\) | −32.1854 | −1.07344 | ||||||||
\(900\) | 0.478162 | − | 29.2570i | 0.0159387 | − | 0.975232i | ||||
\(901\) | −3.08365 | −0.102731 | ||||||||
\(902\) | 0.971936 | + | 2.02018i | 0.0323619 | + | 0.0672648i | ||||
\(903\) | −11.1621 | + | 3.80838i | −0.371452 | + | 0.126735i | ||||
\(904\) | −43.7783 | − | 10.0439i | −1.45605 | − | 0.334056i | ||||
\(905\) | 5.85859i | 0.194746i | ||||||||
\(906\) | 24.0406 | + | 24.4367i | 0.798695 | + | 0.811855i | ||||
\(907\) | − | 36.8608i | − | 1.22394i | −0.790879 | − | 0.611972i | \(-0.790377\pi\) | ||
0.790879 | − | 0.611972i | \(-0.209623\pi\) | |||||||
\(908\) | 5.32083 | − | 6.66186i | 0.176578 | − | 0.221082i | ||||
\(909\) | 22.9634 | + | 29.7347i | 0.761649 | + | 0.986239i | ||||
\(910\) | 5.90657 | − | 2.84173i | 0.195801 | − | 0.0942023i | ||||
\(911\) | −31.6676 | −1.04920 | −0.524598 | − | 0.851350i | \(-0.675784\pi\) | ||||
−0.524598 | + | 0.851350i | \(0.675784\pi\) | |||||||
\(912\) | −8.56516 | + | 5.27144i | −0.283621 | + | 0.174555i | ||||
\(913\) | 11.2437 | 0.372114 | ||||||||
\(914\) | −0.295244 | + | 0.142046i | −0.00976582 | + | 0.00469846i | ||||
\(915\) | 0.674741 | + | 1.97762i | 0.0223062 | + | 0.0653782i | ||||
\(916\) | 23.0854 | − | 28.9037i | 0.762763 | − | 0.955005i | ||||
\(917\) | − | 29.3010i | − | 0.967604i | ||||||
\(918\) | −14.5851 | − | 1.99535i | −0.481380 | − | 0.0658562i | ||||
\(919\) | 19.4847i | 0.642740i | 0.946954 | + | 0.321370i | \(0.104143\pi\) | ||||
−0.946954 | + | 0.321370i | \(0.895857\pi\) | |||||||
\(920\) | −3.37204 | − | 0.773636i | −0.111173 | − | 0.0255060i | ||||
\(921\) | 11.0894 | + | 32.5024i | 0.365409 | + | 1.07099i | ||||
\(922\) | −14.3260 | − | 29.7769i | −0.471803 | − | 0.980649i | ||||
\(923\) | −62.0888 | −2.04368 | ||||||||
\(924\) | −16.4847 | − | 5.92686i | −0.542308 | − | 0.194979i | ||||
\(925\) | −33.3149 | −1.09539 | ||||||||
\(926\) | −6.97466 | − | 14.4969i | −0.229202 | − | 0.476399i | ||||
\(927\) | 6.09483 | + | 7.89204i | 0.200181 | + | 0.259209i | ||||
\(928\) | −13.4614 | + | 10.6939i | −0.441892 | + | 0.351045i | ||||
\(929\) | 10.1296i | 0.332342i | 0.986097 | + | 0.166171i | \(0.0531404\pi\) | ||||
−0.986097 | + | 0.166171i | \(0.946860\pi\) | |||||||
\(930\) | −6.49034 | + | 6.38513i | −0.212826 | + | 0.209377i | ||||
\(931\) | − | 2.74819i | − | 0.0900684i | ||||||
\(932\) | 36.7790 | + | 29.3754i | 1.20474 | + | 0.962225i | ||||
\(933\) | 45.0042 | − | 15.3549i | 1.47337 | − | 0.502696i | ||||
\(934\) | −24.0413 | + | 11.5666i | −0.786654 | + | 0.378469i | ||||
\(935\) | −1.19229 | −0.0389921 | ||||||||
\(936\) | −15.7346 | − | 34.1208i | −0.514302 | − | 1.11527i | ||||
\(937\) | −21.4503 | −0.700749 | −0.350375 | − | 0.936610i | \(-0.613946\pi\) | ||||
−0.350375 | + | 0.936610i | \(0.613946\pi\) | |||||||
\(938\) | 3.80041 | − | 1.82843i | 0.124088 | − | 0.0597003i | ||||
\(939\) | 13.2679 | − | 4.52686i | 0.432983 | − | 0.147729i | ||||
\(940\) | −6.43826 | − | 5.14224i | −0.209993 | − | 0.167721i | ||||
\(941\) | − | 15.1606i | − | 0.494222i | −0.968987 | − | 0.247111i | \(-0.920519\pi\) | ||
0.968987 | − | 0.247111i | \(-0.0794812\pi\) | |||||||
\(942\) | 6.84012 | − | 6.72924i | 0.222863 | − | 0.219251i | ||||
\(943\) | 3.25784i | 0.106090i | ||||||||
\(944\) | 13.1253 | + | 57.9058i | 0.427192 | + | 1.88467i | ||||
\(945\) | −3.00045 | + | 4.53612i | −0.0976046 | + | 0.147560i | ||||
\(946\) | 2.37400 | + | 4.93440i | 0.0771855 | + | 0.160431i | ||||
\(947\) | 2.73350 | 0.0888268 | 0.0444134 | − | 0.999013i | \(-0.485858\pi\) | ||||
0.0444134 | + | 0.999013i | \(0.485858\pi\) | |||||||
\(948\) | −54.5981 | − | 19.6300i | −1.77326 | − | 0.637553i | ||||
\(949\) | 23.4247 | 0.760398 | ||||||||
\(950\) | −4.34059 | − | 9.02198i | −0.140827 | − | 0.292712i | ||||
\(951\) | 0.552363 | + | 1.61894i | 0.0179116 | + | 0.0524977i | ||||
\(952\) | 3.77847 | − | 16.4692i | 0.122461 | − | 0.533770i | ||||
\(953\) | 32.4065i | 1.04975i | 0.851180 | + | 0.524874i | \(0.175888\pi\) | ||||
−0.851180 | + | 0.524874i | \(0.824112\pi\) | |||||||
\(954\) | 5.83801 | + | 2.92717i | 0.189013 | + | 0.0947707i | ||||
\(955\) | 4.09154i | 0.132399i | ||||||||
\(956\) | −11.5975 | + | 14.5205i | −0.375090 | + | 0.469625i | ||||
\(957\) | 2.88243 | + | 8.44822i | 0.0931758 | + | 0.273092i | ||||
\(958\) | 54.1459 | − | 26.0503i | 1.74938 | − | 0.841647i | ||||
\(959\) | 1.79823 | 0.0580678 | ||||||||
\(960\) | −0.593037 | + | 4.82703i | −0.0191402 | + | 0.155792i | ||||
\(961\) | −81.1524 | −2.61782 | ||||||||
\(962\) | −38.5502 | + | 18.5470i | −1.24291 | + | 0.597980i | ||||
\(963\) | −1.24047 | + | 0.957985i | −0.0399736 | + | 0.0308706i | ||||
\(964\) | −21.6472 | + | 27.1030i | −0.697209 | + | 0.872929i | ||||
\(965\) | − | 6.49354i | − | 0.209035i | ||||||
\(966\) | −17.8532 | − | 18.1473i | −0.574416 | − | 0.583881i | ||||
\(967\) | 28.4122i | 0.913676i | 0.889550 | + | 0.456838i | \(0.151018\pi\) | ||||
−0.889550 | + | 0.456838i | \(0.848982\pi\) | |||||||
\(968\) | 5.13858 | − | 22.3975i | 0.165160 | − | 0.719882i | ||||
\(969\) | −4.76705 | + | 1.62646i | −0.153140 | + | 0.0522495i | ||||
\(970\) | 2.08653 | + | 4.33688i | 0.0669945 | + | 0.139249i | ||||
\(971\) | −24.4514 | −0.784684 | −0.392342 | − | 0.919819i | \(-0.628335\pi\) | ||||
−0.392342 | + | 0.919819i | \(0.628335\pi\) | |||||||
\(972\) | 25.7186 | + | 17.6226i | 0.824924 | + | 0.565244i | ||||
\(973\) | −48.9010 | −1.56769 | ||||||||
\(974\) | −1.45959 | − | 3.03378i | −0.0467683 | − | 0.0972085i | ||||
\(975\) | 35.4003 | − | 12.0782i | 1.13372 | − | 0.386811i | ||||
\(976\) | 3.03935 | + | 13.4089i | 0.0972871 | + | 0.429208i | ||||
\(977\) | 14.7929i | 0.473267i | 0.971599 | + | 0.236633i | \(0.0760440\pi\) | ||||
−0.971599 | + | 0.236633i | \(0.923956\pi\) | |||||||
\(978\) | −1.83646 | − | 1.86672i | −0.0587235 | − | 0.0596911i | ||||
\(979\) | 9.51266i | 0.304026i | ||||||||
\(980\) | −1.03837 | − | 0.829344i | −0.0331694 | − | 0.0264924i | ||||
\(981\) | −25.2532 | + | 19.5024i | −0.806271 | + | 0.622664i | ||||
\(982\) | 6.04189 | − | 2.90683i | 0.192805 | − | 0.0927608i | ||||
\(983\) | −22.8355 | −0.728340 | −0.364170 | − | 0.931332i | \(-0.618647\pi\) | ||||
−0.364170 | + | 0.931332i | \(0.618647\pi\) | |||||||
\(984\) | 4.55524 | − | 0.472141i | 0.145216 | − | 0.0150513i | ||||
\(985\) | 2.48101 | 0.0790517 | ||||||||
\(986\) | −7.75883 | + | 3.73288i | −0.247092 | + | 0.118879i | ||||
\(987\) | −19.5782 | − | 57.3825i | −0.623181 | − | 1.82650i | ||||
\(988\) | −10.0454 | − | 8.02327i | −0.319587 | − | 0.255254i | ||||
\(989\) | 7.95745i | 0.253032i | ||||||||
\(990\) | 2.25726 | + | 1.13179i | 0.0717405 | + | 0.0359706i | ||||
\(991\) | − | 16.4157i | − | 0.521462i | −0.965411 | − | 0.260731i | \(-0.916036\pi\) | ||
0.965411 | − | 0.260731i | \(-0.0839636\pi\) | |||||||
\(992\) | −46.9073 | + | 37.2637i | −1.48931 | + | 1.18312i | ||||
\(993\) | 6.98077 | + | 20.4602i | 0.221528 | + | 0.649284i | ||||
\(994\) | 25.6371 | + | 53.2872i | 0.813161 | + | 1.69017i | ||||
\(995\) | −4.75576 | −0.150768 | ||||||||
\(996\) | 7.77113 | − | 21.6143i | 0.246238 | − | 0.684876i | ||||
\(997\) | 11.0803 | 0.350916 | 0.175458 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175458 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(998\) | 15.1401 | + | 31.4689i | 0.479251 | + | 0.996130i | ||||
\(999\) | 19.5829 | − | 29.6057i | 0.619577 | − | 0.936684i |
(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 | 804.2.c.b.671.20 | yes | 128 | |
3.2 | odd | 2 | inner | 804.2.c.b.671.109 | yes | 128 | |
4.3 | odd | 2 | inner | 804.2.c.b.671.110 | yes | 128 | |
12.11 | even | 2 | inner | 804.2.c.b.671.19 | ✓ | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.c.b.671.19 | ✓ | 128 | 12.11 | even | 2 | inner | |
804.2.c.b.671.20 | yes | 128 | 1.1 | even | 1 | trivial | |
804.2.c.b.671.109 | yes | 128 | 3.2 | odd | 2 | inner | |
804.2.c.b.671.110 | yes | 128 | 4.3 | odd | 2 | inner |