Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(751,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.751");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.bc (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 20x^{10} + 150x^{8} + 520x^{6} + 825x^{4} + 512x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 751.1 | ||
Root | \(2.36051i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.751 |
Dual form | 975.2.bc.k.901.1 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04426 | + | 1.18025i | −1.44551 | + | 0.834565i | −0.998209 | − | 0.0598198i | \(-0.980947\pi\) |
−0.447299 | + | 0.894384i | \(0.647614\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.78599 | − | 3.09343i | 0.892996 | − | 1.54671i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.04426 | + | 1.18025i | 0.834565 | + | 0.481836i | ||||
\(7\) | 3.93440 | + | 2.27152i | 1.48706 | + | 0.858556i | 0.999891 | − | 0.0147510i | \(-0.00469555\pi\) |
0.487171 | + | 0.873307i | \(0.338029\pi\) | |||||||
\(8\) | 3.71068i | 1.31192i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.74607 | − | 2.16279i | 1.12948 | − | 0.652106i | 0.185677 | − | 0.982611i | \(-0.440552\pi\) |
0.943804 | + | 0.330505i | \(0.107219\pi\) | |||||||
\(12\) | −3.57199 | −1.03114 | ||||||||
\(13\) | −1.84085 | + | 3.10021i | −0.510560 | + | 0.859842i | ||||
\(14\) | −10.7239 | −2.86608 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.807554 | − | 1.39872i | −0.201888 | − | 0.349681i | ||||
\(17\) | −2.76283 | + | 4.78536i | −0.670085 | + | 1.16062i | 0.307795 | + | 0.951453i | \(0.400409\pi\) |
−0.977880 | + | 0.209169i | \(0.932924\pi\) | |||||||
\(18\) | − | 2.36051i | − | 0.556376i | ||||||
\(19\) | 3.41535 | + | 1.97185i | 0.783535 | + | 0.452374i | 0.837682 | − | 0.546159i | \(-0.183910\pi\) |
−0.0541466 | + | 0.998533i | \(0.517244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.54305i | − | 0.991375i | ||||||
\(22\) | −5.10528 | + | 8.84261i | −1.08845 | + | 1.88525i | ||||
\(23\) | 0.364011 | + | 0.630486i | 0.0759016 | + | 0.131465i | 0.901478 | − | 0.432825i | \(-0.142483\pi\) |
−0.825576 | + | 0.564290i | \(0.809150\pi\) | |||||||
\(24\) | 3.21354 | − | 1.85534i | 0.655962 | − | 0.378720i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.104146 | − | 8.51029i | 0.0204248 | − | 1.66900i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 14.0536 | − | 8.11385i | 2.65588 | − | 1.53337i | ||||
\(29\) | −1.97844 | − | 3.42676i | −0.367387 | − | 0.636333i | 0.621769 | − | 0.783200i | \(-0.286414\pi\) |
−0.989156 | + | 0.146868i | \(0.953081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.599343i | 0.107645i | 0.998551 | + | 0.0538226i | \(0.0171405\pi\) | ||||
−0.998551 | + | 0.0538226i | \(0.982859\pi\) | |||||||
\(32\) | −3.12539 | − | 1.80444i | −0.552496 | − | 0.318984i | ||||
\(33\) | −3.74607 | − | 2.16279i | −0.652106 | − | 0.376494i | ||||
\(34\) | − | 13.0434i | − | 2.23692i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.78599 | + | 3.09343i | 0.297665 | + | 0.515572i | ||||
\(37\) | 3.91499 | − | 2.26032i | 0.643620 | − | 0.371594i | −0.142388 | − | 0.989811i | \(-0.545478\pi\) |
0.786008 | + | 0.618217i | \(0.212145\pi\) | |||||||
\(38\) | −9.30914 | −1.51014 | ||||||||
\(39\) | 3.60528 | + | 0.0441204i | 0.577307 | + | 0.00706491i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.97339 | + | 5.18079i | −1.40141 | + | 0.809104i | −0.994537 | − | 0.104382i | \(-0.966714\pi\) |
−0.406871 | + | 0.913485i | \(0.633380\pi\) | |||||||
\(42\) | 5.36195 | + | 9.28716i | 0.827366 | + | 1.43304i | ||||
\(43\) | 5.45093 | − | 9.44128i | 0.831258 | − | 1.43978i | −0.0657822 | − | 0.997834i | \(-0.520954\pi\) |
0.897041 | − | 0.441948i | \(-0.145712\pi\) | |||||||
\(44\) | − | 15.4509i | − | 2.32931i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.48827 | − | 0.859250i | −0.219433 | − | 0.126690i | ||||
\(47\) | − | 1.42486i | − | 0.207838i | −0.994586 | − | 0.103919i | \(-0.966862\pi\) | ||
0.994586 | − | 0.103919i | \(-0.0331382\pi\) | |||||||
\(48\) | −0.807554 | + | 1.39872i | −0.116560 | + | 0.201888i | ||||
\(49\) | 6.81965 | + | 11.8120i | 0.974236 | + | 1.68743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.52566 | 0.773748 | ||||||||
\(52\) | 6.30252 | + | 11.2315i | 0.874003 | + | 1.55753i | ||||
\(53\) | −0.805400 | −0.110630 | −0.0553151 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553151 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(54\) | −2.04426 | + | 1.18025i | −0.278188 | + | 0.160612i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.42890 | + | 14.5993i | −1.12636 | + | 1.95091i | ||||
\(57\) | − | 3.94371i | − | 0.522357i | ||||||
\(58\) | 8.08888 | + | 4.67012i | 1.06212 | + | 0.613216i | ||||
\(59\) | 9.71559 | + | 5.60930i | 1.26486 | + | 0.730269i | 0.974011 | − | 0.226499i | \(-0.0727282\pi\) |
0.290851 | + | 0.956768i | \(0.406061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.20134 | + | 10.7410i | −0.794001 | + | 1.37525i | 0.129471 | + | 0.991583i | \(0.458672\pi\) |
−0.923472 | + | 0.383666i | \(0.874661\pi\) | |||||||
\(62\) | −0.707376 | − | 1.22521i | −0.0898369 | − | 0.155602i | ||||
\(63\) | −3.93440 | + | 2.27152i | −0.495687 | + | 0.286185i | ||||
\(64\) | 11.7490 | 1.46863 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10.2106 | 1.25683 | ||||||||
\(67\) | −9.12013 | + | 5.26551i | −1.11420 | + | 0.643284i | −0.939914 | − | 0.341411i | \(-0.889095\pi\) |
−0.174287 | + | 0.984695i | \(0.555762\pi\) | |||||||
\(68\) | 9.86879 | + | 17.0933i | 1.19677 | + | 2.07286i | ||||
\(69\) | 0.364011 | − | 0.630486i | 0.0438218 | − | 0.0759016i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.898903 | + | 0.518982i | 0.106680 | + | 0.0615918i | 0.552391 | − | 0.833585i | \(-0.313716\pi\) |
−0.445711 | + | 0.895177i | \(0.647049\pi\) | |||||||
\(72\) | −3.21354 | − | 1.85534i | −0.378720 | − | 0.218654i | ||||
\(73\) | 6.45306i | 0.755274i | 0.925954 | + | 0.377637i | \(0.123263\pi\) | ||||
−0.925954 | + | 0.377637i | \(0.876737\pi\) | |||||||
\(74\) | −5.33550 | + | 9.24135i | −0.620239 | + | 1.07429i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.1996 | − | 7.04343i | 1.39939 | − | 0.807937i | ||||
\(77\) | 19.6513 | 2.23948 | ||||||||
\(78\) | −7.42220 | + | 4.16495i | −0.840398 | + | 0.471588i | ||||
\(79\) | 4.22063 | 0.474857 | 0.237429 | − | 0.971405i | \(-0.423695\pi\) | ||||
0.237429 | + | 0.971405i | \(0.423695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 12.2293 | − | 21.1817i | 1.35050 | − | 2.33913i | ||||
\(83\) | − | 7.69642i | − | 0.844792i | −0.906411 | − | 0.422396i | \(-0.861189\pi\) | ||
0.906411 | − | 0.422396i | \(-0.138811\pi\) | |||||||
\(84\) | −14.0536 | − | 8.11385i | −1.53337 | − | 0.885294i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.7339i | 2.77496i | ||||||||
\(87\) | −1.97844 | + | 3.42676i | −0.212111 | + | 0.367387i | ||||
\(88\) | 8.02543 | + | 13.9004i | 0.855513 | + | 1.48179i | ||||
\(89\) | −5.93532 | + | 3.42676i | −0.629142 | + | 0.363235i | −0.780420 | − | 0.625256i | \(-0.784995\pi\) |
0.151278 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2848 | + | 8.01590i | −1.49746 | + | 0.840295i | ||||
\(92\) | 2.60048 | 0.271119 | ||||||||
\(93\) | 0.519046 | − | 0.299672i | 0.0538226 | − | 0.0310745i | ||||
\(94\) | 1.68170 | + | 2.91279i | 0.173454 | + | 0.300431i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.60889i | 0.368331i | ||||||||
\(97\) | −9.61107 | − | 5.54895i | −0.975856 | − | 0.563411i | −0.0748394 | − | 0.997196i | \(-0.523844\pi\) |
−0.901016 | + | 0.433785i | \(0.857178\pi\) | |||||||
\(98\) | −27.8822 | − | 16.0978i | −2.81653 | − | 1.62613i | ||||
\(99\) | 4.32558i | 0.434737i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.83072 | + | 4.90294i | 0.281667 | + | 0.487861i | 0.971795 | − | 0.235826i | \(-0.0757794\pi\) |
−0.690129 | + | 0.723687i | \(0.742446\pi\) | |||||||
\(102\) | −11.2959 | + | 6.52168i | −1.11846 | + | 0.645742i | ||||
\(103\) | 3.25369 | 0.320595 | 0.160298 | − | 0.987069i | \(-0.448755\pi\) | ||||
0.160298 | + | 0.987069i | \(0.448755\pi\) | |||||||
\(104\) | −11.5039 | − | 6.83080i | −1.12805 | − | 0.669815i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.64645 | − | 0.950576i | 0.159917 | − | 0.0923281i | ||||
\(107\) | 7.25780 | + | 12.5709i | 0.701638 | + | 1.21527i | 0.967891 | + | 0.251370i | \(0.0808809\pi\) |
−0.266253 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(108\) | 1.78599 | − | 3.09343i | 0.171857 | − | 0.297665i | ||||
\(109\) | − | 2.24315i | − | 0.214855i | −0.994213 | − | 0.107428i | \(-0.965739\pi\) | ||
0.994213 | − | 0.107428i | \(-0.0342614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.91499 | − | 2.26032i | −0.371594 | − | 0.214540i | ||||
\(112\) | − | 7.33751i | − | 0.693330i | ||||||
\(113\) | 0.809154 | − | 1.40150i | 0.0761188 | − | 0.131842i | −0.825453 | − | 0.564470i | \(-0.809081\pi\) |
0.901572 | + | 0.432629i | \(0.142414\pi\) | |||||||
\(114\) | 4.65457 | + | 8.06195i | 0.435940 | + | 0.755071i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.1339 | −1.31230 | ||||||||
\(117\) | −1.76443 | − | 3.14433i | −0.163122 | − | 0.290693i | ||||
\(118\) | −26.4816 | −2.43783 | ||||||||
\(119\) | −21.7401 | + | 12.5517i | −1.99292 | + | 1.15061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.85534 | − | 6.67764i | 0.350485 | − | 0.607058i | ||||
\(122\) | − | 29.2766i | − | 2.65058i | ||||||
\(123\) | 8.97339 | + | 5.18079i | 0.809104 | + | 0.467136i | ||||
\(124\) | 1.85403 | + | 1.07042i | 0.166496 | + | 0.0961267i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.36195 | − | 9.28716i | 0.477680 | − | 0.827366i | ||||
\(127\) | 9.33047 | + | 16.1608i | 0.827945 | + | 1.43404i | 0.899648 | + | 0.436617i | \(0.143823\pi\) |
−0.0717028 | + | 0.997426i | \(0.522843\pi\) | |||||||
\(128\) | −17.7672 | + | 10.2579i | −1.57042 | + | 0.906680i | ||||
\(129\) | −10.9019 | −0.959855 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.45787 | 0.826338 | 0.413169 | − | 0.910654i | \(-0.364422\pi\) | ||||
0.413169 | + | 0.910654i | \(0.364422\pi\) | |||||||
\(132\) | −13.3809 | + | 7.72546i | −1.16466 | + | 0.672415i | ||||
\(133\) | 8.95823 | + | 15.5161i | 0.776777 | + | 1.34542i | ||||
\(134\) | 12.4293 | − | 21.5281i | 1.07372 | − | 1.85975i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.7570 | − | 10.2520i | −1.52265 | − | 0.879100i | ||||
\(137\) | −1.98355 | − | 1.14520i | −0.169466 | − | 0.0978414i | 0.412868 | − | 0.910791i | \(-0.364527\pi\) |
−0.582334 | + | 0.812950i | \(0.697860\pi\) | |||||||
\(138\) | 1.71850i | 0.146288i | ||||||||
\(139\) | 4.18650 | − | 7.25122i | 0.355094 | − | 0.615041i | −0.632040 | − | 0.774936i | \(-0.717782\pi\) |
0.987134 | + | 0.159895i | \(0.0511156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.23397 | + | 0.712432i | −0.103919 | + | 0.0599976i | ||||
\(142\) | −2.45012 | −0.205609 | ||||||||
\(143\) | −0.190846 | + | 15.5949i | −0.0159594 | + | 1.30411i | ||||
\(144\) | 1.61511 | 0.134592 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.61624 | − | 13.1917i | −0.630325 | − | 1.09175i | ||||
\(147\) | 6.81965 | − | 11.8120i | 0.562475 | − | 0.974236i | ||||
\(148\) | − | 16.1477i | − | 1.32733i | ||||||
\(149\) | 19.7954 | + | 11.4289i | 1.62170 | + | 0.936291i | 0.986465 | + | 0.163974i | \(0.0524315\pi\) |
0.635238 | + | 0.772316i | \(0.280902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.9011i | − | 1.21263i | −0.795223 | − | 0.606317i | \(-0.792646\pi\) | ||
0.795223 | − | 0.606317i | \(-0.207354\pi\) | |||||||
\(152\) | −7.31692 | + | 12.6733i | −0.593480 | + | 1.02794i | ||||
\(153\) | −2.76283 | − | 4.78536i | −0.223362 | − | 0.386874i | ||||
\(154\) | −40.1724 | + | 23.1935i | −3.23718 | + | 1.86899i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.57549 | − | 11.0739i | 0.526460 | − | 0.886620i | ||||
\(157\) | 0.495803 | 0.0395694 | 0.0197847 | − | 0.999804i | \(-0.493702\pi\) | ||||
0.0197847 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(158\) | −8.62805 | + | 4.98140i | −0.686410 | + | 0.396299i | ||||
\(159\) | 0.402700 | + | 0.697497i | 0.0319362 | + | 0.0553151i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.30744i | 0.260663i | ||||||||
\(162\) | 2.04426 | + | 1.18025i | 0.160612 | + | 0.0927294i | ||||
\(163\) | −1.48871 | − | 0.859509i | −0.116605 | − | 0.0673220i | 0.440563 | − | 0.897722i | \(-0.354779\pi\) |
−0.557168 | + | 0.830400i | \(0.688112\pi\) | |||||||
\(164\) | 37.0114i | 2.89011i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.08372 | + | 15.7335i | 0.705033 | + | 1.22115i | ||||
\(167\) | −4.92273 | + | 2.84214i | −0.380933 | + | 0.219932i | −0.678224 | − | 0.734855i | \(-0.737250\pi\) |
0.297291 | + | 0.954787i | \(0.403917\pi\) | |||||||
\(168\) | 16.8578 | 1.30061 | ||||||||
\(169\) | −6.22254 | − | 11.4140i | −0.478657 | − | 0.878002i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.41535 | + | 1.97185i | −0.261178 | + | 0.150791i | ||||
\(172\) | −19.4706 | − | 33.7241i | −1.48462 | − | 2.57144i | ||||
\(173\) | 3.43576 | − | 5.95091i | 0.261216 | − | 0.452439i | −0.705349 | − | 0.708860i | \(-0.749210\pi\) |
0.966565 | + | 0.256421i | \(0.0825432\pi\) | |||||||
\(174\) | − | 9.34023i | − | 0.708081i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.05030 | − | 3.49314i | −0.456058 | − | 0.263305i | ||||
\(177\) | − | 11.2186i | − | 0.843242i | ||||||
\(178\) | 8.08888 | − | 14.0103i | 0.606287 | − | 1.05012i | ||||
\(179\) | 10.9566 | + | 18.9774i | 0.818937 | + | 1.41844i | 0.906466 | + | 0.422278i | \(0.138769\pi\) |
−0.0875295 | + | 0.996162i | \(0.527897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9404 | −1.33350 | −0.666750 | − | 0.745281i | \(-0.732315\pi\) | ||||
−0.666750 | + | 0.745281i | \(0.732315\pi\) | |||||||
\(182\) | 19.7411 | − | 33.2463i | 1.46331 | − | 2.46438i | ||||
\(183\) | 12.4027 | 0.916833 | ||||||||
\(184\) | −2.33953 | + | 1.35073i | −0.172472 | + | 0.0995770i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.707376 | + | 1.22521i | −0.0518673 | + | 0.0898369i | ||||
\(187\) | 23.9017i | 1.74787i | ||||||||
\(188\) | −4.40772 | − | 2.54480i | −0.321466 | − | 0.185598i | ||||
\(189\) | 3.93440 | + | 2.27152i | 0.286185 | + | 0.165229i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.25521 | − | 2.17409i | 0.0908239 | − | 0.157312i | −0.817034 | − | 0.576589i | \(-0.804383\pi\) |
0.907858 | + | 0.419278i | \(0.137717\pi\) | |||||||
\(192\) | −5.87451 | − | 10.1749i | −0.423956 | − | 0.734313i | ||||
\(193\) | 8.16136 | − | 4.71197i | 0.587468 | − | 0.339175i | −0.176628 | − | 0.984278i | \(-0.556519\pi\) |
0.764096 | + | 0.645103i | \(0.223186\pi\) | |||||||
\(194\) | 26.1967 | 1.88081 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 48.7194 | 3.47996 | ||||||||
\(197\) | 21.3578 | − | 12.3309i | 1.52168 | − | 0.878542i | 0.522007 | − | 0.852941i | \(-0.325183\pi\) |
0.999672 | − | 0.0256008i | \(-0.00814988\pi\) | |||||||
\(198\) | −5.10528 | − | 8.84261i | −0.362817 | − | 0.628417i | ||||
\(199\) | 12.9766 | − | 22.4761i | 0.919886 | − | 1.59329i | 0.120300 | − | 0.992738i | \(-0.461614\pi\) |
0.799586 | − | 0.600552i | \(-0.205052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.12013 | + | 5.26551i | 0.643284 | + | 0.371400i | ||||
\(202\) | −11.5734 | − | 6.68192i | −0.814303 | − | 0.470138i | ||||
\(203\) | − | 17.9763i | − | 1.26169i | ||||||
\(204\) | 9.86879 | − | 17.0933i | 0.690954 | − | 1.19677i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.65137 | + | 3.84017i | −0.463423 | + | 0.267557i | ||||
\(207\) | −0.728022 | −0.0506010 | ||||||||
\(208\) | 5.82292 | + | 0.0712591i | 0.403747 | + | 0.00494093i | ||||
\(209\) | 17.0588 | 1.17998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.77273 | − | 9.99866i | −0.397411 | − | 0.688336i | 0.595994 | − | 0.802989i | \(-0.296758\pi\) |
−0.993406 | + | 0.114652i | \(0.963425\pi\) | |||||||
\(212\) | −1.43844 | + | 2.49145i | −0.0987924 | + | 0.171113i | ||||
\(213\) | − | 1.03796i | − | 0.0711201i | ||||||
\(214\) | −29.6736 | − | 17.1321i | −2.02845 | − | 1.17112i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.71068i | 0.252480i | ||||||||
\(217\) | −1.36142 | + | 2.35805i | −0.0924194 | + | 0.160075i | ||||
\(218\) | 2.64749 | + | 4.58558i | 0.179310 | + | 0.310575i | ||||
\(219\) | 5.58852 | − | 3.22653i | 0.377637 | − | 0.218029i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.74965 | − | 17.3745i | −0.655833 | − | 1.16873i | ||||
\(222\) | 10.6710 | 0.716190 | ||||||||
\(223\) | −7.03409 | + | 4.06113i | −0.471037 | + | 0.271954i | −0.716674 | − | 0.697408i | \(-0.754336\pi\) |
0.245636 | + | 0.969362i | \(0.421003\pi\) | |||||||
\(224\) | −8.19768 | − | 14.1988i | −0.547730 | − | 0.948697i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.82002i | 0.254104i | ||||||||
\(227\) | −11.7666 | − | 6.79346i | −0.780978 | − | 0.450898i | 0.0557990 | − | 0.998442i | \(-0.482229\pi\) |
−0.836777 | + | 0.547544i | \(0.815563\pi\) | |||||||
\(228\) | −12.1996 | − | 7.04343i | −0.807937 | − | 0.466463i | ||||
\(229\) | 3.61042i | 0.238583i | 0.992859 | + | 0.119292i | \(0.0380624\pi\) | ||||
−0.992859 | + | 0.119292i | \(0.961938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.82567 | − | 17.0186i | −0.646482 | − | 1.11974i | ||||
\(232\) | 12.7156 | − | 7.34135i | 0.834820 | − | 0.481983i | ||||
\(233\) | 28.6851 | 1.87922 | 0.939612 | − | 0.342240i | \(-0.111186\pi\) | ||||
0.939612 | + | 0.342240i | \(0.111186\pi\) | |||||||
\(234\) | 7.31805 | + | 4.34534i | 0.478396 | + | 0.284064i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 34.7040 | − | 20.0363i | 2.25904 | − | 1.30425i | ||||
\(237\) | −2.11031 | − | 3.65517i | −0.137080 | − | 0.237429i | ||||
\(238\) | 29.6283 | − | 51.3177i | 1.92052 | − | 3.32643i | ||||
\(239\) | 2.00405i | 0.129631i | 0.997897 | + | 0.0648157i | \(0.0206459\pi\) | ||||
−0.997897 | + | 0.0648157i | \(0.979354\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5161 | + | 14.1544i | 1.57922 | + | 0.911762i | 0.994969 | + | 0.100188i | \(0.0319445\pi\) |
0.584250 | + | 0.811574i | \(0.301389\pi\) | |||||||
\(242\) | 18.2011i | 1.17001i | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 22.1511 | + | 38.3668i | 1.41808 | + | 2.45619i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.4586 | −1.55942 | ||||||||
\(247\) | −12.4003 | + | 6.95840i | −0.789012 | + | 0.442752i | ||||
\(248\) | −2.22397 | −0.141222 | ||||||||
\(249\) | −6.66530 | + | 3.84821i | −0.422396 | + | 0.243870i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.84280 | + | 15.3162i | −0.558152 | + | 0.966748i | 0.439498 | + | 0.898243i | \(0.355156\pi\) |
−0.997651 | + | 0.0685050i | \(0.978177\pi\) | |||||||
\(252\) | 16.2277i | 1.02225i | ||||||||
\(253\) | 2.72722 | + | 1.57456i | 0.171459 | + | 0.0989918i | ||||
\(254\) | −38.1477 | − | 22.0246i | −2.39360 | − | 1.38195i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.4649 | − | 21.5898i | 0.779053 | − | 1.34936i | ||||
\(257\) | 9.97787 | + | 17.2822i | 0.622402 | + | 1.07803i | 0.989037 | + | 0.147668i | \(0.0471766\pi\) |
−0.366635 | + | 0.930365i | \(0.619490\pi\) | |||||||
\(258\) | 22.2862 | − | 12.8669i | 1.38748 | − | 0.801061i | ||||
\(259\) | 20.5375 | 1.27614 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.95688 | 0.244925 | ||||||||
\(262\) | −19.3343 | + | 11.1627i | −1.19448 | + | 0.689633i | ||||
\(263\) | −1.69847 | − | 2.94183i | −0.104732 | − | 0.181401i | 0.808897 | − | 0.587951i | \(-0.200065\pi\) |
−0.913629 | + | 0.406550i | \(0.866732\pi\) | |||||||
\(264\) | 8.02543 | − | 13.9004i | 0.493931 | − | 0.855513i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −36.6258 | − | 21.1459i | −2.24567 | − | 1.29654i | ||||
\(267\) | 5.93532 | + | 3.42676i | 0.363235 | + | 0.209714i | ||||
\(268\) | 37.6166i | 2.29780i | ||||||||
\(269\) | −7.66836 | + | 13.2820i | −0.467548 | + | 0.809817i | −0.999312 | − | 0.0370755i | \(-0.988196\pi\) |
0.531765 | + | 0.846892i | \(0.321529\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8495 | + | 9.15070i | −0.962787 | + | 0.555865i | −0.897030 | − | 0.441970i | \(-0.854280\pi\) |
−0.0657572 | + | 0.997836i | \(0.520946\pi\) | |||||||
\(272\) | 8.92454 | 0.541130 | ||||||||
\(273\) | 14.0844 | + | 8.36307i | 0.852426 | + | 0.506156i | ||||
\(274\) | 5.40652 | 0.326620 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.30024 | − | 2.25209i | −0.0782654 | − | 0.135560i | ||||
\(277\) | −3.90042 | + | 6.75572i | −0.234353 | + | 0.405912i | −0.959085 | − | 0.283120i | \(-0.908631\pi\) |
0.724731 | + | 0.689032i | \(0.241964\pi\) | |||||||
\(278\) | 19.7645i | 1.18540i | ||||||||
\(279\) | −0.519046 | − | 0.299672i | −0.0310745 | − | 0.0179409i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 23.2268i | − | 1.38559i | −0.721134 | − | 0.692796i | \(-0.756379\pi\) | ||
0.721134 | − | 0.692796i | \(-0.243621\pi\) | |||||||
\(282\) | 1.68170 | − | 2.91279i | 0.100144 | − | 0.173454i | ||||
\(283\) | −3.92173 | − | 6.79264i | −0.233123 | − | 0.403780i | 0.725603 | − | 0.688114i | \(-0.241561\pi\) |
−0.958725 | + | 0.284333i | \(0.908228\pi\) | |||||||
\(284\) | 3.21087 | − | 1.85379i | 0.190530 | − | 0.110002i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.0158 | − | 32.1053i | −1.06530 | − | 1.89843i | ||||
\(287\) | −47.0732 | −2.77864 | ||||||||
\(288\) | 3.12539 | − | 1.80444i | 0.184165 | − | 0.106328i | ||||
\(289\) | −6.76647 | − | 11.7199i | −0.398028 | − | 0.689405i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0979i | 0.650571i | ||||||||
\(292\) | 19.9621 | + | 11.5251i | 1.16819 | + | 0.674457i | ||||
\(293\) | −8.90314 | − | 5.14023i | −0.520127 | − | 0.300296i | 0.216859 | − | 0.976203i | \(-0.430419\pi\) |
−0.736987 | + | 0.675907i | \(0.763752\pi\) | |||||||
\(294\) | 32.1956i | 1.87769i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.38732 | + | 14.5273i | 0.487503 | + | 0.844380i | ||||
\(297\) | 3.74607 | − | 2.16279i | 0.217369 | − | 0.125498i | ||||
\(298\) | −53.9559 | −3.12558 | ||||||||
\(299\) | −2.62473 | − | 0.0321206i | −0.151792 | − | 0.00185758i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.8922 | − | 24.7638i | 2.47227 | − | 1.42736i | ||||
\(302\) | 17.5870 | + | 30.4617i | 1.01202 | + | 1.75287i | ||||
\(303\) | 2.83072 | − | 4.90294i | 0.162620 | − | 0.281667i | ||||
\(304\) | − | 6.36951i | − | 0.365317i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.2959 | + | 6.52168i | 0.645742 | + | 0.372820i | ||||
\(307\) | − | 33.8058i | − | 1.92940i | −0.263348 | − | 0.964701i | \(-0.584827\pi\) | ||
0.263348 | − | 0.964701i | \(-0.415173\pi\) | |||||||
\(308\) | 35.0971 | − | 60.7900i | 1.99985 | − | 3.46383i | ||||
\(309\) | −1.62684 | − | 2.81777i | −0.0925478 | − | 0.160298i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.286772 | −0.0162613 | −0.00813066 | − | 0.999967i | \(-0.502588\pi\) | ||||
−0.00813066 | + | 0.999967i | \(0.502588\pi\) | |||||||
\(312\) | −0.163716 | + | 13.3780i | −0.00926862 | + | 0.757383i | ||||
\(313\) | −27.8341 | −1.57328 | −0.786639 | − | 0.617413i | \(-0.788181\pi\) | ||||
−0.786639 | + | 0.617413i | \(0.788181\pi\) | |||||||
\(314\) | −1.01355 | + | 0.585173i | −0.0571979 | + | 0.0330232i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.53801 | − | 13.0562i | 0.424046 | − | 0.734469i | ||||
\(317\) | − | 23.6134i | − | 1.32626i | −0.748504 | − | 0.663130i | \(-0.769228\pi\) | ||
0.748504 | − | 0.663130i | \(-0.230772\pi\) | |||||||
\(318\) | −1.64645 | − | 0.950576i | −0.0923281 | − | 0.0533056i | ||||
\(319\) | −14.8227 | − | 8.55790i | −0.829913 | − | 0.479151i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.25780 | − | 12.5709i | 0.405091 | − | 0.701638i | ||||
\(322\) | −3.90362 | − | 6.76126i | −0.217540 | − | 0.376790i | ||||
\(323\) | −18.8721 | + | 10.8958i | −1.05007 | + | 0.606258i | ||||
\(324\) | −3.57199 | −0.198444 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.05775 | 0.224738 | ||||||||
\(327\) | −1.94263 | + | 1.12158i | −0.107428 | + | 0.0620233i | ||||
\(328\) | −19.2243 | − | 33.2974i | −1.06148 | − | 1.83854i | ||||
\(329\) | 3.23661 | − | 5.60598i | 0.178440 | − | 0.309068i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.51960 | + | 2.60939i | 0.248420 | + | 0.143425i | 0.619041 | − | 0.785359i | \(-0.287522\pi\) |
−0.370621 | + | 0.928784i | \(0.620855\pi\) | |||||||
\(332\) | −23.8083 | − | 13.7457i | −1.30665 | − | 0.754396i | ||||
\(333\) | 4.52064i | 0.247730i | ||||||||
\(334\) | 6.70889 | − | 11.6201i | 0.367094 | − | 0.635826i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.35447 | + | 3.66876i | −0.346665 | + | 0.200147i | ||||
\(337\) | 19.8753 | 1.08268 | 0.541339 | − | 0.840804i | \(-0.317918\pi\) | ||||
0.541339 | + | 0.840804i | \(0.317918\pi\) | |||||||
\(338\) | 26.1919 | + | 15.9890i | 1.42465 | + | 0.869689i | ||||
\(339\) | −1.61831 | −0.0878944 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.29625 | + | 2.24518i | 0.0701961 | + | 0.121583i | ||||
\(342\) | 4.65457 | − | 8.06195i | 0.251690 | − | 0.435940i | ||||
\(343\) | 30.1627i | 1.62863i | ||||||||
\(344\) | 35.0336 | + | 20.2266i | 1.88888 | + | 1.09055i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2203i | 0.872007i | ||||||||
\(347\) | −0.854503 | + | 1.48004i | −0.0458721 | + | 0.0794529i | −0.888050 | − | 0.459747i | \(-0.847940\pi\) |
0.842178 | + | 0.539200i | \(0.181273\pi\) | |||||||
\(348\) | 7.06695 | + | 12.2403i | 0.378828 | + | 0.656150i | ||||
\(349\) | 13.3270 | − | 7.69437i | 0.713380 | − | 0.411870i | −0.0989311 | − | 0.995094i | \(-0.531542\pi\) |
0.812311 | + | 0.583224i | \(0.198209\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.84085 | + | 3.10021i | −0.0982573 | + | 0.165477i | ||||
\(352\) | −15.6105 | −0.832045 | ||||||||
\(353\) | 16.2885 | − | 9.40416i | 0.866948 | − | 0.500533i | 0.000615369 | − | 1.00000i | \(-0.499804\pi\) |
0.866333 | + | 0.499467i | \(0.166471\pi\) | |||||||
\(354\) | 13.2408 | + | 22.9337i | 0.703740 | + | 1.21891i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.4806i | 1.29747i | ||||||||
\(357\) | 21.7401 | + | 12.5517i | 1.15061 | + | 0.664305i | ||||
\(358\) | −44.7963 | − | 25.8632i | −2.36756 | − | 1.36691i | ||||
\(359\) | − | 17.0768i | − | 0.901280i | −0.892706 | − | 0.450640i | \(-0.851196\pi\) | ||
0.892706 | − | 0.450640i | \(-0.148804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.72359 | − | 2.98534i | −0.0907152 | − | 0.157123i | ||||
\(362\) | 36.6748 | − | 21.1742i | 1.92759 | − | 1.11289i | ||||
\(363\) | −7.71067 | −0.404705 | ||||||||
\(364\) | −0.715972 | + | 58.5054i | −0.0375271 | + | 3.06652i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −25.3543 | + | 14.6383i | −1.32529 | + | 0.765156i | ||||
\(367\) | −5.20957 | − | 9.02325i | −0.271938 | − | 0.471010i | 0.697420 | − | 0.716662i | \(-0.254331\pi\) |
−0.969358 | + | 0.245653i | \(0.920998\pi\) | |||||||
\(368\) | 0.587917 | − | 1.01830i | 0.0306473 | − | 0.0530827i | ||||
\(369\) | − | 10.3616i | − | 0.539402i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.16876 | − | 1.82949i | −0.164514 | − | 0.0949822i | ||||
\(372\) | − | 2.14084i | − | 0.110998i | ||||||
\(373\) | −12.0400 | + | 20.8540i | −0.623410 | + | 1.07978i | 0.365437 | + | 0.930836i | \(0.380920\pi\) |
−0.988846 | + | 0.148941i | \(0.952414\pi\) | |||||||
\(374\) | −28.2101 | − | 48.8613i | −1.45871 | − | 2.52656i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.28721 | 0.272667 | ||||||||
\(377\) | 14.2657 | + | 0.174579i | 0.734719 | + | 0.00899127i | ||||
\(378\) | −10.7239 | −0.551578 | ||||||||
\(379\) | −7.64369 | + | 4.41308i | −0.392630 | + | 0.226685i | −0.683299 | − | 0.730139i | \(-0.739455\pi\) |
0.290669 | + | 0.956824i | \(0.406122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.33047 | − | 16.1608i | 0.478014 | − | 0.827945i | ||||
\(382\) | 5.92587i | 0.303194i | ||||||||
\(383\) | −14.0423 | − | 8.10734i | −0.717529 | − | 0.414266i | 0.0963135 | − | 0.995351i | \(-0.469295\pi\) |
−0.813843 | + | 0.581085i | \(0.802628\pi\) | |||||||
\(384\) | 17.7672 | + | 10.2579i | 0.906680 | + | 0.523472i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.1226 | + | 19.2649i | −0.566126 | + | 0.980560i | ||||
\(387\) | 5.45093 | + | 9.44128i | 0.277086 | + | 0.479927i | ||||
\(388\) | −34.3306 | + | 19.8208i | −1.74287 | + | 1.00625i | ||||
\(389\) | −33.1860 | −1.68259 | −0.841297 | − | 0.540573i | \(-0.818208\pi\) | ||||
−0.841297 | + | 0.540573i | \(0.818208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.02281 | −0.203442 | ||||||||
\(392\) | −43.8305 | + | 25.3055i | −2.21377 | + | 1.27812i | ||||
\(393\) | −4.72894 | − | 8.19076i | −0.238543 | − | 0.413169i | ||||
\(394\) | −29.1072 | + | 50.4152i | −1.46640 | + | 2.53988i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 13.3809 | + | 7.72546i | 0.672415 | + | 0.388219i | ||||
\(397\) | −6.49531 | − | 3.75007i | −0.325990 | − | 0.188211i | 0.328069 | − | 0.944654i | \(-0.393602\pi\) |
−0.654060 | + | 0.756443i | \(0.726935\pi\) | |||||||
\(398\) | 61.2626i | 3.07082i | ||||||||
\(399\) | 8.95823 | − | 15.5161i | 0.448472 | − | 0.776777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.95696 | − | 1.70720i | 0.147664 | − | 0.0852536i | −0.424348 | − | 0.905499i | \(-0.639497\pi\) |
0.572011 | + | 0.820246i | \(0.306163\pi\) | |||||||
\(402\) | −24.8585 | −1.23983 | ||||||||
\(403\) | −1.85809 | − | 1.10330i | −0.0925579 | − | 0.0549593i | ||||
\(404\) | 20.2225 | 1.00611 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.2166 | + | 36.7482i | 1.05296 | + | 1.82378i | ||||
\(407\) | 9.77720 | − | 16.9346i | 0.484638 | − | 0.839417i | ||||
\(408\) | 20.5040i | 1.01510i | ||||||||
\(409\) | −12.6543 | − | 7.30598i | −0.625716 | − | 0.361257i | 0.153375 | − | 0.988168i | \(-0.450986\pi\) |
−0.779091 | + | 0.626911i | \(0.784319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.29041i | 0.112978i | ||||||||
\(412\) | 5.81106 | − | 10.0650i | 0.286290 | − | 0.495869i | ||||
\(413\) | 25.4833 | + | 44.1384i | 1.25395 | + | 2.17191i | ||||
\(414\) | 1.48827 | − | 0.859250i | 0.0731442 | − | 0.0422298i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.3475 | − | 6.36764i | 0.556358 | − | 0.312199i | ||||
\(417\) | −8.37299 | −0.410027 | ||||||||
\(418\) | −34.8726 | + | 20.1337i | −1.70568 | + | 0.984773i | ||||
\(419\) | 1.70258 | + | 2.94896i | 0.0831765 | + | 0.144066i | 0.904613 | − | 0.426234i | \(-0.140160\pi\) |
−0.821436 | + | 0.570300i | \(0.806827\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9006i | 0.726213i | 0.931748 | + | 0.363107i | \(0.118284\pi\) | ||||
−0.931748 | + | 0.363107i | \(0.881716\pi\) | |||||||
\(422\) | 23.6019 | + | 13.6266i | 1.14892 | + | 0.663331i | ||||
\(423\) | 1.23397 | + | 0.712432i | 0.0599976 | + | 0.0346396i | ||||
\(424\) | − | 2.98858i | − | 0.145138i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.22506 | + | 2.12186i | 0.0593543 | + | 0.102805i | ||||
\(427\) | −48.7971 | + | 28.1730i | −2.36146 | + | 1.36339i | ||||
\(428\) | 51.8495 | 2.50624 | ||||||||
\(429\) | 13.6010 | − | 7.63219i | 0.656664 | − | 0.368486i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.80354 | − | 2.77332i | 0.231378 | − | 0.133586i | −0.379829 | − | 0.925057i | \(-0.624017\pi\) |
0.611208 | + | 0.791470i | \(0.290684\pi\) | |||||||
\(432\) | −0.807554 | − | 1.39872i | −0.0388535 | − | 0.0672962i | ||||
\(433\) | 6.28072 | − | 10.8785i | 0.301832 | − | 0.522789i | −0.674719 | − | 0.738075i | \(-0.735735\pi\) |
0.976551 | + | 0.215286i | \(0.0690684\pi\) | |||||||
\(434\) | − | 6.42729i | − | 0.308520i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.93904 | − | 4.00625i | −0.332320 | − | 0.191865i | ||||
\(437\) | 2.87111i | 0.137344i | ||||||||
\(438\) | −7.61624 | + | 13.1917i | −0.363918 | + | 0.630325i | ||||
\(439\) | −14.7936 | − | 25.6233i | −0.706060 | − | 1.22293i | −0.966308 | − | 0.257390i | \(-0.917138\pi\) |
0.260248 | − | 0.965542i | \(-0.416196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.6393 | −0.649490 | ||||||||
\(442\) | 40.4371 | + | 24.0109i | 1.92340 | + | 1.14208i | ||||
\(443\) | 29.6951 | 1.41086 | 0.705428 | − | 0.708781i | \(-0.250755\pi\) | ||||
0.705428 | + | 0.708781i | \(0.250755\pi\) | |||||||
\(444\) | −13.9843 | + | 8.07383i | −0.663665 | + | 0.383167i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.58633 | − | 16.6040i | 0.453926 | − | 0.786222i | ||||
\(447\) | − | 22.8578i | − | 1.08114i | ||||||
\(448\) | 46.2253 | + | 26.6882i | 2.18394 | + | 1.26090i | ||||
\(449\) | −9.55371 | − | 5.51584i | −0.450867 | − | 0.260308i | 0.257329 | − | 0.966324i | \(-0.417158\pi\) |
−0.708196 | + | 0.706015i | \(0.750491\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4099 | + | 38.8152i | −1.05524 | + | 1.82773i | ||||
\(452\) | −2.89029 | − | 5.00612i | −0.135948 | − | 0.235468i | ||||
\(453\) | −12.9047 | + | 7.45054i | −0.606317 | + | 0.350057i | ||||
\(454\) | 32.0720 | 1.50521 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.6338 | 0.685292 | ||||||||
\(457\) | 12.3287 | − | 7.11796i | 0.576711 | − | 0.332964i | −0.183114 | − | 0.983092i | \(-0.558618\pi\) |
0.759825 | + | 0.650128i | \(0.225285\pi\) | |||||||
\(458\) | −4.26121 | − | 7.38063i | −0.199113 | − | 0.344874i | ||||
\(459\) | −2.76283 | + | 4.78536i | −0.128958 | + | 0.223362i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3611 | − | 11.1781i | −0.901736 | − | 0.520618i | −0.0239731 | − | 0.999713i | \(-0.507632\pi\) |
−0.877763 | + | 0.479095i | \(0.840965\pi\) | |||||||
\(462\) | 40.1724 | + | 23.1935i | 1.86899 | + | 1.07906i | ||||
\(463\) | 29.9717i | 1.39290i | 0.717604 | + | 0.696451i | \(0.245239\pi\) | ||||
−0.717604 | + | 0.696451i | \(0.754761\pi\) | |||||||
\(464\) | −3.19539 | + | 5.53458i | −0.148342 | + | 0.256936i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −58.6398 | + | 33.8557i | −2.71644 | + | 1.56833i | ||||
\(467\) | −17.3591 | −0.803282 | −0.401641 | − | 0.915797i | \(-0.631560\pi\) | ||||
−0.401641 | + | 0.915797i | \(0.631560\pi\) | |||||||
\(468\) | −12.8780 | − | 0.157597i | −0.595286 | − | 0.00728493i | ||||
\(469\) | −47.8429 | −2.20918 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.247901 | − | 0.429378i | −0.0114227 | − | 0.0197847i | ||||
\(472\) | −20.8143 | + | 36.0515i | −0.958057 | + | 1.65940i | ||||
\(473\) | − | 47.1569i | − | 2.16828i | ||||||
\(474\) | 8.62805 | + | 4.98140i | 0.396299 | + | 0.228803i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 89.6688i | 4.10996i | ||||||||
\(477\) | 0.402700 | − | 0.697497i | 0.0184384 | − | 0.0319362i | ||||
\(478\) | −2.36529 | − | 4.09680i | −0.108186 | − | 0.187383i | ||||
\(479\) | −8.85694 | + | 5.11356i | −0.404684 | + | 0.233644i | −0.688503 | − | 0.725233i | \(-0.741732\pi\) |
0.283819 | + | 0.958878i | \(0.408399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.199452 | + | 16.2982i | −0.00909424 | + | 0.743133i | ||||
\(482\) | −66.8229 | −3.04370 | ||||||||
\(483\) | 2.86433 | − | 1.65372i | 0.130331 | − | 0.0752469i | ||||
\(484\) | −13.7712 | − | 23.8524i | −0.625964 | − | 1.08420i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 2.36051i | − | 0.107075i | ||||||
\(487\) | 14.2659 | + | 8.23642i | 0.646449 | + | 0.373228i | 0.787095 | − | 0.616832i | \(-0.211584\pi\) |
−0.140645 | + | 0.990060i | \(0.544918\pi\) | |||||||
\(488\) | −39.8566 | − | 23.0112i | −1.80422 | − | 1.04167i | ||||
\(489\) | 1.71902i | 0.0777367i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2907 | + | 24.7523i | 0.644931 | + | 1.11705i | 0.984317 | + | 0.176407i | \(0.0564473\pi\) |
−0.339386 | + | 0.940647i | \(0.610219\pi\) | |||||||
\(492\) | 32.0528 | − | 18.5057i | 1.44505 | − | 0.834302i | ||||
\(493\) | 21.8644 | 0.984722 | ||||||||
\(494\) | 17.1367 | − | 28.8602i | 0.771018 | − | 1.29848i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.838316 | − | 0.484002i | 0.0376415 | − | 0.0217323i | ||||
\(497\) | 2.35776 | + | 4.08376i | 0.105760 | + | 0.183182i | ||||
\(498\) | 9.08372 | − | 15.7335i | 0.407051 | − | 0.705033i | ||||
\(499\) | 14.6508i | 0.655858i | 0.944702 | + | 0.327929i | \(0.106351\pi\) | ||||
−0.944702 | + | 0.327929i | \(0.893649\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.92273 | + | 2.84214i | 0.219932 | + | 0.126978i | ||||
\(502\) | − | 41.7469i | − | 1.86326i | ||||||
\(503\) | 1.21181 | − | 2.09892i | 0.0540320 | − | 0.0935861i | −0.837744 | − | 0.546063i | \(-0.816126\pi\) |
0.891776 | + | 0.452477i | \(0.149459\pi\) | |||||||
\(504\) | −8.42890 | − | 14.5993i | −0.375453 | − | 0.650304i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.43352 | −0.330460 | ||||||||
\(507\) | −6.77356 | + | 11.0959i | −0.300825 | + | 0.492786i | ||||
\(508\) | 66.6566 | 2.95741 | ||||||||
\(509\) | −12.3914 | + | 7.15420i | −0.549240 | + | 0.317104i | −0.748816 | − | 0.662778i | \(-0.769377\pi\) |
0.199575 | + | 0.979883i | \(0.436044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6583 | + | 25.3889i | −0.648445 | + | 1.12314i | ||||
\(512\) | 17.8150i | 0.787321i | ||||||||
\(513\) | 3.41535 | + | 1.97185i | 0.150791 | + | 0.0870595i | ||||
\(514\) | −40.7947 | − | 23.5528i | −1.79938 | − | 1.03887i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19.4706 | + | 33.7241i | −0.857147 | + | 1.48462i | ||||
\(517\) | −3.08169 | − | 5.33764i | −0.135532 | − | 0.234749i | ||||
\(518\) | −41.9839 | + | 24.2394i | −1.84467 | + | 1.06502i | ||||
\(519\) | −6.87152 | −0.301626 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.9071 | −1.52931 | −0.764654 | − | 0.644441i | \(-0.777090\pi\) | ||||
−0.764654 | + | 0.644441i | \(0.777090\pi\) | |||||||
\(522\) | −8.08888 | + | 4.67012i | −0.354041 | + | 0.204405i | ||||
\(523\) | 6.57502 | + | 11.3883i | 0.287505 | + | 0.497974i | 0.973214 | − | 0.229902i | \(-0.0738407\pi\) |
−0.685708 | + | 0.727877i | \(0.740507\pi\) | |||||||
\(524\) | 16.8917 | − | 29.2573i | 0.737917 | − | 1.27811i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.94420 | + | 4.00924i | 0.302782 | + | 0.174811i | ||||
\(527\) | −2.86807 | − | 1.65588i | −0.124935 | − | 0.0721314i | ||||
\(528\) | 6.98628i | 0.304039i | ||||||||
\(529\) | 11.2350 | − | 19.4596i | 0.488478 | − | 0.846069i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.71559 | + | 5.60930i | −0.421621 | + | 0.243423i | ||||
\(532\) | 63.9973 | 2.77464 | ||||||||
\(533\) | 0.457157 | − | 37.3564i | 0.0198017 | − | 1.61809i | ||||
\(534\) | −16.1778 | −0.700080 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.5386 | − | 33.8419i | −0.843940 | − | 1.46175i | ||||
\(537\) | 10.9566 | − | 18.9774i | 0.472813 | − | 0.818937i | ||||
\(538\) | − | 36.2024i | − | 1.56080i | ||||||
\(539\) | 51.0937 | + | 29.4990i | 2.20076 | + | 1.27061i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 19.0301i | − | 0.818169i | −0.912496 | − | 0.409085i | \(-0.865848\pi\) | ||
0.912496 | − | 0.409085i | \(-0.134152\pi\) | |||||||
\(542\) | 21.6003 | − | 37.4128i | 0.927811 | − | 1.60702i | ||||
\(543\) | 8.97021 | + | 15.5369i | 0.384948 | + | 0.666750i | ||||
\(544\) | 17.2698 | − | 9.97075i | 0.740439 | − | 0.427492i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −38.6627 | − | 0.473142i | −1.65461 | − | 0.0202486i | ||||
\(547\) | 21.1122 | 0.902694 | 0.451347 | − | 0.892348i | \(-0.350944\pi\) | ||||
0.451347 | + | 0.892348i | \(0.350944\pi\) | |||||||
\(548\) | −7.08522 | + | 4.09065i | −0.302666 | + | 0.174744i | ||||
\(549\) | −6.20134 | − | 10.7410i | −0.264667 | − | 0.458416i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.6048i | − | 0.664785i | ||||||
\(552\) | 2.33953 | + | 1.35073i | 0.0995770 | + | 0.0574908i | ||||
\(553\) | 16.6056 | + | 9.58726i | 0.706143 | + | 0.407692i | ||||
\(554\) | − | 18.4139i | − | 0.782332i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.9541 | − | 25.9013i | −0.634195 | − | 1.09846i | ||||
\(557\) | −8.79709 | + | 5.07900i | −0.372745 | + | 0.215204i | −0.674657 | − | 0.738132i | \(-0.735708\pi\) |
0.301912 | + | 0.953336i | \(0.402375\pi\) | |||||||
\(558\) | 1.41475 | 0.0598912 | ||||||||
\(559\) | 19.2356 | + | 34.2790i | 0.813578 | + | 1.44985i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.6995 | − | 11.9509i | 0.873933 | − | 0.504566i | ||||
\(562\) | 27.4134 | + | 47.4815i | 1.15637 | + | 2.00288i | ||||
\(563\) | −7.46961 | + | 12.9377i | −0.314807 | + | 0.545261i | −0.979396 | − | 0.201947i | \(-0.935273\pi\) |
0.664590 | + | 0.747208i | \(0.268606\pi\) | |||||||
\(564\) | 5.08959i | 0.214311i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.0341 | + | 9.25727i | 0.673962 | + | 0.389112i | ||||
\(567\) | − | 4.54305i | − | 0.190790i | ||||||
\(568\) | −1.92577 | + | 3.33554i | −0.0808037 | + | 0.139956i | ||||
\(569\) | −12.0374 | − | 20.8495i | −0.504636 | − | 0.874055i | −0.999986 | − | 0.00536121i | \(-0.998293\pi\) |
0.495350 | − | 0.868694i | \(-0.335040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.95913 | 0.0819868 | 0.0409934 | − | 0.999159i | \(-0.486948\pi\) | ||||
0.0409934 | + | 0.999159i | \(0.486948\pi\) | |||||||
\(572\) | 47.9010 | + | 28.4428i | 2.00284 | + | 1.18925i | ||||
\(573\) | −2.51042 | −0.104874 | ||||||||
\(574\) | 96.2297 | − | 55.5583i | 4.01655 | − | 2.31896i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.87451 | + | 10.1749i | −0.244771 | + | 0.423956i | ||||
\(577\) | − | 1.22118i | − | 0.0508382i | −0.999677 | − | 0.0254191i | \(-0.991908\pi\) | ||
0.999677 | − | 0.0254191i | \(-0.00809202\pi\) | |||||||
\(578\) | 27.6648 | + | 15.9723i | 1.15071 | + | 0.664360i | ||||
\(579\) | −8.16136 | − | 4.71197i | −0.339175 | − | 0.195823i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.4826 | − | 30.2808i | 0.725301 | − | 1.25626i | ||||
\(582\) | −13.0983 | − | 22.6870i | −0.542943 | − | 0.940405i | ||||
\(583\) | −3.01708 | + | 1.74191i | −0.124955 | + | 0.0721427i | ||||
\(584\) | −23.9452 | −0.990861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.2671 | 1.00246 | ||||||||
\(587\) | 25.6779 | − | 14.8251i | 1.05984 | − | 0.611898i | 0.134451 | − | 0.990920i | \(-0.457073\pi\) |
0.925388 | + | 0.379022i | \(0.123739\pi\) | |||||||
\(588\) | −24.3597 | − | 42.1922i | −1.00458 | − | 1.73998i | ||||
\(589\) | −1.18182 | + | 2.04697i | −0.0486959 | + | 0.0843438i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.3578 | − | 12.3309i | −0.878542 | − | 0.507226i | ||||
\(592\) | −6.32313 | − | 3.65066i | −0.259879 | − | 0.150041i | ||||
\(593\) | 10.2794i | 0.422126i | 0.977473 | + | 0.211063i | \(0.0676925\pi\) | ||||
−0.977473 | + | 0.211063i | \(0.932308\pi\) | |||||||
\(594\) | −5.10528 | + | 8.84261i | −0.209472 | + | 0.362817i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 70.7089 | − | 40.8238i | 2.89635 | − | 1.67221i | ||||
\(597\) | −25.9532 | −1.06219 | ||||||||
\(598\) | 5.40352 | − | 3.03218i | 0.220967 | − | 0.123995i | ||||
\(599\) | −15.0591 | −0.615296 | −0.307648 | − | 0.951500i | \(-0.599542\pi\) | ||||
−0.307648 | + | 0.951500i | \(0.599542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2473 | − | 17.7489i | −0.417998 | − | 0.723993i | 0.577740 | − | 0.816221i | \(-0.303935\pi\) |
−0.995738 | + | 0.0922273i | \(0.970601\pi\) | |||||||
\(602\) | −58.4551 | + | 101.247i | −2.38245 | + | 4.12653i | ||||
\(603\) | − | 10.5310i | − | 0.428856i | ||||||
\(604\) | −46.0955 | − | 26.6132i | −1.87560 | − | 1.08288i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.3638i | 0.542869i | ||||||||
\(607\) | −1.34177 | + | 2.32401i | −0.0544608 | + | 0.0943288i | −0.891971 | − | 0.452094i | \(-0.850677\pi\) |
0.837510 | + | 0.546422i | \(0.184011\pi\) | |||||||
\(608\) | −7.11620 | − | 12.3256i | −0.288600 | − | 0.499870i | ||||
\(609\) | −15.5679 | + | 8.98815i | −0.630844 | + | 0.364218i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.41737 | + | 2.62296i | 0.178708 | + | 0.106114i | ||||
\(612\) | −19.7376 | −0.797845 | ||||||||
\(613\) | 9.16309 | − | 5.29031i | 0.370094 | − | 0.213674i | −0.303406 | − | 0.952862i | \(-0.598124\pi\) |
0.673499 | + | 0.739188i | \(0.264790\pi\) | |||||||
\(614\) | 39.8994 | + | 69.1079i | 1.61021 | + | 2.78897i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 72.9198i | 2.93802i | ||||||||
\(617\) | −15.4896 | − | 8.94290i | −0.623586 | − | 0.360028i | 0.154678 | − | 0.987965i | \(-0.450566\pi\) |
−0.778264 | + | 0.627937i | \(0.783899\pi\) | |||||||
\(618\) | 6.65137 | + | 3.84017i | 0.267557 | + | 0.154474i | ||||
\(619\) | − | 8.37677i | − | 0.336691i | −0.985728 | − | 0.168345i | \(-0.946158\pi\) | ||
0.985728 | − | 0.168345i | \(-0.0538424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.364011 | + | 0.630486i | 0.0146073 | + | 0.0253005i | ||||
\(622\) | 0.586235 | − | 0.338463i | 0.0235059 | − | 0.0135711i | ||||
\(623\) | −31.1358 | −1.24743 | ||||||||
\(624\) | −2.84975 | − | 5.07842i | −0.114081 | − | 0.203300i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 56.9001 | − | 32.8513i | 2.27419 | − | 1.31300i | ||||
\(627\) | −8.52942 | − | 14.7734i | −0.340632 | − | 0.589992i | ||||
\(628\) | 0.885500 | − | 1.53373i | 0.0353353 | − | 0.0612025i | ||||
\(629\) | 24.9795i | 0.995999i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.5045 | − | 17.6118i | −1.21437 | − | 0.701114i | −0.250659 | − | 0.968076i | \(-0.580647\pi\) |
−0.963707 | + | 0.266961i | \(0.913980\pi\) | |||||||
\(632\) | 15.6614i | 0.622977i | ||||||||
\(633\) | −5.77273 | + | 9.99866i | −0.229445 | + | 0.397411i | ||||
\(634\) | 27.8698 | + | 48.2719i | 1.10685 | + | 1.91712i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.87688 | 0.114076 | ||||||||
\(637\) | −49.1735 | − | 0.601771i | −1.94833 | − | 0.0238430i | ||||
\(638\) | 40.4019 | 1.59953 | ||||||||
\(639\) | −0.898903 | + | 0.518982i | −0.0355600 | + | 0.0205306i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.48264 | − | 14.6924i | 0.335044 | − | 0.580313i | −0.648449 | − | 0.761258i | \(-0.724582\pi\) |
0.983493 | + | 0.180945i | \(0.0579155\pi\) | |||||||
\(642\) | 34.2642i | 1.35230i | ||||||||
\(643\) | −39.8916 | − | 23.0314i | −1.57317 | − | 0.908272i | −0.995777 | − | 0.0918073i | \(-0.970736\pi\) |
−0.577396 | − | 0.816464i | \(-0.695931\pi\) | |||||||
\(644\) | 10.2313 | + | 5.90707i | 0.403171 | + | 0.232771i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.7196 | − | 44.5476i | 1.01192 | − | 1.75270i | ||||
\(647\) | 0.851665 | + | 1.47513i | 0.0334824 | + | 0.0579932i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(648\) | 3.21354 | − | 1.85534i | 0.126240 | − | 0.0728846i | ||||
\(649\) | 48.5270 | 1.90485 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.72285 | 0.106717 | ||||||||
\(652\) | −5.31766 | + | 3.07015i | −0.208256 | + | 0.120237i | ||||
\(653\) | −1.37739 | − | 2.38570i | −0.0539013 | − | 0.0933597i | 0.837816 | − | 0.545953i | \(-0.183832\pi\) |
−0.891717 | + | 0.452593i | \(0.850499\pi\) | |||||||
\(654\) | 2.64749 | − | 4.58558i | 0.103525 | − | 0.179310i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.4930 | + | 8.36754i | 0.565857 | + | 0.326697i | ||||
\(657\) | −5.58852 | − | 3.22653i | −0.218029 | − | 0.125879i | ||||
\(658\) | 15.2801i | 0.595680i | ||||||||
\(659\) | 10.7195 | − | 18.5668i | 0.417574 | − | 0.723260i | −0.578121 | − | 0.815951i | \(-0.696214\pi\) |
0.995695 | + | 0.0926917i | \(0.0295471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.93927 | + | 3.42904i | −0.231011 | + | 0.133374i | −0.611038 | − | 0.791601i | \(-0.709248\pi\) |
0.380027 | + | 0.924975i | \(0.375915\pi\) | |||||||
\(662\) | −12.3190 | −0.478791 | ||||||||
\(663\) | −10.1719 | + | 17.1307i | −0.395045 | + | 0.665301i | ||||
\(664\) | 28.5589 | 1.10830 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.33550 | − | 9.24135i | −0.206746 | − | 0.358095i | ||||
\(667\) | 1.44035 | − | 2.49476i | 0.0557705 | − | 0.0965973i | ||||
\(668\) | 20.3042i | 0.785592i | ||||||||
\(669\) | 7.03409 | + | 4.06113i | 0.271954 | + | 0.157012i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.6489i | 2.07109i | ||||||||
\(672\) | −8.19768 | + | 14.1988i | −0.316232 | + | 0.547730i | ||||
\(673\) | 0.450047 | + | 0.779505i | 0.0173481 | + | 0.0300477i | 0.874569 | − | 0.484901i | \(-0.161144\pi\) |
−0.857221 | + | 0.514949i | \(0.827811\pi\) | |||||||
\(674\) | −40.6303 | + | 23.4579i | −1.56502 | + | 0.903565i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.4219 | − | 1.13636i | −1.78546 | − | 0.0437063i | ||||
\(677\) | 40.3221 | 1.54970 | 0.774851 | − | 0.632144i | \(-0.217825\pi\) | ||||
0.774851 | + | 0.632144i | \(0.217825\pi\) | |||||||
\(678\) | 3.30824 | − | 1.91001i | 0.127052 | − | 0.0733536i | ||||
\(679\) | −25.2092 | − | 43.6635i | −0.967439 | − | 1.67565i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5869i | 0.520652i | ||||||||
\(682\) | −5.29975 | − | 3.05981i | −0.202938 | − | 0.117166i | ||||
\(683\) | −6.91828 | − | 3.99427i | −0.264721 | − | 0.152837i | 0.361765 | − | 0.932269i | \(-0.382174\pi\) |
−0.626486 | + | 0.779433i | \(0.715507\pi\) | |||||||
\(684\) | 14.0869i | 0.538625i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −35.5996 | − | 61.6603i | −1.35920 | − | 2.35420i | ||||
\(687\) | 3.12672 | − | 1.80521i | 0.119292 | − | 0.0688731i | ||||
\(688\) | −17.6077 | −0.671286 | ||||||||
\(689\) | 1.48262 | − | 2.49691i | 0.0564834 | − | 0.0951246i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.0446 | − | 16.7689i | 1.10491 | − | 0.637919i | 0.167402 | − | 0.985889i | \(-0.446462\pi\) |
0.937506 | + | 0.347970i | \(0.113129\pi\) | |||||||
\(692\) | −12.2725 | − | 21.2566i | −0.466530 | − | 0.808053i | ||||
\(693\) | −9.82567 | + | 17.0186i | −0.373246 | + | 0.646482i | ||||
\(694\) | − | 4.03412i | − | 0.153133i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.7156 | − | 7.34135i | −0.481983 | − | 0.278273i | ||||
\(697\) | − | 57.2546i | − | 2.16867i | ||||||
\(698\) | −18.1626 | + | 31.4586i | −0.687465 | + | 1.19072i | ||||
\(699\) | −14.3426 | − | 24.8420i | −0.542486 | − | 0.939612i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.96325 | 0.225229 | 0.112614 | − | 0.993639i | \(-0.464078\pi\) | ||||
0.112614 | + | 0.993639i | \(0.464078\pi\) | |||||||
\(702\) | 0.104146 | − | 8.51029i | 0.00393075 | − | 0.321200i | ||||
\(703\) | 17.8281 | 0.672399 | ||||||||
\(704\) | 44.0126 | − | 25.4107i | 1.65879 | − | 0.957701i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.1986 | + | 38.4490i | −0.835454 | + | 1.44705i | ||||
\(707\) | 25.7202i | 0.967306i | ||||||||
\(708\) | −34.7040 | − | 20.0363i | −1.30425 | − | 0.753012i | ||||
\(709\) | −29.4208 | − | 16.9861i | −1.10492 | − | 0.637926i | −0.167411 | − | 0.985887i | \(-0.553541\pi\) |
−0.937509 | + | 0.347961i | \(0.886874\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.11031 | + | 3.65517i | −0.0791429 | + | 0.137080i | ||||
\(712\) | −12.7156 | − | 22.0241i | −0.476537 | − | 0.825386i | ||||
\(713\) | −0.377877 | + | 0.218168i | −0.0141516 | + | 0.00817044i | ||||
\(714\) | −59.2566 | −2.21762 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.2738 | 2.92523 | ||||||||
\(717\) | 1.73556 | − | 1.00203i | 0.0648157 | − | 0.0374213i | ||||
\(718\) | 20.1550 | + | 34.9094i | 0.752177 | + | 1.30281i | ||||
\(719\) | 12.0007 | − | 20.7858i | 0.447549 | − | 0.775178i | −0.550677 | − | 0.834719i | \(-0.685630\pi\) |
0.998226 | + | 0.0595406i | \(0.0189636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8013 | + | 7.39083i | 0.476745 | + | 0.275249i | ||||
\(722\) | 7.04692 | + | 4.06854i | 0.262259 | + | 0.151415i | ||||
\(723\) | − | 28.3087i | − | 1.05281i | ||||||
\(724\) | −32.0414 | + | 55.4974i | −1.19081 | + | 2.06255i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.7626 | − | 9.10054i | 0.585005 | − | 0.337753i | ||||
\(727\) | −26.1991 | −0.971672 | −0.485836 | − | 0.874050i | \(-0.661485\pi\) | ||||
−0.485836 | + | 0.874050i | \(0.661485\pi\) | |||||||
\(728\) | −29.7444 | − | 53.0064i | −1.10240 | − | 1.96455i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.1200 | + | 52.1693i | 1.11403 | + | 1.92955i | ||||
\(732\) | 22.1511 | − | 38.3668i | 0.818728 | − | 1.41808i | ||||
\(733\) | − | 49.2273i | − | 1.81825i | −0.416520 | − | 0.909127i | \(-0.636750\pi\) | ||
0.416520 | − | 0.909127i | \(-0.363250\pi\) | |||||||
\(734\) | 21.2994 | + | 12.2972i | 0.786176 | + | 0.453899i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.62735i | − | 0.0968455i | ||||||
\(737\) | −22.7764 | + | 39.4499i | −0.838979 | + | 1.45315i | ||||
\(738\) | 12.2293 | + | 21.1817i | 0.450166 | + | 0.779711i | ||||
\(739\) | 1.15468 | − | 0.666653i | 0.0424755 | − | 0.0245232i | −0.478612 | − | 0.878027i | \(-0.658860\pi\) |
0.521087 | + | 0.853503i | \(0.325527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.2263 | + | 7.25977i | 0.449144 | + | 0.266694i | ||||
\(742\) | 8.63703 | 0.317075 | ||||||||
\(743\) | −25.8413 | + | 14.9195i | −0.948025 | + | 0.547342i | −0.892467 | − | 0.451113i | \(-0.851027\pi\) |
−0.0555581 | + | 0.998455i | \(0.517694\pi\) | |||||||
\(744\) | 1.11198 | + | 1.92601i | 0.0407673 | + | 0.0706111i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 56.8412i | − | 2.08110i | ||||||
\(747\) | 6.66530 | + | 3.84821i | 0.243870 | + | 0.140799i | ||||
\(748\) | 73.9383 | + | 42.6883i | 2.70345 | + | 1.56084i | ||||
\(749\) | 65.9451i | 2.40958i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.94574 | − | 8.56627i | −0.180473 | − | 0.312588i | 0.761569 | − | 0.648084i | \(-0.224429\pi\) |
−0.942042 | + | 0.335496i | \(0.891096\pi\) | |||||||
\(752\) | −1.99299 | + | 1.15065i | −0.0726770 | + | 0.0419601i | ||||
\(753\) | 17.6856 | 0.644499 | ||||||||
\(754\) | −29.3687 | + | 16.4802i | −1.06955 | + | 0.600173i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 14.0536 | − | 8.11385i | 0.511125 | − | 0.295098i | ||||
\(757\) | 24.2455 | + | 41.9944i | 0.881217 | + | 1.52631i | 0.849989 | + | 0.526800i | \(0.176608\pi\) |
0.0312280 | + | 0.999512i | \(0.490058\pi\) | |||||||
\(758\) | 10.4171 | − | 18.0430i | 0.378366 | − | 0.655350i | ||||
\(759\) | − | 3.14912i | − | 0.114306i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.6052 | + | 12.4738i | 0.783188 | + | 0.452174i | 0.837559 | − | 0.546347i | \(-0.183982\pi\) |
−0.0543707 | + | 0.998521i | \(0.517315\pi\) | |||||||
\(762\) | 44.0492i | 1.59574i | ||||||||
\(763\) | 5.09538 | − | 8.82545i | 0.184465 | − | 0.319503i | ||||
\(764\) | −4.48360 | − | 7.76582i | −0.162211 | − | 0.280957i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.2748 | 1.38293 | ||||||||
\(767\) | −35.2749 | + | 19.7945i | −1.27370 | + | 0.714736i | ||||
\(768\) | −24.9297 | −0.899573 | ||||||||
\(769\) | 7.28560 | − | 4.20634i | 0.262725 | − | 0.151685i | −0.362852 | − | 0.931847i | \(-0.618197\pi\) |
0.625577 | + | 0.780162i | \(0.284864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.97787 | − | 17.2822i | 0.359344 | − | 0.622402i | ||||
\(772\) | − | 33.6621i | − | 1.21153i | ||||||
\(773\) | −32.3114 | − | 18.6550i | −1.16216 | − | 0.670973i | −0.210339 | − | 0.977628i | \(-0.567457\pi\) |
−0.951821 | + | 0.306655i | \(0.900790\pi\) | |||||||
\(774\) | −22.2862 | − | 12.8669i | −0.801061 | − | 0.462493i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.5904 | − | 35.6636i | 0.739151 | − | 1.28025i | ||||
\(777\) | −10.2687 | − | 17.7860i | −0.368389 | − | 0.638069i | ||||
\(778\) | 67.8406 | − | 39.1678i | 2.43220 | − | 1.40423i | ||||
\(779\) | −40.8630 | −1.46407 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.48980 | 0.160658 | ||||||||
\(782\) | 8.22365 | − | 4.74793i | 0.294077 | − | 0.169786i | ||||
\(783\) | −1.97844 | − | 3.42676i | −0.0707036 | − | 0.122462i | ||||
\(784\) | 11.0145 | − | 19.0776i | 0.393374 | − | 0.681344i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.3343 | + | 11.1627i | 0.689633 | + | 0.398160i | ||||
\(787\) | 17.7335 | + | 10.2385i | 0.632133 | + | 0.364962i | 0.781578 | − | 0.623808i | \(-0.214415\pi\) |
−0.149445 | + | 0.988770i | \(0.547749\pi\) | |||||||
\(788\) | − | 88.0918i | − | 3.13814i | ||||||
\(789\) | −1.69847 | + | 2.94183i | −0.0604670 | + | 0.104732i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.36706 | − | 3.67603i | 0.226387 | − | 0.130704i | ||||
\(792\) | −16.0509 | −0.570342 | ||||||||
\(793\) | −21.8837 | − | 38.9981i | −0.777113 | − | 1.38486i | ||||
\(794\) | 17.7041 | 0.628296 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −46.3522 | − | 80.2843i | −1.64291 | − | 2.84560i | ||||
\(797\) | 12.2660 | − | 21.2453i | 0.434484 | − | 0.752548i | −0.562770 | − | 0.826614i | \(-0.690264\pi\) |
0.997253 | + | 0.0740660i | \(0.0235975\pi\) | |||||||
\(798\) | 42.2919i | 1.49712i | ||||||||
\(799\) | 6.81850 | + | 3.93666i | 0.241221 | + | 0.139269i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.85351i | − | 0.242157i | ||||||
\(802\) | −4.02986 | + | 6.97992i | −0.142299 | + | 0.246470i | ||||
\(803\) | 13.9566 | + | 24.1736i | 0.492519 | + | 0.853067i | ||||
\(804\) | 32.5770 | − | 18.8083i | 1.14890 | − | 0.663318i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.10058 | + | 0.0624194i | 0.179660 | + | 0.00219863i | ||||
\(807\) | 15.3367 | 0.539878 | ||||||||
\(808\) | −18.1932 | + | 10.5039i | −0.640036 | + | 0.369525i | ||||
\(809\) | −8.38808 | − | 14.5286i | −0.294909 | − | 0.510798i | 0.680055 | − | 0.733161i | \(-0.261956\pi\) |
−0.974964 | + | 0.222364i | \(0.928623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 50.7808i | − | 1.78315i | −0.452869 | − | 0.891577i | \(-0.649600\pi\) | ||
0.452869 | − | 0.891577i | \(-0.350400\pi\) | |||||||
\(812\) | −55.6084 | − | 32.1055i | −1.95147 | − | 1.12668i | ||||
\(813\) | 15.8495 | + | 9.15070i | 0.555865 | + | 0.320929i | ||||
\(814\) | 46.1583i | 1.61785i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.46227 | − | 7.72888i | −0.156211 | − | 0.270565i | ||||
\(817\) | 37.2336 | − | 21.4969i | 1.30264 | − | 0.752080i | ||||
\(818\) | 34.4916 | 1.20597 | ||||||||
\(819\) | 0.200441 | − | 16.3790i | 0.00700397 | − | 0.572328i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.62188 | − | 3.82315i | 0.231105 | − | 0.133429i | −0.379977 | − | 0.924996i | \(-0.624068\pi\) |
0.611082 | + | 0.791567i | \(0.290735\pi\) | |||||||
\(822\) | −2.70326 | − | 4.68219i | −0.0942871 | − | 0.163310i | ||||
\(823\) | 2.54563 | − | 4.40916i | 0.0887351 | − | 0.153694i | −0.818242 | − | 0.574874i | \(-0.805051\pi\) |
0.906977 | + | 0.421181i | \(0.138384\pi\) | |||||||
\(824\) | 12.0734i | 0.420596i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −104.189 | − | 60.1535i | −3.62520 | − | 2.09301i | ||||
\(827\) | 47.2400i | 1.64270i | 0.570426 | + | 0.821349i | \(0.306778\pi\) | ||||
−0.570426 | + | 0.821349i | \(0.693222\pi\) | |||||||
\(828\) | −1.30024 | + | 2.25209i | −0.0451865 | + | 0.0782654i | ||||
\(829\) | 5.70266 | + | 9.87730i | 0.198062 | + | 0.343053i | 0.947900 | − | 0.318568i | \(-0.103202\pi\) |
−0.749838 | + | 0.661621i | \(0.769869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.80083 | 0.270608 | ||||||||
\(832\) | −21.6282 | + | 36.4244i | −0.749822 | + | 1.26279i | ||||
\(833\) | −75.3662 | −2.61128 | ||||||||
\(834\) | 17.1165 | − | 9.88224i | 0.592698 | − | 0.342194i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.4669 | − | 52.7703i | 1.05372 | − | 1.82510i | ||||
\(837\) | 0.599343i | 0.0207163i | ||||||||
\(838\) | −6.96103 | − | 4.01895i | −0.240465 | − | 0.138832i | ||||
\(839\) | 23.5533 | + | 13.5985i | 0.813151 | + | 0.469473i | 0.848049 | − | 0.529918i | \(-0.177777\pi\) |
−0.0348977 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.67156 | − | 11.5555i | 0.230054 | − | 0.398465i | ||||
\(842\) | −17.5865 | − | 30.4608i | −0.606072 | − | 1.04975i | ||||
\(843\) | −20.1150 | + | 11.6134i | −0.692796 | + | 0.399986i | ||||
\(844\) | −41.2402 | −1.41955 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.36340 | −0.115636 | ||||||||
\(847\) | 30.3368 | − | 17.5150i | 1.04239 | − | 0.601822i | ||||
\(848\) | 0.650404 | + | 1.12653i | 0.0223350 | + | 0.0386853i | ||||
\(849\) | −3.92173 | + | 6.79264i | −0.134593 | + | 0.233123i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.85020 | + | 1.64556i | 0.0977036 | + | 0.0564092i | ||||
\(852\) | −3.21087 | − | 1.85379i | −0.110002 | − | 0.0635100i | ||||
\(853\) | 29.5962i | 1.01335i | 0.862136 | + | 0.506677i | \(0.169126\pi\) | ||||
−0.862136 | + | 0.506677i | \(0.830874\pi\) | |||||||
\(854\) | 66.5025 | − | 115.186i | 2.27567 | − | 3.94158i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.6465 | + | 26.9314i | −1.59434 | + | 0.920495i | ||||
\(857\) | 23.3137 | 0.796382 | 0.398191 | − | 0.917302i | \(-0.369638\pi\) | ||||
0.398191 | + | 0.917302i | \(0.369638\pi\) | |||||||
\(858\) | −18.7961 | + | 31.6548i | −0.641689 | + | 1.08068i | ||||
\(859\) | 46.6719 | 1.59242 | 0.796212 | − | 0.605018i | \(-0.206834\pi\) | ||||
0.796212 | + | 0.605018i | \(0.206834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.5366 | + | 40.7666i | 0.802125 | + | 1.38932i | ||||
\(862\) | −6.54645 | + | 11.3388i | −0.222973 | + | 0.386200i | ||||
\(863\) | − | 52.3597i | − | 1.78234i | −0.453665 | − | 0.891172i | \(-0.649884\pi\) | ||
0.453665 | − | 0.891172i | \(-0.350116\pi\) | |||||||
\(864\) | −3.12539 | − | 1.80444i | −0.106328 | − | 0.0613884i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.6514i | 1.00759i | ||||||||
\(867\) | −6.76647 | + | 11.7199i | −0.229802 | + | 0.398028i | ||||
\(868\) | 4.86298 | + | 8.42293i | 0.165060 | + | 0.285893i | ||||
\(869\) | 15.8107 | − | 9.12833i | 0.536343 | − | 0.309658i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.464632 | − | 37.9673i | 0.0157435 | − | 1.28647i | ||||
\(872\) | 8.32362 | 0.281873 | ||||||||
\(873\) | 9.61107 | − | 5.54895i | 0.325285 | − | 0.187804i | ||||
\(874\) | −3.38863 | − | 5.86928i | −0.114622 | − | 0.198531i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 23.0502i | − | 0.778795i | ||||||
\(877\) | 13.6960 | + | 7.90738i | 0.462480 | + | 0.267013i | 0.713087 | − | 0.701076i | \(-0.247297\pi\) |
−0.250606 | + | 0.968089i | \(0.580630\pi\) | |||||||
\(878\) | 60.4839 | + | 34.9204i | 2.04123 | + | 1.17851i | ||||
\(879\) | 10.2805i | 0.346751i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4105 | + | 37.0841i | 0.721338 | + | 1.24939i | 0.960464 | + | 0.278406i | \(0.0898059\pi\) |
−0.239126 | + | 0.970989i | \(0.576861\pi\) | |||||||
\(882\) | 27.8822 | − | 16.0978i | 0.938844 | − | 0.542042i | ||||
\(883\) | 18.5133 | 0.623024 | 0.311512 | − | 0.950242i | \(-0.399165\pi\) | ||||
0.311512 | + | 0.950242i | \(0.399165\pi\) | |||||||
\(884\) | −71.1595 | − | 0.870829i | −2.39335 | − | 0.0292892i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −60.7044 | + | 35.0477i | −2.03941 | + | 1.17745i | ||||
\(887\) | 16.6949 | + | 28.9164i | 0.560560 | + | 0.970919i | 0.997448 | + | 0.0714024i | \(0.0227474\pi\) |
−0.436888 | + | 0.899516i | \(0.643919\pi\) | |||||||
\(888\) | 8.38732 | − | 14.5273i | 0.281460 | − | 0.487503i | ||||
\(889\) | 84.7775i | 2.84335i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.74607 | − | 2.16279i | −0.125498 | − | 0.0724562i | ||||
\(892\) | 29.0126i | 0.971414i | ||||||||
\(893\) | 2.80962 | − | 4.86641i | 0.0940205 | − | 0.162848i | ||||
\(894\) | 26.9779 | + | 46.7272i | 0.902277 | + | 1.56279i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −93.2045 | −3.11374 | ||||||||
\(897\) | 1.28455 | + | 2.28914i | 0.0428897 | + | 0.0764321i | ||||
\(898\) | 26.0403 | 0.868977 | ||||||||
\(899\) | 2.05380 | − | 1.18576i | 0.0684981 | − | 0.0395474i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.22519 | − | 3.85413i | 0.0741317 | − | 0.128400i | ||||
\(902\) | − | 105.798i | − | 3.52267i | ||||||
\(903\) | −42.8922 | − | 24.7638i | −1.42736 | − | 0.824089i | ||||
\(904\) | 5.20050 | + | 3.00251i | 0.172966 | + | 0.0998620i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.5870 | − | 30.4617i | 0.584291 | − | 1.01202i | ||||
\(907\) | −16.5197 | − | 28.6130i | −0.548528 | − | 0.950078i | −0.998376 | − | 0.0569728i | \(-0.981855\pi\) |
0.449848 | − | 0.893105i | \(-0.351478\pi\) | |||||||
\(908\) | −42.0302 | + | 24.2661i | −1.39482 | + | 0.805300i | ||||
\(909\) | −5.66143 | −0.187778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.00701 | −0.232153 | −0.116076 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116076 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(912\) | −5.51616 | + | 3.18476i | −0.182658 | + | 0.105458i | ||||
\(913\) | −16.6458 | − | 28.8313i | −0.550894 | − | 0.954176i | ||||
\(914\) | −16.8020 | + | 29.1019i | −0.555760 | + | 0.962604i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.1686 | + | 6.44819i | 0.369021 | + | 0.213054i | ||||
\(917\) | 37.2110 | + | 21.4838i | 1.22882 | + | 0.709458i | ||||
\(918\) | − | 13.0434i | − | 0.430495i | ||||||
\(919\) | −5.28827 | + | 9.15956i | −0.174444 | + | 0.302146i | −0.939969 | − | 0.341261i | \(-0.889146\pi\) |
0.765525 | + | 0.643406i | \(0.222479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.2767 | + | 16.9029i | −0.964701 | + | 0.556970i | ||||
\(922\) | 52.7721 | 1.73796 | ||||||||
\(923\) | −3.26369 | + | 1.83141i | −0.107426 | + | 0.0602818i | ||||
\(924\) | −70.1943 | −2.30922 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −35.3742 | − | 61.2698i | −1.16247 | − | 2.01345i | ||||
\(927\) | −1.62684 | + | 2.81777i | −0.0534325 | + | 0.0925478i | ||||
\(928\) | 14.2799i | 0.468762i | ||||||||
\(929\) | −12.6230 | − | 7.28788i | −0.414147 | − | 0.239108i | 0.278423 | − | 0.960459i | \(-0.410188\pi\) |
−0.692570 | + | 0.721351i | \(0.743522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.7894i | 1.76288i | ||||||||
\(932\) | 51.2314 | − | 88.7354i | 1.67814 | − | 2.90663i | ||||
\(933\) | 0.143386 | + | 0.248351i | 0.00469424 | + | 0.00813066i | ||||
\(934\) | 35.4864 | − | 20.4881i | 1.16115 | − | 0.670391i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.6676 | − | 6.54724i | 0.381367 | − | 0.214003i | ||||
\(937\) | 2.03451 | 0.0664644 | 0.0332322 | − | 0.999448i | \(-0.489420\pi\) | ||||
0.0332322 | + | 0.999448i | \(0.489420\pi\) | |||||||
\(938\) | 97.8033 | − | 56.4668i | 3.19339 | − | 1.84370i | ||||
\(939\) | 13.9171 | + | 24.1051i | 0.454166 | + | 0.786639i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6270i | 0.509424i | 0.967017 | + | 0.254712i | \(0.0819807\pi\) | ||||
−0.967017 | + | 0.254712i | \(0.918019\pi\) | |||||||
\(942\) | 1.01355 | + | 0.585173i | 0.0330232 | + | 0.0190660i | ||||
\(943\) | −6.53283 | − | 3.77173i | −0.212738 | − | 0.122824i | ||||
\(944\) | − | 18.1192i | − | 0.589731i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 55.6570 | + | 96.4008i | 1.80957 | + | 3.13426i | ||||
\(947\) | −30.4622 | + | 17.5874i | −0.989890 | + | 0.571513i | −0.905241 | − | 0.424898i | \(-0.860310\pi\) |
−0.0846485 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(948\) | −15.0760 | −0.489646 | ||||||||
\(949\) | −20.0058 | − | 11.8791i | −0.649416 | − | 0.385612i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.4498 | + | 11.8067i | −0.663130 | + | 0.382858i | ||||
\(952\) | −46.5753 | − | 80.6707i | −1.50951 | − | 2.61455i | ||||
\(953\) | −1.59492 | + | 2.76248i | −0.0516645 | + | 0.0894855i | −0.890701 | − | 0.454589i | \(-0.849786\pi\) |
0.839037 | + | 0.544075i | \(0.183119\pi\) | |||||||
\(954\) | 1.90115i | 0.0615521i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.19939 | + | 3.57922i | 0.200503 | + | 0.115760i | ||||
\(957\) | 17.1158i | 0.553275i | ||||||||
\(958\) | 12.0706 | − | 20.9069i | 0.389983 | − | 0.675470i | ||||
\(959\) | −5.20272 | − | 9.01138i | −0.168005 | − | 0.290993i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.6408 | 0.988413 | ||||||||
\(962\) | −18.8282 | − | 33.5531i | −0.607047 | − | 1.08179i | ||||
\(963\) | −14.5156 | −0.467759 | ||||||||
\(964\) | 87.5710 | − | 50.5591i | 2.82047 | − | 1.62840i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.90362 | + | 6.76126i | −0.125597 | + | 0.217540i | ||||
\(967\) | − | 19.5885i | − | 0.629925i | −0.949104 | − | 0.314962i | \(-0.898008\pi\) | ||
0.949104 | − | 0.314962i | \(-0.101992\pi\) | |||||||
\(968\) | 24.7786 | + | 14.3059i | 0.796414 | + | 0.459810i | ||||
\(969\) | 18.8721 | + | 10.8958i | 0.606258 | + | 0.350023i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.75194 | − | 16.8909i | 0.312955 | − | 0.542053i | −0.666046 | − | 0.745911i | \(-0.732015\pi\) |
0.979001 | + | 0.203857i | \(0.0653479\pi\) | |||||||
\(972\) | 1.78599 | + | 3.09343i | 0.0572857 | + | 0.0992218i | ||||
\(973\) | 32.9427 | − | 19.0195i | 1.05609 | − | 0.609736i | ||||
\(974\) | −38.8842 | −1.24593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.0317 | 0.641198 | ||||||||
\(977\) | −9.84958 | + | 5.68666i | −0.315116 | + | 0.181932i | −0.649213 | − | 0.760606i | \(-0.724902\pi\) |
0.334098 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(978\) | −2.02888 | − | 3.51412i | −0.0648763 | − | 0.112369i | ||||
\(979\) | −14.8227 | + | 25.6737i | −0.473736 | + | 0.820535i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.94263 | + | 1.12158i | 0.0620233 | + | 0.0358092i | ||||
\(982\) | −58.4278 | − | 33.7333i | −1.86451 | − | 1.07647i | ||||
\(983\) | − | 29.0243i | − | 0.925732i | −0.886428 | − | 0.462866i | \(-0.846821\pi\) | ||
0.886428 | − | 0.462866i | \(-0.153179\pi\) | |||||||
\(984\) | −19.2243 | + | 33.2974i | −0.612847 | + | 1.06148i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −44.6964 | + | 25.8055i | −1.42342 | + | 0.821814i | ||||
\(987\) | −6.47323 | −0.206045 | ||||||||
\(988\) | −0.621517 | + | 50.7871i | −0.0197731 | + | 1.61575i | ||||
\(989\) | 7.93679 | 0.252375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.12446 | + | 8.87583i | 0.162784 | + | 0.281950i | 0.935866 | − | 0.352356i | \(-0.114619\pi\) |
−0.773082 | + | 0.634306i | \(0.781286\pi\) | |||||||
\(992\) | 1.08148 | − | 1.87318i | 0.0343371 | − | 0.0594735i | ||||
\(993\) | − | 5.21879i | − | 0.165613i | ||||||
\(994\) | −9.63973 | − | 5.56550i | −0.305754 | − | 0.176527i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.4915i | 0.871101i | ||||||||
\(997\) | −7.24112 | + | 12.5420i | −0.229328 | + | 0.397209i | −0.957609 | − | 0.288070i | \(-0.906986\pi\) |
0.728281 | + | 0.685279i | \(0.240320\pi\) | |||||||
\(998\) | −17.2916 | − | 29.9499i | −0.547356 | − | 0.948048i | ||||
\(999\) | 3.91499 | − | 2.26032i | 0.123865 | − | 0.0715134i |
(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 | 975.2.bc.k.751.1 | ✓ | 12 | |
5.2 | odd | 4 | 975.2.w.k.49.2 | 24 | |||
5.3 | odd | 4 | 975.2.w.k.49.11 | 24 | |||
5.4 | even | 2 | 975.2.bc.l.751.6 | yes | 12 | ||
13.4 | even | 6 | inner | 975.2.bc.k.901.1 | yes | 12 | |
65.4 | even | 6 | 975.2.bc.l.901.6 | yes | 12 | ||
65.17 | odd | 12 | 975.2.w.k.199.11 | 24 | |||
65.43 | odd | 12 | 975.2.w.k.199.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.w.k.49.2 | 24 | 5.2 | odd | 4 | |||
975.2.w.k.49.11 | 24 | 5.3 | odd | 4 | |||
975.2.w.k.199.2 | 24 | 65.43 | odd | 12 | |||
975.2.w.k.199.11 | 24 | 65.17 | odd | 12 | |||
975.2.bc.k.751.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
975.2.bc.k.901.1 | yes | 12 | 13.4 | even | 6 | inner | |
975.2.bc.l.751.6 | yes | 12 | 5.4 | even | 2 | ||
975.2.bc.l.901.6 | yes | 12 | 65.4 | even | 6 |