LMFDB - Embedded newform 891.2.n.l.433.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			433.9
Character	$\chi$	$=$	891.433
Dual form			891.2.n.l.784.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142582 - 1.35658i) q^{2} +(0.136314 + 0.0289745i) q^{4} +(-0.217145 - 2.06600i) q^{5} +(-0.0694102 + 0.0770878i) q^{7} +(0.901773 - 2.77537i) q^{8} +O(q^{10})$	\(q+(0.142582 - 1.35658i) q^{2} +(0.136314 + 0.0289745i) q^{4} +(-0.217145 - 2.06600i) q^{5} +(-0.0694102 + 0.0770878i) q^{7} +(0.901773 - 2.77537i) q^{8} -2.83366 q^{10} +(1.05164 - 3.14548i) q^{11} +(-6.05306 + 2.69500i) q^{13} +(0.0946792 + 0.105152i) q^{14} +(-3.38182 - 1.50568i) q^{16} +(-3.06899 + 2.22975i) q^{17} +(2.03958 - 6.27717i) q^{19} +(0.0302613 - 0.287917i) q^{20} +(-4.11715 - 1.87512i) q^{22} +(-1.29054 + 2.23528i) q^{23} +(0.669535 - 0.142314i) q^{25} +(2.79292 + 8.59573i) q^{26} +(-0.0116952 + 0.00849706i) q^{28} +(6.66090 - 7.39768i) q^{29} +(-2.01179 + 0.895705i) q^{31} +(0.393434 - 0.681448i) q^{32} +(2.58725 + 4.48125i) q^{34} +(0.174336 + 0.126662i) q^{35} +(1.00747 + 3.10068i) q^{37} +(-8.22468 - 3.66186i) q^{38} +(-5.92974 - 1.26040i) q^{40} +(-0.959724 - 1.06588i) q^{41} +(-1.91062 - 3.30930i) q^{43} +(0.234492 - 0.398304i) q^{44} +(2.84833 + 2.06943i) q^{46} +(-3.36031 + 0.714255i) q^{47} +(0.730574 + 6.95095i) q^{49} +(-0.0975967 - 0.928570i) q^{50} +(-0.903206 + 0.191982i) q^{52} +(0.0511797 + 0.0371842i) q^{53} +(-6.72692 - 1.48966i) q^{55} +(0.151355 + 0.262155i) q^{56} +(-9.08582 - 10.0908i) q^{58} +(-6.81507 - 1.44859i) q^{59} +(3.87617 + 1.72578i) q^{61} +(0.928251 + 2.85686i) q^{62} +(-6.85808 - 4.98268i) q^{64} +(6.88226 + 11.9204i) q^{65} +(2.71656 - 4.70522i) q^{67} +(-0.482953 + 0.215025i) q^{68} +(0.196685 - 0.218440i) q^{70} +(9.57016 - 6.95313i) q^{71} +(-3.78107 - 11.6369i) q^{73} +(4.34996 - 0.924613i) q^{74} +(0.459902 - 0.796573i) q^{76} +(0.169484 + 0.299397i) q^{77} +(-1.62800 + 15.4894i) q^{79} +(-2.37639 + 7.31378i) q^{80} +(-1.58279 + 1.14997i) q^{82} +(4.49737 + 2.00236i) q^{83} +(5.27308 + 5.85635i) q^{85} +(-4.76175 + 2.12007i) q^{86} +(-7.78155 - 5.75520i) q^{88} -7.99493 q^{89} +(0.212393 - 0.653678i) q^{91} +(-0.240686 + 0.267309i) q^{92} +(0.489824 + 4.66037i) q^{94} +(-13.4115 - 2.85070i) q^{95} +(-0.323021 + 3.07334i) q^{97} +9.53369 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 8 q^{4} + 14 q^{7}+O(q^{10}) $ 96 * q + 8 * q^4 + 14 * q^7	$ 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52} - 72 q^{55} + 10 q^{58} + 6 q^{61} - 104 q^{64} - 76 q^{67} + 8 q^{70} - 92 q^{73} - 204 q^{76} + 102 q^{79} + 24 q^{82} - 54 q^{85} + 44 q^{91} + 118 q^{94} + 66 q^{97}+O(q^{100}) $ 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.142582	−	1.35658i	0.100821	−	0.959247i	−0.820816	−	0.571193i	$-0.806481\pi$
$2$	0.142582	−	1.35658i	0.100821	−	0.959247i	0.921637	−	0.388054i	$-0.126853\pi$
$3$		0			0
$3$		0			0
$4$	0.136314	+	0.0289745i	0.0681572	+	0.0144873i
$5$	−0.217145	−	2.06600i	−0.0971103	−	0.923943i	−0.929269	−	0.369405i	$-0.879562\pi$
$5$	−0.217145	−	2.06600i	−0.0971103	−	0.923943i	0.832158	−	0.554538i	$-0.187105\pi$
$6$		0			0
$7$	−0.0694102	+	0.0770878i	−0.0262346	+	0.0291365i	−0.756119	−	0.654434i	$-0.772907\pi$
$7$	−0.0694102	+	0.0770878i	−0.0262346	+	0.0291365i	0.729885	+	0.683570i	$0.239574\pi$
$8$	0.901773	−	2.77537i	0.318825	−	0.981243i
$9$		0			0
$10$	−2.83366			−0.896081
$11$	1.05164	−	3.14548i	0.317081	−	0.948399i
$11$	1.05164	−	3.14548i	0.317081	−	0.948399i
$12$		0			0
$13$	−6.05306	+	2.69500i	−1.67882	+	0.747458i	−0.678905	+	0.734226i	$0.737545\pi$
$13$	−6.05306	+	2.69500i	−1.67882	+	0.747458i	−0.999912	+	0.0132319i	$0.995788\pi$
$14$	0.0946792	+	0.105152i	0.0253041	+	0.0281030i
$15$		0			0
$16$	−3.38182	−	1.50568i	−0.845454	−	0.376420i
$17$	−3.06899	+	2.22975i	−0.744339	+	0.540794i	−0.894067	−	0.447933i	$-0.852160\pi$
$17$	−3.06899	+	2.22975i	−0.744339	+	0.540794i	0.149728	+	0.988727i	$0.452160\pi$
$18$		0			0
$19$	2.03958	−	6.27717i	0.467911	−	1.44008i	−0.387374	−	0.921923i	$-0.626618\pi$
$19$	2.03958	−	6.27717i	0.467911	−	1.44008i	0.855285	−	0.518158i	$-0.173382\pi$
$20$	0.0302613	−	0.287917i	0.00676664	−	0.0643803i
$21$		0			0
$22$	−4.11715	−	1.87512i	−0.877780	−	0.399777i
$23$	−1.29054	+	2.23528i	−0.269096	+	0.466089i	−0.968629	−	0.248512i	$-0.920058\pi$
$23$	−1.29054	+	2.23528i	−0.269096	+	0.466089i	0.699532	+	0.714601i	$0.253392\pi$
$24$		0			0
$25$	0.669535	−	0.142314i	0.133907	−	0.0284628i
$26$	2.79292	+	8.59573i	0.547737	+	1.68576i
$27$		0			0
$28$	−0.0116952	+	0.00849706i	−0.00221018	+	0.00160579i
$29$	6.66090	−	7.39768i	1.23690	−	1.37371i	0.334739	−	0.942311i	$-0.391352\pi$
$29$	6.66090	−	7.39768i	1.23690	−	1.37371i	0.902159	−	0.431404i	$-0.141981\pi$
$30$		0			0
$31$	−2.01179	+	0.895705i	−0.361327	+	0.160873i	−0.579367	−	0.815066i	$-0.696700\pi$
$31$	−2.01179	+	0.895705i	−0.361327	+	0.160873i	0.218040	+	0.975940i	$0.430034\pi$
$32$	0.393434	−	0.681448i	0.0695500	−	0.120464i
$33$		0			0
$34$	2.58725	+	4.48125i	0.443710	+	0.768528i
$35$	0.174336	+	0.126662i	0.0294681	+	0.0214098i
$36$		0			0
$37$	1.00747	+	3.10068i	0.165627	+	0.509748i	0.999082	−	0.0428396i	$-0.0136405\pi$
$37$	1.00747	+	3.10068i	0.165627	+	0.509748i	−0.833455	+	0.552588i	$0.813640\pi$
$38$	−8.22468	−	3.66186i	−1.33422	−	0.594032i
$39$		0			0
$40$	−5.92974	−	1.26040i	−0.937574	−	0.199287i
$41$	−0.959724	−	1.06588i	−0.149884	−	0.166463i	0.663527	−	0.748152i	$-0.269059\pi$
$41$	−0.959724	−	1.06588i	−0.149884	−	0.166463i	−0.813411	+	0.581689i	$0.802392\pi$
$42$		0			0
$43$	−1.91062	−	3.30930i	−0.291367	−	0.504663i	0.682766	−	0.730637i	$-0.260777\pi$
$43$	−1.91062	−	3.30930i	−0.291367	−	0.504663i	−0.974133	+	0.225974i	$0.927443\pi$
$44$	0.234492	−	0.398304i	0.0353511	−	0.0600466i
$45$		0			0
$46$	2.84833	+	2.06943i	0.419964	+	0.305121i
$47$	−3.36031	+	0.714255i	−0.490151	+	0.104185i	−0.446356	−	0.894856i	$-0.647278\pi$
$47$	−3.36031	+	0.714255i	−0.490151	+	0.104185i	−0.0437955	+	0.999041i	$0.513945\pi$
$48$		0			0
$49$	0.730574	+	6.95095i	0.104368	+	0.992993i
$50$	−0.0975967	−	0.928570i	−0.0138023	−	0.131320i
$51$		0			0
$52$	−0.903206	+	0.191982i	−0.125252	+	0.0266232i
$53$	0.0511797	+	0.0371842i	0.00703007	+	0.00510765i	0.591295	−	0.806456i	$-0.298617\pi$
$53$	0.0511797	+	0.0371842i	0.00703007	+	0.00510765i	−0.584265	+	0.811563i	$0.698617\pi$
$54$		0			0
$55$	−6.72692	−	1.48966i	−0.907058	−	0.200865i
$56$	0.151355	+	0.262155i	0.0202257	+	0.0350319i
$57$		0			0
$58$	−9.08582	−	10.0908i	−1.19303	−	1.32499i
$59$	−6.81507	−	1.44859i	−0.887246	−	0.188590i	−0.258324	−	0.966058i	$-0.583170\pi$
$59$	−6.81507	−	1.44859i	−0.887246	−	0.188590i	−0.628922	+	0.777468i	$0.716504\pi$
$60$		0			0
$61$	3.87617	+	1.72578i	0.496293	+	0.220964i	0.639590	−	0.768716i	$-0.279104\pi$
$61$	3.87617	+	1.72578i	0.496293	+	0.220964i	−0.143298	+	0.989680i	$0.545771\pi$
$62$	0.928251	+	2.85686i	0.117888	+	0.362822i
$63$		0			0
$64$	−6.85808	−	4.98268i	−0.857259	−	0.622835i
$65$	6.88226	+	11.9204i	0.853639	+	1.47855i
$66$		0			0
$67$	2.71656	−	4.70522i	0.331880	−	0.574834i	−0.651000	−	0.759078i	$-0.725650\pi$
$67$	2.71656	−	4.70522i	0.331880	−	0.574834i	0.982881	+	0.184244i	$0.0589837\pi$
$68$	−0.482953	+	0.215025i	−0.0585667	+	0.0260756i
$69$		0			0
$70$	0.196685	−	0.218440i	0.0235083	−	0.0261086i
$71$	9.57016	−	6.95313i	1.13577	−	0.825185i	0.149245	−	0.988800i	$-0.452316\pi$
$71$	9.57016	−	6.95313i	1.13577	−	0.825185i	0.986524	+	0.163616i	$0.0523157\pi$
$72$		0			0
$73$	−3.78107	−	11.6369i	−0.442540	−	1.36200i	−0.885159	−	0.465289i	$-0.845950\pi$
$73$	−3.78107	−	11.6369i	−0.442540	−	1.36200i	0.442618	−	0.896710i	$-0.354050\pi$
$74$	4.34996	−	0.924613i	0.505673	−	0.107484i
$75$		0			0
$76$	0.459902	−	0.796573i	0.0527543	−	0.0913732i
$77$	0.169484	+	0.299397i	0.0193145	+	0.0341195i
$78$		0			0
$79$	−1.62800	+	15.4894i	−0.183165	+	1.74270i	0.387820	+	0.921735i	$0.373228\pi$
$79$	−1.62800	+	15.4894i	−0.183165	+	1.74270i	−0.570984	+	0.820961i	$0.693438\pi$
$80$	−2.37639	+	7.31378i	−0.265689	+	0.817706i
$81$		0			0
$82$	−1.58279	+	1.14997i	−0.174790	+	0.126993i
$83$	4.49737	+	2.00236i	0.493650	+	0.219787i	0.638435	−	0.769676i	$-0.279582\pi$
$83$	4.49737	+	2.00236i	0.493650	+	0.219787i	−0.144784	+	0.989463i	$0.546249\pi$
$84$		0			0
$85$	5.27308	+	5.85635i	0.571946	+	0.635210i
$86$	−4.76175	+	2.12007i	−0.513472	+	0.228613i
$87$		0			0
$88$	−7.78155	−	5.75520i	−0.829516	−	0.613506i
$89$	−7.99493			−0.847461			−0.423731	−	0.905788i	$-0.639280\pi$
$89$	−7.99493			−0.847461			−0.423731	+	0.905788i	$0.639280\pi$
$90$		0			0
$91$	0.212393	−	0.653678i	0.0222648	−	0.0685240i
$92$	−0.240686	+	0.267309i	−0.0250932	+	0.0278688i
$93$		0			0
$94$	0.489824	+	4.66037i	0.0505215	+	0.480680i
$95$	−13.4115	−	2.85070i	−1.37599	−	0.292476i
$96$		0			0
$97$	−0.323021	+	3.07334i	−0.0327978	+	0.312050i	0.965808	+	0.259259i	$0.0834784\pi$
$97$	−0.323021	+	3.07334i	−0.0327978	+	0.312050i	−0.998606	+	0.0527910i	$0.983188\pi$
$98$	9.53369			0.963048
$99$		0			0
$100$	0.0953908			0.00953908
$101$	0.261096	−	2.48416i	0.0259800	−	0.247183i	−0.973822	−	0.227310i	$-0.927007\pi$
$101$	0.261096	−	2.48416i	0.0259800	−	0.247183i	0.999803	−	0.0198736i	$-0.00632637\pi$
$102$		0			0
$103$	13.8417	+	2.94215i	1.36386	+	0.289898i	0.830986	−	0.556294i	$-0.187777\pi$
$103$	13.8417	+	2.94215i	1.36386	+	0.289898i	0.532878	+	0.846192i	$0.321110\pi$
$104$	2.02113	+	19.2298i	0.198188	+	1.88564i
$105$		0			0
$106$	0.0577407	−	0.0641276i	0.00560827	−	0.00622862i
$107$	1.56194	−	4.80716i	0.150999	−	0.464726i	−0.846735	−	0.532015i	$-0.821435\pi$
$107$	1.56194	−	4.80716i	0.150999	−	0.464726i	0.997734	+	0.0672891i	$0.0214350\pi$
$108$		0			0
$109$	16.0865			1.54081			0.770403	−	0.637557i	$-0.220055\pi$
$109$	16.0865			1.54081			0.770403	+	0.637557i	$0.220055\pi$
$110$	−2.97998	+	8.91321i	−0.284130	+	0.849842i
$111$		0			0
$112$	0.350802	−	0.156187i	0.0331477	−	0.0147583i
$113$	6.82611	+	7.58117i	0.642147	+	0.713176i	0.973077	−	0.230479i	$-0.0740293\pi$
$113$	6.82611	+	7.58117i	0.642147	+	0.713176i	−0.330931	+	0.943655i	$0.607363\pi$
$114$		0			0
$115$	4.89833	+	2.18088i	0.456771	+	0.203368i
$116$	1.12232	−	0.815414i	0.104205	−	0.0757093i
$117$		0			0
$118$	−2.93683	+	9.03865i	−0.270358	+	0.832075i
$119$	0.0411324	−	0.391349i	0.00377060	−	0.0358749i
$120$		0			0
$121$	−8.78811	−	6.61582i	−0.798919	−	0.601438i
$122$	2.89383	−	5.01227i	0.261995	−	0.453789i
$123$		0			0
$124$	−0.300188	+	0.0638070i	−0.0269577	+	0.00573003i
$125$	−3.64914	−	11.2309i	−0.326389	−	1.00452i
$126$		0			0
$127$	−2.76775	+	2.01089i	−0.245598	+	0.178438i	−0.703774	−	0.710424i	$-0.748503\pi$
$127$	−2.76775	+	2.01089i	−0.245598	+	0.178438i	0.458175	+	0.888862i	$0.348503\pi$
$128$	−6.68422	+	7.42358i	−0.590807	+	0.656158i
$129$		0			0
$130$	17.1523	−	7.63670i	1.50436	−	0.669782i
$131$	8.87522	−	15.3723i	0.775432	−	1.34309i	−0.159120	−	0.987259i	$-0.550866\pi$
$131$	8.87522	−	15.3723i	0.775432	−	1.34309i	0.934551	−	0.355828i	$-0.115801\pi$
$132$		0			0
$133$	0.342326	+	0.592926i	0.0296834	+	0.0514132i
$134$	−5.99567	−	4.35611i	−0.517947	−	0.376311i
$135$		0			0
$136$	3.42086	+	10.5283i	0.293336	+	0.902796i
$137$	7.95851	+	3.54336i	0.679941	+	0.302729i	0.717493	−	0.696565i	$-0.245289\pi$
$137$	7.95851	+	3.54336i	0.679941	+	0.302729i	−0.0375520	+	0.999295i	$0.511956\pi$
$138$		0			0
$139$	3.74459	+	0.795938i	0.317612	+	0.0675105i	0.363959	−	0.931415i	$-0.381425\pi$
$139$	3.74459	+	0.795938i	0.317612	+	0.0675105i	−0.0463472	+	0.998925i	$0.514758\pi$
$140$	0.0200945	+	0.0223172i	0.00169829	+	0.00188615i
$141$		0			0
$142$	−8.06794	−	13.9741i	−0.677047	−	1.17268i
$143$	2.11143	+	21.8740i	0.176567	+	1.82919i
$144$		0			0
$145$	−16.7300	−	12.1550i	−1.38935	−	1.00942i
$146$	−16.3255	+	3.47010i	−1.35111	+	0.287188i
$147$		0			0
$148$	0.0474922	+	0.451858i	0.00390383	+	0.0371425i
$149$	−1.08256	−	10.2999i	−0.0886867	−	0.843797i	−0.944941	−	0.327242i	$-0.893881\pi$
$149$	−1.08256	−	10.2999i	−0.0886867	−	0.843797i	0.856254	−	0.516555i	$-0.172786\pi$
$150$		0			0
$151$	9.79665	−	2.08234i	0.797240	−	0.169459i	0.208757	−	0.977968i	$-0.433058\pi$
$151$	9.79665	−	2.08234i	0.797240	−	0.169459i	0.588484	+	0.808509i	$0.299725\pi$
$152$	−15.5822	−	11.3212i	−1.26389	−	0.918268i
$153$		0			0
$154$	0.430321	−	0.187230i	0.0346763	−	0.0150874i
$155$	2.28738	+	3.96185i	0.183726	+	0.318224i
$156$		0			0
$157$	7.76202	+	8.62060i	0.619477	+	0.687999i	0.968471	−	0.249126i	$-0.0801434\pi$
$157$	7.76202	+	8.62060i	0.619477	+	0.687999i	−0.348994	+	0.937125i	$0.613477\pi$
$158$	20.7805	+	4.41704i	1.65321	+	0.351401i
$159$		0			0
$160$	−1.49330	−	0.664861i	−0.118056	−	0.0525619i
$161$	−0.0827364	−	0.254636i	−0.00652054	−	0.0200682i
$162$		0			0
$163$	18.4433	+	13.3999i	1.44459	+	1.04956i	0.987057	+	0.160368i	$0.0512682\pi$
$163$	18.4433	+	13.3999i	1.44459	+	1.04956i	0.457537	+	0.889191i	$0.348732\pi$
$164$	−0.0999408	−	0.173103i	−0.00780406	−	0.0135170i
$165$		0			0
$166$	3.35760	−	5.81554i	0.260601	−	0.451374i
$167$	−4.17473	+	1.85871i	−0.323051	+	0.143831i	−0.561854	−	0.827237i	$-0.689912\pi$
$167$	−4.17473	+	1.85871i	−0.323051	+	0.143831i	0.238803	+	0.971068i	$0.423245\pi$
$168$		0			0
$169$	20.6779	−	22.9651i	1.59061	−	1.76655i
$170$	8.69645	−	6.31834i	0.666988	−	0.484595i
$171$		0			0
$172$	−0.164560	−	0.506464i	−0.0125476	−	0.0386175i
$173$	−1.46744	+	0.311914i	−0.111567	+	0.0237144i	−0.263357	−	0.964698i	$-0.584830\pi$
$173$	−1.46744	+	0.311914i	−0.111567	+	0.0237144i	0.151790	+	0.988413i	$0.451496\pi$
$174$		0			0
$175$	−0.0355019	+	0.0614911i	−0.00268369	+	0.00464829i
$176$	−8.29254	+	9.05401i	−0.625074	+	0.682472i
$177$		0			0
$178$	−1.13994	+	10.8458i	−0.0854418	+	0.812925i
$179$	−2.76184	+	8.50007i	−0.206430	+	0.635325i	0.793222	+	0.608933i	$0.208402\pi$
$179$	−2.76184	+	8.50007i	−0.206430	+	0.635325i	−0.999652	+	0.0263926i	$0.991598\pi$
$180$		0			0
$181$	−16.9613	+	12.3231i	−1.26072	+	0.915967i	−0.998793	−	0.0491209i	$-0.984358\pi$
$181$	−16.9613	+	12.3231i	−1.26072	+	0.915967i	−0.261927	+	0.965088i	$0.584358\pi$
$182$	−0.856483	−	0.381331i	−0.0634867	−	0.0282661i
$183$		0			0
$184$	5.03997	+	5.59745i	0.371551	+	0.412650i
$185$	6.18723	−	2.75473i	0.454894	−	0.202532i
$186$		0			0
$187$	3.78617	+	11.9983i	0.276872	+	0.877405i
$188$	−0.478754			−0.0349167
$189$		0			0
$190$	−5.77945	+	17.7873i	−0.419286	+	1.29043i
$191$	−5.98365	+	6.64552i	−0.432962	+	0.480853i	−0.919659	−	0.392718i	$-0.871535\pi$
$191$	−5.98365	+	6.64552i	−0.432962	+	0.480853i	0.486697	+	0.873571i	$0.338202\pi$
$192$		0			0
$193$	−0.597769	−	5.68739i	−0.0430284	−	0.409388i	−0.994743	−	0.102403i	$-0.967347\pi$
$193$	−0.597769	−	5.68739i	−0.0430284	−	0.409388i	0.951715	−	0.306984i	$-0.0993199\pi$
$194$	4.12317	+	0.876407i	0.296027	+	0.0629224i
$195$		0			0
$196$	−0.101813	+	0.968683i	−0.00727234	+	0.0691917i
$197$	6.94318			0.494681			0.247341	−	0.968929i	$-0.420443\pi$
$197$	6.94318			0.494681			0.247341	+	0.968929i	$0.420443\pi$
$198$		0			0
$199$	24.0199			1.70273			0.851363	−	0.524576i	$-0.175776\pi$
$199$	24.0199			1.70273			0.851363	+	0.524576i	$0.175776\pi$
$200$	0.208794	−	1.98655i	0.0147640	−	0.140470i
$201$		0			0
$202$	−3.33274	−	0.708396i	−0.234491	−	0.0498425i
$203$	0.107937	+	1.02695i	0.00757567	+	0.0720777i
$204$		0			0
$205$	−1.99371	+	2.21424i	−0.139247	+	0.154649i
$206$	5.96484	−	18.3579i	0.415590	−	1.27905i
$207$		0			0
$208$	24.5282			1.70072
$209$	−17.5998	−	13.0168i	−1.21741	−	0.900388i
$210$		0			0
$211$	3.70310	−	1.64873i	0.254932	−	0.113503i	−0.275292	−	0.961361i	$-0.588775\pi$
$211$	3.70310	−	1.64873i	0.254932	−	0.113503i	0.530224	+	0.847858i	$0.322108\pi$
$212$	0.00589914	+	0.00655166i	0.000405154	+	0.000449970i
$213$		0			0
$214$	−6.29860	−	2.80432i	−0.430563	−	0.191699i
$215$	−6.42212	+	4.66594i	−0.437985	+	0.318215i
$216$		0			0
$217$	0.0705905	−	0.217255i	0.00479200	−	0.0147482i
$218$	2.29365	−	21.8226i	0.155346	−	1.47801i
$219$		0			0
$220$	−0.873815	−	0.397971i	−0.0589126	−	0.0268312i
$221$	12.5676	−	21.7677i	0.845389	−	1.46426i
$222$		0			0
$223$	9.90516	−	2.10541i	0.663299	−	0.140989i	0.136053	−	0.990702i	$-0.456558\pi$
$223$	9.90516	−	2.10541i	0.663299	−	0.140989i	0.527246	+	0.849713i	$0.323225\pi$
$224$	0.0252230	+	0.0776284i	0.00168528	+	0.00518676i
$225$		0			0
$226$	11.2577	−	8.17923i	0.748854	−	0.544074i
$227$	4.37913	−	4.86351i	0.290653	−	0.322803i	−0.580080	−	0.814560i	$-0.696979\pi$
$227$	4.37913	−	4.86351i	0.290653	−	0.322803i	0.870732	+	0.491757i	$0.163645\pi$
$228$		0			0
$229$	14.1163	−	6.28497i	0.932830	−	0.415323i	0.116684	−	0.993169i	$-0.462773\pi$
$229$	14.1163	−	6.28497i	0.932830	−	0.415323i	0.816145	+	0.577846i	$0.196107\pi$
$230$	3.65695	−	6.33402i	0.241132	−	0.417653i
$231$		0			0
$232$	−14.5247	−	25.1575i	−0.953593	−	1.65167i
$233$	−17.2087	−	12.5028i	−1.12738	−	0.819087i	−0.142066	−	0.989857i	$-0.545375\pi$
$233$	−17.2087	−	12.5028i	−1.12738	−	0.819087i	−0.985311	+	0.170770i	$0.945375\pi$
$234$		0			0
$235$	2.20533	+	6.78730i	0.143860	+	0.442754i
$236$	−0.887020	−	0.394927i	−0.0577401	−	0.0257076i
$237$		0			0
$238$	−0.525032	−	0.111599i	−0.0340327	−	0.00723388i
$239$	11.6052	+	12.8889i	0.750679	+	0.833713i	0.990559	−	0.137090i	$-0.0437748\pi$
$239$	11.6052	+	12.8889i	0.750679	+	0.833713i	−0.239880	+	0.970803i	$0.577108\pi$
$240$		0			0
$241$	−5.32147	−	9.21705i	−0.342786	−	0.593722i	0.642163	−	0.766568i	$-0.278037\pi$
$241$	−5.32147	−	9.21705i	−0.342786	−	0.593722i	−0.984949	+	0.172846i	$0.944704\pi$
$242$	−10.2279	+	10.9785i	−0.657476	+	0.705724i
$243$		0			0
$244$	0.478374	+	0.347559i	0.0306248	+	0.0222502i
$245$	14.2020	−	3.01873i	0.907334	−	0.192860i
$246$		0			0
$247$	4.57127	+	43.4927i	0.290863	+	2.76738i
$248$	0.671740	+	6.39118i	0.0426555	+	0.405840i
$249$		0			0
$250$	−15.7559	+	3.34902i	−0.996491	+	0.211811i
$251$	−22.6506	−	16.4566i	−1.42969	−	1.03873i	−0.990074	−	0.140548i	$-0.955113\pi$
$251$	−22.6506	−	16.4566i	−1.42969	−	1.03873i	−0.439619	−	0.898184i	$-0.644887\pi$
$252$		0			0
$253$	5.67386	+	6.41008i	0.356712	+	0.402998i
$254$	2.33330	+	4.04140i	0.146404	+	0.253580i
$255$		0			0
$256$	−2.22688	−	2.47320i	−0.139180	−	0.154575i
$257$	17.5794	+	3.73662i	1.09657	+	0.233084i	0.720465	−	0.693492i	$-0.243929\pi$
$257$	17.5794	+	3.73662i	1.09657	+	0.233084i	0.376109	+	0.926575i	$0.377262\pi$
$258$		0			0
$259$	−0.308953	−	0.137555i	−0.0191974	−	0.00854724i
$260$	0.592763	+	1.82434i	0.0367616	+	0.113141i
$261$		0			0
$262$	−19.5884	−	14.2318i	−1.21017	−	0.879242i
$263$	6.88012	+	11.9167i	0.424247	+	0.734817i	0.996350	−	0.0853650i	$-0.0272056\pi$
$263$	6.88012	+	11.9167i	0.424247	+	0.734817i	−0.572103	+	0.820182i	$0.693872\pi$
$264$		0			0
$265$	0.0657092	−	0.113812i	0.00403648	−	0.00699139i
$266$	0.853161	−	0.379852i	0.0523107	−	0.0232902i
$267$		0			0
$268$	0.506637	−	0.562678i	0.0309478	−	0.0343710i
$269$	11.5788	−	8.41248i	0.705971	−	0.512918i	−0.175900	−	0.984408i	$-0.556284\pi$
$269$	11.5788	−	8.41248i	0.705971	−	0.512918i	0.881871	+	0.471490i	$0.156284\pi$
$270$		0			0
$271$	−0.475672	−	1.46397i	−0.0288950	−	0.0889296i	0.935569	−	0.353144i	$-0.114887\pi$
$271$	−0.475672	−	1.46397i	−0.0288950	−	0.0889296i	−0.964464	+	0.264214i	$0.914887\pi$
$272$	13.7360	−	2.91969i	0.832870	−	0.177032i
$273$		0			0
$274$	5.94159	−	10.2911i	0.358945	−	0.621711i
$275$	0.256462	−	2.25567i	0.0154653	−	0.136022i
$276$		0			0
$277$	2.49953	−	23.7815i	0.150182	−	1.42889i	−0.616748	−	0.787161i	$-0.711550\pi$
$277$	2.49953	−	23.7815i	0.150182	−	1.42889i	0.766931	−	0.641730i	$-0.221783\pi$
$278$	1.61367	−	4.96635i	0.0967813	−	0.297862i
$279$		0			0
$280$	0.508746	−	0.369625i	0.0304034	−	0.0220893i
$281$	−13.9692	−	6.21947i	−0.833330	−	0.371022i	−0.0546976	−	0.998503i	$-0.517419\pi$
$281$	−13.9692	−	6.21947i	−0.833330	−	0.371022i	−0.778632	+	0.627481i	$0.784086\pi$
$282$		0			0
$283$	13.7064	+	15.2225i	0.814762	+	0.904885i	0.996923	−	0.0783840i	$-0.0249760\pi$
$283$	13.7064	+	15.2225i	0.814762	+	0.904885i	−0.182161	+	0.983269i	$0.558309\pi$
$284$	1.50601	−	0.670521i	0.0893655	−	0.0397881i
$285$		0			0
$286$	29.9748	+	0.254512i	1.77245	+	0.0150496i
$287$	0.148781			0.00878227
$288$		0			0
$289$	−0.806389	+	2.48181i	−0.0474347	+	0.145989i
$290$	−18.8747	+	20.9625i	−1.10836	+	1.23096i
$291$		0			0
$292$	−0.178240	−	1.69584i	−0.0104307	−	0.0992413i
$293$	−10.6538	−	2.26454i	−0.622402	−	0.132296i	−0.114093	−	0.993470i	$-0.536396\pi$
$293$	−10.6538	−	2.26454i	−0.622402	−	0.132296i	−0.508310	+	0.861174i	$0.669729\pi$
$294$		0			0
$295$	−1.51292	+	14.3945i	−0.0880857	+	0.838079i
$296$	9.51404			0.552993
$297$		0			0
$298$	−14.1269			−0.818352
$299$	1.78765	−	17.0083i	0.103382	−	0.983616i
$300$		0			0
$301$	0.387723	+	0.0824131i	0.0223480	+	0.00475021i
$302$	−1.42804	−	13.5869i	−0.0821742	−	0.781836i
$303$		0			0
$304$	−16.3489	+	18.1573i	−0.937673	+	1.04139i
$305$	2.72377	−	8.38291i	0.155963	−	0.480004i
$306$		0			0
$307$	16.2173			0.925568			0.462784	−	0.886471i	$-0.346850\pi$
$307$	16.2173			0.925568			0.462784	+	0.886471i	$0.346850\pi$
$308$	0.0144282	+	0.0457229i	0.000822124	+	0.00260530i
$309$		0			0
$310$	5.70071	−	2.53812i	0.323779	−	0.144155i
$311$	−8.56533	−	9.51277i	−0.485695	−	0.539419i	0.449627	−	0.893217i	$-0.351557\pi$
$311$	−8.56533	−	9.51277i	−0.485695	−	0.539419i	−0.935322	+	0.353797i	$0.884890\pi$
$312$		0			0
$313$	11.0756	+	4.93118i	0.626030	+	0.278727i	0.695131	−	0.718883i	$-0.255346\pi$
$313$	11.0756	+	4.93118i	0.626030	+	0.278727i	−0.0691009	+	0.997610i	$0.522013\pi$
$314$	12.8013	−	9.30066i	0.722417	−	0.524867i
$315$		0			0
$316$	−0.670719	+	2.06426i	−0.0377309	+	0.116124i
$317$	−0.876337	+	8.33778i	−0.0492200	+	0.468297i	0.941955	+	0.335738i	$0.108986\pi$
$317$	−0.876337	+	8.33778i	−0.0492200	+	0.468297i	−0.991175	+	0.132558i	$0.957681\pi$
$318$		0			0
$319$	−16.2644	−	28.7314i	−0.910632	−	1.60865i
$320$	−8.80502	+	15.2507i	−0.492216	+	0.852543i
$321$		0			0
$322$	−0.357231	+	0.0759319i	−0.0199077	+	0.00423152i
$323$	7.73708	+	23.8123i	0.430503	+	1.32495i
$324$		0			0
$325$	−3.66920	+	2.66583i	−0.203531	+	0.147874i
$326$	20.8077	−	23.1093i	1.15243	−	1.27991i
$327$		0			0
$328$	−3.82367	+	1.70241i	−0.211127	+	0.0939997i
$329$	0.178179	−	0.308615i	0.00982333	−	0.0170145i
$330$		0			0
$331$	4.07538	+	7.05877i	0.224003	+	0.387985i	0.956020	−	0.293302i	$-0.0947540\pi$
$331$	4.07538	+	7.05877i	0.224003	+	0.387985i	−0.732017	+	0.681287i	$0.761421\pi$
$332$	0.555039	+	0.403259i	0.0304617	+	0.0221317i
$333$		0			0
$334$	1.92625	+	5.92838i	0.105400	+	0.324387i
$335$	−10.3109	−	4.59069i	−0.563343	−	0.250816i
$336$		0			0
$337$	−29.3746	−	6.24377i	−1.60014	−	0.340120i	−0.680458	−	0.732787i	$-0.738219\pi$
$337$	−29.3746	−	6.24377i	−1.60014	−	0.340120i	−0.919681	+	0.392667i	$0.871552\pi$
$338$	−28.2057	−	31.3256i	−1.53419	−	1.70389i
$339$		0			0
$340$	0.549112	+	0.951090i	0.0297798	+	0.0515801i
$341$	0.701753	+	7.26999i	0.0380020	+	0.393692i
$342$		0			0
$343$	−1.17399	−	0.852953i	−0.0633895	−	0.0460551i
$344$	−10.9075	+	2.31846i	−0.588092	+	0.125003i
$345$		0			0
$346$	0.213905	+	2.03517i	0.0114996	+	0.109412i
$347$	3.55559	+	33.8292i	0.190874	+	1.81605i	0.501107	+	0.865385i	$0.332926\pi$
$347$	3.55559	+	33.8292i	0.190874	+	1.81605i	−0.310233	+	0.950661i	$0.600407\pi$
$348$		0			0
$349$	−23.0322	+	4.89564i	−1.23288	+	0.262057i	−0.777869	−	0.628427i	$-0.783699\pi$
$349$	−23.0322	+	4.89564i	−1.23288	+	0.262057i	−0.455014	+	0.890484i	$0.650366\pi$
$350$	0.0783556	+	0.0569287i	0.00418829	+	0.00304297i
$351$		0			0
$352$	−1.72973	−	1.95418i	−0.0921950	−	0.104158i
$353$	7.91367	+	13.7069i	0.421202	+	0.729544i	0.996057	−	0.0887116i	$-0.0282749\pi$
$353$	7.91367	+	13.7069i	0.421202	+	0.729544i	−0.574855	+	0.818255i	$0.694942\pi$
$354$		0			0
$355$	−16.4433	−	18.2621i	−0.872719	−	0.969252i
$356$	−1.08982	−	0.231649i	−0.0577606	−	0.0122774i
$357$		0			0
$358$	11.1372	+	4.95862i	0.588621	+	0.262071i
$359$	−0.135487	−	0.416986i	−0.00715073	−	0.0220077i	0.947417	−	0.320000i	$-0.103683\pi$
$359$	−0.135487	−	0.416986i	−0.00715073	−	0.0220077i	−0.954568	+	0.297992i	$0.903683\pi$
$360$		0			0
$361$	−19.8716	−	14.4376i	−1.04588	−	0.759873i
$362$	14.2989	+	24.7664i	0.751532	+	1.30169i
$363$		0			0
$364$	0.0478922	−	0.0829517i	0.00251023	−	0.00434785i
$365$	−23.2208	+	10.3386i	−1.21543	+	0.541146i
$366$		0			0
$367$	−9.27145	+	10.2970i	−0.483966	+	0.537499i	−0.934831	−	0.355094i	$-0.884449\pi$
$367$	−9.27145	+	10.2970i	−0.483966	+	0.537499i	0.450865	+	0.892592i	$0.351116\pi$
$368$	7.73000	−	5.61617i	0.402954	−	0.292763i
$369$		0			0
$370$	−2.85483	−	8.78625i	−0.148415	−	0.456775i
$371$	−0.00641884	+	0.00136437i	−0.000333250	+	7.08344e-5i
$372$		0			0
$373$	−3.50784	+	6.07576i	−0.181629	+	0.314591i	−0.942436	−	0.334388i	$-0.891470\pi$
$373$	−3.50784	+	6.07576i	−0.181629	+	0.314591i	0.760806	+	0.648979i	$0.224804\pi$
$374$	16.8165	−	3.42550i	0.869563	−	0.177128i
$375$		0			0
$376$	−1.04791	+	9.97020i	−0.0540418	+	0.514174i
$377$	−20.3821	+	62.7297i	−1.04973	+	3.23075i
$378$		0			0
$379$	8.06973	−	5.86300i	0.414514	−	0.301162i	−0.360913	−	0.932600i	$-0.617535\pi$
$379$	8.06973	−	5.86300i	0.414514	−	0.301162i	0.775427	+	0.631437i	$0.217535\pi$
$380$	−1.74559	−	0.777185i	−0.0895466	−	0.0398687i
$381$		0			0
$382$	8.16202	+	9.06484i	0.417605	+	0.463797i
$383$	−17.2295	+	7.67107i	−0.880387	+	0.391974i	−0.796598	−	0.604510i	$-0.793369\pi$
$383$	−17.2295	+	7.67107i	−0.880387	+	0.391974i	−0.0837894	+	0.996483i	$0.526702\pi$
$384$		0			0
$385$	0.581751	−	0.415166i	0.0296488	−	0.0211588i
$386$	−7.80064			−0.397042
$387$		0			0
$388$	−0.133081	+	0.409581i	−0.00675616	+	0.0207933i
$389$	−15.6225	+	17.3505i	−0.792090	+	0.879705i	−0.995039	−	0.0994841i	$-0.968281\pi$
$389$	−15.6225	+	17.3505i	−0.792090	+	0.879705i	0.202949	+	0.979189i	$0.434947\pi$
$390$		0			0
$391$	−1.02347	−	9.73764i	−0.0517589	−	0.492454i
$392$	19.9503	+	4.24057i	1.00764	+	0.214181i
$393$		0			0
$394$	0.989975	−	9.41898i	0.0498742	−	0.474521i
$395$	32.3547			1.62794
$396$		0			0
$397$	−27.6991			−1.39018			−0.695090	−	0.718923i	$-0.744636\pi$
$397$	−27.6991			−1.39018			−0.695090	+	0.718923i	$0.744636\pi$
$398$	3.42482	−	32.5849i	0.171671	−	1.63334i
$399$		0			0
$400$	−2.47853	−	0.526827i	−0.123926	−	0.0263413i
$401$	−1.57899	−	15.0231i	−0.0788512	−	0.750219i	−0.960494	−	0.278301i	$-0.910229\pi$
$401$	−1.57899	−	15.0231i	−0.0788512	−	0.750219i	0.881643	−	0.471918i	$-0.156438\pi$
$402$		0			0
$403$	9.76355	−	10.8435i	0.486357	−	0.540154i
$404$	0.107569	−	0.331062i	0.00535174	−	0.0164710i
$405$		0			0
$406$	1.40853			0.0699041
$407$	10.8126	+	0.0918083i	0.535961	+	0.00455077i
$408$		0			0
$409$	−8.59465	+	3.82659i	−0.424978	+	0.189213i	−0.608070	−	0.793883i	$-0.708056\pi$
$409$	−8.59465	+	3.82659i	−0.424978	+	0.189213i	0.183092	+	0.983096i	$0.441389\pi$
$410$	2.71953	+	3.02034i	0.134308	+	0.149164i
$411$		0			0
$412$	1.80158	+	0.802114i	0.0887573	+	0.0395173i
$413$	0.584704	−	0.424812i	0.0287714	−	0.0209036i
$414$		0			0
$415$	3.16029	−	9.72636i	0.155132	−	0.477448i
$416$	−0.544981	+	5.18515i	−0.0267199	+	0.254223i
$417$		0			0
$418$	−20.1677	+	22.0196i	−0.986435	+	1.07701i
$419$	−10.0519	+	17.4104i	−0.491069	+	0.850556i	−0.999947	−	0.0102827i	$-0.996727\pi$
$419$	−10.0519	+	17.4104i	−0.491069	+	0.850556i	0.508879	+	0.860838i	$0.330060\pi$
$420$		0			0
$421$	12.5645	−	2.67068i	0.612358	−	0.130161i	0.108716	−	0.994073i	$-0.465326\pi$
$421$	12.5645	−	2.67068i	0.612358	−	0.130161i	0.503643	+	0.863912i	$0.331993\pi$
$422$	−1.70863	−	5.25863i	−0.0831750	−	0.255986i
$423$		0			0
$424$	0.149353	−	0.108511i	0.00725320	−	0.00526976i
$425$	−1.73747	+	1.92966i	−0.0842797	+	0.0936021i
$426$		0			0
$427$	−0.402082	+	0.179019i	−0.0194581	+	0.00866332i
$428$	0.352201	−	0.610029i	0.0170243	−	0.0294869i
$429$		0			0
$430$	5.41405	+	9.37741i	0.261089	+	0.452219i
$431$	12.3785	+	8.99352i	0.596252	+	0.433202i	0.844547	−	0.535482i	$-0.179870\pi$
$431$	12.3785	+	8.99352i	0.596252	+	0.433202i	−0.248295	+	0.968685i	$0.579870\pi$
$432$		0			0
$433$	−3.72241	−	11.4564i	−0.178887	−	0.550559i	0.820902	−	0.571069i	$-0.193471\pi$
$433$	−3.72241	−	11.4564i	−0.178887	−	0.550559i	−0.999790	+	0.0205099i	$0.993471\pi$
$434$	−0.284659	−	0.126738i	−0.0136641	−	0.00608364i
$435$		0			0
$436$	2.19282	+	0.466099i	0.105017	+	0.0223221i
$437$	11.3991	+	12.6600i	0.545292	+	0.605608i
$438$		0			0
$439$	2.07408	+	3.59240i	0.0989902	+	0.171456i	0.911267	−	0.411816i	$-0.135105\pi$
$439$	2.07408	+	3.59240i	0.0989902	+	0.171456i	−0.812277	+	0.583272i	$0.801772\pi$
$440$	−10.2005	+	17.3264i	−0.486290	+	0.826003i
$441$		0			0
$442$	−27.7378	−	20.1527i	−1.31935	−	0.958564i
$443$	−18.6746	+	3.96941i	−0.887258	+	0.188592i	−0.628927	−	0.777464i	$-0.716506\pi$
$443$	−18.6746	+	3.96941i	−0.887258	+	0.188592i	−0.258331	+	0.966057i	$0.583172\pi$
$444$		0			0
$445$	1.73606	+	16.5175i	0.0822972	+	0.783006i
$446$	−1.44385	−	13.7373i	−0.0683684	−	0.650482i
$447$		0			0
$448$	0.860125	−	0.182825i	0.0406371	−	0.00863767i
$449$	−2.76223	−	2.00688i	−0.130358	−	0.0947104i	0.520696	−	0.853742i	$-0.325673\pi$
$449$	−2.76223	−	2.00688i	−0.130358	−	0.0947104i	−0.651053	+	0.759032i	$0.725673\pi$
$450$		0			0
$451$	−4.36199	+	1.89787i	−0.205398	+	0.0893673i
$452$	0.710837	+	1.23121i	0.0334350	+	0.0579111i
$453$		0			0
$454$	−5.97336	−	6.63409i	−0.280344	−	0.311353i
$455$	−1.39662	−	0.296860i	−0.0654745	−	0.0139170i
$456$		0			0
$457$	−26.9900	−	12.0167i	−1.26254	−	0.562119i	−0.337262	−	0.941411i	$-0.609501\pi$
$457$	−26.9900	−	12.0167i	−1.26254	−	0.562119i	−0.925277	+	0.379292i	$0.876168\pi$
$458$	−6.51334	−	20.0460i	−0.304348	−	0.936688i
$459$		0			0
$460$	0.604523	+	0.439212i	0.0281860	+	0.0204784i
$461$	20.3879	+	35.3129i	0.949560	+	1.64469i	0.746353	+	0.665550i	$0.231803\pi$
$461$	20.3879	+	35.3129i	0.949560	+	1.64469i	0.203207	+	0.979136i	$0.434864\pi$
$462$		0			0
$463$	19.3751	−	33.5586i	0.900435	−	1.55960i	0.0735054	−	0.997295i	$-0.476581\pi$
$463$	19.3751	−	33.5586i	0.900435	−	1.55960i	0.826930	−	0.562305i	$-0.190085\pi$
$464$	−33.6645	+	14.9884i	−1.56283	+	0.695819i
$465$		0			0
$466$	−19.4147	+	21.5623i	−0.899370	+	0.998852i
$467$	−22.7043	+	16.4956i	−1.05063	+	0.763327i	−0.972332	−	0.233603i	$-0.924949\pi$
$467$	−22.7043	+	16.4956i	−1.05063	+	0.763327i	−0.0782979	+	0.996930i	$0.524949\pi$
$468$		0			0
$469$	0.174158	+	0.536003i	0.00804187	+	0.0247503i
$470$	9.52195	−	2.02395i	0.439215	−	0.0933580i
$471$		0			0
$472$	−10.1660	+	17.6081i	−0.467929	+	0.810477i
$473$	−12.4186	+	2.52965i	−0.571009	+	0.116313i
$474$		0			0
$475$	0.472238	−	4.49305i	0.0216678	−	0.206155i
$476$	0.0169461	−	0.0521547i	0.000776723	−	0.00239051i
$477$		0			0
$478$	19.1395	−	13.9057i	0.875421	−	0.636031i
$479$	14.4564	+	6.43642i	0.660531	+	0.294088i	0.709492	−	0.704713i	$-0.248924\pi$
$479$	14.4564	+	6.43642i	0.660531	+	0.294088i	−0.0489609	+	0.998801i	$0.515591\pi$
$480$		0			0
$481$	−14.4546	−	16.0535i	−0.659073	−	0.731975i
$482$	−13.2624	+	5.90481i	−0.604087	+	0.268957i
$483$		0			0
$484$	−1.00626	−	1.15646i	−0.0457389	−	0.0525665i
$485$	6.41966			0.291502
$486$		0			0
$487$	−1.77582	+	5.46540i	−0.0804699	+	0.247661i	−0.983195	−	0.182556i	$-0.941563\pi$
$487$	−1.77582	+	5.46540i	−0.0804699	+	0.247661i	0.902726	+	0.430217i	$0.141563\pi$
$488$	8.28511	−	9.20155i	0.375049	−	0.416535i
$489$		0			0
$490$	−2.07020	−	19.6966i	−0.0935220	−	0.889802i
$491$	−34.9000	−	7.41823i	−1.57502	−	0.334780i	−0.664188	−	0.747566i	$-0.731223\pi$
$491$	−34.9000	−	7.41823i	−1.57502	−	0.334780i	−0.910828	+	0.412786i	$0.864556\pi$
$492$		0			0
$493$	−3.94724	+	37.5555i	−0.177775	+	1.69142i
$494$	59.6532			2.68392
$495$		0			0
$496$	8.15214			0.366042
$497$	−0.128265	+	1.22036i	−0.00575348	+	0.0547407i
$498$		0			0
$499$	−26.0215	−	5.53105i	−1.16488	−	0.247604i	−0.415408	−	0.909635i	$-0.636361\pi$
$499$	−26.0215	−	5.53105i	−1.16488	−	0.247604i	−0.749476	+	0.662032i	$0.769694\pi$
$500$	−0.172020	−	1.63666i	−0.00769298	−	0.0731938i
$501$		0			0
$502$	−25.5543	+	28.3809i	−1.14054	+	1.26670i
$503$	9.97834	−	30.7102i	0.444912	−	1.36930i	−0.437668	−	0.899137i	$-0.644195\pi$
$503$	9.97834	−	30.7102i	0.444912	−	1.36930i	0.882580	−	0.470162i	$-0.155805\pi$
$504$		0			0
$505$	−5.18898			−0.230906
$506$	9.50478	−	6.78308i	0.422539	−	0.301545i
$507$		0			0
$508$	−0.435549	+	0.193919i	−0.0193244	+	0.00860376i
$509$	21.7002	+	24.1005i	0.961842	+	1.06823i	0.997625	+	0.0688745i	$0.0219408\pi$
$509$	21.7002	+	24.1005i	0.961842	+	1.06823i	−0.0357831	+	0.999360i	$0.511393\pi$
$510$		0			0
$511$	1.15951	+	0.516247i	0.0512937	+	0.0228374i
$512$	−19.8358	+	14.4116i	−0.876627	+	0.636907i
$513$		0			0
$514$	7.57554	−	23.3151i	0.334143	−	1.02839i
$515$	3.07281	−	29.2358i	0.135404	−	1.28828i
$516$		0			0
$517$	−1.28715	+	11.3209i	−0.0566088	+	0.497894i
$518$	−0.230655	+	0.399507i	−0.0101344	+	0.0175533i
$519$		0			0
$520$	39.2899	−	8.35132i	1.72297	−	0.366229i
$521$	4.14919	+	12.7699i	0.181779	+	0.559460i	0.999878	−	0.0156184i	$-0.00497170\pi$
$521$	4.14919	+	12.7699i	0.181779	+	0.559460i	−0.818099	+	0.575078i	$0.804972\pi$
$522$		0			0
$523$	−14.5065	+	10.5396i	−0.634325	+	0.460864i	−0.857896	−	0.513824i	$-0.828229\pi$
$523$	−14.5065	+	10.5396i	−0.634325	+	0.460864i	0.223571	+	0.974688i	$0.428229\pi$
$524$	1.65523	−	1.83832i	0.0723090	−	0.0803072i
$525$		0			0
$526$	17.1470	−	7.63433i	0.747644	−	0.332872i
$527$	4.17695	−	7.23469i	0.181951	−	0.315148i
$528$		0			0
$529$	8.16901	+	14.1491i	0.355174	+	0.615180i
$530$	−0.145026	−	0.105367i	−0.00629951	−	0.00457686i
$531$		0			0
$532$	0.0294842	+	0.0907431i	0.00127830	+	0.00393421i
$533$	8.68181	+	3.86539i	0.376051	+	0.167429i
$534$		0			0
$535$	−10.2708	−	2.18312i	−0.444044	−	0.0943844i
$536$	−10.6090	−	11.7825i	−0.458239	−	0.508926i
$537$		0			0
$538$	−9.76128	−	16.9070i	−0.420838	−	0.728914i
$539$	22.6324	+	5.01188i	0.974846	+	0.215877i
$540$		0			0
$541$	−11.9701	−	8.69682i	−0.514637	−	0.373906i	0.299943	−	0.953957i	$-0.403032\pi$
$541$	−11.9701	−	8.69682i	−0.514637	−	0.373906i	−0.814580	+	0.580052i	$0.803032\pi$
$542$	−2.05381	+	0.436551i	−0.0882187	+	0.0187515i
$543$		0			0
$544$	0.312014	+	2.96861i	0.0133775	+	0.127278i
$545$	−3.49311	−	33.2347i	−0.149628	−	1.42362i
$546$		0			0
$547$	−19.5093	+	4.14684i	−0.834159	+	0.177306i	−0.605143	−	0.796117i	$-0.706884\pi$
$547$	−19.5093	+	4.14684i	−0.834159	+	0.177306i	−0.229016	+	0.973423i	$0.573551\pi$
$548$	0.982193	+	0.713605i	0.0419572	+	0.0304837i
$549$		0			0
$550$	−3.02344	−	0.669531i	−0.128920	−	0.0285489i
$551$	−32.8511	−	56.8997i	−1.39950	−	2.42401i
$552$		0			0
$553$	−1.08105	−	1.20062i	−0.0459707	−	0.0510557i
$554$	−31.9051	−	6.78164i	−1.35552	−	0.288124i
$555$		0			0
$556$	0.487380	+	0.216996i	0.0206695	+	0.00920266i
$557$	−4.01834	−	12.3672i	−0.170262	−	0.524014i	0.829123	−	0.559066i	$-0.188840\pi$
$557$	−4.01834	−	12.3672i	−0.170262	−	0.524014i	−0.999385	+	0.0350524i	$0.988840\pi$
$558$		0			0
$559$	20.4837	+	14.8823i	0.866367	+	0.629452i
$560$	−0.398858	−	0.690842i	−0.0168548	−	0.0291934i
$561$		0			0
$562$	−10.4290	+	18.0635i	−0.439919	+	0.761962i
$563$	39.9533	−	17.7883i	1.68383	−	0.749689i	0.684034	−	0.729450i	$-0.260224\pi$
$563$	39.9533	−	17.7883i	1.68383	−	0.749689i	0.999795	−	0.0202395i	$-0.00644286\pi$
$564$		0			0
$565$	14.1804	−	15.7490i	0.596575	−	0.662564i
$566$	22.6049	−	16.4234i	0.950153	−	0.690327i
$567$		0			0
$568$	−10.6674	−	32.8309i	−0.447595	−	1.37755i
$569$	0.384824	−	0.0817969i	0.0161327	−	0.00342910i	−0.199838	−	0.979829i	$-0.564042\pi$
$569$	0.384824	−	0.0817969i	0.0161327	−	0.00342910i	0.215971	+	0.976400i	$0.430708\pi$
$570$		0			0
$571$	−19.2502	+	33.3423i	−0.805594	+	1.39533i	0.110295	+	0.993899i	$0.464820\pi$
$571$	−19.2502	+	33.3423i	−0.805594	+	1.39533i	−0.915889	+	0.401431i	$0.868513\pi$
$572$	−0.345969	+	3.04292i	−0.0144657	+	0.127231i
$573$		0			0
$574$	0.0212135	−	0.201833i	0.000885436	−	0.00842436i
$575$	−0.545951	+	1.68026i	−0.0227677	+	0.0700718i
$576$		0			0
$577$	−0.0503581	+	0.0365873i	−0.00209643	+	0.00152315i	−0.588833	−	0.808255i	$-0.700412\pi$
$577$	−0.0503581	+	0.0365873i	−0.00209643	+	0.00152315i	0.586737	+	0.809778i	$0.300412\pi$
$578$	3.25180	+	1.44779i	0.135257	+	0.0602203i
$579$		0			0
$580$	−1.92835	−	2.14165i	−0.0800705	−	0.0889273i
$581$	−0.466521	+	0.207708i	−0.0193545	+	0.00861719i
$582$		0			0
$583$	0.170785	−	0.121880i	0.00707319	−	0.00504777i
$584$	−35.7065			−1.47754
$585$		0			0
$586$	−4.59107	+	14.1299i	−0.189655	+	0.583699i
$587$	7.96448	−	8.84545i	0.328729	−	0.365091i	−0.556011	−	0.831175i	$-0.687669\pi$
$587$	7.96448	−	8.84545i	0.328729	−	0.365091i	0.884740	+	0.466084i	$0.154336\pi$
$588$		0			0
$589$	1.51930	+	14.4552i	0.0626017	+	0.595615i
$590$	19.3116	+	4.10480i	0.795044	+	0.168992i
$591$		0			0
$592$	1.26155	−	12.0028i	0.0518494	−	0.493314i
$593$	−29.3055			−1.20343			−0.601717	−	0.798709i	$-0.705516\pi$
$593$	−29.3055			−1.20343			−0.601717	+	0.798709i	$0.705516\pi$
$594$		0			0
$595$	−0.817458			−0.0335125
$596$	0.150865	−	1.43539i	0.00617968	−	0.0587957i
$597$		0			0
$598$	−22.8183	−	4.85017i	−0.933108	−	0.198338i
$599$	0.887145	+	8.44062i	0.0362478	+	0.344875i	0.997583	+	0.0694920i	$0.0221378\pi$
$599$	0.887145	+	8.44062i	0.0362478	+	0.344875i	−0.961335	+	0.275383i	$0.911195\pi$
$600$		0			0
$601$	13.6227	−	15.1295i	0.555681	−	0.617146i	−0.398212	−	0.917293i	$-0.630369\pi$
$601$	13.6227	−	15.1295i	0.555681	−	0.617146i	0.953893	+	0.300148i	$0.0970359\pi$
$602$	0.167082	−	0.514227i	0.00680977	−	0.0209583i
$603$		0			0
$604$	1.39576			0.0567927
$605$	−11.7600	+	19.5928i	−0.478111	+	0.796562i
$606$		0			0
$607$	27.8666	−	12.4070i	1.13107	−	0.503585i	0.246105	−	0.969243i	$-0.420849\pi$
$607$	27.8666	−	12.4070i	1.13107	−	0.503585i	0.884965	+	0.465658i	$0.154182\pi$
$608$	−3.47512	−	3.85952i	−0.140935	−	0.156524i
$609$		0			0
$610$	−10.9837	−	4.89027i	−0.444718	−	0.198001i
$611$	18.4152	−	13.3794i	0.745001	−	0.541275i
$612$		0			0
$613$	10.6491	−	32.7746i	0.430114	−	1.32376i	−0.467897	−	0.883783i	$-0.654988\pi$
$613$	10.6491	−	32.7746i	0.430114	−	1.32376i	0.898011	−	0.439972i	$-0.145012\pi$
$614$	2.31230	−	22.0000i	0.0933167	−	0.887849i
$615$		0			0
$616$	0.983774	−	0.200393i	0.0396374	−	0.00807406i
$617$	0.112417	−	0.194713i	0.00452576	−	0.00783884i	−0.863754	−	0.503914i	$-0.831893\pi$
$617$	0.112417	−	0.194713i	0.00452576	−	0.00783884i	0.868279	+	0.496075i	$0.165226\pi$
$618$		0			0
$619$	−0.581534	+	0.123609i	−0.0233738	+	0.00496826i	−0.219584	−	0.975594i	$-0.570470\pi$
$619$	−0.581534	+	0.123609i	−0.0233738	+	0.00496826i	0.196210	+	0.980562i	$0.437137\pi$
$620$	0.197010	+	0.606333i	0.00791210	+	0.0243509i
$621$		0			0
$622$	−14.1261	+	10.2632i	−0.566405	+	0.411517i
$623$	0.554930	−	0.616312i	0.0222328	−	0.0246920i
$624$		0			0
$625$	−19.2840	+	8.58580i	−0.771361	+	0.343432i
$626$	8.26872	−	14.3218i	0.330485	−	0.572416i
$627$		0			0
$628$	0.808298	+	1.40001i	0.0322546	+	0.0558666i
$629$	−10.0056	−	7.26953i	−0.398951	−	0.289855i
$630$		0			0
$631$	10.7136	+	32.9732i	0.426504	+	1.31264i	0.901547	+	0.432681i	$0.142432\pi$
$631$	10.7136	+	32.9732i	0.426504	+	1.31264i	−0.475044	+	0.879962i	$0.657568\pi$
$632$	41.5208	+	18.4863i	1.65161	+	0.735344i
$633$		0			0
$634$	11.1859	+	2.37764i	0.444250	+	0.0944282i
$635$	4.75550	+	5.28152i	0.188716	+	0.209591i
$636$		0			0
$637$	−23.1550	−	40.1057i	−0.917435	−	1.58904i
$638$	−41.2955	+	17.9674i	−1.63490	+	0.711336i
$639$		0			0
$640$	16.7886	+	12.1976i	0.663626	+	0.482152i
$641$	−21.3702	+	4.54238i	−0.844073	+	0.179413i	−0.609600	−	0.792709i	$-0.708670\pi$
$641$	−21.3702	+	4.54238i	−0.844073	+	0.179413i	−0.234473	+	0.972123i	$0.575336\pi$
$642$		0			0
$643$	−3.19198	−	30.3697i	−0.125879	−	1.19766i	−0.856964	−	0.515376i	$-0.827652\pi$
$643$	−3.19198	−	30.3697i	−0.125879	−	1.19766i	0.731085	−	0.682287i	$-0.239014\pi$
$644$	−0.00390019	−	0.0371079i	−0.000153689	−	0.00146225i
$645$		0			0
$646$	33.4065	−	7.10076i	1.31436	−	0.279376i
$647$	−21.6341	−	15.7181i	−0.850525	−	0.617943i	0.0747658	−	0.997201i	$-0.476179\pi$
$647$	−21.6341	−	15.7181i	−0.850525	−	0.617943i	−0.925291	+	0.379259i	$0.876179\pi$
$648$		0			0
$649$	−11.7235	+	19.9133i	−0.460187	+	0.781665i
$650$	3.09325	+	5.35767i	0.121327	+	0.210145i
$651$		0			0
$652$	2.12584	+	2.36098i	0.0832543	+	0.0924633i
$653$	28.7173	+	6.10406i	1.12380	+	0.238870i	0.732082	−	0.681217i	$-0.238549\pi$
$653$	28.7173	+	6.10406i	1.12380	+	0.238870i	0.391714	+	0.920087i	$0.371882\pi$
$654$		0			0
$655$	−33.6865	−	14.9982i	−1.31624	−	0.586027i
$656$	1.64073	+	5.04965i	0.0640598	+	0.197156i
$657$		0			0
$658$	−0.393256	−	0.285717i	−0.0153307	−	0.0111384i
$659$	−18.2740	−	31.6515i	−0.711854	−	1.23297i	−0.964161	−	0.265320i	$-0.914523\pi$
$659$	−18.2740	−	31.6515i	−0.711854	−	1.23297i	0.252307	−	0.967647i	$-0.418811\pi$
$660$		0			0
$661$	1.90648	−	3.30212i	0.0741535	−	0.128438i	−0.826564	−	0.562842i	$-0.809708\pi$
$661$	1.90648	−	3.30212i	0.0741535	−	0.128438i	0.900718	+	0.434405i	$0.143041\pi$
$662$	10.1569	−	4.52213i	0.394758	−	0.175758i
$663$		0			0
$664$	9.61290	−	10.6762i	0.373053	−	0.414317i
$665$	1.15065	−	0.835996i	0.0446203	−	0.0324185i
$666$		0			0
$667$	7.93974	+	24.4360i	0.307428	+	0.946166i
$668$	−0.622932	+	0.132408i	−0.0241020	+	0.00512303i
$669$		0			0
$670$	−7.69779	+	13.3330i	−0.297392	+	0.515097i
$671$	9.50474	−	10.3775i	0.366926	−	0.400620i
$672$		0			0
$673$	−1.57168	+	14.9535i	−0.0605837	+	0.576415i	0.921554	+	0.388251i	$0.126921\pi$
$673$	−1.57168	+	14.9535i	−0.0605837	+	0.576415i	−0.982137	+	0.188165i	$0.939746\pi$
$674$	−12.6585	+	38.9588i	−0.487587	+	1.50064i
$675$		0			0
$676$	3.48410	−	2.53134i	0.134004	−	0.0973594i
$677$	−27.5434	−	12.2631i	−1.05858	−	0.471309i	−0.197775	−	0.980247i	$-0.563371\pi$
$677$	−27.5434	−	12.2631i	−1.05858	−	0.471309i	−0.860803	+	0.508938i	$0.830038\pi$
$678$		0			0
$679$	−0.214496	−	0.238222i	−0.00823160	−	0.00914212i
$680$	21.0087	−	9.35366i	0.805646	−	0.358697i
$681$		0			0
$682$	9.96239	+	0.0845892i	0.381480	+	0.00323909i
$683$	45.7767			1.75160			0.875798	−	0.482677i	$-0.160336\pi$
$683$	45.7767			1.75160			0.875798	+	0.482677i	$0.160336\pi$
$684$		0			0
$685$	5.59242	−	17.2117i	0.213675	−	0.657625i
$686$	−1.32449	+	1.47099i	−0.0505692	+	0.0561628i
$687$		0			0
$688$	1.47863	+	14.0682i	0.0563722	+	0.536346i
$689$	−0.410005	−	0.0871493i	−0.0156200	−	0.00332013i
$690$		0			0
$691$	−2.58274	+	24.5732i	−0.0982522	+	0.934807i	0.828717	+	0.559668i	$0.189071\pi$
$691$	−2.58274	+	24.5732i	−0.0982522	+	0.934807i	−0.926969	+	0.375138i	$0.877595\pi$
$692$	−0.209071			−0.00794768
$693$		0			0
$694$	46.3990			1.76128
$695$	0.831286	−	7.90916i	0.0315325	−	0.300012i
$696$		0			0
$697$	5.32203	+	1.13123i	0.201586	+	0.0428485i
$698$	3.35735	+	31.9430i	0.127077	+	1.20906i
$699$		0			0
$700$	−0.00662110	+	0.00735347i	−0.000250254	+	0.000277935i
$701$	11.3822	−	35.0310i	0.429902	−	1.32310i	−0.468320	−	0.883559i	$-0.655141\pi$
$701$	11.3822	−	35.0310i	0.429902	−	1.32310i	0.898222	−	0.439542i	$-0.144859\pi$
$702$		0			0
$703$	21.5183			0.811577
$704$	−22.8852	+	16.3320i	−0.862517	+	0.615534i
$705$		0			0
$706$	19.7228	−	8.78117i	0.742279	−	0.330484i
$707$	0.173376	+	0.192554i	0.00652048	+	0.00724172i
$708$		0			0
$709$	7.44567	+	3.31502i	0.279628	+	0.124498i	0.541759	−	0.840534i	$-0.317759\pi$
$709$	7.44567	+	3.31502i	0.279628	+	0.124498i	−0.262131	+	0.965032i	$0.584425\pi$
$710$	−27.1185	+	19.7028i	−1.01774	+	0.739432i
$711$		0			0
$712$	−7.20962	+	22.1889i	−0.270192	+	0.831565i
$713$	0.594139	−	5.65285i	0.0222507	−	0.211701i
$714$		0			0
$715$	44.7331	−	9.11205i	1.67292	−	0.340771i
$716$	−0.622764	+	1.07866i	−0.0232738	+	0.0403114i
$717$		0			0
$718$	−0.584994	+	0.124344i	−0.0218318	+	0.00464049i
$719$	10.8427	+	33.3703i	0.404363	+	1.24450i	0.921426	+	0.388554i	$0.127025\pi$
$719$	10.8427	+	33.3703i	0.404363	+	1.24450i	−0.517063	+	0.855947i	$0.672975\pi$
$720$		0			0
$721$	−1.18756	+	0.862812i	−0.0442270	+	0.0321328i
$722$	−22.4191	+	24.8989i	−0.834353	+	0.926643i
$723$		0			0
$724$	−2.66912	+	1.18837i	−0.0991970	+	0.0441654i
$725$	3.40691	−	5.90095i	0.126530	−	0.219156i
$726$		0			0
$727$	−11.2832	−	19.5431i	−0.418470	−	0.724812i	0.577316	−	0.816521i	$-0.304100\pi$
$727$	−11.2832	−	19.5431i	−0.418470	−	0.724812i	−0.995786	+	0.0917094i	$0.970767\pi$
$728$	−1.62267	−	1.17894i	−0.0601401	−	0.0436944i
$729$		0			0
$730$	10.7142	+	32.9750i	0.396552	+	1.22046i
$731$	13.2426	+	5.89598i	0.489795	+	0.218071i
$732$		0			0
$733$	33.7559	+	7.17503i	1.24680	+	0.265016i	0.783616	−	0.621246i	$-0.213373\pi$
$733$	33.7559	+	7.17503i	1.24680	+	0.265016i	0.463185	+	0.886262i	$0.346706\pi$
$734$	12.6468	+	14.0456i	0.466800	+	0.518434i
$735$		0			0
$736$	1.01549	+	1.75887i	0.0374313	+	0.0648329i
$737$	−11.9433	−	13.4931i	−0.439938	−	0.497023i
$738$		0			0
$739$	17.2345	+	12.5216i	0.633983	+	0.460616i	0.857778	−	0.514021i	$-0.171845\pi$
$739$	17.2345	+	12.5216i	0.633983	+	0.460616i	−0.223795	+	0.974636i	$0.571845\pi$
$740$	0.923226	−	0.196238i	0.0339385	−	0.00721384i
$741$		0			0
$742$	0.000935660		0.00890221i	3.43492e−5		0.000326810i
$743$	4.62621	+	44.0155i	0.169719	+	1.61477i	0.665551	+	0.746352i	$0.268197\pi$
$743$	4.62621	+	44.0155i	0.169719	+	1.61477i	−0.495832	+	0.868419i	$0.665137\pi$
$744$		0			0
$745$	−21.0444	+	4.47313i	−0.771008	+	0.163883i
$746$	7.74211	+	5.62497i	0.283459	+	0.205945i
$747$		0			0
$748$	0.168464	+	1.74525i	0.00615966	+	0.0638126i
$749$	0.262159	+	0.454073i	0.00957908	+	0.0165915i
$750$		0			0
$751$	−16.7012	−	18.5485i	−0.609435	−	0.676846i	0.356897	−	0.934144i	$-0.383835\pi$
$751$	−16.7012	−	18.5485i	−0.609435	−	0.676846i	−0.966332	+	0.257298i	$0.917168\pi$
$752$	12.4394	+	2.64407i	0.453618	+	0.0964194i
$753$		0			0
$754$	82.1918	+	36.5941i	2.99325	+	1.33268i
$755$	−6.42942	−	19.7877i	−0.233990	−	0.720149i
$756$		0			0
$757$	−32.9524	−	23.9413i	−1.19768	−	0.870162i	−0.203622	−	0.979050i	$-0.565271\pi$
$757$	−32.9524	−	23.9413i	−1.19768	−	0.870162i	−0.994054	+	0.108887i	$0.965271\pi$
$758$	−6.80303	−	11.7832i	−0.247097	−	0.427985i
$759$		0			0
$760$	−20.0059	+	34.6513i	−0.725691	+	1.25693i
$761$	−17.7105	+	7.88522i	−0.642005	+	0.285839i	−0.701803	−	0.712372i	$-0.747621\pi$
$761$	−17.7105	+	7.88522i	−0.642005	+	0.285839i	0.0597977	+	0.998211i	$0.480954\pi$
$762$		0			0
$763$	−1.11657	+	1.24007i	−0.0404224	+	0.0448936i
$764$	−1.00821	+	0.732507i	−0.0364757	+	0.0265012i
$765$		0			0
$766$	7.94980	+	24.4670i	0.287238	+	0.884028i
$767$	45.1560	−	9.59820i	1.63049	−	0.346571i
$768$		0			0
$769$	5.38361	−	9.32469i	0.194138	−	0.336257i	−0.752480	−	0.658616i	$-0.771142\pi$
$769$	5.38361	−	9.32469i	0.194138	−	0.336257i	0.946618	+	0.322359i	$0.104476\pi$
$770$	−0.480259	−	0.848388i	−0.0173073	−	0.0305738i
$771$		0			0
$772$	0.0833050	−	0.792594i	0.00299821	−	0.0285261i
$773$	9.08010	−	27.9457i	0.326589	−	1.00514i	−0.644130	−	0.764916i	$-0.722780\pi$
$773$	9.08010	−	27.9457i	0.326589	−	1.00514i	0.970718	−	0.240220i	$-0.0772197\pi$
$774$		0			0
$775$	−1.21949	+	0.886012i	−0.0438054	+	0.0318265i
$776$	8.23837	+	3.66796i	0.295740	+	0.131672i
$777$		0			0
$778$	21.3099	+	23.6670i	0.763995	+	0.848503i
$779$	−8.64814	+	3.85040i	−0.309852	+	0.137955i
$780$		0			0
$781$	−11.8066	−	37.4149i	−0.422473	−	1.33881i
$782$	−13.3558			−0.477603
$783$		0			0
$784$	7.99525	−	24.6069i	0.285545	−	0.878816i
$785$	16.1247	−	17.9083i	0.575514	−	0.639173i
$786$		0			0
$787$	−0.371829	−	3.53772i	−0.0132543	−	0.126106i	0.985894	−	0.167371i	$-0.0535278\pi$
$787$	−0.371829	−	3.53772i	−0.0132543	−	0.126106i	−0.999148	+	0.0412652i	$0.986861\pi$
$788$	0.946456	+	0.201175i	0.0337161	+	0.00716658i
$789$		0			0
$790$	4.61320	−	43.8917i	0.164130	−	1.56160i
$791$	−1.05822			−0.0376259
$792$		0			0
$793$	−28.1137			−0.998346
$794$	−3.94941	+	37.5761i	−0.140159	+	1.33353i
$795$		0			0
$796$	3.27426	+	0.695966i	0.116053	+	0.0246679i
$797$	−3.66004	−	34.8230i	−0.129645	−	1.23349i	−0.845013	−	0.534745i	$-0.820408\pi$
$797$	−3.66004	−	34.8230i	−0.129645	−	1.23349i	0.715368	−	0.698748i	$-0.246259\pi$
$798$		0			0
$799$	8.72013	−	9.68468i	0.308496	−	0.342619i
$800$	0.166438	−	0.512245i	0.00588448	−	0.0181106i
$801$		0			0
$802$	−20.6052			−0.727595
$803$	−40.5801	−	0.344559i	−1.43204	−	0.0121592i
$804$		0			0
$805$	−0.508113	+	0.226226i	−0.0179086	+	0.00797343i
$806$	−13.3180	−	14.7911i	−0.469106	−	0.520995i
$807$		0			0
$808$	−6.65903	−	2.96479i	−0.234264	−	0.104301i
$809$	15.4959	−	11.2584i	0.544807	−	0.395826i	−0.281060	−	0.959690i	$-0.590686\pi$
$809$	15.4959	−	11.2584i	0.544807	−	0.395826i	0.825867	+	0.563864i	$0.190686\pi$
$810$		0			0
$811$	−1.91663	+	5.89877i	−0.0673019	+	0.207134i	−0.979052	−	0.203612i	$-0.934732\pi$
$811$	−1.91663	+	5.89877i	−0.0673019	+	0.207134i	0.911750	+	0.410746i	$0.134732\pi$
$812$	−0.0150420	+	0.143115i	−0.000527872	+	0.00502236i
$813$		0			0
$814$	1.66623	−	14.6551i	0.0584015	−	0.513661i
$815$	23.6792	−	41.0137i	0.829448	−	1.43665i
$816$		0			0
$817$	−24.6699	+	5.24374i	−0.863089	+	0.183455i
$818$	3.96563	+	12.2049i	0.138655	+	0.426736i
$819$		0			0
$820$	−0.335928	+	0.244066i	−0.0117311	+	0.00852316i
$821$	−16.7725	+	18.6277i	−0.585363	+	0.650112i	−0.960965	−	0.276669i	$-0.910769\pi$
$821$	−16.7725	+	18.6277i	−0.585363	+	0.650112i	0.375602	+	0.926781i	$0.377436\pi$
$822$		0			0
$823$	2.68551	−	1.19567i	0.0936110	−	0.0416783i	−0.359397	−	0.933185i	$-0.617018\pi$
$823$	2.68551	−	1.19567i	0.0936110	−	0.0416783i	0.453008	+	0.891506i	$0.350351\pi$
$824$	20.6476	−	35.7627i	0.719294	−	1.24585i
$825$		0			0
$826$	−0.492923	−	0.853768i	−0.0171510	−	0.0297064i
$827$	−26.1058	−	18.9670i	−0.907789	−	0.659547i	0.0326657	−	0.999466i	$-0.489600\pi$
$827$	−26.1058	−	18.9670i	−0.907789	−	0.659547i	−0.940455	+	0.339919i	$0.889600\pi$
$828$		0			0
$829$	0.324911	+	0.999973i	0.0112846	+	0.0347305i	0.956540	−	0.291600i	$-0.0941877\pi$
$829$	0.324911	+	0.999973i	0.0112846	+	0.0347305i	−0.945256	+	0.326331i	$0.894188\pi$
$830$	−12.7440	−	5.67399i	−0.442351	−	0.196947i
$831$		0			0
$832$	54.9407	+	11.6780i	1.90473	+	0.404862i
$833$	−17.7410	−	19.7034i	−0.614690	−	0.682682i
$834$		0			0
$835$	4.74662	+	8.22139i	0.164264	+	0.284513i
$836$	−2.02196	−	2.28432i	−0.0699308	−	0.0790048i
$837$		0			0
$838$	22.1854	+	16.1187i	0.766383	+	0.556810i
$839$	2.30712	−	0.490392i	0.0796505	−	0.0169302i	−0.167914	−	0.985802i	$-0.553703\pi$
$839$	2.30712	−	0.490392i	0.0796505	−	0.0169302i	0.247565	+	0.968871i	$0.420370\pi$
$840$		0			0
$841$	−7.32674	−	69.7093i	−0.252646	−	2.40377i
$842$	−1.83151	−	17.4256i	−0.0631178	−	0.600526i
$843$		0			0
$844$	0.552557	−	0.117450i	0.0190198	−	0.00404279i
$845$	−51.9360	−	37.7337i	−1.78665	−	1.29808i
$846$		0			0
$847$	1.11998	−	0.218251i	0.0384831	−	0.00749921i
$848$	−0.117093	−	0.202811i	−0.00402098	−	0.00696454i
$849$		0			0
$850$	2.37000	+	2.63215i	0.0812904	+	0.0902821i
$851$	−8.23107	−	1.74957i	−0.282157	−	0.0599744i
$852$		0			0
$853$	−26.7164	−	11.8949i	−0.914754	−	0.407275i	−0.105288	−	0.994442i	$-0.533576\pi$
$853$	−26.7164	−	11.8949i	−0.914754	−	0.407275i	−0.809466	+	0.587167i	$0.800243\pi$
$854$	0.185523	+	0.570982i	0.00634848	+	0.0195386i
$855$		0			0
$856$	−11.9332	−	8.66994i	−0.407867	−	0.296333i
$857$	14.1021	+	24.4256i	0.481720	+	0.834363i	0.999780	−	0.0209813i	$-0.00667903\pi$
$857$	14.1021	+	24.4256i	0.481720	+	0.834363i	−0.518060	+	0.855344i	$0.673346\pi$
$858$		0			0
$859$	−13.3222	+	23.0747i	−0.454548	+	0.787300i	−0.998662	−	0.0517114i	$-0.983532\pi$
$859$	−13.3222	+	23.0747i	−0.454548	+	0.787300i	0.544114	+	0.839011i	$0.316866\pi$
$860$	−1.01062	+	0.449958i	−0.0344619	+	0.0153434i
$861$		0			0
$862$	13.9654	−	15.5101i	0.475663	−	0.528277i
$863$	19.5825	−	14.2275i	0.666596	−	0.484311i	−0.202288	−	0.979326i	$-0.564838\pi$
$863$	19.5825	−	14.2275i	0.666596	−	0.484311i	0.868884	+	0.495015i	$0.164838\pi$
$864$		0			0
$865$	0.963062	+	2.96400i	0.0327451	+	0.100779i
$866$	−16.0723	+	3.41626i	−0.546158	+	0.116089i
$867$		0			0
$868$	0.0159174	−	0.0275697i	0.000540271	−	0.000935777i
$869$	47.0096	+	21.4101i	1.59469	+	0.726289i
$870$		0			0
$871$	−3.76295	+	35.8021i	−0.127503	+	1.21311i
$872$	14.5064	−	44.6460i	0.491248	−	1.51190i
$873$		0			0
$874$	18.7996	−	13.6587i	0.635905	−	0.462012i
$875$	1.11905	+	0.498234i	0.0378308	+	0.0168434i
$876$		0			0
$877$	−6.13414	−	6.81265i	−0.207135	−	0.230047i	0.630622	−	0.776090i	$-0.282800\pi$
$877$	−6.13414	−	6.81265i	−0.207135	−	0.230047i	−0.837757	+	0.546044i	$0.816133\pi$
$878$	5.16911	−	2.30144i	0.174449	−	0.0776697i
$879$		0			0
$880$	20.5063	+	15.1664i	0.691266	+	0.511258i
$881$	32.2415			1.08624			0.543122	−	0.839654i	$-0.317242\pi$
$881$	32.2415			1.08624			0.543122	+	0.839654i	$0.317242\pi$
$882$		0			0
$883$	−13.4868	+	41.5083i	−0.453869	+	1.39686i	0.418590	+	0.908175i	$0.362525\pi$
$883$	−13.4868	+	41.5083i	−0.453869	+	1.39686i	−0.872458	+	0.488689i	$0.837475\pi$
$884$	2.34386	−	2.60312i	0.0788324	−	0.0875523i
$885$		0			0
$886$	2.72216	+	25.8996i	0.0914526	+	0.870114i
$887$	−8.43321	−	1.79253i	−0.283159	−	0.0601874i	0.0641425	−	0.997941i	$-0.479569\pi$
$887$	−8.43321	−	1.79253i	−0.283159	−	0.0601874i	−0.347302	+	0.937753i	$0.612902\pi$
$888$		0			0
$889$	0.0370951	−	0.352936i	0.00124413	−	0.0118371i
$890$	22.6549			0.759393
$891$		0			0
$892$	1.41122			0.0472512
$893$	−2.37010	+	22.5500i	−0.0793123	+	0.754606i
$894$		0			0
$895$	18.1609	+	3.86021i	0.607051	+	0.129033i
$896$	−0.108314	−	1.03054i	−0.00361853	−	0.0344280i
$897$		0			0
$898$	−3.11634	+	3.46104i	−0.103994	+	0.115497i
$899$	−6.77417	+	20.8487i	−0.225931	+	0.695345i
$900$		0			0
$901$	−0.239981			−0.00799494
$902$	1.95267	+	6.18799i	0.0650169	+	0.206038i
$903$		0			0
$904$	27.1962	−	12.1085i	0.904531	−	0.402723i
$905$	29.1425	+	32.3660i	0.968730	+	1.07588i
$906$		0			0
$907$	−7.67196	−	3.41578i	−0.254743	−	0.113419i	0.275392	−	0.961332i	$-0.411192\pi$
$907$	−7.67196	−	3.41578i	−0.254743	−	0.113419i	−0.530135	+	0.847913i	$0.677859\pi$
$908$	0.737856	−	0.536084i	0.0244866	−	0.0177906i
$909$		0			0
$910$	−0.601848	+	1.85230i	−0.0199511	+	0.0614031i
$911$	−3.30178	+	31.4144i	−0.109393	+	1.04080i	0.792803	+	0.609478i	$0.208621\pi$
$911$	−3.30178	+	31.4144i	−0.109393	+	1.04080i	−0.902196	+	0.431327i	$0.858046\pi$
$912$		0			0
$913$	11.0280	−	12.0406i	0.364973	−	0.398487i
$914$	−20.1500	+	34.9007i	−0.666501	+	1.15441i
$915$		0			0
$916$	2.10636	−	0.447720i	0.0695960	−	0.0147931i
$917$	0.568989	+	1.75117i	0.0187897	+	0.0578287i
$918$		0			0
$919$	33.1386	−	24.0766i	1.09314	−	0.794213i	0.113214	−	0.993571i	$-0.463885\pi$
$919$	33.1386	−	24.0766i	1.09314	−	0.794213i	0.979927	+	0.199357i	$0.0638855\pi$
$920$	10.4699	−	11.6280i	0.345183	−	0.383365i
$921$		0			0
$922$	50.8117	−	22.6228i	1.67340	−	0.745044i
$923$	−39.1901	+	67.8793i	−1.28996	+	2.23427i
$924$		0			0
$925$	1.11581	+	1.93264i	0.0366875	+	0.0635447i
$926$	−42.7624	−	31.0687i	−1.40526	−	1.02098i
$927$		0			0
$928$	−2.42051	−	7.44955i	−0.0794570	−	0.244544i
$929$	10.3889	+	4.62543i	0.340848	+	0.151755i	0.570020	−	0.821630i	$-0.306935\pi$
$929$	10.3889	+	4.62543i	0.340848	+	0.151755i	−0.229172	+	0.973386i	$0.573602\pi$
$930$		0			0
$931$	45.1224	+	9.59105i	1.47883	+	0.314334i
$932$	−1.98353	−	2.20293i	−0.0649726	−	0.0721593i
$933$		0			0
$934$	19.1404	+	33.1522i	0.626294	+	1.08477i
$935$	23.9664	−	10.4276i	0.783785	−	0.341020i
$936$		0			0
$937$	0.289552	+	0.210372i	0.00945925	+	0.00687255i	0.592505	−	0.805567i	$-0.298139\pi$
$937$	0.289552	+	0.210372i	0.00945925	+	0.00687255i	−0.583046	+	0.812439i	$0.698139\pi$
$938$	0.751963	−	0.159835i	0.0245525	−	0.00521879i
$939$		0			0
$940$	0.103959	+	0.989105i	0.00339077	+	0.0322610i
$941$	1.91868	+	18.2550i	0.0625472	+	0.595097i	0.980241	+	0.197808i	$0.0633822\pi$
$941$	1.91868	+	18.2550i	0.0625472	+	0.595097i	−0.917694	+	0.397289i	$0.869951\pi$
$942$		0			0
$943$	3.62111	−	0.769690i	0.117919	−	0.0250646i
$944$	20.8662	+	15.1602i	0.679137	+	0.493422i
$945$		0			0
$946$	1.66100	+	17.2075i	0.0540036	+	0.559465i
$947$	25.6076	+	44.3537i	0.832137	+	1.44130i	0.896341	+	0.443366i	$0.146216\pi$
$947$	25.6076	+	44.3537i	0.832137	+	1.44130i	−0.0642039	+	0.997937i	$0.520451\pi$
$948$		0			0
$949$	54.2485	+	60.2491i	1.76098	+	1.95577i
$950$	−6.02785	−	1.28126i	−0.195569	−	0.0415695i
$951$		0			0
$952$	−1.04905	−	0.467066i	−0.0339998	−	0.0151377i
$953$	5.01140	+	15.4235i	0.162335	+	0.499616i	0.998830	−	0.0483587i	$-0.0153991\pi$
$953$	5.01140	+	15.4235i	0.162335	+	0.499616i	−0.836495	+	0.547975i	$0.815399\pi$
$954$		0			0
$955$	15.0290	+	10.9192i	0.486326	+	0.353336i
$956$	1.20851	+	2.09320i	0.0390859	+	0.0676988i
$957$		0			0
$958$	10.7928	−	18.6936i	0.348698	−	0.603963i
$959$	−0.825551	+	0.367559i	−0.0266584	+	0.0118691i
$960$		0			0
$961$	−17.4981	+	19.4336i	−0.564453	+	0.626889i
$962$	−23.8388	+	17.3199i	−0.768593	+	0.558416i
$963$		0			0
$964$	−0.458333	−	1.41060i	−0.0147619	−	0.0454325i
$965$	−11.6204	+	2.46998i	−0.374072	+	0.0795115i
$966$		0			0
$967$	−16.2654	+	28.1725i	−0.523061	+	0.905968i	0.476579	+	0.879132i	$0.341877\pi$
$967$	−16.2654	+	28.1725i	−0.523061	+	0.905968i	−0.999640	+	0.0268364i	$0.991457\pi$
$968$	−26.2862	+	18.4243i	−0.844872	+	0.592180i
$969$		0			0
$970$	0.915330	−	8.70878i	0.0293895	−	0.279622i
$971$	0.685761	−	2.11056i	0.0220071	−	0.0677310i	−0.939450	−	0.342687i	$-0.888663\pi$
$971$	0.685761	−	2.11056i	0.0220071	−	0.0677310i	0.961457	+	0.274956i	$0.0886631\pi$
$972$		0			0
$973$	−0.321270	+	0.233416i	−0.0102994	+	0.00748298i
$974$	7.16105	+	3.18831i	0.229455	+	0.102160i
$975$		0			0
$976$	−10.5100	−	11.6726i	−0.336417	−	0.373629i
$977$	−19.5116	+	8.68712i	−0.624231	+	0.277926i	−0.694377	−	0.719611i	$-0.744320\pi$
$977$	−19.5116	+	8.68712i	−0.624231	+	0.277926i	0.0701460	+	0.997537i	$0.477653\pi$
$978$		0			0
$979$	−8.40777	+	25.1479i	−0.268714	+	0.803731i
$980$	2.02341			0.0646354
$981$		0			0
$982$	−15.0396	+	46.2870i	−0.479931	+	1.47708i
$983$	−9.67356	+	10.7436i	−0.308539	+	0.342667i	−0.877394	−	0.479771i	$-0.840720\pi$
$983$	−9.67356	+	10.7436i	−0.308539	+	0.342667i	0.568855	+	0.822438i	$0.307387\pi$
$984$		0			0
$985$	−1.50768	−	14.3446i	−0.0480386	−	0.457057i
$986$	50.3843	+	10.7095i	1.60456	+	0.341060i
$987$		0			0
$988$	−0.637052	+	6.06114i	−0.0202673	+	0.192831i
$989$	9.86295			0.313624
$990$		0			0
$991$	4.68782			0.148914			0.0744568	−	0.997224i	$-0.476278\pi$
$991$	4.68782			0.148914			0.0744568	+	0.997224i	$0.476278\pi$
$992$	−0.181129	+	1.72333i	−0.00575085	+	0.0547157i
$993$		0			0
$994$	1.63723	+	0.348004i	0.0519298	+	0.0110380i
$995$	−5.21581	−	49.6251i	−0.165352	−	1.57322i
$996$		0			0
$997$	22.6053	−	25.1058i	0.715918	−	0.795107i	−0.269907	−	0.962886i	$-0.586993\pi$
$997$	22.6053	−	25.1058i	0.715918	−	0.795107i	0.985825	+	0.167779i	$0.0536595\pi$
$998$	−11.2135	+	34.5117i	−0.354958	+	1.09245i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.l.433.9		96
3.2	odd	2	inner	891.2.n.l.433.4		96
9.2	odd	6	inner	891.2.n.l.136.9		96
9.4	even	3		891.2.f.g.730.9	yes	48
9.5	odd	6		891.2.f.g.730.4	yes	48
9.7	even	3	inner	891.2.n.l.136.4		96
11.3	even	5	inner	891.2.n.l.190.4		96
33.14	odd	10	inner	891.2.n.l.190.9		96
99.5	odd	30		9801.2.a.cr.1.18		24
99.14	odd	30		891.2.f.g.487.4	✓	48
99.25	even	15	inner	891.2.n.l.784.9		96
99.47	odd	30	inner	891.2.n.l.784.4		96
99.49	even	15		9801.2.a.cr.1.7		24
99.50	even	30		9801.2.a.cq.1.7		24
99.58	even	15		891.2.f.g.487.9	yes	48
99.94	odd	30		9801.2.a.cq.1.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.4	✓	48	99.14	odd	30
891.2.f.g.487.9	yes	48	99.58	even	15
891.2.f.g.730.4	yes	48	9.5	odd	6
891.2.f.g.730.9	yes	48	9.4	even	3
891.2.n.l.136.4		96	9.7	even	3	inner
891.2.n.l.136.9		96	9.2	odd	6	inner
891.2.n.l.190.4		96	11.3	even	5	inner
891.2.n.l.190.9		96	33.14	odd	10	inner
891.2.n.l.433.4		96	3.2	odd	2	inner
891.2.n.l.433.9		96	1.1	even	1	trivial
891.2.n.l.784.4		96	99.47	odd	30	inner
891.2.n.l.784.9		96	99.25	even	15	inner
9801.2.a.cq.1.7		24	99.50	even	30
9801.2.a.cq.1.18		24	99.94	odd	30
9801.2.a.cr.1.7		24	99.49	even	15
9801.2.a.cr.1.18		24	99.5	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.142582 - 1.35658i) q^{2} +(0.136314 + 0.0289745i) q^{4} +(-0.217145 - 2.06600i) q^{5} +(-0.0694102 + 0.0770878i) q^{7} +(0.901773 - 2.77537i) q^{8} +O(q^{10})\)	\(q+(0.142582 - 1.35658i) q^{2} +(0.136314 + 0.0289745i) q^{4} +(-0.217145 - 2.06600i) q^{5} +(-0.0694102 + 0.0770878i) q^{7} +(0.901773 - 2.77537i) q^{8} -2.83366 q^{10} +(1.05164 - 3.14548i) q^{11} +(-6.05306 + 2.69500i) q^{13} +(0.0946792 + 0.105152i) q^{14} +(-3.38182 - 1.50568i) q^{16} +(-3.06899 + 2.22975i) q^{17} +(2.03958 - 6.27717i) q^{19} +(0.0302613 - 0.287917i) q^{20} +(-4.11715 - 1.87512i) q^{22} +(-1.29054 + 2.23528i) q^{23} +(0.669535 - 0.142314i) q^{25} +(2.79292 + 8.59573i) q^{26} +(-0.0116952 + 0.00849706i) q^{28} +(6.66090 - 7.39768i) q^{29} +(-2.01179 + 0.895705i) q^{31} +(0.393434 - 0.681448i) q^{32} +(2.58725 + 4.48125i) q^{34} +(0.174336 + 0.126662i) q^{35} +(1.00747 + 3.10068i) q^{37} +(-8.22468 - 3.66186i) q^{38} +(-5.92974 - 1.26040i) q^{40} +(-0.959724 - 1.06588i) q^{41} +(-1.91062 - 3.30930i) q^{43} +(0.234492 - 0.398304i) q^{44} +(2.84833 + 2.06943i) q^{46} +(-3.36031 + 0.714255i) q^{47} +(0.730574 + 6.95095i) q^{49} +(-0.0975967 - 0.928570i) q^{50} +(-0.903206 + 0.191982i) q^{52} +(0.0511797 + 0.0371842i) q^{53} +(-6.72692 - 1.48966i) q^{55} +(0.151355 + 0.262155i) q^{56} +(-9.08582 - 10.0908i) q^{58} +(-6.81507 - 1.44859i) q^{59} +(3.87617 + 1.72578i) q^{61} +(0.928251 + 2.85686i) q^{62} +(-6.85808 - 4.98268i) q^{64} +(6.88226 + 11.9204i) q^{65} +(2.71656 - 4.70522i) q^{67} +(-0.482953 + 0.215025i) q^{68} +(0.196685 - 0.218440i) q^{70} +(9.57016 - 6.95313i) q^{71} +(-3.78107 - 11.6369i) q^{73} +(4.34996 - 0.924613i) q^{74} +(0.459902 - 0.796573i) q^{76} +(0.169484 + 0.299397i) q^{77} +(-1.62800 + 15.4894i) q^{79} +(-2.37639 + 7.31378i) q^{80} +(-1.58279 + 1.14997i) q^{82} +(4.49737 + 2.00236i) q^{83} +(5.27308 + 5.85635i) q^{85} +(-4.76175 + 2.12007i) q^{86} +(-7.78155 - 5.75520i) q^{88} -7.99493 q^{89} +(0.212393 - 0.653678i) q^{91} +(-0.240686 + 0.267309i) q^{92} +(0.489824 + 4.66037i) q^{94} +(-13.4115 - 2.85070i) q^{95} +(-0.323021 + 3.07334i) q^{97} +9.53369 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 8 q^{4} + 14 q^{7}+O(q^{10}) \) 96 * q + 8 * q^4 + 14 * q^7	\( 96 q + 8 q^{4} + 14 q^{7} + 64 q^{10} + 14 q^{13} + 4 q^{16} - 16 q^{19} - 16 q^{22} + 20 q^{25} - 36 q^{28} + 4 q^{31} - 84 q^{34} - 24 q^{37} + 106 q^{40} - 84 q^{43} - 76 q^{46} + 54 q^{49} - 52 q^{52} - 72 q^{55} + 10 q^{58} + 6 q^{61} - 104 q^{64} - 76 q^{67} + 8 q^{70} - 92 q^{73} - 204 q^{76} + 102 q^{79} + 24 q^{82} - 54 q^{85} + 44 q^{91} + 118 q^{94} + 66 q^{97}+O(q^{100}) \) 96 * q + 8 * q^4 + 14 * q^7 + 64 * q^10 + 14 * q^13 + 4 * q^16 - 16 * q^19 - 16 * q^22 + 20 * q^25 - 36 * q^28 + 4 * q^31 - 84 * q^34 - 24 * q^37 + 106 * q^40 - 84 * q^43 - 76 * q^46 + 54 * q^49 - 52 * q^52 - 72 * q^55 + 10 * q^58 + 6 * q^61 - 104 * q^64 - 76 * q^67 + 8 * q^70 - 92 * q^73 - 204 * q^76 + 102 * q^79 + 24 * q^82 - 54 * q^85 + 44 * q^91 + 118 * q^94 + 66 * q^97

Introduction

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