LMFDB - Embedded newform 891.2.n.l.433.4

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			433.4
Character	$\chi$	$=$	891.433
Dual form			891.2.n.l.784.4

$q$-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	$0.193519\pi$
$2$	−0.142582	+	1.35658i	−0.100821	+	0.959247i	−0.921637	+	0.388054i	$0.873147\pi$
$3$		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	$0.120438\pi$
$5$	0.217145	+	2.06600i	0.0971103	+	0.923943i	−0.832158	+	0.554538i	$0.812895\pi$
$6$		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	−0.149728	−	0.988727i	$-0.547840\pi$
$17$	3.06899	−	2.22975i	0.744339	−	0.540794i	0.894067	+	0.447933i	$0.147840\pi$
$18$		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	−0.699532	−	0.714601i	$-0.746608\pi$
$23$	1.29054	−	2.23528i	0.269096	−	0.466089i	0.968629	+	0.248512i	$0.0799416\pi$
$24$		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	$0.608648\pi$
$29$	−6.66090	+	7.39768i	−1.23690	+	1.37371i	−0.902159	+	0.431404i	$0.858019\pi$
$30$		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	0.813411	−	0.581689i	$-0.197608\pi$
$41$	0.959724	+	1.06588i	0.149884	+	0.166463i	−0.663527	+	0.748152i	$0.730941\pi$
$42$		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	0.0437955	−	0.999041i	$-0.486055\pi$
$47$	3.36031	−	0.714255i	0.490151	−	0.104185i	0.446356	+	0.894856i	$0.352722\pi$
$48$		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	0.584265	−	0.811563i	$-0.301383\pi$
$53$	−0.0511797	−	0.0371842i	−0.00703007	−	0.00510765i	−0.591295	+	0.806456i	$0.701383\pi$
$54$		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	0.628922	−	0.777468i	$-0.283496\pi$
$59$	6.81507	+	1.44859i	0.887246	+	0.188590i	0.258324	+	0.966058i	$0.416830\pi$
$60$		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	−0.986524	−	0.163616i	$-0.947684\pi$
$71$	−9.57016	+	6.95313i	−1.13577	+	0.825185i	−0.149245	+	0.988800i	$0.547684\pi$
$72$		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	0.144784	−	0.989463i	$-0.453751\pi$
$83$	−4.49737	−	2.00236i	−0.493650	−	0.219787i	−0.638435	+	0.769676i	$0.720418\pi$
$84$		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	$-0.360720\pi$
$89$	7.99493			0.847461			0.423731	+	0.905788i	$0.360720\pi$
$90$		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	$0.0729930\pi$
$101$	−0.261096	+	2.48416i	−0.0259800	+	0.247183i	−0.999803	+	0.0198736i	$0.993674\pi$
$102$		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	−0.997734	−	0.0672891i	$-0.978565\pi$
$107$	−1.56194	+	4.80716i	−0.150999	+	0.464726i	0.846735	+	0.532015i	$0.178565\pi$
$108$		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	0.330931	−	0.943655i	$-0.392637\pi$
$113$	−6.82611	−	7.58117i	−0.642147	−	0.713176i	−0.973077	+	0.230479i	$0.925971\pi$
$114$		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	$0.449134\pi$
$131$	−8.87522	+	15.3723i	−0.775432	+	1.34309i	−0.934551	+	0.355828i	$0.884199\pi$
$132$		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	0.0375520	−	0.999295i	$-0.488044\pi$
$137$	−7.95851	−	3.54336i	−0.679941	−	0.302729i	−0.717493	+	0.696565i	$0.754711\pi$
$138$		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	$0.106119\pi$
$149$	1.08256	+	10.2999i	0.0886867	+	0.843797i	−0.856254	+	0.516555i	$0.827214\pi$
$150$		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	−0.238803	−	0.971068i	$-0.576755\pi$
$167$	4.17473	−	1.85871i	0.323051	−	0.143831i	0.561854	+	0.827237i	$0.310088\pi$
$168$		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	−0.151790	−	0.988413i	$-0.548504\pi$
$173$	1.46744	−	0.311914i	0.111567	−	0.0237144i	0.263357	+	0.964698i	$0.415170\pi$
$174$		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	$-0.791598\pi$
$179$	2.76184	−	8.50007i	0.206430	−	0.635325i	0.999652	−	0.0263926i	$-0.00840199\pi$
$180$		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	−0.486697	−	0.873571i	$-0.661798\pi$
$191$	5.98365	−	6.64552i	0.432962	−	0.480853i	0.919659	+	0.392718i	$0.128465\pi$
$192$		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	$-0.579557\pi$
$197$	−6.94318			−0.494681			−0.247341	+	0.968929i	$0.579557\pi$
$198$		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	−0.870732	−	0.491757i	$-0.836355\pi$
$227$	−4.37913	+	4.86351i	−0.290653	+	0.322803i	0.580080	+	0.814560i	$0.303021\pi$
$228$		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	0.985311	−	0.170770i	$-0.0546255\pi$
$233$	17.2087	+	12.5028i	1.12738	+	0.819087i	0.142066	+	0.989857i	$0.454625\pi$
$234$		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	0.239880	−	0.970803i	$-0.422892\pi$
$239$	−11.6052	−	12.8889i	−0.750679	−	0.833713i	−0.990559	+	0.137090i	$0.956225\pi$
$240$		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	$0.0448866\pi$
$251$	22.6506	+	16.4566i	1.42969	+	1.03873i	0.439619	+	0.898184i	$0.355113\pi$
$252$		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	−0.376109	−	0.926575i	$-0.622738\pi$
$257$	−17.5794	−	3.73662i	−1.09657	−	0.233084i	−0.720465	+	0.693492i	$0.756071\pi$
$258$		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	0.572103	−	0.820182i	$-0.306128\pi$
$263$	−6.88012	−	11.9167i	−0.424247	−	0.734817i	−0.996350	+	0.0853650i	$0.972794\pi$
$264$		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	−0.881871	−	0.471490i	$-0.843716\pi$
$269$	−11.5788	+	8.41248i	−0.705971	+	0.512918i	0.175900	+	0.984408i	$0.443716\pi$
$270$		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	0.778632	−	0.627481i	$-0.215914\pi$
$281$	13.9692	+	6.21947i	0.833330	+	0.371022i	0.0546976	+	0.998503i	$0.482581\pi$
$282$		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	0.508310	−	0.861174i	$-0.330271\pi$
$293$	10.6538	+	2.26454i	0.622402	+	0.132296i	0.114093	+	0.993470i	$0.463604\pi$
$294$		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	0.935322	−	0.353797i	$-0.115110\pi$
$311$	8.56533	+	9.51277i	0.485695	+	0.539419i	−0.449627	+	0.893217i	$0.648443\pi$
$312$		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	$-0.891014\pi$
$317$	0.876337	−	8.33778i	0.0492200	−	0.468297i	0.991175	−	0.132558i	$-0.0423192\pi$
$318$		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	$-0.667074\pi$
$347$	−3.55559	−	33.8292i	−0.190874	−	1.81605i	0.310233	−	0.950661i	$-0.399593\pi$
$348$		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	0.574855	−	0.818255i	$-0.305058\pi$
$353$	−7.91367	−	13.7069i	−0.421202	−	0.729544i	−0.996057	+	0.0887116i	$0.971725\pi$
$354$		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	0.954568	−	0.297992i	$-0.0963170\pi$
$359$	0.135487	+	0.416986i	0.00715073	+	0.0220077i	−0.947417	+	0.320000i	$0.896317\pi$
$360$		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	0.0837894	−	0.996483i	$-0.473298\pi$
$383$	17.2295	−	7.67107i	0.880387	−	0.391974i	0.796598	+	0.604510i	$0.206631\pi$
$384$		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	−0.202949	−	0.979189i	$-0.565053\pi$
$389$	15.6225	−	17.3505i	0.792090	−	0.879705i	0.995039	+	0.0994841i	$0.0317192\pi$
$390$		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	$0.0897714\pi$
$401$	1.57899	+	15.0231i	0.0788512	+	0.750219i	−0.881643	+	0.471918i	$0.843562\pi$
$402$		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	−0.508879	−	0.860838i	$-0.669940\pi$
$419$	10.0519	−	17.4104i	0.491069	−	0.850556i	0.999947	+	0.0102827i	$0.00327314\pi$
$420$		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	0.248295	−	0.968685i	$-0.420130\pi$
$431$	−12.3785	−	8.99352i	−0.596252	−	0.433202i	−0.844547	+	0.535482i	$0.820130\pi$
$432$		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	0.258331	−	0.966057i	$-0.416828\pi$
$443$	18.6746	−	3.96941i	0.887258	−	0.188592i	0.628927	+	0.777464i	$0.283494\pi$
$444$		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	0.651053	−	0.759032i	$-0.274327\pi$
$449$	2.76223	+	2.00688i	0.130358	+	0.0947104i	−0.520696	+	0.853742i	$0.674327\pi$
$450$		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	$-0.768197\pi$
$461$	−20.3879	−	35.3129i	−0.949560	−	1.64469i	−0.203207	−	0.979136i	$-0.565136\pi$
$462$		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	0.0782979	−	0.996930i	$-0.475051\pi$
$467$	22.7043	−	16.4956i	1.05063	−	0.763327i	0.972332	+	0.233603i	$0.0750515\pi$
$468$		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	0.0489609	−	0.998801i	$-0.484409\pi$
$479$	−14.4564	−	6.43642i	−0.660531	−	0.294088i	−0.709492	+	0.704713i	$0.751076\pi$
$480$		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	0.910828	−	0.412786i	$-0.135444\pi$
$491$	34.9000	+	7.41823i	1.57502	+	0.334780i	0.664188	+	0.747566i	$0.268777\pi$
$492$		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	$0.355805\pi$
$503$	−9.97834	+	30.7102i	−0.444912	+	1.36930i	−0.882580	+	0.470162i	$0.844195\pi$
$504$		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	$-0.978059\pi$
$509$	−21.7002	−	24.1005i	−0.961842	−	1.06823i	0.0357831	−	0.999360i	$-0.488607\pi$
$510$		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	0.818099	−	0.575078i	$-0.195028\pi$
$521$	−4.14919	−	12.7699i	−0.181779	−	0.559460i	−0.999878	+	0.0156184i	$0.995028\pi$
$522$		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	0.999385	−	0.0350524i	$-0.0111598\pi$
$557$	4.01834	+	12.3672i	0.170262	+	0.524014i	−0.829123	+	0.559066i	$0.811160\pi$
$558$		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	$0.739776\pi$
$563$	−39.9533	+	17.7883i	−1.68383	+	0.749689i	−0.999795	+	0.0202395i	$0.993557\pi$
$564$		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	−0.215971	−	0.976400i	$-0.569292\pi$
$569$	−0.384824	+	0.0817969i	−0.0161327	+	0.00342910i	0.199838	+	0.979829i	$0.435958\pi$
$570$		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	−0.884740	−	0.466084i	$-0.845664\pi$
$587$	−7.96448	+	8.84545i	−0.328729	+	0.365091i	0.556011	+	0.831175i	$0.312331\pi$
$588$		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	$-0.294484\pi$
$593$	29.3055			1.20343			0.601717	+	0.798709i	$0.294484\pi$
$594$		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	$-0.977862\pi$
$599$	−0.887145	−	8.44062i	−0.0362478	−	0.344875i	0.961335	−	0.275383i	$-0.0888045\pi$
$600$		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	−0.868279	−	0.496075i	$-0.834774\pi$
$617$	−0.112417	+	0.194713i	−0.00452576	+	0.00783884i	0.863754	+	0.503914i	$0.168107\pi$
$618$		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	0.234473	−	0.972123i	$-0.424664\pi$
$641$	21.3702	−	4.54238i	0.844073	−	0.179413i	0.609600	+	0.792709i	$0.291330\pi$
$642$		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	0.925291	−	0.379259i	$-0.123821\pi$
$647$	21.6341	+	15.7181i	0.850525	+	0.617943i	−0.0747658	+	0.997201i	$0.523821\pi$
$648$		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	−0.391714	−	0.920087i	$-0.628118\pi$
$653$	−28.7173	−	6.10406i	−1.12380	−	0.238870i	−0.732082	+	0.681217i	$0.761451\pi$
$654$		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	$0.0854775\pi$
$659$	18.2740	+	31.6515i	0.711854	+	1.23297i	−0.252307	+	0.967647i	$0.581189\pi$
$660$		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	0.860803	−	0.508938i	$-0.169962\pi$
$677$	27.5434	+	12.2631i	1.05858	+	0.471309i	0.197775	+	0.980247i	$0.436629\pi$
$678$		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	$-0.839664\pi$
$683$	−45.7767			−1.75160			−0.875798	+	0.482677i	$0.839664\pi$
$684$		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	$0.344859\pi$
$701$	−11.3822	+	35.0310i	−0.429902	+	1.32310i	−0.898222	+	0.439542i	$0.855141\pi$
$702$		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	$-0.872975\pi$
$719$	−10.8427	−	33.3703i	−0.404363	−	1.24450i	0.517063	−	0.855947i	$-0.327025\pi$
$720$		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	$-0.731803\pi$
$743$	−4.62621	−	44.0155i	−0.169719	−	1.61477i	0.495832	−	0.868419i	$-0.334863\pi$
$744$		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	−0.0597977	−	0.998211i	$-0.519046\pi$
$761$	17.7105	−	7.88522i	0.642005	−	0.285839i	0.701803	+	0.712372i	$0.252379\pi$
$762$		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	$0.277220\pi$
$773$	−9.08010	+	27.9457i	−0.326589	+	1.00514i	−0.970718	+	0.240220i	$0.922780\pi$
$774$		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	$0.179592\pi$
$797$	3.66004	+	34.8230i	0.129645	+	1.23349i	−0.715368	+	0.698748i	$0.753741\pi$
$798$		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	−0.825867	−	0.563864i	$-0.809314\pi$
$809$	−15.4959	+	11.2584i	−0.544807	+	0.395826i	0.281060	+	0.959690i	$0.409314\pi$
$810$		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	−0.375602	−	0.926781i	$-0.622564\pi$
$821$	16.7725	−	18.6277i	0.585363	−	0.650112i	0.960965	+	0.276669i	$0.0892307\pi$
$822$		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	0.940455	−	0.339919i	$-0.110400\pi$
$827$	26.1058	+	18.9670i	0.907789	+	0.659547i	−0.0326657	+	0.999466i	$0.510400\pi$
$828$		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	−0.247565	−	0.968871i	$-0.579630\pi$
$839$	−2.30712	+	0.490392i	−0.0796505	+	0.0169302i	0.167914	+	0.985802i	$0.446297\pi$
$840$		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	0.518060	−	0.855344i	$-0.326654\pi$
$857$	−14.1021	−	24.4256i	−0.481720	−	0.834363i	−0.999780	+	0.0209813i	$0.993321\pi$
$858$		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	−0.868884	−	0.495015i	$-0.835162\pi$
$863$	−19.5825	+	14.2275i	−0.666596	+	0.484311i	0.202288	+	0.979326i	$0.435162\pi$
$864$		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	$-0.682758\pi$
$881$	−32.2415			−1.08624			−0.543122	+	0.839654i	$0.682758\pi$
$882$		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	0.347302	−	0.937753i	$-0.387098\pi$
$887$	8.43321	+	1.79253i	0.283159	+	0.0601874i	−0.0641425	+	0.997941i	$0.520431\pi$
$888$		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	$-0.791379\pi$
$911$	3.30178	−	31.4144i	0.109393	−	1.04080i	0.902196	−	0.431327i	$-0.141954\pi$
$912$		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	0.229172	−	0.973386i	$-0.426398\pi$
$929$	−10.3889	−	4.62543i	−0.340848	−	0.151755i	−0.570020	+	0.821630i	$0.693065\pi$
$930$		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	$-0.936618\pi$
$941$	−1.91868	−	18.2550i	−0.0625472	−	0.595097i	0.917694	−	0.397289i	$-0.130049\pi$
$942$		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	$-0.853784\pi$
$947$	−25.6076	−	44.3537i	−0.832137	−	1.44130i	0.0642039	−	0.997937i	$-0.479549\pi$
$948$		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	0.836495	−	0.547975i	$-0.184601\pi$
$953$	−5.01140	−	15.4235i	−0.162335	−	0.499616i	−0.998830	+	0.0483587i	$0.984601\pi$
$954$		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	−0.961457	−	0.274956i	$-0.911337\pi$
$971$	−0.685761	+	2.11056i	−0.0220071	+	0.0677310i	0.939450	+	0.342687i	$0.111337\pi$
$972$		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	−0.0701460	−	0.997537i	$-0.522347\pi$
$977$	19.5116	−	8.68712i	0.624231	−	0.277926i	0.694377	+	0.719611i	$0.255680\pi$
$978$		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	−0.568855	−	0.822438i	$-0.692613\pi$
$983$	9.67356	−	10.7436i	0.308539	−	0.342667i	0.877394	+	0.479771i	$0.159280\pi$
$984$		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.433.4		96
3.2	odd	2	inner	891.2.n.l.433.9		96
9.2	odd	6	inner	891.2.n.l.136.4		96
9.4	even	3		891.2.f.g.730.4	yes	48
9.5	odd	6		891.2.f.g.730.9	yes	48
9.7	even	3	inner	891.2.n.l.136.9		96
11.3	even	5	inner	891.2.n.l.190.9		96
33.14	odd	10	inner	891.2.n.l.190.4		96
99.5	odd	30		9801.2.a.cr.1.7		24
99.14	odd	30		891.2.f.g.487.9	yes	48
99.25	even	15	inner	891.2.n.l.784.4		96
99.47	odd	30	inner	891.2.n.l.784.9		96
99.49	even	15		9801.2.a.cr.1.18		24
99.50	even	30		9801.2.a.cq.1.18		24
99.58	even	15		891.2.f.g.487.4	✓	48
99.94	odd	30		9801.2.a.cq.1.7		24

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

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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