LMFDB - Embedded newform 891.2.f.g.730.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			730.4
Character	$\chi$	$=$	891.730
Dual form			891.2.f.g.487.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10354 - 0.801770i) q^{2} +(-0.0430645 - 0.132539i) q^{4} +(1.68064 - 1.22105i) q^{5} +(-0.0320549 - 0.0986549i) q^{7} +(-0.901773 + 2.77537i) q^{8} +O(q^{10})$	\(q+(-1.10354 - 0.801770i) q^{2} +(-0.0430645 - 0.132539i) q^{4} +(1.68064 - 1.22105i) q^{5} +(-0.0320549 - 0.0986549i) q^{7} +(-0.901773 + 2.77537i) q^{8} -2.83366 q^{10} +(-2.19825 - 2.48349i) q^{11} +(5.36047 + 3.89461i) q^{13} +(-0.0437246 + 0.134570i) q^{14} +(2.99487 - 2.17590i) q^{16} +(3.06899 - 2.22975i) q^{17} +(2.03958 - 6.27717i) q^{19} +(-0.234213 - 0.170166i) q^{20} +(0.434674 + 4.50312i) q^{22} -2.58108 q^{23} +(-0.211520 + 0.650992i) q^{25} +(-2.79292 - 8.59573i) q^{26} +(-0.0116952 + 0.00849706i) q^{28} +(-3.07613 - 9.46735i) q^{29} +(1.78160 + 1.29441i) q^{31} +0.786868 q^{32} -5.17450 q^{34} +(-0.174336 - 0.126662i) q^{35} +(1.00747 + 3.10068i) q^{37} +(-7.28360 + 5.29185i) q^{38} +(1.87333 + 5.76550i) q^{40} +(0.443218 - 1.36409i) q^{41} +3.82125 q^{43} +(-0.234492 + 0.398304i) q^{44} +(2.84833 + 2.06943i) q^{46} +(-1.06159 + 3.26724i) q^{47} +(5.65441 - 4.10817i) q^{49} +(0.755367 - 0.548806i) q^{50} +(0.285342 - 0.878191i) q^{52} +(-0.0511797 - 0.0371842i) q^{53} +(-6.72692 - 1.48966i) q^{55} +0.302710 q^{56} +(-4.19600 + 12.9140i) q^{58} +(-2.15302 - 6.62632i) q^{59} +(-3.43265 + 2.49397i) q^{61} +(-0.928251 - 2.85686i) q^{62} +(-6.85808 - 4.98268i) q^{64} +13.7645 q^{65} -5.43311 q^{67} +(-0.427694 - 0.310738i) q^{68} +(0.0908326 + 0.279554i) q^{70} +(-9.57016 + 6.95313i) q^{71} +(-3.78107 - 11.6369i) q^{73} +(1.37424 - 4.22949i) q^{74} -0.919803 q^{76} +(-0.174543 + 0.296476i) q^{77} +(-12.6002 - 9.15460i) q^{79} +(2.37639 - 7.31378i) q^{80} +(-1.58279 + 1.14997i) q^{82} +(3.98278 - 2.89366i) q^{83} +(2.43521 - 7.49479i) q^{85} +(-4.21690 - 3.06376i) q^{86} +(8.87492 - 3.86142i) q^{88} +7.99493 q^{89} +(0.212393 - 0.653678i) q^{91} +(0.111153 + 0.342094i) q^{92} +(3.79108 - 2.75438i) q^{94} +(-4.23697 - 13.0401i) q^{95} +(-2.50008 - 1.81641i) q^{97} -9.53369 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} - 14 q^{7}+O(q^{10}) $ 48 * q - 8 * q^4 - 14 * q^7	$ 48 q - 8 q^{4} - 14 q^{7} + 32 q^{10} - 14 q^{13} - 4 q^{16} - 8 q^{19} + 16 q^{22} - 20 q^{25} - 18 q^{28} - 4 q^{31} + 84 q^{34} - 12 q^{37} - 106 q^{40} + 84 q^{43} - 38 q^{46} - 54 q^{49} + 52 q^{52} - 36 q^{55} - 10 q^{58} - 6 q^{61} - 52 q^{64} + 76 q^{67} - 8 q^{70} - 46 q^{73} + 204 q^{76} - 102 q^{79} + 12 q^{82} + 54 q^{85} + 22 q^{91} - 118 q^{94} - 66 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 - 14 * q^7 + 32 * q^10 - 14 * q^13 - 4 * q^16 - 8 * q^19 + 16 * q^22 - 20 * q^25 - 18 * q^28 - 4 * q^31 + 84 * q^34 - 12 * q^37 - 106 * q^40 + 84 * q^43 - 38 * q^46 - 54 * q^49 + 52 * q^52 - 36 * q^55 - 10 * q^58 - 6 * q^61 - 52 * q^64 + 76 * q^67 - 8 * q^70 - 46 * q^73 + 204 * q^76 - 102 * q^79 + 12 * q^82 + 54 * q^85 + 22 * q^91 - 118 * q^94 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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 $

$2$	−1.10354	−	0.801770i	−0.780322	−	0.566937i	0.124754	−	0.992188i	$-0.460186\pi$
$2$	−1.10354	−	0.801770i	−0.780322	−	0.566937i	−0.905076	+	0.425251i	$0.860186\pi$
$3$		0			0
$3$		0			0
$4$	−0.0430645	−	0.132539i	−0.0215323	−	0.0662695i
$5$	1.68064	−	1.22105i	0.751603	−	0.546072i	−0.144720	−	0.989473i	$-0.546228\pi$
$5$	1.68064	−	1.22105i	0.751603	−	0.546072i	0.896323	+	0.443401i	$0.146228\pi$
$6$		0			0
$7$	−0.0320549	−	0.0986549i	−0.0121156	−	0.0372880i	0.944816	−	0.327602i	$-0.106240\pi$
$7$	−0.0320549	−	0.0986549i	−0.0121156	−	0.0372880i	−0.956932	+	0.290314i	$0.906240\pi$
$8$	−0.901773	+	2.77537i	−0.318825	+	0.981243i
$9$		0			0
$10$	−2.83366			−0.896081
$11$	−2.19825	−	2.48349i	−0.662797	−	0.748799i
$11$	−2.19825	−	2.48349i	−0.662797	−	0.748799i
$12$		0			0
$13$	5.36047	+	3.89461i	1.48673	+	1.08017i	0.975311	+	0.220836i	$0.0708786\pi$
$13$	5.36047	+	3.89461i	1.48673	+	1.08017i	0.511415	+	0.859334i	$0.329121\pi$
$14$	−0.0437246	+	0.134570i	−0.0116859	+	0.0359655i
$15$		0			0
$16$	2.99487	−	2.17590i	0.748717	−	0.543975i
$17$	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	$-0.173382\pi$
$20$	−0.234213	−	0.170166i	−0.0523716	−	0.0380502i
$21$		0			0
$22$	0.434674	+	4.50312i	0.0926728	+	0.960069i
$23$	−2.58108			−0.538193			−0.269096	−	0.963113i	$-0.586725\pi$
$23$	−2.58108			−0.538193			−0.269096	+	0.963113i	$0.586725\pi$
$24$		0			0
$25$	−0.211520	+	0.650992i	−0.0423040	+	0.130198i
$26$	−2.79292	−	8.59573i	−0.547737	−	1.68576i
$27$		0			0
$28$	−0.0116952	+	0.00849706i	−0.00221018	+	0.00160579i
$29$	−3.07613	−	9.46735i	−0.571223	−	1.75804i	−0.648696	−	0.761048i	$-0.724685\pi$
$29$	−3.07613	−	9.46735i	−0.571223	−	1.75804i	0.0774731	−	0.996994i	$-0.475315\pi$
$30$		0			0
$31$	1.78160	+	1.29441i	0.319984	+	0.232482i	0.736169	−	0.676798i	$-0.236633\pi$
$31$	1.78160	+	1.29441i	0.319984	+	0.232482i	−0.416185	+	0.909280i	$0.636633\pi$
$32$	0.786868			0.139100
$33$		0			0
$34$	−5.17450			−0.887420
$35$	−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	$0.813640\pi$
$38$	−7.28360	+	5.29185i	−1.18156	+	0.858451i
$39$		0			0
$40$	1.87333	+	5.76550i	0.296199	+	0.911606i
$41$	0.443218	−	1.36409i	0.0692191	−	0.213034i	−0.910463	−	0.413590i	$-0.864275\pi$
$41$	0.443218	−	1.36409i	0.0692191	−	0.213034i	0.979682	+	0.200556i	$0.0642747\pi$
$42$		0			0
$43$	3.82125			0.582735			0.291367	−	0.956611i	$-0.405890\pi$
$43$	3.82125			0.582735			0.291367	+	0.956611i	$0.405890\pi$
$44$	−0.234492	+	0.398304i	−0.0353511	+	0.0600466i
$45$		0			0
$46$	2.84833	+	2.06943i	0.419964	+	0.305121i
$47$	−1.06159	+	3.26724i	−0.154849	+	0.476576i	−0.998146	−	0.0608726i	$-0.980612\pi$
$47$	−1.06159	+	3.26724i	−0.154849	+	0.476576i	0.843297	+	0.537448i	$0.180612\pi$
$48$		0			0
$49$	5.65441	−	4.10817i	0.807773	−	0.586882i
$50$	0.755367	−	0.548806i	0.106825	−	0.0776129i
$51$		0			0
$52$	0.285342	−	0.878191i	0.0395697	−	0.121783i
$53$	−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
$56$	0.302710			0.0404514
$57$		0			0
$58$	−4.19600	+	12.9140i	−0.550962	+	1.69569i
$59$	−2.15302	−	6.62632i	−0.280299	−	0.862673i	−0.987768	−	0.155929i	$-0.950163\pi$
$59$	−2.15302	−	6.62632i	−0.280299	−	0.862673i	0.707469	−	0.706744i	$-0.249837\pi$
$60$		0			0
$61$	−3.43265	+	2.49397i	−0.439506	+	0.319320i	−0.785439	−	0.618939i	$-0.787563\pi$
$61$	−3.43265	+	2.49397i	−0.439506	+	0.319320i	0.345932	+	0.938259i	$0.387563\pi$
$62$	−0.928251	−	2.85686i	−0.117888	−	0.362822i
$63$		0			0
$64$	−6.85808	−	4.98268i	−0.857259	−	0.622835i
$65$	13.7645			1.70728
$66$		0			0
$67$	−5.43311			−0.663761			−0.331880	−	0.943322i	$-0.607683\pi$
$67$	−5.43311			−0.663761			−0.331880	+	0.943322i	$0.607683\pi$
$68$	−0.427694	−	0.310738i	−0.0518655	−	0.0376825i
$69$		0			0
$70$	0.0908326	+	0.279554i	0.0108566	+	0.0334131i
$71$	−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	$-0.354050\pi$
$74$	1.37424	−	4.22949i	0.159753	−	0.491668i
$75$		0			0
$76$	−0.919803			−0.105509
$77$	−0.174543	+	0.296476i	−0.0198911	+	0.0337866i
$78$		0			0
$79$	−12.6002	−	9.15460i	−1.41764	−	1.02997i	−0.992156	−	0.125006i	$-0.960105\pi$
$79$	−12.6002	−	9.15460i	−1.41764	−	1.02997i	−0.425481	−	0.904967i	$-0.639895\pi$
$80$	2.37639	−	7.31378i	0.265689	−	0.817706i
$81$		0			0
$82$	−1.58279	+	1.14997i	−0.174790	+	0.126993i
$83$	3.98278	−	2.89366i	0.437167	−	0.317620i	−0.347342	−	0.937739i	$-0.612916\pi$
$83$	3.98278	−	2.89366i	0.437167	−	0.317620i	0.784508	+	0.620119i	$0.212916\pi$
$84$		0			0
$85$	2.43521	−	7.49479i	0.264135	−	0.812925i
$86$	−4.21690	−	3.06376i	−0.454721	−	0.330374i
$87$		0			0
$88$	8.87492	−	3.86142i	0.946070	−	0.411628i
$89$	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
$92$	0.111153	+	0.342094i	0.0115885	+	0.0356658i
$93$		0			0
$94$	3.79108	−	2.75438i	0.391020	−	0.284093i
$95$	−4.23697	−	13.0401i	−0.434704	−	1.33788i
$96$		0			0
$97$	−2.50008	−	1.81641i	−0.253844	−	0.184429i	0.453584	−	0.891213i	$-0.350145\pi$
$97$	−2.50008	−	1.81641i	−0.253844	−	0.184429i	−0.707429	+	0.706784i	$0.750145\pi$
$98$	−9.53369			−0.963048
$99$		0			0
$100$	0.0953908			0.00953908
$101$	−2.02080	−	1.46820i	−0.201077	−	0.146091i	0.482690	−	0.875791i	$-0.339660\pi$
$101$	−2.02080	−	1.46820i	−0.201077	−	0.146091i	−0.683767	+	0.729700i	$0.739660\pi$
$102$		0			0
$103$	−4.37288	−	13.4583i	−0.430873	−	1.32609i	−0.897257	−	0.441508i	$-0.854444\pi$
$103$	−4.37288	−	13.4583i	−0.430873	−	1.32609i	0.466385	−	0.884582i	$-0.345556\pi$
$104$	−15.6429	+	11.3652i	−1.53391	+	1.11445i
$105$		0			0
$106$	0.0266657	+	0.0820687i	0.00259001	+	0.00797122i
$107$	−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	$0.220055\pi$
$110$	6.22908	+	7.03735i	0.593919	+	0.670985i
$111$		0			0
$112$	−0.310663	−	0.225710i	−0.0293549	−	0.0213276i
$113$	−3.15243	+	9.70217i	−0.296555	+	0.912703i	0.686139	+	0.727470i	$0.259304\pi$
$113$	−3.15243	+	9.70217i	−0.296555	+	0.912703i	−0.982695	+	0.185233i	$0.940696\pi$
$114$		0			0
$115$	−4.33786	+	3.15164i	−0.404507	+	0.293892i
$116$	−1.12232	+	0.815414i	−0.104205	+	0.0757093i
$117$		0			0
$118$	−2.93683	+	9.03865i	−0.270358	+	0.832075i
$119$	−0.318352	−	0.231296i	−0.0291833	−	0.0212029i
$120$		0			0
$121$	−1.33541	+	10.9186i	−0.121401	+	0.992604i
$122$	5.78767			0.523991
$123$		0			0
$124$	0.0948356	−	0.291874i	0.00851649	−	0.0262111i
$125$	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	$0.348503\pi$
$128$	3.08690	+	9.50049i	0.272846	+	0.839733i
$129$		0			0
$130$	−15.1897	−	11.0360i	−1.33223	−	0.967919i
$131$	17.7504			1.55086			0.775432	−	0.631431i	$-0.217532\pi$
$131$	17.7504			1.55086			0.775432	+	0.631431i	$0.217532\pi$
$132$		0			0
$133$	−0.684652			−0.0593668
$134$	5.99567	+	4.35611i	0.517947	+	0.376311i
$135$		0			0
$136$	3.42086	+	10.5283i	0.293336	+	0.902796i
$137$	7.04789	−	5.12059i	0.602142	−	0.437482i	−0.244496	−	0.969650i	$-0.578623\pi$
$137$	7.04789	−	5.12059i	0.602142	−	0.437482i	0.846639	+	0.532168i	$0.178623\pi$
$138$		0			0
$139$	−1.18299	−	3.64088i	−0.100340	−	0.308815i	0.888268	−	0.459325i	$-0.151909\pi$
$139$	−1.18299	−	3.64088i	−0.100340	−	0.308815i	−0.988609	+	0.150509i	$0.951909\pi$
$140$	−0.00928000	+	0.0285609i	−0.000784303	+	0.00241384i
$141$		0			0
$142$	16.1359			1.35409
$143$	−2.11143	−	21.8740i	−0.176567	−	1.82919i
$144$		0			0
$145$	−16.7300	−	12.1550i	−1.38935	−	1.00942i
$146$	−5.15757	+	15.8734i	−0.426844	+	1.31369i
$147$		0			0
$148$	0.367574	−	0.267058i	0.0302144	−	0.0219521i
$149$	8.37866	−	6.08745i	0.686407	−	0.498704i	−0.189070	−	0.981964i	$-0.560547\pi$
$149$	8.37866	−	6.08745i	0.686407	−	0.498704i	0.875477	+	0.483260i	$0.160547\pi$
$150$		0			0
$151$	−3.09496	+	9.52532i	−0.251865	+	0.775160i	0.742567	+	0.669772i	$0.233608\pi$
$151$	−3.09496	+	9.52532i	−0.251865	+	0.775160i	−0.994431	+	0.105387i	$0.966392\pi$
$152$	15.5822	+	11.3212i	1.26389	+	0.918268i
$153$		0			0
$154$	0.430321	−	0.187230i	0.0346763	−	0.0150874i
$155$	4.57475			0.367453
$156$		0			0
$157$	3.58465	−	11.0324i	0.286086	−	0.880482i	−0.699985	−	0.714157i	$-0.746810\pi$
$157$	3.58465	−	11.0324i	0.286086	−	0.880482i	0.986071	−	0.166324i	$-0.0531899\pi$
$158$	6.56500	+	20.2050i	0.522283	+	1.60742i
$159$		0			0
$160$	1.32244	−	0.960808i	0.104548	−	0.0759585i
$161$	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	$0.348732\pi$
$164$	−0.199882			−0.0156081
$165$		0			0
$166$	−6.71521			−0.521201
$167$	−3.69706	−	2.68607i	−0.286087	−	0.207854i	0.435481	−	0.900198i	$-0.356578\pi$
$167$	−3.69706	−	2.68607i	−0.286087	−	0.207854i	−0.721568	+	0.692344i	$0.756578\pi$
$168$		0			0
$169$	9.54942	+	29.3901i	0.734571	+	2.26078i
$170$	−8.69645	+	6.31834i	−0.666988	+	0.484595i
$171$		0			0
$172$	−0.164560	−	0.506464i	−0.0125476	−	0.0386175i
$173$	−0.463595	+	1.42680i	−0.0352465	+	0.108477i	−0.967132	−	0.254275i	$-0.918163\pi$
$173$	−0.463595	+	1.42680i	−0.0352465	+	0.108477i	0.931885	+	0.362753i	$0.118163\pi$
$174$		0			0
$175$	0.0710038			0.00536738
$176$	−11.9873	−	2.65455i	−0.903575	−	0.200094i
$177$		0			0
$178$	−8.82274	−	6.41010i	−0.661292	−	0.480457i
$179$	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	$0.584358\pi$
$182$	−0.758484	+	0.551071i	−0.0562225	+	0.0408481i
$183$		0			0
$184$	2.32755	−	7.16346i	0.171589	−	0.528098i
$185$	5.47928	+	3.98093i	0.402845	+	0.292684i
$186$		0			0
$187$	−12.2840	−	2.72024i	−0.898291	−	0.198924i
$188$	0.478754			0.0349167
$189$		0			0
$190$	−5.77945	+	17.7873i	−0.419286	+	1.29043i
$191$	2.76336	+	8.50475i	0.199950	+	0.615382i	0.999883	+	0.0152932i	$0.00486817\pi$
$191$	2.76336	+	8.50475i	0.199950	+	0.615382i	−0.799933	+	0.600089i	$0.795132\pi$
$192$		0			0
$193$	−4.62654	+	3.36138i	−0.333026	+	0.241957i	−0.741713	−	0.670717i	$-0.765987\pi$
$193$	−4.62654	+	3.36138i	−0.333026	+	0.241957i	0.408688	+	0.912674i	$0.365987\pi$
$194$	1.30260	+	4.00898i	0.0935209	+	0.287828i
$195$		0			0
$196$	−0.787998	−	0.572514i	−0.0562856	−	0.0408939i
$197$	−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	$0.175776\pi$
$200$	−1.61600	−	1.17409i	−0.114269	−	0.0830210i
$201$		0			0
$202$	1.05288	+	3.24043i	0.0740805	+	0.227996i
$203$	−0.835395	+	0.606950i	−0.0586332	+	0.0425995i
$204$		0			0
$205$	−0.920733	−	2.83372i	−0.0643068	−	0.197916i
$206$	−5.96484	+	18.3579i	−0.415590	+	1.27905i
$207$		0			0
$208$	24.5282			1.70072
$209$	−20.0728	+	8.73352i	−1.38846	+	0.604110i
$210$		0			0
$211$	−3.27939	−	2.38262i	−0.225763	−	0.164026i	0.469154	−	0.883116i	$-0.344559\pi$
$211$	−3.27939	−	2.38262i	−0.225763	−	0.164026i	−0.694917	+	0.719090i	$0.744559\pi$
$212$	−0.00272433	+	0.00838463i	−0.000187108	+	0.000575859i
$213$		0			0
$214$	5.57791	−	4.05259i	0.381298	−	0.277029i
$215$	6.42212	−	4.66594i	0.437985	−	0.318215i
$216$		0			0
$217$	0.0705905	−	0.217255i	0.00479200	−	0.0147482i
$218$	−17.7521	−	12.8977i	−1.20233	−	0.873540i
$219$		0			0
$220$	0.0922541	+	0.955731i	0.00621977	+	0.0644354i
$221$	25.1352			1.69078
$222$		0			0
$223$	−3.12925	+	9.63083i	−0.209550	+	0.644928i	0.789946	+	0.613176i	$0.210109\pi$
$223$	−3.12925	+	9.63083i	−0.209550	+	0.644928i	−0.999496	+	0.0317515i	$0.989891\pi$
$224$	−0.0252230	−	0.0776284i	−0.00168528	−	0.00518676i
$225$		0			0
$226$	11.2577	−	8.17923i	0.748854	−	0.544074i
$227$	−2.02236	−	6.22419i	−0.134229	−	0.413114i	0.861240	−	0.508198i	$-0.169688\pi$
$227$	−2.02236	−	6.22419i	−0.134229	−	0.413114i	−0.995469	+	0.0950838i	$0.969688\pi$
$228$		0			0
$229$	−12.5011	−	9.08257i	−0.826095	−	0.600193i	0.0923570	−	0.995726i	$-0.470560\pi$
$229$	−12.5011	−	9.08257i	−0.826095	−	0.600193i	−0.918452	+	0.395533i	$0.870560\pi$
$230$	7.31390			0.482264
$231$		0			0
$232$	29.0494			1.90719
$233$	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
$236$	−0.785527	+	0.570719i	−0.0511334	+	0.0371506i
$237$		0			0
$238$	0.165868	+	0.510490i	0.0107516	+	0.0330902i
$239$	−5.35950	+	16.4949i	−0.346677	+	1.06696i	0.614002	+	0.789304i	$0.289559\pi$
$239$	−5.35950	+	16.4949i	−0.346677	+	1.06696i	−0.960680	+	0.277659i	$0.910441\pi$
$240$		0			0
$241$	10.6429			0.685572			0.342786	−	0.939414i	$-0.388629\pi$
$241$	10.6429			0.685572			0.342786	+	0.939414i	$0.388629\pi$
$242$	10.2279	−	10.9785i	0.657476	−	0.705724i
$243$		0			0
$244$	0.478374	+	0.347559i	0.0306248	+	0.0222502i
$245$	4.48671	−	13.8087i	0.286646	−	0.882204i
$246$		0			0
$247$	35.3802	−	25.7052i	2.25119	−	1.63558i
$248$	−5.19905	+	3.77733i	−0.330140	+	0.239861i
$249$		0			0
$250$	4.97761	−	15.3195i	0.314812	−	0.968892i
$251$	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
$254$	4.66660			0.292809
$255$		0			0
$256$	−1.02841	+	3.16513i	−0.0642759	+	0.197821i
$257$	5.55370	+	17.0925i	0.346430	+	1.06620i	0.960814	+	0.277195i	$0.0894048\pi$
$257$	5.55370	+	17.0925i	0.346430	+	1.06620i	−0.614383	+	0.789008i	$0.710595\pi$
$258$		0			0
$259$	0.273602	−	0.198784i	0.0170008	−	0.0123518i
$260$	−0.592763	−	1.82434i	−0.0367616	−	0.113141i
$261$		0			0
$262$	−19.5884	−	14.2318i	−1.21017	−	0.879242i
$263$	13.7602			0.848493			0.424247	−	0.905547i	$-0.360539\pi$
$263$	13.7602			0.848493			0.424247	+	0.905547i	$0.360539\pi$
$264$		0			0
$265$	−0.131418			−0.00807296
$266$	0.755542	+	0.548933i	0.0463252	+	0.0336573i
$267$		0			0
$268$	0.233975	+	0.720100i	0.0142923	+	0.0439871i
$269$	−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	$0.914887\pi$
$272$	4.33950	−	13.3556i	0.263121	−	0.809803i
$273$		0			0
$274$	−11.8832			−0.717889
$275$	2.08170	−	0.905734i	0.125531	−	0.0546178i
$276$		0			0
$277$	19.3456	+	14.0554i	1.16236	+	0.844507i	0.990075	−	0.140539i	$-0.0448836\pi$
$277$	19.3456	+	14.0554i	1.16236	+	0.844507i	0.172289	+	0.985046i	$0.444884\pi$
$278$	−1.61367	+	4.96635i	−0.0967813	+	0.297862i
$279$		0			0
$280$	0.508746	−	0.369625i	0.0304034	−	0.0220893i
$281$	−12.3708	+	8.98791i	−0.737980	+	0.536174i	−0.892078	−	0.451882i	$-0.850753\pi$
$281$	−12.3708	+	8.98791i	−0.737980	+	0.536174i	0.154098	+	0.988056i	$0.450753\pi$
$282$		0			0
$283$	6.32988	−	19.4814i	0.376272	−	1.15805i	−0.566344	−	0.824169i	$-0.691643\pi$
$283$	6.32988	−	19.4814i	0.376272	−	1.15805i	0.942616	−	0.333878i	$-0.108357\pi$
$284$	1.33370	+	0.968987i	0.0791403	+	0.0574988i
$285$		0			0
$286$	−15.2078	+	25.8317i	−0.899258	+	1.52746i
$287$	−0.148781			−0.00878227
$288$		0			0
$289$	−0.806389	+	2.48181i	−0.0474347	+	0.145989i
$290$	8.71669	+	26.8272i	0.511861	+	1.57535i
$291$		0			0
$292$	−1.37952	+	1.00228i	−0.0807301	+	0.0586539i
$293$	−3.36576	−	10.3587i	−0.196630	−	0.605164i	−0.999954	−	0.00962177i	$-0.996937\pi$
$293$	−3.36576	−	10.3587i	−0.196630	−	0.605164i	0.803324	−	0.595542i	$-0.203063\pi$
$294$		0			0
$295$	−11.7095	−	8.50747i	−0.681755	−	0.495324i
$296$	−9.51404			−0.552993
$297$		0			0
$298$	−14.1269			−0.818352
$299$	−13.8358	−	10.0523i	−0.800145	−	0.581340i
$300$		0			0
$301$	−0.122490	−	0.376985i	−0.00706019	−	0.0217290i
$302$	11.0525	−	8.03014i	0.636002	−	0.462083i
$303$		0			0
$304$	−7.55022	−	23.2372i	−0.433035	−	1.33274i
$305$	−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	$0.346850\pi$
$308$	0.0468113	+	0.0103662i	0.00266732	+	0.000590670i
$309$		0			0
$310$	−5.04843	−	3.66790i	−0.286732	−	0.208323i
$311$	3.95563	−	12.1742i	0.224303	−	0.690334i	−0.774058	−	0.633114i	$-0.781776\pi$
$311$	3.95563	−	12.1742i	0.224303	−	0.690334i	0.998362	−	0.0572201i	$-0.0182237\pi$
$312$		0			0
$313$	−9.80832	+	7.12617i	−0.554399	+	0.402795i	−0.829405	−	0.558648i	$-0.811320\pi$
$313$	−9.80832	+	7.12617i	−0.554399	+	0.402795i	0.275006	+	0.961443i	$0.411320\pi$
$314$	−12.8013	+	9.30066i	−0.722417	+	0.524867i
$315$		0			0
$316$	−0.670719	+	2.06426i	−0.0377309	+	0.116124i
$317$	6.78257	+	4.92782i	0.380947	+	0.276774i	0.761736	−	0.647888i	$-0.224348\pi$
$317$	6.78257	+	4.92782i	0.380947	+	0.276774i	−0.380789	+	0.924662i	$0.624348\pi$
$318$		0			0
$319$	−16.7499	+	28.4511i	−0.937816	+	1.59296i
$320$	−17.6100			−0.984432
$321$		0			0
$322$	0.112857	−	0.347337i	0.00628926	−	0.0193564i
$323$	−7.73708	−	23.8123i	−0.430503	−	1.32495i
$324$		0			0
$325$	−3.66920	+	2.66583i	−0.203531	+	0.147874i
$326$	−9.60938	−	29.5746i	−0.532215	−	1.63799i
$327$		0			0
$328$	3.38616	+	2.46019i	0.186970	+	0.135841i
$329$	0.356358			0.0196467
$330$		0			0
$331$	−8.15077			−0.448007			−0.224003	−	0.974588i	$-0.571913\pi$
$331$	−8.15077			−0.448007			−0.224003	+	0.974588i	$0.571913\pi$
$332$	−0.555039	−	0.403259i	−0.0304617	−	0.0221317i
$333$		0			0
$334$	1.92625	+	5.92838i	0.105400	+	0.324387i
$335$	−9.13109	+	6.63412i	−0.498884	+	0.362461i
$336$		0			0
$337$	9.28005	+	28.5611i	0.505517	+	1.55582i	0.799900	+	0.600133i	$0.204886\pi$
$337$	9.28005	+	28.5611i	0.505517	+	1.55582i	−0.294384	+	0.955687i	$0.595114\pi$
$338$	13.0259	−	40.0897i	0.708517	−	2.18059i
$339$		0			0
$340$	−1.09822			−0.0595596
$341$	−0.701753	−	7.26999i	−0.0380020	−	0.393692i
$342$		0			0
$343$	−1.17399	−	0.852953i	−0.0633895	−	0.0460551i
$344$	−3.44590	+	10.6054i	−0.185790	+	0.571804i
$345$		0			0
$346$	1.65556	−	1.20283i	0.0890035	−	0.0646648i
$347$	−27.5191	+	19.9938i	−1.47730	+	1.07332i	−0.498892	+	0.866664i	$0.666260\pi$
$347$	−27.5191	+	19.9938i	−1.47730	+	1.07332i	−0.978413	+	0.206661i	$0.933740\pi$
$348$		0			0
$349$	7.27633	−	22.3943i	0.389493	−	1.19874i	−0.543675	−	0.839296i	$-0.682967\pi$
$349$	7.27633	−	22.3943i	0.389493	−	1.19874i	0.933168	−	0.359441i	$-0.117033\pi$
$350$	−0.0783556	−	0.0569287i	−0.00418829	−	0.00304297i
$351$		0			0
$352$	−1.72973	−	1.95418i	−0.0921950	−	0.104158i
$353$	15.8273			0.842404			0.421202	−	0.906967i	$-0.361608\pi$
$353$	15.8273			0.842404			0.421202	+	0.906967i	$0.361608\pi$
$354$		0			0
$355$	−7.59381	+	23.3714i	−0.403038	+	1.24042i
$356$	−0.344298	−	1.05964i	−0.0182478	−	0.0561608i
$357$		0			0
$358$	−9.86291	+	7.16582i	−0.521271	+	0.378726i
$359$	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
$362$	28.5977			1.50306
$363$		0			0
$364$	−0.0957844			−0.00502047
$365$	−20.5639	−	14.9405i	−1.07636	−	0.782024i
$366$		0			0
$367$	−4.28173	−	13.1778i	−0.223504	−	0.687876i	−0.998440	−	0.0558357i	$-0.982218\pi$
$367$	−4.28173	−	13.1778i	−0.223504	−	0.687876i	0.774936	−	0.632040i	$-0.217782\pi$
$368$	−7.73000	+	5.61617i	−0.402954	+	0.292763i
$369$		0			0
$370$	−2.85483	−	8.78625i	−0.148415	−	0.456775i
$371$	−0.00202784	+	0.00624107i	−0.000105280	+	0.000324020i
$372$		0			0
$373$	7.01569			0.363259			0.181629	−	0.983367i	$-0.441863\pi$
$373$	7.01569			0.363259			0.181629	+	0.983367i	$0.441863\pi$
$374$	11.3748	+	12.8508i	0.588179	+	0.664500i
$375$		0			0
$376$	−8.11049	−	5.89262i	−0.418267	−	0.303889i
$377$	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	$0.217535\pi$
$380$	−1.54585	+	1.12313i	−0.0793006	+	0.0576153i
$381$		0			0
$382$	3.76937	−	11.6009i	0.192858	−	0.593555i
$383$	−15.2581	−	11.0857i	−0.779653	−	0.566451i	0.125222	−	0.992129i	$-0.460036\pi$
$383$	−15.2581	−	11.0857i	−0.779653	−	0.566451i	−0.904875	+	0.425678i	$0.860036\pi$
$384$		0			0
$385$	0.0686690	+	0.711395i	0.00349969	+	0.0362560i
$386$	7.80064			0.397042
$387$		0			0
$388$	−0.133081	+	0.409581i	−0.00675616	+	0.0207933i
$389$	7.21474	+	22.2047i	0.365802	+	1.12582i	0.949477	+	0.313836i	$0.101614\pi$
$389$	7.21474	+	22.2047i	0.365802	+	1.12582i	−0.583675	+	0.811987i	$0.698386\pi$
$390$		0			0
$391$	−7.92131	+	5.75517i	−0.400598	+	0.291051i
$392$	6.30271	+	19.3977i	0.318335	+	0.979734i
$393$		0			0
$394$	7.66209	+	5.56683i	0.386011	+	0.280453i
$395$	−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	$0.744636\pi$
$398$	−26.5070	−	19.2585i	−1.32868	−	0.965339i
$399$		0			0
$400$	0.783017	+	2.40988i	0.0391509	+	0.120494i
$401$	12.2209	−	8.87901i	0.610283	−	0.443397i	−0.239231	−	0.970963i	$-0.576895\pi$
$401$	12.2209	−	8.87901i	0.610283	−	0.443397i	0.849514	+	0.527566i	$0.176895\pi$
$402$		0			0
$403$	4.50899	+	13.8772i	0.224609	+	0.691274i
$404$	−0.107569	+	0.331062i	−0.00535174	+	0.0164710i
$405$		0			0
$406$	1.40853			0.0699041
$407$	5.48582	−	9.31810i	0.271922	−	0.461881i
$408$		0			0
$409$	7.61125	+	5.52990i	0.376352	+	0.273436i	0.759840	−	0.650110i	$-0.225277\pi$
$409$	7.61125	+	5.52990i	0.376352	+	0.273436i	−0.383488	+	0.923546i	$0.625277\pi$
$410$	−1.25593	+	3.86535i	−0.0620259	+	0.190896i
$411$		0			0
$412$	−1.59544	+	1.15915i	−0.0786017	+	0.0571075i
$413$	−0.584704	+	0.424812i	−0.0287714	+	0.0209036i
$414$		0			0
$415$	3.16029	−	9.72636i	0.155132	−	0.477448i
$416$	4.21798	+	3.06454i	0.206804	+	0.150252i
$417$		0			0
$418$	29.1534	+	6.45593i	1.42594	+	0.315770i
$419$	−20.1038			−0.982137			−0.491069	−	0.871121i	$-0.663394\pi$
$419$	−20.1038			−0.982137			−0.491069	+	0.871121i	$0.663394\pi$
$420$		0			0
$421$	−3.96940	+	12.2166i	−0.193457	+	0.595398i	0.806534	+	0.591187i	$0.201341\pi$
$421$	−3.96940	+	12.2166i	−0.193457	+	0.595398i	−0.999991	+	0.00421133i	$0.998659\pi$
$422$	1.70863	+	5.25863i	0.0831750	+	0.255986i
$423$		0			0
$424$	0.149353	−	0.108511i	0.00725320	−	0.00526976i
$425$	0.802396	+	2.46952i	0.0389219	+	0.119789i
$426$		0			0
$427$	0.356076	+	0.258704i	0.0172317	+	0.0125196i
$428$	0.704401			0.0340485
$429$		0			0
$430$	−10.8281			−0.522177
$431$	−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	$0.993471\pi$
$434$	−0.252088	+	0.183153i	−0.0121006	+	0.00879162i
$435$		0			0
$436$	−0.692757	−	2.13209i	−0.0331771	−	0.102109i
$437$	−5.26431	+	16.2019i	−0.251826	+	0.775041i
$438$		0			0
$439$	−4.14815			−0.197980			−0.0989902	−	0.995088i	$-0.531561\pi$
$439$	−4.14815			−0.197980			−0.0989902	+	0.995088i	$0.531561\pi$
$440$	10.2005	−	17.3264i	0.486290	−	0.826003i
$441$		0			0
$442$	−27.7378	−	20.1527i	−1.31935	−	0.958564i
$443$	−5.89970	+	18.1574i	−0.280303	+	0.862684i	0.707464	+	0.706749i	$0.249839\pi$
$443$	−5.89970	+	18.1574i	−0.280303	+	0.862684i	−0.987767	+	0.155935i	$0.950161\pi$
$444$		0			0
$445$	13.4366	−	9.76224i	0.636954	−	0.462774i
$446$	11.1750	−	8.11909i	0.529150	−	0.384450i
$447$		0			0
$448$	−0.271731	+	0.836302i	−0.0128381	+	0.0395116i
$449$	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
$452$	1.42167			0.0668699
$453$		0			0
$454$	−2.75861	+	8.49012i	−0.129468	+	0.398461i
$455$	−0.441220	−	1.35794i	−0.0206847	−	0.0636611i
$456$		0			0
$457$	23.9018	−	17.3657i	1.11808	−	0.812332i	0.134162	−	0.990959i	$-0.457166\pi$
$457$	23.9018	−	17.3657i	1.11808	−	0.812332i	0.983917	+	0.178628i	$0.0571657\pi$
$458$	6.51334	+	20.0460i	0.304348	+	0.936688i
$459$		0			0
$460$	0.604523	+	0.439212i	0.0281860	+	0.0204784i
$461$	40.7758			1.89912			0.949560	−	0.313586i	$-0.101530\pi$
$461$	40.7758			1.89912			0.949560	+	0.313586i	$0.101530\pi$
$462$		0			0
$463$	−38.7501			−1.80087			−0.900435	−	0.434990i	$-0.856752\pi$
$463$	−38.7501			−1.80087			−0.900435	+	0.434990i	$0.856752\pi$
$464$	−29.8126	−	21.6601i	−1.38401	−	1.00555i
$465$		0			0
$466$	−8.96609	−	27.5948i	−0.415346	−	1.27830i
$467$	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
$470$	3.00818	−	9.25823i	0.138757	−	0.427050i
$471$		0			0
$472$	20.3320			0.935858
$473$	−8.40005	−	9.49001i	−0.386235	−	0.436351i
$474$		0			0
$475$	3.65497	+	2.65549i	0.167702	+	0.121842i
$476$	−0.0169461	+	0.0521547i	−0.000776723	+	0.00239051i
$477$		0			0
$478$	19.1395	−	13.9057i	0.875421	−	0.636031i
$479$	12.8023	−	9.30143i	0.584953	−	0.424993i	−0.255553	−	0.966795i	$-0.582258\pi$
$479$	12.8023	−	9.30143i	0.584953	−	0.424993i	0.840506	+	0.541802i	$0.182258\pi$
$480$		0			0
$481$	−6.67540	+	20.5448i	−0.304372	+	0.936761i
$482$	−11.7449	−	8.53319i	−0.534967	−	0.388676i
$483$		0			0
$484$	1.50465	−	0.293212i	0.0683934	−	0.0133278i
$485$	−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	$0.141563\pi$
$488$	−3.82622	−	11.7759i	−0.173205	−	0.533070i
$489$		0			0
$490$	−16.0227	+	11.6411i	−0.723830	+	0.525893i
$491$	−11.0256	−	33.9334i	−0.497580	−	1.53139i	−0.812897	−	0.582407i	$-0.802111\pi$
$491$	−11.0256	−	33.9334i	−0.497580	−	1.53139i	0.315317	−	0.948986i	$-0.397889\pi$
$492$		0			0
$493$	−30.5504	−	22.1962i	−1.37592	−	0.999666i
$494$	−59.6532			−2.68392
$495$		0			0
$496$	8.15214			0.366042
$497$	0.992731	+	0.721261i	0.0445301	+	0.0323530i
$498$		0			0
$499$	8.22074	+	25.3008i	0.368011	+	1.13262i	0.948074	+	0.318049i	$0.103028\pi$
$499$	8.22074	+	25.3008i	0.368011	+	1.13262i	−0.580064	+	0.814571i	$0.696972\pi$
$500$	1.33138	−	0.967306i	0.0595412	−	0.0432592i
$501$		0			0
$502$	−11.8015	−	36.3211i	−0.526725	−	1.62109i
$503$	−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
$506$	−1.12193	−	11.6229i	−0.0498758	−	0.516702i
$507$		0			0
$508$	0.385713	+	0.280237i	0.0171133	+	0.0124335i
$509$	−10.0215	+	30.8431i	−0.444197	+	1.36710i	0.439166	+	0.898406i	$0.355274\pi$
$509$	−10.0215	+	30.8431i	−0.444197	+	1.36710i	−0.883362	+	0.468691i	$0.844726\pi$
$510$		0			0
$511$	−1.02684	+	0.746041i	−0.0454246	+	0.0330029i
$512$	19.8358	−	14.4116i	0.876627	−	0.636907i
$513$		0			0
$514$	7.57554	−	23.3151i	0.334143	−	1.02839i
$515$	−23.7826	−	17.2790i	−1.04799	−	0.761406i
$516$		0			0
$517$	10.4478	−	4.54576i	0.459493	−	0.199922i
$518$	−0.461311			−0.0202688
$519$		0			0
$520$	−12.4125	+	38.2017i	−0.544323	+	1.67525i
$521$	−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	$0.428229\pi$
$524$	−0.764415	−	2.35263i	−0.0333936	−	0.102775i
$525$		0			0
$526$	−15.1850	−	11.0326i	−0.662098	−	0.481042i
$527$	8.35390			0.363901
$528$		0			0
$529$	−16.3380			−0.710349
$530$	0.145026	+	0.105367i	0.00629951	+	0.00457686i
$531$		0			0
$532$	0.0294842	+	0.0907431i	0.00127830	+	0.00393421i
$533$	7.68843	−	5.58597i	0.333023	−	0.241955i
$534$		0			0
$535$	3.24475	+	9.98630i	0.140283	+	0.431746i
$536$	4.89944	−	15.0789i	0.211623	−	0.651310i
$537$		0			0
$538$	19.5226			0.841677
$539$	−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	$0.803032\pi$
$542$	−0.648841	+	1.99693i	−0.0278701	+	0.0857754i
$543$		0			0
$544$	2.41489	−	1.75452i	0.103537	−	0.0752244i
$545$	27.0355	−	19.6425i	1.15807	−	0.841391i
$546$		0			0
$547$	6.16340	−	18.9690i	0.263528	−	0.811056i	−0.728501	−	0.685045i	$-0.759783\pi$
$547$	6.16340	−	18.9690i	0.263528	−	0.811056i	0.992029	−	0.126011i	$-0.0402174\pi$
$548$	−0.982193	−	0.713605i	−0.0419572	−	0.0304837i
$549$		0			0
$550$	−3.02344	−	0.669531i	−0.128920	−	0.0285489i
$551$	−65.7021			−2.79900
$552$		0			0
$553$	−0.499247	+	1.53652i	−0.0212301	+	0.0653397i
$554$	−10.0795	−	31.0214i	−0.428236	−	1.31798i
$555$		0			0
$556$	−0.431614	+	0.313586i	−0.0183045	+	0.0132990i
$557$	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
$560$	−0.797716			−0.0337096
$561$		0			0
$562$	20.8579			0.879838
$563$	35.3818	+	25.7064i	1.49116	+	1.08339i	0.973739	+	0.227666i	$0.0731095\pi$
$563$	35.3818	+	25.7064i	1.49116	+	1.08339i	0.517425	+	0.855728i	$0.326890\pi$
$564$		0			0
$565$	6.54879	+	20.1551i	0.275509	+	0.847931i
$566$	−22.6049	+	16.4234i	−0.950153	+	0.690327i
$567$		0			0
$568$	−10.6674	−	32.8309i	−0.447595	−	1.37755i
$569$	0.121574	−	0.374166i	0.00509664	−	0.0156858i	−0.948476	−	0.316849i	$-0.897375\pi$
$569$	0.121574	−	0.374166i	0.00509664	−	0.0156858i	0.953572	+	0.301164i	$0.0973750\pi$
$570$		0			0
$571$	38.5003			1.61119			0.805594	−	0.592468i	$-0.201846\pi$
$571$	38.5003			1.61119			0.805594	+	0.592468i	$0.201846\pi$
$572$	−2.80823	+	1.22184i	−0.117418	+	0.0510877i
$573$		0			0
$574$	0.164186	+	0.119288i	0.00685300	+	0.00497899i
$575$	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	$0.300412\pi$
$578$	2.87973	−	2.09224i	0.119781	−	0.0870259i
$579$		0			0
$580$	−0.890549	+	2.74083i	−0.0369780	+	0.113807i
$581$	−0.413141	−	0.300164i	−0.0171400	−	0.0124529i
$582$		0			0
$583$	0.0201592	+	0.208844i	0.000834907	+	0.00864945i
$584$	35.7065			1.47754
$585$		0			0
$586$	−4.59107	+	14.1299i	−0.189655	+	0.583699i
$587$	−3.67814	−	11.3202i	−0.151813	−	0.467233i	0.846011	−	0.533166i	$-0.178998\pi$
$587$	−3.67814	−	11.3202i	−0.151813	−	0.467233i	−0.997824	+	0.0659326i	$0.978998\pi$
$588$		0			0
$589$	11.7589	−	8.54334i	0.484517	−	0.352022i
$590$	6.10092	+	18.7767i	0.251171	+	0.773025i
$591$		0			0
$592$	9.76400	+	7.09396i	0.401298	+	0.291560i
$593$	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
$596$	−1.16765	−	0.848346i	−0.0478288	−	0.0347496i
$597$		0			0
$598$	7.20876	+	22.1863i	0.294788	+	0.907264i
$599$	−6.86622	+	4.98860i	−0.280546	+	0.203829i	−0.719156	−	0.694849i	$-0.755471\pi$
$599$	−6.86622	+	4.98860i	−0.280546	+	0.203829i	0.438609	+	0.898678i	$0.355471\pi$
$600$		0			0
$601$	6.29121	+	19.3623i	0.256624	+	0.789806i	0.993505	+	0.113785i	$0.0362974\pi$
$601$	6.29121	+	19.3623i	0.256624	+	0.789806i	−0.736882	+	0.676022i	$0.763703\pi$
$602$	−0.167082	+	0.514227i	−0.00680977	+	0.0209583i
$603$		0			0
$604$	1.39576			0.0567927
$605$	11.0879	+	19.9809i	0.450787	+	0.812337i
$606$		0			0
$607$	−24.6781	−	17.9297i	−1.00165	−	0.727743i	−0.0392104	−	0.999231i	$-0.512484\pi$
$607$	−24.6781	−	17.9297i	−1.00165	−	0.727743i	−0.962442	+	0.271488i	$0.912484\pi$
$608$	1.60488	−	4.93930i	0.0650863	−	0.200315i
$609$		0			0
$610$	9.72696	−	7.06705i	0.393833	−	0.286137i
$611$	−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	$-0.145012\pi$
$614$	−17.8964	−	13.0025i	−0.722241	−	0.524739i
$615$		0			0
$616$	−0.665433	−	0.751777i	−0.0268110	−	0.0302900i
$617$	0.224835			0.00905152			0.00452576	−	0.999990i	$-0.498559\pi$
$617$	0.224835			0.00905152			0.00452576	+	0.999990i	$0.498559\pi$
$618$		0			0
$619$	0.183719	−	0.565428i	0.00738427	−	0.0227265i	−0.947296	−	0.320358i	$-0.896197\pi$
$619$	0.183719	−	0.565428i	0.00738427	−	0.0227265i	0.954681	+	0.297632i	$0.0961967\pi$
$620$	−0.197010	−	0.606333i	−0.00791210	−	0.0243509i
$621$		0			0
$622$	−14.1261	+	10.2632i	−0.566405	+	0.411517i
$623$	−0.256277	−	0.788739i	−0.0102675	−	0.0316002i
$624$		0			0
$625$	17.0775	+	12.4076i	0.683102	+	0.496302i
$626$	16.5374			0.660969
$627$		0			0
$628$	−1.61660			−0.0645092
$629$	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	$0.657568\pi$
$632$	36.7700	−	26.7150i	1.46263	−	1.06266i
$633$		0			0
$634$	−3.53386	−	10.8761i	−0.140348	−	0.431946i
$635$	−2.19618	+	6.75914i	−0.0871527	+	0.268228i
$636$		0			0
$637$	46.3100			1.83487
$638$	41.2955	−	17.9674i	1.63490	−	0.711336i
$639$		0			0
$640$	16.7886	+	12.1976i	0.663626	+	0.482152i
$641$	−6.75129	+	20.7783i	−0.266660	+	0.820695i	0.724646	+	0.689121i	$0.242003\pi$
$641$	−6.75129	+	20.7783i	−0.266660	+	0.820695i	−0.991306	+	0.131574i	$0.957997\pi$
$642$		0			0
$643$	−24.7049	+	17.9492i	−0.974267	+	0.707846i	−0.956420	−	0.291994i	$-0.905681\pi$
$643$	−24.7049	+	17.9492i	−0.974267	+	0.707846i	−0.0178469	+	0.999841i	$0.505681\pi$
$644$	0.0301863	−	0.0219316i	0.00118951	−	0.000864226i
$645$		0			0
$646$	−10.5538	+	32.4812i	−0.415233	+	1.27796i
$647$	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
$650$	6.18651			0.242655
$651$		0			0
$652$	0.981752	−	3.02152i	0.0384484	−	0.118332i
$653$	9.07240	+	27.9220i	0.355030	+	1.09267i	0.955992	+	0.293393i	$0.0947844\pi$
$653$	9.07240	+	27.9220i	0.355030	+	1.09267i	−0.600962	+	0.799278i	$0.705216\pi$
$654$		0			0
$655$	29.8320	−	21.6742i	1.16563	−	0.846883i
$656$	−1.64073	−	5.04965i	−0.0640598	−	0.197156i
$657$		0			0
$658$	−0.393256	−	0.285717i	−0.0153307	−	0.0111384i
$659$	−36.5480			−1.42371			−0.711854	−	0.702328i	$-0.752144\pi$
$659$	−36.5480			−1.42371			−0.711854	+	0.702328i	$0.752144\pi$
$660$		0			0
$661$	−3.81296			−0.148307			−0.0741535	−	0.997247i	$-0.523625\pi$
$661$	−3.81296			−0.148307			−0.0741535	+	0.997247i	$0.523625\pi$
$662$	8.99471	+	6.53504i	0.349589	+	0.253992i
$663$		0			0
$664$	4.43941	+	13.6631i	0.172283	+	0.530232i
$665$	−1.15065	+	0.835996i	−0.0446203	+	0.0324185i
$666$		0			0
$667$	7.93974	+	24.4360i	0.307428	+	0.946166i
$668$	−0.196797	+	0.605679i	−0.00761431	+	0.0234344i
$669$		0			0
$670$	15.3956			0.594783
$671$	13.7396	+	3.04259i	0.530410	+	0.117458i
$672$		0			0
$673$	−12.1643	−	8.83787i	−0.468899	−	0.340675i	0.328113	−	0.944638i	$-0.393587\pi$
$673$	−12.1643	−	8.83787i	−0.468899	−	0.340675i	−0.797012	+	0.603964i	$0.793587\pi$
$674$	12.6585	−	38.9588i	0.487587	−	1.50064i
$675$		0			0
$676$	3.48410	−	2.53134i	0.134004	−	0.0973594i
$677$	−24.3918	+	17.7217i	−0.937455	+	0.681101i	−0.947807	−	0.318846i	$-0.896705\pi$
$677$	−24.3918	+	17.7217i	−0.937455	+	0.681101i	0.0103520	+	0.999946i	$0.496705\pi$
$678$		0			0
$679$	−0.0990582	+	0.304870i	−0.00380151	+	0.0116998i
$680$	18.6048	+	13.5172i	0.713463	+	0.518361i
$681$		0			0
$682$	−5.05445	+	8.58539i	−0.193545	+	0.328752i
$683$	−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
$686$	0.611674	+	1.88254i	0.0233538	+	0.0718757i
$687$		0			0
$688$	11.4441	−	8.31464i	0.436303	−	0.316993i
$689$	−0.129529	−	0.398650i	−0.00493467	−	0.0151873i
$690$		0			0
$691$	−19.9896	−	14.5233i	−0.760440	−	0.552492i	0.138605	−	0.990348i	$-0.455738\pi$
$691$	−19.9896	−	14.5233i	−0.760440	−	0.552492i	−0.899045	+	0.437855i	$0.855738\pi$
$692$	0.209071			0.00794768
$693$		0			0
$694$	46.3990			1.76128
$695$	−6.43389	−	4.67450i	−0.244051	−	0.177314i
$696$		0			0
$697$	−1.68134	−	5.17463i	−0.0636852	−	0.196003i
$698$	−25.9848	+	18.8790i	−0.983539	+	0.714583i
$699$		0			0
$700$	−0.00305775	−	0.00941077i	−0.000115572	−	0.000355694i
$701$	−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
$704$	2.70133	+	27.9851i	0.101810	+	1.05473i
$705$		0			0
$706$	−17.4661	−	12.6899i	−0.657347	−	0.477590i
$707$	−0.0800683	+	0.246425i	−0.00301128	+	0.00926776i
$708$		0			0
$709$	−6.59373	+	4.79063i	−0.247633	+	0.179916i	−0.704677	−	0.709528i	$-0.748908\pi$
$709$	−6.59373	+	4.79063i	−0.247633	+	0.179916i	0.457044	+	0.889444i	$0.348908\pi$
$710$	27.1185	−	19.7028i	1.01774	−	0.739432i
$711$		0			0
$712$	−7.20962	+	22.1889i	−0.270192	+	0.831565i
$713$	−4.59845	−	3.34097i	−0.172213	−	0.125120i
$714$		0			0
$715$	−30.2578	−	34.1840i	−1.13158	−	1.27841i
$716$	−1.24553			−0.0465476
$717$		0			0
$718$	0.184812	−	0.568791i	0.00689710	−	0.0212271i
$719$	−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
$722$	10.3536	+	31.8650i	0.385320	+	1.18589i
$723$		0			0
$724$	2.36372	+	1.71734i	0.0878469	+	0.0638245i
$725$	6.81383			0.253059
$726$		0			0
$727$	22.5664			0.836940			0.418470	−	0.908231i	$-0.362566\pi$
$727$	22.5664			0.836940			0.418470	+	0.908231i	$0.362566\pi$
$728$	1.62267	+	1.17894i	0.0601401	+	0.0436944i
$729$		0			0
$730$	10.7142	+	32.9750i	0.396552	+	1.22046i
$731$	11.7274	−	8.52042i	0.433752	−	0.315139i
$732$		0			0
$733$	−10.6642	−	32.8209i	−0.393890	−	1.21227i	−0.929823	−	0.368008i	$-0.880040\pi$
$733$	−10.6642	−	32.8209i	−0.393890	−	1.21227i	0.535932	−	0.844261i	$-0.319960\pi$
$734$	−5.84051	+	17.9752i	−0.215577	+	0.663478i
$735$		0			0
$736$	−2.03097			−0.0748626
$737$	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	$0.571845\pi$
$740$	0.291666	−	0.897656i	0.0107219	−	0.0329985i
$741$		0			0
$742$	0.00724171	−	0.00526141i	0.000265852	−	0.000193152i
$743$	−35.8054	+	26.0142i	−1.31357	+	0.954367i	−0.313585	+	0.949560i	$0.601530\pi$
$743$	−35.8054	+	26.0142i	−1.31357	+	0.954367i	−0.999988	+	0.00480648i	$0.998470\pi$
$744$		0			0
$745$	6.64837	−	20.4616i	0.243577	−	0.749654i
$746$	−7.74211	−	5.62497i	−0.283459	−	0.205945i
$747$		0			0
$748$	0.168464	+	1.74525i	0.00615966	+	0.0638126i
$749$	0.524318			0.0191582
$750$		0			0
$751$	−7.71292	+	23.7379i	−0.281448	+	0.866209i	0.705992	+	0.708220i	$0.250501\pi$
$751$	−7.71292	+	23.7379i	−0.281448	+	0.866209i	−0.987441	+	0.157990i	$0.949499\pi$
$752$	3.92986	+	12.0949i	0.143307	+	0.441054i
$753$		0			0
$754$	−72.7873	+	52.8831i	−2.65076	+	1.92589i
$755$	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	$0.965271\pi$
$758$	−13.6061			−0.494194
$759$		0			0
$760$	40.0118			1.45138
$761$	−15.6840	−	11.3951i	−0.568546	−	0.413073i	0.266031	−	0.963965i	$-0.414288\pi$
$761$	−15.6840	−	11.3951i	−0.568546	−	0.413073i	−0.834577	+	0.550892i	$0.814288\pi$
$762$		0			0
$763$	−0.515651	−	1.58701i	−0.0186678	−	0.0574537i
$764$	1.00821	−	0.732507i	0.0364757	−	0.0265012i
$765$		0			0
$766$	7.94980	+	24.4670i	0.287238	+	0.884028i
$767$	14.2657	−	43.9053i	0.515105	−	1.58533i
$768$		0			0
$769$	−10.7672			−0.388276			−0.194138	−	0.980974i	$-0.562191\pi$
$769$	−10.7672			−0.388276			−0.194138	+	0.980974i	$0.562191\pi$
$770$	0.494596	−	0.840111i	0.0178240	−	0.0302755i
$771$		0			0
$772$	0.644754	+	0.468441i	0.0232052	+	0.0168596i
$773$	−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
$776$	7.29573	−	5.30066i	0.261901	−	0.190282i
$777$		0			0
$778$	9.84129	−	30.2884i	0.352827	−	1.08589i
$779$	−7.65862	−	5.56431i	−0.274398	−	0.199362i
$780$		0			0
$781$	38.3056	+	8.48266i	1.37068	+	0.303533i
$782$	13.3558			0.477603
$783$		0			0
$784$	7.99525	−	24.6069i	0.285545	−	0.878816i
$785$	−7.44667	−	22.9185i	−0.265783	−	0.817996i
$786$		0			0
$787$	−2.87784	+	2.09087i	−0.102584	+	0.0745315i	−0.637895	−	0.770124i	$-0.720194\pi$
$787$	−2.87784	+	2.09087i	−0.102584	+	0.0745315i	0.535311	+	0.844655i	$0.320194\pi$
$788$	0.299005	+	0.920242i	0.0106516	+	0.0327823i
$789$		0			0
$790$	35.7047	+	25.9410i	1.27032	+	0.922939i
$791$	1.05822			0.0376259
$792$		0			0
$793$	−28.1137			−0.998346
$794$	30.5672	+	22.2084i	1.08479	+	0.788145i
$795$		0			0
$796$	−1.03441	−	3.18358i	−0.0366636	−	0.112839i
$797$	28.3276	−	20.5812i	1.00341	−	0.729023i	0.0405963	−	0.999176i	$-0.487074\pi$
$797$	28.3276	−	20.5812i	1.00341	−	0.729023i	0.962817	+	0.270153i	$0.0870743\pi$
$798$		0			0
$799$	4.02712	+	12.3942i	0.142469	+	0.438475i
$800$	−0.166438	+	0.512245i	−0.00588448	+	0.0181106i
$801$		0			0
$802$	−20.6052			−0.727595
$803$	−20.5884	+	34.9711i	−0.726550	+	1.23410i
$804$		0			0
$805$	0.449974	+	0.326925i	0.0158595	+	0.0115226i
$806$	6.15050	−	18.9293i	0.216642	−	0.666756i
$807$		0			0
$808$	5.89710	−	4.28449i	0.207459	−	0.150728i
$809$	−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	$0.134732\pi$
$812$	0.116421	+	0.0845844i	0.00408556	+	0.00296833i
$813$		0			0
$814$	−13.5248	+	5.88455i	−0.474044	+	0.206253i
$815$	47.3585			1.65890
$816$		0			0
$817$	7.79372	−	23.9866i	0.272668	−	0.839185i
$818$	−3.96563	−	12.2049i	−0.138655	−	0.426736i
$819$		0			0
$820$	−0.335928	+	0.244066i	−0.0117311	+	0.00852316i
$821$	7.74584	+	23.8392i	0.270332	+	0.831995i	0.990417	+	0.138110i	$0.0441026\pi$
$821$	7.74584	+	23.8392i	0.270332	+	0.831995i	−0.720085	+	0.693886i	$0.755897\pi$
$822$		0			0
$823$	−2.37823	−	1.72789i	−0.0829000	−	0.0602303i	0.545563	−	0.838070i	$-0.316316\pi$
$823$	−2.37823	−	1.72789i	−0.0829000	−	0.0602303i	−0.628463	+	0.777839i	$0.716316\pi$
$824$	41.2953			1.43859
$825$		0			0
$826$	0.985847			0.0343020
$827$	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	$0.894188\pi$
$830$	−11.2858	+	8.19963i	−0.391736	+	0.284613i
$831$		0			0
$832$	−17.3569	−	53.4190i	−0.601742	−	1.85197i
$833$	8.19313	−	25.2159i	0.283875	−	0.873678i
$834$		0			0
$835$	−9.49324			−0.328527
$836$	2.02196	+	2.28432i	0.0699308	+	0.0790048i
$837$		0			0
$838$	22.1854	+	16.1187i	0.766383	+	0.556810i
$839$	0.728865	−	2.24322i	0.0251632	−	0.0774444i	−0.937686	−	0.347483i	$-0.887036\pi$
$839$	0.728865	−	2.24322i	0.0251632	−	0.0774444i	0.962850	+	0.270039i	$0.0870364\pi$
$840$		0			0
$841$	−56.7066	+	41.1998i	−1.95540	+	1.42068i
$842$	14.1753	−	10.2989i	0.488512	−	0.354925i
$843$		0			0
$844$	−0.174564	+	0.537254i	−0.00600875	+	0.0184930i
$845$	51.9360	+	37.7337i	1.78665	+	1.29808i
$846$		0			0
$847$	1.11998	−	0.218251i	0.0384831	−	0.00749921i
$848$	−0.234185			−0.00804196
$849$		0			0
$850$	1.09451	−	3.36856i	0.0375414	−	0.115541i
$851$	−2.60036	−	8.00310i	−0.0891393	−	0.274343i
$852$		0			0
$853$	23.6595	−	17.1897i	0.810087	−	0.588563i	−0.103769	−	0.994601i	$-0.533090\pi$
$853$	23.6595	−	17.1897i	0.810087	−	0.588563i	0.913856	+	0.406039i	$0.133090\pi$
$854$	−0.185523	−	0.570982i	−0.00634848	−	0.0195386i
$855$		0			0
$856$	−11.9332	−	8.66994i	−0.407867	−	0.296333i
$857$	28.2043			0.963439			0.481720	−	0.876325i	$-0.340012\pi$
$857$	28.2043			0.963439			0.481720	+	0.876325i	$0.340012\pi$
$858$		0			0
$859$	26.6444			0.909095			0.454548	−	0.890722i	$-0.349801\pi$
$859$	26.6444			0.909095			0.454548	+	0.890722i	$0.349801\pi$
$860$	−0.894986	−	0.650245i	−0.0305188	−	0.0221732i
$861$		0			0
$862$	6.44948	+	19.8494i	0.219670	+	0.676075i
$863$	−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
$866$	−5.07756	+	15.6271i	−0.172542	+	0.531031i
$867$		0			0
$868$	−0.0318348			−0.00108054
$869$	4.96310	+	51.4166i	0.168362	+	1.74419i
$870$		0			0
$871$	−29.1240	−	21.1599i	−0.986830	−	0.716974i
$872$	−14.5064	+	44.6460i	−0.491248	+	1.51190i
$873$		0			0
$874$	18.7996	−	13.6587i	0.635905	−	0.462012i
$875$	0.991009	−	0.720010i	0.0335022	−	0.0243408i
$876$		0			0
$877$	−2.83286	+	8.71864i	−0.0956588	+	0.294408i	−0.987425	−	0.158089i	$-0.949467\pi$
$877$	−2.83286	+	8.71864i	−0.0956588	+	0.294408i	0.891766	+	0.452497i	$0.149467\pi$
$878$	4.57766	+	3.32586i	0.154489	+	0.112242i
$879$		0			0
$880$	−23.3876	+	10.1758i	−0.788395	+	0.343025i
$881$	−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	$0.837475\pi$
$884$	−1.08244	−	3.33140i	−0.0364063	−	0.112047i
$885$		0			0
$886$	21.0686	−	15.3073i	0.707814	−	0.514257i
$887$	−2.66422	−	8.19964i	−0.0894559	−	0.275317i	0.896313	−	0.443421i	$-0.146235\pi$
$887$	−2.66422	−	8.19964i	−0.0894559	−	0.275317i	−0.985769	+	0.168104i	$0.946235\pi$
$888$		0			0
$889$	0.287104	+	0.208593i	0.00962916	+	0.00699600i
$890$	−22.6549			−0.759393
$891$		0			0
$892$	1.41122			0.0472512
$893$	18.3438	+	13.3276i	0.613852	+	0.445990i
$894$		0			0
$895$	−5.73739	−	17.6579i	−0.191780	−	0.590238i
$896$	0.838320	−	0.609075i	0.0280063	−	0.0203478i
$897$		0			0
$898$	−1.43918	−	4.42935i	−0.0480261	−	0.147809i
$899$	6.77417	−	20.8487i	0.225931	−	0.695345i
$900$		0			0
$901$	−0.239981			−0.00799494
$902$	6.33530	+	1.40293i	0.210942	+	0.0467126i
$903$		0			0
$904$	−24.0844	−	17.4983i	−0.801034	−	0.581985i
$905$	−13.4586	+	41.4212i	−0.447378	+	1.37689i
$906$		0			0
$907$	6.79413	−	4.93622i	0.225595	−	0.163905i	−0.469246	−	0.883067i	$-0.655474\pi$
$907$	6.79413	−	4.93622i	0.225595	−	0.163905i	0.694842	+	0.719163i	$0.255474\pi$
$908$	−0.737856	+	0.536084i	−0.0244866	+	0.0177906i
$909$		0			0
$910$	−0.601848	+	1.85230i	−0.0199511	+	0.0614031i
$911$	25.5548	+	18.5666i	0.846667	+	0.615140i	0.924225	−	0.381848i	$-0.124712\pi$
$911$	25.5548	+	18.5666i	0.846667	+	0.615140i	−0.0775581	+	0.996988i	$0.524712\pi$
$912$		0			0
$913$	−15.9415	−	3.53020i	−0.527586	−	0.116832i
$914$	−40.2999			−1.33300
$915$		0			0
$916$	−0.665441	+	2.04802i	−0.0219868	+	0.0676684i
$917$	−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	$0.0638855\pi$
$920$	−4.83521	−	14.8812i	−0.159412	−	0.490620i
$921$		0			0
$922$	−44.9978	−	32.6928i	−1.48192	−	1.07668i
$923$	−78.3802			−2.57992
$924$		0			0
$925$	−2.23161			−0.0733750
$926$	42.7624	+	31.0687i	1.40526	+	1.02098i
$927$		0			0
$928$	−2.42051	−	7.44955i	−0.0794570	−	0.244544i
$929$	9.20018	−	6.68432i	0.301848	−	0.219305i	−0.426543	−	0.904467i	$-0.640269\pi$
$929$	9.20018	−	6.68432i	0.301848	−	0.219305i	0.728391	+	0.685162i	$0.240269\pi$
$930$		0			0
$931$	−14.2551	−	43.8726i	−0.467191	−	1.43787i
$932$	0.916029	−	2.81925i	0.0300055	−	0.0923476i
$933$		0			0
$934$	−38.2809			−1.25259
$935$	−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	$0.698139\pi$
$938$	0.237561	−	0.731137i	0.00775663	−	0.0238725i
$939$		0			0
$940$	0.804610	−	0.584584i	0.0262435	−	0.0190670i
$941$	−14.8500	+	10.7891i	−0.484095	+	0.351716i	−0.802909	−	0.596102i	$-0.796716\pi$
$941$	−14.8500	+	10.7891i	−0.484095	+	0.351716i	0.318814	+	0.947817i	$0.396716\pi$
$942$		0			0
$943$	−1.14398	+	3.52082i	−0.0372532	+	0.114654i
$944$	−20.8662	−	15.1602i	−0.679137	−	0.493422i
$945$		0			0
$946$	1.66100	+	17.2075i	0.0540036	+	0.559465i
$947$	51.2153			1.66427			0.832137	−	0.554571i	$-0.187117\pi$
$947$	51.2153			1.66427			0.832137	+	0.554571i	$0.187117\pi$
$948$		0			0
$949$	25.0530	−	77.1051i	0.813254	−	2.50294i
$950$	−1.90432	−	5.86090i	−0.0617843	−	0.190153i
$951$		0			0
$952$	0.929014	−	0.674968i	0.0301095	−	0.0218759i
$953$	−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
$956$	2.41702			0.0781719
$957$		0			0
$958$	−21.5855			−0.697396
$959$	−0.731091	−	0.531169i	−0.0236082	−	0.0171523i
$960$		0			0
$961$	−8.08093	−	24.8705i	−0.260675	−	0.802275i
$962$	23.8388	−	17.3199i	0.768593	−	0.558416i
$963$		0			0
$964$	−0.458333	−	1.41060i	−0.0147619	−	0.0454325i
$965$	−3.67111	+	11.2985i	−0.118177	+	0.363712i
$966$		0			0
$967$	32.5309			1.04612			0.523061	−	0.852295i	$-0.324790\pi$
$967$	32.5309			1.04612			0.523061	+	0.852295i	$0.324790\pi$
$968$	−29.0991	−	13.5524i	−0.935279	−	0.435591i
$969$		0			0
$970$	7.08436	+	5.14709i	0.227465	+	0.165263i
$971$	−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
$974$	6.34168	−	4.60750i	0.203201	−	0.147634i
$975$		0			0
$976$	−4.85372	+	14.9382i	−0.155364	+	0.478161i
$977$	−17.2791	−	12.5540i	−0.552806	−	0.401637i	0.276013	−	0.961154i	$-0.410987\pi$
$977$	−17.2791	−	12.5540i	−0.552806	−	0.401637i	−0.828819	+	0.559517i	$0.810987\pi$
$978$		0			0
$979$	−17.5748	−	19.8553i	−0.561694	−	0.634578i
$980$	−2.02341			−0.0646354
$981$		0			0
$982$	−15.0396	+	46.2870i	−0.479931	+	1.47708i
$983$	4.46743	+	13.7493i	0.142489	+	0.438536i	0.996680	−	0.0814241i	$-0.0259468\pi$
$983$	4.46743	+	13.7493i	0.142489	+	0.438536i	−0.854191	+	0.519960i	$0.825947\pi$
$984$		0			0
$985$	−11.6690	+	8.47799i	−0.371804	+	0.270131i
$986$	15.9174	+	48.9888i	0.506914	+	1.56012i
$987$		0			0
$988$	−4.93058	−	3.58227i	−0.156863	−	0.113967i
$989$	−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	$0.476278\pi$
$992$	1.40188	+	1.01853i	0.0445098	+	0.0323382i
$993$		0			0
$994$	−0.517234	−	1.59188i	−0.0164057	−	0.0504915i
$995$	40.3687	−	29.3296i	1.27977	−	0.929811i
$996$		0			0
$997$	10.4396	+	32.1297i	0.330624	+	1.01756i	0.968838	+	0.247697i	$0.0796738\pi$
$997$	10.4396	+	32.1297i	0.330624	+	1.01756i	−0.638213	+	0.769860i	$0.720326\pi$
$998$	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.f.g.730.4	yes	48
3.2	odd	2	inner	891.2.f.g.730.9	yes	48
9.2	odd	6		891.2.n.l.433.9		96
9.4	even	3		891.2.n.l.136.9		96
9.5	odd	6		891.2.n.l.136.4		96
9.7	even	3		891.2.n.l.433.4		96
11.3	even	5	inner	891.2.f.g.487.4	✓	48
11.5	even	5		9801.2.a.cr.1.18		24
11.6	odd	10		9801.2.a.cq.1.7		24
33.5	odd	10		9801.2.a.cr.1.7		24
33.14	odd	10	inner	891.2.f.g.487.9	yes	48
33.17	even	10		9801.2.a.cq.1.18		24
99.14	odd	30		891.2.n.l.784.9		96
99.25	even	15		891.2.n.l.190.9		96
99.47	odd	30		891.2.n.l.190.4		96
99.58	even	15		891.2.n.l.784.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.g.487.4	✓	48	11.3	even	5	inner
891.2.f.g.487.9	yes	48	33.14	odd	10	inner
891.2.f.g.730.4	yes	48	1.1	even	1	trivial
891.2.f.g.730.9	yes	48	3.2	odd	2	inner
891.2.n.l.136.4		96	9.5	odd	6
891.2.n.l.136.9		96	9.4	even	3
891.2.n.l.190.4		96	99.47	odd	30
891.2.n.l.190.9		96	99.25	even	15
891.2.n.l.433.4		96	9.7	even	3
891.2.n.l.433.9		96	9.2	odd	6
891.2.n.l.784.4		96	99.58	even	15
891.2.n.l.784.9		96	99.14	odd	30
9801.2.a.cq.1.7		24	11.6	odd	10
9801.2.a.cq.1.18		24	33.17	even	10
9801.2.a.cr.1.7		24	33.5	odd	10
9801.2.a.cr.1.18		24	11.5	even	5

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.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.10354 - 0.801770i) q^{2} +(-0.0430645 - 0.132539i) q^{4} +(1.68064 - 1.22105i) q^{5} +(-0.0320549 - 0.0986549i) q^{7} +(-0.901773 + 2.77537i) q^{8} +O(q^{10})\)	\(q+(-1.10354 - 0.801770i) q^{2} +(-0.0430645 - 0.132539i) q^{4} +(1.68064 - 1.22105i) q^{5} +(-0.0320549 - 0.0986549i) q^{7} +(-0.901773 + 2.77537i) q^{8} -2.83366 q^{10} +(-2.19825 - 2.48349i) q^{11} +(5.36047 + 3.89461i) q^{13} +(-0.0437246 + 0.134570i) q^{14} +(2.99487 - 2.17590i) q^{16} +(3.06899 - 2.22975i) q^{17} +(2.03958 - 6.27717i) q^{19} +(-0.234213 - 0.170166i) q^{20} +(0.434674 + 4.50312i) q^{22} -2.58108 q^{23} +(-0.211520 + 0.650992i) q^{25} +(-2.79292 - 8.59573i) q^{26} +(-0.0116952 + 0.00849706i) q^{28} +(-3.07613 - 9.46735i) q^{29} +(1.78160 + 1.29441i) q^{31} +0.786868 q^{32} -5.17450 q^{34} +(-0.174336 - 0.126662i) q^{35} +(1.00747 + 3.10068i) q^{37} +(-7.28360 + 5.29185i) q^{38} +(1.87333 + 5.76550i) q^{40} +(0.443218 - 1.36409i) q^{41} +3.82125 q^{43} +(-0.234492 + 0.398304i) q^{44} +(2.84833 + 2.06943i) q^{46} +(-1.06159 + 3.26724i) q^{47} +(5.65441 - 4.10817i) q^{49} +(0.755367 - 0.548806i) q^{50} +(0.285342 - 0.878191i) q^{52} +(-0.0511797 - 0.0371842i) q^{53} +(-6.72692 - 1.48966i) q^{55} +0.302710 q^{56} +(-4.19600 + 12.9140i) q^{58} +(-2.15302 - 6.62632i) q^{59} +(-3.43265 + 2.49397i) q^{61} +(-0.928251 - 2.85686i) q^{62} +(-6.85808 - 4.98268i) q^{64} +13.7645 q^{65} -5.43311 q^{67} +(-0.427694 - 0.310738i) q^{68} +(0.0908326 + 0.279554i) q^{70} +(-9.57016 + 6.95313i) q^{71} +(-3.78107 - 11.6369i) q^{73} +(1.37424 - 4.22949i) q^{74} -0.919803 q^{76} +(-0.174543 + 0.296476i) q^{77} +(-12.6002 - 9.15460i) q^{79} +(2.37639 - 7.31378i) q^{80} +(-1.58279 + 1.14997i) q^{82} +(3.98278 - 2.89366i) q^{83} +(2.43521 - 7.49479i) q^{85} +(-4.21690 - 3.06376i) q^{86} +(8.87492 - 3.86142i) q^{88} +7.99493 q^{89} +(0.212393 - 0.653678i) q^{91} +(0.111153 + 0.342094i) q^{92} +(3.79108 - 2.75438i) q^{94} +(-4.23697 - 13.0401i) q^{95} +(-2.50008 - 1.81641i) q^{97} -9.53369 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} - 14 q^{7}+O(q^{10}) \) 48 * q - 8 * q^4 - 14 * q^7	\( 48 q - 8 q^{4} - 14 q^{7} + 32 q^{10} - 14 q^{13} - 4 q^{16} - 8 q^{19} + 16 q^{22} - 20 q^{25} - 18 q^{28} - 4 q^{31} + 84 q^{34} - 12 q^{37} - 106 q^{40} + 84 q^{43} - 38 q^{46} - 54 q^{49} + 52 q^{52} - 36 q^{55} - 10 q^{58} - 6 q^{61} - 52 q^{64} + 76 q^{67} - 8 q^{70} - 46 q^{73} + 204 q^{76} - 102 q^{79} + 12 q^{82} + 54 q^{85} + 22 q^{91} - 118 q^{94} - 66 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 - 14 * q^7 + 32 * q^10 - 14 * q^13 - 4 * q^16 - 8 * q^19 + 16 * q^22 - 20 * q^25 - 18 * q^28 - 4 * q^31 + 84 * q^34 - 12 * q^37 - 106 * q^40 + 84 * q^43 - 38 * q^46 - 54 * q^49 + 52 * q^52 - 36 * q^55 - 10 * q^58 - 6 * q^61 - 52 * q^64 + 76 * q^67 - 8 * q^70 - 46 * q^73 + 204 * q^76 - 102 * q^79 + 12 * q^82 + 54 * q^85 + 22 * q^91 - 118 * q^94 - 66 * q^97

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