LMFDB - Embedded newform 1148.2.r.a.737.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			737.7
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64009 + 0.946908i) q^{3} +(1.83233 - 3.17368i) q^{5} +(0.288265 + 2.63000i) q^{7} +(0.293269 - 0.507958i) q^{9} +O(q^{10})$	\(q+(-1.64009 + 0.946908i) q^{3} +(1.83233 - 3.17368i) q^{5} +(0.288265 + 2.63000i) q^{7} +(0.293269 - 0.507958i) q^{9} +(-4.51759 + 2.60823i) q^{11} -3.89471i q^{13} +6.94018i q^{15} +(1.07071 - 0.618177i) q^{17} +(-3.64815 - 2.10626i) q^{19} +(-2.96315 - 4.04048i) q^{21} +(-1.39290 + 2.41257i) q^{23} +(-4.21484 - 7.30032i) q^{25} -4.57065i q^{27} +4.81157i q^{29} +(4.20891 + 7.29004i) q^{31} +(4.93951 - 8.55549i) q^{33} +(8.87498 + 3.90416i) q^{35} +(-0.952530 + 1.64983i) q^{37} +(3.68793 + 6.38768i) q^{39} +(-4.85100 + 4.17945i) q^{41} -11.5379 q^{43} +(-1.07473 - 1.86149i) q^{45} +(-1.91574 - 1.10605i) q^{47} +(-6.83381 + 1.51628i) q^{49} +(-1.17071 + 2.02774i) q^{51} +(-2.05287 + 1.18522i) q^{53} +19.1165i q^{55} +7.97774 q^{57} +(-6.14495 - 10.6434i) q^{59} +(-1.31229 + 2.27296i) q^{61} +(1.42047 + 0.624872i) q^{63} +(-12.3606 - 7.13637i) q^{65} +(3.49634 - 2.01862i) q^{67} -5.27578i q^{69} -11.2362i q^{71} +(7.92976 + 13.7347i) q^{73} +(13.8255 + 7.98213i) q^{75} +(-8.16192 - 11.1294i) q^{77} +(-5.10404 - 2.94682i) q^{79} +(5.20779 + 9.02016i) q^{81} -17.1398 q^{83} -4.53081i q^{85} +(-4.55611 - 7.89142i) q^{87} +(-1.77294 - 1.02361i) q^{89} +(10.2431 - 1.12271i) q^{91} +(-13.8060 - 7.97090i) q^{93} +(-13.3692 + 7.71871i) q^{95} +2.27201i q^{97} +3.05966i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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			0
$2$		0			0
$3$	−1.64009	+	0.946908i	−0.946908	+	0.546698i	−0.892119	−	0.451800i	$-0.850782\pi$
$3$	−1.64009	+	0.946908i	−0.946908	+	0.546698i	−0.0547889	+	0.998498i	$0.517449\pi$
$4$		0			0
$5$	1.83233	−	3.17368i	0.819441	−	1.41931i	−0.0866531	−	0.996239i	$-0.527617\pi$
$5$	1.83233	−	3.17368i	0.819441	−	1.41931i	0.906094	−	0.423075i	$-0.139049\pi$
$6$		0			0
$7$	0.288265	+	2.63000i	0.108954	+	0.994047i
$7$	0.288265	+	2.63000i	0.108954	+	0.994047i
$8$		0			0
$9$	0.293269	−	0.507958i	0.0977565	−	0.169319i
$10$		0			0
$11$	−4.51759	+	2.60823i	−1.36211	+	0.786412i	−0.989904	−	0.141740i	$-0.954730\pi$
$11$	−4.51759	+	2.60823i	−1.36211	+	0.786412i	−0.372201	+	0.928152i	$0.621397\pi$
$12$		0			0
$13$		−	3.89471i		−	1.08020i	−0.841602	−	0.540098i	$-0.818387\pi$
$13$		−	3.89471i		−	1.08020i	0.841602	−	0.540098i	$-0.181613\pi$
$14$		0			0
$15$			6.94018i			1.79195i
$16$		0			0
$17$	1.07071	−	0.618177i	0.259686	−	0.149930i	−0.364505	−	0.931201i	$-0.618762\pi$
$17$	1.07071	−	0.618177i	0.259686	−	0.149930i	0.624191	+	0.781271i	$0.285429\pi$
$18$		0			0
$19$	−3.64815	−	2.10626i	−0.836943	−	0.483209i	0.0192811	−	0.999814i	$-0.493862\pi$
$19$	−3.64815	−	2.10626i	−0.836943	−	0.483209i	−0.856224	+	0.516605i	$0.827196\pi$
$20$		0			0
$21$	−2.96315	−	4.04048i	−0.646612	−	0.881706i
$22$		0			0
$23$	−1.39290	+	2.41257i	−0.290439	+	0.503055i	−0.973914	−	0.226919i	$-0.927135\pi$
$23$	−1.39290	+	2.41257i	−0.290439	+	0.503055i	0.683475	+	0.729974i	$0.260468\pi$
$24$		0			0
$25$	−4.21484	−	7.30032i	−0.842968	−	1.46006i
$26$		0			0
$27$		−	4.57065i		−	0.879622i
$28$		0			0
$29$			4.81157i			0.893486i	0.894662	+	0.446743i	$0.147416\pi$
$29$			4.81157i			0.893486i	−0.894662	+	0.446743i	$0.852584\pi$
$30$		0			0
$31$	4.20891	+	7.29004i	0.755942	+	1.30933i	0.944904	+	0.327346i	$0.106154\pi$
$31$	4.20891	+	7.29004i	0.755942	+	1.30933i	−0.188962	+	0.981984i	$0.560512\pi$
$32$		0			0
$33$	4.93951	−	8.55549i	0.859859	−	1.48932i
$34$		0			0
$35$	8.87498	+	3.90416i	1.50015	+	0.659923i
$36$		0			0
$37$	−0.952530	+	1.64983i	−0.156595	+	0.271231i	−0.933639	−	0.358216i	$-0.883385\pi$
$37$	−0.952530	+	1.64983i	−0.156595	+	0.271231i	0.777044	+	0.629447i	$0.216718\pi$
$38$		0			0
$39$	3.68793	+	6.38768i	0.590541	+	1.02285i
$40$		0			0
$41$	−4.85100	+	4.17945i	−0.757598	+	0.652721i
$41$	−4.85100	+	4.17945i	−0.757598	+	0.652721i
$42$		0			0
$43$	−11.5379			−1.75951			−0.879753	−	0.475431i	$-0.842292\pi$
$43$	−11.5379			−1.75951			−0.879753	+	0.475431i	$0.842292\pi$
$44$		0			0
$45$	−1.07473	−	1.86149i	−0.160211	−	0.277494i
$46$		0			0
$47$	−1.91574	−	1.10605i	−0.279439	−	0.161334i	0.353730	−	0.935347i	$-0.384913\pi$
$47$	−1.91574	−	1.10605i	−0.279439	−	0.161334i	−0.633170	+	0.774013i	$0.718246\pi$
$48$		0			0
$49$	−6.83381	+	1.51628i	−0.976258	+	0.216611i
$50$		0			0
$51$	−1.17071	+	2.02774i	−0.163933	+	0.283940i
$52$		0			0
$53$	−2.05287	+	1.18522i	−0.281983	+	0.162803i	−0.634321	−	0.773070i	$-0.718720\pi$
$53$	−2.05287	+	1.18522i	−0.281983	+	0.162803i	0.352338	+	0.935873i	$0.385387\pi$
$54$		0			0
$55$			19.1165i			2.57767i
$56$		0			0
$57$	7.97774			1.05668
$58$		0			0
$59$	−6.14495	−	10.6434i	−0.800004	−	1.38565i	−0.919613	−	0.392826i	$-0.871497\pi$
$59$	−6.14495	−	10.6434i	−0.800004	−	1.38565i	0.119609	−	0.992821i	$-0.461836\pi$
$60$		0			0
$61$	−1.31229	+	2.27296i	−0.168022	+	0.291022i	−0.937724	−	0.347380i	$-0.887071\pi$
$61$	−1.31229	+	2.27296i	−0.168022	+	0.291022i	0.769702	+	0.638403i	$0.220405\pi$
$62$		0			0
$63$	1.42047	+	0.624872i	0.178962	+	0.0787265i
$64$		0			0
$65$	−12.3606	−	7.13637i	−1.53314	−	0.885158i
$66$		0			0
$67$	3.49634	−	2.01862i	0.427147	−	0.246613i	−0.270984	−	0.962584i	$-0.587349\pi$
$67$	3.49634	−	2.01862i	0.427147	−	0.246613i	0.698130	+	0.715971i	$0.254016\pi$
$68$		0			0
$69$		−	5.27578i		−	0.635129i
$70$		0			0
$71$		−	11.2362i		−	1.33349i	−0.745286	−	0.666745i	$-0.767687\pi$
$71$		−	11.2362i		−	1.33349i	0.745286	−	0.666745i	$-0.232313\pi$
$72$		0			0
$73$	7.92976	+	13.7347i	0.928108	+	1.60753i	0.786485	+	0.617610i	$0.211899\pi$
$73$	7.92976	+	13.7347i	0.928108	+	1.60753i	0.141624	+	0.989921i	$0.454768\pi$
$74$		0			0
$75$	13.8255	+	7.98213i	1.59643	+	0.921697i
$76$		0			0
$77$	−8.16192	−	11.1294i	−0.930137	−	1.26831i
$78$		0			0
$79$	−5.10404	−	2.94682i	−0.574250	−	0.331543i	0.184595	−	0.982815i	$-0.440903\pi$
$79$	−5.10404	−	2.94682i	−0.574250	−	0.331543i	−0.758845	+	0.651271i	$0.774236\pi$
$80$		0			0
$81$	5.20779	+	9.02016i	0.578644	+	1.00224i
$82$		0			0
$83$	−17.1398			−1.88134			−0.940669	−	0.339326i	$-0.889801\pi$
$83$	−17.1398			−1.88134			−0.940669	+	0.339326i	$0.889801\pi$
$84$		0			0
$85$		−	4.53081i		−	0.491435i
$86$		0			0
$87$	−4.55611	−	7.89142i	−0.488466	−	0.846049i
$88$		0			0
$89$	−1.77294	−	1.02361i	−0.187931	−	0.108502i	0.403082	−	0.915164i	$-0.367939\pi$
$89$	−1.77294	−	1.02361i	−0.187931	−	0.108502i	−0.591014	+	0.806661i	$0.701272\pi$
$90$		0			0
$91$	10.2431	−	1.12271i	1.07377	−	0.117692i
$92$		0			0
$93$	−13.8060	−	7.97090i	−1.43162	−	0.826544i
$94$		0			0
$95$	−13.3692	+	7.71871i	−1.37165	+	0.791923i
$96$		0			0
$97$			2.27201i			0.230688i	0.993326	+	0.115344i	$0.0367971\pi$
$97$			2.27201i			0.230688i	−0.993326	+	0.115344i	$0.963203\pi$
$98$		0			0
$99$			3.05966i			0.307507i
$100$		0			0
$101$	−12.1463	+	7.01265i	−1.20860	+	0.697785i	−0.962453	−	0.271448i	$-0.912498\pi$
$101$	−12.1463	+	7.01265i	−1.20860	+	0.697785i	−0.246146	+	0.969233i	$0.579164\pi$
$102$		0			0
$103$	−0.854239	+	1.47959i	−0.0841707	+	0.145788i	−0.905038	−	0.425332i	$-0.860157\pi$
$103$	−0.854239	+	1.47959i	−0.0841707	+	0.145788i	0.820867	+	0.571120i	$0.193491\pi$
$104$		0			0
$105$	−18.2527	+	2.00061i	−1.78128	+	0.195240i
$106$		0			0
$107$	−1.95166	+	3.38038i	−0.188675	+	0.326794i	−0.944809	−	0.327623i	$-0.893752\pi$
$107$	−1.95166	+	3.38038i	−0.188675	+	0.326794i	0.756134	+	0.654417i	$0.227086\pi$
$108$		0			0
$109$	−9.64979	+	5.57131i	−0.924282	+	0.533634i	−0.884999	−	0.465594i	$-0.845841\pi$
$109$	−9.64979	+	5.57131i	−0.924282	+	0.533634i	−0.0392832	+	0.999228i	$0.512507\pi$
$110$		0			0
$111$		−	3.60783i		−	0.342440i
$112$		0			0
$113$	0.348049			0.0327417			0.0163709	−	0.999866i	$-0.494789\pi$
$113$	0.348049			0.0327417			0.0163709	+	0.999866i	$0.494789\pi$
$114$		0			0
$115$	5.10448	+	8.84122i	0.475995	+	0.824448i
$116$		0			0
$117$	−1.97835	−	1.14220i	−0.182898	−	0.105596i
$118$		0			0
$119$	1.93446	+	2.63778i	0.177331	+	0.241805i
$120$		0			0
$121$	8.10576	−	14.0396i	0.736887	−	1.27633i
$122$		0			0
$123$	3.99852	−	11.4481i	0.360535	−	1.03224i
$124$		0			0
$125$	−12.5686			−1.12417
$126$		0			0
$127$	4.02941			0.357552			0.178776	−	0.983890i	$-0.442786\pi$
$127$	4.02941			0.357552			0.178776	+	0.983890i	$0.442786\pi$
$128$		0			0
$129$	18.9231	−	10.9253i	1.66609	−	0.961918i
$130$		0			0
$131$	8.34975	−	14.4622i	0.729521	−	1.26357i	−0.227565	−	0.973763i	$-0.573076\pi$
$131$	8.34975	−	14.4622i	0.729521	−	1.26357i	0.957086	−	0.289804i	$-0.0935903\pi$
$132$		0			0
$133$	4.48783	−	10.2018i	0.389144	−	0.884608i
$134$		0			0
$135$	−14.5058	−	8.37493i	−1.24846	−	0.720799i
$136$		0			0
$137$	2.10504	−	1.21535i	0.179846	−	0.103834i	−0.407374	−	0.913261i	$-0.633556\pi$
$137$	2.10504	−	1.21535i	0.179846	−	0.103834i	0.587220	+	0.809427i	$0.300222\pi$
$138$		0			0
$139$	−6.19688			−0.525612			−0.262806	−	0.964849i	$-0.584648\pi$
$139$	−6.19688			−0.525612			−0.262806	+	0.964849i	$0.584648\pi$
$140$		0			0
$141$	4.18932			0.352804
$142$		0			0
$143$	10.1583	+	17.5947i	0.849480	+	1.47134i
$144$		0			0
$145$	15.2704	+	8.81636i	1.26814	+	0.732159i
$146$		0			0
$147$	9.77230	−	8.95782i	0.806006	−	0.738828i
$148$		0			0
$149$	−5.33077	−	3.07772i	−0.436714	−	0.252137i	0.265489	−	0.964114i	$-0.414467\pi$
$149$	−5.33077	−	3.07772i	−0.436714	−	0.252137i	−0.702203	+	0.711977i	$0.747800\pi$
$150$		0			0
$151$	2.92747	−	1.69017i	0.238234	−	0.137544i	−0.376131	−	0.926567i	$-0.622746\pi$
$151$	2.92747	−	1.69017i	0.238234	−	0.137544i	0.614365	+	0.789022i	$0.289412\pi$
$152$		0			0
$153$		−	0.725170i		−	0.0586265i
$154$		0			0
$155$	30.8484			2.47780
$156$		0			0
$157$	−8.20835	+	4.73909i	−0.655098	+	0.378221i	−0.790407	−	0.612583i	$-0.790131\pi$
$157$	−8.20835	+	4.73909i	−0.655098	+	0.378221i	0.135309	+	0.990803i	$0.456797\pi$
$158$		0			0
$159$	2.24459	−	3.88775i	0.178008	−	0.308319i
$160$		0			0
$161$	−6.74657	−	2.96786i	−0.531704	−	0.233900i
$162$		0			0
$163$	−8.17620	+	14.1616i	−0.640409	+	1.10922i	0.344932	+	0.938628i	$0.387902\pi$
$163$	−8.17620	+	14.1616i	−0.640409	+	1.10922i	−0.985341	+	0.170594i	$0.945431\pi$
$164$		0			0
$165$	−18.1016	−	31.3529i	−1.40921	−	2.44082i
$166$		0			0
$167$			24.7370i			1.91421i	0.289743	+	0.957105i	$0.406430\pi$
$167$			24.7370i			1.91421i	−0.289743	+	0.957105i	$0.593570\pi$
$168$		0			0
$169$	−2.16873			−0.166825
$170$		0			0
$171$	−2.13978	+	1.23540i	−0.163633	+	0.0944737i
$172$		0			0
$173$	1.22233	−	2.11714i	0.0929320	−	0.160963i	−0.815812	−	0.578318i	$-0.803709\pi$
$173$	1.22233	−	2.11714i	0.0929320	−	0.160963i	0.908744	+	0.417355i	$0.137043\pi$
$174$		0			0
$175$	17.9849	−	13.1895i	1.35953	−	0.997030i
$176$		0			0
$177$	20.1566	+	11.6374i	1.51506	+	0.874720i
$178$		0			0
$179$	14.8979	−	8.60128i	1.11352	−	0.642890i	0.173780	−	0.984785i	$-0.444402\pi$
$179$	14.8979	−	8.60128i	1.11352	−	0.642890i	0.939738	+	0.341895i	$0.111069\pi$
$180$		0			0
$181$			4.03818i			0.300155i	0.988674	+	0.150078i	$0.0479524\pi$
$181$			4.03818i			0.300155i	−0.988674	+	0.150078i	$0.952048\pi$
$182$		0			0
$183$		−	4.97048i		−	0.367429i
$184$		0			0
$185$	3.49069	+	6.04606i	0.256641	+	0.444515i
$186$		0			0
$187$	−3.22470	+	5.58534i	−0.235813	+	0.408441i
$188$		0			0
$189$	12.0208	−	1.31756i	0.874386	−	0.0958384i
$190$		0			0
$191$	−3.95452	−	2.28314i	−0.286139	−	0.165202i	0.350060	−	0.936727i	$-0.386161\pi$
$191$	−3.95452	−	2.28314i	−0.286139	−	0.165202i	−0.636199	+	0.771525i	$0.719494\pi$
$192$		0			0
$193$	4.54784	−	2.62570i	0.327361	−	0.189002i	−0.327308	−	0.944918i	$-0.606141\pi$
$193$	4.54784	−	2.62570i	0.327361	−	0.189002i	0.654669	+	0.755916i	$0.272808\pi$
$194$		0			0
$195$	27.0299			1.93565
$196$		0			0
$197$	18.4396			1.31376			0.656882	−	0.753993i	$-0.271875\pi$
$197$	18.4396			1.31376			0.656882	+	0.753993i	$0.271875\pi$
$198$		0			0
$199$	11.2119	−	6.47319i	0.794790	−	0.458872i	−0.0468561	−	0.998902i	$-0.514920\pi$
$199$	11.2119	−	6.47319i	0.794790	−	0.458872i	0.841646	+	0.540029i	$0.181587\pi$
$200$		0			0
$201$	−3.82289	+	6.62143i	−0.269646	+	0.467040i
$202$		0			0
$203$	−12.6544	+	1.38701i	−0.888167	+	0.0973489i
$204$		0			0
$205$	4.37566	+	23.0536i	0.305609	+	1.61014i
$206$		0			0
$207$	0.816988	+	1.41506i	0.0567846	+	0.0983537i
$208$		0			0
$209$	21.9745			1.52001
$210$		0			0
$211$			18.0321i			1.24138i	0.784054	+	0.620692i	$0.213148\pi$
$211$			18.0321i			1.24138i	−0.784054	+	0.620692i	$0.786852\pi$
$212$		0			0
$213$	10.6396	+	18.4284i	0.729016	+	1.26269i
$214$		0			0
$215$	−21.1411	+	36.6175i	−1.44181	+	2.49729i
$216$		0			0
$217$	−17.9595	+	13.1709i	−1.21917	+	0.894099i
$218$		0			0
$219$	−26.0111	−	15.0175i	−1.75767	−	1.01479i
$220$		0			0
$221$	−2.40762	−	4.17012i	−0.161954	−	0.280512i
$222$		0			0
$223$	17.5505			1.17527			0.587635	−	0.809126i	$-0.300059\pi$
$223$	17.5505			1.17527			0.587635	+	0.809126i	$0.300059\pi$
$224$		0			0
$225$	−4.94434			−0.329622
$226$		0			0
$227$	23.9391	−	13.8212i	1.58889	−	0.917348i	0.595405	−	0.803426i	$-0.296992\pi$
$227$	23.9391	−	13.8212i	1.58889	−	0.917348i	0.993490	−	0.113922i	$-0.0363415\pi$
$228$		0			0
$229$	22.9494	+	13.2498i	1.51654	+	0.875573i	0.999811	+	0.0194226i	$0.00618281\pi$
$229$	22.9494	+	13.2498i	1.51654	+	0.875573i	0.516726	+	0.856151i	$0.327151\pi$
$230$		0			0
$231$	23.9248	+	10.5247i	1.57414	+	0.692473i
$232$		0			0
$233$	−21.3620	−	12.3333i	−1.39947	−	0.807984i	−0.405133	−	0.914258i	$-0.632775\pi$
$233$	−21.3620	−	12.3333i	−1.39947	−	0.807984i	−0.994337	+	0.106274i	$0.966108\pi$
$234$		0			0
$235$	−7.02052	+	4.05330i	−0.457968	+	0.264408i
$236$		0			0
$237$	11.1615			0.725016
$238$		0			0
$239$		−	19.0486i		−	1.23215i	−0.787688	−	0.616075i	$-0.788722\pi$
$239$		−	19.0486i		−	1.23215i	0.787688	−	0.616075i	$-0.211278\pi$
$240$		0			0
$241$	−7.72249	−	13.3757i	−0.497449	−	0.861607i	0.502547	−	0.864550i	$-0.332397\pi$
$241$	−7.72249	−	13.3757i	−0.497449	−	0.861607i	−0.999996	+	0.00294298i	$0.999063\pi$
$242$		0			0
$243$	−5.20763	−	3.00663i	−0.334070	−	0.192875i
$244$		0			0
$245$	−7.70959	+	24.4666i	−0.492547	+	1.56312i
$246$		0			0
$247$	−8.20326	+	14.2085i	−0.521961	+	0.904063i
$248$		0			0
$249$	28.1109	−	16.2298i	1.78145	−	1.02852i
$250$		0			0
$251$	27.2723			1.72141			0.860706	−	0.509102i	$-0.170022\pi$
$251$	27.2723			1.72141			0.860706	+	0.509102i	$0.170022\pi$
$252$		0			0
$253$		−	14.5320i		−	0.913618i
$254$		0			0
$255$	4.29026	+	7.43095i	0.268666	+	0.465344i
$256$		0			0
$257$	−22.6870	−	13.0984i	−1.41518	−	0.817054i	−0.419308	−	0.907844i	$-0.637727\pi$
$257$	−22.6870	−	13.0984i	−1.41518	−	0.817054i	−0.995870	+	0.0907904i	$0.971061\pi$
$258$		0			0
$259$	−4.61364	−	2.02957i	−0.286677	−	0.126111i
$260$		0			0
$261$	2.44407	+	1.41109i	0.151284	+	0.0873440i
$262$		0			0
$263$	−1.60999	+	0.929529i	−0.0992763	+	0.0573172i	−0.548816	−	0.835943i	$-0.684921\pi$
$263$	−1.60999	+	0.929529i	−0.0992763	+	0.0573172i	0.449540	+	0.893260i	$0.351588\pi$
$264$		0			0
$265$			8.68686i			0.533629i
$266$		0			0
$267$	3.87705			0.237272
$268$		0			0
$269$	−6.30864	−	10.9269i	−0.384645	−	0.666224i	0.607075	−	0.794645i	$-0.292343\pi$
$269$	−6.30864	−	10.9269i	−0.384645	−	0.666224i	−0.991720	+	0.128420i	$0.959009\pi$
$270$		0			0
$271$	9.71715	−	16.8306i	0.590275	−	1.02239i	−0.403921	−	0.914794i	$-0.632353\pi$
$271$	9.71715	−	16.8306i	0.590275	−	1.02239i	0.994195	−	0.107591i	$-0.0343138\pi$
$272$		0			0
$273$	−15.7365	+	11.5406i	−0.952416	+	0.698469i
$274$		0			0
$275$	38.0819	+	21.9866i	2.29642	+	1.32584i
$276$		0			0
$277$	6.51902	+	11.2913i	0.391690	+	0.678427i	0.992673	−	0.120835i	$-0.0385573\pi$
$277$	6.51902	+	11.2913i	0.391690	+	0.678427i	−0.600983	+	0.799262i	$0.705224\pi$
$278$		0			0
$279$	4.93738			0.295593
$280$		0			0
$281$		−	3.41321i		−	0.203615i	−0.994804	−	0.101808i	$-0.967537\pi$
$281$		−	3.41321i		−	0.203615i	0.994804	−	0.101808i	$-0.0324626\pi$
$282$		0			0
$283$	−3.26158	−	5.64921i	−0.193881	−	0.335811i	0.752652	−	0.658418i	$-0.228774\pi$
$283$	−3.26158	−	5.64921i	−0.193881	−	0.335811i	−0.946533	+	0.322607i	$0.895441\pi$
$284$		0			0
$285$	14.6178	−	25.3188i	0.865885	−	1.49976i
$286$		0			0
$287$	−12.3903	−	11.5533i	−0.731379	−	0.681971i
$288$		0			0
$289$	−7.73571	+	13.3986i	−0.455042	+	0.788156i
$290$		0			0
$291$	−2.15139	−	3.72631i	−0.126117	−	0.218440i
$292$		0			0
$293$			3.31599i			0.193722i	0.995298	+	0.0968611i	$0.0308803\pi$
$293$			3.31599i			0.193722i	−0.995298	+	0.0968611i	$0.969120\pi$
$294$		0			0
$295$	−45.0382			−2.62222
$296$		0			0
$297$	11.9213	+	20.6483i	0.691745	+	1.19814i
$298$		0			0
$299$	9.39623	+	5.42492i	0.543398	+	0.313731i
$300$		0			0
$301$	−3.32596	−	30.3446i	−0.191705	−	1.74903i
$302$		0			0
$303$	13.2807	−	23.0028i	0.762955	−	1.32148i
$304$		0			0
$305$	4.80910	+	8.32960i	0.275368	+	0.476951i
$306$		0			0
$307$	14.5774			0.831978			0.415989	−	0.909370i	$-0.363435\pi$
$307$	14.5774			0.831978			0.415989	+	0.909370i	$0.363435\pi$
$308$		0			0
$309$		−	3.23554i		−	0.184064i
$310$		0			0
$311$	13.5283	−	7.81059i	0.767121	−	0.442898i	−0.0647254	−	0.997903i	$-0.520617\pi$
$311$	13.5283	−	7.81059i	0.767121	−	0.442898i	0.831847	+	0.555005i	$0.187284\pi$
$312$		0			0
$313$	20.0207	+	11.5589i	1.13163	+	0.653350i	0.944345	−	0.328955i	$-0.106697\pi$
$313$	20.0207	+	11.5589i	1.13163	+	0.653350i	0.187289	+	0.982305i	$0.440030\pi$
$314$		0			0
$315$	4.58591	−	3.36314i	0.258387	−	0.189492i
$316$		0			0
$317$	9.60700	+	5.54660i	0.539583	+	0.311528i	0.744910	−	0.667165i	$-0.232493\pi$
$317$	9.60700	+	5.54660i	0.539583	+	0.311528i	−0.205327	+	0.978693i	$0.565826\pi$
$318$		0			0
$319$	−12.5497	−	21.7367i	−0.702648	−	1.21702i
$320$		0			0
$321$		−	7.39219i		−	0.412592i
$322$		0			0
$323$	−5.20817			−0.289790
$324$		0			0
$325$	−28.4326	+	16.4156i	−1.57716	+	0.910572i
$326$		0			0
$327$	10.5510	−	18.2749i	0.583473	−	1.01061i
$328$		0			0
$329$	2.35668	−	5.35723i	0.129928	−	0.295354i
$330$		0			0
$331$	−7.30258	−	4.21615i	−0.401386	−	0.231740i	0.285696	−	0.958320i	$-0.407775\pi$
$331$	−7.30258	−	4.21615i	−0.401386	−	0.231740i	−0.687082	+	0.726580i	$0.741109\pi$
$332$		0			0
$333$	0.558696	+	0.967690i	0.0306164	+	0.0530291i
$334$		0			0
$335$		−	14.7951i		−	0.808340i
$336$		0			0
$337$	−7.02132			−0.382476			−0.191238	−	0.981544i	$-0.561250\pi$
$337$	−7.02132			−0.382476			−0.191238	+	0.981544i	$0.561250\pi$
$338$		0			0
$339$	−0.570833	+	0.329571i	−0.0310034	+	0.0178998i
$340$		0			0
$341$	−38.0283	−	21.9556i	−2.05935	−	1.18896i
$342$		0			0
$343$	−5.95775	−	17.5358i	−0.321688	−	0.946846i
$344$		0			0
$345$	−16.7436	−	9.66694i	−0.901447	−	0.520451i
$346$		0			0
$347$	6.15674	−	3.55459i	0.330511	−	0.190821i	−0.325557	−	0.945522i	$-0.605552\pi$
$347$	6.15674	−	3.55459i	0.330511	−	0.190821i	0.656068	+	0.754702i	$0.272218\pi$
$348$		0			0
$349$	−15.3432			−0.821302			−0.410651	−	0.911793i	$-0.634699\pi$
$349$	−15.3432			−0.821302			−0.410651	+	0.911793i	$0.634699\pi$
$350$		0			0
$351$	−17.8013			−0.950165
$352$		0			0
$353$	−4.36754	−	7.56481i	−0.232461	−	0.402634i	0.726071	−	0.687620i	$-0.241344\pi$
$353$	−4.36754	−	7.56481i	−0.232461	−	0.402634i	−0.958532	+	0.284986i	$0.908011\pi$
$354$		0			0
$355$	−35.6601	−	20.5884i	−1.89264	−	1.09272i
$356$		0			0
$357$	−5.67042	−	2.49445i	−0.300111	−	0.132020i
$358$		0			0
$359$	−12.0452	+	20.8629i	−0.635721	+	1.10110i	0.350641	+	0.936510i	$0.385964\pi$
$359$	−12.0452	+	20.8629i	−0.635721	+	1.10110i	−0.986362	+	0.164591i	$0.947370\pi$
$360$		0			0
$361$	−0.627339	−	1.08658i	−0.0330178	−	0.0571886i
$362$		0			0
$363$			30.7016i			1.61142i
$364$		0			0
$365$	58.1196			3.04212
$366$		0			0
$367$	16.0359	+	27.7749i	0.837065	+	1.44984i	0.892338	+	0.451368i	$0.149064\pi$
$367$	16.0359	+	27.7749i	0.837065	+	1.44984i	−0.0552726	+	0.998471i	$0.517603\pi$
$368$		0			0
$369$	0.700337	+	3.68981i	0.0364581	+	0.192084i
$370$		0			0
$371$	−3.70891	−	5.05738i	−0.192557	−	0.262566i
$372$		0			0
$373$	4.85101	−	8.40220i	0.251176	−	0.435049i	−0.712674	−	0.701495i	$-0.752516\pi$
$373$	4.85101	−	8.40220i	0.251176	−	0.435049i	0.963850	+	0.266446i	$0.0858494\pi$
$374$		0			0
$375$	20.6137	−	11.9013i	1.06448	−	0.614581i
$376$		0			0
$377$	18.7396			0.965140
$378$		0			0
$379$	−27.5555			−1.41543			−0.707716	−	0.706497i	$-0.750274\pi$
$379$	−27.5555			−1.41543			−0.707716	+	0.706497i	$0.750274\pi$
$380$		0			0
$381$	−6.60861	+	3.81548i	−0.338569	+	0.195473i
$382$		0			0
$383$	−20.0256	−	11.5618i	−1.02326	−	0.590780i	−0.108214	−	0.994128i	$-0.534513\pi$
$383$	−20.0256	−	11.5618i	−1.02326	−	0.590780i	−0.915047	+	0.403348i	$0.867846\pi$
$384$		0			0
$385$	−50.2765	+	5.51063i	−2.56233	+	0.280848i
$386$		0			0
$387$	−3.38370	+	5.86074i	−0.172003	+	0.297918i
$388$		0			0
$389$	−8.41017	−	14.5668i	−0.426413	−	0.738568i	0.570139	−	0.821549i	$-0.306890\pi$
$389$	−8.41017	−	14.5668i	−0.426413	−	0.738568i	−0.996551	+	0.0829802i	$0.973556\pi$
$390$		0			0
$391$			3.44422i			0.174182i
$392$		0			0
$393$			31.6258i			1.59531i
$394$		0			0
$395$	−18.7045	+	10.7991i	−0.941128	+	0.543360i
$396$		0			0
$397$	5.86748	+	3.38759i	0.294480	+	0.170018i	0.639961	−	0.768408i	$-0.278951\pi$
$397$	5.86748	+	3.38759i	0.294480	+	0.170018i	−0.345480	+	0.938426i	$0.612284\pi$
$398$		0			0
$399$	2.29970	+	20.9815i	0.115129	+	1.05039i
$400$		0			0
$401$	−0.208148	+	0.360524i	−0.0103944	+	0.0180037i	−0.871176	−	0.490971i	$-0.836642\pi$
$401$	−0.208148	+	0.360524i	−0.0103944	+	0.0180037i	0.860781	+	0.508975i	$0.169975\pi$
$402$		0			0
$403$	28.3926	−	16.3925i	1.41433	−	0.816567i
$404$		0			0
$405$	38.1695			1.89666
$406$		0			0
$407$		−	9.93768i		−	0.492593i
$408$		0			0
$409$	−16.3809	−	28.3725i	−0.809983	−	1.40293i	−0.912875	−	0.408239i	$-0.866143\pi$
$409$	−16.3809	−	28.3725i	−0.809983	−	1.40293i	0.102892	−	0.994693i	$-0.467190\pi$
$410$		0			0
$411$	−2.30164	+	3.98656i	−0.113532	+	0.196643i
$412$		0			0
$413$	26.2207	−	19.2293i	1.29023	−	0.946213i
$414$		0			0
$415$	−31.4057	+	54.3963i	−1.54165	+	2.67021i
$416$		0			0
$417$	10.1635	−	5.86787i	0.497707	−	0.287351i
$418$		0			0
$419$	0.558726			0.0272955			0.0136478	−	0.999907i	$-0.495656\pi$
$419$	0.558726			0.0272955			0.0136478	+	0.999907i	$0.495656\pi$
$420$		0			0
$421$			8.73292i			0.425617i	0.977094	+	0.212808i	$0.0682610\pi$
$421$			8.73292i			0.425617i	−0.977094	+	0.212808i	$0.931739\pi$
$422$		0			0
$423$	−1.12366	+	0.648743i	−0.0546340	+	0.0315430i
$424$		0			0
$425$	−9.02578	−	5.21104i	−0.437815	−	0.252772i
$426$		0			0
$427$	−6.35617	−	2.79612i	−0.307596	−	0.135314i
$428$		0			0
$429$	−33.3211	−	19.2379i	−1.60876	−	0.928817i
$430$		0			0
$431$	−12.4492	−	21.5627i	−0.599659	−	1.03864i	−0.992871	−	0.119192i	$-0.961970\pi$
$431$	−12.4492	−	21.5627i	−0.599659	−	1.03864i	0.393212	−	0.919448i	$-0.371364\pi$
$432$		0			0
$433$	−21.7044			−1.04305			−0.521524	−	0.853236i	$-0.674636\pi$
$433$	−21.7044			−1.04305			−0.521524	+	0.853236i	$0.674636\pi$
$434$		0			0
$435$	−33.3931			−1.60108
$436$		0			0
$437$	10.1630	−	5.86760i	0.486161	−	0.280685i
$438$		0			0
$439$	14.4592	+	8.34801i	0.690099	+	0.398429i	0.803649	−	0.595104i	$-0.202889\pi$
$439$	14.4592	+	8.34801i	0.690099	+	0.398429i	−0.113550	+	0.993532i	$0.536222\pi$
$440$		0			0
$441$	−1.23394	+	3.91596i	−0.0587592	+	0.186474i
$442$		0			0
$443$	4.20522	−	7.28365i	0.199796	−	0.346057i	−0.748666	−	0.662947i	$-0.769305\pi$
$443$	4.20522	−	7.28365i	0.199796	−	0.346057i	0.948462	+	0.316890i	$0.102639\pi$
$444$		0			0
$445$	−6.49721	+	3.75117i	−0.307997	+	0.177822i
$446$		0			0
$447$	11.6573			0.551370
$448$		0			0
$449$	14.0039			0.660885			0.330443	−	0.943826i	$-0.392802\pi$
$449$	14.0039			0.660885			0.330443	+	0.943826i	$0.392802\pi$
$450$		0			0
$451$	11.0138	−	31.5336i	0.518621	−	1.48486i
$452$		0			0
$453$	−3.20088	+	5.54409i	−0.150390	+	0.260484i
$454$		0			0
$455$	15.2055	−	34.5654i	0.712847	−	1.62045i
$456$		0			0
$457$	10.1207	+	5.84321i	0.473428	+	0.273334i	0.717674	−	0.696380i	$-0.245207\pi$
$457$	10.1207	+	5.84321i	0.473428	+	0.273334i	−0.244246	+	0.969713i	$0.578540\pi$
$458$		0			0
$459$	−2.82547	−	4.89386i	−0.131882	−	0.228426i
$460$		0			0
$461$	7.79184			0.362902			0.181451	−	0.983400i	$-0.441921\pi$
$461$	7.79184			0.362902			0.181451	+	0.983400i	$0.441921\pi$
$462$		0			0
$463$		−	14.6823i		−	0.682346i	−0.940001	−	0.341173i	$-0.889176\pi$
$463$		−	14.6823i		−	0.682346i	0.940001	−	0.341173i	$-0.110824\pi$
$464$		0			0
$465$	−50.5942	+	29.2106i	−2.34625	+	1.35461i
$466$		0			0
$467$	−14.4696	+	25.0622i	−0.669575	+	1.15974i	0.308447	+	0.951241i	$0.400191\pi$
$467$	−14.4696	+	25.0622i	−0.669575	+	1.15974i	−0.978023	+	0.208497i	$0.933143\pi$
$468$		0			0
$469$	6.31684	+	8.61349i	0.291684	+	0.397734i
$470$		0			0
$471$	8.97497	−	15.5451i	0.413545	−	0.716281i
$472$		0			0
$473$	52.1233	−	30.0934i	2.39663	−	1.38370i
$474$		0			0
$475$			35.5102i			1.62932i
$476$		0			0
$477$			1.39036i			0.0636601i
$478$		0			0
$479$	−23.9118	+	13.8055i	−1.09256	+	0.630787i	−0.934256	−	0.356604i	$-0.883935\pi$
$479$	−23.9118	+	13.8055i	−1.09256	+	0.630787i	−0.158300	+	0.987391i	$0.550601\pi$
$480$		0			0
$481$	6.42560	+	3.70982i	0.292982	+	0.169153i
$482$		0			0
$483$	13.8753	−	1.52082i	0.631348	−	0.0691998i
$484$		0			0
$485$	7.21065	+	4.16307i	0.327419	+	0.189035i
$486$		0			0
$487$	21.7662	+	37.7002i	0.986321	+	1.70836i	0.635914	+	0.771760i	$0.280623\pi$
$487$	21.7662	+	37.7002i	0.986321	+	1.70836i	0.350407	+	0.936598i	$0.386043\pi$
$488$		0			0
$489$		−	30.9684i		−	1.40044i
$490$		0			0
$491$	−13.3727			−0.603501			−0.301751	−	0.953387i	$-0.597571\pi$
$491$	−13.3727			−0.603501			−0.301751	+	0.953387i	$0.597571\pi$
$492$		0			0
$493$	2.97440	+	5.15181i	0.133960	+	0.232026i
$494$		0			0
$495$	9.71039	+	5.60630i	0.436450	+	0.251984i
$496$		0			0
$497$	29.5512	−	3.23900i	1.32555	−	0.145289i
$498$		0			0
$499$	6.34984	+	3.66608i	0.284258	+	0.164116i	0.635349	−	0.772225i	$-0.280856\pi$
$499$	6.34984	+	3.66608i	0.284258	+	0.164116i	−0.351092	+	0.936341i	$0.614189\pi$
$500$		0			0
$501$	−23.4237	−	40.5710i	−1.04649	−	1.81258i
$502$		0			0
$503$			29.0022i			1.29314i	0.762853	+	0.646572i	$0.223798\pi$
$503$			29.0022i			1.29314i	−0.762853	+	0.646572i	$0.776202\pi$
$504$		0			0
$505$			51.3979i			2.28718i
$506$		0			0
$507$	3.55691	−	2.05359i	0.157968	−	0.0912029i
$508$		0			0
$509$	30.9454	+	17.8664i	1.37163	+	0.791912i	0.991134	−	0.132869i	$-0.0424190\pi$
$509$	30.9454	+	17.8664i	1.37163	+	0.791912i	0.380499	+	0.924781i	$0.375752\pi$
$510$		0			0
$511$	−33.8365	+	24.8145i	−1.49684	+	1.09773i
$512$		0			0
$513$	−9.62698	+	16.6744i	−0.425042	+	0.736193i
$514$		0			0
$515$	3.13049	+	5.42217i	0.137946	+	0.238929i
$516$		0			0
$517$	11.5394			0.507501
$518$		0			0
$519$			4.62974i			0.203223i
$520$		0			0
$521$	−11.6085	+	6.70218i	−0.508578	+	0.293628i	−0.732249	−	0.681037i	$-0.761529\pi$
$521$	−11.6085	+	6.70218i	−0.508578	+	0.293628i	0.223671	+	0.974665i	$0.428196\pi$
$522$		0			0
$523$	−1.37758	+	2.38604i	−0.0602374	+	0.104334i	−0.894571	−	0.446925i	$-0.852519\pi$
$523$	−1.37758	+	2.38604i	−0.0602374	+	0.104334i	0.834334	+	0.551259i	$0.185852\pi$
$524$		0			0
$525$	−17.0076	+	38.6619i	−0.742273	+	1.68735i
$526$		0			0
$527$	9.01308	+	5.20370i	0.392616	+	0.226677i
$528$		0			0
$529$	7.61968	+	13.1977i	0.331291	+	0.573812i
$530$		0			0
$531$	−7.20850			−0.312822
$532$		0			0
$533$	16.2777	+	18.8932i	0.705067	+	0.818355i
$534$		0			0
$535$	7.15217	+	12.3879i	0.309215	+	0.535577i
$536$		0			0
$537$	−16.2892	+	28.2138i	−0.702933	+	1.21752i
$538$		0			0
$539$	26.9176	−	24.6741i	1.15942	−	1.06279i
$540$		0			0
$541$	11.6537	−	20.1849i	0.501033	−	0.867815i	−0.498966	−	0.866621i	$-0.666287\pi$
$541$	11.6537	−	20.1849i	0.501033	−	0.867815i	0.999999	−	0.00119332i	$-0.000379845\pi$
$542$		0			0
$543$	−3.82378	−	6.62298i	−0.164094	−	0.284219i
$544$		0			0
$545$			40.8338i			1.74913i
$546$		0			0
$547$			46.5607i			1.99079i	0.0958453	+	0.995396i	$0.469445\pi$
$547$			46.5607i			1.99079i	−0.0958453	+	0.995396i	$0.530555\pi$
$548$		0			0
$549$	0.769711	+	1.33318i	0.0328504	+	0.0568986i
$550$		0			0
$551$	10.1344	−	17.5533i	0.431740	−	0.747796i
$552$		0			0
$553$	6.27882	−	14.2731i	0.267003	−	0.606954i
$554$		0			0
$555$	−11.4501	−	6.61073i	−0.486031	−	0.280610i
$556$		0			0
$557$	−19.0318	+	10.9880i	−0.806401	+	0.465576i	−0.845705	−	0.533651i	$-0.820820\pi$
$557$	−19.0318	+	10.9880i	−0.806401	+	0.465576i	0.0393032	+	0.999227i	$0.487486\pi$
$558$		0			0
$559$			44.9365i			1.90061i
$560$		0			0
$561$		−	12.2140i		−	0.515675i
$562$		0			0
$563$	24.3764	−	14.0737i	1.02734	−	0.593137i	0.111122	−	0.993807i	$-0.464556\pi$
$563$	24.3764	−	14.0737i	1.02734	−	0.593137i	0.916223	+	0.400669i	$0.131222\pi$
$564$		0			0
$565$	0.637740	−	1.10460i	0.0268299	−	0.0464708i
$566$		0			0
$567$	−22.2218	+	16.2967i	−0.933228	+	0.684397i
$568$		0			0
$569$	15.4159	−	26.7011i	0.646268	−	1.11937i	−0.337739	−	0.941240i	$-0.609662\pi$
$569$	15.4159	−	26.7011i	0.646268	−	1.11937i	0.984007	−	0.178129i	$-0.0570045\pi$
$570$		0			0
$571$	−15.2134	+	8.78347i	−0.636662	+	0.367577i	−0.783327	−	0.621609i	$-0.786479\pi$
$571$	−15.2134	+	8.78347i	−0.636662	+	0.367577i	0.146666	+	0.989186i	$0.453146\pi$
$572$		0			0
$573$	8.64771			0.361263
$574$		0			0
$575$	23.4833			0.979323
$576$		0			0
$577$	−36.1109	+	20.8486i	−1.50332	+	0.867940i	−0.503324	+	0.864098i	$0.667890\pi$
$577$	−36.1109	+	20.8486i	−1.50332	+	0.867940i	−0.999993	+	0.00384220i	$0.998777\pi$
$578$		0			0
$579$	−4.97258	+	8.61277i	−0.206654	+	0.357934i
$580$		0			0
$581$	−4.94081	−	45.0777i	−0.204979	−	1.87014i
$582$		0			0
$583$	6.18267	−	10.7087i	0.256060	−	0.443509i
$584$		0			0
$585$	−7.24995	+	4.18576i	−0.299748	+	0.173060i
$586$		0			0
$587$		−	14.6646i		−	0.605273i	−0.953106	−	0.302636i	$-0.902133\pi$
$587$		−	14.6646i		−	0.605273i	0.953106	−	0.302636i	$-0.0978667\pi$
$588$		0			0
$589$		−	35.4602i		−	1.46111i
$590$		0			0
$591$	−30.2426	+	17.4606i	−1.24401	+	0.718232i
$592$		0			0
$593$	2.21085	+	1.27644i	0.0907888	+	0.0524169i	0.544707	−	0.838626i	$-0.316641\pi$
$593$	2.21085	+	1.27644i	0.0907888	+	0.0524169i	−0.453918	+	0.891043i	$0.649974\pi$
$594$		0			0
$595$	11.9160	−	1.30607i	0.488510	−	0.0535438i
$596$		0			0
$597$	−12.2590	+	21.2333i	−0.501729	+	0.869020i
$598$		0			0
$599$	17.9208	+	31.0398i	0.732225	+	1.26825i	0.955930	+	0.293594i	$0.0948513\pi$
$599$	17.9208	+	31.0398i	0.732225	+	1.26825i	−0.223705	+	0.974657i	$0.571815\pi$
$600$		0			0
$601$		−	5.61681i		−	0.229115i	−0.993417	−	0.114557i	$-0.963455\pi$
$601$		−	5.61681i		−	0.229115i	0.993417	−	0.114557i	$-0.0365449\pi$
$602$		0			0
$603$		−	2.36799i		−	0.0964321i
$604$		0			0
$605$	−29.7048	−	51.4502i	−1.20767	−	2.09175i
$606$		0			0
$607$	15.9968	−	27.7073i	0.649291	−	1.12460i	−0.334002	−	0.942572i	$-0.608399\pi$
$607$	15.9968	−	27.7073i	0.649291	−	1.12460i	0.983293	−	0.182032i	$-0.0582675\pi$
$608$		0			0
$609$	19.4411	−	14.2574i	0.787792	−	0.577739i
$610$		0			0
$611$	−4.30775	+	7.46124i	−0.174273	+	0.301849i
$612$		0			0
$613$	−10.8506	−	18.7938i	−0.438253	−	0.759076i	0.559302	−	0.828964i	$-0.311069\pi$
$613$	−10.8506	−	18.7938i	−0.438253	−	0.759076i	−0.997555	+	0.0698880i	$0.977736\pi$
$614$		0			0
$615$	−29.0062	−	33.6668i	−1.16964	−	1.35758i
$616$		0			0
$617$	−2.79348			−0.112461			−0.0562307	−	0.998418i	$-0.517908\pi$
$617$	−2.79348			−0.112461			−0.0562307	+	0.998418i	$0.517908\pi$
$618$		0			0
$619$	−16.7463	−	29.0054i	−0.673090	−	1.16583i	−0.977023	−	0.213133i	$-0.931633\pi$
$619$	−16.7463	−	29.0054i	−0.673090	−	1.16583i	0.303933	−	0.952694i	$-0.401700\pi$
$620$		0			0
$621$	11.0270	+	6.36644i	0.442498	+	0.255476i
$622$		0			0
$623$	2.18101	−	4.95791i	0.0873804	−	0.198634i
$624$		0			0
$625$	−1.95556	+	3.38713i	−0.0782225	+	0.135485i
$626$		0			0
$627$	−36.0402	+	20.8078i	−1.43931	+	0.830983i
$628$		0			0
$629$			2.35533i			0.0939131i
$630$		0			0
$631$	−25.3087			−1.00752			−0.503761	−	0.863843i	$-0.668051\pi$
$631$	−25.3087			−1.00752			−0.503761	+	0.863843i	$0.668051\pi$
$632$		0			0
$633$	−17.0748	−	29.5744i	−0.678662	−	1.17548i
$634$		0			0
$635$	7.38320	−	12.7881i	0.292993	−	0.507479i
$636$		0			0
$637$	5.90545	+	26.6157i	0.233982	+	1.05455i
$638$		0			0
$639$	−5.70751	−	3.29523i	−0.225786	−	0.130357i
$640$		0			0
$641$	10.1542	−	5.86254i	0.401068	−	0.231557i	−0.285877	−	0.958266i	$-0.592285\pi$
$641$	10.1542	−	5.86254i	0.401068	−	0.231557i	0.686945	+	0.726710i	$0.258952\pi$
$642$		0			0
$643$		−	17.0067i		−	0.670678i	−0.942098	−	0.335339i	$-0.891149\pi$
$643$		−	17.0067i		−	0.670678i	0.942098	−	0.335339i	$-0.108851\pi$
$644$		0			0
$645$		−	80.0748i		−	3.15294i
$646$		0			0
$647$	−5.07646	−	8.79269i	−0.199576	−	0.345676i	0.748815	−	0.662779i	$-0.230623\pi$
$647$	−5.07646	−	8.79269i	−0.199576	−	0.345676i	−0.948391	+	0.317103i	$0.897290\pi$
$648$		0			0
$649$	55.5207	+	32.0549i	2.17938	+	1.25826i
$650$		0			0
$651$	16.9837	−	38.6075i	0.665643	−	1.51315i
$652$		0			0
$653$	−14.2547	−	8.22998i	−0.557831	−	0.322064i	0.194443	−	0.980914i	$-0.437710\pi$
$653$	−14.2547	−	8.22998i	−0.557831	−	0.322064i	−0.752274	+	0.658850i	$0.771043\pi$
$654$		0			0
$655$	−30.5989	−	52.9989i	−1.19560	−	2.07084i
$656$		0			0
$657$	9.30222			0.362914
$658$		0			0
$659$			13.6757i			0.532728i	0.963873	+	0.266364i	$0.0858223\pi$
$659$			13.6757i			0.532728i	−0.963873	+	0.266364i	$0.914178\pi$
$660$		0			0
$661$	−12.9668	−	22.4592i	−0.504351	−	0.873562i	−0.999987	−	0.00503193i	$-0.998398\pi$
$661$	−12.9668	−	22.4592i	−0.504351	−	0.873562i	0.495636	−	0.868530i	$-0.334935\pi$
$662$		0			0
$663$	7.89743	+	4.55958i	0.306711	+	0.177080i
$664$		0			0
$665$	−24.1541	−	32.9360i	−0.936655	−	1.27720i
$666$		0			0
$667$	−11.6082	−	6.70201i	−0.449472	−	0.259503i
$668$		0			0
$669$	−28.7845	+	16.6187i	−1.11287	+	0.642518i
$670$		0			0
$671$		−	13.6911i		−	0.528537i
$672$		0			0
$673$			33.9367i			1.30816i	0.756423	+	0.654082i	$0.226945\pi$
$673$			33.9367i			1.30816i	−0.756423	+	0.654082i	$0.773055\pi$
$674$		0			0
$675$	−33.3672	+	19.2646i	−1.28430	+	0.741494i
$676$		0			0
$677$	−19.7093	+	34.1375i	−0.757491	+	1.31201i	0.186636	+	0.982429i	$0.440242\pi$
$677$	−19.7093	+	34.1375i	−0.757491	+	1.31201i	−0.944126	+	0.329583i	$0.893092\pi$
$678$		0			0
$679$	−5.97540	+	0.654943i	−0.229315	+	0.0251344i
$680$		0			0
$681$	−26.1749	+	45.3363i	−1.00302	+	1.73729i
$682$		0			0
$683$	−26.1953	+	15.1239i	−1.00233	+	0.578698i	−0.908938	−	0.416931i	$-0.863106\pi$
$683$	−26.1953	+	15.1239i	−1.00233	+	0.578698i	−0.0933966	+	0.995629i	$0.529772\pi$
$684$		0			0
$685$		−	8.90765i		−	0.340344i
$686$		0			0
$687$	−50.1855			−1.91470
$688$		0			0
$689$	4.61609	+	7.99530i	0.175859	+	0.304597i
$690$		0			0
$691$	11.4670	+	6.62049i	0.436226	+	0.251855i	0.701996	−	0.712181i	$-0.252293\pi$
$691$	11.4670	+	6.62049i	0.436226	+	0.251855i	−0.265769	+	0.964037i	$0.585626\pi$
$692$		0			0
$693$	−8.04691	+	0.881994i	−0.305677	+	0.0335042i
$694$		0			0
$695$	−11.3547	+	19.6669i	−0.430709	+	0.746009i
$696$		0			0
$697$	−2.61039	+	7.47378i	−0.0988754	+	0.283089i
$698$		0			0
$699$	46.7142			1.76689
$700$		0			0
$701$	4.53790			0.171394			0.0856971	−	0.996321i	$-0.472688\pi$
$701$	4.53790			0.171394			0.0856971	+	0.996321i	$0.472688\pi$
$702$		0			0
$703$	6.94994	−	4.01255i	0.262122	−	0.151336i
$704$		0			0
$705$	7.67620	−	13.2956i	0.289103	−	0.500740i
$706$		0			0
$707$	−21.9446	−	29.9232i	−0.825313	−	1.12538i
$708$		0			0
$709$	−33.3342	−	19.2455i	−1.25189	−	0.722781i	−0.280409	−	0.959881i	$-0.590470\pi$
$709$	−33.3342	−	19.2455i	−1.25189	−	0.722781i	−0.971485	+	0.237099i	$0.923803\pi$
$710$		0			0
$711$	−2.99372	+	1.72843i	−0.112273	+	0.0648210i
$712$		0			0
$713$	−23.4503			−0.878220
$714$		0			0
$715$	74.4533			2.78439
$716$		0			0
$717$	18.0372	+	31.2414i	0.673613	+	1.16673i
$718$		0			0
$719$	22.2733	+	12.8595i	0.830653	+	0.479578i	0.854076	−	0.520148i	$-0.174123\pi$
$719$	22.2733	+	12.8595i	0.830653	+	0.479578i	−0.0234234	+	0.999726i	$0.507457\pi$
$720$		0			0
$721$	−4.13756	−	1.82014i	−0.154091	−	0.0677854i
$722$		0			0
$723$	25.3312	+	14.6250i	0.942077	+	0.543908i
$724$		0			0
$725$	35.1260	−	20.2800i	1.30455	−	0.753180i
$726$		0			0
$727$			1.59858i			0.0592880i	0.999561	+	0.0296440i	$0.00943736\pi$
$727$			1.59858i			0.0592880i	−0.999561	+	0.0296440i	$0.990563\pi$
$728$		0			0
$729$	−19.8588			−0.735510
$730$		0			0
$731$	−12.3537	+	7.13244i	−0.456920	+	0.263803i
$732$		0			0
$733$	10.7040	−	18.5399i	0.395361	−	0.684786i	−0.597786	−	0.801656i	$-0.703953\pi$
$733$	10.7040	−	18.5399i	0.395361	−	0.684786i	0.993147	+	0.116870i	$0.0372860\pi$
$734$		0			0
$735$	−10.5232	−	47.4278i	−0.388155	−	1.74940i
$736$		0			0
$737$	−10.5300	+	18.2386i	−0.387879	+	0.671826i
$738$		0			0
$739$	11.1617	+	19.3326i	0.410588	+	0.711160i	0.994954	−	0.100330i	$-0.0319900\pi$
$739$	11.1617	+	19.3326i	0.410588	+	0.711160i	−0.584366	+	0.811490i	$0.698657\pi$
$740$		0			0
$741$		−	31.0709i		−	1.14142i
$742$		0			0
$743$	−12.6304			−0.463365			−0.231682	−	0.972792i	$-0.574423\pi$
$743$	−12.6304			−0.463365			−0.231682	+	0.972792i	$0.574423\pi$
$744$		0			0
$745$	−19.5354	+	11.2788i	−0.715722	+	0.413223i
$746$		0			0
$747$	−5.02658	+	8.70629i	−0.183913	+	0.318547i
$748$		0			0
$749$	−9.45300	−	4.15843i	−0.345405	−	0.151946i
$750$		0			0
$751$	−12.6261	−	7.28968i	−0.460733	−	0.266004i	0.251620	−	0.967826i	$-0.419037\pi$
$751$	−12.6261	−	7.28968i	−0.460733	−	0.266004i	−0.712352	+	0.701822i	$0.752370\pi$
$752$		0			0
$753$	−44.7291	+	25.8244i	−1.63002	+	0.941092i
$754$		0			0
$755$		−	12.3878i		−	0.450838i
$756$		0			0
$757$		−	12.9601i		−	0.471042i	−0.971869	−	0.235521i	$-0.924320\pi$
$757$		−	12.9601i		−	0.471042i	0.971869	−	0.235521i	$-0.0756796\pi$
$758$		0			0
$759$	13.7605	+	23.8338i	0.499473	+	0.865112i
$760$		0			0
$761$	1.01386	−	1.75605i	0.0367523	−	0.0636568i	−0.847064	−	0.531491i	$-0.821632\pi$
$761$	1.01386	−	1.75605i	0.0367523	−	0.0636568i	0.883816	+	0.467834i	$0.154965\pi$
$762$		0			0
$763$	−17.4342	−	23.7729i	−0.631162	−	0.860638i
$764$		0			0
$765$	−2.30146	−	1.32875i	−0.0832094	−	0.0480410i
$766$		0			0
$767$	−41.4527	+	23.9327i	−1.49677	+	0.864161i
$768$		0			0
$769$	−50.2600			−1.81242			−0.906211	−	0.422826i	$-0.861038\pi$
$769$	−50.2600			−1.81242			−0.906211	+	0.422826i	$0.861038\pi$
$770$		0			0
$771$	49.6118			1.78672
$772$		0			0
$773$	13.0836	−	7.55380i	0.470583	−	0.271691i	−0.245901	−	0.969295i	$-0.579084\pi$
$773$	13.0836	−	7.55380i	0.470583	−	0.271691i	0.716484	+	0.697604i	$0.245750\pi$
$774$		0			0
$775$	35.4798	−	61.4528i	1.27447	−	2.20745i
$776$		0			0
$777$	9.48861	−	1.04001i	0.340402	−	0.0373103i
$778$		0			0
$779$	26.5002	−	5.02982i	0.949467	−	0.180212i
$780$		0			0
$781$	29.3066	+	50.7605i	1.04867	+	1.81635i
$782$		0			0
$783$	21.9920			0.785930
$784$		0			0
$785$			34.7343i			1.23972i
$786$		0			0
$787$	19.9936	+	34.6299i	0.712693	+	1.23442i	0.963842	+	0.266473i	$0.0858582\pi$
$787$	19.9936	+	34.6299i	0.712693	+	1.23442i	−0.251149	+	0.967948i	$0.580808\pi$
$788$		0			0
$789$	1.76036	−	3.04903i	0.0626703	−	0.108548i
$790$		0			0
$791$	0.100331	+	0.915370i	0.00356734	+	0.0325468i
$792$		0			0
$793$	8.85250	+	5.11099i	0.314361	+	0.181497i
$794$		0			0
$795$	−8.22565	−	14.2473i	−0.291734	−	0.505298i
$796$		0			0
$797$	17.1426			0.607224			0.303612	−	0.952796i	$-0.401807\pi$
$797$	17.1426			0.607224			0.303612	+	0.952796i	$0.401807\pi$
$798$		0			0
$799$	−2.73495			−0.0967554
$800$		0			0
$801$	−1.03990	+	0.600386i	−0.0367430	+	0.0212136i
$802$		0			0
$803$	−71.6468	−	41.3653i	−2.52836	−	1.45975i
$804$		0			0
$805$	−21.7810	+	15.9734i	−0.767678	+	0.562988i
$806$		0			0
$807$	20.6935	+	11.9474i	0.728446	+	0.420569i
$808$		0			0
$809$	1.69809	−	0.980395i	0.0597018	−	0.0344688i	−0.469852	−	0.882745i	$-0.655693\pi$
$809$	1.69809	−	0.980395i	0.0597018	−	0.0344688i	0.529554	+	0.848276i	$0.322359\pi$
$810$		0			0
$811$	−6.67544			−0.234406			−0.117203	−	0.993108i	$-0.537393\pi$
$811$	−6.67544			−0.234406			−0.117203	+	0.993108i	$0.537393\pi$
$812$		0			0
$813$			36.8050i			1.29081i
$814$		0			0
$815$	29.9629	+	51.8973i	1.04956	+	1.81788i
$816$		0			0
$817$	42.0918	+	24.3017i	1.47261	+	0.850209i
$818$		0			0
$819$	2.43369	−	5.53230i	0.0850401	−	0.193314i
$820$		0			0
$821$	−8.35563	+	14.4724i	−0.291613	+	0.505089i	−0.974191	−	0.225723i	$-0.927525\pi$
$821$	−8.35563	+	14.4724i	−0.291613	+	0.505089i	0.682578	+	0.730813i	$0.260859\pi$
$822$		0			0
$823$	−3.35523	+	1.93715i	−0.116956	+	0.0675246i	−0.557337	−	0.830286i	$-0.688177\pi$
$823$	−3.35523	+	1.93715i	−0.116956	+	0.0675246i	0.440381	+	0.897811i	$0.354843\pi$
$824$		0			0
$825$	−83.2771			−2.89933
$826$		0			0
$827$			26.5362i			0.922753i	0.887205	+	0.461376i	$0.152644\pi$
$827$			26.5362i			0.922753i	−0.887205	+	0.461376i	$0.847356\pi$
$828$		0			0
$829$	6.39635	+	11.0788i	0.222155	+	0.384783i	0.955462	−	0.295114i	$-0.0953577\pi$
$829$	6.39635	+	11.0788i	0.222155	+	0.384783i	−0.733307	+	0.679897i	$0.762024\pi$
$830$		0			0
$831$	−21.3836	−	12.3458i	−0.741788	−	0.428272i
$832$		0			0
$833$	−6.37973	+	5.84800i	−0.221044	+	0.202621i
$834$		0			0
$835$	78.5075	+	45.3263i	2.71686	+	1.56858i
$836$		0			0
$837$	33.3202	−	19.2375i	1.15172	−	0.664944i
$838$		0			0
$839$		−	44.8654i		−	1.54893i	−0.632619	−	0.774463i	$-0.718020\pi$
$839$		−	44.8654i		−	1.54893i	0.632619	−	0.774463i	$-0.281980\pi$
$840$		0			0
$841$	5.84882			0.201683
$842$		0			0
$843$	3.23200	+	5.59798i	0.111316	+	0.192805i
$844$		0			0
$845$	−3.97382	+	6.88285i	−0.136703	+	0.236777i
$846$		0			0
$847$	39.2607	+	17.2710i	1.34901	+	0.593440i
$848$		0			0
$849$	10.6986	+	6.17682i	0.367174	+	0.211988i
$850$		0			0
$851$	−2.65355	−	4.59608i	−0.0909625	−	0.157552i
$852$		0			0
$853$	−10.4901			−0.359174			−0.179587	−	0.983742i	$-0.557476\pi$
$853$	−10.4901			−0.359174			−0.179587	+	0.983742i	$0.557476\pi$
$854$		0			0
$855$			9.05465i			0.309662i
$856$		0			0
$857$	−2.17987	−	3.77565i	−0.0744630	−	0.128974i	0.826390	−	0.563099i	$-0.190391\pi$
$857$	−2.17987	−	3.77565i	−0.0744630	−	0.128974i	−0.900853	+	0.434125i	$0.857058\pi$
$858$		0			0
$859$	−27.5172	+	47.6611i	−0.938874	+	1.62618i	−0.171297	+	0.985219i	$0.554796\pi$
$859$	−27.5172	+	47.6611i	−0.938874	+	1.62618i	−0.767577	+	0.640957i	$0.778538\pi$
$860$		0			0
$861$	31.2612	+	7.21602i	1.06538	+	0.245921i
$862$		0			0
$863$	−11.6063	+	20.1027i	−0.395083	+	0.684305i	−0.993112	−	0.117170i	$-0.962618\pi$
$863$	−11.6063	+	20.1027i	−0.395083	+	0.684305i	0.598028	+	0.801475i	$0.295951\pi$
$864$		0			0
$865$	−4.47941	−	7.75857i	−0.152305	−	0.263799i
$866$		0			0
$867$		−	29.3000i		−	0.995081i
$868$		0			0
$869$	30.7440			1.04292
$870$		0			0
$871$	−7.86191	−	13.6172i	−0.266391	−	0.461402i
$872$		0			0
$873$	1.15409	+	0.666313i	0.0390599	+	0.0225513i
$874$		0			0
$875$	−3.62309	−	33.0554i	−0.122483	−	1.11748i
$876$		0			0
$877$	−20.8335	+	36.0846i	−0.703496	+	1.21849i	0.263735	+	0.964595i	$0.415046\pi$
$877$	−20.8335	+	36.0846i	−0.703496	+	1.21849i	−0.967231	+	0.253896i	$0.918288\pi$
$878$		0			0
$879$	−3.13994	−	5.43853i	−0.105907	−	0.183437i
$880$		0			0
$881$	5.32826			0.179514			0.0897569	−	0.995964i	$-0.471391\pi$
$881$	5.32826			0.179514			0.0897569	+	0.995964i	$0.471391\pi$
$882$		0			0
$883$		−	47.3902i		−	1.59481i	−0.603447	−	0.797403i	$-0.706207\pi$
$883$		−	47.3902i		−	1.59481i	0.603447	−	0.797403i	$-0.293793\pi$
$884$		0			0
$885$	73.8668	−	42.6470i	2.48301	−	1.43356i
$886$		0			0
$887$	−30.2398	−	17.4590i	−1.01535	−	0.586214i	−0.102598	−	0.994723i	$-0.532716\pi$
$887$	−30.2398	−	17.4590i	−1.01535	−	0.586214i	−0.912754	+	0.408509i	$0.866049\pi$
$888$		0			0
$889$	1.16154	+	10.5974i	0.0389568	+	0.355424i
$890$		0			0
$891$	−47.0534	−	27.1663i	−1.57635	−	0.910105i
$892$		0			0
$893$	4.65927	+	8.07009i	0.155916	+	0.270055i
$894$		0			0
$895$		−	63.0414i		−	2.10724i
$896$		0			0
$897$	−20.5476			−0.686064
$898$		0			0
$899$	−35.0765	+	20.2515i	−1.16987	+	0.675424i
$900$		0			0
$901$	−1.46535	+	2.53807i	−0.0488180	+	0.0845553i
$902$		0			0
$903$	34.1884	+	46.6185i	1.13772	+	1.55137i
$904$		0			0
$905$	12.8159	+	7.39926i	0.426015	+	0.245960i
$906$		0			0
$907$	−9.21549	−	15.9617i	−0.305995	−	0.530000i	0.671487	−	0.741016i	$-0.265656\pi$
$907$	−9.21549	−	15.9617i	−0.305995	−	0.530000i	−0.977482	+	0.211017i	$0.932323\pi$
$908$		0			0
$909$			8.22639i			0.272852i
$910$		0			0
$911$	−39.0871			−1.29501			−0.647506	−	0.762060i	$-0.724188\pi$
$911$	−39.0871			−1.29501			−0.647506	+	0.762060i	$0.724188\pi$
$912$		0			0
$913$	77.4306	−	44.7046i	2.56258	−	1.47951i
$914$		0			0
$915$	−15.7747	−	9.10754i	−0.521496	−	0.301086i
$916$		0			0
$917$	40.4425	+	17.7909i	1.33553	+	0.587507i
$918$		0			0
$919$	10.2262	+	5.90408i	0.337330	+	0.194758i	0.659091	−	0.752063i	$-0.270941\pi$
$919$	10.2262	+	5.90408i	0.337330	+	0.194758i	−0.321761	+	0.946821i	$0.604275\pi$
$920$		0			0
$921$	−23.9084	+	13.8035i	−0.787807	+	0.454841i
$922$		0			0
$923$	−43.7617			−1.44043
$924$		0			0
$925$	16.0591			0.528018
$926$		0			0
$927$	0.501044	+	0.867835i	0.0164565	+	0.0285034i
$928$		0			0
$929$	−40.0038	−	23.0962i	−1.31248	−	0.757762i	−0.329976	−	0.943989i	$-0.607041\pi$
$929$	−40.0038	−	23.0962i	−1.31248	−	0.757762i	−0.982507	+	0.186227i	$0.940374\pi$
$930$		0			0
$931$	28.1244	+	8.86217i	0.921740	+	0.290446i
$932$		0			0
$933$	−14.7918	+	25.6202i	−0.484262	+	0.838767i
$934$		0			0
$935$	11.8174	+	20.4683i	0.386471	+	0.669387i
$936$		0			0
$937$			49.5868i			1.61993i	0.586477	+	0.809966i	$0.300514\pi$
$937$			49.5868i			1.61993i	−0.586477	+	0.809966i	$0.699486\pi$
$938$		0			0
$939$	−43.7810			−1.42874
$940$		0			0
$941$	−8.00174	−	13.8594i	−0.260849	−	0.451804i	0.705619	−	0.708592i	$-0.250669\pi$
$941$	−8.00174	−	13.8594i	−0.260849	−	0.451804i	−0.966468	+	0.256788i	$0.917336\pi$
$942$		0			0
$943$	−3.32628	−	17.5249i	−0.108319	−	0.570689i
$944$		0			0
$945$	17.8445	−	40.5645i	0.580483	−	1.31956i
$946$		0			0
$947$	−7.79888	+	13.5080i	−0.253429	+	0.438953i	−0.964468	−	0.264201i	$-0.914892\pi$
$947$	−7.79888	+	13.5080i	−0.253429	+	0.438953i	0.711038	+	0.703153i	$0.248225\pi$
$948$		0			0
$949$	53.4928	−	30.8841i	1.73645	−	1.00254i
$950$		0			0
$951$	−21.0085			−0.681247
$952$		0			0
$953$	−37.3993			−1.21148			−0.605740	−	0.795662i	$-0.707123\pi$
$953$	−37.3993			−1.21148			−0.605740	+	0.795662i	$0.707123\pi$
$954$		0			0
$955$	−14.4919	+	8.36693i	−0.468948	+	0.270748i
$956$		0			0
$957$	41.1653	+	23.7668i	1.33069	+	0.768272i
$958$		0			0
$959$	3.80317	+	5.18592i	0.122811	+	0.167462i
$960$		0			0
$961$	−19.9298	+	34.5195i	−0.642898	+	1.11353i
$962$		0			0
$963$	1.14473	+	1.98273i	0.0368883	+	0.0638924i
$964$		0			0
$965$		−	19.2445i		−	0.619503i
$966$		0			0
$967$		−	42.3241i		−	1.36105i	−0.732725	−	0.680525i	$-0.761752\pi$
$967$		−	42.3241i		−	1.36105i	0.732725	−	0.680525i	$-0.238248\pi$
$968$		0			0
$969$	8.54188	−	4.93165i	0.274405	−	0.158428i
$970$		0			0
$971$	−30.1059	−	17.3817i	−0.966144	−	0.557804i	−0.0680858	−	0.997679i	$-0.521689\pi$
$971$	−30.1059	−	17.3817i	−0.966144	−	0.557804i	−0.898059	+	0.439876i	$0.855022\pi$
$972$		0			0
$973$	−1.78634	−	16.2978i	−0.0572676	−	0.522483i
$974$		0			0
$975$	31.0881	−	53.8461i	0.995615	−	1.72445i
$976$		0			0
$977$	1.26714	−	0.731584i	0.0405394	−	0.0234054i	−0.479593	−	0.877491i	$-0.659216\pi$
$977$	1.26714	−	0.731584i	0.0405394	−	0.0234054i	0.520133	+	0.854085i	$0.325882\pi$
$978$		0			0
$979$	10.6792			0.341310
$980$		0			0
$981$			6.53558i			0.208665i
$982$		0			0
$983$	−19.8203	−	34.3298i	−0.632170	−	1.09495i	−0.987107	−	0.160060i	$-0.948831\pi$
$983$	−19.8203	−	34.3298i	−0.632170	−	1.09495i	0.354938	−	0.934890i	$-0.384502\pi$
$984$		0			0
$985$	33.7873	−	58.5213i	1.07655	−	1.86464i
$986$		0			0
$987$	1.20764	+	11.0179i	0.0384395	+	0.350704i
$988$		0			0
$989$	16.0710	−	27.8358i	0.511029	−	0.885128i
$990$		0			0
$991$	25.8148	−	14.9042i	0.820034	−	0.473447i	−0.0303941	−	0.999538i	$-0.509676\pi$
$991$	25.8148	−	14.9042i	0.820034	−	0.473447i	0.850428	+	0.526091i	$0.176343\pi$
$992$		0			0
$993$	15.9692			0.506768
$994$		0			0
$995$		−	47.4440i		−	1.50408i
$996$		0			0
$997$	24.8521	−	14.3484i	0.787074	−	0.454417i	−0.0518574	−	0.998654i	$-0.516514\pi$
$997$	24.8521	−	14.3484i	0.787074	−	0.454417i	0.838931	+	0.544237i	$0.183181\pi$
$998$		0			0
$999$	7.54080	+	4.35368i	0.238580	+	0.137744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.7	yes	56
7.4	even	3	inner	1148.2.r.a.81.22	yes	56
41.40	even	2	inner	1148.2.r.a.737.22	yes	56
287.81	even	6	inner	1148.2.r.a.81.7	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.7	✓	56	287.81	even	6	inner
1148.2.r.a.81.22	yes	56	7.4	even	3	inner
1148.2.r.a.737.7	yes	56	1.1	even	1	trivial
1148.2.r.a.737.22	yes	56	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64009 + 0.946908i) q^{3} +(1.83233 - 3.17368i) q^{5} +(0.288265 + 2.63000i) q^{7} +(0.293269 - 0.507958i) q^{9} +O(q^{10})\)	\(q+(-1.64009 + 0.946908i) q^{3} +(1.83233 - 3.17368i) q^{5} +(0.288265 + 2.63000i) q^{7} +(0.293269 - 0.507958i) q^{9} +(-4.51759 + 2.60823i) q^{11} -3.89471i q^{13} +6.94018i q^{15} +(1.07071 - 0.618177i) q^{17} +(-3.64815 - 2.10626i) q^{19} +(-2.96315 - 4.04048i) q^{21} +(-1.39290 + 2.41257i) q^{23} +(-4.21484 - 7.30032i) q^{25} -4.57065i q^{27} +4.81157i q^{29} +(4.20891 + 7.29004i) q^{31} +(4.93951 - 8.55549i) q^{33} +(8.87498 + 3.90416i) q^{35} +(-0.952530 + 1.64983i) q^{37} +(3.68793 + 6.38768i) q^{39} +(-4.85100 + 4.17945i) q^{41} -11.5379 q^{43} +(-1.07473 - 1.86149i) q^{45} +(-1.91574 - 1.10605i) q^{47} +(-6.83381 + 1.51628i) q^{49} +(-1.17071 + 2.02774i) q^{51} +(-2.05287 + 1.18522i) q^{53} +19.1165i q^{55} +7.97774 q^{57} +(-6.14495 - 10.6434i) q^{59} +(-1.31229 + 2.27296i) q^{61} +(1.42047 + 0.624872i) q^{63} +(-12.3606 - 7.13637i) q^{65} +(3.49634 - 2.01862i) q^{67} -5.27578i q^{69} -11.2362i q^{71} +(7.92976 + 13.7347i) q^{73} +(13.8255 + 7.98213i) q^{75} +(-8.16192 - 11.1294i) q^{77} +(-5.10404 - 2.94682i) q^{79} +(5.20779 + 9.02016i) q^{81} -17.1398 q^{83} -4.53081i q^{85} +(-4.55611 - 7.89142i) q^{87} +(-1.77294 - 1.02361i) q^{89} +(10.2431 - 1.12271i) q^{91} +(-13.8060 - 7.97090i) q^{93} +(-13.3692 + 7.71871i) q^{95} +2.27201i q^{97} +3.05966i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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