LMFDB - Embedded newform 1148.2.r.a.81.7

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			81.7
Character	$\chi$	$=$	1148.81
Dual form			1148.2.r.a.737.7

$q$-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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	−0.0547889	−	0.998498i	$-0.517449\pi$
$3$	−1.64009	−	0.946908i	−0.946908	−	0.546698i	−0.892119	+	0.451800i	$0.850782\pi$
$4$		0			0
$5$	1.83233	+	3.17368i	0.819441	+	1.41931i	0.906094	+	0.423075i	$0.139049\pi$
$5$	1.83233	+	3.17368i	0.819441	+	1.41931i	−0.0866531	+	0.996239i	$0.527617\pi$
$6$		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	−0.372201	−	0.928152i	$-0.621397\pi$
$11$	−4.51759	−	2.60823i	−1.36211	−	0.786412i	−0.989904	+	0.141740i	$0.954730\pi$
$12$		0			0
$13$			3.89471i			1.08020i	0.841602	+	0.540098i	$0.181613\pi$
$13$			3.89471i			1.08020i	−0.841602	+	0.540098i	$0.818387\pi$
$14$		0			0
$15$		−	6.94018i		−	1.79195i
$16$		0			0
$17$	1.07071	+	0.618177i	0.259686	+	0.149930i	0.624191	−	0.781271i	$-0.285429\pi$
$17$	1.07071	+	0.618177i	0.259686	+	0.149930i	−0.364505	+	0.931201i	$0.618762\pi$
$18$		0			0
$19$	−3.64815	+	2.10626i	−0.836943	+	0.483209i	−0.856224	−	0.516605i	$-0.827196\pi$
$19$	−3.64815	+	2.10626i	−0.836943	+	0.483209i	0.0192811	+	0.999814i	$0.493862\pi$
$20$		0			0
$21$	−2.96315	+	4.04048i	−0.646612	+	0.881706i
$22$		0			0
$23$	−1.39290	−	2.41257i	−0.290439	−	0.503055i	0.683475	−	0.729974i	$-0.260468\pi$
$23$	−1.39290	−	2.41257i	−0.290439	−	0.503055i	−0.973914	+	0.226919i	$0.927135\pi$
$24$		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	$-0.852584\pi$
$29$		−	4.81157i		−	0.893486i	0.894662	−	0.446743i	$-0.147416\pi$
$30$		0			0
$31$	4.20891	−	7.29004i	0.755942	−	1.30933i	−0.188962	−	0.981984i	$-0.560512\pi$
$31$	4.20891	−	7.29004i	0.755942	−	1.30933i	0.944904	−	0.327346i	$-0.106154\pi$
$32$		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	0.777044	−	0.629447i	$-0.216718\pi$
$37$	−0.952530	−	1.64983i	−0.156595	−	0.271231i	−0.933639	+	0.358216i	$0.883385\pi$
$38$		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	−0.633170	−	0.774013i	$-0.718246\pi$
$47$	−1.91574	+	1.10605i	−0.279439	+	0.161334i	0.353730	+	0.935347i	$0.384913\pi$
$48$		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	0.352338	−	0.935873i	$-0.385387\pi$
$53$	−2.05287	−	1.18522i	−0.281983	−	0.162803i	−0.634321	+	0.773070i	$0.718720\pi$
$54$		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	0.119609	+	0.992821i	$0.461836\pi$
$59$	−6.14495	+	10.6434i	−0.800004	+	1.38565i	−0.919613	+	0.392826i	$0.871497\pi$
$60$		0			0
$61$	−1.31229	−	2.27296i	−0.168022	−	0.291022i	0.769702	−	0.638403i	$-0.220405\pi$
$61$	−1.31229	−	2.27296i	−0.168022	−	0.291022i	−0.937724	+	0.347380i	$0.887071\pi$
$62$		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	0.698130	−	0.715971i	$-0.254016\pi$
$67$	3.49634	+	2.01862i	0.427147	+	0.246613i	−0.270984	+	0.962584i	$0.587349\pi$
$68$		0			0
$69$			5.27578i			0.635129i
$70$		0			0
$71$			11.2362i			1.33349i	0.745286	+	0.666745i	$0.232313\pi$
$71$			11.2362i			1.33349i	−0.745286	+	0.666745i	$0.767687\pi$
$72$		0			0
$73$	7.92976	−	13.7347i	0.928108	−	1.60753i	0.141624	−	0.989921i	$-0.454768\pi$
$73$	7.92976	−	13.7347i	0.928108	−	1.60753i	0.786485	−	0.617610i	$-0.211899\pi$
$74$		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	−0.758845	−	0.651271i	$-0.774236\pi$
$79$	−5.10404	+	2.94682i	−0.574250	+	0.331543i	0.184595	+	0.982815i	$0.440903\pi$
$80$		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	−0.591014	−	0.806661i	$-0.701272\pi$
$89$	−1.77294	+	1.02361i	−0.187931	+	0.108502i	0.403082	+	0.915164i	$0.367939\pi$
$90$		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	$-0.963203\pi$
$97$		−	2.27201i		−	0.230688i	0.993326	−	0.115344i	$-0.0367971\pi$
$98$		0			0
$99$		−	3.05966i		−	0.307507i
$100$		0			0
$101$	−12.1463	−	7.01265i	−1.20860	−	0.697785i	−0.246146	−	0.969233i	$-0.579164\pi$
$101$	−12.1463	−	7.01265i	−1.20860	−	0.697785i	−0.962453	+	0.271448i	$0.912498\pi$
$102$		0			0
$103$	−0.854239	−	1.47959i	−0.0841707	−	0.145788i	0.820867	−	0.571120i	$-0.193491\pi$
$103$	−0.854239	−	1.47959i	−0.0841707	−	0.145788i	−0.905038	+	0.425332i	$0.860157\pi$
$104$		0			0
$105$	−18.2527	−	2.00061i	−1.78128	−	0.195240i
$106$		0			0
$107$	−1.95166	−	3.38038i	−0.188675	−	0.326794i	0.756134	−	0.654417i	$-0.227086\pi$
$107$	−1.95166	−	3.38038i	−0.188675	−	0.326794i	−0.944809	+	0.327623i	$0.893752\pi$
$108$		0			0
$109$	−9.64979	−	5.57131i	−0.924282	−	0.533634i	−0.0392832	−	0.999228i	$-0.512507\pi$
$109$	−9.64979	−	5.57131i	−0.924282	−	0.533634i	−0.884999	+	0.465594i	$0.845841\pi$
$110$		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	0.957086	+	0.289804i	$0.0935903\pi$
$131$	8.34975	+	14.4622i	0.729521	+	1.26357i	−0.227565	+	0.973763i	$0.573076\pi$
$132$		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	0.587220	−	0.809427i	$-0.300222\pi$
$137$	2.10504	+	1.21535i	0.179846	+	0.103834i	−0.407374	+	0.913261i	$0.633556\pi$
$138$		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	−0.702203	−	0.711977i	$-0.747800\pi$
$149$	−5.33077	+	3.07772i	−0.436714	+	0.252137i	0.265489	+	0.964114i	$0.414467\pi$
$150$		0			0
$151$	2.92747	+	1.69017i	0.238234	+	0.137544i	0.614365	−	0.789022i	$-0.289412\pi$
$151$	2.92747	+	1.69017i	0.238234	+	0.137544i	−0.376131	+	0.926567i	$0.622746\pi$
$152$		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	0.135309	−	0.990803i	$-0.456797\pi$
$157$	−8.20835	−	4.73909i	−0.655098	−	0.378221i	−0.790407	+	0.612583i	$0.790131\pi$
$158$		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	−0.985341	−	0.170594i	$-0.945431\pi$
$163$	−8.17620	−	14.1616i	−0.640409	−	1.10922i	0.344932	−	0.938628i	$-0.387902\pi$
$164$		0			0
$165$	−18.1016	+	31.3529i	−1.40921	+	2.44082i
$166$		0			0
$167$		−	24.7370i		−	1.91421i	−0.289743	−	0.957105i	$-0.593570\pi$
$167$		−	24.7370i		−	1.91421i	0.289743	−	0.957105i	$-0.406430\pi$
$168$		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	0.908744	−	0.417355i	$-0.137043\pi$
$173$	1.22233	+	2.11714i	0.0929320	+	0.160963i	−0.815812	+	0.578318i	$0.803709\pi$
$174$		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	0.939738	−	0.341895i	$-0.111069\pi$
$179$	14.8979	+	8.60128i	1.11352	+	0.642890i	0.173780	+	0.984785i	$0.444402\pi$
$180$		0			0
$181$		−	4.03818i		−	0.300155i	−0.988674	−	0.150078i	$-0.952048\pi$
$181$		−	4.03818i		−	0.300155i	0.988674	−	0.150078i	$-0.0479524\pi$
$182$		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	−0.636199	−	0.771525i	$-0.719494\pi$
$191$	−3.95452	+	2.28314i	−0.286139	+	0.165202i	0.350060	+	0.936727i	$0.386161\pi$
$192$		0			0
$193$	4.54784	+	2.62570i	0.327361	+	0.189002i	0.654669	−	0.755916i	$-0.272808\pi$
$193$	4.54784	+	2.62570i	0.327361	+	0.189002i	−0.327308	+	0.944918i	$0.606141\pi$
$194$		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	0.841646	−	0.540029i	$-0.181587\pi$
$199$	11.2119	+	6.47319i	0.794790	+	0.458872i	−0.0468561	+	0.998902i	$0.514920\pi$
$200$		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	$-0.786852\pi$
$211$		−	18.0321i		−	1.24138i	0.784054	−	0.620692i	$-0.213148\pi$
$212$		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	0.993490	+	0.113922i	$0.0363415\pi$
$227$	23.9391	+	13.8212i	1.58889	+	0.917348i	0.595405	+	0.803426i	$0.296992\pi$
$228$		0			0
$229$	22.9494	−	13.2498i	1.51654	−	0.875573i	0.516726	−	0.856151i	$-0.327151\pi$
$229$	22.9494	−	13.2498i	1.51654	−	0.875573i	0.999811	−	0.0194226i	$-0.00618281\pi$
$230$		0			0
$231$	23.9248	−	10.5247i	1.57414	−	0.692473i
$232$		0			0
$233$	−21.3620	+	12.3333i	−1.39947	+	0.807984i	−0.994337	−	0.106274i	$-0.966108\pi$
$233$	−21.3620	+	12.3333i	−1.39947	+	0.807984i	−0.405133	+	0.914258i	$0.632775\pi$
$234$		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	$0.211278\pi$
$239$			19.0486i			1.23215i	−0.787688	+	0.616075i	$0.788722\pi$
$240$		0			0
$241$	−7.72249	+	13.3757i	−0.497449	+	0.861607i	−0.999996	−	0.00294298i	$-0.999063\pi$
$241$	−7.72249	+	13.3757i	−0.497449	+	0.861607i	0.502547	+	0.864550i	$0.332397\pi$
$242$		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	−0.995870	−	0.0907904i	$-0.971061\pi$
$257$	−22.6870	+	13.0984i	−1.41518	+	0.817054i	−0.419308	+	0.907844i	$0.637727\pi$
$258$		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	0.449540	−	0.893260i	$-0.351588\pi$
$263$	−1.60999	−	0.929529i	−0.0992763	−	0.0573172i	−0.548816	+	0.835943i	$0.684921\pi$
$264$		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	−0.991720	−	0.128420i	$-0.959009\pi$
$269$	−6.30864	+	10.9269i	−0.384645	+	0.666224i	0.607075	+	0.794645i	$0.292343\pi$
$270$		0			0
$271$	9.71715	+	16.8306i	0.590275	+	1.02239i	0.994195	+	0.107591i	$0.0343138\pi$
$271$	9.71715	+	16.8306i	0.590275	+	1.02239i	−0.403921	+	0.914794i	$0.632353\pi$
$272$		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	−0.600983	−	0.799262i	$-0.705224\pi$
$277$	6.51902	−	11.2913i	0.391690	−	0.678427i	0.992673	+	0.120835i	$0.0385573\pi$
$278$		0			0
$279$	4.93738			0.295593
$280$		0			0
$281$			3.41321i			0.203615i	0.994804	+	0.101808i	$0.0324626\pi$
$281$			3.41321i			0.203615i	−0.994804	+	0.101808i	$0.967537\pi$
$282$		0			0
$283$	−3.26158	+	5.64921i	−0.193881	+	0.335811i	−0.946533	−	0.322607i	$-0.895441\pi$
$283$	−3.26158	+	5.64921i	−0.193881	+	0.335811i	0.752652	+	0.658418i	$0.228774\pi$
$284$		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	$-0.969120\pi$
$293$		−	3.31599i		−	0.193722i	0.995298	−	0.0968611i	$-0.0308803\pi$
$294$		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	0.831847	−	0.555005i	$-0.187284\pi$
$311$	13.5283	+	7.81059i	0.767121	+	0.442898i	−0.0647254	+	0.997903i	$0.520617\pi$
$312$		0			0
$313$	20.0207	−	11.5589i	1.13163	−	0.653350i	0.187289	−	0.982305i	$-0.440030\pi$
$313$	20.0207	−	11.5589i	1.13163	−	0.653350i	0.944345	+	0.328955i	$0.106697\pi$
$314$		0			0
$315$	4.58591	+	3.36314i	0.258387	+	0.189492i
$316$		0			0
$317$	9.60700	−	5.54660i	0.539583	−	0.311528i	−0.205327	−	0.978693i	$-0.565826\pi$
$317$	9.60700	−	5.54660i	0.539583	−	0.311528i	0.744910	+	0.667165i	$0.232493\pi$
$318$		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	−0.687082	−	0.726580i	$-0.741109\pi$
$331$	−7.30258	+	4.21615i	−0.401386	+	0.231740i	0.285696	+	0.958320i	$0.407775\pi$
$332$		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	0.656068	−	0.754702i	$-0.272218\pi$
$347$	6.15674	+	3.55459i	0.330511	+	0.190821i	−0.325557	+	0.945522i	$0.605552\pi$
$348$		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	−0.958532	−	0.284986i	$-0.908011\pi$
$353$	−4.36754	+	7.56481i	−0.232461	+	0.402634i	0.726071	+	0.687620i	$0.241344\pi$
$354$		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	−0.986362	−	0.164591i	$-0.947370\pi$
$359$	−12.0452	−	20.8629i	−0.635721	−	1.10110i	0.350641	−	0.936510i	$-0.385964\pi$
$360$		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	−0.0552726	−	0.998471i	$-0.517603\pi$
$367$	16.0359	−	27.7749i	0.837065	−	1.44984i	0.892338	−	0.451368i	$-0.149064\pi$
$368$		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	0.963850	−	0.266446i	$-0.0858494\pi$
$373$	4.85101	+	8.40220i	0.251176	+	0.435049i	−0.712674	+	0.701495i	$0.752516\pi$
$374$		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	−0.915047	−	0.403348i	$-0.867846\pi$
$383$	−20.0256	+	11.5618i	−1.02326	+	0.590780i	−0.108214	+	0.994128i	$0.534513\pi$
$384$		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	−0.996551	−	0.0829802i	$-0.973556\pi$
$389$	−8.41017	+	14.5668i	−0.426413	+	0.738568i	0.570139	+	0.821549i	$0.306890\pi$
$390$		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	−0.345480	−	0.938426i	$-0.612284\pi$
$397$	5.86748	−	3.38759i	0.294480	−	0.170018i	0.639961	+	0.768408i	$0.278951\pi$
$398$		0			0
$399$	2.29970	−	20.9815i	0.115129	−	1.05039i
$400$		0			0
$401$	−0.208148	−	0.360524i	−0.0103944	−	0.0180037i	0.860781	−	0.508975i	$-0.169975\pi$
$401$	−0.208148	−	0.360524i	−0.0103944	−	0.0180037i	−0.871176	+	0.490971i	$0.836642\pi$
$402$		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	0.102892	+	0.994693i	$0.467190\pi$
$409$	−16.3809	+	28.3725i	−0.809983	+	1.40293i	−0.912875	+	0.408239i	$0.866143\pi$
$410$		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	$-0.931739\pi$
$421$		−	8.73292i		−	0.425617i	0.977094	−	0.212808i	$-0.0682610\pi$
$422$		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	0.393212	+	0.919448i	$0.371364\pi$
$431$	−12.4492	+	21.5627i	−0.599659	+	1.03864i	−0.992871	+	0.119192i	$0.961970\pi$
$432$		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	−0.113550	−	0.993532i	$-0.536222\pi$
$439$	14.4592	−	8.34801i	0.690099	−	0.398429i	0.803649	+	0.595104i	$0.202889\pi$
$440$		0			0
$441$	−1.23394	−	3.91596i	−0.0587592	−	0.186474i
$442$		0			0
$443$	4.20522	+	7.28365i	0.199796	+	0.346057i	0.948462	−	0.316890i	$-0.102639\pi$
$443$	4.20522	+	7.28365i	0.199796	+	0.346057i	−0.748666	+	0.662947i	$0.769305\pi$
$444$		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	−0.244246	−	0.969713i	$-0.578540\pi$
$457$	10.1207	−	5.84321i	0.473428	−	0.273334i	0.717674	+	0.696380i	$0.245207\pi$
$458$		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	$0.110824\pi$
$463$			14.6823i			0.682346i	−0.940001	+	0.341173i	$0.889176\pi$
$464$		0			0
$465$	−50.5942	−	29.2106i	−2.34625	−	1.35461i
$466$		0			0
$467$	−14.4696	−	25.0622i	−0.669575	−	1.15974i	−0.978023	−	0.208497i	$-0.933143\pi$
$467$	−14.4696	−	25.0622i	−0.669575	−	1.15974i	0.308447	−	0.951241i	$-0.400191\pi$
$468$		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	−0.158300	−	0.987391i	$-0.550601\pi$
$479$	−23.9118	−	13.8055i	−1.09256	−	0.630787i	−0.934256	+	0.356604i	$0.883935\pi$
$480$		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	0.350407	−	0.936598i	$-0.386043\pi$
$487$	21.7662	−	37.7002i	0.986321	−	1.70836i	0.635914	−	0.771760i	$-0.280623\pi$
$488$		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	−0.351092	−	0.936341i	$-0.614189\pi$
$499$	6.34984	−	3.66608i	0.284258	−	0.164116i	0.635349	+	0.772225i	$0.280856\pi$
$500$		0			0
$501$	−23.4237	+	40.5710i	−1.04649	+	1.81258i
$502$		0			0
$503$		−	29.0022i		−	1.29314i	−0.762853	−	0.646572i	$-0.776202\pi$
$503$		−	29.0022i		−	1.29314i	0.762853	−	0.646572i	$-0.223798\pi$
$504$		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	0.380499	−	0.924781i	$-0.375752\pi$
$509$	30.9454	−	17.8664i	1.37163	−	0.791912i	0.991134	+	0.132869i	$0.0424190\pi$
$510$		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	0.223671	−	0.974665i	$-0.428196\pi$
$521$	−11.6085	−	6.70218i	−0.508578	−	0.293628i	−0.732249	+	0.681037i	$0.761529\pi$
$522$		0			0
$523$	−1.37758	−	2.38604i	−0.0602374	−	0.104334i	0.834334	−	0.551259i	$-0.185852\pi$
$523$	−1.37758	−	2.38604i	−0.0602374	−	0.104334i	−0.894571	+	0.446925i	$0.852519\pi$
$524$		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	0.999999	+	0.00119332i	$0.000379845\pi$
$541$	11.6537	+	20.1849i	0.501033	+	0.867815i	−0.498966	+	0.866621i	$0.666287\pi$
$542$		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	$-0.530555\pi$
$547$		−	46.5607i		−	1.99079i	0.0958453	−	0.995396i	$-0.469445\pi$
$548$		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	0.0393032	−	0.999227i	$-0.487486\pi$
$557$	−19.0318	−	10.9880i	−0.806401	−	0.465576i	−0.845705	+	0.533651i	$0.820820\pi$
$558$		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	0.916223	−	0.400669i	$-0.131222\pi$
$563$	24.3764	+	14.0737i	1.02734	+	0.593137i	0.111122	+	0.993807i	$0.464556\pi$
$564$		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	0.984007	+	0.178129i	$0.0570045\pi$
$569$	15.4159	+	26.7011i	0.646268	+	1.11937i	−0.337739	+	0.941240i	$0.609662\pi$
$570$		0			0
$571$	−15.2134	−	8.78347i	−0.636662	−	0.367577i	0.146666	−	0.989186i	$-0.453146\pi$
$571$	−15.2134	−	8.78347i	−0.636662	−	0.367577i	−0.783327	+	0.621609i	$0.786479\pi$
$572$		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	−0.999993	−	0.00384220i	$-0.998777\pi$
$577$	−36.1109	−	20.8486i	−1.50332	−	0.867940i	−0.503324	−	0.864098i	$-0.667890\pi$
$578$		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	$0.0978667\pi$
$587$			14.6646i			0.605273i	−0.953106	+	0.302636i	$0.902133\pi$
$588$		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	−0.453918	−	0.891043i	$-0.649974\pi$
$593$	2.21085	−	1.27644i	0.0907888	−	0.0524169i	0.544707	+	0.838626i	$0.316641\pi$
$594$		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	−0.223705	−	0.974657i	$-0.571815\pi$
$599$	17.9208	−	31.0398i	0.732225	−	1.26825i	0.955930	−	0.293594i	$-0.0948513\pi$
$600$		0			0
$601$			5.61681i			0.229115i	0.993417	+	0.114557i	$0.0365449\pi$
$601$			5.61681i			0.229115i	−0.993417	+	0.114557i	$0.963455\pi$
$602$		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	0.983293	+	0.182032i	$0.0582675\pi$
$607$	15.9968	+	27.7073i	0.649291	+	1.12460i	−0.334002	+	0.942572i	$0.608399\pi$
$608$		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	−0.997555	−	0.0698880i	$-0.977736\pi$
$613$	−10.8506	+	18.7938i	−0.438253	+	0.759076i	0.559302	+	0.828964i	$0.311069\pi$
$614$		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	0.303933	+	0.952694i	$0.401700\pi$
$619$	−16.7463	+	29.0054i	−0.673090	+	1.16583i	−0.977023	+	0.213133i	$0.931633\pi$
$620$		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	0.686945	−	0.726710i	$-0.258952\pi$
$641$	10.1542	+	5.86254i	0.401068	+	0.231557i	−0.285877	+	0.958266i	$0.592285\pi$
$642$		0			0
$643$			17.0067i			0.670678i	0.942098	+	0.335339i	$0.108851\pi$
$643$			17.0067i			0.670678i	−0.942098	+	0.335339i	$0.891149\pi$
$644$		0			0
$645$			80.0748i			3.15294i
$646$		0			0
$647$	−5.07646	+	8.79269i	−0.199576	+	0.345676i	−0.948391	−	0.317103i	$-0.897290\pi$
$647$	−5.07646	+	8.79269i	−0.199576	+	0.345676i	0.748815	+	0.662779i	$0.230623\pi$
$648$		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	−0.752274	−	0.658850i	$-0.771043\pi$
$653$	−14.2547	+	8.22998i	−0.557831	+	0.322064i	0.194443	+	0.980914i	$0.437710\pi$
$654$		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	$-0.914178\pi$
$659$		−	13.6757i		−	0.532728i	0.963873	−	0.266364i	$-0.0858223\pi$
$660$		0			0
$661$	−12.9668	+	22.4592i	−0.504351	+	0.873562i	0.495636	+	0.868530i	$0.334935\pi$
$661$	−12.9668	+	22.4592i	−0.504351	+	0.873562i	−0.999987	+	0.00503193i	$0.998398\pi$
$662$		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	$-0.773055\pi$
$673$		−	33.9367i		−	1.30816i	0.756423	−	0.654082i	$-0.226945\pi$
$674$		0			0
$675$	−33.3672	−	19.2646i	−1.28430	−	0.741494i
$676$		0			0
$677$	−19.7093	−	34.1375i	−0.757491	−	1.31201i	−0.944126	−	0.329583i	$-0.893092\pi$
$677$	−19.7093	−	34.1375i	−0.757491	−	1.31201i	0.186636	−	0.982429i	$-0.440242\pi$
$678$		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	−0.0933966	−	0.995629i	$-0.529772\pi$
$683$	−26.1953	−	15.1239i	−1.00233	−	0.578698i	−0.908938	+	0.416931i	$0.863106\pi$
$684$		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	−0.265769	−	0.964037i	$-0.585626\pi$
$691$	11.4670	−	6.62049i	0.436226	−	0.251855i	0.701996	+	0.712181i	$0.252293\pi$
$692$		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	−0.971485	−	0.237099i	$-0.923803\pi$
$709$	−33.3342	+	19.2455i	−1.25189	+	0.722781i	−0.280409	+	0.959881i	$0.590470\pi$
$710$		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	−0.0234234	−	0.999726i	$-0.507457\pi$
$719$	22.2733	−	12.8595i	0.830653	−	0.479578i	0.854076	+	0.520148i	$0.174123\pi$
$720$		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	$-0.990563\pi$
$727$		−	1.59858i		−	0.0592880i	0.999561	−	0.0296440i	$-0.00943736\pi$
$728$		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	0.993147	−	0.116870i	$-0.0372860\pi$
$733$	10.7040	+	18.5399i	0.395361	+	0.684786i	−0.597786	+	0.801656i	$0.703953\pi$
$734$		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	−0.584366	−	0.811490i	$-0.698657\pi$
$739$	11.1617	−	19.3326i	0.410588	−	0.711160i	0.994954	+	0.100330i	$0.0319900\pi$
$740$		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	−0.712352	−	0.701822i	$-0.752370\pi$
$751$	−12.6261	+	7.28968i	−0.460733	+	0.266004i	0.251620	+	0.967826i	$0.419037\pi$
$752$		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	$0.0756796\pi$
$757$			12.9601i			0.471042i	−0.971869	+	0.235521i	$0.924320\pi$
$758$		0			0
$759$	13.7605	−	23.8338i	0.499473	−	0.865112i
$760$		0			0
$761$	1.01386	+	1.75605i	0.0367523	+	0.0636568i	0.883816	−	0.467834i	$-0.154965\pi$
$761$	1.01386	+	1.75605i	0.0367523	+	0.0636568i	−0.847064	+	0.531491i	$0.821632\pi$
$762$		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	0.716484	−	0.697604i	$-0.245750\pi$
$773$	13.0836	+	7.55380i	0.470583	+	0.271691i	−0.245901	+	0.969295i	$0.579084\pi$
$774$		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	−0.251149	−	0.967948i	$-0.580808\pi$
$787$	19.9936	−	34.6299i	0.712693	−	1.23442i	0.963842	−	0.266473i	$-0.0858582\pi$
$788$		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	0.529554	−	0.848276i	$-0.322359\pi$
$809$	1.69809	+	0.980395i	0.0597018	+	0.0344688i	−0.469852	+	0.882745i	$0.655693\pi$
$810$		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	0.682578	−	0.730813i	$-0.260859\pi$
$821$	−8.35563	−	14.4724i	−0.291613	−	0.505089i	−0.974191	+	0.225723i	$0.927525\pi$
$822$		0			0
$823$	−3.35523	−	1.93715i	−0.116956	−	0.0675246i	0.440381	−	0.897811i	$-0.354843\pi$
$823$	−3.35523	−	1.93715i	−0.116956	−	0.0675246i	−0.557337	+	0.830286i	$0.688177\pi$
$824$		0			0
$825$	−83.2771			−2.89933
$826$		0			0
$827$		−	26.5362i		−	0.922753i	−0.887205	−	0.461376i	$-0.847356\pi$
$827$		−	26.5362i		−	0.922753i	0.887205	−	0.461376i	$-0.152644\pi$
$828$		0			0
$829$	6.39635	−	11.0788i	0.222155	−	0.384783i	−0.733307	−	0.679897i	$-0.762024\pi$
$829$	6.39635	−	11.0788i	0.222155	−	0.384783i	0.955462	+	0.295114i	$0.0953577\pi$
$830$		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	$0.281980\pi$
$839$			44.8654i			1.54893i	−0.632619	+	0.774463i	$0.718020\pi$
$840$		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	−0.900853	−	0.434125i	$-0.857058\pi$
$857$	−2.17987	+	3.77565i	−0.0744630	+	0.128974i	0.826390	+	0.563099i	$0.190391\pi$
$858$		0			0
$859$	−27.5172	−	47.6611i	−0.938874	−	1.62618i	−0.767577	−	0.640957i	$-0.778538\pi$
$859$	−27.5172	−	47.6611i	−0.938874	−	1.62618i	−0.171297	−	0.985219i	$-0.554796\pi$
$860$		0			0
$861$	31.2612	−	7.21602i	1.06538	−	0.245921i
$862$		0			0
$863$	−11.6063	−	20.1027i	−0.395083	−	0.684305i	0.598028	−	0.801475i	$-0.295951\pi$
$863$	−11.6063	−	20.1027i	−0.395083	−	0.684305i	−0.993112	+	0.117170i	$0.962618\pi$
$864$		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	−0.967231	−	0.253896i	$-0.918288\pi$
$877$	−20.8335	−	36.0846i	−0.703496	−	1.21849i	0.263735	−	0.964595i	$-0.415046\pi$
$878$		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	$0.293793\pi$
$883$			47.3902i			1.59481i	−0.603447	+	0.797403i	$0.706207\pi$
$884$		0			0
$885$	73.8668	+	42.6470i	2.48301	+	1.43356i
$886$		0			0
$887$	−30.2398	+	17.4590i	−1.01535	+	0.586214i	−0.912754	−	0.408509i	$-0.866049\pi$
$887$	−30.2398	+	17.4590i	−1.01535	+	0.586214i	−0.102598	+	0.994723i	$0.532716\pi$
$888$		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	−0.977482	−	0.211017i	$-0.932323\pi$
$907$	−9.21549	+	15.9617i	−0.305995	+	0.530000i	0.671487	+	0.741016i	$0.265656\pi$
$908$		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	−0.321761	−	0.946821i	$-0.604275\pi$
$919$	10.2262	−	5.90408i	0.337330	−	0.194758i	0.659091	+	0.752063i	$0.270941\pi$
$920$		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	−0.982507	−	0.186227i	$-0.940374\pi$
$929$	−40.0038	+	23.0962i	−1.31248	+	0.757762i	−0.329976	+	0.943989i	$0.607041\pi$
$930$		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	$-0.699486\pi$
$937$		−	49.5868i		−	1.61993i	0.586477	−	0.809966i	$-0.300514\pi$
$938$		0			0
$939$	−43.7810			−1.42874
$940$		0			0
$941$	−8.00174	+	13.8594i	−0.260849	+	0.451804i	−0.966468	−	0.256788i	$-0.917336\pi$
$941$	−8.00174	+	13.8594i	−0.260849	+	0.451804i	0.705619	+	0.708592i	$0.250669\pi$
$942$		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	0.711038	−	0.703153i	$-0.248225\pi$
$947$	−7.79888	−	13.5080i	−0.253429	−	0.438953i	−0.964468	+	0.264201i	$0.914892\pi$
$948$		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	$0.238248\pi$
$967$			42.3241i			1.36105i	−0.732725	+	0.680525i	$0.761752\pi$
$968$		0			0
$969$	8.54188	+	4.93165i	0.274405	+	0.158428i
$970$		0			0
$971$	−30.1059	+	17.3817i	−0.966144	+	0.557804i	−0.898059	−	0.439876i	$-0.855022\pi$
$971$	−30.1059	+	17.3817i	−0.966144	+	0.557804i	−0.0680858	+	0.997679i	$0.521689\pi$
$972$		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	0.520133	−	0.854085i	$-0.325882\pi$
$977$	1.26714	+	0.731584i	0.0405394	+	0.0234054i	−0.479593	+	0.877491i	$0.659216\pi$
$978$		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	0.354938	+	0.934890i	$0.384502\pi$
$983$	−19.8203	+	34.3298i	−0.632170	+	1.09495i	−0.987107	+	0.160060i	$0.948831\pi$
$984$		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	0.850428	−	0.526091i	$-0.176343\pi$
$991$	25.8148	+	14.9042i	0.820034	+	0.473447i	−0.0303941	+	0.999538i	$0.509676\pi$
$992$		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	0.838931	−	0.544237i	$-0.183181\pi$
$997$	24.8521	+	14.3484i	0.787074	+	0.454417i	−0.0518574	+	0.998654i	$0.516514\pi$
$998$		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.81.7	✓	56
7.2	even	3	inner	1148.2.r.a.737.22	yes	56
41.40	even	2	inner	1148.2.r.a.81.22	yes	56
287.163	even	6	inner	1148.2.r.a.737.7	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.7	✓	56	1.1	even	1	trivial
1148.2.r.a.81.22	yes	56	41.40	even	2	inner
1148.2.r.a.737.7	yes	56	287.163	even	6	inner
1148.2.r.a.737.22	yes	56	7.2	even	3	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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