LMFDB - Embedded newform 1176.2.u.b.1097.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.3
Root			$0.247636 - 1.71426i$ of defining polynomial
Character	$\chi$	$=$	1176.1097
Dual form			1176.2.u.b.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642670 + 1.60841i) q^{3} +(-1.28955 + 2.23357i) q^{5} +(-2.17395 - 2.06735i) q^{9} +O(q^{10})$	\(q+(-0.642670 + 1.60841i) q^{3} +(-1.28955 + 2.23357i) q^{5} +(-2.17395 - 2.06735i) q^{9} +(-1.43199 + 0.826762i) q^{11} +5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(-3.79313 - 6.56990i) q^{17} +(-2.58961 - 1.49511i) q^{19} +(-0.249340 - 0.143957i) q^{23} +(-0.825879 - 1.43046i) q^{25} +(4.72227 - 2.16798i) q^{27} +2.05856i q^{29} +(5.21209 - 3.00920i) q^{31} +(-0.409472 - 2.83457i) q^{33} +(-0.877523 + 1.51991i) q^{37} +(-9.18685 - 3.67078i) q^{39} -4.28635 q^{41} +2.46537 q^{43} +(7.42098 - 2.18971i) q^{45} +(0.186586 - 0.323176i) q^{47} +(13.0048 - 1.87863i) q^{51} +(-6.73264 + 3.88709i) q^{53} -4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(-4.89610 - 8.48029i) q^{59} +(-0.889794 - 0.513723i) q^{61} +(-12.7576 - 7.36561i) q^{65} +(-1.18281 - 2.04868i) q^{67} +(0.391784 - 0.308524i) q^{69} -15.6655i q^{71} +(3.30170 - 1.90624i) q^{73} +(2.83154 - 0.409034i) q^{75} +(4.56033 - 7.89872i) q^{79} +(0.452128 + 8.98864i) q^{81} +6.65166 q^{83} +19.5657 q^{85} +(-3.31101 - 1.32298i) q^{87} +(-7.25723 + 12.5699i) q^{89} +(1.49037 + 10.3171i) q^{93} +(6.67886 - 3.85604i) q^{95} -4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^9	$ 16 q + 2 q^{9} + 8 q^{15} + 6 q^{19} - 18 q^{25} + 48 q^{31} + 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} + 42 q^{45} + 6 q^{51} - 8 q^{57} - 36 q^{61} + 14 q^{67} - 30 q^{73} - 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} + 16 q^{93} + 20 q^{99}+O(q^{100}) $ 16 * q + 2 * q^9 + 8 * q^15 + 6 * q^19 - 18 * q^25 + 48 * q^31 + 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 + 42 * q^45 + 6 * q^51 - 8 * q^57 - 36 * q^61 + 14 * q^67 - 30 * q^73 - 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 + 16 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.642670	+	1.60841i	−0.371046	+	0.928615i
$3$	−0.642670	+	1.60841i	−0.371046	+	0.928615i
$4$		0			0
$5$	−1.28955	+	2.23357i	−0.576704	+	0.998881i	0.419150	+	0.907917i	$0.362328\pi$
$5$	−1.28955	+	2.23357i	−0.576704	+	0.998881i	−0.995854	+	0.0909641i	$0.971005\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.17395	−	2.06735i	−0.724650	−	0.689117i
$10$		0			0
$11$	−1.43199	+	0.826762i	−0.431763	+	0.249278i	−0.700097	−	0.714048i	$-0.746860\pi$
$11$	−1.43199	+	0.826762i	−0.431763	+	0.249278i	0.268335	+	0.963326i	$0.413527\pi$
$12$		0			0
$13$			5.71177i			1.58416i	0.610418	+	0.792080i	$0.291002\pi$
$13$			5.71177i			1.58416i	−0.610418	+	0.792080i	$0.708998\pi$
$14$		0			0
$15$	−2.76373	−	3.50957i	−0.713592	−	0.906167i
$16$		0			0
$17$	−3.79313	−	6.56990i	−0.919970	−	1.59343i	−0.799458	−	0.600722i	$-0.794880\pi$
$17$	−3.79313	−	6.56990i	−0.919970	−	1.59343i	−0.120512	−	0.992712i	$-0.538453\pi$
$18$		0			0
$19$	−2.58961	−	1.49511i	−0.594097	−	0.343002i	0.172619	−	0.984989i	$-0.444777\pi$
$19$	−2.58961	−	1.49511i	−0.594097	−	0.343002i	−0.766716	+	0.641987i	$0.778110\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.249340	−	0.143957i	−0.0519910	−	0.0300170i	0.473779	−	0.880644i	$-0.342889\pi$
$23$	−0.249340	−	0.143957i	−0.0519910	−	0.0300170i	−0.525770	+	0.850627i	$0.676223\pi$
$24$		0			0
$25$	−0.825879	−	1.43046i	−0.165176	−	0.286093i
$26$		0			0
$27$	4.72227	−	2.16798i	0.908802	−	0.417227i
$28$		0			0
$29$			2.05856i			0.382265i	0.981564	+	0.191133i	$0.0612161\pi$
$29$			2.05856i			0.382265i	−0.981564	+	0.191133i	$0.938784\pi$
$30$		0			0
$31$	5.21209	−	3.00920i	0.936118	−	0.540468i	0.0473770	−	0.998877i	$-0.484914\pi$
$31$	5.21209	−	3.00920i	0.936118	−	0.540468i	0.888741	+	0.458409i	$0.151580\pi$
$32$		0			0
$33$	−0.409472	−	2.83457i	−0.0712798	−	0.493435i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.877523	+	1.51991i	−0.144264	+	0.249872i	−0.929098	−	0.369833i	$-0.879415\pi$
$37$	−0.877523	+	1.51991i	−0.144264	+	0.249872i	0.784834	+	0.619706i	$0.212748\pi$
$38$		0			0
$39$	−9.18685	−	3.67078i	−1.47107	−	0.587795i
$40$		0			0
$41$	−4.28635			−0.669415			−0.334708	−	0.942322i	$-0.608638\pi$
$41$	−4.28635			−0.669415			−0.334708	+	0.942322i	$0.608638\pi$
$42$		0			0
$43$	2.46537			0.375965			0.187982	−	0.982172i	$-0.439805\pi$
$43$	2.46537			0.375965			0.187982	+	0.982172i	$0.439805\pi$
$44$		0			0
$45$	7.42098	−	2.18971i	1.10625	−	0.326423i
$46$		0			0
$47$	0.186586	−	0.323176i	0.0272163	−	0.0471401i	−0.852096	−	0.523385i	$-0.824669\pi$
$47$	0.186586	−	0.323176i	0.0272163	−	0.0471401i	0.879313	+	0.476245i	$0.158002\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	13.0048	−	1.87863i	1.82104	−	0.263061i
$52$		0			0
$53$	−6.73264	+	3.88709i	−0.924799	+	0.533933i	−0.885163	−	0.465281i	$-0.845953\pi$
$53$	−6.73264	+	3.88709i	−0.924799	+	0.533933i	−0.0396361	+	0.999214i	$0.512620\pi$
$54$		0			0
$55$		−	4.26461i		−	0.575039i
$56$		0			0
$57$	4.06901	−	3.20429i	0.538954	−	0.424418i
$58$		0			0
$59$	−4.89610	−	8.48029i	−0.637417	−	1.10404i	−0.985997	−	0.166760i	$-0.946669\pi$
$59$	−4.89610	−	8.48029i	−0.637417	−	1.10404i	0.348580	−	0.937279i	$-0.386664\pi$
$60$		0			0
$61$	−0.889794	−	0.513723i	−0.113926	−	0.0657755i	0.441954	−	0.897038i	$-0.354285\pi$
$61$	−0.889794	−	0.513723i	−0.113926	−	0.0657755i	−0.555880	+	0.831262i	$0.687619\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−12.7576	−	7.36561i	−1.58239	−	0.913592i
$66$		0			0
$67$	−1.18281	−	2.04868i	−0.144503	−	0.250286i	0.784685	−	0.619895i	$-0.212825\pi$
$67$	−1.18281	−	2.04868i	−0.144503	−	0.250286i	−0.929187	+	0.369609i	$0.879492\pi$
$68$		0			0
$69$	0.391784	−	0.308524i	0.0471653	−	0.0371419i
$70$		0			0
$71$		−	15.6655i		−	1.85915i	−0.368631	−	0.929576i	$-0.620174\pi$
$71$		−	15.6655i		−	1.85915i	0.368631	−	0.929576i	$-0.379826\pi$
$72$		0			0
$73$	3.30170	−	1.90624i	0.386434	−	0.223108i	−0.294180	−	0.955750i	$-0.595046\pi$
$73$	3.30170	−	1.90624i	0.386434	−	0.223108i	0.680614	+	0.732642i	$0.261713\pi$
$74$		0			0
$75$	2.83154	−	0.409034i	0.326958	−	0.0472312i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.56033	−	7.89872i	0.513077	−	0.888676i	−0.486808	−	0.873509i	$-0.661839\pi$
$79$	4.56033	−	7.89872i	0.513077	−	0.888676i	0.999885	−	0.0151665i	$-0.00482783\pi$
$80$		0			0
$81$	0.452128	+	8.98864i	0.0502364	+	0.998737i
$82$		0			0
$83$	6.65166			0.730114			0.365057	−	0.930985i	$-0.381049\pi$
$83$	6.65166			0.730114			0.365057	+	0.930985i	$0.381049\pi$
$84$		0			0
$85$	19.5657			2.12220
$86$		0			0
$87$	−3.31101	−	1.32298i	−0.354977	−	0.141838i
$88$		0			0
$89$	−7.25723	+	12.5699i	−0.769265	+	1.33241i	0.168697	+	0.985668i	$0.446044\pi$
$89$	−7.25723	+	12.5699i	−0.769265	+	1.33241i	−0.937962	+	0.346738i	$0.887289\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.49037	+	10.3171i	0.154544	+	1.06983i
$94$		0			0
$95$	6.67886	−	3.85604i	0.685237	−	0.395622i
$96$		0			0
$97$		−	4.43739i		−	0.450548i	−0.974295	−	0.225274i	$-0.927672\pi$
$97$		−	4.43739i		−	0.450548i	0.974295	−	0.225274i	$-0.0723278\pi$
$98$		0			0
$99$	4.82229	+	1.16309i	0.484659	+	0.116895i
$100$		0			0
$101$	2.03628	+	3.52694i	0.202617	+	0.350943i	0.949371	−	0.314157i	$-0.101722\pi$
$101$	2.03628	+	3.52694i	0.202617	+	0.350943i	−0.746754	+	0.665101i	$0.768389\pi$
$102$		0			0
$103$	7.30346	+	4.21666i	0.719632	+	0.415479i	0.814617	−	0.579999i	$-0.196947\pi$
$103$	7.30346	+	4.21666i	0.719632	+	0.415479i	−0.0949855	+	0.995479i	$0.530280\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.6334	−	7.29389i	−1.22132	−	0.705127i	−0.256118	−	0.966646i	$-0.582444\pi$
$107$	−12.6334	−	7.29389i	−1.22132	−	0.705127i	−0.965199	+	0.261518i	$0.915777\pi$
$108$		0			0
$109$	−8.64994	−	14.9821i	−0.828514	−	1.43503i	−0.899204	−	0.437530i	$-0.855853\pi$
$109$	−8.64994	−	14.9821i	−0.828514	−	1.43503i	0.0706901	−	0.997498i	$-0.477480\pi$
$110$		0			0
$111$	−1.88068	−	2.38822i	−0.178507	−	0.226680i
$112$		0			0
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		0			0
$115$	0.643073	−	0.371279i	0.0599669	−	0.0346219i
$116$		0			0
$117$	11.8082	−	12.4171i	1.09167	−	1.14796i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.13293	+	7.15844i	−0.375721	+	0.650767i
$122$		0			0
$123$	2.75471	−	6.89420i	0.248384	−	0.621629i
$124$		0			0
$125$	−8.63545			−0.772378
$126$		0			0
$127$	−16.6481			−1.47728			−0.738641	−	0.674099i	$-0.764532\pi$
$127$	−16.6481			−1.47728			−0.738641	+	0.674099i	$0.764532\pi$
$128$		0			0
$129$	−1.58442	+	3.96531i	−0.139500	+	0.349126i
$130$		0			0
$131$	−8.29744	+	14.3716i	−0.724951	+	1.25565i	0.234043	+	0.972226i	$0.424804\pi$
$131$	−8.29744	+	14.3716i	−0.724951	+	1.25565i	−0.958994	+	0.283426i	$0.908529\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.24729	+	13.3432i	−0.107350	+	1.14840i
$136$		0			0
$137$	−8.61684	+	4.97493i	−0.736186	+	0.425037i	−0.820681	−	0.571387i	$-0.806406\pi$
$137$	−8.61684	+	4.97493i	−0.736186	+	0.425037i	0.0844948	+	0.996424i	$0.473072\pi$
$138$		0			0
$139$		−	3.11952i		−	0.264594i	−0.991210	−	0.132297i	$-0.957765\pi$
$139$		−	3.11952i		−	0.264594i	0.991210	−	0.132297i	$-0.0422353\pi$
$140$		0			0
$141$	0.399886	+	0.507801i	0.0336765	+	0.0427646i
$142$		0			0
$143$	−4.72227	−	8.17922i	−0.394896	−	0.683981i
$144$		0			0
$145$	−4.59794	−	2.65462i	−0.381838	−	0.220454i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.987090	+	0.569897i	0.0808655	+	0.0466877i	0.539888	−	0.841737i	$-0.318467\pi$
$149$	0.987090	+	0.569897i	0.0808655	+	0.0466877i	−0.459022	+	0.888425i	$0.651800\pi$
$150$		0			0
$151$	6.38621	+	11.0612i	0.519702	+	0.900151i	0.999738	+	0.0229016i	$0.00729044\pi$
$151$	6.38621	+	11.0612i	0.519702	+	0.900151i	−0.480036	+	0.877249i	$0.659376\pi$
$152$		0			0
$153$	−5.33619	+	22.1244i	−0.431406	+	1.78865i
$154$		0			0
$155$			15.5221i			1.24676i
$156$		0			0
$157$	−7.82053	+	4.51518i	−0.624146	+	0.360351i	−0.778481	−	0.627668i	$-0.784010\pi$
$157$	−7.82053	+	4.51518i	−0.624146	+	0.360351i	0.154335	+	0.988019i	$0.450676\pi$
$158$		0			0
$159$	−1.92516	−	13.3269i	−0.152675	−	1.05690i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.0498774	+	0.0863903i	−0.00390670	+	0.00676661i	−0.867972	−	0.496613i	$-0.834577\pi$
$163$	−0.0498774	+	0.0863903i	−0.00390670	+	0.00676661i	0.864065	+	0.503379i	$0.167910\pi$
$164$		0			0
$165$	6.85922	+	2.74073i	0.533990	+	0.213366i
$166$		0			0
$167$	−3.08612			−0.238811			−0.119406	−	0.992846i	$-0.538099\pi$
$167$	−3.08612			−0.238811			−0.119406	+	0.992846i	$0.538099\pi$
$168$		0			0
$169$	−19.6243			−1.50956
$170$		0			0
$171$	2.53877	+	8.60393i	0.194144	+	0.657959i
$172$		0			0
$173$	3.73038	−	6.46120i	0.283615	−	0.491236i	−0.688657	−	0.725087i	$-0.741799\pi$
$173$	3.73038	−	6.46120i	0.283615	−	0.491236i	0.972272	+	0.233851i	$0.0751328\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	16.7863	−	2.42490i	1.26174	−	0.182266i
$178$		0			0
$179$	2.61465	−	1.50957i	0.195428	−	0.112830i	−0.399093	−	0.916910i	$-0.630675\pi$
$179$	2.61465	−	1.50957i	0.195428	−	0.112830i	0.594521	+	0.804080i	$0.297342\pi$
$180$		0			0
$181$			0.762552i			0.0566801i	0.999598	+	0.0283400i	$0.00902212\pi$
$181$			0.762552i			0.0566801i	−0.999598	+	0.0283400i	$0.990978\pi$
$182$		0			0
$183$	1.39812	−	1.10100i	0.103352	−	0.0813881i
$184$		0			0
$185$	−2.26322	−	3.92001i	−0.166395	−	0.288205i
$186$		0			0
$187$	10.8635	+	6.27204i	0.794417	+	0.458657i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.05844	+	0.611089i	0.0765859	+	0.0442169i	0.537804	−	0.843070i	$-0.319254\pi$
$191$	1.05844	+	0.611089i	0.0765859	+	0.0442169i	−0.461218	+	0.887287i	$0.652587\pi$
$192$		0			0
$193$	11.7587	+	20.3666i	0.846409	+	1.46602i	0.884392	+	0.466744i	$0.154573\pi$
$193$	11.7587	+	20.3666i	0.846409	+	1.46602i	−0.0379837	+	0.999278i	$0.512093\pi$
$194$		0			0
$195$	20.0458	−	15.7858i	1.43551	−	1.13044i
$196$		0			0
$197$			14.7312i			1.04956i	0.851239	+	0.524778i	$0.175852\pi$
$197$			14.7312i			1.04956i	−0.851239	+	0.524778i	$0.824148\pi$
$198$		0			0
$199$	−5.96032	+	3.44119i	−0.422516	+	0.243940i	−0.696153	−	0.717893i	$-0.745107\pi$
$199$	−5.96032	+	3.44119i	−0.422516	+	0.243940i	0.273637	+	0.961833i	$0.411773\pi$
$200$		0			0
$201$	4.05527	−	0.585810i	0.286036	−	0.0413198i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.52746	−	9.57384i	0.386055	−	0.668666i
$206$		0			0
$207$	0.244445	+	0.828428i	0.0169901	+	0.0575797i
$208$		0			0
$209$	4.94441			0.342012
$210$		0			0
$211$	−19.0897			−1.31419			−0.657093	−	0.753809i	$-0.728214\pi$
$211$	−19.0897			−1.31419			−0.657093	+	0.753809i	$0.728214\pi$
$212$		0			0
$213$	25.1965	+	10.0677i	1.72644	+	0.689830i
$214$		0			0
$215$	−3.17921	+	5.50656i	−0.216821	+	0.375544i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.944103	+	6.53555i	0.0637966	+	0.441632i
$220$		0			0
$221$	37.5257	−	21.6655i	2.52425	−	1.45738i
$222$		0			0
$223$			10.9876i			0.735785i	0.929868	+	0.367892i	$0.119921\pi$
$223$			10.9876i			0.735785i	−0.929868	+	0.367892i	$0.880079\pi$
$224$		0			0
$225$	−1.16185	+	4.81714i	−0.0774567	+	0.321143i
$226$		0			0
$227$	9.45418	+	16.3751i	0.627496	+	1.08686i	0.988052	+	0.154118i	$0.0492535\pi$
$227$	9.45418	+	16.3751i	0.627496	+	1.08686i	−0.360556	+	0.932737i	$0.617413\pi$
$228$		0			0
$229$	−14.9744	−	8.64545i	−0.989533	−	0.571307i	−0.0843986	−	0.996432i	$-0.526897\pi$
$229$	−14.9744	−	8.64545i	−0.989533	−	0.571307i	−0.905135	+	0.425125i	$0.860230\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.45119	+	2.56990i	0.291607	+	0.168360i	0.638666	−	0.769484i	$-0.279486\pi$
$233$	4.45119	+	2.56990i	0.291607	+	0.168360i	−0.347059	+	0.937843i	$0.612820\pi$
$234$		0			0
$235$	0.481223	+	0.833503i	0.0313916	+	0.0543718i
$236$		0			0
$237$	9.77358	+	12.4111i	0.634862	+	0.806190i
$238$		0			0
$239$			5.67983i			0.367398i	0.982983	+	0.183699i	$0.0588071\pi$
$239$			5.67983i			0.367398i	−0.982983	+	0.183699i	$0.941193\pi$
$240$		0			0
$241$	−20.1604	+	11.6396i	−1.29864	+	0.749773i	−0.980170	−	0.198158i	$-0.936504\pi$
$241$	−20.1604	+	11.6396i	−1.29864	+	0.749773i	−0.318475	+	0.947931i	$0.603171\pi$
$242$		0			0
$243$	−14.7480	−	5.04952i	−0.946082	−	0.323927i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.53973	−	14.7913i	0.543370	−	0.941145i
$248$		0			0
$249$	−4.27482	+	10.6986i	−0.270906	+	0.677995i
$250$		0			0
$251$	−21.3799			−1.34949			−0.674744	−	0.738052i	$-0.735746\pi$
$251$	−21.3799			−1.34949			−0.674744	+	0.738052i	$0.735746\pi$
$252$		0			0
$253$	0.476072			0.0299304
$254$		0			0
$255$	−12.5743	+	31.4697i	−0.787433	+	1.97071i
$256$		0			0
$257$	7.09305	−	12.2855i	0.442452	−	0.766349i	−0.555419	−	0.831571i	$-0.687442\pi$
$257$	7.09305	−	12.2855i	0.442452	−	0.766349i	0.997871	+	0.0652214i	$0.0207753\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	4.25577	−	4.47521i	0.263425	−	0.277009i
$262$		0			0
$263$	−1.90698	+	1.10100i	−0.117590	+	0.0678904i	−0.557641	−	0.830082i	$-0.688293\pi$
$263$	−1.90698	+	1.10100i	−0.117590	+	0.0678904i	0.440052	+	0.897973i	$0.354960\pi$
$264$		0			0
$265$		−	20.0504i		−	1.23169i
$266$		0			0
$267$	−15.5535	−	19.7509i	−0.951860	−	1.20873i
$268$		0			0
$269$	7.33275	+	12.7007i	0.447086	+	0.774375i	0.998195	−	0.0600579i	$-0.0191285\pi$
$269$	7.33275	+	12.7007i	0.447086	+	0.774375i	−0.551109	+	0.834433i	$0.685795\pi$
$270$		0			0
$271$	−17.6687	−	10.2010i	−1.07330	−	0.619669i	−0.144217	−	0.989546i	$-0.546066\pi$
$271$	−17.6687	−	10.2010i	−1.07330	−	0.619669i	−0.929081	+	0.369877i	$0.879400\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.36531	+	1.36561i	0.142633	+	0.0823495i
$276$		0			0
$277$	−0.00535275	−	0.00927123i	−0.000321615	−	0.000557054i	0.865865	−	0.500279i	$-0.166769\pi$
$277$	−0.00535275	−	0.00927123i	−0.000321615	−	0.000557054i	−0.866186	+	0.499721i	$0.833436\pi$
$278$		0			0
$279$	−17.5519	−	4.23335i	−1.05080	−	0.253444i
$280$		0			0
$281$		−	8.11712i		−	0.484227i	−0.970248	−	0.242114i	$-0.922159\pi$
$281$		−	8.11712i		−	0.484227i	0.970248	−	0.242114i	$-0.0778406\pi$
$282$		0			0
$283$	3.34466	−	1.93104i	0.198819	−	0.114788i	−0.397285	−	0.917695i	$-0.630048\pi$
$283$	3.34466	−	1.93104i	0.198819	−	0.114788i	0.596105	+	0.802907i	$0.296714\pi$
$284$		0			0
$285$	1.90979	+	13.2205i	0.113126	+	0.783115i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−20.2757	+	35.1185i	−1.19269	+	2.06580i
$290$		0			0
$291$	7.13713	+	2.85177i	0.418386	+	0.167174i
$292$		0			0
$293$	−5.75351			−0.336123			−0.168062	−	0.985776i	$-0.553751\pi$
$293$	−5.75351			−0.336123			−0.168062	+	0.985776i	$0.553751\pi$
$294$		0			0
$295$	25.2550			1.47041
$296$		0			0
$297$	−4.96987	+	7.00873i	−0.288381	+	0.406688i
$298$		0			0
$299$	0.822247	−	1.42417i	0.0475518	−	0.0823621i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.98141	+	1.00851i	−0.401071	+	0.0579374i
$304$		0			0
$305$	2.29487	−	1.32494i	0.131404	−	0.0758660i
$306$		0			0
$307$			23.9041i			1.36428i	0.731221	+	0.682140i	$0.238951\pi$
$307$			23.9041i			1.36428i	−0.731221	+	0.682140i	$0.761049\pi$
$308$		0			0
$309$	−11.4758	+	9.03703i	−0.652836	+	0.514099i
$310$		0			0
$311$	−10.5789	−	18.3232i	−0.599874	−	1.03901i	−0.992839	−	0.119459i	$-0.961884\pi$
$311$	−10.5789	−	18.3232i	−0.599874	−	1.03901i	0.392965	−	0.919553i	$-0.371449\pi$
$312$		0			0
$313$	18.2861	+	10.5575i	1.03359	+	0.596746i	0.918012	−	0.396552i	$-0.129793\pi$
$313$	18.2861	+	10.5575i	1.03359	+	0.596746i	0.115582	+	0.993298i	$0.463127\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.8698	−	8.00775i	−0.779007	−	0.449760i	0.0570712	−	0.998370i	$-0.481824\pi$
$317$	−13.8698	−	8.00775i	−0.779007	−	0.449760i	−0.836078	+	0.548610i	$0.815157\pi$
$318$		0			0
$319$	−1.70194	−	2.94785i	−0.0952904	−	0.165048i
$320$		0			0
$321$	19.8507	−	15.6321i	1.10796	−	0.872498i
$322$		0			0
$323$			22.6846i			1.26221i
$324$		0			0
$325$	8.17048	−	4.71723i	0.453217	−	0.261665i
$326$		0			0
$327$	29.6564	−	4.28406i	1.64000	−	0.236909i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.48985	+	16.4369i	−0.521610	+	0.903454i	0.478074	+	0.878319i	$0.341335\pi$
$331$	−9.48985	+	16.4369i	−0.521610	+	0.903454i	−0.999684	+	0.0251350i	$0.991998\pi$
$332$		0			0
$333$	5.04989	−	1.49007i	0.276732	−	0.0816555i
$334$		0			0
$335$	6.10115			0.333341
$336$		0			0
$337$	0.151144			0.00823337			0.00411668	−	0.999992i	$-0.498690\pi$
$337$	0.151144			0.00823337			0.00411668	+	0.999992i	$0.498690\pi$
$338$		0			0
$339$	−6.43363	−	2.57068i	−0.349427	−	0.139620i
$340$		0			0
$341$	−4.97579	+	8.61831i	−0.269454	+	0.466708i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.183884	+	1.27293i	0.00989996	+	0.0685325i
$346$		0			0
$347$	11.5977	−	6.69596i	0.622599	−	0.359458i	−0.155281	−	0.987870i	$-0.549628\pi$
$347$	11.5977	−	6.69596i	0.622599	−	0.359458i	0.777880	+	0.628412i	$0.216295\pi$
$348$		0			0
$349$		−	13.4025i		−	0.717421i	−0.933449	−	0.358710i	$-0.883217\pi$
$349$		−	13.4025i		−	0.717421i	0.933449	−	0.358710i	$-0.116783\pi$
$350$		0			0
$351$	12.3830	+	26.9725i	0.660955	+	1.43969i
$352$		0			0
$353$	−10.7469	−	18.6141i	−0.571998	−	0.990729i	−0.996361	−	0.0852371i	$-0.972835\pi$
$353$	−10.7469	−	18.6141i	−0.571998	−	0.990729i	0.424363	−	0.905492i	$-0.360498\pi$
$354$		0			0
$355$	34.9899	+	20.2014i	1.85707	+	1.07218i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	24.4173	+	14.0974i	1.28870	+	0.744030i	0.978422	−	0.206616i	$-0.0662452\pi$
$359$	24.4173	+	14.0974i	1.28870	+	0.744030i	0.310276	+	0.950647i	$0.399579\pi$
$360$		0			0
$361$	−5.02928	−	8.71097i	−0.264699	−	0.458472i
$362$		0			0
$363$	−8.85759	−	11.2479i	−0.464903	−	0.590364i
$364$		0			0
$365$			9.83274i			0.514669i
$366$		0			0
$367$	19.6810	−	11.3628i	1.02734	−	0.593135i	0.111118	−	0.993807i	$-0.464557\pi$
$367$	19.6810	−	11.3628i	1.02734	−	0.593135i	0.916221	+	0.400673i	$0.131224\pi$
$368$		0			0
$369$	9.31831	+	8.86138i	0.485092	+	0.461305i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.95699	−	12.0499i	0.360219	−	0.623918i	−0.627778	−	0.778393i	$-0.716035\pi$
$373$	6.95699	−	12.0499i	0.360219	−	0.623918i	0.987997	+	0.154475i	$0.0493686\pi$
$374$		0			0
$375$	5.54974	−	13.8893i	0.286588	−	0.717242i
$376$		0			0
$377$	−11.7580			−0.605569
$378$		0			0
$379$	20.8656			1.07179			0.535897	−	0.844283i	$-0.319973\pi$
$379$	20.8656			1.07179			0.535897	+	0.844283i	$0.319973\pi$
$380$		0			0
$381$	10.6992	−	26.7770i	0.548139	−	1.37183i
$382$		0			0
$383$	1.23577	−	2.14042i	0.0631451	−	0.109371i	−0.832725	−	0.553687i	$-0.813220\pi$
$383$	1.23577	−	2.14042i	0.0631451	−	0.109371i	0.895870	+	0.444317i	$0.146554\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.35959	−	5.09677i	−0.272443	−	0.259084i
$388$		0			0
$389$	−20.4245	+	11.7921i	−1.03556	+	0.597882i	−0.918573	−	0.395251i	$-0.870658\pi$
$389$	−20.4245	+	11.7921i	−1.03556	+	0.597882i	−0.116989	+	0.993133i	$0.537324\pi$
$390$		0			0
$391$			2.18419i			0.110459i
$392$		0			0
$393$	−17.7829	−	22.5819i	−0.897027	−	1.13910i
$394$		0			0
$395$	11.7615	+	20.3716i	0.591788	+	1.02501i
$396$		0			0
$397$	1.79160	+	1.03438i	0.0899181	+	0.0519142i	0.544285	−	0.838901i	$-0.316801\pi$
$397$	1.79160	+	1.03438i	0.0899181	+	0.0519142i	−0.454367	+	0.890815i	$0.650134\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.46052	−	3.72998i	−0.322623	−	0.186266i	0.329938	−	0.944003i	$-0.392972\pi$
$401$	−6.46052	−	3.72998i	−0.322623	−	0.186266i	−0.652561	+	0.757736i	$0.726305\pi$
$402$		0			0
$403$	17.1879	+	29.7702i	0.856188	+	1.48296i
$404$		0			0
$405$	−20.6598	−	10.5814i	−1.02659	−	0.525796i
$406$		0			0
$407$		−	2.90201i		−	0.143847i
$408$		0			0
$409$	−29.2897	+	16.9104i	−1.44828	+	0.836166i	−0.998379	−	0.0569122i	$-0.981874\pi$
$409$	−29.2897	+	16.9104i	−1.44828	+	0.836166i	−0.449902	+	0.893078i	$0.648541\pi$
$410$		0			0
$411$	−2.46394	−	17.0566i	−0.121537	−	0.841342i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−8.57764	+	14.8569i	−0.421060	+	0.729297i
$416$		0			0
$417$	5.01746	+	2.00482i	0.245706	+	0.0981765i
$418$		0			0
$419$	15.2980			0.747358			0.373679	−	0.927558i	$-0.378096\pi$
$419$	15.2980			0.747358			0.373679	+	0.927558i	$0.378096\pi$
$420$		0			0
$421$	11.8931			0.579633			0.289816	−	0.957082i	$-0.406406\pi$
$421$	11.8931			0.579633			0.289816	+	0.957082i	$0.406406\pi$
$422$		0			0
$423$	−1.07375	+	0.316831i	−0.0522073	+	0.0154048i
$424$		0			0
$425$	−6.26534	+	10.8519i	−0.303913	+	0.526393i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	16.1904	−	2.33881i	0.781679	−	0.112919i
$430$		0			0
$431$	−14.9148	+	8.61109i	−0.718423	+	0.414782i	−0.814172	−	0.580624i	$-0.802809\pi$
$431$	−14.9148	+	8.61109i	−0.718423	+	0.414782i	0.0957491	+	0.995405i	$0.469475\pi$
$432$		0			0
$433$		−	1.55093i		−	0.0745329i	−0.999305	−	0.0372664i	$-0.988135\pi$
$433$		−	1.55093i		−	0.0745329i	0.999305	−	0.0372664i	$-0.0118650\pi$
$434$		0			0
$435$	7.22466	−	5.68931i	0.346396	−	0.272782i
$436$		0			0
$437$	0.430463	+	0.745583i	0.0205918	+	0.0356661i
$438$		0			0
$439$	−16.8278	−	9.71551i	−0.803145	−	0.463696i	0.0414249	−	0.999142i	$-0.486810\pi$
$439$	−16.8278	−	9.71551i	−0.803145	−	0.463696i	−0.844570	+	0.535446i	$0.820144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.08964	−	1.78380i	−0.146793	−	0.0847510i	0.424805	−	0.905285i	$-0.360343\pi$
$443$	−3.08964	−	1.78380i	−0.146793	−	0.0847510i	−0.571598	+	0.820534i	$0.693676\pi$
$444$		0			0
$445$	−18.7171	−	32.4190i	−0.887277	−	1.53681i
$446$		0			0
$447$	−1.55100	+	1.22139i	−0.0733597	+	0.0577697i
$448$		0			0
$449$		−	29.5796i		−	1.39595i	−0.716124	−	0.697973i	$-0.754085\pi$
$449$		−	29.5796i		−	1.39595i	0.716124	−	0.697973i	$-0.245915\pi$
$450$		0			0
$451$	6.13803	−	3.54379i	0.289028	−	0.166871i
$452$		0			0
$453$	−21.8952	+	3.16290i	−1.02873	+	0.148606i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.2312	−	19.4530i	0.525374	−	0.909975i	−0.474189	−	0.880423i	$-0.657259\pi$
$457$	11.2312	−	19.4530i	0.525374	−	0.909975i	0.999563	−	0.0295520i	$-0.00940807\pi$
$458$		0			0
$459$	−32.1556	−	22.8014i	−1.50089	−	1.06428i
$460$		0			0
$461$	9.31904			0.434031			0.217015	−	0.976168i	$-0.430368\pi$
$461$	9.31904			0.434031			0.217015	+	0.976168i	$0.430368\pi$
$462$		0			0
$463$	−16.6243			−0.772597			−0.386298	−	0.922374i	$-0.626246\pi$
$463$	−16.6243			−0.772597			−0.386298	+	0.922374i	$0.626246\pi$
$464$		0			0
$465$	−24.9658	−	9.97556i	−1.15776	−	0.462605i
$466$		0			0
$467$	6.06560	−	10.5059i	0.280683	−	0.486156i	−0.690871	−	0.722979i	$-0.742773\pi$
$467$	6.06560	−	10.5059i	0.280683	−	0.486156i	0.971553	+	0.236822i	$0.0761059\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−2.23624	−	15.4804i	−0.103040	−	0.713298i
$472$		0			0
$473$	−3.53039	+	2.03827i	−0.162328	+	0.0937198i
$474$		0			0
$475$			4.93913i			0.226623i
$476$		0			0
$477$	22.6724	+	5.46838i	1.03810	+	0.250380i
$478$		0			0
$479$	13.2594	+	22.9660i	0.605839	+	1.04934i	0.991918	+	0.126878i	$0.0404956\pi$
$479$	13.2594	+	22.9660i	0.605839	+	1.04934i	−0.386080	+	0.922465i	$0.626171\pi$
$480$		0			0
$481$	−8.68140	−	5.01221i	−0.395838	−	0.228537i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.91120	+	5.72223i	0.450044	+	0.259833i
$486$		0			0
$487$	17.5986	+	30.4817i	0.797469	+	1.38126i	0.921260	+	0.388948i	$0.127161\pi$
$487$	17.5986	+	30.4817i	0.797469	+	1.38126i	−0.123791	+	0.992308i	$0.539505\pi$
$488$		0			0
$489$	−0.106896	−	0.135744i	−0.00483401	−	0.00613854i
$490$		0			0
$491$		−	32.5795i		−	1.47029i	−0.677910	−	0.735145i	$-0.737114\pi$
$491$		−	32.5795i		−	1.47029i	0.677910	−	0.735145i	$-0.262886\pi$
$492$		0			0
$493$	13.5245	−	7.80840i	0.609115	−	0.351673i
$494$		0			0
$495$	−8.81643	+	9.27104i	−0.396269	+	0.416702i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.46895	+	4.27635i	−0.110525	+	0.191436i	−0.915982	−	0.401219i	$-0.868587\pi$
$499$	−2.46895	+	4.27635i	−0.110525	+	0.191436i	0.805457	+	0.592655i	$0.201920\pi$
$500$		0			0
$501$	1.98336	−	4.96374i	0.0886099	−	0.221764i
$502$		0			0
$503$	16.7907			0.748661			0.374331	−	0.927295i	$-0.377873\pi$
$503$	16.7907			0.748661			0.374331	+	0.927295i	$0.377873\pi$
$504$		0			0
$505$	−10.5035			−0.467401
$506$		0			0
$507$	12.6119	−	31.5639i	0.560116	−	1.40180i
$508$		0			0
$509$	0.631490	−	1.09377i	0.0279903	−	0.0484806i	−0.851691	−	0.524044i	$-0.824423\pi$
$509$	0.631490	−	1.09377i	0.0279903	−	0.0484806i	0.879681	+	0.475564i	$0.157756\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−15.4702	−	1.44611i	−0.683027	−	0.0638475i
$514$		0			0
$515$	−18.8364	+	10.8752i	−0.830029	+	0.479218i
$516$		0			0
$517$			0.617048i			0.0271378i
$518$		0			0
$519$	7.99485	+	10.1524i	0.350935	+	0.445640i
$520$		0			0
$521$	14.9945	+	25.9713i	0.656922	+	1.13782i	0.981408	+	0.191932i	$0.0614755\pi$
$521$	14.9945	+	25.9713i	0.656922	+	1.13782i	−0.324486	+	0.945891i	$0.605191\pi$
$522$		0			0
$523$	−30.7587	−	17.7586i	−1.34499	−	0.776528i	−0.357451	−	0.933932i	$-0.616354\pi$
$523$	−30.7587	−	17.7586i	−1.34499	−	0.776528i	−0.987534	+	0.157404i	$0.949688\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−39.5403	−	22.8286i	−1.72240	−	0.994429i
$528$		0			0
$529$	−11.4586	−	19.8468i	−0.498198	−	0.862904i
$530$		0			0
$531$	−6.88785	+	28.5577i	−0.298907	+	1.23930i
$532$		0			0
$533$		−	24.4826i		−	1.06046i
$534$		0			0
$535$	32.5828	−	18.8117i	1.40868	−	0.813300i
$536$		0			0
$537$	0.747645	+	5.17557i	0.0322633	+	0.223343i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	11.9158	−	20.6388i	0.512300	−	0.887330i	−0.487598	−	0.873068i	$-0.662127\pi$
$541$	11.9158	−	20.6388i	0.512300	−	0.887330i	0.999898	−	0.0142616i	$-0.00453975\pi$
$542$		0			0
$543$	−1.22649	−	0.490069i	−0.0526339	−	0.0210309i
$544$		0			0
$545$	44.6181			1.91123
$546$		0			0
$547$	21.1040			0.902342			0.451171	−	0.892437i	$-0.351006\pi$
$547$	21.1040			0.902342			0.451171	+	0.892437i	$0.351006\pi$
$548$		0			0
$549$	0.872324	+	2.95632i	0.0372299	+	0.126173i
$550$		0			0
$551$	3.07778	−	5.33087i	0.131118	−	0.227103i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.75948	−	1.12091i	0.329372	−	0.0475799i
$556$		0			0
$557$	19.3020	−	11.1440i	0.817852	−	0.472187i	−0.0318235	−	0.999494i	$-0.510131\pi$
$557$	19.3020	−	11.1440i	0.817852	−	0.472187i	0.849675	+	0.527307i	$0.176798\pi$
$558$		0			0
$559$			14.0816i			0.595588i
$560$		0			0
$561$	−17.0696	+	13.4421i	−0.720680	+	0.567525i
$562$		0			0
$563$	−20.2197	−	35.0215i	−0.852157	−	1.47598i	−0.879258	−	0.476347i	$-0.841961\pi$
$563$	−20.2197	−	35.0215i	−0.852157	−	1.47598i	0.0271005	−	0.999633i	$-0.491373\pi$
$564$		0			0
$565$	−8.93427	−	5.15820i	−0.375867	−	0.217007i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.7717	+	12.5699i	0.912717	+	0.526957i	0.881304	−	0.472549i	$-0.156666\pi$
$569$	21.7717	+	12.5699i	0.912717	+	0.526957i	0.0314127	+	0.999506i	$0.489999\pi$
$570$		0			0
$571$	−0.655344	−	1.13509i	−0.0274253	−	0.0475020i	0.851987	−	0.523563i	$-0.175398\pi$
$571$	−0.655344	−	1.13509i	−0.0274253	−	0.0475020i	−0.879412	+	0.476061i	$0.842064\pi$
$572$		0			0
$573$	−1.66311	+	1.30967i	−0.0694773	+	0.0547123i
$574$		0			0
$575$			0.475563i			0.0198324i
$576$		0			0
$577$	−5.21739	+	3.01226i	−0.217203	+	0.125402i	−0.604654	−	0.796488i	$-0.706689\pi$
$577$	−5.21739	+	3.01226i	−0.217203	+	0.125402i	0.387452	+	0.921890i	$0.373355\pi$
$578$		0			0
$579$	−40.3148	+	5.82374i	−1.67543	+	0.242026i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	6.42740	−	11.1326i	0.266196	−	0.461065i
$584$		0			0
$585$	12.5071	+	42.3869i	0.517106	+	1.75248i
$586$		0			0
$587$	−39.5131			−1.63088			−0.815439	−	0.578843i	$-0.803504\pi$
$587$	−39.5131			−1.63088			−0.815439	+	0.578843i	$0.803504\pi$
$588$		0			0
$589$	−17.9964			−0.741527
$590$		0			0
$591$	−23.6938	−	9.46731i	−0.974633	−	0.389433i
$592$		0			0
$593$	6.75855	−	11.7062i	0.277540	−	0.480714i	−0.693232	−	0.720714i	$-0.743814\pi$
$593$	6.75855	−	11.7062i	0.277540	−	0.480714i	0.970773	+	0.240000i	$0.0771474\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.70432	−	11.7982i	−0.0697533	−	0.482867i
$598$		0			0
$599$	−5.68762	+	3.28375i	−0.232390	+	0.134170i	−0.611674	−	0.791110i	$-0.709504\pi$
$599$	−5.68762	+	3.28375i	−0.232390	+	0.134170i	0.379284	+	0.925280i	$0.376170\pi$
$600$		0			0
$601$			10.0499i			0.409946i	0.978768	+	0.204973i	$0.0657106\pi$
$601$			10.0499i			0.409946i	−0.978768	+	0.204973i	$0.934289\pi$
$602$		0			0
$603$	−1.66398	+	6.89900i	−0.0677623	+	0.280949i
$604$		0			0
$605$	−10.6592	−	18.4623i	−0.433360	−	0.750601i
$606$		0			0
$607$	0.673920	+	0.389088i	0.0273536	+	0.0157926i	0.513614	−	0.858021i	$-0.328306\pi$
$607$	0.673920	+	0.389088i	0.0273536	+	0.0157926i	−0.486261	+	0.873814i	$0.661640\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.84591	+	1.06573i	0.0746774	+	0.0431150i
$612$		0			0
$613$	−19.3349	−	33.4890i	−0.780928	−	1.35261i	−0.931402	−	0.363993i	$-0.881413\pi$
$613$	−19.3349	−	33.4890i	−0.780928	−	1.35261i	0.150474	−	0.988614i	$-0.451920\pi$
$614$		0			0
$615$	11.8463	+	15.0432i	0.477689	+	0.606602i
$616$		0			0
$617$		−	7.83523i		−	0.315434i	−0.987484	−	0.157717i	$-0.949587\pi$
$617$		−	7.83523i		−	0.315434i	0.987484	−	0.157717i	$-0.0504134\pi$
$618$		0			0
$619$	−17.9235	+	10.3481i	−0.720407	+	0.415927i	−0.814902	−	0.579598i	$-0.803209\pi$
$619$	−17.9235	+	10.3481i	−0.720407	+	0.415927i	0.0944957	+	0.995525i	$0.469876\pi$
$620$		0			0
$621$	−1.48955	−	0.139239i	−0.0597735	−	0.00558747i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.2652	−	26.4402i	0.610610	−	1.05761i
$626$		0			0
$627$	−3.17762	+	7.95263i	−0.126902	+	0.317597i
$628$		0			0
$629$	13.3142			0.530874
$630$		0			0
$631$	−7.21022			−0.287034			−0.143517	−	0.989648i	$-0.545841\pi$
$631$	−7.21022			−0.287034			−0.143517	+	0.989648i	$0.545841\pi$
$632$		0			0
$633$	12.2683	−	30.7040i	0.487623	−	1.22037i
$634$		0			0
$635$	21.4686	−	37.1847i	0.851955	−	1.47563i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−32.3860	+	34.0560i	−1.28117	+	1.34723i
$640$		0			0
$641$	−31.9156	+	18.4265i	−1.26059	+	0.727802i	−0.973189	−	0.230009i	$-0.926124\pi$
$641$	−31.9156	+	18.4265i	−1.26059	+	0.727802i	−0.287401	+	0.957810i	$0.592791\pi$
$642$		0			0
$643$			10.5183i			0.414801i	0.978256	+	0.207400i	$0.0665003\pi$
$643$			10.5183i			0.414801i	−0.978256	+	0.207400i	$0.933500\pi$
$644$		0			0
$645$	−6.81361	−	8.65237i	−0.268286	−	0.340687i
$646$		0			0
$647$	10.2057	+	17.6768i	0.401228	+	0.694948i	0.993874	−	0.110515i	$-0.0352501\pi$
$647$	10.2057	+	17.6768i	0.401228	+	0.694948i	−0.592646	+	0.805463i	$0.701917\pi$
$648$		0			0
$649$	14.0224	+	8.09581i	0.550426	+	0.317789i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.7382	+	16.5920i	1.12461	+	0.649295i	0.942574	−	0.333996i	$-0.108397\pi$
$653$	28.7382	+	16.5920i	1.12461	+	0.649295i	0.182038	+	0.983291i	$0.441731\pi$
$654$		0			0
$655$	−21.3999	−	37.0658i	−0.836165	−	1.44828i
$656$		0			0
$657$	−11.1186	−	2.68170i	−0.433777	−	0.104623i
$658$		0			0
$659$			7.18286i			0.279804i	0.990165	+	0.139902i	$0.0446788\pi$
$659$			7.18286i			0.279804i	−0.990165	+	0.139902i	$0.955321\pi$
$660$		0			0
$661$	18.2360	−	10.5285i	0.709297	−	0.409513i	−0.101504	−	0.994835i	$-0.532365\pi$
$661$	18.2360	−	10.5285i	0.709297	−	0.409513i	0.810801	+	0.585323i	$0.199032\pi$
$662$		0			0
$663$	10.7303	+	74.2804i	0.416730	+	2.88481i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.296344	−	0.513282i	0.0114745	−	0.0198744i
$668$		0			0
$669$	−17.6726	−	7.06140i	−0.683261	−	0.273010i
$670$		0			0
$671$	1.69891			0.0655856
$672$		0			0
$673$	−21.5441			−0.830464			−0.415232	−	0.909715i	$-0.636300\pi$
$673$	−21.5441			−0.830464			−0.415232	+	0.909715i	$0.636300\pi$
$674$		0			0
$675$	−7.00124	−	4.96456i	−0.269478	−	0.191086i
$676$		0			0
$677$	−2.69876	+	4.67439i	−0.103722	+	0.179651i	−0.913215	−	0.407477i	$-0.866408\pi$
$677$	−2.69876	+	4.67439i	−0.103722	+	0.179651i	0.809493	+	0.587129i	$0.199742\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−32.4138	+	4.68238i	−1.24210	+	0.179429i
$682$		0			0
$683$	−28.9007	+	16.6858i	−1.10585	+	0.638465i	−0.937752	−	0.347305i	$-0.887097\pi$
$683$	−28.9007	+	16.6858i	−1.10585	+	0.638465i	−0.168101	+	0.985770i	$0.553764\pi$
$684$		0			0
$685$		−	25.6617i		−	0.980483i
$686$		0			0
$687$	23.5290	−	18.5287i	0.897686	−	0.706914i
$688$		0			0
$689$	−22.2022	−	38.4553i	−0.845835	−	1.46503i
$690$		0			0
$691$	34.4696	+	19.9010i	1.31128	+	0.757070i	0.982309	−	0.187268i	$-0.0599634\pi$
$691$	34.4696	+	19.9010i	1.31128	+	0.757070i	0.328975	+	0.944339i	$0.393297\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.96765	+	4.02278i	0.264298	+	0.152593i
$696$		0			0
$697$	16.2587	+	28.1609i	0.615842	+	1.06667i
$698$		0			0
$699$	−6.99409	+	5.50774i	−0.264541	+	0.208322i
$700$		0			0
$701$			10.6583i			0.402559i	0.979534	+	0.201280i	$0.0645100\pi$
$701$			10.6583i			0.402559i	−0.979534	+	0.201280i	$0.935490\pi$
$702$		0			0
$703$	4.54488	−	2.62399i	0.171414	−	0.0989657i
$704$		0			0
$705$	−1.64988	+	0.238336i	−0.0621381	+	0.00897626i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.5727	+	30.4367i	−0.659955	+	1.14308i	0.320672	+	0.947190i	$0.396091\pi$
$709$	−17.5727	+	30.4367i	−0.659955	+	1.14308i	−0.980627	+	0.195885i	$0.937242\pi$
$710$		0			0
$711$	−26.2434	+	7.74364i	−0.984203	+	0.290409i
$712$		0			0
$713$	−1.73278			−0.0648930
$714$		0			0
$715$	24.3584			0.910954
$716$		0			0
$717$	−9.13549	−	3.65026i	−0.341171	−	0.136321i
$718$		0			0
$719$	−15.6309	+	27.0734i	−0.582932	+	1.00967i	0.412197	+	0.911095i	$0.364761\pi$
$719$	−15.6309	+	27.0734i	−0.582932	+	1.00967i	−0.995130	+	0.0985739i	$0.968572\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−5.76476	−	39.9066i	−0.214394	−	1.48414i
$724$		0			0
$725$	2.94470	−	1.70012i	0.109363	−	0.0631410i
$726$		0			0
$727$		−	39.7975i		−	1.47601i	−0.674797	−	0.738003i	$-0.735769\pi$
$727$		−	39.7975i		−	1.47601i	0.674797	−	0.738003i	$-0.264231\pi$
$728$		0			0
$729$	17.5998	−	20.4756i	0.651843	−	0.758354i
$730$		0			0
$731$	−9.35146	−	16.1972i	−0.345876	−	0.599075i
$732$		0			0
$733$	−10.5878	−	6.11289i	−0.391071	−	0.225785i	0.291553	−	0.956555i	$-0.405828\pi$
$733$	−10.5878	−	6.11289i	−0.391071	−	0.225785i	−0.682624	+	0.730770i	$0.739161\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.38754	+	1.95580i	0.124782	+	0.0720428i
$738$		0			0
$739$	−14.5001	−	25.1148i	−0.533393	−	0.923864i	−0.999239	−	0.0389981i	$-0.987583\pi$
$739$	−14.5001	−	25.1148i	−0.533393	−	0.923864i	0.465846	−	0.884866i	$-0.345750\pi$
$740$		0			0
$741$	18.3021	+	23.2413i	0.672346	+	0.853789i
$742$		0			0
$743$			33.4864i			1.22850i	0.789113	+	0.614248i	$0.210541\pi$
$743$			33.4864i			1.22850i	−0.789113	+	0.614248i	$0.789459\pi$
$744$		0			0
$745$	−2.54580	+	1.46982i	−0.0932710	+	0.0538501i
$746$		0			0
$747$	−14.4604	−	13.7513i	−0.529078	−	0.503134i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.86021	+	10.1502i	−0.213842	+	0.370385i	−0.952914	−	0.303242i	$-0.901931\pi$
$751$	−5.86021	+	10.1502i	−0.213842	+	0.370385i	0.739072	+	0.673627i	$0.235264\pi$
$752$		0			0
$753$	13.7402	−	34.3876i	0.500722	−	1.25315i
$754$		0			0
$755$	−32.9413			−1.19886
$756$		0			0
$757$	11.2688			0.409571			0.204785	−	0.978807i	$-0.434350\pi$
$757$	11.2688			0.409571			0.204785	+	0.978807i	$0.434350\pi$
$758$		0			0
$759$	−0.305957	+	0.765717i	−0.0111055	+	0.0277938i
$760$		0			0
$761$	10.0633	−	17.4301i	0.364793	−	0.631841i	−0.623950	−	0.781465i	$-0.714473\pi$
$761$	10.0633	−	17.4301i	0.364793	−	0.631841i	0.988743	+	0.149624i	$0.0478063\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−42.5349	−	40.4492i	−1.53785	−	1.46244i
$766$		0			0
$767$	48.4374	−	27.9654i	1.74897	−	1.00977i
$768$		0			0
$769$		−	7.95157i		−	0.286741i	−0.989669	−	0.143370i	$-0.954206\pi$
$769$		−	7.95157i		−	0.286741i	0.989669	−	0.143370i	$-0.0457940\pi$
$770$		0			0
$771$	15.2016	+	19.3040i	0.547473	+	0.695218i
$772$		0			0
$773$	15.8927	+	27.5269i	0.571620	+	0.990075i	0.996400	+	0.0847784i	$0.0270182\pi$
$773$	15.8927	+	27.5269i	0.571620	+	0.990075i	−0.424780	+	0.905297i	$0.639648\pi$
$774$		0			0
$775$	−8.60911	−	4.97047i	−0.309248	−	0.178545i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.1000	+	6.40857i	0.397698	+	0.229611i
$780$		0			0
$781$	12.9516	+	22.4329i	0.463446	+	0.802712i
$782$		0			0
$783$	4.46291	+	9.72110i	0.159492	+	0.347404i
$784$		0			0
$785$		−	23.2902i		−	0.831264i
$786$		0			0
$787$	−26.3569	+	15.2172i	−0.939523	+	0.542434i	−0.889811	−	0.456330i	$-0.849164\pi$
$787$	−26.3569	+	15.2172i	−0.939523	+	0.542434i	−0.0497122	+	0.998764i	$0.515830\pi$
$788$		0			0
$789$	−0.545292	−	3.77478i	−0.0194129	−	0.134386i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.93427	−	5.08230i	0.104199	−	0.180478i
$794$		0			0
$795$	32.2492	+	12.8858i	1.14376	+	0.457012i
$796$		0			0
$797$	40.0924			1.42015			0.710074	−	0.704127i	$-0.248662\pi$
$797$	40.0924			1.42015			0.710074	+	0.704127i	$0.248662\pi$
$798$		0			0
$799$	−2.83098			−0.100153
$800$		0			0
$801$	41.7632	−	12.3231i	1.47563	−	0.435415i
$802$		0			0
$803$	−3.15201	+	5.45944i	−0.111232	+	0.192659i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−25.1404	+	3.63170i	−0.884985	+	0.127842i
$808$		0			0
$809$	−34.0306	+	19.6476i	−1.19645	+	0.690773i	−0.959763	−	0.280812i	$-0.909396\pi$
$809$	−34.0306	+	19.6476i	−1.19645	+	0.690773i	−0.236691	+	0.971585i	$0.576063\pi$
$810$		0			0
$811$			23.6789i			0.831480i	0.909484	+	0.415740i	$0.136477\pi$
$811$			23.6789i			0.831480i	−0.909484	+	0.415740i	$0.863523\pi$
$812$		0			0
$813$	27.7626	−	21.8626i	0.973676	−	0.766755i
$814$		0			0
$815$	−0.128639	−	0.222809i	−0.00450602	−	0.00780466i
$816$		0			0
$817$	−6.38434	−	3.68600i	−0.223360	−	0.128957i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	37.4772	+	21.6374i	1.30796	+	0.755152i	0.981756	−	0.190146i	$-0.0608963\pi$
$821$	37.4772	+	21.6374i	1.30796	+	0.755152i	0.326206	+	0.945299i	$0.394230\pi$
$822$		0			0
$823$	0.484756	+	0.839623i	0.0168975	+	0.0292674i	0.874351	−	0.485295i	$-0.161288\pi$
$823$	0.484756	+	0.839623i	0.0168975	+	0.0292674i	−0.857453	+	0.514562i	$0.827954\pi$
$824$		0			0
$825$	−3.71657	+	2.92674i	−0.129394	+	0.101896i
$826$		0			0
$827$		−	43.9510i		−	1.52833i	−0.645023	−	0.764163i	$-0.723152\pi$
$827$		−	43.9510i		−	1.52833i	0.645023	−	0.764163i	$-0.276848\pi$
$828$		0			0
$829$	6.57119	−	3.79388i	0.228227	−	0.131767i	−0.381527	−	0.924358i	$-0.624602\pi$
$829$	6.57119	−	3.79388i	0.228227	−	0.131767i	0.609754	+	0.792591i	$0.291268\pi$
$830$		0			0
$831$	0.0183520	−	0.00265106i	0.000636622	−	9.19643e-5i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.97971	−	6.89306i	0.137724	−	0.238544i
$836$		0			0
$837$	18.0890	−	25.5099i	0.625248	−	0.881753i
$838$		0			0
$839$	−8.87477			−0.306391			−0.153196	−	0.988196i	$-0.548956\pi$
$839$	−8.87477			−0.306391			−0.153196	+	0.988196i	$0.548956\pi$
$840$		0			0
$841$	24.7623			0.853873
$842$		0			0
$843$	13.0556	+	5.21663i	0.449660	+	0.179670i
$844$		0			0
$845$	25.3065	−	43.8322i	0.870570	−	1.50787i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.956387	+	6.62059i	0.0328231	+	0.227218i
$850$		0			0
$851$	0.437604	−	0.252651i	0.0150009	−	0.00866075i
$852$		0			0
$853$			0.208510i			0.00713924i	0.999994	+	0.00356962i	$0.00113625\pi$
$853$			0.208510i			0.00713924i	−0.999994	+	0.00356962i	$0.998864\pi$
$854$		0			0
$855$	−22.4913	−	5.42470i	−0.769187	−	0.185521i
$856$		0			0
$857$	14.9945	+	25.9713i	0.512204	+	0.887163i	0.999900	+	0.0141492i	$0.00450398\pi$
$857$	14.9945	+	25.9713i	0.512204	+	0.887163i	−0.487696	+	0.873013i	$0.662163\pi$
$858$		0			0
$859$	−17.9227	−	10.3477i	−0.611513	−	0.353057i	0.162044	−	0.986783i	$-0.448191\pi$
$859$	−17.9227	−	10.3477i	−0.611513	−	0.353057i	−0.773557	+	0.633726i	$0.781525\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.8134	+	8.55253i	0.504254	+	0.291131i	0.730469	−	0.682946i	$-0.239302\pi$
$863$	14.8134	+	8.55253i	0.504254	+	0.291131i	−0.226214	+	0.974078i	$0.572635\pi$
$864$		0			0
$865$	9.62102	+	16.6641i	0.327124	+	0.566596i
$866$		0			0
$867$	−43.4543	−	55.1812i	−1.47579	−	1.87405i
$868$		0			0
$869$			15.0812i			0.511596i
$870$		0			0
$871$	11.7016	−	6.75591i	0.396493	−	0.228915i
$872$		0			0
$873$	−9.17363	+	9.64666i	−0.310480	+	0.326490i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.71713	+	16.8306i	−0.328124	+	0.568328i	−0.982140	−	0.188153i	$-0.939750\pi$
$877$	−9.71713	+	16.8306i	−0.328124	+	0.568328i	0.654015	+	0.756481i	$0.273083\pi$
$878$		0			0
$879$	3.69760	−	9.25398i	0.124717	−	0.312129i
$880$		0			0
$881$	−30.0526			−1.01250			−0.506249	−	0.862387i	$-0.668968\pi$
$881$	−30.0526			−1.01250			−0.506249	+	0.862387i	$0.668968\pi$
$882$		0			0
$883$	−16.8382			−0.566649			−0.283324	−	0.959024i	$-0.591437\pi$
$883$	−16.8382			−0.566649			−0.283324	+	0.959024i	$0.591437\pi$
$884$		0			0
$885$	−16.2307	+	40.6204i	−0.545587	+	1.36544i
$886$		0			0
$887$	13.3283	−	23.0853i	0.447520	−	0.775128i	−0.550704	−	0.834701i	$-0.685641\pi$
$887$	13.3283	−	23.0853i	0.447520	−	0.775128i	0.998224	+	0.0595728i	$0.0189738\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8.07891	−	12.4979i	−0.270654	−	0.418695i
$892$		0			0
$893$	−0.966369	+	0.557933i	−0.0323383	+	0.0186705i
$894$		0			0
$895$			7.78665i			0.260279i
$896$		0			0
$897$	1.76222	+	2.23778i	0.0588388	+	0.0747174i
$898$		0			0
$899$	6.19462	+	10.7294i	0.206602	+	0.357846i
$900$		0			0
$901$	51.0756	+	29.4885i	1.70157	+	0.982404i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.70321	−	0.983349i	−0.0566166	−	0.0326876i
$906$		0			0
$907$	−4.22753	−	7.32230i	−0.140373	−	0.243133i	0.787264	−	0.616616i	$-0.211497\pi$
$907$	−4.22753	−	7.32230i	−0.140373	−	0.243133i	−0.927637	+	0.373483i	$0.878163\pi$
$908$		0			0
$909$	2.86464	−	11.8771i	0.0950143	−	0.393938i
$910$		0			0
$911$		−	15.4171i		−	0.510792i	−0.966837	−	0.255396i	$-0.917794\pi$
$911$		−	15.4171i		−	0.510792i	0.966837	−	0.255396i	$-0.0822058\pi$
$912$		0			0
$913$	−9.52513	+	5.49934i	−0.315236	+	0.182002i
$914$		0			0
$915$	0.656206	+	4.54258i	0.0216935	+	0.150173i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	28.7933	−	49.8714i	0.949802	−	1.64511i	0.203964	−	0.978978i	$-0.434617\pi$
$919$	28.7933	−	49.8714i	0.949802	−	1.64511i	0.745838	−	0.666127i	$-0.232049\pi$
$920$		0			0
$921$	−38.4476	−	15.3625i	−1.26689	−	0.506210i
$922$		0			0
$923$	89.4776			2.94519
$924$		0			0
$925$	2.89891			0.0953156
$926$		0			0
$927$	−7.16007	−	24.2656i	−0.235167	−	0.796988i
$928$		0			0
$929$	−23.6879	+	41.0287i	−0.777176	+	1.34611i	0.156388	+	0.987696i	$0.450015\pi$
$929$	−23.6879	+	41.0287i	−0.777176	+	1.34611i	−0.933563	+	0.358412i	$0.883318\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	36.2699	−	5.23942i	1.18742	−	0.171531i
$934$		0			0
$935$	−28.0180	+	16.1762i	−0.916287	+	0.529019i
$936$		0			0
$937$		−	40.6136i		−	1.32679i	−0.748270	−	0.663394i	$-0.769115\pi$
$937$		−	40.6136i		−	1.32679i	0.748270	−	0.663394i	$-0.230885\pi$
$938$		0			0
$939$	−28.7327	+	22.6266i	−0.937657	+	0.738391i
$940$		0			0
$941$	14.9142	+	25.8322i	0.486189	+	0.842105i	0.999874	−	0.0158745i	$-0.00505322\pi$
$941$	14.9142	+	25.8322i	0.486189	+	0.842105i	−0.513685	+	0.857979i	$0.671720\pi$
$942$		0			0
$943$	1.06876	+	0.617048i	0.0348036	+	0.0200939i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.1139	+	20.2730i	1.14105	+	0.658785i	0.946690	−	0.322145i	$-0.104404\pi$
$947$	35.1139	+	20.2730i	1.14105	+	0.658785i	0.194359	+	0.980930i	$0.437737\pi$
$948$		0			0
$949$	10.8880	+	18.8585i	0.353439	+	0.612174i
$950$		0			0
$951$	21.7934	−	17.1620i	0.706701	−	0.556516i
$952$		0			0
$953$			36.7169i			1.18938i	0.803956	+	0.594688i	$0.202724\pi$
$953$			36.7169i			1.18938i	−0.803956	+	0.594688i	$0.797276\pi$
$954$		0			0
$955$	−2.72982	+	1.57606i	−0.0883348	+	0.0510001i
$956$		0			0
$957$	5.83513	−	0.842923i	0.188623	−	0.0272478i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.61057	−	4.52163i	0.0842118	−	0.145859i
$962$		0			0
$963$	12.3854	+	41.9742i	0.399112	+	1.35260i
$964$		0			0
$965$	−60.6536			−1.95251
$966$		0			0
$967$	30.1106			0.968290			0.484145	−	0.874988i	$-0.339131\pi$
$967$	30.1106			0.968290			0.484145	+	0.874988i	$0.339131\pi$
$968$		0			0
$969$	−36.4861	−	14.5787i	−1.17210	−	0.468336i
$970$		0			0
$971$	11.1290	−	19.2760i	0.357147	−	0.618597i	−0.630336	−	0.776322i	$-0.717083\pi$
$971$	11.1290	−	19.2760i	0.357147	−	0.618597i	0.987483	+	0.157726i	$0.0504162\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.33631	+	16.1731i	0.0748217	+	0.517953i
$976$		0			0
$977$	48.3918	−	27.9390i	1.54819	−	0.893849i	0.549912	−	0.835223i	$-0.314661\pi$
$977$	48.3918	−	27.9390i	1.54819	−	0.893849i	0.998280	−	0.0586266i	$-0.0186721\pi$
$978$		0			0
$979$		−	24.0000i		−	0.767044i
$980$		0			0
$981$	−12.1688	+	50.4529i	−0.388519	+	1.61084i
$982$		0			0
$983$	21.8878	+	37.9109i	0.698114	+	1.20917i	0.969120	+	0.246591i	$0.0793104\pi$
$983$	21.8878	+	37.9109i	0.698114	+	1.20917i	−0.271006	+	0.962578i	$0.587356\pi$
$984$		0			0
$985$	−32.9032	−	18.9966i	−1.04838	−	0.605284i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.614715	−	0.354906i	−0.0195468	−	0.0112853i
$990$		0			0
$991$	11.7736	+	20.3924i	0.374000	+	0.647787i	0.990177	−	0.139821i	$-0.0446528\pi$
$991$	11.7736	+	20.3924i	0.374000	+	0.647787i	−0.616177	+	0.787608i	$0.711319\pi$
$992$		0			0
$993$	−20.3384	−	25.8271i	−0.645420	−	0.819597i
$994$		0			0
$995$		−	17.7504i		−	0.562724i
$996$		0			0
$997$	16.4923	−	9.52186i	0.522318	−	0.301560i	−0.215565	−	0.976490i	$-0.569159\pi$
$997$	16.4923	−	9.52186i	0.522318	−	0.301560i	0.737882	+	0.674929i	$0.235826\pi$
$998$		0			0
$999$	−0.848765	+	9.07990i	−0.0268537	+	0.287275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.b.1097.3		16
3.2	odd	2	inner	1176.2.u.b.1097.1		16
7.2	even	3		1176.2.k.a.881.5		16
7.3	odd	6	inner	1176.2.u.b.521.1		16
7.4	even	3		168.2.u.a.17.8	yes	16
7.5	odd	6		1176.2.k.a.881.12		16
7.6	odd	2		168.2.u.a.89.6	yes	16
21.2	odd	6		1176.2.k.a.881.11		16
21.5	even	6		1176.2.k.a.881.6		16
21.11	odd	6		168.2.u.a.17.6	✓	16
21.17	even	6	inner	1176.2.u.b.521.3		16
21.20	even	2		168.2.u.a.89.8	yes	16
28.11	odd	6		336.2.bc.f.17.1		16
28.19	even	6		2352.2.k.i.881.5		16
28.23	odd	6		2352.2.k.i.881.12		16
28.27	even	2		336.2.bc.f.257.3		16
84.11	even	6		336.2.bc.f.17.3		16
84.23	even	6		2352.2.k.i.881.6		16
84.47	odd	6		2352.2.k.i.881.11		16
84.83	odd	2		336.2.bc.f.257.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.6	✓	16	21.11	odd	6
168.2.u.a.17.8	yes	16	7.4	even	3
168.2.u.a.89.6	yes	16	7.6	odd	2
168.2.u.a.89.8	yes	16	21.20	even	2
336.2.bc.f.17.1		16	28.11	odd	6
336.2.bc.f.17.3		16	84.11	even	6
336.2.bc.f.257.1		16	84.83	odd	2
336.2.bc.f.257.3		16	28.27	even	2
1176.2.k.a.881.5		16	7.2	even	3
1176.2.k.a.881.6		16	21.5	even	6
1176.2.k.a.881.11		16	21.2	odd	6
1176.2.k.a.881.12		16	7.5	odd	6
1176.2.u.b.521.1		16	7.3	odd	6	inner
1176.2.u.b.521.3		16	21.17	even	6	inner
1176.2.u.b.1097.1		16	3.2	odd	2	inner
1176.2.u.b.1097.3		16	1.1	even	1	trivial
2352.2.k.i.881.5		16	28.19	even	6
2352.2.k.i.881.6		16	84.23	even	6
2352.2.k.i.881.11		16	84.47	odd	6
2352.2.k.i.881.12		16	28.23	odd	6

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.642670 + 1.60841i) q^{3} +(-1.28955 + 2.23357i) q^{5} +(-2.17395 - 2.06735i) q^{9} +O(q^{10})\)	\(q+(-0.642670 + 1.60841i) q^{3} +(-1.28955 + 2.23357i) q^{5} +(-2.17395 - 2.06735i) q^{9} +(-1.43199 + 0.826762i) q^{11} +5.71177i q^{13} +(-2.76373 - 3.50957i) q^{15} +(-3.79313 - 6.56990i) q^{17} +(-2.58961 - 1.49511i) q^{19} +(-0.249340 - 0.143957i) q^{23} +(-0.825879 - 1.43046i) q^{25} +(4.72227 - 2.16798i) q^{27} +2.05856i q^{29} +(5.21209 - 3.00920i) q^{31} +(-0.409472 - 2.83457i) q^{33} +(-0.877523 + 1.51991i) q^{37} +(-9.18685 - 3.67078i) q^{39} -4.28635 q^{41} +2.46537 q^{43} +(7.42098 - 2.18971i) q^{45} +(0.186586 - 0.323176i) q^{47} +(13.0048 - 1.87863i) q^{51} +(-6.73264 + 3.88709i) q^{53} -4.26461i q^{55} +(4.06901 - 3.20429i) q^{57} +(-4.89610 - 8.48029i) q^{59} +(-0.889794 - 0.513723i) q^{61} +(-12.7576 - 7.36561i) q^{65} +(-1.18281 - 2.04868i) q^{67} +(0.391784 - 0.308524i) q^{69} -15.6655i q^{71} +(3.30170 - 1.90624i) q^{73} +(2.83154 - 0.409034i) q^{75} +(4.56033 - 7.89872i) q^{79} +(0.452128 + 8.98864i) q^{81} +6.65166 q^{83} +19.5657 q^{85} +(-3.31101 - 1.32298i) q^{87} +(-7.25723 + 12.5699i) q^{89} +(1.49037 + 10.3171i) q^{93} +(6.67886 - 3.85604i) q^{95} -4.43739i q^{97} +(4.82229 + 1.16309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^9	\( 16 q + 2 q^{9} + 8 q^{15} + 6 q^{19} - 18 q^{25} + 48 q^{31} + 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} + 42 q^{45} + 6 q^{51} - 8 q^{57} - 36 q^{61} + 14 q^{67} - 30 q^{73} - 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} + 16 q^{93} + 20 q^{99}+O(q^{100}) \) 16 * q + 2 * q^9 + 8 * q^15 + 6 * q^19 - 18 * q^25 + 48 * q^31 + 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 + 42 * q^45 + 6 * q^51 - 8 * q^57 - 36 * q^61 + 14 * q^67 - 30 * q^73 - 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 + 16 * q^93 + 20 * q^99

Introduction

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