LMFDB - Embedded newform 891.2.g.c.296.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(296,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.296"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-4,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			296.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	891.296
Dual form			891.2.g.c.593.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(2.12132 - 1.22474i) q^{7} +1.73205 q^{8} -2.44949i q^{10} +(1.58346 - 2.91421i) q^{11} +(-4.24264 - 2.44949i) q^{13} +(3.67423 + 2.12132i) q^{14} +(2.50000 + 4.33013i) q^{16} -7.34847i q^{19} +(1.22474 - 0.707107i) q^{20} +(5.74264 - 0.148586i) q^{22} +(2.44949 + 1.41421i) q^{23} +(-1.50000 - 2.59808i) q^{25} -8.48528i q^{26} +2.44949i q^{28} +(3.46410 + 6.00000i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-2.59808 + 4.50000i) q^{32} -3.46410 q^{35} +8.00000 q^{37} +(11.0227 - 6.36396i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(-3.46410 + 6.00000i) q^{41} +(2.12132 - 1.22474i) q^{43} +(1.73205 + 2.82843i) q^{44} +4.89898i q^{46} +(-2.44949 + 1.41421i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.59808 - 4.50000i) q^{50} +(4.24264 - 2.44949i) q^{52} +9.89949i q^{53} +(-4.00000 + 2.44949i) q^{55} +(3.67423 - 2.12132i) q^{56} +(-6.00000 + 10.3923i) q^{58} +(9.79796 + 5.65685i) q^{59} +(-4.24264 + 2.44949i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(3.46410 + 6.00000i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{70} -2.82843i q^{71} +(6.92820 + 12.0000i) q^{74} +(6.36396 + 3.67423i) q^{76} +(-0.210133 - 8.12132i) q^{77} +(-10.6066 + 6.12372i) q^{79} -7.07107i q^{80} -12.0000 q^{82} +(-6.92820 - 12.0000i) q^{83} +(3.67423 + 2.12132i) q^{86} +(2.74264 - 5.04757i) q^{88} -7.07107i q^{89} -12.0000 q^{91} +(-2.44949 + 1.41421i) q^{92} +(-4.24264 - 2.44949i) q^{94} +(-5.19615 + 9.00000i) q^{95} +(5.00000 + 8.66025i) q^{97} -1.73205 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 20 q^{16} + 12 q^{22} - 12 q^{25} + 16 q^{31} + 64 q^{37} - 4 q^{49} - 32 q^{55} - 48 q^{58} + 8 q^{64} + 16 q^{67} - 24 q^{70} - 96 q^{82} - 12 q^{88} - 96 q^{91} + 40 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 + 20 * q^16 + 12 * q^22 - 12 * q^25 + 16 * q^31 + 64 * q^37 - 4 * q^49 - 32 * q^55 - 48 * q^58 + 8 * q^64 + 16 * q^67 - 24 * q^70 - 96 * q^82 - 12 * q^88 - 96 * q^91 + 40 * q^97

Character values

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

$n$	$244$	$650$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	0.200480	−	0.979698i	$-0.435750\pi$
$5$	−1.22474	−	0.707107i	−0.547723	−	0.316228i	−0.748203	+	0.663470i	$0.769083\pi$
$6$		0			0
$7$	2.12132	−	1.22474i	0.801784	−	0.462910i	−0.0423108	−	0.999104i	$-0.513472\pi$
$7$	2.12132	−	1.22474i	0.801784	−	0.462910i	0.844094	+	0.536194i	$0.180139\pi$
$8$	1.73205			0.612372
$9$		0			0
$10$		−	2.44949i		−	0.774597i
$11$	1.58346	−	2.91421i	0.477432	−	0.878668i
$11$	1.58346	−	2.91421i	0.477432	−	0.878668i
$12$		0			0
$13$	−4.24264	−	2.44949i	−1.17670	−	0.679366i	−0.221449	−	0.975172i	$-0.571079\pi$
$13$	−4.24264	−	2.44949i	−1.17670	−	0.679366i	−0.955248	+	0.295806i	$0.904412\pi$
$14$	3.67423	+	2.12132i	0.981981	+	0.566947i
$15$		0			0
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		−	7.34847i		−	1.68585i	−0.538028	−	0.842927i	$-0.680830\pi$
$19$		−	7.34847i		−	1.68585i	0.538028	−	0.842927i	$-0.319170\pi$
$20$	1.22474	−	0.707107i	0.273861	−	0.158114i
$21$		0			0
$22$	5.74264	−	0.148586i	1.22434	−	0.0316787i
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	0.733144	−	0.680074i	$-0.238052\pi$
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	−0.222390	+	0.974958i	$0.571386\pi$
$24$		0			0
$25$	−1.50000	−	2.59808i	−0.300000	−	0.519615i
$26$		−	8.48528i		−	1.66410i
$27$		0			0
$28$			2.44949i			0.462910i
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	0.984699	+	0.174265i	$0.0557550\pi$
$29$	3.46410	+	6.00000i	0.643268	+	1.11417i	−0.341431	+	0.939907i	$0.610912\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$		0			0
$34$		0			0
$35$	−3.46410			−0.585540
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	11.0227	−	6.36396i	1.78812	−	1.03237i
$39$		0			0
$40$	−2.12132	−	1.22474i	−0.335410	−	0.193649i
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	0.457845	+	0.889032i	$0.348621\pi$
$41$	−3.46410	+	6.00000i	−0.541002	+	0.937043i	−0.998847	+	0.0480106i	$0.984712\pi$
$42$		0			0
$43$	2.12132	−	1.22474i	0.323498	−	0.186772i	−0.329452	−	0.944172i	$-0.606864\pi$
$43$	2.12132	−	1.22474i	0.323498	−	0.186772i	0.652951	+	0.757400i	$0.273531\pi$
$44$	1.73205	+	2.82843i	0.261116	+	0.426401i
$45$		0			0
$46$			4.89898i			0.722315i
$47$	−2.44949	+	1.41421i	−0.357295	+	0.206284i	−0.667893	−	0.744257i	$-0.732804\pi$
$47$	−2.44949	+	1.41421i	−0.357295	+	0.206284i	0.310599	+	0.950541i	$0.399470\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.59808	−	4.50000i	0.367423	−	0.636396i
$51$		0			0
$52$	4.24264	−	2.44949i	0.588348	−	0.339683i
$53$			9.89949i			1.35980i	0.733305	+	0.679900i	$0.237977\pi$
$53$			9.89949i			1.35980i	−0.733305	+	0.679900i	$0.762023\pi$
$54$		0			0
$55$	−4.00000	+	2.44949i	−0.539360	+	0.330289i
$56$	3.67423	−	2.12132i	0.490990	−	0.283473i
$57$		0			0
$58$	−6.00000	+	10.3923i	−0.787839	+	1.36458i
$59$	9.79796	+	5.65685i	1.27559	+	0.736460i	0.976034	−	0.217620i	$-0.0698294\pi$
$59$	9.79796	+	5.65685i	1.27559	+	0.736460i	0.299552	+	0.954080i	$0.403163\pi$
$60$		0			0
$61$	−4.24264	+	2.44949i	−0.543214	+	0.313625i	−0.746381	−	0.665519i	$-0.768210\pi$
$61$	−4.24264	+	2.44949i	−0.543214	+	0.313625i	0.203166	+	0.979144i	$0.434877\pi$
$62$	6.92820			0.879883
$63$		0			0
$64$	1.00000			0.125000
$65$	3.46410	+	6.00000i	0.429669	+	0.744208i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$		0			0
$69$		0			0
$70$	−3.00000	−	5.19615i	−0.358569	−	0.621059i
$71$		−	2.82843i		−	0.335673i	−0.985815	−	0.167836i	$-0.946322\pi$
$71$		−	2.82843i		−	0.335673i	0.985815	−	0.167836i	$-0.0536780\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	6.92820	+	12.0000i	0.805387	+	1.39497i
$75$		0			0
$76$	6.36396	+	3.67423i	0.729996	+	0.421464i
$77$	−0.210133	−	8.12132i	−0.0239469	−	0.925510i
$78$		0			0
$79$	−10.6066	+	6.12372i	−1.19334	+	0.688973i	−0.959062	−	0.283198i	$-0.908605\pi$
$79$	−10.6066	+	6.12372i	−1.19334	+	0.688973i	−0.234274	+	0.972171i	$0.575271\pi$
$80$		−	7.07107i		−	0.790569i
$81$		0			0
$82$	−12.0000			−1.32518
$83$	−6.92820	−	12.0000i	−0.760469	−	1.31717i	−0.942609	−	0.333899i	$-0.891636\pi$
$83$	−6.92820	−	12.0000i	−0.760469	−	1.31717i	0.182140	−	0.983273i	$-0.441698\pi$
$84$		0			0
$85$		0			0
$86$	3.67423	+	2.12132i	0.396203	+	0.228748i
$87$		0			0
$88$	2.74264	−	5.04757i	0.292366	−	0.538072i
$89$		−	7.07107i		−	0.749532i	−0.927119	−	0.374766i	$-0.877723\pi$
$89$		−	7.07107i		−	0.749532i	0.927119	−	0.374766i	$-0.122277\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$	−2.44949	+	1.41421i	−0.255377	+	0.147442i
$93$		0			0
$94$	−4.24264	−	2.44949i	−0.437595	−	0.252646i
$95$	−5.19615	+	9.00000i	−0.533114	+	0.923381i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	−1.73205			−0.174964
$99$		0			0
$100$	3.00000			0.300000
$101$	−6.92820	−	12.0000i	−0.689382	−	1.19404i	−0.972038	−	0.234823i	$-0.924549\pi$
$101$	−6.92820	−	12.0000i	−0.689382	−	1.19404i	0.282656	−	0.959221i	$-0.408784\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−7.34847	−	4.24264i	−0.720577	−	0.416025i
$105$		0			0
$106$	−14.8492	+	8.57321i	−1.44229	+	0.832704i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$			14.6969i			1.40771i	0.710343	+	0.703856i	$0.248540\pi$
$109$			14.6969i			1.40771i	−0.710343	+	0.703856i	$0.751460\pi$
$110$	−7.13834	−	3.87868i	−0.680614	−	0.369818i
$111$		0			0
$112$	10.6066	+	6.12372i	1.00223	+	0.578638i
$113$	−1.22474	−	0.707107i	−0.115214	−	0.0665190i	0.441285	−	0.897367i	$-0.354523\pi$
$113$	−1.22474	−	0.707107i	−0.115214	−	0.0665190i	−0.556500	+	0.830848i	$0.687856\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	−6.92820			−0.643268
$117$		0			0
$118$			19.5959i			1.80395i
$119$		0			0
$120$		0			0
$121$	−5.98528	−	9.22911i	−0.544116	−	0.839010i
$122$	−7.34847	−	4.24264i	−0.665299	−	0.384111i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$			11.3137i			1.01193i
$126$		0			0
$127$		−	7.34847i		−	0.652071i	−0.945357	−	0.326036i	$-0.894287\pi$
$127$		−	7.34847i		−	0.652071i	0.945357	−	0.326036i	$-0.105713\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$		0			0
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	−0.780387	−	0.625297i	$-0.784978\pi$
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	0.931717	+	0.363186i	$0.118311\pi$
$132$		0			0
$133$	−9.00000	−	15.5885i	−0.780399	−	1.35169i
$134$	6.92820			0.598506
$135$		0			0
$136$		0			0
$137$	−13.4722	+	7.77817i	−1.15101	+	0.664534i	−0.949132	−	0.314877i	$-0.898037\pi$
$137$	−13.4722	+	7.77817i	−1.15101	+	0.664534i	−0.201875	+	0.979411i	$0.564703\pi$
$138$		0			0
$139$	2.12132	+	1.22474i	0.179928	+	0.103882i	0.587259	−	0.809399i	$-0.300207\pi$
$139$	2.12132	+	1.22474i	0.179928	+	0.103882i	−0.407331	+	0.913281i	$0.633540\pi$
$140$	1.73205	−	3.00000i	0.146385	−	0.253546i
$141$		0			0
$142$	4.24264	−	2.44949i	0.356034	−	0.205557i
$143$	−13.8564	+	8.48528i	−1.15873	+	0.709575i
$144$		0			0
$145$		−	9.79796i		−	0.813676i
$146$		0			0
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	6.92820	−	12.0000i	0.567581	−	0.983078i	−0.429224	−	0.903198i	$-0.641213\pi$
$149$	6.92820	−	12.0000i	0.567581	−	0.983078i	0.996804	−	0.0798802i	$-0.0254538\pi$
$150$		0			0
$151$	2.12132	−	1.22474i	0.172631	−	0.0996683i	−0.411195	−	0.911547i	$-0.634888\pi$
$151$	2.12132	−	1.22474i	0.172631	−	0.0996683i	0.583826	+	0.811879i	$0.301555\pi$
$152$		−	12.7279i		−	1.03237i
$153$		0			0
$154$	12.0000	−	7.34847i	0.966988	−	0.592157i
$155$	−4.89898	+	2.82843i	−0.393496	+	0.227185i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−18.3712	−	10.6066i	−1.46153	−	0.843816i
$159$		0			0
$160$	6.36396	−	3.67423i	0.503115	−	0.290474i
$161$	6.92820			0.546019
$162$		0			0
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−3.46410	−	6.00000i	−0.270501	−	0.468521i
$165$		0			0
$166$	12.0000	−	20.7846i	0.931381	−	1.61320i
$167$	1.73205	−	3.00000i	0.134030	−	0.232147i	−0.791196	−	0.611562i	$-0.790541\pi$
$167$	1.73205	−	3.00000i	0.134030	−	0.232147i	0.925227	+	0.379415i	$0.123875\pi$
$168$		0			0
$169$	5.50000	+	9.52628i	0.423077	+	0.732791i
$170$		0			0
$171$		0			0
$172$			2.44949i			0.186772i
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	0.967135	−	0.254262i	$-0.0818324\pi$
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	−0.703765	+	0.710433i	$0.748499\pi$
$174$		0			0
$175$	−6.36396	−	3.67423i	−0.481070	−	0.277746i
$176$	16.5776	−	0.428932i	1.24958	−	0.0323320i
$177$		0			0
$178$	10.6066	−	6.12372i	0.794998	−	0.458993i
$179$			22.6274i			1.69125i	0.533775	+	0.845626i	$0.320773\pi$
$179$			22.6274i			1.69125i	−0.533775	+	0.845626i	$0.679227\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−10.3923	−	18.0000i	−0.770329	−	1.33425i
$183$		0			0
$184$	4.24264	+	2.44949i	0.312772	+	0.180579i
$185$	−9.79796	−	5.65685i	−0.720360	−	0.415900i
$186$		0			0
$187$		0			0
$188$		−	2.82843i		−	0.206284i
$189$		0			0
$190$	−18.0000			−1.30586
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	8.48528	+	4.89898i	0.610784	+	0.352636i	0.773272	−	0.634074i	$-0.218619\pi$
$193$	8.48528	+	4.89898i	0.610784	+	0.352636i	−0.162488	+	0.986710i	$0.551952\pi$
$194$	−8.66025	+	15.0000i	−0.621770	+	1.07694i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−2.59808	−	4.50000i	−0.183712	−	0.318198i
$201$		0			0
$202$	12.0000	−	20.7846i	0.844317	−	1.46240i
$203$	14.6969	+	8.48528i	1.03152	+	0.595550i
$204$		0			0
$205$	8.48528	−	4.89898i	0.592638	−	0.342160i
$206$	6.92820			0.482711
$207$		0			0
$208$		−	24.4949i		−	1.69842i
$209$	−21.4150	−	11.6360i	−1.48131	−	0.804882i
$210$		0			0
$211$	−10.6066	−	6.12372i	−0.730189	−	0.421575i	0.0883026	−	0.996094i	$-0.471856\pi$
$211$	−10.6066	−	6.12372i	−0.730189	−	0.421575i	−0.818491	+	0.574519i	$0.805189\pi$
$212$	−8.57321	−	4.94975i	−0.588811	−	0.339950i
$213$		0			0
$214$		0			0
$215$	−3.46410			−0.236250
$216$		0			0
$217$		−	9.79796i		−	0.665129i
$218$	−22.0454	+	12.7279i	−1.49310	+	0.862044i
$219$		0			0
$220$	−0.121320	−	4.68885i	−0.00817942	−	0.316122i
$221$		0			0
$222$		0			0
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$			12.7279i			0.850420i
$225$		0			0
$226$		−	2.44949i		−	0.162938i
$227$	13.8564	+	24.0000i	0.919682	+	1.59294i	0.799898	+	0.600136i	$0.204887\pi$
$227$	13.8564	+	24.0000i	0.919682	+	1.59294i	0.119784	+	0.992800i	$0.461780\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	3.46410	−	6.00000i	0.228416	−	0.395628i
$231$		0			0
$232$	6.00000	+	10.3923i	0.393919	+	0.682288i
$233$	−20.7846			−1.36165			−0.680823	−	0.732448i	$-0.738378\pi$
$233$	−20.7846			−1.36165			−0.680823	+	0.732448i	$0.738378\pi$
$234$		0			0
$235$	4.00000			0.260931
$236$	−9.79796	+	5.65685i	−0.637793	+	0.368230i
$237$		0			0
$238$		0			0
$239$	−8.66025	+	15.0000i	−0.560185	+	0.970269i	0.437295	+	0.899318i	$0.355937\pi$
$239$	−8.66025	+	15.0000i	−0.560185	+	0.970269i	−0.997480	+	0.0709510i	$0.977397\pi$
$240$		0			0
$241$	−16.9706	+	9.79796i	−1.09317	+	0.631142i	−0.934419	−	0.356177i	$-0.884080\pi$
$241$	−16.9706	+	9.79796i	−1.09317	+	0.631142i	−0.158751	+	0.987319i	$0.550747\pi$
$242$	8.66025	−	16.9706i	0.556702	−	1.09091i
$243$		0			0
$244$		−	4.89898i		−	0.313625i
$245$	1.22474	−	0.707107i	0.0782461	−	0.0451754i
$246$		0			0
$247$	−18.0000	+	31.1769i	−1.14531	+	1.98374i
$248$	3.46410	−	6.00000i	0.219971	−	0.381000i
$249$		0			0
$250$	−16.9706	+	9.79796i	−1.07331	+	0.619677i
$251$			5.65685i			0.357057i	0.983935	+	0.178529i	$0.0571337\pi$
$251$			5.65685i			0.357057i	−0.983935	+	0.178529i	$0.942866\pi$
$252$		0			0
$253$	8.00000	−	4.89898i	0.502956	−	0.307996i
$254$	11.0227	−	6.36396i	0.691626	−	0.399310i
$255$		0			0
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−8.57321	−	4.94975i	−0.534782	−	0.308757i	0.208179	−	0.978091i	$-0.433246\pi$
$257$	−8.57321	−	4.94975i	−0.534782	−	0.308757i	−0.742962	+	0.669334i	$0.766580\pi$
$258$		0			0
$259$	16.9706	−	9.79796i	1.05450	−	0.608816i
$260$	−6.92820			−0.429669
$261$		0			0
$262$	6.00000			0.370681
$263$	−1.73205	−	3.00000i	−0.106803	−	0.184988i	0.807671	−	0.589634i	$-0.200728\pi$
$263$	−1.73205	−	3.00000i	−0.106803	−	0.184988i	−0.914473	+	0.404646i	$0.867395\pi$
$264$		0			0
$265$	7.00000	−	12.1244i	0.430007	−	0.744793i
$266$	15.5885	−	27.0000i	0.955790	−	1.65548i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$		−	15.5563i		−	0.948487i	−0.880394	−	0.474244i	$-0.842722\pi$
$269$		−	15.5563i		−	0.948487i	0.880394	−	0.474244i	$-0.157278\pi$
$270$		0			0
$271$			7.34847i			0.446388i	0.974774	+	0.223194i	$0.0716483\pi$
$271$			7.34847i			0.446388i	−0.974774	+	0.223194i	$0.928352\pi$
$272$		0			0
$273$		0			0
$274$	−23.3345	−	13.4722i	−1.40969	−	0.813885i
$275$	−9.94655	+	0.257359i	−0.599799	+	0.0155194i
$276$		0			0
$277$	21.2132	−	12.2474i	1.27458	−	0.735878i	0.298732	−	0.954337i	$-0.403436\pi$
$277$	21.2132	−	12.2474i	1.27458	−	0.735878i	0.975846	+	0.218459i	$0.0701031\pi$
$278$			4.24264i			0.254457i
$279$		0			0
$280$	−6.00000			−0.358569
$281$	−6.92820	−	12.0000i	−0.413302	−	0.715860i	0.581947	−	0.813227i	$-0.302291\pi$
$281$	−6.92820	−	12.0000i	−0.413302	−	0.715860i	−0.995249	+	0.0973670i	$0.968958\pi$
$282$		0			0
$283$	2.12132	+	1.22474i	0.126099	+	0.0728035i	0.561723	−	0.827325i	$-0.310139\pi$
$283$	2.12132	+	1.22474i	0.126099	+	0.0728035i	−0.435623	+	0.900129i	$0.643472\pi$
$284$	2.44949	+	1.41421i	0.145350	+	0.0839181i
$285$		0			0
$286$	−24.7279	−	13.4361i	−1.46219	−	0.794496i
$287$			16.9706i			1.00174i
$288$		0			0
$289$	−17.0000			−1.00000
$290$	14.6969	−	8.48528i	0.863034	−	0.498273i
$291$		0			0
$292$		0			0
$293$	−3.46410	+	6.00000i	−0.202375	+	0.350524i	−0.949293	−	0.314392i	$-0.898199\pi$
$293$	−3.46410	+	6.00000i	−0.202375	+	0.350524i	0.746918	+	0.664916i	$0.231533\pi$
$294$		0			0
$295$	−8.00000	−	13.8564i	−0.465778	−	0.806751i
$296$	13.8564			0.805387
$297$		0			0
$298$	24.0000			1.39028
$299$	−6.92820	−	12.0000i	−0.400668	−	0.693978i
$300$		0			0
$301$	3.00000	−	5.19615i	0.172917	−	0.299501i
$302$	3.67423	+	2.12132i	0.211428	+	0.122068i
$303$		0			0
$304$	31.8198	−	18.3712i	1.82499	−	1.05366i
$305$	6.92820			0.396708
$306$		0			0
$307$		−	7.34847i		−	0.419399i	−0.977766	−	0.209700i	$-0.932751\pi$
$307$		−	7.34847i		−	0.419399i	0.977766	−	0.209700i	$-0.0672486\pi$
$308$	7.13834	+	3.87868i	0.406744	+	0.221008i
$309$		0			0
$310$	−8.48528	−	4.89898i	−0.481932	−	0.278243i
$311$	−12.2474	−	7.07107i	−0.694489	−	0.400963i	0.110802	−	0.993842i	$-0.464658\pi$
$311$	−12.2474	−	7.07107i	−0.694489	−	0.400963i	−0.805292	+	0.592879i	$0.797991\pi$
$312$		0			0
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$	−24.2487			−1.36843
$315$		0			0
$316$		−	12.2474i		−	0.688973i
$317$	15.9217	−	9.19239i	0.894251	−	0.516296i	0.0189203	−	0.999821i	$-0.493977\pi$
$317$	15.9217	−	9.19239i	0.894251	−	0.516296i	0.875331	+	0.483525i	$0.160644\pi$
$318$		0			0
$319$	22.9706	−	0.594346i	1.28610	−	0.0332770i
$320$	−1.22474	−	0.707107i	−0.0684653	−	0.0395285i
$321$		0			0
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$		0			0
$324$		0			0
$325$			14.6969i			0.815239i
$326$	6.92820	+	12.0000i	0.383718	+	0.664619i
$327$		0			0
$328$	−6.00000	+	10.3923i	−0.331295	+	0.573819i
$329$	−3.46410	+	6.00000i	−0.190982	+	0.330791i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	13.8564			0.760469
$333$		0			0
$334$	6.00000			0.328305
$335$	−4.89898	+	2.82843i	−0.267660	+	0.154533i
$336$		0			0
$337$	8.48528	+	4.89898i	0.462223	+	0.266864i	0.712978	−	0.701186i	$-0.247346\pi$
$337$	8.48528	+	4.89898i	0.462223	+	0.266864i	−0.250756	+	0.968050i	$0.580679\pi$
$338$	−9.52628	+	16.5000i	−0.518161	+	0.897482i
$339$		0			0
$340$		0			0
$341$	−6.92820	−	11.3137i	−0.375183	−	0.612672i
$342$		0			0
$343$			19.5959i			1.05808i
$344$	3.67423	−	2.12132i	0.198101	−	0.114374i
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	6.92820	−	12.0000i	0.371925	−	0.644194i	−0.617936	−	0.786228i	$-0.712031\pi$
$347$	6.92820	−	12.0000i	0.371925	−	0.644194i	0.989862	+	0.142034i	$0.0453644\pi$
$348$		0			0
$349$	−4.24264	+	2.44949i	−0.227103	+	0.131118i	−0.609235	−	0.792990i	$-0.708523\pi$
$349$	−4.24264	+	2.44949i	−0.227103	+	0.131118i	0.382132	+	0.924108i	$0.375190\pi$
$350$		−	12.7279i		−	0.680336i
$351$		0			0
$352$	9.00000	+	14.6969i	0.479702	+	0.783349i
$353$	−28.1691	+	16.2635i	−1.49929	+	0.865616i	−1.00000		0.000817391i	$-0.999740\pi$
$353$	−28.1691	+	16.2635i	−1.49929	+	0.865616i	−0.499292	+	0.866434i	$0.666406\pi$
$354$		0			0
$355$	−2.00000	+	3.46410i	−0.106149	+	0.183855i
$356$	6.12372	+	3.53553i	0.324557	+	0.187383i
$357$		0			0
$358$	−33.9411	+	19.5959i	−1.79384	+	1.03568i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−35.0000			−1.84211
$362$	6.92820	+	12.0000i	0.364138	+	0.630706i
$363$		0			0
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$		0			0
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$			14.1421i			0.737210i
$369$		0			0
$370$		−	19.5959i		−	1.01874i
$371$	12.1244	+	21.0000i	0.629465	+	1.09027i
$372$		0			0
$373$	21.2132	+	12.2474i	1.09838	+	0.634149i	0.935795	−	0.352546i	$-0.114684\pi$
$373$	21.2132	+	12.2474i	1.09838	+	0.634149i	0.162584	+	0.986695i	$0.448017\pi$
$374$		0			0
$375$		0			0
$376$	−4.24264	+	2.44949i	−0.218797	+	0.126323i
$377$		−	33.9411i		−	1.74806i
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−5.19615	−	9.00000i	−0.266557	−	0.461690i
$381$		0			0
$382$	−4.24264	−	2.44949i	−0.217072	−	0.125327i
$383$	31.8434	+	18.3848i	1.62712	+	0.939418i	0.984947	+	0.172859i	$0.0553004\pi$
$383$	31.8434	+	18.3848i	1.62712	+	0.939418i	0.642173	+	0.766559i	$0.278033\pi$
$384$		0			0
$385$	−5.48528	+	10.0951i	−0.279556	+	0.514496i
$386$			16.9706i			0.863779i
$387$		0			0
$388$	−10.0000			−0.507673
$389$	8.57321	−	4.94975i	0.434679	−	0.250962i	−0.266659	−	0.963791i	$-0.585920\pi$
$389$	8.57321	−	4.94975i	0.434679	−	0.250962i	0.701338	+	0.712829i	$0.252586\pi$
$390$		0			0
$391$		0			0
$392$	−0.866025	+	1.50000i	−0.0437409	+	0.0757614i
$393$		0			0
$394$		0			0
$395$	17.3205			0.871489
$396$		0			0
$397$	8.00000			0.401508			0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000			0.401508			0.200754	+	0.979642i	$0.435661\pi$
$398$	6.92820	+	12.0000i	0.347279	+	0.601506i
$399$		0			0
$400$	7.50000	−	12.9904i	0.375000	−	0.649519i
$401$	−1.22474	−	0.707107i	−0.0611608	−	0.0353112i	0.469108	−	0.883141i	$-0.344576\pi$
$401$	−1.22474	−	0.707107i	−0.0611608	−	0.0353112i	−0.530269	+	0.847830i	$0.677909\pi$
$402$		0			0
$403$	−16.9706	+	9.79796i	−0.845364	+	0.488071i
$404$	13.8564			0.689382
$405$		0			0
$406$			29.3939i			1.45879i
$407$	12.6677	−	23.3137i	0.627915	−	1.15562i
$408$		0			0
$409$	33.9411	+	19.5959i	1.67828	+	0.968956i	0.962757	+	0.270367i	$0.0871450\pi$
$409$	33.9411	+	19.5959i	1.67828	+	0.968956i	0.715523	+	0.698589i	$0.246188\pi$
$410$	14.6969	+	8.48528i	0.725830	+	0.419058i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	27.7128			1.36366
$414$		0			0
$415$			19.5959i			0.961926i
$416$	22.0454	−	12.7279i	1.08087	−	0.624038i
$417$		0			0
$418$	−1.09188	−	42.1996i	−0.0534057	−	2.06405i
$419$	9.79796	+	5.65685i	0.478662	+	0.276355i	0.719859	−	0.694121i	$-0.244207\pi$
$419$	9.79796	+	5.65685i	0.478662	+	0.276355i	−0.241197	+	0.970476i	$0.577540\pi$
$420$		0			0
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	0.751935	−	0.659237i	$-0.229121\pi$
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	−0.946883	+	0.321577i	$0.895787\pi$
$422$		−	21.2132i		−	1.03264i
$423$		0			0
$424$			17.1464i			0.832704i
$425$		0			0
$426$		0			0
$427$	−6.00000	+	10.3923i	−0.290360	+	0.502919i
$428$		0			0
$429$		0			0
$430$	−3.00000	−	5.19615i	−0.144673	−	0.250581i
$431$	−10.3923			−0.500580			−0.250290	−	0.968171i	$-0.580526\pi$
$431$	−10.3923			−0.500580			−0.250290	+	0.968171i	$0.580526\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	14.6969	−	8.48528i	0.705476	−	0.407307i
$435$		0			0
$436$	−12.7279	−	7.34847i	−0.609557	−	0.351928i
$437$	10.3923	−	18.0000i	0.497131	−	0.861057i
$438$		0			0
$439$	2.12132	−	1.22474i	0.101245	−	0.0584539i	−0.448523	−	0.893772i	$-0.648050\pi$
$439$	2.12132	−	1.22474i	0.101245	−	0.0584539i	0.549768	+	0.835318i	$0.314716\pi$
$440$	−6.92820	+	4.24264i	−0.330289	+	0.202260i
$441$		0			0
$442$		0			0
$443$	19.5959	−	11.3137i	0.931030	−	0.537531i	0.0438929	−	0.999036i	$-0.486024\pi$
$443$	19.5959	−	11.3137i	0.931030	−	0.537531i	0.887137	+	0.461506i	$0.152691\pi$
$444$		0			0
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	−13.8564	+	24.0000i	−0.656120	+	1.13643i
$447$		0			0
$448$	2.12132	−	1.22474i	0.100223	−	0.0578638i
$449$			9.89949i			0.467186i	0.972334	+	0.233593i	$0.0750483\pi$
$449$			9.89949i			0.467186i	−0.972334	+	0.233593i	$0.924952\pi$
$450$		0			0
$451$	12.0000	+	19.5959i	0.565058	+	0.922736i
$452$	1.22474	−	0.707107i	0.0576072	−	0.0332595i
$453$		0			0
$454$	−24.0000	+	41.5692i	−1.12638	+	1.95094i
$455$	14.6969	+	8.48528i	0.689003	+	0.397796i
$456$		0			0
$457$	8.48528	−	4.89898i	0.396925	−	0.229165i	−0.288231	−	0.957561i	$-0.593067\pi$
$457$	8.48528	−	4.89898i	0.396925	−	0.229165i	0.685156	+	0.728396i	$0.259734\pi$
$458$	17.3205			0.809334
$459$		0			0
$460$	4.00000			0.186501
$461$	3.46410	+	6.00000i	0.161339	+	0.279448i	0.935349	−	0.353726i	$-0.115085\pi$
$461$	3.46410	+	6.00000i	0.161339	+	0.279448i	−0.774010	+	0.633173i	$0.781752\pi$
$462$		0			0
$463$	14.0000	−	24.2487i	0.650635	−	1.12693i	−0.332334	−	0.943162i	$-0.607836\pi$
$463$	14.0000	−	24.2487i	0.650635	−	1.12693i	0.982969	−	0.183771i	$-0.0588306\pi$
$464$	−17.3205	+	30.0000i	−0.804084	+	1.39272i
$465$		0			0
$466$	−18.0000	−	31.1769i	−0.833834	−	1.44424i
$467$			22.6274i			1.04707i	0.852004	+	0.523536i	$0.175387\pi$
$467$			22.6274i			1.04707i	−0.852004	+	0.523536i	$0.824613\pi$
$468$		0			0
$469$		−	9.79796i		−	0.452428i
$470$	3.46410	+	6.00000i	0.159787	+	0.276759i
$471$		0			0
$472$	16.9706	+	9.79796i	0.781133	+	0.450988i
$473$	−0.210133	−	8.12132i	−0.00966193	−	0.373419i
$474$		0			0
$475$	−19.0919	+	11.0227i	−0.875996	+	0.505756i
$476$		0			0
$477$		0			0
$478$	−30.0000			−1.37217
$479$	19.0526	+	33.0000i	0.870534	+	1.50781i	0.861446	+	0.507850i	$0.169560\pi$
$479$	19.0526	+	33.0000i	0.870534	+	1.50781i	0.00908799	+	0.999959i	$0.497107\pi$
$480$		0			0
$481$	−33.9411	−	19.5959i	−1.54758	−	0.893497i
$482$	−29.3939	−	16.9706i	−1.33885	−	0.772988i
$483$		0			0
$484$	10.9853	−	0.568852i	0.499331	−	0.0258569i
$485$		−	14.1421i		−	0.642161i
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	−7.34847	+	4.24264i	−0.332650	+	0.192055i
$489$		0			0
$490$	2.12132	+	1.22474i	0.0958315	+	0.0553283i
$491$	−13.8564	+	24.0000i	−0.625331	+	1.08310i	0.363146	+	0.931732i	$0.381703\pi$
$491$	−13.8564	+	24.0000i	−0.625331	+	1.08310i	−0.988477	+	0.151373i	$0.951631\pi$
$492$		0			0
$493$		0			0
$494$	−62.3538			−2.80543
$495$		0			0
$496$	20.0000			0.898027
$497$	−3.46410	−	6.00000i	−0.155386	−	0.269137i
$498$		0			0
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−9.79796	−	5.65685i	−0.438178	−	0.252982i
$501$		0			0
$502$	−8.48528	+	4.89898i	−0.378717	+	0.218652i
$503$	−31.1769			−1.39011			−0.695055	−	0.718957i	$-0.744620\pi$
$503$	−31.1769			−1.39011			−0.695055	+	0.718957i	$0.744620\pi$
$504$		0			0
$505$			19.5959i			0.872007i
$506$	14.2767	+	7.75736i	0.634676	+	0.344857i
$507$		0			0
$508$	6.36396	+	3.67423i	0.282355	+	0.163018i
$509$	13.4722	+	7.77817i	0.597144	+	0.344762i	0.767917	−	0.640549i	$-0.221293\pi$
$509$	13.4722	+	7.77817i	0.597144	+	0.344762i	−0.170773	+	0.985310i	$0.554626\pi$
$510$		0			0
$511$		0			0
$512$	−8.66025			−0.382733
$513$		0			0
$514$		−	17.1464i		−	0.756297i
$515$	−4.89898	+	2.82843i	−0.215875	+	0.124635i
$516$		0			0
$517$	0.242641	+	9.37769i	0.0106713	+	0.412430i
$518$	29.3939	+	16.9706i	1.29149	+	0.745644i
$519$		0			0
$520$	6.00000	+	10.3923i	0.263117	+	0.455733i
$521$		−	15.5563i		−	0.681536i	−0.940147	−	0.340768i	$-0.889313\pi$
$521$		−	15.5563i		−	0.681536i	0.940147	−	0.340768i	$-0.110687\pi$
$522$		0			0
$523$		−	22.0454i		−	0.963978i	−0.876177	−	0.481989i	$-0.839914\pi$
$523$		−	22.0454i		−	0.963978i	0.876177	−	0.481989i	$-0.160086\pi$
$524$	1.73205	+	3.00000i	0.0756650	+	0.131056i
$525$		0			0
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$		0			0
$528$		0			0
$529$	−7.50000	−	12.9904i	−0.326087	−	0.564799i
$530$	24.2487			1.05330
$531$		0			0
$532$	18.0000			0.780399
$533$	29.3939	−	16.9706i	1.27319	−	0.735077i
$534$		0			0
$535$		0			0
$536$	3.46410	−	6.00000i	0.149626	−	0.259161i
$537$		0			0
$538$	23.3345	−	13.4722i	1.00602	−	0.580828i
$539$	1.73205	+	2.82843i	0.0746047	+	0.121829i
$540$		0			0
$541$		−	14.6969i		−	0.631871i	−0.948781	−	0.315935i	$-0.897682\pi$
$541$		−	14.6969i		−	0.631871i	0.948781	−	0.315935i	$-0.102318\pi$
$542$	−11.0227	+	6.36396i	−0.473466	+	0.273356i
$543$		0			0
$544$		0			0
$545$	10.3923	−	18.0000i	0.445157	−	0.771035i
$546$		0			0
$547$	27.5772	−	15.9217i	1.17911	−	0.680762i	0.223305	−	0.974749i	$-0.428315\pi$
$547$	27.5772	−	15.9217i	1.17911	−	0.680762i	0.955810	+	0.293987i	$0.0949821\pi$
$548$		−	15.5563i		−	0.664534i
$549$		0			0
$550$	−9.00000	−	14.6969i	−0.383761	−	0.626680i
$551$	44.0908	−	25.4558i	1.87833	−	1.08446i
$552$		0			0
$553$	−15.0000	+	25.9808i	−0.637865	+	1.10481i
$554$	36.7423	+	21.2132i	1.56103	+	0.901263i
$555$		0			0
$556$	−2.12132	+	1.22474i	−0.0899640	+	0.0519408i
$557$	20.7846			0.880672			0.440336	−	0.897833i	$-0.354859\pi$
$557$	20.7846			0.880672			0.440336	+	0.897833i	$0.354859\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$	−8.66025	−	15.0000i	−0.365963	−	0.633866i
$561$		0			0
$562$	12.0000	−	20.7846i	0.506189	−	0.876746i
$563$	−8.66025	+	15.0000i	−0.364986	+	0.632175i	−0.988774	−	0.149419i	$-0.952260\pi$
$563$	−8.66025	+	15.0000i	−0.364986	+	0.632175i	0.623788	+	0.781594i	$0.285593\pi$
$564$		0			0
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$			4.24264i			0.178331i
$567$		0			0
$568$		−	4.89898i		−	0.205557i
$569$	−6.92820	−	12.0000i	−0.290445	−	0.503066i	0.683470	−	0.729979i	$-0.260470\pi$
$569$	−6.92820	−	12.0000i	−0.290445	−	0.503066i	−0.973915	+	0.226913i	$0.927137\pi$
$570$		0			0
$571$	2.12132	+	1.22474i	0.0887745	+	0.0512540i	0.543730	−	0.839260i	$-0.317012\pi$
$571$	2.12132	+	1.22474i	0.0887745	+	0.0512540i	−0.454956	+	0.890514i	$0.650345\pi$
$572$	−0.420266	−	16.2426i	−0.0175722	−	0.679139i
$573$		0			0
$574$	−25.4558	+	14.6969i	−1.06251	+	0.613438i
$575$		−	8.48528i		−	0.353861i
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	−14.7224	−	25.5000i	−0.612372	−	1.06066i
$579$		0			0
$580$	8.48528	+	4.89898i	0.352332	+	0.203419i
$581$	−29.3939	−	16.9706i	−1.21946	−	0.704058i
$582$		0			0
$583$	28.8492	+	15.6755i	1.19481	+	0.649213i
$584$		0			0
$585$		0			0
$586$	−12.0000			−0.495715
$587$	−24.4949	+	14.1421i	−1.01101	+	0.583708i	−0.911488	−	0.411327i	$-0.865066\pi$
$587$	−24.4949	+	14.1421i	−1.01101	+	0.583708i	−0.0995246	+	0.995035i	$0.531732\pi$
$588$		0			0
$589$	−25.4558	−	14.6969i	−1.04889	−	0.605577i
$590$	13.8564	−	24.0000i	0.570459	−	0.988064i
$591$		0			0
$592$	20.0000	+	34.6410i	0.821995	+	1.42374i
$593$	41.5692			1.70704			0.853522	−	0.521057i	$-0.174462\pi$
$593$	41.5692			1.70704			0.853522	+	0.521057i	$0.174462\pi$
$594$		0			0
$595$		0			0
$596$	6.92820	+	12.0000i	0.283790	+	0.491539i
$597$		0			0
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	2.44949	+	1.41421i	0.100083	+	0.0577832i	0.549206	−	0.835687i	$-0.314930\pi$
$599$	2.44949	+	1.41421i	0.100083	+	0.0577832i	−0.449123	+	0.893470i	$0.648263\pi$
$600$		0			0
$601$	−16.9706	+	9.79796i	−0.692244	+	0.399667i	−0.804452	−	0.594018i	$-0.797541\pi$
$601$	−16.9706	+	9.79796i	−0.692244	+	0.399667i	0.112208	+	0.993685i	$0.464208\pi$
$602$	10.3923			0.423559
$603$		0			0
$604$			2.44949i			0.0996683i
$605$	0.804479	+	15.5355i	0.0327067	+	0.631609i
$606$		0			0
$607$	−10.6066	−	6.12372i	−0.430509	−	0.248554i	0.269055	−	0.963125i	$-0.413289\pi$
$607$	−10.6066	−	6.12372i	−0.430509	−	0.248554i	−0.699563	+	0.714571i	$0.746622\pi$
$608$	33.0681	+	19.0919i	1.34109	+	0.774278i
$609$		0			0
$610$	6.00000	+	10.3923i	0.242933	+	0.420772i
$611$	13.8564			0.560570
$612$		0			0
$613$			14.6969i			0.593604i	0.954939	+	0.296802i	$0.0959201\pi$
$613$			14.6969i			0.593604i	−0.954939	+	0.296802i	$0.904080\pi$
$614$	11.0227	−	6.36396i	0.444840	−	0.256829i
$615$		0			0
$616$	−0.363961	−	14.0665i	−0.0146644	−	0.566757i
$617$	−23.2702	−	13.4350i	−0.936821	−	0.540874i	−0.0478587	−	0.998854i	$-0.515240\pi$
$617$	−23.2702	−	13.4350i	−0.936821	−	0.540874i	−0.888962	+	0.457980i	$0.848573\pi$
$618$		0			0
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	0.997259	+	0.0739910i	$0.0235736\pi$
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$620$		−	5.65685i		−	0.227185i
$621$		0			0
$622$		−	24.4949i		−	0.982156i
$623$	−8.66025	−	15.0000i	−0.346966	−	0.600962i
$624$		0			0
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−13.8564	+	24.0000i	−0.553813	+	0.959233i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$		0			0
$630$		0			0
$631$	44.0000			1.75161			0.875806	−	0.482663i	$-0.160330\pi$
$631$	44.0000			1.75161			0.875806	+	0.482663i	$0.160330\pi$
$632$	−18.3712	+	10.6066i	−0.730766	+	0.421908i
$633$		0			0
$634$	27.5772	+	15.9217i	1.09523	+	0.632331i
$635$	−5.19615	+	9.00000i	−0.206203	+	0.357154i
$636$		0			0
$637$	4.24264	−	2.44949i	0.168100	−	0.0970523i
$638$	20.7846	+	33.9411i	0.822871	+	1.34374i
$639$		0			0
$640$		−	17.1464i		−	0.677772i
$641$	−28.1691	+	16.2635i	−1.11261	+	0.642368i	−0.939505	−	0.342535i	$-0.888715\pi$
$641$	−28.1691	+	16.2635i	−1.11261	+	0.642368i	−0.173109	+	0.984903i	$0.555381\pi$
$642$		0			0
$643$	14.0000	−	24.2487i	0.552106	−	0.956276i	−0.446016	−	0.895025i	$-0.647158\pi$
$643$	14.0000	−	24.2487i	0.552106	−	0.956276i	0.998122	−	0.0612510i	$-0.0195090\pi$
$644$	−3.46410	+	6.00000i	−0.136505	+	0.236433i
$645$		0			0
$646$		0			0
$647$		−	19.7990i		−	0.778379i	−0.921158	−	0.389189i	$-0.872755\pi$
$647$		−	19.7990i		−	0.778379i	0.921158	−	0.389189i	$-0.127245\pi$
$648$		0			0
$649$	32.0000	−	19.5959i	1.25611	−	0.769207i
$650$	−22.0454	+	12.7279i	−0.864692	+	0.499230i
$651$		0			0
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−23.2702	−	13.4350i	−0.910631	−	0.525753i	−0.0299972	−	0.999550i	$-0.509550\pi$
$653$	−23.2702	−	13.4350i	−0.910631	−	0.525753i	−0.880634	+	0.473797i	$0.842883\pi$
$654$		0			0
$655$	−4.24264	+	2.44949i	−0.165774	+	0.0957095i
$656$	−34.6410			−1.35250
$657$		0			0
$658$	−12.0000			−0.467809
$659$	19.0526	+	33.0000i	0.742182	+	1.28550i	0.951500	+	0.307650i	$0.0995425\pi$
$659$	19.0526	+	33.0000i	0.742182	+	1.28550i	−0.209317	+	0.977848i	$0.567124\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$	6.92820	−	12.0000i	0.269272	−	0.466393i
$663$		0			0
$664$	−12.0000	−	20.7846i	−0.465690	−	0.806599i
$665$			25.4558i			0.987135i
$666$		0			0
$667$			19.5959i			0.758757i
$668$	1.73205	+	3.00000i	0.0670151	+	0.116073i
$669$		0			0
$670$	−8.48528	−	4.89898i	−0.327815	−	0.189264i
$671$	0.420266	+	16.2426i	0.0162242	+	0.627040i
$672$		0			0
$673$	33.9411	−	19.5959i	1.30833	−	0.755367i	0.326516	−	0.945192i	$-0.394125\pi$
$673$	33.9411	−	19.5959i	1.30833	−	0.755367i	0.981818	+	0.189824i	$0.0607919\pi$
$674$			16.9706i			0.653682i
$675$		0			0
$676$	−11.0000			−0.423077
$677$	13.8564	+	24.0000i	0.532545	+	0.922395i	0.999278	+	0.0379966i	$0.0120976\pi$
$677$	13.8564	+	24.0000i	0.532545	+	0.922395i	−0.466733	+	0.884398i	$0.654569\pi$
$678$		0			0
$679$	21.2132	+	12.2474i	0.814088	+	0.470014i
$680$		0			0
$681$		0			0
$682$	10.9706	−	20.1903i	0.420085	−	0.773125i
$683$		−	28.2843i		−	1.08227i	−0.840937	−	0.541134i	$-0.817995\pi$
$683$		−	28.2843i		−	1.08227i	0.840937	−	0.541134i	$-0.182005\pi$
$684$		0			0
$685$	22.0000			0.840577
$686$	−29.3939	+	16.9706i	−1.12226	+	0.647939i
$687$		0			0
$688$	10.6066	+	6.12372i	0.404373	+	0.233465i
$689$	24.2487	−	42.0000i	0.923802	−	1.60007i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−6.92820			−0.263371
$693$		0			0
$694$	24.0000			0.911028
$695$	−1.73205	−	3.00000i	−0.0657004	−	0.113796i
$696$		0			0
$697$		0			0
$698$	−7.34847	−	4.24264i	−0.278144	−	0.160586i
$699$		0			0
$700$	6.36396	−	3.67423i	0.240535	−	0.138873i
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$		−	58.7878i		−	2.21722i
$704$	1.58346	−	2.91421i	0.0596791	−	0.109834i
$705$		0			0
$706$	−48.7904	−	28.1691i	−1.83625	−	1.06016i
$707$	−29.3939	−	16.9706i	−1.10547	−	0.638244i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	−6.92820			−0.260011
$711$		0			0
$712$		−	12.2474i		−	0.458993i
$713$	9.79796	−	5.65685i	0.366936	−	0.211851i
$714$		0			0
$715$	22.9706	−	0.594346i	0.859050	−	0.0222273i
$716$	−19.5959	−	11.3137i	−0.732334	−	0.422813i
$717$		0			0
$718$		0			0
$719$		−	2.82843i		−	0.105483i	−0.998608	−	0.0527413i	$-0.983204\pi$
$719$		−	2.82843i		−	0.105483i	0.998608	−	0.0527413i	$-0.0167959\pi$
$720$		0			0
$721$		−	9.79796i		−	0.364895i
$722$	−30.3109	−	52.5000i	−1.12805	−	1.95385i
$723$		0			0
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$	10.3923	−	18.0000i	0.385961	−	0.668503i
$726$		0			0
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	0.782267	−	0.622944i	$-0.214063\pi$
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	−0.930618	+	0.365991i	$0.880730\pi$
$728$	−20.7846			−0.770329
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−29.6985	−	17.1464i	−1.09694	−	0.633318i	−0.161523	−	0.986869i	$-0.551641\pi$
$733$	−29.6985	−	17.1464i	−1.09694	−	0.633318i	−0.935415	+	0.353551i	$0.884974\pi$
$734$	6.92820	−	12.0000i	0.255725	−	0.442928i
$735$		0			0
$736$	−12.7279	+	7.34847i	−0.469157	+	0.270868i
$737$	−6.92820	−	11.3137i	−0.255204	−	0.416746i
$738$		0			0
$739$			7.34847i			0.270318i	0.990824	+	0.135159i	$0.0431545\pi$
$739$			7.34847i			0.270318i	−0.990824	+	0.135159i	$0.956846\pi$
$740$	9.79796	−	5.65685i	0.360180	−	0.207950i
$741$		0			0
$742$	−21.0000	+	36.3731i	−0.770934	+	1.33530i
$743$	−13.8564	+	24.0000i	−0.508342	+	0.880475i	0.491611	+	0.870815i	$0.336408\pi$
$743$	−13.8564	+	24.0000i	−0.508342	+	0.880475i	−0.999953	+	0.00965974i	$0.996925\pi$
$744$		0			0
$745$	−16.9706	+	9.79796i	−0.621753	+	0.358969i
$746$			42.4264i			1.55334i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	−12.2474	−	7.07107i	−0.446619	−	0.257855i
$753$		0			0
$754$	50.9117	−	29.3939i	1.85409	−	1.07046i
$755$	−3.46410			−0.126072
$756$		0			0
$757$	8.00000			0.290765			0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000			0.290765			0.145382	+	0.989376i	$0.453559\pi$
$758$	−13.8564	−	24.0000i	−0.503287	−	0.871719i
$759$		0			0
$760$	−9.00000	+	15.5885i	−0.326464	+	0.565453i
$761$	6.92820	−	12.0000i	0.251147	−	0.435000i	−0.712695	−	0.701474i	$-0.752526\pi$
$761$	6.92820	−	12.0000i	0.251147	−	0.435000i	0.963842	+	0.266475i	$0.0858589\pi$
$762$		0			0
$763$	18.0000	+	31.1769i	0.651644	+	1.12868i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$			63.6867i			2.30110i
$767$	−27.7128	−	48.0000i	−1.00065	−	1.73318i
$768$		0			0
$769$	−16.9706	−	9.79796i	−0.611974	−	0.353323i	0.161764	−	0.986830i	$-0.448282\pi$
$769$	−16.9706	−	9.79796i	−0.611974	−	0.353323i	−0.773738	+	0.633506i	$0.781615\pi$
$770$	−19.8931	+	0.514719i	−0.716897	+	0.0185492i
$771$		0			0
$772$	−8.48528	+	4.89898i	−0.305392	+	0.176318i
$773$		−	32.5269i		−	1.16991i	−0.811065	−	0.584956i	$-0.801112\pi$
$773$		−	32.5269i		−	1.16991i	0.811065	−	0.584956i	$-0.198888\pi$
$774$		0			0
$775$	−12.0000			−0.431053
$776$	8.66025	+	15.0000i	0.310885	+	0.538469i
$777$		0			0
$778$	14.8492	+	8.57321i	0.532371	+	0.307365i
$779$	44.0908	+	25.4558i	1.57972	+	0.912050i
$780$		0			0
$781$	−8.24264	−	4.47871i	−0.294945	−	0.160261i
$782$		0			0
$783$		0			0
$784$	−5.00000			−0.178571
$785$	17.1464	−	9.89949i	0.611982	−	0.353328i
$786$		0			0
$787$	−10.6066	−	6.12372i	−0.378085	−	0.218287i	0.298900	−	0.954284i	$-0.403380\pi$
$787$	−10.6066	−	6.12372i	−0.378085	−	0.218287i	−0.676985	+	0.735997i	$0.736714\pi$
$788$		0			0
$789$		0			0
$790$	15.0000	+	25.9808i	0.533676	+	0.924354i
$791$	−3.46410			−0.123169
$792$		0			0
$793$	24.0000			0.852265
$794$	6.92820	+	12.0000i	0.245873	+	0.425864i
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−23.2702	−	13.4350i	−0.824271	−	0.475893i	0.0276160	−	0.999619i	$-0.491208\pi$
$797$	−23.2702	−	13.4350i	−0.824271	−	0.475893i	−0.851887	+	0.523725i	$0.824542\pi$
$798$		0			0
$799$		0			0
$800$	15.5885			0.551135
$801$		0			0
$802$		−	2.44949i		−	0.0864945i
$803$		0			0
$804$		0			0
$805$	−8.48528	−	4.89898i	−0.299067	−	0.172666i
$806$	−29.3939	−	16.9706i	−1.03536	−	0.597763i
$807$		0			0
$808$	−12.0000	−	20.7846i	−0.422159	−	0.731200i
$809$	20.7846			0.730748			0.365374	−	0.930861i	$-0.380941\pi$
$809$	20.7846			0.730748			0.365374	+	0.930861i	$0.380941\pi$
$810$		0			0
$811$		−	22.0454i		−	0.774119i	−0.922055	−	0.387059i	$-0.873491\pi$
$811$		−	22.0454i		−	0.774119i	0.922055	−	0.387059i	$-0.126509\pi$
$812$	−14.6969	+	8.48528i	−0.515761	+	0.297775i
$813$		0			0
$814$	45.9411	−	1.18869i	1.61024	−	0.0416636i
$815$	−9.79796	−	5.65685i	−0.343208	−	0.198151i
$816$		0			0
$817$	−9.00000	−	15.5885i	−0.314870	−	0.545371i
$818$			67.8823i			2.37345i
$819$		0			0
$820$			9.79796i			0.342160i
$821$	−6.92820	−	12.0000i	−0.241796	−	0.418803i	0.719430	−	0.694565i	$-0.244403\pi$
$821$	−6.92820	−	12.0000i	−0.241796	−	0.418803i	−0.961226	+	0.275762i	$0.911070\pi$
$822$		0			0
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$	3.46410	−	6.00000i	0.120678	−	0.209020i
$825$		0			0
$826$	24.0000	+	41.5692i	0.835067	+	1.44638i
$827$	−41.5692			−1.44550			−0.722752	−	0.691108i	$-0.757123\pi$
$827$	−41.5692			−1.44550			−0.722752	+	0.691108i	$0.757123\pi$
$828$		0			0
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$	−29.3939	+	16.9706i	−1.02028	+	0.589057i
$831$		0			0
$832$	−4.24264	−	2.44949i	−0.147087	−	0.0849208i
$833$		0			0
$834$		0			0
$835$	−4.24264	+	2.44949i	−0.146823	+	0.0847681i
$836$	20.7846	−	12.7279i	0.718851	−	0.440204i
$837$		0			0
$838$			19.5959i			0.676930i
$839$	−17.1464	+	9.89949i	−0.591960	+	0.341769i	−0.765872	−	0.642993i	$-0.777693\pi$
$839$	−17.1464	+	9.89949i	−0.591960	+	0.341769i	0.173912	+	0.984761i	$0.444359\pi$
$840$		0			0
$841$	−9.50000	+	16.4545i	−0.327586	+	0.567396i
$842$	6.92820	−	12.0000i	0.238762	−	0.413547i
$843$		0			0
$844$	10.6066	−	6.12372i	0.365094	−	0.210787i
$845$		−	15.5563i		−	0.535155i
$846$		0			0
$847$	−24.0000	−	12.2474i	−0.824650	−	0.420827i
$848$	−42.8661	+	24.7487i	−1.47203	+	0.849875i
$849$		0			0
$850$		0			0
$851$	19.5959	+	11.3137i	0.671739	+	0.387829i
$852$		0			0
$853$	−29.6985	+	17.1464i	−1.01686	+	0.587083i	−0.913192	−	0.407530i	$-0.866390\pi$
$853$	−29.6985	+	17.1464i	−1.01686	+	0.587083i	−0.103665	+	0.994612i	$0.533057\pi$
$854$	−20.7846			−0.711235
$855$		0			0
$856$		0			0
$857$	−17.3205	−	30.0000i	−0.591657	−	1.02478i	−0.994009	−	0.109295i	$-0.965141\pi$
$857$	−17.3205	−	30.0000i	−0.591657	−	1.02478i	0.402352	−	0.915485i	$-0.368193\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$	1.73205	−	3.00000i	0.0590624	−	0.102299i
$861$		0			0
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$		−	19.7990i		−	0.673965i	−0.941511	−	0.336983i	$-0.890594\pi$
$863$		−	19.7990i		−	0.673965i	0.941511	−	0.336983i	$-0.109406\pi$
$864$		0			0
$865$		−	9.79796i		−	0.333141i
$866$	−13.8564	−	24.0000i	−0.470860	−	0.815553i
$867$		0			0
$868$	8.48528	+	4.89898i	0.288009	+	0.166282i
$869$	1.05066	+	40.6066i	0.0356414	+	1.37748i
$870$		0			0
$871$	−16.9706	+	9.79796i	−0.575026	+	0.331991i
$872$			25.4558i			0.862044i
$873$		0			0
$874$	36.0000			1.21772
$875$	13.8564	+	24.0000i	0.468432	+	0.811348i
$876$		0			0
$877$	46.6690	+	26.9444i	1.57590	+	0.909847i	0.995422	+	0.0955723i	$0.0304681\pi$
$877$	46.6690	+	26.9444i	1.57590	+	0.909847i	0.580479	+	0.814275i	$0.302865\pi$
$878$	3.67423	+	2.12132i	0.123999	+	0.0715911i
$879$		0			0
$880$	−20.6066	−	11.1968i	−0.694648	−	0.377444i
$881$			9.89949i			0.333522i	0.985997	+	0.166761i	$0.0533309\pi$
$881$			9.89949i			0.333522i	−0.985997	+	0.166761i	$0.946669\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		0			0
$886$	33.9411	+	19.5959i	1.14027	+	0.658338i
$887$	27.7128	−	48.0000i	0.930505	−	1.61168i	0.148046	−	0.988980i	$-0.452702\pi$
$887$	27.7128	−	48.0000i	0.930505	−	1.61168i	0.782459	−	0.622702i	$-0.213965\pi$
$888$		0			0
$889$	−9.00000	−	15.5885i	−0.301850	−	0.522820i
$890$	−17.3205			−0.580585
$891$		0			0
$892$	−16.0000			−0.535720
$893$	10.3923	+	18.0000i	0.347765	+	0.602347i
$894$		0			0
$895$	16.0000	−	27.7128i	0.534821	−	0.926337i
$896$	25.7196	+	14.8492i	0.859233	+	0.496078i
$897$		0			0
$898$	−14.8492	+	8.57321i	−0.495526	+	0.286092i
$899$	27.7128			0.924274
$900$		0			0
$901$		0			0
$902$	−19.0016	+	34.9706i	−0.632683	+	1.16439i
$903$		0			0
$904$	−2.12132	−	1.22474i	−0.0705541	−	0.0407344i
$905$	−9.79796	−	5.65685i	−0.325695	−	0.188040i
$906$		0			0
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	0.868710	+	0.495321i	$0.164950\pi$
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	−0.00539395	+	0.999985i	$0.501717\pi$
$908$	−27.7128			−0.919682
$909$		0			0
$910$			29.3939i			0.974398i
$911$	−46.5403	+	26.8701i	−1.54195	+	0.890245i	−0.543233	+	0.839582i	$0.682800\pi$
$911$	−46.5403	+	26.8701i	−1.54195	+	0.890245i	−0.998716	+	0.0506629i	$0.983867\pi$
$912$		0			0
$913$	−45.9411	+	1.18869i	−1.52043	+	0.0393400i
$914$	14.6969	+	8.48528i	0.486132	+	0.280668i
$915$		0			0
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$		−	8.48528i		−	0.280209i
$918$		0			0
$919$			36.7423i			1.21202i	0.795458	+	0.606009i	$0.207230\pi$
$919$			36.7423i			1.21202i	−0.795458	+	0.606009i	$0.792770\pi$
$920$	−3.46410	−	6.00000i	−0.114208	−	0.197814i
$921$		0			0
$922$	−6.00000	+	10.3923i	−0.197599	+	0.342252i
$923$	−6.92820	+	12.0000i	−0.228045	+	0.394985i
$924$		0			0
$925$	−12.0000	−	20.7846i	−0.394558	−	0.683394i
$926$	48.4974			1.59372
$927$		0			0
$928$	−36.0000			−1.18176
$929$	8.57321	−	4.94975i	0.281278	−	0.162396i	−0.352724	−	0.935727i	$-0.614744\pi$
$929$	8.57321	−	4.94975i	0.281278	−	0.162396i	0.634002	+	0.773332i	$0.281411\pi$
$930$		0			0
$931$	6.36396	+	3.67423i	0.208570	+	0.120418i
$932$	10.3923	−	18.0000i	0.340411	−	0.589610i
$933$		0			0
$934$	−33.9411	+	19.5959i	−1.11059	+	0.641198i
$935$		0			0
$936$		0			0
$937$			29.3939i			0.960256i	0.877198	+	0.480128i	$0.159410\pi$
$937$			29.3939i			0.960256i	−0.877198	+	0.480128i	$0.840590\pi$
$938$	14.6969	−	8.48528i	0.479872	−	0.277054i
$939$		0			0
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	−13.8564	+	24.0000i	−0.451706	+	0.782378i	−0.998492	−	0.0548946i	$-0.982518\pi$
$941$	−13.8564	+	24.0000i	−0.451706	+	0.782378i	0.546786	+	0.837272i	$0.315851\pi$
$942$		0			0
$943$	−16.9706	+	9.79796i	−0.552638	+	0.319065i
$944$			56.5685i			1.84115i
$945$		0			0
$946$	12.0000	−	7.34847i	0.390154	−	0.238919i
$947$	19.5959	−	11.3137i	0.636782	−	0.367646i	−0.146592	−	0.989197i	$-0.546830\pi$
$947$	19.5959	−	11.3137i	0.636782	−	0.367646i	0.783374	+	0.621551i	$0.213497\pi$
$948$		0			0
$949$		0			0
$950$	−33.0681	−	19.0919i	−1.07287	−	0.619422i
$951$		0			0
$952$		0			0
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$	4.00000			0.129437
$956$	−8.66025	−	15.0000i	−0.280093	−	0.485135i
$957$		0			0
$958$	−33.0000	+	57.1577i	−1.06618	+	1.84668i
$959$	−19.0526	+	33.0000i	−0.615239	+	1.06563i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		−	67.8823i		−	2.18861i
$963$		0			0
$964$		−	19.5959i		−	0.631142i
$965$	−6.92820	−	12.0000i	−0.223027	−	0.386294i
$966$		0			0
$967$	−36.0624	−	20.8207i	−1.15969	−	0.669547i	−0.208460	−	0.978031i	$-0.566845\pi$
$967$	−36.0624	−	20.8207i	−1.15969	−	0.669547i	−0.951230	+	0.308483i	$0.900179\pi$
$968$	−10.3668	−	15.9853i	−0.333202	−	0.513786i
$969$		0			0
$970$	21.2132	−	12.2474i	0.681115	−	0.393242i
$971$			56.5685i			1.81537i	0.419651	+	0.907685i	$0.362152\pi$
$971$			56.5685i			1.81537i	−0.419651	+	0.907685i	$0.637848\pi$
$972$		0			0
$973$	6.00000			0.192351
$974$	6.92820	+	12.0000i	0.221994	+	0.384505i
$975$		0			0
$976$	−21.2132	−	12.2474i	−0.679018	−	0.392031i
$977$	−30.6186	−	17.6777i	−0.979576	−	0.565559i	−0.0774342	−	0.996997i	$-0.524673\pi$
$977$	−30.6186	−	17.6777i	−0.979576	−	0.565559i	−0.902142	+	0.431439i	$0.858006\pi$
$978$		0			0
$979$	−20.6066	−	11.1968i	−0.658590	−	0.357851i
$980$			1.41421i			0.0451754i
$981$		0			0
$982$	−48.0000			−1.53174
$983$	41.6413	−	24.0416i	1.32815	−	0.766809i	0.343138	−	0.939285i	$-0.388510\pi$
$983$	41.6413	−	24.0416i	1.32815	−	0.766809i	0.985014	+	0.172476i	$0.0551767\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−18.0000	−	31.1769i	−0.572656	−	0.991870i
$989$	6.92820			0.220304
$990$		0			0
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$	10.3923	+	18.0000i	0.329956	+	0.571501i
$993$		0			0
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$	−9.79796	−	5.65685i	−0.310616	−	0.179334i
$996$		0			0
$997$	21.2132	−	12.2474i	0.671829	−	0.387881i	−0.124940	−	0.992164i	$-0.539874\pi$
$997$	21.2132	−	12.2474i	0.671829	−	0.387881i	0.796769	+	0.604284i	$0.206541\pi$
$998$	−55.4256			−1.75447
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.g.c.296.3		8
3.2	odd	2	inner	891.2.g.c.296.2		8
9.2	odd	6	inner	891.2.g.c.593.1		8
9.4	even	3		99.2.d.a.98.2	yes	4
9.5	odd	6		99.2.d.a.98.3	yes	4
9.7	even	3	inner	891.2.g.c.593.4		8
11.10	odd	2	inner	891.2.g.c.296.1		8
33.32	even	2	inner	891.2.g.c.296.4		8
36.23	even	6		1584.2.b.e.593.1		4
36.31	odd	6		1584.2.b.e.593.3		4
45.4	even	6		2475.2.f.e.2276.3		4
45.13	odd	12		2475.2.d.a.2474.8		8
45.14	odd	6		2475.2.f.e.2276.1		4
45.22	odd	12		2475.2.d.a.2474.2		8
45.23	even	12		2475.2.d.a.2474.3		8
45.32	even	12		2475.2.d.a.2474.5		8
72.5	odd	6		6336.2.b.s.2177.4		4
72.13	even	6		6336.2.b.s.2177.2		4
72.59	even	6		6336.2.b.t.2177.3		4
72.67	odd	6		6336.2.b.t.2177.1		4
99.32	even	6		99.2.d.a.98.1	✓	4
99.43	odd	6	inner	891.2.g.c.593.2		8
99.65	even	6	inner	891.2.g.c.593.3		8
99.76	odd	6		99.2.d.a.98.4	yes	4
396.131	odd	6		1584.2.b.e.593.2		4
396.175	even	6		1584.2.b.e.593.4		4
495.32	odd	12		2475.2.d.a.2474.4		8
495.274	odd	6		2475.2.f.e.2276.2		4
495.329	even	6		2475.2.f.e.2276.4		4
495.373	even	12		2475.2.d.a.2474.1		8
495.428	odd	12		2475.2.d.a.2474.6		8
495.472	even	12		2475.2.d.a.2474.7		8
792.131	odd	6		6336.2.b.t.2177.4		4
792.373	odd	6		6336.2.b.s.2177.1		4
792.571	even	6		6336.2.b.t.2177.2		4
792.725	even	6		6336.2.b.s.2177.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.d.a.98.1	✓	4	99.32	even	6
99.2.d.a.98.2	yes	4	9.4	even	3
99.2.d.a.98.3	yes	4	9.5	odd	6
99.2.d.a.98.4	yes	4	99.76	odd	6
891.2.g.c.296.1		8	11.10	odd	2	inner
891.2.g.c.296.2		8	3.2	odd	2	inner
891.2.g.c.296.3		8	1.1	even	1	trivial
891.2.g.c.296.4		8	33.32	even	2	inner
891.2.g.c.593.1		8	9.2	odd	6	inner
891.2.g.c.593.2		8	99.43	odd	6	inner
891.2.g.c.593.3		8	99.65	even	6	inner
891.2.g.c.593.4		8	9.7	even	3	inner
1584.2.b.e.593.1		4	36.23	even	6
1584.2.b.e.593.2		4	396.131	odd	6
1584.2.b.e.593.3		4	36.31	odd	6
1584.2.b.e.593.4		4	396.175	even	6
2475.2.d.a.2474.1		8	495.373	even	12
2475.2.d.a.2474.2		8	45.22	odd	12
2475.2.d.a.2474.3		8	45.23	even	12
2475.2.d.a.2474.4		8	495.32	odd	12
2475.2.d.a.2474.5		8	45.32	even	12
2475.2.d.a.2474.6		8	495.428	odd	12
2475.2.d.a.2474.7		8	495.472	even	12
2475.2.d.a.2474.8		8	45.13	odd	12
2475.2.f.e.2276.1		4	45.14	odd	6
2475.2.f.e.2276.2		4	495.274	odd	6
2475.2.f.e.2276.3		4	45.4	even	6
2475.2.f.e.2276.4		4	495.329	even	6
6336.2.b.s.2177.1		4	792.373	odd	6
6336.2.b.s.2177.2		4	72.13	even	6
6336.2.b.s.2177.3		4	792.725	even	6
6336.2.b.s.2177.4		4	72.5	odd	6
6336.2.b.t.2177.1		4	72.67	odd	6
6336.2.b.t.2177.2		4	792.571	even	6
6336.2.b.t.2177.3		4	72.59	even	6
6336.2.b.t.2177.4		4	792.131	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.22474 - 0.707107i) q^{5} +(2.12132 - 1.22474i) q^{7} +1.73205 q^{8} -2.44949i q^{10} +(1.58346 - 2.91421i) q^{11} +(-4.24264 - 2.44949i) q^{13} +(3.67423 + 2.12132i) q^{14} +(2.50000 + 4.33013i) q^{16} -7.34847i q^{19} +(1.22474 - 0.707107i) q^{20} +(5.74264 - 0.148586i) q^{22} +(2.44949 + 1.41421i) q^{23} +(-1.50000 - 2.59808i) q^{25} -8.48528i q^{26} +2.44949i q^{28} +(3.46410 + 6.00000i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-2.59808 + 4.50000i) q^{32} -3.46410 q^{35} +8.00000 q^{37} +(11.0227 - 6.36396i) q^{38} +(-2.12132 - 1.22474i) q^{40} +(-3.46410 + 6.00000i) q^{41} +(2.12132 - 1.22474i) q^{43} +(1.73205 + 2.82843i) q^{44} +4.89898i q^{46} +(-2.44949 + 1.41421i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.59808 - 4.50000i) q^{50} +(4.24264 - 2.44949i) q^{52} +9.89949i q^{53} +(-4.00000 + 2.44949i) q^{55} +(3.67423 - 2.12132i) q^{56} +(-6.00000 + 10.3923i) q^{58} +(9.79796 + 5.65685i) q^{59} +(-4.24264 + 2.44949i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(3.46410 + 6.00000i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{70} -2.82843i q^{71} +(6.92820 + 12.0000i) q^{74} +(6.36396 + 3.67423i) q^{76} +(-0.210133 - 8.12132i) q^{77} +(-10.6066 + 6.12372i) q^{79} -7.07107i q^{80} -12.0000 q^{82} +(-6.92820 - 12.0000i) q^{83} +(3.67423 + 2.12132i) q^{86} +(2.74264 - 5.04757i) q^{88} -7.07107i q^{89} -12.0000 q^{91} +(-2.44949 + 1.41421i) q^{92} +(-4.24264 - 2.44949i) q^{94} +(-5.19615 + 9.00000i) q^{95} +(5.00000 + 8.66025i) q^{97} -1.73205 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 20 q^{16} + 12 q^{22} - 12 q^{25} + 16 q^{31} + 64 q^{37} - 4 q^{49} - 32 q^{55} - 48 q^{58} + 8 q^{64} + 16 q^{67} - 24 q^{70} - 96 q^{82} - 12 q^{88} - 96 q^{91} + 40 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 + 20 * q^16 + 12 * q^22 - 12 * q^25 + 16 * q^31 + 64 * q^37 - 4 * q^49 - 32 * q^55 - 48 * q^58 + 8 * q^64 + 16 * q^67 - 24 * q^70 - 96 * q^82 - 12 * q^88 - 96 * q^91 + 40 * q^97

Introduction

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