LMFDB - Embedded newform 624.2.cn.c.353.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.2
Root			$0.500000 - 1.19293i$ of defining polynomial
Character	$\chi$	$=$	624.353
Dual form			624.2.cn.c.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +O(q^{10})$	\(q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +(1.69293 + 0.453620i) q^{11} +(-1.59808 + 3.23205i) q^{13} +(4.14187 + 0.202571i) q^{15} +(1.07328 - 1.85897i) q^{17} +(0.267949 + 1.00000i) q^{19} +(1.32691 - 2.05896i) q^{21} +0.732051i q^{25} +(-3.09808 - 4.17156i) q^{27} +(4.79122 - 2.76621i) q^{29} +(-4.46410 + 4.46410i) q^{31} +(2.69999 - 1.38761i) q^{33} +(2.93225 + 1.69293i) q^{35} +(-1.76795 + 6.59808i) q^{37} +(1.70983 + 6.00637i) q^{39} +(-0.166037 + 0.619657i) q^{41} +(-7.09808 - 4.09808i) q^{43} +(5.55017 - 4.55896i) q^{45} +(6.77174 - 6.77174i) q^{47} +(-4.33013 + 2.50000i) q^{49} +(-0.785693 - 3.63397i) q^{51} -4.62518i q^{53} +(2.09808 + 3.63397i) q^{55} +(1.50726 + 0.971364i) q^{57} +(-1.23931 - 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-0.692934 - 4.18567i) q^{63} +(-8.17709 + 2.76621i) q^{65} +(8.46410 + 2.26795i) q^{67} +(-4.62518 + 1.23931i) q^{71} +(-6.09808 - 6.09808i) q^{73} +(0.851708 + 0.939303i) q^{75} +2.47863 q^{77} -2.00000 q^{79} +(-8.82860 - 1.74811i) q^{81} +(1.23931 + 1.23931i) q^{83} +(4.96410 - 1.33013i) q^{85} +(2.92931 - 9.12372i) q^{87} +(-9.70398 - 2.60017i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(-0.534160 + 10.9217i) q^{93} +(-1.23931 + 2.14655i) q^{95} +(3.36603 + 12.5622i) q^{97} +(1.84997 - 4.92177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9	$ 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 14 q^{15} + 16 q^{19} + 4 q^{21} - 4 q^{27} - 8 q^{31} + 16 q^{33} - 28 q^{37} + 14 q^{39} - 36 q^{43} - 20 q^{45} - 4 q^{55} + 16 q^{57} + 28 q^{61} + 8 q^{63} + 40 q^{67} - 28 q^{73} - 12 q^{75} - 16 q^{79} + 4 q^{81} + 12 q^{85} + 34 q^{87} - 8 q^{91} + 4 q^{93} + 20 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9 + 8 * q^13 + 14 * q^15 + 16 * q^19 + 4 * q^21 - 4 * q^27 - 8 * q^31 + 16 * q^33 - 28 * q^37 + 14 * q^39 - 36 * q^43 - 20 * q^45 - 4 * q^55 + 16 * q^57 + 28 * q^61 + 8 * q^63 + 40 * q^67 - 28 * q^73 - 12 * q^75 - 16 * q^79 + 4 * q^81 + 12 * q^85 + 34 * q^87 - 8 * q^91 + 4 * q^93 + 20 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.28311	−	1.16345i	0.740805	−	0.671721i
$3$	1.28311	−	1.16345i	0.740805	−	0.671721i
$4$		0			0
$5$	1.69293	+	1.69293i	0.757103	+	0.757103i	0.975794	−	0.218691i	$-0.0701787\pi$
$5$	1.69293	+	1.69293i	0.757103	+	0.757103i	−0.218691	+	0.975794i	$0.570179\pi$
$6$		0			0
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.00875026	−	0.999962i	$-0.497215\pi$
$7$	1.36603	−	0.366025i	0.516309	−	0.138345i	0.507559	+	0.861617i	$0.330548\pi$
$8$		0			0
$9$	0.292748	−	2.98568i	0.0975828	−	0.995227i
$10$		0			0
$11$	1.69293	+	0.453620i	0.510439	+	0.136772i	0.504840	−	0.863213i	$-0.331551\pi$
$11$	1.69293	+	0.453620i	0.510439	+	0.136772i	0.00559833	+	0.999984i	$0.498218\pi$
$12$		0			0
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$		0			0
$15$	4.14187	+	0.202571i	1.06943	+	0.0523036i
$16$		0			0
$17$	1.07328	−	1.85897i	0.260308	−	0.450867i	−0.706016	−	0.708196i	$-0.749509\pi$
$17$	1.07328	−	1.85897i	0.260308	−	0.450867i	0.966324	+	0.257330i	$0.0828426\pi$
$18$		0			0
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	0.989826	−	0.142280i	$-0.0454432\pi$
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	−0.928355	+	0.371695i	$0.878777\pi$
$20$		0			0
$21$	1.32691	−	2.05896i	0.289555	−	0.449302i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$			0.732051i			0.146410i
$26$		0			0
$27$	−3.09808	−	4.17156i	−0.596225	−	0.802817i
$28$		0			0
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.0158603	−	0.999874i	$-0.494951\pi$
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.873847	+	0.486202i	$0.161618\pi$
$30$		0			0
$31$	−4.46410	+	4.46410i	−0.801776	+	0.801776i	−0.983373	−	0.181597i	$-0.941873\pi$
$31$	−4.46410	+	4.46410i	−0.801776	+	0.801776i	0.181597	+	0.983373i	$0.441873\pi$
$32$		0			0
$33$	2.69999	−	1.38761i	0.470008	−	0.241551i
$34$		0			0
$35$	2.93225	+	1.69293i	0.495640	+	0.286158i
$36$		0			0
$37$	−1.76795	+	6.59808i	−0.290649	+	1.08472i	0.653963	+	0.756527i	$0.273105\pi$
$37$	−1.76795	+	6.59808i	−0.290649	+	1.08472i	−0.944612	+	0.328190i	$0.893561\pi$
$38$		0			0
$39$	1.70983	+	6.00637i	0.273793	+	0.961789i
$40$		0			0
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	−0.977678	−	0.210107i	$-0.932619\pi$
$41$	−0.166037	+	0.619657i	−0.0259306	+	0.0967741i	0.951748	+	0.306881i	$0.0992854\pi$
$42$		0			0
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.150891	−	0.988550i	$-0.548214\pi$
$43$	−7.09808	−	4.09808i	−1.08245	−	0.624951i	−0.931555	+	0.363600i	$0.881548\pi$
$44$		0			0
$45$	5.55017	−	4.55896i	0.827370	−	0.679610i
$46$		0			0
$47$	6.77174	−	6.77174i	0.987759	−	0.987759i	−0.0121668	−	0.999926i	$-0.503873\pi$
$47$	6.77174	−	6.77174i	0.987759	−	0.987759i	0.999926	+	0.0121668i	$0.00387290\pi$
$48$		0			0
$49$	−4.33013	+	2.50000i	−0.618590	+	0.357143i
$50$		0			0
$51$	−0.785693	−	3.63397i	−0.110019	−	0.508858i
$52$		0			0
$53$		−	4.62518i		−	0.635318i	−0.948205	−	0.317659i	$-0.897103\pi$
$53$		−	4.62518i		−	0.635318i	0.948205	−	0.317659i	$-0.102897\pi$
$54$		0			0
$55$	2.09808	+	3.63397i	0.282905	+	0.490005i
$56$		0			0
$57$	1.50726	+	0.971364i	0.199642	+	0.128660i
$58$		0			0
$59$	−1.23931	−	4.62518i	−0.161345	−	0.602147i	−0.998478	−	0.0551484i	$-0.982437\pi$
$59$	−1.23931	−	4.62518i	−0.161345	−	0.602147i	0.837133	−	0.546999i	$-0.184230\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	−0.692934	−	4.18567i	−0.0873015	−	0.527345i
$64$		0			0
$65$	−8.17709	+	2.76621i	−1.01424	+	0.343106i
$66$		0			0
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.735647	−	0.677365i	$-0.236878\pi$
$67$	8.46410	+	2.26795i	1.03405	+	0.277074i	0.298407	+	0.954439i	$0.403545\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.62518	+	1.23931i	−0.548908	+	0.147079i	−0.522606	−	0.852575i	$-0.675040\pi$
$71$	−4.62518	+	1.23931i	−0.548908	+	0.147079i	−0.0263025	+	0.999654i	$0.508373\pi$
$72$		0			0
$73$	−6.09808	−	6.09808i	−0.713726	−	0.713726i	0.253587	−	0.967313i	$-0.418390\pi$
$73$	−6.09808	−	6.09808i	−0.713726	−	0.713726i	−0.967313	+	0.253587i	$0.918390\pi$
$74$		0			0
$75$	0.851708	+	0.939303i	0.0983467	+	0.108461i
$76$		0			0
$77$	2.47863			0.282466
$78$		0			0
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	−8.82860	−	1.74811i	−0.980955	−	0.194234i
$82$		0			0
$83$	1.23931	+	1.23931i	0.136032	+	0.136032i	0.771844	−	0.635812i	$-0.219335\pi$
$83$	1.23931	+	1.23931i	0.136032	+	0.136032i	−0.635812	+	0.771844i	$0.719335\pi$
$84$		0			0
$85$	4.96410	−	1.33013i	0.538432	−	0.144273i
$86$		0			0
$87$	2.92931	−	9.12372i	0.314054	−	0.978165i
$88$		0			0
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.295230	−	0.955426i	$-0.595396\pi$
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.733390	+	0.679808i	$0.762063\pi$
$90$		0			0
$91$	−1.00000	+	5.00000i	−0.104828	+	0.524142i
$92$		0			0
$93$	−0.534160	+	10.9217i	−0.0553898	+	1.13253i
$94$		0			0
$95$	−1.23931	+	2.14655i	−0.127151	+	0.220232i
$96$		0			0
$97$	3.36603	+	12.5622i	0.341768	+	1.27550i	0.896343	+	0.443362i	$0.146214\pi$
$97$	3.36603	+	12.5622i	0.341768	+	1.27550i	−0.554575	+	0.832134i	$0.687119\pi$
$98$		0			0
$99$	1.84997	−	4.92177i	0.185929	−	0.494656i
$100$		0			0
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.654160	+	0.756356i	$0.273022\pi$
$101$	9.87002	+	17.0954i	0.982104	+	1.70105i	0.327944	+	0.944697i	$0.393644\pi$
$102$		0			0
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$		0			0
$105$	5.73205	−	1.23931i	0.559391	−	0.120945i
$106$		0			0
$107$	−14.4507	+	8.34312i	−1.39700	+	0.806560i	−0.994078	−	0.108673i	$-0.965340\pi$
$107$	−14.4507	+	8.34312i	−1.39700	+	0.806560i	−0.402925	+	0.915233i	$0.632007\pi$
$108$		0			0
$109$	−2.80385	+	2.80385i	−0.268560	+	0.268560i	−0.828520	−	0.559960i	$-0.810817\pi$
$109$	−2.80385	+	2.80385i	−0.268560	+	0.268560i	0.559960	+	0.828520i	$0.310817\pi$
$110$		0			0
$111$	5.40808	+	10.5230i	0.513313	+	0.998798i
$112$		0			0
$113$	−11.2309	−	6.48415i	−1.05651	−	0.609978i	−0.132047	−	0.991243i	$-0.542155\pi$
$113$	−11.2309	−	6.48415i	−1.05651	−	0.609978i	−0.924465	+	0.381266i	$0.875488\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.18204	+	5.71753i	0.848880	+	0.528585i
$118$		0			0
$119$	0.785693	−	2.93225i	0.0720244	−	0.268799i
$120$		0			0
$121$	−6.86603	−	3.96410i	−0.624184	−	0.360373i
$122$		0			0
$123$	0.507899	+	0.988265i	0.0457957	+	0.0891088i
$124$		0			0
$125$	7.22536	−	7.22536i	0.646255	−	0.646255i
$126$		0			0
$127$	−13.0981	+	7.56218i	−1.16227	+	0.671035i	−0.951846	−	0.306576i	$-0.900817\pi$
$127$	−13.0981	+	7.56218i	−1.16227	+	0.671035i	−0.210420	+	0.977611i	$0.567483\pi$
$128$		0			0
$129$	−13.8755	+	3.00000i	−1.22167	+	0.264135i
$130$		0			0
$131$			0.907241i			0.0792660i	0.999214	+	0.0396330i	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$		0			0
$133$	0.732051	+	1.26795i	0.0634769	+	0.109945i
$134$		0			0
$135$	1.81734	−	12.3070i	0.156412	−	1.05922i
$136$		0			0
$137$	1.52690	+	5.69846i	0.130452	+	0.486852i	0.999975	−	0.00703925i	$-0.00224068\pi$
$137$	1.52690	+	5.69846i	0.130452	+	0.486852i	−0.869524	+	0.493891i	$0.835574\pi$
$138$		0			0
$139$	−1.19615	+	2.07180i	−0.101456	+	0.175728i	−0.912285	−	0.409556i	$-0.865684\pi$
$139$	−1.19615	+	2.07180i	−0.101456	+	0.175728i	0.810829	+	0.585284i	$0.199017\pi$
$140$		0			0
$141$	0.810284	−	16.5675i	0.0682383	−	1.39523i
$142$		0			0
$143$	−4.17156	+	4.74673i	−0.348843	+	0.396941i
$144$		0			0
$145$	12.7942	+	3.42820i	1.06250	+	0.284697i
$146$		0			0
$147$	−2.64740	+	8.24568i	−0.218354	+	0.680092i
$148$		0			0
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	−0.467173	−	0.884166i	$-0.654728\pi$
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	0.0374992	+	0.999297i	$0.488061\pi$
$150$		0			0
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	0.334851	−	0.942271i	$-0.391314\pi$
$151$	−7.46410	−	7.46410i	−0.607420	−	0.607420i	−0.942271	+	0.334851i	$0.891314\pi$
$152$		0			0
$153$	−5.23610	−	3.74867i	−0.423313	−	0.303062i
$154$		0			0
$155$	−15.1149			−1.21405
$156$		0			0
$157$	−15.1962			−1.21278			−0.606392	−	0.795165i	$-0.707384\pi$
$157$	−15.1962			−1.21278			−0.606392	+	0.795165i	$0.707384\pi$
$158$		0			0
$159$	−5.38119	−	5.93462i	−0.426756	−	0.470646i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.378606	−	0.925558i	$-0.376404\pi$
$163$	14.9282	−	4.00000i	1.16927	−	0.313304i	0.790661	+	0.612254i	$0.209737\pi$
$164$		0			0
$165$	6.92003	+	2.22178i	0.538723	+	0.172965i
$166$		0			0
$167$	−11.3969	−	3.05379i	−0.881920	−	0.236310i	−0.210685	−	0.977554i	$-0.567569\pi$
$167$	−11.3969	−	3.05379i	−0.881920	−	0.236310i	−0.671235	+	0.741244i	$0.734236\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	3.06412	−	0.507263i	0.234319	−	0.0387914i
$172$		0			0
$173$	3.71794	−	6.43966i	0.282670	−	0.489598i	−0.689372	−	0.724408i	$-0.742113\pi$
$173$	3.71794	−	6.43966i	0.282670	−	0.489598i	0.972041	+	0.234809i	$0.0754466\pi$
$174$		0			0
$175$	0.267949	+	1.00000i	0.0202551	+	0.0755929i
$176$		0			0
$177$	−6.97136	−	4.49274i	−0.524000	−	0.337695i
$178$		0			0
$179$	9.37191	+	16.2326i	0.700489	+	1.21328i	0.968295	+	0.249810i	$0.0803683\pi$
$179$	9.37191	+	16.2326i	0.700489	+	1.21328i	−0.267805	+	0.963473i	$0.586298\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$		0			0
$183$	−2.56218	−	11.8505i	−0.189402	−	0.876017i
$184$		0			0
$185$	−14.1631	+	8.17709i	−1.04129	+	0.601191i
$186$		0			0
$187$	2.66025	−	2.66025i	0.194537	−	0.194537i
$188$		0			0
$189$	−5.75895	−	4.56448i	−0.418902	−	0.332017i
$190$		0			0
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.964096	−	0.265553i	$-0.0855544\pi$
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.252073	+	0.967708i	$0.418888\pi$
$192$		0			0
$193$	1.86603	−	6.96410i	0.134319	−	0.501287i	−0.865680	−	0.500597i	$-0.833114\pi$
$193$	1.86603	−	6.96410i	0.134319	−	0.501287i	1.00000		0.000689767i	$-0.000219560\pi$
$194$		0			0
$195$	−7.27375	+	13.0630i	−0.520884	+	0.935462i
$196$		0			0
$197$	−0.453620	+	1.69293i	−0.0323191	+	0.120617i	−0.980201	−	0.198006i	$-0.936554\pi$
$197$	−0.453620	+	1.69293i	−0.0323191	+	0.120617i	0.947882	+	0.318622i	$0.103220\pi$
$198$		0			0
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	0.471238	−	0.882006i	$-0.343807\pi$
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	−0.528221	+	0.849107i	$0.677141\pi$
$200$		0			0
$201$	13.4990	−	6.93756i	0.952149	−	0.489338i
$202$		0			0
$203$	5.53242	−	5.53242i	0.388300	−	0.388300i
$204$		0			0
$205$	−1.33013	+	0.767949i	−0.0929001	+	0.0536359i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			1.81448i			0.125510i
$210$		0			0
$211$	−6.09808	−	10.5622i	−0.419809	−	0.727130i	0.576111	−	0.817371i	$-0.304570\pi$
$211$	−6.09808	−	10.5622i	−0.419809	−	0.727130i	−0.995920	+	0.0902411i	$0.971236\pi$
$212$		0			0
$213$	−4.49274	+	6.97136i	−0.307837	+	0.477670i
$214$		0			0
$215$	−5.07880	−	18.9543i	−0.346371	−	1.29268i
$216$		0			0
$217$	−4.46410	+	7.73205i	−0.303043	+	0.524886i
$218$		0			0
$219$	−14.9193	−	0.729677i	−1.00816	−	0.0493070i
$220$		0			0
$221$	4.29311	+	6.43966i	0.288786	+	0.433179i
$222$		0			0
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.582206	−	0.813041i	$-0.697810\pi$
$223$	−22.2942	−	5.97372i	−1.49293	−	0.400030i	−0.910726	+	0.413011i	$0.864477\pi$
$224$		0			0
$225$	2.18567	+	0.214307i	0.145711	+	0.0142871i
$226$		0			0
$227$	15.1149	−	4.05001i	1.00321	−	0.268809i	0.280419	−	0.959878i	$-0.409526\pi$
$227$	15.1149	−	4.05001i	1.00321	−	0.268809i	0.722789	+	0.691069i	$0.242860\pi$
$228$		0			0
$229$	10.1244	+	10.1244i	0.669036	+	0.669036i	0.957493	−	0.288457i	$-0.0931421\pi$
$229$	10.1244	+	10.1244i	0.669036	+	0.669036i	−0.288457	+	0.957493i	$0.593142\pi$
$230$		0			0
$231$	3.18035	−	2.88377i	0.209252	−	0.189738i
$232$		0			0
$233$	−7.43588			−0.487141			−0.243570	−	0.969883i	$-0.578319\pi$
$233$	−7.43588			−0.487141			−0.243570	+	0.969883i	$0.578319\pi$
$234$		0			0
$235$	22.9282			1.49567
$236$		0			0
$237$	−2.56622	+	2.32691i	−0.166694	+	0.151149i
$238$		0			0
$239$	7.10381	+	7.10381i	0.459507	+	0.459507i	0.898494	−	0.438986i	$-0.144662\pi$
$239$	7.10381	+	7.10381i	0.459507	+	0.459507i	−0.438986	+	0.898494i	$0.644662\pi$
$240$		0			0
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	−0.0182524	−	0.999833i	$-0.505810\pi$
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	0.484110	+	0.875007i	$0.339144\pi$
$242$		0			0
$243$	−13.3619	+	8.02865i	−0.857167	+	0.515038i
$244$		0			0
$245$	−11.5630	−	3.09828i	−0.738730	−	0.197942i
$246$		0			0
$247$	−3.66025	−	0.732051i	−0.232896	−	0.0465793i
$248$		0			0
$249$	3.03206	+	0.148292i	0.192149	+	0.00939765i
$250$		0			0
$251$	10.9433	−	18.9543i	0.690735	−	1.19639i	−0.280863	−	0.959748i	$-0.590621\pi$
$251$	10.9433	−	18.9543i	0.690735	−	1.19639i	0.971597	−	0.236640i	$-0.0760461\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	4.82195	−	7.48221i	0.301962	−	0.468554i
$256$		0			0
$257$	8.29863	+	14.3737i	0.517655	+	0.896604i	0.999790	+	0.0205071i	$0.00652807\pi$
$257$	8.29863	+	14.3737i	0.517655	+	0.896604i	−0.482135	+	0.876097i	$0.660139\pi$
$258$		0			0
$259$			9.66025i			0.600259i
$260$		0			0
$261$	−6.85641	−	15.1149i	−0.424401	−	0.935586i
$262$		0			0
$263$	−10.3681	+	5.98604i	−0.639326	+	0.369115i	−0.784355	−	0.620312i	$-0.787006\pi$
$263$	−10.3681	+	5.98604i	−0.639326	+	0.369115i	0.145029	+	0.989427i	$0.453673\pi$
$264$		0			0
$265$	7.83013	−	7.83013i	0.481001	−	0.481001i
$266$		0			0
$267$	−15.4765	+	7.95383i	−0.947145	+	0.486766i
$268$		0			0
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	0.762821	−	0.646610i	$-0.223814\pi$
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	−0.178570	+	0.983927i	$0.557147\pi$
$270$		0			0
$271$	−0.535898	+	2.00000i	−0.0325535	+	0.121491i	−0.980291	−	0.197561i	$-0.936698\pi$
$271$	−0.535898	+	2.00000i	−0.0325535	+	0.121491i	0.947737	+	0.319052i	$0.103365\pi$
$272$		0			0
$273$	4.53416	+	7.57901i	0.274420	+	0.458703i
$274$		0			0
$275$	−0.332073	+	1.23931i	−0.0200248	+	0.0747334i
$276$		0			0
$277$	3.10770	+	1.79423i	0.186723	+	0.107805i	0.590448	−	0.807076i	$-0.298951\pi$
$277$	3.10770	+	1.79423i	0.186723	+	0.107805i	−0.403724	+	0.914881i	$0.632285\pi$
$278$		0			0
$279$	12.0215	+	14.6352i	0.719710	+	0.876189i
$280$		0			0
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	−0.0501922	−	0.998740i	$-0.515983\pi$
$281$	15.9006	−	15.9006i	0.948547	−	0.948547i	0.998740	+	0.0501922i	$0.0159834\pi$
$282$		0			0
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.291618	−	0.956535i	$-0.405806\pi$
$283$	21.2942	−	12.2942i	1.26581	−	0.730816i	0.974192	+	0.225719i	$0.0724731\pi$
$284$		0			0
$285$	0.907241	+	4.19615i	0.0537403	+	0.248559i
$286$		0			0
$287$			0.907241i			0.0535527i
$288$		0			0
$289$	6.19615	+	10.7321i	0.364480	+	0.631297i
$290$		0			0
$291$	18.9345	+	12.2025i	1.10996	+	0.715320i
$292$		0			0
$293$	−5.69846	−	21.2669i	−0.332908	−	1.24243i	−0.906120	−	0.423021i	$-0.860970\pi$
$293$	−5.69846	−	21.2669i	−0.332908	−	1.24243i	0.573212	−	0.819407i	$-0.305697\pi$
$294$		0			0
$295$	5.73205	−	9.92820i	0.333733	−	0.578042i
$296$		0			0
$297$	−3.35253	−	8.46753i	−0.194534	−	0.491336i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−11.1962	−	3.00000i	−0.645335	−	0.172917i
$302$		0			0
$303$	32.5540	+	10.4520i	1.87018	+	0.600449i
$304$		0			0
$305$	16.1881	−	4.33760i	0.926930	−	0.248370i
$306$		0			0
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	0.965960	−	0.258693i	$-0.0832919\pi$
$307$	12.3923	+	12.3923i	0.707266	+	0.707266i	−0.258693	+	0.965960i	$0.583292\pi$
$308$		0			0
$309$	8.06065	+	8.88965i	0.458554	+	0.505715i
$310$		0			0
$311$	−4.29311			−0.243440			−0.121720	−	0.992564i	$-0.538841\pi$
$311$	−4.29311			−0.243440			−0.121720	+	0.992564i	$0.538841\pi$
$312$		0			0
$313$	2.00000			0.113047			0.0565233	−	0.998401i	$-0.481998\pi$
$313$	2.00000			0.113047			0.0565233	+	0.998401i	$0.481998\pi$
$314$		0			0
$315$	5.91297	−	8.25916i	0.333158	−	0.465351i
$316$		0			0
$317$	11.2754	+	11.2754i	0.633288	+	0.633288i	0.948891	−	0.315603i	$-0.102207\pi$
$317$	11.2754	+	11.2754i	0.633288	+	0.633288i	−0.315603	+	0.948891i	$0.602207\pi$
$318$		0			0
$319$	9.36603	−	2.50962i	0.524397	−	0.140512i
$320$		0			0
$321$	−8.83503	+	27.5179i	−0.493123	+	1.53590i
$322$		0			0
$323$	2.14655	+	0.575167i	0.119437	+	0.0320032i
$324$		0			0
$325$	−2.36603	−	1.16987i	−0.131243	−	0.0648929i
$326$		0			0
$327$	−0.335500	+	6.85980i	−0.0185532	+	0.379348i
$328$		0			0
$329$	6.77174	−	11.7290i	0.373338	−	0.646640i
$330$		0			0
$331$	−5.05256	−	18.8564i	−0.277714	−	1.03644i	−0.954001	−	0.299804i	$-0.903079\pi$
$331$	−5.05256	−	18.8564i	−0.277714	−	1.03644i	0.676287	−	0.736638i	$-0.263588\pi$
$332$		0			0
$333$	19.1822	+	7.21011i	1.05118	+	0.395112i
$334$		0			0
$335$	10.4897	+	18.1687i	0.573112	+	0.992660i
$336$		0			0
$337$		−	11.5359i		−	0.628400i	−0.949357	−	0.314200i	$-0.898264\pi$
$337$		−	11.5359i		−	0.628400i	0.949357	−	0.314200i	$-0.101736\pi$
$338$		0			0
$339$	−21.9545	+	4.74673i	−1.19240	+	0.257807i
$340$		0			0
$341$	−9.58244	+	5.53242i	−0.518918	+	0.299597i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.4618	−	12.9683i	−1.20581	−	0.696175i	−0.243969	−	0.969783i	$-0.578450\pi$
$347$	−22.4618	−	12.9683i	−1.20581	−	0.696175i	−0.961841	+	0.273608i	$0.911783\pi$
$348$		0			0
$349$	1.50962	−	5.63397i	0.0808080	−	0.301580i	−0.913679	−	0.406436i	$-0.866772\pi$
$349$	1.50962	−	5.63397i	0.0808080	−	0.301580i	0.994487	+	0.104856i	$0.0334382\pi$
$350$		0			0
$351$	18.4337	−	3.34667i	0.983916	−	0.178632i
$352$		0			0
$353$	7.05932	−	26.3457i	0.375730	−	1.40224i	−0.476546	−	0.879149i	$-0.658111\pi$
$353$	7.05932	−	26.3457i	0.375730	−	1.40224i	0.852276	−	0.523093i	$-0.175222\pi$
$354$		0			0
$355$	−9.92820	−	5.73205i	−0.526934	−	0.304226i
$356$		0			0
$357$	−2.40340	−	4.67652i	−0.127202	−	0.247508i
$358$		0			0
$359$	12.0611	−	12.0611i	0.636559	−	0.636559i	−0.313146	−	0.949705i	$-0.601383\pi$
$359$	12.0611	−	12.0611i	0.636559	−	0.636559i	0.949705	+	0.313146i	$0.101383\pi$
$360$		0			0
$361$	15.5263	−	8.96410i	0.817173	−	0.471795i
$362$		0			0
$363$	−13.4219	+	2.90192i	−0.704468	+	0.152311i
$364$		0			0
$365$		−	20.6473i		−	1.08073i
$366$		0			0
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	0.963735	−	0.266861i	$-0.0859866\pi$
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	−0.712976	+	0.701188i	$0.752653\pi$
$368$		0			0
$369$	1.80149	+	0.677136i	0.0937819	+	0.0352503i
$370$		0			0
$371$	−1.69293	−	6.31812i	−0.0878928	−	0.328020i
$372$		0			0
$373$	9.79423	−	16.9641i	0.507126	−	0.878368i	−0.492840	−	0.870120i	$-0.664041\pi$
$373$	9.79423	−	16.9641i	0.507126	−	0.878368i	0.999966	−	0.00824796i	$-0.00262544\pi$
$374$		0			0
$375$	0.864563	−	17.6773i	0.0446459	−	0.912852i
$376$		0			0
$377$	1.28380	+	19.9061i	0.0661192	+	1.02522i
$378$		0			0
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	0.380729	−	0.924687i	$-0.375673\pi$
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	−0.132622	+	0.991167i	$0.542340\pi$
$380$		0			0
$381$	−8.00804	+	24.9421i	−0.410264	+	1.27782i
$382$		0			0
$383$	13.5435	−	3.62896i	0.692039	−	0.185431i	0.104377	−	0.994538i	$-0.466715\pi$
$383$	13.5435	−	3.62896i	0.692039	−	0.185431i	0.587662	+	0.809106i	$0.300048\pi$
$384$		0			0
$385$	4.19615	+	4.19615i	0.213856	+	0.213856i
$386$		0			0
$387$	−14.3135	+	19.9929i	−0.727596	+	1.01630i
$388$		0			0
$389$	−5.28933			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$389$	−5.28933			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	1.05553	+	1.16409i	0.0532446	+	0.0587206i
$394$		0			0
$395$	−3.38587	−	3.38587i	−0.170362	−	0.170362i
$396$		0			0
$397$	8.56218	−	2.29423i	0.429723	−	0.115144i	−0.0374729	−	0.999298i	$-0.511931\pi$
$397$	8.56218	−	2.29423i	0.429723	−	0.115144i	0.467196	+	0.884154i	$0.345264\pi$
$398$		0			0
$399$	2.41450	+	0.775212i	0.120876	+	0.0388091i
$400$		0			0
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.861933	−	0.507021i	$-0.169253\pi$
$401$	27.1314	+	7.26985i	1.35488	+	0.363039i	0.492946	+	0.870060i	$0.335920\pi$
$402$		0			0
$403$	−7.29423	−	21.5622i	−0.363351	−	1.07409i
$404$		0			0
$405$	−11.9868	−	17.9057i	−0.595629	−	0.889739i
$406$		0			0
$407$	−5.98604	+	10.3681i	−0.296717	+	0.513929i
$408$		0			0
$409$	3.00962	+	11.2321i	0.148816	+	0.555389i	0.999556	+	0.0298020i	$0.00948767\pi$
$409$	3.00962	+	11.2321i	0.148816	+	0.555389i	−0.850740	+	0.525587i	$0.823846\pi$
$410$		0			0
$411$	8.58908	+	5.53528i	0.423668	+	0.273035i
$412$		0			0
$413$	−3.38587	−	5.86450i	−0.166608	−	0.288573i
$414$		0			0
$415$			4.19615i			0.205981i
$416$		0			0
$417$	0.875644	+	4.05001i	0.0428805	+	0.198330i
$418$		0			0
$419$	7.22536	−	4.17156i	0.352982	−	0.203794i	−0.313016	−	0.949748i	$-0.601339\pi$
$419$	7.22536	−	4.17156i	0.352982	−	0.203794i	0.665998	+	0.745954i	$0.268006\pi$
$420$		0			0
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	−0.686588	−	0.727046i	$-0.740893\pi$
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	0.727046	+	0.686588i	$0.240893\pi$
$422$		0			0
$423$	−18.2358	−	22.2007i	−0.886657	−	1.07943i
$424$		0			0
$425$	1.36086	+	0.785693i	0.0660114	+	0.0381117i
$426$		0			0
$427$	2.56218	−	9.56218i	0.123992	−	0.462746i
$428$		0			0
$429$	0.170025	+	10.9440i	0.00820890	+	0.528381i
$430$		0			0
$431$	−0.542599	+	2.02501i	−0.0261361	+	0.0975412i	−0.977762	−	0.209718i	$-0.932745\pi$
$431$	−0.542599	+	2.02501i	−0.0261361	+	0.0975412i	0.951626	+	0.307260i	$0.0994120\pi$
$432$		0			0
$433$	−6.10770	−	3.52628i	−0.293517	−	0.169462i	0.346010	−	0.938231i	$-0.387536\pi$
$433$	−6.10770	−	3.52628i	−0.293517	−	0.169462i	−0.639527	+	0.768769i	$0.720870\pi$
$434$		0			0
$435$	20.4050	−	10.4867i	0.978344	−	0.502800i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	4.09808	−	2.36603i	0.195591	−	0.112924i	−0.399007	−	0.916948i	$-0.630645\pi$
$439$	4.09808	−	2.36603i	0.195591	−	0.112924i	0.594597	+	0.804024i	$0.297312\pi$
$440$		0			0
$441$	6.19657	+	13.6603i	0.295075	+	0.650488i
$442$		0			0
$443$		−	29.5656i		−	1.40470i	−0.711830	−	0.702351i	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$		0			0
$445$	−12.0263	−	20.8301i	−0.570100	−	0.987443i
$446$		0			0
$447$	−5.09465	+	7.90535i	−0.240969	+	0.373910i
$448$		0			0
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	0.891530	−	0.452961i	$-0.149632\pi$
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	−0.998568	+	0.0534890i	$0.982966\pi$
$450$		0			0
$451$	−0.562178	+	0.973721i	−0.0264719	+	0.0458507i
$452$		0			0
$453$	−18.2614	−	0.893131i	−0.857996	−	0.0419629i
$454$		0			0
$455$	−10.1576	+	6.77174i	−0.476196	+	0.317464i
$456$		0			0
$457$	−26.9904	−	7.23205i	−1.26256	−	0.338301i	−0.435382	−	0.900246i	$-0.643387\pi$
$457$	−26.9904	−	7.23205i	−1.26256	−	0.338301i	−0.827175	+	0.561945i	$0.810053\pi$
$458$		0			0
$459$	−11.0799	+	1.28199i	−0.517166	+	0.0598382i
$460$		0			0
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.758880	−	0.651230i	$-0.774253\pi$
$461$	−23.4135	+	6.27363i	−1.09048	+	0.292192i	−0.331595	+	0.943422i	$0.607587\pi$
$462$		0			0
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	0.964314	−	0.264762i	$-0.0852934\pi$
$463$	15.0526	+	15.0526i	0.699552	+	0.699552i	−0.264762	+	0.964314i	$0.585293\pi$
$464$		0			0
$465$	−19.3940	+	17.5854i	−0.899377	+	0.815506i
$466$		0			0
$467$	30.4728			1.41011			0.705057	−	0.709151i	$-0.250921\pi$
$467$	30.4728			1.41011			0.705057	+	0.709151i	$0.250921\pi$
$468$		0			0
$469$	12.3923			0.572223
$470$		0			0
$471$	−19.4984	+	17.6800i	−0.898437	+	0.814653i
$472$		0			0
$473$	−10.1576	−	10.1576i	−0.467047	−	0.467047i
$474$		0			0
$475$	−0.732051	+	0.196152i	−0.0335888	+	0.00900009i
$476$		0			0
$477$	−13.8093	−	1.35401i	−0.632285	−	0.0619960i
$478$		0			0
$479$	−8.46467	−	2.26810i	−0.386761	−	0.103632i	0.0601988	−	0.998186i	$-0.480827\pi$
$479$	−8.46467	−	2.26810i	−0.386761	−	0.103632i	−0.446959	+	0.894554i	$0.647493\pi$
$480$		0			0
$481$	−18.5000	−	16.2583i	−0.843527	−	0.741316i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.5685	+	26.9654i	−0.706928	+	1.22444i
$486$		0			0
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	0.939324	+	0.343030i	$0.111453\pi$
$487$	6.56218	+	24.4904i	0.297361	+	1.10977i	−0.641964	+	0.766735i	$0.721880\pi$
$488$		0			0
$489$	14.5007	−	22.5007i	0.655746	−	1.01752i
$490$		0			0
$491$	12.5147	+	21.6761i	0.564780	+	0.978227i	0.997070	+	0.0764928i	$0.0243722\pi$
$491$	12.5147	+	21.6761i	0.564780	+	0.978227i	−0.432290	+	0.901734i	$0.642294\pi$
$492$		0			0
$493$		−	11.8756i		−	0.534852i
$494$		0			0
$495$	11.4641	−	5.20035i	0.515273	−	0.233738i
$496$		0			0
$497$	−5.86450	+	3.38587i	−0.263059	+	0.151877i
$498$		0			0
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	−0.799932	−	0.600091i	$-0.795131\pi$
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	0.600091	+	0.799932i	$0.295131\pi$
$500$		0			0
$501$	−18.1765	+	9.34143i	−0.812064	+	0.417345i
$502$		0			0
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.168666	−	0.985673i	$-0.553946\pi$
$503$	−24.8188	−	14.3292i	−1.10662	−	0.638906i	−0.937951	+	0.346767i	$0.887279\pi$
$504$		0			0
$505$	−12.2321	+	45.6506i	−0.544319	+	2.03143i
$506$		0			0
$507$	−22.1453	−	4.07236i	−0.983509	−	0.180860i
$508$		0			0
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	0.824865	+	0.565330i	$0.191251\pi$
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	−0.997019	+	0.0771582i	$0.975415\pi$
$510$		0			0
$511$	−10.5622	−	6.09808i	−0.467243	−	0.269763i
$512$		0			0
$513$	3.34143	−	4.21584i	0.147528	−	0.186134i
$514$		0			0
$515$	−11.7290	+	11.7290i	−0.516841	+	0.516841i
$516$		0			0
$517$	14.5359	−	8.39230i	0.639288	−	0.369093i
$518$		0			0
$519$	−2.72172	−	12.5885i	−0.119470	−	0.552572i
$520$		0			0
$521$			33.2835i			1.45818i	0.684419	+	0.729089i	$0.260056\pi$
$521$			33.2835i			1.45818i	−0.684419	+	0.729089i	$0.739944\pi$
$522$		0			0
$523$	6.49038	+	11.2417i	0.283805	+	0.491564i	0.972319	−	0.233659i	$-0.0750700\pi$
$523$	6.49038	+	11.2417i	0.283805	+	0.491564i	−0.688514	+	0.725223i	$0.741737\pi$
$524$		0			0
$525$	1.50726	+	0.971364i	0.0657823	+	0.0423938i
$526$		0			0
$527$	3.50742	+	13.0899i	0.152785	+	0.570203i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	−14.1721	+	2.34618i	−0.615018	+	0.101816i
$532$		0			0
$533$	−1.73742	−	1.52690i	−0.0752562	−	0.0661373i
$534$		0			0
$535$	−38.5885	−	10.3397i	−1.66832	−	0.447026i
$536$		0			0
$537$	30.9111	+	9.92447i	1.33391	+	0.428273i
$538$		0			0
$539$	−8.46467	+	2.26810i	−0.364599	+	0.0976940i
$540$		0			0
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.999828	+	0.0185354i	$0.00590034\pi$
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.0185354	+	0.999828i	$0.494100\pi$
$542$		0			0
$543$	3.49036	+	3.84933i	0.149786	+	0.165191i
$544$		0			0
$545$	−9.49346			−0.406655
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	−17.0751	−	12.2246i	−0.728748	−	0.521732i
$550$		0			0
$551$	4.05001	+	4.05001i	0.172536	+	0.172536i
$552$		0			0
$553$	−2.73205	+	0.732051i	−0.116179	+	0.0311300i
$554$		0			0
$555$	−8.65920	+	26.9703i	−0.367563	+	1.14482i
$556$		0			0
$557$	−39.3140	−	10.5342i	−1.66579	−	0.446347i	−0.701819	−	0.712355i	$-0.747628\pi$
$557$	−39.3140	−	10.5342i	−1.66579	−	0.446347i	−0.963971	+	0.266009i	$0.914295\pi$
$558$		0			0
$559$	24.5885	−	16.3923i	1.03998	−	0.693321i
$560$		0			0
$561$	0.318318	−	6.50849i	0.0134394	−	0.274788i
$562$		0			0
$563$	−2.14655	+	3.71794i	−0.0904665	+	0.156693i	−0.907708	−	0.419603i	$-0.862169\pi$
$563$	−2.14655	+	3.71794i	−0.0904665	+	0.156693i	0.817241	+	0.576296i	$0.195502\pi$
$564$		0			0
$565$	−8.03590	−	29.9904i	−0.338073	−	1.26170i
$566$		0			0
$567$	−12.6999	+	0.843533i	−0.533347	+	0.0354250i
$568$		0			0
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	0.983646	−	0.180113i	$-0.0576463\pi$
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	−0.647805	+	0.761806i	$0.724313\pi$
$570$		0			0
$571$		−	40.0526i		−	1.67615i	−0.545557	−	0.838074i	$-0.683682\pi$
$571$		−	40.0526i		−	1.67615i	0.545557	−	0.838074i	$-0.316318\pi$
$572$		0			0
$573$	32.8564	−	7.10381i	1.37260	−	0.296766i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.49038	−	3.49038i	0.145306	−	0.145306i	−0.630711	−	0.776018i	$-0.717237\pi$
$577$	3.49038	−	3.49038i	0.145306	−	0.145306i	0.776018	+	0.630711i	$0.217237\pi$
$578$		0			0
$579$	−5.70810	−	11.1068i	−0.237220	−	0.461581i
$580$		0			0
$581$	2.14655	+	1.23931i	0.0890541	+	0.0514154i
$582$		0			0
$583$	2.09808	−	7.83013i	0.0868934	−	0.324291i
$584$		0			0
$585$	5.86520	+	25.2240i	0.242496	+	1.04288i
$586$		0			0
$587$	−5.20035	+	19.4080i	−0.214641	+	0.801053i	0.771651	+	0.636046i	$0.219431\pi$
$587$	−5.20035	+	19.4080i	−0.214641	+	0.801053i	−0.986292	+	0.165006i	$0.947235\pi$
$588$		0			0
$589$	−5.66025	−	3.26795i	−0.233227	−	0.134654i
$590$		0			0
$591$	1.38761	+	2.69999i	0.0570785	+	0.111063i
$592$		0			0
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	−0.454828	−	0.890579i	$-0.650299\pi$
$593$	10.6112	−	10.6112i	0.435751	−	0.435751i	0.890579	+	0.454828i	$0.150299\pi$
$594$		0			0
$595$	6.29423	−	3.63397i	0.258038	−	0.148978i
$596$		0			0
$597$	−1.57139	+	0.339746i	−0.0643126	+	0.0139049i
$598$		0			0
$599$			21.2224i			0.867126i	0.901123	+	0.433563i	$0.142744\pi$
$599$			21.2224i			0.867126i	−0.901123	+	0.433563i	$0.857256\pi$
$600$		0			0
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	0.932975	−	0.359941i	$-0.117203\pi$
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	−0.778205	+	0.628010i	$0.783870\pi$
$602$		0			0
$603$	9.24923	−	24.6072i	0.376658	−	1.00208i
$604$		0			0
$605$	−4.91277	−	18.3347i	−0.199732	−	0.745411i
$606$		0			0
$607$	5.09808	−	8.83013i	0.206925	−	0.358404i	−0.743820	−	0.668380i	$-0.766988\pi$
$607$	5.09808	−	8.83013i	0.206925	−	0.358404i	0.950744	+	0.309977i	$0.100321\pi$
$608$		0			0
$609$	0.661992	−	13.5354i	0.0268253	−	0.548483i
$610$		0			0
$611$	11.0648	+	32.7083i	0.447636	+	1.32324i
$612$		0			0
$613$	16.3564	+	4.38269i	0.660629	+	0.177015i	0.573530	−	0.819185i	$-0.305574\pi$
$613$	16.3564	+	4.38269i	0.660629	+	0.177015i	0.0870991	+	0.996200i	$0.472240\pi$
$614$		0			0
$615$	−0.813227	+	2.53291i	−0.0327925	+	0.102137i
$616$		0			0
$617$	36.3818	−	9.74847i	1.46468	−	0.392459i	0.563574	−	0.826066i	$-0.309426\pi$
$617$	36.3818	−	9.74847i	1.46468	−	0.392459i	0.901102	+	0.433607i	$0.142759\pi$
$618$		0			0
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	0.933899	−	0.357536i	$-0.116383\pi$
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	−0.357536	+	0.933899i	$0.616383\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.2076			−0.569216
$624$		0			0
$625$	28.1244			1.12497
$626$		0			0
$627$	2.11107	+	2.32818i	0.0843078	+	0.0929786i
$628$		0			0
$629$	10.3681	+	10.3681i	0.413404	+	0.413404i
$630$		0			0
$631$	−2.26795	+	0.607695i	−0.0902856	+	0.0241920i	−0.303679	−	0.952774i	$-0.598215\pi$
$631$	−2.26795	+	0.607695i	−0.0902856	+	0.0241920i	0.213393	+	0.976966i	$0.431548\pi$
$632$		0			0
$633$	−20.1131	−	6.45761i	−0.799425	−	0.256667i
$634$		0			0
$635$	−34.9764	−	9.37191i	−1.38800	−	0.371913i
$636$		0			0
$637$	−1.16025	−	17.9904i	−0.0459709	−	0.712805i
$638$		0			0
$639$	2.34618	+	14.1721i	0.0928136	+	0.560641i
$640$		0			0
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	−0.991281	−	0.131767i	$-0.957935\pi$
$641$	−9.65949	+	16.7307i	−0.381527	+	0.660824i	0.609754	+	0.792591i	$0.291268\pi$
$642$		0			0
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	−0.955132	−	0.296179i	$-0.904287\pi$
$643$	−7.00000	−	26.1244i	−0.276053	−	1.03024i	0.679079	−	0.734065i	$-0.262379\pi$
$644$		0			0
$645$	−28.5692	−	18.4116i	−1.12491	−	0.724955i
$646$		0			0
$647$	−7.22536	−	12.5147i	−0.284058	−	0.492003i	0.688322	−	0.725405i	$-0.258348\pi$
$647$	−7.22536	−	12.5147i	−0.284058	−	0.492003i	−0.972380	+	0.233402i	$0.925014\pi$
$648$		0			0
$649$		−	8.39230i		−	0.329427i
$650$		0			0
$651$	3.26795	+	15.1149i	0.128081	+	0.592398i
$652$		0			0
$653$	−33.6156	+	19.4080i	−1.31548	+	0.759492i	−0.982998	−	0.183617i	$-0.941219\pi$
$653$	−33.6156	+	19.4080i	−1.31548	+	0.759492i	−0.332482	+	0.943110i	$0.607886\pi$
$654$		0			0
$655$	−1.53590	+	1.53590i	−0.0600125	+	0.0600125i
$656$		0			0
$657$	−19.9921	+	16.4217i	−0.779967	+	0.640672i
$658$		0			0
$659$	−27.1759	−	15.6900i	−1.05862	−	0.611197i	−0.133572	−	0.991039i	$-0.542645\pi$
$659$	−27.1759	−	15.6900i	−1.05862	−	0.611197i	−0.925051	+	0.379842i	$0.875978\pi$
$660$		0			0
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	0.824769	+	0.565470i	$0.191305\pi$
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	−0.997006	+	0.0773274i	$0.975361\pi$
$662$		0			0
$663$	13.0008	+	3.26797i	0.504909	+	0.126917i
$664$		0			0
$665$	−0.907241	+	3.38587i	−0.0351813	+	0.131298i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−35.5561	+	18.2734i	−1.37468	+	0.706489i
$670$		0			0
$671$	8.67520	−	8.67520i	0.334902	−	0.334902i
$672$		0			0
$673$	−11.0096	+	6.35641i	−0.424390	+	0.245021i	−0.696954	−	0.717116i	$-0.745462\pi$
$673$	−11.0096	+	6.35641i	−0.424390	+	0.245021i	0.272564	+	0.962138i	$0.412128\pi$
$674$		0			0
$675$	3.05379	−	2.26795i	0.117541	−	0.0872934i
$676$		0			0
$677$		−	38.8159i		−	1.49182i	−0.666048	−	0.745909i	$-0.732015\pi$
$677$		−	38.8159i		−	1.49182i	0.666048	−	0.745909i	$-0.267985\pi$
$678$		0			0
$679$	9.19615	+	15.9282i	0.352916	+	0.611268i
$680$		0			0
$681$	14.6820	−	22.7821i	0.562617	−	0.873011i
$682$		0			0
$683$	4.26054	+	15.9006i	0.163025	+	0.608418i	0.998284	+	0.0585607i	$0.0186511\pi$
$683$	4.26054	+	15.9006i	0.163025	+	0.608418i	−0.835259	+	0.549857i	$0.814682\pi$
$684$		0			0
$685$	−7.06218	+	12.2321i	−0.269832	+	0.467363i
$686$		0			0
$687$	24.7699	+	1.21145i	0.945031	+	0.0462196i
$688$		0			0
$689$	14.9488	+	7.39139i	0.569505	+	0.281590i
$690$		0			0
$691$	41.8827	+	11.2224i	1.59329	+	0.426921i	0.943008	−	0.332770i	$-0.107983\pi$
$691$	41.8827	+	11.2224i	1.59329	+	0.426921i	0.650284	+	0.759691i	$0.274650\pi$
$692$		0			0
$693$	0.725614	−	7.40039i	0.0275638	−	0.281118i
$694$		0			0
$695$	−5.53242	+	1.48241i	−0.209857	+	0.0562309i
$696$		0			0
$697$	0.973721	+	0.973721i	0.0368823	+	0.0368823i
$698$		0			0
$699$	−9.54106	+	8.65131i	−0.360876	+	0.327223i
$700$		0			0
$701$	20.3152			0.767295			0.383647	−	0.923480i	$-0.374668\pi$
$701$	20.3152			0.767295			0.383647	+	0.923480i	$0.374668\pi$
$702$		0			0
$703$	−7.07180			−0.266718
$704$		0			0
$705$	29.4194	−	26.6759i	1.10800	−	1.00467i
$706$		0			0
$707$	19.7400	+	19.7400i	0.742401	+	0.742401i
$708$		0			0
$709$	−9.96410	+	2.66987i	−0.374210	+	0.100269i	−0.441022	−	0.897496i	$-0.645384\pi$
$709$	−9.96410	+	2.66987i	−0.374210	+	0.100269i	0.0668121	+	0.997766i	$0.478717\pi$
$710$		0			0
$711$	−0.585497	+	5.97136i	−0.0219578	+	0.223944i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−15.0981	+	0.973721i	−0.564636	+	0.0364151i
$716$		0			0
$717$	17.3799	+	0.850019i	0.649065	+	0.0317446i
$718$		0			0
$719$	5.86450	−	10.1576i	0.218709	−	0.378815i	−0.735705	−	0.677302i	$-0.763149\pi$
$719$	5.86450	−	10.1576i	0.218709	−	0.378815i	0.954413	+	0.298488i	$0.0964822\pi$
$720$		0			0
$721$	2.53590	+	9.46410i	0.0944418	+	0.352462i
$722$		0			0
$723$	7.02496	−	10.9006i	0.261261	−	0.405398i
$724$		0			0
$725$	2.02501	+	3.50742i	0.0752069	+	0.130262i
$726$		0			0
$727$		−	25.5167i		−	0.946361i	−0.880966	−	0.473180i	$-0.843106\pi$
$727$		−	25.5167i		−	0.946361i	0.880966	−	0.473180i	$-0.156894\pi$
$728$		0			0
$729$	−7.80385	+	25.8476i	−0.289031	+	0.957320i
$730$		0			0
$731$	−15.2364	+	8.79674i	−0.563539	+	0.325359i
$732$		0			0
$733$	−36.2224	+	36.2224i	−1.33791	+	1.33791i	−0.439820	+	0.898086i	$0.644958\pi$
$733$	−36.2224	+	36.2224i	−1.33791	+	1.33791i	−0.898086	+	0.439820i	$0.855042\pi$
$734$		0			0
$735$	−18.4413	+	9.47753i	−0.680216	+	0.349584i
$736$		0			0
$737$	13.3004	+	7.67898i	0.489926	+	0.282859i
$738$		0			0
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	0.107037	+	0.994255i	$0.465864\pi$
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	−0.589825	+	0.807531i	$0.700803\pi$
$740$		0			0
$741$	−5.54822	+	3.31924i	−0.203819	+	0.121935i
$742$		0			0
$743$	13.5435	−	50.5449i	0.496862	−	1.85431i	−0.0224808	−	0.999747i	$-0.507156\pi$
$743$	13.5435	−	50.5449i	0.496862	−	1.85431i	0.519343	−	0.854566i	$-0.326177\pi$
$744$		0			0
$745$	−11.2583	−	6.50000i	−0.412473	−	0.238142i
$746$		0			0
$747$	4.06300	−	3.33739i	0.148658	−	0.122109i
$748$		0			0
$749$	−16.6862	+	16.6862i	−0.609702	+	0.609702i
$750$		0			0
$751$	−38.2750	+	22.0981i	−1.39667	+	0.806370i	−0.994043	−	0.108992i	$-0.965238\pi$
$751$	−38.2750	+	22.0981i	−1.39667	+	0.806370i	−0.402632	+	0.915362i	$0.631904\pi$
$752$		0			0
$753$	−8.01105	−	37.0526i	−0.291939	−	1.35027i
$754$		0			0
$755$		−	25.2725i		−	0.919759i
$756$		0			0
$757$	12.3923	+	21.4641i	0.450406	+	0.780126i	0.998411	−	0.0563489i	$-0.0179459\pi$
$757$	12.3923	+	21.4641i	0.450406	+	0.780126i	−0.548005	+	0.836475i	$0.684613\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	0.942703	−	0.333634i	$-0.108275\pi$
$761$	−1.11777	−	4.17156i	−0.0405190	−	0.151219i	−0.983222	+	0.182415i	$0.941608\pi$
$762$		0			0
$763$	−2.80385	+	4.85641i	−0.101506	+	0.175814i
$764$		0			0
$765$	−2.51810	−	15.2106i	−0.0910423	−	0.549941i
$766$		0			0
$767$	16.9293	+	3.38587i	0.611283	+	0.122257i
$768$		0			0
$769$	−2.16987	−	0.581416i	−0.0782476	−	0.0209664i	0.219483	−	0.975616i	$-0.429563\pi$
$769$	−2.16987	−	0.581416i	−0.0782476	−	0.0209664i	−0.297730	+	0.954650i	$0.596230\pi$
$770$		0			0
$771$	27.3712	+	8.78792i	0.985748	+	0.316489i
$772$		0			0
$773$	5.98604	−	1.60396i	0.215303	−	0.0576903i	−0.149555	−	0.988753i	$-0.547784\pi$
$773$	5.98604	−	1.60396i	0.215303	−	0.0576903i	0.364858	+	0.931063i	$0.381117\pi$
$774$		0			0
$775$	−3.26795	−	3.26795i	−0.117388	−	0.117388i
$776$		0			0
$777$	11.2393	+	12.3952i	0.403206	+	0.444675i
$778$		0			0
$779$	−0.664146			−0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	−26.3830	−	11.4169i	−0.942851	−	0.408008i
$784$		0			0
$785$	−25.7261	−	25.7261i	−0.918203	−	0.918203i
$786$		0			0
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	−0.0518385	−	0.998655i	$-0.516508\pi$
$787$	11.2942	−	3.02628i	0.402596	−	0.107875i	0.454434	+	0.890780i	$0.349841\pi$
$788$		0			0
$789$	−6.33898	+	19.7436i	−0.225674	+	0.702891i
$790$		0			0
$791$	−17.7150	−	4.74673i	−0.629874	−	0.168774i
$792$		0			0
$793$	14.0000	+	21.0000i	0.497155	+	0.745732i
$794$		0			0
$795$	0.936928	−	19.1569i	0.0332294	−	0.679426i
$796$		0			0
$797$	8.58622	−	14.8718i	0.304139	−	0.526785i	−0.672930	−	0.739706i	$-0.734964\pi$
$797$	8.58622	−	14.8718i	0.304139	−	0.526785i	0.977069	+	0.212921i	$0.0682978\pi$
$798$		0			0
$799$	−5.32051	−	19.8564i	−0.188226	−	0.702469i
$800$		0			0
$801$	−10.6041	+	28.2118i	−0.374678	+	0.996815i
$802$		0			0
$803$	−7.55743	−	13.0899i	−0.266696	−	0.461931i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18.7321	−	4.05001i	0.659399	−	0.142567i
$808$		0			0
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	−0.156097	−	0.987742i	$-0.549891\pi$
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	0.777361	+	0.629055i	$0.216558\pi$
$810$		0			0
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	−0.957062	−	0.289882i	$-0.906384\pi$
$811$	−19.0000	+	19.0000i	−0.667180	+	0.667180i	0.289882	+	0.957062i	$0.406384\pi$
$812$		0			0
$813$	1.63929	+	3.18972i	0.0574925	+	0.111868i
$814$		0			0
$815$	32.0442	+	18.5007i	1.12246	+	0.648052i
$816$		0			0
$817$	2.19615	−	8.19615i	0.0768336	−	0.286747i
$818$		0			0
$819$	14.6357	+	4.44942i	0.511411	+	0.155475i
$820$		0			0
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	−0.988250	−	0.152844i	$-0.951157\pi$
$821$	−1.60396	+	5.98604i	−0.0559784	+	0.208914i	0.932272	+	0.361758i	$0.117823\pi$
$822$		0			0
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	0.248084	−	0.968739i	$-0.420199\pi$
$823$	−13.3923	−	7.73205i	−0.466826	−	0.269522i	−0.714910	+	0.699216i	$0.753532\pi$
$824$		0			0
$825$	1.01580	+	1.97653i	0.0353656	+	0.0688139i
$826$		0			0
$827$	3.62896	−	3.62896i	0.126191	−	0.126191i	−0.641190	−	0.767382i	$-0.721559\pi$
$827$	3.62896	−	3.62896i	0.126191	−	0.126191i	0.767382	+	0.641190i	$0.221559\pi$
$828$		0			0
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	−0.814067	−	0.580771i	$-0.802751\pi$
$829$	−20.6769	+	11.9378i	−0.718139	+	0.414618i	0.0959284	+	0.995388i	$0.469418\pi$
$830$		0			0
$831$	6.07502	−	1.31347i	0.210740	−	0.0455636i
$832$		0			0
$833$			10.7328i			0.371868i
$834$		0			0
$835$	−14.1244	−	24.4641i	−0.488793	−	0.846615i
$836$		0			0
$837$	32.4524	+	4.79215i	1.12172	+	0.165641i
$838$		0			0
$839$	−2.02501	−	7.55743i	−0.0699110	−	0.260911i	0.922120	−	0.386903i	$-0.126455\pi$
$839$	−2.02501	−	7.55743i	−0.0699110	−	0.260911i	−0.992031	+	0.125992i	$0.959789\pi$
$840$		0			0
$841$	0.803848	−	1.39230i	0.0277189	−	0.0480105i
$842$		0			0
$843$	1.90261	−	38.9017i	0.0655294	−	1.33985i
$844$		0			0
$845$	4.12707	−	30.8494i	0.141976	−	1.06125i
$846$		0			0
$847$	−10.8301	−	2.90192i	−0.372128	−	0.0997113i
$848$		0			0
$849$	13.0191	−	40.5497i	0.446814	−	1.39166i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−20.6340	−	20.6340i	−0.706494	−	0.706494i	0.259302	−	0.965796i	$-0.416507\pi$
$853$	−20.6340	−	20.6340i	−0.706494	−	0.706494i	−0.965796	+	0.259302i	$0.916507\pi$
$854$		0			0
$855$	6.04612	+	4.32860i	0.206773	+	0.148035i
$856$		0			0
$857$	−35.7621			−1.22161			−0.610806	−	0.791781i	$-0.709154\pi$
$857$	−35.7621			−1.22161			−0.610806	+	0.791781i	$0.709154\pi$
$858$		0			0
$859$	23.1769			0.790786			0.395393	−	0.918512i	$-0.370608\pi$
$859$	23.1769			0.790786			0.395393	+	0.918512i	$0.370608\pi$
$860$		0			0
$861$	1.05553	+	1.16409i	0.0359725	+	0.0396721i
$862$		0			0
$863$	−12.0611	−	12.0611i	−0.410563	−	0.410563i	0.471371	−	0.881935i	$-0.343759\pi$
$863$	−12.0611	−	12.0611i	−0.410563	−	0.410563i	−0.881935	+	0.471371i	$0.843759\pi$
$864$		0			0
$865$	17.1962	−	4.60770i	0.584687	−	0.156666i
$866$		0			0
$867$	20.4366	+	6.56147i	0.694063	+	0.222839i
$868$		0			0
$869$	−3.38587	−	0.907241i	−0.114858	−	0.0307760i
$870$		0			0
$871$	−20.8564	+	23.7321i	−0.706692	+	0.804130i
$872$		0			0
$873$	38.4921	−	6.37233i	1.30276	−	0.215671i
$874$		0			0
$875$	7.22536	−	12.5147i	0.244262	−	0.423074i
$876$		0			0
$877$	3.00962	+	11.2321i	0.101628	+	0.379279i	0.997941	−	0.0641422i	$-0.0204311\pi$
$877$	3.00962	+	11.2321i	0.101628	+	0.379279i	−0.896313	+	0.443422i	$0.853764\pi$
$878$		0			0
$879$	−32.0549	−	20.6579i	−1.08118	−	0.696775i
$880$		0			0
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	0.541054	−	0.840988i	$-0.318026\pi$
$881$	−13.5880	−	23.5350i	−0.457790	−	0.792916i	−0.998844	+	0.0480724i	$0.984692\pi$
$882$		0			0
$883$			39.3731i			1.32501i	0.749058	+	0.662505i	$0.230506\pi$
$883$			39.3731i			1.32501i	−0.749058	+	0.662505i	$0.769494\pi$
$884$		0			0
$885$	−4.19615	−	19.4080i	−0.141052	−	0.652392i
$886$		0			0
$887$	46.4949	−	26.8438i	1.56115	−	0.901328i	0.564005	−	0.825772i	$-0.309260\pi$
$887$	46.4949	−	26.8438i	1.56115	−	0.901328i	0.997142	−	0.0755567i	$-0.0240734\pi$
$888$		0			0
$889$	−15.1244	+	15.1244i	−0.507255	+	0.507255i
$890$		0			0
$891$	−14.1533	−	6.96426i	−0.474152	−	0.233311i
$892$		0			0
$893$	8.58622	+	4.95725i	0.287327	+	0.165888i
$894$		0			0
$895$	−11.6147	+	43.3468i	−0.388238	+	1.44892i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.03984	+	33.7371i	−0.301495	+	1.12520i
$900$		0			0
$901$	−8.59808	−	4.96410i	−0.286443	−	0.165378i
$902$		0			0
$903$	−17.8563	+	9.17688i	−0.594219	+	0.305387i
$904$		0			0
$905$	−5.07880	+	5.07880i	−0.168825	+	0.168825i
$906$		0			0
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	−0.229848	−	0.973227i	$-0.573823\pi$
$907$	15.0000	−	8.66025i	0.498067	−	0.287559i	0.727915	+	0.685668i	$0.240490\pi$
$908$		0			0
$909$	53.9308	−	24.4641i	1.78877	−	0.811423i
$910$		0			0
$911$		−	9.25036i		−	0.306478i	−0.988189	−	0.153239i	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$		0			0
$913$	1.53590	+	2.66025i	0.0508308	+	0.0880416i
$914$		0			0
$915$	15.7246	−	24.3998i	0.519839	−	0.806632i
$916$		0			0
$917$	0.332073	+	1.23931i	0.0109660	+	0.0409257i
$918$		0			0
$919$	22.2942	−	38.6147i	0.735419	−	1.27378i	−0.219121	−	0.975698i	$-0.570319\pi$
$919$	22.2942	−	38.6147i	0.735419	−	1.27378i	0.954539	−	0.298085i	$-0.0963478\pi$
$920$		0			0
$921$	30.3186	+	1.48282i	0.999031	+	0.0488607i
$922$		0			0
$923$	3.38587	−	16.9293i	0.111447	−	0.557236i
$924$		0			0
$925$	−4.83013	−	1.29423i	−0.158814	−	0.0425540i
$926$		0			0
$927$	20.6854	+	2.02822i	0.679398	+	0.0666155i
$928$		0			0
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.622347	−	0.782742i	$-0.286179\pi$
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.930339	+	0.366701i	$0.119513\pi$
$930$		0			0
$931$	−3.66025	−	3.66025i	−0.119960	−	0.119960i
$932$		0			0
$933$	−5.50854	+	4.99484i	−0.180341	+	0.163524i
$934$		0			0
$935$	9.00727			0.294569
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$		0			0
$939$	2.56622	−	2.32691i	0.0837455	−	0.0759358i
$940$		0			0
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.957206	+	0.289407i	$0.0934582\pi$
$941$	38.2408	+	38.2408i	1.24661	+	1.24661i	0.289407	+	0.957206i	$0.406542\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−2.02215	−	17.4769i	−0.0657805	−	0.568523i
$946$		0			0
$947$	39.6016	+	10.6112i	1.28688	+	0.344818i	0.836475	−	0.548006i	$-0.184613\pi$
$947$	39.6016	+	10.6112i	1.28688	+	0.344818i	0.450405	+	0.892824i	$0.351279\pi$
$948$		0			0
$949$	29.4545	−	9.96410i	0.956133	−	0.323448i
$950$		0			0
$951$	27.5859	+	1.34918i	0.894535	+	0.0437500i
$952$		0			0
$953$	21.8866	−	37.9087i	0.708976	−	1.22798i	−0.256261	−	0.966608i	$-0.582491\pi$
$953$	21.8866	−	37.9087i	0.708976	−	1.22798i	0.965237	−	0.261375i	$-0.0841760\pi$
$954$		0			0
$955$	12.0263	+	44.8827i	0.389161	+	1.45237i
$956$		0			0
$957$	9.09782	−	14.1171i	0.294091	−	0.456340i
$958$		0			0
$959$	4.17156	+	7.22536i	0.134707	+	0.233319i
$960$		0			0
$961$		−	8.85641i		−	0.285691i
$962$		0			0
$963$	20.6795	+	45.5877i	0.666387	+	1.46904i
$964$		0			0
$965$	14.9488	−	8.63071i	0.481220	−	0.277832i
$966$		0			0
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	−0.704794	−	0.709412i	$-0.748961\pi$
$967$	0.143594	−	0.143594i	0.00461766	−	0.00461766i	0.709412	+	0.704794i	$0.248961\pi$
$968$		0			0
$969$	3.42345	−	1.75941i	0.109977	−	0.0565205i
$970$		0			0
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.999101	−	0.0423987i	$-0.0135000\pi$
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.462832	+	0.886446i	$0.346833\pi$
$972$		0			0
$973$	−0.875644	+	3.26795i	−0.0280719	+	0.104766i
$974$		0			0
$975$	−4.39697	+	1.25169i	−0.140816	+	0.0400860i
$976$		0			0
$977$	−7.60192	+	28.3707i	−0.243207	+	0.907661i	0.731069	+	0.682303i	$0.239022\pi$
$977$	−7.60192	+	28.3707i	−0.243207	+	0.907661i	−0.974276	+	0.225357i	$0.927645\pi$
$978$		0			0
$979$	−15.2487	−	8.80385i	−0.487351	−	0.281372i
$980$		0			0
$981$	7.55058	+	9.19222i	0.241071	+	0.293485i
$982$		0			0
$983$	−4.38209	+	4.38209i	−0.139767	+	0.139767i	−0.773528	−	0.633762i	$-0.781510\pi$
$983$	−4.38209	+	4.38209i	−0.139767	+	0.139767i	0.633762	+	0.773528i	$0.281510\pi$
$984$		0			0
$985$	−3.63397	+	2.09808i	−0.115788	+	0.0668503i
$986$		0			0
$987$	−4.95725	−	22.9282i	−0.157791	−	0.729813i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	12.7846	+	22.1436i	0.406117	+	0.703414i	0.994451	−	0.105203i	$-0.0335494\pi$
$991$	12.7846	+	22.1436i	0.406117	+	0.703414i	−0.588334	+	0.808618i	$0.700216\pi$
$992$		0			0
$993$	−28.4216	−	18.3164i	−0.901931	−	0.581255i
$994$		0			0
$995$	−0.575167	−	2.14655i	−0.0182340	−	0.0680503i
$996$		0			0
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$		0			0
$999$	33.0015	−	13.0662i	1.04412	−	0.413397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.c.353.2		8
3.2	odd	2	inner	624.2.cn.c.353.1		8
4.3	odd	2		39.2.k.b.2.2	yes	8
12.11	even	2		39.2.k.b.2.1	✓	8
13.7	odd	12	inner	624.2.cn.c.449.1		8
20.3	even	4		975.2.bp.e.899.1		8
20.7	even	4		975.2.bp.f.899.2		8
20.19	odd	2		975.2.bo.d.626.1		8
39.20	even	12	inner	624.2.cn.c.449.2		8
52.3	odd	6		507.2.f.f.239.4		8
52.7	even	12		39.2.k.b.20.1	yes	8
52.11	even	12		507.2.f.f.437.1		8
52.15	even	12		507.2.f.e.437.4		8
52.19	even	12		507.2.k.d.488.2		8
52.23	odd	6		507.2.f.e.239.1		8
52.31	even	4		507.2.k.f.89.1		8
52.35	odd	6		507.2.k.e.188.1		8
52.43	odd	6		507.2.k.f.188.2		8
52.47	even	4		507.2.k.e.89.2		8
52.51	odd	2		507.2.k.d.80.1		8
60.23	odd	4		975.2.bp.e.899.2		8
60.47	odd	4		975.2.bp.f.899.1		8
60.59	even	2		975.2.bo.d.626.2		8
156.11	odd	12		507.2.f.f.437.4		8
156.23	even	6		507.2.f.e.239.4		8
156.35	even	6		507.2.k.e.188.2		8
156.47	odd	4		507.2.k.e.89.1		8
156.59	odd	12		39.2.k.b.20.2	yes	8
156.71	odd	12		507.2.k.d.488.1		8
156.83	odd	4		507.2.k.f.89.2		8
156.95	even	6		507.2.k.f.188.1		8
156.107	even	6		507.2.f.f.239.1		8
156.119	odd	12		507.2.f.e.437.1		8
156.155	even	2		507.2.k.d.80.2		8
260.7	odd	12		975.2.bp.e.449.2		8
260.59	even	12		975.2.bo.d.176.2		8
260.163	odd	12		975.2.bp.f.449.1		8
780.59	odd	12		975.2.bo.d.176.1		8
780.527	even	12		975.2.bp.e.449.1		8
780.683	even	12		975.2.bp.f.449.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	12.11	even	2
39.2.k.b.2.2	yes	8	4.3	odd	2
39.2.k.b.20.1	yes	8	52.7	even	12
39.2.k.b.20.2	yes	8	156.59	odd	12
507.2.f.e.239.1		8	52.23	odd	6
507.2.f.e.239.4		8	156.23	even	6
507.2.f.e.437.1		8	156.119	odd	12
507.2.f.e.437.4		8	52.15	even	12
507.2.f.f.239.1		8	156.107	even	6
507.2.f.f.239.4		8	52.3	odd	6
507.2.f.f.437.1		8	52.11	even	12
507.2.f.f.437.4		8	156.11	odd	12
507.2.k.d.80.1		8	52.51	odd	2
507.2.k.d.80.2		8	156.155	even	2
507.2.k.d.488.1		8	156.71	odd	12
507.2.k.d.488.2		8	52.19	even	12
507.2.k.e.89.1		8	156.47	odd	4
507.2.k.e.89.2		8	52.47	even	4
507.2.k.e.188.1		8	52.35	odd	6
507.2.k.e.188.2		8	156.35	even	6
507.2.k.f.89.1		8	52.31	even	4
507.2.k.f.89.2		8	156.83	odd	4
507.2.k.f.188.1		8	156.95	even	6
507.2.k.f.188.2		8	52.43	odd	6
624.2.cn.c.353.1		8	3.2	odd	2	inner
624.2.cn.c.353.2		8	1.1	even	1	trivial
624.2.cn.c.449.1		8	13.7	odd	12	inner
624.2.cn.c.449.2		8	39.20	even	12	inner
975.2.bo.d.176.1		8	780.59	odd	12
975.2.bo.d.176.2		8	260.59	even	12
975.2.bo.d.626.1		8	20.19	odd	2
975.2.bo.d.626.2		8	60.59	even	2
975.2.bp.e.449.1		8	780.527	even	12
975.2.bp.e.449.2		8	260.7	odd	12
975.2.bp.e.899.1		8	20.3	even	4
975.2.bp.e.899.2		8	60.23	odd	4
975.2.bp.f.449.1		8	260.163	odd	12
975.2.bp.f.449.2		8	780.683	even	12
975.2.bp.f.899.1		8	60.47	odd	4
975.2.bp.f.899.2		8	20.7	even	4

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +O(q^{10})\)	\(q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +(1.69293 + 0.453620i) q^{11} +(-1.59808 + 3.23205i) q^{13} +(4.14187 + 0.202571i) q^{15} +(1.07328 - 1.85897i) q^{17} +(0.267949 + 1.00000i) q^{19} +(1.32691 - 2.05896i) q^{21} +0.732051i q^{25} +(-3.09808 - 4.17156i) q^{27} +(4.79122 - 2.76621i) q^{29} +(-4.46410 + 4.46410i) q^{31} +(2.69999 - 1.38761i) q^{33} +(2.93225 + 1.69293i) q^{35} +(-1.76795 + 6.59808i) q^{37} +(1.70983 + 6.00637i) q^{39} +(-0.166037 + 0.619657i) q^{41} +(-7.09808 - 4.09808i) q^{43} +(5.55017 - 4.55896i) q^{45} +(6.77174 - 6.77174i) q^{47} +(-4.33013 + 2.50000i) q^{49} +(-0.785693 - 3.63397i) q^{51} -4.62518i q^{53} +(2.09808 + 3.63397i) q^{55} +(1.50726 + 0.971364i) q^{57} +(-1.23931 - 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-0.692934 - 4.18567i) q^{63} +(-8.17709 + 2.76621i) q^{65} +(8.46410 + 2.26795i) q^{67} +(-4.62518 + 1.23931i) q^{71} +(-6.09808 - 6.09808i) q^{73} +(0.851708 + 0.939303i) q^{75} +2.47863 q^{77} -2.00000 q^{79} +(-8.82860 - 1.74811i) q^{81} +(1.23931 + 1.23931i) q^{83} +(4.96410 - 1.33013i) q^{85} +(2.92931 - 9.12372i) q^{87} +(-9.70398 - 2.60017i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(-0.534160 + 10.9217i) q^{93} +(-1.23931 + 2.14655i) q^{95} +(3.36603 + 12.5622i) q^{97} +(1.84997 - 4.92177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9	\( 8 q + 2 q^{3} + 4 q^{7} + 4 q^{9} + 8 q^{13} + 14 q^{15} + 16 q^{19} + 4 q^{21} - 4 q^{27} - 8 q^{31} + 16 q^{33} - 28 q^{37} + 14 q^{39} - 36 q^{43} - 20 q^{45} - 4 q^{55} + 16 q^{57} + 28 q^{61} + 8 q^{63} + 40 q^{67} - 28 q^{73} - 12 q^{75} - 16 q^{79} + 4 q^{81} + 12 q^{85} + 34 q^{87} - 8 q^{91} + 4 q^{93} + 20 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^7 + 4 * q^9 + 8 * q^13 + 14 * q^15 + 16 * q^19 + 4 * q^21 - 4 * q^27 - 8 * q^31 + 16 * q^33 - 28 * q^37 + 14 * q^39 - 36 * q^43 - 20 * q^45 - 4 * q^55 + 16 * q^57 + 28 * q^61 + 8 * q^63 + 40 * q^67 - 28 * q^73 - 12 * q^75 - 16 * q^79 + 4 * q^81 + 12 * q^85 + 34 * q^87 - 8 * q^91 + 4 * q^93 + 20 * q^97 - 40 * q^99

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