LMFDB - Embedded newform 936.2.dg.c.829.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(829,936)] 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("936.829"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.dg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			829.1
Root			$-1.40126 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	936.829
Dual form			936.2.dg.c.901.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +2.23607 q^{5} +(3.43649 + 1.98406i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(-3.13331 - 0.427051i) q^{10} +(0.252009 + 0.436492i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-4.43649 - 3.43649i) q^{14} +(3.42705 + 2.06284i) q^{16} +(2.93649 - 5.08615i) q^{17} +(0.252009 - 0.436492i) q^{19} +(4.30902 + 1.19682i) q^{20} +(-0.269767 - 0.659767i) q^{22} +(4.43649 + 7.68423i) q^{23} +(-3.16312 - 3.99933i) q^{26} +(5.56036 + 5.66271i) q^{28} +(-8.55025 + 4.93649i) q^{29} -4.47214i q^{31} +(-4.40822 - 3.54508i) q^{32} +(-5.08615 + 6.56619i) q^{34} +(7.68423 + 4.43649i) q^{35} +(-3.60611 - 6.24597i) q^{37} +(-0.436492 + 0.563508i) q^{38} +(-5.80948 - 2.50000i) q^{40} +(-1.06351 + 0.614017i) q^{41} +(-7.68423 - 4.43649i) q^{43} +(0.252009 + 0.976025i) q^{44} +(-4.74911 - 11.6149i) q^{46} +3.96812i q^{47} +(4.37298 + 7.57423i) q^{49} +(3.66854 + 6.20820i) q^{52} -7.87298i q^{53} +(0.563508 + 0.976025i) q^{55} +(-6.71002 - 8.99685i) q^{56} +(12.9239 - 5.28435i) q^{58} +(-1.22803 + 2.12702i) q^{59} +(-0.866025 - 0.500000i) q^{61} +(-0.854102 + 6.26662i) q^{62} +(5.50000 + 5.80948i) q^{64} +(5.80948 + 5.59017i) q^{65} +(-0.976025 - 1.69052i) q^{67} +(8.38105 - 8.22957i) q^{68} +(-9.92030 - 7.68423i) q^{70} +(4.30948 + 2.48808i) q^{71} +13.1324i q^{73} +(3.86022 + 9.44092i) q^{74} +(0.719258 - 0.706258i) q^{76} +2.00000i q^{77} +14.0000 q^{79} +(7.66312 + 4.61266i) q^{80} +(1.60752 - 0.657284i) q^{82} +2.96008 q^{83} +(6.56619 - 11.3730i) q^{85} +(9.92030 + 7.68423i) q^{86} +(-0.166725 - 1.41579i) q^{88} +(1.74597 - 1.00803i) q^{89} +(3.96812 + 13.7460i) q^{91} +(4.43649 + 17.1825i) q^{92} +(0.757843 - 5.56036i) q^{94} +(0.563508 - 0.976025i) q^{95} +(-15.0000 - 8.66025i) q^{97} +(-4.68113 - 11.4486i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 12 q^{7} - 20 q^{14} + 14 q^{16} + 8 q^{17} + 30 q^{20} - 6 q^{22} + 20 q^{23} + 6 q^{26} + 6 q^{28} + 12 q^{38} - 24 q^{41} - 30 q^{46} + 4 q^{49} + 20 q^{55} + 10 q^{56} + 36 q^{58} + 20 q^{62}+ \cdots - 60 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 + 12 * q^7 - 20 * q^14 + 14 * q^16 + 8 * q^17 + 30 * q^20 - 6 * q^22 + 20 * q^23 + 6 * q^26 + 6 * q^28 + 12 * q^38 - 24 * q^41 - 30 * q^46 + 4 * q^49 + 20 * q^55 + 10 * q^56 + 36 * q^58 + 20 * q^62 + 44 * q^64 - 4 * q^68 - 12 * q^71 + 6 * q^74 + 30 * q^76 + 112 * q^79 + 30 * q^80 - 10 * q^82 + 18 * q^88 - 48 * q^89 + 20 * q^92 - 10 * q^94 + 20 * q^95 - 120 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$2$	−1.40126	−	0.190983i	−0.990839	−	0.135045i
$3$		0			0
$3$		0			0
$4$	1.92705	+	0.535233i	0.963525	+	0.267617i
$5$	2.23607			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$6$		0			0
$7$	3.43649	+	1.98406i	1.29887	+	0.749904i	0.980209	−	0.197964i	$-0.0634330\pi$
$7$	3.43649	+	1.98406i	1.29887	+	0.749904i	0.318663	+	0.947868i	$0.396766\pi$
$8$	−2.59808	−	1.11803i	−0.918559	−	0.395285i
$9$		0			0
$10$	−3.13331	−	0.427051i	−0.990839	−	0.135045i
$11$	0.252009	+	0.436492i	0.0759834	+	0.131607i	0.901514	−	0.432751i	$-0.142457\pi$
$11$	0.252009	+	0.436492i	0.0759834	+	0.131607i	−0.825530	+	0.564358i	$0.809124\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−4.43649	−	3.43649i	−1.18570	−	0.918441i
$15$		0			0
$16$	3.42705	+	2.06284i	0.856763	+	0.515711i
$17$	2.93649	−	5.08615i	0.712204	−	1.23357i	−0.251824	−	0.967773i	$-0.581030\pi$
$17$	2.93649	−	5.08615i	0.712204	−	1.23357i	0.964028	−	0.265800i	$-0.0856362\pi$
$18$		0			0
$19$	0.252009	−	0.436492i	0.0578147	−	0.100138i	−0.835669	−	0.549233i	$-0.814920\pi$
$19$	0.252009	−	0.436492i	0.0578147	−	0.100138i	0.893484	+	0.449095i	$0.148253\pi$
$20$	4.30902	+	1.19682i	0.963525	+	0.267617i
$21$		0			0
$22$	−0.269767	−	0.659767i	−0.0575145	−	0.140663i
$23$	4.43649	+	7.68423i	0.925072	+	1.60227i	0.791445	+	0.611241i	$0.209329\pi$
$23$	4.43649	+	7.68423i	0.925072	+	1.60227i	0.133628	+	0.991032i	$0.457337\pi$
$24$		0			0
$25$		0			0
$26$	−3.16312	−	3.99933i	−0.620339	−	0.784334i
$27$		0			0
$28$	5.56036	+	5.66271i	1.05081	+	1.07015i
$29$	−8.55025	+	4.93649i	−1.58774	+	0.916683i	−0.594064	+	0.804418i	$0.702477\pi$
$29$	−8.55025	+	4.93649i	−1.58774	+	0.916683i	−0.993678	+	0.112266i	$0.964189\pi$
$30$		0			0
$31$		−	4.47214i		−	0.803219i	−0.915811	−	0.401610i	$-0.868451\pi$
$31$		−	4.47214i		−	0.803219i	0.915811	−	0.401610i	$-0.131549\pi$
$32$	−4.40822	−	3.54508i	−0.779270	−	0.626688i
$33$		0			0
$34$	−5.08615	+	6.56619i	−0.872268	+	1.12609i
$35$	7.68423	+	4.43649i	1.29887	+	0.749904i
$36$		0			0
$37$	−3.60611	−	6.24597i	−0.592841	−	1.02683i	−0.993848	−	0.110756i	$-0.964673\pi$
$37$	−3.60611	−	6.24597i	−0.592841	−	1.02683i	0.401007	−	0.916075i	$-0.368660\pi$
$38$	−0.436492	+	0.563508i	−0.0708083	+	0.0914131i
$39$		0			0
$40$	−5.80948	−	2.50000i	−0.918559	−	0.395285i
$41$	−1.06351	+	0.614017i	−0.166092	+	0.0958933i	−0.580742	−	0.814088i	$-0.697237\pi$
$41$	−1.06351	+	0.614017i	−0.166092	+	0.0958933i	0.414650	+	0.909981i	$0.363904\pi$
$42$		0			0
$43$	−7.68423	−	4.43649i	−1.17183	−	0.676559i	−0.217723	−	0.976011i	$-0.569863\pi$
$43$	−7.68423	−	4.43649i	−1.17183	−	0.676559i	−0.954111	+	0.299452i	$0.903196\pi$
$44$	0.252009	+	0.976025i	0.0379917	+	0.147141i
$45$		0			0
$46$	−4.74911	−	11.6149i	−0.700219	−	1.71252i
$47$			3.96812i			0.578810i	0.957207	+	0.289405i	$0.0934574\pi$
$47$			3.96812i			0.578810i	−0.957207	+	0.289405i	$0.906543\pi$
$48$		0			0
$49$	4.37298	+	7.57423i	0.624712	+	1.08203i
$50$		0			0
$51$		0			0
$52$	3.66854	+	6.20820i	0.508735	+	0.860923i
$53$		−	7.87298i		−	1.08144i	−0.841203	−	0.540719i	$-0.818152\pi$
$53$		−	7.87298i		−	1.08144i	0.841203	−	0.540719i	$-0.181848\pi$
$54$		0			0
$55$	0.563508	+	0.976025i	0.0759834	+	0.131607i
$56$	−6.71002	−	8.99685i	−0.896664	−	1.20225i
$57$		0			0
$58$	12.9239	−	5.28435i	1.69699	−	0.693869i
$59$	−1.22803	+	2.12702i	−0.159876	+	0.276914i	−0.934824	−	0.355112i	$-0.884443\pi$
$59$	−1.22803	+	2.12702i	−0.159876	+	0.276914i	0.774948	+	0.632026i	$0.217776\pi$
$60$		0			0
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	0.443533	−	0.896258i	$-0.353725\pi$
$61$	−0.866025	−	0.500000i	−0.110883	−	0.0640184i	−0.554416	+	0.832240i	$0.687058\pi$
$62$	−0.854102	+	6.26662i	−0.108471	+	0.795861i
$63$		0			0
$64$	5.50000	+	5.80948i	0.687500	+	0.726184i
$65$	5.80948	+	5.59017i	0.720577	+	0.693375i
$66$		0			0
$67$	−0.976025	−	1.69052i	−0.119240	−	0.206530i	0.800226	−	0.599698i	$-0.204713\pi$
$67$	−0.976025	−	1.69052i	−0.119240	−	0.206530i	−0.919467	+	0.393167i	$0.871379\pi$
$68$	8.38105	−	8.22957i	1.01635	−	0.997982i
$69$		0			0
$70$	−9.92030	−	7.68423i	−1.18570	−	0.918441i
$71$	4.30948	+	2.48808i	0.511441	+	0.295280i	0.733426	−	0.679770i	$-0.237920\pi$
$71$	4.30948	+	2.48808i	0.511441	+	0.295280i	−0.221985	+	0.975050i	$0.571254\pi$
$72$		0			0
$73$			13.1324i			1.53703i	0.639832	+	0.768515i	$0.279004\pi$
$73$			13.1324i			1.53703i	−0.639832	+	0.768515i	$0.720996\pi$
$74$	3.86022	+	9.44092i	0.448741	+	1.09748i
$75$		0			0
$76$	0.719258	−	0.706258i	0.0825046	−	0.0810134i
$77$			2.00000i			0.227921i
$78$		0			0
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	7.66312	+	4.61266i	0.856763	+	0.515711i
$81$		0			0
$82$	1.60752	−	0.657284i	0.177521	−	0.0725849i
$83$	2.96008			0.324911			0.162456	−	0.986716i	$-0.448059\pi$
$83$	2.96008			0.324911			0.162456	+	0.986716i	$0.448059\pi$
$84$		0			0
$85$	6.56619	−	11.3730i	0.712204	−	1.23357i
$86$	9.92030	+	7.68423i	1.06973	+	0.828612i
$87$		0			0
$88$	−0.166725	−	1.41579i	−0.0177729	−	0.150924i
$89$	1.74597	−	1.00803i	0.185072	−	0.106851i	−0.404601	−	0.914493i	$-0.632590\pi$
$89$	1.74597	−	1.00803i	0.185072	−	0.106851i	0.589674	+	0.807642i	$0.299256\pi$
$90$		0			0
$91$	3.96812	+	13.7460i	0.415972	+	1.44097i
$92$	4.43649	+	17.1825i	0.462536	+	1.79140i
$93$		0			0
$94$	0.757843	−	5.56036i	0.0781656	−	0.573507i
$95$	0.563508	−	0.976025i	0.0578147	−	0.100138i
$96$		0			0
$97$	−15.0000	−	8.66025i	−1.52302	−	0.879316i	−0.999629	−	0.0272222i	$-0.991334\pi$
$97$	−15.0000	−	8.66025i	−1.52302	−	0.879316i	−0.523390	−	0.852093i	$-0.675333\pi$
$98$	−4.68113	−	11.4486i	−0.472866	−	1.15649i
$99$		0			0
$100$		0			0
$101$	6.81820	−	3.93649i	0.678437	−	0.391696i	−0.120829	−	0.992673i	$-0.538555\pi$
$101$	6.81820	−	3.93649i	0.678437	−	0.391696i	0.799266	+	0.600978i	$0.205222\pi$
$102$		0			0
$103$	10.6190			1.04632			0.523158	−	0.852236i	$-0.324754\pi$
$103$	10.6190			1.04632			0.523158	+	0.852236i	$0.324754\pi$
$104$	−3.95492	−	9.39993i	−0.387811	−	0.921739i
$105$		0			0
$106$	−1.50361	+	11.0321i	−0.146043	+	1.07153i
$107$	−0.756026	+	0.436492i	−0.0730878	+	0.0421972i	−0.536099	−	0.844155i	$-0.680102\pi$
$107$	−0.756026	+	0.436492i	−0.0730878	+	0.0421972i	0.463011	+	0.886353i	$0.346769\pi$
$108$		0			0
$109$	−2.45607			−0.235249			−0.117624	−	0.993058i	$-0.537528\pi$
$109$	−2.45607			−0.235249			−0.117624	+	0.993058i	$0.537528\pi$
$110$	−0.603217	−	1.47528i	−0.0575145	−	0.140663i
$111$		0			0
$112$	7.68423	+	13.8884i	0.726091	+	1.31233i
$113$	4.93649	−	8.55025i	0.464386	−	0.804340i	−0.534788	−	0.844987i	$-0.679608\pi$
$113$	4.93649	−	8.55025i	0.464386	−	0.804340i	0.999174	+	0.0406463i	$0.0129417\pi$
$114$		0			0
$115$	9.92030	+	17.1825i	0.925072	+	1.60227i
$116$	−19.1190	+	4.93649i	−1.77515	+	0.458342i
$117$		0			0
$118$	2.12702	−	2.74597i	0.195808	−	0.252787i
$119$	20.1825	−	11.6523i	1.85012	−	1.06817i
$120$		0			0
$121$	5.37298	−	9.30628i	0.488453	−	0.846025i
$122$	1.11803	+	0.866025i	0.101222	+	0.0784063i
$123$		0			0
$124$	2.39364	−	8.61803i	0.214955	−	0.773922i
$125$	−11.1803			−1.00000
$126$		0			0
$127$	−1.12702	−	1.95205i	−0.100007	−	0.173216i	0.811681	−	0.584102i	$-0.198553\pi$
$127$	−1.12702	−	1.95205i	−0.100007	−	0.173216i	−0.911687	+	0.410885i	$0.865220\pi$
$128$	−6.59741	−	9.19098i	−0.583134	−	0.812376i
$129$		0			0
$130$	−7.07295	−	8.94278i	−0.620339	−	0.784334i
$131$			11.7460i			1.02625i	0.858314	+	0.513125i	$0.171512\pi$
$131$			11.7460i			1.02625i	−0.858314	+	0.513125i	$0.828488\pi$
$132$		0			0
$133$	1.73205	−	1.00000i	0.150188	−	0.0867110i
$134$	1.04480	+	2.55527i	0.0902571	+	0.220741i
$135$		0			0
$136$	−13.3157	+	9.93112i	−1.14181	+	0.851586i
$137$	0.190525	+	0.110000i	0.0162776	+	0.00939790i	0.508117	−	0.861288i	$-0.330342\pi$
$137$	0.190525	+	0.110000i	0.0162776	+	0.00939790i	−0.491839	+	0.870686i	$0.663675\pi$
$138$		0			0
$139$	8.44025	+	4.87298i	0.715893	+	0.413321i	0.813239	−	0.581930i	$-0.197702\pi$
$139$	8.44025	+	4.87298i	0.715893	+	0.413321i	−0.0973462	+	0.995251i	$0.531035\pi$
$140$	12.4333	+	12.6622i	1.05081	+	1.07015i
$141$		0			0
$142$	−5.56351	−	4.30948i	−0.466879	−	0.361643i
$143$	−0.436492	+	1.76406i	−0.0365013	+	0.147518i
$144$		0			0
$145$	−19.1190	+	11.0383i	−1.58774	+	0.916683i
$146$	2.50806	−	18.4019i	0.207569	−	1.52295i
$147$		0			0
$148$	−3.60611	−	13.9664i	−0.296420	−	1.14803i
$149$	4.36214	−	7.55544i	0.357360	−	0.618966i	−0.630159	−	0.776466i	$-0.717010\pi$
$149$	4.36214	−	7.55544i	0.357360	−	0.618966i	0.987519	+	0.157500i	$0.0503436\pi$
$150$		0			0
$151$		−	10.8963i		−	0.886730i	−0.896341	−	0.443365i	$-0.853785\pi$
$151$		−	10.8963i		−	0.886730i	0.896341	−	0.443365i	$-0.146215\pi$
$152$	−1.14275	+	0.852284i	−0.0926893	+	0.0691294i
$153$		0			0
$154$	0.381966	−	2.80252i	0.0307797	−	0.225833i
$155$		−	10.0000i		−	0.803219i
$156$		0			0
$157$			1.25403i			0.100083i	0.998747	+	0.0500414i	$0.0159353\pi$
$157$			1.25403i			0.100083i	−0.998747	+	0.0500414i	$0.984065\pi$
$158$	−19.6176	−	2.67376i	−1.56069	−	0.212713i
$159$		0			0
$160$	−9.85707	−	7.92705i	−0.779270	−	0.626688i
$161$			35.2091i			2.77486i
$162$		0			0
$163$	−8.44025	+	14.6190i	−0.661092	+	1.14504i	0.319237	+	0.947675i	$0.396573\pi$
$163$	−8.44025	+	14.6190i	−0.661092	+	1.14504i	−0.980329	+	0.197370i	$0.936760\pi$
$164$	−2.37808	+	0.614017i	−0.185697	+	0.0479467i
$165$		0			0
$166$	−4.14784	−	0.565326i	−0.321935	−	0.0438778i
$167$	−8.12702	+	4.69214i	−0.628887	+	0.363088i	−0.780321	−	0.625379i	$-0.784944\pi$
$167$	−8.12702	+	4.69214i	−0.628887	+	0.363088i	0.151434	+	0.988467i	$0.451611\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−11.3730	+	14.6825i	−0.872268	+	1.12609i
$171$		0			0
$172$	−12.4333	−	12.6622i	−0.948034	−	0.965484i
$173$	−15.1485	−	8.74597i	−1.15172	−	0.664944i	−0.202411	−	0.979301i	$-0.564878\pi$
$173$	−15.1485	−	8.74597i	−1.15172	−	0.664944i	−0.949305	+	0.314357i	$0.898211\pi$
$174$		0			0
$175$		0			0
$176$	−0.0367676	+	2.01573i	−0.00277146	+	0.151942i
$177$		0			0
$178$	−2.63907	+	1.07907i	−0.197807	+	0.0808795i
$179$	4.44013	−	2.56351i	0.331871	−	0.191606i	−0.324801	−	0.945782i	$-0.605297\pi$
$179$	4.44013	−	2.56351i	0.331871	−	0.191606i	0.656671	+	0.754177i	$0.271964\pi$
$180$		0			0
$181$		−	0.745967i		−	0.0554473i	−0.999616	−	0.0277236i	$-0.991174\pi$
$181$		−	0.745967i		−	0.0554473i	0.999616	−	0.0277236i	$-0.00882584\pi$
$182$	−2.93511	−	20.0195i	−0.217565	−	1.48394i
$183$		0			0
$184$	−2.93511	−	24.9244i	−0.216379	−	1.83745i
$185$	−8.06351	−	13.9664i	−0.592841	−	1.02683i
$186$		0			0
$187$	2.96008			0.216463
$188$	−2.12387	+	7.64677i	−0.154899	+	0.557698i
$189$		0			0
$190$	−0.976025	+	1.26004i	−0.0708083	+	0.0914131i
$191$	9.87298	−	17.1005i	0.714384	−	1.23735i	−0.248813	−	0.968552i	$-0.580040\pi$
$191$	9.87298	−	17.1005i	0.714384	−	1.23735i	0.963197	−	0.268798i	$-0.0866263\pi$
$192$		0			0
$193$	7.11895	−	4.11013i	0.512433	−	0.295853i	−0.221400	−	0.975183i	$-0.571063\pi$
$193$	7.11895	−	4.11013i	0.512433	−	0.295853i	0.733833	+	0.679330i	$0.237729\pi$
$194$	19.3649	+	15.0000i	1.39032	+	1.07694i
$195$		0			0
$196$	4.37298	+	16.9365i	0.312356	+	1.20975i
$197$	−1.22803	−	2.12702i	−0.0874938	−	0.151544i	0.818957	−	0.573854i	$-0.194552\pi$
$197$	−1.22803	−	2.12702i	−0.0874938	−	0.151544i	−0.906451	+	0.422311i	$0.861219\pi$
$198$		0			0
$199$	3.43649	−	5.95218i	0.243606	−	0.421939i	−0.718132	−	0.695906i	$-0.755003\pi$
$199$	3.43649	−	5.95218i	0.243606	−	0.421939i	0.961739	+	0.273968i	$0.0883361\pi$
$200$		0			0
$201$		0			0
$202$	−10.3059	+	4.21388i	−0.725118	+	0.296488i
$203$	−39.1772			−2.74970
$204$		0			0
$205$	−2.37808	+	1.37298i	−0.166092	+	0.0958933i
$206$	−14.8799	−	2.02804i	−1.03673	−	0.141300i
$207$		0			0
$208$	3.74663	+	13.9271i	0.259782	+	0.965667i
$209$	0.254033			0.0175719
$210$		0			0
$211$	12.1244	−	7.00000i	0.834675	−	0.481900i	−0.0207756	−	0.999784i	$-0.506614\pi$
$211$	12.1244	−	7.00000i	0.834675	−	0.481900i	0.855451	+	0.517884i	$0.173280\pi$
$212$	4.21388	−	15.1716i	0.289411	−	1.04199i
$213$		0			0
$214$	1.14275	−	0.467250i	0.0781168	−	0.0319405i
$215$	−17.1825	−	9.92030i	−1.17183	−	0.676559i
$216$		0			0
$217$	8.87298	−	15.3685i	0.602337	−	1.04328i
$218$	3.44159	+	0.469067i	0.233094	+	0.0317692i
$219$		0			0
$220$	0.563508	+	2.18246i	0.0379917	+	0.147141i
$221$	20.3446	−	5.87298i	1.36853	−	0.395060i
$222$		0			0
$223$	−12.4919	+	7.21222i	−0.836522	+	0.482966i	−0.856080	−	0.516843i	$-0.827107\pi$
$223$	−12.4919	+	7.21222i	−0.836522	+	0.482966i	0.0195587	+	0.999809i	$0.493774\pi$
$224$	−8.11514	−	20.9288i	−0.542216	−	1.39837i
$225$		0			0
$226$	−8.55025	+	11.0383i	−0.568754	+	0.734259i
$227$	−0.976025	+	1.69052i	−0.0647811	+	0.112204i	−0.896597	−	0.442848i	$-0.853968\pi$
$227$	−0.976025	+	1.69052i	−0.0647811	+	0.112204i	0.831816	+	0.555052i	$0.187302\pi$
$228$		0			0
$229$	−15.8725			−1.04888			−0.524441	−	0.851447i	$-0.675726\pi$
$229$	−15.8725			−1.04888			−0.524441	+	0.851447i	$0.675726\pi$
$230$	−10.6193	−	25.9717i	−0.700219	−	1.71252i
$231$		0			0
$232$	27.7334	−	3.26591i	1.82079	−	0.214417i
$233$	−22.0000			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$234$		0			0
$235$			8.87298i			0.578810i
$236$	−3.50493	+	3.44159i	−0.228152	+	0.224028i
$237$		0			0
$238$	−30.5062	+	12.4734i	−1.97743	+	0.808533i
$239$		−	1.51205i		−	0.0978065i	−0.998804	−	0.0489032i	$-0.984427\pi$
$239$		−	1.51205i		−	0.0978065i	0.998804	−	0.0489032i	$-0.0155726\pi$
$240$		0			0
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.00239235	−	0.999997i	$-0.500762\pi$
$241$	−13.5000	−	7.79423i	−0.869611	−	0.502070i	−0.867219	+	0.497927i	$0.834095\pi$
$242$	−9.30628	+	12.0144i	−0.598230	+	0.772312i
$243$		0			0
$244$	−1.40126	−	1.42705i	−0.0897064	−	0.0913576i
$245$	9.77829	+	16.9365i	0.624712	+	1.08203i
$246$		0			0
$247$	1.74597	−	0.504017i	0.111093	−	0.0320698i
$248$	−5.00000	+	11.6190i	−0.317500	+	0.737804i
$249$		0			0
$250$	15.6665	+	2.13525i	0.990839	+	0.135045i
$251$	13.1964	+	7.61895i	0.832950	+	0.480904i	0.854862	−	0.518856i	$-0.173642\pi$
$251$	13.1964	+	7.61895i	0.832950	+	0.480904i	−0.0219117	+	0.999760i	$0.506975\pi$
$252$		0			0
$253$	−2.23607	+	3.87298i	−0.140580	+	0.243492i
$254$	1.20643	+	2.95057i	0.0756984	+	0.185135i
$255$		0			0
$256$	7.48936	+	14.1389i	0.468085	+	0.883684i
$257$	−7.68246	−	13.3064i	−0.479219	−	0.830031i	0.520497	−	0.853863i	$-0.325747\pi$
$257$	−7.68246	−	13.3064i	−0.479219	−	0.830031i	−0.999716	+	0.0238323i	$0.992413\pi$
$258$		0			0
$259$		−	28.6190i		−	1.77830i
$260$	8.20311	+	13.8820i	0.508735	+	0.860923i
$261$		0			0
$262$	2.24328	−	16.4591i	0.138590	−	1.01685i
$263$	0.563508	+	0.976025i	0.0347474	+	0.0601843i	0.882876	−	0.469606i	$-0.155604\pi$
$263$	0.563508	+	0.976025i	0.0347474	+	0.0601843i	−0.848129	+	0.529790i	$0.822271\pi$
$264$		0			0
$265$		−	17.6045i		−	1.08144i
$266$	−2.61803	+	1.07047i	−0.160522	+	0.0656345i
$267$		0			0
$268$	−0.976025	−	3.78013i	−0.0596202	−	0.230908i
$269$	17.1005	+	9.87298i	1.04264	+	0.601966i	0.920579	−	0.390557i	$-0.127717\pi$
$269$	17.1005	+	9.87298i	1.04264	+	0.601966i	0.122058	+	0.992523i	$0.461051\pi$
$270$		0			0
$271$	−26.2379	+	15.1485i	−1.59384	+	0.920203i	−0.601199	+	0.799099i	$0.705310\pi$
$271$	−26.2379	+	15.1485i	−1.59384	+	0.920203i	−0.992640	+	0.121104i	$0.961357\pi$
$272$	20.5554	−	11.3730i	1.24636	−	0.689588i
$273$		0			0
$274$	−0.245967	−	0.190525i	−0.0148594	−	0.0115100i
$275$		0			0
$276$		0			0
$277$	0.646026	+	0.372983i	0.0388159	+	0.0224104i	0.519282	−	0.854603i	$-0.326199\pi$
$277$	0.646026	+	0.372983i	0.0388159	+	0.0224104i	−0.480466	+	0.877013i	$0.659533\pi$
$278$	−10.8963	−	8.44025i	−0.653518	−	0.506213i
$279$		0			0
$280$	−15.0041	−	20.1176i	−0.896664	−	1.20225i
$281$			12.1884i			0.727097i	0.931575	+	0.363549i	$0.118435\pi$
$281$			12.1884i			0.727097i	−0.931575	+	0.363549i	$0.881565\pi$
$282$		0			0
$283$	−17.8565	+	10.3095i	−1.06146	+	0.612835i	−0.925836	−	0.377926i	$-0.876638\pi$
$283$	−17.8565	+	10.3095i	−1.06146	+	0.612835i	−0.135625	+	0.990760i	$0.543304\pi$
$284$	6.97288	+	7.10122i	0.413764	+	0.421380i
$285$		0			0
$286$	0.948543	−	2.38854i	0.0560885	−	0.141237i
$287$	−4.87298			−0.287643
$288$		0			0
$289$	−8.74597	−	15.1485i	−0.514469	−	0.891086i
$290$	28.8987	−	11.8162i	1.69699	−	0.693869i
$291$		0			0
$292$	−7.02889	+	25.3068i	−0.411335	+	1.48097i
$293$	3.07008	−	5.31754i	0.179356	−	0.310654i	−0.762304	−	0.647219i	$-0.775932\pi$
$293$	3.07008	−	5.31754i	0.179356	−	0.310654i	0.941660	+	0.336565i	$0.109265\pi$
$294$		0			0
$295$	−2.74597	+	4.75615i	−0.159876	+	0.276914i
$296$	2.38575	+	20.2593i	0.138669	+	1.17755i
$297$		0			0
$298$	−7.55544	+	9.75403i	−0.437675	+	0.565036i
$299$	−7.68423	+	31.0554i	−0.444390	+	1.79598i
$300$		0			0
$301$	−17.6045	−	30.4919i	−1.01471	−	1.75753i
$302$	−2.08101	+	15.2686i	−0.119749	+	0.878607i
$303$		0			0
$304$	1.76406	−	0.976025i	0.101176	−	0.0559789i
$305$	−1.93649	−	1.11803i	−0.110883	−	0.0640184i
$306$		0			0
$307$	−18.8326			−1.07483			−0.537415	−	0.843318i	$-0.680599\pi$
$307$	−18.8326			−1.07483			−0.537415	+	0.843318i	$0.680599\pi$
$308$	−1.07047	+	3.85410i	−0.0609955	+	0.219608i
$309$		0			0
$310$	−1.90983	+	14.0126i	−0.108471	+	0.795861i
$311$	−12.6190			−0.715555			−0.357778	−	0.933807i	$-0.616465\pi$
$311$	−12.6190			−0.715555			−0.357778	+	0.933807i	$0.616465\pi$
$312$		0			0
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$	0.239499	−	1.75722i	0.0135157	−	0.0991659i
$315$		0			0
$316$	26.9787	+	7.49326i	1.51767	+	0.421529i
$317$	−18.5485			−1.04179			−0.520895	−	0.853621i	$-0.674402\pi$
$317$	−18.5485			−1.04179			−0.520895	+	0.853621i	$0.674402\pi$
$318$		0			0
$319$	−4.30948	−	2.48808i	−0.241284	−	0.139306i
$320$	12.2984	+	12.9904i	0.687500	+	0.726184i
$321$		0			0
$322$	6.72433	−	49.3370i	0.374732	−	2.74944i
$323$	−1.48004	−	2.56351i	−0.0823518	−	0.142637i
$324$		0			0
$325$		0			0
$326$	14.6190	−	18.8730i	0.809669	−	1.04528i
$327$		0			0
$328$	3.44957	−	0.406224i	0.190470	−	0.0224300i
$329$	−7.87298	+	13.6364i	−0.434052	+	0.751799i
$330$		0			0
$331$	4.97615	−	8.61895i	0.273514	−	0.473740i	−0.696245	−	0.717804i	$-0.745147\pi$
$331$	4.97615	−	8.61895i	0.273514	−	0.473740i	0.969759	+	0.244064i	$0.0784806\pi$
$332$	5.70423	+	1.58434i	0.313060	+	0.0869517i
$333$		0			0
$334$	12.2842	−	5.02277i	0.672160	−	0.274834i
$335$	−2.18246	−	3.78013i	−0.119240	−	0.206530i
$336$		0			0
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	1.78031	−	18.2984i	0.0968362	−	0.995300i
$339$		0			0
$340$	18.7406	−	18.4019i	1.01635	−	0.997982i
$341$	1.95205	−	1.12702i	0.105709	−	0.0610314i
$342$		0			0
$343$			6.92820i			0.374088i
$344$	15.0041	+	20.1176i	0.808965	+	1.08467i
$345$		0			0
$346$	19.5566	+	15.1485i	1.05137	+	0.814386i
$347$	−6.17218	−	3.56351i	−0.331340	−	0.191299i	0.325096	−	0.945681i	$-0.394603\pi$
$347$	−6.17218	−	3.56351i	−0.331340	−	0.191299i	−0.656436	+	0.754382i	$0.727937\pi$
$348$		0			0
$349$	−13.6364	−	23.6190i	−0.729940	−	1.26429i	−0.956908	−	0.290391i	$-0.906215\pi$
$349$	−13.6364	−	23.6190i	−0.729940	−	1.26429i	0.226968	−	0.973902i	$-0.427119\pi$
$350$		0			0
$351$		0			0
$352$	0.436492	−	2.81754i	0.0232651	−	0.150175i
$353$	23.8095	−	13.7464i	1.26725	−	0.731647i	0.292784	−	0.956179i	$-0.405418\pi$
$353$	23.8095	−	13.7464i	1.26725	−	0.731647i	0.974467	+	0.224531i	$0.0720851\pi$
$354$		0			0
$355$	9.63628	+	5.56351i	0.511441	+	0.295280i
$356$	3.90410	−	1.00803i	0.206917	−	0.0534257i
$357$		0			0
$358$	−6.71135	+	2.74415i	−0.354706	+	0.145033i
$359$		−	13.9204i		−	0.734692i	−0.930084	−	0.367346i	$-0.880267\pi$
$359$		−	13.9204i		−	0.734692i	0.930084	−	0.367346i	$-0.119733\pi$
$360$		0			0
$361$	9.37298	+	16.2345i	0.493315	+	0.854446i
$362$	−0.142467	+	1.04529i	−0.00748790	+	0.0549393i
$363$		0			0
$364$	0.289470	+	28.6130i	0.0151724	+	1.49973i
$365$			29.3649i			1.53703i
$366$		0			0
$367$	−0.309475	−	0.536026i	−0.0161545	−	0.0279804i	0.857835	−	0.513925i	$-0.171809\pi$
$367$	−0.309475	−	0.536026i	−0.0161545	−	0.0279804i	−0.873990	+	0.485945i	$0.838476\pi$
$368$	−0.647275	+	35.4860i	−0.0337416	+	1.84984i
$369$		0			0
$370$	8.63171	+	21.1105i	0.448741	+	1.09748i
$371$	15.6205	−	27.0554i	0.810974	−	1.40465i
$372$		0			0
$373$	26.4068	+	15.2460i	1.36729	+	0.789406i	0.990581	−	0.136925i	$-0.0437219\pi$
$373$	26.4068	+	15.2460i	1.36729	+	0.789406i	0.376710	+	0.926331i	$0.377055\pi$
$374$	−4.14784	−	0.565326i	−0.214480	−	0.0292323i
$375$		0			0
$376$	4.43649	−	10.3095i	0.228795	−	0.531671i
$377$	−34.5554	−	8.55025i	−1.77970	−	0.440361i
$378$		0			0
$379$	5.48017	+	9.49193i	0.281497	+	0.487568i	0.971754	−	0.235997i	$-0.0758356\pi$
$379$	5.48017	+	9.49193i	0.281497	+	0.487568i	−0.690256	+	0.723565i	$0.742502\pi$
$380$	1.60831	−	1.57924i	0.0825046	−	0.0810134i
$381$		0			0
$382$	−17.1005	+	22.0767i	−0.874938	+	1.12954i
$383$	19.7460	+	11.4003i	1.00897	+	0.582530i	0.910890	−	0.412648i	$-0.135396\pi$
$383$	19.7460	+	11.4003i	1.00897	+	0.582530i	0.0980813	+	0.995178i	$0.468729\pi$
$384$		0			0
$385$			4.47214i			0.227921i
$386$	−10.7605	+	4.39975i	−0.547693	+	0.223942i
$387$		0			0
$388$	−24.2705	−	24.7172i	−1.23215	−	1.25483i
$389$		−	11.6190i		−	0.589104i	−0.955635	−	0.294552i	$-0.904830\pi$
$389$		−	11.6190i		−	0.589104i	0.955635	−	0.294552i	$-0.0951704\pi$
$390$		0			0
$391$	52.1109			2.63536
$392$	−2.89310	−	24.5676i	−0.146124	−	1.24085i
$393$		0			0
$394$	1.31457	+	3.21503i	0.0662270	+	0.161971i
$395$	31.3050			1.57512
$396$		0			0
$397$	3.74812	−	6.49193i	0.188113	−	0.325821i	−0.756508	−	0.653984i	$-0.773096\pi$
$397$	3.74812	−	6.49193i	0.188113	−	0.325821i	0.944621	+	0.328163i	$0.106430\pi$
$398$	−5.95218	+	7.68423i	−0.298356	+	0.385176i
$399$		0			0
$400$		0			0
$401$	3.19052	−	1.84205i	0.159327	−	0.0919876i	−0.418216	−	0.908347i	$-0.637345\pi$
$401$	3.19052	−	1.84205i	0.159327	−	0.0919876i	0.577544	+	0.816360i	$0.304011\pi$
$402$		0			0
$403$	11.1803	−	11.6190i	0.556932	−	0.578781i
$404$	15.2460	−	3.93649i	0.758515	−	0.195848i
$405$		0			0
$406$	54.8973	+	7.48217i	2.72451	+	0.371334i
$407$	1.81754	−	3.14807i	0.0900922	−	0.156044i
$408$		0			0
$409$	4.88105	+	2.81808i	0.241352	+	0.139345i	0.615798	−	0.787904i	$-0.288834\pi$
$409$	4.88105	+	2.81808i	0.241352	+	0.139345i	−0.374446	+	0.927249i	$0.622167\pi$
$410$	3.59452	−	1.46973i	0.177521	−	0.0725849i
$411$		0			0
$412$	20.4633	+	5.68361i	1.00815	+	0.280012i
$413$	−8.44025	+	4.87298i	−0.415318	+	0.239784i
$414$		0			0
$415$	6.61895			0.324911
$416$	−2.59017	−	20.2309i	−0.126994	−	0.991904i
$417$		0			0
$418$	−0.355966	−	0.0485160i	−0.0174109	−	0.00237300i
$419$	22.5167	−	13.0000i	1.10001	−	0.635092i	0.163787	−	0.986496i	$-0.447629\pi$
$419$	22.5167	−	13.0000i	1.10001	−	0.635092i	0.936224	+	0.351404i	$0.114296\pi$
$420$		0			0
$421$	−12.1244			−0.590905			−0.295452	−	0.955357i	$-0.595470\pi$
$421$	−12.1244			−0.590905			−0.295452	+	0.955357i	$0.595470\pi$
$422$	−18.3262	+	7.49326i	−0.892107	+	0.364766i
$423$		0			0
$424$	−8.80226	+	20.4546i	−0.427476	+	0.993364i
$425$		0			0
$426$		0			0
$427$	−1.98406	−	3.43649i	−0.0960154	−	0.166303i
$428$	−1.69052	+	0.436492i	−0.0817146	+	0.0210986i
$429$		0			0
$430$	22.1825	+	17.1825i	1.06973	+	0.828612i
$431$	−13.6905	+	7.90423i	−0.659449	+	0.380733i	−0.792067	−	0.610434i	$-0.790995\pi$
$431$	−13.6905	+	7.90423i	−0.659449	+	0.380733i	0.132618	+	0.991167i	$0.457662\pi$
$432$		0			0
$433$	13.3730	−	23.1627i	0.642665	−	1.11313i	−0.342171	−	0.939638i	$-0.611162\pi$
$433$	13.3730	−	23.1627i	0.642665	−	1.11313i	0.984836	−	0.173490i	$-0.0555044\pi$
$434$	−15.3685	+	19.8406i	−0.737710	+	0.952379i
$435$		0			0
$436$	−4.73297	−	1.31457i	−0.226668	−	0.0629564i
$437$	4.47214			0.213931
$438$		0			0
$439$	8.43649	+	14.6124i	0.402652	+	0.697413i	0.994045	−	0.108970i	$-0.0347552\pi$
$439$	8.43649	+	14.6124i	0.402652	+	0.697413i	−0.591393	+	0.806383i	$0.701422\pi$
$440$	−0.372808	−	3.16581i	−0.0177729	−	0.150924i
$441$		0			0
$442$	−29.6297	+	4.34409i	−1.40934	+	0.206627i
$443$		−	40.7298i		−	1.93513i	−0.252617	−	0.967566i	$-0.581291\pi$
$443$		−	40.7298i		−	1.93513i	0.252617	−	0.967566i	$-0.418709\pi$
$444$		0			0
$445$	3.90410	−	2.25403i	0.185072	−	0.106851i
$446$	18.8818	−	7.72044i	0.894081	−	0.365573i
$447$		0			0
$448$	7.37436	+	30.8765i	0.348406	+	1.45878i
$449$	4.25403	+	2.45607i	0.200760	+	0.115909i	0.597010	−	0.802234i	$-0.296355\pi$
$449$	4.25403	+	2.45607i	0.200760	+	0.115909i	−0.396250	+	0.918143i	$0.629689\pi$
$450$		0			0
$451$	−0.536026	−	0.309475i	−0.0252405	−	0.0145726i
$452$	14.0893	−	13.8346i	0.662703	−	0.650725i
$453$		0			0
$454$	1.69052	−	2.18246i	0.0793403	−	0.102428i
$455$	8.87298	+	30.7369i	0.415972	+	1.44097i
$456$		0			0
$457$	−33.3569	+	19.2586i	−1.56037	+	0.900879i	−0.563148	+	0.826356i	$0.690410\pi$
$457$	−33.3569	+	19.2586i	−1.56037	+	0.900879i	−0.997219	+	0.0745228i	$0.976257\pi$
$458$	22.2414	+	3.03137i	1.03927	+	0.141647i
$459$		0			0
$460$	9.92030	+	38.4211i	0.462536	+	1.79140i
$461$	18.2185	−	31.5554i	0.848522	−	1.46968i	−0.0340048	−	0.999422i	$-0.510826\pi$
$461$	18.2185	−	31.5554i	0.848522	−	1.46968i	0.882527	−	0.470262i	$-0.155841\pi$
$462$		0			0
$463$		−	18.3926i		−	0.854775i	−0.904069	−	0.427387i	$-0.859434\pi$
$463$		−	18.3926i		−	0.854775i	0.904069	−	0.427387i	$-0.140566\pi$
$464$	−39.4854	−	0.720224i	−1.83306	−	0.0334356i
$465$		0			0
$466$	30.8277	+	4.20163i	1.42807	+	0.194637i
$467$			12.3649i			0.572180i	0.958203	+	0.286090i	$0.0923557\pi$
$467$			12.3649i			0.572180i	−0.958203	+	0.286090i	$0.907644\pi$
$468$		0			0
$469$		−	7.74597i		−	0.357676i
$470$	1.69459	−	12.4333i	0.0781656	−	0.573507i
$471$		0			0
$472$	5.56860	−	4.15317i	0.256316	−	0.191165i
$473$		−	4.47214i		−	0.205629i
$474$		0			0
$475$		0			0
$476$	45.1293	−	11.6523i	2.06850	−	0.534084i
$477$		0			0
$478$	−0.288776	+	2.11878i	−0.0132083	+	0.0969105i
$479$	−36.1109	+	20.8486i	−1.64995	+	0.952598i	−0.672858	+	0.739771i	$0.734934\pi$
$479$	−36.1109	+	20.8486i	−1.64995	+	0.952598i	−0.977090	+	0.212827i	$0.931733\pi$
$480$		0			0
$481$	6.24597	−	25.2428i	0.284792	−	1.15097i
$482$	17.4284	+	13.5000i	0.793843	+	0.614908i
$483$		0			0
$484$	15.3350	−	15.0579i	0.697047	−	0.684449i
$485$	−33.5410	−	19.3649i	−1.52302	−	0.879316i
$486$		0			0
$487$	−27.9284	−	16.1245i	−1.26556	−	0.730670i	−0.291414	−	0.956597i	$-0.594126\pi$
$487$	−27.9284	−	16.1245i	−1.26556	−	0.730670i	−0.974144	+	0.225927i	$0.927459\pi$
$488$	1.69098	+	2.26728i	0.0765472	+	0.102635i
$489$		0			0
$490$	−10.4673	−	25.5999i	−0.472866	−	1.15649i
$491$	−32.7850	+	18.9284i	−1.47957	+	0.854228i	−0.999732	−	0.0231316i	$-0.992636\pi$
$491$	−32.7850	+	18.9284i	−1.47957	+	0.854228i	−0.479834	+	0.877359i	$0.659303\pi$
$492$		0			0
$493$			57.9839i			2.61146i
$494$	−2.54281	+	0.372808i	−0.114406	+	0.0167734i
$495$		0			0
$496$	9.22531	−	15.3262i	0.414229	−	0.688168i
$497$	9.87298	+	17.1005i	0.442864	+	0.767063i
$498$		0			0
$499$	−2.01607			−0.0902516			−0.0451258	−	0.998981i	$-0.514369\pi$
$499$	−2.01607			−0.0902516			−0.0451258	+	0.998981i	$0.514369\pi$
$500$	−21.5451	−	5.98409i	−0.963525	−	0.267617i
$501$		0			0
$502$	−17.0365	−	13.1964i	−0.760376	−	0.588985i
$503$	10.3095	−	17.8565i	0.459677	−	0.796184i	−0.539267	−	0.842135i	$-0.681299\pi$
$503$	10.3095	−	17.8565i	0.459677	−	0.796184i	0.998944	+	0.0459514i	$0.0146319\pi$
$504$		0			0
$505$	15.2460	−	8.80226i	0.678437	−	0.391696i
$506$	3.87298	−	5.00000i	0.172175	−	0.222277i
$507$		0			0
$508$	−1.12702	−	4.36492i	−0.0500033	−	0.193662i
$509$	4.36214	+	7.55544i	0.193348	+	0.334889i	0.946358	−	0.323121i	$-0.104732\pi$
$509$	4.36214	+	7.55544i	0.193348	+	0.334889i	−0.753010	+	0.658010i	$0.771399\pi$
$510$		0			0
$511$	−26.0554	+	45.1293i	−1.15262	+	1.99640i
$512$	−7.79423	−	21.2426i	−0.344459	−	0.938801i
$513$		0			0
$514$	8.22381	+	20.1129i	0.362737	+	0.887144i
$515$	23.7447			1.04632
$516$		0			0
$517$	−1.73205	+	1.00000i	−0.0761755	+	0.0439799i
$518$	−5.46573	+	40.1025i	−0.240151	+	1.76200i
$519$		0			0
$520$	−8.84346	−	21.0189i	−0.387811	−	0.921739i
$521$	−5.61895			−0.246171			−0.123085	−	0.992396i	$-0.539279\pi$
$521$	−5.61895			−0.246171			−0.123085	+	0.992396i	$0.539279\pi$
$522$		0			0
$523$	29.7609	−	17.1825i	1.30135	−	0.751336i	0.320717	−	0.947175i	$-0.396076\pi$
$523$	29.7609	−	17.1825i	1.30135	−	0.751336i	0.980636	+	0.195839i	$0.0627429\pi$
$524$	−6.28683	+	22.6351i	−0.274641	+	0.988818i
$525$		0			0
$526$	−0.603217	−	1.47528i	−0.0263015	−	0.0643254i
$527$	−22.7460	−	13.1324i	−0.990830	−	0.572056i
$528$		0			0
$529$	−27.8649	+	48.2635i	−1.21152	+	2.09841i
$530$	−3.36217	+	24.6685i	−0.146043	+	1.07153i
$531$		0			0
$532$	3.87298	−	1.00000i	0.167915	−	0.0433555i
$533$	−4.29812	−	1.06351i	−0.186172	−	0.0460657i
$534$		0			0
$535$	−1.69052	+	0.976025i	−0.0730878	+	0.0421972i
$536$	0.645723	+	5.48334i	0.0278910	+	0.236844i
$537$		0			0
$538$	−22.0767	−	17.1005i	−0.951792	−	0.737255i
$539$	−2.20406	+	3.81754i	−0.0949355	+	0.164433i
$540$		0			0
$541$	29.4449			1.26593			0.632967	−	0.774179i	$-0.281837\pi$
$541$	29.4449			1.26593			0.632967	+	0.774179i	$0.281837\pi$
$542$	39.6592	−	16.2159i	1.70351	−	0.696533i
$543$		0			0
$544$	−30.9755	+	12.0107i	−1.32807	+	0.514957i
$545$	−5.49193			−0.235249
$546$		0			0
$547$			24.3649i			1.04177i	0.853627	+	0.520884i	$0.174398\pi$
$547$			24.3649i			1.04177i	−0.853627	+	0.520884i	$0.825602\pi$
$548$	0.308276	+	0.313950i	0.0131689	+	0.0134113i
$549$		0			0
$550$		0			0
$551$			4.97615i			0.211991i
$552$		0			0
$553$	48.1109	+	27.7768i	2.04588	+	1.18119i
$554$	−0.834016	−	0.646026i	−0.0354339	−	0.0274470i
$555$		0			0
$556$	13.6566	+	13.9080i	0.579170	+	0.589830i
$557$	−2.85008	−	4.93649i	−0.120762	−	0.209166i	0.799306	−	0.600924i	$-0.205200\pi$
$557$	−2.85008	−	4.93649i	−0.120762	−	0.209166i	−0.920068	+	0.391758i	$0.871867\pi$
$558$		0			0
$559$	−8.87298	−	30.7369i	−0.375287	−	1.30003i
$560$	17.1825	+	31.0554i	0.726091	+	1.31233i
$561$		0			0
$562$	2.32777	−	17.0791i	0.0981911	−	0.720437i
$563$	−21.6367	−	12.4919i	−0.911877	−	0.526472i	−0.0308422	−	0.999524i	$-0.509819\pi$
$563$	−21.6367	−	12.4919i	−0.911877	−	0.526472i	−0.881034	+	0.473052i	$0.843152\pi$
$564$		0			0
$565$	11.0383	−	19.1190i	0.464386	−	0.804340i
$566$	26.9906	−	11.0359i	1.13450	−	0.463875i
$567$		0			0
$568$	−8.41459	−	11.2824i	−0.353068	−	0.473397i
$569$	−19.4919	−	33.7610i	−0.817144	−	1.41534i	−0.907778	−	0.419451i	$-0.862223\pi$
$569$	−19.4919	−	33.7610i	−0.817144	−	1.41534i	0.0906335	−	0.995884i	$-0.471111\pi$
$570$		0			0
$571$			16.6190i			0.695481i	0.937591	+	0.347741i	$0.113051\pi$
$571$			16.6190i			0.695481i	−0.937591	+	0.347741i	$0.886949\pi$
$572$	−1.78533	+	3.16581i	−0.0746482	+	0.132369i
$573$		0			0
$574$	6.82831	+	0.930657i	0.285008	+	0.0388449i
$575$		0			0
$576$		0			0
$577$			18.6126i			0.774851i	0.921901	+	0.387426i	$0.126636\pi$
$577$			18.6126i			0.774851i	−0.921901	+	0.387426i	$0.873364\pi$
$578$	9.36226	+	22.8972i	0.389419	+	0.952400i
$579$		0			0
$580$	−42.7513	+	11.0383i	−1.77515	+	0.458342i
$581$	10.1723	+	5.87298i	0.422018	+	0.243652i
$582$		0			0
$583$	3.43649	−	1.98406i	0.142325	−	0.0821713i
$584$	14.6825	−	34.1190i	0.607564	−	1.41185i
$585$		0			0
$586$	−5.31754	+	6.86492i	−0.219666	+	0.283587i
$587$	4.47214	+	7.74597i	0.184585	+	0.319710i	0.943437	−	0.331553i	$-0.107573\pi$
$587$	4.47214	+	7.74597i	0.184585	+	0.319710i	−0.758852	+	0.651263i	$0.774239\pi$
$588$		0			0
$589$	−1.95205	−	1.12702i	−0.0804328	−	0.0464379i
$590$	4.75615	−	6.14017i	0.195808	−	0.252787i
$591$		0			0
$592$	0.526124	−	28.8441i	0.0216236	−	1.18548i
$593$			19.5566i			0.803092i	0.915839	+	0.401546i	$0.131527\pi$
$593$			19.5566i			0.803092i	−0.915839	+	0.401546i	$0.868473\pi$
$594$		0			0
$595$	45.1293	−	26.0554i	1.85012	−	1.06817i
$596$	12.4500	−	12.2250i	0.509971	−	0.500754i
$597$		0			0
$598$	16.6987	−	42.0491i	0.682859	−	1.71952i
$599$	10.0000			0.408589			0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000			0.408589			0.204294	+	0.978909i	$0.434510\pi$
$600$		0			0
$601$	8.24597	+	14.2824i	0.336360	+	0.582593i	0.983745	−	0.179570i	$-0.0574708\pi$
$601$	8.24597	+	14.2824i	0.336360	+	0.582593i	−0.647385	+	0.762163i	$0.724137\pi$
$602$	18.8451	+	46.0892i	0.768067	+	1.87846i
$603$		0			0
$604$	5.83207	−	20.9978i	0.237304	−	0.854387i
$605$	12.0144	−	20.8095i	0.488453	−	0.846025i
$606$		0			0
$607$	9.74597	−	16.8805i	0.395577	−	0.685159i	−0.597598	−	0.801796i	$-0.703878\pi$
$607$	9.74597	−	16.8805i	0.395577	−	0.685159i	0.993175	+	0.116637i	$0.0372114\pi$
$608$	−2.65831	+	1.03076i	−0.107809	+	0.0418028i
$609$		0			0
$610$	2.50000	+	1.93649i	0.101222	+	0.0784063i
$611$	−9.92030	+	10.3095i	−0.401332	+	0.417077i
$612$		0			0
$613$	7.35423	+	12.7379i	0.297035	+	0.514479i	0.975456	−	0.220194i	$-0.0706690\pi$
$613$	7.35423	+	12.7379i	0.297035	+	0.514479i	−0.678422	+	0.734673i	$0.737336\pi$
$614$	26.3893	+	3.59670i	1.06498	+	0.145151i
$615$		0			0
$616$	2.23607	−	5.19615i	0.0900937	−	0.209359i
$617$	5.42843	+	3.13410i	0.218540	+	0.126174i	0.605274	−	0.796017i	$-0.293063\pi$
$617$	5.42843	+	3.13410i	0.218540	+	0.126174i	−0.386734	+	0.922191i	$0.626397\pi$
$618$		0			0
$619$	−22.2326			−0.893605			−0.446803	−	0.894633i	$-0.647437\pi$
$619$	−22.2326			−0.893605			−0.446803	+	0.894633i	$0.647437\pi$
$620$	5.35233	−	19.2705i	0.214955	−	0.773922i
$621$		0			0
$622$	17.6824	+	2.41001i	0.709000	+	0.0966324i
$623$	8.00000			0.320513
$624$		0			0
$625$	−25.0000			−1.00000
$626$	−5.60503	−	0.763932i	−0.224022	−	0.0305329i
$627$		0			0
$628$	−0.671200	+	2.41659i	−0.0267838	+	0.0964323i
$629$	−42.3573			−1.68889
$630$		0			0
$631$	12.0000	+	6.92820i	0.477712	+	0.275807i	0.719463	−	0.694531i	$-0.244388\pi$
$631$	12.0000	+	6.92820i	0.477712	+	0.275807i	−0.241750	+	0.970339i	$0.577721\pi$
$632$	−36.3731	−	15.6525i	−1.44684	−	0.622622i
$633$		0			0
$634$	25.9913	+	3.54246i	1.03225	+	0.140689i
$635$	−2.52009	−	4.36492i	−0.100007	−	0.173216i
$636$		0			0
$637$	−7.57423	+	30.6109i	−0.300102	+	1.21285i
$638$	5.56351	+	4.30948i	0.220261	+	0.170614i
$639$		0			0
$640$	−14.7523	−	20.5517i	−0.583134	−	0.812376i
$641$	9.68246	−	16.7705i	0.382434	−	0.662395i	−0.608975	−	0.793189i	$-0.708419\pi$
$641$	9.68246	−	16.7705i	0.382434	−	0.662395i	0.991410	+	0.130794i	$0.0417526\pi$
$642$		0			0
$643$	−2.67607	+	4.63508i	−0.105534	+	0.182790i	−0.913956	−	0.405813i	$-0.866988\pi$
$643$	−2.67607	+	4.63508i	−0.105534	+	0.182790i	0.808422	+	0.588603i	$0.200322\pi$
$644$	−18.8451	+	67.8496i	−0.742599	+	2.67365i
$645$		0			0
$646$	1.58434	+	3.87480i	0.0623348	+	0.152452i
$647$	−8.12702	−	14.0764i	−0.319506	−	0.553401i	0.660879	−	0.750492i	$-0.270184\pi$
$647$	−8.12702	−	14.0764i	−0.319506	−	0.553401i	−0.980385	+	0.197092i	$0.936850\pi$
$648$		0			0
$649$	−1.23790			−0.0485918
$650$		0			0
$651$		0			0
$652$	−24.0893	+	23.6540i	−0.943412	+	0.926360i
$653$	16.6605	−	9.61895i	0.651976	−	0.376419i	−0.137237	−	0.990538i	$-0.543822\pi$
$653$	16.6605	−	9.61895i	0.651976	−	0.376419i	0.789213	+	0.614120i	$0.210489\pi$
$654$		0			0
$655$			26.2648i			1.02625i
$656$	−4.91132	−	0.0895838i	−0.191755	−	0.00349766i
$657$		0			0
$658$	13.6364	−	17.6045i	0.531602	−	0.686296i
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	16.2345	+	28.1190i	0.631448	+	1.09370i	0.987256	+	0.159141i	$0.0508725\pi$
$661$	16.2345	+	28.1190i	0.631448	+	1.09370i	−0.355808	+	0.934559i	$0.615794\pi$
$662$	−8.61895	+	11.1270i	−0.334985	+	0.432464i
$663$		0			0
$664$	−7.69052	−	3.30948i	−0.298450	−	0.128433i
$665$	3.87298	−	2.23607i	0.150188	−	0.0867110i
$666$		0			0
$667$	−75.8663	−	43.8014i	−2.93755	−	1.69600i
$668$	−18.1726	+	4.69214i	−0.703118	+	0.181544i
$669$		0			0
$670$	2.33625	+	5.71375i	0.0902571	+	0.220741i
$671$		−	0.504017i		−	0.0194574i
$672$		0			0
$673$	−11.1190	−	19.2586i	−0.428604	−	0.742364i	0.568145	−	0.822928i	$-0.307661\pi$
$673$	−11.1190	−	19.2586i	−0.428604	−	0.742364i	−0.996749	+	0.0805642i	$0.974328\pi$
$674$	18.2164	+	2.48278i	0.701668	+	0.0956331i
$675$		0			0
$676$	−5.98936	+	25.3007i	−0.230360	+	0.973106i
$677$			15.7460i			0.605167i	0.953123	+	0.302583i	$0.0978491\pi$
$677$			15.7460i			0.605167i	−0.953123	+	0.302583i	$0.902151\pi$
$678$		0			0
$679$	−34.3649	−	59.5218i	−1.31880	−	2.28424i
$680$	−29.7749	+	22.2066i	−1.14181	+	0.851586i
$681$		0			0
$682$	−2.95057	+	1.20643i	−0.112983	+	0.0461967i
$683$	4.25214	−	7.36492i	0.162703	−	0.281811i	−0.773134	−	0.634243i	$-0.781312\pi$
$683$	4.25214	−	7.36492i	0.162703	−	0.281811i	0.935837	+	0.352432i	$0.114645\pi$
$684$		0			0
$685$	0.426027	+	0.245967i	0.0162776	+	0.00939790i
$686$	1.32317	−	9.70820i	0.0505188	−	0.370661i
$687$		0			0
$688$	−17.1825	−	31.0554i	−0.655075	−	1.18398i
$689$	19.6825	−	20.4546i	0.749842	−	0.779259i
$690$		0			0
$691$	−21.3206	−	36.9284i	−0.811075	−	1.40482i	−0.912112	−	0.409941i	$-0.865549\pi$
$691$	−21.3206	−	36.9284i	−0.811075	−	1.40482i	0.101037	−	0.994883i	$-0.467784\pi$
$692$	−24.5107	−	24.9619i	−0.931758	−	0.948908i
$693$		0			0
$694$	7.96825	+	6.17218i	0.302471	+	0.234293i
$695$	18.8730	+	10.8963i	0.715893	+	0.413321i
$696$		0			0
$697$			7.21222i			0.273182i
$698$	14.5973	+	35.7006i	0.552516	+	1.35129i
$699$		0			0
$700$		0			0
$701$			43.7460i			1.65226i	0.563478	+	0.826131i	$0.309463\pi$
$701$			43.7460i			1.65226i	−0.563478	+	0.826131i	$0.690537\pi$
$702$		0			0
$703$	−3.63508			−0.137100
$704$	−1.14974	+	3.86474i	−0.0433325	+	0.145658i
$705$		0			0
$706$	−35.9886	+	14.7151i	−1.35445	+	0.553809i
$707$	31.2409			1.17494
$708$		0			0
$709$	24.8947	−	43.1190i	0.934941	−	1.61937i	0.160203	−	0.987084i	$-0.448785\pi$
$709$	24.8947	−	43.1190i	0.934941	−	1.61937i	0.774738	−	0.632282i	$-0.217882\pi$
$710$	−12.4404	−	9.63628i	−0.466879	−	0.361643i
$711$		0			0
$712$	−5.66317	+	0.666900i	−0.212236	+	0.0249931i
$713$	34.3649	−	19.8406i	1.28698	−	0.743036i
$714$		0			0
$715$	−0.976025	+	3.94456i	−0.0365013	+	0.147518i
$716$	9.92843	−	2.56351i	0.371043	−	0.0958028i
$717$		0			0
$718$	−2.65856	+	19.5061i	−0.0992168	+	0.727962i
$719$	−6.49193	+	11.2444i	−0.242108	+	0.419344i	−0.961315	−	0.275453i	$-0.911172\pi$
$719$	−6.49193	+	11.2444i	−0.242108	+	0.419344i	0.719206	+	0.694797i	$0.244506\pi$
$720$		0			0
$721$	36.4919	+	21.0686i	1.35903	+	0.784637i
$722$	−10.0335	−	24.5388i	−0.373407	−	0.913239i
$723$		0			0
$724$	0.399266	−	1.43752i	0.0148386	−	0.0534249i
$725$		0			0
$726$		0			0
$727$	−25.1270			−0.931909			−0.465955	−	0.884809i	$-0.654289\pi$
$727$	−25.1270			−0.931909			−0.465955	+	0.884809i	$0.654289\pi$
$728$	5.05898	−	40.1496i	0.187498	−	1.48804i
$729$		0			0
$730$	5.60820	−	41.1478i	0.207569	−	1.52295i
$731$	−45.1293	+	26.0554i	−1.66917	+	0.963695i
$732$		0			0
$733$	30.5809			1.12953			0.564766	−	0.825251i	$-0.308966\pi$
$733$	30.5809			1.12953			0.564766	+	0.825251i	$0.308966\pi$
$734$	0.331283	+	0.810216i	0.0122279	+	0.0299056i
$735$		0			0
$736$	7.68423	−	49.6015i	0.283244	−	1.82833i
$737$	0.491933	−	0.852054i	0.0181206	−	0.0313858i
$738$		0			0
$739$	16.3765	+	28.3649i	0.602419	+	1.04342i	0.992454	+	0.122620i	$0.0391297\pi$
$739$	16.3765	+	28.3649i	0.602419	+	1.04342i	−0.390035	+	0.920800i	$0.627537\pi$
$740$	−8.06351	−	31.2298i	−0.296420	−	1.14803i
$741$		0			0
$742$	−27.0554	+	34.9284i	−0.993237	+	1.28226i
$743$	−30.0000	+	17.3205i	−1.10059	+	0.635428i	−0.936377	−	0.350997i	$-0.885843\pi$
$743$	−30.0000	+	17.3205i	−1.10059	+	0.635428i	−0.164216	+	0.986424i	$0.552510\pi$
$744$		0			0
$745$	9.75403	−	16.8945i	0.357360	−	0.618966i
$746$	−34.0910	−	26.4068i	−1.24816	−	0.966821i
$747$		0			0
$748$	5.70423	+	1.58434i	0.208567	+	0.0579290i
$749$	−3.46410			−0.126576
$750$		0			0
$751$	−9.56351	−	16.5645i	−0.348977	−	0.604447i	0.637091	−	0.770789i	$-0.280138\pi$
$751$	−9.56351	−	16.5645i	−0.348977	−	0.604447i	−0.986068	+	0.166342i	$0.946804\pi$
$752$	−8.18561	+	13.5989i	−0.298498	+	0.495903i
$753$		0			0
$754$	46.7882	+	18.5806i	1.70392	+	0.676666i
$755$		−	24.3649i		−	0.886730i
$756$		0			0
$757$	2.39205	−	1.38105i	0.0869405	−	0.0501951i	−0.455899	−	0.890031i	$-0.650682\pi$
$757$	2.39205	−	1.38105i	0.0869405	−	0.0501951i	0.542840	+	0.839836i	$0.317349\pi$
$758$	−5.86634	−	14.3473i	−0.213075	−	0.521116i
$759$		0			0
$760$	−2.55527	+	1.90577i	−0.0926893	+	0.0691294i
$761$	−5.12702	−	2.96008i	−0.185854	−	0.107303i	0.404186	−	0.914677i	$-0.367555\pi$
$761$	−5.12702	−	2.96008i	−0.185854	−	0.107303i	−0.590040	+	0.807374i	$0.700888\pi$
$762$		0			0
$763$	−8.44025	−	4.87298i	−0.305558	−	0.176414i
$764$	28.1785	−	27.6692i	1.01946	−	1.00104i
$765$		0			0
$766$	−25.4919	−	19.7460i	−0.921061	−	0.713451i
$767$	−8.50807	+	2.45607i	−0.307208	+	0.0886834i
$768$		0			0
$769$	24.4919	−	14.1404i	0.883202	−	0.509917i	0.0114890	−	0.999934i	$-0.496343\pi$
$769$	24.4919	−	14.1404i	0.883202	−	0.509917i	0.871713	+	0.490017i	$0.163010\pi$
$770$	0.854102	−	6.26662i	0.0307797	−	0.225833i
$771$		0			0
$772$	15.9185	−	4.11013i	0.572918	−	0.147927i
$773$	1.51205	−	2.61895i	0.0543847	−	0.0941971i	−0.837551	−	0.546359i	$-0.816014\pi$
$773$	1.51205	−	2.61895i	0.0543847	−	0.0941971i	0.891936	+	0.452161i	$0.149347\pi$
$774$		0			0
$775$		0			0
$776$	29.2887	+	39.2705i	1.05140	+	1.40973i
$777$		0			0
$778$	−2.21902	+	16.2812i	−0.0795558	+	0.583708i
$779$			0.618950i			0.0221762i
$780$		0			0
$781$			2.50807i			0.0897457i
$782$	−73.0208	−	9.95229i	−2.61122	−	0.355893i
$783$		0			0
$784$	−0.638010	+	34.9780i	−0.0227861	+	1.24922i
$785$			2.80410i			0.100083i
$786$		0			0
$787$	−3.24410	+	5.61895i	−0.115640	+	0.200294i	−0.918035	−	0.396499i	$-0.870225\pi$
$787$	−3.24410	+	5.61895i	−0.115640	+	0.200294i	0.802396	+	0.596793i	$0.203558\pi$
$788$	−1.22803	−	4.75615i	−0.0437469	−	0.169431i
$789$		0			0
$790$	−43.8663	−	5.97871i	−1.56069	−	0.212713i
$791$	33.9284	−	19.5886i	1.20636	−	0.696490i
$792$		0			0
$793$	−1.00000	−	3.46410i	−0.0355110	−	0.123014i
$794$	−6.49193	+	8.38105i	−0.230390	+	0.297432i
$795$		0			0
$796$	9.80810	−	9.63083i	0.347639	−	0.341356i
$797$	−27.2728	−	15.7460i	−0.966053	−	0.557751i	−0.0680221	−	0.997684i	$-0.521669\pi$
$797$	−27.2728	−	15.7460i	−0.966053	−	0.557751i	−0.898031	+	0.439933i	$0.855002\pi$
$798$		0			0
$799$	20.1825	+	11.6523i	0.714004	+	0.412230i
$800$		0			0
$801$		0			0
$802$	−4.82255	+	1.97185i	−0.170290	+	0.0696285i
$803$	−5.73218	+	3.30948i	−0.202284	+	0.116789i
$804$		0			0
$805$			78.7298i			2.77486i
$806$	−17.8856	+	14.1459i	−0.629992	+	0.498268i
$807$		0			0
$808$	−22.1153	+	2.60432i	−0.778015	+	0.0916197i
$809$	13.9365	+	24.1387i	0.489981	+	0.848672i	0.999934	−	0.0115306i	$-0.00367039\pi$
$809$	13.9365	+	24.1387i	0.489981	+	0.848672i	−0.509953	+	0.860203i	$0.670337\pi$
$810$		0			0
$811$	−36.2171			−1.27175			−0.635877	−	0.771790i	$-0.719361\pi$
$811$	−36.2171			−1.27175			−0.635877	+	0.771790i	$0.719361\pi$
$812$	−75.4964	−	20.9689i	−2.64940	−	0.735865i
$813$		0			0
$814$	−3.14807	+	4.06415i	−0.110340	+	0.142448i
$815$	−18.8730	+	32.6890i	−0.661092	+	1.14504i
$816$		0			0
$817$	−3.87298	+	2.23607i	−0.135499	+	0.0782301i
$818$	−6.30141	−	4.88105i	−0.220324	−	0.170662i
$819$		0			0
$820$	−5.31754	+	1.37298i	−0.185697	+	0.0479467i
$821$	26.3288	+	45.6028i	0.918881	+	1.59155i	0.801117	+	0.598508i	$0.204239\pi$
$821$	26.3288	+	45.6028i	0.918881	+	1.59155i	0.117764	+	0.993042i	$0.462427\pi$
$822$		0			0
$823$	−23.8730	+	41.3492i	−0.832160	+	1.44134i	0.0641621	+	0.997939i	$0.479563\pi$
$823$	−23.8730	+	41.3492i	−0.832160	+	1.44134i	−0.896322	+	0.443404i	$0.853771\pi$
$824$	−27.5888	−	11.8723i	−0.961103	−	0.413593i
$825$		0			0
$826$	12.7576	−	5.21636i	0.443895	−	0.181501i
$827$	−35.2091			−1.22434			−0.612169	−	0.790727i	$-0.709703\pi$
$827$	−35.2091			−1.22434			−0.612169	+	0.790727i	$0.709703\pi$
$828$		0			0
$829$	−26.1868	+	15.1190i	−0.909505	+	0.525103i	−0.880272	−	0.474470i	$-0.842640\pi$
$829$	−26.1868	+	15.1190i	−0.909505	+	0.525103i	−0.0292330	+	0.999573i	$0.509306\pi$
$830$	−9.27486	−	1.26411i	−0.321935	−	0.0438778i
$831$		0			0
$832$	−0.234268	+	28.8435i	−0.00812179	+	0.999967i
$833$	51.3649			1.77969
$834$		0			0
$835$	−18.1726	+	10.4919i	−0.628887	+	0.363088i
$836$	0.489535	+	0.135967i	0.0169309	+	0.00470252i
$837$		0			0
$838$	−34.0344	+	13.9161i	−1.17570	+	0.480722i
$839$	−6.00000	−	3.46410i	−0.207143	−	0.119594i	0.392840	−	0.919607i	$-0.371493\pi$
$839$	−6.00000	−	3.46410i	−0.207143	−	0.119594i	−0.599983	+	0.800013i	$0.704826\pi$
$840$		0			0
$841$	34.2379	−	59.3018i	1.18062	−	2.04489i
$842$	16.9894	+	2.31555i	0.585492	+	0.0797990i
$843$		0			0
$844$	27.1109	−	7.00000i	0.933195	−	0.240950i
$845$	1.11803	+	29.0474i	0.0384615	+	0.999260i
$846$		0			0
$847$	36.9284	−	21.3206i	1.26888	−	0.732586i
$848$	16.2407	−	26.9811i	0.557709	−	0.926535i
$849$		0			0
$850$		0			0
$851$	31.9970	−	55.4204i	1.09684	−	1.89979i
$852$		0			0
$853$	−25.5408			−0.874499			−0.437250	−	0.899340i	$-0.644047\pi$
$853$	−25.5408			−0.874499			−0.437250	+	0.899340i	$0.644047\pi$
$854$	2.12387	+	5.19433i	0.0726773	+	0.177746i
$855$		0			0
$856$	2.45223	−	0.288776i	0.0838153	−	0.00987017i
$857$	15.6190			0.533533			0.266767	−	0.963761i	$-0.414045\pi$
$857$	15.6190			0.533533			0.266767	+	0.963761i	$0.414045\pi$
$858$		0			0
$859$		−	43.6028i		−	1.48771i	−0.668342	−	0.743854i	$-0.732996\pi$
$859$		−	43.6028i		−	1.48771i	0.668342	−	0.743854i	$-0.267004\pi$
$860$	−27.8018	−	28.3135i	−0.948034	−	0.965484i
$861$		0			0
$862$	20.6935	−	8.46121i	0.704825	−	0.288190i
$863$		−	17.2565i		−	0.587418i	−0.955895	−	0.293709i	$-0.905110\pi$
$863$		−	17.2565i		−	0.587418i	0.955895	−	0.293709i	$-0.0948896\pi$
$864$		0			0
$865$	−33.8730	−	19.5566i	−1.15172	−	0.664944i
$866$	−23.1627	+	29.9029i	−0.787100	+	1.01614i
$867$		0			0
$868$	25.3244	−	24.8667i	0.859566	−	0.844030i
$869$	3.52812	+	6.11088i	0.119683	+	0.207298i
$870$		0			0
$871$	1.69052	−	6.83218i	0.0572813	−	0.231499i
$872$	6.38105	+	2.74597i	0.216090	+	0.0929902i
$873$		0			0
$874$	−6.26662	−	0.854102i	−0.211972	−	0.0288904i
$875$	−38.4211	−	22.1825i	−1.29887	−	0.749904i
$876$		0			0
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	−0.906552	−	0.422095i	$-0.861295\pi$
$877$	−2.59808	+	4.50000i	−0.0877308	+	0.151954i	0.818821	+	0.574049i	$0.194628\pi$
$878$	−9.03098	−	22.0870i	−0.304781	−	0.745401i
$879$		0			0
$880$	−0.0822148	+	4.50732i	−0.00277146	+	0.151942i
$881$	5.55544	+	9.62231i	0.187168	+	0.324184i	0.944305	−	0.329072i	$-0.106736\pi$
$881$	5.55544	+	9.62231i	0.187168	+	0.324184i	−0.757137	+	0.653256i	$0.773403\pi$
$882$		0			0
$883$		−	50.9839i		−	1.71574i	−0.513864	−	0.857872i	$-0.671786\pi$
$883$		−	50.9839i		−	1.71574i	0.513864	−	0.857872i	$-0.328214\pi$
$884$	42.3485	−	0.428428i	1.42433	−	0.0144096i
$885$		0			0
$886$	−7.77871	+	57.0730i	−0.261331	+	1.91741i
$887$	−17.8730	−	30.9569i	−0.600116	−	1.03943i	−0.992803	−	0.119759i	$-0.961788\pi$
$887$	−17.8730	−	30.9569i	−0.600116	−	1.03943i	0.392687	−	0.919672i	$-0.371546\pi$
$888$		0			0
$889$		−	8.94427i		−	0.299981i
$890$	−5.90114	+	2.41287i	−0.197807	+	0.0808795i
$891$		0			0
$892$	−27.9328	+	7.21222i	−0.935260	+	0.241483i
$893$	1.73205	+	1.00000i	0.0579609	+	0.0334637i
$894$		0			0
$895$	9.92843	−	5.73218i	0.331871	−	0.191606i
$896$	−4.43649	−	44.6744i	−0.148213	−	1.49247i
$897$		0			0
$898$	−5.49193	−	4.25403i	−0.183268	−	0.141959i
$899$	22.0767	+	38.2379i	0.736298	+	1.27531i
$900$		0			0
$901$	−40.0432	−	23.1190i	−1.33403	−	0.770204i
$902$	0.692007	+	0.536026i	0.0230413	+	0.0178477i
$903$		0			0
$904$	−22.3849	+	16.6950i	−0.744509	+	0.555269i
$905$		−	1.66803i		−	0.0554473i
$906$		0			0
$907$	−27.2728	+	15.7460i	−0.905579	+	0.522836i	−0.879006	−	0.476811i	$-0.841793\pi$
$907$	−27.2728	+	15.7460i	−0.905579	+	0.522836i	−0.0265729	+	0.999647i	$0.508459\pi$
$908$	−2.78568	+	2.73533i	−0.0924459	+	0.0907750i
$909$		0			0
$910$	−6.56312	−	44.7650i	−0.217565	−	1.48394i
$911$	38.7298			1.28318			0.641588	−	0.767049i	$-0.278276\pi$
$911$	38.7298			1.28318			0.641588	+	0.767049i	$0.278276\pi$
$912$		0			0
$913$	0.745967	+	1.29205i	0.0246879	+	0.0427607i
$914$	50.4196	−	20.6157i	1.66773	−	0.681906i
$915$		0			0
$916$	−30.5871	−	8.49547i	−1.01063	−	0.280698i
$917$	−23.3047	+	40.3649i	−0.769589	+	1.33297i
$918$		0			0
$919$	−22.8730	+	39.6172i	−0.754510	+	1.30685i	0.191107	+	0.981569i	$0.438792\pi$
$919$	−22.8730	+	39.6172i	−0.754510	+	1.30685i	−0.945618	+	0.325281i	$0.894541\pi$
$920$	−6.56312	−	55.7326i	−0.216379	−	1.83745i
$921$		0			0
$922$	−31.5554	+	40.7379i	−1.03922	+	1.34163i
$923$	4.97615	+	17.2379i	0.163792	+	0.567392i
$924$		0			0
$925$		0			0
$926$	−3.51267	+	25.7727i	−0.115433	+	0.846945i
$927$		0			0
$928$	55.1917	+	8.55025i	1.81175	+	0.280676i
$929$	−23.4284	−	13.5264i	−0.768662	−	0.443787i	0.0637353	−	0.997967i	$-0.479699\pi$
$929$	−23.4284	−	13.5264i	−0.768662	−	0.443787i	−0.832397	+	0.554180i	$0.813032\pi$
$930$		0			0
$931$	4.40812			0.144470
$932$	−42.3951	−	11.7751i	−1.38870	−	0.385707i
$933$		0			0
$934$	2.36149	−	17.3264i	0.0772703	−	0.566939i
$935$	6.61895			0.216463
$936$		0			0
$937$	12.2379			0.399795			0.199897	−	0.979817i	$-0.435939\pi$
$937$	12.2379			0.399795			0.199897	+	0.979817i	$0.435939\pi$
$938$	−1.47935	+	10.8541i	−0.0483024	+	0.354399i
$939$		0			0
$940$	−4.74911	+	17.0987i	−0.154899	+	0.557698i
$941$	34.6410			1.12926			0.564632	−	0.825342i	$-0.309018\pi$
$941$	34.6410			1.12926			0.564632	+	0.825342i	$0.309018\pi$
$942$		0			0
$943$	−9.43649	−	5.44816i	−0.307294	−	0.177417i
$944$	−8.59624	+	4.75615i	−0.279784	+	0.154800i
$945$		0			0
$946$	−0.854102	+	6.26662i	−0.0277693	+	0.203745i
$947$	−0.504017	−	0.872983i	−0.0163784	−	0.0283681i	0.857720	−	0.514117i	$-0.171880\pi$
$947$	−0.504017	−	0.872983i	−0.0163784	−	0.0283681i	−0.874098	+	0.485749i	$0.838547\pi$
$948$		0			0
$949$	−32.8310	+	34.1190i	−1.06574	+	1.10755i
$950$		0			0
$951$		0			0
$952$	−65.4633	+	7.70901i	−2.12168	+	0.249851i
$953$	−17.7460	+	30.7369i	−0.574848	+	0.995666i	0.421210	+	0.906963i	$0.361606\pi$
$953$	−17.7460	+	30.7369i	−0.574848	+	0.995666i	−0.996058	+	0.0887032i	$0.971728\pi$
$954$		0			0
$955$	22.0767	−	38.2379i	0.714384	−	1.23735i
$956$	0.809300	−	2.91380i	0.0261746	−	0.0942390i
$957$		0			0
$958$	54.5824	−	22.3178i	1.76348	−	0.721054i
$959$	0.436492	+	0.756026i	0.0140951	+	0.0244133i
$960$		0			0
$961$	11.0000			0.354839
$962$	−13.5732	+	34.1788i	−0.437616	+	1.10197i
$963$		0			0
$964$	−21.8435	−	22.2455i	−0.703530	−	0.716480i
$965$	15.9185	−	9.19052i	0.512433	−	0.295853i
$966$		0			0
$967$		−	11.3363i		−	0.364551i	−0.983247	−	0.182276i	$-0.941654\pi$
$967$		−	11.3363i		−	0.364551i	0.983247	−	0.182276i	$-0.0583464\pi$
$968$	−24.3642	+	18.1712i	−0.783094	+	0.584046i
$969$		0			0
$970$	43.3013	+	33.5410i	1.39032	+	1.07694i
$971$	50.6415	+	29.2379i	1.62516	+	0.938289i	0.985508	+	0.169627i	$0.0542564\pi$
$971$	50.6415	+	29.2379i	1.62516	+	0.938289i	0.639656	+	0.768662i	$0.279077\pi$
$972$		0			0
$973$	19.3366	+	33.4919i	0.619902	+	1.07370i
$974$	36.0554	+	27.9284i	1.15529	+	0.894884i
$975$		0			0
$976$	−1.93649	−	3.50000i	−0.0619856	−	0.112032i
$977$	−27.3014	+	15.7625i	−0.873449	+	0.504286i	−0.868493	−	0.495701i	$-0.834911\pi$
$977$	−27.3014	+	15.7625i	−0.873449	+	0.504286i	−0.00495645	+	0.999988i	$0.501578\pi$
$978$		0			0
$979$	0.879997	+	0.508067i	0.0281248	+	0.0162379i
$980$	9.77829	+	37.8711i	0.312356	+	1.20975i
$981$		0			0
$982$	49.5553	−	20.2622i	1.58137	−	0.646594i
$983$			27.2728i			0.869868i	0.900462	+	0.434934i	$0.143228\pi$
$983$			27.2728i			0.869868i	−0.900462	+	0.434934i	$0.856772\pi$
$984$		0			0
$985$	−2.74597	−	4.75615i	−0.0874938	−	0.151544i
$986$	11.0739	−	81.2504i	0.352666	−	2.58754i
$987$		0			0
$988$	3.63433	−	0.0367676i	0.115624	−	0.00116973i
$989$		−	78.7298i		−	2.50346i
$990$		0			0
$991$	6.18246	+	10.7083i	0.196392	+	0.340161i	0.947356	−	0.320182i	$-0.103744\pi$
$991$	6.18246	+	10.7083i	0.196392	+	0.340161i	−0.750964	+	0.660343i	$0.770411\pi$
$992$	−15.8541	+	19.7141i	−0.503368	+	0.625925i
$993$		0			0
$994$	−10.5687	−	25.8478i	−0.335219	−	0.819843i
$995$	7.68423	−	13.3095i	0.243606	−	0.421939i
$996$		0			0
$997$	6.50218	+	3.75403i	0.205926	+	0.118891i	0.599417	−	0.800437i	$-0.295399\pi$
$997$	6.50218	+	3.75403i	0.205926	+	0.118891i	−0.393491	+	0.919329i	$0.628733\pi$
$998$	2.82503	+	0.385035i	0.0894249	+	0.0121881i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.dg.c.829.1		8
3.2	odd	2		312.2.bk.a.205.4	yes	8
8.5	even	2	inner	936.2.dg.c.829.2		8
12.11	even	2		1248.2.ca.a.49.3		8
13.4	even	6	inner	936.2.dg.c.901.2		8
24.5	odd	2		312.2.bk.a.205.3	✓	8
24.11	even	2		1248.2.ca.a.49.2		8
39.17	odd	6		312.2.bk.a.277.3	yes	8
104.69	even	6	inner	936.2.dg.c.901.1		8
156.95	even	6		1248.2.ca.a.433.2		8
312.173	odd	6		312.2.bk.a.277.4	yes	8
312.251	even	6		1248.2.ca.a.433.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bk.a.205.3	✓	8	24.5	odd	2
312.2.bk.a.205.4	yes	8	3.2	odd	2
312.2.bk.a.277.3	yes	8	39.17	odd	6
312.2.bk.a.277.4	yes	8	312.173	odd	6
936.2.dg.c.829.1		8	1.1	even	1	trivial
936.2.dg.c.829.2		8	8.5	even	2	inner
936.2.dg.c.901.1		8	104.69	even	6	inner
936.2.dg.c.901.2		8	13.4	even	6	inner
1248.2.ca.a.49.2		8	24.11	even	2
1248.2.ca.a.49.3		8	12.11	even	2
1248.2.ca.a.433.2		8	156.95	even	6
1248.2.ca.a.433.3		8	312.251	even	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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.dg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40126 - 0.190983i) q^{2} +(1.92705 + 0.535233i) q^{4} +2.23607 q^{5} +(3.43649 + 1.98406i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(-3.13331 - 0.427051i) q^{10} +(0.252009 + 0.436492i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-4.43649 - 3.43649i) q^{14} +(3.42705 + 2.06284i) q^{16} +(2.93649 - 5.08615i) q^{17} +(0.252009 - 0.436492i) q^{19} +(4.30902 + 1.19682i) q^{20} +(-0.269767 - 0.659767i) q^{22} +(4.43649 + 7.68423i) q^{23} +(-3.16312 - 3.99933i) q^{26} +(5.56036 + 5.66271i) q^{28} +(-8.55025 + 4.93649i) q^{29} -4.47214i q^{31} +(-4.40822 - 3.54508i) q^{32} +(-5.08615 + 6.56619i) q^{34} +(7.68423 + 4.43649i) q^{35} +(-3.60611 - 6.24597i) q^{37} +(-0.436492 + 0.563508i) q^{38} +(-5.80948 - 2.50000i) q^{40} +(-1.06351 + 0.614017i) q^{41} +(-7.68423 - 4.43649i) q^{43} +(0.252009 + 0.976025i) q^{44} +(-4.74911 - 11.6149i) q^{46} +3.96812i q^{47} +(4.37298 + 7.57423i) q^{49} +(3.66854 + 6.20820i) q^{52} -7.87298i q^{53} +(0.563508 + 0.976025i) q^{55} +(-6.71002 - 8.99685i) q^{56} +(12.9239 - 5.28435i) q^{58} +(-1.22803 + 2.12702i) q^{59} +(-0.866025 - 0.500000i) q^{61} +(-0.854102 + 6.26662i) q^{62} +(5.50000 + 5.80948i) q^{64} +(5.80948 + 5.59017i) q^{65} +(-0.976025 - 1.69052i) q^{67} +(8.38105 - 8.22957i) q^{68} +(-9.92030 - 7.68423i) q^{70} +(4.30948 + 2.48808i) q^{71} +13.1324i q^{73} +(3.86022 + 9.44092i) q^{74} +(0.719258 - 0.706258i) q^{76} +2.00000i q^{77} +14.0000 q^{79} +(7.66312 + 4.61266i) q^{80} +(1.60752 - 0.657284i) q^{82} +2.96008 q^{83} +(6.56619 - 11.3730i) q^{85} +(9.92030 + 7.68423i) q^{86} +(-0.166725 - 1.41579i) q^{88} +(1.74597 - 1.00803i) q^{89} +(3.96812 + 13.7460i) q^{91} +(4.43649 + 17.1825i) q^{92} +(0.757843 - 5.56036i) q^{94} +(0.563508 - 0.976025i) q^{95} +(-15.0000 - 8.66025i) q^{97} +(-4.68113 - 11.4486i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 12 q^{7} - 20 q^{14} + 14 q^{16} + 8 q^{17} + 30 q^{20} - 6 q^{22} + 20 q^{23} + 6 q^{26} + 6 q^{28} + 12 q^{38} - 24 q^{41} - 30 q^{46} + 4 q^{49} + 20 q^{55} + 10 q^{56} + 36 q^{58} + 20 q^{62}+ \cdots - 60 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 + 12 * q^7 - 20 * q^14 + 14 * q^16 + 8 * q^17 + 30 * q^20 - 6 * q^22 + 20 * q^23 + 6 * q^26 + 6 * q^28 + 12 * q^38 - 24 * q^41 - 30 * q^46 + 4 * q^49 + 20 * q^55 + 10 * q^56 + 36 * q^58 + 20 * q^62 + 44 * q^64 - 4 * q^68 - 12 * q^71 + 6 * q^74 + 30 * q^76 + 112 * q^79 + 30 * q^80 - 10 * q^82 + 18 * q^88 - 48 * q^89 + 20 * q^92 - 10 * q^94 + 20 * q^95 - 120 * q^97 - 60 * q^98

Introduction

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