LMFDB - Embedded newform 936.2.be.a.685.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(685,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.685"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [24,1,0,-1,0,0,-2,10,0,-3,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			685.11
Character	$\chi$	$=$	936.685
Dual form			936.2.be.a.757.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39150 - 0.252450i) q^{2} +(1.87254 - 0.702569i) q^{4} +4.18204i q^{5} +(0.818571 + 1.41781i) q^{7} +(2.42827 - 1.45035i) q^{8} +(1.05576 + 5.81931i) q^{10} +(-0.112523 - 0.0649654i) q^{11} +(-2.30757 + 2.77040i) q^{13} +(1.49697 + 1.76623i) q^{14} +(3.01279 - 2.63117i) q^{16} +(-1.60044 - 2.77205i) q^{17} +(-3.31858 + 1.91598i) q^{19} +(2.93817 + 7.83103i) q^{20} +(-0.172977 - 0.0619926i) q^{22} +(1.09184 - 1.89113i) q^{23} -12.4895 q^{25} +(-2.51159 + 4.43756i) q^{26} +(2.52891 + 2.07979i) q^{28} +(4.98269 + 2.87676i) q^{29} +4.16704 q^{31} +(3.52806 - 4.42186i) q^{32} +(-2.92682 - 3.45327i) q^{34} +(-5.92932 + 3.42330i) q^{35} +(-0.156315 - 0.0902485i) q^{37} +(-4.13411 + 3.50386i) q^{38} +(6.06541 + 10.1551i) q^{40} +(-2.25610 + 3.90767i) q^{41} +(5.84408 - 3.37408i) q^{43} +(-0.256347 - 0.0425947i) q^{44} +(1.04188 - 2.90714i) q^{46} +4.71041 q^{47} +(2.15988 - 3.74103i) q^{49} +(-17.3791 + 3.15297i) q^{50} +(-2.37461 + 6.80891i) q^{52} -4.75546i q^{53} +(0.271688 - 0.470577i) q^{55} +(4.04402 + 2.25560i) q^{56} +(7.65965 + 2.74512i) q^{58} +(9.37008 - 5.40982i) q^{59} +(-1.24545 + 0.719063i) q^{61} +(5.79842 - 1.05197i) q^{62} +(3.79299 - 7.04367i) q^{64} +(-11.5859 - 9.65035i) q^{65} +(11.0310 + 6.36874i) q^{67} +(-4.94445 - 4.06634i) q^{68} +(-7.38643 + 6.26037i) q^{70} +(-2.53663 - 4.39358i) q^{71} +3.28487 q^{73} +(-0.240295 - 0.0861189i) q^{74} +(-4.86805 + 5.91928i) q^{76} -0.212715i q^{77} -9.44449 q^{79} +(11.0037 + 12.5996i) q^{80} +(-2.15286 + 6.00707i) q^{82} +5.48783i q^{83} +(11.5928 - 6.69312i) q^{85} +(7.28024 - 6.17037i) q^{86} +(-0.367459 + 0.00544441i) q^{88} +(0.386337 - 0.669155i) q^{89} +(-5.81680 - 1.00392i) q^{91} +(0.715870 - 4.30830i) q^{92} +(6.55453 - 1.18915i) q^{94} +(-8.01272 - 13.8784i) q^{95} +(-5.07163 - 8.78432i) q^{97} +(2.06105 - 5.75090i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) $ 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

Character values

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

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	1.39150	−	0.252450i	0.983938	−	0.178509i
$2$	1.39150	−	0.252450i	0.983938	−	0.178509i
$3$		0			0
$3$		0			0
$4$	1.87254	−	0.702569i	0.936269	−	0.351285i
$5$			4.18204i			1.87027i	0.354297	+	0.935133i	$0.384720\pi$
$5$			4.18204i			1.87027i	−0.354297	+	0.935133i	$0.615280\pi$
$6$		0			0
$7$	0.818571	+	1.41781i	0.309391	+	0.535880i	0.978229	−	0.207527i	$-0.0665416\pi$
$7$	0.818571	+	1.41781i	0.309391	+	0.535880i	−0.668839	+	0.743408i	$0.733208\pi$
$8$	2.42827	−	1.45035i	0.858523	−	0.512775i
$9$		0			0
$10$	1.05576	+	5.81931i	0.333860	+	1.84023i
$11$	−0.112523	−	0.0649654i	−0.0339270	−	0.0195878i	0.482941	−	0.875653i	$-0.339569\pi$
$11$	−0.112523	−	0.0649654i	−0.0339270	−	0.0195878i	−0.516868	+	0.856065i	$0.672902\pi$
$12$		0			0
$13$	−2.30757	+	2.77040i	−0.640005	+	0.768371i
$13$	−2.30757	+	2.77040i	−0.640005	+	0.768371i
$14$	1.49697	+	1.76623i	0.400081	+	0.472044i
$15$		0			0
$16$	3.01279	−	2.63117i	0.753198	−	0.657793i
$17$	−1.60044	−	2.77205i	−0.388165	−	0.672321i	0.604038	−	0.796955i	$-0.293557\pi$
$17$	−1.60044	−	2.77205i	−0.388165	−	0.672321i	−0.992203	+	0.124635i	$0.960224\pi$
$18$		0			0
$19$	−3.31858	+	1.91598i	−0.761334	+	0.439556i	−0.829775	−	0.558099i	$-0.811531\pi$
$19$	−3.31858	+	1.91598i	−0.761334	+	0.439556i	0.0684404	+	0.997655i	$0.478198\pi$
$20$	2.93817	+	7.83103i	0.656995	+	1.75107i
$21$		0			0
$22$	−0.172977	−	0.0619926i	−0.0368787	−	0.0132169i
$23$	1.09184	−	1.89113i	0.227665	−	0.394327i	−0.729451	−	0.684033i	$-0.760224\pi$
$23$	1.09184	−	1.89113i	0.227665	−	0.394327i	0.957116	+	0.289706i	$0.0935575\pi$
$24$		0			0
$25$	−12.4895			−2.49789
$26$	−2.51159	+	4.43756i	−0.492563	+	0.870277i
$27$		0			0
$28$	2.52891	+	2.07979i	0.477919	+	0.393044i
$29$	4.98269	+	2.87676i	0.925263	+	0.534201i	0.885310	−	0.465001i	$-0.153946\pi$
$29$	4.98269	+	2.87676i	0.925263	+	0.534201i	0.0399526	+	0.999202i	$0.487279\pi$
$30$		0			0
$31$	4.16704			0.748422			0.374211	−	0.927344i	$-0.377914\pi$
$31$	4.16704			0.748422			0.374211	+	0.927344i	$0.377914\pi$
$32$	3.52806	−	4.42186i	0.623678	−	0.781681i
$33$		0			0
$34$	−2.92682	−	3.45327i	−0.501946	−	0.592231i
$35$	−5.92932	+	3.42330i	−1.00224	+	0.578643i
$36$		0			0
$37$	−0.156315	−	0.0902485i	−0.0256980	−	0.0148368i	0.487096	−	0.873348i	$-0.338056\pi$
$37$	−0.156315	−	0.0902485i	−0.0256980	−	0.0148368i	−0.512794	+	0.858512i	$0.671390\pi$
$38$	−4.13411	+	3.50386i	−0.670641	+	0.568402i
$39$		0			0
$40$	6.06541	+	10.1551i	0.959026	+	1.60567i
$41$	−2.25610	+	3.90767i	−0.352343	+	0.610276i	−0.986660	−	0.162798i	$-0.947948\pi$
$41$	−2.25610	+	3.90767i	−0.352343	+	0.610276i	0.634317	+	0.773073i	$0.281282\pi$
$42$		0			0
$43$	5.84408	−	3.37408i	0.891213	−	0.514542i	0.0168740	−	0.999858i	$-0.494629\pi$
$43$	5.84408	−	3.37408i	0.891213	−	0.514542i	0.874339	+	0.485315i	$0.161295\pi$
$44$	−0.256347	−	0.0425947i	−0.0386457	−	0.00642139i
$45$		0			0
$46$	1.04188	−	2.90714i	0.153617	−	0.428634i
$47$	4.71041			0.687084			0.343542	−	0.939137i	$-0.388373\pi$
$47$	4.71041			0.687084			0.343542	+	0.939137i	$0.388373\pi$
$48$		0			0
$49$	2.15988	−	3.74103i	0.308555	−	0.534433i
$50$	−17.3791	+	3.15297i	−2.45777	+	0.445898i
$51$		0			0
$52$	−2.37461	+	6.80891i	−0.329299	+	0.944226i
$53$		−	4.75546i		−	0.653213i	−0.945160	−	0.326606i	$-0.894095\pi$
$53$		−	4.75546i		−	0.653213i	0.945160	−	0.326606i	$-0.105905\pi$
$54$		0			0
$55$	0.271688	−	0.470577i	0.0366344	−	0.0634526i
$56$	4.04402	+	2.25560i	0.540405	+	0.301418i
$57$		0			0
$58$	7.65965	+	2.74512i	1.00576	+	0.360452i
$59$	9.37008	−	5.40982i	1.21988	−	0.704298i	0.254988	−	0.966944i	$-0.417929\pi$
$59$	9.37008	−	5.40982i	1.21988	−	0.704298i	0.964892	+	0.262646i	$0.0845952\pi$
$60$		0			0
$61$	−1.24545	+	0.719063i	−0.159464	+	0.0920666i	−0.577608	−	0.816314i	$-0.696014\pi$
$61$	−1.24545	+	0.719063i	−0.159464	+	0.0920666i	0.418144	+	0.908381i	$0.362681\pi$
$62$	5.79842	−	1.05197i	0.736401	−	0.133600i
$63$		0			0
$64$	3.79299	−	7.04367i	0.474123	−	0.880458i
$65$	−11.5859	−	9.65035i	−1.43706	−	1.19698i
$66$		0			0
$67$	11.0310	+	6.36874i	1.34765	+	0.778065i	0.987916	−	0.154991i	$-0.0495347\pi$
$67$	11.0310	+	6.36874i	1.34765	+	0.778065i	0.359732	+	0.933056i	$0.382868\pi$
$68$	−4.94445	−	4.06634i	−0.599602	−	0.493117i
$69$		0			0
$70$	−7.38643	+	6.26037i	−0.882848	+	0.748258i
$71$	−2.53663	−	4.39358i	−0.301043	−	0.521422i	0.675329	−	0.737516i	$-0.264001\pi$
$71$	−2.53663	−	4.39358i	−0.301043	−	0.521422i	−0.976373	+	0.216094i	$0.930668\pi$
$72$		0			0
$73$	3.28487			0.384464			0.192232	−	0.981349i	$-0.438427\pi$
$73$	3.28487			0.384464			0.192232	+	0.981349i	$0.438427\pi$
$74$	−0.240295	−	0.0861189i	−0.0279338	−	0.0100111i
$75$		0			0
$76$	−4.86805	+	5.91928i	−0.558404	+	0.678988i
$77$		−	0.212715i		−	0.0242411i
$78$		0			0
$79$	−9.44449			−1.06259			−0.531294	−	0.847188i	$-0.678294\pi$
$79$	−9.44449			−1.06259			−0.531294	+	0.847188i	$0.678294\pi$
$80$	11.0037	+	12.5996i	1.23025	+	1.40868i
$81$		0			0
$82$	−2.15286	+	6.00707i	−0.237744	+	0.663370i
$83$			5.48783i			0.602368i	0.953566	+	0.301184i	$0.0973818\pi$
$83$			5.48783i			0.602368i	−0.953566	+	0.301184i	$0.902618\pi$
$84$		0			0
$85$	11.5928	−	6.69312i	1.25742	−	0.725971i
$86$	7.28024	−	6.17037i	0.785048	−	0.665368i
$87$		0			0
$88$	−0.367459	+	0.00544441i	−0.0391713	+	0.000580376i
$89$	0.386337	−	0.669155i	0.0409516	−	0.0709303i	−0.844823	−	0.535046i	$-0.820294\pi$
$89$	0.386337	−	0.669155i	0.0409516	−	0.0709303i	0.885775	+	0.464115i	$0.153628\pi$
$90$		0			0
$91$	−5.81680	−	1.00392i	−0.609766	−	0.105239i
$92$	0.715870	−	4.30830i	0.0746346	−	0.449172i
$93$		0			0
$94$	6.55453	−	1.18915i	0.676048	−	0.122651i
$95$	−8.01272	−	13.8784i	−0.822087	−	1.42390i
$96$		0			0
$97$	−5.07163	−	8.78432i	−0.514946	−	0.891913i	−0.999850	−	0.0173453i	$-0.994479\pi$
$97$	−5.07163	−	8.78432i	−0.514946	−	0.891913i	0.484903	−	0.874568i	$-0.338855\pi$
$98$	2.06105	−	5.75090i	0.208198	−	0.580929i
$99$		0			0
$100$	−23.3870	+	8.77472i	−2.33870	+	0.877472i
$101$	−1.06784	−	0.616520i	−0.106254	−	0.0613460i	0.445931	−	0.895067i	$-0.352873\pi$
$101$	−1.06784	−	0.616520i	−0.106254	−	0.0613460i	−0.552185	+	0.833721i	$0.686206\pi$
$102$		0			0
$103$	17.8494			1.75876			0.879378	−	0.476124i	$-0.157959\pi$
$103$	17.8494			1.75876			0.879378	+	0.476124i	$0.157959\pi$
$104$	−1.58536	+	10.0741i	−0.155457	+	0.987843i
$105$		0			0
$106$	−1.20052	−	6.61722i	−0.116605	−	0.642721i
$107$	−5.60755	−	3.23752i	−0.542102	−	0.312983i	0.203828	−	0.979007i	$-0.434662\pi$
$107$	−5.60755	−	3.23752i	−0.542102	−	0.312983i	−0.745930	+	0.666024i	$0.767995\pi$
$108$		0			0
$109$		−	6.68786i		−	0.640581i	−0.947319	−	0.320291i	$-0.896219\pi$
$109$		−	6.68786i		−	0.640581i	0.947319	−	0.320291i	$-0.103781\pi$
$110$	0.259256	−	0.723395i	0.0247191	−	0.0689730i
$111$		0			0
$112$	6.19668	+	2.11776i	0.585531	+	0.200109i
$113$	2.97574	+	5.15414i	0.279935	+	0.484861i	0.971368	−	0.237579i	$-0.0763539\pi$
$113$	2.97574	+	5.15414i	0.279935	+	0.484861i	−0.691434	+	0.722440i	$0.743021\pi$
$114$		0			0
$115$	7.90878	+	4.56613i	0.737497	+	0.425794i
$116$	11.3514	+	1.88615i	1.05395	+	0.175125i
$117$		0			0
$118$	11.6727	−	9.89323i	1.07456	−	0.910746i
$119$	2.62015	−	4.53824i	0.240189	−	0.416019i
$120$		0			0
$121$	−5.49156	−	9.51166i	−0.499233	−	0.864696i
$122$	−1.55152	+	1.31499i	−0.140468	+	0.119054i
$123$		0			0
$124$	7.80293	−	2.92763i	0.700724	−	0.262909i
$125$		−	31.3213i		−	2.80146i
$126$		0			0
$127$	−2.12829	+	3.68631i	−0.188855	+	0.327107i	−0.944869	−	0.327449i	$-0.893811\pi$
$127$	−2.12829	+	3.68631i	−0.188855	+	0.327107i	0.756014	+	0.654556i	$0.227144\pi$
$128$	3.49976	−	10.7588i	0.309338	−	0.950952i
$129$		0			0
$130$	−18.5580	−	10.5036i	−1.62765	−	0.921225i
$131$			6.87969i			0.601082i	0.953769	+	0.300541i	$0.0971672\pi$
$131$			6.87969i			0.601082i	−0.953769	+	0.300541i	$0.902833\pi$
$132$		0			0
$133$	−5.43298	−	3.13673i	−0.471099	−	0.271989i
$134$	16.9574	+	6.07731i	1.46489	+	0.525000i
$135$		0			0
$136$	−7.90674	−	4.41009i	−0.677998	−	0.378162i
$137$	−2.17602	−	3.76898i	−0.185910	−	0.322006i	0.757973	−	0.652286i	$-0.226190\pi$
$137$	−2.17602	−	3.76898i	−0.185910	−	0.322006i	−0.943883	+	0.330280i	$0.892857\pi$
$138$		0			0
$139$	−10.5694	+	6.10225i	−0.896485	+	0.517586i	−0.876058	−	0.482206i	$-0.839836\pi$
$139$	−10.5694	+	6.10225i	−0.896485	+	0.517586i	−0.0204268	+	0.999791i	$0.506503\pi$
$140$	−8.69778	+	10.5760i	−0.735096	+	0.893836i
$141$		0			0
$142$	−4.63889	−	5.47329i	−0.389287	−	0.459308i
$143$	0.439635	−	0.161823i	0.0367642	−	0.0135323i
$144$		0			0
$145$	−12.0307	+	20.8378i	−0.999097	+	1.73049i
$146$	4.57089	−	0.829266i	0.378289	−	0.0686305i
$147$		0			0
$148$	−0.356112	−	0.0591716i	−0.0292722	−	0.00486388i
$149$	−1.30871	+	0.755584i	−0.107214	+	0.0618999i	−0.552648	−	0.833415i	$-0.686383\pi$
$149$	−1.30871	+	0.755584i	−0.107214	+	0.0618999i	0.445434	+	0.895315i	$0.353049\pi$
$150$		0			0
$151$	18.5064			1.50603			0.753016	−	0.658002i	$-0.228598\pi$
$151$	18.5064			1.50603			0.753016	+	0.658002i	$0.228598\pi$
$152$	−5.27956	+	9.46561i	−0.428229	+	0.767762i
$153$		0			0
$154$	−0.0537000	−	0.295993i	−0.00432727	−	0.0238518i
$155$			17.4267i			1.39975i
$156$		0			0
$157$		−	12.3725i		−	0.987436i	−0.869622	−	0.493718i	$-0.835638\pi$
$157$		−	12.3725i		−	0.987436i	0.869622	−	0.493718i	$-0.164362\pi$
$158$	−13.1420	+	2.38427i	−1.04552	+	0.189682i
$159$		0			0
$160$	18.4924	+	14.7545i	1.46195	+	1.16644i
$161$	3.57500			0.281750
$162$		0			0
$163$	−16.7151	+	9.65045i	−1.30922	+	0.755881i	−0.981967	−	0.189054i	$-0.939458\pi$
$163$	−16.7151	+	9.65045i	−1.30922	+	0.755881i	−0.327258	+	0.944935i	$0.606125\pi$
$164$	−1.47921	+	8.90233i	−0.115507	+	0.695155i
$165$		0			0
$166$	1.38541	+	7.63631i	0.107528	+	0.592693i
$167$	−7.37018	+	12.7655i	−0.570322	+	0.987826i	0.426211	+	0.904624i	$0.359848\pi$
$167$	−7.37018	+	12.7655i	−0.570322	+	0.987826i	−0.996533	+	0.0832023i	$0.973485\pi$
$168$		0			0
$169$	−2.35025	−	12.7858i	−0.180788	−	0.983522i
$170$	14.4417	−	12.2401i	1.10763	−	0.938772i
$171$		0			0
$172$	8.57273	−	10.4240i	0.653664	−	0.794819i
$173$	−17.3427	+	10.0128i	−1.31854	+	0.761261i	−0.983494	−	0.180940i	$-0.942086\pi$
$173$	−17.3427	+	10.0128i	−1.31854	+	0.761261i	−0.335049	+	0.942201i	$0.608753\pi$
$174$		0			0
$175$	−10.2235	−	17.7076i	−0.772825	−	1.33857i
$176$	−0.509945	+	0.100341i	−0.0384385	+	0.00756350i
$177$		0			0
$178$	0.368659	−	1.02866i	0.0276322	−	0.0771013i
$179$	−18.1523	−	10.4802i	−1.35677	−	0.783330i	−0.367581	−	0.929992i	$-0.619814\pi$
$179$	−18.1523	−	10.4802i	−1.35677	−	0.783330i	−0.989187	+	0.146662i	$0.953147\pi$
$180$		0			0
$181$			7.45173i			0.553883i	0.960887	+	0.276941i	$0.0893208\pi$
$181$			7.45173i			0.553883i	−0.960887	+	0.276941i	$0.910679\pi$
$182$	−8.34751	+	0.0715061i	−0.618759	+	0.00530039i
$183$		0			0
$184$	−0.0915017	−	6.17572i	−0.00674560	−	0.455280i
$185$	0.377423	−	0.653716i	0.0277487	−	0.0480621i
$186$		0			0
$187$			0.415894i			0.0304131i
$188$	8.82042	−	3.30939i	0.643295	−	0.241362i
$189$		0			0
$190$	−14.6533	−	17.2890i	−1.06306	−	1.25428i
$191$	−2.54530	−	4.40859i	−0.184171	−	0.318994i	0.759126	−	0.650944i	$-0.225627\pi$
$191$	−2.54530	−	4.40859i	−0.184171	−	0.318994i	−0.943297	+	0.331950i	$0.892293\pi$
$192$		0			0
$193$	−2.32009	+	4.01852i	−0.167004	+	0.289259i	−0.937365	−	0.348348i	$-0.886743\pi$
$193$	−2.32009	+	4.01852i	−0.167004	+	0.289259i	0.770361	+	0.637608i	$0.220076\pi$
$194$	−9.27478	−	10.9430i	−0.665890	−	0.785665i
$195$		0			0
$196$	1.41613	−	8.52269i	0.101152	−	0.608763i
$197$	−8.23896	−	4.75677i	−0.587002	−	0.338906i	0.176909	−	0.984227i	$-0.443390\pi$
$197$	−8.23896	−	4.75677i	−0.587002	−	0.338906i	−0.763911	+	0.645322i	$0.776723\pi$
$198$		0			0
$199$	−3.19043	−	5.52598i	−0.226163	−	0.391727i	0.730504	−	0.682908i	$-0.239285\pi$
$199$	−3.19043	−	5.52598i	−0.226163	−	0.391727i	−0.956668	+	0.291181i	$0.905952\pi$
$200$	−30.3278	+	18.1141i	−2.14450	+	1.28086i
$201$		0			0
$202$	−1.64154	−	0.588309i	−0.115499	−	0.0413933i
$203$			9.41932i			0.661107i
$204$		0			0
$205$	−16.3420	−	9.43509i	−1.14138	−	0.658975i
$206$	24.8375	−	4.50610i	1.73051	−	0.313955i
$207$		0			0
$208$	0.337178	+	14.4183i	0.0233791	+	0.999727i
$209$	0.497890			0.0344398
$210$		0			0
$211$	−0.393007	−	0.226903i	−0.0270557	−	0.0156206i	0.486411	−	0.873730i	$-0.338306\pi$
$211$	−0.393007	−	0.226903i	−0.0270557	−	0.0156206i	−0.513467	+	0.858109i	$0.671639\pi$
$212$	−3.34104	−	8.90478i	−0.229463	−	0.611582i
$213$		0			0
$214$	−8.62021	−	3.08938i	−0.589265	−	0.211185i
$215$	14.1105	+	24.4402i	0.962331	+	1.66681i
$216$		0			0
$217$	3.41101	+	5.90805i	0.231555	+	0.401064i
$218$	−1.68835	−	9.30615i	−0.114350	−	0.630292i
$219$		0			0
$220$	0.178133	−	1.07205i	0.0120097	−	0.0722778i
$221$	11.3728	+	1.96282i	0.765019	+	0.132034i
$222$		0			0
$223$	−5.57308	+	9.65286i	−0.373201	+	0.646403i	−0.990056	−	0.140674i	$-0.955073\pi$
$223$	−5.57308	+	9.65286i	−0.373201	+	0.646403i	0.616855	+	0.787077i	$0.288407\pi$
$224$	9.15730	+	1.38250i	0.611848	+	0.0923721i
$225$		0			0
$226$	5.44191	+	6.42075i	0.361991	+	0.427102i
$227$	6.69076	−	3.86291i	0.444082	−	0.256391i	−0.261246	−	0.965272i	$-0.584133\pi$
$227$	6.69076	−	3.86291i	0.444082	−	0.256391i	0.705327	+	0.708882i	$0.250800\pi$
$228$		0			0
$229$		−	11.1426i		−	0.736326i	−0.929761	−	0.368163i	$-0.879987\pi$
$229$		−	11.1426i		−	0.736326i	0.929761	−	0.368163i	$-0.120013\pi$
$230$	12.1578	+	4.35720i	0.801660	+	0.287305i
$231$		0			0
$232$	16.2716	−	0.241086i	1.06828	−	0.0158281i
$233$	6.04221			0.395838			0.197919	−	0.980218i	$-0.436582\pi$
$233$	6.04221			0.395838			0.197919	+	0.980218i	$0.436582\pi$
$234$		0			0
$235$			19.6991i			1.28503i
$236$	13.7450	−	16.7132i	0.894726	−	1.08794i
$237$		0			0
$238$	2.50026	−	6.97641i	0.162068	−	0.452213i
$239$	8.18119			0.529197			0.264599	−	0.964359i	$-0.414761\pi$
$239$	8.18119			0.529197			0.264599	+	0.964359i	$0.414761\pi$
$240$		0			0
$241$	3.58510	+	6.20958i	0.230937	+	0.399994i	0.958084	−	0.286487i	$-0.0924876\pi$
$241$	3.58510	+	6.20958i	0.230937	+	0.399994i	−0.727147	+	0.686481i	$0.759154\pi$
$242$	−10.0427	−	11.8491i	−0.645571	−	0.761690i
$243$		0			0
$244$	−1.82697	+	2.22149i	−0.116960	+	0.142216i
$245$	15.6451	+	9.03273i	0.999531	+	0.577080i
$246$		0			0
$247$	2.34981	−	13.6151i	0.149515	−	0.866305i
$248$	10.1187	−	6.04365i	0.642537	−	0.383772i
$249$		0			0
$250$	−7.90707	−	43.5835i	−0.500087	−	2.75646i
$251$	0.0364204	−	0.0210273i	0.00229884	−	0.00132723i	−0.498850	−	0.866688i	$-0.666244\pi$
$251$	0.0364204	−	0.0210273i	0.00229884	−	0.00132723i	0.501149	+	0.865361i	$0.332911\pi$
$252$		0			0
$253$	−0.245716	+	0.141864i	−0.0154480	+	0.00891891i
$254$	−2.03090	+	5.66678i	−0.127430	+	0.355565i
$255$		0			0
$256$	2.15385	−	15.8544i	0.134616	−	0.990898i
$257$	12.7818	−	22.1387i	0.797306	−	1.38097i	−0.124059	−	0.992275i	$-0.539591\pi$
$257$	12.7818	−	22.1387i	0.797306	−	1.38097i	0.921365	−	0.388699i	$-0.127075\pi$
$258$		0			0
$259$		−	0.295499i		−	0.0183614i
$260$	−28.4751	−	9.93072i	−1.76595	−	0.615877i
$261$		0			0
$262$	1.73678	+	9.57309i	0.107299	+	0.591427i
$263$	11.5182	−	19.9501i	0.710241	−	1.23017i	−0.254526	−	0.967066i	$-0.581919\pi$
$263$	11.5182	−	19.9501i	0.710241	−	1.23017i	0.964767	−	0.263107i	$-0.0847472\pi$
$264$		0			0
$265$	19.8875			1.22168
$266$	−8.35186	−	2.99320i	−0.512085	−	0.183525i
$267$		0			0
$268$	25.1304	+	4.17568i	1.53508	+	0.255070i
$269$	−11.1829	+	6.45647i	−0.681836	+	0.393658i	−0.800546	−	0.599271i	$-0.795457\pi$
$269$	−11.1829	+	6.45647i	−0.681836	+	0.393658i	0.118711	+	0.992929i	$0.462124\pi$
$270$		0			0
$271$	9.32018	−	16.1430i	0.566161	−	0.980619i	−0.430780	−	0.902457i	$-0.641762\pi$
$271$	9.32018	−	16.1430i	0.566161	−	0.980619i	0.996941	−	0.0781619i	$-0.0249051\pi$
$272$	−12.1156	−	4.14057i	−0.734613	−	0.251059i
$273$		0			0
$274$	−3.97941	−	4.69520i	−0.240405	−	0.283647i
$275$	1.40536	+	0.811383i	0.0847462	+	0.0489282i
$276$		0			0
$277$	−14.4955	+	8.36900i	−0.870953	+	0.502845i	−0.867665	−	0.497150i	$-0.834380\pi$
$277$	−14.4955	+	8.36900i	−0.870953	+	0.502845i	−0.00328797	+	0.999995i	$0.501047\pi$
$278$	−13.1668	+	11.1595i	−0.789692	+	0.669303i
$279$		0			0
$280$	−9.43303	+	16.9123i	−0.563731	+	1.01070i
$281$	−12.2103			−0.728407			−0.364203	−	0.931319i	$-0.618659\pi$
$281$	−12.2103			−0.728407			−0.364203	+	0.931319i	$0.618659\pi$
$282$		0			0
$283$	−18.9020	−	10.9131i	−1.12361	−	0.648717i	−0.181290	−	0.983430i	$-0.558027\pi$
$283$	−18.9020	−	10.9131i	−1.12361	−	0.648717i	−0.942320	+	0.334713i	$0.891361\pi$
$284$	−7.83674	−	6.44498i	−0.465025	−	0.382439i
$285$		0			0
$286$	0.570900	−	0.336162i	0.0337580	−	0.0198777i
$287$	−7.38710			−0.436046
$288$		0			0
$289$	3.37716	−	5.84941i	0.198657	−	0.344083i
$290$	−11.4802	+	32.0330i	−0.674142	+	1.88104i
$291$		0			0
$292$	6.15103	−	2.30785i	0.359962	−	0.135056i
$293$	4.85556	−	2.80336i	0.283665	−	0.163774i	−0.351417	−	0.936219i	$-0.614300\pi$
$293$	4.85556	−	2.80336i	0.283665	−	0.163774i	0.635081	+	0.772445i	$0.280967\pi$
$294$		0			0
$295$	22.6241	+	39.1860i	1.31722	+	2.28150i
$296$	−0.510467	+	0.00756326i	−0.0296703	+	0.000439605i
$297$		0			0
$298$	−1.63032	+	1.38178i	−0.0944420	+	0.0800443i
$299$	2.71968	+	7.38875i	0.157283	+	0.427303i
$300$		0			0
$301$	9.56758	+	5.52384i	0.551466	+	0.318389i
$302$	25.7517	−	4.67196i	1.48184	−	0.268841i
$303$		0			0
$304$	−4.95691	+	14.5042i	−0.284298	+	0.831874i
$305$	−3.00715	−	5.20854i	−0.172189	−	0.298240i
$306$		0			0
$307$			10.4756i			0.597873i	0.954273	+	0.298937i	$0.0966319\pi$
$307$			10.4756i			0.597873i	−0.954273	+	0.298937i	$0.903368\pi$
$308$	−0.149447	−	0.398317i	−0.00851553	−	0.0226962i
$309$		0			0
$310$	4.39938	+	24.2493i	0.249868	+	1.37726i
$311$	8.46570			0.480046			0.240023	−	0.970767i	$-0.422845\pi$
$311$	8.46570			0.480046			0.240023	+	0.970767i	$0.422845\pi$
$312$		0			0
$313$	−11.5873			−0.654953			−0.327477	−	0.944859i	$-0.606198\pi$
$313$	−11.5873			−0.654953			−0.327477	+	0.944859i	$0.606198\pi$
$314$	−3.12345	−	17.2164i	−0.176267	−	0.971576i
$315$		0			0
$316$	−17.6852	+	6.63540i	−0.994868	+	0.373271i
$317$		−	10.0772i		−	0.565993i	−0.959121	−	0.282997i	$-0.908671\pi$
$317$		−	10.0772i		−	0.565993i	0.959121	−	0.282997i	$-0.0913285\pi$
$318$		0			0
$319$	−0.373779	−	0.647405i	−0.0209276	−	0.0362477i
$320$	29.4569	+	15.8624i	1.64669	+	0.886737i
$321$		0			0
$322$	4.97461	−	0.902511i	0.277224	−	0.0502950i
$323$	10.6224	+	6.13284i	0.591046	+	0.341240i
$324$		0			0
$325$	28.8203	−	34.6009i	1.59866	−	1.91931i
$326$	−20.8227	+	17.6483i	−1.15326	+	0.977450i
$327$		0			0
$328$	0.189072	+	12.7610i	0.0104397	+	0.704609i
$329$	3.85580	+	6.67845i	0.212577	+	0.368195i
$330$		0			0
$331$	22.9049	−	13.2242i	1.25897	−	0.726865i	0.286094	−	0.958202i	$-0.407643\pi$
$331$	22.9049	−	13.2242i	1.25897	−	0.726865i	0.972874	+	0.231336i	$0.0743097\pi$
$332$	3.85558	+	10.2762i	0.211602	+	0.563978i
$333$		0			0
$334$	−7.03293	+	19.6238i	−0.384825	+	1.07377i
$335$	−26.6343	+	46.1320i	−1.45519	+	2.52046i
$336$		0			0
$337$	−9.74324			−0.530748			−0.265374	−	0.964146i	$-0.585495\pi$
$337$	−9.74324			−0.530748			−0.265374	+	0.964146i	$0.585495\pi$
$338$	−6.49815	−	17.1981i	−0.353453	−	0.935452i
$339$		0			0
$340$	17.0056	−	20.6779i	0.922259	−	1.12142i
$341$	−0.468889	−	0.270713i	−0.0253917	−	0.0146599i
$342$		0			0
$343$	18.5321			1.00064
$344$	9.29741	−	16.6691i	0.501283	−	0.898738i
$345$		0			0
$346$	−21.6046	+	18.3110i	−1.16147	+	0.984406i
$347$	26.5385	−	15.3220i	1.42466	−	0.822527i	0.427967	−	0.903795i	$-0.359230\pi$
$347$	26.5385	−	15.3220i	1.42466	−	0.822527i	0.996692	+	0.0812673i	$0.0258967\pi$
$348$		0			0
$349$	18.8036	+	10.8563i	1.00653	+	0.581122i	0.910175	−	0.414225i	$-0.135947\pi$
$349$	18.8036	+	10.8563i	1.00653	+	0.581122i	0.0963582	+	0.995347i	$0.469281\pi$
$350$	−18.6963	−	22.0592i	−0.999360	−	1.17912i
$351$		0			0
$352$	−0.684256	+	0.268360i	−0.0364710	+	0.0143037i
$353$	−14.8743	+	25.7630i	−0.791679	+	1.37123i	0.133248	+	0.991083i	$0.457459\pi$
$353$	−14.8743	+	25.7630i	−0.791679	+	1.37123i	−0.924927	+	0.380145i	$0.875874\pi$
$354$		0			0
$355$	18.3741	−	10.6083i	0.975198	−	0.563031i
$356$	0.253303	−	1.52445i	0.0134250	−	0.0807955i
$357$		0			0
$358$	−27.9047	−	10.0007i	−1.47481	−	0.528553i
$359$	35.4019			1.86844			0.934220	−	0.356697i	$-0.116097\pi$
$359$	35.4019			1.86844			0.934220	+	0.356697i	$0.116097\pi$
$360$		0			0
$361$	−2.15802	+	3.73781i	−0.113580	+	0.196727i
$362$	1.88119	+	10.3691i	0.0988733	+	0.544986i
$363$		0			0
$364$	−11.5975	+	2.20683i	−0.607874	+	0.115669i
$365$			13.7374i			0.719051i
$366$		0			0
$367$	−11.1967	+	19.3933i	−0.584465	+	1.01232i	0.410477	+	0.911871i	$0.365362\pi$
$367$	−11.1967	+	19.3933i	−0.584465	+	1.01232i	−0.994942	+	0.100452i	$0.967971\pi$
$368$	−1.68639	−	8.57041i	−0.0879091	−	0.446763i
$369$		0			0
$370$	0.360153	−	1.00493i	0.0187235	−	0.0522436i
$371$	6.74232	−	3.89268i	0.350044	−	0.202098i
$372$		0			0
$373$	−7.02394	+	4.05527i	−0.363686	+	0.209974i	−0.670696	−	0.741732i	$-0.734005\pi$
$373$	−7.02394	+	4.05527i	−0.363686	+	0.209974i	0.307011	+	0.951706i	$0.400671\pi$
$374$	0.104993	+	0.578715i	0.00542903	+	0.0299247i
$375$		0			0
$376$	11.4381	−	6.83173i	0.589877	−	0.352320i
$377$	−19.4677	+	7.16574i	−1.00264	+	0.369054i
$378$		0			0
$379$	−31.5220	−	18.1993i	−1.61918	−	0.934833i	−0.987133	−	0.159901i	$-0.948883\pi$
$379$	−31.5220	−	18.1993i	−1.61918	−	0.934833i	−0.632045	−	0.774932i	$-0.717784\pi$
$380$	−24.7547	−	20.3584i	−1.26989	−	1.04436i
$381$		0			0
$382$	−4.65473	−	5.49198i	−0.238157	−	0.280994i
$383$	6.06507	+	10.5050i	0.309911	+	0.536781i	0.978343	−	0.206992i	$-0.0663675\pi$
$383$	6.06507	+	10.5050i	0.309911	+	0.536781i	−0.668432	+	0.743773i	$0.733034\pi$
$384$		0			0
$385$	0.889583			0.0453373
$386$	−2.21393	+	6.17747i	−0.112686	+	0.314425i
$387$		0			0
$388$	−15.6684	−	12.8858i	−0.795443	−	0.654178i
$389$			9.92534i			0.503235i	0.967827	+	0.251617i	$0.0809624\pi$
$389$			9.92534i			0.503235i	−0.967827	+	0.251617i	$0.919038\pi$
$390$		0			0
$391$	−6.98974			−0.353486
$392$	−0.181009	−	12.2168i	−0.00914232	−	0.617042i
$393$		0			0
$394$	−12.6654	−	4.53911i	−0.638071	−	0.228677i
$395$		−	39.4972i		−	1.98732i
$396$		0			0
$397$	6.08746	−	3.51459i	0.305521	−	0.176392i	−0.339400	−	0.940642i	$-0.610224\pi$
$397$	6.08746	−	3.51459i	0.305521	−	0.176392i	0.644920	+	0.764250i	$0.276891\pi$
$398$	−5.83451	−	6.88397i	−0.292458	−	0.345062i
$399$		0			0
$400$	−37.6282	+	32.8620i	−1.88141	+	1.64310i
$401$	−13.2273	+	22.9104i	−0.660540	+	1.14409i	0.319934	+	0.947440i	$0.396339\pi$
$401$	−13.2273	+	22.9104i	−0.660540	+	1.14409i	−0.980474	+	0.196649i	$0.936994\pi$
$402$		0			0
$403$	−9.61572	+	11.5444i	−0.478993	+	0.575066i
$404$	−2.43272	−	0.404222i	−0.121033	−	0.0201108i
$405$		0			0
$406$	2.37791	+	13.1070i	0.118014	+	0.650488i
$407$	0.0117261	+	0.0203101i	0.000581239	+	0.00100674i
$408$		0			0
$409$	−10.3029	−	17.8452i	−0.509448	−	0.882389i	−0.999940	−	0.0109437i	$-0.996516\pi$
$409$	−10.3029	−	17.8452i	−0.509448	−	0.882389i	0.490493	−	0.871445i	$-0.336817\pi$
$410$	−25.1218	−	9.00335i	−1.24068	−	0.444644i
$411$		0			0
$412$	33.4237	−	12.5405i	1.64667	−	0.617824i
$413$	15.3401	+	8.85663i	0.754839	+	0.435806i
$414$		0			0
$415$	−22.9503			−1.12659
$416$	4.10908	+	19.9779i	0.201464	+	0.979496i
$417$		0			0
$418$	0.692813	−	0.125693i	0.0338866	−	0.00614782i
$419$	0.0293062	+	0.0169200i	0.00143170	+	0.000826594i	0.500716	−	0.865612i	$-0.333070\pi$
$419$	0.0293062	+	0.0169200i	0.00143170	+	0.000826594i	−0.499284	+	0.866438i	$0.666404\pi$
$420$		0			0
$421$			31.4805i			1.53427i	0.641488	+	0.767133i	$0.278317\pi$
$421$			31.4805i			1.53427i	−0.641488	+	0.767133i	$0.721683\pi$
$422$	−0.604150	−	0.216520i	−0.0294096	−	0.0105400i
$423$		0			0
$424$	−6.89707	−	11.5475i	−0.334951	−	0.560798i
$425$	19.9887	+	34.6214i	0.969594	+	1.67939i
$426$		0			0
$427$	−2.03898	−	1.17721i	−0.0986733	−	0.0569691i
$428$	−12.7749	−	2.12269i	−0.617499	−	0.102604i
$429$		0			0
$430$	25.8047	+	30.4462i	1.24441	+	1.46825i
$431$	8.74777	−	15.1516i	0.421365	−	0.729826i	−0.574708	−	0.818359i	$-0.694884\pi$
$431$	8.74777	−	15.1516i	0.421365	−	0.729826i	0.996073	+	0.0885325i	$0.0282177\pi$
$432$		0			0
$433$	12.0881	+	20.9371i	0.580915	+	1.00617i	0.995371	+	0.0961049i	$0.0306384\pi$
$433$	12.0881	+	20.9371i	0.580915	+	1.00617i	−0.414456	+	0.910069i	$0.636028\pi$
$434$	6.23791	+	7.35993i	0.299429	+	0.353288i
$435$		0			0
$436$	−4.69869	−	12.5233i	−0.225026	−	0.599756i
$437$			8.36781i			0.400287i
$438$		0			0
$439$	−5.67437	+	9.82831i	−0.270823	+	0.469079i	−0.969073	−	0.246775i	$-0.920629\pi$
$439$	−5.67437	+	9.82831i	−0.270823	+	0.469079i	0.698250	+	0.715854i	$0.253963\pi$
$440$	−0.0227687	−	1.53673i	−0.00108546	−	0.0732607i
$441$		0			0
$442$	16.3208	−	0.139806i	0.776301	−	0.00664992i
$443$		−	23.6211i		−	1.12227i	−0.827723	−	0.561137i	$-0.810364\pi$
$443$		−	23.6211i		−	1.12227i	0.827723	−	0.561137i	$-0.189636\pi$
$444$		0			0
$445$	2.79844	+	1.61568i	0.132659	+	0.0765905i
$446$	−5.31807	+	14.8389i	−0.251818	+	0.702641i
$447$		0			0
$448$	13.0914	−	0.388018i	0.618510	−	0.0183321i
$449$	−13.5758	−	23.5140i	−0.640683	−	1.10970i	−0.985281	−	0.170945i	$-0.945318\pi$
$449$	−13.5758	−	23.5140i	−0.640683	−	1.10970i	0.344597	−	0.938751i	$-0.388015\pi$
$450$		0			0
$451$	0.507727	−	0.293136i	0.0239079	−	0.0138032i
$452$	9.19333	+	7.56066i	0.432418	+	0.355623i
$453$		0			0
$454$	8.33499	−	7.06433i	0.391181	−	0.331545i
$455$	4.19842	−	24.3261i	0.196825	−	1.14043i
$456$		0			0
$457$	−19.6700	+	34.0695i	−0.920124	+	1.59370i	−0.120903	+	0.992664i	$0.538579\pi$
$457$	−19.6700	+	34.0695i	−0.920124	+	1.59370i	−0.799221	+	0.601038i	$0.794754\pi$
$458$	−2.81296	−	15.5050i	−0.131441	−	0.724499i
$459$		0			0
$460$	18.0175	+	2.99380i	0.840071	+	0.139586i
$461$	−30.5545	+	17.6406i	−1.42306	+	0.821606i	−0.996560	−	0.0828789i	$-0.973589\pi$
$461$	−30.5545	+	17.6406i	−1.42306	+	0.821606i	−0.426505	+	0.904485i	$0.640255\pi$
$462$		0			0
$463$	3.79130			0.176197			0.0880984	−	0.996112i	$-0.471921\pi$
$463$	3.79130			0.176197			0.0880984	+	0.996112i	$0.471921\pi$
$464$	22.5811	−	4.44325i	1.04830	−	0.206273i
$465$		0			0
$466$	8.40773	−	1.52536i	0.389481	−	0.0706609i
$467$			5.84443i			0.270448i	0.990815	+	0.135224i	$0.0431754\pi$
$467$			5.84443i			0.270448i	−0.990815	+	0.135224i	$0.956825\pi$
$468$		0			0
$469$			20.8530i			0.962904i
$470$	4.97306	+	27.4113i	0.229390	+	1.26439i
$471$		0			0
$472$	14.9070	−	26.7264i	0.686148	−	1.23018i
$473$	−0.876793			−0.0403150
$474$		0			0
$475$	41.4473	−	23.9296i	1.90173	−	1.09797i
$476$	1.71791	−	10.3389i	0.0787402	−	0.473881i
$477$		0			0
$478$	11.3841	−	2.06535i	0.520697	−	0.0944667i
$479$	3.67249	−	6.36093i	0.167800	−	0.290638i	−0.769846	−	0.638230i	$-0.779667\pi$
$479$	3.67249	−	6.36093i	0.167800	−	0.290638i	0.937646	+	0.347591i	$0.113000\pi$
$480$		0			0
$481$	0.610732	−	0.224801i	0.0278470	−	0.0102500i
$482$	6.55628	+	7.73556i	0.298630	+	0.352345i
$483$		0			0
$484$	−16.9657	−	13.9527i	−0.771170	−	0.634215i
$485$	36.7364	−	21.2098i	1.66811	−	0.963086i
$486$		0			0
$487$	−9.78062	−	16.9405i	−0.443202	−	0.767649i	0.554723	−	0.832035i	$-0.312824\pi$
$487$	−9.78062	−	16.9405i	−0.443202	−	0.767649i	−0.997925	+	0.0643866i	$0.979491\pi$
$488$	−1.98141	+	3.55242i	−0.0896941	+	0.160810i
$489$		0			0
$490$	24.0505	+	8.61940i	1.08649	+	0.389385i
$491$	−23.1454	−	13.3630i	−1.04454	−	0.603065i	−0.123424	−	0.992354i	$-0.539387\pi$
$491$	−23.1454	−	13.3630i	−1.04454	−	0.603065i	−0.921116	+	0.389289i	$0.872721\pi$
$492$		0			0
$493$		−	18.4164i		−	0.829431i
$494$	−0.167370	−	19.5385i	−0.00753035	−	0.879081i
$495$		0			0
$496$	12.5544	−	10.9642i	0.563710	−	0.492307i
$497$	4.15283	−	7.19291i	0.186280	−	0.322646i
$498$		0			0
$499$		−	22.3087i		−	0.998674i	−0.866408	−	0.499337i	$-0.833577\pi$
$499$		−	22.3087i		−	0.998674i	0.866408	−	0.499337i	$-0.166423\pi$
$500$	−22.0054	−	58.6503i	−0.984110	−	2.62292i
$501$		0			0
$502$	0.0453706	−	0.0384539i	0.00202499	−	0.00171628i
$503$	21.2109	+	36.7383i	0.945746	+	1.63808i	0.754250	+	0.656587i	$0.228001\pi$
$503$	21.2109	+	36.7383i	0.945746	+	1.63808i	0.191496	+	0.981493i	$0.438666\pi$
$504$		0			0
$505$	2.57831	−	4.46576i	0.114733	−	0.198724i
$506$	−0.306099	+	0.259435i	−0.0136078	+	0.0115333i
$507$		0			0
$508$	−1.39542	+	8.39802i	−0.0619117	+	0.372602i
$509$	−32.8492	−	18.9655i	−1.45602	−	0.840631i	−0.457204	−	0.889362i	$-0.651149\pi$
$509$	−32.8492	−	18.9655i	−1.45602	−	0.840631i	−0.998812	+	0.0487309i	$0.984482\pi$
$510$		0			0
$511$	2.68889	+	4.65730i	0.118950	+	0.206027i
$512$	−1.00536	−	22.6051i	−0.0444312	−	0.999012i
$513$		0			0
$514$	12.1969	−	34.0327i	0.537983	−	1.50112i
$515$			74.6471i			3.28934i
$516$		0			0
$517$	−0.530031	−	0.306013i	−0.0233107	−	0.0134585i
$518$	−0.0745989	−	0.411187i	−0.00327769	−	0.0180665i
$519$		0			0
$520$	−42.1301	−	6.63003i	−1.84753	−	0.290746i
$521$	31.2115			1.36740			0.683699	−	0.729764i	$-0.260370\pi$
$521$	31.2115			1.36740			0.683699	+	0.729764i	$0.260370\pi$
$522$		0			0
$523$	17.2006	+	9.93079i	0.752131	+	0.434243i	0.826463	−	0.562990i	$-0.190349\pi$
$523$	17.2006	+	9.93079i	0.752131	+	0.434243i	−0.0743322	+	0.997234i	$0.523683\pi$
$524$	4.83346	+	12.8825i	0.211151	+	0.562774i
$525$		0			0
$526$	10.9911	−	30.6682i	0.479235	−	1.33720i
$527$	−6.66910	−	11.5512i	−0.290511	−	0.503179i
$528$		0			0
$529$	9.11576	+	15.7890i	0.396337	+	0.686476i
$530$	27.6735	−	5.02062i	1.20206	−	0.218082i
$531$		0			0
$532$	−12.3772	−	2.05661i	−0.536621	−	0.0891652i
$533$	−5.61972	−	15.2675i	−0.243417	−	0.661310i
$534$		0			0
$535$	13.5394	−	23.4510i	0.585361	−	1.01388i
$536$	36.0231	−	0.533731i	1.55596	−	0.0230537i
$537$		0			0
$538$	−13.9311	+	11.8073i	−0.600613	+	0.509049i
$539$	−0.486075	+	0.280635i	−0.0209367	+	0.0120878i
$540$		0			0
$541$			19.0860i			0.820573i	0.911957	+	0.410286i	$0.134571\pi$
$541$			19.0860i			0.820573i	−0.911957	+	0.410286i	$0.865429\pi$
$542$	8.89370	−	24.8159i	0.382017	−	1.06593i
$543$		0			0
$544$	−17.9041	−	2.70302i	−0.767630	−	0.115891i
$545$	27.9689			1.19806
$546$		0			0
$547$			34.9201i			1.49307i	0.665343	+	0.746537i	$0.268285\pi$
$547$			34.9201i			1.49307i	−0.665343	+	0.746537i	$0.731715\pi$
$548$	−6.72265	−	5.52875i	−0.287178	−	0.236177i
$549$		0			0
$550$	2.16039	+	0.774255i	0.0921192	+	0.0330144i
$551$	−22.0473			−0.939245
$552$		0			0
$553$	−7.73098	−	13.3905i	−0.328755	−	0.569420i
$554$	−18.0578	+	15.3049i	−0.767201	+	0.650241i
$555$		0			0
$556$	−15.5044	+	18.8524i	−0.657531	+	0.799521i
$557$	23.7593	+	13.7174i	1.00671	+	0.581225i	0.910227	−	0.414109i	$-0.135907\pi$
$557$	23.7593	+	13.7174i	1.00671	+	0.581225i	0.0964847	+	0.995334i	$0.469240\pi$
$558$		0			0
$559$	−4.13806	+	23.9764i	−0.175021	+	1.01409i
$560$	−8.85654	+	25.9148i	−0.374257	+	1.09510i
$561$		0			0
$562$	−16.9906	+	3.08250i	−0.716707	+	0.130027i
$563$	18.8753	−	10.8976i	0.795498	−	0.459281i	−0.0463964	−	0.998923i	$-0.514774\pi$
$563$	18.8753	−	10.8976i	0.795498	−	0.459281i	0.841895	+	0.539642i	$0.181440\pi$
$564$		0			0
$565$	−21.5548	+	12.4447i	−0.906819	+	0.523552i
$566$	−29.0572	−	10.4137i	−1.22136	−	0.437722i
$567$		0			0
$568$	−12.5318	−	6.98980i	−0.525825	−	0.293285i
$569$	4.13482	−	7.16172i	0.173341	−	0.300235i	−0.766245	−	0.642548i	$-0.777877\pi$
$569$	4.13482	−	7.16172i	0.173341	−	0.300235i	0.939586	+	0.342314i	$0.111210\pi$
$570$		0			0
$571$			23.8709i			0.998967i	0.866323	+	0.499484i	$0.166477\pi$
$571$			23.8709i			0.998967i	−0.866323	+	0.499484i	$0.833523\pi$
$572$	0.709542	−	0.611893i	0.0296674	−	0.0255845i
$573$		0			0
$574$	−10.2791	+	1.86488i	−0.429043	+	0.0778384i
$575$	−13.6365	+	23.6192i	−0.568683	+	0.984988i
$576$		0			0
$577$	−11.0017			−0.458005			−0.229003	−	0.973426i	$-0.573546\pi$
$577$	−11.0017			−0.458005			−0.229003	+	0.973426i	$0.573546\pi$
$578$	3.22263	−	8.99202i	0.134044	−	0.374019i
$579$		0			0
$580$	−7.88797	+	47.4720i	−0.327530	+	1.97117i
$581$	−7.78068	+	4.49218i	−0.322797	+	0.186367i
$582$		0			0
$583$	−0.308940	+	0.535100i	−0.0127950	+	0.0221616i
$584$	7.97654	−	4.76420i	0.330072	−	0.197144i
$585$		0			0
$586$	6.04879	−	5.12666i	0.249873	−	0.211780i
$587$	−23.7398	−	13.7062i	−0.979846	−	0.565714i	−0.0776224	−	0.996983i	$-0.524733\pi$
$587$	−23.7398	−	13.7062i	−0.979846	−	0.565714i	−0.902224	+	0.431268i	$0.858066\pi$
$588$		0			0
$589$	−13.8286	+	7.98396i	−0.569799	+	0.328974i
$590$	41.3739	+	48.8159i	1.70334	+	2.00972i
$591$		0			0
$592$	−0.708404	+	0.139392i	−0.0291152	+	0.00572897i
$593$	−27.9342			−1.14712			−0.573560	−	0.819163i	$-0.694438\pi$
$593$	−27.9342			−1.14712			−0.573560	+	0.819163i	$0.694438\pi$
$594$		0			0
$595$	18.9791	+	10.9576i	0.778067	+	0.449217i
$596$	−1.91976	+	2.33432i	−0.0786364	+	0.0956174i
$597$		0			0
$598$	5.64973	+	9.59486i	0.231034	+	0.392363i
$599$	−28.5235			−1.16544			−0.582720	−	0.812673i	$-0.698011\pi$
$599$	−28.5235			−1.16544			−0.582720	+	0.812673i	$0.698011\pi$
$600$		0			0
$601$	14.9335	−	25.8655i	0.609149	−	1.05508i	−0.382232	−	0.924066i	$-0.624845\pi$
$601$	14.9335	−	25.8655i	0.609149	−	1.05508i	0.991381	−	0.131010i	$-0.0418221\pi$
$602$	14.7078	+	5.27108i	0.599444	+	0.214833i
$603$		0			0
$604$	34.6540	−	13.0021i	1.41005	−	0.529046i
$605$	39.7782	−	22.9659i	1.61721	−	0.933698i
$606$		0			0
$607$	−1.42147	−	2.46206i	−0.0576958	−	0.0999320i	0.835735	−	0.549133i	$-0.185042\pi$
$607$	−1.42147	−	2.46206i	−0.0576958	−	0.0999320i	−0.893431	+	0.449201i	$0.851709\pi$
$608$	−3.23594	+	21.4340i	−0.131235	+	0.869262i
$609$		0			0
$610$	−5.49934	−	6.48852i	−0.222662	−	0.262712i
$611$	−10.8696	+	13.0497i	−0.439737	+	0.527936i
$612$		0			0
$613$	−29.0756	−	16.7868i	−1.17435	−	0.678012i	−0.219650	−	0.975579i	$-0.570491\pi$
$613$	−29.0756	−	16.7868i	−1.17435	−	0.678012i	−0.954701	+	0.297567i	$0.903825\pi$
$614$	2.64457	+	14.5768i	0.106726	+	0.588270i
$615$		0			0
$616$	−0.308510	−	0.516529i	−0.0124302	−	0.0208116i
$617$	20.6348	+	35.7406i	0.830728	+	1.43886i	0.897462	+	0.441092i	$0.145409\pi$
$617$	20.6348	+	35.7406i	0.830728	+	1.43886i	−0.0667344	+	0.997771i	$0.521258\pi$
$618$		0			0
$619$		−	15.5402i		−	0.624612i	−0.949981	−	0.312306i	$-0.898899\pi$
$619$		−	15.5402i		−	0.624612i	0.949981	−	0.312306i	$-0.101101\pi$
$620$	12.2435	+	32.6322i	0.491710	+	1.31054i
$621$		0			0
$622$	11.7800	−	2.13717i	0.472335	−	0.0856927i
$623$	1.26498			0.0506802
$624$		0			0
$625$	68.5395			2.74158
$626$	−16.1237	+	2.92522i	−0.644434	+	0.116915i
$627$		0			0
$628$	−8.69256	−	23.1680i	−0.346871	−	0.924505i
$629$			0.577751i			0.0230364i
$630$		0			0
$631$	7.60667	+	13.1751i	0.302817	+	0.524494i	0.976773	−	0.214277i	$-0.0687396\pi$
$631$	7.60667	+	13.1751i	0.302817	+	0.524494i	−0.673956	+	0.738771i	$0.735406\pi$
$632$	−22.9338	+	13.6978i	−0.912256	+	0.544869i
$633$		0			0
$634$	−2.54400	−	14.0224i	−0.101035	−	0.556902i
$635$	−15.4163	−	8.90060i	−0.611777	−	0.353209i
$636$		0			0
$637$	5.38007	+	14.6164i	0.213166	+	0.579124i
$638$	−0.683551	−	0.806502i	−0.0270620	−	0.0319297i
$639$		0			0
$640$	44.9937	+	14.6361i	1.77853	+	0.578544i
$641$	−6.58777	−	11.4104i	−0.260201	−	0.450682i	0.706094	−	0.708118i	$-0.250456\pi$
$641$	−6.58777	−	11.4104i	−0.260201	−	0.450682i	−0.966295	+	0.257436i	$0.917122\pi$
$642$		0			0
$643$	−15.6244	+	9.02073i	−0.616165	+	0.355743i	−0.775374	−	0.631502i	$-0.782439\pi$
$643$	−15.6244	+	9.02073i	−0.616165	+	0.355743i	0.159209	+	0.987245i	$0.449105\pi$
$644$	6.69433	−	2.51169i	0.263794	−	0.0989743i
$645$		0			0
$646$	16.3293	+	5.85221i	0.642467	+	0.230252i
$647$	−13.2156	+	22.8901i	−0.519560	+	0.899904i	0.480181	+	0.877169i	$0.340571\pi$
$647$	−13.2156	+	22.8901i	−0.519560	+	0.899904i	−0.999742	+	0.0227353i	$0.992763\pi$
$648$		0			0
$649$	−1.40580			−0.0551826
$650$	31.3684	−	55.4227i	1.23037	−	2.17386i
$651$		0			0
$652$	−24.5195	+	29.8143i	−0.960257	+	1.16762i
$653$	−0.343032	−	0.198049i	−0.0134239	−	0.00775027i	0.493273	−	0.869875i	$-0.335800\pi$
$653$	−0.343032	−	0.198049i	−0.0134239	−	0.00775027i	−0.506697	+	0.862124i	$0.669134\pi$
$654$		0			0
$655$	−28.7712			−1.12418
$656$	3.48461	+	17.7092i	0.136051	+	0.691428i
$657$		0			0
$658$	7.05132	+	8.31965i	0.274889	+	0.324334i
$659$	−10.9574	+	6.32627i	−0.426841	+	0.246437i	−0.698000	−	0.716098i	$-0.745926\pi$
$659$	−10.9574	+	6.32627i	−0.426841	+	0.246437i	0.271159	+	0.962535i	$0.412593\pi$
$660$		0			0
$661$	−12.6635	−	7.31128i	−0.492554	−	0.284376i	0.233080	−	0.972458i	$-0.425120\pi$
$661$	−12.6635	−	7.31128i	−0.492554	−	0.284376i	−0.725633	+	0.688082i	$0.758453\pi$
$662$	28.5337	−	24.1838i	1.10899	−	0.939928i
$663$		0			0
$664$	7.95926	+	13.3259i	0.308879	+	0.517147i
$665$	13.1179	−	22.7210i	0.508692	−	0.881081i
$666$		0			0
$667$	10.8806	−	6.28194i	0.421300	−	0.243238i
$668$	−4.83228	+	29.0820i	−0.186966	+	1.12522i
$669$		0			0
$670$	−25.4156	+	70.9165i	−0.981890	+	2.73974i
$671$	0.186857			0.00721352
$672$		0			0
$673$	−5.72681	+	9.91913i	−0.220752	+	0.382354i	−0.955037	−	0.296488i	$-0.904185\pi$
$673$	−5.72681	+	9.91913i	−0.220752	+	0.382354i	0.734284	+	0.678842i	$0.237518\pi$
$674$	−13.5577	+	2.45968i	−0.522223	+	0.0947435i
$675$		0			0
$676$	−13.3838	−	22.2907i	−0.514763	−	0.857333i
$677$			32.2006i			1.23757i	0.785561	+	0.618784i	$0.212375\pi$
$677$			32.2006i			1.23757i	−0.785561	+	0.618784i	$0.787625\pi$
$678$		0			0
$679$	8.30298	−	14.3812i	0.318639	−	0.551899i
$680$	18.4432	−	33.0663i	0.707263	−	1.26804i
$681$		0			0
$682$	−0.720799	−	0.258326i	−0.0276008	−	0.00989180i
$683$	10.2725	−	5.93085i	0.393067	−	0.226938i	−0.290421	−	0.956899i	$-0.593795\pi$
$683$	10.2725	−	5.93085i	0.393067	−	0.226938i	0.683488	+	0.729961i	$0.260462\pi$
$684$		0			0
$685$	15.7620	−	9.10022i	0.602237	−	0.347701i
$686$	25.7873	−	4.67843i	0.984565	−	0.178623i
$687$		0			0
$688$	8.72921	−	25.5422i	0.332798	−	0.973786i
$689$	13.1745	+	10.9736i	0.501910	+	0.418059i
$690$		0			0
$691$	−6.81210	−	3.93297i	−0.259145	−	0.149617i	0.364800	−	0.931086i	$-0.381137\pi$
$691$	−6.81210	−	3.93297i	−0.259145	−	0.149617i	−0.623944	+	0.781469i	$0.714471\pi$
$692$	−25.4402	+	30.9339i	−0.967091	+	1.17593i
$693$		0			0
$694$	33.0602	−	28.0202i	1.25495	−	1.06363i
$695$	−25.5199	−	44.2017i	−0.968023	−	1.67667i
$696$		0			0
$697$	14.4430			0.547068
$698$	28.9058	+	10.3595i	1.09410	+	0.392113i
$699$		0			0
$700$	−31.5848	−	25.9755i	−1.19379	−	0.981782i
$701$			25.2255i			0.952752i	0.879242	+	0.476376i	$0.158050\pi$
$701$			25.2255i			0.952752i	−0.879242	+	0.476376i	$0.841950\pi$
$702$		0			0
$703$	0.691658			0.0260864
$704$	−0.884394	+	0.546164i	−0.0333318	+	0.0205843i
$705$		0			0
$706$	−14.1937	+	39.6043i	−0.534186	+	1.49053i
$707$		−	2.01866i		−	0.0759195i
$708$		0			0
$709$	3.83979	−	2.21690i	0.144206	−	0.0832576i	−0.426161	−	0.904647i	$-0.640134\pi$
$709$	3.83979	−	2.21690i	0.144206	−	0.0832576i	0.570367	+	0.821390i	$0.306801\pi$
$710$	22.8895	−	19.4000i	0.859028	−	0.728069i
$711$		0			0
$712$	−0.0323769	−	2.18521i	−0.00121338	−	0.0818943i
$713$	4.54975	−	7.88040i	0.170389	−	0.295123i
$714$		0			0
$715$	0.676749	+	1.83857i	0.0253090	+	0.0687587i
$716$	−41.3540	−	6.87139i	−1.54547	−	0.256796i
$717$		0			0
$718$	49.2617	−	8.93722i	1.83843	−	0.333534i
$719$	−14.9536	−	25.9004i	−0.557675	−	0.965922i	−0.997690	−	0.0679313i	$-0.978360\pi$
$719$	−14.9536	−	25.9004i	−0.557675	−	0.965922i	0.440015	−	0.897991i	$-0.354973\pi$
$720$		0			0
$721$	14.6110	+	25.3070i	0.544143	+	0.942483i
$722$	−2.05928	+	5.74595i	−0.0766384	+	0.213842i
$723$		0			0
$724$	5.23536	+	13.9536i	0.194570	+	0.518583i
$725$	−62.2312	−	35.9292i	−2.31121	−	1.33438i
$726$		0			0
$727$	−3.63561			−0.134837			−0.0674186	−	0.997725i	$-0.521476\pi$
$727$	−3.63561			−0.134837			−0.0674186	+	0.997725i	$0.521476\pi$
$728$	−15.5808	+	5.99860i	−0.577462	+	0.222323i
$729$		0			0
$730$	3.46802	+	19.1156i	0.128357	+	0.707502i
$731$	−18.7062	−	10.8000i	−0.691875	−	0.399454i
$732$		0			0
$733$			19.1009i			0.705507i	0.935716	+	0.352753i	$0.114754\pi$
$733$			19.1009i			0.705507i	−0.935716	+	0.352753i	$0.885246\pi$
$734$	−10.6844	+	29.8124i	−0.394368	+	1.10040i
$735$		0			0
$736$	−4.51021	−	11.5000i	−0.166249	−	0.423895i
$737$	−0.827494	−	1.43326i	−0.0304811	−	0.0527949i
$738$		0			0
$739$	−19.9646	−	11.5266i	−0.734410	−	0.424012i	0.0856233	−	0.996328i	$-0.472712\pi$
$739$	−19.9646	−	11.5266i	−0.734410	−	0.424012i	−0.820033	+	0.572316i	$0.806045\pi$
$740$	0.247458	−	1.48927i	0.00909675	−	0.0547468i
$741$		0			0
$742$	8.39922	−	7.11876i	0.308345	−	0.261338i
$743$	0.368260	−	0.637844i	0.0135101	−	0.0234002i	−0.859191	−	0.511654i	$-0.829033\pi$
$743$	0.368260	−	0.637844i	0.0135101	−	0.0234002i	0.872701	+	0.488254i	$0.162366\pi$
$744$		0			0
$745$	−3.15988	−	5.47308i	−0.115769	−	0.200518i
$746$	−8.75004	+	7.41610i	−0.320362	+	0.271523i
$747$		0			0
$748$	0.292194	+	0.778776i	0.0106837	+	0.0284749i
$749$		−	10.6006i		−	0.387336i
$750$		0			0
$751$	−19.4794	+	33.7394i	−0.710815	+	1.23117i	0.253737	+	0.967273i	$0.418340\pi$
$751$	−19.4794	+	33.7394i	−0.710815	+	1.23117i	−0.964552	+	0.263894i	$0.914993\pi$
$752$	14.1915	−	12.3939i	0.517511	−	0.451959i
$753$		0			0
$754$	−25.2803	+	14.8857i	−0.920653	+	0.542107i
$755$			77.3947i			2.81668i
$756$		0			0
$757$	43.5113	+	25.1213i	1.58144	+	0.913047i	0.994649	+	0.103312i	$0.0329441\pi$
$757$	43.5113	+	25.1213i	1.58144	+	0.913047i	0.586796	+	0.809735i	$0.300389\pi$
$758$	−48.4573	−	17.3665i	−1.76005	−	0.630779i
$759$		0			0
$760$	−39.5856	−	22.0794i	−1.43592	−	0.800903i
$761$	13.3039	+	23.0431i	0.482268	+	0.835312i	0.999793	−	0.0203558i	$-0.00647990\pi$
$761$	13.3039	+	23.0431i	0.482268	+	0.835312i	−0.517525	+	0.855668i	$0.673147\pi$
$762$		0			0
$763$	9.48209	−	5.47449i	0.343275	−	0.198190i
$764$	−7.86350	−	6.46699i	−0.284491	−	0.233968i
$765$		0			0
$766$	11.0915	+	13.0866i	0.400753	+	0.472837i
$767$	−6.63474	+	38.4424i	−0.239566	+	1.38807i
$768$		0			0
$769$	24.9857	−	43.2765i	0.901006	−	1.56059i	0.0748162	−	0.997197i	$-0.476163\pi$
$769$	24.9857	−	43.2765i	0.901006	−	1.56059i	0.826190	−	0.563391i	$-0.190504\pi$
$770$	1.23785	−	0.224576i	0.0446091	−	0.00809314i
$771$		0			0
$772$	−1.52117	+	9.15485i	−0.0547482	+	0.329490i
$773$	25.4987	−	14.7217i	0.917124	−	0.529502i	0.0344079	−	0.999408i	$-0.489045\pi$
$773$	25.4987	−	14.7217i	0.917124	−	0.529502i	0.882717	+	0.469906i	$0.155712\pi$
$774$		0			0
$775$	−52.0441			−1.86948
$776$	−25.0556	−	13.9751i	−0.899444	−	0.501676i
$777$		0			0
$778$	2.50566	+	13.8111i	0.0898321	+	0.495152i
$779$		−	17.2906i		−	0.619499i
$780$		0			0
$781$			0.659173i			0.0235871i
$782$	−9.72621	+	1.76456i	−0.347808	+	0.0631006i
$783$		0			0
$784$	−3.33601	−	16.9540i	−0.119143	−	0.605499i
$785$	51.7424			1.84677
$786$		0			0
$787$	25.2518	−	14.5791i	0.900129	−	0.519689i	0.0228866	−	0.999738i	$-0.492714\pi$
$787$	25.2518	−	14.5791i	0.900129	−	0.519689i	0.877242	+	0.480049i	$0.159381\pi$
$788$	−18.7697	−	3.11879i	−0.668644	−	0.111102i
$789$		0			0
$790$	−9.97110	−	54.9604i	−0.354756	−	1.95540i
$791$	−4.87171	+	8.43806i	−0.173218	+	0.300023i
$792$		0			0
$793$	0.881877	−	5.10969i	0.0313164	−	0.181451i
$794$	7.58343	−	6.42733i	0.269126	−	0.228098i
$795$		0			0
$796$	−9.85658	−	8.10611i	−0.349357	−	0.287314i
$797$	−12.9474	+	7.47521i	−0.458622	+	0.264786i	−0.711465	−	0.702722i	$-0.751968\pi$
$797$	−12.9474	+	7.47521i	−0.458622	+	0.264786i	0.252843	+	0.967507i	$0.418634\pi$
$798$		0			0
$799$	−7.53875	−	13.0575i	−0.266702	−	0.461941i
$800$	−44.0636	+	55.2266i	−1.55788	+	1.95256i
$801$		0			0
$802$	−12.6220	+	35.2190i	−0.445700	+	1.24363i
$803$	−0.369624	−	0.213402i	−0.0130437	−	0.00753081i
$804$		0			0
$805$			14.9508i			0.526947i
$806$	−10.4659	+	18.4915i	−0.368645	+	0.651334i
$807$		0			0
$808$	−3.48718	+	0.0516673i	−0.122679	+	0.00181765i
$809$	15.1416	−	26.2260i	0.532350	−	0.922057i	−0.466936	−	0.884291i	$-0.654642\pi$
$809$	15.1416	−	26.2260i	0.532350	−	0.922057i	0.999287	−	0.0377666i	$-0.0120243\pi$
$810$		0			0
$811$		−	26.0266i		−	0.913917i	−0.889488	−	0.456959i	$-0.848939\pi$
$811$		−	26.0266i		−	0.913917i	0.889488	−	0.456959i	$-0.151061\pi$
$812$	6.61772	+	17.6380i	0.232237	+	0.618974i
$813$		0			0
$814$	0.0214441	+	0.0253013i	0.000751615	+	0.000886809i
$815$	−40.3586	−	69.9031i	−1.41370	−	2.44860i
$816$		0			0
$817$	−12.9293	+	22.3943i	−0.452341	+	0.783477i
$818$	−18.8416	−	22.2306i	−0.658780	−	0.777275i
$819$		0			0
$820$	−37.2299	−	6.18614i	−1.30012	−	0.216029i
$821$	9.80725	+	5.66222i	0.342275	+	0.197613i	0.661278	−	0.750141i	$-0.270014\pi$
$821$	9.80725	+	5.66222i	0.342275	+	0.197613i	−0.319002	+	0.947754i	$0.603348\pi$
$822$		0			0
$823$	4.84592	+	8.39339i	0.168918	+	0.292575i	0.938040	−	0.346527i	$-0.112639\pi$
$823$	4.84592	+	8.39339i	0.168918	+	0.292575i	−0.769122	+	0.639103i	$0.779306\pi$
$824$	43.3432	−	25.8879i	1.50993	−	0.901847i
$825$		0			0
$826$	23.5816	+	8.45137i	0.820510	+	0.294061i
$827$		−	25.1340i		−	0.873995i	−0.899463	−	0.436998i	$-0.856042\pi$
$827$		−	25.1340i		−	0.873995i	0.899463	−	0.436998i	$-0.143958\pi$
$828$		0			0
$829$	−23.6743	−	13.6684i	−0.822243	−	0.474722i	0.0289466	−	0.999581i	$-0.490785\pi$
$829$	−23.6743	−	13.6684i	−0.822243	−	0.474722i	−0.851189	+	0.524859i	$0.824118\pi$
$830$	−31.9354	+	5.79382i	−1.10849	+	0.201107i
$831$		0			0
$832$	10.7612	+	26.7618i	0.373078	+	0.927800i
$833$	−13.8271			−0.479080
$834$		0			0
$835$	−53.3860	−	30.8224i	−1.84750	−	1.06665i
$836$	0.932317	−	0.349802i	0.0322449	−	0.0120982i
$837$		0			0
$838$	0.0450510	+	0.0161457i	0.00155626	+	0.000557745i
$839$	−20.2439	−	35.0635i	−0.698898	−	1.21053i	−0.968849	−	0.247652i	$-0.920341\pi$
$839$	−20.2439	−	35.0635i	−0.698898	−	1.21053i	0.269951	−	0.962874i	$-0.412992\pi$
$840$		0			0
$841$	2.05148	+	3.55327i	0.0707408	+	0.122527i
$842$	7.94727	+	43.8051i	0.273881	+	1.50962i
$843$		0			0
$844$	−0.895335	−	0.148769i	−0.0308187	−	0.00512085i
$845$	53.4707	−	9.82884i	1.83945	−	0.338122i
$846$		0			0
$847$	8.99046	−	15.5719i	0.308916	−	0.535058i
$848$	−12.5124	−	14.3272i	−0.429679	−	0.491999i
$849$		0			0
$850$	36.5544	+	43.1295i	1.25381	+	1.47933i
$851$	−0.341343	+	0.197074i	−0.0117011	+	0.00675563i
$852$		0			0
$853$		−	19.3717i		−	0.663274i	−0.943407	−	0.331637i	$-0.892399\pi$
$853$		−	19.3717i		−	0.663274i	0.943407	−	0.331637i	$-0.107601\pi$
$854$	−3.13443	−	1.12334i	−0.107258	−	0.0384399i
$855$		0			0
$856$	−18.3122	+	0.271320i	−0.625897	+	0.00927351i
$857$	−42.7949			−1.46185			−0.730923	−	0.682459i	$-0.760910\pi$
$857$	−42.7949			−1.46185			−0.730923	+	0.682459i	$0.760910\pi$
$858$		0			0
$859$		−	13.5425i		−	0.462062i	−0.972946	−	0.231031i	$-0.925790\pi$
$859$		−	13.5425i		−	0.462062i	0.972946	−	0.231031i	$-0.0742100\pi$
$860$	43.5934	+	35.8515i	1.48652	+	1.22253i
$861$		0			0
$862$	8.34749	−	23.2918i	0.284317	−	0.793321i
$863$	31.5933			1.07545			0.537724	−	0.843121i	$-0.319284\pi$
$863$	31.5933			1.07545			0.537724	+	0.843121i	$0.319284\pi$
$864$		0			0
$865$	−41.8741	−	72.5280i	−1.42376	−	2.46603i
$866$	22.1061	+	26.0824i	0.751196	+	0.886314i
$867$		0			0
$868$	10.5381	+	8.66657i	0.357685	+	0.294162i
$869$	1.06272	+	0.613564i	0.0360505	+	0.0208137i
$870$		0			0
$871$	−43.0987	+	15.8639i	−1.46034	+	0.537529i
$872$	−9.69972	−	16.2399i	−0.328474	−	0.549954i
$873$		0			0
$874$	2.11246	+	11.6438i	0.0714549	+	0.393857i
$875$	44.4075	−	25.6387i	1.50125	−	0.866746i
$876$		0			0
$877$	14.3595	−	8.29048i	0.484887	−	0.279950i	−0.237564	−	0.971372i	$-0.576349\pi$
$877$	14.3595	−	8.29048i	0.484887	−	0.279950i	0.722451	+	0.691422i	$0.243016\pi$
$878$	−5.41472	+	15.1086i	−0.182738	+	0.509890i
$879$		0			0
$880$	−0.419631	−	2.13261i	−0.0141458	−	0.0718902i
$881$	5.68180	−	9.84117i	0.191425	−	0.331557i	−0.754298	−	0.656532i	$-0.772023\pi$
$881$	5.68180	−	9.84117i	0.191425	−	0.331557i	0.945723	+	0.324975i	$0.105356\pi$
$882$		0			0
$883$		−	27.3539i		−	0.920531i	−0.887781	−	0.460266i	$-0.847754\pi$
$883$		−	27.3539i		−	0.920531i	0.887781	−	0.460266i	$-0.152246\pi$
$884$	22.6751	−	4.31473i	0.762645	−	0.145120i
$885$		0			0
$886$	−5.96316	−	32.8688i	−0.200336	−	1.10425i
$887$	11.3696	−	19.6927i	0.381754	−	0.661217i	−0.609559	−	0.792741i	$-0.708654\pi$
$887$	11.3696	−	19.6927i	0.381754	−	0.661217i	0.991313	+	0.131523i	$0.0419868\pi$
$888$		0			0
$889$	−6.96862			−0.233720
$890$	4.30190	+	1.54175i	0.144200	+	0.0516795i
$891$		0			0
$892$	−3.65400	+	21.9908i	−0.122345	+	0.736307i
$893$	−15.6319	+	9.02506i	−0.523100	+	0.302012i
$894$		0			0
$895$	43.8288	−	75.9137i	1.46504	−	2.53752i
$896$	18.1187	−	3.84485i	0.605303	−	0.128448i
$897$		0			0
$898$	−24.8269	−	29.2925i	−0.828484	−	0.977504i
$899$	20.7631	+	11.9876i	0.692487	+	0.399807i
$900$		0			0
$901$	−13.1824	+	7.61084i	−0.439168	+	0.253554i
$902$	0.632499	−	0.536074i	0.0210599	−	0.0178493i
$903$		0			0
$904$	14.7012	+	8.19978i	0.488955	+	0.272721i
$905$	−31.1635			−1.03591
$906$		0			0
$907$	−8.59306	−	4.96121i	−0.285328	−	0.164734i	0.350505	−	0.936561i	$-0.386010\pi$
$907$	−8.59306	−	4.96121i	−0.285328	−	0.164734i	−0.635833	+	0.771827i	$0.719343\pi$
$908$	9.81474	−	11.9342i	0.325714	−	0.396049i
$909$		0			0
$910$	−0.299042	−	34.9096i	−0.00991313	−	1.15724i
$911$	44.1121			1.46150			0.730749	−	0.682646i	$-0.239171\pi$
$911$	44.1121			1.46150			0.730749	+	0.682646i	$0.239171\pi$
$912$		0			0
$913$	0.356519	−	0.617509i	0.0117991	−	0.0204366i
$914$	−18.7699	+	52.3733i	−0.620855	+	1.73236i
$915$		0			0
$916$	−7.82847	−	20.8650i	−0.258660	−	0.689399i
$917$	−9.75407	+	5.63152i	−0.322108	+	0.185969i
$918$		0			0
$919$	−14.9559	−	25.9044i	−0.493351	−	0.854509i	0.506620	−	0.862169i	$-0.330895\pi$
$919$	−14.9559	−	25.9044i	−0.493351	−	0.854509i	−0.999971	+	0.00766098i	$0.997561\pi$
$920$	25.8271	−	0.382664i	0.851495	−	0.0126161i
$921$		0			0
$922$	−38.0631	+	32.2604i	−1.25354	+	1.06244i
$923$	18.0254	+	3.11099i	0.593315	+	0.102400i
$924$		0			0
$925$	1.95229	+	1.12716i	0.0641910	+	0.0370607i
$926$	5.27559	−	0.957116i	0.173367	−	0.0314528i
$927$		0			0
$928$	30.2998	−	11.8834i	0.994641	−	0.390091i
$929$	−21.2926	−	36.8800i	−0.698589	−	1.20999i	−0.968956	−	0.247234i	$-0.920478\pi$
$929$	−21.2926	−	36.8800i	−0.698589	−	1.20999i	0.270367	−	0.962757i	$-0.412855\pi$
$930$		0			0
$931$			16.5532i			0.542509i
$932$	11.3143	−	4.24507i	0.370611	−	0.139052i
$933$		0			0
$934$	1.47543	+	8.13251i	0.0482775	+	0.266104i
$935$	−1.73928			−0.0568807
$936$		0			0
$937$	48.8727			1.59660			0.798301	−	0.602259i	$-0.205733\pi$
$937$	48.8727			1.59660			0.798301	+	0.602259i	$0.205733\pi$
$938$	5.26436	+	29.0170i	0.171887	+	0.947438i
$939$		0			0
$940$	13.8400	+	36.8874i	0.451411	+	1.20313i
$941$			0.373985i			0.0121916i	0.999981	+	0.00609579i	$0.00194036\pi$
$941$			0.373985i			0.0121916i	−0.999981	+	0.00609579i	$0.998060\pi$
$942$		0			0
$943$	4.92661	+	8.53313i	0.160432	+	0.277877i
$944$	13.9959	−	40.9530i	0.455529	−	1.33291i
$945$		0			0
$946$	−1.22006	+	0.221347i	−0.0396674	+	0.00719660i
$947$	−32.8305	−	18.9547i	−1.06685	−	0.615945i	−0.139529	−	0.990218i	$-0.544559\pi$
$947$	−32.8305	−	18.9547i	−1.06685	−	0.615945i	−0.927318	+	0.374273i	$0.877892\pi$
$948$		0			0
$949$	−7.58006	+	9.10040i	−0.246059	+	0.295411i
$950$	51.6328	−	43.7614i	1.67519	−	1.41981i
$951$		0			0
$952$	−0.219581	−	14.8202i	−0.00711667	−	0.480325i
$953$	6.10919	+	10.5814i	0.197896	+	0.342766i	0.947846	−	0.318728i	$-0.103256\pi$
$953$	6.10919	+	10.5814i	0.197896	+	0.342766i	−0.749950	+	0.661495i	$0.769922\pi$
$954$		0			0
$955$	18.4369	−	10.6445i	0.596604	−	0.344449i
$956$	15.3196	−	5.74785i	0.495471	−	0.185899i
$957$		0			0
$958$	3.50444	−	9.77835i	0.113223	−	0.315924i
$959$	3.56246	−	6.17036i	0.115038	−	0.199251i
$960$		0			0
$961$	−13.6358			−0.439865
$962$	0.793082	−	0.466989i	0.0255700	−	0.0150563i
$963$		0			0
$964$	11.0759	+	9.10889i	0.356731	+	0.293378i
$965$	−16.8056	−	9.70272i	−0.540992	−	0.312342i
$966$		0			0
$967$	−21.0836			−0.678003			−0.339002	−	0.940786i	$-0.610089\pi$
$967$	−21.0836			−0.678003			−0.339002	+	0.940786i	$0.610089\pi$
$968$	−27.1302	−	15.1322i	−0.871997	−	0.486368i
$969$		0			0
$970$	45.7643	−	38.7875i	1.46940	−	1.24539i
$971$	−18.0110	+	10.3987i	−0.578002	+	0.333710i	−0.760339	−	0.649526i	$-0.774967\pi$
$971$	−18.0110	+	10.3987i	−0.578002	+	0.333710i	0.182337	+	0.983236i	$0.441634\pi$
$972$		0			0
$973$	−17.3036	−	9.99024i	−0.554728	−	0.320272i
$974$	−17.8864	−	21.1036i	−0.573116	−	0.676203i
$975$		0			0
$976$	−1.86031	+	5.44339i	−0.0595472	+	0.174239i
$977$	2.19054	−	3.79413i	0.0700817	−	0.121385i	−0.828855	−	0.559463i	$-0.811007\pi$
$977$	2.19054	−	3.79413i	0.0700817	−	0.121385i	0.898937	+	0.438078i	$0.144341\pi$
$978$		0			0
$979$	−0.0869438	+	0.0501970i	−0.00277874	+	0.00160430i
$980$	35.6422	+	5.92233i	1.13855	+	0.189182i
$981$		0			0
$982$	−35.5804	−	12.7516i	−1.13542	−	0.406919i
$983$	−11.6609			−0.371925			−0.185962	−	0.982557i	$-0.559540\pi$
$983$	−11.6609			−0.371925			−0.185962	+	0.982557i	$0.559540\pi$
$984$		0			0
$985$	19.8930	−	34.4557i	0.633844	−	1.09785i
$986$	−4.64922	−	25.6263i	−0.148061	−	0.816109i
$987$		0			0
$988$	−5.16541	−	27.1456i	−0.164334	−	0.863617i
$989$		−	14.7359i		−	0.468573i
$990$		0			0
$991$	6.53708	−	11.3226i	0.207657	−	0.359673i	−0.743319	−	0.668937i	$-0.766749\pi$
$991$	6.53708	−	11.3226i	0.207657	−	0.359673i	0.950976	+	0.309264i	$0.100083\pi$
$992$	14.7015	−	18.4260i	0.466774	−	0.585027i
$993$		0			0
$994$	3.96280	−	11.0573i	0.125692	−	0.350717i
$995$	23.1099	−	13.3425i	0.732633	−	0.422986i
$996$		0			0
$997$	28.2743	−	16.3242i	0.895456	−	0.516992i	0.0197330	−	0.999805i	$-0.493718\pi$
$997$	28.2743	−	16.3242i	0.895456	−	0.516992i	0.875723	+	0.482813i	$0.160385\pi$
$998$	−5.63184	−	31.0425i	−0.178273	−	0.982633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.685.11		24
3.2	odd	2		104.2.r.a.61.2	yes	24
8.5	even	2	inner	936.2.be.a.685.5		24
12.11	even	2		416.2.z.a.113.2		24
13.3	even	3	inner	936.2.be.a.757.5		24
24.5	odd	2		104.2.r.a.61.8	yes	24
24.11	even	2		416.2.z.a.113.11		24
39.29	odd	6		104.2.r.a.29.8	yes	24
104.29	even	6	inner	936.2.be.a.757.11		24
156.107	even	6		416.2.z.a.81.11		24
312.29	odd	6		104.2.r.a.29.2	✓	24
312.107	even	6		416.2.z.a.81.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.2	✓	24	312.29	odd	6
104.2.r.a.29.8	yes	24	39.29	odd	6
104.2.r.a.61.2	yes	24	3.2	odd	2
104.2.r.a.61.8	yes	24	24.5	odd	2
416.2.z.a.81.2		24	312.107	even	6
416.2.z.a.81.11		24	156.107	even	6
416.2.z.a.113.2		24	12.11	even	2
416.2.z.a.113.11		24	24.11	even	2
936.2.be.a.685.5		24	8.5	even	2	inner
936.2.be.a.685.11		24	1.1	even	1	trivial
936.2.be.a.757.5		24	13.3	even	3	inner
936.2.be.a.757.11		24	104.29	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.39150 - 0.252450i) q^{2} +(1.87254 - 0.702569i) q^{4} +4.18204i q^{5} +(0.818571 + 1.41781i) q^{7} +(2.42827 - 1.45035i) q^{8} +(1.05576 + 5.81931i) q^{10} +(-0.112523 - 0.0649654i) q^{11} +(-2.30757 + 2.77040i) q^{13} +(1.49697 + 1.76623i) q^{14} +(3.01279 - 2.63117i) q^{16} +(-1.60044 - 2.77205i) q^{17} +(-3.31858 + 1.91598i) q^{19} +(2.93817 + 7.83103i) q^{20} +(-0.172977 - 0.0619926i) q^{22} +(1.09184 - 1.89113i) q^{23} -12.4895 q^{25} +(-2.51159 + 4.43756i) q^{26} +(2.52891 + 2.07979i) q^{28} +(4.98269 + 2.87676i) q^{29} +4.16704 q^{31} +(3.52806 - 4.42186i) q^{32} +(-2.92682 - 3.45327i) q^{34} +(-5.92932 + 3.42330i) q^{35} +(-0.156315 - 0.0902485i) q^{37} +(-4.13411 + 3.50386i) q^{38} +(6.06541 + 10.1551i) q^{40} +(-2.25610 + 3.90767i) q^{41} +(5.84408 - 3.37408i) q^{43} +(-0.256347 - 0.0425947i) q^{44} +(1.04188 - 2.90714i) q^{46} +4.71041 q^{47} +(2.15988 - 3.74103i) q^{49} +(-17.3791 + 3.15297i) q^{50} +(-2.37461 + 6.80891i) q^{52} -4.75546i q^{53} +(0.271688 - 0.470577i) q^{55} +(4.04402 + 2.25560i) q^{56} +(7.65965 + 2.74512i) q^{58} +(9.37008 - 5.40982i) q^{59} +(-1.24545 + 0.719063i) q^{61} +(5.79842 - 1.05197i) q^{62} +(3.79299 - 7.04367i) q^{64} +(-11.5859 - 9.65035i) q^{65} +(11.0310 + 6.36874i) q^{67} +(-4.94445 - 4.06634i) q^{68} +(-7.38643 + 6.26037i) q^{70} +(-2.53663 - 4.39358i) q^{71} +3.28487 q^{73} +(-0.240295 - 0.0861189i) q^{74} +(-4.86805 + 5.91928i) q^{76} -0.212715i q^{77} -9.44449 q^{79} +(11.0037 + 12.5996i) q^{80} +(-2.15286 + 6.00707i) q^{82} +5.48783i q^{83} +(11.5928 - 6.69312i) q^{85} +(7.28024 - 6.17037i) q^{86} +(-0.367459 + 0.00544441i) q^{88} +(0.386337 - 0.669155i) q^{89} +(-5.81680 - 1.00392i) q^{91} +(0.715870 - 4.30830i) q^{92} +(6.55453 - 1.18915i) q^{94} +(-8.01272 - 13.8784i) q^{95} +(-5.07163 - 8.78432i) q^{97} +(2.06105 - 5.75090i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

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