LMFDB - Embedded newform 936.2.be.a.685.3

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			685.3
Character	$\chi$	$=$	936.685
Dual form			936.2.be.a.757.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02392 + 0.975496i) q^{2} +(0.0968157 - 1.99766i) q^{4} -2.24007i q^{5} +(0.471952 + 0.817445i) q^{7} +(1.84957 + 2.13988i) q^{8} +(2.18518 + 2.29365i) q^{10} +(4.82849 + 2.78773i) q^{11} +(-0.108823 + 3.60391i) q^{13} +(-1.28065 - 0.376609i) q^{14} +(-3.98125 - 0.386809i) q^{16} +(-3.03119 - 5.25017i) q^{17} +(1.43961 - 0.831159i) q^{19} +(-4.47489 - 0.216874i) q^{20} +(-7.66340 + 1.85577i) q^{22} +(-1.07746 + 1.86621i) q^{23} -0.0179136 q^{25} +(-3.40417 - 3.79626i) q^{26} +(1.67867 - 0.863656i) q^{28} +(1.68452 + 0.972558i) q^{29} -1.91161 q^{31} +(4.45381 - 3.48764i) q^{32} +(8.22520 + 2.41883i) q^{34} +(1.83113 - 1.05721i) q^{35} +(4.54154 + 2.62206i) q^{37} +(-0.663250 + 2.25537i) q^{38} +(4.79348 - 4.14317i) q^{40} +(0.332039 - 0.575109i) q^{41} +(6.97919 - 4.02944i) q^{43} +(6.03640 - 9.37576i) q^{44} +(-0.717252 - 2.96190i) q^{46} +10.5778 q^{47} +(3.05452 - 5.29059i) q^{49} +(0.0183420 - 0.0174746i) q^{50} +(7.18883 + 0.566307i) q^{52} +10.3882i q^{53} +(6.24471 - 10.8162i) q^{55} +(-0.876323 + 2.52184i) q^{56} +(-2.67354 + 0.647422i) q^{58} +(-0.411368 + 0.237503i) q^{59} +(-3.06666 + 1.77054i) q^{61} +(1.95733 - 1.86477i) q^{62} +(-1.15816 + 7.91572i) q^{64} +(8.07301 + 0.243772i) q^{65} +(3.91067 + 2.25783i) q^{67} +(-10.7815 + 5.54696i) q^{68} +(-0.843631 + 2.86876i) q^{70} +(-5.81695 - 10.0753i) q^{71} -1.91680 q^{73} +(-7.20797 + 1.74548i) q^{74} +(-1.52099 - 2.95631i) q^{76} +5.26270i q^{77} +13.6120 q^{79} +(-0.866479 + 8.91829i) q^{80} +(0.221035 + 0.912767i) q^{82} -11.5623i q^{83} +(-11.7607 + 6.79007i) q^{85} +(-3.21542 + 10.9340i) q^{86} +(2.96524 + 15.4885i) q^{88} +(0.373638 - 0.647161i) q^{89} +(-2.99736 + 1.61192i) q^{91} +(3.62373 + 2.33306i) q^{92} +(-10.8308 + 10.3186i) q^{94} +(-1.86185 - 3.22483i) q^{95} +(0.640742 + 1.10980i) q^{97} +(2.03337 + 8.39680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.02392	+	0.975496i	−0.724019	+	0.689780i
$2$	−1.02392	+	0.975496i	−0.724019	+	0.689780i
$3$		0			0
$3$		0			0
$4$	0.0968157	−	1.99766i	0.0484079	−	0.998828i
$5$		−	2.24007i		−	1.00179i	−0.865508	−	0.500895i	$-0.833004\pi$
$5$		−	2.24007i		−	1.00179i	0.865508	−	0.500895i	$-0.166996\pi$
$6$		0			0
$7$	0.471952	+	0.817445i	0.178381	+	0.308965i	0.941326	−	0.337498i	$-0.109581\pi$
$7$	0.471952	+	0.817445i	0.178381	+	0.308965i	−0.762945	+	0.646463i	$0.776247\pi$
$8$	1.84957	+	2.13988i	0.653923	+	0.756561i
$9$		0			0
$10$	2.18518	+	2.29365i	0.691014	+	0.725315i
$11$	4.82849	+	2.78773i	1.45584	+	0.840532i	0.998803	−	0.0489128i	$-0.0155756\pi$
$11$	4.82849	+	2.78773i	1.45584	+	0.840532i	0.457042	+	0.889445i	$0.348909\pi$
$12$		0			0
$13$	−0.108823	+	3.60391i	−0.0301821	+	0.999544i
$13$	−0.108823	+	3.60391i	−0.0301821	+	0.999544i
$14$	−1.28065	−	0.376609i	−0.342269	−	0.100653i
$15$		0			0
$16$	−3.98125	−	0.386809i	−0.995313	−	0.0967022i
$17$	−3.03119	−	5.25017i	−0.735170	−	1.27335i	−0.954649	−	0.297735i	$-0.903769\pi$
$17$	−3.03119	−	5.25017i	−0.735170	−	1.27335i	0.219478	−	0.975617i	$-0.429565\pi$
$18$		0			0
$19$	1.43961	−	0.831159i	0.330269	−	0.190681i	−0.325692	−	0.945476i	$-0.605597\pi$
$19$	1.43961	−	0.831159i	0.330269	−	0.190681i	0.655961	+	0.754795i	$0.272264\pi$
$20$	−4.47489	−	0.216874i	−1.00062	−	0.0484945i
$21$		0			0
$22$	−7.66340	+	1.85577i	−1.63384	+	0.395651i
$23$	−1.07746	+	1.86621i	−0.224665	+	0.389131i	−0.956219	−	0.292652i	$-0.905462\pi$
$23$	−1.07746	+	1.86621i	−0.224665	+	0.389131i	0.731554	+	0.681784i	$0.238795\pi$
$24$		0			0
$25$	−0.0179136			−0.00358271
$26$	−3.40417	−	3.79626i	−0.667613	−	0.744508i
$27$		0			0
$28$	1.67867	−	0.863656i	0.317238	−	0.163216i
$29$	1.68452	+	0.972558i	0.312807	+	0.180599i	0.648182	−	0.761485i	$-0.275530\pi$
$29$	1.68452	+	0.972558i	0.312807	+	0.180599i	−0.335375	+	0.942085i	$0.608863\pi$
$30$		0			0
$31$	−1.91161			−0.343335			−0.171668	−	0.985155i	$-0.554916\pi$
$31$	−1.91161			−0.343335			−0.171668	+	0.985155i	$0.554916\pi$
$32$	4.45381	−	3.48764i	0.787329	−	0.616533i
$33$		0			0
$34$	8.22520	+	2.41883i	1.41061	+	0.414826i
$35$	1.83113	−	1.05721i	0.309518	−	0.178700i
$36$		0			0
$37$	4.54154	+	2.62206i	0.746624	+	0.431064i	0.824473	−	0.565902i	$-0.191472\pi$
$37$	4.54154	+	2.62206i	0.746624	+	0.431064i	−0.0778488	+	0.996965i	$0.524805\pi$
$38$	−0.663250	+	2.25537i	−0.107593	+	0.365870i
$39$		0			0
$40$	4.79348	−	4.14317i	0.757915	−	0.655093i
$41$	0.332039	−	0.575109i	0.0518558	−	0.0898169i	−0.838932	−	0.544236i	$-0.816820\pi$
$41$	0.332039	−	0.575109i	0.0518558	−	0.0898169i	0.890788	+	0.454419i	$0.150153\pi$
$42$		0			0
$43$	6.97919	−	4.02944i	1.06432	−	0.614483i	0.137693	−	0.990475i	$-0.456031\pi$
$43$	6.97919	−	4.02944i	1.06432	−	0.614483i	0.926623	+	0.375992i	$0.122698\pi$
$44$	6.03640	−	9.37576i	0.910021	−	1.41345i
$45$		0			0
$46$	−0.717252	−	2.96190i	−0.105753	−	0.436708i
$47$	10.5778			1.54293			0.771466	−	0.636270i	$-0.219524\pi$
$47$	10.5778			1.54293			0.771466	+	0.636270i	$0.219524\pi$
$48$		0			0
$49$	3.05452	−	5.29059i	0.436360	−	0.755798i
$50$	0.0183420	−	0.0174746i	0.00259395	−	0.00247128i
$51$		0			0
$52$	7.18883	+	0.566307i	0.996912	+	0.0785326i
$53$			10.3882i			1.42693i	0.700691	+	0.713465i	$0.252875\pi$
$53$			10.3882i			1.42693i	−0.700691	+	0.713465i	$0.747125\pi$
$54$		0			0
$55$	6.24471	−	10.8162i	0.842037	−	1.45845i
$56$	−0.876323	+	2.52184i	−0.117104	+	0.336996i
$57$		0			0
$58$	−2.67354	+	0.647422i	−0.351052	+	0.0850107i
$59$	−0.411368	+	0.237503i	−0.0535555	+	0.0309203i	−0.526539	−	0.850151i	$-0.676510\pi$
$59$	−0.411368	+	0.237503i	−0.0535555	+	0.0309203i	0.472983	+	0.881071i	$0.343177\pi$
$60$		0			0
$61$	−3.06666	+	1.77054i	−0.392646	+	0.226694i	−0.683306	−	0.730132i	$-0.739459\pi$
$61$	−3.06666	+	1.77054i	−0.392646	+	0.226694i	0.290660	+	0.956826i	$0.406125\pi$
$62$	1.95733	−	1.86477i	0.248581	−	0.236826i
$63$		0			0
$64$	−1.15816	+	7.91572i	−0.144770	+	0.989465i
$65$	8.07301	+	0.243772i	1.00133	+	0.0302362i
$66$		0			0
$67$	3.91067	+	2.25783i	0.477764	+	0.275837i	0.719484	−	0.694509i	$-0.244378\pi$
$67$	3.91067	+	2.25783i	0.477764	+	0.275837i	−0.241720	+	0.970346i	$0.577712\pi$
$68$	−10.7815	+	5.54696i	−1.30745	+	0.672668i
$69$		0			0
$70$	−0.843631	+	2.86876i	−0.100833	+	0.342882i
$71$	−5.81695	−	10.0753i	−0.690345	−	1.19571i	−0.971725	−	0.236117i	$-0.924125\pi$
$71$	−5.81695	−	10.0753i	−0.690345	−	1.19571i	0.281379	−	0.959597i	$-0.409208\pi$
$72$		0			0
$73$	−1.91680			−0.224345			−0.112172	−	0.993689i	$-0.535781\pi$
$73$	−1.91680			−0.224345			−0.112172	+	0.993689i	$0.535781\pi$
$74$	−7.20797	+	1.74548i	−0.837909	+	0.202908i
$75$		0			0
$76$	−1.52099	−	2.95631i	−0.174470	−	0.339112i
$77$			5.26270i			0.599741i
$78$		0			0
$79$	13.6120			1.53147			0.765737	−	0.643154i	$-0.222374\pi$
$79$	13.6120			1.53147			0.765737	+	0.643154i	$0.222374\pi$
$80$	−0.866479	+	8.91829i	−0.0968753	+	0.997095i
$81$		0			0
$82$	0.221035	+	0.912767i	0.0244093	+	0.100798i
$83$		−	11.5623i		−	1.26913i	−0.772871	−	0.634564i	$-0.781180\pi$
$83$		−	11.5623i		−	1.26913i	0.772871	−	0.634564i	$-0.218820\pi$
$84$		0			0
$85$	−11.7607	+	6.79007i	−1.27563	+	0.736486i
$86$	−3.21542	+	10.9340i	−0.346727	+	1.17904i
$87$		0			0
$88$	2.96524	+	15.4885i	0.316096	+	1.65108i
$89$	0.373638	−	0.647161i	0.0396056	−	0.0685989i	−0.845543	−	0.533907i	$-0.820723\pi$
$89$	0.373638	−	0.647161i	0.0396056	−	0.0685989i	0.885149	+	0.465308i	$0.154057\pi$
$90$		0			0
$91$	−2.99736	+	1.61192i	−0.314208	+	0.168975i
$92$	3.62373	+	2.33306i	0.377800	+	0.243239i
$93$		0			0
$94$	−10.8308	+	10.3186i	−1.11711	+	1.06428i
$95$	−1.86185	−	3.22483i	−0.191022	−	0.330860i
$96$		0			0
$97$	0.640742	+	1.10980i	0.0650575	+	0.112683i	0.896719	−	0.442599i	$-0.145944\pi$
$97$	0.640742	+	1.10980i	0.0650575	+	0.112683i	−0.831662	+	0.555282i	$0.812610\pi$
$98$	2.03337	+	8.39680i	0.205401	+	0.848205i
$99$		0			0
$100$	−0.00173431	+	0.0357851i	−0.000173431	+	0.00357851i
$101$	8.45583	+	4.88197i	0.841386	+	0.485775i	0.857735	−	0.514092i	$-0.171871\pi$
$101$	8.45583	+	4.88197i	0.841386	+	0.485775i	−0.0163490	+	0.999866i	$0.505204\pi$
$102$		0			0
$103$	−15.0755			−1.48544			−0.742719	−	0.669604i	$-0.766464\pi$
$103$	−15.0755			−1.48544			−0.742719	+	0.669604i	$0.766464\pi$
$104$	−7.91320	+	6.43282i	−0.775953	+	0.630790i
$105$		0			0
$106$	−10.1337	−	10.6367i	−0.984267	−	1.03312i
$107$	13.6044	+	7.85448i	1.31518	+	0.759321i	0.982949	−	0.183876i	$-0.0588646\pi$
$107$	13.6044	+	7.85448i	1.31518	+	0.759321i	0.332233	+	0.943197i	$0.392198\pi$
$108$		0			0
$109$		−	9.69920i		−	0.929015i	−0.885569	−	0.464508i	$-0.846231\pi$
$109$		−	9.69920i		−	0.929015i	0.885569	−	0.464508i	$-0.153769\pi$
$110$	4.15704	+	17.1665i	0.396359	+	1.63677i
$111$		0			0
$112$	−1.56277	−	3.43701i	−0.147668	−	0.324767i
$113$	−3.78116	−	6.54916i	−0.355701	−	0.616093i	0.631536	−	0.775346i	$-0.282425\pi$
$113$	−3.78116	−	6.54916i	−0.355701	−	0.616093i	−0.987238	+	0.159253i	$0.949091\pi$
$114$		0			0
$115$	4.18044	+	2.41358i	0.389828	+	0.225067i
$116$	2.10592	−	3.27093i	0.195530	−	0.303698i
$117$		0			0
$118$	0.189523	−	0.644472i	0.0174470	−	0.0593284i
$119$	2.86115	−	4.95566i	0.262281	−	0.454284i
$120$		0			0
$121$	10.0429	+	17.3948i	0.912989	+	1.58134i
$122$	1.41286	−	4.80441i	0.127914	−	0.434970i
$123$		0			0
$124$	−0.185074	+	3.81874i	−0.0166201	+	0.342933i
$125$		−	11.1602i		−	0.998201i
$126$		0			0
$127$	−1.53962	+	2.66670i	−0.136619	+	0.236632i	−0.926215	−	0.376996i	$-0.876957\pi$
$127$	−1.53962	+	2.66670i	−0.136619	+	0.236632i	0.789596	+	0.613628i	$0.210290\pi$
$128$	−6.53589	−	9.23483i	−0.577697	−	0.816251i
$129$		0			0
$130$	−8.50390	+	7.62558i	−0.745841	+	0.668808i
$131$		−	11.9145i		−	1.04098i	−0.853869	−	0.520488i	$-0.825750\pi$
$131$		−	11.9145i		−	1.04098i	0.853869	−	0.520488i	$-0.174250\pi$
$132$		0			0
$133$	1.35885	+	0.784534i	0.117828	+	0.0680278i
$134$	−6.20671	+	1.50301i	−0.536178	+	0.129841i
$135$		0			0
$136$	5.62832	−	16.1969i	0.482624	−	1.38888i
$137$	10.2342	+	17.7261i	0.874365	+	1.51444i	0.857437	+	0.514588i	$0.172055\pi$
$137$	10.2342	+	17.7261i	0.874365	+	1.51444i	0.0169276	+	0.999857i	$0.494612\pi$
$138$		0			0
$139$	7.01589	−	4.05062i	0.595080	−	0.343570i	−0.172024	−	0.985093i	$-0.555031\pi$
$139$	7.01589	−	4.05062i	0.595080	−	0.343570i	0.767104	+	0.641523i	$0.221697\pi$
$140$	−1.93465	−	3.76033i	−0.163508	−	0.317806i
$141$		0			0
$142$	15.7845	+	4.64182i	1.32460	+	0.389533i
$143$	−10.5722	+	17.0981i	−0.884090	+	1.42981i
$144$		0			0
$145$	2.17860	−	3.77344i	0.180923	−	0.313367i
$146$	1.96265	−	1.86983i	0.162430	−	0.154748i
$147$		0			0
$148$	5.67766	−	8.81857i	0.466701	−	0.724882i
$149$	3.13501	−	1.81000i	0.256830	−	0.148281i	−0.366058	−	0.930592i	$-0.619293\pi$
$149$	3.13501	−	1.81000i	0.256830	−	0.148281i	0.622888	+	0.782311i	$0.285959\pi$
$150$		0			0
$151$	−16.0939			−1.30970			−0.654850	−	0.755759i	$-0.727268\pi$
$151$	−16.0939			−1.30970			−0.654850	+	0.755759i	$0.727268\pi$
$152$	4.44124	+	1.54330i	0.360232	+	0.125178i
$153$		0			0
$154$	−5.13374	−	5.38857i	−0.413689	−	0.434224i
$155$			4.28214i			0.343950i
$156$		0			0
$157$			15.4274i			1.23124i	0.788042	+	0.615621i	$0.211095\pi$
$157$			15.4274i			1.23124i	−0.788042	+	0.615621i	$0.788905\pi$
$158$	−13.9376	+	13.2785i	−1.10882	+	1.05638i
$159$		0			0
$160$	−7.81255	−	9.97684i	−0.617636	−	0.788738i
$161$	−2.03403			−0.160304
$162$		0			0
$163$	4.33867	−	2.50493i	0.339831	−	0.196201i	−0.320366	−	0.947294i	$-0.603806\pi$
$163$	4.33867	−	2.50493i	0.339831	−	0.196201i	0.660197	+	0.751092i	$0.270473\pi$
$164$	−1.11672	−	0.718980i	−0.0872014	−	0.0561429i
$165$		0			0
$166$	11.2790	+	11.8388i	0.875418	+	0.918873i
$167$	0.532199	−	0.921796i	0.0411828	−	0.0713308i	−0.844699	−	0.535241i	$-0.820221\pi$
$167$	0.532199	−	0.921796i	0.0411828	−	0.0713308i	0.885882	+	0.463910i	$0.153554\pi$
$168$		0			0
$169$	−12.9763	−	0.784378i	−0.998178	−	0.0603368i
$170$	5.41835	−	18.4250i	0.415569	−	1.41314i
$171$		0			0
$172$	−7.37373	−	14.3321i	−0.562241	−	1.09281i
$173$	−18.9047	+	10.9146i	−1.43730	+	0.829825i	−0.997661	−	0.0683503i	$-0.978226\pi$
$173$	−18.9047	+	10.9146i	−1.43730	+	0.829825i	−0.439638	+	0.898175i	$0.644893\pi$
$174$		0			0
$175$	−0.00845434	−	0.0146433i	−0.000639088	−	0.00110693i
$176$	−18.1451	−	12.9664i	−1.36774	−	0.977377i
$177$		0			0
$178$	0.248728	+	1.02712i	0.0186429	+	0.0769861i
$179$	2.82862	+	1.63310i	0.211421	+	0.122064i	0.601972	−	0.798517i	$-0.294382\pi$
$179$	2.82862	+	1.63310i	0.211421	+	0.122064i	−0.390551	+	0.920581i	$0.627715\pi$
$180$		0			0
$181$			13.1229i			0.975420i	0.873006	+	0.487710i	$0.162168\pi$
$181$			13.1229i			0.975420i	−0.873006	+	0.487710i	$0.837832\pi$
$182$	1.49663	−	4.57438i	0.110938	−	0.339075i
$183$		0			0
$184$	−5.98629	+	1.14606i	−0.441315	+	0.0844890i
$185$	5.87359	−	10.1734i	0.431835	−	0.747960i
$186$		0			0
$187$		−	33.8005i		−	2.47174i
$188$	1.02410	−	21.1308i	0.0746901	−	1.54112i
$189$		0			0
$190$	5.05219	+	1.48573i	0.366524	+	0.107786i
$191$	−4.02136	−	6.96520i	−0.290975	−	0.503984i	0.683065	−	0.730357i	$-0.260646\pi$
$191$	−4.02136	−	6.96520i	−0.290975	−	0.503984i	−0.974041	+	0.226373i	$0.927313\pi$
$192$		0			0
$193$	0.417932	−	0.723880i	0.0300834	−	0.0521060i	−0.850592	−	0.525827i	$-0.823756\pi$
$193$	0.417932	−	0.723880i	0.0300834	−	0.0521060i	0.880675	+	0.473721i	$0.157089\pi$
$194$	−1.73867	−	0.511300i	−0.124829	−	0.0367092i
$195$		0			0
$196$	−10.2730	−	6.61409i	−0.733789	−	0.472435i
$197$	−6.06608	−	3.50225i	−0.432190	−	0.249525i	0.268089	−	0.963394i	$-0.413608\pi$
$197$	−6.06608	−	3.50225i	−0.432190	−	0.249525i	−0.700279	+	0.713869i	$0.746941\pi$
$198$		0			0
$199$	−7.51756	−	13.0208i	−0.532906	−	0.923019i	−0.999262	−	0.0384223i	$-0.987767\pi$
$199$	−7.51756	−	13.0208i	−0.532906	−	0.923019i	0.466356	−	0.884597i	$-0.345567\pi$
$200$	−0.0331324	−	0.0383328i	−0.00234282	−	0.00271054i
$201$		0			0
$202$	−13.4204	+	3.24988i	−0.944257	+	0.228661i
$203$			1.83600i			0.128862i
$204$		0			0
$205$	−1.28828	−	0.743791i	−0.0899777	−	0.0519486i
$206$	15.4361	−	14.7061i	1.07549	−	1.02462i
$207$		0			0
$208$	1.82728	−	14.3060i	0.126699	−	0.991941i
$209$	9.26819			0.641094
$210$		0			0
$211$	5.82236	+	3.36154i	0.400828	+	0.231418i	0.686841	−	0.726808i	$-0.258997\pi$
$211$	5.82236	+	3.36154i	0.400828	+	0.231418i	−0.286013	+	0.958226i	$0.592330\pi$
$212$	20.7521	+	1.00574i	1.42526	+	0.0690746i
$213$		0			0
$214$	−21.5918	+	5.22865i	−1.47598	+	0.357423i
$215$	−9.02622	−	15.6339i	−0.615583	−	1.06622i
$216$		0			0
$217$	−0.902189	−	1.56264i	−0.0612446	−	0.106079i
$218$	9.46153	+	9.93119i	0.640816	+	0.672625i
$219$		0			0
$220$	−21.0024	−	13.5220i	−1.41598	−	0.911650i
$221$	19.2510	−	10.3528i	1.29496	−	0.696403i
$222$		0			0
$223$	−10.4340	+	18.0723i	−0.698715	+	1.21021i	0.270198	+	0.962805i	$0.412911\pi$
$223$	−10.4340	+	18.0723i	−0.698715	+	1.21021i	−0.968912	+	0.247404i	$0.920422\pi$
$224$	4.95293	+	1.99475i	0.330932	+	0.133280i
$225$		0			0
$226$	10.2603	+	3.01730i	0.682503	+	0.200707i
$227$	−16.7688	+	9.68145i	−1.11298	+	0.642580i	−0.939600	−	0.342274i	$-0.888803\pi$
$227$	−16.7688	+	9.68145i	−1.11298	+	0.642580i	−0.173382	+	0.984855i	$0.555469\pi$
$228$		0			0
$229$		−	17.6044i		−	1.16333i	−0.813428	−	0.581666i	$-0.802401\pi$
$229$		−	17.6044i		−	1.16333i	0.813428	−	0.581666i	$-0.197599\pi$
$230$	−6.63486	+	1.60669i	−0.437490	+	0.105942i
$231$		0			0
$232$	1.03449	+	5.40348i	0.0679174	+	0.354756i
$233$	−15.3281			−1.00417			−0.502087	−	0.864817i	$-0.667434\pi$
$233$	−15.3281			−1.00417			−0.502087	+	0.864817i	$0.667434\pi$
$234$		0			0
$235$		−	23.6950i		−	1.54569i
$236$	0.434623	+	0.844765i	0.0282915	+	0.0549895i
$237$		0			0
$238$	1.90464	+	7.86522i	0.123459	+	0.509827i
$239$	14.0854			0.911111			0.455556	−	0.890207i	$-0.349441\pi$
$239$	14.0854			0.911111			0.455556	+	0.890207i	$0.349441\pi$
$240$		0			0
$241$	−7.24993	−	12.5572i	−0.467009	−	0.808883i	0.532281	−	0.846568i	$-0.321335\pi$
$241$	−7.24993	−	12.5572i	−0.467009	−	0.808883i	−0.999290	+	0.0376849i	$0.988002\pi$
$242$	−27.2516	−	8.01404i	−1.75180	−	0.515162i
$243$		0			0
$244$	3.24003	+	6.29756i	0.207421	+	0.403160i
$245$	−11.8513	−	6.84234i	−0.757151	−	0.437141i
$246$		0			0
$247$	2.83876	+	5.27867i	0.180626	+	0.335874i
$248$	−3.53566	−	4.09061i	−0.224515	−	0.259754i
$249$		0			0
$250$	10.8868	+	11.4272i	0.688539	+	0.722717i
$251$	24.8381	−	14.3403i	1.56777	−	0.905151i	0.571340	−	0.820714i	$-0.306424\pi$
$251$	24.8381	−	14.3403i	1.56777	−	0.905151i	0.996429	−	0.0844378i	$-0.0269094\pi$
$252$		0			0
$253$	−10.4050	+	6.00731i	−0.654155	+	0.377677i
$254$	−1.02491	−	4.23238i	−0.0643087	−	0.265563i
$255$		0			0
$256$	15.7008	+	3.07997i	0.981297	+	0.192498i
$257$	−5.81269	+	10.0679i	−0.362586	+	0.628017i	−0.988386	−	0.151967i	$-0.951439\pi$
$257$	−5.81269	+	10.0679i	−0.362586	+	0.628017i	0.625800	+	0.779984i	$0.284773\pi$
$258$		0			0
$259$			4.94994i			0.307574i
$260$	1.26857	−	16.1035i	0.0786731	−	0.998696i
$261$		0			0
$262$	11.6226	+	12.1995i	0.718044	+	0.753687i
$263$	−8.47469	+	14.6786i	−0.522572	+	0.905121i	0.477083	+	0.878858i	$0.341694\pi$
$263$	−8.47469	+	14.6786i	−0.522572	+	0.905121i	−0.999655	+	0.0262631i	$0.991639\pi$
$264$		0			0
$265$	23.2703			1.42948
$266$	−2.15666	+	0.522257i	−0.132234	+	0.0320216i
$267$		0			0
$268$	4.88897	−	7.59358i	0.298642	−	0.463852i
$269$	−6.45180	+	3.72495i	−0.393373	+	0.227114i	−0.683621	−	0.729837i	$-0.739596\pi$
$269$	−6.45180	+	3.72495i	−0.393373	+	0.227114i	0.290247	+	0.956952i	$0.406262\pi$
$270$		0			0
$271$	7.61248	−	13.1852i	0.462425	−	0.800944i	−0.536656	−	0.843801i	$-0.680313\pi$
$271$	7.61248	−	13.1852i	0.462425	−	0.800944i	0.999081	+	0.0428569i	$0.0136459\pi$
$272$	10.0371	+	22.0747i	0.608589	+	1.33848i
$273$		0			0
$274$	−27.7707	−	8.16669i	−1.67769	−	0.493368i
$275$	−0.0864954	−	0.0499382i	−0.00521587	−	0.00301138i
$276$		0			0
$277$	−13.9928	+	8.07878i	−0.840749	+	0.485407i	−0.857519	−	0.514453i	$-0.827995\pi$
$277$	−13.9928	+	8.07878i	−0.840749	+	0.485407i	0.0167699	+	0.999859i	$0.494662\pi$
$278$	−3.23233	+	10.9915i	−0.193862	+	0.659225i
$279$		0			0
$280$	5.64911	+	1.96303i	0.337599	+	0.117313i
$281$	−27.7204			−1.65366			−0.826831	−	0.562450i	$-0.809859\pi$
$281$	−27.7204			−1.65366			−0.826831	+	0.562450i	$0.809859\pi$
$282$		0			0
$283$	3.28760	+	1.89810i	0.195428	+	0.112830i	0.594521	−	0.804080i	$-0.297342\pi$
$283$	3.28760	+	1.89810i	0.195428	+	0.112830i	−0.399093	+	0.916910i	$0.630675\pi$
$284$	−20.6901	+	10.6448i	−1.22773	+	0.631654i
$285$		0			0
$286$	−5.85405	−	27.8201i	−0.346157	−	1.64504i
$287$	0.626827			0.0370004
$288$		0			0
$289$	−9.87617	+	17.1060i	−0.580951	+	1.00624i
$290$	1.45027	+	5.98891i	0.0851629	+	0.351681i
$291$		0			0
$292$	−0.185577	+	3.82911i	−0.0108600	+	0.224082i
$293$	−4.14791	+	2.39480i	−0.242324	+	0.139906i	−0.616244	−	0.787555i	$-0.711347\pi$
$293$	−4.14791	+	2.39480i	−0.242324	+	0.139906i	0.373921	+	0.927461i	$0.378013\pi$
$294$		0			0
$295$	0.532024	+	0.921493i	0.0309756	+	0.0536514i
$296$	2.78902	+	14.5680i	0.162108	+	0.846749i
$297$		0			0
$298$	−1.44435	+	4.91148i	−0.0836687	+	0.284514i
$299$	−6.60839	−	4.08614i	−0.382173	−	0.236308i
$300$		0			0
$301$	6.58768	+	3.80340i	0.379708	+	0.219224i
$302$	16.4788	−	15.6995i	0.948249	−	0.903405i
$303$		0			0
$304$	−6.05295	+	2.75220i	−0.347160	+	0.157849i
$305$	3.96613	+	6.86954i	0.227100	+	0.393349i
$306$		0			0
$307$			8.95981i			0.511363i	0.966761	+	0.255682i	$0.0822999\pi$
$307$			8.95981i			0.511363i	−0.966761	+	0.255682i	$0.917700\pi$
$308$	10.5131	+	0.509512i	0.599037	+	0.0290322i
$309$		0			0
$310$	−4.17721	−	4.38456i	−0.237250	−	0.249026i
$311$	−9.35196			−0.530301			−0.265150	−	0.964207i	$-0.585422\pi$
$311$	−9.35196			−0.530301			−0.265150	+	0.964207i	$0.585422\pi$
$312$		0			0
$313$	−11.7834			−0.666039			−0.333019	−	0.942920i	$-0.608067\pi$
$313$	−11.7834			−0.666039			−0.333019	+	0.942920i	$0.608067\pi$
$314$	−15.0494	−	15.7964i	−0.849286	−	0.891443i
$315$		0			0
$316$	1.31786	−	27.1922i	0.0741354	−	1.52968i
$317$		−	0.828044i		−	0.0465076i	−0.999730	−	0.0232538i	$-0.992597\pi$
$317$		−	0.828044i		−	0.0465076i	0.999730	−	0.0232538i	$-0.00740258\pi$
$318$		0			0
$319$	5.42246	+	9.39197i	0.303599	+	0.525850i
$320$	17.7318	+	2.59436i	0.991236	+	0.145029i
$321$		0			0
$322$	2.08268	−	1.98419i	0.116063	−	0.110574i
$323$	−8.72745	−	5.03879i	−0.485608	−	0.280366i
$324$		0			0
$325$	0.00194941	−	0.0645588i	0.000108134	−	0.00358108i
$326$	−1.99889	+	6.79720i	−0.110708	+	0.376462i
$327$		0			0
$328$	1.84479	−	0.353182i	0.101862	−	0.0195012i
$329$	4.99222	+	8.64678i	0.275230	+	0.476712i
$330$		0			0
$331$	−12.8419	+	7.41425i	−0.705853	+	0.407524i	−0.809524	−	0.587087i	$-0.800274\pi$
$331$	−12.8419	+	7.41425i	−0.705853	+	0.407524i	0.103671	+	0.994612i	$0.466941\pi$
$332$	−23.0975	−	1.11941i	−1.26764	−	0.0614357i
$333$		0			0
$334$	0.354280	+	1.46300i	0.0193853	+	0.0800519i
$335$	5.05769	−	8.76018i	0.276331	−	0.478620i
$336$		0			0
$337$	5.53901			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$337$	5.53901			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$338$	14.0518	−	11.8552i	0.764319	−	0.644838i
$339$		0			0
$340$	12.4256	+	24.1513i	0.673872	+	1.30979i
$341$	−9.23019	−	5.32906i	−0.499843	−	0.288585i
$342$		0			0
$343$	12.3737			0.668116
$344$	21.5310	+	7.48188i	1.16087	+	0.403396i
$345$		0			0
$346$	8.70969	−	29.6172i	0.468236	−	1.59223i
$347$	−13.9803	+	8.07154i	−0.750503	+	0.433303i	−0.825876	−	0.563852i	$-0.809319\pi$
$347$	−13.9803	+	8.07154i	−0.750503	+	0.433303i	0.0753728	+	0.997155i	$0.475985\pi$
$348$		0			0
$349$	−20.7087	−	11.9562i	−1.10851	−	0.640000i	−0.170068	−	0.985432i	$-0.554399\pi$
$349$	−20.7087	−	11.9562i	−1.10851	−	0.640000i	−0.938444	+	0.345432i	$0.887732\pi$
$350$	0.0229411	+	0.00674641i	0.00122625	+	0.000360611i
$351$		0			0
$352$	31.2278	−	4.42400i	1.66445	−	0.235800i
$353$	2.77899	−	4.81335i	0.147911	−	0.256189i	−0.782544	−	0.622595i	$-0.786079\pi$
$353$	2.77899	−	4.81335i	0.147911	−	0.256189i	0.930455	+	0.366406i	$0.119412\pi$
$354$		0			0
$355$	−22.5693	+	13.0304i	−1.19785	+	0.691581i
$356$	−1.25663	−	0.809056i	−0.0666013	−	0.0428799i
$357$		0			0
$358$	−4.48936	+	1.08714i	−0.237270	+	0.0574572i
$359$	8.55135			0.451323			0.225661	−	0.974206i	$-0.427546\pi$
$359$	8.55135			0.451323			0.225661	+	0.974206i	$0.427546\pi$
$360$		0			0
$361$	−8.11835	+	14.0614i	−0.427282	+	0.740073i
$362$	−12.8014	−	13.4368i	−0.672825	−	0.706223i
$363$		0			0
$364$	2.92986	+	6.14374i	0.153566	+	0.322020i
$365$			4.29377i			0.224746i
$366$		0			0
$367$	1.96700	−	3.40695i	0.102677	−	0.177841i	−0.810110	−	0.586278i	$-0.800593\pi$
$367$	1.96700	−	3.40695i	0.102677	−	0.177841i	0.912787	+	0.408437i	$0.133926\pi$
$368$	5.01149	−	7.01308i	0.261242	−	0.365582i
$369$		0			0
$370$	3.90999	+	16.1463i	0.203271	+	0.839409i
$371$	−8.49179	+	4.90274i	−0.440872	+	0.254537i
$372$		0			0
$373$	−6.86329	+	3.96253i	−0.355368	+	0.205172i	−0.667047	−	0.745016i	$-0.732442\pi$
$373$	−6.86329	+	3.96253i	−0.355368	+	0.205172i	0.311679	+	0.950187i	$0.399109\pi$
$374$	32.9723	+	34.6090i	1.70495	+	1.78959i
$375$		0			0
$376$	19.5644	+	22.6352i	1.00896	+	1.16732i
$377$	−3.68832	+	5.96502i	−0.189958	+	0.307214i
$378$		0			0
$379$	22.8779	+	13.2086i	1.17516	+	0.678479i	0.954890	−	0.296959i	$-0.0959726\pi$
$379$	22.8779	+	13.2086i	1.17516	+	0.678479i	0.220271	+	0.975439i	$0.429306\pi$
$380$	−6.62235	+	3.40713i	−0.339719	+	0.174782i
$381$		0			0
$382$	10.9121	+	3.20897i	0.558310	+	0.164185i
$383$	0.947088	+	1.64041i	0.0483940	+	0.0838208i	0.889208	−	0.457504i	$-0.151256\pi$
$383$	0.947088	+	1.64041i	0.0483940	+	0.0838208i	−0.840814	+	0.541325i	$0.817923\pi$
$384$		0			0
$385$	11.7888			0.600814
$386$	0.278214	+	1.14888i	0.0141607	+	0.0584767i
$387$		0			0
$388$	2.27903	−	1.17254i	0.115700	−	0.0595265i
$389$			25.0808i			1.27165i	0.771835	+	0.635823i	$0.219339\pi$
$389$			25.0808i			1.27165i	−0.771835	+	0.635823i	$0.780661\pi$
$390$		0			0
$391$	13.0639			0.660669
$392$	16.9708	−	3.24902i	0.857154	−	0.164100i
$393$		0			0
$394$	9.62760	−	2.33141i	0.485031	−	0.117455i
$395$		−	30.4919i		−	1.53422i
$396$		0			0
$397$	7.99993	−	4.61876i	0.401505	−	0.231809i	−0.285628	−	0.958341i	$-0.592202\pi$
$397$	7.99993	−	4.61876i	0.401505	−	0.231809i	0.687133	+	0.726532i	$0.258869\pi$
$398$	20.3991	+	5.99888i	1.02251	+	0.300696i
$399$		0			0
$400$	0.0713184	+	0.00692912i	0.00356592	+	0.000346456i
$401$	2.21136	−	3.83018i	0.110430	−	0.191270i	−0.805514	−	0.592577i	$-0.798111\pi$
$401$	2.21136	−	3.83018i	0.110430	−	0.191270i	0.915944	+	0.401307i	$0.131444\pi$
$402$		0			0
$403$	0.208028	−	6.88927i	0.0103626	−	0.343179i
$404$	10.5712	−	16.4192i	0.525935	−	0.816884i
$405$		0			0
$406$	−1.79101	−	1.87992i	−0.0888865	−	0.0932987i
$407$	14.6192	+	25.3212i	0.724646	+	1.25512i
$408$		0			0
$409$	−13.2341	−	22.9221i	−0.654384	−	1.13343i	−0.982048	−	0.188631i	$-0.939595\pi$
$409$	−13.2341	−	22.9221i	−0.654384	−	1.13343i	0.327664	−	0.944794i	$-0.393738\pi$
$410$	2.04466	−	0.495135i	0.100979	−	0.0244530i
$411$		0			0
$412$	−1.45955	+	30.1157i	−0.0719068	+	1.48370i
$413$	−0.388292	−	0.224180i	−0.0191066	−	0.0110312i
$414$		0			0
$415$	−25.9004			−1.27140
$416$	12.0844	+	16.4307i	0.592489	+	0.805579i
$417$		0			0
$418$	−9.48986	+	9.04108i	−0.464164	+	0.442214i
$419$	−4.30501	−	2.48550i	−0.210314	−	0.121425i	0.391144	−	0.920330i	$-0.372080\pi$
$419$	−4.30501	−	2.48550i	−0.210314	−	0.121425i	−0.601457	+	0.798905i	$0.705413\pi$
$420$		0			0
$421$		−	24.0575i		−	1.17249i	−0.810134	−	0.586244i	$-0.800606\pi$
$421$		−	24.0575i		−	1.17249i	0.810134	−	0.586244i	$-0.199394\pi$
$422$	−9.24078	+	2.23774i	−0.449834	+	0.108932i
$423$		0			0
$424$	−22.2295	+	19.2137i	−1.07956	+	0.933102i
$425$	0.0542993	+	0.0940492i	0.00263390	+	0.00456205i
$426$		0			0
$427$	−2.89464	−	1.67122i	−0.140081	−	0.0808760i
$428$	17.0077	−	26.4164i	0.822096	−	1.27688i
$429$		0			0
$430$	24.4929	+	7.20276i	1.18115	+	0.347348i
$431$	5.28961	−	9.16188i	0.254792	−	0.441312i	−0.710047	−	0.704154i	$-0.751326\pi$
$431$	5.28961	−	9.16188i	0.254792	−	0.441312i	0.964839	+	0.262842i	$0.0846598\pi$
$432$		0			0
$433$	6.11293	+	10.5879i	0.293769	+	0.508822i	0.974698	−	0.223527i	$-0.0717572\pi$
$433$	6.11293	+	10.5879i	0.293769	+	0.508822i	−0.680929	+	0.732349i	$0.738424\pi$
$434$	2.44811	+	0.719930i	0.117513	+	0.0345578i
$435$		0			0
$436$	−19.3757	−	0.939036i	−0.927926	−	0.0449717i
$437$			3.58215i			0.171357i
$438$		0			0
$439$	−6.46417	+	11.1963i	−0.308518	+	0.534369i	−0.978038	−	0.208425i	$-0.933166\pi$
$439$	−6.46417	+	11.1963i	−0.308518	+	0.534369i	0.669520	+	0.742794i	$0.266500\pi$
$440$	34.6953	−	6.64235i	1.65403	−	0.316662i
$441$		0			0
$442$	−9.61234	+	29.3796i	−0.457212	+	1.39745i
$443$		−	14.0440i		−	0.667248i	−0.942706	−	0.333624i	$-0.891728\pi$
$443$		−	14.0440i		−	0.667248i	0.942706	−	0.333624i	$-0.108272\pi$
$444$		0			0
$445$	−1.44969	−	0.836976i	−0.0687217	−	0.0396765i
$446$	−6.94584	−	28.6829i	−0.328895	−	1.35817i
$447$		0			0
$448$	−7.01726	+	2.78911i	−0.331535	+	0.131773i
$449$	0.857113	+	1.48456i	0.0404497	+	0.0700609i	0.885541	−	0.464560i	$-0.153788\pi$
$449$	0.857113	+	1.48456i	0.0404497	+	0.0700609i	−0.845092	+	0.534621i	$0.820454\pi$
$450$		0			0
$451$	3.20650	−	1.85127i	0.150988	−	0.0871730i
$452$	−13.4490	+	6.91939i	−0.632589	+	0.325461i
$453$		0			0
$454$	7.72562	−	26.2709i	0.362581	−	1.23295i
$455$	3.61080	+	6.71429i	0.169277	+	0.314771i
$456$		0			0
$457$	14.5822	−	25.2571i	0.682126	−	1.18148i	−0.292205	−	0.956356i	$-0.594389\pi$
$457$	14.5822	−	25.2571i	0.682126	−	1.18148i	0.974331	−	0.225121i	$-0.0722778\pi$
$458$	17.1730	+	18.0255i	0.802443	+	0.842275i
$459$		0			0
$460$	5.22623	−	8.11740i	0.243674	−	0.378476i
$461$	−22.4501	+	12.9616i	−1.04561	+	0.603681i	−0.921416	−	0.388577i	$-0.872967\pi$
$461$	−22.4501	+	12.9616i	−1.04561	+	0.603681i	−0.124190	+	0.992258i	$0.539633\pi$
$462$		0			0
$463$	36.7003			1.70561			0.852803	−	0.522233i	$-0.174901\pi$
$463$	36.7003			1.70561			0.852803	+	0.522233i	$0.174901\pi$
$464$	−6.33030	−	4.52359i	−0.293877	−	0.210002i
$465$		0			0
$466$	15.6947	−	14.9525i	0.727042	−	0.692659i
$467$			27.9836i			1.29492i	0.762097	+	0.647462i	$0.224170\pi$
$467$			27.9836i			1.29492i	−0.762097	+	0.647462i	$0.775830\pi$
$468$		0			0
$469$			4.26234i			0.196817i
$470$	23.1144	+	24.2618i	1.06619	+	1.11911i
$471$		0			0
$472$	−1.26908	−	0.440997i	−0.0584143	−	0.0202986i
$473$	44.9319			2.06597
$474$		0			0
$475$	−0.0257885	+	0.0148890i	−0.00118326	+	0.000683155i
$476$	−9.62269	−	6.19537i	−0.441055	−	0.283965i
$477$		0			0
$478$	−14.4223	+	13.7403i	−0.659662	+	0.628466i
$479$	−16.2482	+	28.1426i	−0.742397	+	1.28587i	0.209004	+	0.977915i	$0.432978\pi$
$479$	−16.2482	+	28.1426i	−0.742397	+	1.28587i	−0.951401	+	0.307955i	$0.900355\pi$
$480$		0			0
$481$	−9.94388	+	16.0819i	−0.453402	+	0.733273i
$482$	19.6729	+	5.78531i	0.896074	+	0.263514i
$483$		0			0
$484$	35.7211	−	18.3781i	1.62369	−	0.835370i
$485$	2.48602	−	1.43531i	0.112885	−	0.0651739i
$486$		0			0
$487$	−5.79695	−	10.0406i	−0.262685	−	0.454983i	0.704270	−	0.709933i	$-0.251275\pi$
$487$	−5.79695	−	10.0406i	−0.262685	−	0.454983i	−0.966954	+	0.254949i	$0.917941\pi$
$488$	−9.46076	−	3.28755i	−0.428268	−	0.148820i
$489$		0			0
$490$	18.8094	−	4.55488i	0.849723	−	0.205769i
$491$	−36.2077	−	20.9045i	−1.63403	−	0.943407i	−0.982833	−	0.184498i	$-0.940934\pi$
$491$	−36.2077	−	20.9045i	−1.63403	−	0.943407i	−0.651197	−	0.758909i	$-0.725733\pi$
$492$		0			0
$493$		−	11.7920i		−	0.531085i
$494$	−8.05597	−	2.63573i	−0.362455	−	0.118587i
$495$		0			0
$496$	7.61061	+	0.739428i	0.341726	+	0.0332013i
$497$	5.49065	−	9.51008i	0.246289	−	0.426585i
$498$		0			0
$499$			17.9011i			0.801363i	0.916217	+	0.400682i	$0.131227\pi$
$499$			17.9011i			0.801363i	−0.916217	+	0.400682i	$0.868773\pi$
$500$	−22.2943	−	1.08049i	−0.997030	−	0.0483208i
$501$		0			0
$502$	−11.4433	+	38.9128i	−0.510739	+	1.73676i
$503$	7.29456	+	12.6345i	0.325248	+	0.563346i	0.981563	−	0.191141i	$-0.0612188\pi$
$503$	7.29456	+	12.6345i	0.325248	+	0.563346i	−0.656314	+	0.754488i	$0.727886\pi$
$504$		0			0
$505$	10.9360	−	18.9416i	0.486644	−	0.842892i
$506$	4.79373	−	16.3010i	0.213107	−	0.724668i
$507$		0			0
$508$	5.17810	+	3.33381i	0.229741	+	0.147914i
$509$	1.08621	+	0.627122i	0.0481453	+	0.0277967i	0.523879	−	0.851792i	$-0.324484\pi$
$509$	1.08621	+	0.627122i	0.0481453	+	0.0277967i	−0.475734	+	0.879589i	$0.657818\pi$
$510$		0			0
$511$	−0.904639	−	1.56688i	−0.0400189	−	0.0693147i
$512$	−19.0808	+	12.1624i	−0.843259	+	0.537507i
$513$		0			0
$514$	−3.86945	−	15.9789i	−0.170674	−	0.704801i
$515$			33.7703i			1.48810i
$516$		0			0
$517$	51.0749	+	29.4881i	2.24627	+	1.29688i
$518$	−4.82865	−	5.06833i	−0.212159	−	0.222690i
$519$		0			0
$520$	14.4100	+	17.7261i	0.631919	+	0.777342i
$521$	−8.42526			−0.369117			−0.184559	−	0.982822i	$-0.559086\pi$
$521$	−8.42526			−0.369117			−0.184559	+	0.982822i	$0.559086\pi$
$522$		0			0
$523$	−20.6677	−	11.9325i	−0.903736	−	0.521772i	−0.0253256	−	0.999679i	$-0.508062\pi$
$523$	−20.6677	−	11.9325i	−0.903736	−	0.521772i	−0.878410	+	0.477907i	$0.841396\pi$
$524$	−23.8011	−	1.15351i	−1.03976	−	0.0503914i
$525$		0			0
$526$	−5.64152	−	23.2967i	−0.245982	−	1.01578i
$527$	5.79445	+	10.0363i	0.252410	+	0.437187i
$528$		0			0
$529$	9.17818	+	15.8971i	0.399051	+	0.691177i
$530$	−23.8269	+	22.7001i	−1.03497	+	0.986029i
$531$		0			0
$532$	1.69879	−	2.63857i	0.0736518	−	0.114396i
$533$	2.03651	+	1.25922i	0.0882109	+	0.0545431i
$534$		0			0
$535$	17.5946	−	30.4747i	0.760680	−	1.31754i
$536$	2.40160	+	12.5444i	0.103733	+	0.541834i
$537$		0			0
$538$	2.97244	−	10.1077i	0.128151	−	0.435776i
$539$	29.4975	−	17.0304i	1.27055	−	0.733550i
$540$		0			0
$541$			19.4928i			0.838059i	0.907973	+	0.419030i	$0.137630\pi$
$541$			19.4928i			0.838059i	−0.907973	+	0.419030i	$0.862370\pi$
$542$	5.06756	+	20.9265i	0.217670	+	0.898871i
$543$		0			0
$544$	−31.8110	−	12.8116i	−1.36388	−	0.549291i
$545$	−21.7269			−0.930678
$546$		0			0
$547$		−	2.18538i		−	0.0934399i	−0.998908	−	0.0467200i	$-0.985123\pi$
$547$		−	2.18538i		−	0.0934399i	0.998908	−	0.0467200i	$-0.0148768\pi$
$548$	36.4015	−	18.7282i	1.55500	−	0.800029i
$549$		0			0
$550$	0.137279	−	0.0332434i	0.00585358	−	0.00141750i
$551$	3.23340			0.137747
$552$		0			0
$553$	6.42423	+	11.1271i	0.273186	+	0.473172i
$554$	6.44672	−	21.9220i	0.273895	−	0.931375i
$555$		0			0
$556$	−7.41250	−	14.4075i	−0.314360	−	0.611014i
$557$	−29.5902	−	17.0839i	−1.25378	−	0.723869i	−0.281921	−	0.959438i	$-0.590972\pi$
$557$	−29.5902	−	17.0839i	−1.25378	−	0.723869i	−0.971858	+	0.235568i	$0.924305\pi$
$558$		0			0
$559$	13.7622	+	25.5908i	0.582080	+	1.08238i
$560$	−7.69915	+	3.50071i	−0.325348	+	0.147932i
$561$		0			0
$562$	28.3834	−	27.0412i	1.19728	−	1.14066i
$563$	−20.4379	+	11.7998i	−0.861353	+	0.497302i	−0.864465	−	0.502693i	$-0.832343\pi$
$563$	−20.4379	+	11.7998i	−0.861353	+	0.497302i	0.00311215	+	0.999995i	$0.499009\pi$
$564$		0			0
$565$	−14.6706	+	8.47006i	−0.617195	+	0.356338i
$566$	−5.21782	+	1.26355i	−0.219321	+	0.0531108i
$567$		0			0
$568$	10.8009	−	31.0825i	0.453198	−	1.30419i
$569$	1.38906	−	2.40592i	0.0582323	−	0.100861i	−0.835440	−	0.549582i	$-0.814787\pi$
$569$	1.38906	−	2.40592i	0.0582323	−	0.100861i	0.893672	+	0.448721i	$0.148120\pi$
$570$		0			0
$571$			19.2497i			0.805577i	0.915293	+	0.402788i	$0.131959\pi$
$571$			19.2497i			0.805577i	−0.915293	+	0.402788i	$0.868041\pi$
$572$	33.1325	+	22.7749i	1.38534	+	0.952268i
$573$		0			0
$574$	−0.641819	+	0.611467i	−0.0267890	+	0.0255221i
$575$	0.0193011	−	0.0334304i	0.000804910	−	0.00139415i
$576$		0			0
$577$	6.64617			0.276683			0.138342	−	0.990385i	$-0.455823\pi$
$577$	6.64617			0.276683			0.138342	+	0.990385i	$0.455823\pi$
$578$	−6.57447	−	27.1493i	−0.273462	−	1.12926i
$579$		0			0
$580$	−7.32711	−	4.71742i	−0.304242	−	0.195880i
$581$	9.45154	−	5.45685i	0.392116	−	0.226388i
$582$		0			0
$583$	−28.9595	+	50.1594i	−1.19938	+	2.07739i
$584$	−3.54526	−	4.10172i	−0.146704	−	0.169730i
$585$		0			0
$586$	1.91101	−	6.49835i	0.0789430	−	0.268444i
$587$	23.1016	+	13.3377i	0.953505	+	0.550507i	0.894168	−	0.447731i	$-0.147768\pi$
$587$	23.1016	+	13.3377i	0.953505	+	0.550507i	0.0593374	+	0.998238i	$0.481101\pi$
$588$		0			0
$589$	−2.75197	+	1.58885i	−0.113393	+	0.0654675i
$590$	−1.44366	−	0.424546i	−0.0594346	−	0.0174783i
$591$		0			0
$592$	−17.0668	−	12.1958i	−0.701440	−	0.501244i
$593$	−6.61409			−0.271608			−0.135804	−	0.990736i	$-0.543362\pi$
$593$	−6.61409			−0.271608			−0.135804	+	0.990736i	$0.543362\pi$
$594$		0			0
$595$	−11.1010	−	6.40917i	−0.455097	−	0.262751i
$596$	−3.31223	−	6.43790i	−0.135674	−	0.263707i
$597$		0			0
$598$	10.7525	−	2.26259i	0.439701	−	0.0925241i
$599$	−11.9319			−0.487523			−0.243762	−	0.969835i	$-0.578381\pi$
$599$	−11.9319			−0.487523			−0.243762	+	0.969835i	$0.578381\pi$
$600$		0			0
$601$	6.15610	−	10.6627i	0.251113	−	0.434940i	−0.712720	−	0.701449i	$-0.752537\pi$
$601$	6.15610	−	10.6627i	0.251113	−	0.434940i	0.963832	+	0.266509i	$0.0858702\pi$
$602$	−10.4555	+	2.53189i	−0.426132	+	0.103192i
$603$		0			0
$604$	−1.55814	+	32.1500i	−0.0633998	+	1.30817i
$605$	38.9655	−	22.4968i	1.58417	−	0.914623i
$606$		0			0
$607$	4.35738	+	7.54720i	0.176860	+	0.306331i	0.940804	−	0.338952i	$-0.110073\pi$
$607$	4.35738	+	7.54720i	0.176860	+	0.306331i	−0.763943	+	0.645284i	$0.776739\pi$
$608$	3.51296	−	8.72265i	0.142469	−	0.353750i
$609$		0			0
$610$	−10.7622	−	3.16490i	−0.435749	−	0.128143i
$611$	−1.15111	+	38.1215i	−0.0465690	+	1.54223i
$612$		0			0
$613$	−30.7480	−	17.7523i	−1.24190	−	0.717010i	−0.272418	−	0.962179i	$-0.587823\pi$
$613$	−30.7480	−	17.7523i	−1.24190	−	0.717010i	−0.969480	+	0.245169i	$0.921157\pi$
$614$	−8.74025	−	9.17411i	−0.352728	−	0.370237i
$615$		0			0
$616$	−11.2615	+	9.73375i	−0.453740	+	0.392184i
$617$	−12.0318	−	20.8396i	−0.484380	−	0.838971i	0.515459	−	0.856914i	$-0.327622\pi$
$617$	−12.0318	−	20.8396i	−0.484380	−	0.838971i	−0.999839	+	0.0179431i	$0.994288\pi$
$618$		0			0
$619$			21.6806i			0.871417i	0.900088	+	0.435708i	$0.143502\pi$
$619$			21.6806i			0.871417i	−0.900088	+	0.435708i	$0.856498\pi$
$620$	8.55424	+	0.414579i	0.343547	+	0.0166499i
$621$		0			0
$622$	9.57564	−	9.12280i	0.383948	−	0.365791i
$623$	0.705358			0.0282596
$624$		0			0
$625$	−25.0892			−1.00357
$626$	12.0653	−	11.4947i	0.482225	−	0.459420i
$627$		0			0
$628$	30.8187	+	1.49362i	1.22980	+	0.0596018i
$629$		−	31.7918i		−	1.26762i
$630$		0			0
$631$	−9.48379	−	16.4264i	−0.377544	−	0.653925i	0.613161	−	0.789958i	$-0.289898\pi$
$631$	−9.48379	−	16.4264i	−0.377544	−	0.653925i	−0.990704	+	0.136033i	$0.956565\pi$
$632$	25.1765	+	29.1281i	1.00147	+	1.15865i
$633$		0			0
$634$	0.807754	+	0.847849i	0.0320800	+	0.0336724i
$635$	5.97360	+	3.44886i	0.237055	+	0.136864i
$636$		0			0
$637$	18.7344	+	11.5840i	0.742284	+	0.458973i
$638$	−14.7140	−	4.32702i	−0.582532	−	0.171309i
$639$		0			0
$640$	−20.6867	+	14.6409i	−0.817712	+	0.578731i
$641$	12.4294	+	21.5284i	0.490934	+	0.850322i	0.999946	−	0.0104375i	$-0.00332243\pi$
$641$	12.4294	+	21.5284i	0.490934	+	0.850322i	−0.509012	+	0.860759i	$0.669989\pi$
$642$		0			0
$643$	−3.25429	+	1.87887i	−0.128337	+	0.0740952i	−0.562794	−	0.826597i	$-0.690274\pi$
$643$	−3.25429	+	1.87887i	−0.128337	+	0.0740952i	0.434457	+	0.900692i	$0.356940\pi$
$644$	−0.196926	+	4.06329i	−0.00775998	+	0.160116i
$645$		0			0
$646$	13.8515	−	3.35428i	0.544980	−	0.131972i
$647$	24.0878	−	41.7213i	0.946989	−	1.64023i	0.195271	−	0.980749i	$-0.437441\pi$
$647$	24.0878	−	41.7213i	0.946989	−	1.64023i	0.751718	−	0.659484i	$-0.229225\pi$
$648$		0			0
$649$	−2.64838			−0.103958
$650$	0.0609808	+	0.0680046i	0.00239186	+	0.00266736i
$651$		0			0
$652$	−4.58394	−	8.90969i	−0.179521	−	0.348930i
$653$	21.5793	+	12.4588i	0.844463	+	0.487551i	0.858779	−	0.512346i	$-0.171224\pi$
$653$	21.5793	+	12.4588i	0.844463	+	0.487551i	−0.0143156	+	0.999898i	$0.504557\pi$
$654$		0			0
$655$	−26.6894			−1.04284
$656$	−1.54439	+	2.16122i	−0.0602983	+	0.0843814i
$657$		0			0
$658$	−13.5465	−	3.98370i	−0.528098	−	0.155301i
$659$	1.75765	−	1.01478i	0.0684684	−	0.0395302i	−0.465375	−	0.885114i	$-0.654081\pi$
$659$	1.75765	−	1.01478i	0.0684684	−	0.0395302i	0.533843	+	0.845583i	$0.320747\pi$
$660$		0			0
$661$	9.61763	+	5.55274i	0.374082	+	0.215977i	0.675240	−	0.737598i	$-0.264040\pi$
$661$	9.61763	+	5.55274i	0.374082	+	0.215977i	−0.301158	+	0.953574i	$0.597373\pi$
$662$	5.91644	−	20.1188i	0.229949	−	0.781938i
$663$		0			0
$664$	24.7419	−	21.3853i	0.960172	−	0.829911i
$665$	1.75741	−	3.04393i	0.0681495	−	0.118038i
$666$		0			0
$667$	−3.62999	+	2.09578i	−0.140554	+	0.0811488i
$668$	−1.78991	−	1.15240i	−0.0692536	−	0.0445875i
$669$		0			0
$670$	3.36686	+	13.9035i	0.130073	+	0.537137i
$671$	−19.7432			−0.762176
$672$		0			0
$673$	−17.0389	+	29.5122i	−0.656800	+	1.13761i	0.324639	+	0.945838i	$0.394757\pi$
$673$	−17.0389	+	29.5122i	−0.656800	+	1.13761i	−0.981439	+	0.191773i	$0.938576\pi$
$674$	−5.67149	+	5.40328i	−0.218458	+	0.208127i
$675$		0			0
$676$	−2.82323	+	25.8463i	−0.108586	+	0.994087i
$677$		−	28.8974i		−	1.11062i	−0.831645	−	0.555308i	$-0.812600\pi$
$677$		−	28.8974i		−	1.11062i	0.831645	−	0.555308i	$-0.187400\pi$
$678$		0			0
$679$	−0.604799	+	1.04754i	−0.0232100	+	0.0402010i
$680$	−36.2823	−	12.6078i	−1.39136	−	0.483488i
$681$		0			0
$682$	14.6494	−	3.54750i	0.560956	−	0.135841i
$683$	18.5350	−	10.7012i	0.709221	−	0.409469i	−0.101551	−	0.994830i	$-0.532381\pi$
$683$	18.5350	−	10.7012i	0.709221	−	0.409469i	0.810773	+	0.585361i	$0.199047\pi$
$684$		0			0
$685$	39.7078	−	22.9253i	1.51716	−	0.875930i
$686$	−12.6696	+	12.0705i	−0.483729	+	0.460853i
$687$		0			0
$688$	−29.3445	+	13.3426i	−1.11875	+	0.508682i
$689$	−37.4381	−	1.13048i	−1.42628	−	0.0430678i
$690$		0			0
$691$	−42.9878	−	24.8190i	−1.63533	−	0.944159i	−0.982411	−	0.186733i	$-0.940210\pi$
$691$	−42.9878	−	24.8190i	−1.63533	−	0.944159i	−0.652921	−	0.757426i	$-0.726457\pi$
$692$	19.9734	+	38.8218i	0.759276	+	1.47578i
$693$		0			0
$694$	6.44094	−	21.9023i	0.244495	−	0.831401i
$695$	−9.07368	−	15.7161i	−0.344184	−	0.596145i
$696$		0			0
$697$	−4.02589			−0.152491
$698$	32.8672	−	7.95912i	1.24404	−	0.301257i
$699$		0			0
$700$	−0.0300709	+	0.0154712i	−0.00113657	+	0.000584755i
$701$		−	23.3855i		−	0.883258i	−0.897198	−	0.441629i	$-0.854401\pi$
$701$		−	23.3855i		−	0.883258i	0.897198	−	0.441629i	$-0.145599\pi$
$702$		0			0
$703$	8.71738			0.328782
$704$	−27.6591	+	34.9924i	−1.04244	+	1.31882i
$705$		0			0
$706$	1.84995	+	7.63936i	0.0696236	+	0.287511i
$707$			9.21623i			0.346612i
$708$		0			0
$709$	41.1118	−	23.7359i	1.54399	−	0.891421i	0.545405	−	0.838172i	$-0.316376\pi$
$709$	41.1118	−	23.7359i	1.54399	−	0.891421i	0.998581	−	0.0532487i	$-0.0169576\pi$
$710$	10.3980	−	35.3583i	0.390230	−	1.32697i
$711$		0			0
$712$	2.07592	−	0.397430i	0.0777983	−	0.0148943i
$713$	2.05968	−	3.56746i	0.0771355	−	0.133603i
$714$		0			0
$715$	38.3009	+	23.6824i	1.43237	+	0.885672i
$716$	3.53624	−	5.49250i	0.132155	−	0.205264i
$717$		0			0
$718$	−8.75588	+	8.34180i	−0.326766	+	0.311313i
$719$	−22.6840	−	39.2899i	−0.845972	−	1.46527i	−0.884774	−	0.466020i	$-0.845688\pi$
$719$	−22.6840	−	39.2899i	−0.845972	−	1.46527i	0.0388023	−	0.999247i	$-0.487646\pi$
$720$		0			0
$721$	−7.11493	−	12.3234i	−0.264974	−	0.458948i
$722$	−5.40431	−	22.3171i	−0.201128	−	0.830558i
$723$		0			0
$724$	26.2151	+	1.27051i	0.974276	+	0.0472180i
$725$	−0.0301757	−	0.0174220i	−0.00112070	−	0.000647036i
$726$		0			0
$727$	27.1042			1.00524			0.502619	−	0.864508i	$-0.332370\pi$
$727$	27.1042			1.00524			0.502619	+	0.864508i	$0.332370\pi$
$728$	−8.99313	−	3.43262i	−0.333308	−	0.127222i
$729$		0			0
$730$	−4.18855	−	4.39647i	−0.155025	−	0.162721i
$731$	−42.3104	−	24.4279i	−1.56491	−	0.903500i
$732$		0			0
$733$			21.1225i			0.780179i	0.920777	+	0.390090i	$0.127556\pi$
$733$			21.1225i			0.780179i	−0.920777	+	0.390090i	$0.872444\pi$
$734$	1.30941	+	5.40723i	0.0483314	+	0.199585i
$735$		0			0
$736$	1.70987	+	12.0695i	0.0630268	+	0.444888i
$737$	12.5884	+	21.8038i	0.463701	+	0.803153i
$738$		0			0
$739$	−25.6746	−	14.8233i	−0.944457	−	0.545283i	−0.0531023	−	0.998589i	$-0.516911\pi$
$739$	−25.6746	−	14.8233i	−0.944457	−	0.545283i	−0.891355	+	0.453307i	$0.850244\pi$
$740$	−19.7542	−	12.7184i	−0.726179	−	0.467536i
$741$		0			0
$742$	3.91230	−	13.3037i	0.143625	−	0.488394i
$743$	−5.52318	+	9.56643i	−0.202626	+	0.350958i	−0.949374	−	0.314149i	$-0.898281\pi$
$743$	−5.52318	+	9.56643i	−0.202626	+	0.350958i	0.746748	+	0.665107i	$0.231614\pi$
$744$		0			0
$745$	−4.05452	−	7.02264i	−0.148546	−	0.257290i
$746$	3.16202	−	10.7524i	0.115770	−	0.393674i
$747$		0			0
$748$	−67.5218	−	3.27242i	−2.46884	−	0.119652i
$749$			14.8277i			0.541794i
$750$		0			0
$751$	18.6034	−	32.2220i	0.678846	−	1.17580i	−0.296483	−	0.955038i	$-0.595814\pi$
$751$	18.6034	−	32.2220i	0.678846	−	1.17580i	0.975329	−	0.220758i	$-0.0708530\pi$
$752$	−42.1130	−	4.09159i	−1.53570	−	0.149205i
$753$		0			0
$754$	−2.04231	−	9.70563i	−0.0743765	−	0.353458i
$755$			36.0514i			1.31204i
$756$		0			0
$757$	−17.2083	−	9.93522i	−0.625446	−	0.361102i	0.153540	−	0.988142i	$-0.450933\pi$
$757$	−17.2083	−	9.93522i	−0.625446	−	0.361102i	−0.778986	+	0.627041i	$0.784266\pi$
$758$	−36.3100	+	8.79283i	−1.31884	+	0.319370i
$759$		0			0
$760$	3.45710	−	9.94869i	0.125402	−	0.360877i
$761$	4.52926	+	7.84491i	0.164186	+	0.284378i	0.936366	−	0.351026i	$-0.114167\pi$
$761$	4.52926	+	7.84491i	0.164186	+	0.284378i	−0.772180	+	0.635404i	$0.780834\pi$
$762$		0			0
$763$	7.92857	−	4.57756i	0.287033	−	0.165719i
$764$	−14.3034	+	7.35895i	−0.517479	+	0.266237i
$765$		0			0
$766$	−2.56995	−	0.755759i	−0.0928560	−	0.0273067i
$767$	−0.811174	−	1.50838i	−0.0292898	−	0.0544644i
$768$		0			0
$769$	−5.28678	+	9.15697i	−0.190646	+	0.330209i	−0.945465	−	0.325725i	$-0.894392\pi$
$769$	−5.28678	+	9.15697i	−0.190646	+	0.330209i	0.754818	+	0.655934i	$0.227725\pi$
$770$	−12.0708	+	11.4999i	−0.435001	+	0.414429i
$771$		0			0
$772$	−1.40560	−	0.904968i	−0.0505887	−	0.0325705i
$773$	−22.3264	+	12.8902i	−0.803026	+	0.463627i	−0.844528	−	0.535511i	$-0.820119\pi$
$773$	−22.3264	+	12.8902i	−0.803026	+	0.463627i	0.0415022	+	0.999138i	$0.486786\pi$
$774$		0			0
$775$	0.0342437			0.00123007
$776$	−1.18973	+	3.42376i	−0.0427089	+	0.122906i
$777$		0			0
$778$	−24.4662	−	25.6807i	−0.877156	−	0.920697i
$779$		−	1.10391i		−	0.0395517i
$780$		0			0
$781$		−	64.8644i		−	2.32103i
$782$	−13.3763	+	12.7438i	−0.478337	+	0.455716i
$783$		0			0
$784$	−14.2073	+	19.8817i	−0.507403	+	0.710059i
$785$	34.5585			1.23345
$786$		0			0
$787$	−12.1719	+	7.02745i	−0.433881	+	0.250502i	−0.700999	−	0.713162i	$-0.747262\pi$
$787$	−12.1719	+	7.02745i	−0.433881	+	0.250502i	0.267117	+	0.963664i	$0.413929\pi$
$788$	−7.58358	+	11.7789i	−0.270154	+	0.419604i
$789$		0			0
$790$	29.7447	+	31.2212i	1.05827	+	1.11080i
$791$	3.56905	−	6.18178i	0.126901	−	0.219799i
$792$		0			0
$793$	−6.04714	−	11.2447i	−0.214740	−	0.399309i
$794$	−3.68569	+	12.5331i	−0.130800	+	0.444784i
$795$		0			0
$796$	−26.7389	+	13.7569i	−0.947734	+	0.487599i
$797$	19.1331	−	11.0465i	0.677731	−	0.391288i	−0.121269	−	0.992620i	$-0.538696\pi$
$797$	19.1331	−	11.0465i	0.677731	−	0.391288i	0.798999	+	0.601332i	$0.205363\pi$
$798$		0			0
$799$	−32.0633	−	55.5353i	−1.13432	−	1.96470i
$800$	−0.0797835	+	0.0624759i	−0.00282077	+	0.00220886i
$801$		0			0
$802$	1.47208	+	6.07896i	0.0519809	+	0.214656i
$803$	−9.25526	−	5.34353i	−0.326611	−	0.188569i
$804$		0			0
$805$			4.55637i			0.160591i
$806$	6.50745	+	7.25698i	0.229215	+	0.255616i
$807$		0			0
$808$	5.19284	+	27.1240i	0.182683	+	0.954219i
$809$	2.02317	−	3.50424i	0.0711310	−	0.123202i	−0.828266	−	0.560335i	$-0.810672\pi$
$809$	2.02317	−	3.50424i	0.0711310	−	0.123202i	0.899397	+	0.437132i	$0.144006\pi$
$810$		0			0
$811$			18.7132i			0.657109i	0.944485	+	0.328555i	$0.106561\pi$
$811$			18.7132i			0.657109i	−0.944485	+	0.328555i	$0.893439\pi$
$812$	3.66770	+	0.177754i	0.128711	+	0.00623794i
$813$		0			0
$814$	−39.6695	−	11.6658i	−1.39042	−	0.408888i
$815$	−5.61122	−	9.71893i	−0.196553	−	0.340439i
$816$		0			0
$817$	6.69820	−	11.6016i	0.234340	−	0.405889i
$818$	35.9110	+	10.5606i	1.25560	+	0.369241i
$819$		0			0
$820$	−1.61056	+	2.50154i	−0.0562434	+	0.0873575i
$821$	−6.46202	−	3.73085i	−0.225526	−	0.130208i	0.382980	−	0.923757i	$-0.374898\pi$
$821$	−6.46202	−	3.73085i	−0.225526	−	0.130208i	−0.608506	+	0.793549i	$0.708231\pi$
$822$		0			0
$823$	−9.81336	−	16.9972i	−0.342072	−	0.592486i	0.642745	−	0.766080i	$-0.277795\pi$
$823$	−9.81336	−	16.9972i	−0.342072	−	0.592486i	−0.984817	+	0.173594i	$0.944462\pi$
$824$	−27.8833	−	32.2598i	−0.971361	−	1.12382i
$825$		0			0
$826$	0.616266	−	0.149235i	0.0214426	−	0.00519254i
$827$		−	19.2616i		−	0.669792i	−0.942255	−	0.334896i	$-0.891299\pi$
$827$		−	19.2616i		−	0.669792i	0.942255	−	0.334896i	$-0.108701\pi$
$828$		0			0
$829$	−18.7148	−	10.8050i	−0.649993	−	0.375273i	0.138461	−	0.990368i	$-0.455785\pi$
$829$	−18.7148	−	10.8050i	−0.649993	−	0.375273i	−0.788453	+	0.615094i	$0.789118\pi$
$830$	26.5198	−	25.2657i	0.920517	−	0.876985i
$831$		0			0
$832$	−28.4015	−	5.03531i	−0.984645	−	0.174568i
$833$	−37.0353			−1.28320
$834$		0			0
$835$	−2.06489	−	1.19216i	−0.0714584	−	0.0412565i
$836$	0.897306	−	18.5146i	0.0310340	−	0.640342i
$837$		0			0
$838$	6.83257	−	1.65457i	0.236027	−	0.0571563i
$839$	21.0839	+	36.5183i	0.727895	+	1.26075i	0.957771	+	0.287532i	$0.0928347\pi$
$839$	21.0839	+	36.5183i	0.727895	+	1.26075i	−0.229876	+	0.973220i	$0.573832\pi$
$840$		0			0
$841$	−12.6083	−	21.8382i	−0.434768	−	0.753040i
$842$	23.4680	+	24.6329i	0.808759	+	0.848905i
$843$		0			0
$844$	7.27889	−	11.3056i	0.250550	−	0.389155i
$845$	−1.75706	+	29.0679i	−0.0604448	+	0.999965i
$846$		0			0
$847$	−9.47952	+	16.4190i	−0.325720	+	0.564164i
$848$	4.01825	−	41.3581i	0.137987	−	1.42024i
$849$		0			0
$850$	−0.147343	−	0.0433299i	−0.00505381	−	0.00148620i
$851$	−9.78661	+	5.65030i	−0.335481	+	0.193690i
$852$		0			0
$853$		−	40.2417i		−	1.37785i	−0.724833	−	0.688924i	$-0.758083\pi$
$853$		−	40.2417i		−	1.37785i	0.724833	−	0.688924i	$-0.241917\pi$
$854$	4.59414	−	1.11252i	0.157208	−	0.0380695i
$855$		0			0
$856$	8.35462	+	43.6391i	0.285555	+	1.49155i
$857$	−7.37621			−0.251966			−0.125983	−	0.992032i	$-0.540209\pi$
$857$	−7.37621			−0.251966			−0.125983	+	0.992032i	$0.540209\pi$
$858$		0			0
$859$			31.9493i			1.09010i	0.838405	+	0.545048i	$0.183489\pi$
$859$			31.9493i			1.09010i	−0.838405	+	0.545048i	$0.816511\pi$
$860$	−32.1050	+	16.5177i	−1.09477	+	0.563248i
$861$		0			0
$862$	3.52124	+	14.5410i	0.119934	+	0.495269i
$863$	16.1143			0.548536			0.274268	−	0.961653i	$-0.411564\pi$
$863$	16.1143			0.548536			0.274268	+	0.961653i	$0.411564\pi$
$864$		0			0
$865$	24.4496	+	42.3479i	0.831310	+	1.43987i
$866$	−16.5876	−	4.87801i	−0.563669	−	0.165761i
$867$		0			0
$868$	−3.20896	+	1.65097i	−0.108919	+	0.0560377i
$869$	65.7256	+	37.9467i	2.22959	+	1.28725i
$870$		0			0
$871$	−8.56257	+	13.8480i	−0.290132	+	0.469221i
$872$	20.7551	−	17.9394i	0.702857	−	0.607504i
$873$		0			0
$874$	−3.49437	−	3.66783i	−0.118199	−	0.124066i
$875$	9.12287	−	5.26709i	0.308409	−	0.178060i
$876$		0			0
$877$	0.181562	−	0.104825i	0.00613091	−	0.00353968i	−0.496931	−	0.867790i	$-0.665540\pi$
$877$	0.181562	−	0.104825i	0.00613091	−	0.00353968i	0.503062	+	0.864250i	$0.332207\pi$
$878$	−4.30314	−	17.7698i	−0.145224	−	0.599703i
$879$		0			0
$880$	−29.0456	+	40.6464i	−0.979126	+	1.37019i
$881$	20.1008	−	34.8157i	0.677214	−	1.17297i	−0.298602	−	0.954378i	$-0.596520\pi$
$881$	20.1008	−	34.8157i	0.677214	−	1.17297i	0.975816	−	0.218592i	$-0.0701464\pi$
$882$		0			0
$883$			4.69019i			0.157837i	0.996881	+	0.0789187i	$0.0251467\pi$
$883$			4.69019i			0.157837i	−0.996881	+	0.0789187i	$0.974853\pi$
$884$	−18.8175	−	39.4591i	−0.632900	−	1.32715i
$885$		0			0
$886$	13.6998	+	14.3799i	0.460254	+	0.483101i
$887$	11.6991	−	20.2635i	0.392819	−	0.680382i	−0.600002	−	0.799999i	$-0.704833\pi$
$887$	11.6991	−	20.2635i	0.392819	−	0.680382i	0.992820	+	0.119617i	$0.0381667\pi$
$888$		0			0
$889$	−2.90651			−0.0974813
$890$	2.30083	−	0.557167i	0.0771239	−	0.0186763i
$891$		0			0
$892$	35.0920	+	22.5933i	1.17497	+	0.756479i
$893$	15.2279	−	8.79184i	0.509583	−	0.294208i
$894$		0			0
$895$	3.65827	−	6.33631i	0.122282	−	0.211799i
$896$	4.46434	−	9.70113i	0.149143	−	0.324092i
$897$		0			0
$898$	−2.32580	−	0.683961i	−0.0776129	−	0.0228241i
$899$	−3.22015	−	1.85915i	−0.107398	−	0.0620062i
$900$		0			0
$901$	54.5398	−	31.4886i	1.81698	−	1.04904i
$902$	−1.47728	+	5.02348i	−0.0491881	+	0.167263i
$903$		0			0
$904$	7.02087	−	20.2044i	0.233511	−	0.671987i
$905$	29.3963			0.977166
$906$		0			0
$907$	3.93422	+	2.27142i	0.130634	+	0.0754213i	0.563893	−	0.825848i	$-0.309303\pi$
$907$	3.93422	+	2.27142i	0.130634	+	0.0754213i	−0.433259	+	0.901269i	$0.642637\pi$
$908$	17.7167	+	34.4355i	0.587950	+	1.14278i
$909$		0			0
$910$	−10.2469	−	3.35256i	−0.339682	−	0.111136i
$911$	29.5451			0.978873			0.489436	−	0.872039i	$-0.337203\pi$
$911$	29.5451			0.978873			0.489436	+	0.872039i	$0.337203\pi$
$912$		0			0
$913$	32.2326	−	55.8285i	1.06674	−	1.84765i
$914$	9.70722	+	40.0860i	0.321086	+	1.32593i
$915$		0			0
$916$	−35.1675	−	1.70438i	−1.16197	−	0.0563144i
$917$	9.73946	−	5.62308i	0.321625	−	0.185691i
$918$		0			0
$919$	15.5647	+	26.9588i	0.513431	+	0.889288i	0.999879	+	0.0155787i	$0.00495905\pi$
$919$	15.5647	+	26.9588i	0.513431	+	0.889288i	−0.486448	+	0.873710i	$0.661708\pi$
$920$	2.56726	+	13.4097i	0.0846402	+	0.442105i
$921$		0			0
$922$	10.3431	−	35.1716i	0.340632	−	1.15831i
$923$	36.9433	−	19.8673i	1.21600	−	0.653942i
$924$		0			0
$925$	−0.0813551	−	0.0469704i	−0.00267494	−	0.00154438i
$926$	−37.5781	+	35.8009i	−1.23489	+	1.17649i
$927$		0			0
$928$	10.8945	−	1.54341i	0.357628	−	0.0506648i
$929$	−11.9251	−	20.6548i	−0.391249	−	0.677663i	0.601366	−	0.798974i	$-0.294624\pi$
$929$	−11.9251	−	20.6548i	−0.391249	−	0.677663i	−0.992615	+	0.121311i	$0.961290\pi$
$930$		0			0
$931$		−	10.1552i		−	0.332822i
$932$	−1.48400	+	30.6202i	−0.0486100	+	1.00300i
$933$		0			0
$934$	−27.2978	−	28.6529i	−0.893213	−	0.937550i
$935$	−75.7155			−2.47616
$936$		0			0
$937$	−9.97996			−0.326031			−0.163016	−	0.986623i	$-0.552122\pi$
$937$	−9.97996			−0.326031			−0.163016	+	0.986623i	$0.552122\pi$
$938$	−4.15790	−	4.36429i	−0.135760	−	0.142499i
$939$		0			0
$940$	−47.3345	−	2.29405i	−1.54388	−	0.0748238i
$941$			12.2242i			0.398498i	0.979949	+	0.199249i	$0.0638502\pi$
$941$			12.2242i			0.398498i	−0.979949	+	0.199249i	$0.936150\pi$
$942$		0			0
$943$	0.715515	+	1.23931i	0.0233004	+	0.0403575i
$944$	1.72963	−	0.786440i	0.0562946	−	0.0255965i
$945$		0			0
$946$	−46.0066	+	43.8309i	−1.49580	+	1.42507i
$947$	−2.80497	−	1.61945i	−0.0911494	−	0.0526251i	0.453732	−	0.891138i	$-0.350092\pi$
$947$	−2.80497	−	1.61945i	−0.0911494	−	0.0526251i	−0.544882	+	0.838513i	$0.683426\pi$
$948$		0			0
$949$	0.208593	−	6.90798i	0.00677120	−	0.224242i
$950$	0.0118812	−	0.0404017i	0.000385476	−	0.00131080i
$951$		0			0
$952$	15.8964	−	3.04334i	0.515205	−	0.0986351i
$953$	3.08301	+	5.33994i	0.0998686	+	0.172977i	0.911630	−	0.411012i	$-0.134824\pi$
$953$	3.08301	+	5.33994i	0.0998686	+	0.172977i	−0.811762	+	0.583989i	$0.801491\pi$
$954$		0			0
$955$	−15.6025	+	9.00813i	−0.504886	+	0.291496i
$956$	1.36369	−	28.1379i	0.0441050	−	0.910043i
$957$		0			0
$958$	−10.8162	−	44.6658i	−0.349457	−	1.44309i
$959$	−9.66009	+	16.7318i	−0.311941	+	0.540297i
$960$		0			0
$961$	−27.3457			−0.882121
$962$	−5.50615	−	26.1668i	−0.177525	−	0.843652i
$963$		0			0
$964$	−25.7869	+	13.2671i	−0.830541	+	0.427305i
$965$	−1.62154	−	0.936197i	−0.0521993	−	0.0301373i
$966$		0			0
$967$	44.1828			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$967$	44.1828			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$968$	−18.6477	+	53.6635i	−0.599359	+	1.72481i
$969$		0			0
$970$	−1.14535	+	3.89474i	−0.0367749	+	0.125053i
$971$	33.2299	−	19.1853i	1.06640	−	0.615686i	0.139204	−	0.990264i	$-0.455546\pi$
$971$	33.2299	−	19.1853i	1.06640	−	0.615686i	0.927195	+	0.374578i	$0.122212\pi$
$972$		0			0
$973$	6.62233	+	3.82340i	0.212302	+	0.122573i
$974$	15.7302	+	4.62586i	0.504027	+	0.148222i
$975$		0			0
$976$	12.8940	−	5.86275i	0.412728	−	0.187662i
$977$	9.04005	−	15.6578i	0.289217	−	0.500938i	−0.684406	−	0.729101i	$-0.739938\pi$
$977$	9.04005	−	15.6578i	0.289217	−	0.500938i	0.973623	+	0.228163i	$0.0732718\pi$
$978$		0			0
$979$	3.60822	−	2.08321i	0.115319	−	0.0665796i
$980$	−14.8160	+	23.0123i	−0.473281	+	0.735102i
$981$		0			0
$982$	57.4660	−	13.9159i	1.83381	−	0.444075i
$983$	−18.8329			−0.600677			−0.300339	−	0.953833i	$-0.597100\pi$
$983$	−18.8329			−0.600677			−0.300339	+	0.953833i	$0.597100\pi$
$984$		0			0
$985$	−7.84529	+	13.5884i	−0.249972	+	0.432964i
$986$	11.5031	+	12.0741i	0.366332	+	0.384516i
$987$		0			0
$988$	10.8198	−	5.15980i	0.344224	−	0.164155i
$989$			17.3662i			0.552212i
$990$		0			0
$991$	−24.8600	+	43.0588i	−0.789704	+	1.36781i	0.136444	+	0.990648i	$0.456433\pi$
$991$	−24.8600	+	43.0588i	−0.789704	+	1.36781i	−0.926148	+	0.377160i	$0.876901\pi$
$992$	−8.51395	+	6.66700i	−0.270318	+	0.211677i
$993$		0			0
$994$	3.65507	+	15.0936i	0.115932	+	0.478741i
$995$	−29.1675	+	16.8399i	−0.924671	+	0.533859i
$996$		0			0
$997$	−41.6202	+	24.0294i	−1.31812	+	0.761020i	−0.983427	−	0.181306i	$-0.941968\pi$
$997$	−41.6202	+	24.0294i	−1.31812	+	0.761020i	−0.334698	+	0.942325i	$0.608634\pi$
$998$	−17.4624	−	18.3293i	−0.552764	−	0.580202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.685.3		24
3.2	odd	2		104.2.r.a.61.10	yes	24
8.5	even	2	inner	936.2.be.a.685.6		24
12.11	even	2		416.2.z.a.113.5		24
13.3	even	3	inner	936.2.be.a.757.6		24
24.5	odd	2		104.2.r.a.61.7	yes	24
24.11	even	2		416.2.z.a.113.8		24
39.29	odd	6		104.2.r.a.29.7	✓	24
104.29	even	6	inner	936.2.be.a.757.3		24
156.107	even	6		416.2.z.a.81.8		24
312.29	odd	6		104.2.r.a.29.10	yes	24
312.107	even	6		416.2.z.a.81.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.7	✓	24	39.29	odd	6
104.2.r.a.29.10	yes	24	312.29	odd	6
104.2.r.a.61.7	yes	24	24.5	odd	2
104.2.r.a.61.10	yes	24	3.2	odd	2
416.2.z.a.81.5		24	312.107	even	6
416.2.z.a.81.8		24	156.107	even	6
416.2.z.a.113.5		24	12.11	even	2
416.2.z.a.113.8		24	24.11	even	2
936.2.be.a.685.3		24	1.1	even	1	trivial
936.2.be.a.685.6		24	8.5	even	2	inner
936.2.be.a.757.3		24	104.29	even	6	inner
936.2.be.a.757.6		24	13.3	even	3	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)

\(f(q)\)	\(=\)	\(q+(-1.02392 + 0.975496i) q^{2} +(0.0968157 - 1.99766i) q^{4} -2.24007i q^{5} +(0.471952 + 0.817445i) q^{7} +(1.84957 + 2.13988i) q^{8} +(2.18518 + 2.29365i) q^{10} +(4.82849 + 2.78773i) q^{11} +(-0.108823 + 3.60391i) q^{13} +(-1.28065 - 0.376609i) q^{14} +(-3.98125 - 0.386809i) q^{16} +(-3.03119 - 5.25017i) q^{17} +(1.43961 - 0.831159i) q^{19} +(-4.47489 - 0.216874i) q^{20} +(-7.66340 + 1.85577i) q^{22} +(-1.07746 + 1.86621i) q^{23} -0.0179136 q^{25} +(-3.40417 - 3.79626i) q^{26} +(1.67867 - 0.863656i) q^{28} +(1.68452 + 0.972558i) q^{29} -1.91161 q^{31} +(4.45381 - 3.48764i) q^{32} +(8.22520 + 2.41883i) q^{34} +(1.83113 - 1.05721i) q^{35} +(4.54154 + 2.62206i) q^{37} +(-0.663250 + 2.25537i) q^{38} +(4.79348 - 4.14317i) q^{40} +(0.332039 - 0.575109i) q^{41} +(6.97919 - 4.02944i) q^{43} +(6.03640 - 9.37576i) q^{44} +(-0.717252 - 2.96190i) q^{46} +10.5778 q^{47} +(3.05452 - 5.29059i) q^{49} +(0.0183420 - 0.0174746i) q^{50} +(7.18883 + 0.566307i) q^{52} +10.3882i q^{53} +(6.24471 - 10.8162i) q^{55} +(-0.876323 + 2.52184i) q^{56} +(-2.67354 + 0.647422i) q^{58} +(-0.411368 + 0.237503i) q^{59} +(-3.06666 + 1.77054i) q^{61} +(1.95733 - 1.86477i) q^{62} +(-1.15816 + 7.91572i) q^{64} +(8.07301 + 0.243772i) q^{65} +(3.91067 + 2.25783i) q^{67} +(-10.7815 + 5.54696i) q^{68} +(-0.843631 + 2.86876i) q^{70} +(-5.81695 - 10.0753i) q^{71} -1.91680 q^{73} +(-7.20797 + 1.74548i) q^{74} +(-1.52099 - 2.95631i) q^{76} +5.26270i q^{77} +13.6120 q^{79} +(-0.866479 + 8.91829i) q^{80} +(0.221035 + 0.912767i) q^{82} -11.5623i q^{83} +(-11.7607 + 6.79007i) q^{85} +(-3.21542 + 10.9340i) q^{86} +(2.96524 + 15.4885i) q^{88} +(0.373638 - 0.647161i) q^{89} +(-2.99736 + 1.61192i) q^{91} +(3.62373 + 2.33306i) q^{92} +(-10.8308 + 10.3186i) q^{94} +(-1.86185 - 3.22483i) q^{95} +(0.640742 + 1.10980i) q^{97} +(2.03337 + 8.39680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 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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