LMFDB - Embedded newform 567.2.be.a.62.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			62.15
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(-0.253991 - 1.44045i) q^{5} +(1.07486 - 2.41758i) q^{7} +(2.64668 + 1.52806i) q^{8} +(1.56488 - 0.903482i) q^{10} +(-4.32398 - 0.762434i) q^{11} +(1.72073 - 4.72766i) q^{13} +(3.26067 + 0.226294i) q^{14} +(-0.491047 + 2.78487i) q^{16} +(-0.691322 - 1.19740i) q^{17} +(-4.13271 - 2.38602i) q^{19} +(-0.530913 - 0.445489i) q^{20} +(-0.941898 - 5.34177i) q^{22} +(3.82383 + 4.55707i) q^{23} +(2.68807 - 0.978376i) q^{25} +6.21530 q^{26} +(-0.346179 - 1.20489i) q^{28} +(-1.96611 - 5.40183i) q^{29} +(4.06150 + 4.84031i) q^{31} +(2.57902 - 0.454750i) q^{32} +(1.09794 - 1.30848i) q^{34} +(-3.75541 - 0.934242i) q^{35} +(4.81181 + 8.33429i) q^{37} +(1.02371 - 5.80574i) q^{38} +(1.52887 - 4.20054i) q^{40} +(-1.26265 - 0.459567i) q^{41} +(-0.613355 + 3.47851i) q^{43} +(-1.80171 + 1.04022i) q^{44} +(-3.67454 + 6.36449i) q^{46} +(5.55855 + 4.66418i) q^{47} +(-4.68936 - 5.19711i) q^{49} +(2.27156 + 2.70713i) q^{50} +(-0.815330 - 2.24010i) q^{52} +0.811158i q^{53} +6.42214i q^{55} +(6.53902 - 4.75611i) q^{56} +(5.44015 - 4.56483i) q^{58} +(0.933219 + 5.29255i) q^{59} +(-5.13083 + 6.11468i) q^{61} +(-3.90293 + 6.76007i) q^{62} +(4.44544 + 7.69973i) q^{64} +(-7.24703 - 1.27785i) q^{65} +(-4.21835 - 1.53535i) q^{67} +(-0.615627 - 0.224070i) q^{68} +(-0.502216 - 4.75433i) q^{70} +(11.6889 - 6.74856i) q^{71} +(6.23051 + 3.59719i) q^{73} +(-7.64200 + 9.10738i) q^{74} +(-2.22678 + 0.392641i) q^{76} +(-6.49091 + 9.63404i) q^{77} +(-8.07721 + 2.93986i) q^{79} +4.13619 q^{80} -1.65997i q^{82} +(-4.57620 + 1.66560i) q^{83} +(-1.54922 + 1.29995i) q^{85} +(-4.29729 + 0.757728i) q^{86} +(-10.2791 - 8.62523i) q^{88} +(-0.219556 + 0.380281i) q^{89} +(-9.57994 - 9.24156i) q^{91} +(2.77590 + 0.489467i) q^{92} +(-3.06592 + 8.42355i) q^{94} +(-2.38728 + 6.55901i) q^{95} +(-3.66832 - 0.646825i) q^{97} +(4.05185 - 7.63969i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	0.422526	+	1.16088i	0.298771	+	0.820866i	0.994706	+	0.102762i	$0.0327679\pi$
$2$	0.422526	+	1.16088i	0.298771	+	0.820866i	−0.695935	+	0.718105i	$0.745010\pi$
$3$		0			0
$3$		0			0
$4$	0.362974	−	0.304571i	0.181487	−	0.152286i
$5$	−0.253991	−	1.44045i	−0.113588	−	0.644191i	−0.987440	−	0.157997i	$-0.949496\pi$
$5$	−0.253991	−	1.44045i	−0.113588	−	0.644191i	0.873851	−	0.486193i	$-0.161615\pi$
$6$		0			0
$7$	1.07486	−	2.41758i	0.406258	−	0.913758i
$7$	1.07486	−	2.41758i	0.406258	−	0.913758i
$8$	2.64668	+	1.52806i	0.935744	+	0.540252i
$9$		0			0
$10$	1.56488	−	0.903482i	0.494858	−	0.285706i
$11$	−4.32398	−	0.762434i	−1.30373	−	0.229882i	−0.521702	−	0.853128i	$-0.674703\pi$
$11$	−4.32398	−	0.762434i	−1.30373	−	0.229882i	−0.782026	+	0.623246i	$0.785814\pi$
$12$		0			0
$13$	1.72073	−	4.72766i	0.477244	−	1.31122i	−0.434579	−	0.900634i	$-0.643103\pi$
$13$	1.72073	−	4.72766i	0.477244	−	1.31122i	0.911823	−	0.410583i	$-0.134675\pi$
$14$	3.26067	+	0.226294i	0.871452	+	0.0604795i
$15$		0			0
$16$	−0.491047	+	2.78487i	−0.122762	+	0.696217i
$17$	−0.691322	−	1.19740i	−0.167670	−	0.290413i	0.769930	−	0.638128i	$-0.220291\pi$
$17$	−0.691322	−	1.19740i	−0.167670	−	0.290413i	−0.937600	+	0.347715i	$0.886958\pi$
$18$		0			0
$19$	−4.13271	−	2.38602i	−0.948109	−	0.547391i	−0.0556159	−	0.998452i	$-0.517712\pi$
$19$	−4.13271	−	2.38602i	−0.948109	−	0.547391i	−0.892493	+	0.451061i	$0.851046\pi$
$20$	−0.530913	−	0.445489i	−0.118716	−	0.0996144i
$21$		0			0
$22$	−0.941898	−	5.34177i	−0.200813	−	1.13887i
$23$	3.82383	+	4.55707i	0.797324	+	0.950214i	0.999576	−	0.0291193i	$-0.00927028\pi$
$23$	3.82383	+	4.55707i	0.797324	+	0.950214i	−0.202251	+	0.979334i	$0.564826\pi$
$24$		0			0
$25$	2.68807	−	0.978376i	0.537613	−	0.195675i
$26$	6.21530			1.21892
$27$		0			0
$28$	−0.346179	−	1.20489i	−0.0654217	−	0.227703i
$29$	−1.96611	−	5.40183i	−0.365097	−	1.00310i	−0.977201	−	0.212318i	$-0.931899\pi$
$29$	−1.96611	−	5.40183i	−0.365097	−	1.00310i	0.612104	−	0.790777i	$-0.290323\pi$
$30$		0			0
$31$	4.06150	+	4.84031i	0.729467	+	0.869345i	0.995514	−	0.0946154i	$-0.0301621\pi$
$31$	4.06150	+	4.84031i	0.729467	+	0.869345i	−0.266047	+	0.963960i	$0.585718\pi$
$32$	2.57902	−	0.454750i	0.455910	−	0.0803892i
$33$		0			0
$34$	1.09794	−	1.30848i	0.188295	−	0.224402i
$35$	−3.75541	−	0.934242i	−0.634781	−	0.157916i
$36$		0			0
$37$	4.81181	+	8.33429i	0.791056	+	1.37015i	0.925314	+	0.379203i	$0.123802\pi$
$37$	4.81181	+	8.33429i	0.791056	+	1.37015i	−0.134258	+	0.990946i	$0.542865\pi$
$38$	1.02371	−	5.80574i	0.166067	−	0.941815i
$39$		0			0
$40$	1.52887	−	4.20054i	0.241736	−	0.664164i
$41$	−1.26265	−	0.459567i	−0.197193	−	0.0717724i	0.241536	−	0.970392i	$-0.422349\pi$
$41$	−1.26265	−	0.459567i	−0.197193	−	0.0717724i	−0.438729	+	0.898620i	$0.644571\pi$
$42$		0			0
$43$	−0.613355	+	3.47851i	−0.0935357	+	0.530467i	0.901651	+	0.432465i	$0.142356\pi$
$43$	−0.613355	+	3.47851i	−0.0935357	+	0.530467i	−0.995186	+	0.0980019i	$0.968755\pi$
$44$	−1.80171	+	1.04022i	−0.271617	+	0.156818i
$45$		0			0
$46$	−3.67454	+	6.36449i	−0.541782	+	0.938393i
$47$	5.55855	+	4.66418i	0.810798	+	0.680341i	0.950798	−	0.309811i	$-0.100266\pi$
$47$	5.55855	+	4.66418i	0.810798	+	0.680341i	−0.140000	+	0.990152i	$0.544710\pi$
$48$		0			0
$49$	−4.68936	−	5.19711i	−0.669908	−	0.742444i
$50$	2.27156	+	2.70713i	0.321246	+	0.382847i
$51$		0			0
$52$	−0.815330	−	2.24010i	−0.113066	−	0.310646i
$53$			0.811158i			0.111421i	0.998447	+	0.0557105i	$0.0177424\pi$
$53$			0.811158i			0.111421i	−0.998447	+	0.0557105i	$0.982258\pi$
$54$		0			0
$55$			6.42214i			0.865961i
$56$	6.53902	−	4.75611i	0.873813	−	0.635562i
$57$		0			0
$58$	5.44015	−	4.56483i	0.714327	−	0.599391i
$59$	0.933219	+	5.29255i	0.121495	+	0.689031i	0.983328	+	0.181839i	$0.0582051\pi$
$59$	0.933219	+	5.29255i	0.121495	+	0.689031i	−0.861834	+	0.507191i	$0.830684\pi$
$60$		0			0
$61$	−5.13083	+	6.11468i	−0.656935	+	0.782905i	−0.986942	−	0.161073i	$-0.948504\pi$
$61$	−5.13083	+	6.11468i	−0.656935	+	0.782905i	0.330007	+	0.943978i	$0.392949\pi$
$62$	−3.90293	+	6.76007i	−0.495672	+	0.858530i
$63$		0			0
$64$	4.44544	+	7.69973i	0.555680	+	0.962466i
$65$	−7.24703	−	1.27785i	−0.898883	−	0.158497i
$66$		0			0
$67$	−4.21835	−	1.53535i	−0.515353	−	0.187573i	0.0712336	−	0.997460i	$-0.477306\pi$
$67$	−4.21835	−	1.53535i	−0.515353	−	0.187573i	−0.586587	+	0.809886i	$0.699529\pi$
$68$	−0.615627	−	0.224070i	−0.0746557	−	0.0271725i
$69$		0			0
$70$	−0.502216	−	4.75433i	−0.0600263	−	0.568251i
$71$	11.6889	−	6.74856i	1.38721	−	0.800907i	0.394211	−	0.919020i	$-0.371018\pi$
$71$	11.6889	−	6.74856i	1.38721	−	0.800907i	0.993000	+	0.118113i	$0.0376845\pi$
$72$		0			0
$73$	6.23051	+	3.59719i	0.729226	+	0.421019i	0.818139	−	0.575020i	$-0.195006\pi$
$73$	6.23051	+	3.59719i	0.729226	+	0.421019i	−0.0889127	+	0.996039i	$0.528339\pi$
$74$	−7.64200	+	9.10738i	−0.888365	+	1.05871i
$75$		0			0
$76$	−2.22678	+	0.392641i	−0.255429	+	0.0450391i
$77$	−6.49091	+	9.63404i	−0.739707	+	1.09790i
$78$		0			0
$79$	−8.07721	+	2.93986i	−0.908757	+	0.330760i	−0.753756	−	0.657154i	$-0.771760\pi$
$79$	−8.07721	+	2.93986i	−0.908757	+	0.330760i	−0.155000	+	0.987914i	$0.549538\pi$
$80$	4.13619			0.462441
$81$		0			0
$82$		−	1.65997i		−	0.183313i
$83$	−4.57620	+	1.66560i	−0.502303	+	0.182823i	−0.580729	−	0.814097i	$-0.697233\pi$
$83$	−4.57620	+	1.66560i	−0.502303	+	0.182823i	0.0784266	+	0.996920i	$0.475010\pi$
$84$		0			0
$85$	−1.54922	+	1.29995i	−0.168036	+	0.140999i
$86$	−4.29729	+	0.757728i	−0.463388	+	0.0817079i
$87$		0			0
$88$	−10.2791	−	8.62523i	−1.09576	−	0.919453i
$89$	−0.219556	+	0.380281i	−0.0232728	+	0.0403097i	−0.877427	−	0.479710i	$-0.840742\pi$
$89$	−0.219556	+	0.380281i	−0.0232728	+	0.0403097i	0.854154	+	0.520019i	$0.174075\pi$
$90$		0			0
$91$	−9.57994	−	9.24156i	−1.00425	−	0.968778i
$92$	2.77590	+	0.489467i	0.289408	+	0.0510305i
$93$		0			0
$94$	−3.06592	+	8.42355i	−0.316226	+	0.868823i
$95$	−2.38728	+	6.55901i	−0.244930	+	0.672940i
$96$		0			0
$97$	−3.66832	−	0.646825i	−0.372462	−	0.0656751i	−0.0157159	−	0.999876i	$-0.505003\pi$
$97$	−3.66832	−	0.646825i	−0.372462	−	0.0656751i	−0.356746	+	0.934201i	$0.616114\pi$
$98$	4.05185	−	7.63969i	0.409298	−	0.771726i
$99$		0			0
$100$	0.677713	−	1.17383i	0.0677713	−	0.117383i
$101$	−12.1379	−	10.1849i	−1.20777	−	1.01344i	−0.999374	−	0.0353913i	$-0.988732\pi$
$101$	−12.1379	−	10.1849i	−1.20777	−	1.01344i	−0.208393	−	0.978045i	$-0.566823\pi$
$102$		0			0
$103$	5.45514	−	0.961888i	0.537511	−	0.0947776i	0.101698	−	0.994815i	$-0.467572\pi$
$103$	5.45514	−	0.961888i	0.537511	−	0.0947776i	0.435812	+	0.900038i	$0.356461\pi$
$104$	11.7784	−	9.88324i	1.15497	−	0.969131i
$105$		0			0
$106$	−0.941657	+	0.342735i	−0.0914618	+	0.0332894i
$107$		−	2.86545i		−	0.277014i	−0.990361	−	0.138507i	$-0.955770\pi$
$107$		−	2.86545i		−	0.277014i	0.990361	−	0.138507i	$-0.0442303\pi$
$108$		0			0
$109$	13.5547			1.29831			0.649154	−	0.760657i	$-0.275123\pi$
$109$	13.5547			1.29831			0.649154	+	0.760657i	$0.275123\pi$
$110$	−7.45534	+	2.71352i	−0.710838	+	0.258724i
$111$		0			0
$112$	6.20482	+	4.18048i	0.586301	+	0.395019i
$113$	10.0678	−	1.77523i	0.947100	−	0.166999i	0.321295	−	0.946979i	$-0.395882\pi$
$113$	10.0678	−	1.77523i	0.947100	−	0.166999i	0.625805	+	0.779980i	$0.284771\pi$
$114$		0			0
$115$	5.59303	−	6.66551i	0.521552	−	0.621562i
$116$	−2.35889	−	1.36191i	−0.219017	−	0.126450i
$117$		0			0
$118$	−5.74970	+	3.31959i	−0.529303	+	0.305593i
$119$	−3.63789	+	0.384283i	−0.333485	+	0.0352272i
$120$		0			0
$121$	7.77885	+	2.83127i	0.707168	+	0.257388i
$122$	−9.26632	−	3.37267i	−0.838934	−	0.305347i
$123$		0			0
$124$	2.94844	+	0.519889i	0.264777	+	0.0466874i
$125$	−5.74874	−	9.95711i	−0.514183	−	0.890591i
$126$		0			0
$127$	3.57642	−	6.19455i	0.317356	−	0.549677i	−0.662579	−	0.748992i	$-0.730538\pi$
$127$	3.57642	−	6.19455i	0.317356	−	0.549677i	0.979936	+	0.199315i	$0.0638715\pi$
$128$	−3.69348	+	4.40172i	−0.326461	+	0.389061i
$129$		0			0
$130$	−1.57863	−	8.95285i	−0.138455	−	0.785217i
$131$	−11.8367	+	9.93219i	−1.03418	+	0.867779i	−0.991342	−	0.131303i	$-0.958084\pi$
$131$	−11.8367	+	9.93219i	−1.03418	+	0.867779i	−0.0428368	+	0.999082i	$0.513640\pi$
$132$		0			0
$133$	−10.2105	+	7.42651i	−0.885360	+	0.643960i
$134$		−	5.54572i		−	0.479077i
$135$		0			0
$136$		−	4.22553i		−	0.362336i
$137$	−2.61871	−	7.19484i	−0.223731	−	0.614697i	0.776143	−	0.630557i	$-0.217174\pi$
$137$	−2.61871	−	7.19484i	−0.223731	−	0.614697i	−0.999874	+	0.0158603i	$0.994951\pi$
$138$		0			0
$139$	6.08203	+	7.24828i	0.515871	+	0.614791i	0.959599	−	0.281370i	$-0.0907889\pi$
$139$	6.08203	+	7.24828i	0.515871	+	0.614791i	−0.443728	+	0.896161i	$0.646344\pi$
$140$	−1.64766	+	0.804686i	−0.139253	+	0.0680083i
$141$		0			0
$142$	12.7731	+	10.7179i	1.07190	+	0.899428i
$143$	−11.0449	+	19.1303i	−0.923622	+	1.59976i
$144$		0			0
$145$	−7.28172	+	4.20410i	−0.604714	+	0.349132i
$146$	−1.54335	+	8.75278i	−0.127729	+	0.724386i
$147$		0			0
$148$	4.28495	+	1.55959i	0.352220	+	0.128198i
$149$	−6.17318	+	16.9607i	−0.505726	+	1.38947i	0.379880	+	0.925036i	$0.375965\pi$
$149$	−6.17318	+	16.9607i	−0.505726	+	1.38947i	−0.885607	+	0.464436i	$0.846257\pi$
$150$		0			0
$151$	−1.75618	+	9.95978i	−0.142916	+	0.810515i	0.826101	+	0.563521i	$0.190554\pi$
$151$	−1.75618	+	9.95978i	−0.142916	+	0.810515i	−0.969017	+	0.246994i	$0.920557\pi$
$152$	−7.29198	−	12.6301i	−0.591458	−	1.02444i
$153$		0			0
$154$	−13.9265	−	3.46454i	−1.12223	−	0.279180i
$155$	5.94065	−	7.07980i	0.477165	−	0.568663i
$156$		0			0
$157$	−21.0842	+	3.71772i	−1.68270	+	0.296706i	−0.931602	−	0.363481i	$-0.881588\pi$
$157$	−21.0842	+	3.71772i	−1.68270	+	0.296706i	−0.751101	+	0.660187i	$0.770477\pi$
$158$	−6.82566	−	8.13450i	−0.543020	−	0.647146i
$159$		0			0
$160$	−1.31009	−	3.59945i	−0.103572	−	0.284562i
$161$	15.1271	−	4.34621i	1.19219	−	0.342529i
$162$		0			0
$163$	−5.89950			−0.462084			−0.231042	−	0.972944i	$-0.574214\pi$
$163$	−5.89950			−0.462084			−0.231042	+	0.972944i	$0.574214\pi$
$164$	−0.598280	+	0.217756i	−0.0467179	+	0.0170039i
$165$		0			0
$166$	−3.86712	−	4.60866i	−0.300147	−	0.357701i
$167$	−1.77762	−	10.0814i	−0.137557	−	0.780123i	−0.973045	−	0.230615i	$-0.925926\pi$
$167$	−1.77762	−	10.0814i	−0.137557	−	0.780123i	0.835488	−	0.549508i	$-0.185185\pi$
$168$		0			0
$169$	−9.43129	−	7.91379i	−0.725483	−	0.608753i
$170$	−2.16367	−	1.24919i	−0.165946	−	0.0958088i
$171$		0			0
$172$	0.836822	+	1.44942i	0.0638071	+	0.110517i
$173$	0.404033	−	2.29139i	0.0307181	−	0.174211i	−0.965589	−	0.260073i	$-0.916253\pi$
$173$	0.404033	−	2.29139i	0.0307181	−	0.174211i	0.996307	+	0.0858621i	$0.0273645\pi$
$174$		0			0
$175$	0.523992	−	7.55023i	0.0396101	−	0.570743i
$176$	4.24655	−	11.6673i	0.320096	−	0.879457i
$177$		0			0
$178$	−0.534229	−	0.0941990i	−0.0400422	−	0.00706051i
$179$	6.11585	−	3.53099i	0.457120	−	0.263919i	−0.253712	−	0.967280i	$-0.581652\pi$
$179$	6.11585	−	3.53099i	0.457120	−	0.263919i	0.710833	+	0.703361i	$0.248318\pi$
$180$		0			0
$181$	13.6823	+	7.89950i	1.01700	+	0.587165i	0.913234	−	0.407436i	$-0.133577\pi$
$181$	13.6823	+	7.89950i	1.01700	+	0.587165i	0.103766	+	0.994602i	$0.466911\pi$
$182$	6.68057	−	15.0260i	0.495197	−	1.11380i
$183$		0			0
$184$	3.15699	+	17.9042i	0.232736	+	1.31991i
$185$	10.7830	−	9.04802i	0.792783	−	0.665224i
$186$		0			0
$187$	2.07632	+	5.70464i	0.151835	+	0.417164i
$188$	3.43819			0.250756
$189$		0			0
$190$	−8.62291			−0.625572
$191$	4.22356	+	11.6041i	0.305606	+	0.839646i	0.993500	+	0.113835i	$0.0363134\pi$
$191$	4.22356	+	11.6041i	0.305606	+	0.839646i	−0.687893	+	0.725812i	$0.741464\pi$
$192$		0			0
$193$	−2.51840	+	2.11318i	−0.181278	+	0.152110i	−0.728911	−	0.684608i	$-0.759973\pi$
$193$	−2.51840	+	2.11318i	−0.181278	+	0.152110i	0.547633	+	0.836718i	$0.315529\pi$
$194$	−0.799076	−	4.53179i	−0.0573703	−	0.325363i
$195$		0			0
$196$	−3.28501	−	0.458171i	−0.234643	−	0.0327265i
$197$	−9.63928	−	5.56524i	−0.686770	−	0.396507i	0.115631	−	0.993292i	$-0.463111\pi$
$197$	−9.63928	−	5.56524i	−0.686770	−	0.396507i	−0.802401	+	0.596785i	$0.796444\pi$
$198$		0			0
$199$	8.51003	−	4.91327i	0.603260	−	0.348292i	−0.167063	−	0.985946i	$-0.553428\pi$
$199$	8.51003	−	4.91327i	0.603260	−	0.348292i	0.770323	+	0.637654i	$0.220095\pi$
$200$	8.60948	+	1.51808i	0.608782	+	0.107345i
$201$		0			0
$202$	6.69488	−	18.3940i	0.471050	−	1.29420i
$203$	−15.1726	−	1.05299i	−1.06491	−	0.0739057i
$204$		0			0
$205$	−0.341284	+	1.93552i	−0.0238363	+	0.135182i
$206$	3.42157	+	5.92634i	0.238392	+	0.412908i
$207$		0			0
$208$	12.3209	+	7.11350i	0.854304	+	0.493233i
$209$	16.0506	+	13.4680i	1.11024	+	0.931602i
$210$		0			0
$211$	0.351313	+	1.99239i	0.0241854	+	0.137162i	0.994510	−	0.104646i	$-0.0333708\pi$
$211$	0.351313	+	1.99239i	0.0241854	+	0.137162i	−0.970324	+	0.241808i	$0.922260\pi$
$212$	0.247055	+	0.294429i	0.0169678	+	0.0202215i
$213$		0			0
$214$	3.32644	−	1.21073i	0.227391	−	0.0827636i
$215$	5.16642			0.352347
$216$		0			0
$217$	16.0674	−	4.61634i	1.09072	−	0.313378i
$218$	5.72723	+	15.7354i	0.387897	+	1.06574i
$219$		0			0
$220$	1.95600	+	2.33107i	0.131873	+	0.157161i
$221$	−6.85050	+	1.20793i	−0.460814	+	0.0812540i
$222$		0			0
$223$	−14.1148	+	16.8214i	−0.945198	+	1.12644i	0.0466367	+	0.998912i	$0.485150\pi$
$223$	−14.1148	+	16.8214i	−0.945198	+	1.12644i	−0.991835	+	0.127531i	$0.959295\pi$
$224$	1.67268	−	6.72376i	0.111761	−	0.449250i
$225$		0			0
$226$	6.31473	+	10.9374i	0.420050	+	0.727548i
$227$	1.17595	−	6.66915i	0.0780506	−	0.442647i	−0.920590	−	0.390530i	$-0.872292\pi$
$227$	1.17595	−	6.66915i	0.0780506	−	0.442647i	0.998641	−	0.0521174i	$-0.0165970\pi$
$228$		0			0
$229$	2.81930	−	7.74596i	0.186304	−	0.511867i	−0.811016	−	0.585024i	$-0.801085\pi$
$229$	2.81930	−	7.74596i	0.186304	−	0.511867i	0.997320	+	0.0731567i	$0.0233073\pi$
$230$	10.1011	+	3.67648i	0.666044	+	0.242420i
$231$		0			0
$232$	3.05068	−	17.3013i	0.200287	−	1.13588i
$233$	−7.87577	+	4.54708i	−0.515959	+	0.297889i	−0.735280	−	0.677764i	$-0.762949\pi$
$233$	−7.87577	+	4.54708i	−0.515959	+	0.297889i	0.219321	+	0.975653i	$0.429616\pi$
$234$		0			0
$235$	5.30672	−	9.19150i	0.346172	−	0.599587i
$236$	1.95069	+	1.63682i	0.126979	+	0.106548i
$237$		0			0
$238$	−1.98321	−	4.06079i	−0.128552	−	0.263222i
$239$	−2.30552	−	2.74761i	−0.149132	−	0.177728i	0.686307	−	0.727312i	$-0.259231\pi$
$239$	−2.30552	−	2.74761i	−0.149132	−	0.177728i	−0.835439	+	0.549584i	$0.814786\pi$
$240$		0			0
$241$	−4.59174	−	12.6157i	−0.295780	−	0.812649i	−0.995193	−	0.0979312i	$-0.968777\pi$
$241$	−4.59174	−	12.6157i	−0.295780	−	0.812649i	0.699413	−	0.714718i	$-0.253445\pi$
$242$			10.2266i			0.657391i
$243$		0			0
$244$			3.78218i			0.242129i
$245$	−6.29514	+	8.07482i	−0.402182	+	0.515881i
$246$		0			0
$247$	−18.3916	+	15.4324i	−1.17023	+	0.981937i
$248$	3.35321	+	19.0170i	0.212929	+	1.20758i
$249$		0			0
$250$	9.13002	−	10.8807i	0.577433	−	0.688158i
$251$	−6.38510	+	11.0593i	−0.403024	+	0.698057i	−0.994089	−	0.108566i	$-0.965374\pi$
$251$	−6.38510	+	11.0593i	−0.403024	+	0.698057i	0.591066	+	0.806624i	$0.298707\pi$
$252$		0			0
$253$	−13.0597	−	22.6201i	−0.821057	−	1.42211i
$254$	8.70226	+	1.53444i	0.546028	+	0.0962795i
$255$		0			0
$256$	10.0389	+	3.65387i	0.627433	+	0.228367i
$257$	8.05762	+	2.93273i	0.502620	+	0.182939i	0.580872	−	0.813995i	$-0.302712\pi$
$257$	8.05762	+	2.93273i	0.502620	+	0.182939i	−0.0782518	+	0.996934i	$0.524934\pi$
$258$		0			0
$259$	25.3208	−	2.67472i	1.57336	−	0.166199i
$260$	−3.01968	+	1.74341i	−0.187272	+	0.108122i
$261$		0			0
$262$	−16.5314	−	9.54441i	−1.02131	−	0.589656i
$263$	−2.26452	+	2.69875i	−0.139636	+	0.166412i	−0.831330	−	0.555779i	$-0.812420\pi$
$263$	−2.26452	+	2.69875i	−0.139636	+	0.166412i	0.691694	+	0.722191i	$0.256865\pi$
$264$		0			0
$265$	1.16844	−	0.206027i	0.0717764	−	0.0126561i
$266$	−12.9355	−	8.71524i	−0.793125	−	0.534366i
$267$		0			0
$268$	−1.99877	+	0.727494i	−0.122095	+	0.0444388i
$269$	32.0022			1.95121			0.975604	−	0.219536i	$-0.0704544\pi$
$269$	32.0022			1.95121			0.975604	+	0.219536i	$0.0704544\pi$
$270$		0			0
$271$			12.5643i			0.763225i	0.924322	+	0.381612i	$0.124631\pi$
$271$			12.5643i			0.763225i	−0.924322	+	0.381612i	$0.875369\pi$
$272$	3.67408	−	1.33726i	0.222774	−	0.0810831i
$273$		0			0
$274$	7.24588	−	6.08001i	0.437739	−	0.367307i
$275$	−12.3691	+	2.18100i	−0.745884	+	0.131519i
$276$		0			0
$277$	11.1823	+	9.38308i	0.671880	+	0.563774i	0.913621	−	0.406566i	$-0.133274\pi$
$277$	11.1823	+	9.38308i	0.671880	+	0.563774i	−0.241741	+	0.970341i	$0.577718\pi$
$278$	−5.84457	+	10.1231i	−0.350534	+	0.607143i
$279$		0			0
$280$	−8.51181	−	8.21115i	−0.508678	−	0.490710i
$281$	3.55531	+	0.626897i	0.212092	+	0.0373975i	0.278684	−	0.960383i	$-0.410102\pi$
$281$	3.55531	+	0.626897i	0.212092	+	0.0373975i	−0.0665925	+	0.997780i	$0.521213\pi$
$282$		0			0
$283$	−7.18235	+	19.7333i	−0.426946	+	1.17303i	0.520710	+	0.853733i	$0.325667\pi$
$283$	−7.18235	+	19.7333i	−0.426946	+	1.17303i	−0.947656	+	0.319292i	$0.896555\pi$
$284$	2.18733	−	6.00964i	0.129794	−	0.356607i
$285$		0			0
$286$	−26.8748	−	4.73875i	−1.58914	−	0.280208i
$287$	−2.46821	+	2.55859i	−0.145694	+	0.151029i
$288$		0			0
$289$	7.54415	−	13.0668i	0.443773	−	0.768638i
$290$	−7.95717	−	6.67686i	−0.467261	−	0.392079i
$291$		0			0
$292$	3.35711	−	0.591950i	0.196460	−	0.0346412i
$293$	4.25738	−	3.57236i	0.248719	−	0.208700i	−0.509902	−	0.860233i	$-0.670318\pi$
$293$	4.25738	−	3.57236i	0.248719	−	0.208700i	0.758620	+	0.651533i	$0.225874\pi$
$294$		0			0
$295$	7.38664	−	2.68852i	0.430067	−	0.156532i
$296$			29.4110i			1.70948i
$297$		0			0
$298$	−22.2976			−1.29167
$299$	28.1240	−	10.2363i	1.62646	−	0.591981i
$300$		0			0
$301$	7.75029	+	5.22174i	0.446719	+	0.300976i
$302$	−12.3041	+	2.16955i	−0.708024	+	0.124844i
$303$		0			0
$304$	8.67411	−	10.3374i	0.497494	−	0.592891i
$305$	10.1111	+	5.83765i	0.578960	+	0.334263i
$306$		0			0
$307$	26.1410	−	15.0925i	1.49195	−	0.861375i	0.491989	−	0.870602i	$-0.336270\pi$
$307$	26.1410	−	15.0925i	1.49195	−	0.861375i	0.999957	+	0.00922626i	$0.00293685\pi$
$308$	0.578222	+	5.47385i	0.0329472	+	0.311902i
$309$		0			0
$310$	10.7289	+	3.90499i	0.609359	+	0.221789i
$311$	24.1028	+	8.77272i	1.36675	+	0.497455i	0.918134	−	0.396271i	$-0.129696\pi$
$311$	24.1028	+	8.77272i	1.36675	+	0.497455i	0.448613	+	0.893726i	$0.351918\pi$
$312$		0			0
$313$	−1.77245	−	0.312531i	−0.100185	−	0.0176653i	0.123331	−	0.992366i	$-0.460642\pi$
$313$	−1.77245	−	0.312531i	−0.100185	−	0.0176653i	−0.223516	+	0.974700i	$0.571753\pi$
$314$	−13.2244	−	22.9054i	−0.746299	−	1.29263i
$315$		0			0
$316$	−2.03642	+	3.52718i	−0.114557	+	0.198419i
$317$	3.17281	−	3.78121i	0.178203	−	0.212374i	−0.669548	−	0.742769i	$-0.733512\pi$
$317$	3.17281	−	3.78121i	0.178203	−	0.212374i	0.847751	+	0.530395i	$0.177956\pi$
$318$		0			0
$319$	4.38286	+	24.8564i	0.245393	+	1.39169i
$320$	9.96200	−	8.35911i	0.556893	−	0.467289i
$321$		0			0
$322$	11.4370	+	15.7244i	0.637361	+	0.876287i
$323$			6.59804i			0.367124i
$324$		0			0
$325$		−	14.3918i		−	0.798313i
$326$	−2.49269	−	6.84861i	−0.138057	−	0.379310i
$327$		0			0
$328$	−2.63959	−	3.14574i	−0.145747	−	0.173694i
$329$	17.2507	−	8.42490i	0.951061	−	0.464480i
$330$		0			0
$331$	10.3974	+	8.72442i	0.571491	+	0.479538i	0.882140	−	0.470987i	$-0.156102\pi$
$331$	10.3974	+	8.72442i	0.571491	+	0.479538i	−0.310650	+	0.950525i	$0.600547\pi$
$332$	−1.15375	+	1.99835i	−0.0633201	+	0.109674i
$333$		0			0
$334$	10.9522	−	6.32326i	0.599278	−	0.345994i
$335$	−1.14018	+	6.46630i	−0.0622949	+	0.353292i
$336$		0			0
$337$	−21.7478	−	7.91556i	−1.18468	−	0.431188i	−0.326827	−	0.945084i	$-0.605980\pi$
$337$	−21.7478	−	7.91556i	−1.18468	−	0.431188i	−0.857853	+	0.513896i	$0.828202\pi$
$338$	5.20200	−	14.2924i	0.282951	−	0.777403i
$339$		0			0
$340$	−0.166399	+	0.943694i	−0.00902424	+	0.0511790i
$341$	−13.8714	−	24.0260i	−0.751179	−	1.30108i
$342$		0			0
$343$	−17.6048	+	5.75073i	−0.950570	+	0.310510i
$344$	−6.93873	+	8.26926i	−0.374111	+	0.445849i
$345$		0			0
$346$	2.83074	−	0.499136i	0.152182	−	0.0268337i
$347$	14.4789	+	17.2552i	0.777266	+	0.926310i	0.998807	−	0.0488415i	$-0.0155529\pi$
$347$	14.4789	+	17.2552i	0.777266	+	0.926310i	−0.221540	+	0.975151i	$0.571108\pi$
$348$		0			0
$349$	−10.9711	−	30.1428i	−0.587269	−	1.61351i	−0.775475	−	0.631378i	$-0.782489\pi$
$349$	−10.9711	−	30.1428i	−0.587269	−	1.61351i	0.188206	−	0.982130i	$-0.439733\pi$
$350$	8.98631	−	2.58187i	0.480338	−	0.138007i
$351$		0			0
$352$	−11.4983			−0.612863
$353$	1.94119	−	0.706536i	0.103319	−	0.0376051i	−0.289843	−	0.957074i	$-0.593603\pi$
$353$	1.94119	−	0.706536i	0.103319	−	0.0376051i	0.393163	+	0.919469i	$0.371381\pi$
$354$		0			0
$355$	−12.6899	−	15.1232i	−0.673508	−	0.802655i
$356$	0.0361299	+	0.204903i	0.00191488	+	0.0108598i
$357$		0			0
$358$	6.68316	+	5.60784i	0.353216	+	0.296384i
$359$	−5.58124	−	3.22233i	−0.294567	−	0.170068i	0.345433	−	0.938443i	$-0.387732\pi$
$359$	−5.58124	−	3.22233i	−0.294567	−	0.170068i	−0.639999	+	0.768375i	$0.721065\pi$
$360$		0			0
$361$	1.88620	+	3.26699i	0.0992736	+	0.171947i
$362$	−3.38923	+	19.2213i	−0.178134	+	1.01025i
$363$		0			0
$364$	−6.29198	−	0.436669i	−0.329790	−	0.0228877i
$365$	3.59909	−	9.88842i	0.188385	−	0.517584i
$366$		0			0
$367$	13.8164	+	2.43620i	0.721208	+	0.127168i	0.522192	−	0.852828i	$-0.325114\pi$
$367$	13.8164	+	2.43620i	0.721208	+	0.127168i	0.199016	+	0.979996i	$0.436225\pi$
$368$	−14.5685	+	8.41113i	−0.759436	+	0.438461i
$369$		0			0
$370$	15.0598	+	8.69476i	0.782920	+	0.452019i
$371$	1.96104	+	0.871880i	0.101812	+	0.0452657i
$372$		0			0
$373$	−3.27412	−	18.5684i	−0.169527	−	0.961437i	−0.944273	−	0.329164i	$-0.893233\pi$
$373$	−3.27412	−	18.5684i	−0.169527	−	0.961437i	0.774745	−	0.632273i	$-0.217878\pi$
$374$	−5.74510	+	4.82071i	−0.297072	+	0.249273i
$375$		0			0
$376$	7.58457	+	20.8384i	0.391144	+	1.07466i
$377$	−28.9212			−1.48952
$378$		0			0
$379$	1.19709			0.0614903			0.0307452	−	0.999527i	$-0.490212\pi$
$379$	1.19709			0.0614903			0.0307452	+	0.999527i	$0.490212\pi$
$380$	1.13116	+	3.10785i	0.0580275	+	0.159429i
$381$		0			0
$382$	−11.6865	+	9.80610i	−0.597931	+	0.501724i
$383$	0.200482	+	1.13699i	0.0102442	+	0.0580975i	0.989501	−	0.144524i	$-0.0461651\pi$
$383$	0.200482	+	1.13699i	0.0102442	+	0.0580975i	−0.979257	+	0.202621i	$0.935054\pi$
$384$		0			0
$385$	15.5260	+	6.90289i	0.791279	+	0.351804i
$386$	−3.51724	−	2.03068i	−0.179023	−	0.103359i
$387$		0			0
$388$	−1.52851	+	0.882486i	−0.0775984	+	0.0448014i
$389$	33.3699	+	5.88401i	1.69192	+	0.298331i	0.934860	−	0.355016i	$-0.115525\pi$
$389$	33.3699	+	5.88401i	1.69192	+	0.298331i	0.757059	+	0.653347i	$0.226636\pi$
$390$		0			0
$391$	2.81315	−	7.72908i	0.142267	−	0.390876i
$392$	−4.46973	−	20.9207i	−0.225756	−	1.05666i
$393$		0			0
$394$	2.38773	−	13.5415i	0.120292	−	0.682211i
$395$	6.28627	+	10.8881i	0.316297	+	0.547842i
$396$		0			0
$397$	−20.5615	−	11.8712i	−1.03195	−	0.595798i	−0.114409	−	0.993434i	$-0.536497\pi$
$397$	−20.5615	−	11.8712i	−1.03195	−	0.595798i	−0.917543	+	0.397636i	$0.869831\pi$
$398$	9.29942	+	7.80314i	0.466138	+	0.391136i
$399$		0			0
$400$	1.40468	+	7.96634i	0.0702340	+	0.398317i
$401$	−14.6379	−	17.4448i	−0.730984	−	0.871152i	0.264665	−	0.964340i	$-0.414739\pi$
$401$	−14.6379	−	17.4448i	−0.730984	−	0.871152i	−0.995649	+	0.0931880i	$0.970294\pi$
$402$		0			0
$403$	29.8721	−	10.8725i	1.48803	−	0.541600i
$404$	−7.50778			−0.373526
$405$		0			0
$406$	−5.18843	−	18.0585i	−0.257497	−	0.896230i
$407$	−14.4518	−	39.7060i	−0.716349	−	1.96815i
$408$		0			0
$409$	−15.1400	−	18.0432i	−0.748625	−	0.892177i	0.248447	−	0.968646i	$-0.420080\pi$
$409$	−15.1400	−	18.0432i	−0.748625	−	0.892177i	−0.997072	+	0.0764689i	$0.975635\pi$
$410$	−2.39110	+	0.421616i	−0.118088	+	0.0208221i
$411$		0			0
$412$	1.68711	−	2.01062i	0.0831179	−	0.0990561i
$413$	13.7982	+	3.43261i	0.678966	+	0.168908i
$414$		0			0
$415$	3.56153	+	6.16875i	0.174829	+	0.302812i
$416$	2.28788	−	12.9752i	0.112173	−	0.636162i
$417$		0			0
$418$	−8.85298	+	24.3234i	−0.433013	+	1.18969i
$419$	24.7436	+	9.00593i	1.20880	+	0.439968i	0.866289	−	0.499544i	$-0.166499\pi$
$419$	24.7436	+	9.00593i	1.20880	+	0.439968i	0.342515	+	0.939512i	$0.388721\pi$
$420$		0			0
$421$	−1.75667	+	9.96255i	−0.0856147	+	0.485545i	0.911608	+	0.411062i	$0.134842\pi$
$421$	−1.75667	+	9.96255i	−0.0856147	+	0.485545i	−0.997222	+	0.0744834i	$0.976269\pi$
$422$	−2.16449	+	1.24967i	−0.105366	+	0.0608330i
$423$		0			0
$424$	−1.23950	+	2.14688i	−0.0601954	+	0.104262i
$425$	−3.02983	−	2.54233i	−0.146968	−	0.123321i
$426$		0			0
$427$	9.26780	+	18.9766i	0.448500	+	0.918342i
$428$	−0.872734	−	1.04008i	−0.0421852	−	0.0502744i
$429$		0			0
$430$	2.18294	+	5.99759i	0.105271	+	0.289229i
$431$		−	3.21277i		−	0.154754i	−0.997002	−	0.0773769i	$-0.975346\pi$
$431$		−	3.21277i		−	0.154754i	0.997002	−	0.0773769i	$-0.0246545\pi$
$432$		0			0
$433$			15.4984i			0.744805i	0.928071	+	0.372403i	$0.121466\pi$
$433$			15.4984i			0.744805i	−0.928071	+	0.372403i	$0.878534\pi$
$434$	12.1479	+	16.7017i	0.583117	+	0.801709i
$435$		0			0
$436$	4.92002	−	4.12839i	0.235626	−	0.197714i
$437$	−4.92954	−	27.9568i	−0.235812	−	1.33735i
$438$		0			0
$439$	−15.7258	+	18.7413i	−0.750551	+	0.894472i	−0.997211	−	0.0746301i	$-0.976222\pi$
$439$	−15.7258	+	18.7413i	−0.750551	+	0.894472i	0.246660	+	0.969102i	$0.420667\pi$
$440$	−9.81344	+	16.9974i	−0.467837	+	0.810318i
$441$		0			0
$442$	−4.29677	−	7.44223i	−0.204377	−	0.353991i
$443$	−33.6606	−	5.93527i	−1.59926	−	0.281993i	−0.698272	−	0.715832i	$-0.746048\pi$
$443$	−33.6606	−	5.93527i	−1.59926	−	0.281993i	−0.900990	+	0.433839i	$0.857159\pi$
$444$		0			0
$445$	0.603543	+	0.219672i	0.0286107	+	0.0104134i
$446$	−25.4915	−	9.27814i	−1.20706	−	0.439333i
$447$		0			0
$448$	23.3929	−	2.47107i	1.10521	−	0.116747i
$449$	−9.72152	+	5.61272i	−0.458787	+	0.264881i	−0.711534	−	0.702652i	$-0.751999\pi$
$449$	−9.72152	+	5.61272i	−0.458787	+	0.264881i	0.252747	+	0.967532i	$0.418666\pi$
$450$		0			0
$451$	5.10928	+	2.94985i	0.240587	+	0.138903i
$452$	3.11367	−	3.71073i	0.146455	−	0.174538i
$453$		0			0
$454$	8.23896	−	1.45275i	0.386673	−	0.0681809i
$455$	−10.8788	+	16.1467i	−0.510007	+	0.756971i
$456$		0			0
$457$	24.0852	−	8.76630i	1.12666	−	0.410070i	0.289581	−	0.957154i	$-0.406484\pi$
$457$	24.0852	−	8.76630i	1.12666	−	0.410070i	0.837078	+	0.547083i	$0.184262\pi$
$458$	10.1834			0.475837
$459$		0			0
$460$		−	4.12288i		−	0.192230i
$461$	−18.4071	+	6.69964i	−0.857305	+	0.312033i	−0.733015	−	0.680213i	$-0.761887\pi$
$461$	−18.4071	+	6.69964i	−0.857305	+	0.312033i	−0.124290	+	0.992246i	$0.539665\pi$
$462$		0			0
$463$	−5.40665	+	4.53671i	−0.251268	+	0.210839i	−0.759718	−	0.650252i	$-0.774663\pi$
$463$	−5.40665	+	4.53671i	−0.251268	+	0.210839i	0.508450	+	0.861092i	$0.330219\pi$
$464$	16.0088	−	2.82279i	0.743192	−	0.131045i
$465$		0			0
$466$	−8.60633	−	7.22156i	−0.398680	−	0.334533i
$467$	6.73186	−	11.6599i	0.311513	−	0.539557i	−0.667177	−	0.744899i	$-0.732498\pi$
$467$	6.73186	−	11.6599i	0.311513	−	0.539557i	0.978690	+	0.205343i	$0.0658309\pi$
$468$		0			0
$469$	−8.24596	+	8.54789i	−0.380763	+	0.394705i
$470$	12.9125	+	2.27681i	0.595607	+	0.105022i
$471$		0			0
$472$	−5.61741	+	15.4337i	−0.258562	+	0.710394i
$473$	5.30426	−	14.5733i	0.243890	−	0.670083i
$474$		0			0
$475$	−13.4434	−	2.37044i	−0.616827	−	0.108763i
$476$	−1.20342	+	1.24748i	−0.0551586	+	0.0571782i
$477$		0			0
$478$	2.21551	−	3.83737i	0.101335	−	0.175517i
$479$	−19.6234	−	16.4660i	−0.896614	−	0.752349i	0.0729114	−	0.997338i	$-0.476771\pi$
$479$	−19.6234	−	16.4660i	−0.896614	−	0.752349i	−0.969526	+	0.244990i	$0.921215\pi$
$480$		0			0
$481$	47.6815	−	8.40753i	2.17409	−	0.383351i
$482$	12.7052	−	10.6609i	0.578706	−	0.485592i
$483$		0			0
$484$	3.68584	−	1.34154i	0.167538	−	0.0609790i
$485$			5.44834i			0.247396i
$486$		0			0
$487$	−7.30424			−0.330987			−0.165493	−	0.986211i	$-0.552922\pi$
$487$	−7.30424			−0.330987			−0.165493	+	0.986211i	$0.552922\pi$
$488$	−22.9233	+	8.34340i	−1.03769	+	0.377688i
$489$		0			0
$490$	−12.0338	−	3.89608i	−0.543630	−	0.176007i
$491$	−21.2089	+	3.73971i	−0.957146	+	0.168771i	−0.630339	−	0.776320i	$-0.717084\pi$
$491$	−21.2089	+	3.73971i	−0.957146	+	0.168771i	−0.326807	+	0.945091i	$0.605973\pi$
$492$		0			0
$493$	−5.10897	+	6.08863i	−0.230096	+	0.274218i
$494$	−25.6860	−	14.8298i	−1.15567	−	0.667226i
$495$		0			0
$496$	−15.4740	+	8.93392i	−0.694803	+	0.401145i
$497$	−3.75130	−	35.5125i	−0.168269	−	1.59295i
$498$		0			0
$499$	−26.2483	−	9.55359i	−1.17503	−	0.427678i	−0.320589	−	0.947218i	$-0.603881\pi$
$499$	−26.2483	−	9.55359i	−1.17503	−	0.427678i	−0.854446	+	0.519541i	$0.826103\pi$
$500$	−5.11929	−	1.86327i	−0.228942	−	0.0833280i
$501$		0			0
$502$	−15.5364	−	2.73949i	−0.693424	−	0.122269i
$503$	−6.80712	−	11.7903i	−0.303514	−	0.525702i	0.673415	−	0.739265i	$-0.264827\pi$
$503$	−6.80712	−	11.7903i	−0.303514	−	0.525702i	−0.976929	+	0.213562i	$0.931493\pi$
$504$		0			0
$505$	−11.5880	+	20.0710i	−0.515658	+	0.893146i
$506$	20.7411	−	24.7183i	0.922056	−	1.09886i
$507$		0			0
$508$	−0.588533	−	3.33774i	−0.0261119	−	0.148088i
$509$	1.52700	−	1.28130i	0.0676830	−	0.0567928i	−0.608319	−	0.793693i	$-0.708156\pi$
$509$	1.52700	−	1.28130i	0.0676830	−	0.0567928i	0.676002	+	0.736900i	$0.263711\pi$
$510$		0			0
$511$	15.3934	−	11.1963i	0.680964	−	0.495294i
$512$			24.6899i			1.09115i
$513$		0			0
$514$			10.5931i			0.467241i
$515$	−2.77111	−	7.61356i	−0.122110	−	0.335494i
$516$		0			0
$517$	−20.4789	−	24.4058i	−0.900662	−	1.07337i
$518$	13.8037	+	28.2643i	0.606501	+	1.24186i
$519$		0			0
$520$	−17.2279	−	14.4560i	−0.755495	−	0.633936i
$521$	−3.88589	+	6.73055i	−0.170244	+	0.294871i	−0.938505	−	0.345266i	$-0.887789\pi$
$521$	−3.88589	+	6.73055i	−0.170244	+	0.294871i	0.768261	+	0.640136i	$0.221122\pi$
$522$		0			0
$523$	−17.4428	+	10.0706i	−0.762720	+	0.440356i	−0.830271	−	0.557359i	$-0.811815\pi$
$523$	−17.4428	+	10.0706i	−0.762720	+	0.440356i	0.0675518	+	0.997716i	$0.478481\pi$
$524$	−1.27136	+	7.21025i	−0.0555397	+	0.314981i
$525$		0			0
$526$	−4.08975	−	1.48855i	−0.178321	−	0.0649037i
$527$	2.98800	−	8.20947i	0.130159	−	0.357610i
$528$		0			0
$529$	−2.15125	+	12.2004i	−0.0935327	+	0.530451i
$530$	0.732866	+	1.26936i	0.0318337	+	0.0551375i
$531$		0			0
$532$	−1.44423	+	5.80545i	−0.0626155	+	0.251698i
$533$	−4.34536	+	5.17859i	−0.188218	+	0.224310i
$534$		0			0
$535$	−4.12755	+	0.727798i	−0.178450	+	0.0314655i
$536$	−8.81851	−	10.5095i	−0.380902	−	0.453941i
$537$		0			0
$538$	13.5218	+	37.1507i	0.582964	+	1.60168i
$539$	16.3142	+	26.0475i	0.702703	+	1.12195i
$540$		0			0
$541$	−33.5967			−1.44444			−0.722219	−	0.691665i	$-0.756877\pi$
$541$	−33.5967			−1.44444			−0.722219	+	0.691665i	$0.756877\pi$
$542$	−14.5856	+	5.30873i	−0.626506	+	0.228029i
$543$		0			0
$544$	−2.32745	−	2.77375i	−0.0997886	−	0.118923i
$545$	−3.44278	−	19.5250i	−0.147473	−	0.836358i
$546$		0			0
$547$	−8.29582	−	6.96102i	−0.354704	−	0.297632i	0.447972	−	0.894048i	$-0.352146\pi$
$547$	−8.29582	−	6.96102i	−0.354704	−	0.297632i	−0.802675	+	0.596416i	$0.796591\pi$
$548$	−3.14187	−	1.81396i	−0.134214	−	0.0774884i
$549$		0			0
$550$	−7.75814	−	13.4375i	−0.330808	−	0.572977i
$551$	−4.76354	+	27.0154i	−0.202934	+	1.15089i
$552$		0			0
$553$	−1.57451	+	22.6872i	−0.0669550	+	0.964758i
$554$	−6.16781	+	16.9459i	−0.262045	+	0.719963i
$555$		0			0
$556$	4.41524	+	0.778525i	0.187248	+	0.0330168i
$557$	2.65395	−	1.53226i	0.112451	−	0.0649239i	−0.442719	−	0.896660i	$-0.645986\pi$
$557$	2.65395	−	1.53226i	0.112451	−	0.0649239i	0.555171	+	0.831736i	$0.312653\pi$
$558$		0			0
$559$	15.3898	+	8.88529i	0.650918	+	0.375808i
$560$	4.44583	−	9.99957i	0.187870	−	0.422559i
$561$		0			0
$562$	0.774458	+	4.39217i	0.0326685	+	0.185272i
$563$	−35.1445	+	29.4898i	−1.48117	+	1.24285i	−0.576237	+	0.817283i	$0.695479\pi$
$563$	−35.1445	+	29.4898i	−1.48117	+	1.24285i	−0.904929	+	0.425563i	$0.860076\pi$
$564$		0			0
$565$	−5.11426	−	14.0513i	−0.215159	−	0.591144i
$566$	−25.9428			−1.09046
$567$		0			0
$568$	41.2489			1.73077
$569$	9.66650	+	26.5585i	0.405241	+	1.11339i	0.959663	+	0.281154i	$0.0907171\pi$
$569$	9.66650	+	26.5585i	0.405241	+	1.11339i	−0.554422	+	0.832236i	$0.687061\pi$
$570$		0			0
$571$	31.2950	−	26.2596i	1.30966	−	1.09893i	0.321266	−	0.946989i	$-0.395892\pi$
$571$	31.2950	−	26.2596i	1.30966	−	1.09893i	0.988389	−	0.151943i	$-0.0485529\pi$
$572$	1.81754	+	10.3078i	0.0759952	+	0.430990i
$573$		0			0
$574$	−4.01309	−	1.78423i	−0.167503	−	0.0744723i
$575$	14.7372	+	8.50855i	0.614586	+	0.354831i
$576$		0			0
$577$	0.564874	−	0.326130i	0.0235160	−	0.0135770i	−0.488196	−	0.872734i	$-0.662345\pi$
$577$	0.564874	−	0.326130i	0.0235160	−	0.0135770i	0.511712	+	0.859157i	$0.329012\pi$
$578$	18.3566	+	3.23677i	0.763536	+	0.134632i
$579$		0			0
$580$	−1.36263	+	3.74378i	−0.0565799	+	0.155452i
$581$	−0.892050	+	12.8536i	−0.0370085	+	0.533257i
$582$		0			0
$583$	0.618454	−	3.50743i	0.0256137	−	0.145263i
$584$	10.9935	+	19.0412i	0.454913	+	0.787932i
$585$		0			0
$586$	5.94594	+	3.43289i	0.245624	+	0.141811i
$587$	3.87979	+	3.25553i	0.160136	+	0.134370i	0.719335	−	0.694664i	$-0.244447\pi$
$587$	3.87979	+	3.25553i	0.160136	+	0.134370i	−0.559199	+	0.829034i	$0.688891\pi$
$588$		0			0
$589$	−5.23593	−	29.6944i	−0.215743	−	1.22354i
$590$	6.24209	+	7.43904i	0.256983	+	0.306260i
$591$		0			0
$592$	−25.5727	+	9.30771i	−1.05103	+	0.382544i
$593$	−1.95836			−0.0804204			−0.0402102	−	0.999191i	$-0.512803\pi$
$593$	−1.95836			−0.0804204			−0.0402102	+	0.999191i	$0.512803\pi$
$594$		0			0
$595$	1.47753	+	5.14261i	0.0605729	+	0.210826i
$596$	2.92503	+	8.03645i	0.119814	+	0.329186i
$597$		0			0
$598$	23.7663	+	28.3235i	0.971875	+	1.15824i
$599$	28.4407	−	5.01487i	1.16206	−	0.204902i	0.440823	−	0.897594i	$-0.354687\pi$
$599$	28.4407	−	5.01487i	1.16206	−	0.204902i	0.721234	+	0.692692i	$0.243575\pi$
$600$		0			0
$601$	−5.22977	+	6.23259i	−0.213327	+	0.254233i	−0.862087	−	0.506760i	$-0.830843\pi$
$601$	−5.22977	+	6.23259i	−0.213327	+	0.254233i	0.648761	+	0.760992i	$0.275288\pi$
$602$	−2.78711	+	11.2035i	−0.113594	+	0.456620i
$603$		0			0
$604$	2.39602	+	4.15002i	0.0974925	+	0.168862i
$605$	2.10256	−	11.9242i	0.0854811	−	0.484787i
$606$		0			0
$607$	6.22814	−	17.1117i	0.252792	−	0.694542i	−0.746773	−	0.665079i	$-0.768398\pi$
$607$	6.22814	−	17.1117i	0.252792	−	0.694542i	0.999566	−	0.0294631i	$-0.00937975\pi$
$608$	−11.7434	−	4.27424i	−0.476257	−	0.173343i
$609$		0			0
$610$	−2.50461	+	14.2043i	−0.101409	+	0.575117i
$611$	31.6154	−	18.2532i	1.27902	−	0.738444i
$612$		0			0
$613$	4.24675	−	7.35559i	0.171525	−	0.297089i	−0.767428	−	0.641135i	$-0.778464\pi$
$613$	4.24675	−	7.35559i	0.171525	−	0.297089i	0.938953	+	0.344045i	$0.111797\pi$
$614$	28.5659	+	23.9696i	1.15282	+	0.967334i
$615$		0			0
$616$	−31.9008	+	15.5797i	−1.28532	+	0.627725i
$617$	−4.56438	−	5.43962i	−0.183755	−	0.218991i	0.666301	−	0.745683i	$-0.267877\pi$
$617$	−4.56438	−	5.43962i	−0.183755	−	0.218991i	−0.850056	+	0.526692i	$0.823432\pi$
$618$		0			0
$619$	7.83037	+	21.5138i	0.314729	+	0.864711i	0.991685	+	0.128688i	$0.0410764\pi$
$619$	7.83037	+	21.5138i	0.314729	+	0.864711i	−0.676956	+	0.736023i	$0.736701\pi$
$620$		−	4.37914i		−	0.175870i
$621$		0			0
$622$			31.6872i			1.27054i
$623$	0.683368	+	0.939541i	0.0273786	+	0.0376419i
$624$		0			0
$625$	−1.92597	+	1.61608i	−0.0770387	+	0.0646431i
$626$	−0.386095	−	2.18966i	−0.0154315	−	0.0875163i
$627$		0			0
$628$	−6.52071	+	7.77108i	−0.260205	+	0.310100i
$629$	6.65301	−	11.5234i	0.265273	−	0.459466i
$630$		0			0
$631$	−21.5784	−	37.3748i	−0.859021	−	1.48787i	−0.872863	−	0.487965i	$-0.837740\pi$
$631$	−21.5784	−	37.3748i	−0.859021	−	1.48787i	0.0138420	−	0.999904i	$-0.495594\pi$
$632$	−25.8701	−	4.56160i	−1.02906	−	0.181451i
$633$		0			0
$634$	5.73013	+	2.08560i	0.227572	+	0.0828296i
$635$	−9.83134	−	3.57832i	−0.390145	−	0.142001i
$636$		0			0
$637$	−32.6393	+	13.2269i	−1.29321	+	0.524068i
$638$	−27.0035	+	15.5905i	−1.06908	+	0.617232i
$639$		0			0
$640$	7.27859	+	4.20229i	0.287711	+	0.166110i
$641$	−27.2005	+	32.4163i	−1.07436	+	1.28037i	−0.116478	+	0.993193i	$0.537161\pi$
$641$	−27.2005	+	32.4163i	−1.07436	+	1.28037i	−0.957878	+	0.287175i	$0.907284\pi$
$642$		0			0
$643$	7.14787	−	1.26036i	0.281884	−	0.0497038i	−0.0309184	−	0.999522i	$-0.509843\pi$
$643$	7.14787	−	1.26036i	0.281884	−	0.0497038i	0.312803	+	0.949818i	$0.398732\pi$
$644$	4.16703	−	6.18486i	0.164204	−	0.243717i
$645$		0			0
$646$	−7.65953	+	2.78784i	−0.301360	+	0.109686i
$647$	−30.4657			−1.19773			−0.598865	−	0.800850i	$-0.704381\pi$
$647$	−30.4657			−1.19773			−0.598865	+	0.800850i	$0.704381\pi$
$648$		0			0
$649$		−	23.5964i		−	0.926238i
$650$	16.7071	−	6.08090i	0.655308	−	0.238513i
$651$		0			0
$652$	−2.14136	+	1.79682i	−0.0838623	+	0.0703688i
$653$	14.6823	−	2.58888i	0.574561	−	0.101311i	0.121185	−	0.992630i	$-0.461331\pi$
$653$	14.6823	−	2.58888i	0.574561	−	0.101311i	0.453376	+	0.891319i	$0.350219\pi$
$654$		0			0
$655$	17.3133	+	14.5276i	0.676486	+	0.567639i
$656$	1.89986	−	3.29065i	0.0741769	−	0.128478i
$657$		0			0
$658$	17.0692	+	16.4662i	0.665425	+	0.641921i
$659$	−15.1310	−	2.66800i	−0.589420	−	0.103931i	−0.129019	−	0.991642i	$-0.541183\pi$
$659$	−15.1310	−	2.66800i	−0.589420	−	0.103931i	−0.460400	+	0.887711i	$0.652294\pi$
$660$		0			0
$661$	−13.5122	+	37.1245i	−0.525564	+	1.44398i	0.338679	+	0.940902i	$0.390020\pi$
$661$	−13.5122	+	37.1245i	−0.525564	+	1.44398i	−0.864244	+	0.503074i	$0.832202\pi$
$662$	−5.73485	+	15.7564i	−0.222891	+	0.612389i
$663$		0			0
$664$	−14.6569	−	2.58440i	−0.568797	−	0.100294i
$665$	13.2909	+	12.8214i	0.515399	+	0.497194i
$666$		0			0
$667$	17.0985	−	29.6154i	0.662055	−	1.14671i
$668$	−3.71574	−	3.11788i	−0.143766	−	0.120634i
$669$		0			0
$670$	−7.98836	+	1.40856i	−0.308617	+	0.0544175i
$671$	26.8476	−	22.5278i	1.03644	−	0.869677i
$672$		0			0
$673$	−17.0901	+	6.22029i	−0.658776	+	0.239775i	−0.649708	−	0.760184i	$-0.725109\pi$
$673$	−17.0901	+	6.22029i	−0.658776	+	0.239775i	−0.00906796	+	0.999959i	$0.502886\pi$
$674$		−	28.5912i		−	1.10129i
$675$		0			0
$676$	−5.83362			−0.224370
$677$	12.6704	−	4.61166i	0.486965	−	0.177241i	−0.0868572	−	0.996221i	$-0.527682\pi$
$677$	12.6704	−	4.61166i	0.486965	−	0.177241i	0.573822	+	0.818980i	$0.305460\pi$
$678$		0			0
$679$	−5.50668	+	8.17321i	−0.211327	+	0.313659i
$680$	−6.08669	+	1.07325i	−0.233414	+	0.0411571i
$681$		0			0
$682$	22.0303	−	26.2547i	0.843583	−	1.00534i
$683$	−1.56791	−	0.905232i	−0.0599943	−	0.0346377i	0.469703	−	0.882825i	$-0.344361\pi$
$683$	−1.56791	−	0.905232i	−0.0599943	−	0.0346377i	−0.529697	+	0.848187i	$0.677694\pi$
$684$		0			0
$685$	−9.69871	+	5.59955i	−0.370569	+	0.213948i
$686$	−14.1144	−	18.0072i	−0.538890	−	0.687520i
$687$		0			0
$688$	−9.38599	−	3.41622i	−0.357838	−	0.130242i
$689$	3.83488	+	1.39578i	0.146097	+	0.0531750i
$690$		0			0
$691$	17.8283	+	3.14362i	0.678222	+	0.119589i	0.502140	−	0.864787i	$-0.332546\pi$
$691$	17.8283	+	3.14362i	0.678222	+	0.119589i	0.176083	+	0.984375i	$0.443657\pi$
$692$	−0.551237	−	0.954771i	−0.0209549	−	0.0362949i
$693$		0			0
$694$	−13.9136	+	24.0990i	−0.528152	+	0.914786i
$695$	8.89603	−	10.6019i	0.337446	−	0.402152i
$696$		0			0
$697$	0.322610	+	1.82961i	0.0122197	+	0.0693015i
$698$	30.3566	−	25.4722i	1.14902	−	0.964139i
$699$		0			0
$700$	−2.10939	−	2.90013i	−0.0797273	−	0.109615i
$701$		−	44.5178i		−	1.68141i	−0.541490	−	0.840707i	$-0.682140\pi$
$701$		−	44.5178i		−	1.68141i	0.541490	−	0.840707i	$-0.317860\pi$
$702$		0			0
$703$		−	45.9243i		−	1.73207i
$704$	−13.3514	−	36.6828i	−0.503201	−	1.38253i
$705$		0			0
$706$	1.64041	+	1.95496i	0.0617375	+	0.0735759i
$707$	−37.6693	+	18.3970i	−1.41670	+	0.691889i
$708$		0			0
$709$	−28.5175	−	23.9291i	−1.07100	−	0.898675i	−0.0758564	−	0.997119i	$-0.524169\pi$
$709$	−28.5175	−	23.9291i	−1.07100	−	0.898675i	−0.995143	+	0.0984439i	$0.968614\pi$
$710$	12.1944	−	21.1213i	0.457648	−	0.792670i
$711$		0			0
$712$	−1.16219	+	0.670989i	−0.0435548	+	0.0251464i
$713$	−6.52711	+	37.0171i	−0.244442	+	1.38630i
$714$		0			0
$715$	30.3617	+	11.0508i	1.13546	+	0.413275i
$716$	1.14446	−	3.14437i	0.0427704	−	0.117511i
$717$		0			0
$718$	1.38252	−	7.84067i	0.0515952	−	0.292611i
$719$	22.9381	+	39.7300i	0.855447	+	1.48168i	0.876230	+	0.481894i	$0.160051\pi$
$719$	22.9381	+	39.7300i	0.855447	+	1.48168i	−0.0207825	+	0.999784i	$0.506616\pi$
$720$		0			0
$721$	3.53806	−	14.2221i	0.131764	−	0.529659i
$722$	−2.99562	+	3.57004i	−0.111485	+	0.132863i
$723$		0			0
$724$	7.37229	−	1.29993i	0.273989	−	0.0483117i
$725$	−10.5701	−	12.5969i	−0.392562	−	0.467837i
$726$		0			0
$727$	−3.02410	−	8.30865i	−0.112158	−	0.308151i	0.870896	−	0.491467i	$-0.163539\pi$
$727$	−3.02410	−	8.30865i	−0.112158	−	0.308151i	−0.983054	+	0.183316i	$0.941317\pi$
$728$	−11.2334	−	39.0982i	−0.416337	−	1.44908i
$729$		0			0
$730$	13.0000			0.481151
$731$	4.58920	−	1.67033i	0.169738	−	0.0617795i
$732$		0			0
$733$	2.71245	+	3.23257i	0.100187	+	0.119398i	0.813808	−	0.581134i	$-0.197391\pi$
$733$	2.71245	+	3.23257i	0.100187	+	0.119398i	−0.713621	+	0.700532i	$0.752946\pi$
$734$	3.00964	+	17.0685i	0.111088	+	0.630009i
$735$		0			0
$736$	11.9341	+	10.0139i	0.439895	+	0.369116i
$737$	17.0694	+	9.85504i	0.628760	+	0.363015i
$738$		0			0
$739$	23.4859	+	40.6787i	0.863941	+	1.49639i	0.868095	+	0.496398i	$0.165344\pi$
$739$	23.4859	+	40.6787i	0.863941	+	1.49639i	−0.00415394	+	0.999991i	$0.501322\pi$
$740$	1.15818	−	6.56839i	0.0425757	−	0.241459i
$741$		0			0
$742$	−0.183560	+	2.64492i	−0.00673869	+	0.0970981i
$743$	−7.59281	+	20.8611i	−0.278553	+	0.765319i	0.718974	+	0.695037i	$0.244612\pi$
$743$	−7.59281	+	20.8611i	−0.278553	+	0.765319i	−0.997527	+	0.0702816i	$0.977610\pi$
$744$		0			0
$745$	25.9990	+	4.58432i	0.952529	+	0.167957i
$746$	20.1723	−	11.6465i	0.738562	−	0.426409i
$747$		0			0
$748$	2.49112	+	1.43825i	0.0910843	+	0.0525875i
$749$	−6.92745	−	3.07995i	−0.253123	−	0.112539i
$750$		0			0
$751$	−1.64819	−	9.34735i	−0.0601433	−	0.341090i	0.939857	−	0.341569i	$-0.110958\pi$
$751$	−1.64819	−	9.34735i	−0.0601433	−	0.341090i	−1.00000		0.000479731i	$0.999847\pi$
$752$	−15.7186	+	13.1895i	−0.573200	+	0.480972i
$753$		0			0
$754$	−12.2199	−	33.5740i	−0.445024	−	1.22269i
$755$	14.7927			0.538360
$756$		0			0
$757$	39.9101			1.45056			0.725279	−	0.688456i	$-0.241711\pi$
$757$	39.9101			1.45056			0.725279	+	0.688456i	$0.241711\pi$
$758$	0.505801	+	1.38968i	0.0183715	+	0.0504753i
$759$		0			0
$760$	−16.3410	+	13.7117i	−0.592749	+	0.497375i
$761$	0.165785	+	0.940211i	0.00600969	+	0.0340826i	0.987665	−	0.156581i	$-0.0500472\pi$
$761$	0.165785	+	0.940211i	0.00600969	+	0.0340826i	−0.981655	+	0.190663i	$0.938936\pi$
$762$		0			0
$763$	14.5694	−	32.7696i	0.527449	−	1.18634i
$764$	5.06733	+	2.92563i	0.183330	+	0.105845i
$765$		0			0
$766$	−1.23520	+	0.713143i	−0.0446296	+	0.0257669i
$767$	26.6272	+	4.69509i	0.961451	+	0.169530i
$768$		0			0
$769$	15.5790	−	42.8029i	0.561792	−	1.54351i	−0.255216	−	0.966884i	$-0.582146\pi$
$769$	15.5790	−	42.8029i	0.561792	−	1.54351i	0.817008	−	0.576627i	$-0.195631\pi$
$770$	−1.45329	+	20.9405i	−0.0523729	+	0.754643i
$771$		0			0
$772$	−0.270497	+	1.53406i	−0.00973538	+	0.0552121i
$773$	−24.2021	−	41.9192i	−0.870488	−	1.50773i	−0.861492	−	0.507771i	$-0.830470\pi$
$773$	−24.2021	−	41.9192i	−0.870488	−	1.50773i	−0.00899604	−	0.999960i	$-0.502864\pi$
$774$		0			0
$775$	15.6532	+	9.03739i	0.562280	+	0.324633i
$776$	−8.72050	−	7.31737i	−0.313048	−	0.262678i
$777$		0			0
$778$	7.26900	+	41.2245i	0.260606	+	1.47797i
$779$	4.12163	+	4.91197i	0.147673	+	0.175990i
$780$		0			0
$781$	−55.6877	+	20.2686i	−1.99266	+	0.725269i
$782$	10.1612			0.363362
$783$		0			0
$784$	16.7760	−	10.5072i	0.599141	−	0.375258i
$785$	10.7104	+	29.4266i	0.382270	+	1.05028i
$786$		0			0
$787$	1.37685	+	1.64087i	0.0490795	+	0.0584906i	0.790026	−	0.613074i	$-0.210067\pi$
$787$	1.37685	+	1.64087i	0.0490795	+	0.0584906i	−0.740946	+	0.671564i	$0.765623\pi$
$788$	−5.19382	+	0.915811i	−0.185022	+	0.0326244i
$789$		0			0
$790$	−9.98372	+	11.8981i	−0.355205	+	0.423317i
$791$	6.52973	−	26.2478i	0.232170	−	0.933265i
$792$		0			0
$793$	20.0794	+	34.7785i	0.713040	+	1.23502i
$794$	5.09326	−	28.8853i	0.180753	−	1.02510i
$795$		0			0
$796$	1.59248	−	4.37530i	0.0564439	−	0.155078i
$797$	−0.360086	−	0.131061i	−0.0127549	−	0.00464241i	0.335635	−	0.941992i	$-0.391049\pi$
$797$	−0.360086	−	0.131061i	−0.0127549	−	0.00464241i	−0.348390	+	0.937350i	$0.613271\pi$
$798$		0			0
$799$	1.74216	−	9.88029i	0.0616332	−	0.349539i
$800$	6.48765	−	3.74565i	0.229373	−	0.132429i
$801$		0			0
$802$	14.0664	−	24.3638i	0.496703	−	0.860315i
$803$	−24.1980	−	20.3045i	−0.853928	−	0.716531i
$804$		0			0
$805$	−10.1027	−	20.6861i	−0.356072	−	0.729088i
$806$	25.2434	+	30.0839i	0.889162	+	1.05966i
$807$		0			0
$808$	−16.5620	−	45.5037i	−0.582649	−	1.60081i
$809$		−	9.37609i		−	0.329646i	−0.986323	−	0.164823i	$-0.947295\pi$
$809$		−	9.37609i		−	0.329646i	0.986323	−	0.164823i	$-0.0527052\pi$
$810$		0			0
$811$			10.9268i			0.383692i	0.981425	+	0.191846i	$0.0614474\pi$
$811$			10.9268i			0.383692i	−0.981425	+	0.191846i	$0.938553\pi$
$812$	−5.82798	+	4.23894i	−0.204522	+	0.148758i
$813$		0			0
$814$	39.9876	−	33.5536i	1.40157	−	1.17605i
$815$	1.49842	+	8.49796i	0.0524873	+	0.297670i
$816$		0			0
$817$	10.8346	−	12.9122i	0.379055	−	0.451740i
$818$	14.5489	−	25.1994i	0.508690	−	0.881077i
$819$		0			0
$820$	0.465626	+	0.806487i	0.0162604	+	0.0281638i
$821$	38.4318	+	6.77656i	1.34128	+	0.236504i	0.797801	−	0.602920i	$-0.205996\pi$
$821$	38.4318	+	6.77656i	1.34128	+	0.236504i	0.543477	+	0.839424i	$0.317107\pi$
$822$		0			0
$823$	−14.4443	−	5.25731i	−0.503498	−	0.183258i	0.0777686	−	0.996971i	$-0.475220\pi$
$823$	−14.4443	−	5.25731i	−0.503498	−	0.183258i	−0.581267	+	0.813713i	$0.697443\pi$
$824$	15.9078	+	5.78998i	0.554176	+	0.201704i
$825$		0			0
$826$	1.84525	+	17.4684i	0.0642045	+	0.607805i
$827$	21.5267	−	12.4285i	0.748558	−	0.432180i	−0.0766147	−	0.997061i	$-0.524411\pi$
$827$	21.5267	−	12.4285i	0.748558	−	0.432180i	0.825173	+	0.564881i	$0.191078\pi$
$828$		0			0
$829$	−40.8365	−	23.5770i	−1.41831	−	0.818862i	−0.422160	−	0.906521i	$-0.638728\pi$
$829$	−40.8365	−	23.5770i	−1.41831	−	0.818862i	−0.996150	+	0.0876596i	$0.972061\pi$
$830$	−5.65634	+	6.74097i	−0.196335	+	0.233982i
$831$		0			0
$832$	44.0511	−	7.76739i	1.52720	−	0.269286i
$833$	−2.98119	+	9.20793i	−0.103292	+	0.319036i
$834$		0			0
$835$	−14.0703	+	5.12117i	−0.486923	+	0.177225i
$836$	9.92791			0.343364
$837$		0			0
$838$			32.5296i			1.12372i
$839$	6.72893	−	2.44913i	0.232309	−	0.0845534i	−0.223243	−	0.974763i	$-0.571664\pi$
$839$	6.72893	−	2.44913i	0.232309	−	0.0845534i	0.455551	+	0.890209i	$0.349442\pi$
$840$		0			0
$841$	−3.09894	+	2.60032i	−0.106860	+	0.0896661i
$842$	−12.3076	+	2.17016i	−0.424147	+	0.0747885i
$843$		0			0
$844$	0.734343	+	0.616187i	0.0252771	+	0.0212100i
$845$	−9.00399	+	15.5954i	−0.309747	+	0.536497i
$846$		0			0
$847$	15.2060	−	15.7628i	0.522484	−	0.541615i
$848$	−2.25897	−	0.398317i	−0.0775732	−	0.0136783i
$849$		0			0
$850$	1.67116	−	4.59147i	0.0573203	−	0.157486i
$851$	−19.5804	+	53.7967i	−0.671207	+	1.84413i
$852$		0			0
$853$	5.45780	+	0.962357i	0.186871	+	0.0329505i	0.266301	−	0.963890i	$-0.414199\pi$
$853$	5.45780	+	0.962357i	0.186871	+	0.0329505i	−0.0794291	+	0.996841i	$0.525310\pi$
$854$	−18.1137	+	18.7769i	−0.619837	+	0.642533i
$855$		0			0
$856$	4.37859	−	7.58394i	0.149657	−	0.259214i
$857$	38.9684	+	32.6983i	1.33113	+	1.11695i	0.983811	+	0.179208i	$0.0573535\pi$
$857$	38.9684	+	32.6983i	1.33113	+	1.11695i	0.347322	+	0.937746i	$0.387091\pi$
$858$		0			0
$859$	−9.91290	+	1.74791i	−0.338224	+	0.0596380i	−0.340181	−	0.940360i	$-0.610488\pi$
$859$	−9.91290	+	1.74791i	−0.338224	+	0.0596380i	0.00195691	+	0.999998i	$0.499377\pi$
$860$	1.87527	−	1.57354i	0.0639463	−	0.0536573i
$861$		0			0
$862$	3.72964	−	1.35748i	0.127032	−	0.0462359i
$863$		−	51.7414i		−	1.76130i	−0.473768	−	0.880649i	$-0.657107\pi$
$863$		−	51.7414i		−	1.76130i	0.473768	−	0.880649i	$-0.342893\pi$
$864$		0			0
$865$	−3.40326			−0.115714
$866$	−17.9918	+	6.54847i	−0.611386	+	0.222526i
$867$		0			0
$868$	4.42603	−	6.56927i	0.150229	−	0.222975i
$869$	37.1671	−	6.55356i	1.26081	−	0.222314i
$870$		0			0
$871$	−14.5172	+	17.3010i	−0.491898	+	0.586221i
$872$	35.8751	+	20.7125i	1.21488	+	0.701414i
$873$		0			0
$874$	30.3716	−	17.5351i	1.02734	−	0.593133i
$875$	−30.2512	+	3.19553i	−1.02268	+	0.108029i
$876$		0			0
$877$	−5.63056	−	2.04936i	−0.190131	−	0.0692019i	0.245200	−	0.969472i	$-0.421146\pi$
$877$	−5.63056	−	2.04936i	−0.190131	−	0.0692019i	−0.435331	+	0.900271i	$0.643369\pi$
$878$	−28.4009	−	10.3371i	−0.958485	−	0.348860i
$879$		0			0
$880$	−17.8848	−	3.15357i	−0.602897	−	0.106307i
$881$	28.7112	+	49.7293i	0.967306	+	1.67542i	0.703288	+	0.710905i	$0.251714\pi$
$881$	28.7112	+	49.7293i	0.967306	+	1.67542i	0.264017	+	0.964518i	$0.414952\pi$
$882$		0			0
$883$	−26.5130	+	45.9219i	−0.892235	+	1.54540i	−0.0550448	+	0.998484i	$0.517530\pi$
$883$	−26.5130	+	45.9219i	−0.892235	+	1.54540i	−0.837190	+	0.546912i	$0.815803\pi$
$884$	−2.11865	+	2.52491i	−0.0712580	+	0.0849220i
$885$		0			0
$886$	−7.33233	−	41.5837i	−0.246334	−	1.39703i
$887$	−10.9003	+	9.14647i	−0.365997	+	0.307108i	−0.807176	−	0.590311i	$-0.799005\pi$
$887$	−10.9003	+	9.14647i	−0.365997	+	0.307108i	0.441178	+	0.897419i	$0.354561\pi$
$888$		0			0
$889$	−11.1316	−	15.3045i	−0.373343	−	0.513298i
$890$			0.793458i			0.0265968i
$891$		0			0
$892$			10.4047i			0.348375i
$893$	−11.8431	−	32.5385i	−0.396313	−	1.08886i
$894$		0			0
$895$	−6.63960	−	7.91277i	−0.221937	−	0.264495i
$896$	6.67153	+	13.6605i	0.222880	+	0.456365i
$897$		0			0
$898$	−10.6233	−	8.91400i	−0.354504	−	0.297464i
$899$	18.1612	−	31.4561i	0.605709	−	1.04912i
$900$		0			0
$901$	0.971284	−	0.560771i	0.0323582	−	0.0186820i
$902$	−1.26561	+	7.17765i	−0.0421403	+	0.238990i
$903$		0			0
$904$	29.3590	+	10.6858i	0.976464	+	0.355404i
$905$	7.90368	−	21.7152i	0.262727	−	0.721837i
$906$		0			0
$907$	7.77690	−	44.1050i	0.258228	−	1.46448i	−0.529422	−	0.848359i	$-0.677591\pi$
$907$	7.77690	−	44.1050i	0.258228	−	1.46448i	0.787649	−	0.616124i	$-0.211298\pi$
$908$	−1.60439	−	2.77889i	−0.0532436	−	0.0922207i
$909$		0			0
$910$	−23.3410	−	5.80659i	−0.773747	−	0.192487i
$911$	−24.5858	+	29.3003i	−0.814565	+	0.970761i	−0.999929	−	0.0119092i	$-0.996209\pi$
$911$	−24.5858	+	29.3003i	−0.814565	+	0.970761i	0.185364	+	0.982670i	$0.440654\pi$
$912$		0			0
$913$	21.0573	−	3.71297i	0.696894	−	0.122881i
$914$	20.3533	+	24.2561i	0.673226	+	0.802319i
$915$		0			0
$916$	−1.33586	−	3.67026i	−0.0441382	−	0.121269i
$917$	11.2890	+	39.2919i	0.372797	+	1.29753i
$918$		0			0
$919$	−39.5867			−1.30584			−0.652922	−	0.757425i	$-0.726457\pi$
$919$	−39.5867			−1.30584			−0.652922	+	0.757425i	$0.726457\pi$
$920$	24.9883	−	9.09499i	0.823840	−	0.299853i
$921$		0			0
$922$	−15.5550	−	18.5377i	−0.512275	−	0.610506i
$923$	−11.7916	−	66.8734i	−0.388124	−	2.20116i
$924$		0			0
$925$	21.0885	+	17.6954i	0.693387	+	0.581820i
$926$	−7.55103	−	4.35959i	−0.248142	−	0.143265i
$927$		0			0
$928$	−7.52710	−	13.0373i	−0.247089	−	0.427971i
$929$	9.95917	−	56.4812i	0.326750	−	1.85309i	−0.170333	−	0.985387i	$-0.554484\pi$
$929$	9.95917	−	56.4812i	0.326750	−	1.85309i	0.497083	−	0.867703i	$-0.334404\pi$
$930$		0			0
$931$	6.97935	+	32.6671i	0.228739	+	1.07062i
$932$	−1.47379	+	4.04920i	−0.0482756	+	0.132636i
$933$		0			0
$934$	16.3801	+	2.88826i	0.535975	+	0.0945068i
$935$	7.68990	−	4.43977i	0.251487	−	0.145196i
$936$		0			0
$937$	22.4359	+	12.9533i	0.732948	+	0.423167i	0.819500	−	0.573080i	$-0.194252\pi$
$937$	22.4359	+	12.9533i	0.732948	+	0.423167i	−0.0865519	+	0.996247i	$0.527585\pi$
$938$	−13.4072	−	5.96087i	−0.437761	−	0.194629i
$939$		0			0
$940$	−0.873268	−	4.95255i	−0.0284829	−	0.161534i
$941$	−15.8590	+	13.3072i	−0.516987	+	0.433804i	−0.863580	−	0.504212i	$-0.831783\pi$
$941$	−15.8590	+	13.3072i	−0.516987	+	0.433804i	0.346593	+	0.938016i	$0.387339\pi$
$942$		0			0
$943$	−2.73389	−	7.51129i	−0.0890276	−	0.244601i
$944$	−15.1973			−0.494630
$945$		0			0
$946$	19.1591			0.622916
$947$	−8.96478	−	24.6305i	−0.291316	−	0.800385i	−0.995875	−	0.0907390i	$-0.971077\pi$
$947$	−8.96478	−	24.6305i	−0.291316	−	0.800385i	0.704558	−	0.709646i	$-0.251145\pi$
$948$		0			0
$949$	27.7273	−	23.2660i	0.900066	−	0.755245i
$950$	−2.92840	−	16.6078i	−0.0950099	−	0.538828i
$951$		0			0
$952$	−10.2156	−	4.54185i	−0.331088	−	0.147202i
$953$	−30.8895	−	17.8340i	−1.00061	−	0.577701i	−0.0921795	−	0.995742i	$-0.529383\pi$
$953$	−30.8895	−	17.8340i	−1.00061	−	0.577701i	−0.908428	+	0.418041i	$0.862717\pi$
$954$		0			0
$955$	15.6425	−	9.03119i	0.506179	−	0.292243i
$956$	−1.67369	−	0.295117i	−0.0541310	−	0.00954475i
$957$		0			0
$958$	10.8236	−	29.7377i	0.349695	−	0.960780i
$959$	−20.2088	−	1.40251i	−0.652577	−	0.0452894i
$960$		0			0
$961$	−1.54969	+	8.78876i	−0.0499902	+	0.283508i
$962$	29.9068	+	51.8001i	0.964234	+	1.67010i
$963$		0			0
$964$	−5.50906	−	3.18066i	−0.177435	−	0.102442i
$965$	3.68359	+	3.09090i	0.118579	+	0.0994997i
$966$		0			0
$967$	3.02065	+	17.1310i	0.0971377	+	0.550895i	0.994071	+	0.108730i	$0.0346784\pi$
$967$	3.02065	+	17.1310i	0.0971377	+	0.550895i	−0.896934	+	0.442165i	$0.854210\pi$
$968$	16.2618	+	19.3800i	0.522674	+	0.622898i
$969$		0			0
$970$	−6.32487	+	2.30206i	−0.203079	+	0.0739148i
$971$	−48.7070			−1.56308			−0.781540	−	0.623855i	$-0.785566\pi$
$971$	−48.7070			−1.56308			−0.781540	+	0.623855i	$0.785566\pi$
$972$		0			0
$973$	24.0606	−	6.91290i	0.771347	−	0.221617i
$974$	−3.08623	−	8.47934i	−0.0988891	−	0.271696i
$975$		0			0
$976$	−14.5091	−	17.2913i	−0.464425	−	0.553480i
$977$	−18.0628	+	3.18497i	−0.577881	+	0.101896i	−0.454947	−	0.890519i	$-0.650342\pi$
$977$	−18.0628	+	3.18497i	−0.577881	+	0.101896i	−0.122935	+	0.992415i	$0.539231\pi$
$978$		0			0
$979$	1.23929	−	1.47693i	0.0396080	−	0.0472029i
$980$	0.174387	+	4.84827i	0.00557058	+	0.154872i
$981$		0			0
$982$	−13.3027	−	23.0409i	−0.424505	−	0.735265i
$983$	−1.43166	+	8.11934i	−0.0456628	+	0.258967i	−0.999090	−	0.0426573i	$-0.986418\pi$
$983$	−1.43166	+	8.11934i	−0.0456628	+	0.258967i	0.953427	+	0.301624i	$0.0975287\pi$
$984$		0			0
$985$	−5.56819	+	15.2985i	−0.177417	+	0.487450i
$986$	−9.22684	−	3.35830i	−0.293842	−	0.106950i
$987$		0			0
$988$	−1.97541	+	11.2031i	−0.0628461	+	0.356418i
$989$	−18.1972	+	10.5061i	−0.578636	+	0.334076i
$990$		0			0
$991$	8.03577	−	13.9184i	0.255265	−	0.442131i	−0.709703	−	0.704501i	$-0.751171\pi$
$991$	8.03577	−	13.9184i	0.255265	−	0.442131i	0.964967	+	0.262370i	$0.0845040\pi$
$992$	12.6758	+	10.6363i	0.402457	+	0.337702i
$993$		0			0
$994$	39.6407	−	19.3597i	1.25733	−	0.614054i
$995$	−9.23880	−	11.0104i	−0.292890	−	0.349052i
$996$		0			0
$997$	20.2279	+	55.5756i	0.640623	+	1.76010i	0.649760	+	0.760139i	$0.274869\pi$
$997$	20.2279	+	55.5756i	0.640623	+	1.76010i	−0.00913679	+	0.999958i	$0.502908\pi$
$998$		−	34.5078i		−	1.09232i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.62.15		132
3.2	odd	2		189.2.be.a.20.7	✓	132
7.6	odd	2	inner	567.2.be.a.62.16		132
21.20	even	2		189.2.be.a.20.8	yes	132
27.4	even	9		189.2.be.a.104.8	yes	132
27.23	odd	18	inner	567.2.be.a.503.16		132
189.104	even	18	inner	567.2.be.a.503.15		132
189.139	odd	18		189.2.be.a.104.7	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.7	✓	132	3.2	odd	2
189.2.be.a.20.8	yes	132	21.20	even	2
189.2.be.a.104.7	yes	132	189.139	odd	18
189.2.be.a.104.8	yes	132	27.4	even	9
567.2.be.a.62.15		132	1.1	even	1	trivial
567.2.be.a.62.16		132	7.6	odd	2	inner
567.2.be.a.503.15		132	189.104	even	18	inner
567.2.be.a.503.16		132	27.23	odd	18	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(-0.253991 - 1.44045i) q^{5} +(1.07486 - 2.41758i) q^{7} +(2.64668 + 1.52806i) q^{8} +(1.56488 - 0.903482i) q^{10} +(-4.32398 - 0.762434i) q^{11} +(1.72073 - 4.72766i) q^{13} +(3.26067 + 0.226294i) q^{14} +(-0.491047 + 2.78487i) q^{16} +(-0.691322 - 1.19740i) q^{17} +(-4.13271 - 2.38602i) q^{19} +(-0.530913 - 0.445489i) q^{20} +(-0.941898 - 5.34177i) q^{22} +(3.82383 + 4.55707i) q^{23} +(2.68807 - 0.978376i) q^{25} +6.21530 q^{26} +(-0.346179 - 1.20489i) q^{28} +(-1.96611 - 5.40183i) q^{29} +(4.06150 + 4.84031i) q^{31} +(2.57902 - 0.454750i) q^{32} +(1.09794 - 1.30848i) q^{34} +(-3.75541 - 0.934242i) q^{35} +(4.81181 + 8.33429i) q^{37} +(1.02371 - 5.80574i) q^{38} +(1.52887 - 4.20054i) q^{40} +(-1.26265 - 0.459567i) q^{41} +(-0.613355 + 3.47851i) q^{43} +(-1.80171 + 1.04022i) q^{44} +(-3.67454 + 6.36449i) q^{46} +(5.55855 + 4.66418i) q^{47} +(-4.68936 - 5.19711i) q^{49} +(2.27156 + 2.70713i) q^{50} +(-0.815330 - 2.24010i) q^{52} +0.811158i q^{53} +6.42214i q^{55} +(6.53902 - 4.75611i) q^{56} +(5.44015 - 4.56483i) q^{58} +(0.933219 + 5.29255i) q^{59} +(-5.13083 + 6.11468i) q^{61} +(-3.90293 + 6.76007i) q^{62} +(4.44544 + 7.69973i) q^{64} +(-7.24703 - 1.27785i) q^{65} +(-4.21835 - 1.53535i) q^{67} +(-0.615627 - 0.224070i) q^{68} +(-0.502216 - 4.75433i) q^{70} +(11.6889 - 6.74856i) q^{71} +(6.23051 + 3.59719i) q^{73} +(-7.64200 + 9.10738i) q^{74} +(-2.22678 + 0.392641i) q^{76} +(-6.49091 + 9.63404i) q^{77} +(-8.07721 + 2.93986i) q^{79} +4.13619 q^{80} -1.65997i q^{82} +(-4.57620 + 1.66560i) q^{83} +(-1.54922 + 1.29995i) q^{85} +(-4.29729 + 0.757728i) q^{86} +(-10.2791 - 8.62523i) q^{88} +(-0.219556 + 0.380281i) q^{89} +(-9.57994 - 9.24156i) q^{91} +(2.77590 + 0.489467i) q^{92} +(-3.06592 + 8.42355i) q^{94} +(-2.38728 + 6.55901i) q^{95} +(-3.66832 - 0.646825i) q^{97} +(4.05185 - 7.63969i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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