LMFDB - Embedded newform 567.2.be.a.62.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(62,567)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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			62.16
Character	$\chi$	$=$	567.62
Dual form			567.2.be.a.503.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(0.253991 + 1.44045i) q^{5} +(-2.19420 + 1.47834i) q^{7} +(2.64668 + 1.52806i) q^{8} +O(q^{10})$	\(q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(0.253991 + 1.44045i) q^{5} +(-2.19420 + 1.47834i) q^{7} +(2.64668 + 1.52806i) q^{8} +(-1.56488 + 0.903482i) q^{10} +(-4.32398 - 0.762434i) q^{11} +(-1.72073 + 4.72766i) q^{13} +(-2.64328 - 1.92257i) q^{14} +(-0.491047 + 2.78487i) q^{16} +(0.691322 + 1.19740i) q^{17} +(4.13271 + 2.38602i) q^{19} +(0.530913 + 0.445489i) q^{20} +(-0.941898 - 5.34177i) q^{22} +(3.82383 + 4.55707i) q^{23} +(2.68807 - 0.978376i) q^{25} -6.21530 q^{26} +(-0.346179 + 1.20489i) q^{28} +(-1.96611 - 5.40183i) q^{29} +(-4.06150 - 4.84031i) q^{31} +(2.57902 - 0.454750i) q^{32} +(-1.09794 + 1.30848i) q^{34} +(-2.68678 - 2.78516i) q^{35} +(4.81181 + 8.33429i) q^{37} +(-1.02371 + 5.80574i) q^{38} +(-1.52887 + 4.20054i) q^{40} +(1.26265 + 0.459567i) q^{41} +(-0.613355 + 3.47851i) q^{43} +(-1.80171 + 1.04022i) q^{44} +(-3.67454 + 6.36449i) q^{46} +(-5.55855 - 4.66418i) q^{47} +(2.62904 - 6.48754i) q^{49} +(2.27156 + 2.70713i) q^{50} +(0.815330 + 2.24010i) q^{52} +0.811158i q^{53} -6.42214i q^{55} +(-8.06635 + 0.559812i) q^{56} +(5.44015 - 4.56483i) q^{58} +(-0.933219 - 5.29255i) q^{59} +(5.13083 - 6.11468i) q^{61} +(3.90293 - 6.76007i) q^{62} +(4.44544 + 7.69973i) q^{64} +(-7.24703 - 1.27785i) q^{65} +(-4.21835 - 1.53535i) q^{67} +(0.615627 + 0.224070i) q^{68} +(2.09800 - 4.29584i) q^{70} +(11.6889 - 6.74856i) q^{71} +(-6.23051 - 3.59719i) q^{73} +(-7.64200 + 9.10738i) q^{74} +(2.22678 - 0.392641i) q^{76} +(10.6148 - 4.71936i) q^{77} +(-8.07721 + 2.93986i) q^{79} -4.13619 q^{80} +1.65997i q^{82} +(4.57620 - 1.66560i) q^{83} +(-1.54922 + 1.29995i) q^{85} +(-4.29729 + 0.757728i) q^{86} +(-10.2791 - 8.62523i) q^{88} +(0.219556 - 0.380281i) q^{89} +(-3.21345 - 12.9173i) q^{91} +(2.77590 + 0.489467i) q^{92} +(3.06592 - 8.42355i) q^{94} +(-2.38728 + 6.55901i) q^{95} +(3.66832 + 0.646825i) q^{97} +(8.64209 + 0.310846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.0505038\pi$
$5$	0.253991	+	1.44045i	0.113588	+	0.644191i	−0.873851	+	0.486193i	$0.838385\pi$
$6$		0			0
$7$	−2.19420	+	1.47834i	−0.829330	+	0.558759i
$7$	−2.19420	+	1.47834i	−0.829330	+	0.558759i
$8$	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	$0.356897\pi$
$13$	−1.72073	+	4.72766i	−0.477244	+	1.31122i	−0.911823	+	0.410583i	$0.865325\pi$
$14$	−2.64328	−	1.92257i	−0.706446	−	0.513828i
$15$		0			0
$16$	−0.491047	+	2.78487i	−0.122762	+	0.696217i
$17$	0.691322	+	1.19740i	0.167670	+	0.290413i	0.937600	−	0.347715i	$-0.113042\pi$
$17$	0.691322	+	1.19740i	0.167670	+	0.290413i	−0.769930	+	0.638128i	$0.779709\pi$
$18$		0			0
$19$	4.13271	+	2.38602i	0.948109	+	0.547391i	0.892493	−	0.451061i	$-0.148954\pi$
$19$	4.13271	+	2.38602i	0.948109	+	0.547391i	0.0556159	+	0.998452i	$0.482288\pi$
$20$	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	0.266047	−	0.963960i	$-0.414282\pi$
$31$	−4.06150	−	4.84031i	−0.729467	−	0.869345i	−0.995514	+	0.0946154i	$0.969838\pi$
$32$	2.57902	−	0.454750i	0.455910	−	0.0803892i
$33$		0			0
$34$	−1.09794	+	1.30848i	−0.188295	+	0.224402i
$35$	−2.68678	−	2.78516i	−0.454149	−	0.470778i
$36$		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	0.438729	−	0.898620i	$-0.355429\pi$
$41$	1.26265	+	0.459567i	0.197193	+	0.0717724i	−0.241536	+	0.970392i	$0.577651\pi$
$42$		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	0.140000	−	0.990152i	$-0.455290\pi$
$47$	−5.55855	−	4.66418i	−0.810798	−	0.680341i	−0.950798	+	0.309811i	$0.899734\pi$
$48$		0			0
$49$	2.62904	−	6.48754i	0.375577	−	0.926791i
$50$	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
$56$	−8.06635	+	0.559812i	−1.07791	+	0.0748080i
$57$		0			0
$58$	5.44015	−	4.56483i	0.714327	−	0.599391i
$59$	−0.933219	−	5.29255i	−0.121495	−	0.689031i	−0.983328	−	0.181839i	$-0.941795\pi$
$59$	−0.933219	−	5.29255i	−0.121495	−	0.689031i	0.861834	−	0.507191i	$-0.169316\pi$
$60$		0			0
$61$	5.13083	−	6.11468i	0.656935	−	0.782905i	−0.330007	−	0.943978i	$-0.607051\pi$
$61$	5.13083	−	6.11468i	0.656935	−	0.782905i	0.986942	+	0.161073i	$0.0514956\pi$
$62$	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
$70$	2.09800	−	4.29584i	0.250759	−	0.513451i
$71$	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	0.0889127	−	0.996039i	$-0.471661\pi$
$73$	−6.23051	−	3.59719i	−0.729226	−	0.421019i	−0.818139	+	0.575020i	$0.804994\pi$
$74$	−7.64200	+	9.10738i	−0.888365	+	1.05871i
$75$		0			0
$76$	2.22678	−	0.392641i	0.255429	−	0.0450391i
$77$	10.6148	−	4.71936i	1.20967	−	0.537821i
$78$		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	−0.0784266	−	0.996920i	$-0.524990\pi$
$83$	4.57620	−	1.66560i	0.502303	−	0.182823i	0.580729	+	0.814097i	$0.302767\pi$
$84$		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	−0.854154	−	0.520019i	$-0.825925\pi$
$89$	0.219556	−	0.380281i	0.0232728	−	0.0403097i	0.877427	+	0.479710i	$0.159258\pi$
$90$		0			0
$91$	−3.21345	−	12.9173i	−0.336861	−	1.35410i
$92$	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	0.356746	−	0.934201i	$-0.383886\pi$
$97$	3.66832	+	0.646825i	0.372462	+	0.0656751i	0.0157159	+	0.999876i	$0.494997\pi$
$98$	8.64209	+	0.310846i	0.872983	+	0.0314002i
$99$		0			0
$100$	0.677713	−	1.17383i	0.0677713	−	0.117383i
$101$	12.1379	+	10.1849i	1.20777	+	1.01344i	0.999374	+	0.0353913i	$0.0112677\pi$
$101$	12.1379	+	10.1849i	1.20777	+	1.01344i	0.208393	+	0.978045i	$0.433177\pi$
$102$		0			0
$103$	−5.45514	+	0.961888i	−0.537511	+	0.0947776i	−0.435812	−	0.900038i	$-0.643539\pi$
$103$	−5.45514	+	0.961888i	−0.537511	+	0.0947776i	−0.101698	+	0.994815i	$0.532428\pi$
$104$	−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
$112$	−3.03952	−	6.83649i	−0.287207	−	0.645988i
$113$	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
$119$	−3.28707	−	1.60534i	−0.301325	−	0.147161i
$120$		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	0.0428368	−	0.999082i	$-0.486360\pi$
$131$	11.8367	−	9.93219i	1.03418	−	0.867779i	0.991342	+	0.131303i	$0.0419160\pi$
$132$		0			0
$133$	−12.5953	+	0.874128i	−1.09215	+	0.0757965i
$134$		−	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	0.443728	−	0.896161i	$-0.353656\pi$
$139$	−6.08203	−	7.24828i	−0.515871	−	0.614791i	−0.959599	+	0.281370i	$0.909211\pi$
$140$	−1.82351	−	0.192624i	−0.154115	−	0.0162797i
$141$		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
$154$	9.96365	+	10.3285i	0.802893	+	0.832292i
$155$	5.94065	−	7.07980i	0.477165	−	0.568663i
$156$		0			0
$157$	21.0842	−	3.71772i	1.68270	−	0.296706i	0.751101	−	0.660187i	$-0.229523\pi$
$157$	21.0842	−	3.71772i	1.68270	−	0.296706i	0.931602	+	0.363481i	$0.118412\pi$
$158$	−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	$0.0740737\pi$
$167$	1.77762	+	10.0814i	0.137557	+	0.780123i	−0.835488	+	0.549508i	$0.814815\pi$
$168$		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	−0.996307	−	0.0858621i	$-0.972636\pi$
$173$	−0.404033	+	2.29139i	−0.0307181	+	0.174211i	0.965589	+	0.260073i	$0.0837466\pi$
$174$		0			0
$175$	−4.45179	+	6.12062i	−0.336524	+	0.462676i
$176$	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	−0.103766	−	0.994602i	$-0.533089\pi$
$181$	−13.6823	−	7.89950i	−1.01700	−	0.587165i	−0.913234	+	0.407436i	$0.866423\pi$
$182$	13.6376	−	9.18831i	1.01089	−	0.681083i
$183$		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
$196$	−1.02165	−	3.15554i	−0.0729747	−	0.225396i
$197$	−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	−0.770323	−	0.637654i	$-0.779905\pi$
$199$	−8.51003	+	4.91327i	−0.603260	+	0.348292i	0.167063	+	0.985946i	$0.446572\pi$
$200$	8.60948	+	1.51808i	0.608782	+	0.107345i
$201$		0			0
$202$	−6.69488	+	18.3940i	−0.471050	+	1.29420i
$203$	12.2998	+	8.94614i	0.863274	+	0.627896i
$204$		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	$-0.514850\pi$
$223$	14.1148	−	16.8214i	0.945198	−	1.12644i	0.991835	−	0.127531i	$-0.0407053\pi$
$224$	−4.98661	+	4.81047i	−0.333182	+	0.321413i
$225$		0			0
$226$	6.31473	+	10.9374i	0.420050	+	0.727548i
$227$	−1.17595	+	6.66915i	−0.0780506	+	0.442647i	0.920590	+	0.390530i	$0.127708\pi$
$227$	−1.17595	+	6.66915i	−0.0780506	+	0.442647i	−0.998641	+	0.0521174i	$0.983403\pi$
$228$		0			0
$229$	−2.81930	+	7.74596i	−0.186304	+	0.511867i	−0.997320	−	0.0731567i	$-0.976693\pi$
$229$	−2.81930	+	7.74596i	−0.186304	+	0.511867i	0.811016	+	0.585024i	$0.198915\pi$
$230$	−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
$238$	0.474737	−	4.49419i	0.0307726	−	0.291315i
$239$	−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	$0.0312225\pi$
$241$	4.59174	+	12.6157i	0.295780	+	0.812649i	−0.699413	+	0.714718i	$0.746555\pi$
$242$			10.2266i			0.657391i
$243$		0			0
$244$		−	3.78218i		−	0.242129i
$245$	10.0128	+	2.13923i	0.639691	+	0.136671i
$246$		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	−0.591066	−	0.806624i	$-0.701293\pi$
$251$	6.38510	−	11.0593i	0.403024	−	0.698057i	0.994089	+	0.108566i	$0.0346259\pi$
$252$		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	0.0782518	−	0.996934i	$-0.475066\pi$
$257$	−8.05762	−	2.93273i	−0.502620	−	0.182939i	−0.580872	+	0.813995i	$0.697288\pi$
$258$		0			0
$259$	−22.8790	−	11.1736i	−1.42163	−	0.694296i
$260$	−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
$266$	−6.33662	−	14.2523i	−0.388523	−	0.873867i
$267$		0			0
$268$	−1.99877	+	0.727494i	−0.122095	+	0.0444388i
$269$	−32.0022			−1.95121			−0.975604	−	0.219536i	$-0.929546\pi$
$269$	−32.0022			−1.95121			−0.975604	+	0.219536i	$0.929546\pi$
$270$		0			0
$271$		−	12.5643i		−	0.763225i	−0.924322	−	0.381612i	$-0.875369\pi$
$271$		−	12.5643i		−	0.763225i	0.924322	−	0.381612i	$-0.124631\pi$
$272$	−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
$280$	−2.85516	−	11.4770i	−0.170629	−	0.685883i
$281$	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	$-0.674333\pi$
$283$	7.18235	−	19.7333i	0.426946	−	1.17303i	0.947656	−	0.319292i	$-0.103445\pi$
$284$	2.18733	−	6.00964i	0.129794	−	0.356607i
$285$		0			0
$286$	26.8748	+	4.73875i	1.58914	+	0.280208i
$287$	−3.44991	+	0.858240i	−0.203641	+	0.0506603i
$288$		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	−0.758620	−	0.651533i	$-0.774126\pi$
$293$	−4.25738	+	3.57236i	−0.248719	+	0.208700i	0.509902	+	0.860233i	$0.329682\pi$
$294$		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
$301$	−3.79658	−	8.53929i	−0.218831	−	0.492196i
$302$	−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	−0.999957	−	0.00922626i	$-0.997063\pi$
$307$	−26.1410	+	15.0925i	−1.49195	+	0.861375i	−0.491989	+	0.870602i	$0.663730\pi$
$308$	2.41552	−	4.94597i	0.137637	−	0.281823i
$309$		0			0
$310$	10.7289	+	3.90499i	0.609359	+	0.221789i
$311$	−24.1028	−	8.77272i	−1.36675	−	0.497455i	−0.448613	−	0.893726i	$-0.648082\pi$
$311$	−24.1028	−	8.77272i	−1.36675	−	0.497455i	−0.918134	+	0.396271i	$0.870304\pi$
$312$		0			0
$313$	1.77245	+	0.312531i	0.100185	+	0.0176653i	0.223516	−	0.974700i	$-0.428247\pi$
$313$	1.77245	+	0.312531i	0.100185	+	0.0176653i	−0.123331	+	0.992366i	$0.539358\pi$
$314$	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
$322$	−1.34618	−	19.3972i	−0.0750198	−	1.08096i
$323$			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
$329$	19.0918	+	2.01673i	1.05257	+	0.111186i
$330$		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
$343$	3.82213	+	18.1216i	0.206376	+	0.978473i
$344$	−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	$0.217511\pi$
$349$	10.9711	+	30.1428i	0.587269	+	1.61351i	−0.188206	+	0.982130i	$0.560267\pi$
$350$	−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	−0.393163	−	0.919469i	$-0.628619\pi$
$353$	−1.94119	+	0.706536i	−0.103319	+	0.0376051i	0.289843	+	0.957074i	$0.406397\pi$
$354$		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
$364$	−5.10062	−	3.70990i	−0.267345	−	0.194452i
$365$	3.59909	−	9.88842i	0.188385	−	0.517584i
$366$		0			0
$367$	−13.8164	−	2.43620i	−0.721208	−	0.127168i	−0.199016	−	0.979996i	$-0.563775\pi$
$367$	−13.8164	−	2.43620i	−0.721208	−	0.127168i	−0.522192	+	0.852828i	$0.674886\pi$
$368$	−14.5685	+	8.41113i	−0.759436	+	0.438461i
$369$		0			0
$370$	−15.0598	−	8.69476i	−0.782920	−	0.452019i
$371$	−1.19916	−	1.77984i	−0.0622575	−	0.0924048i
$372$		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	0.979257	−	0.202621i	$-0.0649461\pi$
$383$	−0.200482	−	1.13699i	−0.0102442	−	0.0580975i	−0.989501	+	0.144524i	$0.953835\pi$
$384$		0			0
$385$	9.49409	+	14.0915i	0.483864	+	0.718168i
$386$	−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
$392$	16.8716	−	13.1531i	0.852144	−	0.664333i
$393$		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	0.917543	−	0.397636i	$-0.130169\pi$
$397$	20.5615	+	11.8712i	1.03195	+	0.595798i	0.114409	+	0.993434i	$0.463503\pi$
$398$	−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	0.997072	−	0.0764689i	$-0.0243646\pi$
$409$	15.1400	+	18.0432i	0.748625	+	0.892177i	−0.248447	+	0.968646i	$0.579920\pi$
$410$	−2.39110	+	0.421616i	−0.118088	+	0.0208221i
$411$		0			0
$412$	−1.68711	+	2.01062i	−0.0831179	+	0.0990561i
$413$	9.87184	+	10.2333i	0.485761	+	0.503548i
$414$		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	−0.342515	−	0.939512i	$-0.611279\pi$
$419$	−24.7436	−	9.00593i	−1.20880	−	0.439968i	−0.866289	+	0.499544i	$0.833501\pi$
$420$		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
$427$	−2.21851	+	21.0019i	−0.107361	+	1.01636i
$428$	−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	$-0.878534\pi$
$433$		−	15.4984i		−	0.744805i	0.928071	−	0.372403i	$-0.121466\pi$
$434$	1.42985	+	20.6028i	0.0686351	+	0.988966i
$435$		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	−0.246660	−	0.969102i	$-0.579333\pi$
$439$	15.7258	−	18.7413i	0.750551	−	0.894472i	0.997211	+	0.0746301i	$0.0237776\pi$
$440$	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
$448$	−21.1370	−	10.3229i	−0.998629	−	0.487711i
$449$	−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
$455$	17.7905	−	7.90969i	0.834032	−	0.370812i
$456$		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	0.124290	−	0.992246i	$-0.460335\pi$
$461$	18.4071	−	6.69964i	0.857305	−	0.312033i	0.733015	+	0.680213i	$0.238113\pi$
$462$		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	−0.978690	−	0.205343i	$-0.934169\pi$
$467$	−6.73186	+	11.6599i	−0.311513	+	0.539557i	0.667177	+	0.744899i	$0.267502\pi$
$468$		0			0
$469$	11.5257	−	2.86727i	0.532206	−	0.132398i
$470$	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
$476$	−1.68206	+	0.418450i	−0.0770971	+	0.0191796i
$477$		0			0
$478$	2.21551	−	3.83737i	0.101335	−	0.175517i
$479$	19.6234	+	16.4660i	0.896614	+	0.752349i	0.969526	−	0.244990i	$-0.0787846\pi$
$479$	19.6234	+	16.4660i	0.896614	+	0.752349i	−0.0729114	+	0.997338i	$0.523229\pi$
$480$		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
$490$	1.74725	+	12.5275i	0.0789328	+	0.565934i
$491$	−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
$497$	−15.6710	+	32.0878i	−0.702942	+	1.43933i
$498$		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	0.976929	−	0.213562i	$-0.0685066\pi$
$503$	6.80712	+	11.7903i	0.303514	+	0.525702i	−0.673415	+	0.739265i	$0.735173\pi$
$504$		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	−0.676002	−	0.736900i	$-0.736289\pi$
$509$	−1.52700	+	1.28130i	−0.0676830	+	0.0567928i	0.608319	+	0.793693i	$0.291844\pi$
$510$		0			0
$511$	18.9889	−	1.31784i	0.840018	−	0.0582979i
$512$			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
$518$	3.30431	−	31.2809i	0.145183	−	1.37440i
$519$		0			0
$520$	−17.2279	−	14.4560i	−0.755495	−	0.633936i
$521$	3.88589	−	6.73055i	0.170244	−	0.294871i	−0.768261	−	0.640136i	$-0.778878\pi$
$521$	3.88589	−	6.73055i	0.170244	−	0.294871i	0.938505	+	0.345266i	$0.112211\pi$
$522$		0			0
$523$	17.4428	−	10.0706i	0.762720	−	0.440356i	−0.0675518	−	0.997716i	$-0.521519\pi$
$523$	17.4428	−	10.0706i	0.762720	−	0.440356i	0.830271	+	0.557359i	$0.188185\pi$
$524$	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
$532$	−4.30555	+	4.15347i	−0.186669	+	0.180076i
$533$	−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
$553$	13.3769	−	18.3915i	0.568844	−	0.782085i
$554$	−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
$560$	9.07564	−	6.11469i	0.383516	−	0.258393i
$561$		0			0
$562$	0.774458	+	4.39217i	0.0326685	+	0.185272i
$563$	35.1445	−	29.4898i	1.48117	−	1.24285i	0.576237	−	0.817283i	$-0.304521\pi$
$563$	35.1445	−	29.4898i	1.48117	−	1.24285i	0.904929	−	0.425563i	$-0.139924\pi$
$564$		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
$574$	−2.45399	−	3.64230i	−0.102428	−	0.152027i
$575$	14.7372	+	8.50855i	0.614586	+	0.354831i
$576$		0			0
$577$	−0.564874	+	0.326130i	−0.0235160	+	0.0135770i	−0.511712	−	0.859157i	$-0.670988\pi$
$577$	−0.564874	+	0.326130i	−0.0235160	+	0.0135770i	0.488196	+	0.872734i	$0.337655\pi$
$578$	18.3566	+	3.23677i	0.763536	+	0.134632i
$579$		0			0
$580$	1.36263	−	3.74378i	0.0565799	−	0.155452i
$581$	−7.57878	+	10.4198i	−0.314421	+	0.432287i
$582$		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	0.559199	−	0.829034i	$-0.311109\pi$
$587$	−3.87979	−	3.25553i	−0.160136	−	0.134370i	−0.719335	+	0.694664i	$0.755553\pi$
$588$		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	$-0.487197\pi$
$593$	1.95836			0.0804204			0.0402102	+	0.999191i	$0.487197\pi$
$594$		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	−0.648761	−	0.760992i	$-0.724712\pi$
$601$	5.22977	−	6.23259i	0.213327	−	0.254233i	0.862087	+	0.506760i	$0.169157\pi$
$602$	8.30894	−	8.01545i	0.338647	−	0.326685i
$603$		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	$0.231602\pi$
$607$	−6.22814	+	17.1117i	−0.252792	+	0.694542i	−0.999566	+	0.0294631i	$0.990620\pi$
$608$	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
$616$	35.3055	+	3.72944i	1.42250	+	0.150264i
$617$	−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	$-0.958924\pi$
$619$	−7.83037	−	21.5138i	−0.314729	−	0.864711i	0.676956	−	0.736023i	$-0.263299\pi$
$620$		−	4.37914i		−	0.175870i
$621$		0			0
$622$		−	31.6872i		−	1.27054i
$623$	0.0804350	+	1.15899i	0.00322256	+	0.0464340i
$624$		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
$637$	26.1470	+	23.5925i	1.03598	+	0.934768i
$638$	−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	−0.312803	−	0.949818i	$-0.601268\pi$
$643$	−7.14787	+	1.26036i	−0.281884	+	0.0497038i	0.0309184	+	0.999522i	$0.490157\pi$
$644$	−6.81449	+	3.02973i	−0.268529	+	0.119388i
$645$		0			0
$646$	−7.65953	+	2.78784i	−0.301360	+	0.109686i
$647$	30.4657			1.19773			0.598865	−	0.800850i	$-0.295619\pi$
$647$	30.4657			1.19773			0.598865	+	0.800850i	$0.295619\pi$
$648$		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
$658$	5.72560	+	23.0154i	0.223207	+	0.897235i
$659$	−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	$-0.609980\pi$
$661$	13.5122	−	37.1245i	0.525564	−	1.44398i	0.864244	−	0.503074i	$-0.167798\pi$
$662$	−5.73485	+	15.7564i	−0.222891	+	0.612389i
$663$		0			0
$664$	14.6569	+	2.58440i	0.568797	+	0.100294i
$665$	−4.45824	−	17.9210i	−0.172883	−	0.694946i
$666$		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	−0.573822	−	0.818980i	$-0.694540\pi$
$677$	−12.6704	+	4.61166i	−0.486965	+	0.177241i	0.0868572	+	0.996221i	$0.472318\pi$
$678$		0			0
$679$	−9.00527	+	4.00376i	−0.345590	+	0.153650i
$680$	−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
$686$	−19.4220	+	12.0939i	−0.741536	+	0.461746i
$687$		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	−0.176083	−	0.984375i	$-0.556343\pi$
$691$	−17.8283	−	3.14362i	−0.678222	−	0.119589i	−0.502140	+	0.864787i	$0.667454\pi$
$692$	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
$700$	0.248283	+	3.57752i	0.00938420	+	0.135217i
$701$		−	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
$707$	−41.6897	−	4.40383i	−1.56790	−	0.165623i
$708$		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	$-0.839949\pi$
$719$	−22.9381	−	39.7300i	−0.855447	−	1.48168i	0.0207825	−	0.999784i	$-0.493384\pi$
$720$		0			0
$721$	10.5477	−	10.1751i	0.392816	−	0.378941i
$722$	−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	0.983054	−	0.183316i	$-0.0586831\pi$
$727$	3.02410	+	8.30865i	0.112158	+	0.308151i	−0.870896	+	0.491467i	$0.836461\pi$
$728$	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	0.713621	−	0.700532i	$-0.247054\pi$
$733$	−2.71245	−	3.23257i	−0.100187	−	0.119398i	−0.813808	+	0.581134i	$0.802609\pi$
$734$	−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
$742$	1.55951	−	2.14412i	0.0572513	−	0.0787130i
$743$	−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
$749$	4.23610	+	6.28737i	0.154784	+	0.229736i
$750$		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	0.981655	−	0.190663i	$-0.0610639\pi$
$761$	−0.165785	−	0.940211i	−0.00600969	−	0.0340826i	−0.987665	+	0.156581i	$0.949953\pi$
$762$		0			0
$763$	−29.7418	+	20.0385i	−1.07673	+	0.725442i
$764$	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	$0.417854\pi$
$769$	−15.5790	+	42.8029i	−0.561792	+	1.54351i	−0.817008	+	0.576627i	$0.804369\pi$
$770$	−12.3470	+	16.9755i	−0.444955	+	0.611755i
$771$		0			0
$772$	−0.270497	+	1.53406i	−0.00973538	+	0.0552121i
$773$	24.2021	+	41.9192i	0.870488	+	1.50773i	0.861492	+	0.507771i	$0.169530\pi$
$773$	24.2021	+	41.9192i	0.870488	+	1.50773i	0.00899604	+	0.999960i	$0.497136\pi$
$774$		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	0.740946	−	0.671564i	$-0.234377\pi$
$787$	−1.37685	−	1.64087i	−0.0490795	−	0.0584906i	−0.790026	+	0.613074i	$0.789933\pi$
$788$	−5.19382	+	0.915811i	−0.185022	+	0.0326244i
$789$		0			0
$790$	9.98372	−	11.8981i	0.355205	−	0.423317i
$791$	−19.4664	+	18.7788i	−0.692146	+	0.667698i
$792$		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	0.348390	−	0.937350i	$-0.386729\pi$
$797$	0.360086	+	0.131061i	0.0127549	+	0.00464241i	−0.335635	+	0.941992i	$0.608951\pi$
$798$		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
$805$	2.41836	−	22.8939i	0.0852359	−	0.806902i
$806$	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	$-0.938553\pi$
$811$		−	10.9268i		−	0.383692i	0.981425	−	0.191846i	$-0.0614474\pi$
$812$	7.18923	−	0.498939i	0.252293	−	0.0175093i
$813$		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
$826$	−7.70853	+	15.7839i	−0.268214	+	0.549190i
$827$	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	0.996150	−	0.0876596i	$-0.0279388\pi$
$829$	40.8365	+	23.5770i	1.41831	+	0.818862i	0.422160	+	0.906521i	$0.361272\pi$
$830$	−5.65634	+	6.74097i	−0.196335	+	0.233982i
$831$		0			0
$832$	−44.0511	+	7.76739i	−1.52720	+	0.269286i
$833$	9.58572	−	1.33695i	0.332125	−	0.0463227i
$834$		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	−0.455551	−	0.890209i	$-0.650558\pi$
$839$	−6.72893	+	2.44913i	−0.232309	+	0.0845534i	0.223243	+	0.974763i	$0.428336\pi$
$840$		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
$847$	−21.2539	+	5.28739i	−0.730294	+	0.181677i
$848$	−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	0.0794291	−	0.996841i	$-0.474690\pi$
$853$	−5.45780	−	0.962357i	−0.186871	−	0.0329505i	−0.266301	+	0.963890i	$0.585801\pi$
$854$	−25.3181	+	6.29844i	−0.866368	+	0.215528i
$855$		0			0
$856$	4.37859	−	7.58394i	0.149657	−	0.259214i
$857$	−38.9684	−	32.6983i	−1.33113	−	1.11695i	−0.983811	−	0.179208i	$-0.942647\pi$
$857$	−38.9684	−	32.6983i	−1.33113	−	1.11695i	−0.347322	−	0.937746i	$-0.612909\pi$
$858$		0			0
$859$	9.91290	−	1.74791i	0.338224	−	0.0596380i	−0.00195691	−	0.999998i	$-0.500623\pi$
$859$	9.91290	−	1.74791i	0.338224	−	0.0596380i	0.340181	+	0.940360i	$0.389512\pi$
$860$	−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
$868$	7.23804	−	3.21804i	0.245675	−	0.109227i
$869$	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
$875$	−27.3339	−	13.3493i	−0.924053	−	0.451290i
$876$		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	$-0.748286\pi$
$881$	−28.7112	−	49.7293i	−0.967306	−	1.67542i	−0.264017	−	0.964518i	$-0.585048\pi$
$882$		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	−0.441178	−	0.897419i	$-0.645439\pi$
$887$	10.9003	−	9.14647i	0.365997	−	0.307108i	0.807176	+	0.590311i	$0.200995\pi$
$888$		0			0
$889$	1.31024	+	18.8792i	0.0439439	+	0.633190i
$890$			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
$896$	1.59702	−	15.1185i	0.0533526	−	0.505073i
$897$		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
$910$	16.6992	+	17.3106i	0.553572	+	0.573841i
$911$	−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	$0.445516\pi$
$929$	−9.95917	+	56.4812i	−0.326750	+	1.85309i	−0.497083	+	0.867703i	$0.665596\pi$
$930$		0			0
$931$	26.3445	−	20.5382i	0.863405	−	0.673112i
$932$	−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	0.0865519	−	0.996247i	$-0.472415\pi$
$937$	−22.4359	−	12.9533i	−0.732948	−	0.423167i	−0.819500	+	0.573080i	$0.805748\pi$
$938$	8.19845	+	12.1684i	0.267689	+	0.397313i
$939$		0			0
$940$	−0.873268	−	4.95255i	−0.0284829	−	0.161534i
$941$	15.8590	−	13.3072i	0.516987	−	0.433804i	−0.346593	−	0.938016i	$-0.612661\pi$
$941$	15.8590	−	13.3072i	0.516987	−	0.433804i	0.863580	+	0.504212i	$0.168217\pi$
$942$		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
$952$	−6.24676	−	9.27167i	−0.202459	−	0.300497i
$953$	−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
$959$	16.3824	+	11.9156i	0.529014	+	0.384775i
$960$		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	$-0.214434\pi$
$971$	48.7070			1.56308			0.781540	+	0.623855i	$0.214434\pi$
$972$		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
$980$	4.28592	−	2.27311i	0.136909	−	0.0726119i
$981$		0			0
$982$	−13.3027	−	23.0409i	−0.424505	−	0.735265i
$983$	1.43166	−	8.11934i	0.0456628	−	0.258967i	−0.953427	−	0.301624i	$-0.902471\pi$
$983$	1.43166	−	8.11934i	0.0456628	−	0.258967i	0.999090	+	0.0426573i	$0.0135824\pi$
$984$		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
$994$	−43.8715	−	4.63430i	−1.39152	−	0.146991i
$995$	−9.23880	−	11.0104i	−0.292890	−	0.349052i
$996$		0			0
$997$	−20.2279	−	55.5756i	−0.640623	−	1.76010i	−0.649760	−	0.760139i	$-0.725131\pi$
$997$	−20.2279	−	55.5756i	−0.640623	−	1.76010i	0.00913679	−	0.999958i	$-0.497092\pi$
$998$		−	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.62.16		132
3.2	odd	2		189.2.be.a.20.8	yes	132
7.6	odd	2	inner	567.2.be.a.62.15		132
21.20	even	2		189.2.be.a.20.7	✓	132
27.4	even	9		189.2.be.a.104.7	yes	132
27.23	odd	18	inner	567.2.be.a.503.15		132
189.104	even	18	inner	567.2.be.a.503.16		132
189.139	odd	18		189.2.be.a.104.8	yes	132

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

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

\(f(q)\)	\(=\)	\(q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(0.253991 + 1.44045i) q^{5} +(-2.19420 + 1.47834i) q^{7} +(2.64668 + 1.52806i) q^{8} +O(q^{10})\)	\(q+(0.422526 + 1.16088i) q^{2} +(0.362974 - 0.304571i) q^{4} +(0.253991 + 1.44045i) q^{5} +(-2.19420 + 1.47834i) q^{7} +(2.64668 + 1.52806i) q^{8} +(-1.56488 + 0.903482i) q^{10} +(-4.32398 - 0.762434i) q^{11} +(-1.72073 + 4.72766i) q^{13} +(-2.64328 - 1.92257i) q^{14} +(-0.491047 + 2.78487i) q^{16} +(0.691322 + 1.19740i) q^{17} +(4.13271 + 2.38602i) q^{19} +(0.530913 + 0.445489i) q^{20} +(-0.941898 - 5.34177i) q^{22} +(3.82383 + 4.55707i) q^{23} +(2.68807 - 0.978376i) q^{25} -6.21530 q^{26} +(-0.346179 + 1.20489i) q^{28} +(-1.96611 - 5.40183i) q^{29} +(-4.06150 - 4.84031i) q^{31} +(2.57902 - 0.454750i) q^{32} +(-1.09794 + 1.30848i) q^{34} +(-2.68678 - 2.78516i) q^{35} +(4.81181 + 8.33429i) q^{37} +(-1.02371 + 5.80574i) q^{38} +(-1.52887 + 4.20054i) q^{40} +(1.26265 + 0.459567i) q^{41} +(-0.613355 + 3.47851i) q^{43} +(-1.80171 + 1.04022i) q^{44} +(-3.67454 + 6.36449i) q^{46} +(-5.55855 - 4.66418i) q^{47} +(2.62904 - 6.48754i) q^{49} +(2.27156 + 2.70713i) q^{50} +(0.815330 + 2.24010i) q^{52} +0.811158i q^{53} -6.42214i q^{55} +(-8.06635 + 0.559812i) q^{56} +(5.44015 - 4.56483i) q^{58} +(-0.933219 - 5.29255i) q^{59} +(5.13083 - 6.11468i) q^{61} +(3.90293 - 6.76007i) q^{62} +(4.44544 + 7.69973i) q^{64} +(-7.24703 - 1.27785i) q^{65} +(-4.21835 - 1.53535i) q^{67} +(0.615627 + 0.224070i) q^{68} +(2.09800 - 4.29584i) q^{70} +(11.6889 - 6.74856i) q^{71} +(-6.23051 - 3.59719i) q^{73} +(-7.64200 + 9.10738i) q^{74} +(2.22678 - 0.392641i) q^{76} +(10.6148 - 4.71936i) q^{77} +(-8.07721 + 2.93986i) q^{79} -4.13619 q^{80} +1.65997i q^{82} +(4.57620 - 1.66560i) q^{83} +(-1.54922 + 1.29995i) q^{85} +(-4.29729 + 0.757728i) q^{86} +(-10.2791 - 8.62523i) q^{88} +(0.219556 - 0.380281i) q^{89} +(-3.21345 - 12.9173i) q^{91} +(2.77590 + 0.489467i) q^{92} +(3.06592 - 8.42355i) q^{94} +(-2.38728 + 6.55901i) q^{95} +(3.66832 + 0.646825i) q^{97} +(8.64209 + 0.310846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44} - 6 q^{46} - 24 q^{49} - 18 q^{50} - 57 q^{56} - 12 q^{58} + 18 q^{64} - 78 q^{65} - 12 q^{67} - 69 q^{70} - 18 q^{71} + 6 q^{74} + 57 q^{77} + 24 q^{79} + 54 q^{85} + 42 q^{86} - 72 q^{88} + 6 q^{91} + 120 q^{92} - 126 q^{95} - 126 q^{98}+O(q^{100}) \) 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

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