LMFDB - Embedded newform 567.2.w.a.235.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(37,567)]

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([14, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("567.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.w (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			235.20
Character	$\chi$	$=$	567.235
Dual form			567.2.w.a.415.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11851 - 0.771075i) q^{2} +(2.36145 - 1.98149i) q^{4} +(1.51793 + 0.552482i) q^{5} +(2.02397 + 1.70398i) q^{7} +(1.22040 - 2.11380i) q^{8} +O(q^{10})$	\(q+(2.11851 - 0.771075i) q^{2} +(2.36145 - 1.98149i) q^{4} +(1.51793 + 0.552482i) q^{5} +(2.02397 + 1.70398i) q^{7} +(1.22040 - 2.11380i) q^{8} +3.64176 q^{10} +(-0.906628 + 0.329986i) q^{11} +(-0.0325017 - 0.184326i) q^{13} +(5.60170 + 2.04928i) q^{14} +(-0.115055 + 0.652508i) q^{16} -4.70815 q^{17} +0.504342 q^{19} +(4.67925 - 1.70311i) q^{20} +(-1.66626 + 1.39816i) q^{22} +(-1.36276 - 7.72859i) q^{23} +(-1.83134 - 1.53668i) q^{25} +(-0.210985 - 0.365436i) q^{26} +(8.15591 + 0.0133961i) q^{28} +(1.02634 - 5.82066i) q^{29} +(-2.85990 + 2.39974i) q^{31} +(1.10707 + 6.27850i) q^{32} +(-9.97427 + 3.63034i) q^{34} +(2.13082 + 3.70473i) q^{35} +(4.84361 - 8.38937i) q^{37} +(1.06846 - 0.388886i) q^{38} +(3.02032 - 2.53435i) q^{40} +(1.93086 + 10.9505i) q^{41} +(-6.60401 - 5.54143i) q^{43} +(-1.48709 + 2.57572i) q^{44} +(-8.84634 - 15.3223i) q^{46} +(1.15853 + 0.972120i) q^{47} +(1.19289 + 6.89761i) q^{49} +(-5.06461 - 1.84337i) q^{50} +(-0.441991 - 0.370875i) q^{52} +(-1.38569 + 2.40009i) q^{53} -1.55851 q^{55} +(6.07193 - 2.19871i) q^{56} +(-2.31386 - 13.1225i) q^{58} +(0.120799 + 0.685087i) q^{59} +(-6.80963 - 5.71396i) q^{61} +(-4.20835 + 7.28908i) q^{62} +(6.52397 + 11.2998i) q^{64} +(0.0525016 - 0.297751i) q^{65} +(2.99646 + 1.09062i) q^{67} +(-11.1180 + 9.32915i) q^{68} +(7.37080 + 6.20550i) q^{70} +(1.43937 + 2.49307i) q^{71} +(0.0174169 + 0.0301670i) q^{73} +(3.79240 - 21.5078i) q^{74} +(1.19098 - 0.999349i) q^{76} +(-2.39727 - 0.876998i) q^{77} +(-7.85664 + 2.85958i) q^{79} +(-0.535144 + 0.926896i) q^{80} +(12.5342 + 21.7098i) q^{82} +(-2.38942 + 13.5510i) q^{83} +(-7.14665 - 2.60117i) q^{85} +(-18.2635 - 6.64738i) q^{86} +(-0.408927 + 2.31914i) q^{88} +11.4122 q^{89} +(0.248306 - 0.428452i) q^{91} +(-18.5322 - 15.5503i) q^{92} +(3.20393 + 1.16614i) q^{94} +(0.765557 + 0.278640i) q^{95} +(-7.73226 - 6.48814i) q^{97} +(7.84572 + 13.6929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	2.11851	−	0.771075i	1.49801	−	0.545233i	0.542468	−	0.840076i	$-0.317490\pi$
$2$	2.11851	−	0.771075i	1.49801	−	0.545233i	0.955546	+	0.294844i	$0.0952676\pi$
$3$		0			0
$3$		0			0
$4$	2.36145	−	1.98149i	1.18072	−	0.990744i
$5$	1.51793	+	0.552482i	0.678840	+	0.247077i	0.658349	−	0.752713i	$-0.271255\pi$
$5$	1.51793	+	0.552482i	0.678840	+	0.247077i	0.0204904	+	0.999790i	$0.493477\pi$
$6$		0			0
$7$	2.02397	+	1.70398i	0.764988	+	0.644045i
$7$	2.02397	+	1.70398i	0.764988	+	0.644045i
$8$	1.22040	−	2.11380i	0.431477	−	0.747340i
$9$		0			0
$10$	3.64176			1.15163
$11$	−0.906628	+	0.329986i	−0.273359	+	0.0994944i	−0.475062	−	0.879952i	$-0.657574\pi$
$11$	−0.906628	+	0.329986i	−0.273359	+	0.0994944i	0.201704	+	0.979447i	$0.435352\pi$
$12$		0			0
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	0.979969	−	0.199151i	$-0.0638185\pi$
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	−0.988983	+	0.148028i	$0.952707\pi$
$14$	5.60170	+	2.04928i	1.49712	+	0.547692i
$15$		0			0
$16$	−0.115055	+	0.652508i	−0.0287637	+	0.163127i
$17$	−4.70815			−1.14189			−0.570947	−	0.820987i	$-0.693424\pi$
$17$	−4.70815			−1.14189			−0.570947	+	0.820987i	$0.693424\pi$
$18$		0			0
$19$	0.504342			0.115704			0.0578520	−	0.998325i	$-0.481575\pi$
$19$	0.504342			0.115704			0.0578520	+	0.998325i	$0.481575\pi$
$20$	4.67925	−	1.70311i	1.04631	−	0.380826i
$21$		0			0
$22$	−1.66626	+	1.39816i	−0.355247	+	0.298088i
$23$	−1.36276	−	7.72859i	−0.284155	−	1.61152i	−0.708289	−	0.705922i	$-0.750533\pi$
$23$	−1.36276	−	7.72859i	−0.284155	−	1.61152i	0.424135	−	0.905599i	$-0.360578\pi$
$24$		0			0
$25$	−1.83134	−	1.53668i	−0.366268	−	0.307336i
$26$	−0.210985	−	0.365436i	−0.0413775	−	0.0716679i
$27$		0			0
$28$	8.15591	+	0.0133961i	1.54132	+	0.00253162i
$29$	1.02634	−	5.82066i	0.190587	−	1.08087i	−0.727978	−	0.685600i	$-0.759540\pi$
$29$	1.02634	−	5.82066i	0.190587	−	1.08087i	0.918565	−	0.395270i	$-0.129349\pi$
$30$		0			0
$31$	−2.85990	+	2.39974i	−0.513653	+	0.431006i	−0.862413	−	0.506206i	$-0.831048\pi$
$31$	−2.85990	+	2.39974i	−0.513653	+	0.431006i	0.348759	+	0.937212i	$0.386603\pi$
$32$	1.10707	+	6.27850i	0.195704	+	1.10989i
$33$		0			0
$34$	−9.97427	+	3.63034i	−1.71057	+	0.622598i
$35$	2.13082	+	3.70473i	0.360175	+	0.626214i
$36$		0			0
$37$	4.84361	−	8.38937i	0.796284	−	1.37920i	−0.125737	−	0.992064i	$-0.540129\pi$
$37$	4.84361	−	8.38937i	0.796284	−	1.37920i	0.922021	−	0.387141i	$-0.126537\pi$
$38$	1.06846	−	0.388886i	0.173326	−	0.0630856i
$39$		0			0
$40$	3.02032	−	2.53435i	0.477555	−	0.400716i
$41$	1.93086	+	10.9505i	0.301550	+	1.71017i	0.639316	+	0.768944i	$0.279217\pi$
$41$	1.93086	+	10.9505i	0.301550	+	1.71017i	−0.337767	+	0.941230i	$0.609671\pi$
$42$		0			0
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.0191503	−	0.999817i	$-0.506096\pi$
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.987953	+	0.154757i	$0.950541\pi$
$44$	−1.48709	+	2.57572i	−0.224187	+	0.388304i
$45$		0			0
$46$	−8.84634	−	15.3223i	−1.30432	−	2.25915i
$47$	1.15853	+	0.972120i	0.168989	+	0.141798i	0.723360	−	0.690471i	$-0.242597\pi$
$47$	1.15853	+	0.972120i	0.168989	+	0.141798i	−0.554371	+	0.832269i	$0.687041\pi$
$48$		0			0
$49$	1.19289	+	6.89761i	0.170412	+	0.985373i
$50$	−5.06461	−	1.84337i	−0.716245	−	0.260692i
$51$		0			0
$52$	−0.441991	−	0.370875i	−0.0612932	−	0.0514311i
$53$	−1.38569	+	2.40009i	−0.190340	+	0.329678i	−0.945363	−	0.326020i	$-0.894292\pi$
$53$	−1.38569	+	2.40009i	−0.190340	+	0.329678i	0.755023	+	0.655698i	$0.227626\pi$
$54$		0			0
$55$	−1.55851			−0.210149
$56$	6.07193	−	2.19871i	0.811395	−	0.293815i
$57$		0			0
$58$	−2.31386	−	13.1225i	−0.303824	−	1.72307i
$59$	0.120799	+	0.685087i	0.0157267	+	0.0891908i	0.991661	−	0.128875i	$-0.0411365\pi$
$59$	0.120799	+	0.685087i	0.0157267	+	0.0891908i	−0.975934	+	0.218065i	$0.930025\pi$
$60$		0			0
$61$	−6.80963	−	5.71396i	−0.871884	−	0.731598i	0.0926097	−	0.995702i	$-0.470479\pi$
$61$	−6.80963	−	5.71396i	−0.871884	−	0.731598i	−0.964494	+	0.264105i	$0.914924\pi$
$62$	−4.20835	+	7.28908i	−0.534461	+	0.925714i
$63$		0			0
$64$	6.52397	+	11.2998i	0.815496	+	1.41248i
$65$	0.0525016	−	0.297751i	0.00651202	−	0.0369315i
$66$		0			0
$67$	2.99646	+	1.09062i	0.366076	+	0.133241i	0.518507	−	0.855073i	$-0.326488\pi$
$67$	2.99646	+	1.09062i	0.366076	+	0.133241i	−0.152431	+	0.988314i	$0.548710\pi$
$68$	−11.1180	+	9.32915i	−1.34826	+	1.13133i
$69$		0			0
$70$	7.37080	+	6.20550i	0.880980	+	0.741699i
$71$	1.43937	+	2.49307i	0.170822	+	0.295873i	0.938708	−	0.344714i	$-0.112024\pi$
$71$	1.43937	+	2.49307i	0.170822	+	0.295873i	−0.767885	+	0.640587i	$0.778691\pi$
$72$		0			0
$73$	0.0174169	+	0.0301670i	0.00203850	+	0.00353078i	0.867043	−	0.498234i	$-0.166018\pi$
$73$	0.0174169	+	0.0301670i	0.00203850	+	0.00353078i	−0.865004	+	0.501764i	$0.832684\pi$
$74$	3.79240	−	21.5078i	0.440858	−	2.50023i
$75$		0			0
$76$	1.19098	−	0.999349i	0.136614	−	0.114633i
$77$	−2.39727	−	0.876998i	−0.273195	−	0.0999432i
$78$		0			0
$79$	−7.85664	+	2.85958i	−0.883941	+	0.321728i	−0.743799	−	0.668403i	$-0.766978\pi$
$79$	−7.85664	+	2.85958i	−0.883941	+	0.321728i	−0.140142	+	0.990131i	$0.544756\pi$
$80$	−0.535144	+	0.926896i	−0.0598309	+	0.103630i
$81$		0			0
$82$	12.5342	+	21.7098i	1.38417	+	2.39745i
$83$	−2.38942	+	13.5510i	−0.262272	+	1.48742i	0.514419	+	0.857539i	$0.328008\pi$
$83$	−2.38942	+	13.5510i	−0.262272	+	1.48742i	−0.776691	+	0.629882i	$0.783103\pi$
$84$		0			0
$85$	−7.14665	−	2.60117i	−0.775163	−	0.282136i
$86$	−18.2635	−	6.64738i	−1.96941	−	0.716806i
$87$		0			0
$88$	−0.408927	+	2.31914i	−0.0435918	+	0.247221i
$89$	11.4122			1.20970			0.604848	−	0.796341i	$-0.293234\pi$
$89$	11.4122			1.20970			0.604848	+	0.796341i	$0.293234\pi$
$90$		0			0
$91$	0.248306	−	0.428452i	0.0260296	−	0.0449140i
$92$	−18.5322	−	15.5503i	−1.93211	−	1.62124i
$93$		0			0
$94$	3.20393	+	1.16614i	0.330460	+	0.120278i
$95$	0.765557	+	0.278640i	0.0785445	+	0.0285879i
$96$		0			0
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	0.159433	−	0.987209i	$-0.449033\pi$
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	−0.944525	+	0.328438i	$0.893478\pi$
$98$	7.84572	+	13.6929i	0.792537	+	1.38319i
$99$		0			0
$100$	−7.36953			−0.736953
$101$	0.358407	−	2.03263i	0.0356628	−	0.202254i	−0.961770	−	0.273857i	$-0.911700\pi$
$101$	0.358407	−	2.03263i	0.0356628	−	0.202254i	0.997433	+	0.0716032i	$0.0228115\pi$
$102$		0			0
$103$	16.6558	+	6.06221i	1.64114	+	0.597328i	0.987239	−	0.159248i	$-0.0509070\pi$
$103$	16.6558	+	6.06221i	1.64114	+	0.597328i	0.653906	+	0.756576i	$0.273129\pi$
$104$	−0.429293	−	0.156250i	−0.0420957	−	0.0153216i
$105$		0			0
$106$	−1.08496	+	6.15310i	−0.105380	+	0.597642i
$107$	8.44399	+	14.6254i	0.816311	+	1.41389i	0.908383	+	0.418140i	$0.137318\pi$
$107$	8.44399	+	14.6254i	0.816311	+	1.41389i	−0.0920719	+	0.995752i	$0.529349\pi$
$108$		0			0
$109$	−6.03251	+	10.4486i	−0.577810	+	1.00080i	0.417920	+	0.908484i	$0.362759\pi$
$109$	−6.03251	+	10.4486i	−0.577810	+	1.00080i	−0.995730	+	0.0923121i	$0.970574\pi$
$110$	−3.30172	+	1.20173i	−0.314807	+	0.114580i
$111$		0			0
$112$	−1.34473	+	1.12460i	−0.127065	+	0.106265i
$113$	12.9494	−	10.8658i	1.21818	−	1.02217i	0.219258	−	0.975667i	$-0.429636\pi$
$113$	12.9494	−	10.8658i	1.21818	−	1.02217i	0.998918	−	0.0465043i	$-0.0148081\pi$
$114$		0			0
$115$	2.20133	−	12.4844i	0.205275	−	1.16417i
$116$	−9.10993	−	15.7789i	−0.845836	−	1.46503i
$117$		0			0
$118$	0.784169	+	1.35822i	0.0721886	+	0.125034i
$119$	−9.52914	−	8.02261i	−0.873535	−	0.735431i
$120$		0			0
$121$	−7.71341	+	6.47232i	−0.701219	+	0.588392i
$122$	−18.8322	−	6.85435i	−1.70499	−	0.620564i
$123$		0			0
$124$	−1.99844	+	11.3337i	−0.179465	+	1.01780i
$125$	−5.96924	−	10.3390i	−0.533905	−	0.924750i
$126$		0			0
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	−0.973461	−	0.228852i	$-0.926503\pi$
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	0.684922	+	0.728616i	$0.259836\pi$
$128$	12.7665	+	10.7124i	1.12841	+	0.946849i
$129$		0			0
$130$	−0.118363	−	0.671272i	−0.0103812	−	0.0588744i
$131$	−0.392080	−	2.22359i	−0.0342562	−	0.194276i	0.962877	−	0.269940i	$-0.0870037\pi$
$131$	−0.392080	−	2.22359i	−0.0342562	−	0.194276i	−0.997133	+	0.0756632i	$0.975893\pi$
$132$		0			0
$133$	1.02077	+	0.859391i	0.0885122	+	0.0745186i
$134$	7.18899			0.621034
$135$		0			0
$136$	−5.74583	+	9.95208i	−0.492701	+	0.853383i
$137$	−8.19370	−	6.87533i	−0.700035	−	0.587399i	0.221749	−	0.975104i	$-0.428824\pi$
$137$	−8.19370	−	6.87533i	−0.700035	−	0.587399i	−0.921784	+	0.387705i	$0.873268\pi$
$138$		0			0
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	0.550911	−	0.834564i	$-0.314281\pi$
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	−0.114426	+	0.993432i	$0.536503\pi$
$140$	12.3727	+	4.52633i	1.04569	+	0.382545i
$141$		0			0
$142$	4.97168	+	4.17173i	0.417214	+	0.350084i
$143$	0.0902919	+	0.156390i	0.00755059	+	0.0130780i
$144$		0			0
$145$	4.77372	−	8.26833i	0.396436	−	0.686648i
$146$	0.0601590	+	0.0504794i	0.00497880	+	0.00417771i
$147$		0			0
$148$	−5.18553	−	29.4086i	−0.426248	−	2.41737i
$149$	8.99259	−	7.54568i	0.736702	−	0.618166i	−0.195248	−	0.980754i	$-0.562551\pi$
$149$	8.99259	−	7.54568i	0.736702	−	0.618166i	0.931950	+	0.362588i	$0.118107\pi$
$150$		0			0
$151$	−0.205412	+	0.0747638i	−0.0167162	+	0.00608419i	−0.350365	−	0.936613i	$-0.613942\pi$
$151$	−0.205412	+	0.0747638i	−0.0167162	+	0.00608419i	0.333649	+	0.942698i	$0.391720\pi$
$152$	0.615500	−	1.06608i	0.0499237	−	0.0864703i
$153$		0			0
$154$	−5.75489	−	0.00945238i	−0.463742	−	0.000761695i
$155$	−5.66695	+	2.06260i	−0.455180	+	0.165672i
$156$		0			0
$157$	−3.76555	−	21.3555i	−0.300524	−	1.70435i	−0.643861	−	0.765142i	$-0.722669\pi$
$157$	−3.76555	−	21.3555i	−0.300524	−	1.70435i	0.343338	−	0.939212i	$-0.388442\pi$
$158$	−14.4394	+	12.1161i	−1.14874	+	0.963907i
$159$		0			0
$160$	−1.78830	+	10.1420i	−0.141378	+	0.801794i
$161$	10.4112	−	17.9645i	0.820517	−	1.41580i
$162$		0			0
$163$	4.59071	+	7.95135i	0.359572	+	0.622798i	0.987889	−	0.155160i	$-0.0495892\pi$
$163$	4.59071	+	7.95135i	0.359572	+	0.622798i	−0.628317	+	0.777957i	$0.716256\pi$
$164$	26.2578	+	22.0329i	2.05039	+	1.72048i
$165$		0			0
$166$	5.38687	+	30.5505i	0.418102	+	2.37118i
$167$	−6.56510	+	5.50878i	−0.508023	+	0.426282i	−0.860433	−	0.509564i	$-0.829807\pi$
$167$	−6.56510	+	5.50878i	−0.508023	+	0.426282i	0.352410	+	0.935846i	$0.385362\pi$
$168$		0			0
$169$	12.1831	−	4.43428i	0.937160	−	0.341098i
$170$	−17.1460			−1.31504
$171$		0			0
$172$	−26.5753			−2.02635
$173$	−3.39752	+	19.2683i	−0.258309	+	1.46494i	0.529126	+	0.848543i	$0.322520\pi$
$173$	−3.39752	+	19.2683i	−0.258309	+	1.46494i	−0.787435	+	0.616398i	$0.788591\pi$
$174$		0			0
$175$	−1.08810	−	6.23076i	−0.0822528	−	0.471001i
$176$	−0.111006	−	0.629548i	−0.00836742	−	0.0474540i
$177$		0			0
$178$	24.1770	−	8.79970i	1.81214	−	0.659565i
$179$	−5.85235			−0.437425			−0.218713	−	0.975789i	$-0.570186\pi$
$179$	−5.85235			−0.437425			−0.218713	+	0.975789i	$0.570186\pi$
$180$		0			0
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	−0.878079	−	0.478515i	$-0.841175\pi$
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	0.853446	+	0.521181i	$0.174509\pi$
$182$	0.195671	−	1.09914i	0.0145041	−	0.0814740i
$183$		0			0
$184$	−17.9998	−	6.55138i	−1.32696	−	0.482974i
$185$	11.9872	−	10.0585i	0.881319	−	0.739515i
$186$		0			0
$187$	4.26854	−	1.55362i	0.312147	−	0.113612i
$188$	4.66205			0.340015
$189$		0			0
$190$	1.83669			0.133248
$191$	8.29180	−	3.01797i	0.599974	−	0.218372i	−0.0241369	−	0.999709i	$-0.507684\pi$
$191$	8.29180	−	3.01797i	0.599974	−	0.218372i	0.624110	+	0.781336i	$0.285462\pi$
$192$		0			0
$193$	6.59508	−	5.53393i	0.474725	−	0.398341i	−0.373790	−	0.927513i	$-0.621942\pi$
$193$	6.59508	−	5.53393i	0.474725	−	0.398341i	0.848514	+	0.529172i	$0.177497\pi$
$194$	−21.3837	−	7.78304i	−1.53526	−	0.558790i
$195$		0			0
$196$	16.4845	+	13.9246i	1.17746	+	0.994618i
$197$	8.50014	−	14.7227i	0.605610	−	1.04895i	−0.386345	−	0.922354i	$-0.626263\pi$
$197$	8.50014	−	14.7227i	0.605610	−	1.04895i	0.991955	−	0.126593i	$-0.0404041\pi$
$198$		0			0
$199$	22.9181			1.62462			0.812309	−	0.583228i	$-0.198210\pi$
$199$	22.9181			1.62462			0.812309	+	0.583228i	$0.198210\pi$
$200$	−5.48320	+	1.99572i	−0.387721	+	0.141119i
$201$		0			0
$202$	−0.808019	−	4.58250i	−0.0568520	−	0.322424i
$203$	11.9956	−	10.0320i	0.841925	−	0.704106i
$204$		0			0
$205$	−3.11901	+	17.6888i	−0.217841	+	1.23544i
$206$	39.9599			2.78414
$207$		0			0
$208$	0.124014			0.00859881
$209$	−0.457251	+	0.166426i	−0.0316287	+	0.0115119i
$210$		0			0
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	−0.123700	−	0.992320i	$-0.539476\pi$
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	0.955764	+	0.294135i	$0.0950316\pi$
$212$	1.48351	+	8.41343i	0.101888	+	0.577837i
$213$		0			0
$214$	29.1660	+	24.4732i	1.99375	+	1.67295i
$215$	−6.96290	−	12.0601i	−0.474866	−	0.822492i
$216$		0			0
$217$	−9.87747	−	0.0162237i	−0.670526	−	0.00110134i
$218$	−4.72328	+	26.7870i	−0.319901	+	1.81425i
$219$		0			0
$220$	−3.68034	+	3.08817i	−0.248128	+	0.208204i
$221$	0.153023	+	0.867836i	0.0102934	+	0.0583769i
$222$		0			0
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.649271	−	0.760557i	$-0.724926\pi$
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.00849389	+	0.999964i	$0.502704\pi$
$224$	−8.45779	+	14.5939i	−0.565110	+	0.975097i
$225$		0			0
$226$	19.0551	−	33.0043i	1.26752	−	2.19542i
$227$	−3.25983	+	1.18648i	−0.216363	+	0.0787496i	−0.447928	−	0.894070i	$-0.647838\pi$
$227$	−3.25983	+	1.18648i	−0.216363	+	0.0787496i	0.231565	+	0.972820i	$0.425616\pi$
$228$		0			0
$229$	−14.9694	+	12.5608i	−0.989206	+	0.830043i	−0.985453	−	0.169950i	$-0.945639\pi$
$229$	−14.9694	+	12.5608i	−0.989206	+	0.830043i	−0.00375378	+	0.999993i	$0.501195\pi$
$230$	−4.96284	−	28.1457i	−0.327240	−	1.85587i
$231$		0			0
$232$	−11.0512	−	9.27302i	−0.725544	−	0.608804i
$233$	0.00761848	−	0.0131956i	0.000499103	−	0.000864472i	−0.865776	−	0.500432i	$-0.833174\pi$
$233$	0.00761848	−	0.0131956i	0.000499103	−	0.000864472i	0.866275	+	0.499568i	$0.166508\pi$
$234$		0			0
$235$	1.22149	+	2.11568i	0.0796810	+	0.138012i
$236$	1.64275	+	1.37843i	0.106934	+	0.0897284i
$237$		0			0
$238$	−26.3736	−	9.64830i	−1.70955	−	0.625407i
$239$	10.5505	+	3.84008i	0.682458	+	0.248394i	0.659902	−	0.751351i	$-0.270598\pi$
$239$	10.5505	+	3.84008i	0.682458	+	0.248394i	0.0225552	+	0.999746i	$0.492820\pi$
$240$		0			0
$241$	−23.1336	−	19.4114i	−1.49016	−	1.25040i	−0.894425	−	0.447218i	$-0.852415\pi$
$241$	−23.1336	−	19.4114i	−1.49016	−	1.25040i	−0.595739	−	0.803178i	$-0.703141\pi$
$242$	−11.3503	+	19.6593i	−0.729625	+	1.26375i
$243$		0			0
$244$	−27.4027			−1.75428
$245$	−2.00009	+	11.1291i	−0.127781	+	0.711015i
$246$		0			0
$247$	−0.0163920	−	0.0929635i	−0.00104300	−	0.00591513i
$248$	1.58234	+	8.97390i	0.100479	+	0.569843i
$249$		0			0
$250$	−20.6181	−	17.3006i	−1.30400	−	1.09419i
$251$	−3.95625	+	6.85242i	−0.249716	+	0.432521i	−0.963447	−	0.267899i	$-0.913671\pi$
$251$	−3.95625	+	6.85242i	−0.249716	+	0.432521i	0.713731	+	0.700420i	$0.247004\pi$
$252$		0			0
$253$	3.78584	+	6.55726i	0.238013	+	0.412251i
$254$	−2.54596	+	14.4389i	−0.159748	+	0.905976i
$255$		0			0
$256$	10.7839	+	3.92503i	0.673996	+	0.245315i
$257$	−0.461057	+	0.386873i	−0.0287600	+	0.0241325i	−0.657054	−	0.753843i	$-0.728198\pi$
$257$	−0.461057	+	0.386873i	−0.0287600	+	0.0241325i	0.628294	+	0.777976i	$0.283753\pi$
$258$		0			0
$259$	24.0986	−	8.72639i	1.49742	−	0.542232i
$260$	−0.466011	−	0.807154i	−0.0289008	−	0.0500576i
$261$		0			0
$262$	−2.54518	−	4.40839i	−0.157242	−	0.272351i
$263$	0.0903211	−	0.512236i	0.00556943	−	0.0315858i	−0.981896	−	0.189419i	$-0.939340\pi$
$263$	0.0903211	−	0.512236i	0.00556943	−	0.0315858i	0.987466	+	0.157833i	$0.0504507\pi$
$264$		0			0
$265$	−3.42940	+	2.87761i	−0.210666	+	0.176770i
$266$	2.82517	+	1.03354i	0.173222	+	0.0633702i
$267$		0			0
$268$	9.23704	−	3.36201i	0.564242	−	0.205367i
$269$	0.0763972	−	0.132324i	0.00465802	−	0.00806793i	−0.863687	−	0.504029i	$-0.831851\pi$
$269$	0.0763972	−	0.132324i	0.00465802	−	0.00806793i	0.868345	+	0.495961i	$0.165184\pi$
$270$		0			0
$271$	−9.93447	−	17.2070i	−0.603476	−	1.04525i	−0.992290	−	0.123935i	$-0.960449\pi$
$271$	−9.93447	−	17.2070i	−0.603476	−	1.04525i	0.388814	−	0.921316i	$-0.372885\pi$
$272$	0.541695	−	3.07211i	0.0328451	−	0.186274i
$273$		0			0
$274$	−22.6598	−	8.24751i	−1.36893	−	0.498250i
$275$	2.16743	+	0.788879i	0.130701	+	0.0475712i
$276$		0			0
$277$	−0.951869	+	5.39832i	−0.0571923	+	0.324353i	−0.999959	−	0.00910069i	$-0.997103\pi$
$277$	−0.951869	+	5.39832i	−0.0571923	+	0.324353i	0.942766	+	0.333454i	$0.108214\pi$
$278$	12.3463			0.740480
$279$		0			0
$280$	10.4315	+	0.0171337i	0.623402	+	0.00102394i
$281$	−14.9522	−	12.5464i	−0.891972	−	0.748454i	0.0766325	−	0.997059i	$-0.475583\pi$
$281$	−14.9522	−	12.5464i	−0.891972	−	0.748454i	−0.968605	+	0.248606i	$0.920028\pi$
$282$		0			0
$283$	21.2428	+	7.73174i	1.26275	+	0.459604i	0.884692	−	0.466177i	$-0.154369\pi$
$283$	21.2428	+	7.73174i	1.26275	+	0.459604i	0.378061	+	0.925781i	$0.376591\pi$
$284$	8.33899	+	3.03515i	0.494828	+	0.180103i
$285$		0			0
$286$	0.311873	+	0.261693i	0.0184414	+	0.0154742i
$287$	−14.7514	+	25.4535i	−0.870747	+	1.50247i
$288$		0			0
$289$	5.16669			0.303923
$290$	3.73768	−	21.1975i	0.219484	−	1.24476i
$291$		0			0
$292$	0.100905	+	0.0367263i	0.00590501	+	0.00214925i
$293$	10.9601	+	3.98916i	0.640298	+	0.233049i	0.641707	−	0.766950i	$-0.278226\pi$
$293$	10.9601	+	3.98916i	0.640298	+	0.233049i	−0.00140924	+	0.999999i	$0.500449\pi$
$294$		0			0
$295$	−0.195133	+	1.10666i	−0.0113611	+	0.0644320i
$296$	−11.8223	−	20.4768i	−0.687157	−	1.19019i
$297$		0			0
$298$	13.2326	−	22.9196i	0.766545	−	1.32769i
$299$	−1.38029	+	0.502384i	−0.0798242	+	0.0290536i
$300$		0			0
$301$	−3.92381	−	22.4688i	−0.226165	−	1.29508i
$302$	−0.377519	+	0.316776i	−0.0217238	+	0.0182284i
$303$		0			0
$304$	−0.0580270	+	0.329087i	−0.00332808	+	0.0188745i
$305$	−7.17970	−	12.4356i	−0.411108	−	0.712061i
$306$		0			0
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	0.704901	−	0.709305i	$-0.250991\pi$
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	−0.966727	+	0.255810i	$0.917658\pi$
$308$	−7.39880	+	2.67919i	−0.421586	+	0.152661i
$309$		0			0
$310$	−10.4151	+	8.73929i	−0.591537	+	0.496358i
$311$	−6.79138	−	2.47186i	−0.385104	−	0.140166i	0.142211	−	0.989836i	$-0.454579\pi$
$311$	−6.79138	−	2.47186i	−0.385104	−	0.140166i	−0.527315	+	0.849670i	$0.676801\pi$
$312$		0			0
$313$	−0.801216	+	4.54392i	−0.0452874	+	0.256838i	−0.999043	−	0.0437467i	$-0.986071\pi$
$313$	−0.801216	+	4.54392i	−0.0452874	+	0.256838i	0.953755	+	0.300584i	$0.0971817\pi$
$314$	−24.4441	−	42.3383i	−1.37946	−	2.38929i
$315$		0			0
$316$	−12.8868	+	22.3206i	−0.724939	+	1.25563i
$317$	−8.07739	−	6.77774i	−0.453672	−	0.380676i	0.387125	−	0.922027i	$-0.373468\pi$
$317$	−8.07739	−	6.77774i	−0.453672	−	0.380676i	−0.840796	+	0.541352i	$0.817913\pi$
$318$		0			0
$319$	0.990226	+	5.61585i	0.0554420	+	0.314427i
$320$	3.65998	+	20.7568i	0.204599	+	1.16034i
$321$		0			0
$322$	8.20425	−	46.0859i	0.457205	−	2.56826i
$323$	−2.37452			−0.132122
$324$		0			0
$325$	−0.223728	+	0.387509i	−0.0124102	+	0.0214951i
$326$	15.8566	+	13.3052i	0.878214	+	0.736909i
$327$		0			0
$328$	25.5035	+	9.28250i	1.40819	+	0.512540i
$329$	0.688346	+	3.94165i	0.0379497	+	0.217310i
$330$		0			0
$331$	19.2351	+	16.1402i	1.05726	+	0.887146i	0.993838	−	0.110841i	$-0.0353544\pi$
$331$	19.2351	+	16.1402i	1.05726	+	0.887146i	0.0634211	+	0.997987i	$0.479799\pi$
$332$	21.2088	+	36.7347i	1.16398	+	2.01608i
$333$		0			0
$334$	−9.66057	+	16.7326i	−0.528603	+	0.915567i
$335$	3.94588	+	3.31098i	0.215586	+	0.180898i
$336$		0			0
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	0.992221	+	0.124491i	$0.0397298\pi$
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	−0.889804	+	0.456343i	$0.849159\pi$
$338$	22.3908	−	18.7881i	1.21790	−	1.02194i
$339$		0			0
$340$	−22.0306	+	8.01849i	−1.19478	+	0.434864i
$341$	1.80099	−	3.11940i	0.0975289	−	0.168925i
$342$		0			0
$343$	−9.33905	+	15.9932i	−0.504261	+	0.863551i
$344$	−19.7730	+	7.19678i	−1.06609	+	0.388025i
$345$		0			0
$346$	7.65961	+	43.4398i	0.411783	+	2.33534i
$347$	1.28400	−	1.07741i	0.0689289	−	0.0578382i	−0.607672	−	0.794188i	$-0.707897\pi$
$347$	1.28400	−	1.07741i	0.0689289	−	0.0578382i	0.676601	+	0.736350i	$0.263452\pi$
$348$		0			0
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	−0.911283	−	0.411782i	$-0.864907\pi$
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	0.997163	−	0.0752713i	$-0.0239823\pi$
$350$	−7.10954	−	12.3609i	−0.380021	−	0.660720i
$351$		0			0
$352$	−3.07552	−	5.32695i	−0.163926	−	0.283927i
$353$	−12.7820	−	10.7253i	−0.680315	−	0.570852i	0.235783	−	0.971806i	$-0.424234\pi$
$353$	−12.7820	−	10.7253i	−0.680315	−	0.570852i	−0.916098	+	0.400953i	$0.868679\pi$
$354$		0			0
$355$	0.807496	+	4.57954i	0.0428574	+	0.243057i
$356$	26.9494	−	22.6132i	1.42832	−	1.19850i
$357$		0			0
$358$	−12.3983	+	4.51260i	−0.655269	+	0.238498i
$359$	6.85278			0.361676			0.180838	−	0.983513i	$-0.442119\pi$
$359$	6.85278			0.361676			0.180838	+	0.983513i	$0.442119\pi$
$360$		0			0
$361$	−18.7456			−0.986613
$362$	−0.259483	+	1.47160i	−0.0136381	+	0.0773455i
$363$		0			0
$364$	−0.262612	−	1.50378i	−0.0137646	−	0.0788197i
$365$	0.00977099	+	0.0554140i	0.000511437	+	0.00290050i
$366$		0			0
$367$	6.75224	−	2.45761i	0.352464	−	0.128286i	−0.159720	−	0.987162i	$-0.551059\pi$
$367$	6.75224	−	2.45761i	0.352464	−	0.128286i	0.512183	+	0.858876i	$0.328837\pi$
$368$	5.19975			0.271056
$369$		0			0
$370$	17.6393	−	30.5521i	0.917021	−	1.58833i
$371$	−6.89432	+	2.49651i	−0.357935	+	0.129612i
$372$		0			0
$373$	27.5343	+	10.0217i	1.42567	+	0.518902i	0.935688	−	0.352830i	$-0.114780\pi$
$373$	27.5343	+	10.0217i	1.42567	+	0.518902i	0.489984	+	0.871732i	$0.337003\pi$
$374$	7.84499	−	6.58273i	0.405655	−	0.340385i
$375$		0			0
$376$	3.46873	−	1.26252i	0.178886	−	0.0651093i
$377$	−1.10626			−0.0569752
$378$		0			0
$379$	0.333430			0.0171272			0.00856359	−	0.999963i	$-0.497274\pi$
$379$	0.333430			0.0171272			0.00856359	+	0.999963i	$0.497274\pi$
$380$	2.35994	−	0.858949i	0.121063	−	0.0440632i
$381$		0			0
$382$	15.2392	−	12.7872i	0.779705	−	0.654250i
$383$	−13.5363	−	4.92681i	−0.691672	−	0.251748i	−0.0278213	−	0.999613i	$-0.508857\pi$
$383$	−13.5363	−	4.92681i	−0.691672	−	0.251748i	−0.663851	+	0.747865i	$0.731079\pi$
$384$		0			0
$385$	−3.15437	−	2.65567i	−0.160762	−	0.135346i
$386$	9.70468	−	16.8090i	0.493955	−	0.855556i
$387$		0			0
$388$	−31.1155			−1.57965
$389$	21.4697	−	7.81432i	1.08855	−	0.396202i	0.265470	−	0.964119i	$-0.414473\pi$
$389$	21.4697	−	7.81432i	1.08855	−	0.396202i	0.823085	+	0.567918i	$0.192251\pi$
$390$		0			0
$391$	6.41607	+	36.3873i	0.324475	+	1.84019i
$392$	16.0359	+	5.89634i	0.809938	+	0.297810i
$393$		0			0
$394$	6.65536	−	37.7444i	0.335292	−	1.90154i
$395$	−13.5057			−0.679546
$396$		0			0
$397$	22.6020			1.13436			0.567181	−	0.823593i	$-0.308034\pi$
$397$	22.6020			1.13436			0.567181	+	0.823593i	$0.308034\pi$
$398$	48.5522	−	17.6715i	2.43370	−	0.885794i
$399$		0			0
$400$	1.21340	−	1.01816i	0.0606700	−	0.0509081i
$401$	2.29230	+	13.0003i	0.114472	+	0.649203i	0.987010	+	0.160657i	$0.0513614\pi$
$401$	2.29230	+	13.0003i	0.114472	+	0.649203i	−0.872538	+	0.488546i	$0.837527\pi$
$402$		0			0
$403$	0.535287	+	0.449159i	0.0266645	+	0.0223742i
$404$	−3.18127	−	5.51012i	−0.158274	−	0.274139i
$405$		0			0
$406$	17.6774	−	30.5023i	0.877314	−	1.51381i
$407$	−1.62298	+	9.20436i	−0.0804480	+	0.456243i
$408$		0			0
$409$	2.05094	−	1.72095i	0.101413	−	0.0850953i	−0.590672	−	0.806912i	$-0.701137\pi$
$409$	2.05094	−	1.72095i	0.101413	−	0.0850953i	0.692084	+	0.721817i	$0.256693\pi$
$410$	7.03173	+	39.8789i	0.347273	+	1.96948i
$411$		0			0
$412$	51.3440	−	18.6877i	2.52954	−	0.920676i
$413$	−0.922883	+	1.59243i	−0.0454121	+	0.0783586i
$414$		0			0
$415$	−11.1137	+	19.2495i	−0.545549	+	0.944919i
$416$	1.12131	−	0.408124i	0.0549768	−	0.0200099i
$417$		0			0
$418$	−0.840365	+	0.705150i	−0.0411036	+	0.0344900i
$419$	4.94281	+	28.0321i	0.241472	+	1.36946i	0.828545	+	0.559922i	$0.189169\pi$
$419$	4.94281	+	28.0321i	0.241472	+	1.36946i	−0.587073	+	0.809534i	$0.699720\pi$
$420$		0			0
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	0.0602237	−	0.998185i	$-0.480819\pi$
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	−0.972562	+	0.232642i	$0.925263\pi$
$422$	17.7852	−	30.8049i	0.865770	−	1.49956i
$423$		0			0
$424$	3.38221	+	5.85816i	0.164255	+	0.284497i
$425$	8.62224	+	7.23491i	0.418240	+	0.350945i
$426$		0			0
$427$	−4.04598	−	23.1684i	−0.195799	−	1.12120i
$428$	48.9201	+	17.8055i	2.36464	+	0.860659i
$429$		0			0
$430$	−24.0502	−	20.1806i	−1.15981	−	0.973193i
$431$	−11.9105	+	20.6296i	−0.573709	+	0.993692i	0.422472	+	0.906376i	$0.361162\pi$
$431$	−11.9105	+	20.6296i	−0.573709	+	0.993692i	−0.996181	+	0.0873164i	$0.972171\pi$
$432$		0			0
$433$	32.7062			1.57176			0.785880	−	0.618379i	$-0.212210\pi$
$433$	32.7062			1.57176			0.785880	+	0.618379i	$0.212210\pi$
$434$	−20.9380	+	7.58190i	−1.00506	+	0.363943i
$435$		0			0
$436$	6.45836	+	36.6272i	0.309299	+	1.75412i
$437$	−0.687297	−	3.89785i	−0.0328779	−	0.186460i
$438$		0			0
$439$	−18.7534	−	15.7360i	−0.895050	−	0.751036i	0.0741666	−	0.997246i	$-0.476370\pi$
$439$	−18.7534	−	15.7360i	−0.895050	−	0.751036i	−0.969217	+	0.246210i	$0.920815\pi$
$440$	−1.90201	+	3.29437i	−0.0906747	+	0.157053i
$441$		0			0
$442$	0.993347	+	1.72053i	0.0472487	+	0.0818372i
$443$	0.643330	−	3.64851i	0.0305655	−	0.173346i	−0.965704	−	0.259647i	$-0.916394\pi$
$443$	0.643330	−	3.64851i	0.0305655	−	0.173346i	0.996269	+	0.0863015i	$0.0275048\pi$
$444$		0			0
$445$	17.3230	+	6.30506i	0.821189	+	0.298888i
$446$	−18.0525	+	15.1478i	−0.854809	+	0.717270i
$447$		0			0
$448$	−6.05044	+	33.9872i	−0.285856	+	1.60575i
$449$	4.45575	+	7.71759i	0.210280	+	0.364215i	0.951802	−	0.306713i	$-0.0992291\pi$
$449$	4.45575	+	7.71759i	0.210280	+	0.364215i	−0.741522	+	0.670928i	$0.765896\pi$
$450$		0			0
$451$	−5.36406	−	9.29083i	−0.252584	−	0.437488i
$452$	9.04877	−	51.3181i	0.425618	−	2.41380i
$453$		0			0
$454$	−5.99113	+	5.02716i	−0.281178	+	0.235936i
$455$	0.613624	−	0.513177i	0.0287671	−	0.0240581i
$456$		0			0
$457$	−6.80857	+	2.47812i	−0.318492	+	0.115921i	−0.496319	−	0.868140i	$-0.665315\pi$
$457$	−6.80857	+	2.47812i	−0.318492	+	0.115921i	0.177827	+	0.984062i	$0.443093\pi$
$458$	−22.0275	+	38.1528i	−1.02928	+	1.78276i
$459$		0			0
$460$	−19.5393	−	33.8431i	−0.911025	−	1.57794i
$461$	0.937013	−	5.31406i	0.0436410	−	0.247501i	−0.955181	−	0.296022i	$-0.904340\pi$
$461$	0.937013	−	5.31406i	0.0436410	−	0.247501i	0.998822	+	0.0485214i	$0.0154509\pi$
$462$		0			0
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	0.242904	−	0.970050i	$-0.421900\pi$
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	−0.437461	+	0.899237i	$0.644122\pi$
$464$	3.67994	+	1.33939i	0.170837	+	0.0621796i
$465$		0			0
$466$	0.00596504	−	0.0338294i	0.000276325	−	0.00156712i
$467$	28.6791			1.32711			0.663554	−	0.748128i	$-0.269047\pi$
$467$	28.6791			1.32711			0.663554	+	0.748128i	$0.269047\pi$
$468$		0			0
$469$	4.20634	+	7.31331i	0.194231	+	0.337697i
$470$	4.21908	+	3.54023i	0.194612	+	0.163299i
$471$		0			0
$472$	1.59556	+	0.580736i	0.0734416	+	0.0267305i
$473$	7.81597	+	2.84478i	0.359379	+	0.130803i
$474$		0			0
$475$	−0.923624	−	0.775012i	−0.0423788	−	0.0355600i
$476$	−38.3993	−	0.0630707i	−1.76003	−	0.00289084i
$477$		0			0
$478$	25.3124			1.15776
$479$	1.94837	−	11.0498i	0.0890235	−	0.504877i	−0.907392	−	0.420285i	$-0.861930\pi$
$479$	1.94837	−	11.0498i	0.0890235	−	0.504877i	0.996416	−	0.0845923i	$-0.0269588\pi$
$480$		0			0
$481$	−1.70381	−	0.620135i	−0.0776869	−	0.0282757i
$482$	−63.9764	−	23.2855i	−2.91404	−	1.06062i
$483$		0			0
$484$	−5.38997	+	30.5680i	−0.244999	+	1.38946i
$485$	−8.15246	−	14.1205i	−0.370184	−	0.641178i
$486$		0			0
$487$	−13.8374	+	23.9671i	−0.627033	+	1.08605i	0.361111	+	0.932523i	$0.382398\pi$
$487$	−13.8374	+	23.9671i	−0.627033	+	1.08605i	−0.988144	+	0.153530i	$0.950936\pi$
$488$	−20.3886	+	7.42086i	−0.922951	+	0.335927i
$489$		0			0
$490$	4.34420	+	25.1194i	0.196251	+	1.13478i
$491$	−23.0453	+	19.3373i	−1.04002	+	0.872682i	−0.992009	−	0.126165i	$-0.959733\pi$
$491$	−23.0453	+	19.3373i	−1.04002	+	0.872682i	−0.0480122	+	0.998847i	$0.515289\pi$
$492$		0			0
$493$	−4.83216	+	27.4046i	−0.217630	+	1.23424i
$494$	−0.106408	−	0.184305i	−0.00478754	−	0.00829227i
$495$		0			0
$496$	−1.23681	−	2.14221i	−0.0555342	−	0.0961880i
$497$	−1.33490	+	7.49856i	−0.0598785	+	0.336356i
$498$		0			0
$499$	−9.73355	+	8.16742i	−0.435734	+	0.365624i	−0.834110	−	0.551598i	$-0.814018\pi$
$499$	−9.73355	+	8.16742i	−0.435734	+	0.365624i	0.398376	+	0.917222i	$0.369574\pi$
$500$	−34.5827	−	12.5871i	−1.54658	−	0.562911i
$501$		0			0
$502$	−3.09762	+	17.5675i	−0.138254	+	0.784076i
$503$	−5.27617	−	9.13860i	−0.235253	−	0.407470i	0.724093	−	0.689702i	$-0.242259\pi$
$503$	−5.27617	−	9.13860i	−0.235253	−	0.407470i	−0.959346	+	0.282232i	$0.908925\pi$
$504$		0			0
$505$	1.66703	−	2.88738i	0.0741817	−	0.128487i
$506$	13.0765	+	10.9725i	0.581320	+	0.487786i
$507$		0			0
$508$	3.48122	+	19.7430i	0.154454	+	0.875952i
$509$	−0.763789	−	4.33166i	−0.0338543	−	0.191998i	0.963190	−	0.268820i	$-0.0866337\pi$
$509$	−0.763789	−	4.33166i	−0.0338543	−	0.191998i	−0.997045	+	0.0768224i	$0.975523\pi$
$510$		0			0
$511$	−0.0161528	+	0.0907352i	−0.000714557	+	0.00401389i
$512$	−7.45857			−0.329625
$513$		0			0
$514$	−0.678447	+	1.17511i	−0.0299250	+	0.0518317i
$515$	21.9331	+	18.4041i	0.966488	+	0.810979i
$516$		0			0
$517$	−1.37114	−	0.499054i	−0.0603026	−	0.0219484i
$518$	44.3246	−	37.0688i	1.94751	−	1.62871i
$519$		0			0
$520$	−0.565313	−	0.474354i	−0.0247906	−	0.0208018i
$521$	−11.1596	−	19.3289i	−0.488909	−	0.846816i	0.511009	−	0.859575i	$-0.329272\pi$
$521$	−11.1596	−	19.3289i	−0.488909	−	0.846816i	−0.999919	+	0.0127592i	$0.995938\pi$
$522$		0			0
$523$	−9.08231	+	15.7310i	−0.397142	+	0.687869i	−0.993372	−	0.114944i	$-0.963331\pi$
$523$	−9.08231	+	15.7310i	−0.397142	+	0.687869i	0.596230	+	0.802813i	$0.296664\pi$
$524$	−5.33190	−	4.47400i	−0.232925	−	0.195447i
$525$		0			0
$526$	−0.203626	−	1.15482i	−0.00887853	−	0.0503527i
$527$	13.4648	−	11.2983i	0.586538	−	0.492164i
$528$		0			0
$529$	−36.2610	+	13.1979i	−1.57656	+	0.573823i
$530$	−5.04637	+	8.74057i	−0.219200	+	0.379666i
$531$		0			0
$532$	4.11337	+	0.00675620i	0.178337	+	0.000292918i
$533$	1.95570	−	0.711816i	0.0847107	−	0.0308322i
$534$		0			0
$535$	4.73712	+	26.8655i	0.204803	+	1.16150i
$536$	5.96224	−	5.00292i	0.257530	−	0.216093i
$537$		0			0
$538$	0.0598168	−	0.339238i	0.00257888	−	0.0146256i
$539$	−3.35761	−	5.85993i	−0.144623	−	0.252405i
$540$		0			0
$541$	−14.1984	−	24.5924i	−0.610438	−	1.05731i	−0.991167	−	0.132623i	$-0.957660\pi$
$541$	−14.1984	−	24.5924i	−0.610438	−	1.05731i	0.380729	−	0.924687i	$-0.375673\pi$
$542$	−34.3142	−	28.7930i	−1.47392	−	1.23677i
$543$		0			0
$544$	−5.21225	−	29.5601i	−0.223473	−	1.26738i
$545$	−14.9296	+	12.5274i	−0.639514	+	0.536616i
$546$		0			0
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	−0.0509474	−	0.998701i	$-0.516224\pi$
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	0.602925	+	0.797798i	$0.294002\pi$
$548$	−32.9724			−1.40851
$549$		0			0
$550$	5.20001			0.221729
$551$	0.517627	−	2.93561i	0.0220516	−	0.125061i
$552$		0			0
$553$	−20.7743	−	7.59988i	−0.883412	−	0.323180i
$554$	2.14596	+	12.1704i	0.0911732	+	0.517069i
$555$		0			0
$556$	15.8636	−	5.77386i	0.672765	−	0.244866i
$557$	−10.5881			−0.448631			−0.224316	−	0.974517i	$-0.572015\pi$
$557$	−10.5881			−0.448631			−0.224316	+	0.974517i	$0.572015\pi$
$558$		0			0
$559$	−0.806788	+	1.39740i	−0.0341235	+	0.0591037i
$560$	−2.66253	+	0.964132i	−0.112512	+	0.0407420i
$561$		0			0
$562$	−41.3506	−	15.0504i	−1.74427	−	0.634862i
$563$	−11.5992	+	9.73288i	−0.488848	+	0.410192i	−0.853613	−	0.520907i	$-0.825594\pi$
$563$	−11.5992	+	9.73288i	−0.488848	+	0.410192i	0.364765	+	0.931100i	$0.381149\pi$
$564$		0			0
$565$	25.6595	−	9.33928i	1.07950	−	0.392906i
$566$	50.9648			2.14221
$567$		0			0
$568$	7.02646			0.294824
$569$	−21.1188	+	7.68663i	−0.885348	+	0.322240i	−0.744366	−	0.667772i	$-0.767248\pi$
$569$	−21.1188	+	7.68663i	−0.885348	+	0.322240i	−0.140982	+	0.990012i	$0.545026\pi$
$570$		0			0
$571$	−7.29087	+	6.11777i	−0.305114	+	0.256021i	−0.782469	−	0.622690i	$-0.786040\pi$
$571$	−7.29087	+	6.11777i	−0.305114	+	0.256021i	0.477355	+	0.878710i	$0.341595\pi$
$572$	0.523105	+	0.190395i	0.0218721	+	0.00796080i
$573$		0			0
$574$	−11.6244	+	65.2980i	−0.485194	+	2.72549i
$575$	−9.38068	+	16.2478i	−0.391201	+	0.677580i
$576$		0			0
$577$	−42.3017			−1.76104			−0.880521	−	0.474007i	$-0.842807\pi$
$577$	−42.3017			−1.76104			−0.880521	+	0.474007i	$0.842807\pi$
$578$	10.9457	−	3.98390i	0.455280	−	0.165709i
$579$		0			0
$580$	−5.11071	−	28.9843i	−0.212211	−	1.20351i
$581$	−27.9269	+	23.3554i	−1.15860	+	0.968943i
$582$		0			0
$583$	0.464313	−	2.63325i	0.0192299	−	0.109058i
$584$	0.0850226			0.00351826
$585$		0			0
$586$	26.2951			1.08624
$587$	−12.4550	+	4.53327i	−0.514075	+	0.187108i	−0.586014	−	0.810301i	$-0.699304\pi$
$587$	−12.4550	+	4.53327i	−0.514075	+	0.187108i	0.0719389	+	0.997409i	$0.477081\pi$
$588$		0			0
$589$	−1.44237	+	1.21029i	−0.0594318	+	0.0498692i
$590$	0.439923	+	2.49492i	0.0181113	+	0.102714i
$591$		0			0
$592$	4.91685	+	4.12573i	0.202081	+	0.169566i
$593$	−22.2156	−	38.4786i	−0.912287	−	1.58013i	−0.810826	−	0.585287i	$-0.800982\pi$
$593$	−22.2156	−	38.4786i	−0.912287	−	1.58013i	−0.101460	−	0.994840i	$-0.532351\pi$
$594$		0			0
$595$	−10.0322	−	17.4424i	−0.411282	−	0.715071i
$596$	6.28384	−	35.6374i	0.257396	−	1.45977i
$597$		0			0
$598$	−2.53678	+	2.12861i	−0.103737	+	0.0870455i
$599$	−6.77975	−	38.4499i	−0.277013	−	1.57102i	−0.732494	−	0.680774i	$-0.761644\pi$
$599$	−6.77975	−	38.4499i	−0.277013	−	1.57102i	0.455480	−	0.890246i	$-0.349467\pi$
$600$		0			0
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.322240	−	0.946658i	$-0.395564\pi$
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.855350	+	0.518050i	$0.173342\pi$
$602$	−25.6378	−	44.5748i	−1.04492	−	1.81674i
$603$		0			0
$604$	−0.336925	+	0.583572i	−0.0137093	+	0.0237452i
$605$	−15.2843	+	5.56302i	−0.621393	+	0.226169i
$606$		0			0
$607$	−5.67351	+	4.76064i	−0.230281	+	0.193228i	−0.750626	−	0.660728i	$-0.770248\pi$
$607$	−5.67351	+	4.76064i	−0.230281	+	0.193228i	0.520345	+	0.853956i	$0.325803\pi$
$608$	0.558342	+	3.16652i	0.0226438	+	0.128419i
$609$		0			0
$610$	−24.7991	−	20.8089i	−1.00408	−	0.842527i
$611$	0.141533	−	0.245143i	0.00572582	−	0.00991741i
$612$		0			0
$613$	11.9455	+	20.6902i	0.482475	+	0.835671i	0.999798	−	0.0201196i	$-0.00640471\pi$
$613$	11.9455	+	20.6902i	0.482475	+	0.835671i	−0.517323	+	0.855790i	$0.673071\pi$
$614$	−15.8457	−	13.2961i	−0.639479	−	0.536587i
$615$		0			0
$616$	−4.77943	+	3.99706i	−0.192569	+	0.161046i
$617$	−12.6845	−	4.61680i	−0.510661	−	0.185865i	0.0738220	−	0.997271i	$-0.476480\pi$
$617$	−12.6845	−	4.61680i	−0.510661	−	0.185865i	−0.584483	+	0.811406i	$0.698703\pi$
$618$		0			0
$619$	20.9806	+	17.6048i	0.843280	+	0.707596i	0.958299	−	0.285767i	$-0.0922484\pi$
$619$	20.9806	+	17.6048i	0.843280	+	0.707596i	−0.115019	+	0.993363i	$0.536693\pi$
$620$	−9.29517	+	16.0997i	−0.373303	+	0.646580i
$621$		0			0
$622$	−16.2936			−0.653314
$623$	23.0980	+	19.4463i	0.925402	+	0.779098i
$624$		0			0
$625$	−1.27311	−	7.22018i	−0.0509245	−	0.288807i
$626$	1.80632	+	10.2441i	0.0721951	+	0.409439i
$627$		0			0
$628$	−51.2078	−	42.9685i	−2.04341	−	1.71463i
$629$	−22.8044	+	39.4984i	−0.909272	+	1.57491i
$630$		0			0
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	0.995384	+	0.0959739i	$0.0305965\pi$
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	−0.414576	+	0.910015i	$0.636070\pi$
$632$	−3.54368	+	20.0972i	−0.140960	+	0.799423i
$633$		0			0
$634$	−22.3382	−	8.13044i	−0.887163	−	0.322901i
$635$	−8.04743	+	6.75260i	−0.319353	+	0.267969i
$636$		0			0
$637$	1.23264	−	0.444064i	0.0488390	−	0.0175945i
$638$	6.42805	+	11.1337i	0.254489	+	0.440788i
$639$		0			0
$640$	13.4603	+	23.3139i	0.532065	+	0.921563i
$641$	−7.93557	+	45.0049i	−0.313436	+	1.77759i	0.267421	+	0.963580i	$0.413829\pi$
$641$	−7.93557	+	45.0049i	−0.313436	+	1.77759i	−0.580857	+	0.814005i	$0.697283\pi$
$642$		0			0
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	−0.678497	−	0.734603i	$-0.737368\pi$
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	0.605623	+	0.795751i	$0.292924\pi$
$644$	−11.0110	−	63.0519i	−0.433894	−	2.48459i
$645$		0			0
$646$	−5.03045	+	1.83093i	−0.197920	+	0.0720371i
$647$	10.6983	−	18.5300i	0.420594	−	0.728491i	−0.575403	−	0.817870i	$-0.695155\pi$
$647$	10.6983	−	18.5300i	0.420594	−	0.728491i	0.995998	+	0.0893790i	$0.0284882\pi$
$648$		0			0
$649$	−0.335589	−	0.581257i	−0.0131730	−	0.0228163i
$650$	−0.175173	+	0.993454i	−0.00687084	+	0.0389665i
$651$		0			0
$652$	26.5962	+	9.68023i	1.04159	+	0.379107i
$653$	39.5114	+	14.3810i	1.54620	+	0.562771i	0.967522	−	0.252785i	$-0.0813466\pi$
$653$	39.5114	+	14.3810i	1.54620	+	0.562771i	0.578678	+	0.815556i	$0.303569\pi$
$654$		0			0
$655$	0.633345	−	3.59188i	0.0247469	−	0.140346i
$656$	−7.36741			−0.287649
$657$		0			0
$658$	4.49758	+	7.81967i	0.175334	+	0.304842i
$659$	−18.8582	−	15.8239i	−0.734612	−	0.616413i	0.196772	−	0.980449i	$-0.436954\pi$
$659$	−18.8582	−	15.8239i	−0.734612	−	0.616413i	−0.931385	+	0.364036i	$0.881398\pi$
$660$		0			0
$661$	−18.3545	−	6.68048i	−0.713906	−	0.259841i	−0.0405697	−	0.999177i	$-0.512917\pi$
$661$	−18.3545	−	6.68048i	−0.713906	−	0.259841i	−0.673337	+	0.739336i	$0.735140\pi$
$662$	53.1952	+	19.3615i	2.06749	+	0.752505i
$663$		0			0
$664$	25.7281	+	21.5885i	0.998445	+	0.837795i
$665$	1.07466	+	1.86845i	0.0416737	+	0.0724556i
$666$		0			0
$667$	−46.3841			−1.79600
$668$	−4.58756	+	26.0174i	−0.177498	+	1.00664i
$669$		0			0
$670$	10.9124	+	3.97179i	0.421583	+	0.153444i
$671$	8.05933	+	2.93336i	0.311127	+	0.113241i
$672$		0			0
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	0.858361	+	0.513046i	$0.171483\pi$
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	−0.982068	+	0.188529i	$0.939628\pi$
$674$	12.2048	+	21.1393i	0.470111	+	0.814256i
$675$		0			0
$676$	19.9832	−	34.6120i	0.768585	−	1.33123i
$677$	6.42342	−	2.33793i	0.246872	−	0.0898540i	−0.215621	−	0.976477i	$-0.569177\pi$
$677$	6.42342	−	2.33793i	0.246872	−	0.0898540i	0.462492	+	0.886623i	$0.346955\pi$
$678$		0			0
$679$	−4.59417	−	26.3074i	−0.176308	−	1.00959i
$680$	−14.2201	+	11.9321i	−0.545317	+	0.457575i
$681$		0			0
$682$	1.41012	−	7.99718i	0.0539962	−	0.306228i
$683$	−8.17274	−	14.1556i	−0.312721	−	0.541649i	0.666229	−	0.745747i	$-0.267907\pi$
$683$	−8.17274	−	14.1556i	−0.312721	−	0.541649i	−0.978950	+	0.204098i	$0.934574\pi$
$684$		0			0
$685$	−8.63898	−	14.9631i	−0.330078	−	0.571713i
$686$	−7.45293	+	41.0829i	−0.284554	+	1.56855i
$687$		0			0
$688$	4.37565	−	3.67160i	0.166820	−	0.139979i
$689$	0.487438	+	0.177413i	0.0185699	+	0.00675889i
$690$		0			0
$691$	−4.69295	+	26.6151i	−0.178528	+	1.01248i	0.755464	+	0.655191i	$0.227412\pi$
$691$	−4.69295	+	26.6151i	−0.178528	+	1.01248i	−0.933992	+	0.357294i	$0.883699\pi$
$692$	30.1568	+	52.2332i	1.14639	+	1.98561i
$693$		0			0
$694$	1.88941	−	3.27256i	0.0717212	−	0.124225i
$695$	6.77659	+	5.68623i	0.257051	+	0.215691i
$696$		0			0
$697$	−9.09078	−	51.5564i	−0.344338	−	1.95284i
$698$	−3.61704	−	20.5132i	−0.136907	−	0.776437i
$699$		0			0
$700$	−14.9157	−	12.5575i	−0.563760	−	0.474631i
$701$	10.3899			0.392422			0.196211	−	0.980562i	$-0.437136\pi$
$701$	10.3899			0.392422			0.196211	+	0.980562i	$0.437136\pi$
$702$		0			0
$703$	2.44284	−	4.23112i	0.0921333	−	0.159580i
$704$	−9.64359	−	8.09193i	−0.363457	−	0.304976i
$705$		0			0
$706$	−35.3488	−	12.8659i	−1.33037	−	0.484215i
$707$	4.18897	−	3.50325i	0.157542	−	0.131753i
$708$		0			0
$709$	1.99047	+	1.67020i	0.0747536	+	0.0627257i	0.679399	−	0.733769i	$-0.262241\pi$
$709$	1.99047	+	1.67020i	0.0747536	+	0.0627257i	−0.604645	+	0.796495i	$0.706685\pi$
$710$	5.24186	+	9.07916i	0.196723	+	0.340735i
$711$		0			0
$712$	13.9275	−	24.1232i	0.521956	−	0.904054i
$713$	22.4440	+	18.8327i	0.840533	+	0.705291i
$714$		0			0
$715$	0.0506542	+	0.287274i	0.00189436	+	0.0107434i
$716$	−13.8200	+	11.5964i	−0.516478	+	0.433377i
$717$		0			0
$718$	14.5177	−	5.28401i	0.541795	−	0.197197i
$719$	−2.82487	+	4.89282i	−0.105350	+	0.182471i	−0.913881	−	0.405982i	$-0.866930\pi$
$719$	−2.82487	+	4.89282i	−0.105350	+	0.182471i	0.808531	+	0.588453i	$0.200263\pi$
$720$		0			0
$721$	23.3809	+	40.6509i	0.870749	+	1.51392i
$722$	−39.7129	+	14.4543i	−1.47796	+	0.537933i
$723$		0			0
$724$	0.354803	+	2.01219i	0.0131861	+	0.0747824i
$725$	−10.8241	+	9.08247i	−0.401996	+	0.337315i
$726$		0			0
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	−0.983186	−	0.182608i	$-0.941546\pi$
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	0.986348	+	0.164674i	$0.0526570\pi$
$728$	−0.602628	−	1.04775i	−0.0223349	−	0.0388323i
$729$		0			0
$730$	0.0634283	+	0.109861i	0.00234759	+	0.00406614i
$731$	31.0927	+	26.0899i	1.15001	+	0.964969i
$732$		0			0
$733$	−4.35051	−	24.6730i	−0.160690	−	0.911316i	−0.953398	−	0.301715i	$-0.902441\pi$
$733$	−4.35051	−	24.6730i	−0.160690	−	0.911316i	0.792708	−	0.609601i	$-0.208670\pi$
$734$	12.4097	−	10.4130i	0.458050	−	0.384350i
$735$		0			0
$736$	47.0153	−	17.1122i	1.73301	−	0.630763i
$737$	−3.07657			−0.113327
$738$		0			0
$739$	−9.83748			−0.361877			−0.180939	−	0.983494i	$-0.557914\pi$
$739$	−9.83748			−0.361877			−0.180939	+	0.983494i	$0.557914\pi$
$740$	8.37644	−	47.5052i	0.307924	−	1.74632i
$741$		0			0
$742$	−12.6807	+	10.6049i	−0.465523	+	0.389319i
$743$	1.59945	+	9.07091i	0.0586780	+	0.332779i	0.999989	−	0.00476202i	$-0.00151581\pi$
$743$	1.59945	+	9.07091i	0.0586780	+	0.332779i	−0.941311	+	0.337541i	$0.890405\pi$
$744$		0			0
$745$	17.8190	−	6.48558i	0.652837	−	0.237613i
$746$	66.0592			2.41860
$747$		0			0
$748$	7.00144	−	12.1269i	0.255998	−	0.443402i
$749$	−7.83110	+	43.9898i	−0.286142	+	1.60735i
$750$		0			0
$751$	37.5722	+	13.6752i	1.37103	+	0.499014i	0.919446	−	0.393215i	$-0.128637\pi$
$751$	37.5722	+	13.6752i	1.37103	+	0.499014i	0.451583	+	0.892229i	$0.350860\pi$
$752$	−0.767610	+	0.644101i	−0.0279919	+	0.0234880i
$753$		0			0
$754$	−2.34362	+	0.853008i	−0.0853497	+	0.0310647i
$755$	−0.353107			−0.0128509
$756$		0			0
$757$	28.8482			1.04850			0.524252	−	0.851563i	$-0.324345\pi$
$757$	28.8482			1.04850			0.524252	+	0.851563i	$0.324345\pi$
$758$	0.706376	−	0.257100i	0.0256567	−	0.00933829i
$759$		0			0
$760$	1.52328	−	1.27818i	0.0552550	−	0.0463645i
$761$	17.4626	+	6.35586i	0.633018	+	0.230400i	0.638544	−	0.769585i	$-0.279537\pi$
$761$	17.4626	+	6.35586i	0.633018	+	0.230400i	−0.00552629	+	0.999985i	$0.501759\pi$
$762$		0			0
$763$	−30.0139	+	10.8684i	−1.08657	+	0.393461i
$764$	13.6006	−	23.5569i	0.492051	−	0.852258i
$765$		0			0
$766$	−32.4757			−1.17340
$767$	0.122353	−	0.0445330i	0.00441792	−	0.00160799i
$768$		0			0
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	0.975269	+	0.221021i	$0.0709389\pi$
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	−0.840860	+	0.541253i	$0.817950\pi$
$770$	−8.73030	−	3.19382i	−0.314618	−	0.115097i
$771$		0			0
$772$	4.60851	−	26.1362i	0.165864	−	0.940661i
$773$	18.6930			0.672340			0.336170	−	0.941801i	$-0.390868\pi$
$773$	18.6930			0.672340			0.336170	+	0.941801i	$0.390868\pi$
$774$		0			0
$775$	8.92509			0.320599
$776$	−23.1511	+	8.42630i	−0.831075	+	0.302486i
$777$		0			0
$778$	39.4583	−	33.1094i	1.41465	−	1.18703i
$779$	0.973815	+	5.52278i	0.0348905	+	0.197874i
$780$		0			0
$781$	−2.12765	−	1.78531i	−0.0761334	−	0.0638835i
$782$	41.6499	+	72.1398i	1.48940	+	2.57971i
$783$		0			0
$784$	−4.63799	−	0.0152358i	−0.165643	−	0.000544136i
$785$	6.08268	−	34.4966i	0.217100	−	1.23124i
$786$		0			0
$787$	6.04767	−	5.07460i	0.215576	−	0.180890i	−0.528604	−	0.848868i	$-0.677285\pi$
$787$	6.04767	−	5.07460i	0.215576	−	0.180890i	0.744181	+	0.667978i	$0.232840\pi$
$788$	−9.10019	−	51.6097i	−0.324181	−	1.83852i
$789$		0			0
$790$	−28.6120	+	10.4139i	−1.01797	+	0.370511i
$791$	44.7243	+	0.0734596i	1.59021	+	0.00261192i
$792$		0			0
$793$	−0.831908	+	1.44091i	−0.0295419	+	0.0511681i
$794$	47.8826	−	17.4279i	1.69929	−	0.618491i
$795$		0			0
$796$	54.1197	−	45.4119i	1.91822	−	1.60958i
$797$	0.0774178	+	0.439058i	0.00274228	+	0.0155522i	0.986148	−	0.165867i	$-0.0530421\pi$
$797$	0.0774178	+	0.439058i	0.00274228	+	0.0155522i	−0.983406	+	0.181419i	$0.941931\pi$
$798$		0			0
$799$	−5.45452	−	4.57689i	−0.192967	−	0.161919i
$800$	7.62062	−	13.1993i	0.269430	−	0.466666i
$801$		0			0
$802$	14.8805	+	25.7737i	0.525448	+	0.910102i
$803$	−0.0257454	−	0.0216029i	−0.000908534	−	0.000762351i
$804$		0			0
$805$	25.7286	−	21.5169i	0.906813	−	0.758371i
$806$	1.48035	+	0.538802i	0.0521430	+	0.0189785i
$807$		0			0
$808$	−3.85916	−	3.23822i	−0.135765	−	0.113920i
$809$	23.7254	−	41.0936i	0.834140	−	1.44477i	−0.0605883	−	0.998163i	$-0.519298\pi$
$809$	23.7254	−	41.0936i	0.834140	−	1.44477i	0.894729	−	0.446610i	$-0.147369\pi$
$810$		0			0
$811$	−16.8993			−0.593416			−0.296708	−	0.954968i	$-0.595889\pi$
$811$	−16.8993			−0.593416			−0.296708	+	0.954968i	$0.595889\pi$
$812$	8.44871	−	47.4591i	0.296492	−	1.66549i
$813$		0			0
$814$	3.65896	+	20.7510i	0.128246	+	0.727321i
$815$	2.57541	+	14.6059i	0.0902128	+	0.511622i
$816$		0			0
$817$	−3.33068	−	2.79478i	−0.116526	−	0.0977769i
$818$	3.01797	−	5.22728i	0.105521	−	0.182767i
$819$		0			0
$820$	27.6848	+	47.9515i	0.966795	+	1.67454i
$821$	−2.80743	+	15.9217i	−0.0979798	+	0.555671i	0.895814	+	0.444430i	$0.146594\pi$
$821$	−2.80743	+	15.9217i	−0.0979798	+	0.555671i	−0.993793	+	0.111241i	$0.964517\pi$
$822$		0			0
$823$	−21.8344	−	7.94707i	−0.761099	−	0.277017i	−0.0678307	−	0.997697i	$-0.521608\pi$
$823$	−21.8344	−	7.94707i	−0.761099	−	0.277017i	−0.693268	+	0.720679i	$0.743830\pi$
$824$	33.1410	−	27.8086i	1.15452	−	0.968760i
$825$		0			0
$826$	−0.727252	+	4.08520i	−0.0253043	+	0.142142i
$827$	1.36430	+	2.36304i	0.0474415	+	0.0821710i	0.888771	−	0.458352i	$-0.151560\pi$
$827$	1.36430	+	2.36304i	0.0474415	+	0.0821710i	−0.841330	+	0.540523i	$0.818227\pi$
$828$		0			0
$829$	−6.01275	−	10.4144i	−0.208831	−	0.361706i	0.742515	−	0.669829i	$-0.233633\pi$
$829$	−6.01275	−	10.4144i	−0.208831	−	0.361706i	−0.951347	+	0.308123i	$0.900299\pi$
$830$	−8.70168	+	49.3497i	−0.302040	+	1.71295i
$831$		0			0
$832$	1.87082	−	1.56980i	0.0648589	−	0.0544231i
$833$	−5.61628	−	32.4750i	−0.194593	−	1.12519i
$834$		0			0
$835$	−13.0089	+	4.73484i	−0.450191	+	0.163856i
$836$	−0.750003	+	1.29904i	−0.0259394	+	0.0449283i
$837$		0			0
$838$	32.0862	+	55.5750i	1.10840	+	1.91981i
$839$	7.27989	−	41.2863i	0.251330	−	1.42536i	−0.553991	−	0.832522i	$-0.686896\pi$
$839$	7.27989	−	41.2863i	0.251330	−	1.42536i	0.805321	−	0.592839i	$-0.201993\pi$
$840$		0			0
$841$	−5.57566	−	2.02937i	−0.192264	−	0.0699784i
$842$	−51.7695	−	18.8426i	−1.78410	−	0.649358i
$843$		0			0
$844$	8.44575	−	47.8982i	0.290715	−	1.64872i
$845$	20.9429			0.720459
$846$		0			0
$847$	−26.6404	−	0.0437568i	−0.915375	−	0.00150350i
$848$	−1.40665	−	1.18032i	−0.0483045	−	0.0405323i
$849$		0			0
$850$	23.8450	+	8.67886i	0.817876	+	0.297682i
$851$	−71.4386	−	26.0015i	−2.44889	−	0.891321i
$852$		0			0
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	0.853096	−	0.521754i	$-0.174722\pi$
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	−0.365689	+	0.930737i	$0.619167\pi$
$854$	−26.4360	−	45.9627i	−0.904622	−	1.57281i
$855$		0			0
$856$	41.2202			1.40888
$857$	10.1401	−	57.5074i	0.346379	−	1.96442i	0.101675	−	0.994818i	$-0.467580\pi$
$857$	10.1401	−	57.5074i	0.346379	−	1.96442i	0.244704	−	0.969598i	$-0.421309\pi$
$858$		0			0
$859$	−27.3328	−	9.94833i	−0.932584	−	0.339433i	−0.169351	−	0.985556i	$-0.554167\pi$
$859$	−27.3328	−	9.94833i	−0.932584	−	0.339433i	−0.763233	+	0.646123i	$0.776389\pi$
$860$	−40.3395	−	14.6824i	−1.37556	−	0.500665i
$861$		0			0
$862$	−9.32557	+	52.8879i	−0.317630	+	1.80137i
$863$	−1.95160	−	3.38027i	−0.0664332	−	0.115066i	0.830896	−	0.556428i	$-0.187829\pi$
$863$	−1.95160	−	3.38027i	−0.0664332	−	0.115066i	−0.897329	+	0.441363i	$0.854495\pi$
$864$		0			0
$865$	−15.8026	+	27.3709i	−0.537304	+	0.930638i
$866$	69.2885	−	25.2190i	2.35452	−	0.856975i
$867$		0			0
$868$	−23.3572	+	19.5338i	−0.792797	+	0.663019i
$869$	6.17943	−	5.18516i	0.209623	−	0.175894i
$870$		0			0
$871$	0.103640	−	0.587774i	0.00351172	−	0.0199159i
$872$	14.7242	+	25.5030i	0.498623	+	0.863641i
$873$		0			0
$874$	−4.46158	−	7.72769i	−0.150915	−	0.261393i
$875$	5.53598	−	31.0973i	0.187150	−	1.05128i
$876$		0			0
$877$	30.9522	−	25.9720i	1.04518	−	0.877013i	0.0526043	−	0.998615i	$-0.483248\pi$
$877$	30.9522	−	25.9720i	1.04518	−	0.877013i	0.992579	+	0.121603i	$0.0388033\pi$
$878$	−51.8629	−	18.8765i	−1.75029	−	0.637052i
$879$		0			0
$880$	0.179314	−	1.01694i	0.00604467	−	0.0342810i
$881$	2.36050	+	4.08851i	0.0795274	+	0.137745i	0.903046	−	0.429544i	$-0.141326\pi$
$881$	2.36050	+	4.08851i	0.0795274	+	0.137745i	−0.823519	+	0.567289i	$0.807992\pi$
$882$		0			0
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.0931577	−	0.995651i	$-0.470304\pi$
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.815681	−	0.578503i	$-0.196363\pi$
$884$	2.08096	+	1.74613i	0.0699903	+	0.0587288i
$885$		0			0
$886$	−1.45037	−	8.22546i	−0.0487261	−	0.276340i
$887$	6.28643	+	35.6521i	0.211078	+	1.19708i	0.887585	+	0.460644i	$0.152382\pi$
$887$	6.28643	+	35.6521i	0.211078	+	1.19708i	−0.676507	+	0.736436i	$0.736507\pi$
$888$		0			0
$889$	−16.1782	+	5.85831i	−0.542600	+	0.196482i
$890$	41.5607			1.39312
$891$		0			0
$892$	−16.1113	+	27.9056i	−0.539447	+	0.934350i
$893$	0.584295	+	0.490281i	0.0195527	+	0.0164066i
$894$		0			0
$895$	−8.88347	−	3.23332i	−0.296942	−	0.108078i
$896$	7.58529	+	43.4354i	0.253407	+	1.45107i
$897$		0			0
$898$	15.3904	+	12.9141i	0.513584	+	0.430948i
$899$	11.0329	+	19.1095i	0.367966	+	0.637337i
$900$		0			0
$901$	6.52406	−	11.3000i	0.217348	−	0.376458i
$902$	−18.5278	−	15.5466i	−0.616907	−	0.517646i
$903$		0			0
$904$	−7.16470	−	40.6331i	−0.238295	−	1.35144i
$905$	−0.820188	+	0.688219i	−0.0272640	+	0.0228772i
$906$		0			0
$907$	47.2375	−	17.1931i	1.56850	−	0.570886i	0.595833	−	0.803108i	$-0.296822\pi$
$907$	47.2375	−	17.1931i	1.56850	−	0.570886i	0.972663	+	0.232222i	$0.0745996\pi$
$908$	−5.34692	+	9.26114i	−0.177444	+	0.307342i
$909$		0			0
$910$	0.904272	−	1.56032i	0.0299763	−	0.0517242i
$911$	10.2931	−	3.74638i	0.341026	−	0.124123i	−0.165829	−	0.986154i	$-0.553030\pi$
$911$	10.2931	−	3.74638i	0.341026	−	0.124123i	0.506855	+	0.862031i	$0.330808\pi$
$912$		0			0
$913$	−2.30534	−	13.0742i	−0.0762956	−	0.432694i
$914$	−12.5132	+	10.4998i	−0.413901	+	0.347304i
$915$		0			0
$916$	−10.4603	+	59.3234i	−0.345619	+	1.96010i
$917$	2.99541	−	5.16858i	0.0989171	−	0.170681i
$918$		0			0
$919$	6.42767	+	11.1330i	0.212029	+	0.367245i	0.952349	−	0.305009i	$-0.0986595\pi$
$919$	6.42767	+	11.1330i	0.212029	+	0.367245i	−0.740320	+	0.672254i	$0.765326\pi$
$920$	−23.7029	−	19.8891i	−0.781462	−	0.655724i
$921$		0			0
$922$	−2.11247	−	11.9804i	−0.0695705	−	0.394554i
$923$	0.412756	−	0.346343i	0.0135860	−	0.0114000i
$924$		0			0
$925$	−21.7621	+	7.92075i	−0.715532	+	0.260433i
$926$	−10.0438			−0.330060
$927$		0			0
$928$	37.6813			1.23695
$929$	4.60291	−	26.1044i	0.151017	−	0.856457i	−0.811321	−	0.584601i	$-0.801251\pi$
$929$	4.60291	−	26.1044i	0.151017	−	0.856457i	0.962338	−	0.271857i	$-0.0876377\pi$
$930$		0			0
$931$	0.601623	+	3.47876i	0.0197174	+	0.114012i
$932$	−0.00815629	−	0.0462566i	−0.000267168	−	0.00151519i
$933$		0			0
$934$	60.7569	−	22.1137i	1.98803	−	0.723583i
$935$	7.33770			0.239968
$936$		0			0
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	0.485980	+	0.873970i	$0.338463\pi$
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	−0.999870	+	0.0161137i	$0.994871\pi$
$938$	14.5503	+	12.2499i	0.475084	+	0.399974i
$939$		0			0
$940$	7.07667	+	2.57570i	0.230815	+	0.0840099i
$941$	−19.6665	+	16.5022i	−0.641111	+	0.537956i	−0.904359	−	0.426772i	$-0.859651\pi$
$941$	−19.6665	+	16.5022i	−0.641111	+	0.537956i	0.263248	+	0.964728i	$0.415206\pi$
$942$		0			0
$943$	82.0002	−	29.8456i	2.67029	−	0.971908i
$944$	−0.460923			−0.0150018
$945$		0			0
$946$	18.7518			0.609673
$947$	−24.2480	+	8.82557i	−0.787956	+	0.286792i	−0.704486	−	0.709718i	$-0.748822\pi$
$947$	−24.2480	+	8.82557i	−0.787956	+	0.286792i	−0.0834696	+	0.996510i	$0.526600\pi$
$948$		0			0
$949$	0.00499449	−	0.00419088i	0.000162128	−	0.000136042i
$950$	−2.55430	−	0.929689i	−0.0828724	−	0.0301631i
$951$		0			0
$952$	−28.5875	+	10.3519i	−0.926528	+	0.335506i
$953$	11.0856	−	19.2009i	0.359098	−	0.621977i	−0.628712	−	0.777638i	$-0.716418\pi$
$953$	11.0856	−	19.2009i	0.359098	−	0.621977i	0.987810	+	0.155661i	$0.0497509\pi$
$954$		0			0
$955$	14.2538			0.461241
$956$	32.5236	−	11.8376i	1.05189	−	0.382856i
$957$		0			0
$958$	−4.39256	−	24.9114i	−0.141917	−	0.804852i
$959$	−4.86833	−	27.8774i	−0.157207	−	0.900207i
$960$		0			0
$961$	−2.96282	+	16.8030i	−0.0955749	+	0.542032i
$962$	−4.08770			−0.131793
$963$		0			0
$964$	−93.0921			−2.99829
$965$	13.0683	−	4.75647i	0.420683	−	0.153116i
$966$		0			0
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	−0.959582	−	0.281428i	$-0.909192\pi$
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	0.110523	+	0.993874i	$0.464747\pi$
$968$	4.26771	+	24.2034i	0.137169	+	0.777927i
$969$		0			0
$970$	−28.1590	−	23.6282i	−0.904132	−	0.758657i
$971$	0.797770	+	1.38178i	0.0256017	+	0.0443434i	0.878542	−	0.477664i	$-0.158517\pi$
$971$	0.797770	+	1.38178i	0.0256017	+	0.0443434i	−0.852941	+	0.522008i	$0.825183\pi$
$972$		0			0
$973$	7.22390	+	12.5598i	0.231588	+	0.402648i
$974$	−10.8343	+	61.4443i	−0.347153	+	1.96880i
$975$		0			0
$976$	4.51188	−	3.78592i	0.144422	−	0.121184i
$977$	−2.95474	−	16.7572i	−0.0945306	−	0.536109i	−0.994890	−	0.100963i	$-0.967808\pi$
$977$	−2.95474	−	16.7572i	−0.0945306	−	0.536109i	0.900360	−	0.435147i	$-0.143303\pi$
$978$		0			0
$979$	−10.3467	+	3.76588i	−0.330681	+	0.120358i
$980$	17.3292	+	30.2440i	0.553560	+	0.966110i
$981$		0			0
$982$	−33.9113	+	58.7361i	−1.08215	+	1.87434i
$983$	8.18574	−	2.97936i	0.261084	−	0.0950270i	−0.208162	−	0.978094i	$-0.566748\pi$
$983$	8.18574	−	2.97936i	0.261084	−	0.0950270i	0.469246	+	0.883067i	$0.344526\pi$
$984$		0			0
$985$	21.0366	−	17.6518i	0.670283	−	0.562434i
$986$	10.8940	+	61.7828i	0.346935	+	1.96757i
$987$		0			0
$988$	−0.222915	−	0.187048i	−0.00709187	−	0.00595078i
$989$	−33.8277	+	58.5913i	−1.07566	+	1.86310i
$990$		0			0
$991$	−19.5540	−	33.8686i	−0.621154	−	1.07587i	−0.989271	−	0.146091i	$-0.953331\pi$
$991$	−19.5540	−	33.8686i	−0.621154	−	1.07587i	0.368117	−	0.929779i	$-0.380002\pi$
$992$	−18.2329	−	15.2992i	−0.578895	−	0.485751i
$993$		0			0
$994$	2.95395	+	16.9151i	0.0936936	+	0.536514i
$995$	34.7880	+	12.6618i	1.10285	+	0.401406i
$996$		0			0
$997$	−15.5949	−	13.0857i	−0.493896	−	0.414428i	0.361524	−	0.932363i	$-0.382257\pi$
$997$	−15.5949	−	13.0857i	−0.493896	−	0.414428i	−0.855420	+	0.517935i	$0.826701\pi$
$998$	−14.3230	+	24.8081i	−0.453385	+	0.785286i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.w.a.235.20		132
3.2	odd	2		189.2.w.a.25.3	yes	132
7.2	even	3		567.2.u.a.478.3		132
21.2	odd	6		189.2.u.a.79.20	yes	132
27.13	even	9		567.2.u.a.172.3		132
27.14	odd	18		189.2.u.a.67.20	✓	132
189.121	even	9	inner	567.2.w.a.415.20		132
189.149	odd	18		189.2.w.a.121.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.20	✓	132	27.14	odd	18
189.2.u.a.79.20	yes	132	21.2	odd	6
189.2.w.a.25.3	yes	132	3.2	odd	2
189.2.w.a.121.3	yes	132	189.149	odd	18
567.2.u.a.172.3		132	27.13	even	9
567.2.u.a.478.3		132	7.2	even	3
567.2.w.a.235.20		132	1.1	even	1	trivial
567.2.w.a.415.20		132	189.121	even	9	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.w (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.11851 - 0.771075i) q^{2} +(2.36145 - 1.98149i) q^{4} +(1.51793 + 0.552482i) q^{5} +(2.02397 + 1.70398i) q^{7} +(1.22040 - 2.11380i) q^{8} +O(q^{10})\)	\(q+(2.11851 - 0.771075i) q^{2} +(2.36145 - 1.98149i) q^{4} +(1.51793 + 0.552482i) q^{5} +(2.02397 + 1.70398i) q^{7} +(1.22040 - 2.11380i) q^{8} +3.64176 q^{10} +(-0.906628 + 0.329986i) q^{11} +(-0.0325017 - 0.184326i) q^{13} +(5.60170 + 2.04928i) q^{14} +(-0.115055 + 0.652508i) q^{16} -4.70815 q^{17} +0.504342 q^{19} +(4.67925 - 1.70311i) q^{20} +(-1.66626 + 1.39816i) q^{22} +(-1.36276 - 7.72859i) q^{23} +(-1.83134 - 1.53668i) q^{25} +(-0.210985 - 0.365436i) q^{26} +(8.15591 + 0.0133961i) q^{28} +(1.02634 - 5.82066i) q^{29} +(-2.85990 + 2.39974i) q^{31} +(1.10707 + 6.27850i) q^{32} +(-9.97427 + 3.63034i) q^{34} +(2.13082 + 3.70473i) q^{35} +(4.84361 - 8.38937i) q^{37} +(1.06846 - 0.388886i) q^{38} +(3.02032 - 2.53435i) q^{40} +(1.93086 + 10.9505i) q^{41} +(-6.60401 - 5.54143i) q^{43} +(-1.48709 + 2.57572i) q^{44} +(-8.84634 - 15.3223i) q^{46} +(1.15853 + 0.972120i) q^{47} +(1.19289 + 6.89761i) q^{49} +(-5.06461 - 1.84337i) q^{50} +(-0.441991 - 0.370875i) q^{52} +(-1.38569 + 2.40009i) q^{53} -1.55851 q^{55} +(6.07193 - 2.19871i) q^{56} +(-2.31386 - 13.1225i) q^{58} +(0.120799 + 0.685087i) q^{59} +(-6.80963 - 5.71396i) q^{61} +(-4.20835 + 7.28908i) q^{62} +(6.52397 + 11.2998i) q^{64} +(0.0525016 - 0.297751i) q^{65} +(2.99646 + 1.09062i) q^{67} +(-11.1180 + 9.32915i) q^{68} +(7.37080 + 6.20550i) q^{70} +(1.43937 + 2.49307i) q^{71} +(0.0174169 + 0.0301670i) q^{73} +(3.79240 - 21.5078i) q^{74} +(1.19098 - 0.999349i) q^{76} +(-2.39727 - 0.876998i) q^{77} +(-7.85664 + 2.85958i) q^{79} +(-0.535144 + 0.926896i) q^{80} +(12.5342 + 21.7098i) q^{82} +(-2.38942 + 13.5510i) q^{83} +(-7.14665 - 2.60117i) q^{85} +(-18.2635 - 6.64738i) q^{86} +(-0.408927 + 2.31914i) q^{88} +11.4122 q^{89} +(0.248306 - 0.428452i) q^{91} +(-18.5322 - 15.5503i) q^{92} +(3.20393 + 1.16614i) q^{94} +(0.765557 + 0.278640i) q^{95} +(-7.73226 - 6.48814i) q^{97} +(7.84572 + 13.6929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} - 6 q^{10} - 3 q^{11} - 12 q^{13} - 15 q^{14} - 9 q^{16} + 54 q^{17} - 6 q^{19} + 18 q^{20} - 12 q^{22} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} - 51 q^{32} - 18 q^{34} + 12 q^{35} + 3 q^{37} + 57 q^{38} - 66 q^{40} - 12 q^{43} - 3 q^{44} + 3 q^{46} + 21 q^{47} + 12 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 57 q^{56} - 3 q^{58} + 18 q^{59} + 33 q^{61} - 75 q^{62} - 30 q^{64} - 81 q^{65} - 3 q^{67} - 6 q^{68} - 42 q^{70} + 18 q^{71} + 21 q^{73} + 93 q^{74} - 24 q^{76} - 87 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} - 159 q^{86} + 57 q^{88} + 150 q^{89} + 6 q^{91} + 66 q^{92} + 33 q^{94} + 147 q^{95} - 12 q^{97} - 99 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 - 6 * q^10 - 3 * q^11 - 12 * q^13 - 15 * q^14 - 9 * q^16 + 54 * q^17 - 6 * q^19 + 18 * q^20 - 12 * q^22 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 - 51 * q^32 - 18 * q^34 + 12 * q^35 + 3 * q^37 + 57 * q^38 - 66 * q^40 - 12 * q^43 - 3 * q^44 + 3 * q^46 + 21 * q^47 + 12 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 57 * q^56 - 3 * q^58 + 18 * q^59 + 33 * q^61 - 75 * q^62 - 30 * q^64 - 81 * q^65 - 3 * q^67 - 6 * q^68 - 42 * q^70 + 18 * q^71 + 21 * q^73 + 93 * q^74 - 24 * q^76 - 87 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 - 159 * q^86 + 57 * q^88 + 150 * q^89 + 6 * q^91 + 66 * q^92 + 33 * q^94 + 147 * q^95 - 12 * q^97 - 99 * q^98

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