LMFDB - Embedded newform 819.2.et.c.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +O(q^{10})$	\(q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +(2.97888 - 5.15957i) q^{10} +(-0.872699 - 3.25696i) q^{11} +(-3.03769 + 1.94228i) q^{13} +(-1.06413 - 4.05349i) q^{14} +4.75894 q^{16} +3.33792 q^{17} +(0.733837 + 0.196631i) q^{19} +(-1.84932 + 0.495525i) q^{20} +(-2.67049 + 4.62542i) q^{22} +3.56245i q^{23} +(-7.92144 + 4.57345i) q^{25} +(5.57781 + 1.22692i) q^{26} +(-0.679283 + 1.16289i) q^{28} +(1.42199 + 2.46295i) q^{29} +(-8.90596 - 2.38635i) q^{31} +(-1.99032 - 1.99032i) q^{32} +(-3.73864 - 3.73864i) q^{34} +(-2.62430 + 9.59903i) q^{35} +(-8.01070 + 8.01070i) q^{37} +(-0.601698 - 1.04217i) q^{38} +(-7.69280 - 4.44144i) q^{40} +(-6.84386 - 1.83381i) q^{41} +(10.9295 + 6.31017i) q^{43} +(1.65787 - 0.444225i) q^{44} +(3.99012 - 3.99012i) q^{46} +(-1.32905 + 0.356118i) q^{47} +(3.43833 + 6.09737i) q^{49} +(13.9949 + 3.74992i) q^{50} +(-0.988666 - 1.54626i) q^{52} +(3.59290 + 6.22308i) q^{53} +(10.9832 - 6.34116i) q^{55} +(-6.04366 + 1.58659i) q^{56} +(1.16593 - 4.35132i) q^{58} +(2.23105 + 2.23105i) q^{59} +(0.902515 - 0.521067i) q^{61} +(7.30230 + 12.6480i) q^{62} -5.05937i q^{64} +(-10.0136 - 9.14539i) q^{65} +(2.85760 - 0.765690i) q^{67} +1.69908i q^{68} +(13.6907 - 7.81204i) q^{70} +(7.00412 - 1.87675i) q^{71} +(0.559835 - 2.08933i) q^{73} +17.9448 q^{74} +(-0.100090 + 0.373541i) q^{76} +(2.35262 - 8.60528i) q^{77} +(-5.54357 + 9.60175i) q^{79} +(4.63273 + 17.2896i) q^{80} +(5.61151 + 9.71942i) q^{82} +(1.51210 - 1.51210i) q^{83} +(3.24940 + 12.1269i) q^{85} +(-5.17392 - 19.3093i) q^{86} +(6.89639 + 3.98163i) q^{88} +(2.23766 + 2.23766i) q^{89} +(-9.53168 + 0.383488i) q^{91} -1.81337 q^{92} +(1.88747 + 1.08973i) q^{94} +2.85750i q^{95} +(-3.23001 - 12.0545i) q^{97} +(2.97826 - 10.6805i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.12005	−	1.12005i	−0.791995	−	0.791995i	0.189823	−	0.981818i	$-0.439208\pi$
$2$	−1.12005	−	1.12005i	−0.791995	−	0.791995i	−0.981818	+	0.189823i	$0.939208\pi$
$3$		0			0
$3$		0			0
$4$			0.509024i			0.254512i
$5$	0.973479	+	3.63307i	0.435353	+	1.62476i	0.740219	+	0.672365i	$0.234722\pi$
$5$	0.973479	+	3.63307i	0.435353	+	1.62476i	−0.304866	+	0.952395i	$0.598612\pi$
$6$		0			0
$7$	2.28455	+	1.33448i	0.863478	+	0.504386i
$7$	2.28455	+	1.33448i	0.863478	+	0.504386i
$8$	−1.66997	+	1.66997i	−0.590423	+	0.590423i
$9$		0			0
$10$	2.97888	−	5.15957i	0.942005	−	1.63160i
$11$	−0.872699	−	3.25696i	−0.263129	−	0.982010i	−0.963386	−	0.268119i	$-0.913598\pi$
$11$	−0.872699	−	3.25696i	−0.263129	−	0.982010i	0.700257	−	0.713891i	$-0.253069\pi$
$12$		0			0
$13$	−3.03769	+	1.94228i	−0.842504	+	0.538690i
$13$	−3.03769	+	1.94228i	−0.842504	+	0.538690i
$14$	−1.06413	−	4.05349i	−0.284400	−	1.08334i
$15$		0			0
$16$	4.75894			1.18974
$17$	3.33792			0.809565			0.404782	−	0.914413i	$-0.367347\pi$
$17$	3.33792			0.809565			0.404782	+	0.914413i	$0.367347\pi$
$18$		0			0
$19$	0.733837	+	0.196631i	0.168354	+	0.0451103i	0.342011	−	0.939696i	$-0.388892\pi$
$19$	0.733837	+	0.196631i	0.168354	+	0.0451103i	−0.173657	+	0.984806i	$0.555559\pi$
$20$	−1.84932	+	0.495525i	−0.413521	+	0.110803i
$21$		0			0
$22$	−2.67049	+	4.62542i	−0.569350	+	0.986143i
$23$			3.56245i			0.742822i	0.928469	+	0.371411i	$0.121126\pi$
$23$			3.56245i			0.742822i	−0.928469	+	0.371411i	$0.878874\pi$
$24$		0			0
$25$	−7.92144	+	4.57345i	−1.58429	+	0.914690i
$26$	5.57781	+	1.22692i	1.09390	+	0.240619i
$27$		0			0
$28$	−0.679283	+	1.16289i	−0.128372	+	0.219766i
$29$	1.42199	+	2.46295i	0.264056	+	0.457358i	0.967316	−	0.253574i	$-0.0816063\pi$
$29$	1.42199	+	2.46295i	0.264056	+	0.457358i	−0.703260	+	0.710933i	$0.748273\pi$
$30$		0			0
$31$	−8.90596	−	2.38635i	−1.59956	−	0.428600i	−0.654649	−	0.755933i	$-0.727184\pi$
$31$	−8.90596	−	2.38635i	−1.59956	−	0.428600i	−0.944909	+	0.327332i	$0.893850\pi$
$32$	−1.99032	−	1.99032i	−0.351842	−	0.351842i
$33$		0			0
$34$	−3.73864	−	3.73864i	−0.641171	−	0.641171i
$35$	−2.62430	+	9.59903i	−0.443588	+	1.62253i
$36$		0			0
$37$	−8.01070	+	8.01070i	−1.31695	+	1.31695i	−0.400775	+	0.916177i	$0.631259\pi$
$37$	−8.01070	+	8.01070i	−1.31695	+	1.31695i	−0.916177	+	0.400775i	$0.868741\pi$
$38$	−0.601698	−	1.04217i	−0.0976083	−	0.169063i
$39$		0			0
$40$	−7.69280	−	4.44144i	−1.21634	−	0.702253i
$41$	−6.84386	−	1.83381i	−1.06883	−	0.286393i	−0.318819	−	0.947816i	$-0.603286\pi$
$41$	−6.84386	−	1.83381i	−1.06883	−	0.286393i	−0.750013	+	0.661423i	$0.769953\pi$
$42$		0			0
$43$	10.9295	+	6.31017i	1.66674	+	0.962291i	0.969379	+	0.245568i	$0.0789746\pi$
$43$	10.9295	+	6.31017i	1.66674	+	0.962291i	0.697358	+	0.716723i	$0.254359\pi$
$44$	1.65787	−	0.444225i	0.249933	−	0.0669695i
$45$		0			0
$46$	3.99012	−	3.99012i	0.588311	−	0.588311i
$47$	−1.32905	+	0.356118i	−0.193862	+	0.0519452i	−0.354444	−	0.935077i	$-0.615330\pi$
$47$	−1.32905	+	0.356118i	−0.193862	+	0.0519452i	0.160582	+	0.987023i	$0.448663\pi$
$48$		0			0
$49$	3.43833	+	6.09737i	0.491190	+	0.871052i
$50$	13.9949	+	3.74992i	1.97918	+	0.530319i
$51$		0			0
$52$	−0.988666	−	1.54626i	−0.137103	−	0.214427i
$53$	3.59290	+	6.22308i	0.493523	+	0.854806i	0.999972	−	0.00746338i	$-0.00237569\pi$
$53$	3.59290	+	6.22308i	0.493523	+	0.854806i	−0.506450	+	0.862270i	$0.669042\pi$
$54$		0			0
$55$	10.9832	−	6.34116i	1.48098	−	0.855042i
$56$	−6.04366	+	1.58659i	−0.807618	+	0.212016i
$57$		0			0
$58$	1.16593	−	4.35132i	0.153095	−	0.571357i
$59$	2.23105	+	2.23105i	0.290458	+	0.290458i	0.837261	−	0.546803i	$-0.184156\pi$
$59$	2.23105	+	2.23105i	0.290458	+	0.290458i	−0.546803	+	0.837261i	$0.684156\pi$
$60$		0			0
$61$	0.902515	−	0.521067i	0.115555	−	0.0667158i	−0.441108	−	0.897454i	$-0.645415\pi$
$61$	0.902515	−	0.521067i	0.115555	−	0.0667158i	0.556664	+	0.830738i	$0.312081\pi$
$62$	7.30230	+	12.6480i	0.927393	+	1.60629i
$63$		0			0
$64$		−	5.05937i		−	0.632421i
$65$	−10.0136	−	9.14539i	−1.24203	−	1.13435i
$66$		0			0
$67$	2.85760	−	0.765690i	0.349111	−	0.0935440i	−0.0800024	−	0.996795i	$-0.525493\pi$
$67$	2.85760	−	0.765690i	0.349111	−	0.0935440i	0.429113	+	0.903251i	$0.358826\pi$
$68$			1.69908i			0.206044i
$69$		0			0
$70$	13.6907	−	7.81204i	1.63636	−	0.933717i
$71$	7.00412	−	1.87675i	0.831236	−	0.222729i	0.181983	−	0.983302i	$-0.441748\pi$
$71$	7.00412	−	1.87675i	0.831236	−	0.222729i	0.649253	+	0.760573i	$0.275082\pi$
$72$		0			0
$73$	0.559835	−	2.08933i	0.0655238	−	0.244538i	−0.925394	−	0.379006i	$-0.876266\pi$
$73$	0.559835	−	2.08933i	0.0655238	−	0.244538i	0.990918	+	0.134468i	$0.0429326\pi$
$74$	17.9448			2.08604
$75$		0			0
$76$	−0.100090	+	0.373541i	−0.0114811	+	0.0428481i
$77$	2.35262	−	8.60528i	0.268106	−	0.980663i
$78$		0			0
$79$	−5.54357	+	9.60175i	−0.623700	+	1.08028i	0.365090	+	0.930972i	$0.381038\pi$
$79$	−5.54357	+	9.60175i	−0.623700	+	1.08028i	−0.988791	+	0.149309i	$0.952295\pi$
$80$	4.63273	+	17.2896i	0.517955	+	1.93304i
$81$		0			0
$82$	5.61151	+	9.71942i	0.619688	+	1.07333i
$83$	1.51210	−	1.51210i	0.165975	−	0.165975i	−0.619233	−	0.785208i	$-0.712556\pi$
$83$	1.51210	−	1.51210i	0.165975	−	0.165975i	0.785208	+	0.619233i	$0.212556\pi$
$84$		0			0
$85$	3.24940	+	12.1269i	0.352447	+	1.31535i
$86$	−5.17392	−	19.3093i	−0.557918	−	2.08218i
$87$		0			0
$88$	6.89639	+	3.98163i	0.735158	+	0.424444i
$89$	2.23766	+	2.23766i	0.237192	+	0.237192i	0.815686	−	0.578494i	$-0.196360\pi$
$89$	2.23766	+	2.23766i	0.237192	+	0.237192i	−0.578494	+	0.815686i	$0.696360\pi$
$90$		0			0
$91$	−9.53168	+	0.383488i	−0.999192	+	0.0402005i
$92$	−1.81337			−0.189057
$93$		0			0
$94$	1.88747	+	1.08973i	0.194678	+	0.112397i
$95$			2.85750i			0.293174i
$96$		0			0
$97$	−3.23001	−	12.0545i	−0.327957	−	1.22395i	−0.911305	−	0.411731i	$-0.864924\pi$
$97$	−3.23001	−	12.0545i	−0.327957	−	1.22395i	0.583348	−	0.812222i	$-0.301742\pi$
$98$	2.97826	−	10.6805i	0.300849	−	1.07889i
$99$		0			0
$100$	−2.32800	−	4.03221i	−0.232800	−	0.403221i
$101$	2.19617	−	3.80388i	0.218527	−	0.378500i	−0.735831	−	0.677165i	$-0.763208\pi$
$101$	2.19617	−	3.80388i	0.218527	−	0.378500i	0.954358	+	0.298665i	$0.0965415\pi$
$102$		0			0
$103$	6.67838	−	11.5673i	0.658040	−	1.13976i	−0.323082	−	0.946371i	$-0.604719\pi$
$103$	6.67838	−	11.5673i	0.658040	−	1.13976i	0.981122	−	0.193389i	$-0.0619478\pi$
$104$	1.82931	−	8.31638i	0.179378	−	0.815488i
$105$		0			0
$106$	2.94594	−	10.9944i	0.286135	−	1.06787i
$107$	−0.177558			−0.0171652			−0.00858260	−	0.999963i	$-0.502732\pi$
$107$	−0.177558			−0.0171652			−0.00858260	+	0.999963i	$0.502732\pi$
$108$		0			0
$109$	−1.34434	+	5.01713i	−0.128764	+	0.480554i	−0.999946	−	0.0104068i	$-0.996687\pi$
$109$	−1.34434	+	5.01713i	−0.128764	+	0.480554i	0.871182	+	0.490960i	$0.163354\pi$
$110$	−19.4042	−	5.19933i	−1.85012	−	0.495737i
$111$		0			0
$112$	10.8720	+	6.35071i	1.02731	+	0.600086i
$113$	−10.0079	+	17.3342i	−0.941462	+	1.63066i	−0.178778	+	0.983889i	$0.557215\pi$
$113$	−10.0079	+	17.3342i	−0.941462	+	1.63066i	−0.762684	+	0.646771i	$0.776119\pi$
$114$		0			0
$115$	−12.9426	+	3.46797i	−1.20691	+	0.323390i
$116$	−1.25370	+	0.723825i	−0.116403	+	0.0672055i
$117$		0			0
$118$		−	4.99777i		−	0.460082i
$119$	7.62564	+	4.45439i	0.699042	+	0.408333i
$120$		0			0
$121$	−0.319891	+	0.184689i	−0.0290810	+	0.0167899i
$122$	−1.59448	−	0.427240i	−0.144358	−	0.0386805i
$123$		0			0
$124$	1.21471	−	4.53335i	0.109084	−	0.407107i
$125$	−11.0291	−	11.0291i	−0.986469	−	0.986469i
$126$		0			0
$127$	6.74547	−	3.89450i	0.598564	−	0.345581i	−0.169913	−	0.985459i	$-0.554349\pi$
$127$	6.74547	−	3.89450i	0.598564	−	0.345581i	0.768476	+	0.639878i	$0.221015\pi$
$128$	−9.64739	+	9.64739i	−0.852717	+	0.852717i
$129$		0			0
$130$	0.972393	+	21.4590i	0.0852845	+	1.88208i
$131$	−8.40782	−	4.85426i	−0.734595	−	0.424118i	0.0855060	−	0.996338i	$-0.472749\pi$
$131$	−8.40782	−	4.85426i	−0.734595	−	0.424118i	−0.820101	+	0.572219i	$0.806083\pi$
$132$		0			0
$133$	1.41409	+	1.42850i	0.122617	+	0.123867i
$134$	−4.05826	−	2.34304i	−0.350580	−	0.202408i
$135$		0			0
$136$	−5.57422	+	5.57422i	−0.477985	+	0.477985i
$137$	6.42607	−	6.42607i	0.549017	−	0.549017i	−0.377140	−	0.926156i	$-0.623092\pi$
$137$	6.42607	−	6.42607i	0.549017	−	0.549017i	0.926156	+	0.377140i	$0.123092\pi$
$138$		0			0
$139$	8.85473	+	5.11228i	0.751048	+	0.433618i	0.826073	−	0.563564i	$-0.190570\pi$
$139$	8.85473	+	5.11228i	0.751048	+	0.433618i	−0.0750244	+	0.997182i	$0.523903\pi$
$140$	−4.88614	−	1.33583i	−0.412954	−	0.112899i
$141$		0			0
$142$	−9.94701	−	5.74291i	−0.834735	−	0.481934i
$143$	8.97690	+	8.19861i	0.750686	+	0.685602i
$144$		0			0
$145$	−7.56381	+	7.56381i	−0.628140	+	0.628140i
$146$	−2.96720	+	1.71311i	−0.245567	+	0.141778i
$147$		0			0
$148$	−4.07764	−	4.07764i	−0.335180	−	0.335180i
$149$	−3.88850	+	14.5121i	−0.318559	+	1.18888i	0.602072	+	0.798442i	$0.294342\pi$
$149$	−3.88850	+	14.5121i	−0.318559	+	1.18888i	−0.920630	+	0.390435i	$0.872325\pi$
$150$		0			0
$151$	−0.268230	−	0.0718719i	−0.0218282	−	0.00584885i	0.247888	−	0.968789i	$-0.420263\pi$
$151$	−0.268230	−	0.0718719i	−0.0218282	−	0.00584885i	−0.269717	+	0.962940i	$0.586930\pi$
$152$	−1.55385	+	0.897117i	−0.126034	+	0.0727658i
$153$		0			0
$154$	−12.2734	+	7.00329i	−0.989018	+	0.564341i
$155$		−	34.6791i		−	2.78549i
$156$		0			0
$157$	0.272321	−	0.157225i	0.0217336	−	0.0125479i	−0.489094	−	0.872231i	$-0.662672\pi$
$157$	0.272321	−	0.157225i	0.0217336	−	0.0125479i	0.510827	+	0.859683i	$0.329339\pi$
$158$	16.9635	−	4.54536i	1.34954	−	0.361609i
$159$		0			0
$160$	5.29344	−	9.16852i	0.418484	−	0.724835i
$161$	−4.75401	+	8.13859i	−0.374669	+	0.641410i
$162$		0			0
$163$	−0.911958	−	0.244358i	−0.0714300	−	0.0191396i	0.222927	−	0.974835i	$-0.428439\pi$
$163$	−0.911958	−	0.244358i	−0.0714300	−	0.0191396i	−0.294357	+	0.955696i	$0.595105\pi$
$164$	0.933452	−	3.48369i	0.0728904	−	0.272031i
$165$		0			0
$166$	−3.38726			−0.262903
$167$	−0.626601	+	2.33851i	−0.0484878	+	0.180959i	−0.985923	−	0.167202i	$-0.946527\pi$
$167$	−0.626601	+	2.33851i	−0.0484878	+	0.180959i	0.937435	+	0.348161i	$0.113194\pi$
$168$		0			0
$169$	5.45513	−	11.8001i	0.419626	−	0.907697i
$170$	9.94326	−	17.2222i	0.762614	−	1.32089i
$171$		0			0
$172$	−3.21203	+	5.56340i	−0.244915	+	0.424205i
$173$	−8.61076	−	14.9143i	−0.654664	−	1.13391i	−0.981978	−	0.188996i	$-0.939477\pi$
$173$	−8.61076	−	14.9143i	−0.654664	−	1.13391i	0.327314	−	0.944916i	$-0.393857\pi$
$174$		0			0
$175$	−24.2001	−	0.122737i	−1.82936	−	0.00927805i
$176$	−4.15313	−	15.4997i	−0.313054	−	1.16833i
$177$		0			0
$178$		−	5.01259i		−	0.375710i
$179$	−2.98125	−	1.72123i	−0.222829	−	0.128651i	0.384430	−	0.923154i	$-0.374398\pi$
$179$	−2.98125	−	1.72123i	−0.222829	−	0.128651i	−0.607260	+	0.794503i	$0.707731\pi$
$180$		0			0
$181$	25.9767			1.93084			0.965418	−	0.260708i	$-0.0839561\pi$
$181$	25.9767			1.93084			0.965418	+	0.260708i	$0.0839561\pi$
$182$	11.1055	+	10.2464i	0.823193	+	0.759516i
$183$		0			0
$184$	−5.94917	−	5.94917i	−0.438579	−	0.438579i
$185$	−36.9017	−	21.3052i	−2.71307	−	1.56639i
$186$		0			0
$187$	−2.91300	−	10.8715i	−0.213020	−	0.795000i
$188$	−0.181273	−	0.676520i	−0.0132207	−	0.0493403i
$189$		0			0
$190$	3.20055	−	3.20055i	0.232192	−	0.232192i
$191$	1.49154	+	2.58342i	0.107924	+	0.186930i	0.914929	−	0.403615i	$-0.132246\pi$
$191$	1.49154	+	2.58342i	0.107924	+	0.186930i	−0.807005	+	0.590544i	$0.798913\pi$
$192$		0			0
$193$	0.676598	+	2.52510i	0.0487026	+	0.181761i	0.985992	−	0.166791i	$-0.0533404\pi$
$193$	0.676598	+	2.52510i	0.0487026	+	0.181761i	−0.937290	+	0.348551i	$0.886674\pi$
$194$	−9.88393	+	17.1195i	−0.709624	+	1.22911i
$195$		0			0
$196$	−3.10371	+	1.75019i	−0.221693	+	0.125014i
$197$	−0.213689	+	0.797498i	−0.0152247	+	0.0568194i	−0.973120	−	0.230297i	$-0.926030\pi$
$197$	−0.213689	+	0.797498i	−0.0152247	+	0.0568194i	0.957896	+	0.287117i	$0.0926968\pi$
$198$		0			0
$199$	−8.20173			−0.581405			−0.290703	−	0.956813i	$-0.593889\pi$
$199$	−8.20173			−0.581405			−0.290703	+	0.956813i	$0.593889\pi$
$200$	5.59104	−	20.8661i	0.395347	−	1.47545i
$201$		0			0
$202$	−6.72036	+	1.80071i	−0.472843	+	0.126698i
$203$	−0.0381616	+	7.52434i	−0.00267842	+	0.528105i
$204$		0			0
$205$		−	26.6494i		−	1.86128i
$206$	−20.4361	+	5.47583i	−1.42385	+	0.381519i
$207$		0			0
$208$	−14.4562	+	9.24318i	−1.00236	+	0.640899i
$209$		−	2.56168i		−	0.177195i
$210$		0			0
$211$	5.37441	+	9.30875i	0.369989	+	0.640841i	0.989563	−	0.144098i	$-0.0460280\pi$
$211$	5.37441	+	9.30875i	0.369989	+	0.640841i	−0.619574	+	0.784938i	$0.712695\pi$
$212$	−3.16770	+	1.82887i	−0.217559	+	0.125608i
$213$		0			0
$214$	0.198874	+	0.198874i	0.0135947	+	0.0135947i
$215$	−12.2856	+	45.8506i	−0.837873	+	3.12699i
$216$		0			0
$217$	−17.1616	−	17.3365i	−1.16500	−	1.17688i
$218$	7.12516	−	4.11371i	0.482576	−	0.278616i
$219$		0			0
$220$	3.22781	+	5.59072i	0.217619	+	0.376927i
$221$	−10.1396	+	6.48316i	−0.682061	+	0.436105i
$222$		0			0
$223$	5.74055	+	1.53818i	0.384416	+	0.103004i	0.445851	−	0.895107i	$-0.352901\pi$
$223$	5.74055	+	1.53818i	0.384416	+	0.103004i	−0.0614354	+	0.998111i	$0.519568\pi$
$224$	−1.89094	−	7.20302i	−0.126344	−	0.481272i
$225$		0			0
$226$	30.6245	−	8.20580i	2.03711	−	0.545842i
$227$	14.4159	−	14.4159i	0.956815	−	0.956815i	−0.0422908	−	0.999105i	$-0.513466\pi$
$227$	14.4159	−	14.4159i	0.956815	−	0.956815i	0.999105	+	0.0422908i	$0.0134656\pi$
$228$		0			0
$229$	−8.29019	+	2.22135i	−0.547831	+	0.146791i	−0.522110	−	0.852878i	$-0.674855\pi$
$229$	−8.29019	+	2.22135i	−0.547831	+	0.146791i	−0.0257212	+	0.999669i	$0.508188\pi$
$230$	18.3807	+	10.6121i	1.21199	+	0.699741i
$231$		0			0
$232$	−6.48772	−	1.73838i	−0.425939	−	0.114130i
$233$	−4.35471	−	2.51419i	−0.285286	−	0.164710i	0.350528	−	0.936552i	$-0.386002\pi$
$233$	−4.35471	−	2.51419i	−0.285286	−	0.164710i	−0.635814	+	0.771842i	$0.719336\pi$
$234$		0			0
$235$	−2.58761	−	4.48187i	−0.168797	−	0.292365i
$236$	−1.13566	+	1.13566i	−0.0739250	+	0.0739250i
$237$		0			0
$238$	−3.55197	−	13.5302i	−0.230240	−	0.877035i
$239$	11.6568	+	11.6568i	0.754018	+	0.754018i	0.975227	−	0.221208i	$-0.0710001\pi$
$239$	11.6568	+	11.6568i	0.754018	+	0.754018i	−0.221208	+	0.975227i	$0.571000\pi$
$240$		0			0
$241$	3.99187	+	3.99187i	0.257139	+	0.257139i	0.823889	−	0.566751i	$-0.191800\pi$
$241$	3.99187	+	3.99187i	0.257139	+	0.257139i	−0.566751	+	0.823889i	$0.691800\pi$
$242$	0.565154	+	0.151433i	0.0363295	+	0.00973446i
$243$		0			0
$244$	0.265236	+	0.459402i	0.0169800	+	0.0294102i
$245$	−18.8050	+	18.4274i	−1.20141	+	1.17728i
$246$		0			0
$247$	−2.61108	+	0.828010i	−0.166139	+	0.0526850i
$248$	18.8578	−	10.8875i	1.19747	−	0.691360i
$249$		0			0
$250$			24.7062i			1.56256i
$251$	5.54226	−	9.59948i	0.349825	−	0.605914i	−0.636394	−	0.771365i	$-0.719575\pi$
$251$	5.54226	−	9.59948i	0.349825	−	0.605914i	0.986218	+	0.165451i	$0.0529079\pi$
$252$		0			0
$253$	11.6027	−	3.10894i	0.729458	−	0.195458i
$254$	−11.9173	−	3.19323i	−0.747758	−	0.200361i
$255$		0			0
$256$	11.4924			0.718273
$257$	2.40321			0.149908			0.0749540	−	0.997187i	$-0.476119\pi$
$257$	2.40321			0.149908			0.0749540	+	0.997187i	$0.476119\pi$
$258$		0			0
$259$	−28.9910	+	7.61073i	−1.80141	+	0.472908i
$260$	4.65523	−	5.09715i	0.288705	−	0.316112i
$261$		0			0
$262$	3.98017	+	14.8542i	0.245896	+	0.917695i
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	0.110527	+	0.993873i	$0.464746\pi$
$263$	−13.0623	+	22.6246i	−0.805456	+	1.39509i	−0.915983	+	0.401218i	$0.868587\pi$
$264$		0			0
$265$	−19.1113	+	19.1113i	−1.17400	+	1.17400i
$266$	0.0161477	−	3.18385i	0.000990079	−	0.195214i
$267$		0			0
$268$	0.389755	+	1.45459i	0.0238081	+	0.0888530i
$269$		−	26.4202i		−	1.61087i	−0.592684	−	0.805435i	$-0.701932\pi$
$269$		−	26.4202i		−	1.61087i	0.592684	−	0.805435i	$-0.298068\pi$
$270$		0			0
$271$	−5.35562	−	5.35562i	−0.325330	−	0.325330i	0.525477	−	0.850808i	$-0.323887\pi$
$271$	−5.35562	−	5.35562i	−0.325330	−	0.325330i	−0.850808	+	0.525477i	$0.823887\pi$
$272$	15.8850			0.963168
$273$		0			0
$274$	−14.3950			−0.869637
$275$	21.8086	+	21.8086i	1.31511	+	1.31511i
$276$		0			0
$277$		−	22.5430i		−	1.35448i	−0.735764	−	0.677238i	$-0.763177\pi$
$277$		−	22.5430i		−	1.35448i	0.735764	−	0.677238i	$-0.236823\pi$
$278$	−4.19173	−	15.6437i	−0.251403	−	0.938250i
$279$		0			0
$280$	−11.6476	−	20.4126i	−0.696075	−	1.21988i
$281$	7.73479	−	7.73479i	0.461419	−	0.461419i	−0.437701	−	0.899120i	$-0.644207\pi$
$281$	7.73479	−	7.73479i	0.461419	−	0.461419i	0.899120	+	0.437701i	$0.144207\pi$
$282$		0			0
$283$	8.86524	−	15.3550i	0.526984	−	0.912763i	−0.472522	−	0.881319i	$-0.656656\pi$
$283$	8.86524	−	15.3550i	0.526984	−	0.912763i	0.999506	−	0.0314437i	$-0.0100105\pi$
$284$	0.955310	+	3.56527i	0.0566872	+	0.211560i
$285$		0			0
$286$	−0.871725	−	19.2374i	−0.0515462	−	1.13753i
$287$	−13.1880	−	13.3224i	−0.778461	−	0.786397i
$288$		0			0
$289$	−5.85829			−0.344605
$290$	16.9437			0.994968
$291$		0			0
$292$	1.06352	+	0.284970i	0.0622379	+	0.0166766i
$293$	12.4507	−	3.33616i	0.727379	−	0.194901i	0.123917	−	0.992293i	$-0.460454\pi$
$293$	12.4507	−	3.33616i	0.727379	−	0.194901i	0.603462	+	0.797392i	$0.293788\pi$
$294$		0			0
$295$	−5.93368	+	10.2774i	−0.345472	+	0.598376i
$296$		−	26.7552i		−	1.55512i
$297$		0			0
$298$	20.6096	−	11.8990i	1.19388	−	0.689288i
$299$	−6.91925	−	10.8216i	−0.400151	−	0.625830i
$300$		0			0
$301$	16.5483	+	29.0011i	0.953826	+	1.67160i
$302$	0.219930	+	0.380931i	0.0126556	+	0.0219201i
$303$		0			0
$304$	3.49229	+	0.935756i	0.200297	+	0.0536693i
$305$	2.77166	+	2.77166i	0.158705	+	0.158705i
$306$		0			0
$307$	−5.82305	−	5.82305i	−0.332339	−	0.332339i	0.521135	−	0.853474i	$-0.325509\pi$
$307$	−5.82305	−	5.82305i	−0.332339	−	0.332339i	−0.853474	+	0.521135i	$0.825509\pi$
$308$	4.38030	+	1.19754i	0.249591	+	0.0682362i
$309$		0			0
$310$	−38.8423	+	38.8423i	−2.20610	+	2.20610i
$311$	13.5284	+	23.4318i	0.767124	+	1.32870i	0.939116	+	0.343600i	$0.111646\pi$
$311$	13.5284	+	23.4318i	0.767124	+	1.32870i	−0.171992	+	0.985098i	$0.555020\pi$
$312$		0			0
$313$	11.8883	+	6.86374i	0.671969	+	0.387962i	0.796822	−	0.604214i	$-0.206513\pi$
$313$	11.8883	+	6.86374i	0.671969	+	0.387962i	−0.124853	+	0.992175i	$0.539846\pi$
$314$	−0.481113	−	0.128914i	−0.0271508	−	0.00727502i
$315$		0			0
$316$	−4.88752	−	2.82181i	−0.274945	−	0.158739i
$317$	−2.23807	+	0.599689i	−0.125702	+	0.0336819i	−0.321122	−	0.947038i	$-0.604060\pi$
$317$	−2.23807	+	0.599689i	−0.125702	+	0.0336819i	0.195419	+	0.980720i	$0.437393\pi$
$318$		0			0
$319$	6.78076	−	6.78076i	0.379650	−	0.379650i
$320$	18.3811	−	4.92519i	1.02753	−	0.275327i
$321$		0			0
$322$	14.4404	−	3.79089i	0.804730	−	0.211258i
$323$	2.44949	+	0.656339i	0.136293	+	0.0365197i
$324$		0			0
$325$	15.1800	−	29.2783i	0.842035	−	1.62407i
$326$	0.747745	+	1.29513i	0.0414138	+	0.0717307i
$327$		0			0
$328$	14.4914	−	8.36663i	0.800155	−	0.461970i
$329$	−3.51152	−	0.960022i	−0.193596	−	0.0529277i
$330$		0			0
$331$	6.68605	−	24.9527i	0.367498	−	1.37152i	−0.496504	−	0.868035i	$-0.665383\pi$
$331$	6.68605	−	24.9527i	0.367498	−	1.37152i	0.864002	−	0.503488i	$-0.167950\pi$
$332$	0.769698	+	0.769698i	0.0422427	+	0.0422427i
$333$		0			0
$334$	3.32107	−	1.91742i	0.181721	−	0.104917i
$335$	5.56362	+	9.63647i	0.303973	+	0.526497i
$336$		0			0
$337$		−	32.4074i		−	1.76534i	−0.469990	−	0.882672i	$-0.655743\pi$
$337$		−	32.4074i		−	1.76534i	0.469990	−	0.882672i	$-0.344257\pi$
$338$	−19.3267	+	7.10664i	−1.05123	+	0.386550i
$339$		0			0
$340$	−6.17289	+	1.65402i	−0.334772	+	0.0897019i
$341$			31.0889i			1.68356i
$342$		0			0
$343$	−0.281778	+	18.5181i	−0.0152146	+	0.999884i
$344$	−28.7897	+	7.71418i	−1.55224	+	0.415921i
$345$		0			0
$346$	−7.06025	+	26.3492i	−0.379562	+	1.41654i
$347$	31.0215			1.66532			0.832660	−	0.553784i	$-0.186817\pi$
$347$	31.0215			1.66532			0.832660	+	0.553784i	$0.186817\pi$
$348$		0			0
$349$	0.142223	−	0.530784i	0.00761303	−	0.0284122i	−0.962015	−	0.272997i	$-0.911985\pi$
$349$	0.142223	−	0.530784i	0.00761303	−	0.0284122i	0.969628	+	0.244585i	$0.0786517\pi$
$350$	26.9679	+	27.2428i	1.44149	+	1.45619i
$351$		0			0
$352$	−4.74544	+	8.21934i	−0.252933	+	0.438092i
$353$	−3.20193	−	11.9498i	−0.170422	−	0.636022i	−0.997286	−	0.0736213i	$-0.976544\pi$
$353$	−3.20193	−	11.9498i	−0.170422	−	0.636022i	0.826865	−	0.562401i	$-0.190122\pi$
$354$		0			0
$355$	13.6367	+	23.6195i	0.723762	+	1.25359i
$356$	−1.13903	+	1.13903i	−0.0603682	+	0.0603682i
$357$		0			0
$358$	1.41129	+	5.26701i	0.0745891	+	0.278370i
$359$	−1.88465	−	7.03362i	−0.0994682	−	0.371220i	0.898191	−	0.439606i	$-0.144882\pi$
$359$	−1.88465	−	7.03362i	−0.0994682	−	0.371220i	−0.997659	+	0.0683856i	$0.978215\pi$
$360$		0			0
$361$	−15.9546	−	9.21141i	−0.839717	−	0.484811i
$362$	−29.0952	−	29.0952i	−1.52921	−	1.52921i
$363$		0			0
$364$	−0.195205	−	4.85186i	−0.0102315	−	0.254306i
$365$	8.13569			0.425842
$366$		0			0
$367$	3.73411	+	2.15589i	0.194919	+	0.112536i	0.594283	−	0.804256i	$-0.297436\pi$
$367$	3.73411	+	2.15589i	0.194919	+	0.112536i	−0.399364	+	0.916792i	$0.630769\pi$
$368$			16.9535i			0.883761i
$369$		0			0
$370$	17.4689	+	65.1947i	0.908163	+	3.38931i
$371$	−0.0964222	+	19.0116i	−0.00500599	+	0.987032i
$372$		0			0
$373$	8.58752	+	14.8740i	0.444645	+	0.770147i	0.998027	−	0.0627799i	$-0.0199966\pi$
$373$	8.58752	+	14.8740i	0.444645	+	0.770147i	−0.553383	+	0.832927i	$0.686663\pi$
$374$	−8.91388	+	15.4393i	−0.460926	+	0.798347i
$375$		0			0
$376$	1.62477	−	2.81418i	0.0837909	−	0.145130i
$377$	−9.10328	−	4.71980i	−0.468843	−	0.243082i
$378$		0			0
$379$	0.602843	−	2.24984i	0.0309659	−	0.115566i	−0.948713	−	0.316139i	$-0.897613\pi$
$379$	0.602843	−	2.24984i	0.0309659	−	0.115566i	0.979679	+	0.200572i	$0.0642801\pi$
$380$	−1.45454			−0.0746163
$381$		0			0
$382$	1.22296	−	4.56415i	0.0625721	−	0.233522i
$383$	26.6204	+	7.13293i	1.36024	+	0.364476i	0.863905	−	0.503655i	$-0.168012\pi$
$383$	26.6204	+	7.13293i	1.36024	+	0.364476i	0.496336	+	0.868130i	$0.334678\pi$
$384$		0			0
$385$	33.5538	+	0.170177i	1.71006	+	0.00867302i
$386$	2.07041	−	3.58606i	0.105381	−	0.182526i
$387$		0			0
$388$	6.13606	−	1.64415i	0.311511	−	0.0834691i
$389$	10.7596	−	6.21203i	0.545531	−	0.314962i	−0.201787	−	0.979430i	$-0.564675\pi$
$389$	10.7596	−	6.21203i	0.545531	−	0.314962i	0.747318	+	0.664467i	$0.231341\pi$
$390$		0			0
$391$			11.8912i			0.601362i
$392$	−15.9243	−	4.44051i	−0.804299	−	0.224279i
$393$		0			0
$394$	1.13258	−	0.653895i	0.0570585	−	0.0329428i
$395$	−40.2804	−	10.7931i	−2.02673	−	0.543060i
$396$		0			0
$397$	−8.36351	+	31.2130i	−0.419752	+	1.56654i	0.355369	+	0.934726i	$0.384355\pi$
$397$	−8.36351	+	31.2130i	−0.419752	+	1.56654i	−0.775122	+	0.631812i	$0.782312\pi$
$398$	9.18635	+	9.18635i	0.460470	+	0.460470i
$399$		0			0
$400$	−37.6977	+	21.7648i	−1.88488	+	1.08824i
$401$	9.95929	−	9.95929i	0.497343	−	0.497343i	−0.413267	−	0.910610i	$-0.635612\pi$
$401$	9.95929	−	9.95929i	0.497343	−	0.497343i	0.910610	+	0.413267i	$0.135612\pi$
$402$		0			0
$403$	31.6885	−	10.0489i	1.57852	−	0.500569i
$404$	1.93627	+	1.11790i	0.0963329	+	0.0556178i
$405$		0			0
$406$	8.47038	−	8.38490i	0.420378	−	0.416135i
$407$	33.0815	+	19.0996i	1.63979	+	0.946731i
$408$		0			0
$409$	−20.8373	+	20.8373i	−1.03034	+	1.03034i	−0.0308137	+	0.999525i	$0.509810\pi$
$409$	−20.8373	+	20.8373i	−1.03034	+	1.03034i	−0.999525	+	0.0308137i	$0.990190\pi$
$410$	−29.8487	+	29.8487i	−1.47412	+	1.47412i
$411$		0			0
$412$	5.88804	+	3.39946i	0.290083	+	0.167479i
$413$	2.11965	+	8.07422i	0.104301	+	0.397307i
$414$		0			0
$415$	6.96559	+	4.02159i	0.341927	+	0.197412i
$416$	9.91172	+	2.18023i	0.485962	+	0.106894i
$417$		0			0
$418$	−2.86921	+	2.86921i	−0.140338	+	0.140338i
$419$	10.6429	−	6.14470i	0.519941	−	0.300188i	−0.216970	−	0.976178i	$-0.569617\pi$
$419$	10.6429	−	6.14470i	0.519941	−	0.300188i	0.736911	+	0.675990i	$0.236284\pi$
$420$		0			0
$421$	6.08177	+	6.08177i	0.296407	+	0.296407i	0.839605	−	0.543197i	$-0.182787\pi$
$421$	6.08177	+	6.08177i	0.296407	+	0.296407i	−0.543197	+	0.839605i	$0.682787\pi$
$422$	4.40666	−	16.4459i	0.214513	−	0.800572i
$423$		0			0
$424$	−16.3924	−	4.39232i	−0.796084	−	0.213310i
$425$	−26.4411	+	15.2658i	−1.28258	+	0.740500i
$426$		0			0
$427$	2.75719	+	0.0139838i	0.133430	+	0.000676724i
$428$		−	0.0903814i		−	0.00436875i
$429$		0			0
$430$	65.1155	−	37.5945i	3.14015	−	1.81297i
$431$	−32.9505	+	8.82906i	−1.58717	+	0.425281i	−0.941136	−	0.338029i	$-0.890240\pi$
$431$	−32.9505	+	8.82906i	−1.58717	+	0.425281i	−0.646033	+	0.763309i	$0.723573\pi$
$432$		0			0
$433$	14.7993	−	25.6331i	0.711209	−	1.23185i	−0.253194	−	0.967415i	$-0.581481\pi$
$433$	14.7993	−	25.6331i	0.711209	−	1.23185i	0.964403	−	0.264435i	$-0.0851855\pi$
$434$	−0.195971	+	38.6396i	−0.00940690	+	1.85476i
$435$		0			0
$436$	−2.55384	−	0.684299i	−0.122307	−	0.0327720i
$437$	−0.700488	+	2.61426i	−0.0335089	+	0.125057i
$438$		0			0
$439$	18.4285			0.879545			0.439772	−	0.898109i	$-0.355059\pi$
$439$	18.4285			0.879545			0.439772	+	0.898109i	$0.355059\pi$
$440$	−7.75208	+	28.9311i	−0.369566	+	1.37924i
$441$		0			0
$442$	18.6183	+	4.09536i	0.885582	+	0.194796i
$443$	2.87530	−	4.98017i	0.136610	−	0.236615i	−0.789601	−	0.613620i	$-0.789713\pi$
$443$	2.87530	−	4.98017i	0.136610	−	0.236615i	0.926211	+	0.377005i	$0.123046\pi$
$444$		0			0
$445$	−5.95128	+	10.3079i	−0.282118	+	0.488642i
$446$	−4.70687	−	8.15254i	−0.222877	−	0.386034i
$447$		0			0
$448$	6.75163	−	11.5584i	0.318984	−	0.546082i
$449$	−5.09748	−	19.0241i	−0.240565	−	0.897801i	−0.975561	−	0.219729i	$-0.929483\pi$
$449$	−5.09748	−	19.0241i	−0.240565	−	0.897801i	0.734996	−	0.678072i	$-0.237184\pi$
$450$		0			0
$451$			23.8905i			1.12496i
$452$	−8.82351	−	5.09426i	−0.415023	−	0.239614i
$453$		0			0
$454$	−32.2930			−1.51558
$455$	−10.6721	−	34.2560i	−0.500317	−	1.60595i
$456$		0			0
$457$	2.19914	+	2.19914i	0.102871	+	0.102871i	0.756669	−	0.653798i	$-0.226825\pi$
$457$	2.19914	+	2.19914i	0.102871	+	0.102871i	−0.653798	+	0.756669i	$0.726825\pi$
$458$	11.7734	+	6.79740i	0.550137	+	0.317622i
$459$		0			0
$460$	−1.76528	−	6.58812i	−0.0823066	−	0.307173i
$461$	−8.13643	−	30.3656i	−0.378951	−	1.41427i	−0.847485	−	0.530820i	$-0.821884\pi$
$461$	−8.13643	−	30.3656i	−0.378951	−	1.41427i	0.468533	−	0.883446i	$-0.344783\pi$
$462$		0			0
$463$	10.2951	−	10.2951i	0.478455	−	0.478455i	−0.426182	−	0.904637i	$-0.640142\pi$
$463$	10.2951	−	10.2951i	0.478455	−	0.478455i	0.904637	+	0.426182i	$0.140142\pi$
$464$	6.76715	+	11.7210i	0.314157	+	0.544136i
$465$		0			0
$466$	2.06147	+	7.69351i	0.0954958	+	0.356395i
$467$	6.26532	−	10.8518i	0.289924	−	0.502164i	−0.683867	−	0.729607i	$-0.739703\pi$
$467$	6.26532	−	10.8518i	0.289924	−	0.502164i	0.973791	+	0.227443i	$0.0730365\pi$
$468$		0			0
$469$	7.55012	+	2.06414i	0.348632	+	0.0953133i
$470$	−2.12167	+	7.91817i	−0.0978652	+	0.365238i
$471$		0			0
$472$	−7.45155			−0.342985
$473$	11.0138	−	41.1039i	0.506413	−	1.88996i
$474$		0			0
$475$	−6.71233	+	1.79856i	−0.307983	+	0.0825238i
$476$	−2.26739	+	3.88164i	−0.103926	+	0.177915i
$477$		0			0
$478$		−	26.1125i		−	1.19436i
$479$	−20.2529	+	5.42675i	−0.925379	+	0.247954i	−0.689883	−	0.723921i	$-0.742338\pi$
$479$	−20.2529	+	5.42675i	−0.925379	+	0.247954i	−0.235496	+	0.971875i	$0.575671\pi$
$480$		0			0
$481$	8.77505	−	39.8930i	0.400108	−	1.81897i
$482$		−	8.94218i		−	0.407305i
$483$		0			0
$484$	−0.0940112	−	0.162832i	−0.00427324	−	0.00740146i
$485$	40.6507	−	23.4697i	1.84585	−	1.06570i
$486$		0			0
$487$	7.62705	+	7.62705i	0.345615	+	0.345615i	0.858473	−	0.512858i	$-0.171413\pi$
$487$	7.62705	+	7.62705i	0.345615	+	0.345615i	−0.512858	+	0.858473i	$0.671413\pi$
$488$	−0.637005	+	2.37734i	−0.0288359	+	0.107617i
$489$		0			0
$490$	41.7022	+	0.423018i	1.88391	+	0.0191100i
$491$	−30.7318	+	17.7430i	−1.38691	+	0.800730i	−0.992965	−	0.118406i	$-0.962222\pi$
$491$	−30.7318	+	17.7430i	−1.38691	+	0.800730i	−0.393940	+	0.919136i	$0.628888\pi$
$492$		0			0
$493$	4.74647	+	8.22113i	0.213770	+	0.370261i
$494$	3.85196	+	1.99713i	0.173308	+	0.0898552i
$495$		0			0
$496$	−42.3830	−	11.3565i	−1.90305	−	0.509921i
$497$	18.5057	+	5.05933i	0.830096	+	0.226942i
$498$		0			0
$499$	−4.95983	+	1.32898i	−0.222033	+	0.0594935i	−0.368120	−	0.929778i	$-0.619999\pi$
$499$	−4.95983	+	1.32898i	−0.222033	+	0.0594935i	0.146088	+	0.989272i	$0.453332\pi$
$500$	5.61406	−	5.61406i	0.251069	−	0.251069i
$501$		0			0
$502$	−16.9595	+	4.54429i	−0.756940	+	0.202821i
$503$	31.3005	+	18.0713i	1.39562	+	0.805761i	0.993930	−	0.110015i	$-0.0350897\pi$
$503$	31.3005	+	18.0713i	1.39562	+	0.805761i	0.401690	+	0.915776i	$0.368423\pi$
$504$		0			0
$505$	15.9577	+	4.27585i	0.710108	+	0.190273i
$506$	−16.4778	−	9.51348i	−0.732529	−	0.422926i
$507$		0			0
$508$	1.98239	+	3.43361i	0.0879546	+	0.152342i
$509$	20.3768	−	20.3768i	0.903184	−	0.903184i	−0.0925266	−	0.995710i	$-0.529494\pi$
$509$	20.3768	−	20.3768i	0.903184	−	0.903184i	0.995710	+	0.0925266i	$0.0294943\pi$
$510$		0			0
$511$	4.06714	−	4.02610i	0.179920	−	0.178104i
$512$	6.42274	+	6.42274i	0.283848	+	0.283848i
$513$		0			0
$514$	−2.69171	−	2.69171i	−0.118726	−	0.118726i
$515$	48.5261	+	13.0025i	2.13832	+	0.572960i
$516$		0			0
$517$	2.31972	+	4.01788i	0.102021	+	0.176706i
$518$	40.9957	+	23.9469i	1.80125	+	1.05217i
$519$		0			0
$520$	31.9948	−	1.44981i	1.40307	−	0.0635785i
$521$	−15.6852	+	9.05586i	−0.687182	+	0.396745i	−0.802555	−	0.596578i	$-0.796527\pi$
$521$	−15.6852	+	9.05586i	−0.687182	+	0.396745i	0.115374	+	0.993322i	$0.463193\pi$
$522$		0			0
$523$			1.70402i			0.0745115i	0.999306	+	0.0372557i	$0.0118616\pi$
$523$			1.70402i			0.0745115i	−0.999306	+	0.0372557i	$0.988138\pi$
$524$	2.47094	−	4.27979i	0.107943	−	0.186963i
$525$		0			0
$526$	39.9711	−	10.7102i	1.74282	−	0.466988i
$527$	−29.7274	−	7.96543i	−1.29495	−	0.346980i
$528$		0			0
$529$	10.3090			0.448216
$530$	42.8113			1.85960
$531$		0			0
$532$	−0.727144	+	0.719805i	−0.0315257	+	0.0312075i
$533$	24.3513	−	7.72212i	1.05477	−	0.334482i
$534$		0			0
$535$	−0.172849	−	0.645082i	−0.00747292	−	0.0278893i
$536$	−3.49341	+	6.05077i	−0.150892	+	0.261353i
$537$		0			0
$538$	−29.5920	+	29.5920i	−1.27580	+	1.27580i
$539$	16.8582	−	16.5197i	0.726136	−	0.711552i
$540$		0			0
$541$	−2.05747	−	7.67860i	−0.0884577	−	0.330129i	0.907489	−	0.420076i	$-0.137997\pi$
$541$	−2.05747	−	7.67860i	−0.0884577	−	0.330129i	−0.995946	+	0.0899476i	$0.971330\pi$
$542$			11.9971i			0.515320i
$543$		0			0
$544$	−6.64353	−	6.64353i	−0.284839	−	0.284839i
$545$	−19.5363			−0.836842
$546$		0			0
$547$	−45.6503			−1.95187			−0.975933	−	0.218072i	$-0.930023\pi$
$547$	−45.6503			−1.95187			−0.975933	+	0.218072i	$0.930023\pi$
$548$	3.27103	+	3.27103i	0.139731	+	0.139731i
$549$		0			0
$550$		−	48.8534i		−	2.08311i
$551$	0.559213	+	2.08701i	0.0238233	+	0.0889097i
$552$		0			0
$553$	−25.4779	+	14.5379i	−1.08343	+	0.618214i
$554$	−25.2493	+	25.2493i	−1.07274	+	1.07274i
$555$		0			0
$556$	−2.60227	+	4.50727i	−0.110361	+	0.191151i
$557$	3.24461	+	12.1091i	0.137479	+	0.513077i	0.999975	+	0.00701474i	$0.00223288\pi$
$557$	3.24461	+	12.1091i	0.137479	+	0.513077i	−0.862497	+	0.506063i	$0.831100\pi$
$558$		0			0
$559$	−45.4566	+	2.05982i	−1.92261	+	0.0871211i
$560$	−12.4889	+	45.6812i	−0.527752	+	1.93038i
$561$		0			0
$562$	−17.3267			−0.730883
$563$	14.7021			0.619621			0.309810	−	0.950798i	$-0.399734\pi$
$563$	14.7021			0.619621			0.309810	+	0.950798i	$0.399734\pi$
$564$		0			0
$565$	−72.7188	−	19.4849i	−3.05930	−	0.819737i
$566$	−27.1279	+	7.26891i	−1.14027	+	0.305535i
$567$		0			0
$568$	−8.56254	+	14.8308i	−0.359276	+	0.622285i
$569$		−	21.1424i		−	0.886335i	−0.896439	−	0.443167i	$-0.853855\pi$
$569$		−	21.1424i		−	0.886335i	0.896439	−	0.443167i	$-0.146145\pi$
$570$		0			0
$571$	−2.38493	+	1.37694i	−0.0998064	+	0.0576232i	−0.549072	−	0.835775i	$-0.685019\pi$
$571$	−2.38493	+	1.37694i	−0.0998064	+	0.0576232i	0.449266	+	0.893398i	$0.351686\pi$
$572$	−4.17329	+	4.56946i	−0.174494	+	0.191059i
$573$		0			0
$574$	−0.150595	+	29.6929i	−0.00628573	+	1.23936i
$575$	−16.2927	−	28.2197i	−0.679451	−	1.17684i
$576$		0			0
$577$	−6.04026	−	1.61848i	−0.251459	−	0.0673783i	0.130888	−	0.991397i	$-0.458217\pi$
$577$	−6.04026	−	1.61848i	−0.251459	−	0.0673783i	−0.382347	+	0.924019i	$0.624884\pi$
$578$	6.56158	+	6.56158i	0.272926	+	0.272926i
$579$		0			0
$580$	−3.85016	−	3.85016i	−0.159869	−	0.159869i
$581$	5.47235	−	1.43660i	0.227031	−	0.0596004i
$582$		0			0
$583$	17.1328	−	17.1328i	0.709568	−	0.709568i
$584$	2.55421	+	4.42403i	0.105694	+	0.183067i
$585$		0			0
$586$	−17.6821	−	10.2088i	−0.730441	−	0.421720i
$587$	15.8338	+	4.24265i	0.653530	+	0.175113i	0.570324	−	0.821420i	$-0.306817\pi$
$587$	15.8338	+	4.24265i	0.653530	+	0.175113i	0.0832057	+	0.996532i	$0.473484\pi$
$588$		0			0
$589$	−6.06630	−	3.50238i	−0.249958	−	0.144313i
$590$	18.1573	−	4.86523i	0.747523	−	0.200298i
$591$		0			0
$592$	−38.1225	+	38.1225i	−1.56682	+	1.56682i
$593$	−14.8765	+	3.98614i	−0.610904	+	0.163691i	−0.550989	−	0.834512i	$-0.685750\pi$
$593$	−14.8765	+	3.98614i	−0.610904	+	0.163691i	−0.0599148	+	0.998203i	$0.519083\pi$
$594$		0			0
$595$	−8.75971	+	32.0408i	−0.359113	+	1.31354i
$596$	−7.38701	−	1.97934i	−0.302584	−	0.0810770i
$597$		0			0
$598$	−4.37084	+	19.8707i	−0.178737	+	0.812572i
$599$	−13.0357	−	22.5784i	−0.532623	−	0.922530i	−0.999274	−	0.0380886i	$-0.987873\pi$
$599$	−13.0357	−	22.5784i	−0.532623	−	0.922530i	0.466651	−	0.884441i	$-0.345460\pi$
$600$		0			0
$601$	−36.7529	+	21.2193i	−1.49918	+	0.865554i	−1.00000		0.000942846i	$-0.999700\pi$
$601$	−36.7529	+	21.2193i	−1.49918	+	0.865554i	−0.499183	+	0.866496i	$0.666367\pi$
$602$	13.9478	−	51.0176i	0.568471	−	2.07932i
$603$		0			0
$604$	0.0365845	−	0.136535i	0.00148860	−	0.00555555i
$605$	−0.982396	−	0.982396i	−0.0399401	−	0.0399401i
$606$		0			0
$607$	−5.87620	+	3.39263i	−0.238508	+	0.137702i	−0.614491	−	0.788924i	$-0.710638\pi$
$607$	−5.87620	+	3.39263i	−0.238508	+	0.137702i	0.375983	+	0.926627i	$0.377305\pi$
$608$	−1.06921	−	1.85193i	−0.0433623	−	0.0751057i
$609$		0			0
$610$		−	6.20879i		−	0.251386i
$611$	3.34557	−	3.66316i	0.135347	−	0.148196i
$612$		0			0
$613$	32.8333	−	8.79765i	1.32612	−	0.355334i	0.474855	−	0.880064i	$-0.342501\pi$
$613$	32.8333	−	8.79765i	1.32612	−	0.355334i	0.851269	+	0.524730i	$0.175834\pi$
$614$			13.0442i			0.526422i
$615$		0			0
$616$	10.4417	+	18.2993i	0.420710	+	0.737301i
$617$	7.13892	−	1.91287i	0.287402	−	0.0770091i	−0.112238	−	0.993681i	$-0.535802\pi$
$617$	7.13892	−	1.91287i	0.287402	−	0.0770091i	0.399640	+	0.916672i	$0.369135\pi$
$618$		0			0
$619$	0.183786	−	0.685897i	0.00738697	−	0.0275685i	−0.962134	−	0.272577i	$-0.912124\pi$
$619$	0.183786	−	0.685897i	0.00738697	−	0.0275685i	0.969521	+	0.245008i	$0.0787907\pi$
$620$	17.6525			0.708942
$621$		0			0
$622$	11.0924	−	41.3973i	0.444764	−	1.65988i
$623$	2.12594	+	8.09817i	0.0851739	+	0.324446i
$624$		0			0
$625$	6.46561	−	11.1988i	0.258624	−	0.447951i
$626$	−5.62781	−	21.0033i	−0.224933	−	0.839460i
$627$		0			0
$628$	0.0800312	+	0.138618i	0.00319359	+	0.00553146i
$629$	−26.7391	+	26.7391i	−1.06616	+	1.06616i
$630$		0			0
$631$	7.80744	+	29.1378i	0.310809	+	1.15996i	0.927828	+	0.373008i	$0.121674\pi$
$631$	7.80744	+	29.1378i	0.310809	+	1.15996i	−0.617019	+	0.786948i	$0.711660\pi$
$632$	−6.77702	−	25.2922i	−0.269575	−	1.00607i
$633$		0			0
$634$	3.17843	+	1.83507i	0.126232	+	0.0728798i
$635$	20.7156	+	20.7156i	0.822073	+	0.822073i
$636$		0			0
$637$	−22.2874	−	11.8437i	−0.883057	−	0.469266i
$638$	−15.1896			−0.601361
$639$		0			0
$640$	−44.4412	−	25.6581i	−1.75669	−	1.01423i
$641$			14.4376i			0.570251i	0.958490	+	0.285126i	$0.0920353\pi$
$641$			14.4376i			0.570251i	−0.958490	+	0.285126i	$0.907965\pi$
$642$		0			0
$643$	−4.71705	−	17.6043i	−0.186022	−	0.694244i	−0.994409	−	0.105593i	$-0.966326\pi$
$643$	−4.71705	−	17.6043i	−0.186022	−	0.694244i	0.808387	−	0.588651i	$-0.200341\pi$
$644$	−4.14274	−	2.41991i	−0.163247	−	0.0953577i
$645$		0			0
$646$	−2.00842	−	3.47868i	−0.0790202	−	0.136867i
$647$	−18.8833	+	32.7068i	−0.742379	+	1.28584i	0.209031	+	0.977909i	$0.432969\pi$
$647$	−18.8833	+	32.7068i	−0.742379	+	1.28584i	−0.951409	+	0.307929i	$0.900364\pi$
$648$		0			0
$649$	5.31939	−	9.21346i	0.208804	−	0.361660i
$650$	−49.7956	+	15.7909i	−1.95314	+	0.619368i
$651$		0			0
$652$	0.124384	−	0.464209i	0.00487127	−	0.0181798i
$653$	26.5542			1.03915			0.519573	−	0.854426i	$-0.326091\pi$
$653$	26.5542			1.03915			0.519573	+	0.854426i	$0.326091\pi$
$654$		0			0
$655$	9.45104	−	35.2718i	0.369283	−	1.37818i
$656$	−32.5695	−	8.72698i	−1.27163	−	0.340731i
$657$		0			0
$658$	2.85780	+	5.00835i	0.111409	+	0.195246i
$659$	−2.28186	+	3.95230i	−0.0888888	+	0.153960i	−0.907042	−	0.421041i	$-0.861665\pi$
$659$	−2.28186	+	3.95230i	−0.0888888	+	0.153960i	0.818153	+	0.575001i	$0.194998\pi$
$660$		0			0
$661$	40.6603	−	10.8949i	1.58150	−	0.423762i	0.642111	−	0.766612i	$-0.278059\pi$
$661$	40.6603	−	10.8949i	1.58150	−	0.423762i	0.939390	+	0.342850i	$0.111392\pi$
$662$	−35.4369	+	20.4595i	−1.37730	+	0.795182i
$663$		0			0
$664$			5.05033i			0.195991i
$665$	−3.81328	+	6.52811i	−0.147873	+	0.253149i
$666$		0			0
$667$	−8.77413	+	5.06575i	−0.339736	+	0.196146i
$668$	−1.19036	−	0.318955i	−0.0460563	−	0.0123407i
$669$		0			0
$670$	4.56180	−	17.0249i	0.176238	−	0.657728i
$671$	−2.48472	−	2.48472i	−0.0959215	−	0.0959215i
$672$		0			0
$673$	−22.4576	+	12.9659i	−0.865675	+	0.499798i	−0.865909	−	0.500202i	$-0.833259\pi$
$673$	−22.4576	+	12.9659i	−0.865675	+	0.499798i	0.000233516		1.00000i	$0.499926\pi$
$674$	−36.2979	+	36.2979i	−1.39814	+	1.39814i
$675$		0			0
$676$	6.00652	+	2.77679i	0.231020	+	0.106800i
$677$	−15.4910	−	8.94374i	−0.595368	−	0.343736i	0.171849	−	0.985123i	$-0.445026\pi$
$677$	−15.4910	−	8.94374i	−0.595368	−	0.343736i	−0.767217	+	0.641387i	$0.778359\pi$
$678$		0			0
$679$	8.70743	−	31.8496i	0.334161	−	1.22227i
$680$	−25.6779	−	14.8252i	−0.984704	−	0.568519i
$681$		0			0
$682$	34.8211	−	34.8211i	1.33337	−	1.33337i
$683$	22.6009	−	22.6009i	0.864799	−	0.864799i	−0.127092	−	0.991891i	$-0.540564\pi$
$683$	22.6009	−	22.6009i	0.864799	−	0.864799i	0.991891	+	0.127092i	$0.0405643\pi$
$684$		0			0
$685$	29.6021	+	17.0908i	1.13104	+	0.653004i
$686$	21.0568	−	20.4256i	0.803953	−	0.779853i
$687$		0			0
$688$	52.0130	+	30.0297i	1.98298	+	1.14487i
$689$	−23.0011	−	11.9254i	−0.876271	−	0.454322i
$690$		0			0
$691$	10.6170	−	10.6170i	0.403889	−	0.403889i	−0.475712	−	0.879601i	$-0.657809\pi$
$691$	10.6170	−	10.6170i	0.403889	−	0.403889i	0.879601	+	0.475712i	$0.157809\pi$
$692$	7.59173	−	4.38309i	0.288594	−	0.166620i
$693$		0			0
$694$	−34.7456	−	34.7456i	−1.31893	−	1.31893i
$695$	−9.95340	+	37.1466i	−0.377554	+	1.40905i
$696$		0			0
$697$	−22.8443	−	6.12110i	−0.865288	−	0.231853i
$698$	−0.753802	+	0.435208i	−0.0285318	+	0.0164729i
$699$		0			0
$700$	0.0624761	−	12.3184i	0.00236138	−	0.465593i
$701$		−	17.3022i		−	0.653495i	−0.945112	−	0.326747i	$-0.894047\pi$
$701$		−	17.3022i		−	0.653495i	0.945112	−	0.326747i	$-0.105953\pi$
$702$		0			0
$703$	−7.45371	+	4.30340i	−0.281122	+	0.162306i
$704$	−16.4782	+	4.41531i	−0.621044	+	0.166408i
$705$		0			0
$706$	−9.79802	+	16.9707i	−0.368753	+	0.638700i
$707$	10.0935	−	5.75940i	0.379604	−	0.216605i
$708$		0			0
$709$	−13.4262	−	3.59754i	−0.504231	−	0.135108i	−0.00226813	−	0.999997i	$-0.500722\pi$
$709$	−13.4262	−	3.59754i	−0.504231	−	0.135108i	−0.501963	+	0.864889i	$0.667389\pi$
$710$	11.1812	−	41.7289i	0.419623	−	1.56606i
$711$		0			0
$712$	−7.47365			−0.280087
$713$	8.50123	−	31.7270i	0.318374	−	1.18819i
$714$		0			0
$715$	−21.0473	+	40.5949i	−0.787126	+	1.51816i
$716$	0.876146	−	1.51753i	0.0327431	−	0.0567128i
$717$		0			0
$718$	−5.76710	+	9.98891i	−0.215226	+	0.372783i
$719$	−24.5650	−	42.5477i	−0.916118	−	1.58676i	−0.805256	−	0.592927i	$-0.797972\pi$
$719$	−24.5650	−	42.5477i	−0.916118	−	1.58676i	−0.110862	−	0.993836i	$-0.535361\pi$
$720$		0			0
$721$	30.6934	−	17.5139i	1.14308	−	0.652252i
$722$	7.55274	+	28.1872i	0.281084	+	1.04902i
$723$		0			0
$724$			13.2228i			0.491421i
$725$	−22.5283	−	13.0067i	−0.836682	−	0.483059i
$726$		0			0
$727$	19.4676			0.722014			0.361007	−	0.932563i	$-0.382433\pi$
$727$	19.4676			0.722014			0.361007	+	0.932563i	$0.382433\pi$
$728$	15.2772	−	16.5580i	0.566210	−	0.613681i
$729$		0			0
$730$	−9.11238	−	9.11238i	−0.337264	−	0.337264i
$731$	36.4819	+	21.0628i	1.34933	+	0.779037i
$732$		0			0
$733$	1.81677	+	6.78026i	0.0671038	+	0.250435i	0.991327	−	0.131418i	$-0.0419529\pi$
$733$	1.81677	+	6.78026i	0.0671038	+	0.250435i	−0.924223	+	0.381852i	$0.875286\pi$
$734$	−1.76768	−	6.59709i	−0.0652464	−	0.243503i
$735$		0			0
$736$	7.09041	−	7.09041i	0.261356	−	0.261356i
$737$	−4.98764	−	8.63885i	−0.183722	−	0.318216i
$738$		0			0
$739$	10.3392	+	38.5863i	0.380332	+	1.41942i	0.845395	+	0.534142i	$0.179365\pi$
$739$	10.3392	+	38.5863i	0.380332	+	1.41942i	−0.465063	+	0.885278i	$0.653968\pi$
$740$	10.8449	−	18.7839i	0.398666	−	0.690509i
$741$		0			0
$742$	21.4019	−	21.1859i	0.785690	−	0.777760i
$743$	9.49010	−	35.4175i	0.348158	−	1.29934i	−0.540721	−	0.841202i	$-0.681849\pi$
$743$	9.49010	−	35.4175i	0.348158	−	1.29934i	0.888879	−	0.458141i	$-0.151485\pi$
$744$		0			0
$745$	−56.5089			−2.07033
$746$	7.04119	−	26.2781i	0.257796	−	0.962109i
$747$		0			0
$748$	5.53384	−	1.48279i	0.202337	−	0.0542161i
$749$	−0.405640	−	0.236948i	−0.0148218	−	0.00865788i
$750$		0			0
$751$		−	19.4504i		−	0.709755i	−0.934913	−	0.354877i	$-0.884523\pi$
$751$		−	19.4504i		−	0.709755i	0.934913	−	0.354877i	$-0.115477\pi$
$752$	−6.32488	+	1.69475i	−0.230645	+	0.0618010i
$753$		0			0
$754$	4.90972	+	15.4825i	0.178802	+	0.563841i
$755$		−	1.04446i		−	0.0380119i
$756$		0			0
$757$	3.02968	+	5.24756i	0.110116	+	0.190726i	0.915817	−	0.401597i	$-0.131545\pi$
$757$	3.02968	+	5.24756i	0.110116	+	0.190726i	−0.805701	+	0.592322i	$0.798211\pi$
$758$	−3.19515	+	1.84472i	−0.116053	+	0.0670032i
$759$		0			0
$760$	−4.77194	−	4.77194i	−0.173096	−	0.173096i
$761$	7.80535	−	29.1300i	0.282944	−	1.05596i	−0.667385	−	0.744713i	$-0.732587\pi$
$761$	7.80535	−	29.1300i	0.282944	−	1.05596i	0.950329	−	0.311247i	$-0.100747\pi$
$762$		0			0
$763$	−9.76645	+	9.66789i	−0.353569	+	0.350001i
$764$	−1.31502	+	0.759229i	−0.0475759	+	0.0274679i
$765$		0			0
$766$	−21.8270	−	37.8055i	−0.788641	−	1.36597i
$767$	−11.1105	−	2.44392i	−0.401178	−	0.0882450i
$768$		0			0
$769$	22.1109	+	5.92460i	0.797339	+	0.213646i	0.634415	−	0.772992i	$-0.281241\pi$
$769$	22.1109	+	5.92460i	0.797339	+	0.213646i	0.162924	+	0.986639i	$0.447908\pi$
$770$	−37.3914	−	37.7726i	−1.34749	−	1.36123i
$771$		0			0
$772$	−1.28534	+	0.344405i	−0.0462603	+	0.0123954i
$773$	−10.6208	+	10.6208i	−0.382004	+	0.382004i	−0.871824	−	0.489820i	$-0.837063\pi$
$773$	−10.6208	+	10.6208i	−0.382004	+	0.382004i	0.489820	+	0.871824i	$0.337063\pi$
$774$		0			0
$775$	81.4619	−	21.8277i	2.92620	−	0.784073i
$776$	25.5247	+	14.7367i	0.916283	+	0.529016i
$777$		0			0
$778$	−19.0090	−	5.09345i	−0.681506	−	0.182609i
$779$	−4.66170	−	2.69143i	−0.167023	−	0.0964306i
$780$		0			0
$781$	−12.2250	−	21.1743i	−0.437444	−	0.757675i
$782$	13.3187	−	13.3187i	0.476276	−	0.476276i
$783$		0			0
$784$	16.3628	+	29.0170i	0.584386	+	1.03632i
$785$	0.836308	+	0.836308i	0.0298491	+	0.0298491i
$786$		0			0
$787$	−6.19869	−	6.19869i	−0.220959	−	0.220959i	0.587943	−	0.808902i	$-0.299938\pi$
$787$	−6.19869	−	6.19869i	−0.220959	−	0.220959i	−0.808902	+	0.587943i	$0.799938\pi$
$788$	−0.405946	−	0.108773i	−0.0144612	−	0.00387487i
$789$		0			0
$790$	33.0273	+	57.2049i	1.17506	+	2.03526i
$791$	−45.9956	+	26.2454i	−1.63541	+	0.933180i
$792$		0			0
$793$	−1.72951	+	3.33577i	−0.0614165	+	0.118457i
$794$	44.3277	−	25.5926i	1.57313	−	0.908248i
$795$		0			0
$796$		−	4.17488i		−	0.147975i
$797$	−21.7995	+	37.7578i	−0.772177	+	1.33745i	0.164190	+	0.986429i	$0.447499\pi$
$797$	−21.7995	+	37.7578i	−0.772177	+	1.33745i	−0.936367	+	0.351021i	$0.885834\pi$
$798$		0			0
$799$	−4.43627	+	1.18869i	−0.156944	+	0.0420530i
$800$	24.8688	+	6.66358i	0.879246	+	0.235593i
$801$		0			0
$802$	−22.3098			−0.787787
$803$	−7.29344			−0.257380
$804$		0			0
$805$	−34.1960	−	9.34894i	−1.20525	−	0.329507i
$806$	−46.7479	−	24.2375i	−1.64663	−	0.853729i
$807$		0			0
$808$	2.68482	+	10.0199i	0.0944517	+	0.352498i
$809$	6.30114	−	10.9139i	0.221536	−	0.383712i	−0.733738	−	0.679432i	$-0.762226\pi$
$809$	6.30114	−	10.9139i	0.221536	−	0.383712i	0.955275	+	0.295720i	$0.0955596\pi$
$810$		0			0
$811$	−13.6469	+	13.6469i	−0.479208	+	0.479208i	−0.904878	−	0.425670i	$-0.860038\pi$
$811$	−13.6469	+	13.6469i	−0.479208	+	0.479208i	0.425670	+	0.904878i	$0.360038\pi$
$812$	−3.83007	−	0.0194252i	−0.134409	−	0.000681691i
$813$		0			0
$814$	−15.6604	−	58.4454i	−0.548896	−	2.04851i
$815$		−	3.55109i		−	0.124389i
$816$		0			0
$817$	6.77972	+	6.77972i	0.237192	+	0.237192i
$818$	46.6777			1.63205
$819$		0			0
$820$	13.5652			0.473718
$821$	19.5518	+	19.5518i	0.682363	+	0.682363i	0.960532	−	0.278169i	$-0.0897276\pi$
$821$	19.5518	+	19.5518i	0.682363	+	0.682363i	−0.278169	+	0.960532i	$0.589728\pi$
$822$		0			0
$823$			14.0080i			0.488288i	0.969739	+	0.244144i	$0.0785070\pi$
$823$			14.0080i			0.488288i	−0.969739	+	0.244144i	$0.921493\pi$
$824$	8.16433	+	30.4697i	0.284418	+	1.06146i
$825$		0			0
$826$	6.66942	−	11.4176i	0.232059	−	0.397271i
$827$	−25.9908	+	25.9908i	−0.903790	+	0.903790i	−0.995762	−	0.0919718i	$-0.970683\pi$
$827$	−25.9908	+	25.9908i	−0.903790	+	0.903790i	0.0919718	+	0.995762i	$0.470683\pi$
$828$		0			0
$829$	−1.59143	+	2.75645i	−0.0552728	+	0.0957353i	−0.892338	−	0.451368i	$-0.850936\pi$
$829$	−1.59143	+	2.75645i	−0.0552728	+	0.0957353i	0.837065	+	0.547103i	$0.184270\pi$
$830$	−3.29743	−	12.3062i	−0.114456	−	0.427154i
$831$		0			0
$832$	9.82669	+	15.3688i	0.340679	+	0.532817i
$833$	11.4769	+	20.3525i	0.397650	+	0.705173i
$834$		0			0
$835$	−9.10595			−0.315124
$836$	1.30396			0.0450983
$837$		0			0
$838$	−18.8030	−	5.03824i	−0.649538	−	0.174043i
$839$	−15.7489	+	4.21991i	−0.543713	+	0.145687i	−0.520213	−	0.854036i	$-0.674148\pi$
$839$	−15.7489	+	4.21991i	−0.543713	+	0.145687i	−0.0234997	+	0.999724i	$0.507481\pi$
$840$		0			0
$841$	10.4559	−	18.1102i	0.360549	−	0.624489i
$842$		−	13.6238i		−	0.469506i
$843$		0			0
$844$	−4.73838	+	2.73570i	−0.163102	+	0.0941668i
$845$	48.1810	+	8.33178i	1.65748	+	0.286622i
$846$		0			0
$847$	−0.977270	−	0.00495647i	−0.0335794	−	0.000170306i
$848$	17.0984	+	29.6153i	0.587161	+	1.01699i
$849$		0			0
$850$	46.7139	+	12.5169i	1.60227	+	0.429328i
$851$	−28.5377	−	28.5377i	−0.978260	−	0.978260i
$852$		0			0
$853$	1.18686	+	1.18686i	0.0406374	+	0.0406374i	0.727133	−	0.686496i	$-0.240852\pi$
$853$	1.18686	+	1.18686i	0.0406374	+	0.0406374i	−0.686496	+	0.727133i	$0.740852\pi$
$854$	−3.07253	−	3.10386i	−0.105140	−	0.106212i
$855$		0			0
$856$	0.296516	−	0.296516i	0.0101347	−	0.0101347i
$857$	13.8735	+	24.0297i	0.473911	+	0.820838i	0.999554	−	0.0298676i	$-0.00950857\pi$
$857$	13.8735	+	24.0297i	0.473911	+	0.820838i	−0.525643	+	0.850705i	$0.676175\pi$
$858$		0			0
$859$	33.2801	+	19.2142i	1.13550	+	0.655582i	0.945313	−	0.326166i	$-0.105757\pi$
$859$	33.2801	+	19.2142i	1.13550	+	0.655582i	0.190188	+	0.981748i	$0.439090\pi$
$860$	−23.3391	−	6.25369i	−0.795856	−	0.213249i
$861$		0			0
$862$	46.7952	+	27.0172i	1.59385	+	0.920210i
$863$	35.6421	−	9.55027i	1.21327	−	0.325095i	0.405226	−	0.914216i	$-0.367193\pi$
$863$	35.6421	−	9.55027i	1.21327	−	0.325095i	0.808044	+	0.589122i	$0.200526\pi$
$864$		0			0
$865$	45.8023	−	45.8023i	1.55732	−	1.55732i
$866$	−45.2864	+	12.1344i	−1.53889	+	0.412345i
$867$		0			0
$868$	8.82473	−	8.73566i	0.299531	−	0.296508i
$869$	36.1104	+	9.67574i	1.22496	+	0.328227i
$870$		0			0
$871$	−7.19331	+	7.87617i	−0.243736	+	0.266874i
$872$	−6.13344	−	10.6234i	−0.207705	−	0.359755i
$873$		0			0
$874$	3.71268	−	2.14352i	0.125583	−	0.0725055i
$875$	−10.4784	−	39.9145i	−0.354234	−	1.34936i
$876$		0			0
$877$	−12.2105	+	45.5701i	−0.412318	+	1.53879i	0.377830	+	0.925875i	$0.376670\pi$
$877$	−12.2105	+	45.5701i	−0.412318	+	1.53879i	−0.790148	+	0.612916i	$0.789996\pi$
$878$	−20.6409	−	20.6409i	−0.696595	−	0.696595i
$879$		0			0
$880$	52.2685	−	30.1772i	1.76197	−	1.01727i
$881$	−6.77602	−	11.7364i	−0.228290	−	0.395410i	0.729011	−	0.684501i	$-0.239980\pi$
$881$	−6.77602	−	11.7364i	−0.228290	−	0.395410i	−0.957301	+	0.289092i	$0.906647\pi$
$882$		0			0
$883$			35.2962i			1.18781i	0.804534	+	0.593907i	$0.202415\pi$
$883$			35.2962i			1.18781i	−0.804534	+	0.593907i	$0.797585\pi$
$884$	−3.30009	−	5.16129i	−0.110994	−	0.173593i
$885$		0			0
$886$	−8.79853	+	2.35756i	−0.295592	+	0.0792037i
$887$		−	12.5265i		−	0.420599i	−0.977637	−	0.210300i	$-0.932556\pi$
$887$		−	12.5265i		−	0.420599i	0.977637	−	0.210300i	$-0.0674440\pi$
$888$		0			0
$889$	20.6075	+	0.104516i	0.691153	+	0.00350536i
$890$	18.2111	−	4.87966i	0.610438	−	0.163566i
$891$		0			0
$892$	−0.782969	+	2.92208i	−0.0262157	+	0.0978384i
$893$	−1.04533			−0.0349807
$894$		0			0
$895$	3.35116	−	12.5067i	0.112017	−	0.418053i
$896$	−34.9142	+	9.16569i	−1.16640	+	0.306204i
$897$		0			0
$898$	−15.5985	+	27.0173i	−0.520528	+	0.901580i
$899$	−6.78670	−	25.3283i	−0.226349	−	0.844746i
$900$		0			0
$901$	11.9928	+	20.7722i	0.399538	+	0.692021i
$902$	26.7586	−	26.7586i	0.890963	−	0.890963i
$903$		0			0
$904$	−12.2346	−	45.6603i	−0.406918	−	1.51864i
$905$	25.2878	+	94.3754i	0.840595	+	3.13714i
$906$		0			0
$907$	32.7297	+	18.8965i	1.08677	+	0.627447i	0.932715	−	0.360615i	$-0.117433\pi$
$907$	32.7297	+	18.8965i	1.08677	+	0.627447i	0.154056	+	0.988062i	$0.450767\pi$
$908$	7.33803	+	7.33803i	0.243521	+	0.243521i
$909$		0			0
$910$	−26.4151	+	50.3218i	−0.875652	+	1.66815i
$911$	15.1976			0.503520			0.251760	−	0.967790i	$-0.418991\pi$
$911$	15.1976			0.503520			0.251760	+	0.967790i	$0.418991\pi$
$912$		0			0
$913$	−6.24447	−	3.60525i	−0.206662	−	0.119316i
$914$		−	4.92629i		−	0.162947i
$915$		0			0
$916$	−1.13072	−	4.21991i	−0.0373601	−	0.139430i
$917$	−12.7302	−	22.3099i	−0.420387	−	0.736736i
$918$		0			0
$919$	9.49306	+	16.4425i	0.313147	+	0.542387i	0.979042	−	0.203659i	$-0.0652834\pi$
$919$	9.49306	+	16.4425i	0.313147	+	0.542387i	−0.665895	+	0.746046i	$0.731950\pi$
$920$	15.8224	−	27.4052i	0.521649	−	0.903522i
$921$		0			0
$922$	−24.8978	+	43.1242i	−0.819964	+	1.42022i
$923$	−17.6312	+	19.3049i	−0.580337	+	0.635429i
$924$		0			0
$925$	26.8198	−	100.093i	0.881830	−	3.29103i
$926$	−23.0621			−0.757868
$927$		0			0
$928$	2.07185	−	7.73226i	0.0680119	−	0.253824i
$929$	−25.9735	−	6.95959i	−0.852164	−	0.228337i	−0.193804	−	0.981040i	$-0.562083\pi$
$929$	−25.9735	−	6.95959i	−0.852164	−	0.228337i	−0.658360	+	0.752704i	$0.728749\pi$
$930$		0			0
$931$	1.32424	+	5.15056i	0.0434003	+	0.168803i
$932$	1.27978	−	2.21665i	0.0419207	−	0.0726089i
$933$		0			0
$934$	−19.1721	+	5.13714i	−0.627330	+	0.168092i
$935$	36.6611	−	21.1663i	1.19895	−	0.692212i
$936$		0			0
$937$		−	55.8288i		−	1.82385i	−0.410358	−	0.911924i	$-0.634596\pi$
$937$		−	55.8288i		−	1.82385i	0.410358	−	0.911924i	$-0.365404\pi$
$938$	−6.14456	−	10.7685i	−0.200627	−	0.351602i
$939$		0			0
$940$	2.28138	−	1.31716i	0.0744104	−	0.0429609i
$941$	48.0434	+	12.8732i	1.56617	+	0.419654i	0.934610	−	0.355675i	$-0.115749\pi$
$941$	48.0434	+	12.8732i	1.56617	+	0.419654i	0.631559	+	0.775328i	$0.282416\pi$
$942$		0			0
$943$	6.53284	−	24.3809i	0.212739	−	0.793951i
$944$	10.6174	+	10.6174i	0.345568	+	0.345568i
$945$		0			0
$946$	−58.3744	+	33.7025i	−1.89791	+	1.09576i
$947$	−22.6510	+	22.6510i	−0.736057	+	0.736057i	−0.971812	−	0.235755i	$-0.924244\pi$
$947$	−22.6510	+	22.6510i	−0.736057	+	0.736057i	0.235755	+	0.971812i	$0.424244\pi$
$948$		0			0
$949$	2.35746	+	7.43410i	0.0765262	+	0.241321i
$950$	9.53263	+	5.50367i	0.309279	+	0.178563i
$951$		0			0
$952$	−20.1733	+	5.29590i	−0.653819	+	0.171641i
$953$	25.2887	+	14.6005i	0.819182	+	0.472955i	0.850134	−	0.526566i	$-0.176521\pi$
$953$	25.2887	+	14.6005i	0.819182	+	0.472955i	−0.0309522	+	0.999521i	$0.509854\pi$
$954$		0			0
$955$	−7.93377	+	7.93377i	−0.256731	+	0.256731i
$956$	−5.93361	+	5.93361i	−0.191907	+	0.191907i
$957$		0			0
$958$	28.7625	+	16.6060i	0.929274	+	0.536517i
$959$	23.2561	−	6.10522i	0.750980	−	0.197148i
$960$		0			0
$961$	46.7748	+	27.0054i	1.50886	+	0.871143i
$962$	−54.5107	+	34.8537i	−1.75749	+	1.12373i
$963$		0			0
$964$	−2.03196	+	2.03196i	−0.0654450	+	0.0654450i
$965$	−8.51522	+	4.91627i	−0.274115	+	0.158260i
$966$		0			0
$967$	−28.2620	−	28.2620i	−0.908844	−	0.908844i	0.0873352	−	0.996179i	$-0.472165\pi$
$967$	−28.2620	−	28.2620i	−0.908844	−	0.908844i	−0.996179	+	0.0873352i	$0.972165\pi$
$968$	0.225782	−	0.842631i	0.00725692	−	0.0270832i
$969$		0			0
$970$	−71.8181	−	19.2436i	−2.30594	−	0.617875i
$971$	12.1286	−	7.00245i	0.389225	−	0.224719i	−0.292599	−	0.956235i	$-0.594520\pi$
$971$	12.1286	−	7.00245i	0.389225	−	0.224719i	0.681824	+	0.731516i	$0.261187\pi$
$972$		0			0
$973$	13.4068	+	23.4957i	0.429803	+	0.753238i
$974$		−	17.0854i		−	0.547450i
$975$		0			0
$976$	4.29502	−	2.47973i	0.137480	−	0.0793742i
$977$	20.3161	−	5.44369i	0.649970	−	0.174159i	0.0812550	−	0.996693i	$-0.474107\pi$
$977$	20.3161	−	5.44369i	0.649970	−	0.174159i	0.568716	+	0.822534i	$0.307441\pi$
$978$		0			0
$979$	5.33517	−	9.24079i	0.170513	−	0.295337i
$980$	−9.37998	−	9.57223i	−0.299633	−	0.305774i
$981$		0			0
$982$	54.2942	+	14.5481i	1.73260	+	0.464248i
$983$	−1.96757	+	7.34307i	−0.0627558	+	0.234208i	−0.990179	−	0.139806i	$-0.955352\pi$
$983$	−1.96757	+	7.34307i	−0.0627558	+	0.234208i	0.927423	+	0.374014i	$0.122019\pi$
$984$		0			0
$985$	−3.10539			−0.0989460
$986$	3.89179	−	14.5244i	0.123940	−	0.462550i
$987$		0			0
$988$	−0.421477	−	1.32910i	−0.0134090	−	0.0422845i
$989$	−22.4796	+	38.9359i	−0.714811	+	1.23809i
$990$		0			0
$991$	−12.3131	+	21.3269i	−0.391138	+	0.677470i	−0.992600	−	0.121431i	$-0.961252\pi$
$991$	−12.3131	+	21.3269i	−0.391138	+	0.677470i	0.601462	+	0.798901i	$0.294585\pi$
$992$	12.9761	+	22.4753i	0.411992	+	0.713592i
$993$		0			0
$994$	−15.0606	−	26.3940i	−0.477695	−	0.837168i
$995$	−7.98422	−	29.7975i	−0.253117	−	0.944645i
$996$		0			0
$997$			16.4760i			0.521801i	0.965366	+	0.260901i	$0.0840195\pi$
$997$			16.4760i			0.521801i	−0.965366	+	0.260901i	$0.915980\pi$
$998$	7.04379	+	4.06674i	0.222967	+	0.128730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.2		36
3.2	odd	2		273.2.bt.a.271.8	yes	36
7.3	odd	6		819.2.gh.c.388.8		36
13.6	odd	12		819.2.gh.c.19.8		36
21.17	even	6		273.2.cg.a.115.2	yes	36
39.32	even	12		273.2.cg.a.19.2	yes	36
91.45	even	12	inner	819.2.et.c.136.2		36
273.227	odd	12		273.2.bt.a.136.8	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.8	✓	36	273.227	odd	12
273.2.bt.a.271.8	yes	36	3.2	odd	2
273.2.cg.a.19.2	yes	36	39.32	even	12
273.2.cg.a.115.2	yes	36	21.17	even	6
819.2.et.c.136.2		36	91.45	even	12	inner
819.2.et.c.271.2		36	1.1	even	1	trivial
819.2.gh.c.19.8		36	13.6	odd	12
819.2.gh.c.388.8		36	7.3	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +O(q^{10})\)	\(q+(-1.12005 - 1.12005i) q^{2} +0.509024i q^{4} +(0.973479 + 3.63307i) q^{5} +(2.28455 + 1.33448i) q^{7} +(-1.66997 + 1.66997i) q^{8} +(2.97888 - 5.15957i) q^{10} +(-0.872699 - 3.25696i) q^{11} +(-3.03769 + 1.94228i) q^{13} +(-1.06413 - 4.05349i) q^{14} +4.75894 q^{16} +3.33792 q^{17} +(0.733837 + 0.196631i) q^{19} +(-1.84932 + 0.495525i) q^{20} +(-2.67049 + 4.62542i) q^{22} +3.56245i q^{23} +(-7.92144 + 4.57345i) q^{25} +(5.57781 + 1.22692i) q^{26} +(-0.679283 + 1.16289i) q^{28} +(1.42199 + 2.46295i) q^{29} +(-8.90596 - 2.38635i) q^{31} +(-1.99032 - 1.99032i) q^{32} +(-3.73864 - 3.73864i) q^{34} +(-2.62430 + 9.59903i) q^{35} +(-8.01070 + 8.01070i) q^{37} +(-0.601698 - 1.04217i) q^{38} +(-7.69280 - 4.44144i) q^{40} +(-6.84386 - 1.83381i) q^{41} +(10.9295 + 6.31017i) q^{43} +(1.65787 - 0.444225i) q^{44} +(3.99012 - 3.99012i) q^{46} +(-1.32905 + 0.356118i) q^{47} +(3.43833 + 6.09737i) q^{49} +(13.9949 + 3.74992i) q^{50} +(-0.988666 - 1.54626i) q^{52} +(3.59290 + 6.22308i) q^{53} +(10.9832 - 6.34116i) q^{55} +(-6.04366 + 1.58659i) q^{56} +(1.16593 - 4.35132i) q^{58} +(2.23105 + 2.23105i) q^{59} +(0.902515 - 0.521067i) q^{61} +(7.30230 + 12.6480i) q^{62} -5.05937i q^{64} +(-10.0136 - 9.14539i) q^{65} +(2.85760 - 0.765690i) q^{67} +1.69908i q^{68} +(13.6907 - 7.81204i) q^{70} +(7.00412 - 1.87675i) q^{71} +(0.559835 - 2.08933i) q^{73} +17.9448 q^{74} +(-0.100090 + 0.373541i) q^{76} +(2.35262 - 8.60528i) q^{77} +(-5.54357 + 9.60175i) q^{79} +(4.63273 + 17.2896i) q^{80} +(5.61151 + 9.71942i) q^{82} +(1.51210 - 1.51210i) q^{83} +(3.24940 + 12.1269i) q^{85} +(-5.17392 - 19.3093i) q^{86} +(6.89639 + 3.98163i) q^{88} +(2.23766 + 2.23766i) q^{89} +(-9.53168 + 0.383488i) q^{91} -1.81337 q^{92} +(1.88747 + 1.08973i) q^{94} +2.85750i q^{95} +(-3.23001 - 12.0545i) q^{97} +(2.97826 - 10.6805i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

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