LMFDB - Embedded newform 795.2.m.a.158.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [795,2,Mod(158,795)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("795.158"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(795, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 795 = 3 \cdot 5 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	795.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.34810696069$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label			158.1
Character	$\chi$	$=$	795.158
Dual form			795.2.m.a.317.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96968 + 1.96968i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.75926i q^{4} +(2.19865 + 0.407360i) q^{5} +4.82471 q^{6} +(2.79770 - 2.79770i) q^{7} +(7.40454 + 7.40454i) q^{8} +3.00000i q^{9} +(-5.13300 + 3.52826i) q^{10} +(-7.05363 + 7.05363i) q^{12} +(2.99303 + 2.99303i) q^{13} +11.0212i q^{14} +(-2.19387 - 3.19170i) q^{15} -17.6506 q^{16} +(-5.90903 - 5.90903i) q^{18} +(2.34609 - 12.6626i) q^{20} -6.85295 q^{21} +(5.77550 + 5.77550i) q^{23} -18.1373i q^{24} +(4.66812 + 1.79128i) q^{25} -11.7906 q^{26} +(3.67423 - 3.67423i) q^{27} +(-16.1127 - 16.1127i) q^{28} +(10.6078 + 1.96539i) q^{30} +(19.9569 - 19.9569i) q^{32} +(7.29084 - 5.01150i) q^{35} +17.2778 q^{36} +(-1.49035 + 1.49035i) q^{37} -7.33140i q^{39} +(13.2637 + 19.2963i) q^{40} -12.5768 q^{41} +(13.4981 - 13.4981i) q^{42} +(9.25416 + 9.25416i) q^{43} +(-1.22208 + 6.59595i) q^{45} -22.7517 q^{46} +(21.6175 + 21.6175i) q^{48} -8.65429i q^{49} +(-12.7229 + 5.66643i) q^{50} +(17.2377 - 17.2377i) q^{52} +(-5.14782 - 5.14782i) q^{53} +14.4741i q^{54} +41.4314 q^{56} +(-18.3818 + 12.6351i) q^{60} +(8.39311 + 8.39311i) q^{63} +43.3161i q^{64} +(5.36139 + 7.79987i) q^{65} -14.1470i q^{69} +(-4.48957 + 24.2316i) q^{70} +13.3708 q^{71} +(-22.2136 + 22.2136i) q^{72} -5.87103i q^{74} +(-3.52339 - 7.91112i) q^{75} +(14.4405 + 14.4405i) q^{78} +(-38.8074 - 7.19014i) q^{80} -9.00000 q^{81} +(24.7722 - 24.7722i) q^{82} +(-3.82177 - 3.82177i) q^{83} +39.4679i q^{84} -36.4554 q^{86} +(-10.5848 - 15.3990i) q^{90} +16.7472 q^{91} +(33.2626 - 33.2626i) q^{92} -48.8842 q^{96} +(-2.13252 + 2.13252i) q^{97} +(17.0462 + 17.0462i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 160 q^{16} + 240 q^{36} + 20 q^{40} + 60 q^{42} - 140 q^{52} - 180 q^{60} + 220 q^{70} - 360 q^{81} + 260 q^{82}+O(q^{100}) $ 40 * q - 160 * q^16 + 240 * q^36 + 20 * q^40 + 60 * q^42 - 140 * q^52 - 180 * q^60 + 220 * q^70 - 360 * q^81 + 260 * q^82

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/795\mathbb{Z}\right)^\times$.

$n$	$266$	$637$	$691$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.96968	+	1.96968i	−1.39277	+	1.39277i	−0.573724	+	0.819049i	$0.694502\pi$
$2$	−1.96968	+	1.96968i	−1.39277	+	1.39277i	−0.819049	+	0.573724i	$0.805498\pi$
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$4$		−	5.75926i		−	2.87963i
$5$	2.19865	+	0.407360i	0.983266	+	0.182177i
$5$	2.19865	+	0.407360i	0.983266	+	0.182177i
$6$	4.82471			1.96968
$7$	2.79770	−	2.79770i	1.05743	−	1.05743i	0.0591855	−	0.998247i	$-0.481150\pi$
$7$	2.79770	−	2.79770i	1.05743	−	1.05743i	0.998247	−	0.0591855i	$-0.0188504\pi$
$8$	7.40454	+	7.40454i	2.61790	+	2.61790i
$9$			3.00000i			1.00000i
$10$	−5.13300	+	3.52826i	−1.62320	+	1.11573i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	−7.05363	+	7.05363i	−2.03621	+	2.03621i
$13$	2.99303	+	2.99303i	0.830118	+	0.830118i	0.987533	−	0.157415i	$-0.0503159\pi$
$13$	2.99303	+	2.99303i	0.830118	+	0.830118i	−0.157415	+	0.987533i	$0.550316\pi$
$14$			11.0212i			2.94553i
$15$	−2.19387	−	3.19170i	−0.566455	−	0.824092i
$16$	−17.6506			−4.41265
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	−5.90903	−	5.90903i	−1.39277	−	1.39277i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	2.34609	−	12.6626i	0.524602	−	2.83144i
$21$	−6.85295			−1.49544
$22$		0			0
$23$	5.77550	+	5.77550i	1.20427	+	1.20427i	0.972854	+	0.231420i	$0.0743373\pi$
$23$	5.77550	+	5.77550i	1.20427	+	1.20427i	0.231420	+	0.972854i	$0.425663\pi$
$24$		−	18.1373i		−	3.70227i
$25$	4.66812	+	1.79128i	0.933623	+	0.358257i
$26$	−11.7906			−2.31233
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$	−16.1127	−	16.1127i	−3.04502	−	3.04502i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	10.6078	+	1.96539i	1.93672	+	0.358830i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	19.9569	−	19.9569i	3.52791	−	3.52791i
$33$		0			0
$34$		0			0
$35$	7.29084	−	5.01150i	1.23238	−	0.847097i
$36$	17.2778			2.87963
$37$	−1.49035	+	1.49035i	−0.245012	+	0.245012i	−0.818920	−	0.573908i	$-0.805427\pi$
$37$	−1.49035	+	1.49035i	−0.245012	+	0.245012i	0.573908	+	0.818920i	$0.305427\pi$
$38$		0			0
$39$		−	7.33140i		−	1.17396i
$40$	13.2637	+	19.2963i	2.09717	+	3.05101i
$41$	−12.5768			−1.96416			−0.982080	−	0.188465i	$-0.939649\pi$
$41$	−12.5768			−1.96416			−0.982080	+	0.188465i	$0.939649\pi$
$42$	13.4981	−	13.4981i	2.08280	−	2.08280i
$43$	9.25416	+	9.25416i	1.41125	+	1.41125i	0.751410	+	0.659835i	$0.229374\pi$
$43$	9.25416	+	9.25416i	1.41125	+	1.41125i	0.659835	+	0.751410i	$0.270626\pi$
$44$		0			0
$45$	−1.22208	+	6.59595i	−0.182177	+	0.983266i
$46$	−22.7517			−3.35456
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	21.6175	+	21.6175i	3.12021	+	3.12021i
$49$		−	8.65429i		−	1.23633i
$50$	−12.7229	+	5.66643i	−1.79929	+	0.801355i
$51$		0			0
$52$	17.2377	−	17.2377i	2.39043	−	2.39043i
$53$	−5.14782	−	5.14782i	−0.707107	−	0.707107i
$53$	−5.14782	−	5.14782i	−0.707107	−	0.707107i
$54$			14.4741i			1.96968i
$55$		0			0
$56$	41.4314			5.53650
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−18.3818	+	12.6351i	−2.37308	+	1.63118i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$	8.39311	+	8.39311i	1.05743	+	1.05743i
$64$			43.3161i			5.41452i
$65$	5.36139	+	7.79987i	0.664998	+	0.967455i
$66$		0			0
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$		0			0
$69$		−	14.1470i		−	1.70310i
$70$	−4.48957	+	24.2316i	−0.536607	+	2.89624i
$71$	13.3708			1.58682			0.793410	−	0.608688i	$-0.208304\pi$
$71$	13.3708			1.58682			0.793410	+	0.608688i	$0.208304\pi$
$72$	−22.2136	+	22.2136i	−2.61790	+	2.61790i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		−	5.87103i		−	0.682493i
$75$	−3.52339	−	7.91112i	−0.406846	−	0.913497i
$76$		0			0
$77$		0			0
$78$	14.4405	+	14.4405i	1.63507	+	1.63507i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−38.8074	−	7.19014i	−4.33880	−	0.803882i
$81$	−9.00000			−1.00000
$82$	24.7722	−	24.7722i	2.73563	−	2.73563i
$83$	−3.82177	−	3.82177i	−0.419494	−	0.419494i	0.465536	−	0.885029i	$-0.345862\pi$
$83$	−3.82177	−	3.82177i	−0.419494	−	0.419494i	−0.885029	+	0.465536i	$0.845862\pi$
$84$			39.4679i			4.30630i
$85$		0			0
$86$	−36.4554			−3.93109
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	−10.5848	−	15.3990i	−1.11573	−	1.62320i
$91$	16.7472			1.75559
$92$	33.2626	−	33.2626i	3.46787	−	3.46787i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−48.8842			−4.98922
$97$	−2.13252	+	2.13252i	−0.216524	+	0.216524i	−0.807032	−	0.590508i	$-0.798928\pi$
$97$	−2.13252	+	2.13252i	−0.216524	+	0.216524i	0.590508	+	0.807032i	$0.298928\pi$
$98$	17.0462	+	17.0462i	1.72192	+	1.72192i
$99$		0			0
$100$	10.3165	−	26.8849i	1.03165	−	2.68849i
$101$	0.497671			0.0495201			0.0247601	−	0.999693i	$-0.492118\pi$
$101$	0.497671			0.0495201			0.0247601	+	0.999693i	$0.492118\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$			44.3240i			4.34633i
$105$	−15.0672	−	2.79162i	−1.47041	−	0.272434i
$106$	20.2791			1.96968
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	−21.1609	−	21.1609i	−2.03621	−	2.03621i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	3.65060			0.346500
$112$	−49.3811	+	49.3811i	−4.66608	+	4.66608i
$113$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$113$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$114$		0			0
$115$	10.3456	+	15.0510i	0.964731	+	1.40351i
$116$		0			0
$117$	−8.97910	+	8.97910i	−0.830118	+	0.830118i
$118$		0			0
$119$		0			0
$120$	7.38842	−	39.8776i	0.674468	−	3.64031i
$121$	11.0000			1.00000
$122$		0			0
$123$	15.4033	+	15.4033i	1.38887	+	1.38887i
$124$		0			0
$125$	9.53385	+	5.84001i	0.852734	+	0.522346i
$126$	−33.0635			−2.94553
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−45.4050	−	45.4050i	−4.01328	−	4.01328i
$129$		−	22.6680i		−	1.99580i
$130$	−25.9234	−	4.80303i	−2.27364	−	0.421253i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	9.57509	−	6.58162i	0.824092	−	0.566455i
$136$		0			0
$137$	5.38651	−	5.38651i	0.460200	−	0.460200i	−0.438521	−	0.898721i	$-0.644497\pi$
$137$	5.38651	−	5.38651i	0.460200	−	0.460200i	0.898721	+	0.438521i	$0.144497\pi$
$138$	27.8651	+	27.8651i	2.37203	+	2.37203i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−28.8625	−	41.9899i	−2.43933	−	3.54879i
$141$		0			0
$142$	−26.3361	+	26.3361i	−2.21008	+	2.21008i
$143$		0			0
$144$		−	52.9517i		−	4.41265i
$145$		0			0
$146$		0			0
$147$	−10.5993	+	10.5993i	−0.874215	+	0.874215i
$148$	8.58333	+	8.58333i	0.705546	+	0.705546i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	22.5223	+	8.64241i	1.83894	+	0.705650i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−42.2235			−3.38058
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$			12.6095i			1.00000i
$160$	52.0078	−	35.7486i	4.11158	−	2.82617i
$161$	32.3163			2.54688
$162$	17.7271	−	17.7271i	1.39277	−	1.39277i
$163$	−10.6095	−	10.6095i	−0.831002	−	0.831002i	0.156652	−	0.987654i	$-0.449930\pi$
$163$	−10.6095	−	10.6095i	−0.831002	−	0.831002i	−0.987654	+	0.156652i	$0.949930\pi$
$164$			72.4329i			5.65606i
$165$		0			0
$166$	15.0553			1.16852
$167$	15.8868	−	15.8868i	1.22936	−	1.22936i	0.265151	−	0.964207i	$-0.414578\pi$
$167$	15.8868	−	15.8868i	1.22936	−	1.22936i	0.964207	−	0.265151i	$-0.0854219\pi$
$168$	−50.7429	−	50.7429i	−3.91490	−	3.91490i
$169$			4.91649i			0.378192i
$170$		0			0
$171$		0			0
$172$	53.2971	−	53.2971i	4.06387	−	4.06387i
$173$	9.24491	+	9.24491i	0.702878	+	0.702878i	0.965027	−	0.262149i	$-0.0844313\pi$
$173$	9.24491	+	9.24491i	0.702878	+	0.702878i	−0.262149	+	0.965027i	$0.584431\pi$
$174$		0			0
$175$	18.0715	−	8.04853i	1.36608	−	0.608411i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	21.5029i		−	1.60720i	−0.595168	−	0.803602i	$-0.702914\pi$
$179$		−	21.5029i		−	1.60720i	0.595168	−	0.803602i	$-0.297086\pi$
$180$	37.9878	+	7.03828i	2.83144	+	0.524602i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−32.9867	+	32.9867i	−2.44513	+	2.44513i
$183$		0			0
$184$			85.5298i			6.30534i
$185$	−3.88387	+	2.66965i	−0.285548	+	0.196277i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		−	20.5588i		−	1.49544i
$190$		0			0
$191$	16.3133			1.18039			0.590193	−	0.807262i	$-0.299052\pi$
$191$	16.3133			1.18039			0.590193	+	0.807262i	$0.299052\pi$
$192$	53.0512	−	53.0512i	3.82864	−	3.82864i
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$		−	8.40075i		−	0.603139i
$195$	2.98652	−	16.1192i	0.213869	−	1.15432i
$196$	−49.8423			−3.56017
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$		0			0
$199$		−	15.3216i		−	1.08612i	−0.839695	−	0.543058i	$-0.817266\pi$
$199$		−	15.3216i		−	1.08612i	0.839695	−	0.543058i	$-0.182734\pi$
$200$	21.3016	+	47.8289i	1.50625	+	3.38201i
$201$		0			0
$202$	−0.980252	+	0.980252i	−0.0689703	+	0.0689703i
$203$		0			0
$204$		0			0
$205$	−27.6519	−	5.12327i	−1.93129	−	0.357825i
$206$		0			0
$207$	−17.3265	+	17.3265i	−1.20427	+	1.20427i
$208$	−52.8288	−	52.8288i	−3.66302	−	3.66302i
$209$		0			0
$210$	35.1762	−	24.1790i	2.42739	−	1.66851i
$211$	−17.7329			−1.22078			−0.610392	−	0.792099i	$-0.708988\pi$
$211$	−17.7329			−1.22078			−0.610392	+	0.792099i	$0.708988\pi$
$212$	−29.6476	+	29.6476i	−2.03621	+	2.03621i
$213$	−16.3758	−	16.3758i	−1.12205	−	1.12205i
$214$		0			0
$215$	16.5769	+	24.1164i	1.13053	+	1.64473i
$216$	54.4120			3.70227
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−7.19051	+	7.19051i	−0.482596	+	0.482596i
$223$	−20.6095	−	20.6095i	−1.38012	−	1.38012i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$	−20.6095	−	20.6095i	−1.38012	−	1.38012i	−0.535720	−	0.844396i	$-0.679960\pi$
$224$		−	111.667i		−	7.46106i
$225$	−5.37385	+	14.0043i	−0.358257	+	0.933623i
$226$		0			0
$227$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$227$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$228$		0			0
$229$		−	11.2153i		−	0.741129i	−0.928807	−	0.370564i	$-0.879164\pi$
$229$		−	11.2153i		−	0.741129i	0.928807	−	0.370564i	$-0.120836\pi$
$230$	−50.0231	−	9.26815i	−3.29842	−	0.611123i
$231$		0			0
$232$		0			0
$233$	−4.90428	−	4.90428i	−0.321290	−	0.321290i	0.527972	−	0.849262i	$-0.322953\pi$
$233$	−4.90428	−	4.90428i	−0.321290	−	0.321290i	−0.849262	+	0.527972i	$0.822953\pi$
$234$		−	35.3719i		−	2.31233i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	13.2428i		−	0.856605i	−0.903635	−	0.428302i	$-0.859112\pi$
$239$		−	13.2428i		−	0.856605i	0.903635	−	0.428302i	$-0.140888\pi$
$240$	38.7231	+	56.3353i	2.49957	+	3.63643i
$241$	−10.3812			−0.668712			−0.334356	−	0.942447i	$-0.608519\pi$
$241$	−10.3812			−0.668712			−0.334356	+	0.942447i	$0.608519\pi$
$242$	−21.6665	+	21.6665i	−1.39277	+	1.39277i
$243$	11.0227	+	11.0227i	0.707107	+	0.707107i
$244$		0			0
$245$	3.52541	−	19.0277i	0.225230	−	1.21564i
$246$	−60.6792			−3.86876
$247$		0			0
$248$		0			0
$249$			9.36138i			0.593254i
$250$	−30.2815	+	7.27569i	−1.91517	+	0.460155i
$251$	−30.0191			−1.89479			−0.947396	−	0.320064i	$-0.896295\pi$
$251$	−30.0191			−1.89479			−0.947396	+	0.320064i	$0.896295\pi$
$252$	48.3381	−	48.3381i	3.04502	−	3.04502i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	92.2344			5.76465
$257$	−20.7959	+	20.7959i	−1.29721	+	1.29721i	−0.366987	+	0.930226i	$0.619611\pi$
$257$	−20.7959	+	20.7959i	−1.29721	+	1.29721i	−0.930226	+	0.366987i	$0.880389\pi$
$258$	44.6486	+	44.6486i	2.77970	+	2.77970i
$259$			8.33913i			0.518168i
$260$	44.9215	−	30.8776i	2.78591	−	1.91495i
$261$		0			0
$262$		0			0
$263$	22.2383	+	22.2383i	1.37127	+	1.37127i	0.858559	+	0.512714i	$0.171360\pi$
$263$	22.2383	+	22.2383i	1.37127	+	1.37127i	0.512714	+	0.858559i	$0.328640\pi$
$264$		0			0
$265$	−9.22123	−	13.4153i	−0.566455	−	0.824092i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	−5.89618	+	31.8235i	−0.358830	+	1.93672i
$271$	−1.84286			−0.111946			−0.0559729	−	0.998432i	$-0.517826\pi$
$271$	−1.84286			−0.111946			−0.0559729	+	0.998432i	$0.517826\pi$
$272$		0			0
$273$	−20.5111	−	20.5111i	−1.24139	−	1.24139i
$274$			21.2194i			1.28191i
$275$		0			0
$276$	−81.4764			−4.90430
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$		0			0
$279$		0			0
$280$	91.0931	+	16.8775i	5.44385	+	1.00862i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$283$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$284$		−	77.0058i		−	4.56946i
$285$		0			0
$286$		0			0
$287$	−35.1860	+	35.1860i	−2.07697	+	2.07697i
$288$	59.8707	+	59.8707i	3.52791	+	3.52791i
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$	5.22358			0.306212
$292$		0			0
$293$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$293$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$294$		−	41.7544i		−	2.43517i
$295$		0			0
$296$	−22.0707			−1.28284
$297$		0			0
$298$		0			0
$299$			34.5725i			1.99938i
$300$	−45.5622	+	20.2921i	−2.63053	+	1.17157i
$301$	51.7808			2.98459
$302$		0			0
$303$	−0.609520	−	0.609520i	−0.0350160	−	0.0350160i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−20.9418	+	20.9418i	−1.19521	+	1.19521i	−0.219626	+	0.975584i	$0.570484\pi$
$307$	−20.9418	+	20.9418i	−1.19521	+	1.19521i	−0.975584	+	0.219626i	$0.929516\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	54.2856	−	54.2856i	3.07332	−	3.07332i
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$		0			0
$315$	15.0345	+	21.8725i	0.847097	+	1.23238i
$316$		0			0
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$	−24.8367	−	24.8367i	−1.39277	−	1.39277i
$319$		0			0
$320$	−17.6453	+	95.2370i	−0.986400	+	5.32391i
$321$		0			0
$322$	−63.6526	+	63.6526i	−3.54722	+	3.54722i
$323$		0			0
$324$			51.8334i			2.87963i
$325$	8.61045	+	19.3332i	0.477622	+	1.07241i
$326$	41.7947			2.31479
$327$		0			0
$328$	−93.1251	−	93.1251i	−5.14197	−	5.14197i
$329$		0			0
$330$		0			0
$331$	−20.8647			−1.14683			−0.573415	−	0.819265i	$-0.694382\pi$
$331$	−20.8647			−1.14683			−0.573415	+	0.819265i	$0.694382\pi$
$332$	−22.0106	+	22.0106i	−1.20799	+	1.20799i
$333$	−4.47106	−	4.47106i	−0.245012	−	0.245012i
$334$			62.5838i			3.42443i
$335$		0			0
$336$	120.958			6.59883
$337$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$337$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$338$	−9.68390	−	9.68390i	−0.526735	−	0.526735i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−4.62821	−	4.62821i	−0.249900	−	0.249900i
$344$			137.045i			7.38900i
$345$	5.76293	−	31.1043i	0.310266	−	1.67460i
$346$	−36.4190			−1.95790
$347$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$347$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−19.7420	+	51.4480i	−1.05525	+	2.75001i
$351$	21.9942			1.17396
$352$		0			0
$353$	−10.2956	−	10.2956i	−0.547981	−	0.547981i	0.377875	−	0.925856i	$-0.376655\pi$
$353$	−10.2956	−	10.2956i	−0.547981	−	0.547981i	−0.925856	+	0.377875i	$0.876655\pi$
$354$		0			0
$355$	29.3977	+	5.44672i	1.56027	+	0.289082i
$356$		0			0
$357$		0			0
$358$	42.3538	+	42.3538i	2.23847	+	2.23847i
$359$		−	37.7377i		−	1.99172i	−0.0909056	−	0.995860i	$-0.528976\pi$
$359$		−	37.7377i		−	1.99172i	0.0909056	−	0.995860i	$-0.471024\pi$
$360$	−57.8889	+	39.7910i	−3.05101	+	2.09717i
$361$	−19.0000			−1.00000
$362$		0			0
$363$	−13.4722	−	13.4722i	−0.707107	−	0.707107i
$364$		−	96.4517i		−	5.05544i
$365$		0			0
$366$		0			0
$367$	18.3840	−	18.3840i	0.959638	−	0.959638i	−0.0395781	−	0.999216i	$-0.512601\pi$
$367$	18.3840	−	18.3840i	0.959638	−	0.959638i	0.999216	+	0.0395781i	$0.0126014\pi$
$368$	−101.941	−	101.941i	−5.31404	−	5.31404i
$369$		−	37.7303i		−	1.96416i
$370$	2.39162	−	12.9083i	0.124335	−	0.671072i
$371$	−28.8041			−1.49544
$372$		0			0
$373$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$373$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$374$		0			0
$375$	−4.52402	−	18.8291i	−0.233619	−	0.972328i
$376$		0			0
$377$		0			0
$378$	40.4943	+	40.4943i	2.08280	+	2.08280i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$	−32.1319	+	32.1319i	−1.64401	+	1.64401i
$383$	11.8346	+	11.8346i	0.604722	+	0.604722i	0.941562	−	0.336840i	$-0.109358\pi$
$383$	11.8346	+	11.8346i	0.604722	+	0.604722i	−0.336840	+	0.941562i	$0.609358\pi$
$384$			111.219i			5.67563i
$385$		0			0
$386$		0			0
$387$	−27.7625	+	27.7625i	−1.41125	+	1.41125i
$388$	12.2817	+	12.2817i	0.623511	+	0.623511i
$389$		−	5.27555i		−	0.267481i	−0.991016	−	0.133741i	$-0.957301\pi$
$389$		−	5.27555i		−	0.267481i	0.991016	−	0.133741i	$-0.0426989\pi$
$390$	25.8671	+	37.6321i	1.30983	+	1.90557i
$391$		0			0
$392$	64.0810	−	64.0810i	3.23658	−	3.23658i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	30.1785	+	30.1785i	1.51271	+	1.51271i
$399$		0			0
$400$	−82.3950	−	31.6172i	−4.11975	−	1.58086i
$401$	−36.6493			−1.83018			−0.915089	−	0.403251i	$-0.867880\pi$
$401$	−36.6493			−1.83018			−0.915089	+	0.403251i	$0.867880\pi$
$402$		0			0
$403$		0			0
$404$		−	2.86622i		−	0.142600i
$405$	−19.7878	−	3.66624i	−0.983266	−	0.182177i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			38.6752i			1.91237i	0.292767	+	0.956184i	$0.405424\pi$
$409$			38.6752i			1.91237i	−0.292767	+	0.956184i	$0.594576\pi$
$410$	64.5565	−	44.3741i	3.18822	−	2.19148i
$411$	−13.1942			−0.650821
$412$		0			0
$413$		0			0
$414$		−	68.2552i		−	3.35456i
$415$	−6.84589	−	9.95957i	−0.336052	−	0.488896i
$416$	119.463			5.85717
$417$		0			0
$418$		0			0
$419$			36.6416i			1.79006i	0.446008	+	0.895029i	$0.352845\pi$
$419$			36.6416i			1.79006i	−0.446008	+	0.895029i	$0.647155\pi$
$420$	−16.0776	+	86.7761i	−0.784509	+	4.23424i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	34.9281	−	34.9281i	1.70028	−	1.70028i
$423$		0			0
$424$		−	76.2344i		−	3.70227i
$425$		0			0
$426$	64.5101			3.12552
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−80.1527	−	14.8505i	−3.86530	−	0.716153i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−64.8524	+	64.8524i	−3.12021	+	3.12021i
$433$	−29.3163	−	29.3163i	−1.40885	−	1.40885i	−0.765946	−	0.642905i	$-0.777729\pi$
$433$	−29.3163	−	29.3163i	−1.40885	−	1.40885i	−0.642905	−	0.765946i	$-0.722271\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$			37.0317i			1.76743i	0.468027	+	0.883714i	$0.344965\pi$
$439$			37.0317i			1.76743i	−0.468027	+	0.883714i	$0.655035\pi$
$440$		0			0
$441$	25.9629			1.23633
$442$		0			0
$443$	29.7475	+	29.7475i	1.41335	+	1.41335i	0.731410	+	0.681938i	$0.238863\pi$
$443$	29.7475	+	29.7475i	1.41335	+	1.41335i	0.681938	+	0.731410i	$0.261137\pi$
$444$		−	21.0248i		−	0.997792i
$445$		0			0
$446$	81.1882			3.84437
$447$		0			0
$448$	121.186	+	121.186i	5.72549	+	5.72549i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−16.9993	−	38.1688i	−0.801355	−	1.79929i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	36.8213	+	6.82215i	1.72621	+	0.319827i
$456$		0			0
$457$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$457$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$458$	22.0906	+	22.0906i	1.03222	+	1.03222i
$459$		0			0
$460$	86.6826	−	59.5829i	4.04160	−	2.77807i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$		0			0
$465$		0			0
$466$	19.3197			0.894968
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$	51.7130	+	51.7130i	2.39043	+	2.39043i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	15.4434	−	15.4434i	0.707107	−	0.707107i
$478$	26.0840	+	26.0840i	1.19306	+	1.19306i
$479$		−	43.7250i		−	1.99785i	−0.0463783	−	0.998924i	$-0.514768\pi$
$479$		−	43.7250i		−	1.99785i	0.0463783	−	0.998924i	$-0.485232\pi$
$480$	−107.479	−	19.9135i	−4.90573	−	0.908921i
$481$	−8.92135			−0.406778
$482$	20.4476	−	20.4476i	0.931364	−	0.931364i
$483$	−39.5792	−	39.5792i	−1.80091	−	1.80091i
$484$		−	63.3519i		−	2.87963i
$485$	−5.55736	+	3.81996i	−0.252347	+	0.173455i
$486$	−43.4224			−1.96968
$487$	13.5192	−	13.5192i	0.612613	−	0.612613i	−0.331013	−	0.943626i	$-0.607390\pi$
$487$	13.5192	−	13.5192i	0.612613	−	0.612613i	0.943626	+	0.331013i	$0.107390\pi$
$488$		0			0
$489$			25.9879i			1.17521i
$490$	30.5346	+	44.4225i	1.37941	+	2.00680i
$491$	−21.9788			−0.991888			−0.495944	−	0.868354i	$-0.665178\pi$
$491$	−21.9788			−0.991888			−0.495944	+	0.868354i	$0.665178\pi$
$492$	88.7118	−	88.7118i	3.99944	−	3.99944i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	37.4075	−	37.4075i	1.67795	−	1.67795i
$498$	−18.4389	−	18.4389i	−0.826267	−	0.826267i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	33.6341	−	54.9080i	1.50416	−	2.45556i
$501$	−38.9146			−1.73857
$502$	59.1280	−	59.1280i	2.63901	−	2.63901i
$503$	2.02153	+	2.02153i	0.0901353	+	0.0901353i	0.750737	−	0.660601i	$-0.229699\pi$
$503$	2.02153	+	2.02153i	0.0901353	+	0.0901353i	−0.660601	+	0.750737i	$0.729699\pi$
$504$			124.294i			5.53650i
$505$	1.09420	+	0.202731i	0.0486915	+	0.00902142i
$506$		0			0
$507$	6.02145	−	6.02145i	0.267422	−	0.267422i
$508$		0			0
$509$			7.33912i			0.325301i	0.986684	+	0.162650i	$0.0520043\pi$
$509$			7.33912i			0.325301i	−0.986684	+	0.162650i	$0.947996\pi$
$510$		0			0
$511$		0			0
$512$	−90.8619	+	90.8619i	−4.01557	+	4.01557i
$513$		0			0
$514$		−	81.9225i		−	3.61345i
$515$		0			0
$516$	−130.551			−5.74718
$517$		0			0
$518$	−16.4254	−	16.4254i	−0.721691	−	0.721691i
$519$		−	22.6453i		−	0.994019i
$520$	−18.0558	+	97.4530i	−0.791801	+	4.27360i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−9.44191	−	9.44191i	−0.412866	−	0.412866i	0.469870	−	0.882736i	$-0.344301\pi$
$523$	−9.44191	−	9.44191i	−0.412866	−	0.412866i	−0.882736	+	0.469870i	$0.844301\pi$
$524$		0			0
$525$	−31.9903	−	12.2756i	−1.39617	−	0.535750i
$526$	−87.6047			−3.81974
$527$		0			0
$528$		0			0
$529$			43.7127i			1.90055i
$530$	44.5866	+	8.26088i	1.93672	+	0.358830i
$531$		0			0
$532$		0			0
$533$	−37.6427	−	37.6427i	−1.63048	−	1.63048i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−26.3356	+	26.3356i	−1.13646	+	1.13646i
$538$		0			0
$539$		0			0
$540$	−37.9053	−	55.1455i	−1.63118	−	2.37308i
$541$	32.2974			1.38857			0.694287	−	0.719698i	$-0.255720\pi$
$541$	32.2974			1.38857			0.694287	+	0.719698i	$0.255720\pi$
$542$	3.62984	−	3.62984i	0.155915	−	0.155915i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	80.8005			3.45794
$547$	32.9139	−	32.9139i	1.40730	−	1.40730i	0.633801	−	0.773496i	$-0.281494\pi$
$547$	32.9139	−	32.9139i	1.40730	−	1.40730i	0.773496	−	0.633801i	$-0.218506\pi$
$548$	−31.0223	−	31.0223i	−1.32521	−	1.32521i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	104.752	−	104.752i	4.45855	−	4.45855i
$553$		0			0
$554$		0			0
$555$	8.02640	+	1.48711i	0.340702	+	0.0631243i
$556$		0			0
$557$	−13.8571	+	13.8571i	−0.587143	+	0.587143i	−0.936857	−	0.349714i	$-0.886279\pi$
$557$	−13.8571	+	13.8571i	−0.587143	+	0.587143i	0.349714	+	0.936857i	$0.386279\pi$
$558$		0			0
$559$			55.3960i			2.34300i
$560$	−128.688	+	88.4558i	−5.43804	+	3.73794i
$561$		0			0
$562$		0			0
$563$	5.85719	+	5.85719i	0.246851	+	0.246851i	0.819677	−	0.572826i	$-0.194153\pi$
$563$	5.85719	+	5.85719i	0.246851	+	0.246851i	−0.572826	+	0.819677i	$0.694153\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−25.1793	+	25.1793i	−1.05743	+	1.05743i
$568$	99.0044	+	99.0044i	4.15413	+	4.15413i
$569$		−	14.5208i		−	0.608742i	−0.952554	−	0.304371i	$-0.901554\pi$
$569$		−	14.5208i		−	0.608742i	0.952554	−	0.304371i	$-0.0984463\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−19.9796	−	19.9796i	−0.834659	−	0.834659i
$574$		−	138.610i		−	5.78548i
$575$	16.6151	+	37.3062i	0.692899	+	1.55578i
$576$	−129.948			−5.41452
$577$	−25.5750	+	25.5750i	−1.06470	+	1.06470i	−0.0669435	+	0.997757i	$0.521325\pi$
$577$	−25.5750	+	25.5750i	−1.06470	+	1.06470i	−0.997757	+	0.0669435i	$0.978675\pi$
$578$	33.4845	+	33.4845i	1.39277	+	1.39277i
$579$		0			0
$580$		0			0
$581$	−21.3844			−0.887173
$582$	−10.2888	+	10.2888i	−0.426483	+	0.426483i
$583$		0			0
$584$		0			0
$585$	−23.3996	+	16.0842i	−0.967455	+	0.664998i
$586$		0			0
$587$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$587$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$588$	61.0441	+	61.0441i	2.51742	+	2.51742i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	26.3056	−	26.3056i	1.08115	−	1.08115i
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−18.7650	+	18.7650i	−0.768000	+	0.768000i
$598$	−68.0967	−	68.0967i	−2.78468	−	2.78468i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	32.4891	−	84.6672i	1.32636	−	3.45652i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−101.991	+	101.991i	−4.15686	+	4.15686i
$603$		0			0
$604$		0			0
$605$	24.1851	+	4.48096i	0.983266	+	0.182177i
$606$	2.40112			0.0975387
$607$	23.4974	−	23.4974i	0.953731	−	0.953731i	−0.0452446	−	0.998976i	$-0.514407\pi$
$607$	23.4974	−	23.4974i	0.953731	−	0.953731i	0.998976	+	0.0452446i	$0.0144067\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$		−	82.4971i		−	3.32931i
$615$	27.5918	+	40.1412i	1.11261	+	1.61865i
$616$		0			0
$617$	9.79654	−	9.79654i	0.394394	−	0.394394i	−0.481856	−	0.876250i	$-0.660037\pi$
$617$	9.79654	−	9.79654i	0.394394	−	0.394394i	0.876250	+	0.481856i	$0.160037\pi$
$618$		0			0
$619$			46.9540i			1.88724i	0.331029	+	0.943621i	$0.392604\pi$
$619$			46.9540i			1.88724i	−0.331029	+	0.943621i	$0.607396\pi$
$620$		0			0
$621$	42.4411			1.70310
$622$		0			0
$623$		0			0
$624$			129.404i			5.18029i
$625$	18.5826	+	16.7238i	0.743304	+	0.668953i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−72.6949	−	13.4687i	−2.89624	−	0.536607i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	21.7183	+	21.7183i	0.863225	+	0.863225i
$634$		0			0
$635$		0			0
$636$	72.6215			2.87963
$637$	25.9026	−	25.9026i	1.02630	−	1.02630i
$638$		0			0
$639$			40.1123i			1.58682i
$640$	−81.3336	−	118.326i	−3.21499	−	4.67724i
$641$	−23.9972			−0.947833			−0.473917	−	0.880570i	$-0.657160\pi$
$641$	−23.9972			−0.947833			−0.473917	+	0.880570i	$0.657160\pi$
$642$		0			0
$643$	9.39048	+	9.39048i	0.370324	+	0.370324i	0.867595	−	0.497271i	$-0.165665\pi$
$643$	9.39048	+	9.39048i	0.370324	+	0.370324i	−0.497271	+	0.867595i	$0.665665\pi$
$644$		−	186.118i		−	7.33407i
$645$	9.23402	−	49.8389i	0.363589	−	1.96240i
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−66.6408	−	66.6408i	−2.61790	−	2.61790i
$649$		0			0
$650$	−55.0400	−	21.1203i	−2.15885	−	0.828408i
$651$		0			0
$652$	−61.1030	+	61.1030i	−2.39298	+	2.39298i
$653$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$653$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$654$		0			0
$655$		0			0
$656$	221.987			8.66714
$657$		0			0
$658$		0			0
$659$		−	51.3044i		−	1.99854i	−0.0382670	−	0.999268i	$-0.512184\pi$
$659$		−	51.3044i		−	1.99854i	0.0382670	−	0.999268i	$-0.487816\pi$
$660$		0			0
$661$	50.4381			1.96181			0.980907	−	0.194477i	$-0.0623011\pi$
$661$	50.4381			1.96181			0.980907	+	0.194477i	$0.0623011\pi$
$662$	41.0968	−	41.0968i	1.59727	−	1.59727i
$663$		0			0
$664$		−	56.5969i		−	2.19638i
$665$		0			0
$666$	17.6131			0.682493
$667$		0			0
$668$	−91.4963	−	91.4963i	−3.54010	−	3.54010i
$669$			50.4828i			1.95178i
$670$		0			0
$671$		0			0
$672$	−136.763	+	136.763i	−5.27577	+	5.27577i
$673$	34.8841	+	34.8841i	1.34468	+	1.34468i	0.891332	+	0.453352i	$0.149772\pi$
$673$	34.8841	+	34.8841i	1.34468	+	1.34468i	0.453352	+	0.891332i	$0.350228\pi$
$674$		0			0
$675$	23.7333	−	10.5702i	0.913497	−	0.406846i
$676$	28.3154			1.08905
$677$	−36.6779	+	36.6779i	−1.40965	+	1.40965i	−0.648038	+	0.761608i	$0.724410\pi$
$677$	−36.6779	+	36.6779i	−1.40965	+	1.40965i	−0.761608	+	0.648038i	$0.775590\pi$
$678$		0			0
$679$			11.9323i			0.457920i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$683$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$684$		0			0
$685$	14.0373	−	9.64879i	0.536337	−	0.368661i
$686$	18.2322			0.696108
$687$	−13.7359	+	13.7359i	−0.524057	+	0.524057i
$688$	−163.341	−	163.341i	−6.22733	−	6.22733i
$689$		−	30.8152i		−	1.17396i
$690$	49.9144	+	72.6166i	1.90021	+	2.76447i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$	53.2439	−	53.2439i	2.02403	−	2.02403i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$			12.0130i			0.454373i
$700$	−46.3536	−	104.078i	−1.75200	−	3.93379i
$701$	−49.4095			−1.86617			−0.933086	−	0.359654i	$-0.882895\pi$
$701$	−49.4095			−1.86617			−0.933086	+	0.359654i	$0.882895\pi$
$702$	−43.3215	+	43.3215i	−1.63507	+	1.63507i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	40.5582			1.52643
$707$	1.39234	−	1.39234i	0.0523642	−	0.0523642i
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	−68.6322	+	47.1756i	−2.57572	+	1.77047i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−123.841			−4.62815
$717$	−16.2190	+	16.2190i	−0.605711	+	0.605711i
$718$	74.3311	+	74.3311i	2.77401	+	2.77401i
$719$			11.2521i			0.419633i	0.977741	+	0.209816i	$0.0672866\pi$
$719$			11.2521i			0.419633i	−0.977741	+	0.209816i	$0.932713\pi$
$720$	21.5704	−	116.422i	0.803882	−	4.33880i
$721$		0			0
$722$	37.4239	−	37.4239i	1.39277	−	1.39277i
$723$	12.7143	+	12.7143i	0.472851	+	0.472851i
$724$		0			0
$725$		0			0
$726$	53.0718			1.96968
$727$	2.98358	−	2.98358i	0.110655	−	0.110655i	−0.649611	−	0.760266i	$-0.725068\pi$
$727$	2.98358	−	2.98358i	0.110655	−	0.110655i	0.760266	+	0.649611i	$0.225068\pi$
$728$	124.006	+	124.006i	4.59595	+	4.59595i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	8.78876	+	8.78876i	0.324620	+	0.324620i	0.850536	−	0.525916i	$-0.176277\pi$
$733$	8.78876	+	8.78876i	0.324620	+	0.324620i	−0.525916	+	0.850536i	$0.676277\pi$
$734$			72.4212i			2.67312i
$735$	−27.6219	+	18.9864i	−1.01885	+	0.700324i
$736$	230.522			8.49715
$737$		0			0
$738$	74.3165	+	74.3165i	2.73563	+	2.73563i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	15.3752	+	22.3682i	0.565205	+	0.822273i
$741$		0			0
$742$	56.7348	−	56.7348i	2.08280	−	2.08280i
$743$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$743$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	11.4653	−	11.4653i	0.419494	−	0.419494i
$748$		0			0
$749$		0			0
$750$	45.9980	+	28.1763i	1.67961	+	1.02885i
$751$	−52.5818			−1.91874			−0.959369	−	0.282153i	$-0.908951\pi$
$751$	−52.5818			−1.91874			−0.959369	+	0.282153i	$0.908951\pi$
$752$		0			0
$753$	36.7658	+	36.7658i	1.33982	+	1.33982i
$754$		0			0
$755$		0			0
$756$	−118.404			−4.30630
$757$	−36.2190	+	36.2190i	−1.31640	+	1.31640i	−0.399802	+	0.916602i	$0.630921\pi$
$757$	−36.2190	+	36.2190i	−1.31640	+	1.31640i	−0.916602	+	0.399802i	$0.869079\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	39.4794			1.43113			0.715564	−	0.698547i	$-0.246170\pi$
$761$	39.4794			1.43113			0.715564	+	0.698547i	$0.246170\pi$
$762$		0			0
$763$		0			0
$764$		−	93.9523i		−	3.39908i
$765$		0			0
$766$	−46.6209			−1.68448
$767$		0			0
$768$	−112.964	−	112.964i	−4.07622	−	4.07622i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	50.9394			1.83454
$772$		0			0
$773$	−17.6753	−	17.6753i	−0.635735	−	0.635735i	0.313766	−	0.949500i	$-0.398409\pi$
$773$	−17.6753	−	17.6753i	−0.635735	−	0.635735i	−0.949500	+	0.313766i	$0.898409\pi$
$774$		−	109.366i		−	3.93109i
$775$		0			0
$776$	−31.5806			−1.13368
$777$	10.2133	−	10.2133i	0.366400	−	0.366400i
$778$	10.3911	+	10.3911i	0.372540	+	0.372540i
$779$		0			0
$780$	−92.8346	−	17.2002i	−3.32401	−	0.615864i
$781$		0			0
$782$		0			0
$783$		0			0
$784$			152.753i			5.45547i
$785$		0			0
$786$		0			0
$787$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$787$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$788$		0			0
$789$		−	54.4725i		−	1.93927i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−5.13661	+	27.7239i	−0.182177	+	0.983266i
$796$	−88.2409			−3.12762
$797$	−29.5970	+	29.5970i	−1.04838	+	1.04838i	−0.0496115	+	0.998769i	$0.515798\pi$
$797$	−29.5970	+	29.5970i	−1.04838	+	1.04838i	−0.998769	+	0.0496115i	$0.984202\pi$
$798$		0			0
$799$		0			0
$800$	128.910	−	57.4126i	4.55764	−	2.02984i
$801$		0			0
$802$	72.1873	−	72.1873i	2.54902	−	2.54902i
$803$		0			0
$804$		0			0
$805$	71.0521	+	13.1643i	2.50426	+	0.463982i
$806$		0			0
$807$		0			0
$808$	3.68502	+	3.68502i	0.129639	+	0.129639i
$809$			25.7736i			0.906150i	0.891472	+	0.453075i	$0.149673\pi$
$809$			25.7736i			0.906150i	−0.891472	+	0.453075i	$0.850327\pi$
$810$	46.1970	−	31.7544i	1.62320	−	1.11573i
$811$	−54.7052			−1.92096			−0.960479	−	0.278352i	$-0.910212\pi$
$811$	−54.7052			−1.92096			−0.960479	+	0.278352i	$0.910212\pi$
$812$		0			0
$813$	2.25703	+	2.25703i	0.0791576	+	0.0791576i
$814$		0			0
$815$	−19.0047	−	27.6485i	−0.665706	−	0.968485i
$816$		0			0
$817$		0			0
$818$	−76.1778	−	76.1778i	−2.66349	−	2.66349i
$819$			50.2417i			1.75559i
$820$	−29.5062	+	159.254i	−1.03040	+	5.56141i
$821$	49.4875			1.72712			0.863562	−	0.504242i	$-0.168228\pi$
$821$	49.4875			1.72712			0.863562	+	0.504242i	$0.168228\pi$
$822$	25.9883	−	25.9883i	0.906446	−	0.906446i
$823$	−38.9000	−	38.9000i	−1.35597	−	1.35597i	−0.878827	−	0.477141i	$-0.841673\pi$
$823$	−38.9000	−	38.9000i	−1.35597	−	1.35597i	−0.477141	−	0.878827i	$-0.658327\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−40.6549	+	40.6549i	−1.41371	+	1.41371i	−0.687956	+	0.725752i	$0.741492\pi$
$827$	−40.6549	+	40.6549i	−1.41371	+	1.41371i	−0.725752	+	0.687956i	$0.758508\pi$
$828$	99.7878	+	99.7878i	3.46787	+	3.46787i
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$	33.1013	+	6.13293i	1.14896	+	0.212877i
$831$		0			0
$832$	−129.647	+	129.647i	−4.49469	+	4.49469i
$833$		0			0
$834$		0			0
$835$	41.4012	−	28.4579i	1.43275	−	0.984825i
$836$		0			0
$837$		0			0
$838$	−72.1721	−	72.1721i	−2.49314	−	2.49314i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−90.8952	−	132.236i	−3.13618	−	4.56259i
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$			102.129i			3.51541i
$845$	−2.00278	+	10.8096i	−0.0688978	+	0.371863i
$846$		0			0
$847$	30.7747	−	30.7747i	1.05743	−	1.05743i
$848$	90.8619	+	90.8619i	3.12021	+	3.12021i
$849$		0			0
$850$		0			0
$851$	−17.2151			−0.590124
$852$	−94.3125	+	94.3125i	−3.23109	+	3.23109i
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$		−	56.3306i		−	1.92197i	−0.276593	−	0.960987i	$-0.589205\pi$
$859$		−	56.3306i		−	1.92197i	0.276593	−	0.960987i	$-0.410795\pi$
$860$	138.893	−	95.4705i	4.73620	−	3.25552i
$861$	86.1878			2.93727
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$		−	146.653i		−	4.98922i
$865$	16.5603	+	24.0923i	0.563068	+	0.819164i
$866$	115.487			3.92442
$867$	−20.8207	+	20.8207i	−0.707107	+	0.707107i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−6.39755	−	6.39755i	−0.216524	−	0.216524i
$874$		0			0
$875$	43.0115	−	10.3343i	1.45405	−	0.349363i
$876$		0			0
$877$	−12.1108	+	12.1108i	−0.408951	+	0.408951i	−0.881373	−	0.472422i	$-0.843380\pi$
$877$	−12.1108	+	12.1108i	−0.408951	+	0.408951i	0.472422	+	0.881373i	$0.343380\pi$
$878$	−72.9406	−	72.9406i	−2.46163	−	2.46163i
$879$		0			0
$880$		0			0
$881$	−53.1853			−1.79186			−0.895930	−	0.444196i	$-0.853490\pi$
$881$	−53.1853			−1.79186			−0.895930	+	0.444196i	$0.853490\pi$
$882$	−51.1385	+	51.1385i	−1.72192	+	1.72192i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$		0			0
$886$	−117.186			−3.93694
$887$	−20.5913	+	20.5913i	−0.691387	+	0.691387i	−0.962537	−	0.271150i	$-0.912596\pi$
$887$	−20.5913	+	20.5913i	−0.691387	+	0.691387i	0.271150	+	0.962537i	$0.412596\pi$
$888$	27.0310	+	27.0310i	0.907102	+	0.907102i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−118.696	+	118.696i	−3.97422	+	3.97422i
$893$		0			0
$894$		0			0
$895$	8.75942	−	47.2774i	0.292795	−	1.58031i
$896$	−254.060			−8.48754
$897$	42.3425	−	42.3425i	1.41377	−	1.41377i
$898$		0			0
$899$		0			0
$900$	80.6547	+	30.9494i	2.68849	+	1.03165i
$901$		0			0
$902$		0			0
$903$	−63.4182	−	63.4182i	−2.11043	−	2.11043i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−21.3647	+	21.3647i	−0.709404	+	0.709404i	−0.966410	−	0.257006i	$-0.917264\pi$
$907$	−21.3647	+	21.3647i	−0.709404	+	0.709404i	0.257006	+	0.966410i	$0.417264\pi$
$908$		0			0
$909$			1.49301i			0.0495201i
$910$	−85.9635	+	59.0887i	−2.84966	+	1.95877i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−64.5919			−2.13418
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−34.8414	+	188.050i	−1.14869	+	6.19982i
$921$	51.2967			1.69028
$922$		0			0
$923$	40.0192	+	40.0192i	1.31725	+	1.31725i
$924$		0			0
$925$	−9.62678	+	4.28750i	−0.316527	+	0.140972i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$	−28.2450	+	28.2450i	−0.925197	+	0.925197i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−132.972			−4.34633
$937$	23.3549	−	23.3549i	0.762971	−	0.762971i	−0.213888	−	0.976858i	$-0.568613\pi$
$937$	23.3549	−	23.3549i	0.762971	−	0.762971i	0.976858	+	0.213888i	$0.0686126\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$	−72.6370	−	72.6370i	−2.36539	−	2.36539i
$944$		0			0
$945$	8.37485	−	45.2017i	0.272434	−	1.47041i
$946$		0			0
$947$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$947$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$953$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$954$			60.8372i			1.96968i
$955$	35.8671	+	6.64536i	1.16063	+	0.215039i
$956$	−76.2687			−2.46671
$957$		0			0
$958$	86.1242	+	86.1242i	2.78255	+	2.78255i
$959$		−	30.1397i		−	0.973262i
$960$	138.252	−	95.0301i	4.46206	−	3.06708i
$961$	31.0000			1.00000
$962$	17.5722	−	17.5722i	0.566550	−	0.566550i
$963$		0			0
$964$			59.7881i			1.92565i
$965$		0			0
$966$	155.916			5.01653
$967$	43.2293	−	43.2293i	1.39016	−	1.39016i	0.565217	−	0.824942i	$-0.308793\pi$
$967$	43.2293	−	43.2293i	1.39016	−	1.39016i	0.824942	−	0.565217i	$-0.191207\pi$
$968$	81.4499	+	81.4499i	2.61790	+	2.61790i
$969$		0			0
$970$	3.42213	−	18.4703i	0.109878	−	0.593046i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	63.4826	−	63.4826i	2.03621	−	2.03621i
$973$		0			0
$974$			53.2569i			1.70646i
$975$	13.1326	−	34.2238i	0.420580	−	1.09604i
$976$		0			0
$977$	43.8979	−	43.8979i	1.40442	−	1.40442i	0.619128	−	0.785290i	$-0.287486\pi$
$977$	43.8979	−	43.8979i	1.40442	−	1.40442i	0.785290	−	0.619128i	$-0.212514\pi$
$978$	−51.1878	−	51.1878i	−1.63681	−	1.63681i
$979$		0			0
$980$	−109.586	−	20.3038i	−3.50059	−	0.648580i
$981$		0			0
$982$	43.2911	−	43.2911i	1.38147	−	1.38147i
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$			228.109i			7.27185i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$			106.895i			3.39905i
$990$		0			0
$991$	61.9911			1.96921			0.984606	−	0.174791i	$-0.0559250\pi$
$991$	61.9911			1.96921			0.984606	+	0.174791i	$0.0559250\pi$
$992$		0			0
$993$	25.5540	+	25.5540i	0.810931	+	0.810931i
$994$			147.361i			4.67402i
$995$	6.24139	−	33.6867i	0.197865	−	1.06794i
$996$	53.9147			1.70835
$997$	−6.21904	+	6.21904i	−0.196959	+	0.196959i	−0.798695	−	0.601736i	$-0.794476\pi$
$997$	−6.21904	+	6.21904i	−0.196959	+	0.196959i	0.601736	+	0.798695i	$0.294476\pi$
$998$		0			0
$999$			10.9518i			0.346500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	795.2.m.a.158.1	✓	40
3.2	odd	2	inner	795.2.m.a.158.20	yes	40
5.2	odd	4	inner	795.2.m.a.317.1	yes	40
15.2	even	4	inner	795.2.m.a.317.20	yes	40
53.52	even	2	inner	795.2.m.a.158.20	yes	40
159.158	odd	2	CM	795.2.m.a.158.1	✓	40
265.52	odd	4	inner	795.2.m.a.317.20	yes	40
795.317	even	4	inner	795.2.m.a.317.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
795.2.m.a.158.1	✓	40	1.1	even	1	trivial
795.2.m.a.158.1	✓	40	159.158	odd	2	CM
795.2.m.a.158.20	yes	40	3.2	odd	2	inner
795.2.m.a.158.20	yes	40	53.52	even	2	inner
795.2.m.a.317.1	yes	40	5.2	odd	4	inner
795.2.m.a.317.1	yes	40	795.317	even	4	inner
795.2.m.a.317.20	yes	40	15.2	even	4	inner
795.2.m.a.317.20	yes	40	265.52	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 795 = 3 \cdot 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	795.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96968 + 1.96968i) q^{2} +(-1.22474 - 1.22474i) q^{3} -5.75926i q^{4} +(2.19865 + 0.407360i) q^{5} +4.82471 q^{6} +(2.79770 - 2.79770i) q^{7} +(7.40454 + 7.40454i) q^{8} +3.00000i q^{9} +(-5.13300 + 3.52826i) q^{10} +(-7.05363 + 7.05363i) q^{12} +(2.99303 + 2.99303i) q^{13} +11.0212i q^{14} +(-2.19387 - 3.19170i) q^{15} -17.6506 q^{16} +(-5.90903 - 5.90903i) q^{18} +(2.34609 - 12.6626i) q^{20} -6.85295 q^{21} +(5.77550 + 5.77550i) q^{23} -18.1373i q^{24} +(4.66812 + 1.79128i) q^{25} -11.7906 q^{26} +(3.67423 - 3.67423i) q^{27} +(-16.1127 - 16.1127i) q^{28} +(10.6078 + 1.96539i) q^{30} +(19.9569 - 19.9569i) q^{32} +(7.29084 - 5.01150i) q^{35} +17.2778 q^{36} +(-1.49035 + 1.49035i) q^{37} -7.33140i q^{39} +(13.2637 + 19.2963i) q^{40} -12.5768 q^{41} +(13.4981 - 13.4981i) q^{42} +(9.25416 + 9.25416i) q^{43} +(-1.22208 + 6.59595i) q^{45} -22.7517 q^{46} +(21.6175 + 21.6175i) q^{48} -8.65429i q^{49} +(-12.7229 + 5.66643i) q^{50} +(17.2377 - 17.2377i) q^{52} +(-5.14782 - 5.14782i) q^{53} +14.4741i q^{54} +41.4314 q^{56} +(-18.3818 + 12.6351i) q^{60} +(8.39311 + 8.39311i) q^{63} +43.3161i q^{64} +(5.36139 + 7.79987i) q^{65} -14.1470i q^{69} +(-4.48957 + 24.2316i) q^{70} +13.3708 q^{71} +(-22.2136 + 22.2136i) q^{72} -5.87103i q^{74} +(-3.52339 - 7.91112i) q^{75} +(14.4405 + 14.4405i) q^{78} +(-38.8074 - 7.19014i) q^{80} -9.00000 q^{81} +(24.7722 - 24.7722i) q^{82} +(-3.82177 - 3.82177i) q^{83} +39.4679i q^{84} -36.4554 q^{86} +(-10.5848 - 15.3990i) q^{90} +16.7472 q^{91} +(33.2626 - 33.2626i) q^{92} -48.8842 q^{96} +(-2.13252 + 2.13252i) q^{97} +(17.0462 + 17.0462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 160 q^{16} + 240 q^{36} + 20 q^{40} + 60 q^{42} - 140 q^{52} - 180 q^{60} + 220 q^{70} - 360 q^{81} + 260 q^{82}+O(q^{100}) \) 40 * q - 160 * q^16 + 240 * q^36 + 20 * q^40 + 60 * q^42 - 140 * q^52 - 180 * q^60 + 220 * q^70 - 360 * q^81 + 260 * q^82

Introduction

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