LMFDB - Embedded newform 795.2.m.a.158.11

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			158.11
Character	$\chi$	$=$	795.158
Dual form			795.2.m.a.317.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.278703 - 0.278703i) q^{2} +(-1.22474 - 1.22474i) q^{3} +1.84465i q^{4} +(0.962772 - 2.01818i) q^{5} -0.682680 q^{6} +(3.42853 - 3.42853i) q^{7} +(1.07151 + 1.07151i) q^{8} +3.00000i q^{9} +(-0.294146 - 0.830801i) q^{10} +(2.25923 - 2.25923i) q^{12} +(5.09902 + 5.09902i) q^{13} -1.91108i q^{14} +(-3.65091 + 1.29261i) q^{15} -3.09203 q^{16} +(0.836108 + 0.836108i) q^{18} +(3.72284 + 1.77598i) q^{20} -8.39816 q^{21} +(-1.59703 - 1.59703i) q^{23} -2.62466i q^{24} +(-3.14614 - 3.88611i) q^{25} +2.84222 q^{26} +(3.67423 - 3.67423i) q^{27} +(6.32444 + 6.32444i) q^{28} +(-0.657265 + 1.37777i) q^{30} +(-3.00479 + 3.00479i) q^{32} +(-3.61852 - 10.2203i) q^{35} -5.53395 q^{36} +(4.03548 - 4.03548i) q^{37} -12.4900i q^{39} +(3.19414 - 1.13089i) q^{40} +12.7070 q^{41} +(-2.34059 + 2.34059i) q^{42} +(-4.95364 - 4.95364i) q^{43} +(6.05455 + 2.88832i) q^{45} -0.890194 q^{46} +(3.78695 + 3.78695i) q^{48} -16.5097i q^{49} +(-1.95991 - 0.206231i) q^{50} +(-9.40590 + 9.40590i) q^{52} +(5.14782 + 5.14782i) q^{53} -2.04804i q^{54} +7.34745 q^{56} +(-2.38441 - 6.73465i) q^{60} +(10.2856 + 10.2856i) q^{63} -4.50918i q^{64} +(15.2000 - 5.38156i) q^{65} +3.91191i q^{69} +(-3.85692 - 1.83994i) q^{70} -16.1579 q^{71} +(-3.21454 + 3.21454i) q^{72} -2.24940i q^{74} +(-0.906270 + 8.61270i) q^{75} +(-3.48099 - 3.48099i) q^{78} +(-2.97692 + 6.24029i) q^{80} -9.00000 q^{81} +(3.54148 - 3.54148i) q^{82} +(-4.14037 - 4.14037i) q^{83} -15.4917i q^{84} -2.76119 q^{86} +(2.49240 - 0.882439i) q^{90} +34.9643 q^{91} +(2.94596 - 2.94596i) q^{92} +7.36019 q^{96} +(-9.88198 + 9.88198i) q^{97} +(-4.60130 - 4.60130i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.278703	−	0.278703i	0.197073	−	0.197073i	−0.601671	−	0.798744i	$-0.705498\pi$
$2$	0.278703	−	0.278703i	0.197073	−	0.197073i	0.798744	+	0.601671i	$0.205498\pi$
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$3$	−1.22474	−	1.22474i	−0.707107	−	0.707107i
$4$			1.84465i			0.922325i
$5$	0.962772	−	2.01818i	0.430565	−	0.902560i
$5$	0.962772	−	2.01818i	0.430565	−	0.902560i
$6$	−0.682680			−0.278703
$7$	3.42853	−	3.42853i	1.29586	−	1.29586i	0.364764	−	0.931100i	$-0.381150\pi$
$7$	3.42853	−	3.42853i	1.29586	−	1.29586i	0.931100	−	0.364764i	$-0.118850\pi$
$8$	1.07151	+	1.07151i	0.378838	+	0.378838i
$9$			3.00000i			1.00000i
$10$	−0.294146	−	0.830801i	−0.0930172	−	0.262722i
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	2.25923	−	2.25923i	0.652182	−	0.652182i
$13$	5.09902	+	5.09902i	1.41421	+	1.41421i	0.707808	+	0.706405i	$0.249684\pi$
$13$	5.09902	+	5.09902i	1.41421	+	1.41421i	0.706405	+	0.707808i	$0.250316\pi$
$14$		−	1.91108i		−	0.510759i
$15$	−3.65091	+	1.29261i	−0.942661	+	0.333751i
$16$	−3.09203			−0.773008
$17$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$	0.836108	+	0.836108i	0.197073	+	0.197073i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	3.72284	+	1.77598i	0.832453	+	0.397121i
$21$	−8.39816			−1.83263
$22$		0			0
$23$	−1.59703	−	1.59703i	−0.333004	−	0.333004i	0.520722	−	0.853726i	$-0.325663\pi$
$23$	−1.59703	−	1.59703i	−0.333004	−	0.333004i	−0.853726	+	0.520722i	$0.825663\pi$
$24$		−	2.62466i		−	0.535757i
$25$	−3.14614	−	3.88611i	−0.629228	−	0.777221i
$26$	2.84222			0.557405
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$	6.32444	+	6.32444i	1.19521	+	1.19521i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−0.657265	+	1.37777i	−0.120000	+	0.251546i
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−3.00479	+	3.00479i	−0.531176	+	0.531176i
$33$		0			0
$34$		0			0
$35$	−3.61852	−	10.2203i	−0.611641	−	1.72755i
$36$	−5.53395			−0.922325
$37$	4.03548	−	4.03548i	0.663428	−	0.663428i	−0.292758	−	0.956186i	$-0.594573\pi$
$37$	4.03548	−	4.03548i	0.663428	−	0.663428i	0.956186	+	0.292758i	$0.0945731\pi$
$38$		0			0
$39$		−	12.4900i		−	2.00000i
$40$	3.19414	−	1.13089i	0.505038	−	0.178809i
$41$	12.7070			1.98450			0.992252	−	0.124238i	$-0.0396487\pi$
$41$	12.7070			1.98450			0.992252	+	0.124238i	$0.0396487\pi$
$42$	−2.34059	+	2.34059i	−0.361161	+	0.361161i
$43$	−4.95364	−	4.95364i	−0.755424	−	0.755424i	0.220062	−	0.975486i	$-0.429374\pi$
$43$	−4.95364	−	4.95364i	−0.755424	−	0.755424i	−0.975486	+	0.220062i	$0.929374\pi$
$44$		0			0
$45$	6.05455	+	2.88832i	0.902560	+	0.430565i
$46$	−0.890194			−0.131252
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$	3.78695	+	3.78695i	0.546599	+	0.546599i
$49$		−	16.5097i		−	2.35853i
$50$	−1.95991	−	0.206231i	−0.277173	−	0.0291654i
$51$		0			0
$52$	−9.40590	+	9.40590i	−1.30436	+	1.30436i
$53$	5.14782	+	5.14782i	0.707107	+	0.707107i
$53$	5.14782	+	5.14782i	0.707107	+	0.707107i
$54$		−	2.04804i		−	0.278703i
$55$		0			0
$56$	7.34745			0.981844
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−2.38441	−	6.73465i	−0.307826	−	0.869440i
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$		0			0
$63$	10.2856	+	10.2856i	1.29586	+	1.29586i
$64$		−	4.50918i		−	0.563647i
$65$	15.2000	−	5.38156i	1.88532	−	0.667501i
$66$		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
$69$			3.91191i			0.470939i
$70$	−3.85692	−	1.83994i	−0.460990	−	0.219915i
$71$	−16.1579			−1.91759			−0.958793	−	0.284104i	$-0.908304\pi$
$71$	−16.1579			−1.91759			−0.958793	+	0.284104i	$0.908304\pi$
$72$	−3.21454	+	3.21454i	−0.378838	+	0.378838i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		−	2.24940i		−	0.261487i
$75$	−0.906270	+	8.61270i	−0.104647	+	0.994509i
$76$		0			0
$77$		0			0
$78$	−3.48099	−	3.48099i	−0.394145	−	0.394145i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	−2.97692	+	6.24029i	−0.332830	+	0.697686i
$81$	−9.00000			−1.00000
$82$	3.54148	−	3.54148i	0.391092	−	0.391092i
$83$	−4.14037	−	4.14037i	−0.454464	−	0.454464i	0.442369	−	0.896833i	$-0.354138\pi$
$83$	−4.14037	−	4.14037i	−0.454464	−	0.454464i	−0.896833	+	0.442369i	$0.854138\pi$
$84$		−	15.4917i		−	1.69028i
$85$		0			0
$86$	−2.76119			−0.297747
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	2.49240	−	0.882439i	0.262722	−	0.0930172i
$91$	34.9643			3.66526
$92$	2.94596	−	2.94596i	0.307138	−	0.307138i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	7.36019			0.751197
$97$	−9.88198	+	9.88198i	−1.00336	+	1.00336i	−0.00336917	+	0.999994i	$0.501072\pi$
$97$	−9.88198	+	9.88198i	−1.00336	+	1.00336i	−0.999994	+	0.00336917i	$0.998928\pi$
$98$	−4.60130	−	4.60130i	−0.464801	−	0.464801i
$99$		0			0
$100$	7.16850	−	5.80352i	0.716850	−	0.580352i
$101$	−20.0936			−1.99939			−0.999693	−	0.0247601i	$-0.992118\pi$
$101$	−20.0936			−1.99939			−0.999693	+	0.0247601i	$0.992118\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$			10.9273i			1.07151i
$105$	−8.08552	+	16.9490i	−0.789066	+	1.65406i
$106$	2.86942			0.278703
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$	6.77768	+	6.77768i	0.652182	+	0.652182i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−9.88486			−0.938229
$112$	−10.6011	+	10.6011i	−1.00171	+	1.00171i
$113$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$113$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$114$		0			0
$115$	−4.76068	+	1.68553i	−0.443936	+	0.157176i
$116$		0			0
$117$	−15.2971	+	15.2971i	−1.41421	+	1.41421i
$118$		0			0
$119$		0			0
$120$	−5.29706	−	2.52695i	−0.483553	−	0.230678i
$121$	11.0000			1.00000
$122$		0			0
$123$	−15.5629	−	15.5629i	−1.40326	−	1.40326i
$124$		0			0
$125$	−10.8719	+	2.60805i	−0.972412	+	0.233271i
$126$	5.73325			0.510759
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−7.26629	−	7.26629i	−0.642256	−	0.642256i
$129$			12.1339i			1.06833i
$130$	2.73641	−	5.73612i	0.239999	−	0.503091i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.87783	−	10.9527i	−0.333751	−	0.942661i
$136$		0			0
$137$	−13.5578	+	13.5578i	−1.15832	+	1.15832i	−0.173484	+	0.984837i	$0.555503\pi$
$137$	−13.5578	+	13.5578i	−1.15832	+	1.15832i	−0.984837	+	0.173484i	$0.944497\pi$
$138$	1.09026	+	1.09026i	0.0928091	+	0.0928091i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	18.8529	−	6.67490i	1.59336	−	0.564132i
$141$		0			0
$142$	−4.50324	+	4.50324i	−0.377904	+	0.377904i
$143$		0			0
$144$		−	9.27609i		−	0.773008i
$145$		0			0
$146$		0			0
$147$	−20.2202	+	20.2202i	−1.66773	+	1.66773i
$148$	7.44404	+	7.44404i	0.611896	+	0.611896i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	2.14780	+	2.65296i	0.175367	+	0.216614i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	23.0397			1.84465
$157$		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
$160$	3.17129	+	8.95714i	0.250712	+	0.708124i
$161$	−10.9509			−0.863056
$162$	−2.50832	+	2.50832i	−0.197073	+	0.197073i
$163$	14.6095	+	14.6095i	1.14431	+	1.14431i	0.987654	+	0.156652i	$0.0500701\pi$
$163$	14.6095	+	14.6095i	1.14431	+	1.14431i	0.156652	+	0.987654i	$0.449930\pi$
$164$			23.4400i			1.83036i
$165$		0			0
$166$	−2.30786			−0.179125
$167$	18.1626	−	18.1626i	1.40547	−	1.40547i	0.624208	−	0.781258i	$-0.285422\pi$
$167$	18.1626	−	18.1626i	1.40547	−	1.40547i	0.781258	−	0.624208i	$-0.214578\pi$
$168$	−8.99875	−	8.99875i	−0.694268	−	0.694268i
$169$			38.9999i			3.00000i
$170$		0			0
$171$		0			0
$172$	9.13774	−	9.13774i	0.696746	−	0.696746i
$173$	18.2078	+	18.2078i	1.38432	+	1.38432i	0.836787	+	0.547529i	$0.184431\pi$
$173$	18.2078	+	18.2078i	1.38432	+	1.38432i	0.547529	+	0.836787i	$0.315569\pi$
$174$		0			0
$175$	−24.1103	−	2.53700i	−1.82257	−	0.191779i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			15.5292i			1.16071i	0.814365	+	0.580354i	$0.197086\pi$
$179$			15.5292i			1.16071i	−0.814365	+	0.580354i	$0.802914\pi$
$180$	−5.32793	+	11.1685i	−0.397121	+	0.832453i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	9.74465	−	9.74465i	0.722321	−	0.722321i
$183$		0			0
$184$		−	3.42248i		−	0.252309i
$185$	−4.25909	−	12.0296i	−0.313135	−	0.884432i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		−	25.1945i		−	1.83263i
$190$		0			0
$191$	8.61967			0.623698			0.311849	−	0.950132i	$-0.399052\pi$
$191$	8.61967			0.623698			0.311849	+	0.950132i	$0.399052\pi$
$192$	−5.52259	+	5.52259i	−0.398559	+	0.398559i
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$			5.50827i			0.395471i
$195$	−25.2071	−	12.0250i	−1.80512	−	0.861129i
$196$	30.4546			2.17533
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$		0			0
$199$			1.52965i			0.108434i	0.998529	+	0.0542169i	$0.0172662\pi$
$199$			1.52965i			0.108434i	−0.998529	+	0.0542169i	$0.982734\pi$
$200$	0.792885	−	7.53515i	0.0560654	−	0.532816i
$201$		0			0
$202$	−5.60014	+	5.60014i	−0.394024	+	0.394024i
$203$		0			0
$204$		0			0
$205$	12.2340	−	25.6451i	0.854458	−	1.79113i
$206$		0			0
$207$	4.79109	−	4.79109i	0.333004	−	0.333004i
$208$	−15.7663	−	15.7663i	−1.09320	−	1.09320i
$209$		0			0
$210$	2.47029	+	6.97720i	0.170466	+	0.481472i
$211$	27.3653			1.88391			0.941953	−	0.335745i	$-0.108988\pi$
$211$	27.3653			1.88391			0.941953	+	0.335745i	$0.108988\pi$
$212$	−9.49591	+	9.49591i	−0.652182	+	0.652182i
$213$	19.7893	+	19.7893i	1.35594	+	1.35594i
$214$		0			0
$215$	−14.7666	+	5.22814i	−1.00707	+	0.356556i
$216$	7.87399			0.535757
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−2.75494	+	2.75494i	−0.184899	+	0.184899i
$223$	4.60952	+	4.60952i	0.308676	+	0.308676i	0.844396	−	0.535720i	$-0.179960\pi$
$223$	4.60952	+	4.60952i	0.308676	+	0.308676i	−0.535720	+	0.844396i	$0.679960\pi$
$224$			20.6040i			1.37666i
$225$	11.6583	−	9.43842i	0.777221	−	0.629228i
$226$		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
$229$		−	23.2692i		−	1.53767i	−0.639445	−	0.768837i	$-0.720836\pi$
$229$		−	23.2692i		−	1.53767i	0.639445	−	0.768837i	$-0.279164\pi$
$230$	−0.857054	+	1.79658i	−0.0565125	+	0.118463i
$231$		0			0
$232$		0			0
$233$	8.38911	+	8.38911i	0.549589	+	0.549589i	0.926322	−	0.376733i	$-0.122953\pi$
$233$	8.38911	+	8.38911i	0.549589	+	0.549589i	−0.376733	+	0.926322i	$0.622953\pi$
$234$			8.52666i			0.557405i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$			27.9397i			1.80727i	0.428302	+	0.903635i	$0.359112\pi$
$239$			27.9397i			1.80727i	−0.428302	+	0.903635i	$0.640888\pi$
$240$	11.2887	−	3.99679i	0.728685	−	0.257992i
$241$	−31.0372			−1.99928			−0.999642	−	0.0267596i	$-0.991481\pi$
$241$	−31.0372			−1.99928			−0.999642	+	0.0267596i	$0.991481\pi$
$242$	3.06573	−	3.06573i	0.197073	−	0.197073i
$243$	11.0227	+	11.0227i	0.707107	+	0.707107i
$244$		0			0
$245$	−33.3196	−	15.8951i	−2.12871	−	1.01550i
$246$	−8.67483			−0.553087
$247$		0			0
$248$		0			0
$249$			10.1418i			0.642710i
$250$	−2.30315	+	3.75690i	−0.145664	+	0.237607i
$251$	−25.4160			−1.60424			−0.802122	−	0.597161i	$-0.796295\pi$
$251$	−25.4160			−1.60424			−0.802122	+	0.597161i	$0.796295\pi$
$252$	−18.9733	+	18.9733i	−1.19521	+	1.19521i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	4.96808			0.310505
$257$	−15.0138	+	15.0138i	−0.936533	+	0.936533i	−0.998103	−	0.0615696i	$-0.980389\pi$
$257$	−15.0138	+	15.0138i	−0.936533	+	0.936533i	0.0615696	+	0.998103i	$0.480389\pi$
$258$	3.38175	+	3.38175i	0.210539	+	0.210539i
$259$		−	27.6715i		−	1.71943i
$260$	9.92710	+	28.0386i	0.615653	+	1.73888i
$261$		0			0
$262$		0			0
$263$	−14.6945	−	14.6945i	−0.906101	−	0.906101i	0.0898538	−	0.995955i	$-0.471360\pi$
$263$	−14.6945	−	14.6945i	−0.906101	−	0.906101i	−0.995955	+	0.0898538i	$0.971360\pi$
$264$		0			0
$265$	15.3454	−	5.43307i	0.942661	−	0.333751i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	−4.13332	−	1.97180i	−0.251546	−	0.120000i
$271$	−17.8311			−1.08316			−0.541581	−	0.840649i	$-0.682174\pi$
$271$	−17.8311			−1.08316			−0.541581	+	0.840649i	$0.682174\pi$
$272$		0			0
$273$	−42.8224	−	42.8224i	−2.59173	−	2.59173i
$274$			7.55719i			0.456547i
$275$		0			0
$276$	−7.21610			−0.434358
$277$		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
$280$	7.07392	−	14.8285i	0.422748	−	0.886173i
$281$		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	$0.250000\pi$
$284$		−	29.8056i		−	1.76864i
$285$		0			0
$286$		0			0
$287$	43.5665	−	43.5665i	2.57165	−	2.57165i
$288$	−9.01436	−	9.01436i	−0.531176	−	0.531176i
$289$		−	17.0000i		−	1.00000i
$290$		0			0
$291$	24.2058			1.41897
$292$		0			0
$293$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$293$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$294$			11.2708i			0.657328i
$295$		0			0
$296$	8.64814			0.502663
$297$		0			0
$298$		0			0
$299$		−	16.2866i		−	0.941877i
$300$	−15.8874	−	1.67175i	−0.917261	−	0.0965186i
$301$	−33.9675			−1.95785
$302$		0			0
$303$	24.6095	+	24.6095i	1.41378	+	1.41378i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.59347	+	1.59347i	−0.0909442	+	0.0909442i	−0.751115	−	0.660171i	$-0.770484\pi$
$307$	−1.59347	+	1.59347i	−0.0909442	+	0.0909442i	0.660171	+	0.751115i	$0.270484\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	13.3832	−	13.3832i	0.757675	−	0.757675i
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$		0			0
$315$	30.6609	−	10.8556i	1.72755	−	0.611641i
$316$		0			0
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$	−3.51431	−	3.51431i	−0.197073	−	0.197073i
$319$		0			0
$320$	−9.10035	−	4.34131i	−0.508725	−	0.242687i
$321$		0			0
$322$	−3.05206	+	3.05206i	−0.170085	+	0.170085i
$323$		0			0
$324$		−	16.6018i		−	0.922325i
$325$	3.77310	−	35.8575i	0.209294	−	1.98902i
$326$	8.14343			0.451023
$327$		0			0
$328$	13.6158	+	13.6158i	0.751805	+	0.751805i
$329$		0			0
$330$		0			0
$331$	−21.9039			−1.20395			−0.601973	−	0.798517i	$-0.705618\pi$
$331$	−21.9039			−1.20395			−0.601973	+	0.798517i	$0.705618\pi$
$332$	7.63753	−	7.63753i	0.419164	−	0.419164i
$333$	12.1064	+	12.1064i	0.663428	+	0.663428i
$334$		−	10.1239i		−	0.553958i
$335$		0			0
$336$	25.9674			1.41664
$337$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$337$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$338$	10.8694	+	10.8694i	0.591217	+	0.591217i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−32.6043	−	32.6043i	−1.76047	−	1.76047i
$344$		−	10.6158i		−	0.572366i
$345$	7.89496	+	3.76628i	0.425050	+	0.202770i
$346$	10.1491			0.545621
$347$		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	$0.5\pi$
$350$	−7.42667	+	6.01253i	−0.396972	+	0.321383i
$351$	37.4700			2.00000
$352$		0			0
$353$	10.2956	+	10.2956i	0.547981	+	0.547981i	0.925856	−	0.377875i	$-0.123345\pi$
$353$	10.2956	+	10.2956i	0.547981	+	0.547981i	−0.377875	+	0.925856i	$0.623345\pi$
$354$		0			0
$355$	−15.5564	+	32.6096i	−0.825646	+	1.73074i
$356$		0			0
$357$		0			0
$358$	4.32803	+	4.32803i	0.228744	+	0.228744i
$359$			3.44483i			0.181811i	0.995860	+	0.0909056i	$0.0289762\pi$
$359$			3.44483i			0.181811i	−0.995860	+	0.0909056i	$0.971024\pi$
$360$	3.39267	+	9.58242i	0.178809	+	0.505038i
$361$	−19.0000			−1.00000
$362$		0			0
$363$	−13.4722	−	13.4722i	−0.707107	−	0.707107i
$364$			64.4969i			3.38056i
$365$		0			0
$366$		0			0
$367$	−23.6338	+	23.6338i	−1.23368	+	1.23368i	−0.271134	+	0.962542i	$0.587399\pi$
$367$	−23.6338	+	23.6338i	−1.23368	+	1.23368i	−0.962542	+	0.271134i	$0.912601\pi$
$368$	4.93807	+	4.93807i	0.257415	+	0.257415i
$369$			38.1211i			1.98450i
$370$	−4.53970	−	2.16566i	−0.236008	−	0.112587i
$371$	35.2989			1.83263
$372$		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
$375$	16.5095	+	10.1211i	0.852547	+	0.522651i
$376$		0			0
$377$		0			0
$378$	−7.02177	−	7.02177i	−0.361161	−	0.361161i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		0			0
$382$	2.40233	−	2.40233i	0.122914	−	0.122914i
$383$	−5.13127	−	5.13127i	−0.262195	−	0.262195i	0.563750	−	0.825945i	$-0.309358\pi$
$383$	−5.13127	−	5.13127i	−0.262195	−	0.262195i	−0.825945	+	0.563750i	$0.809358\pi$
$384$			17.7987i			0.908287i
$385$		0			0
$386$		0			0
$387$	14.8609	−	14.8609i	0.755424	−	0.755424i
$388$	−18.2288	−	18.2288i	−0.925427	−	0.925427i
$389$		−	7.06268i		−	0.358092i	−0.983841	−	0.179046i	$-0.942699\pi$
$389$		−	7.06268i		−	0.358092i	0.983841	−	0.179046i	$-0.0573011\pi$
$390$	−10.3767	+	3.67388i	−0.525444	+	0.186034i
$391$		0			0
$392$	17.6904	−	17.6904i	0.893499	−	0.893499i
$393$		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	$0.750000\pi$
$398$	0.426317	+	0.426317i	0.0213693	+	0.0213693i
$399$		0			0
$400$	9.72796	+	12.0160i	0.486398	+	0.600798i
$401$	−34.6077			−1.72823			−0.864113	−	0.503298i	$-0.832120\pi$
$401$	−34.6077			−1.72823			−0.864113	+	0.503298i	$0.832120\pi$
$402$		0			0
$403$		0			0
$404$		−	37.0656i		−	1.84408i
$405$	−8.66495	+	18.1637i	−0.430565	+	0.902560i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			23.2134i			1.14783i	0.818915	+	0.573915i	$0.194576\pi$
$409$			23.2134i			1.14783i	−0.818915	+	0.573915i	$0.805424\pi$
$410$	−3.73773	−	10.5570i	−0.184593	−	0.521374i
$411$	33.2097			1.63811
$412$		0			0
$413$		0			0
$414$		−	2.67058i		−	0.131252i
$415$	−12.3423	+	4.36980i	−0.605858	+	0.214505i
$416$	−30.6429			−1.50239
$417$		0			0
$418$		0			0
$419$			6.76546i			0.330514i	0.986251	+	0.165257i	$0.0528454\pi$
$419$			6.76546i			0.330514i	−0.986251	+	0.165257i	$0.947155\pi$
$420$	−31.2650	−	14.9149i	−1.52558	−	0.727775i
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	7.62679	−	7.62679i	0.371266	−	0.371266i
$423$		0			0
$424$			11.0319i			0.535757i
$425$		0			0
$426$	11.0306			0.534437
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−2.65840	+	5.57259i	−0.128199	+	0.268734i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−11.3608	+	11.3608i	−0.546599	+	0.546599i
$433$	27.0903	+	27.0903i	1.30188	+	1.30188i	0.927126	+	0.374749i	$0.122271\pi$
$433$	27.0903	+	27.0903i	1.30188	+	1.30188i	0.374749	+	0.927126i	$0.377729\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		−	30.0960i		−	1.43640i	−0.695834	−	0.718202i	$-0.744965\pi$
$439$		−	30.0960i		−	1.43640i	0.695834	−	0.718202i	$-0.255035\pi$
$440$		0			0
$441$	49.5291			2.35853
$442$		0			0
$443$	24.6783	+	24.6783i	1.17250	+	1.17250i	0.981611	+	0.190890i	$0.0611375\pi$
$443$	24.6783	+	24.6783i	1.17250	+	1.17250i	0.190890	+	0.981611i	$0.438863\pi$
$444$		−	18.2341i		−	0.865352i
$445$		0			0
$446$	2.56937			0.121663
$447$		0			0
$448$	−15.4599	−	15.4599i	−0.730410	−	0.730410i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	0.618692	−	5.87972i	0.0291654	−	0.277173i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	33.6627	−	70.5644i	1.57813	−	3.30811i
$456$		0			0
$457$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$457$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$458$	−6.48520	−	6.48520i	−0.303033	−	0.303033i
$459$		0			0
$460$	−3.10920	−	8.78179i	−0.144967	−	0.409453i
$461$		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
$466$	4.67613			0.216618
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$	−28.2177	−	28.2177i	−1.30436	−	1.30436i
$469$		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
$478$	7.78688	+	7.78688i	0.356164	+	0.356164i
$479$		−	42.2123i		−	1.92873i	−0.264576	−	0.964365i	$-0.585232\pi$
$479$		−	42.2123i		−	1.92873i	0.264576	−	0.964365i	$-0.414768\pi$
$480$	7.08619	−	14.8542i	0.323439	−	0.678000i
$481$	41.1539			1.87646
$482$	−8.65016	+	8.65016i	−0.394004	+	0.394004i
$483$	13.4121	+	13.4121i	0.610272	+	0.610272i
$484$			20.2911i			0.922325i
$485$	10.4296	+	29.4578i	0.473582	+	1.33761i
$486$	6.14412			0.278703
$487$	14.8103	−	14.8103i	0.671120	−	0.671120i	−0.286854	−	0.957974i	$-0.592610\pi$
$487$	14.8103	−	14.8103i	0.671120	−	0.671120i	0.957974	+	0.286854i	$0.0926096\pi$
$488$		0			0
$489$		−	35.7859i		−	1.61829i
$490$	−13.7163	+	4.85626i	−0.619638	+	0.219384i
$491$	18.2145			0.822010			0.411005	−	0.911633i	$-0.365178\pi$
$491$	18.2145			0.822010			0.411005	+	0.911633i	$0.365178\pi$
$492$	28.7080	−	28.7080i	1.29426	−	1.29426i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−55.3978	+	55.3978i	−2.48493	+	2.48493i
$498$	2.82654	+	2.82654i	0.126661	+	0.126661i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−4.81094	−	20.0548i	−0.215152	−	0.896879i
$501$	−44.4892			−1.98763
$502$	−7.08351	+	7.08351i	−0.316152	+	0.316152i
$503$	−30.7285	−	30.7285i	−1.37012	−	1.37012i	−0.860260	−	0.509856i	$-0.829699\pi$
$503$	−30.7285	−	30.7285i	−1.37012	−	1.37012i	−0.509856	−	0.860260i	$-0.670301\pi$
$504$			22.0423i			0.981844i
$505$	−19.3456	+	40.5526i	−0.860866	+	1.80457i
$506$		0			0
$507$	47.7650	−	47.7650i	2.12132	−	2.12132i
$508$		0			0
$509$			40.3322i			1.78769i	0.448371	+	0.893847i	$0.352004\pi$
$509$			40.3322i			1.78769i	−0.448371	+	0.893847i	$0.647996\pi$
$510$		0			0
$511$		0			0
$512$	15.9172	−	15.9172i	0.703448	−	0.703448i
$513$		0			0
$514$			8.36876i			0.369130i
$515$		0			0
$516$	−22.3828			−0.985348
$517$		0			0
$518$	−7.71213	−	7.71213i	−0.338852	−	0.338852i
$519$		−	44.5999i		−	1.95772i
$520$	22.0534	+	10.5205i	0.967105	+	0.461356i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−0.579032	−	0.579032i	−0.0253193	−	0.0253193i	0.694334	−	0.719653i	$-0.255699\pi$
$523$	−0.579032	−	0.579032i	−0.0253193	−	0.0253193i	−0.719653	+	0.694334i	$0.755699\pi$
$524$		0			0
$525$	26.4218	+	32.6361i	1.15314	+	1.42436i
$526$	−8.19079			−0.357135
$527$		0			0
$528$		0			0
$529$		−	17.8990i		−	0.778217i
$530$	2.76260	−	5.79102i	0.120000	−	0.251546i
$531$		0			0
$532$		0			0
$533$	64.7934	+	64.7934i	2.80651	+	2.80651i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	19.0193	−	19.0193i	0.820744	−	0.820744i
$538$		0			0
$539$		0			0
$540$	20.2040	−	7.15324i	0.869440	−	0.307826i
$541$	6.45040			0.277324			0.138662	−	0.990340i	$-0.455720\pi$
$541$	6.45040			0.277324			0.138662	+	0.990340i	$0.455720\pi$
$542$	−4.96957	+	4.96957i	−0.213461	+	0.213461i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−23.8694			−1.02152
$547$	21.9895	−	21.9895i	0.940205	−	0.940205i	−0.0581056	−	0.998310i	$-0.518506\pi$
$547$	21.9895	−	21.9895i	0.940205	−	0.940205i	0.998310	+	0.0581056i	$0.0185060\pi$
$548$	−25.0094	−	25.0094i	−1.06835	−	1.06835i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−4.19167	+	4.19167i	−0.178409	+	0.178409i
$553$		0			0
$554$		0			0
$555$	−9.51687	+	19.9495i	−0.403969	+	0.846808i
$556$		0			0
$557$	24.5960	−	24.5960i	1.04216	−	1.04216i	0.0430928	−	0.999071i	$-0.486279\pi$
$557$	24.5960	−	24.5960i	1.04216	−	1.04216i	0.999071	−	0.0430928i	$-0.0137211\pi$
$558$		0			0
$559$		−	50.5174i		−	2.13666i
$560$	11.1886	+	31.6015i	0.472803	+	1.33541i
$561$		0			0
$562$		0			0
$563$	29.6137	+	29.6137i	1.24807	+	1.24807i	0.956572	+	0.291496i	$0.0941529\pi$
$563$	29.6137	+	29.6137i	1.24807	+	1.24807i	0.291496	+	0.956572i	$0.405847\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−30.8568	+	30.8568i	−1.29586	+	1.29586i
$568$	−17.3134	−	17.3134i	−0.726454	−	0.726454i
$569$		−	28.2298i		−	1.18345i	−0.806138	−	0.591727i	$-0.798446\pi$
$569$		−	28.2298i		−	1.18345i	0.806138	−	0.591727i	$-0.201554\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−10.5569	−	10.5569i	−0.441021	−	0.441021i
$574$		−	24.2842i		−	1.01360i
$575$	−1.18175	+	11.2307i	−0.0492823	+	0.468353i
$576$	13.5275			0.563647
$577$	−17.4140	+	17.4140i	−0.724953	+	0.724953i	−0.969610	−	0.244657i	$-0.921325\pi$
$577$	−17.4140	+	17.4140i	−0.724953	+	0.724953i	0.244657	+	0.969610i	$0.421325\pi$
$578$	−4.73795	−	4.73795i	−0.197073	−	0.197073i
$579$		0			0
$580$		0			0
$581$	−28.3908			−1.17785
$582$	6.74623	−	6.74623i	0.279640	−	0.279640i
$583$		0			0
$584$		0			0
$585$	16.1447	+	45.5999i	0.667501	+	1.88532i
$586$		0			0
$587$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$587$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$588$	−37.2991	−	37.2991i	−1.53819	−	1.53819i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−12.4778	+	12.4778i	−0.512835	+	0.512835i
$593$		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
$597$	1.87343	−	1.87343i	0.0766742	−	0.0766742i
$598$	−4.53911	−	4.53911i	−0.185618	−	0.185618i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−10.1997	+	8.25755i	−0.416402	+	0.337113i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−9.46683	+	9.46683i	−0.385839	+	0.385839i
$603$		0			0
$604$		0			0
$605$	10.5905	−	22.2000i	0.430565	−	0.902560i
$606$	13.7175			0.557235
$607$	−34.6249	+	34.6249i	−1.40538	+	1.40538i	−0.623787	+	0.781594i	$0.714407\pi$
$607$	−34.6249	+	34.6249i	−1.40538	+	1.40538i	−0.781594	+	0.623787i	$0.785593\pi$
$608$		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	$0.250000\pi$
$614$			0.888210i			0.0358452i
$615$	−46.3923	+	16.4252i	−1.87072	+	0.662330i
$616$		0			0
$617$	29.0563	−	29.0563i	1.16976	−	1.16976i	0.187496	−	0.982265i	$-0.439963\pi$
$617$	29.0563	−	29.0563i	1.16976	−	1.16976i	0.982265	−	0.187496i	$-0.0600373\pi$
$618$		0			0
$619$		−	28.3047i		−	1.13766i	−0.822454	−	0.568831i	$-0.807396\pi$
$619$		−	28.3047i		−	1.13766i	0.822454	−	0.568831i	$-0.192604\pi$
$620$		0			0
$621$	−11.7357			−0.470939
$622$		0			0
$623$		0			0
$624$			38.6194i			1.54601i
$625$	−5.20363	+	24.4524i	−0.208145	+	0.978098i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	5.51982	−	11.5708i	0.219915	−	0.460990i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−33.5155	−	33.5155i	−1.33212	−	1.33212i
$634$		0			0
$635$		0			0
$636$	23.2601			0.922325
$637$	84.1832	−	84.1832i	3.33546	−	3.33546i
$638$		0			0
$639$		−	48.4736i		−	1.91759i
$640$	−21.6605	+	7.66893i	−0.856207	+	0.303141i
$641$	−44.5885			−1.76114			−0.880570	−	0.473917i	$-0.842840\pi$
$641$	−44.5885			−1.76114			−0.880570	+	0.473917i	$0.842840\pi$
$642$		0			0
$643$	34.6095	+	34.6095i	1.36487	+	1.36487i	0.867595	+	0.497271i	$0.165665\pi$
$643$	34.6095	+	34.6095i	1.36487	+	1.36487i	0.497271	+	0.867595i	$0.334335\pi$
$644$		−	20.2007i		−	0.796018i
$645$	24.4885	+	11.6822i	0.964232	+	0.459986i
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−9.64363	−	9.64363i	−0.378838	−	0.378838i
$649$		0			0
$650$	−8.94202	−	11.0452i	−0.350735	−	0.433227i
$651$		0			0
$652$	−26.9494	+	26.9494i	−1.05542	+	1.05542i
$653$		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
$656$	−39.2905			−1.53404
$657$		0			0
$658$		0			0
$659$		−	31.7454i		−	1.23663i	−0.785932	−	0.618313i	$-0.787816\pi$
$659$		−	31.7454i		−	1.23663i	0.785932	−	0.618313i	$-0.212184\pi$
$660$		0			0
$661$	−50.4381			−1.96181			−0.980907	−	0.194477i	$-0.937699\pi$
$661$	−50.4381			−1.96181			−0.980907	+	0.194477i	$0.937699\pi$
$662$	−6.10467	+	6.10467i	−0.237265	+	0.237265i
$663$		0			0
$664$		−	8.87293i		−	0.344336i
$665$		0			0
$666$	6.74819			0.261487
$667$		0			0
$668$	33.5037	+	33.5037i	1.29630	+	1.29630i
$669$		−	11.2910i		−	0.436534i
$670$		0			0
$671$		0			0
$672$	25.2347	−	25.2347i	0.973449	−	0.973449i
$673$	−29.6966	−	29.6966i	−1.14472	−	1.14472i	−0.987576	−	0.157142i	$-0.949772\pi$
$673$	−29.6966	−	29.6966i	−1.14472	−	1.14472i	−0.157142	−	0.987576i	$-0.550228\pi$
$674$		0			0
$675$	−25.8381	−	2.71881i	−0.994509	−	0.104647i
$676$	−71.9412			−2.76697
$677$	−27.9361	+	27.9361i	−1.07367	+	1.07367i	−0.0766123	+	0.997061i	$0.524410\pi$
$677$	−27.9361	+	27.9361i	−1.07367	+	1.07367i	−0.997061	+	0.0766123i	$0.975590\pi$
$678$		0			0
$679$			67.7614i			2.60045i
$680$		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
$685$	14.3091	+	40.4152i	0.546721	+	1.54419i
$686$	−18.1738			−0.693880
$687$	−28.4989	+	28.4989i	−1.08730	+	1.08730i
$688$	15.3168	+	15.3168i	0.583948	+	0.583948i
$689$			52.4976i			2.00000i
$690$	3.25002	−	1.15067i	0.123726	−	0.0438054i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$	−33.5871	+	33.5871i	−1.27679	+	1.27679i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	20.5490i		−	0.777236i
$700$	4.67988	−	44.4750i	0.176883	−	1.68100i
$701$	44.4496			1.67884			0.839420	−	0.543483i	$-0.182895\pi$
$701$	44.4496			1.67884			0.839420	+	0.543483i	$0.182895\pi$
$702$	10.4430	−	10.4430i	0.394145	−	0.394145i
$703$		0			0
$704$		0			0
$705$		0			0
$706$	5.73884			0.215984
$707$	−68.8916	+	68.8916i	−2.59093	+	2.59093i
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	4.75278	+	13.4240i	0.178369	+	0.503793i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−28.6459			−1.07055
$717$	34.2190	−	34.2190i	1.27793	−	1.27793i
$718$	0.960084	+	0.960084i	0.0358300	+	0.0358300i
$719$			52.4346i			1.95548i	0.209816	+	0.977741i	$0.432713\pi$
$719$			52.4346i			1.95548i	−0.209816	+	0.977741i	$0.567287\pi$
$720$	−18.7209	−	8.93077i	−0.697686	−	0.332830i
$721$		0			0
$722$	−5.29535	+	5.29535i	−0.197073	+	0.197073i
$723$	38.0127	+	38.0127i	1.41371	+	1.41371i
$724$		0			0
$725$		0			0
$726$	−7.50947			−0.278703
$727$	−29.0006	+	29.0006i	−1.07557	+	1.07557i	−0.0786734	+	0.996900i	$0.525068\pi$
$727$	−29.0006	+	29.0006i	−1.07557	+	1.07557i	−0.996900	+	0.0786734i	$0.974932\pi$
$728$	37.4648	+	37.4648i	1.38854	+	1.38854i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−3.15724	−	3.15724i	−0.116615	−	0.116615i	0.646391	−	0.763006i	$-0.276277\pi$
$733$	−3.15724	−	3.15724i	−0.116615	−	0.116615i	−0.763006	+	0.646391i	$0.776277\pi$
$734$			13.1736i			0.486247i
$735$	21.3406	+	60.2754i	0.787160	+	2.22329i
$736$	9.59747			0.353767
$737$		0			0
$738$	10.6245	+	10.6245i	0.391092	+	0.391092i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	22.1904	−	7.85653i	0.815734	−	0.288812i
$741$		0			0
$742$	9.83791	−	9.83791i	0.361161	−	0.361161i
$743$		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
$747$	12.4211	−	12.4211i	0.454464	−	0.454464i
$748$		0			0
$749$		0			0
$750$	7.42202	−	1.78046i	0.271014	−	0.0650134i
$751$	−33.4498			−1.22060			−0.610301	−	0.792170i	$-0.708951\pi$
$751$	−33.4498			−1.22060			−0.610301	+	0.792170i	$0.708951\pi$
$752$		0			0
$753$	31.1281	+	31.1281i	1.13437	+	1.13437i
$754$		0			0
$755$		0			0
$756$	46.4750			1.69028
$757$	14.2190	−	14.2190i	0.516800	−	0.516800i	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	14.2190	−	14.2190i	0.516800	−	0.516800i	0.916602	+	0.399802i	$0.130921\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.6375			0.929359			0.464679	−	0.885479i	$-0.346170\pi$
$761$	25.6375			0.929359			0.464679	+	0.885479i	$0.346170\pi$
$762$		0			0
$763$		0			0
$764$			15.9003i			0.575252i
$765$		0			0
$766$	−2.86020			−0.103343
$767$		0			0
$768$	−6.08464	−	6.08464i	−0.219560	−	0.219560i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	36.7761			1.32446
$772$		0			0
$773$	−27.9415	−	27.9415i	−1.00498	−	1.00498i	−0.999988	−	0.00499715i	$-0.998409\pi$
$773$	−27.9415	−	27.9415i	−1.00498	−	1.00498i	−0.00499715	−	0.999988i	$-0.501591\pi$
$774$		−	8.28357i		−	0.297747i
$775$		0			0
$776$	−21.1774			−0.760224
$777$	−33.8906	+	33.8906i	−1.21582	+	1.21582i
$778$	−1.96839	−	1.96839i	−0.0705702	−	0.0705702i
$779$		0			0
$780$	22.1819	−	46.4983i	0.794241	−	1.66491i
$781$		0			0
$782$		0			0
$783$		0			0
$784$			51.0485i			1.82316i
$785$		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
$789$			35.9940i			1.28142i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−25.4483	−	12.1401i	−0.902560	−	0.430565i
$796$	−2.82166			−0.100011
$797$	34.6303	−	34.6303i	1.22667	−	1.22667i	0.261453	−	0.965216i	$-0.415798\pi$
$797$	34.6303	−	34.6303i	1.22667	−	1.22667i	0.965216	−	0.261453i	$-0.0842017\pi$
$798$		0			0
$799$		0			0
$800$	21.1304	+	2.22344i	0.747072	+	0.0786105i
$801$		0			0
$802$	−9.64526	+	9.64526i	−0.340586	+	0.340586i
$803$		0			0
$804$		0			0
$805$	−10.5433	+	22.1010i	−0.371601	+	0.778959i
$806$		0			0
$807$		0			0
$808$	−21.5306	−	21.5306i	−0.757443	−	0.757443i
$809$			8.84119i			0.310840i	0.987849	+	0.155420i	$0.0496730\pi$
$809$			8.84119i			0.310840i	−0.987849	+	0.155420i	$0.950327\pi$
$810$	2.64732	+	7.47721i	0.0930172	+	0.262722i
$811$	−1.82693			−0.0641522			−0.0320761	−	0.999485i	$-0.510212\pi$
$811$	−1.82693			−0.0641522			−0.0320761	+	0.999485i	$0.510212\pi$
$812$		0			0
$813$	21.8385	+	21.8385i	0.765911	+	0.765911i
$814$		0			0
$815$	43.5504	−	15.4191i	1.52550	−	0.540106i
$816$		0			0
$817$		0			0
$818$	6.46964	+	6.46964i	0.226206	+	0.226206i
$819$			104.893i			3.66526i
$820$	47.3063	+	22.5674i	1.65201	+	0.788088i
$821$	28.8962			1.00848			0.504242	−	0.863562i	$-0.331772\pi$
$821$	28.8962			1.00848			0.504242	+	0.863562i	$0.331772\pi$
$822$	9.25563	−	9.25563i	0.322827	−	0.322827i
$823$	−32.1876	−	32.1876i	−1.12199	−	1.12199i	−0.991442	−	0.130546i	$-0.958327\pi$
$823$	−32.1876	−	32.1876i	−1.12199	−	1.12199i	−0.130546	−	0.991442i	$-0.541673\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.5294	−	33.5294i	1.16593	−	1.16593i	0.182775	−	0.983155i	$-0.441492\pi$
$827$	33.5294	−	33.5294i	1.16593	−	1.16593i	0.983155	−	0.182775i	$-0.0585080\pi$
$828$	8.83788	+	8.83788i	0.307138	+	0.307138i
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$	−2.22195	+	4.65770i	−0.0771249	+	0.161671i
$831$		0			0
$832$	22.9924	−	22.9924i	0.797117	−	0.797117i
$833$		0			0
$834$		0			0
$835$	−19.1691	−	54.1420i	−0.663373	−	1.87366i
$836$		0			0
$837$		0			0
$838$	1.88555	+	1.88555i	0.0651353	+	0.0651353i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−26.8249	+	9.49739i	−0.925546	+	0.327691i
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$			50.4794i			1.73757i
$845$	78.7091	+	37.5481i	2.70768	+	1.29169i
$846$		0			0
$847$	37.7139	−	37.7139i	1.29586	−	1.29586i
$848$	−15.9172	−	15.9172i	−0.546599	−	0.546599i
$849$		0			0
$850$		0			0
$851$	−12.8896			−0.441848
$852$	−36.5043	+	36.5043i	−1.25062	+	1.25062i
$853$		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
$859$			32.8267i			1.12003i	0.828481	+	0.560017i	$0.189205\pi$
$859$			32.8267i			1.12003i	−0.828481	+	0.560017i	$0.810795\pi$
$860$	−9.64408	−	27.2392i	−0.328860	−	0.928849i
$861$	−106.716			−3.63686
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$			22.0806i			0.751197i
$865$	54.2768	−	19.2168i	1.84547	−	0.653390i
$866$	15.1003			0.513128
$867$	−20.8207	+	20.8207i	−0.707107	+	0.707107i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−29.6460	−	29.6460i	−1.00336	−	1.00336i
$874$		0			0
$875$	−28.3329	+	46.2165i	−0.957825	+	1.56240i
$876$		0			0
$877$	39.5532	−	39.5532i	1.33562	−	1.33562i	0.435363	−	0.900255i	$-0.356620\pi$
$877$	39.5532	−	39.5532i	1.33562	−	1.33562i	0.900255	−	0.435363i	$-0.143380\pi$
$878$	−8.38784	−	8.38784i	−0.283076	−	0.283076i
$879$		0			0
$880$		0			0
$881$	−42.4338			−1.42963			−0.714816	−	0.699313i	$-0.753490\pi$
$881$	−42.4338			−1.42963			−0.714816	+	0.699313i	$0.753490\pi$
$882$	13.8039	−	13.8039i	0.464801	−	0.464801i
$883$		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
$886$	13.7558			0.462136
$887$	20.5913	−	20.5913i	0.691387	−	0.691387i	−0.271150	−	0.962537i	$-0.587404\pi$
$887$	20.5913	−	20.5913i	0.691387	−	0.691387i	0.962537	+	0.271150i	$0.0874040\pi$
$888$	−10.5918	−	10.5918i	−0.355436	−	0.355436i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−8.50295	+	8.50295i	−0.284700	+	0.284700i
$893$		0			0
$894$		0			0
$895$	31.3408	+	14.9511i	1.04761	+	0.499760i
$896$	−49.8255			−1.66455
$897$	−19.9469	+	19.9469i	−0.666007	+	0.666007i
$898$		0			0
$899$		0			0
$900$	17.4106	+	21.5055i	0.580352	+	0.716850i
$901$		0			0
$902$		0			0
$903$	41.6015	+	41.6015i	1.38441	+	1.38441i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	31.7048	−	31.7048i	1.05274	−	1.05274i	0.0542102	−	0.998530i	$-0.482736\pi$
$907$	31.7048	−	31.7048i	1.05274	−	1.05274i	0.998530	−	0.0542102i	$-0.0172641\pi$
$908$		0			0
$909$		−	60.2808i		−	1.99939i
$910$	−10.2846	−	29.0484i	−0.340932	−	0.962944i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	42.9236			1.41823
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−6.90720	−	3.29507i	−0.227724	−	0.108635i
$921$	3.90319			0.128615
$922$		0			0
$923$	−82.3893	−	82.3893i	−2.71188	−	2.71188i
$924$		0			0
$925$	−28.3784	−	2.98612i	−0.933078	−	0.0981829i
$926$		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
$932$	−15.4750	+	15.4750i	−0.506899	+	0.506899i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−32.7820			−1.07151
$937$	−10.9484	+	10.9484i	−0.357667	+	0.357667i	−0.862952	−	0.505285i	$-0.831387\pi$
$937$	−10.9484	+	10.9484i	−0.357667	+	0.357667i	0.505285	+	0.862952i	$0.331387\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$	−20.2935	−	20.2935i	−0.660848	−	0.660848i
$944$		0			0
$945$	−50.8471	−	24.2565i	−1.65406	−	0.789066i
$946$		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	$0.250000\pi$
$954$			8.60826i			0.278703i
$955$	8.29878	−	17.3961i	0.268542	−	0.562924i
$956$	−51.5390			−1.66689
$957$		0			0
$958$	−11.7647	−	11.7647i	−0.380100	−	0.380100i
$959$			92.9667i			3.00205i
$960$	5.82861	+	16.4626i	0.188118	+	0.531328i
$961$	31.0000			1.00000
$962$	11.4697	−	11.4697i	0.369798	−	0.369798i
$963$		0			0
$964$		−	57.2528i		−	1.84399i
$965$		0			0
$966$	7.47599			0.240536
$967$	−38.6177	+	38.6177i	−1.24186	+	1.24186i	−0.282632	+	0.959228i	$0.591207\pi$
$967$	−38.6177	+	38.6177i	−1.24186	+	1.24186i	−0.959228	+	0.282632i	$0.908793\pi$
$968$	11.7867	+	11.7867i	0.378838	+	0.378838i
$969$		0			0
$970$	11.1167	+	5.30321i	0.356936	+	0.170276i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−20.3330	+	20.3330i	−0.652182	+	0.652182i
$973$		0			0
$974$		−	8.25536i		−	0.264519i
$975$	−48.5374	+	39.2952i	−1.55444	+	1.25845i
$976$		0			0
$977$	8.62565	−	8.62565i	0.275959	−	0.275959i	−0.555535	−	0.831493i	$-0.687486\pi$
$977$	8.62565	−	8.62565i	0.275959	−	0.275959i	0.831493	+	0.555535i	$0.187486\pi$
$978$	−9.97362	−	9.97362i	−0.318921	−	0.318921i
$979$		0			0
$980$	29.3208	−	61.4630i	0.936620	−	1.96336i
$981$		0			0
$982$	5.07644	−	5.07644i	0.161996	−	0.161996i
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		−	33.3517i		−	1.06321i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$			15.8222i			0.503118i
$990$		0			0
$991$	−43.6833			−1.38765			−0.693823	−	0.720146i	$-0.744075\pi$
$991$	−43.6833			−1.38765			−0.693823	+	0.720146i	$0.744075\pi$
$992$		0			0
$993$	26.8267	+	26.8267i	0.851318	+	0.851318i
$994$			30.8790i			0.979424i
$995$	3.08711	+	1.47270i	0.0978679	+	0.0466878i
$996$	−18.7080			−0.592787
$997$	44.2190	−	44.2190i	1.40043	−	1.40043i	0.601736	−	0.798695i	$-0.294476\pi$
$997$	44.2190	−	44.2190i	1.40043	−	1.40043i	0.798695	−	0.601736i	$-0.205524\pi$
$998$		0			0
$999$		−	29.6546i		−	0.938229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	795.2.m.a.158.11	yes	40
3.2	odd	2	inner	795.2.m.a.158.10	✓	40
5.2	odd	4	inner	795.2.m.a.317.11	yes	40
15.2	even	4	inner	795.2.m.a.317.10	yes	40
53.52	even	2	inner	795.2.m.a.158.10	✓	40
159.158	odd	2	CM	795.2.m.a.158.11	yes	40
265.52	odd	4	inner	795.2.m.a.317.10	yes	40
795.317	even	4	inner	795.2.m.a.317.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
795.2.m.a.158.10	✓	40	3.2	odd	2	inner
795.2.m.a.158.10	✓	40	53.52	even	2	inner
795.2.m.a.158.11	yes	40	1.1	even	1	trivial
795.2.m.a.158.11	yes	40	159.158	odd	2	CM
795.2.m.a.317.10	yes	40	15.2	even	4	inner
795.2.m.a.317.10	yes	40	265.52	odd	4	inner
795.2.m.a.317.11	yes	40	5.2	odd	4	inner
795.2.m.a.317.11	yes	40	795.317	even	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)

\(f(q)\)	\(=\)	\(q+(0.278703 - 0.278703i) q^{2} +(-1.22474 - 1.22474i) q^{3} +1.84465i q^{4} +(0.962772 - 2.01818i) q^{5} -0.682680 q^{6} +(3.42853 - 3.42853i) q^{7} +(1.07151 + 1.07151i) q^{8} +3.00000i q^{9} +(-0.294146 - 0.830801i) q^{10} +(2.25923 - 2.25923i) q^{12} +(5.09902 + 5.09902i) q^{13} -1.91108i q^{14} +(-3.65091 + 1.29261i) q^{15} -3.09203 q^{16} +(0.836108 + 0.836108i) q^{18} +(3.72284 + 1.77598i) q^{20} -8.39816 q^{21} +(-1.59703 - 1.59703i) q^{23} -2.62466i q^{24} +(-3.14614 - 3.88611i) q^{25} +2.84222 q^{26} +(3.67423 - 3.67423i) q^{27} +(6.32444 + 6.32444i) q^{28} +(-0.657265 + 1.37777i) q^{30} +(-3.00479 + 3.00479i) q^{32} +(-3.61852 - 10.2203i) q^{35} -5.53395 q^{36} +(4.03548 - 4.03548i) q^{37} -12.4900i q^{39} +(3.19414 - 1.13089i) q^{40} +12.7070 q^{41} +(-2.34059 + 2.34059i) q^{42} +(-4.95364 - 4.95364i) q^{43} +(6.05455 + 2.88832i) q^{45} -0.890194 q^{46} +(3.78695 + 3.78695i) q^{48} -16.5097i q^{49} +(-1.95991 - 0.206231i) q^{50} +(-9.40590 + 9.40590i) q^{52} +(5.14782 + 5.14782i) q^{53} -2.04804i q^{54} +7.34745 q^{56} +(-2.38441 - 6.73465i) q^{60} +(10.2856 + 10.2856i) q^{63} -4.50918i q^{64} +(15.2000 - 5.38156i) q^{65} +3.91191i q^{69} +(-3.85692 - 1.83994i) q^{70} -16.1579 q^{71} +(-3.21454 + 3.21454i) q^{72} -2.24940i q^{74} +(-0.906270 + 8.61270i) q^{75} +(-3.48099 - 3.48099i) q^{78} +(-2.97692 + 6.24029i) q^{80} -9.00000 q^{81} +(3.54148 - 3.54148i) q^{82} +(-4.14037 - 4.14037i) q^{83} -15.4917i q^{84} -2.76119 q^{86} +(2.49240 - 0.882439i) q^{90} +34.9643 q^{91} +(2.94596 - 2.94596i) q^{92} +7.36019 q^{96} +(-9.88198 + 9.88198i) q^{97} +(-4.60130 - 4.60130i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 160 q^{16} + 240 q^{36} + 20 q^{40} + 60 q^{42} - 140 q^{52} - 180 q^{60} + 220 q^{70} - 360 q^{81} + 260 q^{82}+O(q^{100}) \) 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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