LMFDB - Embedded newform 820.2.x.a.273.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			273.3
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.53901 - 1.05169i) q^{3} +(-0.771074 + 2.09892i) q^{5} +(0.595144 - 1.43680i) q^{7} +(3.21921 + 3.21921i) q^{9} +(-2.33163 - 5.62905i) q^{11} +(5.44842 + 2.25681i) q^{13} +(4.16518 - 4.51824i) q^{15} +(-3.78859 + 1.56929i) q^{17} +(0.941956 - 2.27408i) q^{19} +(-3.02216 + 3.02216i) q^{21} +(-3.60761 + 3.60761i) q^{23} +(-3.81089 - 3.23684i) q^{25} +(-1.63291 - 3.94219i) q^{27} +(-1.53963 - 3.71699i) q^{29} +3.63486i q^{31} +16.7444i q^{33} +(2.55683 + 2.35704i) q^{35} +(-3.14703 + 3.14703i) q^{37} +(-11.4601 - 11.4601i) q^{39} +(-5.62080 + 3.06702i) q^{41} +8.27605i q^{43} +(-9.23909 + 4.27460i) q^{45} +(-9.41426 + 3.89951i) q^{47} +(3.23954 + 3.23954i) q^{49} +11.2697 q^{51} +(3.35740 - 8.10547i) q^{53} +(13.6128 - 0.553476i) q^{55} +(-4.78328 + 4.78328i) q^{57} +8.50003i q^{59} +(-6.25449 - 6.25449i) q^{61} +(6.54127 - 2.70948i) q^{63} +(-8.93799 + 9.69561i) q^{65} +(-6.79531 + 2.81471i) q^{67} +(12.9539 - 5.36567i) q^{69} +(2.31864 - 0.960413i) q^{71} +16.8505i q^{73} +(6.27174 + 12.2263i) q^{75} -9.47550 q^{77} +(-12.7201 + 5.26883i) q^{79} -1.93134i q^{81} +(0.0356030 + 0.0356030i) q^{83} +(-0.372513 - 9.16197i) q^{85} +11.0567i q^{87} +(-4.20305 - 10.1471i) q^{89} +(6.48519 - 6.48519i) q^{91} +(3.82276 - 9.22896i) q^{93} +(4.04679 + 3.73057i) q^{95} +(1.60089 + 3.86488i) q^{97} +(10.6151 - 25.6271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.53901	−	1.05169i	−1.46590	−	0.607196i	−0.499980	−	0.866037i	$-0.666659\pi$
$3$	−2.53901	−	1.05169i	−1.46590	−	0.607196i	−0.965920	+	0.258841i	$0.916659\pi$
$4$		0			0
$5$	−0.771074	+	2.09892i	−0.344835	+	0.938663i
$5$	−0.771074	+	2.09892i	−0.344835	+	0.938663i
$6$		0			0
$7$	0.595144	−	1.43680i	0.224943	−	0.543061i	−0.770605	−	0.637313i	$-0.780046\pi$
$7$	0.595144	−	1.43680i	0.224943	−	0.543061i	0.995548	+	0.0942518i	$0.0300459\pi$
$8$		0			0
$9$	3.21921	+	3.21921i	1.07307	+	1.07307i
$10$		0			0
$11$	−2.33163	−	5.62905i	−0.703013	−	1.69722i	−0.716763	−	0.697317i	$-0.754377\pi$
$11$	−2.33163	−	5.62905i	−0.703013	−	1.69722i	0.0137503	−	0.999905i	$-0.495623\pi$
$12$		0			0
$13$	5.44842	+	2.25681i	1.51112	+	0.625927i	0.975789	−	0.218715i	$-0.0701865\pi$
$13$	5.44842	+	2.25681i	1.51112	+	0.625927i	0.535332	+	0.844642i	$0.320187\pi$
$14$		0			0
$15$	4.16518	−	4.51824i	1.07545	−	1.16660i
$16$		0			0
$17$	−3.78859	+	1.56929i	−0.918869	+	0.380608i	−0.791445	−	0.611240i	$-0.790671\pi$
$17$	−3.78859	+	1.56929i	−0.918869	+	0.380608i	−0.127424	+	0.991848i	$0.540671\pi$
$18$		0			0
$19$	0.941956	−	2.27408i	0.216099	−	0.521710i	−0.778239	−	0.627968i	$-0.783887\pi$
$19$	0.941956	−	2.27408i	0.216099	−	0.521710i	0.994339	+	0.106258i	$0.0338869\pi$
$20$		0			0
$21$	−3.02216	+	3.02216i	−0.659489	+	0.659489i
$22$		0			0
$23$	−3.60761	+	3.60761i	−0.752239	+	0.752239i	−0.974897	−	0.222658i	$-0.928527\pi$
$23$	−3.60761	+	3.60761i	−0.752239	+	0.752239i	0.222658	+	0.974897i	$0.428527\pi$
$24$		0			0
$25$	−3.81089	−	3.23684i	−0.762178	−	0.647368i
$26$		0			0
$27$	−1.63291	−	3.94219i	−0.314254	−	0.758676i
$28$		0			0
$29$	−1.53963	−	3.71699i	−0.285902	−	0.690228i	0.714050	−	0.700095i	$-0.246859\pi$
$29$	−1.53963	−	3.71699i	−0.285902	−	0.690228i	−0.999951	+	0.00986733i	$0.996859\pi$
$30$		0			0
$31$			3.63486i			0.652840i	0.945225	+	0.326420i	$0.105842\pi$
$31$			3.63486i			0.652840i	−0.945225	+	0.326420i	$0.894158\pi$
$32$		0			0
$33$			16.7444i			2.91482i
$34$		0			0
$35$	2.55683	+	2.35704i	0.432183	+	0.398412i
$36$		0			0
$37$	−3.14703	+	3.14703i	−0.517369	+	0.517369i	−0.916774	−	0.399406i	$-0.869216\pi$
$37$	−3.14703	+	3.14703i	−0.517369	+	0.517369i	0.399406	+	0.916774i	$0.369216\pi$
$38$		0			0
$39$	−11.4601	−	11.4601i	−1.83509	−	1.83509i
$40$		0			0
$41$	−5.62080	+	3.06702i	−0.877821	+	0.478988i
$41$	−5.62080	+	3.06702i	−0.877821	+	0.478988i
$42$		0			0
$43$			8.27605i			1.26209i	0.775748	+	0.631043i	$0.217373\pi$
$43$			8.27605i			1.26209i	−0.775748	+	0.631043i	$0.782627\pi$
$44$		0			0
$45$	−9.23909	+	4.27460i	−1.37728	+	0.637219i
$46$		0			0
$47$	−9.41426	+	3.89951i	−1.37321	+	0.568802i	−0.942657	−	0.333763i	$-0.891682\pi$
$47$	−9.41426	+	3.89951i	−1.37321	+	0.568802i	−0.430553	+	0.902565i	$0.641682\pi$
$48$		0			0
$49$	3.23954	+	3.23954i	0.462791	+	0.462791i
$50$		0			0
$51$	11.2697			1.57807
$52$		0			0
$53$	3.35740	−	8.10547i	0.461174	−	1.11337i	−0.506742	−	0.862098i	$-0.669150\pi$
$53$	3.35740	−	8.10547i	0.461174	−	1.11337i	0.967916	−	0.251275i	$-0.0808497\pi$
$54$		0			0
$55$	13.6128	−	0.553476i	1.83554	−	0.0746307i
$56$		0			0
$57$	−4.78328	+	4.78328i	−0.633560	+	0.633560i
$58$		0			0
$59$			8.50003i			1.10661i	0.832979	+	0.553305i	$0.186634\pi$
$59$			8.50003i			1.10661i	−0.832979	+	0.553305i	$0.813366\pi$
$60$		0			0
$61$	−6.25449	−	6.25449i	−0.800806	−	0.800806i	0.182416	−	0.983221i	$-0.441608\pi$
$61$	−6.25449	−	6.25449i	−0.800806	−	0.800806i	−0.983221	+	0.182416i	$0.941608\pi$
$62$		0			0
$63$	6.54127	−	2.70948i	0.824122	−	0.341363i
$64$		0			0
$65$	−8.93799	+	9.69561i	−1.10862	+	1.20259i
$66$		0			0
$67$	−6.79531	+	2.81471i	−0.830179	+	0.343872i	−0.756974	−	0.653445i	$-0.773323\pi$
$67$	−6.79531	+	2.81471i	−0.830179	+	0.343872i	−0.0732056	+	0.997317i	$0.523323\pi$
$68$		0			0
$69$	12.9539	−	5.36567i	1.55946	−	0.645951i
$70$		0			0
$71$	2.31864	−	0.960413i	0.275172	−	0.113980i	−0.240830	−	0.970567i	$-0.577420\pi$
$71$	2.31864	−	0.960413i	0.275172	−	0.113980i	0.516002	+	0.856587i	$0.327420\pi$
$72$		0			0
$73$			16.8505i			1.97220i	0.166159	+	0.986099i	$0.446863\pi$
$73$			16.8505i			1.97220i	−0.166159	+	0.986099i	$0.553137\pi$
$74$		0			0
$75$	6.27174	+	12.2263i	0.724198	+	1.41177i
$76$		0			0
$77$	−9.47550			−1.07983
$78$		0			0
$79$	−12.7201	+	5.26883i	−1.43112	+	0.592789i	−0.957628	−	0.288009i	$-0.907007\pi$
$79$	−12.7201	+	5.26883i	−1.43112	+	0.592789i	−0.473492	+	0.880798i	$0.657007\pi$
$80$		0			0
$81$		−	1.93134i		−	0.214593i
$82$		0			0
$83$	0.0356030	+	0.0356030i	0.00390793	+	0.00390793i	0.709058	−	0.705150i	$-0.249120\pi$
$83$	0.0356030	+	0.0356030i	0.00390793	+	0.00390793i	−0.705150	+	0.709058i	$0.749120\pi$
$84$		0			0
$85$	−0.372513	−	9.16197i	−0.0404047	−	0.993755i
$86$		0			0
$87$			11.0567i			1.18540i
$88$		0			0
$89$	−4.20305	−	10.1471i	−0.445522	−	1.07559i	−0.973982	−	0.226627i	$-0.927230\pi$
$89$	−4.20305	−	10.1471i	−0.445522	−	1.07559i	0.528459	−	0.848959i	$-0.322770\pi$
$90$		0			0
$91$	6.48519	−	6.48519i	0.679833	−	0.679833i
$92$		0			0
$93$	3.82276	−	9.22896i	0.396402	−	0.956999i
$94$		0			0
$95$	4.04679	+	3.73057i	0.415192	+	0.382748i
$96$		0			0
$97$	1.60089	+	3.86488i	0.162545	+	0.392419i	0.984077	−	0.177744i	$-0.0568800\pi$
$97$	1.60089	+	3.86488i	0.162545	+	0.392419i	−0.821531	+	0.570163i	$0.806880\pi$
$98$		0			0
$99$	10.6151	−	25.6271i	1.06686	−	2.57562i
$100$		0			0
$101$	−1.05066	−	0.435196i	−0.104544	−	0.0433036i	0.329798	−	0.944051i	$-0.393019\pi$
$101$	−1.05066	−	0.435196i	−0.104544	−	0.0433036i	−0.434342	+	0.900748i	$0.643019\pi$
$102$		0			0
$103$	−4.63000			−0.456208			−0.228104	−	0.973637i	$-0.573253\pi$
$103$	−4.63000			−0.456208			−0.228104	+	0.973637i	$0.573253\pi$
$104$		0			0
$105$	−4.01294	−	8.67356i	−0.391623	−	0.846453i
$106$		0			0
$107$	−3.02910	−	3.02910i	−0.292835	−	0.292835i	0.545364	−	0.838199i	$-0.316391\pi$
$107$	−3.02910	−	3.02910i	−0.292835	−	0.292835i	−0.838199	+	0.545364i	$0.816391\pi$
$108$		0			0
$109$	5.99561	+	2.48346i	0.574276	+	0.237873i	0.650870	−	0.759190i	$-0.274404\pi$
$109$	5.99561	+	2.48346i	0.574276	+	0.237873i	−0.0765938	+	0.997062i	$0.524404\pi$
$110$		0			0
$111$	11.3001	−	4.68064i	1.07255	−	0.444267i
$112$		0			0
$113$	5.26738	−	5.26738i	0.495513	−	0.495513i	−0.414525	−	0.910038i	$-0.636052\pi$
$113$	5.26738	−	5.26738i	0.495513	−	0.495513i	0.910038	+	0.414525i	$0.136052\pi$
$114$		0			0
$115$	−4.79033	−	10.3538i	−0.446701	−	0.965497i
$116$		0			0
$117$	10.2745	+	24.8048i	0.949875	+	2.29320i
$118$		0			0
$119$			6.37742i			0.584617i
$120$		0			0
$121$	−18.4715	+	18.4715i	−1.67923	+	1.67923i
$122$		0			0
$123$	17.4969	−	1.87585i	1.57764	−	0.169140i
$124$		0			0
$125$	9.73233	−	5.50289i	0.870486	−	0.492194i
$126$		0			0
$127$	−4.07898	−	4.07898i	−0.361951	−	0.361951i	0.502580	−	0.864531i	$-0.332384\pi$
$127$	−4.07898	−	4.07898i	−0.361951	−	0.361951i	−0.864531	+	0.502580i	$0.832384\pi$
$128$		0			0
$129$	8.70387	−	21.0130i	0.766333	−	1.85009i
$130$		0			0
$131$	7.46398	−	7.46398i	0.652131	−	0.652131i	−0.301375	−	0.953506i	$-0.597445\pi$
$131$	7.46398	−	7.46398i	0.652131	−	0.652131i	0.953506	+	0.301375i	$0.0974454\pi$
$132$		0			0
$133$	−2.70681	−	2.70681i	−0.234710	−	0.234710i
$134$		0			0
$135$	9.53343	−	0.387616i	0.820507	−	0.0333607i
$136$		0			0
$137$	−20.2442	+	8.38542i	−1.72958	+	0.716415i	−0.730127	+	0.683312i	$0.760539\pi$
$137$	−20.2442	+	8.38542i	−1.72958	+	0.716415i	−0.999452	+	0.0331030i	$0.989461\pi$
$138$		0			0
$139$		−	13.0176i		−	1.10414i	−0.833799	−	0.552068i	$-0.813839\pi$
$139$		−	13.0176i		−	1.10414i	0.833799	−	0.552068i	$-0.186161\pi$
$140$		0			0
$141$	28.0040			2.35836
$142$		0			0
$143$		−	35.9315i		−	3.00474i
$144$		0			0
$145$	8.98881	−	0.365473i	0.746480	−	0.0303509i
$146$		0			0
$147$	−4.81823	−	11.6322i	−0.397401	−	0.959410i
$148$		0			0
$149$	−2.27929	+	5.50270i	−0.186727	+	0.450798i	−0.989326	−	0.145721i	$-0.953450\pi$
$149$	−2.27929	+	5.50270i	−0.186727	+	0.450798i	0.802599	+	0.596519i	$0.203450\pi$
$150$		0			0
$151$	−1.40942	−	3.40263i	−0.114697	−	0.276902i	0.856098	−	0.516813i	$-0.172882\pi$
$151$	−1.40942	−	3.40263i	−0.114697	−	0.276902i	−0.970795	+	0.239911i	$0.922882\pi$
$152$		0			0
$153$	−17.2481	−	7.14441i	−1.39443	−	0.577591i
$154$		0			0
$155$	−7.62927	−	2.80275i	−0.612797	−	0.225122i
$156$		0			0
$157$	0.589043	+	0.243990i	0.0470108	+	0.0194725i	0.406065	−	0.913844i	$-0.366901\pi$
$157$	0.589043	+	0.243990i	0.0470108	+	0.0194725i	−0.359054	+	0.933317i	$0.616901\pi$
$158$		0			0
$159$	−17.0489	+	17.0489i	−1.35207	+	1.35207i
$160$		0			0
$161$	3.03638	+	7.33048i	0.239301	+	0.577723i
$162$		0			0
$163$	−2.02442	+	2.02442i	−0.158565	+	0.158565i	−0.781931	−	0.623366i	$-0.785765\pi$
$163$	−2.02442	+	2.02442i	−0.158565	+	0.158565i	0.623366	+	0.781931i	$0.285765\pi$
$164$		0			0
$165$	−35.1451	−	12.9112i	−2.73604	−	1.00513i
$166$		0			0
$167$	9.17706	−	22.1554i	0.710142	−	1.71444i	0.0104976	−	0.999945i	$-0.496658\pi$
$167$	9.17706	−	22.1554i	0.710142	−	1.71444i	0.699645	−	0.714491i	$-0.253342\pi$
$168$		0			0
$169$	15.3997	+	15.3997i	1.18459	+	1.18459i
$170$		0			0
$171$	10.3531	−	4.28839i	0.791721	−	0.327942i
$172$		0			0
$173$	3.56592			0.271112			0.135556	−	0.990770i	$-0.456718\pi$
$173$	3.56592			0.271112			0.135556	+	0.990770i	$0.456718\pi$
$174$		0			0
$175$	−6.91873	+	3.54912i	−0.523007	+	0.268288i
$176$		0			0
$177$	8.93943	−	21.5817i	0.671929	−	1.62218i
$178$		0			0
$179$	19.5164	+	8.08397i	1.45873	+	0.604224i	0.964257	−	0.264970i	$-0.0853622\pi$
$179$	19.5164	+	8.08397i	1.45873	+	0.604224i	0.494470	+	0.869195i	$0.335362\pi$
$180$		0			0
$181$	−4.27893	−	1.77239i	−0.318051	−	0.131741i	0.217946	−	0.975961i	$-0.430064\pi$
$181$	−4.27893	−	1.77239i	−0.318051	−	0.131741i	−0.535997	+	0.844220i	$0.680064\pi$
$182$		0			0
$183$	9.30243	+	22.4580i	0.687655	+	1.66015i
$184$		0			0
$185$	−4.17876	−	9.03194i	−0.307228	−	0.664042i
$186$		0			0
$187$	17.6672	+	17.6672i	1.29195	+	1.29195i
$188$		0			0
$189$	−6.63598			−0.482697
$190$		0			0
$191$	−5.07548	+	12.2533i	−0.367249	+	0.886617i	0.626950	+	0.779059i	$0.284303\pi$
$191$	−5.07548	+	12.2533i	−0.367249	+	0.886617i	−0.994199	+	0.107557i	$0.965697\pi$
$192$		0			0
$193$	3.92371	+	1.62525i	0.282435	+	0.116988i	0.519404	−	0.854529i	$-0.326154\pi$
$193$	3.92371	+	1.62525i	0.282435	+	0.116988i	−0.236969	+	0.971517i	$0.576154\pi$
$194$		0			0
$195$	32.8905	−	15.2173i	2.35534	−	1.08973i
$196$		0			0
$197$	−9.15299			−0.652124			−0.326062	−	0.945348i	$-0.605722\pi$
$197$	−9.15299			−0.652124			−0.326062	+	0.945348i	$0.605722\pi$
$198$		0			0
$199$	7.05505	+	2.92230i	0.500119	+	0.207156i	0.618459	−	0.785817i	$-0.287757\pi$
$199$	7.05505	+	2.92230i	0.500119	+	0.207156i	−0.118340	+	0.992973i	$0.537757\pi$
$200$		0			0
$201$	20.2136			1.42576
$202$		0			0
$203$	−6.25689			−0.439148
$204$		0			0
$205$	−2.10337	−	14.1625i	−0.146906	−	0.989151i
$206$		0			0
$207$	−23.2273			−1.61441
$208$		0			0
$209$	−14.9972			−1.03738
$210$		0			0
$211$	−15.9472	−	6.60554i	−1.09785	−	0.454744i	−0.241112	−	0.970497i	$-0.577512\pi$
$211$	−15.9472	−	6.60554i	−1.09785	−	0.454744i	−0.856737	+	0.515753i	$0.827512\pi$
$212$		0			0
$213$	−6.89712			−0.472583
$214$		0			0
$215$	−17.3707	−	6.38145i	−1.18467	−	0.435211i
$216$		0			0
$217$	5.22259	+	2.16327i	0.354532	+	0.146852i
$218$		0			0
$219$	17.7215	−	42.7836i	1.19751	−	2.89104i
$220$		0			0
$221$	−24.1834			−1.62675
$222$		0			0
$223$	3.22913	+	3.22913i	0.216238	+	0.216238i	0.806911	−	0.590673i	$-0.201138\pi$
$223$	3.22913	+	3.22913i	0.216238	+	0.216238i	−0.590673	+	0.806911i	$0.701138\pi$
$224$		0			0
$225$	−1.84799	−	22.6881i	−0.123199	−	1.51254i
$226$		0			0
$227$	3.76258	+	9.08367i	0.249731	+	0.602904i	0.998181	−	0.0602869i	$-0.0192016\pi$
$227$	3.76258	+	9.08367i	0.249731	+	0.602904i	−0.748450	+	0.663191i	$0.769202\pi$
$228$		0			0
$229$	0.978616	+	0.405356i	0.0646688	+	0.0267867i	0.414783	−	0.909920i	$-0.363857\pi$
$229$	0.978616	+	0.405356i	0.0646688	+	0.0267867i	−0.350115	+	0.936707i	$0.613857\pi$
$230$		0			0
$231$	24.0584	+	9.96532i	1.58293	+	0.655670i
$232$		0			0
$233$	−1.45063	+	3.50214i	−0.0950341	+	0.229433i	−0.964247	−	0.265006i	$-0.914626\pi$
$233$	−1.45063	+	3.50214i	−0.0950341	+	0.229433i	0.869213	+	0.494438i	$0.164626\pi$
$234$		0			0
$235$	−0.925657	−	22.7665i	−0.0603832	−	1.48513i
$236$		0			0
$237$	37.8376			2.45782
$238$		0			0
$239$	−10.1731	+	4.21384i	−0.658044	+	0.272571i	−0.686615	−	0.727021i	$-0.740904\pi$
$239$	−10.1731	+	4.21384i	−0.658044	+	0.272571i	0.0285713	+	0.999592i	$0.490904\pi$
$240$		0			0
$241$	16.6240	+	16.6240i	1.07084	+	1.07084i	0.997291	+	0.0735522i	$0.0234336\pi$
$241$	16.6240	+	16.6240i	1.07084	+	1.07084i	0.0735522	+	0.997291i	$0.476566\pi$
$242$		0			0
$243$	−6.92991	+	16.7303i	−0.444554	+	1.07325i
$244$		0			0
$245$	−9.29743	+	4.30159i	−0.593991	+	0.274818i
$246$		0			0
$247$	10.2643	−	10.2643i	0.653105	−	0.653105i
$248$		0			0
$249$	−0.0529530	−	0.127840i	−0.00335576	−	0.00810152i
$250$		0			0
$251$	−19.4996	+	19.4996i	−1.23080	+	1.23080i	−0.267148	+	0.963655i	$0.586081\pi$
$251$	−19.4996	+	19.4996i	−1.23080	+	1.23080i	−0.963655	+	0.267148i	$0.913919\pi$
$252$		0			0
$253$	28.7190	+	11.8958i	1.80555	+	0.747883i
$254$		0			0
$255$	−8.68977	+	23.6541i	−0.544175	+	1.48128i
$256$		0			0
$257$	9.60332	+	3.97783i	0.599039	+	0.248130i	0.661534	−	0.749915i	$-0.269906\pi$
$257$	9.60332	+	3.97783i	0.599039	+	0.248130i	−0.0624951	+	0.998045i	$0.519906\pi$
$258$		0			0
$259$	2.64873	+	6.39460i	0.164584	+	0.397341i
$260$		0			0
$261$	7.00938	−	16.9221i	0.433870	−	1.04745i
$262$		0			0
$263$	10.2656	+	24.7833i	0.633002	+	1.52820i	0.835831	+	0.548987i	$0.184986\pi$
$263$	10.2656	+	24.7833i	0.633002	+	1.52820i	−0.202829	+	0.979214i	$0.565014\pi$
$264$		0			0
$265$	14.4239	+	13.2968i	0.886053	+	0.816817i
$266$		0			0
$267$			30.1838i			1.84722i
$268$		0			0
$269$	20.5672			1.25401			0.627003	−	0.779017i	$-0.284281\pi$
$269$	20.5672			1.25401			0.627003	+	0.779017i	$0.284281\pi$
$270$		0			0
$271$		−	6.85930i		−	0.416673i	−0.978057	−	0.208336i	$-0.933195\pi$
$271$		−	6.85930i		−	0.416673i	0.978057	−	0.208336i	$-0.0668049\pi$
$272$		0			0
$273$	−23.2864	+	9.64555i	−1.40936	+	0.583775i
$274$		0			0
$275$	−9.33475	+	28.9988i	−0.562906	+	1.74869i
$276$		0			0
$277$	−12.2463	−	12.2463i	−0.735810	−	0.735810i	0.235954	−	0.971764i	$-0.424178\pi$
$277$	−12.2463	−	12.2463i	−0.735810	−	0.735810i	−0.971764	+	0.235954i	$0.924178\pi$
$278$		0			0
$279$	−11.7014	+	11.7014i	−0.700543	+	0.700543i
$280$		0			0
$281$	−3.51648	+	8.48952i	−0.209775	+	0.506443i	−0.993388	−	0.114808i	$-0.963375\pi$
$281$	−3.51648	+	8.48952i	−0.209775	+	0.506443i	0.783612	+	0.621250i	$0.213375\pi$
$282$		0			0
$283$	−10.1308	−	10.1308i	−0.602216	−	0.602216i	0.338684	−	0.940900i	$-0.390018\pi$
$283$	−10.1308	−	10.1308i	−0.602216	−	0.602216i	−0.940900	+	0.338684i	$0.890018\pi$
$284$		0			0
$285$	−6.35143	−	13.7279i	−0.376226	−	0.813174i
$286$		0			0
$287$	1.06153	+	9.90131i	0.0626600	+	0.584456i
$288$		0			0
$289$	−0.130040	+	0.130040i	−0.00764940	+	0.00764940i
$290$		0			0
$291$		−	11.4966i		−	0.673944i
$292$		0			0
$293$	2.11466	+	5.10525i	0.123540	+	0.298252i	0.973535	−	0.228539i	$-0.0733950\pi$
$293$	2.11466	+	5.10525i	0.123540	+	0.298252i	−0.849995	+	0.526791i	$0.823395\pi$
$294$		0			0
$295$	−17.8409	−	6.55416i	−1.03873	−	0.381598i
$296$		0			0
$297$	−18.3835	+	18.3835i	−1.06672	+	1.06672i
$298$		0			0
$299$	−27.7975	+	11.5141i	−1.60757	+	0.665877i
$300$		0			0
$301$	11.8911	+	4.92544i	0.685390	+	0.283898i
$302$		0			0
$303$	2.20994	+	2.20994i	0.126957	+	0.126957i
$304$		0			0
$305$	17.9503	−	8.30497i	1.02783	−	0.475541i
$306$		0			0
$307$	14.0870			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$307$	14.0870			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$308$		0			0
$309$	11.7556	+	4.86935i	0.668755	+	0.277007i
$310$		0			0
$311$	2.66645	−	6.43737i	0.151200	−	0.365030i	−0.830072	−	0.557656i	$-0.811701\pi$
$311$	2.66645	−	6.43737i	0.151200	−	0.365030i	0.981272	+	0.192627i	$0.0617007\pi$
$312$		0			0
$313$	−12.5649	−	30.3344i	−0.710212	−	1.71460i	−0.699470	−	0.714662i	$-0.746580\pi$
$313$	−12.5649	−	30.3344i	−0.710212	−	1.71460i	−0.0107425	−	0.999942i	$-0.503420\pi$
$314$		0			0
$315$	0.643170	+	15.8188i	0.0362385	+	0.891287i
$316$		0			0
$317$	−5.80082	+	14.0044i	−0.325806	+	0.786566i	0.673088	+	0.739562i	$0.264967\pi$
$317$	−5.80082	+	14.0044i	−0.325806	+	0.786566i	−0.998895	+	0.0470041i	$0.985033\pi$
$318$		0			0
$319$	−17.3333	+	17.3333i	−0.970478	+	0.970478i
$320$		0			0
$321$	4.50525	+	10.8766i	0.251458	+	0.607074i
$322$		0			0
$323$			10.0938i			0.561632i
$324$		0			0
$325$	−13.4584	−	26.2361i	−0.746538	−	1.45532i
$326$		0			0
$327$	−12.6111	−	12.6111i	−0.697395	−	0.697395i
$328$		0			0
$329$			15.8472i			0.873686i
$330$		0			0
$331$	0.633412	−	0.262368i	0.0348155	−	0.0144210i	−0.365208	−	0.930926i	$-0.619002\pi$
$331$	0.633412	−	0.262368i	0.0348155	−	0.0144210i	0.400023	+	0.916505i	$0.369002\pi$
$332$		0			0
$333$	−20.2619			−1.11034
$334$		0			0
$335$	−0.668149	−	16.4331i	−0.0365049	−	0.897838i
$336$		0			0
$337$		−	22.8135i		−	1.24273i	−0.783520	−	0.621366i	$-0.786578\pi$
$337$		−	22.8135i		−	1.24273i	0.783520	−	0.621366i	$-0.213422\pi$
$338$		0			0
$339$	−18.9136	+	7.83428i	−1.02725	+	0.425500i
$340$		0			0
$341$	20.4608	−	8.47515i	1.10802	−	0.458955i
$342$		0			0
$343$	16.6402	−	6.89260i	0.898487	−	0.372165i
$344$		0			0
$345$	1.27369	+	31.3264i	0.0685731	+	1.68656i
$346$		0			0
$347$	−5.30546	+	2.19759i	−0.284812	+	0.117973i	−0.520516	−	0.853852i	$-0.674260\pi$
$347$	−5.30546	+	2.19759i	−0.284812	+	0.117973i	0.235704	+	0.971825i	$0.424260\pi$
$348$		0			0
$349$	−7.14286	−	7.14286i	−0.382348	−	0.382348i	0.489599	−	0.871948i	$-0.337143\pi$
$349$	−7.14286	−	7.14286i	−0.382348	−	0.382348i	−0.871948	+	0.489599i	$0.837143\pi$
$350$		0			0
$351$		−	25.1639i		−	1.34315i
$352$		0			0
$353$	1.12494	−	1.12494i	0.0598745	−	0.0598745i	−0.676535	−	0.736410i	$-0.736519\pi$
$353$	1.12494	−	1.12494i	0.0598745	−	0.0598745i	0.736410	+	0.676535i	$0.236519\pi$
$354$		0			0
$355$	0.227980	+	5.60718i	0.0120999	+	0.297598i
$356$		0			0
$357$	6.70709	−	16.1924i	0.354977	−	0.856990i
$358$		0			0
$359$	−12.6782			−0.669129			−0.334565	−	0.942373i	$-0.608589\pi$
$359$	−12.6782			−0.669129			−0.334565	+	0.942373i	$0.608589\pi$
$360$		0			0
$361$	9.15086	+	9.15086i	0.481624	+	0.481624i
$362$		0			0
$363$	66.3259	−	27.4731i	3.48121	−	1.44196i
$364$		0			0
$365$	−35.3677	−	12.9930i	−1.85123	−	0.680083i
$366$		0			0
$367$			5.67372i			0.296166i	0.988975	+	0.148083i	$0.0473102\pi$
$367$			5.67372i			0.296166i	−0.988975	+	0.148083i	$0.952690\pi$
$368$		0			0
$369$	−27.9679	−	8.22114i	−1.45595	−	0.427975i
$370$		0			0
$371$	−9.64785	−	9.64785i	−0.500891	−	0.500891i
$372$		0			0
$373$	16.6980	−	16.6980i	0.864592	−	0.864592i	−0.127275	−	0.991867i	$-0.540623\pi$
$373$	16.6980	−	16.6980i	0.864592	−	0.864592i	0.991867	+	0.127275i	$0.0406232\pi$
$374$		0			0
$375$	−30.4979	+	3.73649i	−1.57490	+	0.192951i
$376$		0			0
$377$		−	23.7264i		−	1.22197i
$378$		0			0
$379$		−	34.8490i		−	1.79007i	−0.445992	−	0.895037i	$-0.647149\pi$
$379$		−	34.8490i		−	1.79007i	0.445992	−	0.895037i	$-0.352851\pi$
$380$		0			0
$381$	6.06674	+	14.6464i	0.310809	+	0.750358i
$382$		0			0
$383$	−4.36946	−	10.5488i	−0.223269	−	0.539019i	0.772061	−	0.635548i	$-0.219226\pi$
$383$	−4.36946	−	10.5488i	−0.223269	−	0.539019i	−0.995330	+	0.0965293i	$0.969226\pi$
$384$		0			0
$385$	7.30631	−	19.8883i	0.372364	−	1.01360i
$386$		0			0
$387$	−26.6423	+	26.6423i	−1.35431	+	1.35431i
$388$		0			0
$389$	−0.172107	+	0.172107i	−0.00872615	+	0.00872615i	−0.711456	−	0.702730i	$-0.751964\pi$
$389$	−0.172107	+	0.172107i	−0.00872615	+	0.00872615i	0.702730	+	0.711456i	$0.251964\pi$
$390$		0			0
$391$	8.00639	−	19.3291i	0.404901	−	0.977517i
$392$		0			0
$393$	−26.8010	+	11.1013i	−1.35193	+	0.559988i
$394$		0			0
$395$	−1.25070	−	30.7610i	−0.0629296	−	1.54775i
$396$		0			0
$397$	−17.8073	−	7.37603i	−0.893724	−	0.370193i	−0.111920	−	0.993717i	$-0.535700\pi$
$397$	−17.8073	−	7.37603i	−0.893724	−	0.370193i	−0.781804	+	0.623525i	$0.785700\pi$
$398$		0			0
$399$	4.02589	+	9.71937i	0.201547	+	0.486577i
$400$		0			0
$401$	−20.0793	−	20.0793i	−1.00271	−	1.00271i	−0.999996	−	0.00271719i	$-0.999135\pi$
$401$	−20.0793	−	20.0793i	−1.00271	−	1.00271i	−0.00271719	−	0.999996i	$-0.500865\pi$
$402$		0			0
$403$	−8.20320	+	19.8043i	−0.408630	+	0.986521i
$404$		0			0
$405$	4.05372	+	1.48921i	0.201431	+	0.0739992i
$406$		0			0
$407$	25.0525	+	10.3771i	1.24181	+	0.514373i
$408$		0			0
$409$	32.9769			1.63060			0.815301	−	0.579038i	$-0.196572\pi$
$409$	32.9769			1.63060			0.815301	+	0.579038i	$0.196572\pi$
$410$		0			0
$411$	60.2192			2.97039
$412$		0			0
$413$	12.2129	+	5.05874i	0.600957	+	0.248925i
$414$		0			0
$415$	−0.102180	+	0.0472751i	−0.00501583	+	0.00232064i
$416$		0			0
$417$	−13.6905	+	33.0518i	−0.670427	+	1.61855i
$418$		0			0
$419$	−7.01049	−	7.01049i	−0.342485	−	0.342485i	0.514816	−	0.857301i	$-0.327860\pi$
$419$	−7.01049	−	7.01049i	−0.342485	−	0.342485i	−0.857301	+	0.514816i	$0.827860\pi$
$420$		0			0
$421$	−11.6357	−	28.0911i	−0.567091	−	1.36908i	−0.903997	−	0.427539i	$-0.859380\pi$
$421$	−11.6357	−	28.0911i	−0.567091	−	1.36908i	0.336906	−	0.941538i	$-0.390620\pi$
$422$		0			0
$423$	−42.8598	−	17.7531i	−2.08392	−	0.863186i
$424$		0			0
$425$	19.5174	+	6.28269i	0.946735	+	0.304755i
$426$		0			0
$427$	−12.7088	+	5.26416i	−0.615022	+	0.254751i
$428$		0			0
$429$	−37.7889	+	91.2305i	−1.82447	+	4.40465i
$430$		0			0
$431$	−19.6109	+	19.6109i	−0.944624	+	0.944624i	−0.998545	−	0.0539216i	$-0.982828\pi$
$431$	−19.6109	+	19.6109i	−0.944624	+	0.944624i	0.0539216	+	0.998545i	$0.482828\pi$
$432$		0			0
$433$	−13.1295	+	13.1295i	−0.630965	+	0.630965i	−0.948310	−	0.317345i	$-0.897209\pi$
$433$	−13.1295	+	13.1295i	−0.630965	+	0.630965i	0.317345	+	0.948310i	$0.397209\pi$
$434$		0			0
$435$	−23.2071	−	8.52554i	−1.11269	−	0.408768i
$436$		0			0
$437$	4.80579	+	11.6022i	0.229892	+	0.555009i
$438$		0			0
$439$	0.815559	+	1.96893i	0.0389245	+	0.0939720i	0.942146	−	0.335202i	$-0.108805\pi$
$439$	0.815559	+	1.96893i	0.0389245	+	0.0939720i	−0.903222	+	0.429174i	$0.858805\pi$
$440$		0			0
$441$			20.8575i			0.993214i
$442$		0			0
$443$			14.2660i			0.677796i	0.940823	+	0.338898i	$0.110054\pi$
$443$			14.2660i			0.677796i	−0.940823	+	0.338898i	$0.889946\pi$
$444$		0			0
$445$	24.5387	−	0.997709i	1.16324	−	0.0472959i
$446$		0			0
$447$	11.5743	−	11.5743i	0.547446	−	0.547446i
$448$		0			0
$449$	−5.78673	−	5.78673i	−0.273093	−	0.273093i	0.557251	−	0.830344i	$-0.311856\pi$
$449$	−5.78673	−	5.78673i	−0.273093	−	0.273093i	−0.830344	+	0.557251i	$0.811856\pi$
$450$		0			0
$451$	30.3700	+	24.4886i	1.43007	+	1.15312i
$452$		0			0
$453$			10.1216i			0.475554i
$454$		0			0
$455$	8.61130	+	18.6124i	0.403704	+	0.872564i
$456$		0			0
$457$	9.10762	−	3.77250i	0.426037	−	0.176470i	−0.159354	−	0.987221i	$-0.550941\pi$
$457$	9.10762	−	3.77250i	0.426037	−	0.176470i	0.585391	+	0.810751i	$0.300941\pi$
$458$		0			0
$459$	12.3729	+	12.3729i	0.577516	+	0.577516i
$460$		0			0
$461$	−10.3760			−0.483259			−0.241629	−	0.970369i	$-0.577682\pi$
$461$	−10.3760			−0.483259			−0.241629	+	0.970369i	$0.577682\pi$
$462$		0			0
$463$	7.36256	−	17.7748i	0.342167	−	0.826065i	−0.655329	−	0.755344i	$-0.727470\pi$
$463$	7.36256	−	17.7748i	0.342167	−	0.826065i	0.997496	−	0.0707211i	$-0.0225300\pi$
$464$		0			0
$465$	16.4232	+	15.1399i	0.761607	+	0.702094i
$466$		0			0
$467$	−1.50463	+	1.50463i	−0.0696261	+	0.0696261i	−0.741062	−	0.671436i	$-0.765678\pi$
$467$	−1.50463	+	1.50463i	−0.0696261	+	0.0696261i	0.671436	+	0.741062i	$0.265678\pi$
$468$		0			0
$469$			11.4387i			0.528190i
$470$		0			0
$471$	−1.23899	−	1.23899i	−0.0570895	−	0.0570895i
$472$		0			0
$473$	46.5863	−	19.2967i	2.14204	−	0.887263i
$474$		0			0
$475$	−10.9505	+	5.61732i	−0.502445	+	0.257740i
$476$		0			0
$477$	36.9014	−	15.2850i	1.68960	−	0.699854i
$478$		0			0
$479$	10.1085	−	4.18709i	0.461871	−	0.191313i	−0.139600	−	0.990208i	$-0.544582\pi$
$479$	10.1085	−	4.18709i	0.461871	−	0.191313i	0.601471	+	0.798895i	$0.294582\pi$
$480$		0			0
$481$	−24.2486	+	10.0441i	−1.10564	+	0.457971i
$482$		0			0
$483$		−	21.8055i		−	0.992186i
$484$		0			0
$485$	−9.34645	+	0.380014i	−0.424401	+	0.0172556i
$486$		0			0
$487$	−29.9270			−1.35612			−0.678060	−	0.735007i	$-0.737179\pi$
$487$	−29.9270			−1.35612			−0.678060	+	0.735007i	$0.737179\pi$
$488$		0			0
$489$	7.26910	−	3.01096i	0.328720	−	0.136160i
$490$		0			0
$491$			5.48110i			0.247358i	0.992322	+	0.123679i	$0.0394694\pi$
$491$			5.48110i			0.247358i	−0.992322	+	0.123679i	$0.960531\pi$
$492$		0			0
$493$	11.6660	+	11.6660i	0.525412	+	0.525412i
$494$		0			0
$495$	45.6041	+	42.0405i	2.04975	+	1.88958i
$496$		0			0
$497$		−	3.90302i		−	0.175074i
$498$		0			0
$499$	−4.81613	−	11.6272i	−0.215600	−	0.520504i	0.778666	−	0.627438i	$-0.215897\pi$
$499$	−4.81613	−	11.6272i	−0.215600	−	0.520504i	−0.994266	+	0.106934i	$0.965897\pi$
$500$		0			0
$501$	−46.6014	+	46.6014i	−2.08200	+	2.08200i
$502$		0			0
$503$	5.71607	−	13.7998i	0.254867	−	0.615303i	−0.743718	−	0.668494i	$-0.766939\pi$
$503$	5.71607	−	13.7998i	0.254867	−	0.615303i	0.998584	+	0.0531912i	$0.0169393\pi$
$504$		0			0
$505$	1.72357	−	1.86967i	0.0766979	−	0.0831991i
$506$		0			0
$507$	−22.9043	−	55.2959i	−1.01722	−	2.45578i
$508$		0			0
$509$	−9.64913	+	23.2950i	−0.427690	+	1.03253i	0.552328	+	0.833627i	$0.313740\pi$
$509$	−9.64913	+	23.2950i	−0.427690	+	1.03253i	−0.980018	+	0.198908i	$0.936260\pi$
$510$		0			0
$511$	24.2108	+	10.0285i	1.07102	+	0.443633i
$512$		0			0
$513$	−10.5030			−0.463719
$514$		0			0
$515$	3.57008	−	9.71798i	0.157316	−	0.428226i
$516$		0			0
$517$	43.9011	+	43.9011i	1.93077	+	1.93077i
$518$		0			0
$519$	−9.05391	−	3.75025i	−0.397423	−	0.164618i
$520$		0			0
$521$	−0.462590	+	0.191611i	−0.0202664	+	0.00839463i	−0.392794	−	0.919627i	$-0.628491\pi$
$521$	−0.462590	+	0.191611i	−0.0202664	+	0.00839463i	0.372527	+	0.928021i	$0.378491\pi$
$522$		0			0
$523$	−12.8634	+	12.8634i	−0.562479	+	0.562479i	−0.930011	−	0.367532i	$-0.880203\pi$
$523$	−12.8634	+	12.8634i	−0.562479	+	0.562479i	0.367532	+	0.930011i	$0.380203\pi$
$524$		0			0
$525$	21.2993	−	1.73487i	0.929579	−	0.0757160i
$526$		0			0
$527$	−5.70414	−	13.7710i	−0.248476	−	0.599875i
$528$		0			0
$529$		−	3.02972i		−	0.131727i
$530$		0			0
$531$	−27.3634	+	27.3634i	−1.18747	+	1.18747i
$532$		0			0
$533$	−37.5462	+	4.02536i	−1.62631	+	0.174358i
$534$		0			0
$535$	8.69350	−	4.02217i	0.375853	−	0.173894i
$536$		0			0
$537$	−41.0506	−	41.0506i	−1.77146	−	1.77146i
$538$		0			0
$539$	10.6821	−	25.7889i	0.460111	−	1.11081i
$540$		0			0
$541$	26.6195	−	26.6195i	1.14446	−	1.14446i	0.156838	−	0.987624i	$-0.449870\pi$
$541$	26.6195	−	26.6195i	1.14446	−	1.14446i	0.987624	−	0.156838i	$-0.0501301\pi$
$542$		0			0
$543$	9.00026	+	9.00026i	0.386238	+	0.386238i
$544$		0			0
$545$	−9.83565	+	10.6694i	−0.421313	+	0.457025i
$546$		0			0
$547$	6.58818	−	2.72891i	0.281690	−	0.116680i	−0.237365	−	0.971420i	$-0.576284\pi$
$547$	6.58818	−	2.72891i	0.281690	−	0.116680i	0.519055	+	0.854741i	$0.326284\pi$
$548$		0			0
$549$		−	40.2690i		−	1.71864i
$550$		0			0
$551$	−9.90300			−0.421882
$552$		0			0
$553$			21.4120i			0.910529i
$554$		0			0
$555$	1.11108	+	27.3270i	0.0471626	+	1.15997i
$556$		0			0
$557$	−9.83885	−	23.7531i	−0.416885	−	1.00645i	−0.983245	−	0.182292i	$-0.941649\pi$
$557$	−9.83885	−	23.7531i	−0.416885	−	1.00645i	0.566359	−	0.824158i	$-0.308351\pi$
$558$		0			0
$559$	−18.6775	+	45.0914i	−0.789974	+	1.90716i
$560$		0			0
$561$	−26.2768	−	63.4377i	−1.10941	−	2.67834i
$562$		0			0
$563$	−3.89605	−	1.61380i	−0.164199	−	0.0680135i	0.299070	−	0.954231i	$-0.403324\pi$
$563$	−3.89605	−	1.61380i	−0.164199	−	0.0680135i	−0.463269	+	0.886218i	$0.653324\pi$
$564$		0			0
$565$	6.99424	+	15.1173i	0.294250	+	0.635991i
$566$		0			0
$567$	−2.77496	−	1.14942i	−0.116537	−	0.0482713i
$568$		0			0
$569$	22.3777	−	22.3777i	0.938121	−	0.938121i	−0.0600726	−	0.998194i	$-0.519133\pi$
$569$	22.3777	−	22.3777i	0.938121	−	0.938121i	0.998194	+	0.0600726i	$0.0191332\pi$
$570$		0			0
$571$	0.973313	+	2.34979i	0.0407319	+	0.0983355i	0.942936	−	0.332973i	$-0.108052\pi$
$571$	0.973313	+	2.34979i	0.0407319	+	0.0983355i	−0.902204	+	0.431309i	$0.858052\pi$
$572$		0			0
$573$	25.7734	−	25.7734i	1.07670	−	1.07670i
$574$		0			0
$575$	25.4255	−	2.07095i	1.06031	−	0.0863647i
$576$		0			0
$577$	−8.20000	+	19.7965i	−0.341370	+	0.824141i	0.656207	+	0.754581i	$0.272160\pi$
$577$	−8.20000	+	19.7965i	−0.341370	+	0.824141i	−0.997578	+	0.0695603i	$0.977840\pi$
$578$		0			0
$579$	−8.25308	−	8.25308i	−0.342986	−	0.342986i
$580$		0			0
$581$	0.0723434	−	0.0299656i	0.00300131	−	0.00124318i
$582$		0			0
$583$	−53.4543			−2.21385
$584$		0			0
$585$	−59.9854	+	2.43893i	−2.48009	+	0.100837i
$586$		0			0
$587$	12.7299	−	30.7327i	0.525419	−	1.26847i	−0.409077	−	0.912500i	$-0.634149\pi$
$587$	12.7299	−	30.7327i	0.525419	−	1.26847i	0.934496	−	0.355974i	$-0.115851\pi$
$588$		0			0
$589$	8.26597	+	3.42388i	0.340594	+	0.141078i
$590$		0			0
$591$	23.2396	+	9.62614i	0.955948	+	0.395967i
$592$		0			0
$593$	16.4790	+	39.7837i	0.676709	+	1.63372i	0.769971	+	0.638079i	$0.220271\pi$
$593$	16.4790	+	39.7837i	0.676709	+	1.63372i	−0.0932611	+	0.995642i	$0.529729\pi$
$594$		0			0
$595$	−13.3857	−	4.91746i	−0.548759	−	0.201596i
$596$		0			0
$597$	−14.8395	−	14.8395i	−0.607341	−	0.607341i
$598$		0			0
$599$	16.7678			0.685114			0.342557	−	0.939497i	$-0.388707\pi$
$599$	16.7678			0.685114			0.342557	+	0.939497i	$0.388707\pi$
$600$		0			0
$601$	−6.12648	+	14.7906i	−0.249904	+	0.603322i	−0.998195	−	0.0600481i	$-0.980875\pi$
$601$	−6.12648	+	14.7906i	−0.249904	+	0.603322i	0.748291	+	0.663370i	$0.230875\pi$
$602$		0			0
$603$	−30.9367	−	12.8144i	−1.25984	−	0.521842i
$604$		0			0
$605$	−24.5273	−	53.0131i	−0.997175	−	2.15529i
$606$		0			0
$607$	−25.4726			−1.03390			−0.516951	−	0.856015i	$-0.672933\pi$
$607$	−25.4726			−1.03390			−0.516951	+	0.856015i	$0.672933\pi$
$608$		0			0
$609$	15.8863	+	6.58033i	0.643746	+	0.266648i
$610$		0			0
$611$	−60.0933			−2.43112
$612$		0			0
$613$	−44.1630			−1.78372			−0.891862	−	0.452307i	$-0.850601\pi$
$613$	−44.1630			−1.78372			−0.891862	+	0.452307i	$0.850601\pi$
$614$		0			0
$615$	−9.55412	+	38.1708i	−0.385259	+	1.53920i
$616$		0			0
$617$	1.30787			0.0526528			0.0263264	−	0.999653i	$-0.491619\pi$
$617$	1.30787			0.0526528			0.0263264	+	0.999653i	$0.491619\pi$
$618$		0			0
$619$	−9.18340			−0.369112			−0.184556	−	0.982822i	$-0.559085\pi$
$619$	−9.18340			−0.369112			−0.184556	+	0.982822i	$0.559085\pi$
$620$		0			0
$621$	20.1128	+	8.33100i	0.807099	+	0.334311i
$622$		0			0
$623$	−17.0808			−0.684326
$624$		0			0
$625$	4.04575	+	24.6705i	0.161830	+	0.986819i
$626$		0			0
$627$	38.0781	+	15.7725i	1.52069	+	0.629892i
$628$		0			0
$629$	6.98422	−	16.8614i	0.278479	−	0.672308i
$630$		0			0
$631$	12.0431			0.479429			0.239715	−	0.970843i	$-0.422946\pi$
$631$	12.0431			0.479429			0.239715	+	0.970843i	$0.422946\pi$
$632$		0			0
$633$	33.5431	+	33.5431i	1.33322	+	1.33322i
$634$		0			0
$635$	11.7066	−	5.41623i	0.464563	−	0.214937i
$636$		0			0
$637$	10.3393	+	24.9614i	0.409660	+	0.989006i
$638$		0			0
$639$	10.5560	+	4.37242i	0.417587	+	0.172970i
$640$		0			0
$641$	−0.714431	−	0.295927i	−0.0282183	−	0.0116884i	0.368530	−	0.929616i	$-0.379861\pi$
$641$	−0.714431	−	0.295927i	−0.0282183	−	0.0116884i	−0.396748	+	0.917928i	$0.629861\pi$
$642$		0			0
$643$	−9.29811	+	22.4476i	−0.366682	+	0.885248i	0.627608	+	0.778530i	$0.284034\pi$
$643$	−9.29811	+	22.4476i	−0.366682	+	0.885248i	−0.994289	+	0.106718i	$0.965966\pi$
$644$		0			0
$645$	37.3932	+	34.4713i	1.47236	+	1.35731i
$646$		0			0
$647$	39.0339			1.53458			0.767291	−	0.641299i	$-0.221604\pi$
$647$	39.0339			1.53458			0.767291	+	0.641299i	$0.221604\pi$
$648$		0			0
$649$	47.8471	−	19.8189i	1.87816	−	0.777961i
$650$		0			0
$651$	−10.9851	−	10.9851i	−0.430541	−	0.430541i
$652$		0			0
$653$	−15.4677	+	37.3424i	−0.605300	+	1.46132i	0.262759	+	0.964861i	$0.415367\pi$
$653$	−15.4677	+	37.3424i	−0.605300	+	1.46132i	−0.868059	+	0.496461i	$0.834633\pi$
$654$		0			0
$655$	9.91098	+	21.4216i	0.387254	+	0.837009i
$656$		0			0
$657$	−54.2452	+	54.2452i	−2.11631	+	2.11631i
$658$		0			0
$659$	−11.7951	−	28.4759i	−0.459472	−	1.10926i	−0.968611	−	0.248580i	$-0.920036\pi$
$659$	−11.7951	−	28.4759i	−0.459472	−	1.10926i	0.509139	−	0.860684i	$-0.329964\pi$
$660$		0			0
$661$	14.7579	−	14.7579i	0.574014	−	0.574014i	−0.359233	−	0.933248i	$-0.616962\pi$
$661$	14.7579	−	14.7579i	0.574014	−	0.574014i	0.933248	+	0.359233i	$0.116962\pi$
$662$		0			0
$663$	61.4021	+	25.4336i	2.38466	+	0.987758i
$664$		0			0
$665$	7.76852	−	3.59422i	0.301250	−	0.139378i
$666$		0			0
$667$	18.9638	+	7.85508i	0.734283	+	0.304150i
$668$		0			0
$669$	−4.80275	−	11.5949i	−0.185685	−	0.448283i
$670$		0			0
$671$	−20.6237	+	49.7900i	−0.796169	+	1.92212i
$672$		0			0
$673$	3.95671	+	9.55233i	0.152520	+	0.368215i	0.981609	−	0.190900i	$-0.0611407\pi$
$673$	3.95671	+	9.55233i	0.152520	+	0.368215i	−0.829090	+	0.559116i	$0.811141\pi$
$674$		0			0
$675$	−6.53741	+	20.3087i	−0.251625	+	0.781684i
$676$		0			0
$677$		−	26.2292i		−	1.00807i	−0.863683	−	0.504036i	$-0.831848\pi$
$677$		−	26.2292i		−	1.00807i	0.863683	−	0.504036i	$-0.168152\pi$
$678$		0			0
$679$	6.50583			0.249671
$680$		0			0
$681$		−	27.0206i		−	1.03543i
$682$		0			0
$683$	4.74229	−	1.96432i	0.181459	−	0.0751627i	−0.290104	−	0.956995i	$-0.593690\pi$
$683$	4.74229	−	1.96432i	0.181459	−	0.0751627i	0.471563	+	0.881832i	$0.343690\pi$
$684$		0			0
$685$	−1.99051	−	48.9566i	−0.0760535	−	1.87054i
$686$		0			0
$687$	−2.05841	−	2.05841i	−0.0785332	−	0.0785332i
$688$		0			0
$689$	36.5850	−	36.5850i	1.39378	−	1.39378i
$690$		0			0
$691$	14.6694	−	35.4152i	0.558052	−	1.34726i	−0.353254	−	0.935527i	$-0.614925\pi$
$691$	14.6694	−	35.4152i	0.558052	−	1.34726i	0.911306	−	0.411730i	$-0.135075\pi$
$692$		0			0
$693$	−30.5036	−	30.5036i	−1.15874	−	1.15874i
$694$		0			0
$695$	27.3228	+	10.0375i	1.03641	+	0.380745i
$696$		0			0
$697$	16.4819	−	20.4403i	0.624296	−	0.774233i
$698$		0			0
$699$	7.36635	−	7.36635i	0.278621	−	0.278621i
$700$		0			0
$701$			12.8764i			0.486333i	0.969985	+	0.243167i	$0.0781862\pi$
$701$			12.8764i			0.486333i	−0.969985	+	0.243167i	$0.921814\pi$
$702$		0			0
$703$	4.19224	+	10.1210i	0.158113	+	0.381719i
$704$		0			0
$705$	−21.5932	+	58.7781i	−0.813246	+	2.21371i
$706$		0			0
$707$	−1.25058	+	1.25058i	−0.0470330	+	0.0470330i
$708$		0			0
$709$	−27.5745	+	11.4217i	−1.03558	+	0.428952i	−0.834724	−	0.550668i	$-0.814373\pi$
$709$	−27.5745	+	11.4217i	−1.03558	+	0.428952i	−0.200858	+	0.979620i	$0.564373\pi$
$710$		0			0
$711$	−57.9100	−	23.9871i	−2.17180	−	0.899587i
$712$		0			0
$713$	−13.1132	−	13.1132i	−0.491092	−	0.491092i
$714$		0			0
$715$	75.4172	+	27.7058i	2.82044	+	1.03614i
$716$		0			0
$717$	30.2613			1.13013
$718$		0			0
$719$	12.0241	+	4.98055i	0.448423	+	0.185743i	0.595455	−	0.803389i	$-0.296972\pi$
$719$	12.0241	+	4.98055i	0.448423	+	0.185743i	−0.147031	+	0.989132i	$0.546972\pi$
$720$		0			0
$721$	−2.75552	+	6.65241i	−0.102621	+	0.247749i
$722$		0			0
$723$	−24.7251	−	59.6918i	−0.919538	−	2.21996i
$724$		0			0
$725$	−6.16395	+	19.1486i	−0.228923	+	0.711160i
$726$		0			0
$727$	16.1188	−	38.9143i	0.597814	−	1.44325i	−0.277989	−	0.960584i	$-0.589668\pi$
$727$	16.1188	−	38.9143i	0.597814	−	1.44325i	0.875804	−	0.482667i	$-0.160332\pi$
$728$		0			0
$729$	31.0933	−	31.0933i	1.15160	−	1.15160i
$730$		0			0
$731$	−12.9875	−	31.3546i	−0.480360	−	1.15969i
$732$		0			0
$733$		−	32.8312i		−	1.21265i	−0.795218	−	0.606324i	$-0.792643\pi$
$733$		−	32.8312i		−	1.21265i	0.795218	−	0.606324i	$-0.207357\pi$
$734$		0			0
$735$	28.1303	−	1.14374i	1.03760	−	0.0421874i
$736$		0			0
$737$	31.6883	+	31.6883i	1.16725	+	1.16725i
$738$		0			0
$739$			13.9872i			0.514528i	0.966341	+	0.257264i	$0.0828209\pi$
$739$			13.9872i			0.514528i	−0.966341	+	0.257264i	$0.917179\pi$
$740$		0			0
$741$	−36.8563	+	15.2664i	−1.35395	+	0.560824i
$742$		0			0
$743$	−7.89369			−0.289591			−0.144796	−	0.989462i	$-0.546253\pi$
$743$	−7.89369			−0.289591			−0.144796	+	0.989462i	$0.546253\pi$
$744$		0			0
$745$	−9.79219	−	9.02703i	−0.358758	−	0.330725i
$746$		0			0
$747$			0.229227i			0.00838697i
$748$		0			0
$749$	−6.15498	+	2.54948i	−0.224898	+	0.0931559i
$750$		0			0
$751$	−42.9761	+	17.8013i	−1.56822	+	0.649578i	−0.986493	−	0.163805i	$-0.947623\pi$
$751$	−42.9761	+	17.8013i	−1.56822	+	0.649578i	−0.581728	+	0.813383i	$0.697623\pi$
$752$		0			0
$753$	70.0174	−	29.0021i	2.55157	−	1.05690i
$754$		0			0
$755$	8.22860	−	0.334563i	0.299469	−	0.0121760i
$756$		0			0
$757$	11.7631	−	4.87242i	0.427536	−	0.177091i	−0.158531	−	0.987354i	$-0.550676\pi$
$757$	11.7631	−	4.87242i	0.427536	−	0.177091i	0.586067	+	0.810263i	$0.300676\pi$
$758$		0			0
$759$	−60.4073	−	60.4073i	−2.19264	−	2.19264i
$760$		0			0
$761$		−	34.1623i		−	1.23838i	−0.785240	−	0.619192i	$-0.787460\pi$
$761$		−	34.1623i		−	1.23838i	0.785240	−	0.619192i	$-0.212540\pi$
$762$		0			0
$763$	7.13651	−	7.13651i	0.258359	−	0.258359i
$764$		0			0
$765$	28.2951	−	30.6935i	1.02301	−	1.10973i
$766$		0			0
$767$	−19.1830	+	46.3118i	−0.692657	+	1.67222i
$768$		0			0
$769$	40.7281			1.46869			0.734346	−	0.678775i	$-0.237489\pi$
$769$	40.7281			1.46869			0.734346	+	0.678775i	$0.237489\pi$
$770$		0			0
$771$	−20.1995	−	20.1995i	−0.727467	−	0.727467i
$772$		0			0
$773$	−14.4533	+	5.98673i	−0.519847	+	0.215328i	−0.627150	−	0.778899i	$-0.715779\pi$
$773$	−14.4533	+	5.98673i	−0.519847	+	0.215328i	0.107302	+	0.994226i	$0.465779\pi$
$774$		0			0
$775$	11.7655	−	13.8521i	0.422628	−	0.497581i
$776$		0			0
$777$		−	19.0216i		−	0.682397i
$778$		0			0
$779$	1.68012	+	15.6712i	0.0601965	+	0.561477i
$780$		0			0
$781$	−10.8124	−	10.8124i	−0.386899	−	0.386899i
$782$		0			0
$783$	−12.1390	+	12.1390i	−0.433813	+	0.433813i
$784$		0			0
$785$	−0.966310	+	1.04822i	−0.0344891	+	0.0374125i
$786$		0			0
$787$			18.0808i			0.644510i	0.946653	+	0.322255i	$0.104441\pi$
$787$			18.0808i			0.644510i	−0.946653	+	0.322255i	$0.895559\pi$
$788$		0			0
$789$		−	73.7212i		−	2.62455i
$790$		0			0
$791$	−4.43335	−	10.7030i	−0.157632	−	0.380556i
$792$		0			0
$793$	−19.9619	−	48.1923i	−0.708868	−	1.71136i
$794$		0			0
$795$	−22.6383	−	48.9303i	−0.802898	−	1.73538i
$796$		0			0
$797$	−35.4612	+	35.4612i	−1.25610	+	1.25610i	−0.303159	+	0.952940i	$0.598041\pi$
$797$	−35.4612	+	35.4612i	−1.25610	+	1.25610i	−0.952940	+	0.303159i	$0.901959\pi$
$798$		0			0
$799$	29.5473	−	29.5473i	1.04531	−	1.04531i
$800$		0			0
$801$	19.1350	−	46.1960i	0.676102	−	1.63225i
$802$		0			0
$803$	94.8521	−	39.2890i	3.34726	−	1.38648i
$804$		0			0
$805$	−17.7273	+	0.720769i	−0.624806	+	0.0254038i
$806$		0			0
$807$	−52.2205	−	21.6304i	−1.83825	−	0.761427i
$808$		0			0
$809$	−1.74606	−	4.21536i	−0.0613882	−	0.148204i	0.890209	−	0.455553i	$-0.150558\pi$
$809$	−1.74606	−	4.21536i	−0.0613882	−	0.148204i	−0.951597	+	0.307348i	$0.900558\pi$
$810$		0			0
$811$	2.75780	+	2.75780i	0.0968395	+	0.0968395i	0.753867	−	0.657027i	$-0.228186\pi$
$811$	2.75780	+	2.75780i	0.0968395	+	0.0968395i	−0.657027	+	0.753867i	$0.728186\pi$
$812$		0			0
$813$	−7.21388	+	17.4158i	−0.253002	+	0.610801i
$814$		0			0
$815$	−2.68811	−	5.81007i	−0.0941604	−	0.203518i
$816$		0			0
$817$	18.8204	+	7.79568i	0.658443	+	0.272736i
$818$		0			0
$819$	41.7544			1.45902
$820$		0			0
$821$	38.3872			1.33972			0.669862	−	0.742486i	$-0.266353\pi$
$821$	38.3872			1.33972			0.669862	+	0.742486i	$0.266353\pi$
$822$		0			0
$823$	29.9685	+	12.4134i	1.04464	+	0.432703i	0.837975	−	0.545709i	$-0.183740\pi$
$823$	29.9685	+	12.4134i	1.04464	+	0.432703i	0.206663	+	0.978412i	$0.433740\pi$
$824$		0			0
$825$	54.1989	−	63.8110i	1.88696	−	2.22161i
$826$		0			0
$827$	10.5595	−	25.4929i	0.367189	−	0.886473i	−0.627019	−	0.779004i	$-0.715725\pi$
$827$	10.5595	−	25.4929i	0.367189	−	0.886473i	0.994208	−	0.107469i	$-0.0342748\pi$
$828$		0			0
$829$	−15.5952	−	15.5952i	−0.541643	−	0.541643i	0.382368	−	0.924010i	$-0.375109\pi$
$829$	−15.5952	−	15.5952i	−0.541643	−	0.541643i	−0.924010	+	0.382368i	$0.875109\pi$
$830$		0			0
$831$	18.2142	+	43.9729i	0.631843	+	1.52540i
$832$		0			0
$833$	−17.3570	−	7.18952i	−0.601386	−	0.249102i
$834$		0			0
$835$	39.4261	+	36.3453i	1.36440	+	1.25778i
$836$		0			0
$837$	14.3293	−	5.93540i	0.495294	−	0.205158i
$838$		0			0
$839$	−17.0443	+	41.1485i	−0.588434	+	1.42061i	0.296565	+	0.955013i	$0.404159\pi$
$839$	−17.0443	+	41.1485i	−0.588434	+	1.42061i	−0.884999	+	0.465593i	$0.845841\pi$
$840$		0			0
$841$	9.06053	−	9.06053i	0.312432	−	0.312432i
$842$		0			0
$843$	17.8568	−	17.8568i	0.615019	−	0.615019i
$844$		0			0
$845$	−44.1971	+	20.4484i	−1.52043	+	0.703446i
$846$		0			0
$847$	15.5468	+	37.5332i	0.534193	+	1.28966i
$848$		0			0
$849$	15.0678	+	36.3769i	0.517125	+	1.24845i
$850$		0			0
$851$		−	22.7065i		−	0.778369i
$852$		0			0
$853$			14.7581i			0.505307i	0.967557	+	0.252653i	$0.0813032\pi$
$853$			14.7581i			0.505307i	−0.967557	+	0.252653i	$0.918697\pi$
$854$		0			0
$855$	1.01797	+	25.0369i	0.0348138	+	0.856245i
$856$		0			0
$857$	18.6904	−	18.6904i	0.638453	−	0.638453i	−0.311720	−	0.950174i	$-0.600905\pi$
$857$	18.6904	−	18.6904i	0.638453	−	0.638453i	0.950174	+	0.311720i	$0.100905\pi$
$858$		0			0
$859$	2.76827	+	2.76827i	0.0944523	+	0.0944523i	0.752754	−	0.658302i	$-0.228725\pi$
$859$	2.76827	+	2.76827i	0.0944523	+	0.0944523i	−0.658302	+	0.752754i	$0.728725\pi$
$860$		0			0
$861$	7.71791	−	26.2560i	0.263026	−	0.894801i
$862$		0			0
$863$		−	38.7456i		−	1.31892i	−0.751741	−	0.659458i	$-0.770786\pi$
$863$		−	38.7456i		−	1.31892i	0.751741	−	0.659458i	$-0.229214\pi$
$864$		0			0
$865$	−2.74959	+	7.48456i	−0.0934887	+	0.254483i
$866$		0			0
$867$	0.466935	−	0.193411i	0.0158579	−	0.00656857i
$868$		0			0
$869$	59.3170	+	59.3170i	2.01219	+	2.01219i
$870$		0			0
$871$	−43.3760			−1.46974
$872$		0			0
$873$	−7.28827	+	17.5954i	−0.246671	+	0.595515i
$874$		0			0
$875$	−2.11444	−	17.2585i	−0.0714812	−	0.583443i
$876$		0			0
$877$	10.0697	−	10.0697i	0.340028	−	0.340028i	−0.516350	−	0.856378i	$-0.672710\pi$
$877$	10.0697	−	10.0697i	0.340028	−	0.340028i	0.856378	+	0.516350i	$0.172710\pi$
$878$		0			0
$879$		−	15.1863i		−	0.512220i
$880$		0			0
$881$	−23.0343	−	23.0343i	−0.776045	−	0.776045i	0.203111	−	0.979156i	$-0.434895\pi$
$881$	−23.0343	−	23.0343i	−0.776045	−	0.776045i	−0.979156	+	0.203111i	$0.934895\pi$
$882$		0			0
$883$	−22.6328	+	9.37481i	−0.761655	+	0.315488i	−0.729487	−	0.683995i	$-0.760241\pi$
$883$	−22.6328	+	9.37481i	−0.761655	+	0.315488i	−0.0321677	+	0.999482i	$0.510241\pi$
$884$		0			0
$885$	38.4052	+	35.4042i	1.29098	+	1.19010i
$886$		0			0
$887$	3.52337	−	1.45943i	0.118303	−	0.0490027i	−0.322747	−	0.946485i	$-0.604606\pi$
$887$	3.52337	−	1.45943i	0.118303	−	0.0490027i	0.441050	+	0.897483i	$0.354606\pi$
$888$		0			0
$889$	−8.28827	+	3.43311i	−0.277980	+	0.115143i
$890$		0			0
$891$	−10.8716	+	4.50316i	−0.364212	+	0.150862i
$892$		0			0
$893$			25.0820i			0.839336i
$894$		0			0
$895$	−32.0162	+	34.7300i	−1.07018	+	1.16090i
$896$		0			0
$897$	82.6875			2.76086
$898$		0			0
$899$	13.5107	−	5.59633i	0.450609	−	0.186648i
$900$		0			0
$901$			35.9771i			1.19857i
$902$		0			0
$903$	−25.0115	−	25.0115i	−0.832332	−	0.832332i
$904$		0			0
$905$	7.01948	−	7.61447i	0.233335	−	0.253114i
$906$		0			0
$907$		−	3.89068i		−	0.129188i	−0.997912	−	0.0645940i	$-0.979425\pi$
$907$		−	3.89068i		−	0.129188i	0.997912	−	0.0645940i	$-0.0205752\pi$
$908$		0			0
$909$	−1.98129	−	4.78326i	−0.0657153	−	0.158651i
$910$		0			0
$911$	−25.8414	+	25.8414i	−0.856165	+	0.856165i	−0.990884	−	0.134719i	$-0.956987\pi$
$911$	−25.8414	+	25.8414i	−0.856165	+	0.856165i	0.134719	+	0.990884i	$0.456987\pi$
$912$		0			0
$913$	0.117398	−	0.283424i	0.00388531	−	0.00937996i
$914$		0			0
$915$	−54.3104	+	2.20819i	−1.79545	+	0.0730004i
$916$		0			0
$917$	−6.28214	−	15.1664i	−0.207455	−	0.500840i
$918$		0			0
$919$	13.4174	−	32.3924i	0.442598	−	1.06853i	−0.532436	−	0.846470i	$-0.678723\pi$
$919$	13.4174	−	32.3924i	0.442598	−	1.06853i	0.975034	−	0.222056i	$-0.0712768\pi$
$920$		0			0
$921$	−35.7672	−	14.8153i	−1.17857	−	0.488179i
$922$		0			0
$923$	14.8004			0.487162
$924$		0			0
$925$	22.1794	−	1.80656i	0.729254	−	0.0593992i
$926$		0			0
$927$	−14.9049	−	14.9049i	−0.489543	−	0.489543i
$928$		0			0
$929$	−48.6863	−	20.1665i	−1.59734	−	0.661642i	−0.606308	−	0.795230i	$-0.707350\pi$
$929$	−48.6863	−	20.1665i	−1.59734	−	0.661642i	−0.991037	+	0.133588i	$0.957350\pi$
$930$		0			0
$931$	10.4185	−	4.31547i	0.341452	−	0.141434i
$932$		0			0
$933$	−13.5403	+	13.5403i	−0.443289	+	0.443289i
$934$		0			0
$935$	−50.7046	+	23.4592i	−1.65822	+	0.767198i
$936$		0			0
$937$	−18.6802	−	45.0981i	−0.610257	−	1.47329i	−0.862719	−	0.505684i	$-0.831240\pi$
$937$	−18.6802	−	45.0981i	−0.610257	−	1.47329i	0.252462	−	0.967607i	$-0.418760\pi$
$938$		0			0
$939$			90.2340i			2.94468i
$940$		0			0
$941$	14.8009	−	14.8009i	0.482497	−	0.482497i	−0.423431	−	0.905928i	$-0.639175\pi$
$941$	14.8009	−	14.8009i	0.482497	−	0.482497i	0.905928	+	0.423431i	$0.139175\pi$
$942$		0			0
$943$	9.21303	−	31.3423i	0.300018	−	1.02064i
$944$		0			0
$945$	5.11683	−	13.9284i	0.166451	−	0.453090i
$946$		0			0
$947$	28.2996	+	28.2996i	0.919614	+	0.919614i	0.997001	−	0.0773869i	$-0.0246577\pi$
$947$	28.2996	+	28.2996i	0.919614	+	0.919614i	−0.0773869	+	0.997001i	$0.524658\pi$
$948$		0			0
$949$	−38.0283	+	91.8085i	−1.23445	+	2.98023i
$950$		0			0
$951$	29.4567	−	29.4567i	0.955199	−	0.955199i
$952$		0			0
$953$	15.7361	+	15.7361i	0.509742	+	0.509742i	0.914447	−	0.404705i	$-0.132626\pi$
$953$	15.7361	+	15.7361i	0.509742	+	0.509742i	−0.404705	+	0.914447i	$0.632626\pi$
$954$		0			0
$955$	−21.8050	−	20.1012i	−0.705595	−	0.650459i
$956$		0			0
$957$	62.2387	−	25.7801i	2.01189	−	0.833353i
$958$		0			0
$959$			34.0775i			1.10042i
$960$		0			0
$961$	17.7878			0.573799
$962$		0			0
$963$		−	19.5026i		−	0.628464i
$964$		0			0
$965$	−6.43674	+	6.98234i	−0.207206	+	0.224770i
$966$		0			0
$967$	−7.64058	−	18.4460i	−0.245705	−	0.593183i	0.752126	−	0.659019i	$-0.229029\pi$
$967$	−7.64058	−	18.4460i	−0.245705	−	0.593183i	−0.997830	+	0.0658362i	$0.979029\pi$
$968$		0			0
$969$	10.6156	−	25.6282i	0.341021	−	0.823297i
$970$		0			0
$971$	18.9995	+	45.8688i	0.609722	+	1.47200i	0.863303	+	0.504686i	$0.168392\pi$
$971$	18.9995	+	45.8688i	0.609722	+	1.47200i	−0.253581	+	0.967314i	$0.581608\pi$
$972$		0			0
$973$	−18.7037	−	7.74733i	−0.599613	−	0.248368i
$974$		0			0
$975$	6.57871	+	80.7680i	0.210687	+	2.58665i
$976$		0			0
$977$	−39.9839	−	16.5619i	−1.27920	−	0.529862i	−0.363451	−	0.931613i	$-0.618401\pi$
$977$	−39.9839	−	16.5619i	−1.27920	−	0.529862i	−0.915749	+	0.401752i	$0.868401\pi$
$978$		0			0
$979$	−47.3183	+	47.3183i	−1.51230	+	1.51230i
$980$		0			0
$981$	11.3063	+	27.2959i	0.360984	+	0.871492i
$982$		0			0
$983$	−12.8617	+	12.8617i	−0.410224	+	0.410224i	−0.881816	−	0.471593i	$-0.843679\pi$
$983$	−12.8617	+	12.8617i	−0.410224	+	0.410224i	0.471593	+	0.881816i	$0.343679\pi$
$984$		0			0
$985$	7.05764	−	19.2114i	0.224875	−	0.612125i
$986$		0			0
$987$	16.6664	−	40.2363i	0.530498	−	1.28074i
$988$		0			0
$989$	−29.8568	−	29.8568i	−0.949391	−	0.949391i
$990$		0			0
$991$	−44.0757	+	18.2567i	−1.40011	+	0.579944i	−0.949780	−	0.312918i	$-0.898693\pi$
$991$	−44.0757	+	18.2567i	−1.40011	+	0.579944i	−0.450329	+	0.892863i	$0.648693\pi$
$992$		0			0
$993$	−1.88417			−0.0597924
$994$		0			0
$995$	−11.5736	+	12.5546i	−0.366909	+	0.398009i
$996$		0			0
$997$	10.5831	−	25.5499i	0.335170	−	0.809172i	−0.662995	−	0.748624i	$-0.730715\pi$
$997$	10.5831	−	25.5499i	0.335170	−	0.809172i	0.998165	−	0.0605485i	$-0.0192850\pi$
$998$		0			0
$999$	17.5450	+	7.26739i	0.555100	+	0.229930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.3	✓	84
5.2	odd	4		820.2.y.a.437.3	yes	84
41.38	odd	8		820.2.y.a.653.3	yes	84
205.202	even	8	inner	820.2.x.a.817.3	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.3	✓	84	1.1	even	1	trivial
820.2.x.a.817.3	yes	84	205.202	even	8	inner
820.2.y.a.437.3	yes	84	5.2	odd	4
820.2.y.a.653.3	yes	84	41.38	odd	8

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.53901 - 1.05169i) q^{3} +(-0.771074 + 2.09892i) q^{5} +(0.595144 - 1.43680i) q^{7} +(3.21921 + 3.21921i) q^{9} +(-2.33163 - 5.62905i) q^{11} +(5.44842 + 2.25681i) q^{13} +(4.16518 - 4.51824i) q^{15} +(-3.78859 + 1.56929i) q^{17} +(0.941956 - 2.27408i) q^{19} +(-3.02216 + 3.02216i) q^{21} +(-3.60761 + 3.60761i) q^{23} +(-3.81089 - 3.23684i) q^{25} +(-1.63291 - 3.94219i) q^{27} +(-1.53963 - 3.71699i) q^{29} +3.63486i q^{31} +16.7444i q^{33} +(2.55683 + 2.35704i) q^{35} +(-3.14703 + 3.14703i) q^{37} +(-11.4601 - 11.4601i) q^{39} +(-5.62080 + 3.06702i) q^{41} +8.27605i q^{43} +(-9.23909 + 4.27460i) q^{45} +(-9.41426 + 3.89951i) q^{47} +(3.23954 + 3.23954i) q^{49} +11.2697 q^{51} +(3.35740 - 8.10547i) q^{53} +(13.6128 - 0.553476i) q^{55} +(-4.78328 + 4.78328i) q^{57} +8.50003i q^{59} +(-6.25449 - 6.25449i) q^{61} +(6.54127 - 2.70948i) q^{63} +(-8.93799 + 9.69561i) q^{65} +(-6.79531 + 2.81471i) q^{67} +(12.9539 - 5.36567i) q^{69} +(2.31864 - 0.960413i) q^{71} +16.8505i q^{73} +(6.27174 + 12.2263i) q^{75} -9.47550 q^{77} +(-12.7201 + 5.26883i) q^{79} -1.93134i q^{81} +(0.0356030 + 0.0356030i) q^{83} +(-0.372513 - 9.16197i) q^{85} +11.0567i q^{87} +(-4.20305 - 10.1471i) q^{89} +(6.48519 - 6.48519i) q^{91} +(3.82276 - 9.22896i) q^{93} +(4.04679 + 3.73057i) q^{95} +(1.60089 + 3.86488i) q^{97} +(10.6151 - 25.6271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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