LMFDB - Embedded newform 464.2.bl.c.15.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,2,Mod(15,464)] 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("464.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 0, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.bl (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [120] 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:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			15.3
Character	$\chi$	$=$	464.15
Dual form			464.2.bl.c.31.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.823357 - 1.31036i) q^{3} +(-2.32413 - 1.85343i) q^{5} +(-2.47691 - 0.565338i) q^{7} +(0.262512 - 0.545111i) q^{9} +(-1.89664 + 5.42028i) q^{11} +(0.674824 + 1.40129i) q^{13} +(-0.515083 + 4.57149i) q^{15} +(5.07675 + 5.07675i) q^{17} +(-0.886325 - 0.556915i) q^{19} +(1.29858 + 3.71113i) q^{21} +(-0.405531 + 0.323400i) q^{23} +(0.853764 + 3.74058i) q^{25} +(-5.54395 + 0.624653i) q^{27} +(-3.18817 - 4.34000i) q^{29} +(-0.207994 - 1.84600i) q^{31} +(8.66415 - 1.97754i) q^{33} +(4.70883 + 5.90469i) q^{35} +(-5.14048 + 1.79873i) q^{37} +(1.28058 - 2.03802i) q^{39} +(-5.15895 + 5.15895i) q^{41} +(-10.1596 - 1.14471i) q^{43} +(-1.62044 + 0.780361i) q^{45} +(3.48702 + 1.22016i) q^{47} +(-0.491326 - 0.236610i) q^{49} +(2.47242 - 10.8324i) q^{51} +(7.51501 - 9.42353i) q^{53} +(14.4541 - 9.08214i) q^{55} +1.61995i q^{57} +8.01950i q^{59} +(-12.4768 + 7.83971i) q^{61} +(-0.958388 + 1.20178i) q^{63} +(1.02881 - 4.50751i) q^{65} +(-2.21191 - 1.06520i) q^{67} +(0.757669 + 0.265120i) q^{69} +(-4.92140 + 2.37002i) q^{71} +(-4.92030 - 0.554385i) q^{73} +(4.19858 - 4.19858i) q^{75} +(7.76208 - 12.3533i) q^{77} +(-6.57935 + 2.30221i) q^{79} +(4.25149 + 5.33120i) q^{81} +(10.2799 - 2.34632i) q^{83} +(-2.38961 - 21.2084i) q^{85} +(-3.06198 + 7.75103i) q^{87} +(-2.88852 + 0.325458i) q^{89} +(-0.879275 - 3.85236i) q^{91} +(-2.24768 + 1.79247i) q^{93} +(1.02773 + 2.93708i) q^{95} +(-0.0192149 - 0.0120735i) q^{97} +(2.45676 + 2.45676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) $ 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{27}{28}\right)$

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
$3$	−0.823357	−	1.31036i	−0.475365	−	0.756540i	0.519849	−	0.854258i	$-0.325988\pi$
$3$	−0.823357	−	1.31036i	−0.475365	−	0.756540i	−0.995214	+	0.0977188i	$0.968845\pi$
$4$		0			0
$5$	−2.32413	−	1.85343i	−1.03938	−	0.828879i	−0.0538806	−	0.998547i	$-0.517159\pi$
$5$	−2.32413	−	1.85343i	−1.03938	−	0.828879i	−0.985501	+	0.169668i	$0.945730\pi$
$6$		0			0
$7$	−2.47691	−	0.565338i	−0.936182	−	0.213678i	−0.272896	−	0.962043i	$-0.587982\pi$
$7$	−2.47691	−	0.565338i	−0.936182	−	0.213678i	−0.663286	+	0.748366i	$0.730839\pi$
$8$		0			0
$9$	0.262512	−	0.545111i	0.0875038	−	0.181704i
$10$		0			0
$11$	−1.89664	+	5.42028i	−0.571858	+	1.63428i	0.186513	+	0.982453i	$0.440281\pi$
$11$	−1.89664	+	5.42028i	−0.571858	+	1.63428i	−0.758371	+	0.651823i	$0.774004\pi$
$12$		0			0
$13$	0.674824	+	1.40129i	0.187162	+	0.388647i	0.973344	−	0.229348i	$-0.0736594\pi$
$13$	0.674824	+	1.40129i	0.187162	+	0.388647i	−0.786182	+	0.617995i	$0.787945\pi$
$14$		0			0
$15$	−0.515083	+	4.57149i	−0.132994	+	1.18035i
$16$		0			0
$17$	5.07675	+	5.07675i	1.23129	+	1.23129i	0.963468	+	0.267824i	$0.0863047\pi$
$17$	5.07675	+	5.07675i	1.23129	+	1.23129i	0.267824	+	0.963468i	$0.413695\pi$
$18$		0			0
$19$	−0.886325	−	0.556915i	−0.203337	−	0.127765i	0.426514	−	0.904481i	$-0.359741\pi$
$19$	−0.886325	−	0.556915i	−0.203337	−	0.127765i	−0.629851	+	0.776716i	$0.716884\pi$
$20$		0			0
$21$	1.29858	+	3.71113i	0.283373	+	0.809834i
$22$		0			0
$23$	−0.405531	+	0.323400i	−0.0845591	+	0.0674336i	−0.664857	−	0.746971i	$-0.731508\pi$
$23$	−0.405531	+	0.323400i	−0.0845591	+	0.0674336i	0.580298	+	0.814404i	$0.302936\pi$
$24$		0			0
$25$	0.853764	+	3.74058i	0.170753	+	0.748117i
$26$		0			0
$27$	−5.54395	+	0.624653i	−1.06693	+	0.120215i
$28$		0			0
$29$	−3.18817	−	4.34000i	−0.592028	−	0.805917i
$29$	−3.18817	−	4.34000i	−0.592028	−	0.805917i
$30$		0			0
$31$	−0.207994	−	1.84600i	−0.0373569	−	0.331552i	−0.998465	−	0.0553803i	$-0.982363\pi$
$31$	−0.207994	−	1.84600i	−0.0373569	−	0.331552i	0.961108	−	0.276171i	$-0.0890657\pi$
$32$		0			0
$33$	8.66415	−	1.97754i	1.50824	−	0.344245i
$34$		0			0
$35$	4.70883	+	5.90469i	0.795938	+	0.998075i
$36$		0			0
$37$	−5.14048	+	1.79873i	−0.845090	+	0.295710i	−0.717881	−	0.696166i	$-0.754888\pi$
$37$	−5.14048	+	1.79873i	−0.845090	+	0.295710i	−0.127209	+	0.991876i	$0.540602\pi$
$38$		0			0
$39$	1.28058	−	2.03802i	0.205056	−	0.326345i
$40$		0			0
$41$	−5.15895	+	5.15895i	−0.805693	+	0.805693i	−0.983979	−	0.178286i	$-0.942945\pi$
$41$	−5.15895	+	5.15895i	−0.805693	+	0.805693i	0.178286	+	0.983979i	$0.442945\pi$
$42$		0			0
$43$	−10.1596	−	1.14471i	−1.54932	−	0.174567i	−0.704536	−	0.709668i	$-0.748845\pi$
$43$	−10.1596	−	1.14471i	−1.54932	−	0.174567i	−0.844788	+	0.535101i	$0.820274\pi$
$44$		0			0
$45$	−1.62044	+	0.780361i	−0.241560	+	0.116329i
$46$		0			0
$47$	3.48702	+	1.22016i	0.508634	+	0.177979i	0.572382	−	0.819987i	$-0.306020\pi$
$47$	3.48702	+	1.22016i	0.508634	+	0.177979i	−0.0637479	+	0.997966i	$0.520305\pi$
$48$		0			0
$49$	−0.491326	−	0.236610i	−0.0701895	−	0.0338015i
$50$		0			0
$51$	2.47242	−	10.8324i	0.346208	−	1.51683i
$52$		0			0
$53$	7.51501	−	9.42353i	1.03227	−	1.29442i	0.0775229	−	0.996991i	$-0.475299\pi$
$53$	7.51501	−	9.42353i	1.03227	−	1.29442i	0.954743	−	0.297431i	$-0.0961297\pi$
$54$		0			0
$55$	14.4541	−	9.08214i	1.94900	−	1.22464i
$56$		0			0
$57$			1.61995i			0.214567i
$58$		0			0
$59$			8.01950i			1.04405i	0.852930	+	0.522025i	$0.174823\pi$
$59$			8.01950i			1.04405i	−0.852930	+	0.522025i	$0.825177\pi$
$60$		0			0
$61$	−12.4768	+	7.83971i	−1.59749	+	1.00377i	−0.622201	+	0.782858i	$0.713761\pi$
$61$	−12.4768	+	7.83971i	−1.59749	+	1.00377i	−0.975293	+	0.220914i	$0.929096\pi$
$62$		0			0
$63$	−0.958388	+	1.20178i	−0.120746	+	0.151410i
$64$		0			0
$65$	1.02881	−	4.50751i	0.127608	−	0.559088i
$66$		0			0
$67$	−2.21191	−	1.06520i	−0.270228	−	0.130135i	0.293863	−	0.955848i	$-0.405059\pi$
$67$	−2.21191	−	1.06520i	−0.270228	−	0.130135i	−0.564091	+	0.825713i	$0.690773\pi$
$68$		0			0
$69$	0.757669	+	0.265120i	0.0912126	+	0.0319167i
$70$		0			0
$71$	−4.92140	+	2.37002i	−0.584063	+	0.281270i	−0.702491	−	0.711693i	$-0.747929\pi$
$71$	−4.92140	+	2.37002i	−0.584063	+	0.281270i	0.118428	+	0.992963i	$0.462214\pi$
$72$		0			0
$73$	−4.92030	−	0.554385i	−0.575878	−	0.0648859i	−0.180778	−	0.983524i	$-0.557862\pi$
$73$	−4.92030	−	0.554385i	−0.575878	−	0.0648859i	−0.395100	+	0.918638i	$0.629290\pi$
$74$		0			0
$75$	4.19858	−	4.19858i	0.484810	−	0.484810i
$76$		0			0
$77$	7.76208	−	12.3533i	0.884571	−	1.40779i
$78$		0			0
$79$	−6.57935	+	2.30221i	−0.740234	+	0.259019i	−0.673945	−	0.738781i	$-0.735402\pi$
$79$	−6.57935	+	2.30221i	−0.740234	+	0.259019i	−0.0662890	+	0.997800i	$0.521116\pi$
$80$		0			0
$81$	4.25149	+	5.33120i	0.472388	+	0.592355i
$82$		0			0
$83$	10.2799	−	2.34632i	1.12837	−	0.257542i	0.382707	−	0.923870i	$-0.374992\pi$
$83$	10.2799	−	2.34632i	1.12837	−	0.257542i	0.745659	+	0.666328i	$0.232135\pi$
$84$		0			0
$85$	−2.38961	−	21.2084i	−0.259190	−	2.30038i
$86$		0			0
$87$	−3.06198	+	7.75103i	−0.328278	+	0.830998i
$88$		0			0
$89$	−2.88852	+	0.325458i	−0.306183	+	0.0344985i	−0.263719	−	0.964600i	$-0.584949\pi$
$89$	−2.88852	+	0.325458i	−0.306183	+	0.0344985i	−0.0424636	+	0.999098i	$0.513521\pi$
$90$		0			0
$91$	−0.879275	−	3.85236i	−0.0921731	−	0.403837i
$92$		0			0
$93$	−2.24768	+	1.79247i	−0.233074	+	0.185870i
$94$		0			0
$95$	1.02773	+	2.93708i	0.105443	+	0.301338i
$96$		0			0
$97$	−0.0192149	−	0.0120735i	−0.00195098	−	0.00122588i	0.531056	−	0.847337i	$-0.321795\pi$
$97$	−0.0192149	−	0.0120735i	−0.00195098	−	0.00122588i	−0.533007	+	0.846111i	$0.678938\pi$
$98$		0			0
$99$	2.45676	+	2.45676i	0.246914	+	0.246914i
$100$		0			0
$101$	−0.418477	+	3.71408i	−0.0416400	+	0.369565i	0.955561	+	0.294794i	$0.0952511\pi$
$101$	−0.418477	+	3.71408i	−0.0416400	+	0.369565i	−0.997201	+	0.0747709i	$0.976177\pi$
$102$		0			0
$103$	−0.287652	−	0.597315i	−0.0283432	−	0.0588552i	0.886317	−	0.463080i	$-0.153256\pi$
$103$	−0.287652	−	0.597315i	−0.0283432	−	0.0588552i	−0.914660	+	0.404225i	$0.867541\pi$
$104$		0			0
$105$	3.86025	−	11.0320i	0.376722	−	1.07661i
$106$		0			0
$107$	8.11361	−	16.8481i	0.784372	−	1.62877i	0.00679537	−	0.999977i	$-0.497837\pi$
$107$	8.11361	−	16.8481i	0.784372	−	1.62877i	0.777577	−	0.628788i	$-0.216449\pi$
$108$		0			0
$109$	−0.0679013	−	0.0154980i	−0.00650376	−	0.00148444i	0.219268	−	0.975665i	$-0.429633\pi$
$109$	−0.0679013	−	0.0154980i	−0.00650376	−	0.00148444i	−0.225772	+	0.974180i	$0.572490\pi$
$110$		0			0
$111$	6.58945	+	5.25491i	0.625443	+	0.498774i
$112$		0			0
$113$	0.919112	+	1.46276i	0.0864628	+	0.137605i	0.887156	−	0.461470i	$-0.152678\pi$
$113$	0.919112	+	1.46276i	0.0864628	+	0.137605i	−0.800693	+	0.599075i	$0.795535\pi$
$114$		0			0
$115$	1.54191			0.143784
$116$		0			0
$117$	0.941005			0.0869960
$118$		0			0
$119$	−9.70455	−	15.4447i	−0.889615	−	1.41581i
$120$		0			0
$121$	−17.1821	−	13.7022i	−1.56200	−	1.24566i
$122$		0			0
$123$	11.0078	+	2.51245i	0.992537	+	0.226540i
$124$		0			0
$125$	−1.50031	+	3.11544i	−0.134192	+	0.278653i
$126$		0			0
$127$	6.15227	−	17.5822i	0.545926	−	1.56017i	−0.258437	−	0.966028i	$-0.583207\pi$
$127$	6.15227	−	17.5822i	0.545926	−	1.56017i	0.804363	−	0.594138i	$-0.202507\pi$
$128$		0			0
$129$	6.86499	+	14.2553i	0.604428	+	1.25511i
$130$		0			0
$131$	−0.841249	+	7.46629i	−0.0735003	+	0.652333i	0.901908	+	0.431928i	$0.142167\pi$
$131$	−0.841249	+	7.46629i	−0.0735003	+	0.652333i	−0.975408	+	0.220405i	$0.929262\pi$
$132$		0			0
$133$	1.88050	+	1.88050i	0.163060	+	0.163060i
$134$		0			0
$135$	14.0426	+	8.82356i	1.20860	+	0.759411i
$136$		0			0
$137$	5.12448	+	14.6449i	0.437814	+	1.25120i	0.925688	+	0.378287i	$0.123487\pi$
$137$	5.12448	+	14.6449i	0.437814	+	1.25120i	−0.487874	+	0.872914i	$0.662228\pi$
$138$		0			0
$139$	14.8997	−	11.8821i	1.26378	−	1.00783i	0.264725	−	0.964324i	$-0.414719\pi$
$139$	14.8997	−	11.8821i	1.26378	−	1.00783i	0.999053	−	0.0435055i	$-0.0138526\pi$
$140$		0			0
$141$	−1.27220	−	5.57389i	−0.107139	−	0.469406i
$142$		0			0
$143$	−8.87526	+	1.00000i	−0.742187	+	0.0836243i
$144$		0			0
$145$	−0.634163	+	15.9958i	−0.0526644	+	1.32838i
$146$		0			0
$147$	0.0944910	+	0.838631i	0.00779349	+	0.0691691i
$148$		0			0
$149$	−18.8568	+	4.30394i	−1.54481	+	0.352593i	−0.908181	−	0.418578i	$-0.862529\pi$
$149$	−18.8568	+	4.30394i	−1.54481	+	0.352593i	−0.636628	+	0.771171i	$0.719671\pi$
$150$		0			0
$151$	−2.25472	−	2.82733i	−0.183486	−	0.230085i	0.681578	−	0.731745i	$-0.261294\pi$
$151$	−2.25472	−	2.82733i	−0.183486	−	0.230085i	−0.865064	+	0.501661i	$0.832723\pi$
$152$		0			0
$153$	4.10009	−	1.43469i	0.331473	−	0.115987i
$154$		0			0
$155$	−2.93803	+	4.67585i	−0.235988	+	0.375573i
$156$		0			0
$157$	−1.21363	+	1.21363i	−0.0968584	+	0.0968584i	−0.753876	−	0.657017i	$-0.771818\pi$
$157$	−1.21363	+	1.21363i	−0.0968584	+	0.0968584i	0.657017	+	0.753876i	$0.271818\pi$
$158$		0			0
$159$	−18.5358	−	2.08848i	−1.46998	−	0.165627i
$160$		0			0
$161$	1.18729	−	0.571770i	0.0935718	−	0.0450618i
$162$		0			0
$163$	18.9617	+	6.63499i	1.48520	+	0.519692i	0.946471	−	0.322789i	$-0.104621\pi$
$163$	18.9617	+	6.63499i	1.48520	+	0.519692i	0.538725	+	0.842482i	$0.318906\pi$
$164$		0			0
$165$	−23.8018	−	11.4624i	−1.85297	−	0.892344i
$166$		0			0
$167$	1.96549	−	8.61137i	0.152094	−	0.666368i	−0.840181	−	0.542307i	$-0.817551\pi$
$167$	1.96549	−	8.61137i	0.152094	−	0.666368i	0.992275	−	0.124061i	$-0.0395918\pi$
$168$		0			0
$169$	6.59715	−	8.27257i	0.507473	−	0.636351i
$170$		0			0
$171$	−0.536251	+	0.336949i	−0.0410081	+	0.0257671i
$172$		0			0
$173$			8.38655i			0.637617i	0.947819	+	0.318809i	$0.103283\pi$
$173$			8.38655i			0.637617i	−0.947819	+	0.318809i	$0.896717\pi$
$174$		0			0
$175$		−	9.74774i		−	0.736860i
$176$		0			0
$177$	10.5085	−	6.60291i	0.789865	−	0.496305i
$178$		0			0
$179$	−7.24834	+	9.08913i	−0.541766	+	0.679353i	−0.975071	−	0.221894i	$-0.928776\pi$
$179$	−7.24834	+	9.08913i	−0.541766	+	0.679353i	0.433305	+	0.901248i	$0.357347\pi$
$180$		0			0
$181$	−1.77618	+	7.78196i	−0.132023	+	0.578429i	0.865031	+	0.501719i	$0.167299\pi$
$181$	−1.77618	+	7.78196i	−0.132023	+	0.578429i	−0.997053	+	0.0767100i	$0.975558\pi$
$182$		0			0
$183$	20.5458	+	9.89432i	1.51879	+	0.731409i
$184$		0			0
$185$	15.2810	+	5.34704i	1.12348	+	0.393122i
$186$		0			0
$187$	−37.1461	+	17.8886i	−2.71640	+	1.30815i
$188$		0			0
$189$	14.0850	+	1.58700i	1.02453	+	0.115437i
$190$		0			0
$191$	−11.0701	+	11.0701i	−0.801003	+	0.801003i	−0.983252	−	0.182249i	$-0.941662\pi$
$191$	−11.0701	+	11.0701i	−0.801003	+	0.801003i	0.182249	+	0.983252i	$0.441662\pi$
$192$		0			0
$193$	4.98727	−	7.93719i	0.358991	−	0.571331i	−0.617585	−	0.786504i	$-0.711889\pi$
$193$	4.98727	−	7.93719i	0.358991	−	0.571331i	0.976576	+	0.215173i	$0.0690316\pi$
$194$		0			0
$195$	−6.75356	+	2.36317i	−0.483632	+	0.169230i
$196$		0			0
$197$	−4.30109	−	5.39339i	−0.306440	−	0.384263i	0.604636	−	0.796502i	$-0.293318\pi$
$197$	−4.30109	−	5.39339i	−0.306440	−	0.384263i	−0.911076	+	0.412238i	$0.864747\pi$
$198$		0			0
$199$	−22.4820	+	5.13136i	−1.59370	+	0.363753i	−0.925058	−	0.379827i	$-0.875984\pi$
$199$	−22.4820	+	5.13136i	−1.59370	+	0.363753i	−0.668647	+	0.743580i	$0.733126\pi$
$200$		0			0
$201$	0.425392	+	3.77545i	0.0300048	+	0.266300i
$202$		0			0
$203$	5.44324	+	12.5522i	0.382040	+	0.880989i
$204$		0			0
$205$	21.5518	−	2.42831i	1.50524	−	0.169600i
$206$		0			0
$207$	0.0698324	+	0.305956i	0.00485369	+	0.0212654i
$208$		0			0
$209$	4.69967	−	3.74786i	0.325083	−	0.259245i
$210$		0			0
$211$	−7.85722	−	22.4546i	−0.540913	−	1.54584i	−0.812222	−	0.583348i	$-0.801742\pi$
$211$	−7.85722	−	22.4546i	−0.540913	−	1.54584i	0.271309	−	0.962492i	$-0.412543\pi$
$212$		0			0
$213$	7.15766	+	4.49746i	0.490435	+	0.308161i
$214$		0			0
$215$	21.4906	+	21.4906i	1.46564	+	1.46564i
$216$		0			0
$217$	−0.528431	+	4.68996i	−0.0358723	+	0.318375i
$218$		0			0
$219$	3.32472	+	6.90385i	0.224664	+	0.466519i
$220$		0			0
$221$	−3.68807	+	10.5399i	−0.248086	+	0.708990i
$222$		0			0
$223$	0.307371	−	0.638262i	0.0205831	−	0.0427412i	−0.890424	−	0.455132i	$-0.849592\pi$
$223$	0.307371	−	0.638262i	0.0205831	−	0.0427412i	0.911007	+	0.412391i	$0.135306\pi$
$224$		0			0
$225$	2.26316	+	0.516550i	0.150877	+	0.0344367i
$226$		0			0
$227$	−15.8089	−	12.6072i	−1.04927	−	0.836769i	−0.0623667	−	0.998053i	$-0.519865\pi$
$227$	−15.8089	−	12.6072i	−1.04927	−	0.836769i	−0.986908	+	0.161285i	$0.948436\pi$
$228$		0			0
$229$	−2.89574	−	4.60855i	−0.191356	−	0.304542i	0.737242	−	0.675629i	$-0.236128\pi$
$229$	−2.89574	−	4.60855i	−0.191356	−	0.304542i	−0.928598	+	0.371087i	$0.878985\pi$
$230$		0			0
$231$	−22.5783			−1.48554
$232$		0			0
$233$	−8.11633			−0.531719			−0.265859	−	0.964012i	$-0.585656\pi$
$233$	−8.11633			−0.531719			−0.265859	+	0.964012i	$0.585656\pi$
$234$		0			0
$235$	−5.84279	−	9.29875i	−0.381142	−	0.606584i
$236$		0			0
$237$	8.43389	+	6.72580i	0.547840	+	0.436888i
$238$		0			0
$239$	5.89664	+	1.34587i	0.381422	+	0.0870571i	0.408933	−	0.912564i	$-0.365901\pi$
$239$	5.89664	+	1.34587i	0.381422	+	0.0870571i	−0.0275110	+	0.999622i	$0.508758\pi$
$240$		0			0
$241$	−0.630445	+	1.30913i	−0.0406105	+	0.0843287i	−0.920287	−	0.391244i	$-0.872045\pi$
$241$	−0.630445	+	1.30913i	−0.0406105	+	0.0843287i	0.879676	+	0.475573i	$0.157759\pi$
$242$		0			0
$243$	−2.04259	+	5.83738i	−0.131032	+	0.374468i
$244$		0			0
$245$	0.703365	+	1.46055i	0.0449363	+	0.0933112i
$246$		0			0
$247$	0.182284	−	1.61781i	0.0115984	−	0.102939i
$248$		0			0
$249$	−11.5386	−	11.5386i	−0.731227	−	0.731227i
$250$		0			0
$251$	−2.71367	−	1.70511i	−0.171285	−	0.107626i	0.443661	−	0.896195i	$-0.353679\pi$
$251$	−2.71367	−	1.70511i	−0.171285	−	0.107626i	−0.614946	+	0.788569i	$0.710822\pi$
$252$		0			0
$253$	−0.983774	−	2.81147i	−0.0618494	−	0.176755i
$254$		0			0
$255$	−25.8233	+	20.5934i	−1.61712	+	1.28961i
$256$		0			0
$257$	−2.08608	−	9.13971i	−0.130126	−	0.570120i	−0.997386	−	0.0722632i	$-0.976978\pi$
$257$	−2.08608	−	9.13971i	−0.130126	−	0.570120i	0.867260	−	0.497856i	$-0.165879\pi$
$258$		0			0
$259$	13.7494	−	1.54918i	0.854345	−	0.0962616i
$260$		0			0
$261$	−3.20271	+	0.598607i	−0.198243	+	0.0370529i
$262$		0			0
$263$	1.21678	+	10.7992i	0.0750299	+	0.665909i	0.973787	+	0.227462i	$0.0730427\pi$
$263$	1.21678	+	10.7992i	0.0750299	+	0.665909i	−0.898757	+	0.438447i	$0.855529\pi$
$264$		0			0
$265$	−34.9317	+	7.97294i	−2.14584	+	0.489774i
$266$		0			0
$267$	2.80475	+	3.51705i	0.171648	+	0.215240i
$268$		0			0
$269$	18.9216	−	6.62095i	1.15367	−	0.403686i	0.315408	−	0.948956i	$-0.397859\pi$
$269$	18.9216	−	6.62095i	1.15367	−	0.403686i	0.838261	+	0.545270i	$0.183573\pi$
$270$		0			0
$271$	−0.0862405	+	0.137251i	−0.00523873	+	0.00833740i	−0.849333	−	0.527857i	$-0.822996\pi$
$271$	−0.0862405	+	0.137251i	−0.00523873	+	0.00833740i	0.844095	+	0.536194i	$0.180139\pi$
$272$		0			0
$273$	−4.32404	+	4.32404i	−0.261703	+	0.261703i
$274$		0			0
$275$	−21.8943	−	2.46689i	−1.32028	−	0.148759i
$276$		0			0
$277$	−14.2634	+	6.86891i	−0.857007	+	0.412713i	−0.810174	−	0.586190i	$-0.800627\pi$
$277$	−14.2634	+	6.86891i	−0.857007	+	0.412713i	−0.0468332	+	0.998903i	$0.514913\pi$
$278$		0			0
$279$	−1.06088	−	0.371217i	−0.0635130	−	0.0222242i
$280$		0			0
$281$	−12.4582	−	5.99954i	−0.743193	−	0.357903i	0.0236649	−	0.999720i	$-0.492467\pi$
$281$	−12.4582	−	5.99954i	−0.743193	−	0.357903i	−0.766858	+	0.641817i	$0.778181\pi$
$282$		0			0
$283$	0.174871	−	0.766159i	0.0103950	−	0.0455434i	−0.969464	−	0.245232i	$-0.921136\pi$
$283$	0.174871	−	0.766159i	0.0103950	−	0.0455434i	0.979859	+	0.199689i	$0.0639930\pi$
$284$		0			0
$285$	3.00246	−	3.76497i	0.177850	−	0.223017i
$286$		0			0
$287$	15.6948	−	9.86168i	0.926434	−	0.582117i
$288$		0			0
$289$			34.5467i			2.03216i
$290$		0			0
$291$			0.0351194i			0.00205874i
$292$		0			0
$293$	−0.353741	+	0.222270i	−0.0206658	+	0.0129852i	−0.542325	−	0.840169i	$-0.682456\pi$
$293$	−0.353741	+	0.222270i	−0.0206658	+	0.0129852i	0.521660	+	0.853154i	$0.325313\pi$
$294$		0			0
$295$	14.8636	−	18.6383i	0.865391	−	1.08517i
$296$		0			0
$297$	7.12907	−	31.2345i	0.413671	−	1.81241i
$298$		0			0
$299$	−0.726838	−	0.350027i	−0.0420341	−	0.0202426i
$300$		0			0
$301$	24.5172	+	8.57895i	1.41315	+	0.494482i
$302$		0			0
$303$	5.21136	−	2.50966i	0.299385	−	0.144176i
$304$		0			0
$305$	43.5281	+	4.90444i	2.49241	+	0.280827i
$306$		0			0
$307$	−6.78309	+	6.78309i	−0.387132	+	0.387132i	−0.873663	−	0.486531i	$-0.838262\pi$
$307$	−6.78309	+	6.78309i	−0.387132	+	0.387132i	0.486531	+	0.873663i	$0.338262\pi$
$308$		0			0
$309$	−0.545861	+	0.868733i	−0.0310529	+	0.0494205i
$310$		0			0
$311$	−16.4157	+	5.74410i	−0.930849	+	0.325718i	−0.752759	−	0.658296i	$-0.771277\pi$
$311$	−16.4157	+	5.74410i	−0.930849	+	0.325718i	−0.178090	+	0.984014i	$0.556992\pi$
$312$		0			0
$313$	12.8999	+	16.1759i	0.729144	+	0.914318i	0.998817	−	0.0486340i	$-0.0154868\pi$
$313$	12.8999	+	16.1759i	0.729144	+	0.914318i	−0.269672	+	0.962952i	$0.586915\pi$
$314$		0			0
$315$	4.45483	−	1.01679i	0.251001	−	0.0572894i
$316$		0			0
$317$	2.64628	+	23.4864i	0.148630	+	1.31913i	0.817578	+	0.575818i	$0.195316\pi$
$317$	2.64628	+	23.4864i	0.148630	+	1.31913i	−0.668948	+	0.743309i	$0.733255\pi$
$318$		0			0
$319$	29.5708	−	9.04938i	1.65565	−	0.506668i
$320$		0			0
$321$	−28.7575	+	3.24019i	−1.60509	+	0.180850i
$322$		0			0
$323$	−1.67233	−	7.32696i	−0.0930510	−	0.407683i
$324$		0			0
$325$	−4.66549	+	3.72060i	−0.258795	+	0.206382i
$326$		0			0
$327$	0.0355989	+	0.101736i	0.00196862	+	0.00562601i
$328$		0			0
$329$	−7.94721	−	4.99356i	−0.438144	−	0.275304i
$330$		0			0
$331$	−10.9412	−	10.9412i	−0.601380	−	0.601380i	0.339298	−	0.940679i	$-0.389810\pi$
$331$	−10.9412	−	10.9412i	−0.601380	−	0.601380i	−0.940679	+	0.339298i	$0.889810\pi$
$332$		0			0
$333$	−0.368927	+	3.27432i	−0.0202171	+	0.179432i
$334$		0			0
$335$	3.16649	+	6.57529i	0.173004	+	0.359247i
$336$		0			0
$337$	8.14791	−	23.2854i	0.443845	−	1.26844i	−0.477136	−	0.878829i	$-0.658325\pi$
$337$	8.14791	−	23.2854i	0.443845	−	1.26844i	0.920981	−	0.389607i	$-0.127389\pi$
$338$		0			0
$339$	1.15999	−	2.40874i	0.0630020	−	0.130825i
$340$		0			0
$341$	10.4003	+	2.37381i	0.563210	+	0.128549i
$342$		0			0
$343$	14.9875	+	11.9521i	0.809248	+	0.645353i
$344$		0			0
$345$	−1.26954	−	2.02046i	−0.0683497	−	0.108778i
$346$		0			0
$347$	1.38821			0.0745230			0.0372615	−	0.999306i	$-0.488137\pi$
$347$	1.38821			0.0745230			0.0372615	+	0.999306i	$0.488137\pi$
$348$		0			0
$349$	27.1106			1.45119			0.725597	−	0.688119i	$-0.241564\pi$
$349$	27.1106			1.45119			0.725597	+	0.688119i	$0.241564\pi$
$350$		0			0
$351$	−4.61651	−	7.34713i	−0.246411	−	0.392161i
$352$		0			0
$353$	−24.5630	−	19.5884i	−1.30736	−	1.04258i	−0.995724	−	0.0923808i	$-0.970552\pi$
$353$	−24.5630	−	19.5884i	−1.30736	−	1.04258i	−0.311634	−	0.950202i	$-0.600876\pi$
$354$		0			0
$355$	15.8306	+	3.61324i	0.840203	+	0.191771i
$356$		0			0
$357$	−12.2479	+	25.4330i	−0.648227	+	1.34606i
$358$		0			0
$359$	10.2703	−	29.3509i	0.542048	−	1.54908i	−0.268421	−	0.963302i	$-0.586502\pi$
$359$	10.2703	−	29.3509i	0.542048	−	1.54908i	0.810469	−	0.585782i	$-0.199212\pi$
$360$		0			0
$361$	−7.76837	−	16.1312i	−0.408862	−	0.849010i
$362$		0			0
$363$	−3.80796	+	33.7966i	−0.199866	+	1.77386i
$364$		0			0
$365$	10.4079	+	10.4079i	0.544775	+	0.544775i
$366$		0			0
$367$	−13.8633	−	8.71091i	−0.723660	−	0.454706i	0.119178	−	0.992873i	$-0.461974\pi$
$367$	−13.8633	−	8.71091i	−0.723660	−	0.454706i	−0.842838	+	0.538167i	$0.819117\pi$
$368$		0			0
$369$	1.45792	+	4.16648i	0.0758960	+	0.216898i
$370$		0			0
$371$	−23.9415	+	19.0927i	−1.24298	+	0.991242i
$372$		0			0
$373$	−2.19756	−	9.62815i	−0.113785	−	0.498527i	−0.999417	−	0.0341384i	$-0.989131\pi$
$373$	−2.19756	−	9.62815i	−0.113785	−	0.498527i	0.885632	−	0.464388i	$-0.153726\pi$
$374$		0			0
$375$	5.31765	−	0.599156i	0.274602	−	0.0309403i
$376$		0			0
$377$	3.93012	−	7.39627i	0.202412	−	0.380927i
$378$		0			0
$379$	3.51508	+	31.1972i	0.180558	+	1.60249i	0.678044	+	0.735022i	$0.262828\pi$
$379$	3.51508	+	31.1972i	0.180558	+	1.60249i	−0.497486	+	0.867472i	$0.665743\pi$
$380$		0			0
$381$	−28.1046	+	6.41469i	−1.43984	+	0.328634i
$382$		0			0
$383$	15.7683	+	19.7729i	0.805724	+	1.01035i	0.999570	+	0.0293144i	$0.00933239\pi$
$383$	15.7683	+	19.7729i	0.805724	+	1.01035i	−0.193846	+	0.981032i	$0.562096\pi$
$384$		0			0
$385$	−40.9360	+	14.3241i	−2.08629	+	0.730026i
$386$		0			0
$387$	−3.29101	+	5.23761i	−0.167291	+	0.266243i
$388$		0			0
$389$	25.6964	−	25.6964i	1.30286	−	1.30286i	0.376404	−	0.926456i	$-0.377160\pi$
$389$	25.6964	−	25.6964i	1.30286	−	1.30286i	0.926456	−	0.376404i	$-0.122840\pi$
$390$		0			0
$391$	−3.70060	−	0.416958i	−0.187147	−	0.0210864i
$392$		0			0
$393$	10.4762	−	5.04508i	0.528455	−	0.254491i
$394$		0			0
$395$	19.5582	+	6.84372i	0.984082	+	0.344345i
$396$		0			0
$397$	25.0854	+	12.0805i	1.25900	+	0.606304i	0.939911	−	0.341420i	$-0.110908\pi$
$397$	25.0854	+	12.0805i	1.25900	+	0.606304i	0.319092	+	0.947724i	$0.396622\pi$
$398$		0			0
$399$	0.915818	−	4.01246i	0.0458482	−	0.200874i
$400$		0			0
$401$	−3.09115	+	3.87618i	−0.154365	+	0.193567i	−0.853000	−	0.521910i	$-0.825219\pi$
$401$	−3.09115	+	3.87618i	−0.154365	+	0.193567i	0.698636	+	0.715478i	$0.253791\pi$
$402$		0			0
$403$	2.44642	−	1.53719i	0.121865	−	0.0765727i
$404$		0			0
$405$		−	20.2702i		−	1.00724i
$406$		0			0
$407$		−	31.2744i		−	1.55021i
$408$		0			0
$409$	−8.20860	+	5.15781i	−0.405889	+	0.255037i	−0.719469	−	0.694525i	$-0.755615\pi$
$409$	−8.20860	+	5.15781i	−0.405889	+	0.255037i	0.313580	+	0.949562i	$0.398472\pi$
$410$		0			0
$411$	14.9709	−	18.7729i	0.738461	−	0.926001i
$412$		0			0
$413$	4.53372	−	19.8635i	0.223090	−	0.977421i
$414$		0			0
$415$	−28.2406	−	13.5999i	−1.38627	−	0.667595i
$416$		0			0
$417$	−27.8377	−	9.74084i	−1.36322	−	0.477011i
$418$		0			0
$419$	18.8605	−	9.08272i	0.921394	−	0.443720i	0.0878253	−	0.996136i	$-0.472008\pi$
$419$	18.8605	−	9.08272i	0.921394	−	0.443720i	0.833569	+	0.552416i	$0.186294\pi$
$420$		0			0
$421$	−6.95615	−	0.783770i	−0.339022	−	0.0381986i	−0.0591876	−	0.998247i	$-0.518851\pi$
$421$	−6.95615	−	0.783770i	−0.339022	−	0.0381986i	−0.279834	+	0.960048i	$0.590280\pi$
$422$		0			0
$423$	1.58050	−	1.58050i	0.0768468	−	0.0768468i
$424$		0			0
$425$	−14.6557	+	23.3243i	−0.710904	+	1.13140i
$426$		0			0
$427$	35.3360	−	12.3646i	1.71003	−	0.598365i
$428$		0			0
$429$	8.61787	+	10.8065i	0.416075	+	0.521741i
$430$		0			0
$431$	30.9686	−	7.06837i	1.49170	−	0.340472i	0.602550	−	0.798081i	$-0.294151\pi$
$431$	30.9686	−	7.06837i	1.49170	−	0.340472i	0.889153	+	0.457609i	$0.151294\pi$
$432$		0			0
$433$	−2.05748	−	18.2607i	−0.0988763	−	0.877551i	−0.941032	−	0.338317i	$-0.890142\pi$
$433$	−2.05748	−	18.2607i	−0.0988763	−	0.877551i	0.842156	−	0.539234i	$-0.181286\pi$
$434$		0			0
$435$	21.4824	−	12.3392i	1.03000	−	0.591621i
$436$		0			0
$437$	0.539539	−	0.0607914i	0.0258096	−	0.00290805i
$438$		0			0
$439$	−7.66537	−	33.5842i	−0.365848	−	1.60289i	−0.738058	−	0.674737i	$-0.764257\pi$
$439$	−7.66537	−	33.5842i	−0.365848	−	1.60289i	0.372210	−	0.928148i	$-0.378600\pi$
$440$		0			0
$441$	−0.257958	+	0.205714i	−0.0122837	+	0.00979592i
$442$		0			0
$443$	−7.27895	−	20.8021i	−0.345834	−	0.988336i	−0.977102	−	0.212771i	$-0.931751\pi$
$443$	−7.27895	−	20.8021i	−0.345834	−	0.988336i	0.631269	−	0.775564i	$-0.282535\pi$
$444$		0			0
$445$	7.31651	+	4.59727i	0.346836	+	0.217931i
$446$		0			0
$447$	21.1656	+	21.1656i	1.00110	+	1.00110i
$448$		0			0
$449$	1.46602	−	13.0113i	0.0691858	−	0.614041i	−0.910501	−	0.413507i	$-0.864304\pi$
$449$	1.46602	−	13.0113i	0.0691858	−	0.614041i	0.979687	−	0.200534i	$-0.0642677\pi$
$450$		0			0
$451$	−18.1783	−	37.7476i	−0.855982	−	1.77747i
$452$		0			0
$453$	−1.84839	+	5.28241i	−0.0868451	+	0.248189i
$454$		0			0
$455$	−5.09653	+	10.5831i	−0.238929	+	0.496141i
$456$		0			0
$457$	−33.1983	−	7.57729i	−1.55295	−	0.354451i	−0.641914	−	0.766776i	$-0.721859\pi$
$457$	−33.1983	−	7.57729i	−1.55295	−	0.354451i	−0.911037	+	0.412326i	$0.864717\pi$
$458$		0			0
$459$	−31.3165	−	24.9740i	−1.46173	−	1.16569i
$460$		0			0
$461$	−2.05600	−	3.27211i	−0.0957576	−	0.152397i	0.795410	−	0.606072i	$-0.207256\pi$
$461$	−2.05600	−	3.27211i	−0.0957576	−	0.152397i	−0.891167	+	0.453675i	$0.850113\pi$
$462$		0			0
$463$	−2.38429			−0.110807			−0.0554036	−	0.998464i	$-0.517645\pi$
$463$	−2.38429			−0.110807			−0.0554036	+	0.998464i	$0.517645\pi$
$464$		0			0
$465$	8.54611			0.396317
$466$		0			0
$467$	2.64301	+	4.20632i	0.122304	+	0.194645i	0.902264	−	0.431183i	$-0.141904\pi$
$467$	2.64301	+	4.20632i	0.122304	+	0.194645i	−0.779961	+	0.625829i	$0.784761\pi$
$468$		0			0
$469$	4.87650	+	3.88888i	0.225176	+	0.179572i
$470$		0			0
$471$	2.58955	+	0.591049i	0.119320	+	0.0272341i
$472$		0			0
$473$	25.4737	−	52.8968i	1.17128	−	2.43220i
$474$		0			0
$475$	1.32647	−	3.79084i	0.0608628	−	0.173936i
$476$		0			0
$477$	−3.16409	−	6.57030i	−0.144874	−	0.300833i
$478$		0			0
$479$	−2.88117	+	25.5711i	−0.131644	+	1.16837i	0.738038	+	0.674760i	$0.235753\pi$
$479$	−2.88117	+	25.5711i	−0.131644	+	1.16837i	−0.869682	+	0.493613i	$0.835676\pi$
$480$		0			0
$481$	−5.98946	−	5.98946i	−0.273096	−	0.273096i
$482$		0			0
$483$	−1.72679	−	1.08502i	−0.0785718	−	0.0493699i
$484$		0			0
$485$	0.0222805	+	0.0636740i	0.00101171	+	0.00289129i
$486$		0			0
$487$	−23.1511	+	18.4624i	−1.04908	+	0.836610i	−0.986880	−	0.161454i	$-0.948382\pi$
$487$	−23.1511	+	18.4624i	−1.04908	+	0.836610i	−0.0621951	+	0.998064i	$0.519810\pi$
$488$		0			0
$489$	−6.91800	−	30.3097i	−0.312843	−	1.37065i
$490$		0			0
$491$	30.7117	−	3.46038i	1.38600	−	0.156165i	0.612756	−	0.790272i	$-0.290061\pi$
$491$	30.7117	−	3.46038i	1.38600	−	0.156165i	0.773245	+	0.634107i	$0.218632\pi$
$492$		0			0
$493$	5.84753	−	38.2186i	0.263359	−	1.72128i
$494$		0			0
$495$	−1.15639	−	10.2633i	−0.0519760	−	0.461300i
$496$		0			0
$497$	13.5297	−	3.08807i	0.606890	−	0.138519i
$498$		0			0
$499$	22.7692	+	28.5516i	1.01929	+	1.27815i	0.960028	+	0.279904i	$0.0903027\pi$
$499$	22.7692	+	28.5516i	1.01929	+	1.27815i	0.0592600	+	0.998243i	$0.481126\pi$
$500$		0			0
$501$	−12.9023	+	4.51472i	−0.576434	+	0.201703i
$502$		0			0
$503$	−10.7426	+	17.0968i	−0.478989	+	0.762307i	−0.995579	−	0.0939258i	$-0.970058\pi$
$503$	−10.7426	+	17.0968i	−0.478989	+	0.762307i	0.516590	+	0.856233i	$0.327201\pi$
$504$		0			0
$505$	7.85639	−	7.85639i	0.349605	−	0.349605i
$506$		0			0
$507$	−16.2719	−	1.83340i	−0.722660	−	0.0814242i
$508$		0			0
$509$	−32.8506	+	15.8200i	−1.45608	+	0.701211i	−0.983639	−	0.180152i	$-0.942341\pi$
$509$	−32.8506	+	15.8200i	−1.45608	+	0.701211i	−0.472440	+	0.881363i	$0.656627\pi$
$510$		0			0
$511$	11.8737	+	4.15479i	0.525262	+	0.183797i
$512$		0			0
$513$	5.26162	+	2.53386i	0.232306	+	0.111873i
$514$		0			0
$515$	−0.438543	+	1.92138i	−0.0193245	+	0.0846661i
$516$		0			0
$517$	−13.2272	+	16.5864i	−0.581732	+	0.729469i
$518$		0			0
$519$	10.9894	−	6.90512i	0.482383	−	0.303101i
$520$		0			0
$521$			11.6841i			0.511891i	0.966691	+	0.255946i	$0.0823868\pi$
$521$			11.6841i			0.511891i	−0.966691	+	0.255946i	$0.917613\pi$
$522$		0			0
$523$		−	25.8163i		−	1.12887i	−0.825478	−	0.564434i	$-0.809095\pi$
$523$		−	25.8163i		−	1.12887i	0.825478	−	0.564434i	$-0.190905\pi$
$524$		0			0
$525$	−12.7731	+	8.02587i	−0.557463	+	0.350278i
$526$		0			0
$527$	8.31575	−	10.4276i	0.362240	−	0.454234i
$528$		0			0
$529$	−5.05811	+	22.1610i	−0.219918	+	0.963524i
$530$		0			0
$531$	4.37152	+	2.10521i	0.189708	+	0.0913584i
$532$		0			0
$533$	−10.7105	−	3.74778i	−0.463925	−	0.162334i
$534$		0			0
$535$	−50.0838	+	24.1191i	−2.16531	+	1.04276i
$536$		0			0
$537$	17.8780	+	2.01437i	0.771494	+	0.0869265i
$538$		0			0
$539$	2.21436	−	2.21436i	0.0953793	−	0.0953793i
$540$		0			0
$541$	14.7829	−	23.5268i	0.635566	−	1.01150i	−0.361305	−	0.932448i	$-0.617669\pi$
$541$	14.7829	−	23.5268i	0.635566	−	1.01150i	0.996871	−	0.0790496i	$-0.0251885\pi$
$542$		0			0
$543$	11.6596	−	4.07988i	0.500363	−	0.175085i
$544$		0			0
$545$	0.129087	+	0.161870i	0.00552947	+	0.00693374i
$546$		0			0
$547$	−18.0555	+	4.12105i	−0.771997	+	0.176203i	−0.590336	−	0.807158i	$-0.701005\pi$
$547$	−18.0555	+	4.12105i	−0.771997	+	0.176203i	−0.181661	+	0.983361i	$0.558147\pi$
$548$		0			0
$549$	0.998200	+	8.85927i	0.0426021	+	0.378104i
$550$		0			0
$551$	0.408747	+	5.62218i	0.0174132	+	0.239513i
$552$		0			0
$553$	17.5979	−	1.98281i	0.748341	−	0.0843178i
$554$		0			0
$555$	−5.57511	−	24.4262i	−0.236650	−	1.03683i
$556$		0			0
$557$	−20.2320	+	16.1344i	−0.857255	+	0.683638i	−0.950067	−	0.312045i	$-0.898986\pi$
$557$	−20.2320	+	16.1344i	−0.857255	+	0.683638i	0.0928118	+	0.995684i	$0.470415\pi$
$558$		0			0
$559$	−5.25187	−	15.0090i	−0.222131	−	0.634813i
$560$		0			0
$561$	54.0252	+	33.9463i	2.28094	+	1.43321i
$562$		0			0
$563$	20.4641	+	20.4641i	0.862460	+	0.862460i	0.991623	−	0.129163i	$-0.0412292\pi$
$563$	20.4641	+	20.4641i	0.862460	+	0.862460i	−0.129163	+	0.991623i	$0.541229\pi$
$564$		0			0
$565$	0.574987	−	5.10315i	0.0241899	−	0.214691i
$566$		0			0
$567$	−7.51661	−	15.6084i	−0.315668	−	0.655491i
$568$		0			0
$569$	−9.14639	+	26.1389i	−0.383436	+	1.09580i	0.576866	+	0.816839i	$0.304275\pi$
$569$	−9.14639	+	26.1389i	−0.383436	+	1.09580i	−0.960303	+	0.278960i	$0.910010\pi$
$570$		0			0
$571$	7.90904	−	16.4233i	0.330983	−	0.687294i	−0.667366	−	0.744730i	$-0.732578\pi$
$571$	7.90904	−	16.4233i	0.330983	−	0.687294i	0.998349	+	0.0574362i	$0.0182926\pi$
$572$		0			0
$573$	23.6205	+	5.39122i	0.986760	+	0.225221i
$574$		0			0
$575$	−1.55593	−	1.24082i	−0.0648869	−	0.0517456i
$576$		0			0
$577$	2.77911	+	4.42292i	0.115696	+	0.184129i	0.899552	−	0.436814i	$-0.143893\pi$
$577$	2.77911	+	4.42292i	0.115696	+	0.184129i	−0.783856	+	0.620942i	$0.786750\pi$
$578$		0			0
$579$	−14.5069			−0.602887
$580$		0			0
$581$	−26.7888			−1.11139
$582$		0			0
$583$	36.8249	+	58.6065i	1.52513	+	2.42723i
$584$		0			0
$585$	−2.18702	−	1.74409i	−0.0904220	−	0.0721092i
$586$		0			0
$587$	29.6874	+	6.77594i	1.22533	+	0.279673i	0.785757	−	0.618535i	$-0.212273\pi$
$587$	29.6874	+	6.77594i	1.22533	+	0.279673i	0.439571	+	0.898208i	$0.355131\pi$
$588$		0			0
$589$	−0.843715	+	1.75199i	−0.0347647	+	0.0721896i
$590$		0			0
$591$	−3.52598	+	10.0767i	−0.145040	+	0.414499i
$592$		0			0
$593$	3.40712	+	7.07495i	0.139913	+	0.290533i	0.959138	−	0.282940i	$-0.0913098\pi$
$593$	3.40712	+	7.07495i	0.139913	+	0.290533i	−0.819224	+	0.573474i	$0.805596\pi$
$594$		0			0
$595$	−6.07106	+	53.8822i	−0.248889	+	2.20895i
$596$		0			0
$597$	25.2346	+	25.2346i	1.03279	+	1.03279i
$598$		0			0
$599$	7.68929	+	4.83150i	0.314176	+	0.197410i	0.679884	−	0.733320i	$-0.262030\pi$
$599$	7.68929	+	4.83150i	0.314176	+	0.197410i	−0.365708	+	0.930730i	$0.619173\pi$
$600$		0			0
$601$	3.68520	+	10.5317i	0.150323	+	0.429597i	0.994279	−	0.106815i	$-0.0340651\pi$
$601$	3.68520	+	10.5317i	0.150323	+	0.429597i	−0.843956	+	0.536412i	$0.819779\pi$
$602$		0			0
$603$	−1.16131	+	0.926110i	−0.0472920	+	0.0377141i
$604$		0			0
$605$	14.5372	+	63.6915i	0.591020	+	2.58943i
$606$		0			0
$607$	−5.38884	+	0.607176i	−0.218726	+	0.0246445i	−0.220647	−	0.975354i	$-0.570817\pi$
$607$	−5.38884	+	0.607176i	−0.218726	+	0.0246445i	0.00192130	+	0.999998i	$0.499388\pi$
$608$		0			0
$609$	11.9662	−	17.4675i	0.484894	−	0.707820i
$610$		0			0
$611$	0.643329	+	5.70970i	0.0260263	+	0.230990i
$612$		0			0
$613$	5.78133	−	1.31955i	0.233506	−	0.0532961i	−0.104167	−	0.994560i	$-0.533218\pi$
$613$	5.78133	−	1.31955i	0.233506	−	0.0532961i	0.337672	+	0.941264i	$0.390360\pi$
$614$		0			0
$615$	−20.9268	−	26.2414i	−0.843850	−	1.05815i
$616$		0			0
$617$	−22.4307	+	7.84886i	−0.903028	+	0.315983i	−0.741553	−	0.670894i	$-0.765911\pi$
$617$	−22.4307	+	7.84886i	−0.903028	+	0.315983i	−0.161474	+	0.986877i	$0.551625\pi$
$618$		0			0
$619$	−12.4673	+	19.8416i	−0.501103	+	0.797501i	−0.997505	−	0.0705919i	$-0.977511\pi$
$619$	−12.4673	+	19.8416i	−0.501103	+	0.797501i	0.496402	+	0.868093i	$0.334654\pi$
$620$		0			0
$621$	2.04623	−	2.04623i	0.0821125	−	0.0821125i
$622$		0			0
$623$	7.33859	+	0.826861i	0.294014	+	0.0331275i
$624$		0			0
$625$	26.5453	−	12.7835i	1.06181	−	0.511341i
$626$		0			0
$627$	−8.78057	−	3.07246i	−0.350662	−	0.122702i
$628$		0			0
$629$	−35.2286	−	16.9652i	−1.40466	−	0.676448i
$630$		0			0
$631$	−5.50703	+	24.1279i	−0.219232	+	0.960516i	0.738816	+	0.673907i	$0.235385\pi$
$631$	−5.50703	+	24.1279i	−0.219232	+	0.960516i	−0.958048	+	0.286609i	$0.907472\pi$
$632$		0			0
$633$	−22.9545	+	28.7840i	−0.912358	+	1.14406i
$634$		0			0
$635$	−46.8860	+	29.4604i	−1.86062	+	1.16910i
$636$		0			0
$637$		−	0.848159i		−	0.0336053i
$638$		0			0
$639$			3.30487i			0.130738i
$640$		0			0
$641$	7.86143	−	4.93966i	0.310508	−	0.195105i	−0.367758	−	0.929921i	$-0.619875\pi$
$641$	7.86143	−	4.93966i	0.310508	−	0.195105i	0.678266	+	0.734817i	$0.262732\pi$
$642$		0			0
$643$	11.8012	−	14.7982i	0.465392	−	0.583583i	−0.492644	−	0.870231i	$-0.663969\pi$
$643$	11.8012	−	14.7982i	0.465392	−	0.583583i	0.958036	+	0.286648i	$0.0925409\pi$
$644$		0			0
$645$	10.4661	−	45.8549i	0.412102	−	1.80554i
$646$		0			0
$647$	−16.2507	−	7.82595i	−0.638883	−	0.307670i	0.0862555	−	0.996273i	$-0.472510\pi$
$647$	−16.2507	−	7.82595i	−0.638883	−	0.307670i	−0.725138	+	0.688603i	$0.758224\pi$
$648$		0			0
$649$	−43.4679	−	15.2101i	−1.70627	−	0.597048i
$650$		0			0
$651$	6.58064	−	3.16907i	0.257916	−	0.124206i
$652$		0			0
$653$	8.82155	+	0.993950i	0.345214	+	0.0388963i	0.282869	−	0.959158i	$-0.408714\pi$
$653$	8.82155	+	0.993950i	0.345214	+	0.0388963i	0.0623445	+	0.998055i	$0.480142\pi$
$654$		0			0
$655$	15.7934	−	15.7934i	0.617100	−	0.617100i
$656$		0			0
$657$	−1.59384	+	2.53658i	−0.0621815	+	0.0989614i
$658$		0			0
$659$	−28.8086	+	10.0806i	−1.12222	+	0.392683i	−0.826694	−	0.562651i	$-0.809781\pi$
$659$	−28.8086	+	10.0806i	−1.12222	+	0.392683i	−0.295528	+	0.955334i	$0.595496\pi$
$660$		0			0
$661$	27.6060	+	34.6169i	1.07375	+	1.34644i	0.934412	+	0.356195i	$0.115926\pi$
$661$	27.6060	+	34.6169i	1.07375	+	1.34644i	0.139338	+	0.990245i	$0.455503\pi$
$662$		0			0
$663$	16.8477	−	3.84538i	0.654310	−	0.149342i
$664$		0			0
$665$	−0.885146	−	7.85589i	−0.0343245	−	0.304638i
$666$		0			0
$667$	2.69646	+	0.728948i	0.104407	+	0.0282250i
$668$		0			0
$669$	−1.08943	+	0.122749i	−0.0421198	+	0.00474577i
$670$		0			0
$671$	−18.8294	−	82.4970i	−0.726901	−	3.18476i
$672$		0			0
$673$	4.45437	−	3.55224i	0.171703	−	0.136929i	−0.533868	−	0.845568i	$-0.679262\pi$
$673$	4.45437	−	3.55224i	0.171703	−	0.136929i	0.705571	+	0.708639i	$0.250691\pi$
$674$		0			0
$675$	−7.06979	−	20.2043i	−0.272116	−	0.777664i
$676$		0			0
$677$	−6.07180	−	3.81516i	−0.233358	−	0.146629i	0.410277	−	0.911961i	$-0.365432\pi$
$677$	−6.07180	−	3.81516i	−0.233358	−	0.146629i	−0.643636	+	0.765332i	$0.722575\pi$
$678$		0			0
$679$	0.0407680	+	0.0407680i	0.00156453	+	0.00156453i
$680$		0			0
$681$	−3.50364	+	31.0957i	−0.134260	+	1.19159i
$682$		0			0
$683$	3.52631	+	7.32246i	0.134930	+	0.280186i	0.957476	−	0.288514i	$-0.0931610\pi$
$683$	3.52631	+	7.32246i	0.134930	+	0.280186i	−0.822545	+	0.568700i	$0.807447\pi$
$684$		0			0
$685$	15.2334	−	43.5346i	0.582039	−	1.66337i
$686$		0			0
$687$	−3.65465	+	7.58896i	−0.139434	+	0.289537i
$688$		0			0
$689$	18.2764	+	4.17146i	0.696274	+	0.158920i
$690$		0			0
$691$	7.90778	+	6.30625i	0.300826	+	0.239901i	0.762256	−	0.647276i	$-0.224092\pi$
$691$	7.90778	+	6.30625i	0.300826	+	0.239901i	−0.461429	+	0.887177i	$0.652663\pi$
$692$		0			0
$693$	−4.69627	−	7.47407i	−0.178397	−	0.283917i
$694$		0			0
$695$	−56.6516			−2.14892
$696$		0			0
$697$	−52.3814			−1.98409
$698$		0			0
$699$	6.68264	+	10.6354i	0.252761	+	0.402266i
$700$		0			0
$701$	−12.9112	−	10.2964i	−0.487651	−	0.388889i	0.348569	−	0.937283i	$-0.386668\pi$
$701$	−12.9112	−	10.2964i	−0.487651	−	0.388889i	−0.836220	+	0.548395i	$0.815239\pi$
$702$		0			0
$703$	5.55788	+	1.26855i	0.209619	+	0.0478442i
$704$		0			0
$705$	−7.37405	+	15.3124i	−0.277723	+	0.576698i
$706$		0			0
$707$	3.13624	−	8.96286i	0.117950	−	0.337083i
$708$		0			0
$709$	12.7491	+	26.4738i	0.478802	+	0.994243i	0.990810	+	0.135262i	$0.0431876\pi$
$709$	12.7491	+	26.4738i	0.478802	+	0.994243i	−0.512008	+	0.858981i	$0.671098\pi$
$710$		0			0
$711$	−0.472193	+	4.19083i	−0.0177086	+	0.157168i
$712$		0			0
$713$	0.681345	+	0.681345i	0.0255166	+	0.0255166i
$714$		0			0
$715$	22.4807	+	14.1255i	0.840730	+	0.528266i
$716$		0			0
$717$	−3.09146	−	8.83488i	−0.115453	−	0.329945i
$718$		0			0
$719$	−17.0617	+	13.6062i	−0.636293	+	0.507426i	−0.887680	−	0.460460i	$-0.847684\pi$
$719$	−17.0617	+	13.6062i	−0.636293	+	0.507426i	0.251388	+	0.967886i	$0.419113\pi$
$720$		0			0
$721$	0.374802	+	1.64211i	0.0139584	+	0.0611555i
$722$		0			0
$723$	2.23452	−	0.251770i	0.0831028	−	0.00936344i
$724$		0			0
$725$	13.5122	−	15.6310i	0.501829	−	0.580519i
$726$		0			0
$727$	6.02755	+	53.4960i	0.223550	+	1.98406i	0.169595	+	0.985514i	$0.445754\pi$
$727$	6.02755	+	53.4960i	0.223550	+	1.98406i	0.0539544	+	0.998543i	$0.482817\pi$
$728$		0			0
$729$	29.2746	−	6.68173i	1.08424	−	0.247471i
$730$		0			0
$731$	−45.7663	−	57.3891i	−1.69273	−	2.12261i
$732$		0			0
$733$	29.5458	−	10.3385i	1.09130	−	0.381862i	0.276151	−	0.961114i	$-0.410941\pi$
$733$	29.5458	−	10.3385i	1.09130	−	0.381862i	0.815149	+	0.579252i	$0.196655\pi$
$734$		0			0
$735$	1.33474	−	2.12422i	0.0492325	−	0.0783530i
$736$		0			0
$737$	9.96889	−	9.96889i	0.367209	−	0.367209i
$738$		0			0
$739$	−18.1132	−	2.04087i	−0.666305	−	0.0750745i	−0.227668	−	0.973739i	$-0.573110\pi$
$739$	−18.1132	−	2.04087i	−0.666305	−	0.0750745i	−0.438637	+	0.898664i	$0.644539\pi$
$740$		0			0
$741$	−2.27001	+	1.09318i	−0.0833909	+	0.0401590i
$742$		0			0
$743$	4.09112	+	1.43154i	0.150089	+	0.0525183i	0.404278	−	0.914636i	$-0.367523\pi$
$743$	4.09112	+	1.43154i	0.150089	+	0.0525183i	−0.254189	+	0.967155i	$0.581809\pi$
$744$		0			0
$745$	51.8027	+	24.9469i	1.89790	+	0.913982i
$746$		0			0
$747$	1.41959	−	6.21962i	0.0519400	−	0.227564i
$748$		0			0
$749$	−29.6215	+	37.1442i	−1.08235	+	1.35722i
$750$		0			0
$751$	−32.7647	+	20.5874i	−1.19560	+	0.751246i	−0.974584	−	0.224024i	$-0.928081\pi$
$751$	−32.7647	+	20.5874i	−1.19560	+	0.751246i	−0.221017	+	0.975270i	$0.570938\pi$
$752$		0			0
$753$			4.95981i			0.180746i
$754$		0			0
$755$			10.7500i			0.391234i
$756$		0			0
$757$	−0.480142	+	0.301693i	−0.0174511	+	0.0109652i	−0.540729	−	0.841197i	$-0.681852\pi$
$757$	−0.480142	+	0.301693i	−0.0174511	+	0.0109652i	0.523278	+	0.852162i	$0.324709\pi$
$758$		0			0
$759$	−2.87405	+	3.60394i	−0.104321	+	0.130815i
$760$		0			0
$761$	3.41051	−	14.9424i	0.123631	−	0.541663i	−0.874739	−	0.484594i	$-0.838967\pi$
$761$	3.41051	−	14.9424i	0.123631	−	0.541663i	0.998370	−	0.0570689i	$-0.0181755\pi$
$762$		0			0
$763$	0.159423	+	0.0767743i	0.00577152	+	0.00277942i
$764$		0			0
$765$	−12.1882	−	4.26485i	−0.440667	−	0.154196i
$766$		0			0
$767$	−11.2376	+	5.41175i	−0.405767	+	0.195407i
$768$		0			0
$769$	1.79498	+	0.202245i	0.0647285	+	0.00729315i	0.144269	−	0.989538i	$-0.453917\pi$
$769$	1.79498	+	0.202245i	0.0647285	+	0.00729315i	−0.0795408	+	0.996832i	$0.525345\pi$
$770$		0			0
$771$	−10.2588	+	10.2588i	−0.369461	+	0.369461i
$772$		0			0
$773$	1.85455	−	2.95150i	0.0667036	−	0.106158i	−0.811707	−	0.584065i	$-0.801461\pi$
$773$	1.85455	−	2.95150i	0.0667036	−	0.106158i	0.878411	+	0.477907i	$0.158604\pi$
$774$		0			0
$775$	6.72754	−	2.35407i	0.241660	−	0.0845607i
$776$		0			0
$777$	−13.3506	−	16.7412i	−0.478952	−	0.600586i
$778$		0			0
$779$	7.44560	−	1.69941i	0.266766	−	0.0608877i
$780$		0			0
$781$	−3.51206	−	31.1704i	−0.125672	−	1.11537i
$782$		0			0
$783$	20.3861	+	22.0692i	0.728538	+	0.788690i
$784$		0			0
$785$	5.07002	−	0.571254i	0.180957	−	0.0203889i
$786$		0			0
$787$	5.81947	+	25.4968i	0.207442	+	0.908861i	0.966262	+	0.257561i	$0.0829189\pi$
$787$	5.81947	+	25.4968i	0.207442	+	0.908861i	−0.758820	+	0.651300i	$0.774224\pi$
$788$		0			0
$789$	13.1491	−	10.4860i	0.468120	−	0.373313i
$790$		0			0
$791$	−1.44960	−	4.14272i	−0.0515419	−	0.147298i
$792$		0			0
$793$	−19.4053	−	12.1932i	−0.689104	−	0.432993i
$794$		0			0
$795$	39.2087	+	39.2087i	1.39059	+	1.39059i
$796$		0			0
$797$	−4.85465	+	43.0862i	−0.171960	+	1.52619i	0.550533	+	0.834814i	$0.314425\pi$
$797$	−4.85465	+	43.0862i	−0.171960	+	1.52619i	−0.722493	+	0.691378i	$0.757004\pi$
$798$		0			0
$799$	11.5083	+	23.8971i	0.407133	+	0.845420i
$800$		0			0
$801$	−0.580859	+	1.66000i	−0.0205237	+	0.0586533i
$802$		0			0
$803$	12.3370	−	25.6180i	0.435362	−	0.904038i
$804$		0			0
$805$	−3.81916	−	0.871698i	−0.134608	−	0.0307233i
$806$		0			0
$807$	−24.2551	−	19.3428i	−0.853819	−	0.680898i
$808$		0			0
$809$	−3.67496	−	5.84867i	−0.129205	−	0.205628i	0.775856	−	0.630910i	$-0.217318\pi$
$809$	−3.67496	−	5.84867i	−0.129205	−	0.205628i	−0.905061	+	0.425281i	$0.860175\pi$
$810$		0			0
$811$	−47.2942			−1.66072			−0.830362	−	0.557225i	$-0.811866\pi$
$811$	−47.2942			−1.66072			−0.830362	+	0.557225i	$0.811866\pi$
$812$		0			0
$813$	0.250855			0.00879788
$814$		0			0
$815$	−31.7720	−	50.5648i	−1.11292	−	1.77121i
$816$		0			0
$817$	8.36720	+	6.67262i	0.292731	+	0.233445i
$818$		0			0
$819$	−2.33078	−	0.531986i	−0.0814441	−	0.0185891i
$820$		0			0
$821$	−1.53479	+	3.18703i	−0.0535646	+	0.111228i	−0.926033	−	0.377442i	$-0.876804\pi$
$821$	−1.53479	+	3.18703i	−0.0535646	+	0.111228i	0.872468	+	0.488670i	$0.162518\pi$
$822$		0			0
$823$	2.19926	−	6.28513i	0.0766615	−	0.219086i	−0.899174	−	0.437590i	$-0.855832\pi$
$823$	2.19926	−	6.28513i	0.0766615	−	0.219086i	0.975836	+	0.218504i	$0.0701178\pi$
$824$		0			0
$825$	14.7943	+	30.7206i	0.515071	+	1.06956i
$826$		0			0
$827$	0.00607682	−	0.0539332i	0.000211312	−	0.00187544i	−0.993606	−	0.112902i	$-0.963985\pi$
$827$	0.00607682	−	0.0539332i	0.000211312	−	0.00187544i	0.993817	+	0.111027i	$0.0354139\pi$
$828$		0			0
$829$	−23.5838	−	23.5838i	−0.819098	−	0.819098i	0.166879	−	0.985977i	$-0.446631\pi$
$829$	−23.5838	−	23.5838i	−0.819098	−	0.819098i	−0.985977	+	0.166879i	$0.946631\pi$
$830$		0			0
$831$	20.7447	+	13.0347i	0.719625	+	0.452170i
$832$		0			0
$833$	−1.29313	−	3.69555i	−0.0448042	−	0.128043i
$834$		0			0
$835$	−20.5286	+	16.3710i	−0.710422	+	0.566543i
$836$		0			0
$837$	2.30622	+	10.1042i	0.0797147	+	0.349253i
$838$		0			0
$839$	−24.5036	+	2.76089i	−0.845958	+	0.0953166i	−0.524294	−	0.851537i	$-0.675671\pi$
$839$	−24.5036	+	2.76089i	−0.845958	+	0.0953166i	−0.321664	+	0.946854i	$0.604242\pi$
$840$		0			0
$841$	−8.67113	+	27.6733i	−0.299005	+	0.954252i
$842$		0			0
$843$	2.39594	+	21.2645i	0.0825204	+	0.732389i
$844$		0			0
$845$	−30.6653	+	6.99914i	−1.05492	+	0.240778i
$846$		0			0
$847$	34.8119	+	43.6528i	1.19615	+	1.49993i
$848$		0			0
$849$	−1.14793	+	0.401678i	−0.0393968	+	0.0137855i
$850$		0			0
$851$	1.50291	−	2.39187i	0.0515192	−	0.0819924i
$852$		0			0
$853$	24.4332	−	24.4332i	0.836576	−	0.836576i	−0.151830	−	0.988407i	$-0.548517\pi$
$853$	24.4332	−	24.4332i	0.836576	−	0.836576i	0.988407	+	0.151830i	$0.0485167\pi$
$854$		0			0
$855$	1.87083	+	0.210792i	0.0639809	+	0.00720892i
$856$		0			0
$857$	43.5668	−	20.9807i	1.48821	−	0.716686i	0.499473	−	0.866329i	$-0.333527\pi$
$857$	43.5668	−	20.9807i	1.48821	−	0.716686i	0.988740	+	0.149644i	$0.0478127\pi$
$858$		0			0
$859$	35.2264	+	12.3262i	1.20191	+	0.420566i	0.855641	−	0.517570i	$-0.173163\pi$
$859$	35.2264	+	12.3262i	1.20191	+	0.420566i	0.346267	+	0.938136i	$0.387449\pi$
$860$		0			0
$861$	−25.8448	−	12.4462i	−0.880789	−	0.424166i
$862$		0			0
$863$	−5.67979	+	24.8848i	−0.193342	+	0.847087i	0.781449	+	0.623969i	$0.214481\pi$
$863$	−5.67979	+	24.8848i	−0.193342	+	0.847087i	−0.974791	+	0.223119i	$0.928376\pi$
$864$		0			0
$865$	15.5439	−	19.4914i	0.528508	−	0.662728i
$866$		0			0
$867$	45.2688	−	28.4443i	1.53741	−	0.966019i
$868$		0			0
$869$		−	40.0284i		−	1.35787i
$870$		0			0
$871$		−	3.81835i		−	0.129380i
$872$		0			0
$873$	−0.0116256	+	0.00730483i	−0.000393466	+	0.000247231i
$874$		0			0
$875$	5.47741	−	6.86846i	0.185170	−	0.232196i
$876$		0			0
$877$	−8.48578	+	37.1786i	−0.286545	+	1.25543i	0.602688	+	0.797977i	$0.294097\pi$
$877$	−8.48578	+	37.1786i	−0.286545	+	1.25543i	−0.889232	+	0.457456i	$0.848761\pi$
$878$		0			0
$879$	0.582510	+	0.280522i	0.0196476	+	0.00946177i
$880$		0			0
$881$	−15.0794	−	5.27650i	−0.508037	−	0.177770i	0.0640754	−	0.997945i	$-0.479590\pi$
$881$	−15.0794	−	5.27650i	−0.508037	−	0.177770i	−0.572112	+	0.820175i	$0.693876\pi$
$882$		0			0
$883$	4.44862	−	2.14234i	0.149708	−	0.0720956i	−0.357530	−	0.933902i	$-0.616381\pi$
$883$	4.44862	−	2.14234i	0.149708	−	0.0720956i	0.507238	+	0.861806i	$0.330667\pi$
$884$		0			0
$885$	−36.6611	−	4.13071i	−1.23235	−	0.138852i
$886$		0			0
$887$	17.5805	−	17.5805i	0.590294	−	0.590294i	−0.347417	−	0.937711i	$-0.612941\pi$
$887$	17.5805	−	17.5805i	0.590294	−	0.590294i	0.937711	+	0.347417i	$0.112941\pi$
$888$		0			0
$889$	−25.1785	+	40.0713i	−0.844459	+	1.34395i
$890$		0			0
$891$	−36.9601	+	12.9329i	−1.23821	+	0.433269i
$892$		0			0
$893$	−2.41110	−	3.02343i	−0.0806845	−	0.101175i
$894$		0			0
$895$	33.6921	−	7.69001i	1.12620	−	0.257049i
$896$		0			0
$897$	0.139784	+	1.24062i	0.00466726	+	0.0414231i
$898$		0			0
$899$	−7.34852	+	6.78806i	−0.245087	+	0.226395i
$900$		0			0
$901$	85.9927	−	9.68905i	2.86483	−	0.322789i
$902$		0			0
$903$	−8.94487	−	39.1900i	−0.297667	−	1.30416i
$904$		0			0
$905$	18.5514	−	14.7942i	0.616669	−	0.491777i
$906$		0			0
$907$	2.74154	+	7.83488i	0.0910315	+	0.260153i	0.980393	−	0.197051i	$-0.0631365\pi$
$907$	2.74154	+	7.83488i	0.0910315	+	0.260153i	−0.889362	+	0.457204i	$0.848851\pi$
$908$		0			0
$909$	1.91473	+	1.20311i	0.0635077	+	0.0399045i
$910$		0			0
$911$	−27.2620	−	27.2620i	−0.903232	−	0.903232i	0.0924825	−	0.995714i	$-0.470520\pi$
$911$	−27.2620	−	27.2620i	−0.903232	−	0.903232i	−0.995714	+	0.0924825i	$0.970520\pi$
$912$		0			0
$913$	−6.77954	+	60.1701i	−0.224370	+	1.99134i
$914$		0			0
$915$	−29.4126	−	61.0758i	−0.972349	−	2.01910i
$916$		0			0
$917$	6.30467	−	18.0177i	0.208199	−	0.594997i
$918$		0			0
$919$	1.91567	−	3.97792i	0.0631920	−	0.131220i	−0.866981	−	0.498342i	$-0.833943\pi$
$919$	1.91567	−	3.97792i	0.0631920	−	0.131220i	0.930173	+	0.367122i	$0.119657\pi$
$920$		0			0
$921$	14.4732	+	3.30342i	0.476909	+	0.108851i
$922$		0			0
$923$	−6.64216	−	5.29694i	−0.218629	−	0.174351i
$924$		0			0
$925$	−11.1171	−	17.6927i	−0.365527	−	0.581733i
$926$		0			0
$927$	−0.401115			−0.0131743
$928$		0			0
$929$	−31.8119			−1.04372			−0.521858	−	0.853032i	$-0.674761\pi$
$929$	−31.8119			−1.04372			−0.521858	+	0.853032i	$0.674761\pi$
$930$		0			0
$931$	0.303703	+	0.483340i	0.00995346	+	0.0158408i
$932$		0			0
$933$	21.0428	+	16.7811i	0.688912	+	0.549389i
$934$		0			0
$935$	119.488	+	27.2723i	3.90767	+	0.891900i
$936$		0			0
$937$	3.77449	−	7.83780i	0.123307	−	0.256050i	−0.830173	−	0.557506i	$-0.811758\pi$
$937$	3.77449	−	7.83780i	0.123307	−	0.256050i	0.953480	+	0.301456i	$0.0974727\pi$
$938$		0			0
$939$	10.5752	−	30.2221i	0.345108	−	0.986262i
$940$		0			0
$941$	0.0173255	+	0.0359768i	0.000564796	+	0.00117281i	0.901251	−	0.433297i	$-0.142650\pi$
$941$	0.0173255	+	0.0359768i	0.000564796	+	0.00117281i	−0.900686	+	0.434470i	$0.856936\pi$
$942$		0			0
$943$	0.423709	−	3.76052i	0.0137979	−	0.122459i
$944$		0			0
$945$	−29.7939	−	29.7939i	−0.969197	−	0.969197i
$946$		0			0
$947$	−48.1894	−	30.2794i	−1.56594	−	0.983948i	−0.985505	−	0.169644i	$-0.945738\pi$
$947$	−48.1894	−	30.2794i	−1.56594	−	0.983948i	−0.580439	−	0.814304i	$-0.697119\pi$
$948$		0			0
$949$	−2.54349	−	7.26887i	−0.0825651	−	0.235957i
$950$		0			0
$951$	28.5969	−	22.8053i	0.927319	−	0.739512i
$952$		0			0
$953$	−1.60808	−	7.04544i	−0.0520907	−	0.228224i	0.942181	−	0.335104i	$-0.108771\pi$
$953$	−1.60808	−	7.04544i	−0.0520907	−	0.228224i	−0.994272	+	0.106879i	$0.965914\pi$
$954$		0			0
$955$	46.2459	−	5.21067i	1.49648	−	0.168613i
$956$		0			0
$957$	−36.2053	−	31.2977i	−1.17035	−	1.01171i
$958$		0			0
$959$	−4.41353	−	39.1712i	−0.142520	−	1.26490i
$960$		0			0
$961$	26.8583	−	6.13023i	0.866397	−	0.197749i
$962$		0			0
$963$	−7.05415	−	8.84563i	−0.227317	−	0.285046i
$964$		0			0
$965$	−26.3021	+	9.20350i	−0.846694	+	0.296271i
$966$		0			0
$967$	−2.18729	+	3.48105i	−0.0703384	+	0.111943i	−0.880041	−	0.474897i	$-0.842485\pi$
$967$	−2.18729	+	3.48105i	−0.0703384	+	0.111943i	0.809703	+	0.586840i	$0.199628\pi$
$968$		0			0
$969$	−8.22407	+	8.22407i	−0.264195	+	0.264195i
$970$		0			0
$971$	27.6572	+	3.11622i	0.887562	+	0.100004i	0.543960	−	0.839111i	$-0.316924\pi$
$971$	27.6572	+	3.11622i	0.887562	+	0.100004i	0.343602	+	0.939115i	$0.388353\pi$
$972$		0			0
$973$	−43.6226	+	21.0076i	−1.39848	+	0.673471i
$974$		0			0
$975$	8.71671	+	3.05011i	0.279158	+	0.0976816i
$976$		0			0
$977$	8.69828	+	4.18887i	0.278283	+	0.134014i	0.567820	−	0.823153i	$-0.307787\pi$
$977$	8.69828	+	4.18887i	0.278283	+	0.134014i	−0.289537	+	0.957167i	$0.593501\pi$
$978$		0			0
$979$	3.71441	−	16.2739i	0.118713	−	0.520115i
$980$		0			0
$981$	−0.0262730	+	0.0329453i	−0.000838833	+	0.00105186i
$982$		0			0
$983$	26.9625	−	16.9417i	0.859972	−	0.540356i	−0.0283393	−	0.999598i	$-0.509022\pi$
$983$	26.9625	−	16.9417i	0.859972	−	0.540356i	0.888311	+	0.459242i	$0.151879\pi$
$984$		0			0
$985$			20.5067i			0.653398i
$986$		0			0
$987$			14.5252i			0.462343i
$988$		0			0
$989$	4.49023	−	2.82140i	0.142781	−	0.0897153i
$990$		0			0
$991$	31.0578	−	38.9453i	0.986584	−	1.23714i	0.0151358	−	0.999885i	$-0.495182\pi$
$991$	31.0578	−	38.9453i	0.986584	−	1.23714i	0.971448	−	0.237252i	$-0.0762466\pi$
$992$		0			0
$993$	−5.32843	+	23.3454i	−0.169093	+	0.740843i
$994$		0			0
$995$	61.7616	+	29.7428i	1.95798	+	0.942911i
$996$		0			0
$997$	−10.2181	−	3.57547i	−0.323611	−	0.113236i	0.163585	−	0.986529i	$-0.447694\pi$
$997$	−10.2181	−	3.57547i	−0.323611	−	0.113236i	−0.487195	+	0.873293i	$0.661980\pi$
$998$		0			0
$999$	27.3750	−	13.1831i	0.866107	−	0.417095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.bl.c.15.3	✓	120
4.3	odd	2	inner	464.2.bl.c.15.8	yes	120
29.2	odd	28	inner	464.2.bl.c.31.8	yes	120
116.31	even	28	inner	464.2.bl.c.31.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.bl.c.15.3	✓	120	1.1	even	1	trivial
464.2.bl.c.15.8	yes	120	4.3	odd	2	inner
464.2.bl.c.31.3	yes	120	116.31	even	28	inner
464.2.bl.c.31.8	yes	120	29.2	odd	28	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:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bl (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.823357 - 1.31036i) q^{3} +(-2.32413 - 1.85343i) q^{5} +(-2.47691 - 0.565338i) q^{7} +(0.262512 - 0.545111i) q^{9} +(-1.89664 + 5.42028i) q^{11} +(0.674824 + 1.40129i) q^{13} +(-0.515083 + 4.57149i) q^{15} +(5.07675 + 5.07675i) q^{17} +(-0.886325 - 0.556915i) q^{19} +(1.29858 + 3.71113i) q^{21} +(-0.405531 + 0.323400i) q^{23} +(0.853764 + 3.74058i) q^{25} +(-5.54395 + 0.624653i) q^{27} +(-3.18817 - 4.34000i) q^{29} +(-0.207994 - 1.84600i) q^{31} +(8.66415 - 1.97754i) q^{33} +(4.70883 + 5.90469i) q^{35} +(-5.14048 + 1.79873i) q^{37} +(1.28058 - 2.03802i) q^{39} +(-5.15895 + 5.15895i) q^{41} +(-10.1596 - 1.14471i) q^{43} +(-1.62044 + 0.780361i) q^{45} +(3.48702 + 1.22016i) q^{47} +(-0.491326 - 0.236610i) q^{49} +(2.47242 - 10.8324i) q^{51} +(7.51501 - 9.42353i) q^{53} +(14.4541 - 9.08214i) q^{55} +1.61995i q^{57} +8.01950i q^{59} +(-12.4768 + 7.83971i) q^{61} +(-0.958388 + 1.20178i) q^{63} +(1.02881 - 4.50751i) q^{65} +(-2.21191 - 1.06520i) q^{67} +(0.757669 + 0.265120i) q^{69} +(-4.92140 + 2.37002i) q^{71} +(-4.92030 - 0.554385i) q^{73} +(4.19858 - 4.19858i) q^{75} +(7.76208 - 12.3533i) q^{77} +(-6.57935 + 2.30221i) q^{79} +(4.25149 + 5.33120i) q^{81} +(10.2799 - 2.34632i) q^{83} +(-2.38961 - 21.2084i) q^{85} +(-3.06198 + 7.75103i) q^{87} +(-2.88852 + 0.325458i) q^{89} +(-0.879275 - 3.85236i) q^{91} +(-2.24768 + 1.79247i) q^{93} +(1.02773 + 2.93708i) q^{95} +(-0.0192149 - 0.0120735i) q^{97} +(2.45676 + 2.45676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) \) 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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