LMFDB - Embedded newform 840.2.cp.b.521.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(521,840)] 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("840.521"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.9
Character	$\chi$	$=$	840.521
Dual form			840.2.cp.b.761.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0468355 - 1.73142i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.719245 + 2.54611i) q^{7} +(-2.99561 - 0.162184i) q^{9} +(-1.50258 - 0.867515i) q^{11} -4.52010i q^{13} +(1.52287 - 0.825148i) q^{15} +(1.11074 - 1.92386i) q^{17} +(6.20617 - 3.58314i) q^{19} +(4.44207 - 1.12607i) q^{21} +(5.12760 - 2.96042i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.421109 + 5.17906i) q^{27} -9.11607i q^{29} +(5.76540 + 3.32866i) q^{31} +(-1.57240 + 2.56096i) q^{33} +(-1.84538 + 1.89594i) q^{35} +(0.687757 + 1.19123i) q^{37} +(-7.82619 - 0.211701i) q^{39} -3.20604 q^{41} +9.02575 q^{43} +(-1.35735 - 2.67537i) q^{45} +(0.561320 + 0.972234i) q^{47} +(-5.96537 + 3.66256i) q^{49} +(-3.27898 - 2.01326i) q^{51} +(-6.60510 - 3.81346i) q^{53} -1.73503i q^{55} +(-5.91323 - 10.9133i) q^{57} +(0.244352 - 0.423231i) q^{59} +(7.58163 - 4.37726i) q^{61} +(-1.74164 - 7.74382i) q^{63} +(3.91452 - 2.26005i) q^{65} +(-7.12780 + 12.3457i) q^{67} +(-4.88558 - 9.01668i) q^{69} -7.93299i q^{71} +(-1.22652 - 0.708133i) q^{73} +(1.47603 + 0.906269i) q^{75} +(1.12807 - 4.44969i) q^{77} +(3.04459 + 5.27338i) q^{79} +(8.94739 + 0.971678i) q^{81} -15.6055 q^{83} +2.22148 q^{85} +(-15.7837 - 0.426955i) q^{87} +(2.27711 + 3.94408i) q^{89} +(11.5087 - 3.25106i) q^{91} +(6.03332 - 9.82642i) q^{93} +(6.20617 + 3.58314i) q^{95} +6.94223i q^{97} +(4.36045 + 2.84243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) $ 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0468355	−	1.73142i	0.0270405	−	0.999634i
$3$	0.0468355	−	1.73142i	0.0270405	−	0.999634i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.719245	+	2.54611i	0.271849	+	0.962340i
$7$	0.719245	+	2.54611i	0.271849	+	0.962340i
$8$		0			0
$9$	−2.99561	−	0.162184i	−0.998538	−	0.0540612i
$10$		0			0
$11$	−1.50258	−	0.867515i	−0.453045	−	0.261566i	0.256070	−	0.966658i	$-0.417572\pi$
$11$	−1.50258	−	0.867515i	−0.453045	−	0.261566i	−0.709115	+	0.705093i	$0.750905\pi$
$12$		0			0
$13$		−	4.52010i		−	1.25365i	−0.779160	−	0.626826i	$-0.784354\pi$
$13$		−	4.52010i		−	1.25365i	0.779160	−	0.626826i	$-0.215646\pi$
$14$		0			0
$15$	1.52287	−	0.825148i	0.393203	−	0.213052i
$16$		0			0
$17$	1.11074	−	1.92386i	0.269394	−	0.466604i	−0.699312	−	0.714817i	$-0.746510\pi$
$17$	1.11074	−	1.92386i	0.269394	−	0.466604i	0.968705	+	0.248213i	$0.0798433\pi$
$18$		0			0
$19$	6.20617	−	3.58314i	1.42379	−	0.822028i	0.427173	−	0.904170i	$-0.359510\pi$
$19$	6.20617	−	3.58314i	1.42379	−	0.822028i	0.996621	+	0.0821424i	$0.0261762\pi$
$20$		0			0
$21$	4.44207	−	1.12607i	0.969339	−	0.245728i
$22$		0			0
$23$	5.12760	−	2.96042i	1.06918	−	0.617291i	0.141222	−	0.989978i	$-0.454897\pi$
$23$	5.12760	−	2.96042i	1.06918	−	0.617291i	0.927957	+	0.372687i	$0.121563\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−0.421109	+	5.17906i	−0.0810424	+	0.996711i
$28$		0			0
$29$		−	9.11607i		−	1.69281i	−0.532539	−	0.846405i	$-0.678762\pi$
$29$		−	9.11607i		−	1.69281i	0.532539	−	0.846405i	$-0.321238\pi$
$30$		0			0
$31$	5.76540	+	3.32866i	1.03550	+	0.597845i	0.918555	−	0.395294i	$-0.129357\pi$
$31$	5.76540	+	3.32866i	1.03550	+	0.597845i	0.116943	+	0.993139i	$0.462691\pi$
$32$		0			0
$33$	−1.57240	+	2.56096i	−0.273720	+	0.445806i
$34$		0			0
$35$	−1.84538	+	1.89594i	−0.311925	+	0.320472i
$36$		0			0
$37$	0.687757	+	1.19123i	0.113067	+	0.195837i	0.917005	−	0.398875i	$-0.130599\pi$
$37$	0.687757	+	1.19123i	0.113067	+	0.195837i	−0.803939	+	0.594712i	$0.797266\pi$
$38$		0			0
$39$	−7.82619	−	0.211701i	−1.25319	−	0.0338993i
$40$		0			0
$41$	−3.20604			−0.500699			−0.250350	−	0.968155i	$-0.580546\pi$
$41$	−3.20604			−0.500699			−0.250350	+	0.968155i	$0.580546\pi$
$42$		0			0
$43$	9.02575			1.37641			0.688207	−	0.725514i	$-0.258398\pi$
$43$	9.02575			1.37641			0.688207	+	0.725514i	$0.258398\pi$
$44$		0			0
$45$	−1.35735	−	2.67537i	−0.202342	−	0.398820i
$46$		0			0
$47$	0.561320	+	0.972234i	0.0818769	+	0.141815i	0.904056	−	0.427414i	$-0.140575\pi$
$47$	0.561320	+	0.972234i	0.0818769	+	0.141815i	−0.822179	+	0.569229i	$0.807242\pi$
$48$		0			0
$49$	−5.96537	+	3.66256i	−0.852196	+	0.523223i
$50$		0			0
$51$	−3.27898	−	2.01326i	−0.459149	−	0.281913i
$52$		0			0
$53$	−6.60510	−	3.81346i	−0.907281	−	0.523819i	−0.0277255	−	0.999616i	$-0.508826\pi$
$53$	−6.60510	−	3.81346i	−0.907281	−	0.523819i	−0.879555	+	0.475797i	$0.842160\pi$
$54$		0			0
$55$		−	1.73503i		−	0.233951i
$56$		0			0
$57$	−5.91323	−	10.9133i	−0.783227	−	1.44550i
$58$		0			0
$59$	0.244352	−	0.423231i	0.0318120	−	0.0551000i	−0.849681	−	0.527297i	$-0.823206\pi$
$59$	0.244352	−	0.423231i	0.0318120	−	0.0551000i	0.881493	+	0.472197i	$0.156539\pi$
$60$		0			0
$61$	7.58163	−	4.37726i	0.970729	−	0.560450i	0.0712703	−	0.997457i	$-0.477295\pi$
$61$	7.58163	−	4.37726i	0.970729	−	0.560450i	0.899458	+	0.437007i	$0.143961\pi$
$62$		0			0
$63$	−1.74164	−	7.74382i	−0.219426	−	0.975629i
$64$		0			0
$65$	3.91452	−	2.26005i	0.485537	−	0.280325i
$66$		0			0
$67$	−7.12780	+	12.3457i	−0.870800	+	1.50827i	−0.00962884	+	0.999954i	$0.503065\pi$
$67$	−7.12780	+	12.3457i	−0.870800	+	1.50827i	−0.861171	+	0.508316i	$0.830268\pi$
$68$		0			0
$69$	−4.88558	−	9.01668i	−0.588154	−	1.08548i
$70$		0			0
$71$		−	7.93299i		−	0.941473i	−0.882274	−	0.470737i	$-0.843988\pi$
$71$		−	7.93299i		−	0.941473i	0.882274	−	0.470737i	$-0.156012\pi$
$72$		0			0
$73$	−1.22652	−	0.708133i	−0.143554	−	0.0828807i	0.426503	−	0.904486i	$-0.359745\pi$
$73$	−1.22652	−	0.708133i	−0.143554	−	0.0828807i	−0.570057	+	0.821605i	$0.693079\pi$
$74$		0			0
$75$	1.47603	+	0.906269i	0.170438	+	0.104647i
$76$		0			0
$77$	1.12807	−	4.44969i	0.128555	−	0.507089i
$78$		0			0
$79$	3.04459	+	5.27338i	0.342543	+	0.593302i	0.984904	−	0.173100i	$-0.0553785\pi$
$79$	3.04459	+	5.27338i	0.342543	+	0.593302i	−0.642361	+	0.766402i	$0.722045\pi$
$80$		0			0
$81$	8.94739	+	0.971678i	0.994155	+	0.107964i
$82$		0			0
$83$	−15.6055			−1.71292			−0.856462	−	0.516211i	$-0.827342\pi$
$83$	−15.6055			−1.71292			−0.856462	+	0.516211i	$0.827342\pi$
$84$		0			0
$85$	2.22148			0.240953
$86$		0			0
$87$	−15.7837	−	0.426955i	−1.69219	−	0.0457744i
$88$		0			0
$89$	2.27711	+	3.94408i	0.241374	+	0.418071i	0.961106	−	0.276180i	$-0.0890687\pi$
$89$	2.27711	+	3.94408i	0.241374	+	0.418071i	−0.719732	+	0.694252i	$0.755735\pi$
$90$		0			0
$91$	11.5087	−	3.25106i	1.20644	−	0.340804i
$92$		0			0
$93$	6.03332	−	9.82642i	0.625626	−	1.01895i
$94$		0			0
$95$	6.20617	+	3.58314i	0.636740	+	0.367622i
$96$		0			0
$97$			6.94223i			0.704877i	0.935835	+	0.352438i	$0.114647\pi$
$97$			6.94223i			0.704877i	−0.935835	+	0.352438i	$0.885353\pi$
$98$		0			0
$99$	4.36045	+	2.84243i	0.438242	+	0.285675i
$100$		0			0
$101$	−1.42009	+	2.45967i	−0.141304	+	0.244746i	−0.927988	−	0.372610i	$-0.878463\pi$
$101$	−1.42009	+	2.45967i	−0.141304	+	0.244746i	0.786684	+	0.617356i	$0.211796\pi$
$102$		0			0
$103$	−14.1465	+	8.16751i	−1.39390	+	0.804768i	−0.993744	−	0.111679i	$-0.964377\pi$
$103$	−14.1465	+	8.16751i	−1.39390	+	0.804768i	−0.400155	+	0.916447i	$0.631044\pi$
$104$		0			0
$105$	3.19624	+	3.28391i	0.311921	+	0.320477i
$106$		0			0
$107$	6.40143	−	3.69587i	0.618850	−	0.357293i	−0.157571	−	0.987508i	$-0.550366\pi$
$107$	6.40143	−	3.69587i	0.618850	−	0.357293i	0.776421	+	0.630214i	$0.217033\pi$
$108$		0			0
$109$	2.64239	−	4.57675i	0.253095	−	0.438373i	−0.711282	−	0.702907i	$-0.751885\pi$
$109$	2.64239	−	4.57675i	0.253095	−	0.438373i	0.964376	+	0.264534i	$0.0852182\pi$
$110$		0			0
$111$	2.09473	−	1.13500i	0.198823	−	0.107730i
$112$		0			0
$113$			15.9020i			1.49594i	0.663734	+	0.747968i	$0.268971\pi$
$113$			15.9020i			1.49594i	−0.663734	+	0.747968i	$0.731029\pi$
$114$		0			0
$115$	5.12760	+	2.96042i	0.478152	+	0.276061i
$116$		0			0
$117$	−0.733087	+	13.5405i	−0.0677739	+	1.25182i
$118$		0			0
$119$	5.69725	+	1.44434i	0.522266	+	0.132403i
$120$		0			0
$121$	−3.99484	−	6.91926i	−0.363167	−	0.629024i
$122$		0			0
$123$	−0.150156	+	5.55099i	−0.0135392	+	0.500516i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.29106			−0.558242			−0.279121	−	0.960256i	$-0.590043\pi$
$127$	−6.29106			−0.558242			−0.279121	+	0.960256i	$0.590043\pi$
$128$		0			0
$129$	0.422726	−	15.6273i	0.0372189	−	1.37591i
$130$		0			0
$131$	6.56624	+	11.3731i	0.573695	+	0.993668i	0.996182	+	0.0872995i	$0.0278237\pi$
$131$	6.56624	+	11.3731i	0.573695	+	0.993668i	−0.422487	+	0.906369i	$0.638843\pi$
$132$		0			0
$133$	13.5868	+	13.2245i	1.17813	+	1.14671i
$134$		0			0
$135$	−4.69575	+	2.22484i	−0.404146	+	0.191484i
$136$		0			0
$137$	−4.99494	−	2.88383i	−0.426746	−	0.246382i	0.271213	−	0.962519i	$-0.412575\pi$
$137$	−4.99494	−	2.88383i	−0.426746	−	0.246382i	−0.697960	+	0.716137i	$0.745908\pi$
$138$		0			0
$139$		−	1.66017i		−	0.140814i	−0.997518	−	0.0704068i	$-0.977570\pi$
$139$		−	1.66017i		−	0.140814i	0.997518	−	0.0704068i	$-0.0224297\pi$
$140$		0			0
$141$	1.70963	−	0.926344i	0.143977	−	0.0780122i
$142$		0			0
$143$	−3.92126	+	6.79181i	−0.327912	+	0.567960i
$144$		0			0
$145$	7.89474	−	4.55803i	0.655623	−	0.378524i
$146$		0			0
$147$	6.06203	+	10.5001i	0.499987	+	0.866033i
$148$		0			0
$149$	−11.4737	+	6.62433i	−0.939961	+	0.542686i	−0.889948	−	0.456062i	$-0.849259\pi$
$149$	−11.4737	+	6.62433i	−0.939961	+	0.542686i	−0.0500126	+	0.998749i	$0.515926\pi$
$150$		0			0
$151$	6.42140	−	11.1222i	0.522566	−	0.905111i	−0.477089	−	0.878855i	$-0.658308\pi$
$151$	6.42140	−	11.1222i	0.522566	−	0.905111i	0.999655	−	0.0262559i	$-0.00835848\pi$
$152$		0			0
$153$	−3.63936	+	5.58299i	−0.294225	+	0.451358i
$154$		0			0
$155$			6.65732i			0.534729i
$156$		0			0
$157$	3.96267	+	2.28785i	0.316255	+	0.182590i	0.649722	−	0.760172i	$-0.274885\pi$
$157$	3.96267	+	2.28785i	0.316255	+	0.182590i	−0.333467	+	0.942762i	$0.608219\pi$
$158$		0			0
$159$	−6.91204	+	11.2576i	−0.548161	+	0.892785i
$160$		0			0
$161$	11.2256	+	10.9262i	0.884699	+	0.861104i
$162$		0			0
$163$	−1.63146	−	2.82578i	−0.127786	−	0.221332i	0.795032	−	0.606567i	$-0.207454\pi$
$163$	−1.63146	−	2.82578i	−0.127786	−	0.221332i	−0.922819	+	0.385235i	$0.874120\pi$
$164$		0			0
$165$	−3.00406	−	0.0812610i	−0.233866	−	0.00632616i
$166$		0			0
$167$	−16.1809			−1.25212			−0.626060	−	0.779775i	$-0.715333\pi$
$167$	−16.1809			−1.25212			−0.626060	+	0.779775i	$0.715333\pi$
$168$		0			0
$169$	−7.43133			−0.571641
$170$		0			0
$171$	−19.1724	+	9.72715i	−1.46615	+	0.743853i
$172$		0			0
$173$	8.94446	+	15.4923i	0.680035	+	1.17785i	0.974970	+	0.222337i	$0.0713686\pi$
$173$	8.94446	+	15.4923i	0.680035	+	1.17785i	−0.294935	+	0.955517i	$0.595298\pi$
$174$		0			0
$175$	−2.56462	−	0.650171i	−0.193867	−	0.0491483i
$176$		0			0
$177$	−0.721345	−	0.442898i	−0.0542196	−	0.0332903i
$178$		0			0
$179$	13.9108	+	8.03141i	1.03974	+	0.600296i	0.919760	−	0.392480i	$-0.128383\pi$
$179$	13.9108	+	8.03141i	1.03974	+	0.600296i	0.119982	+	0.992776i	$0.461716\pi$
$180$		0			0
$181$		−	10.4957i		−	0.780142i	−0.920785	−	0.390071i	$-0.872450\pi$
$181$		−	10.4957i		−	0.780142i	0.920785	−	0.390071i	$-0.127550\pi$
$182$		0			0
$183$	−7.22377	−	13.3320i	−0.533997	−	0.985529i
$184$		0			0
$185$	−0.687757	+	1.19123i	−0.0505649	+	0.0875810i
$186$		0			0
$187$	−3.33795	+	1.92717i	−0.244095	+	0.140928i
$188$		0			0
$189$	−13.4893	+	2.65283i	−0.981206	+	0.192965i
$190$		0			0
$191$	7.10655	−	4.10297i	0.514212	−	0.296881i	−0.220351	−	0.975421i	$-0.570720\pi$
$191$	7.10655	−	4.10297i	0.514212	−	0.296881i	0.734563	+	0.678540i	$0.237387\pi$
$192$		0			0
$193$	9.61343	−	16.6509i	0.691990	−	1.19856i	−0.279195	−	0.960234i	$-0.590068\pi$
$193$	9.61343	−	16.6509i	0.691990	−	1.19856i	0.971185	−	0.238327i	$-0.0765989\pi$
$194$		0			0
$195$	−3.72975	−	6.88353i	−0.267093	−	0.492940i
$196$		0			0
$197$		−	22.5041i		−	1.60335i	−0.597761	−	0.801674i	$-0.703943\pi$
$197$		−	22.5041i		−	1.60335i	0.597761	−	0.801674i	$-0.296057\pi$
$198$		0			0
$199$	9.27053	+	5.35234i	0.657171	+	0.379418i	0.791198	−	0.611560i	$-0.209458\pi$
$199$	9.27053	+	5.35234i	0.657171	+	0.379418i	−0.134027	+	0.990978i	$0.542791\pi$
$200$		0			0
$201$	21.0418	+	12.9194i	1.48417	+	0.911266i
$202$		0			0
$203$	23.2105	−	6.55669i	1.62906	−	0.460189i
$204$		0			0
$205$	−1.60302	−	2.77651i	−0.111960	−	0.193920i
$206$		0			0
$207$	−15.8404	+	8.03667i	−1.10099	+	0.558587i
$208$		0			0
$209$	−12.4337			−0.860056
$210$		0			0
$211$	24.4415			1.68262			0.841310	−	0.540554i	$-0.181785\pi$
$211$	24.4415			1.68262			0.841310	+	0.540554i	$0.181785\pi$
$212$		0			0
$213$	−13.7353	−	0.371546i	−0.941129	−	0.0254579i
$214$		0			0
$215$	4.51288	+	7.81653i	0.307776	+	0.533083i
$216$		0			0
$217$	−4.32840	+	17.0735i	−0.293831	+	1.15902i
$218$		0			0
$219$	−1.28352	+	2.09046i	−0.0867321	+	0.141260i
$220$		0			0
$221$	−8.69603	−	5.02066i	−0.584959	−	0.337726i
$222$		0			0
$223$			16.4054i			1.09859i	0.835630	+	0.549293i	$0.185103\pi$
$223$			16.4054i			1.09859i	−0.835630	+	0.549293i	$0.814897\pi$
$224$		0			0
$225$	1.63826	−	2.51319i	0.109217	−	0.167546i
$226$		0			0
$227$	−9.24824	+	16.0184i	−0.613827	+	1.06318i	0.376762	+	0.926310i	$0.377037\pi$
$227$	−9.24824	+	16.0184i	−0.613827	+	1.06318i	−0.990589	+	0.136870i	$0.956296\pi$
$228$		0			0
$229$	−19.3784	+	11.1881i	−1.28056	+	0.739333i	−0.976951	−	0.213463i	$-0.931526\pi$
$229$	−19.3784	+	11.1881i	−1.28056	+	0.739333i	−0.303611	+	0.952796i	$0.598192\pi$
$230$		0			0
$231$	−7.65144	−	2.16156i	−0.503428	−	0.142220i
$232$		0			0
$233$	−22.2560	+	12.8495i	−1.45804	+	0.841799i	−0.998915	−	0.0465740i	$-0.985170\pi$
$233$	−22.2560	+	12.8495i	−1.45804	+	0.841799i	−0.459123	+	0.888373i	$0.651836\pi$
$234$		0			0
$235$	−0.561320	+	0.972234i	−0.0366165	+	0.0634216i
$236$		0			0
$237$	9.27302	−	5.02447i	0.602347	−	0.326374i
$238$		0			0
$239$		−	21.7943i		−	1.40976i	−0.709328	−	0.704879i	$-0.751001\pi$
$239$		−	21.7943i		−	1.40976i	0.709328	−	0.704879i	$-0.248999\pi$
$240$		0			0
$241$	−1.97789	−	1.14194i	−0.127407	−	0.0735587i	0.434942	−	0.900459i	$-0.356769\pi$
$241$	−1.97789	−	1.14194i	−0.127407	−	0.0735587i	−0.562349	+	0.826900i	$0.690102\pi$
$242$		0			0
$243$	2.10144	−	15.4462i	0.134807	−	0.990872i
$244$		0			0
$245$	−6.15455	−	3.33489i	−0.393200	−	0.213058i
$246$		0			0
$247$	−16.1961	−	28.0525i	−1.03054	−	1.78494i
$248$		0			0
$249$	−0.730890	+	27.0196i	−0.0463183	+	1.71230i
$250$		0			0
$251$	17.1557			1.08286			0.541429	−	0.840747i	$-0.317884\pi$
$251$	17.1557			1.08286			0.541429	+	0.840747i	$0.317884\pi$
$252$		0			0
$253$	−10.2728			−0.645848
$254$		0			0
$255$	0.104044	−	3.84631i	0.00651549	−	0.240865i
$256$		0			0
$257$	−1.87411	−	3.24605i	−0.116904	−	0.202483i	0.801636	−	0.597813i	$-0.203964\pi$
$257$	−1.87411	−	3.24605i	−0.116904	−	0.202483i	−0.918539	+	0.395330i	$0.870630\pi$
$258$		0			0
$259$	−2.53834	+	2.60789i	−0.157725	+	0.162047i
$260$		0			0
$261$	−1.47848	+	27.3082i	−0.0915154	+	1.69034i
$262$		0			0
$263$	17.7647	+	10.2564i	1.09542	+	0.632439i	0.935014	−	0.354612i	$-0.115387\pi$
$263$	17.7647	+	10.2564i	1.09542	+	0.632439i	0.160404	+	0.987051i	$0.448720\pi$
$264$		0			0
$265$		−	7.62692i		−	0.468518i
$266$		0			0
$267$	6.93550	−	3.75791i	0.424445	−	0.229981i
$268$		0			0
$269$	−9.77038	+	16.9228i	−0.595711	+	1.03180i	0.397735	+	0.917500i	$0.369796\pi$
$269$	−9.77038	+	16.9228i	−0.595711	+	1.03180i	−0.993446	+	0.114301i	$0.963537\pi$
$270$		0			0
$271$	−19.7609	+	11.4090i	−1.20039	+	0.693047i	−0.960642	−	0.277788i	$-0.910399\pi$
$271$	−19.7609	+	11.4090i	−1.20039	+	0.693047i	−0.239750	+	0.970835i	$0.577065\pi$
$272$		0			0
$273$	−5.08993	−	20.0786i	−0.308057	−	1.21521i
$274$		0			0
$275$	1.50258	−	0.867515i	0.0906090	−	0.0523131i
$276$		0			0
$277$	−3.27512	+	5.67267i	−0.196783	+	0.340838i	−0.947484	−	0.319805i	$-0.896383\pi$
$277$	−3.27512	+	5.67267i	−0.196783	+	0.340838i	0.750701	+	0.660643i	$0.229716\pi$
$278$		0			0
$279$	−16.7311	−	10.9064i	−1.00166	−	0.652951i
$280$		0			0
$281$		−	12.6670i		−	0.755651i	−0.925877	−	0.377825i	$-0.876672\pi$
$281$		−	12.6670i		−	0.755651i	0.925877	−	0.377825i	$-0.123328\pi$
$282$		0			0
$283$	−2.06081	−	1.18981i	−0.122502	−	0.0707267i	0.437497	−	0.899220i	$-0.355865\pi$
$283$	−2.06081	−	1.18981i	−0.122502	−	0.0707267i	−0.559999	+	0.828493i	$0.689198\pi$
$284$		0			0
$285$	6.49457	−	10.5777i	0.384705	−	0.626566i
$286$		0			0
$287$	−2.30593	−	8.16294i	−0.136115	−	0.481843i
$288$		0			0
$289$	6.03252	+	10.4486i	0.354854	+	0.614625i
$290$		0			0
$291$	12.0199	+	0.325143i	0.704619	+	0.0190602i
$292$		0			0
$293$	17.6255			1.02969			0.514847	−	0.857282i	$-0.327849\pi$
$293$	17.6255			1.02969			0.514847	+	0.857282i	$0.327849\pi$
$294$		0			0
$295$	0.488705			0.0284535
$296$		0			0
$297$	5.12566	−	7.41663i	0.297421	−	0.430357i
$298$		0			0
$299$	−13.3814	−	23.1773i	−0.773868	−	1.34038i
$300$		0			0
$301$	6.49173	+	22.9806i	0.374177	+	1.32458i
$302$		0			0
$303$	4.19221	+	2.57397i	0.240836	+	0.147871i
$304$		0			0
$305$	7.58163	+	4.37726i	0.434123	+	0.250641i
$306$		0			0
$307$		−	17.8269i		−	1.01743i	−0.860934	−	0.508717i	$-0.830120\pi$
$307$		−	17.8269i		−	1.01743i	0.860934	−	0.508717i	$-0.169880\pi$
$308$		0			0
$309$	13.4788	+	24.8761i	0.766782	+	1.41515i
$310$		0			0
$311$	3.30272	−	5.72047i	0.187280	−	0.324378i	−0.757063	−	0.653342i	$-0.773366\pi$
$311$	3.30272	−	5.72047i	0.187280	−	0.324378i	0.944342	+	0.328964i	$0.106700\pi$
$312$		0			0
$313$	−14.7063	+	8.49066i	−0.831246	+	0.479920i	−0.854279	−	0.519814i	$-0.826001\pi$
$313$	−14.7063	+	8.49066i	−0.831246	+	0.479920i	0.0230328	+	0.999735i	$0.492668\pi$
$314$		0			0
$315$	5.83552	−	5.38021i	0.328794	−	0.303141i
$316$		0			0
$317$	2.83413	−	1.63629i	0.159181	−	0.0919031i	−0.418294	−	0.908312i	$-0.637372\pi$
$317$	2.83413	−	1.63629i	0.159181	−	0.0919031i	0.577474	+	0.816409i	$0.304038\pi$
$318$		0			0
$319$	−7.90832	+	13.6976i	−0.442781	+	0.766919i
$320$		0			0
$321$	−6.09928	−	11.2567i	−0.340429	−	0.628285i
$322$		0			0
$323$		−	15.9197i		−	0.885797i
$324$		0			0
$325$	3.91452	+	2.26005i	0.217139	+	0.125365i
$326$		0			0
$327$	−7.80050	−	4.78943i	−0.431369	−	0.264856i
$328$		0			0
$329$	−2.07169	+	2.12846i	−0.114216	+	0.117346i
$330$		0			0
$331$	3.57149	+	6.18601i	0.196307	+	0.340014i	0.947328	−	0.320264i	$-0.103772\pi$
$331$	3.57149	+	6.18601i	0.196307	+	0.340014i	−0.751021	+	0.660278i	$0.770438\pi$
$332$		0			0
$333$	−1.86706	−	3.68001i	−0.102314	−	0.201663i
$334$		0			0
$335$	−14.2556			−0.778867
$336$		0			0
$337$	−1.33490			−0.0727168			−0.0363584	−	0.999339i	$-0.511576\pi$
$337$	−1.33490			−0.0727168			−0.0363584	+	0.999339i	$0.511576\pi$
$338$		0			0
$339$	27.5330	+	0.744779i	1.49539	+	0.0404509i
$340$		0			0
$341$	−5.77532	−	10.0031i	−0.312751	−	0.541701i
$342$		0			0
$343$	−13.6158	−	12.5542i	−0.735187	−	0.677865i
$344$		0			0
$345$	5.36588	−	8.73937i	0.288889	−	0.470512i
$346$		0			0
$347$	−2.53870	−	1.46572i	−0.136284	−	0.0786838i	0.430308	−	0.902682i	$-0.358405\pi$
$347$	−2.53870	−	1.46572i	−0.136284	−	0.0786838i	−0.566592	+	0.823998i	$0.691738\pi$
$348$		0			0
$349$		−	14.1947i		−	0.759823i	−0.925023	−	0.379912i	$-0.875954\pi$
$349$		−	14.1947i		−	0.759823i	0.925023	−	0.379912i	$-0.124046\pi$
$350$		0			0
$351$	23.4099	+	1.90345i	1.24953	+	0.101599i
$352$		0			0
$353$	−6.34424	+	10.9885i	−0.337670	+	0.584861i	−0.983994	−	0.178202i	$-0.942972\pi$
$353$	−6.34424	+	10.9885i	−0.337670	+	0.584861i	0.646324	+	0.763063i	$0.276305\pi$
$354$		0			0
$355$	6.87017	−	3.96650i	0.364631	−	0.210520i
$356$		0			0
$357$	2.76759	−	9.79667i	0.146477	−	0.518495i
$358$		0			0
$359$	7.00432	−	4.04395i	0.369674	−	0.213431i	−0.303642	−	0.952786i	$-0.598203\pi$
$359$	7.00432	−	4.04395i	0.369674	−	0.213431i	0.673316	+	0.739355i	$0.264869\pi$
$360$		0			0
$361$	16.1777	−	28.0206i	0.851459	−	1.47477i
$362$		0			0
$363$	−12.1672	+	6.59266i	−0.638614	+	0.346025i
$364$		0			0
$365$		−	1.41627i		−	0.0741307i
$366$		0			0
$367$	−10.8649	−	6.27287i	−0.567145	−	0.327441i	0.188863	−	0.982003i	$-0.439520\pi$
$367$	−10.8649	−	6.27287i	−0.567145	−	0.327441i	−0.756008	+	0.654562i	$0.772853\pi$
$368$		0			0
$369$	9.60406	+	0.519967i	0.499967	+	0.0270684i
$370$		0			0
$371$	4.95880	−	19.5601i	0.257448	−	1.01551i
$372$		0			0
$373$	15.5352	+	26.9078i	0.804382	+	1.39323i	0.916707	+	0.399560i	$0.130837\pi$
$373$	15.5352	+	26.9078i	0.804382	+	1.39323i	−0.112325	+	0.993672i	$0.535830\pi$
$374$		0			0
$375$	−0.0468355	+	1.73142i	−0.00241857	+	0.0894100i
$376$		0			0
$377$	−41.2056			−2.12219
$378$		0			0
$379$	−0.0979431			−0.00503100			−0.00251550	−	0.999997i	$-0.500801\pi$
$379$	−0.0979431			−0.00503100			−0.00251550	+	0.999997i	$0.500801\pi$
$380$		0			0
$381$	−0.294645	+	10.8925i	−0.0150951	+	0.558038i
$382$		0			0
$383$	9.57846	+	16.5904i	0.489436	+	0.847729i	0.999926	−	0.0121553i	$-0.00386924\pi$
$383$	9.57846	+	16.5904i	0.489436	+	0.847729i	−0.510490	+	0.859884i	$0.670536\pi$
$384$		0			0
$385$	4.41758	−	1.24791i	0.225141	−	0.0635995i
$386$		0			0
$387$	−27.0377	−	1.46383i	−1.37440	−	0.0744106i
$388$		0			0
$389$	21.6644	+	12.5079i	1.09843	+	0.634178i	0.935808	−	0.352511i	$-0.114672\pi$
$389$	21.6644	+	12.5079i	1.09843	+	0.634178i	0.162620	+	0.986689i	$0.448005\pi$
$390$		0			0
$391$		−	13.1530i		−	0.665178i
$392$		0			0
$393$	19.9990	−	10.8362i	1.00882	−	0.546616i
$394$		0			0
$395$	−3.04459	+	5.27338i	−0.153190	+	0.265332i
$396$		0			0
$397$	22.8951	−	13.2185i	1.14907	−	0.663417i	0.200411	−	0.979712i	$-0.435772\pi$
$397$	22.8951	−	13.2185i	1.14907	−	0.663417i	0.948661	+	0.316295i	$0.102439\pi$
$398$		0			0
$399$	23.5334	−	22.9051i	1.17814	−	1.14669i
$400$		0			0
$401$	−11.7907	+	6.80738i	−0.588801	+	0.339944i	−0.764623	−	0.644478i	$-0.777075\pi$
$401$	−11.7907	+	6.80738i	−0.588801	+	0.339944i	0.175822	+	0.984422i	$0.443742\pi$
$402$		0			0
$403$	15.0459	−	26.0602i	0.749489	−	1.29815i
$404$		0			0
$405$	3.63220	+	8.23451i	0.180485	+	0.409176i
$406$		0			0
$407$		−	2.38656i		−	0.118297i
$408$		0			0
$409$	23.3342	+	13.4720i	1.15380	+	0.666146i	0.949810	−	0.312827i	$-0.101276\pi$
$409$	23.3342	+	13.4720i	1.15380	+	0.666146i	0.203989	+	0.978973i	$0.434609\pi$
$410$		0			0
$411$	−5.22705	+	8.51326i	−0.257831	+	0.419928i
$412$		0			0
$413$	1.25334	+	0.317742i	0.0616730	+	0.0156351i
$414$		0			0
$415$	−7.80274	−	13.5147i	−0.383021	−	0.663412i
$416$		0			0
$417$	−2.87444	−	0.0777548i	−0.140762	−	0.00380767i
$418$		0			0
$419$	−2.39230			−0.116871			−0.0584357	−	0.998291i	$-0.518611\pi$
$419$	−2.39230			−0.116871			−0.0584357	+	0.998291i	$0.518611\pi$
$420$		0			0
$421$	−19.4713			−0.948972			−0.474486	−	0.880263i	$-0.657366\pi$
$421$	−19.4713			−0.948972			−0.474486	+	0.880263i	$0.657366\pi$
$422$		0			0
$423$	−1.52382	−	3.00347i	−0.0740905	−	0.146034i
$424$		0			0
$425$	1.11074	+	1.92386i	0.0538788	+	0.0933208i
$426$		0			0
$427$	16.5980	+	16.1554i	0.803236	+	0.781813i
$428$		0			0
$429$	11.5758	+	7.10743i	0.558886	+	0.343150i
$430$		0			0
$431$	−9.21326	−	5.31928i	−0.443787	−	0.256221i	0.261416	−	0.965226i	$-0.415811\pi$
$431$	−9.21326	−	5.31928i	−0.443787	−	0.256221i	−0.705203	+	0.709006i	$0.749144\pi$
$432$		0			0
$433$		−	11.4141i		−	0.548527i	−0.961655	−	0.274263i	$-0.911566\pi$
$433$		−	11.4141i		−	0.548527i	0.961655	−	0.274263i	$-0.0884340\pi$
$434$		0			0
$435$	−7.52210	−	13.8826i	−0.360657	−	0.665619i
$436$		0			0
$437$	21.2152	−	36.7458i	1.01486	−	1.75779i
$438$		0			0
$439$	−27.2069	+	15.7079i	−1.29851	+	0.749698i	−0.980147	−	0.198270i	$-0.936468\pi$
$439$	−27.2069	+	15.7079i	−1.29851	+	0.749698i	−0.318367	+	0.947968i	$0.603134\pi$
$440$		0			0
$441$	18.4640	−	10.0041i	0.879236	−	0.476387i
$442$		0			0
$443$	2.27390	−	1.31284i	0.108036	−	0.0623747i	−0.445008	−	0.895526i	$-0.646799\pi$
$443$	2.27390	−	1.31284i	0.108036	−	0.0623747i	0.553044	+	0.833152i	$0.313466\pi$
$444$		0			0
$445$	−2.27711	+	3.94408i	−0.107946	+	0.186967i
$446$		0			0
$447$	10.9321	+	20.1760i	0.517071	+	0.954291i
$448$		0			0
$449$		−	16.3605i		−	0.772100i	−0.922478	−	0.386050i	$-0.873839\pi$
$449$		−	16.3605i		−	0.772100i	0.922478	−	0.386050i	$-0.126161\pi$
$450$		0			0
$451$	4.81733	+	2.78129i	0.226839	+	0.130966i
$452$		0			0
$453$	−18.9564	−	11.6390i	−0.890649	−	0.546849i
$454$		0			0
$455$	8.56985	+	8.34129i	0.401761	+	0.391045i
$456$		0			0
$457$	13.8490	+	23.9872i	0.647831	+	1.12208i	0.983640	+	0.180146i	$0.0576569\pi$
$457$	13.8490	+	23.9872i	0.647831	+	1.12208i	−0.335809	+	0.941930i	$0.609010\pi$
$458$		0			0
$459$	9.49603	+	6.56274i	0.443237	+	0.306322i
$460$		0			0
$461$	2.25024			0.104804			0.0524022	−	0.998626i	$-0.483312\pi$
$461$	2.25024			0.104804			0.0524022	+	0.998626i	$0.483312\pi$
$462$		0			0
$463$	−3.66223			−0.170198			−0.0850991	−	0.996372i	$-0.527121\pi$
$463$	−3.66223			−0.170198			−0.0850991	+	0.996372i	$0.527121\pi$
$464$		0			0
$465$	11.5266	+	0.311799i	0.534533	+	0.0144593i
$466$		0			0
$467$	12.8340	+	22.2291i	0.593885	+	1.02864i	0.993703	+	0.112044i	$0.0357398\pi$
$467$	12.8340	+	22.2291i	0.593885	+	1.02864i	−0.399819	+	0.916594i	$0.630927\pi$
$468$		0			0
$469$	−36.5602	−	9.26859i	−1.68819	−	0.427984i
$470$		0			0
$471$	4.14681	−	6.75388i	0.191075	−	0.311202i
$472$		0			0
$473$	−13.5619	−	7.82997i	−0.623577	−	0.360023i
$474$		0			0
$475$			7.16627i			0.328811i
$476$		0			0
$477$	19.1679	+	12.4949i	0.877636	+	0.572101i
$478$		0			0
$479$	14.8176	−	25.6648i	0.677032	−	1.17265i	−0.298838	−	0.954304i	$-0.596599\pi$
$479$	14.8176	−	25.6648i	0.677032	−	1.17265i	0.975870	−	0.218350i	$-0.0700676\pi$
$480$		0			0
$481$	5.38448	−	3.10873i	0.245511	−	0.141746i
$482$		0			0
$483$	19.4435	−	18.9244i	0.884712	−	0.861091i
$484$		0			0
$485$	−6.01215	+	3.47112i	−0.272998	+	0.157615i
$486$		0			0
$487$	9.71448	−	16.8260i	0.440205	−	0.762458i	−0.557499	−	0.830178i	$-0.688239\pi$
$487$	9.71448	−	16.8260i	0.440205	−	0.762458i	0.997704	+	0.0677196i	$0.0215723\pi$
$488$		0			0
$489$	−4.96901	+	2.69240i	−0.224707	+	0.121755i
$490$		0			0
$491$			28.6905i			1.29478i	0.762158	+	0.647391i	$0.224140\pi$
$491$			28.6905i			1.29478i	−0.762158	+	0.647391i	$0.775860\pi$
$492$		0			0
$493$	−17.5380	−	10.1256i	−0.789872	−	0.456033i
$494$		0			0
$495$	−0.281393	+	5.19748i	−0.0126477	+	0.233609i
$496$		0			0
$497$	20.1983	−	5.70577i	0.906017	−	0.255939i
$498$		0			0
$499$	−16.4576	−	28.5054i	−0.736743	−	1.27608i	−0.953954	−	0.299952i	$-0.903029\pi$
$499$	−16.4576	−	28.5054i	−0.736743	−	1.27608i	0.217211	−	0.976125i	$-0.430304\pi$
$500$		0			0
$501$	−0.757843	+	28.0160i	−0.0338579	+	1.25166i
$502$		0			0
$503$	12.2651			0.546874			0.273437	−	0.961890i	$-0.411840\pi$
$503$	12.2651			0.546874			0.273437	+	0.961890i	$0.411840\pi$
$504$		0			0
$505$	−2.84018			−0.126387
$506$		0			0
$507$	−0.348050	+	12.8667i	−0.0154574	+	0.571432i
$508$		0			0
$509$	−7.21563	−	12.4978i	−0.319827	−	0.553957i	0.660625	−	0.750716i	$-0.270291\pi$
$509$	−7.21563	−	12.4978i	−0.319827	−	0.553957i	−0.980452	+	0.196760i	$0.936958\pi$
$510$		0			0
$511$	0.920815	−	3.63218i	0.0407345	−	0.160678i
$512$		0			0
$513$	15.9438	+	33.6510i	0.703936	+	1.48573i
$514$		0			0
$515$	−14.1465	−	8.16751i	−0.623371	−	0.359903i
$516$		0			0
$517$		−	1.94781i		−	0.0856647i
$518$		0			0
$519$	27.2425	−	14.7610i	1.19581	−	0.647936i
$520$		0			0
$521$	3.78222	−	6.55100i	0.165702	−	0.287005i	−0.771202	−	0.636590i	$-0.780344\pi$
$521$	3.78222	−	6.55100i	0.165702	−	0.287005i	0.936904	+	0.349586i	$0.113678\pi$
$522$		0			0
$523$	8.64129	−	4.98905i	0.377857	−	0.218156i	−0.299028	−	0.954244i	$-0.596662\pi$
$523$	8.64129	−	4.98905i	0.377857	−	0.218156i	0.676886	+	0.736088i	$0.263329\pi$
$524$		0			0
$525$	−1.24583	+	4.40998i	−0.0543726	+	0.192467i
$526$		0			0
$527$	12.8077	−	7.39454i	0.557913	−	0.322111i
$528$		0			0
$529$	6.02822	−	10.4412i	0.262096	−	0.453964i
$530$		0			0
$531$	−0.800626	+	1.22821i	−0.0347442	+	0.0532996i
$532$		0			0
$533$			14.4916i			0.627702i
$534$		0			0
$535$	6.40143	+	3.69587i	0.276758	+	0.159786i
$536$		0			0
$537$	14.5572	−	23.7093i	0.628191	−	1.02313i
$538$		0			0
$539$	12.1408	−	0.328237i	0.522940	−	0.0141381i
$540$		0			0
$541$	−16.5475	−	28.6612i	−0.711434	−	1.23224i	−0.964319	−	0.264744i	$-0.914713\pi$
$541$	−16.5475	−	28.6612i	−0.711434	−	1.23224i	0.252884	−	0.967496i	$-0.418621\pi$
$542$		0			0
$543$	−18.1725	−	0.491573i	−0.779857	−	0.0210954i
$544$		0			0
$545$	5.28477			0.226375
$546$		0			0
$547$	−45.0112			−1.92454			−0.962270	−	0.272096i	$-0.912283\pi$
$547$	−45.0112			−1.92454			−0.962270	+	0.272096i	$0.912283\pi$
$548$		0			0
$549$	−23.4216	+	11.8830i	−0.999608	+	0.507152i
$550$		0			0
$551$	−32.6641	−	56.5759i	−1.39154	−	2.41021i
$552$		0			0
$553$	−11.2368	+	11.5447i	−0.477838	+	0.490931i
$554$		0			0
$555$	2.03031	+	1.24659i	0.0861817	+	0.0529146i
$556$		0			0
$557$	−1.45160	−	0.838083i	−0.0615064	−	0.0355107i	0.468931	−	0.883235i	$-0.344639\pi$
$557$	−1.45160	−	0.838083i	−0.0615064	−	0.0355107i	−0.530438	+	0.847724i	$0.677972\pi$
$558$		0			0
$559$		−	40.7973i		−	1.72554i
$560$		0			0
$561$	3.18039	+	5.86964i	0.134276	+	0.247817i
$562$		0			0
$563$	−21.4502	+	37.1529i	−0.904020	+	1.56581i	−0.0817930	+	0.996649i	$0.526065\pi$
$563$	−21.4502	+	37.1529i	−0.904020	+	1.56581i	−0.822227	+	0.569159i	$0.807269\pi$
$564$		0			0
$565$	−13.7716	+	7.95101i	−0.579374	+	0.334502i
$566$		0			0
$567$	3.96137	+	23.4799i	0.166362	+	0.986065i
$568$		0			0
$569$	−35.5051	+	20.4989i	−1.48845	+	0.859357i	−0.999913	−	0.0131862i	$-0.995803\pi$
$569$	−35.5051	+	20.4989i	−1.48845	+	0.859357i	−0.488537	+	0.872543i	$0.662469\pi$
$570$		0			0
$571$	−7.30655	+	12.6553i	−0.305770	+	0.529609i	−0.977432	−	0.211248i	$-0.932247\pi$
$571$	−7.30655	+	12.6553i	−0.305770	+	0.529609i	0.671663	+	0.740857i	$0.265580\pi$
$572$		0			0
$573$	−6.77112	−	12.4966i	−0.282867	−	0.522052i
$574$		0			0
$575$			5.92085i			0.246916i
$576$		0			0
$577$	−11.8401	−	6.83587i	−0.492909	−	0.284581i	0.232872	−	0.972508i	$-0.425188\pi$
$577$	−11.8401	−	6.83587i	−0.492909	−	0.284581i	−0.725780	+	0.687926i	$0.758521\pi$
$578$		0			0
$579$	−28.3795	−	17.4247i	−1.17941	−	0.724146i
$580$		0			0
$581$	−11.2242	−	39.7333i	−0.465657	−	1.64841i
$582$		0			0
$583$	6.61646	+	11.4601i	0.274026	+	0.474627i
$584$		0			0
$585$	−12.0929	+	6.13537i	−0.499982	+	0.253666i
$586$		0			0
$587$	1.12952			0.0466203			0.0233102	−	0.999728i	$-0.492579\pi$
$587$	1.12952			0.0466203			0.0233102	+	0.999728i	$0.492579\pi$
$588$		0			0
$589$	47.7081			1.96578
$590$		0			0
$591$	−38.9639	−	1.05399i	−1.60276	−	0.0433553i
$592$		0			0
$593$	5.52609	+	9.57146i	0.226929	+	0.393053i	0.956896	−	0.290429i	$-0.0937981\pi$
$593$	5.52609	+	9.57146i	0.226929	+	0.393053i	−0.729967	+	0.683482i	$0.760465\pi$
$594$		0			0
$595$	1.59779	+	5.65613i	0.0655029	+	0.231879i
$596$		0			0
$597$	9.70133	−	15.8005i	0.397049	−	0.646671i
$598$		0			0
$599$	−13.6283	−	7.86831i	−0.556838	−	0.321490i	0.195038	−	0.980796i	$-0.437517\pi$
$599$	−13.6283	−	7.86831i	−0.556838	−	0.321490i	−0.751875	+	0.659305i	$0.770850\pi$
$600$		0			0
$601$			36.9336i			1.50655i	0.657704	+	0.753276i	$0.271528\pi$
$601$			36.9336i			1.50655i	−0.657704	+	0.753276i	$0.728472\pi$
$602$		0			0
$603$	23.3544	−	35.8270i	0.951065	−	1.45899i
$604$		0			0
$605$	3.99484	−	6.91926i	0.162413	−	0.281308i
$606$		0			0
$607$	−6.08775	+	3.51476i	−0.247094	+	0.142660i	−0.618433	−	0.785838i	$-0.712232\pi$
$607$	−6.08775	+	3.51476i	−0.247094	+	0.142660i	0.371339	+	0.928497i	$0.378899\pi$
$608$		0			0
$609$	−10.2653	−	40.4942i	−0.415970	−	1.64091i
$610$		0			0
$611$	4.39460	−	2.53722i	0.177786	−	0.102645i
$612$		0			0
$613$	6.83385	−	11.8366i	0.276017	−	0.478075i	−0.694374	−	0.719614i	$-0.744319\pi$
$613$	6.83385	−	11.8366i	0.276017	−	0.478075i	0.970391	+	0.241539i	$0.0776522\pi$
$614$		0			0
$615$	−4.88238	+	2.64546i	−0.196877	+	0.106675i
$616$		0			0
$617$		−	29.1859i		−	1.17498i	−0.809232	−	0.587489i	$-0.800116\pi$
$617$		−	29.1859i		−	1.17498i	0.809232	−	0.587489i	$-0.199884\pi$
$618$		0			0
$619$	30.1847	+	17.4271i	1.21322	+	0.700455i	0.963460	−	0.267852i	$-0.0863137\pi$
$619$	30.1847	+	17.4271i	1.21322	+	0.700455i	0.249764	+	0.968307i	$0.419647\pi$
$620$		0			0
$621$	13.1729	+	27.8028i	0.528612	+	1.11569i
$622$		0			0
$623$	−8.40426	+	8.63455i	−0.336710	+	0.345936i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.582338	+	21.5279i	−0.0232563	+	0.859742i
$628$		0			0
$629$	3.05568			0.121838
$630$		0			0
$631$	−17.5038			−0.696816			−0.348408	−	0.937343i	$-0.613278\pi$
$631$	−17.5038			−0.696816			−0.348408	+	0.937343i	$0.613278\pi$
$632$		0			0
$633$	1.14473	−	42.3184i	0.0454988	−	1.68200i
$634$		0			0
$635$	−3.14553	−	5.44822i	−0.124827	−	0.216206i
$636$		0			0
$637$	16.5551	+	26.9641i	0.655939	+	1.06836i
$638$		0			0
$639$	−1.28660	+	23.7642i	−0.0508972	+	0.940096i
$640$		0			0
$641$	12.8017	+	7.39109i	0.505638	+	0.291930i	0.731039	−	0.682336i	$-0.239036\pi$
$641$	12.8017	+	7.39109i	0.505638	+	0.291930i	−0.225401	+	0.974266i	$0.572369\pi$
$642$		0			0
$643$			8.75484i			0.345257i	0.984987	+	0.172629i	$0.0552260\pi$
$643$			8.75484i			0.345257i	−0.984987	+	0.172629i	$0.944774\pi$
$644$		0			0
$645$	13.7450	−	7.44758i	0.541210	−	0.293248i
$646$		0			0
$647$	2.25035	−	3.89772i	0.0884703	−	0.153235i	−0.818394	−	0.574657i	$-0.805136\pi$
$647$	2.25035	−	3.89772i	0.0884703	−	0.153235i	0.906865	+	0.421422i	$0.138469\pi$
$648$		0			0
$649$	−0.734318	+	0.423959i	−0.0288245	+	0.0166418i
$650$		0			0
$651$	29.3586	+	8.29391i	1.15065	+	0.325064i
$652$		0			0
$653$	−18.4630	+	10.6596i	−0.722514	+	0.417144i	−0.815677	−	0.578507i	$-0.803636\pi$
$653$	−18.4630	+	10.6596i	−0.722514	+	0.417144i	0.0931631	+	0.995651i	$0.470302\pi$
$654$		0			0
$655$	−6.56624	+	11.3731i	−0.256564	+	0.444382i
$656$		0			0
$657$	3.55934	+	2.32021i	0.138863	+	0.0905202i
$658$		0			0
$659$			29.9255i			1.16573i	0.812569	+	0.582865i	$0.198069\pi$
$659$			29.9255i			1.16573i	−0.812569	+	0.582865i	$0.801931\pi$
$660$		0			0
$661$	−23.9971	−	13.8547i	−0.933379	−	0.538886i	−0.0455001	−	0.998964i	$-0.514488\pi$
$661$	−23.9971	−	13.8547i	−0.933379	−	0.538886i	−0.887879	+	0.460078i	$0.847821\pi$
$662$		0			0
$663$	−9.10014	+	14.8213i	−0.353420	+	0.575612i
$664$		0			0
$665$	−4.65930	+	18.3788i	−0.180680	+	0.712698i
$666$		0			0
$667$	−26.9874	−	46.7436i	−1.04496	−	1.80992i
$668$		0			0
$669$	28.4046	+	0.768354i	1.09818	+	0.0297063i
$670$		0			0
$671$	−15.1893			−0.586378
$672$		0			0
$673$	−28.8495			−1.11206			−0.556032	−	0.831161i	$-0.687677\pi$
$673$	−28.8495			−1.11206			−0.556032	+	0.831161i	$0.687677\pi$
$674$		0			0
$675$	−4.27464	−	2.95422i	−0.164531	−	0.113708i
$676$		0			0
$677$	21.9030	+	37.9372i	0.841802	+	1.45804i	0.888370	+	0.459128i	$0.151838\pi$
$677$	21.9030	+	37.9372i	0.841802	+	1.45804i	−0.0465685	+	0.998915i	$0.514829\pi$
$678$		0			0
$679$	−17.6757	+	4.99317i	−0.678331	+	0.191620i
$680$		0			0
$681$	27.3014	+	16.7628i	1.04619	+	0.642352i
$682$		0			0
$683$	10.2915	+	5.94181i	0.393794	+	0.227357i	0.683803	−	0.729667i	$-0.260325\pi$
$683$	10.2915	+	5.94181i	0.393794	+	0.227357i	−0.290009	+	0.957024i	$0.593658\pi$
$684$		0			0
$685$		−	5.76766i		−	0.220371i
$686$		0			0
$687$	18.4637	+	34.0761i	0.704435	+	1.30009i
$688$		0			0
$689$	−17.2372	+	29.8558i	−0.656686	+	1.13741i
$690$		0			0
$691$	−25.8888	+	14.9469i	−0.984858	+	0.568608i	−0.903733	−	0.428096i	$-0.859185\pi$
$691$	−25.8888	+	14.9469i	−0.984858	+	0.568608i	−0.0811246	+	0.996704i	$0.525851\pi$
$692$		0			0
$693$	−4.10092	+	13.1466i	−0.155781	+	0.499398i
$694$		0			0
$695$	1.43775	−	0.830084i	0.0545369	−	0.0314869i
$696$		0			0
$697$	−3.56108	+	6.16796i	−0.134885	+	0.233628i
$698$		0			0
$699$	21.2055	+	39.1362i	0.802065	+	1.48027i
$700$		0			0
$701$		−	25.1116i		−	0.948451i	−0.880403	−	0.474226i	$-0.842728\pi$
$701$		−	25.1116i		−	0.948451i	0.880403	−	0.474226i	$-0.157272\pi$
$702$		0			0
$703$	8.53668	+	4.92865i	0.321967	+	0.185888i
$704$		0			0
$705$	1.65705	+	1.01741i	0.0624083	+	0.0383180i
$706$		0			0
$707$	−7.28399	−	1.84661i	−0.273943	−	0.0694488i
$708$		0			0
$709$	13.8755	+	24.0330i	0.521104	+	0.902578i	0.999699	+	0.0245424i	$0.00781286\pi$
$709$	13.8755	+	24.0330i	0.521104	+	0.902578i	−0.478595	+	0.878036i	$0.658854\pi$
$710$		0			0
$711$	−8.26515	−	16.2908i	−0.309967	−	0.610952i
$712$		0			0
$713$	39.4170			1.47618
$714$		0			0
$715$	−7.84251			−0.293293
$716$		0			0
$717$	−37.7351	−	1.02075i	−1.40924	−	0.0381205i
$718$		0			0
$719$	−3.02336	−	5.23662i	−0.112752	−	0.195293i	0.804127	−	0.594458i	$-0.202633\pi$
$719$	−3.02336	−	5.23662i	−0.112752	−	0.195293i	−0.916879	+	0.399165i	$0.869300\pi$
$720$		0			0
$721$	−30.9702	−	30.1442i	−1.15339	−	1.12263i
$722$		0			0
$723$	−2.06981	+	3.37108i	−0.0769769	+	0.125372i
$724$		0			0
$725$	7.89474	+	4.55803i	0.293203	+	0.169281i
$726$		0			0
$727$			24.4800i			0.907915i	0.891023	+	0.453957i	$0.149988\pi$
$727$			24.4800i			0.907915i	−0.891023	+	0.453957i	$0.850012\pi$
$728$		0			0
$729$	−26.6453	−	4.36189i	−0.986864	−	0.161552i
$730$		0			0
$731$	10.0253	−	17.3643i	0.370798	−	0.642240i
$732$		0			0
$733$	−14.6881	+	8.48017i	−0.542517	+	0.313222i	−0.746098	−	0.665836i	$-0.768075\pi$
$733$	−14.6881	+	8.48017i	−0.542517	+	0.313222i	0.203582	+	0.979058i	$0.434742\pi$
$734$		0			0
$735$	−6.06233	+	10.4999i	−0.223612	+	0.387295i
$736$		0			0
$737$	21.4202	−	12.3669i	0.789023	−	0.455542i
$738$		0			0
$739$	15.6634	−	27.1299i	0.576189	−	0.997988i	−0.419723	−	0.907652i	$-0.637873\pi$
$739$	15.6634	−	27.1299i	0.576189	−	0.997988i	0.995911	−	0.0903358i	$-0.0287940\pi$
$740$		0			0
$741$	−49.3292	+	26.7284i	−1.81215	+	0.981893i
$742$		0			0
$743$			25.2739i			0.927208i	0.886043	+	0.463604i	$0.153444\pi$
$743$			25.2739i			0.927208i	−0.886043	+	0.463604i	$0.846556\pi$
$744$		0			0
$745$	−11.4737	−	6.62433i	−0.420363	−	0.242697i
$746$		0			0
$747$	46.7480	+	2.53095i	1.71042	+	0.0926027i
$748$		0			0
$749$	14.0143	+	13.6405i	0.512071	+	0.498414i
$750$		0			0
$751$	16.3393	+	28.3005i	0.596229	+	1.03270i	0.993372	+	0.114942i	$0.0366684\pi$
$751$	16.3393	+	28.3005i	0.596229	+	1.03270i	−0.397143	+	0.917757i	$0.629998\pi$
$752$		0			0
$753$	0.803495	−	29.7037i	0.0292810	−	1.08246i
$754$		0			0
$755$	12.8428			0.467397
$756$		0			0
$757$	−18.5359			−0.673697			−0.336848	−	0.941559i	$-0.609361\pi$
$757$	−18.5359			−0.673697			−0.336848	+	0.941559i	$0.609361\pi$
$758$		0			0
$759$	−0.481134	+	17.7866i	−0.0174641	+	0.645612i
$760$		0			0
$761$	15.3810	+	26.6407i	0.557561	+	0.965723i	0.997699	+	0.0677935i	$0.0215959\pi$
$761$	15.3810	+	26.6407i	0.557561	+	0.965723i	−0.440139	+	0.897930i	$0.645071\pi$
$762$		0			0
$763$	13.5534	+	3.43601i	0.490667	+	0.124392i
$764$		0			0
$765$	−6.65469	−	0.360287i	−0.240601	−	0.0130262i
$766$		0			0
$767$	−1.91305	−	1.10450i	−0.0690761	−	0.0398811i
$768$		0			0
$769$		−	34.0455i		−	1.22771i	−0.789418	−	0.613855i	$-0.789618\pi$
$769$		−	34.0455i		−	1.22771i	0.789418	−	0.613855i	$-0.210382\pi$
$770$		0			0
$771$	−5.70804	+	3.09283i	−0.205570	+	0.111386i
$772$		0			0
$773$	6.68565	−	11.5799i	0.240466	−	0.416499i	−0.720381	−	0.693578i	$-0.756033\pi$
$773$	6.68565	−	11.5799i	0.240466	−	0.416499i	0.960847	+	0.277079i	$0.0893664\pi$
$774$		0			0
$775$	−5.76540	+	3.32866i	−0.207099	+	0.119569i
$776$		0			0
$777$	4.39647	+	4.51707i	0.157722	+	0.162049i
$778$		0			0
$779$	−19.8972	+	11.4877i	−0.712892	+	0.411589i
$780$		0			0
$781$	−6.88199	+	11.9200i	−0.246257	+	0.426530i
$782$		0			0
$783$	47.2127	+	3.83885i	1.68724	+	0.137189i
$784$		0			0
$785$			4.57569i			0.163313i
$786$		0			0
$787$	22.4629	+	12.9690i	0.800717	+	0.462294i	0.843722	−	0.536781i	$-0.180360\pi$
$787$	22.4629	+	12.9690i	0.800717	+	0.462294i	−0.0430051	+	0.999075i	$0.513693\pi$
$788$		0			0
$789$	18.5902	−	30.2777i	0.661829	−	1.07792i
$790$		0			0
$791$	−40.4883	+	11.4375i	−1.43960	+	0.406669i
$792$		0			0
$793$	−19.7857	−	34.2698i	−0.702609	−	1.21695i
$794$		0			0
$795$	−13.2054	−	0.357210i	−0.468346	−	0.0126689i
$796$		0			0
$797$	30.9797			1.09736			0.548679	−	0.836033i	$-0.315131\pi$
$797$	30.9797			1.09736			0.548679	+	0.836033i	$0.315131\pi$
$798$		0			0
$799$	2.49392			0.0882286
$800$		0			0
$801$	−6.18169	−	12.1842i	−0.218419	−	0.430509i
$802$		0			0
$803$	1.22863	+	2.12805i	0.0433575	+	0.0750973i
$804$		0			0
$805$	−3.84957	+	15.1847i	−0.135679	+	0.535191i
$806$		0			0
$807$	28.8428	+	17.7092i	1.01532	+	0.623393i
$808$		0			0
$809$	24.1436	+	13.9393i	0.848845	+	0.490081i	0.860261	−	0.509854i	$-0.170301\pi$
$809$	24.1436	+	13.9393i	0.848845	+	0.490081i	−0.0114160	+	0.999935i	$0.503634\pi$
$810$		0			0
$811$			26.1528i			0.918349i	0.888346	+	0.459175i	$0.151855\pi$
$811$			26.1528i			0.918349i	−0.888346	+	0.459175i	$0.848145\pi$
$812$		0			0
$813$	18.8282	+	34.7488i	0.660334	+	1.21869i
$814$		0			0
$815$	1.63146	−	2.82578i	0.0571477	−	0.0989827i
$816$		0			0
$817$	56.0154	−	32.3405i	1.95973	−	1.13145i
$818$		0			0
$819$	−35.0028	+	7.87241i	−1.22310	+	0.275084i
$820$		0			0
$821$	2.42107	−	1.39781i	0.0844959	−	0.0487837i	−0.457157	−	0.889386i	$-0.651132\pi$
$821$	2.42107	−	1.39781i	0.0844959	−	0.0487837i	0.541653	+	0.840602i	$0.317799\pi$
$822$		0			0
$823$	12.4881	−	21.6300i	0.435308	−	0.753976i	−0.562012	−	0.827129i	$-0.689973\pi$
$823$	12.4881	−	21.6300i	0.435308	−	0.753976i	0.997321	+	0.0731527i	$0.0233060\pi$
$824$		0			0
$825$	−1.43166	−	2.64222i	−0.0498439	−	0.0919904i
$826$		0			0
$827$			44.4134i			1.54440i	0.635377	+	0.772202i	$0.280845\pi$
$827$			44.4134i			1.54440i	−0.635377	+	0.772202i	$0.719155\pi$
$828$		0			0
$829$	−27.6610	−	15.9701i	−0.960705	−	0.554663i	−0.0643148	−	0.997930i	$-0.520486\pi$
$829$	−27.6610	−	15.9701i	−0.960705	−	0.554663i	−0.896390	+	0.443267i	$0.853820\pi$
$830$		0			0
$831$	9.66837	+	5.93628i	0.335392	+	0.205927i
$832$		0			0
$833$	0.420264	+	15.5447i	0.0145613	+	0.538591i
$834$		0			0
$835$	−8.09047	−	14.0131i	−0.279982	−	0.484944i
$836$		0			0
$837$	−19.6672	+	28.4577i	−0.679797	+	0.983640i
$838$		0			0
$839$	−11.3366			−0.391384			−0.195692	−	0.980665i	$-0.562695\pi$
$839$	−11.3366			−0.391384			−0.195692	+	0.980665i	$0.562695\pi$
$840$		0			0
$841$	−54.1027			−1.86561
$842$		0			0
$843$	−21.9319	−	0.593266i	−0.755374	−	0.0204332i
$844$		0			0
$845$	−3.71567	−	6.43572i	−0.127823	−	0.221396i
$846$		0			0
$847$	14.7439	−	15.1479i	0.506608	−	0.520490i
$848$		0			0
$849$	−2.15657	+	3.51239i	−0.0740133	+	0.120545i
$850$		0			0
$851$	7.05309	+	4.07210i	0.241777	+	0.139590i
$852$		0			0
$853$		−	41.8866i		−	1.43417i	−0.696986	−	0.717085i	$-0.745476\pi$
$853$		−	41.8866i		−	1.43417i	0.696986	−	0.717085i	$-0.254524\pi$
$854$		0			0
$855$	−18.0102	−	11.7402i	−0.615935	−	0.401507i
$856$		0			0
$857$	−20.1484	+	34.8980i	−0.688255	+	1.19209i	0.284147	+	0.958781i	$0.408290\pi$
$857$	−20.1484	+	34.8980i	−0.688255	+	1.19209i	−0.972402	+	0.233312i	$0.925044\pi$
$858$		0			0
$859$	−4.51782	+	2.60837i	−0.154146	+	0.0889963i	−0.575089	−	0.818091i	$-0.695033\pi$
$859$	−4.51782	+	2.60837i	−0.154146	+	0.0889963i	0.420943	+	0.907087i	$0.361699\pi$
$860$		0			0
$861$	−14.2415	+	3.61021i	−0.485347	+	0.123036i
$862$		0			0
$863$	−7.10243	+	4.10059i	−0.241769	+	0.139586i	−0.615990	−	0.787754i	$-0.711244\pi$
$863$	−7.10243	+	4.10059i	−0.241769	+	0.139586i	0.374220	+	0.927340i	$0.377910\pi$
$864$		0			0
$865$	−8.94446	+	15.4923i	−0.304121	+	0.526753i
$866$		0			0
$867$	18.3735	−	9.95544i	0.623996	−	0.338104i
$868$		0			0
$869$		−	10.5649i		−	0.358390i
$870$		0			0
$871$	55.8039	+	32.2184i	1.89084	+	1.09168i
$872$		0			0
$873$	1.12592	−	20.7962i	0.0381065	−	0.703846i
$874$		0			0
$875$	−0.719245	−	2.54611i	−0.0243149	−	0.0860743i
$876$		0			0
$877$	−17.5894	−	30.4657i	−0.593951	−	1.02875i	−0.993694	−	0.112126i	$-0.964234\pi$
$877$	−17.5894	−	30.4657i	−0.593951	−	1.02875i	0.399743	−	0.916627i	$-0.369099\pi$
$878$		0			0
$879$	0.825500	−	30.5171i	0.0278434	−	1.02932i
$880$		0			0
$881$	13.3867			0.451011			0.225505	−	0.974242i	$-0.427597\pi$
$881$	13.3867			0.451011			0.225505	+	0.974242i	$0.427597\pi$
$882$		0			0
$883$	−3.79780			−0.127806			−0.0639031	−	0.997956i	$-0.520355\pi$
$883$	−3.79780			−0.127806			−0.0639031	+	0.997956i	$0.520355\pi$
$884$		0			0
$885$	0.0228887	−	0.846152i	0.000769396	−	0.0284431i
$886$		0			0
$887$	13.8288	+	23.9521i	0.464325	+	0.804234i	0.999171	−	0.0407153i	$-0.0129637\pi$
$887$	13.8288	+	23.9521i	0.464325	+	0.804234i	−0.534846	+	0.844950i	$0.679630\pi$
$888$		0			0
$889$	−4.52482	−	16.0178i	−0.151758	−	0.537218i
$890$		0			0
$891$	−12.6012	−	9.22202i	−0.422157	−	0.308949i
$892$		0			0
$893$	6.96729	+	4.02257i	0.233152	+	0.134610i
$894$		0			0
$895$			16.0628i			0.536921i
$896$		0			0
$897$	−40.7563	+	22.0833i	−1.36081	+	0.737340i
$898$		0			0
$899$	30.3443	−	52.5578i	1.01204	−	1.75290i
$900$		0			0
$901$	−14.6731	+	8.47152i	−0.488832	+	0.282227i
$902$		0			0
$903$	40.0930	−	10.1636i	1.33421	−	0.338223i
$904$		0			0
$905$	9.08958	−	5.24787i	0.302148	−	0.174445i
$906$		0			0
$907$	−10.9484	+	18.9633i	−0.363537	+	0.629665i	−0.988540	−	0.150957i	$-0.951764\pi$
$907$	−10.9484	+	18.9633i	−0.363537	+	0.629665i	0.625003	+	0.780622i	$0.285098\pi$
$908$		0			0
$909$	4.65296	−	7.13791i	0.154329	−	0.236749i
$910$		0			0
$911$			13.0835i			0.433477i	0.976230	+	0.216739i	$0.0695419\pi$
$911$			13.0835i			0.433477i	−0.976230	+	0.216739i	$0.930458\pi$
$912$		0			0
$913$	23.4485	+	13.5380i	0.776031	+	0.448042i
$914$		0			0
$915$	7.93395	−	12.9220i	0.262288	−	0.427187i
$916$		0			0
$917$	−24.2343	+	24.8984i	−0.800288	+	0.822217i
$918$		0			0
$919$	−3.62558	−	6.27969i	−0.119597	−	0.207148i	0.800011	−	0.599985i	$-0.204827\pi$
$919$	−3.62558	−	6.27969i	−0.119597	−	0.207148i	−0.919608	+	0.392837i	$0.871494\pi$
$920$		0			0
$921$	−30.8658	−	0.834931i	−1.01706	−	0.0275119i
$922$		0			0
$923$	−35.8580			−1.18028
$924$		0			0
$925$	−1.37551			−0.0452266
$926$		0			0
$927$	43.7022	−	22.1724i	1.43537	−	0.728236i
$928$		0			0
$929$	16.5819	+	28.7207i	0.544035	+	0.942297i	0.998667	+	0.0516174i	$0.0164376\pi$
$929$	16.5819	+	28.7207i	0.544035	+	0.942297i	−0.454631	+	0.890680i	$0.650229\pi$
$930$		0			0
$931$	−23.8987	+	44.1052i	−0.783248	+	1.44549i
$932$		0			0
$933$	−9.74984	−	5.98630i	−0.319195	−	0.195983i
$934$		0			0
$935$	−3.33795	−	1.92717i	−0.109163	−	0.0630251i
$936$		0			0
$937$			31.3774i			1.02506i	0.858671	+	0.512528i	$0.171291\pi$
$937$			31.3774i			1.02506i	−0.858671	+	0.512528i	$0.828709\pi$
$938$		0			0
$939$	14.0121	+	25.8603i	0.457268	+	0.843920i
$940$		0			0
$941$	10.0272	−	17.3676i	0.326876	−	0.566167i	−0.655014	−	0.755617i	$-0.727337\pi$
$941$	10.0272	−	17.3676i	0.326876	−	0.566167i	0.981890	+	0.189450i	$0.0606706\pi$
$942$		0			0
$943$	−16.4393	+	9.49124i	−0.535337	+	0.309077i
$944$		0			0
$945$	−9.04209	−	10.3557i	−0.294139	−	0.336871i
$946$		0			0
$947$	10.3813	−	5.99364i	0.337346	−	0.194767i	−0.321752	−	0.946824i	$-0.604272\pi$
$947$	10.3813	−	5.99364i	0.337346	−	0.194767i	0.659098	+	0.752057i	$0.270938\pi$
$948$		0			0
$949$	−3.20083	+	5.54401i	−0.103903	+	0.179966i
$950$		0			0
$951$	−2.70036	−	4.98371i	−0.0875652	−	0.161608i
$952$		0			0
$953$			18.3262i			0.593643i	0.954933	+	0.296821i	$0.0959266\pi$
$953$			18.3262i			0.593643i	−0.954933	+	0.296821i	$0.904073\pi$
$954$		0			0
$955$	7.10655	+	4.10297i	0.229963	+	0.132769i
$956$		0			0
$957$	23.3459	+	14.3341i	0.754666	+	0.463357i
$958$		0			0
$959$	3.74997	−	14.7919i	0.121093	−	0.477654i
$960$		0			0
$961$	6.65993	+	11.5353i	0.214836	+	0.372108i
$962$		0			0
$963$	−19.7756	+	10.0332i	−0.637261	+	0.323315i
$964$		0			0
$965$	19.2269			0.618934
$966$		0			0
$967$	30.4904			0.980506			0.490253	−	0.871580i	$-0.336904\pi$
$967$	30.4904			0.980506			0.490253	+	0.871580i	$0.336904\pi$
$968$		0			0
$969$	−27.5637	−	0.745608i	−0.885473	−	0.0239524i
$970$		0			0
$971$	−14.5995	−	25.2872i	−0.468522	−	0.811503i	0.530831	−	0.847478i	$-0.321880\pi$
$971$	−14.5995	−	25.2872i	−0.468522	−	0.811503i	−0.999353	+	0.0359742i	$0.988547\pi$
$972$		0			0
$973$	4.22697	−	1.19407i	0.135511	−	0.0382801i
$974$		0			0
$975$	4.09643	−	6.67182i	0.131191	−	0.213669i
$976$		0			0
$977$	−24.2834	−	14.0200i	−0.776894	−	0.448540i	0.0584344	−	0.998291i	$-0.481389\pi$
$977$	−24.2834	−	14.0200i	−0.776894	−	0.448540i	−0.835328	+	0.549751i	$0.814722\pi$
$978$		0			0
$979$		−	7.90172i		−	0.252540i
$980$		0			0
$981$	−8.65784	+	13.2816i	−0.276424	+	0.424049i
$982$		0			0
$983$	−24.2928	+	42.0763i	−0.774819	+	1.34203i	0.160078	+	0.987104i	$0.448826\pi$
$983$	−24.2928	+	42.0763i	−0.774819	+	1.34203i	−0.934896	+	0.354921i	$0.884508\pi$
$984$		0			0
$985$	19.4891	−	11.2520i	0.620974	−	0.358520i
$986$		0			0
$987$	3.58822	+	3.68665i	0.114214	+	0.117347i
$988$		0			0
$989$	46.2805	−	26.7201i	1.47163	−	0.849648i
$990$		0			0
$991$	0.953533	−	1.65157i	0.0302900	−	0.0524638i	−0.850483	−	0.526002i	$-0.823690\pi$
$991$	0.953533	−	1.65157i	0.0302900	−	0.0524638i	0.880773	+	0.473539i	$0.157024\pi$
$992$		0			0
$993$	10.8778	−	5.89402i	0.345198	−	0.187041i
$994$		0			0
$995$			10.7047i			0.339361i
$996$		0			0
$997$	36.5101	+	21.0791i	1.15629	+	0.667582i	0.950411	−	0.310996i	$-0.100663\pi$
$997$	36.5101	+	21.0791i	1.15629	+	0.667582i	0.205875	+	0.978578i	$0.433996\pi$
$998$		0			0
$999$	−6.45907	+	3.06030i	−0.204356	+	0.0968236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cp.b.521.9	yes	32
3.2	odd	2		840.2.cp.a.521.3	✓	32
7.5	odd	6		840.2.cp.a.761.3	yes	32
21.5	even	6	inner	840.2.cp.b.761.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cp.a.521.3	✓	32	3.2	odd	2
840.2.cp.a.761.3	yes	32	7.5	odd	6
840.2.cp.b.521.9	yes	32	1.1	even	1	trivial
840.2.cp.b.761.9	yes	32	21.5	even	6	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0468355 - 1.73142i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.719245 + 2.54611i) q^{7} +(-2.99561 - 0.162184i) q^{9} +(-1.50258 - 0.867515i) q^{11} -4.52010i q^{13} +(1.52287 - 0.825148i) q^{15} +(1.11074 - 1.92386i) q^{17} +(6.20617 - 3.58314i) q^{19} +(4.44207 - 1.12607i) q^{21} +(5.12760 - 2.96042i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-0.421109 + 5.17906i) q^{27} -9.11607i q^{29} +(5.76540 + 3.32866i) q^{31} +(-1.57240 + 2.56096i) q^{33} +(-1.84538 + 1.89594i) q^{35} +(0.687757 + 1.19123i) q^{37} +(-7.82619 - 0.211701i) q^{39} -3.20604 q^{41} +9.02575 q^{43} +(-1.35735 - 2.67537i) q^{45} +(0.561320 + 0.972234i) q^{47} +(-5.96537 + 3.66256i) q^{49} +(-3.27898 - 2.01326i) q^{51} +(-6.60510 - 3.81346i) q^{53} -1.73503i q^{55} +(-5.91323 - 10.9133i) q^{57} +(0.244352 - 0.423231i) q^{59} +(7.58163 - 4.37726i) q^{61} +(-1.74164 - 7.74382i) q^{63} +(3.91452 - 2.26005i) q^{65} +(-7.12780 + 12.3457i) q^{67} +(-4.88558 - 9.01668i) q^{69} -7.93299i q^{71} +(-1.22652 - 0.708133i) q^{73} +(1.47603 + 0.906269i) q^{75} +(1.12807 - 4.44969i) q^{77} +(3.04459 + 5.27338i) q^{79} +(8.94739 + 0.971678i) q^{81} -15.6055 q^{83} +2.22148 q^{85} +(-15.7837 - 0.426955i) q^{87} +(2.27711 + 3.94408i) q^{89} +(11.5087 - 3.25106i) q^{91} +(6.03332 - 9.82642i) q^{93} +(6.20617 + 3.58314i) q^{95} +6.94223i q^{97} +(4.36045 + 2.84243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{5} - 2 q^{7} + 8 q^{9} + 6 q^{19} - 14 q^{21} + 24 q^{23} - 16 q^{25} + 24 q^{27} + 42 q^{31} + 18 q^{33} + 2 q^{35} + 6 q^{37} + 12 q^{39} + 44 q^{41} - 20 q^{43} + 10 q^{45} + 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) \) 32 * q + 16 * q^5 - 2 * q^7 + 8 * q^9 + 6 * q^19 - 14 * q^21 + 24 * q^23 - 16 * q^25 + 24 * q^27 + 42 * q^31 + 18 * q^33 + 2 * q^35 + 6 * q^37 + 12 * q^39 + 44 * q^41 - 20 * q^43 + 10 * q^45 + 4 * q^47 + 16 * q^49 - 36 * q^51 + 12 * q^59 - 18 * q^61 + 34 * q^63 - 6 * q^65 - 6 * q^67 - 34 * q^69 - 6 * q^73 + 40 * q^77 - 2 * q^79 - 12 * q^81 - 88 * q^83 - 72 * q^87 - 6 * q^89 - 26 * q^91 + 50 * q^93 + 6 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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