LMFDB - Embedded newform 840.2.cp.a.761.3

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			761.3
Character	$\chi$	$=$	840.761
Dual form			840.2.cp.a.521.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47603 - 0.906269i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.719245 - 2.54611i) q^{7} +(1.35735 + 2.67537i) q^{9} +(1.50258 - 0.867515i) q^{11} +4.52010i q^{13} +(1.52287 - 0.825148i) q^{15} +(-1.11074 - 1.92386i) q^{17} +(6.20617 + 3.58314i) q^{19} +(-3.36909 + 3.10632i) q^{21} +(-5.12760 - 2.96042i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.421109 - 5.17906i) q^{27} -9.11607i q^{29} +(5.76540 - 3.32866i) q^{31} +(-3.00406 - 0.0812610i) q^{33} +(1.84538 + 1.89594i) q^{35} +(0.687757 - 1.19123i) q^{37} +(4.09643 - 6.67182i) q^{39} +3.20604 q^{41} +9.02575 q^{43} +(-2.99561 - 0.162184i) q^{45} +(-0.561320 + 0.972234i) q^{47} +(-5.96537 - 3.66256i) q^{49} +(-0.104044 + 3.84631i) q^{51} +(6.60510 - 3.81346i) q^{53} +1.73503i q^{55} +(-5.91323 - 10.9133i) q^{57} +(-0.244352 - 0.423231i) q^{59} +(7.58163 + 4.37726i) q^{61} +(7.78806 - 1.53172i) q^{63} +(-3.91452 - 2.26005i) q^{65} +(-7.12780 - 12.3457i) q^{67} +(4.88558 + 9.01668i) q^{69} -7.93299i q^{71} +(-1.22652 + 0.708133i) q^{73} +(-0.0468355 + 1.73142i) q^{75} +(-1.12807 - 4.44969i) q^{77} +(3.04459 - 5.27338i) q^{79} +(-5.31519 + 7.26283i) q^{81} +15.6055 q^{83} +2.22148 q^{85} +(-8.26161 + 13.4556i) q^{87} +(-2.27711 + 3.94408i) q^{89} +(11.5087 + 3.25106i) q^{91} +(-11.5266 - 0.311799i) q^{93} +(-6.20617 + 3.58314i) q^{95} -6.94223i q^{97} +(4.36045 + 2.84243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{19} - 4 q^{21} - 24 q^{23} - 16 q^{25} - 24 q^{27} + 42 q^{31} + 6 q^{33} - 2 q^{35} + 6 q^{37} + 12 q^{39} - 44 q^{41} - 20 q^{43} + 8 q^{45} - 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) $ 32 * q - 16 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^19 - 4 * q^21 - 24 * q^23 - 16 * q^25 - 24 * q^27 + 42 * q^31 + 6 * q^33 - 2 * q^35 + 6 * q^37 + 12 * q^39 - 44 * q^41 - 20 * q^43 + 8 * q^45 - 4 * q^47 + 16 * q^49 + 24 * q^51 - 12 * q^59 - 18 * q^61 - 6 * q^63 + 6 * q^65 - 6 * q^67 + 34 * q^69 - 6 * q^73 - 40 * q^77 - 2 * q^79 - 18 * q^81 + 88 * q^83 - 84 * q^87 + 6 * q^89 - 26 * q^91 - 58 * q^93 - 6 * q^95 - 8 * q^99

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$	$1$

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
$3$	−1.47603	−	0.906269i	−0.852188	−	0.523235i
$3$	−1.47603	−	0.906269i	−0.852188	−	0.523235i
$4$		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
$9$	1.35735	+	2.67537i	0.452450	+	0.891790i
$10$		0			0
$11$	1.50258	−	0.867515i	0.453045	−	0.261566i	−0.256070	−	0.966658i	$-0.582428\pi$
$11$	1.50258	−	0.867515i	0.453045	−	0.261566i	0.709115	+	0.705093i	$0.249095\pi$
$12$		0			0
$13$			4.52010i			1.25365i	0.779160	+	0.626826i	$0.215646\pi$
$13$			4.52010i			1.25365i	−0.779160	+	0.626826i	$0.784354\pi$
$14$		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	$-0.253490\pi$
$17$	−1.11074	−	1.92386i	−0.269394	−	0.466604i	−0.968705	+	0.248213i	$0.920157\pi$
$18$		0			0
$19$	6.20617	+	3.58314i	1.42379	+	0.822028i	0.996621	−	0.0821424i	$-0.0261762\pi$
$19$	6.20617	+	3.58314i	1.42379	+	0.822028i	0.427173	+	0.904170i	$0.359510\pi$
$20$		0			0
$21$	−3.36909	+	3.10632i	−0.735197	+	0.677854i
$22$		0			0
$23$	−5.12760	−	2.96042i	−1.06918	−	0.617291i	−0.141222	−	0.989978i	$-0.545103\pi$
$23$	−5.12760	−	2.96042i	−1.06918	−	0.617291i	−0.927957	+	0.372687i	$0.878437\pi$
$24$		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	0.116943	−	0.993139i	$-0.462691\pi$
$31$	5.76540	−	3.32866i	1.03550	−	0.597845i	0.918555	+	0.395294i	$0.129357\pi$
$32$		0			0
$33$	−3.00406	−	0.0812610i	−0.522940	−	0.0141457i
$34$		0			0
$35$	1.84538	+	1.89594i	0.311925	+	0.320472i
$36$		0			0
$37$	0.687757	−	1.19123i	0.113067	−	0.195837i	−0.803939	−	0.594712i	$-0.797266\pi$
$37$	0.687757	−	1.19123i	0.113067	−	0.195837i	0.917005	+	0.398875i	$0.130599\pi$
$38$		0			0
$39$	4.09643	−	6.67182i	0.655954	−	1.06835i
$40$		0			0
$41$	3.20604			0.500699			0.250350	−	0.968155i	$-0.419454\pi$
$41$	3.20604			0.500699			0.250350	+	0.968155i	$0.419454\pi$
$42$		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
$45$	−2.99561	−	0.162184i	−0.446560	−	0.0241769i
$46$		0			0
$47$	−0.561320	+	0.972234i	−0.0818769	+	0.141815i	−0.904056	−	0.427414i	$-0.859425\pi$
$47$	−0.561320	+	0.972234i	−0.0818769	+	0.141815i	0.822179	+	0.569229i	$0.192758\pi$
$48$		0			0
$49$	−5.96537	−	3.66256i	−0.852196	−	0.523223i
$50$		0			0
$51$	−0.104044	+	3.84631i	−0.0145691	+	0.538591i
$52$		0			0
$53$	6.60510	−	3.81346i	0.907281	−	0.523819i	0.0277255	−	0.999616i	$-0.491174\pi$
$53$	6.60510	−	3.81346i	0.907281	−	0.523819i	0.879555	+	0.475797i	$0.157840\pi$
$54$		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	$-0.176794\pi$
$59$	−0.244352	−	0.423231i	−0.0318120	−	0.0551000i	−0.881493	+	0.472197i	$0.843461\pi$
$60$		0			0
$61$	7.58163	+	4.37726i	0.970729	+	0.560450i	0.899458	−	0.437007i	$-0.143961\pi$
$61$	7.58163	+	4.37726i	0.970729	+	0.560450i	0.0712703	+	0.997457i	$0.477295\pi$
$62$		0			0
$63$	7.78806	−	1.53172i	0.981203	−	0.192979i
$64$		0			0
$65$	−3.91452	−	2.26005i	−0.485537	−	0.280325i
$66$		0			0
$67$	−7.12780	−	12.3457i	−0.870800	−	1.50827i	−0.861171	−	0.508316i	$-0.830268\pi$
$67$	−7.12780	−	12.3457i	−0.870800	−	1.50827i	−0.00962884	−	0.999954i	$-0.503065\pi$
$68$		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	−0.570057	−	0.821605i	$-0.693079\pi$
$73$	−1.22652	+	0.708133i	−0.143554	+	0.0828807i	0.426503	+	0.904486i	$0.359745\pi$
$74$		0			0
$75$	−0.0468355	+	1.73142i	−0.00540810	+	0.199927i
$76$		0			0
$77$	−1.12807	−	4.44969i	−0.128555	−	0.507089i
$78$		0			0
$79$	3.04459	−	5.27338i	0.342543	−	0.593302i	−0.642361	−	0.766402i	$-0.722045\pi$
$79$	3.04459	−	5.27338i	0.342543	−	0.593302i	0.984904	+	0.173100i	$0.0553785\pi$
$80$		0			0
$81$	−5.31519	+	7.26283i	−0.590577	+	0.806981i
$82$		0			0
$83$	15.6055			1.71292			0.856462	−	0.516211i	$-0.172658\pi$
$83$	15.6055			1.71292			0.856462	+	0.516211i	$0.172658\pi$
$84$		0			0
$85$	2.22148			0.240953
$86$		0			0
$87$	−8.26161	+	13.4556i	−0.885738	+	1.44259i
$88$		0			0
$89$	−2.27711	+	3.94408i	−0.241374	+	0.418071i	−0.961106	−	0.276180i	$-0.910931\pi$
$89$	−2.27711	+	3.94408i	−0.241374	+	0.418071i	0.719732	+	0.694252i	$0.244265\pi$
$90$		0			0
$91$	11.5087	+	3.25106i	1.20644	+	0.340804i
$92$		0			0
$93$	−11.5266	−	0.311799i	−1.19525	−	0.0323320i
$94$		0			0
$95$	−6.20617	+	3.58314i	−0.636740	+	0.367622i
$96$		0			0
$97$		−	6.94223i		−	0.704877i	−0.935835	−	0.352438i	$-0.885353\pi$
$97$		−	6.94223i		−	0.704877i	0.935835	−	0.352438i	$-0.114647\pi$
$98$		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	$-0.121537\pi$
$101$	1.42009	+	2.45967i	0.141304	+	0.244746i	−0.786684	+	0.617356i	$0.788204\pi$
$102$		0			0
$103$	−14.1465	−	8.16751i	−1.39390	−	0.804768i	−0.400155	−	0.916447i	$-0.631044\pi$
$103$	−14.1465	−	8.16751i	−1.39390	−	0.804768i	−0.993744	+	0.111679i	$0.964377\pi$
$104$		0			0
$105$	−1.00560	−	4.47088i	−0.0981368	−	0.436313i
$106$		0			0
$107$	−6.40143	−	3.69587i	−0.618850	−	0.357293i	0.157571	−	0.987508i	$-0.449634\pi$
$107$	−6.40143	−	3.69587i	−0.618850	−	0.357293i	−0.776421	+	0.630214i	$0.782967\pi$
$108$		0			0
$109$	2.64239	+	4.57675i	0.253095	+	0.438373i	0.964376	−	0.264534i	$-0.0852182\pi$
$109$	2.64239	+	4.57675i	0.253095	+	0.438373i	−0.711282	+	0.702907i	$0.751885\pi$
$110$		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
$117$	−12.0929	+	6.13537i	−1.11799	+	0.567215i
$118$		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
$123$	−4.73222	−	2.90554i	−0.426690	−	0.261983i
$124$		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
$129$	−13.3223	−	8.17976i	−1.17296	−	0.720188i
$130$		0			0
$131$	−6.56624	+	11.3731i	−0.573695	+	0.993668i	0.422487	+	0.906369i	$0.361157\pi$
$131$	−6.56624	+	11.3731i	−0.573695	+	0.993668i	−0.996182	+	0.0872995i	$0.972176\pi$
$132$		0			0
$133$	13.5868	−	13.2245i	1.17813	−	1.14671i
$134$		0			0
$135$	4.27464	+	2.95422i	0.367903	+	0.254259i
$136$		0			0
$137$	4.99494	−	2.88383i	0.426746	−	0.246382i	−0.271213	−	0.962519i	$-0.587425\pi$
$137$	4.99494	−	2.88383i	0.426746	−	0.246382i	0.697960	+	0.716137i	$0.254092\pi$
$138$		0			0
$139$			1.66017i			0.140814i	0.997518	+	0.0704068i	$0.0224297\pi$
$139$			1.66017i			0.140814i	−0.997518	+	0.0704068i	$0.977570\pi$
$140$		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
$147$	5.48583	+	10.8123i	0.452463	+	0.891783i
$148$		0			0
$149$	11.4737	+	6.62433i	0.939961	+	0.542686i	0.889948	−	0.456062i	$-0.150741\pi$
$149$	11.4737	+	6.62433i	0.939961	+	0.542686i	0.0500126	+	0.998749i	$0.484074\pi$
$150$		0			0
$151$	6.42140	+	11.1222i	0.522566	+	0.905111i	0.999655	+	0.0262559i	$0.00835848\pi$
$151$	6.42140	+	11.1222i	0.522566	+	0.905111i	−0.477089	+	0.878855i	$0.658308\pi$
$152$		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	−0.333467	−	0.942762i	$-0.608219\pi$
$157$	3.96267	−	2.28785i	0.316255	−	0.182590i	0.649722	+	0.760172i	$0.274885\pi$
$158$		0			0
$159$	−13.2054	−	0.357210i	−1.04725	−	0.0283286i
$160$		0			0
$161$	−11.2256	+	10.9262i	−0.884699	+	0.861104i
$162$		0			0
$163$	−1.63146	+	2.82578i	−0.127786	+	0.221332i	−0.922819	−	0.385235i	$-0.874120\pi$
$163$	−1.63146	+	2.82578i	−0.127786	+	0.221332i	0.795032	+	0.606567i	$0.207454\pi$
$164$		0			0
$165$	1.57240	−	2.56096i	0.122412	−	0.199371i
$166$		0			0
$167$	16.1809			1.25212			0.626060	−	0.779775i	$-0.284667\pi$
$167$	16.1809			1.25212			0.626060	+	0.779775i	$0.284667\pi$
$168$		0			0
$169$	−7.43133			−0.571641
$170$		0			0
$171$	−1.16225	+	21.4674i	−0.0888796	+	1.64165i
$172$		0			0
$173$	−8.94446	+	15.4923i	−0.680035	+	1.17785i	0.294935	+	0.955517i	$0.404702\pi$
$173$	−8.94446	+	15.4923i	−0.680035	+	1.17785i	−0.974970	+	0.222337i	$0.928631\pi$
$174$		0			0
$175$	−2.56462	+	0.650171i	−0.193867	+	0.0491483i
$176$		0			0
$177$	−0.0228887	+	0.846152i	−0.00172042	+	0.0636007i
$178$		0			0
$179$	−13.9108	+	8.03141i	−1.03974	+	0.600296i	−0.919760	−	0.392480i	$-0.871617\pi$
$179$	−13.9108	+	8.03141i	−1.03974	+	0.600296i	−0.119982	+	0.992776i	$0.538284\pi$
$180$		0			0
$181$			10.4957i			0.780142i	0.920785	+	0.390071i	$0.127550\pi$
$181$			10.4957i			0.780142i	−0.920785	+	0.390071i	$0.872450\pi$
$182$		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
$189$	−12.8836	−	4.79720i	−0.937143	−	0.348945i
$190$		0			0
$191$	−7.10655	−	4.10297i	−0.514212	−	0.296881i	0.220351	−	0.975421i	$-0.429280\pi$
$191$	−7.10655	−	4.10297i	−0.514212	−	0.296881i	−0.734563	+	0.678540i	$0.762613\pi$
$192$		0			0
$193$	9.61343	+	16.6509i	0.691990	+	1.19856i	0.971185	+	0.238327i	$0.0765989\pi$
$193$	9.61343	+	16.6509i	0.691990	+	1.19856i	−0.279195	+	0.960234i	$0.590068\pi$
$194$		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	−0.134027	−	0.990978i	$-0.542791\pi$
$199$	9.27053	−	5.35234i	0.657171	−	0.379418i	0.791198	+	0.611560i	$0.209458\pi$
$200$		0			0
$201$	−0.667668	+	24.6824i	−0.0470937	+	1.74096i
$202$		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
$207$	0.960264	−	17.7366i	0.0667430	−	1.23278i
$208$		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
$213$	−7.18943	+	11.7094i	−0.492612	+	0.802313i
$214$		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
$219$	2.45215	+	0.0663315i	0.165701	+	0.00448227i
$220$		0			0
$221$	8.69603	−	5.02066i	0.584959	−	0.337726i
$222$		0			0
$223$		−	16.4054i		−	1.09859i	−0.835630	−	0.549293i	$-0.814897\pi$
$223$		−	16.4054i		−	1.09859i	0.835630	−	0.549293i	$-0.185103\pi$
$224$		0			0
$225$	1.63826	−	2.51319i	0.109217	−	0.167546i
$226$		0			0
$227$	9.24824	+	16.0184i	0.613827	+	1.06318i	0.990589	+	0.136870i	$0.0437041\pi$
$227$	9.24824	+	16.0184i	0.613827	+	1.06318i	−0.376762	+	0.926310i	$0.622963\pi$
$228$		0			0
$229$	−19.3784	−	11.1881i	−1.28056	−	0.739333i	−0.303611	−	0.952796i	$-0.598192\pi$
$229$	−19.3784	−	11.1881i	−1.28056	−	0.739333i	−0.976951	+	0.213463i	$0.931526\pi$
$230$		0			0
$231$	−2.36756	+	7.59023i	−0.155774	+	0.499400i
$232$		0			0
$233$	22.2560	+	12.8495i	1.45804	+	0.841799i	0.998915	−	0.0465740i	$-0.0148303\pi$
$233$	22.2560	+	12.8495i	1.45804	+	0.841799i	0.459123	+	0.888373i	$0.348164\pi$
$234$		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	−0.562349	−	0.826900i	$-0.690102\pi$
$241$	−1.97789	+	1.14194i	−0.127407	+	0.0735587i	0.434942	+	0.900459i	$0.356769\pi$
$242$		0			0
$243$	14.4275	−	5.90318i	0.925524	−	0.378689i
$244$		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
$249$	−23.0342	−	14.1428i	−1.45973	−	0.896261i
$250$		0			0
$251$	−17.1557			−1.08286			−0.541429	−	0.840747i	$-0.682116\pi$
$251$	−17.1557			−1.08286			−0.541429	+	0.840747i	$0.682116\pi$
$252$		0			0
$253$	−10.2728			−0.645848
$254$		0			0
$255$	−3.27898	−	2.01326i	−0.205338	−	0.126075i
$256$		0			0
$257$	1.87411	−	3.24605i	0.116904	−	0.202483i	−0.801636	−	0.597813i	$-0.796036\pi$
$257$	1.87411	−	3.24605i	0.116904	−	0.202483i	0.918539	+	0.395330i	$0.129370\pi$
$258$		0			0
$259$	−2.53834	−	2.60789i	−0.157725	−	0.162047i
$260$		0			0
$261$	24.3888	−	12.3737i	1.50963	−	0.765913i
$262$		0			0
$263$	−17.7647	+	10.2564i	−1.09542	+	0.632439i	−0.935014	−	0.354612i	$-0.884613\pi$
$263$	−17.7647	+	10.2564i	−1.09542	+	0.632439i	−0.160404	+	0.987051i	$0.551280\pi$
$264$		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	0.993446	+	0.114301i	$0.0364629\pi$
$269$	9.77038	+	16.9228i	0.595711	+	1.03180i	−0.397735	+	0.917500i	$0.630204\pi$
$270$		0			0
$271$	−19.7609	−	11.4090i	−1.20039	−	0.693047i	−0.239750	−	0.970835i	$-0.577065\pi$
$271$	−19.7609	−	11.4090i	−1.20039	−	0.693047i	−0.960642	+	0.277788i	$0.910399\pi$
$272$		0			0
$273$	−14.0409	−	15.2287i	−0.849792	−	0.921680i
$274$		0			0
$275$	−1.50258	−	0.867515i	−0.0906090	−	0.0523131i
$276$		0			0
$277$	−3.27512	−	5.67267i	−0.196783	−	0.340838i	0.750701	−	0.660643i	$-0.229716\pi$
$277$	−3.27512	−	5.67267i	−0.196783	−	0.340838i	−0.947484	+	0.319805i	$0.896383\pi$
$278$		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	−0.559999	−	0.828493i	$-0.689198\pi$
$283$	−2.06081	+	1.18981i	−0.122502	+	0.0707267i	0.437497	+	0.899220i	$0.355865\pi$
$284$		0			0
$285$	12.4078	+	0.335636i	0.734975	+	0.0198813i
$286$		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
$291$	−6.29153	+	10.2470i	−0.368816	+	0.600688i
$292$		0			0
$293$	−17.6255			−1.02969			−0.514847	−	0.857282i	$-0.672151\pi$
$293$	−17.6255			−1.02969			−0.514847	+	0.857282i	$0.672151\pi$
$294$		0			0
$295$	0.488705			0.0284535
$296$		0			0
$297$	−3.86016	−	8.14727i	−0.223989	−	0.472752i
$298$		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
$303$	0.133021	−	4.91754i	0.00764188	−	0.282506i
$304$		0			0
$305$	−7.58163	+	4.37726i	−0.434123	+	0.250641i
$306$		0			0
$307$			17.8269i			1.01743i	0.860934	+	0.508717i	$0.169880\pi$
$307$			17.8269i			1.01743i	−0.860934	+	0.508717i	$0.830120\pi$
$308$		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	$-0.226634\pi$
$311$	−3.30272	−	5.72047i	−0.187280	−	0.324378i	−0.944342	+	0.328964i	$0.893300\pi$
$312$		0			0
$313$	−14.7063	−	8.49066i	−0.831246	−	0.479920i	0.0230328	−	0.999735i	$-0.492668\pi$
$313$	−14.7063	−	8.49066i	−0.831246	−	0.479920i	−0.854279	+	0.519814i	$0.826001\pi$
$314$		0			0
$315$	−2.56752	+	7.51052i	−0.144663	+	0.423170i
$316$		0			0
$317$	−2.83413	−	1.63629i	−0.159181	−	0.0919031i	0.418294	−	0.908312i	$-0.362628\pi$
$317$	−2.83413	−	1.63629i	−0.159181	−	0.0919031i	−0.577474	+	0.816409i	$0.695962\pi$
$318$		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
$327$	0.247515	−	9.15015i	0.0136876	−	0.506004i
$328$		0			0
$329$	2.07169	+	2.12846i	0.114216	+	0.117346i
$330$		0			0
$331$	3.57149	−	6.18601i	0.196307	−	0.340014i	−0.751021	−	0.660278i	$-0.770438\pi$
$331$	3.57149	−	6.18601i	0.196307	−	0.340014i	0.947328	+	0.320264i	$0.103772\pi$
$332$		0			0
$333$	4.12051	+	0.223086i	0.225802	+	0.0122250i
$334$		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
$339$	14.4115	−	23.4719i	0.782726	−	1.27482i
$340$		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
$345$	−10.2515	−	0.277306i	−0.551920	−	0.0149296i
$346$		0			0
$347$	2.53870	−	1.46572i	0.136284	−	0.0786838i	−0.430308	−	0.902682i	$-0.641595\pi$
$347$	2.53870	−	1.46572i	0.136284	−	0.0786838i	0.566592	+	0.823998i	$0.308262\pi$
$348$		0			0
$349$			14.1947i			0.759823i	0.925023	+	0.379912i	$0.124046\pi$
$349$			14.1947i			0.759823i	−0.925023	+	0.379912i	$0.875954\pi$
$350$		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	$-0.0570280\pi$
$353$	6.34424	+	10.9885i	0.337670	+	0.584861i	−0.646324	+	0.763063i	$0.723695\pi$
$354$		0			0
$355$	6.87017	+	3.96650i	0.364631	+	0.210520i
$356$		0			0
$357$	9.71830	+	3.03135i	0.514347	+	0.160436i
$358$		0			0
$359$	−7.00432	−	4.04395i	−0.369674	−	0.213431i	0.303642	−	0.952786i	$-0.401797\pi$
$359$	−7.00432	−	4.04395i	−0.369674	−	0.213431i	−0.673316	+	0.739355i	$0.735131\pi$
$360$		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	−0.756008	−	0.654562i	$-0.772853\pi$
$367$	−10.8649	+	6.27287i	−0.567145	+	0.327441i	0.188863	+	0.982003i	$0.439520\pi$
$368$		0			0
$369$	4.35172	+	8.57734i	0.226542	+	0.446518i
$370$		0			0
$371$	−4.95880	−	19.5601i	−0.257448	−	1.01551i
$372$		0			0
$373$	15.5352	−	26.9078i	0.804382	−	1.39323i	−0.112325	−	0.993672i	$-0.535830\pi$
$373$	15.5352	−	26.9078i	0.804382	−	1.39323i	0.916707	−	0.399560i	$-0.130837\pi$
$374$		0			0
$375$	−1.47603	−	0.906269i	−0.0762221	−	0.0467996i
$376$		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
$381$	9.28582	+	5.70140i	0.475727	+	0.292092i
$382$		0			0
$383$	−9.57846	+	16.5904i	−0.489436	+	0.847729i	−0.999926	−	0.0121553i	$-0.996131\pi$
$383$	−9.57846	+	16.5904i	−0.489436	+	0.847729i	0.510490	+	0.859884i	$0.329464\pi$
$384$		0			0
$385$	4.41758	+	1.24791i	0.225141	+	0.0635995i
$386$		0			0
$387$	12.2511	+	24.1472i	0.622759	+	1.22747i
$388$		0			0
$389$	−21.6644	+	12.5079i	−1.09843	+	0.634178i	−0.935808	−	0.352511i	$-0.885328\pi$
$389$	−21.6644	+	12.5079i	−1.09843	+	0.634178i	−0.162620	+	0.986689i	$0.551995\pi$
$390$		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	0.948661	−	0.316295i	$-0.102439\pi$
$397$	22.8951	+	13.2185i	1.14907	+	0.663417i	0.200411	+	0.979712i	$0.435772\pi$
$398$		0			0
$399$	−32.0395	+	7.20642i	−1.60398	+	0.360772i
$400$		0			0
$401$	11.7907	+	6.80738i	0.588801	+	0.339944i	0.764623	−	0.644478i	$-0.222925\pi$
$401$	11.7907	+	6.80738i	0.588801	+	0.339944i	−0.175822	+	0.984422i	$0.556258\pi$
$402$		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	0.203989	−	0.978973i	$-0.434609\pi$
$409$	23.3342	−	13.4720i	1.15380	−	0.666146i	0.949810	+	0.312827i	$0.101276\pi$
$410$		0			0
$411$	−9.98622	−	0.270131i	−0.492584	−	0.0133246i
$412$		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
$417$	1.50456	−	2.45046i	0.0736786	−	0.120000i
$418$		0			0
$419$	2.39230			0.116871			0.0584357	−	0.998291i	$-0.481389\pi$
$419$	2.39230			0.116871			0.0584357	+	0.998291i	$0.481389\pi$
$420$		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
$423$	−3.36299	−	0.182074i	−0.163514	−	0.00885273i
$424$		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
$429$	0.367308	−	13.5787i	0.0177338	−	0.655584i
$430$		0			0
$431$	9.21326	−	5.31928i	0.443787	−	0.256221i	−0.261416	−	0.965226i	$-0.584189\pi$
$431$	9.21326	−	5.31928i	0.443787	−	0.256221i	0.705203	+	0.709006i	$0.250856\pi$
$432$		0			0
$433$			11.4141i			0.548527i	0.961655	+	0.274263i	$0.0884340\pi$
$433$			11.4141i			0.548527i	−0.961655	+	0.274263i	$0.911566\pi$
$434$		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	−0.318367	−	0.947968i	$-0.603134\pi$
$439$	−27.2069	−	15.7079i	−1.29851	−	0.749698i	−0.980147	+	0.198270i	$0.936468\pi$
$440$		0			0
$441$	1.70159	−	20.9309i	0.0810279	−	0.996712i
$442$		0			0
$443$	−2.27390	−	1.31284i	−0.108036	−	0.0623747i	0.445008	−	0.895526i	$-0.353201\pi$
$443$	−2.27390	−	1.31284i	−0.108036	−	0.0623747i	−0.553044	+	0.833152i	$0.686534\pi$
$444$		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
$453$	0.601499	−	22.2362i	0.0282609	−	1.04475i
$454$		0			0
$455$	−8.56985	+	8.34129i	−0.401761	+	0.391045i
$456$		0			0
$457$	13.8490	−	23.9872i	0.647831	−	1.12208i	−0.335809	−	0.941930i	$-0.609010\pi$
$457$	13.8490	−	23.9872i	0.647831	−	1.12208i	0.983640	−	0.180146i	$-0.0576569\pi$
$458$		0			0
$459$	−10.4315	+	4.94243i	−0.486901	+	0.230693i
$460$		0			0
$461$	−2.25024			−0.104804			−0.0524022	−	0.998626i	$-0.516688\pi$
$461$	−2.25024			−0.104804			−0.0524022	+	0.998626i	$0.516688\pi$
$462$		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
$465$	6.03332	−	9.82642i	0.279789	−	0.455689i
$466$		0			0
$467$	−12.8340	+	22.2291i	−0.593885	+	1.02864i	0.399819	+	0.916594i	$0.369073\pi$
$467$	−12.8340	+	22.2291i	−0.593885	+	1.02864i	−0.993703	+	0.112044i	$0.964260\pi$
$468$		0			0
$469$	−36.5602	+	9.26859i	−1.68819	+	0.427984i
$470$		0			0
$471$	−7.92243	−	0.214305i	−0.365047	−	0.00987465i
$472$		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	−0.975870	−	0.218350i	$-0.929932\pi$
$479$	−14.8176	−	25.6648i	−0.677032	−	1.17265i	0.298838	−	0.954304i	$-0.403401\pi$
$480$		0			0
$481$	5.38448	+	3.10873i	0.245511	+	0.141746i
$482$		0			0
$483$	26.4714	−	5.95402i	1.20449	−	0.270917i
$484$		0			0
$485$	6.01215	+	3.47112i	0.272998	+	0.157615i
$486$		0			0
$487$	9.71448	+	16.8260i	0.440205	+	0.762458i	0.997704	−	0.0677196i	$-0.0215723\pi$
$487$	9.71448	+	16.8260i	0.440205	+	0.762458i	−0.557499	+	0.830178i	$0.688239\pi$
$488$		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
$495$	−4.64184	+	2.35504i	−0.208635	+	0.105851i
$496$		0			0
$497$	−20.1983	−	5.70577i	−0.906017	−	0.255939i
$498$		0			0
$499$	−16.4576	+	28.5054i	−0.736743	+	1.27608i	0.217211	+	0.976125i	$0.430304\pi$
$499$	−16.4576	+	28.5054i	−0.736743	+	1.27608i	−0.953954	+	0.299952i	$0.903029\pi$
$500$		0			0
$501$	−23.8836	−	14.6643i	−1.06704	−	0.655153i
$502$		0			0
$503$	−12.2651			−0.546874			−0.273437	−	0.961890i	$-0.588160\pi$
$503$	−12.2651			−0.546874			−0.273437	+	0.961890i	$0.588160\pi$
$504$		0			0
$505$	−2.84018			−0.126387
$506$		0			0
$507$	10.9689	+	6.73479i	0.487146	+	0.299102i
$508$		0			0
$509$	7.21563	−	12.4978i	0.319827	−	0.553957i	−0.660625	−	0.750716i	$-0.729709\pi$
$509$	7.21563	−	12.4978i	0.319827	−	0.553957i	0.980452	+	0.196760i	$0.0630419\pi$
$510$		0			0
$511$	0.920815	+	3.63218i	0.0407345	+	0.160678i
$512$		0			0
$513$	21.1707	−	30.6333i	0.934711	−	1.35249i
$514$		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	$-0.219656\pi$
$521$	−3.78222	−	6.55100i	−0.165702	−	0.287005i	−0.936904	+	0.349586i	$0.886322\pi$
$522$		0			0
$523$	8.64129	+	4.98905i	0.377857	+	0.218156i	0.676886	−	0.736088i	$-0.263329\pi$
$523$	8.64129	+	4.98905i	0.377857	+	0.218156i	−0.299028	+	0.954244i	$0.596662\pi$
$524$		0			0
$525$	4.37470	+	1.36456i	0.190927	+	0.0595544i
$526$		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
$537$	27.8114	+	0.752310i	1.20015	+	0.0324646i
$538$		0			0
$539$	−12.1408	−	0.328237i	−0.522940	−	0.0141381i
$540$		0			0
$541$	−16.5475	+	28.6612i	−0.711434	+	1.23224i	0.252884	+	0.967496i	$0.418621\pi$
$541$	−16.5475	+	28.6612i	−0.711434	+	1.23224i	−0.964319	+	0.264744i	$0.914713\pi$
$542$		0			0
$543$	9.51197	−	15.4921i	0.408198	−	0.664828i
$544$		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
$549$	−1.41984	+	26.2251i	−0.0605972	+	1.11926i
$550$		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
$555$	0.0644229	−	2.38159i	0.00273460	−	0.101093i
$556$		0			0
$557$	1.45160	−	0.838083i	0.0615064	−	0.0355107i	−0.468931	−	0.883235i	$-0.655361\pi$
$557$	1.45160	−	0.838083i	0.0615064	−	0.0355107i	0.530438	+	0.847724i	$0.322028\pi$
$558$		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	0.822227	+	0.569159i	$0.192731\pi$
$563$	21.4502	+	37.1529i	0.904020	+	1.56581i	0.0817930	+	0.996649i	$0.473935\pi$
$564$		0			0
$565$	−13.7716	−	7.95101i	−0.579374	−	0.334502i
$566$		0			0
$567$	14.6691	+	18.7568i	0.616042	+	0.787713i
$568$		0			0
$569$	35.5051	+	20.4989i	1.48845	+	0.859357i	0.999913	−	0.0131862i	$-0.00419740\pi$
$569$	35.5051	+	20.4989i	1.48845	+	0.859357i	0.488537	+	0.872543i	$0.337531\pi$
$570$		0			0
$571$	−7.30655	−	12.6553i	−0.305770	−	0.529609i	0.671663	−	0.740857i	$-0.265580\pi$
$571$	−7.30655	−	12.6553i	−0.305770	−	0.529609i	−0.977432	+	0.211248i	$0.932247\pi$
$572$		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	−0.725780	−	0.687926i	$-0.758521\pi$
$577$	−11.8401	+	6.83587i	−0.492909	+	0.284581i	0.232872	+	0.972508i	$0.425188\pi$
$578$		0			0
$579$	0.900499	−	33.2897i	0.0374235	−	1.38347i
$580$		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
$585$	0.733087	−	13.5405i	0.0303094	−	0.559830i
$586$		0			0
$587$	−1.12952			−0.0466203			−0.0233102	−	0.999728i	$-0.507421\pi$
$587$	−1.12952			−0.0466203			−0.0233102	+	0.999728i	$0.507421\pi$
$588$		0			0
$589$	47.7081			1.96578
$590$		0			0
$591$	−20.3947	+	33.2168i	−0.838928	+	1.36635i
$592$		0			0
$593$	−5.52609	+	9.57146i	−0.226929	+	0.393053i	−0.956896	−	0.290429i	$-0.906202\pi$
$593$	−5.52609	+	9.57146i	−0.226929	+	0.393053i	0.729967	+	0.683482i	$0.239535\pi$
$594$		0			0
$595$	1.59779	−	5.65613i	0.0655029	−	0.231879i
$596$		0			0
$597$	−18.5343	−	0.501359i	−0.758558	−	0.0205193i
$598$		0			0
$599$	13.6283	−	7.86831i	0.556838	−	0.321490i	−0.195038	−	0.980796i	$-0.562483\pi$
$599$	13.6283	−	7.86831i	0.556838	−	0.321490i	0.751875	+	0.659305i	$0.229150\pi$
$600$		0			0
$601$		−	36.9336i		−	1.50655i	−0.657704	−	0.753276i	$-0.728472\pi$
$601$		−	36.9336i		−	1.50655i	0.657704	−	0.753276i	$-0.271528\pi$
$602$		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	0.371339	−	0.928497i	$-0.378899\pi$
$607$	−6.08775	−	3.51476i	−0.247094	−	0.142660i	−0.618433	+	0.785838i	$0.712232\pi$
$608$		0			0
$609$	28.3174	+	30.7129i	1.14748	+	1.24455i
$610$		0			0
$611$	−4.39460	−	2.53722i	−0.177786	−	0.102645i
$612$		0			0
$613$	6.83385	+	11.8366i	0.276017	+	0.478075i	0.970391	−	0.241539i	$-0.0776522\pi$
$613$	6.83385	+	11.8366i	0.276017	+	0.478075i	−0.694374	+	0.719614i	$0.744319\pi$
$614$		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	0.249764	−	0.968307i	$-0.419647\pi$
$619$	30.1847	−	17.4271i	1.21322	−	0.700455i	0.963460	+	0.267852i	$0.0863137\pi$
$620$		0			0
$621$	−17.4915	+	25.3095i	−0.701909	+	1.01564i
$622$		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
$627$	−18.3525	−	11.2683i	−0.732930	−	0.450012i
$628$		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
$633$	−36.0764	−	22.1505i	−1.43391	−	0.880405i
$634$		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
$639$	21.2237	−	10.7679i	0.839596	−	0.425970i
$640$		0			0
$641$	−12.8017	+	7.39109i	−0.505638	+	0.291930i	−0.731039	−	0.682336i	$-0.760964\pi$
$641$	−12.8017	+	7.39109i	−0.505638	+	0.291930i	0.225401	+	0.974266i	$0.427631\pi$
$642$		0			0
$643$		−	8.75484i		−	0.345257i	−0.984987	−	0.172629i	$-0.944774\pi$
$643$		−	8.75484i		−	0.345257i	0.984987	−	0.172629i	$-0.0552260\pi$
$644$		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	$-0.194864\pi$
$647$	−2.25035	−	3.89772i	−0.0884703	−	0.153235i	−0.906865	+	0.421422i	$0.861531\pi$
$648$		0			0
$649$	−0.734318	−	0.423959i	−0.0288245	−	0.0166418i
$650$		0			0
$651$	−9.08432	+	29.1237i	−0.356043	+	1.14145i
$652$		0			0
$653$	18.4630	+	10.6596i	0.722514	+	0.417144i	0.815677	−	0.578507i	$-0.196364\pi$
$653$	18.4630	+	10.6596i	0.722514	+	0.417144i	−0.0931631	+	0.995651i	$0.529698\pi$
$654$		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	−0.887879	−	0.460078i	$-0.847821\pi$
$661$	−23.9971	+	13.8547i	−0.933379	+	0.538886i	−0.0455001	+	0.998964i	$0.514488\pi$
$662$		0			0
$663$	−17.3857	−	0.470290i	−0.675205	−	0.0182645i
$664$		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
$669$	−14.8677	+	24.2149i	−0.574818	+	0.936202i
$670$		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
$675$	−4.69575	+	2.22484i	−0.180740	+	0.0856341i
$676$		0			0
$677$	−21.9030	+	37.9372i	−0.841802	+	1.45804i	0.0465685	+	0.998915i	$0.485171\pi$
$677$	−21.9030	+	37.9372i	−0.841802	+	1.45804i	−0.888370	+	0.459128i	$0.848162\pi$
$678$		0			0
$679$	−17.6757	−	4.99317i	−0.678331	−	0.191620i
$680$		0			0
$681$	0.866292	−	32.0251i	0.0331964	−	1.22721i
$682$		0			0
$683$	−10.2915	+	5.94181i	−0.393794	+	0.227357i	−0.683803	−	0.729667i	$-0.739675\pi$
$683$	−10.2915	+	5.94181i	−0.393794	+	0.227357i	0.290009	+	0.957024i	$0.406342\pi$
$684$		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	−0.0811246	−	0.996704i	$-0.525851\pi$
$691$	−25.8888	−	14.9469i	−0.984858	−	0.568608i	−0.903733	+	0.428096i	$0.859185\pi$
$692$		0			0
$693$	10.3734	−	9.05779i	0.394052	−	0.344077i
$694$		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
$705$	−0.0525794	+	1.94376i	−0.00198025	+	0.0732062i
$706$		0			0
$707$	7.28399	−	1.84661i	0.273943	−	0.0694488i
$708$		0			0
$709$	13.8755	−	24.0330i	0.521104	−	0.902578i	−0.478595	−	0.878036i	$-0.658854\pi$
$709$	13.8755	−	24.0330i	0.521104	−	0.902578i	0.999699	−	0.0245424i	$-0.00781286\pi$
$710$		0			0
$711$	18.2408	+	0.987564i	0.684084	+	0.0370365i
$712$		0			0
$713$	−39.4170			−1.47618
$714$		0			0
$715$	−7.84251			−0.293293
$716$		0			0
$717$	−19.7515	+	32.1692i	−0.737634	+	1.20138i
$718$		0			0
$719$	3.02336	−	5.23662i	0.112752	−	0.195293i	−0.804127	−	0.594458i	$-0.797367\pi$
$719$	3.02336	−	5.23662i	0.112752	−	0.195293i	0.916879	+	0.399165i	$0.130700\pi$
$720$		0			0
$721$	−30.9702	+	30.1442i	−1.15339	+	1.12263i
$722$		0			0
$723$	3.95434	+	0.106966i	0.147064	+	0.00397812i
$724$		0			0
$725$	−7.89474	+	4.55803i	−0.293203	+	0.169281i
$726$		0			0
$727$		−	24.4800i		−	0.907915i	−0.891023	−	0.453957i	$-0.850012\pi$
$727$		−	24.4800i		−	0.907915i	0.891023	−	0.453957i	$-0.149988\pi$
$728$		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	0.203582	−	0.979058i	$-0.434742\pi$
$733$	−14.6881	−	8.48017i	−0.542517	−	0.313222i	−0.746098	+	0.665836i	$0.768075\pi$
$734$		0			0
$735$	−12.1066	−	0.655282i	−0.446560	−	0.0241704i
$736$		0			0
$737$	−21.4202	−	12.3669i	−0.789023	−	0.455542i
$738$		0			0
$739$	15.6634	+	27.1299i	0.576189	+	0.997988i	0.995911	+	0.0903358i	$0.0287940\pi$
$739$	15.6634	+	27.1299i	0.576189	+	0.997988i	−0.419723	+	0.907652i	$0.637873\pi$
$740$		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
$747$	21.1821	+	41.7504i	0.775013	+	1.52757i
$748$		0			0
$749$	−14.0143	+	13.6405i	−0.512071	+	0.498414i
$750$		0			0
$751$	16.3393	−	28.3005i	0.596229	−	1.03270i	−0.397143	−	0.917757i	$-0.629998\pi$
$751$	16.3393	−	28.3005i	0.596229	−	1.03270i	0.993372	−	0.114942i	$-0.0366684\pi$
$752$		0			0
$753$	25.3224	+	15.5477i	0.922799	+	0.566589i
$754$		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
$759$	15.1631	+	9.30997i	0.550384	+	0.337930i
$760$		0			0
$761$	−15.3810	+	26.6407i	−0.557561	+	0.965723i	0.440139	+	0.897930i	$0.354929\pi$
$761$	−15.3810	+	26.6407i	−0.557561	+	0.965723i	−0.997699	+	0.0677935i	$0.978404\pi$
$762$		0			0
$763$	13.5534	−	3.43601i	0.490667	−	0.124392i
$764$		0			0
$765$	3.01533	+	5.94328i	0.109019	+	0.214880i
$766$		0			0
$767$	1.91305	−	1.10450i	0.0690761	−	0.0398811i
$768$		0			0
$769$			34.0455i			1.22771i	0.789418	+	0.613855i	$0.210382\pi$
$769$			34.0455i			1.22771i	−0.789418	+	0.613855i	$0.789618\pi$
$770$		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	$-0.243967\pi$
$773$	−6.68565	−	11.5799i	−0.240466	−	0.416499i	−0.960847	+	0.277079i	$0.910634\pi$
$774$		0			0
$775$	−5.76540	−	3.32866i	−0.207099	−	0.119569i
$776$		0			0
$777$	1.38322	+	6.14976i	0.0496228	+	0.220621i
$778$		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	−0.0430051	−	0.999075i	$-0.513693\pi$
$787$	22.4629	−	12.9690i	0.800717	−	0.462294i	0.843722	+	0.536781i	$0.180360\pi$
$788$		0			0
$789$	35.5164	+	0.960731i	1.26442	+	0.0342029i
$790$		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
$795$	6.91204	−	11.2576i	0.245145	−	0.399265i
$796$		0			0
$797$	−30.9797			−1.09736			−0.548679	−	0.836033i	$-0.684869\pi$
$797$	−30.9797			−1.09736			−0.548679	+	0.836033i	$0.684869\pi$
$798$		0			0
$799$	2.49392			0.0882286
$800$		0			0
$801$	−13.6427	−	0.738621i	−0.482041	−	0.0260979i
$802$		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
$807$	0.915202	−	33.8332i	0.0322166	−	1.19099i
$808$		0			0
$809$	−24.1436	+	13.9393i	−0.848845	+	0.490081i	−0.860261	−	0.509854i	$-0.829699\pi$
$809$	−24.1436	+	13.9393i	−0.848845	+	0.490081i	0.0114160	+	0.999935i	$0.496366\pi$
$810$		0			0
$811$		−	26.1528i		−	0.918349i	−0.888346	−	0.459175i	$-0.848145\pi$
$811$		−	26.1528i		−	0.918349i	0.888346	−	0.459175i	$-0.151855\pi$
$812$		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
$819$	6.92354	+	35.2028i	0.241928	+	1.23009i
$820$		0			0
$821$	−2.42107	−	1.39781i	−0.0844959	−	0.0487837i	0.457157	−	0.889386i	$-0.348868\pi$
$821$	−2.42107	−	1.39781i	−0.0844959	−	0.0487837i	−0.541653	+	0.840602i	$0.682201\pi$
$822$		0			0
$823$	12.4881	+	21.6300i	0.435308	+	0.753976i	0.997321	−	0.0731527i	$-0.0233060\pi$
$823$	12.4881	+	21.6300i	0.435308	+	0.753976i	−0.562012	+	0.827129i	$0.689973\pi$
$824$		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	−0.896390	−	0.443267i	$-0.853820\pi$
$829$	−27.6610	+	15.9701i	−0.960705	+	0.554663i	−0.0643148	+	0.997930i	$0.520486\pi$
$830$		0			0
$831$	−0.306784	+	11.3412i	−0.0106422	+	0.393422i
$832$		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
$837$	−14.8115	−	31.2611i	−0.511959	−	1.08054i
$838$		0			0
$839$	11.3366			0.391384			0.195692	−	0.980665i	$-0.437305\pi$
$839$	11.3366			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$840$		0			0
$841$	−54.1027			−1.86561
$842$		0			0
$843$	−11.4797	+	18.6969i	−0.395383	+	0.643957i
$844$		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
$849$	4.12011	+	0.111450i	0.141402	+	0.00382497i
$850$		0			0
$851$	−7.05309	+	4.07210i	−0.241777	+	0.139590i
$852$		0			0
$853$			41.8866i			1.43417i	0.696986	+	0.717085i	$0.254524\pi$
$853$			41.8866i			1.43417i	−0.696986	+	0.717085i	$0.745476\pi$
$854$		0			0
$855$	−18.0102	−	11.7402i	−0.615935	−	0.401507i
$856$		0			0
$857$	20.1484	+	34.8980i	0.688255	+	1.19209i	0.972402	+	0.233312i	$0.0749563\pi$
$857$	20.1484	+	34.8980i	0.688255	+	1.19209i	−0.284147	+	0.958781i	$0.591710\pi$
$858$		0			0
$859$	−4.51782	−	2.60837i	−0.154146	−	0.0889963i	0.420943	−	0.907087i	$-0.361699\pi$
$859$	−4.51782	−	2.60837i	−0.154146	−	0.0889963i	−0.575089	+	0.818091i	$0.695033\pi$
$860$		0			0
$861$	−10.8015	+	9.95898i	−0.368112	+	0.339401i
$862$		0			0
$863$	7.10243	+	4.10059i	0.241769	+	0.139586i	0.615990	−	0.787754i	$-0.288756\pi$
$863$	7.10243	+	4.10059i	0.241769	+	0.139586i	−0.374220	+	0.927340i	$0.622090\pi$
$864$		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
$873$	18.5730	−	9.42305i	0.628602	−	0.318922i
$874$		0			0
$875$	0.719245	−	2.54611i	0.0243149	−	0.0860743i
$876$		0			0
$877$	−17.5894	+	30.4657i	−0.593951	+	1.02875i	0.399743	+	0.916627i	$0.369099\pi$
$877$	−17.5894	+	30.4657i	−0.593951	+	1.02875i	−0.993694	+	0.112126i	$0.964234\pi$
$878$		0			0
$879$	26.0159	+	15.9735i	0.877494	+	0.538772i
$880$		0			0
$881$	−13.3867			−0.451011			−0.225505	−	0.974242i	$-0.572403\pi$
$881$	−13.3867			−0.451011			−0.225505	+	0.974242i	$0.572403\pi$
$882$		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
$885$	−0.721345	−	0.442898i	−0.0242477	−	0.0148879i
$886$		0			0
$887$	−13.8288	+	23.9521i	−0.464325	+	0.804234i	−0.999171	−	0.0407153i	$-0.987036\pi$
$887$	−13.8288	+	23.9521i	−0.464325	+	0.804234i	0.534846	+	0.844950i	$0.320370\pi$
$888$		0			0
$889$	−4.52482	+	16.0178i	−0.151758	+	0.537218i
$890$		0			0
$891$	−1.68589	+	15.5240i	−0.0564795	+	0.520073i
$892$		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
$903$	−30.4086	+	28.0369i	−1.01194	+	0.933008i
$904$		0			0
$905$	−9.08958	−	5.24787i	−0.302148	−	0.174445i
$906$		0			0
$907$	−10.9484	−	18.9633i	−0.363537	−	0.629665i	0.625003	−	0.780622i	$-0.285098\pi$
$907$	−10.9484	−	18.9633i	−0.363537	−	0.629665i	−0.988540	+	0.150957i	$0.951764\pi$
$908$		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
$915$	15.1577	+	0.410022i	0.501099	+	0.0135549i
$916$		0			0
$917$	24.2343	+	24.8984i	0.800288	+	0.822217i
$918$		0			0
$919$	−3.62558	+	6.27969i	−0.119597	+	0.207148i	−0.919608	−	0.392837i	$-0.871494\pi$
$919$	−3.62558	+	6.27969i	−0.119597	+	0.207148i	0.800011	+	0.599985i	$0.204827\pi$
$920$		0			0
$921$	16.1560	−	26.3131i	0.532357	−	0.867046i
$922$		0			0
$923$	35.8580			1.18028
$924$		0			0
$925$	−1.37551			−0.0452266
$926$		0			0
$927$	2.64927	−	48.9334i	0.0870135	−	1.60718i
$928$		0			0
$929$	−16.5819	+	28.7207i	−0.544035	+	0.942297i	0.454631	+	0.890680i	$0.349771\pi$
$929$	−16.5819	+	28.7207i	−0.544035	+	0.942297i	−0.998667	+	0.0516174i	$0.983562\pi$
$930$		0			0
$931$	−23.8987	−	44.1052i	−0.783248	−	1.44549i
$932$		0			0
$933$	−0.309369	+	11.4368i	−0.0101283	+	0.374423i
$934$		0			0
$935$	3.33795	−	1.92717i	0.109163	−	0.0630251i
$936$		0			0
$937$		−	31.3774i		−	1.02506i	−0.858671	−	0.512528i	$-0.828709\pi$
$937$		−	31.3774i		−	1.02506i	0.858671	−	0.512528i	$-0.171291\pi$
$938$		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	$-0.272663\pi$
$941$	−10.0272	−	17.3676i	−0.326876	−	0.566167i	−0.981890	+	0.189450i	$0.939329\pi$
$942$		0			0
$943$	−16.4393	−	9.49124i	−0.535337	−	0.309077i
$944$		0			0
$945$	10.5963	−	8.75891i	0.344697	−	0.284927i
$946$		0			0
$947$	−10.3813	−	5.99364i	−0.337346	−	0.194767i	0.321752	−	0.946824i	$-0.395728\pi$
$947$	−10.3813	−	5.99364i	−0.337346	−	0.194767i	−0.659098	+	0.752057i	$0.729062\pi$
$948$		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
$957$	−0.740780	+	27.3852i	−0.0239460	+	0.885238i
$958$		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
$963$	1.19882	−	22.1428i	0.0386314	−	0.713541i
$964$		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
$969$	−14.4276	+	23.4980i	−0.463480	+	0.754866i
$970$		0			0
$971$	14.5995	−	25.2872i	0.468522	−	0.811503i	−0.530831	−	0.847478i	$-0.678120\pi$
$971$	14.5995	−	25.2872i	0.468522	−	0.811503i	0.999353	+	0.0359742i	$0.0114534\pi$
$972$		0			0
$973$	4.22697	+	1.19407i	0.135511	+	0.0382801i
$974$		0			0
$975$	−7.82619	−	0.211701i	−0.250639	−	0.00677987i
$976$		0			0
$977$	24.2834	−	14.0200i	0.776894	−	0.448540i	−0.0584344	−	0.998291i	$-0.518611\pi$
$977$	24.2834	−	14.0200i	0.776894	−	0.448540i	0.835328	+	0.549751i	$0.185278\pi$
$978$		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	0.934896	+	0.354921i	$0.115492\pi$
$983$	24.2928	+	42.0763i	0.774819	+	1.34203i	−0.160078	+	0.987104i	$0.551174\pi$
$984$		0			0
$985$	19.4891	+	11.2520i	0.620974	+	0.358520i
$986$		0			0
$987$	−1.12893	−	5.01919i	−0.0359342	−	0.159762i
$988$		0			0
$989$	−46.2805	−	26.7201i	−1.47163	−	0.849648i
$990$		0			0
$991$	0.953533	+	1.65157i	0.0302900	+	0.0524638i	0.880773	−	0.473539i	$-0.157024\pi$
$991$	0.953533	+	1.65157i	0.0302900	+	0.0524638i	−0.850483	+	0.526002i	$0.823690\pi$
$992$		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	0.205875	−	0.978578i	$-0.433996\pi$
$997$	36.5101	−	21.0791i	1.15629	−	0.667582i	0.950411	+	0.310996i	$0.100663\pi$
$998$		0			0
$999$	−5.87983	−	4.06357i	−0.186030	−	0.128566i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cp.a.521.3	✓	32	21.17	even	6	inner
840.2.cp.a.761.3	yes	32	1.1	even	1	trivial
840.2.cp.b.521.9	yes	32	7.3	odd	6
840.2.cp.b.761.9	yes	32	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.47603 - 0.906269i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.719245 - 2.54611i) q^{7} +(1.35735 + 2.67537i) q^{9} +(1.50258 - 0.867515i) q^{11} +4.52010i q^{13} +(1.52287 - 0.825148i) q^{15} +(-1.11074 - 1.92386i) q^{17} +(6.20617 + 3.58314i) q^{19} +(-3.36909 + 3.10632i) q^{21} +(-5.12760 - 2.96042i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(0.421109 - 5.17906i) q^{27} -9.11607i q^{29} +(5.76540 - 3.32866i) q^{31} +(-3.00406 - 0.0812610i) q^{33} +(1.84538 + 1.89594i) q^{35} +(0.687757 - 1.19123i) q^{37} +(4.09643 - 6.67182i) q^{39} +3.20604 q^{41} +9.02575 q^{43} +(-2.99561 - 0.162184i) q^{45} +(-0.561320 + 0.972234i) q^{47} +(-5.96537 - 3.66256i) q^{49} +(-0.104044 + 3.84631i) q^{51} +(6.60510 - 3.81346i) q^{53} +1.73503i q^{55} +(-5.91323 - 10.9133i) q^{57} +(-0.244352 - 0.423231i) q^{59} +(7.58163 + 4.37726i) q^{61} +(7.78806 - 1.53172i) q^{63} +(-3.91452 - 2.26005i) q^{65} +(-7.12780 - 12.3457i) q^{67} +(4.88558 + 9.01668i) q^{69} -7.93299i q^{71} +(-1.22652 + 0.708133i) q^{73} +(-0.0468355 + 1.73142i) q^{75} +(-1.12807 - 4.44969i) q^{77} +(3.04459 - 5.27338i) q^{79} +(-5.31519 + 7.26283i) q^{81} +15.6055 q^{83} +2.22148 q^{85} +(-8.26161 + 13.4556i) q^{87} +(-2.27711 + 3.94408i) q^{89} +(11.5087 + 3.25106i) q^{91} +(-11.5266 - 0.311799i) q^{93} +(-6.20617 + 3.58314i) q^{95} -6.94223i q^{97} +(4.36045 + 2.84243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{19} - 4 q^{21} - 24 q^{23} - 16 q^{25} - 24 q^{27} + 42 q^{31} + 6 q^{33} - 2 q^{35} + 6 q^{37} + 12 q^{39} - 44 q^{41} - 20 q^{43} + 8 q^{45} - 4 q^{47} + 16 q^{49}+ \cdots - 8 q^{99}+O(q^{100}) \) 32 * q - 16 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^19 - 4 * q^21 - 24 * q^23 - 16 * q^25 - 24 * q^27 + 42 * q^31 + 6 * q^33 - 2 * q^35 + 6 * q^37 + 12 * q^39 - 44 * q^41 - 20 * q^43 + 8 * q^45 - 4 * q^47 + 16 * q^49 + 24 * q^51 - 12 * q^59 - 18 * q^61 - 6 * q^63 + 6 * q^65 - 6 * q^67 + 34 * q^69 - 6 * q^73 - 40 * q^77 - 2 * q^79 - 18 * q^81 + 88 * q^83 - 84 * q^87 + 6 * q^89 - 26 * q^91 - 58 * q^93 - 6 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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