LMFDB - Embedded newform 588.2.o.e.19.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,-12,4,0,8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	588.19
Dual form			588.2.o.e.31.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.381130 - 1.36189i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.70948 + 1.03811i) q^{4} +(0.977624 + 0.564431i) q^{5} +(-0.988865 + 1.01101i) q^{6} +(2.06533 + 1.93246i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.396091 - 1.54654i) q^{10} +(-1.16914 + 0.675002i) q^{11} +(1.75377 + 0.961396i) q^{12} +5.58489i q^{13} -1.12886i q^{15} +(1.84464 - 3.54927i) q^{16} +(-3.44113 + 1.98674i) q^{17} +(1.36999 + 0.350876i) q^{18} +(-3.07204 + 5.32093i) q^{19} +(-2.25717 + 0.0500006i) q^{20} +(1.36487 + 1.33497i) q^{22} +(5.72784 + 3.30697i) q^{23} +(0.640898 - 2.75486i) q^{24} +(-1.86283 - 3.22652i) q^{25} +(7.60600 - 2.12857i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(-1.53738 + 0.430244i) q^{30} +(1.46111 + 2.53071i) q^{31} +(-5.53675 - 1.15946i) q^{32} +(1.16914 + 0.675002i) q^{33} +(4.01723 + 3.92923i) q^{34} +(-0.0442929 - 1.99951i) q^{36} +(-3.16249 + 5.47759i) q^{37} +(8.41736 + 2.15581i) q^{38} +(4.83666 - 2.79245i) q^{39} +(0.928372 + 3.05496i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(1.29789 - 2.36760i) q^{44} +(-0.977624 + 0.564431i) q^{45} +(2.32067 - 9.06107i) q^{46} +(1.79746 - 3.11329i) q^{47} +(-3.99608 + 0.177128i) q^{48} +(-3.68418 + 3.76670i) q^{50} +(3.44113 + 1.98674i) q^{51} +(-5.79775 - 9.54726i) q^{52} +(-0.366793 - 0.635305i) q^{53} +(-0.381130 - 1.36189i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(-3.25969 - 11.6478i) q^{58} +(7.20270 + 12.4754i) q^{59} +(1.17189 + 1.92977i) q^{60} +(-7.89372 - 4.55744i) q^{61} +(2.88967 - 2.95439i) q^{62} +(0.531167 + 7.98235i) q^{64} +(-3.15229 + 5.45992i) q^{65} +(0.473683 - 1.84950i) q^{66} +(0.202730 - 0.117046i) q^{67} +(3.82008 - 6.96857i) q^{68} -6.61394i q^{69} +8.74104i q^{71} +(-2.70623 + 0.822395i) q^{72} +(1.52893 - 0.882729i) q^{73} +(8.66518 + 2.21928i) q^{74} +(-1.86283 + 3.22652i) q^{75} +(-0.272139 - 12.2852i) q^{76} +(-5.64640 - 5.52270i) q^{78} +(-7.28129 - 4.20385i) q^{79} +(3.80668 - 2.42868i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.203226 - 0.0568736i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(-14.5119 + 4.06122i) q^{86} +(-4.27635 - 7.40685i) q^{87} +(-3.71907 - 0.865215i) q^{88} +(-6.86538 - 3.96373i) q^{89} +(1.14129 + 1.11629i) q^{90} +(-13.2246 + 0.292951i) q^{92} +(1.46111 - 2.53071i) q^{93} +(-4.92502 - 1.26137i) q^{94} +(-6.00660 + 3.46791i) q^{95} +(1.76425 + 5.37470i) q^{96} +6.23063i q^{97} -1.35000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.381130	−	1.36189i	−0.269500	−	0.963000i
$2$	−0.381130	−	1.36189i	−0.269500	−	0.963000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.70948	+	1.03811i	−0.854740	+	0.519057i
$5$	0.977624	+	0.564431i	0.437207	+	0.252421i	0.702412	−	0.711771i	$-0.252106\pi$
$5$	0.977624	+	0.564431i	0.437207	+	0.252421i	−0.265205	+	0.964192i	$0.585440\pi$
$6$	−0.988865	+	1.01101i	−0.403702	+	0.412744i
$7$		0			0
$7$		0			0
$8$	2.06533	+	1.93246i	0.730204	+	0.683229i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.396091	−	1.54654i	0.125255	−	0.489058i
$11$	−1.16914	+	0.675002i	−0.352508	+	0.203521i	−0.665789	−	0.746140i	$-0.731905\pi$
$11$	−1.16914	+	0.675002i	−0.352508	+	0.203521i	0.313281	+	0.949660i	$0.398572\pi$
$12$	1.75377	+	0.961396i	0.506271	+	0.277531i
$13$			5.58489i			1.54897i	0.632592	+	0.774485i	$0.281991\pi$
$13$			5.58489i			1.54897i	−0.632592	+	0.774485i	$0.718009\pi$
$14$		0			0
$15$		−	1.12886i		−	0.291471i
$16$	1.84464	−	3.54927i	0.461160	−	0.887317i
$17$	−3.44113	+	1.98674i	−0.834597	+	0.481855i	−0.855424	−	0.517929i	$-0.826703\pi$
$17$	−3.44113	+	1.98674i	−0.834597	+	0.481855i	0.0208273	+	0.999783i	$0.493370\pi$
$18$	1.36999	+	0.350876i	0.322911	+	0.0827022i
$19$	−3.07204	+	5.32093i	−0.704775	+	1.22071i	0.261998	+	0.965068i	$0.415619\pi$
$19$	−3.07204	+	5.32093i	−0.704775	+	1.22071i	−0.966773	+	0.255637i	$0.917715\pi$
$20$	−2.25717	+	0.0500006i	−0.504719	+	0.0111805i
$21$		0			0
$22$	1.36487	+	1.33497i	0.290991	+	0.284617i
$23$	5.72784	+	3.30697i	1.19434	+	0.689551i	0.959287	−	0.282432i	$-0.0911411\pi$
$23$	5.72784	+	3.30697i	1.19434	+	0.689551i	0.235051	+	0.971983i	$0.424474\pi$
$24$	0.640898	−	2.75486i	0.130823	−	0.562333i
$25$	−1.86283	−	3.22652i	−0.372567	−	0.645305i
$26$	7.60600	−	2.12857i	1.49166	−	0.417447i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.55270			1.58820			0.794098	−	0.607790i	$-0.207944\pi$
$29$	8.55270			1.58820			0.794098	+	0.607790i	$0.207944\pi$
$30$	−1.53738	+	0.430244i	−0.280687	+	0.0785514i
$31$	1.46111	+	2.53071i	0.262422	+	0.454529i	0.966885	−	0.255212i	$-0.0821453\pi$
$31$	1.46111	+	2.53071i	0.262422	+	0.454529i	−0.704463	+	0.709741i	$0.748812\pi$
$32$	−5.53675	−	1.15946i	−0.978769	−	0.204966i
$33$	1.16914	+	0.675002i	0.203521	+	0.117503i
$34$	4.01723	+	3.92923i	0.688950	+	0.673857i
$35$		0			0
$36$	−0.0442929	−	1.99951i	−0.00738215	−	0.333252i
$37$	−3.16249	+	5.47759i	−0.519910	+	0.900510i	0.479823	+	0.877366i	$0.340701\pi$
$37$	−3.16249	+	5.47759i	−0.519910	+	0.900510i	−0.999732	+	0.0231442i	$0.992632\pi$
$38$	8.41736	+	2.15581i	1.36548	+	0.349719i
$39$	4.83666	−	2.79245i	0.774485	−	0.447149i
$40$	0.928372	+	3.05496i	0.146788	+	0.483031i
$41$			0.149223i			0.0233048i	0.999932	+	0.0116524i	$0.00370916\pi$
$41$			0.149223i			0.0233048i	−0.999932	+	0.0116524i	$0.996291\pi$
$42$		0			0
$43$		−	10.6557i		−	1.62498i	−0.582974	−	0.812491i	$-0.698111\pi$
$43$		−	10.6557i		−	1.62498i	0.582974	−	0.812491i	$-0.301889\pi$
$44$	1.29789	−	2.36760i	0.195664	−	0.356929i
$45$	−0.977624	+	0.564431i	−0.145736	+	0.0841405i
$46$	2.32067	−	9.06107i	0.342164	−	1.33598i
$47$	1.79746	−	3.11329i	0.262186	−	0.454120i	−0.704636	−	0.709569i	$-0.748890\pi$
$47$	1.79746	−	3.11329i	0.262186	−	0.454120i	0.966823	+	0.255448i	$0.0822231\pi$
$48$	−3.99608	+	0.177128i	−0.576784	+	0.0255663i
$49$		0			0
$50$	−3.68418	+	3.76670i	−0.521022	+	0.532692i
$51$	3.44113	+	1.98674i	0.481855	+	0.278199i
$52$	−5.79775	−	9.54726i	−0.804003	−	1.32397i
$53$	−0.366793	−	0.635305i	−0.0503830	−	0.0872658i	0.839734	−	0.542998i	$-0.182711\pi$
$53$	−0.366793	−	0.635305i	−0.0503830	−	0.0872658i	−0.890117	+	0.455732i	$0.849378\pi$
$54$	−0.381130	−	1.36189i	−0.0518653	−	0.185330i
$55$	−1.52397			−0.205492
$56$		0			0
$57$	6.14408			0.813804
$58$	−3.25969	−	11.6478i	−0.428018	−	1.52943i
$59$	7.20270	+	12.4754i	0.937712	+	1.62416i	0.769726	+	0.638375i	$0.220393\pi$
$59$	7.20270	+	12.4754i	0.937712	+	1.62416i	0.167986	+	0.985789i	$0.446274\pi$
$60$	1.17189	+	1.92977i	0.151290	+	0.249132i
$61$	−7.89372	−	4.55744i	−1.01069	−	0.583520i	−0.0992943	−	0.995058i	$-0.531659\pi$
$61$	−7.89372	−	4.55744i	−1.01069	−	0.583520i	−0.911393	+	0.411538i	$0.864992\pi$
$62$	2.88967	−	2.95439i	0.366989	−	0.375208i
$63$		0			0
$64$	0.531167	+	7.98235i	0.0663959	+	0.997793i
$65$	−3.15229	+	5.45992i	−0.390993	+	0.677220i
$66$	0.473683	−	1.84950i	0.0583064	−	0.227657i
$67$	0.202730	−	0.117046i	0.0247674	−	0.0142995i	−0.487565	−	0.873087i	$-0.662115\pi$
$67$	0.202730	−	0.117046i	0.0247674	−	0.0142995i	0.512333	+	0.858787i	$0.328782\pi$
$68$	3.82008	−	6.96857i	0.463253	−	0.845063i
$69$		−	6.61394i		−	0.796225i
$70$		0			0
$71$			8.74104i			1.03737i	0.854965	+	0.518685i	$0.173578\pi$
$71$			8.74104i			1.03737i	−0.854965	+	0.518685i	$0.826422\pi$
$72$	−2.70623	+	0.822395i	−0.318932	+	0.0969202i
$73$	1.52893	−	0.882729i	0.178948	−	0.103316i	−0.407850	−	0.913049i	$-0.633721\pi$
$73$	1.52893	−	0.882729i	0.178948	−	0.103316i	0.586798	+	0.809733i	$0.300388\pi$
$74$	8.66518	+	2.21928i	1.00731	+	0.257986i
$75$	−1.86283	+	3.22652i	−0.215102	+	0.372567i
$76$	−0.272139	−	12.2852i	−0.0312165	−	1.40920i
$77$		0			0
$78$	−5.64640	−	5.52270i	−0.639328	−	0.625323i
$79$	−7.28129	−	4.20385i	−0.819209	−	0.472971i	0.0309346	−	0.999521i	$-0.490152\pi$
$79$	−7.28129	−	4.20385i	−0.819209	−	0.472971i	−0.850144	+	0.526551i	$0.823485\pi$
$80$	3.80668	−	2.42868i	0.425600	−	0.271534i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.203226	−	0.0568736i	0.0224425	−	0.00628063i
$83$	9.12928			1.00207			0.501035	−	0.865427i	$-0.332953\pi$
$83$	9.12928			1.00207			0.501035	+	0.865427i	$0.332953\pi$
$84$		0			0
$85$	−4.48551			−0.486522
$86$	−14.5119	+	4.06122i	−1.56486	+	0.437932i
$87$	−4.27635	−	7.40685i	−0.458473	−	0.794098i
$88$	−3.71907	−	0.865215i	−0.396454	−	0.0922322i
$89$	−6.86538	−	3.96373i	−0.727729	−	0.420155i	0.0898617	−	0.995954i	$-0.471358\pi$
$89$	−6.86538	−	3.96373i	−0.727729	−	0.420155i	−0.817591	+	0.575800i	$0.804691\pi$
$90$	1.14129	+	1.11629i	0.120303	+	0.117668i
$91$		0			0
$92$	−13.2246	+	0.292951i	−1.37876	+	0.0305422i
$93$	1.46111	−	2.53071i	0.151510	−	0.262422i
$94$	−4.92502	−	1.26137i	−0.507977	−	0.130100i
$95$	−6.00660	+	3.46791i	−0.616264	+	0.355800i
$96$	1.76425	+	5.37470i	0.180063	+	0.548553i
$97$			6.23063i			0.632624i	0.948655	+	0.316312i	$0.102445\pi$
$97$			6.23063i			0.632624i	−0.948655	+	0.316312i	$0.897555\pi$
$98$		0			0
$99$		−	1.35000i		−	0.135680i
$100$	6.53398	+	3.58184i	0.653398	+	0.358184i
$101$	−0.688456	+	0.397480i	−0.0685040	+	0.0395508i	−0.533861	−	0.845572i	$-0.679259\pi$
$101$	−0.688456	+	0.397480i	−0.0685040	+	0.0395508i	0.465357	+	0.885123i	$0.345926\pi$
$102$	1.39420	−	5.44364i	0.138046	−	0.539001i
$103$	−1.67738	+	2.90531i	−0.165277	+	0.286268i	−0.936754	−	0.349989i	$-0.886185\pi$
$103$	−1.67738	+	2.90531i	−0.165277	+	0.286268i	0.771477	+	0.636258i	$0.219518\pi$
$104$	−10.7926	+	11.5346i	−1.05830	+	1.13106i
$105$		0			0
$106$	−0.725418	+	0.741666i	−0.0704589	+	0.0720369i
$107$	10.8695	+	6.27550i	1.05079	+	0.606675i	0.922871	−	0.385109i	$-0.125836\pi$
$107$	10.8695	+	6.27550i	1.05079	+	0.606675i	0.127921	+	0.991784i	$0.459169\pi$
$108$	−1.70948	+	1.03811i	−0.164495	+	0.0998925i
$109$	7.62660	+	13.2097i	0.730496	+	1.26526i	0.956672	+	0.291169i	$0.0940442\pi$
$109$	7.62660	+	13.2097i	0.730496	+	1.26526i	−0.226176	+	0.974086i	$0.572622\pi$
$110$	0.580830	+	2.07547i	0.0553800	+	0.197889i
$111$	6.32497			0.600340
$112$		0			0
$113$	−11.7783			−1.10801			−0.554004	−	0.832514i	$-0.686901\pi$
$113$	−11.7783			−1.10801			−0.554004	+	0.832514i	$0.686901\pi$
$114$	−2.34170	−	8.36756i	−0.219320	−	0.783693i
$115$	3.73312	+	6.46595i	0.348115	+	0.602953i
$116$	−14.6207	+	8.87867i	−1.35749	+	0.824364i
$117$	−4.83666	−	2.79245i	−0.447149	−	0.258162i
$118$	14.2450	−	14.5640i	1.31136	−	1.34073i
$119$		0			0
$120$	2.18149	−	2.33147i	0.199142	−	0.212833i
$121$	−4.58875	+	7.94794i	−0.417159	+	0.722540i
$122$	−3.19819	+	12.4873i	−0.289551	+	1.13055i
$123$	0.129231	−	0.0746117i	0.0116524	−	0.00672751i
$124$	−5.12489	−	2.80940i	−0.460229	−	0.252292i
$125$		−	9.85008i		−	0.881018i
$126$		0			0
$127$		−	3.52444i		−	0.312743i	−0.987698	−	0.156372i	$-0.950020\pi$
$127$		−	3.52444i		−	0.312743i	0.987698	−	0.156372i	$-0.0499798\pi$
$128$	10.6686	−	3.76570i	0.942982	−	0.332844i
$129$	−9.22813	+	5.32786i	−0.812491	+	0.469092i
$130$	8.63724	+	2.21212i	0.757536	+	0.194016i
$131$	1.18600	−	2.05421i	0.103621	−	0.179477i	−0.809553	−	0.587047i	$-0.800290\pi$
$131$	1.18600	−	2.05421i	0.103621	−	0.179477i	0.913174	+	0.407570i	$0.133624\pi$
$132$	−2.69934	+	0.0597956i	−0.234948	+	0.00520454i
$133$		0			0
$134$	−0.236671	−	0.231486i	−0.0204452	−	0.0199973i
$135$	0.977624	+	0.564431i	0.0841405	+	0.0485785i
$136$	−10.9464	−	2.54659i	−0.938643	−	0.218369i
$137$	3.58780	+	6.21426i	0.306527	+	0.530920i	0.977600	−	0.210471i	$-0.0674997\pi$
$137$	3.58780	+	6.21426i	0.306527	+	0.530920i	−0.671073	+	0.741391i	$0.734166\pi$
$138$	−9.00745	+	2.52077i	−0.766765	+	0.214583i
$139$	−22.5888			−1.91595			−0.957977	−	0.286845i	$-0.907394\pi$
$139$	−22.5888			−1.91595			−0.957977	+	0.286845i	$0.907394\pi$
$140$		0			0
$141$	−3.59492			−0.302747
$142$	11.9043	−	3.33147i	0.998988	−	0.279571i
$143$	−3.76981	−	6.52950i	−0.315247	−	0.546025i
$144$	2.15144	+	3.37214i	0.179286	+	0.281012i
$145$	8.36132	+	4.82741i	0.694370	+	0.400895i
$146$	−1.78490	−	1.74580i	−0.147719	−	0.144483i
$147$		0			0
$148$	−0.280151	−	12.6468i	−0.0230283	−	1.03956i
$149$	5.52532	−	9.57014i	0.452652	−	0.784016i	−0.545898	−	0.837852i	$-0.683811\pi$
$149$	5.52532	−	9.57014i	0.452652	−	0.784016i	0.998550	+	0.0538356i	$0.0171447\pi$
$150$	5.10415	+	1.30725i	0.416752	+	0.106736i
$151$	−1.33325	+	0.769750i	−0.108498	+	0.0626413i	−0.553267	−	0.833004i	$-0.686619\pi$
$151$	−1.33325	+	0.769750i	−0.108498	+	0.0626413i	0.444769	+	0.895645i	$0.353286\pi$
$152$	−16.6273	+	5.05287i	−1.34865	+	0.409842i
$153$		−	3.97347i		−	0.321236i
$154$		0			0
$155$			3.29878i			0.264964i
$156$	−5.36929	+	9.79463i	−0.429887	+	0.784198i
$157$	7.41273	−	4.27974i	0.591600	−	0.341560i	−0.174130	−	0.984723i	$-0.555711\pi$
$157$	7.41273	−	4.27974i	0.591600	−	0.341560i	0.765730	+	0.643162i	$0.222378\pi$
$158$	−2.95006	+	11.5185i	−0.234694	+	0.916364i
$159$	−0.366793	+	0.635305i	−0.0290886	+	0.0503830i
$160$	−4.75843	−	4.25863i	−0.376187	−	0.336675i
$161$		0			0
$162$	−0.988865	+	1.01101i	−0.0776926	+	0.0794327i
$163$	4.90167	+	2.82998i	0.383929	+	0.221661i	0.679526	−	0.733651i	$-0.262185\pi$
$163$	4.90167	+	2.82998i	0.383929	+	0.221661i	−0.295598	+	0.955313i	$0.595519\pi$
$164$	−0.154911	−	0.255094i	−0.0120965	−	0.0199195i
$165$	0.761984	+	1.31980i	0.0593204	+	0.102746i
$166$	−3.47945	−	12.4331i	−0.270057	−	0.964993i
$167$	4.84357			0.374807			0.187403	−	0.982283i	$-0.439993\pi$
$167$	4.84357			0.374807			0.187403	+	0.982283i	$0.439993\pi$
$168$		0			0
$169$	−18.1910			−1.39931
$170$	1.70956	+	6.10876i	0.131117	+	0.468520i
$171$	−3.07204	−	5.32093i	−0.234925	−	0.406902i
$172$	11.0618	+	18.2157i	0.843458	+	1.38894i
$173$	−1.82184	−	1.05184i	−0.138512	−	0.0799701i	0.429143	−	0.903237i	$-0.358816\pi$
$173$	−1.82184	−	1.05184i	−0.138512	−	0.0799701i	−0.567655	+	0.823267i	$0.692149\pi$
$174$	−8.45746	+	8.64689i	−0.641159	+	0.655519i
$175$		0			0
$176$	0.239124	+	5.39472i	0.0180246	+	0.406642i
$177$	7.20270	−	12.4754i	0.541388	−	0.937712i
$178$	−2.78155	+	10.8606i	−0.208486	+	0.814035i
$179$	3.47076	−	2.00384i	0.259417	−	0.149774i	−0.364652	−	0.931144i	$-0.618812\pi$
$179$	3.47076	−	2.00384i	0.259417	−	0.149774i	0.624068	+	0.781370i	$0.285479\pi$
$180$	1.08528	−	1.97977i	0.0808923	−	0.147563i
$181$			5.89663i			0.438293i	0.975692	+	0.219146i	$0.0703272\pi$
$181$			5.89663i			0.438293i	−0.975692	+	0.219146i	$0.929673\pi$
$182$		0			0
$183$			9.11488i			0.673791i
$184$	5.43928	+	17.8988i	0.400989	+	1.31952i
$185$	−6.18344	+	3.57001i	−0.454616	+	0.262473i
$186$	−4.00341	−	1.02533i	−0.293545	−	0.0751811i
$187$	2.68210	−	4.64554i	0.196135	−	0.339715i
$188$	0.159229	+	7.18808i	0.0116130	+	0.524244i
$189$		0			0
$190$	7.01221	+	6.85859i	0.508719	+	0.497575i
$191$	−21.9900	−	12.6959i	−1.59114	−	0.918645i	−0.993112	−	0.117170i	$-0.962618\pi$
$191$	−21.9900	−	12.6959i	−1.59114	−	0.918645i	−0.598028	−	0.801475i	$-0.704049\pi$
$192$	6.64733	−	4.45118i	0.479730	−	0.321236i
$193$	−0.0366935	−	0.0635549i	−0.00264125	−	0.00457478i	0.864702	−	0.502286i	$-0.167507\pi$
$193$	−0.0366935	−	0.0635549i	−0.00264125	−	0.00457478i	−0.867343	+	0.497711i	$0.834174\pi$
$194$	8.48542	−	2.37468i	0.609218	−	0.170492i
$195$	6.30457			0.451480
$196$		0			0
$197$	7.23506			0.515477			0.257739	−	0.966215i	$-0.417023\pi$
$197$	7.23506			0.515477			0.257739	+	0.966215i	$0.417023\pi$
$198$	−1.83855	+	0.514527i	−0.130660	+	0.0365658i
$199$	−7.65598	−	13.2605i	−0.542718	−	0.940015i	−0.998747	−	0.0500500i	$-0.984062\pi$
$199$	−7.65598	−	13.2605i	−0.542718	−	0.940015i	0.456029	−	0.889965i	$-0.349271\pi$
$200$	2.38777	−	10.2637i	0.168841	−	0.725753i
$201$	−0.202730	−	0.117046i	−0.0142995	−	0.00825581i
$202$	0.803715	+	0.786109i	0.0565492	+	0.0553104i
$203$		0			0
$204$	−7.94500	+	0.175997i	−0.556261	+	0.0123222i
$205$	−0.0842264	+	0.145884i	−0.00588263	+	0.0101890i
$206$	4.59600	+	1.17710i	0.320219	+	0.0820127i
$207$	−5.72784	+	3.30697i	−0.398113	+	0.229850i
$208$	19.8223	+	10.3021i	1.37443	+	0.714323i
$209$		−	8.29453i		−	0.573745i
$210$		0			0
$211$		−	13.7540i		−	0.946861i	−0.880831	−	0.473431i	$-0.843015\pi$
$211$		−	13.7540i		−	0.946861i	0.880831	−	0.473431i	$-0.156985\pi$
$212$	1.28654	+	0.705268i	0.0883602	+	0.0484380i
$213$	7.56996	−	4.37052i	0.518685	−	0.299463i
$214$	4.40384	−	17.1948i	0.301040	−	1.17541i
$215$	6.01442	−	10.4173i	0.410180	−	0.710453i
$216$	2.06533	+	1.93246i	0.140528	+	0.131488i
$217$		0			0
$218$	15.0833	−	15.4212i	1.02157	−	1.04445i
$219$	−1.52893	−	0.882729i	−0.103316	−	0.0596493i
$220$	2.60519	−	1.58205i	0.175642	−	0.106662i
$221$	−11.0957	−	19.2183i	−0.746378	−	1.29277i
$222$	−2.41064	−	8.61391i	−0.161791	−	0.578127i
$223$	−16.4120			−1.09903			−0.549516	−	0.835483i	$-0.685188\pi$
$223$	−16.4120			−1.09903			−0.549516	+	0.835483i	$0.685188\pi$
$224$		0			0
$225$	3.72567			0.248378
$226$	4.48906	+	16.0407i	0.298608	+	1.06701i
$227$	−8.06595	−	13.9706i	−0.535356	−	0.927263i	−0.999146	−	0.0413183i	$-0.986844\pi$
$227$	−8.06595	−	13.9706i	−0.535356	−	0.927263i	0.463790	−	0.885945i	$-0.346489\pi$
$228$	−10.5032	+	6.37826i	−0.695590	+	0.422410i
$229$	18.7652	+	10.8341i	1.24004	+	0.715937i	0.969102	−	0.246660i	$-0.0793331\pi$
$229$	18.7652	+	10.8341i	1.24004	+	0.715937i	0.270937	+	0.962597i	$0.412666\pi$
$230$	7.38310	−	7.54846i	0.486827	−	0.497731i
$231$		0			0
$232$	17.6641	+	16.5278i	1.15971	+	1.08510i
$233$	9.51561	−	16.4815i	0.623389	−	1.07974i	−0.365461	−	0.930826i	$-0.619089\pi$
$233$	9.51561	−	16.4815i	0.623389	−	1.07974i	0.988850	−	0.148914i	$-0.0475779\pi$
$234$	−1.95960	+	7.65127i	−0.128103	+	0.500179i
$235$	3.51448	−	2.02909i	0.229259	−	0.132363i
$236$	−25.2638	−	13.8493i	−1.64453	−	0.901512i
$237$			8.40771i			0.546139i
$238$		0			0
$239$			15.6878i			1.01476i	0.861722	+	0.507381i	$0.169386\pi$
$239$			15.6878i			1.01476i	−0.861722	+	0.507381i	$0.830614\pi$
$240$	−4.00664	−	2.08235i	−0.258627	−	0.134415i
$241$	10.3066	−	5.95053i	0.663908	−	0.383307i	−0.129857	−	0.991533i	$-0.541452\pi$
$241$	10.3066	−	5.95053i	0.663908	−	0.383307i	0.793764	+	0.608225i	$0.208118\pi$
$242$	12.5731	+	3.22016i	0.808231	+	0.207000i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	18.2253	−	0.403725i	1.16675	−	0.0258458i
$245$		0			0
$246$	−0.150867	−	0.147562i	−0.00961891	−	0.00940820i
$247$	−29.7168	−	17.1570i	−1.89084	−	1.09167i
$248$	−1.87284	+	8.05028i	−0.118925	+	0.511193i
$249$	−4.56464	−	7.90619i	−0.289272	−	0.501035i
$250$	−13.4147	+	3.75416i	−0.848421	+	0.237434i
$251$	−1.68715			−0.106492			−0.0532459	−	0.998581i	$-0.516957\pi$
$251$	−1.68715			−0.106492			−0.0532459	+	0.998581i	$0.516957\pi$
$252$		0			0
$253$	−8.92885			−0.561352
$254$	−4.79989	+	1.34327i	−0.301172	+	0.0842843i
$255$	2.24275	+	3.88456i	0.140447	+	0.243261i
$256$	−9.19460	−	13.0942i	−0.574663	−	0.818390i
$257$	18.4612	+	10.6586i	1.15158	+	0.664862i	0.949271	−	0.314460i	$-0.101824\pi$
$257$	18.4612	+	10.6586i	1.15158	+	0.664862i	0.202305	+	0.979323i	$0.435157\pi$
$258$	10.7731	+	10.5371i	0.670702	+	0.656009i
$259$		0			0
$260$	−0.279248	−	12.6061i	−0.0173182	−	0.781794i
$261$	−4.27635	+	7.40685i	−0.264699	+	0.458473i
$262$	−3.24962	−	0.832274i	−0.200762	−	0.0514181i
$263$	10.0326	−	5.79230i	0.618634	−	0.357169i	−0.157703	−	0.987487i	$-0.550409\pi$
$263$	10.0326	−	5.79230i	0.618634	−	0.357169i	0.776337	+	0.630318i	$0.217075\pi$
$264$	1.11024	+	3.65342i	0.0683303	+	0.224852i
$265$		−	0.828119i		−	0.0508709i
$266$		0			0
$267$			7.92746i			0.485153i
$268$	−0.225056	+	0.410545i	−0.0137475	+	0.0250780i
$269$	6.28171	−	3.62675i	0.383003	−	0.221127i	−0.296121	−	0.955150i	$-0.595693\pi$
$269$	6.28171	−	3.62675i	0.383003	−	0.221127i	0.679124	+	0.734024i	$0.262360\pi$
$270$	0.396091	−	1.54654i	0.0241053	−	0.0941192i
$271$	14.5072	−	25.1272i	0.881249	−	1.52637i	0.0312948	−	0.999510i	$-0.490037\pi$
$271$	14.5072	−	25.1272i	0.881249	−	1.52637i	0.849954	−	0.526857i	$-0.176630\pi$
$272$	0.703814	+	15.8783i	0.0426750	+	0.962764i
$273$		0			0
$274$	7.09571	−	7.25463i	0.428667	−	0.438268i
$275$	4.35582	+	2.51483i	0.262666	+	0.151650i
$276$	6.86603	+	11.3064i	0.413286	+	0.680565i
$277$	0.172570	+	0.298901i	0.0103688	+	0.0179592i	0.871163	−	0.490994i	$-0.163366\pi$
$277$	0.172570	+	0.298901i	0.0103688	+	0.0179592i	−0.860794	+	0.508953i	$0.830033\pi$
$278$	8.60926	+	30.7634i	0.516349	+	1.84506i
$279$	−2.92221			−0.174948
$280$		0			0
$281$	6.62734			0.395354			0.197677	−	0.980267i	$-0.436660\pi$
$281$	6.62734			0.395354			0.197677	+	0.980267i	$0.436660\pi$
$282$	1.37013	+	4.89588i	0.0815902	+	0.291545i
$283$	13.8906	+	24.0593i	0.825713	+	1.43018i	0.901373	+	0.433044i	$0.142560\pi$
$283$	13.8906	+	24.0593i	0.825713	+	1.43018i	−0.0756596	+	0.997134i	$0.524106\pi$
$284$	−9.07419	−	14.9426i	−0.538454	−	0.886682i
$285$	6.00660	+	3.46791i	0.355800	+	0.205421i
$286$	−7.45567	+	7.62265i	−0.440863	+	0.450737i
$287$		0			0
$288$	3.77250	−	4.21524i	0.222297	−	0.248385i
$289$	−0.605750	+	1.04919i	−0.0356324	+	0.0617171i
$290$	3.38764	−	13.2271i	0.198929	−	0.776720i
$291$	5.39588	−	3.11531i	0.316312	−	0.182623i
$292$	−1.69730	+	3.09621i	−0.0993272	+	0.181192i
$293$		−	7.28491i		−	0.425589i	−0.977097	−	0.212794i	$-0.931744\pi$
$293$		−	7.28491i		−	0.425589i	0.977097	−	0.212794i	$-0.0682565\pi$
$294$		0			0
$295$			16.2617i			0.946794i
$296$	−17.1168	+	5.20163i	−0.994894	+	0.302339i
$297$	−1.16914	+	0.675002i	−0.0678402	+	0.0391676i
$298$	−15.1393	−	3.87740i	−0.876997	−	0.224612i
$299$	−18.4691	+	31.9894i	−1.06809	+	1.84999i
$300$	−0.165021	−	7.44951i	−0.00952748	−	0.430098i
$301$		0			0
$302$	1.55645	+	1.52236i	0.0895638	+	0.0876018i
$303$	0.688456	+	0.397480i	0.0395508	+	0.0228347i
$304$	13.2186	+	20.7187i	0.758139	+	1.18830i
$305$	−5.14472	−	8.91092i	−0.294586	−	0.510238i
$306$	−5.41143	+	1.51441i	−0.309351	+	0.0865731i
$307$	27.1911			1.55188			0.775939	−	0.630808i	$-0.217276\pi$
$307$	27.1911			1.55188			0.775939	+	0.630808i	$0.217276\pi$
$308$		0			0
$309$	3.35476			0.190846
$310$	4.49256	−	1.25726i	0.255160	−	0.0714077i
$311$	−10.4609	−	18.1188i	−0.593182	−	1.02742i	−0.993801	−	0.111177i	$-0.964538\pi$
$311$	−10.4609	−	18.1188i	−0.593182	−	1.02742i	0.400618	−	0.916245i	$-0.368795\pi$
$312$	15.3856	+	3.57935i	0.871037	+	0.202641i
$313$	−2.26674	−	1.30871i	−0.128124	−	0.0739724i	0.434568	−	0.900639i	$-0.356901\pi$
$313$	−2.26674	−	1.30871i	−0.128124	−	0.0739724i	−0.562692	+	0.826667i	$0.690234\pi$
$314$	−8.65374	−	8.46417i	−0.488359	−	0.477661i
$315$		0			0
$316$	16.8113	−	0.372402i	0.945709	−	0.0209492i
$317$	6.47430	−	11.2138i	0.363633	−	0.629831i	−0.624923	−	0.780687i	$-0.714870\pi$
$317$	6.47430	−	11.2138i	0.363633	−	0.629831i	0.988556	+	0.150856i	$0.0482028\pi$
$318$	1.00501	+	0.257398i	0.0563582	+	0.0144342i
$319$	−9.99928	+	5.77309i	−0.559852	+	0.323231i
$320$	−3.98620	+	8.10354i	−0.222836	+	0.453002i
$321$		−	12.5510i		−	0.700528i
$322$		0			0
$323$		−	24.4134i		−	1.35840i
$324$	1.75377	+	0.961396i	0.0974318	+	0.0534109i
$325$	18.0198	−	10.4037i	0.999558	−	0.577095i
$326$	1.98594	−	7.75412i	0.109991	−	0.429461i
$327$	7.62660	−	13.2097i	0.421752	−	0.730496i
$328$	−0.288369	+	0.308195i	−0.0159225	+	0.0170172i
$329$		0			0
$330$	1.50700	−	1.54075i	0.0829575	−	0.0848156i
$331$	4.53796	+	2.61999i	0.249429	+	0.144008i	0.619503	−	0.784994i	$-0.287334\pi$
$331$	4.53796	+	2.61999i	0.249429	+	0.144008i	−0.370074	+	0.929002i	$0.620668\pi$
$332$	−15.6063	+	9.47723i	−0.856508	+	0.520131i
$333$	−3.16249	−	5.47759i	−0.173303	−	0.300170i
$334$	−1.84603	−	6.59640i	−0.101010	−	0.360939i
$335$	0.264258			0.0144380
$336$		0			0
$337$	21.6837			1.18119			0.590594	−	0.806969i	$-0.298894\pi$
$337$	21.6837			1.18119			0.590594	+	0.806969i	$0.298894\pi$
$338$	6.93314	+	24.7741i	0.377113	+	1.34753i
$339$	5.88914	+	10.2003i	0.319854	+	0.554004i
$340$	7.66788	−	4.65647i	0.415849	−	0.252532i
$341$	−3.41647	−	1.97250i	−0.185012	−	0.106817i
$342$	−6.07567	+	6.21175i	−0.328534	+	0.335893i
$343$		0			0
$344$	20.5918	−	22.0076i	1.11024	−	1.18657i
$345$	3.73312	−	6.46595i	0.200984	−	0.348115i
$346$	−0.738131	+	2.88204i	−0.0396822	+	0.154939i
$347$	0.567776	−	0.327806i	0.0304798	−	0.0175975i	−0.484683	−	0.874690i	$-0.661065\pi$
$347$	0.567776	−	0.327806i	0.0304798	−	0.0175975i	0.515162	+	0.857093i	$0.327732\pi$
$348$	14.9995	+	8.22253i	0.804057	+	0.440774i
$349$			19.4157i			1.03930i	0.854380	+	0.519649i	$0.173937\pi$
$349$			19.4157i			1.03930i	−0.854380	+	0.519649i	$0.826063\pi$
$350$		0			0
$351$			5.58489i			0.298099i
$352$	7.25586	−	2.38175i	0.386739	−	0.126948i
$353$	25.8806	−	14.9422i	1.37749	−	0.795292i	0.385630	−	0.922653i	$-0.373984\pi$
$353$	25.8806	−	14.9422i	1.37749	−	0.795292i	0.991856	+	0.127361i	$0.0406507\pi$
$354$	−19.7353	−	5.05450i	−1.04892	−	0.268644i
$355$	−4.93372	+	8.54545i	−0.261854	+	0.453545i
$356$	15.8510	−	0.351130i	0.840103	−	0.0186099i
$357$		0			0
$358$	−4.05182	−	3.96306i	−0.214145	−	0.209454i
$359$	−10.9061	−	6.29666i	−0.575604	−	0.332325i	0.183781	−	0.982967i	$-0.441166\pi$
$359$	−10.9061	−	6.29666i	−0.575604	−	0.332325i	−0.759384	+	0.650642i	$0.774500\pi$
$360$	−3.10986	−	0.723486i	−0.163904	−	0.0381311i
$361$	−9.37488	−	16.2378i	−0.493415	−	0.854619i
$362$	8.03055	−	2.24738i	0.422076	−	0.118120i
$363$	9.17749			0.481693
$364$		0			0
$365$	1.99296			0.104316
$366$	12.4134	−	3.47396i	0.648861	−	0.181587i
$367$	−2.73446	−	4.73623i	−0.142738	−	0.247229i	0.785789	−	0.618495i	$-0.212257\pi$
$367$	−2.73446	−	4.73623i	−0.142738	−	0.247229i	−0.928527	+	0.371266i	$0.878924\pi$
$368$	22.3031	−	14.2295i	1.16263	−	0.741763i
$369$	−0.129231	−	0.0746117i	−0.00672751	−	0.00388413i
$370$	7.21866	+	7.06052i	0.375280	+	0.367059i
$371$		0			0
$372$	0.129433	+	5.84299i	0.00671080	+	0.302945i
$373$	7.42404	−	12.8588i	0.384402	−	0.665805i	−0.607284	−	0.794485i	$-0.707741\pi$
$373$	7.42404	−	12.8588i	0.384402	−	0.665805i	0.991686	+	0.128681i	$0.0410742\pi$
$374$	−7.34893	−	1.88217i	−0.380004	−	0.0973246i
$375$	−8.53042	+	4.92504i	−0.440509	+	0.254328i
$376$	9.72867	−	2.95645i	0.501718	−	0.152467i
$377$			47.7659i			2.46007i
$378$		0			0
$379$			30.6135i			1.57251i	0.617901	+	0.786256i	$0.287983\pi$
$379$			30.6135i			1.57251i	−0.617901	+	0.786256i	$0.712017\pi$
$380$	6.66808	−	12.1639i	0.342065	−	0.623993i
$381$	−3.05225	+	1.76222i	−0.156372	+	0.0902812i
$382$	−8.90939	+	34.7867i	−0.455844	+	1.77984i
$383$	11.7392	−	20.3329i	0.599844	−	1.03896i	−0.392999	−	0.919539i	$-0.628562\pi$
$383$	11.7392	−	20.3329i	0.599844	−	1.03896i	0.992844	−	0.119422i	$-0.0381042\pi$
$384$	−8.59551	−	7.35644i	−0.438638	−	0.375407i
$385$		0			0
$386$	−0.0725697	+	0.0741951i	−0.00369370	+	0.00377643i
$387$	9.22813	+	5.32786i	0.469092	+	0.270830i
$388$	−6.46810	−	10.6511i	−0.328368	−	0.540729i
$389$	18.0887	+	31.3306i	0.917134	+	1.58852i	0.803747	+	0.594972i	$0.202837\pi$
$389$	18.0887	+	31.3306i	0.917134	+	1.58852i	0.113387	+	0.993551i	$0.463830\pi$
$390$	−2.40286	−	8.58613i	−0.121674	−	0.434775i
$391$	−26.2803			−1.32905
$392$		0			0
$393$	−2.37199			−0.119651
$394$	−2.75750	−	9.85335i	−0.138921	−	0.496405i
$395$	−4.74557	−	8.21958i	−0.238776	−	0.413572i
$396$	1.40146	+	2.30780i	0.0704259	+	0.115971i
$397$	−1.15332	−	0.665868i	−0.0578833	−	0.0334189i	0.470779	−	0.882251i	$-0.343973\pi$
$397$	−1.15332	−	0.665868i	−0.0578833	−	0.0334189i	−0.528662	+	0.848832i	$0.677306\pi$
$398$	−15.1415	+	15.4806i	−0.758973	+	0.775971i
$399$		0			0
$400$	−14.8881	+	0.659921i	−0.744403	+	0.0329961i
$401$	−13.0298	+	22.5683i	−0.650677	+	1.12701i	0.332282	+	0.943180i	$0.392181\pi$
$401$	−13.0298	+	22.5683i	−0.650677	+	1.12701i	−0.982959	+	0.183825i	$0.941152\pi$
$402$	−0.0821374	+	0.320706i	−0.00409664	+	0.0159953i
$403$	−14.1337	+	8.16012i	−0.704051	+	0.406484i
$404$	0.764272	−	1.39418i	0.0380240	−	0.0693631i
$405$		−	1.12886i		−	0.0560936i
$406$		0			0
$407$		−	8.53873i		−	0.423249i
$408$	3.26777	+	10.7531i	0.161779	+	0.532359i
$409$	−11.5362	+	6.66044i	−0.570429	+	0.329337i	−0.757321	−	0.653043i	$-0.773492\pi$
$409$	−11.5362	+	6.66044i	−0.570429	+	0.329337i	0.186892	+	0.982381i	$0.440159\pi$
$410$	0.230779	+	0.0591060i	0.0113974	+	0.00291904i
$411$	3.58780	−	6.21426i	0.176973	−	0.306527i
$412$	−0.148592	−	6.70787i	−0.00732060	−	0.330473i
$413$		0			0
$414$	6.68678	+	6.54030i	0.328637	+	0.321438i
$415$	8.92501	+	5.15285i	0.438111	+	0.252944i
$416$	6.47547	−	30.9222i	0.317486	−	1.51608i
$417$	11.2944	+	19.5624i	0.553088	+	0.957977i
$418$	−11.2962	+	3.16130i	−0.552517	+	0.154624i
$419$	−7.54663			−0.368677			−0.184339	−	0.982863i	$-0.559014\pi$
$419$	−7.54663			−0.368677			−0.184339	+	0.982863i	$0.559014\pi$
$420$		0			0
$421$	2.67060			0.130157			0.0650785	−	0.997880i	$-0.479270\pi$
$421$	2.67060			0.130157			0.0650785	+	0.997880i	$0.479270\pi$
$422$	−18.7313	+	5.24205i	−0.911828	+	0.255179i
$423$	1.79746	+	3.11329i	0.0873955	+	0.151373i
$424$	0.470155	−	2.02093i	0.0228327	−	0.0981450i
$425$	12.8205	+	7.40193i	0.621886	+	0.359046i
$426$	−8.83730	−	8.64371i	−0.428169	−	0.418789i
$427$		0			0
$428$	−25.0958	+	0.555920i	−1.21305	+	0.0268714i
$429$	−3.76981	+	6.52950i	−0.182008	+	0.315247i
$430$	−16.4795	−	4.22063i	−0.794710	−	0.203537i
$431$	10.2938	−	5.94311i	0.495833	−	0.286269i	−0.231158	−	0.972916i	$-0.574251\pi$
$431$	10.2938	−	5.94311i	0.495833	−	0.286269i	0.726991	+	0.686647i	$0.240918\pi$
$432$	1.84464	−	3.54927i	0.0887503	−	0.170764i
$433$		−	20.6667i		−	0.993177i	−0.867986	−	0.496589i	$-0.834586\pi$
$433$		−	20.6667i		−	0.993177i	0.867986	−	0.496589i	$-0.165414\pi$
$434$		0			0
$435$		−	9.65482i		−	0.462913i
$436$	−26.7506	−	14.6644i	−1.28112	−	0.702296i
$437$	−35.1924	+	20.3183i	−1.68348	+	0.971957i
$438$	−0.619456	+	2.41867i	−0.0295988	+	0.115568i
$439$	−2.71032	+	4.69441i	−0.129356	+	0.224052i	−0.923427	−	0.383773i	$-0.874624\pi$
$439$	−2.71032	+	4.69441i	−0.129356	+	0.224052i	0.794071	+	0.607825i	$0.207958\pi$
$440$	−3.14750	−	2.94501i	−0.150051	−	0.140398i
$441$		0			0
$442$	−21.9443	+	22.4358i	−1.04378	+	1.06716i
$443$	19.6620	+	11.3519i	0.934172	+	0.539344i	0.888129	−	0.459595i	$-0.152005\pi$
$443$	19.6620	+	11.3519i	0.934172	+	0.539344i	0.0460432	+	0.998939i	$0.485339\pi$
$444$	−10.8124	+	6.56604i	−0.513134	+	0.311610i
$445$	−4.47451	−	7.75008i	−0.212112	−	0.367389i
$446$	6.25512	+	22.3514i	0.296189	+	1.05837i
$447$	−11.0506			−0.522677
$448$		0			0
$449$	−15.6516			−0.738645			−0.369322	−	0.929301i	$-0.620410\pi$
$449$	−15.6516			−0.738645			−0.369322	+	0.929301i	$0.620410\pi$
$450$	−1.41996	−	5.07395i	−0.0669378	−	0.239188i
$451$	−0.100726	−	0.174463i	−0.00474301	−	0.00821513i
$452$	20.1347	−	12.2272i	0.947059	−	0.575119i
$453$	1.33325	+	0.769750i	0.0626413	+	0.0361660i
$454$	−15.9523	+	16.3095i	−0.748677	+	0.765445i
$455$		0			0
$456$	12.6896	+	11.8732i	0.594243	+	0.556014i
$457$	8.51329	−	14.7454i	0.398235	−	0.689763i	−0.595274	−	0.803523i	$-0.702956\pi$
$457$	8.51329	−	14.7454i	0.398235	−	0.689763i	0.993508	+	0.113760i	$0.0362896\pi$
$458$	7.60284	−	29.6853i	0.355257	−	1.38710i
$459$	−3.44113	+	1.98674i	−0.160618	+	0.0927330i
$460$	−13.0941	−	7.17801i	−0.610514	−	0.334676i
$461$		−	38.1090i		−	1.77491i	−0.460891	−	0.887457i	$-0.652470\pi$
$461$		−	38.1090i		−	1.77491i	0.460891	−	0.887457i	$-0.347530\pi$
$462$		0			0
$463$		−	1.38958i		−	0.0645794i	−0.999479	−	0.0322897i	$-0.989720\pi$
$463$		−	1.38958i		−	0.0645794i	0.999479	−	0.0322897i	$-0.0102799\pi$
$464$	15.7767	−	30.3558i	0.732413	−	1.40923i
$465$	2.85682	−	1.64939i	0.132482	−	0.0764885i
$466$	−26.0727	−	6.67760i	−1.20779	−	0.309334i
$467$	1.74691	−	3.02573i	0.0808372	−	0.140014i	−0.822773	−	0.568371i	$-0.807574\pi$
$467$	1.74691	−	3.02573i	0.0808372	−	0.140014i	0.903610	+	0.428357i	$0.140907\pi$
$468$	11.1670	−	0.247371i	0.516197	−	0.0114347i
$469$		0			0
$470$	−4.10286	−	4.01298i	−0.189251	−	0.185105i
$471$	−7.41273	−	4.27974i	−0.341560	−	0.197200i
$472$	−9.23240	+	39.6848i	−0.424955	+	1.82664i
$473$	7.19263	+	12.4580i	0.330717	+	0.572819i
$474$	11.4504	−	3.20443i	0.525932	−	0.147184i
$475$	22.8908			1.05030
$476$		0			0
$477$	0.733587			0.0335886
$478$	21.3651	−	5.97911i	0.977216	−	0.273478i
$479$	−6.86079	−	11.8832i	−0.313478	−	0.542959i	0.665635	−	0.746277i	$-0.268161\pi$
$479$	−6.86079	−	11.8832i	−0.313478	−	0.542959i	−0.979113	+	0.203318i	$0.934827\pi$
$480$	−1.30887	+	6.25024i	−0.0597416	+	0.285283i
$481$	−30.5917	−	17.6621i	−1.39486	−	0.805324i
$482$	−12.0321	−	11.7685i	−0.548048	−	0.536042i
$483$		0			0
$484$	−0.406498	−	18.3505i	−0.0184772	−	0.834113i
$485$	−3.51676	+	6.09121i	−0.159688	+	0.276588i
$486$	1.36999	+	0.350876i	0.0621442	+	0.0159160i
$487$	3.25655	−	1.88017i	0.147569	−	0.0851987i	−0.424398	−	0.905476i	$-0.639514\pi$
$487$	3.25655	−	1.88017i	0.147569	−	0.0851987i	0.571966	+	0.820277i	$0.306181\pi$
$488$	−7.49604	−	24.6669i	−0.339330	−	1.11662i
$489$		−	5.65996i		−	0.255952i
$490$		0			0
$491$		−	8.60497i		−	0.388337i	−0.980968	−	0.194168i	$-0.937799\pi$
$491$		−	8.60497i		−	0.388337i	0.980968	−	0.194168i	$-0.0622008\pi$
$492$	−0.143463	+	0.261704i	−0.00646780	+	0.0117985i
$493$	−29.4309	+	16.9920i	−1.32550	+	0.765280i
$494$	−12.0400	+	47.0101i	−0.541704	+	2.11508i
$495$	0.761984	−	1.31980i	0.0342486	−	0.0593204i
$496$	11.6774	−	0.517606i	0.524330	−	0.0232412i
$497$		0			0
$498$	−9.02763	+	9.22982i	−0.404538	+	0.413598i
$499$	16.0929	+	9.29123i	0.720416	+	0.415933i	0.814906	−	0.579593i	$-0.196789\pi$
$499$	16.0929	+	9.29123i	0.720416	+	0.415933i	−0.0944896	+	0.995526i	$0.530122\pi$
$500$	10.2255	+	16.8385i	0.457298	+	0.753041i
$501$	−2.42178	−	4.19465i	−0.108197	−	0.187403i
$502$	0.643022	+	2.29771i	0.0286995	+	0.102552i
$503$	−33.4544			−1.49166			−0.745828	−	0.666139i	$-0.767946\pi$
$503$	−33.4544			−1.49166			−0.745828	+	0.666139i	$0.767946\pi$
$504$		0			0
$505$	−0.897402			−0.0399338
$506$	3.40305	+	12.1601i	0.151284	+	0.540582i
$507$	9.09550	+	15.7539i	0.403946	+	0.699654i
$508$	3.65877	+	6.02496i	0.162332	+	0.267314i
$509$	−20.7781	−	11.9963i	−0.920974	−	0.531725i	−0.0370283	−	0.999314i	$-0.511789\pi$
$509$	−20.7781	−	11.9963i	−0.920974	−	0.531725i	−0.883946	+	0.467590i	$0.845122\pi$
$510$	4.43556	−	4.53490i	0.196410	−	0.200809i
$511$		0			0
$512$	−14.3286	+	17.5126i	−0.633239	+	0.773956i
$513$	−3.07204	+	5.32093i	−0.135634	+	0.234925i
$514$	7.47966	−	29.2043i	0.329913	−	1.28815i
$515$	−3.27969	+	1.89353i	−0.144520	+	0.0834389i
$516$	10.2444	−	18.6877i	0.450983	−	0.822681i
$517$			4.85315i			0.213441i
$518$		0			0
$519$			2.10368i			0.0923415i
$520$	−17.0616	+	5.18485i	−0.748201	+	0.227371i
$521$	12.1946	−	7.04055i	0.534255	−	0.308452i	−0.208493	−	0.978024i	$-0.566856\pi$
$521$	12.1946	−	7.04055i	0.534255	−	0.308452i	0.742747	+	0.669572i	$0.233522\pi$
$522$	11.7172	+	3.00093i	0.512846	+	0.131347i
$523$	−17.5726	+	30.4366i	−0.768396	+	1.33090i	0.170037	+	0.985438i	$0.445611\pi$
$523$	−17.5726	+	30.4366i	−0.768396	+	1.33090i	−0.938432	+	0.345463i	$0.887722\pi$
$524$	0.105062	+	4.74282i	0.00458967	+	0.207191i
$525$		0			0
$526$	−11.7122	−	11.4556i	−0.510675	−	0.499488i
$527$	−10.0557	−	5.80567i	−0.438034	−	0.252899i
$528$	4.55240	−	2.90445i	0.198118	−	0.126400i
$529$	10.3721	+	17.9651i	0.450962	+	0.781089i
$530$	−1.12781	+	0.315621i	−0.0489887	+	0.0137097i
$531$	−14.4054			−0.625141
$532$		0			0
$533$	−0.833397			−0.0360984
$534$	10.7963	−	3.02140i	0.467202	−	0.130749i
$535$	7.08418	+	12.2702i	0.306276	+	0.530485i
$536$	0.644892	+	0.150030i	0.0278551	+	0.00648029i
$537$	−3.47076	−	2.00384i	−0.149774	−	0.0864722i
$538$	−7.33338	−	7.17273i	−0.316164	−	0.309238i
$539$		0			0
$540$	−2.25717	+	0.0500006i	−0.0971332	+	0.00215168i
$541$	−6.35759	+	11.0117i	−0.273334	+	0.473429i	−0.969714	−	0.244245i	$-0.921460\pi$
$541$	−6.35759	+	11.0117i	−0.273334	+	0.473429i	0.696379	+	0.717674i	$0.254793\pi$
$542$	−39.7495	−	10.1804i	−1.70739	−	0.437287i
$543$	5.10663	−	2.94831i	0.219146	−	0.126524i
$544$	21.3562	−	7.01022i	0.915641	−	0.300561i
$545$			17.2188i			0.737571i
$546$		0			0
$547$		−	42.0999i		−	1.80006i	−0.435828	−	0.900030i	$-0.643544\pi$
$547$		−	42.0999i		−	1.80006i	0.435828	−	0.900030i	$-0.356456\pi$
$548$	−12.5844	−	6.89860i	−0.537578	−	0.294694i
$549$	7.89372	−	4.55744i	0.336896	−	0.194507i
$550$	1.76479	−	6.89062i	0.0752508	−	0.293817i
$551$	−26.2742	+	45.5083i	−1.11932	+	1.93872i
$552$	12.7812	−	13.6600i	0.544004	−	0.581407i
$553$		0			0
$554$	0.341298	−	0.348942i	0.0145003	−	0.0148251i
$555$	6.18344	+	3.57001i	0.262473	+	0.151539i
$556$	38.6150	−	23.4497i	1.63764	−	0.994489i
$557$	−7.94263	−	13.7570i	−0.336540	−	0.582905i	0.647239	−	0.762287i	$-0.275923\pi$
$557$	−7.94263	−	13.7570i	−0.336540	−	0.582905i	−0.983779	+	0.179382i	$0.942590\pi$
$558$	1.11374	+	3.97973i	0.0471485	+	0.168475i
$559$	59.5110			2.51705
$560$		0			0
$561$	−5.36420			−0.226477
$562$	−2.52588	−	9.02569i	−0.106548	−	0.380726i
$563$	16.4594	+	28.5085i	0.693681	+	1.20149i	0.970623	+	0.240604i	$0.0773454\pi$
$563$	16.4594	+	28.5085i	0.693681	+	1.20149i	−0.276943	+	0.960886i	$0.589321\pi$
$564$	6.14544	−	3.73194i	0.258770	−	0.157143i
$565$	−11.5147	−	6.64803i	−0.484428	−	0.279685i
$566$	27.4719	−	28.0872i	1.15473	−	1.18059i
$567$		0			0
$568$	−16.8917	+	18.0531i	−0.708762	+	0.757492i
$569$	−17.4920	+	30.2971i	−0.733304	+	1.27012i	0.222159	+	0.975010i	$0.428690\pi$
$569$	−17.4920	+	30.2971i	−0.733304	+	1.27012i	−0.955463	+	0.295110i	$0.904644\pi$
$570$	2.43361	−	9.50205i	0.101933	−	0.397997i
$571$	5.63066	−	3.25087i	0.235636	−	0.136044i	−0.377533	−	0.925996i	$-0.623228\pi$
$571$	5.63066	−	3.25087i	0.235636	−	0.136044i	0.613169	+	0.789951i	$0.289894\pi$
$572$	13.2228	+	7.24856i	0.552872	+	0.303078i
$573$			25.3919i			1.06076i
$574$		0			0
$575$		−	24.6414i		−	1.02762i
$576$	−7.17850	−	3.53117i	−0.299104	−	0.147132i
$577$	−32.2277	+	18.6067i	−1.34166	+	0.774606i	−0.987051	−	0.160409i	$-0.948719\pi$
$577$	−32.2277	+	18.6067i	−1.34166	+	0.774606i	−0.354607	+	0.935016i	$0.615385\pi$
$578$	1.65975	+	0.425086i	0.0690365	+	0.0176812i
$579$	−0.0366935	+	0.0635549i	−0.00152493	+	0.00264125i
$580$	−19.3049	+	0.427640i	−0.801593	+	0.0177568i
$581$		0			0
$582$	−6.29924	−	6.16125i	−0.261112	−	0.255392i
$583$	0.857664	+	0.495172i	0.0355208	+	0.0205079i
$584$	4.86359	+	1.13148i	0.201257	+	0.0468209i
$585$	−3.15229	−	5.45992i	−0.130331	−	0.225740i
$586$	−9.92123	+	2.77650i	−0.409842	+	0.114696i
$587$	24.7914			1.02325			0.511625	−	0.859209i	$-0.329044\pi$
$587$	24.7914			1.02325			0.511625	+	0.859209i	$0.329044\pi$
$588$		0			0
$589$	−17.9543			−0.739794
$590$	22.1466	−	6.19783i	0.911763	−	0.255161i
$591$	−3.61753	−	6.26575i	−0.148805	−	0.257739i
$592$	13.6078	+	21.3287i	0.559276	+	0.876604i
$593$	−26.8491	−	15.5014i	−1.10256	−	0.636565i	−0.165670	−	0.986181i	$-0.552979\pi$
$593$	−26.8491	−	15.5014i	−1.10256	−	0.636565i	−0.936893	+	0.349617i	$0.886312\pi$
$594$	1.36487	+	1.33497i	0.0560013	+	0.0547745i
$595$		0			0
$596$	0.489465	+	22.0959i	0.0200493	+	0.905082i
$597$	−7.65598	+	13.2605i	−0.313338	+	0.542718i
$598$	50.6051	+	12.9607i	2.06940	+	0.530003i
$599$	7.12727	−	4.11493i	0.291212	−	0.168131i	−0.347276	−	0.937763i	$-0.612893\pi$
$599$	7.12727	−	4.11493i	0.291212	−	0.168131i	0.638488	+	0.769631i	$0.279560\pi$
$600$	−10.0825	+	3.06397i	−0.411617	+	0.125086i
$601$		−	47.6805i		−	1.94493i	−0.233053	−	0.972464i	$-0.574872\pi$
$601$		−	47.6805i		−	1.94493i	0.233053	−	0.972464i	$-0.425128\pi$
$602$		0			0
$603$			0.234093i			0.00953299i
$604$	1.48007	−	2.69993i	0.0602231	−	0.109859i
$605$	−8.97213	+	5.18006i	−0.364769	+	0.210600i
$606$	0.278932	−	1.08909i	0.0113309	−	0.0442413i
$607$	6.32713	−	10.9589i	0.256810	−	0.444808i	−0.708575	−	0.705635i	$-0.750662\pi$
$607$	6.32713	−	10.9589i	0.256810	−	0.444808i	0.965386	+	0.260827i	$0.0839951\pi$
$608$	23.1786	−	25.8988i	0.940015	−	1.05033i
$609$		0			0
$610$	−10.1749	+	10.4028i	−0.411969	+	0.421196i
$611$	17.3874	+	10.0386i	0.703419	+	0.406119i
$612$	4.12492	+	6.79257i	0.166740	+	0.274574i
$613$	−0.226457	−	0.392236i	−0.00914652	−	0.0158422i	0.861416	−	0.507900i	$-0.169578\pi$
$613$	−0.226457	−	0.392236i	−0.00914652	−	0.0158422i	−0.870562	+	0.492058i	$0.836245\pi$
$614$	−10.3633	−	37.0312i	−0.418231	−	1.49446i
$615$	0.168453			0.00679267
$616$		0			0
$617$	−0.575345			−0.0231625			−0.0115813	−	0.999933i	$-0.503687\pi$
$617$	−0.575345			−0.0231625			−0.0115813	+	0.999933i	$0.503687\pi$
$618$	−1.27860	−	4.56881i	−0.0514328	−	0.183784i
$619$	−1.02161	−	1.76949i	−0.0410622	−	0.0711218i	0.844764	−	0.535139i	$-0.179741\pi$
$619$	−1.02161	−	1.76949i	−0.0410622	−	0.0711218i	−0.885826	+	0.464017i	$0.846408\pi$
$620$	−3.42450	−	5.63919i	−0.137531	−	0.226475i
$621$	5.72784	+	3.30697i	0.229850	+	0.132704i
$622$	−20.6888	+	21.1522i	−0.829545	+	0.848125i
$623$		0			0
$624$	−0.989242	−	22.3177i	−0.0396014	−	0.893421i
$625$	−3.75448	+	6.50295i	−0.150179	+	0.260118i
$626$	−0.918386	+	3.58584i	−0.0367061	+	0.143319i
$627$	−7.18328	+	4.14727i	−0.286872	+	0.165626i
$628$	−8.22905	+	15.0114i	−0.328375	+	0.599019i
$629$		−	25.1321i		−	1.00208i
$630$		0			0
$631$			38.8983i			1.54852i	0.632870	+	0.774258i	$0.281877\pi$
$631$			38.8983i			1.54852i	−0.632870	+	0.774258i	$0.718123\pi$
$632$	−6.91446	−	22.7532i	−0.275043	−	0.905073i
$633$	−11.9113	+	6.87698i	−0.473431	+	0.273335i
$634$	−17.7395	−	4.54335i	−0.704527	−	0.180440i
$635$	1.98930	−	3.44558i	0.0789431	−	0.136733i
$636$	−0.0324927	−	1.46681i	−0.00128842	−	0.0581630i
$637$		0			0
$638$	11.6733	+	11.4176i	0.462151	+	0.452027i
$639$	−7.56996	−	4.37052i	−0.299463	−	0.172895i
$640$	12.5554	+	2.34026i	0.496295	+	0.0925070i
$641$	1.03036	+	1.78464i	0.0406969	+	0.0704891i	0.885656	−	0.464341i	$-0.153709\pi$
$641$	1.03036	+	1.78464i	0.0406969	+	0.0704891i	−0.844959	+	0.534830i	$0.820376\pi$
$642$	−17.0931	+	4.78356i	−0.674609	+	0.188792i
$643$	−2.86029			−0.112799			−0.0563994	−	0.998408i	$-0.517962\pi$
$643$	−2.86029			−0.112799			−0.0563994	+	0.998408i	$0.517962\pi$
$644$		0			0
$645$	−12.0288			−0.473635
$646$	−33.2483	+	9.30467i	−1.30814	+	0.366087i
$647$	9.70418	+	16.8081i	0.381511	+	0.660796i	0.991278	−	0.131784i	$-0.0420706\pi$
$647$	9.70418	+	16.8081i	0.381511	+	0.660796i	−0.609768	+	0.792580i	$0.708737\pi$
$648$	0.640898	−	2.75486i	0.0251769	−	0.108221i
$649$	−16.8419	−	9.72367i	−0.661102	−	0.381687i
$650$	−21.0366	−	20.5758i	−0.825123	−	0.807048i
$651$		0			0
$652$	−11.3171	+	0.250696i	−0.443214	+	0.00981802i
$653$	0.364864	−	0.631964i	0.0142783	−	0.0247307i	−0.858798	−	0.512314i	$-0.828788\pi$
$653$	0.364864	−	0.631964i	0.0142783	−	0.0247307i	0.873076	+	0.487584i	$0.162122\pi$
$654$	−20.8968	−	5.35198i	−0.817130	−	0.209279i
$655$	2.31892	−	1.33883i	0.0906075	−	0.0523123i
$656$	0.529634	+	0.275264i	0.0206787	+	0.0107472i
$657$			1.76546i			0.0688771i
$658$		0			0
$659$		−	19.6921i		−	0.767097i	−0.923521	−	0.383548i	$-0.874702\pi$
$659$		−	19.6921i		−	0.767097i	0.923521	−	0.383548i	$-0.125298\pi$
$660$	−2.67269	−	1.46514i	−0.104034	−	0.0570304i
$661$	8.14536	−	4.70273i	0.316818	−	0.182915i	−0.333156	−	0.942872i	$-0.608113\pi$
$661$	8.14536	−	4.70273i	0.316818	−	0.182915i	0.649973	+	0.759957i	$0.274780\pi$
$662$	1.83858	−	7.17876i	0.0714586	−	0.279010i
$663$	−11.0957	+	19.2183i	−0.430922	+	0.746378i
$664$	18.8550	+	17.6420i	0.731715	+	0.684643i
$665$		0			0
$666$	−6.25454	+	6.39463i	−0.242359	+	0.247787i
$667$	48.9885	+	28.2835i	1.89684	+	1.09514i
$668$	−8.27998	+	5.02817i	−0.320362	+	0.194546i
$669$	8.20602	+	14.2132i	0.317263	+	0.549516i
$670$	−0.100717	−	0.359890i	−0.00389103	−	0.0139038i
$671$	12.3051			0.475034
$672$		0			0
$673$	30.0031			1.15653			0.578266	−	0.815848i	$-0.303729\pi$
$673$	30.0031			1.15653			0.578266	+	0.815848i	$0.303729\pi$
$674$	−8.26432	−	29.5308i	−0.318330	−	1.13748i
$675$	−1.86283	−	3.22652i	−0.0717005	−	0.124189i
$676$	31.0972	−	18.8843i	1.19604	−	0.726320i
$677$	26.6823	+	15.4050i	1.02548	+	0.592063i	0.915687	−	0.401891i	$-0.131647\pi$
$677$	26.6823	+	15.4050i	1.02548	+	0.592063i	0.109796	+	0.993954i	$0.464980\pi$
$678$	11.6471	−	11.9080i	0.447305	−	0.457324i
$679$		0			0
$680$	−9.26405	−	8.66808i	−0.355260	−	0.332406i
$681$	−8.06595	+	13.9706i	−0.309088	+	0.535356i
$682$	−1.38420	+	5.40462i	−0.0530039	+	0.206954i
$683$	36.0508	−	20.8140i	1.37945	−	0.796424i	0.387354	−	0.921931i	$-0.373389\pi$
$683$	36.0508	−	20.8140i	1.37945	−	0.796424i	0.992093	+	0.125507i	$0.0400558\pi$
$684$	10.7753	+	5.90690i	0.412005	+	0.225856i
$685$			8.10028i			0.309496i
$686$		0			0
$687$		−	21.6682i		−	0.826693i
$688$	−37.8200	−	19.6560i	−1.44187	−	0.749377i
$689$	3.54811	−	2.04850i	0.135172	−	0.0780417i
$690$	−10.2287	−	2.61972i	−0.389400	−	0.0997311i
$691$	4.39414	−	7.61087i	0.167161	−	0.289531i	−0.770260	−	0.637730i	$-0.779873\pi$
$691$	4.39414	−	7.61087i	0.167161	−	0.289531i	0.937421	+	0.348199i	$0.113207\pi$
$692$	4.20634	−	0.0931783i	0.159901	−	0.00354211i
$693$		0			0
$694$	−0.662831	−	0.648311i	−0.0251607	−	0.0246095i
$695$	−22.0833	−	12.7498i	−0.837668	−	0.483628i
$696$	5.48141	−	23.5615i	0.207772	−	0.893096i
$697$	−0.296468	−	0.513497i	−0.0112295	−	0.0194501i
$698$	26.4420	−	7.39990i	1.00084	−	0.280090i
$699$	−19.0312			−0.719827
$700$		0			0
$701$	−0.0621184			−0.00234618			−0.00117309	−	0.999999i	$-0.500373\pi$
$701$	−0.0621184			−0.00234618			−0.00117309	+	0.999999i	$0.500373\pi$
$702$	7.60600	−	2.12857i	0.287070	−	0.0803377i
$703$	−19.4306	−	33.6547i	−0.732838	−	1.26931i
$704$	−6.00911	−	8.97392i	−0.226477	−	0.338217i
$705$	−3.51448	−	2.02909i	−0.132363	−	0.0764198i
$706$	−30.2135	−	29.5516i	−1.13710	−	1.11219i
$707$		0			0
$708$	0.638057	+	28.8037i	0.0239797	+	1.08251i
$709$	−16.6018	+	28.7551i	−0.623492	+	1.07992i	0.365338	+	0.930875i	$0.380953\pi$
$709$	−16.6018	+	28.7551i	−0.623492	+	1.07992i	−0.988830	+	0.149045i	$0.952380\pi$
$710$	13.5183	+	3.46224i	0.507334	+	0.129936i
$711$	7.28129	−	4.20385i	0.273070	−	0.157657i
$712$	−6.51951	−	21.4535i	−0.244329	−	0.804004i
$713$			19.3273i			0.723815i
$714$		0			0
$715$		−	8.51120i		−	0.318301i
$716$	−3.85297	+	7.02857i	−0.143992	+	0.262670i
$717$	13.5861	−	7.84392i	0.507381	−	0.292937i
$718$	−4.41869	+	17.2528i	−0.164904	+	0.643868i
$719$	15.9535	−	27.6323i	0.594966	−	1.03051i	−0.398586	−	0.917131i	$-0.630499\pi$
$719$	15.9535	−	27.6323i	0.594966	−	1.03051i	0.993552	−	0.113380i	$-0.0361677\pi$
$720$	0.199953	+	4.51102i	0.00745182	+	0.168116i
$721$		0			0
$722$	−18.5410	+	18.9562i	−0.690024	+	0.705478i
$723$	−10.3066	−	5.95053i	−0.383307	−	0.221303i
$724$	−6.12137	−	10.0802i	−0.227499	−	0.374626i
$725$	−15.9323	−	27.5955i	−0.591709	−	1.02487i
$726$	−3.49782	−	12.4987i	−0.129816	−	0.463871i
$727$	−11.8242			−0.438535			−0.219268	−	0.975665i	$-0.570367\pi$
$727$	−11.8242			−0.438535			−0.219268	+	0.975665i	$0.570367\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−0.759577	−	2.71419i	−0.0281132	−	0.100457i
$731$	21.1701	+	36.6677i	0.783005	+	1.35620i
$732$	−9.46228	−	15.5817i	−0.349736	−	0.575916i
$733$	10.2349	+	5.90910i	0.378033	+	0.218258i	0.676962	−	0.736018i	$-0.263296\pi$
$733$	10.2349	+	5.90910i	0.378033	+	0.218258i	−0.298929	+	0.954275i	$0.596629\pi$
$734$	−5.40803	+	5.52915i	−0.199614	+	0.204085i
$735$		0			0
$736$	−27.8794	−	24.9511i	−1.02765	−	0.919710i
$737$	−0.158013	+	0.273686i	−0.00582048	+	0.0100814i
$738$	−0.0523589	+	0.204435i	−0.00192736	+	0.00752537i
$739$	23.0318	−	13.2974i	0.847237	−	0.489153i	−0.0124806	−	0.999922i	$-0.503973\pi$
$739$	23.0318	−	13.2974i	0.847237	−	0.489153i	0.859718	+	0.510770i	$0.170639\pi$
$740$	6.86439	−	12.5220i	0.252340	−	0.460317i
$741$			34.3140i			1.26056i
$742$		0			0
$743$			34.9119i			1.28079i	0.768045	+	0.640396i	$0.221230\pi$
$743$			34.9119i			1.28079i	−0.768045	+	0.640396i	$0.778770\pi$
$744$	7.90817	−	2.40321i	0.289927	−	0.0881061i
$745$	10.8034	−	6.23733i	0.395805	−	0.228518i
$746$	−20.3418	−	5.20983i	−0.744766	−	0.190746i
$747$	−4.56464	+	7.90619i	−0.167012	+	0.289272i
$748$	0.237596	+	10.7258i	0.00868738	+	0.392173i
$749$		0			0
$750$	9.95856	+	9.74040i	0.363635	+	0.355669i
$751$	−1.48965	−	0.860048i	−0.0543580	−	0.0313836i	0.472575	−	0.881291i	$-0.343325\pi$
$751$	−1.48965	−	0.860048i	−0.0543580	−	0.0313836i	−0.526933	+	0.849907i	$0.676658\pi$
$752$	−7.73424	−	12.1226i	−0.282039	−	0.442065i
$753$	0.843573	+	1.46111i	0.0307415	+	0.0532459i
$754$	65.0518	−	18.2050i	2.36905	−	0.662988i
$755$	−1.73788			−0.0632480
$756$		0			0
$757$	33.2057			1.20688			0.603440	−	0.797408i	$-0.293796\pi$
$757$	33.2057			1.20688			0.603440	+	0.797408i	$0.293796\pi$
$758$	41.6922	−	11.6677i	1.51433	−	0.423792i
$759$	4.46442	+	7.73261i	0.162048	+	0.280676i
$760$	−19.1072	−	4.44516i	−0.693092	−	0.161243i
$761$	−23.5363	−	13.5887i	−0.853191	−	0.492590i	0.00853557	−	0.999964i	$-0.497283\pi$
$761$	−23.5363	−	13.5887i	−0.853191	−	0.492590i	−0.861726	+	0.507374i	$0.830616\pi$
$762$	3.56325	+	3.48519i	0.129083	+	0.126255i
$763$		0			0
$764$	50.7713	−	1.12468i	1.83684	−	0.0406895i
$765$	2.24275	−	3.88456i	0.0810869	−	0.140447i
$766$	−32.1653	−	8.23799i	−1.16218	−	0.297651i
$767$	−69.6740	+	40.2263i	−2.51578	+	1.45249i
$768$	−6.74265	+	14.5099i	−0.243304	+	0.523580i
$769$		−	7.13960i		−	0.257460i	−0.991680	−	0.128730i	$-0.958910\pi$
$769$		−	7.13960i		−	0.257460i	0.991680	−	0.128730i	$-0.0410901\pi$
$770$		0			0
$771$		−	21.3171i		−	0.767717i
$772$	0.128704	+	0.0705539i	0.00463216	+	0.00253929i
$773$	−22.9995	+	13.2788i	−0.827234	+	0.477604i	−0.852905	−	0.522067i	$-0.825161\pi$
$773$	−22.9995	+	13.2788i	−0.827234	+	0.477604i	0.0256709	+	0.999670i	$0.491828\pi$
$774$	3.73883	−	14.5983i	0.134390	−	0.524725i
$775$	5.44360	−	9.42858i	0.195540	−	0.338685i
$776$	−12.0405	+	12.8683i	−0.432227	+	0.461945i
$777$		0			0
$778$	35.7746	−	36.5758i	1.28258	−	1.31131i
$779$	−0.794008	−	0.458421i	−0.0284483	−	0.0164246i
$780$	−10.7775	+	6.54486i	−0.385898	+	0.234344i
$781$	−5.90022	−	10.2195i	−0.211126	−	0.365682i
$782$	10.0162	+	35.7909i	0.358180	+	1.27988i
$783$	8.55270			0.305648
$784$		0			0
$785$	9.66247			0.344869
$786$	0.904038	+	3.23039i	0.0322460	+	0.115224i
$787$	−12.2335	−	21.1890i	−0.436077	−	0.755307i	0.561306	−	0.827608i	$-0.310299\pi$
$787$	−12.2335	−	21.1890i	−0.436077	−	0.755307i	−0.997383	+	0.0723013i	$0.976966\pi$
$788$	−12.3682	+	7.51082i	−0.440599	+	0.267562i
$789$	−10.0326	−	5.79230i	−0.357169	−	0.206211i
$790$	−9.38546	+	9.59567i	−0.333920	+	0.341399i
$791$		0			0
$792$	2.60883	−	2.78820i	0.0927008	−	0.0990744i
$793$	25.4528	−	44.0856i	0.903856	−	1.56552i
$794$	−0.467274	+	1.82447i	−0.0165829	+	0.0647481i
$795$	−0.717172	+	0.414059i	−0.0254355	+	0.0146852i
$796$	26.8537	+	14.7209i	0.951804	+	0.521767i
$797$			26.0084i			0.921265i	0.887591	+	0.460632i	$0.152377\pi$
$797$			26.0084i			0.921265i	−0.887591	+	0.460632i	$0.847623\pi$
$798$		0			0
$799$			14.2843i			0.505343i
$800$	6.57303	+	20.0244i	0.232392	+	0.707968i
$801$	6.86538	−	3.96373i	0.242576	−	0.140052i
$802$	35.7015	+	9.14368i	1.26066	+	0.322875i
$803$	−1.19169	+	2.06406i	−0.0420537	+	0.0728392i
$804$	0.468070	−	0.0103686i	0.0165076	−	0.000365674i
$805$		0			0
$806$	16.5000	+	16.1385i	0.581186	+	0.568454i
$807$	−6.28171	−	3.62675i	−0.221127	−	0.127668i
$808$	−2.19001	−	0.509489i	−0.0770441	−	0.0179238i
$809$	6.59877	+	11.4294i	0.232000	+	0.401836i	0.958397	−	0.285440i	$-0.0921396\pi$
$809$	6.59877	+	11.4294i	0.232000	+	0.401836i	−0.726396	+	0.687276i	$0.758806\pi$
$810$	−1.53738	+	0.430244i	−0.0540182	+	0.0151172i
$811$	4.87597			0.171219			0.0856093	−	0.996329i	$-0.472716\pi$
$811$	4.87597			0.171219			0.0856093	+	0.996329i	$0.472716\pi$
$812$		0			0
$813$	−29.0144			−1.01758
$814$	−11.6288	+	3.25437i	−0.407589	+	0.114066i
$815$	3.19466	+	5.53331i	0.111904	+	0.193824i
$816$	13.3991	−	8.54867i	0.469063	−	0.299263i
$817$	56.6984	+	32.7348i	1.98362	+	1.14525i
$818$	13.4676	+	13.1725i	0.470883	+	0.460567i
$819$		0			0
$820$	−0.00746126	−	0.336823i	−0.000260559	−	0.0117624i
$821$	−3.53291	+	6.11917i	−0.123299	+	0.213561i	−0.921067	−	0.389404i	$-0.872681\pi$
$821$	−3.53291	+	6.11917i	−0.123299	+	0.213561i	0.797768	+	0.602965i	$0.206014\pi$
$822$	−9.83055	−	2.51775i	−0.342880	−	0.0878165i
$823$	19.0192	−	10.9807i	0.662966	−	0.382764i	−0.130440	−	0.991456i	$-0.541639\pi$
$823$	19.0192	−	10.9807i	0.662966	−	0.382764i	0.793406	+	0.608692i	$0.208306\pi$
$824$	−9.07874	+	2.75894i	−0.316273	+	0.0961121i
$825$		−	5.02967i		−	0.175110i
$826$		0			0
$827$			17.4897i			0.608175i	0.952644	+	0.304088i	$0.0983515\pi$
$827$			17.4897i			0.608175i	−0.952644	+	0.304088i	$0.901648\pi$
$828$	6.35862	−	11.5994i	0.220977	−	0.403105i
$829$	−22.1721	+	12.8011i	−0.770069	+	0.444599i	−0.832899	−	0.553425i	$-0.813321\pi$
$829$	−22.1721	+	12.8011i	−0.770069	+	0.444599i	0.0628304	+	0.998024i	$0.479987\pi$
$830$	3.61602	−	14.1188i	0.125514	−	0.490070i
$831$	0.172570	−	0.298901i	0.00598640	−	0.0103688i
$832$	−44.5805	+	2.96651i	−1.54555	+	0.102845i
$833$		0			0
$834$	22.3372	−	22.8375i	0.773475	−	0.790799i
$835$	4.73519	+	2.73386i	0.163868	+	0.0946092i
$836$	8.61067	+	14.1793i	0.297806	+	0.490403i
$837$	1.46111	+	2.53071i	0.0505032	+	0.0874741i
$838$	2.87625	+	10.2777i	0.0993584	+	0.355036i
$839$	−9.04513			−0.312273			−0.156136	−	0.987736i	$-0.549904\pi$
$839$	−9.04513			−0.312273			−0.156136	+	0.987736i	$0.549904\pi$
$840$		0			0
$841$	44.1486			1.52237
$842$	−1.01785	−	3.63705i	−0.0350773	−	0.125341i
$843$	−3.31367	−	5.73944i	−0.114129	−	0.197677i
$844$	14.2782	+	23.5121i	0.491475	+	0.809320i
$845$	−17.7840	−	10.2676i	−0.611787	−	0.353215i
$846$	3.55489	−	3.63451i	0.122220	−	0.124957i
$847$		0			0
$848$	−2.93147	+	0.129939i	−0.100667	+	0.00446212i
$849$	13.8906	−	24.0593i	0.476726	−	0.825713i
$850$	5.19431	−	20.2812i	0.178163	−	0.695639i
$851$	−36.2285	+	20.9165i	−1.24190	+	0.717009i
$852$	−8.40360	+	15.3298i	−0.287903	+	0.525190i
$853$		−	28.8642i		−	0.988292i	−0.869379	−	0.494146i	$-0.835481\pi$
$853$		−	28.8642i		−	0.988292i	0.869379	−	0.494146i	$-0.164519\pi$
$854$		0			0
$855$		−	6.93583i		−	0.237200i
$856$	10.3219	+	33.9659i	0.352795	+	1.16093i
$857$	41.9058	−	24.1943i	1.43148	−	0.826463i	0.434242	−	0.900796i	$-0.357016\pi$
$857$	41.9058	−	24.1943i	1.43148	−	0.826463i	0.997233	+	0.0743338i	$0.0236830\pi$
$858$	10.3292	+	2.64547i	0.352635	+	0.0903149i
$859$	−9.91892	+	17.1801i	−0.338429	+	0.586176i	−0.984137	−	0.177408i	$-0.943229\pi$
$859$	−9.91892	+	17.1801i	−0.338429	+	0.586176i	0.645708	+	0.763584i	$0.276562\pi$
$860$	0.532793	+	24.0518i	0.0181681	+	0.820159i
$861$		0			0
$862$	−12.0171	−	11.7539i	−0.409304	−	0.400338i
$863$	33.6011	+	19.3996i	1.14379	+	0.660370i	0.947367	−	0.320148i	$-0.103733\pi$
$863$	33.6011	+	19.3996i	1.14379	+	0.660370i	0.196427	+	0.980518i	$0.437066\pi$
$864$	−5.53675	−	1.15946i	−0.188364	−	0.0394457i
$865$	−1.18738	−	2.05661i	−0.0403723	−	0.0699269i
$866$	−28.1457	+	7.87669i	−0.956430	+	0.267661i
$867$	1.21150			0.0411447
$868$		0			0
$869$	11.3504			0.385037
$870$	−13.1488	+	3.67974i	−0.445786	+	0.124755i
$871$	0.653691	+	1.13223i	0.0221495	+	0.0383640i
$872$	−9.77575	+	42.0204i	−0.331049	+	1.42299i
$873$	−5.39588	−	3.11531i	−0.182623	−	0.105437i
$874$	41.0841	+	40.1841i	1.38969	+	1.35925i
$875$		0			0
$876$	3.53005	−	0.0781973i	0.119269	−	0.00264204i
$877$	7.48487	−	12.9642i	0.252746	−	0.437769i	−0.711535	−	0.702651i	$-0.752000\pi$
$877$	7.48487	−	12.9642i	0.252746	−	0.437769i	0.964281	+	0.264882i	$0.0853330\pi$
$878$	7.42625	+	1.90197i	0.250624	+	0.0641884i
$879$	−6.30891	+	3.64245i	−0.212794	+	0.122857i
$880$	−2.81117	+	5.40897i	−0.0947647	+	0.182336i
$881$			44.9991i			1.51606i	0.652221	+	0.758029i	$0.273837\pi$
$881$			44.9991i			1.51606i	−0.652221	+	0.758029i	$0.726163\pi$
$882$		0			0
$883$			20.0940i			0.676217i	0.941107	+	0.338109i	$0.109787\pi$
$883$			20.0940i			0.676217i	−0.941107	+	0.338109i	$0.890213\pi$
$884$	38.9187	+	21.3347i	1.30898	+	0.717565i
$885$	14.0831	−	8.13086i	0.473397	−	0.273316i
$886$	7.96620	−	31.1040i	0.267630	−	1.04496i
$887$	7.60734	−	13.1763i	0.255430	−	0.442417i	−0.709583	−	0.704622i	$-0.751116\pi$
$887$	7.60734	−	13.1763i	0.255430	−	0.442417i	0.965012	+	0.262205i	$0.0844498\pi$
$888$	13.0631	+	12.2228i	0.438371	+	0.410170i
$889$		0			0
$890$	−8.84937	+	9.04757i	−0.296631	+	0.303275i
$891$	1.16914	+	0.675002i	0.0391676	+	0.0226134i
$892$	28.0560	−	17.0376i	0.939386	−	0.570460i
$893$	11.0437	+	19.1283i	0.369565	+	0.640105i
$894$	4.21173	+	15.0497i	0.140861	+	0.503339i
$895$	4.52413			0.151225
$896$		0			0
$897$	36.9382			1.23333
$898$	5.96530	+	21.3157i	0.199065	+	0.711315i
$899$	12.4964	+	21.6444i	0.416778	+	0.721881i
$900$	−6.36896	+	3.86767i	−0.212299	+	0.128922i
$901$	2.52437	+	1.45744i	0.0840989	+	0.0485545i
$902$	−0.199209	+	0.203671i	−0.00663293	+	0.00678149i
$903$		0			0
$904$	−24.3260	−	22.7611i	−0.809072	−	0.757023i
$905$	−3.32824	+	5.76468i	−0.110634	+	0.191625i
$906$	0.540173	−	2.10911i	0.0179460	−	0.0700704i
$907$	12.2298	−	7.06089i	0.406084	−	0.234453i	−0.283022	−	0.959114i	$-0.591337\pi$
$907$	12.2298	−	7.06089i	0.406084	−	0.234453i	0.689106	+	0.724661i	$0.258003\pi$
$908$	28.2917	+	15.5091i	0.938892	+	0.514689i
$909$		−	0.794961i		−	0.0263672i
$910$		0			0
$911$			12.5510i			0.415832i	0.978147	+	0.207916i	$0.0666681\pi$
$911$			12.5510i			0.415832i	−0.978147	+	0.207916i	$0.933332\pi$
$912$	11.3336	−	21.8070i	0.375294	−	0.722102i
$913$	−10.6734	+	6.16228i	−0.353238	+	0.203942i
$914$	−23.3263	−	5.97421i	−0.771566	−	0.197609i
$915$	−5.14472	+	8.91092i	−0.170079	+	0.294586i
$916$	−43.3257	+	0.959747i	−1.43152	+	0.0317109i
$917$		0			0
$918$	4.01723	+	3.92923i	0.132588	+	0.129684i
$919$	30.7045	+	17.7272i	1.01285	+	0.584768i	0.912024	−	0.410136i	$-0.134519\pi$
$919$	30.7045	+	17.7272i	1.01285	+	0.584768i	0.100824	+	0.994904i	$0.467852\pi$
$920$	−4.78510	+	20.5684i	−0.157760	+	0.678121i
$921$	−13.5955	−	23.5482i	−0.447989	−	0.775939i
$922$	−51.9002	+	14.5245i	−1.70924	+	0.478339i
$923$	−48.8178			−1.60686
$924$		0			0
$925$	23.5648			0.774804
$926$	−1.89246	+	0.529612i	−0.0621899	+	0.0174041i
$927$	−1.67738	−	2.90531i	−0.0550924	−	0.0954228i
$928$	−47.3542	−	9.91652i	−1.55448	−	0.325526i
$929$	48.0685	+	27.7524i	1.57708	+	0.910526i	0.995264	+	0.0972040i	$0.0309899\pi$
$929$	48.0685	+	27.7524i	1.57708	+	0.910526i	0.581813	+	0.813322i	$0.302343\pi$
$930$	−3.33510	−	3.26204i	−0.109362	−	0.106967i
$931$		0			0
$932$	0.842949	+	38.0531i	0.0276117	+	1.24647i
$933$	−10.4609	+	18.1188i	−0.342474	+	0.593182i
$934$	−4.78650	−	1.22589i	−0.156619	−	0.0401125i
$935$	5.24417	−	3.02772i	0.171503	−	0.0990172i
$936$	−4.59299	−	15.1140i	−0.150127	−	0.494016i
$937$			18.8683i			0.616400i	0.951322	+	0.308200i	$0.0997265\pi$
$937$			18.8683i			0.616400i	−0.951322	+	0.308200i	$0.900273\pi$
$938$		0			0
$939$			2.61741i			0.0854160i
$940$	−3.90151	+	7.11711i	−0.127253	+	0.232134i
$941$	34.8394	−	20.1145i	1.13573	−	0.655715i	0.190361	−	0.981714i	$-0.439034\pi$
$941$	34.8394	−	20.1145i	1.13573	−	0.655715i	0.945370	+	0.325999i	$0.105701\pi$
$942$	−3.00331	+	11.7264i	−0.0978532	+	0.382068i
$943$	−0.493478	+	0.854729i	−0.0160698	+	0.0278338i
$944$	57.5651	−	2.55160i	1.87358	−	0.0830476i
$945$		0			0
$946$	14.2251	−	14.5437i	0.462497	−	0.472856i
$947$	−42.9382	−	24.7904i	−1.39530	−	0.805579i	−0.401408	−	0.915899i	$-0.631479\pi$
$947$	−42.9382	−	24.7904i	−1.39530	−	0.805579i	−0.993896	+	0.110320i	$0.964812\pi$
$948$	−8.72816	−	14.3728i	−0.283477	−	0.466807i
$949$	4.92995	+	8.53892i	0.160033	+	0.277185i
$950$	−8.72438	−	31.1747i	−0.283056	−	1.01144i
$951$	−12.9486			−0.419887
$952$		0			0
$953$	−35.9273			−1.16380			−0.581900	−	0.813260i	$-0.697691\pi$
$953$	−35.9273			−1.16380			−0.581900	+	0.813260i	$0.697691\pi$
$954$	−0.279592	−	0.999063i	−0.00905213	−	0.0323459i
$955$	−14.3320	−	24.8237i	−0.463771	−	0.803275i
$956$	−16.2858	−	26.8180i	−0.526719	−	0.867358i
$957$	9.99928	+	5.77309i	0.323231	+	0.186617i
$958$	−13.5688	+	13.8727i	−0.438388	+	0.448206i
$959$		0			0
$960$	9.01097	−	0.599615i	0.290828	−	0.0193525i
$961$	11.2303	−	19.4515i	0.362269	−	0.627468i
$962$	−12.3944	+	48.3941i	−0.399613	+	1.56029i
$963$	−10.8695	+	6.27550i	−0.350264	+	0.202225i
$964$	−11.4416	+	20.8717i	−0.368510	+	0.672234i
$965$		−	0.0828437i		−	0.00266683i
$966$		0			0
$967$		−	33.5277i		−	1.07818i	−0.842249	−	0.539089i	$-0.818769\pi$
$967$		−	33.5277i		−	1.07818i	0.842249	−	0.539089i	$-0.181231\pi$
$968$	−24.8364	+	7.54753i	−0.798271	+	0.242587i
$969$	−21.1426	+	12.2067i	−0.679198	+	0.392135i
$970$	9.63589	+	2.46789i	0.309390	+	0.0792393i
$971$	7.35991	−	12.7477i	0.236191	−	0.409094i	−0.723427	−	0.690401i	$-0.757434\pi$
$971$	7.35991	−	12.7477i	0.236191	−	0.409094i	0.959618	+	0.281306i	$0.0907677\pi$
$972$	−0.0442929	−	1.99951i	−0.00142070	−	0.0641343i
$973$		0			0
$974$	−3.80175	−	3.71847i	−0.121816	−	0.119148i
$975$	−18.0198	−	10.4037i	−0.577095	−	0.333186i
$976$	−30.7366	+	19.6101i	−0.983856	+	0.627703i
$977$	4.48644	+	7.77075i	0.143534	+	0.248608i	0.928825	−	0.370519i	$-0.120820\pi$
$977$	4.48644	+	7.77075i	0.143534	+	0.248608i	−0.785291	+	0.619127i	$0.787487\pi$
$978$	−7.70824	+	2.15718i	−0.246482	+	0.0689791i
$979$	10.7021			0.342041
$980$		0			0
$981$	−15.2532			−0.486997
$982$	−11.7190	+	3.27961i	−0.373968	+	0.104657i
$983$	0.933162	+	1.61628i	0.0297633	+	0.0515515i	0.880523	−	0.474003i	$-0.157191\pi$
$983$	0.933162	+	1.61628i	0.0297633	+	0.0515515i	−0.850760	+	0.525554i	$0.823858\pi$
$984$	0.411090	+	0.0956370i	0.0131051	+	0.00304880i
$985$	7.07317	+	4.08370i	0.225370	+	0.130117i
$986$	34.3582	+	33.6055i	1.09419	+	1.07022i
$987$		0			0
$988$	68.6112	−	1.51987i	2.18281	−	0.0483535i
$989$	35.2382	−	61.0343i	1.12051	−	1.94078i
$990$	−2.08783	−	0.534724i	−0.0663556	−	0.0169946i
$991$	−5.62256	+	3.24619i	−0.178607	+	0.103119i	−0.586638	−	0.809849i	$-0.699549\pi$
$991$	−5.62256	+	3.24619i	−0.178607	+	0.103119i	0.408031	+	0.912968i	$0.366215\pi$
$992$	−5.15552	−	15.7060i	−0.163688	−	0.498666i
$993$		−	5.23999i		−	0.166286i
$994$		0			0
$995$		−	17.2851i		−	0.547974i
$996$	16.0107	+	8.77686i	0.507318	+	0.278105i
$997$	10.6805	−	6.16637i	0.338254	−	0.195291i	−0.321246	−	0.946996i	$-0.604102\pi$
$997$	10.6805	−	6.16637i	0.338254	−	0.195291i	0.659500	+	0.751705i	$0.270768\pi$
$998$	6.52013	−	25.4579i	0.206391	−	0.805855i
$999$	−3.16249	+	5.47759i	−0.100057	+	0.173303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.e.19.6		24
4.3	odd	2		588.2.o.f.19.11		24
7.2	even	3		588.2.b.d.391.2	yes	12
7.3	odd	6		588.2.o.f.31.11		24
7.4	even	3	inner	588.2.o.e.31.11		24
7.5	odd	6		588.2.b.c.391.2	yes	12
7.6	odd	2		588.2.o.f.19.6		24
21.2	odd	6		1764.2.b.m.1567.11		12
21.5	even	6		1764.2.b.l.1567.11		12
28.3	even	6	inner	588.2.o.e.31.6		24
28.11	odd	6		588.2.o.f.31.6		24
28.19	even	6		588.2.b.d.391.1	yes	12
28.23	odd	6		588.2.b.c.391.1	✓	12
28.27	even	2	inner	588.2.o.e.19.11		24
84.23	even	6		1764.2.b.l.1567.12		12
84.47	odd	6		1764.2.b.m.1567.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.1	✓	12	28.23	odd	6
588.2.b.c.391.2	yes	12	7.5	odd	6
588.2.b.d.391.1	yes	12	28.19	even	6
588.2.b.d.391.2	yes	12	7.2	even	3
588.2.o.e.19.6		24	1.1	even	1	trivial
588.2.o.e.19.11		24	28.27	even	2	inner
588.2.o.e.31.6		24	28.3	even	6	inner
588.2.o.e.31.11		24	7.4	even	3	inner
588.2.o.f.19.6		24	7.6	odd	2
588.2.o.f.19.11		24	4.3	odd	2
588.2.o.f.31.6		24	28.11	odd	6
588.2.o.f.31.11		24	7.3	odd	6
1764.2.b.l.1567.11		12	21.5	even	6
1764.2.b.l.1567.12		12	84.23	even	6
1764.2.b.m.1567.11		12	21.2	odd	6
1764.2.b.m.1567.12		12	84.47	odd	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.381130 - 1.36189i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.70948 + 1.03811i) q^{4} +(0.977624 + 0.564431i) q^{5} +(-0.988865 + 1.01101i) q^{6} +(2.06533 + 1.93246i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.396091 - 1.54654i) q^{10} +(-1.16914 + 0.675002i) q^{11} +(1.75377 + 0.961396i) q^{12} +5.58489i q^{13} -1.12886i q^{15} +(1.84464 - 3.54927i) q^{16} +(-3.44113 + 1.98674i) q^{17} +(1.36999 + 0.350876i) q^{18} +(-3.07204 + 5.32093i) q^{19} +(-2.25717 + 0.0500006i) q^{20} +(1.36487 + 1.33497i) q^{22} +(5.72784 + 3.30697i) q^{23} +(0.640898 - 2.75486i) q^{24} +(-1.86283 - 3.22652i) q^{25} +(7.60600 - 2.12857i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(-1.53738 + 0.430244i) q^{30} +(1.46111 + 2.53071i) q^{31} +(-5.53675 - 1.15946i) q^{32} +(1.16914 + 0.675002i) q^{33} +(4.01723 + 3.92923i) q^{34} +(-0.0442929 - 1.99951i) q^{36} +(-3.16249 + 5.47759i) q^{37} +(8.41736 + 2.15581i) q^{38} +(4.83666 - 2.79245i) q^{39} +(0.928372 + 3.05496i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(1.29789 - 2.36760i) q^{44} +(-0.977624 + 0.564431i) q^{45} +(2.32067 - 9.06107i) q^{46} +(1.79746 - 3.11329i) q^{47} +(-3.99608 + 0.177128i) q^{48} +(-3.68418 + 3.76670i) q^{50} +(3.44113 + 1.98674i) q^{51} +(-5.79775 - 9.54726i) q^{52} +(-0.366793 - 0.635305i) q^{53} +(-0.381130 - 1.36189i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(-3.25969 - 11.6478i) q^{58} +(7.20270 + 12.4754i) q^{59} +(1.17189 + 1.92977i) q^{60} +(-7.89372 - 4.55744i) q^{61} +(2.88967 - 2.95439i) q^{62} +(0.531167 + 7.98235i) q^{64} +(-3.15229 + 5.45992i) q^{65} +(0.473683 - 1.84950i) q^{66} +(0.202730 - 0.117046i) q^{67} +(3.82008 - 6.96857i) q^{68} -6.61394i q^{69} +8.74104i q^{71} +(-2.70623 + 0.822395i) q^{72} +(1.52893 - 0.882729i) q^{73} +(8.66518 + 2.21928i) q^{74} +(-1.86283 + 3.22652i) q^{75} +(-0.272139 - 12.2852i) q^{76} +(-5.64640 - 5.52270i) q^{78} +(-7.28129 - 4.20385i) q^{79} +(3.80668 - 2.42868i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.203226 - 0.0568736i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(-14.5119 + 4.06122i) q^{86} +(-4.27635 - 7.40685i) q^{87} +(-3.71907 - 0.865215i) q^{88} +(-6.86538 - 3.96373i) q^{89} +(1.14129 + 1.11629i) q^{90} +(-13.2246 + 0.292951i) q^{92} +(1.46111 - 2.53071i) q^{93} +(-4.92502 - 1.26137i) q^{94} +(-6.00660 + 3.46791i) q^{95} +(1.76425 + 5.37470i) q^{96} +6.23063i q^{97} -1.35000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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