LMFDB - Embedded newform 588.2.o.e.31.11

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			31.11
Character	$\chi$	$=$	588.31
Dual form			588.2.o.e.19.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36999 + 0.350876i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.75377 + 0.961396i) 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} +(-1.53738 + 0.430244i) q^{10} +(1.16914 + 0.675002i) q^{11} +(-1.70948 + 1.03811i) q^{12} +5.58489i q^{13} -1.12886i q^{15} +(2.15144 + 3.37214i) q^{16} +(3.44113 + 1.98674i) q^{17} +(-0.381130 - 1.36189i) 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} +(-2.70623 + 0.822395i) q^{24} +(-1.86283 + 3.22652i) q^{25} +(-1.95960 + 7.65127i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(0.396091 - 1.54654i) q^{30} +(1.46111 - 2.53071i) q^{31} +(1.76425 + 5.37470i) 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} +(-2.34170 - 8.36756i) q^{38} +(-4.83666 - 2.79245i) q^{39} +(-3.10986 - 0.723486i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(1.40146 + 2.30780i) q^{44} +(0.977624 + 0.564431i) q^{45} +(-9.00745 + 2.52077i) 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} +(-5.36929 + 9.79463i) q^{52} +(-0.366793 + 0.635305i) q^{53} +(1.36999 + 0.350876i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(11.7172 + 3.00093i) q^{58} +(7.20270 - 12.4754i) q^{59} +(1.08528 - 1.97977i) 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} +(-1.83855 + 0.514527i) q^{66} +(-0.202730 - 0.117046i) q^{67} +(4.12492 + 6.79257i) q^{68} -6.61394i q^{69} +8.74104i q^{71} +(0.640898 - 2.75486i) q^{72} +(-1.52893 - 0.882729i) q^{73} +(-2.41064 - 8.61391i) 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} +(-4.00664 - 2.08235i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0523589 + 0.204435i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(3.73883 - 14.5983i) q^{86} +(-4.27635 + 7.40685i) q^{87} +(1.11024 + 3.65342i) 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} +(1.37013 + 4.89588i) q^{94} +(6.00660 + 3.46791i) q^{95} +(-5.53675 - 1.15946i) 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.36999	+	0.350876i	0.968733	+	0.248107i
$2$	1.36999	+	0.350876i	0.968733	+	0.248107i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.75377	+	0.961396i	0.876886	+	0.480698i
$5$	−0.977624	+	0.564431i	−0.437207	+	0.252421i	−0.702412	−	0.711771i	$-0.747894\pi$
$5$	−0.977624	+	0.564431i	−0.437207	+	0.252421i	0.265205	+	0.964192i	$0.414560\pi$
$6$	−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
$10$	−1.53738	+	0.430244i	−0.486164	+	0.136055i
$11$	1.16914	+	0.675002i	0.352508	+	0.203521i	0.665789	−	0.746140i	$-0.268095\pi$
$11$	1.16914	+	0.675002i	0.352508	+	0.203521i	−0.313281	+	0.949660i	$0.601428\pi$
$12$	−1.70948	+	1.03811i	−0.493484	+	0.299678i
$13$			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
$16$	2.15144	+	3.37214i	0.537859	+	0.843035i
$17$	3.44113	+	1.98674i	0.834597	+	0.481855i	0.855424	−	0.517929i	$-0.173297\pi$
$17$	3.44113	+	1.98674i	0.834597	+	0.481855i	−0.0208273	+	0.999783i	$0.506630\pi$
$18$	−0.381130	−	1.36189i	−0.0898332	−	0.321000i
$19$	−3.07204	−	5.32093i	−0.704775	−	1.22071i	−0.966773	−	0.255637i	$-0.917715\pi$
$19$	−3.07204	−	5.32093i	−0.704775	−	1.22071i	0.261998	−	0.965068i	$-0.415619\pi$
$20$	−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	$-0.908859\pi$
$23$	−5.72784	+	3.30697i	−1.19434	+	0.689551i	−0.235051	+	0.971983i	$0.575526\pi$
$24$	−2.70623	+	0.822395i	−0.552406	+	0.167871i
$25$	−1.86283	+	3.22652i	−0.372567	+	0.645305i
$26$	−1.95960	+	7.65127i	−0.384310	+	1.50054i
$27$	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	$0.207944\pi$
$30$	0.396091	−	1.54654i	0.0723159	−	0.282358i
$31$	1.46111	−	2.53071i	0.262422	−	0.454529i	−0.704463	−	0.709741i	$-0.748812\pi$
$31$	1.46111	−	2.53071i	0.262422	−	0.454529i	0.966885	+	0.255212i	$0.0821453\pi$
$32$	1.76425	+	5.37470i	0.311879	+	0.950122i
$33$	−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	−0.999732	−	0.0231442i	$-0.992632\pi$
$37$	−3.16249	−	5.47759i	−0.519910	−	0.900510i	0.479823	−	0.877366i	$-0.340701\pi$
$38$	−2.34170	−	8.36756i	−0.379873	−	1.35740i
$39$	−4.83666	−	2.79245i	−0.774485	−	0.447149i
$40$	−3.10986	−	0.723486i	−0.491712	−	0.114393i
$41$			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	$-0.301889\pi$
$44$	1.40146	+	2.30780i	0.211278	+	0.347914i
$45$	0.977624	+	0.564431i	0.145736	+	0.0841405i
$46$	−9.00745	+	2.52077i	−1.32808	+	0.371668i
$47$	1.79746	+	3.11329i	0.262186	+	0.454120i	0.966823	−	0.255448i	$-0.0822231\pi$
$47$	1.79746	+	3.11329i	0.262186	+	0.454120i	−0.704636	+	0.709569i	$0.748890\pi$
$48$	−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
$52$	−5.36929	+	9.79463i	−0.744587	+	1.35827i
$53$	−0.366793	+	0.635305i	−0.0503830	+	0.0872658i	−0.890117	−	0.455732i	$-0.849378\pi$
$53$	−0.366793	+	0.635305i	−0.0503830	+	0.0872658i	0.839734	+	0.542998i	$0.182711\pi$
$54$	1.36999	+	0.350876i	0.186433	+	0.0477481i
$55$	−1.52397			−0.205492
$56$		0			0
$57$	6.14408			0.813804
$58$	11.7172	+	3.00093i	1.53854	+	0.394042i
$59$	7.20270	−	12.4754i	0.937712	−	1.62416i	0.167986	−	0.985789i	$-0.446274\pi$
$59$	7.20270	−	12.4754i	0.937712	−	1.62416i	0.769726	−	0.638375i	$-0.220393\pi$
$60$	1.08528	−	1.97977i	0.140110	−	0.255587i
$61$	7.89372	−	4.55744i	1.01069	−	0.583520i	0.0992943	−	0.995058i	$-0.468341\pi$
$61$	7.89372	−	4.55744i	1.01069	−	0.583520i	0.911393	+	0.411538i	$0.135008\pi$
$62$	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
$66$	−1.83855	+	0.514527i	−0.226310	+	0.0633339i
$67$	−0.202730	−	0.117046i	−0.0247674	−	0.0142995i	0.487565	−	0.873087i	$-0.337885\pi$
$67$	−0.202730	−	0.117046i	−0.0247674	−	0.0142995i	−0.512333	+	0.858787i	$0.671218\pi$
$68$	4.12492	+	6.79257i	0.500220	+	0.823721i
$69$		−	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	$0.826422\pi$
$72$	0.640898	−	2.75486i	0.0755306	−	0.324663i
$73$	−1.52893	−	0.882729i	−0.178948	−	0.103316i	0.407850	−	0.913049i	$-0.366279\pi$
$73$	−1.52893	−	0.882729i	−0.178948	−	0.103316i	−0.586798	+	0.809733i	$0.699612\pi$
$74$	−2.41064	−	8.61391i	−0.280231	−	1.00135i
$75$	−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	$-0.509848\pi$
$79$	7.28129	−	4.20385i	0.819209	−	0.472971i	0.850144	+	0.526551i	$0.176515\pi$
$80$	−4.00664	−	2.08235i	−0.447955	−	0.232813i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.0523589	+	0.204435i	−0.00578207	+	0.0225761i
$83$	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
$86$	3.73883	−	14.5983i	0.403169	−	1.57417i
$87$	−4.27635	+	7.40685i	−0.458473	+	0.794098i
$88$	1.11024	+	3.65342i	0.118352	+	0.389455i
$89$	6.86538	−	3.96373i	0.727729	−	0.420155i	−0.0898617	−	0.995954i	$-0.528642\pi$
$89$	6.86538	−	3.96373i	0.727729	−	0.420155i	0.817591	+	0.575800i	$0.195309\pi$
$90$	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
$94$	1.37013	+	4.89588i	0.141318	+	0.504971i
$95$	6.00660	+	3.46791i	0.616264	+	0.355800i
$96$	−5.53675	−	1.15946i	−0.565093	−	0.118337i
$97$			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
$100$	−6.36896	+	3.86767i	−0.636896	+	0.386767i
$101$	0.688456	+	0.397480i	0.0685040	+	0.0395508i	0.533861	−	0.845572i	$-0.320741\pi$
$101$	0.688456	+	0.397480i	0.0685040	+	0.0395508i	−0.465357	+	0.885123i	$0.654074\pi$
$102$	−5.41143	+	1.51441i	−0.535811	+	0.149949i
$103$	−1.67738	−	2.90531i	−0.165277	−	0.286268i	0.771477	−	0.636258i	$-0.219518\pi$
$103$	−1.67738	−	2.90531i	−0.165277	−	0.286268i	−0.936754	+	0.349989i	$0.886185\pi$
$104$	−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	$-0.874164\pi$
$107$	−10.8695	+	6.27550i	−1.05079	+	0.606675i	−0.127921	+	0.991784i	$0.540831\pi$
$108$	1.75377	+	0.961396i	0.168757	+	0.0925104i
$109$	7.62660	−	13.2097i	0.730496	−	1.26526i	−0.226176	−	0.974086i	$-0.572622\pi$
$109$	7.62660	−	13.2097i	0.730496	−	1.26526i	0.956672	−	0.291169i	$-0.0940442\pi$
$110$	−2.08783	−	0.534724i	−0.199067	−	0.0509839i
$111$	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	$0.686901\pi$
$114$	8.41736	+	2.15581i	0.788358	+	0.201910i
$115$	3.73312	−	6.46595i	0.348115	−	0.602953i
$116$	14.9995	+	8.22253i	1.39267	+	0.763443i
$117$	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
$122$	12.4134	−	3.47396i	1.12386	−	0.314517i
$123$	−0.129231	−	0.0746117i	−0.0116524	−	0.00672751i
$124$	4.99546	−	3.03359i	0.448606	−	0.272424i
$125$		−	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	$-0.0499798\pi$
$128$	−2.07312	+	11.1221i	−0.183239	+	0.983068i
$129$	9.22813	+	5.32786i	0.812491	+	0.469092i
$130$	−2.40286	−	8.58613i	−0.210745	−	0.753053i
$131$	1.18600	+	2.05421i	0.103621	+	0.179477i	0.913174	−	0.407570i	$-0.133624\pi$
$131$	1.18600	+	2.05421i	0.103621	+	0.179477i	−0.809553	+	0.587047i	$0.800290\pi$
$132$	−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
$136$	3.26777	+	10.7531i	0.280209	+	0.922073i
$137$	3.58780	−	6.21426i	0.306527	−	0.530920i	−0.671073	−	0.741391i	$-0.734166\pi$
$137$	3.58780	−	6.21426i	0.306527	−	0.530920i	0.977600	+	0.210471i	$0.0674997\pi$
$138$	2.32067	−	9.06107i	0.197549	−	0.771330i
$139$	−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
$142$	−3.06702	+	11.9752i	−0.257378	+	1.00493i
$143$	−3.76981	+	6.52950i	−0.315247	+	0.546025i
$144$	1.84464	−	3.54927i	0.153720	−	0.295772i
$145$	−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	0.998550	−	0.0538356i	$-0.0171447\pi$
$149$	5.52532	+	9.57014i	0.452652	+	0.784016i	−0.545898	+	0.837852i	$0.683811\pi$
$150$	−1.41996	−	5.07395i	−0.115940	−	0.414286i
$151$	1.33325	+	0.769750i	0.108498	+	0.0626413i	0.553267	−	0.833004i	$-0.313381\pi$
$151$	1.33325	+	0.769750i	0.108498	+	0.0626413i	−0.444769	+	0.895645i	$0.646714\pi$
$152$	3.93773	−	16.9261i	0.319392	−	1.37289i
$153$		−	3.97347i		−	0.321236i
$154$		0			0
$155$			3.29878i			0.264964i
$156$	−5.79775	−	9.54726i	−0.464192	−	0.764392i
$157$	−7.41273	−	4.27974i	−0.591600	−	0.341560i	0.174130	−	0.984723i	$-0.444289\pi$
$157$	−7.41273	−	4.27974i	−0.591600	−	0.341560i	−0.765730	+	0.643162i	$0.777622\pi$
$158$	11.4504	−	3.20443i	0.910942	−	0.254931i
$159$	−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	$-0.737815\pi$
$163$	−4.90167	+	2.82998i	−0.383929	+	0.221661i	0.295598	+	0.955313i	$0.404481\pi$
$164$	−0.143463	+	0.261704i	−0.0112026	+	0.0204356i
$165$	0.761984	−	1.31980i	0.0593204	−	0.102746i
$166$	12.5071	+	3.20324i	0.970737	+	0.248620i
$167$	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
$170$	−6.14512	−	1.57386i	−0.471309	−	0.120709i
$171$	−3.07204	+	5.32093i	−0.234925	+	0.406902i
$172$	10.2444	−	18.6877i	0.781126	−	1.42492i
$173$	1.82184	−	1.05184i	0.138512	−	0.0799701i	−0.429143	−	0.903237i	$-0.641184\pi$
$173$	1.82184	−	1.05184i	0.138512	−	0.0799701i	0.567655	+	0.823267i	$0.307851\pi$
$174$	−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
$178$	10.7963	−	3.02140i	0.809218	−	0.226463i
$179$	−3.47076	−	2.00384i	−0.259417	−	0.149774i	0.364652	−	0.931144i	$-0.381188\pi$
$179$	−3.47076	−	2.00384i	−0.259417	−	0.149774i	−0.624068	+	0.781370i	$0.714521\pi$
$180$	1.17189	+	1.92977i	0.0873473	+	0.143836i
$181$			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
$184$	−18.2205	−	4.23887i	−1.34323	−	0.312493i
$185$	6.18344	+	3.57001i	0.454616	+	0.262473i
$186$	1.11374	+	3.97973i	0.0816636	+	0.291808i
$187$	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	0.598028	−	0.801475i	$-0.295951\pi$
$191$	21.9900	−	12.6959i	1.59114	−	0.918645i	0.993112	−	0.117170i	$-0.0373823\pi$
$192$	−7.17850	−	3.53117i	−0.518064	−	0.254840i
$193$	−0.0366935	+	0.0635549i	−0.00264125	+	0.00457478i	−0.867343	−	0.497711i	$-0.834174\pi$
$193$	−0.0366935	+	0.0635549i	−0.00264125	+	0.00457478i	0.864702	+	0.502286i	$0.167507\pi$
$194$	−2.18618	+	8.53593i	−0.156958	+	0.612844i
$195$	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	$0.417023\pi$
$198$	0.473683	−	1.84950i	0.0336632	−	0.131438i
$199$	−7.65598	+	13.2605i	−0.542718	+	0.940015i	0.456029	+	0.889965i	$0.349271\pi$
$199$	−7.65598	+	13.2605i	−0.542718	+	0.940015i	−0.998747	+	0.0500500i	$0.984062\pi$
$200$	−10.0825	+	3.06397i	−0.712941	+	0.216656i
$201$	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
$206$	−1.27860	−	4.56881i	−0.0890843	−	0.318324i
$207$	5.72784	+	3.30697i	0.398113	+	0.229850i
$208$	−18.8330	+	12.0155i	−1.30584	+	0.833127i
$209$		−	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	$-0.156985\pi$
$212$	−1.25405	+	0.761547i	−0.0861286	+	0.0523032i
$213$	−7.56996	−	4.37052i	−0.518685	−	0.299463i
$214$	−17.0931	+	4.78356i	−1.16846	+	0.326998i
$215$	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
$220$	−2.67269	−	1.46514i	−0.180193	−	0.0987795i
$221$	−11.0957	+	19.2183i	−0.746378	+	1.29277i
$222$	8.66518	+	2.21928i	0.581569	+	0.148948i
$223$	−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
$226$	−16.1362	−	4.13272i	−1.07336	−	0.274904i
$227$	−8.06595	+	13.9706i	−0.535356	+	0.927263i	0.463790	+	0.885945i	$0.346489\pi$
$227$	−8.06595	+	13.9706i	−0.535356	+	0.927263i	−0.999146	+	0.0413183i	$0.986844\pi$
$228$	10.7753	+	5.90690i	0.713613	+	0.391194i
$229$	−18.7652	+	10.8341i	−1.24004	+	0.715937i	−0.969102	−	0.246660i	$-0.920667\pi$
$229$	−18.7652	+	10.8341i	−1.24004	+	0.715937i	−0.270937	+	0.962597i	$0.587334\pi$
$230$	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	0.988850	+	0.148914i	$0.0475779\pi$
$233$	9.51561	+	16.4815i	0.623389	+	1.07974i	−0.365461	+	0.930826i	$0.619089\pi$
$234$	7.60600	−	2.12857i	0.497220	−	0.139149i
$235$	−3.51448	−	2.02909i	−0.229259	−	0.132363i
$236$	24.6257	−	14.9544i	1.60300	−	0.973451i
$237$			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	$0.830614\pi$
$240$	3.80668	−	2.42868i	0.245720	−	0.156770i
$241$	−10.3066	−	5.95053i	−0.663908	−	0.383307i	0.129857	−	0.991533i	$-0.458548\pi$
$241$	−10.3066	−	5.95053i	−0.663908	−	0.383307i	−0.793764	+	0.608225i	$0.791882\pi$
$242$	−3.49782	−	12.4987i	−0.224848	−	0.803448i
$243$	−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
$248$	7.90817	−	2.40321i	0.502169	−	0.152604i
$249$	−4.56464	+	7.90619i	−0.289272	+	0.501035i
$250$	3.45615	−	13.4946i	0.218586	−	0.853471i
$251$	−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
$254$	1.23664	−	4.82846i	0.0775937	−	0.302965i
$255$	2.24275	−	3.88456i	0.140447	−	0.243261i
$256$	−6.74265	+	14.5099i	−0.421416	+	0.906868i
$257$	−18.4612	+	10.6586i	−1.15158	+	0.664862i	−0.949271	−	0.314460i	$-0.898176\pi$
$257$	−18.4612	+	10.6586i	−1.15158	+	0.664862i	−0.202305	+	0.979323i	$0.564843\pi$
$258$	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
$262$	0.904038	+	3.23039i	0.0558516	+	0.199574i
$263$	−10.0326	−	5.79230i	−0.618634	−	0.357169i	0.157703	−	0.987487i	$-0.449591\pi$
$263$	−10.0326	−	5.79230i	−0.618634	−	0.357169i	−0.776337	+	0.630318i	$0.782925\pi$
$264$	−3.71907	−	0.865215i	−0.228893	−	0.0532503i
$265$		−	0.828119i		−	0.0508709i
$266$		0			0
$267$			7.92746i			0.485153i
$268$	−0.243015	−	0.400177i	−0.0148445	−	0.0244447i
$269$	−6.28171	−	3.62675i	−0.383003	−	0.221127i	0.296121	−	0.955150i	$-0.404307\pi$
$269$	−6.28171	−	3.62675i	−0.383003	−	0.221127i	−0.679124	+	0.734024i	$0.737640\pi$
$270$	−1.53738	+	0.430244i	−0.0935623	+	0.0261838i
$271$	14.5072	+	25.1272i	0.881249	+	1.52637i	0.849954	+	0.526857i	$0.176630\pi$
$271$	14.5072	+	25.1272i	0.881249	+	1.52637i	0.0312948	+	0.999510i	$0.490037\pi$
$272$	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
$276$	6.35862	−	11.5994i	0.382744	−	0.698199i
$277$	0.172570	−	0.298901i	0.0103688	−	0.0179592i	−0.860794	−	0.508953i	$-0.830033\pi$
$277$	0.172570	−	0.298901i	0.0103688	−	0.0179592i	0.871163	+	0.490994i	$0.163366\pi$
$278$	−30.9465	−	7.92585i	−1.85605	−	0.475361i
$279$	−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	$0.436660\pi$
$282$	−4.92502	−	1.26137i	−0.293281	−	0.0751135i
$283$	13.8906	−	24.0593i	0.825713	−	1.43018i	−0.0756596	−	0.997134i	$-0.524106\pi$
$283$	13.8906	−	24.0593i	0.825713	−	1.43018i	0.901373	−	0.433044i	$-0.142560\pi$
$284$	−8.40360	+	15.3298i	−0.498662	+	0.909656i
$285$	−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
$290$	−13.1488	+	3.67974i	−0.772123	+	0.216082i
$291$	−5.39588	−	3.11531i	−0.316312	−	0.182623i
$292$	−1.83275	−	3.01801i	−0.107253	−	0.176616i
$293$		−	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
$296$	4.05366	−	17.4244i	0.235614	−	1.01277i
$297$	1.16914	+	0.675002i	0.0678402	+	0.0391676i
$298$	4.21173	+	15.0497i	0.243979	+	0.871808i
$299$	−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
$304$	11.3336	−	21.8070i	0.650028	−	1.25072i
$305$	−5.14472	+	8.91092i	−0.294586	+	0.510238i
$306$	1.39420	−	5.44364i	0.0797009	−	0.311192i
$307$	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
$310$	−1.15746	+	4.51931i	−0.0657393	+	0.256679i
$311$	−10.4609	+	18.1188i	−0.593182	+	1.02742i	0.400618	+	0.916245i	$0.368795\pi$
$311$	−10.4609	+	18.1188i	−0.593182	+	1.02742i	−0.993801	+	0.111177i	$0.964538\pi$
$312$	−4.59299	−	15.1140i	−0.260027	−	0.855661i
$313$	2.26674	−	1.30871i	0.128124	−	0.0739724i	−0.434568	−	0.900639i	$-0.643099\pi$
$313$	2.26674	−	1.30871i	0.128124	−	0.0739724i	0.562692	+	0.826667i	$0.309766\pi$
$314$	−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	0.988556	−	0.150856i	$-0.0482028\pi$
$317$	6.47430	+	11.2138i	0.363633	+	0.629831i	−0.624923	+	0.780687i	$0.714870\pi$
$318$	−0.279592	−	0.999063i	−0.0156787	−	0.0560247i
$319$	9.99928	+	5.77309i	0.559852	+	0.323231i
$320$	−5.02477	−	7.50392i	−0.280893	−	0.419482i
$321$		−	12.5510i		−	0.700528i
$322$		0			0
$323$		−	24.4134i		−	1.35840i
$324$	−1.70948	+	1.03811i	−0.0949711	+	0.0576730i
$325$	−18.0198	−	10.4037i	−0.999558	−	0.577095i
$326$	−7.70824	+	2.15718i	−0.426920	+	0.119475i
$327$	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	$-0.712666\pi$
$331$	−4.53796	+	2.61999i	−0.249429	+	0.144008i	0.370074	+	0.929002i	$0.379332\pi$
$332$	16.0107	+	8.77686i	0.878701	+	0.481693i
$333$	−3.16249	+	5.47759i	−0.173303	+	0.300170i
$334$	6.63566	+	1.69949i	0.363087	+	0.0929920i
$335$	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	$0.298894\pi$
$338$	−24.9216	−	6.38278i	−1.35556	−	0.347178i
$339$	5.88914	−	10.2003i	0.319854	−	0.554004i
$340$	−7.86656	−	4.31235i	−0.426624	−	0.233870i
$341$	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
$346$	2.86498	−	0.801777i	0.154022	−	0.0431038i
$347$	−0.567776	−	0.327806i	−0.0304798	−	0.0175975i	0.484683	−	0.874690i	$-0.338935\pi$
$347$	−0.567776	−	0.327806i	−0.0304798	−	0.0175975i	−0.515162	+	0.857093i	$0.672268\pi$
$348$	−14.6207	+	8.87867i	−0.783750	+	0.475947i
$349$			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
$352$	−1.56528	+	7.47464i	−0.0834295	+	0.398400i
$353$	−25.8806	−	14.9422i	−1.37749	−	0.795292i	−0.385630	−	0.922653i	$-0.626016\pi$
$353$	−25.8806	−	14.9422i	−1.37749	−	0.795292i	−0.991856	+	0.127361i	$0.959349\pi$
$354$	5.49033	+	19.6185i	0.291808	+	1.04271i
$355$	−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	$-0.558834\pi$
$359$	10.9061	−	6.29666i	0.575604	−	0.332325i	0.759384	+	0.650642i	$0.225500\pi$
$360$	0.928372	+	3.05496i	0.0489295	+	0.161010i
$361$	−9.37488	+	16.2378i	−0.493415	+	0.854619i
$362$	−2.06898	+	8.07835i	−0.108743	+	0.424589i
$363$	9.17749			0.481693
$364$		0			0
$365$	1.99296			0.104316
$366$	−3.19819	+	12.4873i	−0.167172	+	0.652724i
$367$	−2.73446	+	4.73623i	−0.142738	+	0.247229i	−0.928527	−	0.371266i	$-0.878924\pi$
$367$	−2.73446	+	4.73623i	−0.142738	+	0.247229i	0.785789	+	0.618495i	$0.212257\pi$
$368$	−23.4747	−	12.2004i	−1.22370	−	0.635987i
$369$	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	0.991686	−	0.128681i	$-0.0410742\pi$
$373$	7.42404	+	12.8588i	0.384402	+	0.665805i	−0.607284	+	0.794485i	$0.707741\pi$
$374$	2.04446	+	7.30545i	0.105717	+	0.377756i
$375$	8.53042	+	4.92504i	0.440509	+	0.254328i
$376$	−2.30398	+	9.90350i	−0.118819	+	0.510734i
$377$			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	$0.712017\pi$
$380$	7.20018	+	11.8567i	0.369361	+	0.608233i
$381$	3.05225	+	1.76222i	0.156372	+	0.0902812i
$382$	34.5809	−	9.67760i	1.76931	−	0.495149i
$383$	11.7392	+	20.3329i	0.599844	+	1.03896i	0.992844	+	0.119422i	$0.0381042\pi$
$383$	11.7392	+	20.3329i	0.599844	+	1.03896i	−0.392999	+	0.919539i	$0.628562\pi$
$384$	−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
$388$	−5.99010	+	10.9271i	−0.304101	+	0.554740i
$389$	18.0887	−	31.3306i	0.917134	−	1.58852i	0.113387	−	0.993551i	$-0.463830\pi$
$389$	18.0887	−	31.3306i	0.917134	−	1.58852i	0.803747	−	0.594972i	$-0.202837\pi$
$390$	8.63724	+	2.21212i	0.437363	+	0.112015i
$391$	−26.2803			−1.32905
$392$		0			0
$393$	−2.37199			−0.119651
$394$	9.91200	+	2.53861i	0.499359	+	0.127893i
$395$	−4.74557	+	8.21958i	−0.238776	+	0.413572i
$396$	1.29789	−	2.36760i	0.0652213	−	0.118976i
$397$	1.15332	−	0.665868i	0.0578833	−	0.0334189i	−0.470779	−	0.882251i	$-0.656027\pi$
$397$	1.15332	−	0.665868i	0.0578833	−	0.0334189i	0.528662	+	0.848832i	$0.322694\pi$
$398$	−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	−0.982959	−	0.183825i	$-0.941152\pi$
$401$	−13.0298	−	22.5683i	−0.650677	−	1.12701i	0.332282	−	0.943180i	$-0.392181\pi$
$402$	0.318808	−	0.0892198i	0.0159007	−	0.00444988i
$403$	14.1337	+	8.16012i	0.704051	+	0.406484i
$404$	0.825260	+	1.35897i	0.0410582	+	0.0676112i
$405$		−	1.12886i		−	0.0560936i
$406$		0			0
$407$		−	8.53873i		−	0.423249i
$408$	−10.9464	−	2.54659i	−0.541926	−	0.126075i
$409$	11.5362	+	6.66044i	0.570429	+	0.329337i	0.757321	−	0.653043i	$-0.226508\pi$
$409$	11.5362	+	6.66044i	0.570429	+	0.329337i	−0.186892	+	0.982381i	$0.559841\pi$
$410$	−0.0642024	−	0.229414i	−0.00317073	−	0.0113299i
$411$	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
$416$	−30.0171	+	9.85317i	−1.47171	+	0.483091i
$417$	11.2944	−	19.5624i	0.553088	−	0.957977i
$418$	2.91035	−	11.3635i	0.142350	−	0.555805i
$419$	−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	$0.479270\pi$
$422$	4.82593	−	18.8428i	0.234922	−	0.917255i
$423$	1.79746	−	3.11329i	0.0873955	−	0.151373i
$424$	−1.98525	+	0.603299i	−0.0964124	+	0.0292988i
$425$	−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
$430$	4.58456	+	16.3819i	0.221087	+	0.790008i
$431$	−10.2938	−	5.94311i	−0.495833	−	0.286269i	0.231158	−	0.972916i	$-0.425749\pi$
$431$	−10.2938	−	5.94311i	−0.495833	−	0.286269i	−0.726991	+	0.686647i	$0.759082\pi$
$432$	2.15144	+	3.37214i	0.103511	+	0.162242i
$433$		−	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
$436$	26.0750	−	15.8345i	1.24877	−	0.758337i
$437$	35.1924	+	20.3183i	1.68348	+	0.971957i
$438$	2.40436	−	0.672869i	0.114885	−	0.0321509i
$439$	−2.71032	−	4.69441i	−0.129356	−	0.224052i	0.794071	−	0.607825i	$-0.207958\pi$
$439$	−2.71032	−	4.69441i	−0.129356	−	0.224052i	−0.923427	+	0.383773i	$0.874624\pi$
$440$	−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	$-0.847995\pi$
$443$	−19.6620	+	11.3519i	−0.934172	+	0.539344i	−0.0460432	+	0.998939i	$0.514661\pi$
$444$	11.0926	+	6.08080i	0.526430	+	0.288582i
$445$	−4.47451	+	7.75008i	−0.212112	+	0.367389i
$446$	−22.4844	−	5.75858i	−1.06467	−	0.272677i
$447$	−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	$0.620410\pi$
$450$	5.10415	+	1.30725i	0.240612	+	0.0616242i
$451$	−0.100726	+	0.174463i	−0.00474301	+	0.00821513i
$452$	−20.6564	−	11.3236i	−0.971597	−	0.532617i
$453$	−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	0.993508	−	0.113760i	$-0.0362896\pi$
$457$	8.51329	+	14.7454i	0.398235	+	0.689763i	−0.595274	+	0.803523i	$0.702956\pi$
$458$	−29.5096	+	8.25840i	−1.37890	+	0.385890i
$459$	3.44113	+	1.98674i	0.160618	+	0.0927330i
$460$	12.7634	−	7.75080i	0.595095	−	0.361383i
$461$		−	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	$-0.0102799\pi$
$464$	18.4006	+	28.8409i	0.854225	+	1.33890i
$465$	−2.85682	−	1.64939i	−0.132482	−	0.0764885i
$466$	7.25338	+	25.9184i	0.336006	+	1.20065i
$467$	1.74691	+	3.02573i	0.0808372	+	0.140014i	0.903610	−	0.428357i	$-0.140907\pi$
$467$	1.74691	+	3.02573i	0.0808372	+	0.140014i	−0.822773	+	0.568371i	$0.807574\pi$
$468$	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
$472$	38.9843	−	11.8469i	1.79440	−	0.545299i
$473$	7.19263	−	12.4580i	0.330717	−	0.572819i
$474$	−2.95006	+	11.5185i	−0.135501	+	0.529063i
$475$	22.8908			1.05030
$476$		0			0
$477$	0.733587			0.0335886
$478$	−5.50448	+	21.4923i	−0.251769	+	0.983033i
$479$	−6.86079	+	11.8832i	−0.313478	+	0.542959i	−0.979113	−	0.203318i	$-0.934827\pi$
$479$	−6.86079	+	11.8832i	−0.313478	+	0.542959i	0.665635	+	0.746277i	$0.268161\pi$
$480$	6.06730	−	1.99160i	0.276933	−	0.0909037i
$481$	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
$486$	−0.381130	−	1.36189i	−0.0172884	−	0.0617765i
$487$	−3.25655	−	1.88017i	−0.147569	−	0.0851987i	0.424398	−	0.905476i	$-0.360486\pi$
$487$	−3.25655	−	1.88017i	−0.147569	−	0.0851987i	−0.571966	+	0.820277i	$0.693819\pi$
$488$	25.1102	+	5.84171i	1.13669	+	0.264442i
$489$		−	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	$-0.0622008\pi$
$492$	−0.154911	−	0.255094i	−0.00698392	−	0.0115005i
$493$	29.4309	+	16.9920i	1.32550	+	0.765280i
$494$	46.7319	−	13.0781i	2.10257	−	0.588412i
$495$	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	$-0.803211\pi$
$499$	−16.0929	+	9.29123i	−0.720416	+	0.415933i	0.0944896	+	0.995526i	$0.469878\pi$
$500$	9.46983	−	17.2748i	0.423504	−	0.772553i
$501$	−2.42178	+	4.19465i	−0.108197	+	0.187403i
$502$	−2.31138	−	0.591979i	−0.103162	−	0.0264213i
$503$	−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
$506$	−12.2325	−	3.13292i	−0.543800	−	0.139275i
$507$	9.09550	−	15.7539i	0.403946	−	0.699654i
$508$	3.38838	−	6.18106i	0.150335	−	0.274240i
$509$	20.7781	−	11.9963i	0.920974	−	0.531725i	0.0370283	−	0.999314i	$-0.488211\pi$
$509$	20.7781	−	11.9963i	0.920974	−	0.531725i	0.883946	+	0.467590i	$0.154878\pi$
$510$	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
$514$	−29.0315	+	8.12459i	−1.28053	+	0.358360i
$515$	3.27969	+	1.89353i	0.144520	+	0.0834389i
$516$	11.0618	+	18.2157i	0.486971	+	0.801903i
$517$			4.85315i			0.213441i
$518$		0			0
$519$			2.10368i			0.0923415i
$520$	4.04059	−	17.3682i	0.177192	−	0.761647i
$521$	−12.1946	−	7.04055i	−0.534255	−	0.308452i	0.208493	−	0.978024i	$-0.433144\pi$
$521$	−12.1946	−	7.04055i	−0.534255	−	0.308452i	−0.742747	+	0.669572i	$0.766478\pi$
$522$	−3.25969	−	11.6478i	−0.142673	−	0.509811i
$523$	−17.5726	−	30.4366i	−0.768396	−	1.33090i	−0.938432	−	0.345463i	$-0.887722\pi$
$523$	−17.5726	−	30.4366i	−0.768396	−	1.33090i	0.170037	−	0.985438i	$-0.445611\pi$
$524$	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
$528$	−4.79152	−	2.49027i	−0.208524	−	0.108375i
$529$	10.3721	−	17.9651i	0.450962	−	0.781089i
$530$	0.290567	−	1.13452i	0.0126214	−	0.0492803i
$531$	−14.4054			−0.625141
$532$		0			0
$533$	−0.833397			−0.0360984
$534$	−2.78155	+	10.8606i	−0.120370	+	0.469983i
$535$	7.08418	−	12.2702i	0.306276	−	0.530485i
$536$	−0.192517	−	0.633508i	−0.00831545	−	0.0273634i
$537$	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	0.696379	−	0.717674i	$-0.254793\pi$
$541$	−6.35759	−	11.0117i	−0.273334	−	0.473429i	−0.969714	+	0.244245i	$0.921460\pi$
$542$	11.0583	+	39.5143i	0.474993	+	1.69729i
$543$	−5.10663	−	2.94831i	−0.219146	−	0.126524i
$544$	−4.60709	+	22.0002i	−0.197527	+	0.943249i
$545$			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	$-0.356456\pi$
$548$	12.2666	−	7.44910i	0.524001	−	0.318210i
$549$	−7.89372	−	4.55744i	−0.336896	−	0.194507i
$550$	−6.84984	+	1.91696i	−0.292078	+	0.0817393i
$551$	−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
$556$	−39.6156	−	21.7167i	−1.68007	−	0.920995i
$557$	−7.94263	+	13.7570i	−0.336540	+	0.582905i	−0.983779	−	0.179382i	$-0.942590\pi$
$557$	−7.94263	+	13.7570i	−0.336540	+	0.582905i	0.647239	+	0.762287i	$0.275923\pi$
$558$	−4.00341	−	1.02533i	−0.169478	−	0.0434058i
$559$	59.5110			2.51705
$560$		0			0
$561$	−5.36420			−0.226477
$562$	9.07942	+	2.32537i	0.382992	+	0.0980899i
$563$	16.4594	−	28.5085i	0.693681	−	1.20149i	−0.276943	−	0.960886i	$-0.589321\pi$
$563$	16.4594	−	28.5085i	0.693681	−	1.20149i	0.970623	−	0.240604i	$-0.0773454\pi$
$564$	−6.30467	−	3.45614i	−0.265475	−	0.145530i
$565$	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	−0.955463	−	0.295110i	$-0.904644\pi$
$569$	−17.4920	−	30.2971i	−0.733304	−	1.27012i	0.222159	−	0.975010i	$-0.428690\pi$
$570$	−9.44582	+	2.64345i	−0.395642	+	0.110722i
$571$	−5.63066	−	3.25087i	−0.235636	−	0.136044i	0.377533	−	0.925996i	$-0.376772\pi$
$571$	−5.63066	−	3.25087i	−0.235636	−	0.136044i	−0.613169	+	0.789951i	$0.710106\pi$
$572$	−12.8888	+	7.82698i	−0.538909	+	0.327263i
$573$			25.3919i			1.06076i
$574$		0			0
$575$		−	24.6414i		−	1.02762i
$576$	6.64733	−	4.45118i	0.276972	−	0.185466i
$577$	32.2277	+	18.6067i	1.34166	+	0.774606i	0.987051	−	0.160409i	$-0.0512814\pi$
$577$	32.2277	+	18.6067i	1.34166	+	0.774606i	0.354607	+	0.935016i	$0.384615\pi$
$578$	−0.461739	−	1.64993i	−0.0192058	−	0.0686280i
$579$	−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
$584$	−1.45190	−	4.77773i	−0.0600802	−	0.197704i
$585$	−3.15229	+	5.45992i	−0.130331	+	0.225740i
$586$	2.55610	−	9.98029i	0.105591	−	0.412282i
$587$	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
$590$	−5.70584	+	22.2785i	−0.234906	+	0.917190i
$591$	−3.61753	+	6.26575i	−0.148805	+	0.257739i
$592$	11.6673	−	22.4490i	0.479523	−	0.922649i
$593$	26.8491	−	15.5014i	1.10256	−	0.636565i	0.165670	−	0.986181i	$-0.447021\pi$
$593$	26.8491	−	15.5014i	1.10256	−	0.636565i	0.936893	+	0.349617i	$0.113688\pi$
$594$	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
$598$	−14.0782	−	50.3056i	−0.575702	−	2.05715i
$599$	−7.12727	−	4.11493i	−0.291212	−	0.168131i	0.347276	−	0.937763i	$-0.387107\pi$
$599$	−7.12727	−	4.11493i	−0.291212	−	0.168131i	−0.638488	+	0.769631i	$0.720440\pi$
$600$	2.38777	−	10.2637i	0.0974805	−	0.419014i
$601$		−	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
$604$	1.59817	+	2.63174i	0.0650288	+	0.107084i
$605$	8.97213	+	5.18006i	0.364769	+	0.210600i
$606$	−1.08265	+	0.302984i	−0.0439796	+	0.0123079i
$607$	6.32713	+	10.9589i	0.256810	+	0.444808i	0.965386	−	0.260827i	$-0.0839951\pi$
$607$	6.32713	+	10.9589i	0.256810	+	0.444808i	−0.708575	+	0.705635i	$0.750662\pi$
$608$	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
$612$	3.82008	−	6.96857i	0.154418	−	0.281688i
$613$	−0.226457	+	0.392236i	−0.00914652	+	0.0158422i	−0.870562	−	0.492058i	$-0.836245\pi$
$613$	−0.226457	+	0.392236i	−0.00914652	+	0.0158422i	0.861416	+	0.507900i	$0.169578\pi$
$614$	37.2517	+	9.54070i	1.50335	+	0.385031i
$615$	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	$0.503687\pi$
$618$	4.59600	+	1.17710i	0.184878	+	0.0473500i
$619$	−1.02161	+	1.76949i	−0.0410622	+	0.0711218i	−0.885826	−	0.464017i	$-0.846408\pi$
$619$	−1.02161	+	1.76949i	−0.0410622	+	0.0711218i	0.844764	+	0.535139i	$0.179741\pi$
$620$	−3.17143	+	5.78530i	−0.127368	+	0.232343i
$621$	−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
$626$	3.56462	−	0.997574i	0.142471	−	0.0398711i
$627$	7.18328	+	4.14727i	0.286872	+	0.165626i
$628$	−8.88571	−	14.6323i	−0.354578	−	0.583890i
$629$		−	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	$0.718123\pi$
$632$	23.1621	+	5.38849i	0.921337	+	0.214342i
$633$	11.9113	+	6.87698i	0.473431	+	0.273335i
$634$	4.93511	+	17.6346i	0.195998	+	0.700358i
$635$	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
$640$	−4.25096	−	12.0434i	−0.168034	−	0.476057i
$641$	1.03036	−	1.78464i	0.0406969	−	0.0704891i	−0.844959	−	0.534830i	$-0.820376\pi$
$641$	1.03036	−	1.78464i	0.0406969	−	0.0704891i	0.885656	+	0.464341i	$0.153709\pi$
$642$	4.40384	−	17.1948i	0.173806	−	0.678625i
$643$	−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
$646$	8.56605	−	33.4462i	0.337027	−	1.31592i
$647$	9.70418	−	16.8081i	0.381511	−	0.660796i	−0.609768	−	0.792580i	$-0.708737\pi$
$647$	9.70418	−	16.8081i	0.381511	−	0.660796i	0.991278	+	0.131784i	$0.0420706\pi$
$648$	−2.70623	+	0.822395i	−0.106311	+	0.0323067i
$649$	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	0.873076	−	0.487584i	$-0.162122\pi$
$653$	0.364864	+	0.631964i	0.0142783	+	0.0247307i	−0.858798	+	0.512314i	$0.828788\pi$
$654$	5.81345	+	20.7732i	0.227324	+	0.812294i
$655$	−2.31892	−	1.33883i	−0.0906075	−	0.0523123i
$656$	−0.503202	+	0.321045i	−0.0196467	+	0.0125347i
$657$			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	$-0.125298\pi$
$660$	2.60519	−	1.58205i	0.101407	−	0.0615813i
$661$	−8.14536	−	4.70273i	−0.316818	−	0.182915i	0.333156	−	0.942872i	$-0.391887\pi$
$661$	−8.14536	−	4.70273i	−0.316818	−	0.182915i	−0.649973	+	0.759957i	$0.725220\pi$
$662$	−7.13628	+	1.99712i	−0.277359	+	0.0776202i
$663$	−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
$668$	8.49452	+	4.65659i	0.328663	+	0.180169i
$669$	8.20602	−	14.2132i	0.317263	−	0.549516i
$670$	0.362033	+	0.0927219i	0.0139865	+	0.00358216i
$671$	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	$0.303729\pi$
$674$	29.7066	+	7.60829i	1.14426	+	0.293060i
$675$	−1.86283	+	3.22652i	−0.0717005	+	0.124189i
$676$	−31.9029	−	17.4888i	−1.22703	−	0.672645i
$677$	−26.6823	+	15.4050i	−1.02548	+	0.592063i	−0.915687	−	0.401891i	$-0.868353\pi$
$677$	−26.6823	+	15.4050i	−1.02548	+	0.592063i	−0.109796	+	0.993954i	$0.535020\pi$
$678$	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
$682$	5.37264	−	1.50356i	0.205729	−	0.0575742i
$683$	−36.0508	−	20.8140i	−1.37945	−	0.796424i	−0.387354	−	0.921931i	$-0.626611\pi$
$683$	−36.0508	−	20.8140i	−1.37945	−	0.796424i	−0.992093	+	0.125507i	$0.959944\pi$
$684$	−10.5032	+	6.37826i	−0.401599	+	0.243879i
$685$			8.10028i			0.309496i
$686$		0			0
$687$		−	21.6682i		−	0.826693i
$688$	35.9326	−	22.9251i	1.36992	−	0.874011i
$689$	−3.54811	−	2.04850i	−0.135172	−	0.0780417i
$690$	2.84561	+	10.1682i	0.108330	+	0.387096i
$691$	4.39414	+	7.61087i	0.167161	+	0.289531i	0.937421	−	0.348199i	$-0.113207\pi$
$691$	4.39414	+	7.61087i	0.167161	+	0.289531i	−0.770260	+	0.637730i	$0.779873\pi$
$692$	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
$696$	−23.1455	+	7.03370i	−0.877330	+	0.266612i
$697$	−0.296468	+	0.513497i	−0.0112295	+	0.0194501i
$698$	−6.81249	+	26.5994i	−0.257856	+	1.00680i
$699$	−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	$0.500373\pi$
$702$	−1.95960	+	7.65127i	−0.0739604	+	0.288779i
$703$	−19.4306	+	33.6547i	−0.732838	+	1.26931i
$704$	−4.76709	+	9.69100i	−0.179666	+	0.365243i
$705$	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	−0.988830	−	0.149045i	$-0.952380\pi$
$709$	−16.6018	−	28.7551i	−0.623492	−	1.07992i	0.365338	−	0.930875i	$-0.380953\pi$
$710$	−3.76078	−	13.4383i	−0.141139	−	0.504332i
$711$	−7.28129	−	4.20385i	−0.273070	−	0.157657i
$712$	21.8390	+	5.08070i	0.818453	+	0.190407i
$713$			19.3273i			0.723815i
$714$		0			0
$715$		−	8.51120i		−	0.318301i
$716$	−4.16043	−	6.85106i	−0.155483	−	0.256036i
$717$	−13.5861	−	7.84392i	−0.507381	−	0.292937i
$718$	17.1507	−	4.79969i	0.640058	−	0.179123i
$719$	15.9535	+	27.6323i	0.594966	+	1.03051i	0.993552	+	0.113380i	$0.0361677\pi$
$719$	15.9535	+	27.6323i	0.594966	+	1.03051i	−0.398586	+	0.917131i	$0.630499\pi$
$720$	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
$724$	−5.66899	+	10.3413i	−0.210687	+	0.384333i
$725$	−15.9323	+	27.5955i	−0.591709	+	1.02487i
$726$	12.5731	+	3.22016i	0.466632	+	0.119511i
$727$	−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
$730$	2.73035	+	0.699281i	0.101055	+	0.0258816i
$731$	21.1701	−	36.6677i	0.783005	−	1.35620i
$732$	−8.76301	+	15.9854i	−0.323890	+	0.590838i
$733$	−10.2349	+	5.90910i	−0.378033	+	0.218258i	−0.676962	−	0.736018i	$-0.736704\pi$
$733$	−10.2349	+	5.90910i	−0.378033	+	0.218258i	0.298929	+	0.954275i	$0.403371\pi$
$734$	−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
$738$	0.203226	−	0.0568736i	0.00748084	−	0.00209354i
$739$	−23.0318	−	13.2974i	−0.847237	−	0.489153i	0.0124806	−	0.999922i	$-0.496027\pi$
$739$	−23.0318	−	13.2974i	−0.847237	−	0.489153i	−0.859718	+	0.510770i	$0.829361\pi$
$740$	7.41216	+	12.2057i	0.272476	+	0.448691i
$741$			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	$0.778770\pi$
$744$	−1.87284	+	8.05028i	−0.0686616	+	0.295138i
$745$	−10.8034	−	6.23733i	−0.395805	−	0.228518i
$746$	5.65905	+	20.2214i	0.207193	+	0.740359i
$747$	−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	$-0.656675\pi$
$751$	1.48965	−	0.860048i	0.0543580	−	0.0313836i	0.526933	+	0.849907i	$0.323342\pi$
$752$	−6.63134	+	12.7593i	−0.241820	+	0.465285i
$753$	0.843573	−	1.46111i	0.0307415	−	0.0532459i
$754$	−16.7599	+	65.4390i	−0.610359	+	2.38315i
$755$	−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	$0.293796\pi$
$758$	−10.7416	+	41.9404i	−0.390151	+	1.52334i
$759$	4.46442	−	7.73261i	0.162048	−	0.280676i
$760$	5.70399	+	18.7699i	0.206906	+	0.680857i
$761$	23.5363	−	13.5887i	0.853191	−	0.492590i	−0.00853557	−	0.999964i	$-0.502717\pi$
$761$	23.5363	−	13.5887i	0.853191	−	0.492590i	0.861726	+	0.507374i	$0.169384\pi$
$762$	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
$766$	8.94832	+	31.9749i	0.323316	+	1.15530i
$767$	69.6740	+	40.2263i	2.51578	+	1.45249i
$768$	−9.19460	−	13.0942i	−0.331782	−	0.472498i
$769$		−	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
$772$	−0.125453	+	0.0761839i	−0.00451517	+	0.00274192i
$773$	22.9995	+	13.2788i	0.827234	+	0.477604i	0.852905	−	0.522067i	$-0.174839\pi$
$773$	22.9995	+	13.2788i	0.827234	+	0.477604i	−0.0256709	+	0.999670i	$0.508172\pi$
$774$	−14.5119	+	4.06122i	−0.521620	+	0.145977i
$775$	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
$780$	11.0568	+	6.06119i	0.395897	+	0.217026i
$781$	−5.90022	+	10.2195i	−0.211126	+	0.365682i
$782$	−36.0039	−	9.22113i	−1.28750	−	0.329747i
$783$	8.55270			0.305648
$784$		0			0
$785$	9.66247			0.344869
$786$	−3.24962	−	0.832274i	−0.115910	−	0.0296862i
$787$	−12.2335	+	21.1890i	−0.436077	+	0.755307i	−0.997383	−	0.0723013i	$-0.976966\pi$
$787$	−12.2335	+	21.1890i	−0.436077	+	0.755307i	0.561306	+	0.827608i	$0.310299\pi$
$788$	12.6887	+	6.95576i	0.452015	+	0.247789i
$789$	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
$794$	1.81368	−	0.507565i	0.0643649	−	0.0180128i
$795$	0.717172	+	0.414059i	0.0254355	+	0.0146852i
$796$	−26.1755	+	15.8955i	−0.927765	+	0.563403i
$797$			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
$800$	−20.6281	−	4.31977i	−0.729314	−	0.152727i
$801$	−6.86538	−	3.96373i	−0.242576	−	0.140052i
$802$	−9.93210	−	35.4903i	−0.350715	−	1.25320i
$803$	−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
$808$	0.653772	+	2.15134i	0.0229996	+	0.0756840i
$809$	6.59877	−	11.4294i	0.232000	−	0.401836i	−0.726396	−	0.687276i	$-0.758806\pi$
$809$	6.59877	−	11.4294i	0.232000	−	0.401836i	0.958397	+	0.285440i	$0.0921396\pi$
$810$	0.396091	−	1.54654i	0.0139172	−	0.0543397i
$811$	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
$814$	2.99603	−	11.6980i	0.105011	−	0.410015i
$815$	3.19466	−	5.53331i	0.111904	−	0.193824i
$816$	−14.1029	−	7.32963i	−0.493701	−	0.256588i
$817$	−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	0.797768	−	0.602965i	$-0.206014\pi$
$821$	−3.53291	−	6.11917i	−0.123299	−	0.213561i	−0.921067	+	0.389404i	$0.872681\pi$
$822$	2.73484	+	9.77238i	0.0953885	+	0.340851i
$823$	−19.0192	−	10.9807i	−0.662966	−	0.382764i	0.130440	−	0.991456i	$-0.458361\pi$
$823$	−19.0192	−	10.9807i	−0.662966	−	0.382764i	−0.793406	+	0.608692i	$0.791694\pi$
$824$	2.15006	−	9.24189i	0.0749008	−	0.321956i
$825$		−	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	$0.901648\pi$
$828$	6.86603	+	11.3064i	0.238611	+	0.392925i
$829$	22.1721	+	12.8011i	0.770069	+	0.444599i	0.832899	−	0.553425i	$-0.186679\pi$
$829$	22.1721	+	12.8011i	0.770069	+	0.444599i	−0.0628304	+	0.998024i	$0.520013\pi$
$830$	−14.0352	+	3.92782i	−0.487170	+	0.136337i
$831$	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
$836$	7.97433	−	14.5467i	0.275798	−	0.503109i
$837$	1.46111	−	2.53071i	0.0505032	−	0.0874741i
$838$	−10.3388	−	2.64793i	−0.357150	−	0.0914712i
$839$	−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
$842$	3.65870	+	0.937048i	0.126087	+	0.0322928i
$843$	−3.31367	+	5.73944i	−0.114129	+	0.197677i
$844$	13.2230	−	24.1213i	0.455154	−	0.830289i
$845$	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
$850$	−20.1612	+	5.64219i	−0.691523	+	0.193526i
$851$	36.2285	+	20.9165i	1.24190	+	0.717009i
$852$	−9.07419	−	14.9426i	−0.310877	−	0.511926i
$853$		−	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
$856$	−34.5762	−	8.04391i	−1.18179	−	0.274935i
$857$	−41.9058	−	24.1943i	−1.43148	−	0.826463i	−0.434242	−	0.900796i	$-0.642984\pi$
$857$	−41.9058	−	24.1943i	−1.43148	−	0.826463i	−0.997233	+	0.0743338i	$0.976317\pi$
$858$	−2.87358	−	10.2681i	−0.0981023	−	0.350548i
$859$	−9.91892	−	17.1801i	−0.338429	−	0.586176i	0.645708	−	0.763584i	$-0.276562\pi$
$859$	−9.91892	−	17.1801i	−0.338429	−	0.586176i	−0.984137	+	0.177408i	$0.943229\pi$
$860$	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	$-0.896267\pi$
$863$	−33.6011	+	19.3996i	−1.14379	+	0.660370i	−0.196427	+	0.980518i	$0.562934\pi$
$864$	1.76425	+	5.37470i	0.0600211	+	0.182851i
$865$	−1.18738	+	2.05661i	−0.0403723	+	0.0699269i
$866$	7.25144	−	28.3132i	0.246414	−	0.962123i
$867$	1.21150			0.0411447
$868$		0			0
$869$	11.3504			0.385037
$870$	3.38764	−	13.2271i	0.114852	−	0.448439i
$871$	0.653691	−	1.13223i	0.0221495	−	0.0383640i
$872$	41.2786	−	12.5442i	1.39787	−	0.424799i
$873$	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	0.964281	−	0.264882i	$-0.0853330\pi$
$877$	7.48487	+	12.9642i	0.252746	+	0.437769i	−0.711535	+	0.702651i	$0.752000\pi$
$878$	−2.06597	−	7.38230i	−0.0697231	−	0.249141i
$879$	6.30891	+	3.64245i	0.212794	+	0.122857i
$880$	−3.27872	−	5.13903i	−0.110526	−	0.173237i
$881$			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	$0.890213\pi$
$884$	−37.9358	+	23.0372i	−1.27592	+	0.774825i
$885$	−14.0831	−	8.13086i	−0.473397	−	0.273316i
$886$	−30.9200	+	8.65309i	−1.03878	+	0.290706i
$887$	7.60734	+	13.1763i	0.255430	+	0.442417i	0.965012	−	0.262205i	$-0.0844498\pi$
$887$	7.60734	+	13.1763i	0.255430	+	0.442417i	−0.709583	+	0.704622i	$0.751116\pi$
$888$	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
$892$	−28.7830	−	15.7785i	−0.963725	−	0.528302i
$893$	11.0437	−	19.1283i	0.369565	−	0.640105i
$894$	−15.1393	−	3.87740i	−0.506335	−	0.129680i
$895$	4.52413			0.151225
$896$		0			0
$897$	36.9382			1.23333
$898$	−21.4426	−	5.49177i	−0.715549	−	0.183263i
$899$	12.4964	−	21.6444i	0.416778	−	0.721881i
$900$	6.53398	+	3.58184i	0.217799	+	0.119395i
$901$	−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
$906$	−2.09663	+	0.586750i	−0.0696557	+	0.0194935i
$907$	−12.2298	−	7.06089i	−0.406084	−	0.234453i	0.283022	−	0.959114i	$-0.408663\pi$
$907$	−12.2298	−	7.06089i	−0.406084	−	0.234453i	−0.689106	+	0.724661i	$0.741997\pi$
$908$	−27.5771	+	16.7467i	−0.915180	+	0.555760i
$909$		−	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	$0.933332\pi$
$912$	13.2186	+	20.7187i	0.437712	+	0.686065i
$913$	10.6734	+	6.16228i	0.353238	+	0.203942i
$914$	6.48934	+	23.1883i	0.214648	+	0.767000i
$915$	−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	$-0.865481\pi$
$919$	−30.7045	+	17.7272i	−1.01285	+	0.584768i	−0.100824	+	0.994904i	$0.532148\pi$
$920$	20.2053	−	6.14020i	0.666150	−	0.202436i
$921$	−13.5955	+	23.5482i	−0.447989	+	0.775939i
$922$	13.3715	−	52.2092i	0.440368	−	1.71942i
$923$	−48.8178			−1.60686
$924$		0			0
$925$	23.5648			0.774804
$926$	0.487571	−	1.90372i	0.0160226	−	0.0625601i
$927$	−1.67738	+	2.90531i	−0.0550924	+	0.0954228i
$928$	15.0891	+	45.9682i	0.495325	+	1.50898i
$929$	−48.0685	+	27.7524i	−1.57708	+	0.910526i	−0.581813	+	0.813322i	$0.697657\pi$
$929$	−48.0685	+	27.7524i	−1.57708	+	0.910526i	−0.995264	+	0.0972040i	$0.969010\pi$
$930$	−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
$934$	1.33160	+	4.75818i	0.0435712	+	0.155692i
$935$	−5.24417	−	3.02772i	−0.171503	−	0.0990172i
$936$	15.3856	+	3.57935i	0.502894	+	0.116995i
$937$			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
$940$	−4.21284	−	6.93736i	−0.137408	−	0.226272i
$941$	−34.8394	−	20.1145i	−1.13573	−	0.655715i	−0.190361	−	0.981714i	$-0.560966\pi$
$941$	−34.8394	−	20.1145i	−1.13573	−	0.655715i	−0.945370	+	0.325999i	$0.894299\pi$
$942$	11.6571	−	3.26228i	0.379807	−	0.106291i
$943$	−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	$-0.368521\pi$
$947$	42.9382	−	24.7904i	1.39530	−	0.805579i	0.993896	+	0.110320i	$0.0351877\pi$
$948$	−8.08314	+	14.7452i	−0.262528	+	0.478902i
$949$	4.92995	−	8.53892i	0.160033	−	0.277185i
$950$	31.3603	+	8.03183i	1.01746	+	0.260587i
$951$	−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	$0.697691\pi$
$954$	1.00501	+	0.257398i	0.0325384	+	0.00833356i
$955$	−14.3320	+	24.8237i	−0.463771	+	0.803275i
$956$	−15.0822	+	27.5129i	−0.487794	+	0.889831i
$957$	−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
$962$	48.1077	−	13.4631i	1.55106	−	0.434069i
$963$	10.8695	+	6.27550i	0.350264	+	0.202225i
$964$	−12.3547	−	20.3446i	−0.397916	−	0.655256i
$965$		−	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	$-0.181231\pi$
$968$	5.88184	−	25.2827i	0.189049	−	0.812617i
$969$	21.1426	+	12.2067i	0.679198	+	0.392135i
$970$	−2.68069	−	9.57887i	−0.0860717	−	0.307559i
$971$	7.35991	+	12.7477i	0.236191	+	0.409094i	0.959618	−	0.281306i	$-0.0907677\pi$
$971$	7.35991	+	12.7477i	0.236191	+	0.409094i	−0.723427	+	0.690401i	$0.757434\pi$
$972$	−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
$976$	32.3512	+	16.8137i	1.03554	+	0.538193i
$977$	4.48644	−	7.77075i	0.143534	−	0.248608i	−0.785291	−	0.619127i	$-0.787487\pi$
$977$	4.48644	−	7.77075i	0.143534	−	0.248608i	0.928825	+	0.370519i	$0.120820\pi$
$978$	1.98594	−	7.75412i	0.0635035	−	0.247949i
$979$	10.7021			0.342041
$980$		0			0
$981$	−15.2532			−0.486997
$982$	3.01927	−	11.7888i	0.0963489	−	0.376195i
$983$	0.933162	−	1.61628i	0.0297633	−	0.0515515i	−0.850760	−	0.525554i	$-0.823858\pi$
$983$	0.933162	−	1.61628i	0.0297633	−	0.0515515i	0.880523	+	0.474003i	$0.157191\pi$
$984$	−0.122721	−	0.403833i	−0.00391219	−	0.0128737i
$985$	−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
$990$	0.580830	+	2.07547i	0.0184600	+	0.0659629i
$991$	5.62256	+	3.24619i	0.178607	+	0.103119i	0.586638	−	0.809849i	$-0.300451\pi$
$991$	5.62256	+	3.24619i	0.178607	+	0.103119i	−0.408031	+	0.912968i	$0.633785\pi$
$992$	16.1796	+	3.38819i	0.513702	+	0.107575i
$993$		−	5.23999i		−	0.166286i
$994$		0			0
$995$		−	17.2851i		−	0.547974i
$996$	−15.6063	+	9.47723i	−0.494505	+	0.300298i
$997$	−10.6805	−	6.16637i	−0.338254	−	0.195291i	0.321246	−	0.946996i	$-0.395898\pi$
$997$	−10.6805	−	6.16637i	−0.338254	−	0.195291i	−0.659500	+	0.751705i	$0.729232\pi$
$998$	−25.3072	+	7.08234i	−0.801086	+	0.224187i
$999$	−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.31.11		24
4.3	odd	2		588.2.o.f.31.6		24
7.2	even	3	inner	588.2.o.e.19.6		24
7.3	odd	6		588.2.b.c.391.2	yes	12
7.4	even	3		588.2.b.d.391.2	yes	12
7.5	odd	6		588.2.o.f.19.6		24
7.6	odd	2		588.2.o.f.31.11		24
21.11	odd	6		1764.2.b.m.1567.11		12
21.17	even	6		1764.2.b.l.1567.11		12
28.3	even	6		588.2.b.d.391.1	yes	12
28.11	odd	6		588.2.b.c.391.1	✓	12
28.19	even	6	inner	588.2.o.e.19.11		24
28.23	odd	6		588.2.o.f.19.11		24
28.27	even	2	inner	588.2.o.e.31.6		24
84.11	even	6		1764.2.b.l.1567.12		12
84.59	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	28.11	odd	6
588.2.b.c.391.2	yes	12	7.3	odd	6
588.2.b.d.391.1	yes	12	28.3	even	6
588.2.b.d.391.2	yes	12	7.4	even	3
588.2.o.e.19.6		24	7.2	even	3	inner
588.2.o.e.19.11		24	28.19	even	6	inner
588.2.o.e.31.6		24	28.27	even	2	inner
588.2.o.e.31.11		24	1.1	even	1	trivial
588.2.o.f.19.6		24	7.5	odd	6
588.2.o.f.19.11		24	28.23	odd	6
588.2.o.f.31.6		24	4.3	odd	2
588.2.o.f.31.11		24	7.6	odd	2
1764.2.b.l.1567.11		12	21.17	even	6
1764.2.b.l.1567.12		12	84.11	even	6
1764.2.b.m.1567.11		12	21.11	odd	6
1764.2.b.m.1567.12		12	84.59	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+(1.36999 + 0.350876i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(1.75377 + 0.961396i) 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} +(-1.53738 + 0.430244i) q^{10} +(1.16914 + 0.675002i) q^{11} +(-1.70948 + 1.03811i) q^{12} +5.58489i q^{13} -1.12886i q^{15} +(2.15144 + 3.37214i) q^{16} +(3.44113 + 1.98674i) q^{17} +(-0.381130 - 1.36189i) 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} +(-2.70623 + 0.822395i) q^{24} +(-1.86283 + 3.22652i) q^{25} +(-1.95960 + 7.65127i) q^{26} +1.00000 q^{27} +8.55270 q^{29} +(0.396091 - 1.54654i) q^{30} +(1.46111 - 2.53071i) q^{31} +(1.76425 + 5.37470i) 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} +(-2.34170 - 8.36756i) q^{38} +(-4.83666 - 2.79245i) q^{39} +(-3.10986 - 0.723486i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(1.40146 + 2.30780i) q^{44} +(0.977624 + 0.564431i) q^{45} +(-9.00745 + 2.52077i) 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} +(-5.36929 + 9.79463i) q^{52} +(-0.366793 + 0.635305i) q^{53} +(1.36999 + 0.350876i) q^{54} -1.52397 q^{55} +6.14408 q^{57} +(11.7172 + 3.00093i) q^{58} +(7.20270 - 12.4754i) q^{59} +(1.08528 - 1.97977i) 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} +(-1.83855 + 0.514527i) q^{66} +(-0.202730 - 0.117046i) q^{67} +(4.12492 + 6.79257i) q^{68} -6.61394i q^{69} +8.74104i q^{71} +(0.640898 - 2.75486i) q^{72} +(-1.52893 - 0.882729i) q^{73} +(-2.41064 - 8.61391i) 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} +(-4.00664 - 2.08235i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0523589 + 0.204435i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(3.73883 - 14.5983i) q^{86} +(-4.27635 + 7.40685i) q^{87} +(1.11024 + 3.65342i) 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} +(1.37013 + 4.89588i) q^{94} +(6.00660 + 3.46791i) q^{95} +(-5.53675 - 1.15946i) 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

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Representations

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Database

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