LMFDB - Embedded newform 588.2.o.f.19.11

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			19.11
Character	$\chi$	$=$	588.19
Dual form			588.2.o.f.31.11

$q$-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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	$-0.252106\pi$
$5$	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
$10$	1.53738	+	0.430244i	0.486164	+	0.136055i
$11$	1.16914	−	0.675002i	0.352508	−	0.203521i	−0.313281	−	0.949660i	$-0.601428\pi$
$11$	1.16914	−	0.675002i	0.352508	−	0.203521i	0.665789	+	0.746140i	$0.268095\pi$
$12$	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	$-0.826703\pi$
$17$	−3.44113	+	1.98674i	−0.834597	+	0.481855i	0.0208273	+	0.999783i	$0.493370\pi$
$18$	−0.381130	+	1.36189i	−0.0898332	+	0.321000i
$19$	3.07204	−	5.32093i	0.704775	−	1.22071i	−0.261998	−	0.965068i	$-0.584381\pi$
$19$	3.07204	−	5.32093i	0.704775	−	1.22071i	0.966773	−	0.255637i	$-0.0822853\pi$
$20$	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	−0.235051	−	0.971983i	$-0.575526\pi$
$23$	−5.72784	−	3.30697i	−1.19434	−	0.689551i	−0.959287	+	0.282432i	$0.908859\pi$
$24$	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	$-0.251188\pi$
$31$	−1.46111	−	2.53071i	−0.262422	−	0.454529i	−0.966885	+	0.255212i	$0.917855\pi$
$32$	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	0.479823	+	0.877366i	$0.340701\pi$
$37$	−3.16249	+	5.47759i	−0.519910	+	0.900510i	−0.999732	+	0.0231442i	$0.992632\pi$
$38$	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	$0.301889\pi$
$43$			10.6557i			1.62498i	−0.582974	+	0.812491i	$0.698111\pi$
$44$	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	$-0.917777\pi$
$47$	−1.79746	+	3.11329i	−0.262186	+	0.454120i	0.704636	+	0.709569i	$0.251110\pi$
$48$	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	0.839734	−	0.542998i	$-0.182711\pi$
$53$	−0.366793	−	0.635305i	−0.0503830	−	0.0872658i	−0.890117	+	0.455732i	$0.849378\pi$
$54$	−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	−0.769726	−	0.638375i	$-0.779607\pi$
$59$	−7.20270	−	12.4754i	−0.937712	−	1.62416i	−0.167986	−	0.985789i	$-0.553726\pi$
$60$	1.08528	+	1.97977i	0.140110	+	0.255587i
$61$	−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
$66$	1.83855	+	0.514527i	0.226310	+	0.0633339i
$67$	−0.202730	+	0.117046i	−0.0247674	+	0.0142995i	−0.512333	−	0.858787i	$-0.671218\pi$
$67$	−0.202730	+	0.117046i	−0.0247674	+	0.0142995i	0.487565	+	0.873087i	$0.337885\pi$
$68$	−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	$-0.826422\pi$
$71$		−	8.74104i		−	1.03737i	0.854965	−	0.518685i	$-0.173578\pi$
$72$	0.640898	+	2.75486i	0.0755306	+	0.324663i
$73$	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	$0.300388\pi$
$74$	−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	0.850144	−	0.526551i	$-0.176515\pi$
$79$	7.28129	+	4.20385i	0.819209	+	0.472971i	−0.0309346	+	0.999521i	$0.509848\pi$
$80$	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	$-0.667047\pi$
$83$	−9.12928			−1.00207			−0.501035	+	0.865427i	$0.667047\pi$
$84$		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	$-0.471358\pi$
$89$	−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
$94$	−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	$-0.679259\pi$
$101$	−0.688456	+	0.397480i	−0.0685040	+	0.0395508i	0.465357	+	0.885123i	$0.345926\pi$
$102$	−5.41143	−	1.51441i	−0.535811	−	0.149949i
$103$	1.67738	−	2.90531i	0.165277	−	0.286268i	−0.771477	−	0.636258i	$-0.780482\pi$
$103$	1.67738	−	2.90531i	0.165277	−	0.286268i	0.936754	+	0.349989i	$0.113815\pi$
$104$	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	−0.127921	−	0.991784i	$-0.540831\pi$
$107$	−10.8695	−	6.27550i	−1.05079	−	0.606675i	−0.922871	+	0.385109i	$0.874164\pi$
$108$	−1.75377	+	0.961396i	−0.168757	+	0.0925104i
$109$	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	$0.572622\pi$
$110$	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	$0.0499798\pi$
$127$			3.52444i			0.312743i	−0.987698	+	0.156372i	$0.950020\pi$
$128$	−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	$-0.866376\pi$
$131$	−1.18600	+	2.05421i	−0.103621	+	0.179477i	0.809553	+	0.587047i	$0.199710\pi$
$132$	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	0.977600	−	0.210471i	$-0.0674997\pi$
$137$	3.58780	+	6.21426i	0.306527	+	0.530920i	−0.671073	+	0.741391i	$0.734166\pi$
$138$	−2.32067	−	9.06107i	−0.197549	−	0.771330i
$139$	22.5888			1.91595			0.957977	−	0.286845i	$-0.0926064\pi$
$139$	22.5888			1.91595			0.957977	+	0.286845i	$0.0926064\pi$
$140$		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	−0.545898	−	0.837852i	$-0.683811\pi$
$149$	5.52532	−	9.57014i	0.452652	−	0.784016i	0.998550	+	0.0538356i	$0.0171447\pi$
$150$	1.41996	−	5.07395i	0.115940	−	0.414286i
$151$	1.33325	−	0.769750i	0.108498	−	0.0626413i	−0.444769	−	0.895645i	$-0.646714\pi$
$151$	1.33325	−	0.769750i	0.108498	−	0.0626413i	0.553267	+	0.833004i	$0.313381\pi$
$152$	−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	$-0.555711\pi$
$157$	7.41273	−	4.27974i	0.591600	−	0.341560i	0.765730	+	0.643162i	$0.222378\pi$
$158$	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	0.295598	−	0.955313i	$-0.404481\pi$
$163$	−4.90167	−	2.82998i	−0.383929	−	0.221661i	−0.679526	+	0.733651i	$0.737815\pi$
$164$	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	$-0.560007\pi$
$167$	−4.84357			−0.374807			−0.187403	+	0.982283i	$0.560007\pi$
$168$		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	$-0.358816\pi$
$173$	−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
$178$	−10.7963	−	3.02140i	−0.809218	−	0.226463i
$179$	−3.47076	+	2.00384i	−0.259417	+	0.149774i	−0.624068	−	0.781370i	$-0.714521\pi$
$179$	−3.47076	+	2.00384i	−0.259417	+	0.149774i	0.364652	+	0.931144i	$0.381188\pi$
$180$	−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	0.993112	+	0.117170i	$0.0373823\pi$
$191$	21.9900	+	12.6959i	1.59114	+	0.918645i	0.598028	+	0.801475i	$0.295951\pi$
$192$	7.17850	−	3.53117i	0.518064	−	0.254840i
$193$	−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	$0.834174\pi$
$194$	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	0.998747	+	0.0500500i	$0.0159381\pi$
$199$	7.65598	+	13.2605i	0.542718	+	0.940015i	−0.456029	+	0.889965i	$0.650729\pi$
$200$	−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	$0.156985\pi$
$211$			13.7540i			0.946861i	−0.880831	+	0.473431i	$0.843015\pi$
$212$	−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	$-0.314812\pi$
$223$	16.4120			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$224$		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	0.999146	+	0.0413183i	$0.0131558\pi$
$227$	8.06595	+	13.9706i	0.535356	+	0.927263i	−0.463790	+	0.885945i	$0.653511\pi$
$228$	10.7753	−	5.90690i	0.713613	−	0.391194i
$229$	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	$-0.0475779\pi$
$234$	−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	$-0.830614\pi$
$239$		−	15.6878i		−	1.01476i	0.861722	−	0.507381i	$-0.169386\pi$
$240$	3.80668	+	2.42868i	0.245720	+	0.156770i
$241$	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	$0.208118\pi$
$242$	−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	$-0.483043\pi$
$251$	1.68715			0.106492			0.0532459	+	0.998581i	$0.483043\pi$
$252$		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	$-0.101824\pi$
$257$	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
$262$	−0.904038	+	3.23039i	−0.0558516	+	0.199574i
$263$	−10.0326	+	5.79230i	−0.618634	+	0.357169i	−0.776337	−	0.630318i	$-0.782925\pi$
$263$	−10.0326	+	5.79230i	−0.618634	+	0.357169i	0.157703	+	0.987487i	$0.449591\pi$
$264$	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	$-0.595693\pi$
$269$	6.28171	−	3.62675i	0.383003	−	0.221127i	0.679124	+	0.734024i	$0.262360\pi$
$270$	−1.53738	−	0.430244i	−0.0935623	−	0.0261838i
$271$	−14.5072	+	25.1272i	−0.881249	+	1.52637i	−0.0312948	+	0.999510i	$0.509963\pi$
$271$	−14.5072	+	25.1272i	−0.881249	+	1.52637i	−0.849954	+	0.526857i	$0.823370\pi$
$272$	−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	0.871163	−	0.490994i	$-0.163366\pi$
$277$	0.172570	+	0.298901i	0.0103688	+	0.0179592i	−0.860794	+	0.508953i	$0.830033\pi$
$278$	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	−0.901373	−	0.433044i	$-0.857440\pi$
$283$	−13.8906	−	24.0593i	−0.825713	−	1.43018i	0.0756596	−	0.997134i	$-0.475894\pi$
$284$	−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	$-0.782724\pi$
$307$	−27.1911			−1.55188			−0.775939	+	0.630808i	$0.782724\pi$
$308$		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	0.993801	+	0.111177i	$0.0354620\pi$
$311$	10.4609	+	18.1188i	0.593182	+	1.02742i	−0.400618	+	0.916245i	$0.631205\pi$
$312$	−4.59299	+	15.1140i	−0.260027	+	0.855661i
$313$	−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	$0.0482028\pi$
$318$	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	0.370074	−	0.929002i	$-0.379332\pi$
$331$	−4.53796	−	2.61999i	−0.249429	−	0.144008i	−0.619503	+	0.784994i	$0.712666\pi$
$332$	−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	−0.515162	−	0.857093i	$-0.672268\pi$
$347$	−0.567776	+	0.327806i	−0.0304798	+	0.0175975i	0.484683	+	0.874690i	$0.338935\pi$
$348$	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	$-0.373984\pi$
$353$	25.8806	−	14.9422i	1.37749	−	0.795292i	0.991856	+	0.127361i	$0.0406507\pi$
$354$	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	0.759384	−	0.650642i	$-0.225500\pi$
$359$	10.9061	+	6.29666i	0.575604	+	0.332325i	−0.183781	+	0.982967i	$0.558834\pi$
$360$	−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	$-0.121076\pi$
$367$	2.73446	+	4.73623i	0.142738	+	0.247229i	−0.785789	+	0.618495i	$0.787743\pi$
$368$	−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	−0.607284	−	0.794485i	$-0.707741\pi$
$373$	7.42404	−	12.8588i	0.384402	−	0.665805i	0.991686	+	0.128681i	$0.0410742\pi$
$374$	−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	$-0.712017\pi$
$379$		−	30.6135i		−	1.57251i	0.617901	−	0.786256i	$-0.287983\pi$
$380$	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	0.392999	+	0.919539i	$0.371438\pi$
$383$	−11.7392	+	20.3329i	−0.599844	+	1.03896i	−0.992844	+	0.119422i	$0.961896\pi$
$384$	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	0.803747	+	0.594972i	$0.202837\pi$
$389$	18.0887	+	31.3306i	0.917134	+	1.58852i	0.113387	+	0.993551i	$0.463830\pi$
$390$	−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	$-0.343973\pi$
$397$	−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	$0.941152\pi$
$402$	−0.318808	−	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	$-0.773492\pi$
$409$	−11.5362	+	6.66044i	−0.570429	+	0.329337i	0.186892	+	0.982381i	$0.440159\pi$
$410$	−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	$-0.440986\pi$
$419$	7.54663			0.368677			0.184339	+	0.982863i	$0.440986\pi$
$420$		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	−0.726991	−	0.686647i	$-0.759082\pi$
$431$	−10.2938	+	5.94311i	−0.495833	+	0.286269i	0.231158	+	0.972916i	$0.425749\pi$
$432$	−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	$-0.792042\pi$
$439$	2.71032	−	4.69441i	0.129356	−	0.224052i	0.923427	+	0.383773i	$0.125376\pi$
$440$	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	−0.0460432	−	0.998939i	$-0.514661\pi$
$443$	−19.6620	−	11.3519i	−0.934172	−	0.539344i	−0.888129	+	0.459595i	$0.847995\pi$
$444$	−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	−0.595274	−	0.803523i	$-0.702956\pi$
$457$	8.51329	−	14.7454i	0.398235	−	0.689763i	0.993508	+	0.113760i	$0.0362896\pi$
$458$	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	$0.0102799\pi$
$463$			1.38958i			0.0645794i	−0.999479	+	0.0322897i	$0.989720\pi$
$464$	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	$-0.859093\pi$
$467$	−1.74691	+	3.02573i	−0.0808372	+	0.140014i	0.822773	+	0.568371i	$0.192426\pi$
$468$	−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	$-0.0651726\pi$
$479$	6.86079	+	11.8832i	0.313478	+	0.542959i	−0.665635	+	0.746277i	$0.731839\pi$
$480$	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	−0.571966	−	0.820277i	$-0.693819\pi$
$487$	−3.25655	+	1.88017i	−0.147569	+	0.0851987i	0.424398	+	0.905476i	$0.360486\pi$
$488$	−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	$0.0622008\pi$
$491$			8.60497i			0.388337i	−0.980968	+	0.194168i	$0.937799\pi$
$492$	−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	0.0944896	−	0.995526i	$-0.469878\pi$
$499$	−16.0929	−	9.29123i	−0.720416	−	0.415933i	−0.814906	+	0.579593i	$0.803211\pi$
$500$	−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	$-0.232054\pi$
$503$	33.4544			1.49166			0.745828	+	0.666139i	$0.232054\pi$
$504$		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	$-0.511789\pi$
$509$	−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
$514$	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	$-0.566856\pi$
$521$	12.1946	−	7.04055i	0.534255	−	0.308452i	0.742747	+	0.669572i	$0.233522\pi$
$522$	−3.25969	+	11.6478i	−0.142673	+	0.509811i
$523$	17.5726	−	30.4366i	0.768396	−	1.33090i	−0.170037	−	0.985438i	$-0.554389\pi$
$523$	17.5726	−	30.4366i	0.768396	−	1.33090i	0.938432	−	0.345463i	$-0.112278\pi$
$524$	−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	−0.969714	−	0.244245i	$-0.921460\pi$
$541$	−6.35759	+	11.0117i	−0.273334	+	0.473429i	0.696379	+	0.717674i	$0.254793\pi$
$542$	−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	$0.356456\pi$
$547$			42.0999i			1.80006i	−0.435828	+	0.900030i	$0.643544\pi$
$548$	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	0.647239	−	0.762287i	$-0.275923\pi$
$557$	−7.94263	−	13.7570i	−0.336540	−	0.582905i	−0.983779	+	0.179382i	$0.942590\pi$
$558$	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	−0.970623	−	0.240604i	$-0.922655\pi$
$563$	−16.4594	−	28.5085i	−0.693681	−	1.20149i	0.276943	−	0.960886i	$-0.410679\pi$
$564$	−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	0.222159	+	0.975010i	$0.428690\pi$
$569$	−17.4920	+	30.2971i	−0.733304	+	1.27012i	−0.955463	+	0.295110i	$0.904644\pi$
$570$	9.44582	+	2.64345i	0.395642	+	0.110722i
$571$	−5.63066	+	3.25087i	−0.235636	+	0.136044i	−0.613169	−	0.789951i	$-0.710106\pi$
$571$	−5.63066	+	3.25087i	−0.235636	+	0.136044i	0.377533	+	0.925996i	$0.376772\pi$
$572$	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	$-0.948719\pi$
$577$	−32.2277	+	18.6067i	−1.34166	+	0.774606i	−0.354607	+	0.935016i	$0.615385\pi$
$578$	−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	$-0.670956\pi$
$587$	−24.7914			−1.02325			−0.511625	+	0.859209i	$0.670956\pi$
$588$		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	$-0.552979\pi$
$593$	−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
$598$	14.0782	−	50.3056i	0.575702	−	2.05715i
$599$	−7.12727	+	4.11493i	−0.291212	+	0.168131i	−0.638488	−	0.769631i	$-0.720440\pi$
$599$	−7.12727	+	4.11493i	−0.291212	+	0.168131i	0.347276	+	0.937763i	$0.387107\pi$
$600$	−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	$-0.916005\pi$
$607$	−6.32713	+	10.9589i	−0.256810	+	0.444808i	0.708575	+	0.705635i	$0.249338\pi$
$608$	−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	0.861416	−	0.507900i	$-0.169578\pi$
$613$	−0.226457	−	0.392236i	−0.00914652	−	0.0158422i	−0.870562	+	0.492058i	$0.836245\pi$
$614$	−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	$-0.153592\pi$
$619$	1.02161	+	1.76949i	0.0410622	+	0.0711218i	−0.844764	+	0.535139i	$0.820259\pi$
$620$	−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	$-0.718123\pi$
$631$		−	38.8983i		−	1.54852i	0.632870	−	0.774258i	$-0.281877\pi$
$632$	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	0.885656	−	0.464341i	$-0.153709\pi$
$641$	1.03036	+	1.78464i	0.0406969	+	0.0704891i	−0.844959	+	0.534830i	$0.820376\pi$
$642$	−4.40384	−	17.1948i	−0.173806	−	0.678625i
$643$	2.86029			0.112799			0.0563994	−	0.998408i	$-0.482038\pi$
$643$	2.86029			0.112799			0.0563994	+	0.998408i	$0.482038\pi$
$644$		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	$-0.291263\pi$
$647$	−9.70418	−	16.8081i	−0.381511	−	0.660796i	−0.991278	+	0.131784i	$0.957929\pi$
$648$	−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	−0.858798	−	0.512314i	$-0.828788\pi$
$653$	0.364864	−	0.631964i	0.0142783	−	0.0247307i	0.873076	+	0.487584i	$0.162122\pi$
$654$	−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	$0.125298\pi$
$659$			19.6921i			0.767097i	−0.923521	+	0.383548i	$0.874702\pi$
$660$	2.60519	+	1.58205i	0.101407	+	0.0615813i
$661$	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	$0.274780\pi$
$662$	−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	$-0.131647\pi$
$677$	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
$682$	−5.37264	−	1.50356i	−0.205729	−	0.0575742i
$683$	−36.0508	+	20.8140i	−1.37945	+	0.796424i	−0.992093	−	0.125507i	$-0.959944\pi$
$683$	−36.0508	+	20.8140i	−1.37945	+	0.796424i	−0.387354	+	0.921931i	$0.626611\pi$
$684$	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	$-0.886793\pi$
$691$	−4.39414	+	7.61087i	−0.167161	+	0.289531i	0.770260	+	0.637730i	$0.220127\pi$
$692$	−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	0.365338	+	0.930875i	$0.380953\pi$
$709$	−16.6018	+	28.7551i	−0.623492	+	1.07992i	−0.988830	+	0.149045i	$0.952380\pi$
$710$	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	0.398586	+	0.917131i	$0.369501\pi$
$719$	−15.9535	+	27.6323i	−0.594966	+	1.03051i	−0.993552	+	0.113380i	$0.963832\pi$
$720$	−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	$-0.429633\pi$
$727$	11.8242			0.438535			0.219268	+	0.975665i	$0.429633\pi$
$728$		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	$-0.263296\pi$
$733$	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
$738$	−0.203226	−	0.0568736i	−0.00748084	−	0.00209354i
$739$	−23.0318	+	13.2974i	−0.847237	+	0.489153i	−0.859718	−	0.510770i	$-0.829361\pi$
$739$	−23.0318	+	13.2974i	−0.847237	+	0.489153i	0.0124806	+	0.999922i	$0.496027\pi$
$740$	−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	$-0.778770\pi$
$743$		−	34.9119i		−	1.28079i	0.768045	−	0.640396i	$-0.221230\pi$
$744$	−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	0.526933	−	0.849907i	$-0.323342\pi$
$751$	1.48965	+	0.860048i	0.0543580	+	0.0313836i	−0.472575	+	0.881291i	$0.656675\pi$
$752$	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	$-0.497283\pi$
$761$	−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
$766$	−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	$-0.825161\pi$
$773$	−22.9995	+	13.2788i	−0.827234	+	0.477604i	0.0256709	+	0.999670i	$0.491828\pi$
$774$	−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	$-0.0230343\pi$
$787$	12.2335	+	21.1890i	0.436077	+	0.755307i	−0.561306	+	0.827608i	$0.689701\pi$
$788$	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	0.958397	−	0.285440i	$-0.0921396\pi$
$809$	6.59877	+	11.4294i	0.232000	+	0.401836i	−0.726396	+	0.687276i	$0.758806\pi$
$810$	−0.396091	−	1.54654i	−0.0139172	−	0.0543397i
$811$	−4.87597			−0.171219			−0.0856093	−	0.996329i	$-0.527284\pi$
$811$	−4.87597			−0.171219			−0.0856093	+	0.996329i	$0.527284\pi$
$812$		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	−0.921067	−	0.389404i	$-0.872681\pi$
$821$	−3.53291	+	6.11917i	−0.123299	+	0.213561i	0.797768	+	0.602965i	$0.206014\pi$
$822$	−2.73484	+	9.77238i	−0.0953885	+	0.340851i
$823$	−19.0192	+	10.9807i	−0.662966	+	0.382764i	−0.793406	−	0.608692i	$-0.791694\pi$
$823$	−19.0192	+	10.9807i	−0.662966	+	0.382764i	0.130440	+	0.991456i	$0.458361\pi$
$824$	−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	$-0.901648\pi$
$827$		−	17.4897i		−	0.608175i	0.952644	−	0.304088i	$-0.0983515\pi$
$828$	6.86603	−	11.3064i	0.238611	−	0.392925i
$829$	−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	$0.479987\pi$
$830$	−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	$-0.450096\pi$
$839$	9.04513			0.312273			0.156136	+	0.987736i	$0.450096\pi$
$840$		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	$-0.357016\pi$
$857$	41.9058	−	24.1943i	1.43148	−	0.826463i	0.997233	+	0.0743338i	$0.0236830\pi$
$858$	−2.87358	+	10.2681i	−0.0981023	+	0.350548i
$859$	9.91892	−	17.1801i	0.338429	−	0.586176i	−0.645708	−	0.763584i	$-0.723438\pi$
$859$	9.91892	−	17.1801i	0.338429	−	0.586176i	0.984137	+	0.177408i	$0.0567711\pi$
$860$	−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	−0.196427	−	0.980518i	$-0.562934\pi$
$863$	−33.6011	−	19.3996i	−1.14379	−	0.660370i	−0.947367	+	0.320148i	$0.896267\pi$
$864$	−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	−0.711535	−	0.702651i	$-0.752000\pi$
$877$	7.48487	−	12.9642i	0.252746	−	0.437769i	0.964281	+	0.264882i	$0.0853330\pi$
$878$	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	$-0.890213\pi$
$883$		−	20.0940i		−	0.676217i	0.941107	−	0.338109i	$-0.109787\pi$
$884$	−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	$-0.915550\pi$
$887$	−7.60734	+	13.1763i	−0.255430	+	0.442417i	0.709583	+	0.704622i	$0.248884\pi$
$888$	−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	−0.689106	−	0.724661i	$-0.741997\pi$
$907$	−12.2298	+	7.06089i	−0.406084	+	0.234453i	0.283022	+	0.959114i	$0.408663\pi$
$908$	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	$-0.933332\pi$
$911$		−	12.5510i		−	0.415832i	0.978147	−	0.207916i	$-0.0666681\pi$
$912$	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	−0.100824	−	0.994904i	$-0.532148\pi$
$919$	−30.7045	−	17.7272i	−1.01285	−	0.584768i	−0.912024	+	0.410136i	$0.865481\pi$
$920$	−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	0.995264	+	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
$934$	−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	$-0.439034\pi$
$941$	34.8394	−	20.1145i	1.13573	−	0.655715i	0.945370	+	0.325999i	$0.105701\pi$
$942$	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	0.993896	−	0.110320i	$-0.0351877\pi$
$947$	42.9382	+	24.7904i	1.39530	+	0.805579i	0.401408	+	0.915899i	$0.368521\pi$
$948$	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	$0.181231\pi$
$967$			33.5277i			1.07818i	−0.842249	+	0.539089i	$0.818769\pi$
$968$	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	$-0.909232\pi$
$971$	−7.35991	+	12.7477i	−0.236191	+	0.409094i	0.723427	+	0.690401i	$0.242566\pi$
$972$	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	0.928825	−	0.370519i	$-0.120820\pi$
$977$	4.48644	+	7.77075i	0.143534	+	0.248608i	−0.785291	+	0.619127i	$0.787487\pi$
$978$	−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	$-0.176142\pi$
$983$	−0.933162	−	1.61628i	−0.0297633	−	0.0515515i	−0.880523	+	0.474003i	$0.842809\pi$
$984$	−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	−0.408031	−	0.912968i	$-0.633785\pi$
$991$	5.62256	−	3.24619i	0.178607	−	0.103119i	0.586638	+	0.809849i	$0.300451\pi$
$992$	−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	$-0.604102\pi$
$997$	10.6805	−	6.16637i	0.338254	−	0.195291i	0.659500	+	0.751705i	$0.270768\pi$
$998$	−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.f.19.11		24
4.3	odd	2		588.2.o.e.19.6		24
7.2	even	3		588.2.b.c.391.1	✓	12
7.3	odd	6		588.2.o.e.31.6		24
7.4	even	3	inner	588.2.o.f.31.6		24
7.5	odd	6		588.2.b.d.391.1	yes	12
7.6	odd	2		588.2.o.e.19.11		24
21.2	odd	6		1764.2.b.l.1567.12		12
21.5	even	6		1764.2.b.m.1567.12		12
28.3	even	6	inner	588.2.o.f.31.11		24
28.11	odd	6		588.2.o.e.31.11		24
28.19	even	6		588.2.b.c.391.2	yes	12
28.23	odd	6		588.2.b.d.391.2	yes	12
28.27	even	2	inner	588.2.o.f.19.6		24
84.23	even	6		1764.2.b.m.1567.11		12
84.47	odd	6		1764.2.b.l.1567.11		12

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

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