LMFDB - Embedded newform 90.2.i.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,2,Mod(49,90)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("90.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	90.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	90.49
Dual form			90.2.i.b.79.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.57313 - 0.724745i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.03906 + 0.917738i) q^{5} +(1.72474 - 0.158919i) q^{6} +(3.85337 - 2.22474i) q^{7} +1.00000i q^{8} +(1.94949 + 2.28024i) q^{9} +(-2.22474 + 0.224745i) q^{10} +(-0.724745 - 1.25529i) q^{11} +(-1.41421 + 1.00000i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(-2.22474 + 3.85337i) q^{14} +(-2.54258 - 2.92152i) q^{15} +(-0.500000 - 0.866025i) q^{16} +3.89898i q^{17} +(-2.82843 - 1.00000i) q^{18} +0.550510 q^{19} +(1.81431 - 1.30701i) q^{20} +(-7.67423 + 0.707107i) q^{21} +(1.25529 + 0.724745i) q^{22} +(-2.51059 - 1.44949i) q^{23} +(0.724745 - 1.57313i) q^{24} +(3.31552 + 3.74264i) q^{25} +2.44949 q^{26} +(-1.41421 - 5.00000i) q^{27} -4.44949i q^{28} +(-3.00000 - 5.19615i) q^{29} +(3.66270 + 1.25882i) q^{30} +(-3.22474 + 5.58542i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.230351 + 2.50000i) q^{33} +(-1.94949 - 3.37662i) q^{34} +(9.89898 - 1.00000i) q^{35} +(2.94949 - 0.548188i) q^{36} +8.00000i q^{37} +(-0.476756 + 0.275255i) q^{38} +(2.44949 + 3.46410i) q^{39} +(-0.917738 + 2.03906i) q^{40} +(0.500000 - 0.866025i) q^{41} +(6.29253 - 4.44949i) q^{42} +(-6.45145 + 3.72474i) q^{43} -1.44949 q^{44} +(1.88246 + 6.43866i) q^{45} +2.89898 q^{46} +(0.389270 - 0.224745i) q^{47} +(0.158919 + 1.72474i) q^{48} +(6.39898 - 11.0834i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(2.82577 - 6.13361i) q^{51} +(-2.12132 + 1.22474i) q^{52} -8.44949i q^{53} +(3.72474 + 3.62302i) q^{54} +(-0.325765 - 3.22474i) q^{55} +(2.22474 + 3.85337i) q^{56} +(-0.866025 - 0.398979i) q^{57} +(5.19615 + 3.00000i) q^{58} +(-5.62372 + 9.74058i) q^{59} +(-3.80140 + 0.741181i) q^{60} +(0.224745 + 0.389270i) q^{61} -6.44949i q^{62} +(12.5851 + 4.44949i) q^{63} -1.00000 q^{64} +(-3.20150 - 4.44414i) q^{65} +(-1.44949 - 2.04989i) q^{66} +(-8.18350 - 4.72474i) q^{67} +(3.37662 + 1.94949i) q^{68} +(2.89898 + 4.09978i) q^{69} +(-8.07277 + 5.81552i) q^{70} +2.44949 q^{71} +(-2.28024 + 1.94949i) q^{72} +4.79796i q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.50328 - 8.29057i) q^{75} +(0.275255 - 0.476756i) q^{76} +(-5.58542 - 3.22474i) q^{77} +(-3.85337 - 1.77526i) q^{78} +(-3.67423 - 6.36396i) q^{79} +(-0.224745 - 2.22474i) q^{80} +(-1.39898 + 8.89060i) q^{81} +1.00000i q^{82} +(3.46410 - 2.00000i) q^{83} +(-3.22474 + 6.99964i) q^{84} +(-3.57824 + 7.95025i) q^{85} +(3.72474 - 6.45145i) q^{86} +(0.953512 + 10.3485i) q^{87} +(1.25529 - 0.724745i) q^{88} -12.8990 q^{89} +(-4.84959 - 4.63481i) q^{90} -10.8990 q^{91} +(-2.51059 + 1.44949i) q^{92} +(9.12096 - 6.44949i) q^{93} +(-0.224745 + 0.389270i) q^{94} +(1.12252 + 0.505224i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(11.2583 - 6.50000i) q^{97} +12.7980i q^{98} +(1.44949 - 4.09978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{9} - 8 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{15} - 4 q^{16} + 24 q^{19} + 4 q^{20} - 32 q^{21} - 4 q^{24} - 24 q^{29} + 16 q^{30} - 16 q^{31} + 4 q^{34} + 40 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^9 - 8 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^15 - 4 * q^16 + 24 * q^19 + 4 * q^20 - 32 * q^21 - 4 * q^24 - 24 * q^29 + 16 * q^30 - 16 * q^31 + 4 * q^34 + 40 * q^35 + 4 * q^36 - 4 * q^40 + 4 * q^41 + 8 * q^44 + 20 * q^45 - 16 * q^46 + 12 * q^49 - 4 * q^50 + 52 * q^51 + 20 * q^54 - 32 * q^55 + 8 * q^56 + 4 * q^59 - 16 * q^60 - 8 * q^61 - 8 * q^64 - 12 * q^65 + 8 * q^66 - 16 * q^69 + 4 * q^70 - 32 * q^74 - 4 * q^75 + 12 * q^76 + 8 * q^80 + 28 * q^81 - 16 * q^84 - 20 * q^85 + 20 * q^86 - 64 * q^89 - 20 * q^90 - 48 * q^91 + 8 * q^94 - 24 * q^95 - 8 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.57313	−	0.724745i	−0.908248	−	0.418432i
$3$	−1.57313	−	0.724745i	−0.908248	−	0.418432i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.03906	+	0.917738i	0.911894	+	0.410425i
$5$	2.03906	+	0.917738i	0.911894	+	0.410425i
$6$	1.72474	−	0.158919i	0.704124	−	0.0648783i
$7$	3.85337	−	2.22474i	1.45644	−	0.840875i	0.457604	−	0.889156i	$-0.348708\pi$
$7$	3.85337	−	2.22474i	1.45644	−	0.840875i	0.998834	+	0.0482818i	$0.0153745\pi$
$8$			1.00000i			0.353553i
$9$	1.94949	+	2.28024i	0.649830	+	0.760080i
$10$	−2.22474	+	0.224745i	−0.703526	+	0.0710706i
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	0.735837	−	0.677159i	$-0.236789\pi$
$11$	−0.724745	−	1.25529i	−0.218519	−	0.378486i	−0.954355	+	0.298674i	$0.903456\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	0.176096	−	0.984373i	$-0.443653\pi$
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	−0.764444	+	0.644690i	$0.776986\pi$
$14$	−2.22474	+	3.85337i	−0.594588	+	1.02986i
$15$	−2.54258	−	2.92152i	−0.656492	−	0.754333i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			3.89898i			0.945641i	0.881159	+	0.472821i	$0.156764\pi$
$17$			3.89898i			0.945641i	−0.881159	+	0.472821i	$0.843236\pi$
$18$	−2.82843	−	1.00000i	−0.666667	−	0.235702i
$19$	0.550510			0.126296			0.0631479	−	0.998004i	$-0.479886\pi$
$19$	0.550510			0.126296			0.0631479	+	0.998004i	$0.479886\pi$
$20$	1.81431	−	1.30701i	0.405693	−	0.292256i
$21$	−7.67423	+	0.707107i	−1.67466	+	0.154303i
$22$	1.25529	+	0.724745i	0.267630	+	0.154516i
$23$	−2.51059	−	1.44949i	−0.523494	−	0.302240i	0.214869	−	0.976643i	$-0.431068\pi$
$23$	−2.51059	−	1.44949i	−0.523494	−	0.302240i	−0.738363	+	0.674403i	$0.764401\pi$
$24$	0.724745	−	1.57313i	0.147938	−	0.321114i
$25$	3.31552	+	3.74264i	0.663103	+	0.748528i
$26$	2.44949			0.480384
$27$	−1.41421	−	5.00000i	−0.272166	−	0.962250i
$28$		−	4.44949i		−	0.840875i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	3.66270	+	1.25882i	0.668715	+	0.229828i
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	0.416392	+	0.909185i	$0.363294\pi$
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	−0.995573	+	0.0939863i	$0.970039\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.230351	+	2.50000i	0.0400989	+	0.435194i
$34$	−1.94949	−	3.37662i	−0.334335	−	0.579085i
$35$	9.89898	−	1.00000i	1.67323	−	0.169031i
$36$	2.94949	−	0.548188i	0.491582	−	0.0913647i
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	−0.476756	+	0.275255i	−0.0773400	+	0.0446523i
$39$	2.44949	+	3.46410i	0.392232	+	0.554700i
$40$	−0.917738	+	2.03906i	−0.145107	+	0.322403i
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	−0.824338	−	0.566099i	$-0.808452\pi$
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i	0.902424	+	0.430848i	$0.141786\pi$
$42$	6.29253	−	4.44949i	0.970958	−	0.686571i
$43$	−6.45145	+	3.72474i	−0.983836	+	0.568018i	−0.903426	−	0.428744i	$-0.858956\pi$
$43$	−6.45145	+	3.72474i	−0.983836	+	0.568018i	−0.0804103	+	0.996762i	$0.525623\pi$
$44$	−1.44949			−0.218519
$45$	1.88246	+	6.43866i	0.280621	+	0.959819i
$46$	2.89898			0.427431
$47$	0.389270	−	0.224745i	0.0567808	−	0.0327824i	−0.471341	−	0.881951i	$-0.656230\pi$
$47$	0.389270	−	0.224745i	0.0567808	−	0.0327824i	0.528122	+	0.849169i	$0.322896\pi$
$48$	0.158919	+	1.72474i	0.0229379	+	0.248945i
$49$	6.39898	−	11.0834i	0.914140	−	1.58334i
$50$	−4.74264	−	1.58346i	−0.670711	−	0.223936i
$51$	2.82577	−	6.13361i	0.395686	−	0.858877i
$52$	−2.12132	+	1.22474i	−0.294174	+	0.169842i
$53$		−	8.44949i		−	1.16063i	−0.814393	−	0.580313i	$-0.802930\pi$
$53$		−	8.44949i		−	1.16063i	0.814393	−	0.580313i	$-0.197070\pi$
$54$	3.72474	+	3.62302i	0.506874	+	0.493031i
$55$	−0.325765	−	3.22474i	−0.0439262	−	0.434825i
$56$	2.22474	+	3.85337i	0.297294	+	0.514928i
$57$	−0.866025	−	0.398979i	−0.114708	−	0.0528461i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	−5.62372	+	9.74058i	−0.732147	+	1.26812i	0.223817	+	0.974631i	$0.428148\pi$
$59$	−5.62372	+	9.74058i	−0.732147	+	1.26812i	−0.955964	+	0.293484i	$0.905185\pi$
$60$	−3.80140	+	0.741181i	−0.490759	+	0.0956860i
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	0.880055	−	0.474873i	$-0.157506\pi$
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	−0.851279	+	0.524713i	$0.824173\pi$
$62$		−	6.44949i		−	0.819086i
$63$	12.5851	+	4.44949i	1.58557	+	0.560583i
$64$	−1.00000			−0.125000
$65$	−3.20150	−	4.44414i	−0.397097	−	0.551228i
$66$	−1.44949	−	2.04989i	−0.178420	−	0.252324i
$67$	−8.18350	−	4.72474i	−0.999773	−	0.577219i	−0.0915922	−	0.995797i	$-0.529196\pi$
$67$	−8.18350	−	4.72474i	−0.999773	−	0.577219i	−0.908181	+	0.418577i	$0.862529\pi$
$68$	3.37662	+	1.94949i	0.409475	+	0.236410i
$69$	2.89898	+	4.09978i	0.348996	+	0.493555i
$70$	−8.07277	+	5.81552i	−0.964880	+	0.695087i
$71$	2.44949			0.290701			0.145350	−	0.989380i	$-0.453569\pi$
$71$	2.44949			0.290701			0.145350	+	0.989380i	$0.453569\pi$
$72$	−2.28024	+	1.94949i	−0.268729	+	0.229750i
$73$			4.79796i			0.561559i	0.959772	+	0.280779i	$0.0905929\pi$
$73$			4.79796i			0.561559i	−0.959772	+	0.280779i	$0.909407\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	−2.50328	−	8.29057i	−0.289054	−	0.957313i
$76$	0.275255	−	0.476756i	0.0315739	−	0.0546876i
$77$	−5.58542	−	3.22474i	−0.636518	−	0.367494i
$78$	−3.85337	−	1.77526i	−0.436308	−	0.201008i
$79$	−3.67423	−	6.36396i	−0.413384	−	0.716002i	0.581874	−	0.813279i	$-0.302320\pi$
$79$	−3.67423	−	6.36396i	−0.413384	−	0.716002i	−0.995257	+	0.0972777i	$0.968987\pi$
$80$	−0.224745	−	2.22474i	−0.0251272	−	0.248734i
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$			1.00000i			0.110432i
$83$	3.46410	−	2.00000i	0.380235	−	0.219529i	−0.297686	−	0.954664i	$-0.596215\pi$
$83$	3.46410	−	2.00000i	0.380235	−	0.219529i	0.677920	+	0.735135i	$0.262881\pi$
$84$	−3.22474	+	6.99964i	−0.351849	+	0.763723i
$85$	−3.57824	+	7.95025i	−0.388115	+	0.862325i
$86$	3.72474	−	6.45145i	0.401650	−	0.695677i
$87$	0.953512	+	10.3485i	0.102227	+	1.10947i
$88$	1.25529	−	0.724745i	0.133815	−	0.0772581i
$89$	−12.8990			−1.36729			−0.683645	−	0.729815i	$-0.739606\pi$
$89$	−12.8990			−1.36729			−0.683645	+	0.729815i	$0.739606\pi$
$90$	−4.84959	−	4.63481i	−0.511192	−	0.488552i
$91$	−10.8990			−1.14252
$92$	−2.51059	+	1.44949i	−0.261747	+	0.151120i
$93$	9.12096	−	6.44949i	0.945799	−	0.668781i
$94$	−0.224745	+	0.389270i	−0.0231807	+	0.0401501i
$95$	1.12252	+	0.505224i	0.115168	+	0.0518349i
$96$	−1.00000	−	1.41421i	−0.102062	−	0.144338i
$97$	11.2583	−	6.50000i	1.14311	−	0.659975i	0.195911	−	0.980622i	$-0.437234\pi$
$97$	11.2583	−	6.50000i	1.14311	−	0.659975i	0.947199	+	0.320647i	$0.103900\pi$
$98$			12.7980i			1.29279i
$99$	1.44949	−	4.09978i	0.145679	−	0.412043i
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	0.619620	+	6.72474i	0.0613516	+	0.665849i
$103$	8.87455	+	5.12372i	0.874435	+	0.504856i	0.868820	−	0.495129i	$-0.164879\pi$
$103$	8.87455	+	5.12372i	0.874435	+	0.504856i	0.00561582	+	0.999984i	$0.498212\pi$
$104$	1.22474	−	2.12132i	0.120096	−	0.208013i
$105$	−16.2971	−	5.60110i	−1.59044	−	0.546612i
$106$	4.22474	+	7.31747i	0.410343	+	0.710736i
$107$			1.65153i			0.159660i	0.996809	+	0.0798298i	$0.0254377\pi$
$107$			1.65153i			0.159660i	−0.996809	+	0.0798298i	$0.974562\pi$
$108$	−5.03723	−	1.27526i	−0.484708	−	0.122711i
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	1.89449	+	2.62983i	0.180633	+	0.250744i
$111$	5.79796	−	12.5851i	0.550318	−	1.19452i
$112$	−3.85337	−	2.22474i	−0.364109	−	0.210219i
$113$	4.24264	+	2.44949i	0.399114	+	0.230429i	0.686102	−	0.727506i	$-0.259321\pi$
$113$	4.24264	+	2.44949i	0.399114	+	0.230429i	−0.286988	+	0.957934i	$0.592654\pi$
$114$	0.949490	−	0.0874863i	0.0889279	−	0.00819385i
$115$	−3.78899	−	5.25966i	−0.353325	−	0.490466i
$116$	−6.00000			−0.557086
$117$	−1.34278	−	7.22474i	−0.124140	−	0.667928i
$118$		−	11.2474i		−	1.03541i
$119$	8.67423	+	15.0242i	0.795166	+	1.37727i
$120$	2.92152	−	2.54258i	0.266697	−	0.232105i
$121$	4.44949	−	7.70674i	0.404499	−	0.700613i
$122$	−0.389270	−	0.224745i	−0.0352428	−	0.0203474i
$123$	−1.41421	+	1.00000i	−0.127515	+	0.0901670i
$124$	3.22474	+	5.58542i	0.289591	+	0.501586i
$125$	3.32577	+	10.6742i	0.297465	+	0.954733i
$126$	−13.1237	+	2.43916i	−1.16915	+	0.217297i
$127$		−	2.89898i		−	0.257243i	−0.991694	−	0.128621i	$-0.958945\pi$
$127$		−	2.89898i		−	0.257243i	0.991694	−	0.128621i	$-0.0410552\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	12.8485	−	1.18386i	1.13124	−	0.104233i
$130$	4.99465	+	2.24799i	0.438060	+	0.197162i
$131$	2.44949	−	4.24264i	0.214013	−	0.370681i	−0.738954	−	0.673756i	$-0.764680\pi$
$131$	2.44949	−	4.24264i	0.214013	−	0.370681i	0.952967	+	0.303075i	$0.0980132\pi$
$132$	2.28024	+	1.05051i	0.198469	+	0.0914352i
$133$	2.12132	−	1.22474i	0.183942	−	0.106199i
$134$	9.44949			0.816312
$135$	1.70502	−	11.4932i	0.146745	−	0.989174i
$136$	−3.89898			−0.334335
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	−0.384893	−	0.922961i	$-0.625762\pi$
$137$	2.59808	−	1.50000i	0.221969	−	0.128154i	0.606861	+	0.794808i	$0.292428\pi$
$138$	−4.56048	−	2.10102i	−0.388214	−	0.178851i
$139$	−5.62372	+	9.74058i	−0.476998	+	0.826185i	−0.999653	−	0.0263597i	$-0.991608\pi$
$139$	−5.62372	+	9.74058i	−0.476998	+	0.826185i	0.522654	+	0.852545i	$0.324942\pi$
$140$	4.08346	−	9.07277i	0.345116	−	0.766789i
$141$	−0.775255	+	0.0714323i	−0.0652883	+	0.00601568i
$142$	−2.12132	+	1.22474i	−0.178017	+	0.102778i
$143$			3.55051i			0.296909i
$144$	1.00000	−	2.82843i	0.0833333	−	0.235702i
$145$	−1.34847	−	13.3485i	−0.111984	−	1.10853i
$146$	−2.39898	−	4.15515i	−0.198541	−	0.343883i
$147$	−18.0990	+	12.7980i	−1.49278	+	1.05556i
$148$	6.92820	+	4.00000i	0.569495	+	0.328798i
$149$	8.12372	−	14.0707i	0.665521	−	1.15272i	−0.313622	−	0.949548i	$-0.601543\pi$
$149$	8.12372	−	14.0707i	0.665521	−	1.15272i	0.979144	−	0.203169i	$-0.0651241\pi$
$150$	6.31319	+	5.92820i	0.515470	+	0.484036i
$151$	3.44949	+	5.97469i	0.280715	+	0.486213i	0.971561	−	0.236789i	$-0.0760949\pi$
$151$	3.44949	+	5.97469i	0.280715	+	0.486213i	−0.690846	+	0.723002i	$0.742762\pi$
$152$			0.550510i			0.0446523i
$153$	−8.89060	+	7.60102i	−0.718763	+	0.614506i
$154$	6.44949			0.519715
$155$	−11.7014	+	8.42953i	−0.939879	+	0.677076i
$156$	4.22474	−	0.389270i	0.338250	−	0.0311665i
$157$	−13.8564	−	8.00000i	−1.10586	−	0.638470i	−0.168107	−	0.985769i	$-0.553765\pi$
$157$	−13.8564	−	8.00000i	−1.10586	−	0.638470i	−0.937754	+	0.347299i	$0.887099\pi$
$158$	6.36396	+	3.67423i	0.506290	+	0.292306i
$159$	−6.12372	+	13.2922i	−0.485643	+	1.05414i
$160$	1.30701	+	1.81431i	0.103328	+	0.143434i
$161$	−12.8990			−1.01658
$162$	−3.23375	−	8.39898i	−0.254067	−	0.659886i
$163$			0.898979i			0.0704135i	0.999380	+	0.0352068i	$0.0112090\pi$
$163$			0.898979i			0.0704135i	−0.999380	+	0.0352068i	$0.988791\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$	−1.82465	+	5.30905i	−0.142048	+	0.413309i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	20.9989	+	12.1237i	1.62494	+	0.938162i	0.985570	+	0.169266i	$0.0541397\pi$
$167$	20.9989	+	12.1237i	1.62494	+	0.938162i	0.639374	+	0.768896i	$0.279194\pi$
$168$	−0.707107	−	7.67423i	−0.0545545	−	0.592080i
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$	−0.876276	−	8.67423i	−0.0672073	−	0.665283i
$171$	1.07321	+	1.25529i	0.0820707	+	0.0959948i
$172$			7.44949i			0.568018i
$173$	−6.75323	+	3.89898i	−0.513439	+	0.296434i	−0.734246	−	0.678884i	$-0.762464\pi$
$173$	−6.75323	+	3.89898i	−0.513439	+	0.296434i	0.220807	+	0.975317i	$0.429131\pi$
$174$	−6.00000	−	8.48528i	−0.454859	−	0.643268i
$175$	21.1023	+	7.04561i	1.59519	+	0.532598i
$176$	−0.724745	+	1.25529i	−0.0546297	+	0.0946214i
$177$	15.9063	−	11.2474i	1.19559	−	0.845410i
$178$	11.1708	−	6.44949i	0.837290	−	0.483410i
$179$	−8.89898			−0.665141			−0.332570	−	0.943078i	$-0.607916\pi$
$179$	−8.89898			−0.665141			−0.332570	+	0.943078i	$0.607916\pi$
$180$	6.51727	+	1.58907i	0.485769	+	0.118442i
$181$	10.4495			0.776704			0.388352	−	0.921511i	$-0.373044\pi$
$181$	10.4495			0.776704			0.388352	+	0.921511i	$0.373044\pi$
$182$	9.43879	−	5.44949i	0.699650	−	0.403943i
$183$	−0.0714323	−	0.775255i	−0.00528043	−	0.0573085i
$184$	1.44949	−	2.51059i	0.106858	−	0.185083i
$185$	−7.34190	+	16.3125i	−0.539787	+	1.19932i
$186$	−4.67423	+	10.1459i	−0.342732	+	0.743933i
$187$	4.89437	−	2.82577i	0.357912	−	0.206640i
$188$		−	0.449490i		−	0.0327824i
$189$	−16.5732	−	16.1206i	−1.20552	−	1.17260i
$190$	−1.22474	+	0.123724i	−0.0888523	+	0.00897591i
$191$	3.12372	+	5.41045i	0.226025	+	0.391486i	0.956626	−	0.291318i	$-0.0940936\pi$
$191$	3.12372	+	5.41045i	0.226025	+	0.391486i	−0.730602	+	0.682804i	$0.760760\pi$
$192$	1.57313	+	0.724745i	0.113531	+	0.0523040i
$193$	−13.5939	−	7.84847i	−0.978514	−	0.564945i	−0.0766927	−	0.997055i	$-0.524436\pi$
$193$	−13.5939	−	7.84847i	−0.978514	−	0.564945i	−0.901821	+	0.432110i	$0.857769\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	1.81552	+	9.31149i	0.130012	+	0.666810i
$196$	−6.39898	−	11.0834i	−0.457070	−	0.791668i
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$	0.794593	+	4.27526i	0.0564693	+	0.303829i
$199$	−20.4495			−1.44963			−0.724813	−	0.688946i	$-0.758074\pi$
$199$	−20.4495			−1.44963			−0.724813	+	0.688946i	$0.758074\pi$
$200$	−3.74264	+	3.31552i	−0.264645	+	0.234442i
$201$	9.44949	+	13.3636i	0.666516	+	0.942595i
$202$	−6.92820	−	4.00000i	−0.487467	−	0.281439i
$203$	−23.1202	−	13.3485i	−1.62272	−	0.936879i
$204$	−3.89898	−	5.51399i	−0.272983	−	0.386056i
$205$	1.81431	−	1.30701i	0.126717	−	0.0912853i
$206$	−10.2474			−0.713974
$207$	−1.58919	−	8.55051i	−0.110456	−	0.594302i
$208$			2.44949i			0.169842i
$209$	−0.398979	−	0.691053i	−0.0275980	−	0.0478011i
$210$	16.9143	−	3.29788i	1.16720	−	0.227575i
$211$	7.89898	−	13.6814i	0.543788	−	0.941869i	−0.454894	−	0.890546i	$-0.650323\pi$
$211$	7.89898	−	13.6814i	0.543788	−	0.941869i	0.998682	−	0.0513231i	$-0.0163438\pi$
$212$	−7.31747	−	4.22474i	−0.502566	−	0.290157i
$213$	−3.85337	−	1.77526i	−0.264029	−	0.121638i
$214$	−0.825765	−	1.43027i	−0.0564482	−	0.0977711i
$215$	−16.5732	+	1.67423i	−1.13028	+	0.114182i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$			28.6969i			1.94808i
$218$	−6.92820	+	4.00000i	−0.469237	+	0.270914i
$219$	3.47730	−	7.54782i	0.234974	−	0.510035i
$220$	−2.95559	−	1.33025i	−0.199266	−	0.0896855i
$221$	4.77526	−	8.27098i	0.321218	−	0.556367i
$222$	1.27135	+	13.7980i	0.0853274	+	0.926058i
$223$	−16.3670	+	9.44949i	−1.09602	+	0.632785i	−0.935171	−	0.354195i	$-0.884755\pi$
$223$	−16.3670	+	9.44949i	−1.09602	+	0.632785i	−0.160844	+	0.986980i	$0.551421\pi$
$224$	4.44949			0.297294
$225$	−2.07055	+	14.8564i	−0.138037	+	0.990427i
$226$	−4.89898			−0.325875
$227$	1.25529	−	0.724745i	0.0833169	−	0.0481030i	−0.457763	−	0.889074i	$-0.651349\pi$
$227$	1.25529	−	0.724745i	0.0833169	−	0.0481030i	0.541080	+	0.840971i	$0.318016\pi$
$228$	−0.778539	+	0.550510i	−0.0515600	+	0.0364584i
$229$	−6.77526	+	11.7351i	−0.447721	+	0.775476i	−0.998237	−	0.0593484i	$-0.981098\pi$
$229$	−6.77526	+	11.7351i	−0.447721	+	0.775476i	0.550516	+	0.834825i	$0.314431\pi$
$230$	5.91119	+	2.66050i	0.389772	+	0.175428i
$231$	6.44949	+	9.12096i	0.424345	+	0.600115i
$232$	5.19615	−	3.00000i	0.341144	−	0.196960i
$233$		−	15.6969i		−	1.02834i	−0.857688	−	0.514170i	$-0.828100\pi$
$233$		−	15.6969i		−	1.02834i	0.857688	−	0.514170i	$-0.171900\pi$
$234$	4.77526	+	5.58542i	0.312168	+	0.365130i
$235$	1.00000	−	0.101021i	0.0652328	−	0.00658985i
$236$	5.62372	+	9.74058i	0.366073	+	0.634058i
$237$	1.16781	+	12.6742i	0.0758573	+	0.823280i
$238$	−15.0242	−	8.67423i	−0.973875	−	0.562267i
$239$	14.3485	−	24.8523i	0.928125	−	1.60756i	0.141669	−	0.989914i	$-0.454753\pi$
$239$	14.3485	−	24.8523i	0.928125	−	1.60756i	0.786456	−	0.617646i	$-0.211914\pi$
$240$	−1.25882	+	3.66270i	−0.0812564	+	0.236426i
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	0.849472	−	0.527633i	$-0.176921\pi$
$241$	−0.500000	−	0.866025i	−0.0322078	−	0.0557856i	−0.881680	+	0.471848i	$0.843587\pi$
$242$			8.89898i			0.572048i
$243$	8.64420	−	12.9722i	0.554526	−	0.832167i
$244$	0.449490			0.0287756
$245$	23.2195	−	16.7270i	1.48344	−	1.06865i
$246$	0.724745	−	1.57313i	0.0462080	−	0.100299i
$247$	−1.16781	−	0.674235i	−0.0743059	−	0.0429005i
$248$	−5.58542	−	3.22474i	−0.354675	−	0.204772i
$249$	−6.89898	+	0.635674i	−0.437205	+	0.0402842i
$250$	−8.21731	−	7.58128i	−0.519709	−	0.479482i
$251$	11.4495			0.722685			0.361343	−	0.932433i	$-0.382318\pi$
$251$	11.4495			0.722685			0.361343	+	0.932433i	$0.382318\pi$
$252$	10.1459	−	8.67423i	0.639132	−	0.546425i
$253$			4.20204i			0.264180i
$254$	1.44949	+	2.51059i	0.0909491	+	0.157528i
$255$	11.3909	−	9.91348i	0.713329	−	0.620806i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.2330	−	9.94949i	−1.07497	−	0.620632i	−0.145432	−	0.989368i	$-0.546457\pi$
$257$	−17.2330	−	9.94949i	−1.07497	−	0.620632i	−0.929534	+	0.368736i	$0.879791\pi$
$258$	−10.5352	+	7.44949i	−0.655891	+	0.463785i
$259$	17.7980	+	30.8270i	1.10591	+	1.91549i
$260$	−5.44949	+	0.550510i	−0.337963	+	0.0341412i
$261$	6.00000	−	16.9706i	0.371391	−	1.05045i
$262$			4.89898i			0.302660i
$263$	6.53893	−	3.77526i	0.403208	−	0.232792i	−0.284659	−	0.958629i	$-0.591880\pi$
$263$	6.53893	−	3.77526i	0.403208	−	0.232792i	0.687867	+	0.725837i	$0.258547\pi$
$264$	−2.50000	+	0.230351i	−0.153864	+	0.0141771i
$265$	7.75442	−	17.2290i	0.476350	−	1.05837i
$266$	−1.22474	+	2.12132i	−0.0750939	+	0.130066i
$267$	20.2918	+	9.34847i	1.24184	+	0.572117i
$268$	−8.18350	+	4.72474i	−0.499887	+	0.288610i
$269$	28.0454			1.70996			0.854979	−	0.518662i	$-0.173570\pi$
$269$	28.0454			1.70996			0.854979	+	0.518662i	$0.173570\pi$
$270$	4.26999	+	10.8059i	0.259863	+	0.657625i
$271$	23.5959			1.43335			0.716675	−	0.697407i	$-0.245663\pi$
$271$	23.5959			1.43335			0.716675	+	0.697407i	$0.245663\pi$
$272$	3.37662	−	1.94949i	0.204737	−	0.118205i
$273$	17.1455	+	7.89898i	1.03770	+	0.478068i
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	2.29522	−	6.87441i	0.138407	−	0.414542i
$276$	5.00000	−	0.460702i	0.300965	−	0.0277310i
$277$	8.31031	−	4.79796i	0.499318	−	0.288281i	−0.229114	−	0.973400i	$-0.573583\pi$
$277$	8.31031	−	4.79796i	0.499318	−	0.288281i	0.728432	+	0.685118i	$0.240249\pi$
$278$		−	11.2474i		−	0.674577i
$279$	−19.0227	+	3.53553i	−1.13886	+	0.211667i
$280$	1.00000	+	9.89898i	0.0597614	+	0.591577i
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	0.629685	−	0.776851i	$-0.283184\pi$
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	−0.987615	+	0.156898i	$0.949851\pi$
$282$	0.635674	−	0.449490i	0.0378539	−	0.0267667i
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	0.599414	−	0.800439i	$-0.295400\pi$
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	−0.393494	+	0.919327i	$0.628734\pi$
$284$	1.22474	−	2.12132i	0.0726752	−	0.125877i
$285$	−1.39972	−	1.60833i	−0.0829121	−	0.0952690i
$286$	−1.77526	−	3.07483i	−0.104973	−	0.181819i
$287$		−	4.44949i		−	0.262645i
$288$	0.548188	+	2.94949i	0.0323023	+	0.173800i
$289$	1.79796			0.105762
$290$	7.84204	+	10.8859i	0.460501	+	0.639241i
$291$	−22.4217	+	2.06594i	−1.31438	+	0.121108i
$292$	4.15515	+	2.39898i	0.243162	+	0.140390i
$293$	15.5885	+	9.00000i	0.910687	+	0.525786i	0.880652	−	0.473763i	$-0.157105\pi$
$293$	15.5885	+	9.00000i	0.910687	+	0.525786i	0.0300351	+	0.999549i	$0.490438\pi$
$294$	9.27526	−	20.1329i	0.540944	−	1.17417i
$295$	−20.4064	+	14.7005i	−1.18811	+	0.855896i
$296$	−8.00000			−0.464991
$297$	−5.25153	+	5.39898i	−0.304725	+	0.313281i
$298$			16.2474i			0.941189i
$299$	3.55051	+	6.14966i	0.205331	+	0.355644i
$300$	−8.43149	−	1.97738i	−0.486792	−	0.114164i
$301$	−16.5732	+	28.7056i	−0.955264	+	1.65457i
$302$	−5.97469	−	3.44949i	−0.343805	−	0.198496i
$303$	−1.27135	−	13.7980i	−0.0730371	−	0.792672i
$304$	−0.275255	−	0.476756i	−0.0157870	−	0.0273438i
$305$	0.101021	+	1.00000i	0.00578442	+	0.0572598i
$306$	3.89898	−	11.0280i	0.222890	−	0.630428i
$307$		−	23.9444i		−	1.36658i	−0.730148	−	0.683289i	$-0.760549\pi$
$307$		−	23.9444i		−	1.36658i	0.730148	−	0.683289i	$-0.239451\pi$
$308$	−5.58542	+	3.22474i	−0.318259	+	0.183747i
$309$	−10.2474	−	14.4921i	−0.582957	−	0.824426i
$310$	5.91894	−	13.1509i	0.336173	−	0.746920i
$311$	−11.4495	+	19.8311i	−0.649241	+	1.12452i	0.334063	+	0.942551i	$0.391580\pi$
$311$	−11.4495	+	19.8311i	−0.649241	+	1.12452i	−0.983304	+	0.181968i	$0.941753\pi$
$312$	−3.46410	+	2.44949i	−0.196116	+	0.138675i
$313$	−6.66574	+	3.84847i	−0.376770	+	0.217528i	−0.676412	−	0.736523i	$-0.736466\pi$
$313$	−6.66574	+	3.84847i	−0.376770	+	0.217528i	0.299642	+	0.954052i	$0.403133\pi$
$314$	16.0000			0.902932
$315$	21.5782	+	20.6225i	1.21579	+	1.16195i
$316$	−7.34847			−0.413384
$317$	−26.7986	+	15.4722i	−1.50516	+	0.869005i	−0.505179	+	0.863015i	$0.668573\pi$
$317$	−26.7986	+	15.4722i	−1.50516	+	0.869005i	−0.999982	+	0.00599020i	$0.998093\pi$
$318$	−1.34278	−	14.5732i	−0.0752994	−	0.817225i
$319$	−4.34847	+	7.53177i	−0.243468	+	0.421698i
$320$	−2.03906	−	0.917738i	−0.113987	−	0.0513031i
$321$	1.19694	−	2.59808i	0.0668066	−	0.145010i
$322$	11.1708	−	6.44949i	0.622527	−	0.359416i
$323$			2.14643i			0.119430i
$324$	7.00000	+	5.65685i	0.388889	+	0.314270i
$325$	−2.44949	−	12.0000i	−0.135873	−	0.665640i
$326$	−0.449490	−	0.778539i	−0.0248949	−	0.0431193i
$327$	−12.5851	−	5.79796i	−0.695955	−	0.320628i
$328$	0.866025	+	0.500000i	0.0478183	+	0.0276079i
$329$	1.00000	−	1.73205i	0.0551318	−	0.0954911i
$330$	−1.07433	−	5.51009i	−0.0591402	−	0.303321i
$331$	−16.6969	−	28.9199i	−0.917747	−	1.58958i	−0.802829	−	0.596209i	$-0.796673\pi$
$331$	−16.6969	−	28.9199i	−0.917747	−	1.58958i	−0.114917	−	0.993375i	$-0.536660\pi$
$332$		−	4.00000i		−	0.219529i
$333$	−18.2419	+	15.5959i	−0.999651	+	0.854651i
$334$	−24.2474			−1.32676
$335$	−12.3506	−	17.1443i	−0.674783	−	0.936695i
$336$	4.44949	+	6.29253i	0.242740	+	0.343286i
$337$	17.8366	+	10.2980i	0.971621	+	0.560966i	0.899730	−	0.436447i	$-0.143763\pi$
$337$	17.8366	+	10.2980i	0.971621	+	0.560966i	0.0718909	+	0.997413i	$0.477097\pi$
$338$	6.06218	+	3.50000i	0.329739	+	0.190375i
$339$	−4.89898	−	6.92820i	−0.266076	−	0.376288i
$340$	5.09599	+	7.07397i	0.276369	+	0.383640i
$341$	9.34847			0.506248
$342$	−1.55708	−	0.550510i	−0.0841971	−	0.0297682i
$343$		−	25.7980i		−	1.39296i
$344$	−3.72474	−	6.45145i	−0.200825	−	0.347839i
$345$	2.14867	+	11.0202i	0.115680	+	0.593307i
$346$	3.89898	−	6.75323i	0.209610	−	0.363056i
$347$	13.2047	+	7.62372i	0.708864	+	0.409263i	0.810640	−	0.585544i	$-0.199119\pi$
$347$	13.2047	+	7.62372i	0.708864	+	0.409263i	−0.101776	+	0.994807i	$0.532453\pi$
$348$	9.43879	+	4.34847i	0.505972	+	0.233102i
$349$	5.79796	+	10.0424i	0.310358	+	0.537555i	0.978440	−	0.206532i	$-0.0662179\pi$
$349$	5.79796	+	10.0424i	0.310358	+	0.537555i	−0.668082	+	0.744088i	$0.732885\pi$
$350$	−21.7980	+	4.44949i	−1.16515	+	0.237835i
$351$	−3.12372	+	12.3387i	−0.166732	+	0.658589i
$352$		−	1.44949i		−	0.0772581i
$353$	5.71223	−	3.29796i	0.304031	−	0.175533i	−0.340221	−	0.940345i	$-0.610502\pi$
$353$	5.71223	−	3.29796i	0.304031	−	0.175533i	0.644253	+	0.764813i	$0.277169\pi$
$354$	−8.15153	+	17.6937i	−0.433249	+	0.940411i
$355$	4.99465	+	2.24799i	0.265089	+	0.119311i
$356$	−6.44949	+	11.1708i	−0.341822	+	0.592054i
$357$	−2.75699	−	29.9217i	−0.145916	−	1.58362i
$358$	7.70674	−	4.44949i	0.407314	−	0.235163i
$359$	−8.44949			−0.445947			−0.222974	−	0.974825i	$-0.571576\pi$
$359$	−8.44949			−0.445947			−0.222974	+	0.974825i	$0.571576\pi$
$360$	−6.43866	+	1.88246i	−0.339347	+	0.0992144i
$361$	−18.6969			−0.984049
$362$	−9.04952	+	5.22474i	−0.475632	+	0.274606i
$363$	−12.5851	+	8.89898i	−0.660544	+	0.467075i
$364$	−5.44949	+	9.43879i	−0.285631	+	0.494727i
$365$	−4.40327	+	9.78332i	−0.230478	+	0.512082i
$366$	0.449490	+	0.635674i	0.0234952	+	0.0332272i
$367$	−10.0424	+	5.79796i	−0.524207	+	0.302651i	−0.738654	−	0.674085i	$-0.764538\pi$
$367$	−10.0424	+	5.79796i	−0.524207	+	0.302651i	0.214447	+	0.976736i	$0.431205\pi$
$368$			2.89898i			0.151120i
$369$	2.94949	−	0.548188i	0.153544	−	0.0285375i
$370$	−1.79796	−	17.7980i	−0.0934714	−	0.925272i
$371$	−18.7980	−	32.5590i	−0.975941	−	1.69038i
$372$	−1.02494	−	11.1237i	−0.0531409	−	0.576738i
$373$	22.1667	+	12.7980i	1.14775	+	0.662653i	0.948338	−	0.317263i	$-0.102764\pi$
$373$	22.1667	+	12.7980i	1.14775	+	0.662653i	0.199411	+	0.979916i	$0.436097\pi$
$374$	−2.82577	+	4.89437i	−0.146117	+	0.253082i
$375$	2.50423	−	19.2023i	0.129318	−	0.991603i
$376$	0.224745	+	0.389270i	0.0115903	+	0.0200750i
$377$			14.6969i			0.756931i
$378$	22.4131	+	5.67423i	1.15281	+	0.291851i
$379$	30.1464			1.54852			0.774259	−	0.632869i	$-0.218123\pi$
$379$	30.1464			1.54852			0.774259	+	0.632869i	$0.218123\pi$
$380$	0.998798	−	0.719521i	0.0512373	−	0.0369106i
$381$	−2.10102	+	4.56048i	−0.107639	+	0.233640i
$382$	−5.41045	−	3.12372i	−0.276823	−	0.159824i
$383$	1.55708	+	0.898979i	0.0795630	+	0.0459357i	0.539254	−	0.842143i	$-0.318706\pi$
$383$	1.55708	+	0.898979i	0.0795630	+	0.0459357i	−0.459691	+	0.888079i	$0.652040\pi$
$384$	−1.72474	+	0.158919i	−0.0880155	+	0.00810978i
$385$	−8.42953	−	11.7014i	−0.429609	−	0.596358i
$386$	15.6969			0.798953
$387$	−21.0703	−	7.44949i	−1.07107	−	0.378679i
$388$		−	13.0000i		−	0.659975i
$389$	11.2247	+	19.4418i	0.569117	+	0.985740i	0.996654	+	0.0817417i	$0.0260483\pi$
$389$	11.2247	+	19.4418i	0.569117	+	0.985740i	−0.427536	+	0.903998i	$0.640618\pi$
$390$	−6.22803	−	7.15623i	−0.315368	−	0.362370i
$391$	5.65153	−	9.78874i	0.285810	−	0.495038i
$392$	11.0834	+	6.39898i	0.559794	+	0.323197i
$393$	−6.92820	+	4.89898i	−0.349482	+	0.247121i
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$	−1.65153	−	16.3485i	−0.0830975	−	0.822581i
$396$	−2.82577	−	3.30518i	−0.142000	−	0.166092i
$397$			17.7980i			0.893254i	0.894720	+	0.446627i	$0.147375\pi$
$397$			17.7980i			0.893254i	−0.894720	+	0.446627i	$0.852625\pi$
$398$	17.7098	−	10.2247i	0.887711	−	0.512520i
$399$	−4.22474	+	0.389270i	−0.211502	+	0.0194879i
$400$	1.58346	−	4.74264i	0.0791732	−	0.237132i
$401$	−14.3990	+	24.9398i	−0.719051	+	1.24543i	0.242326	+	0.970195i	$0.422090\pi$
$401$	−14.3990	+	24.9398i	−0.719051	+	1.24543i	−0.961376	+	0.275237i	$0.911244\pi$
$402$	−14.8653	−	6.84847i	−0.741414	−	0.341571i
$403$	13.6814	−	7.89898i	0.681521	−	0.393476i
$404$	8.00000			0.398015
$405$	−11.0118	+	16.8446i	−0.547183	+	0.837013i
$406$	26.6969			1.32495
$407$	10.0424	−	5.79796i	0.497781	−	0.287394i
$408$	6.13361	+	2.82577i	0.303659	+	0.139896i
$409$	3.05051	−	5.28364i	0.150838	−	0.261259i	−0.780698	−	0.624909i	$-0.785136\pi$
$409$	3.05051	−	5.28364i	0.150838	−	0.261259i	0.931536	+	0.363650i	$0.118469\pi$
$410$	−0.917738	+	2.03906i	−0.0453238	+	0.100702i
$411$	−5.17423	+	0.476756i	−0.255226	+	0.0235166i
$412$	8.87455	−	5.12372i	0.437218	−	0.252428i
$413$			50.0454i			2.46257i
$414$	5.65153	+	6.61037i	0.277758	+	0.324882i
$415$	8.89898	−	0.898979i	0.436834	−	0.0441292i
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$	15.9063	−	11.2474i	0.778935	−	0.550790i
$418$	0.691053	+	0.398979i	0.0338005	+	0.0195147i
$419$	0.449490	−	0.778539i	0.0219590	−	0.0380341i	−0.854837	−	0.518896i	$-0.826343\pi$
$419$	0.449490	−	0.778539i	0.0219590	−	0.0380341i	0.876796	+	0.480862i	$0.159676\pi$
$420$	−12.9993	+	11.3132i	−0.634299	+	0.552027i
$421$	8.22474	+	14.2457i	0.400850	+	0.694292i	0.993829	−	0.110926i	$-0.0353817\pi$
$421$	8.22474	+	14.2457i	0.400850	+	0.694292i	−0.592979	+	0.805218i	$0.702048\pi$
$422$			15.7980i			0.769033i
$423$	1.27135	+	0.449490i	0.0618151	+	0.0218549i
$424$	8.44949			0.410343
$425$	−14.5925	+	12.9271i	−0.707839	+	0.627058i
$426$	4.22474	−	0.389270i	0.204690	−	0.0188602i
$427$	1.73205	+	1.00000i	0.0838198	+	0.0483934i
$428$	1.43027	+	0.825765i	0.0691346	+	0.0399149i
$429$	2.57321	−	5.58542i	0.124236	−	0.269667i
$430$	13.5157	−	9.73654i	0.651785	−	0.469537i
$431$	13.7526			0.662437			0.331219	−	0.943554i	$-0.392540\pi$
$431$	13.7526			0.662437			0.331219	+	0.943554i	$0.392540\pi$
$432$	−3.62302	+	3.72474i	−0.174313	+	0.179207i
$433$		−	23.0000i		−	1.10531i	−0.833410	−	0.552655i	$-0.813615\pi$
$433$		−	23.0000i		−	1.10531i	0.833410	−	0.552655i	$-0.186385\pi$
$434$	−14.3485	−	24.8523i	−0.688749	−	1.19295i
$435$	−7.55291	+	21.9762i	−0.362135	+	1.05368i
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$	−1.38211	−	0.797959i	−0.0661151	−	0.0381716i
$438$	0.762485	+	8.27526i	0.0364329	+	0.395407i
$439$	−11.0227	−	19.0919i	−0.526085	−	0.911206i	−0.999538	−	0.0303869i	$-0.990326\pi$
$439$	−11.0227	−	19.0919i	−0.526085	−	0.911206i	0.473453	−	0.880819i	$-0.343007\pi$
$440$	3.22474	−	0.325765i	0.153734	−	0.0155303i
$441$	37.7474	−	7.01569i	1.79750	−	0.334080i
$442$			9.55051i			0.454271i
$443$	2.81237	−	1.62372i	0.133620	−	0.0771455i	−0.431700	−	0.902017i	$-0.642086\pi$
$443$	2.81237	−	1.62372i	0.133620	−	0.0771455i	0.565320	+	0.824872i	$0.308753\pi$
$444$	−8.00000	−	11.3137i	−0.379663	−	0.536925i
$445$	−26.3018	−	11.8379i	−1.24682	−	0.561169i
$446$	9.44949	−	16.3670i	0.447446	−	0.775000i
$447$	−22.9774	+	16.2474i	−1.08679	+	0.768478i
$448$	−3.85337	+	2.22474i	−0.182055	+	0.105109i
$449$	0.797959			0.0376580			0.0188290	−	0.999823i	$-0.494006\pi$
$449$	0.797959			0.0376580			0.0188290	+	0.999823i	$0.494006\pi$
$450$	−5.63505	−	13.9013i	−0.265639	−	0.655314i
$451$	−1.44949			−0.0682538
$452$	4.24264	−	2.44949i	0.199557	−	0.115214i
$453$	−1.09638	−	11.8990i	−0.0515123	−	0.559063i
$454$	−0.724745	+	1.25529i	−0.0340140	+	0.0589139i
$455$	−22.2237	−	10.0024i	−1.04186	−	0.468920i
$456$	0.398979	−	0.866025i	0.0186839	−	0.0405554i
$457$	−7.01569	+	4.05051i	−0.328180	+	0.189475i	−0.655033	−	0.755600i	$-0.727345\pi$
$457$	−7.01569	+	4.05051i	−0.328180	+	0.189475i	0.326853	+	0.945075i	$0.394012\pi$
$458$		−	13.5505i		−	0.633174i
$459$	19.4949	−	5.51399i	0.909944	−	0.257371i
$460$	−6.44949	+	0.651531i	−0.300709	+	0.0303778i
$461$	−1.22474	−	2.12132i	−0.0570421	−	0.0987997i	0.836094	−	0.548586i	$-0.184834\pi$
$461$	−1.22474	−	2.12132i	−0.0570421	−	0.0987997i	−0.893136	+	0.449786i	$0.851500\pi$
$462$	−10.1459	−	4.67423i	−0.472030	−	0.217465i
$463$	20.7846	+	12.0000i	0.965943	+	0.557687i	0.897997	−	0.440002i	$-0.145022\pi$
$463$	20.7846	+	12.0000i	0.965943	+	0.557687i	0.0679458	+	0.997689i	$0.478356\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	24.5171	−	4.78024i	1.13695	−	0.221678i
$466$	7.84847	+	13.5939i	0.363573	+	0.629727i
$467$			4.34847i			0.201223i	0.994926	+	0.100612i	$0.0320799\pi$
$467$			4.34847i			0.201223i	−0.994926	+	0.100612i	$0.967920\pi$
$468$	−6.92820	−	2.44949i	−0.320256	−	0.113228i
$469$	−42.0454			−1.94148
$470$	−0.815515	+	0.587486i	−0.0376169	+	0.0270987i
$471$	16.0000	+	22.6274i	0.737241	+	1.04262i
$472$	−9.74058	−	5.62372i	−0.448346	−	0.258853i
$473$	9.35131	+	5.39898i	0.429974	+	0.248245i
$474$	−7.34847	−	10.3923i	−0.337526	−	0.477334i
$475$	1.82523	+	2.06036i	0.0837471	+	0.0945359i
$476$	17.3485			0.795166
$477$	19.2669	−	16.4722i	0.882169	−	0.754210i
$478$			28.6969i			1.31257i
$479$	−6.34847	−	10.9959i	−0.290069	−	0.502414i	0.683757	−	0.729710i	$-0.260345\pi$
$479$	−6.34847	−	10.9959i	−0.290069	−	0.502414i	−0.973826	+	0.227296i	$0.927012\pi$
$480$	−0.741181	−	3.80140i	−0.0338301	−	0.173509i
$481$	9.79796	−	16.9706i	0.446748	−	0.773791i
$482$	0.866025	+	0.500000i	0.0394464	+	0.0227744i
$483$	20.2918	+	9.34847i	0.923309	+	0.425370i
$484$	−4.44949	−	7.70674i	−0.202250	−	0.350306i
$485$	28.9217	−	2.92168i	1.31327	−	0.132667i
$486$	−1.00000	+	15.5563i	−0.0453609	+	0.705650i
$487$		−	34.8990i		−	1.58142i	−0.612188	−	0.790712i	$-0.709711\pi$
$487$		−	34.8990i		−	1.58142i	0.612188	−	0.790712i	$-0.290289\pi$
$488$	−0.389270	+	0.224745i	−0.0176214	+	0.0101737i
$489$	0.651531	−	1.41421i	0.0294632	−	0.0639529i
$490$	−11.7452	+	26.0958i	−0.530593	+	1.17889i
$491$	−11.7247	+	20.3079i	−0.529130	+	0.916481i	0.470293	+	0.882511i	$0.344148\pi$
$491$	−11.7247	+	20.3079i	−0.529130	+	0.916481i	−0.999423	+	0.0339700i	$0.989185\pi$
$492$	0.158919	+	1.72474i	0.00716460	+	0.0777575i
$493$	20.2597	−	11.6969i	0.912451	−	0.526804i
$494$	1.34847			0.0606705
$495$	6.71811	−	7.02943i	0.301957	−	0.315949i
$496$	6.44949			0.289591
$497$	9.43879	−	5.44949i	0.423388	−	0.244443i
$498$	5.65685	−	4.00000i	0.253490	−	0.179244i
$499$	1.62372	−	2.81237i	0.0726879	−	0.125899i	−0.827391	−	0.561627i	$-0.810176\pi$
$499$	1.62372	−	2.81237i	0.0726879	−	0.125899i	0.900078	+	0.435728i	$0.143509\pi$
$500$	10.9070	+	2.45692i	0.487778	+	0.109877i
$501$	−24.2474	−	34.2911i	−1.08330	−	1.53201i
$502$	−9.91555	+	5.72474i	−0.442553	+	0.255508i
$503$		−	9.55051i		−	0.425836i	−0.977070	−	0.212918i	$-0.931703\pi$
$503$		−	9.55051i		−	0.425836i	0.977070	−	0.212918i	$-0.0682968\pi$
$504$	−4.44949	+	12.5851i	−0.198196	+	0.560583i
$505$	1.79796	+	17.7980i	0.0800081	+	0.791999i
$506$	−2.10102	−	3.63907i	−0.0934018	−	0.161777i
$507$	1.11243	+	12.0732i	0.0494048	+	0.536190i
$508$	−2.51059	−	1.44949i	−0.111389	−	0.0643107i
$509$	−3.79796	+	6.57826i	−0.168342	+	0.291576i	−0.937837	−	0.347076i	$-0.887174\pi$
$509$	−3.79796	+	6.57826i	−0.168342	+	0.291576i	0.769495	+	0.638652i	$0.220508\pi$
$510$	−4.90811	+	14.2808i	−0.217335	+	0.632364i
$511$	10.6742	+	18.4883i	0.472200	+	0.817875i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.778539	−	2.75255i	−0.0343733	−	0.121528i
$514$	19.8990			0.877706
$515$	13.3935	+	18.5921i	0.590188	+	0.819265i
$516$	5.39898	−	11.7190i	0.237677	−	0.515902i
$517$	−0.564242	−	0.325765i	−0.0248153	−	0.0143271i
$518$	−30.8270	−	17.7980i	−1.35446	−	0.781997i
$519$	13.4495	−	1.23924i	0.590367	−	0.0543966i
$520$	4.44414	−	3.20150i	0.194888	−	0.140395i
$521$	−7.69694			−0.337209			−0.168604	−	0.985684i	$-0.553926\pi$
$521$	−7.69694			−0.337209			−0.168604	+	0.985684i	$0.553926\pi$
$522$	3.28913	+	17.6969i	0.143961	+	0.774574i
$523$			29.7980i			1.30297i	0.758660	+	0.651487i	$0.225854\pi$
$523$			29.7980i			1.30297i	−0.758660	+	0.651487i	$0.774146\pi$
$524$	−2.44949	−	4.24264i	−0.107006	−	0.185341i
$525$	−28.0905	−	26.3775i	−1.22597	−	1.15121i
$526$	−3.77526	+	6.53893i	−0.164609	+	0.285111i
$527$	−21.7774	−	12.5732i	−0.948640	−	0.547698i
$528$	2.04989	−	1.44949i	0.0892099	−	0.0630809i
$529$	−7.29796	−	12.6404i	−0.317303	−	0.549584i
$530$	1.89898	+	18.7980i	0.0824864	+	0.816531i
$531$	−33.1742	+	6.16572i	−1.43964	+	0.267569i
$532$		−	2.44949i		−	0.106199i
$533$	−2.12132	+	1.22474i	−0.0918846	+	0.0530496i
$534$	−22.2474	+	2.04989i	−0.962741	+	0.0887073i
$535$	−1.51567	+	3.36757i	−0.0655282	+	0.145593i
$536$	4.72474	−	8.18350i	0.204078	−	0.353473i
$537$	13.9993	+	6.44949i	0.604113	+	0.278316i
$538$	−24.2880	+	14.0227i	−1.04713	+	0.604562i
$539$	−18.5505			−0.799027
$540$	−9.10086	−	7.22318i	−0.391639	−	0.310836i
$541$	−39.5959			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$541$	−39.5959			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$542$	−20.4347	+	11.7980i	−0.877744	+	0.506766i
$543$	−16.4384	−	7.57321i	−0.705440	−	0.324998i
$544$	−1.94949	+	3.37662i	−0.0835837	+	0.144771i
$545$	16.3125	+	7.34190i	0.698749	+	0.314493i
$546$	−18.7980	+	1.73205i	−0.804478	+	0.0741249i
$547$	−6.27647	+	3.62372i	−0.268363	+	0.154939i	−0.628143	−	0.778098i	$-0.716185\pi$
$547$	−6.27647	+	3.62372i	−0.268363	+	0.154939i	0.359781	+	0.933037i	$0.382852\pi$
$548$		−	3.00000i		−	0.128154i
$549$	−0.449490	+	1.27135i	−0.0191838	+	0.0542599i
$550$	1.44949	+	7.10102i	0.0618065	+	0.302789i
$551$	−1.65153	−	2.86054i	−0.0703576	−	0.121863i
$552$	−4.09978	+	2.89898i	−0.174498	+	0.123389i
$553$	−28.3164	−	16.3485i	−1.20413	−	0.695208i
$554$	−4.79796	+	8.31031i	−0.203846	+	0.353071i
$555$	23.3722	−	20.3407i	0.992093	−	0.863413i
$556$	5.62372	+	9.74058i	0.238499	+	0.413092i
$557$		−	38.9444i		−	1.65013i	−0.565040	−	0.825063i	$-0.691139\pi$
$557$		−	38.9444i		−	1.65013i	0.565040	−	0.825063i	$-0.308861\pi$
$558$	14.7064	−	12.5732i	0.622571	−	0.532267i
$559$	18.2474			0.771785
$560$	−5.81552	−	8.07277i	−0.245750	−	0.341137i
$561$	−9.74745	+	0.898133i	−0.411538	+	0.0379192i
$562$	10.3923	+	6.00000i	0.438373	+	0.253095i
$563$	31.3037	+	18.0732i	1.31929	+	0.761695i	0.983615	−	0.180281i	$-0.0577007\pi$
$563$	31.3037	+	18.0732i	1.31929	+	0.761695i	0.335680	+	0.941976i	$0.391034\pi$
$564$	−0.325765	+	0.707107i	−0.0137172	+	0.0297746i
$565$	6.40300	+	8.88828i	0.269376	+	0.373933i
$566$	−4.00000			−0.168133
$567$	14.3885	+	37.3712i	0.604262	+	1.56944i
$568$			2.44949i			0.102778i
$569$	8.74745	+	15.1510i	0.366712	+	0.635164i	0.989049	−	0.147585i	$-0.0471501\pi$
$569$	8.74745	+	15.1510i	0.366712	+	0.635164i	−0.622337	+	0.782749i	$0.713817\pi$
$570$	2.01635	+	0.692993i	0.0844558	+	0.0290263i
$571$	−6.37628	+	11.0440i	−0.266839	+	0.462178i	−0.968044	−	0.250781i	$-0.919312\pi$
$571$	−6.37628	+	11.0440i	−0.266839	+	0.462178i	0.701205	+	0.712960i	$0.252646\pi$
$572$	3.07483	+	1.77526i	0.128565	+	0.0742271i
$573$	−0.992836	−	10.7753i	−0.0414763	−	0.450143i
$574$	2.22474	+	3.85337i	0.0928591	+	0.160837i
$575$	−2.89898	−	14.2020i	−0.120896	−	0.592266i
$576$	−1.94949	−	2.28024i	−0.0812287	−	0.0950100i
$577$			13.6969i			0.570211i	0.958496	+	0.285106i	$0.0920286\pi$
$577$			13.6969i			0.570211i	−0.958496	+	0.285106i	$0.907971\pi$
$578$	−1.55708	+	0.898979i	−0.0647659	+	0.0373926i
$579$	15.6969	+	22.1988i	0.652343	+	0.922552i
$580$	−12.2343	−	5.50643i	−0.508004	−	0.228642i
$581$	8.89898	−	15.4135i	0.369192	−	0.639459i
$582$	18.3848	−	13.0000i	0.762073	−	0.538867i
$583$	−10.6066	+	6.12372i	−0.439281	+	0.253619i
$584$	−4.79796			−0.198541
$585$	3.89241	−	15.9640i	0.160931	−	0.660030i
$586$	−18.0000			−0.743573
$587$	25.9326	−	14.9722i	1.07035	−	0.617969i	0.142075	−	0.989856i	$-0.454623\pi$
$587$	25.9326	−	14.9722i	1.07035	−	0.617969i	0.928278	+	0.371887i	$0.121289\pi$
$588$	2.03383	+	22.0732i	0.0838739	+	0.910284i
$589$	−1.77526	+	3.07483i	−0.0731481	+	0.126696i
$590$	10.3222	−	22.9342i	0.424959	−	0.944186i
$591$	−5.79796	+	12.5851i	−0.238496	+	0.517680i
$592$	6.92820	−	4.00000i	0.284747	−	0.164399i
$593$		−	41.3939i		−	1.69984i	−0.526910	−	0.849921i	$-0.676649\pi$
$593$		−	41.3939i		−	1.69984i	0.526910	−	0.849921i	$-0.323351\pi$
$594$	1.84847	−	7.30142i	0.0758436	−	0.299581i
$595$	3.89898	+	38.5959i	0.159843	+	1.58228i
$596$	−8.12372	−	14.0707i	−0.332761	−	0.576358i
$597$	32.1698	+	14.8207i	1.31662	+	0.606569i
$598$	−6.14966	−	3.55051i	−0.251478	−	0.145191i
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	−0.683703	−	0.729761i	$-0.739632\pi$
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	0.973843	+	0.227224i	$0.0729648\pi$
$600$	8.29057	−	2.50328i	0.338461	−	0.102196i
$601$	−9.60102	−	16.6295i	−0.391634	−	0.678330i	0.601031	−	0.799225i	$-0.294757\pi$
$601$	−9.60102	−	16.6295i	−0.391634	−	0.678330i	−0.992665	+	0.120896i	$0.961423\pi$
$602$		−	33.1464i		−	1.35095i
$603$	−5.18010	−	27.8712i	−0.210950	−	1.13500i
$604$	6.89898			0.280715
$605$	16.1455	−	11.6310i	0.656409	−	0.472869i
$606$	8.00000	+	11.3137i	0.324978	+	0.459588i
$607$	−10.0424	−	5.79796i	−0.407607	−	0.235332i	0.282154	−	0.959369i	$-0.408951\pi$
$607$	−10.0424	−	5.79796i	−0.407607	−	0.235332i	−0.689761	+	0.724037i	$0.742284\pi$
$608$	0.476756	+	0.275255i	0.0193350	+	0.0111631i
$609$	26.6969	+	37.7552i	1.08181	+	1.52992i
$610$	−0.587486	−	0.815515i	−0.0237866	−	0.0330192i
$611$	−1.10102			−0.0445425
$612$	2.13737	+	11.5000i	0.0863982	+	0.464860i
$613$		−	16.9444i		−	0.684377i	−0.939631	−	0.342189i	$-0.888832\pi$
$613$		−	16.9444i		−	0.684377i	0.939631	−	0.342189i	$-0.111168\pi$
$614$	11.9722	+	20.7364i	0.483158	+	0.836855i
$615$	−3.80140	+	0.741181i	−0.153287	+	0.0298873i
$616$	3.22474	−	5.58542i	0.129929	−	0.225043i
$617$	−32.6465	−	18.8485i	−1.31430	−	0.758811i	−0.331494	−	0.943457i	$-0.607553\pi$
$617$	−32.6465	−	18.8485i	−1.31430	−	0.758811i	−0.982805	+	0.184647i	$0.940886\pi$
$618$	16.1206	+	7.42679i	0.648465	+	0.298749i
$619$	−16.7247	−	28.9681i	−0.672224	−	1.16433i	−0.977272	−	0.211989i	$-0.932006\pi$
$619$	−16.7247	−	28.9681i	−0.672224	−	1.16433i	0.305048	−	0.952337i	$-0.401328\pi$
$620$	1.44949	+	14.3485i	0.0582129	+	0.576248i
$621$	−3.69694	+	14.6028i	−0.148353	+	0.585992i
$622$		−	22.8990i		−	0.918165i
$623$	−49.7046	+	28.6969i	−1.99137	+	1.14972i
$624$	1.77526	−	3.85337i	0.0710671	−	0.154258i
$625$	−3.01472	+	24.8176i	−0.120589	+	0.992703i
$626$	3.84847	−	6.66574i	0.153816	−	0.266417i
$627$	0.126811	+	1.37628i	0.00506433	+	0.0549632i
$628$	−13.8564	+	8.00000i	−0.552931	+	0.319235i
$629$	−31.1918			−1.24370
$630$	−28.9985	−	7.07055i	−1.15533	−	0.281698i
$631$	3.34847			0.133300			0.0666502	−	0.997776i	$-0.478769\pi$
$631$	3.34847			0.133300			0.0666502	+	0.997776i	$0.478769\pi$
$632$	6.36396	−	3.67423i	0.253145	−	0.146153i
$633$	−22.3417	+	15.7980i	−0.888002	+	0.627912i
$634$	15.4722	−	26.7986i	0.614479	−	1.06431i
$635$	2.66050	−	5.91119i	0.105579	−	0.234578i
$636$	8.44949	+	11.9494i	0.335044	+	0.473824i
$637$	−27.1486	+	15.6742i	−1.07567	+	0.621036i
$638$		−	8.69694i		−	0.344315i
$639$	4.77526	+	5.58542i	0.188906	+	0.220956i
$640$	2.22474	−	0.224745i	0.0879408	−	0.00888382i
$641$	18.5000	+	32.0429i	0.730706	+	1.26562i	0.956582	+	0.291464i	$0.0941423\pi$
$641$	18.5000	+	32.0429i	0.730706	+	1.26562i	−0.225876	+	0.974156i	$0.572524\pi$
$642$	0.262459	+	2.84847i	0.0103584	+	0.112420i
$643$	−8.00853	−	4.62372i	−0.315825	−	0.182342i	0.333705	−	0.942678i	$-0.391701\pi$
$643$	−8.00853	−	4.62372i	−0.315825	−	0.182342i	−0.649530	+	0.760336i	$0.725034\pi$
$644$	−6.44949	+	11.1708i	−0.254145	+	0.440193i
$645$	27.2852	+	9.37756i	1.07436	+	0.369241i
$646$	−1.07321	−	1.85886i	−0.0422250	−	0.0731359i
$647$			25.1010i			0.986823i	0.869796	+	0.493411i	$0.164250\pi$
$647$			25.1010i			0.986823i	−0.869796	+	0.493411i	$0.835750\pi$
$648$	−8.89060	−	1.39898i	−0.349256	−	0.0549571i
$649$	16.3031			0.639951
$650$	8.12132	+	9.16756i	0.318544	+	0.359581i
$651$	20.7980	−	45.1441i	0.815136	−	1.76934i
$652$	0.778539	+	0.449490i	0.0304899	+	0.0176034i
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.202828	−	0.979214i	$-0.565013\pi$
$653$	−29.4449	−	17.0000i	−1.15227	−	0.665261i	−0.949439	+	0.313953i	$0.898347\pi$
$654$	13.7980	−	1.27135i	0.539543	−	0.0497137i
$655$	8.88828	−	6.40300i	0.347294	−	0.250186i
$656$	−1.00000			−0.0390434
$657$	−10.9405	+	9.35357i	−0.426829	+	0.364918i
$658$			2.00000i			0.0779681i
$659$	−8.10102	−	14.0314i	−0.315571	−	0.546585i	0.663988	−	0.747743i	$-0.268863\pi$
$659$	−8.10102	−	14.0314i	−0.315571	−	0.546585i	−0.979559	+	0.201159i	$0.935529\pi$
$660$	3.68545	+	4.23471i	0.143456	+	0.164836i
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	−0.700094	−	0.714051i	$-0.746859\pi$
$661$	6.89898	−	11.9494i	0.268339	−	0.464777i	0.968433	+	0.249274i	$0.0801919\pi$
$662$	28.9199	+	16.6969i	1.12401	+	0.648945i
$663$	−13.5065	+	9.55051i	−0.524547	+	0.370911i
$664$	2.00000	+	3.46410i	0.0776151	+	0.134433i
$665$	5.44949	−	0.550510i	0.211322	−	0.0213479i
$666$	8.00000	−	22.6274i	0.309994	−	0.876795i
$667$			17.3939i			0.673494i
$668$	20.9989	−	12.1237i	0.812472	−	0.469081i
$669$	32.5959	−	3.00340i	1.26023	−	0.116118i
$670$	19.2681	+	8.67215i	0.744390	+	0.335034i
$671$	0.325765	−	0.564242i	0.0125760	−	0.0217823i
$672$	−6.99964	−	3.22474i	−0.270017	−	0.124397i
$673$	16.5420	−	9.55051i	0.637646	−	0.368145i	−0.146061	−	0.989276i	$-0.546660\pi$
$673$	16.5420	−	9.55051i	0.637646	−	0.368145i	0.783707	+	0.621130i	$0.213326\pi$
$674$	−20.5959			−0.793325
$675$	14.0244	−	21.8705i	0.539798	−	0.841795i
$676$	−7.00000			−0.269231
$677$	0.349945	−	0.202041i	0.0134495	−	0.00776507i	−0.493260	−	0.869882i	$-0.664195\pi$
$677$	0.349945	−	0.202041i	0.0134495	−	0.00776507i	0.506710	+	0.862117i	$0.330862\pi$
$678$	7.70674	+	3.55051i	0.295976	+	0.136357i
$679$	28.9217	−	50.0938i	1.10991	−	1.92242i
$680$	−7.95025	−	3.57824i	−0.304878	−	0.137219i
$681$	−2.50000	+	0.230351i	−0.0958002	+	0.00882707i
$682$	−8.09601	+	4.67423i	−0.310012	+	0.178986i
$683$			40.5505i			1.55162i	0.630965	+	0.775811i	$0.282659\pi$
$683$			40.5505i			1.55162i	−0.630965	+	0.775811i	$0.717341\pi$
$684$	1.62372	−	0.301783i	0.0620847	−	0.0115390i
$685$	6.67423	−	0.674235i	0.255009	−	0.0257612i
$686$	12.8990	+	22.3417i	0.492485	+	0.853010i
$687$	19.1633	−	13.5505i	0.731126	−	0.516984i
$688$	6.45145	+	3.72474i	0.245959	+	0.142005i
$689$	−10.3485	+	17.9241i	−0.394245	+	0.682853i
$690$	−7.37089	−	8.46943i	−0.280605	−	0.322426i
$691$	10.7980	+	18.7026i	0.410774	+	0.711481i	0.994975	−	0.100128i	$-0.0319253\pi$
$691$	10.7980	+	18.7026i	0.410774	+	0.711481i	−0.584201	+	0.811609i	$0.698592\pi$
$692$			7.79796i			0.296434i
$693$	−3.53553	−	19.0227i	−0.134304	−	0.722613i
$694$	−15.2474			−0.578785
$695$	−20.4064	+	14.7005i	−0.774059	+	0.557622i
$696$	−10.3485	+	0.953512i	−0.392258	+	0.0361428i
$697$	3.37662	+	1.94949i	0.127898	+	0.0738422i
$698$	−10.0424	−	5.79796i	−0.380109	−	0.219456i
$699$	−11.3763	+	24.6934i	−0.430290	+	0.933989i
$700$	16.6528	−	14.7524i	0.629418	−	0.557586i
$701$	19.3939			0.732497			0.366248	−	0.930517i	$-0.380642\pi$
$701$	19.3939			0.732497			0.366248	+	0.930517i	$0.380642\pi$
$702$	−3.46410	−	12.2474i	−0.130744	−	0.462250i
$703$			4.40408i			0.166103i
$704$	0.724745	+	1.25529i	0.0273149	+	0.0473107i
$705$	−1.64635	−	0.565826i	−0.0620050	−	0.0213102i
$706$	−3.29796	+	5.71223i	−0.124120	+	0.214983i
$707$	30.8270	+	17.7980i	1.15937	+	0.669361i
$708$	−1.78743	−	19.3990i	−0.0671757	−	0.729058i
$709$	11.3258	+	19.6168i	0.425348	+	0.736724i	0.996453	−	0.0841527i	$-0.0268184\pi$
$709$	11.3258	+	19.6168i	0.425348	+	0.736724i	−0.571105	+	0.820877i	$0.693485\pi$
$710$	−5.44949	+	0.550510i	−0.204516	+	0.0206603i
$711$	7.34847	−	20.7846i	0.275589	−	0.779484i
$712$		−	12.8990i		−	0.483410i
$713$	16.1920	−	9.34847i	0.606396	−	0.350103i
$714$	17.3485	+	24.5344i	0.649250	+	0.918178i
$715$	−3.25844	+	7.23970i	−0.121859	+	0.270749i
$716$	−4.44949	+	7.70674i	−0.166285	+	0.288014i
$717$	−40.5836	+	28.6969i	−1.51562	+	1.07171i
$718$	7.31747	−	4.22474i	0.273086	−	0.157666i
$719$	−22.2020			−0.827996			−0.413998	−	0.910278i	$-0.635868\pi$
$719$	−22.2020			−0.827996			−0.413998	+	0.910278i	$0.635868\pi$
$720$	4.63481	−	4.84959i	0.172729	−	0.180734i
$721$	45.5959			1.69808
$722$	16.1920	−	9.34847i	0.602605	−	0.347914i
$723$	0.158919	+	1.72474i	0.00591025	+	0.0641440i
$724$	5.22474	−	9.04952i	0.194176	−	0.336323i
$725$	9.50079	−	28.4558i	0.352850	−	1.05682i
$726$	6.44949	−	13.9993i	0.239363	−	0.519562i
$727$	−9.22450	+	5.32577i	−0.342118	+	0.197522i	−0.661208	−	0.750203i	$-0.729956\pi$
$727$	−9.22450	+	5.32577i	−0.342118	+	0.197522i	0.319090	+	0.947724i	$0.396623\pi$
$728$		−	10.8990i		−	0.403943i
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$	−1.07832	−	10.6742i	−0.0399103	−	0.395071i
$731$	−14.5227	−	25.1541i	−0.537142	−	0.930357i
$732$	−0.707107	−	0.325765i	−0.0261354	−	0.0120406i
$733$	−11.3851	−	6.57321i	−0.420520	−	0.242787i	0.274780	−	0.961507i	$-0.411395\pi$
$733$	−11.3851	−	6.57321i	−0.420520	−	0.242787i	−0.695300	+	0.718720i	$0.744728\pi$
$734$	5.79796	−	10.0424i	0.214007	−	0.370670i
$735$	−48.6502	+	9.48560i	−1.79449	+	0.349882i
$736$	−1.44949	−	2.51059i	−0.0534289	−	0.0925416i
$737$			13.6969i			0.504533i
$738$	−2.28024	+	1.94949i	−0.0839368	+	0.0717617i
$739$	−7.24745			−0.266602			−0.133301	−	0.991076i	$-0.542558\pi$
$739$	−7.24745			−0.266602			−0.133301	+	0.991076i	$0.542558\pi$
$740$	10.4561	+	14.5145i	0.384372	+	0.533564i
$741$	1.34847	+	1.90702i	0.0495373	+	0.0700563i
$742$	32.5590	+	18.7980i	1.19528	+	0.690095i
$743$	−11.3458	−	6.55051i	−0.416238	−	0.240315i	0.277229	−	0.960804i	$-0.410584\pi$
$743$	−11.3458	−	6.55051i	−0.416238	−	0.240315i	−0.693466	+	0.720489i	$0.743917\pi$
$744$	6.44949	+	9.12096i	0.236450	+	0.334390i
$745$	29.4780	−	21.2355i	1.07999	−	0.778010i
$746$	−25.5959			−0.937133
$747$	11.3137	+	4.00000i	0.413947	+	0.146352i
$748$		−	5.65153i		−	0.206640i
$749$	3.67423	+	6.36396i	0.134254	+	0.232534i
$750$	7.43243	+	17.8818i	0.271394	+	0.652951i
$751$	−22.4949	+	38.9623i	−0.820850	+	1.42175i	0.0841993	+	0.996449i	$0.473167\pi$
$751$	−22.4949	+	38.9623i	−0.820850	+	1.42175i	−0.905050	+	0.425306i	$0.860167\pi$
$752$	−0.389270	−	0.224745i	−0.0141952	−	0.00819560i
$753$	−18.0116	−	8.29796i	−0.656378	−	0.302394i
$754$	−7.34847	−	12.7279i	−0.267615	−	0.463524i
$755$	1.55051	+	15.3485i	0.0564288	+	0.558588i
$756$	−22.2474	+	6.29253i	−0.809132	+	0.228857i
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−26.1076	+	15.0732i	−0.948270	+	0.547484i
$759$	3.04541	−	6.61037i	0.110541	−	0.239941i
$760$	−0.505224	+	1.12252i	−0.0183264	+	0.0407182i
$761$	24.2474	−	41.9978i	0.878969	−	1.52242i	0.0264959	−	0.999649i	$-0.491565\pi$
$761$	24.2474	−	41.9978i	0.878969	−	1.52242i	0.852473	−	0.522771i	$-0.175102\pi$
$762$	−0.460702	−	5.00000i	−0.0166895	−	0.181131i
$763$	30.8270	−	17.7980i	1.11601	−	0.644329i
$764$	6.24745			0.226025
$765$	−25.1042	+	7.33968i	−0.907644	+	0.265367i
$766$	−1.79796			−0.0649629
$767$	23.8594	−	13.7753i	0.861515	−	0.497396i
$768$	1.41421	−	1.00000i	0.0510310	−	0.0360844i
$769$	−12.2474	+	21.2132i	−0.441654	+	0.764968i	−0.997812	−	0.0661088i	$-0.978942\pi$
$769$	−12.2474	+	21.2132i	−0.441654	+	0.764968i	0.556158	+	0.831076i	$0.312275\pi$
$770$	13.1509	+	5.91894i	0.473925	+	0.213304i
$771$	19.8990	+	28.1414i	0.716644	+	1.01349i
$772$	−13.5939	+	7.84847i	−0.489257	+	0.282473i
$773$			23.3939i			0.841419i	0.907195	+	0.420710i	$0.138219\pi$
$773$			23.3939i			0.841419i	−0.907195	+	0.420710i	$0.861781\pi$
$774$	21.9722	−	4.08372i	0.789774	−	0.146786i
$775$	−31.5959	+	6.44949i	−1.13496	+	0.231673i
$776$	6.50000	+	11.2583i	0.233336	+	0.404151i
$777$	−5.65685	−	61.3939i	−0.202939	−	2.20249i
$778$	−19.4418	−	11.2247i	−0.697023	−	0.402427i
$779$	0.275255	−	0.476756i	0.00986204	−	0.0170816i
$780$	8.97175	+	3.08346i	0.321240	+	0.110406i
$781$	−1.77526	−	3.07483i	−0.0635236	−	0.110026i
$782$			11.3031i			0.404197i
$783$	−21.7381	+	22.3485i	−0.776857	+	0.798669i
$784$	−12.7980			−0.457070
$785$	−20.9121	−	29.0290i	−0.746385	−	1.03609i
$786$	3.55051	−	7.70674i	0.126643	−	0.274890i
$787$	−6.40329	−	3.69694i	−0.228252	−	0.131782i	0.381513	−	0.924363i	$-0.375403\pi$
$787$	−6.40329	−	3.69694i	−0.228252	−	0.131782i	−0.609766	+	0.792582i	$0.708736\pi$
$788$	−6.92820	−	4.00000i	−0.246807	−	0.142494i
$789$	−13.0227	+	1.19992i	−0.463621	+	0.0427182i
$790$	9.60450	+	13.3324i	0.341713	+	0.474346i
$791$	21.7980			0.775046
$792$	4.09978	+	1.44949i	0.145679	+	0.0515054i
$793$		−	1.10102i		−	0.0390984i
$794$	−8.89898	−	15.4135i	−0.315813	−	0.547004i
$795$	−24.6853	+	21.4835i	−0.875499	+	0.761942i
$796$	−10.2247	+	17.7098i	−0.362406	+	0.627706i
$797$	30.8270	+	17.7980i	1.09195	+	0.630436i	0.934094	−	0.357027i	$-0.116209\pi$
$797$	30.8270	+	17.7980i	1.09195	+	0.630436i	0.157853	+	0.987463i	$0.449543\pi$
$798$	3.46410	−	2.44949i	0.122628	−	0.0867110i
$799$	0.876276	+	1.51775i	0.0310004	+	0.0536943i
$800$	1.00000	+	4.89898i	0.0353553	+	0.173205i
$801$	−25.1464	−	29.4128i	−0.888505	−	1.03925i
$802$		−	28.7980i		−	1.01689i
$803$	6.02285	−	3.47730i	0.212542	−	0.122711i
$804$	16.2980	−	1.50170i	0.574785	−	0.0529609i
$805$	−26.3018	−	11.8379i	−0.927015	−	0.417230i
$806$	−7.89898	+	13.6814i	−0.278230	+	0.481908i
$807$	−44.1191	−	20.3258i	−1.55307	−	0.715501i
$808$	−6.92820	+	4.00000i	−0.243733	+	0.140720i
$809$	−47.0908			−1.65562			−0.827812	−	0.561005i	$-0.810415\pi$
$809$	−47.0908			−1.65562			−0.827812	+	0.561005i	$0.810415\pi$
$810$	1.11425	−	20.0937i	0.0391509	−	0.706022i
$811$	−17.2474			−0.605640			−0.302820	−	0.953048i	$-0.597928\pi$
$811$	−17.2474			−0.605640			−0.302820	+	0.953048i	$0.597928\pi$
$812$	−23.1202	+	13.3485i	−0.811361	+	0.468439i
$813$	−37.1195	−	17.1010i	−1.30184	−	0.599759i
$814$	−5.79796	+	10.0424i	−0.203218	+	0.351985i
$815$	−0.825027	+	1.83307i	−0.0288994	+	0.0642097i
$816$	−6.72474	+	0.619620i	−0.235413	+	0.0216911i
$817$	−3.55159	+	2.05051i	−0.124254	+	0.0717383i
$818$			6.10102i			0.213317i
$819$	−21.2474	−	24.8523i	−0.742446	−	0.868409i
$820$	−0.224745	−	2.22474i	−0.00784843	−	0.0776915i
$821$	21.0227	+	36.4124i	0.733697	+	1.27080i	0.955292	+	0.295662i	$0.0955404\pi$
$821$	21.0227	+	36.4124i	0.733697	+	1.27080i	−0.221595	+	0.975139i	$0.571126\pi$
$822$	4.24264	−	3.00000i	0.147979	−	0.104637i
$823$	6.57826	+	3.79796i	0.229304	+	0.132389i	0.610251	−	0.792208i	$-0.291069\pi$
$823$	6.57826	+	3.79796i	0.229304	+	0.132389i	−0.380947	+	0.924597i	$0.624402\pi$
$824$	−5.12372	+	8.87455i	−0.178493	+	0.309160i
$825$	−8.59287	+	9.15091i	−0.299165	+	0.318594i
$826$	−25.0227	−	43.3406i	−0.870651	−	1.50801i
$827$		−	13.7980i		−	0.479802i	−0.970797	−	0.239901i	$-0.922885\pi$
$827$		−	13.7980i		−	0.479802i	0.970797	−	0.239901i	$-0.0771150\pi$
$828$	−8.19955	−	2.89898i	−0.284954	−	0.100747i
$829$	21.5505			0.748480			0.374240	−	0.927332i	$-0.377904\pi$
$829$	21.5505			0.748480			0.374240	+	0.927332i	$0.377904\pi$
$830$	−7.25725	+	5.22803i	−0.251903	+	0.181468i
$831$	−16.5505	+	1.52497i	−0.574131	+	0.0529006i
$832$	2.12132	+	1.22474i	0.0735436	+	0.0424604i
$833$	43.2138	+	24.9495i	1.49727	+	0.864449i
$834$	−8.15153	+	17.6937i	−0.282264	+	0.612684i
$835$	31.6916	+	43.9925i	1.09673	+	1.52242i
$836$	−0.797959			−0.0275980
$837$	32.4876	+	8.22474i	1.12294	+	0.284289i
$838$			0.898979i			0.0310547i
$839$	7.87628	+	13.6421i	0.271919	+	0.470978i	0.969353	−	0.245671i	$-0.0790083\pi$
$839$	7.87628	+	13.6421i	0.271919	+	0.470978i	−0.697434	+	0.716649i	$0.745675\pi$
$840$	5.60110	−	16.2971i	0.193256	−	0.562305i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−14.2457	−	8.22474i	−0.490938	−	0.283443i
$843$	1.90702	+	20.6969i	0.0656814	+	0.712840i
$844$	−7.89898	−	13.6814i	−0.271894	−	0.470934i
$845$	−1.57321	−	15.5732i	−0.0541202	−	0.535735i
$846$	−1.32577	+	0.246405i	−0.0455808	+	0.00847158i
$847$		−	39.5959i		−	1.36053i
$848$	−7.31747	+	4.22474i	−0.251283	+	0.145078i
$849$	−4.00000	−	5.65685i	−0.137280	−	0.194143i
$850$	6.17389	−	18.4915i	0.211763	−	0.634252i
$851$	11.5959	−	20.0847i	0.397503	−	0.688495i
$852$	−3.46410	+	2.44949i	−0.118678	+	0.0839181i
$853$	21.7774	−	12.5732i	0.745646	−	0.430499i	−0.0784728	−	0.996916i	$-0.525004\pi$
$853$	21.7774	−	12.5732i	0.745646	−	0.430499i	0.824118	+	0.566418i	$0.191671\pi$
$854$	−2.00000			−0.0684386
$855$	1.03631	+	3.54455i	0.0354412	+	0.121221i
$856$	−1.65153			−0.0564482
$857$	−46.2405	+	26.6969i	−1.57954	+	0.911950i	−0.584621	+	0.811306i	$0.698757\pi$
$857$	−46.2405	+	26.6969i	−1.57954	+	0.911950i	−0.994923	+	0.100644i	$0.967910\pi$
$858$	0.564242	+	6.12372i	0.0192629	+	0.209061i
$859$	17.8712	−	30.9538i	0.609757	−	1.05613i	−0.381524	−	0.924359i	$-0.624601\pi$
$859$	17.8712	−	30.9538i	0.609757	−	1.05613i	0.991280	−	0.131770i	$-0.0420661\pi$
$860$	−6.83668	+	15.1899i	−0.233129	+	0.517973i
$861$	−3.22474	+	6.99964i	−0.109899	+	0.238547i
$862$	−11.9101	+	6.87628i	−0.405658	+	0.234207i
$863$		−	21.5505i		−	0.733588i	−0.930302	−	0.366794i	$-0.880455\pi$
$863$		−	21.5505i		−	0.733588i	0.930302	−	0.366794i	$-0.119545\pi$
$864$	1.27526	−	5.03723i	0.0433851	−	0.171370i
$865$	−17.3485	+	1.75255i	−0.589866	+	0.0595885i
$866$	11.5000	+	19.9186i	0.390786	+	0.676861i
$867$	−2.82843	−	1.30306i	−0.0960584	−	0.0442543i
$868$	24.8523	+	14.3485i	0.843541	+	0.487019i
$869$	−5.32577	+	9.22450i	−0.180664	+	0.312920i
$870$	−4.44709	−	22.8084i	−0.150770	−	0.773277i
$871$	11.5732	+	20.0454i	0.392143	+	0.679212i
$872$			8.00000i			0.270914i
$873$	36.7696	+	13.0000i	1.24446	+	0.439983i
$874$	1.59592			0.0539827
$875$	36.5629	+	33.7328i	1.23605	+	1.14038i
$876$	−4.79796	−	6.78534i	−0.162108	−	0.229255i
$877$	47.7582	+	27.5732i	1.61268	+	0.931081i	0.988746	+	0.149604i	$0.0478000\pi$
$877$	47.7582	+	27.5732i	1.61268	+	0.931081i	0.623934	+	0.781477i	$0.285533\pi$
$878$	19.0919	+	11.0227i	0.644320	+	0.371998i
$879$	−18.0000	−	25.4558i	−0.607125	−	0.858604i
$880$	−2.62983	+	1.89449i	−0.0886515	+	0.0638634i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	−29.1824	+	24.9495i	−0.982623	+	0.840093i
$883$			11.4495i			0.385306i	0.981267	+	0.192653i	$0.0617092\pi$
$883$			11.4495i			0.385306i	−0.981267	+	0.192653i	$0.938291\pi$
$884$	−4.77526	−	8.27098i	−0.160609	−	0.278183i
$885$	42.7561	−	8.33639i	1.43723	−	0.280225i
$886$	−1.62372	+	2.81237i	−0.0545501	+	0.0944835i
$887$	−4.02834	−	2.32577i	−0.135259	−	0.0780916i	0.430844	−	0.902427i	$-0.358216\pi$
$887$	−4.02834	−	2.32577i	−0.135259	−	0.0780916i	−0.566102	+	0.824335i	$0.691549\pi$
$888$	12.5851	+	5.79796i	0.422327	+	0.194567i
$889$	−6.44949	−	11.1708i	−0.216309	−	0.374658i
$890$	28.6969	−	2.89898i	0.961924	−	0.0971740i
$891$	12.1742	−	4.68729i	0.407852	−	0.157030i
$892$			18.8990i			0.632785i
$893$	0.214297	−	0.123724i	0.00717117	−	0.00414028i
$894$	11.7753	−	25.5594i	0.393823	−	0.854834i
$895$	−18.1455	−	8.16693i	−0.606538	−	0.272990i
$896$	2.22474	−	3.85337i	0.0743235	−	0.128732i
$897$	−1.12848	−	12.2474i	−0.0376790	−	0.408930i
$898$	−0.691053	+	0.398979i	−0.0230607	+	0.0133141i
$899$	38.6969			1.29062
$900$	11.8307	+	9.22135i	0.394358	+	0.307378i
$901$	32.9444			1.09754
$902$	1.25529	−	0.724745i	0.0417967	−	0.0241314i
$903$	46.8761	−	33.1464i	1.55994	−	1.10304i
$904$	−2.44949	+	4.24264i	−0.0814688	+	0.141108i
$905$	21.3071	+	9.58989i	0.708272	+	0.318779i
$906$	6.89898	+	9.75663i	0.229203	+	0.324142i
$907$	29.2217	−	16.8712i	0.970292	−	0.560198i	0.0709665	−	0.997479i	$-0.477392\pi$
$907$	29.2217	−	16.8712i	0.970292	−	0.560198i	0.899325	+	0.437281i	$0.144058\pi$
$908$		−	1.44949i		−	0.0481030i
$909$	−8.00000	+	22.6274i	−0.265343	+	0.750504i
$910$	24.2474	−	2.44949i	0.803795	−	0.0811998i
$911$	0.123724	+	0.214297i	0.00409917	+	0.00709997i	0.868068	−	0.496446i	$-0.165362\pi$
$911$	0.123724	+	0.214297i	0.00409917	+	0.00709997i	−0.863969	+	0.503546i	$0.832029\pi$
$912$	0.0874863	+	0.949490i	0.00289696	+	0.0314407i
$913$	−5.02118	−	2.89898i	−0.166177	−	0.0959422i
$914$	4.05051	−	7.01569i	0.133979	−	0.232058i
$915$	0.565826	−	1.64635i	0.0187056	−	0.0544265i
$916$	6.77526	+	11.7351i	0.223861	+	0.387738i
$917$		−	21.7980i		−	0.719832i
$918$	−14.1261	+	14.5227i	−0.466230	+	0.479321i
$919$	−10.8990			−0.359524			−0.179762	−	0.983710i	$-0.557533\pi$
$919$	−10.8990			−0.359524			−0.179762	+	0.983710i	$0.557533\pi$
$920$	5.25966	−	3.78899i	0.173406	−	0.124919i
$921$	−17.3536	+	37.6677i	−0.571820	+	1.24119i
$922$	2.12132	+	1.22474i	0.0698620	+	0.0403348i
$923$	−5.19615	−	3.00000i	−0.171033	−	0.0987462i
$924$	11.1237	−	1.02494i	0.365944	−	0.0337182i
$925$	−29.9411	+	26.5241i	−0.984458	+	0.872108i
$926$	−24.0000			−0.788689
$927$	5.61753	+	30.2247i	0.184504	+	0.992711i
$928$		−	6.00000i		−	0.196960i
$929$	−27.7980	−	48.1475i	−0.912021	−	1.57967i	−0.811205	−	0.584762i	$-0.801188\pi$
$929$	−27.7980	−	48.1475i	−0.912021	−	1.57967i	−0.100817	−	0.994905i	$-0.532146\pi$
$930$	−18.8423	+	16.3984i	−0.617864	+	0.537723i
$931$	3.52270	−	6.10150i	0.115452	−	0.199969i
$932$	−13.5939	−	7.84847i	−0.445285	−	0.257085i
$933$	32.3840	−	22.8990i	1.06021	−	0.749679i
$934$	−2.17423	−	3.76588i	−0.0711431	−	0.123224i
$935$	12.5732	−	1.27015i	0.411188	−	0.0415384i
$936$	7.22474	−	1.34278i	0.236148	−	0.0438902i
$937$		−	39.5959i		−	1.29354i	−0.762684	−	0.646771i	$-0.776119\pi$
$937$		−	39.5959i		−	1.29354i	0.762684	−	0.646771i	$-0.223881\pi$
$938$	36.4124	−	21.0227i	1.18891	−	0.686416i
$939$	13.2753	−	1.22319i	0.433222	−	0.0399172i
$940$	0.412514	−	0.916536i	0.0134547	−	0.0298941i
$941$	24.8990	−	43.1263i	0.811684	−	1.40588i	−0.100001	−	0.994987i	$-0.531885\pi$
$941$	24.8990	−	43.1263i	0.811684	−	1.40588i	0.911685	−	0.410890i	$-0.134782\pi$
$942$	−25.1701	−	11.5959i	−0.820087	−	0.377815i
$943$	−2.51059	+	1.44949i	−0.0817561	+	0.0472019i
$944$	11.2474			0.366073
$945$	−18.9993	−	48.0807i	−0.618046	−	1.56406i
$946$	−10.7980			−0.351072
$947$	−18.4008	+	10.6237i	−0.597947	+	0.345225i	−0.768233	−	0.640170i	$-0.778864\pi$
$947$	−18.4008	+	10.6237i	−0.597947	+	0.345225i	0.170287	+	0.985395i	$0.445531\pi$
$948$	11.5601	+	5.32577i	0.375455	+	0.172973i
$949$	5.87628	−	10.1780i	0.190752	−	0.330392i
$950$	−2.61087	−	0.871713i	−0.0847079	−	0.0282821i
$951$	53.3712	−	4.91764i	1.73068	−	0.159465i
$952$	−15.0242	+	8.67423i	−0.486938	+	0.281134i
$953$			50.7980i			1.64551i	0.568398	+	0.822754i	$0.307563\pi$
$953$			50.7980i			1.64551i	−0.568398	+	0.822754i	$0.692437\pi$
$954$	−8.44949	+	23.8988i	−0.273562	+	0.773751i
$955$	1.40408	+	13.8990i	0.0454350	+	0.449760i
$956$	−14.3485	−	24.8523i	−0.464063	−	0.803780i
$957$	12.2993	−	8.69694i	0.397581	−	0.281132i
$958$	10.9959	+	6.34847i	0.355260	+	0.205110i
$959$	6.67423	−	11.5601i	0.215522	−	0.373296i
$960$	2.54258	+	2.92152i	0.0820615	+	0.0942916i
$961$	−5.29796	−	9.17633i	−0.170902	−	0.296011i
$962$			19.5959i			0.631798i
$963$	−3.76588	+	3.21964i	−0.121354	+	0.103752i
$964$	−1.00000			−0.0322078
$965$	−20.5160	−	28.4792i	−0.660434	−	0.916777i
$966$	−22.2474	+	2.04989i	−0.715800	+	0.0659541i
$967$	24.8523	+	14.3485i	0.799195	+	0.461416i	0.843190	−	0.537616i	$-0.180675\pi$
$967$	24.8523	+	14.3485i	0.799195	+	0.461416i	−0.0439944	+	0.999032i	$0.514008\pi$
$968$	7.70674	+	4.44949i	0.247704	+	0.143012i
$969$	1.55561	−	3.37662i	0.0499735	−	0.108473i
$970$	−23.5861	+	16.9911i	−0.757303	+	0.545551i
$971$	−23.3939			−0.750745			−0.375373	−	0.926874i	$-0.622485\pi$
$971$	−23.3939			−0.750745			−0.375373	+	0.926874i	$0.622485\pi$
$972$	−6.91215	−	13.9722i	−0.221707	−	0.448158i
$973$			50.0454i			1.60438i
$974$	17.4495	+	30.2234i	0.559118	+	0.968420i
$975$	−4.84357	+	20.6528i	−0.155118	+	0.661420i
$976$	0.224745	−	0.389270i	0.00719391	−	0.0124602i
$977$	−32.8215	−	18.9495i	−1.05005	−	0.606248i	−0.127388	−	0.991853i	$-0.540659\pi$
$977$	−32.8215	−	18.9495i	−1.05005	−	0.606248i	−0.922664	+	0.385605i	$0.873993\pi$
$978$	0.142865	+	1.55051i	0.00456831	+	0.0495799i
$979$	9.34847	+	16.1920i	0.298778	+	0.517499i
$980$	−2.87628	−	28.4722i	−0.0918793	−	0.909511i
$981$	15.5959	+	18.2419i	0.497939	+	0.582419i
$982$		−	23.4495i		−	0.748303i
$983$	32.3840	−	18.6969i	1.03289	−	0.596340i	0.115079	−	0.993356i	$-0.463288\pi$
$983$	32.3840	−	18.6969i	1.03289	−	0.596340i	0.917811	+	0.397017i	$0.129954\pi$
$984$	−1.00000	−	1.41421i	−0.0318788	−	0.0450835i
$985$	7.34190	−	16.3125i	0.233932	−	0.519758i
$986$	−11.6969	+	20.2597i	−0.372506	+	0.645200i
$987$	−2.82843	+	2.00000i	−0.0900298	+	0.0636607i
$988$	−1.16781	+	0.674235i	−0.0371529	+	0.0214503i
$989$	21.5959			0.686710
$990$	−2.30334	+	9.44672i	−0.0732050	+	0.300237i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	−5.58542	+	3.22474i	−0.177337	+	0.102386i
$993$	5.30691	+	57.5959i	0.168410	+	1.82775i
$994$	−5.44949	+	9.43879i	−0.172847	+	0.299380i
$995$	−41.6977	−	18.7673i	−1.32191	−	0.594962i
$996$	−2.89898	+	6.29253i	−0.0918577	+	0.199386i
$997$	−28.5307	+	16.4722i	−0.903576	+	0.521680i	−0.878359	−	0.478002i	$-0.841361\pi$
$997$	−28.5307	+	16.4722i	−0.903576	+	0.521680i	−0.0252170	+	0.999682i	$0.508028\pi$
$998$			3.24745i			0.102796i
$999$	40.0000	−	11.3137i	1.26554	−	0.357950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.i.b.49.1	✓	8
3.2	odd	2		270.2.i.b.199.3		8
4.3	odd	2		720.2.by.c.49.4		8
5.2	odd	4		450.2.e.k.301.1		4
5.3	odd	4		450.2.e.n.301.2		4
5.4	even	2	inner	90.2.i.b.49.4	yes	8
9.2	odd	6		270.2.i.b.19.2		8
9.4	even	3		810.2.c.f.649.1		4
9.5	odd	6		810.2.c.e.649.4		4
9.7	even	3	inner	90.2.i.b.79.4	yes	8
12.11	even	2		2160.2.by.d.1009.1		8
15.2	even	4		1350.2.e.m.901.2		4
15.8	even	4		1350.2.e.j.901.1		4
15.14	odd	2		270.2.i.b.199.2		8
20.19	odd	2		720.2.by.c.49.1		8
36.7	odd	6		720.2.by.c.529.1		8
36.11	even	6		2160.2.by.d.289.4		8
45.2	even	12		1350.2.e.m.451.2		4
45.4	even	6		810.2.c.f.649.3		4
45.7	odd	12		450.2.e.k.151.1		4
45.13	odd	12		4050.2.a.bq.1.2		2
45.14	odd	6		810.2.c.e.649.2		4
45.22	odd	12		4050.2.a.bs.1.1		2
45.23	even	12		4050.2.a.bz.1.2		2
45.29	odd	6		270.2.i.b.19.3		8
45.32	even	12		4050.2.a.bm.1.1		2
45.34	even	6	inner	90.2.i.b.79.1	yes	8
45.38	even	12		1350.2.e.j.451.1		4
45.43	odd	12		450.2.e.n.151.2		4
60.59	even	2		2160.2.by.d.1009.4		8
180.79	odd	6		720.2.by.c.529.4		8
180.119	even	6		2160.2.by.d.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.1	✓	8	1.1	even	1	trivial
90.2.i.b.49.4	yes	8	5.4	even	2	inner
90.2.i.b.79.1	yes	8	45.34	even	6	inner
90.2.i.b.79.4	yes	8	9.7	even	3	inner
270.2.i.b.19.2		8	9.2	odd	6
270.2.i.b.19.3		8	45.29	odd	6
270.2.i.b.199.2		8	15.14	odd	2
270.2.i.b.199.3		8	3.2	odd	2
450.2.e.k.151.1		4	45.7	odd	12
450.2.e.k.301.1		4	5.2	odd	4
450.2.e.n.151.2		4	45.43	odd	12
450.2.e.n.301.2		4	5.3	odd	4
720.2.by.c.49.1		8	20.19	odd	2
720.2.by.c.49.4		8	4.3	odd	2
720.2.by.c.529.1		8	36.7	odd	6
720.2.by.c.529.4		8	180.79	odd	6
810.2.c.e.649.2		4	45.14	odd	6
810.2.c.e.649.4		4	9.5	odd	6
810.2.c.f.649.1		4	9.4	even	3
810.2.c.f.649.3		4	45.4	even	6
1350.2.e.j.451.1		4	45.38	even	12
1350.2.e.j.901.1		4	15.8	even	4
1350.2.e.m.451.2		4	45.2	even	12
1350.2.e.m.901.2		4	15.2	even	4
2160.2.by.d.289.1		8	180.119	even	6
2160.2.by.d.289.4		8	36.11	even	6
2160.2.by.d.1009.1		8	12.11	even	2
2160.2.by.d.1009.4		8	60.59	even	2
4050.2.a.bm.1.1		2	45.32	even	12
4050.2.a.bq.1.2		2	45.13	odd	12
4050.2.a.bs.1.1		2	45.22	odd	12
4050.2.a.bz.1.2		2	45.23	even	12

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	90.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.57313 - 0.724745i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.03906 + 0.917738i) q^{5} +(1.72474 - 0.158919i) q^{6} +(3.85337 - 2.22474i) q^{7} +1.00000i q^{8} +(1.94949 + 2.28024i) q^{9} +(-2.22474 + 0.224745i) q^{10} +(-0.724745 - 1.25529i) q^{11} +(-1.41421 + 1.00000i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(-2.22474 + 3.85337i) q^{14} +(-2.54258 - 2.92152i) q^{15} +(-0.500000 - 0.866025i) q^{16} +3.89898i q^{17} +(-2.82843 - 1.00000i) q^{18} +0.550510 q^{19} +(1.81431 - 1.30701i) q^{20} +(-7.67423 + 0.707107i) q^{21} +(1.25529 + 0.724745i) q^{22} +(-2.51059 - 1.44949i) q^{23} +(0.724745 - 1.57313i) q^{24} +(3.31552 + 3.74264i) q^{25} +2.44949 q^{26} +(-1.41421 - 5.00000i) q^{27} -4.44949i q^{28} +(-3.00000 - 5.19615i) q^{29} +(3.66270 + 1.25882i) q^{30} +(-3.22474 + 5.58542i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.230351 + 2.50000i) q^{33} +(-1.94949 - 3.37662i) q^{34} +(9.89898 - 1.00000i) q^{35} +(2.94949 - 0.548188i) q^{36} +8.00000i q^{37} +(-0.476756 + 0.275255i) q^{38} +(2.44949 + 3.46410i) q^{39} +(-0.917738 + 2.03906i) q^{40} +(0.500000 - 0.866025i) q^{41} +(6.29253 - 4.44949i) q^{42} +(-6.45145 + 3.72474i) q^{43} -1.44949 q^{44} +(1.88246 + 6.43866i) q^{45} +2.89898 q^{46} +(0.389270 - 0.224745i) q^{47} +(0.158919 + 1.72474i) q^{48} +(6.39898 - 11.0834i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(2.82577 - 6.13361i) q^{51} +(-2.12132 + 1.22474i) q^{52} -8.44949i q^{53} +(3.72474 + 3.62302i) q^{54} +(-0.325765 - 3.22474i) q^{55} +(2.22474 + 3.85337i) q^{56} +(-0.866025 - 0.398979i) q^{57} +(5.19615 + 3.00000i) q^{58} +(-5.62372 + 9.74058i) q^{59} +(-3.80140 + 0.741181i) q^{60} +(0.224745 + 0.389270i) q^{61} -6.44949i q^{62} +(12.5851 + 4.44949i) q^{63} -1.00000 q^{64} +(-3.20150 - 4.44414i) q^{65} +(-1.44949 - 2.04989i) q^{66} +(-8.18350 - 4.72474i) q^{67} +(3.37662 + 1.94949i) q^{68} +(2.89898 + 4.09978i) q^{69} +(-8.07277 + 5.81552i) q^{70} +2.44949 q^{71} +(-2.28024 + 1.94949i) q^{72} +4.79796i q^{73} +(-4.00000 - 6.92820i) q^{74} +(-2.50328 - 8.29057i) q^{75} +(0.275255 - 0.476756i) q^{76} +(-5.58542 - 3.22474i) q^{77} +(-3.85337 - 1.77526i) q^{78} +(-3.67423 - 6.36396i) q^{79} +(-0.224745 - 2.22474i) q^{80} +(-1.39898 + 8.89060i) q^{81} +1.00000i q^{82} +(3.46410 - 2.00000i) q^{83} +(-3.22474 + 6.99964i) q^{84} +(-3.57824 + 7.95025i) q^{85} +(3.72474 - 6.45145i) q^{86} +(0.953512 + 10.3485i) q^{87} +(1.25529 - 0.724745i) q^{88} -12.8990 q^{89} +(-4.84959 - 4.63481i) q^{90} -10.8990 q^{91} +(-2.51059 + 1.44949i) q^{92} +(9.12096 - 6.44949i) q^{93} +(-0.224745 + 0.389270i) q^{94} +(1.12252 + 0.505224i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(11.2583 - 6.50000i) q^{97} +12.7980i q^{98} +(1.44949 - 4.09978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{9} - 8 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{15} - 4 q^{16} + 24 q^{19} + 4 q^{20} - 32 q^{21} - 4 q^{24} - 24 q^{29} + 16 q^{30} - 16 q^{31} + 4 q^{34} + 40 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^9 - 8 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^15 - 4 * q^16 + 24 * q^19 + 4 * q^20 - 32 * q^21 - 4 * q^24 - 24 * q^29 + 16 * q^30 - 16 * q^31 + 4 * q^34 + 40 * q^35 + 4 * q^36 - 4 * q^40 + 4 * q^41 + 8 * q^44 + 20 * q^45 - 16 * q^46 + 12 * q^49 - 4 * q^50 + 52 * q^51 + 20 * q^54 - 32 * q^55 + 8 * q^56 + 4 * q^59 - 16 * q^60 - 8 * q^61 - 8 * q^64 - 12 * q^65 + 8 * q^66 - 16 * q^69 + 4 * q^70 - 32 * q^74 - 4 * q^75 + 12 * q^76 + 8 * q^80 + 28 * q^81 - 16 * q^84 - 20 * q^85 + 20 * q^86 - 64 * q^89 - 20 * q^90 - 48 * q^91 + 8 * q^94 - 24 * q^95 - 8 * q^96 - 8 * q^99

Introduction

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