LMFDB - Embedded newform 90.2.i.b.49.3

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			49.3
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	90.49
Dual form			90.2.i.b.79.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.158919 - 1.72474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.917738 + 2.03906i) q^{5} +(-0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(-2.94949 - 0.548188i) q^{9} +(0.224745 + 2.22474i) q^{10} +(1.72474 + 2.98735i) q^{11} +(-1.41421 - 1.00000i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(0.224745 - 0.389270i) q^{14} +(3.37101 + 1.90691i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.89898i q^{17} +(-2.82843 + 1.00000i) q^{18} +5.44949 q^{19} +(1.30701 + 1.81431i) q^{20} +(-0.325765 - 0.707107i) q^{21} +(2.98735 + 1.72474i) q^{22} +(-5.97469 - 3.44949i) q^{23} +(-1.72474 - 0.158919i) q^{24} +(-3.31552 - 3.74264i) q^{25} -2.44949 q^{26} +(-1.41421 + 5.00000i) q^{27} -0.449490i q^{28} +(-3.00000 - 5.19615i) q^{29} +(3.87283 - 0.0340742i) q^{30} +(-0.775255 + 1.34278i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.42650 - 2.50000i) q^{33} +(2.94949 + 5.10867i) q^{34} +(0.101021 + 1.00000i) q^{35} +(-1.94949 + 2.28024i) q^{36} -8.00000i q^{37} +(4.71940 - 2.72474i) q^{38} +(-2.44949 + 3.46410i) q^{39} +(2.03906 + 0.917738i) q^{40} +(0.500000 - 0.866025i) q^{41} +(-0.635674 - 0.449490i) q^{42} +(2.20881 - 1.27526i) q^{43} +3.44949 q^{44} +(3.82465 - 5.51109i) q^{45} -6.89898 q^{46} +(3.85337 - 2.22474i) q^{47} +(-1.57313 + 0.724745i) q^{48} +(-3.39898 + 5.88721i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(10.1742 + 0.937458i) q^{51} +(-2.12132 + 1.22474i) q^{52} +3.55051i q^{53} +(1.27526 + 5.03723i) q^{54} +(-7.67423 + 0.775255i) q^{55} +(-0.224745 - 0.389270i) q^{56} +(0.866025 - 9.39898i) q^{57} +(-5.19615 - 3.00000i) q^{58} +(6.62372 - 11.4726i) q^{59} +(3.33694 - 1.96593i) q^{60} +(-2.22474 - 3.85337i) q^{61} +1.55051i q^{62} +(-1.27135 + 0.449490i) q^{63} -1.00000 q^{64} +(4.44414 - 3.20150i) q^{65} +(3.44949 - 4.87832i) q^{66} +(3.94086 + 2.27526i) q^{67} +(5.10867 + 2.94949i) q^{68} +(-6.89898 + 9.75663i) q^{69} +(0.587486 + 0.815515i) q^{70} -2.44949 q^{71} +(-0.548188 + 2.94949i) q^{72} +14.7980i q^{73} +(-4.00000 - 6.92820i) q^{74} +(-6.98200 + 5.12364i) q^{75} +(2.72474 - 4.71940i) q^{76} +(1.34278 + 0.775255i) q^{77} +(-0.389270 + 4.22474i) q^{78} +(3.67423 + 6.36396i) q^{79} +(2.22474 - 0.224745i) q^{80} +(8.39898 + 3.23375i) q^{81} -1.00000i q^{82} +(-3.46410 + 2.00000i) q^{83} +(-0.775255 - 0.0714323i) q^{84} +(-12.0284 - 5.41372i) q^{85} +(1.27526 - 2.20881i) q^{86} +(-9.43879 + 4.34847i) q^{87} +(2.98735 - 1.72474i) q^{88} -3.10102 q^{89} +(0.556696 - 6.68506i) q^{90} -1.10102 q^{91} +(-5.97469 + 3.44949i) q^{92} +(2.19275 + 1.55051i) q^{93} +(2.22474 - 3.85337i) q^{94} +(-5.00120 + 11.1118i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(-11.2583 + 6.50000i) q^{97} +6.79796i q^{98} +(-3.44949 - 9.75663i) 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
$3$	0.158919	−	1.72474i	0.0917517	−	0.995782i
$3$	0.158919	−	1.72474i	0.0917517	−	0.995782i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.917738	+	2.03906i	−0.410425	+	0.911894i
$5$	−0.917738	+	2.03906i	−0.410425	+	0.911894i
$6$	−0.724745	−	1.57313i	−0.295876	−	0.642229i
$7$	0.389270	−	0.224745i	0.147130	−	0.0849456i	−0.424628	−	0.905368i	$-0.639595\pi$
$7$	0.389270	−	0.224745i	0.147130	−	0.0849456i	0.571758	+	0.820422i	$0.306262\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.94949	−	0.548188i	−0.983163	−	0.182729i
$10$	0.224745	+	2.22474i	0.0710706	+	0.703526i
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	0.999729	+	0.0232854i	$0.00741263\pi$
$11$	1.72474	+	2.98735i	0.520030	+	0.900719i	−0.479699	+	0.877433i	$0.659254\pi$
$12$	−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	$0.776986\pi$
$14$	0.224745	−	0.389270i	0.0600656	−	0.104037i
$15$	3.37101	+	1.90691i	0.870391	+	0.492361i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			5.89898i			1.43071i	0.698760	+	0.715356i	$0.253736\pi$
$17$			5.89898i			1.43071i	−0.698760	+	0.715356i	$0.746264\pi$
$18$	−2.82843	+	1.00000i	−0.666667	+	0.235702i
$19$	5.44949			1.25020			0.625099	−	0.780545i	$-0.285058\pi$
$19$	5.44949			1.25020			0.625099	+	0.780545i	$0.285058\pi$
$20$	1.30701	+	1.81431i	0.292256	+	0.405693i
$21$	−0.325765	−	0.707107i	−0.0710878	−	0.154303i
$22$	2.98735	+	1.72474i	0.636904	+	0.367717i
$23$	−5.97469	−	3.44949i	−1.24581	−	0.719268i	−0.275538	−	0.961290i	$-0.588856\pi$
$23$	−5.97469	−	3.44949i	−1.24581	−	0.719268i	−0.970271	+	0.242022i	$0.922189\pi$
$24$	−1.72474	−	0.158919i	−0.352062	−	0.0324391i
$25$	−3.31552	−	3.74264i	−0.663103	−	0.748528i
$26$	−2.44949			−0.480384
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$		−	0.449490i		−	0.0849456i
$29$	−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	$-0.354747\pi$
$30$	3.87283	−	0.0340742i	0.707079	−	0.00622106i
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	−0.927209	−	0.374544i	$-0.877799\pi$
$31$	−0.775255	+	1.34278i	−0.139240	+	0.241171i	0.787969	+	0.615715i	$0.211133\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	5.42650	−	2.50000i	0.944633	−	0.435194i
$34$	2.94949	+	5.10867i	0.505833	+	0.876129i
$35$	0.101021	+	1.00000i	0.0170756	+	0.169031i
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	4.71940	−	2.72474i	0.765587	−	0.442012i
$39$	−2.44949	+	3.46410i	−0.392232	+	0.554700i
$40$	2.03906	+	0.917738i	0.322403	+	0.145107i
$41$	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	$0.141786\pi$
$42$	−0.635674	−	0.449490i	−0.0980867	−	0.0693578i
$43$	2.20881	−	1.27526i	0.336840	−	0.194475i	−0.322034	−	0.946728i	$-0.604366\pi$
$43$	2.20881	−	1.27526i	0.336840	−	0.194475i	0.658874	+	0.752254i	$0.271033\pi$
$44$	3.44949			0.520030
$45$	3.82465	−	5.51109i	0.570144	−	0.821544i
$46$	−6.89898			−1.01720
$47$	3.85337	−	2.22474i	0.562072	−	0.324512i	−0.191905	−	0.981414i	$-0.561466\pi$
$47$	3.85337	−	2.22474i	0.562072	−	0.324512i	0.753977	+	0.656901i	$0.228133\pi$
$48$	−1.57313	+	0.724745i	−0.227062	+	0.104608i
$49$	−3.39898	+	5.88721i	−0.485568	+	0.841029i
$50$	−4.74264	−	1.58346i	−0.670711	−	0.223936i
$51$	10.1742	+	0.937458i	1.42468	+	0.131270i
$52$	−2.12132	+	1.22474i	−0.294174	+	0.169842i
$53$			3.55051i			0.487700i	0.969813	+	0.243850i	$0.0784105\pi$
$53$			3.55051i			0.487700i	−0.969813	+	0.243850i	$0.921590\pi$
$54$	1.27526	+	5.03723i	0.173540	+	0.685481i
$55$	−7.67423	+	0.775255i	−1.03479	+	0.104535i
$56$	−0.224745	−	0.389270i	−0.0300328	−	0.0520183i
$57$	0.866025	−	9.39898i	0.114708	−	1.24493i
$58$	−5.19615	−	3.00000i	−0.682288	−	0.393919i
$59$	6.62372	−	11.4726i	0.862335	−	1.49361i	−0.00733331	−	0.999973i	$-0.502334\pi$
$59$	6.62372	−	11.4726i	0.862335	−	1.49361i	0.869669	−	0.493636i	$-0.164332\pi$
$60$	3.33694	−	1.96593i	0.430796	−	0.253800i
$61$	−2.22474	−	3.85337i	−0.284849	−	0.493374i	0.687723	−	0.725973i	$-0.258610\pi$
$61$	−2.22474	−	3.85337i	−0.284849	−	0.493374i	−0.972573	+	0.232599i	$0.925277\pi$
$62$			1.55051i			0.196915i
$63$	−1.27135	+	0.449490i	−0.160175	+	0.0566304i
$64$	−1.00000			−0.125000
$65$	4.44414	−	3.20150i	0.551228	−	0.397097i
$66$	3.44949	−	4.87832i	0.424603	−	0.600479i
$67$	3.94086	+	2.27526i	0.481452	+	0.277967i	0.721022	−	0.692913i	$-0.243673\pi$
$67$	3.94086	+	2.27526i	0.481452	+	0.277967i	−0.239569	+	0.970879i	$0.577006\pi$
$68$	5.10867	+	2.94949i	0.619517	+	0.357678i
$69$	−6.89898	+	9.75663i	−0.830540	+	1.17456i
$70$	0.587486	+	0.815515i	0.0702180	+	0.0974727i
$71$	−2.44949			−0.290701			−0.145350	−	0.989380i	$-0.546431\pi$
$71$	−2.44949			−0.290701			−0.145350	+	0.989380i	$0.546431\pi$
$72$	−0.548188	+	2.94949i	−0.0646046	+	0.347601i
$73$			14.7980i			1.73197i	0.500070	+	0.865985i	$0.333308\pi$
$73$			14.7980i			1.73197i	−0.500070	+	0.865985i	$0.666692\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	−6.98200	+	5.12364i	−0.806212	+	0.591627i
$76$	2.72474	−	4.71940i	0.312550	−	0.541352i
$77$	1.34278	+	0.775255i	0.153024	+	0.0883485i
$78$	−0.389270	+	4.22474i	−0.0440761	+	0.478358i
$79$	3.67423	+	6.36396i	0.413384	+	0.716002i	0.995257	−	0.0972777i	$-0.0310135\pi$
$79$	3.67423	+	6.36396i	0.413384	+	0.716002i	−0.581874	+	0.813279i	$0.697680\pi$
$80$	2.22474	−	0.224745i	0.248734	−	0.0251272i
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$		−	1.00000i		−	0.110432i
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	−0.677920	−	0.735135i	$-0.737119\pi$
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	0.297686	+	0.954664i	$0.403785\pi$
$84$	−0.775255	−	0.0714323i	−0.0845873	−	0.00779390i
$85$	−12.0284	−	5.41372i	−1.30466	−	0.587200i
$86$	1.27526	−	2.20881i	0.137514	−	0.238182i
$87$	−9.43879	+	4.34847i	−1.01194	+	0.466205i
$88$	2.98735	−	1.72474i	0.318452	−	0.183858i
$89$	−3.10102			−0.328708			−0.164354	−	0.986401i	$-0.552554\pi$
$89$	−3.10102			−0.328708			−0.164354	+	0.986401i	$0.552554\pi$
$90$	0.556696	−	6.68506i	0.0586809	−	0.704668i
$91$	−1.10102			−0.115418
$92$	−5.97469	+	3.44949i	−0.622905	+	0.359634i
$93$	2.19275	+	1.55051i	0.227378	+	0.160780i
$94$	2.22474	−	3.85337i	0.229465	−	0.397445i
$95$	−5.00120	+	11.1118i	−0.513112	+	1.14005i
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	−11.2583	+	6.50000i	−1.14311	+	0.659975i	−0.947199	−	0.320647i	$-0.896100\pi$
$97$	−11.2583	+	6.50000i	−1.14311	+	0.659975i	−0.195911	+	0.980622i	$0.562766\pi$
$98$			6.79796i			0.686698i
$99$	−3.44949	−	9.75663i	−0.346687	−	0.980578i
$100$	−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	$0.703033\pi$
$102$	9.27987	−	4.27526i	0.918844	−	0.423313i
$103$	12.3387	+	7.12372i	1.21576	+	0.701921i	0.964009	−	0.265870i	$-0.0856591\pi$
$103$	12.3387	+	7.12372i	1.21576	+	0.701921i	0.251755	+	0.967791i	$0.418992\pi$
$104$	−1.22474	+	2.12132i	−0.120096	+	0.208013i
$105$	1.74080	−	0.0153160i	0.169885	−	0.00149469i
$106$	1.77526	+	3.07483i	0.172428	+	0.298654i
$107$		−	16.3485i		−	1.58047i	−0.612806	−	0.790233i	$-0.709959\pi$
$107$		−	16.3485i		−	1.58047i	0.612806	−	0.790233i	$-0.290041\pi$
$108$	3.62302	+	3.72474i	0.348625	+	0.358414i
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	−6.25845	+	4.50851i	−0.596720	+	0.429869i
$111$	−13.7980	−	1.27135i	−1.30964	−	0.120671i
$112$	−0.389270	−	0.224745i	−0.0367825	−	0.0212364i
$113$	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	$0.592654\pi$
$114$	−3.94949	−	8.57277i	−0.369904	−	0.802913i
$115$	12.5169	−	9.01702i	1.16721	−	0.840841i
$116$	−6.00000			−0.557086
$117$	5.58542	+	4.77526i	0.516372	+	0.441472i
$118$		−	13.2474i		−	1.21953i
$119$	1.32577	+	2.29629i	0.121533	+	0.210501i
$120$	1.90691	−	3.37101i	0.174076	−	0.307730i
$121$	−0.449490	+	0.778539i	−0.0408627	+	0.0707763i
$122$	−3.85337	−	2.22474i	−0.348868	−	0.201419i
$123$	−1.41421	−	1.00000i	−0.127515	−	0.0901670i
$124$	0.775255	+	1.34278i	0.0696200	+	0.120585i
$125$	10.6742	−	3.32577i	0.954733	−	0.297465i
$126$	−0.876276	+	1.02494i	−0.0780648	+	0.0913093i
$127$		−	6.89898i		−	0.612185i	−0.952002	−	0.306093i	$-0.900978\pi$
$127$		−	6.89898i		−	0.612185i	0.952002	−	0.306093i	$-0.0990218\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.84847	−	4.01229i	−0.162749	−	0.353262i
$130$	2.24799	−	4.99465i	0.197162	−	0.438060i
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	−0.952967	−	0.303075i	$-0.901987\pi$
$131$	−2.44949	+	4.24264i	−0.214013	+	0.370681i	0.738954	+	0.673756i	$0.235320\pi$
$132$	0.548188	−	5.94949i	0.0477137	−	0.517837i
$133$	2.12132	−	1.22474i	0.183942	−	0.106199i
$134$	4.55051			0.393104
$135$	−8.89741	−	7.47235i	−0.765767	−	0.643118i
$136$	5.89898			0.505833
$137$	−2.59808	+	1.50000i	−0.221969	+	0.128154i	−0.606861	−	0.794808i	$-0.707572\pi$
$137$	−2.59808	+	1.50000i	−0.221969	+	0.128154i	0.384893	+	0.922961i	$0.374238\pi$
$138$	−1.09638	+	11.8990i	−0.0933298	+	1.01291i
$139$	6.62372	−	11.4726i	0.561817	−	0.973096i	−0.435521	−	0.900179i	$-0.643436\pi$
$139$	6.62372	−	11.4726i	0.561817	−	0.973096i	0.997338	−	0.0729170i	$-0.0232308\pi$
$140$	0.916536	+	0.412514i	0.0774614	+	0.0348638i
$141$	−3.22474	−	6.99964i	−0.271573	−	0.589476i
$142$	−2.12132	+	1.22474i	−0.178017	+	0.102778i
$143$		−	8.44949i		−	0.706582i
$144$	1.00000	+	2.82843i	0.0833333	+	0.235702i
$145$	13.3485	−	1.34847i	1.10853	−	0.111984i
$146$	7.39898	+	12.8154i	0.612344	+	1.06061i
$147$	9.61377	+	6.79796i	0.792930	+	0.560686i
$148$	−6.92820	−	4.00000i	−0.569495	−	0.328798i
$149$	−4.12372	+	7.14250i	−0.337829	+	0.585136i	−0.984024	−	0.178036i	$-0.943026\pi$
$149$	−4.12372	+	7.14250i	−0.337829	+	0.585136i	0.646195	+	0.763172i	$0.276359\pi$
$150$	−3.48477	+	7.92820i	−0.284530	+	0.647335i
$151$	−1.44949	−	2.51059i	−0.117958	−	0.204309i	0.801000	−	0.598664i	$-0.204301\pi$
$151$	−1.44949	−	2.51059i	−0.117958	−	0.204309i	−0.918958	+	0.394355i	$0.870968\pi$
$152$		−	5.44949i		−	0.442012i
$153$	3.23375	−	17.3990i	0.261433	−	1.40662i
$154$	1.55051			0.124944
$155$	−2.02653	−	2.81311i	−0.162775	−	0.225955i
$156$	1.77526	+	3.85337i	0.142134	+	0.308517i
$157$	13.8564	+	8.00000i	1.10586	+	0.638470i	0.937754	−	0.347299i	$-0.112901\pi$
$157$	13.8564	+	8.00000i	1.10586	+	0.638470i	0.168107	+	0.985769i	$0.446235\pi$
$158$	6.36396	+	3.67423i	0.506290	+	0.292306i
$159$	6.12372	+	0.564242i	0.485643	+	0.0447473i
$160$	1.81431	−	1.30701i	0.143434	−	0.103328i
$161$	−3.10102			−0.244395
$162$	8.89060	−	1.39898i	0.698512	−	0.109914i
$163$			8.89898i			0.697022i	0.937305	+	0.348511i	$0.113313\pi$
$163$			8.89898i			0.697022i	−0.937305	+	0.348511i	$0.886687\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$	0.117539	+	13.3593i	0.00915036	+	1.04002i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	0.214297	+	0.123724i	0.0165828	+	0.00957408i	0.508268	−	0.861199i	$-0.330286\pi$
$167$	0.214297	+	0.123724i	0.0165828	+	0.00957408i	−0.491686	+	0.870773i	$0.663619\pi$
$168$	−0.707107	+	0.325765i	−0.0545545	+	0.0251333i
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$	−13.1237	+	1.32577i	−1.00654	+	0.101682i
$171$	−16.0732	−	2.98735i	−1.22915	−	0.228448i
$172$		−	2.55051i		−	0.194475i
$173$	−10.2173	+	5.89898i	−0.776809	+	0.448491i	−0.835298	−	0.549797i	$-0.814705\pi$
$173$	−10.2173	+	5.89898i	−0.776809	+	0.448491i	0.0584890	+	0.998288i	$0.481372\pi$
$174$	−6.00000	+	8.48528i	−0.454859	+	0.643268i
$175$	−2.13177	−	0.711751i	−0.161147	−	0.0538033i
$176$	1.72474	−	2.98735i	0.130008	−	0.225180i
$177$	−18.7347	−	13.2474i	−1.40819	−	0.995739i
$178$	−2.68556	+	1.55051i	−0.201291	+	0.116216i
$179$	0.898979			0.0671929			0.0335964	−	0.999435i	$-0.489304\pi$
$179$	0.898979			0.0671929			0.0335964	+	0.999435i	$0.489304\pi$
$180$	−2.86042	−	6.06778i	−0.213203	−	0.452266i
$181$	5.55051			0.412566			0.206283	−	0.978492i	$-0.433863\pi$
$181$	5.55051			0.412566			0.206283	+	0.978492i	$0.433863\pi$
$182$	−0.953512	+	0.550510i	−0.0706790	+	0.0408065i
$183$	−6.99964	+	3.22474i	−0.517428	+	0.238380i
$184$	−3.44949	+	5.97469i	−0.254300	+	0.440460i
$185$	16.3125	+	7.34190i	1.19932	+	0.539787i
$186$	2.67423	+	0.246405i	0.196084	+	0.0180673i
$187$	−17.6223	+	10.1742i	−1.28867	+	0.744014i
$188$		−	4.44949i		−	0.324512i
$189$	0.573214	+	2.26418i	0.0416952	+	0.164695i
$190$	1.22474	+	12.1237i	0.0888523	+	0.879547i
$191$	−9.12372	−	15.8028i	−0.660170	−	1.14345i	−0.980571	−	0.196165i	$-0.937151\pi$
$191$	−9.12372	−	15.8028i	−0.660170	−	1.14345i	0.320401	−	0.947282i	$-0.396182\pi$
$192$	−0.158919	+	1.72474i	−0.0114690	+	0.124473i
$193$	−11.8619	−	6.84847i	−0.853838	−	0.492964i	0.00810596	−	0.999967i	$-0.497420\pi$
$193$	−11.8619	−	6.84847i	−0.853838	−	0.492964i	−0.861944	+	0.507004i	$0.830753\pi$
$194$	−6.50000	+	11.2583i	−0.466673	+	0.808301i
$195$	−4.81552	−	8.17379i	−0.344846	−	0.585337i
$196$	3.39898	+	5.88721i	0.242784	+	0.420515i
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	−7.86566	−	6.72474i	−0.558988	−	0.477907i
$199$	−15.5505			−1.10235			−0.551173	−	0.834391i	$-0.685820\pi$
$199$	−15.5505			−1.10235			−0.551173	+	0.834391i	$0.685820\pi$
$200$	−3.74264	+	3.31552i	−0.264645	+	0.234442i
$201$	4.55051	−	6.43539i	0.320968	−	0.453918i
$202$	6.92820	+	4.00000i	0.487467	+	0.281439i
$203$	−2.33562	−	1.34847i	−0.163928	−	0.0946440i
$204$	5.89898	−	8.34242i	0.413011	−	0.584086i
$205$	1.30701	+	1.81431i	0.0912853	+	0.126717i
$206$	14.2474			0.992667
$207$	15.7313	+	13.4495i	1.09340	+	0.934804i
$208$			2.44949i			0.169842i
$209$	9.39898	+	16.2795i	0.650141	+	1.12608i
$210$	1.49992	−	0.883663i	0.103504	−	0.0609786i
$211$	−1.89898	+	3.28913i	−0.130731	+	0.226433i	−0.923959	−	0.382492i	$-0.875066\pi$
$211$	−1.89898	+	3.28913i	−0.130731	+	0.226433i	0.793227	+	0.608925i	$0.208399\pi$
$212$	3.07483	+	1.77526i	0.211180	+	0.121925i
$213$	−0.389270	+	4.22474i	−0.0266723	+	0.289475i
$214$	−8.17423	−	14.1582i	−0.558779	−	0.967834i
$215$	0.573214	+	5.67423i	0.0390929	+	0.386980i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$			0.696938i			0.0473113i
$218$	6.92820	−	4.00000i	0.469237	−	0.270914i
$219$	25.5227	+	2.35167i	1.72466	+	0.158911i
$220$	−3.16573	+	7.03371i	−0.213433	+	0.474213i
$221$	7.22474	−	12.5136i	0.485989	−	0.841758i
$222$	−12.5851	+	5.79796i	−0.844654	+	0.389134i
$223$	7.88171	−	4.55051i	0.527799	−	0.304725i	−0.212321	−	0.977200i	$-0.568102\pi$
$223$	7.88171	−	4.55051i	0.527799	−	0.304725i	0.740120	+	0.672475i	$0.234769\pi$
$224$	−0.449490			−0.0300328
$225$	7.72741	+	12.8564i	0.515160	+	0.857094i
$226$	4.89898			0.325875
$227$	2.98735	−	1.72474i	0.198277	−	0.114475i	−0.397574	−	0.917570i	$-0.630148\pi$
$227$	2.98735	−	1.72474i	0.198277	−	0.114475i	0.595852	+	0.803095i	$0.296815\pi$
$228$	−7.70674	−	5.44949i	−0.510391	−	0.360901i
$229$	−9.22474	+	15.9777i	−0.609588	+	1.05584i	0.381720	+	0.924278i	$0.375332\pi$
$229$	−9.22474	+	15.9777i	−0.609588	+	1.05584i	−0.991308	+	0.131560i	$0.958001\pi$
$230$	6.33145	−	14.0674i	0.417484	−	0.927578i
$231$	1.55051	−	2.19275i	0.102016	−	0.144273i
$232$	−5.19615	+	3.00000i	−0.341144	+	0.196960i
$233$		−	13.6969i		−	0.897316i	−0.893703	−	0.448658i	$-0.851902\pi$
$233$		−	13.6969i		−	0.897316i	0.893703	−	0.448658i	$-0.148098\pi$
$234$	7.22474	+	1.34278i	0.472296	+	0.0877804i
$235$	1.00000	+	9.89898i	0.0652328	+	0.645738i
$236$	−6.62372	−	11.4726i	−0.431168	−	0.746804i
$237$	11.5601	−	5.32577i	0.750910	−	0.345946i
$238$	2.29629	+	1.32577i	0.148847	+	0.0859366i
$239$	−0.348469	+	0.603566i	−0.0225406	+	0.0390415i	−0.877076	−	0.480352i	$-0.840509\pi$
$239$	−0.348469	+	0.603566i	−0.0225406	+	0.0390415i	0.854535	+	0.519394i	$0.173842\pi$
$240$	−0.0340742	−	3.87283i	−0.00219948	−	0.249990i
$241$	−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	$0.843587\pi$
$242$			0.898979i			0.0577886i
$243$	6.91215	−	13.9722i	0.443415	−	0.896317i
$244$	−4.44949			−0.284849
$245$	−8.88498	−	12.3336i	−0.567641	−	0.787966i
$246$	−1.72474	−	0.158919i	−0.109966	−	0.0101323i
$247$	−11.5601	−	6.67423i	−0.735552	−	0.424671i
$248$	1.34278	+	0.775255i	0.0852667	+	0.0492287i
$249$	2.89898	+	6.29253i	0.183715	+	0.398773i
$250$	7.58128	−	8.21731i	0.479482	−	0.519709i
$251$	6.55051			0.413465			0.206732	−	0.978398i	$-0.433717\pi$
$251$	6.55051			0.413465			0.206732	+	0.978398i	$0.433717\pi$
$252$	−0.246405	+	1.32577i	−0.0155221	+	0.0835154i
$253$		−	23.7980i		−	1.49616i
$254$	−3.44949	−	5.97469i	−0.216440	−	0.374885i
$255$	−11.2488	+	19.8855i	−0.704428	+	1.24528i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.74774	+	5.05051i	0.545669	+	0.315042i	0.747373	−	0.664404i	$-0.231315\pi$
$257$	8.74774	+	5.05051i	0.545669	+	0.315042i	−0.201704	+	0.979446i	$0.564648\pi$
$258$	−3.60697	−	2.55051i	−0.224560	−	0.158788i
$259$	−1.79796	−	3.11416i	−0.111720	−	0.193504i
$260$	−0.550510	−	5.44949i	−0.0341412	−	0.337963i
$261$	6.00000	+	16.9706i	0.371391	+	1.05045i
$262$			4.89898i			0.302660i
$263$	−10.7816	+	6.22474i	−0.664820	+	0.383834i	−0.794111	−	0.607773i	$-0.792063\pi$
$263$	−10.7816	+	6.22474i	−0.664820	+	0.383834i	0.129291	+	0.991607i	$0.458730\pi$
$264$	−2.50000	−	5.42650i	−0.153864	−	0.333978i
$265$	−7.23970	−	3.25844i	−0.444731	−	0.200164i
$266$	1.22474	−	2.12132i	0.0750939	−	0.130066i
$267$	−0.492810	+	5.34847i	−0.0301595	+	0.327321i
$268$	3.94086	−	2.27526i	0.240726	−	0.138983i
$269$	−16.0454			−0.978306			−0.489153	−	0.872198i	$-0.662694\pi$
$269$	−16.0454			−0.978306			−0.489153	+	0.872198i	$0.662694\pi$
$270$	−11.4416	−	2.02254i	−0.696311	−	0.123088i
$271$	−15.5959			−0.947385			−0.473692	−	0.880690i	$-0.657079\pi$
$271$	−15.5959			−0.947385			−0.473692	+	0.880690i	$0.657079\pi$
$272$	5.10867	−	2.94949i	0.309758	−	0.178839i
$273$	−0.174973	+	1.89898i	−0.0105898	+	0.114931i
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	5.46214	−	16.3597i	0.329380	−	0.986526i
$276$	5.00000	+	10.8530i	0.300965	+	0.653274i
$277$	25.6308	−	14.7980i	1.54001	−	0.889123i	0.541169	−	0.840914i	$-0.317982\pi$
$277$	25.6308	−	14.7980i	1.54001	−	0.889123i	0.998837	−	0.0482095i	$-0.0153515\pi$
$278$		−	13.2474i		−	0.794529i
$279$	3.02270	−	3.53553i	0.180965	−	0.211667i
$280$	1.00000	−	0.101021i	0.0597614	−	0.00603713i
$281$	−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	$0.949851\pi$
$282$	−6.29253	−	4.44949i	−0.374715	−	0.264963i
$283$	−3.46410	−	2.00000i	−0.205919	−	0.118888i	0.393494	−	0.919327i	$-0.371266\pi$
$283$	−3.46410	−	2.00000i	−0.205919	−	0.118888i	−0.599414	+	0.800439i	$0.704600\pi$
$284$	−1.22474	+	2.12132i	−0.0726752	+	0.125877i
$285$	18.3703	+	10.3917i	1.08816	+	0.615550i
$286$	−4.22474	−	7.31747i	−0.249814	−	0.432691i
$287$		−	0.449490i		−	0.0265325i
$288$	2.28024	+	1.94949i	0.134364	+	0.114875i
$289$	−17.7980			−1.04694
$290$	10.8859	−	7.84204i	0.639241	−	0.460501i
$291$	9.42168	+	20.4507i	0.552309	+	1.19884i
$292$	12.8154	+	7.39898i	0.749965	+	0.432993i
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.0300351	−	0.999549i	$-0.509562\pi$
$293$	−15.5885	−	9.00000i	−0.910687	−	0.525786i	−0.880652	+	0.473763i	$0.842895\pi$
$294$	11.7247	+	1.08032i	0.683801	+	0.0630057i
$295$	17.3145	+	24.0350i	1.00809	+	1.39937i
$296$	−8.00000			−0.464991
$297$	−17.3759	+	4.39898i	−1.00825	+	0.255255i
$298$			8.24745i			0.477762i
$299$	8.44949	+	14.6349i	0.488647	+	0.846361i
$300$	0.946206	+	8.60841i	0.0546292	+	0.497007i
$301$	0.573214	−	0.992836i	0.0330395	−	0.0572261i
$302$	−2.51059	−	1.44949i	−0.144468	−	0.0834088i
$303$	12.5851	−	5.79796i	0.722993	−	0.333084i
$304$	−2.72474	−	4.71940i	−0.156275	−	0.270676i
$305$	9.89898	−	1.00000i	0.566814	−	0.0572598i
$306$	−5.89898	−	16.6848i	−0.337222	−	0.953808i
$307$		−	29.9444i		−	1.70902i	−0.519438	−	0.854508i	$-0.673859\pi$
$307$		−	29.9444i		−	1.70902i	0.519438	−	0.854508i	$-0.326141\pi$
$308$	1.34278	−	0.775255i	0.0765121	−	0.0441743i
$309$	14.2474	−	20.1489i	0.810509	−	1.14623i
$310$	−3.16158	−	1.42296i	−0.179566	−	0.0808188i
$311$	−6.55051	+	11.3458i	−0.371445	+	0.643362i	−0.989788	−	0.142546i	$-0.954471\pi$
$311$	−6.55051	+	11.3458i	−0.371445	+	0.643362i	0.618343	+	0.785909i	$0.287804\pi$
$312$	3.46410	+	2.44949i	0.196116	+	0.138675i
$313$	−18.7901	+	10.8485i	−1.06208	+	0.613192i	−0.926007	−	0.377507i	$-0.876781\pi$
$313$	−18.7901	+	10.8485i	−1.06208	+	0.613192i	−0.136073	+	0.990699i	$0.543448\pi$
$314$	16.0000			0.902932
$315$	0.250229	−	3.00487i	0.0140988	−	0.169305i
$316$	7.34847			0.413384
$317$	−19.8704	+	11.4722i	−1.11603	+	0.644343i	−0.940386	−	0.340110i	$-0.889536\pi$
$317$	−19.8704	+	11.4722i	−1.11603	+	0.644343i	−0.175649	+	0.984453i	$0.556202\pi$
$318$	5.58542	−	2.57321i	0.313215	−	0.144299i
$319$	10.3485	−	17.9241i	0.579403	−	1.00356i
$320$	0.917738	−	2.03906i	0.0513031	−	0.113987i
$321$	−28.1969	−	2.59808i	−1.57380	−	0.145010i
$322$	−2.68556	+	1.55051i	−0.149661	+	0.0864066i
$323$			32.1464i			1.78868i
$324$	7.00000	−	5.65685i	0.388889	−	0.314270i
$325$	2.44949	+	12.0000i	0.135873	+	0.665640i
$326$	4.44949	+	7.70674i	0.246434	+	0.426837i
$327$	1.27135	−	13.7980i	0.0703058	−	0.763029i
$328$	−0.866025	−	0.500000i	−0.0478183	−	0.0276079i
$329$	1.00000	−	1.73205i	0.0551318	−	0.0954911i
$330$	6.78144	+	11.5107i	0.373306	+	0.633644i
$331$	12.6969	+	21.9917i	0.697887	+	1.20878i	0.969198	+	0.246284i	$0.0792095\pi$
$331$	12.6969	+	21.9917i	0.697887	+	1.20878i	−0.271311	+	0.962492i	$0.587457\pi$
$332$			4.00000i			0.219529i
$333$	−4.38551	+	23.5959i	−0.240324	+	1.29305i
$334$	0.247449			0.0135398
$335$	−8.25605	+	5.94755i	−0.451076	+	0.324949i
$336$	−0.449490	+	0.635674i	−0.0245217	+	0.0346789i
$337$	16.1045	+	9.29796i	0.877270	+	0.506492i	0.869757	−	0.493480i	$-0.164275\pi$
$337$	16.1045	+	9.29796i	0.877270	+	0.506492i	0.00751272	+	0.999972i	$0.497609\pi$
$338$	−6.06218	−	3.50000i	−0.329739	−	0.190375i
$339$	4.89898	−	6.92820i	0.266076	−	0.376288i
$340$	−10.7026	+	7.71001i	−0.580430	+	0.418134i
$341$	−5.34847			−0.289636
$342$	−15.4135	+	5.44949i	−0.833466	+	0.294675i
$343$			6.20204i			0.334879i
$344$	−1.27526	−	2.20881i	−0.0687571	−	0.119091i
$345$	−13.5629	−	23.0214i	−0.730201	−	1.23943i
$346$	−5.89898	+	10.2173i	−0.317131	+	0.549287i
$347$	8.00853	+	4.62372i	0.429920	+	0.248215i	0.699313	−	0.714816i	$-0.253490\pi$
$347$	8.00853	+	4.62372i	0.429920	+	0.248215i	−0.269392	+	0.963030i	$0.586823\pi$
$348$	−0.953512	+	10.3485i	−0.0511136	+	0.554736i
$349$	−13.7980	−	23.8988i	−0.738588	−	1.27927i	−0.953131	−	0.302557i	$-0.902160\pi$
$349$	−13.7980	−	23.8988i	−0.738588	−	1.27927i	0.214543	−	0.976714i	$-0.431174\pi$
$350$	−2.20204	+	0.449490i	−0.117704	+	0.0240262i
$351$	9.12372	−	8.87455i	0.486988	−	0.473688i
$352$		−	3.44949i		−	0.183858i
$353$	28.2289	−	16.2980i	1.50247	−	0.867453i	0.502476	−	0.864591i	$-0.332422\pi$
$353$	28.2289	−	16.2980i	1.50247	−	0.867453i	0.999996	−	0.00286194i	$-0.000910986\pi$
$354$	−22.8485	−	2.10527i	−1.21438	−	0.111894i
$355$	2.24799	−	4.99465i	0.119311	−	0.265089i
$356$	−1.55051	+	2.68556i	−0.0821769	+	0.142335i
$357$	4.17121	−	1.92168i	0.220764	−	0.101706i
$358$	0.778539	−	0.449490i	0.0411471	−	0.0237563i
$359$	−3.55051			−0.187389			−0.0936944	−	0.995601i	$-0.529868\pi$
$359$	−3.55051			−0.187389			−0.0936944	+	0.995601i	$0.529868\pi$
$360$	−5.51109	−	3.82465i	−0.290460	−	0.201577i
$361$	10.6969			0.562997
$362$	4.80688	−	2.77526i	0.252644	−	0.145864i
$363$	1.27135	+	0.898979i	0.0667285	+	0.0471842i
$364$	−0.550510	+	0.953512i	−0.0288546	+	0.0499776i
$365$	−30.1739	−	13.5806i	−1.57937	−	0.710843i
$366$	−4.44949	+	6.29253i	−0.232579	+	0.328916i
$367$	−23.8988	+	13.7980i	−1.24751	+	0.720248i	−0.970611	−	0.240653i	$-0.922638\pi$
$367$	−23.8988	+	13.7980i	−1.24751	+	0.720248i	−0.276894	+	0.960900i	$0.589305\pi$
$368$			6.89898i			0.359634i
$369$	−1.94949	+	2.28024i	−0.101486	+	0.118704i
$370$	17.7980	−	1.79796i	0.925272	−	0.0934714i
$371$	0.797959	+	1.38211i	0.0414280	+	0.0717553i
$372$	2.43916	−	1.12372i	0.126464	−	0.0582624i
$373$	11.7744	+	6.79796i	0.609656	+	0.351985i	0.772831	−	0.634612i	$-0.218840\pi$
$373$	11.7744	+	6.79796i	0.609656	+	0.351985i	−0.163175	+	0.986597i	$0.552173\pi$
$374$	−10.1742	+	17.6223i	−0.526097	+	0.911227i
$375$	−4.03976	−	18.9389i	−0.208612	−	0.977998i
$376$	−2.22474	−	3.85337i	−0.114732	−	0.198722i
$377$			14.6969i			0.756931i
$378$	1.62851	+	1.67423i	0.0837615	+	0.0861133i
$379$	−4.14643			−0.212988			−0.106494	−	0.994313i	$-0.533962\pi$
$379$	−4.14643			−0.212988			−0.106494	+	0.994313i	$0.533962\pi$
$380$	7.12252	+	9.88708i	0.365378	+	0.507197i
$381$	−11.8990	−	1.09638i	−0.609603	−	0.0561691i
$382$	−15.8028	−	9.12372i	−0.808539	−	0.466810i
$383$	15.4135	+	8.89898i	0.787592	+	0.454717i	0.839114	−	0.543955i	$-0.183074\pi$
$383$	15.4135	+	8.89898i	0.787592	+	0.454717i	−0.0515220	+	0.998672i	$0.516407\pi$
$384$	0.724745	+	1.57313i	0.0369845	+	0.0802786i
$385$	−2.81311	+	2.02653i	−0.143369	+	0.103281i
$386$	−13.6969			−0.697156
$387$	−7.21393	+	2.55051i	−0.366705	+	0.129650i
$388$			13.0000i			0.659975i
$389$	8.77526	+	15.1992i	0.444923	+	0.770629i	0.998047	−	0.0624697i	$-0.0198977\pi$
$389$	8.77526	+	15.1992i	0.444923	+	0.770629i	−0.553124	+	0.833099i	$0.686564\pi$
$390$	−8.25725	−	4.67095i	−0.418122	−	0.236523i
$391$	20.3485	−	35.2446i	1.02907	−	1.78240i
$392$	5.88721	+	3.39898i	0.297349	+	0.171674i
$393$	6.92820	+	4.89898i	0.349482	+	0.247121i
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$	−16.3485	+	1.65153i	−0.822581	+	0.0830975i
$396$	−10.1742	−	1.89097i	−0.511275	−	0.0950248i
$397$			1.79796i			0.0902370i	0.998982	+	0.0451185i	$0.0143665\pi$
$397$			1.79796i			0.0902370i	−0.998982	+	0.0451185i	$0.985633\pi$
$398$	−13.4671	+	7.77526i	−0.675047	+	0.389738i
$399$	−1.77526	−	3.85337i	−0.0888739	−	0.192910i
$400$	−1.58346	+	4.74264i	−0.0791732	+	0.237132i
$401$	−4.60102	+	7.96920i	−0.229764	+	0.397963i	−0.957738	−	0.287642i	$-0.907129\pi$
$401$	−4.60102	+	7.96920i	−0.229764	+	0.397963i	0.727974	+	0.685605i	$0.240462\pi$
$402$	0.723161	−	7.84847i	0.0360680	−	0.391446i
$403$	3.28913	−	1.89898i	0.163843	−	0.0945949i
$404$	8.00000			0.398015
$405$	−14.3019	+	14.1583i	−0.710665	+	0.703530i
$406$	−2.69694			−0.133847
$407$	23.8988	−	13.7980i	1.18462	−	0.683939i
$408$	0.937458	−	10.1742i	0.0464111	−	0.503700i
$409$	7.94949	−	13.7689i	0.393077	−	0.680829i	−0.599777	−	0.800167i	$-0.704744\pi$
$409$	7.94949	−	13.7689i	0.393077	−	0.680829i	0.992854	+	0.119338i	$0.0380773\pi$
$410$	2.03906	+	0.917738i	0.100702	+	0.0453238i
$411$	2.17423	+	4.71940i	0.107247	+	0.232791i
$412$	12.3387	−	7.12372i	0.607882	−	0.350961i
$413$		−	5.95459i		−	0.293006i
$414$	20.3485	+	3.78194i	1.00007	+	0.185872i
$415$	−0.898979	−	8.89898i	−0.0441292	−	0.436834i
$416$	1.22474	+	2.12132i	0.0600481	+	0.104006i
$417$	−18.7347	−	13.2474i	−0.917443	−	0.648730i
$418$	16.2795	+	9.39898i	0.796257	+	0.459719i
$419$	−4.44949	+	7.70674i	−0.217372	+	0.376499i	−0.954004	−	0.299795i	$-0.903082\pi$
$419$	−4.44949	+	7.70674i	−0.217372	+	0.376499i	0.736632	+	0.676294i	$0.236415\pi$
$420$	0.857135	−	1.51523i	0.0418239	−	0.0739359i
$421$	5.77526	+	10.0030i	0.281469	+	0.487518i	0.971747	−	0.236026i	$-0.0758451\pi$
$421$	5.77526	+	10.0030i	0.281469	+	0.487518i	−0.690278	+	0.723544i	$0.742512\pi$
$422$			3.79796i			0.184882i
$423$	−12.5851	+	4.44949i	−0.611906	+	0.216342i
$424$	3.55051			0.172428
$425$	22.0778	−	19.5582i	1.07093	−	0.948710i
$426$	1.77526	+	3.85337i	0.0860114	+	0.186696i
$427$	−1.73205	−	1.00000i	−0.0838198	−	0.0483934i
$428$	−14.1582	−	8.17423i	−0.684362	−	0.395117i
$429$	−14.5732	−	1.34278i	−0.703601	−	0.0648301i
$430$	3.33354	+	4.62742i	0.160757	+	0.223154i
$431$	38.2474			1.84231			0.921157	−	0.389190i	$-0.127245\pi$
$431$	38.2474			1.84231			0.921157	+	0.389190i	$0.127245\pi$
$432$	5.03723	−	1.27526i	0.242354	−	0.0613557i
$433$			23.0000i			1.10531i	0.833410	+	0.552655i	$0.186385\pi$
$433$			23.0000i			1.10531i	−0.833410	+	0.552655i	$0.813615\pi$
$434$	0.348469	+	0.603566i	0.0167271	+	0.0289721i
$435$	−0.204445	−	23.2370i	−0.00980239	−	1.11413i
$436$	4.00000	−	6.92820i	0.191565	−	0.331801i
$437$	−32.5590	−	18.7980i	−1.55751	−	0.899228i
$438$	23.2791	−	10.7247i	1.11232	−	0.512448i
$439$	11.0227	+	19.0919i	0.526085	+	0.911206i	0.999538	+	0.0303869i	$0.00967395\pi$
$439$	11.0227	+	19.0919i	0.526085	+	0.911206i	−0.473453	+	0.880819i	$0.656993\pi$
$440$	0.775255	+	7.67423i	0.0369588	+	0.365855i
$441$	13.2526	−	15.5010i	0.631074	−	0.738141i
$442$		−	14.4495i		−	0.687292i
$443$	18.4008	−	10.6237i	0.874250	−	0.504748i	0.00549166	−	0.999985i	$-0.498252\pi$
$443$	18.4008	−	10.6237i	0.874250	−	0.504748i	0.868758	+	0.495237i	$0.164919\pi$
$444$	−8.00000	+	11.3137i	−0.379663	+	0.536925i
$445$	2.84592	−	6.32316i	0.134910	−	0.299747i
$446$	4.55051	−	7.88171i	0.215473	−	0.373210i
$447$	11.6637	+	8.24745i	0.551672	+	0.390091i
$448$	−0.389270	+	0.224745i	−0.0183913	+	0.0106182i
$449$	−18.7980			−0.887131			−0.443565	−	0.896242i	$-0.646287\pi$
$449$	−18.7980			−0.887131			−0.443565	+	0.896242i	$0.646287\pi$
$450$	13.1203	+	7.27027i	0.618498	+	0.342724i
$451$	3.44949			0.162430
$452$	4.24264	−	2.44949i	0.199557	−	0.115214i
$453$	−4.56048	+	2.10102i	−0.214270	+	0.0987146i
$454$	1.72474	−	2.98735i	0.0809463	−	0.140203i
$455$	1.01045	−	2.24504i	0.0473705	−	0.105249i
$456$	−9.39898	−	0.866025i	−0.440148	−	0.0405554i
$457$	15.5010	−	8.94949i	0.725105	−	0.418639i	−0.0915238	−	0.995803i	$-0.529174\pi$
$457$	15.5010	−	8.94949i	0.725105	−	0.418639i	0.816629	+	0.577163i	$0.195840\pi$
$458$			18.4495i			0.862088i
$459$	−29.4949	−	8.34242i	−1.37670	−	0.389391i
$460$	−1.55051	−	15.3485i	−0.0722929	−	0.715626i
$461$	1.22474	+	2.12132i	0.0570421	+	0.0987997i	0.893136	−	0.449786i	$-0.148500\pi$
$461$	1.22474	+	2.12132i	0.0570421	+	0.0987997i	−0.836094	+	0.548586i	$0.815166\pi$
$462$	0.246405	−	2.67423i	0.0114638	−	0.124417i
$463$	−20.7846	−	12.0000i	−0.965943	−	0.557687i	−0.0679458	−	0.997689i	$-0.521644\pi$
$463$	−20.7846	−	12.0000i	−0.965943	−	0.557687i	−0.897997	+	0.440002i	$0.854978\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−5.17395	+	3.04819i	−0.239936	+	0.141356i
$466$	−6.84847	−	11.8619i	−0.317249	−	0.549492i
$467$			10.3485i			0.478870i	0.970912	+	0.239435i	$0.0769622\pi$
$467$			10.3485i			0.478870i	−0.970912	+	0.239435i	$0.923038\pi$
$468$	6.92820	−	2.44949i	0.320256	−	0.113228i
$469$	2.04541			0.0944482
$470$	5.81552	+	8.07277i	0.268250	+	0.372369i
$471$	16.0000	−	22.6274i	0.737241	−	1.04262i
$472$	−11.4726	−	6.62372i	−0.528070	−	0.304882i
$473$	7.61926	+	4.39898i	0.350334	+	0.202265i
$474$	7.34847	−	10.3923i	0.337526	−	0.477334i
$475$	−18.0679	−	20.3955i	−0.829011	−	0.935809i
$476$	2.65153			0.121533
$477$	1.94635	−	10.4722i	0.0891171	−	0.479489i
$478$			0.696938i			0.0318772i
$479$	8.34847	+	14.4600i	0.381451	+	0.660693i	0.991270	−	0.131848i	$-0.0420911\pi$
$479$	8.34847	+	14.4600i	0.381451	+	0.660693i	−0.609819	+	0.792541i	$0.708758\pi$
$480$	−1.96593	−	3.33694i	−0.0897318	−	0.152310i
$481$	−9.79796	+	16.9706i	−0.446748	+	0.773791i
$482$	−0.866025	−	0.500000i	−0.0394464	−	0.0227744i
$483$	−0.492810	+	5.34847i	−0.0224236	+	0.243364i
$484$	0.449490	+	0.778539i	0.0204314	+	0.0353881i
$485$	−2.92168	−	28.9217i	−0.132667	−	1.31327i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$			25.1010i			1.13744i	0.822533	+	0.568718i	$0.192560\pi$
$487$			25.1010i			1.13744i	−0.822533	+	0.568718i	$0.807440\pi$
$488$	−3.85337	+	2.22474i	−0.174434	+	0.100709i
$489$	15.3485	+	1.41421i	0.694082	+	0.0639529i
$490$	−13.8614	−	6.23874i	−0.626196	−	0.281838i
$491$	−9.27526	+	16.0652i	−0.418586	+	0.725013i	−0.995798	−	0.0915820i	$-0.970808\pi$
$491$	−9.27526	+	16.0652i	−0.418586	+	0.725013i	0.577211	+	0.816595i	$0.304141\pi$
$492$	−1.57313	+	0.724745i	−0.0709223	+	0.0326740i
$493$	30.6520	−	17.6969i	1.38050	−	0.797030i
$494$	−13.3485			−0.600576
$495$	23.0601	+	1.92032i	1.03647	+	0.0863119i
$496$	1.55051			0.0696200
$497$	−0.953512	+	0.550510i	−0.0427708	+	0.0246938i
$498$	5.65685	+	4.00000i	0.253490	+	0.179244i
$499$	−10.6237	+	18.4008i	−0.475583	+	0.823734i	−0.999609	−	0.0279682i	$-0.991096\pi$
$499$	−10.6237	+	18.4008i	−0.475583	+	0.823734i	0.524026	+	0.851703i	$0.324430\pi$
$500$	2.45692	−	10.9070i	0.109877	−	0.487778i
$501$	0.247449	−	0.349945i	0.0110552	−	0.0156344i
$502$	5.67291	−	3.27526i	0.253194	−	0.146182i
$503$			14.4495i			0.644271i	0.946694	+	0.322135i	$0.104401\pi$
$503$			14.4495i			0.644271i	−0.946694	+	0.322135i	$0.895599\pi$
$504$	0.449490	+	1.27135i	0.0200219	+	0.0566304i
$505$	−17.7980	+	1.79796i	−0.791999	+	0.0800081i
$506$	−11.8990	−	20.6096i	−0.528974	−	0.916210i
$507$	−11.0119	+	5.07321i	−0.489057	+	0.225309i
$508$	−5.97469	−	3.44949i	−0.265084	−	0.153046i
$509$	15.7980	−	27.3629i	0.700232	−	1.21284i	−0.268153	−	0.963376i	$-0.586413\pi$
$509$	15.7980	−	27.3629i	0.700232	−	1.21284i	0.968385	−	0.249461i	$-0.0802535\pi$
$510$	0.201003	+	22.8458i	0.00890056	+	1.01163i
$511$	3.32577	+	5.76039i	0.147123	+	0.254825i
$512$			1.00000i			0.0441942i
$513$	−7.70674	+	27.2474i	−0.340261	+	1.20300i
$514$	10.1010			0.445537
$515$	−25.8493	+	18.6215i	−1.13906	+	0.820562i
$516$	−4.39898	−	0.405324i	−0.193654	−	0.0178434i
$517$	13.2922	+	7.67423i	0.584589	+	0.337512i
$518$	−3.11416	−	1.79796i	−0.136828	−	0.0789978i
$519$	8.55051	+	18.5597i	0.375326	+	0.814683i
$520$	−3.20150	−	4.44414i	−0.140395	−	0.194888i
$521$	21.6969			0.950560			0.475280	−	0.879835i	$-0.342347\pi$
$521$	21.6969			0.950560			0.475280	+	0.879835i	$0.342347\pi$
$522$	13.6814	+	11.6969i	0.598820	+	0.511961i
$523$		−	10.2020i		−	0.446104i	−0.974807	−	0.223052i	$-0.928398\pi$
$523$		−	10.2020i		−	0.446104i	0.974807	−	0.223052i	$-0.0716020\pi$
$524$	2.44949	+	4.24264i	0.107006	+	0.185341i
$525$	−1.56637	+	3.56365i	−0.0683618	+	0.155530i
$526$	−6.22474	+	10.7816i	−0.271412	+	0.470099i
$527$	−7.92104	−	4.57321i	−0.345046	−	0.199212i
$528$	−4.87832	−	3.44949i	−0.212301	−	0.150120i
$529$	12.2980	+	21.3007i	0.534694	+	0.926117i
$530$	−7.89898	+	0.797959i	−0.343110	+	0.0346611i
$531$	−25.8258	+	30.2073i	−1.12074	+	1.31089i
$532$		−	2.44949i		−	0.106199i
$533$	−2.12132	+	1.22474i	−0.0918846	+	0.0530496i
$534$	2.24745	+	4.87832i	0.0972566	+	0.211105i
$535$	33.3355	+	15.0036i	1.44122	+	0.648662i
$536$	2.27526	−	3.94086i	0.0982761	−	0.170219i
$537$	0.142865	−	1.55051i	0.00616506	−	0.0669095i
$538$	−13.8957	+	8.02270i	−0.599087	+	0.345883i
$539$	−23.4495			−1.01004
$540$	−10.9200	+	3.96921i	−0.469920	+	0.170808i
$541$	−0.404082			−0.0173728			−0.00868642	−	0.999962i	$-0.502765\pi$
$541$	−0.404082			−0.0173728			−0.00868642	+	0.999962i	$0.502765\pi$
$542$	−13.5065	+	7.79796i	−0.580152	+	0.334951i
$543$	0.882079	−	9.57321i	0.0378537	−	0.410826i
$544$	2.94949	−	5.10867i	0.126458	−	0.219032i
$545$	−7.34190	+	16.3125i	−0.314493	+	0.698749i
$546$	0.797959	+	1.73205i	0.0341495	+	0.0741249i
$547$	−14.9367	+	8.62372i	−0.638648	+	0.368724i	−0.784094	−	0.620642i	$-0.786872\pi$
$547$	−14.9367	+	8.62372i	−0.638648	+	0.368724i	0.145445	+	0.989366i	$0.453539\pi$
$548$			3.00000i			0.128154i
$549$	4.44949	+	12.5851i	0.189900	+	0.537117i
$550$	−3.44949	−	16.8990i	−0.147087	−	0.720575i
$551$	−16.3485	−	28.3164i	−0.696468	−	1.20632i
$552$	9.75663	+	6.89898i	0.415270	+	0.293640i
$553$	2.86054	+	1.65153i	0.121642	+	0.0702302i
$554$	14.7980	−	25.6308i	0.628705	−	1.08895i
$555$	15.2553	−	26.9681i	0.647550	−	1.14473i
$556$	−6.62372	−	11.4726i	−0.280908	−	0.486548i
$557$		−	14.9444i		−	0.633214i	−0.948557	−	0.316607i	$-0.897456\pi$
$557$		−	14.9444i		−	0.633214i	0.948557	−	0.316607i	$-0.102544\pi$
$558$	0.849971	−	4.57321i	0.0359822	−	0.193600i
$559$	−6.24745			−0.264239
$560$	0.815515	−	0.587486i	0.0344618	−	0.0248258i
$561$	14.7474	+	32.0108i	0.622638	+	1.35150i
$562$	−10.3923	−	6.00000i	−0.438373	−	0.253095i
$563$	−1.60524	−	0.926786i	−0.0676528	−	0.0390594i	0.465792	−	0.884894i	$-0.345769\pi$
$563$	−1.60524	−	0.926786i	−0.0676528	−	0.0390594i	−0.533445	+	0.845835i	$0.679103\pi$
$564$	−7.67423	−	0.707107i	−0.323144	−	0.0297746i
$565$	−8.88828	+	6.40300i	−0.373933	+	0.269376i
$566$	−4.00000			−0.168133
$567$	3.99624	−	0.628827i	0.167826	−	0.0264082i
$568$			2.44949i			0.102778i
$569$	−15.7474	−	27.2754i	−0.660167	−	1.14344i	−0.980571	−	0.196162i	$-0.937152\pi$
$569$	−15.7474	−	27.2754i	−0.660167	−	1.14344i	0.320404	−	0.947281i	$-0.396181\pi$
$570$	21.1050	−	0.185687i	0.883990	−	0.00777757i
$571$	−18.6237	+	32.2572i	−0.779379	+	1.34992i	0.152922	+	0.988238i	$0.451132\pi$
$571$	−18.6237	+	32.2572i	−0.779379	+	1.34992i	−0.932300	+	0.361685i	$0.882202\pi$
$572$	−7.31747	−	4.22474i	−0.305959	−	0.176645i
$573$	−28.7056	+	13.2247i	−1.19920	+	0.552472i
$574$	−0.224745	−	0.389270i	−0.00938067	−	0.0162478i
$575$	6.89898	+	33.7980i	0.287707	+	1.40947i
$576$	2.94949	+	0.548188i	0.122895	+	0.0228412i
$577$			15.6969i			0.653472i	0.945116	+	0.326736i	$0.105949\pi$
$577$			15.6969i			0.653472i	−0.945116	+	0.326736i	$0.894051\pi$
$578$	−15.4135	+	8.89898i	−0.641116	+	0.370149i
$579$	−13.6969	+	19.3704i	−0.569225	+	0.805006i
$580$	5.50643	−	12.2343i	0.228642	−	0.508004i
$581$	−0.898979	+	1.55708i	−0.0372960	+	0.0645985i
$582$	18.3848	+	13.0000i	0.762073	+	0.538867i
$583$	−10.6066	+	6.12372i	−0.439281	+	0.253619i
$584$	14.7980			0.612344
$585$	−14.8630	+	7.00657i	−0.614508	+	0.289686i
$586$	−18.0000			−0.743573
$587$	20.7364	−	11.9722i	0.855885	−	0.494145i	−0.00674727	−	0.999977i	$-0.502148\pi$
$587$	20.7364	−	11.9722i	0.855885	−	0.494145i	0.862632	+	0.505832i	$0.168814\pi$
$588$	10.6941	−	4.92679i	0.441017	−	0.203177i
$589$	−4.22474	+	7.31747i	−0.174078	+	0.301511i
$590$	27.0123	+	12.1577i	1.11208	+	0.500524i
$591$	13.7980	+	1.27135i	0.567572	+	0.0522963i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$		−	17.3939i		−	0.714281i	−0.934051	−	0.357140i	$-0.883752\pi$
$593$		−	17.3939i		−	0.714281i	0.934051	−	0.357140i	$-0.116248\pi$
$594$	−12.8485	+	12.4976i	−0.527179	+	0.512782i
$595$	−5.89898	+	0.595918i	−0.241835	+	0.0244303i
$596$	4.12372	+	7.14250i	0.168914	+	0.292568i
$597$	−2.47127	+	26.8207i	−0.101142	+	1.09770i
$598$	14.6349	+	8.44949i	0.598467	+	0.345525i
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	−0.281209	−	0.959646i	$-0.590736\pi$
$599$	16.8990	−	29.2699i	0.690474	−	1.19594i	0.971683	−	0.236289i	$-0.0759312\pi$
$600$	5.12364	+	6.98200i	0.209172	+	0.285039i
$601$	−19.3990	−	33.6000i	−0.791301	−	1.37057i	−0.925162	−	0.379573i	$-0.876071\pi$
$601$	−19.3990	−	33.6000i	−0.791301	−	1.37057i	0.133861	−	0.991000i	$-0.457262\pi$
$602$		−	1.14643i		−	0.0467249i
$603$	−10.3763	−	8.87117i	−0.422554	−	0.361262i
$604$	−2.89898			−0.117958
$605$	−1.17497	−	1.63103i	−0.0477694	−	0.0663108i
$606$	8.00000	−	11.3137i	0.324978	−	0.459588i
$607$	−23.8988	−	13.7980i	−0.970021	−	0.560042i	−0.0707783	−	0.997492i	$-0.522548\pi$
$607$	−23.8988	−	13.7980i	−0.970021	−	0.560042i	−0.899243	+	0.437450i	$0.855882\pi$
$608$	−4.71940	−	2.72474i	−0.191397	−	0.110503i
$609$	−2.69694	+	3.81405i	−0.109285	+	0.154553i
$610$	8.07277	−	5.81552i	0.326857	−	0.235463i
$611$	−10.8990			−0.440926
$612$	−13.4511	−	11.5000i	−0.543728	−	0.464860i
$613$		−	36.9444i		−	1.49217i	−0.665851	−	0.746085i	$-0.731931\pi$
$613$		−	36.9444i		−	1.49217i	0.665851	−	0.746085i	$-0.268069\pi$
$614$	−14.9722	−	25.9326i	−0.604229	−	1.04655i
$615$	3.33694	−	1.96593i	0.134558	−	0.0792738i
$616$	0.775255	−	1.34278i	0.0312359	−	0.0541022i
$617$	7.19066	+	4.15153i	0.289485	+	0.167134i	0.637710	−	0.770277i	$-0.279882\pi$
$617$	7.19066	+	4.15153i	0.289485	+	0.167134i	−0.348224	+	0.937411i	$0.613215\pi$
$618$	2.26418	−	24.5732i	0.0910789	−	0.988480i
$619$	−14.2753	−	24.7255i	−0.573771	−	0.993800i	−0.996174	−	0.0873923i	$-0.972147\pi$
$619$	−14.2753	−	24.7255i	−0.573771	−	0.993800i	0.422403	−	0.906408i	$-0.361187\pi$
$620$	−3.44949	+	0.348469i	−0.138535	+	0.0139949i
$621$	25.6969	−	24.9951i	1.03118	−	1.00302i
$622$			13.1010i			0.525303i
$623$	−1.20713	+	0.696938i	−0.0483628	+	0.0279222i
$624$	4.22474	+	0.389270i	0.169125	+	0.0155833i
$625$	−3.01472	+	24.8176i	−0.120589	+	0.992703i
$626$	−10.8485	+	18.7901i	−0.433592	+	0.751003i
$627$	29.5717	−	13.6237i	1.18098	−	0.544079i
$628$	13.8564	−	8.00000i	0.552931	−	0.319235i
$629$	47.1918			1.88166
$630$	−1.28573	−	2.72741i	−0.0512247	−	0.108662i
$631$	−11.3485			−0.451775			−0.225888	−	0.974153i	$-0.572528\pi$
$631$	−11.3485			−0.451775			−0.225888	+	0.974153i	$0.572528\pi$
$632$	6.36396	−	3.67423i	0.253145	−	0.146153i
$633$	5.37113	+	3.79796i	0.213483	+	0.150955i
$634$	−11.4722	+	19.8704i	−0.455619	+	0.789155i
$635$	14.0674	+	6.33145i	0.558249	+	0.251256i
$636$	3.55051	−	5.02118i	0.140787	−	0.199103i
$637$	14.4206	−	8.32577i	0.571367	−	0.329879i
$638$		−	20.6969i		−	0.819400i
$639$	7.22474	+	1.34278i	0.285806	+	0.0531196i
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$	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	$0.572524\pi$
$642$	−25.7183	+	11.8485i	−1.01502	+	0.467622i
$643$	−13.2047	−	7.62372i	−0.520742	−	0.300650i	0.216496	−	0.976283i	$-0.430537\pi$
$643$	−13.2047	−	7.62372i	−0.520742	−	0.300650i	−0.737238	+	0.675633i	$0.763870\pi$
$644$	−1.55051	+	2.68556i	−0.0610987	+	0.105826i
$645$	9.87770	−	0.0869065i	0.388934	−	0.00342194i
$646$	16.0732	+	27.8396i	0.632392	+	1.09534i
$647$		−	34.8990i		−	1.37202i	−0.727592	−	0.686010i	$-0.759361\pi$
$647$		−	34.8990i		−	1.37202i	0.727592	−	0.686010i	$-0.240639\pi$
$648$	3.23375	−	8.39898i	0.127034	−	0.329943i
$649$	45.6969			1.79376
$650$	8.12132	+	9.16756i	0.318544	+	0.359581i
$651$	1.20204	+	0.110756i	0.0471117	+	0.00434089i
$652$	7.70674	+	4.44949i	0.301819	+	0.174255i
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.949439	−	0.313953i	$-0.101653\pi$
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.202828	+	0.979214i	$0.434987\pi$
$654$	−5.79796	−	12.5851i	−0.226718	−	0.492115i
$655$	−6.40300	−	8.88828i	−0.250186	−	0.347294i
$656$	−1.00000			−0.0390434
$657$	8.11207	−	43.6464i	0.316482	−	1.70281i
$658$		−	2.00000i		−	0.0779681i
$659$	−17.8990	−	31.0019i	−0.697245	−	1.20766i	−0.969418	−	0.245416i	$-0.921076\pi$
$659$	−17.8990	−	31.0019i	−0.697245	−	1.20766i	0.272173	−	0.962248i	$-0.412258\pi$
$660$	11.6283	+	6.57786i	0.452629	+	0.256043i
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	−0.916881	−	0.399161i	$-0.869302\pi$
$661$	−2.89898	+	5.02118i	−0.112757	+	0.195301i	0.804124	+	0.594462i	$0.202635\pi$
$662$	21.9917	+	12.6969i	0.854733	+	0.493481i
$663$	−20.4347	−	14.4495i	−0.793617	−	0.561172i
$664$	2.00000	+	3.46410i	0.0776151	+	0.134433i
$665$	0.550510	+	5.44949i	0.0213479	+	0.211322i
$666$	8.00000	+	22.6274i	0.309994	+	0.876795i
$667$			41.3939i			1.60278i
$668$	0.214297	−	0.123724i	0.00829139	−	0.00478704i
$669$	−6.59592	−	14.3171i	−0.255013	−	0.553531i
$670$	−4.17617	+	9.27875i	−0.161340	+	0.358470i
$671$	7.67423	−	13.2922i	0.296261	−	0.513138i
$672$	−0.0714323	+	0.775255i	−0.00275556	+	0.0299061i
$673$	−25.0273	+	14.4495i	−0.964730	+	0.556987i	−0.897625	−	0.440759i	$-0.854709\pi$
$673$	−25.0273	+	14.4495i	−0.964730	+	0.556987i	−0.0671042	+	0.997746i	$0.521376\pi$
$674$	18.5959			0.716288
$675$	23.4020	−	11.2847i	0.900745	−	0.434348i
$676$	−7.00000			−0.269231
$677$	−34.2911	+	19.7980i	−1.31791	+	0.760897i	−0.983393	−	0.181491i	$-0.941908\pi$
$677$	−34.2911	+	19.7980i	−1.31791	+	0.760897i	−0.334520	+	0.942389i	$0.608574\pi$
$678$	0.778539	−	8.44949i	0.0298996	−	0.324501i
$679$	−2.92168	+	5.06050i	−0.112124	+	0.194204i
$680$	−5.41372	+	12.0284i	−0.207607	+	0.461267i
$681$	−2.50000	−	5.42650i	−0.0958002	−	0.207944i
$682$	−4.63191	+	2.67423i	−0.177365	+	0.102402i
$683$		−	45.4495i		−	1.73908i	−0.493866	−	0.869538i	$-0.664417\pi$
$683$		−	45.4495i		−	1.73908i	0.493866	−	0.869538i	$-0.335583\pi$
$684$	−10.6237	+	12.4261i	−0.406208	+	0.475125i
$685$	−0.674235	−	6.67423i	−0.0257612	−	0.255009i
$686$	3.10102	+	5.37113i	0.118398	+	0.205071i
$687$	26.0915	+	18.4495i	0.995454	+	0.703892i
$688$	−2.20881	−	1.27526i	−0.0842100	−	0.0486186i
$689$	4.34847	−	7.53177i	0.165663	−	0.286938i
$690$	−23.2565	−	13.1557i	−0.885361	−	0.500830i
$691$	−8.79796	−	15.2385i	−0.334690	−	0.579700i	0.648735	−	0.761014i	$-0.275298\pi$
$691$	−8.79796	−	15.2385i	−0.334690	−	0.579700i	−0.983425	+	0.181314i	$0.941965\pi$
$692$			11.7980i			0.448491i
$693$	−3.53553	−	3.02270i	−0.134304	−	0.114823i
$694$	9.24745			0.351028
$695$	17.3145	+	24.0350i	0.656777	+	0.911700i
$696$	4.34847	+	9.43879i	0.164828	+	0.357777i
$697$	5.10867	+	2.94949i	0.193505	+	0.111720i
$698$	−23.8988	−	13.7980i	−0.904582	−	0.522260i
$699$	−23.6237	−	2.17670i	−0.893531	−	0.0823303i
$700$	−1.68228	+	1.49029i	−0.0635842	+	0.0563277i
$701$	−39.3939			−1.48789			−0.743943	−	0.668243i	$-0.767047\pi$
$701$	−39.3939			−1.48789			−0.743943	+	0.668243i	$0.767047\pi$
$702$	3.46410	−	12.2474i	0.130744	−	0.462250i
$703$		−	43.5959i		−	1.64425i
$704$	−1.72474	−	2.98735i	−0.0650038	−	0.112590i
$705$	17.2321	−	0.151613i	0.649000	−	0.00571006i
$706$	16.2980	−	28.2289i	0.613382	−	1.06241i
$707$	3.11416	+	1.79796i	0.117120	+	0.0676192i
$708$	−20.8400	+	9.60102i	−0.783215	+	0.360828i
$709$	18.6742	+	32.3447i	0.701326	+	1.21473i	0.968001	+	0.250945i	$0.0807414\pi$
$709$	18.6742	+	32.3447i	0.701326	+	1.21473i	−0.266676	+	0.963786i	$0.585925\pi$
$710$	−0.550510	−	5.44949i	−0.0206603	−	0.204516i
$711$	−7.34847	−	20.7846i	−0.275589	−	0.779484i
$712$			3.10102i			0.116216i
$713$	9.26382	−	5.34847i	0.346933	−	0.200302i
$714$	2.65153	−	3.74983i	0.0992310	−	0.140334i
$715$	17.2290	+	7.75442i	0.644328	+	0.289999i
$716$	0.449490	−	0.778539i	0.0167982	−	0.0290954i
$717$	0.985620	+	0.696938i	0.0368086	+	0.0260276i
$718$	−3.07483	+	1.77526i	−0.114752	+	0.0662519i
$719$	−41.7980			−1.55880			−0.779400	−	0.626526i	$-0.784476\pi$
$719$	−41.7980			−1.55880			−0.779400	+	0.626526i	$0.784476\pi$
$720$	−6.68506	−	0.556696i	−0.249138	−	0.0207468i
$721$	6.40408			0.238500
$722$	9.26382	−	5.34847i	0.344764	−	0.199049i
$723$	−1.57313	+	0.724745i	−0.0585054	+	0.0269536i
$724$	2.77526	−	4.80688i	0.103142	−	0.178646i
$725$	−9.50079	+	28.4558i	−0.352850	+	1.05682i
$726$	1.55051	+	0.142865i	0.0575448	+	0.00530220i
$727$	21.9524	−	12.6742i	0.814170	−	0.470061i	−0.0342318	−	0.999414i	$-0.510898\pi$
$727$	21.9524	−	12.6742i	0.814170	−	0.470061i	0.848402	+	0.529353i	$0.177565\pi$
$728$			1.10102i			0.0408065i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$	−32.9217	+	3.32577i	−1.21849	+	0.123092i
$731$	7.52270	+	13.0297i	0.278237	+	0.481921i
$732$	−0.707107	+	7.67423i	−0.0261354	+	0.283648i
$733$	−18.3133	−	10.5732i	−0.676419	−	0.390531i	0.122086	−	0.992520i	$-0.461042\pi$
$733$	−18.3133	−	10.5732i	−0.676419	−	0.390531i	−0.798504	+	0.601989i	$0.794375\pi$
$734$	−13.7980	+	23.8988i	−0.509292	+	0.882120i
$735$	−22.6843	+	13.3643i	−0.836725	+	0.492949i
$736$	3.44949	+	5.97469i	0.127150	+	0.220230i
$737$			15.6969i			0.578204i
$738$	−0.548188	+	2.94949i	−0.0201791	+	0.108572i
$739$	17.2474			0.634458			0.317229	−	0.948349i	$-0.397248\pi$
$739$	17.2474			0.634458			0.317229	+	0.948349i	$0.397248\pi$
$740$	14.5145	−	10.4561i	0.533564	−	0.384372i
$741$	−13.3485	+	18.8776i	−0.490368	+	0.693485i
$742$	1.38211	+	0.797959i	0.0507387	+	0.0292940i
$743$	19.8311	+	11.4495i	0.727532	+	0.420041i	0.817519	−	0.575902i	$-0.195349\pi$
$743$	19.8311	+	11.4495i	0.727532	+	0.420041i	−0.0899863	+	0.995943i	$0.528682\pi$
$744$	1.55051	−	2.19275i	0.0568445	−	0.0803902i
$745$	−10.7795	−	14.9635i	−0.394929	−	0.548219i
$746$	13.5959			0.497782
$747$	11.3137	−	4.00000i	0.413947	−	0.146352i
$748$			20.3485i			0.744014i
$749$	−3.67423	−	6.36396i	−0.134254	−	0.232534i
$750$	−12.9680	−	14.3817i	−0.473523	−	0.525144i
$751$	26.4949	−	45.8905i	0.966813	−	1.67457i	0.262148	−	0.965028i	$-0.415569\pi$
$751$	26.4949	−	45.8905i	0.966813	−	1.67457i	0.704664	−	0.709541i	$-0.251098\pi$
$752$	−3.85337	−	2.22474i	−0.140518	−	0.0811281i
$753$	1.04100	−	11.2980i	0.0379361	−	0.411721i
$754$	7.34847	+	12.7279i	0.267615	+	0.463524i
$755$	6.44949	−	0.651531i	0.234721	−	0.0237116i
$756$	2.24745	+	0.635674i	0.0817389	+	0.0231193i
$757$			10.0000i			0.363456i	0.983349	+	0.181728i	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	−3.59091	+	2.07321i	−0.130428	+	0.0753025i
$759$	−41.0454	−	3.78194i	−1.48985	−	0.137276i
$760$	11.1118	+	5.00120i	0.403068	+	0.181413i
$761$	−0.247449	+	0.428594i	−0.00897001	+	0.0155365i	−0.870476	−	0.492212i	$-0.836189\pi$
$761$	−0.247449	+	0.428594i	−0.00897001	+	0.0155365i	0.861506	+	0.507748i	$0.169522\pi$
$762$	−10.8530	+	5.00000i	−0.393163	+	0.181131i
$763$	3.11416	−	1.79796i	0.112740	−	0.0650905i
$764$	−18.2474			−0.660170
$765$	32.5098	+	22.5615i	1.17539	+	0.815713i
$766$	17.7980			0.643066
$767$	−28.1021	+	16.2247i	−1.01471	+	0.585842i
$768$	1.41421	+	1.00000i	0.0510310	+	0.0360844i
$769$	12.2474	−	21.2132i	0.441654	−	0.764968i	−0.556158	−	0.831076i	$-0.687725\pi$
$769$	12.2474	−	21.2132i	0.441654	−	0.764968i	0.997812	+	0.0661088i	$0.0210584\pi$
$770$	−1.42296	+	3.16158i	−0.0512800	+	0.113935i
$771$	10.1010	−	14.2850i	0.363779	−	0.514462i
$772$	−11.8619	+	6.84847i	−0.426919	+	0.246482i
$773$			35.3939i			1.27303i	0.771265	+	0.636515i	$0.219625\pi$
$773$			35.3939i			1.27303i	−0.771265	+	0.636515i	$0.780375\pi$
$774$	−4.97219	+	5.81577i	−0.178722	+	0.209044i
$775$	7.59592	−	1.55051i	0.272853	−	0.0556960i
$776$	6.50000	+	11.2583i	0.233336	+	0.404151i
$777$	−5.65685	+	2.60612i	−0.202939	+	0.0934941i
$778$	15.1992	+	8.77526i	0.544917	+	0.314608i
$779$	2.72474	−	4.71940i	0.0976241	−	0.169090i
$780$	−9.48647	+	0.0834643i	−0.339670	+	0.00298850i
$781$	−4.22474	−	7.31747i	−0.151173	−	0.261840i
$782$		−	40.6969i		−	1.45532i
$783$	30.2234	−	7.65153i	1.08010	−	0.273443i
$784$	6.79796			0.242784
$785$	−29.0290	+	20.9121i	−1.03609	+	0.746385i
$786$	8.44949	+	0.778539i	0.301383	+	0.0277696i
$787$	−44.5084	−	25.6969i	−1.58655	−	0.915997i	−0.993869	−	0.110562i	$-0.964735\pi$
$787$	−44.5084	−	25.6969i	−1.58655	−	0.915997i	−0.592684	−	0.805435i	$-0.701932\pi$
$788$	6.92820	+	4.00000i	0.246807	+	0.142494i
$789$	9.02270	+	19.5847i	0.321217	+	0.697234i
$790$	−13.3324	+	9.60450i	−0.474346	+	0.341713i
$791$	2.20204			0.0782956
$792$	−9.75663	+	3.44949i	−0.346687	+	0.122572i
$793$			10.8990i			0.387034i
$794$	0.898979	+	1.55708i	0.0319036	+	0.0552586i
$795$	−6.77050	+	11.9688i	−0.240125	+	0.424490i
$796$	−7.77526	+	13.4671i	−0.275587	+	0.477330i
$797$	3.11416	+	1.79796i	0.110309	+	0.0636870i	0.554139	−	0.832424i	$-0.313047\pi$
$797$	3.11416	+	1.79796i	0.110309	+	0.0636870i	−0.443830	+	0.896111i	$0.646381\pi$
$798$	−3.46410	−	2.44949i	−0.122628	−	0.0867110i
$799$	13.1237	+	22.7310i	0.464284	+	0.804163i
$800$	1.00000	+	4.89898i	0.0353553	+	0.173205i
$801$	9.14643	+	1.69994i	0.323173	+	0.0600645i
$802$			9.20204i			0.324935i
$803$	−44.2066	+	25.5227i	−1.56002	+	0.900677i
$804$	−3.29796	−	7.15855i	−0.116310	−	0.252463i
$805$	2.84592	−	6.32316i	0.100306	−	0.222862i
$806$	1.89898	−	3.28913i	0.0668887	−	0.115855i
$807$	−2.54991	+	27.6742i	−0.0897612	+	0.974179i
$808$	6.92820	−	4.00000i	0.243733	−	0.140720i
$809$	41.0908			1.44468			0.722338	−	0.691540i	$-0.243067\pi$
$809$	41.0908			1.44468			0.722338	+	0.691540i	$0.243067\pi$
$810$	−5.30664	+	19.4124i	−0.186456	+	0.682081i
$811$	7.24745			0.254492			0.127246	−	0.991871i	$-0.459386\pi$
$811$	7.24745			0.254492			0.127246	+	0.991871i	$0.459386\pi$
$812$	−2.33562	+	1.34847i	−0.0819641	+	0.0473220i
$813$	−2.47848	+	26.8990i	−0.0869242	+	0.943388i
$814$	13.7980	−	23.8988i	0.483618	−	0.837651i
$815$	−18.1455	−	8.16693i	−0.635610	−	0.286075i
$816$	−4.27526	−	9.27987i	−0.149664	−	0.324861i
$817$	12.0369	−	6.94949i	0.421117	−	0.243132i
$818$		−	15.8990i		−	0.555895i
$819$	3.24745	+	0.603566i	0.113475	+	0.0210903i
$820$	2.22474	−	0.224745i	0.0776915	−	0.00784843i
$821$	−1.02270	−	1.77138i	−0.0356926	−	0.0618214i	0.847627	−	0.530592i	$-0.178030\pi$
$821$	−1.02270	−	1.77138i	−0.0356926	−	0.0618214i	−0.883320	+	0.468771i	$0.844697\pi$
$822$	4.24264	+	3.00000i	0.147979	+	0.104637i
$823$	27.3629	+	15.7980i	0.953810	+	0.550682i	0.894262	−	0.447543i	$-0.147701\pi$
$823$	27.3629	+	15.7980i	0.953810	+	0.550682i	0.0595473	+	0.998225i	$0.481034\pi$
$824$	7.12372	−	12.3387i	0.248167	−	0.429837i
$825$	−27.3483	−	12.0207i	−0.952144	−	0.418506i
$826$	−2.97730	−	5.15683i	−0.103593	−	0.179429i
$827$		−	5.79796i		−	0.201615i	−0.994906	−	0.100807i	$-0.967857\pi$
$827$		−	5.79796i		−	0.201615i	0.994906	−	0.100807i	$-0.0321426\pi$
$828$	19.5133	−	6.89898i	0.678133	−	0.239756i
$829$	26.4495			0.918629			0.459314	−	0.888274i	$-0.348095\pi$
$829$	26.4495			0.918629			0.459314	+	0.888274i	$0.348095\pi$
$830$	−5.22803	−	7.25725i	−0.181468	−	0.251903i
$831$	−21.4495	−	46.5583i	−0.744075	−	1.61509i
$832$	2.12132	+	1.22474i	0.0735436	+	0.0424604i
$833$	−34.7285	−	20.0505i	−1.20327	−	0.694709i
$834$	−22.8485	−	2.10527i	−0.791178	−	0.0728994i
$835$	−0.448949	+	0.323417i	−0.0155365	+	0.0111923i
$836$	18.7980			0.650141
$837$	−5.61753	−	5.77526i	−0.194170	−	0.199622i
$838$			8.89898i			0.307410i
$839$	20.1237	+	34.8553i	0.694748	+	1.20334i	0.970266	+	0.242043i	$0.0778175\pi$
$839$	20.1237	+	34.8553i	0.694748	+	1.20334i	−0.275517	+	0.961296i	$0.588849\pi$
$840$	−0.0153160	−	1.74080i	−0.000528452	−	0.0600633i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	10.0030	+	5.77526i	0.344727	+	0.199028i
$843$	−18.8776	+	8.69694i	−0.650179	+	0.299538i
$844$	1.89898	+	3.28913i	0.0653656	+	0.113216i
$845$	15.5732	−	1.57321i	0.535735	−	0.0541202i
$846$	−8.67423	+	10.1459i	−0.298226	+	0.348823i
$847$			0.404082i			0.0138844i
$848$	3.07483	−	1.77526i	0.105590	−	0.0609625i
$849$	−4.00000	+	5.65685i	−0.137280	+	0.194143i
$850$	9.34082	−	27.9767i	0.320388	−	0.959594i
$851$	−27.5959	+	47.7975i	−0.945976	+	1.63848i
$852$	3.46410	+	2.44949i	0.118678	+	0.0839181i
$853$	7.92104	−	4.57321i	0.271211	−	0.156584i	−0.358227	−	0.933635i	$-0.616619\pi$
$853$	7.92104	−	4.57321i	0.271211	−	0.156584i	0.629438	+	0.777051i	$0.283285\pi$
$854$	−2.00000			−0.0684386
$855$	20.8424	−	30.0326i	0.712794	−	1.02709i
$856$	−16.3485			−0.558779
$857$	−4.67123	+	2.69694i	−0.159566	+	0.0921257i	−0.577657	−	0.816280i	$-0.696033\pi$
$857$	−4.67123	+	2.69694i	−0.159566	+	0.0921257i	0.418091	+	0.908405i	$0.362699\pi$
$858$	−13.2922	+	6.12372i	−0.453787	+	0.209061i
$859$	−18.8712	+	32.6858i	−0.643876	+	1.11523i	0.340684	+	0.940178i	$0.389341\pi$
$859$	−18.8712	+	32.6858i	−0.643876	+	1.11523i	−0.984560	+	0.175048i	$0.943992\pi$
$860$	5.20064	+	2.34070i	0.177340	+	0.0798172i
$861$	−0.775255	−	0.0714323i	−0.0264206	−	0.00243441i
$862$	33.1233	−	19.1237i	1.12818	−	0.651357i
$863$			26.4495i			0.900351i	0.892940	+	0.450176i	$0.148639\pi$
$863$			26.4495i			0.900351i	−0.892940	+	0.450176i	$0.851361\pi$
$864$	3.72474	−	3.62302i	0.126718	−	0.123258i
$865$	−2.65153	−	26.2474i	−0.0901548	−	0.892440i
$866$	11.5000	+	19.9186i	0.390786	+	0.676861i
$867$	−2.82843	+	30.6969i	−0.0960584	+	1.04252i
$868$	0.603566	+	0.348469i	0.0204864	+	0.0118278i
$869$	−12.6742	+	21.9524i	−0.429944	+	0.744685i
$870$	−11.7956	−	20.0216i	−0.399907	−	0.678796i
$871$	−5.57321	−	9.65309i	−0.188841	−	0.327082i
$872$		−	8.00000i		−	0.270914i
$873$	36.7696	−	13.0000i	1.24446	−	0.439983i
$874$	−37.5959			−1.27170
$875$	3.40771	−	3.69360i	0.115201	−	0.124866i
$876$	14.7980	−	20.9275i	0.499977	−	0.707074i
$877$	−18.0597	−	10.4268i	−0.609834	−	0.352088i	0.163067	−	0.986615i	$-0.447861\pi$
$877$	−18.0597	−	10.4268i	−0.609834	−	0.352088i	−0.772900	+	0.634527i	$0.781195\pi$
$878$	19.0919	+	11.0227i	0.644320	+	0.371998i
$879$	−18.0000	+	25.4558i	−0.607125	+	0.858604i
$880$	4.50851	+	6.25845i	0.151982	+	0.210972i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$	3.72656	−	20.0505i	0.125480	−	0.675136i
$883$		−	6.55051i		−	0.220442i	−0.993907	−	0.110221i	$-0.964844\pi$
$883$		−	6.55051i		−	0.220442i	0.993907	−	0.110221i	$-0.0351559\pi$
$884$	−7.22474	−	12.5136i	−0.242994	−	0.420879i
$885$	44.2059	−	26.0435i	1.48596	−	0.875443i
$886$	10.6237	−	18.4008i	0.356911	−	0.618188i
$887$	16.7563	+	9.67423i	0.562620	+	0.324829i	0.754197	−	0.656649i	$-0.228027\pi$
$887$	16.7563	+	9.67423i	0.562620	+	0.324829i	−0.191576	+	0.981478i	$0.561360\pi$
$888$	−1.27135	+	13.7980i	−0.0426637	+	0.463029i
$889$	−1.55051	−	2.68556i	−0.0520024	−	0.0900709i
$890$	−0.696938	−	6.89898i	−0.0233614	−	0.231254i
$891$	4.82577	+	30.6681i	0.161669	+	1.02742i
$892$		−	9.10102i		−	0.304725i
$893$	20.9989	−	12.1237i	0.702702	−	0.405705i
$894$	14.2247	+	1.31067i	0.475747	+	0.0438355i
$895$	−0.825027	+	1.83307i	−0.0275776	+	0.0612728i
$896$	−0.224745	+	0.389270i	−0.00750820	+	0.0130046i
$897$	26.5843	−	12.2474i	0.887625	−	0.408930i
$898$	−16.2795	+	9.39898i	−0.543254	+	0.313648i
$899$	9.30306			0.310274
$900$	14.9977	−	0.263927i	0.499923	−	0.00879757i
$901$	−20.9444			−0.697759
$902$	2.98735	−	1.72474i	0.0994677	−	0.0574277i
$903$	−1.62129	−	1.14643i	−0.0539533	−	0.0381507i
$904$	2.44949	−	4.24264i	0.0814688	−	0.141108i
$905$	−5.09391	+	11.3178i	−0.169327	+	0.376217i
$906$	−2.89898	+	4.09978i	−0.0963121	+	0.136206i
$907$	34.4179	−	19.8712i	1.14283	−	0.659811i	0.195698	−	0.980664i	$-0.437303\pi$
$907$	34.4179	−	19.8712i	1.14283	−	0.659811i	0.947129	+	0.320853i	$0.103969\pi$
$908$		−	3.44949i		−	0.114475i
$909$	−8.00000	−	22.6274i	−0.265343	−	0.750504i
$910$	−0.247449	−	2.44949i	−0.00820284	−	0.0811998i
$911$	−12.1237	−	20.9989i	−0.401677	−	0.695725i	0.592252	−	0.805753i	$-0.298239\pi$
$911$	−12.1237	−	20.9989i	−0.401677	−	0.695725i	−0.993928	+	0.110028i	$0.964906\pi$
$912$	−8.57277	+	3.94949i	−0.283873	+	0.130781i
$913$	−11.9494	−	6.89898i	−0.395467	−	0.228323i
$914$	8.94949	−	15.5010i	0.296023	−	0.512727i
$915$	−0.151613	−	17.2321i	−0.00501216	−	0.569677i
$916$	9.22474	+	15.9777i	0.304794	+	0.527919i
$917$			2.20204i			0.0727178i
$918$	−29.7145	+	7.52270i	−0.980726	+	0.248286i
$919$	−1.10102			−0.0363193			−0.0181597	−	0.999835i	$-0.505781\pi$
$919$	−1.10102			−0.0363193			−0.0181597	+	0.999835i	$0.505781\pi$
$920$	−9.01702	−	12.5169i	−0.297282	−	0.412670i
$921$	−51.6464	−	4.75872i	−1.70181	−	0.156805i
$922$	2.12132	+	1.22474i	0.0698620	+	0.0403348i
$923$	5.19615	+	3.00000i	0.171033	+	0.0987462i
$924$	−1.12372	−	2.43916i	−0.0369678	−	0.0802424i
$925$	−29.9411	+	26.5241i	−0.984458	+	0.872108i
$926$	−24.0000			−0.788689
$927$	−32.4876	−	27.7753i	−1.06703	−	0.912259i
$928$			6.00000i			0.196960i
$929$	−8.20204	−	14.2064i	−0.269100	−	0.466095i	0.699529	−	0.714604i	$-0.253393\pi$
$929$	−8.20204	−	14.2064i	−0.269100	−	0.466095i	−0.968630	+	0.248508i	$0.920060\pi$
$930$	−2.95668	+	5.22678i	−0.0969534	+	0.171393i
$931$	−18.5227	+	32.0823i	−0.607057	+	1.05145i
$932$	−11.8619	−	6.84847i	−0.388549	−	0.224329i
$933$	18.5276	+	13.1010i	0.606568	+	0.428908i
$934$	5.17423	+	8.96204i	0.169306	+	0.293247i
$935$	−4.57321	−	45.2702i	−0.149560	−	1.48049i
$936$	4.77526	−	5.58542i	0.156084	−	0.182565i
$937$			0.404082i			0.0132008i	0.999978	+	0.00660039i	$0.00210099\pi$
$937$			0.404082i			0.0132008i	−0.999978	+	0.00660039i	$0.997899\pi$
$938$	1.77138	−	1.02270i	0.0578374	−	0.0333925i
$939$	15.7247	+	34.1322i	0.513158	+	1.11386i
$940$	9.07277	+	4.08346i	0.295921	+	0.133188i
$941$	15.1010	−	26.1557i	0.492279	−	0.852653i	−0.507681	−	0.861545i	$-0.669497\pi$
$941$	15.1010	−	26.1557i	0.492279	−	0.852653i	0.999960	+	0.00889239i	$0.00283057\pi$
$942$	2.54270	−	27.5959i	0.0828456	−	0.899124i
$943$	−5.97469	+	3.44949i	−0.194563	+	0.112331i
$944$	−13.2474			−0.431168
$945$	−5.14286	−	0.909111i	−0.167297	−	0.0295734i
$946$	8.79796			0.286046
$947$	−2.81237	+	1.62372i	−0.0913898	+	0.0527640i	−0.544998	−	0.838437i	$-0.683470\pi$
$947$	−2.81237	+	1.62372i	−0.0913898	+	0.0527640i	0.453609	+	0.891201i	$0.350136\pi$
$948$	1.16781	−	12.6742i	0.0379287	−	0.411640i
$949$	18.1237	−	31.3912i	0.588321	−	1.01900i
$950$	−25.8450	−	8.62907i	−0.838522	−	0.279964i
$951$	16.6288	+	36.0946i	0.539227	+	1.17045i
$952$	2.29629	−	1.32577i	0.0744233	−	0.0429683i
$953$		−	31.2020i		−	1.01073i	−0.862905	−	0.505367i	$-0.831357\pi$
$953$		−	31.2020i		−	1.01073i	0.862905	−	0.505367i	$-0.168643\pi$
$954$	−3.55051	−	10.0424i	−0.114952	−	0.325133i
$955$	40.5959	−	4.10102i	1.31365	−	0.132706i
$956$	0.348469	+	0.603566i	0.0112703	+	0.0195207i
$957$	−29.2699	−	20.6969i	−0.946161	−	0.669037i
$958$	14.4600	+	8.34847i	0.467181	+	0.269727i
$959$	−0.674235	+	1.16781i	−0.0217722	+	0.0377105i
$960$	−3.37101	−	1.90691i	−0.108799	−	0.0615452i
$961$	14.2980	+	24.7648i	0.461224	+	0.798864i
$962$			19.5959i			0.631798i
$963$	−8.96204	+	48.2196i	−0.288798	+	1.55386i
$964$	−1.00000			−0.0322078
$965$	24.8505	−	17.9020i	0.799967	−	0.576286i
$966$	2.24745	+	4.87832i	0.0723105	+	0.156957i
$967$	0.603566	+	0.348469i	0.0194094	+	0.0112060i	0.509673	−	0.860368i	$-0.329766\pi$
$967$	0.603566	+	0.348469i	0.0194094	+	0.0112060i	−0.490264	+	0.871574i	$0.663100\pi$
$968$	0.778539	+	0.449490i	0.0250232	+	0.0144471i
$969$	55.4444	+	5.10867i	1.78113	+	0.164114i
$970$	−16.9911	−	23.5861i	−0.545551	−	0.757303i
$971$	35.3939			1.13584			0.567922	−	0.823083i	$-0.307748\pi$
$971$	35.3939			1.13584			0.567922	+	0.823083i	$0.307748\pi$
$972$	−8.64420	−	12.9722i	−0.277263	−	0.416083i
$973$		−	5.95459i		−	0.190895i
$974$	12.5505	+	21.7381i	0.402144	+	0.696534i
$975$	21.0862	−	2.31772i	0.675299	−	0.0742265i
$976$	−2.22474	+	3.85337i	−0.0712123	+	0.123343i
$977$	24.3362	+	14.0505i	0.778584	+	0.449516i	0.835928	−	0.548839i	$-0.184930\pi$
$977$	24.3362	+	14.0505i	0.778584	+	0.449516i	−0.0573443	+	0.998354i	$0.518263\pi$
$978$	13.9993	−	6.44949i	0.447647	−	0.206232i
$979$	−5.34847	−	9.26382i	−0.170938	−	0.296073i
$980$	−15.1237	+	1.52781i	−0.483110	+	0.0488040i
$981$	−23.5959	−	4.38551i	−0.753360	−	0.140018i
$982$			18.5505i			0.591971i
$983$	18.5276	−	10.6969i	0.590940	−	0.341179i	−0.174529	−	0.984652i	$-0.555840\pi$
$983$	18.5276	−	10.6969i	0.590940	−	0.341179i	0.765469	+	0.643473i	$0.222507\pi$
$984$	−1.00000	+	1.41421i	−0.0318788	+	0.0450835i
$985$	−16.3125	−	7.34190i	−0.519758	−	0.233932i
$986$	17.6969	−	30.6520i	0.563585	−	0.976158i
$987$	−2.82843	−	2.00000i	−0.0900298	−	0.0636607i
$988$	−11.5601	+	6.67423i	−0.367776	+	0.212336i
$989$	−17.5959			−0.559518
$990$	20.9308	−	9.86699i	0.665223	−	0.313593i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	1.34278	−	0.775255i	0.0426333	−	0.0246144i
$993$	39.9479	−	18.4041i	1.26771	−	0.584036i
$994$	−0.550510	+	0.953512i	−0.0174611	+	0.0302436i
$995$	14.2713	−	31.7084i	0.452430	−	1.00522i
$996$	6.89898	+	0.635674i	0.218603	+	0.0201421i
$997$	−18.1384	+	10.4722i	−0.574448	+	0.331658i	−0.758924	−	0.651179i	$-0.774275\pi$
$997$	−18.1384	+	10.4722i	−0.574448	+	0.331658i	0.184476	+	0.982837i	$0.440941\pi$
$998$			21.2474i			0.672576i
$999$	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.49.3	yes	8
3.2	odd	2		270.2.i.b.199.1		8
4.3	odd	2		720.2.by.c.49.2		8
5.2	odd	4		450.2.e.n.301.1		4
5.3	odd	4		450.2.e.k.301.2		4
5.4	even	2	inner	90.2.i.b.49.2	✓	8
9.2	odd	6		270.2.i.b.19.4		8
9.4	even	3		810.2.c.f.649.4		4
9.5	odd	6		810.2.c.e.649.1		4
9.7	even	3	inner	90.2.i.b.79.2	yes	8
12.11	even	2		2160.2.by.d.1009.2		8
15.2	even	4		1350.2.e.j.901.2		4
15.8	even	4		1350.2.e.m.901.1		4
15.14	odd	2		270.2.i.b.199.4		8
20.19	odd	2		720.2.by.c.49.3		8
36.7	odd	6		720.2.by.c.529.3		8
36.11	even	6		2160.2.by.d.289.3		8
45.2	even	12		1350.2.e.j.451.2		4
45.4	even	6		810.2.c.f.649.2		4
45.7	odd	12		450.2.e.n.151.1		4
45.13	odd	12		4050.2.a.bs.1.2		2
45.14	odd	6		810.2.c.e.649.3		4
45.22	odd	12		4050.2.a.bq.1.1		2
45.23	even	12		4050.2.a.bm.1.2		2
45.29	odd	6		270.2.i.b.19.1		8
45.32	even	12		4050.2.a.bz.1.1		2
45.34	even	6	inner	90.2.i.b.79.3	yes	8
45.38	even	12		1350.2.e.m.451.1		4
45.43	odd	12		450.2.e.k.151.2		4
60.59	even	2		2160.2.by.d.1009.3		8
180.79	odd	6		720.2.by.c.529.2		8
180.119	even	6		2160.2.by.d.289.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.2	✓	8	5.4	even	2	inner
90.2.i.b.49.3	yes	8	1.1	even	1	trivial
90.2.i.b.79.2	yes	8	9.7	even	3	inner
90.2.i.b.79.3	yes	8	45.34	even	6	inner
270.2.i.b.19.1		8	45.29	odd	6
270.2.i.b.19.4		8	9.2	odd	6
270.2.i.b.199.1		8	3.2	odd	2
270.2.i.b.199.4		8	15.14	odd	2
450.2.e.k.151.2		4	45.43	odd	12
450.2.e.k.301.2		4	5.3	odd	4
450.2.e.n.151.1		4	45.7	odd	12
450.2.e.n.301.1		4	5.2	odd	4
720.2.by.c.49.2		8	4.3	odd	2
720.2.by.c.49.3		8	20.19	odd	2
720.2.by.c.529.2		8	180.79	odd	6
720.2.by.c.529.3		8	36.7	odd	6
810.2.c.e.649.1		4	9.5	odd	6
810.2.c.e.649.3		4	45.14	odd	6
810.2.c.f.649.2		4	45.4	even	6
810.2.c.f.649.4		4	9.4	even	3
1350.2.e.j.451.2		4	45.2	even	12
1350.2.e.j.901.2		4	15.2	even	4
1350.2.e.m.451.1		4	45.38	even	12
1350.2.e.m.901.1		4	15.8	even	4
2160.2.by.d.289.2		8	180.119	even	6
2160.2.by.d.289.3		8	36.11	even	6
2160.2.by.d.1009.2		8	12.11	even	2
2160.2.by.d.1009.3		8	60.59	even	2
4050.2.a.bm.1.2		2	45.23	even	12
4050.2.a.bq.1.1		2	45.22	odd	12
4050.2.a.bs.1.2		2	45.13	odd	12
4050.2.a.bz.1.1		2	45.32	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} +(0.158919 - 1.72474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.917738 + 2.03906i) q^{5} +(-0.724745 - 1.57313i) q^{6} +(0.389270 - 0.224745i) q^{7} -1.00000i q^{8} +(-2.94949 - 0.548188i) q^{9} +(0.224745 + 2.22474i) q^{10} +(1.72474 + 2.98735i) q^{11} +(-1.41421 - 1.00000i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(0.224745 - 0.389270i) q^{14} +(3.37101 + 1.90691i) q^{15} +(-0.500000 - 0.866025i) q^{16} +5.89898i q^{17} +(-2.82843 + 1.00000i) q^{18} +5.44949 q^{19} +(1.30701 + 1.81431i) q^{20} +(-0.325765 - 0.707107i) q^{21} +(2.98735 + 1.72474i) q^{22} +(-5.97469 - 3.44949i) q^{23} +(-1.72474 - 0.158919i) q^{24} +(-3.31552 - 3.74264i) q^{25} -2.44949 q^{26} +(-1.41421 + 5.00000i) q^{27} -0.449490i q^{28} +(-3.00000 - 5.19615i) q^{29} +(3.87283 - 0.0340742i) q^{30} +(-0.775255 + 1.34278i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(5.42650 - 2.50000i) q^{33} +(2.94949 + 5.10867i) q^{34} +(0.101021 + 1.00000i) q^{35} +(-1.94949 + 2.28024i) q^{36} -8.00000i q^{37} +(4.71940 - 2.72474i) q^{38} +(-2.44949 + 3.46410i) q^{39} +(2.03906 + 0.917738i) q^{40} +(0.500000 - 0.866025i) q^{41} +(-0.635674 - 0.449490i) q^{42} +(2.20881 - 1.27526i) q^{43} +3.44949 q^{44} +(3.82465 - 5.51109i) q^{45} -6.89898 q^{46} +(3.85337 - 2.22474i) q^{47} +(-1.57313 + 0.724745i) q^{48} +(-3.39898 + 5.88721i) q^{49} +(-4.74264 - 1.58346i) q^{50} +(10.1742 + 0.937458i) q^{51} +(-2.12132 + 1.22474i) q^{52} +3.55051i q^{53} +(1.27526 + 5.03723i) q^{54} +(-7.67423 + 0.775255i) q^{55} +(-0.224745 - 0.389270i) q^{56} +(0.866025 - 9.39898i) q^{57} +(-5.19615 - 3.00000i) q^{58} +(6.62372 - 11.4726i) q^{59} +(3.33694 - 1.96593i) q^{60} +(-2.22474 - 3.85337i) q^{61} +1.55051i q^{62} +(-1.27135 + 0.449490i) q^{63} -1.00000 q^{64} +(4.44414 - 3.20150i) q^{65} +(3.44949 - 4.87832i) q^{66} +(3.94086 + 2.27526i) q^{67} +(5.10867 + 2.94949i) q^{68} +(-6.89898 + 9.75663i) q^{69} +(0.587486 + 0.815515i) q^{70} -2.44949 q^{71} +(-0.548188 + 2.94949i) q^{72} +14.7980i q^{73} +(-4.00000 - 6.92820i) q^{74} +(-6.98200 + 5.12364i) q^{75} +(2.72474 - 4.71940i) q^{76} +(1.34278 + 0.775255i) q^{77} +(-0.389270 + 4.22474i) q^{78} +(3.67423 + 6.36396i) q^{79} +(2.22474 - 0.224745i) q^{80} +(8.39898 + 3.23375i) q^{81} -1.00000i q^{82} +(-3.46410 + 2.00000i) q^{83} +(-0.775255 - 0.0714323i) q^{84} +(-12.0284 - 5.41372i) q^{85} +(1.27526 - 2.20881i) q^{86} +(-9.43879 + 4.34847i) q^{87} +(2.98735 - 1.72474i) q^{88} -3.10102 q^{89} +(0.556696 - 6.68506i) q^{90} -1.10102 q^{91} +(-5.97469 + 3.44949i) q^{92} +(2.19275 + 1.55051i) q^{93} +(2.22474 - 3.85337i) q^{94} +(-5.00120 + 11.1118i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(-11.2583 + 6.50000i) q^{97} +6.79796i q^{98} +(-3.44949 - 9.75663i) 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

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