LMFDB - Embedded newform 630.2.bi.a.479.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(479,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.479"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.5
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.a.509.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-1.49245 - 0.878978i) q^{3} +1.00000 q^{4} +(0.796362 - 2.08945i) q^{5} +(1.49245 + 0.878978i) q^{6} +(-2.55753 + 0.677517i) q^{7} -1.00000 q^{8} +(1.45479 + 2.62366i) q^{9} +(-0.796362 + 2.08945i) q^{10} +(-2.46056 + 1.42061i) q^{11} +(-1.49245 - 0.878978i) q^{12} +(2.51471 + 4.35560i) q^{13} +(2.55753 - 0.677517i) q^{14} +(-3.02511 + 2.41841i) q^{15} +1.00000 q^{16} +(3.91852 + 2.26236i) q^{17} +(-1.45479 - 2.62366i) q^{18} +(-3.40172 + 1.96399i) q^{19} +(0.796362 - 2.08945i) q^{20} +(4.41250 + 1.23686i) q^{21} +(2.46056 - 1.42061i) q^{22} +(3.21075 - 5.56118i) q^{23} +(1.49245 + 0.878978i) q^{24} +(-3.73162 - 3.32792i) q^{25} +(-2.51471 - 4.35560i) q^{26} +(0.134933 - 5.19440i) q^{27} +(-2.55753 + 0.677517i) q^{28} +(3.16363 + 1.82652i) q^{29} +(3.02511 - 2.41841i) q^{30} +2.04291i q^{31} -1.00000 q^{32} +(4.92094 + 0.0426013i) q^{33} +(-3.91852 - 2.26236i) q^{34} +(-0.621082 + 5.88339i) q^{35} +(1.45479 + 2.62366i) q^{36} +(-0.925584 + 0.534386i) q^{37} +(3.40172 - 1.96399i) q^{38} +(0.0754114 - 8.71088i) q^{39} +(-0.796362 + 2.08945i) q^{40} +(2.85368 + 4.94272i) q^{41} +(-4.41250 - 1.23686i) q^{42} +(6.76731 + 3.90711i) q^{43} +(-2.46056 + 1.42061i) q^{44} +(6.64055 - 0.950343i) q^{45} +(-3.21075 + 5.56118i) q^{46} -2.23938i q^{47} +(-1.49245 - 0.878978i) q^{48} +(6.08194 - 3.46554i) q^{49} +(3.73162 + 3.32792i) q^{50} +(-3.85962 - 6.82074i) q^{51} +(2.51471 + 4.35560i) q^{52} +(2.88164 - 4.99115i) q^{53} +(-0.134933 + 5.19440i) q^{54} +(1.00879 + 6.27254i) q^{55} +(2.55753 - 0.677517i) q^{56} +(6.80319 + 0.0588963i) q^{57} +(-3.16363 - 1.82652i) q^{58} +12.8102 q^{59} +(-3.02511 + 2.41841i) q^{60} +10.4338i q^{61} -2.04291i q^{62} +(-5.49826 - 5.72444i) q^{63} +1.00000 q^{64} +(11.1034 - 1.78572i) q^{65} +(-4.92094 - 0.0426013i) q^{66} -5.99972i q^{67} +(3.91852 + 2.26236i) q^{68} +(-9.68003 + 5.47759i) q^{69} +(0.621082 - 5.88339i) q^{70} +7.81664i q^{71} +(-1.45479 - 2.62366i) q^{72} +(-7.04158 + 12.1964i) q^{73} +(0.925584 - 0.534386i) q^{74} +(2.64407 + 8.24675i) q^{75} +(-3.40172 + 1.96399i) q^{76} +(5.33048 - 5.30032i) q^{77} +(-0.0754114 + 8.71088i) q^{78} +4.51074 q^{79} +(0.796362 - 2.08945i) q^{80} +(-4.76714 + 7.63376i) q^{81} +(-2.85368 - 4.94272i) q^{82} +(10.9918 + 6.34613i) q^{83} +(4.41250 + 1.23686i) q^{84} +(7.84765 - 6.38590i) q^{85} +(-6.76731 - 3.90711i) q^{86} +(-3.11608 - 5.50675i) q^{87} +(2.46056 - 1.42061i) q^{88} +(-5.33519 - 9.24081i) q^{89} +(-6.64055 + 0.950343i) q^{90} +(-9.38244 - 9.43583i) q^{91} +(3.21075 - 5.56118i) q^{92} +(1.79567 - 3.04893i) q^{93} +2.23938i q^{94} +(1.39465 + 8.67178i) q^{95} +(1.49245 + 0.878978i) q^{96} +(-8.91744 + 15.4455i) q^{97} +(-6.08194 + 3.46554i) q^{98} +(-7.30680 - 4.38898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.49245	−	0.878978i	−0.861665	−	0.507478i
$3$	−1.49245	−	0.878978i	−0.861665	−	0.507478i
$4$	1.00000			0.500000
$5$	0.796362	−	2.08945i	0.356144	−	0.934431i
$5$	0.796362	−	2.08945i	0.356144	−	0.934431i
$6$	1.49245	+	0.878978i	0.609289	+	0.358841i
$7$	−2.55753	+	0.677517i	−0.966656	+	0.256077i
$7$	−2.55753	+	0.677517i	−0.966656	+	0.256077i
$8$	−1.00000			−0.353553
$9$	1.45479	+	2.62366i	0.484932	+	0.874552i
$10$	−0.796362	+	2.08945i	−0.251832	+	0.660743i
$11$	−2.46056	+	1.42061i	−0.741887	+	0.428329i	−0.822755	−	0.568396i	$-0.807564\pi$
$11$	−2.46056	+	1.42061i	−0.741887	+	0.428329i	0.0808677	+	0.996725i	$0.474231\pi$
$12$	−1.49245	−	0.878978i	−0.430832	−	0.253739i
$13$	2.51471	+	4.35560i	0.697455	+	1.20803i	0.969346	+	0.245699i	$0.0790174\pi$
$13$	2.51471	+	4.35560i	0.697455	+	1.20803i	−0.271892	+	0.962328i	$0.587649\pi$
$14$	2.55753	−	0.677517i	0.683529	−	0.181074i
$15$	−3.02511	+	2.41841i	−0.781080	+	0.624431i
$16$	1.00000			0.250000
$17$	3.91852	+	2.26236i	0.950381	+	0.548703i	0.893199	−	0.449661i	$-0.148455\pi$
$17$	3.91852	+	2.26236i	0.950381	+	0.548703i	0.0571816	+	0.998364i	$0.481789\pi$
$18$	−1.45479	−	2.62366i	−0.342898	−	0.618402i
$19$	−3.40172	+	1.96399i	−0.780409	+	0.450569i	−0.836575	−	0.547852i	$-0.815446\pi$
$19$	−3.40172	+	1.96399i	−0.780409	+	0.450569i	0.0561661	+	0.998421i	$0.482112\pi$
$20$	0.796362	−	2.08945i	0.178072	−	0.467216i
$21$	4.41250	+	1.23686i	0.962887	+	0.269904i
$22$	2.46056	−	1.42061i	0.524594	−	0.302874i
$23$	3.21075	−	5.56118i	0.669487	−	1.15959i	−0.308560	−	0.951205i	$-0.599847\pi$
$23$	3.21075	−	5.56118i	0.669487	−	1.15959i	0.978048	−	0.208381i	$-0.0668195\pi$
$24$	1.49245	+	0.878978i	0.304644	+	0.179421i
$25$	−3.73162	−	3.32792i	−0.746323	−	0.665584i
$26$	−2.51471	−	4.35560i	−0.493175	−	0.854204i
$27$	0.134933	−	5.19440i	0.0259679	−	0.999663i
$28$	−2.55753	+	0.677517i	−0.483328	+	0.128039i
$29$	3.16363	+	1.82652i	0.587472	+	0.339177i	0.764097	−	0.645101i	$-0.223185\pi$
$29$	3.16363	+	1.82652i	0.587472	+	0.339177i	−0.176626	+	0.984278i	$0.556518\pi$
$30$	3.02511	−	2.41841i	0.552307	−	0.441539i
$31$			2.04291i			0.366917i	0.983027	+	0.183459i	$0.0587294\pi$
$31$			2.04291i			0.366917i	−0.983027	+	0.183459i	$0.941271\pi$
$32$	−1.00000			−0.176777
$33$	4.92094	+	0.0426013i	0.856626	+	0.00741594i
$34$	−3.91852	−	2.26236i	−0.672021	−	0.387991i
$35$	−0.621082	+	5.88339i	−0.104982	+	0.994474i
$36$	1.45479	+	2.62366i	0.242466	+	0.437276i
$37$	−0.925584	+	0.534386i	−0.152165	+	0.0878526i	−0.574149	−	0.818751i	$-0.694667\pi$
$37$	−0.925584	+	0.534386i	−0.152165	+	0.0878526i	0.421984	+	0.906603i	$0.361334\pi$
$38$	3.40172	−	1.96399i	0.551833	−	0.318601i
$39$	0.0754114	−	8.71088i	0.0120755	−	1.39486i
$40$	−0.796362	+	2.08945i	−0.125916	+	0.330371i
$41$	2.85368	+	4.94272i	0.445670	+	0.771923i	0.998099	−	0.0616375i	$-0.0196323\pi$
$41$	2.85368	+	4.94272i	0.445670	+	0.771923i	−0.552429	+	0.833560i	$0.686299\pi$
$42$	−4.41250	−	1.23686i	−0.680864	−	0.190851i
$43$	6.76731	+	3.90711i	1.03201	+	0.595829i	0.917559	−	0.397601i	$-0.130157\pi$
$43$	6.76731	+	3.90711i	1.03201	+	0.595829i	0.114447	+	0.993429i	$0.463490\pi$
$44$	−2.46056	+	1.42061i	−0.370944	+	0.214164i
$45$	6.64055	−	0.950343i	0.989914	−	0.141669i
$46$	−3.21075	+	5.56118i	−0.473399	+	0.819951i
$47$		−	2.23938i		−	0.326647i	−0.986573	−	0.163323i	$-0.947779\pi$
$47$		−	2.23938i		−	0.326647i	0.986573	−	0.163323i	$-0.0522213\pi$
$48$	−1.49245	−	0.878978i	−0.215416	−	0.126870i
$49$	6.08194	−	3.46554i	0.868849	−	0.495078i
$50$	3.73162	+	3.32792i	0.527730	+	0.470639i
$51$	−3.85962	−	6.82074i	−0.540455	−	0.955095i
$52$	2.51471	+	4.35560i	0.348727	+	0.604013i
$53$	2.88164	−	4.99115i	0.395824	−	0.685587i	−0.597382	−	0.801957i	$-0.703792\pi$
$53$	2.88164	−	4.99115i	0.395824	−	0.685587i	0.993206	+	0.116370i	$0.0371258\pi$
$54$	−0.134933	+	5.19440i	−0.0183621	+	0.706868i
$55$	1.00879	+	6.27254i	0.136025	+	0.845789i
$56$	2.55753	−	0.677517i	0.341765	−	0.0905371i
$57$	6.80319	+	0.0588963i	0.901105	+	0.00780100i
$58$	−3.16363	−	1.82652i	−0.415405	−	0.239834i
$59$	12.8102			1.66775			0.833875	−	0.551953i	$-0.186117\pi$
$59$	12.8102			1.66775			0.833875	+	0.551953i	$0.186117\pi$
$60$	−3.02511	+	2.41841i	−0.390540	+	0.312215i
$61$			10.4338i			1.33592i	0.744199	+	0.667958i	$0.232831\pi$
$61$			10.4338i			1.33592i	−0.744199	+	0.667958i	$0.767169\pi$
$62$		−	2.04291i		−	0.259450i
$63$	−5.49826	−	5.72444i	−0.692715	−	0.721211i
$64$	1.00000			0.125000
$65$	11.1034	−	1.78572i	1.37721	−	0.221492i
$66$	−4.92094	−	0.0426013i	−0.605726	−	0.00524386i
$67$		−	5.99972i		−	0.732982i	−0.930422	−	0.366491i	$-0.880559\pi$
$67$		−	5.99972i		−	0.732982i	0.930422	−	0.366491i	$-0.119441\pi$
$68$	3.91852	+	2.26236i	0.475190	+	0.274351i
$69$	−9.68003	+	5.47759i	−1.16534	+	0.659424i
$70$	0.621082	−	5.88339i	0.0742335	−	0.703199i
$71$			7.81664i			0.927664i	0.885923	+	0.463832i	$0.153526\pi$
$71$			7.81664i			0.927664i	−0.885923	+	0.463832i	$0.846474\pi$
$72$	−1.45479	−	2.62366i	−0.171449	−	0.309201i
$73$	−7.04158	+	12.1964i	−0.824154	+	1.42748i	0.0784100	+	0.996921i	$0.475016\pi$
$73$	−7.04158	+	12.1964i	−0.824154	+	1.42748i	−0.902564	+	0.430556i	$0.858318\pi$
$74$	0.925584	−	0.534386i	0.107597	−	0.0621212i
$75$	2.64407	+	8.24675i	0.305311	+	0.952253i
$76$	−3.40172	+	1.96399i	−0.390205	+	0.225285i
$77$	5.33048	−	5.30032i	0.607465	−	0.604028i
$78$	−0.0754114	+	8.71088i	−0.00853865	+	0.986313i
$79$	4.51074			0.507498			0.253749	−	0.967270i	$-0.418336\pi$
$79$	4.51074			0.507498			0.253749	+	0.967270i	$0.418336\pi$
$80$	0.796362	−	2.08945i	0.0890360	−	0.233608i
$81$	−4.76714	+	7.63376i	−0.529683	+	0.848196i
$82$	−2.85368	−	4.94272i	−0.315136	−	0.545832i
$83$	10.9918	+	6.34613i	1.20651	+	0.696578i	0.961995	−	0.273068i	$-0.0880385\pi$
$83$	10.9918	+	6.34613i	1.20651	+	0.696578i	0.244513	+	0.969646i	$0.421372\pi$
$84$	4.41250	+	1.23686i	0.481444	+	0.134952i
$85$	7.84765	−	6.38590i	0.851197	−	0.692648i
$86$	−6.76731	−	3.90711i	−0.729738	−	0.421315i
$87$	−3.11608	−	5.50675i	−0.334079	−	0.590386i
$88$	2.46056	−	1.42061i	0.262297	−	0.151437i
$89$	−5.33519	−	9.24081i	−0.565529	−	0.979524i	−0.997000	−	0.0773979i	$-0.975339\pi$
$89$	−5.33519	−	9.24081i	−0.565529	−	0.979524i	0.431472	−	0.902127i	$-0.357995\pi$
$90$	−6.64055	+	0.950343i	−0.699975	+	0.100175i
$91$	−9.38244	−	9.43583i	−0.983547	−	0.989144i
$92$	3.21075	−	5.56118i	0.334744	−	0.579793i
$93$	1.79567	−	3.04893i	0.186203	−	0.316160i
$94$			2.23938i			0.230974i
$95$	1.39465	+	8.67178i	0.143088	+	0.889706i
$96$	1.49245	+	0.878978i	0.152322	+	0.0897103i
$97$	−8.91744	+	15.4455i	−0.905429	+	1.56825i	−0.0850876	+	0.996373i	$0.527117\pi$
$97$	−8.91744	+	15.4455i	−0.905429	+	1.56825i	−0.820341	+	0.571875i	$0.806216\pi$
$98$	−6.08194	+	3.46554i	−0.614369	+	0.350073i
$99$	−7.30680	−	4.38898i	−0.734361	−	0.441109i
$100$	−3.73162	−	3.32792i	−0.373162	−	0.332792i
$101$	−5.04091	−	8.73112i	−0.501590	−	0.868779i	−0.999998	−	0.00183643i	$-0.999415\pi$
$101$	−5.04091	−	8.73112i	−0.501590	−	0.868779i	0.498409	−	0.866942i	$-0.333918\pi$
$102$	3.85962	+	6.82074i	0.382159	+	0.675354i
$103$	−1.03484	+	1.79239i	−0.101965	+	0.176609i	−0.912494	−	0.409089i	$-0.865846\pi$
$103$	−1.03484	+	1.79239i	−0.101965	+	0.176609i	0.810529	+	0.585699i	$0.199180\pi$
$104$	−2.51471	−	4.35560i	−0.246587	−	0.427102i
$105$	6.09830	−	8.23473i	0.595133	−	0.803627i
$106$	−2.88164	+	4.99115i	−0.279890	+	0.484783i
$107$	1.27205	+	2.20325i	0.122973	+	0.212996i	0.920939	−	0.389707i	$-0.127424\pi$
$107$	1.27205	+	2.20325i	0.122973	+	0.212996i	−0.797966	+	0.602703i	$0.794090\pi$
$108$	0.134933	−	5.19440i	0.0129839	−	0.499831i
$109$	5.96532	−	10.3322i	0.571374	−	0.989649i	−0.425051	−	0.905170i	$-0.639744\pi$
$109$	5.96532	−	10.3322i	0.571374	−	0.989649i	0.996425	−	0.0844800i	$-0.0269229\pi$
$110$	−1.00879	−	6.27254i	−0.0961843	−	0.598063i
$111$	1.85110	+	0.0160252i	0.175699	+	0.00152105i
$112$	−2.55753	+	0.677517i	−0.241664	+	0.0640194i
$113$	−4.09453	−	7.09194i	−0.385181	−	0.667153i	0.606613	−	0.794997i	$-0.292528\pi$
$113$	−4.09453	−	7.09194i	−0.385181	−	0.667153i	−0.991794	+	0.127844i	$0.959194\pi$
$114$	−6.80319	−	0.0588963i	−0.637178	−	0.00551614i
$115$	−9.06290	−	11.1374i	−0.845119	−	1.03857i
$116$	3.16363	+	1.82652i	0.293736	+	0.169588i
$117$	−7.76922	+	12.9342i	−0.718265	+	1.19577i
$118$	−12.8102			−1.17928
$119$	−11.5545	−	3.13119i	−1.05920	−	0.287036i
$120$	3.02511	−	2.41841i	0.276154	−	0.220770i
$121$	−1.46376	+	2.53530i	−0.133069	+	0.230482i
$122$		−	10.4338i		−	0.944635i
$123$	0.0855764	−	9.88506i	0.00771617	−	0.891306i
$124$			2.04291i			0.183459i
$125$	−9.92524	+	5.14680i	−0.887741	+	0.460344i
$126$	5.49826	+	5.72444i	0.489824	+	0.509973i
$127$			18.1709i			1.61240i	0.591641	+	0.806202i	$0.298480\pi$
$127$			18.1709i			1.61240i	−0.591641	+	0.806202i	$0.701520\pi$
$128$	−1.00000			−0.0883883
$129$	−6.66559	−	11.7795i	−0.586873	−	1.03712i
$130$	−11.1034	+	1.78572i	−0.973836	+	0.156618i
$131$	−8.55442	+	14.8167i	−0.747403	+	1.29454i	0.201661	+	0.979455i	$0.435366\pi$
$131$	−8.55442	+	14.8167i	−0.747403	+	1.29454i	−0.949064	+	0.315084i	$0.897967\pi$
$132$	4.92094	+	0.0426013i	0.428313	+	0.00370797i
$133$	7.36938	−	7.32769i	0.639007	−	0.635391i
$134$			5.99972i			0.518296i
$135$	−10.7460	−	4.41856i	−0.924868	−	0.380289i
$136$	−3.91852	−	2.26236i	−0.336010	−	0.193996i
$137$	3.10008	+	5.36950i	0.264858	+	0.458747i	0.967526	−	0.252770i	$-0.0813416\pi$
$137$	3.10008	+	5.36950i	0.264858	+	0.458747i	−0.702668	+	0.711517i	$0.748008\pi$
$138$	9.68003	−	5.47759i	0.824019	−	0.466283i
$139$	13.0131	−	7.51311i	1.10376	−	0.637253i	0.166550	−	0.986033i	$-0.446737\pi$
$139$	13.0131	−	7.51311i	1.10376	−	0.637253i	0.937205	+	0.348780i	$0.113404\pi$
$140$	−0.621082	+	5.88339i	−0.0524910	+	0.497237i
$141$	−1.96836	+	3.34215i	−0.165766	+	0.281460i
$142$		−	7.81664i		−	0.655958i
$143$	−12.3752	−	7.14482i	−1.03487	−	0.597480i
$144$	1.45479	+	2.62366i	0.121233	+	0.218638i
$145$	6.33583	−	5.15568i	0.526162	−	0.428156i
$146$	7.04158	−	12.1964i	0.582765	−	1.00938i
$147$	−12.1231	−	0.173752i	−0.999897	−	0.0143309i
$148$	−0.925584	+	0.534386i	−0.0760826	+	0.0439263i
$149$	−1.97748	−	1.14170i	−0.162001	−	0.0935314i	0.416808	−	0.908995i	$-0.363149\pi$
$149$	−1.97748	−	1.14170i	−0.162001	−	0.0935314i	−0.578809	+	0.815463i	$0.696482\pi$
$150$	−2.64407	−	8.24675i	−0.215887	−	0.673344i
$151$	−6.59525	−	11.4233i	−0.536714	−	0.929616i	−0.999078	−	0.0429256i	$-0.986332\pi$
$151$	−6.59525	−	11.4233i	−0.536714	−	0.929616i	0.462365	−	0.886690i	$-0.347001\pi$
$152$	3.40172	−	1.96399i	0.275916	−	0.159300i
$153$	−0.235009	+	13.5721i	−0.0189994	+	1.09724i
$154$	−5.33048	+	5.30032i	−0.429542	+	0.427112i
$155$	4.26856	+	1.62690i	0.342859	+	0.130675i
$156$	0.0754114	−	8.71088i	0.00603774	−	0.697428i
$157$	17.9261			1.43066			0.715330	−	0.698786i	$-0.246276\pi$
$157$	17.9261			1.43066			0.715330	+	0.698786i	$0.246276\pi$
$158$	−4.51074			−0.358855
$159$	−8.68780	+	4.91612i	−0.688988	+	0.389874i
$160$	−0.796362	+	2.08945i	−0.0629579	+	0.165186i
$161$	−4.44380	+	16.3982i	−0.350220	+	1.29236i
$162$	4.76714	−	7.63376i	0.374542	−	0.599765i
$163$	3.27021	−	1.88806i	0.256143	−	0.147884i	−0.366431	−	0.930445i	$-0.619420\pi$
$163$	3.27021	−	1.88806i	0.256143	−	0.147884i	0.622574	+	0.782561i	$0.286087\pi$
$164$	2.85368	+	4.94272i	0.222835	+	0.385961i
$165$	4.00786	−	10.2481i	0.312012	−	0.797817i
$166$	−10.9918	−	6.34613i	−0.853130	−	0.492555i
$167$	−20.8655	+	12.0467i	−1.61462	+	0.932201i	−0.626340	+	0.779550i	$0.715448\pi$
$167$	−20.8655	+	12.0467i	−1.61462	+	0.932201i	−0.988280	+	0.152651i	$0.951219\pi$
$168$	−4.41250	−	1.23686i	−0.340432	−	0.0954255i
$169$	−6.14752	+	10.6478i	−0.472886	+	0.819062i
$170$	−7.84765	+	6.38590i	−0.601887	+	0.489776i
$171$	−10.1016	−	6.06776i	−0.772491	−	0.464013i
$172$	6.76731	+	3.90711i	0.516003	+	0.297914i
$173$		−	12.1734i		−	0.925523i	−0.886483	−	0.462762i	$-0.846859\pi$
$173$		−	12.1734i		−	0.925523i	0.886483	−	0.462762i	$-0.153141\pi$
$174$	3.11608	+	5.50675i	0.236229	+	0.417466i
$175$	11.7984	+	5.98303i	0.891879	+	0.452274i
$176$	−2.46056	+	1.42061i	−0.185472	+	0.107082i
$177$	−19.1186	−	11.2599i	−1.43704	−	0.846347i
$178$	5.33519	+	9.24081i	0.399889	+	0.692628i
$179$	−3.16979	−	1.83008i	−0.236921	−	0.136786i	0.376840	−	0.926278i	$-0.377011\pi$
$179$	−3.16979	−	1.83008i	−0.236921	−	0.136786i	−0.613761	+	0.789492i	$0.710344\pi$
$180$	6.64055	−	0.950343i	0.494957	−	0.0708344i
$181$		−	11.5653i		−	0.859645i	−0.902914	−	0.429822i	$-0.858576\pi$
$181$		−	11.5653i		−	0.859645i	0.902914	−	0.429822i	$-0.141424\pi$
$182$	9.38244	+	9.43583i	0.695473	+	0.699431i
$183$	9.17111	−	15.5719i	0.677948	−	1.15111i
$184$	−3.21075	+	5.56118i	−0.236700	+	0.409976i
$185$	0.379474	+	2.35953i	0.0278995	+	0.173476i
$186$	−1.79567	+	3.04893i	−0.131665	+	0.223559i
$187$	−12.8557			−0.940101
$188$		−	2.23938i		−	0.163323i
$189$	3.17420	+	13.3763i	0.230889	+	0.972980i
$190$	−1.39465	−	8.67178i	−0.101179	−	0.629117i
$191$			9.43103i			0.682405i	0.939990	+	0.341203i	$0.110834\pi$
$191$			9.43103i			0.682405i	−0.939990	+	0.341203i	$0.889166\pi$
$192$	−1.49245	−	0.878978i	−0.107708	−	0.0634348i
$193$		−	1.48521i		−	0.106908i	−0.998570	−	0.0534540i	$-0.982977\pi$
$193$		−	1.48521i		−	0.106908i	0.998570	−	0.0534540i	$-0.0170230\pi$
$194$	8.91744	−	15.4455i	0.640235	−	1.10892i
$195$	−18.1409	−	7.09458i	−1.29910	−	0.508053i
$196$	6.08194	−	3.46554i	0.434424	−	0.247539i
$197$	17.6493			1.25746			0.628729	−	0.777624i	$-0.283575\pi$
$197$	17.6493			1.25746			0.628729	+	0.777624i	$0.283575\pi$
$198$	7.30680	+	4.38898i	0.519271	+	0.311911i
$199$	17.8938	+	10.3310i	1.26846	+	0.732344i	0.974696	−	0.223534i	$-0.0717595\pi$
$199$	17.8938	+	10.3310i	1.26846	+	0.732344i	0.293762	+	0.955879i	$0.405093\pi$
$200$	3.73162	+	3.32792i	0.263865	+	0.235319i
$201$	−5.27362	+	8.95426i	−0.371972	+	0.631585i
$202$	5.04091	+	8.73112i	0.354677	+	0.614319i
$203$	−9.32859	−	2.52798i	−0.654739	−	0.177429i
$204$	−3.85962	−	6.82074i	−0.270227	−	0.477548i
$205$	12.6001	−	2.02643i	0.880031	−	0.141532i
$206$	1.03484	−	1.79239i	0.0721004	−	0.124882i
$207$	19.2616	+	0.333526i	1.33877	+	0.0231817i
$208$	2.51471	+	4.35560i	0.174364	+	0.302007i
$209$	5.58010	−	9.66502i	0.385984	−	0.668544i
$210$	−6.09830	+	8.23473i	−0.420823	+	0.568250i
$211$	5.63953	+	9.76796i	0.388241	+	0.672454i	0.992213	−	0.124552i	$-0.0397493\pi$
$211$	5.63953	+	9.76796i	0.388241	+	0.672454i	−0.603972	+	0.797006i	$0.706416\pi$
$212$	2.88164	−	4.99115i	0.197912	−	0.342793i
$213$	6.87065	−	11.6659i	0.470769	−	0.799335i
$214$	−1.27205	−	2.20325i	−0.0869553	−	0.150611i
$215$	13.5529	−	11.0285i	0.924303	−	0.752137i
$216$	−0.134933	+	5.19440i	−0.00918103	+	0.353434i
$217$	−1.38411	−	5.22481i	−0.0939593	−	0.354683i
$218$	−5.96532	+	10.3322i	−0.404023	+	0.699788i
$219$	21.2295	−	12.0130i	1.43456	−	0.811766i
$220$	1.00879	+	6.27254i	0.0680126	+	0.422895i
$221$			22.7567i			1.53078i
$222$	−1.85110	−	0.0160252i	−0.124238	−	0.00107554i
$223$	−6.07248	+	10.5178i	−0.406643	+	0.704327i	−0.994511	−	0.104630i	$-0.966634\pi$
$223$	−6.07248	+	10.5178i	−0.406643	+	0.704327i	0.587868	+	0.808957i	$0.299968\pi$
$224$	2.55753	−	0.677517i	0.170882	−	0.0452685i
$225$	3.30258	−	14.6319i	0.220172	−	0.975461i
$226$	4.09453	+	7.09194i	0.272364	+	0.471749i
$227$	−20.5863	+	11.8855i	−1.36636	+	0.788868i	−0.990461	−	0.137793i	$-0.955999\pi$
$227$	−20.5863	+	11.8855i	−1.36636	+	0.788868i	−0.375898	+	0.926661i	$0.622666\pi$
$228$	6.80319	+	0.0588963i	0.450553	+	0.00390050i
$229$	9.88508	+	5.70716i	0.653225	+	0.377139i	0.789691	−	0.613505i	$-0.210241\pi$
$229$	9.88508	+	5.70716i	0.653225	+	0.377139i	−0.136466	+	0.990645i	$0.543574\pi$
$230$	9.06290	+	11.1374i	0.597590	+	0.734379i
$231$	−12.6143	+	3.22507i	−0.829962	+	0.212194i
$232$	−3.16363	−	1.82652i	−0.207703	−	0.119917i
$233$	−4.16132	−	7.20762i	−0.272617	−	0.472187i	0.696914	−	0.717155i	$-0.254556\pi$
$233$	−4.16132	−	7.20762i	−0.272617	−	0.472187i	−0.969531	+	0.244968i	$0.921223\pi$
$234$	7.76922	−	12.9342i	0.507890	−	0.845538i
$235$	−4.67907	−	1.78335i	−0.305229	−	0.116333i
$236$	12.8102			0.833875
$237$	−6.73204	−	3.96484i	−0.437293	−	0.257544i
$238$	11.5545	+	3.13119i	0.748969	+	0.202965i
$239$	−6.41684	+	3.70476i	−0.415071	+	0.239641i	−0.692966	−	0.720970i	$-0.743696\pi$
$239$	−6.41684	+	3.70476i	−0.415071	+	0.239641i	0.277895	+	0.960611i	$0.410363\pi$
$240$	−3.02511	+	2.41841i	−0.195270	+	0.156108i
$241$	−7.50748	+	4.33445i	−0.483599	+	0.279206i	−0.721915	−	0.691981i	$-0.756738\pi$
$241$	−7.50748	+	4.33445i	−0.483599	+	0.279206i	0.238316	+	0.971188i	$0.423405\pi$
$242$	1.46376	−	2.53530i	0.0940937	−	0.162975i
$243$	13.8246	−	7.20277i	0.886850	−	0.462058i
$244$			10.4338i			0.667958i
$245$	−2.39766	−	15.4677i	−0.153181	−	0.988198i
$246$	−0.0855764	+	9.88506i	−0.00545615	+	0.630249i
$247$	−17.1087	−	9.87771i	−1.08860	−	0.628503i
$248$		−	2.04291i		−	0.129725i
$249$	−10.8266	−	19.1328i	−0.686107	−	1.21249i
$250$	9.92524	−	5.14680i	0.627727	−	0.325512i
$251$	−15.4449			−0.974871			−0.487436	−	0.873159i	$-0.662068\pi$
$251$	−15.4449			−0.974871			−0.487436	+	0.873159i	$0.662068\pi$
$252$	−5.49826	−	5.72444i	−0.346358	−	0.360606i
$253$			18.2448i			1.14704i
$254$		−	18.1709i		−	1.14014i
$255$	−17.3253	+	2.63271i	−1.08495	+	0.164866i
$256$	1.00000			0.0625000
$257$	5.03816	+	2.90878i	0.314272	+	0.181445i	0.648836	−	0.760928i	$-0.275256\pi$
$257$	5.03816	+	2.90878i	0.314272	+	0.181445i	−0.334565	+	0.942373i	$0.608589\pi$
$258$	6.66559	+	11.7795i	0.414982	+	0.733358i
$259$	2.00516	−	1.99381i	0.124594	−	0.123889i
$260$	11.1034	−	1.78572i	0.688606	−	0.110746i
$261$	−0.189736	+	10.9575i	−0.0117443	+	0.678252i
$262$	8.55442	−	14.8167i	0.528494	−	0.915378i
$263$	−1.08784	−	1.88419i	−0.0670790	−	0.116184i	0.830535	−	0.556966i	$-0.188035\pi$
$263$	−1.08784	−	1.88419i	−0.0670790	−	0.116184i	−0.897614	+	0.440782i	$0.854701\pi$
$264$	−4.92094	−	0.0426013i	−0.302863	−	0.00262193i
$265$	−8.13393	−	9.99581i	−0.499663	−	0.614037i
$266$	−7.36938	+	7.32769i	−0.451846	+	0.449289i
$267$	−0.159992	+	18.4809i	−0.00979136	+	1.13101i
$268$		−	5.99972i		−	0.366491i
$269$	1.75606	−	3.04158i	0.107069	−	0.185449i	−0.807513	−	0.589850i	$-0.799187\pi$
$269$	1.75606	−	3.04158i	0.107069	−	0.185449i	0.914582	+	0.404401i	$0.132520\pi$
$270$	10.7460	+	4.41856i	0.653980	+	0.268905i
$271$	1.39309	−	0.804303i	0.0846244	−	0.0488579i	−0.457091	−	0.889420i	$-0.651109\pi$
$271$	1.39309	−	0.804303i	0.0846244	−	0.0488579i	0.541715	+	0.840562i	$0.317775\pi$
$272$	3.91852	+	2.26236i	0.237595	+	0.137176i
$273$	5.70890	+	22.3294i	0.345519	+	1.35144i
$274$	−3.10008	−	5.36950i	−0.187283	−	0.324383i
$275$	13.9095	+	2.88740i	0.838777	+	0.174117i
$276$	−9.68003	+	5.47759i	−0.582669	+	0.329712i
$277$	3.87815	−	2.23905i	0.233015	−	0.134531i	−0.378947	−	0.925418i	$-0.623714\pi$
$277$	3.87815	−	2.23905i	0.233015	−	0.134531i	0.611962	+	0.790887i	$0.290380\pi$
$278$	−13.0131	+	7.51311i	−0.780473	+	0.450606i
$279$	−5.35989	+	2.97201i	−0.320888	+	0.177930i
$280$	0.621082	−	5.88339i	0.0371167	−	0.351600i
$281$	−9.04334	−	5.22117i	−0.539480	−	0.311469i	0.205388	−	0.978681i	$-0.434154\pi$
$281$	−9.04334	−	5.22117i	−0.539480	−	0.311469i	−0.744868	+	0.667211i	$0.767488\pi$
$282$	1.96836	−	3.34215i	0.117214	−	0.199022i
$283$	−18.5038			−1.09994			−0.549969	−	0.835185i	$-0.685360\pi$
$283$	−18.5038			−1.09994			−0.549969	+	0.835185i	$0.685360\pi$
$284$			7.81664i			0.463832i
$285$	5.54087	−	14.1680i	0.328213	−	0.839242i
$286$	12.3752	+	7.14482i	0.731761	+	0.422482i
$287$	−10.6471	−	10.7077i	−0.628481	−	0.632058i
$288$	−1.45479	−	2.62366i	−0.0857246	−	0.154600i
$289$	1.73653	+	3.00776i	0.102149	+	0.176927i
$290$	−6.33583	+	5.15568i	−0.372053	+	0.302752i
$291$	26.8850	−	15.2133i	1.57603	−	0.891819i
$292$	−7.04158	+	12.1964i	−0.412077	+	0.713738i
$293$	−0.317382	+	0.183240i	−0.0185416	+	0.0107050i	−0.509242	−	0.860623i	$-0.670074\pi$
$293$	−0.317382	+	0.183240i	−0.0185416	+	0.0107050i	0.490701	+	0.871328i	$0.336741\pi$
$294$	12.1231	+	0.173752i	0.707034	+	0.0101334i
$295$	10.2016	−	26.7664i	0.593959	−	1.55840i
$296$	0.925584	−	0.534386i	0.0537985	−	0.0310606i
$297$	7.04719	+	12.9728i	0.408919	+	0.752760i
$298$	1.97748	+	1.14170i	0.114552	+	0.0661367i
$299$	32.2964			1.86775
$300$	2.64407	+	8.24675i	0.152655	+	0.476126i
$301$	−19.9548	−	5.40759i	−1.15017	−	0.311688i
$302$	6.59525	+	11.4233i	0.379514	+	0.657337i
$303$	−0.151167	+	17.4616i	−0.00868434	+	1.00314i
$304$	−3.40172	+	1.96399i	−0.195102	+	0.112642i
$305$	21.8010	+	8.30911i	1.24832	+	0.475778i
$306$	0.235009	−	13.5721i	0.0134346	−	0.775866i
$307$	24.9894			1.42622			0.713110	−	0.701053i	$-0.247286\pi$
$307$	24.9894			1.42622			0.713110	+	0.701053i	$0.247286\pi$
$308$	5.33048	−	5.30032i	0.303732	−	0.302014i
$309$	3.11991	−	1.76545i	0.177485	−	0.100433i
$310$	−4.26856	−	1.62690i	−0.242438	−	0.0924015i
$311$	24.0318			1.36272			0.681358	−	0.731950i	$-0.261390\pi$
$311$	24.0318			1.36272			0.681358	+	0.731950i	$0.261390\pi$
$312$	−0.0754114	+	8.71088i	−0.00426933	+	0.493156i
$313$	−6.50477			−0.367671			−0.183836	−	0.982957i	$-0.558851\pi$
$313$	−6.50477			−0.367671			−0.183836	+	0.982957i	$0.558851\pi$
$314$	−17.9261			−1.01163
$315$	−16.3395	+	6.92962i	−0.920629	+	0.390440i
$316$	4.51074			0.253749
$317$	−7.38882			−0.414997			−0.207499	−	0.978235i	$-0.566532\pi$
$317$	−7.38882			−0.414997			−0.207499	+	0.978235i	$0.566532\pi$
$318$	8.68780	−	4.91612i	0.487188	−	0.275682i
$319$	−10.3791			−0.581117
$320$	0.796362	−	2.08945i	0.0445180	−	0.116804i
$321$	0.0381463	−	4.40633i	0.00212912	−	0.245938i
$322$	4.44380	−	16.3982i	0.247643	−	0.913838i
$323$	−17.7730			−0.988914
$324$	−4.76714	+	7.63376i	−0.264841	+	0.424098i
$325$	5.11117	−	24.6222i	0.283517	−	1.36579i
$326$	−3.27021	+	1.88806i	−0.181120	+	0.104570i
$327$	−17.9847	+	10.1769i	−0.994559	+	0.562786i
$328$	−2.85368	−	4.94272i	−0.157568	−	0.272916i
$329$	1.51722	+	5.72727i	0.0836468	+	0.315755i
$330$	−4.00786	+	10.2481i	−0.220626	+	0.564142i
$331$	26.3139			1.44634			0.723171	−	0.690669i	$-0.242684\pi$
$331$	26.3139			1.44634			0.723171	+	0.690669i	$0.242684\pi$
$332$	10.9918	+	6.34613i	0.603254	+	0.348289i
$333$	−2.74858	−	1.65099i	−0.150621	−	0.0904739i
$334$	20.8655	−	12.0467i	1.14171	−	0.659166i
$335$	−12.5361	−	4.77795i	−0.684921	−	0.261047i
$336$	4.41250	+	1.23686i	0.240722	+	0.0674760i
$337$	5.78970	−	3.34269i	0.315385	−	0.182088i	−0.333949	−	0.942591i	$-0.608381\pi$
$337$	5.78970	−	3.34269i	0.315385	−	0.182088i	0.649334	+	0.760504i	$0.275048\pi$
$338$	6.14752	−	10.6478i	0.334381	−	0.579164i
$339$	−0.122787	+	14.1833i	−0.00666889	+	0.770334i
$340$	7.84765	−	6.38590i	0.425599	−	0.346324i
$341$	−2.90217	−	5.02671i	−0.157161	−	0.272211i
$342$	10.1016	+	6.06776i	0.546234	+	0.328107i
$343$	−13.2068	+	12.9839i	−0.713100	+	0.701063i
$344$	−6.76731	−	3.90711i	−0.364869	−	0.210657i
$345$	3.73635	+	24.5881i	0.201158	+	1.32378i
$346$			12.1734i			0.654444i
$347$	−2.41396			−0.129588			−0.0647940	−	0.997899i	$-0.520639\pi$
$347$	−2.41396			−0.129588			−0.0647940	+	0.997899i	$0.520639\pi$
$348$	−3.11608	−	5.50675i	−0.167039	−	0.295193i
$349$	−0.654664	−	0.377971i	−0.0350434	−	0.0202323i	0.482376	−	0.875964i	$-0.339774\pi$
$349$	−0.654664	−	0.377971i	−0.0350434	−	0.0202323i	−0.517419	+	0.855732i	$0.673107\pi$
$350$	−11.7984	−	5.98303i	−0.630654	−	0.319806i
$351$	22.9641	−	12.4747i	1.22573	−	0.665849i
$352$	2.46056	−	1.42061i	0.131148	−	0.0757186i
$353$	−8.10821	+	4.68128i	−0.431557	+	0.249159i	−0.700010	−	0.714133i	$-0.746821\pi$
$353$	−8.10821	+	4.68128i	−0.431557	+	0.249159i	0.268453	+	0.963293i	$0.413488\pi$
$354$	19.1186	+	11.2599i	1.01614	+	0.598458i
$355$	16.3325	+	6.22487i	0.866838	+	0.330382i
$356$	−5.33519	−	9.24081i	−0.282764	−	0.489762i
$357$	14.4923	+	14.8293i	0.767012	+	0.784850i
$358$	3.16979	+	1.83008i	0.167529	+	0.0967227i
$359$	−20.7136	+	11.9590i	−1.09322	+	0.631172i	−0.934433	−	0.356140i	$-0.884093\pi$
$359$	−20.7136	+	11.9590i	−1.09322	+	0.631172i	−0.158790	+	0.987312i	$0.550759\pi$
$360$	−6.64055	+	0.950343i	−0.349987	+	0.0500875i
$361$	−1.78551	+	3.09260i	−0.0939744	+	0.162768i
$362$			11.5653i			0.607860i
$363$	4.41305	−	2.49719i	0.231625	−	0.131068i
$364$	−9.38244	−	9.43583i	−0.491774	−	0.494572i
$365$	19.8761	+	24.4258i	1.04036	+	1.27850i
$366$	−9.17111	+	15.5719i	−0.479382	+	0.813958i
$367$	−2.63628	−	4.56616i	−0.137612	−	0.238352i	0.788980	−	0.614419i	$-0.210610\pi$
$367$	−2.63628	−	4.56616i	−0.137612	−	0.238352i	−0.926592	+	0.376067i	$0.877276\pi$
$368$	3.21075	−	5.56118i	0.167372	−	0.289896i
$369$	−8.81647	+	14.6777i	−0.458967	+	0.764091i
$370$	−0.379474	−	2.35953i	−0.0197279	−	0.122666i
$371$	−3.98830	+	14.7174i	−0.207062	+	0.764088i
$372$	1.79567	−	3.04893i	0.0931013	−	0.158080i
$373$	−6.37029	−	3.67789i	−0.329841	−	0.190434i	0.325930	−	0.945394i	$-0.394323\pi$
$373$	−6.37029	−	3.67789i	−0.329841	−	0.190434i	−0.655770	+	0.754960i	$0.727656\pi$
$374$	12.8557			0.664752
$375$	19.3368	+	1.04275i	0.998549	+	0.0538472i
$376$			2.23938i			0.115487i
$377$			18.3727i			0.946242i
$378$	−3.17420	−	13.3763i	−0.163263	−	0.688001i
$379$	−6.48462			−0.333092			−0.166546	−	0.986034i	$-0.553261\pi$
$379$	−6.48462			−0.333092			−0.166546	+	0.986034i	$0.553261\pi$
$380$	1.39465	+	8.67178i	0.0715441	+	0.444853i
$381$	15.9718	−	27.1190i	0.818260	−	1.38935i
$382$		−	9.43103i		−	0.482534i
$383$	8.50872	+	4.91251i	0.434775	+	0.251018i	0.701379	−	0.712789i	$-0.252568\pi$
$383$	8.50872	+	4.91251i	0.434775	+	0.251018i	−0.266604	+	0.963806i	$0.585901\pi$
$384$	1.49245	+	0.878978i	0.0761611	+	0.0448552i
$385$	−6.82977	−	15.3588i	−0.348077	−	0.782755i
$386$			1.48521i			0.0755953i
$387$	−0.405863	+	23.4391i	−0.0206312	+	1.19148i
$388$	−8.91744	+	15.4455i	−0.452714	+	0.784124i
$389$	7.18549	−	4.14854i	0.364319	−	0.210340i	−0.306655	−	0.951821i	$-0.599210\pi$
$389$	7.18549	−	4.14854i	0.364319	−	0.210340i	0.670974	+	0.741481i	$0.265876\pi$
$390$	18.1409	+	7.09458i	0.918600	+	0.359248i
$391$	25.1628	−	14.5277i	1.27254	−	0.734699i
$392$	−6.08194	+	3.46554i	−0.307184	+	0.175036i
$393$	25.7906	−	14.5940i	1.30096	−	0.736168i
$394$	−17.6493			−0.889158
$395$	3.59218	−	9.42498i	0.180742	−	0.474222i
$396$	−7.30680	−	4.38898i	−0.367180	−	0.220555i
$397$	−6.65037	−	11.5188i	−0.333772	−	0.578111i	0.649476	−	0.760382i	$-0.274988\pi$
$397$	−6.65037	−	11.5188i	−0.333772	−	0.578111i	−0.983248	+	0.182272i	$0.941655\pi$
$398$	−17.8938	−	10.3310i	−0.896935	−	0.517846i
$399$	−17.4393	+	4.45865i	−0.873057	+	0.223212i
$400$	−3.73162	−	3.32792i	−0.186581	−	0.166396i
$401$	18.0899	+	10.4442i	0.903367	+	0.521559i	0.878291	−	0.478126i	$-0.158684\pi$
$401$	18.0899	+	10.4442i	0.903367	+	0.521559i	0.0250758	+	0.999686i	$0.492017\pi$
$402$	5.27362	−	8.95426i	0.263024	−	0.446598i
$403$	−8.89810	+	5.13732i	−0.443246	+	0.255908i
$404$	−5.04091	−	8.73112i	−0.250795	−	0.434389i
$405$	12.1540	+	16.0400i	0.603937	+	0.797032i
$406$	9.32859	+	2.52798i	0.462970	+	0.125461i
$407$	1.51831	−	2.62978i	0.0752596	−	0.130353i
$408$	3.85962	+	6.82074i	0.191080	+	0.337677i
$409$			28.3129i			1.39998i	0.714151	+	0.699992i	$0.246813\pi$
$409$			28.3129i			1.39998i	−0.714151	+	0.699992i	$0.753187\pi$
$410$	−12.6001	+	2.02643i	−0.622276	+	0.100078i
$411$	0.0929656	−	10.7386i	0.00458566	−	0.529696i
$412$	−1.03484	+	1.79239i	−0.0509827	+	0.0883046i
$413$	−32.7626	+	8.67915i	−1.61214	+	0.427073i
$414$	−19.2616	−	0.333526i	−0.946656	−	0.0163919i
$415$	22.0134	−	17.9130i	1.08059	−	0.879317i
$416$	−2.51471	−	4.35560i	−0.123294	−	0.213551i
$417$	−26.0252	−	0.225304i	−1.27446	−	0.0110332i
$418$	−5.58010	+	9.66502i	−0.272932	+	0.472732i
$419$	−7.85403	−	13.6036i	−0.383695	−	0.664578i	0.607893	−	0.794019i	$-0.292015\pi$
$419$	−7.85403	−	13.6036i	−0.383695	−	0.664578i	−0.991587	+	0.129441i	$0.958682\pi$
$420$	6.09830	−	8.23473i	0.297567	−	0.401814i
$421$	−13.2658	+	22.9771i	−0.646537	+	1.11983i	0.337408	+	0.941359i	$0.390450\pi$
$421$	−13.2658	+	22.9771i	−0.646537	+	1.11983i	−0.983944	+	0.178476i	$0.942883\pi$
$422$	−5.63953	−	9.76796i	−0.274528	−	0.475497i
$423$	5.87535	−	3.25783i	0.285669	−	0.158401i
$424$	−2.88164	+	4.99115i	−0.139945	+	0.242391i
$425$	−7.09346	−	21.4828i	−0.344083	−	1.04207i
$426$	−6.87065	+	11.6659i	−0.332884	+	0.565216i
$427$	−7.06910	−	26.6849i	−0.342098	−	1.29137i
$428$	1.27205	+	2.20325i	0.0614867	+	0.106498i
$429$	12.1892	+	21.5408i	0.588499	+	1.04000i
$430$	−13.5529	+	11.0285i	−0.653581	+	0.531841i
$431$	−14.0479	−	8.11059i	−0.676666	−	0.390673i	0.121932	−	0.992538i	$-0.461091\pi$
$431$	−14.0479	−	8.11059i	−0.676666	−	0.390673i	−0.798598	+	0.601865i	$0.794424\pi$
$432$	0.134933	−	5.19440i	0.00649197	−	0.249916i
$433$	19.7268			0.948010			0.474005	−	0.880522i	$-0.342808\pi$
$433$	19.7268			0.948010			0.474005	+	0.880522i	$0.342808\pi$
$434$	1.38411	+	5.22481i	0.0664392	+	0.250799i
$435$	−13.9876	+	2.12552i	−0.670655	+	0.101911i
$436$	5.96532	−	10.3322i	0.285687	−	0.494825i
$437$			25.2235i			1.20660i
$438$	−21.2295	+	12.0130i	−1.01439	+	0.574005i
$439$			13.1264i			0.626488i	0.949673	+	0.313244i	$0.101416\pi$
$439$			13.1264i			0.626488i	−0.949673	+	0.313244i	$0.898584\pi$
$440$	−1.00879	−	6.27254i	−0.0480922	−	0.299032i
$441$	17.9404	+	10.9153i	0.854303	+	0.519775i
$442$		−	22.7567i		−	1.08243i
$443$	−8.62000			−0.409548			−0.204774	−	0.978809i	$-0.565646\pi$
$443$	−8.62000			−0.409548			−0.204774	+	0.978809i	$0.565646\pi$
$444$	1.85110	+	0.0160252i	0.0878493	+	0.000760524i
$445$	−23.5570	+	3.78858i	−1.11671	+	0.179596i
$446$	6.07248	−	10.5178i	0.287540	−	0.498034i
$447$	1.94775	+	3.44208i	0.0921254	+	0.162805i
$448$	−2.55753	+	0.677517i	−0.120832	+	0.0320097i
$449$		−	37.2222i		−	1.75663i	−0.478086	−	0.878313i	$-0.658669\pi$
$449$		−	37.2222i		−	1.75663i	0.478086	−	0.878313i	$-0.341331\pi$
$450$	−3.30258	+	14.6319i	−0.155685	+	0.689755i
$451$	−14.0433	−	8.10791i	−0.661274	−	0.381786i
$452$	−4.09453	−	7.09194i	−0.192591	−	0.333577i
$453$	−0.197779	+	22.8458i	−0.00929247	+	1.07339i
$454$	20.5863	−	11.8855i	0.966162	−	0.557814i
$455$	−27.1875	+	12.0898i	−1.27457	+	0.566780i
$456$	−6.80319	−	0.0588963i	−0.318589	−	0.00275807i
$457$		−	40.5035i		−	1.89467i	−0.320238	−	0.947337i	$-0.603763\pi$
$457$		−	40.5035i		−	1.89467i	0.320238	−	0.947337i	$-0.396237\pi$
$458$	−9.88508	−	5.70716i	−0.461900	−	0.266678i
$459$	12.2803	−	20.0491i	0.573197	−	0.935812i
$460$	−9.06290	−	11.1374i	−0.422560	−	0.519285i
$461$	16.8755	−	29.2292i	0.785971	−	1.36134i	−0.142446	−	0.989803i	$-0.545497\pi$
$461$	16.8755	−	29.2292i	0.785971	−	1.36134i	0.928417	−	0.371539i	$-0.121170\pi$
$462$	12.6143	−	3.22507i	0.586872	−	0.150044i
$463$	23.0998	−	13.3367i	1.07354	−	0.619809i	0.144394	−	0.989520i	$-0.453877\pi$
$463$	23.0998	−	13.3367i	1.07354	−	0.619809i	0.929147	+	0.369712i	$0.120543\pi$
$464$	3.16363	+	1.82652i	0.146868	+	0.0847942i
$465$	−4.94059	−	6.18003i	−0.229115	−	0.286592i
$466$	4.16132	+	7.20762i	0.192769	+	0.333886i
$467$	4.89263	−	2.82476i	0.226404	−	0.130714i	−0.382508	−	0.923952i	$-0.624940\pi$
$467$	4.89263	−	2.82476i	0.226404	−	0.130714i	0.608912	+	0.793238i	$0.291606\pi$
$468$	−7.76922	+	12.9342i	−0.359132	+	0.597885i
$469$	4.06491	+	15.3445i	0.187700	+	0.708542i
$470$	4.67907	+	1.78335i	0.215829	+	0.0822600i
$471$	−26.7538	−	15.7567i	−1.23275	−	0.726029i
$472$	−12.8102			−0.589639
$473$	−22.2019			−1.02084
$474$	6.73204	+	3.96484i	0.309213	+	0.182111i
$475$	19.2299	+	3.99182i	0.882329	+	0.183157i
$476$	−11.5545	−	3.13119i	−0.529601	−	0.143518i
$477$	17.2872	+	0.299339i	0.791529	+	0.0137058i
$478$	6.41684	−	3.70476i	0.293499	−	0.169452i
$479$	0.136929	+	0.237168i	0.00625644	+	0.0108365i	0.869137	−	0.494572i	$-0.164675\pi$
$479$	0.136929	+	0.237168i	0.00625644	+	0.0108365i	−0.862880	+	0.505408i	$0.831342\pi$
$480$	3.02511	−	2.41841i	0.138077	−	0.110385i
$481$	−4.65515	−	2.68765i	−0.212257	−	0.122546i
$482$	7.50748	−	4.33445i	0.341956	−	0.197429i
$483$	21.0458	−	20.5675i	0.957618	−	0.935853i
$484$	−1.46376	+	2.53530i	−0.0665343	+	0.115241i
$485$	25.1710	+	30.9327i	1.14296	+	1.40458i
$486$	−13.8246	+	7.20277i	−0.627098	+	0.326724i
$487$	−12.4072	−	7.16329i	−0.562223	−	0.324600i	0.191814	−	0.981431i	$-0.438563\pi$
$487$	−12.4072	−	7.16329i	−0.562223	−	0.324600i	−0.754037	+	0.656832i	$0.771896\pi$
$488$		−	10.4338i		−	0.472317i
$489$	−6.54018	−	0.0566193i	−0.295757	−	0.00256041i
$490$	2.39766	+	15.4677i	0.108315	+	0.698762i
$491$	31.8165	−	18.3692i	1.43586	−	0.828992i	0.438298	−	0.898830i	$-0.355581\pi$
$491$	31.8165	−	18.3692i	1.43586	−	0.828992i	0.997558	+	0.0698374i	$0.0222480\pi$
$492$	0.0855764	−	9.88506i	0.00385808	−	0.445653i
$493$	8.26450	+	14.3145i	0.372214	+	0.644694i
$494$	17.1087	+	9.87771i	0.769756	+	0.444419i
$495$	−14.9894	+	11.7720i	−0.673724	+	0.529111i
$496$			2.04291i			0.0917294i
$497$	−5.29591	−	19.9913i	−0.237554	−	0.896733i
$498$	10.8266	+	19.1328i	0.485151	+	0.857362i
$499$	16.0396	−	27.7814i	0.718032	−	1.24367i	−0.243746	−	0.969839i	$-0.578376\pi$
$499$	16.0396	−	27.7814i	0.718032	−	1.24367i	0.961778	−	0.273829i	$-0.0882902\pi$
$500$	−9.92524	+	5.14680i	−0.443870	+	0.230172i
$501$	41.7294	+	0.361258i	1.86433	+	0.0161398i
$502$	15.4449			0.689338
$503$		−	35.1778i		−	1.56850i	−0.620445	−	0.784250i	$-0.713048\pi$
$503$		−	35.1778i		−	1.56850i	0.620445	−	0.784250i	$-0.286952\pi$
$504$	5.49826	+	5.72444i	0.244912	+	0.254987i
$505$	−22.2576	+	3.57961i	−0.990452	+	0.159291i
$506$		−	18.2448i		−	0.811082i
$507$	18.5340	−	10.4878i	0.823125	−	0.465778i
$508$			18.1709i			0.806202i
$509$	−11.7471	+	20.3465i	−0.520679	+	0.901843i	0.479032	+	0.877798i	$0.340988\pi$
$509$	−11.7471	+	20.3465i	−0.520679	+	0.901843i	−0.999711	+	0.0240450i	$0.992345\pi$
$510$	17.3253	−	2.63271i	0.767176	−	0.116578i
$511$	9.74581	−	35.9634i	0.431129	−	1.59093i
$512$	−1.00000			−0.0441942
$513$	9.74273	+	17.9349i	0.430152	+	0.791846i
$514$	−5.03816	−	2.90878i	−0.222224	−	0.128301i
$515$	2.92100	+	3.58963i	0.128715	+	0.158178i
$516$	−6.66559	−	11.7795i	−0.293436	−	0.518562i
$517$	3.18127	+	5.51012i	0.139912	+	0.242335i
$518$	−2.00516	+	1.99381i	−0.0881015	+	0.0876030i
$519$	−10.7001	+	18.1681i	−0.469683	+	0.797491i
$520$	−11.1034	+	1.78572i	−0.486918	+	0.0783092i
$521$	−0.581200	+	1.00667i	−0.0254628	+	0.0441029i	−0.878476	−	0.477786i	$-0.841439\pi$
$521$	−0.581200	+	1.00667i	−0.0254628	+	0.0441029i	0.853013	+	0.521889i	$0.174773\pi$
$522$	0.189736	−	10.9575i	0.00830450	−	0.479597i
$523$	−1.24452	−	2.15558i	−0.0544191	−	0.0942567i	0.837533	−	0.546387i	$-0.183997\pi$
$523$	−1.24452	−	2.15558i	−0.0544191	−	0.0942567i	−0.891952	+	0.452131i	$0.850664\pi$
$524$	−8.55442	+	14.8167i	−0.373701	+	0.647270i
$525$	−12.3496	−	19.2999i	−0.538981	−	0.842318i
$526$	1.08784	+	1.88419i	0.0474320	+	0.0821547i
$527$	−4.62179	+	8.00518i	−0.201329	+	0.348711i
$528$	4.92094	+	0.0426013i	0.214156	+	0.00185398i
$529$	−9.11781	−	15.7925i	−0.396426	−	0.686631i
$530$	8.13393	+	9.99581i	0.353315	+	0.434190i
$531$	18.6363	+	33.6096i	0.808745	+	1.45853i
$532$	7.36938	−	7.32769i	0.319503	−	0.317695i
$533$	−14.3523	+	24.8590i	−0.621669	+	1.07676i
$534$	0.159992	−	18.4809i	0.00692354	−	0.799748i
$535$	5.61659	−	0.903296i	0.242827	−	0.0390529i
$536$			5.99972i			0.259148i
$537$	3.12214	+	5.51747i	0.134730	+	0.238096i
$538$	−1.75606	+	3.04158i	−0.0757091	+	0.131132i
$539$	−10.0418	+	17.1672i	−0.432532	+	0.739445i
$540$	−10.7460	−	4.41856i	−0.462434	−	0.190144i
$541$	−10.4582	−	18.1142i	−0.449634	−	0.778789i	0.548728	−	0.836001i	$-0.315112\pi$
$541$	−10.4582	−	18.1142i	−0.449634	−	0.778789i	−0.998362	+	0.0572120i	$0.981779\pi$
$542$	−1.39309	+	0.804303i	−0.0598385	+	0.0345478i
$543$	−10.1657	+	17.2606i	−0.436251	+	0.740725i
$544$	−3.91852	−	2.26236i	−0.168005	−	0.0969978i
$545$	−16.8382	−	20.6925i	−0.721268	−	0.886368i
$546$	−5.70890	−	22.3294i	−0.244319	−	0.955612i
$547$	0.150888	+	0.0871155i	0.00645152	+	0.00372479i	0.503222	−	0.864157i	$-0.332148\pi$
$547$	0.150888	+	0.0871155i	0.00645152	+	0.00372479i	−0.496771	+	0.867882i	$0.665481\pi$
$548$	3.10008	+	5.36950i	0.132429	+	0.229374i
$549$	−27.3748	+	15.1791i	−1.16833	+	0.647827i
$550$	−13.9095	−	2.88740i	−0.593105	−	0.123119i
$551$	−14.3491			−0.611291
$552$	9.68003	−	5.47759i	0.412009	−	0.233142i
$553$	−11.5364	+	3.05611i	−0.490576	+	0.129959i
$554$	−3.87815	+	2.23905i	−0.164767	+	0.0951281i
$555$	1.50763	−	3.85502i	0.0639953	−	0.163637i
$556$	13.0131	−	7.51311i	0.551878	−	0.318627i
$557$	10.1509	−	17.5819i	0.430109	−	0.744971i	−0.566773	−	0.823874i	$-0.691808\pi$
$557$	10.1509	−	17.5819i	0.430109	−	0.744971i	0.996882	+	0.0789031i	$0.0251418\pi$
$558$	5.35989	−	2.97201i	0.226902	−	0.125815i
$559$			39.3010i			1.66225i
$560$	−0.621082	+	5.88339i	−0.0262455	+	0.248619i
$561$	19.1864	+	11.2999i	0.810051	+	0.477081i
$562$	9.04334	+	5.22117i	0.381470	+	0.220242i
$563$		−	12.0047i		−	0.505938i	−0.967474	−	0.252969i	$-0.918593\pi$
$563$		−	12.0047i		−	0.505938i	0.967474	−	0.252969i	$-0.0814070\pi$
$564$	−1.96836	+	3.34215i	−0.0828830	+	0.140730i
$565$	−18.0790	+	2.90758i	−0.760589	+	0.122323i
$566$	18.5038			0.777773
$567$	7.02012	−	22.7534i	0.294817	−	0.955554i
$568$		−	7.81664i		−	0.327979i
$569$		−	32.3222i		−	1.35502i	−0.735515	−	0.677509i	$-0.763060\pi$
$569$		−	32.3222i		−	1.35502i	0.735515	−	0.677509i	$-0.236940\pi$
$570$	−5.54087	+	14.1680i	−0.232081	+	0.593434i
$571$	−39.7878			−1.66507			−0.832535	−	0.553973i	$-0.813111\pi$
$571$	−39.7878			−1.66507			−0.832535	+	0.553973i	$0.813111\pi$
$572$	−12.3752	−	7.14482i	−0.517433	−	0.298740i
$573$	8.28967	−	14.0753i	0.346306	−	0.588005i
$574$	10.6471	+	10.7077i	0.444403	+	0.446932i
$575$	−30.4884	+	10.0671i	−1.27146	+	0.419826i
$576$	1.45479	+	2.62366i	0.0606164	+	0.109319i
$577$	5.59098	−	9.68386i	0.232756	−	0.403144i	−0.725862	−	0.687840i	$-0.758559\pi$
$577$	5.59098	−	9.68386i	0.232756	−	0.403144i	0.958618	+	0.284695i	$0.0918925\pi$
$578$	−1.73653	−	3.00776i	−0.0722303	−	0.125107i
$579$	−1.30547	+	2.21660i	−0.0542535	+	0.0921188i
$580$	6.33583	−	5.15568i	0.263081	−	0.214078i
$581$	−32.4115	−	8.78328i	−1.34466	−	0.364392i
$582$	−26.8850	+	15.2133i	−1.11442	+	0.630611i
$583$			16.3747i			0.678171i
$584$	7.04158	−	12.1964i	0.291382	−	0.504689i
$585$	20.8384	+	26.5337i	0.861560	+	1.09704i
$586$	0.317382	−	0.183240i	0.0131109	−	0.00756959i
$587$	2.92497	+	1.68873i	0.120726	+	0.0697015i	0.559147	−	0.829068i	$-0.311129\pi$
$587$	2.92497	+	1.68873i	0.120726	+	0.0697015i	−0.438421	+	0.898770i	$0.644462\pi$
$588$	−12.1231	−	0.173752i	−0.499949	−	0.00716543i
$589$	−4.01225	−	6.94942i	−0.165322	−	0.286346i
$590$	−10.2016	+	26.7664i	−0.419992	+	1.10195i
$591$	−26.3406	−	15.5133i	−1.08351	−	0.638133i
$592$	−0.925584	+	0.534386i	−0.0380413	+	0.0219631i
$593$	−28.6406	+	16.5357i	−1.17613	+	0.679039i	−0.955116	−	0.296232i	$-0.904270\pi$
$593$	−28.6406	+	16.5357i	−1.17613	+	0.679039i	−0.221014	+	0.975271i	$0.570937\pi$
$594$	−7.04719	−	12.9728i	−0.289150	−	0.532282i
$595$	−15.7441	+	21.6491i	−0.645443	+	0.887525i
$596$	−1.97748	−	1.14170i	−0.0810005	−	0.0467657i
$597$	−17.6248	−	31.1467i	−0.721336	−	1.27475i
$598$	−32.2964			−1.32070
$599$			15.0631i			0.615461i	0.951474	+	0.307730i	$0.0995695\pi$
$599$			15.0631i			0.615461i	−0.951474	+	0.307730i	$0.900431\pi$
$600$	−2.64407	−	8.24675i	−0.107944	−	0.336672i
$601$	−38.2212	−	22.0670i	−1.55908	−	0.900133i	−0.997346	−	0.0728123i	$-0.976803\pi$
$601$	−38.2212	−	22.0670i	−1.55908	−	0.900133i	−0.561730	−	0.827321i	$-0.689864\pi$
$602$	19.9548	+	5.40759i	0.813295	+	0.220397i
$603$	15.7412	−	8.72835i	0.641031	−	0.355446i
$604$	−6.59525	−	11.4233i	−0.268357	−	0.464808i
$605$	4.13170	+	5.07746i	0.167978	+	0.206428i
$606$	0.151167	−	17.4616i	0.00614076	−	0.709328i
$607$	−9.73116	+	16.8549i	−0.394976	+	0.684118i	−0.993098	−	0.117287i	$-0.962580\pi$
$607$	−9.73116	+	16.8549i	−0.394976	+	0.684118i	0.598122	+	0.801405i	$0.295914\pi$
$608$	3.40172	−	1.96399i	0.137958	−	0.0796502i
$609$	11.7004	+	11.9725i	0.474124	+	0.485150i
$610$	−21.8010	−	8.30911i	−0.882696	−	0.336426i
$611$	9.75383	−	5.63138i	0.394598	−	0.227821i
$612$	−0.235009	+	13.5721i	−0.00949969	+	0.548620i
$613$	26.5030	+	15.3015i	1.07045	+	0.618023i	0.928304	−	0.371823i	$-0.121267\pi$
$613$	26.5030	+	15.3015i	1.07045	+	0.618023i	0.142144	+	0.989846i	$0.454600\pi$
$614$	−24.9894			−1.00849
$615$	−20.5862	−	8.05089i	−0.830116	−	0.324643i
$616$	−5.33048	+	5.30032i	−0.214771	+	0.213556i
$617$	−18.9195	−	32.7695i	−0.761671	−	1.31925i	−0.941989	−	0.335644i	$-0.891046\pi$
$617$	−18.9195	−	32.7695i	−0.761671	−	1.31925i	0.180318	−	0.983608i	$-0.442287\pi$
$618$	−3.11991	+	1.76545i	−0.125501	+	0.0710166i
$619$	−42.1495	+	24.3350i	−1.69413	+	0.978107i	−0.743015	+	0.669274i	$0.766605\pi$
$619$	−42.1495	+	24.3350i	−1.69413	+	0.978107i	−0.951116	+	0.308833i	$0.900062\pi$
$620$	4.26856	+	1.62690i	0.171430	+	0.0653377i
$621$	−28.4538	−	17.4283i	−1.14181	−	0.699374i
$622$	−24.0318			−0.963586
$623$	19.9057	+	20.0190i	0.797506	+	0.802044i
$624$	0.0754114	−	8.71088i	0.00301887	−	0.348714i
$625$	2.84990	+	24.8370i	0.113996	+	0.993481i
$626$	6.50477			0.259983
$627$	−16.8234	+	9.51974i	−0.671860	+	0.380182i
$628$	17.9261			0.715330
$629$	−4.83590			−0.192820
$630$	16.3395	−	6.92962i	0.650983	−	0.276083i
$631$	40.7671			1.62291			0.811456	−	0.584414i	$-0.198675\pi$
$631$	40.7671			1.62291			0.811456	+	0.584414i	$0.198675\pi$
$632$	−4.51074			−0.179428
$633$	0.169119	−	19.5352i	0.00672187	−	0.776454i
$634$	7.38882			0.293447
$635$	37.9671	+	14.4706i	1.50668	+	0.574248i
$636$	−8.68780	+	4.91612i	−0.344494	+	0.194937i
$637$	30.3888	+	17.7757i	1.20405	+	0.704298i
$638$	10.3791			0.410912
$639$	−20.5082	+	11.3716i	−0.811291	+	0.449854i
$640$	−0.796362	+	2.08945i	−0.0314790	+	0.0825928i
$641$	−16.8354	+	9.71990i	−0.664957	+	0.383913i	−0.794163	−	0.607705i	$-0.792090\pi$
$641$	−16.8354	+	9.71990i	−0.664957	+	0.383913i	0.129206	+	0.991618i	$0.458757\pi$
$642$	−0.0381463	+	4.40633i	−0.00150551	+	0.173904i
$643$	−3.29651	−	5.70972i	−0.130002	−	0.225169i	0.793675	−	0.608342i	$-0.208165\pi$
$643$	−3.29651	−	5.70972i	−0.130002	−	0.225169i	−0.923677	+	0.383172i	$0.874832\pi$
$644$	−4.44380	+	16.3982i	−0.175110	+	0.646181i
$645$	−29.9209	+	4.54670i	−1.17813	+	0.179026i
$646$	17.7730			0.699268
$647$	34.2506	+	19.7746i	1.34653	+	0.777419i	0.987756	−	0.156006i	$-0.0498620\pi$
$647$	34.2506	+	19.7746i	1.34653	+	0.777419i	0.358773	+	0.933425i	$0.383195\pi$
$648$	4.76714	−	7.63376i	0.187271	−	0.299883i
$649$	−31.5204	+	18.1983i	−1.23728	+	0.714346i
$650$	−5.11117	+	24.6222i	−0.200477	+	0.965761i
$651$	−2.52679	+	9.01435i	−0.0990325	+	0.353300i
$652$	3.27021	−	1.88806i	0.128071	−	0.0739421i
$653$	10.3809	−	17.9803i	0.406236	−	0.703622i	−0.588228	−	0.808695i	$-0.700174\pi$
$653$	10.3809	−	17.9803i	0.406236	−	0.703622i	0.994464	+	0.105073i	$0.0335077\pi$
$654$	17.9847	−	10.1769i	0.703259	−	0.397950i
$655$	24.1463	+	29.6735i	0.943475	+	1.15944i
$656$	2.85368	+	4.94272i	0.111417	+	0.192981i
$657$	−42.2431	−	0.731465i	−1.64806	−	0.0285372i
$658$	−1.51722	−	5.72727i	−0.0591472	−	0.223272i
$659$	4.81761	+	2.78145i	0.187667	+	0.108350i	0.590890	−	0.806752i	$-0.298777\pi$
$659$	4.81761	+	2.78145i	0.187667	+	0.108350i	−0.403223	+	0.915102i	$0.632110\pi$
$660$	4.00786	−	10.2481i	0.156006	−	0.398908i
$661$			43.2382i			1.68177i	0.541214	+	0.840885i	$0.317965\pi$
$661$			43.2382i			1.68177i	−0.541214	+	0.840885i	$0.682035\pi$
$662$	−26.3139			−1.02272
$663$	20.0026	−	33.9631i	0.776838	−	1.31902i
$664$	−10.9918	−	6.34613i	−0.426565	−	0.246277i
$665$	−9.44215	−	21.2335i	−0.366151	−	0.823398i
$666$	2.74858	+	1.65099i	0.106505	+	0.0639747i
$667$	20.3152	−	11.7290i	0.786609	−	0.454149i
$668$	−20.8655	+	12.0467i	−0.807310	+	0.466101i
$669$	18.3078	−	10.3597i	0.707821	−	0.400531i
$670$	12.5361	+	4.77795i	0.484312	+	0.184588i
$671$	−14.8224	−	25.6731i	−0.572211	−	0.991099i
$672$	−4.41250	−	1.23686i	−0.170216	−	0.0477128i
$673$	−11.8398	−	6.83568i	−0.456389	−	0.263496i	0.254136	−	0.967169i	$-0.418209\pi$
$673$	−11.8398	−	6.83568i	−0.456389	−	0.263496i	−0.710525	+	0.703672i	$0.751542\pi$
$674$	−5.78970	+	3.34269i	−0.223011	+	0.128755i
$675$	−17.7901	+	18.9345i	−0.684740	+	0.728788i
$676$	−6.14752	+	10.6478i	−0.236443	+	0.409531i
$677$			8.29461i			0.318788i	0.987215	+	0.159394i	$0.0509540\pi$
$677$			8.29461i			0.318788i	−0.987215	+	0.159394i	$0.949046\pi$
$678$	0.122787	−	14.1833i	0.00471562	−	0.544708i
$679$	12.3421	−	45.5440i	0.473645	−	1.74782i
$680$	−7.84765	+	6.38590i	−0.300944	+	0.244888i
$681$	41.1710	+	0.356423i	1.57768	+	0.0136582i
$682$	2.90217	+	5.02671i	0.111130	+	0.192483i
$683$	20.1186	−	34.8465i	0.769817	−	1.33336i	−0.167845	−	0.985813i	$-0.553681\pi$
$683$	20.1186	−	34.8465i	0.769817	−	1.33336i	0.937662	−	0.347549i	$-0.112986\pi$
$684$	−10.1016	−	6.06776i	−0.386246	−	0.232007i
$685$	13.6881	−	2.20141i	0.522995	−	0.0841114i
$686$	13.2068	−	12.9839i	0.504238	−	0.495726i
$687$	−9.73650	−	17.2064i	−0.371470	−	0.656465i
$688$	6.76731	+	3.90711i	0.258001	+	0.148957i
$689$	28.9859			1.10428
$690$	−3.73635	−	24.5881i	−0.142240	−	0.936052i
$691$		−	7.62789i		−	0.290179i	−0.989419	−	0.145089i	$-0.953653\pi$
$691$		−	7.62789i		−	0.290179i	0.989419	−	0.145089i	$-0.0463470\pi$
$692$		−	12.1734i		−	0.462762i
$693$	21.6610	+	6.27447i	0.822832	+	0.238348i
$694$	2.41396			0.0916325
$695$	−5.33515	−	33.1734i	−0.202374	−	1.25834i
$696$	3.11608	+	5.50675i	0.118115	+	0.208733i
$697$			25.8242i			0.978160i
$698$	0.654664	+	0.377971i	0.0247794	+	0.0143064i
$699$	−0.124790	+	14.4147i	−0.00471999	+	0.545214i
$700$	11.7984	+	5.98303i	0.445939	+	0.226137i
$701$		−	31.4440i		−	1.18762i	−0.804604	−	0.593812i	$-0.797622\pi$
$701$		−	31.4440i		−	1.18762i	0.804604	−	0.593812i	$-0.202378\pi$
$702$	−22.9641	+	12.4747i	−0.866723	+	0.470827i
$703$	2.09906	−	3.63567i	0.0791674	−	0.137122i
$704$	−2.46056	+	1.42061i	−0.0927359	+	0.0535411i
$705$	5.41573	+	6.77436i	0.203968	+	0.255137i
$706$	8.10821	−	4.68128i	0.305157	−	0.176182i
$707$	18.8078	+	18.9148i	0.707339	+	0.711364i
$708$	−19.1186	−	11.2599i	−0.718520	−	0.423173i
$709$	−20.1317			−0.756061			−0.378030	−	0.925793i	$-0.623398\pi$
$709$	−20.1317			−0.756061			−0.378030	+	0.925793i	$0.623398\pi$
$710$	−16.3325	−	6.22487i	−0.612947	−	0.233615i
$711$	6.56220	+	11.8346i	0.246102	+	0.443834i
$712$	5.33519	+	9.24081i	0.199945	+	0.346314i
$713$	11.3610	+	6.55927i	0.425472	+	0.245647i
$714$	−14.4923	−	14.8293i	−0.542360	−	0.554973i
$715$	−24.7839	+	20.1675i	−0.926865	+	0.754222i
$716$	−3.16979	−	1.83008i	−0.118461	−	0.0683932i
$717$	12.8332	+	0.111099i	0.479265	+	0.00414906i
$718$	20.7136	−	11.9590i	0.773025	−	0.446306i
$719$	12.4736	+	21.6049i	0.465187	+	0.805728i	0.999210	−	0.0397421i	$-0.0126536\pi$
$719$	12.4736	+	21.6049i	0.465187	+	0.805728i	−0.534023	+	0.845470i	$0.679320\pi$
$720$	6.64055	−	0.950343i	0.247479	−	0.0354172i
$721$	1.43225	−	5.28521i	0.0533398	−	0.196831i
$722$	1.78551	−	3.09260i	0.0664499	−	0.115095i
$723$	15.0144	+	0.129982i	0.558391	+	0.00483408i
$724$		−	11.5653i		−	0.429822i
$725$	−5.72693	−	17.3442i	−0.212693	−	0.644147i
$726$	−4.41305	+	2.49719i	−0.163784	+	0.0926794i
$727$	0.756579	−	1.31043i	0.0280600	−	0.0486013i	−0.851654	−	0.524104i	$-0.824400\pi$
$727$	0.756579	−	1.31043i	0.0280600	−	0.0486013i	0.879714	+	0.475502i	$0.157734\pi$
$728$	9.38244	+	9.43583i	0.347736	+	0.349715i
$729$	−26.9636	−	1.40179i	−0.998651	−	0.0519182i
$730$	−19.8761	−	24.4258i	−0.735646	−	0.904038i
$731$	17.6786	+	30.6202i	0.653866	+	1.13253i
$732$	9.17111	−	15.5719i	0.338974	−	0.575555i
$733$	4.96247	−	8.59526i	0.183293	−	0.317473i	−0.759707	−	0.650266i	$-0.774658\pi$
$733$	4.96247	−	8.59526i	0.183293	−	0.317473i	0.943000	+	0.332793i	$0.107991\pi$
$734$	2.63628	+	4.56616i	0.0973067	+	0.168540i
$735$	−10.0174	+	25.1923i	−0.369499	+	0.929231i
$736$	−3.21075	+	5.56118i	−0.118350	+	0.204988i
$737$	8.52323	+	14.7627i	0.313957	+	0.543790i
$738$	8.81647	−	14.6777i	0.324539	−	0.540294i
$739$	7.69829	−	13.3338i	0.283186	−	0.490493i	−0.688981	−	0.724779i	$-0.741942\pi$
$739$	7.69829	−	13.3338i	0.283186	−	0.490493i	0.972168	+	0.234286i	$0.0752752\pi$
$740$	0.379474	+	2.35953i	0.0139498	+	0.0867380i
$741$	16.8515	+	29.7801i	0.619056	+	1.09400i
$742$	3.98830	−	14.7174i	0.146415	−	0.540292i
$743$	−22.7782	−	39.4530i	−0.835651	−	1.44739i	−0.893499	−	0.449065i	$-0.851757\pi$
$743$	−22.7782	−	39.4530i	−0.835651	−	1.44739i	0.0578475	−	0.998325i	$-0.481576\pi$
$744$	−1.79567	+	3.04893i	−0.0658326	+	0.111779i
$745$	−3.96030	+	3.22264i	−0.145094	+	0.118068i
$746$	6.37029	+	3.67789i	0.233233	+	0.134657i
$747$	−0.659223	+	38.0710i	−0.0241197	+	1.39295i
$748$	−12.8557			−0.470050
$749$	−4.74604	−	4.77305i	−0.173417	−	0.174403i
$750$	−19.3368	−	1.04275i	−0.706081	−	0.0380757i
$751$	−0.490251	+	0.849139i	−0.0178895	+	0.0309855i	−0.874832	−	0.484427i	$-0.839028\pi$
$751$	−0.490251	+	0.849139i	−0.0178895	+	0.0309855i	0.856942	+	0.515413i	$0.172361\pi$
$752$		−	2.23938i		−	0.0816616i
$753$	23.0506	+	13.5757i	0.840012	+	0.494726i
$754$		−	18.3727i		−	0.669094i
$755$	−29.1207	+	4.68337i	−1.05981	+	0.170445i
$756$	3.17420	+	13.3763i	0.115445	+	0.486490i
$757$			16.9068i			0.614489i	0.951631	+	0.307245i	$0.0994070\pi$
$757$			16.9068i			0.614489i	−0.951631	+	0.307245i	$0.900593\pi$
$758$	6.48462			0.235532
$759$	16.0368	−	27.2294i	0.582099	−	0.988366i
$760$	−1.39465	−	8.67178i	−0.0505893	−	0.314559i
$761$	16.0830	−	27.8566i	0.583010	−	1.00980i	−0.412111	−	0.911134i	$-0.635208\pi$
$761$	16.0830	−	27.8566i	0.583010	−	1.00980i	0.995120	−	0.0986685i	$-0.0314584\pi$
$762$	−15.9718	+	27.1190i	−0.578597	+	0.982419i
$763$	−8.25623	+	30.4667i	−0.298896	+	1.10297i
$764$			9.43103i			0.341203i
$765$	28.1711	+	11.2994i	1.01853	+	0.408529i
$766$	−8.50872	−	4.91251i	−0.307432	−	0.177496i
$767$	32.2140	+	55.7963i	1.16318	+	2.01469i
$768$	−1.49245	−	0.878978i	−0.0538540	−	0.0317174i
$769$	44.2257	−	25.5337i	1.59482	−	0.920770i	0.602358	−	0.798226i	$-0.294228\pi$
$769$	44.2257	−	25.5337i	1.59482	−	0.920770i	0.992463	−	0.122545i	$-0.0391054\pi$
$770$	6.82977	+	15.3588i	0.246128	+	0.553491i
$771$	−4.96243	−	8.76963i	−0.178717	−	0.315831i
$772$		−	1.48521i		−	0.0534540i
$773$	21.9215	+	12.6564i	0.788463	+	0.455219i	0.839421	−	0.543482i	$-0.182894\pi$
$773$	21.9215	+	12.6564i	0.788463	+	0.455219i	−0.0509584	+	0.998701i	$0.516228\pi$
$774$	0.405863	−	23.4391i	0.0145884	−	0.842503i
$775$	6.79864	−	7.62335i	0.244214	−	0.273839i
$776$	8.91744	−	15.4455i	0.320117	−	0.554459i
$777$	−4.74510	+	1.21317i	−0.170230	+	0.0435221i
$778$	−7.18549	+	4.14854i	−0.257612	+	0.148733i
$779$	−19.4149	−	11.2092i	−0.695609	−	0.401610i
$780$	−18.1409	−	7.09458i	−0.649549	−	0.254027i
$781$	−11.1044	−	19.2333i	−0.397345	−	0.688223i
$782$	−25.1628	+	14.5277i	−0.899819	+	0.519511i
$783$	9.91457	−	16.1867i	0.354318	−	0.578466i
$784$	6.08194	−	3.46554i	0.217212	−	0.123769i
$785$	14.2757	−	37.4558i	0.509521	−	1.33685i
$786$	−25.7906	+	14.5940i	−0.919919	+	0.520550i
$787$	25.7571			0.918141			0.459071	−	0.888400i	$-0.348182\pi$
$787$	25.7571			0.918141			0.459071	+	0.888400i	$0.348182\pi$
$788$	17.6493			0.628729
$789$	−0.0326222	+	3.76824i	−0.00116138	+	0.134153i
$790$	−3.59218	+	9.42498i	−0.127804	+	0.335326i
$791$	15.2768	+	15.3637i	0.543181	+	0.546272i
$792$	7.30680	+	4.38898i	0.259636	+	0.155956i
$793$	−45.4456	+	26.2380i	−1.61382	+	0.931740i
$794$	6.65037	+	11.5188i	0.236013	+	0.408786i
$795$	3.35336	+	22.0678i	0.118932	+	0.782663i
$796$	17.8938	+	10.3310i	0.634229	+	0.366172i
$797$	42.2492	−	24.3926i	1.49655	−	0.864031i	0.496553	−	0.868006i	$-0.334599\pi$
$797$	42.2492	−	24.3926i	1.49655	−	0.864031i	0.999992	+	0.00397561i	$0.00126548\pi$
$798$	17.4393	−	4.45865i	0.617344	−	0.157835i
$799$	5.06627	−	8.77504i	0.179232	−	0.310439i
$800$	3.73162	+	3.32792i	0.131933	+	0.117660i
$801$	16.4831	−	27.4412i	0.582402	−	0.969587i
$802$	−18.0899	−	10.4442i	−0.638777	−	0.368798i
$803$		−	40.0132i		−	1.41204i
$804$	−5.27362	+	8.95426i	−0.185986	+	0.315792i
$805$	30.7244	+	22.3440i	1.08289	+	0.787523i
$806$	8.89810	−	5.13732i	0.313422	−	0.180954i
$807$	−5.29431	+	2.99586i	−0.186369	+	0.105459i
$808$	5.04091	+	8.73112i	0.177339	+	0.307160i
$809$	19.3683	+	11.1823i	0.680953	+	0.393148i	0.800214	−	0.599715i	$-0.204719\pi$
$809$	19.3683	+	11.1823i	0.680953	+	0.393148i	−0.119261	+	0.992863i	$0.538053\pi$
$810$	−12.1540	−	16.0400i	−0.427048	−	0.563587i
$811$			0.819585i			0.0287795i	0.999896	+	0.0143898i	$0.00458056\pi$
$811$			0.819585i			0.0287795i	−0.999896	+	0.0143898i	$0.995419\pi$
$812$	−9.32859	−	2.52798i	−0.327369	−	0.0887146i
$813$	−2.78608	−	0.0241195i	−0.0977122	−	0.000845909i
$814$	−1.51831	+	2.62978i	−0.0532166	+	0.0921738i
$815$	−1.34073	−	8.33653i	−0.0469638	−	0.292016i
$816$	−3.85962	−	6.82074i	−0.135114	−	0.238774i
$817$	−30.6940			−1.07385
$818$		−	28.3129i		−	0.989938i
$819$	11.1069	−	38.3435i	0.388105	−	1.33983i
$820$	12.6001	−	2.02643i	0.440016	−	0.0707661i
$821$			53.8484i			1.87932i	0.342108	+	0.939661i	$0.388859\pi$
$821$			53.8484i			1.87932i	−0.342108	+	0.939661i	$0.611141\pi$
$822$	−0.0929656	+	10.7386i	−0.00324255	+	0.374552i
$823$		−	44.7612i		−	1.56028i	−0.625608	−	0.780138i	$-0.715149\pi$
$823$		−	44.7612i		−	1.56028i	0.625608	−	0.780138i	$-0.284851\pi$
$824$	1.03484	−	1.79239i	0.0360502	−	0.0624408i
$825$	−18.2213	−	16.5355i	−0.634384	−	0.575691i
$826$	32.7626	−	8.67915i	1.13996	−	0.301986i
$827$	14.5517			0.506014			0.253007	−	0.967464i	$-0.418580\pi$
$827$	14.5517			0.506014			0.253007	+	0.967464i	$0.418580\pi$
$828$	19.2616	+	0.333526i	0.669387	+	0.0115908i
$829$	29.5474	+	17.0592i	1.02623	+	0.592491i	0.915901	−	0.401404i	$-0.131478\pi$
$829$	29.5474	+	17.0592i	1.02623	+	0.592491i	0.110324	+	0.993896i	$0.464811\pi$
$830$	−22.0134	+	17.9130i	−0.764096	+	0.621771i
$831$	−7.75600	−	0.0671449i	−0.269053	−	0.00232923i
$832$	2.51471	+	4.35560i	0.0871818	+	0.151003i
$833$	31.6725	+	0.179725i	1.09739	+	0.00622710i
$834$	26.0252	+	0.225304i	0.901178	+	0.00780163i
$835$	8.55450	+	53.1910i	0.296041	+	1.84075i
$836$	5.58010	−	9.66502i	0.192992	−	0.334272i
$837$	10.6117	+	0.275656i	0.366794	+	0.00952807i
$838$	7.85403	+	13.6036i	0.271313	+	0.469928i
$839$	−23.2722	+	40.3087i	−0.803446	+	1.39161i	0.113889	+	0.993493i	$0.463669\pi$
$839$	−23.2722	+	40.3087i	−0.803446	+	1.39161i	−0.917335	+	0.398116i	$0.869664\pi$
$840$	−6.09830	+	8.23473i	−0.210411	+	0.284125i
$841$	−7.82763	−	13.5578i	−0.269918	−	0.467512i
$842$	13.2658	−	22.9771i	0.457171	−	0.791843i
$843$	8.90740	+	15.7412i	0.306787	+	0.542157i
$844$	5.63953	+	9.76796i	0.194121	+	0.336227i
$845$	17.3524	+	21.3244i	0.596942	+	0.733583i
$846$	−5.87535	+	3.25783i	−0.201999	+	0.112007i
$847$	2.02589	−	7.47583i	0.0696105	−	0.256872i
$848$	2.88164	−	4.99115i	0.0989559	−	0.171397i
$849$	27.6160	+	16.2645i	0.947777	+	0.558195i
$850$	7.09346	+	21.4828i	0.243304	+	0.736853i
$851$			6.86312i			0.235265i
$852$	6.87065	−	11.6659i	0.235385	−	0.399668i
$853$	19.2187	−	33.2878i	0.658037	−	1.13975i	−0.323086	−	0.946369i	$-0.604720\pi$
$853$	19.2187	−	33.2878i	0.658037	−	1.13975i	0.981123	−	0.193384i	$-0.0619462\pi$
$854$	7.06910	+	26.6849i	0.241900	+	0.913137i
$855$	−20.7228	+	16.2747i	−0.708706	+	0.556585i
$856$	−1.27205	−	2.20325i	−0.0434777	−	0.0753055i
$857$	23.5713	−	13.6089i	0.805180	−	0.464871i	−0.0400992	−	0.999196i	$-0.512767\pi$
$857$	23.5713	−	13.6089i	0.805180	−	0.464871i	0.845279	+	0.534325i	$0.179434\pi$
$858$	−12.1892	−	21.5408i	−0.416132	−	0.735390i
$859$	−27.7376	−	16.0143i	−0.946395	−	0.546402i	−0.0544359	−	0.998517i	$-0.517336\pi$
$859$	−27.7376	−	16.0143i	−0.946395	−	0.546402i	−0.891959	+	0.452116i	$0.850669\pi$
$860$	13.5529	−	11.0285i	0.462152	−	0.376069i
$861$	6.47844	+	25.3393i	0.220785	+	0.863562i
$862$	14.0479	+	8.11059i	0.478475	+	0.276248i
$863$	14.0979	+	24.4183i	0.479898	+	0.831208i	0.999734	−	0.0230584i	$-0.00734037\pi$
$863$	14.0979	+	24.4183i	0.479898	+	0.831208i	−0.519836	+	0.854266i	$0.674007\pi$
$864$	−0.134933	+	5.19440i	−0.00459051	+	0.176717i
$865$	−25.4356	−	9.69440i	−0.864838	−	0.329620i
$866$	−19.7268			−0.670344
$867$	0.0520754	−	6.01530i	0.00176857	−	0.204290i
$868$	−1.38411	−	5.22481i	−0.0469796	−	0.177342i
$869$	−11.0990	+	6.40799i	−0.376507	+	0.217376i
$870$	13.9876	−	2.12552i	0.474225	−	0.0720620i
$871$	26.1324	−	15.0875i	0.885462	−	0.511222i
$872$	−5.96532	+	10.3322i	−0.202011	+	0.349894i
$873$	−53.4966	−	0.926325i	−1.81059	−	0.0313514i
$874$		−	25.2235i		−	0.853196i
$875$	21.8971	−	19.8876i	0.740256	−	0.672325i
$876$	21.2295	−	12.0130i	0.717279	−	0.405883i
$877$	−20.2119	−	11.6694i	−0.682508	−	0.394046i	0.118291	−	0.992979i	$-0.462258\pi$
$877$	−20.2119	−	11.6694i	−0.682508	−	0.394046i	−0.800799	+	0.598933i	$0.795592\pi$
$878$		−	13.1264i		−	0.442994i
$879$	0.634740	+	0.00549504i	0.0214092	+	0.000185343i
$880$	1.00879	+	6.27254i	0.0340063	+	0.211447i
$881$	18.3044			0.616690			0.308345	−	0.951275i	$-0.400225\pi$
$881$	18.3044			0.616690			0.308345	+	0.951275i	$0.400225\pi$
$882$	−17.9404	−	10.9153i	−0.604084	−	0.367536i
$883$			7.38295i			0.248456i	0.992254	+	0.124228i	$0.0396454\pi$
$883$			7.38295i			0.248456i	−0.992254	+	0.124228i	$0.960355\pi$
$884$			22.7567i			0.765390i
$885$	−38.7524	+	30.9804i	−1.30265	+	1.04139i
$886$	8.62000			0.289595
$887$	−9.64775	−	5.57013i	−0.323940	−	0.187027i	0.329207	−	0.944258i	$-0.393218\pi$
$887$	−9.64775	−	5.57013i	−0.323940	−	0.187027i	−0.653147	+	0.757231i	$0.726552\pi$
$888$	−1.85110	−	0.0160252i	−0.0621188	−	0.000537772i
$889$	−12.3111	−	46.4726i	−0.412900	−	1.55864i
$890$	23.5570	−	3.78858i	0.789632	−	0.126994i
$891$	0.885286	−	25.5556i	0.0296582	−	0.856144i
$892$	−6.07248	+	10.5178i	−0.203322	+	0.352164i
$893$	4.39810	+	7.61774i	0.147177	+	0.254918i
$894$	−1.94775	−	3.44208i	−0.0651425	−	0.115120i
$895$	−6.34816	+	5.16572i	−0.212196	+	0.172671i
$896$	2.55753	−	0.677517i	0.0854411	−	0.0226343i
$897$	−48.2006	−	28.3878i	−1.60937	−	0.947842i
$898$			37.2222i			1.24212i
$899$	−3.73142	+	6.46301i	−0.124450	+	0.215554i
$900$	3.30258	−	14.6319i	0.110086	−	0.487731i
$901$	22.5835	−	13.0386i	0.752366	−	0.434379i
$902$	14.0433	+	8.10791i	0.467591	+	0.269964i
$903$	25.0283	+	25.6103i	0.832888	+	0.852258i
$904$	4.09453	+	7.09194i	0.136182	+	0.235874i
$905$	−24.1652	−	9.21019i	−0.803279	−	0.306157i
$906$	0.197779	−	22.8458i	0.00657077	−	0.758999i
$907$	−21.6780	+	12.5158i	−0.719806	+	0.415580i	−0.814681	−	0.579909i	$-0.803088\pi$
$907$	−21.6780	+	12.5158i	−0.719806	+	0.415580i	0.0948756	+	0.995489i	$0.469755\pi$
$908$	−20.5863	+	11.8855i	−0.683180	+	0.394434i
$909$	15.5740	−	25.9276i	0.516556	−	0.859964i
$910$	27.1875	−	12.0898i	0.901258	−	0.400774i
$911$	10.1366	+	5.85238i	0.335841	+	0.193898i	0.658431	−	0.752641i	$-0.271220\pi$
$911$	10.1366	+	5.85238i	0.335841	+	0.193898i	−0.322590	+	0.946539i	$0.604554\pi$
$912$	6.80319	+	0.0588963i	0.225276	+	0.00195025i
$913$	−36.0614			−1.19346
$914$			40.5035i			1.33974i
$915$	−25.2333	−	31.5635i	−0.834187	−	1.04346i
$916$	9.88508	+	5.70716i	0.326612	+	0.188570i
$917$	11.8396	−	43.6899i	0.390979	−	1.44277i
$918$	−12.2803	+	20.0491i	−0.405311	+	0.661719i
$919$	15.3085	+	26.5152i	0.504982	+	0.874655i	0.999983	+	0.00576276i	$0.00183435\pi$
$919$	15.3085	+	26.5152i	0.504982	+	0.874655i	−0.495001	+	0.868892i	$0.664832\pi$
$920$	9.06290	+	11.1374i	0.298795	+	0.367190i
$921$	−37.2953	−	21.9651i	−1.22892	−	0.723775i
$922$	−16.8755	+	29.2292i	−0.555765	+	0.962614i
$923$	−34.0462	+	19.6566i	−1.12064	+	0.647004i
$924$	−12.6143	+	3.22507i	−0.414981	+	0.106097i
$925$	5.23232	+	1.08615i	0.172038	+	0.0357123i
$926$	−23.0998	+	13.3367i	−0.759108	+	0.438271i
$927$	−6.20808	−	0.107497i	−0.203900	−	0.00353065i
$928$	−3.16363	−	1.82652i	−0.103851	−	0.0599586i
$929$	13.3528			0.438093			0.219046	−	0.975714i	$-0.429705\pi$
$929$	13.3528			0.438093			0.219046	+	0.975714i	$0.429705\pi$
$930$	4.94059	+	6.18003i	0.162008	+	0.202651i
$931$	−13.8828	+	23.7337i	−0.454991	+	0.777840i
$932$	−4.16132	−	7.20762i	−0.136309	−	0.236093i
$933$	−35.8661	−	21.1234i	−1.17420	−	0.691549i
$934$	−4.89263	+	2.82476i	−0.160092	+	0.0924289i
$935$	−10.2378	+	26.8613i	−0.334811	+	0.878459i
$936$	7.76922	−	12.9342i	0.253945	−	0.422769i
$937$	−32.6519			−1.06669			−0.533345	−	0.845898i	$-0.679065\pi$
$937$	−32.6519			−1.06669			−0.533345	+	0.845898i	$0.679065\pi$
$938$	−4.06491	−	15.3445i	−0.132724	−	0.501015i
$939$	9.70802	+	5.71755i	0.316809	+	0.186585i
$940$	−4.67907	−	1.78335i	−0.152614	−	0.0581666i
$941$	35.8078			1.16730			0.583650	−	0.812006i	$-0.301624\pi$
$941$	35.8078			1.16730			0.583650	+	0.812006i	$0.301624\pi$
$942$	26.7538	+	15.7567i	0.871686	+	0.513380i
$943$	36.6498			1.19348
$944$	12.8102			0.416937
$945$	30.4769	+	4.02001i	0.991413	+	0.130771i
$946$	22.2019			0.721845
$947$	−34.3826			−1.11729			−0.558643	−	0.829408i	$-0.688678\pi$
$947$	−34.3826			−1.11729			−0.558643	+	0.829408i	$0.688678\pi$
$948$	−6.73204	−	3.96484i	−0.218647	−	0.128772i
$949$	−70.8300			−2.29924
$950$	−19.2299	−	3.99182i	−0.623901	−	0.129512i
$951$	11.0274	+	6.49461i	0.357588	+	0.210602i
$952$	11.5545	+	3.13119i	0.374484	+	0.101482i
$953$	−44.0113			−1.42566			−0.712832	−	0.701334i	$-0.752588\pi$
$953$	−44.0113			−1.42566			−0.712832	+	0.701334i	$0.752588\pi$
$954$	−17.2872	−	0.299339i	−0.559695	−	0.00969145i
$955$	19.7057	+	7.51051i	0.637661	+	0.243035i
$956$	−6.41684	+	3.70476i	−0.207535	+	0.119821i
$957$	15.4902	+	9.12299i	0.500728	+	0.294904i
$958$	−0.136929	−	0.237168i	−0.00442397	−	0.00766254i
$959$	−11.5665	−	11.6323i	−0.373501	−	0.375627i
$960$	−3.02511	+	2.41841i	−0.0976350	+	0.0780539i
$961$	26.8265			0.865372
$962$	4.65515	+	2.68765i	0.150088	+	0.0866534i
$963$	−3.93000	+	6.54269i	−0.126643	+	0.210835i
$964$	−7.50748	+	4.33445i	−0.241800	+	0.139603i
$965$	−3.10328	−	1.18277i	−0.0998981	−	0.0380746i
$966$	−21.0458	+	20.5675i	−0.677138	+	0.661748i
$967$	−6.03415	+	3.48382i	−0.194045	+	0.112032i	−0.593875	−	0.804557i	$-0.702403\pi$
$967$	−6.03415	+	3.48382i	−0.194045	+	0.112032i	0.399830	+	0.916589i	$0.369069\pi$
$968$	1.46376	−	2.53530i	0.0470469	−	0.0814876i
$969$	26.5252	+	15.6221i	0.852112	+	0.501853i
$970$	−25.1710	−	30.9327i	−0.808193	−	0.993190i
$971$	−12.3672	−	21.4206i	−0.396883	−	0.687421i	0.596457	−	0.802645i	$-0.296575\pi$
$971$	−12.3672	−	21.4206i	−0.396883	−	0.687421i	−0.993340	+	0.115224i	$0.963241\pi$
$972$	13.8246	−	7.20277i	0.443425	−	0.231029i
$973$	−28.1911	+	28.0316i	−0.903766	+	0.898652i
$974$	12.4072	+	7.16329i	0.397552	+	0.229527i
$975$	−29.2705	+	32.2547i	−0.937406	+	1.03298i
$976$			10.4338i			0.333979i
$977$	−45.1109			−1.44323			−0.721613	−	0.692296i	$-0.756599\pi$
$977$	−45.1109			−1.44323			−0.721613	+	0.692296i	$0.756599\pi$
$978$	6.54018	+	0.0566193i	0.209132	+	0.00181049i
$979$	26.2551	+	15.1584i	0.839117	+	0.484465i
$980$	−2.39766	−	15.4677i	−0.0765905	−	0.494099i
$981$	35.7866	+	0.619666i	1.14258	+	0.0197844i
$982$	−31.8165	+	18.3692i	−1.01530	+	0.586186i
$983$	31.8263	−	18.3749i	1.01510	−	0.586068i	0.102419	−	0.994741i	$-0.467342\pi$
$983$	31.8263	−	18.3749i	1.01510	−	0.586068i	0.912681	+	0.408673i	$0.134008\pi$
$984$	−0.0855764	+	9.88506i	−0.00272808	+	0.315124i
$985$	14.0552	−	36.8773i	0.447836	−	1.17501i
$986$	−8.26450	−	14.3145i	−0.263195	−	0.455868i
$987$	2.76979	−	9.88125i	0.0881633	−	0.314524i
$988$	−17.1087	−	9.87771i	−0.544300	−	0.314252i
$989$	43.4563	−	25.0895i	1.38183	−	0.797800i
$990$	14.9894	−	11.7720i	0.476395	−	0.374138i
$991$	5.67076	−	9.82205i	0.180138	−	0.312008i	−0.761790	−	0.647825i	$-0.775679\pi$
$991$	5.67076	−	9.82205i	0.180138	−	0.312008i	0.941927	+	0.335817i	$0.109012\pi$
$992$		−	2.04291i		−	0.0648624i
$993$	−39.2721	−	23.1293i	−1.24626	−	0.733987i
$994$	5.29591	+	19.9913i	0.167976	+	0.634086i
$995$	35.8360	−	29.1610i	1.13608	−	0.924466i
$996$	−10.8266	−	19.1328i	−0.343054	−	0.606246i
$997$	4.30265	+	7.45242i	0.136266	+	0.236020i	0.926081	−	0.377326i	$-0.123156\pi$
$997$	4.30265	+	7.45242i	0.136266	+	0.236020i	−0.789814	+	0.613346i	$0.789823\pi$
$998$	−16.0396	+	27.7814i	−0.507725	+	0.879406i
$999$	2.65093	+	4.87996i	0.0838716	+	0.154395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.a.479.5	yes	48
3.2	odd	2		1890.2.bi.b.899.11		48
5.4	even	2		630.2.bi.b.479.20	yes	48
7.5	odd	6		630.2.r.b.299.5	yes	48
9.4	even	3		1890.2.r.b.1529.2		48
9.5	odd	6		630.2.r.a.59.20	✓	48
15.14	odd	2		1890.2.bi.a.899.6		48
21.5	even	6		1890.2.r.a.89.2		48
35.19	odd	6		630.2.r.a.299.20	yes	48
45.4	even	6		1890.2.r.a.1529.2		48
45.14	odd	6		630.2.r.b.59.5	yes	48
63.5	even	6		630.2.bi.b.509.20	yes	48
63.40	odd	6		1890.2.bi.a.719.6		48
105.89	even	6		1890.2.r.b.89.2		48
315.194	even	6	inner	630.2.bi.a.509.5	yes	48
315.229	odd	6		1890.2.bi.b.719.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.20	✓	48	9.5	odd	6
630.2.r.a.299.20	yes	48	35.19	odd	6
630.2.r.b.59.5	yes	48	45.14	odd	6
630.2.r.b.299.5	yes	48	7.5	odd	6
630.2.bi.a.479.5	yes	48	1.1	even	1	trivial
630.2.bi.a.509.5	yes	48	315.194	even	6	inner
630.2.bi.b.479.20	yes	48	5.4	even	2
630.2.bi.b.509.20	yes	48	63.5	even	6
1890.2.r.a.89.2		48	21.5	even	6
1890.2.r.a.1529.2		48	45.4	even	6
1890.2.r.b.89.2		48	105.89	even	6
1890.2.r.b.1529.2		48	9.4	even	3
1890.2.bi.a.719.6		48	63.40	odd	6
1890.2.bi.a.899.6		48	15.14	odd	2
1890.2.bi.b.719.11		48	315.229	odd	6
1890.2.bi.b.899.11		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.49245 - 0.878978i) q^{3} +1.00000 q^{4} +(0.796362 - 2.08945i) q^{5} +(1.49245 + 0.878978i) q^{6} +(-2.55753 + 0.677517i) q^{7} -1.00000 q^{8} +(1.45479 + 2.62366i) q^{9} +(-0.796362 + 2.08945i) q^{10} +(-2.46056 + 1.42061i) q^{11} +(-1.49245 - 0.878978i) q^{12} +(2.51471 + 4.35560i) q^{13} +(2.55753 - 0.677517i) q^{14} +(-3.02511 + 2.41841i) q^{15} +1.00000 q^{16} +(3.91852 + 2.26236i) q^{17} +(-1.45479 - 2.62366i) q^{18} +(-3.40172 + 1.96399i) q^{19} +(0.796362 - 2.08945i) q^{20} +(4.41250 + 1.23686i) q^{21} +(2.46056 - 1.42061i) q^{22} +(3.21075 - 5.56118i) q^{23} +(1.49245 + 0.878978i) q^{24} +(-3.73162 - 3.32792i) q^{25} +(-2.51471 - 4.35560i) q^{26} +(0.134933 - 5.19440i) q^{27} +(-2.55753 + 0.677517i) q^{28} +(3.16363 + 1.82652i) q^{29} +(3.02511 - 2.41841i) q^{30} +2.04291i q^{31} -1.00000 q^{32} +(4.92094 + 0.0426013i) q^{33} +(-3.91852 - 2.26236i) q^{34} +(-0.621082 + 5.88339i) q^{35} +(1.45479 + 2.62366i) q^{36} +(-0.925584 + 0.534386i) q^{37} +(3.40172 - 1.96399i) q^{38} +(0.0754114 - 8.71088i) q^{39} +(-0.796362 + 2.08945i) q^{40} +(2.85368 + 4.94272i) q^{41} +(-4.41250 - 1.23686i) q^{42} +(6.76731 + 3.90711i) q^{43} +(-2.46056 + 1.42061i) q^{44} +(6.64055 - 0.950343i) q^{45} +(-3.21075 + 5.56118i) q^{46} -2.23938i q^{47} +(-1.49245 - 0.878978i) q^{48} +(6.08194 - 3.46554i) q^{49} +(3.73162 + 3.32792i) q^{50} +(-3.85962 - 6.82074i) q^{51} +(2.51471 + 4.35560i) q^{52} +(2.88164 - 4.99115i) q^{53} +(-0.134933 + 5.19440i) q^{54} +(1.00879 + 6.27254i) q^{55} +(2.55753 - 0.677517i) q^{56} +(6.80319 + 0.0588963i) q^{57} +(-3.16363 - 1.82652i) q^{58} +12.8102 q^{59} +(-3.02511 + 2.41841i) q^{60} +10.4338i q^{61} -2.04291i q^{62} +(-5.49826 - 5.72444i) q^{63} +1.00000 q^{64} +(11.1034 - 1.78572i) q^{65} +(-4.92094 - 0.0426013i) q^{66} -5.99972i q^{67} +(3.91852 + 2.26236i) q^{68} +(-9.68003 + 5.47759i) q^{69} +(0.621082 - 5.88339i) q^{70} +7.81664i q^{71} +(-1.45479 - 2.62366i) q^{72} +(-7.04158 + 12.1964i) q^{73} +(0.925584 - 0.534386i) q^{74} +(2.64407 + 8.24675i) q^{75} +(-3.40172 + 1.96399i) q^{76} +(5.33048 - 5.30032i) q^{77} +(-0.0754114 + 8.71088i) q^{78} +4.51074 q^{79} +(0.796362 - 2.08945i) q^{80} +(-4.76714 + 7.63376i) q^{81} +(-2.85368 - 4.94272i) q^{82} +(10.9918 + 6.34613i) q^{83} +(4.41250 + 1.23686i) q^{84} +(7.84765 - 6.38590i) q^{85} +(-6.76731 - 3.90711i) q^{86} +(-3.11608 - 5.50675i) q^{87} +(2.46056 - 1.42061i) q^{88} +(-5.33519 - 9.24081i) q^{89} +(-6.64055 + 0.950343i) q^{90} +(-9.38244 - 9.43583i) q^{91} +(3.21075 - 5.56118i) q^{92} +(1.79567 - 3.04893i) q^{93} +2.23938i q^{94} +(1.39465 + 8.67178i) q^{95} +(1.49245 + 0.878978i) q^{96} +(-8.91744 + 15.4455i) q^{97} +(-6.08194 + 3.46554i) q^{98} +(-7.30680 - 4.38898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 + 42 * q^55 + 3 * q^56 + 22 * q^57 + 3 * q^58 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * q^70 + 18 * q^73 + 18 * q^75 + 12 * q^77 + 18 * q^78 + 8 * q^81 + 3 * q^82 - 9 * q^83 + 8 * q^84 + 33 * q^85 + 15 * q^87 - 6 * q^88 - 33 * q^89 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more