LMFDB - Embedded newform 600.2.bm.a.61.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(61,600)] 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("600.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bm (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.10
Character	$\chi$	$=$	600.61
Dual form			600.2.bm.a.541.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19482 + 0.756580i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.855174 - 1.80795i) q^{4} +(2.02065 - 0.957578i) q^{5} +(-1.37013 + 0.350332i) q^{6} +1.19999 q^{7} +(0.346081 + 2.80717i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.68983 + 2.67292i) q^{10} +(0.523260 + 0.720206i) q^{11} +(1.37201 - 1.45520i) q^{12} +(-0.209858 + 0.288844i) q^{13} +(-1.43376 + 0.907885i) q^{14} +(2.21766 - 0.286294i) q^{15} +(-2.53736 - 3.09222i) q^{16} +(0.934888 + 2.87729i) q^{17} +(-1.41133 - 0.0902097i) q^{18} +(1.42873 - 0.464223i) q^{19} +(-0.00324108 - 4.47213i) q^{20} +(1.14125 + 0.370816i) q^{21} +(-1.17009 - 0.464626i) q^{22} +(-2.29796 + 1.66957i) q^{23} +(-0.538322 + 2.77673i) q^{24} +(3.16609 - 3.86987i) q^{25} +(0.0322077 - 0.503890i) q^{26} +(0.587785 + 0.809017i) q^{27} +(1.02620 - 2.16951i) q^{28} +(6.48859 + 2.10827i) q^{29} +(-2.43310 + 2.01991i) q^{30} +(-3.02296 - 9.30373i) q^{31} +(5.37119 + 1.77492i) q^{32} +(0.275094 + 0.846653i) q^{33} +(-3.29392 - 2.73052i) q^{34} +(2.42476 - 1.14908i) q^{35} +(1.75454 - 0.960002i) q^{36} +(4.89385 - 6.73581i) q^{37} +(-1.35585 + 1.63561i) q^{38} +(-0.288844 + 0.209858i) q^{39} +(3.38740 + 5.34093i) q^{40} +(-4.99458 - 3.62877i) q^{41} +(-1.64414 + 0.420393i) q^{42} +5.64606i q^{43} +(1.74957 - 0.330126i) q^{44} +(2.19759 + 0.413014i) q^{45} +(1.48248 - 3.73342i) q^{46} +(-1.33700 + 4.11488i) q^{47} +(-1.45762 - 3.72496i) q^{48} -5.56004 q^{49} +(-0.855030 + 7.01918i) q^{50} +3.02536i q^{51} +(0.342751 + 0.626424i) q^{52} +(12.5009 + 4.06177i) q^{53} +(-1.31438 - 0.521921i) q^{54} +(1.74698 + 0.954224i) q^{55} +(0.415293 + 3.36857i) q^{56} +1.50226 q^{57} +(-9.34775 + 2.39014i) q^{58} +(-5.81937 + 8.00968i) q^{59} +(1.37888 - 4.25425i) q^{60} +(1.35375 + 1.86327i) q^{61} +(10.6509 + 8.82914i) q^{62} +(0.970808 + 0.705334i) q^{63} +(-7.76046 + 1.94302i) q^{64} +(-0.147459 + 0.784610i) q^{65} +(-0.969247 - 0.803464i) q^{66} +(-1.55489 + 0.505216i) q^{67} +(6.00148 + 0.770353i) q^{68} +(-2.70141 + 0.877743i) q^{69} +(-2.02777 + 3.20746i) q^{70} +(2.67467 - 8.23178i) q^{71} +(-1.37003 + 2.47447i) q^{72} +(0.208588 - 0.151548i) q^{73} +(-0.751078 + 11.7506i) q^{74} +(4.20698 - 2.70209i) q^{75} +(0.382523 - 2.98007i) q^{76} +(0.627904 + 0.864236i) q^{77} +(0.186342 - 0.469275i) q^{78} +(-1.60329 + 4.93442i) q^{79} +(-8.08816 - 3.81859i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.71306 + 0.556922i) q^{82} +(-3.73634 + 1.21401i) q^{83} +(1.64639 - 1.74622i) q^{84} +(4.64431 + 4.91878i) q^{85} +(-4.27170 - 6.74601i) q^{86} +(5.51952 + 4.01017i) q^{87} +(-1.84065 + 1.71813i) q^{88} +(-11.3302 + 8.23184i) q^{89} +(-2.93820 + 1.16918i) q^{90} +(-0.251826 + 0.346609i) q^{91} +(1.05333 + 5.58236i) q^{92} -9.78252i q^{93} +(-1.51576 - 5.92807i) q^{94} +(2.44244 - 2.30616i) q^{95} +(4.55982 + 3.34784i) q^{96} +(0.401170 - 1.23467i) q^{97} +(6.64322 - 4.20661i) q^{98} +0.890223i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) $ 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.19482	+	0.756580i	−0.844863	+	0.534983i
$2$	−1.19482	+	0.756580i	−0.844863	+	0.534983i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.855174	−	1.80795i	0.427587	−	0.903974i
$5$	2.02065	−	0.957578i	0.903664	−	0.428242i
$5$	2.02065	−	0.957578i	0.903664	−	0.428242i
$6$	−1.37013	+	0.350332i	−0.559355	+	0.143022i
$7$	1.19999			0.453552			0.226776	−	0.973947i	$-0.427182\pi$
$7$	1.19999			0.453552			0.226776	+	0.973947i	$0.427182\pi$
$8$	0.346081	+	2.80717i	0.122358	+	0.992486i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.68983	+	2.67292i	−0.534370	+	0.845250i
$11$	0.523260	+	0.720206i	0.157769	+	0.217150i	0.880583	−	0.473893i	$-0.157152\pi$
$11$	0.523260	+	0.720206i	0.157769	+	0.217150i	−0.722814	+	0.691043i	$0.757152\pi$
$12$	1.37201	−	1.45520i	0.396064	−	0.420079i
$13$	−0.209858	+	0.288844i	−0.0582041	+	0.0801110i	−0.837127	−	0.547009i	$-0.815766\pi$
$13$	−0.209858	+	0.288844i	−0.0582041	+	0.0801110i	0.778923	+	0.627120i	$0.215766\pi$
$14$	−1.43376	+	0.907885i	−0.383189	+	0.242642i
$15$	2.21766	−	0.286294i	0.572598	−	0.0739209i
$16$	−2.53736	−	3.09222i	−0.634339	−	0.773055i
$17$	0.934888	+	2.87729i	0.226744	+	0.697845i	0.998110	+	0.0614537i	$0.0195736\pi$
$17$	0.934888	+	2.87729i	0.226744	+	0.697845i	−0.771366	+	0.636391i	$0.780426\pi$
$18$	−1.41133	−	0.0902097i	−0.332654	−	0.0212626i
$19$	1.42873	−	0.464223i	0.327774	−	0.106500i	−0.140508	−	0.990080i	$-0.544873\pi$
$19$	1.42873	−	0.464223i	0.327774	−	0.106500i	0.468281	+	0.883579i	$0.344873\pi$
$20$	−0.00324108	−	4.47213i	−0.000724727	−	1.00000i
$21$	1.14125	+	0.370816i	0.249042	+	0.0809186i
$22$	−1.17009	−	0.464626i	−0.249465	−	0.0990585i
$23$	−2.29796	+	1.66957i	−0.479158	+	0.348129i	−0.801000	−	0.598665i	$-0.795698\pi$
$23$	−2.29796	+	1.66957i	−0.479158	+	0.348129i	0.321842	+	0.946793i	$0.395698\pi$
$24$	−0.538322	+	2.77673i	−0.109884	+	0.566797i
$25$	3.16609	−	3.86987i	0.633218	−	0.773974i
$26$	0.0322077	−	0.503890i	0.00631644	−	0.0988210i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	1.02620	−	2.16951i	0.193933	−	0.409999i
$29$	6.48859	+	2.10827i	1.20490	+	0.391496i	0.841562	−	0.540161i	$-0.181637\pi$
$29$	6.48859	+	2.10827i	1.20490	+	0.391496i	0.363339	+	0.931657i	$0.381637\pi$
$30$	−2.43310	+	2.01991i	−0.444221	+	0.368783i
$31$	−3.02296	−	9.30373i	−0.542941	−	1.67100i	−0.725837	−	0.687867i	$-0.758547\pi$
$31$	−3.02296	−	9.30373i	−0.542941	−	1.67100i	0.182896	−	0.983132i	$-0.441453\pi$
$32$	5.37119	+	1.77492i	0.949501	+	0.313765i
$33$	0.275094	+	0.846653i	0.0478877	+	0.147383i
$34$	−3.29392	−	2.73052i	−0.564902	−	0.468280i
$35$	2.42476	−	1.14908i	0.409858	−	0.194230i
$36$	1.75454	−	0.960002i	0.292423	−	0.160000i
$37$	4.89385	−	6.73581i	0.804544	−	1.10736i	−0.187598	−	0.982246i	$-0.560070\pi$
$37$	4.89385	−	6.73581i	0.804544	−	1.10736i	0.992142	−	0.125115i	$-0.0399298\pi$
$38$	−1.35585	+	1.63561i	−0.219948	+	0.265331i
$39$	−0.288844	+	0.209858i	−0.0462521	+	0.0336041i
$40$	3.38740	+	5.34093i	0.535595	+	0.844475i
$41$	−4.99458	−	3.62877i	−0.780022	−	0.566719i	0.124963	−	0.992161i	$-0.460119\pi$
$41$	−4.99458	−	3.62877i	−0.780022	−	0.566719i	−0.904986	+	0.425442i	$0.860119\pi$
$42$	−1.64414	+	0.420393i	−0.253696	+	0.0648680i
$43$			5.64606i			0.861016i	0.902587	+	0.430508i	$0.141666\pi$
$43$			5.64606i			0.861016i	−0.902587	+	0.430508i	$0.858334\pi$
$44$	1.74957	−	0.330126i	0.263758	−	0.0497684i
$45$	2.19759	+	0.413014i	0.327598	+	0.0615685i
$46$	1.48248	−	3.73342i	0.218580	−	0.550462i
$47$	−1.33700	+	4.11488i	−0.195022	+	0.600216i	0.804954	+	0.593337i	$0.202190\pi$
$47$	−1.33700	+	4.11488i	−0.195022	+	0.600216i	−0.999976	+	0.00687939i	$0.997810\pi$
$48$	−1.45762	−	3.72496i	−0.210389	−	0.537652i
$49$	−5.56004			−0.794291
$50$	−0.855030	+	7.01918i	−0.120920	+	0.992662i
$51$			3.02536i			0.423635i
$52$	0.342751	+	0.626424i	0.0475310	+	0.0868694i
$53$	12.5009	+	4.06177i	1.71712	+	0.557927i	0.991493	−	0.130157i	$-0.0415481\pi$
$53$	12.5009	+	4.06177i	1.71712	+	0.557927i	0.725631	+	0.688084i	$0.241548\pi$
$54$	−1.31438	−	0.521921i	−0.178865	−	0.0710244i
$55$	1.74698	+	0.954224i	0.235563	+	0.128668i
$56$	0.415293	+	3.36857i	0.0554958	+	0.450144i
$57$	1.50226			0.198979
$58$	−9.34775	+	2.39014i	−1.22742	+	0.313841i
$59$	−5.81937	+	8.00968i	−0.757618	+	1.04277i	0.239790	+	0.970825i	$0.422921\pi$
$59$	−5.81937	+	8.00968i	−0.757618	+	1.04277i	−0.997408	+	0.0719471i	$0.977079\pi$
$60$	1.37888	−	4.25425i	0.178013	−	0.549222i
$61$	1.35375	+	1.86327i	0.173329	+	0.238568i	0.886840	−	0.462077i	$-0.152896\pi$
$61$	1.35375	+	1.86327i	0.173329	+	0.238568i	−0.713510	+	0.700645i	$0.752896\pi$
$62$	10.6509	+	8.82914i	1.35267	+	1.12130i
$63$	0.970808	+	0.705334i	0.122310	+	0.0888637i
$64$	−7.76046	+	1.94302i	−0.970057	+	0.242878i
$65$	−0.147459	+	0.784610i	−0.0182900	+	0.0973189i
$66$	−0.969247	−	0.803464i	−0.119306	−	0.0988996i
$67$	−1.55489	+	0.505216i	−0.189961	+	0.0617220i	−0.402452	−	0.915441i	$-0.631842\pi$
$67$	−1.55489	+	0.505216i	−0.189961	+	0.0617220i	0.212492	+	0.977163i	$0.431842\pi$
$68$	6.00148	+	0.770353i	0.727787	+	0.0934190i
$69$	−2.70141	+	0.877743i	−0.325212	+	0.105668i
$70$	−2.02777	+	3.20746i	−0.242365	+	0.383365i
$71$	2.67467	−	8.23178i	0.317425	−	0.976932i	−0.657320	−	0.753611i	$-0.728310\pi$
$71$	2.67467	−	8.23178i	0.317425	−	0.976932i	0.974745	−	0.223321i	$-0.0716899\pi$
$72$	−1.37003	+	2.47447i	−0.161460	+	0.291619i
$73$	0.208588	−	0.151548i	0.0244134	−	0.0177374i	−0.575512	−	0.817794i	$-0.695197\pi$
$73$	0.208588	−	0.151548i	0.0244134	−	0.0177374i	0.599925	+	0.800056i	$0.295197\pi$
$74$	−0.751078	+	11.7506i	−0.0873111	+	1.36599i
$75$	4.20698	−	2.70209i	0.485781	−	0.312010i
$76$	0.382523	−	2.98007i	0.0438784	−	0.341837i
$77$	0.627904	+	0.864236i	0.0715563	+	0.0984889i
$78$	0.186342	−	0.469275i	0.0210991	−	0.0531350i
$79$	−1.60329	+	4.93442i	−0.180384	+	0.555165i	−0.999838	−	0.0179794i	$-0.994277\pi$
$79$	−1.60329	+	4.93442i	−0.180384	+	0.555165i	0.819454	+	0.573145i	$0.194277\pi$
$80$	−8.08816	−	3.81859i	−0.904284	−	0.426932i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	8.71306	+	0.556922i	0.962197	+	0.0615017i
$83$	−3.73634	+	1.21401i	−0.410117	+	0.133255i	−0.506807	−	0.862060i	$-0.669174\pi$
$83$	−3.73634	+	1.21401i	−0.410117	+	0.133255i	0.0966905	+	0.995315i	$0.469174\pi$
$84$	1.64639	−	1.74622i	0.179635	−	0.190528i
$85$	4.64431	+	4.91878i	0.503747	+	0.533516i
$86$	−4.27170	−	6.74601i	−0.460629	−	0.727441i
$87$	5.51952	+	4.01017i	0.591755	+	0.429935i
$88$	−1.84065	+	1.71813i	−0.196214	+	0.183153i
$89$	−11.3302	+	8.23184i	−1.20099	+	0.872574i	−0.994382	−	0.105849i	$-0.966244\pi$
$89$	−11.3302	+	8.23184i	−1.20099	+	0.872574i	−0.206612	+	0.978423i	$0.566244\pi$
$90$	−2.93820	+	1.16918i	−0.309713	+	0.123242i
$91$	−0.251826	+	0.346609i	−0.0263986	+	0.0363345i
$92$	1.05333	+	5.58236i	0.109818	+	0.582002i
$93$		−	9.78252i		−	1.01440i
$94$	−1.51576	−	5.92807i	−0.156338	−	0.611434i
$95$	2.44244	−	2.30616i	0.250589	−	0.236607i
$96$	4.55982	+	3.34784i	0.465385	+	0.341688i
$97$	0.401170	−	1.23467i	0.0407326	−	0.125362i	−0.928622	−	0.371026i	$-0.879006\pi$
$97$	0.401170	−	1.23467i	0.0407326	−	0.125362i	0.969355	+	0.245664i	$0.0790060\pi$
$98$	6.64322	−	4.20661i	0.671067	−	0.424932i
$99$			0.890223i			0.0894708i
$100$	−4.28897	−	9.03354i	−0.428897	−	0.903354i
$101$		−	9.02480i		−	0.898001i	−0.893531	−	0.449001i	$-0.851780\pi$
$101$		−	9.02480i		−	0.898001i	0.893531	−	0.449001i	$-0.148220\pi$
$102$	−2.28893	−	3.61475i	−0.226638	−	0.357914i
$103$	0.0131643	−	0.0405154i	0.00129711	−	0.00399210i	−0.950406	−	0.311012i	$-0.899332\pi$
$103$	0.0131643	−	0.0405154i	0.00129711	−	0.00399210i	0.951703	+	0.307020i	$0.0993319\pi$
$104$	−0.883464	−	0.489144i	−0.0866308	−	0.0479645i
$105$	2.66116	−	0.343549i	0.259703	−	0.0335269i
$106$	−18.0093	+	4.60482i	−1.74922	+	0.447260i
$107$			1.56942i			0.151722i	0.997118	+	0.0758610i	$0.0241705\pi$
$107$			1.56942i			0.151722i	−0.997118	+	0.0758610i	$0.975829\pi$
$108$	1.96532	−	0.370835i	0.189113	−	0.0356836i
$109$	5.13562	−	7.06857i	0.491903	−	0.677047i	−0.488834	−	0.872377i	$-0.662578\pi$
$109$	5.13562	−	7.06857i	0.491903	−	0.677047i	0.980738	+	0.195330i	$0.0625778\pi$
$110$	−2.80927	+	0.181607i	−0.267853	+	0.0173156i
$111$	6.73581	−	4.89385i	0.639335	−	0.464504i
$112$	−3.04479	−	3.71062i	−0.287706	−	0.350621i
$113$	2.98687	+	2.17009i	0.280981	+	0.204145i	0.719345	−	0.694653i	$-0.244442\pi$
$113$	2.98687	+	2.17009i	0.280981	+	0.204145i	−0.438364	+	0.898798i	$0.644442\pi$
$114$	−1.79492	+	1.13658i	−0.168110	+	0.106450i
$115$	−3.04464	+	5.57409i	−0.283914	+	0.519787i
$116$	9.36051	−	9.92809i	0.869102	−	0.921800i
$117$	−0.339557	+	0.110329i	−0.0313921	+	0.0101999i
$118$	0.893122	−	13.9729i	0.0822185	−	1.28631i
$119$	1.12185	+	3.45270i	0.102840	+	0.316509i
$120$	1.57117	+	6.12629i	0.143428	+	0.559251i
$121$	3.15429	−	9.70791i	0.286754	−	0.882537i
$122$	−3.02719	−	1.20205i	−0.274069	−	0.108829i
$123$	−3.62877	−	4.99458i	−0.327196	−	0.450346i
$124$	−19.4058	−	2.49094i	−1.74269	−	0.223693i
$125$	2.69187	−	10.8514i	0.240768	−	0.970583i
$126$	−1.69358	−	0.108250i	−0.150876	−	0.00964370i
$127$	−12.9857	+	9.43469i	−1.15230	+	0.837193i	−0.988785	−	0.149348i	$-0.952283\pi$
$127$	−12.9857	+	9.43469i	−1.15230	+	0.837193i	−0.163513	+	0.986541i	$0.552283\pi$
$128$	7.80227	−	8.19296i	0.689630	−	0.724162i
$129$	−1.74473	+	5.36972i	−0.153615	+	0.472778i
$130$	−0.417434	−	1.04903i	−0.0366114	−	0.0920060i
$131$	−8.55387	+	2.77932i	−0.747355	+	0.242830i	−0.657843	−	0.753155i	$-0.728531\pi$
$131$	−8.55387	+	2.77932i	−0.747355	+	0.242830i	−0.0895125	+	0.995986i	$0.528531\pi$
$132$	1.76596	+	0.226679i	0.153707	+	0.0197299i
$133$	1.71446	−	0.557061i	0.148662	−	0.0483033i
$134$	1.47558	−	1.78004i	0.127471	−	0.153772i
$135$	1.96241	+	1.07189i	0.168897	+	0.0922539i
$136$	−7.75350	+	3.62017i	−0.664857	+	0.310427i
$137$	−14.1199	−	10.2587i	−1.20635	−	0.876461i	−0.211452	−	0.977388i	$-0.567819\pi$
$137$	−14.1199	−	10.2587i	−1.20635	−	0.876461i	−0.994894	+	0.100927i	$0.967819\pi$
$138$	2.56361	−	3.09258i	0.218229	−	0.263258i
$139$	−6.49106	−	8.93418i	−0.550565	−	0.757787i	0.439524	−	0.898231i	$-0.355147\pi$
$139$	−6.49106	−	8.93418i	−0.550565	−	0.757787i	−0.990089	+	0.140443i	$0.955147\pi$
$140$	−0.00388924	−	5.36650i	−0.000328701	−	0.453552i
$141$	−2.54313	+	3.50032i	−0.214170	+	0.294780i
$142$	3.03226	+	11.8591i	0.254462	+	0.995191i
$143$	−0.317838			−0.0265789
$144$	−0.235202	−	3.99308i	−0.0196002	−	0.332757i
$145$	15.1300	−	1.95324i	1.25648	−	0.162208i
$146$	−0.134566	+	0.338886i	−0.0111368	+	0.0280464i
$147$	−5.28791	−	1.71815i	−0.436139	−	0.141710i
$148$	−7.99290	−	14.6081i	−0.657013	−	1.20078i
$149$			3.06306i			0.250936i	0.992098	+	0.125468i	$0.0400432\pi$
$149$			3.06306i			0.250936i	−0.992098	+	0.125468i	$0.959957\pi$
$150$	−2.98223	+	6.41142i	−0.243498	+	0.523490i
$151$	−7.34602			−0.597810			−0.298905	−	0.954283i	$-0.596621\pi$
$151$	−7.34602			−0.597810			−0.298905	+	0.954283i	$0.596621\pi$
$152$	1.79761	+	3.85004i	0.145806	+	0.312280i
$153$	−0.934888	+	2.87729i	−0.0755812	+	0.232615i
$154$	−1.40409	−	0.557544i	−0.113145	−	0.0449282i
$155$	−15.0174	−	15.9049i	−1.20623	−	1.27751i
$156$	0.132400	+	0.701681i	0.0106005	+	0.0561794i
$157$		−	11.2164i		−	0.895165i	−0.894243	−	0.447582i	$-0.852285\pi$
$157$		−	11.2164i		−	0.895165i	0.894243	−	0.447582i	$-0.147715\pi$
$158$	−1.81764	−	7.10874i	−0.144604	−	0.565541i
$159$	10.6339	+	7.72595i	0.843320	+	0.612708i
$160$	12.5529	−	1.55682i	0.992397	−	0.123078i
$161$	−2.75752	+	2.00345i	−0.217323	+	0.157894i
$162$	−1.08877	−	0.902542i	−0.0855418	−	0.0709104i
$163$	−3.58955	+	4.94059i	−0.281155	+	0.386977i	−0.926116	−	0.377238i	$-0.876874\pi$
$163$	−3.58955	+	4.94059i	−0.281155	+	0.386977i	0.644961	+	0.764216i	$0.276874\pi$
$164$	−10.8319	+	5.92671i	−0.845827	+	0.462798i
$165$	1.36661	+	1.44737i	0.106390	+	0.112677i
$166$	3.54574	−	4.27736i	0.275203	−	0.331987i
$167$	0.950709	+	2.92598i	0.0735681	+	0.226419i	0.981079	−	0.193610i	$-0.0620197\pi$
$167$	0.950709	+	2.92598i	0.0735681	+	0.226419i	−0.907510	+	0.420030i	$0.862020\pi$
$168$	−0.645978	+	3.33203i	−0.0498383	+	0.257072i
$169$	3.97783	+	12.2425i	0.305987	+	0.941731i
$170$	−9.27055	−	2.36324i	−0.711019	−	0.181253i
$171$	1.42873	+	0.464223i	0.109258	+	0.0355000i
$172$	10.2078	+	4.82836i	0.778337	+	0.368159i
$173$	−4.97362	−	6.84560i	−0.378137	−	0.520461i	0.576952	−	0.816778i	$-0.304242\pi$
$173$	−4.97362	−	6.84560i	−0.378137	−	0.520461i	−0.955090	+	0.296316i	$0.904242\pi$
$174$	−9.62883	−	0.615456i	−0.729960	−	0.0466576i
$175$	3.79926	−	4.64379i	0.287197	−	0.351037i
$176$	0.899338	−	3.44545i	0.0677902	−	0.259711i
$177$	−8.00968	+	5.81937i	−0.602045	+	0.437411i
$178$	7.30942	−	18.4077i	0.547864	−	1.37972i
$179$	−12.3543	−	4.01417i	−0.923407	−	0.300033i	−0.191543	−	0.981484i	$-0.561349\pi$
$179$	−12.3543	−	4.01417i	−0.923407	−	0.300033i	−0.731864	+	0.681451i	$0.761349\pi$
$180$	2.62603	−	3.61994i	0.195733	−	0.269814i
$181$	−11.9209	+	3.87333i	−0.886073	+	0.287902i	−0.716477	−	0.697611i	$-0.754246\pi$
$181$	−11.9209	+	3.87333i	−0.886073	+	0.287902i	−0.169596	+	0.985514i	$0.554246\pi$
$182$	0.0386487	−	0.604661i	0.00286483	−	0.0448204i
$183$	0.711707	+	2.19041i	0.0526109	+	0.161920i
$184$	−5.48204	−	5.87297i	−0.404142	−	0.432961i
$185$	3.43872	−	18.2970i	0.252820	−	1.34522i
$186$	7.40126	+	11.6883i	0.542687	+	0.857029i
$187$	−1.58305	+	2.17888i	−0.115764	+	0.159336i
$188$	6.29611	+	5.93617i	0.459191	+	0.432940i
$189$	0.705334	+	0.970808i	0.0513055	+	0.0706159i
$190$	−1.17348	+	4.60334i	−0.0851332	+	0.333961i
$191$	−20.7473	−	15.0738i	−1.50122	−	1.09070i	−0.969892	−	0.243534i	$-0.921693\pi$
$191$	−20.7473	−	15.0738i	−1.50122	−	1.09070i	−0.531328	−	0.847166i	$-0.678307\pi$
$192$	−7.98106	−	0.550189i	−0.575983	−	0.0397065i
$193$	17.3497			1.24886			0.624429	−	0.781082i	$-0.285332\pi$
$193$	17.3497			1.24886			0.624429	+	0.781082i	$0.285332\pi$
$194$	0.454805	+	1.77873i	0.0326531	+	0.127705i
$195$	−0.382700	+	0.700641i	−0.0274057	+	0.0501739i
$196$	−4.75480	+	10.0523i	−0.339628	+	0.718018i
$197$	−7.52964	−	2.44653i	−0.536465	−	0.174308i	0.0282398	−	0.999601i	$-0.491010\pi$
$197$	−7.52964	−	2.44653i	−0.536465	−	0.174308i	−0.564704	+	0.825293i	$0.691010\pi$
$198$	−0.673525	−	1.06365i	−0.0478653	−	0.0755906i
$199$	3.77605			0.267677			0.133838	−	0.991003i	$-0.457270\pi$
$199$	3.77605			0.267677			0.133838	+	0.991003i	$0.457270\pi$
$200$	11.9591	+	7.54847i	0.845638	+	0.533758i
$201$	−1.63491			−0.115318
$202$	6.82798	+	10.7830i	0.480415	+	0.758688i
$203$	7.78621	+	2.52989i	0.546485	+	0.177564i
$204$	5.46970	+	2.58721i	0.382955	+	0.181141i
$205$	−13.5672	−	2.54980i	−0.947571	−	0.178086i
$206$	0.0149243	+	0.0583683i	0.00103982	+	0.00406671i
$207$	−2.84044			−0.197424
$208$	1.42565	−	0.0839745i	0.0988513	−	0.00582258i
$209$	1.08193	+	0.786072i	0.0748390	+	0.0543737i
$210$	−2.91968	+	2.42386i	−0.201477	+	0.167262i
$211$	2.63847	+	3.63154i	0.181640	+	0.250006i	0.890121	−	0.455724i	$-0.150619\pi$
$211$	2.63847	+	3.63154i	0.181640	+	0.250006i	−0.708482	+	0.705729i	$0.750619\pi$
$212$	18.0339	−	19.1274i	1.23857	−	1.31367i
$213$	5.08752	−	7.00237i	0.348591	−	0.479794i
$214$	−1.18739	−	1.87517i	−0.0811686	−	0.128184i
$215$	5.40655	+	11.4087i	0.368723	+	0.778070i
$216$	−2.06763	+	1.93000i	−0.140684	+	0.131320i
$217$	−3.62751	−	11.1643i	−0.246252	−	0.757885i
$218$	−0.788183	+	12.3312i	−0.0533825	+	0.835171i
$219$	0.245210	−	0.0796735i	0.0165698	−	0.00538384i
$220$	3.21916	−	2.34242i	0.217036	−	0.157926i
$221$	−1.02728	−	0.333784i	−0.0691025	−	0.0224528i
$222$	−4.34547	+	10.9434i	−0.291649	+	0.734475i
$223$	−19.5689	+	14.2176i	−1.31043	+	0.952084i	−0.310432	+	0.950595i	$0.600474\pi$
$223$	−19.5689	+	14.2176i	−1.31043	+	0.952084i	−0.999999	+	0.00148865i	$0.999526\pi$
$224$	6.44534	+	2.12988i	0.430648	+	0.142309i
$225$	4.83607	−	1.26981i	0.322405	−	0.0846540i
$226$	−5.21061	−	0.333052i	−0.346605	−	0.0221543i
$227$	13.8895	+	19.1173i	0.921881	+	1.26886i	0.962943	+	0.269704i	$0.0869257\pi$
$227$	13.8895	+	19.1173i	0.921881	+	1.26886i	−0.0410625	+	0.999157i	$0.513074\pi$
$228$	1.28469	−	2.71601i	0.0850808	−	0.179872i
$229$	15.7791	+	5.12695i	1.04271	+	0.338798i	0.779805	−	0.626023i	$-0.215318\pi$
$229$	15.7791	+	5.12695i	1.04271	+	0.338798i	0.262909	+	0.964821i	$0.415318\pi$
$230$	−0.579454	−	8.96353i	−0.0382081	−	0.591038i
$231$	0.330109	+	1.01597i	0.0217196	+	0.0668460i
$232$	−3.67270	+	18.9442i	−0.241125	+	1.24375i
$233$	−2.21629	−	6.82105i	−0.145194	−	0.446862i	0.851842	−	0.523799i	$-0.175486\pi$
$233$	−2.21629	−	6.82105i	−0.145194	−	0.446862i	−0.997036	+	0.0769375i	$0.975486\pi$
$234$	0.322236	−	0.388725i	0.0210652	−	0.0254117i
$235$	1.23869	+	9.59503i	0.0808033	+	0.625911i
$236$	9.50451	+	17.3708i	0.618691	+	1.13074i
$237$	−3.04964	+	4.19747i	−0.198095	+	0.272655i
$238$	−3.95265	−	3.27658i	−0.256212	−	0.212389i
$239$	6.51199	−	4.73124i	0.421226	−	0.306038i	−0.356905	−	0.934141i	$-0.616168\pi$
$239$	6.51199	−	4.73124i	0.421226	−	0.306038i	0.778131	+	0.628102i	$0.216168\pi$
$240$	−6.51229	−	6.13108i	−0.420366	−	0.395759i
$241$	12.7492	+	9.26287i	0.821251	+	0.596674i	0.917071	−	0.398725i	$-0.130547\pi$
$241$	12.7492	+	9.26287i	0.821251	+	0.596674i	−0.0958195	+	0.995399i	$0.530547\pi$
$242$	3.57601	+	13.9856i	0.229875	+	0.899032i
$243$			1.00000i			0.0641500i
$244$	4.52639	−	0.854082i	0.289772	−	0.0546770i
$245$	−11.2349	+	5.32417i	−0.717772	+	0.340149i
$246$	8.11452	+	3.22215i	0.517363	+	0.205437i
$247$	−0.165742	+	0.510102i	−0.0105459	+	0.0324570i
$248$	25.0710	−	11.7058i	1.59201	−	0.743321i
$249$	−3.92862			−0.248966
$250$	4.99369	+	15.0021i	0.315829	+	0.948816i
$251$		−	4.77894i		−	0.301644i	−0.988561	−	0.150822i	$-0.951808\pi$
$251$		−	4.77894i		−	0.301644i	0.988561	−	0.150822i	$-0.0481920\pi$
$252$	2.10542	−	1.15199i	0.132629	−	0.0725685i
$253$	−2.40486	−	0.781387i	−0.151192	−	0.0491254i
$254$	8.37748	−	21.0975i	0.525650	−	1.32377i
$255$	2.89702	+	6.11321i	0.181418	+	0.382824i
$256$	−3.12366	+	15.6921i	−0.195228	+	0.980758i
$257$	−24.5585			−1.53192			−0.765958	−	0.642890i	$-0.777735\pi$
$257$	−24.5585			−1.53192			−0.765958	+	0.642890i	$0.777735\pi$
$258$	−1.97799	−	7.73586i	−0.123145	−	0.481614i
$259$	5.87255	−	8.08287i	0.364903	−	0.502245i
$260$	1.29243	+	0.937576i	0.0801532	+	0.0581460i
$261$	4.01017	+	5.51952i	0.248223	+	0.341650i
$262$	8.11753	−	9.79247i	0.501503	−	0.604981i
$263$	−14.5961	−	10.6047i	−0.900036	−	0.653914i	0.0384396	−	0.999261i	$-0.487761\pi$
$263$	−14.5961	−	10.6047i	−0.900036	−	0.653914i	−0.938475	+	0.345347i	$0.887761\pi$
$264$	−2.28150	+	1.06525i	−0.140416	+	0.0655615i
$265$	29.1494	−	3.76310i	1.79063	−	0.231166i
$266$	−1.62700	+	1.96271i	−0.0997579	+	0.120341i
$267$	−13.3194	+	4.32774i	−0.815134	+	0.264853i
$268$	−0.416301	+	3.24322i	−0.0254296	+	0.198111i
$269$	−20.7693	+	6.74836i	−1.26633	+	0.411455i	−0.863745	−	0.503929i	$-0.831887\pi$
$269$	−20.7693	+	6.74836i	−1.26633	+	0.411455i	−0.402583	+	0.915384i	$0.631887\pi$
$270$	−3.15569	+	0.204002i	−0.192049	+	0.0124152i
$271$	3.54113	−	10.8985i	0.215108	−	0.662035i	−0.784038	−	0.620713i	$-0.786843\pi$
$271$	3.54113	−	10.8985i	0.215108	−	0.662035i	0.999146	−	0.0413219i	$-0.0131569\pi$
$272$	6.52507	−	10.1916i	0.395640	−	0.617956i
$273$	−0.346609	+	0.251826i	−0.0209777	+	0.0152412i
$274$	24.6322	+	1.57444i	1.48809	+	0.0951157i
$275$	4.44379	+	0.255287i	0.267971	+	0.0153944i
$276$	−0.723265	+	5.63464i	−0.0435355	+	0.339165i
$277$	12.2885	+	16.9136i	0.738342	+	1.01624i	0.998712	+	0.0507322i	$0.0161555\pi$
$277$	12.2885	+	16.9136i	0.738342	+	1.01624i	−0.260370	+	0.965509i	$0.583845\pi$
$278$	14.5151	+	5.76370i	0.870555	+	0.345684i
$279$	3.02296	−	9.30373i	0.180980	−	0.557000i
$280$	4.06483	+	6.40904i	0.242920	+	0.383013i
$281$	−1.21159	−	3.72889i	−0.0722774	−	0.222447i	0.908392	−	0.418120i	$-0.137311\pi$
$281$	−1.21159	−	3.72889i	−0.0722774	−	0.222447i	−0.980669	+	0.195673i	$0.937311\pi$
$282$	0.390304	−	6.10633i	0.0232423	−	0.363626i
$283$	−26.5374	+	8.62252i	−1.57748	+	0.512556i	−0.961407	−	0.275131i	$-0.911279\pi$
$283$	−26.5374	+	8.62252i	−1.57748	+	0.512556i	−0.616077	+	0.787686i	$0.711279\pi$
$284$	−12.5953	−	11.8753i	−0.747395	−	0.704667i
$285$	3.03554	−	1.43853i	0.179810	−	0.0852111i
$286$	0.379758	−	0.240469i	0.0224555	−	0.0142193i
$287$	−5.99342	−	4.35448i	−0.353780	−	0.257037i
$288$	3.30211	+	4.59305i	0.194578	+	0.270648i
$289$	6.34851	−	4.61246i	0.373442	−	0.271321i
$290$	−16.5998	+	13.7808i	−0.974775	+	0.809239i
$291$	0.763070	−	1.05028i	0.0447320	−	0.0615683i
$292$	−0.0956121	−	0.506716i	−0.00559527	−	0.0296533i
$293$			21.3016i			1.24445i	0.782838	+	0.622225i	$0.213771\pi$
$293$			21.3016i			1.24445i	−0.782838	+	0.622225i	$0.786229\pi$
$294$	7.61799	−	1.94786i	0.444290	−	0.113601i
$295$	−4.08905	+	21.7573i	−0.238074	+	1.26676i
$296$	20.6023	+	11.4068i	1.19748	+	0.663004i
$297$	−0.275094	+	0.846653i	−0.0159626	+	0.0491278i
$298$	−2.31745	−	3.65979i	−0.134246	−	0.212006i
$299$		−	1.01412i		−	0.0586483i
$300$	−1.28753	−	9.91677i	−0.0743358	−	0.572545i
$301$			6.77519i			0.390516i
$302$	8.77714	−	5.55785i	0.505068	−	0.319818i
$303$	2.78882	−	8.58310i	0.160213	−	0.493086i
$304$	−5.06068	−	3.24006i	−0.290250	−	0.185830i
$305$	4.51968	+	2.46871i	0.258796	+	0.141358i
$306$	−1.05988	−	4.14515i	−0.0605893	−	0.236962i
$307$		−	17.8908i		−	1.02108i	−0.859853	−	0.510542i	$-0.829445\pi$
$307$		−	17.8908i		−	1.02108i	0.859853	−	0.510542i	$-0.170555\pi$
$308$	2.09946	−	0.396147i	0.119628	−	0.0225725i
$309$	0.0250399	−	0.0344645i	0.00142447	−	0.00196062i
$310$	29.9764	+	7.64156i	1.70254	+	0.434012i
$311$	16.6338	−	12.0852i	0.943217	−	0.685287i	−0.00597607	−	0.999982i	$-0.501902\pi$
$311$	16.6338	−	12.0852i	0.943217	−	0.685287i	0.949193	+	0.314695i	$0.101902\pi$
$312$	−0.689071	−	0.738209i	−0.0390110	−	0.0417928i
$313$	15.7992	+	11.4788i	0.893025	+	0.648821i	0.936665	−	0.350226i	$-0.113895\pi$
$313$	15.7992	+	11.4788i	0.893025	+	0.648821i	−0.0436396	+	0.999047i	$0.513895\pi$
$314$	8.48609	+	13.4015i	0.478898	+	0.756292i
$315$	2.63708	+	0.495611i	0.148583	+	0.0279245i
$316$	7.55008	+	7.11845i	0.424725	+	0.400444i
$317$	−0.864173	+	0.280787i	−0.0485368	+	0.0157706i	−0.333185	−	0.942862i	$-0.608123\pi$
$317$	−0.864173	+	0.280787i	−0.0485368	+	0.0157706i	0.284648	+	0.958632i	$0.408123\pi$
$318$	−18.5508	−	1.18573i	−1.04028	−	0.0664925i
$319$	1.87683	+	5.77629i	0.105082	+	0.323410i
$320$	−13.8206	+	11.3574i	−0.772595	+	0.634899i
$321$	−0.484979	+	1.49261i	−0.0270689	+	0.0833094i
$322$	1.77896	−	4.48004i	0.0991373	−	0.249663i
$323$	2.67141	+	3.67688i	0.148641	+	0.204587i
$324$	1.98372	+	0.254632i	0.110207	+	0.0141462i
$325$	0.453362	+	1.72663i	0.0251480	+	0.0957761i
$326$	0.550902	−	8.61889i	0.0305117	−	0.477356i
$327$	7.06857	−	5.13562i	0.390893	−	0.284000i
$328$	8.45807	−	15.2765i	0.467019	−	0.843504i
$329$	−1.60439	+	4.93779i	−0.0884526	+	0.272229i
$330$	−2.72789	−	0.695393i	−0.150166	−	0.0382801i
$331$	−8.40470	+	2.73085i	−0.461964	+	0.150101i	−0.530747	−	0.847530i	$-0.678089\pi$
$331$	−8.40470	+	2.73085i	−0.461964	+	0.150101i	0.0687826	+	0.997632i	$0.478089\pi$
$332$	−1.00035	+	7.79330i	−0.0549014	+	0.427713i
$333$	7.91842	−	2.57285i	0.433927	−	0.140991i
$334$	−3.34966	−	2.77672i	−0.183285	−	0.151936i
$335$	−2.65812	+	2.50980i	−0.145229	+	0.137125i
$336$	−1.74912	−	4.46990i	−0.0954224	−	0.243853i
$337$	−7.90164	−	5.74088i	−0.430430	−	0.312726i	0.351391	−	0.936229i	$-0.385709\pi$
$337$	−7.90164	−	5.74088i	−0.430430	−	0.312726i	−0.781821	+	0.623503i	$0.785709\pi$
$338$	−14.0152	−	11.6180i	−0.762327	−	0.631936i
$339$	2.17009	+	2.98687i	0.117863	+	0.162225i
$340$	12.8646	−	4.19027i	0.697681	−	0.227249i
$341$	5.11880	−	7.04543i	0.277199	−	0.381531i
$342$	−2.05830	+	0.526288i	−0.111300	+	0.0284584i
$343$	−15.0719			−0.813804
$344$	−15.8495	+	1.95400i	−0.854547	+	0.105352i
$345$	−4.61812	+	4.36043i	−0.248631	+	0.234758i
$346$	11.1218	+	4.41630i	0.597912	+	0.237422i
$347$	13.4040	+	4.35523i	0.719565	+	0.233801i	0.645835	−	0.763477i	$-0.276510\pi$
$347$	13.4040	+	4.35523i	0.719565	+	0.233801i	0.0737303	+	0.997278i	$0.476510\pi$
$348$	11.9703	−	6.54962i	0.641677	−	0.351097i
$349$		−	26.7074i		−	1.42962i	−0.699321	−	0.714808i	$-0.746514\pi$
$349$		−	26.7074i		−	1.42962i	0.699321	−	0.714808i	$-0.253486\pi$
$350$	−1.02602	+	8.42292i	−0.0548433	+	0.450224i
$351$	−0.357031			−0.0190569
$352$	1.53222	+	4.79711i	0.0816674	+	0.255687i
$353$	−6.95208	+	21.3963i	−0.370022	+	1.13881i	0.576755	+	0.816917i	$0.304319\pi$
$353$	−6.95208	+	21.3963i	−0.370022	+	1.13881i	−0.946776	+	0.321892i	$0.895681\pi$
$354$	5.16728	−	13.0130i	0.274638	−	0.691636i
$355$	−2.47799	−	19.1948i	−0.131518	−	1.01875i
$356$	5.19349	+	27.5240i	0.275255	+	1.45877i
$357$			3.63039i			0.192140i
$358$	17.7982	−	4.55085i	0.940665	−	0.240520i
$359$	26.1750	+	19.0172i	1.38146	+	1.00369i	0.996742	+	0.0806579i	$0.0257021\pi$
$359$	26.1750	+	19.0172i	1.38146	+	1.00369i	0.384720	+	0.923033i	$0.374298\pi$
$360$	−0.398856	+	6.31197i	−0.0210215	+	0.332670i
$361$	−13.5456	+	9.84142i	−0.712924	+	0.517969i
$362$	11.3128	−	13.6470i	0.594587	−	0.717272i
$363$	5.99982	−	8.25804i	0.314909	−	0.433435i
$364$	0.411296	+	0.751700i	0.0215578	+	0.0393998i
$365$	0.276365	−	0.505966i	0.0144656	−	0.0264835i
$366$	−2.50758	−	2.07867i	−0.131073	−	0.108654i
$367$	6.84476	+	21.0660i	0.357293	+	1.09964i	0.954668	+	0.297674i	$0.0962107\pi$
$367$	6.84476	+	21.0660i	0.357293	+	1.09964i	−0.597374	+	0.801963i	$0.703789\pi$
$368$	10.9934	+	2.86952i	0.573071	+	0.149584i
$369$	−1.90776	−	5.87148i	−0.0993140	−	0.305657i
$370$	9.73449	+	24.4632i	0.506072	+	1.27178i
$371$	15.0008	+	4.87407i	0.778805	+	0.253049i
$372$	−17.6863	−	8.36576i	−0.916992	−	0.433744i
$373$	−10.7791	−	14.8362i	−0.558123	−	0.768190i	0.432963	−	0.901412i	$-0.357468\pi$
$373$	−10.7791	−	14.8362i	−0.558123	−	0.768190i	−0.991086	+	0.133221i	$0.957468\pi$
$374$	0.242957	−	3.80107i	0.0125630	−	0.196549i
$375$	5.91340	−	9.48850i	0.305367	−	0.489984i
$376$	−12.0139	−	2.32912i	−0.619569	−	0.120115i
$377$	−1.97064	+	1.43176i	−0.101493	+	0.0737391i
$378$	−1.57724	−	0.626297i	−0.0811244	−	0.0322132i
$379$	33.6616	+	10.9373i	1.72908	+	0.561812i	0.993316	−	0.115428i	$-0.0368239\pi$
$379$	33.6616	+	10.9373i	1.72908	+	0.561812i	0.735763	+	0.677240i	$0.236824\pi$
$380$	−2.08070	−	6.38798i	−0.106738	−	0.327696i
$381$	−15.2656	+	4.96011i	−0.782083	+	0.254114i
$382$	36.1937	+	2.31343i	1.85183	+	0.118365i
$383$	−5.26298	−	16.1978i	−0.268926	−	0.827668i	−0.990763	−	0.135605i	$-0.956702\pi$
$383$	−5.26298	−	16.1978i	−0.268926	−	0.827668i	0.721837	−	0.692063i	$-0.243298\pi$
$384$	9.95216	−	5.38093i	0.507869	−	0.274595i
$385$	2.09635	+	1.14506i	0.106840	+	0.0583574i
$386$	−20.7297	+	13.1264i	−1.05511	+	0.668117i
$387$	−3.31867	+	4.56776i	−0.168698	+	0.232192i
$388$	−1.88916	−	1.78116i	−0.0959074	−	0.0904245i
$389$	10.7150	+	14.7479i	0.543272	+	0.747750i	0.989080	−	0.147379i	$-0.0470836\pi$
$389$	10.7150	+	14.7479i	0.543272	+	0.747750i	−0.445808	+	0.895129i	$0.647084\pi$
$390$	−0.0728351	−	1.12668i	−0.00368815	−	0.0570517i
$391$	−6.95216	−	5.05104i	−0.351586	−	0.255442i
$392$	−1.92422	−	15.6080i	−0.0971880	−	0.788322i
$393$	−8.99408			−0.453691
$394$	10.8475	−	2.77362i	0.546491	−	0.139733i
$395$	1.48540	+	11.5060i	0.0747384	+	0.578931i
$396$	1.60948	+	0.761296i	0.0808793	+	0.0382565i
$397$	−31.8102	−	10.3357i	−1.59651	−	0.518736i	−0.630266	−	0.776380i	$-0.717054\pi$
$397$	−31.8102	−	10.3357i	−1.59651	−	0.518736i	−0.966240	+	0.257643i	$0.917054\pi$
$398$	−4.51168	+	2.85688i	−0.226150	+	0.143203i
$399$	1.80269			0.0902473
$400$	−20.0000	+	0.0289891i	−0.999999	+	0.00144945i
$401$	−18.8872			−0.943179			−0.471590	−	0.881818i	$-0.656320\pi$
$401$	−18.8872			−0.943179			−0.471590	+	0.881818i	$0.656320\pi$
$402$	1.95342	−	1.23694i	0.0974278	−	0.0616931i
$403$	3.32172	+	1.07929i	0.165467	+	0.0537634i
$404$	−16.3164	−	7.71777i	−0.811770	−	0.383974i
$405$	1.53513	+	1.62585i	0.0762811	+	0.0807891i
$406$	−11.2172	+	2.86813i	−0.556698	+	0.142343i
$407$	7.41193			0.367396
$408$	−8.49271	+	1.04702i	−0.420452	+	0.0518353i
$409$	6.13013	+	4.45380i	0.303116	+	0.220226i	0.728937	−	0.684581i	$-0.240015\pi$
$409$	6.13013	+	4.45380i	0.303116	+	0.220226i	−0.425821	+	0.904807i	$0.640015\pi$
$410$	18.1394	−	7.21809i	0.895840	−	0.356476i
$411$	−10.2587	−	14.1199i	−0.506025	−	0.696484i
$412$	−0.0619921	−	0.0584480i	−0.00305413	−	0.00287953i
$413$	−6.98316	+	9.61150i	−0.343619	+	0.472951i
$414$	3.39380	−	2.14902i	0.166796	−	0.105618i
$415$	−6.38734	+	6.03093i	−0.313542	+	0.296047i
$416$	−1.63986	+	1.17896i	−0.0804008	+	0.0578030i
$417$	−3.41255	−	10.5028i	−0.167113	−	0.514322i
$418$	−1.88744	−	0.120641i	−0.0923177	−	0.00590077i
$419$	−22.1954	+	7.21172i	−1.08432	+	0.352316i	−0.796048	−	0.605234i	$-0.793079\pi$
$419$	−22.1954	+	7.21172i	−1.08432	+	0.352316i	−0.288268	+	0.957550i	$0.593079\pi$
$420$	1.65464	−	5.10504i	0.0807381	−	0.249101i
$421$	18.6087	+	6.04632i	0.906931	+	0.294680i	0.725095	−	0.688649i	$-0.241796\pi$
$421$	18.6087	+	6.04632i	0.906931	+	0.294680i	0.181836	+	0.983329i	$0.441796\pi$
$422$	−5.90004	−	2.34281i	−0.287209	−	0.114046i
$423$	−3.50032	+	2.54313i	−0.170191	+	0.123651i
$424$	−7.07579	+	36.4978i	−0.343631	+	1.77249i
$425$	14.0947	+	5.49186i	0.683692	+	0.266394i
$426$	−0.780801	+	12.2157i	−0.0378299	+	0.591851i
$427$	1.62448	+	2.23590i	0.0786139	+	0.108203i
$428$	2.83744	+	1.34213i	0.137153	+	0.0648743i
$429$	−0.302281	−	0.0982172i	−0.0145943	−	0.00474197i
$430$	−15.0915	−	9.54087i	−0.727775	−	0.460102i
$431$	−1.59072	−	4.89572i	−0.0766221	−	0.235819i	0.905408	−	0.424542i	$-0.139565\pi$
$431$	−1.59072	−	4.89572i	−0.0766221	−	0.235819i	−0.982030	+	0.188724i	$0.939565\pi$
$432$	1.01024	−	3.87033i	0.0486051	−	0.186211i
$433$	3.49806	+	10.7659i	0.168106	+	0.517377i	0.999252	−	0.0386775i	$-0.0123145\pi$
$433$	3.49806	+	10.7659i	0.168106	+	0.517377i	−0.831146	+	0.556055i	$0.812315\pi$
$434$	12.7809	+	10.5948i	0.613504	+	0.508568i
$435$	14.9931	+	2.81779i	0.718864	+	0.135103i
$436$	−8.38777	−	15.3298i	−0.401701	−	0.734164i
$437$	−2.50812	+	3.45213i	−0.119980	+	0.165138i
$438$	−0.232702	+	0.280716i	−0.0111189	+	0.0134131i
$439$	20.9506	−	15.2215i	0.999917	−	0.726482i	0.0378463	−	0.999284i	$-0.487950\pi$
$439$	20.9506	−	15.2215i	0.999917	−	0.726482i	0.962070	+	0.272802i	$0.0879503\pi$
$440$	−2.07408	+	5.23432i	−0.0988777	+	0.249536i
$441$	−4.49816	−	3.26811i	−0.214198	−	0.155624i
$442$	1.47995	−	0.378410i	0.0703940	−	0.0179991i
$443$		−	28.5698i		−	1.35739i	−0.734418	−	0.678697i	$-0.762545\pi$
$443$		−	28.5698i		−	1.35739i	0.734418	−	0.678697i	$-0.237455\pi$
$444$	−3.08754	−	16.3631i	−0.146528	−	0.776558i
$445$	−15.0117	+	27.4832i	−0.711623	+	1.30283i
$446$	12.6245	−	31.7929i	0.597786	−	1.50544i
$447$	−0.946537	+	2.91314i	−0.0447697	+	0.137787i
$448$	−9.31243	+	2.33160i	−0.439971	+	0.110158i
$449$	−8.52161			−0.402160			−0.201080	−	0.979575i	$-0.564445\pi$
$449$	−8.52161			−0.402160			−0.201080	+	0.979575i	$0.564445\pi$
$450$	−4.81751	+	5.17606i	−0.227099	+	0.244002i
$451$		−	5.49592i		−	0.258793i
$452$	6.47771	−	3.54431i	0.304686	−	0.166710i
$453$	−6.98648	−	2.27004i	−0.328253	−	0.106656i
$454$	−31.0592	−	12.3331i	−1.45768	−	0.578823i
$455$	−0.176948	+	0.941520i	−0.00829547	+	0.0441391i
$456$	0.519904	+	4.21710i	0.0243467	+	0.197484i
$457$	−18.3363			−0.857738			−0.428869	−	0.903367i	$-0.641088\pi$
$457$	−18.3363			−0.857738			−0.428869	+	0.903367i	$0.641088\pi$
$458$	−22.7321	+	5.81240i	−1.06220	+	0.271596i
$459$	−1.77826	+	2.44757i	−0.0830022	+	0.114243i
$460$	7.47397	+	10.2714i	0.348476	+	0.478905i
$461$	−22.8752	−	31.4850i	−1.06540	−	1.46640i	−0.874644	−	0.484766i	$-0.838905\pi$
$461$	−22.8752	−	31.4850i	−1.06540	−	1.46640i	−0.190760	−	0.981637i	$-0.561095\pi$
$462$	−1.16308	−	0.964145i	−0.0541115	−	0.0448561i
$463$	−14.3557	−	10.4301i	−0.667168	−	0.484726i	0.201908	−	0.979405i	$-0.435286\pi$
$463$	−14.3557	−	10.4301i	−0.667168	−	0.484726i	−0.869076	+	0.494678i	$0.835286\pi$
$464$	−9.94462	−	25.4136i	−0.461667	−	1.17980i
$465$	−9.36753	−	19.7671i	−0.434409	−	0.916677i
$466$	7.80873	+	6.47310i	0.361733	+	0.299861i
$467$	29.9026	−	9.71593i	1.38373	−	0.449600i	0.479833	−	0.877360i	$-0.340697\pi$
$467$	29.9026	−	9.71593i	1.38373	−	0.449600i	0.903892	+	0.427760i	$0.140697\pi$
$468$	−0.0909115	+	0.708252i	−0.00420239	+	0.0327389i
$469$	−1.86585	+	0.606252i	−0.0861570	+	0.0279941i
$470$	−8.73941	−	10.5271i	−0.403119	−	0.485580i
$471$	3.46605	−	10.6674i	0.159707	−	0.491529i
$472$	−24.4985	−	13.5640i	−1.12764	−	0.624334i
$473$	−4.06633	+	2.95436i	−0.186970	+	0.135842i
$474$	0.468040	−	7.32250i	0.0214978	−	0.336333i
$475$	2.72701	−	6.99878i	0.125124	−	0.321126i
$476$	7.20169	+	0.924412i	0.330089	+	0.0423704i
$477$	7.72595	+	10.6339i	0.353747	+	0.486891i
$478$	−4.20108	+	10.5798i	−0.192153	+	0.483909i
$479$	5.09633	−	15.6849i	0.232857	−	0.716662i	−0.764541	−	0.644575i	$-0.777034\pi$
$479$	5.09633	−	15.6849i	0.232857	−	0.716662i	0.997398	−	0.0720864i	$-0.0229657\pi$
$480$	12.4196	+	2.39845i	0.566876	+	0.109474i
$481$	0.918588	+	2.82712i	0.0418840	+	0.128906i
$482$	−22.2411	−	1.42161i	−1.01305	−	0.0647525i
$483$	−3.24166	+	1.05328i	−0.147501	+	0.0479258i
$484$	−14.8539	−	14.0047i	−0.675179	−	0.636580i
$485$	−0.371671	−	2.87900i	−0.0168767	−	0.130729i
$486$	−0.756580	−	1.19482i	−0.0343192	−	0.0541980i
$487$	−12.3288	−	8.95738i	−0.558670	−	0.405897i	0.272302	−	0.962212i	$-0.412215\pi$
$487$	−12.3288	−	8.95738i	−0.558670	−	0.405897i	−0.830972	+	0.556314i	$0.812215\pi$
$488$	−4.76202	+	4.44505i	−0.215567	+	0.201218i
$489$	−4.94059	+	3.58955i	−0.223421	+	0.162325i
$490$	9.39550	−	14.8615i	0.424445	−	0.671375i
$491$	15.5840	−	21.4496i	0.703297	−	0.968005i	−0.296618	−	0.954996i	$-0.595859\pi$
$491$	15.5840	−	21.4496i	0.703297	−	0.968005i	0.999915	−	0.0130091i	$-0.00414106\pi$
$492$	−12.1332	+	2.28940i	−0.547006	+	0.103214i
$493$			20.6405i			0.929603i
$494$	−0.187901	−	0.734876i	−0.00845408	−	0.0330636i
$495$	0.852458	+	1.79883i	0.0383151	+	0.0808516i
$496$	−21.0988	+	32.9545i	−0.947366	+	1.47970i
$497$	3.20956	−	9.87801i	0.143968	−	0.443089i
$498$	4.69398	−	2.97231i	0.210342	−	0.133193i
$499$		−	42.6525i		−	1.90939i	−0.297589	−	0.954694i	$-0.596182\pi$
$499$		−	42.6525i		−	1.90939i	0.297589	−	0.954694i	$-0.403818\pi$
$500$	−17.3168	−	14.1466i	−0.774432	−	0.632657i
$501$			3.07656i			0.137451i
$502$	3.61565	+	5.70995i	0.161374	+	0.254848i
$503$	−10.8538	+	33.4046i	−0.483947	+	1.48944i	0.349553	+	0.936917i	$0.386334\pi$
$503$	−10.8538	+	33.4046i	−0.483947	+	1.48944i	−0.833500	+	0.552520i	$0.813666\pi$
$504$	−1.64402	+	2.96933i	−0.0732303	+	0.132265i
$505$	−8.64195	−	18.2360i	−0.384562	−	0.811492i
$506$	3.46455	−	0.885856i	0.154018	−	0.0393811i
$507$			12.8725i			0.571689i
$508$	5.95237	+	31.5458i	0.264094	+	1.39962i
$509$	−11.6008	+	15.9672i	−0.514198	+	0.707733i	−0.984620	−	0.174709i	$-0.944102\pi$
$509$	−11.6008	+	15.9672i	−0.514198	+	0.707733i	0.470422	+	0.882441i	$0.344102\pi$
$510$	−8.08654	−	5.11234i	−0.358078	−	0.226378i
$511$	0.250303	−	0.181855i	0.0110727	−	0.00804481i
$512$	−8.14015	−	21.1125i	−0.359747	−	0.933050i
$513$	1.21535	+	0.883005i	0.0536591	+	0.0389856i
$514$	29.3429	−	18.5805i	1.29426	−	0.819549i
$515$	−0.0121963	−	0.0944735i	−0.000537432	−	0.00416300i
$516$	8.21614	+	7.74643i	0.361695	+	0.341017i
$517$	−3.66316	+	1.19023i	−0.161105	+	0.0523463i
$518$	−0.901283	+	14.1006i	−0.0396001	+	0.619545i
$519$	−2.61479	−	8.04749i	−0.114776	−	0.353246i
$520$	−2.25357	−	0.142404i	−0.0988256	−	0.00624482i
$521$	−8.23015	+	25.3298i	−0.360570	+	1.10972i	0.592140	+	0.805835i	$0.298283\pi$
$521$	−8.23015	+	25.3298i	−0.360570	+	1.10972i	−0.952709	+	0.303884i	$0.901717\pi$
$522$	−8.96737	−	3.56080i	−0.392491	−	0.155852i
$523$	19.4523	+	26.7738i	0.850589	+	1.17073i	0.983733	+	0.179638i	$0.0574927\pi$
$523$	19.4523	+	26.7738i	0.850589	+	1.17073i	−0.133144	+	0.991097i	$0.542507\pi$
$524$	−2.29018	+	17.8418i	−0.100047	+	0.779421i
$525$	5.04832	−	3.24247i	0.220327	−	0.141513i
$526$	25.4630	+	1.62754i	1.11024	+	0.0709643i
$527$	23.9434	−	17.3959i	1.04299	−	0.757777i
$528$	1.92003	−	2.99891i	0.0835584	−	0.130511i
$529$	−4.61422	+	14.2011i	−0.200618	+	0.617439i
$530$	−31.9811	+	26.5500i	−1.38917	+	1.15326i
$531$	−9.41595	+	3.05943i	−0.408617	+	0.132768i
$532$	0.459022	−	3.57604i	0.0199011	−	0.155041i
$533$	2.09630	−	0.681130i	0.0908009	−	0.0295030i
$534$	12.6400	−	15.2480i	0.546985	−	0.659847i
$535$	1.50285	+	3.17126i	0.0649737	+	0.137106i
$536$	−1.95635	−	4.19001i	−0.0845014	−	0.180981i
$537$	−10.5092	−	7.63541i	−0.453507	−	0.329492i
$538$	19.7099	−	23.7767i	0.849752	−	1.02509i
$539$	−2.90934	−	4.00437i	−0.125314	−	0.172480i
$540$	3.61613	−	2.63128i	0.155613	−	0.113232i
$541$	5.97099	−	8.21837i	0.256713	−	0.353335i	−0.661135	−	0.750267i	$-0.729925\pi$
$541$	5.97099	−	8.21837i	0.256713	−	0.353335i	0.917848	+	0.396932i	$0.129925\pi$
$542$	4.01457	+	15.7008i	0.172440	+	0.674408i
$543$	−12.5344			−0.537901
$544$	−0.0855143	+	17.1138i	−0.00366640	+	0.733749i
$545$	3.60860	−	19.2009i	0.154575	−	0.822476i
$546$	0.223608	−	0.563123i	0.00956952	−	0.0240995i
$547$	−35.0642	−	11.3931i	−1.49924	−	0.487132i	−0.559442	−	0.828870i	$-0.688985\pi$
$547$	−35.0642	−	11.3931i	−1.49924	−	0.487132i	−0.939795	+	0.341738i	$0.888985\pi$
$548$	−30.6222	+	16.7551i	−1.30812	+	0.715742i
$549$			2.30313i			0.0982952i
$550$	−5.50266	+	3.05706i	−0.234634	+	0.130353i
$551$	10.2492			0.436629
$552$	−3.39889	−	7.27957i	−0.144666	−	0.309839i
$553$	−1.92392	+	5.92123i	−0.0818135	+	0.251796i
$554$	−27.4790	−	10.9115i	−1.16747	−	0.463584i
$555$	8.92450	−	16.3389i	0.378824	−	0.693546i
$556$	−21.7035	+	4.09523i	−0.920435	+	0.173676i
$557$			3.05713i			0.129535i	0.997900	+	0.0647673i	$0.0206305\pi$
$557$			3.05713i			0.129535i	−0.997900	+	0.0647673i	$0.979369\pi$
$558$	3.42713	+	13.4034i	0.145082	+	0.567410i
$559$	−1.63083	−	1.18487i	−0.0689769	−	0.0501147i
$560$	−9.70567	−	4.58226i	−0.410140	−	0.193636i
$561$	−2.17888	+	1.58305i	−0.0919925	+	0.0668364i
$562$	4.26883	+	3.53868i	0.180070	+	0.149270i
$563$	19.0940	−	26.2807i	0.804717	−	1.10760i	−0.187400	−	0.982284i	$-0.560006\pi$
$563$	19.0940	−	26.2807i	0.804717	−	1.10760i	0.992117	−	0.125314i	$-0.0399939\pi$
$564$	4.15358	+	7.59124i	0.174897	+	0.319649i
$565$	8.11347	+	1.52484i	0.341336	+	0.0641504i
$566$	25.1837	−	30.3800i	1.05855	−	1.27697i
$567$	0.370816	+	1.14125i	0.0155728	+	0.0479282i
$568$	24.0337	+	4.65939i	1.00843	+	0.195504i
$569$	6.90082	+	21.2386i	0.289298	+	0.890366i	0.985077	+	0.172111i	$0.0550589\pi$
$569$	6.90082	+	21.2386i	0.289298	+	0.890366i	−0.695780	+	0.718255i	$0.744941\pi$
$570$	−2.53856	+	4.01541i	−0.106328	+	0.168187i
$571$	40.5032	+	13.1603i	1.69501	+	0.550741i	0.987727	−	0.156191i	$-0.0499216\pi$
$571$	40.5032	+	13.1603i	1.69501	+	0.550741i	0.707281	+	0.706933i	$0.249922\pi$
$572$	−0.271806	+	0.574634i	−0.0113648	+	0.0240267i
$573$	−15.0738	−	20.7473i	−0.629716	−	0.866730i
$574$	10.4555	+	0.668298i	0.436406	+	0.0278942i
$575$	−0.814544	+	14.1788i	−0.0339689	+	0.591297i
$576$	−7.42042	−	2.98954i	−0.309184	−	0.124564i
$577$	9.56473	−	6.94918i	0.398185	−	0.289298i	−0.370616	−	0.928786i	$-0.620854\pi$
$577$	9.56473	−	6.94918i	0.398185	−	0.289298i	0.768801	+	0.639488i	$0.220854\pi$
$578$	−4.09561	+	10.3142i	−0.170355	+	0.429014i
$579$	16.5005	+	5.36134i	0.685738	+	0.222810i
$580$	9.40744	−	29.0247i	0.390623	−	1.20518i
$581$	−4.48355	+	1.45679i	−0.186009	+	0.0604380i
$582$	−0.117111	+	1.83221i	−0.00485442	+	0.0759476i
$583$	3.61588	+	11.1285i	0.149755	+	0.460897i
$584$	0.497610	+	0.533095i	0.0205913	+	0.0220596i
$585$	−0.580479	+	0.548089i	−0.0239998	+	0.0226607i
$586$	−16.1163	−	25.4515i	−0.665759	−	1.05139i
$587$	16.7702	−	23.0822i	0.692181	−	0.952705i	−0.307819	−	0.951445i	$-0.599599\pi$
$587$	16.7702	−	23.0822i	0.692181	−	0.952705i	0.999999	−	0.00125990i	$-0.000401038\pi$
$588$	−7.62840	+	8.09095i	−0.314590	+	0.333665i
$589$	−8.63802	−	11.8892i	−0.355923	−	0.489886i
$590$	−11.5755	−	29.0897i	−0.476555	−	1.19760i
$591$	−6.40509	−	4.65357i	−0.263470	−	0.191422i
$592$	−33.2461	+	1.95827i	−1.36640	+	0.0804845i
$593$	31.5447			1.29539			0.647693	−	0.761901i	$-0.275734\pi$
$593$	31.5447			1.29539			0.647693	+	0.761901i	$0.275734\pi$
$594$	−0.311873	−	1.21973i	−0.0127963	−	0.0500459i
$595$	5.57311	+	5.90246i	0.228475	+	0.241977i
$596$	5.53785	+	2.61945i	0.226839	+	0.107297i
$597$	3.59123	+	1.16686i	0.146979	+	0.0477565i
$598$	0.767266	+	1.21169i	0.0313758	+	0.0495498i
$599$	32.5134			1.32846			0.664230	−	0.747528i	$-0.268760\pi$
$599$	32.5134			1.32846			0.664230	+	0.747528i	$0.268760\pi$
$600$	9.04119	+	10.8746i	0.369105	+	0.443953i
$601$	36.4957			1.48869			0.744345	−	0.667795i	$-0.232762\pi$
$601$	36.4957			1.48869			0.744345	+	0.667795i	$0.232762\pi$
$602$	−5.12597	−	8.09511i	−0.208919	−	0.329932i
$603$	−1.55489	−	0.505216i	−0.0633202	−	0.0205740i
$604$	−6.28212	+	13.2812i	−0.255616	+	0.540405i
$605$	−2.92235	−	22.6368i	−0.118810	−	0.920317i
$606$	3.16167	+	12.3652i	0.128434	+	0.502302i
$607$	7.47915			0.303569			0.151785	−	0.988414i	$-0.451498\pi$
$607$	7.47915			0.303569			0.151785	+	0.988414i	$0.451498\pi$
$608$	8.49795	+	0.0424626i	0.344637	+	0.00172208i
$609$	6.62334	+	4.81214i	0.268391	+	0.194998i
$610$	−7.26797	+	0.469843i	−0.294271	+	0.0190234i
$611$	−0.907978	−	1.24972i	−0.0367329	−	0.0505584i
$612$	4.40250	+	4.15081i	0.177960	+	0.167787i
$613$	−10.4658	+	14.4049i	−0.422710	+	0.581810i	−0.966261	−	0.257566i	$-0.917080\pi$
$613$	−10.4658	+	14.4049i	−0.422710	+	0.581810i	0.543551	+	0.839376i	$0.317080\pi$
$614$	13.5359	+	21.3763i	0.546263	+	0.862676i
$615$	−12.1152	−	6.61748i	−0.488532	−	0.266843i
$616$	−2.20876	+	2.06173i	−0.0889933	+	0.0830696i
$617$	−11.7372	−	36.1233i	−0.472521	−	1.45427i	−0.849272	−	0.527955i	$-0.822959\pi$
$617$	−11.7372	−	36.1233i	−0.472521	−	1.45427i	0.376752	−	0.926314i	$-0.377041\pi$
$618$	−0.00384297	+	0.0601234i	−0.000154587	+	0.00241852i
$619$	44.4253	−	14.4347i	1.78561	−	0.580178i	0.786314	−	0.617827i	$-0.211987\pi$
$619$	44.4253	−	14.4347i	1.78561	−	0.580178i	0.999291	+	0.0376486i	$0.0119868\pi$
$620$	−41.5977	+	13.5493i	−1.67061	+	0.544151i
$621$	−2.70141	−	0.877743i	−0.108404	−	0.0352226i
$622$	−10.7310	+	27.0244i	−0.430272	+	1.08358i
$623$	−13.5960	+	9.87809i	−0.544713	+	0.395757i
$624$	1.38183	+	0.360687i	0.0553174	+	0.0144390i
$625$	−4.95177	−	24.5047i	−0.198071	−	0.980188i
$626$	−27.5618	−	1.76170i	−1.10159	−	0.0704116i
$627$	0.786072	+	1.08193i	0.0313927	+	0.0432083i
$628$	−20.2786	−	9.59196i	−0.809206	−	0.382761i
$629$	23.9561	+	7.78380i	0.955191	+	0.310360i
$630$	−3.52580	+	1.40300i	−0.140471	+	0.0558968i
$631$	−5.91139	−	18.1934i	−0.235329	−	0.724268i	−0.997078	−	0.0763953i	$-0.975659\pi$
$631$	−5.91139	−	18.1934i	−0.235329	−	0.724268i	0.761749	−	0.647873i	$-0.224341\pi$
$632$	−14.4066	−	2.79300i	−0.573065	−	0.111100i
$633$	1.38713	+	4.26913i	0.0551333	+	0.169683i
$634$	0.820091	−	0.989305i	0.0325700	−	0.0392903i
$635$	−17.2052	+	31.4991i	−0.682769	+	1.25000i
$636$	23.0619	−	12.6184i	0.914465	−	0.500354i
$637$	1.16682	−	1.60599i	0.0462309	−	0.0636314i
$638$	−6.61269	−	5.48164i	−0.261799	−	0.217020i
$639$	7.00237	−	5.08752i	0.277009	−	0.201259i
$640$	7.92029	−	24.0264i	0.313077	−	0.949728i
$641$	34.3957	+	24.9900i	1.35855	+	0.987044i	0.998536	+	0.0540974i	$0.0172282\pi$
$641$	34.3957	+	24.9900i	1.35855	+	0.987044i	0.360014	+	0.932947i	$0.382772\pi$
$642$	−0.549819	−	2.15032i	−0.0216996	−	0.0848664i
$643$			5.63992i			0.222417i	0.993797	+	0.111208i	$0.0354721\pi$
$643$			5.63992i			0.222417i	−0.993797	+	0.111208i	$0.964528\pi$
$644$	1.26398	+	6.69875i	0.0498080	+	0.263968i
$645$	1.61644	+	12.5211i	0.0636471	+	0.493017i
$646$	−5.97370	−	2.37206i	−0.235032	−	0.0933275i
$647$	−9.09625	+	27.9954i	−0.357610	+	1.10061i	0.596870	+	0.802338i	$0.296411\pi$
$647$	−9.09625	+	27.9954i	−0.357610	+	1.10061i	−0.954480	+	0.298274i	$0.903589\pi$
$648$	−2.56284	+	1.19661i	−0.100678	+	0.0470072i
$649$	−8.81366			−0.345967
$650$	−1.84802	−	1.72000i	−0.0724852	−	0.0674640i
$651$		−	11.7389i		−	0.460083i
$652$	5.86265	+	10.7148i	0.229599	+	0.419624i
$653$	−5.27901	−	1.71525i	−0.206584	−	0.0671231i	0.203897	−	0.978992i	$-0.434639\pi$
$653$	−5.27901	−	1.71525i	−0.206584	−	0.0671231i	−0.410481	+	0.911869i	$0.634639\pi$
$654$	−4.56014	+	11.4841i	−0.178316	+	0.449063i
$655$	−14.6230	+	13.8071i	−0.571368	+	0.539486i
$656$	1.45205	+	24.6518i	0.0566931	+	0.962492i
$657$	0.257829			0.0100589
$658$	−1.81889	−	7.11360i	−0.0709076	−	0.277317i
$659$	−16.8359	+	23.1727i	−0.655834	+	0.902678i	−0.999335	−	0.0364741i	$-0.988387\pi$
$659$	−16.8359	+	23.1727i	−0.655834	+	0.902678i	0.343500	+	0.939153i	$0.388387\pi$
$660$	3.78545	−	1.23300i	0.147349	−	0.0479945i
$661$	27.3779	+	37.6825i	1.06488	+	1.46568i	0.875157	+	0.483840i	$0.160758\pi$
$661$	27.3779	+	37.6825i	1.06488	+	1.46568i	0.189720	+	0.981838i	$0.439242\pi$
$662$	7.97597	−	9.62170i	0.309995	−	0.373958i
$663$	−0.873858	−	0.634895i	−0.0339378	−	0.0246573i
$664$	−4.70102	−	10.0684i	−0.182435	−	0.390730i
$665$	2.93090	−	2.76735i	0.113655	−	0.107313i
$666$	−7.51449	+	9.06500i	−0.291181	+	0.351262i
$667$	−18.4304	+	5.98840i	−0.713628	+	0.231872i
$668$	6.10305	+	0.783390i	0.236134	+	0.0303103i
$669$	−23.0046	+	7.47466i	−0.889411	+	0.288987i
$670$	1.27710	−	5.00983i	0.0493388	−	0.193547i
$671$	−0.633578	+	1.94995i	−0.0244590	+	0.0752771i
$672$	5.47172	+	4.01736i	0.211076	+	0.154973i
$673$	0.465376	−	0.338116i	0.0179389	−	0.0130334i	−0.578780	−	0.815484i	$-0.696471\pi$
$673$	0.465376	−	0.338116i	0.0179389	−	0.0130334i	0.596719	+	0.802451i	$0.296471\pi$
$674$	13.7845	+	0.881075i	0.530957	+	0.0339377i
$675$	4.99177	+	0.286768i	0.192133	+	0.0110377i
$676$	25.5355	+	3.27776i	0.982137	+	0.126068i
$677$	29.3094	+	40.3409i	1.12645	+	1.55043i	0.794641	+	0.607080i	$0.207659\pi$
$677$	29.3094	+	40.3409i	1.12645	+	1.55043i	0.331810	+	0.943346i	$0.392341\pi$
$678$	−4.85267	−	1.92692i	−0.186366	−	0.0740029i
$679$	0.481398	−	1.48159i	0.0184744	−	0.0568582i
$680$	−12.2006	+	14.7397i	−0.467870	+	0.565242i
$681$	7.30216	+	22.4737i	0.279819	+	0.861196i
$682$	−0.785602	+	12.2908i	−0.0300823	+	0.470638i
$683$	9.13636	−	2.96858i	0.349593	−	0.113590i	−0.128956	−	0.991650i	$-0.541163\pi$
$683$	9.13636	−	2.96858i	0.349593	−	0.113590i	0.478549	+	0.878061i	$0.341163\pi$
$684$	2.06111	−	2.18608i	0.0788084	−	0.0835870i
$685$	−38.3550	−	7.20840i	−1.46547	−	0.275419i
$686$	18.0081	−	11.4031i	0.687553	−	0.435371i
$687$	13.4225	+	9.75203i	0.512101	+	0.372063i
$688$	17.4589	−	14.3261i	0.665613	−	0.546176i
$689$	−3.79662	+	2.75841i	−0.144640	+	0.105087i
$690$	2.21879	−	8.70389i	0.0844679	−	0.331351i
$691$	4.05333	−	5.57893i	0.154196	−	0.212232i	−0.724929	−	0.688823i	$-0.758128\pi$
$691$	4.05333	−	5.57893i	0.154196	−	0.212232i	0.879125	+	0.476591i	$0.158128\pi$
$692$	−16.6298	+	3.13787i	−0.632170	+	0.119284i
$693$			1.06825i			0.0405796i
$694$	−19.3104	+	4.93751i	−0.733013	+	0.187425i
$695$	−21.6714	−	11.8372i	−0.822042	−	0.449010i
$696$	−9.34703	+	16.8821i	−0.354298	+	0.639915i
$697$	5.77166	−	17.7633i	0.218617	−	0.672835i
$698$	20.2063	+	31.9105i	0.764820	+	1.20783i
$699$		−	7.17208i		−	0.271273i
$700$	−5.14670	−	10.8401i	−0.194527	−	0.409718i
$701$		−	17.4892i		−	0.660559i	−0.943883	−	0.330279i	$-0.892857\pi$
$701$		−	17.4892i		−	0.660559i	0.943883	−	0.330279i	$-0.107143\pi$
$702$	0.426587	−	0.270123i	0.0161005	−	0.0101951i
$703$	3.86509	−	11.8955i	0.145774	−	0.448648i
$704$	−5.46011	−	4.57242i	−0.205786	−	0.172330i
$705$	−1.78696	+	9.50819i	−0.0673008	+	0.358099i
$706$	−7.88154	−	30.8244i	−0.296626	−	1.16009i
$707$		−	10.8296i		−	0.407290i
$708$	3.67146	+	19.4577i	0.137982	+	0.731264i
$709$	7.09301	−	9.76269i	0.266384	−	0.366646i	−0.654781	−	0.755819i	$-0.727239\pi$
$709$	7.09301	−	9.76269i	0.266384	−	0.366646i	0.921165	+	0.389173i	$0.127239\pi$
$710$	17.4831	+	21.0594i	0.656130	+	0.790347i
$711$	−4.19747	+	3.04964i	−0.157417	+	0.114370i
$712$	−27.0294	−	28.9568i	−1.01297	−	1.08520i
$713$	22.4798	+	16.3326i	0.841877	+	0.611659i
$714$	−2.74668	−	4.33765i	−0.102792	−	0.162332i
$715$	−0.642240	+	0.304354i	−0.0240184	+	0.0113822i
$716$	−17.8225	+	18.9032i	−0.666059	+	0.706446i
$717$	7.65531	−	2.48736i	0.285893	−	0.0928922i
$718$	−45.6623	−	2.91865i	−1.70410	−	0.108923i
$719$	−1.40968	−	4.33855i	−0.0525722	−	0.161801i	0.921323	−	0.388797i	$-0.127109\pi$
$719$	−1.40968	−	4.33855i	−0.0525722	−	0.161801i	−0.973896	+	0.226997i	$0.927109\pi$
$720$	−4.29895	−	7.84341i	−0.160212	−	0.292307i
$721$	0.0157969	−	0.0486179i	0.000588308	−	0.00181063i
$722$	8.73863	−	22.0070i	0.325218	−	0.819015i
$723$	9.26287	+	12.7492i	0.344490	+	0.474150i
$724$	−3.19165	+	24.8647i	−0.118617	+	0.924090i
$725$	28.7022	−	18.4350i	1.06597	−	0.684659i
$726$	−0.920815	+	14.4062i	−0.0341747	+	0.534664i
$727$	−2.69557	+	1.95844i	−0.0999731	+	0.0726347i	−0.636649	−	0.771154i	$-0.719680\pi$
$727$	−2.69557	+	1.95844i	−0.0999731	+	0.0726347i	0.536676	+	0.843789i	$0.319680\pi$
$728$	−1.06014	−	0.586965i	−0.0392916	−	0.0217544i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	0.0525976	+	0.813629i	0.00194673	+	0.0301137i
$731$	−16.2454	+	5.27843i	−0.600856	+	0.195230i
$732$	4.56878	+	0.586451i	0.168867	+	0.0216758i
$733$	5.28312	−	1.71659i	0.195136	−	0.0634037i	−0.209818	−	0.977740i	$-0.567287\pi$
$733$	5.28312	−	1.71659i	0.195136	−	0.0634037i	0.404955	+	0.914337i	$0.367287\pi$
$734$	−24.1163	−	19.9914i	−0.890150	−	0.737896i
$735$	−12.3303	+	1.59181i	−0.454810	+	0.0587147i
$736$	−15.3061	+	4.88884i	−0.564191	+	0.180205i
$737$	−1.17747	−	0.855485i	−0.0433728	−	0.0315122i
$738$	6.72167	+	5.57197i	0.247428	+	0.205107i
$739$	28.1458	+	38.7394i	1.03536	+	1.42505i	0.900845	+	0.434141i	$0.142948\pi$
$739$	28.1458	+	38.7394i	1.03536	+	1.42505i	0.134516	+	0.990911i	$0.457052\pi$
$740$	−30.1393	−	21.8641i	−1.10794	−	0.803742i
$741$	−0.315260	+	0.433919i	−0.0115814	+	0.0159404i
$742$	−21.6109	+	5.52571i	−0.793360	+	0.202855i
$743$	24.1480			0.885904			0.442952	−	0.896545i	$-0.353931\pi$
$743$	24.1480			0.885904			0.442952	+	0.896545i	$0.353931\pi$
$744$	27.4612	−	3.38555i	1.00678	−	0.124120i
$745$	2.93312	+	6.18938i	0.107461	+	0.226761i
$746$	24.1039	+	9.57128i	0.882506	+	0.350429i
$747$	−3.73634	−	1.21401i	−0.136706	−	0.0444183i
$748$	2.58552	+	4.72540i	0.0945361	+	0.172778i
$749$			1.88329i			0.0688138i
$750$	0.113382	+	15.8110i	0.00414011	+	0.577335i
$751$	17.6424			0.643779			0.321890	−	0.946777i	$-0.395682\pi$
$751$	17.6424			0.643779			0.321890	+	0.946777i	$0.395682\pi$
$752$	16.1166	−	6.30659i	0.587710	−	0.229978i
$753$	1.47677	−	4.54504i	0.0538166	−	0.165630i
$754$	1.27132	−	3.20163i	0.0462987	−	0.116597i
$755$	−14.8438	+	7.03438i	−0.540220	+	0.256007i
$756$	2.35835	−	0.444997i	0.0857725	−	0.0161844i
$757$		−	18.0496i		−	0.656024i	−0.944673	−	0.328012i	$-0.893621\pi$
$757$		−	18.0496i		−	0.656024i	0.944673	−	0.328012i	$-0.106379\pi$
$758$	−48.4943	+	12.3996i	−1.76139	+	0.450373i
$759$	−2.04570	−	1.48629i	−0.0742541	−	0.0539488i
$760$	7.31907	+	6.05825i	0.265491	+	0.219756i
$761$	18.1490	−	13.1860i	0.657900	−	0.477993i	−0.208053	−	0.978118i	$-0.566713\pi$
$761$	18.1490	−	13.1860i	0.657900	−	0.477993i	0.865953	+	0.500125i	$0.166713\pi$
$762$	14.4869	−	17.4761i	0.524806	−	0.633093i
$763$	6.16267	−	8.48219i	0.223104	−	0.307076i
$764$	−44.9951	+	24.6193i	−1.62787	+	0.890695i
$765$	0.866144	+	6.70923i	0.0313155	+	0.242573i
$766$	18.5432	+	15.3715i	0.669993	+	0.555395i
$767$	−1.09231	−	3.36179i	−0.0394411	−	0.121387i
$768$	−7.81991	+	13.9588i	−0.282177	+	0.503696i
$769$	−13.8647	−	42.6711i	−0.499973	−	1.53876i	−0.809060	−	0.587726i	$-0.800023\pi$
$769$	−13.8647	−	42.6711i	−0.499973	−	1.53876i	0.309087	−	0.951034i	$-0.399977\pi$
$770$	−3.37108	+	0.217926i	−0.121485	+	0.00785351i
$771$	−23.3565	−	7.58899i	−0.841164	−	0.273311i
$772$	14.8370	−	31.3673i	0.533995	−	1.12893i
$773$	13.7572	+	18.9352i	0.494814	+	0.681052i	0.981267	−	0.192654i	$-0.0617096\pi$
$773$	13.7572	+	18.9352i	0.494814	+	0.681052i	−0.486453	+	0.873707i	$0.661710\pi$
$774$	0.509329	−	7.96848i	0.0183075	−	0.286421i
$775$	−45.5752	−	17.7580i	−1.63711	−	0.637884i
$776$	3.60478	+	0.698856i	0.129404	+	0.0250875i
$777$	8.08287	−	5.87255i	0.289971	−	0.210677i
$778$	−23.9605	−	9.51432i	−0.859024	−	0.341105i
$779$	−8.82048	−	2.86595i	−0.316026	−	0.102683i
$780$	0.939448	+	1.29107i	0.0336376	+	0.0462278i
$781$	7.32812	−	2.38105i	0.262221	−	0.0852007i
$782$	12.1281	+	0.775202i	0.433699	+	0.0277212i
$783$	2.10827	+	6.48859i	0.0753434	+	0.231883i
$784$	14.1078	+	17.1929i	0.503850	+	0.614031i
$785$	−10.7406	−	22.6644i	−0.383347	−	0.808928i
$786$	10.7463	−	6.80474i	0.383307	−	0.242717i
$787$	15.2445	−	20.9822i	0.543406	−	0.747934i	−0.445693	−	0.895186i	$-0.647043\pi$
$787$	15.2445	−	20.9822i	0.543406	−	0.747934i	0.989099	+	0.147251i	$0.0470427\pi$
$788$	−10.8623	+	11.5210i	−0.386955	+	0.410418i
$789$	−10.6047	−	14.5961i	−0.377537	−	0.519636i
$790$	−10.4800	−	12.6238i	−0.372862	−	0.449134i
$791$	3.58420	+	2.60408i	0.127440	+	0.0925903i
$792$	−2.49901	+	0.308090i	−0.0887985	+	0.0109475i
$793$	−0.822290			−0.0292004
$794$	45.8271	−	11.7176i	1.62634	−	0.415842i
$795$	28.8856	+	5.42873i	1.02447	+	0.192537i
$796$	3.22918	−	6.82690i	0.114455	−	0.241973i
$797$	−31.2556	−	10.1556i	−1.10713	−	0.359729i	−0.302288	−	0.953216i	$-0.597751\pi$
$797$	−31.2556	−	10.1556i	−1.10713	−	0.359729i	−0.804843	+	0.593488i	$0.797751\pi$
$798$	−2.15388	+	1.36388i	−0.0762466	+	0.0482807i
$799$	−13.0896			−0.463078
$800$	23.8744	−	15.1662i	0.844087	−	0.536207i
$801$	−14.0048			−0.494837
$802$	22.5667	−	14.2896i	0.796857	−	0.504585i
$803$	0.218292	+	0.0709272i	0.00770334	+	0.00250297i
$804$	−1.39813	+	2.95584i	−0.0493084	+	0.104244i
$805$	−3.65353	+	6.68883i	−0.128770	+	0.235750i
$806$	−4.78542	+	1.22359i	−0.168559	+	0.0430992i
$807$	−21.8382			−0.768740
$808$	25.3342	−	3.12332i	0.891254	−	0.109878i
$809$	−3.01631	−	2.19148i	−0.106048	−	0.0770483i	0.533497	−	0.845802i	$-0.320877\pi$
$809$	−3.01631	−	2.19148i	−0.106048	−	0.0770483i	−0.639545	+	0.768753i	$0.720877\pi$
$810$	−3.06428	−	0.781145i	−0.107668	−	0.0274466i
$811$	1.37626	+	1.89426i	0.0483271	+	0.0665165i	0.832497	−	0.554030i	$-0.186911\pi$
$811$	1.37626	+	1.89426i	0.0483271	+	0.0665165i	−0.784170	+	0.620547i	$0.786911\pi$
$812$	11.2325	−	11.9136i	0.394183	−	0.418084i
$813$	6.73563	−	9.27080i	0.236229	−	0.325141i
$814$	−8.85589	+	5.60772i	−0.310399	+	0.196550i
$815$	−2.52224	+	13.4205i	−0.0883502	+	0.470100i
$816$	9.35508	−	7.67641i	0.327493	−	0.268728i
$817$	2.62103	+	8.06671i	0.0916983	+	0.282218i
$818$	−10.6940	−	0.683542i	−0.373909	−	0.0238995i
$819$	−0.407463	+	0.132393i	−0.0142379	+	0.00462618i
$820$	−16.2122	+	22.3482i	−0.566154	+	0.780433i
$821$	1.31190	+	0.426263i	0.0457858	+	0.0148767i	0.331820	−	0.943343i	$-0.392337\pi$
$821$	1.31190	+	0.426263i	0.0457858	+	0.0148767i	−0.286035	+	0.958219i	$0.592337\pi$
$822$	22.9401	+	9.10917i	0.800129	+	0.317719i
$823$	−22.7590	+	16.5353i	−0.793327	+	0.576386i	−0.908949	−	0.416907i	$-0.863114\pi$
$823$	−22.7590	+	16.5353i	−0.793327	+	0.576386i	0.115622	+	0.993293i	$0.463114\pi$
$824$	0.118290	+	0.0229327i	0.00412082	+	0.000798900i
$825$	4.14741	+	1.61600i	0.144394	+	0.0562619i
$826$	1.07173	−	16.7673i	0.0372904	−	0.583409i
$827$	18.9449	+	26.0754i	0.658779	+	0.906731i	0.999440	−	0.0334546i	$-0.0106509\pi$
$827$	18.9449	+	26.0754i	0.658779	+	0.906731i	−0.340661	+	0.940186i	$0.610651\pi$
$828$	−2.42907	+	5.13536i	−0.0844159	+	0.178466i
$829$	12.2210	+	3.97085i	0.424454	+	0.137913i	0.513452	−	0.858118i	$-0.328366\pi$
$829$	12.2210	+	3.97085i	0.424454	+	0.137913i	−0.0889981	+	0.996032i	$0.528366\pi$
$830$	3.06882	−	12.0384i	0.106520	−	0.417859i
$831$	6.46043	+	19.8832i	0.224110	+	0.689739i
$832$	1.06736	−	2.64932i	0.0370041	−	0.0918487i
$833$	−5.19801	−	15.9978i	−0.180100	−	0.554292i
$834$	12.0236	+	9.96700i	0.416342	+	0.345129i
$835$	4.72291	+	5.00202i	0.163443	+	0.173102i
$836$	2.34642	−	1.28385i	0.0811526	−	0.0444030i
$837$	5.75002	−	7.91422i	0.198750	−	0.273556i
$838$	21.0632	−	25.4093i	0.727616	−	0.877749i
$839$	0.0187228	−	0.0136029i	0.000646384	−	0.000469626i	−0.587462	−	0.809252i	$-0.699873\pi$
$839$	0.0187228	−	0.0136029i	0.000646384	−	0.000469626i	0.588108	+	0.808782i	$0.299873\pi$
$840$	1.88538	+	7.35146i	0.0650518	+	0.253649i
$841$	14.1955	+	10.3136i	0.489499	+	0.355642i
$842$	−26.8085	+	6.85470i	−0.923881	+	0.236228i
$843$		−	3.92079i		−	0.135039i
$844$	8.82199	−	1.66462i	0.303665	−	0.0572985i
$845$	19.7610	+	20.9288i	0.679798	+	0.719972i
$846$	2.25816	−	5.68685i	0.0776371	−	0.195518i
$847$	3.78510	−	11.6494i	0.130058	−	0.400276i
$848$	−19.1592	−	48.9616i	−0.657930	−	1.68135i
$849$	−27.9031			−0.957630
$850$	−20.9956	+	4.10198i	−0.720142	+	0.140697i
$851$			23.6492i			0.810685i
$852$	−8.30921	−	15.1862i	−0.284669	−	0.520271i
$853$	17.0920	+	5.55353i	0.585220	+	0.190149i	0.586638	−	0.809850i	$-0.300451\pi$
$853$	17.0920	+	5.55353i	0.585220	+	0.190149i	−0.00141787	+	0.999999i	$0.500451\pi$
$854$	−3.63259	−	1.44244i	−0.124305	−	0.0493594i
$855$	3.33150	−	0.430088i	0.113935	−	0.0147087i
$856$	−4.40565	+	0.543149i	−0.150582	+	0.0185644i
$857$	45.8146			1.56500			0.782499	−	0.622652i	$-0.213945\pi$
$857$	45.8146			1.56500			0.782499	+	0.622652i	$0.213945\pi$
$858$	0.435480	−	0.111349i	0.0148670	−	0.00380138i
$859$	−26.0236	+	35.8184i	−0.887913	+	1.22211i	0.0862525	+	0.996273i	$0.472511\pi$
$859$	−26.0236	+	35.8184i	−0.887913	+	1.22211i	−0.974166	+	0.225834i	$0.927489\pi$
$860$	25.2500	−	0.0182993i	0.861016	−	0.000624002i
$861$	−4.35448	−	5.99342i	−0.148400	−	0.204255i
$862$	5.60462	+	4.64599i	0.190894	+	0.158243i
$863$	−6.92045	−	5.02800i	−0.235575	−	0.171155i	0.463735	−	0.885974i	$-0.346509\pi$
$863$	−6.92045	−	5.02800i	−0.235575	−	0.171155i	−0.699310	+	0.714819i	$0.746509\pi$
$864$	1.72116	+	5.38866i	0.0585550	+	0.183326i
$865$	−16.6052	−	9.06997i	−0.564593	−	0.308388i
$866$	−12.3248	−	10.2167i	−0.418814	−	0.347179i
$867$	7.46312	−	2.42492i	0.253461	−	0.0823545i
$868$	−23.2867	−	2.98909i	−0.790402	−	0.101456i
$869$	−4.39273	+	1.42729i	−0.149013	+	0.0484173i
$870$	−20.0459	+	7.97673i	−0.679619	+	0.270437i
$871$	0.180378	−	0.555146i	0.00611187	−	0.0188104i
$872$	21.6201	+	11.9703i	0.732148	+	0.405365i
$873$	1.05028	−	0.763070i	0.0355465	−	0.0258260i
$874$	0.384931	−	6.02225i	0.0130205	−	0.203706i
$875$	3.23020	−	13.0216i	0.109201	−	0.440210i
$876$	0.0656515	−	0.511462i	0.00221816	−	0.0172807i
$877$	−4.76978	−	6.56504i	−0.161064	−	0.221685i	0.720856	−	0.693085i	$-0.243749\pi$
$877$	−4.76978	−	6.56504i	−0.161064	−	0.221685i	−0.881920	+	0.471400i	$0.843749\pi$
$878$	−13.5158	+	34.0377i	−0.456137	+	1.14872i
$879$	−6.58254	+	20.2590i	−0.222024	+	0.683319i
$880$	−1.48204	−	7.82326i	−0.0499595	−	0.263722i
$881$	8.82346	+	27.1558i	0.297270	+	0.914903i	0.982450	+	0.186529i	$0.0597237\pi$
$881$	8.82346	+	27.1558i	0.297270	+	0.914903i	−0.685180	+	0.728374i	$0.740276\pi$
$882$	7.84706	+	0.501569i	0.264224	+	0.0168887i
$883$	7.53805	−	2.44926i	0.253676	−	0.0824242i	−0.179419	−	0.983773i	$-0.557422\pi$
$883$	7.53805	−	2.44926i	0.253676	−	0.0824242i	0.433094	+	0.901349i	$0.357422\pi$
$884$	−1.48197	+	1.57183i	−0.0498440	+	0.0528664i
$885$	−10.6123	+	19.4288i	−0.356728	+	0.653093i
$886$	21.6154	+	34.1357i	0.726183	+	1.14681i
$887$	25.8251	+	18.7630i	0.867121	+	0.630000i	0.929813	−	0.368033i	$-0.119969\pi$
$887$	25.8251	+	18.7630i	0.867121	+	0.630000i	−0.0626922	+	0.998033i	$0.519969\pi$
$888$	16.0690	+	17.2149i	0.539242	+	0.577695i
$889$	−15.5827	+	11.3215i	−0.522627	+	0.379711i
$890$	−2.85702	−	44.1950i	−0.0957674	−	1.48142i
$891$	−0.523260	+	0.720206i	−0.0175299	+	0.0241278i
$892$	8.96995	+	47.5381i	0.300336	+	1.59169i
$893$			6.49972i			0.217505i
$894$	−1.07309	−	4.19680i	−0.0358894	−	0.140362i
$895$	−28.8077	+	3.71900i	−0.962937	+	0.124312i
$896$	9.36261	−	9.83143i	0.312783	−	0.328445i
$897$	0.313382	−	0.964489i	0.0104635	−	0.0322034i
$898$	10.1818	−	6.44728i	0.339770	−	0.215149i
$899$		−	66.7413i		−	2.22595i
$900$	1.83993	−	9.82928i	0.0613310	−	0.327643i
$901$			39.7659i			1.32479i
$902$	4.15810	+	6.56661i	0.138450	+	0.218644i
$903$	−2.09365	+	6.44359i	−0.0696723	+	0.214429i
$904$	−5.05812	+	9.13570i	−0.168231	+	0.303849i
$905$	−20.3790	+	19.2418i	−0.677420	+	0.639621i
$906$	10.0650	−	2.57354i	0.334388	−	0.0855002i
$907$		−	11.2763i		−	0.374425i	−0.982319	−	0.187212i	$-0.940055\pi$
$907$		−	11.2763i		−	0.374425i	0.982319	−	0.187212i	$-0.0599452\pi$
$908$	46.4411	−	8.76295i	1.54120	−	0.290809i
$909$	5.30465	−	7.30122i	0.175944	−	0.242166i
$910$	−0.500914	−	1.25882i	−0.0166051	−	0.0417295i
$911$	31.3779	−	22.7974i	1.03960	−	0.755311i	0.0693892	−	0.997590i	$-0.477895\pi$
$911$	31.3779	−	22.7974i	1.03960	−	0.755311i	0.970207	+	0.242279i	$0.0778950\pi$
$912$	−3.81176	−	4.64531i	−0.126220	−	0.153822i
$913$	−2.82941	−	2.05569i	−0.0936399	−	0.0680334i
$914$	21.9086	−	13.8729i	0.724671	−	0.458875i
$915$	3.53560	+	3.74454i	0.116883	+	0.123791i
$916$	22.7631	−	24.1434i	0.752115	−	0.797720i
$917$	−10.2645	+	3.33515i	−0.338964	+	0.110136i
$918$	0.272917	−	4.26979i	0.00900760	−	0.140924i
$919$	−2.46540	−	7.58773i	−0.0813262	−	0.250296i	0.902123	−	0.431478i	$-0.142008\pi$
$919$	−2.46540	−	7.58773i	−0.0813262	−	0.250296i	−0.983450	+	0.181182i	$0.942008\pi$
$920$	−16.7011	−	6.61776i	−0.550620	−	0.218181i
$921$	5.52858	−	17.0152i	0.182173	−	0.560670i
$922$	51.1526	+	20.3119i	1.68462	+	0.668937i
$923$	1.81640	+	2.50007i	0.0597877	+	0.0822906i
$924$	2.11912	+	0.272012i	0.0697140	+	0.00894853i
$925$	−10.5723	−	40.2647i	−0.347616	−	1.32390i
$926$	25.0437	+	1.60074i	0.822986	+	0.0526036i
$927$	0.0344645	−	0.0250399i	0.00113196	−	0.000822418i
$928$	31.1094	+	22.8407i	1.02122	+	0.749781i
$929$	7.86839	−	24.2164i	0.258154	−	0.794515i	−0.735038	−	0.678025i	$-0.762836\pi$
$929$	7.86839	−	24.2164i	0.258154	−	0.794515i	0.993192	−	0.116489i	$-0.0371641\pi$
$930$	26.1479	+	16.5308i	0.857422	+	0.542065i
$931$	−7.94380	+	2.58110i	−0.260348	+	0.0845921i
$932$	−14.2274	−	1.82624i	−0.466035	−	0.0598204i
$933$	19.5542	−	6.35355i	0.640176	−	0.208006i
$934$	−28.3772	+	34.2324i	−0.928530	+	1.12012i
$935$	−1.11235	+	5.91866i	−0.0363777	+	0.193561i
$936$	−0.427226	−	0.915013i	−0.0139643	−	0.0299081i
$937$	−15.9591	−	11.5949i	−0.521360	−	0.378790i	0.295756	−	0.955264i	$-0.404428\pi$
$937$	−15.9591	−	11.5949i	−0.521360	−	0.378790i	−0.817116	+	0.576473i	$0.804428\pi$
$938$	1.77067	−	2.13602i	0.0578145	−	0.0697437i
$939$	11.4788	+	15.7992i	0.374597	+	0.515588i
$940$	18.4066	+	5.96593i	0.600357	+	0.194587i
$941$	23.4403	−	32.2628i	0.764131	−	1.05174i	−0.232728	−	0.972542i	$-0.574765\pi$
$941$	23.4403	−	32.2628i	0.764131	−	1.05174i	0.996859	−	0.0791948i	$-0.0252349\pi$
$942$	3.92945	+	15.3680i	0.128029	+	0.500715i
$943$	17.5358			0.571045
$944$	39.5335	−	2.32862i	1.28671	−	0.0757901i
$945$	2.35486	+	1.28626i	0.0766036	+	0.0418419i
$946$	2.62331	−	6.60642i	0.0852910	−	0.214793i
$947$	−4.17660	−	1.35706i	−0.135721	−	0.0440985i	0.240369	−	0.970682i	$-0.422732\pi$
$947$	−4.17660	−	1.35706i	−0.135721	−	0.0440985i	−0.376090	+	0.926583i	$0.622732\pi$
$948$	4.98083	+	9.10315i	0.161770	+	0.295657i
$949$			0.0920530i			0.00298817i
$950$	2.03686	+	10.4255i	0.0660844	+	0.338247i
$951$	−0.908645			−0.0294648
$952$	−9.30409	+	4.34415i	−0.301547	+	0.140795i
$953$	−9.87095	+	30.3797i	−0.319751	+	0.984094i	0.654003	+	0.756492i	$0.273088\pi$
$953$	−9.87095	+	30.3797i	−0.319751	+	0.984094i	−0.973754	+	0.227602i	$0.926912\pi$
$954$	−17.2765	−	6.86021i	−0.559346	−	0.222108i
$955$	−56.3574	−	10.5918i	−1.82368	−	0.342741i
$956$	−2.98495	−	15.8194i	−0.0965402	−	0.511635i
$957$			6.07355i			0.196330i
$958$	5.77770	+	22.5964i	0.186669	+	0.730055i
$959$	−16.9437	−	12.3103i	−0.547140	−	0.397521i
$960$	−16.6538	+	6.53074i	−0.537499	+	0.210779i
$961$	−52.3415	+	38.0284i	−1.68844	+	1.22672i
$962$	−3.23649	−	2.68291i	−0.104349	−	0.0865005i
$963$	−0.922485	+	1.26969i	−0.0297266	+	0.0409152i
$964$	27.6496	−	15.1286i	0.890534	−	0.487260i
$965$	35.0577	−	16.6137i	1.12855	−	0.534813i
$966$	3.07630	−	3.71105i	0.0989782	−	0.119401i
$967$	−1.53342	−	4.71937i	−0.0493113	−	0.151765i	0.923369	−	0.383914i	$-0.125424\pi$
$967$	−1.53342	−	4.71937i	−0.0493113	−	0.151765i	−0.972680	+	0.232149i	$0.925424\pi$
$968$	28.3434	+	5.49492i	0.910993	+	0.176613i
$969$	1.40444	+	4.32243i	0.0451172	+	0.138856i
$970$	2.62227	+	3.15868i	0.0841961	+	0.101419i
$971$	−12.5985	−	4.09350i	−0.404305	−	0.131367i	0.0998030	−	0.995007i	$-0.468179\pi$
$971$	−12.5985	−	4.09350i	−0.404305	−	0.131367i	−0.504108	+	0.863640i	$0.668179\pi$
$972$	1.80795	+	0.855174i	0.0579900	+	0.0274297i
$973$	−7.78918	−	10.7209i	−0.249710	−	0.343696i
$974$	21.5076	+	1.37472i	0.689148	+	0.0440490i
$975$	−0.102385	+	1.78222i	−0.00327894	+	0.0570767i
$976$	2.32671	−	8.91387i	0.0744763	−	0.285326i
$977$	23.8714	−	17.3436i	0.763714	−	0.554871i	−0.136333	−	0.990663i	$-0.543532\pi$
$977$	23.8714	−	17.3436i	0.763714	−	0.554871i	0.900047	+	0.435792i	$0.143532\pi$
$978$	3.18732	−	8.02681i	0.101919	−	0.256669i
$979$	−11.8572	−	3.85265i	−0.378959	−	0.123131i
$980$	0.0180205	+	24.8652i	0.000575644	+	0.794291i
$981$	8.30961	−	2.69996i	0.265305	−	0.0862029i
$982$	−2.39174	+	37.4189i	−0.0763235	+	1.19408i
$983$	−3.30682	−	10.1773i	−0.105471	−	0.324606i	0.884370	−	0.466787i	$-0.154589\pi$
$983$	−3.30682	−	10.1773i	−0.105471	−	0.324606i	−0.989841	+	0.142181i	$0.954589\pi$
$984$	12.7648	−	11.9151i	0.406927	−	0.379841i
$985$	−17.5575	+	2.26663i	−0.559430	+	0.0722208i
$986$	−15.6162	−	24.6617i	−0.497322	−	0.785387i
$987$	−3.05172	+	4.20033i	−0.0971374	+	0.133698i
$988$	0.780500	+	0.735879i	0.0248310	+	0.0234114i
$989$	−9.42647	−	12.9744i	−0.299744	−	0.412563i
$990$	−2.37949	−	1.50432i	−0.0756252	−	0.0478105i
$991$	−8.72892	−	6.34193i	−0.277283	−	0.201458i	0.440448	−	0.897778i	$-0.354820\pi$
$991$	−8.72892	−	6.34193i	−0.277283	−	0.201458i	−0.717732	+	0.696320i	$0.754820\pi$
$992$	0.276511	−	55.3376i	0.00877923	−	1.75697i
$993$	−8.83723			−0.280441
$994$	3.63867	+	14.2307i	0.115412	+	0.451371i
$995$	7.63009	−	3.61586i	0.241890	−	0.114630i
$996$	−3.35965	+	7.10274i	−0.106455	+	0.225059i
$997$	−16.8382	−	5.47107i	−0.533271	−	0.173270i	0.0299884	−	0.999550i	$-0.490453\pi$
$997$	−16.8382	−	5.47107i	−0.533271	−	0.173270i	−0.563260	+	0.826280i	$0.690453\pi$
$998$	32.2700	+	50.9619i	1.02149	+	1.61317i
$999$	8.32592			0.263420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bm.a.61.10	✓	240
8.5	even	2	inner	600.2.bm.a.61.13	yes	240
25.16	even	5	inner	600.2.bm.a.541.13	yes	240
200.141	even	10	inner	600.2.bm.a.541.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bm.a.61.10	✓	240	1.1	even	1	trivial
600.2.bm.a.61.13	yes	240	8.5	even	2	inner
600.2.bm.a.541.10	yes	240	200.141	even	10	inner
600.2.bm.a.541.13	yes	240	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bm (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19482 + 0.756580i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.855174 - 1.80795i) q^{4} +(2.02065 - 0.957578i) q^{5} +(-1.37013 + 0.350332i) q^{6} +1.19999 q^{7} +(0.346081 + 2.80717i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.68983 + 2.67292i) q^{10} +(0.523260 + 0.720206i) q^{11} +(1.37201 - 1.45520i) q^{12} +(-0.209858 + 0.288844i) q^{13} +(-1.43376 + 0.907885i) q^{14} +(2.21766 - 0.286294i) q^{15} +(-2.53736 - 3.09222i) q^{16} +(0.934888 + 2.87729i) q^{17} +(-1.41133 - 0.0902097i) q^{18} +(1.42873 - 0.464223i) q^{19} +(-0.00324108 - 4.47213i) q^{20} +(1.14125 + 0.370816i) q^{21} +(-1.17009 - 0.464626i) q^{22} +(-2.29796 + 1.66957i) q^{23} +(-0.538322 + 2.77673i) q^{24} +(3.16609 - 3.86987i) q^{25} +(0.0322077 - 0.503890i) q^{26} +(0.587785 + 0.809017i) q^{27} +(1.02620 - 2.16951i) q^{28} +(6.48859 + 2.10827i) q^{29} +(-2.43310 + 2.01991i) q^{30} +(-3.02296 - 9.30373i) q^{31} +(5.37119 + 1.77492i) q^{32} +(0.275094 + 0.846653i) q^{33} +(-3.29392 - 2.73052i) q^{34} +(2.42476 - 1.14908i) q^{35} +(1.75454 - 0.960002i) q^{36} +(4.89385 - 6.73581i) q^{37} +(-1.35585 + 1.63561i) q^{38} +(-0.288844 + 0.209858i) q^{39} +(3.38740 + 5.34093i) q^{40} +(-4.99458 - 3.62877i) q^{41} +(-1.64414 + 0.420393i) q^{42} +5.64606i q^{43} +(1.74957 - 0.330126i) q^{44} +(2.19759 + 0.413014i) q^{45} +(1.48248 - 3.73342i) q^{46} +(-1.33700 + 4.11488i) q^{47} +(-1.45762 - 3.72496i) q^{48} -5.56004 q^{49} +(-0.855030 + 7.01918i) q^{50} +3.02536i q^{51} +(0.342751 + 0.626424i) q^{52} +(12.5009 + 4.06177i) q^{53} +(-1.31438 - 0.521921i) q^{54} +(1.74698 + 0.954224i) q^{55} +(0.415293 + 3.36857i) q^{56} +1.50226 q^{57} +(-9.34775 + 2.39014i) q^{58} +(-5.81937 + 8.00968i) q^{59} +(1.37888 - 4.25425i) q^{60} +(1.35375 + 1.86327i) q^{61} +(10.6509 + 8.82914i) q^{62} +(0.970808 + 0.705334i) q^{63} +(-7.76046 + 1.94302i) q^{64} +(-0.147459 + 0.784610i) q^{65} +(-0.969247 - 0.803464i) q^{66} +(-1.55489 + 0.505216i) q^{67} +(6.00148 + 0.770353i) q^{68} +(-2.70141 + 0.877743i) q^{69} +(-2.02777 + 3.20746i) q^{70} +(2.67467 - 8.23178i) q^{71} +(-1.37003 + 2.47447i) q^{72} +(0.208588 - 0.151548i) q^{73} +(-0.751078 + 11.7506i) q^{74} +(4.20698 - 2.70209i) q^{75} +(0.382523 - 2.98007i) q^{76} +(0.627904 + 0.864236i) q^{77} +(0.186342 - 0.469275i) q^{78} +(-1.60329 + 4.93442i) q^{79} +(-8.08816 - 3.81859i) q^{80} +(0.309017 + 0.951057i) q^{81} +(8.71306 + 0.556922i) q^{82} +(-3.73634 + 1.21401i) q^{83} +(1.64639 - 1.74622i) q^{84} +(4.64431 + 4.91878i) q^{85} +(-4.27170 - 6.74601i) q^{86} +(5.51952 + 4.01017i) q^{87} +(-1.84065 + 1.71813i) q^{88} +(-11.3302 + 8.23184i) q^{89} +(-2.93820 + 1.16918i) q^{90} +(-0.251826 + 0.346609i) q^{91} +(1.05333 + 5.58236i) q^{92} -9.78252i q^{93} +(-1.51576 - 5.92807i) q^{94} +(2.44244 - 2.30616i) q^{95} +(4.55982 + 3.34784i) q^{96} +(0.401170 - 1.23467i) q^{97} +(6.64322 - 4.20661i) q^{98} +0.890223i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) \) 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more