LMFDB - Embedded newform 780.2.g.e.131.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(131,780)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("780.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	780.131
Dual form			780.2.g.e.131.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41093 - 0.0963462i) q^{2} +(1.70974 + 0.277108i) q^{3} +(1.98143 + 0.271875i) q^{4} +1.00000i q^{5} +(-2.38562 - 0.555706i) q^{6} +4.66235i q^{7} +(-2.76947 - 0.574500i) q^{8} +(2.84642 + 0.947565i) q^{9} +(0.0963462 - 1.41093i) q^{10} +5.03741 q^{11} +(3.31240 + 1.01391i) q^{12} -1.00000 q^{13} +(0.449199 - 6.57823i) q^{14} +(-0.277108 + 1.70974i) q^{15} +(3.85217 + 1.07741i) q^{16} -6.55169i q^{17} +(-3.92480 - 1.61119i) q^{18} +0.699987i q^{19} +(-0.271875 + 1.98143i) q^{20} +(-1.29197 + 7.97140i) q^{21} +(-7.10742 - 0.485335i) q^{22} -5.65505 q^{23} +(-4.57587 - 1.74969i) q^{24} -1.00000 q^{25} +(1.41093 + 0.0963462i) q^{26} +(4.60406 + 2.40886i) q^{27} +(-1.26758 + 9.23814i) q^{28} +5.09126i q^{29} +(0.555706 - 2.38562i) q^{30} +6.88919i q^{31} +(-5.33133 - 1.89128i) q^{32} +(8.61266 + 1.39591i) q^{33} +(-0.631231 + 9.24397i) q^{34} -4.66235 q^{35} +(5.38238 + 2.65141i) q^{36} -1.52653 q^{37} +(0.0674411 - 0.987632i) q^{38} +(-1.70974 - 0.277108i) q^{39} +(0.574500 - 2.76947i) q^{40} -6.16631i q^{41} +(2.59090 - 11.1226i) q^{42} -0.390638i q^{43} +(9.98130 + 1.36955i) q^{44} +(-0.947565 + 2.84642i) q^{45} +(7.97886 + 0.544842i) q^{46} -0.483058 q^{47} +(6.28765 + 2.90955i) q^{48} -14.7375 q^{49} +(1.41093 + 0.0963462i) q^{50} +(1.81553 - 11.2017i) q^{51} +(-1.98143 - 0.271875i) q^{52} -0.793745i q^{53} +(-6.26392 - 3.84231i) q^{54} +5.03741i q^{55} +(2.67852 - 12.9122i) q^{56} +(-0.193972 + 1.19680i) q^{57} +(0.490524 - 7.18341i) q^{58} -6.19480 q^{59} +(-1.01391 + 3.31240i) q^{60} +9.05980 q^{61} +(0.663747 - 9.72015i) q^{62} +(-4.41788 + 13.2710i) q^{63} +(7.33990 + 3.18212i) q^{64} -1.00000i q^{65} +(-12.0174 - 2.79932i) q^{66} +1.64274i q^{67} +(1.78124 - 12.9818i) q^{68} +(-9.66866 - 1.56706i) q^{69} +(6.57823 + 0.449199i) q^{70} +11.9195 q^{71} +(-7.33870 - 4.25952i) q^{72} +10.7627 q^{73} +(2.15383 + 0.147076i) q^{74} +(-1.70974 - 0.277108i) q^{75} +(-0.190309 + 1.38698i) q^{76} +23.4862i q^{77} +(2.38562 + 0.555706i) q^{78} -13.0445i q^{79} +(-1.07741 + 3.85217i) q^{80} +(7.20424 + 5.39434i) q^{81} +(-0.594101 + 8.70022i) q^{82} -2.16081 q^{83} +(-4.72719 + 15.4436i) q^{84} +6.55169 q^{85} +(-0.0376365 + 0.551162i) q^{86} +(-1.41083 + 8.70474i) q^{87} +(-13.9509 - 2.89399i) q^{88} +7.02840i q^{89} +(1.61119 - 3.92480i) q^{90} -4.66235i q^{91} +(-11.2051 - 1.53747i) q^{92} +(-1.90905 + 11.7787i) q^{93} +(0.681560 + 0.0465408i) q^{94} -0.699987 q^{95} +(-8.59109 - 4.71096i) q^{96} +5.31043 q^{97} +(20.7935 + 1.41990i) q^{98} +(14.3386 + 4.77327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} - 2 q^{6} - 14 q^{12} - 40 q^{13} + 12 q^{16} - 16 q^{18} - 24 q^{21} + 44 q^{22} - 10 q^{24} - 40 q^{25} - 48 q^{28} - 6 q^{30} - 8 q^{33} - 56 q^{34} + 36 q^{36} - 72 q^{37} - 20 q^{42}+ \cdots + 72 q^{97}+O(q^{100}) $ 40 * q + 4 * q^4 - 2 * q^6 - 14 * q^12 - 40 * q^13 + 12 * q^16 - 16 * q^18 - 24 * q^21 + 44 * q^22 - 10 * q^24 - 40 * q^25 - 48 * q^28 - 6 * q^30 - 8 * q^33 - 56 * q^34 + 36 * q^36 - 72 * q^37 - 20 * q^42 + 8 * q^45 + 84 * q^46 + 70 * q^48 - 96 * q^49 - 4 * q^52 - 14 * q^54 + 80 * q^57 + 18 * q^60 + 40 * q^61 + 28 * q^64 - 24 * q^66 - 56 * q^69 + 24 * q^70 + 12 * q^72 - 68 * q^76 + 2 * q^78 + 96 * q^82 - 48 * q^84 + 8 * q^85 - 116 * q^88 - 8 * q^90 - 24 * q^93 - 8 * q^94 - 10 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41093	−	0.0963462i	−0.997677	−	0.0681271i
$2$	−1.41093	−	0.0963462i	−0.997677	−	0.0681271i
$3$	1.70974	+	0.277108i	0.987119	+	0.159988i
$3$	1.70974	+	0.277108i	0.987119	+	0.159988i
$4$	1.98143	+	0.271875i	0.990717	+	0.135938i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.38562	−	0.555706i	−0.973926	−	0.226866i
$7$			4.66235i			1.76220i	0.472929	+	0.881101i	$0.343197\pi$
$7$			4.66235i			1.76220i	−0.472929	+	0.881101i	$0.656803\pi$
$8$	−2.76947	−	0.574500i	−0.979155	−	0.203116i
$9$	2.84642	+	0.947565i	0.948807	+	0.315855i
$10$	0.0963462	−	1.41093i	0.0304673	−	0.446175i
$11$	5.03741			1.51884			0.759418	−	0.650603i	$-0.225484\pi$
$11$	5.03741			1.51884			0.759418	+	0.650603i	$0.225484\pi$
$12$	3.31240	+	1.01391i	0.956207	+	0.292690i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	0.449199	−	6.57823i	0.120054	−	1.75811i
$15$	−0.277108	+	1.70974i	−0.0715490	+	0.441453i
$16$	3.85217	+	1.07741i	0.963042	+	0.269351i
$17$		−	6.55169i		−	1.58902i	−0.607251	−	0.794510i	$-0.707728\pi$
$17$		−	6.55169i		−	1.58902i	0.607251	−	0.794510i	$-0.292272\pi$
$18$	−3.92480	−	1.61119i	−0.925085	−	0.379761i
$19$			0.699987i			0.160588i	0.996771	+	0.0802941i	$0.0255859\pi$
$19$			0.699987i			0.160588i	−0.996771	+	0.0802941i	$0.974414\pi$
$20$	−0.271875	+	1.98143i	−0.0607931	+	0.443062i
$21$	−1.29197	+	7.97140i	−0.281932	+	1.73950i
$22$	−7.10742	−	0.485335i	−1.51531	−	0.103474i
$23$	−5.65505			−1.17916			−0.589580	−	0.807710i	$-0.700707\pi$
$23$	−5.65505			−1.17916			−0.589580	+	0.807710i	$0.700707\pi$
$24$	−4.57587	−	1.74969i	−0.934046	−	0.357153i
$25$	−1.00000			−0.200000
$26$	1.41093	+	0.0963462i	0.276706	+	0.0188950i
$27$	4.60406	+	2.40886i	0.886053	+	0.463585i
$28$	−1.26758	+	9.23814i	−0.239549	+	1.74584i
$29$			5.09126i			0.945424i	0.881217	+	0.472712i	$0.156725\pi$
$29$			5.09126i			0.945424i	−0.881217	+	0.472712i	$0.843275\pi$
$30$	0.555706	−	2.38562i	0.101458	−	0.435553i
$31$			6.88919i			1.23733i	0.785653	+	0.618667i	$0.212327\pi$
$31$			6.88919i			1.23733i	−0.785653	+	0.618667i	$0.787673\pi$
$32$	−5.33133	−	1.89128i	−0.942454	−	0.334335i
$33$	8.61266	+	1.39591i	1.49927	+	0.242996i
$34$	−0.631231	+	9.24397i	−0.108255	+	1.58533i
$35$	−4.66235			−0.788080
$36$	5.38238	+	2.65141i	0.897063	+	0.441902i
$37$	−1.52653			−0.250961			−0.125480	−	0.992096i	$-0.540047\pi$
$37$	−1.52653			−0.250961			−0.125480	+	0.992096i	$0.540047\pi$
$38$	0.0674411	−	0.987632i	0.0109404	−	0.160215i
$39$	−1.70974	−	0.277108i	−0.273778	−	0.0443728i
$40$	0.574500	−	2.76947i	0.0908364	−	0.437891i
$41$		−	6.16631i		−	0.963016i	−0.876442	−	0.481508i	$-0.840089\pi$
$41$		−	6.16631i		−	0.963016i	0.876442	−	0.481508i	$-0.159911\pi$
$42$	2.59090	−	11.1226i	0.399784	−	1.71625i
$43$		−	0.390638i		−	0.0595718i	−0.999556	−	0.0297859i	$-0.990517\pi$
$43$		−	0.390638i		−	0.0595718i	0.999556	−	0.0297859i	$-0.00948255\pi$
$44$	9.98130	+	1.36955i	1.50474	+	0.206467i
$45$	−0.947565	+	2.84642i	−0.141255	+	0.424320i
$46$	7.97886	+	0.544842i	1.17642	+	0.0803326i
$47$	−0.483058			−0.0704613			−0.0352306	−	0.999379i	$-0.511217\pi$
$47$	−0.483058			−0.0704613			−0.0352306	+	0.999379i	$0.511217\pi$
$48$	6.28765	+	2.90955i	0.907544	+	0.419957i
$49$	−14.7375			−2.10535
$50$	1.41093	+	0.0963462i	0.199535	+	0.0136254i
$51$	1.81553	−	11.2017i	0.254225	−	1.56855i
$52$	−1.98143	−	0.271875i	−0.274776	−	0.0377023i
$53$		−	0.793745i		−	0.109029i	−0.998513	−	0.0545146i	$-0.982639\pi$
$53$		−	0.793745i		−	0.109029i	0.998513	−	0.0545146i	$-0.0173612\pi$
$54$	−6.26392	−	3.84231i	−0.852411	−	0.522872i
$55$			5.03741i			0.679244i
$56$	2.67852	−	12.9122i	0.357932	−	1.72547i
$57$	−0.193972	+	1.19680i	−0.0256922	+	0.158520i
$58$	0.490524	−	7.18341i	0.0644090	−	0.943227i
$59$	−6.19480			−0.806495			−0.403247	−	0.915091i	$-0.632119\pi$
$59$	−6.19480			−0.806495			−0.403247	+	0.915091i	$0.632119\pi$
$60$	−1.01391	+	3.31240i	−0.130895	+	0.427629i
$61$	9.05980			1.15999			0.579994	−	0.814621i	$-0.303055\pi$
$61$	9.05980			1.15999			0.579994	+	0.814621i	$0.303055\pi$
$62$	0.663747	−	9.72015i	0.0842960	−	1.23446i
$63$	−4.41788	+	13.2710i	−0.556600	+	1.67199i
$64$	7.33990	+	3.18212i	0.917487	+	0.397765i
$65$		−	1.00000i		−	0.124035i
$66$	−12.0174	−	2.79932i	−1.47923	−	0.344573i
$67$			1.64274i			0.200693i	0.994953	+	0.100346i	$0.0319951\pi$
$67$			1.64274i			0.200693i	−0.994953	+	0.100346i	$0.968005\pi$
$68$	1.78124	−	12.9818i	0.216007	−	1.57427i
$69$	−9.66866	−	1.56706i	−1.16397	−	0.188652i
$70$	6.57823	+	0.449199i	0.786249	+	0.0536896i
$71$	11.9195			1.41458			0.707292	−	0.706921i	$-0.249916\pi$
$71$	11.9195			1.41458			0.707292	+	0.706921i	$0.249916\pi$
$72$	−7.33870	−	4.25952i	−0.864874	−	0.501989i
$73$	10.7627			1.25968			0.629840	−	0.776725i	$-0.283121\pi$
$73$	10.7627			1.25968			0.629840	+	0.776725i	$0.283121\pi$
$74$	2.15383	+	0.147076i	0.250378	+	0.0170972i
$75$	−1.70974	−	0.277108i	−0.197424	−	0.0319977i
$76$	−0.190309	+	1.38698i	−0.0218300	+	0.159097i
$77$			23.4862i			2.67650i
$78$	2.38562	+	0.555706i	0.270118	+	0.0629213i
$79$		−	13.0445i		−	1.46762i	−0.679354	−	0.733810i	$-0.737740\pi$
$79$		−	13.0445i		−	1.46762i	0.679354	−	0.733810i	$-0.262260\pi$
$80$	−1.07741	+	3.85217i	−0.120458	+	0.430685i
$81$	7.20424	+	5.39434i	0.800471	+	0.599371i
$82$	−0.594101	+	8.70022i	−0.0656074	+	0.960778i
$83$	−2.16081			−0.237180			−0.118590	−	0.992943i	$-0.537837\pi$
$83$	−2.16081			−0.237180			−0.118590	+	0.992943i	$0.537837\pi$
$84$	−4.72719	+	15.4436i	−0.515778	+	1.68503i
$85$	6.55169			0.710631
$86$	−0.0376365	+	0.551162i	−0.00405845	+	0.0594334i
$87$	−1.41083	+	8.70474i	−0.151257	+	0.933246i
$88$	−13.9509	−	2.89399i	−1.48718	−	0.308501i
$89$			7.02840i			0.745009i	0.928030	+	0.372505i	$0.121501\pi$
$89$			7.02840i			0.745009i	−0.928030	+	0.372505i	$0.878499\pi$
$90$	1.61119	−	3.92480i	0.169834	−	0.413710i
$91$		−	4.66235i		−	0.488747i
$92$	−11.2051	−	1.53747i	−1.16821	−	0.160292i
$93$	−1.90905	+	11.7787i	−0.197959	+	1.22140i
$94$	0.681560	+	0.0465408i	0.0702976	+	0.00480032i
$95$	−0.699987			−0.0718172
$96$	−8.59109	−	4.71096i	−0.876825	−	0.480810i
$97$	5.31043			0.539193			0.269596	−	0.962973i	$-0.413110\pi$
$97$	5.31043			0.539193			0.269596	+	0.962973i	$0.413110\pi$
$98$	20.7935	+	1.41990i	2.10046	+	0.143432i
$99$	14.3386	+	4.77327i	1.44108	+	0.479732i
$100$	−1.98143	−	0.271875i	−0.198143	−	0.0271875i
$101$		−	0.169975i		−	0.0169131i	−0.999964	−	0.00845657i	$-0.997308\pi$
$101$		−	0.169975i		−	0.0169131i	0.999964	−	0.00845657i	$-0.00269184\pi$
$102$	−3.64082	+	15.6299i	−0.360495	+	1.54759i
$103$		−	19.6851i		−	1.93963i	−0.243843	−	0.969815i	$-0.578408\pi$
$103$		−	19.6851i		−	1.93963i	0.243843	−	0.969815i	$-0.421592\pi$
$104$	2.76947	+	0.574500i	0.271569	+	0.0563344i
$105$	−7.97140	−	1.29197i	−0.777929	−	0.126084i
$106$	−0.0764743	+	1.11992i	−0.00742784	+	0.108776i
$107$	−5.80500			−0.561191			−0.280595	−	0.959826i	$-0.590532\pi$
$107$	−5.80500			−0.561191			−0.280595	+	0.959826i	$0.590532\pi$
$108$	8.46775	+	6.02472i	0.814809	+	0.579729i
$109$	−14.2735			−1.36715			−0.683575	−	0.729880i	$-0.739576\pi$
$109$	−14.2735			−1.36715			−0.683575	+	0.729880i	$0.739576\pi$
$110$	0.485335	−	7.10742i	0.0462749	−	0.677666i
$111$	−2.60998	−	0.423015i	−0.247728	−	0.0401508i
$112$	−5.02324	+	17.9601i	−0.474651	+	1.69707i
$113$			10.5746i			0.994776i	0.867528	+	0.497388i	$0.165708\pi$
$113$			10.5746i			0.994776i	−0.867528	+	0.497388i	$0.834292\pi$
$114$	0.388987	−	1.66990i	0.0364320	−	0.156401i
$115$		−	5.65505i		−	0.527336i
$116$	−1.38419	+	10.0880i	−0.128519	+	0.936648i
$117$	−2.84642	−	0.947565i	−0.263152	−	0.0876024i
$118$	8.74042	+	0.596846i	0.804621	+	0.0549441i
$119$	30.5463			2.80017
$120$	1.74969	−	4.57587i	0.159724	−	0.417718i
$121$	14.3755			1.30686
$122$	−12.7827	−	0.872877i	−1.15729	−	0.0790266i
$123$	1.70873	−	10.5428i	0.154071	−	0.950611i
$124$	−1.87300	+	13.6505i	−0.168200	+	1.22585i
$125$		−	1.00000i		−	0.0894427i
$126$	7.51192	−	18.2988i	0.669215	−	1.63019i
$127$		−	0.0692154i		−	0.00614187i	−0.999995	−	0.00307093i	$-0.999022\pi$
$127$		−	0.0692154i		−	0.00614187i	0.999995	−	0.00307093i	$-0.000977510\pi$
$128$	−10.0495	−	5.19691i	−0.888257	−	0.459346i
$129$	0.108249	−	0.667890i	0.00953079	−	0.0588044i
$130$	−0.0963462	+	1.41093i	−0.00845012	+	0.123747i
$131$	−1.07164			−0.0936293			−0.0468147	−	0.998904i	$-0.514907\pi$
$131$	−1.07164			−0.0936293			−0.0468147	+	0.998904i	$0.514907\pi$
$132$	16.6859	+	5.10747i	1.45232	+	0.444548i
$133$	−3.26358			−0.282989
$134$	0.158272	−	2.31779i	0.0136726	−	0.200226i
$135$	−2.40886	+	4.60406i	−0.207321	+	0.396255i
$136$	−3.76395	+	18.1447i	−0.322756	+	1.55590i
$137$			19.0915i			1.63110i	0.578688	+	0.815549i	$0.303565\pi$
$137$			19.0915i			1.63110i	−0.578688	+	0.815549i	$0.696435\pi$
$138$	13.4908	+	3.14255i	1.14841	+	0.267511i
$139$			0.101483i			0.00860771i	0.999991	+	0.00430385i	$0.00136996\pi$
$139$			0.101483i			0.00860771i	−0.999991	+	0.00430385i	$0.998630\pi$
$140$	−9.23814	−	1.26758i	−0.780765	−	0.107130i
$141$	−0.825904	−	0.133859i	−0.0695536	−	0.0112730i
$142$	−16.8176	−	1.14840i	−1.41130	−	0.0963715i
$143$	−5.03741			−0.421249
$144$	9.94398	+	6.71693i	0.828665	+	0.559744i
$145$	−5.09126			−0.422806
$146$	−15.1854	−	1.03695i	−1.25675	−	0.0858183i
$147$	−25.1973	−	4.08387i	−2.07823	−	0.336832i
$148$	−3.02473	−	0.415027i	−0.248631	−	0.0341150i
$149$		−	10.7234i		−	0.878497i	−0.898366	−	0.439249i	$-0.855245\pi$
$149$		−	10.7234i		−	0.878497i	0.898366	−	0.439249i	$-0.144755\pi$
$150$	2.38562	+	0.555706i	0.194785	+	0.0453732i
$151$		−	15.8824i		−	1.29249i	−0.763129	−	0.646246i	$-0.776338\pi$
$151$		−	15.8824i		−	1.29249i	0.763129	−	0.646246i	$-0.223662\pi$
$152$	0.402143	−	1.93859i	0.0326181	−	0.157241i
$153$	6.20816	−	18.6489i	0.501900	−	1.50767i
$154$	2.26280	−	33.1373i	0.182342	−	2.67028i
$155$	−6.88919			−0.553353
$156$	−3.31240	−	1.01391i	−0.265204	−	0.0811775i
$157$	5.44604			0.434641			0.217321	−	0.976100i	$-0.430268\pi$
$157$	5.44604			0.434641			0.217321	+	0.976100i	$0.430268\pi$
$158$	−1.25679	+	18.4048i	−0.0999847	+	1.46421i
$159$	0.219953	−	1.35710i	0.0174434	−	0.107625i
$160$	1.89128	−	5.33133i	0.149519	−	0.421478i
$161$		−	26.3658i		−	2.07792i
$162$	−9.64494	−	8.30513i	−0.757778	−	0.652512i
$163$		−	1.85125i		−	0.145001i	−0.997368	−	0.0725004i	$-0.976902\pi$
$163$		−	1.85125i		−	0.145001i	0.997368	−	0.0725004i	$-0.0230979\pi$
$164$	1.67647	−	12.2181i	0.130910	−	0.954077i
$165$	−1.39591	+	8.61266i	−0.108671	+	0.670495i
$166$	3.04875	+	0.208186i	0.236629	+	0.0161583i
$167$	−2.96476			−0.229420			−0.114710	−	0.993399i	$-0.536594\pi$
$167$	−2.96476			−0.229420			−0.114710	+	0.993399i	$0.536594\pi$
$168$	8.15765	−	21.3343i	0.629376	−	1.64598i
$169$	1.00000			0.0769231
$170$	−9.24397	−	0.631231i	−0.708980	−	0.0484132i
$171$	−0.663284	+	1.99246i	−0.0507226	+	0.152367i
$172$	0.106205	−	0.774024i	0.00809804	−	0.0590188i
$173$		−	14.4696i		−	1.10011i	−0.835130	−	0.550053i	$-0.814608\pi$
$173$		−	14.4696i		−	1.10011i	0.835130	−	0.550053i	$-0.185392\pi$
$174$	2.82925	−	12.1458i	0.214485	−	0.920773i
$175$		−	4.66235i		−	0.352440i
$176$	19.4049	+	5.42733i	1.46270	+	0.409101i
$177$	−10.5915	−	1.71663i	−0.796106	−	0.129030i
$178$	0.677160	−	9.91657i	0.0507553	−	0.743278i
$179$	7.47837			0.558959			0.279480	−	0.960152i	$-0.409838\pi$
$179$	7.47837			0.558959			0.279480	+	0.960152i	$0.409838\pi$
$180$	−2.65141	+	5.38238i	−0.197624	+	0.401179i
$181$	9.12919			0.678567			0.339284	−	0.940684i	$-0.389815\pi$
$181$	9.12919			0.678567			0.339284	+	0.940684i	$0.389815\pi$
$182$	−0.449199	+	6.57823i	−0.0332969	+	0.487611i
$183$	15.4899	+	2.51054i	1.14505	+	0.185585i
$184$	15.6615	+	3.24882i	1.15458	+	0.239507i
$185$		−	1.52653i		−	0.112233i
$186$	3.82836	−	16.4350i	0.280709	−	1.20507i
$187$		−	33.0036i		−	2.41346i
$188$	−0.957148	−	0.131331i	−0.0698072	−	0.00957833i
$189$	−11.2309	+	21.4657i	−0.816929	+	1.56140i
$190$	0.987632	+	0.0674411i	0.0716503	+	0.00489269i
$191$	−15.8608			−1.14765			−0.573824	−	0.818979i	$-0.694541\pi$
$191$	−15.8608			−1.14765			−0.573824	+	0.818979i	$0.694541\pi$
$192$	11.6675	+	7.47454i	0.842031	+	0.539428i
$193$	9.13915			0.657850			0.328925	−	0.944356i	$-0.393314\pi$
$193$	9.13915			0.657850			0.328925	+	0.944356i	$0.393314\pi$
$194$	−7.49264	−	0.511640i	−0.537940	−	0.0367336i
$195$	0.277108	−	1.70974i	0.0198441	−	0.122437i
$196$	−29.2014	−	4.00675i	−2.08581	−	0.286197i
$197$		−	23.5638i		−	1.67885i	−0.543475	−	0.839425i	$-0.682892\pi$
$197$		−	23.5638i		−	1.67885i	0.543475	−	0.839425i	$-0.317108\pi$
$198$	−19.7708	−	8.11621i	−1.40505	−	0.576794i
$199$		−	1.29778i		−	0.0919972i	−0.998942	−	0.0459986i	$-0.985353\pi$
$199$		−	1.29778i		−	0.0919972i	0.998942	−	0.0459986i	$-0.0146470\pi$
$200$	2.76947	+	0.574500i	0.195831	+	0.0406233i
$201$	−0.455216	+	2.80866i	−0.0321085	+	0.198108i
$202$	−0.0163764	+	0.239822i	−0.00115224	+	0.0168738i
$203$	−23.7372			−1.66603
$204$	6.64281	−	21.7018i	0.465090	−	1.51943i
$205$	6.16631			0.430674
$206$	−1.89658	+	27.7742i	−0.132141	+	1.93512i
$207$	−16.0967	−	5.35853i	−1.11879	−	0.372443i
$208$	−3.85217	−	1.07741i	−0.267100	−	0.0747046i
$209$			3.52612i			0.243907i
$210$	11.1226	+	2.59090i	0.767532	+	0.178789i
$211$		−	7.56242i		−	0.520618i	−0.965525	−	0.260309i	$-0.916176\pi$
$211$		−	7.56242i		−	0.520618i	0.965525	−	0.260309i	$-0.0838245\pi$
$212$	0.215799	−	1.57275i	0.0148212	−	0.108017i
$213$	20.3793	+	3.30299i	1.39636	+	0.226317i
$214$	8.19044	+	0.559290i	0.559887	+	0.0382323i
$215$	0.390638			0.0266413
$216$	−11.3669	−	9.31628i	−0.773421	−	0.633893i
$217$	−32.1198			−2.18043
$218$	20.1388	+	1.37520i	1.36397	+	0.0931400i
$219$	18.4014	+	2.98243i	1.24345	+	0.201534i
$220$	−1.36955	+	9.98130i	−0.0923348	+	0.672939i
$221$			6.55169i			0.440715i
$222$	3.64173	+	0.848305i	0.244417	+	0.0569345i
$223$			25.8560i			1.73144i	0.500525	+	0.865722i	$0.333140\pi$
$223$			25.8560i			1.73144i	−0.500525	+	0.865722i	$0.666860\pi$
$224$	8.81782	−	24.8565i	0.589165	−	1.66079i
$225$	−2.84642	−	0.947565i	−0.189761	−	0.0631710i
$226$	1.01882	−	14.9200i	0.0677712	−	0.992465i
$227$	−3.44287			−0.228512			−0.114256	−	0.993451i	$-0.536448\pi$
$227$	−3.44287			−0.228512			−0.114256	+	0.993451i	$0.536448\pi$
$228$	−0.709722	+	2.31864i	−0.0470025	+	0.153556i
$229$	17.3504			1.14654			0.573272	−	0.819365i	$-0.305674\pi$
$229$	17.3504			1.14654			0.573272	+	0.819365i	$0.305674\pi$
$230$	−0.544842	+	7.97886i	−0.0359258	+	0.526111i
$231$	−6.50820	+	40.1552i	−0.428208	+	2.64202i
$232$	2.92493	−	14.1001i	0.192031	−	0.925716i
$233$		−	16.6488i		−	1.09070i	−0.838209	−	0.545349i	$-0.816397\pi$
$233$		−	16.6488i		−	1.09070i	0.838209	−	0.545349i	$-0.183603\pi$
$234$	3.92480	+	1.61119i	0.256572	+	0.105327i
$235$		−	0.483058i		−	0.0315112i
$236$	−12.2746	−	1.68421i	−0.799008	−	0.109633i
$237$	3.61473	−	22.3027i	0.234802	−	1.44872i
$238$	−43.0986	−	2.94302i	−2.79367	−	0.190768i
$239$	−26.9359			−1.74234			−0.871169	−	0.490983i	$-0.836638\pi$
$239$	−26.9359			−1.74234			−0.871169	+	0.490983i	$0.836638\pi$
$240$	−2.90955	+	6.28765i	−0.187811	+	0.405866i
$241$	−10.9600			−0.705996			−0.352998	−	0.935624i	$-0.614838\pi$
$241$	−10.9600			−0.705996			−0.352998	+	0.935624i	$0.614838\pi$
$242$	−20.2828	−	1.38502i	−1.30383	−	0.0890328i
$243$	10.8226	+	11.2193i	0.694268	+	0.719717i
$244$	17.9514	+	2.46313i	1.14922	+	0.157686i
$245$		−	14.7375i		−	0.941543i
$246$	−3.42666	+	14.7105i	−0.218476	+	0.937906i
$247$		−	0.699987i		−	0.0445391i
$248$	3.95784	−	19.0794i	0.251323	−	1.21154i
$249$	−3.69442	−	0.598777i	−0.234124	−	0.0379460i
$250$	−0.0963462	+	1.41093i	−0.00609347	+	0.0892349i
$251$	19.2428			1.21460			0.607299	−	0.794474i	$-0.292253\pi$
$251$	19.2428			1.21460			0.607299	+	0.794474i	$0.292253\pi$
$252$	−12.3618	+	25.0945i	−0.778720	+	1.58081i
$253$	−28.4868			−1.79095
$254$	−0.00666864	+	0.0976579i	−0.000418428	+	0.00612760i
$255$	11.2017	+	1.81553i	0.701477	+	0.113693i
$256$	13.6784	+	8.30069i	0.854900	+	0.518793i
$257$		−	1.20455i		−	0.0751375i	−0.999294	−	0.0375687i	$-0.988039\pi$
$257$		−	1.20455i		−	0.0751375i	0.999294	−	0.0375687i	$-0.0119613\pi$
$258$	−0.217080	+	0.931915i	−0.0135148	+	0.0580185i
$259$		−	7.11723i		−	0.442243i
$260$	0.271875	−	1.98143i	0.0168610	−	0.122883i
$261$	−4.82430	+	14.4919i	−0.298617	+	0.897025i
$262$	1.51200	+	0.103248i	0.0934118	+	0.00637869i
$263$	9.66287			0.595838			0.297919	−	0.954591i	$-0.403707\pi$
$263$	9.66287			0.595838			0.297919	+	0.954591i	$0.403707\pi$
$264$	−23.0505	−	8.81389i	−1.41866	−	0.542457i
$265$	0.793745			0.0487594
$266$	4.60468	+	0.314434i	0.282331	+	0.0192792i
$267$	−1.94763	+	12.0167i	−0.119193	+	0.735413i
$268$	−0.446620	+	3.25498i	−0.0272817	+	0.198830i
$269$		−	14.4066i		−	0.878385i	−0.898393	−	0.439193i	$-0.855265\pi$
$269$		−	14.4066i		−	0.878385i	0.898393	−	0.439193i	$-0.144735\pi$
$270$	3.84231	−	6.26392i	0.233835	−	0.381210i
$271$		−	5.47269i		−	0.332442i	−0.986089	−	0.166221i	$-0.946843\pi$
$271$		−	5.47269i		−	0.332442i	0.986089	−	0.166221i	$-0.0531566\pi$
$272$	7.05883	−	25.2382i	0.428005	−	1.53029i
$273$	1.29197	−	7.97140i	0.0781938	−	0.482451i
$274$	1.83939	−	26.9367i	0.111122	−	1.62731i
$275$	−5.03741			−0.303767
$276$	−18.7318	−	5.73369i	−1.12752	−	0.345128i
$277$	1.64011			0.0985444			0.0492722	−	0.998785i	$-0.484310\pi$
$277$	1.64011			0.0985444			0.0492722	+	0.998785i	$0.484310\pi$
$278$	0.00977754	−	0.143186i	0.000586418	−	0.00858771i
$279$	−6.52795	+	19.6095i	−0.390818	+	1.17399i
$280$	12.9122	+	2.67852i	0.771653	+	0.160072i
$281$		−	23.9044i		−	1.42602i	−0.701156	−	0.713008i	$-0.747333\pi$
$281$		−	23.9044i		−	1.42602i	0.701156	−	0.713008i	$-0.252667\pi$
$282$	1.15239	+	0.268438i	0.0686241	+	0.0159853i
$283$			19.7669i			1.17502i	0.809218	+	0.587509i	$0.199891\pi$
$283$			19.7669i			1.17502i	−0.809218	+	0.587509i	$0.800109\pi$
$284$	23.6177	+	3.24062i	1.40145	+	0.192295i
$285$	−1.19680	−	0.193972i	−0.0708921	−	0.0114899i
$286$	7.10742	+	0.485335i	0.420271	+	0.0286985i
$287$	28.7495			1.69703
$288$	−13.3831	−	10.4352i	−0.788606	−	0.614898i
$289$	−25.9247			−1.52498
$290$	7.18341	+	0.490524i	0.421824	+	0.0288046i
$291$	9.07946	+	1.47156i	0.532247	+	0.0862646i
$292$	21.3256	+	2.92611i	1.24799	+	0.171238i
$293$			24.9188i			1.45577i	0.685700	+	0.727884i	$0.259496\pi$
$293$			24.9188i			1.45577i	−0.685700	+	0.727884i	$0.740504\pi$
$294$	35.1580	+	8.18971i	2.05046	+	0.477634i
$295$		−	6.19480i		−	0.360675i
$296$	4.22769	+	0.876994i	0.245729	+	0.0509742i
$297$	23.1926	+	12.1344i	1.34577	+	0.704109i
$298$	−1.03316	+	15.1300i	−0.0598494	+	0.876456i
$299$	5.65505			0.327040
$300$	−3.31240	−	1.01391i	−0.191241	−	0.0585380i
$301$	1.82129			0.104977
$302$	−1.53021	+	22.4089i	−0.0880537	+	1.28949i
$303$	0.0471014	−	0.290613i	0.00270590	−	0.0166953i
$304$	−0.754170	+	2.69647i	−0.0432546	+	0.154653i
$305$			9.05980i			0.518763i
$306$	−10.5560	+	25.7141i	−0.603447	+	1.46998i
$307$			1.88922i			0.107824i	0.998546	+	0.0539118i	$0.0171690\pi$
$307$			1.88922i			0.107824i	−0.998546	+	0.0539118i	$0.982831\pi$
$308$	−6.38530	+	46.5363i	−0.363836	+	2.65165i
$309$	5.45490	−	33.6564i	0.310318	−	1.91465i
$310$	9.72015	+	0.663747i	0.552067	+	0.0376983i
$311$	11.9419			0.677161			0.338581	−	0.940937i	$-0.390053\pi$
$311$	11.9419			0.677161			0.338581	+	0.940937i	$0.390053\pi$
$312$	4.57587	+	1.74969i	0.259058	+	0.0990565i
$313$	9.16738			0.518171			0.259086	−	0.965854i	$-0.416579\pi$
$313$	9.16738			0.518171			0.259086	+	0.965854i	$0.416579\pi$
$314$	−7.68397	−	0.524705i	−0.433632	−	0.0296108i
$315$	−13.2710	−	4.41788i	−0.747737	−	0.248919i
$316$	3.54647	−	25.8468i	0.199505	−	1.45400i
$317$		−	28.1638i		−	1.58184i	−0.611920	−	0.790920i	$-0.709603\pi$
$317$		−	28.1638i		−	1.58184i	0.611920	−	0.790920i	$-0.290397\pi$
$318$	−0.441089	+	1.89358i	−0.0247350	+	0.106186i
$319$			25.6468i			1.43594i
$320$	−3.18212	+	7.33990i	−0.177886	+	0.410313i
$321$	−9.92504	−	1.60861i	−0.553962	−	0.0897840i
$322$	−2.54024	+	37.2002i	−0.141562	+	2.07309i
$323$	4.58610			0.255178
$324$	12.8081	+	12.6472i	0.711564	+	0.702622i
$325$	1.00000			0.0554700
$326$	−0.178361	+	2.61197i	−0.00987848	+	0.144664i
$327$	−24.4039	−	3.95529i	−1.34954	−	0.218728i
$328$	−3.54254	+	17.0774i	−0.195604	+	0.942941i
$329$		−	2.25218i		−	0.124167i
$330$	2.79932	−	12.0174i	0.154098	−	0.661534i
$331$		−	32.9408i		−	1.81059i	−0.424782	−	0.905296i	$-0.639649\pi$
$331$		−	32.9408i		−	1.81059i	0.424782	−	0.905296i	$-0.360351\pi$
$332$	−4.28150	−	0.587470i	−0.234978	−	0.0322416i
$333$	−4.34516	−	1.44649i	−0.238113	−	0.0792672i
$334$	4.18306	+	0.285643i	0.228887	+	0.0156297i
$335$	−1.64274			−0.0897525
$336$	−13.5653	+	29.3152i	−0.740049	+	1.59928i
$337$	−7.16724			−0.390425			−0.195212	−	0.980761i	$-0.562540\pi$
$337$	−7.16724			−0.390425			−0.195212	+	0.980761i	$0.562540\pi$
$338$	−1.41093	−	0.0963462i	−0.0767444	−	0.00524054i
$339$	−2.93031	+	18.0798i	−0.159153	+	0.981963i
$340$	12.9818	+	1.78124i	0.704035	+	0.0966015i
$341$			34.7037i			1.87931i
$342$	1.12781	−	2.74731i	0.0609850	−	0.148558i
$343$		−	36.0748i		−	1.94786i
$344$	−0.224422	+	1.08186i	−0.0121000	+	0.0583300i
$345$	1.56706	−	9.66866i	0.0843676	−	0.520543i
$346$	−1.39409	+	20.4156i	−0.0749469	+	1.09755i
$347$	24.0269			1.28983			0.644916	−	0.764253i	$-0.276892\pi$
$347$	24.0269			1.28983			0.644916	+	0.764253i	$0.276892\pi$
$348$	−5.16207	+	16.8643i	−0.276716	+	0.904022i
$349$	−10.7310			−0.574417			−0.287208	−	0.957868i	$-0.592727\pi$
$349$	−10.7310			−0.574417			−0.287208	+	0.957868i	$0.592727\pi$
$350$	−0.449199	+	6.57823i	−0.0240107	+	0.351621i
$351$	−4.60406	−	2.40886i	−0.245747	−	0.128575i
$352$	−26.8561	−	9.52717i	−1.43143	−	0.507800i
$353$			12.0331i			0.640459i	0.947340	+	0.320229i	$0.103760\pi$
$353$			12.0331i			0.640459i	−0.947340	+	0.320229i	$0.896240\pi$
$354$	14.7785	+	3.44249i	0.785466	+	0.182966i
$355$			11.9195i			0.632622i
$356$	−1.91085	+	13.9263i	−0.101275	+	0.738094i
$357$	52.2262	+	8.46462i	2.76410	+	0.447995i
$358$	−10.5514	−	0.720512i	−0.557661	−	0.0380803i
$359$	−10.3443			−0.545951			−0.272975	−	0.962021i	$-0.588008\pi$
$359$	−10.3443			−0.545951			−0.272975	+	0.962021i	$0.588008\pi$
$360$	4.25952	−	7.33870i	0.224496	−	0.386783i
$361$	18.5100			0.974211
$362$	−12.8806	−	0.879563i	−0.676991	−	0.0462288i
$363$	24.5784	+	3.98356i	1.29003	+	0.209083i
$364$	1.26758	−	9.23814i	0.0664390	−	0.484210i
$365$			10.7627i			0.563346i
$366$	−21.6132	−	5.03459i	−1.12974	−	0.263162i
$367$		−	11.6121i		−	0.606146i	−0.952967	−	0.303073i	$-0.901987\pi$
$367$		−	11.6121i		−	0.606146i	0.952967	−	0.303073i	$-0.0980126\pi$
$368$	−21.7842	−	6.09278i	−1.13558	−	0.317608i
$369$	5.84298	−	17.5519i	0.304173	−	0.913717i
$370$	−0.147076	+	2.15383i	−0.00764611	+	0.111972i
$371$	3.70071			0.192131
$372$	−6.98500	+	22.8197i	−0.362155	+	1.18315i
$373$	35.0545			1.81505			0.907525	−	0.419997i	$-0.137969\pi$
$373$	35.0545			1.81505			0.907525	+	0.419997i	$0.137969\pi$
$374$	−3.17977	+	46.5657i	−0.164422	+	2.40785i
$375$	0.277108	−	1.70974i	0.0143098	−	0.0882906i
$376$	1.33781	+	0.277517i	0.0689925	+	0.0143118i
$377$		−	5.09126i		−	0.262213i
$378$	17.9142	−	29.2046i	0.921405	−	1.50212i
$379$		−	8.91238i		−	0.457798i	−0.973450	−	0.228899i	$-0.926487\pi$
$379$		−	8.91238i		−	0.457798i	0.973450	−	0.228899i	$-0.0735126\pi$
$380$	−1.38698	−	0.190309i	−0.0711505	−	0.00976265i
$381$	0.0191801	−	0.118340i	0.000982628	−	0.00606276i
$382$	22.3784	+	1.52813i	1.14498	+	0.0781858i
$383$	29.8922			1.52742			0.763710	−	0.645559i	$-0.223376\pi$
$383$	29.8922			1.52742			0.763710	+	0.645559i	$0.223376\pi$
$384$	−15.7419	−	11.6702i	−0.803325	−	0.595540i
$385$	−23.4862			−1.19697
$386$	−12.8947	−	0.880522i	−0.656322	−	0.0448174i
$387$	0.370155	−	1.11192i	0.0188160	−	0.0565221i
$388$	10.5223	+	1.44377i	0.534188	+	0.0732965i
$389$			14.5837i			0.739424i	0.929146	+	0.369712i	$0.120544\pi$
$389$			14.5837i			0.739424i	−0.929146	+	0.369712i	$0.879456\pi$
$390$	−0.555706	+	2.38562i	−0.0281393	+	0.120801i
$391$			37.0501i			1.87371i
$392$	40.8150	+	8.46668i	2.06147	+	0.427632i
$393$	−1.83222	−	0.296959i	−0.0924233	−	0.0149796i
$394$	−2.27028	+	33.2468i	−0.114375	+	1.67495i
$395$	13.0445			0.656340
$396$	27.1133	+	13.3562i	1.36249	+	0.671176i
$397$	−7.65512			−0.384200			−0.192100	−	0.981375i	$-0.561530\pi$
$397$	−7.65512			−0.384200			−0.192100	+	0.981375i	$0.561530\pi$
$398$	−0.125036	+	1.83107i	−0.00626750	+	0.0917834i
$399$	−5.57988	−	0.904365i	−0.279343	−	0.0452749i
$400$	−3.85217	−	1.07741i	−0.192608	−	0.0538703i
$401$		−	4.25810i		−	0.212639i	−0.994332	−	0.106320i	$-0.966093\pi$
$401$		−	4.25810i		−	0.212639i	0.994332	−	0.106320i	$-0.0339067\pi$
$402$	0.912881	−	3.91896i	0.0455304	−	0.195460i
$403$		−	6.88919i		−	0.343175i
$404$	0.0462119	−	0.336794i	0.00229913	−	0.0167561i
$405$	−5.39434	+	7.20424i	−0.268047	+	0.357982i
$406$	33.4915	+	2.28699i	1.66216	+	0.113502i
$407$	−7.68978			−0.381168
$408$	−11.4634	+	29.9797i	−0.567524	+	1.48422i
$409$	−24.7154			−1.22210			−0.611049	−	0.791593i	$-0.709252\pi$
$409$	−24.7154			−1.22210			−0.611049	+	0.791593i	$0.709252\pi$
$410$	−8.70022	−	0.594101i	−0.429673	−	0.0293405i
$411$	−5.29041	+	32.6415i	−0.260957	+	1.61009i
$412$	5.35189	−	39.0047i	0.263669	−	1.92162i
$413$		−	28.8823i		−	1.42121i
$414$	22.1949	+	9.11135i	1.09082	+	0.447798i
$415$		−	2.16081i		−	0.106070i
$416$	5.33133	+	1.89128i	0.261390	+	0.0927278i
$417$	−0.0281218	+	0.173510i	−0.00137713	+	0.00849683i
$418$	0.339729	−	4.97510i	0.0166167	−	0.243340i
$419$	−2.59833			−0.126937			−0.0634683	−	0.997984i	$-0.520216\pi$
$419$	−2.59833			−0.126937			−0.0634683	+	0.997984i	$0.520216\pi$
$420$	−15.4436	−	4.72719i	−0.753568	−	0.230663i
$421$	−16.6272			−0.810358			−0.405179	−	0.914237i	$-0.632791\pi$
$421$	−16.6272			−0.810358			−0.405179	+	0.914237i	$0.632791\pi$
$422$	−0.728610	+	10.6700i	−0.0354682	+	0.519409i
$423$	−1.37499	−	0.457729i	−0.0668542	−	0.0222555i
$424$	−0.456006	+	2.19825i	−0.0221456	+	0.106756i
$425$			6.55169i			0.317804i
$426$	−28.4354	−	6.62374i	−1.37770	−	0.320921i
$427$			42.2399i			2.04413i
$428$	−11.5022	−	1.57824i	−0.555981	−	0.0762869i
$429$	−8.61266	−	1.39591i	−0.415823	−	0.0673950i
$430$	−0.551162	−	0.0376365i	−0.0265794	−	0.00181499i
$431$	−35.5765			−1.71366			−0.856829	−	0.515600i	$-0.827569\pi$
$431$	−35.5765			−1.71366			−0.856829	+	0.515600i	$0.827569\pi$
$432$	15.1403	+	14.2398i	0.728439	+	0.685111i
$433$	0.306543			0.0147315			0.00736576	−	0.999973i	$-0.497655\pi$
$433$	0.306543			0.0147315			0.00736576	+	0.999973i	$0.497655\pi$
$434$	45.3187	+	3.09462i	2.17537	+	0.148546i
$435$	−8.70474	−	1.41083i	−0.417360	−	0.0676441i
$436$	−28.2820	−	3.88060i	−1.35446	−	0.185847i
$437$		−	3.95846i		−	0.189359i
$438$	−25.6757	−	5.98090i	−1.22683	−	0.285779i
$439$			24.1138i			1.15089i	0.817840	+	0.575445i	$0.195171\pi$
$439$			24.1138i			1.15089i	−0.817840	+	0.575445i	$0.804829\pi$
$440$	2.89399	−	13.9509i	0.137966	−	0.665085i
$441$	−41.9491	−	13.9647i	−1.99758	−	0.664987i
$442$	0.631231	−	9.24397i	0.0300246	−	0.439691i
$443$	−39.8814			−1.89482			−0.947411	−	0.320018i	$-0.896311\pi$
$443$	−39.8814			−1.89482			−0.947411	+	0.320018i	$0.896311\pi$
$444$	−5.05649	−	1.54776i	−0.239971	−	0.0734537i
$445$	−7.02840			−0.333178
$446$	2.49113	−	36.4809i	0.117958	−	1.72742i
$447$	2.97155	−	18.3343i	0.140549	−	0.867181i
$448$	−14.8361	+	34.2212i	−0.700942	+	1.61680i
$449$			16.8351i			0.794498i	0.917711	+	0.397249i	$0.130035\pi$
$449$			16.8351i			0.794498i	−0.917711	+	0.397249i	$0.869965\pi$
$450$	3.92480	+	1.61119i	0.185017	+	0.0759521i
$451$		−	31.0622i		−	1.46266i
$452$	−2.87498	+	20.9529i	−0.135227	+	0.985542i
$453$	4.40114	−	27.1548i	0.206784	−	1.27584i
$454$	4.85765	+	0.331708i	0.227981	+	0.0155678i
$455$	4.66235			0.218574
$456$	1.22476	−	3.20305i	0.0573546	−	0.149997i
$457$	26.4440			1.23700			0.618499	−	0.785785i	$-0.287741\pi$
$457$	26.4440			1.23700			0.618499	+	0.785785i	$0.287741\pi$
$458$	−24.4801	−	1.67164i	−1.14388	−	0.0781107i
$459$	15.7821	−	30.1644i	0.736645	−	1.40795i
$460$	1.53747	−	11.2051i	0.0716848	−	0.522441i
$461$			2.38547i			0.111102i	0.998456	+	0.0555512i	$0.0176916\pi$
$461$			2.38547i			0.111102i	−0.998456	+	0.0555512i	$0.982308\pi$
$462$	13.0514	−	56.0291i	0.607206	−	2.60671i
$463$			17.2209i			0.800324i	0.916444	+	0.400162i	$0.131046\pi$
$463$			17.2209i			0.800324i	−0.916444	+	0.400162i	$0.868954\pi$
$464$	−5.48536	+	19.6124i	−0.254651	+	0.910483i
$465$	−11.7787	−	1.90905i	−0.546225	−	0.0885300i
$466$	−1.60405	+	23.4902i	−0.0743060	+	1.08816i
$467$	−29.3709			−1.35912			−0.679561	−	0.733619i	$-0.737830\pi$
$467$	−29.3709			−1.35912			−0.679561	+	0.733619i	$0.737830\pi$
$468$	−5.38238	−	2.65141i	−0.248801	−	0.122561i
$469$	−7.65902			−0.353661
$470$	−0.0465408	+	0.681560i	−0.00214677	+	0.0314380i
$471$	9.31131	+	1.50914i	0.429043	+	0.0695375i
$472$	17.1563	+	3.55891i	0.789683	+	0.163812i
$473$		−	1.96781i		−	0.0904798i
$474$	−7.24891	+	31.1192i	−0.332953	+	1.42935i
$475$		−	0.699987i		−	0.0321176i
$476$	60.5254	+	8.30477i	2.77418	+	0.380649i
$477$	0.752125	−	2.25933i	0.0344374	−	0.103448i
$478$	38.0046	+	2.59517i	1.73829	+	0.118700i
$479$	−8.14856			−0.372317			−0.186159	−	0.982520i	$-0.559604\pi$
$479$	−8.14856			−0.372317			−0.186159	+	0.982520i	$0.559604\pi$
$480$	4.71096	−	8.59109i	0.215025	−	0.392128i
$481$	1.52653			0.0696040
$482$	15.4638	+	1.05595i	0.704356	+	0.0480974i
$483$	7.30617	−	45.0787i	0.332442	−	2.05115i
$484$	28.4841	+	3.90834i	1.29473	+	0.177652i
$485$			5.31043i			0.241134i
$486$	−14.1889	−	16.8723i	−0.643623	−	0.765343i
$487$			28.9133i			1.31019i	0.755548	+	0.655093i	$0.227371\pi$
$487$			28.9133i			1.31019i	−0.755548	+	0.655093i	$0.772629\pi$
$488$	−25.0908	−	5.20485i	−1.13581	−	0.235613i
$489$	0.512995	−	3.16515i	0.0231984	−	0.143133i
$490$	−1.41990	+	20.7935i	−0.0641446	+	0.939355i
$491$	−3.40523			−0.153676			−0.0768379	−	0.997044i	$-0.524482\pi$
$491$	−3.40523			−0.153676			−0.0768379	+	0.997044i	$0.524482\pi$
$492$	6.25207	−	20.4253i	0.281865	−	0.920843i
$493$	33.3564			1.50230
$494$	−0.0674411	+	0.987632i	−0.00303432	+	0.0444356i
$495$	−4.77327	+	14.3386i	−0.214543	+	0.644472i
$496$	−7.42245	+	26.5383i	−0.333278	+	1.19161i
$497$			55.5729i			2.49278i
$498$	5.15487	+	1.20078i	0.230995	+	0.0538080i
$499$		−	35.3026i		−	1.58036i	−0.612874	−	0.790180i	$-0.709987\pi$
$499$		−	35.3026i		−	1.58036i	0.612874	−	0.790180i	$-0.290013\pi$
$500$	0.271875	−	1.98143i	0.0121586	−	0.0886125i
$501$	−5.06897	−	0.821558i	−0.226465	−	0.0367045i
$502$	−27.1503	−	1.85398i	−1.21178	−	0.0827470i
$503$	6.76294			0.301544			0.150772	−	0.988569i	$-0.451824\pi$
$503$	6.76294			0.301544			0.150772	+	0.988569i	$0.451824\pi$
$504$	19.8594	−	34.2156i	0.884606	−	1.52408i
$505$	0.169975			0.00756378
$506$	40.1928	+	2.74459i	1.78679	+	0.122012i
$507$	1.70974	+	0.277108i	0.0759322	+	0.0123068i
$508$	0.0188179	−	0.137146i	0.000834911	−	0.00608486i
$509$		−	8.84100i		−	0.391870i	−0.980617	−	0.195935i	$-0.937226\pi$
$509$		−	8.84100i		−	0.391870i	0.980617	−	0.195935i	$-0.0627742\pi$
$510$	−15.6299	−	3.64082i	−0.692102	−	0.161218i
$511$			50.1795i			2.21981i
$512$	−18.4995	−	13.0295i	−0.817570	−	0.575830i
$513$	−1.68617	+	3.22279i	−0.0744462	+	0.142290i
$514$	−0.116053	+	1.69953i	−0.00511890	+	0.0749629i
$515$	19.6851			0.867429
$516$	0.396071	−	1.29395i	0.0174361	−	0.0569630i
$517$	−2.43336			−0.107019
$518$	−0.685719	+	10.0419i	−0.0301287	+	0.441216i
$519$	4.00965	−	24.7393i	0.176004	−	1.08593i
$520$	−0.574500	+	2.76947i	−0.0251935	+	0.121449i
$521$		−	6.96646i		−	0.305206i	−0.988288	−	0.152603i	$-0.951234\pi$
$521$		−	6.96646i		−	0.305206i	0.988288	−	0.152603i	$-0.0487656\pi$
$522$	8.20298	−	19.9822i	0.359035	−	0.874597i
$523$		−	20.1239i		−	0.879955i	−0.898009	−	0.439977i	$-0.854986\pi$
$523$		−	20.1239i		−	0.879955i	0.898009	−	0.439977i	$-0.145014\pi$
$524$	−2.12338	−	0.291351i	−0.0927602	−	0.0127277i
$525$	1.29197	−	7.97140i	0.0563863	−	0.347900i
$526$	−13.6336	−	0.930981i	−0.594454	−	0.0405927i
$527$	45.1358			1.96615
$528$	31.6735	+	14.6566i	1.37841	+	0.637846i
$529$	8.97957			0.390416
$530$	−1.11992	−	0.0764743i	−0.0486461	−	0.00332183i
$531$	−17.6330	−	5.86998i	−0.765208	−	0.254735i
$532$	−6.46658	−	0.887287i	−0.280362	−	0.0384688i
$533$			6.16631i			0.267093i
$534$	3.90573	−	16.7671i	0.169017	−	0.725584i
$535$		−	5.80500i		−	0.250972i
$536$	0.943754	−	4.54952i	0.0407640	−	0.196509i
$537$	12.7861	+	2.07232i	0.551759	+	0.0894270i
$538$	−1.38802	+	20.3267i	−0.0598418	+	0.876344i
$539$	−74.2387			−3.19769
$540$	−6.02472	+	8.46775i	−0.259263	+	0.364394i
$541$	32.7478			1.40794			0.703969	−	0.710231i	$-0.251409\pi$
$541$	32.7478			1.40794			0.703969	+	0.710231i	$0.251409\pi$
$542$	−0.527273	+	7.72157i	−0.0226483	+	0.331670i
$543$	15.6085	+	2.52977i	0.669826	+	0.108563i
$544$	−12.3911	+	34.9292i	−0.531265	+	1.49758i
$545$		−	14.2735i		−	0.611409i
$546$	−2.59090	+	11.1226i	−0.110880	+	0.476003i
$547$		−	34.5794i		−	1.47851i	−0.673426	−	0.739254i	$-0.735178\pi$
$547$		−	34.5794i		−	1.47851i	0.673426	−	0.739254i	$-0.264822\pi$
$548$	−5.19051	+	37.8286i	−0.221727	+	1.61596i
$549$	25.7880	+	8.58475i	1.10061	+	0.366388i
$550$	7.10742	+	0.485335i	0.303061	+	0.0206948i
$551$	−3.56382			−0.151824
$552$	25.8768	+	9.89456i	1.10139	+	0.421141i
$553$	60.8180			2.58624
$554$	−2.31407	−	0.158018i	−0.0983154	−	0.00671354i
$555$	0.423015	−	2.60998i	0.0179560	−	0.110787i
$556$	−0.0275908	+	0.201083i	−0.00117011	+	0.00852780i
$557$		−	34.1118i		−	1.44536i	−0.691181	−	0.722681i	$-0.742909\pi$
$557$		−	34.1118i		−	1.44536i	0.691181	−	0.722681i	$-0.257091\pi$
$558$	11.0998	−	27.0387i	0.469891	−	1.14464i
$559$			0.390638i			0.0165222i
$560$	−17.9601	−	5.02324i	−0.758955	−	0.212271i
$561$	9.14555	−	56.4275i	0.386126	−	2.38237i
$562$	−2.30310	+	33.7273i	−0.0971502	+	1.42270i
$563$	−10.5450			−0.444419			−0.222210	−	0.974999i	$-0.571327\pi$
$563$	−10.5450			−0.444419			−0.222210	+	0.974999i	$0.571327\pi$
$564$	−1.60008	−	0.489776i	−0.0673756	−	0.0206233i
$565$	−10.5746			−0.444878
$566$	1.90446	−	27.8896i	0.0800505	−	1.17229i
$567$	−25.1503	+	33.5887i	−1.05621	+	1.41059i
$568$	−33.0107	−	6.84775i	−1.38510	−	0.287325i
$569$			21.9273i			0.919238i	0.888116	+	0.459619i	$0.152014\pi$
$569$			21.9273i			0.919238i	−0.888116	+	0.459619i	$0.847986\pi$
$570$	1.66990	+	0.388987i	0.0699446	+	0.0162929i
$571$		−	9.37041i		−	0.392139i	−0.980590	−	0.196070i	$-0.937182\pi$
$571$		−	9.37041i		−	0.392139i	0.980590	−	0.196070i	$-0.0628179\pi$
$572$	−9.98130	−	1.36955i	−0.417339	−	0.0572636i
$573$	−27.1178	−	4.39515i	−1.13286	−	0.183610i
$574$	−40.5634	−	2.76990i	−1.69309	−	0.115614i
$575$	5.65505			0.235832
$576$	17.8772	+	16.0127i	0.744883	+	0.667195i
$577$	−24.8818			−1.03584			−0.517921	−	0.855429i	$-0.673294\pi$
$577$	−24.8818			−1.03584			−0.517921	+	0.855429i	$0.673294\pi$
$578$	36.5779	+	2.49775i	1.52144	+	0.103893i
$579$	15.6256	+	2.53253i	0.649376	+	0.105248i
$580$	−10.0880	−	1.38419i	−0.418882	−	0.0574753i
$581$		−	10.0744i		−	0.417958i
$582$	−12.6687	−	2.95104i	−0.525134	−	0.122325i
$583$		−	3.99842i		−	0.165598i
$584$	−29.8070	−	6.18317i	−1.23342	−	0.255862i
$585$	0.947565	−	2.84642i	0.0391770	−	0.117685i
$586$	2.40083	−	35.1586i	0.0991773	−	1.45239i
$587$	−9.18323			−0.379032			−0.189516	−	0.981878i	$-0.560692\pi$
$587$	−9.18323			−0.379032			−0.189516	+	0.981878i	$0.560692\pi$
$588$	−48.8164	−	14.9424i	−2.01316	−	0.616216i
$589$	−4.82234			−0.198701
$590$	−0.596846	+	8.74042i	−0.0245718	+	0.359837i
$591$	6.52971	−	40.2879i	0.268596	−	1.65722i
$592$	−5.88047	−	1.64470i	−0.241686	−	0.0675966i
$593$			10.7692i			0.442238i	0.975247	+	0.221119i	$0.0709709\pi$
$593$			10.7692i			0.442238i	−0.975247	+	0.221119i	$0.929029\pi$
$594$	−31.5539	−	19.3553i	−1.29467	−	0.794156i
$595$			30.5463i			1.25228i
$596$	2.91543	−	21.2478i	0.119421	−	0.870342i
$597$	0.359625	−	2.21887i	0.0147185	−	0.0908121i
$598$	−7.97886	−	0.544842i	−0.326280	−	0.0222803i
$599$	2.31068			0.0944120			0.0472060	−	0.998885i	$-0.484968\pi$
$599$	2.31068			0.0944120			0.0472060	+	0.998885i	$0.484968\pi$
$600$	4.57587	+	1.74969i	0.186809	+	0.0714307i
$601$	−0.0150889			−0.000615489			−0.000307744	−	1.00000i	$-0.500098\pi$
$601$	−0.0150889			−0.000615489			−0.000307744		1.00000i	$0.500098\pi$
$602$	−2.56971	−	0.175475i	−0.104734	−	0.00715181i
$603$	−1.55660	+	4.67593i	−0.0633898	+	0.190419i
$604$	4.31803	−	31.4700i	0.175698	−	1.28049i
$605$			14.3755i			0.584447i
$606$	−0.0944561	+	0.405496i	−0.00383702	+	0.0164721i
$607$			27.8774i			1.13151i	0.824574	+	0.565754i	$0.191415\pi$
$607$			27.8774i			1.13151i	−0.824574	+	0.565754i	$0.808585\pi$
$608$	1.32387	−	3.73186i	0.0536902	−	0.151347i
$609$	−40.5845	−	6.57778i	−1.64457	−	0.266545i
$610$	0.872877	−	12.7827i	0.0353418	−	0.517557i
$611$	0.483058			0.0195424
$612$	17.3712	−	35.2637i	0.702190	−	1.42545i
$613$	−1.84020			−0.0743249			−0.0371625	−	0.999309i	$-0.511832\pi$
$613$	−1.84020			−0.0743249			−0.0371625	+	0.999309i	$0.511832\pi$
$614$	0.182019	−	2.66556i	0.00734570	−	0.107573i
$615$	10.5428	+	1.70873i	0.425126	+	0.0689028i
$616$	13.4928	−	65.0441i	0.543640	−	2.62070i
$617$		−	29.3158i		−	1.18021i	−0.807327	−	0.590105i	$-0.799086\pi$
$617$		−	29.3158i		−	1.18021i	0.807327	−	0.590105i	$-0.200914\pi$
$618$	−10.9391	+	46.9612i	−0.440036	+	1.88906i
$619$		−	39.7422i		−	1.59737i	−0.601748	−	0.798686i	$-0.705529\pi$
$619$		−	39.7422i		−	1.59737i	0.601748	−	0.798686i	$-0.294471\pi$
$620$	−13.6505	−	1.87300i	−0.548216	−	0.0752214i
$621$	−26.0362	−	13.6222i	−1.04480	−	0.546640i
$622$	−16.8491	−	1.15055i	−0.675588	−	0.0461330i
$623$	−32.7689			−1.31286
$624$	−6.28765	−	2.90955i	−0.251707	−	0.116475i
$625$	1.00000			0.0400000
$626$	−12.9345	−	0.883243i	−0.516967	−	0.0353015i
$627$	−0.977117	+	6.02875i	−0.0390223	+	0.240765i
$628$	10.7910	+	1.48064i	0.430607	+	0.0590841i
$629$			10.0014i			0.398782i
$630$	18.2988	+	7.51192i	0.729041	+	0.299282i
$631$		−	31.0663i		−	1.23673i	−0.785891	−	0.618365i	$-0.787795\pi$
$631$		−	31.0663i		−	1.23673i	0.785891	−	0.618365i	$-0.212205\pi$
$632$	−7.49406	+	36.1263i	−0.298098	+	1.43703i
$633$	2.09561	−	12.9298i	0.0832929	−	0.513912i
$634$	−2.71348	+	39.7372i	−0.107766	+	1.57816i
$635$	0.0692154			0.00274673
$636$	0.804784	−	2.62920i	0.0319117	−	0.104255i
$637$	14.7375			0.583920
$638$	2.47097	−	36.1858i	0.0978267	−	1.43261i
$639$	33.9279	+	11.2945i	1.34217	+	0.446804i
$640$	5.19691	−	10.0495i	0.205426	−	0.397241i
$641$			37.1590i			1.46769i	0.679316	+	0.733846i	$0.262277\pi$
$641$			37.1590i			1.46769i	−0.679316	+	0.733846i	$0.737723\pi$
$642$	13.8485	+	3.22588i	0.546558	+	0.127315i
$643$			34.6620i			1.36694i	0.729981	+	0.683468i	$0.239529\pi$
$643$			34.6620i			1.36694i	−0.729981	+	0.683468i	$0.760471\pi$
$644$	7.16820	−	52.2421i	0.282467	−	2.05863i
$645$	0.667890	+	0.108249i	0.0262981	+	0.00426230i
$646$	−6.47066	−	0.441854i	−0.254585	−	0.0173845i
$647$	44.5213			1.75031			0.875157	−	0.483840i	$-0.160758\pi$
$647$	44.5213			1.75031			0.875157	+	0.483840i	$0.160758\pi$
$648$	−16.8529	−	19.0783i	−0.662043	−	0.749466i
$649$	−31.2058			−1.22493
$650$	−1.41093	−	0.0963462i	−0.0553411	−	0.00377901i
$651$	−54.9165	−	8.90065i	−2.15235	−	0.348844i
$652$	0.503308	−	3.66812i	0.0197111	−	0.143655i
$653$		−	4.45001i		−	0.174142i	−0.996202	−	0.0870711i	$-0.972249\pi$
$653$		−	4.45001i		−	0.174142i	0.996202	−	0.0870711i	$-0.0277507\pi$
$654$	34.0511	+	7.93186i	1.33150	+	0.310160i
$655$		−	1.07164i		−	0.0418723i
$656$	6.64362	−	23.7537i	0.259390	−	0.927425i
$657$	30.6352	+	10.1984i	1.19519	+	0.397876i
$658$	−0.216989	+	3.17767i	−0.00845913	+	0.123878i
$659$	28.0983			1.09455			0.547277	−	0.836951i	$-0.315664\pi$
$659$	28.0983			1.09455			0.547277	+	0.836951i	$0.315664\pi$
$660$	−5.10747	+	16.6859i	−0.198808	+	0.649498i
$661$	−33.8444			−1.31639			−0.658197	−	0.752845i	$-0.728681\pi$
$661$	−33.8444			−1.31639			−0.658197	+	0.752845i	$0.728681\pi$
$662$	−3.17372	+	46.4771i	−0.123350	+	1.80638i
$663$	−1.81553	+	11.2017i	−0.0705092	+	0.435038i
$664$	5.98429	+	1.24138i	0.232235	+	0.0481751i
$665$		−	3.26358i		−	0.126556i
$666$	5.99135	+	2.45953i	0.232160	+	0.0953050i
$667$		−	28.7913i		−	1.11481i
$668$	−5.87448	−	0.806044i	−0.227290	−	0.0311868i
$669$	−7.16490	+	44.2070i	−0.277011	+	1.70914i
$670$	2.31779	+	0.158272i	0.0895440	+	0.00611457i
$671$	45.6379			1.76183
$672$	21.9641	−	40.0547i	0.847284	−	1.54514i
$673$	−13.3369			−0.514098			−0.257049	−	0.966398i	$-0.582750\pi$
$673$	−13.3369			−0.514098			−0.257049	+	0.966398i	$0.582750\pi$
$674$	10.1125	+	0.690537i	0.389518	+	0.0265985i
$675$	−4.60406	−	2.40886i	−0.177211	−	0.0927169i
$676$	1.98143	+	0.271875i	0.0762090	+	0.0104567i
$677$			16.6664i			0.640543i	0.947326	+	0.320272i	$0.103774\pi$
$677$			16.6664i			0.640543i	−0.947326	+	0.320272i	$0.896226\pi$
$678$	5.87638	−	25.2270i	0.225681	−	0.968839i
$679$			24.7591i			0.950166i
$680$	−18.1447	−	3.76395i	−0.695818	−	0.144341i
$681$	−5.88642	−	0.954048i	−0.225568	−	0.0365592i
$682$	3.34357	−	48.9644i	0.128032	−	1.87494i
$683$	11.2952			0.432198			0.216099	−	0.976371i	$-0.430667\pi$
$683$	11.2952			0.432198			0.216099	+	0.976371i	$0.430667\pi$
$684$	−1.85595	+	3.76760i	−0.0709641	+	0.144058i
$685$	−19.0915			−0.729449
$686$	−3.47567	+	50.8989i	−0.132702	+	1.94333i
$687$	29.6646	+	4.80792i	1.13178	+	0.183434i
$688$	0.420876	−	1.50480i	0.0160457	−	0.0573701i
$689$			0.793745i			0.0302393i
$690$	−3.14255	+	13.4908i	−0.119635	+	0.513586i
$691$			29.7699i			1.13250i	0.824234	+	0.566250i	$0.191606\pi$
$691$			29.7699i			1.13250i	−0.824234	+	0.566250i	$0.808394\pi$
$692$	3.93393	−	28.6706i	0.149546	−	1.08989i
$693$	−22.2547	+	66.8515i	−0.845385	+	2.53948i
$694$	−33.9002	−	2.31490i	−1.28684	−	0.0878725i
$695$	−0.101483			−0.00384948
$696$	8.90812	−	23.2970i	0.337661	−	0.883069i
$697$	−40.3998			−1.53025
$698$	15.1407	+	1.03389i	0.573082	+	0.0391333i
$699$	4.61351	−	28.4651i	0.174499	−	1.07665i
$700$	1.26758	−	9.23814i	0.0479099	−	0.349169i
$701$			17.6604i			0.667023i	0.942746	+	0.333511i	$0.108234\pi$
$701$			17.6604i			0.667023i	−0.942746	+	0.333511i	$0.891766\pi$
$702$	6.26392	+	3.84231i	0.236416	+	0.145019i
$703$		−	1.06855i		−	0.0403013i
$704$	36.9741	+	16.0296i	1.39351	+	0.604139i
$705$	0.133859	−	0.825904i	0.00504143	−	0.0311053i
$706$	1.15935	−	16.9779i	0.0436326	−	0.638971i
$707$	0.792482			0.0298043
$708$	−20.5197	−	6.28095i	−0.771176	−	0.236053i
$709$	−19.8003			−0.743617			−0.371809	−	0.928309i	$-0.621262\pi$
$709$	−19.8003			−0.743617			−0.371809	+	0.928309i	$0.621262\pi$
$710$	1.14840	−	16.8176i	0.0430986	−	0.631152i
$711$	12.3605	−	37.1301i	0.463555	−	1.39249i
$712$	4.03782	−	19.4649i	0.151324	−	0.729479i
$713$		−	38.9587i		−	1.45901i
$714$	−72.8718	−	16.9748i	−2.72716	−	0.635264i
$715$		−	5.03741i		−	0.188388i
$716$	14.8179	+	2.03318i	0.553771	+	0.0759836i
$717$	−46.0534	−	7.46415i	−1.71990	−	0.278754i
$718$	14.5950	+	0.996633i	0.544682	+	0.0371940i
$719$	28.2461			1.05340			0.526701	−	0.850050i	$-0.323429\pi$
$719$	28.2461			1.05340			0.526701	+	0.850050i	$0.323429\pi$
$720$	−6.71693	+	9.94398i	−0.250325	+	0.370590i
$721$	91.7787			3.41802
$722$	−26.1163	−	1.78337i	−0.971948	−	0.0663702i
$723$	−18.7388	−	3.03710i	−0.696902	−	0.112951i
$724$	18.0889	+	2.48200i	0.672268	+	0.0922428i
$725$		−	5.09126i		−	0.189085i
$726$	−34.2945	−	7.98855i	−1.27279	−	0.296483i
$727$		−	6.45726i		−	0.239486i	−0.992805	−	0.119743i	$-0.961793\pi$
$727$		−	6.45726i		−	0.239486i	0.992805	−	0.119743i	$-0.0382071\pi$
$728$	−2.67852	+	12.9122i	−0.0992725	+	0.478559i
$729$	15.3948	+	22.1811i	0.570179	+	0.821521i
$730$	1.03695	−	15.1854i	0.0383791	−	0.562037i
$731$	−2.55934			−0.0946607
$732$	30.0097	+	9.18579i	1.10919	+	0.339517i
$733$	−21.9265			−0.809872			−0.404936	−	0.914345i	$-0.632706\pi$
$733$	−21.9265			−0.809872			−0.404936	+	0.914345i	$0.632706\pi$
$734$	−1.11878	+	16.3838i	−0.0412949	+	0.604738i
$735$	4.08387	−	25.1973i	0.150636	−	0.929415i
$736$	30.1489	+	10.6953i	1.11130	+	0.394234i
$737$			8.27516i			0.304819i
$738$	−9.93509	+	24.2015i	−0.365716	+	0.890871i
$739$			52.2170i			1.92083i	0.278567	+	0.960417i	$0.410140\pi$
$739$			52.2170i			1.92083i	−0.278567	+	0.960417i	$0.589860\pi$
$740$	0.415027	−	3.02473i	0.0152567	−	0.111191i
$741$	0.193972	−	1.19680i	0.00712574	−	0.0439654i
$742$	−5.22144	−	0.356550i	−0.191685	−	0.0130894i
$743$	−21.9568			−0.805518			−0.402759	−	0.915306i	$-0.631949\pi$
$743$	−21.9568			−0.805518			−0.402759	+	0.915306i	$0.631949\pi$
$744$	12.0539	−	31.5240i	0.441918	−	1.15573i
$745$	10.7234			0.392876
$746$	−49.4593	−	3.37736i	−1.81083	−	0.123654i
$747$	−6.15057	−	2.04751i	−0.225038	−	0.0749144i
$748$	8.97285	−	65.3944i	0.328080	−	2.39106i
$749$		−	27.0649i		−	0.988931i
$750$	−0.555706	+	2.38562i	−0.0202915	+	0.0871106i
$751$			26.2721i			0.958684i	0.877628	+	0.479342i	$0.159125\pi$
$751$			26.2721i			0.958684i	−0.877628	+	0.479342i	$0.840875\pi$
$752$	−1.86082	−	0.520450i	−0.0678572	−	0.0189788i
$753$	32.9003	+	5.33235i	1.19895	+	0.194321i
$754$	−0.490524	+	7.18341i	−0.0178638	+	0.261604i
$755$	15.8824			0.578020
$756$	−28.0893	+	39.4796i	−1.02160	+	1.43586i
$757$	38.6203			1.40368			0.701840	−	0.712335i	$-0.252362\pi$
$757$	38.6203			1.40368			0.701840	+	0.712335i	$0.252362\pi$
$758$	−0.858674	+	12.5747i	−0.0311885	+	0.456735i
$759$	−48.7050	−	7.89392i	−1.76788	−	0.286531i
$760$	1.93859	+	0.402143i	0.0703201	+	0.0145872i
$761$			43.9828i			1.59438i	0.603731	+	0.797188i	$0.293680\pi$
$761$			43.9828i			1.59438i	−0.603731	+	0.797188i	$0.706320\pi$
$762$	−0.0384634	+	0.165122i	−0.00139338	+	0.00598173i
$763$		−	66.5479i		−	2.40920i
$764$	−31.4271	−	4.31216i	−1.13699	−	0.156008i
$765$	18.6489	+	6.20816i	0.674252	+	0.224456i
$766$	−42.1757	−	2.88000i	−1.52387	−	0.104059i
$767$	6.19480			0.223681
$768$	21.0863	+	17.9824i	0.760887	+	0.648885i
$769$	−7.07498			−0.255130			−0.127565	−	0.991830i	$-0.540716\pi$
$769$	−7.07498			−0.255130			−0.127565	+	0.991830i	$0.540716\pi$
$770$	33.1373	+	2.26280i	1.19418	+	0.0815457i
$771$	0.333789	−	2.05946i	0.0120211	−	0.0741696i
$772$	18.1086	+	2.48471i	0.651744	+	0.0894266i
$773$			8.39439i			0.301925i	0.988539	+	0.150963i	$0.0482373\pi$
$773$			8.39439i			0.301925i	−0.988539	+	0.150963i	$0.951763\pi$
$774$	−0.629392	+	1.53318i	−0.0226230	+	0.0551089i
$775$		−	6.88919i		−	0.247467i
$776$	−14.7071	−	3.05084i	−0.527953	−	0.109519i
$777$	1.97224	−	12.1686i	0.0707538	−	0.436547i
$778$	1.40509	−	20.5766i	0.0503748	−	0.737706i
$779$	4.31634			0.154649
$780$	1.01391	−	3.31240i	0.0363037	−	0.118603i
$781$	60.0434			2.14852
$782$	3.56964	−	52.2751i	0.127650	−	1.86935i
$783$	−12.2641	+	23.4405i	−0.438284	+	0.837695i
$784$	−56.7712	−	15.8782i	−2.02754	−	0.567080i
$785$			5.44604i			0.194378i
$786$	2.55652	+	0.595515i	0.0911880	+	0.0212413i
$787$			10.1504i			0.361823i	0.983499	+	0.180911i	$0.0579048\pi$
$787$			10.1504i			0.361823i	−0.983499	+	0.180911i	$0.942095\pi$
$788$	6.40641	−	46.6901i	0.228219	−	1.66327i
$789$	16.5210	+	2.67766i	0.588163	+	0.0953271i
$790$	−18.4048	−	1.25679i	−0.654815	−	0.0447145i
$791$	−49.3025			−1.75300
$792$	−36.9680	−	21.4569i	−1.31360	−	0.762439i
$793$	−9.05980			−0.321723
$794$	10.8008	+	0.737542i	0.383307	+	0.0261744i
$795$	1.35710	+	0.219953i	0.0481313	+	0.00780093i
$796$	0.352834	−	2.57147i	0.0125059	−	0.0911432i
$797$			12.4302i			0.440301i	0.975466	+	0.220150i	$0.0706548\pi$
$797$			12.4302i			0.440301i	−0.975466	+	0.220150i	$0.929345\pi$
$798$	7.78568	+	1.81359i	0.275610	+	0.0642005i
$799$			3.16485i			0.111964i
$800$	5.33133	+	1.89128i	0.188491	+	0.0668670i
$801$	−6.65987	+	20.0058i	−0.235315	+	0.706870i
$802$	−0.410252	+	6.00787i	−0.0144865	+	0.212145i
$803$	54.2162			1.91325
$804$	−1.66559	+	5.44141i	−0.0587407	+	0.191904i
$805$	26.3658			0.929272
$806$	−0.663747	+	9.72015i	−0.0233795	+	0.342378i
$807$	3.99218	−	24.6315i	0.140531	−	0.867071i
$808$	−0.0976506	+	0.470740i	−0.00343533	+	0.0165606i
$809$			26.1598i			0.919728i	0.887989	+	0.459864i	$0.152102\pi$
$809$			26.1598i			0.919728i	−0.887989	+	0.459864i	$0.847898\pi$
$810$	8.30513	−	9.64494i	0.291812	−	0.338889i
$811$			36.6442i			1.28675i	0.765550	+	0.643376i	$0.222467\pi$
$811$			36.6442i			1.28675i	−0.765550	+	0.643376i	$0.777533\pi$
$812$	−47.0338	−	6.45356i	−1.65056	−	0.226476i
$813$	1.51653	−	9.35688i	0.0531869	−	0.328160i
$814$	10.8497	+	0.740881i	0.380283	+	0.0259679i
$815$	1.85125			0.0648463
$816$	19.0625	−	41.1948i	0.667320	−	1.44210i
$817$	0.273442			0.00956652
$818$	34.8716	+	2.38124i	1.21926	+	0.0832579i
$819$	4.41788	−	13.2710i	0.154373	−	0.463727i
$820$	12.2181	+	1.67647i	0.426676	+	0.0585447i
$821$			53.0153i			1.85025i	0.379667	+	0.925123i	$0.376038\pi$
$821$			53.0153i			1.85025i	−0.379667	+	0.925123i	$0.623962\pi$
$822$	10.6093	−	45.5451i	0.370041	−	1.58857i
$823$		−	2.88863i		−	0.100691i	−0.998732	−	0.0503457i	$-0.983968\pi$
$823$		−	2.88863i		−	0.100691i	0.998732	−	0.0503457i	$-0.0160323\pi$
$824$	−11.3091	+	54.5172i	−0.393971	+	1.89920i
$825$	−8.61266	−	1.39591i	−0.299854	−	0.0485992i
$826$	−2.78270	+	40.7509i	−0.0968226	+	1.41790i
$827$	−6.34477			−0.220629			−0.110315	−	0.993897i	$-0.535186\pi$
$827$	−6.34477			−0.220629			−0.110315	+	0.993897i	$0.535186\pi$
$828$	−30.4376	−	14.9939i	−1.05778	−	0.521072i
$829$	−16.9177			−0.587575			−0.293787	−	0.955871i	$-0.594916\pi$
$829$	−16.9177			−0.587575			−0.293787	+	0.955871i	$0.594916\pi$
$830$	−0.208186	+	3.04875i	−0.00722623	+	0.105823i
$831$	2.80415	+	0.454486i	0.0972750	+	0.0157659i
$832$	−7.33990	−	3.18212i	−0.254465	−	0.110320i
$833$			96.5555i			3.34545i
$834$	0.0563949	−	0.242101i	0.00195280	−	0.00838327i
$835$		−	2.96476i		−	0.102600i
$836$	−0.958665	+	6.98678i	−0.0331561	+	0.241643i
$837$	−16.5951	+	31.7183i	−0.573609	+	1.09634i
$838$	3.66605	+	0.250339i	0.126642	+	0.00864781i
$839$	−40.0419			−1.38240			−0.691199	−	0.722664i	$-0.742917\pi$
$839$	−40.0419			−1.38240			−0.691199	+	0.722664i	$0.742917\pi$
$840$	21.3343	+	8.15765i	0.736103	+	0.281466i
$841$	3.07903			0.106173
$842$	23.4597	+	1.60196i	0.808475	+	0.0552073i
$843$	6.62409	−	40.8703i	0.228146	−	1.40765i
$844$	2.05603	−	14.9844i	0.0707716	−	0.515786i
$845$			1.00000i			0.0344010i
$846$	1.89591	+	0.778297i	0.0651826	+	0.0267584i
$847$			67.0235i			2.30296i
$848$	0.855185	−	3.05764i	0.0293672	−	0.105000i
$849$	−5.47755	+	33.7962i	−0.187989	+	1.15988i
$850$	0.631231	−	9.24397i	0.0216510	−	0.317066i
$851$	8.63263			0.295923
$852$	39.4822	+	12.0853i	1.35264	+	0.414035i
$853$	11.1409			0.381457			0.190728	−	0.981643i	$-0.438915\pi$
$853$	11.1409			0.381457			0.190728	+	0.981643i	$0.438915\pi$
$854$	4.06966	−	59.5975i	0.139261	−	2.03938i
$855$	−1.99246	−	0.663284i	−0.0681407	−	0.0226838i
$856$	16.0768	+	3.33497i	0.549492	+	0.113987i
$857$		−	21.1520i		−	0.722539i	−0.932461	−	0.361269i	$-0.882343\pi$
$857$		−	21.1520i		−	0.722539i	0.932461	−	0.361269i	$-0.117657\pi$
$858$	12.0174	+	2.79932i	0.410266	+	0.0955672i
$859$		−	38.5891i		−	1.31664i	−0.752737	−	0.658321i	$-0.771267\pi$
$859$		−	38.5891i		−	1.31664i	0.752737	−	0.658321i	$-0.228733\pi$
$860$	0.774024	+	0.106205i	0.0263940	+	0.00362155i
$861$	49.1541	+	7.96671i	1.67517	+	0.271505i
$862$	50.1959	+	3.42766i	1.70968	+	0.116747i
$863$	27.3063			0.929517			0.464759	−	0.885437i	$-0.346141\pi$
$863$	27.3063			0.929517			0.464759	+	0.885437i	$0.346141\pi$
$864$	−19.9899	−	21.5500i	−0.680072	−	0.733146i
$865$	14.4696			0.491982
$866$	−0.432510	−	0.0295342i	−0.0146973	−	0.00100361i
$867$	−44.3245	−	7.18394i	−1.50534	−	0.243979i
$868$	−63.6432	−	8.73257i	−2.16019	−	0.296403i
$869$		−	65.7105i		−	2.22908i
$870$	12.1458	+	2.82925i	0.411782	+	0.0959205i
$871$		−	1.64274i		−	0.0556621i
$872$	39.5299	+	8.20011i	1.33865	+	0.277691i
$873$	15.1157	+	5.03198i	0.511590	+	0.170307i
$874$	−0.381383	+	5.58510i	−0.0129005	+	0.188919i
$875$	4.66235			0.157616
$876$	35.6504	+	10.9124i	1.20451	+	0.368695i
$877$	−47.0015			−1.58713			−0.793564	−	0.608487i	$-0.791777\pi$
$877$	−47.0015			−1.58713			−0.793564	+	0.608487i	$0.791777\pi$
$878$	2.32328	−	34.0229i	0.0784068	−	1.14822i
$879$	−6.90518	+	42.6046i	−0.232906	+	1.43702i
$880$	−5.42733	+	19.4049i	−0.182955	+	0.654141i
$881$			6.99986i			0.235831i	0.993024	+	0.117916i	$0.0376213\pi$
$881$			6.99986i			0.235831i	−0.993024	+	0.117916i	$0.962379\pi$
$882$	57.8417	+	23.7448i	1.94763	+	0.799531i
$883$			2.57175i			0.0865463i	0.999063	+	0.0432731i	$0.0137786\pi$
$883$			2.57175i			0.0865463i	−0.999063	+	0.0432731i	$0.986221\pi$
$884$	−1.78124	+	12.9818i	−0.0599097	+	0.436624i
$885$	1.71663	−	10.5915i	0.0577039	−	0.356029i
$886$	56.2698	+	3.84242i	1.89042	+	0.129089i
$887$	28.0488			0.941787			0.470893	−	0.882190i	$-0.343932\pi$
$887$	28.0488			0.941787			0.470893	+	0.882190i	$0.343932\pi$
$888$	6.98523	+	2.67096i	0.234409	+	0.0896315i
$889$	0.322706			0.0108232
$890$	9.91657	+	0.677160i	0.332404	+	0.0226985i
$891$	36.2907	+	27.1735i	1.21578	+	0.910347i
$892$	−7.02960	+	51.2319i	−0.235368	+	1.71537i
$893$		−	0.338135i		−	0.0113152i
$894$	−5.95907	+	25.5820i	−0.199301	+	0.855591i
$895$			7.47837i			0.249974i
$896$	24.2298	−	46.8542i	0.809461	−	1.56529i
$897$	9.66866	+	1.56706i	0.322827	+	0.0523226i
$898$	1.62200	−	23.7531i	0.0541268	−	0.792652i
$899$	−35.0747			−1.16981
$900$	−5.38238	−	2.65141i	−0.179413	−	0.0883803i
$901$	−5.20037			−0.173250
$902$	−2.99273	+	43.8266i	−0.0996470	+	1.45926i
$903$	3.11393	+	0.504694i	0.103625	+	0.0167952i
$904$	6.07512	−	29.2861i	0.202055	−	0.974040i
$905$			9.12919i			0.303464i
$906$	−8.82595	+	37.8894i	−0.293223	+	1.25879i
$907$		−	45.0883i		−	1.49713i	−0.663060	−	0.748567i	$-0.730742\pi$
$907$		−	45.0883i		−	1.49713i	0.663060	−	0.748567i	$-0.269258\pi$
$908$	−6.82183	−	0.936032i	−0.226390	−	0.0310633i
$909$	0.161062	−	0.483820i	0.00534210	−	0.0160473i
$910$	−6.57823	−	0.449199i	−0.218066	−	0.0148908i
$911$	−42.4273			−1.40568			−0.702839	−	0.711349i	$-0.748085\pi$
$911$	−42.4273			−1.40568			−0.702839	+	0.711349i	$0.748085\pi$
$912$	−2.03665	+	4.40127i	−0.0674402	+	0.145741i
$913$	−10.8849			−0.360237
$914$	−37.3106	−	2.54778i	−1.23412	−	0.0842731i
$915$	−2.51054	+	15.4899i	−0.0829960	+	0.512080i
$916$	34.3786	+	4.71713i	1.13590	+	0.155858i
$917$		−	4.99634i		−	0.164994i
$918$	−25.1736	+	41.0393i	−0.830853	+	1.35450i
$919$			23.7166i			0.782338i	0.920319	+	0.391169i	$0.127929\pi$
$919$			23.7166i			0.782338i	−0.920319	+	0.391169i	$0.872071\pi$
$920$	−3.24882	+	15.6615i	−0.107111	+	0.516343i
$921$	−0.523518	+	3.23008i	−0.0172505	+	0.106435i
$922$	0.229831	−	3.36572i	0.00756907	−	0.110844i
$923$	−11.9195			−0.392335
$924$	−23.8128	+	77.7955i	−0.783383	+	2.55928i
$925$	1.52653			0.0501922
$926$	1.65917	−	24.2975i	0.0545237	−	0.798465i
$927$	18.6529	−	56.0321i	0.612642	−	1.84034i
$928$	9.62902	−	27.1432i	0.316088	−	0.891019i
$929$			25.8095i			0.846782i	0.905947	+	0.423391i	$0.139160\pi$
$929$			25.8095i			0.846782i	−0.905947	+	0.423391i	$0.860840\pi$
$930$	16.4350	+	3.82836i	0.538925	+	0.125537i
$931$		−	10.3160i		−	0.338095i
$932$	4.52639	−	32.9885i	0.148267	−	1.08057i
$933$	20.4175	+	3.30919i	0.668438	+	0.108338i
$934$	41.4402	+	2.82977i	1.35596	+	0.0925930i
$935$	33.0036			1.07933
$936$	7.33870	+	4.25952i	0.239873	+	0.139227i
$937$	19.5668			0.639219			0.319610	−	0.947549i	$-0.396448\pi$
$937$	19.5668			0.639219			0.319610	+	0.947549i	$0.396448\pi$
$938$	10.8063	+	0.737918i	0.352839	+	0.0240939i
$939$	15.6738	+	2.54035i	0.511496	+	0.0829013i
$940$	0.131331	−	0.957148i	0.00428356	−	0.0312187i
$941$			3.96139i			0.129138i	0.997913	+	0.0645688i	$0.0205672\pi$
$941$			3.96139i			0.129138i	−0.997913	+	0.0645688i	$0.979433\pi$
$942$	−12.9922	−	3.02640i	−0.423308	−	0.0986054i
$943$			34.8708i			1.13555i
$944$	−23.8634	−	6.67431i	−0.776688	−	0.217230i
$945$	−21.4657	−	11.2309i	−0.698281	−	0.365342i
$946$	−0.189591	+	2.77643i	−0.00616412	+	0.0902696i
$947$	46.1474			1.49959			0.749794	−	0.661671i	$-0.230152\pi$
$947$	46.1474			1.49959			0.749794	+	0.661671i	$0.230152\pi$
$948$	13.2259	−	43.2086i	0.429558	−	1.40335i
$949$	−10.7627			−0.349372
$950$	−0.0674411	+	0.987632i	−0.00218808	+	0.0320430i
$951$	7.80443	−	48.1529i	0.253076	−	1.56146i
$952$	−84.5969	−	17.5488i	−2.74180	−	0.568761i
$953$		−	15.7481i		−	0.510133i	−0.966924	−	0.255066i	$-0.917903\pi$
$953$		−	15.7481i		−	0.510133i	0.966924	−	0.255066i	$-0.0820973\pi$
$954$	−1.27887	+	3.11529i	−0.0414050	+	0.100861i
$955$		−	15.8608i		−	0.513243i
$956$	−53.3717	−	7.32320i	−1.72617	−	0.236849i
$957$	−7.10693	+	43.8493i	−0.229734	+	1.41745i
$958$	11.4970	+	0.785083i	0.371452	+	0.0253649i
$959$	−89.0112			−2.87432
$960$	−7.47454	+	11.6675i	−0.241240	+	0.376568i
$961$	−16.4609			−0.530997
$962$	−2.15383	−	0.147076i	−0.0694423	−	0.00474192i
$963$	−16.5235	−	5.50062i	−0.532462	−	0.177255i
$964$	−21.7165	−	2.97975i	−0.699442	−	0.0959714i
$965$			9.13915i			0.294200i
$966$	−14.6516	+	62.8988i	−0.471409	+	2.02374i
$967$		−	4.57125i		−	0.147002i	−0.997295	−	0.0735008i	$-0.976583\pi$
$967$		−	4.57125i		−	0.147002i	0.997295	−	0.0735008i	$-0.0234171\pi$
$968$	−39.8125	−	8.25872i	−1.27962	−	0.265445i
$969$	7.84104	+	1.27085i	0.251891	+	0.0408254i
$970$	0.511640	−	7.49264i	0.0164278	−	0.240574i
$971$	−36.1836			−1.16119			−0.580594	−	0.814193i	$-0.697180\pi$
$971$	−36.1836			−1.16119			−0.580594	+	0.814193i	$0.697180\pi$
$972$	18.3940	+	25.1726i	0.589987	+	0.807413i
$973$	−0.473151			−0.0151685
$974$	2.78569	−	40.7946i	0.0892592	−	1.30714i
$975$	1.70974	+	0.277108i	0.0547555	+	0.00887456i
$976$	34.8999	+	9.76108i	1.11712	+	0.312444i
$977$			37.4974i			1.19965i	0.800132	+	0.599824i	$0.204763\pi$
$977$			37.4974i			1.19965i	−0.800132	+	0.599824i	$0.795237\pi$
$978$	−1.02875	+	4.41637i	−0.0328958	+	0.141220i
$979$			35.4049i			1.13155i
$980$	4.00675	−	29.2014i	0.127991	−	0.932803i
$981$	−40.6283	−	13.5250i	−1.29716	−	0.431822i
$982$	4.80453	+	0.328081i	0.153319	+	0.0104695i
$983$	−13.0053			−0.414803			−0.207402	−	0.978256i	$-0.566501\pi$
$983$	−13.0053			−0.414803			−0.207402	+	0.978256i	$0.566501\pi$
$984$	−10.7891	+	28.2162i	−0.343944	+	0.899501i
$985$	23.5638			0.750805
$986$	−47.0635	−	3.21376i	−1.49881	−	0.102347i
$987$	0.624098	−	3.85065i	0.0198653	−	0.122568i
$988$	0.190309	−	1.38698i	0.00605454	−	0.0441257i
$989$			2.20908i			0.0702446i
$990$	8.11621	−	19.7708i	0.257950	−	0.628358i
$991$			35.7174i			1.13460i	0.823511	+	0.567301i	$0.192012\pi$
$991$			35.7174i			1.13460i	−0.823511	+	0.567301i	$0.807988\pi$
$992$	13.0294	−	36.7285i	0.413684	−	1.16613i
$993$	9.12816	−	56.3202i	0.289673	−	1.78727i
$994$	5.35423	−	78.4093i	0.169826	−	2.48699i
$995$	1.29778			0.0411424
$996$	−7.15746	−	2.19086i	−0.226793	−	0.0694200i
$997$	−60.1926			−1.90632			−0.953159	−	0.302469i	$-0.902189\pi$
$997$	−60.1926			−1.90632			−0.953159	+	0.302469i	$0.902189\pi$
$998$	−3.40127	+	49.8094i	−0.107665	+	1.57669i
$999$	−7.02826	−	3.67720i	−0.222364	−	0.116342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.e.131.1	✓	40
3.2	odd	2	inner	780.2.g.e.131.40	yes	40
4.3	odd	2	inner	780.2.g.e.131.39	yes	40
12.11	even	2	inner	780.2.g.e.131.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.e.131.1	✓	40	1.1	even	1	trivial
780.2.g.e.131.2	yes	40	12.11	even	2	inner
780.2.g.e.131.39	yes	40	4.3	odd	2	inner
780.2.g.e.131.40	yes	40	3.2	odd	2	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:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41093 - 0.0963462i) q^{2} +(1.70974 + 0.277108i) q^{3} +(1.98143 + 0.271875i) q^{4} +1.00000i q^{5} +(-2.38562 - 0.555706i) q^{6} +4.66235i q^{7} +(-2.76947 - 0.574500i) q^{8} +(2.84642 + 0.947565i) q^{9} +(0.0963462 - 1.41093i) q^{10} +5.03741 q^{11} +(3.31240 + 1.01391i) q^{12} -1.00000 q^{13} +(0.449199 - 6.57823i) q^{14} +(-0.277108 + 1.70974i) q^{15} +(3.85217 + 1.07741i) q^{16} -6.55169i q^{17} +(-3.92480 - 1.61119i) q^{18} +0.699987i q^{19} +(-0.271875 + 1.98143i) q^{20} +(-1.29197 + 7.97140i) q^{21} +(-7.10742 - 0.485335i) q^{22} -5.65505 q^{23} +(-4.57587 - 1.74969i) q^{24} -1.00000 q^{25} +(1.41093 + 0.0963462i) q^{26} +(4.60406 + 2.40886i) q^{27} +(-1.26758 + 9.23814i) q^{28} +5.09126i q^{29} +(0.555706 - 2.38562i) q^{30} +6.88919i q^{31} +(-5.33133 - 1.89128i) q^{32} +(8.61266 + 1.39591i) q^{33} +(-0.631231 + 9.24397i) q^{34} -4.66235 q^{35} +(5.38238 + 2.65141i) q^{36} -1.52653 q^{37} +(0.0674411 - 0.987632i) q^{38} +(-1.70974 - 0.277108i) q^{39} +(0.574500 - 2.76947i) q^{40} -6.16631i q^{41} +(2.59090 - 11.1226i) q^{42} -0.390638i q^{43} +(9.98130 + 1.36955i) q^{44} +(-0.947565 + 2.84642i) q^{45} +(7.97886 + 0.544842i) q^{46} -0.483058 q^{47} +(6.28765 + 2.90955i) q^{48} -14.7375 q^{49} +(1.41093 + 0.0963462i) q^{50} +(1.81553 - 11.2017i) q^{51} +(-1.98143 - 0.271875i) q^{52} -0.793745i q^{53} +(-6.26392 - 3.84231i) q^{54} +5.03741i q^{55} +(2.67852 - 12.9122i) q^{56} +(-0.193972 + 1.19680i) q^{57} +(0.490524 - 7.18341i) q^{58} -6.19480 q^{59} +(-1.01391 + 3.31240i) q^{60} +9.05980 q^{61} +(0.663747 - 9.72015i) q^{62} +(-4.41788 + 13.2710i) q^{63} +(7.33990 + 3.18212i) q^{64} -1.00000i q^{65} +(-12.0174 - 2.79932i) q^{66} +1.64274i q^{67} +(1.78124 - 12.9818i) q^{68} +(-9.66866 - 1.56706i) q^{69} +(6.57823 + 0.449199i) q^{70} +11.9195 q^{71} +(-7.33870 - 4.25952i) q^{72} +10.7627 q^{73} +(2.15383 + 0.147076i) q^{74} +(-1.70974 - 0.277108i) q^{75} +(-0.190309 + 1.38698i) q^{76} +23.4862i q^{77} +(2.38562 + 0.555706i) q^{78} -13.0445i q^{79} +(-1.07741 + 3.85217i) q^{80} +(7.20424 + 5.39434i) q^{81} +(-0.594101 + 8.70022i) q^{82} -2.16081 q^{83} +(-4.72719 + 15.4436i) q^{84} +6.55169 q^{85} +(-0.0376365 + 0.551162i) q^{86} +(-1.41083 + 8.70474i) q^{87} +(-13.9509 - 2.89399i) q^{88} +7.02840i q^{89} +(1.61119 - 3.92480i) q^{90} -4.66235i q^{91} +(-11.2051 - 1.53747i) q^{92} +(-1.90905 + 11.7787i) q^{93} +(0.681560 + 0.0465408i) q^{94} -0.699987 q^{95} +(-8.59109 - 4.71096i) q^{96} +5.31043 q^{97} +(20.7935 + 1.41990i) q^{98} +(14.3386 + 4.77327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} - 2 q^{6} - 14 q^{12} - 40 q^{13} + 12 q^{16} - 16 q^{18} - 24 q^{21} + 44 q^{22} - 10 q^{24} - 40 q^{25} - 48 q^{28} - 6 q^{30} - 8 q^{33} - 56 q^{34} + 36 q^{36} - 72 q^{37} - 20 q^{42}+ \cdots + 72 q^{97}+O(q^{100}) \) 40 * q + 4 * q^4 - 2 * q^6 - 14 * q^12 - 40 * q^13 + 12 * q^16 - 16 * q^18 - 24 * q^21 + 44 * q^22 - 10 * q^24 - 40 * q^25 - 48 * q^28 - 6 * q^30 - 8 * q^33 - 56 * q^34 + 36 * q^36 - 72 * q^37 - 20 * q^42 + 8 * q^45 + 84 * q^46 + 70 * q^48 - 96 * q^49 - 4 * q^52 - 14 * q^54 + 80 * q^57 + 18 * q^60 + 40 * q^61 + 28 * q^64 - 24 * q^66 - 56 * q^69 + 24 * q^70 + 12 * q^72 - 68 * q^76 + 2 * q^78 + 96 * q^82 - 48 * q^84 + 8 * q^85 - 116 * q^88 - 8 * q^90 - 24 * q^93 - 8 * q^94 - 10 * q^96 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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