LMFDB - Embedded newform 840.2.dj.a.403.64

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] 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("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			403.64
Character	$\chi$	$=$	840.403
Dual form			840.2.dj.a.667.64

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.635612 - 1.26333i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.19199 - 1.60597i) q^{4} +(0.422435 + 2.19580i) q^{5} +(0.286981 - 1.38479i) q^{6} +(1.48397 + 2.19039i) q^{7} +(-2.78652 + 0.485105i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.04252 + 0.862005i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-1.56703 - 1.24274i) q^{12} +(4.22999 - 4.22999i) q^{13} +(3.71042 - 0.482505i) q^{14} +(0.976356 + 2.01165i) q^{15} +(-1.15830 + 3.82862i) q^{16} +(-0.0957741 - 0.357434i) q^{17} +(-0.0812078 - 1.41188i) q^{18} +(3.88557 - 2.24334i) q^{19} +(3.02286 - 3.29580i) q^{20} +(2.00032 + 1.73168i) q^{21} +(4.32459 + 6.58559i) q^{22} +(5.12067 + 1.37208i) q^{23} +(-2.56601 + 1.18978i) q^{24} +(-4.64310 + 1.85517i) q^{25} +(-2.65523 - 8.03249i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.74882 - 4.99416i) q^{28} +2.15497 q^{29} +(3.16196 + 0.0451698i) q^{30} +(7.57009 + 4.37059i) q^{31} +(4.10058 + 3.89683i) q^{32} +(-1.44188 + 5.38117i) q^{33} +(-0.512431 - 0.106195i) q^{34} +(-4.18279 + 4.18381i) q^{35} +(-1.83528 - 0.794816i) q^{36} +(0.398738 - 1.48811i) q^{37} +(-0.364353 - 6.33465i) q^{38} +(2.99105 - 5.18066i) q^{39} +(-2.24232 - 5.91371i) q^{40} -6.48184 q^{41} +(3.45911 - 1.42639i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(11.0685 - 1.27749i) q^{44} +(1.46374 + 1.69040i) q^{45} +(4.98815 - 5.59698i) q^{46} +(-0.335928 + 1.25370i) q^{47} +(-0.127909 + 3.99795i) q^{48} +(-2.59564 + 6.50097i) q^{49} +(-0.607525 + 7.04492i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(-11.8354 - 1.75112i) q^{52} +(-0.463759 - 1.73077i) q^{53} +(-0.443862 - 1.34275i) q^{54} +(-11.7706 - 4.07832i) q^{55} +(-5.19769 - 5.38368i) q^{56} +(3.17256 - 3.17256i) q^{57} +(1.36973 - 2.72244i) q^{58} +(2.91223 + 1.68137i) q^{59} +(2.06684 - 3.96588i) q^{60} +(-9.74986 + 5.62909i) q^{61} +(10.3331 - 6.78550i) q^{62} +(2.38036 + 1.15495i) q^{63} +(7.52935 - 2.70350i) q^{64} +(11.0751 + 7.50133i) q^{65} +(5.88171 + 5.24190i) q^{66} +(-3.73855 - 13.9525i) q^{67} +(-0.459867 + 0.579870i) q^{68} +5.30131 q^{69} +(2.62689 + 7.94351i) q^{70} -10.8638i q^{71} +(-2.17064 + 1.81337i) q^{72} +(-7.09104 + 1.90004i) q^{73} +(-1.62653 - 1.44960i) q^{74} +(-4.00474 + 2.99368i) q^{75} +(-8.23432 - 3.56608i) q^{76} +(-14.7014 + 1.05828i) q^{77} +(-4.64372 - 7.07157i) q^{78} +(-0.655100 - 1.13467i) q^{79} +(-8.89620 - 0.926049i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-4.11994 + 8.18869i) q^{82} +(6.80401 + 6.80401i) q^{83} +(0.396650 - 5.27662i) q^{84} +(0.744396 - 0.361294i) q^{85} +(-9.12916 + 3.01775i) q^{86} +(2.08154 - 0.557748i) q^{87} +(5.42139 - 14.7952i) q^{88} +(-3.23303 + 1.86659i) q^{89} +(3.06590 - 0.774744i) q^{90} +(15.5425 + 2.98815i) q^{91} +(-3.90029 - 9.85917i) q^{92} +(8.44333 + 2.26238i) q^{93} +(1.37031 + 1.22125i) q^{94} +(6.56733 + 7.58429i) q^{95} +(4.96943 + 2.70274i) q^{96} +(5.31523 - 5.31523i) q^{97} +(6.56304 + 7.41125i) q^{98} +5.57100i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	0.635612	−	1.26333i	0.449446	−	0.893308i
$2$	0.635612	−	1.26333i	0.449446	−	0.893308i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−1.19199	−	1.60597i	−0.595997	−	0.802986i
$5$	0.422435	+	2.19580i	0.188919	+	0.981993i
$5$	0.422435	+	2.19580i	0.188919	+	0.981993i
$6$	0.286981	−	1.38479i	0.117159	−	0.565338i
$7$	1.48397	+	2.19039i	0.560889	+	0.827891i
$7$	1.48397	+	2.19039i	0.560889	+	0.827891i
$8$	−2.78652	+	0.485105i	−0.985182	+	0.171510i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	3.04252	+	0.862005i	0.962130	+	0.272590i
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	0.0501521	+	0.998742i	$0.484029\pi$
$11$	−2.78550	+	4.82463i	−0.839860	+	1.45468i	−0.890012	+	0.455938i	$0.849304\pi$
$12$	−1.56703	−	1.24274i	−0.452364	−	0.358748i
$13$	4.22999	−	4.22999i	1.17319	−	1.17319i	0.191742	−	0.981445i	$-0.438586\pi$
$13$	4.22999	−	4.22999i	1.17319	−	1.17319i	0.981445	−	0.191742i	$-0.0614138\pi$
$14$	3.71042	−	0.482505i	0.991650	−	0.128955i
$15$	0.976356	+	2.01165i	0.252094	+	0.519405i
$16$	−1.15830	+	3.82862i	−0.289574	+	0.957156i
$17$	−0.0957741	−	0.357434i	−0.0232286	−	0.0866904i	0.953338	−	0.301904i	$-0.0976221\pi$
$17$	−0.0957741	−	0.357434i	−0.0232286	−	0.0866904i	−0.976567	+	0.215213i	$0.930955\pi$
$18$	−0.0812078	−	1.41188i	−0.0191409	−	0.332783i
$19$	3.88557	−	2.24334i	0.891412	−	0.514657i	0.0170079	−	0.999855i	$-0.494586\pi$
$19$	3.88557	−	2.24334i	0.891412	−	0.514657i	0.874404	+	0.485198i	$0.161253\pi$
$20$	3.02286	−	3.29580i	0.675932	−	0.736964i
$21$	2.00032	+	1.73168i	0.436506	+	0.377883i
$22$	4.32459	+	6.58559i	0.922005	+	1.40405i
$23$	5.12067	+	1.37208i	1.06773	+	0.286098i	0.749562	−	0.661934i	$-0.230264\pi$
$23$	5.12067	+	1.37208i	1.06773	+	0.286098i	0.318172	+	0.948033i	$0.396931\pi$
$24$	−2.56601	+	1.18978i	−0.523785	+	0.242863i
$25$	−4.64310	+	1.85517i	−0.928620	+	0.371033i
$26$	−2.65523	−	8.03249i	−0.520734	−	1.57530i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.74882	−	4.99416i	0.330496	−	0.943807i
$29$	2.15497			0.400168			0.200084	−	0.979779i	$-0.435878\pi$
$29$	2.15497			0.400168			0.200084	+	0.979779i	$0.435878\pi$
$30$	3.16196	+	0.0451698i	0.577291	+	0.00824684i
$31$	7.57009	+	4.37059i	1.35963	+	0.784981i	0.989574	−	0.144029i	$-0.0460058\pi$
$31$	7.57009	+	4.37059i	1.35963	+	0.784981i	0.370054	+	0.929010i	$0.379339\pi$
$32$	4.10058	+	3.89683i	0.724887	+	0.688868i
$33$	−1.44188	+	5.38117i	−0.250999	+	0.936742i
$34$	−0.512431	−	0.106195i	−0.0878813	−	0.0182123i
$35$	−4.18279	+	4.18381i	−0.707020	+	0.707193i
$36$	−1.83528	−	0.794816i	−0.305881	−	0.132469i
$37$	0.398738	−	1.48811i	0.0655522	−	0.244644i	−0.925373	−	0.379057i	$-0.876248\pi$
$37$	0.398738	−	1.48811i	0.0655522	−	0.244644i	0.990925	+	0.134413i	$0.0429150\pi$
$38$	−0.364353	−	6.33465i	−0.0591059	−	1.02762i
$39$	2.99105	−	5.18066i	0.478952	−	0.829569i
$40$	−2.24232	−	5.91371i	−0.354541	−	0.935040i
$41$	−6.48184			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$41$	−6.48184			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$42$	3.45911	−	1.42639i	0.533752	−	0.220097i
$43$	−4.80750	−	4.80750i	−0.733137	−	0.733137i	0.238103	−	0.971240i	$-0.423474\pi$
$43$	−4.80750	−	4.80750i	−0.733137	−	0.733137i	−0.971240	+	0.238103i	$0.923474\pi$
$44$	11.0685	−	1.27749i	1.66864	−	0.192589i
$45$	1.46374	+	1.69040i	0.218202	+	0.251990i
$46$	4.98815	−	5.59698i	0.735462	−	0.825229i
$47$	−0.335928	+	1.25370i	−0.0490001	+	0.182871i	−0.986088	−	0.166221i	$-0.946843\pi$
$47$	−0.335928	+	1.25370i	−0.0490001	+	0.182871i	0.937088	+	0.349092i	$0.113510\pi$
$48$	−0.127909	+	3.99795i	−0.0184620	+	0.577055i
$49$	−2.59564	+	6.50097i	−0.370806	+	0.928710i
$50$	−0.607525	+	7.04492i	−0.0859170	+	0.996302i
$51$	−0.185021	−	0.320466i	−0.0259082	−	0.0448743i
$52$	−11.8354	−	1.75112i	−1.64127	−	0.242837i
$53$	−0.463759	−	1.73077i	−0.0637022	−	0.237740i	0.926733	−	0.375722i	$-0.122605\pi$
$53$	−0.463759	−	1.73077i	−0.0637022	−	0.237740i	−0.990435	+	0.137982i	$0.955938\pi$
$54$	−0.443862	−	1.34275i	−0.0604020	−	0.182726i
$55$	−11.7706	−	4.07832i	−1.58715	−	0.549920i
$56$	−5.19769	−	5.38368i	−0.694570	−	0.719425i
$57$	3.17256	−	3.17256i	0.420216	−	0.420216i
$58$	1.36973	−	2.72244i	0.179854	−	0.357473i
$59$	2.91223	+	1.68137i	0.379140	+	0.218896i	0.677444	−	0.735574i	$-0.263088\pi$
$59$	2.91223	+	1.68137i	0.379140	+	0.218896i	−0.298304	+	0.954471i	$0.596421\pi$
$60$	2.06684	−	3.96588i	0.266828	−	0.511992i
$61$	−9.74986	+	5.62909i	−1.24834	+	0.720731i	−0.970779	−	0.239977i	$-0.922860\pi$
$61$	−9.74986	+	5.62909i	−1.24834	+	0.720731i	−0.277563	+	0.960707i	$0.589527\pi$
$62$	10.3331	−	6.78550i	1.31231	−	0.861760i
$63$	2.38036	+	1.15495i	0.299897	+	0.145510i
$64$	7.52935	−	2.70350i	0.941168	−	0.337938i
$65$	11.0751	+	7.50133i	1.37370	+	0.930425i
$66$	5.88171	+	5.24190i	0.723988	+	0.645234i
$67$	−3.73855	−	13.9525i	−0.456736	−	1.70456i	−0.682933	−	0.730481i	$-0.739296\pi$
$67$	−3.73855	−	13.9525i	−0.456736	−	1.70456i	0.226196	−	0.974082i	$-0.427371\pi$
$68$	−0.459867	+	0.579870i	−0.0557670	+	0.0703196i
$69$	5.30131			0.638203
$70$	2.62689	+	7.94351i	0.313974	+	0.949432i
$71$		−	10.8638i		−	1.28929i	−0.764481	−	0.644646i	$-0.777005\pi$
$71$		−	10.8638i		−	1.28929i	0.764481	−	0.644646i	$-0.222995\pi$
$72$	−2.17064	+	1.81337i	−0.255813	+	0.213708i
$73$	−7.09104	+	1.90004i	−0.829944	+	0.222383i	−0.648689	−	0.761053i	$-0.724682\pi$
$73$	−7.09104	+	1.90004i	−0.829944	+	0.222383i	−0.181255	+	0.983436i	$0.558016\pi$
$74$	−1.62653	−	1.44960i	−0.189080	−	0.168512i
$75$	−4.00474	+	2.99368i	−0.462427	+	0.345680i
$76$	−8.23432	−	3.56608i	−0.944542	−	0.409057i
$77$	−14.7014	+	1.05828i	−1.67538	+	0.120602i
$78$	−4.64372	−	7.07157i	−0.525798	−	0.800698i
$79$	−0.655100	−	1.13467i	−0.0737045	−	0.127660i	0.826818	−	0.562470i	$-0.190149\pi$
$79$	−0.655100	−	1.13467i	−0.0737045	−	0.127660i	−0.900522	+	0.434810i	$0.856816\pi$
$80$	−8.89620	−	0.926049i	−0.994626	−	0.103535i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−4.11994	+	8.18869i	−0.454971	+	0.904290i
$83$	6.80401	+	6.80401i	0.746837	+	0.746837i	0.973884	−	0.227047i	$-0.0729070\pi$
$83$	6.80401	+	6.80401i	0.746837	+	0.746837i	−0.227047	+	0.973884i	$0.572907\pi$
$84$	0.396650	−	5.27662i	0.0432781	−	0.575726i
$85$	0.744396	−	0.361294i	0.0807411	−	0.0391878i
$86$	−9.12916	+	3.01775i	−0.984422	+	0.325412i
$87$	2.08154	−	0.557748i	0.223165	−	0.0597968i
$88$	5.42139	−	14.7952i	0.577922	−	1.57717i
$89$	−3.23303	+	1.86659i	−0.342700	+	0.197858i	−0.661465	−	0.749976i	$-0.730065\pi$
$89$	−3.23303	+	1.86659i	−0.342700	+	0.197858i	0.318765	+	0.947834i	$0.396732\pi$
$90$	3.06590	−	0.774744i	0.323175	−	0.0816651i
$91$	15.5425	+	2.98815i	1.62930	+	0.313243i
$92$	−3.90029	−	9.85917i	−0.406633	−	1.02789i
$93$	8.44333	+	2.26238i	0.875533	+	0.234598i
$94$	1.37031	+	1.22125i	0.141337	+	0.125963i
$95$	6.56733	+	7.58429i	0.673794	+	0.778132i
$96$	4.96943	+	2.70274i	0.507190	+	0.275847i
$97$	5.31523	−	5.31523i	0.539679	−	0.539679i	−0.383755	−	0.923435i	$-0.625369\pi$
$97$	5.31523	−	5.31523i	0.539679	−	0.539679i	0.923435	+	0.383755i	$0.125369\pi$
$98$	6.56304	+	7.41125i	0.662967	+	0.748649i
$99$			5.57100i			0.559906i
$100$	8.51390	+	5.24534i	0.851390	+	0.524534i
$101$	−12.1989	−	7.04305i	−1.21384	−	0.700810i	−0.250245	−	0.968183i	$-0.580511\pi$
$101$	−12.1989	−	7.04305i	−1.21384	−	0.700810i	−0.963593	+	0.267373i	$0.913844\pi$
$102$	−0.522456	+	0.0300504i	−0.0517309	+	0.00297543i
$103$	−8.90017	−	2.38479i	−0.876960	−	0.234981i	−0.207865	−	0.978158i	$-0.566651\pi$
$103$	−8.90017	−	2.38479i	−0.876960	−	0.234981i	−0.669095	+	0.743177i	$0.733318\pi$
$104$	−9.73495	+	13.8389i	−0.954590	+	1.35702i
$105$	−2.95741	+	5.12384i	−0.288614	+	0.500035i
$106$	−2.48130	−	0.514220i	−0.241005	−	0.0499454i
$107$	−7.47856	−	2.00387i	−0.722979	−	0.193722i	−0.121479	−	0.992594i	$-0.538764\pi$
$107$	−7.47856	−	2.00387i	−0.722979	−	0.193722i	−0.601501	+	0.798872i	$0.705430\pi$
$108$	−1.97846	−	0.292727i	−0.190378	−	0.0281676i
$109$	−2.51427	+	4.35484i	−0.240823	+	0.417118i	−0.960949	−	0.276725i	$-0.910751\pi$
$109$	−2.51427	+	4.35484i	−0.240823	+	0.417118i	0.720126	+	0.693844i	$0.244084\pi$
$110$	−12.6338	+	12.2779i	−1.20459	+	1.17065i
$111$		−	1.54061i		−	0.146228i
$112$	−10.1051	+	3.14445i	−0.954839	+	0.297122i
$113$	1.95011	+	1.95011i	0.183451	+	0.183451i	0.792858	−	0.609407i	$-0.208592\pi$
$113$	1.95011	+	1.95011i	0.183451	+	0.183451i	−0.609407	+	0.792858i	$0.708592\pi$
$114$	−1.99147	−	6.02450i	−0.186518	−	0.564246i
$115$	−0.849667	+	11.8236i	−0.0792318	+	1.10256i
$116$	−2.56871	−	3.46083i	−0.238499	−	0.321330i
$117$	1.54828	−	5.77827i	0.143139	−	0.534201i
$118$	3.97517	−	2.61040i	0.365944	−	0.240306i
$119$	0.640794	−	0.740205i	0.0587415	−	0.0678545i
$120$	−3.69649	−	5.13186i	−0.337442	−	0.468472i
$121$	−10.0180	−	17.3517i	−0.910728	−	1.57743i
$122$	0.914251	+	15.8952i	0.0827724	+	1.43908i
$123$	−6.26098	+	1.67762i	−0.564534	+	0.151266i
$124$	−2.00445	−	17.3671i	−0.180005	−	1.55961i
$125$	−6.03499	−	9.41164i	−0.539786	−	0.841803i
$126$	2.97206	−	2.27307i	0.264772	−	0.202501i
$127$	14.2525	+	14.2525i	1.26471	+	1.26471i	0.948786	+	0.315919i	$0.102313\pi$
$127$	14.2525	+	14.2525i	1.26471	+	1.26471i	0.315919	+	0.948786i	$0.397687\pi$
$128$	1.37033	−	11.2304i	0.121121	−	0.992638i
$129$	−5.88796	−	3.39942i	−0.518406	−	0.299302i
$130$	16.5161	−	9.22357i	1.44856	−	0.808960i
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	0.912707	−	0.408614i	$-0.133988\pi$
$131$	1.17297	+	2.03165i	0.102483	+	0.177506i	−0.810224	+	0.586120i	$0.800655\pi$
$132$	10.3607	−	4.09871i	0.901786	−	0.356747i
$133$	10.6799	+	5.18188i	0.926063	+	0.449326i
$134$	−20.0028	−	4.14533i	−1.72798	−	0.358102i
$135$	1.85137	+	1.25396i	0.159341	+	0.107924i
$136$	0.440269	+	0.949535i	0.0377528	+	0.0814219i
$137$	1.12053	+	4.18186i	0.0957331	+	0.357281i	0.997130	−	0.0757139i	$-0.0241236\pi$
$137$	1.12053	+	4.18186i	0.0957331	+	0.357281i	−0.901396	+	0.432995i	$0.857457\pi$
$138$	3.36958	−	6.69729i	0.286837	−	0.570111i
$139$		−	19.6140i		−	1.66364i	−0.555046	−	0.831819i	$-0.687300\pi$
$139$		−	19.6140i		−	1.66364i	0.555046	−	0.831819i	$-0.312700\pi$
$140$	11.7049	+	1.73036i	0.989249	+	0.146242i
$141$			1.29792i			0.109305i
$142$	−13.7245	−	6.90514i	−1.15173	−	0.579467i
$143$	8.62548	+	32.1907i	0.721299	+	2.69192i
$144$	0.911196	+	3.89483i	0.0759330	+	0.324569i
$145$	0.910335	+	4.73189i	0.0755992	+	0.392962i
$146$	−2.10678	+	10.1660i	−0.174358	+	0.841344i
$147$	−0.824624	+	6.95126i	−0.0680139	+	0.573330i
$148$	−2.86516	+	1.13346i	−0.235515	+	0.0931697i
$149$	−9.37590	−	16.2395i	−0.768103	−	1.33039i	−0.938590	−	0.345034i	$-0.887867\pi$
$149$	−9.37590	−	16.2395i	−0.768103	−	1.33039i	0.170487	−	0.985360i	$-0.445466\pi$
$150$	1.23654	+	6.96211i	0.100963	+	0.568454i
$151$	11.9413	+	6.89433i	0.971771	+	0.561052i	0.899776	−	0.436352i	$-0.143730\pi$
$151$	11.9413	+	6.89433i	0.971771	+	0.561052i	0.0719956	+	0.997405i	$0.477063\pi$
$152$	−9.73896	+	8.13601i	−0.789934	+	0.659917i
$153$	−0.261660	−	0.261660i	−0.0211539	−	0.0211539i
$154$	−8.00745	+	19.2454i	−0.645259	+	1.55084i
$155$	−6.39909	+	18.4687i	−0.513987	+	1.48344i
$156$	−11.8853	+	1.37176i	−0.951587	+	0.109829i
$157$	−4.68010	+	1.25403i	−0.373512	+	0.100082i	−0.440692	−	0.897659i	$-0.645267\pi$
$157$	−4.68010	+	1.25403i	−0.373512	+	0.100082i	0.0671792	+	0.997741i	$0.478600\pi$
$158$	−1.84985	+	0.106399i	−0.147166	+	0.00846461i
$159$	−0.895913	−	1.55177i	−0.0710506	−	0.123063i
$160$	−6.82444	+	10.6502i	−0.539519	+	0.841973i
$161$	4.59355	+	13.2524i	0.362022	+	1.04444i
$162$	−0.776268	−	1.18212i	−0.0609894	−	0.0928761i
$163$	0.692231	−	2.58344i	0.0542197	−	0.202351i	−0.933503	−	0.358571i	$-0.883264\pi$
$163$	0.692231	−	2.58344i	0.0542197	−	0.202351i	0.987722	+	0.156220i	$0.0499309\pi$
$164$	7.72632	+	10.4097i	0.603324	+	0.812858i
$165$	−12.4251	−	0.892891i	−0.967292	−	0.0695115i
$166$	12.9204	−	4.27099i	1.00282	−	0.331493i
$167$	13.5322	+	13.5322i	1.04715	+	1.04715i	0.998832	+	0.0483210i	$0.0153870\pi$
$167$	13.5322	+	13.5322i	1.04715	+	1.04715i	0.0483210	+	0.998832i	$0.484613\pi$
$168$	−6.41398	−	3.85498i	−0.494849	−	0.297418i
$169$		−	22.7856i		−	1.75274i
$170$	0.0167148	−	1.17006i	0.00128196	−	0.0897394i
$171$	2.24334	−	3.88557i	0.171552	−	0.297137i
$172$	−1.99020	+	13.4512i	−0.151751	+	1.02565i
$173$	−6.51581	−	1.74590i	−0.495388	−	0.132739i	0.00247098	−	0.999997i	$-0.499213\pi$
$173$	−6.51581	−	1.74590i	−0.495388	−	0.132739i	−0.497859	+	0.867258i	$0.665880\pi$
$174$	0.618435	−	2.98418i	0.0468835	−	0.226230i
$175$	−10.9538	−	7.41719i	−0.828028	−	0.560687i
$176$	−15.2452	−	16.2530i	−1.14915	−	1.22511i
$177$	3.24817	+	0.870344i	0.244147	+	0.0654190i
$178$	0.303163	+	5.27080i	0.0227230	+	0.395063i
$179$	−1.10843	−	0.639953i	−0.0828481	−	0.0478324i	0.458004	−	0.888950i	$-0.348565\pi$
$179$	−1.10843	−	0.639953i	−0.0828481	−	0.0478324i	−0.540852	+	0.841118i	$0.681898\pi$
$180$	0.969971	−	4.36568i	0.0722974	−	0.325399i
$181$		−	19.3108i		−	1.43536i	−0.696374	−	0.717679i	$-0.745205\pi$
$181$		−	19.3108i		−	1.43536i	0.696374	−	0.717679i	$-0.254795\pi$
$182$	13.6540	−	17.7360i	1.01210	−	1.31468i
$183$	−7.96073	+	7.96073i	−0.588474	+	0.588474i
$184$	−14.9344	−	1.33926i	−1.10098	−	0.0987317i
$185$	3.43604	+	0.246921i	0.252623	+	0.0181540i
$186$	8.22482	−	9.22870i	0.603073	−	0.676681i
$187$	1.99126	+	0.533557i	0.145616	+	0.0390176i
$188$	2.41383	−	0.954912i	0.176047	−	0.0696441i
$189$	2.59817	+	0.499514i	0.188989	+	0.0363343i
$190$	13.7557	−	3.47602i	0.997945	−	0.252177i
$191$	−11.9792	+	6.91618i	−0.866783	+	0.500437i	−0.866278	−	0.499563i	$-0.833494\pi$
$191$	−11.9792	+	6.91618i	−0.866783	+	0.500437i	−0.000505095		1.00000i	$0.500161\pi$
$192$	6.57307	−	4.56012i	0.474371	−	0.329098i
$193$	18.6186	−	4.98883i	1.34019	−	0.359104i	0.483688	−	0.875241i	$-0.339297\pi$
$193$	18.6186	−	4.98883i	1.34019	−	0.359104i	0.856506	+	0.516137i	$0.172630\pi$
$194$	−3.33645	−	10.0933i	−0.239543	−	0.724656i
$195$	12.6392	+	4.37927i	0.905114	+	0.313606i
$196$	13.5344	−	3.58059i	0.966741	−	0.255756i
$197$	8.87857	+	8.87857i	0.632572	+	0.632572i	0.948712	−	0.316140i	$-0.102387\pi$
$197$	8.87857	+	8.87857i	0.632572	+	0.632572i	−0.316140	+	0.948712i	$0.602387\pi$
$198$	7.03800	+	3.54099i	0.500169	+	0.251647i
$199$	6.58171	−	11.3999i	0.466565	−	0.808115i	−0.532705	−	0.846301i	$-0.678825\pi$
$199$	6.58171	−	11.3999i	0.466565	−	0.808115i	0.999271	+	0.0381859i	$0.0121579\pi$
$200$	12.0381	−	7.42184i	0.851223	−	0.524803i
$201$	−7.22232	−	12.5094i	−0.509423	−	0.882347i
$202$	−16.6515	+	10.9346i	−1.17159	+	0.769355i
$203$	3.19792	+	4.72024i	0.224450	+	0.331296i
$204$	−0.294116	+	0.679134i	−0.0205922	+	0.0475489i
$205$	−2.73816	−	14.2328i	−0.191241	−	0.994065i
$206$	−8.66983	+	9.72803i	−0.604056	+	0.677784i
$207$	5.12067	−	1.37208i	0.355911	−	0.0953662i
$208$	11.2954	+	21.0946i	0.783198	+	1.46265i
$209$			24.9953i			1.72896i
$210$	4.59332	+	6.99296i	0.316969	+	0.482560i
$211$	−0.281828			−0.0194019			−0.00970093	−	0.999953i	$-0.503088\pi$
$211$	−0.281828			−0.0194019			−0.00970093	+	0.999953i	$0.503088\pi$
$212$	−2.22677	+	2.80785i	−0.152935	+	0.192844i
$213$	−2.81175	−	10.4936i	−0.192658	−	0.719009i
$214$	−7.28501	+	8.17418i	−0.497993	+	0.558776i
$215$	8.52547	−	12.5872i	0.581432	−	0.858439i
$216$	−1.62734	+	2.31339i	−0.110727	+	0.157406i
$217$	1.66050	+	23.0673i	0.112722	+	1.56591i
$218$	3.90349	+	5.94434i	0.264378	+	0.402601i
$219$	−6.35766	+	3.67059i	−0.429611	+	0.248036i
$220$	7.48085	+	23.7646i	0.504359	+	1.60221i
$221$	−1.91706	−	1.10682i	−0.128956	−	0.0744526i
$222$	−1.94629	−	0.979228i	−0.130627	−	0.0657215i
$223$	0.661316	−	0.661316i	0.0442850	−	0.0442850i	−0.684618	−	0.728902i	$-0.740031\pi$
$223$	0.661316	−	0.661316i	0.0442850	−	0.0442850i	0.728902	+	0.684618i	$0.240031\pi$
$224$	−2.45043	+	14.7647i	−0.163727	+	0.986506i
$225$	−3.09346	+	3.92817i	−0.206230	+	0.261878i
$226$	3.70314	−	1.22412i	0.246329	−	0.0814269i
$227$	−5.73653	−	21.4090i	−0.380747	−	1.42097i	−0.844763	−	0.535140i	$-0.820259\pi$
$227$	−5.73653	−	21.4090i	−0.380747	−	1.42097i	0.464016	−	0.885827i	$-0.346408\pi$
$228$	−8.87672	−	1.31337i	−0.587875	−	0.0869800i
$229$	−2.38356	−	4.12844i	−0.157510	−	0.272815i	0.776460	−	0.630166i	$-0.217013\pi$
$229$	−2.38356	−	4.12844i	−0.157510	−	0.272815i	−0.933970	+	0.357351i	$0.883680\pi$
$230$	14.3970	+	8.58863i	0.949312	+	0.566317i
$231$	−13.9266	+	4.82723i	−0.916302	+	0.317608i
$232$	−6.00486	+	1.04539i	−0.394239	+	0.0686330i
$233$	−0.00292416	+	0.0109131i	−0.000191568	+	0.000714941i	−0.966022	−	0.258462i	$-0.916784\pi$
$233$	−0.00292416	+	0.0109131i	−0.000191568	+	0.000714941i	0.965830	+	0.259176i	$0.0834511\pi$
$234$	−6.31574	−	5.62873i	−0.412873	−	0.367961i
$235$	−2.89478	−	0.208025i	−0.188835	−	0.0135700i
$236$	−0.771117	−	6.68115i	−0.0501954	−	0.434906i
$237$	−0.926452	−	0.926452i	−0.0601795	−	0.0601795i
$238$	−0.527826	−	1.28002i	−0.0342138	−	0.0829712i
$239$	10.3228			0.667723			0.333862	−	0.942622i	$-0.391648\pi$
$239$	10.3228			0.667723			0.333862	+	0.942622i	$0.391648\pi$
$240$	−8.83275	+	1.40801i	−0.570152	+	0.0908868i
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	−0.982779	−	0.184783i	$-0.940842\pi$
$241$	−5.14413	+	8.90990i	−0.331363	+	0.573937i	0.651417	+	0.758720i	$0.274175\pi$
$242$	−28.2885	+	1.62708i	−1.81845	+	0.104593i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	20.6619	+	8.94817i	1.32275	+	0.572848i
$245$	−15.3713	−	2.95329i	−0.982039	−	0.188678i
$246$	−1.86016	+	8.97599i	−0.118600	+	0.572288i
$247$	6.94664	−	25.9252i	0.442004	−	1.64958i
$248$	−23.2144	−	8.50644i	−1.47411	−	0.540160i
$249$	8.33318	+	4.81116i	0.528094	+	0.304895i
$250$	−15.7259	+	1.64201i	−0.994593	+	0.103850i
$251$	−1.10630			−0.0698290			−0.0349145	−	0.999390i	$-0.511116\pi$
$251$	−1.10630			−0.0698290			−0.0349145	+	0.999390i	$0.511116\pi$
$252$	−0.982554	−	5.19948i	−0.0618951	−	0.327536i
$253$	−20.8834	+	20.8834i	−1.31293	+	1.31293i
$254$	27.0646	−	8.94652i	1.69819	−	0.561355i
$255$	0.625522	−	0.541647i	0.0391717	−	0.0339192i
$256$	−13.3167	−	8.86936i	−0.832293	−	0.554335i
$257$	−19.6781	−	5.27272i	−1.22748	−	0.328903i	−0.413884	−	0.910329i	$-0.635828\pi$
$257$	−19.6781	−	5.27272i	−1.22748	−	0.328903i	−0.813599	+	0.581426i	$0.802495\pi$
$258$	−8.03704	+	5.27772i	−0.500364	+	0.328576i
$259$	3.85127	−	1.33493i	0.239306	−	0.0829482i
$260$	−1.15455	−	26.7279i	−0.0716023	−	1.65759i
$261$	1.86626	−	1.07749i	0.115519	−	0.0666947i
$262$	3.31219	−	0.190509i	0.204628	−	0.0117697i
$263$	4.20813	+	15.7050i	0.259485	+	0.968410i	0.965540	+	0.260254i	$0.0838062\pi$
$263$	4.20813	+	15.7050i	0.259485	+	0.968410i	−0.706056	+	0.708156i	$0.749527\pi$
$264$	1.40739	−	15.6942i	0.0866190	−	0.965910i
$265$	3.60453	−	1.74946i	0.221424	−	0.107469i
$266$	13.3347	−	10.1985i	0.817602	−	0.625312i
$267$	−2.63976	+	2.63976i	−0.161550	+	0.161550i
$268$	−17.9509	+	22.6353i	−1.09653	+	1.38267i
$269$	2.46307	−	4.26616i	0.150176	−	0.260112i	−0.781116	−	0.624386i	$-0.785349\pi$
$269$	2.46307	−	4.26616i	0.150176	−	0.260112i	0.931292	+	0.364274i	$0.118683\pi$
$270$	2.76092	−	1.54186i	0.168024	−	0.0938346i
$271$	−9.47009	+	5.46756i	−0.575267	+	0.332130i	−0.759250	−	0.650799i	$-0.774434\pi$
$271$	−9.47009	+	5.46756i	−0.575267	+	0.332130i	0.183983	+	0.982929i	$0.441101\pi$
$272$	1.47941	+	0.0473317i	0.0897027	+	0.00286991i
$273$	15.7863	−	1.13638i	0.955432	−	0.0687766i
$274$	5.99529	+	1.24245i	0.362188	+	0.0750591i
$275$	3.98286	−	27.5688i	0.240175	−	1.66246i
$276$	−6.31913	−	8.51376i	−0.380367	−	0.512468i
$277$	10.8608	−	2.91014i	0.652562	−	0.174854i	0.0826752	−	0.996577i	$-0.473654\pi$
$277$	10.8608	−	2.91014i	0.652562	−	0.174854i	0.569887	+	0.821723i	$0.306987\pi$
$278$	−24.7789	−	12.4669i	−1.48614	−	0.747715i
$279$	8.74118			0.523321
$280$	9.62582	−	13.6873i	0.575253	−	0.817976i
$281$	−12.9485			−0.772444			−0.386222	−	0.922406i	$-0.626220\pi$
$281$	−12.9485			−0.772444			−0.386222	+	0.922406i	$0.626220\pi$
$282$	1.63970	+	0.824976i	0.0976430	+	0.0491266i
$283$	−22.2576	+	5.96390i	−1.32308	+	0.354517i	−0.850129	−	0.526574i	$-0.823476\pi$
$283$	−22.2576	+	5.96390i	−1.32308	+	0.354517i	−0.472947	+	0.881091i	$0.656810\pi$
$284$	−17.4469	+	12.9496i	−1.03528	+	0.768415i
$285$	8.30651	+	5.62611i	0.492035	+	0.333262i
$286$	46.1499	+	9.56401i	2.72890	+	0.565532i
$287$	−9.61888	−	14.1978i	−0.567785	−	0.838069i
$288$	5.49962	+	1.32446i	0.324068	+	0.0780447i
$289$	14.6038	−	8.43153i	0.859050	−	0.495973i
$290$	6.55655	+	1.85760i	0.385014	+	0.109082i
$291$	3.75843	−	6.50980i	0.220323	−	0.381611i
$292$	11.5039	+	9.12319i	0.673215	+	0.533894i
$293$	7.48370	−	7.48370i	0.437203	−	0.437203i	−0.453867	−	0.891070i	$-0.649956\pi$
$293$	7.48370	−	7.48370i	0.437203	−	0.437203i	0.891070	+	0.453867i	$0.149956\pi$
$294$	8.25758	+	5.46007i	0.481592	+	0.318438i
$295$	−2.46174	+	7.10495i	−0.143328	+	0.413666i
$296$	−0.389201	+	4.34008i	−0.0226219	+	0.252262i
$297$	1.44188	+	5.38117i	0.0836664	+	0.312247i
$298$	−26.4753	+	1.52279i	−1.53367	+	0.0882130i
$299$	27.4643	−	15.8565i	1.58830	−	0.917005i
$300$	9.58139	+	2.86305i	0.553182	+	0.165298i
$301$	3.39611	−	17.6645i	0.195749	−	1.01817i
$302$	16.2998	−	10.7037i	0.937951	−	0.615928i
$303$	−13.6061	−	3.64575i	−0.781652	−	0.209443i
$304$	4.08824	+	17.4748i	0.234477	+	1.00225i
$305$	−16.4790	−	19.0309i	−0.943587	−	1.08970i
$306$	−0.496876	+	0.164248i	−0.0284045	+	0.00938943i
$307$	−20.7138	+	20.7138i	−1.18220	+	1.18220i	−0.203028	+	0.979173i	$0.565078\pi$
$307$	−20.7138	+	20.7138i	−1.18220	+	1.18220i	−0.979173	+	0.203028i	$0.934922\pi$
$308$	19.2236	+	22.3486i	1.09537	+	1.27343i
$309$	−9.21414			−0.524174
$310$	19.2647	+	19.8231i	1.09416	+	1.12588i
$311$	9.94499	+	5.74174i	0.563928	+	0.325584i	0.754721	−	0.656046i	$-0.227772\pi$
$311$	9.94499	+	5.74174i	0.563928	+	0.325584i	−0.190792	+	0.981630i	$0.561106\pi$
$312$	−5.82146	+	15.8870i	−0.329575	+	0.899422i
$313$	−2.95266	+	11.0195i	−0.166894	+	0.622857i	0.830897	+	0.556426i	$0.187828\pi$
$313$	−2.95266	+	11.0195i	−0.166894	+	0.622857i	−0.997791	+	0.0664309i	$0.978839\pi$
$314$	−1.39048	+	6.70957i	−0.0784692	+	0.378643i
$315$	−1.53050	+	5.71468i	−0.0862337	+	0.321986i
$316$	−1.04137	+	2.40459i	−0.0585815	+	0.135269i
$317$	−1.27621	+	4.76290i	−0.0716794	+	0.267511i	−0.992460	−	0.122570i	$-0.960886\pi$
$317$	−1.27621	+	4.76290i	−0.0716794	+	0.267511i	0.920780	+	0.390081i	$0.127553\pi$
$318$	−2.52984	+	0.145510i	−0.141867	+	0.00815981i
$319$	−6.00267	+	10.3969i	−0.336085	+	0.582116i
$320$	9.11702	+	15.3909i	0.509657	+	0.860378i
$321$	−7.74237			−0.432137
$322$	19.6619	+	2.62024i	1.09571	+	0.146020i
$323$	−1.17398	−	1.17398i	−0.0653221	−	0.0653221i
$324$	−1.98681	+	0.229311i	−0.110378	+	0.0127395i
$325$	−11.7929	+	27.4876i	−0.654153	+	1.52474i
$326$	−2.82374	−	2.51658i	−0.156393	−	0.139381i
$327$	−1.30148	+	4.85720i	−0.0719721	+	0.268604i
$328$	18.0618	−	3.14437i	0.997294	−	0.173619i
$329$	−3.24460	+	1.12464i	−0.178881	+	0.0620035i
$330$	−9.02555	+	15.1294i	−0.496840	+	0.832848i
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	0.935749	−	0.352666i	$-0.114725\pi$
$331$	2.95564	+	5.11931i	0.162456	+	0.281383i	−0.773293	+	0.634049i	$0.781392\pi$
$332$	2.81671	−	19.0374i	0.154587	−	1.04481i
$333$	−0.398738	−	1.48811i	−0.0218507	−	0.0815480i
$334$	25.6968	−	8.49437i	1.40607	−	0.464792i
$335$	29.0575	−	14.1031i	1.58758	−	0.770535i
$336$	−8.94691	+	5.65269i	−0.488094	+	0.308379i
$337$	22.1222	−	22.1222i	1.20507	−	1.20507i	0.232469	−	0.972604i	$-0.425320\pi$
$337$	22.1222	−	22.1222i	1.20507	−	1.20507i	0.972604	−	0.232469i	$-0.0746804\pi$
$338$	−28.7857	−	14.4828i	−1.56574	−	0.787761i
$339$	2.38839	+	1.37894i	0.129719	+	0.0748935i
$340$	−1.46754	−	0.764820i	−0.0795887	−	0.0414782i
$341$	−42.1729	+	24.3486i	−2.28379	+	1.31855i
$342$	−3.48286	−	5.30379i	−0.188332	−	0.286796i
$343$	−18.0916	+	3.96179i	−0.976852	+	0.213917i
$344$	15.7283	+	11.0640i	0.848014	+	0.596533i
$345$	2.23946	+	11.6406i	0.120568	+	0.626710i
$346$	−6.34718	+	7.12188i	−0.341226	+	0.382875i
$347$	4.35285	+	16.2451i	0.233673	+	0.872081i	0.978742	+	0.205094i	$0.0657499\pi$
$347$	4.35285	+	16.2451i	0.233673	+	0.872081i	−0.745069	+	0.666988i	$0.767583\pi$
$348$	−3.37692	−	2.67807i	−0.181022	−	0.143560i
$349$	0.714880			0.0382667			0.0191333	−	0.999817i	$-0.493909\pi$
$349$	0.714880			0.0382667			0.0191333	+	0.999817i	$0.493909\pi$
$350$	−16.3327	+	9.12376i	−0.873019	+	0.487685i
$351$		−	5.98211i		−	0.319301i
$352$	−30.2229	+	8.92914i	−1.61089	+	0.475925i
$353$	−1.47233	+	0.394510i	−0.0783643	+	0.0209977i	−0.297788	−	0.954632i	$-0.596249\pi$
$353$	−1.47233	+	0.394510i	−0.0783643	+	0.0209977i	0.219424	+	0.975630i	$0.429582\pi$
$354$	3.16410	−	3.55030i	0.168170	−	0.188696i
$355$	23.8547	−	4.58923i	1.26608	−	0.243571i
$356$	6.85144	+	2.96719i	0.363126	+	0.157261i
$357$	0.427381	−	0.880833i	0.0226194	−	0.0466186i
$358$	−1.51300	+	0.993551i	−0.0799647	+	0.0525108i
$359$	−8.03539	−	13.9177i	−0.424092	−	0.734548i	0.572243	−	0.820084i	$-0.306073\pi$
$359$	−8.03539	−	13.9177i	−0.424092	−	0.734548i	−0.996335	+	0.0855354i	$0.972740\pi$
$360$	−4.89876	−	4.00027i	−0.258187	−	0.210833i
$361$	0.565127	−	0.978828i	0.0297435	−	0.0515173i
$362$	−24.3958	−	12.2742i	−1.28222	−	0.645115i
$363$	−14.1676	−	14.1676i	−0.743606	−	0.743606i
$364$	−13.7277	−	28.5227i	−0.719529	−	1.49500i
$365$	−7.16761	−	14.7679i	−0.375170	−	0.772987i
$366$	4.99708	+	15.1169i	0.261201	+	0.790176i
$367$	−17.6035	+	4.71685i	−0.918897	+	0.246218i	−0.687114	−	0.726550i	$-0.741123\pi$
$367$	−17.6035	+	4.71685i	−0.918897	+	0.246218i	−0.231783	+	0.972767i	$0.574456\pi$
$368$	−11.1844	+	18.0158i	−0.583029	+	0.939141i
$369$	−5.61344	+	3.24092i	−0.292224	+	0.168716i
$370$	2.49593	−	4.18390i	0.129757	−	0.217511i
$371$	3.10286	−	3.58423i	0.161093	−	0.186084i
$372$	−6.43108	−	16.2565i	−0.333436	−	0.842861i
$373$	14.3013	+	3.83202i	0.740493	+	0.198414i	0.609297	−	0.792942i	$-0.291452\pi$
$373$	14.3013	+	3.83202i	0.740493	+	0.198414i	0.131196	+	0.991356i	$0.458118\pi$
$374$	1.93973	−	2.17648i	0.100301	−	0.112543i
$375$	−8.26526	−	7.52898i	−0.426816	−	0.388795i
$376$	0.327893	−	3.65641i	0.0169098	−	0.188565i
$377$	9.11551	−	9.11551i	0.469472	−	0.469472i
$378$	2.28248	−	2.96484i	0.117398	−	0.152495i
$379$		−	21.4047i		−	1.09949i	−0.835334	−	0.549743i	$-0.814726\pi$
$379$		−	21.4047i		−	1.09949i	0.835334	−	0.549743i	$-0.185274\pi$
$380$	4.35194	−	19.5874i	0.223250	−	1.00481i
$381$	17.4557	+	10.0780i	0.894282	+	0.516314i
$382$	1.12330	+	19.5296i	0.0574728	+	0.999223i
$383$	17.8415	+	4.78061i	0.911658	+	0.244278i	0.684016	−	0.729467i	$-0.260232\pi$
$383$	17.8415	+	4.78061i	0.911658	+	0.244278i	0.227642	+	0.973745i	$0.426899\pi$
$384$	−1.58301	−	11.2024i	−0.0807824	−	0.571671i
$385$	−8.53417	−	31.8344i	−0.434942	−	1.62243i
$386$	5.53166	−	26.6923i	0.281554	−	1.35860i
$387$	−6.56717	−	1.75967i	−0.333828	−	0.0894489i
$388$	−14.8718	−	2.20039i	−0.755003	−	0.111708i
$389$	12.1014	−	20.9602i	0.613563	−	1.06272i	−0.377072	−	0.926184i	$-0.623069\pi$
$389$	12.1014	−	20.9602i	0.613563	−	1.06272i	0.990635	−	0.136538i	$-0.0435977\pi$
$390$	13.5661	−	13.1840i	0.686946	−	0.667596i
$391$		−	1.96171i		−	0.0992080i
$392$	4.07915	−	19.3742i	0.206028	−	0.978546i
$393$	1.65883	+	1.65883i	0.0836771	+	0.0836771i
$394$	16.8599	−	5.57322i	0.849388	−	0.280775i
$395$	2.21477	−	1.91779i	0.111437	−	0.0964947i
$396$	8.94687	−	6.64060i	0.449597	−	0.333703i
$397$	−1.12078	+	4.18281i	−0.0562504	+	0.209929i	−0.988331	−	0.152322i	$-0.951325\pi$
$397$	−1.12078	+	4.18281i	−0.0562504	+	0.209929i	0.932081	+	0.362251i	$0.117992\pi$
$398$	−10.2183	−	15.5608i	−0.512200	−	0.779990i
$399$	11.6571	+	2.24116i	0.583587	+	0.112198i
$400$	−1.72465	−	19.9255i	−0.0862323	−	0.996275i
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	−0.977915	−	0.209001i	$-0.932979\pi$
$401$	−13.4159	−	23.2370i	−0.669958	−	1.16040i	0.307958	−	0.951400i	$-0.400355\pi$
$402$	−20.3941	+	1.17302i	−1.01717	+	0.0585048i
$403$	50.5089	−	13.5338i	2.51603	−	0.674168i
$404$	3.23010	+	27.9864i	0.160704	+	1.39238i
$405$	2.11284	+	0.732062i	0.104988	+	0.0363765i
$406$	7.99584	−	1.03979i	0.396827	−	0.0516037i
$407$	6.06890	+	6.06890i	0.300824	+	0.300824i
$408$	0.671025	+	0.803230i	0.0332207	+	0.0397658i
$409$	12.0607	+	6.96325i	0.596364	+	0.344311i	0.767610	−	0.640918i	$-0.221446\pi$
$409$	12.0607	+	6.96325i	0.596364	+	0.344311i	−0.171246	+	0.985228i	$0.554779\pi$
$410$	−19.7212	−	5.58738i	−0.973959	−	0.275941i
$411$	2.16469	+	3.74936i	0.106776	+	0.184942i
$412$	6.77904	+	17.1361i	0.333980	+	0.844235i
$413$	0.638796	+	8.87404i	0.0314331	+	0.436663i
$414$	1.52137	−	7.34120i	0.0747715	−	0.360800i
$415$	−12.0660	+	17.8145i	−0.592297	+	0.874480i
$416$	33.8289	−	0.861861i	1.65860	−	0.0422562i
$417$	−5.07648	−	18.9457i	−0.248596	−	0.927774i
$418$	31.5772	+	15.8873i	1.54449	+	0.777073i
$419$		−	1.69659i		−	0.0828841i	−0.999141	−	0.0414420i	$-0.986805\pi$
$419$		−	1.69659i		−	0.0828841i	0.999141	−	0.0414420i	$-0.0131952\pi$
$420$	11.7540	−	1.35806i	0.573535	−	0.0662666i
$421$		−	10.8090i		−	0.526800i	−0.964687	−	0.263400i	$-0.915156\pi$
$421$		−	10.8090i		−	0.526800i	0.964687	−	0.263400i	$-0.0848439\pi$
$422$	−0.179133	+	0.356042i	−0.00872008	+	0.0173318i
$423$	0.335928	+	1.25370i	0.0163334	+	0.0609569i
$424$	2.13188	+	4.59785i	0.103533	+	0.223291i
$425$	1.10779	+	1.48192i	0.0537356	+	0.0718838i
$426$	−15.0440	−	3.11769i	−0.728886	−	0.151053i
$427$	−26.7985	−	13.0026i	−1.29687	−	0.629241i
$428$	5.69623	+	14.3990i	0.275338	+	0.696000i
$429$	16.6632	+	28.8614i	0.804505	+	1.39344i
$430$	−10.4828	−	18.7710i	−0.505528	−	0.905219i
$431$	−2.61429	−	1.50936i	−0.125926	−	0.0727034i	0.435714	−	0.900085i	$-0.356496\pi$
$431$	−2.61429	−	1.50936i	−0.125926	−	0.0727034i	−0.561640	+	0.827382i	$0.689829\pi$
$432$	1.88820	+	3.52628i	0.0908463	+	0.169658i
$433$	−8.45880	−	8.45880i	−0.406504	−	0.406504i	0.474014	−	0.880518i	$-0.342805\pi$
$433$	−8.45880	−	8.45880i	−0.406504	−	0.406504i	−0.880518	+	0.474014i	$0.842805\pi$
$434$	30.1970	+	12.5641i	1.44950	+	0.603096i
$435$	2.10402	+	4.33505i	0.100880	+	0.207850i
$436$	9.99075	−	1.15310i	0.478470	−	0.0552235i
$437$	22.9748	−	6.15608i	1.09903	−	0.294485i
$438$	0.596162	+	10.3649i	0.0284857	+	0.495253i
$439$	−5.28278	−	9.15005i	−0.252133	−	0.436708i	0.711980	−	0.702200i	$-0.247799\pi$
$439$	−5.28278	−	9.15005i	−0.252133	−	0.436708i	−0.964113	+	0.265492i	$0.914466\pi$
$440$	34.7774	+	5.65431i	1.65795	+	0.269559i
$441$	1.00259	+	6.92783i	0.0477425	+	0.329897i
$442$	−2.61678	+	1.71837i	−0.124468	+	0.0817347i
$443$	7.74694	−	28.9120i	0.368068	−	1.37365i	−0.495145	−	0.868810i	$-0.664885\pi$
$443$	7.74694	−	28.9120i	0.368068	−	1.37365i	0.863213	−	0.504839i	$-0.168448\pi$
$444$	−2.47417	+	1.83640i	−0.117419	+	0.0871515i
$445$	−5.46440	−	6.31058i	−0.259038	−	0.299150i
$446$	−0.415118	−	1.25580i	−0.0196564	−	0.0594638i
$447$	−13.2595	−	13.2595i	−0.627154	−	0.627154i
$448$	17.0951	+	12.4803i	0.807667	+	0.589639i
$449$			4.41290i			0.208257i	0.994564	+	0.104129i	$0.0332054\pi$
$449$			4.41290i			0.208257i	−0.994564	+	0.104129i	$0.966795\pi$
$450$	2.99633	+	6.40484i	0.141248	+	0.301927i
$451$	18.0552	−	31.2725i	0.850185	−	1.47256i
$452$	0.807303	−	5.45635i	0.0379723	−	0.256645i
$453$	13.3188	+	3.56877i	0.625773	+	0.167675i
$454$	−30.6928	−	6.36071i	−1.44049	−	0.298523i
$455$	0.00432617	+	35.3906i	0.000202814	+	1.65914i
$456$	−7.30136	+	10.3794i	−0.341918	+	0.486060i
$457$	−35.8936	−	9.61767i	−1.67903	−	0.449896i	−0.711510	−	0.702676i	$-0.751988\pi$
$457$	−35.8936	−	9.61767i	−1.67903	−	0.449896i	−0.967524	+	0.252780i	$0.918655\pi$
$458$	−6.73059	+	0.387127i	−0.314500	+	0.0180892i
$459$	−0.320466	−	0.185021i	−0.0149581	−	0.00863606i
$460$	20.0012	−	12.7291i	0.932560	−	0.593499i
$461$		−	15.8272i		−	0.737148i	−0.929598	−	0.368574i	$-0.879846\pi$
$461$		−	15.8272i		−	0.737148i	0.929598	−	0.368574i	$-0.120154\pi$
$462$	−2.75353	+	20.6621i	−0.128106	+	0.961288i
$463$	8.81202	−	8.81202i	0.409529	−	0.409529i	−0.472045	−	0.881574i	$-0.656484\pi$
$463$	8.81202	−	8.81202i	0.409529	−	0.409529i	0.881574	+	0.472045i	$0.156484\pi$
$464$	−2.49610	+	8.25057i	−0.115878	+	0.383023i
$465$	−1.40099	+	19.4956i	−0.0649694	+	0.904087i
$466$	0.0119282	+	0.0106307i	0.000552563	+	0.000492456i
$467$	32.7580	+	8.77747i	1.51586	+	0.406173i	0.918376	−	0.395709i	$-0.129501\pi$
$467$	32.7580	+	8.77747i	1.51586	+	0.406173i	0.597482	+	0.801882i	$0.296168\pi$
$468$	−11.1253	+	4.40117i	−0.514267	+	0.203444i
$469$	25.0134	−	28.8940i	1.15501	−	1.33420i
$470$	−2.10276	+	3.52484i	−0.0969932	+	0.162589i
$471$	−4.19606	+	2.42260i	−0.193344	+	0.111627i
$472$	−8.93061	−	3.27244i	−0.411065	−	0.150626i
$473$	36.5857	−	9.80311i	1.68221	−	0.450747i
$474$	−1.75928	+	0.581548i	−0.0808062	+	0.0267114i
$475$	−13.8793	+	17.6244i	−0.636828	+	0.808664i
$476$	−1.95257	−	0.146777i	−0.0894961	−	0.00672753i
$477$	−1.26701	−	1.26701i	−0.0580125	−	0.0580125i
$478$	6.56126	−	13.0410i	0.300105	−	0.596482i
$479$	9.32972	−	16.1595i	0.426286	−	0.738348i	−0.570254	−	0.821468i	$-0.693155\pi$
$479$	9.32972	−	16.1595i	0.426286	−	0.738348i	0.996540	+	0.0831201i	$0.0264885\pi$
$480$	−3.83542	+	12.0536i	−0.175062	+	0.550170i
$481$	−4.60804	−	7.98136i	−0.210108	−	0.363918i
$482$	7.98645	+	12.1620i	0.363773	+	0.553962i
$483$	7.86700	+	11.6120i	0.357961	+	0.528362i
$484$	−15.9249	+	36.7718i	−0.723861	+	1.67144i
$485$	13.9165	+	9.42585i	0.631917	+	0.428006i
$486$	−1.05577	−	0.940927i	−0.0478908	−	0.0426813i
$487$	17.4237	−	4.66866i	0.789542	−	0.211557i	0.158554	−	0.987350i	$-0.449317\pi$
$487$	17.4237	−	4.66866i	0.789542	−	0.211557i	0.630987	+	0.775793i	$0.282650\pi$
$488$	24.4375	−	20.4152i	1.10623	−	0.924155i
$489$		−	2.67457i		−	0.120948i
$490$	−13.5012	+	17.5419i	−0.609921	+	0.792462i
$491$	20.1191			0.907962			0.453981	−	0.891011i	$-0.350003\pi$
$491$	20.1191			0.907962			0.453981	+	0.891011i	$0.350003\pi$
$492$	10.1573	+	8.05524i	0.457925	+	0.363158i
$493$	−0.206391	−	0.770260i	−0.00929536	−	0.0346908i
$494$	−28.3367	−	25.2543i	−1.27493	−	1.13624i
$495$	−12.2328	+	2.35338i	−0.549824	+	0.105777i
$496$	−25.5018	+	23.9206i	−1.14506	+	1.07406i
$497$	23.7959	−	16.1215i	1.06739	−	0.723150i
$498$	11.3747	−	7.46950i	0.509714	−	0.334716i
$499$	−8.51618	+	4.91682i	−0.381237	+	0.220107i	−0.678356	−	0.734733i	$-0.737307\pi$
$499$	−8.51618	+	4.91682i	−0.381237	+	0.220107i	0.297119	+	0.954840i	$0.403974\pi$
$500$	−7.92116	+	20.9106i	−0.354245	+	0.935153i
$501$	16.5735	+	9.56871i	0.740449	+	0.427498i
$502$	−0.703177	+	1.39762i	−0.0313843	+	0.0623788i
$503$	11.2005	−	11.2005i	0.499406	−	0.499406i	−0.411847	−	0.911253i	$-0.635116\pi$
$503$	11.2005	−	11.2005i	0.499406	−	0.499406i	0.911253	+	0.411847i	$0.135116\pi$
$504$	−7.19317	−	2.06356i	−0.320409	−	0.0919184i
$505$	10.3119	−	29.7616i	0.458873	−	1.32438i
$506$	13.1088	+	39.6563i	0.582759	+	1.76294i
$507$	−5.89735	−	22.0092i	−0.261910	−	0.977463i
$508$	5.90022	−	39.8780i	0.261780	−	1.76930i
$509$	2.28874	+	3.96422i	0.101447	+	0.175711i	0.912281	−	0.409565i	$-0.134320\pi$
$509$	2.28874	+	3.96422i	0.101447	+	0.175711i	−0.810834	+	0.585276i	$0.800986\pi$
$510$	−0.286688	−	1.13452i	−0.0126948	−	0.0502372i
$511$	−14.6848	−	12.7126i	−0.649615	−	0.562371i
$512$	−19.6692	+	11.1859i	−0.869263	+	0.494351i
$513$	1.16124	−	4.33380i	0.0512699	−	0.191342i
$514$	−19.1688	+	21.5084i	−0.845499	+	0.948696i
$515$	1.47679	−	20.5504i	0.0650753	−	0.905561i
$516$	1.55905	+	13.5080i	0.0686333	+	0.594656i
$517$	−5.11290	−	5.11290i	−0.224865	−	0.224865i
$518$	0.761464	−	5.71391i	0.0334568	−	0.251055i
$519$	−6.74566			−0.296102
$520$	−34.4999	−	15.5300i	−1.51292	−	0.681035i
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	−0.999030	−	0.0440323i	$-0.985980\pi$
$521$	−10.5312	+	18.2406i	−0.461382	+	0.799137i	0.537648	+	0.843169i	$0.319313\pi$
$522$	−0.175001	−	3.04256i	−0.00765956	−	0.133169i
$523$	0.144603	−	0.539666i	0.00632305	−	0.0235980i	−0.962692	−	0.270599i	$-0.912778\pi$
$523$	0.144603	−	0.539666i	0.00632305	−	0.0235980i	0.969015	+	0.247001i	$0.0794450\pi$
$524$	1.86459	−	4.30548i	0.0814552	−	0.188086i
$525$	−12.5002	−	4.32941i	−0.545556	−	0.188951i
$526$	22.5153	+	4.66601i	0.981712	+	0.203448i
$527$	0.837179	−	3.12439i	0.0364681	−	0.136101i
$528$	−18.9323	−	11.7534i	−0.823925	−	0.511502i
$529$	4.42010	+	2.55195i	0.192178	+	0.110954i
$530$	0.0809365	−	5.66568i	0.00351565	−	0.246101i
$531$	3.36275			0.145931
$532$	−4.40840	−	23.3284i	−0.191128	−	1.01141i
$533$	−27.4181	+	27.4181i	−1.18761	+	1.18761i
$534$	1.65702	+	5.01274i	0.0717061	+	0.216922i
$535$	1.24091	−	17.2679i	0.0536491	−	0.746558i
$536$	17.1859	+	37.0651i	0.742319	+	1.60097i
$537$	−1.23630	−	0.331264i	−0.0533501	−	0.0142951i
$538$	−3.82400	−	5.82328i	−0.164864	−	0.251060i
$539$	−24.1346	−	30.6315i	−1.03955	−	1.31939i
$540$	−0.193001	−	4.46797i	−0.00830544	−	0.192271i
$541$	−11.9490	+	6.89877i	−0.513728	+	0.296601i	−0.734365	−	0.678755i	$-0.762520\pi$
$541$	−11.9490	+	6.89877i	−0.513728	+	0.296601i	0.220637	+	0.975356i	$0.429187\pi$
$542$	0.888016	+	15.4391i	0.0381436	+	0.663165i
$543$	−4.99799	−	18.6528i	−0.214484	−	0.800467i
$544$	1.00013	−	1.83890i	0.0428802	−	0.0788422i
$545$	−10.6245	−	3.68120i	−0.455103	−	0.157685i
$546$	8.59836	−	20.6656i	0.367976	−	0.884406i
$547$	−2.63775	+	2.63775i	−0.112782	+	0.112782i	−0.761246	−	0.648464i	$-0.775412\pi$
$547$	−2.63775	+	2.63775i	−0.112782	+	0.112782i	0.648464	+	0.761246i	$0.275412\pi$
$548$	5.38030	−	6.78430i	0.229835	−	0.289811i
$549$	−5.62909	+	9.74986i	−0.240244	+	0.416114i
$550$	−32.2968	−	22.5547i	−1.37714	−	0.961736i
$551$	8.37330	−	4.83433i	0.356715	−	0.205949i
$552$	−14.7722	+	2.57169i	−0.628746	+	0.109458i
$553$	1.51322	−	3.11874i	0.0643485	−	0.132622i
$554$	3.22679	−	15.5705i	0.137093	−	0.661526i
$555$	3.38287	−	0.650806i	0.143595	−	0.0276252i
$556$	−31.4996	+	23.3798i	−1.33588	+	0.991524i
$557$	17.5592	−	4.70498i	0.744008	−	0.199356i	0.133149	−	0.991096i	$-0.457491\pi$
$557$	17.5592	−	4.70498i	0.744008	−	0.199356i	0.610859	+	0.791740i	$0.290824\pi$
$558$	5.55600	−	11.0430i	0.235204	−	0.467487i
$559$	−40.6714			−1.72022
$560$	−11.1733	−	20.8604i	−0.472159	−	0.881513i
$561$	2.06151			0.0870369
$562$	−8.23024	+	16.3582i	−0.347172	+	0.690030i
$563$	−24.3030	+	6.51198i	−1.02425	+	0.274447i	−0.731572	−	0.681764i	$-0.761213\pi$
$563$	−24.3030	+	6.51198i	−1.02425	+	0.274447i	−0.292678	+	0.956211i	$0.594547\pi$
$564$	2.08443	−	1.54712i	0.0877704	−	0.0651455i
$565$	−3.45826	+	5.10585i	−0.145490	+	0.214805i
$566$	−6.61283	+	31.9094i	−0.277958	+	1.34125i
$567$	2.63892	−	0.189962i	0.110824	−	0.00797767i
$568$	5.27006	+	30.2721i	0.221127	+	1.27019i
$569$	−13.9329	+	8.04416i	−0.584097	+	0.337229i	−0.762760	−	0.646682i	$-0.776156\pi$
$569$	−13.9329	+	8.04416i	−0.584097	+	0.337229i	0.178663	+	0.983910i	$0.442823\pi$
$570$	12.3873	−	6.91782i	0.518849	−	0.289756i
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.00848298	+	0.999964i	$0.502700\pi$
$571$	−20.7948	+	36.0177i	−0.870236	+	1.50729i	−0.861753	+	0.507328i	$0.830633\pi$
$572$	41.4159	−	52.2235i	1.73169	−	2.18357i
$573$	−9.78096	+	9.78096i	−0.408605	+	0.408605i
$574$	−24.0503	+	3.12752i	−1.00384	+	0.130540i
$575$	−26.3212	+	3.12900i	−1.09767	+	0.130488i
$576$	5.16885	−	6.10598i	0.215369	−	0.254416i
$577$	8.56429	+	31.9623i	0.356536	+	1.33061i	0.878541	+	0.477667i	$0.158518\pi$
$577$	8.56429	+	31.9623i	0.356536	+	1.33061i	−0.522005	+	0.852943i	$0.674816\pi$
$578$	−1.36941	−	23.8086i	−0.0569601	−	0.990308i
$579$	16.6929	−	9.63768i	0.693735	−	0.400528i
$580$	6.51418	−	7.10236i	0.270486	−	0.294910i
$581$	−4.80649	+	25.0004i	−0.199407	+	1.03719i
$582$	−5.83510	−	8.88584i	−0.241873	−	0.368330i
$583$	9.64213	+	2.58360i	0.399336	+	0.107002i
$584$	18.8376	−	8.73439i	0.779505	−	0.361432i
$585$	13.3420	+	0.958781i	0.551623	+	0.0396407i
$586$	−4.69764	−	14.2111i	−0.194058	−	0.587055i
$587$	−22.3262	+	22.3262i	−0.921501	+	0.921501i	−0.997136	−	0.0756346i	$-0.975902\pi$
$587$	−22.3262	+	22.3262i	−0.921501	+	0.921501i	0.0756346	+	0.997136i	$0.475902\pi$
$588$	12.1465	−	6.96154i	0.500912	−	0.287089i
$589$	39.2188			1.61598
$590$	7.41116	+	7.62598i	0.305113	+	0.313956i
$591$	10.8740	+	6.27810i	0.447296	+	0.258247i
$592$	5.23556	+	3.25029i	0.215180	+	0.133586i
$593$	−4.18981	+	15.6366i	−0.172055	+	0.642117i	0.824980	+	0.565162i	$0.191186\pi$
$593$	−4.18981	+	15.6366i	−0.172055	+	0.642117i	−0.997035	+	0.0769548i	$0.975480\pi$
$594$	7.71466	+	1.59877i	0.316536	+	0.0655983i
$595$	1.89604	+	1.09437i	0.0777300	+	0.0448648i
$596$	−14.9042	+	34.4149i	−0.610501	+	1.40969i
$597$	3.40695	−	12.7149i	0.139437	−	0.520386i
$598$	−2.57534	−	44.7750i	−0.105314	−	1.83098i
$599$	1.79982	−	3.11738i	0.0735386	−	0.127373i	−0.826911	−	0.562332i	$-0.809904\pi$
$599$	1.79982	−	3.11738i	0.0735386	−	0.127373i	0.900450	+	0.434960i	$0.143237\pi$
$600$	9.70702	−	10.2846i	0.396287	−	0.419869i
$601$	17.5729			0.716814			0.358407	−	0.933565i	$-0.383320\pi$
$601$	17.5729			0.716814			0.358407	+	0.933565i	$0.383320\pi$
$602$	−20.1575	−	15.5182i	−0.821558	−	0.632474i
$603$	−10.2139	−	10.2139i	−0.415942	−	0.415942i
$604$	−3.16190	−	27.3954i	−0.128656	−	1.11470i
$605$	33.8690	−	29.3275i	1.37697	−	1.19233i
$606$	−13.2540	+	14.8717i	−0.538407	+	0.604122i
$607$	−11.5490	+	43.1013i	−0.468758	+	1.74943i	0.175362	+	0.984504i	$0.443890\pi$
$607$	−11.5490	+	43.1013i	−0.468758	+	1.74943i	−0.644120	+	0.764924i	$0.722776\pi$
$608$	24.6750	+	5.94243i	1.00070	+	0.240998i
$609$	4.31064	+	3.73171i	0.174676	+	0.151217i
$610$	−34.5165	+	8.72220i	−1.39753	+	0.353151i
$611$	3.88216	+	6.72410i	0.157055	+	0.272028i
$612$	−0.108321	+	0.732115i	−0.00437863	+	0.0295940i
$613$	10.4904	+	39.1507i	0.423703	+	1.58128i	0.766738	+	0.641960i	$0.221879\pi$
$613$	10.4904	+	39.1507i	0.423703	+	1.58128i	−0.343035	+	0.939323i	$0.611455\pi$
$614$	13.0024	+	39.3343i	0.524734	+	1.58740i
$615$	−6.32859	−	13.0392i	−0.255193	−	0.525791i
$616$	40.4524	−	10.0806i	1.62987	−	0.406161i
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	−0.556815	−	0.830637i	$-0.687977\pi$
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	0.830637	+	0.556815i	$0.187977\pi$
$618$	−5.85662	+	11.6405i	−0.235588	+	0.468249i
$619$	−17.8113	−	10.2834i	−0.715898	−	0.413324i	0.0973433	−	0.995251i	$-0.468966\pi$
$619$	−17.8113	−	10.2834i	−0.715898	−	0.413324i	−0.813241	+	0.581927i	$0.802299\pi$
$620$	37.2879	−	11.7378i	1.49752	−	0.471403i
$621$	4.59107	−	2.65066i	0.184233	−	0.106367i
$622$	13.5749	−	8.91426i	0.544302	−	0.357429i
$623$	−8.88629	−	4.31163i	−0.356022	−	0.172742i
$624$	16.3702	+	17.4524i	0.655334	+	0.698653i
$625$	18.1167	−	17.2274i	0.724669	−	0.689098i
$626$	12.0445	+	10.7343i	0.481393	+	0.429028i
$627$	6.46925	+	24.1436i	0.258357	+	0.964201i
$628$	7.59259	+	6.02131i	0.302977	+	0.240277i
$629$	−0.570090			−0.0227310
$630$	6.24672	+	5.56584i	0.248875	+	0.221748i
$631$		−	39.2014i		−	1.56058i	−0.625416	−	0.780291i	$-0.715071\pi$
$631$		−	39.2014i		−	1.56058i	0.625416	−	0.780291i	$-0.284929\pi$
$632$	2.37588	+	2.84398i	0.0945074	+	0.113127i
$633$	−0.272225	+	0.0729425i	−0.0108200	+	0.00289921i
$634$	5.20593	+	4.63963i	0.206754	+	0.184263i
$635$	−25.2749	+	37.3164i	−1.00301	+	1.48086i
$636$	−1.42417	+	3.28851i	−0.0564721	+	0.130398i
$637$	16.5195	+	38.4786i	0.654526	+	1.52458i
$638$	9.31936	+	14.1918i	0.368957	+	0.561857i
$639$	−5.43188	−	9.40830i	−0.214882	−	0.372187i
$640$	25.2386	−	1.73514i	0.997645	−	0.0685874i
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	−0.900101	−	0.435680i	$-0.856508\pi$
$641$	−1.84164	+	3.18982i	−0.0727406	+	0.125990i	0.827361	+	0.561671i	$0.189841\pi$
$642$	−4.92114	+	9.78115i	−0.194222	+	0.386031i
$643$	−1.34191	−	1.34191i	−0.0529196	−	0.0529196i	0.680152	−	0.733071i	$-0.261914\pi$
$643$	−1.34191	−	1.34191i	−0.0529196	−	0.0529196i	−0.733071	+	0.680152i	$0.761914\pi$
$644$	15.8075	−	23.1739i	0.622904	−	0.913181i
$645$	4.97717	−	14.3648i	0.195976	−	0.565615i
$646$	−2.22932	+	0.736927i	−0.0877115	+	0.0289940i
$647$	−28.6343	+	7.67253i	−1.12573	+	0.301638i	−0.773200	−	0.634162i	$-0.781345\pi$
$647$	−28.6343	+	7.67253i	−1.12573	+	0.301638i	−0.352530	+	0.935801i	$0.614678\pi$
$648$	−0.973145	+	2.65575i	−0.0382288	+	0.104328i
$649$	−16.2240	+	9.36694i	−0.636848	+	0.367684i
$650$	27.2301	+	32.3698i	1.06805	+	1.26965i
$651$	7.57417	+	21.8515i	0.296855	+	0.856429i
$652$	−4.97407	+	1.96774i	−0.194800	+	0.0770628i
$653$	−31.0796	−	8.32776i	−1.21624	−	0.325890i	−0.407032	−	0.913414i	$-0.633436\pi$
$653$	−31.0796	−	8.32776i	−1.21624	−	0.325890i	−0.809207	+	0.587523i	$0.800103\pi$
$654$	5.30899	+	4.73149i	0.207598	+	0.185016i
$655$	−3.96559	+	3.43385i	−0.154949	+	0.134172i
$656$	7.50790	−	24.8165i	0.293134	−	0.968923i
$657$	−5.19100	+	5.19100i	−0.202520	+	0.202520i
$658$	−0.641515	+	4.81383i	−0.0250089	+	0.187663i
$659$			45.5239i			1.77336i	0.462382	+	0.886681i	$0.346995\pi$
$659$			45.5239i			1.77336i	−0.462382	+	0.886681i	$0.653005\pi$
$660$	13.3767	+	21.0187i	0.520687	+	0.818151i
$661$	27.4916	+	15.8723i	1.06930	+	0.617360i	0.927990	−	0.372606i	$-0.121536\pi$
$661$	27.4916	+	15.8723i	1.06930	+	0.617360i	0.141309	+	0.989966i	$0.454869\pi$
$662$	8.34601	−	0.480041i	0.324377	−	0.0186573i
$663$	−2.13821	−	0.572931i	−0.0830411	−	0.0222508i
$664$	−22.2601	−	15.6588i	−0.863861	−	0.607680i
$665$	−6.86684	+	25.6399i	−0.266284	+	0.994273i
$666$	−2.13342	−	0.442125i	−0.0826682	−	0.0171320i
$667$	11.0349	+	2.95679i	0.427273	+	0.114488i
$668$	5.60203	−	37.8626i	0.216749	−	1.46495i
$669$	0.467621	−	0.809943i	0.0180793	−	0.0313142i
$670$	0.652461	−	45.6733i	0.0252068	−	1.76451i
$671$		−	62.7193i		−	2.42125i
$672$	1.45444	+	14.8958i	0.0561062	+	0.574618i
$673$	26.2642	+	26.2642i	1.01241	+	1.01241i	0.999922	+	0.0124869i	$0.00397481\pi$
$673$	26.2642	+	26.2642i	1.01241	+	1.01241i	0.0124869	+	0.999922i	$0.496025\pi$
$674$	−13.8865	−	42.0087i	−0.534886	−	1.61812i
$675$	−1.97136	+	4.59497i	−0.0758779	+	0.176860i
$676$	−36.5931	+	27.1603i	−1.40743	+	1.04463i
$677$	−1.90486	+	7.10904i	−0.0732098	+	0.273223i	−0.992821	−	0.119606i	$-0.961837\pi$
$677$	−1.90486	+	7.10904i	−0.0732098	+	0.273223i	0.919612	+	0.392829i	$0.128504\pi$
$678$	3.26014	−	2.14085i	0.125205	−	0.0822188i
$679$	19.5301	+	3.75478i	0.749496	+	0.144095i
$680$	−1.89901	+	1.36786i	−0.0728236	+	0.0524550i
$681$	−11.0821	−	19.1948i	−0.424668	−	0.735546i
$682$	3.95459	+	68.7545i	0.151429	+	2.63275i
$683$	−14.5409	+	3.89621i	−0.556391	+	0.149084i	−0.526048	−	0.850455i	$-0.676327\pi$
$683$	−14.5409	+	3.89621i	−0.556391	+	0.149084i	−0.0303430	+	0.999540i	$0.509660\pi$
$684$	−8.91417	+	1.02885i	−0.340842	+	0.0393389i
$685$	−8.70920	+	4.22702i	−0.332761	+	0.161506i
$686$	−6.49417	+	25.3737i	−0.247948	+	0.968773i
$687$	−3.37086	−	3.37086i	−0.128606	−	0.128606i
$688$	23.9746	−	12.8376i	0.914024	−	0.489429i
$689$	−9.28284	−	5.35945i	−0.353648	−	0.204179i
$690$	16.1294	+	4.56976i	0.614034	+	0.173968i
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	0.931135	+	0.364674i	$0.118820\pi$
$691$	20.5402	+	35.5766i	0.781385	+	1.35340i	−0.149750	+	0.988724i	$0.547847\pi$
$692$	4.96293	+	12.5453i	0.188662	+	0.476901i
$693$	−12.2027	+	8.26721i	−0.463541	+	0.314046i
$694$	23.2896	+	4.82648i	0.884061	+	0.183211i
$695$	43.0685	−	8.28564i	1.63368	−	0.314292i
$696$	−5.52969	+	2.56394i	−0.209602	+	0.0971859i
$697$	0.620793	+	2.31683i	0.0235142	+	0.0877562i
$698$	0.454386	−	0.903128i	0.0171988	−	0.0341839i
$699$			0.0112981i			0.000427332i
$700$	1.14504	+	26.4327i	0.0432785	+	0.999063i
$701$			34.1172i			1.28859i	0.764777	+	0.644295i	$0.222849\pi$
$701$			34.1172i			1.28859i	−0.764777	+	0.644295i	$0.777151\pi$
$702$	−7.55736	−	3.80230i	−0.285234	−	0.143509i
$703$	−1.78901	−	6.67668i	−0.0674738	−	0.251816i
$704$	−7.92959	+	43.8569i	−0.298858	+	1.65292i
$705$	−2.84999	+	0.548288i	−0.107337	+	0.0206497i
$706$	−0.437436	+	2.11079i	−0.0164631	+	0.0794408i
$707$	−2.67583	−	37.1721i	−0.100635	−	1.39800i
$708$	−2.47405	−	6.25391i	−0.0929805	−	0.235036i
$709$	−0.746144	−	1.29236i	−0.0280220	−	0.0485356i	0.851674	−	0.524071i	$-0.175588\pi$
$709$	−0.746144	−	1.29236i	−0.0280220	−	0.0485356i	−0.879696	+	0.475536i	$0.842254\pi$
$710$	9.36462	−	33.0533i	0.351448	−	1.24047i
$711$	−1.13467	−	0.655100i	−0.0425533	−	0.0245682i
$712$	8.10339	−	6.76964i	0.303687	−	0.253703i
$713$	32.7671	+	32.7671i	1.22714	+	1.22714i
$714$	−0.841133	−	1.09979i	−0.0314786	−	0.0411586i
$715$	−67.0408	+	32.5383i	−2.50718	+	1.21687i
$716$	0.293497	+	2.54293i	0.0109685	+	0.0950338i
$717$	9.97101	−	2.67172i	0.372374	−	0.0997774i
$718$	−22.6900	+	1.30507i	−0.846784	+	0.0487049i
$719$	4.78565	+	8.28900i	0.178475	+	0.309127i	0.941358	−	0.337409i	$-0.109550\pi$
$719$	4.78565	+	8.28900i	0.178475	+	0.309127i	−0.762884	+	0.646536i	$0.776217\pi$
$720$	−8.16736	+	3.64612i	−0.304380	+	0.135883i
$721$	−7.98398	−	23.0338i	−0.297339	−	0.857825i
$722$	−0.877380	−	1.33610i	−0.0326527	−	0.0497243i
$723$	−2.66280	+	9.93770i	−0.0990305	+	0.369587i
$724$	−31.0126	+	23.0183i	−1.15257	+	0.855469i
$725$	−10.0057	+	3.99783i	−0.371604	+	0.148476i
$726$	−26.9034	+	8.89323i	−0.998480	+	0.330059i
$727$	−5.91197	−	5.91197i	−0.219263	−	0.219263i	0.588925	−	0.808188i	$-0.299551\pi$
$727$	−5.91197	−	5.91197i	−0.219263	−	0.219263i	−0.808188	+	0.588925i	$0.799551\pi$
$728$	−44.7591	−	0.786765i	−1.65888	−	0.0291595i
$729$		−	1.00000i		−	0.0370370i
$730$	−23.2125	−	0.331600i	−0.859133	−	0.0122731i
$731$	−1.25793	+	2.17880i	−0.0465262	+	0.0805858i
$732$	22.2739	+	3.29557i	0.823266	+	0.121808i
$733$	−11.6657	−	3.12580i	−0.430881	−	0.115454i	0.0368587	−	0.999320i	$-0.488265\pi$
$733$	−11.6657	−	3.12580i	−0.430881	−	0.115454i	−0.467740	+	0.883866i	$0.654932\pi$
$734$	−5.23009	+	25.2371i	−0.193046	+	0.931519i
$735$	−15.6119	+	1.12574i	−0.575855	+	0.0415236i
$736$	15.6510	+	25.5807i	0.576902	+	0.942917i
$737$	77.7291	+	20.8274i	2.86319	+	0.767189i
$738$	0.526376	+	9.15159i	0.0193762	+	0.336875i
$739$	0.587739	+	0.339331i	0.0216203	+	0.0124825i	0.510771	−	0.859717i	$-0.329360\pi$
$739$	0.587739	+	0.339331i	0.0216203	+	0.0124825i	−0.489151	+	0.872199i	$0.662693\pi$
$740$	−3.69920	−	5.81252i	−0.135985	−	0.213672i
$741$		−	26.8398i		−	0.985984i
$742$	−2.55584	−	6.19812i	−0.0938280	−	0.227540i
$743$	−24.0328	+	24.0328i	−0.881679	+	0.881679i	−0.993705	−	0.112026i	$-0.964266\pi$
$743$	−24.0328	+	24.0328i	−0.881679	+	0.881679i	0.112026	+	0.993705i	$0.464266\pi$
$744$	−24.6250	−	2.20827i	−0.902796	−	0.0809592i
$745$	31.6981	−	27.4478i	1.16133	−	1.00561i
$746$	13.9312	−	15.6315i	0.510056	−	0.572311i
$747$	9.29445	+	2.49044i	0.340066	+	0.0911205i
$748$	−1.51670	−	3.83391i	−0.0554559	−	0.140182i
$749$	−6.70871	−	19.3547i	−0.245131	−	0.707204i
$750$	−14.7651	+	5.65623i	−0.539144	+	0.206536i
$751$	2.78825	−	1.60979i	0.101745	−	0.0587422i	−0.448264	−	0.893901i	$-0.647958\pi$
$751$	2.78825	−	1.60979i	0.101745	−	0.0587422i	0.550009	+	0.835159i	$0.314624\pi$
$752$	−4.41083	−	2.73830i	−0.160847	−	0.0998554i
$753$	−1.06860	+	0.286331i	−0.0389420	+	0.0104345i
$754$	−5.72195	−	17.3098i	−0.208381	−	0.630386i
$755$	−10.0942	+	29.1332i	−0.367364	+	1.06027i
$756$	−2.29480	−	4.76801i	−0.0834610	−	0.173411i
$757$	−15.5635	−	15.5635i	−0.565666	−	0.565666i	0.365245	−	0.930911i	$-0.380985\pi$
$757$	−15.5635	−	15.5635i	−0.565666	−	0.565666i	−0.930911	+	0.365245i	$0.880985\pi$
$758$	−27.0412	−	13.6051i	−0.982179	−	0.494159i
$759$	−14.7668	+	25.5768i	−0.536001	+	0.928380i
$760$	−21.9791	−	17.9479i	−0.797267	−	0.651039i
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	−0.954552	−	0.298046i	$-0.903665\pi$
$761$	−20.2867	−	35.1375i	−0.735391	−	1.27373i	0.219161	−	0.975689i	$-0.429668\pi$
$762$	23.8269	−	15.6465i	0.863158	−	0.566814i
$763$	−13.2699	+	0.955233i	−0.480404	+	0.0345818i
$764$	25.3863	+	10.9942i	0.918445	+	0.397756i
$765$	0.464019	−	0.685087i	0.0167766	−	0.0247694i
$766$	17.3797	−	19.5010i	0.627956	−	0.704601i
$767$	19.4309	−	5.20649i	0.701608	−	0.187995i
$768$	−15.1585	−	5.12053i	−0.546985	−	0.184771i
$769$			7.68776i			0.277228i	0.990347	+	0.138614i	$0.0442647\pi$
$769$			7.68776i			0.277228i	−0.990347	+	0.138614i	$0.955735\pi$
$770$	−45.6417	−	9.45287i	−1.64481	−	0.340658i
$771$	−20.3722			−0.733688
$772$	−30.2052	−	23.9543i	−1.08711	−	0.862132i
$773$	3.15384	+	11.7703i	0.113436	+	0.423348i	0.999165	−	0.0408542i	$-0.0130079\pi$
$773$	3.15384	+	11.7703i	0.113436	+	0.423348i	−0.885729	+	0.464202i	$0.846341\pi$
$774$	−6.39721	+	7.17802i	−0.229943	+	0.258009i
$775$	−43.2568	−	6.24931i	−1.55383	−	0.224482i
$776$	−12.2325	+	17.3894i	−0.439122	+	0.624243i
$777$	3.37453	−	2.28622i	0.121061	−	0.0820177i
$778$	−18.7878	−	28.6105i	−0.673575	−	1.02574i
$779$	−25.1857	+	14.5410i	−0.902371	+	0.520984i
$780$	−8.03289	−	25.5183i	−0.287624	−	0.913702i
$781$	52.4136	+	30.2610i	1.87551	+	1.08282i
$782$	−2.47828	−	1.24689i	−0.0886233	−	0.0445886i
$783$	1.52380	−	1.52380i	0.0544560	−	0.0544560i
$784$	−21.8832	−	17.4678i	−0.781544	−	0.623850i
$785$	−4.73063	−	9.74682i	−0.168844	−	0.347879i
$786$	3.15003	−	1.04128i	0.112358	−	0.0371411i
$787$	−1.00173	−	3.73852i	−0.0357079	−	0.133264i	0.945771	−	0.324834i	$-0.105309\pi$
$787$	−1.00173	−	3.73852i	−0.0357079	−	0.133264i	−0.981479	+	0.191571i	$0.938642\pi$
$788$	3.67553	−	24.8420i	0.130936	−	0.884958i
$789$	8.12949	+	14.0807i	0.289418	+	0.501286i
$790$	−1.01507	−	4.01695i	−0.0361146	−	0.142917i
$791$	−1.37760	+	7.16542i	−0.0489817	+	0.254773i
$792$	−2.70252	−	15.5237i	−0.0960297	−	0.551610i
$793$	−17.4308	+	65.0528i	−0.618987	+	2.31009i
$794$	4.57188	+	4.07456i	0.162250	+	0.144601i
$795$	3.02891	−	2.62277i	0.107424	−	0.0930200i
$796$	−26.1532	+	3.01852i	−0.926977	+	0.106989i
$797$	−13.1189	−	13.1189i	−0.464694	−	0.464694i	0.435496	−	0.900191i	$-0.356573\pi$
$797$	−13.1189	−	13.1189i	−0.464694	−	0.464694i	−0.900191	+	0.435496i	$0.856573\pi$
$798$	10.2407	−	13.3023i	0.362518	−	0.470896i
$799$	0.480288			0.0169914
$800$	−26.2686	−	10.4861i	−0.928737	−	0.370739i
$801$	−1.86659	+	3.23303i	−0.0659527	+	0.114233i
$802$	−37.8833	+	2.17895i	−1.33770	+	0.0769414i
$803$	10.5851	−	39.5042i	0.373541	−	1.39407i
$804$	−11.4808	+	26.5100i	−0.404898	+	0.934936i
$805$	−27.1592	+	15.6848i	−0.957237	+	0.552817i
$806$	15.0064	−	72.4116i	0.528579	−	2.55059i
$807$	1.27498	−	4.75828i	0.0448813	−	0.167499i
$808$	37.4091	+	13.7078i	1.31605	+	0.482239i
$809$	−37.5240	−	21.6645i	−1.31927	−	0.761683i	−0.335662	−	0.941983i	$-0.608960\pi$
$809$	−37.5240	−	21.6645i	−1.31927	−	0.761683i	−0.983612	+	0.180300i	$0.942293\pi$
$810$	2.26778	−	2.20390i	0.0796817	−	0.0774372i
$811$	37.8178			1.32796			0.663981	−	0.747749i	$-0.268865\pi$
$811$	37.8178			1.32796			0.663981	+	0.747749i	$0.268865\pi$
$812$	3.76866	−	10.7623i	0.132254	−	0.377682i
$813$	−7.73229	+	7.73229i	−0.271183	+	0.271183i
$814$	11.5245	−	3.80954i	0.403933	−	0.133524i
$815$	5.96515	+	0.428667i	0.208950	+	0.0150156i
$816$	1.44125	−	0.337182i	0.0504540	−	0.0118037i
$817$	−29.4648	−	7.89506i	−1.03084	−	0.276213i
$818$	16.4628	−	10.8107i	0.575608	−	0.377987i
$819$	14.9543	−	5.18345i	0.522545	−	0.181125i
$820$	−19.5937	+	21.3629i	−0.684242	+	0.746024i
$821$	32.9300	−	19.0121i	1.14926	−	0.663528i	0.200557	−	0.979682i	$-0.435725\pi$
$821$	32.9300	−	19.0121i	1.14926	−	0.663528i	0.948708	+	0.316154i	$0.102392\pi$
$822$	6.11257	−	0.351580i	0.213200	−	0.0122628i
$823$	1.70018	+	6.34518i	0.0592647	+	0.221179i	0.989207	−	0.146528i	$-0.0468097\pi$
$823$	1.70018	+	6.34518i	0.0592647	+	0.221179i	−0.929942	+	0.367707i	$0.880143\pi$
$824$	25.9573	+	2.32775i	0.904267	+	0.0810911i
$825$	−3.28818	−	27.6602i	−0.114480	−	0.963006i
$826$	11.6168	+	4.83344i	0.404202	+	0.168177i
$827$	−7.93806	+	7.93806i	−0.276033	+	0.276033i	−0.831523	−	0.555490i	$-0.812531\pi$
$827$	−7.93806	+	7.93806i	−0.276033	+	0.276033i	0.555490	+	0.831523i	$0.312531\pi$
$828$	−8.30734	−	6.58815i	−0.288700	−	0.228954i
$829$	−14.2927	+	24.7556i	−0.496405	+	0.859798i	−0.999991	−	0.00414644i	$-0.998680\pi$
$829$	−14.2927	+	24.7556i	−0.496405	+	0.859798i	0.503587	+	0.863945i	$0.332013\pi$
$830$	14.8363	+	26.5665i	0.514974	+	0.922135i
$831$	9.73753	−	5.62196i	0.337791	−	0.195024i
$832$	20.4133	−	43.2848i	0.707702	−	1.50063i
$833$	2.57226	+	0.305146i	0.0891236	+	0.0105727i
$834$	−27.1613	−	5.62884i	−0.940518	−	0.194911i
$835$	−23.9976	+	35.4305i	−0.830470	+	1.22612i
$836$	40.1417	−	29.7942i	1.38833	−	1.03045i
$837$	8.44333	−	2.26238i	0.291844	−	0.0781995i
$838$	−2.14335	−	1.07838i	−0.0740410	−	0.0372519i
$839$	−38.6351			−1.33383			−0.666916	−	0.745133i	$-0.732386\pi$
$839$	−38.6351			−1.33383			−0.666916	+	0.745133i	$0.732386\pi$
$840$	5.75528	−	15.7123i	0.198576	−	0.542126i
$841$	−24.3561			−0.839865
$842$	−13.6554	−	6.87035i	−0.470595	−	0.236768i
$843$	−12.5073	+	3.35132i	−0.430775	+	0.115426i
$844$	0.335938	+	0.452609i	0.0115635	+	0.0155794i
$845$	50.0327	−	9.62543i	1.72118	−	0.331125i
$846$	1.79735	+	0.372479i	0.0617942	+	0.0128061i
$847$	23.1406	−	47.6928i	0.795120	−	1.63875i
$848$	7.16364	+	0.229190i	0.246000	+	0.00787043i
$849$	−19.9556	+	11.5214i	−0.684875	+	0.395413i
$850$	2.57628	−	0.457571i	0.0883656	−	0.0156946i
$851$	4.08362	−	7.07303i	0.139985	−	0.242460i
$852$	−13.5008	+	17.0239i	−0.462531	+	0.583229i
$853$	−4.38108	+	4.38108i	−0.150005	+	0.150005i	−0.778120	−	0.628115i	$-0.783827\pi$
$853$	−4.38108	+	4.38108i	−0.150005	+	0.150005i	0.628115	+	0.778120i	$0.283827\pi$
$854$	−33.4600	+	25.5906i	−1.14498	+	0.875693i
$855$	9.47962	+	3.28452i	0.324196	+	0.112328i
$856$	21.8112	+	1.95594i	0.745492	+	0.0668528i
$857$	−6.87991	−	25.6762i	−0.235013	−	0.877082i	−0.978143	−	0.207934i	$-0.933326\pi$
$857$	−6.87991	−	25.6762i	−0.235013	−	0.877082i	0.743129	−	0.669148i	$-0.233341\pi$
$858$	47.0527	−	2.70636i	1.60635	−	0.0923935i
$859$	24.4080	−	14.0920i	0.832791	−	0.480812i	−0.0220160	−	0.999758i	$-0.507008\pi$
$859$	24.4080	−	14.0920i	0.832791	−	0.480812i	0.854807	+	0.518945i	$0.173675\pi$
$860$	−30.3770	+	1.31218i	−1.03585	+	0.0447450i
$861$	−12.9658	−	11.2245i	−0.441873	−	0.382528i
$862$	−3.56849	+	2.34334i	−0.121543	+	0.0798145i
$863$	30.6688	+	8.21769i	1.04398	+	0.279733i	0.739761	−	0.672869i	$-0.234938\pi$
$863$	30.6688	+	8.21769i	1.04398	+	0.279733i	0.304218	+	0.952603i	$0.401605\pi$
$864$	5.65502	−	0.144073i	0.192388	−	0.00490147i
$865$	1.08116	−	15.0450i	0.0367605	−	0.511544i
$866$	−16.0628	+	5.30972i	−0.545835	+	0.180432i
$867$	11.9240	−	11.9240i	0.404960	−	0.404960i
$868$	35.0662	−	30.1628i	1.19022	−	1.02379i
$869$	7.29913			0.247606
$870$	6.81392	+	0.0973396i	0.231014	+	0.00330012i
$871$	−74.8327	−	43.2047i	−2.53561	−	1.46394i
$872$	4.89350	−	13.3545i	0.165715	−	0.452241i
$873$	1.94551	−	7.26073i	0.0658455	−	0.245739i
$874$	6.82591	−	32.9376i	0.230890	−	1.11413i
$875$	11.6594	−	27.1856i	0.394161	−	0.919042i
$876$	13.4732	+	5.83489i	0.455216	+	0.197143i
$877$	10.4889	−	39.1450i	0.354184	−	1.32183i	−0.527324	−	0.849664i	$-0.676805\pi$
$877$	10.4889	−	39.1450i	0.354184	−	1.32183i	0.881508	−	0.472169i	$-0.156529\pi$
$878$	−14.9173	+	0.858006i	−0.503435	+	0.0289563i
$879$	5.29178	−	9.16563i	0.178487	−	0.309149i
$880$	29.2482	−	40.3413i	0.985957	−	1.35991i
$881$	−4.02287			−0.135534			−0.0677669	−	0.997701i	$-0.521587\pi$
$881$	−4.02287			−0.135534			−0.0677669	+	0.997701i	$0.521587\pi$
$882$	9.38938	+	3.13681i	0.316157	+	0.105622i
$883$	40.5197	+	40.5197i	1.36360	+	1.36360i	0.869283	+	0.494314i	$0.164581\pi$
$883$	40.5197	+	40.5197i	1.36360	+	1.36360i	0.494314	+	0.869283i	$0.335419\pi$
$884$	0.507612	+	4.39807i	0.0170728	+	0.147923i
$885$	−0.538964	+	7.50000i	−0.0181171	+	0.252110i
$886$	−31.6013	−	28.1637i	−1.06166	−	0.946179i
$887$	−4.77718	+	17.8287i	−0.160402	+	0.598628i	0.838180	+	0.545394i	$0.183620\pi$
$887$	−4.77718	+	17.8287i	−0.160402	+	0.598628i	−0.998582	+	0.0532347i	$0.983047\pi$
$888$	0.747356	+	4.29293i	0.0250796	+	0.144061i
$889$	−10.0682	+	52.3689i	−0.337678	+	1.75640i
$890$	−11.4456	+	2.89226i	−0.383656	+	0.0969486i
$891$	2.78550	+	4.82463i	0.0933177	+	0.161631i
$892$	−1.85034	−	0.273770i	−0.0619540	−	0.00916650i
$893$	1.50720	+	5.62494i	0.0504365	+	0.188231i
$894$	−25.1790	+	8.32321i	−0.842113	+	0.278370i
$895$	0.936971	−	2.70424i	0.0313195	−	0.0903926i
$896$	26.6326	−	13.6641i	0.889731	−	0.456485i
$897$	22.4245	−	22.4245i	0.748732	−	0.748732i
$898$	5.57494	+	2.80489i	0.186038	+	0.0936004i
$899$	16.3133	+	9.41850i	0.544080	+	0.314125i
$900$	9.99592	+	0.285650i	0.333197	+	0.00952166i
$901$	−0.574220	+	0.331526i	−0.0191301	+	0.0110447i
$902$	−28.0313	−	42.6868i	−0.933340	−	1.42131i
$903$	−1.29152	−	17.9416i	−0.0429792	−	0.597059i
$904$	−6.38002	−	4.48801i	−0.212196	−	0.149269i
$905$	42.4026	−	8.15754i	1.40951	−	0.271166i
$906$	12.9741	−	14.5577i	0.431036	−	0.483647i
$907$	0.679115	+	2.53449i	0.0225496	+	0.0841564i	0.976284	−	0.216495i	$-0.0694626\pi$
$907$	0.679115	+	2.53449i	0.0225496	+	0.0841564i	−0.953734	+	0.300652i	$0.902796\pi$
$908$	−27.5444	+	34.7322i	−0.914093	+	1.15263i
$909$	−14.0861			−0.467206
$910$	44.7127	+	22.4892i	1.48221	+	0.745511i
$911$			38.3707i			1.27128i	0.771986	+	0.635639i	$0.219263\pi$
$911$			38.3707i			1.27128i	−0.771986	+	0.635639i	$0.780737\pi$
$912$	8.47176	+	15.8213i	0.280528	+	0.523895i
$913$	−51.7794	+	13.8742i	−1.71365	+	0.459170i
$914$	−34.9647	+	39.2323i	−1.15653	+	1.29769i
$915$	−20.8431	−	14.1173i	−0.689051	−	0.466704i
$916$	−3.78898	+	8.74900i	−0.125191	+	0.289075i
$917$	−2.70945	+	5.58418i	−0.0894738	+	0.184406i
$918$	−0.437435	+	0.287252i	−0.0144375	+	0.00948074i
$919$	27.3963	+	47.4518i	0.903722	+	1.56529i	0.822624	+	0.568586i	$0.192509\pi$
$919$	27.3963	+	47.4518i	0.903722	+	1.56529i	0.0810976	+	0.996706i	$0.474157\pi$
$920$	−3.36807	−	33.3588i	−0.111042	−	1.09981i
$921$	−14.6469	+	25.3692i	−0.482631	+	0.835942i
$922$	−19.9950	−	10.0600i	−0.658500	−	0.331308i
$923$	−45.9536	−	45.9536i	−1.51258	−	1.51258i
$924$	24.3528	+	16.6117i	0.801149	+	0.546485i
$925$	0.909314	+	7.64918i	0.0298981	+	0.251503i
$926$	−5.53144	−	16.7335i	−0.181774	−	0.549897i
$927$	−8.90017	+	2.38479i	−0.292320	+	0.0783269i
$928$	8.83663	+	8.39755i	0.290077	+	0.275663i
$929$	−33.4605	+	19.3184i	−1.09780	+	0.633817i	−0.935643	−	0.352948i	$-0.885179\pi$
$929$	−33.4605	+	19.3184i	−1.09780	+	0.633817i	−0.162160	+	0.986764i	$0.551846\pi$
$930$	23.7389	+	14.1616i	0.778428	+	0.464376i
$931$	4.49830	+	31.0829i	0.147426	+	1.01870i
$932$	0.0210117	−	0.00831224i	0.000688262	−	0.000272276i
$933$	11.0922	+	2.97214i	0.363142	+	0.0973036i
$934$	31.9102	−	35.8050i	1.04413	−	1.17158i
$935$	−0.330408	+	4.59781i	−0.0108055	+	0.150365i
$936$	−1.51125	+	16.8523i	−0.0493968	+	0.550836i
$937$	−30.8098	+	30.8098i	−1.00651	+	1.00651i	−0.00653468	+	0.999979i	$0.502080\pi$
$937$	−30.8098	+	30.8098i	−1.00651	+	1.00651i	−0.999979	+	0.00653468i	$0.997920\pi$
$938$	−20.6037	−	49.9655i	−0.672735	−	1.63143i
$939$			11.4082i			0.372292i
$940$	3.11648	+	4.89691i	0.101648	+	0.159719i
$941$	−44.6989	−	25.8069i	−1.45714	−	0.841282i	−0.458273	−	0.888812i	$-0.651532\pi$
$941$	−44.6989	−	25.8069i	−1.45714	−	0.841282i	−0.998870	+	0.0475297i	$0.984865\pi$
$942$	0.393467	+	6.84083i	0.0128199	+	0.222886i
$943$	−33.1914	−	8.89361i	−1.08086	−	0.289616i
$944$	−9.81057	+	9.20228i	−0.319307	+	0.299509i
$945$	0.000723185		5.91608i	2.35252e−5		0.192450i
$946$	10.8698	−	52.4507i	0.353407	−	1.70532i
$947$	−1.63709	−	0.438657i	−0.0531983	−	0.0142544i	0.232122	−	0.972687i	$-0.425433\pi$
$947$	−1.63709	−	0.438657i	−0.0531983	−	0.0142544i	−0.285320	+	0.958432i	$0.592100\pi$
$948$	−0.383531	+	2.59218i	−0.0124565	+	0.0841902i
$949$	−21.9579	+	38.0322i	−0.712783	+	1.23458i
$950$	13.4436	+	28.7365i	0.436166	+	0.932334i
$951$			4.93092i			0.159896i
$952$	−1.42651	+	2.37345i	−0.0462334	+	0.0769239i
$953$	−4.60430	−	4.60430i	−0.149148	−	0.149148i	0.628589	−	0.777737i	$-0.283633\pi$
$953$	−4.60430	−	4.60430i	−0.149148	−	0.149148i	−0.777737	+	0.628589i	$0.783633\pi$
$954$	−2.40598	+	0.795324i	−0.0778965	+	0.0257496i
$955$	−20.2470	−	23.3823i	−0.655177	−	0.756633i
$956$	−12.3047	−	16.5781i	−0.397961	−	0.536173i
$957$	−3.10721	+	11.5963i	−0.100442	+	0.374854i
$958$	−14.4847	−	22.0577i	−0.467980	−	0.712652i
$959$	−7.49709	+	8.66017i	−0.242094	+	0.279652i
$960$	12.7898	+	12.5068i	0.412790	+	0.403656i
$961$	22.7041	+	39.3247i	0.732392	+	1.26854i
$962$	−13.0120	+	0.748417i	−0.419523	+	0.0241299i
$963$	−7.47856	+	2.00387i	−0.240993	+	0.0645739i
$964$	20.4408	−	2.35922i	0.658355	−	0.0759852i
$965$	18.8196	+	38.7752i	0.605825	+	1.24822i
$966$	19.6701	−	2.55791i	0.632874	−	0.0822994i
$967$	11.1120	+	11.1120i	0.357336	+	0.357336i	0.862830	−	0.505494i	$-0.168690\pi$
$967$	11.1120	+	11.1120i	0.357336	+	0.357336i	−0.505494	+	0.862830i	$0.668690\pi$
$968$	36.3327	+	43.4910i	1.16778	+	1.39785i
$969$	−1.43783	−	0.830131i	−0.0461897	−	0.0266676i
$970$	20.7534	−	11.5899i	0.666353	−	0.372131i
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.599986	+	0.800011i	$0.295173\pi$
$971$	30.9372	+	53.5848i	0.992822	+	1.71962i	0.392837	+	0.919608i	$0.371494\pi$
$972$	−1.85976	+	0.735722i	−0.0596519	+	0.0235983i
$973$	42.9624	−	29.1067i	1.37731	−	0.933117i
$974$	5.17665	−	24.9793i	0.165870	−	0.800387i
$975$	−4.27677	+	29.6032i	−0.136966	+	0.948061i
$976$	−10.2584	−	43.8487i	−0.328364	−	1.40356i
$977$	−5.42070	−	20.2303i	−0.173424	−	0.647226i	−0.996815	−	0.0797515i	$-0.974587\pi$
$977$	−5.42070	−	20.2303i	−0.173424	−	0.647226i	0.823391	−	0.567474i	$-0.192079\pi$
$978$	−3.37886	−	1.69999i	−0.108044	−	0.0543597i
$979$		−	20.7975i		−	0.664692i
$980$	13.5797	+	28.2063i	0.433786	+	0.901016i
$981$			5.02854i			0.160549i
$982$	12.7879	−	25.4170i	0.408079	−	0.811089i
$983$	−8.59852	−	32.0901i	−0.274250	−	1.02352i	−0.956342	−	0.292249i	$-0.905596\pi$
$983$	−8.59852	−	32.0901i	−0.274250	−	1.02352i	0.682092	−	0.731266i	$-0.261070\pi$
$984$	16.6325	−	7.71196i	0.530225	−	0.245848i
$985$	−15.7450	+	23.2462i	−0.501677	+	0.740686i
$986$	−1.10428	−	0.228848i	−0.0351673	−	0.00728799i
$987$	−2.84296	+	1.92609i	−0.0904926	+	0.0613080i
$988$	−49.9156	+	19.7466i	−1.58803	+	0.628223i
$989$	−18.0214	−	31.2139i	−0.573046	−	0.992545i
$990$	−4.80223	+	16.9499i	−0.152625	+	0.538703i
$991$	23.8565	+	13.7735i	0.757826	+	0.437531i	0.828515	−	0.559967i	$-0.189186\pi$
$991$	23.8565	+	13.7735i	0.757826	+	0.437531i	−0.0706886	+	0.997498i	$0.522520\pi$
$992$	14.0103	+	47.4213i	0.444827	+	1.50563i
$993$	4.17990	+	4.17990i	0.132645	+	0.132645i
$994$	−5.24182	−	40.3091i	−0.166261	−	1.27853i
$995$	27.8122	+	9.63645i	0.881706	+	0.305496i
$996$	−2.20651	−	19.1177i	−0.0699159	−	0.605769i
$997$	44.3628	−	11.8870i	1.40498	−	0.376464i	0.524852	−	0.851194i	$-0.324121\pi$
$997$	44.3628	−	11.8870i	1.40498	−	0.376464i	0.880132	+	0.474730i	$0.157454\pi$
$998$	0.798568	+	13.8839i	0.0252782	+	0.439488i
$999$	−0.770303	−	1.33420i	−0.0243713	−	0.0422124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.403.64	yes	384
5.2	odd	4	inner	840.2.dj.a.67.82	yes	384
7.2	even	3	inner	840.2.dj.a.163.3	yes	384
8.3	odd	2	inner	840.2.dj.a.403.48	yes	384
35.2	odd	12	inner	840.2.dj.a.667.48	yes	384
40.27	even	4	inner	840.2.dj.a.67.3	✓	384
56.51	odd	6	inner	840.2.dj.a.163.82	yes	384
280.107	even	12	inner	840.2.dj.a.667.64	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.3	✓	384	40.27	even	4	inner
840.2.dj.a.67.82	yes	384	5.2	odd	4	inner
840.2.dj.a.163.3	yes	384	7.2	even	3	inner
840.2.dj.a.163.82	yes	384	56.51	odd	6	inner
840.2.dj.a.403.48	yes	384	8.3	odd	2	inner
840.2.dj.a.403.64	yes	384	1.1	even	1	trivial
840.2.dj.a.667.48	yes	384	35.2	odd	12	inner
840.2.dj.a.667.64	yes	384	280.107	even	12	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.635612 - 1.26333i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-1.19199 - 1.60597i) q^{4} +(0.422435 + 2.19580i) q^{5} +(0.286981 - 1.38479i) q^{6} +(1.48397 + 2.19039i) q^{7} +(-2.78652 + 0.485105i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.04252 + 0.862005i) q^{10} +(-2.78550 + 4.82463i) q^{11} +(-1.56703 - 1.24274i) q^{12} +(4.22999 - 4.22999i) q^{13} +(3.71042 - 0.482505i) q^{14} +(0.976356 + 2.01165i) q^{15} +(-1.15830 + 3.82862i) q^{16} +(-0.0957741 - 0.357434i) q^{17} +(-0.0812078 - 1.41188i) q^{18} +(3.88557 - 2.24334i) q^{19} +(3.02286 - 3.29580i) q^{20} +(2.00032 + 1.73168i) q^{21} +(4.32459 + 6.58559i) q^{22} +(5.12067 + 1.37208i) q^{23} +(-2.56601 + 1.18978i) q^{24} +(-4.64310 + 1.85517i) q^{25} +(-2.65523 - 8.03249i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.74882 - 4.99416i) q^{28} +2.15497 q^{29} +(3.16196 + 0.0451698i) q^{30} +(7.57009 + 4.37059i) q^{31} +(4.10058 + 3.89683i) q^{32} +(-1.44188 + 5.38117i) q^{33} +(-0.512431 - 0.106195i) q^{34} +(-4.18279 + 4.18381i) q^{35} +(-1.83528 - 0.794816i) q^{36} +(0.398738 - 1.48811i) q^{37} +(-0.364353 - 6.33465i) q^{38} +(2.99105 - 5.18066i) q^{39} +(-2.24232 - 5.91371i) q^{40} -6.48184 q^{41} +(3.45911 - 1.42639i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(11.0685 - 1.27749i) q^{44} +(1.46374 + 1.69040i) q^{45} +(4.98815 - 5.59698i) q^{46} +(-0.335928 + 1.25370i) q^{47} +(-0.127909 + 3.99795i) q^{48} +(-2.59564 + 6.50097i) q^{49} +(-0.607525 + 7.04492i) q^{50} +(-0.185021 - 0.320466i) q^{51} +(-11.8354 - 1.75112i) q^{52} +(-0.463759 - 1.73077i) q^{53} +(-0.443862 - 1.34275i) q^{54} +(-11.7706 - 4.07832i) q^{55} +(-5.19769 - 5.38368i) q^{56} +(3.17256 - 3.17256i) q^{57} +(1.36973 - 2.72244i) q^{58} +(2.91223 + 1.68137i) q^{59} +(2.06684 - 3.96588i) q^{60} +(-9.74986 + 5.62909i) q^{61} +(10.3331 - 6.78550i) q^{62} +(2.38036 + 1.15495i) q^{63} +(7.52935 - 2.70350i) q^{64} +(11.0751 + 7.50133i) q^{65} +(5.88171 + 5.24190i) q^{66} +(-3.73855 - 13.9525i) q^{67} +(-0.459867 + 0.579870i) q^{68} +5.30131 q^{69} +(2.62689 + 7.94351i) q^{70} -10.8638i q^{71} +(-2.17064 + 1.81337i) q^{72} +(-7.09104 + 1.90004i) q^{73} +(-1.62653 - 1.44960i) q^{74} +(-4.00474 + 2.99368i) q^{75} +(-8.23432 - 3.56608i) q^{76} +(-14.7014 + 1.05828i) q^{77} +(-4.64372 - 7.07157i) q^{78} +(-0.655100 - 1.13467i) q^{79} +(-8.89620 - 0.926049i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-4.11994 + 8.18869i) q^{82} +(6.80401 + 6.80401i) q^{83} +(0.396650 - 5.27662i) q^{84} +(0.744396 - 0.361294i) q^{85} +(-9.12916 + 3.01775i) q^{86} +(2.08154 - 0.557748i) q^{87} +(5.42139 - 14.7952i) q^{88} +(-3.23303 + 1.86659i) q^{89} +(3.06590 - 0.774744i) q^{90} +(15.5425 + 2.98815i) q^{91} +(-3.90029 - 9.85917i) q^{92} +(8.44333 + 2.26238i) q^{93} +(1.37031 + 1.22125i) q^{94} +(6.56733 + 7.58429i) q^{95} +(4.96943 + 2.70274i) q^{96} +(5.31523 - 5.31523i) q^{97} +(6.56304 + 7.41125i) q^{98} +5.57100i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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