LMFDB - Embedded newform 840.2.dj.a.163.82

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)

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")

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);

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			163.82
Character	$\chi$	$=$	840.163
Dual form			840.2.dj.a.67.82

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26333 - 0.635612i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.19199 - 1.60597i) q^{4} +(-1.69040 + 1.46374i) q^{5} +(0.286981 + 1.38479i) q^{6} +(-2.19039 - 1.48397i) q^{7} +(0.485105 - 2.78652i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.20516 + 2.92362i) q^{10} +(-2.78550 - 4.82463i) q^{11} +(1.24274 + 1.56703i) 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} +(0.357434 + 0.0957741i) q^{17} +(-1.41188 - 0.0812078i) q^{18} +(-3.88557 - 2.24334i) q^{19} +(0.335775 + 4.45951i) q^{20} +(2.00032 - 1.73168i) q^{21} +(-6.58559 - 4.32459i) q^{22} +(1.37208 + 5.12067i) q^{23} +(2.56601 + 1.18978i) q^{24} +(0.714927 - 4.94862i) q^{25} +(-2.65523 + 8.03249i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.99416 + 1.74882i) q^{28} -2.15497 q^{29} +(-2.51209 - 1.92079i) q^{30} +(7.57009 - 4.37059i) q^{31} +(-3.89683 - 4.10058i) q^{32} +(5.38117 - 1.44188i) q^{33} +(0.512431 - 0.106195i) q^{34} +(5.87480 - 0.697653i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(1.48811 - 0.398738i) q^{37} +(-6.33465 - 0.364353i) q^{38} +(-2.99105 - 5.18066i) q^{39} +(3.25871 + 5.42040i) q^{40} -6.48184 q^{41} +(1.42639 - 3.45911i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(-11.0685 - 1.27749i) q^{44} +(2.19580 - 0.422435i) q^{45} +(4.98815 + 5.59698i) q^{46} +(-1.25370 + 0.335928i) q^{47} +(3.99795 - 0.127909i) q^{48} +(2.59564 + 6.50097i) q^{49} +(-2.24222 - 6.70615i) q^{50} +(-0.185021 + 0.320466i) q^{51} +(1.75112 + 11.8354i) q^{52} +(-1.73077 - 0.463759i) 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} +(-2.72244 + 1.36973i) q^{58} +(-2.91223 + 1.68137i) q^{59} +(-4.39446 - 0.829873i) q^{60} +(-9.74986 - 5.62909i) q^{61} +(6.78550 - 10.3331i) q^{62} +(1.15495 + 2.38036i) q^{63} +(-7.52935 - 2.70350i) q^{64} +(0.958781 - 13.3420i) q^{65} +(5.88171 - 5.24190i) q^{66} +(13.9525 + 3.73855i) q^{67} +(0.579870 - 0.459867i) q^{68} -5.30131 q^{69} +(6.97836 - 4.61546i) q^{70} +10.8638i q^{71} +(-1.81337 + 2.17064i) q^{72} +(1.90004 - 7.09104i) q^{73} +(1.62653 - 1.44960i) q^{74} +(4.59497 + 1.97136i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(-1.05828 + 14.7014i) q^{77} +(-7.07157 - 4.64372i) q^{78} +(0.655100 - 1.13467i) q^{79} +(7.56210 + 4.77647i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-8.18869 + 4.11994i) 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} +(0.557748 - 2.08154i) q^{87} +(-14.7952 + 5.42139i) q^{88} +(3.23303 + 1.86659i) q^{89} +(2.50551 - 1.92935i) q^{90} +(15.5425 - 2.98815i) q^{91} +(9.85917 + 3.90029i) q^{92} +(2.26238 + 8.44333i) q^{93} +(-1.37031 + 1.22125i) q^{94} +(9.85185 - 1.89533i) q^{95} +(4.96943 - 2.70274i) q^{96} +(5.31523 - 5.31523i) q^{97} +(7.41125 + 6.56304i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.26333	−	0.635612i	0.893308	−	0.449446i
$2$	1.26333	−	0.635612i	0.893308	−	0.449446i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	1.19199	−	1.60597i	0.595997	−	0.802986i
$5$	−1.69040	+	1.46374i	−0.755971	+	0.654605i
$5$	−1.69040	+	1.46374i	−0.755971	+	0.654605i
$6$	0.286981	+	1.38479i	0.117159	+	0.565338i
$7$	−2.19039	−	1.48397i	−0.827891	−	0.560889i
$7$	−2.19039	−	1.48397i	−0.827891	−	0.560889i
$8$	0.485105	−	2.78652i	0.171510	−	0.985182i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.20516	+	2.92362i	−0.381106	+	0.924531i
$11$	−2.78550	−	4.82463i	−0.839860	−	1.45468i	−0.890012	−	0.455938i	$-0.849304\pi$
$11$	−2.78550	−	4.82463i	−0.839860	−	1.45468i	0.0501521	−	0.998742i	$-0.484029\pi$
$12$	1.24274	+	1.56703i	0.358748	+	0.452364i
$13$	−4.22999	+	4.22999i	−1.17319	+	1.17319i	−0.191742	+	0.981445i	$0.561414\pi$
$13$	−4.22999	+	4.22999i	−1.17319	+	1.17319i	−0.981445	+	0.191742i	$0.938586\pi$
$14$	−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
$17$	0.357434	+	0.0957741i	0.0866904	+	0.0232286i	0.301904	−	0.953338i	$-0.402378\pi$
$17$	0.357434	+	0.0957741i	0.0866904	+	0.0232286i	−0.215213	+	0.976567i	$0.569045\pi$
$18$	−1.41188	−	0.0812078i	−0.332783	−	0.0191409i
$19$	−3.88557	−	2.24334i	−0.891412	−	0.514657i	−0.0170079	−	0.999855i	$-0.505414\pi$
$19$	−3.88557	−	2.24334i	−0.891412	−	0.514657i	−0.874404	+	0.485198i	$0.838747\pi$
$20$	0.335775	+	4.45951i	0.0750817	+	0.997177i
$21$	2.00032	−	1.73168i	0.436506	−	0.377883i
$22$	−6.58559	−	4.32459i	−1.40405	−	0.922005i
$23$	1.37208	+	5.12067i	0.286098	+	1.06773i	0.948033	+	0.318172i	$0.103069\pi$
$23$	1.37208	+	5.12067i	0.286098	+	1.06773i	−0.661934	+	0.749562i	$0.730264\pi$
$24$	2.56601	+	1.18978i	0.523785	+	0.242863i
$25$	0.714927	−	4.94862i	0.142985	−	0.989725i
$26$	−2.65523	+	8.03249i	−0.520734	+	1.57530i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−4.99416	+	1.74882i	−0.943807	+	0.330496i
$29$	−2.15497			−0.400168			−0.200084	−	0.979779i	$-0.564122\pi$
$29$	−2.15497			−0.400168			−0.200084	+	0.979779i	$0.564122\pi$
$30$	−2.51209	−	1.92079i	−0.458642	−	0.350686i
$31$	7.57009	−	4.37059i	1.35963	−	0.784981i	0.370054	−	0.929010i	$-0.379339\pi$
$31$	7.57009	−	4.37059i	1.35963	−	0.784981i	0.989574	+	0.144029i	$0.0460058\pi$
$32$	−3.89683	−	4.10058i	−0.688868	−	0.724887i
$33$	5.38117	−	1.44188i	0.936742	−	0.250999i
$34$	0.512431	−	0.106195i	0.0878813	−	0.0182123i
$35$	5.87480	−	0.697653i	0.993023	−	0.117925i
$36$	−1.83528	+	0.794816i	−0.305881	+	0.132469i
$37$	1.48811	−	0.398738i	0.244644	−	0.0655522i	−0.134413	−	0.990925i	$-0.542915\pi$
$37$	1.48811	−	0.398738i	0.244644	−	0.0655522i	0.379057	+	0.925373i	$0.376248\pi$
$38$	−6.33465	−	0.364353i	−1.02762	−	0.0591059i
$39$	−2.99105	−	5.18066i	−0.478952	−	0.829569i
$40$	3.25871	+	5.42040i	0.515248	+	0.857041i
$41$	−6.48184			−1.01229			−0.506147	−	0.862447i	$-0.668931\pi$
$41$	−6.48184			−1.01229			−0.506147	+	0.862447i	$0.668931\pi$
$42$	1.42639	−	3.45911i	0.220097	−	0.533752i
$43$	−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
$45$	2.19580	−	0.422435i	0.327331	−	0.0629729i
$46$	4.98815	+	5.59698i	0.735462	+	0.825229i
$47$	−1.25370	+	0.335928i	−0.182871	+	0.0490001i	−0.349092	−	0.937088i	$-0.613510\pi$
$47$	−1.25370	+	0.335928i	−0.182871	+	0.0490001i	0.166221	+	0.986088i	$0.446843\pi$
$48$	3.99795	−	0.127909i	0.577055	−	0.0184620i
$49$	2.59564	+	6.50097i	0.370806	+	0.928710i
$50$	−2.24222	−	6.70615i	−0.317097	−	0.948393i
$51$	−0.185021	+	0.320466i	−0.0259082	+	0.0448743i
$52$	1.75112	+	11.8354i	0.242837	+	1.64127i
$53$	−1.73077	−	0.463759i	−0.237740	−	0.0637022i	0.137982	−	0.990435i	$-0.455938\pi$
$53$	−1.73077	−	0.463759i	−0.237740	−	0.0637022i	−0.375722	+	0.926733i	$0.622605\pi$
$54$	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
$58$	−2.72244	+	1.36973i	−0.357473	+	0.179854i
$59$	−2.91223	+	1.68137i	−0.379140	+	0.218896i	−0.677444	−	0.735574i	$-0.736912\pi$
$59$	−2.91223	+	1.68137i	−0.379140	+	0.218896i	0.298304	+	0.954471i	$0.403579\pi$
$60$	−4.39446	−	0.829873i	−0.567323	−	0.107136i
$61$	−9.74986	−	5.62909i	−1.24834	−	0.720731i	−0.277563	−	0.960707i	$-0.589527\pi$
$61$	−9.74986	−	5.62909i	−1.24834	−	0.720731i	−0.970779	+	0.239977i	$0.922860\pi$
$62$	6.78550	−	10.3331i	0.861760	−	1.31231i
$63$	1.15495	+	2.38036i	0.145510	+	0.299897i
$64$	−7.52935	−	2.70350i	−0.941168	−	0.337938i
$65$	0.958781	−	13.3420i	0.118922	−	1.65487i
$66$	5.88171	−	5.24190i	0.723988	−	0.645234i
$67$	13.9525	+	3.73855i	1.70456	+	0.456736i	0.974082	−	0.226196i	$-0.0726291\pi$
$67$	13.9525	+	3.73855i	1.70456	+	0.456736i	0.730481	+	0.682933i	$0.239296\pi$
$68$	0.579870	−	0.459867i	0.0703196	−	0.0557670i
$69$	−5.30131			−0.638203
$70$	6.97836	−	4.61546i	0.834074	−	0.551653i
$71$			10.8638i			1.28929i	0.764481	+	0.644646i	$0.222995\pi$
$71$			10.8638i			1.28929i	−0.764481	+	0.644646i	$0.777005\pi$
$72$	−1.81337	+	2.17064i	−0.213708	+	0.255813i
$73$	1.90004	−	7.09104i	0.222383	−	0.829944i	−0.761053	−	0.648689i	$-0.775318\pi$
$73$	1.90004	−	7.09104i	0.222383	−	0.829944i	0.983436	−	0.181255i	$-0.0580158\pi$
$74$	1.62653	−	1.44960i	0.189080	−	0.168512i
$75$	4.59497	+	1.97136i	0.530581	+	0.227634i
$76$	−8.23432	+	3.56608i	−0.944542	+	0.409057i
$77$	−1.05828	+	14.7014i	−0.120602	+	1.67538i
$78$	−7.07157	−	4.64372i	−0.800698	−	0.525798i
$79$	0.655100	−	1.13467i	0.0737045	−	0.127660i	−0.826818	−	0.562470i	$-0.809851\pi$
$79$	0.655100	−	1.13467i	0.0737045	−	0.127660i	0.900522	+	0.434810i	$0.143184\pi$
$80$	7.56210	+	4.77647i	0.845468	+	0.534026i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−8.18869	+	4.11994i	−0.904290	+	0.454971i
$83$	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
$87$	0.557748	−	2.08154i	0.0597968	−	0.223165i
$88$	−14.7952	+	5.42139i	−1.57717	+	0.577922i
$89$	3.23303	+	1.86659i	0.342700	+	0.197858i	0.661465	−	0.749976i	$-0.269935\pi$
$89$	3.23303	+	1.86659i	0.342700	+	0.197858i	−0.318765	+	0.947834i	$0.603268\pi$
$90$	2.50551	−	1.92935i	0.264104	−	0.203372i
$91$	15.5425	−	2.98815i	1.62930	−	0.313243i
$92$	9.85917	+	3.90029i	1.02789	+	0.406633i
$93$	2.26238	+	8.44333i	0.234598	+	0.875533i
$94$	−1.37031	+	1.22125i	−0.141337	+	0.125963i
$95$	9.85185	−	1.89533i	1.01078	−	0.194457i
$96$	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	$0.125369\pi$
$98$	7.41125	+	6.56304i	0.748649	+	0.662967i
$99$			5.57100i			0.559906i
$100$	−7.09517	−	7.04689i	−0.709517	−	0.704689i
$101$	−12.1989	+	7.04305i	−1.21384	+	0.700810i	−0.963593	−	0.267373i	$-0.913844\pi$
$101$	−12.1989	+	7.04305i	−1.21384	+	0.700810i	−0.250245	+	0.968183i	$0.580511\pi$
$102$	−0.0300504	+	0.522456i	−0.00297543	+	0.0517309i
$103$	−2.38479	−	8.90017i	−0.234981	−	0.876960i	−0.978158	−	0.207865i	$-0.933349\pi$
$103$	−2.38479	−	8.90017i	−0.234981	−	0.876960i	0.743177	−	0.669095i	$-0.233318\pi$
$104$	9.73495	+	13.8389i	0.954590	+	1.35702i
$105$	−0.846629	+	5.85519i	−0.0826226	+	0.571408i
$106$	−2.48130	+	0.514220i	−0.241005	+	0.0499454i
$107$	2.00387	+	7.47856i	0.193722	+	0.722979i	0.992594	+	0.121479i	$0.0387636\pi$
$107$	2.00387	+	7.47856i	0.193722	+	0.722979i	−0.798872	+	0.601501i	$0.794570\pi$
$108$	−0.292727	−	1.97846i	−0.0281676	−	0.190378i
$109$	2.51427	+	4.35484i	0.240823	+	0.417118i	0.960949	−	0.276725i	$-0.0892492\pi$
$109$	2.51427	+	4.35484i	0.240823	+	0.417118i	−0.720126	+	0.693844i	$0.755916\pi$
$110$	17.4624	−	2.32930i	1.66497	−	0.222090i
$111$			1.54061i			0.146228i
$112$	−3.14445	+	10.1051i	−0.297122	+	0.954839i
$113$	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
$115$	−9.81470	−	6.64763i	−0.915226	−	0.619895i
$116$	−2.56871	+	3.46083i	−0.238499	+	0.321330i
$117$	5.77827	−	1.54828i	0.534201	−	0.143139i
$118$	−2.61040	+	3.97517i	−0.240306	+	0.365944i
$119$	−0.640794	−	0.740205i	−0.0587415	−	0.0678545i
$120$	−6.07913	+	1.74477i	−0.554946	+	0.159275i
$121$	−10.0180	+	17.3517i	−0.910728	+	1.57743i
$122$	−15.8952	−	0.914251i	−1.43908	−	0.0827724i
$123$	1.67762	−	6.26098i	0.151266	−	0.564534i
$124$	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	$-0.897687\pi$
$127$	−14.2525	−	14.2525i	−1.26471	−	1.26471i	−0.315919	−	0.948786i	$-0.602313\pi$
$128$	−11.2304	+	1.37033i	−0.992638	+	0.121121i
$129$	5.88796	−	3.39942i	0.518406	−	0.299302i
$130$	−7.26908	−	17.4647i	−0.637540	−	1.53176i
$131$	1.17297	−	2.03165i	0.102483	−	0.177506i	−0.810224	−	0.586120i	$-0.800655\pi$
$131$	1.17297	−	2.03165i	0.102483	−	0.177506i	0.912707	+	0.408614i	$0.133988\pi$
$132$	4.09871	−	10.3607i	0.356747	−	0.901786i
$133$	5.18188	+	10.6799i	0.449326	+	0.926063i
$134$	20.0028	−	4.14533i	1.72798	−	0.358102i
$135$	−0.160275	+	2.23032i	−0.0137943	+	0.191955i
$136$	0.440269	−	0.949535i	0.0377528	−	0.0814219i
$137$	−4.18186	−	1.12053i	−0.357281	−	0.0957331i	0.0757139	−	0.997130i	$-0.475876\pi$
$137$	−4.18186	−	1.12053i	−0.357281	−	0.0957331i	−0.432995	+	0.901396i	$0.642543\pi$
$138$	−6.69729	+	3.36958i	−0.570111	+	0.286837i
$139$		−	19.6140i		−	1.66364i	−0.555046	−	0.831819i	$-0.687300\pi$
$139$		−	19.6140i		−	1.66364i	0.555046	−	0.831819i	$-0.312700\pi$
$140$	5.88232	−	10.2664i	0.497147	−	0.867666i
$141$		−	1.29792i		−	0.109305i
$142$	6.90514	+	13.7245i	0.579467	+	1.15173i
$143$	32.1907	+	8.62548i	2.69192	+	0.721299i
$144$	−0.911196	+	3.89483i	−0.0759330	+	0.324569i
$145$	3.64277	−	3.15432i	0.302516	−	0.261952i
$146$	−2.10678	−	10.1660i	−0.174358	−	0.841344i
$147$	−6.95126	+	0.824624i	−0.573330	+	0.0680139i
$148$	1.13346	−	2.86516i	0.0931697	−	0.235515i
$149$	9.37590	−	16.2395i	0.768103	−	1.33039i	−0.170487	−	0.985360i	$-0.554534\pi$
$149$	9.37590	−	16.2395i	0.768103	−	1.33039i	0.938590	−	0.345034i	$-0.112133\pi$
$150$	7.05797	−	0.430136i	0.576281	−	0.0351204i
$151$	11.9413	−	6.89433i	0.971771	−	0.561052i	0.0719956	−	0.997405i	$-0.477063\pi$
$151$	11.9413	−	6.89433i	0.971771	−	0.561052i	0.899776	+	0.436352i	$0.143730\pi$
$152$	−8.13601	+	9.73896i	−0.659917	+	0.789934i
$153$	−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
$157$	−1.25403	+	4.68010i	−0.100082	+	0.373512i	−0.997741	−	0.0671792i	$-0.978600\pi$
$157$	−1.25403	+	4.68010i	−0.100082	+	0.373512i	0.897659	+	0.440692i	$0.145267\pi$
$158$	0.106399	−	1.84985i	0.00846461	−	0.147166i
$159$	0.895913	−	1.55177i	0.0710506	−	0.123063i
$160$	12.5894	+	1.22769i	0.995279	+	0.0970571i
$161$	4.59355	−	13.2524i	0.362022	−	1.04444i
$162$	1.18212	+	0.776268i	0.0928761	+	0.0609894i
$163$	−2.58344	+	0.692231i	−0.202351	+	0.0542197i	−0.358571	−	0.933503i	$-0.616736\pi$
$163$	−2.58344	+	0.692231i	−0.202351	+	0.0542197i	0.156220	+	0.987722i	$0.450069\pi$
$164$	−7.72632	+	10.4097i	−0.603324	+	0.812858i
$165$	−6.98581	+	10.3140i	−0.543845	+	0.802944i
$166$	12.9204	+	4.27099i	1.00282	+	0.331493i
$167$	−13.5322	−	13.5322i	−1.04715	−	1.04715i	−0.998832	−	0.0483210i	$-0.984613\pi$
$167$	−13.5322	−	13.5322i	−1.04715	−	1.04715i	−0.0483210	−	0.998832i	$-0.515387\pi$
$168$	−3.85498	−	6.41398i	−0.297418	−	0.494849i
$169$		−	22.7856i		−	1.75274i
$170$	−0.710774	+	0.929579i	−0.0545138	+	0.0712955i
$171$	2.24334	+	3.88557i	0.171552	+	0.297137i
$172$	−13.4512	+	1.99020i	−1.02565	+	0.151751i
$173$	−1.74590	−	6.51581i	−0.132739	−	0.495388i	0.867258	−	0.497859i	$-0.165880\pi$
$173$	−1.74590	−	6.51581i	−0.132739	−	0.495388i	−0.999997	+	0.00247098i	$0.999213\pi$
$174$	−0.618435	−	2.98418i	−0.0468835	−	0.226230i
$175$	−8.90960	+	9.77850i	−0.673502	+	0.739185i
$176$	−15.2452	+	16.2530i	−1.14915	+	1.22511i
$177$	−0.870344	−	3.24817i	−0.0654190	−	0.244147i
$178$	5.27080	+	0.303163i	0.395063	+	0.0227230i
$179$	1.10843	−	0.639953i	0.0828481	−	0.0478324i	−0.458004	−	0.888950i	$-0.651435\pi$
$179$	1.10843	−	0.639953i	0.0828481	−	0.0478324i	0.540852	+	0.841118i	$0.318102\pi$
$180$	1.93897	−	4.02994i	0.144522	−	0.300374i
$181$			19.3108i			1.43536i	0.696374	+	0.717679i	$0.254795\pi$
$181$			19.3108i			1.43536i	−0.696374	+	0.717679i	$0.745205\pi$
$182$	17.7360	−	13.6540i	1.31468	−	1.01210i
$183$	7.96073	−	7.96073i	0.588474	−	0.588474i
$184$	14.9344	−	1.33926i	1.10098	−	0.0987317i
$185$	−1.93186	+	2.85224i	−0.142033	+	0.209701i
$186$	8.22482	+	9.22870i	0.603073	+	0.676681i
$187$	−0.533557	−	1.99126i	−0.0390176	−	0.145616i
$188$	−0.954912	+	2.41383i	−0.0696441	+	0.176047i
$189$	−2.59817	+	0.499514i	−0.188989	+	0.0363343i
$190$	11.2414	−	8.65638i	0.815539	−	0.628000i
$191$	−11.9792	−	6.91618i	−0.866783	−	0.500437i	−0.000505095	−	1.00000i	$-0.500161\pi$
$191$	−11.9792	−	6.91618i	−0.866783	−	0.500437i	−0.866278	+	0.499563i	$0.833494\pi$
$192$	4.56012	−	6.57307i	0.329098	−	0.474371i
$193$	−4.98883	+	18.6186i	−0.359104	+	1.34019i	0.516137	+	0.856506i	$0.327370\pi$
$193$	−4.98883	+	18.6186i	−0.359104	+	1.34019i	−0.875241	+	0.483688i	$0.839297\pi$
$194$	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	0.316140	−	0.948712i	$-0.397613\pi$
$197$	−8.87857	−	8.87857i	−0.632572	−	0.632572i	−0.948712	+	0.316140i	$0.897613\pi$
$198$	3.54099	+	7.03800i	0.251647	+	0.500169i
$199$	−6.58171	−	11.3999i	−0.466565	−	0.808115i	0.532705	−	0.846301i	$-0.321175\pi$
$199$	−6.58171	−	11.3999i	−0.466565	−	0.808115i	−0.999271	+	0.0381859i	$0.987842\pi$
$200$	−13.4426	−	4.39276i	−0.950536	−	0.310615i
$201$	−7.22232	+	12.5094i	−0.509423	+	0.882347i
$202$	−10.9346	+	16.6515i	−0.769355	+	1.17159i
$203$	4.72024	+	3.19792i	0.331296	+	0.224450i
$204$	0.294116	+	0.679134i	0.0205922	+	0.0475489i
$205$	10.9569	−	9.48774i	0.765265	−	0.662652i
$206$	−8.66983	−	9.72803i	−0.604056	−	0.677784i
$207$	1.37208	−	5.12067i	0.0953662	−	0.355911i
$208$	21.0946	+	11.2954i	1.46265	+	0.783198i
$209$			24.9953i			1.72896i
$210$	2.65206	+	7.93515i	0.183009	+	0.547577i
$211$	−0.281828			−0.0194019			−0.00970093	−	0.999953i	$-0.503088\pi$
$211$	−0.281828			−0.0194019			−0.00970093	+	0.999953i	$0.503088\pi$
$212$	−2.80785	+	2.22677i	−0.192844	+	0.152935i
$213$	−10.4936	−	2.81175i	−0.719009	−	0.192658i
$214$	7.28501	+	8.17418i	0.497993	+	0.558776i
$215$	15.1636	+	1.08968i	1.03415	+	0.0743157i
$216$	−1.62734	−	2.31339i	−0.110727	−	0.157406i
$217$	−23.0673	−	1.66050i	−1.56591	−	0.112722i
$218$	5.94434	+	3.90349i	0.402601	+	0.264378i
$219$	6.35766	+	3.67059i	0.429611	+	0.248036i
$220$	20.5802	−	14.0420i	1.38752	−	0.946709i
$221$	−1.91706	+	1.10682i	−0.128956	+	0.0744526i
$222$	0.979228	+	1.94629i	0.0657215	+	0.130627i
$223$	−0.661316	+	0.661316i	−0.0442850	+	0.0442850i	−0.728902	−	0.684618i	$-0.759969\pi$
$223$	−0.661316	+	0.661316i	−0.0442850	+	0.0442850i	0.684618	+	0.728902i	$0.259969\pi$
$224$	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
$227$	21.4090	+	5.73653i	1.42097	+	0.380747i	0.885827	−	0.464016i	$-0.153592\pi$
$227$	21.4090	+	5.73653i	1.42097	+	0.380747i	0.535140	+	0.844763i	$0.320259\pi$
$228$	−1.31337	−	8.87672i	−0.0869800	−	0.587875i
$229$	2.38356	−	4.12844i	0.157510	−	0.272815i	−0.776460	−	0.630166i	$-0.782987\pi$
$229$	2.38356	−	4.12844i	0.157510	−	0.272815i	0.933970	+	0.357351i	$0.116320\pi$
$230$	−16.6245	−	2.15980i	−1.09619	−	0.142413i
$231$	−13.9266	−	4.82723i	−0.916302	−	0.317608i
$232$	−1.04539	+	6.00486i	−0.0686330	+	0.394239i
$233$	0.0109131	−	0.00292416i	0.000714941	−	0.000191568i	−0.258462	−	0.966022i	$-0.583216\pi$
$233$	0.0109131	−	0.00292416i	0.000714941	−	0.000191568i	0.259176	+	0.965830i	$0.416549\pi$
$234$	6.31574	−	5.62873i	0.412873	−	0.367961i
$235$	1.62755	−	2.40294i	0.106169	−	0.156751i
$236$	−0.771117	+	6.68115i	−0.0501954	+	0.434906i
$237$	0.926452	+	0.926452i	0.0601795	+	0.0601795i
$238$	−1.28002	−	0.527826i	−0.0829712	−	0.0342138i
$239$	−10.3228			−0.667723			−0.333862	−	0.942622i	$-0.608352\pi$
$239$	−10.3228			−0.667723			−0.333862	+	0.942622i	$0.608352\pi$
$240$	−6.57093	+	6.06819i	−0.424152	+	0.391700i
$241$	−5.14413	−	8.90990i	−0.331363	−	0.573937i	0.651417	−	0.758720i	$-0.274175\pi$
$241$	−5.14413	−	8.90990i	−0.331363	−	0.573937i	−0.982779	+	0.184783i	$0.940842\pi$
$242$	−1.62708	+	28.2885i	−0.104593	+	1.81845i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−20.6619	+	8.94817i	−1.32275	+	0.572848i
$245$	−13.9034	−	7.18992i	−0.888257	−	0.459347i
$246$	−1.86016	−	8.97599i	−0.118600	−	0.572288i
$247$	25.9252	−	6.94664i	1.64958	−	0.442004i
$248$	−8.50644	−	23.2144i	−0.540160	−	1.47411i
$249$	−8.33318	+	4.81116i	−0.528094	+	0.304895i
$250$	13.6063	+	8.05408i	0.860539	+	0.509385i
$251$	−1.10630			−0.0698290			−0.0349145	−	0.999390i	$-0.511116\pi$
$251$	−1.10630			−0.0698290			−0.0349145	+	0.999390i	$0.511116\pi$
$252$	5.19948	+	0.982554i	0.327536	+	0.0618951i
$253$	20.8834	−	20.8834i	1.31293	−	1.31293i
$254$	−27.0646	−	8.94652i	−1.69819	−	0.561355i
$255$	−0.156319	−	0.812541i	−0.00978907	−	0.0508833i
$256$	−13.3167	+	8.86936i	−0.832293	+	0.554335i
$257$	5.27272	+	19.6781i	0.328903	+	1.22748i	0.910329	+	0.413884i	$0.135828\pi$
$257$	5.27272	+	19.6781i	0.328903	+	1.22748i	−0.581426	+	0.813599i	$0.697505\pi$
$258$	5.27772	−	8.03704i	0.328576	−	0.500364i
$259$	−3.85127	−	1.33493i	−0.239306	−	0.0829482i
$260$	−20.2840	−	17.4434i	−1.25796	−	1.08179i
$261$	1.86626	+	1.07749i	0.115519	+	0.0666947i
$262$	0.190509	−	3.31219i	0.0117697	−	0.204628i
$263$	15.7050	+	4.20813i	0.968410	+	0.259485i	0.708156	−	0.706056i	$-0.249527\pi$
$263$	15.7050	+	4.20813i	0.968410	+	0.259485i	0.260254	+	0.965540i	$0.416194\pi$
$264$	−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
$268$	22.6353	−	17.9509i	1.38267	−	1.09653i
$269$	−2.46307	−	4.26616i	−0.150176	−	0.260112i	0.781116	−	0.624386i	$-0.214651\pi$
$269$	−2.46307	−	4.26616i	−0.150176	−	0.260112i	−0.931292	+	0.364274i	$0.881317\pi$
$270$	1.21514	+	2.91949i	0.0739508	+	0.177675i
$271$	−9.47009	−	5.46756i	−0.575267	−	0.332130i	0.183983	−	0.982929i	$-0.441101\pi$
$271$	−9.47009	−	5.46756i	−0.575267	−	0.332130i	−0.759250	+	0.650799i	$0.774434\pi$
$272$	−0.0473317	−	1.47941i	−0.00286991	−	0.0897027i
$273$	−1.13638	+	15.7863i	−0.0687766	+	0.955432i
$274$	−5.99529	+	1.24245i	−0.362188	+	0.0750591i
$275$	−25.8667	+	10.3351i	−1.55982	+	0.623232i
$276$	−6.31913	+	8.51376i	−0.380367	+	0.512468i
$277$	2.91014	−	10.8608i	0.174854	−	0.652562i	−0.821723	−	0.569887i	$-0.806987\pi$
$277$	2.91014	−	10.8608i	0.174854	−	0.652562i	0.996577	−	0.0826752i	$-0.0263464\pi$
$278$	−12.4669	−	24.7789i	−0.747715	−	1.48614i
$279$	−8.74118			−0.523321
$280$	0.905871	−	16.7087i	0.0541362	−	0.998534i
$281$	−12.9485			−0.772444			−0.386222	−	0.922406i	$-0.626220\pi$
$281$	−12.9485			−0.772444			−0.386222	+	0.922406i	$0.626220\pi$
$282$	−0.824976	−	1.63970i	−0.0491266	−	0.0976430i
$283$	5.96390	−	22.2576i	0.354517	−	1.32308i	−0.526574	−	0.850129i	$-0.676524\pi$
$283$	5.96390	−	22.2576i	0.354517	−	1.32308i	0.881091	−	0.472947i	$-0.156810\pi$
$284$	17.4469	+	12.9496i	1.03528	+	0.768415i
$285$	−0.719101	+	10.0067i	−0.0425959	+	0.592746i
$286$	46.1499	−	9.56401i	2.72890	−	0.565532i
$287$	14.1978	+	9.61888i	0.838069	+	0.567785i
$288$	1.32446	+	5.49962i	0.0780447	+	0.324068i
$289$	−14.6038	−	8.43153i	−0.859050	−	0.495973i
$290$	2.59709	−	6.30033i	0.152506	−	0.369968i
$291$	3.75843	+	6.50980i	0.220323	+	0.381611i
$292$	−9.12319	−	11.5039i	−0.533894	−	0.673215i
$293$	−7.48370	+	7.48370i	−0.437203	+	0.437203i	−0.891070	−	0.453867i	$-0.850044\pi$
$293$	−7.48370	+	7.48370i	−0.437203	+	0.437203i	0.453867	+	0.891070i	$0.350044\pi$
$294$	−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
$297$	−5.38117	−	1.44188i	−0.312247	−	0.0836664i
$298$	1.52279	−	26.4753i	0.0882130	−	1.53367i
$299$	−27.4643	−	15.8565i	−1.58830	−	0.917005i
$300$	8.64313	−	5.02954i	0.499012	−	0.290380i
$301$	3.39611	+	17.6645i	0.195749	+	1.01817i
$302$	10.7037	−	16.2998i	0.615928	−	0.937951i
$303$	−3.64575	−	13.6061i	−0.209443	−	0.781652i
$304$	−4.08824	+	17.4748i	−0.234477	+	1.00225i
$305$	24.7207	−	4.75584i	1.41550	−	0.272319i
$306$	−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	$0.934922\pi$
$308$	22.3486	+	19.2236i	1.27343	+	1.09537i
$309$	9.21414			0.524174
$310$	3.65478	+	27.3994i	0.207578	+	1.55618i
$311$	9.94499	−	5.74174i	0.563928	−	0.325584i	−0.190792	−	0.981630i	$-0.561106\pi$
$311$	9.94499	−	5.74174i	0.563928	−	0.325584i	0.754721	+	0.656046i	$0.227772\pi$
$312$	−15.8870	+	5.82146i	−0.899422	+	0.329575i
$313$	11.0195	−	2.95266i	0.622857	−	0.166894i	0.0664309	−	0.997791i	$-0.478839\pi$
$313$	11.0195	−	2.95266i	0.622857	−	0.166894i	0.556426	+	0.830897i	$0.312172\pi$
$314$	1.39048	+	6.70957i	0.0784692	+	0.378643i
$315$	−5.43655	−	2.33322i	−0.306315	−	0.131462i
$316$	−1.04137	−	2.40459i	−0.0585815	−	0.135269i
$317$	−4.76290	+	1.27621i	−0.267511	+	0.0716794i	−0.390081	−	0.920780i	$-0.627553\pi$
$317$	−4.76290	+	1.27621i	−0.267511	+	0.0716794i	0.122570	+	0.992460i	$0.460886\pi$
$318$	0.145510	−	2.52984i	0.00815981	−	0.141867i
$319$	6.00267	+	10.3969i	0.336085	+	0.582116i
$320$	16.6849	−	6.45100i	0.932712	−	0.360622i
$321$	−7.74237			−0.432137
$322$	−2.62024	−	19.6619i	−0.146020	−	1.09571i
$323$	−1.17398	−	1.17398i	−0.0653221	−	0.0653221i
$324$	1.98681	+	0.229311i	0.110378	+	0.0127395i
$325$	17.9085	+	23.9568i	0.993384	+	1.32888i
$326$	−2.82374	+	2.51658i	−0.156393	+	0.139381i
$327$	−4.85720	+	1.30148i	−0.268604	+	0.0719721i
$328$	−3.14437	+	18.0618i	−0.173619	+	0.997294i
$329$	3.24460	+	1.12464i	0.178881	+	0.0620035i
$330$	−2.26967	+	17.4702i	−0.124941	+	0.961704i
$331$	2.95564	−	5.11931i	0.162456	−	0.281383i	−0.773293	−	0.634049i	$-0.781392\pi$
$331$	2.95564	−	5.11931i	0.162456	−	0.281383i	0.935749	+	0.352666i	$0.114725\pi$
$332$	19.0374	−	2.81671i	1.04481	−	0.154587i
$333$	−1.48811	−	0.398738i	−0.0815480	−	0.0218507i
$334$	−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	$-0.0746804\pi$
$338$	−14.4828	−	28.7857i	−0.787761	−	1.56574i
$339$	−2.38839	+	1.37894i	−0.129719	+	0.0748935i
$340$	−0.307088	+	1.62614i	−0.0166542	+	0.0881898i
$341$	−42.1729	−	24.3486i	−2.28379	−	1.31855i
$342$	5.30379	+	3.48286i	0.286796	+	0.188332i
$343$	3.96179	−	18.0916i	0.213917	−	0.976852i
$344$	−15.7283	+	11.0640i	−0.848014	+	0.596533i
$345$	8.96135	−	7.75974i	0.482463	−	0.417770i
$346$	−6.34718	−	7.12188i	−0.341226	−	0.382875i
$347$	−16.2451	−	4.35285i	−0.872081	−	0.233673i	−0.205094	−	0.978742i	$-0.565750\pi$
$347$	−16.2451	−	4.35285i	−0.872081	−	0.233673i	−0.666988	+	0.745069i	$0.732417\pi$
$348$	−2.67807	−	3.37692i	−0.143560	−	0.181022i
$349$	−0.714880			−0.0382667			−0.0191333	−	0.999817i	$-0.506091\pi$
$349$	−0.714880			−0.0382667			−0.0191333	+	0.999817i	$0.506091\pi$
$350$	−5.04041	+	18.0165i	−0.269422	+	0.963022i
$351$			5.98211i			0.319301i
$352$	−8.92914	+	30.2229i	−0.475925	+	1.61089i
$353$	0.394510	−	1.47233i	0.0209977	−	0.0783643i	−0.954632	−	0.297788i	$-0.903751\pi$
$353$	0.394510	−	1.47233i	0.0209977	−	0.0783643i	0.975630	+	0.219424i	$0.0704178\pi$
$354$	−3.16410	−	3.55030i	−0.168170	−	0.188696i
$355$	−15.9017	−	18.3641i	−0.843976	−	0.974668i
$356$	6.85144	−	2.96719i	0.363126	−	0.157261i
$357$	0.880833	−	0.427381i	0.0466186	−	0.0226194i
$358$	0.993551	−	1.51300i	0.0525108	−	0.0799647i
$359$	8.03539	−	13.9177i	0.424092	−	0.734548i	−0.572243	−	0.820084i	$-0.693927\pi$
$359$	8.03539	−	13.9177i	0.424092	−	0.734548i	0.996335	+	0.0855354i	$0.0272601\pi$
$360$	−0.111927	−	6.32356i	−0.00589910	−	0.333281i
$361$	0.565127	+	0.978828i	0.0297435	+	0.0515173i
$362$	12.2742	+	24.3958i	0.645115	+	1.28222i
$363$	−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
$367$	−4.71685	+	17.6035i	−0.246218	+	0.918897i	0.726550	+	0.687114i	$0.241123\pi$
$367$	−4.71685	+	17.6035i	−0.246218	+	0.918897i	−0.972767	+	0.231783i	$0.925544\pi$
$368$	18.0158	−	11.1844i	0.939141	−	0.583029i
$369$	5.61344	+	3.24092i	0.292224	+	0.168716i
$370$	−0.627656	+	4.83123i	−0.0326303	+	0.251163i
$371$	3.10286	+	3.58423i	0.161093	+	0.186084i
$372$	16.2565	+	6.43108i	0.842861	+	0.333436i
$373$	3.83202	+	14.3013i	0.198414	+	0.740493i	0.991356	+	0.131196i	$0.0418816\pi$
$373$	3.83202	+	14.3013i	0.198414	+	0.740493i	−0.792942	+	0.609297i	$0.791452\pi$
$374$	−1.93973	−	2.17648i	−0.100301	−	0.112543i
$375$	−10.6529	+	3.39344i	−0.550114	+	0.175236i
$376$	0.327893	+	3.65641i	0.0169098	+	0.188565i
$377$	9.11551	−	9.11551i	0.469472	−	0.469472i
$378$	−2.96484	+	2.28248i	−0.152495	+	0.117398i
$379$		−	21.4047i		−	1.09949i	−0.835334	−	0.549743i	$-0.814726\pi$
$379$		−	21.4047i		−	1.09949i	0.835334	−	0.549743i	$-0.185274\pi$
$380$	8.69951	−	18.0810i	0.446276	−	0.927537i
$381$	17.4557	−	10.0780i	0.894282	−	0.516314i
$382$	−19.5296	−	1.12330i	−0.999223	−	0.0574728i
$383$	4.78061	+	17.8415i	0.244278	+	0.911658i	0.973745	+	0.227642i	$0.0731015\pi$
$383$	4.78061	+	17.8415i	0.244278	+	0.911658i	−0.729467	+	0.684016i	$0.760232\pi$
$384$	1.58301	−	11.2024i	0.0807824	−	0.571671i
$385$	−19.7302	−	26.4004i	−1.00554	−	1.34549i
$386$	5.53166	+	26.6923i	0.281554	+	1.35860i
$387$	1.75967	+	6.56717i	0.0894489	+	0.333828i
$388$	−2.20039	−	14.8718i	−0.111708	−	0.755003i
$389$	−12.1014	−	20.9602i	−0.613563	−	1.06272i	−0.990635	−	0.136538i	$-0.956402\pi$
$389$	−12.1014	−	20.9602i	−0.613563	−	1.06272i	0.377072	−	0.926184i	$-0.376931\pi$
$390$	18.7510	−	2.50118i	0.949494	−	0.126652i
$391$			1.96171i			0.0992080i
$392$	19.3742	−	4.07915i	0.978546	−	0.206028i
$393$	1.65883	+	1.65883i	0.0836771	+	0.0836771i
$394$	−16.8599	−	5.57322i	−0.849388	−	0.280775i
$395$	0.553474	+	2.87694i	0.0278483	+	0.144755i
$396$	8.94687	+	6.64060i	0.449597	+	0.333703i
$397$	−4.18281	+	1.12078i	−0.209929	+	0.0562504i	−0.362251	−	0.932081i	$-0.617992\pi$
$397$	−4.18281	+	1.12078i	−0.209929	+	0.0562504i	0.152322	+	0.988331i	$0.451325\pi$
$398$	−15.5608	−	10.2183i	−0.779990	−	0.512200i
$399$	−11.6571	+	2.24116i	−0.583587	+	0.112198i
$400$	−19.7745	+	2.99479i	−0.988725	+	0.149740i
$401$	−13.4159	+	23.2370i	−0.669958	+	1.16040i	0.307958	+	0.951400i	$0.400355\pi$
$401$	−13.4159	+	23.2370i	−0.669958	+	1.16040i	−0.977915	+	0.209001i	$0.932979\pi$
$402$	−1.17302	+	20.3941i	−0.0585048	+	1.01717i
$403$	−13.5338	+	50.5089i	−0.674168	+	2.51603i
$404$	−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
$408$	0.803230	+	0.671025i	0.0397658	+	0.0332207i
$409$	−12.0607	+	6.96325i	−0.596364	+	0.344311i	−0.767610	−	0.640918i	$-0.778554\pi$
$409$	−12.0607	+	6.96325i	−0.596364	+	0.344311i	0.171246	+	0.985228i	$0.445221\pi$
$410$	7.81168	−	18.9505i	0.385791	−	0.935897i
$411$	2.16469	−	3.74936i	0.106776	−	0.184942i
$412$	−17.1361	−	6.77904i	−0.844235	−	0.333980i
$413$	8.87404	+	0.638796i	0.436663	+	0.0314331i
$414$	−1.52137	−	7.34120i	−0.0747715	−	0.360800i
$415$	−21.4608	−	1.54222i	−1.05347	−	0.0757044i
$416$	33.8289	+	0.861861i	1.65860	+	0.0422562i
$417$	18.9457	+	5.07648i	0.927774	+	0.248596i
$418$	15.8873	+	31.5772i	0.777073	+	1.54449i
$419$		−	1.69659i		−	0.0828841i	−0.999141	−	0.0414420i	$-0.986805\pi$
$419$		−	1.69659i		−	0.0828841i	0.999141	−	0.0414420i	$-0.0131952\pi$
$420$	8.39409	+	8.33902i	0.409590	+	0.406902i
$421$			10.8090i			0.526800i	0.964687	+	0.263400i	$0.0848439\pi$
$421$			10.8090i			0.526800i	−0.964687	+	0.263400i	$0.915156\pi$
$422$	−0.356042	+	0.179133i	−0.0173318	+	0.00872008i
$423$	1.25370	+	0.335928i	0.0609569	+	0.0163334i
$424$	−2.13188	+	4.59785i	−0.103533	+	0.223291i
$425$	0.729489	−	1.70033i	0.0353854	−	0.0824783i
$426$	−15.0440	+	3.11769i	−0.728886	+	0.151053i
$427$	13.0026	+	26.7985i	0.629241	+	1.29687i
$428$	14.3990	+	5.69623i	0.696000	+	0.275338i
$429$	−16.6632	+	28.8614i	−0.804505	+	1.39344i
$430$	19.8492	−	8.26151i	0.957211	−	0.398405i
$431$	−2.61429	+	1.50936i	−0.125926	+	0.0727034i	−0.561640	−	0.827382i	$-0.689829\pi$
$431$	−2.61429	+	1.50936i	−0.125926	+	0.0727034i	0.435714	+	0.900085i	$0.356496\pi$
$432$	−3.52628	−	1.88820i	−0.169658	−	0.0908463i
$433$	−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
$437$	6.15608	−	22.9748i	0.294485	−	1.09903i
$438$	10.3649	+	0.596162i	0.495253	+	0.0284857i
$439$	5.28278	−	9.15005i	0.252133	−	0.436708i	−0.711980	−	0.702200i	$-0.752201\pi$
$439$	5.28278	−	9.15005i	0.252133	−	0.436708i	0.964113	+	0.265492i	$0.0855345\pi$
$440$	17.0743	−	30.8206i	0.813984	−	1.46931i
$441$	1.00259	−	6.92783i	0.0477425	−	0.329897i
$442$	−1.71837	+	2.61678i	−0.0817347	+	0.124468i
$443$	−28.9120	+	7.74694i	−1.37365	+	0.368068i	−0.868810	−	0.495145i	$-0.835115\pi$
$443$	−28.9120	+	7.74694i	−1.37365	+	0.368068i	−0.504839	+	0.863213i	$0.668448\pi$
$444$	2.47417	+	1.83640i	0.117419	+	0.0871515i
$445$	−8.19732	+	1.57702i	−0.388590	+	0.0747581i
$446$	−0.415118	+	1.25580i	−0.0196564	+	0.0594638i
$447$	13.2595	+	13.2595i	0.627154	+	0.627154i
$448$	12.4803	+	17.0951i	0.589639	+	0.807667i
$449$			4.41290i			0.208257i	0.994564	+	0.104129i	$0.0332054\pi$
$449$			4.41290i			0.208257i	−0.994564	+	0.104129i	$0.966795\pi$
$450$	−1.41126	+	6.92881i	−0.0665274	+	0.326627i
$451$	18.0552	+	31.2725i	0.850185	+	1.47256i
$452$	5.45635	−	0.807303i	0.256645	−	0.0379723i
$453$	3.56877	+	13.3188i	0.167675	+	0.625773i
$454$	30.6928	−	6.36071i	1.44049	−	0.298523i
$455$	−21.8993	+	27.8014i	−1.02665	+	1.30335i
$456$	−7.30136	−	10.3794i	−0.341918	−	0.486060i
$457$	9.61767	+	35.8936i	0.449896	+	1.67903i	0.702676	+	0.711510i	$0.251988\pi$
$457$	9.61767	+	35.8936i	0.449896	+	1.67903i	−0.252780	+	0.967524i	$0.581345\pi$
$458$	0.387127	−	6.73059i	0.0180892	−	0.314500i
$459$	0.320466	−	0.185021i	0.0149581	−	0.00863606i
$460$	−22.3750	+	7.83820i	−1.04324	+	0.365458i
$461$			15.8272i			0.737148i	0.929598	+	0.368574i	$0.120154\pi$
$461$			15.8272i			0.737148i	−0.929598	+	0.368574i	$0.879846\pi$
$462$	−20.6621	+	2.75353i	−0.961288	+	0.128106i
$463$	−8.81202	+	8.81202i	−0.409529	+	0.409529i	−0.881574	−	0.472045i	$-0.843516\pi$
$463$	−8.81202	+	8.81202i	−0.409529	+	0.409529i	0.472045	+	0.881574i	$0.343516\pi$
$464$	2.49610	+	8.25057i	0.115878	+	0.383023i
$465$	−16.1832	−	10.9611i	−0.750478	−	0.508309i
$466$	0.0119282	−	0.0106307i	0.000552563	−	0.000492456i
$467$	−8.77747	−	32.7580i	−0.406173	−	1.51586i	−0.801882	−	0.597482i	$-0.796168\pi$
$467$	−8.77747	−	32.7580i	−0.406173	−	1.51586i	0.395709	−	0.918376i	$-0.370499\pi$
$468$	4.40117	−	11.1253i	0.203444	−	0.514267i
$469$	−25.0134	−	28.8940i	−1.15501	−	1.33420i
$470$	0.528785	−	4.07019i	0.0243910	−	0.187744i
$471$	−4.19606	−	2.42260i	−0.193344	−	0.111627i
$472$	3.27244	+	8.93061i	0.150626	+	0.411065i
$473$	−9.80311	+	36.5857i	−0.450747	+	1.68221i
$474$	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
$478$	−13.0410	+	6.56126i	−0.596482	+	0.300105i
$479$	−9.32972	−	16.1595i	−0.426286	−	0.738348i	0.570254	−	0.821468i	$-0.306845\pi$
$479$	−9.32972	−	16.1595i	−0.426286	−	0.738348i	−0.996540	+	0.0831201i	$0.973511\pi$
$480$	−4.44423	+	11.8427i	−0.202850	+	0.540541i
$481$	−4.60804	+	7.98136i	−0.210108	+	0.363918i
$482$	−12.1620	−	7.98645i	−0.553962	−	0.363773i
$483$	11.6120	+	7.86700i	0.528362	+	0.357961i
$484$	15.9249	+	36.7718i	0.723861	+	1.67144i
$485$	−1.20476	+	16.7650i	−0.0547055	+	0.761259i
$486$	−1.05577	+	0.940927i	−0.0478908	+	0.0426813i
$487$	4.66866	−	17.4237i	0.211557	−	0.789542i	−0.775793	−	0.630987i	$-0.782650\pi$
$487$	4.66866	−	17.4237i	0.211557	−	0.789542i	0.987350	−	0.158554i	$-0.0506834\pi$
$488$	−20.4152	+	24.4375i	−0.924155	+	1.10623i
$489$		−	2.67457i		−	0.120948i
$490$	−22.1346	−	0.246039i	−0.999938	−	0.0111149i
$491$	20.1191			0.907962			0.453981	−	0.891011i	$-0.350003\pi$
$491$	20.1191			0.907962			0.453981	+	0.891011i	$0.350003\pi$
$492$	−8.05524	−	10.1573i	−0.363158	−	0.457925i
$493$	−0.770260	−	0.206391i	−0.0346908	−	0.00929536i
$494$	28.3367	−	25.2543i	1.27493	−	1.13624i
$495$	−8.15450	−	9.41723i	−0.366517	−	0.423273i
$496$	−25.5018	−	23.9206i	−1.14506	−	1.07406i
$497$	16.1215	−	23.7959i	0.723150	−	1.06739i
$498$	−7.46950	+	11.3747i	−0.334716	+	0.509714i
$499$	8.51618	+	4.91682i	0.381237	+	0.220107i	0.678356	−	0.734733i	$-0.262693\pi$
$499$	8.51618	+	4.91682i	0.381237	+	0.220107i	−0.297119	+	0.954840i	$0.596026\pi$
$500$	22.3085	+	1.52660i	0.997667	+	0.0682717i
$501$	16.5735	−	9.56871i	0.740449	−	0.427498i
$502$	−1.39762	+	0.703177i	−0.0623788	+	0.0313843i
$503$	−11.2005	+	11.2005i	−0.499406	+	0.499406i	−0.911253	−	0.411847i	$-0.864884\pi$
$503$	−11.2005	+	11.2005i	−0.499406	+	0.499406i	0.411847	+	0.911253i	$0.364884\pi$
$504$	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
$507$	22.0092	+	5.89735i	0.977463	+	0.261910i
$508$	−39.8780	+	5.90022i	−1.76930	+	0.261780i
$509$	−2.28874	+	3.96422i	−0.101447	+	0.175711i	−0.912281	−	0.409565i	$-0.865680\pi$
$509$	−2.28874	+	3.96422i	−0.101447	+	0.175711i	0.810834	+	0.585276i	$0.199014\pi$
$510$	−0.713943	−	0.927147i	−0.0316139	−	0.0410548i
$511$	−14.6848	+	12.7126i	−0.649615	+	0.562371i
$512$	−11.1859	+	19.6692i	−0.494351	+	0.869263i
$513$	−4.33380	+	1.16124i	−0.191342	+	0.0512699i
$514$	19.1688	+	21.5084i	0.845499	+	0.948696i
$515$	17.0588	+	11.5542i	0.751701	+	0.509137i
$516$	1.55905	−	13.5080i	0.0686333	−	0.594656i
$517$	5.11290	+	5.11290i	0.224865	+	0.224865i
$518$	−5.71391	+	0.761464i	−0.251055	+	0.0334568i
$519$	6.74566			0.296102
$520$	−36.7126	−	9.14392i	−1.60995	−	0.400987i
$521$	−10.5312	−	18.2406i	−0.461382	−	0.799137i	0.537648	−	0.843169i	$-0.319313\pi$
$521$	−10.5312	−	18.2406i	−0.461382	−	0.799137i	−0.999030	+	0.0440323i	$0.985980\pi$
$522$	3.04256	+	0.175001i	0.133169	+	0.00765956i
$523$	−0.539666	+	0.144603i	−0.0235980	+	0.00632305i	−0.270599	−	0.962692i	$-0.587222\pi$
$523$	−0.539666	+	0.144603i	−0.0235980	+	0.00632305i	0.247001	+	0.969015i	$0.420555\pi$
$524$	−1.86459	−	4.30548i	−0.0814552	−	0.188086i
$525$	−7.13933	−	11.1369i	−0.311586	−	0.486053i
$526$	22.5153	−	4.66601i	0.981712	−	0.203448i
$527$	3.12439	−	0.837179i	0.136101	−	0.0364681i
$528$	−11.7534	−	18.9323i	−0.511502	−	0.823925i
$529$	−4.42010	+	2.55195i	−0.192178	+	0.110954i
$530$	3.44172	−	4.50122i	0.149499	−	0.195521i
$531$	3.36275			0.145931
$532$	23.3284	+	4.40840i	1.01141	+	0.191128i
$533$	27.4181	−	27.4181i	1.18761	−	1.18761i
$534$	−1.65702	+	5.01274i	−0.0717061	+	0.216922i
$535$	−14.3340	−	9.70863i	−0.619714	−	0.419741i
$536$	17.1859	−	37.0651i	0.742319	−	1.60097i
$537$	0.331264	+	1.23630i	0.0142951	+	0.0533501i
$538$	−5.82328	−	3.82400i	−0.251060	−	0.164864i
$539$	24.1346	−	30.6315i	1.03955	−	1.31939i
$540$	3.39078	+	2.91592i	0.145916	+	0.125481i
$541$	−11.9490	−	6.89877i	−0.513728	−	0.296601i	0.220637	−	0.975356i	$-0.429187\pi$
$541$	−11.9490	−	6.89877i	−0.513728	−	0.296601i	−0.734365	+	0.678755i	$0.762520\pi$
$542$	−15.4391	−	0.888016i	−0.663165	−	0.0381436i
$543$	−18.6528	−	4.99799i	−0.800467	−	0.214484i
$544$	−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	$0.275412\pi$
$548$	−6.78430	+	5.38030i	−0.289811	+	0.229835i
$549$	5.62909	+	9.74986i	0.240244	+	0.416114i
$550$	−26.1090	+	29.4978i	−1.11329	+	1.25779i
$551$	8.37330	+	4.83433i	0.356715	+	0.205949i
$552$	−2.57169	+	14.7722i	−0.109458	+	0.628746i
$553$	−3.11874	+	1.51322i	−0.132622	+	0.0643485i
$554$	−3.22679	−	15.5705i	−0.137093	−	0.661526i
$555$	−2.25505	−	2.60425i	−0.0957215	−	0.110544i
$556$	−31.4996	−	23.3798i	−1.33588	−	0.991524i
$557$	4.70498	−	17.5592i	0.199356	−	0.744008i	−0.791740	−	0.610859i	$-0.790824\pi$
$557$	4.70498	−	17.5592i	0.199356	−	0.744008i	0.991096	−	0.133149i	$-0.0425089\pi$
$558$	−11.0430	+	5.55600i	−0.467487	+	0.235204i
$559$	40.6714			1.72022
$560$	−9.47581	−	21.6843i	−0.400426	−	0.916329i
$561$	2.06151			0.0870369
$562$	−16.3582	+	8.23024i	−0.690030	+	0.347172i
$563$	6.51198	−	24.3030i	0.274447	−	1.02425i	−0.681764	−	0.731572i	$-0.738787\pi$
$563$	6.51198	−	24.3030i	0.274447	−	1.02425i	0.956211	−	0.292678i	$-0.0945465\pi$
$564$	−2.08443	−	1.54712i	−0.0877704	−	0.0651455i
$565$	−6.15093	−	0.442018i	−0.258772	−	0.0185958i
$566$	−6.61283	−	31.9094i	−0.277958	−	1.34125i
$567$	0.189962	−	2.63892i	0.00797767	−	0.110824i
$568$	30.2721	+	5.27006i	1.27019	+	0.221127i
$569$	13.9329	+	8.04416i	0.584097	+	0.337229i	0.762760	−	0.646682i	$-0.223844\pi$
$569$	13.9329	+	8.04416i	0.584097	+	0.337229i	−0.178663	+	0.983910i	$0.557177\pi$
$570$	5.45192	+	13.0988i	0.228356	+	0.548649i
$571$	−20.7948	−	36.0177i	−0.870236	−	1.50729i	−0.861753	−	0.507328i	$-0.830633\pi$
$571$	−20.7948	−	36.0177i	−0.870236	−	1.50729i	−0.00848298	−	0.999964i	$-0.502700\pi$
$572$	52.2235	−	41.4159i	2.18357	−	1.73169i
$573$	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
$577$	−31.9623	−	8.56429i	−1.33061	−	0.356536i	−0.477667	−	0.878541i	$-0.658518\pi$
$577$	−31.9623	−	8.56429i	−1.33061	−	0.356536i	−0.852943	+	0.522005i	$0.825184\pi$
$578$	−23.8086	−	1.36941i	−0.990308	−	0.0569601i
$579$	−16.6929	−	9.63768i	−0.693735	−	0.400528i
$580$	−0.723587	−	9.61012i	−0.0300453	−	0.399039i
$581$	−4.80649	−	25.0004i	−0.199407	−	1.03719i
$582$	8.88584	+	5.83510i	0.368330	+	0.241873i
$583$	2.58360	+	9.64213i	0.107002	+	0.399336i
$584$	−18.8376	−	8.73439i	−0.779505	−	0.361432i
$585$	−7.50133	+	11.0751i	−0.310142	+	0.457900i
$586$	−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	$0.475902\pi$
$588$	−6.96154	+	12.1465i	−0.287089	+	0.500912i
$589$	−39.2188			−1.61598
$590$	−1.40600	−	10.5406i	−0.0578842	−	0.433949i
$591$	10.8740	−	6.27810i	0.447296	−	0.258247i
$592$	−3.25029	−	5.23556i	−0.133586	−	0.215180i
$593$	15.6366	−	4.18981i	0.642117	−	0.172055i	0.0769548	−	0.997035i	$-0.475480\pi$
$593$	15.6366	−	4.18981i	0.642117	−	0.172055i	0.565162	+	0.824980i	$0.308814\pi$
$594$	−7.71466	+	1.59877i	−0.316536	+	0.0655983i
$595$	2.16667	+	0.313289i	0.0888248	+	0.0128436i
$596$	−14.9042	−	34.4149i	−0.610501	−	1.40969i
$597$	12.7149	−	3.40695i	0.520386	−	0.139437i
$598$	−44.7750	−	2.57534i	−1.83098	−	0.105314i
$599$	−1.79982	−	3.11738i	−0.0735386	−	0.127373i	0.826911	−	0.562332i	$-0.190096\pi$
$599$	−1.79982	−	3.11738i	−0.0735386	−	0.127373i	−0.900450	+	0.434960i	$0.856763\pi$
$600$	7.72228	−	11.8476i	0.315261	−	0.483678i
$601$	17.5729			0.716814			0.358407	−	0.933565i	$-0.383320\pi$
$601$	17.5729			0.716814			0.358407	+	0.933565i	$0.383320\pi$
$602$	15.5182	+	20.1575i	0.632474	+	0.821558i
$603$	−10.2139	−	10.2139i	−0.415942	−	0.415942i
$604$	3.16190	−	27.3954i	0.128656	−	1.11470i
$605$	−8.46391	−	43.9951i	−0.344107	−	1.78866i
$606$	−13.2540	−	14.8717i	−0.538407	−	0.604122i
$607$	−43.1013	+	11.5490i	−1.74943	+	0.468758i	−0.984504	−	0.175362i	$-0.943890\pi$
$607$	−43.1013	+	11.5490i	−1.74943	+	0.468758i	−0.764924	+	0.644120i	$0.777224\pi$
$608$	5.94243	+	24.6750i	0.240998	+	1.00070i
$609$	−4.31064	+	3.73171i	−0.174676	+	0.151217i
$610$	28.2075	−	21.7210i	1.14209	−	0.879457i
$611$	3.88216	−	6.72410i	0.157055	−	0.272028i
$612$	−0.732115	+	0.108321i	−0.0295940	+	0.00437863i
$613$	39.1507	+	10.4904i	1.58128	+	0.423703i	0.939323	−	0.343035i	$-0.111455\pi$
$613$	39.1507	+	10.4904i	1.58128	+	0.423703i	0.641960	+	0.766738i	$0.278121\pi$
$614$	−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	$0.187977\pi$
$618$	11.6405	−	5.85662i	0.468249	−	0.235588i
$619$	17.8113	−	10.2834i	0.715898	−	0.413324i	−0.0973433	−	0.995251i	$-0.531034\pi$
$619$	17.8113	−	10.2834i	0.715898	−	0.413324i	0.813241	+	0.581927i	$0.197701\pi$
$620$	22.0326	+	32.2914i	0.884849	+	1.29685i
$621$	4.59107	+	2.65066i	0.184233	+	0.106367i
$622$	8.91426	−	13.5749i	0.357429	−	0.544302i
$623$	−4.31163	−	8.88629i	−0.172742	−	0.356022i
$624$	−16.3702	+	17.4524i	−0.655334	+	0.698653i
$625$	−23.9778	−	7.07581i	−0.959110	−	0.283033i
$626$	12.0445	−	10.7343i	0.481393	−	0.429028i
$627$	−24.1436	−	6.46925i	−0.964201	−	0.258357i
$628$	6.02131	+	7.59259i	0.240277	+	0.302977i
$629$	0.570090			0.0227310
$630$	−8.35117	+	0.507923i	−0.332719	+	0.0202361i
$631$			39.2014i			1.56058i	0.625416	+	0.780291i	$0.284929\pi$
$631$			39.2014i			1.56058i	−0.625416	+	0.780291i	$0.715071\pi$
$632$	−2.84398	−	2.37588i	−0.113127	−	0.0945074i
$633$	0.0729425	−	0.272225i	0.00289921	−	0.0108200i
$634$	−5.20593	+	4.63963i	−0.206754	+	0.184263i
$635$	44.9544	+	3.23051i	1.78396	+	0.128199i
$636$	−1.42417	−	3.28851i	−0.0564721	−	0.130398i
$637$	−38.4786	−	16.5195i	−1.52458	−	0.654526i
$638$	14.1918	+	9.31936i	0.561857	+	0.368957i
$639$	5.43188	−	9.40830i	0.214882	−	0.372187i
$640$	16.9781	−	18.7548i	0.671119	−	0.741350i
$641$	−1.84164	−	3.18982i	−0.0727406	−	0.125990i	0.827361	−	0.561671i	$-0.189841\pi$
$641$	−1.84164	−	3.18982i	−0.0727406	−	0.125990i	−0.900101	+	0.435680i	$0.856508\pi$
$642$	−9.78115	+	4.92114i	−0.386031	+	0.194222i
$643$	−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
$647$	−7.67253	+	28.6343i	−0.301638	+	1.12573i	0.634162	+	0.773200i	$0.281345\pi$
$647$	−7.67253	+	28.6343i	−0.301638	+	1.12573i	−0.935801	+	0.352530i	$0.885322\pi$
$648$	2.65575	−	0.973145i	0.104328	−	0.0382288i
$649$	16.2240	+	9.36694i	0.636848	+	0.367684i
$650$	37.8515	+	18.8824i	1.48466	+	0.740628i
$651$	7.57417	−	21.8515i	0.296855	−	0.856429i
$652$	−1.96774	+	4.97407i	−0.0770628	+	0.194800i
$653$	−8.32776	−	31.0796i	−0.325890	−	1.21624i	−0.913414	−	0.407032i	$-0.866564\pi$
$653$	−8.32776	−	31.0796i	−0.325890	−	1.21624i	0.587523	−	0.809207i	$-0.300103\pi$
$654$	−5.30899	+	4.73149i	−0.207598	+	0.185016i
$655$	0.991009	+	5.15123i	0.0387219	+	0.201275i
$656$	7.50790	+	24.8165i	0.293134	+	0.968923i
$657$	−5.19100	+	5.19100i	−0.202520	+	0.202520i
$658$	4.81383	−	0.641515i	0.187663	−	0.0250089i
$659$			45.5239i			1.77336i	0.462382	+	0.886681i	$0.346995\pi$
$659$			45.5239i			1.77336i	−0.462382	+	0.886681i	$0.653005\pi$
$660$	8.23695	+	23.5133i	0.320623	+	0.915252i
$661$	27.4916	−	15.8723i	1.06930	−	0.617360i	0.141309	−	0.989966i	$-0.454869\pi$
$661$	27.4916	−	15.8723i	1.06930	−	0.617360i	0.927990	+	0.372606i	$0.121536\pi$
$662$	0.480041	−	8.34601i	0.0186573	−	0.324377i
$663$	−0.572931	−	2.13821i	−0.0222508	−	0.0830411i
$664$	22.2601	−	15.6588i	0.863861	−	0.607680i
$665$	−24.3920	−	10.4684i	−0.945883	−	0.405946i
$666$	−2.13342	+	0.442125i	−0.0826682	+	0.0171320i
$667$	−2.95679	−	11.0349i	−0.114488	−	0.427273i
$668$	−37.8626	+	5.60203i	−1.46495	+	0.216749i
$669$	−0.467621	−	0.809943i	−0.0180793	−	0.0313142i
$670$	−27.7451	+	36.2862i	−1.07189	+	1.40186i
$671$			62.7193i			2.42125i
$672$	−14.8958	−	1.45444i	−0.574618	−	0.0561062i
$673$	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
$675$	−2.99368	−	4.00474i	−0.115227	−	0.154142i
$676$	−36.5931	−	27.1603i	−1.40743	−	1.04463i
$677$	−7.10904	+	1.90486i	−0.273223	+	0.0732098i	−0.392829	−	0.919612i	$-0.628504\pi$
$677$	−7.10904	+	1.90486i	−0.273223	+	0.0732098i	0.119606	+	0.992821i	$0.461837\pi$
$678$	−2.14085	+	3.26014i	−0.0822188	+	0.125205i
$679$	−19.5301	+	3.75478i	−0.749496	+	0.144095i
$680$	0.645641	+	2.24954i	0.0247592	+	0.0862658i
$681$	−11.0821	+	19.1948i	−0.424668	+	0.735546i
$682$	−68.7545	−	3.95459i	−2.63275	−	0.151429i
$683$	3.89621	−	14.5409i	0.149084	−	0.556391i	−0.850455	−	0.526048i	$-0.823673\pi$
$683$	3.89621	−	14.5409i	0.149084	−	0.556391i	0.999540	−	0.0303430i	$-0.00965997\pi$
$684$	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
$688$	−12.8376	+	23.9746i	−0.489429	+	0.914024i
$689$	9.28284	−	5.35945i	0.353648	−	0.204179i
$690$	6.38894	−	15.4990i	0.243223	−	0.590038i
$691$	20.5402	−	35.5766i	0.781385	−	1.35340i	−0.149750	−	0.988724i	$-0.547847\pi$
$691$	20.5402	−	35.5766i	0.781385	−	1.35340i	0.931135	−	0.364674i	$-0.118820\pi$
$692$	−12.5453	−	4.96293i	−0.476901	−	0.188662i
$693$	8.26721	−	12.2027i	0.314046	−	0.463541i
$694$	−23.2896	+	4.82648i	−0.884061	+	0.183211i
$695$	28.7098	+	33.1556i	1.08903	+	1.25766i
$696$	−5.52969	−	2.56394i	−0.209602	−	0.0971859i
$697$	−2.31683	−	0.620793i	−0.0877562	−	0.0235142i
$698$	−0.903128	+	0.454386i	−0.0341839	+	0.0171988i
$699$			0.0112981i			0.000427332i
$700$	5.08381	+	25.9645i	0.192150	+	0.981366i
$701$		−	34.1172i		−	1.28859i	−0.764777	−	0.644295i	$-0.777151\pi$
$701$		−	34.1172i		−	1.28859i	0.764777	−	0.644295i	$-0.222849\pi$
$702$	3.80230	+	7.55736i	0.143509	+	0.285234i
$703$	−6.67668	−	1.78901i	−0.251816	−	0.0674738i
$704$	7.92959	+	43.8569i	0.298858	+	1.65292i
$705$	1.89982	+	2.19402i	0.0715515	+	0.0826314i
$706$	−0.437436	−	2.11079i	−0.0164631	−	0.0794408i
$707$	37.1721	+	2.67583i	1.39800	+	0.100635i
$708$	−6.25391	−	2.47405i	−0.235036	−	0.0929805i
$709$	0.746144	−	1.29236i	0.0280220	−	0.0485356i	−0.851674	−	0.524071i	$-0.824412\pi$
$709$	0.746144	−	1.29236i	0.0280220	−	0.0485356i	0.879696	+	0.475536i	$0.157746\pi$
$710$	−31.7616	−	13.0926i	−1.19199	−	0.491357i
$711$	−1.13467	+	0.655100i	−0.0425533	+	0.0245682i
$712$	6.76964	−	8.10339i	0.253703	−	0.303687i
$713$	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
$717$	2.67172	−	9.97101i	0.0997774	−	0.372374i
$718$	1.30507	−	22.6900i	0.0487049	−	0.846784i
$719$	−4.78565	+	8.28900i	−0.178475	+	0.309127i	−0.941358	−	0.337409i	$-0.890450\pi$
$719$	−4.78565	+	8.28900i	−0.178475	+	0.309127i	0.762884	+	0.646536i	$0.223783\pi$
$720$	−4.16073	−	7.91759i	−0.155061	−	0.295071i
$721$	−7.98398	+	23.0338i	−0.297339	+	0.857825i
$722$	1.33610	+	0.877380i	0.0497243	+	0.0326527i
$723$	9.93770	−	2.66280i	0.369587	−	0.0990305i
$724$	31.0126	+	23.0183i	1.15257	+	0.855469i
$725$	−1.54065	+	10.6641i	−0.0572182	+	0.396056i
$726$	−26.9034	−	8.89323i	−0.998480	−	0.330059i
$727$	5.91197	+	5.91197i	0.219263	+	0.219263i	0.808188	−	0.588925i	$-0.200449\pi$
$727$	5.91197	+	5.91197i	0.219263	+	0.219263i	−0.588925	+	0.808188i	$0.700449\pi$
$728$	−0.786765	−	44.7591i	−0.0291595	−	1.65888i
$729$		−	1.00000i		−	0.0370370i
$730$	18.4417	+	14.1009i	0.682558	+	0.521896i
$731$	−1.25793	−	2.17880i	−0.0465262	−	0.0805858i
$732$	−3.29557	−	22.2739i	−0.121808	−	0.823266i
$733$	−3.12580	−	11.6657i	−0.115454	−	0.430881i	0.883866	−	0.467740i	$-0.154932\pi$
$733$	−3.12580	−	11.6657i	−0.115454	−	0.430881i	−0.999320	+	0.0368587i	$0.988265\pi$
$734$	5.23009	+	25.2371i	0.193046	+	0.931519i
$735$	10.5434	−	11.5688i	0.388899	−	0.426721i
$736$	15.6510	−	25.5807i	0.576902	−	0.942917i
$737$	−20.8274	−	77.7291i	−0.767189	−	2.86319i
$738$	9.15159	+	0.526376i	0.336875	+	0.0193762i
$739$	−0.587739	+	0.339331i	−0.0216203	+	0.0124825i	−0.510771	−	0.859717i	$-0.670640\pi$
$739$	−0.587739	+	0.339331i	−0.0216203	+	0.0124825i	0.489151	+	0.872199i	$0.337307\pi$
$740$	2.27785	+	6.50237i	0.0837355	+	0.239032i
$741$			26.8398i			0.985984i
$742$	6.19812	+	2.55584i	0.227540	+	0.0938280i
$743$	24.0328	−	24.0328i	0.881679	−	0.881679i	−0.112026	−	0.993705i	$-0.535734\pi$
$743$	24.0328	−	24.0328i	0.881679	−	0.881679i	0.993705	+	0.112026i	$0.0357339\pi$
$744$	24.6250	−	2.20827i	0.902796	−	0.0809592i
$745$	7.92141	+	41.1752i	0.290218	+	1.50854i
$746$	13.9312	+	15.6315i	0.510056	+	0.572311i
$747$	−2.49044	−	9.29445i	−0.0911205	−	0.340066i
$748$	−3.83391	−	1.51670i	−0.140182	−	0.0554559i
$749$	6.70871	−	19.3547i	0.245131	−	0.707204i
$750$	−11.3012	+	11.0581i	−0.412662	+	0.403786i
$751$	2.78825	+	1.60979i	0.101745	+	0.0587422i	0.550009	−	0.835159i	$-0.314624\pi$
$751$	2.78825	+	1.60979i	0.101745	+	0.0587422i	−0.448264	+	0.893901i	$0.647958\pi$
$752$	2.73830	+	4.41083i	0.0998554	+	0.160847i
$753$	0.286331	−	1.06860i	0.0104345	−	0.0389420i
$754$	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	0.930911	−	0.365245i	$-0.119015\pi$
$757$	15.5635	+	15.5635i	0.565666	+	0.565666i	−0.365245	+	0.930911i	$0.619015\pi$
$758$	−13.6051	−	27.0412i	−0.494159	−	0.982179i
$759$	14.7668	+	25.5768i	0.536001	+	0.928380i
$760$	−0.502182	−	28.3718i	−0.0182161	−	1.02915i
$761$	−20.2867	+	35.1375i	−0.735391	+	1.27373i	0.219161	+	0.975689i	$0.429668\pi$
$761$	−20.2867	+	35.1375i	−0.735391	+	1.27373i	−0.954552	+	0.298046i	$0.903665\pi$
$762$	15.6465	−	23.8269i	0.566814	−	0.863158i
$763$	0.955233	−	13.2699i	0.0345818	−	0.480404i
$764$	−25.3863	+	10.9942i	−0.918445	+	0.397756i
$765$	0.825313	+	0.0593086i	0.0298392	+	0.00214431i
$766$	17.3797	+	19.5010i	0.627956	+	0.704601i
$767$	5.20649	−	19.4309i	0.187995	−	0.701608i
$768$	−5.12053	−	15.1585i	−0.184771	−	0.546985i
$769$			7.68776i			0.277228i	0.990347	+	0.138614i	$0.0442647\pi$
$769$			7.68776i			0.277228i	−0.990347	+	0.138614i	$0.955735\pi$
$770$	−41.7061	−	20.8116i	−1.50298	−	0.749999i
$771$	−20.3722			−0.733688
$772$	23.9543	+	30.2052i	0.862132	+	1.08711i
$773$	11.7703	+	3.15384i	0.423348	+	0.113436i	0.464202	−	0.885729i	$-0.346341\pi$
$773$	11.7703	+	3.15384i	0.423348	+	0.113436i	−0.0408542	+	0.999165i	$0.513008\pi$
$774$	6.39721	+	7.17802i	0.229943	+	0.258009i
$775$	−16.2164	−	40.5862i	−0.582509	−	1.45790i
$776$	−12.2325	−	17.3894i	−0.439122	−	0.624243i
$777$	2.28622	−	3.37453i	0.0820177	−	0.121061i
$778$	−28.6105	−	18.7878i	−1.02574	−	0.673575i
$779$	25.1857	+	14.5410i	0.902371	+	0.520984i
$780$	22.0989	−	15.0782i	0.791267	−	0.539885i
$781$	52.4136	−	30.2610i	1.87551	−	1.08282i
$782$	1.24689	+	2.47828i	0.0445886	+	0.0886233i
$783$	−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
$787$	3.73852	+	1.00173i	0.133264	+	0.0357079i	0.324834	−	0.945771i	$-0.394691\pi$
$787$	3.73852	+	1.00173i	0.133264	+	0.0357079i	−0.191571	+	0.981479i	$0.561358\pi$
$788$	−24.8420	+	3.67553i	−0.884958	+	0.130936i
$789$	−8.12949	+	14.0807i	−0.289418	+	0.501286i
$790$	2.52784	+	3.28273i	0.0899365	+	0.116794i
$791$	−1.37760	−	7.16542i	−0.0489817	−	0.254773i
$792$	15.5237	+	2.70252i	0.551610	+	0.0960297i
$793$	65.0528	−	17.4308i	2.31009	−	0.618987i
$794$	−4.57188	+	4.07456i	−0.162250	+	0.144601i
$795$	0.756930	+	3.93450i	0.0268455	+	0.139542i
$796$	−26.1532	−	3.01852i	−0.926977	−	0.106989i
$797$	13.1189	+	13.1189i	0.464694	+	0.464694i	0.900191	−	0.435496i	$-0.143427\pi$
$797$	13.1189	+	13.1189i	0.464694	+	0.464694i	−0.435496	+	0.900191i	$0.643427\pi$
$798$	−13.3023	+	10.2407i	−0.470896	+	0.362518i
$799$	−0.480288			−0.0169914
$800$	−23.0782	+	16.3523i	−0.815936	+	0.578142i
$801$	−1.86659	−	3.23303i	−0.0659527	−	0.114233i
$802$	−2.17895	+	37.8833i	−0.0769414	+	1.33770i
$803$	−39.5042	+	10.5851i	−1.39407	+	0.373541i
$804$	11.4808	+	26.5100i	0.404898	+	0.934936i
$805$	11.6331	+	29.1257i	0.410015	+	1.02655i
$806$	15.0064	+	72.4116i	0.528579	+	2.55059i
$807$	4.75828	−	1.27498i	0.167499	−	0.0448813i
$808$	13.7078	+	37.4091i	0.482239	+	1.31605i
$809$	37.5240	−	21.6645i	1.31927	−	0.761683i	0.335662	−	0.941983i	$-0.391040\pi$
$809$	37.5240	−	21.6645i	1.31927	−	0.761683i	0.983612	+	0.180300i	$0.0577067\pi$
$810$	−3.13451	+	0.418111i	−0.110136	+	0.0146909i
$811$	37.8178			1.32796			0.663981	−	0.747749i	$-0.268865\pi$
$811$	37.8178			1.32796			0.663981	+	0.747749i	$0.268865\pi$
$812$	10.7623	−	3.76866i	0.377682	−	0.132254i
$813$	7.73229	−	7.73229i	0.271183	−	0.271183i
$814$	−11.5245	−	3.80954i	−0.403933	−	0.133524i
$815$	3.35381	−	4.95164i	0.117479	−	0.173448i
$816$	1.44125	+	0.337182i	0.0504540	+	0.0118037i
$817$	7.89506	+	29.4648i	0.276213	+	1.03084i
$818$	−10.8107	+	16.4628i	−0.377987	+	0.575608i
$819$	−14.9543	−	5.18345i	−0.522545	−	0.181125i
$820$	−2.17644	−	28.9059i	−0.0760047	−	1.00944i
$821$	32.9300	+	19.0121i	1.14926	+	0.663528i	0.948708	−	0.316154i	$-0.102392\pi$
$821$	32.9300	+	19.0121i	1.14926	+	0.663528i	0.200557	+	0.979682i	$0.435725\pi$
$822$	0.351580	−	6.11257i	0.0122628	−	0.213200i
$823$	6.34518	+	1.70018i	0.221179	+	0.0592647i	0.367707	−	0.929942i	$-0.380143\pi$
$823$	6.34518	+	1.70018i	0.221179	+	0.0592647i	−0.146528	+	0.989207i	$0.546810\pi$
$824$	−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	$0.312531\pi$
$828$	−6.58815	−	8.30734i	−0.228954	−	0.288700i
$829$	14.2927	+	24.7556i	0.496405	+	0.859798i	0.999991	−	0.00414644i	$-0.00131986\pi$
$829$	14.2927	+	24.7556i	0.496405	+	0.859798i	−0.503587	+	0.863945i	$0.667987\pi$
$830$	−28.0923	+	11.6924i	−0.975099	+	0.405850i
$831$	9.73753	+	5.62196i	0.337791	+	0.195024i
$832$	43.2848	−	20.4133i	1.50063	−	0.707702i
$833$	0.305146	+	2.57226i	0.0105727	+	0.0891236i
$834$	27.1613	−	5.62884i	0.940518	−	0.194911i
$835$	42.6825	+	3.06725i	1.47709	+	0.106146i
$836$	40.1417	+	29.7942i	1.38833	+	1.03045i
$837$	2.26238	−	8.44333i	0.0781995	−	0.291844i
$838$	−1.07838	−	2.14335i	−0.0372519	−	0.0740410i
$839$	38.6351			1.33383			0.666916	−	0.745133i	$-0.267614\pi$
$839$	38.6351			1.33383			0.666916	+	0.745133i	$0.267614\pi$
$840$	15.9049	+	5.19952i	0.548770	+	0.179401i
$841$	−24.3561			−0.839865
$842$	6.87035	+	13.6554i	0.236768	+	0.470595i
$843$	3.35132	−	12.5073i	0.115426	−	0.430775i
$844$	−0.335938	+	0.452609i	−0.0115635	+	0.0155794i
$845$	33.3522	+	38.5169i	1.14735	+	1.32502i
$846$	1.79735	−	0.372479i	0.0617942	−	0.0128061i
$847$	47.6928	−	23.1406i	1.63875	−	0.795120i
$848$	0.229190	+	7.16364i	0.00787043	+	0.246000i
$849$	19.9556	+	11.5214i	0.684875	+	0.395413i
$850$	−0.159169	−	2.61175i	−0.00545944	−	0.0895823i
$851$	4.08362	+	7.07303i	0.139985	+	0.242460i
$852$	−17.0239	+	13.5008i	−0.583229	+	0.462531i
$853$	4.38108	−	4.38108i	0.150005	−	0.150005i	−0.628115	−	0.778120i	$-0.716173\pi$
$853$	4.38108	−	4.38108i	0.150005	−	0.150005i	0.778120	+	0.628115i	$0.216173\pi$
$854$	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
$857$	25.6762	+	6.87991i	0.877082	+	0.235013i	0.669148	−	0.743129i	$-0.266659\pi$
$857$	25.6762	+	6.87991i	0.877082	+	0.235013i	0.207934	+	0.978143i	$0.433326\pi$
$858$	−2.70636	+	47.0527i	−0.0923935	+	1.60635i
$859$	−24.4080	−	14.0920i	−0.832791	−	0.480812i	0.0220160	−	0.999758i	$-0.492992\pi$
$859$	−24.4080	−	14.0920i	−0.832791	−	0.480812i	−0.854807	+	0.518945i	$0.826325\pi$
$860$	19.8249	−	23.0534i	0.676023	−	0.786113i
$861$	−12.9658	+	11.2245i	−0.441873	+	0.382528i
$862$	−2.34334	+	3.56849i	−0.0798145	+	0.121543i
$863$	8.21769	+	30.6688i	0.279733	+	1.04398i	0.952603	+	0.304218i	$0.0983950\pi$
$863$	8.21769	+	30.6688i	0.279733	+	1.04398i	−0.672869	+	0.739761i	$0.734938\pi$
$864$	−5.65502	−	0.144073i	−0.192388	−	0.00490147i
$865$	12.4887	+	8.45879i	0.424630	+	0.287607i
$866$	−16.0628	−	5.30972i	−0.545835	−	0.180432i
$867$	11.9240	−	11.9240i	0.404960	−	0.404960i
$868$	−30.1628	+	35.0662i	−1.02379	+	1.19022i
$869$	−7.29913			−0.247606
$870$	5.41347	+	4.13924i	0.183534	+	0.140333i
$871$	−74.8327	+	43.2047i	−2.53561	+	1.46394i
$872$	13.3545	−	4.89350i	0.452241	−	0.165715i
$873$	−7.26073	+	1.94551i	−0.245739	+	0.0658455i
$874$	−6.82591	−	32.9376i	−0.230890	−	1.11413i
$875$	0.747633	−	29.5709i	0.0252746	−	0.999681i
$876$	13.4732	−	5.83489i	0.455216	−	0.197143i
$877$	39.1450	−	10.4889i	1.32183	−	0.354184i	0.472169	−	0.881508i	$-0.343471\pi$
$877$	39.1450	−	10.4889i	1.32183	−	0.354184i	0.849664	+	0.527324i	$0.176805\pi$
$878$	0.858006	−	14.9173i	0.0289563	−	0.503435i
$879$	−5.29178	−	9.16563i	−0.178487	−	0.309149i
$880$	1.98046	−	49.7891i	0.0667613	−	1.67839i
$881$	−4.02287			−0.135534			−0.0677669	−	0.997701i	$-0.521587\pi$
$881$	−4.02287			−0.135534			−0.0677669	+	0.997701i	$0.521587\pi$
$882$	−3.13681	−	9.38938i	−0.105622	−	0.316157i
$883$	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
$885$	6.22571	+	4.21675i	0.209275	+	0.141745i
$886$	−31.6013	+	28.1637i	−1.06166	+	0.946179i
$887$	−17.8287	+	4.77718i	−0.598628	+	0.160402i	−0.545394	−	0.838180i	$-0.683620\pi$
$887$	−17.8287	+	4.77718i	−0.598628	+	0.160402i	−0.0532347	+	0.998582i	$0.516953\pi$
$888$	4.29293	+	0.747356i	0.144061	+	0.0250796i
$889$	10.0682	+	52.3689i	0.337678	+	1.75640i
$890$	−9.35353	+	7.20262i	−0.313531	+	0.241432i
$891$	2.78550	−	4.82463i	0.0933177	−	0.161631i
$892$	0.273770	+	1.85034i	0.00916650	+	0.0619540i
$893$	5.62494	+	1.50720i	0.188231	+	0.0504365i
$894$	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
$898$	2.80489	+	5.57494i	0.0936004	+	0.186038i
$899$	−16.3133	+	9.41850i	−0.544080	+	0.314125i
$900$	2.62115	+	9.65037i	0.0873717	+	0.321679i
$901$	−0.574220	−	0.331526i	−0.0191301	−	0.0110447i
$902$	42.6868	+	28.0313i	1.42131	+	0.933340i
$903$	−17.9416	−	1.29152i	−0.597059	−	0.0429792i
$904$	6.38002	−	4.48801i	0.212196	−	0.149269i
$905$	−28.2659	−	32.6430i	−0.939592	−	1.08509i
$906$	12.9741	+	14.5577i	0.431036	+	0.483647i
$907$	−2.53449	−	0.679115i	−0.0841564	−	0.0225496i	0.216495	−	0.976284i	$-0.430537\pi$
$907$	−2.53449	−	0.679115i	−0.0841564	−	0.0225496i	−0.300652	+	0.953734i	$0.597204\pi$
$908$	34.7322	−	27.5444i	1.15263	−	0.914093i
$909$	14.0861			0.467206
$910$	−9.99506	+	49.0417i	−0.331333	+	1.62572i
$911$		−	38.3707i		−	1.27128i	−0.771986	−	0.635639i	$-0.780737\pi$
$911$		−	38.3707i		−	1.27128i	0.771986	−	0.635639i	$-0.219263\pi$
$912$	−15.8213	−	8.47176i	−0.523895	−	0.280528i
$913$	13.8742	−	51.7794i	0.459170	−	1.71365i
$914$	34.9647	+	39.2323i	1.15653	+	1.29769i
$915$	−1.80440	+	25.1093i	−0.0596517	+	0.830087i
$916$	−3.78898	−	8.74900i	−0.125191	−	0.289075i
$917$	−5.58418	+	2.70945i	−0.184406	+	0.0894738i
$918$	0.287252	−	0.437435i	0.00948074	−	0.0144375i
$919$	−27.3963	+	47.4518i	−0.903722	+	1.56529i	−0.0810976	+	0.996706i	$0.525843\pi$
$919$	−27.3963	+	47.4518i	−0.903722	+	1.56529i	−0.822624	+	0.568586i	$0.807491\pi$
$920$	−23.2849	+	24.1240i	−0.767680	+	0.795346i
$921$	−14.6469	−	25.3692i	−0.482631	−	0.835942i
$922$	10.0600	+	19.9950i	0.331308	+	0.658500i
$923$	−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
$927$	−2.38479	+	8.90017i	−0.0783269	+	0.292320i
$928$	8.39755	+	8.83663i	0.275663	+	0.290077i
$929$	33.4605	+	19.3184i	1.09780	+	0.633817i	0.935643	−	0.352948i	$-0.114821\pi$
$929$	33.4605	+	19.3184i	1.09780	+	0.633817i	0.162160	+	0.986764i	$0.448154\pi$
$930$	−27.4117	−	3.56123i	−0.898865	−	0.116777i
$931$	4.49830	−	31.0829i	0.147426	−	1.01870i
$932$	0.00831224	−	0.0210117i	0.000272276	−	0.000688262i
$933$	2.97214	+	11.0922i	0.0973036	+	0.363142i
$934$	−31.9102	−	35.8050i	−1.04413	−	1.17158i
$935$	3.81662	+	2.58505i	0.124817	+	0.0845401i
$936$	−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	$0.997920\pi$
$938$	−49.9655	−	20.6037i	−1.63143	−	0.672735i
$939$			11.4082i			0.372292i
$940$	−1.91903	−	5.47809i	−0.0625920	−	0.178676i
$941$	−44.6989	+	25.8069i	−1.45714	+	0.841282i	−0.998870	−	0.0475297i	$-0.984865\pi$
$941$	−44.6989	+	25.8069i	−1.45714	+	0.841282i	−0.458273	+	0.888812i	$0.651532\pi$
$942$	−6.84083	−	0.393467i	−0.222886	−	0.0128199i
$943$	−8.89361	−	33.1914i	−0.289616	−	1.08086i
$944$	9.81057	+	9.20228i	0.319307	+	0.299509i
$945$	3.66080	−	4.64743i	0.119086	−	0.151181i
$946$	10.8698	+	52.4507i	0.353407	+	1.70532i
$947$	0.438657	+	1.63709i	0.0142544	+	0.0531983i	0.972687	−	0.232122i	$-0.0745668\pi$
$947$	0.438657	+	1.63709i	0.0142544	+	0.0531983i	−0.958432	+	0.285320i	$0.907900\pi$
$948$	2.59218	−	0.383531i	0.0841902	−	0.0124565i
$949$	21.9579	+	38.0322i	0.712783	+	1.23458i
$950$	−6.33186	+	31.0873i	−0.205433	+	1.00861i
$951$		−	4.93092i		−	0.159896i
$952$	−2.37345	+	1.42651i	−0.0769239	+	0.0462334i
$953$	−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
$955$	30.3731	−	5.84327i	0.982852	−	0.189084i
$956$	−12.3047	+	16.5781i	−0.397961	+	0.536173i
$957$	−11.5963	+	3.10721i	−0.374854	+	0.100442i
$958$	−22.0577	−	14.4847i	−0.712652	−	0.467980i
$959$	7.49709	+	8.66017i	0.242094	+	0.279652i
$960$	1.91283	+	17.7860i	0.0617362	+	0.574040i
$961$	22.7041	−	39.3247i	0.732392	−	1.26854i
$962$	−0.748417	+	13.0120i	−0.0241299	+	0.419523i
$963$	2.00387	−	7.47856i	0.0645739	−	0.240993i
$964$	−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	0.505494	−	0.862830i	$-0.331310\pi$
$967$	−11.1120	−	11.1120i	−0.357336	−	0.357336i	−0.862830	+	0.505494i	$0.831310\pi$
$968$	43.4910	+	36.3327i	1.39785	+	1.16778i
$969$	1.43783	−	0.830131i	0.0461897	−	0.0266676i
$970$	9.13401	+	21.9454i	0.293276	+	0.704626i
$971$	30.9372	−	53.5848i	0.992822	−	1.71962i	0.392837	−	0.919608i	$-0.371494\pi$
$971$	30.9372	−	53.5848i	0.992822	−	1.71962i	0.599986	−	0.800011i	$-0.295173\pi$
$972$	−0.735722	+	1.85976i	−0.0235983	+	0.0596519i
$973$	−29.1067	+	42.9624i	−0.933117	+	1.37731i
$974$	−5.17665	−	24.9793i	−0.165870	−	0.800387i
$975$	−27.7755	+	11.0978i	−0.889528	+	0.355414i
$976$	−10.2584	+	43.8487i	−0.328364	+	1.40356i
$977$	20.2303	+	5.42070i	0.647226	+	0.173424i	0.567474	−	0.823391i	$-0.307921\pi$
$977$	20.2303	+	5.42070i	0.647226	+	0.173424i	0.0797515	+	0.996815i	$0.474587\pi$
$978$	−1.69999	−	3.37886i	−0.0543597	−	0.108044i
$979$		−	20.7975i		−	0.664692i
$980$	−28.1196	+	13.7582i	−0.898248	+	0.439489i
$981$		−	5.02854i		−	0.160549i
$982$	25.4170	−	12.7879i	0.811089	−	0.408079i
$983$	−32.0901	−	8.59852i	−1.02352	−	0.274250i	−0.292249	−	0.956342i	$-0.594404\pi$
$983$	−32.0901	−	8.59852i	−1.02352	−	0.274250i	−0.731266	+	0.682092i	$0.761070\pi$
$984$	−16.6325	−	7.71196i	−0.530225	−	0.245848i
$985$	28.0043	+	2.01244i	0.892291	+	0.0641218i
$986$	−1.10428	+	0.228848i	−0.0351673	+	0.00728799i
$987$	−1.92609	+	2.84296i	−0.0613080	+	0.0904926i
$988$	19.7466	−	49.9156i	0.628223	−	1.58803i
$989$	18.0214	−	31.2139i	0.573046	−	0.992545i
$990$	−16.2875	−	6.71396i	−0.517651	−	0.213384i
$991$	23.8565	−	13.7735i	0.757826	−	0.437531i	−0.0706886	−	0.997498i	$-0.522520\pi$
$991$	23.8565	−	13.7735i	0.757826	−	0.437531i	0.828515	+	0.559967i	$0.189186\pi$
$992$	−47.4213	−	14.0103i	−1.50563	−	0.444827i
$993$	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
$997$	11.8870	−	44.3628i	0.376464	−	1.40498i	−0.474730	−	0.880132i	$-0.657454\pi$
$997$	11.8870	−	44.3628i	0.376464	−	1.40498i	0.851194	−	0.524852i	$-0.175879\pi$
$998$	13.8839	+	0.798568i	0.439488	+	0.0252782i
$999$	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.163.82	yes	384
5.2	odd	4	inner	840.2.dj.a.667.64	yes	384
7.4	even	3	inner	840.2.dj.a.403.48	yes	384
8.3	odd	2	inner	840.2.dj.a.163.3	yes	384
35.32	odd	12	inner	840.2.dj.a.67.3	✓	384
40.27	even	4	inner	840.2.dj.a.667.48	yes	384
56.11	odd	6	inner	840.2.dj.a.403.64	yes	384
280.67	even	12	inner	840.2.dj.a.67.82	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.3	✓	384	35.32	odd	12	inner
840.2.dj.a.67.82	yes	384	280.67	even	12	inner
840.2.dj.a.163.3	yes	384	8.3	odd	2	inner
840.2.dj.a.163.82	yes	384	1.1	even	1	trivial
840.2.dj.a.403.48	yes	384	7.4	even	3	inner
840.2.dj.a.403.64	yes	384	56.11	odd	6	inner
840.2.dj.a.667.48	yes	384	40.27	even	4	inner
840.2.dj.a.667.64	yes	384	5.2	odd	4	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+(1.26333 - 0.635612i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(1.19199 - 1.60597i) q^{4} +(-1.69040 + 1.46374i) q^{5} +(0.286981 + 1.38479i) q^{6} +(-2.19039 - 1.48397i) q^{7} +(0.485105 - 2.78652i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.20516 + 2.92362i) q^{10} +(-2.78550 - 4.82463i) q^{11} +(1.24274 + 1.56703i) 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} +(0.357434 + 0.0957741i) q^{17} +(-1.41188 - 0.0812078i) q^{18} +(-3.88557 - 2.24334i) q^{19} +(0.335775 + 4.45951i) q^{20} +(2.00032 - 1.73168i) q^{21} +(-6.58559 - 4.32459i) q^{22} +(1.37208 + 5.12067i) q^{23} +(2.56601 + 1.18978i) q^{24} +(0.714927 - 4.94862i) q^{25} +(-2.65523 + 8.03249i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-4.99416 + 1.74882i) q^{28} -2.15497 q^{29} +(-2.51209 - 1.92079i) q^{30} +(7.57009 - 4.37059i) q^{31} +(-3.89683 - 4.10058i) q^{32} +(5.38117 - 1.44188i) q^{33} +(0.512431 - 0.106195i) q^{34} +(5.87480 - 0.697653i) q^{35} +(-1.83528 + 0.794816i) q^{36} +(1.48811 - 0.398738i) q^{37} +(-6.33465 - 0.364353i) q^{38} +(-2.99105 - 5.18066i) q^{39} +(3.25871 + 5.42040i) q^{40} -6.48184 q^{41} +(1.42639 - 3.45911i) q^{42} +(-4.80750 - 4.80750i) q^{43} +(-11.0685 - 1.27749i) q^{44} +(2.19580 - 0.422435i) q^{45} +(4.98815 + 5.59698i) q^{46} +(-1.25370 + 0.335928i) q^{47} +(3.99795 - 0.127909i) q^{48} +(2.59564 + 6.50097i) q^{49} +(-2.24222 - 6.70615i) q^{50} +(-0.185021 + 0.320466i) q^{51} +(1.75112 + 11.8354i) q^{52} +(-1.73077 - 0.463759i) 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} +(-2.72244 + 1.36973i) q^{58} +(-2.91223 + 1.68137i) q^{59} +(-4.39446 - 0.829873i) q^{60} +(-9.74986 - 5.62909i) q^{61} +(6.78550 - 10.3331i) q^{62} +(1.15495 + 2.38036i) q^{63} +(-7.52935 - 2.70350i) q^{64} +(0.958781 - 13.3420i) q^{65} +(5.88171 - 5.24190i) q^{66} +(13.9525 + 3.73855i) q^{67} +(0.579870 - 0.459867i) q^{68} -5.30131 q^{69} +(6.97836 - 4.61546i) q^{70} +10.8638i q^{71} +(-1.81337 + 2.17064i) q^{72} +(1.90004 - 7.09104i) q^{73} +(1.62653 - 1.44960i) q^{74} +(4.59497 + 1.97136i) q^{75} +(-8.23432 + 3.56608i) q^{76} +(-1.05828 + 14.7014i) q^{77} +(-7.07157 - 4.64372i) q^{78} +(0.655100 - 1.13467i) q^{79} +(7.56210 + 4.77647i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-8.18869 + 4.11994i) 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} +(0.557748 - 2.08154i) q^{87} +(-14.7952 + 5.42139i) q^{88} +(3.23303 + 1.86659i) q^{89} +(2.50551 - 1.92935i) q^{90} +(15.5425 - 2.98815i) q^{91} +(9.85917 + 3.90029i) q^{92} +(2.26238 + 8.44333i) q^{93} +(-1.37031 + 1.22125i) q^{94} +(9.85185 - 1.89533i) q^{95} +(4.96943 - 2.70274i) q^{96} +(5.31523 - 5.31523i) q^{97} +(7.41125 + 6.56304i) 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

Related objects

Downloads

Learn more