LMFDB - Embedded newform 85.2.j.c.4.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [85,2,Mod(4,85)] 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("85.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(85, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.2
Root			$-0.803330i$ of defining polynomial
Character	$\chi$	$=$	85.4
Dual form			85.2.j.c.64.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80333 q^{2} +(-0.397180 - 0.397180i) q^{3} +1.25200 q^{4} +(1.45011 + 1.70211i) q^{5} +(0.716248 + 0.716248i) q^{6} +(2.20051 - 2.20051i) q^{7} +1.34889 q^{8} -2.68450i q^{9} +(-2.61503 - 3.06947i) q^{10} +(3.96825 + 3.96825i) q^{11} +(-0.497270 - 0.497270i) q^{12} +1.24880i q^{13} +(-3.96825 + 3.96825i) q^{14} +(0.100090 - 1.25200i) q^{15} -4.93650 q^{16} +(-4.10393 + 0.397180i) q^{17} +4.84103i q^{18} -4.00000i q^{19} +(1.81554 + 2.13104i) q^{20} -1.74800 q^{21} +(-7.15606 - 7.15606i) q^{22} +(1.64598 - 1.64598i) q^{23} +(-0.535753 - 0.535753i) q^{24} +(-0.794361 + 4.93650i) q^{25} -2.25200i q^{26} +(-2.25777 + 2.25777i) q^{27} +(2.75504 - 2.75504i) q^{28} +(-4.68450 + 4.68450i) q^{29} +(-0.180495 + 2.25777i) q^{30} +(3.22025 - 3.22025i) q^{31} +6.20435 q^{32} -3.15222i q^{33} +(7.40074 - 0.716248i) q^{34} +(6.93650 + 0.554530i) q^{35} -3.36099i q^{36} +(1.34889 + 1.34889i) q^{37} +7.21332i q^{38} +(0.495999 - 0.495999i) q^{39} +(1.95604 + 2.29596i) q^{40} +(-4.18850 - 4.18850i) q^{41} +3.15222 q^{42} -2.04316 q^{43} +(4.96825 + 4.96825i) q^{44} +(4.56931 - 3.89281i) q^{45} +(-2.96825 + 2.96825i) q^{46} -4.85546i q^{47} +(1.96068 + 1.96068i) q^{48} -2.68450i q^{49} +(1.43250 - 8.90213i) q^{50} +(1.78775 + 1.47225i) q^{51} +1.56350i q^{52} -9.11674 q^{53} +(4.07151 - 4.07151i) q^{54} +(-1.00000 + 12.5088i) q^{55} +(2.96825 - 2.96825i) q^{56} +(-1.58872 + 1.58872i) q^{57} +(8.44769 - 8.44769i) q^{58} +6.00000i q^{59} +(0.125312 - 1.56750i) q^{60} +(-4.00000 - 4.00000i) q^{61} +(-5.80717 + 5.80717i) q^{62} +(-5.90726 - 5.90726i) q^{63} -1.31550 q^{64} +(-2.12560 + 1.81090i) q^{65} +5.68450i q^{66} +8.46212i q^{67} +(-5.13812 + 0.497270i) q^{68} -1.30750 q^{69} +(-12.5088 - 1.00000i) q^{70} +(-6.22025 + 6.22025i) q^{71} -3.62109i q^{72} +(-1.10906 - 1.10906i) q^{73} +(-2.43250 - 2.43250i) q^{74} +(2.27618 - 1.64517i) q^{75} -5.00800i q^{76} +17.4643 q^{77} +(-0.894450 + 0.894450i) q^{78} +(-3.47225 - 3.47225i) q^{79} +(-7.15846 - 8.40246i) q^{80} -6.26000 q^{81} +(7.55324 + 7.55324i) q^{82} +3.94658 q^{83} -2.18850 q^{84} +(-6.62720 - 6.40939i) q^{85} +3.68450 q^{86} +3.72118 q^{87} +(5.35273 + 5.35273i) q^{88} -10.6130 q^{89} +(-8.23997 + 7.02003i) q^{90} +(2.74800 + 2.74800i) q^{91} +(2.06077 - 2.06077i) q^{92} -2.55804 q^{93} +8.75600i q^{94} +(6.80844 - 5.80044i) q^{95} +(-2.46425 - 2.46425i) q^{96} +(8.76239 + 8.76239i) q^{97} +4.84103i q^{98} +(10.6527 - 10.6527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.80333			−1.27515			−0.637574	−	0.770389i	$-0.720062\pi$
$2$	−1.80333			−1.27515			−0.637574	+	0.770389i	$0.720062\pi$
$3$	−0.397180	−	0.397180i	−0.229312	−	0.229312i	0.583093	−	0.812405i	$-0.301842\pi$
$3$	−0.397180	−	0.397180i	−0.229312	−	0.229312i	−0.812405	+	0.583093i	$0.801842\pi$
$4$	1.25200			0.626000
$5$	1.45011	+	1.70211i	0.648509	+	0.761207i
$5$	1.45011	+	1.70211i	0.648509	+	0.761207i
$6$	0.716248	+	0.716248i	0.292407	+	0.292407i
$7$	2.20051	−	2.20051i	0.831715	−	0.831715i	−0.156036	−	0.987751i	$-0.549872\pi$
$7$	2.20051	−	2.20051i	0.831715	−	0.831715i	0.987751	+	0.156036i	$0.0498717\pi$
$8$	1.34889			0.476905
$9$		−	2.68450i		−	0.894832i
$10$	−2.61503	−	3.06947i	−0.826944	−	0.970651i
$11$	3.96825	+	3.96825i	1.19647	+	1.19647i	0.975216	+	0.221256i	$0.0710156\pi$
$11$	3.96825	+	3.96825i	1.19647	+	1.19647i	0.221256	+	0.975216i	$0.428984\pi$
$12$	−0.497270	−	0.497270i	−0.143549	−	0.143549i
$13$			1.24880i			0.346355i	0.984891	+	0.173178i	$0.0554034\pi$
$13$			1.24880i			0.346355i	−0.984891	+	0.173178i	$0.944597\pi$
$14$	−3.96825	+	3.96825i	−1.06056	+	1.06056i
$15$	0.100090	−	1.25200i	0.0258430	−	0.323265i
$16$	−4.93650			−1.23412
$17$	−4.10393	+	0.397180i	−0.995349	+	0.0963304i
$17$	−4.10393	+	0.397180i	−0.995349	+	0.0963304i
$18$			4.84103i			1.14104i
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	1.81554	+	2.13104i	0.405967	+	0.476516i
$21$	−1.74800			−0.381445
$22$	−7.15606	−	7.15606i	−1.52568	−	1.52568i
$23$	1.64598	−	1.64598i	0.343211	−	0.343211i	−0.514362	−	0.857573i	$-0.671971\pi$
$23$	1.64598	−	1.64598i	0.343211	−	0.343211i	0.857573	+	0.514362i	$0.171971\pi$
$24$	−0.535753	−	0.535753i	−0.109360	−	0.109360i
$25$	−0.794361	+	4.93650i	−0.158872	+	0.987299i
$26$		−	2.25200i		−	0.441654i
$27$	−2.25777	+	2.25777i	−0.434508	+	0.434508i
$28$	2.75504	−	2.75504i	0.520654	−	0.520654i
$29$	−4.68450	+	4.68450i	−0.869889	+	0.869889i	−0.992460	−	0.122571i	$-0.960886\pi$
$29$	−4.68450	+	4.68450i	−0.869889	+	0.869889i	0.122571	+	0.992460i	$0.460886\pi$
$30$	−0.180495	+	2.25777i	−0.0329537	+	0.412211i
$31$	3.22025	−	3.22025i	0.578374	−	0.578374i	−0.356081	−	0.934455i	$-0.615887\pi$
$31$	3.22025	−	3.22025i	0.578374	−	0.578374i	0.934455	+	0.356081i	$0.115887\pi$
$32$	6.20435			1.09678
$33$		−	3.15222i		−	0.548731i
$34$	7.40074	−	0.716248i	1.26922	−	0.122835i
$35$	6.93650	+	0.554530i	1.17248	+	0.0937326i
$36$		−	3.36099i		−	0.560165i
$37$	1.34889	+	1.34889i	0.221756	+	0.221756i	0.809238	−	0.587481i	$-0.199880\pi$
$37$	1.34889	+	1.34889i	0.221756	+	0.221756i	−0.587481	+	0.809238i	$0.699880\pi$
$38$			7.21332i			1.17016i
$39$	0.495999	−	0.495999i	0.0794234	−	0.0794234i
$40$	1.95604	+	2.29596i	0.309277	+	0.363023i
$41$	−4.18850	−	4.18850i	−0.654133	−	0.654133i	0.299852	−	0.953986i	$-0.403063\pi$
$41$	−4.18850	−	4.18850i	−0.654133	−	0.654133i	−0.953986	+	0.299852i	$0.903063\pi$
$42$	3.15222			0.486398
$43$	−2.04316			−0.311579			−0.155790	−	0.987790i	$-0.549792\pi$
$43$	−2.04316			−0.311579			−0.155790	+	0.987790i	$0.549792\pi$
$44$	4.96825	+	4.96825i	0.748992	+	0.748992i
$45$	4.56931	−	3.89281i	0.681152	−	0.580306i
$46$	−2.96825	+	2.96825i	−0.437644	+	0.437644i
$47$		−	4.85546i		−	0.708242i	−0.935200	−	0.354121i	$-0.884780\pi$
$47$		−	4.85546i		−	0.708242i	0.935200	−	0.354121i	$-0.115220\pi$
$48$	1.96068	+	1.96068i	0.283000	+	0.283000i
$49$		−	2.68450i		−	0.383499i
$50$	1.43250	−	8.90213i	0.202585	−	1.25895i
$51$	1.78775	+	1.47225i	0.250336	+	0.206156i
$52$			1.56350i			0.216818i
$53$	−9.11674			−1.25228			−0.626140	−	0.779710i	$-0.715366\pi$
$53$	−9.11674			−1.25228			−0.626140	+	0.779710i	$0.715366\pi$
$54$	4.07151	−	4.07151i	0.554062	−	0.554062i
$55$	−1.00000	+	12.5088i	−0.134840	+	1.68669i
$56$	2.96825	−	2.96825i	0.396649	−	0.396649i
$57$	−1.58872	+	1.58872i	−0.210431	+	0.210431i
$58$	8.44769	−	8.44769i	1.10924	−	1.10924i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$	0.125312	−	1.56750i	0.0161777	−	0.202364i
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	0.403036	−	0.915184i	$-0.367955\pi$
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	−0.915184	+	0.403036i	$0.867955\pi$
$62$	−5.80717	+	5.80717i	−0.737512	+	0.737512i
$63$	−5.90726	−	5.90726i	−0.744245	−	0.744245i
$64$	−1.31550			−0.164438
$65$	−2.12560	+	1.81090i	−0.263648	+	0.224614i
$66$			5.68450i			0.699713i
$67$			8.46212i			1.03381i	0.856042	+	0.516906i	$0.172916\pi$
$67$			8.46212i			1.03381i	−0.856042	+	0.516906i	$0.827084\pi$
$68$	−5.13812	+	0.497270i	−0.623089	+	0.0603029i
$69$	−1.30750			−0.157405
$70$	−12.5088	−	1.00000i	−1.49509	−	0.119523i
$71$	−6.22025	+	6.22025i	−0.738208	+	0.738208i	−0.972231	−	0.234023i	$-0.924811\pi$
$71$	−6.22025	+	6.22025i	−0.738208	+	0.738208i	0.234023	+	0.972231i	$0.424811\pi$
$72$		−	3.62109i		−	0.426750i
$73$	−1.10906	−	1.10906i	−0.129806	−	0.129806i	0.639219	−	0.769025i	$-0.279258\pi$
$73$	−1.10906	−	1.10906i	−0.129806	−	0.129806i	−0.769025	+	0.639219i	$0.779258\pi$
$74$	−2.43250	−	2.43250i	−0.282772	−	0.282772i
$75$	2.27618	−	1.64517i	0.262831	−	0.189968i
$76$		−	5.00800i		−	0.574457i
$77$	17.4643			1.99025
$78$	−0.894450	+	0.894450i	−0.101277	+	0.101277i
$79$	−3.47225	−	3.47225i	−0.390658	−	0.390658i	0.484264	−	0.874922i	$-0.339088\pi$
$79$	−3.47225	−	3.47225i	−0.390658	−	0.390658i	−0.874922	+	0.484264i	$0.839088\pi$
$80$	−7.15846	−	8.40246i	−0.800340	−	0.939424i
$81$	−6.26000			−0.695556
$82$	7.55324	+	7.55324i	0.834116	+	0.834116i
$83$	3.94658			0.433194			0.216597	−	0.976261i	$-0.430504\pi$
$83$	3.94658			0.433194			0.216597	+	0.976261i	$0.430504\pi$
$84$	−2.18850			−0.238785
$85$	−6.62720	−	6.40939i	−0.718820	−	0.695196i
$86$	3.68450			0.397309
$87$	3.72118			0.398952
$88$	5.35273	+	5.35273i	0.570603	+	0.570603i
$89$	−10.6130			−1.12497			−0.562487	−	0.826806i	$-0.690155\pi$
$89$	−10.6130			−1.12497			−0.562487	+	0.826806i	$0.690155\pi$
$90$	−8.23997	+	7.02003i	−0.868569	+	0.739976i
$91$	2.74800	+	2.74800i	0.288069	+	0.288069i
$92$	2.06077	−	2.06077i	0.214850	−	0.214850i
$93$	−2.55804			−0.265256
$94$			8.75600i			0.903113i
$95$	6.80844	−	5.80044i	0.698531	−	0.595113i
$96$	−2.46425	−	2.46425i	−0.251506	−	0.251506i
$97$	8.76239	+	8.76239i	0.889686	+	0.889686i	0.994493	−	0.104807i	$-0.0334224\pi$
$97$	8.76239	+	8.76239i	0.889686	+	0.889686i	−0.104807	+	0.994493i	$0.533422\pi$
$98$			4.84103i			0.489018i
$99$	10.6527	−	10.6527i	1.07064	−	1.07064i
$100$	−0.994540	+	6.18049i	−0.0994540	+	0.618049i
$101$	9.62099			0.957324			0.478662	−	0.877999i	$-0.341122\pi$
$101$	9.62099			0.957324			0.478662	+	0.877999i	$0.341122\pi$
$102$	−3.22391	−	2.65495i	−0.319215	−	0.262879i
$103$			1.84298i			0.181594i	0.995869	+	0.0907972i	$0.0289415\pi$
$103$			1.84298i			0.181594i	−0.995869	+	0.0907972i	$0.971058\pi$
$104$			1.68450i			0.165178i
$105$	−2.53479	−	2.97529i	−0.247370	−	0.290358i
$106$	16.4405			1.59684
$107$	−12.0115	−	12.0115i	−1.16120	−	1.16120i	−0.984214	−	0.176984i	$-0.943366\pi$
$107$	−12.0115	−	12.0115i	−1.16120	−	1.16120i	−0.176984	−	0.984214i	$-0.556634\pi$
$108$	−2.82673	+	2.82673i	−0.272002	+	0.272002i
$109$	−0.315505	−	0.315505i	−0.0302199	−	0.0302199i	0.691835	−	0.722055i	$-0.256802\pi$
$109$	−0.315505	−	0.315505i	−0.0302199	−	0.0302199i	−0.722055	+	0.691835i	$0.756802\pi$
$110$	1.80333	−	22.5575i	0.171941	−	2.15077i
$111$		−	1.07151i		−	0.101703i
$112$	−10.8628	+	10.8628i	−1.02644	+	1.02644i
$113$	8.00768	−	8.00768i	0.753299	−	0.753299i	−0.221794	−	0.975094i	$-0.571191\pi$
$113$	8.00768	−	8.00768i	0.753299	−	0.753299i	0.975094	+	0.221794i	$0.0711913\pi$
$114$	2.86499	−	2.86499i	0.268331	−	0.268331i
$115$	5.18850	+	0.414788i	0.483830	+	0.0386792i
$116$	−5.86499	+	5.86499i	−0.544551	+	0.544551i
$117$	3.35240			0.309929
$118$		−	10.8200i		−	0.996060i
$119$	−8.15674	+	9.90474i	−0.747728	+	0.907966i
$120$	0.135010	−	1.68881i	0.0123247	−	0.154167i
$121$			20.4940i			1.86309i
$122$	7.21332	+	7.21332i	0.653063	+	0.653063i
$123$			3.32718i			0.300001i
$124$	4.03175	−	4.03175i	0.362062	−	0.362062i
$125$	−9.55437	+	5.80637i	−0.854569	+	0.519338i
$126$	10.6527	+	10.6527i	0.949022	+	0.949022i
$127$	−5.85000			−0.519104			−0.259552	−	0.965729i	$-0.583575\pi$
$127$	−5.85000			−0.519104			−0.259552	+	0.965729i	$0.583575\pi$
$128$	−10.0364			−0.887102
$129$	0.811504	+	0.811504i	0.0714489	+	0.0714489i
$130$	3.83315	−	3.26565i	0.336190	−	0.286416i
$131$	13.8332	−	13.8332i	1.20862	−	1.20862i	0.237140	−	0.971475i	$-0.423790\pi$
$131$	13.8332	−	13.8332i	1.20862	−	1.20862i	0.971475	−	0.237140i	$-0.0762101\pi$
$132$		−	3.94658i		−	0.343506i
$133$	−8.80204	−	8.80204i	−0.763234	−	0.763234i
$134$		−	15.2600i		−	1.31826i
$135$	−7.11699	−	0.568959i	−0.612533	−	0.0489682i
$136$	−5.53575	+	0.535753i	−0.474687	+	0.0459404i
$137$			13.8577i			1.18394i	0.805959	+	0.591971i	$0.201650\pi$
$137$			13.8577i			1.18394i	−0.805959	+	0.591971i	$0.798350\pi$
$138$	2.35786			0.200714
$139$	7.21225	−	7.21225i	0.611735	−	0.611735i	−0.331663	−	0.943398i	$-0.607610\pi$
$139$	7.21225	−	7.21225i	0.611735	−	0.611735i	0.943398	+	0.331663i	$0.107610\pi$
$140$	8.68450	+	0.694271i	0.733974	+	0.0586766i
$141$	−1.92849	+	1.92849i	−0.162409	+	0.162409i
$142$	11.2172	−	11.2172i	0.941323	−	0.941323i
$143$	−4.95555	+	4.95555i	−0.414404	+	0.414404i
$144$			13.2520i			1.10433i
$145$	−14.7666	−	1.18049i	−1.22630	−	0.0980347i
$146$	2.00000	+	2.00000i	0.165521	+	0.165521i
$147$	−1.06623	+	1.06623i	−0.0879411	+	0.0879411i
$148$	1.68881	+	1.68881i	0.138819	+	0.138819i
$149$	15.9365			1.30557			0.652784	−	0.757544i	$-0.273601\pi$
$149$	15.9365			1.30557			0.652784	+	0.757544i	$0.273601\pi$
$150$	−4.10471	+	2.96679i	−0.335148	+	0.242238i
$151$		−	3.36899i		−	0.274165i	−0.990560	−	0.137082i	$-0.956228\pi$
$151$		−	3.36899i		−	0.274165i	0.990560	−	0.137082i	$-0.0437725\pi$
$152$		−	5.39556i		−	0.437638i
$153$	1.06623	+	11.0170i	0.0861995	+	0.890670i
$154$	−31.4940			−2.53786
$155$	10.1509	+	0.811504i	0.815343	+	0.0651816i
$156$	0.620991	−	0.620991i	0.0497191	−	0.0497191i
$157$		−	3.92136i		−	0.312959i	−0.987681	−	0.156479i	$-0.949986\pi$
$157$		−	3.92136i		−	0.312959i	0.987681	−	0.156479i	$-0.0500144\pi$
$158$	6.26161	+	6.26161i	0.498147	+	0.498147i
$159$	3.62099	+	3.62099i	0.287163	+	0.287163i
$160$	8.99699	+	10.5605i	0.711275	+	0.834880i
$161$		−	7.24400i		−	0.570907i
$162$	11.2889			0.886936
$163$	10.4084	−	10.4084i	0.815247	−	0.815247i	−0.170168	−	0.985415i	$-0.554431\pi$
$163$	10.4084	−	10.4084i	0.815247	−	0.815247i	0.985415	+	0.170168i	$0.0544312\pi$
$164$	−5.24400	−	5.24400i	−0.409488	−	0.409488i
$165$	5.36543	−	4.57107i	0.417698	−	0.355857i
$166$	−7.11699			−0.552386
$167$	0.297091	+	0.297091i	0.0229896	+	0.0229896i	0.718508	−	0.695519i	$-0.244825\pi$
$167$	0.297091	+	0.297091i	0.0229896	+	0.0229896i	−0.695519	+	0.718508i	$0.744825\pi$
$168$	−2.35786			−0.181913
$169$	11.4405			0.880038
$170$	11.9510	+	11.5582i	0.916602	+	0.886477i
$171$	−10.7380			−0.821154
$172$	−2.55804			−0.195049
$173$	−11.7397	−	11.7397i	−0.892549	−	0.892549i	0.102213	−	0.994763i	$-0.467408\pi$
$173$	−11.7397	−	11.7397i	−0.892549	−	0.892549i	−0.994763	+	0.102213i	$0.967408\pi$
$174$	−6.71052			−0.508723
$175$	9.11481	+	12.6108i	0.689015	+	0.953288i
$176$	−19.5892	−	19.5892i	−1.47659	−	1.47659i
$177$	2.38308	−	2.38308i	0.179123	−	0.179123i
$178$	19.1387			1.43451
$179$			19.7935i			1.47943i	0.672918	+	0.739717i	$0.265041\pi$
$179$			19.7935i			1.47943i	−0.672918	+	0.739717i	$0.734959\pi$
$180$	5.72078	−	4.87380i	0.426401	−	0.363272i
$181$	−6.62099	−	6.62099i	−0.492134	−	0.492134i	0.416844	−	0.908978i	$-0.363136\pi$
$181$	−6.62099	−	6.62099i	−0.492134	−	0.492134i	−0.908978	+	0.416844i	$0.863136\pi$
$182$	−4.95555	−	4.95555i	−0.367330	−	0.367330i
$183$			3.17744i			0.234883i
$184$	2.22025	−	2.22025i	0.163679	−	0.163679i
$185$	−0.339921	+	4.25200i	−0.0249915	+	0.312613i
$186$	4.61299			0.338241
$187$	−17.8615	−	14.7093i	−1.30616	−	1.07565i
$188$		−	6.07904i		−	0.443360i
$189$			9.93650i			0.722774i
$190$	−12.2779	+	10.4601i	−0.890730	+	0.758856i
$191$	−13.9365			−1.00841			−0.504205	−	0.863584i	$-0.668214\pi$
$191$	−13.9365			−1.00841			−0.504205	+	0.863584i	$0.668214\pi$
$192$	0.522493	+	0.522493i	0.0377077	+	0.0377077i
$193$	2.95204	−	2.95204i	0.212493	−	0.212493i	−0.592833	−	0.805325i	$-0.701991\pi$
$193$	2.95204	−	2.95204i	0.212493	−	0.212493i	0.805325	+	0.592833i	$0.201991\pi$
$194$	−15.8015	−	15.8015i	−1.13448	−	1.13448i
$195$	1.56350	+	0.124992i	0.111964	+	0.00895086i
$196$		−	3.36099i		−	0.240071i
$197$	−12.5088	+	12.5088i	−0.891215	+	0.891215i	−0.994637	−	0.103423i	$-0.967021\pi$
$197$	−12.5088	+	12.5088i	−0.891215	+	0.891215i	0.103423	+	0.994637i	$0.467021\pi$
$198$	−19.2104	+	19.2104i	−1.36522	+	1.36522i
$199$	−3.96025	+	3.96025i	−0.280734	+	0.280734i	−0.833402	−	0.552667i	$-0.813610\pi$
$199$	−3.96025	+	3.96025i	−0.280734	+	0.280734i	0.552667	+	0.833402i	$0.313610\pi$
$200$	−1.07151	+	6.65879i	−0.0757669	+	0.470848i
$201$	3.36099	−	3.36099i	0.237066	−	0.237066i
$202$	−17.3498			−1.22073
$203$			20.6166i			1.44700i
$204$	2.23827	+	1.84326i	0.156710	+	0.129054i
$205$	1.05550	−	13.2031i	0.0737195	−	0.922142i
$206$		−	3.32351i		−	0.231560i
$207$	−4.41863	−	4.41863i	−0.307116	−	0.307116i
$208$		−	6.16470i		−	0.427445i
$209$	15.8730	−	15.8730i	1.09796	−	1.09796i
$210$	4.57107	+	5.36543i	0.315434	+	0.370250i
$211$	0.652743	+	0.652743i	0.0449367	+	0.0449367i	0.729218	−	0.684281i	$-0.239884\pi$
$211$	0.652743	+	0.652743i	0.0449367	+	0.0449367i	−0.684281	+	0.729218i	$0.739884\pi$
$212$	−11.4142			−0.783928
$213$	4.94112			0.338560
$214$	21.6607	+	21.6607i	1.48070	+	1.48070i
$215$	−2.96281	−	3.47769i	−0.202062	−	0.237176i
$216$	−3.04548	+	3.04548i	−0.207219	+	0.207219i
$217$		−	14.1724i		−	0.962084i
$218$	0.568959	+	0.568959i	0.0385348	+	0.0385348i
$219$			0.880993i			0.0595320i
$220$	−1.25200	+	15.6610i	−0.0844098	+	1.05587i
$221$	−0.495999	−	5.12499i	−0.0333645	−	0.344744i
$222$			1.93228i			0.129686i
$223$	1.24880			0.0836259			0.0418129	−	0.999125i	$-0.486687\pi$
$223$	1.24880			0.0836259			0.0418129	+	0.999125i	$0.486687\pi$
$224$	13.6527	−	13.6527i	0.912212	−	0.912212i
$225$	13.2520	+	2.13246i	0.883467	+	0.142164i
$226$	−14.4405	+	14.4405i	−0.960568	+	0.960568i
$227$	8.19025	−	8.19025i	0.543606	−	0.543606i	−0.380978	−	0.924584i	$-0.624413\pi$
$227$	8.19025	−	8.19025i	0.543606	−	0.543606i	0.924584	+	0.380978i	$0.124413\pi$
$228$	−1.98908	+	1.98908i	−0.131730	+	0.131730i
$229$			11.7480i			0.776330i	0.921590	+	0.388165i	$0.126891\pi$
$229$			11.7480i			0.776330i	−0.921590	+	0.388165i	$0.873109\pi$
$230$	−9.35657	−	0.748000i	−0.616954	−	0.0493216i
$231$	−6.93650	−	6.93650i	−0.456388	−	0.456388i
$232$	−6.31887	+	6.31887i	−0.414854	+	0.414854i
$233$	7.99325	+	7.99325i	0.523655	+	0.523655i	0.918673	−	0.395018i	$-0.129262\pi$
$233$	7.99325	+	7.99325i	0.523655	+	0.523655i	−0.395018	+	0.918673i	$0.629262\pi$
$234$	−6.04548			−0.395206
$235$	8.26453	−	7.04095i	0.539119	−	0.459301i
$236$			7.51200i			0.488990i
$237$			2.75822i			0.179166i
$238$	14.7093	−	17.8615i	0.953463	−	1.15779i
$239$	−5.13501			−0.332156			−0.166078	−	0.986113i	$-0.553110\pi$
$239$	−5.13501			−0.332156			−0.166078	+	0.986113i	$0.553110\pi$
$240$	−0.494092	+	6.18049i	−0.0318935	+	0.398949i
$241$	6.00000	−	6.00000i	0.386494	−	0.386494i	−0.486941	−	0.873435i	$-0.661887\pi$
$241$	6.00000	−	6.00000i	0.386494	−	0.386494i	0.873435	+	0.486941i	$0.161887\pi$
$242$		−	36.9574i		−	2.37571i
$243$	9.25966	+	9.25966i	0.594008	+	0.594008i
$244$	−5.00800	−	5.00800i	−0.320604	−	0.320604i
$245$	4.56931	−	3.89281i	0.291922	−	0.248703i
$246$		−	6.00000i		−	0.382546i
$247$	4.99520			0.317837
$248$	4.34376	−	4.34376i	0.275829	−	0.275829i
$249$	−1.56750	−	1.56750i	−0.0993366	−	0.0993366i
$250$	17.2297	−	10.4708i	1.08970	−	0.662232i
$251$	19.8095			1.25036			0.625182	−	0.780479i	$-0.285025\pi$
$251$	19.8095			1.25036			0.625182	+	0.780479i	$0.285025\pi$
$252$	−7.39589	−	7.39589i	−0.465897	−	0.465897i
$253$	13.0633			0.821284
$254$	10.5495			0.661934
$255$	0.0865092	+	5.17788i	0.00541741	+	0.324251i
$256$	20.7300			1.29562
$257$	24.3982			1.52192			0.760958	−	0.648801i	$-0.224729\pi$
$257$	24.3982			1.52192			0.760958	+	0.648801i	$0.224729\pi$
$258$	−1.46341	−	1.46341i	−0.0911079	−	0.0911079i
$259$	5.93650			0.368876
$260$	−2.66125	+	2.26725i	−0.165044	+	0.140609i
$261$	12.5755	+	12.5755i	0.778404	+	0.778404i
$262$	−24.9459	+	24.9459i	−1.54116	+	1.54116i
$263$	−18.0585			−1.11354			−0.556768	−	0.830668i	$-0.687959\pi$
$263$	−18.0585			−1.11354			−0.556768	+	0.830668i	$0.687959\pi$
$264$		−	4.25200i		−	0.261693i
$265$	−13.2203	−	15.5177i	−0.812115	−	0.953245i
$266$	15.8730	+	15.8730i	0.973236	+	0.973236i
$267$	4.21527	+	4.21527i	0.257970	+	0.257970i
$268$			10.5946i			0.647167i
$269$	−12.6290	+	12.6290i	−0.770003	+	0.770003i	−0.978107	−	0.208104i	$-0.933271\pi$
$269$	−12.6290	+	12.6290i	−0.770003	+	0.770003i	0.208104	+	0.978107i	$0.433271\pi$
$270$	12.8343	+	1.02602i	0.781070	+	0.0624417i
$271$	−15.8570			−0.963243			−0.481622	−	0.876379i	$-0.659952\pi$
$271$	−15.8570			−0.963243			−0.481622	+	0.876379i	$0.659952\pi$
$272$	20.2590	−	1.96068i	1.22838	−	0.118884i
$273$		−	2.18290i		−	0.132115i
$274$		−	24.9900i		−	1.50970i
$275$	−22.7415	+	16.4370i	−1.37136	+	0.991190i
$276$	−1.63699			−0.0985355
$277$	10.0256	+	10.0256i	0.602381	+	0.602381i	0.940944	−	0.338563i	$-0.109941\pi$
$277$	10.0256	+	10.0256i	0.602381	+	0.602381i	−0.338563	+	0.940944i	$0.609941\pi$
$278$	−13.0061	+	13.0061i	−0.780052	+	0.780052i
$279$	−8.64474	−	8.64474i	−0.517547	−	0.517547i
$280$	9.35657	+	0.748000i	0.559162	+	0.0447015i
$281$			7.80949i			0.465875i	0.972492	+	0.232937i	$0.0748338\pi$
$281$			7.80949i			0.465875i	−0.972492	+	0.232937i	$0.925166\pi$
$282$	3.47771	−	3.47771i	0.207095	−	0.207095i
$283$	14.7842	−	14.7842i	0.878828	−	0.878828i	−0.114586	−	0.993413i	$-0.536554\pi$
$283$	14.7842	−	14.7842i	0.878828	−	0.878828i	0.993413	+	0.114586i	$0.0365540\pi$
$284$	−7.78775	+	7.78775i	−0.462118	+	0.462118i
$285$	−5.00800	−	0.400358i	−0.296648	−	0.0237152i
$286$	8.93650	−	8.93650i	0.528426	−	0.528426i
$287$	−18.4337			−1.08810
$288$		−	16.6556i		−	0.981438i
$289$	16.6845	−	3.26000i	0.981441	−	0.191765i
$290$	26.6290	+	2.12882i	1.56371	+	0.125009i
$291$		−	6.96050i		−	0.408032i
$292$	−1.38854	−	1.38854i	−0.0812583	−	0.0812583i
$293$			4.79502i			0.280128i	0.990142	+	0.140064i	$0.0447309\pi$
$293$			4.79502i			0.280128i	−0.990142	+	0.140064i	$0.955269\pi$
$294$	1.92276	−	1.92276i	0.112138	−	0.112138i
$295$	−10.2127	+	8.70066i	−0.594604	+	0.506572i
$296$	1.81951	+	1.81951i	0.105757	+	0.105757i
$297$	−17.9188			−1.03975
$298$	−28.7388			−1.66479
$299$	2.05550	+	2.05550i	0.118873	+	0.118873i
$300$	2.84978	−	2.05976i	0.164532	−	0.118920i
$301$	−4.49600	+	4.49600i	−0.259145	+	0.259145i
$302$			6.07540i			0.349600i
$303$	−3.82127	−	3.82127i	−0.219526	−	0.219526i
$304$			19.7460i			1.13251i
$305$	1.00800	−	12.6089i	0.0577180	−	0.721983i
$306$	−1.92276	−	19.8673i	−0.109917	−	1.13574i
$307$		−	24.9924i		−	1.42639i	−0.700966	−	0.713195i	$-0.747247\pi$
$307$		−	24.9924i		−	1.42639i	0.700966	−	0.713195i	$-0.252753\pi$
$308$	21.8654			1.24589
$309$	0.731997	−	0.731997i	0.0416418	−	0.0416418i
$310$	−18.3055	−	1.46341i	−1.03968	−	0.0831161i
$311$	−2.85126	+	2.85126i	−0.161680	+	0.161680i	−0.783311	−	0.621631i	$-0.786471\pi$
$311$	−2.85126	+	2.85126i	−0.161680	+	0.161680i	0.621631	+	0.783311i	$0.286471\pi$
$312$	0.669049	−	0.669049i	0.0378774	−	0.0378774i
$313$	−16.0154	+	16.0154i	−0.905242	+	0.905242i	−0.995884	−	0.0906416i	$-0.971108\pi$
$313$	−16.0154	+	16.0154i	−0.905242	+	0.905242i	0.0906416	+	0.995884i	$0.471108\pi$
$314$			7.07151i			0.399068i
$315$	1.48863	−	18.6210i	0.0838749	−	1.04917i
$316$	−4.34726	−	4.34726i	−0.244552	−	0.244552i
$317$	−5.85000	+	5.85000i	−0.328569	+	0.328569i	−0.852042	−	0.523473i	$-0.824636\pi$
$317$	−5.85000	+	5.85000i	−0.328569	+	0.328569i	0.523473	+	0.852042i	$0.324636\pi$
$318$	−6.52984	−	6.52984i	−0.366175	−	0.366175i
$319$	−37.1785			−2.08160
$320$	−1.90763	−	2.23913i	−0.106640	−	0.125171i
$321$			9.54148i			0.532554i
$322$			13.0633i			0.727991i
$323$	1.58872	+	16.4157i	0.0883988	+	0.913395i
$324$	−7.83752			−0.435418
$325$	−6.16470	−	0.991998i	−0.341956	−	0.0550262i
$326$	−18.7697	+	18.7697i	−1.03956	+	1.03956i
$327$			0.250624i			0.0138596i
$328$	−5.64982	−	5.64982i	−0.311959	−	0.311959i
$329$	−10.6845	−	10.6845i	−0.589055	−	0.589055i
$330$	−9.67564	+	8.24314i	−0.532626	+	0.453770i
$331$			5.51200i			0.302967i	0.988460	+	0.151484i	$0.0484050\pi$
$331$			5.51200i			0.302967i	−0.988460	+	0.151484i	$0.951595\pi$
$332$	4.94112			0.271179
$333$	3.62109	−	3.62109i	0.198435	−	0.198435i
$334$	−0.535753	−	0.535753i	−0.0293151	−	0.0293151i
$335$	−14.4035	+	12.2710i	−0.786946	+	0.670437i
$336$	8.62899			0.470750
$337$	6.74445	+	6.74445i	0.367394	+	0.367394i	0.866526	−	0.499132i	$-0.166348\pi$
$337$	6.74445	+	6.74445i	0.367394	+	0.367394i	−0.499132	+	0.866526i	$0.666348\pi$
$338$	−20.6310			−1.12218
$339$	−6.36099			−0.345482
$340$	−8.29725	−	8.02456i	−0.449982	−	0.435193i
$341$	25.5575			1.38402
$342$	19.3641			1.04709
$343$	9.49631	+	9.49631i	0.512753	+	0.512753i
$344$	−2.75600			−0.148594
$345$	−1.89602	−	2.22551i	−0.102078	−	0.119818i
$346$	21.1705	+	21.1705i	1.13813	+	1.13813i
$347$	−8.16503	+	8.16503i	−0.438322	+	0.438322i	−0.891447	−	0.453125i	$-0.850309\pi$
$347$	−8.16503	+	8.16503i	−0.438322	+	0.438322i	0.453125	+	0.891447i	$0.350309\pi$
$348$	4.65892			0.249744
$349$		−	11.4325i		−	0.611967i	−0.952037	−	0.305984i	$-0.901015\pi$
$349$		−	11.4325i		−	0.611967i	0.952037	−	0.305984i	$-0.0989853\pi$
$350$	−16.4370	−	22.7415i	−0.878596	−	1.21558i
$351$	−2.81951	−	2.81951i	−0.150494	−	0.150494i
$352$	24.6204	+	24.6204i	1.31227	+	1.31227i
$353$		−	31.8017i		−	1.69263i	−0.532680	−	0.846317i	$-0.678815\pi$
$353$		−	31.8017i		−	1.69263i	0.532680	−	0.846317i	$-0.321185\pi$
$354$	−4.29749	+	4.29749i	−0.228409	+	0.228409i
$355$	−19.6076	−	1.56750i	−1.04066	−	0.0831945i
$356$	−13.2875			−0.704234
$357$	7.17367	−	0.694271i	0.379671	−	0.0367447i
$358$		−	35.6942i		−	1.88650i
$359$		−	25.1785i		−	1.32887i	−0.747346	−	0.664435i	$-0.768672\pi$
$359$		−	25.1785i		−	1.32887i	0.747346	−	0.664435i	$-0.231328\pi$
$360$	6.16350	−	5.25098i	0.324845	−	0.276751i
$361$	3.00000			0.157895
$362$	11.9398	+	11.9398i	0.627544	+	0.627544i
$363$	8.13981	−	8.13981i	0.427229	−	0.427229i
$364$	3.44050	+	3.44050i	0.180331	+	0.180331i
$365$	0.279483	−	3.49600i	0.0146288	−	0.182989i
$366$		−	5.72998i		−	0.299511i
$367$	4.30411	−	4.30411i	0.224673	−	0.224673i	−0.585790	−	0.810463i	$-0.699216\pi$
$367$	4.30411	−	4.30411i	0.224673	−	0.224673i	0.810463	+	0.585790i	$0.199216\pi$
$368$	−8.12538	+	8.12538i	−0.423565	+	0.423565i
$369$	−11.2440	+	11.2440i	−0.585339	+	0.585339i
$370$	0.612990	−	7.66776i	0.0318678	−	0.398628i
$371$	−20.0615	+	20.0615i	−1.04154	+	1.04154i
$372$	−3.20267			−0.166050
$373$			30.0732i			1.55713i	0.627562	+	0.778566i	$0.284053\pi$
$373$			30.0732i			1.55713i	−0.627562	+	0.778566i	$0.715947\pi$
$374$	32.2102	+	26.5257i	1.66555	+	1.37161i
$375$	6.10099	+	1.48863i	0.315054	+	0.0768726i
$376$		−	6.54949i		−	0.337764i
$377$	−5.85000	−	5.85000i	−0.301290	−	0.301290i
$378$		−	17.9188i		−	0.921643i
$379$	0.716248	−	0.716248i	0.0367912	−	0.0367912i	−0.688472	−	0.725263i	$-0.741718\pi$
$379$	0.716248	−	0.716248i	0.0367912	−	0.0367912i	0.725263	+	0.688472i	$0.241718\pi$
$380$	8.52417	−	7.26215i	0.437281	−	0.372541i
$381$	2.32351	+	2.32351i	0.119037	+	0.119037i
$382$	25.1321			1.28587
$383$	25.8660			1.32169			0.660846	−	0.750521i	$-0.270198\pi$
$383$	25.8660			1.32169			0.660846	+	0.750521i	$0.270198\pi$
$384$	3.98627	+	3.98627i	0.203423	+	0.203423i
$385$	25.3252	+	29.7262i	1.29069	+	1.51499i
$386$	−5.32351	+	5.32351i	−0.270959	+	0.270959i
$387$			5.48486i			0.278811i
$388$	10.9705	+	10.9705i	0.556944	+	0.556944i
$389$		−	33.0695i		−	1.67669i	−0.545140	−	0.838345i	$-0.683524\pi$
$389$		−	33.0695i		−	1.67669i	0.545140	−	0.838345i	$-0.316476\pi$
$390$	−2.81951	−	0.225402i	−0.142771	−	0.0114137i
$391$	−6.10124	+	7.40874i	−0.308553	+	0.374676i
$392$		−	3.62109i		−	0.182893i
$393$	−10.9886			−0.554301
$394$	22.5575	−	22.5575i	1.13643	−	1.13643i
$395$	0.875008	−	10.9453i	0.0440264	−	0.550718i
$396$	13.3372	−	13.3372i	0.670221	−	0.670221i
$397$	−5.76434	+	5.76434i	−0.289304	+	0.289304i	−0.836805	−	0.547501i	$-0.815579\pi$
$397$	−5.76434	+	5.76434i	−0.289304	+	0.289304i	0.547501	+	0.836805i	$0.315579\pi$
$398$	7.14163	−	7.14163i	0.357978	−	0.357978i
$399$			6.99200i			0.350038i
$400$	3.92136	−	24.3690i	0.196068	−	1.21845i
$401$	0.116990	+	0.116990i	0.00584222	+	0.00584222i	0.710022	−	0.704180i	$-0.248685\pi$
$401$	0.116990	+	0.116990i	0.00584222	+	0.00584222i	−0.704180	+	0.710022i	$0.748685\pi$
$402$	−6.06097	+	6.06097i	−0.302294	+	0.302294i
$403$	4.02145	+	4.02145i	0.200323	+	0.200323i
$404$	12.0455			0.599285
$405$	−9.07769	−	10.6552i	−0.451074	−	0.529462i
$406$		−	37.1785i		−	1.84514i
$407$			10.7055i			0.530650i
$408$	2.41148	+	1.98590i	0.119386	+	0.0983168i
$409$	−13.3690			−0.661054			−0.330527	−	0.943797i	$-0.607226\pi$
$409$	−13.3690			−0.661054			−0.330527	+	0.943797i	$0.607226\pi$
$410$	−1.90342	+	23.8095i	−0.0940032	+	1.17587i
$411$	5.50400	−	5.50400i	0.271492	−	0.271492i
$412$			2.30741i			0.113678i
$413$	13.2031	+	13.2031i	0.649680	+	0.649680i
$414$	7.96825	+	7.96825i	0.391618	+	0.391618i
$415$	5.72298	+	6.71752i	0.280930	+	0.329750i
$416$			7.74800i			0.379877i
$417$	−5.72913			−0.280557
$418$	−28.6242	+	28.6242i	−1.40006	+	1.40006i
$419$	16.6687	+	16.6687i	0.814322	+	0.814322i	0.985278	−	0.170957i	$-0.0546859\pi$
$419$	16.6687	+	16.6687i	0.814322	+	0.814322i	−0.170957	+	0.985278i	$0.554686\pi$
$420$	−3.17356	−	3.72506i	−0.154854	−	0.181764i
$421$	5.82751			0.284015			0.142008	−	0.989866i	$-0.454644\pi$
$421$	5.82751			0.284015			0.142008	+	0.989866i	$0.454644\pi$
$422$	−1.17711	−	1.17711i	−0.0573009	−	0.0573009i
$423$	−13.0345			−0.633757
$424$	−12.2975			−0.597219
$425$	1.29932	−	20.5745i	0.0630264	−	0.998012i
$426$	−8.91047			−0.431714
$427$	−17.6041			−0.851921
$428$	−15.0384	−	15.0384i	−0.726910	−	0.726910i
$429$	3.93650			0.190056
$430$	5.34292	+	6.27142i	0.257659	+	0.302435i
$431$	4.90474	+	4.90474i	0.236253	+	0.236253i	0.815297	−	0.579043i	$-0.196574\pi$
$431$	4.90474	+	4.90474i	0.236253	+	0.236253i	−0.579043	+	0.815297i	$0.696574\pi$
$432$	11.1455	−	11.1455i	0.536237	−	0.536237i
$433$	−15.4464			−0.742307			−0.371153	−	0.928572i	$-0.621038\pi$
$433$	−15.4464			−0.742307			−0.371153	+	0.928572i	$0.621038\pi$
$434$			25.5575i			1.22680i
$435$	5.39612	+	6.33386i	0.258724	+	0.303685i
$436$	−0.395012	−	0.395012i	−0.0189176	−	0.0189176i
$437$	−6.58392	−	6.58392i	−0.314952	−	0.314952i
$438$		−	1.58872i		−	0.0759121i
$439$	1.03975	−	1.03975i	0.0496247	−	0.0496247i	−0.681859	−	0.731484i	$-0.738828\pi$
$439$	1.03975	−	1.03975i	0.0496247	−	0.0496247i	0.731484	+	0.681859i	$0.238828\pi$
$440$	−1.34889	+	16.8730i	−0.0643058	+	0.804388i
$441$	−7.20652			−0.343167
$442$	0.894450	+	9.24205i	0.0425447	+	0.439600i
$443$			12.7838i			0.607379i	0.952771	+	0.303689i	$0.0982185\pi$
$443$			12.7838i			0.607379i	−0.952771	+	0.303689i	$0.901782\pi$
$444$		−	1.34153i		−	0.0636660i
$445$	−15.3900	−	18.0645i	−0.729556	−	0.856339i
$446$	−2.25200			−0.106635
$447$	−6.32966	−	6.32966i	−0.299383	−	0.299383i
$448$	−2.89478	+	2.89478i	−0.136766	+	0.136766i
$449$	6.88099	+	6.88099i	0.324734	+	0.324734i	0.850580	−	0.525846i	$-0.176251\pi$
$449$	6.88099	+	6.88099i	0.324734	+	0.324734i	−0.525846	+	0.850580i	$0.676251\pi$
$450$	−23.8977	−	3.84553i	−1.12655	−	0.181280i
$451$		−	33.2420i		−	1.56530i
$452$	10.0256	−	10.0256i	0.471566	−	0.471566i
$453$	−1.33810	+	1.33810i	−0.0628693	+	0.0628693i
$454$	−14.7697	+	14.7697i	−0.693178	+	0.693178i
$455$	−0.692497	+	8.66230i	−0.0324648	+	0.406095i
$456$	−2.14301	+	2.14301i	−0.100356	+	0.100356i
$457$	36.2279			1.69467			0.847336	−	0.531058i	$-0.178205\pi$
$457$	36.2279			1.69467			0.847336	+	0.531058i	$0.178205\pi$
$458$		−	21.1855i		−	0.989935i
$459$	8.36899	−	10.1625i	0.390631	−	0.474344i
$460$	6.49600	+	0.519315i	0.302878	+	0.0242132i
$461$		−	40.0595i		−	1.86576i	−0.360193	−	0.932878i	$-0.617289\pi$
$461$		−	40.0595i		−	1.86576i	0.360193	−	0.932878i	$-0.382711\pi$
$462$	12.5088	+	12.5088i	0.581962	+	0.581962i
$463$		−	15.3607i		−	0.713874i	−0.934128	−	0.356937i	$-0.883821\pi$
$463$		−	15.3607i		−	0.713874i	0.934128	−	0.356937i	$-0.116179\pi$
$464$	23.1250	−	23.1250i	1.07355	−	1.07355i
$465$	−3.70944	−	4.35407i	−0.172021	−	0.201915i
$466$	−14.4145	−	14.4145i	−0.667738	−	0.667738i
$467$	19.4471			0.899903			0.449952	−	0.893053i	$-0.351441\pi$
$467$	19.4471			0.899903			0.449952	+	0.893053i	$0.351441\pi$
$468$	4.19721			0.194016
$469$	18.6210	+	18.6210i	0.859837	+	0.859837i
$470$	−14.9037	+	12.6972i	−0.687456	+	0.585677i
$471$	−1.55749	+	1.55749i	−0.0717652	+	0.0717652i
$472$			8.09334i			0.372526i
$473$	−8.10777	−	8.10777i	−0.372796	−	0.372796i
$474$		−	4.97398i		−	0.228462i
$475$	19.7460	+	3.17744i	0.906008	+	0.145791i
$476$	−10.2122	+	12.4007i	−0.468078	+	0.568387i
$477$			24.4739i			1.12058i
$478$	9.26012			0.423548
$479$	10.2918	−	10.2918i	0.470242	−	0.470242i	−0.431751	−	0.901993i	$-0.642104\pi$
$479$	10.2918	−	10.2918i	0.470242	−	0.470242i	0.901993	+	0.431751i	$0.142104\pi$
$480$	0.620991	−	7.76785i	0.0283442	−	0.354552i
$481$	−1.68450	+	1.68450i	−0.0768064	+	0.0768064i
$482$	−10.8200	+	10.8200i	−0.492837	+	0.492837i
$483$	−2.87717	+	2.87717i	−0.130916	+	0.130916i
$484$			25.6585i			1.16629i
$485$	−2.20813	+	27.6210i	−0.100266	+	1.25420i
$486$	−16.6982	−	16.6982i	−0.757447	−	0.757447i
$487$	20.9993	−	20.9993i	0.951570	−	0.951570i	−0.0473104	−	0.998880i	$-0.515065\pi$
$487$	20.9993	−	20.9993i	0.951570	−	0.951570i	0.998880	+	0.0473104i	$0.0150650\pi$
$488$	−5.39556	−	5.39556i	−0.244246	−	0.244246i
$489$	−8.26800			−0.373892
$490$	−8.23997	+	7.02003i	−0.372244	+	0.317133i
$491$			21.0715i			0.950944i	0.879731	+	0.475472i	$0.157723\pi$
$491$			21.0715i			0.950944i	−0.879731	+	0.475472i	$0.842277\pi$
$492$			4.16563i			0.187801i
$493$	17.3643	−	21.0854i	0.782047	−	0.949640i
$494$	−9.00800			−0.405289
$495$	33.5798	+	2.68450i	1.50930	+	0.120659i
$496$	−15.8967	+	15.8967i	−0.713785	+	0.713785i
$497$			27.3754i			1.22796i
$498$	2.82673	+	2.82673i	0.126669	+	0.126669i
$499$	−6.65274	−	6.65274i	−0.297818	−	0.297818i	0.542341	−	0.840159i	$-0.317538\pi$
$499$	−6.65274	−	6.65274i	−0.297818	−	0.297818i	−0.840159	+	0.542341i	$0.817538\pi$
$500$	−11.9621	+	7.26958i	−0.534960	+	0.325106i
$501$		−	0.235997i		−	0.0105436i
$502$	−35.7231			−1.59440
$503$	20.7739	−	20.7739i	0.926263	−	0.926263i	−0.0711991	−	0.997462i	$-0.522683\pi$
$503$	20.7739	−	20.7739i	0.926263	−	0.926263i	0.997462	+	0.0711991i	$0.0226826\pi$
$504$	−7.96825	−	7.96825i	−0.354934	−	0.354934i
$505$	13.9515	+	16.3760i	0.620833	+	0.728722i
$506$	−23.5575			−1.04726
$507$	−4.54394	−	4.54394i	−0.201804	−	0.201804i
$508$	−7.32420			−0.324959
$509$	−14.3930			−0.637958			−0.318979	−	0.947762i	$-0.603340\pi$
$509$	−14.3930			−0.637958			−0.318979	+	0.947762i	$0.603340\pi$
$510$	−0.156005	−	9.33742i	−0.00690800	−	0.413468i
$511$	−4.88099			−0.215922
$512$	−17.3102			−0.765009
$513$	9.03108	+	9.03108i	0.398732	+	0.398732i
$514$	−43.9980			−1.94067
$515$	−3.13696	+	2.67253i	−0.138231	+	0.117766i
$516$	1.01600	+	1.01600i	0.0447270	+	0.0447270i
$517$	19.2677	−	19.2677i	0.847391	−	0.847391i
$518$	−10.7055			−0.470371
$519$			9.32552i			0.409345i
$520$	−2.86720	+	2.44270i	−0.125735	+	0.107120i
$521$	−19.5655	−	19.5655i	−0.857180	−	0.857180i	0.133825	−	0.991005i	$-0.457274\pi$
$521$	−19.5655	−	19.5655i	−0.857180	−	0.857180i	−0.991005	+	0.133825i	$0.957274\pi$
$522$	−22.6778	−	22.6778i	−0.992580	−	0.992580i
$523$			37.4867i			1.63918i	0.572950	+	0.819590i	$0.305799\pi$
$523$			37.4867i			1.63918i	−0.572950	+	0.819590i	$0.694201\pi$
$524$	17.3192	−	17.3192i	0.756594	−	0.756594i
$525$	1.38854	−	8.62899i	0.0606010	−	0.376600i
$526$	32.5655			1.41992
$527$	−11.9367	+	14.4947i	−0.519969	+	0.631399i
$528$			15.5609i			0.677202i
$529$			17.5815i			0.764413i
$530$	23.8405	+	27.9835i	1.03557	+	1.21553i
$531$	16.1070			0.698983
$532$	−11.0202	−	11.0202i	−0.477785	−	0.477785i
$533$	5.23060	−	5.23060i	0.226562	−	0.226562i
$534$	−7.60153	−	7.60153i	−0.328950	−	0.328950i
$535$	3.02691	−	37.8630i	0.130865	−	1.63696i
$536$			11.4145i			0.493030i
$537$	7.86158	−	7.86158i	0.339252	−	0.339252i
$538$	22.7742	−	22.7742i	0.981867	−	0.981867i
$539$	10.6527	−	10.6527i	0.458846	−	0.458846i
$540$	−8.91047	−	0.712337i	−0.383446	−	0.0306541i
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	28.5954			1.22828
$543$			5.25946i			0.225705i
$544$	−25.4622	+	2.46425i	−1.09168	+	0.105654i
$545$	0.0795073	−	0.994540i	0.00340572	−	0.0426014i
$546$			3.93650i			0.168466i
$547$	−20.3591	−	20.3591i	−0.870493	−	0.870493i	0.122033	−	0.992526i	$-0.461059\pi$
$547$	−20.3591	−	20.3591i	−0.870493	−	0.870493i	−0.992526	+	0.122033i	$0.961059\pi$
$548$			17.3498i			0.741148i
$549$	−10.7380	+	10.7380i	−0.458286	+	0.458286i
$550$	41.0104	−	29.6414i	1.74869	−	1.26391i
$551$	18.7380	+	18.7380i	0.798265	+	0.798265i
$552$	−1.76368			−0.0750671
$553$	−15.2814			−0.649833
$554$	−18.0795	−	18.0795i	−0.768125	−	0.768125i
$555$	1.82382	−	1.55380i	0.0774169	−	0.0659552i
$556$	9.02974	−	9.02974i	0.382946	−	0.382946i
$557$			4.93477i			0.209093i	0.994520	+	0.104546i	$0.0333391\pi$
$557$			4.93477i			0.209093i	−0.994520	+	0.104546i	$0.966661\pi$
$558$	15.5893	+	15.5893i	0.659949	+	0.659949i
$559$		−	2.55150i		−	0.107917i
$560$	−34.2420	−	2.73743i	−1.44699	−	0.115678i
$561$	1.25200	+	12.9365i	0.0528595	+	0.546179i
$562$		−	14.0831i		−	0.594059i
$563$	−3.97544			−0.167545			−0.0837724	−	0.996485i	$-0.526697\pi$
$563$	−3.97544			−0.167545			−0.0837724	+	0.996485i	$0.526697\pi$
$564$	−2.41448	+	2.41448i	−0.101668	+	0.101668i
$565$	25.2420	+	2.01794i	1.06194	+	0.0848953i
$566$	−26.6607	+	26.6607i	−1.12063	+	1.12063i
$567$	−13.7752	+	13.7752i	−0.578504	+	0.578504i
$568$	−8.39043	+	8.39043i	−0.352055	+	0.352055i
$569$		−	5.49600i		−	0.230404i	−0.993342	−	0.115202i	$-0.963248\pi$
$569$		−	5.49600i		−	0.230404i	0.993342	−	0.115202i	$-0.0367516\pi$
$570$	9.03108	+	0.721979i	0.378270	+	0.0302404i
$571$	12.3372	+	12.3372i	0.516297	+	0.516297i	0.916449	−	0.400152i	$-0.131043\pi$
$571$	12.3372	+	12.3372i	0.516297	+	0.516297i	−0.400152	+	0.916449i	$0.631043\pi$
$572$	−6.20435	+	6.20435i	−0.259417	+	0.259417i
$573$	5.53530	+	5.53530i	0.231241	+	0.231241i
$574$	33.2420			1.38749
$575$	6.81788	+	9.43288i	0.284325	+	0.393378i
$576$			3.53147i			0.147144i
$577$		−	32.3418i		−	1.34641i	−0.739458	−	0.673203i	$-0.764918\pi$
$577$		−	32.3418i		−	1.34641i	0.739458	−	0.673203i	$-0.235082\pi$
$578$	−30.0877	+	5.87886i	−1.25148	+	0.244528i
$579$	−2.34499			−0.0974543
$580$	−18.4877	−	1.47798i	−0.767662	−	0.0613698i
$581$	8.68450	−	8.68450i	0.360294	−	0.360294i
$582$			12.5521i			0.520301i
$583$	−36.1775	−	36.1775i	−1.49832	−	1.49832i
$584$	−1.49600	−	1.49600i	−0.0619049	−	0.0619049i
$585$	4.86135	+	5.70616i	0.200992	+	0.235920i
$586$		−	8.64701i		−	0.357205i
$587$	−28.6847			−1.18394			−0.591972	−	0.805959i	$-0.701650\pi$
$587$	−28.6847			−1.18394			−0.591972	+	0.805959i	$0.701650\pi$
$588$	−1.33492	+	1.33492i	−0.0550511	+	0.0550511i
$589$	−12.8810	−	12.8810i	−0.530752	−	0.530752i
$590$	18.4168	−	15.6902i	0.758208	−	0.645954i
$591$	9.93650			0.408733
$592$	−6.65879	−	6.65879i	−0.273675	−	0.273675i
$593$	9.74614			0.400226			0.200113	−	0.979773i	$-0.435869\pi$
$593$	9.74614			0.400226			0.200113	+	0.979773i	$0.435869\pi$
$594$	32.3135			1.32584
$595$	−28.6871	+	0.479289i	−1.17606	+	0.0196490i
$596$	19.9525			0.817286
$597$	3.14586			0.128752
$598$	−3.70675	−	3.70675i	−0.151580	−	0.151580i
$599$	8.07951			0.330120			0.165060	−	0.986284i	$-0.447218\pi$
$599$	8.07951			0.330120			0.165060	+	0.986284i	$0.447218\pi$
$600$	3.07032	−	2.21916i	0.125345	−	0.0905969i
$601$	−12.8810	−	12.8810i	−0.525427	−	0.525427i	0.393779	−	0.919205i	$-0.371168\pi$
$601$	−12.8810	−	12.8810i	−0.525427	−	0.525427i	−0.919205	+	0.393779i	$0.871168\pi$
$602$	8.10777	−	8.10777i	0.330448	−	0.330448i
$603$	22.7165			0.925089
$604$		−	4.21798i		−	0.171627i
$605$	−34.8830	+	29.7185i	−1.41820	+	1.20823i
$606$	6.89101	+	6.89101i	0.279928	+	0.279928i
$607$	−8.37964	−	8.37964i	−0.340119	−	0.340119i	0.516293	−	0.856412i	$-0.327312\pi$
$607$	−8.37964	−	8.37964i	−0.340119	−	0.340119i	−0.856412	+	0.516293i	$0.827312\pi$
$608$		−	24.8174i		−	1.00648i
$609$	8.18850	−	8.18850i	0.331815	−	0.331815i
$610$	−1.81776	+	22.7380i	−0.0735989	+	0.920634i
$611$	6.06350			0.245303
$612$	1.33492	+	13.7933i	0.0539609	+	0.557560i
$613$			23.1494i			0.934995i	0.883994	+	0.467497i	$0.154844\pi$
$613$			23.1494i			0.934995i	−0.883994	+	0.467497i	$0.845156\pi$
$614$			45.0695i			1.81886i
$615$	−5.66322	+	4.82477i	−0.228363	+	0.194554i
$616$	23.5575			0.949158
$617$	7.41350	+	7.41350i	0.298456	+	0.298456i	0.840409	−	0.541953i	$-0.182315\pi$
$617$	7.41350	+	7.41350i	0.298456	+	0.298456i	−0.541953	+	0.840409i	$0.682315\pi$
$618$	−1.32003	+	1.32003i	−0.0530995	+	0.0530995i
$619$	−16.4702	−	16.4702i	−0.661995	−	0.661995i	0.293855	−	0.955850i	$-0.405062\pi$
$619$	−16.4702	−	16.4702i	−0.661995	−	0.661995i	−0.955850	+	0.293855i	$0.905062\pi$
$620$	12.7090	+	1.01600i	0.510405	+	0.0408037i
$621$			7.43250i			0.298256i
$622$	5.14176	−	5.14176i	0.206166	−	0.206166i
$623$	−23.3540	+	23.3540i	−0.935658	+	0.935658i
$624$	−2.44850	+	2.44850i	−0.0980184	+	0.0980184i
$625$	−23.7380	−	7.84272i	−0.949519	−	0.313709i
$626$	28.8810	−	28.8810i	1.15432	−	1.15432i
$627$	−12.6089			−0.503550
$628$		−	4.90954i		−	0.195912i
$629$	−6.07151	−	5.00000i	−0.242087	−	0.199363i
$630$	−2.68450	+	33.5798i	−0.106953	+	1.33785i
$631$			41.1310i			1.63740i	0.574223	+	0.818699i	$0.305304\pi$
$631$			41.1310i			1.63740i	−0.574223	+	0.818699i	$0.694696\pi$
$632$	−4.68368	−	4.68368i	−0.186307	−	0.186307i
$633$		−	0.518514i		−	0.0206091i
$634$	10.5495	−	10.5495i	0.418974	−	0.418974i
$635$	−8.48315	−	9.95735i	−0.336643	−	0.395145i
$636$	4.53348	+	4.53348i	0.179764	+	0.179764i
$637$	3.35240			0.132827
$638$	67.0451			2.65434
$639$	16.6982	+	16.6982i	0.660572	+	0.660572i
$640$	−14.5539	−	17.0831i	−0.575294	−	0.675268i
$641$	33.4325	−	33.4325i	1.32050	−	1.32050i	0.407137	−	0.913367i	$-0.366527\pi$
$641$	33.4325	−	33.4325i	1.32050	−	1.32050i	0.913367	−	0.407137i	$-0.133473\pi$
$642$		−	17.2064i		−	0.679084i
$643$	4.99838	+	4.99838i	0.197117	+	0.197117i	0.798763	−	0.601646i	$-0.205488\pi$
$643$	4.99838	+	4.99838i	0.197117	+	0.197117i	−0.601646	+	0.798763i	$0.705488\pi$
$644$		−	9.06949i		−	0.357388i
$645$	−0.204499	+	2.55804i	−0.00805215	+	0.100723i
$646$	−2.86499	−	29.6030i	−0.112722	−	1.16471i
$647$		−	26.9462i		−	1.05937i	−0.848196	−	0.529683i	$-0.822311\pi$
$647$		−	26.9462i		−	1.05937i	0.848196	−	0.529683i	$-0.177689\pi$
$648$	−8.44406			−0.331714
$649$	−23.8095	+	23.8095i	−0.934604	+	0.934604i
$650$	11.1170	+	1.78890i	0.436044	+	0.0701665i
$651$	−5.62899	+	5.62899i	−0.220618	+	0.220618i
$652$	13.0313	−	13.0313i	0.510345	−	0.510345i
$653$	19.9764	−	19.9764i	0.781736	−	0.781736i	−0.198388	−	0.980124i	$-0.563570\pi$
$653$	19.9764	−	19.9764i	0.781736	−	0.781736i	0.980124	+	0.198388i	$0.0635705\pi$
$654$		−	0.451959i		−	0.0176730i
$655$	43.6054	+	3.48598i	1.70380	+	0.136209i
$656$	20.6765	+	20.6765i	0.807281	+	0.807281i
$657$	−2.97726	+	2.97726i	−0.116154	+	0.116154i
$658$	19.2677	+	19.2677i	0.751132	+	0.751132i
$659$	14.1230			0.550153			0.275077	−	0.961422i	$-0.411297\pi$
$659$	14.1230			0.550153			0.275077	+	0.961422i	$0.411297\pi$
$660$	6.71752	−	5.72298i	0.261479	−	0.222767i
$661$			49.0355i			1.90726i	0.300984	+	0.953629i	$0.402685\pi$
$661$			49.0355i			1.90726i	−0.300984	+	0.953629i	$0.597315\pi$
$662$		−	9.93996i		−	0.386328i
$663$	−1.83855	+	2.23255i	−0.0714032	+	0.0867050i
$664$	5.32351			0.206592
$665$	2.21812	−	27.7460i	0.0860149	−	1.07594i
$666$	−6.53002	+	6.53002i	−0.253033	+	0.253033i
$667$			15.4212i			0.597111i
$668$	0.371958	+	0.371958i	0.0143915	+	0.0143915i
$669$	−0.495999	−	0.495999i	−0.0191764	−	0.0191764i
$670$	25.9742	−	22.1287i	1.00347	−	0.854906i
$671$		−	31.7460i		−	1.22554i
$672$	−10.8452			−0.418363
$673$	−22.2405	+	22.2405i	−0.857308	+	0.857308i	−0.991020	−	0.133712i	$-0.957310\pi$
$673$	−22.2405	+	22.2405i	−0.857308	+	0.857308i	0.133712	+	0.991020i	$0.457310\pi$
$674$	−12.1625	−	12.1625i	−0.468481	−	0.468481i
$675$	−9.35199	−	12.9390i	−0.359958	−	0.498021i
$676$	14.3235			0.550904
$677$	−21.4109	−	21.4109i	−0.822889	−	0.822889i	0.163633	−	0.986521i	$-0.447679\pi$
$677$	−21.4109	−	21.4109i	−0.822889	−	0.822889i	−0.986521	+	0.163633i	$0.947679\pi$
$678$	11.4710			0.440540
$679$	38.5635			1.47993
$680$	−8.93936	−	8.64556i	−0.342809	−	0.331542i
$681$	−6.50602			−0.249311
$682$	−46.0886			−1.76482
$683$	32.6533	+	32.6533i	1.24944	+	1.24944i	0.955966	+	0.293479i	$0.0948129\pi$
$683$	32.6533	+	32.6533i	1.24944	+	1.24944i	0.293479	+	0.955966i	$0.405187\pi$
$684$	−13.4440			−0.514043
$685$	−23.5873	+	20.0952i	−0.901225	+	0.767797i
$686$	−17.1250	−	17.1250i	−0.653835	−	0.653835i
$687$	4.66608	−	4.66608i	0.178022	−	0.178022i
$688$	10.0861			0.384527
$689$		−	11.3850i		−	0.433734i
$690$	3.41916	+	4.01334i	0.130165	+	0.152785i
$691$	−7.52775	−	7.52775i	−0.286369	−	0.286369i	0.549273	−	0.835643i	$-0.314905\pi$
$691$	−7.52775	−	7.52775i	−0.286369	−	0.286369i	−0.835643	+	0.549273i	$0.814905\pi$
$692$	−14.6981	−	14.6981i	−0.558736	−	0.558736i
$693$		−	46.8830i		−	1.78094i
$694$	14.7242	−	14.7242i	0.558925	−	0.558925i
$695$	22.7346	+	1.81749i	0.862372	+	0.0689413i
$696$	5.01946			0.190262
$697$	18.8529	+	15.5257i	0.714104	+	0.588078i
$698$			20.6166i			0.780349i
$699$		−	6.34953i		−	0.240161i
$700$	11.4117	+	15.7887i	0.431324	+	0.596758i
$701$	−39.4145			−1.48866			−0.744332	−	0.667810i	$-0.767232\pi$
$701$	−39.4145			−1.48866			−0.744332	+	0.667810i	$0.767232\pi$
$702$	5.08450	+	5.08450i	0.191902	+	0.191902i
$703$	5.39556	−	5.39556i	0.203497	−	0.203497i
$704$	−5.22025	−	5.22025i	−0.196746	−	0.196746i
$705$	−6.07904	−	0.485981i	−0.228950	−	0.0183031i
$706$			57.3490i			2.15836i
$707$	21.1711	−	21.1711i	0.796221	−	0.796221i
$708$	2.98362	−	2.98362i	0.112131	−	0.112131i
$709$	10.7460	−	10.7460i	0.403574	−	0.403574i	−0.475917	−	0.879490i	$-0.657884\pi$
$709$	10.7460	−	10.7460i	0.403574	−	0.403574i	0.879490	+	0.475917i	$0.157884\pi$
$710$	35.3590	+	2.82673i	1.32700	+	0.106085i
$711$	−9.32124	+	9.32124i	−0.349574	+	0.349574i
$712$	−14.3158			−0.536506
$713$		−	10.6009i		−	0.397008i
$714$	−12.9365	+	1.25200i	−0.484136	+	0.0468549i
$715$	−15.6210	−	1.24880i	−0.584192	−	0.0467025i
$716$			24.7815i			0.926126i
$717$	2.03953	+	2.03953i	0.0761675	+	0.0761675i
$718$			45.4051i			1.69450i
$719$	−4.84924	+	4.84924i	−0.180846	+	0.180846i	−0.791724	−	0.610878i	$-0.790816\pi$
$719$	−4.84924	+	4.84924i	−0.180846	+	0.180846i	0.610878	+	0.791724i	$0.290816\pi$
$720$	−22.5564	+	19.2169i	−0.840626	+	0.716170i
$721$	4.05550	+	4.05550i	0.151035	+	0.151035i
$722$	−5.40999			−0.201339
$723$	−4.76617			−0.177256
$724$	−8.28948	−	8.28948i	−0.308076	−	0.308076i
$725$	−19.4038	−	26.8462i	−0.720639	−	0.997042i
$726$	−14.6788	+	14.6788i	−0.544780	+	0.544780i
$727$			38.5606i			1.43013i	0.699057	+	0.715066i	$0.253603\pi$
$727$			38.5606i			1.43013i	−0.699057	+	0.715066i	$0.746397\pi$
$728$	3.70675	+	3.70675i	0.137381	+	0.137381i
$729$			11.4245i			0.423129i
$730$	−0.504001	+	6.30444i	−0.0186539	+	0.233338i
$731$	8.38499	−	0.811504i	0.310130	−	0.0300146i
$732$			3.97816i			0.147037i
$733$	−42.7425			−1.57873			−0.789366	−	0.613923i	$-0.789591\pi$
$733$	−42.7425			−1.57873			−0.789366	+	0.613923i	$0.789591\pi$
$734$	−7.76173	+	7.76173i	−0.286491	+	0.286491i
$735$	−3.36099	−	0.268690i	−0.123972	−	0.00991078i
$736$	10.2122	−	10.2122i	0.376428	−	0.376428i
$737$	−33.5798	+	33.5798i	−1.23693	+	1.23693i
$738$	20.2766	−	20.2766i	0.746394	−	0.746394i
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$	−0.425581	+	5.32351i	−0.0156447	+	0.195696i
$741$	−1.98400	−	1.98400i	−0.0728839	−	0.0728839i
$742$	36.1775	−	36.1775i	1.32812	−	1.32812i
$743$	−36.9750	−	36.9750i	−1.35648	−	1.35648i	−0.878214	−	0.478269i	$-0.841265\pi$
$743$	−36.9750	−	36.9750i	−1.35648	−	1.35648i	−0.478269	−	0.878214i	$-0.658735\pi$
$744$	−3.45051			−0.126502
$745$	23.1097	+	27.1257i	0.846673	+	0.993808i
$746$		−	54.2320i		−	1.98557i
$747$		−	10.5946i		−	0.387635i
$748$	−22.3626	−	18.4161i	−0.817659	−	0.673358i
$749$	−52.8630			−1.93157
$750$	−11.0021	−	2.68450i	−0.401740	−	0.0980239i
$751$	27.9027	−	27.9027i	1.01818	−	1.01818i	0.0183534	−	0.999832i	$-0.494158\pi$
$751$	27.9027	−	27.9027i	1.01818	−	1.01818i	0.999832	−	0.0183534i	$-0.00584240\pi$
$752$			23.9690i			0.874058i
$753$	−7.86794	−	7.86794i	−0.286724	−	0.286724i
$754$	10.5495	+	10.5495i	0.384190	+	0.384190i
$755$	5.73439	−	4.88541i	0.208696	−	0.177798i
$756$			12.4405i			0.452456i
$757$	−8.61186			−0.313003			−0.156502	−	0.987678i	$-0.550022\pi$
$757$	−8.61186			−0.313003			−0.156502	+	0.987678i	$0.550022\pi$
$758$	−1.29163	+	1.29163i	−0.0469141	+	0.0469141i
$759$	−5.18850	−	5.18850i	−0.188330	−	0.188330i
$760$	9.18384	−	7.82416i	0.333133	−	0.283812i
$761$	−41.2400			−1.49495			−0.747474	−	0.664291i	$-0.768733\pi$
$761$	−41.2400			−1.49495			−0.747474	+	0.664291i	$0.768733\pi$
$762$	−4.19005	−	4.19005i	−0.151789	−	0.151789i
$763$	−1.38854			−0.0502686
$764$	−17.4485			−0.631265
$765$	−17.2060	+	17.7907i	−0.622083	+	0.643223i
$766$	−46.6450			−1.68535
$767$	−7.49280			−0.270549
$768$	−8.23354	−	8.23354i	−0.297102	−	0.297102i
$769$	17.3510			0.625692			0.312846	−	0.949804i	$-0.398718\pi$
$769$	17.3510			0.625692			0.312846	+	0.949804i	$0.398718\pi$
$770$	−45.6697	−	53.6062i	−1.64582	−	1.93183i
$771$	−9.69048	−	9.69048i	−0.348994	−	0.348994i
$772$	3.69596	−	3.69596i	0.133020	−	0.133020i
$773$	−20.0124			−0.719796			−0.359898	−	0.932992i	$-0.617188\pi$
$773$	−20.0124			−0.719796			−0.359898	+	0.932992i	$0.617188\pi$
$774$		−	9.89101i		−	0.355525i
$775$	13.3387	+	18.4548i	0.479140	+	0.662915i
$776$	11.8195	+	11.8195i	0.424296	+	0.424296i
$777$	−2.35786	−	2.35786i	−0.0845878	−	0.0845878i
$778$			59.6352i			2.13803i
$779$	−16.7540	+	16.7540i	−0.600274	+	0.600274i
$780$	1.95750	+	0.156490i	0.0700898	+	0.00560324i
$781$	−49.3670			−1.76649
$782$	11.0026	−	13.3604i	0.393451	−	0.477767i
$783$		−	21.1530i		−	0.755948i
$784$			13.2520i			0.473286i
$785$	6.67459	−	5.68640i	0.238226	−	0.202956i
$786$	19.8160			0.706815
$787$	23.9802	+	23.9802i	0.854802	+	0.854802i	0.990720	−	0.135918i	$-0.0433983\pi$
$787$	23.9802	+	23.9802i	0.854802	+	0.854802i	−0.135918	+	0.990720i	$0.543398\pi$
$788$	−15.6610	+	15.6610i	−0.557901	+	0.557901i
$789$	7.17249	+	7.17249i	0.255348	+	0.255348i
$790$	−1.57793	+	19.7380i	−0.0561402	+	0.702246i
$791$		−	35.2420i		−	1.25306i
$792$	14.3694	−	14.3694i	0.510594	−	0.510594i
$793$	4.99520	−	4.99520i	0.177385	−	0.177385i
$794$	10.3950	−	10.3950i	0.368905	−	0.368905i
$795$	−0.912491	+	11.4142i	−0.0323627	+	0.404819i
$796$	−4.95823	+	4.95823i	−0.175740	+	0.175740i
$797$	−0.730287			−0.0258681			−0.0129340	−	0.999916i	$-0.504117\pi$
$797$	−0.730287			−0.0258681			−0.0129340	+	0.999916i	$0.504117\pi$
$798$		−	12.6089i		−	0.446350i
$799$	1.92849	+	19.9265i	0.0682252	+	0.704948i
$800$	−4.92849	+	30.6278i	−0.174249	+	1.08285i
$801$			28.4905i			1.00666i
$802$	−0.210972	−	0.210972i	−0.00744970	−	0.00744970i
$803$		−	8.80204i		−	0.310617i
$804$	4.20796	−	4.20796i	0.148403	−	0.148403i
$805$	12.3301	−	10.5046i	0.434578	−	0.370238i
$806$	−7.25200	−	7.25200i	−0.255441	−	0.255441i
$807$	10.0320			0.353142
$808$	12.9777			0.456553
$809$	14.4485	+	14.4485i	0.507982	+	0.507982i	0.913907	−	0.405924i	$-0.133050\pi$
$809$	14.4485	+	14.4485i	0.507982	+	0.507982i	−0.405924	+	0.913907i	$0.633050\pi$
$810$	16.3701	+	19.2149i	0.575186	+	0.675142i
$811$	−1.77975	+	1.77975i	−0.0624955	+	0.0624955i	−0.737664	−	0.675168i	$-0.764071\pi$
$811$	−1.77975	+	1.77975i	−0.0624955	+	0.0624955i	0.675168	+	0.737664i	$0.264071\pi$
$812$			25.8119i			0.905822i
$813$	6.29809	+	6.29809i	0.220883	+	0.220883i
$814$		−	19.3055i		−	0.676657i
$815$	32.8095	+	2.62291i	1.14927	+	0.0918767i
$816$	−8.82524	−	7.26775i	−0.308945	−	0.254422i
$817$			8.17265i			0.285925i
$818$	24.1087			0.842941
$819$	7.37699	−	7.37699i	0.257773	−	0.257773i
$820$	1.32149	−	16.5302i	0.0461484	−	0.577261i
$821$	10.8175	−	10.8175i	0.377533	−	0.377533i	−0.492678	−	0.870211i	$-0.663982\pi$
$821$	10.8175	−	10.8175i	0.377533	−	0.377533i	0.870211	+	0.492678i	$0.163982\pi$
$822$	−9.92553	+	9.92553i	−0.346193	+	0.346193i
$823$	−10.1433	+	10.1433i	−0.353574	+	0.353574i	−0.861437	−	0.507864i	$-0.830435\pi$
$823$	−10.1433	+	10.1433i	−0.353574	+	0.353574i	0.507864	+	0.861437i	$0.330435\pi$
$824$			2.48598i			0.0866033i
$825$	15.5609	+	2.50400i	0.541762	+	0.0871781i
$826$	−23.8095	−	23.8095i	−0.828438	−	0.828438i
$827$	28.5066	−	28.5066i	0.991270	−	0.991270i	−0.00869233	−	0.999962i	$-0.502767\pi$
$827$	28.5066	−	28.5066i	0.991270	−	0.991270i	0.999962	+	0.00869233i	$0.00276689\pi$
$828$	−5.53213	−	5.53213i	−0.192255	−	0.192255i
$829$	37.1150			1.28906			0.644528	−	0.764581i	$-0.277054\pi$
$829$	37.1150			1.28906			0.644528	+	0.764581i	$0.277054\pi$
$830$	−10.3204	−	12.1139i	−0.358227	−	0.420480i
$831$		−	7.96396i		−	0.276267i
$832$		−	1.64280i		−	0.0569540i
$833$	1.06623	+	11.0170i	0.0369426	+	0.381716i
$834$	10.3315			0.357751
$835$	−0.0748670	+	0.936496i	−0.00259088	+	0.0324088i
$836$	19.8730	−	19.8730i	0.687322	−	0.687322i
$837$			14.5412i			0.502616i
$838$	−30.0593	−	30.0593i	−1.03838	−	1.03838i
$839$	−5.02173	−	5.02173i	−0.173370	−	0.173370i	0.615089	−	0.788458i	$-0.289120\pi$
$839$	−5.02173	−	5.02173i	−0.173370	−	0.173370i	−0.788458	+	0.615089i	$0.789120\pi$
$840$	−3.41916	−	4.01334i	−0.117972	−	0.138473i
$841$		−	14.8890i		−	0.513414i
$842$	−10.5089			−0.362161
$843$	3.10178	−	3.10178i	0.106831	−	0.106831i
$844$	0.817235	+	0.817235i	0.0281304	+	0.0281304i
$845$	16.5900	+	19.4730i	0.570713	+	0.669891i
$846$	23.5054			0.808134
$847$	45.0972	+	45.0972i	1.54956	+	1.54956i
$848$	45.0048			1.54547
$849$	−11.7440			−0.403052
$850$	−2.34311	+	37.1027i	−0.0803679	+	1.27261i
$851$	4.44050			0.152218
$852$	6.18629			0.211939
$853$	27.1104	+	27.1104i	0.928242	+	0.928242i	0.997592	−	0.0693502i	$-0.0220926\pi$
$853$	27.1104	+	27.1104i	0.928242	+	0.928242i	−0.0693502	+	0.997592i	$0.522093\pi$
$854$	31.7460			1.08633
$855$	−15.5713	−	18.2772i	−0.532526	−	0.625068i
$856$	−16.2022	−	16.2022i	−0.553781	−	0.553781i
$857$	1.22358	−	1.22358i	0.0417966	−	0.0417966i	−0.685900	−	0.727696i	$-0.740591\pi$
$857$	1.22358	−	1.22358i	0.0417966	−	0.0417966i	0.727696	+	0.685900i	$0.240591\pi$
$858$	−7.09880			−0.242349
$859$			30.9245i			1.05513i	0.849515	+	0.527565i	$0.176895\pi$
$859$			30.9245i			1.05513i	−0.849515	+	0.527565i	$0.823105\pi$
$860$	−3.70944	−	4.35407i	−0.126491	−	0.148472i
$861$	7.32149	+	7.32149i	0.249516	+	0.249516i
$862$	−8.84487	−	8.84487i	−0.301258	−	0.301258i
$863$		−	40.2134i		−	1.36888i	−0.729070	−	0.684439i	$-0.760047\pi$
$863$		−	40.2134i		−	1.36888i	0.729070	−	0.684439i	$-0.239953\pi$
$864$	−14.0080	+	14.0080i	−0.476562	+	0.476562i
$865$	2.95840	−	37.0060i	0.100589	−	1.25824i
$866$	27.8550			0.946550
$867$	−7.92156	−	5.33195i	−0.269030	−	0.181082i
$868$		−	17.7438i		−	0.602265i
$869$		−	27.5575i		−	0.934824i
$870$	−9.73099	−	11.4220i	−0.329911	−	0.387243i
$871$	−10.5675			−0.358066
$872$	−0.425581	−	0.425581i	−0.0144120	−	0.0144120i
$873$	23.5226	−	23.5226i	0.796119	−	0.796119i
$874$	11.8730	+	11.8730i	0.401610	+	0.401610i
$875$	−8.24751	+	33.8015i	−0.278817	+	1.14270i
$876$			1.10300i			0.0372670i
$877$	0.715057	−	0.715057i	0.0241458	−	0.0241458i	−0.694931	−	0.719077i	$-0.744565\pi$
$877$	0.715057	−	0.715057i	0.0241458	−	0.0241458i	0.719077	+	0.694931i	$0.244565\pi$
$878$	−1.87502	+	1.87502i	−0.0632788	+	0.0632788i
$879$	1.90449	−	1.90449i	0.0642368	−	0.0642368i
$880$	4.93650	−	61.7496i	0.166409	−	2.08158i
$881$	13.8095	−	13.8095i	0.465253	−	0.465253i	−0.435119	−	0.900373i	$-0.643294\pi$
$881$	13.8095	−	13.8095i	0.465253	−	0.465253i	0.900373	+	0.435119i	$0.143294\pi$
$882$	12.9957			0.437589
$883$			12.6125i			0.424445i	0.977221	+	0.212223i	$0.0680702\pi$
$883$			12.6125i			0.424445i	−0.977221	+	0.212223i	$0.931930\pi$
$884$	−0.620991	−	6.41649i	−0.0208862	−	0.215810i
$885$	7.51200	+	0.600538i	0.252513	+	0.0201869i
$886$		−	23.0535i		−	0.774497i
$887$	26.2443	+	26.2443i	0.881199	+	0.881199i	0.993657	−	0.112458i	$-0.0358723\pi$
$887$	26.2443	+	26.2443i	0.881199	+	0.881199i	−0.112458	+	0.993657i	$0.535872\pi$
$888$		−	1.44534i		−	0.0485026i
$889$	−12.8730	+	12.8730i	−0.431746	+	0.431746i
$890$	27.7533	+	32.5762i	0.930291	+	1.09196i
$891$	−24.8412	−	24.8412i	−0.832213	−	0.832213i
$892$	1.56350			0.0523498
$893$	−19.4218			−0.649927
$894$	11.4145	+	11.4145i	0.381757	+	0.381757i
$895$	−33.6907	+	28.7027i	−1.12616	+	0.959427i
$896$	−22.0852	+	22.0852i	−0.737816	+	0.737816i
$897$		−	1.63281i		−	0.0545180i
$898$	−12.4087	−	12.4087i	−0.414084	−	0.414084i
$899$			30.1705i			1.00624i
$900$	16.5915	+	2.66984i	0.553050	+	0.0889946i
$901$	37.4145	−	3.62099i	1.24646	−	0.120633i
$902$			59.9463i			1.99599i
$903$	3.57145			0.118850
$904$	10.8015	−	10.8015i	0.359252	−	0.359252i
$905$	1.66849	−	20.8708i	0.0554626	−	0.693770i
$906$	2.41303	−	2.41303i	0.0801676	−	0.0801676i
$907$	24.3554	−	24.3554i	0.808706	−	0.808706i	−0.175732	−	0.984438i	$-0.556229\pi$
$907$	24.3554	−	24.3554i	0.808706	−	0.808706i	0.984438	+	0.175732i	$0.0562292\pi$
$908$	10.2542	−	10.2542i	0.340298	−	0.340298i
$909$		−	25.8275i		−	0.856644i
$910$	1.24880	−	15.6210i	0.0413973	−	0.517831i
$911$	−7.21023	−	7.21023i	−0.238886	−	0.238886i	0.577503	−	0.816389i	$-0.304027\pi$
$911$	−7.21023	−	7.21023i	−0.238886	−	0.238886i	−0.816389	+	0.577503i	$0.804027\pi$
$912$	7.84272	−	7.84272i	0.259698	−	0.259698i
$913$	15.6610	+	15.6610i	0.518304	+	0.518304i
$914$	−65.3309			−2.16096
$915$	−5.40836	+	4.60764i	−0.178795	+	0.152324i
$916$			14.7085i			0.485983i
$917$		−	60.8804i		−	2.01045i
$918$	−15.0921	+	18.3263i	−0.498112	+	0.604858i
$919$	50.5315			1.66688			0.833440	−	0.552611i	$-0.186368\pi$
$919$	50.5315			1.66688			0.833440	+	0.552611i	$0.186368\pi$
$920$	6.99871	+	0.559503i	0.230741	+	0.0184463i
$921$	−9.92648	+	9.92648i	−0.327089	+	0.327089i
$922$			72.2405i			2.37911i
$923$	−7.76785	−	7.76785i	−0.255682	−	0.255682i
$924$	−8.68450	−	8.68450i	−0.285699	−	0.285699i
$925$	−7.73030	+	5.58729i	−0.254171	+	0.183709i
$926$			27.7005i			0.910295i
$927$	4.94748			0.162496
$928$	−29.0643	+	29.0643i	−0.954081	+	0.954081i
$929$	20.0615	+	20.0615i	0.658196	+	0.658196i	0.954953	−	0.296757i	$-0.0959051\pi$
$929$	20.0615	+	20.0615i	0.658196	+	0.658196i	−0.296757	+	0.954953i	$0.595905\pi$
$930$	6.68934	+	7.85182i	0.219352	+	0.257471i
$931$	−10.7380			−0.351923
$932$	10.0076	+	10.0076i	0.327808	+	0.327808i
$933$	2.26493			0.0741504
$934$	−35.0695			−1.14751
$935$	−0.864317	−	51.7324i	−0.0282662	−	1.69183i
$936$	4.52202			0.147807
$937$	−47.5024			−1.55183			−0.775917	−	0.630835i	$-0.782713\pi$
$937$	−47.5024			−1.55183			−0.775917	+	0.630835i	$0.782713\pi$
$938$	−33.5798	−	33.5798i	−1.09642	−	1.09642i
$939$	12.7220			0.415166
$940$	10.3472	−	8.81528i	0.337488	−	0.287523i
$941$	32.5555	+	32.5555i	1.06128	+	1.06128i	0.997996	+	0.0632823i	$0.0201569\pi$
$941$	32.5555	+	32.5555i	1.06128	+	1.06128i	0.0632823	+	0.997996i	$0.479843\pi$
$942$	2.80866	−	2.80866i	0.0915112	−	0.0915112i
$943$	−13.7884			−0.449011
$944$		−	29.6190i		−	0.964016i
$945$	−16.9130	+	14.4090i	−0.550180	+	0.468725i
$946$	14.6210	+	14.6210i	0.475369	+	0.475369i
$947$	−21.0282	−	21.0282i	−0.683324	−	0.683324i	0.277424	−	0.960748i	$-0.410519\pi$
$947$	−21.0282	−	21.0282i	−0.683324	−	0.683324i	−0.960748	+	0.277424i	$0.910519\pi$
$948$			3.45329i			0.112158i
$949$	1.38499	−	1.38499i	0.0449588	−	0.0449588i
$950$	−35.6085	−	5.72998i	−1.15529	−	0.185905i
$951$	4.64701			0.150690
$952$	−11.0026	+	13.3604i	−0.356595	+	0.433014i
$953$			9.02109i			0.292222i	0.989268	+	0.146111i	$0.0466756\pi$
$953$			9.02109i			0.292222i	−0.989268	+	0.146111i	$0.953324\pi$
$954$		−	44.1344i		−	1.42891i
$955$	−20.2095	−	23.7215i	−0.653963	−	0.767608i
$956$	−6.42903			−0.207930
$957$	14.7666	+	14.7666i	0.477335	+	0.477335i
$958$	−18.5594	+	18.5594i	−0.599628	+	0.599628i
$959$	30.4940	+	30.4940i	0.984702	+	0.984702i
$960$	−0.131668	+	1.64701i	−0.00424958	+	0.0531571i
$961$			10.2600i			0.330968i
$962$	3.03770	−	3.03770i	0.0979394	−	0.0979394i
$963$	−32.2449	+	32.2449i	−1.03908	+	1.03908i
$964$	7.51200	−	7.51200i	0.241945	−	0.241945i
$965$	9.30549	+	0.743916i	0.299554	+	0.0239475i
$966$	5.18850	−	5.18850i	0.166937	−	0.166937i
$967$	−11.7541			−0.377986			−0.188993	−	0.981978i	$-0.560522\pi$
$967$	−11.7541			−0.377986			−0.188993	+	0.981978i	$0.560522\pi$
$968$			27.6441i			0.888516i
$969$	5.88899	−	7.15101i	0.189182	−	0.229724i
$970$	3.98198	−	49.8098i	0.127854	−	1.59930i
$971$			19.9525i			0.640306i	0.947366	+	0.320153i	$0.103734\pi$
$971$			19.9525i			0.640306i	−0.947366	+	0.320153i	$0.896266\pi$
$972$	11.5931	+	11.5931i	0.371849	+	0.371849i
$973$		−	31.7413i		−	1.01758i
$974$	−37.8687	+	37.8687i	−1.21339	+	1.21339i
$975$	2.05450	+	2.84250i	0.0657965	+	0.0910329i
$976$	19.7460	+	19.7460i	0.632054	+	0.632054i
$977$	27.2005			0.870221			0.435110	−	0.900377i	$-0.356709\pi$
$977$	27.2005			0.870221			0.435110	+	0.900377i	$0.356709\pi$
$978$	14.9099			0.476767
$979$	−42.1150	−	42.1150i	−1.34600	−	1.34600i
$980$	5.72078	−	4.87380i	0.182743	−	0.155688i
$981$	−0.846971	+	0.846971i	−0.0270417	+	0.0270417i
$982$		−	37.9989i		−	1.21259i
$983$	−5.03803	−	5.03803i	−0.160688	−	0.160688i	0.622183	−	0.782872i	$-0.286246\pi$
$983$	−5.03803	−	5.03803i	−0.160688	−	0.160688i	−0.782872	+	0.622183i	$0.786246\pi$
$984$			4.48800i			0.143072i
$985$	−39.4305	−	3.15222i	−1.25636	−	0.100438i
$986$	−31.3135	+	38.0240i	−0.997225	+	1.21093i
$987$			8.48734i			0.270155i
$988$	6.25400			0.198966
$989$	−3.36301	+	3.36301i	−0.106937	+	0.106937i
$990$	−60.5555	−	4.84103i	−1.92458	−	0.153858i
$991$	40.2817	−	40.2817i	1.27959	−	1.27959i	0.338695	−	0.940896i	$-0.390014\pi$
$991$	40.2817	−	40.2817i	1.27959	−	1.27959i	0.940896	−	0.338695i	$-0.109986\pi$
$992$	19.9796	−	19.9796i	0.634351	−	0.634351i
$993$	2.18926	−	2.18926i	0.0694740	−	0.0694740i
$994$		−	49.3670i		−	1.56583i
$995$	−12.4836	−	0.997984i	−0.395756	−	0.0316382i
$996$	−1.96252	−	1.96252i	−0.0621847	−	0.0621847i
$997$	−3.56701	+	3.56701i	−0.112968	+	0.112968i	−0.761331	−	0.648363i	$-0.775454\pi$
$997$	−3.56701	+	3.56701i	−0.112968	+	0.112968i	0.648363	+	0.761331i	$0.275454\pi$
$998$	11.9971	+	11.9971i	0.379761	+	0.379761i
$999$	−6.09097			−0.192710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.j.c.4.2	✓	12
3.2	odd	2		765.2.t.e.514.5		12
5.2	odd	4		425.2.e.d.276.2		12
5.3	odd	4		425.2.e.d.276.5		12
5.4	even	2	inner	85.2.j.c.4.5	yes	12
15.14	odd	2		765.2.t.e.514.2		12
17.8	even	8		1445.2.b.f.579.10		12
17.9	even	8		1445.2.b.f.579.9		12
17.13	even	4	inner	85.2.j.c.64.5	yes	12
51.47	odd	4		765.2.t.e.64.2		12
85.8	odd	8		7225.2.a.bp.1.9		12
85.9	even	8		1445.2.b.f.579.4		12
85.13	odd	4		425.2.e.d.251.2		12
85.42	odd	8		7225.2.a.bp.1.4		12
85.43	odd	8		7225.2.a.bp.1.10		12
85.47	odd	4		425.2.e.d.251.5		12
85.59	even	8		1445.2.b.f.579.3		12
85.64	even	4	inner	85.2.j.c.64.2	yes	12
85.77	odd	8		7225.2.a.bp.1.3		12
255.149	odd	4		765.2.t.e.64.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.2	✓	12	1.1	even	1	trivial
85.2.j.c.4.5	yes	12	5.4	even	2	inner
85.2.j.c.64.2	yes	12	85.64	even	4	inner
85.2.j.c.64.5	yes	12	17.13	even	4	inner
425.2.e.d.251.2		12	85.13	odd	4
425.2.e.d.251.5		12	85.47	odd	4
425.2.e.d.276.2		12	5.2	odd	4
425.2.e.d.276.5		12	5.3	odd	4
765.2.t.e.64.2		12	51.47	odd	4
765.2.t.e.64.5		12	255.149	odd	4
765.2.t.e.514.2		12	15.14	odd	2
765.2.t.e.514.5		12	3.2	odd	2
1445.2.b.f.579.3		12	85.59	even	8
1445.2.b.f.579.4		12	85.9	even	8
1445.2.b.f.579.9		12	17.9	even	8
1445.2.b.f.579.10		12	17.8	even	8
7225.2.a.bp.1.3		12	85.77	odd	8
7225.2.a.bp.1.4		12	85.42	odd	8
7225.2.a.bp.1.9		12	85.8	odd	8
7225.2.a.bp.1.10		12	85.43	odd	8

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.80333 q^{2} +(-0.397180 - 0.397180i) q^{3} +1.25200 q^{4} +(1.45011 + 1.70211i) q^{5} +(0.716248 + 0.716248i) q^{6} +(2.20051 - 2.20051i) q^{7} +1.34889 q^{8} -2.68450i q^{9} +(-2.61503 - 3.06947i) q^{10} +(3.96825 + 3.96825i) q^{11} +(-0.497270 - 0.497270i) q^{12} +1.24880i q^{13} +(-3.96825 + 3.96825i) q^{14} +(0.100090 - 1.25200i) q^{15} -4.93650 q^{16} +(-4.10393 + 0.397180i) q^{17} +4.84103i q^{18} -4.00000i q^{19} +(1.81554 + 2.13104i) q^{20} -1.74800 q^{21} +(-7.15606 - 7.15606i) q^{22} +(1.64598 - 1.64598i) q^{23} +(-0.535753 - 0.535753i) q^{24} +(-0.794361 + 4.93650i) q^{25} -2.25200i q^{26} +(-2.25777 + 2.25777i) q^{27} +(2.75504 - 2.75504i) q^{28} +(-4.68450 + 4.68450i) q^{29} +(-0.180495 + 2.25777i) q^{30} +(3.22025 - 3.22025i) q^{31} +6.20435 q^{32} -3.15222i q^{33} +(7.40074 - 0.716248i) q^{34} +(6.93650 + 0.554530i) q^{35} -3.36099i q^{36} +(1.34889 + 1.34889i) q^{37} +7.21332i q^{38} +(0.495999 - 0.495999i) q^{39} +(1.95604 + 2.29596i) q^{40} +(-4.18850 - 4.18850i) q^{41} +3.15222 q^{42} -2.04316 q^{43} +(4.96825 + 4.96825i) q^{44} +(4.56931 - 3.89281i) q^{45} +(-2.96825 + 2.96825i) q^{46} -4.85546i q^{47} +(1.96068 + 1.96068i) q^{48} -2.68450i q^{49} +(1.43250 - 8.90213i) q^{50} +(1.78775 + 1.47225i) q^{51} +1.56350i q^{52} -9.11674 q^{53} +(4.07151 - 4.07151i) q^{54} +(-1.00000 + 12.5088i) q^{55} +(2.96825 - 2.96825i) q^{56} +(-1.58872 + 1.58872i) q^{57} +(8.44769 - 8.44769i) q^{58} +6.00000i q^{59} +(0.125312 - 1.56750i) q^{60} +(-4.00000 - 4.00000i) q^{61} +(-5.80717 + 5.80717i) q^{62} +(-5.90726 - 5.90726i) q^{63} -1.31550 q^{64} +(-2.12560 + 1.81090i) q^{65} +5.68450i q^{66} +8.46212i q^{67} +(-5.13812 + 0.497270i) q^{68} -1.30750 q^{69} +(-12.5088 - 1.00000i) q^{70} +(-6.22025 + 6.22025i) q^{71} -3.62109i q^{72} +(-1.10906 - 1.10906i) q^{73} +(-2.43250 - 2.43250i) q^{74} +(2.27618 - 1.64517i) q^{75} -5.00800i q^{76} +17.4643 q^{77} +(-0.894450 + 0.894450i) q^{78} +(-3.47225 - 3.47225i) q^{79} +(-7.15846 - 8.40246i) q^{80} -6.26000 q^{81} +(7.55324 + 7.55324i) q^{82} +3.94658 q^{83} -2.18850 q^{84} +(-6.62720 - 6.40939i) q^{85} +3.68450 q^{86} +3.72118 q^{87} +(5.35273 + 5.35273i) q^{88} -10.6130 q^{89} +(-8.23997 + 7.02003i) q^{90} +(2.74800 + 2.74800i) q^{91} +(2.06077 - 2.06077i) q^{92} -2.55804 q^{93} +8.75600i q^{94} +(6.80844 - 5.80044i) q^{95} +(-2.46425 - 2.46425i) q^{96} +(8.76239 + 8.76239i) q^{97} +4.84103i q^{98} +(10.6527 - 10.6527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 20 q^{6} - 4 q^{10} + 16 q^{11} - 16 q^{14} + 4 q^{16} - 32 q^{20} - 24 q^{21} - 32 q^{24} + 4 q^{29} + 52 q^{30} + 4 q^{31} + 20 q^{35} + 12 q^{39} + 24 q^{40} + 16 q^{41} + 28 q^{44}+ \cdots + 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^4 - 20 * q^6 - 4 * q^10 + 16 * q^11 - 16 * q^14 + 4 * q^16 - 32 * q^20 - 24 * q^21 - 32 * q^24 + 4 * q^29 + 52 * q^30 + 4 * q^31 + 20 * q^35 + 12 * q^39 + 24 * q^40 + 16 * q^41 + 28 * q^44 - 20 * q^45 - 4 * q^46 - 40 * q^50 + 44 * q^51 + 100 * q^54 - 12 * q^55 + 4 * q^56 - 48 * q^61 - 76 * q^64 + 8 * q^65 - 88 * q^69 - 40 * q^71 + 28 * q^74 + 64 * q^75 - 4 * q^79 + 12 * q^80 - 60 * q^81 + 40 * q^84 - 52 * q^85 - 16 * q^86 - 16 * q^89 - 84 * q^90 + 36 * q^91 - 4 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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