LMFDB - Embedded newform 85.2.j.c.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(4,85)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			64.5
Root			$-2.80333i$ of defining polynomial
Character	$\chi$	$=$	85.64
Dual form			85.2.j.c.4.5

$q$-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} +(-1.70211 + 1.45011i) q^{5} +(0.716248 - 0.716248i) q^{6} +(-2.20051 - 2.20051i) q^{7} -1.34889 q^{8} +2.68450i q^{9} +(-3.06947 + 2.61503i) 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} +(-2.13104 + 1.81554i) 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} +(2.29596 - 1.95604i) q^{40} +(-4.18850 + 4.18850i) q^{41} -3.15222 q^{42} +2.04316 q^{43} +(4.96825 - 4.96825i) q^{44} +(-3.89281 - 4.56931i) 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} +(-1.81090 - 2.12560i) 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} +(-1.64517 - 2.27618i) q^{75} +5.00800i q^{76} -17.4643 q^{77} +(0.894450 + 0.894450i) q^{78} +(-3.47225 + 3.47225i) q^{79} +(8.40246 - 7.15846i) q^{80} -6.26000 q^{81} +(-7.55324 + 7.55324i) q^{82} -3.94658 q^{83} -2.18850 q^{84} +(-7.56130 + 5.27511i) q^{85} +3.68450 q^{86} -3.72118 q^{87} +(-5.35273 + 5.35273i) q^{88} -10.6130 q^{89} +(-7.02003 - 8.23997i) q^{90} +(2.74800 - 2.74800i) q^{91} +(-2.06077 - 2.06077i) q^{92} +2.55804 q^{93} -8.75600i q^{94} +(-5.80044 - 6.80844i) 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 $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

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

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	$-0.279938\pi$
$2$	1.80333			1.27515			0.637574	+	0.770389i	$0.279938\pi$
$3$	0.397180	−	0.397180i	0.229312	−	0.229312i	−0.583093	−	0.812405i	$-0.698158\pi$
$3$	0.397180	−	0.397180i	0.229312	−	0.229312i	0.812405	+	0.583093i	$0.198158\pi$
$4$	1.25200			0.626000
$5$	−1.70211	+	1.45011i	−0.761207	+	0.648509i
$5$	−1.70211	+	1.45011i	−0.761207	+	0.648509i
$6$	0.716248	−	0.716248i	0.292407	−	0.292407i
$7$	−2.20051	−	2.20051i	−0.831715	−	0.831715i	0.156036	−	0.987751i	$-0.450128\pi$
$7$	−2.20051	−	2.20051i	−0.831715	−	0.831715i	−0.987751	+	0.156036i	$0.950128\pi$
$8$	−1.34889			−0.476905
$9$			2.68450i			0.894832i
$10$	−3.06947	+	2.61503i	−0.970651	+	0.826944i
$11$	3.96825	−	3.96825i	1.19647	−	1.19647i	0.221256	−	0.975216i	$-0.428984\pi$
$11$	3.96825	−	3.96825i	1.19647	−	1.19647i	0.975216	−	0.221256i	$-0.0710156\pi$
$12$	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	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−2.13104	+	1.81554i	−0.476516	+	0.405967i
$21$	−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	$-0.328029\pi$
$23$	−1.64598	−	1.64598i	−0.343211	−	0.343211i	−0.857573	+	0.514362i	$0.828029\pi$
$24$	−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	0.122571	−	0.992460i	$-0.460886\pi$
$29$	−4.68450	−	4.68450i	−0.869889	−	0.869889i	−0.992460	+	0.122571i	$0.960886\pi$
$30$	−0.180495	+	2.25777i	−0.0329537	+	0.412211i
$31$	3.22025	+	3.22025i	0.578374	+	0.578374i	0.934455	−	0.356081i	$-0.115887\pi$
$31$	3.22025	+	3.22025i	0.578374	+	0.578374i	−0.356081	+	0.934455i	$0.615887\pi$
$32$	−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	$-0.800120\pi$
$37$	−1.34889	+	1.34889i	−0.221756	+	0.221756i	0.587481	+	0.809238i	$0.300120\pi$
$38$			7.21332i			1.17016i
$39$	0.495999	+	0.495999i	0.0794234	+	0.0794234i
$40$	2.29596	−	1.95604i	0.363023	−	0.309277i
$41$	−4.18850	+	4.18850i	−0.654133	+	0.654133i	−0.953986	−	0.299852i	$-0.903063\pi$
$41$	−4.18850	+	4.18850i	−0.654133	+	0.654133i	0.299852	+	0.953986i	$0.403063\pi$
$42$	−3.15222			−0.486398
$43$	2.04316			0.311579			0.155790	−	0.987790i	$-0.450208\pi$
$43$	2.04316			0.311579			0.155790	+	0.987790i	$0.450208\pi$
$44$	4.96825	−	4.96825i	0.748992	−	0.748992i
$45$	−3.89281	−	4.56931i	−0.580306	−	0.681152i
$46$	−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	$-0.284634\pi$
$53$	9.11674			1.25228			0.626140	+	0.779710i	$0.284634\pi$
$54$	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	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$	−0.125312	+	1.56750i	−0.0161777	+	0.202364i
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	5.80717	+	5.80717i	0.737512	+	0.737512i
$63$	5.90726	−	5.90726i	0.744245	−	0.744245i
$64$	−1.31550			−0.164438
$65$	−1.81090	−	2.12560i	−0.224614	−	0.263648i
$66$		−	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	0.234023	−	0.972231i	$-0.424811\pi$
$71$	−6.22025	−	6.22025i	−0.738208	−	0.738208i	−0.972231	+	0.234023i	$0.924811\pi$
$72$		−	3.62109i		−	0.426750i
$73$	1.10906	−	1.10906i	0.129806	−	0.129806i	−0.639219	−	0.769025i	$-0.720742\pi$
$73$	1.10906	−	1.10906i	0.129806	−	0.129806i	0.769025	+	0.639219i	$0.220742\pi$
$74$	−2.43250	+	2.43250i	−0.282772	+	0.282772i
$75$	−1.64517	−	2.27618i	−0.189968	−	0.262831i
$76$			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	−0.874922	−	0.484264i	$-0.839088\pi$
$79$	−3.47225	+	3.47225i	−0.390658	+	0.390658i	0.484264	+	0.874922i	$0.339088\pi$
$80$	8.40246	−	7.15846i	0.939424	−	0.800340i
$81$	−6.26000			−0.695556
$82$	−7.55324	+	7.55324i	−0.834116	+	0.834116i
$83$	−3.94658			−0.433194			−0.216597	−	0.976261i	$-0.569496\pi$
$83$	−3.94658			−0.433194			−0.216597	+	0.976261i	$0.569496\pi$
$84$	−2.18850			−0.238785
$85$	−7.56130	+	5.27511i	−0.820138	+	0.572166i
$86$	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	$0.690155\pi$
$90$	−7.02003	−	8.23997i	−0.739976	−	0.868569i
$91$	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
$95$	−5.80044	−	6.80844i	−0.595113	−	0.698531i
$96$	−2.46425	+	2.46425i	−0.251506	+	0.251506i
$97$	−8.76239	+	8.76239i	−0.889686	+	0.889686i	−0.994493	−	0.104807i	$-0.966578\pi$
$97$	−8.76239	+	8.76239i	−0.889686	+	0.889686i	0.104807	+	0.994493i	$0.466578\pi$
$98$			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
$105$	2.97529	−	2.53479i	0.290358	−	0.247370i
$106$	16.4405			1.59684
$107$	12.0115	−	12.0115i	1.16120	−	1.16120i	0.176984	−	0.984214i	$-0.443366\pi$
$107$	12.0115	−	12.0115i	1.16120	−	1.16120i	0.984214	−	0.176984i	$-0.0566341\pi$
$108$	2.82673	+	2.82673i	0.272002	+	0.272002i
$109$	−0.315505	+	0.315505i	−0.0302199	+	0.0302199i	−0.722055	−	0.691835i	$-0.756802\pi$
$109$	−0.315505	+	0.315505i	−0.0302199	+	0.0302199i	0.691835	+	0.722055i	$0.256802\pi$
$110$	−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	$-0.428809\pi$
$113$	−8.00768	−	8.00768i	−0.753299	−	0.753299i	−0.975094	+	0.221794i	$0.928809\pi$
$114$	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
$125$	5.80637	+	9.55437i	0.519338	+	0.854569i
$126$	10.6527	−	10.6527i	0.949022	−	0.949022i
$127$	5.85000			0.519104			0.259552	−	0.965729i	$-0.416425\pi$
$127$	5.85000			0.519104			0.259552	+	0.965729i	$0.416425\pi$
$128$	10.0364			0.887102
$129$	0.811504	−	0.811504i	0.0714489	−	0.0714489i
$130$	−3.26565	−	3.83315i	−0.286416	−	0.336190i
$131$	13.8332	+	13.8332i	1.20862	+	1.20862i	0.971475	+	0.237140i	$0.0762101\pi$
$131$	13.8332	+	13.8332i	1.20862	+	1.20862i	0.237140	+	0.971475i	$0.423790\pi$
$132$		−	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	0.943398	−	0.331663i	$-0.107610\pi$
$139$	7.21225	+	7.21225i	0.611735	+	0.611735i	−0.331663	+	0.943398i	$0.607610\pi$
$140$	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	$0.273601\pi$
$150$	−2.96679	−	4.10471i	−0.242238	−	0.335148i
$151$			3.36899i			0.274165i	0.990560	+	0.137082i	$0.0437725\pi$
$151$			3.36899i			0.274165i	−0.990560	+	0.137082i	$0.956228\pi$
$152$		−	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
$160$	10.5605	−	8.99699i	0.834880	−	0.711275i
$161$			7.24400i			0.570907i
$162$	−11.2889			−0.886936
$163$	−10.4084	−	10.4084i	−0.815247	−	0.815247i	0.170168	−	0.985415i	$-0.445569\pi$
$163$	−10.4084	−	10.4084i	−0.815247	−	0.815247i	−0.985415	+	0.170168i	$0.945569\pi$
$164$	−5.24400	+	5.24400i	−0.409488	+	0.409488i
$165$	4.57107	+	5.36543i	0.355857	+	0.417698i
$166$	−7.11699			−0.552386
$167$	−0.297091	+	0.297091i	−0.0229896	+	0.0229896i	−0.718508	−	0.695519i	$-0.755175\pi$
$167$	−0.297091	+	0.297091i	−0.0229896	+	0.0229896i	0.695519	+	0.718508i	$0.255175\pi$
$168$	2.35786			0.181913
$169$	11.4405			0.880038
$170$	−13.6355	+	9.51276i	−1.04580	+	0.729595i
$171$	−10.7380			−0.821154
$172$	2.55804			0.195049
$173$	11.7397	−	11.7397i	0.892549	−	0.892549i	−0.102213	−	0.994763i	$-0.532592\pi$
$173$	11.7397	−	11.7397i	0.892549	−	0.892549i	0.994763	+	0.102213i	$0.0325924\pi$
$174$	−6.71052			−0.508723
$175$	−12.6108	+	9.11481i	−0.953288	+	0.689015i
$176$	−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	$-0.734959\pi$
$179$		−	19.7935i		−	1.47943i	0.672918	−	0.739717i	$-0.265041\pi$
$180$	−4.87380	−	5.72078i	−0.363272	−	0.426401i
$181$	−6.62099	+	6.62099i	−0.492134	+	0.492134i	−0.908978	−	0.416844i	$-0.863136\pi$
$181$	−6.62099	+	6.62099i	−0.492134	+	0.492134i	0.416844	+	0.908978i	$0.363136\pi$
$182$	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
$190$	−10.4601	−	12.2779i	−0.758856	−	0.890730i
$191$	−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	$-0.298009\pi$
$193$	−2.95204	−	2.95204i	−0.212493	−	0.212493i	−0.805325	+	0.592833i	$0.798009\pi$
$194$	−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	$-0.0329795\pi$
$197$	12.5088	+	12.5088i	0.891215	+	0.891215i	−0.103423	+	0.994637i	$0.532979\pi$
$198$	19.2104	+	19.2104i	1.36522	+	1.36522i
$199$	−3.96025	−	3.96025i	−0.280734	−	0.280734i	0.552667	−	0.833402i	$-0.313610\pi$
$199$	−3.96025	−	3.96025i	−0.280734	−	0.280734i	−0.833402	+	0.552667i	$0.813610\pi$
$200$	−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
$210$	5.36543	−	4.57107i	0.370250	−	0.315434i
$211$	0.652743	−	0.652743i	0.0449367	−	0.0449367i	−0.684281	−	0.729218i	$-0.739884\pi$
$211$	0.652743	−	0.652743i	0.0449367	−	0.0449367i	0.729218	+	0.684281i	$0.239884\pi$
$212$	11.4142			0.783928
$213$	−4.94112			−0.338560
$214$	21.6607	−	21.6607i	1.48070	−	1.48070i
$215$	−3.47769	+	2.96281i	−0.237176	+	0.202062i
$216$	−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	$-0.513313\pi$
$223$	−1.24880			−0.0836259			−0.0418129	+	0.999125i	$0.513313\pi$
$224$	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	$-0.375587\pi$
$227$	−8.19025	−	8.19025i	−0.543606	−	0.543606i	−0.924584	+	0.380978i	$0.875587\pi$
$228$	1.98908	+	1.98908i	0.131730	+	0.131730i
$229$		−	11.7480i		−	0.776330i	−0.921590	−	0.388165i	$-0.873109\pi$
$229$		−	11.7480i		−	0.776330i	0.921590	−	0.388165i	$-0.126891\pi$
$230$	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	$-0.870738\pi$
$233$	−7.99325	+	7.99325i	−0.523655	+	0.523655i	0.395018	+	0.918673i	$0.370738\pi$
$234$	−6.04548			−0.395206
$235$	7.04095	+	8.26453i	0.459301	+	0.539119i
$236$		−	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	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$		−	36.9574i		−	2.37571i
$243$	−9.25966	+	9.25966i	−0.594008	+	0.594008i
$244$	−5.00800	+	5.00800i	−0.320604	+	0.320604i
$245$	−3.89281	−	4.56931i	−0.248703	−	0.291922i
$246$			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
$250$	10.4708	+	17.2297i	0.662232	+	1.08970i
$251$	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
$255$	−0.908031	+	5.09837i	−0.0568631	+	0.319272i
$256$	20.7300			1.29562
$257$	−24.3982			−1.52192			−0.760958	−	0.648801i	$-0.775271\pi$
$257$	−24.3982			−1.52192			−0.760958	+	0.648801i	$0.775271\pi$
$258$	1.46341	−	1.46341i	0.0911079	−	0.0911079i
$259$	5.93650			0.368876
$260$	−2.26725	−	2.66125i	−0.140609	−	0.165044i
$261$	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	$-0.312041\pi$
$263$	18.0585			1.11354			0.556768	+	0.830668i	$0.312041\pi$
$264$			4.25200i			0.261693i
$265$	−15.5177	+	13.2203i	−0.953245	+	0.812115i
$266$	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	0.208104	−	0.978107i	$-0.433271\pi$
$269$	−12.6290	−	12.6290i	−0.770003	−	0.770003i	−0.978107	+	0.208104i	$0.933271\pi$
$270$	−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
$275$	−16.4370	−	22.7415i	−0.991190	−	1.37136i
$276$	−1.63699			−0.0985355
$277$	−10.0256	+	10.0256i	−0.602381	+	0.602381i	−0.940944	−	0.338563i	$-0.890059\pi$
$277$	−10.0256	+	10.0256i	−0.602381	+	0.602381i	0.338563	+	0.940944i	$0.390059\pi$
$278$	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	$-0.925166\pi$
$281$		−	7.80949i		−	0.465875i	0.972492	−	0.232937i	$-0.0748338\pi$
$282$	−3.47771	−	3.47771i	−0.207095	−	0.207095i
$283$	−14.7842	−	14.7842i	−0.878828	−	0.878828i	0.114586	−	0.993413i	$-0.463446\pi$
$283$	−14.7842	−	14.7842i	−0.878828	−	0.878828i	−0.993413	+	0.114586i	$0.963446\pi$
$284$	−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
$295$	8.70066	+	10.2127i	0.506572	+	0.594604i
$296$	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
$300$	−2.05976	−	2.84978i	−0.118920	−	0.164532i
$301$	−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	0.621631	−	0.783311i	$-0.286471\pi$
$311$	−2.85126	−	2.85126i	−0.161680	−	0.161680i	−0.783311	+	0.621631i	$0.786471\pi$
$312$	−0.669049	−	0.669049i	−0.0378774	−	0.0378774i
$313$	16.0154	+	16.0154i	0.905242	+	0.905242i	0.995884	−	0.0906416i	$-0.0288918\pi$
$313$	16.0154	+	16.0154i	0.905242	+	0.905242i	−0.0906416	+	0.995884i	$0.528892\pi$
$314$		−	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	$-0.175364\pi$
$317$	5.85000	+	5.85000i	0.328569	+	0.328569i	−0.523473	+	0.852042i	$0.675364\pi$
$318$	6.52984	−	6.52984i	0.366175	−	0.366175i
$319$	−37.1785			−2.08160
$320$	2.23913	−	1.90763i	0.125171	−	0.106640i
$321$		−	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
$330$	8.24314	+	9.67564i	0.453770	+	0.532626i
$331$		−	5.51200i		−	0.302967i	−0.988460	−	0.151484i	$-0.951595\pi$
$331$		−	5.51200i		−	0.302967i	0.988460	−	0.151484i	$-0.0484050\pi$
$332$	−4.94112			−0.271179
$333$	−3.62109	−	3.62109i	−0.198435	−	0.198435i
$334$	−0.535753	+	0.535753i	−0.0293151	+	0.0293151i
$335$	−12.2710	−	14.4035i	−0.670437	−	0.786946i
$336$	8.62899			0.470750
$337$	−6.74445	+	6.74445i	−0.367394	+	0.367394i	−0.866526	−	0.499132i	$-0.833652\pi$
$337$	−6.74445	+	6.74445i	−0.367394	+	0.367394i	0.499132	+	0.866526i	$0.333652\pi$
$338$	20.6310			1.12218
$339$	−6.36099			−0.345482
$340$	−9.46675	+	6.60444i	−0.513407	+	0.358176i
$341$	25.5575			1.38402
$342$	−19.3641			−1.04709
$343$	−9.49631	+	9.49631i	−0.512753	+	0.512753i
$344$	−2.75600			−0.148594
$345$	2.22551	−	1.89602i	0.119818	−	0.102078i
$346$	21.1705	−	21.1705i	1.13813	−	1.13813i
$347$	8.16503	+	8.16503i	0.438322	+	0.438322i	0.891447	−	0.453125i	$-0.149691\pi$
$347$	8.16503	+	8.16503i	0.438322	+	0.438322i	−0.453125	+	0.891447i	$0.649691\pi$
$348$	−4.65892			−0.249744
$349$			11.4325i			0.611967i	0.952037	+	0.305984i	$0.0989853\pi$
$349$			11.4325i			0.611967i	−0.952037	+	0.305984i	$0.901015\pi$
$350$	−22.7415	+	16.4370i	−1.21558	+	0.878596i
$351$	−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	$0.231328\pi$
$359$			25.1785i			1.32887i	−0.747346	+	0.664435i	$0.768672\pi$
$360$	5.25098	+	6.16350i	0.276751	+	0.324845i
$361$	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	$-0.300784\pi$
$367$	−4.30411	−	4.30411i	−0.224673	−	0.224673i	−0.810463	+	0.585790i	$0.800784\pi$
$368$	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	0.725263	−	0.688472i	$-0.241718\pi$
$379$	0.716248	+	0.716248i	0.0367912	+	0.0367912i	−0.688472	+	0.725263i	$0.741718\pi$
$380$	−7.26215	−	8.52417i	−0.372541	−	0.437281i
$381$	2.32351	−	2.32351i	0.119037	−	0.119037i
$382$	−25.1321			−1.28587
$383$	−25.8660			−1.32169			−0.660846	−	0.750521i	$-0.729802\pi$
$383$	−25.8660			−1.32169			−0.660846	+	0.750521i	$0.729802\pi$
$384$	3.98627	−	3.98627i	0.203423	−	0.203423i
$385$	29.7262	−	25.3252i	1.51499	−	1.29069i
$386$	−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	$0.316476\pi$
$389$			33.0695i			1.67669i	−0.545140	+	0.838345i	$0.683524\pi$
$390$	−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	$-0.184421\pi$
$397$	5.76434	+	5.76434i	0.289304	+	0.289304i	−0.547501	+	0.836805i	$0.684421\pi$
$398$	−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	−0.704180	−	0.710022i	$-0.748685\pi$
$401$	0.116990	−	0.116990i	0.00584222	−	0.00584222i	0.710022	+	0.704180i	$0.248685\pi$
$402$	6.06097	+	6.06097i	0.302294	+	0.302294i
$403$	−4.02145	+	4.02145i	−0.200323	+	0.200323i
$404$	12.0455			0.599285
$405$	10.6552	−	9.07769i	0.529462	−	0.451074i
$406$			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
$415$	6.71752	−	5.72298i	0.329750	−	0.280930i
$416$		−	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	−0.170957	−	0.985278i	$-0.554686\pi$
$419$	16.6687	−	16.6687i	0.814322	−	0.814322i	0.985278	+	0.170957i	$0.0546859\pi$
$420$	3.72506	−	3.17356i	0.181764	−	0.154854i
$421$	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
$425$	5.22068	−	19.9435i	0.253240	−	0.967403i
$426$	−8.91047			−0.431714
$427$	17.6041			0.851921
$428$	15.0384	−	15.0384i	0.726910	−	0.726910i
$429$	3.93650			0.190056
$430$	−6.27142	+	5.34292i	−0.302435	+	0.257659i
$431$	4.90474	−	4.90474i	0.236253	−	0.236253i	−0.579043	−	0.815297i	$-0.696574\pi$
$431$	4.90474	−	4.90474i	0.236253	−	0.236253i	0.815297	+	0.579043i	$0.196574\pi$
$432$	−11.1455	−	11.1455i	−0.536237	−	0.536237i
$433$	15.4464			0.742307			0.371153	−	0.928572i	$-0.378962\pi$
$433$	15.4464			0.742307			0.371153	+	0.928572i	$0.378962\pi$
$434$		−	25.5575i		−	1.22680i
$435$	6.33386	−	5.39612i	0.303685	−	0.258724i
$436$	−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	0.731484	−	0.681859i	$-0.238828\pi$
$439$	1.03975	+	1.03975i	0.0496247	+	0.0496247i	−0.681859	+	0.731484i	$0.738828\pi$
$440$	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
$445$	18.0645	−	15.3900i	0.856339	−	0.729556i
$446$	−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	−0.525846	−	0.850580i	$-0.676251\pi$
$449$	6.88099	−	6.88099i	0.324734	−	0.324734i	0.850580	+	0.525846i	$0.176251\pi$
$450$	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	$-0.821795\pi$
$457$	−36.2279			−1.69467			−0.847336	+	0.531058i	$0.821795\pi$
$458$		−	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	$0.382711\pi$
$461$			40.0595i			1.86576i	−0.360193	+	0.932878i	$0.617289\pi$
$462$	−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
$465$	−4.35407	+	3.70944i	−0.201915	+	0.172021i
$466$	−14.4145	+	14.4145i	−0.667738	+	0.667738i
$467$	−19.4471			−0.899903			−0.449952	−	0.893053i	$-0.648559\pi$
$467$	−19.4471			−0.899903			−0.449952	+	0.893053i	$0.648559\pi$
$468$	−4.19721			−0.194016
$469$	18.6210	−	18.6210i	0.859837	−	0.859837i
$470$	12.6972	+	14.9037i	0.585677	+	0.687456i
$471$	−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	0.901993	−	0.431751i	$-0.142104\pi$
$479$	10.2918	+	10.2918i	0.470242	+	0.470242i	−0.431751	+	0.901993i	$0.642104\pi$
$480$	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	$-0.484935\pi$
$487$	−20.9993	−	20.9993i	−0.951570	−	0.951570i	−0.998880	+	0.0473104i	$0.984935\pi$
$488$	5.39556	−	5.39556i	0.244246	−	0.244246i
$489$	−8.26800			−0.373892
$490$	−7.02003	−	8.23997i	−0.317133	−	0.372244i
$491$		−	21.0715i		−	0.950944i	−0.879731	−	0.475472i	$-0.842277\pi$
$491$		−	21.0715i		−	0.950944i	0.879731	−	0.475472i	$-0.157723\pi$
$492$			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	−0.840159	−	0.542341i	$-0.817538\pi$
$499$	−6.65274	+	6.65274i	−0.297818	+	0.297818i	0.542341	+	0.840159i	$0.317538\pi$
$500$	7.26958	+	11.9621i	0.325106	+	0.534960i
$501$			0.235997i			0.0105436i
$502$	35.7231			1.59440
$503$	−20.7739	−	20.7739i	−0.926263	−	0.926263i	0.0711991	−	0.997462i	$-0.477317\pi$
$503$	−20.7739	−	20.7739i	−0.926263	−	0.926263i	−0.997462	+	0.0711991i	$0.977317\pi$
$504$	−7.96825	+	7.96825i	−0.354934	+	0.354934i
$505$	−16.3760	+	13.9515i	−0.728722	+	0.620833i
$506$	−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	$0.603340\pi$
$510$	−1.63748	+	9.19404i	−0.0725088	+	0.407119i
$511$	−4.88099			−0.215922
$512$	17.3102			0.765009
$513$	−9.03108	+	9.03108i	−0.398732	+	0.398732i
$514$	−43.9980			−1.94067
$515$	−2.67253	−	3.13696i	−0.117766	−	0.138231i
$516$	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
$520$	2.44270	+	2.86720i	0.107120	+	0.125735i
$521$	−19.5655	+	19.5655i	−0.857180	+	0.857180i	−0.991005	−	0.133825i	$-0.957274\pi$
$521$	−19.5655	+	19.5655i	−0.857180	+	0.857180i	0.133825	+	0.991005i	$0.457274\pi$
$522$	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
$530$	−27.9835	+	23.8405i	−1.21553	+	1.03557i
$531$	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	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−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	$-0.538941\pi$
$547$	20.3591	−	20.3591i	0.870493	−	0.870493i	0.992526	+	0.122033i	$0.0389413\pi$
$548$			17.3498i			0.741148i
$549$	−10.7380	−	10.7380i	−0.458286	−	0.458286i
$550$	−29.6414	−	41.0104i	−1.26391	−	1.74869i
$551$	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
$555$	−1.55380	−	1.82382i	−0.0659552	−	0.0774169i
$556$	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	$-0.473303\pi$
$563$	3.97544			0.167545			0.0837724	+	0.996485i	$0.473303\pi$
$564$	−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	$0.0367516\pi$
$569$			5.49600i			0.230404i	−0.993342	+	0.115202i	$0.963248\pi$
$570$	−9.03108	−	0.721979i	−0.378270	−	0.0302404i
$571$	12.3372	−	12.3372i	0.516297	−	0.516297i	−0.400152	−	0.916449i	$-0.631043\pi$
$571$	12.3372	−	12.3372i	0.516297	−	0.516297i	0.916449	+	0.400152i	$0.131043\pi$
$572$	6.20435	+	6.20435i	0.259417	+	0.259417i
$573$	−5.53530	+	5.53530i	−0.231241	+	0.231241i
$574$	33.2420			1.38749
$575$	−9.43288	+	6.81788i	−0.393378	+	0.284325i
$576$		−	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
$585$	5.70616	−	4.86135i	0.235920	−	0.200992i
$586$			8.64701i			0.357205i
$587$	28.6847			1.18394			0.591972	−	0.805959i	$-0.298350\pi$
$587$	28.6847			1.18394			0.591972	+	0.805959i	$0.298350\pi$
$588$	1.33492	+	1.33492i	0.0550511	+	0.0550511i
$589$	−12.8810	+	12.8810i	−0.530752	+	0.530752i
$590$	15.6902	+	18.4168i	0.645954	+	0.758208i
$591$	9.93650			0.408733
$592$	6.65879	−	6.65879i	0.273675	−	0.273675i
$593$	−9.74614			−0.400226			−0.200113	−	0.979773i	$-0.564131\pi$
$593$	−9.74614			−0.400226			−0.200113	+	0.979773i	$0.564131\pi$
$594$	32.3135			1.32584
$595$	28.2467	+	5.03079i	1.15800	+	0.206242i
$596$	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	$0.447218\pi$
$600$	2.21916	+	3.07032i	0.0905969	+	0.125345i
$601$	−12.8810	+	12.8810i	−0.525427	+	0.525427i	−0.919205	−	0.393779i	$-0.871168\pi$
$601$	−12.8810	+	12.8810i	−0.525427	+	0.525427i	0.393779	+	0.919205i	$0.371168\pi$
$602$	−8.10777	−	8.10777i	−0.330448	−	0.330448i
$603$	−22.7165			−0.925089
$604$			4.21798i			0.171627i
$605$	29.7185	+	34.8830i	1.20823	+	1.41820i
$606$	6.89101	−	6.89101i	0.279928	−	0.279928i
$607$	8.37964	−	8.37964i	0.340119	−	0.340119i	−0.516293	−	0.856412i	$-0.672688\pi$
$607$	8.37964	−	8.37964i	0.340119	−	0.340119i	0.856412	+	0.516293i	$0.172688\pi$
$608$		−	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
$615$	−4.82477	−	5.66322i	−0.194554	−	0.228363i
$616$	23.5575			0.949158
$617$	−7.41350	+	7.41350i	−0.298456	+	0.298456i	−0.840409	−	0.541953i	$-0.817685\pi$
$617$	−7.41350	+	7.41350i	−0.298456	+	0.298456i	0.541953	+	0.840409i	$0.317685\pi$
$618$	1.32003	+	1.32003i	0.0530995	+	0.0530995i
$619$	−16.4702	+	16.4702i	−0.661995	+	0.661995i	−0.955850	−	0.293855i	$-0.905062\pi$
$619$	−16.4702	+	16.4702i	−0.661995	+	0.661995i	0.293855	+	0.955850i	$0.405062\pi$
$620$	−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	$-0.694696\pi$
$631$		−	41.1310i		−	1.63740i	0.574223	−	0.818699i	$-0.305304\pi$
$632$	4.68368	−	4.68368i	0.186307	−	0.186307i
$633$		−	0.518514i		−	0.0206091i
$634$	10.5495	+	10.5495i	0.418974	+	0.418974i
$635$	−9.95735	+	8.48315i	−0.395145	+	0.336643i
$636$	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
$640$	−17.0831	+	14.5539i	−0.675268	+	0.575294i
$641$	33.4325	+	33.4325i	1.32050	+	1.32050i	0.913367	+	0.407137i	$0.133473\pi$
$641$	33.4325	+	33.4325i	1.32050	+	1.32050i	0.407137	+	0.913367i	$0.366527\pi$
$642$		−	17.2064i		−	0.679084i
$643$	−4.99838	+	4.99838i	−0.197117	+	0.197117i	−0.798763	−	0.601646i	$-0.794512\pi$
$643$	−4.99838	+	4.99838i	−0.197117	+	0.197117i	0.601646	+	0.798763i	$0.294512\pi$
$644$			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	$-0.436430\pi$
$653$	−19.9764	−	19.9764i	−0.781736	−	0.781736i	−0.980124	+	0.198388i	$0.936430\pi$
$654$			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	$0.411297\pi$
$660$	5.72298	+	6.71752i	0.222767	+	0.261479i
$661$		−	49.0355i		−	1.90726i	−0.300984	−	0.953629i	$-0.597315\pi$
$661$		−	49.0355i		−	1.90726i	0.300984	−	0.953629i	$-0.402685\pi$
$662$		−	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
$670$	−22.1287	−	25.9742i	−0.854906	−	1.00347i
$671$			31.7460i			1.22554i
$672$	10.8452			0.418363
$673$	22.2405	+	22.2405i	0.857308	+	0.857308i	0.991020	−	0.133712i	$-0.0426897\pi$
$673$	22.2405	+	22.2405i	0.857308	+	0.857308i	−0.133712	+	0.991020i	$0.542690\pi$
$674$	−12.1625	+	12.1625i	−0.468481	+	0.468481i
$675$	12.9390	−	9.35199i	0.498021	−	0.359958i
$676$	14.3235			0.550904
$677$	21.4109	−	21.4109i	0.822889	−	0.822889i	−0.163633	−	0.986521i	$-0.552321\pi$
$677$	21.4109	−	21.4109i	0.822889	−	0.822889i	0.986521	+	0.163633i	$0.0523212\pi$
$678$	−11.4710			−0.440540
$679$	38.5635			1.47993
$680$	10.1994	−	7.11554i	0.391128	−	0.272869i
$681$	−6.50602			−0.249311
$682$	46.0886			1.76482
$683$	−32.6533	+	32.6533i	−1.24944	+	1.24944i	−0.293479	+	0.955966i	$0.594813\pi$
$683$	−32.6533	+	32.6533i	−1.24944	+	1.24944i	−0.955966	+	0.293479i	$0.905187\pi$
$684$	−13.4440			−0.514043
$685$	−20.0952	−	23.5873i	−0.767797	−	0.901225i
$686$	−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
$690$	4.01334	−	3.41916i	0.152785	−	0.130165i
$691$	−7.52775	+	7.52775i	−0.286369	+	0.286369i	−0.835643	−	0.549273i	$-0.814905\pi$
$691$	−7.52775	+	7.52775i	−0.286369	+	0.286369i	0.549273	+	0.835643i	$0.314905\pi$
$692$	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
$700$	−15.7887	+	11.4117i	−0.596758	+	0.431324i
$701$	−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	0.879490	−	0.475917i	$-0.157884\pi$
$709$	10.7460	+	10.7460i	0.403574	+	0.403574i	−0.475917	+	0.879490i	$0.657884\pi$
$710$	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	0.610878	−	0.791724i	$-0.290816\pi$
$719$	−4.84924	−	4.84924i	−0.180846	−	0.180846i	−0.791724	+	0.610878i	$0.790816\pi$
$720$	19.2169	+	22.5564i	0.716170	+	0.840626i
$721$	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
$725$	−26.8462	+	19.4038i	−0.997042	+	0.720639i
$726$	−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	$-0.210409\pi$
$733$	42.7425			1.57873			0.789366	+	0.613923i	$0.210409\pi$
$734$	−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	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$	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	0.478269	−	0.878214i	$-0.341265\pi$
$743$	36.9750	−	36.9750i	1.35648	−	1.35648i	0.878214	−	0.478269i	$-0.158735\pi$
$744$	−3.45051			−0.126502
$745$	−27.1257	+	23.1097i	−0.993808	+	0.846673i
$746$			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	0.999832	+	0.0183534i	$0.00584240\pi$
$751$	27.9027	+	27.9027i	1.01818	+	1.01818i	0.0183534	+	0.999832i	$0.494158\pi$
$752$			23.9690i			0.874058i
$753$	7.86794	−	7.86794i	0.286724	−	0.286724i
$754$	10.5495	−	10.5495i	0.384190	−	0.384190i
$755$	−4.88541	−	5.73439i	−0.177798	−	0.208696i
$756$		−	12.4405i		−	0.452456i
$757$	8.61186			0.313003			0.156502	−	0.987678i	$-0.449978\pi$
$757$	8.61186			0.313003			0.156502	+	0.987678i	$0.449978\pi$
$758$	1.29163	+	1.29163i	0.0469141	+	0.0469141i
$759$	−5.18850	+	5.18850i	−0.188330	+	0.188330i
$760$	7.82416	+	9.18384i	0.283812	+	0.333133i
$761$	−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
$765$	−14.1610	−	20.2983i	−0.511992	−	0.733886i
$766$	−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	$0.398718\pi$
$770$	53.6062	−	45.6697i	1.93183	−	1.64582i
$771$	−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	$-0.382812\pi$
$773$	20.0124			0.719796			0.359898	+	0.932992i	$0.382812\pi$
$774$			9.89101i			0.355525i
$775$	18.4548	−	13.3387i	0.662915	−	0.479140i
$776$	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
$785$	5.68640	+	6.67459i	0.202956	+	0.238226i
$786$	19.8160			0.706815
$787$	−23.9802	+	23.9802i	−0.854802	+	0.854802i	−0.990720	−	0.135918i	$-0.956602\pi$
$787$	−23.9802	+	23.9802i	−0.854802	+	0.854802i	0.135918	+	0.990720i	$0.456602\pi$
$788$	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	$-0.495883\pi$
$797$	0.730287			0.0258681			0.0129340	+	0.999916i	$0.495883\pi$
$798$		−	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
$805$	−10.5046	−	12.3301i	−0.370238	−	0.434578i
$806$	−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	−0.405924	−	0.913907i	$-0.633050\pi$
$809$	14.4485	−	14.4485i	0.507982	−	0.507982i	0.913907	+	0.405924i	$0.133050\pi$
$810$	19.2149	−	16.3701i	0.675142	−	0.575186i
$811$	−1.77975	−	1.77975i	−0.0624955	−	0.0624955i	0.675168	−	0.737664i	$-0.264071\pi$
$811$	−1.77975	−	1.77975i	−0.0624955	−	0.0624955i	−0.737664	+	0.675168i	$0.764071\pi$
$812$			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	0.870211	−	0.492678i	$-0.163982\pi$
$821$	10.8175	+	10.8175i	0.377533	+	0.377533i	−0.492678	+	0.870211i	$0.663982\pi$
$822$	9.92553	+	9.92553i	0.346193	+	0.346193i
$823$	10.1433	+	10.1433i	0.353574	+	0.353574i	0.861437	−	0.507864i	$-0.169565\pi$
$823$	10.1433	+	10.1433i	0.353574	+	0.353574i	−0.507864	+	0.861437i	$0.669565\pi$
$824$		−	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	$-0.497233\pi$
$827$	−28.5066	−	28.5066i	−0.991270	−	0.991270i	−0.999962	+	0.00869233i	$0.997233\pi$
$828$	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	$0.277054\pi$
$830$	12.1139	−	10.3204i	0.420480	−	0.358227i
$831$			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	−0.788458	−	0.615089i	$-0.789120\pi$
$839$	−5.02173	+	5.02173i	−0.173370	+	0.173370i	0.615089	+	0.788458i	$0.289120\pi$
$840$	−4.01334	+	3.41916i	−0.138473	+	0.117972i
$841$			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
$845$	−19.4730	+	16.5900i	−0.669891	+	0.570713i
$846$	23.5054			0.808134
$847$	−45.0972	+	45.0972i	−1.54956	+	1.54956i
$848$	−45.0048			−1.54547
$849$	−11.7440			−0.403052
$850$	9.41461	−	35.9648i	0.322919	−	1.23358i
$851$	4.44050			0.152218
$852$	−6.18629			−0.211939
$853$	−27.1104	+	27.1104i	−0.928242	+	0.928242i	−0.997592	−	0.0693502i	$-0.977907\pi$
$853$	−27.1104	+	27.1104i	−0.928242	+	0.928242i	0.0693502	+	0.997592i	$0.477907\pi$
$854$	31.7460			1.08633
$855$	18.2772	−	15.5713i	0.625068	−	0.532526i
$856$	−16.2022	+	16.2022i	−0.553781	+	0.553781i
$857$	−1.22358	−	1.22358i	−0.0417966	−	0.0417966i	0.685900	−	0.727696i	$-0.259409\pi$
$857$	−1.22358	−	1.22358i	−0.0417966	−	0.0417966i	−0.727696	+	0.685900i	$0.759409\pi$
$858$	7.09880			0.242349
$859$		−	30.9245i		−	1.05513i	−0.849515	−	0.527565i	$-0.823105\pi$
$859$		−	30.9245i		−	1.05513i	0.849515	−	0.527565i	$-0.176895\pi$
$860$	−4.35407	+	3.70944i	−0.148472	+	0.126491i
$861$	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
$870$	11.4220	−	9.73099i	0.387243	−	0.329911i
$871$	−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	$-0.255435\pi$
$877$	−0.715057	−	0.715057i	−0.0241458	−	0.0241458i	−0.719077	+	0.694931i	$0.755435\pi$
$878$	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	0.900373	−	0.435119i	$-0.143294\pi$
$881$	13.8095	+	13.8095i	0.465253	+	0.465253i	−0.435119	+	0.900373i	$0.643294\pi$
$882$	−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	$-0.964128\pi$
$887$	−26.2443	+	26.2443i	−0.881199	+	0.881199i	0.112458	+	0.993657i	$0.464128\pi$
$888$		−	1.44534i		−	0.0485026i
$889$	−12.8730	−	12.8730i	−0.431746	−	0.431746i
$890$	32.5762	−	27.7533i	1.09196	−	0.930291i
$891$	−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
$895$	28.7027	+	33.6907i	0.959427	+	1.12616i
$896$	−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	$-0.443771\pi$
$907$	−24.3554	−	24.3554i	−0.808706	−	0.808706i	−0.984438	+	0.175732i	$0.943771\pi$
$908$	−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	−0.816389	−	0.577503i	$-0.804027\pi$
$911$	−7.21023	+	7.21023i	−0.238886	+	0.238886i	0.577503	+	0.816389i	$0.304027\pi$
$912$	−7.84272	−	7.84272i	−0.259698	−	0.259698i
$913$	−15.6610	+	15.6610i	−0.518304	+	0.518304i
$914$	−65.3309			−2.16096
$915$	−4.60764	−	5.40836i	−0.152324	−	0.178795i
$916$		−	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
$925$	5.58729	+	7.73030i	0.183709	+	0.254171i
$926$		−	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	−0.296757	−	0.954953i	$-0.595905\pi$
$929$	20.0615	−	20.0615i	0.658196	−	0.658196i	0.954953	+	0.296757i	$0.0959051\pi$
$930$	−7.85182	+	6.68934i	−0.257471	+	0.219352i
$931$	−10.7380			−0.351923
$932$	−10.0076	+	10.0076i	−0.327808	+	0.327808i
$933$	−2.26493			−0.0741504
$934$	−35.0695			−1.14751
$935$	−9.07218	+	50.9380i	−0.296692	+	1.66585i
$936$	4.52202			0.147807
$937$	47.5024			1.55183			0.775917	−	0.630835i	$-0.217287\pi$
$937$	47.5024			1.55183			0.775917	+	0.630835i	$0.217287\pi$
$938$	33.5798	−	33.5798i	1.09642	−	1.09642i
$939$	12.7220			0.415166
$940$	8.81528	+	10.3472i	0.287523	+	0.337488i
$941$	32.5555	−	32.5555i	1.06128	−	1.06128i	0.0632823	−	0.997996i	$-0.479843\pi$
$941$	32.5555	−	32.5555i	1.06128	−	1.06128i	0.997996	−	0.0632823i	$-0.0201569\pi$
$942$	−2.80866	−	2.80866i	−0.0915112	−	0.0915112i
$943$	13.7884			0.449011
$944$			29.6190i			0.964016i
$945$	14.4090	+	16.9130i	0.468725	+	0.550180i
$946$	14.6210	−	14.6210i	0.475369	−	0.475369i
$947$	21.0282	−	21.0282i	0.683324	−	0.683324i	−0.277424	−	0.960748i	$-0.589481\pi$
$947$	21.0282	−	21.0282i	0.683324	−	0.683324i	0.960748	+	0.277424i	$0.0894806\pi$
$948$			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
$955$	23.7215	−	20.2095i	0.767608	−	0.653963i
$956$	−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	$-0.439478\pi$
$967$	11.7541			0.377986			0.188993	+	0.981978i	$0.439478\pi$
$968$			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	$-0.896266\pi$
$971$		−	19.9525i		−	0.640306i	0.947366	−	0.320153i	$-0.103734\pi$
$972$	−11.5931	+	11.5931i	−0.371849	+	0.371849i
$973$		−	31.7413i		−	1.01758i
$974$	−37.8687	−	37.8687i	−1.21339	−	1.21339i
$975$	2.84250	−	2.05450i	0.0910329	−	0.0657965i
$976$	19.7460	−	19.7460i	0.632054	−	0.632054i
$977$	−27.2005			−0.870221			−0.435110	−	0.900377i	$-0.643291\pi$
$977$	−27.2005			−0.870221			−0.435110	+	0.900377i	$0.643291\pi$
$978$	−14.9099			−0.476767
$979$	−42.1150	+	42.1150i	−1.34600	+	1.34600i
$980$	−4.87380	−	5.72078i	−0.155688	−	0.182743i
$981$	−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	$-0.713754\pi$
$983$	5.03803	−	5.03803i	0.160688	−	0.160688i	0.782872	+	0.622183i	$0.213754\pi$
$984$		−	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	0.940896	+	0.338695i	$0.109986\pi$
$991$	40.2817	+	40.2817i	1.27959	+	1.27959i	0.338695	+	0.940896i	$0.390014\pi$
$992$	−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	$-0.224546\pi$
$997$	3.56701	+	3.56701i	0.112968	+	0.112968i	−0.648363	+	0.761331i	$0.724546\pi$
$998$	−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.64.5	yes	12
3.2	odd	2		765.2.t.e.64.2		12
5.2	odd	4		425.2.e.d.251.5		12
5.3	odd	4		425.2.e.d.251.2		12
5.4	even	2	inner	85.2.j.c.64.2	yes	12
15.14	odd	2		765.2.t.e.64.5		12
17.2	even	8		1445.2.b.f.579.9		12
17.4	even	4	inner	85.2.j.c.4.2	✓	12
17.15	even	8		1445.2.b.f.579.10		12
51.38	odd	4		765.2.t.e.514.5		12
85.2	odd	8		7225.2.a.bp.1.3		12
85.4	even	4	inner	85.2.j.c.4.5	yes	12
85.19	even	8		1445.2.b.f.579.4		12
85.32	odd	8		7225.2.a.bp.1.4		12
85.38	odd	4		425.2.e.d.276.5		12
85.49	even	8		1445.2.b.f.579.3		12
85.53	odd	8		7225.2.a.bp.1.10		12
85.72	odd	4		425.2.e.d.276.2		12
85.83	odd	8		7225.2.a.bp.1.9		12
255.89	odd	4		765.2.t.e.514.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.2	✓	12	17.4	even	4	inner
85.2.j.c.4.5	yes	12	85.4	even	4	inner
85.2.j.c.64.2	yes	12	5.4	even	2	inner
85.2.j.c.64.5	yes	12	1.1	even	1	trivial
425.2.e.d.251.2		12	5.3	odd	4
425.2.e.d.251.5		12	5.2	odd	4
425.2.e.d.276.2		12	85.72	odd	4
425.2.e.d.276.5		12	85.38	odd	4
765.2.t.e.64.2		12	3.2	odd	2
765.2.t.e.64.5		12	15.14	odd	2
765.2.t.e.514.2		12	255.89	odd	4
765.2.t.e.514.5		12	51.38	odd	4
1445.2.b.f.579.3		12	85.49	even	8
1445.2.b.f.579.4		12	85.19	even	8
1445.2.b.f.579.9		12	17.2	even	8
1445.2.b.f.579.10		12	17.15	even	8
7225.2.a.bp.1.3		12	85.2	odd	8
7225.2.a.bp.1.4		12	85.32	odd	8
7225.2.a.bp.1.9		12	85.83	odd	8
7225.2.a.bp.1.10		12	85.53	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 $\F_{q}$

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} +(-1.70211 + 1.45011i) q^{5} +(0.716248 - 0.716248i) q^{6} +(-2.20051 - 2.20051i) q^{7} -1.34889 q^{8} +2.68450i q^{9} +(-3.06947 + 2.61503i) 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} +(-2.13104 + 1.81554i) 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} +(2.29596 - 1.95604i) q^{40} +(-4.18850 + 4.18850i) q^{41} -3.15222 q^{42} +2.04316 q^{43} +(4.96825 - 4.96825i) q^{44} +(-3.89281 - 4.56931i) 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} +(-1.81090 - 2.12560i) 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} +(-1.64517 - 2.27618i) q^{75} +5.00800i q^{76} -17.4643 q^{77} +(0.894450 + 0.894450i) q^{78} +(-3.47225 + 3.47225i) q^{79} +(8.40246 - 7.15846i) q^{80} -6.26000 q^{81} +(-7.55324 + 7.55324i) q^{82} -3.94658 q^{83} -2.18850 q^{84} +(-7.56130 + 5.27511i) q^{85} +3.68450 q^{86} -3.72118 q^{87} +(-5.35273 + 5.35273i) q^{88} -10.6130 q^{89} +(-7.02003 - 8.23997i) q^{90} +(2.74800 - 2.74800i) q^{91} +(-2.06077 - 2.06077i) q^{92} +2.55804 q^{93} -8.75600i q^{94} +(-5.80044 - 6.80844i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more