LMFDB - Embedded newform 735.2.s.l.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (of order $6$, degree $2$, not 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Root			$-1.07834i$ of defining polynomial
Character	$\chi$	$=$	735.521
Dual form			735.2.s.l.656.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.933868 - 0.539169i) q^{2} +(-1.73096 - 0.0613278i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(2.99248 + 0.212312i) q^{9} +O(q^{10})$	\(q+(0.933868 - 0.539169i) q^{2} +(-1.73096 - 0.0613278i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(2.99248 + 0.212312i) q^{9} +(0.933868 + 0.539169i) q^{10} +(-3.84494 - 2.21988i) q^{11} +(0.769035 - 1.22932i) q^{12} -0.955682i q^{13} +(-0.812371 - 1.52972i) q^{15} +(0.812371 + 1.40707i) q^{16} +(-0.253761 + 0.439527i) q^{17} +(2.90905 - 1.41518i) q^{18} +(-4.41107 + 2.54673i) q^{19} -0.837188 q^{20} -4.78755 q^{22} +(-3.72142 + 2.14856i) q^{23} +(0.187629 - 5.29579i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.515274 - 0.892481i) q^{26} +(-5.16685 - 0.551027i) q^{27} +6.89526i q^{29} +(-1.58343 - 0.990554i) q^{30} +(-5.10397 - 2.94678i) q^{31} +(-3.78182 - 2.18344i) q^{32} +(6.51931 + 4.07833i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-3.76353 - 6.51863i) q^{37} +(-2.74624 + 4.75663i) q^{38} +(-0.0586099 + 1.65425i) q^{39} +(-2.64956 + 1.52972i) q^{40} -4.65529 q^{41} -0.492478 q^{43} +(3.21894 - 1.85845i) q^{44} +(1.31237 + 2.69772i) q^{45} +(-2.31688 + 4.01295i) q^{46} +(3.32967 + 5.76715i) q^{47} +(-1.31989 - 2.48541i) q^{48} +1.07834i q^{50} +(0.466207 - 0.745243i) q^{51} +(0.692894 + 0.400043i) q^{52} +(7.90881 + 4.56616i) q^{53} +(-5.12226 + 2.27122i) q^{54} -4.43975i q^{55} +(7.79159 - 4.13778i) q^{57} +(3.71771 + 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(1.44914 + 0.0513428i) q^{60} +(-0.399509 + 0.230657i) q^{61} -6.35524 q^{62} -7.95845 q^{64} +(0.827645 - 0.477841i) q^{65} +(8.28709 + 0.293610i) q^{66} +(1.85246 - 3.20856i) q^{67} +(-0.212446 - 0.367967i) q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(-0.649559 + 9.15533i) q^{72} +(5.46846 + 3.15721i) q^{73} +(-7.02929 - 4.05836i) q^{74} +(0.918594 - 1.46840i) q^{75} -4.26419i q^{76} +(0.837188 + 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-0.812371 + 1.40707i) q^{80} +(8.90985 + 1.27068i) q^{81} +(-4.34743 + 2.50999i) q^{82} +10.7916 q^{83} -0.507522 q^{85} +(-0.459909 + 0.265529i) q^{86} +(0.422871 - 11.9355i) q^{87} +(6.79159 - 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(2.68011 + 1.81172i) q^{90} -3.59750i q^{92} +(8.65407 + 5.41378i) q^{93} +(6.21894 + 3.59050i) q^{94} +(-4.41107 - 2.54673i) q^{95} +(6.41230 + 4.01138i) q^{96} -6.91148i q^{97} +(-11.0346 - 7.45926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9	$ 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9} + 3 q^{10} + 18 q^{12} - q^{15} + q^{16} - 12 q^{17} + 26 q^{18} - 9 q^{19} + 6 q^{20} - 40 q^{22} - 27 q^{23} + 7 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 10 q^{30} + 21 q^{31} - 21 q^{32} - 4 q^{33} + 9 q^{36} + 7 q^{37} - 12 q^{38} + 15 q^{39} - 3 q^{40} - 30 q^{41} + 16 q^{43} + 5 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} + 12 q^{51} - 30 q^{52} - 24 q^{53} - 7 q^{54} + 6 q^{57} - 13 q^{58} - 12 q^{59} + 9 q^{60} - 15 q^{61} + 24 q^{62} + 38 q^{64} + 3 q^{65} + 16 q^{66} + 4 q^{67} - 13 q^{69} + 13 q^{72} - 15 q^{73} - 54 q^{74} + q^{75} - 6 q^{78} - 29 q^{79} - q^{80} + 28 q^{81} - 27 q^{82} + 30 q^{83} - 24 q^{85} - 9 q^{86} + 29 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} + 45 q^{93} + 24 q^{94} - 9 q^{95} + 42 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9 + 3 * q^10 + 18 * q^12 - q^15 + q^16 - 12 * q^17 + 26 * q^18 - 9 * q^19 + 6 * q^20 - 40 * q^22 - 27 * q^23 + 7 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 10 * q^30 + 21 * q^31 - 21 * q^32 - 4 * q^33 + 9 * q^36 + 7 * q^37 - 12 * q^38 + 15 * q^39 - 3 * q^40 - 30 * q^41 + 16 * q^43 + 5 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 + 12 * q^51 - 30 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^57 - 13 * q^58 - 12 * q^59 + 9 * q^60 - 15 * q^61 + 24 * q^62 + 38 * q^64 + 3 * q^65 + 16 * q^66 + 4 * q^67 - 13 * q^69 + 13 * q^72 - 15 * q^73 - 54 * q^74 + q^75 - 6 * q^78 - 29 * q^79 - q^80 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 24 * q^85 - 9 * q^86 + 29 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 + 45 * q^93 + 24 * q^94 - 9 * q^95 + 42 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.933868	−	0.539169i	0.660344	−	0.381250i	−0.132064	−	0.991241i	$-0.542160\pi$
$2$	0.933868	−	0.539169i	0.660344	−	0.381250i	0.792408	+	0.609991i	$0.208827\pi$
$3$	−1.73096	−	0.0613278i	−0.999373	−	0.0354076i
$3$	−1.73096	−	0.0613278i	−0.999373	−	0.0354076i
$4$	−0.418594	+	0.725026i	−0.209297	+	0.362513i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.64956	+	0.876010i	−0.673429	+	0.357630i
$7$		0			0
$7$		0			0
$8$			3.05945i			1.08168i
$9$	2.99248	+	0.212312i	0.997493	+	0.0707708i
$10$	0.933868	+	0.539169i	0.295315	+	0.170500i
$11$	−3.84494	−	2.21988i	−1.15929	−	0.669318i	−0.208158	−	0.978095i	$-0.566747\pi$
$11$	−3.84494	−	2.21988i	−1.15929	−	0.669318i	−0.951134	+	0.308777i	$0.900080\pi$
$12$	0.769035	−	1.22932i	0.222001	−	0.354875i
$13$		−	0.955682i		−	0.265059i	−0.991179	−	0.132529i	$-0.957690\pi$
$13$		−	0.955682i		−	0.265059i	0.991179	−	0.132529i	$-0.0423099\pi$
$14$		0			0
$15$	−0.812371	−	1.52972i	−0.209753	−	0.394973i
$16$	0.812371	+	1.40707i	0.203093	+	0.351767i
$17$	−0.253761	+	0.439527i	−0.0615461	+	0.106601i	−0.895157	−	0.445752i	$-0.852936\pi$
$17$	−0.253761	+	0.439527i	−0.0615461	+	0.106601i	0.833611	+	0.552353i	$0.186270\pi$
$18$	2.90905	−	1.41518i	0.685670	−	0.333561i
$19$	−4.41107	+	2.54673i	−1.01197	+	0.584261i	−0.911768	−	0.410706i	$-0.865282\pi$
$19$	−4.41107	+	2.54673i	−1.01197	+	0.584261i	−0.100202	+	0.994967i	$0.531949\pi$
$20$	−0.837188			−0.187201
$21$		0			0
$22$	−4.78755			−1.02071
$23$	−3.72142	+	2.14856i	−0.775970	+	0.448007i	−0.835000	−	0.550250i	$-0.814533\pi$
$23$	−3.72142	+	2.14856i	−0.775970	+	0.448007i	0.0590300	+	0.998256i	$0.481199\pi$
$24$	0.187629	−	5.29579i	0.0382996	−	1.08100i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.515274	−	0.892481i	−0.101054	−	0.175030i
$27$	−5.16685	−	0.551027i	−0.994361	−	0.106045i
$28$		0			0
$29$			6.89526i			1.28042i	0.768201	+	0.640209i	$0.221152\pi$
$29$			6.89526i			1.28042i	−0.768201	+	0.640209i	$0.778848\pi$
$30$	−1.58343	−	0.990554i	−0.289093	−	0.180850i
$31$	−5.10397	−	2.94678i	−0.916699	−	0.529257i	−0.0341187	−	0.999418i	$-0.510862\pi$
$31$	−5.10397	−	2.94678i	−0.916699	−	0.529257i	−0.882581	+	0.470161i	$0.844196\pi$
$32$	−3.78182	−	2.18344i	−0.668538	−	0.385981i
$33$	6.51931	+	4.07833i	1.13487	+	0.709946i
$34$			0.547280i			0.0938578i
$35$		0			0
$36$	−1.40656	+	2.08075i	−0.234427	+	0.346792i
$37$	−3.76353	−	6.51863i	−0.618721	−	1.07166i	−0.989719	−	0.143023i	$-0.954318\pi$
$37$	−3.76353	−	6.51863i	−0.618721	−	1.07166i	0.370998	−	0.928634i	$-0.379016\pi$
$38$	−2.74624	+	4.75663i	−0.445499	+	0.771627i
$39$	−0.0586099	+	1.65425i	−0.00938509	+	0.264892i
$40$	−2.64956	+	1.52972i	−0.418932	+	0.241870i
$41$	−4.65529			−0.727034			−0.363517	−	0.931588i	$-0.618424\pi$
$41$	−4.65529			−0.727034			−0.363517	+	0.931588i	$0.618424\pi$
$42$		0			0
$43$	−0.492478			−0.0751022			−0.0375511	−	0.999295i	$-0.511956\pi$
$43$	−0.492478			−0.0751022			−0.0375511	+	0.999295i	$0.511956\pi$
$44$	3.21894	−	1.85845i	0.485273	−	0.280172i
$45$	1.31237	+	2.69772i	0.195637	+	0.402152i
$46$	−2.31688	+	4.01295i	−0.341605	+	0.591677i
$47$	3.32967	+	5.76715i	0.485682	+	0.841225i	0.999865	−	0.0164553i	$-0.00523812\pi$
$47$	3.32967	+	5.76715i	0.485682	+	0.841225i	−0.514183	+	0.857681i	$0.671905\pi$
$48$	−1.31989	−	2.48541i	−0.190510	−	0.358737i
$49$		0			0
$50$			1.07834i			0.152500i
$51$	0.466207	−	0.745243i	0.0652820	−	0.104355i
$52$	0.692894	+	0.400043i	0.0960871	+	0.0554759i
$53$	7.90881	+	4.56616i	1.08636	+	0.627210i	0.932605	−	0.360899i	$-0.117530\pi$
$53$	7.90881	+	4.56616i	1.08636	+	0.627210i	0.153754	+	0.988109i	$0.450864\pi$
$54$	−5.12226	+	2.27122i	−0.697051	+	0.309074i
$55$		−	4.43975i		−	0.598656i
$56$		0			0
$57$	7.79159	−	4.13778i	1.03202	−	0.548063i
$58$	3.71771	+	6.43926i	0.488159	+	0.845517i
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	0.187420	+	0.982280i	$0.439987\pi$
$59$	−5.81439	+	10.0708i	−0.756969	+	1.31111i	−0.944389	+	0.328829i	$0.893346\pi$
$60$	1.44914	+	0.0513428i	0.187083	+	0.00662833i
$61$	−0.399509	+	0.230657i	−0.0511519	+	0.0295326i	−0.525358	−	0.850881i	$-0.676069\pi$
$61$	−0.399509	+	0.230657i	−0.0511519	+	0.0295326i	0.474206	+	0.880414i	$0.342735\pi$
$62$	−6.35524			−0.807116
$63$		0			0
$64$	−7.95845			−0.994806
$65$	0.827645	−	0.477841i	0.102657	−	0.0592689i
$66$	8.28709	+	0.293610i	1.02007	+	0.0361409i
$67$	1.85246	−	3.20856i	0.226314	−	0.391988i	−0.730399	−	0.683021i	$-0.760666\pi$
$67$	1.85246	−	3.20856i	0.226314	−	0.391988i	0.956713	+	0.291033i	$0.0939991\pi$
$68$	−0.212446	−	0.367967i	−0.0257628	−	0.0446225i
$69$	6.57342	−	3.49086i	0.791346	−	0.420250i
$70$		0			0
$71$			7.90386i			0.938015i	0.883194	+	0.469008i	$0.155388\pi$
$71$			7.90386i			0.938015i	−0.883194	+	0.469008i	$0.844612\pi$
$72$	−0.649559	+	9.15533i	−0.0765512	+	1.07897i
$73$	5.46846	+	3.15721i	0.640034	+	0.369524i	0.784628	−	0.619967i	$-0.212854\pi$
$73$	5.46846	+	3.15721i	0.640034	+	0.369524i	−0.144593	+	0.989491i	$0.546187\pi$
$74$	−7.02929	−	4.05836i	−0.817138	−	0.471775i
$75$	0.918594	−	1.46840i	0.106070	−	0.169556i
$76$		−	4.26419i		−	0.489136i
$77$		0			0
$78$	0.837188	+	1.57645i	0.0947928	+	0.178498i
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	−0.897742	−	0.440521i	$-0.854794\pi$
$79$	−7.38052	−	12.7834i	−0.830374	−	1.43825i	0.0673684	−	0.997728i	$-0.478540\pi$
$80$	−0.812371	+	1.40707i	−0.0908258	+	0.157315i
$81$	8.90985	+	1.27068i	0.989983	+	0.141187i
$82$	−4.34743	+	2.50999i	−0.480093	+	0.277182i
$83$	10.7916			1.18453			0.592266	−	0.805743i	$-0.298234\pi$
$83$	10.7916			1.18453			0.592266	+	0.805743i	$0.298234\pi$
$84$		0			0
$85$	−0.507522			−0.0550485
$86$	−0.459909	+	0.265529i	−0.0495933	+	0.0286327i
$87$	0.422871	−	11.9355i	0.0453365	−	1.27962i
$88$	6.79159	−	11.7634i	0.723986	−	1.25398i
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	0.611768	−	0.791038i	$-0.290459\pi$
$89$	−3.57713	−	6.19577i	−0.379175	−	0.656750i	−0.990942	+	0.134287i	$0.957125\pi$
$90$	2.68011	+	1.81172i	0.282508	+	0.190972i
$91$		0			0
$92$		−	3.59750i		−	0.375066i
$93$	8.65407	+	5.41378i	0.897385	+	0.561383i
$94$	6.21894	+	3.59050i	0.641434	+	0.370332i
$95$	−4.41107	−	2.54673i	−0.452566	−	0.261289i
$96$	6.41230	+	4.01138i	0.654452	+	0.409410i
$97$		−	6.91148i		−	0.701755i	−0.936421	−	0.350877i	$-0.885883\pi$
$97$		−	6.91148i		−	0.701755i	0.936421	−	0.350877i	$-0.114117\pi$
$98$		0			0
$99$	−11.0346	−	7.45926i	−1.10902	−	0.749684i
$100$	−0.418594	−	0.725026i	−0.0418594	−	0.0725026i
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	−0.800405	−	0.599460i	$-0.795382\pi$
$101$	1.19538	−	2.07046i	0.118945	−	0.206019i	0.919350	+	0.393441i	$0.128715\pi$
$102$	0.0335635	−	0.947323i	0.00332328	−	0.0937990i
$103$	12.9577	−	7.48110i	1.27676	−	0.737135i	0.300505	−	0.953780i	$-0.402845\pi$
$103$	12.9577	−	7.48110i	1.27676	−	0.737135i	0.976250	+	0.216645i	$0.0695115\pi$
$104$	2.92386			0.286708
$105$		0			0
$106$	9.84772			0.956495
$107$	−11.7445	+	6.78072i	−1.13539	+	0.655517i	−0.945284	−	0.326247i	$-0.894216\pi$
$107$	−11.7445	+	6.78072i	−1.13539	+	0.655517i	−0.190104	+	0.981764i	$0.560882\pi$
$108$	2.56232	−	3.51544i	0.246559	−	0.338274i
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	0.164359	+	0.986401i	$0.447444\pi$
$109$	−8.06063	+	13.9614i	−0.772068	+	1.33726i	−0.936428	+	0.350861i	$0.885889\pi$
$110$	−2.39378	−	4.14614i	−0.228238	−	0.395319i
$111$	6.11477	+	11.5143i	0.580388	+	1.09289i
$112$		0			0
$113$		−	5.05678i		−	0.475702i	−0.971302	−	0.237851i	$-0.923557\pi$
$113$		−	5.05678i		−	0.475702i	0.971302	−	0.237851i	$-0.0764429\pi$
$114$	5.04536	−	8.06513i	0.472541	−	0.755369i
$115$	−3.72142	−	2.14856i	−0.347024	−	0.200355i
$116$	−4.99924	−	2.88631i	−0.464168	−	0.267987i
$117$	0.202903	−	2.85986i	0.0187584	−	0.264394i
$118$			12.5398i			1.15438i
$119$		0			0
$120$	4.68011	−	2.48541i	0.427233	−	0.226885i
$121$	4.35571	+	7.54431i	0.395973	+	0.685846i
$122$	−0.248726	+	0.430806i	−0.0225186	+	0.0390033i
$123$	8.05814	+	0.285499i	0.726578	+	0.0257425i
$124$	4.27298	−	2.46700i	0.383725	−	0.221544i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.05009			0.714330			0.357165	−	0.934041i	$-0.383743\pi$
$127$	8.05009			0.714330			0.357165	+	0.934041i	$0.383743\pi$
$128$	0.131506	−	0.0759250i	0.0116236	−	0.00671089i
$129$	0.852462	+	0.0302026i	0.0750551	+	0.00265919i
$130$	0.515274	−	0.892481i	0.0451925	−	0.0782758i
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	0.816523	−	0.577314i	$-0.195899\pi$
$131$	−1.04963	−	1.81802i	−0.0917069	−	0.158841i	−0.908229	+	0.418473i	$0.862566\pi$
$132$	−5.68584	+	3.01951i	−0.494889	+	0.262814i
$133$		0			0
$134$		−	3.99516i		−	0.345129i
$135$	−2.10622	−	4.75014i	−0.181275	−	0.408827i
$136$	−1.34471	−	0.776369i	−0.115308	−	0.0665731i
$137$	4.28431	+	2.47355i	0.366033	+	0.211329i	0.671724	−	0.740801i	$-0.265554\pi$
$137$	4.28431	+	2.47355i	0.366033	+	0.211329i	−0.305691	+	0.952131i	$0.598887\pi$
$138$	4.25654	−	6.80419i	0.362341	−	0.579211i
$139$			10.7217i			0.909406i	0.890643	+	0.454703i	$0.150255\pi$
$139$			10.7217i			0.909406i	−0.890643	+	0.454703i	$0.849745\pi$
$140$		0			0
$141$	−5.40985	−	10.1869i	−0.455591	−	0.857895i
$142$	4.26151	+	7.38116i	0.357618	+	0.619413i
$143$	−2.12150	+	3.67454i	−0.177408	+	0.307281i
$144$	2.13226	+	4.38310i	0.177689	+	0.365258i
$145$	−5.97147	+	3.44763i	−0.495904	+	0.286310i
$146$	6.80909			0.563524
$147$		0			0
$148$	6.30157			0.517986
$149$	4.55837	−	2.63178i	0.373436	−	0.215604i	−0.301522	−	0.953459i	$-0.597495\pi$
$149$	4.55837	−	2.63178i	0.373436	−	0.215604i	0.674959	+	0.737855i	$0.264161\pi$
$150$	0.0661321	−	1.86656i	0.00539966	−	0.152404i
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	−0.687463	−	0.726219i	$-0.741276\pi$
$151$	3.50451	−	6.06998i	0.285193	−	0.493968i	0.972656	+	0.232251i	$0.0746091\pi$
$152$	−7.79159	−	13.4954i	−0.631982	−	1.09462i
$153$	−0.852692	+	1.26140i	−0.0689360	+	0.101978i
$154$		0			0
$155$		−	5.89355i		−	0.473381i
$156$	−1.17484	−	0.734953i	−0.0940626	−	0.0588434i
$157$	−2.51156	−	1.45005i	−0.200445	−	0.115727i	0.396418	−	0.918070i	$-0.370253\pi$
$157$	−2.51156	−	1.45005i	−0.200445	−	0.115727i	−0.596863	+	0.802343i	$0.703586\pi$
$158$	−13.7849	−	7.95870i	−1.09667	−	0.633160i
$159$	−13.4098	−	8.38889i	−1.06347	−	0.665282i
$160$		−	4.36687i		−	0.345232i
$161$		0			0
$162$	9.00573	−	3.61726i	0.707557	−	0.284199i
$163$	6.37930	+	11.0493i	0.499665	+	0.865446i	1.00000		0.000386523i	$-0.000123034\pi$
$163$	6.37930	+	11.0493i	0.499665	+	0.865446i	−0.500335	+	0.865832i	$0.666790\pi$
$164$	1.94868	−	3.37521i	0.152166	−	0.263559i
$165$	−0.272280	+	7.68506i	−0.0211970	+	0.598281i
$166$	10.0779	−	5.81849i	0.782199	−	0.451603i
$167$	15.7766			1.22083			0.610413	−	0.792083i	$-0.291003\pi$
$167$	15.7766			1.22083			0.610413	+	0.792083i	$0.291003\pi$
$168$		0			0
$169$	12.0867			0.929744
$170$	−0.473959	+	0.273640i	−0.0363510	+	0.0209872i
$171$	−13.7407	+	6.68452i	−1.05078	+	0.511178i
$172$	0.206148	−	0.357059i	0.0157186	−	0.0272255i
$173$	5.08667	+	8.81037i	0.386732	+	0.669840i	0.992008	−	0.126176i	$-0.0402704\pi$
$173$	5.08667	+	8.81037i	0.386732	+	0.669840i	−0.605275	+	0.796016i	$0.706937\pi$
$174$	−6.04032	−	11.3741i	−0.457916	−	0.862271i
$175$		0			0
$176$		−	7.21345i		−	0.543735i
$177$	10.6821	−	17.0757i	0.802918	−	1.28348i
$178$	−6.68113	−	3.85735i	−0.500772	−	0.289121i
$179$	4.55716	+	2.63107i	0.340618	+	0.196656i	0.660545	−	0.750786i	$-0.270325\pi$
$179$	4.55716	+	2.63107i	0.340618	+	0.196656i	−0.319927	+	0.947442i	$0.603659\pi$
$180$	−2.50527	−	0.177745i	−0.186731	−	0.0132484i
$181$			9.71314i			0.721972i	0.932571	+	0.360986i	$0.117560\pi$
$181$			9.71314i			0.721972i	−0.932571	+	0.360986i	$0.882440\pi$
$182$		0			0
$183$	0.705682	−	0.374757i	0.0521655	−	0.0277029i
$184$	−6.57342	−	11.3855i	−0.484599	−	0.839350i
$185$	3.76353	−	6.51863i	0.276700	−	0.479259i
$186$	11.0007	+	0.389753i	0.806610	+	0.0285781i
$187$	1.95139	−	1.12664i	0.142700	−	0.0823878i
$188$	−5.57511			−0.406607
$189$		0			0
$190$	−5.49248			−0.398466
$191$	−8.30561	+	4.79524i	−0.600973	+	0.346972i	−0.769424	−	0.638738i	$-0.779457\pi$
$191$	−8.30561	+	4.79524i	−0.600973	+	0.346972i	0.168451	+	0.985710i	$0.446123\pi$
$192$	13.7758	+	0.488074i	0.994182	+	0.0352237i
$193$	−4.17583	+	7.23275i	−0.300583	+	0.520625i	−0.976268	−	0.216566i	$-0.930515\pi$
$193$	−4.17583	+	7.23275i	−0.300583	+	0.520625i	0.675685	+	0.737190i	$0.263848\pi$
$194$	−3.72646	−	6.45441i	−0.267544	−	0.463400i
$195$	−1.46193	+	0.776369i	−0.104691	+	0.0555969i
$196$		0			0
$197$			1.77574i			0.126516i	0.997997	+	0.0632580i	$0.0201491\pi$
$197$			1.77574i			0.126516i	−0.997997	+	0.0632580i	$0.979851\pi$
$198$	−14.3267	−	1.01646i	−1.01815	−	0.0722365i
$199$	3.25502	+	1.87929i	0.230742	+	0.133219i	0.610915	−	0.791697i	$-0.290802\pi$
$199$	3.25502	+	1.87929i	0.230742	+	0.133219i	−0.380172	+	0.924916i	$0.624135\pi$
$200$	−2.64956	−	1.52972i	−0.187352	−	0.108168i
$201$	−3.40332	+	5.44029i	−0.240052	+	0.383729i
$202$		−	2.57805i		−	0.181391i
$203$		0			0
$204$	0.345169	+	0.649966i	0.0241667	+	0.0455067i
$205$	−2.32765	−	4.03160i	−0.162570	−	0.281579i
$206$	8.06716	−	13.9727i	0.562065	−	0.973526i
$207$	−11.5924	+	5.63943i	−0.805730	+	0.391967i
$208$	1.34471	−	0.776369i	0.0932388	−	0.0538315i
$209$	22.6137			1.56422
$210$		0			0
$211$	−9.12126			−0.627933			−0.313967	−	0.949434i	$-0.601658\pi$
$211$	−9.12126			−0.627933			−0.313967	+	0.949434i	$0.601658\pi$
$212$	−6.62116	+	3.82273i	−0.454743	+	0.262546i
$213$	0.484726	−	13.6813i	0.0332129	−	0.937427i
$214$	−7.31190	+	12.6646i	−0.499831	+	0.865734i
$215$	−0.246239	−	0.426498i	−0.0167934	−	0.0290869i
$216$	1.68584	−	15.8077i	0.114707	−	1.07558i
$217$		0			0
$218$			17.3842i			1.17740i
$219$	−9.27208	−	5.80040i	−0.626549	−	0.391954i
$220$	3.21894	+	1.85845i	0.217021	+	0.125297i
$221$	0.420048	+	0.242515i	0.0282555	+	0.0163133i
$222$	11.9186	+	7.45597i	0.799921	+	0.500412i
$223$			11.7397i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$223$			11.7397i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$224$		0			0
$225$	−1.68011	+	2.48541i	−0.112007	+	0.165694i
$226$	−2.72646	−	4.72236i	−0.181361	−	0.314127i
$227$	−12.1105	+	20.9760i	−0.803802	+	1.39223i	0.113295	+	0.993561i	$0.463859\pi$
$227$	−12.1105	+	20.9760i	−0.803802	+	1.39223i	−0.917097	+	0.398664i	$0.869474\pi$
$228$	−0.261513	+	7.38116i	−0.0173191	+	0.488829i
$229$	−18.8003	+	10.8544i	−1.24236	+	0.717278i	−0.969574	−	0.244797i	$-0.921279\pi$
$229$	−18.8003	+	10.8544i	−1.24236	+	0.717278i	−0.272787	+	0.962075i	$0.587945\pi$
$230$	−4.63376			−0.305541
$231$		0			0
$232$	−21.0957			−1.38500
$233$	−9.52303	+	5.49812i	−0.623874	+	0.360194i	−0.778376	−	0.627799i	$-0.783956\pi$
$233$	−9.52303	+	5.49812i	−0.623874	+	0.360194i	0.154502	+	0.987993i	$0.450623\pi$
$234$	−1.35246	−	2.78013i	−0.0884132	−	0.181743i
$235$	−3.32967	+	5.76715i	−0.217203	+	0.376207i
$236$	−4.86774	−	8.43117i	−0.316863	−	0.548822i
$237$	11.9914	+	22.5803i	0.778928	+	1.46675i
$238$		0			0
$239$		−	9.02649i		−	0.583875i	−0.956437	−	0.291938i	$-0.905700\pi$
$239$		−	9.02649i		−	0.583875i	0.956437	−	0.291938i	$-0.0942999\pi$
$240$	1.49248	−	2.38576i	0.0963390	−	0.154000i
$241$	4.40027	+	2.54050i	0.283446	+	0.163648i	0.634982	−	0.772527i	$-0.281007\pi$
$241$	4.40027	+	2.54050i	0.283446	+	0.163648i	−0.351536	+	0.936174i	$0.614341\pi$
$242$	8.13531	+	4.69692i	0.522958	+	0.301930i
$243$	−15.3447	−	2.74592i	−0.984363	−	0.176151i
$244$		−	0.386206i		−	0.0247243i
$245$		0			0
$246$	7.67917	−	4.07808i	0.489606	−	0.260009i
$247$	2.43387	+	4.21558i	0.154863	+	0.268231i
$248$	9.01550	−	15.6153i	0.572485	−	0.991573i
$249$	−18.6799	−	0.661824i	−1.18379	−	0.0419414i
$250$	−0.933868	+	0.539169i	−0.0590630	+	0.0341000i
$251$	−18.6748			−1.17875			−0.589373	−	0.807861i	$-0.700625\pi$
$251$	−18.6748			−1.17875			−0.589373	+	0.807861i	$0.700625\pi$
$252$		0			0
$253$	19.0782			1.19944
$254$	7.51772	−	4.34036i	0.471704	−	0.272338i
$255$	0.878503	+	0.0311252i	0.0550140	+	0.00194914i
$256$	8.04032	−	13.9262i	0.502520	−	0.870390i
$257$	6.04132	+	10.4639i	0.376847	+	0.652718i	0.990602	−	0.136779i	$-0.0436750\pi$
$257$	6.04132	+	10.4639i	0.376847	+	0.652718i	−0.613755	+	0.789497i	$0.710342\pi$
$258$	0.812371	−	0.431416i	0.0505760	−	0.0268588i
$259$		0			0
$260$			0.800085i			0.0496192i
$261$	−1.46395	+	20.6339i	−0.0906162	+	1.27721i
$262$	−1.96044	−	1.13186i	−0.121116	−	0.0699265i
$263$	11.1611	+	6.44388i	0.688224	+	0.397346i	0.802946	−	0.596051i	$-0.203264\pi$
$263$	11.1611	+	6.44388i	0.688224	+	0.397346i	−0.114722	+	0.993398i	$0.536598\pi$
$264$	−12.4774	+	19.9455i	−0.767933	+	1.22756i
$265$			9.13231i			0.560993i
$266$		0			0
$267$	5.81191	+	10.9440i	0.355683	+	0.669764i
$268$	1.55086	+	2.68616i	0.0947337	+	0.164084i
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	−0.858828	−	0.512264i	$-0.828807\pi$
$269$	0.233222	−	0.403952i	0.0142198	−	0.0246294i	0.873048	+	0.487635i	$0.162140\pi$
$270$	−4.52806	−	3.30039i	−0.275569	−	0.200856i
$271$	20.1703	−	11.6453i	1.22526	−	0.707404i	0.259225	−	0.965817i	$-0.416533\pi$
$271$	20.1703	−	11.6453i	1.22526	−	0.707404i	0.966035	+	0.258413i	$0.0831994\pi$
$272$	−0.824593			−0.0499983
$273$		0			0
$274$	5.33464			0.322277
$275$	3.84494	−	2.21988i	0.231859	−	0.133864i
$276$	−0.220627	+	6.22715i	−0.0132802	+	0.374830i
$277$	6.94543	−	12.0298i	0.417310	−	0.722803i	−0.578357	−	0.815783i	$-0.696306\pi$
$277$	6.94543	−	12.0298i	0.417310	−	0.722803i	0.995668	+	0.0929805i	$0.0296394\pi$
$278$	5.78083	+	10.0127i	0.346711	+	0.600521i
$279$	−14.6479	−	9.90180i	−0.876945	−	0.592805i
$280$		0			0
$281$			6.85483i			0.408925i	0.978874	+	0.204462i	$0.0655446\pi$
$281$			6.85483i			0.408925i	−0.978874	+	0.204462i	$0.934455\pi$
$282$	−10.5446	−	6.59643i	−0.627919	−	0.392812i
$283$	−3.84212	−	2.21825i	−0.228391	−	0.131861i	0.381439	−	0.924394i	$-0.375429\pi$
$283$	−3.84212	−	2.21825i	−0.228391	−	0.131861i	−0.609829	+	0.792533i	$0.708762\pi$
$284$	−5.73050	−	3.30850i	−0.340043	−	0.196324i
$285$	7.47922	+	4.67883i	0.443031	+	0.277150i
$286$			4.57538i			0.270548i
$287$		0			0
$288$	−10.8534	−	7.33681i	−0.639546	−	0.432326i
$289$	8.37121	+	14.4994i	0.492424	+	0.852904i
$290$	−3.71771	+	6.43926i	−0.218311	+	0.378127i
$291$	−0.423866	+	11.9635i	−0.0248475	+	0.701315i
$292$	−4.57812	+	2.64318i	−0.267914	+	0.154680i
$293$	−30.0822			−1.75742			−0.878709	−	0.477357i	$-0.841595\pi$
$293$	−30.0822			−1.75742			−0.878709	+	0.477357i	$0.841595\pi$
$294$		0			0
$295$	−11.6288			−0.677054
$296$	19.9434	−	11.5143i	1.15919	−	0.669257i
$297$	18.6430	+	13.5884i	1.08178	+	0.788481i
$298$	2.83795	−	4.91547i	0.164398	−	0.284745i
$299$	2.05334	+	3.55650i	0.118748	+	0.205678i
$300$	0.680107	+	1.28067i	0.0392660	+	0.0739392i
$301$		0			0
$302$		−	7.55808i		−	0.434919i
$303$	−2.19614	+	3.51058i	−0.126165	+	0.201678i
$304$	−7.16685	−	4.13778i	−0.411047	−	0.237318i
$305$	−0.399509	−	0.230657i	−0.0228758	−	0.0132074i
$306$	−0.116194	+	1.63772i	−0.00664239	+	0.0936225i
$307$		−	32.8300i		−	1.87371i	−0.349722	−	0.936853i	$-0.613724\pi$
$307$		−	32.8300i		−	1.87371i	0.349722	−	0.936853i	$-0.386276\pi$
$308$		0			0
$309$	−22.8880	+	12.1549i	−1.30206	+	0.691466i
$310$	−3.17762	−	5.50380i	−0.180477	−	0.312595i
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	−0.999277	−	0.0380092i	$-0.987898\pi$
$311$	−8.23073	+	14.2560i	−0.466722	+	0.808386i	0.532556	+	0.846395i	$0.321232\pi$
$312$	−5.06110	−	0.179314i	−0.286528	−	0.0101516i
$313$	3.99102	−	2.30422i	0.225586	−	0.130242i	−0.382948	−	0.923770i	$-0.625091\pi$
$313$	3.99102	−	2.30422i	0.225586	−	0.130242i	0.608534	+	0.793528i	$0.291758\pi$
$314$	−3.12729			−0.176483
$315$		0			0
$316$	12.3578			0.695179
$317$	25.4873	−	14.7151i	1.43151	−	0.826481i	0.434272	−	0.900782i	$-0.357006\pi$
$317$	25.4873	−	14.7151i	1.43151	−	0.826481i	0.997236	+	0.0743007i	$0.0236725\pi$
$318$	−17.0461	−	0.603939i	−0.955895	−	0.0338672i
$319$	15.3066	−	26.5119i	0.857007	−	1.48438i
$320$	−3.97922	−	6.89222i	−0.222445	−	0.385287i
$321$	20.7452	−	11.0169i	1.15789	−	0.614904i
$322$		0			0
$323$		−	2.58505i		−	0.143836i
$324$	−4.65088	+	5.92797i	−0.258382	+	0.329332i
$325$	0.827645	+	0.477841i	0.0459095	+	0.0265059i
$326$	11.9148	+	6.87904i	0.659902	+	0.380995i
$327$	14.8089	−	23.6724i	0.818933	−	1.30909i
$328$		−	14.2426i		−	0.786417i
$329$		0			0
$330$	3.88927	+	7.32363i	0.214097	+	0.403153i
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	0.827222	−	0.561875i	$-0.189920\pi$
$331$	−1.32787	−	2.29995i	−0.0729866	−	0.126417i	−0.900209	+	0.435458i	$0.856586\pi$
$332$	−4.51729	+	7.82418i	−0.247919	+	0.429408i
$333$	−9.87830	−	20.3059i	−0.541328	−	1.11276i
$334$	14.7332	−	8.50623i	0.806166	−	0.465440i
$335$	3.70492			0.202422
$336$		0			0
$337$	−21.4599			−1.16900			−0.584499	−	0.811395i	$-0.698709\pi$
$337$	−21.4599			−1.16900			−0.584499	+	0.811395i	$0.698709\pi$
$338$	11.2874	−	6.51676i	0.613951	−	0.354465i
$339$	−0.310121	+	8.75311i	−0.0168435	+	0.475403i
$340$	0.212446	−	0.367967i	0.0115215	−	0.0199558i
$341$	13.0830	+	22.6604i	0.708482	+	1.22713i
$342$	−9.22795	+	13.6510i	−0.498990	+	0.738163i
$343$		0			0
$344$		−	1.50671i		−	0.0812363i
$345$	6.30988	+	3.94732i	0.339713	+	0.212516i
$346$	9.50056	+	5.48515i	0.510753	+	0.294883i
$347$	15.7302	+	9.08183i	0.844441	+	0.487538i	0.858771	−	0.512359i	$-0.171228\pi$
$347$	15.7302	+	9.08183i	0.844441	+	0.487538i	−0.0143301	+	0.999897i	$0.504562\pi$
$348$	8.47650	+	5.30270i	0.454388	+	0.284255i
$349$		−	13.1543i		−	0.704135i	−0.935975	−	0.352067i	$-0.885479\pi$
$349$		−	13.1543i		−	0.704135i	0.935975	−	0.352067i	$-0.114521\pi$
$350$		0			0
$351$	−0.526607	+	4.93787i	−0.0281082	+	0.263564i
$352$	9.69392	+	16.7904i	0.516688	+	0.894929i
$353$	5.14707	−	8.91499i	0.273951	−	0.474497i	−0.695919	−	0.718120i	$-0.745003\pi$
$353$	5.14707	−	8.91499i	0.273951	−	0.474497i	0.969870	+	0.243623i	$0.0783361\pi$
$354$	0.769035	−	21.7059i	0.0408738	−	1.15365i
$355$	−6.84494	+	3.95193i	−0.363292	+	0.209747i
$356$	5.98946			0.317441
$357$		0			0
$358$	5.67438			0.299900
$359$	−10.2193	+	5.90010i	−0.539352	+	0.311395i	−0.744816	−	0.667270i	$-0.767463\pi$
$359$	−10.2193	+	5.90010i	−0.539352	+	0.311395i	0.205464	+	0.978665i	$0.434130\pi$
$360$	−8.25352	+	4.01513i	−0.434999	+	0.211616i
$361$	3.47170	−	6.01316i	0.182721	−	0.316482i
$362$	5.23703	+	9.07079i	0.275252	+	0.476750i
$363$	−7.07690	−	13.3261i	−0.371441	−	0.699436i
$364$		0			0
$365$			6.31443i			0.330512i
$366$	0.456956	−	0.730456i	0.0238855	−	0.0381815i
$367$	−13.8338	−	7.98697i	−0.722120	−	0.416916i	0.0934122	−	0.995628i	$-0.470223\pi$
$367$	−13.8338	−	7.98697i	−0.722120	−	0.416916i	−0.815533	+	0.578711i	$0.803556\pi$
$368$	−6.04635	−	3.49086i	−0.315188	−	0.181974i
$369$	−13.9309	−	0.988376i	−0.725211	−	0.0514528i
$370$		−	8.11672i		−	0.421968i
$371$		0			0
$372$	−7.54767	+	4.00825i	−0.391328	+	0.207818i
$373$	−2.65834	−	4.60438i	−0.137644	−	0.238406i	0.788961	−	0.614444i	$-0.210620\pi$
$373$	−2.65834	−	4.60438i	−0.137644	−	0.238406i	−0.926604	+	0.376038i	$0.877286\pi$
$374$	1.21490	−	2.10426i	0.0628207	−	0.108809i
$375$	1.73096	+	0.0613278i	0.0893866	+	0.00316695i
$376$	−17.6443	+	10.1869i	−0.909935	+	0.525351i
$377$	6.58968			0.339386
$378$		0			0
$379$	24.0427			1.23499			0.617494	−	0.786575i	$-0.288148\pi$
$379$	24.0427			1.23499			0.617494	+	0.786575i	$0.288148\pi$
$380$	3.69289	−	2.13209i	0.189441	−	0.109374i
$381$	−13.9344	−	0.493694i	−0.713882	−	0.0252927i
$382$	−5.17089	+	8.95625i	−0.264566	+	0.458242i
$383$	−9.40053	−	16.2822i	−0.480345	−	0.831982i	0.519401	−	0.854531i	$-0.326155\pi$
$383$	−9.40053	−	16.2822i	−0.480345	−	0.831982i	−0.999746	+	0.0225490i	$0.992822\pi$
$384$	−0.232289	+	0.123359i	−0.0118539	+	0.00629512i
$385$		0			0
$386$			9.00591i			0.458389i
$387$	−1.47373	−	0.104559i	−0.0749139	−	0.00531504i
$388$	5.01100	+	2.89310i	0.254395	+	0.146875i
$389$	10.5804	+	6.10860i	0.536448	+	0.309718i	0.743638	−	0.668582i	$-0.233099\pi$
$389$	10.5804	+	6.10860i	0.536448	+	0.309718i	−0.207190	+	0.978301i	$0.566432\pi$
$390$	−0.946655	+	1.51325i	−0.0479358	+	0.0766265i
$391$		−	2.18089i		−	0.110292i
$392$		0			0
$393$	1.70538	+	3.21130i	0.0860252	+	0.161988i
$394$	0.957422	+	1.65830i	0.0482342	+	0.0835442i
$395$	7.38052	−	12.7834i	0.371354	−	0.643205i
$396$	10.0272	−	4.87796i	0.503884	−	0.245127i
$397$	−16.2510	+	9.38254i	−0.815616	+	0.470896i	−0.848902	−	0.528550i	$-0.822736\pi$
$397$	−16.2510	+	9.38254i	−0.815616	+	0.470896i	0.0332862	+	0.999446i	$0.489403\pi$
$398$	4.05302			0.203159
$399$		0			0
$400$	−1.62474			−0.0812371
$401$	−20.7823	+	11.9987i	−1.03782	+	0.599184i	−0.919214	−	0.393757i	$-0.871175\pi$
$401$	−20.7823	+	11.9987i	−1.03782	+	0.599184i	−0.118603	+	0.992942i	$0.537842\pi$
$402$	−0.245014	+	6.91548i	−0.0122202	+	0.344913i
$403$	−2.81618	+	4.87777i	−0.140284	+	0.242979i
$404$	1.00076	+	1.73336i	0.0497896	+	0.0862381i
$405$	3.35448	+	8.35149i	0.166686	+	0.414989i
$406$		0			0
$407$			33.4183i			1.65648i
$408$	2.28003	+	1.42633i	0.112878	+	0.0706141i
$409$	14.7941	+	8.54140i	0.731523	+	0.422345i	0.818979	−	0.573823i	$-0.194540\pi$
$409$	14.7941	+	8.54140i	0.731523	+	0.422345i	−0.0874559	+	0.996168i	$0.527874\pi$
$410$	−4.34743	−	2.50999i	−0.214704	−	0.123959i
$411$	−7.26429	−	4.54437i	−0.358321	−	0.224157i
$412$			12.5262i			0.617120i
$413$		0			0
$414$	−7.78521	+	11.5168i	−0.382622	+	0.566018i
$415$	5.39580	+	9.34580i	0.264869	+	0.458767i
$416$	−2.08667	+	3.61422i	−0.102307	+	0.177202i
$417$	0.657540	−	18.5590i	0.0321999	−	0.908836i
$418$	21.1182	−	12.1926i	1.03293	−	0.596361i
$419$	−39.6524			−1.93714			−0.968572	−	0.248732i	$-0.919986\pi$
$419$	−39.6524			−1.93714			−0.968572	+	0.248732i	$0.919986\pi$
$420$		0			0
$421$	−34.1423			−1.66399			−0.831997	−	0.554779i	$-0.812803\pi$
$421$	−34.1423			−1.66399			−0.831997	+	0.554779i	$0.812803\pi$
$422$	−8.51805	+	4.91790i	−0.414652	+	0.239400i
$423$	8.73951	+	17.9650i	0.424930	+	0.873488i
$424$	−13.9699	+	24.1966i	−0.678439	+	1.17509i
$425$	−0.253761	−	0.439527i	−0.0123092	−	0.0213202i
$426$	−6.92386	−	13.0379i	−0.335462	−	0.631687i
$427$		0			0
$428$		−	11.3535i		−	0.548790i
$429$	3.89759	−	6.23039i	0.188177	−	0.300806i
$430$	−0.459909	−	0.265529i	−0.0221788	−	0.0128049i
$431$	−22.3182	−	12.8854i	−1.07503	−	0.620668i	−0.145478	−	0.989361i	$-0.546472\pi$
$431$	−22.3182	−	12.8854i	−1.07503	−	0.620668i	−0.929551	+	0.368693i	$0.879805\pi$
$432$	−3.42207	−	7.71775i	−0.164644	−	0.371320i
$433$			11.9120i			0.572454i	0.958162	+	0.286227i	$0.0924011\pi$
$433$			11.9120i			0.572454i	−0.958162	+	0.286227i	$0.907599\pi$
$434$		0			0
$435$	10.5478	−	5.60151i	0.505730	−	0.268572i
$436$	−6.74826	−	11.6883i	−0.323183	−	0.559769i
$437$	10.9436	−	18.9549i	0.523505	−	0.906738i
$438$	−11.7863	−	0.417586i	−0.563171	−	0.0199530i
$439$	14.5260	−	8.38661i	0.693290	−	0.400271i	−0.111553	−	0.993758i	$-0.535583\pi$
$439$	14.5260	−	8.38661i	0.693290	−	0.400271i	0.804843	+	0.593487i	$0.202249\pi$
$440$	13.5832			0.647553
$441$		0			0
$442$	0.523026			0.0248778
$443$	−2.07491	+	1.19795i	−0.0985819	+	0.0569163i	−0.548480	−	0.836163i	$-0.684793\pi$
$443$	−2.07491	+	1.19795i	−0.0985819	+	0.0569163i	0.449899	+	0.893080i	$0.351460\pi$
$444$	−10.9078	−	0.386461i	−0.517661	−	0.0183406i
$445$	3.57713	−	6.19577i	0.169572	−	0.293708i
$446$	6.32967	+	10.9633i	0.299718	+	0.519127i
$447$	−8.05178	+	4.27596i	−0.380836	+	0.202246i
$448$		0			0
$449$		−	25.4692i		−	1.20196i	−0.799262	−	0.600982i	$-0.794776\pi$
$449$		−	25.4692i		−	1.20196i	0.799262	−	0.600982i	$-0.205224\pi$
$450$	−0.228945	+	3.22690i	−0.0107925	+	0.152118i
$451$	17.8993	+	10.3342i	0.842846	+	0.486617i
$452$	3.66629	+	2.11674i	0.172448	+	0.0995629i
$453$	−6.43844	+	10.2920i	−0.302504	+	0.483561i
$454$			26.1184i			1.22580i
$455$		0			0
$456$	12.6593	+	23.8380i	0.592827	+	1.11632i
$457$	1.72096	+	2.98078i	0.0805029	+	0.139435i	0.903466	−	0.428660i	$-0.141014\pi$
$457$	1.72096	+	2.98078i	0.0805029	+	0.139435i	−0.822963	+	0.568095i	$0.807681\pi$
$458$	−11.7047	+	20.2731i	−0.546924	+	0.947300i
$459$	1.55334	−	2.13114i	0.0725036	−	0.0994732i
$460$	3.11553	−	1.79875i	0.145262	−	0.0838672i
$461$	−13.5376			−0.630509			−0.315254	−	0.949007i	$-0.602090\pi$
$461$	−13.5376			−0.630509			−0.315254	+	0.949007i	$0.602090\pi$
$462$		0			0
$463$	−5.13770			−0.238769			−0.119385	−	0.992848i	$-0.538092\pi$
$463$	−5.13770			−0.238769			−0.119385	+	0.992848i	$0.538092\pi$
$464$	−9.70210	+	5.60151i	−0.450409	+	0.260044i
$465$	−0.361438	+	10.2015i	−0.0167613	+	0.473085i
$466$	−5.92883	+	10.2690i	−0.274648	+	0.475704i
$467$	4.60894	+	7.98292i	0.213276	+	0.369405i	0.952738	−	0.303793i	$-0.0982532\pi$
$467$	4.60894	+	7.98292i	0.213276	+	0.369405i	−0.739462	+	0.673199i	$0.764920\pi$
$468$	1.98854	+	1.34423i	0.0919201	+	0.0621370i
$469$		0			0
$470$			7.18101i			0.331235i
$471$	4.25850	+	2.66402i	0.196221	+	0.122751i
$472$	−30.8111	−	17.7888i	−1.41820	−	0.818797i
$473$	1.89355	+	1.09324i	0.0870654	+	0.0502672i
$474$	23.3730	+	14.6216i	1.07356	+	0.671593i
$475$		−	5.09347i		−	0.233704i
$476$		0			0
$477$	22.6975	+	15.3433i	1.03925	+	0.702520i
$478$	−4.86680	−	8.42955i	−0.222602	−	0.385559i
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	−0.527996	−	0.849247i	$-0.677056\pi$
$479$	10.3187	−	17.8724i	0.471472	−	0.816613i	0.999467	+	0.0326342i	$0.0103896\pi$
$480$	−0.267811	+	7.55890i	−0.0122238	+	0.345015i
$481$	−6.22974	+	3.59674i	−0.284052	+	0.163997i
$482$	5.47902			0.249563
$483$		0			0
$484$	−7.29309			−0.331504
$485$	5.98552	−	3.45574i	0.271789	−	0.156917i
$486$	−15.8104	+	5.70906i	−0.717176	+	0.258968i
$487$	−1.23749	+	2.14340i	−0.0560761	+	0.0971267i	−0.892701	−	0.450650i	$-0.851192\pi$
$487$	−1.23749	+	2.14340i	−0.0560761	+	0.0971267i	0.836625	+	0.547777i	$0.184526\pi$
$488$	−0.705682	−	1.22228i	−0.0319447	−	0.0553298i
$489$	−10.3647	−	19.5171i	−0.468709	−	0.882595i
$490$		0			0
$491$		−	21.2827i		−	0.960476i	−0.877138	−	0.480238i	$-0.840550\pi$
$491$		−	21.2827i		−	0.960476i	0.877138	−	0.480238i	$-0.159450\pi$
$492$	−3.58008	+	5.72285i	−0.161403	+	0.258006i
$493$	−3.03065	−	1.74975i	−0.136494	−	0.0788047i
$494$	4.54582	+	2.62453i	0.204526	+	0.118083i
$495$	0.942615	−	13.2859i	0.0423674	−	0.597155i
$496$		−	9.57550i		−	0.429953i
$497$		0			0
$498$	−17.8014	+	9.45355i	−0.797698	+	0.423624i
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	−0.955693	−	0.294366i	$-0.904891\pi$
$499$	−16.3690	−	28.3519i	−0.732775	−	1.26920i	0.222918	−	0.974837i	$-0.428442\pi$
$500$	0.418594	−	0.725026i	0.0187201	−	0.0324241i
$501$	−27.3087	−	0.967541i	−1.22006	−	0.0432265i
$502$	−17.4398	+	10.0689i	−0.778378	+	0.449397i
$503$	0.675693			0.0301277			0.0150638	−	0.999887i	$-0.495205\pi$
$503$	0.675693			0.0301277			0.0150638	+	0.999887i	$0.495205\pi$
$504$		0			0
$505$	2.39076			0.106388
$506$	17.8165	−	10.2864i	0.792041	−	0.457285i
$507$	−20.9216	−	0.741249i	−0.929161	−	0.0329200i
$508$	−3.36972	+	5.83652i	−0.149507	+	0.258954i
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	0.955313	+	0.295595i	$0.0955178\pi$
$509$	16.5519	+	28.6687i	0.733649	+	1.27072i	−0.221664	+	0.975123i	$0.571149\pi$
$510$	0.837188	−	0.444595i	0.0370713	−	0.0196870i
$511$		0			0
$512$		−	17.0367i		−	0.752921i
$513$	24.1947	−	10.7280i	1.06822	−	0.473652i
$514$	11.2836	+	6.51458i	0.497697	+	0.287346i
$515$	12.9577	+	7.48110i	0.570982	+	0.329657i
$516$	−0.378733	+	0.605414i	−0.0166728	+	0.0266519i
$517$		−	29.5658i		−	1.30030i
$518$		0			0
$519$	−8.26453	−	15.5624i	−0.362773	−	0.683114i
$520$	1.46193	+	2.53214i	0.0641098	+	0.111042i
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.176634	−	0.984277i	$-0.443479\pi$
$521$	21.4725	−	37.1914i	0.940726	−	1.62938i	0.764092	−	0.645108i	$-0.223188\pi$
$522$	9.75803	+	20.0587i	0.427097	+	0.877944i
$523$	−33.0751	+	19.0959i	−1.44627	+	0.835007i	−0.998257	−	0.0590174i	$-0.981203\pi$
$523$	−33.0751	+	19.0959i	−1.44627	+	0.835007i	−0.448018	+	0.894025i	$0.647870\pi$
$524$	1.75748			0.0767759
$525$		0			0
$526$	13.8974			0.605953
$527$	2.59038	−	1.49555i	0.112839	−	0.0651474i
$528$	−0.442385	+	12.4862i	−0.0192523	+	0.543394i
$529$	−2.26734	+	3.92715i	−0.0985802	+	0.170746i
$530$	4.92386	+	8.52837i	0.213879	+	0.370449i
$531$	−19.5376	+	28.9022i	−0.847859	+	1.25425i
$532$		0			0
$533$			4.44898i			0.192707i
$534$	11.3282	+	7.08668i	0.490221	+	0.306671i
$535$	−11.7445	−	6.78072i	−0.507761	−	0.293156i
$536$	9.81641	+	5.66751i	0.424004	+	0.244799i
$537$	−7.72692	−	4.83378i	−0.333441	−	0.208593i
$538$		−	0.502984i		−	0.0216852i
$539$		0			0
$540$	4.32562	+	0.461313i	0.186145	+	0.0198518i
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	0.870397	−	0.492351i	$-0.163862\pi$
$541$	0.204923	+	0.354938i	0.00881035	+	0.0152600i	−0.861587	+	0.507611i	$0.830529\pi$
$542$	12.5576	−	21.7504i	0.539396	−	0.934261i
$543$	0.595685	−	16.8131i	0.0255633	−	0.721520i
$544$	1.91936	−	1.10814i	0.0822918	−	0.0475112i
$545$	−16.1213			−0.690559
$546$		0			0
$547$	−10.9605			−0.468638			−0.234319	−	0.972160i	$-0.575286\pi$
$547$	−10.9605			−0.468638			−0.234319	+	0.972160i	$0.575286\pi$
$548$	−3.58677	+	2.07082i	−0.153219	+	0.0884612i
$549$	−1.24449	+	0.605414i	−0.0531137	+	0.0258384i
$550$	2.39378	−	4.14614i	0.102071	−	0.176792i
$551$	−17.5604	−	30.4155i	−0.748098	−	1.29574i
$552$	10.6801	+	20.1110i	0.454576	+	0.855982i
$553$		0			0
$554$		−	14.9790i		−	0.636398i
$555$	−6.91432	+	11.0527i	−0.293496	+	0.469161i
$556$	−7.77354	−	4.48805i	−0.329671	−	0.190336i
$557$	−5.21291	−	3.00967i	−0.220878	−	0.127524i	0.385479	−	0.922717i	$-0.374036\pi$
$557$	−5.21291	−	3.00967i	−0.220878	−	0.127524i	−0.606357	+	0.795193i	$0.707370\pi$
$558$	−19.0179	−	1.34930i	−0.805093	−	0.0571203i
$559$			0.470652i			0.0199065i
$560$		0			0
$561$	−3.44689	+	1.83049i	−0.145528	+	0.0772835i
$562$	3.69591	+	6.40150i	0.155903	+	0.270031i
$563$	7.43466	−	12.8772i	0.313334	−	0.542710i	−0.665748	−	0.746176i	$-0.731887\pi$
$563$	7.43466	−	12.8772i	0.313334	−	0.542710i	0.979082	+	0.203467i	$0.0652208\pi$
$564$	9.65032	+	0.341909i	0.406352	+	0.0143970i
$565$	4.37930	−	2.52839i	0.184238	−	0.106370i
$566$	−4.78405			−0.201089
$567$		0			0
$568$	−24.1814			−1.01463
$569$	−4.55880	+	2.63203i	−0.191115	+	0.110340i	−0.592504	−	0.805567i	$-0.701861\pi$
$569$	−4.55880	+	2.63203i	−0.191115	+	0.110340i	0.401389	+	0.915907i	$0.368527\pi$
$570$	9.50729	+	0.336841i	0.398216	+	0.0141087i
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.228601	+	0.973520i	$0.573415\pi$
$571$	−22.8775	+	39.6250i	−0.957394	+	1.65825i	−0.728793	+	0.684734i	$0.759918\pi$
$572$	−1.77609	−	3.07628i	−0.0742621	−	0.128626i
$573$	14.6708	−	7.79103i	0.612881	−	0.325475i
$574$		0			0
$575$		−	4.29713i		−	0.179203i
$576$	−23.8155	−	1.68968i	−0.992312	−	0.0704032i
$577$	4.35716	+	2.51561i	0.181391	+	0.104726i	0.587946	−	0.808900i	$-0.299937\pi$
$577$	4.35716	+	2.51561i	0.181391	+	0.104726i	−0.406555	+	0.913626i	$0.633270\pi$
$578$	15.6352	+	9.02699i	0.650339	+	0.375473i
$579$	7.67178	−	12.2635i	0.318828	−	0.509655i
$580$		−	5.77263i		−	0.239695i
$581$		0			0
$582$	6.05453	+	11.4009i	0.250968	+	0.472582i
$583$	−20.2726	−	35.1132i	−0.839606	−	1.45424i
$584$	−9.65933	+	16.7305i	−0.399706	+	0.692311i
$585$	2.57816	−	1.25421i	0.106594	−	0.0518552i
$586$	−28.0928	+	16.2194i	−1.16050	+	0.670016i
$587$	18.5075			0.763887			0.381944	−	0.924186i	$-0.375255\pi$
$587$	18.5075			0.763887			0.381944	+	0.924186i	$0.375255\pi$
$588$		0			0
$589$	30.0186			1.23690
$590$	−10.8597	+	6.26988i	−0.447089	+	0.258127i
$591$	0.108902	−	3.07374i	0.00447963	−	0.126437i
$592$	6.11477	−	10.5911i	0.251316	−	0.435291i
$593$	9.26927	+	16.0548i	0.380643	+	0.659293i	0.991154	−	0.132714i	$-0.0423693\pi$
$593$	9.26927	+	16.0548i	0.380643	+	0.659293i	−0.610511	+	0.792008i	$0.709036\pi$
$594$	24.7366	+	2.63807i	1.01495	+	0.108241i
$595$		0			0
$596$			4.40658i			0.180501i
$597$	−5.51908	−	3.45261i	−0.225881	−	0.141306i
$598$	3.83511	+	2.21420i	0.156829	+	0.0905453i
$599$	0.501417	+	0.289493i	0.0204873	+	0.0118284i	0.510209	−	0.860051i	$-0.329568\pi$
$599$	0.501417	+	0.289493i	0.0204873	+	0.0118284i	−0.489721	+	0.871879i	$0.662901\pi$
$600$	4.49248	+	2.81039i	0.183405	+	0.114734i
$601$			29.8618i			1.21809i	0.793137	+	0.609044i	$0.208447\pi$
$601$			29.8618i			1.21809i	−0.793137	+	0.609044i	$0.791553\pi$
$602$		0			0
$603$	6.22467	−	9.20824i	0.253488	−	0.374988i
$604$	2.93393	+	5.08172i	0.119380	+	0.206772i
$605$	−4.35571	+	7.54431i	−0.177085	+	0.306720i
$606$	−0.158106	+	4.46251i	−0.00642262	+	0.181277i
$607$	−21.7458	+	12.5550i	−0.882637	+	0.509591i	−0.871527	−	0.490348i	$-0.836870\pi$
$607$	−21.7458	+	12.5550i	−0.882637	+	0.509591i	−0.0111098	+	0.999938i	$0.503536\pi$
$608$	22.2425			0.902053
$609$		0			0
$610$	−0.497451			−0.0201412
$611$	5.51156	−	3.18210i	0.222974	−	0.128734i
$612$	−0.557615	−	1.14624i	−0.0225402	−	0.0463339i
$613$	0.729932	−	1.26428i	0.0294817	−	0.0510638i	−0.850908	−	0.525315i	$-0.823948\pi$
$613$	0.729932	−	1.26428i	0.0294817	−	0.0510638i	0.880390	+	0.474251i	$0.157281\pi$
$614$	−17.7009	−	30.6589i	−0.714351	−	1.23729i
$615$	3.78182	+	7.12131i	0.152498	+	0.287159i
$616$		0			0
$617$		−	6.56208i		−	0.264179i	−0.991238	−	0.132090i	$-0.957831\pi$
$617$		−	6.56208i		−	0.264179i	0.991238	−	0.132090i	$-0.0421687\pi$
$618$	−14.8209	+	23.6916i	−0.596183	+	0.953014i
$619$	−18.2419	−	10.5319i	−0.733202	−	0.423315i	0.0863902	−	0.996261i	$-0.472467\pi$
$619$	−18.2419	−	10.5319i	−0.733202	−	0.423315i	−0.819593	+	0.572947i	$0.805800\pi$
$620$	4.27298	+	2.46700i	0.171607	+	0.0990773i
$621$	20.4120	−	9.05071i	0.819104	−	0.363192i
$622$			17.7510i			0.711751i
$623$		0			0
$624$	−2.37526	+	1.26140i	−0.0950864	+	0.0504964i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.48473	−	4.30367i	0.0993096	−	0.172009i
$627$	−39.1436	−	1.38685i	−1.56324	−	0.0553855i
$628$	2.10265	−	1.21396i	0.0839048	−	0.0484425i
$629$	3.82015			0.152319
$630$		0			0
$631$	17.5069			0.696937			0.348468	−	0.937321i	$-0.386702\pi$
$631$	17.5069			0.696937			0.348468	+	0.937321i	$0.386702\pi$
$632$	39.1103	−	22.5803i	1.55572	−	0.898197i
$633$	15.7886	+	0.559387i	0.627540	+	0.0222336i
$634$	15.8678	−	27.4839i	0.630192	−	1.09152i
$635$	4.02505	+	6.97158i	0.159729	+	0.276659i
$636$	11.6954	−	6.21095i	0.463754	−	0.246280i
$637$		0			0
$638$		−	33.0114i		−	1.30694i
$639$	−1.67809	+	23.6521i	−0.0663841	+	0.935663i
$640$	0.131506	+	0.0759250i	0.00519823	+	0.00300120i
$641$	−9.98943	−	5.76740i	−0.394559	−	0.227798i	0.289575	−	0.957155i	$-0.406486\pi$
$641$	−9.98943	−	5.76740i	−0.394559	−	0.227798i	−0.684133	+	0.729357i	$0.739819\pi$
$642$	13.4333	−	21.4735i	0.530172	−	0.847493i
$643$		−	17.3489i		−	0.684173i	−0.939668	−	0.342087i	$-0.888866\pi$
$643$		−	17.3489i		−	0.684173i	0.939668	−	0.342087i	$-0.111134\pi$
$644$		0			0
$645$	0.400075	+	0.753355i	0.0157529	+	0.0296633i
$646$	−1.39378	−	2.41409i	−0.0548374	−	0.0949812i
$647$	3.93387	−	6.81366i	0.154656	−	0.267873i	−0.778278	−	0.627920i	$-0.783906\pi$
$647$	3.93387	−	6.81366i	0.154656	−	0.267873i	0.932934	+	0.360048i	$0.117240\pi$
$648$	−3.88758	+	27.2592i	−0.152719	+	1.07084i
$649$	44.7120	−	25.8145i	1.75510	−	1.01331i
$650$	1.03055			0.0404214
$651$		0			0
$652$	−10.6813			−0.418314
$653$	1.73516	−	1.00180i	0.0679021	−	0.0392033i	−0.465665	−	0.884961i	$-0.654185\pi$
$653$	1.73516	−	1.00180i	0.0679021	−	0.0392033i	0.533567	+	0.845758i	$0.320851\pi$
$654$	1.06613	−	30.0914i	0.0416891	−	1.17667i
$655$	1.04963	−	1.81802i	0.0410126	−	0.0710358i
$656$	−3.78182	−	6.55031i	−0.147655	−	0.255747i
$657$	15.6939	+	10.6089i	0.612278	+	0.413893i
$658$		0			0
$659$			44.8494i			1.74709i	0.486747	+	0.873543i	$0.338183\pi$
$659$			44.8494i			1.74709i	−0.486747	+	0.873543i	$0.661817\pi$
$660$	−5.45789	−	3.41433i	−0.212448	−	0.132903i
$661$	−10.4404	−	6.02776i	−0.406084	−	0.234453i	0.283022	−	0.959113i	$-0.408663\pi$
$661$	−10.4404	−	6.02776i	−0.406084	−	0.234453i	−0.689106	+	0.724661i	$0.741996\pi$
$662$	−2.48012	−	1.43190i	−0.0963926	−	0.0556523i
$663$	−0.712216	−	0.445546i	−0.0276602	−	0.0173036i
$664$			33.0163i			1.28128i
$665$		0			0
$666$	−20.1733	−	13.6370i	−0.781701	−	0.528421i
$667$	−14.8149	−	25.6602i	−0.573636	−	0.993566i
$668$	−6.60397	+	11.4384i	−0.255515	+	0.442565i
$669$	0.719968	−	20.3210i	0.0278356	−	0.785654i
$670$	3.45991	−	1.99758i	0.133668	−	0.0771732i
$671$	2.04812			0.0790667
$672$		0			0
$673$	11.5641			0.445763			0.222882	−	0.974845i	$-0.428454\pi$
$673$	11.5641			0.445763			0.222882	+	0.974845i	$0.428454\pi$
$674$	−20.0407	+	11.5705i	−0.771941	+	0.445680i
$675$	3.06063	−	4.19911i	0.117804	−	0.161624i
$676$	−5.05941	+	8.76315i	−0.194593	+	0.337044i
$677$	−10.7467	−	18.6138i	−0.413029	−	0.715388i	0.582190	−	0.813053i	$-0.302196\pi$
$677$	−10.7467	−	18.6138i	−0.413029	−	0.715388i	−0.995219	+	0.0976651i	$0.968863\pi$
$678$	4.42979	+	8.34145i	0.170125	+	0.320352i
$679$		0			0
$680$		−	1.55274i		−	0.0595447i
$681$	22.2492	−	35.5660i	0.852593	−	1.36289i
$682$	24.4355	+	14.1079i	0.935684	+	0.540218i
$683$	15.0140	+	8.66837i	0.574497	+	0.331686i	0.758943	−	0.651157i	$-0.225716\pi$
$683$	15.0140	+	8.66837i	0.574497	+	0.331686i	−0.184447	+	0.982843i	$0.559049\pi$
$684$	0.905340	−	12.7605i	0.0346165	−	0.487909i
$685$			4.94709i			0.189019i
$686$		0			0
$687$	33.2084	−	17.6356i	1.26698	−	0.672839i
$688$	−0.400075	−	0.692950i	−0.0152527	−	0.0264185i
$689$	4.36379	−	7.55831i	0.166247	−	0.287949i
$690$	8.02087	+	0.284178i	0.305349	+	0.0108185i
$691$	11.7251	−	6.76951i	0.446045	−	0.257524i	−0.260114	−	0.965578i	$-0.583760\pi$
$691$	11.7251	−	6.76951i	0.446045	−	0.257524i	0.706158	+	0.708054i	$0.250427\pi$
$692$	−8.51700			−0.323768
$693$		0			0
$694$	19.5866			0.743496
$695$	−9.28530	+	5.36087i	−0.352211	+	0.203349i
$696$	36.5159	+	1.29375i	1.38413	+	0.0490395i
$697$	1.18133	−	2.04613i	0.0447461	−	0.0775026i
$698$	−7.09240	−	12.2844i	−0.268451	−	0.464971i
$699$	16.8212	−	8.93303i	0.636237	−	0.337878i
$700$		0			0
$701$		−	41.8503i		−	1.58066i	−0.612679	−	0.790332i	$-0.709908\pi$
$701$		−	41.8503i		−	1.58066i	0.612679	−	0.790332i	$-0.290092\pi$
$702$	2.17056	+	4.89525i	0.0819227	+	0.184759i
$703$	33.2024	+	19.1694i	1.25225	+	0.722989i
$704$	30.5998	+	17.6668i	1.15327	+	0.665842i
$705$	6.11722	−	9.77853i	0.230388	−	0.368281i
$706$		−	11.1006i		−	0.417775i
$707$		0			0
$708$	7.90881	+	14.8926i	0.297231	+	0.559697i
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	0.877563	+	0.479462i	$0.159168\pi$
$709$	22.7397	+	39.3863i	0.854008	+	1.47918i	−0.0235552	+	0.999723i	$0.507499\pi$
$710$	−4.26151	+	7.38116i	−0.159932	+	0.277010i
$711$	−19.3720	−	39.8211i	−0.726506	−	1.49341i
$712$	18.9556	−	10.9440i	0.710392	−	0.410145i
$713$	25.3253			0.948442
$714$		0			0
$715$	−4.24299			−0.158679
$716$	−3.81519	+	2.20270i	−0.142580	+	0.0823189i
$717$	−0.553574	+	15.6245i	−0.0206736	+	0.583509i
$718$	−6.36230	+	11.0198i	−0.237439	+	0.411256i
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	0.863886	−	0.503687i	$-0.168024\pi$
$719$	−0.114311	−	0.197992i	−0.00426307	−	0.00738386i	−0.868149	+	0.496304i	$0.834690\pi$
$720$	−2.72974	+	4.03814i	−0.101731	+	0.150493i
$721$		0			0
$722$		−	7.48733i		−	0.278650i
$723$	−7.46090	−	4.66737i	−0.277474	−	0.173581i
$724$	−7.04228	−	4.06586i	−0.261724	−	0.151107i
$725$	−5.97147	−	3.44763i	−0.221775	−	0.128042i
$726$	−13.7939	−	8.62913i	−0.511939	−	0.320257i
$727$		−	19.2284i		−	0.713140i	−0.934269	−	0.356570i	$-0.883946\pi$
$727$		−	19.2284i		−	0.713140i	0.934269	−	0.356570i	$-0.116054\pi$
$728$		0			0
$729$	26.3927	+	5.69415i	0.977509	+	0.210895i
$730$	3.40454	+	5.89684i	0.126008	+	0.218252i
$731$	0.124972	−	0.216457i	0.00462225	−	0.00800596i
$732$	−0.0236851	+	0.668508i	−0.000875428	+	0.0247088i
$733$	7.15035	−	4.12825i	0.264104	−	0.152481i	−0.362101	−	0.932139i	$-0.617941\pi$
$733$	7.15035	−	4.12825i	0.264104	−	0.152481i	0.626205	+	0.779658i	$0.284607\pi$
$734$	−17.2253			−0.635797
$735$		0			0
$736$	18.7650			0.691688
$737$	−14.2452	+	8.22447i	−0.524729	+	0.302952i
$738$	−13.5425	+	6.58807i	−0.498506	+	0.242510i
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	−0.755088	−	0.655623i	$-0.772406\pi$
$739$	5.17166	−	8.95758i	0.190243	−	0.329510i	0.945331	+	0.326114i	$0.105739\pi$
$740$	3.15078	+	5.45732i	0.115825	+	0.200615i
$741$	−3.95441	−	7.44629i	−0.145269	−	0.273546i
$742$		0			0
$743$		−	37.7580i		−	1.38521i	−0.721318	−	0.692604i	$-0.756463\pi$
$743$		−	37.7580i		−	1.38521i	0.721318	−	0.692604i	$-0.243537\pi$
$744$	−16.5632	+	26.4767i	−0.607235	+	0.970681i
$745$	4.55837	+	2.63178i	0.167006	+	0.0964209i
$746$	−4.96508	−	2.86659i	−0.181785	−	0.104953i
$747$	32.2936	+	2.29119i	1.18156	+	0.0838302i
$748$			1.88641i			0.0689741i
$749$		0			0
$750$	1.64956	−	0.876010i	0.0602334	−	0.0319874i
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	0.930476	+	0.366352i	$0.119394\pi$
$751$	21.4442	+	37.1424i	0.782509	+	1.35534i	−0.147968	+	0.988992i	$0.547273\pi$
$752$	−5.40985	+	9.37013i	−0.197277	+	0.341693i
$753$	32.3255	+	1.14529i	1.17801	+	0.0417365i
$754$	6.15389	−	3.55295i	0.224111	−	0.129391i
$755$	7.00901			0.255084
$756$		0			0
$757$	−30.1051			−1.09419			−0.547094	−	0.837071i	$-0.684266\pi$
$757$	−30.1051			−1.09419			−0.547094	+	0.837071i	$0.684266\pi$
$758$	22.4527	−	12.9631i	0.815518	−	0.470840i
$759$	−33.0237	−	1.17002i	−1.19868	−	0.0424691i
$760$	7.79159	−	13.4954i	0.282631	−	0.489531i
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	−0.973557	−	0.228445i	$-0.926636\pi$
$761$	−18.8860	−	32.7115i	−0.684618	−	1.18579i	0.288939	−	0.957347i	$-0.406697\pi$
$762$	−13.2791	+	7.05196i	−0.481051	+	0.255466i
$763$		0			0
$764$		−	8.02904i		−	0.290480i
$765$	−1.51875	−	0.107753i	−0.0549105	−	0.00389583i
$766$	−17.5577	−	10.1370i	−0.634386	−	0.366263i
$767$	9.62451	+	5.55671i	0.347521	+	0.200641i
$768$	−14.7716	+	23.6127i	−0.533023	+	0.852051i
$769$			33.3656i			1.20319i	0.798800	+	0.601597i	$0.205469\pi$
$769$			33.3656i			1.20319i	−0.798800	+	0.601597i	$0.794531\pi$
$770$		0			0
$771$	−9.81558	−	18.4831i	−0.353499	−	0.665652i
$772$	−3.49595	−	6.05517i	−0.125822	−	0.217930i
$773$	−0.573356	+	0.993081i	−0.0206222	+	0.0357186i	−0.876152	−	0.482034i	$-0.839898\pi$
$773$	−0.573356	+	0.993081i	−0.0206222	+	0.0357186i	0.855530	+	0.517753i	$0.173231\pi$
$774$	−1.43264	+	0.696944i	−0.0514953	+	0.0250511i
$775$	5.10397	−	2.94678i	0.183340	−	0.105851i
$776$	21.1453			0.759073
$777$		0			0
$778$	13.1743			0.472321
$779$	20.5348	−	11.8558i	0.735736	−	0.424778i
$780$	0.0490674	−	1.38492i	0.00175690	−	0.0495881i
$781$	17.5456	−	30.3898i	0.627830	−	1.08743i
$782$	−1.17587	−	2.03666i	−0.0420489	−	0.0728309i
$783$	3.79948	−	35.6268i	0.135782	−	1.27320i
$784$		0			0
$785$		−	2.90010i		−	0.103509i
$786$	3.32403	+	2.07944i	0.118564	+	0.0741711i
$787$	35.9215	+	20.7393i	1.28046	+	0.739276i	0.976933	−	0.213546i	$-0.0685014\pi$
$787$	35.9215	+	20.7393i	1.28046	+	0.739276i	0.303530	+	0.952822i	$0.401835\pi$
$788$	−1.28746	−	0.743313i	−0.0458637	−	0.0264794i
$789$	−18.9243	−	11.8386i	−0.673724	−	0.421466i
$790$		−	15.9174i		−	0.566315i
$791$		0			0
$792$	22.8212	−	33.7597i	0.810916	−	1.19960i
$793$	0.220434	+	0.381804i	0.00782786	+	0.0135582i
$794$	−10.1175	+	17.5241i	−0.359058	+	0.621907i
$795$	0.560064	−	15.8077i	0.0198634	−	0.560642i
$796$	−2.72506	+	1.57332i	−0.0965874	+	0.0557647i
$797$	−49.5086			−1.75369			−0.876843	−	0.480777i	$-0.840355\pi$
$797$	−49.5086			−1.75369			−0.876843	+	0.480777i	$0.840355\pi$
$798$		0			0
$799$	−3.37976			−0.119567
$800$	3.78182	−	2.18344i	0.133708	−	0.0771961i
$801$	−9.38904	−	19.3002i	−0.331745	−	0.681938i
$802$	−12.9386	+	22.4103i	−0.456878	+	0.791336i
$803$	−14.0173	−	24.2786i	−0.494658	−	0.856773i
$804$	−2.51974	−	4.74477i	−0.0888645	−	0.167335i
$805$		0			0
$806$			6.07359i			0.213933i
$807$	−0.428472	+	0.684924i	−0.0150829	+	0.0241105i
$808$	6.33446	+	3.65720i	0.222846	+	0.128660i
$809$	−21.7594	−	12.5628i	−0.765018	−	0.441683i	0.0660764	−	0.997815i	$-0.478952\pi$
$809$	−21.7594	−	12.5628i	−0.765018	−	0.441683i	−0.831095	+	0.556131i	$0.812285\pi$
$810$	7.63551	+	5.99056i	0.268284	+	0.210487i
$811$		−	4.97517i		−	0.174702i	−0.996178	−	0.0873509i	$-0.972160\pi$
$811$		−	4.97517i		−	0.174702i	0.996178	−	0.0873509i	$-0.0278401\pi$
$812$		0			0
$813$	−35.6283	+	18.9207i	−1.24954	+	0.663577i
$814$	18.0181	+	31.2083i	0.631535	+	1.09385i
$815$	−6.37930	+	11.0493i	−0.223457	+	0.387039i
$816$	1.42734	+	0.0505704i	0.0499669	+	0.00177032i
$817$	2.17235	−	1.25421i	0.0760011	−	0.0438792i
$818$	18.4210			0.644076
$819$		0			0
$820$	3.89735			0.136101
$821$	12.0008	−	6.92866i	0.418830	−	0.241812i	−0.275746	−	0.961230i	$-0.588925\pi$
$821$	12.0008	−	6.92866i	0.418830	−	0.241812i	0.694577	+	0.719419i	$0.255592\pi$
$822$	−9.23407	−	0.327162i	−0.322075	−	0.0114111i
$823$	−23.0779	+	39.9721i	−0.804446	+	1.39334i	0.112219	+	0.993684i	$0.464204\pi$
$823$	−23.0779	+	39.9721i	−0.804446	+	1.39334i	−0.916665	+	0.399658i	$0.869129\pi$
$824$	22.8880	+	39.6432i	0.797343	+	1.38104i
$825$	−6.79159	+	3.60673i	−0.236453	+	0.125570i
$826$		0			0
$827$		−	18.6880i		−	0.649844i	−0.945741	−	0.324922i	$-0.894662\pi$
$827$		−	18.6880i		−	0.649844i	0.945741	−	0.324922i	$-0.105338\pi$
$828$	0.763794	−	10.7654i	0.0265437	−	0.374125i
$829$	14.9458	+	8.62894i	0.519088	+	0.299695i	0.736561	−	0.676371i	$-0.236448\pi$
$829$	14.9458	+	8.62894i	0.519088	+	0.299695i	−0.217474	+	0.976066i	$0.569782\pi$
$830$	10.0779	+	5.81849i	0.349810	+	0.201963i
$831$	−12.7601	+	20.3973i	−0.442642	+	0.707574i
$832$			7.60575i			0.263682i
$833$		0			0
$834$	−9.39235	−	17.6861i	−0.325231	−	0.612421i
$835$	7.88828	+	13.6629i	0.272985	+	0.472824i
$836$	−9.46597	+	16.3955i	−0.327387	+	0.567052i
$837$	24.7477	+	18.0380i	0.855405	+	0.623484i
$838$	−37.0301	+	21.3793i	−1.27918	+	0.738536i
$839$	49.1689			1.69750			0.848750	−	0.528795i	$-0.177356\pi$
$839$	49.1689			1.69750			0.848750	+	0.528795i	$0.177356\pi$
$840$		0			0
$841$	−18.5446			−0.639470
$842$	−31.8844	+	18.4085i	−1.09881	+	0.634398i
$843$	0.420391	−	11.8655i	0.0144790	−	0.408668i
$844$	3.81810	−	6.61315i	0.131425	−	0.227634i
$845$	6.04334	+	10.4674i	0.207897	+	0.360088i
$846$	17.8477	+	12.0649i	0.613617	+	0.414798i
$847$		0			0
$848$			14.8377i			0.509527i
$849$	6.51454	+	4.07534i	0.223578	+	0.139865i
$850$	−0.473959	−	0.273640i	−0.0162566	−	0.00938578i
$851$	28.0114	+	16.1724i	0.960218	+	0.554382i
$852$	9.71639	+	6.07834i	0.332878	+	0.208241i
$853$			8.86218i			0.303435i	0.988424	+	0.151718i	$0.0484804\pi$
$853$			8.86218i			0.303435i	−0.988424	+	0.151718i	$0.951520\pi$
$854$		0			0
$855$	−12.6593	−	8.55757i	−0.432940	−	0.292663i
$856$	−20.7452	−	35.9318i	−0.709058	−	1.22812i
$857$	0.491781	−	0.851790i	0.0167989	−	0.0290966i	−0.857504	−	0.514478i	$-0.827986\pi$
$857$	0.491781	−	0.851790i	0.0167989	−	0.0290966i	0.874303	+	0.485381i	$0.161319\pi$
$858$	0.280598	−	7.91982i	0.00957945	−	0.270378i
$859$	23.6244	−	13.6395i	0.806053	−	0.465375i	−0.0395302	−	0.999218i	$-0.512586\pi$
$859$	23.6244	−	13.6395i	0.806053	−	0.465375i	0.845583	+	0.533843i	$0.179253\pi$
$860$	0.412296			0.0140592
$861$		0			0
$862$	−27.7897			−0.946519
$863$	3.94265	−	2.27629i	0.134209	−	0.0774857i	−0.431392	−	0.902165i	$-0.641977\pi$
$863$	3.94265	−	2.27629i	0.134209	−	0.0774857i	0.565601	+	0.824679i	$0.308644\pi$
$864$	18.3370	+	13.3654i	0.623837	+	0.454700i
$865$	−5.08667	+	8.81037i	−0.172952	+	0.299562i
$866$	6.42257	+	11.1242i	0.218248	+	0.378016i
$867$	−13.6011	−	25.6113i	−0.461916	−	0.869804i
$868$		0			0
$869$			65.5354i			2.22314i
$870$	6.83013	−	10.9181i	0.231563	−	0.370160i
$871$	−3.06636	−	1.77036i	−0.103900	−	0.0599865i
$872$	−42.7142	−	24.6611i	−1.44649	−	0.835129i
$873$	1.46739	−	20.6825i	0.0496638	−	0.699995i
$874$		−	23.6019i		−	0.798346i
$875$		0			0
$876$	8.08667	−	4.29449i	0.273223	−	0.145097i
$877$	−10.6784	−	18.4956i	−0.360584	−	0.624551i	0.627473	−	0.778639i	$-0.284089\pi$
$877$	−10.6784	−	18.4956i	−0.360584	−	0.624551i	−0.988057	+	0.154088i	$0.950756\pi$
$878$	9.04360	−	15.6640i	0.305207	−	0.528634i
$879$	52.0712	+	1.84487i	1.75632	+	0.0622260i
$880$	6.24703	−	3.60673i	0.210587	−	0.121583i
$881$	33.2551			1.12039			0.560196	−	0.828360i	$-0.310726\pi$
$881$	33.2551			1.12039			0.560196	+	0.828360i	$0.310726\pi$
$882$		0			0
$883$	12.0561			0.405721			0.202860	−	0.979208i	$-0.434976\pi$
$883$	12.0561			0.405721			0.202860	+	0.979208i	$0.434976\pi$
$884$	−0.351659	+	0.203031i	−0.0118276	+	0.00682866i
$885$	20.1290	+	0.713167i	0.676629	+	0.0239729i
$886$	−1.29179	+	2.23745i	−0.0433987	+	0.0751687i
$887$	−11.7064	−	20.2760i	−0.393062	−	0.680803i	0.599790	−	0.800157i	$-0.295251\pi$
$887$	−11.7064	−	20.2760i	−0.393062	−	0.680803i	−0.992852	+	0.119355i	$0.961917\pi$
$888$	−35.2275	+	18.7078i	−1.18216	+	0.627793i
$889$		0			0
$890$		−	7.71471i		−	0.258598i
$891$	−31.4371	−	24.6645i	−1.05318	−	0.826290i
$892$	−8.51156	−	4.91415i	−0.284988	−	0.164538i
$893$	−29.3748	−	16.9595i	−0.982990	−	0.567529i
$894$	−5.21384	+	8.33445i	−0.174377	+	0.278746i
$895$			5.26215i			0.175894i
$896$		0			0
$897$	−3.33616	−	6.28210i	−0.111391	−	0.209753i
$898$	−13.7322	−	23.7848i	−0.458249	−	0.793711i
$899$	20.3188	−	35.1932i	0.677670	−	1.17376i
$900$	−1.09870	−	2.25850i	−0.0366234	−	0.0752832i
$901$	−4.01390	+	2.31743i	−0.133722	+	0.0772046i
$902$	22.2875			0.742091
$903$		0			0
$904$	15.4709			0.514556
$905$	−8.41183	+	4.85657i	−0.279619	+	0.161438i
$906$	−0.463521	+	13.0828i	−0.0153994	+	0.434646i
$907$	20.7508	−	35.9415i	0.689020	−	1.19342i	−0.283135	−	0.959080i	$-0.591374\pi$
$907$	20.7508	−	35.9415i	0.689020	−	1.19342i	0.972155	−	0.234338i	$-0.0752922\pi$
$908$	−10.1388	−	17.5608i	−0.336466	−	0.582777i
$909$	4.01674	−	5.94201i	0.133227	−	0.197084i
$910$		0			0
$911$			57.6428i			1.90979i	0.296941	+	0.954896i	$0.404034\pi$
$911$			57.6428i			1.90979i	−0.296941	+	0.954896i	$0.595966\pi$
$912$	12.1518	+	7.60189i	0.402387	+	0.251724i
$913$	−41.4930	−	23.9560i	−1.37322	−	0.792828i
$914$	3.21429	+	1.85577i	0.106319	+	0.0613835i
$915$	0.677390	+	0.423759i	0.0223938	+	0.0140091i
$916$		−	18.1743i		−	0.600496i
$917$		0			0
$918$	0.301566	−	2.82772i	0.00995318	−	0.0933286i
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	0.941891	−	0.335918i	$-0.109046\pi$
$919$	5.45769	+	9.45300i	0.180033	+	0.311826i	−0.761859	+	0.647743i	$0.775713\pi$
$920$	6.57342	−	11.3855i	0.216719	−	0.375369i
$921$	−2.01339	+	56.8276i	−0.0663435	+	1.87253i
$922$	−12.6423	+	7.29905i	−0.416353	+	0.240381i
$923$	7.55357			0.248629
$924$		0			0
$925$	7.52707			0.247488
$926$	−4.79793	+	2.77009i	−0.157670	+	0.0910307i
$927$	40.3638	−	19.6360i	1.32572	−	0.644930i
$928$	15.0554	−	26.0767i	0.494217	−	0.856008i
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	0.979837	+	0.199799i	$0.0640289\pi$
$929$	20.2064	+	34.9985i	0.662950	+	1.14826i	−0.316887	+	0.948463i	$0.602638\pi$
$930$	5.16281	+	9.72176i	0.169295	+	0.318789i
$931$		0			0
$932$		−	9.20592i		−	0.301550i
$933$	15.1214	−	24.1719i	0.495052	−	0.791353i
$934$	8.60828	+	4.96999i	0.281672	+	0.162623i
$935$	1.95139	+	1.12664i	0.0638173	+	0.0368450i
$936$	8.74958	+	0.620772i	0.285989	+	0.0202906i
$937$		−	5.67805i		−	0.185494i	−0.995690	−	0.0927468i	$-0.970435\pi$
$937$		−	5.67805i		−	0.185494i	0.995690	−	0.0927468i	$-0.0295647\pi$
$938$		0			0
$939$	−7.04963	+	3.74376i	−0.230056	+	0.122173i
$940$	−2.78755	−	4.82819i	−0.0909200	−	0.157478i
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	−0.950214	−	0.311598i	$-0.899136\pi$
$941$	−6.29634	+	10.9056i	−0.205255	+	0.355512i	0.744959	+	0.667110i	$0.232469\pi$
$942$	5.41323	+	0.191790i	0.176373	+	0.00624885i
$943$	17.3243	−	10.0022i	0.564157	−	0.325716i
$944$	−18.8938			−0.614940
$945$		0			0
$946$	2.35776			0.0766575
$947$	−27.1427	+	15.6709i	−0.882020	+	0.509234i	−0.871324	−	0.490708i	$-0.836738\pi$
$947$	−27.1427	+	15.6709i	−0.882020	+	0.509234i	−0.0106960	+	0.999943i	$0.503405\pi$
$948$	−21.3909	−	0.757874i	−0.694743	−	0.0246146i
$949$	3.01729	−	5.22611i	0.0979455	−	0.169647i
$950$	−2.74624	−	4.75663i	−0.0890998	−	0.154325i
$951$	−45.0200	+	23.9082i	−1.45987	+	0.775277i
$952$		0			0
$953$			43.7751i			1.41802i	0.705200	+	0.709008i	$0.250857\pi$
$953$			43.7751i			1.41802i	−0.705200	+	0.709008i	$0.749143\pi$
$954$	29.4691	+	2.09079i	0.954097	+	0.0676919i
$955$	−8.30561	−	4.79524i	−0.268763	−	0.155170i
$956$	6.54444	+	3.77843i	0.211662	+	0.122203i
$957$	−28.1212	+	44.9524i	−0.909028	+	1.45310i
$958$		−	22.2540i		−	0.718994i
$959$		0			0
$960$	6.46521	+	12.1742i	0.208664	+	0.392921i
$961$	1.86698	+	3.23370i	0.0602251	+	0.104313i
$962$	−3.87850	+	6.71776i	−0.125048	+	0.216589i
$963$	−36.5849	+	17.7976i	−1.17893	+	0.573521i
$964$	−3.68385	+	2.12687i	−0.118649	+	0.0685019i
$965$	−8.35166			−0.268849
$966$		0			0
$967$	36.3052			1.16750			0.583748	−	0.811935i	$-0.301585\pi$
$967$	36.3052			1.16750			0.583748	+	0.811935i	$0.301585\pi$
$968$	−23.0814	+	13.3261i	−0.741864	+	0.428316i
$969$	−0.158535	+	4.47463i	−0.00509288	+	0.143746i
$970$	3.72646	−	6.45441i	0.119649	−	0.207239i
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	0.919948	+	0.392041i	$0.128231\pi$
$971$	24.9129	+	43.1503i	0.799492	+	1.38476i	−0.120456	+	0.992719i	$0.538436\pi$
$972$	8.41406	−	9.97588i	0.269881	−	0.319976i
$973$		0			0
$974$			2.66887i			0.0855161i
$975$	−1.40332	−	0.877884i	−0.0449422	−	0.0281148i
$976$	−0.649099	−	0.374757i	−0.0207772	−	0.0119957i
$977$	−24.0369	−	13.8777i	−0.769008	−	0.443987i	0.0635127	−	0.997981i	$-0.479770\pi$
$977$	−24.0369	−	13.8777i	−0.769008	−	0.443987i	−0.832521	+	0.553994i	$0.813103\pi$
$978$	−20.2023	−	12.6381i	−0.645998	−	0.404121i
$979$			31.7631i			1.01515i
$980$		0			0
$981$	−27.0854	+	40.0679i	−0.864772	+	1.27927i
$982$	−11.4750	−	19.8753i	−0.366181	−	0.634245i
$983$	−21.0396	+	36.4417i	−0.671060	+	1.16231i	0.306544	+	0.951856i	$0.400827\pi$
$983$	−21.0396	+	36.4417i	−0.671060	+	1.16231i	−0.977604	+	0.210453i	$0.932506\pi$
$984$	−0.873468	+	24.6535i	−0.0278451	+	0.785924i
$985$	−1.53783	+	0.887869i	−0.0489995	+	0.0282898i
$986$	−3.77364			−0.120177
$987$		0			0
$988$	−4.07521			−0.129650
$989$	1.83272	−	1.05812i	0.0582770	−	0.0336463i
$990$	−6.28305	−	12.9155i	−0.199688	−	0.410481i
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	−0.907890	−	0.419209i	$-0.862308\pi$
$991$	−2.86154	+	4.95633i	−0.0908997	+	0.157443i	0.816990	+	0.576652i	$0.195641\pi$
$992$	12.8682	+	22.2884i	0.408566	+	0.707656i
$993$	2.15745	+	4.06256i	0.0684647	+	0.128922i
$994$		0			0
$995$			3.75858i			0.119155i
$996$	8.29912	−	13.2663i	0.262968	−	0.420360i
$997$	−9.64266	−	5.56719i	−0.305386	−	0.176315i	0.339474	−	0.940615i	$-0.389751\pi$
$997$	−9.64266	−	5.56719i	−0.305386	−	0.176315i	−0.644860	+	0.764301i	$0.723084\pi$
$998$	−30.5729	−	17.6513i	−0.967768	−	0.558741i
$999$	15.8537	+	35.7546i	0.501588	+	1.13123i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.l.521.3		8
3.2	odd	2		735.2.s.k.521.2		8
7.2	even	3		105.2.s.c.26.2	✓	8
7.3	odd	6		735.2.b.c.146.6		8
7.4	even	3		735.2.b.d.146.6		8
7.5	odd	6		735.2.s.k.656.2		8
7.6	odd	2		105.2.s.d.101.3	yes	8
21.2	odd	6		105.2.s.d.26.3	yes	8
21.5	even	6	inner	735.2.s.l.656.3		8
21.11	odd	6		735.2.b.c.146.3		8
21.17	even	6		735.2.b.d.146.3		8
21.20	even	2		105.2.s.c.101.2	yes	8
35.2	odd	12		525.2.q.f.299.6		16
35.9	even	6		525.2.t.g.26.3		8
35.13	even	4		525.2.q.e.374.3		16
35.23	odd	12		525.2.q.f.299.3		16
35.27	even	4		525.2.q.e.374.6		16
35.34	odd	2		525.2.t.f.101.2		8
105.2	even	12		525.2.q.e.299.3		16
105.23	even	12		525.2.q.e.299.6		16
105.44	odd	6		525.2.t.f.26.2		8
105.62	odd	4		525.2.q.f.374.3		16
105.83	odd	4		525.2.q.f.374.6		16
105.104	even	2		525.2.t.g.101.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	7.2	even	3
105.2.s.c.101.2	yes	8	21.20	even	2
105.2.s.d.26.3	yes	8	21.2	odd	6
105.2.s.d.101.3	yes	8	7.6	odd	2
525.2.q.e.299.3		16	105.2	even	12
525.2.q.e.299.6		16	105.23	even	12
525.2.q.e.374.3		16	35.13	even	4
525.2.q.e.374.6		16	35.27	even	4
525.2.q.f.299.3		16	35.23	odd	12
525.2.q.f.299.6		16	35.2	odd	12
525.2.q.f.374.3		16	105.62	odd	4
525.2.q.f.374.6		16	105.83	odd	4
525.2.t.f.26.2		8	105.44	odd	6
525.2.t.f.101.2		8	35.34	odd	2
525.2.t.g.26.3		8	35.9	even	6
525.2.t.g.101.3		8	105.104	even	2
735.2.b.c.146.3		8	21.11	odd	6
735.2.b.c.146.6		8	7.3	odd	6
735.2.b.d.146.3		8	21.17	even	6
735.2.b.d.146.6		8	7.4	even	3
735.2.s.k.521.2		8	3.2	odd	2
735.2.s.k.656.2		8	7.5	odd	6
735.2.s.l.521.3		8	1.1	even	1	trivial
735.2.s.l.656.3		8	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.933868 - 0.539169i) q^{2} +(-1.73096 - 0.0613278i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(2.99248 + 0.212312i) q^{9} +O(q^{10})\)	\(q+(0.933868 - 0.539169i) q^{2} +(-1.73096 - 0.0613278i) q^{3} +(-0.418594 + 0.725026i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.64956 + 0.876010i) q^{6} +3.05945i q^{8} +(2.99248 + 0.212312i) q^{9} +(0.933868 + 0.539169i) q^{10} +(-3.84494 - 2.21988i) q^{11} +(0.769035 - 1.22932i) q^{12} -0.955682i q^{13} +(-0.812371 - 1.52972i) q^{15} +(0.812371 + 1.40707i) q^{16} +(-0.253761 + 0.439527i) q^{17} +(2.90905 - 1.41518i) q^{18} +(-4.41107 + 2.54673i) q^{19} -0.837188 q^{20} -4.78755 q^{22} +(-3.72142 + 2.14856i) q^{23} +(0.187629 - 5.29579i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.515274 - 0.892481i) q^{26} +(-5.16685 - 0.551027i) q^{27} +6.89526i q^{29} +(-1.58343 - 0.990554i) q^{30} +(-5.10397 - 2.94678i) q^{31} +(-3.78182 - 2.18344i) q^{32} +(6.51931 + 4.07833i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-3.76353 - 6.51863i) q^{37} +(-2.74624 + 4.75663i) q^{38} +(-0.0586099 + 1.65425i) q^{39} +(-2.64956 + 1.52972i) q^{40} -4.65529 q^{41} -0.492478 q^{43} +(3.21894 - 1.85845i) q^{44} +(1.31237 + 2.69772i) q^{45} +(-2.31688 + 4.01295i) q^{46} +(3.32967 + 5.76715i) q^{47} +(-1.31989 - 2.48541i) q^{48} +1.07834i q^{50} +(0.466207 - 0.745243i) q^{51} +(0.692894 + 0.400043i) q^{52} +(7.90881 + 4.56616i) q^{53} +(-5.12226 + 2.27122i) q^{54} -4.43975i q^{55} +(7.79159 - 4.13778i) q^{57} +(3.71771 + 6.43926i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(1.44914 + 0.0513428i) q^{60} +(-0.399509 + 0.230657i) q^{61} -6.35524 q^{62} -7.95845 q^{64} +(0.827645 - 0.477841i) q^{65} +(8.28709 + 0.293610i) q^{66} +(1.85246 - 3.20856i) q^{67} +(-0.212446 - 0.367967i) q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(-0.649559 + 9.15533i) q^{72} +(5.46846 + 3.15721i) q^{73} +(-7.02929 - 4.05836i) q^{74} +(0.918594 - 1.46840i) q^{75} -4.26419i q^{76} +(0.837188 + 1.57645i) q^{78} +(-7.38052 - 12.7834i) q^{79} +(-0.812371 + 1.40707i) q^{80} +(8.90985 + 1.27068i) q^{81} +(-4.34743 + 2.50999i) q^{82} +10.7916 q^{83} -0.507522 q^{85} +(-0.459909 + 0.265529i) q^{86} +(0.422871 - 11.9355i) q^{87} +(6.79159 - 11.7634i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(2.68011 + 1.81172i) q^{90} -3.59750i q^{92} +(8.65407 + 5.41378i) q^{93} +(6.21894 + 3.59050i) q^{94} +(-4.41107 - 2.54673i) q^{95} +(6.41230 + 4.01138i) q^{96} -6.91148i q^{97} +(-11.0346 - 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9	\( 8 q + 3 q^{2} - 2 q^{3} + 3 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{9} + 3 q^{10} + 18 q^{12} - q^{15} + q^{16} - 12 q^{17} + 26 q^{18} - 9 q^{19} + 6 q^{20} - 40 q^{22} - 27 q^{23} + 7 q^{24} - 4 q^{25} - 6 q^{26} + 4 q^{27} + 10 q^{30} + 21 q^{31} - 21 q^{32} - 4 q^{33} + 9 q^{36} + 7 q^{37} - 12 q^{38} + 15 q^{39} - 3 q^{40} - 30 q^{41} + 16 q^{43} + 5 q^{45} - 7 q^{46} - 6 q^{47} - 25 q^{48} + 12 q^{51} - 30 q^{52} - 24 q^{53} - 7 q^{54} + 6 q^{57} - 13 q^{58} - 12 q^{59} + 9 q^{60} - 15 q^{61} + 24 q^{62} + 38 q^{64} + 3 q^{65} + 16 q^{66} + 4 q^{67} - 13 q^{69} + 13 q^{72} - 15 q^{73} - 54 q^{74} + q^{75} - 6 q^{78} - 29 q^{79} - q^{80} + 28 q^{81} - 27 q^{82} + 30 q^{83} - 24 q^{85} - 9 q^{86} + 29 q^{87} - 2 q^{88} - 3 q^{89} + 7 q^{90} + 45 q^{93} + 24 q^{94} - 9 q^{95} + 42 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^9 + 3 * q^10 + 18 * q^12 - q^15 + q^16 - 12 * q^17 + 26 * q^18 - 9 * q^19 + 6 * q^20 - 40 * q^22 - 27 * q^23 + 7 * q^24 - 4 * q^25 - 6 * q^26 + 4 * q^27 + 10 * q^30 + 21 * q^31 - 21 * q^32 - 4 * q^33 + 9 * q^36 + 7 * q^37 - 12 * q^38 + 15 * q^39 - 3 * q^40 - 30 * q^41 + 16 * q^43 + 5 * q^45 - 7 * q^46 - 6 * q^47 - 25 * q^48 + 12 * q^51 - 30 * q^52 - 24 * q^53 - 7 * q^54 + 6 * q^57 - 13 * q^58 - 12 * q^59 + 9 * q^60 - 15 * q^61 + 24 * q^62 + 38 * q^64 + 3 * q^65 + 16 * q^66 + 4 * q^67 - 13 * q^69 + 13 * q^72 - 15 * q^73 - 54 * q^74 + q^75 - 6 * q^78 - 29 * q^79 - q^80 + 28 * q^81 - 27 * q^82 + 30 * q^83 - 24 * q^85 - 9 * q^86 + 29 * q^87 - 2 * q^88 - 3 * q^89 + 7 * q^90 + 45 * q^93 + 24 * q^94 - 9 * q^95 + 42 * q^96 - 34 * q^99

Introduction

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