LMFDB - Embedded newform 735.2.s.l.656.3

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			656.3
Root			$1.07834i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.l.521.3

$q$-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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	0.792408	−	0.609991i	$-0.208827\pi$
$2$	0.933868	+	0.539169i	0.660344	+	0.381250i	−0.132064	+	0.991241i	$0.542160\pi$
$3$	−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	−0.951134	−	0.308777i	$-0.900080\pi$
$11$	−3.84494	+	2.21988i	−1.15929	+	0.669318i	−0.208158	+	0.978095i	$0.566747\pi$
$12$	0.769035	+	1.22932i	0.222001	+	0.354875i
$13$			0.955682i			0.265059i	0.991179	+	0.132529i	$0.0423099\pi$
$13$			0.955682i			0.265059i	−0.991179	+	0.132529i	$0.957690\pi$
$14$		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	0.833611	−	0.552353i	$-0.186270\pi$
$17$	−0.253761	−	0.439527i	−0.0615461	−	0.106601i	−0.895157	+	0.445752i	$0.852936\pi$
$18$	2.90905	+	1.41518i	0.685670	+	0.333561i
$19$	−4.41107	−	2.54673i	−1.01197	−	0.584261i	−0.100202	−	0.994967i	$-0.531949\pi$
$19$	−4.41107	−	2.54673i	−1.01197	−	0.584261i	−0.911768	+	0.410706i	$0.865282\pi$
$20$	−0.837188			−0.187201
$21$		0			0
$22$	−4.78755			−1.02071
$23$	−3.72142	−	2.14856i	−0.775970	−	0.448007i	0.0590300	−	0.998256i	$-0.481199\pi$
$23$	−3.72142	−	2.14856i	−0.775970	−	0.448007i	−0.835000	+	0.550250i	$0.814533\pi$
$24$	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	$-0.778848\pi$
$29$		−	6.89526i		−	1.28042i	0.768201	−	0.640209i	$-0.221152\pi$
$30$	−1.58343	+	0.990554i	−0.289093	+	0.180850i
$31$	−5.10397	+	2.94678i	−0.916699	+	0.529257i	−0.882581	−	0.470161i	$-0.844196\pi$
$31$	−5.10397	+	2.94678i	−0.916699	+	0.529257i	−0.0341187	+	0.999418i	$0.510862\pi$
$32$	−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	0.370998	+	0.928634i	$0.379016\pi$
$37$	−3.76353	+	6.51863i	−0.618721	+	1.07166i	−0.989719	+	0.143023i	$0.954318\pi$
$38$	−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	−0.514183	−	0.857681i	$-0.671905\pi$
$47$	3.32967	−	5.76715i	0.485682	−	0.841225i	0.999865	+	0.0164553i	$0.00523812\pi$
$48$	−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	0.153754	−	0.988109i	$-0.450864\pi$
$53$	7.90881	−	4.56616i	1.08636	−	0.627210i	0.932605	+	0.360899i	$0.117530\pi$
$54$	−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	−0.944389	−	0.328829i	$-0.893346\pi$
$59$	−5.81439	−	10.0708i	−0.756969	−	1.31111i	0.187420	−	0.982280i	$-0.439987\pi$
$60$	1.44914	−	0.0513428i	0.187083	−	0.00662833i
$61$	−0.399509	−	0.230657i	−0.0511519	−	0.0295326i	0.474206	−	0.880414i	$-0.342735\pi$
$61$	−0.399509	−	0.230657i	−0.0511519	−	0.0295326i	−0.525358	+	0.850881i	$0.676069\pi$
$62$	−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	0.956713	−	0.291033i	$-0.0939991\pi$
$67$	1.85246	+	3.20856i	0.226314	+	0.391988i	−0.730399	+	0.683021i	$0.760666\pi$
$68$	−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	$-0.844612\pi$
$71$		−	7.90386i		−	0.938015i	0.883194	−	0.469008i	$-0.155388\pi$
$72$	−0.649559	−	9.15533i	−0.0765512	−	1.07897i
$73$	5.46846	−	3.15721i	0.640034	−	0.369524i	−0.144593	−	0.989491i	$-0.546187\pi$
$73$	5.46846	−	3.15721i	0.640034	−	0.369524i	0.784628	+	0.619967i	$0.212854\pi$
$74$	−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	0.0673684	+	0.997728i	$0.478540\pi$
$79$	−7.38052	+	12.7834i	−0.830374	+	1.43825i	−0.897742	+	0.440521i	$0.854794\pi$
$80$	−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	−0.990942	−	0.134287i	$-0.957125\pi$
$89$	−3.57713	+	6.19577i	−0.379175	+	0.656750i	0.611768	+	0.791038i	$0.290459\pi$
$90$	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	$0.114117\pi$
$97$			6.91148i			0.701755i	−0.936421	+	0.350877i	$0.885883\pi$
$98$		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	0.919350	−	0.393441i	$-0.128715\pi$
$101$	1.19538	+	2.07046i	0.118945	+	0.206019i	−0.800405	+	0.599460i	$0.795382\pi$
$102$	0.0335635	+	0.947323i	0.00332328	+	0.0937990i
$103$	12.9577	+	7.48110i	1.27676	+	0.737135i	0.976250	−	0.216645i	$-0.0695115\pi$
$103$	12.9577	+	7.48110i	1.27676	+	0.737135i	0.300505	+	0.953780i	$0.402845\pi$
$104$	2.92386			0.286708
$105$		0			0
$106$	9.84772			0.956495
$107$	−11.7445	−	6.78072i	−1.13539	−	0.655517i	−0.190104	−	0.981764i	$-0.560882\pi$
$107$	−11.7445	−	6.78072i	−1.13539	−	0.655517i	−0.945284	+	0.326247i	$0.894216\pi$
$108$	2.56232	+	3.51544i	0.246559	+	0.338274i
$109$	−8.06063	−	13.9614i	−0.772068	−	1.33726i	−0.936428	−	0.350861i	$-0.885889\pi$
$109$	−8.06063	−	13.9614i	−0.772068	−	1.33726i	0.164359	−	0.986401i	$-0.447444\pi$
$110$	−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	$0.0764429\pi$
$113$			5.05678i			0.475702i	−0.971302	+	0.237851i	$0.923557\pi$
$114$	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	−0.908229	−	0.418473i	$-0.862566\pi$
$131$	−1.04963	+	1.81802i	−0.0917069	+	0.158841i	0.816523	+	0.577314i	$0.195899\pi$
$132$	−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	−0.305691	−	0.952131i	$-0.598887\pi$
$137$	4.28431	−	2.47355i	0.366033	−	0.211329i	0.671724	+	0.740801i	$0.265554\pi$
$138$	4.25654	+	6.80419i	0.362341	+	0.579211i
$139$		−	10.7217i		−	0.909406i	−0.890643	−	0.454703i	$-0.849745\pi$
$139$		−	10.7217i		−	0.909406i	0.890643	−	0.454703i	$-0.150255\pi$
$140$		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	0.674959	−	0.737855i	$-0.264161\pi$
$149$	4.55837	+	2.63178i	0.373436	+	0.215604i	−0.301522	+	0.953459i	$0.597495\pi$
$150$	0.0661321	+	1.86656i	0.00539966	+	0.152404i
$151$	3.50451	+	6.06998i	0.285193	+	0.493968i	0.972656	−	0.232251i	$-0.0746091\pi$
$151$	3.50451	+	6.06998i	0.285193	+	0.493968i	−0.687463	+	0.726219i	$0.741276\pi$
$152$	−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	−0.596863	−	0.802343i	$-0.703586\pi$
$157$	−2.51156	+	1.45005i	−0.200445	+	0.115727i	0.396418	+	0.918070i	$0.370253\pi$
$158$	−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	−0.500335	−	0.865832i	$-0.666790\pi$
$163$	6.37930	−	11.0493i	0.499665	−	0.865446i	1.00000		0.000386523i	$0.000123034\pi$
$164$	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	−0.605275	−	0.796016i	$-0.706937\pi$
$173$	5.08667	−	8.81037i	0.386732	−	0.669840i	0.992008	+	0.126176i	$0.0402704\pi$
$174$	−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	−0.319927	−	0.947442i	$-0.603659\pi$
$179$	4.55716	−	2.63107i	0.340618	−	0.196656i	0.660545	+	0.750786i	$0.270325\pi$
$180$	−2.50527	+	0.177745i	−0.186731	+	0.0132484i
$181$		−	9.71314i		−	0.721972i	−0.932571	−	0.360986i	$-0.882440\pi$
$181$		−	9.71314i		−	0.721972i	0.932571	−	0.360986i	$-0.117560\pi$
$182$		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	0.168451	−	0.985710i	$-0.446123\pi$
$191$	−8.30561	−	4.79524i	−0.600973	−	0.346972i	−0.769424	+	0.638738i	$0.779457\pi$
$192$	13.7758	−	0.488074i	0.994182	−	0.0352237i
$193$	−4.17583	−	7.23275i	−0.300583	−	0.520625i	0.675685	−	0.737190i	$-0.263848\pi$
$193$	−4.17583	−	7.23275i	−0.300583	−	0.520625i	−0.976268	+	0.216566i	$0.930515\pi$
$194$	−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	$-0.979851\pi$
$197$		−	1.77574i		−	0.126516i	0.997997	−	0.0632580i	$-0.0201491\pi$
$198$	−14.3267	+	1.01646i	−1.01815	+	0.0722365i
$199$	3.25502	−	1.87929i	0.230742	−	0.133219i	−0.380172	−	0.924916i	$-0.624135\pi$
$199$	3.25502	−	1.87929i	0.230742	−	0.133219i	0.610915	+	0.791697i	$0.290802\pi$
$200$	−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	$-0.871412\pi$
$223$		−	11.7397i		−	0.786146i	0.919507	−	0.393073i	$-0.128588\pi$
$224$		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	−0.917097	−	0.398664i	$-0.869474\pi$
$227$	−12.1105	−	20.9760i	−0.803802	−	1.39223i	0.113295	−	0.993561i	$-0.463859\pi$
$228$	−0.261513	−	7.38116i	−0.0173191	−	0.488829i
$229$	−18.8003	−	10.8544i	−1.24236	−	0.717278i	−0.272787	−	0.962075i	$-0.587945\pi$
$229$	−18.8003	−	10.8544i	−1.24236	−	0.717278i	−0.969574	+	0.244797i	$0.921279\pi$
$230$	−4.63376			−0.305541
$231$		0			0
$232$	−21.0957			−1.38500
$233$	−9.52303	−	5.49812i	−0.623874	−	0.360194i	0.154502	−	0.987993i	$-0.450623\pi$
$233$	−9.52303	−	5.49812i	−0.623874	−	0.360194i	−0.778376	+	0.627799i	$0.783956\pi$
$234$	−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	$0.0942999\pi$
$239$			9.02649i			0.583875i	−0.956437	+	0.291938i	$0.905700\pi$
$240$	1.49248	+	2.38576i	0.0963390	+	0.154000i
$241$	4.40027	−	2.54050i	0.283446	−	0.163648i	−0.351536	−	0.936174i	$-0.614341\pi$
$241$	4.40027	−	2.54050i	0.283446	−	0.163648i	0.634982	+	0.772527i	$0.281007\pi$
$242$	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	−0.613755	−	0.789497i	$-0.710342\pi$
$257$	6.04132	−	10.4639i	0.376847	−	0.652718i	0.990602	+	0.136779i	$0.0436750\pi$
$258$	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	−0.114722	−	0.993398i	$-0.536598\pi$
$263$	11.1611	−	6.44388i	0.688224	−	0.397346i	0.802946	+	0.596051i	$0.203264\pi$
$264$	−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	0.873048	−	0.487635i	$-0.162140\pi$
$269$	0.233222	+	0.403952i	0.0142198	+	0.0246294i	−0.858828	+	0.512264i	$0.828807\pi$
$270$	−4.52806	+	3.30039i	−0.275569	+	0.200856i
$271$	20.1703	+	11.6453i	1.22526	+	0.707404i	0.966035	−	0.258413i	$-0.0831994\pi$
$271$	20.1703	+	11.6453i	1.22526	+	0.707404i	0.259225	+	0.965817i	$0.416533\pi$
$272$	−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	0.995668	−	0.0929805i	$-0.0296394\pi$
$277$	6.94543	+	12.0298i	0.417310	+	0.722803i	−0.578357	+	0.815783i	$0.696306\pi$
$278$	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	$-0.934455\pi$
$281$		−	6.85483i		−	0.408925i	0.978874	−	0.204462i	$-0.0655446\pi$
$282$	−10.5446	+	6.59643i	−0.627919	+	0.392812i
$283$	−3.84212	+	2.21825i	−0.228391	+	0.131861i	−0.609829	−	0.792533i	$-0.708762\pi$
$283$	−3.84212	+	2.21825i	−0.228391	+	0.131861i	0.381439	+	0.924394i	$0.375429\pi$
$284$	−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	$0.386276\pi$
$307$			32.8300i			1.87371i	−0.349722	+	0.936853i	$0.613724\pi$
$308$		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	0.532556	−	0.846395i	$-0.321232\pi$
$311$	−8.23073	−	14.2560i	−0.466722	−	0.808386i	−0.999277	+	0.0380092i	$0.987898\pi$
$312$	−5.06110	+	0.179314i	−0.286528	+	0.0101516i
$313$	3.99102	+	2.30422i	0.225586	+	0.130242i	0.608534	−	0.793528i	$-0.291758\pi$
$313$	3.99102	+	2.30422i	0.225586	+	0.130242i	−0.382948	+	0.923770i	$0.625091\pi$
$314$	−3.12729			−0.176483
$315$		0			0
$316$	12.3578			0.695179
$317$	25.4873	+	14.7151i	1.43151	+	0.826481i	0.997236	−	0.0743007i	$-0.0236725\pi$
$317$	25.4873	+	14.7151i	1.43151	+	0.826481i	0.434272	+	0.900782i	$0.357006\pi$
$318$	−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	−0.900209	−	0.435458i	$-0.856586\pi$
$331$	−1.32787	+	2.29995i	−0.0729866	+	0.126417i	0.827222	+	0.561875i	$0.189920\pi$
$332$	−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	−0.0143301	−	0.999897i	$-0.504562\pi$
$347$	15.7302	−	9.08183i	0.844441	−	0.487538i	0.858771	+	0.512359i	$0.171228\pi$
$348$	8.47650	−	5.30270i	0.454388	−	0.284255i
$349$			13.1543i			0.704135i	0.935975	+	0.352067i	$0.114521\pi$
$349$			13.1543i			0.704135i	−0.935975	+	0.352067i	$0.885479\pi$
$350$		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	0.969870	−	0.243623i	$-0.0783361\pi$
$353$	5.14707	+	8.91499i	0.273951	+	0.474497i	−0.695919	+	0.718120i	$0.745003\pi$
$354$	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	0.205464	−	0.978665i	$-0.434130\pi$
$359$	−10.2193	−	5.90010i	−0.539352	−	0.311395i	−0.744816	+	0.667270i	$0.767463\pi$
$360$	−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	−0.815533	−	0.578711i	$-0.803556\pi$
$367$	−13.8338	+	7.98697i	−0.722120	+	0.416916i	0.0934122	+	0.995628i	$0.470223\pi$
$368$	−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	−0.926604	−	0.376038i	$-0.877286\pi$
$373$	−2.65834	+	4.60438i	−0.137644	+	0.238406i	0.788961	+	0.614444i	$0.210620\pi$
$374$	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	−0.999746	−	0.0225490i	$-0.992822\pi$
$383$	−9.40053	+	16.2822i	−0.480345	+	0.831982i	0.519401	+	0.854531i	$0.326155\pi$
$384$	−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	−0.207190	−	0.978301i	$-0.566432\pi$
$389$	10.5804	−	6.10860i	0.536448	−	0.309718i	0.743638	+	0.668582i	$0.233099\pi$
$390$	−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	0.0332862	−	0.999446i	$-0.489403\pi$
$397$	−16.2510	−	9.38254i	−0.815616	−	0.470896i	−0.848902	+	0.528550i	$0.822736\pi$
$398$	4.05302			0.203159
$399$		0			0
$400$	−1.62474			−0.0812371
$401$	−20.7823	−	11.9987i	−1.03782	−	0.599184i	−0.118603	−	0.992942i	$-0.537842\pi$
$401$	−20.7823	−	11.9987i	−1.03782	−	0.599184i	−0.919214	+	0.393757i	$0.871175\pi$
$402$	−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	−0.0874559	−	0.996168i	$-0.527874\pi$
$409$	14.7941	−	8.54140i	0.731523	−	0.422345i	0.818979	+	0.573823i	$0.194540\pi$
$410$	−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	−0.929551	−	0.368693i	$-0.879805\pi$
$431$	−22.3182	+	12.8854i	−1.07503	+	0.620668i	−0.145478	+	0.989361i	$0.546472\pi$
$432$	−3.42207	+	7.71775i	−0.164644	+	0.371320i
$433$		−	11.9120i		−	0.572454i	−0.958162	−	0.286227i	$-0.907599\pi$
$433$		−	11.9120i		−	0.572454i	0.958162	−	0.286227i	$-0.0924011\pi$
$434$		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	0.804843	−	0.593487i	$-0.202249\pi$
$439$	14.5260	+	8.38661i	0.693290	+	0.400271i	−0.111553	+	0.993758i	$0.535583\pi$
$440$	13.5832			0.647553
$441$		0			0
$442$	0.523026			0.0248778
$443$	−2.07491	−	1.19795i	−0.0985819	−	0.0569163i	0.449899	−	0.893080i	$-0.351460\pi$
$443$	−2.07491	−	1.19795i	−0.0985819	−	0.0569163i	−0.548480	+	0.836163i	$0.684793\pi$
$444$	−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	$0.205224\pi$
$449$			25.4692i			1.20196i	−0.799262	+	0.600982i	$0.794776\pi$
$450$	−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	−0.822963	−	0.568095i	$-0.807681\pi$
$457$	1.72096	−	2.98078i	0.0805029	−	0.139435i	0.903466	+	0.428660i	$0.141014\pi$
$458$	−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	−0.739462	−	0.673199i	$-0.764920\pi$
$467$	4.60894	−	7.98292i	0.213276	−	0.369405i	0.952738	+	0.303793i	$0.0982532\pi$
$468$	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	0.999467	−	0.0326342i	$-0.0103896\pi$
$479$	10.3187	+	17.8724i	0.471472	+	0.816613i	−0.527996	+	0.849247i	$0.677056\pi$
$480$	−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	0.836625	−	0.547777i	$-0.184526\pi$
$487$	−1.23749	−	2.14340i	−0.0560761	−	0.0971267i	−0.892701	+	0.450650i	$0.851192\pi$
$488$	−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	$0.159450\pi$
$491$			21.2827i			0.960476i	−0.877138	+	0.480238i	$0.840550\pi$
$492$	−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	0.222918	+	0.974837i	$0.428442\pi$
$499$	−16.3690	+	28.3519i	−0.732775	+	1.26920i	−0.955693	+	0.294366i	$0.904891\pi$
$500$	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	−0.221664	−	0.975123i	$-0.571149\pi$
$509$	16.5519	−	28.6687i	0.733649	−	1.27072i	0.955313	−	0.295595i	$-0.0955178\pi$
$510$	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	0.764092	+	0.645108i	$0.223188\pi$
$521$	21.4725	+	37.1914i	0.940726	+	1.62938i	0.176634	+	0.984277i	$0.443479\pi$
$522$	9.75803	−	20.0587i	0.427097	−	0.877944i
$523$	−33.0751	−	19.0959i	−1.44627	−	0.835007i	−0.448018	−	0.894025i	$-0.647870\pi$
$523$	−33.0751	−	19.0959i	−1.44627	−	0.835007i	−0.998257	+	0.0590174i	$0.981203\pi$
$524$	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	−0.861587	−	0.507611i	$-0.830529\pi$
$541$	0.204923	−	0.354938i	0.00881035	−	0.0152600i	0.870397	+	0.492351i	$0.163862\pi$
$542$	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	−0.606357	−	0.795193i	$-0.707370\pi$
$557$	−5.21291	+	3.00967i	−0.220878	+	0.127524i	0.385479	+	0.922717i	$0.374036\pi$
$558$	−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	0.979082	−	0.203467i	$-0.0652208\pi$
$563$	7.43466	+	12.8772i	0.313334	+	0.542710i	−0.665748	+	0.746176i	$0.731887\pi$
$564$	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	0.401389	−	0.915907i	$-0.368527\pi$
$569$	−4.55880	−	2.63203i	−0.191115	−	0.110340i	−0.592504	+	0.805567i	$0.701861\pi$
$570$	9.50729	−	0.336841i	0.398216	−	0.0141087i
$571$	−22.8775	−	39.6250i	−0.957394	−	1.65825i	−0.728793	−	0.684734i	$-0.759918\pi$
$571$	−22.8775	−	39.6250i	−0.957394	−	1.65825i	−0.228601	−	0.973520i	$-0.573415\pi$
$572$	−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	−0.406555	−	0.913626i	$-0.633270\pi$
$577$	4.35716	−	2.51561i	0.181391	−	0.104726i	0.587946	+	0.808900i	$0.299937\pi$
$578$	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	−0.610511	−	0.792008i	$-0.709036\pi$
$593$	9.26927	−	16.0548i	0.380643	−	0.659293i	0.991154	+	0.132714i	$0.0423693\pi$
$594$	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	−0.489721	−	0.871879i	$-0.662901\pi$
$599$	0.501417	−	0.289493i	0.0204873	−	0.0118284i	0.510209	+	0.860051i	$0.329568\pi$
$600$	4.49248	−	2.81039i	0.183405	−	0.114734i
$601$		−	29.8618i		−	1.21809i	−0.793137	−	0.609044i	$-0.791553\pi$
$601$		−	29.8618i		−	1.21809i	0.793137	−	0.609044i	$-0.208447\pi$
$602$		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	−0.0111098	−	0.999938i	$-0.503536\pi$
$607$	−21.7458	−	12.5550i	−0.882637	−	0.509591i	−0.871527	+	0.490348i	$0.836870\pi$
$608$	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	0.880390	−	0.474251i	$-0.157281\pi$
$613$	0.729932	+	1.26428i	0.0294817	+	0.0510638i	−0.850908	+	0.525315i	$0.823948\pi$
$614$	−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	$0.0421687\pi$
$617$			6.56208i			0.264179i	−0.991238	+	0.132090i	$0.957831\pi$
$618$	−14.8209	−	23.6916i	−0.596183	−	0.953014i
$619$	−18.2419	+	10.5319i	−0.733202	+	0.423315i	−0.819593	−	0.572947i	$-0.805800\pi$
$619$	−18.2419	+	10.5319i	−0.733202	+	0.423315i	0.0863902	+	0.996261i	$0.472467\pi$
$620$	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	−0.684133	−	0.729357i	$-0.739819\pi$
$641$	−9.98943	+	5.76740i	−0.394559	+	0.227798i	0.289575	+	0.957155i	$0.406486\pi$
$642$	13.4333	+	21.4735i	0.530172	+	0.847493i
$643$			17.3489i			0.684173i	0.939668	+	0.342087i	$0.111134\pi$
$643$			17.3489i			0.684173i	−0.939668	+	0.342087i	$0.888866\pi$
$644$		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	0.932934	−	0.360048i	$-0.117240\pi$
$647$	3.93387	+	6.81366i	0.154656	+	0.267873i	−0.778278	+	0.627920i	$0.783906\pi$
$648$	−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	0.533567	−	0.845758i	$-0.320851\pi$
$653$	1.73516	+	1.00180i	0.0679021	+	0.0392033i	−0.465665	+	0.884961i	$0.654185\pi$
$654$	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	$-0.661817\pi$
$659$		−	44.8494i		−	1.74709i	0.486747	−	0.873543i	$-0.338183\pi$
$660$	−5.45789	+	3.41433i	−0.212448	+	0.132903i
$661$	−10.4404	+	6.02776i	−0.406084	+	0.234453i	−0.689106	−	0.724661i	$-0.741996\pi$
$661$	−10.4404	+	6.02776i	−0.406084	+	0.234453i	0.283022	+	0.959113i	$0.408663\pi$
$662$	−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	−0.995219	−	0.0976651i	$-0.968863\pi$
$677$	−10.7467	+	18.6138i	−0.413029	+	0.715388i	0.582190	+	0.813053i	$0.302196\pi$
$678$	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	−0.184447	−	0.982843i	$-0.559049\pi$
$683$	15.0140	−	8.66837i	0.574497	−	0.331686i	0.758943	+	0.651157i	$0.225716\pi$
$684$	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	0.706158	−	0.708054i	$-0.250427\pi$
$691$	11.7251	+	6.76951i	0.446045	+	0.257524i	−0.260114	+	0.965578i	$0.583760\pi$
$692$	−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	$0.290092\pi$
$701$			41.8503i			1.58066i	−0.612679	+	0.790332i	$0.709908\pi$
$702$	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	−0.0235552	−	0.999723i	$-0.507499\pi$
$709$	22.7397	−	39.3863i	0.854008	−	1.47918i	0.877563	−	0.479462i	$-0.159168\pi$
$710$	−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	−0.868149	−	0.496304i	$-0.834690\pi$
$719$	−0.114311	+	0.197992i	−0.00426307	+	0.00738386i	0.863886	+	0.503687i	$0.168024\pi$
$720$	−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	$0.116054\pi$
$727$			19.2284i			0.713140i	−0.934269	+	0.356570i	$0.883946\pi$
$728$		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	0.626205	−	0.779658i	$-0.284607\pi$
$733$	7.15035	+	4.12825i	0.264104	+	0.152481i	−0.362101	+	0.932139i	$0.617941\pi$
$734$	−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	0.945331	−	0.326114i	$-0.105739\pi$
$739$	5.17166	+	8.95758i	0.190243	+	0.329510i	−0.755088	+	0.655623i	$0.772406\pi$
$740$	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	$0.243537\pi$
$743$			37.7580i			1.38521i	−0.721318	+	0.692604i	$0.756463\pi$
$744$	−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	−0.147968	−	0.988992i	$-0.547273\pi$
$751$	21.4442	−	37.1424i	0.782509	−	1.35534i	0.930476	−	0.366352i	$-0.119394\pi$
$752$	−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	0.288939	+	0.957347i	$0.406697\pi$
$761$	−18.8860	+	32.7115i	−0.684618	+	1.18579i	−0.973557	+	0.228445i	$0.926636\pi$
$762$	−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	$-0.794531\pi$
$769$		−	33.3656i		−	1.20319i	0.798800	−	0.601597i	$-0.205469\pi$
$770$		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	0.855530	−	0.517753i	$-0.173231\pi$
$773$	−0.573356	−	0.993081i	−0.0206222	−	0.0357186i	−0.876152	+	0.482034i	$0.839898\pi$
$774$	−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	0.303530	−	0.952822i	$-0.401835\pi$
$787$	35.9215	−	20.7393i	1.28046	−	0.739276i	0.976933	+	0.213546i	$0.0685014\pi$
$788$	−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	−0.831095	−	0.556131i	$-0.812285\pi$
$809$	−21.7594	+	12.5628i	−0.765018	+	0.441683i	0.0660764	+	0.997815i	$0.478952\pi$
$810$	7.63551	−	5.99056i	0.268284	−	0.210487i
$811$			4.97517i			0.174702i	0.996178	+	0.0873509i	$0.0278401\pi$
$811$			4.97517i			0.174702i	−0.996178	+	0.0873509i	$0.972160\pi$
$812$		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	0.694577	−	0.719419i	$-0.255592\pi$
$821$	12.0008	+	6.92866i	0.418830	+	0.241812i	−0.275746	+	0.961230i	$0.588925\pi$
$822$	−9.23407	+	0.327162i	−0.322075	+	0.0114111i
$823$	−23.0779	−	39.9721i	−0.804446	−	1.39334i	−0.916665	−	0.399658i	$-0.869129\pi$
$823$	−23.0779	−	39.9721i	−0.804446	−	1.39334i	0.112219	−	0.993684i	$-0.464204\pi$
$824$	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	$0.105338\pi$
$827$			18.6880i			0.649844i	−0.945741	+	0.324922i	$0.894662\pi$
$828$	0.763794	+	10.7654i	0.0265437	+	0.374125i
$829$	14.9458	−	8.62894i	0.519088	−	0.299695i	−0.217474	−	0.976066i	$-0.569782\pi$
$829$	14.9458	−	8.62894i	0.519088	−	0.299695i	0.736561	+	0.676371i	$0.236448\pi$
$830$	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	$-0.951520\pi$
$853$		−	8.86218i		−	0.303435i	0.988424	−	0.151718i	$-0.0484804\pi$
$854$		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	0.874303	−	0.485381i	$-0.161319\pi$
$857$	0.491781	+	0.851790i	0.0167989	+	0.0290966i	−0.857504	+	0.514478i	$0.827986\pi$
$858$	0.280598	+	7.91982i	0.00957945	+	0.270378i
$859$	23.6244	+	13.6395i	0.806053	+	0.465375i	0.845583	−	0.533843i	$-0.179253\pi$
$859$	23.6244	+	13.6395i	0.806053	+	0.465375i	−0.0395302	+	0.999218i	$0.512586\pi$
$860$	0.412296			0.0140592
$861$		0			0
$862$	−27.7897			−0.946519
$863$	3.94265	+	2.27629i	0.134209	+	0.0774857i	0.565601	−	0.824679i	$-0.308644\pi$
$863$	3.94265	+	2.27629i	0.134209	+	0.0774857i	−0.431392	+	0.902165i	$0.641977\pi$
$864$	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	−0.988057	−	0.154088i	$-0.950756\pi$
$877$	−10.6784	+	18.4956i	−0.360584	+	0.624551i	0.627473	+	0.778639i	$0.284089\pi$
$878$	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	−0.992852	−	0.119355i	$-0.961917\pi$
$887$	−11.7064	+	20.2760i	−0.393062	+	0.680803i	0.599790	+	0.800157i	$0.295251\pi$
$888$	−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	0.972155	+	0.234338i	$0.0752922\pi$
$907$	20.7508	+	35.9415i	0.689020	+	1.19342i	−0.283135	+	0.959080i	$0.591374\pi$
$908$	−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	$-0.595966\pi$
$911$		−	57.6428i		−	1.90979i	0.296941	−	0.954896i	$-0.404034\pi$
$912$	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	−0.761859	−	0.647743i	$-0.775713\pi$
$919$	5.45769	−	9.45300i	0.180033	−	0.311826i	0.941891	+	0.335918i	$0.109046\pi$
$920$	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	−0.316887	−	0.948463i	$-0.602638\pi$
$929$	20.2064	−	34.9985i	0.662950	−	1.14826i	0.979837	−	0.199799i	$-0.0640289\pi$
$930$	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	$0.0295647\pi$
$937$			5.67805i			0.185494i	−0.995690	+	0.0927468i	$0.970435\pi$
$938$		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	0.744959	−	0.667110i	$-0.232469\pi$
$941$	−6.29634	−	10.9056i	−0.205255	−	0.355512i	−0.950214	+	0.311598i	$0.899136\pi$
$942$	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	−0.0106960	−	0.999943i	$-0.503405\pi$
$947$	−27.1427	−	15.6709i	−0.882020	−	0.509234i	−0.871324	+	0.490708i	$0.836738\pi$
$948$	−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	$-0.749143\pi$
$953$		−	43.7751i		−	1.41802i	0.705200	−	0.709008i	$-0.250857\pi$
$954$	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	−0.120456	−	0.992719i	$-0.538436\pi$
$971$	24.9129	−	43.1503i	0.799492	−	1.38476i	0.919948	−	0.392041i	$-0.128231\pi$
$972$	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	−0.832521	−	0.553994i	$-0.813103\pi$
$977$	−24.0369	+	13.8777i	−0.769008	+	0.443987i	0.0635127	+	0.997981i	$0.479770\pi$
$978$	−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	−0.977604	−	0.210453i	$-0.932506\pi$
$983$	−21.0396	−	36.4417i	−0.671060	−	1.16231i	0.306544	−	0.951856i	$-0.400827\pi$
$984$	−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	0.816990	−	0.576652i	$-0.195641\pi$
$991$	−2.86154	−	4.95633i	−0.0908997	−	0.157443i	−0.907890	+	0.419209i	$0.862308\pi$
$992$	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	−0.644860	−	0.764301i	$-0.723084\pi$
$997$	−9.64266	+	5.56719i	−0.305386	+	0.176315i	0.339474	+	0.940615i	$0.389751\pi$
$998$	−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.656.3		8
3.2	odd	2		735.2.s.k.656.2		8
7.2	even	3		735.2.b.d.146.3		8
7.3	odd	6		735.2.s.k.521.2		8
7.4	even	3		105.2.s.c.101.2	yes	8
7.5	odd	6		735.2.b.c.146.3		8
7.6	odd	2		105.2.s.d.26.3	yes	8
21.2	odd	6		735.2.b.c.146.6		8
21.5	even	6		735.2.b.d.146.6		8
21.11	odd	6		105.2.s.d.101.3	yes	8
21.17	even	6	inner	735.2.s.l.521.3		8
21.20	even	2		105.2.s.c.26.2	✓	8
35.4	even	6		525.2.t.g.101.3		8
35.13	even	4		525.2.q.e.299.6		16
35.18	odd	12		525.2.q.f.374.6		16
35.27	even	4		525.2.q.e.299.3		16
35.32	odd	12		525.2.q.f.374.3		16
35.34	odd	2		525.2.t.f.26.2		8
105.32	even	12		525.2.q.e.374.6		16
105.53	even	12		525.2.q.e.374.3		16
105.62	odd	4		525.2.q.f.299.6		16
105.74	odd	6		525.2.t.f.101.2		8
105.83	odd	4		525.2.q.f.299.3		16
105.104	even	2		525.2.t.g.26.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.2	✓	8	21.20	even	2
105.2.s.c.101.2	yes	8	7.4	even	3
105.2.s.d.26.3	yes	8	7.6	odd	2
105.2.s.d.101.3	yes	8	21.11	odd	6
525.2.q.e.299.3		16	35.27	even	4
525.2.q.e.299.6		16	35.13	even	4
525.2.q.e.374.3		16	105.53	even	12
525.2.q.e.374.6		16	105.32	even	12
525.2.q.f.299.3		16	105.83	odd	4
525.2.q.f.299.6		16	105.62	odd	4
525.2.q.f.374.3		16	35.32	odd	12
525.2.q.f.374.6		16	35.18	odd	12
525.2.t.f.26.2		8	35.34	odd	2
525.2.t.f.101.2		8	105.74	odd	6
525.2.t.g.26.3		8	105.104	even	2
525.2.t.g.101.3		8	35.4	even	6
735.2.b.c.146.3		8	7.5	odd	6
735.2.b.c.146.6		8	21.2	odd	6
735.2.b.d.146.3		8	7.2	even	3
735.2.b.d.146.6		8	21.5	even	6
735.2.s.k.521.2		8	7.3	odd	6
735.2.s.k.656.2		8	3.2	odd	2
735.2.s.l.521.3		8	21.17	even	6	inner
735.2.s.l.656.3		8	1.1	even	1	trivial

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

L-functions

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