LMFDB - Embedded newform 735.2.s.k.656.2

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			656.2
Root			$-1.07834i$ of defining polynomial
Character	$\chi$	$=$	735.656
Dual form			735.2.s.k.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933868 - 0.539169i) q^{2} +(-0.918594 + 1.46840i) q^{3} +(-0.418594 - 0.725026i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.64956 - 0.876010i) q^{6} +3.05945i q^{8} +(-1.31237 - 2.69772i) q^{9} +O(q^{10})$	\(q+(-0.933868 - 0.539169i) q^{2} +(-0.918594 + 1.46840i) q^{3} +(-0.418594 - 0.725026i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.64956 - 0.876010i) q^{6} +3.05945i q^{8} +(-1.31237 - 2.69772i) q^{9} +(0.933868 - 0.539169i) q^{10} +(3.84494 - 2.21988i) q^{11} +(1.44914 + 0.0513428i) q^{12} +0.955682i q^{13} +(-0.812371 - 1.52972i) q^{15} +(0.812371 - 1.40707i) q^{16} +(0.253761 + 0.439527i) q^{17} +(-0.228945 + 3.22690i) q^{18} +(-4.41107 - 2.54673i) q^{19} +0.837188 q^{20} -4.78755 q^{22} +(3.72142 + 2.14856i) q^{23} +(-4.49248 - 2.81039i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.515274 - 0.892481i) q^{26} +(5.16685 + 0.551027i) q^{27} +6.89526i q^{29} +(-0.0661321 + 1.86656i) q^{30} +(-5.10397 + 2.94678i) q^{31} +(3.78182 - 2.18344i) q^{32} +(-0.272280 + 7.68506i) q^{33} -0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-3.76353 + 6.51863i) q^{37} +(2.74624 + 4.75663i) q^{38} +(-1.40332 - 0.877884i) q^{39} +(-2.64956 - 1.52972i) q^{40} +4.65529 q^{41} -0.492478 q^{43} +(-3.21894 - 1.85845i) q^{44} +(2.99248 + 0.212312i) q^{45} +(-2.31688 - 4.01295i) q^{46} +(-3.32967 + 5.76715i) q^{47} +(1.31989 + 2.48541i) q^{48} +1.07834i q^{50} +(-0.878503 - 0.0311252i) q^{51} +(0.692894 - 0.400043i) q^{52} +(-7.90881 + 4.56616i) q^{53} +(-4.52806 - 3.30039i) q^{54} +4.43975i q^{55} +(7.79159 - 4.13778i) q^{57} +(3.71771 - 6.43926i) q^{58} +(5.81439 + 10.0708i) q^{59} +(-0.769035 + 1.22932i) q^{60} +(-0.399509 - 0.230657i) q^{61} +6.35524 q^{62} -7.95845 q^{64} +(-0.827645 - 0.477841i) q^{65} +(4.39782 - 7.03002i) q^{66} +(1.85246 + 3.20856i) q^{67} +(0.212446 - 0.367967i) q^{68} +(-6.57342 + 3.49086i) q^{69} +7.90386i q^{71} +(8.25352 - 4.01513i) q^{72} +(5.46846 - 3.15721i) q^{73} +(7.02929 - 4.05836i) q^{74} +(1.73096 + 0.0613278i) q^{75} +4.26419i q^{76} +(0.837188 + 1.57645i) q^{78} +(-7.38052 + 12.7834i) q^{79} +(0.812371 + 1.40707i) q^{80} +(-5.55536 + 7.08081i) q^{81} +(-4.34743 - 2.50999i) q^{82} -10.7916 q^{83} -0.507522 q^{85} +(0.459909 + 0.265529i) q^{86} +(-10.1250 - 6.33394i) q^{87} +(6.79159 + 11.7634i) q^{88} +(3.57713 - 6.19577i) q^{89} +(-2.68011 - 1.81172i) q^{90} -3.59750i q^{92} +(0.361438 - 10.2015i) q^{93} +(6.21894 - 3.59050i) q^{94} +(4.41107 - 2.54673i) q^{95} +(-0.267811 + 7.55890i) q^{96} +6.91148i q^{97} +(-11.0346 - 7.45926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	$ 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * 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	0.132064	−	0.991241i	$-0.457840\pi$
$2$	−0.933868	−	0.539169i	−0.660344	−	0.381250i	−0.792408	+	0.609991i	$0.791173\pi$
$3$	−0.918594	+	1.46840i	−0.530350	+	0.847779i
$3$	−0.918594	+	1.46840i	−0.530350	+	0.847779i
$4$	−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
$9$	−1.31237	−	2.69772i	−0.437457	−	0.899239i
$10$	0.933868	−	0.539169i	0.295315	−	0.170500i
$11$	3.84494	−	2.21988i	1.15929	−	0.669318i	0.208158	−	0.978095i	$-0.433253\pi$
$11$	3.84494	−	2.21988i	1.15929	−	0.669318i	0.951134	+	0.308777i	$0.0999197\pi$
$12$	1.44914	+	0.0513428i	0.418331	+	0.0148214i
$13$			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	0.895157	−	0.445752i	$-0.147064\pi$
$17$	0.253761	+	0.439527i	0.0615461	+	0.106601i	−0.833611	+	0.552353i	$0.813730\pi$
$18$	−0.228945	+	3.22690i	−0.0539627	+	0.760588i
$19$	−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	0.835000	−	0.550250i	$-0.185467\pi$
$23$	3.72142	+	2.14856i	0.775970	+	0.448007i	−0.0590300	+	0.998256i	$0.518801\pi$
$24$	−4.49248	−	2.81039i	−0.917023	−	0.573668i
$25$	−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	$0.778848\pi$
$30$	−0.0661321	+	1.86656i	−0.0120740	+	0.340787i
$31$	−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
$33$	−0.272280	+	7.68506i	−0.0473979	+	1.33780i
$34$		−	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
$39$	−1.40332	−	0.877884i	−0.224711	−	0.140574i
$40$	−2.64956	−	1.52972i	−0.418932	−	0.241870i
$41$	4.65529			0.727034			0.363517	−	0.931588i	$-0.381576\pi$
$41$	4.65529			0.727034			0.363517	+	0.931588i	$0.381576\pi$
$42$		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
$45$	2.99248	+	0.212312i	0.446092	+	0.0316497i
$46$	−2.31688	−	4.01295i	−0.341605	−	0.591677i
$47$	−3.32967	+	5.76715i	−0.485682	+	0.841225i	−0.999865	−	0.0164553i	$-0.994762\pi$
$47$	−3.32967	+	5.76715i	−0.485682	+	0.841225i	0.514183	+	0.857681i	$0.328095\pi$
$48$	1.31989	+	2.48541i	0.190510	+	0.358737i
$49$		0			0
$50$			1.07834i			0.152500i
$51$	−0.878503	−	0.0311252i	−0.123015	−	0.00435840i
$52$	0.692894	−	0.400043i	0.0960871	−	0.0554759i
$53$	−7.90881	+	4.56616i	−1.08636	+	0.627210i	−0.932605	−	0.360899i	$-0.882470\pi$
$53$	−7.90881	+	4.56616i	−1.08636	+	0.627210i	−0.153754	+	0.988109i	$0.549136\pi$
$54$	−4.52806	−	3.30039i	−0.616191	−	0.449127i
$55$			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	$0.106654\pi$
$59$	5.81439	+	10.0708i	0.756969	+	1.31111i	−0.187420	+	0.982280i	$0.560013\pi$
$60$	−0.769035	+	1.22932i	−0.0992820	+	0.158705i
$61$	−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
$66$	4.39782	−	7.03002i	0.541334	−	0.865336i
$67$	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	$0.155388\pi$
$71$			7.90386i			0.938015i	−0.883194	+	0.469008i	$0.844612\pi$
$72$	8.25352	−	4.01513i	0.972687	−	0.473187i
$73$	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
$75$	1.73096	+	0.0613278i	0.199875	+	0.00708152i
$76$			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
$81$	−5.55536	+	7.08081i	−0.617263	+	0.786757i
$82$	−4.34743	−	2.50999i	−0.480093	−	0.277182i
$83$	−10.7916			−1.18453			−0.592266	−	0.805743i	$-0.701766\pi$
$83$	−10.7916			−1.18453			−0.592266	+	0.805743i	$0.701766\pi$
$84$		0			0
$85$	−0.507522			−0.0550485
$86$	0.459909	+	0.265529i	0.0495933	+	0.0286327i
$87$	−10.1250	−	6.33394i	−1.08551	−	0.679070i
$88$	6.79159	+	11.7634i	0.723986	+	1.25398i
$89$	3.57713	−	6.19577i	0.379175	−	0.656750i	−0.611768	−	0.791038i	$-0.709541\pi$
$89$	3.57713	−	6.19577i	0.379175	−	0.656750i	0.990942	+	0.134287i	$0.0428745\pi$
$90$	−2.68011	−	1.81172i	−0.282508	−	0.190972i
$91$		0			0
$92$		−	3.59750i		−	0.375066i
$93$	0.361438	−	10.2015i	0.0374794	−	1.05785i
$94$	6.21894	−	3.59050i	0.641434	−	0.370332i
$95$	4.41107	−	2.54673i	0.452566	−	0.261289i
$96$	−0.267811	+	7.55890i	−0.0273333	+	0.771477i
$97$			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	0.800405	−	0.599460i	$-0.204618\pi$
$101$	−1.19538	−	2.07046i	−0.118945	−	0.206019i	−0.919350	+	0.393441i	$0.871285\pi$
$102$	0.803624	+	0.502728i	0.0795706	+	0.0497775i
$103$	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	0.945284	−	0.326247i	$-0.105784\pi$
$107$	11.7445	+	6.78072i	1.13539	+	0.655517i	0.190104	+	0.981764i	$0.439118\pi$
$108$	−1.76330	−	3.97676i	−0.169674	−	0.382664i
$109$	−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	$-0.923557\pi$
$113$		−	5.05678i		−	0.475702i	0.971302	−	0.237851i	$-0.0764429\pi$
$114$	−9.50729	−	0.336841i	−0.890439	−	0.0315481i
$115$	−3.72142	+	2.14856i	−0.347024	+	0.200355i
$116$	4.99924	−	2.88631i	0.464168	−	0.267987i
$117$	2.57816	−	1.25421i	0.238351	−	0.115952i
$118$		−	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
$123$	−4.27632	+	6.83581i	−0.385583	+	0.616364i
$124$	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
$129$	0.452387	−	0.723152i	0.0398305	−	0.0636700i
$130$	0.515274	+	0.892481i	0.0451925	+	0.0782758i
$131$	1.04963	−	1.81802i	0.0917069	−	0.158841i	−0.816523	−	0.577314i	$-0.804101\pi$
$131$	1.04963	−	1.81802i	0.0917069	−	0.158841i	0.908229	+	0.418473i	$0.137434\pi$
$132$	5.68584	−	3.01951i	0.494889	−	0.262814i
$133$		0			0
$134$		−	3.99516i		−	0.345129i
$135$	−3.06063	+	4.19911i	−0.263417	+	0.361402i
$136$	−1.34471	+	0.776369i	−0.115308	+	0.0665731i
$137$	−4.28431	+	2.47355i	−0.366033	+	0.211329i	−0.671724	−	0.740801i	$-0.734446\pi$
$137$	−4.28431	+	2.47355i	−0.366033	+	0.211329i	0.305691	+	0.952131i	$0.401113\pi$
$138$	8.02087	+	0.284178i	0.682782	+	0.0241908i
$139$		−	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
$144$	−4.86200	−	0.344953i	−0.405167	−	0.0287461i
$145$	−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	$-0.402505\pi$
$149$	−4.55837	−	2.63178i	−0.373436	−	0.215604i	−0.674959	+	0.737855i	$0.735839\pi$
$150$	−1.58343	−	0.990554i	−0.129286	−	0.0808784i
$151$	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
$156$	−0.0490674	+	1.38492i	−0.00392854	+	0.110882i
$157$	−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
$159$	0.560064	−	15.8077i	0.0444160	−	1.25363i
$160$			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
$165$	−6.51931	−	4.07833i	−0.507528	−	0.317498i
$166$	10.0779	+	5.81849i	0.782199	+	0.451603i
$167$	−15.7766			−1.22083			−0.610413	−	0.792083i	$-0.708997\pi$
$167$	−15.7766			−1.22083			−0.610413	+	0.792083i	$0.708997\pi$
$168$		0			0
$169$	12.0867			0.929744
$170$	0.473959	+	0.273640i	0.0363510	+	0.0209872i
$171$	−1.08141	+	15.2421i	−0.0826972	+	1.16559i
$172$	0.206148	+	0.357059i	0.0157186	+	0.0272255i
$173$	−5.08667	+	8.81037i	−0.386732	+	0.669840i	−0.992008	−	0.126176i	$-0.959730\pi$
$173$	−5.08667	+	8.81037i	−0.386732	+	0.669840i	0.605275	+	0.796016i	$0.293063\pi$
$174$	6.04032	+	11.3741i	0.457916	+	0.862271i
$175$		0			0
$176$		−	7.21345i		−	0.543735i
$177$	−20.1290	−	0.713167i	−1.51299	−	0.0536049i
$178$	−6.68113	+	3.85735i	−0.500772	+	0.289121i
$179$	−4.55716	+	2.63107i	−0.340618	+	0.196656i	−0.660545	−	0.750786i	$-0.729675\pi$
$179$	−4.55716	+	2.63107i	−0.340618	+	0.196656i	0.319927	+	0.947442i	$0.396341\pi$
$180$	−1.09870	−	2.25850i	−0.0818923	−	0.168338i
$181$		−	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
$186$	−5.83788	+	9.33201i	−0.428054	+	0.684256i
$187$	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	$-0.220543\pi$
$191$	8.30561	+	4.79524i	0.600973	+	0.346972i	−0.168451	+	0.985710i	$0.553877\pi$
$192$	7.31058	−	11.6861i	0.527596	−	0.843375i
$193$	−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	$0.0201491\pi$
$197$			1.77574i			0.126516i	−0.997997	+	0.0632580i	$0.979851\pi$
$198$	6.28305	+	12.9155i	0.446517	+	0.917863i
$199$	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
$201$	−6.41309	−	0.227215i	−0.452345	−	0.0160265i
$202$			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
$207$	0.912334	−	12.8591i	0.0634116	−	0.893767i
$208$	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
$213$	−11.6060	−	7.26043i	−0.795229	−	0.497477i
$214$	−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
$219$	−0.387250	+	10.9301i	−0.0261679	+	0.738585i
$220$	3.21894	−	1.85845i	0.217021	−	0.125297i
$221$	−0.420048	+	0.242515i	−0.0282555	+	0.0163133i
$222$	−0.497780	+	14.0498i	−0.0334088	+	0.942958i
$223$		−	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	$0.130526\pi$
$227$	12.1105	+	20.9760i	0.803802	+	1.39223i	−0.113295	+	0.993561i	$0.536141\pi$
$228$	−6.26151	−	3.91706i	−0.414679	−	0.259413i
$229$	−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	0.778376	−	0.627799i	$-0.216044\pi$
$233$	9.52303	+	5.49812i	0.623874	+	0.360194i	−0.154502	+	0.987993i	$0.549377\pi$
$234$	−3.08389	−	0.218798i	−0.201600	−	0.0143033i
$235$	−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	$-0.0942999\pi$
$240$	−2.81237	−	0.0996418i	−0.181538	−	0.00643185i
$241$	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
$243$	−5.29431	−	14.6619i	−0.339630	−	0.940559i
$244$			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
$249$	9.91309	−	15.8463i	0.628217	−	1.00422i
$250$	−0.933868	−	0.539169i	−0.0590630	−	0.0341000i
$251$	18.6748			1.17875			0.589373	−	0.807861i	$-0.299375\pi$
$251$	18.6748			1.17875			0.589373	+	0.807861i	$0.299375\pi$
$252$		0			0
$253$	19.0782			1.19944
$254$	−7.51772	−	4.34036i	−0.471704	−	0.272338i
$255$	0.466207	−	0.745243i	0.0291950	−	0.0466689i
$256$	8.04032	+	13.9262i	0.502520	+	0.870390i
$257$	−6.04132	+	10.4639i	−0.376847	+	0.652718i	−0.990602	−	0.136779i	$-0.956325\pi$
$257$	−6.04132	+	10.4639i	−0.376847	+	0.652718i	0.613755	+	0.789497i	$0.289658\pi$
$258$	−0.812371	+	0.431416i	−0.0505760	+	0.0268588i
$259$		0			0
$260$			0.800085i			0.0496192i
$261$	18.6015	−	9.04914i	1.15140	−	0.560128i
$262$	−1.96044	+	1.13186i	−0.121116	+	0.0699265i
$263$	−11.1611	+	6.44388i	−0.688224	+	0.397346i	−0.802946	−	0.596051i	$-0.796736\pi$
$263$	−11.1611	+	6.44388i	−0.688224	+	0.397346i	0.114722	+	0.993398i	$0.463402\pi$
$264$	−23.5120	−	0.833027i	−1.44706	−	0.0512693i
$265$		−	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	$-0.171193\pi$
$269$	−0.233222	−	0.403952i	−0.0142198	−	0.0246294i	−0.873048	+	0.487635i	$0.837860\pi$
$270$	5.12226	−	2.27122i	0.311731	−	0.138222i
$271$	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
$276$	5.28256	+	3.30464i	0.317973	+	0.198916i
$277$	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	$0.0655446\pi$
$281$			6.85483i			0.408925i	−0.978874	+	0.204462i	$0.934455\pi$
$282$	−0.440395	+	12.4301i	−0.0262252	+	0.740200i
$283$	−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
$285$	−0.312371	+	8.81661i	−0.0185033	+	0.522251i
$286$		−	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
$291$	−10.1488	−	6.34885i	−0.594933	−	0.372176i
$292$	−4.57812	−	2.64318i	−0.267914	−	0.154680i
$293$	30.0822			1.75742			0.878709	−	0.477357i	$-0.158405\pi$
$293$	30.0822			1.75742			0.878709	+	0.477357i	$0.158405\pi$
$294$		0			0
$295$	−11.6288			−0.677054
$296$	−19.9434	−	11.5143i	−1.15919	−	0.669257i
$297$	21.0894	−	9.35111i	1.22373	−	0.542606i
$298$	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
$303$	4.13832	+	0.146620i	0.237741	+	0.00842311i
$304$	−7.16685	+	4.13778i	−0.411047	+	0.237318i
$305$	0.399509	−	0.230657i	0.0228758	−	0.0132074i
$306$	−1.47641	+	0.718235i	−0.0844006	+	0.0410588i
$307$			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	0.999277	−	0.0380092i	$-0.0121016\pi$
$311$	8.23073	+	14.2560i	0.466722	+	0.808386i	−0.532556	+	0.846395i	$0.678768\pi$
$312$	2.68584	−	4.29338i	0.152056	−	0.243065i
$313$	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	−0.434272	−	0.900782i	$-0.642994\pi$
$317$	−25.4873	−	14.7151i	−1.43151	−	0.826481i	−0.997236	+	0.0743007i	$0.976328\pi$
$318$	−9.04605	+	14.4603i	−0.507277	+	0.810896i
$319$	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
$324$	7.45921	+	1.06380i	0.414401	+	0.0590999i
$325$	0.827645	−	0.477841i	0.0459095	−	0.0265059i
$326$	−11.9148	+	6.87904i	−0.659902	+	0.380995i
$327$	27.9053	+	0.988681i	1.54317	+	0.0546742i
$328$			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
$333$	22.5246	+	1.59809i	1.23434	+	0.0875748i
$334$	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
$339$	7.42535	+	4.64513i	0.403290	+	0.252289i
$340$	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
$345$	0.263533	−	7.43818i	0.0141882	−	0.400458i
$346$	9.50056	−	5.48515i	0.510753	−	0.294883i
$347$	−15.7302	+	9.08183i	−0.844441	+	0.487538i	−0.858771	−	0.512359i	$-0.828772\pi$
$347$	−15.7302	+	9.08183i	−0.844441	+	0.487538i	0.0143301	+	0.999897i	$0.495438\pi$
$348$	−0.354022	+	9.99221i	−0.0189776	+	0.535639i
$349$			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	0.695919	−	0.718120i	$-0.254997\pi$
$353$	−5.14707	−	8.91499i	−0.273951	−	0.474497i	−0.969870	+	0.243623i	$0.921664\pi$
$354$	18.4133	+	11.5189i	0.978657	+	0.612225i
$355$	−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	$-0.232537\pi$
$359$	10.2193	+	5.90010i	0.539352	+	0.311395i	−0.205464	+	0.978665i	$0.565870\pi$
$360$	−0.649559	+	9.15533i	−0.0342347	+	0.482528i
$361$	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
$366$	−0.861071	−	0.0305076i	−0.0450089	−	0.00159466i
$367$	−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
$369$	−6.10947	−	12.5587i	−0.318046	−	0.653778i
$370$			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
$375$	−0.918594	+	1.46840i	−0.0474360	+	0.0758276i
$376$	−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
$381$	−7.39477	+	11.8207i	−0.378845	+	0.605594i
$382$	−5.17089	−	8.95625i	−0.264566	−	0.458242i
$383$	9.40053	−	16.2822i	0.480345	−	0.831982i	−0.519401	−	0.854531i	$-0.673845\pi$
$383$	9.40053	−	16.2822i	0.480345	−	0.831982i	0.999746	+	0.0225490i	$0.00717818\pi$
$384$	0.232289	−	0.123359i	0.0118539	−	0.00629512i
$385$		0			0
$386$			9.00591i			0.458389i
$387$	0.646314	+	1.32857i	0.0328540	+	0.0675348i
$388$	5.01100	−	2.89310i	0.254395	−	0.146875i
$389$	−10.5804	+	6.10860i	−0.536448	+	0.309718i	−0.743638	−	0.668582i	$-0.766901\pi$
$389$	−10.5804	+	6.10860i	−0.536448	+	0.309718i	0.207190	+	0.978301i	$0.433568\pi$
$390$	−1.78384	−	0.0632012i	−0.0903284	−	0.00320032i
$391$			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
$396$	−0.789145	+	11.1228i	−0.0396560	+	0.558940i
$397$	−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	0.919214	−	0.393757i	$-0.128825\pi$
$401$	20.7823	+	11.9987i	1.03782	+	0.599184i	0.118603	+	0.992942i	$0.462158\pi$
$402$	5.86647	+	3.66993i	0.292593	+	0.183039i
$403$	−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
$408$	0.0952259	−	2.68773i	0.00471438	−	0.133063i
$409$	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
$411$	0.303394	−	8.56325i	0.0149653	−	0.422394i
$412$		−	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
$417$	15.7438	+	9.84892i	0.770975	+	0.482304i
$418$	21.1182	+	12.1926i	1.03293	+	0.596361i
$419$	39.6524			1.93714			0.968572	−	0.248732i	$-0.0800137\pi$
$419$	39.6524			1.93714			0.968572	+	0.248732i	$0.0800137\pi$
$420$		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
$423$	19.9279	+	1.41386i	0.968928	+	0.0687442i
$424$	−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
$429$	−7.34447	−	0.260213i	−0.354594	−	0.0125632i
$430$	−0.459909	+	0.265529i	−0.0221788	+	0.0128049i
$431$	22.3182	−	12.8854i	1.07503	−	0.620668i	0.145478	−	0.989361i	$-0.453528\pi$
$431$	22.3182	−	12.8854i	1.07503	−	0.620668i	0.929551	+	0.368693i	$0.120195\pi$
$432$	4.97273	−	6.82247i	0.239251	−	0.328246i
$433$		−	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
$438$	6.25479	−	9.99844i	0.298865	−	0.477744i
$439$	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	0.548480	−	0.836163i	$-0.315207\pi$
$443$	2.07491	+	1.19795i	0.0985819	+	0.0569163i	−0.449899	+	0.893080i	$0.648540\pi$
$444$	−5.78858	+	9.25319i	−0.274714	+	0.439137i
$445$	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	$-0.205224\pi$
$450$	2.90905	−	1.41518i	0.137134	−	0.0667122i
$451$	17.8993	−	10.3342i	0.842846	−	0.486617i
$452$	−3.66629	+	2.11674i	−0.172448	+	0.0995629i
$453$	−12.1324	−	0.429847i	−0.570028	−	0.0201960i
$454$		−	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
$459$	1.06895	+	2.41080i	0.0498945	+	0.112527i
$460$	3.11553	+	1.79875i	0.145262	+	0.0838672i
$461$	13.5376			0.630509			0.315254	−	0.949007i	$-0.397910\pi$
$461$	13.5376			0.630509			0.315254	+	0.949007i	$0.397910\pi$
$462$		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
$465$	8.65407	+	5.41378i	0.401323	+	0.251058i
$466$	−5.92883	−	10.2690i	−0.274648	−	0.475704i
$467$	−4.60894	+	7.98292i	−0.213276	+	0.369405i	−0.952738	−	0.303793i	$-0.901747\pi$
$467$	−4.60894	+	7.98292i	−0.213276	+	0.369405i	0.739462	+	0.673199i	$0.235080\pi$
$468$	−1.98854	−	1.34423i	−0.0919201	−	0.0621370i
$469$		0			0
$470$			7.18101i			0.331235i
$471$	0.177857	−	5.01998i	0.00819521	−	0.231308i
$472$	−30.8111	+	17.7888i	−1.41820	+	0.818797i
$473$	−1.89355	+	1.09324i	−0.0870654	+	0.0502672i
$474$	−0.976178	+	27.5524i	−0.0448374	+	1.26553i
$475$			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	$-0.322944\pi$
$479$	−10.3187	−	17.8724i	−0.471472	−	0.816613i	−0.999467	+	0.0326342i	$0.989610\pi$
$480$	−6.41230	−	4.01138i	−0.292680	−	0.183094i
$481$	−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
$486$	−2.96103	+	16.5468i	−0.134315	+	0.750577i
$487$	−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	$-0.840550\pi$
$491$		−	21.2827i		−	0.960476i	0.877138	−	0.480238i	$-0.159450\pi$
$492$	6.74618	+	0.239016i	0.304141	+	0.0107757i
$493$	−3.03065	+	1.74975i	−0.136494	+	0.0788047i
$494$	−4.54582	+	2.62453i	−0.204526	+	0.118083i
$495$	11.9772	−	5.82660i	0.538335	−	0.261886i
$496$			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
$501$	14.4922	−	23.1662i	0.647466	−	1.03499i
$502$	−17.4398	−	10.0689i	−0.778378	−	0.449397i
$503$	−0.675693			−0.0301277			−0.0150638	−	0.999887i	$-0.504795\pi$
$503$	−0.675693			−0.0301277			−0.0150638	+	0.999887i	$0.504795\pi$
$504$		0			0
$505$	2.39076			0.106388
$506$	−17.8165	−	10.2864i	−0.792041	−	0.457285i
$507$	−11.1027	+	17.7480i	−0.493090	+	0.788217i
$508$	−3.36972	−	5.83652i	−0.149507	−	0.258954i
$509$	−16.5519	+	28.6687i	−0.733649	+	1.27072i	0.221664	+	0.975123i	$0.428851\pi$
$509$	−16.5519	+	28.6687i	−0.733649	+	1.27072i	−0.955313	+	0.295595i	$0.904482\pi$
$510$	−0.837188	+	0.444595i	−0.0370713	+	0.0196870i
$511$		0			0
$512$		−	17.0367i		−	0.752921i
$513$	−21.3880	−	15.5892i	−0.944305	−	0.688281i
$514$	11.2836	−	6.51458i	0.497697	−	0.287346i
$515$	−12.9577	+	7.48110i	−0.570982	+	0.329657i
$516$	−0.713670	−	0.0252852i	−0.0314176	−	0.00111312i
$517$			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	$-0.776812\pi$
$521$	−21.4725	−	37.1914i	−0.940726	−	1.62938i	−0.176634	−	0.984277i	$-0.556521\pi$
$522$	−22.2503	−	1.57863i	−0.973871	−	0.0690949i
$523$	−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
$528$	10.5922	+	6.62623i	0.460966	+	0.288370i
$529$	−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
$534$	0.473126	−	13.3539i	0.0204742	−	0.577879i
$535$	−11.7445	+	6.78072i	−0.507761	+	0.293156i
$536$	−9.81641	+	5.66751i	−0.424004	+	0.244799i
$537$	0.322716	−	9.10860i	0.0139262	−	0.393065i
$538$			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
$543$	14.2627	+	8.92243i	0.612073	+	0.382898i
$544$	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
$549$	−0.0979425	+	1.38047i	−0.00418008	+	0.0589170i
$550$	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
$555$	13.0291	+	0.461618i	0.553054	+	0.0195946i
$556$	−7.77354	+	4.48805i	−0.329671	+	0.190336i
$557$	5.21291	−	3.00967i	0.220878	−	0.127524i	−0.385479	−	0.922717i	$-0.625964\pi$
$557$	5.21291	−	3.00967i	0.220878	−	0.127524i	0.606357	+	0.795193i	$0.292630\pi$
$558$	−8.34043	−	17.1446i	−0.353079	−	0.725791i
$559$		−	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	$-0.268113\pi$
$563$	−7.43466	−	12.8772i	−0.313334	−	0.542710i	−0.979082	+	0.203467i	$0.934779\pi$
$564$	−5.12126	+	8.18646i	−0.215644	+	0.344712i
$565$	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	$-0.298139\pi$
$569$	4.55880	+	2.63203i	0.191115	+	0.110340i	−0.401389	+	0.915907i	$0.631473\pi$
$570$	5.04536	−	8.06513i	0.211327	−	0.337811i
$571$	−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
$576$	10.4444	+	21.4696i	0.435185	+	0.894569i
$577$	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
$579$	14.4564	+	0.512189i	0.600789	+	0.0212858i
$580$			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
$585$	−0.202903	+	2.85986i	−0.00838902	+	0.118241i
$586$	−28.0928	−	16.2194i	−1.16050	−	0.670016i
$587$	−18.5075			−0.763887			−0.381944	−	0.924186i	$-0.624745\pi$
$587$	−18.5075			−0.763887			−0.381944	+	0.924186i	$0.624745\pi$
$588$		0			0
$589$	30.0186			1.23690
$590$	10.8597	+	6.26988i	0.447089	+	0.258127i
$591$	−2.60748	−	1.63118i	−0.107258	−	0.0670978i
$592$	6.11477	+	10.5911i	0.251316	+	0.435291i
$593$	−9.26927	+	16.0548i	−0.380643	+	0.659293i	−0.991154	−	0.132714i	$-0.957631\pi$
$593$	−9.26927	+	16.0548i	−0.380643	+	0.659293i	0.610511	+	0.792008i	$0.290964\pi$
$594$	−24.7366	−	2.63807i	−1.01495	−	0.108241i
$595$		0			0
$596$			4.40658i			0.180501i
$597$	−0.230505	+	6.50596i	−0.00943395	+	0.266271i
$598$	3.83511	−	2.21420i	0.156829	−	0.0905453i
$599$	−0.501417	+	0.289493i	−0.0204873	+	0.0118284i	−0.510209	−	0.860051i	$-0.670432\pi$
$599$	−0.501417	+	0.289493i	−0.0204873	+	0.0118284i	0.489721	+	0.871879i	$0.337099\pi$
$600$	−0.187629	+	5.29579i	−0.00765992	+	0.216200i
$601$		−	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
$606$	−3.78560	−	2.36818i	−0.153779	−	0.0962007i
$607$	−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
$612$	−1.27148	−	0.0902097i	−0.0513964	−	0.00364651i
$613$	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	$-0.957831\pi$
$617$		−	6.56208i		−	0.264179i	0.991238	−	0.132090i	$-0.0421687\pi$
$618$	27.9279	+	0.989482i	1.12343	+	0.0398028i
$619$	−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
$621$	18.0441	+	13.1519i	0.724086	+	0.527768i
$622$		−	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
$627$	20.7728	−	33.2059i	0.829587	−	1.32612i
$628$	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
$633$	8.37873	−	13.3936i	0.333025	−	0.532349i
$634$	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
$639$	21.3224	−	10.3728i	0.843500	−	0.410341i
$640$	0.131506	−	0.0759250i	0.00519823	−	0.00300120i
$641$	9.98943	−	5.76740i	0.394559	−	0.227798i	−0.289575	−	0.957155i	$-0.593514\pi$
$641$	9.98943	−	5.76740i	0.394559	−	0.227798i	0.684133	+	0.729357i	$0.260181\pi$
$642$	25.3133	+	0.896846i	0.999036	+	0.0353957i
$643$			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	0.778278	−	0.627920i	$-0.216094\pi$
$647$	−3.93387	−	6.81366i	−0.154656	−	0.267873i	−0.932934	+	0.360048i	$0.882760\pi$
$648$	−21.6634	−	16.9963i	−0.851018	−	0.667679i
$649$	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	$-0.345815\pi$
$653$	−1.73516	−	1.00180i	−0.0679021	−	0.0392033i	−0.533567	+	0.845758i	$0.679149\pi$
$654$	−25.5268	−	15.9690i	−0.998178	−	0.624437i
$655$	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	$0.661817\pi$
$660$	−0.227950	+	6.43383i	−0.00887293	+	0.250437i
$661$	−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
$663$	0.0297458	−	0.839570i	0.00115523	−	0.0326062i
$664$		−	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
$669$	17.2385	+	10.7840i	0.666478	+	0.416933i
$670$	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
$675$	−2.10622	−	4.75014i	−0.0810686	−	0.182833i
$676$	−5.05941	−	8.76315i	−0.194593	−	0.337044i
$677$	10.7467	−	18.6138i	0.413029	−	0.715388i	−0.582190	−	0.813053i	$-0.697804\pi$
$677$	10.7467	−	18.6138i	0.413029	−	0.715388i	0.995219	+	0.0976651i	$0.0311374\pi$
$678$	−4.42979	−	8.34145i	−0.170125	−	0.320352i
$679$		0			0
$680$		−	1.55274i		−	0.0595447i
$681$	−41.9257	−	1.48542i	−1.60660	−	0.0569214i
$682$	24.4355	−	14.1079i	0.935684	−	0.540218i
$683$	−15.0140	+	8.66837i	−0.574497	+	0.331686i	−0.758943	−	0.651157i	$-0.774284\pi$
$683$	−15.0140	+	8.66837i	−0.574497	+	0.331686i	0.184447	+	0.982843i	$0.440951\pi$
$684$	11.5036	−	5.59620i	0.439850	−	0.213976i
$685$		−	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
$690$	−4.25654	+	6.80419i	−0.162044	+	0.259031i
$691$	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
$696$	19.3784	−	30.9768i	0.734535	−	1.17417i
$697$	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	$-0.290092\pi$
$702$	3.15413	−	4.32739i	0.119045	−	0.163327i
$703$	33.2024	−	19.1694i	1.25225	−	0.722989i
$704$	−30.5998	+	17.6668i	−1.15327	+	0.665842i
$705$	11.5271	+	0.408402i	0.434134	+	0.0153813i
$706$			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
$711$	44.1721	+	3.13395i	1.65658	+	0.117532i
$712$	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
$717$	13.2545	+	8.29168i	0.494997	+	0.309658i
$718$	−6.36230	−	11.0198i	−0.237439	−	0.411256i
$719$	0.114311	−	0.197992i	0.00426307	−	0.00738386i	−0.863886	−	0.503687i	$-0.831976\pi$
$719$	0.114311	−	0.197992i	0.00426307	−	0.00738386i	0.868149	+	0.496304i	$0.165310\pi$
$720$	2.72974	−	4.03814i	0.101731	−	0.150493i
$721$		0			0
$722$		−	7.48733i		−	0.278650i
$723$	−0.311606	+	8.79502i	−0.0115887	+	0.327090i
$724$	−7.04228	+	4.06586i	−0.261724	+	0.151107i
$725$	5.97147	−	3.44763i	0.221775	−	0.128042i
$726$	0.576104	−	16.2604i	0.0213812	−	0.603481i
$727$			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
$732$	−0.567103	−	0.354766i	−0.0209607	−	0.0131125i
$733$	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
$738$	−1.06580	+	15.0222i	−0.0392328	+	0.552974i
$739$	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	$-0.756463\pi$
$743$		−	37.7580i		−	1.38521i	0.721318	−	0.692604i	$-0.243537\pi$
$744$	31.2110	+	1.10580i	1.14425	+	0.0405407i
$745$	4.55837	−	2.63178i	0.167006	−	0.0964209i
$746$	4.96508	−	2.86659i	0.181785	−	0.104953i
$747$	14.1626	+	29.1127i	0.518182	+	1.06518i
$748$		−	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
$753$	−17.1546	+	27.4220i	−0.625148	+	0.999315i
$754$	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
$759$	−17.5251	+	28.0143i	−0.636121	+	1.01686i
$760$	7.79159	+	13.4954i	0.282631	+	0.489531i
$761$	18.8860	−	32.7115i	0.684618	−	1.18579i	−0.288939	−	0.957347i	$-0.593303\pi$
$761$	18.8860	−	32.7115i	0.684618	−	1.18579i	0.973557	−	0.228445i	$-0.0733641\pi$
$762$	13.2791	−	7.05196i	0.481051	−	0.255466i
$763$		0			0
$764$		−	8.02904i		−	0.290480i
$765$	0.666057	+	1.36915i	0.0240814	+	0.0495018i
$766$	−17.5577	+	10.1370i	−0.634386	+	0.366263i
$767$	−9.62451	+	5.55671i	−0.347521	+	0.200641i
$768$	−27.8350	−	0.986190i	−1.00441	−	0.0355861i
$769$		−	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	0.876152	−	0.482034i	$-0.160102\pi$
$773$	0.573356	+	0.993081i	0.0206222	+	0.0357186i	−0.855530	+	0.517753i	$0.826769\pi$
$774$	0.112750	−	1.58918i	0.00405272	−	0.0571218i
$775$	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
$780$	−1.17484	−	0.734953i	−0.0420661	−	0.0263156i
$781$	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
$786$	0.138829	−	3.91842i	0.00495186	−	0.139765i
$787$	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
$789$	0.790377	−	22.3082i	0.0281382	−	0.794195i
$790$			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
$795$	13.4098	+	8.38889i	0.475598	+	0.297523i
$796$	−2.72506	−	1.57332i	−0.0965874	−	0.0557647i
$797$	49.5086			1.75369			0.876843	−	0.480777i	$-0.159645\pi$
$797$	49.5086			1.75369			0.876843	+	0.480777i	$0.159645\pi$
$798$		0			0
$799$	−3.37976			−0.119567
$800$	−3.78182	−	2.18344i	−0.133708	−	0.0771961i
$801$	−21.4090	−	1.51894i	−0.756448	−	0.0536690i
$802$	−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
$807$	0.807397	+	0.0286059i	0.0284217	+	0.00100698i
$808$	6.33446	−	3.65720i	0.222846	−	0.128660i
$809$	21.7594	−	12.5628i	0.765018	−	0.441683i	−0.0660764	−	0.997815i	$-0.521048\pi$
$809$	21.7594	−	12.5628i	0.765018	−	0.441683i	0.831095	+	0.556131i	$0.187715\pi$
$810$	−1.37022	+	9.60782i	−0.0481447	+	0.337585i
$811$			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
$816$	−0.757466	+	1.21083i	−0.0265166	+	0.0423875i
$817$	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	$-0.411075\pi$
$821$	−12.0008	−	6.92866i	−0.418830	−	0.241812i	−0.694577	+	0.719419i	$0.744408\pi$
$822$	−4.90037	+	7.83336i	−0.170920	+	0.273220i
$823$	−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	$-0.894662\pi$
$827$		−	18.6880i		−	0.649844i	0.945741	−	0.324922i	$-0.105338\pi$
$828$	−9.70505	+	4.72126i	−0.337274	+	0.164075i
$829$	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
$831$	−24.0446	−	0.851896i	−0.834098	−	0.0295519i
$832$		−	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
$837$	−27.9952	+	12.4131i	−0.967655	+	0.429061i
$838$	−37.0301	−	21.3793i	−1.27918	−	0.738536i
$839$	−49.1689			−1.69750			−0.848750	−	0.528795i	$-0.822644\pi$
$839$	−49.1689			−1.69750			−0.848750	+	0.528795i	$0.822644\pi$
$840$		0			0
$841$	−18.5446			−0.639470
$842$	31.8844	+	18.4085i	1.09881	+	0.634398i
$843$	−10.0656	−	6.29680i	−0.346678	−	0.216873i
$844$	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
$849$	0.272081	−	7.67943i	0.00933779	−	0.263557i
$850$	−0.473959	+	0.273640i	−0.0162566	+	0.00938578i
$851$	−28.0114	+	16.1724i	−0.960218	+	0.554382i
$852$	−0.405806	+	11.4538i	−0.0139027	+	0.392401i
$853$		−	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	0.857504	−	0.514478i	$-0.172014\pi$
$857$	−0.491781	−	0.851790i	−0.0167989	−	0.0290966i	−0.874303	+	0.485381i	$0.838681\pi$
$858$	6.71847	+	4.20292i	0.229365	+	0.143485i
$859$	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	0.431392	−	0.902165i	$-0.358023\pi$
$863$	−3.94265	−	2.27629i	−0.134209	−	0.0774857i	−0.565601	+	0.824679i	$0.691356\pi$
$864$	20.7433	−	9.19761i	0.705700	−	0.312909i
$865$	−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
$870$	−12.8705	−	0.455998i	−0.436349	−	0.0154598i
$871$	−3.06636	+	1.77036i	−0.103900	+	0.0599865i
$872$	42.7142	−	24.6611i	1.44649	−	0.835129i
$873$	18.6452	−	9.07043i	0.631046	−	0.306988i
$874$			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
$879$	−27.6333	+	44.1725i	−0.932047	+	1.48990i
$880$	6.24703	+	3.60673i	0.210587	+	0.121583i
$881$	−33.2551			−1.12039			−0.560196	−	0.828360i	$-0.689274\pi$
$881$	−33.2551			−1.12039			−0.560196	+	0.828360i	$0.689274\pi$
$882$		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
$885$	10.6821	−	17.0757i	0.359076	−	0.573992i
$886$	−1.29179	−	2.23745i	−0.0433987	−	0.0751687i
$887$	11.7064	−	20.2760i	0.393062	−	0.680803i	−0.599790	−	0.800157i	$-0.704749\pi$
$887$	11.7064	−	20.2760i	0.393062	−	0.680803i	0.992852	+	0.119355i	$0.0380825\pi$
$888$	35.2275	−	18.7078i	1.18216	−	0.627793i
$889$		0			0
$890$		−	7.71471i		−	0.258598i
$891$	−5.64151	+	39.5575i	−0.188998	+	1.32523i
$892$	−8.51156	+	4.91415i	−0.284988	+	0.164538i
$893$	29.3748	−	16.9595i	0.982990	−	0.567529i
$894$	−9.82477	−	0.348090i	−0.328589	−	0.0116419i
$895$		−	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
$900$	2.50527	+	0.177745i	0.0835088	+	0.00592484i
$901$	−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
$906$	11.0983	+	6.94281i	0.368715	+	0.230659i
$907$	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	$0.404034\pi$
$911$			57.6428i			1.90979i	−0.296941	+	0.954896i	$0.595966\pi$
$912$	0.507522	−	14.3247i	0.0168057	−	0.474339i
$913$	−41.4930	+	23.9560i	−1.37322	+	0.792828i
$914$	−3.21429	+	1.85577i	−0.106319	+	0.0613835i
$915$	−0.0282913	+	0.798517i	−0.000935282	+	0.0263982i
$916$			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
$921$	−48.2074	−	30.1574i	−1.58849	−	0.993721i
$922$	−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
$927$	3.17666	−	44.7741i	0.104335	−	1.47057i
$928$	15.0554	+	26.0767i	0.494217	+	0.856008i
$929$	−20.2064	+	34.9985i	−0.662950	+	1.14826i	0.316887	+	0.948463i	$0.397362\pi$
$929$	−20.2064	+	34.9985i	−0.662950	+	1.14826i	−0.979837	+	0.199799i	$0.935971\pi$
$930$	−5.16281	−	9.72176i	−0.169295	−	0.318789i
$931$		0			0
$932$		−	9.20592i		−	0.301550i
$933$	−28.4942	−	1.00954i	−0.932858	−	0.0330510i
$934$	8.60828	−	4.96999i	0.281672	−	0.162623i
$935$	−1.95139	+	1.12664i	−0.0638173	+	0.0368450i
$936$	3.83719	+	7.88775i	0.125422	+	0.257819i
$937$			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	0.950214	−	0.311598i	$-0.100864\pi$
$941$	6.29634	+	10.9056i	0.205255	+	0.355512i	−0.744959	+	0.667110i	$0.767531\pi$
$942$	−2.87271	+	4.59210i	−0.0935979	+	0.149619i
$943$	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	$-0.163262\pi$
$947$	27.1427	+	15.6709i	0.882020	+	0.509234i	0.0106960	+	0.999943i	$0.496595\pi$
$948$	−11.3518	+	18.1461i	−0.368688	+	0.589357i
$949$	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	$0.749143\pi$
$954$	−12.9239	−	26.5664i	−0.418425	−	0.860118i
$955$	−8.30561	+	4.79524i	−0.268763	+	0.155170i
$956$	−6.54444	+	3.77843i	−0.211662	+	0.122203i
$957$	−52.9905	−	1.87744i	−1.71294	−	0.0606891i
$958$			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
$963$	2.87926	−	40.5823i	0.0927829	−	1.30775i
$964$	−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
$969$	3.79587	+	2.37461i	0.121941	+	0.0762834i
$970$	3.72646	+	6.45441i	0.119649	+	0.207239i
$971$	−24.9129	+	43.1503i	−0.799492	+	1.38476i	0.120456	+	0.992719i	$0.461564\pi$
$971$	−24.9129	+	43.1503i	−0.799492	+	1.38476i	−0.919948	+	0.392041i	$0.871769\pi$
$972$	−8.41406	+	9.97588i	−0.269881	+	0.319976i
$973$		0			0
$974$			2.66887i			0.0855161i
$975$	−0.0586099	+	1.65425i	−0.00187702	+	0.0529785i
$976$	−0.649099	+	0.374757i	−0.0207772	+	0.0119957i
$977$	24.0369	−	13.8777i	0.769008	−	0.443987i	−0.0635127	−	0.997981i	$-0.520230\pi$
$977$	24.0369	−	13.8777i	0.769008	−	0.443987i	0.832521	+	0.553994i	$0.186897\pi$
$978$	0.843752	−	23.8147i	0.0269802	−	0.761512i
$979$		−	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	$0.0674940\pi$
$983$	21.0396	+	36.4417i	0.671060	+	1.16231i	−0.306544	+	0.951856i	$0.599173\pi$
$984$	−20.9138	−	13.0832i	−0.666707	−	0.417076i
$985$	−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
$990$	−14.3267	−	1.01646i	−0.455331	−	0.0323051i
$991$	−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
$996$	−15.6386	−	0.554071i	−0.495527	−	0.0175564i
$997$	−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
$999$	−23.0376	+	31.6070i	−0.728876	+	1.00000i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.933868 - 0.539169i) q^{2} +(-0.918594 + 1.46840i) q^{3} +(-0.418594 - 0.725026i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.64956 - 0.876010i) q^{6} +3.05945i q^{8} +(-1.31237 - 2.69772i) q^{9} +O(q^{10})\)	\(q+(-0.933868 - 0.539169i) q^{2} +(-0.918594 + 1.46840i) q^{3} +(-0.418594 - 0.725026i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.64956 - 0.876010i) q^{6} +3.05945i q^{8} +(-1.31237 - 2.69772i) q^{9} +(0.933868 - 0.539169i) q^{10} +(3.84494 - 2.21988i) q^{11} +(1.44914 + 0.0513428i) q^{12} +0.955682i q^{13} +(-0.812371 - 1.52972i) q^{15} +(0.812371 - 1.40707i) q^{16} +(0.253761 + 0.439527i) q^{17} +(-0.228945 + 3.22690i) q^{18} +(-4.41107 - 2.54673i) q^{19} +0.837188 q^{20} -4.78755 q^{22} +(3.72142 + 2.14856i) q^{23} +(-4.49248 - 2.81039i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.515274 - 0.892481i) q^{26} +(5.16685 + 0.551027i) q^{27} +6.89526i q^{29} +(-0.0661321 + 1.86656i) q^{30} +(-5.10397 + 2.94678i) q^{31} +(3.78182 - 2.18344i) q^{32} +(-0.272280 + 7.68506i) q^{33} -0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(-3.76353 + 6.51863i) q^{37} +(2.74624 + 4.75663i) q^{38} +(-1.40332 - 0.877884i) q^{39} +(-2.64956 - 1.52972i) q^{40} +4.65529 q^{41} -0.492478 q^{43} +(-3.21894 - 1.85845i) q^{44} +(2.99248 + 0.212312i) q^{45} +(-2.31688 - 4.01295i) q^{46} +(-3.32967 + 5.76715i) q^{47} +(1.31989 + 2.48541i) q^{48} +1.07834i q^{50} +(-0.878503 - 0.0311252i) q^{51} +(0.692894 - 0.400043i) q^{52} +(-7.90881 + 4.56616i) q^{53} +(-4.52806 - 3.30039i) q^{54} +4.43975i q^{55} +(7.79159 - 4.13778i) q^{57} +(3.71771 - 6.43926i) q^{58} +(5.81439 + 10.0708i) q^{59} +(-0.769035 + 1.22932i) q^{60} +(-0.399509 - 0.230657i) q^{61} +6.35524 q^{62} -7.95845 q^{64} +(-0.827645 - 0.477841i) q^{65} +(4.39782 - 7.03002i) q^{66} +(1.85246 + 3.20856i) q^{67} +(0.212446 - 0.367967i) q^{68} +(-6.57342 + 3.49086i) q^{69} +7.90386i q^{71} +(8.25352 - 4.01513i) q^{72} +(5.46846 - 3.15721i) q^{73} +(7.02929 - 4.05836i) q^{74} +(1.73096 + 0.0613278i) q^{75} +4.26419i q^{76} +(0.837188 + 1.57645i) q^{78} +(-7.38052 + 12.7834i) q^{79} +(0.812371 + 1.40707i) q^{80} +(-5.55536 + 7.08081i) q^{81} +(-4.34743 - 2.50999i) q^{82} -10.7916 q^{83} -0.507522 q^{85} +(0.459909 + 0.265529i) q^{86} +(-10.1250 - 6.33394i) q^{87} +(6.79159 + 11.7634i) q^{88} +(3.57713 - 6.19577i) q^{89} +(-2.68011 - 1.81172i) q^{90} -3.59750i q^{92} +(0.361438 - 10.2015i) q^{93} +(6.21894 - 3.59050i) q^{94} +(4.41107 - 2.54673i) q^{95} +(-0.267811 + 7.55890i) q^{96} +6.91148i q^{97} +(-11.0346 - 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9	\( 8 q - 3 q^{2} - q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} - 5 q^{9} + 3 q^{10} + 9 q^{12} - q^{15} + q^{16} + 12 q^{17} - 19 q^{18} - 9 q^{19} - 6 q^{20} - 40 q^{22} + 27 q^{23} - 16 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} - 5 q^{30} + 21 q^{31} + 21 q^{32} - 2 q^{33} + 9 q^{36} + 7 q^{37} + 12 q^{38} - 3 q^{39} - 3 q^{40} + 30 q^{41} + 16 q^{43} + 4 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 6 q^{51} - 30 q^{52} + 24 q^{53} - 17 q^{54} + 6 q^{57} - 13 q^{58} + 12 q^{59} - 18 q^{60} - 15 q^{61} - 24 q^{62} + 38 q^{64} - 3 q^{65} - 22 q^{66} + 4 q^{67} + 13 q^{69} - 14 q^{72} - 15 q^{73} + 54 q^{74} + 2 q^{75} - 6 q^{78} - 29 q^{79} + q^{80} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 24 q^{85} + 9 q^{86} - 32 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 9 q^{93} + 24 q^{94} + 9 q^{95} + 3 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - q^3 + 3 * q^4 - 4 * q^5 - 5 * q^6 - 5 * q^9 + 3 * q^10 + 9 * q^12 - q^15 + q^16 + 12 * q^17 - 19 * q^18 - 9 * q^19 - 6 * q^20 - 40 * q^22 + 27 * q^23 - 16 * q^24 - 4 * q^25 + 6 * q^26 - 4 * q^27 - 5 * q^30 + 21 * q^31 + 21 * q^32 - 2 * q^33 + 9 * q^36 + 7 * q^37 + 12 * q^38 - 3 * q^39 - 3 * q^40 + 30 * q^41 + 16 * q^43 + 4 * q^45 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 6 * q^51 - 30 * q^52 + 24 * q^53 - 17 * q^54 + 6 * q^57 - 13 * q^58 + 12 * q^59 - 18 * q^60 - 15 * q^61 - 24 * q^62 + 38 * q^64 - 3 * q^65 - 22 * q^66 + 4 * q^67 + 13 * q^69 - 14 * q^72 - 15 * q^73 + 54 * q^74 + 2 * q^75 - 6 * q^78 - 29 * q^79 + q^80 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 24 * q^85 + 9 * q^86 - 32 * q^87 - 2 * q^88 + 3 * q^89 - 7 * q^90 - 9 * q^93 + 24 * q^94 + 9 * q^95 + 3 * q^96 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more