LMFDB - Embedded newform 600.2.d.e.349.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(349,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.349"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$600 = 2^{3} \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	600.d (of order $2$ , degree $1$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8$ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{3}$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.6
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	600.349
Dual form			600.2.d.e.349.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38923 + 0.264658i) q^{2} -1.00000 q^{3} +(1.85991 + 0.735342i) q^{4} +(-1.38923 - 0.264658i) q^{6} +0.941367i q^{7} +(2.38923 + 1.51380i) q^{8} +1.00000 q^{9} -4.49828i q^{11} +(-1.85991 - 0.735342i) q^{12} +5.55691 q^{13} +(-0.249141 + 1.30777i) q^{14} +(2.91855 + 2.73534i) q^{16} +7.55691i q^{17} +(1.38923 + 0.264658i) q^{18} +1.05863i q^{19} -0.941367i q^{21} +(1.19051 - 6.24914i) q^{22} +1.05863i q^{23} +(-2.38923 - 1.51380i) q^{24} +(7.71982 + 1.47068i) q^{26} -1.00000 q^{27} +(-0.692226 + 1.75086i) q^{28} -2.00000i q^{29} +3.55691 q^{31} +(3.33060 + 4.57243i) q^{32} +4.49828i q^{33} +(-2.00000 + 10.4983i) q^{34} +(1.85991 + 0.735342i) q^{36} -7.43965 q^{37} +(-0.280176 + 1.47068i) q^{38} -5.55691 q^{39} -3.88273 q^{41} +(0.249141 - 1.30777i) q^{42} +1.88273 q^{43} +(3.30777 - 8.36641i) q^{44} +(-0.280176 + 1.47068i) q^{46} -10.0552i q^{47} +(-2.91855 - 2.73534i) q^{48} +6.11383 q^{49} -7.55691i q^{51} +(10.3354 + 4.08623i) q^{52} -2.00000 q^{53} +(-1.38923 - 0.264658i) q^{54} +(-1.42504 + 2.24914i) q^{56} -1.05863i q^{57} +(0.529317 - 2.77846i) q^{58} -8.49828i q^{59} -8.99656i q^{61} +(4.94137 + 0.941367i) q^{62} +0.941367i q^{63} +(3.41683 + 7.23362i) q^{64} +(-1.19051 + 6.24914i) q^{66} -4.00000 q^{67} +(-5.55691 + 14.0552i) q^{68} -1.05863i q^{69} -12.9966 q^{71} +(2.38923 + 1.51380i) q^{72} +6.00000i q^{73} +(-10.3354 - 1.96896i) q^{74} +(-0.778457 + 1.96896i) q^{76} +4.23453 q^{77} +(-7.71982 - 1.47068i) q^{78} -11.5569 q^{79} +1.00000 q^{81} +(-5.39400 - 1.02760i) q^{82} -5.88273 q^{83} +(0.692226 - 1.75086i) q^{84} +(2.61555 + 0.498281i) q^{86} +2.00000i q^{87} +(6.80949 - 10.7474i) q^{88} +4.11727 q^{89} +5.23109i q^{91} +(-0.778457 + 1.96896i) q^{92} -3.55691 q^{93} +(2.66119 - 13.9690i) q^{94} +(-3.33060 - 4.57243i) q^{96} +17.1138i q^{97} +(8.49351 + 1.61808i) q^{98} -4.49828i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 6 q^{3} + 2 q^{4} + 6 q^{8} + 6 q^{9} - 2 q^{12} + 16 q^{14} + 10 q^{16} - 12 q^{22} - 6 q^{24} + 28 q^{26} - 6 q^{27} - 20 q^{28} - 12 q^{31} + 10 q^{32} - 12 q^{34} + 2 q^{36} - 8 q^{37} - 20 q^{38}+ \cdots + 56 q^{98}+O(q^{100})$ 6 * q - 6 * q^3 + 2 * q^4 + 6 * q^8 + 6 * q^9 - 2 * q^12 + 16 * q^14 + 10 * q^16 - 12 * q^22 - 6 * q^24 + 28 * q^26 - 6 * q^27 - 20 * q^28 - 12 * q^31 + 10 * q^32 - 12 * q^34 + 2 * q^36 - 8 * q^37 - 20 * q^38 - 20 * q^41 - 16 * q^42 + 8 * q^43 + 4 * q^44 - 20 * q^46 - 10 * q^48 - 30 * q^49 + 12 * q^52 - 12 * q^53 + 4 * q^56 + 4 * q^58 + 28 * q^62 - 22 * q^64 + 12 * q^66 - 24 * q^67 - 8 * q^71 + 6 * q^72 - 12 * q^74 + 12 * q^76 + 32 * q^77 - 28 * q^78 - 36 * q^79 + 6 * q^81 + 16 * q^82 - 32 * q^83 + 20 * q^84 - 16 * q^86 + 60 * q^88 + 28 * q^89 + 12 * q^92 + 12 * q^93 - 4 * q^94 - 10 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$ .

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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

)

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

$2$	1.38923	+	0.264658i	0.982333	+	0.187142i
$2$	1.38923	+	0.264658i	0.982333	+	0.187142i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.85991	+	0.735342i	0.929956	+	0.367671i
$5$		0			0
$5$		0			0
$6$	−1.38923	−	0.264658i	−0.567150	−	0.108046i
$7$			0.941367i			0.355803i	0.984048	+	0.177902i	$0.0569309\pi$
$7$			0.941367i			0.355803i	−0.984048	+	0.177902i	$0.943069\pi$
$8$	2.38923	+	1.51380i	0.844720	+	0.535209i
$9$	1.00000			0.333333
$10$		0			0
$11$		−	4.49828i		−	1.35628i	−0.734931	−	0.678141i	$-0.762786\pi$
$11$		−	4.49828i		−	1.35628i	0.734931	−	0.678141i	$-0.237214\pi$
$12$	−1.85991	−	0.735342i	−0.536910	−	0.212275i
$13$	5.55691			1.54121			0.770605	−	0.637313i	$-0.219954\pi$
$13$	5.55691			1.54121			0.770605	+	0.637313i	$0.219954\pi$
$14$	−0.249141	+	1.30777i	−0.0665856	+	0.349517i
$15$		0			0
$16$	2.91855	+	2.73534i	0.729636	+	0.683835i
$17$			7.55691i			1.83282i	0.400240	+	0.916410i	$0.368927\pi$
$17$			7.55691i			1.83282i	−0.400240	+	0.916410i	$0.631073\pi$
$18$	1.38923	+	0.264658i	0.327444	+	0.0623806i
$19$			1.05863i			0.242867i	0.992600	+	0.121434i	$0.0387491\pi$
$19$			1.05863i			0.242867i	−0.992600	+	0.121434i	$0.961251\pi$
$20$		0			0
$21$		−	0.941367i		−	0.205423i
$22$	1.19051	−	6.24914i	0.253817	−	1.33232i
$23$			1.05863i			0.220740i	0.993891	+	0.110370i	$0.0352036\pi$
$23$			1.05863i			0.220740i	−0.993891	+	0.110370i	$0.964796\pi$
$24$	−2.38923	−	1.51380i	−0.487699	−	0.309003i
$25$		0			0
$26$	7.71982	+	1.47068i	1.51398	+	0.288425i
$27$	−1.00000			−0.192450
$28$	−0.692226	+	1.75086i	−0.130818	+	0.330881i
$29$		−	2.00000i		−	0.371391i	−0.982607	−	0.185695i	$-0.940546\pi$
$29$		−	2.00000i		−	0.371391i	0.982607	−	0.185695i	$-0.0594537\pi$
$30$		0			0
$31$	3.55691			0.638841			0.319420	−	0.947613i	$-0.396512\pi$
$31$	3.55691			0.638841			0.319420	+	0.947613i	$0.396512\pi$
$32$	3.33060	+	4.57243i	0.588772	+	0.808299i
$33$			4.49828i			0.783050i
$34$	−2.00000	+	10.4983i	−0.342997	+	1.80044i
$35$		0			0
$36$	1.85991	+	0.735342i	0.309985	+	0.122557i
$37$	−7.43965			−1.22307			−0.611535	−	0.791217i	$-0.709448\pi$
$37$	−7.43965			−1.22307			−0.611535	+	0.791217i	$0.709448\pi$
$38$	−0.280176	+	1.47068i	−0.0454506	+	0.238576i
$39$	−5.55691			−0.889818
$40$		0			0
$41$	−3.88273			−0.606381			−0.303191	−	0.952930i	$-0.598052\pi$
$41$	−3.88273			−0.606381			−0.303191	+	0.952930i	$0.598052\pi$
$42$	0.249141	−	1.30777i	0.0384432	−	0.201794i
$43$	1.88273			0.287114			0.143557	−	0.989642i	$-0.454146\pi$
$43$	1.88273			0.287114			0.143557	+	0.989642i	$0.454146\pi$
$44$	3.30777	−	8.36641i	0.498666	−	1.26128i
$45$		0			0
$46$	−0.280176	+	1.47068i	−0.0413097	+	0.216840i
$47$		−	10.0552i		−	1.46670i	−0.679851	−	0.733350i	$-0.737955\pi$
$47$		−	10.0552i		−	1.46670i	0.679851	−	0.733350i	$-0.262045\pi$
$48$	−2.91855	−	2.73534i	−0.421256	−	0.394813i
$49$	6.11383			0.873404
$50$		0			0
$51$		−	7.55691i		−	1.05818i
$52$	10.3354	+	4.08623i	1.43326	+	0.566658i
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.38923	−	0.264658i	−0.189050	−	0.0360154i
$55$		0			0
$56$	−1.42504	+	2.24914i	−0.190429	+	0.300554i
$57$		−	1.05863i		−	0.140219i
$58$	0.529317	−	2.77846i	0.0695027	−	0.364829i
$59$		−	8.49828i		−	1.10638i	−0.833054	−	0.553191i	$-0.813410\pi$
$59$		−	8.49828i		−	1.10638i	0.833054	−	0.553191i	$-0.186590\pi$
$60$		0			0
$61$		−	8.99656i		−	1.15189i	−0.817488	−	0.575946i	$-0.804634\pi$
$61$		−	8.99656i		−	1.15189i	0.817488	−	0.575946i	$-0.195366\pi$
$62$	4.94137	+	0.941367i	0.627554	+	0.119554i
$63$			0.941367i			0.118601i
$64$	3.41683	+	7.23362i	0.427103	+	0.904203i
$65$		0			0
$66$	−1.19051	+	6.24914i	−0.146541	+	0.769216i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−5.55691	+	14.0552i	−0.673875	+	1.70444i
$69$		−	1.05863i		−	0.127444i
$70$		0			0
$71$	−12.9966			−1.54241			−0.771204	−	0.636588i	$-0.780345\pi$
$71$	−12.9966			−1.54241			−0.771204	+	0.636588i	$0.780345\pi$
$72$	2.38923	+	1.51380i	0.281573	+	0.178403i
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−10.3354	−	1.96896i	−1.20146	−	0.228887i
$75$		0			0
$76$	−0.778457	+	1.96896i	−0.0892952	+	0.225856i
$77$	4.23453			0.482570
$78$	−7.71982	−	1.47068i	−0.874098	−	0.166522i
$79$	−11.5569			−1.30025			−0.650127	−	0.759825i	$-0.725284\pi$
$79$	−11.5569			−1.30025			−0.650127	+	0.759825i	$0.725284\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−5.39400	−	1.02760i	−0.595668	−	0.113479i
$83$	−5.88273			−0.645714			−0.322857	−	0.946448i	$-0.604643\pi$
$83$	−5.88273			−0.645714			−0.322857	+	0.946448i	$0.604643\pi$
$84$	0.692226	−	1.75086i	0.0755281	−	0.191034i
$85$		0			0
$86$	2.61555	+	0.498281i	0.282042	+	0.0537310i
$87$			2.00000i			0.214423i
$88$	6.80949	−	10.7474i	0.725894	−	1.14568i
$89$	4.11727			0.436429			0.218215	−	0.975901i	$-0.429977\pi$
$89$	4.11727			0.436429			0.218215	+	0.975901i	$0.429977\pi$
$90$		0			0
$91$			5.23109i			0.548368i
$92$	−0.778457	+	1.96896i	−0.0811598	+	0.205279i
$93$	−3.55691			−0.368835
$94$	2.66119	−	13.9690i	0.274481	−	1.44079i
$95$		0			0
$96$	−3.33060	−	4.57243i	−0.339927	−	0.466672i
$97$			17.1138i			1.73765i	0.495123	+	0.868823i	$0.335123\pi$
$97$			17.1138i			1.73765i	−0.495123	+	0.868823i	$0.664877\pi$
$98$	8.49351	+	1.61808i	0.857974	+	0.163450i
$99$		−	4.49828i		−	0.452094i
$100$		0			0
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$	2.00000	−	10.4983i	0.198030	−	1.03948i
$103$		−	10.1725i		−	1.00232i	−0.865354	−	0.501161i	$-0.832906\pi$
$103$		−	10.1725i		−	1.00232i	0.865354	−	0.501161i	$-0.167094\pi$
$104$	13.2767	+	8.41205i	1.30189	+	0.824869i
$105$		0			0
$106$	−2.77846	−	0.529317i	−0.269868	−	0.0514118i
$107$	−17.2311			−1.66579			−0.832896	−	0.553429i	$-0.813319\pi$
$107$	−17.2311			−1.66579			−0.832896	+	0.553429i	$0.813319\pi$
$108$	−1.85991	−	0.735342i	−0.178970	−	0.0707583i
$109$			1.88273i			0.180333i	0.995927	+	0.0901666i	$0.0287399\pi$
$109$			1.88273i			0.180333i	−0.995927	+	0.0901666i	$0.971260\pi$
$110$		0			0
$111$	7.43965			0.706140
$112$	−2.57496	+	2.74742i	−0.243311	+	0.259607i
$113$		−	15.3224i		−	1.44141i	−0.693243	−	0.720704i	$-0.743819\pi$
$113$		−	15.3224i		−	1.44141i	0.693243	−	0.720704i	$-0.256181\pi$
$114$	0.280176	−	1.47068i	0.0262409	−	0.137742i
$115$		0			0
$116$	1.47068	−	3.71982i	0.136550	−	0.345377i
$117$	5.55691			0.513737
$118$	2.24914	−	11.8061i	0.207050	−	1.08684i
$119$	−7.11383			−0.652124
$120$		0			0
$121$	−9.23453			−0.839503
$122$	2.38101	−	12.4983i	0.215567	−	1.13154i
$123$	3.88273			0.350094
$124$	6.61555	+	2.61555i	0.594094	+	0.234883i
$125$		0			0
$126$	−0.249141	+	1.30777i	−0.0221952	+	0.116506i
$127$		−	18.1725i		−	1.61255i	−0.591544	−	0.806273i	$-0.701481\pi$
$127$		−	18.1725i		−	1.61255i	0.591544	−	0.806273i	$-0.298519\pi$
$128$	2.83231	+	10.9534i	0.250344	+	0.968157i
$129$	−1.88273			−0.165765
$130$		0			0
$131$			6.38101i			0.557512i	0.960362	+	0.278756i	$0.0899220\pi$
$131$			6.38101i			0.557512i	−0.960362	+	0.278756i	$0.910078\pi$
$132$	−3.30777	+	8.36641i	−0.287905	+	0.728202i
$133$	−0.996562			−0.0864129
$134$	−5.55691	−	1.05863i	−0.480044	−	0.0914520i
$135$		0			0
$136$	−11.4396	+	18.0552i	−0.980942	+	1.54822i
$137$		−	4.44309i		−	0.379598i	−0.981823	−	0.189799i	$-0.939216\pi$
$137$		−	4.44309i		−	0.379598i	0.981823	−	0.189799i	$-0.0607837\pi$
$138$	0.280176	−	1.47068i	0.0238502	−	0.125193i
$139$			20.1725i			1.71101i	0.517798	+	0.855503i	$0.326752\pi$
$139$			20.1725i			1.71101i	−0.517798	+	0.855503i	$0.673248\pi$
$140$		0			0
$141$			10.0552i			0.846800i
$142$	−18.0552	−	3.43965i	−1.51516	−	0.288649i
$143$		−	24.9966i		−	2.09032i
$144$	2.91855	+	2.73534i	0.243212	+	0.227945i
$145$		0			0
$146$	−1.58795	+	8.33537i	−0.131420	+	0.689840i
$147$	−6.11383			−0.504260
$148$	−13.8371	−	5.47068i	−1.13740	−	0.449687i
$149$		−	2.00000i		−	0.163846i	−0.996639	−	0.0819232i	$-0.973894\pi$
$149$		−	2.00000i		−	0.163846i	0.996639	−	0.0819232i	$-0.0261062\pi$
$150$		0			0
$151$	9.67418			0.787274			0.393637	−	0.919266i	$-0.371217\pi$
$151$	9.67418			0.787274			0.393637	+	0.919266i	$0.371217\pi$
$152$	−1.60256	+	2.52932i	−0.129985	+	0.205155i
$153$			7.55691i			0.610940i
$154$	5.88273	+	1.12070i	0.474044	+	0.0903089i
$155$		0			0
$156$	−10.3354	−	4.08623i	−0.827492	−	0.327160i
$157$	4.32582			0.345238			0.172619	−	0.984989i	$-0.444777\pi$
$157$	4.32582			0.345238			0.172619	+	0.984989i	$0.444777\pi$
$158$	−16.0552	−	3.05863i	−1.27728	−	0.243332i
$159$	2.00000			0.158610
$160$		0			0
$161$	−0.996562			−0.0785401
$162$	1.38923	+	0.264658i	0.109148	+	0.0207935i
$163$	6.11727			0.479141			0.239571	−	0.970879i	$-0.422993\pi$
$163$	6.11727			0.479141			0.239571	+	0.970879i	$0.422993\pi$
$164$	−7.22154	−	2.85514i	−0.563908	−	0.222949i
$165$		0			0
$166$	−8.17246	−	1.55691i	−0.634306	−	0.120840i
$167$		−	6.05520i		−	0.468565i	−0.972169	−	0.234283i	$-0.924726\pi$
$167$		−	6.05520i		−	0.468565i	0.972169	−	0.234283i	$-0.0752741\pi$
$168$	1.42504	−	2.24914i	0.109944	−	0.173525i
$169$	17.8793			1.37533
$170$		0			0
$171$			1.05863i			0.0809557i
$172$	3.50172	+	1.38445i	0.267004	+	0.105564i
$173$	−16.8793			−1.28331			−0.641655	−	0.766994i	$-0.721752\pi$
$173$	−16.8793			−1.28331			−0.641655	+	0.766994i	$0.721752\pi$
$174$	−0.529317	+	2.77846i	−0.0401274	+	0.210634i
$175$		0			0
$176$	12.3043	−	13.1284i	0.927474	−	0.989593i
$177$			8.49828i			0.638770i
$178$	5.71982	+	1.08967i	0.428719	+	0.0816741i
$179$			10.6155i			0.793443i	0.917939	+	0.396722i	$0.129852\pi$
$179$			10.6155i			0.793443i	−0.917939	+	0.396722i	$0.870148\pi$
$180$		0			0
$181$		−	14.1173i		−	1.04933i	−0.851309	−	0.524664i	$-0.824191\pi$
$181$		−	14.1173i		−	1.04933i	0.851309	−	0.524664i	$-0.175809\pi$
$182$	−1.38445	+	7.26719i	−0.102622	+	0.538680i
$183$			8.99656i			0.665045i
$184$	−1.60256	+	2.52932i	−0.118142	+	0.186464i
$185$		0			0
$186$	−4.94137	−	0.941367i	−0.362319	−	0.0690244i
$187$	33.9931			2.48582
$188$	7.39400	−	18.7018i	0.539263	−	1.36397i
$189$		−	0.941367i		−	0.0684744i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−3.41683	−	7.23362i	−0.246588	−	0.522042i
$193$			4.87930i			0.351219i	0.984460	+	0.175610i	$0.0561897\pi$
$193$			4.87930i			0.351219i	−0.984460	+	0.175610i	$0.943810\pi$
$194$	−4.52932	+	23.7750i	−0.325186	+	1.70695i
$195$		0			0
$196$	11.3712	+	4.49575i	0.812227	+	0.321125i
$197$	−2.88617			−0.205631			−0.102816	−	0.994700i	$-0.532785\pi$
$197$	−2.88617			−0.205631			−0.102816	+	0.994700i	$0.532785\pi$
$198$	1.19051	−	6.24914i	0.0846057	−	0.444107i
$199$	17.6742			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$199$	17.6742			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	0.529317	−	2.77846i	0.0372426	−	0.195492i
$203$	1.88273			0.132142
$204$	5.55691	−	14.0552i	0.389062	−	0.984061i
$205$		0			0
$206$	2.69223	−	14.1319i	0.187576	−	0.984614i
$207$			1.05863i			0.0735801i
$208$	16.2181	+	15.2001i	1.12452	+	1.05393i
$209$	4.76203			0.329396
$210$		0			0
$211$			23.9379i			1.64795i	0.566623	+	0.823977i	$0.308250\pi$
$211$			23.9379i			1.64795i	−0.566623	+	0.823977i	$0.691750\pi$
$212$	−3.71982	−	1.47068i	−0.255479	−	0.101007i
$213$	12.9966			0.890510
$214$	−23.9379	−	4.56035i	−1.63636	−	0.311739i
$215$		0			0
$216$	−2.38923	−	1.51380i	−0.162566	−	0.103001i
$217$			3.34836i			0.227302i
$218$	−0.498281	+	2.61555i	−0.0337479	+	0.177147i
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$			41.9931i			2.82476i
$222$	10.3354	+	1.96896i	0.693665	+	0.132148i
$223$			24.0552i			1.61086i	0.592694	+	0.805428i	$0.298064\pi$
$223$			24.0552i			1.61086i	−0.592694	+	0.805428i	$0.701936\pi$
$224$	−4.30434	+	3.13531i	−0.287596	+	0.209487i
$225$		0			0
$226$	4.05520	−	21.2863i	0.269748	−	1.41594i
$227$	11.1138			0.737651			0.368825	−	0.929499i	$-0.379760\pi$
$227$	11.1138			0.737651			0.368825	+	0.929499i	$0.379760\pi$
$228$	0.778457	−	1.96896i	0.0515546	−	0.130398i
$229$		−	17.2311i		−	1.13866i	−0.822108	−	0.569331i	$-0.807202\pi$
$229$		−	17.2311i		−	1.13866i	0.822108	−	0.569331i	$-0.192798\pi$
$230$		0			0
$231$	−4.23453			−0.278612
$232$	3.02760	−	4.77846i	0.198772	−	0.313721i
$233$			8.44309i			0.553125i	0.960996	+	0.276562i	$0.0891953\pi$
$233$			8.44309i			0.553125i	−0.960996	+	0.276562i	$0.910805\pi$
$234$	7.71982	+	1.47068i	0.504661	+	0.0961416i
$235$		0			0
$236$	6.24914	−	15.8061i	0.406784	−	1.02889i
$237$	11.5569			0.750702
$238$	−9.88273	−	1.88273i	−0.640602	−	0.122039i
$239$	−10.1173			−0.654432			−0.327216	−	0.944950i	$-0.606110\pi$
$239$	−10.1173			−0.654432			−0.327216	+	0.944950i	$0.606110\pi$
$240$		0			0
$241$	16.8793			1.08729			0.543646	−	0.839315i	$-0.317044\pi$
$241$	16.8793			1.08729			0.543646	+	0.839315i	$0.317044\pi$
$242$	−12.8289	−	2.44400i	−0.824671	−	0.157106i
$243$	−1.00000			−0.0641500
$244$	6.61555	−	16.7328i	0.423517	−	1.07121i
$245$		0			0
$246$	5.39400	+	1.02760i	0.343909	+	0.0655172i
$247$			5.88273i			0.374309i
$248$	8.49828	+	5.38445i	0.539641	+	0.341913i
$249$	5.88273			0.372803
$250$		0			0
$251$		−	11.8466i		−	0.747753i	−0.927478	−	0.373877i	$-0.878028\pi$
$251$		−	11.8466i		−	0.747753i	0.927478	−	0.373877i	$-0.121972\pi$
$252$	−0.692226	+	1.75086i	−0.0436062	+	0.110294i
$253$	4.76203			0.299386
$254$	4.80949	−	25.2457i	0.301774	−	1.58406i
$255$		0			0
$256$	1.03581	+	15.9664i	0.0647382	+	0.997902i
$257$		−	10.6707i		−	0.665623i	−0.942993	−	0.332811i	$-0.892003\pi$
$257$		−	10.6707i		−	0.665623i	0.942993	−	0.332811i	$-0.107997\pi$
$258$	−2.61555	−	0.498281i	−0.162837	−	0.0310216i
$259$		−	7.00344i		−	0.435172i
$260$		0			0
$261$		−	2.00000i		−	0.123797i
$262$	−1.68879	+	8.86469i	−0.104334	+	0.547662i
$263$			1.94480i			0.119922i	0.998201	+	0.0599609i	$0.0190976\pi$
$263$			1.94480i			0.119922i	−0.998201	+	0.0599609i	$0.980902\pi$
$264$	−6.80949	+	10.7474i	−0.419095	+	0.661458i
$265$		0			0
$266$	−1.38445	−	0.263748i	−0.0848862	−	0.0161715i
$267$	−4.11727			−0.251973
$268$	−7.43965	−	2.94137i	−0.454449	−	0.179673i
$269$			9.76547i			0.595411i	0.954658	+	0.297706i	$0.0962214\pi$
$269$			9.76547i			0.595411i	−0.954658	+	0.297706i	$0.903779\pi$
$270$		0			0
$271$	3.44652			0.209361			0.104681	−	0.994506i	$-0.466618\pi$
$271$	3.44652			0.209361			0.104681	+	0.994506i	$0.466618\pi$
$272$	−20.6707	+	22.0552i	−1.25335	+	1.33729i
$273$		−	5.23109i		−	0.316600i
$274$	1.17590	−	6.17246i	0.0710387	−	0.372892i
$275$		0			0
$276$	0.778457	−	1.96896i	0.0468576	−	0.118518i
$277$	−18.7880			−1.12886			−0.564431	−	0.825480i	$-0.690904\pi$
$277$	−18.7880			−1.12886			−0.564431	+	0.825480i	$0.690904\pi$
$278$	−5.33881	+	28.0242i	−0.320200	+	1.68078i
$279$	3.55691			0.212947
$280$		0			0
$281$	−16.8793			−1.00693			−0.503467	−	0.864014i	$-0.667943\pi$
$281$	−16.8793			−1.00693			−0.503467	+	0.864014i	$0.667943\pi$
$282$	−2.66119	+	13.9690i	−0.158472	+	0.831840i
$283$	−20.0000			−1.18888			−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000			−1.18888			−0.594438	+	0.804141i	$0.702626\pi$
$284$	−24.1725	−	9.55691i	−1.43437	−	0.567099i
$285$		0			0
$286$	6.61555	−	34.7259i	0.391186	−	2.05339i
$287$		−	3.65508i		−	0.215752i
$288$	3.33060	+	4.57243i	0.196257	+	0.269433i
$289$	−40.1070			−2.35923
$290$		0			0
$291$		−	17.1138i		−	1.00323i
$292$	−4.41205	+	11.1595i	−0.258196	+	0.653059i
$293$	20.2277			1.18171			0.590856	−	0.806777i	$-0.298790\pi$
$293$	20.2277			1.18171			0.590856	+	0.806777i	$0.298790\pi$
$294$	−8.49351	−	1.61808i	−0.495351	−	0.0943681i
$295$		0			0
$296$	−17.7750	−	11.2621i	−1.03315	−	0.654598i
$297$			4.49828i			0.261017i
$298$	0.529317	−	2.77846i	0.0306625	−	0.160952i
$299$			5.88273i			0.340207i
$300$		0			0
$301$			1.77234i			0.102156i
$302$	13.4396	+	2.56035i	0.773365	+	0.147332i
$303$			2.00000i			0.114897i
$304$	−2.89572	+	3.08967i	−0.166081	+	0.177205i
$305$		0			0
$306$	−2.00000	+	10.4983i	−0.114332	+	0.600147i
$307$	8.11039			0.462884			0.231442	−	0.972849i	$-0.425656\pi$
$307$	8.11039			0.462884			0.231442	+	0.972849i	$0.425656\pi$
$308$	7.87586	+	3.11383i	0.448769	+	0.177427i
$309$			10.1725i			0.578691i
$310$		0			0
$311$	31.8759			1.80751			0.903757	−	0.428046i	$-0.140798\pi$
$311$	31.8759			1.80751			0.903757	+	0.428046i	$0.140798\pi$
$312$	−13.2767	−	8.41205i	−0.751647	−	0.476239i
$313$			5.11383i			0.289051i	0.989501	+	0.144525i	$0.0461655\pi$
$313$			5.11383i			0.289051i	−0.989501	+	0.144525i	$0.953834\pi$
$314$	6.00955	+	1.14486i	0.339139	+	0.0646084i
$315$		0			0
$316$	−21.4948	−	8.49828i	−1.20918	−	0.478066i
$317$	24.6448			1.38419			0.692094	−	0.721807i	$-0.256688\pi$
$317$	24.6448			1.38419			0.692094	+	0.721807i	$0.256688\pi$
$318$	2.77846	+	0.529317i	0.155808	+	0.0296826i
$319$	−8.99656			−0.503711
$320$		0			0
$321$	17.2311			0.961746
$322$	−1.38445	−	0.263748i	−0.0771525	−	0.0146981i
$323$	−8.00000			−0.445132
$324$	1.85991	+	0.735342i	0.103328	+	0.0408523i
$325$		0			0
$326$	8.49828	+	1.61899i	0.470676	+	0.0896673i
$327$		−	1.88273i		−	0.104115i
$328$	−9.27674	−	5.87768i	−0.512222	−	0.324540i
$329$	9.46563			0.521857
$330$		0			0
$331$			11.0518i			0.607460i	0.952758	+	0.303730i	$0.0982320\pi$
$331$			11.0518i			0.607460i	−0.952758	+	0.303730i	$0.901768\pi$
$332$	−10.9414	−	4.32582i	−0.600486	−	0.237410i
$333$	−7.43965			−0.407690
$334$	1.60256	−	8.41205i	0.0876881	−	0.460287i
$335$		0			0
$336$	2.57496	−	2.74742i	0.140476	−	0.149884i
$337$		−	19.9931i		−	1.08909i	−0.838730	−	0.544547i	$-0.816701\pi$
$337$		−	19.9931i		−	1.08909i	0.838730	−	0.544547i	$-0.183299\pi$
$338$	24.8384	+	4.73190i	1.35103	+	0.257382i
$339$			15.3224i			0.832198i
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$	−0.280176	+	1.47068i	−0.0151502	+	0.0795255i
$343$			12.3449i			0.666563i
$344$	4.49828	+	2.85008i	0.242531	+	0.153666i
$345$		0			0
$346$	−23.4492	−	4.46725i	−1.26064	−	0.240161i
$347$	−6.87930			−0.369300			−0.184650	−	0.982804i	$-0.559115\pi$
$347$	−6.87930			−0.369300			−0.184650	+	0.982804i	$0.559115\pi$
$348$	−1.47068	+	3.71982i	−0.0788369	+	0.199403i
$349$		−	4.76203i		−	0.254906i	−0.991845	−	0.127453i	$-0.959320\pi$
$349$		−	4.76203i		−	0.254906i	0.991845	−	0.127453i	$-0.0406801\pi$
$350$		0			0
$351$	−5.55691			−0.296606
$352$	20.5681	−	14.9820i	1.09628	−	0.798541i
$353$			3.79145i			0.201798i	0.994897	+	0.100899i	$0.0321720\pi$
$353$			3.79145i			0.201798i	−0.994897	+	0.100899i	$0.967828\pi$
$354$	−2.24914	+	11.8061i	−0.119540	+	0.627485i
$355$		0			0
$356$	7.65775	+	3.02760i	0.405860	+	0.160462i
$357$	7.11383			0.376504
$358$	−2.80949	+	14.7474i	−0.148486	+	0.779425i
$359$	12.9966			0.685932			0.342966	−	0.939348i	$-0.388568\pi$
$359$	12.9966			0.685932			0.342966	+	0.939348i	$0.388568\pi$
$360$		0			0
$361$	17.8793			0.941016
$362$	3.73625	−	19.6121i	0.196373	−	1.03079i
$363$	9.23453			0.484687
$364$	−3.84664	+	9.72938i	−0.201619	+	0.509958i
$365$		0			0
$366$	−2.38101	+	12.4983i	−0.124458	+	0.653296i
$367$			22.9345i			1.19717i	0.801059	+	0.598585i	$0.204270\pi$
$367$			22.9345i			1.19717i	−0.801059	+	0.598585i	$0.795730\pi$
$368$	−2.89572	+	3.08967i	−0.150950	+	0.161060i
$369$	−3.88273			−0.202127
$370$		0			0
$371$		−	1.88273i		−	0.0977467i
$372$	−6.61555	−	2.61555i	−0.343000	−	0.135610i
$373$	−15.4396			−0.799435			−0.399717	−	0.916638i	$-0.630892\pi$
$373$	−15.4396			−0.799435			−0.399717	+	0.916638i	$0.630892\pi$
$374$	47.2242	+	8.99656i	2.44191	+	0.465201i
$375$		0			0
$376$	15.2215	−	24.0242i	0.784991	−	1.23895i
$377$		−	11.1138i		−	0.572391i
$378$	0.249141	−	1.30777i	0.0128144	−	0.0672646i
$379$		−	6.28973i		−	0.323082i	−0.986866	−	0.161541i	$-0.948354\pi$
$379$		−	6.28973i		−	0.323082i	0.986866	−	0.161541i	$-0.0516463\pi$
$380$		0			0
$381$			18.1725i			0.931003i
$382$	−11.1138	−	2.11727i	−0.568633	−	0.108329i
$383$		−	2.94137i		−	0.150297i	−0.997172	−	0.0751484i	$-0.976057\pi$
$383$		−	2.94137i		−	0.150297i	0.997172	−	0.0751484i	$-0.0239431\pi$
$384$	−2.83231	−	10.9534i	−0.144536	−	0.558966i
$385$		0			0
$386$	−1.29135	+	6.77846i	−0.0657278	+	0.345014i
$387$	1.88273			0.0957047
$388$	−12.5845	+	31.8302i	−0.638882	+	1.61593i
$389$			12.2277i			0.619967i	0.950742	+	0.309983i	$0.100324\pi$
$389$			12.2277i			0.619967i	−0.950742	+	0.309983i	$0.899676\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	14.6073	+	9.25511i	0.737782	+	0.467453i
$393$		−	6.38101i		−	0.321880i
$394$	−4.00955	−	0.763849i	−0.201998	−	0.0384822i
$395$		0			0
$396$	3.30777	−	8.36641i	0.166222	−	0.420428i
$397$	−5.32238			−0.267123			−0.133561	−	0.991041i	$-0.542641\pi$
$397$	−5.32238			−0.267123			−0.133561	+	0.991041i	$0.542641\pi$
$398$	24.5535	+	4.67762i	1.23075	+	0.234468i
$399$	0.996562			0.0498905
$400$		0			0
$401$	6.99656			0.349392			0.174696	−	0.984622i	$-0.444106\pi$
$401$	6.99656			0.349392			0.174696	+	0.984622i	$0.444106\pi$
$402$	5.55691	+	1.05863i	0.277154	+	0.0527998i
$403$	19.7655			0.984588
$404$	1.47068	−	3.71982i	0.0731692	−	0.185068i
$405$		0			0
$406$	2.61555	+	0.498281i	0.129807	+	0.0247293i
$407$			33.4656i			1.65883i
$408$	11.4396	−	18.0552i	0.566347	−	0.893865i
$409$	−16.2277			−0.802406			−0.401203	−	0.915989i	$-0.631408\pi$
$409$	−16.2277			−0.802406			−0.401203	+	0.915989i	$0.631408\pi$
$410$		0			0
$411$			4.44309i			0.219161i
$412$	7.48024	−	18.9199i	0.368525	−	0.932116i
$413$	8.00000			0.393654
$414$	−0.280176	+	1.47068i	−0.0137699	+	0.0722801i
$415$		0			0
$416$	18.5078	+	25.4086i	0.907421	+	1.24576i
$417$		−	20.1725i		−	0.987850i
$418$	6.61555	+	1.26031i	0.323577	+	0.0616438i
$419$		−	15.6121i		−	0.762701i	−0.924430	−	0.381351i	$-0.875459\pi$
$419$		−	15.6121i		−	0.762701i	0.924430	−	0.381351i	$-0.124541\pi$
$420$		0			0
$421$		−	33.2311i		−	1.61958i	−0.586717	−	0.809792i	$-0.699580\pi$
$421$		−	33.2311i		−	1.61958i	0.586717	−	0.809792i	$-0.300420\pi$
$422$	−6.33537	+	33.2553i	−0.308401	+	1.61884i
$423$		−	10.0552i		−	0.488900i
$424$	−4.77846	−	3.02760i	−0.232062	−	0.147033i
$425$		0			0
$426$	18.0552	+	3.43965i	0.874777	+	0.166651i
$427$	8.46907			0.409847
$428$	−32.0483	−	12.6707i	−1.54911	−	0.612463i
$429$			24.9966i			1.20685i
$430$		0			0
$431$	−12.9966			−0.626022			−0.313011	−	0.949749i	$-0.601338\pi$
$431$	−12.9966			−0.626022			−0.313011	+	0.949749i	$0.601338\pi$
$432$	−2.91855	−	2.73534i	−0.140419	−	0.131604i
$433$		−	20.2277i		−	0.972079i	−0.873937	−	0.486040i	$-0.838441\pi$
$433$		−	20.2277i		−	0.972079i	0.873937	−	0.486040i	$-0.161559\pi$
$434$	−0.886172	+	4.65164i	−0.0425376	+	0.223286i
$435$		0			0
$436$	−1.38445	+	3.50172i	−0.0663033	+	0.167702i
$437$	−1.12070			−0.0536106
$438$	1.58795	−	8.33537i	0.0758752	−	0.398279i
$439$	5.43965			0.259620			0.129810	−	0.991539i	$-0.458563\pi$
$439$	5.43965			0.259620			0.129810	+	0.991539i	$0.458563\pi$
$440$		0			0
$441$	6.11383			0.291135
$442$	−11.1138	+	58.3380i	−0.528631	+	2.77486i
$443$	15.3484			0.729223			0.364611	−	0.931160i	$-0.381202\pi$
$443$	15.3484			0.729223			0.364611	+	0.931160i	$0.381202\pi$
$444$	13.8371	+	5.47068i	0.656679	+	0.259627i
$445$		0			0
$446$	−6.36641	+	33.4182i	−0.301458	+	1.58240i
$447$			2.00000i			0.0945968i
$448$	−6.80949	+	3.21649i	−0.321718	+	0.151965i
$449$	−4.22766			−0.199515			−0.0997577	−	0.995012i	$-0.531807\pi$
$449$	−4.22766			−0.199515			−0.0997577	+	0.995012i	$0.531807\pi$
$450$		0			0
$451$			17.4656i			0.822424i
$452$	11.2672	−	28.4983i	0.529964	−	1.34045i
$453$	−9.67418			−0.454533
$454$	15.4396	+	2.94137i	0.724619	+	0.138045i
$455$		0			0
$456$	1.60256	−	2.52932i	0.0750466	−	0.118446i
$457$			2.65164i			0.124038i	0.998075	+	0.0620192i	$0.0197540\pi$
$457$			2.65164i			0.124038i	−0.998075	+	0.0620192i	$0.980246\pi$
$458$	4.56035	−	23.9379i	0.213091	−	1.11855i
$459$		−	7.55691i		−	0.352727i
$460$		0			0
$461$			10.2345i			0.476670i	0.971183	+	0.238335i	$0.0766016\pi$
$461$			10.2345i			0.476670i	−0.971183	+	0.238335i	$0.923398\pi$
$462$	−5.88273	−	1.12070i	−0.273690	−	0.0521399i
$463$		−	19.0586i		−	0.885730i	−0.896588	−	0.442865i	$-0.853962\pi$
$463$		−	19.0586i		−	0.885730i	0.896588	−	0.442865i	$-0.146038\pi$
$464$	5.47068	−	5.83709i	0.253970	−	0.270980i
$465$		0			0
$466$	−2.23453	+	11.7294i	−0.103513	+	0.543353i
$467$	−4.11039			−0.190206			−0.0951031	−	0.995467i	$-0.530318\pi$
$467$	−4.11039			−0.190206			−0.0951031	+	0.995467i	$0.530318\pi$
$468$	10.3354	+	4.08623i	0.477753	+	0.188886i
$469$		−	3.76547i		−	0.173873i
$470$		0			0
$471$	−4.32582			−0.199323
$472$	12.8647	−	20.3043i	0.592145	−	0.934583i
$473$		−	8.46907i		−	0.389408i
$474$	16.0552	+	3.05863i	0.737440	+	0.140488i
$475$		0			0
$476$	−13.2311	−	5.23109i	−0.606446	−	0.239767i
$477$	−2.00000			−0.0915737
$478$	−14.0552	−	2.67762i	−0.642870	−	0.122471i
$479$	25.2311			1.15284			0.576419	−	0.817154i	$-0.304450\pi$
$479$	25.2311			1.15284			0.576419	+	0.817154i	$0.304450\pi$
$480$		0			0
$481$	−41.3415			−1.88501
$482$	23.4492	+	4.46725i	1.06808	+	0.203477i
$483$	0.996562			0.0453451
$484$	−17.1754	−	6.79054i	−0.780701	−	0.308661i
$485$		0			0
$486$	−1.38923	−	0.264658i	−0.0630167	−	0.0120051i
$487$		−	21.9379i		−	0.994102i	−0.867721	−	0.497051i	$-0.834416\pi$
$487$		−	21.9379i		−	0.994102i	0.867721	−	0.497051i	$-0.165584\pi$
$488$	13.6190	−	21.4948i	0.616502	−	0.973026i
$489$	−6.11727			−0.276632
$490$		0			0
$491$			7.50172i			0.338548i	0.985569	+	0.169274i	$0.0541423\pi$
$491$			7.50172i			0.338548i	−0.985569	+	0.169274i	$0.945858\pi$
$492$	7.22154	+	2.85514i	0.325572	+	0.128719i
$493$	15.1138			0.680693
$494$	−1.55691	+	8.17246i	−0.0700489	+	0.367696i
$495$		0			0
$496$	10.3810	+	9.72938i	0.466121	+	0.436862i
$497$		−	12.2345i		−	0.548794i
$498$	8.17246	+	1.55691i	0.366217	+	0.0697670i
$499$		−	29.1690i		−	1.30578i	−0.757451	−	0.652892i	$-0.773555\pi$
$499$		−	29.1690i		−	1.30578i	0.757451	−	0.652892i	$-0.226445\pi$
$500$		0			0
$501$			6.05520i			0.270526i
$502$	3.13531	−	16.4577i	0.139936	−	0.734543i
$503$			23.9379i			1.06734i	0.845693	+	0.533670i	$0.179187\pi$
$503$			23.9379i			1.06734i	−0.845693	+	0.533670i	$0.820813\pi$
$504$	−1.42504	+	2.24914i	−0.0634763	+	0.100185i
$505$		0			0
$506$	6.61555	+	1.26031i	0.294097	+	0.0560276i
$507$	−17.8793			−0.794047
$508$	13.3630	−	33.7992i	0.592886	−	1.49960i
$509$			28.6967i			1.27196i	0.771706	+	0.635980i	$0.219404\pi$
$509$			28.6967i			1.27196i	−0.771706	+	0.635980i	$0.780596\pi$
$510$		0			0
$511$	−5.64820			−0.249862
$512$	−2.78667	+	22.4552i	−0.123155	+	0.992387i
$513$		−	1.05863i		−	0.0467398i
$514$	2.82410	−	14.8241i	0.124566	−	0.653863i
$515$		0			0
$516$	−3.50172	−	1.38445i	−0.154155	−	0.0609471i
$517$	−45.2311			−1.98926
$518$	1.85352	−	9.72938i	0.0814389	−	0.427484i
$519$	16.8793			0.740919
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$	0.529317	−	2.77846i	0.0231676	−	0.121610i
$523$	−25.7586			−1.12634			−0.563172	−	0.826340i	$-0.690419\pi$
$523$	−25.7586			−1.12634			−0.563172	+	0.826340i	$0.690419\pi$
$524$	−4.69223	+	11.8681i	−0.204981	+	0.518461i
$525$		0			0
$526$	−0.514709	+	2.70178i	−0.0224424	+	0.117803i
$527$			26.8793i			1.17088i
$528$	−12.3043	+	13.1284i	−0.535477	+	0.571342i
$529$	21.8793			0.951274
$530$		0			0
$531$		−	8.49828i		−	0.368794i
$532$	−1.85352	−	0.732814i	−0.0803602	−	0.0317715i
$533$	−21.5760			−0.934561
$534$	−5.71982	−	1.08967i	−0.247521	−	0.0471546i
$535$		0			0
$536$	−9.55691	−	6.05520i	−0.412796	−	0.261545i
$537$		−	10.6155i		−	0.458095i
$538$	−2.58451	+	13.5665i	−0.111426	+	0.584892i
$539$		−	27.5017i		−	1.18458i
$540$		0			0
$541$		−	12.3449i		−	0.530750i	−0.964145	−	0.265375i	$-0.914504\pi$
$541$		−	12.3449i		−	0.530750i	0.964145	−	0.265375i	$-0.0854957\pi$
$542$	4.78801	+	0.912151i	0.205663	+	0.0391802i
$543$			14.1173i			0.605830i
$544$	−34.5535	+	25.1690i	−1.48147	+	1.07911i
$545$		0			0
$546$	1.38445	−	7.26719i	0.0592491	−	0.311007i
$547$	−19.8759			−0.849830			−0.424915	−	0.905233i	$-0.639696\pi$
$547$	−19.8759			−0.849830			−0.424915	+	0.905233i	$0.639696\pi$
$548$	3.26719	−	8.26375i	0.139567	−	0.353010i
$549$		−	8.99656i		−	0.383964i
$550$		0			0
$551$	2.11727			0.0901986
$552$	1.60256	−	2.52932i	0.0682094	−	0.107655i
$553$		−	10.8793i		−	0.462635i
$554$	−26.1008	−	4.97240i	−1.10892	−	0.211257i
$555$		0			0
$556$	−14.8337	+	37.5190i	−0.629087	+	1.59116i
$557$	3.12070			0.132228			0.0661142	−	0.997812i	$-0.478940\pi$
$557$	3.12070			0.132228			0.0661142	+	0.997812i	$0.478940\pi$
$558$	4.94137	+	0.941367i	0.209185	+	0.0398512i
$559$	10.4622			0.442503
$560$		0			0
$561$	−33.9931			−1.43519
$562$	−23.4492	−	4.46725i	−0.989145	−	0.188439i
$563$	0.651639			0.0274633			0.0137317	−	0.999906i	$-0.495629\pi$
$563$	0.651639			0.0274633			0.0137317	+	0.999906i	$0.495629\pi$
$564$	−7.39400	+	18.7018i	−0.311344	+	0.787487i
$565$		0			0
$566$	−27.7846	−	5.29317i	−1.16787	−	0.222488i
$567$			0.941367i			0.0395337i
$568$	−31.0518	−	19.6742i	−1.30290	−	0.825510i
$569$	−26.9966			−1.13175			−0.565877	−	0.824489i	$-0.691462\pi$
$569$	−26.9966			−1.13175			−0.565877	+	0.824489i	$0.691462\pi$
$570$		0			0
$571$		−	14.9414i		−	0.625277i	−0.949872	−	0.312638i	$-0.898787\pi$
$571$		−	14.9414i		−	0.625277i	0.949872	−	0.312638i	$-0.101213\pi$
$572$	18.3810	−	46.4914i	0.768549	−	1.94390i
$573$	8.00000			0.334205
$574$	0.967346	−	5.07774i	0.0403763	−	0.211941i
$575$		0			0
$576$	3.41683	+	7.23362i	0.142368	+	0.301401i
$577$		−	8.87930i		−	0.369650i	−0.982771	−	0.184825i	$-0.940828\pi$
$577$		−	8.87930i		−	0.369650i	0.982771	−	0.184825i	$-0.0591718\pi$
$578$	−55.7177	−	10.6146i	−2.31755	−	0.441511i
$579$		−	4.87930i		−	0.202777i
$580$		0			0
$581$		−	5.53781i		−	0.229747i
$582$	4.52932	−	23.7750i	0.187746	−	0.985506i
$583$			8.99656i			0.372600i
$584$	−9.08279	+	14.3354i	−0.375849	+	0.593202i
$585$		0			0
$586$	28.1008	+	5.35342i	1.16083	+	0.221148i
$587$	1.23109			0.0508127			0.0254064	−	0.999677i	$-0.491912\pi$
$587$	1.23109			0.0508127			0.0254064	+	0.999677i	$0.491912\pi$
$588$	−11.3712	−	4.49575i	−0.468940	−	0.185402i
$589$			3.76547i			0.155153i
$590$		0			0
$591$	2.88617			0.118721
$592$	−21.7129	−	20.3500i	−0.892397	−	0.836379i
$593$		−	3.55691i		−	0.146065i	−0.997330	−	0.0730325i	$-0.976732\pi$
$593$		−	3.55691i		−	0.146065i	0.997330	−	0.0730325i	$-0.0232677\pi$
$594$	−1.19051	+	6.24914i	−0.0488471	+	0.256405i
$595$		0			0
$596$	1.47068	−	3.71982i	0.0602415	−	0.152370i
$597$	−17.6742			−0.723356
$598$	−1.55691	+	8.17246i	−0.0636670	+	0.334197i
$599$	19.2242			0.785480			0.392740	−	0.919649i	$-0.371527\pi$
$599$	19.2242			0.785480			0.392740	+	0.919649i	$0.371527\pi$
$600$		0			0
$601$	−27.7586			−1.13230			−0.566148	−	0.824303i	$-0.691567\pi$
$601$	−27.7586			−1.13230			−0.566148	+	0.824303i	$0.691567\pi$
$602$	−0.469065	+	2.46219i	−0.0191177	+	0.100351i
$603$	−4.00000			−0.162893
$604$	17.9931	+	7.11383i	0.732130	+	0.289458i
$605$		0			0
$606$	−0.529317	+	2.77846i	−0.0215020	+	0.112867i
$607$			7.16902i			0.290982i	0.989360	+	0.145491i	$0.0464761\pi$
$607$			7.16902i			0.290982i	−0.989360	+	0.145491i	$0.953524\pi$
$608$	−4.84053	+	3.52588i	−0.196309	+	0.142993i
$609$	−1.88273			−0.0762922
$610$		0			0
$611$		−	55.8759i		−	2.26050i
$612$	−5.55691	+	14.0552i	−0.224625	+	0.568148i
$613$	−9.55691			−0.386000			−0.193000	−	0.981199i	$-0.561822\pi$
$613$	−9.55691			−0.386000			−0.193000	+	0.981199i	$0.561822\pi$
$614$	11.2672	+	2.14648i	0.454707	+	0.0866250i
$615$		0			0
$616$	10.1173	+	6.41023i	0.407636	+	0.258276i
$617$			1.32926i			0.0535139i	0.999642	+	0.0267569i	$0.00851802\pi$
$617$			1.32926i			0.0535139i	−0.999642	+	0.0267569i	$0.991482\pi$
$618$	−2.69223	+	14.1319i	−0.108297	+	0.568467i
$619$			28.1725i			1.13235i	0.824286	+	0.566173i	$0.191577\pi$
$619$			28.1725i			1.13235i	−0.824286	+	0.566173i	$0.808423\pi$
$620$		0			0
$621$		−	1.05863i		−	0.0424815i
$622$	44.2829	+	8.43621i	1.77558	+	0.338261i
$623$			3.87586i			0.155283i
$624$	−16.2181	−	15.2001i	−0.649244	−	0.608489i
$625$		0			0
$626$	−1.35342	+	7.10428i	−0.0540934	+	0.283944i
$627$	−4.76203			−0.190177
$628$	8.04564	+	3.18096i	0.321056	+	0.126934i
$629$		−	56.2208i		−	2.24167i
$630$		0			0
$631$	−23.3224			−0.928449			−0.464225	−	0.885717i	$-0.653667\pi$
$631$	−23.3224			−0.928449			−0.464225	+	0.885717i	$0.653667\pi$
$632$	−27.6121	−	17.4948i	−1.09835	−	0.695907i
$633$		−	23.9379i		−	0.951447i
$634$	34.2372	+	6.52244i	1.35973	+	0.259039i
$635$		0			0
$636$	3.71982	+	1.47068i	0.147501	+	0.0583164i
$637$	33.9740			1.34610
$638$	−12.4983	−	2.38101i	−0.494812	−	0.0942653i
$639$	−12.9966			−0.514136
$640$		0			0
$641$	27.1070			1.07066			0.535330	−	0.844643i	$-0.320187\pi$
$641$	27.1070			1.07066			0.535330	+	0.844643i	$0.320187\pi$
$642$	23.9379	+	4.56035i	0.944755	+	0.179983i
$643$	−20.3449			−0.802325			−0.401163	−	0.916007i	$-0.631394\pi$
$643$	−20.3449			−0.802325			−0.401163	+	0.916007i	$0.631394\pi$
$644$	−1.85352	−	0.732814i	−0.0730388	−	0.0288769i
$645$		0			0
$646$	−11.1138	−	2.11727i	−0.437268	−	0.0833027i
$647$			37.6965i			1.48200i	0.671503	+	0.741002i	$0.265649\pi$
$647$			37.6965i			1.48200i	−0.671503	+	0.741002i	$0.734351\pi$
$648$	2.38923	+	1.51380i	0.0938578	+	0.0594676i
$649$	−38.2277			−1.50057
$650$		0			0
$651$		−	3.34836i		−	0.131233i
$652$	11.3776	+	4.49828i	0.445580	+	0.176166i
$653$	8.64476			0.338296			0.169148	−	0.985591i	$-0.445898\pi$
$653$	8.64476			0.338296			0.169148	+	0.985591i	$0.445898\pi$
$654$	0.498281	−	2.61555i	0.0194843	−	0.102276i
$655$		0			0
$656$	−11.3319	−	10.6206i	−0.442438	−	0.414665i
$657$			6.00000i			0.234082i
$658$	13.1499	+	2.50516i	0.512637	+	0.0976612i
$659$			29.2603i			1.13982i	0.821707	+	0.569910i	$0.193022\pi$
$659$			29.2603i			1.13982i	−0.821707	+	0.569910i	$0.806978\pi$
$660$		0			0
$661$		−	28.7620i		−	1.11871i	−0.828927	−	0.559357i	$-0.811048\pi$
$661$		−	28.7620i		−	1.11871i	0.828927	−	0.559357i	$-0.188952\pi$
$662$	−2.92494	+	15.3534i	−0.113681	+	0.596728i
$663$		−	41.9931i		−	1.63088i
$664$	−14.0552	−	8.90528i	−0.545447	−	0.345592i
$665$		0			0
$666$	−10.3354	−	1.96896i	−0.400488	−	0.0762958i
$667$	2.11727			0.0819809
$668$	4.45264	−	11.2621i	0.172278	−	0.435745i
$669$		−	24.0552i		−	0.930028i
$670$		0			0
$671$	−40.4691			−1.56229
$672$	4.30434	−	3.13531i	0.166043	−	0.120947i
$673$			18.0000i			0.693849i	0.937893	+	0.346925i	$0.112774\pi$
$673$			18.0000i			0.693849i	−0.937893	+	0.346925i	$0.887226\pi$
$674$	5.29135	−	27.7750i	0.203815	−	1.06985i
$675$		0			0
$676$	33.2539	+	13.1474i	1.27900	+	0.505669i
$677$	−42.8724			−1.64772			−0.823860	−	0.566793i	$-0.808184\pi$
$677$	−42.8724			−1.64772			−0.823860	+	0.566793i	$0.808184\pi$
$678$	−4.05520	+	21.2863i	−0.155739	+	0.817495i
$679$	−16.1104			−0.618260
$680$		0			0
$681$	−11.1138			−0.425883
$682$	4.23453	−	22.2277i	0.162149	−	0.851141i
$683$	26.1173			0.999349			0.499675	−	0.866213i	$-0.333453\pi$
$683$	26.1173			0.999349			0.499675	+	0.866213i	$0.333453\pi$
$684$	−0.778457	+	1.96896i	−0.0297651	+	0.0752852i
$685$		0			0
$686$	−3.26719	+	17.1499i	−0.124742	+	0.654787i
$687$			17.2311i			0.657407i
$688$	5.49484	+	5.14992i	0.209489	+	0.196339i
$689$	−11.1138			−0.423403
$690$		0			0
$691$			5.29317i			0.201362i	0.994919	+	0.100681i	$0.0321021\pi$
$691$			5.29317i			0.201362i	−0.994919	+	0.100681i	$0.967898\pi$
$692$	−31.3940	−	12.4121i	−1.19342	−	0.471835i
$693$	4.23453			0.160857
$694$	−9.55691	−	1.82066i	−0.362776	−	0.0691114i
$695$		0			0
$696$	−3.02760	+	4.77846i	−0.114761	+	0.181127i
$697$		−	29.3415i		−	1.11139i
$698$	1.26031	−	6.61555i	0.0477035	−	0.250402i
$699$		−	8.44309i		−	0.319347i
$700$		0			0
$701$		−	7.99312i		−	0.301896i	−0.988542	−	0.150948i	$-0.951767\pi$
$701$		−	7.99312i		−	0.301896i	0.988542	−	0.150948i	$-0.0482326\pi$
$702$	−7.71982	−	1.47068i	−0.291366	−	0.0555074i
$703$		−	7.87586i		−	0.297044i
$704$	32.5389	−	15.3698i	1.22635	−	0.579273i
$705$		0			0
$706$	−1.00344	+	5.26719i	−0.0377649	+	0.198233i
$707$	1.88273			0.0708075
$708$	−6.24914	+	15.8061i	−0.234857	+	0.594028i
$709$		−	28.9966i		−	1.08899i	−0.838764	−	0.544494i	$-0.816722\pi$
$709$		−	28.9966i		−	1.08899i	0.838764	−	0.544494i	$-0.183278\pi$
$710$		0			0
$711$	−11.5569			−0.433418
$712$	9.83709	+	6.23271i	0.368661	+	0.233581i
$713$			3.76547i			0.141018i
$714$	9.88273	+	1.88273i	0.369852	+	0.0704595i
$715$		0			0
$716$	−7.80605	+	19.7440i	−0.291726	+	0.737867i
$717$	10.1173			0.377836
$718$	18.0552	+	3.43965i	0.673814	+	0.128367i
$719$	−26.8793			−1.00243			−0.501214	−	0.865323i	$-0.667113\pi$
$719$	−26.8793			−1.00243			−0.501214	+	0.865323i	$0.667113\pi$
$720$		0			0
$721$	9.57602			0.356630
$722$	24.8384	+	4.73190i	0.924391	+	0.176103i
$723$	−16.8793			−0.627748
$724$	10.3810	−	26.2569i	0.385807	−	0.975829i
$725$		0			0
$726$	12.8289	+	2.44400i	0.476124	+	0.0907052i
$727$			41.8138i			1.55079i	0.631478	+	0.775394i	$0.282449\pi$
$727$			41.8138i			1.55079i	−0.631478	+	0.775394i	$0.717551\pi$
$728$	−7.91883	+	12.4983i	−0.293491	+	0.463217i
$729$	1.00000			0.0370370
$730$		0			0
$731$			14.2277i			0.526229i
$732$	−6.61555	+	16.7328i	−0.244518	+	0.618463i
$733$	−30.0844			−1.11119			−0.555597	−	0.831452i	$-0.687510\pi$
$733$	−30.0844			−1.11119			−0.555597	+	0.831452i	$0.687510\pi$
$734$	−6.06980	+	31.8613i	−0.224041	+	1.17602i
$735$		0			0
$736$	−4.84053	+	3.52588i	−0.178424	+	0.129966i
$737$			17.9931i			0.662785i
$738$	−5.39400	−	1.02760i	−0.198556	−	0.0378264i
$739$			29.0449i			1.06843i	0.845348	+	0.534217i	$0.179393\pi$
$739$			29.0449i			1.06843i	−0.845348	+	0.534217i	$0.820607\pi$
$740$		0			0
$741$		−	5.88273i		−	0.216108i
$742$	0.498281	−	2.61555i	0.0182925	−	0.0960198i
$743$			43.2863i			1.58802i	0.607905	+	0.794010i	$0.292010\pi$
$743$			43.2863i			1.58802i	−0.607905	+	0.794010i	$0.707990\pi$
$744$	−8.49828	−	5.38445i	−0.311562	−	0.197404i
$745$		0			0
$746$	−21.4492	−	4.08623i	−0.785311	−	0.149608i
$747$	−5.88273			−0.215238
$748$	63.2242	+	24.9966i	2.31171	+	0.913965i
$749$		−	16.2208i		−	0.592694i
$750$		0			0
$751$	41.7846			1.52474			0.762370	−	0.647141i	$-0.224036\pi$
$751$	41.7846			1.52474			0.762370	+	0.647141i	$0.224036\pi$
$752$	27.5044	−	29.3465i	1.00298	−	1.07016i
$753$			11.8466i			0.431716i
$754$	2.94137	−	15.4396i	0.107118	−	0.562279i
$755$		0			0
$756$	0.692226	−	1.75086i	0.0251760	−	0.0636781i
$757$	−16.3258			−0.593372			−0.296686	−	0.954975i	$-0.595881\pi$
$757$	−16.3258			−0.593372			−0.296686	+	0.954975i	$0.595881\pi$
$758$	1.66463	−	8.73787i	0.0604620	−	0.317374i
$759$	−4.76203			−0.172851
$760$		0			0
$761$	50.2208			1.82050			0.910251	−	0.414057i	$-0.135889\pi$
$761$	50.2208			1.82050			0.910251	+	0.414057i	$0.135889\pi$
$762$	−4.80949	+	25.2457i	−0.174230	+	0.914555i
$763$	−1.77234			−0.0641631
$764$	−14.8793	−	5.88273i	−0.538314	−	0.212830i
$765$		0			0
$766$	0.778457	−	4.08623i	0.0281268	−	0.147642i
$767$		−	47.2242i		−	1.70517i
$768$	−1.03581	−	15.9664i	−0.0373766	−	0.576139i
$769$	31.3415			1.13020			0.565101	−	0.825021i	$-0.308837\pi$
$769$	31.3415			1.13020			0.565101	+	0.825021i	$0.308837\pi$
$770$		0			0
$771$			10.6707i			0.384297i
$772$	−3.58795	+	9.07506i	−0.129133	+	0.326619i
$773$	9.11383			0.327802			0.163901	−	0.986477i	$-0.447592\pi$
$773$	9.11383			0.327802			0.163901	+	0.986477i	$0.447592\pi$
$774$	2.61555	+	0.498281i	0.0940139	+	0.0179103i
$775$		0			0
$776$	−25.9069	+	40.8888i	−0.930003	+	1.46782i
$777$			7.00344i			0.251247i
$778$	−3.23615	+	16.9870i	−0.116022	+	0.609014i
$779$		−	4.11039i		−	0.147270i
$780$		0			0
$781$			58.4622i			2.09194i
$782$	−11.1138	−	2.11727i	−0.397430	−	0.0757133i
$783$			2.00000i			0.0714742i
$784$	17.8435	+	16.7234i	0.637267	+	0.597265i
$785$		0			0
$786$	1.68879	−	8.86469i	0.0602371	−	0.316193i
$787$	36.2208			1.29113			0.645566	−	0.763705i	$-0.276622\pi$
$787$	36.2208			1.29113			0.645566	+	0.763705i	$0.276622\pi$
$788$	−5.36802	−	2.12232i	−0.191228	−	0.0756046i
$789$		−	1.94480i		−	0.0692369i
$790$		0			0
$791$	14.4240			0.512858
$792$	6.80949	−	10.7474i	0.241965	−	0.381893i
$793$		−	49.9931i		−	1.77531i
$794$	−7.39400	−	1.40861i	−0.262403	−	0.0499898i
$795$		0			0
$796$	32.8724	+	12.9966i	1.16513	+	0.460651i
$797$	10.0000			0.354218			0.177109	−	0.984191i	$-0.443325\pi$
$797$	10.0000			0.354218			0.177109	+	0.984191i	$0.443325\pi$
$798$	1.38445	+	0.263748i	0.0490091	+	0.00933659i
$799$	75.9862			2.68820
$800$		0			0
$801$	4.11727			0.145476
$802$	9.71982	+	1.85170i	0.343219	+	0.0653857i
$803$	26.9897			0.952445
$804$	7.43965	+	2.94137i	0.262376	+	0.103734i
$805$		0			0
$806$	27.4588	+	5.23109i	0.967193	+	0.184257i
$807$		−	9.76547i		−	0.343761i
$808$	3.02760	−	4.77846i	0.106511	−	0.168106i
$809$	−47.5760			−1.67268			−0.836342	−	0.548208i	$-0.815310\pi$
$809$	−47.5760			−1.67268			−0.836342	+	0.548208i	$0.815310\pi$
$810$		0			0
$811$		−	20.5174i		−	0.720463i	−0.932863	−	0.360231i	$-0.882698\pi$
$811$		−	20.5174i		−	0.720463i	0.932863	−	0.360231i	$-0.117302\pi$
$812$	3.50172	+	1.38445i	0.122886	+	0.0485848i
$813$	−3.44652			−0.120875
$814$	−8.85696	+	46.4914i	−0.310436	+	1.62952i
$815$		0			0
$816$	20.6707	−	22.0552i	0.723621	−	0.772086i
$817$			1.99312i			0.0697306i
$818$	−22.5439	−	4.29478i	−0.788230	−	0.150164i
$819$			5.23109i			0.182789i
$820$		0			0
$821$		−	44.4622i		−	1.55174i	−0.630892	−	0.775871i	$-0.717311\pi$
$821$		−	44.4622i		−	1.55174i	0.630892	−	0.775871i	$-0.282689\pi$
$822$	−1.17590	+	6.17246i	−0.0410142	+	0.215289i
$823$		−	32.1656i		−	1.12122i	−0.828079	−	0.560611i	$-0.810566\pi$
$823$		−	32.1656i		−	1.12122i	0.828079	−	0.560611i	$-0.189434\pi$
$824$	15.3991	−	24.3043i	0.536452	−	0.846682i
$825$		0			0
$826$	11.1138	+	2.11727i	0.386700	+	0.0736691i
$827$	−20.0000			−0.695468			−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000			−0.695468			−0.347734	+	0.937593i	$0.613049\pi$
$828$	−0.778457	+	1.96896i	−0.0270533	+	0.0684262i
$829$			33.8827i			1.17680i	0.808571	+	0.588398i	$0.200241\pi$
$829$			33.8827i			1.17680i	−0.808571	+	0.588398i	$0.799759\pi$
$830$		0			0
$831$	18.7880			0.651749
$832$	18.9870	+	40.1966i	0.658256	+	1.39357i
$833$			46.2017i			1.60079i
$834$	5.33881	−	28.0242i	0.184868	−	0.970397i
$835$		0			0
$836$	8.85696	+	3.50172i	0.306324	+	0.121109i
$837$	−3.55691			−0.122945
$838$	4.13187	−	21.6888i	0.142733	−	0.749227i
$839$	−4.52750			−0.156307			−0.0781533	−	0.996941i	$-0.524902\pi$
$839$	−4.52750			−0.156307			−0.0781533	+	0.996941i	$0.524902\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	8.79488	−	46.1656i	0.303092	−	1.59097i
$843$	16.8793			0.581354
$844$	−17.6026	+	44.5224i	−0.605905	+	1.53253i
$845$		0			0
$846$	2.66119	−	13.9690i	0.0914936	−	0.480263i
$847$		−	8.69308i		−	0.298698i
$848$	−5.83709	−	5.47068i	−0.200447	−	0.187864i
$849$	20.0000			0.686398
$850$		0			0
$851$		−	7.87586i		−	0.269981i
$852$	24.1725	+	9.55691i	0.828135	+	0.327414i
$853$	50.4293			1.72667			0.863334	−	0.504633i	$-0.168372\pi$
$853$	50.4293			1.72667			0.863334	+	0.504633i	$0.168372\pi$
$854$	11.7655	+	2.24141i	0.402606	+	0.0766994i
$855$		0			0
$856$	−41.1690	−	26.0844i	−1.40713	−	0.891547i
$857$			26.4362i			0.903044i	0.892260	+	0.451522i	$0.149119\pi$
$857$			26.4362i			0.903044i	−0.892260	+	0.451522i	$0.850881\pi$
$858$	−6.61555	+	34.7259i	−0.225851	+	1.18552i
$859$			0.406994i			0.0138865i	0.999976	+	0.00694323i	$0.00221012\pi$
$859$			0.406994i			0.0138865i	−0.999976	+	0.00694323i	$0.997790\pi$
$860$		0			0
$861$			3.65508i			0.124565i
$862$	−18.0552	−	3.43965i	−0.614962	−	0.117155i
$863$			29.9311i			1.01886i	0.860511	+	0.509432i	$0.170145\pi$
$863$			29.9311i			1.01886i	−0.860511	+	0.509432i	$0.829855\pi$
$864$	−3.33060	−	4.57243i	−0.113309	−	0.155557i
$865$		0			0
$866$	5.35342	−	28.1008i	0.181917	−	0.954905i
$867$	40.1070			1.36210
$868$	−2.46219	+	6.22766i	−0.0835722	+	0.211380i
$869$			51.9862i			1.76351i
$870$		0			0
$871$	−22.2277			−0.753155
$872$	−2.85008	+	4.49828i	−0.0965159	+	0.152331i
$873$			17.1138i			0.579215i
$874$	−1.55691	−	0.296604i	−0.0526634	−	0.0100328i
$875$		0			0
$876$	4.41205	−	11.1595i	0.149069	−	0.377044i
$877$	−11.2051			−0.378370			−0.189185	−	0.981941i	$-0.560585\pi$
$877$	−11.2051			−0.378370			−0.189185	+	0.981941i	$0.560585\pi$
$878$	7.55691	+	1.43965i	0.255034	+	0.0485858i
$879$	−20.2277			−0.682262
$880$		0			0
$881$	−48.3380			−1.62855			−0.814275	−	0.580479i	$-0.802865\pi$
$881$	−48.3380			−1.62855			−0.814275	+	0.580479i	$0.802865\pi$
$882$	8.49351	+	1.61808i	0.285991	+	0.0544834i
$883$	50.5726			1.70190			0.850951	−	0.525244i	$-0.176026\pi$
$883$	50.5726			1.70190			0.850951	+	0.525244i	$0.176026\pi$
$884$	−30.8793	+	78.1035i	−1.03858	+	2.62691i
$885$		0			0
$886$	21.3224	+	4.06207i	0.716339	+	0.136468i
$887$		−	48.0483i		−	1.61330i	−0.591026	−	0.806652i	$-0.701277\pi$
$887$		−	48.0483i		−	1.61330i	0.591026	−	0.806652i	$-0.298723\pi$
$888$	17.7750	+	11.2621i	0.596491	+	0.377932i
$889$	17.1070			0.573749
$890$		0			0
$891$		−	4.49828i		−	0.150698i
$892$	−17.6888	+	44.7405i	−0.592264	+	1.49802i
$893$	10.6448			0.356213
$894$	−0.529317	+	2.77846i	−0.0177030	+	0.0929255i
$895$		0			0
$896$	−10.3112	+	2.66625i	−0.344473	+	0.0890731i
$897$		−	5.88273i		−	0.196419i
$898$	−5.87318	−	1.11888i	−0.195991	−	0.0373377i
$899$		−	7.11383i		−	0.237259i
$900$		0			0
$901$		−	15.1138i		−	0.503515i
$902$	−4.62242	+	24.2637i	−0.153910	+	0.807894i
$903$		−	1.77234i		−	0.0589799i
$904$	23.1950	−	36.6087i	0.771454	−	1.21759i
$905$		0			0
$906$	−13.4396	−	2.56035i	−0.446502	−	0.0850620i
$907$	−6.46219			−0.214573			−0.107287	−	0.994228i	$-0.534216\pi$
$907$	−6.46219			−0.214573			−0.107287	+	0.994228i	$0.534216\pi$
$908$	20.6707	+	8.17246i	0.685983	+	0.271213i
$909$		−	2.00000i		−	0.0663358i
$910$		0			0
$911$	50.3380			1.66777			0.833887	−	0.551935i	$-0.186110\pi$
$911$	50.3380			1.66777			0.833887	+	0.551935i	$0.186110\pi$
$912$	2.89572	−	3.08967i	0.0958870	−	0.102309i
$913$			26.4622i			0.875771i
$914$	−0.701778	+	3.68373i	−0.0232128	+	0.121847i
$915$		0			0
$916$	12.6707	−	32.0483i	0.418653	−	1.05891i
$917$	−6.00688			−0.198365
$918$	2.00000	−	10.4983i	0.0660098	−	0.346495i
$919$	−46.4362			−1.53179			−0.765895	−	0.642966i	$-0.777704\pi$
$919$	−46.4362			−1.53179			−0.765895	+	0.642966i	$0.777704\pi$
$920$		0			0
$921$	−8.11039			−0.267246
$922$	−2.70865	+	14.2181i	−0.0892048	+	0.468248i
$923$	−72.2208			−2.37718
$924$	−7.87586	−	3.11383i	−0.259097	−	0.102437i
$925$		0			0
$926$	5.04403	−	26.4768i	0.165757	−	0.870082i
$927$		−	10.1725i		−	0.334107i
$928$	9.14486	−	6.66119i	0.300195	−	0.218664i
$929$	35.9931			1.18090			0.590448	−	0.807076i	$-0.298951\pi$
$929$	35.9931			1.18090			0.590448	+	0.807076i	$0.298951\pi$
$930$		0			0
$931$			6.47230i			0.212121i
$932$	−6.20855	+	15.7034i	−0.203368	+	0.514382i
$933$	−31.8759			−1.04357
$934$	−5.71027	−	1.08785i	−0.186846	−	0.0355955i
$935$		0			0
$936$	13.2767	+	8.41205i	0.433964	+	0.274956i
$937$			2.70360i			0.0883227i	0.999024	+	0.0441613i	$0.0140616\pi$
$937$			2.70360i			0.0883227i	−0.999024	+	0.0441613i	$0.985938\pi$
$938$	0.996562	−	5.23109i	0.0325389	−	0.170801i
$939$		−	5.11383i		−	0.166883i
$940$		0			0
$941$			17.7655i			0.579138i	0.957157	+	0.289569i	$0.0935119\pi$
$941$			17.7655i			0.579138i	−0.957157	+	0.289569i	$0.906488\pi$
$942$	−6.00955	−	1.14486i	−0.195802	−	0.0373017i
$943$		−	4.11039i		−	0.133853i
$944$	23.2457	−	24.8026i	0.756583	−	0.807256i
$945$		0			0
$946$	2.24141	−	11.7655i	0.0728745	−	0.382528i
$947$	−26.2277			−0.852284			−0.426142	−	0.904656i	$-0.640128\pi$
$947$	−26.2277			−0.852284			−0.426142	+	0.904656i	$0.640128\pi$
$948$	21.4948	+	8.49828i	0.698120	+	0.276011i
$949$			33.3415i			1.08231i
$950$		0			0
$951$	−24.6448			−0.799161
$952$	−16.9966	−	10.7689i	−0.550862	−	0.349022i
$953$		−	9.09472i		−	0.294607i	−0.989091	−	0.147304i	$-0.952941\pi$
$953$		−	9.09472i		−	0.294607i	0.989091	−	0.147304i	$-0.0470594\pi$
$954$	−2.77846	−	0.529317i	−0.0899559	−	0.0171373i
$955$		0			0
$956$	−18.8172	−	7.43965i	−0.608593	−	0.240615i
$957$	8.99656			0.290818
$958$	35.0518	+	6.67762i	1.13247	+	0.215744i
$959$	4.18257			0.135062
$960$		0			0
$961$	−18.3484			−0.591883
$962$	−57.4328	−	10.9414i	−1.85171	−	0.352764i
$963$	−17.2311			−0.555264
$964$	31.3940	+	12.4121i	1.01113	+	0.399765i
$965$		0			0
$966$	1.38445	+	0.263748i	0.0445440	+	0.00848597i
$967$		−	7.47574i		−	0.240404i	−0.992749	−	0.120202i	$-0.961646\pi$
$967$		−	7.47574i		−	0.240404i	0.992749	−	0.120202i	$-0.0383542\pi$
$968$	−22.0634	−	13.9792i	−0.709145	−	0.449309i
$969$	8.00000			0.256997
$970$		0			0
$971$			41.0777i			1.31825i	0.752035	+	0.659124i	$0.229073\pi$
$971$			41.0777i			1.31825i	−0.752035	+	0.659124i	$0.770927\pi$
$972$	−1.85991	−	0.735342i	−0.0596567	−	0.0235861i
$973$	−18.9897			−0.608781
$974$	5.80605	−	30.4768i	0.186038	−	0.976540i
$975$		0			0
$976$	24.6087	−	26.2569i	0.787704	−	0.840462i
$977$		−	4.20855i		−	0.134644i	−0.997731	−	0.0673218i	$-0.978555\pi$
$977$		−	4.20855i		−	0.134644i	0.997731	−	0.0673218i	$-0.0214454\pi$
$978$	−8.49828	−	1.61899i	−0.271745	−	0.0517694i
$979$		−	18.5206i		−	0.591922i
$980$		0			0
$981$			1.88273i			0.0601111i
$982$	−1.98539	+	10.4216i	−0.0633564	+	0.332567i
$983$			8.35504i			0.266484i	0.991084	+	0.133242i	$0.0425388\pi$
$983$			8.35504i			0.266484i	−0.991084	+	0.133242i	$0.957461\pi$
$984$	9.27674	+	5.87768i	0.295732	+	0.187374i
$985$		0			0
$986$	20.9966	+	4.00000i	0.668667	+	0.127386i
$987$	−9.46563			−0.301294
$988$	−4.32582	+	10.9414i	−0.137623	+	0.348091i
$989$			1.99312i			0.0633777i
$990$		0			0
$991$	−13.9087			−0.441825			−0.220912	−	0.975294i	$-0.570903\pi$
$991$	−13.9087			−0.441825			−0.220912	+	0.975294i	$0.570903\pi$
$992$	11.8466	+	16.2637i	0.376131	+	0.516375i
$993$		−	11.0518i		−	0.350717i
$994$	3.23797	−	16.9966i	0.102702	−	0.539098i
$995$		0			0
$996$	10.9414	+	4.32582i	0.346690	+	0.137069i
$997$	34.8984			1.10524			0.552622	−	0.833432i	$-0.313627\pi$
$997$	34.8984			1.10524			0.552622	+	0.833432i	$0.313627\pi$
$998$	7.71982	−	40.5224i	0.244367	−	1.28272i
$999$	7.43965			0.235380

Display

a_p

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p

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a_n

instead) (See

a_n

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a_n

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n

up to: 50 250 1000 (See only

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a_p

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.d.e.349.6		6
3.2	odd	2		1800.2.d.q.1549.1		6
4.3	odd	2		2400.2.d.f.49.3		6
5.2	odd	4		600.2.k.c.301.4		6
5.3	odd	4		120.2.k.b.61.3	✓	6
5.4	even	2		600.2.d.f.349.1		6
8.3	odd	2		2400.2.d.e.49.3		6
8.5	even	2		600.2.d.f.349.2		6
12.11	even	2		7200.2.d.q.2449.3		6
15.2	even	4		1800.2.k.p.901.3		6
15.8	even	4		360.2.k.f.181.4		6
15.14	odd	2		1800.2.d.r.1549.6		6
20.3	even	4		480.2.k.b.241.5		6
20.7	even	4		2400.2.k.c.1201.2		6
20.19	odd	2		2400.2.d.e.49.4		6
24.5	odd	2		1800.2.d.r.1549.5		6
24.11	even	2		7200.2.d.r.2449.3		6
40.3	even	4		480.2.k.b.241.2		6
40.13	odd	4		120.2.k.b.61.4	yes	6
40.19	odd	2		2400.2.d.f.49.4		6
40.27	even	4		2400.2.k.c.1201.5		6
40.29	even	2	inner	600.2.d.e.349.5		6
40.37	odd	4		600.2.k.c.301.3		6
60.23	odd	4		1440.2.k.f.721.5		6
60.47	odd	4		7200.2.k.p.3601.3		6
60.59	even	2		7200.2.d.r.2449.4		6
80.3	even	4		3840.2.a.bo.1.2		3
80.13	odd	4		3840.2.a.bq.1.2		3
80.43	even	4		3840.2.a.br.1.2		3
80.53	odd	4		3840.2.a.bp.1.2		3
120.29	odd	2		1800.2.d.q.1549.2		6
120.53	even	4		360.2.k.f.181.3		6
120.59	even	2		7200.2.d.q.2449.4		6
120.77	even	4		1800.2.k.p.901.4		6
120.83	odd	4		1440.2.k.f.721.2		6
120.107	odd	4		7200.2.k.p.3601.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.3	✓	6	5.3	odd	4
120.2.k.b.61.4	yes	6	40.13	odd	4
360.2.k.f.181.3		6	120.53	even	4
360.2.k.f.181.4		6	15.8	even	4
480.2.k.b.241.2		6	40.3	even	4
480.2.k.b.241.5		6	20.3	even	4
600.2.d.e.349.5		6	40.29	even	2	inner
600.2.d.e.349.6		6	1.1	even	1	trivial
600.2.d.f.349.1		6	5.4	even	2
600.2.d.f.349.2		6	8.5	even	2
600.2.k.c.301.3		6	40.37	odd	4
600.2.k.c.301.4		6	5.2	odd	4
1440.2.k.f.721.2		6	120.83	odd	4
1440.2.k.f.721.5		6	60.23	odd	4
1800.2.d.q.1549.1		6	3.2	odd	2
1800.2.d.q.1549.2		6	120.29	odd	2
1800.2.d.r.1549.5		6	24.5	odd	2
1800.2.d.r.1549.6		6	15.14	odd	2
1800.2.k.p.901.3		6	15.2	even	4
1800.2.k.p.901.4		6	120.77	even	4
2400.2.d.e.49.3		6	8.3	odd	2
2400.2.d.e.49.4		6	20.19	odd	2
2400.2.d.f.49.3		6	4.3	odd	2
2400.2.d.f.49.4		6	40.19	odd	2
2400.2.k.c.1201.2		6	20.7	even	4
2400.2.k.c.1201.5		6	40.27	even	4
3840.2.a.bo.1.2		3	80.3	even	4
3840.2.a.bp.1.2		3	80.53	odd	4
3840.2.a.bq.1.2		3	80.13	odd	4
3840.2.a.br.1.2		3	80.43	even	4
7200.2.d.q.2449.3		6	12.11	even	2
7200.2.d.q.2449.4		6	120.59	even	2
7200.2.d.r.2449.3		6	24.11	even	2
7200.2.d.r.2449.4		6	60.59	even	2
7200.2.k.p.3601.3		6	60.47	odd	4
7200.2.k.p.3601.4		6	120.107	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	600.2.d.e.349.6

Level	$600$
Weight	$2$
Character	600.349
Analytic conductor	$4.791$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$