LMFDB - Embedded newform 600.2.k.c.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(301,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, 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:	$4.79102412128$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.3
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.c.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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 $

$2$	−0.264658	−	1.38923i	−0.187142	−	0.982333i
$2$	−0.264658	−	1.38923i	−0.187142	−	0.982333i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.85991	+	0.735342i	−0.929956	+	0.367671i
$5$		0			0
$5$		0			0
$6$	−1.38923	+	0.264658i	−0.567150	+	0.108046i
$7$	−0.941367			−0.355803			−0.177902	−	0.984048i	$-0.556931\pi$
$7$	−0.941367			−0.355803			−0.177902	+	0.984048i	$0.556931\pi$
$8$	1.51380	+	2.38923i	0.535209	+	0.844720i
$9$	−1.00000			−0.333333
$10$		0			0
$11$			4.49828i			1.35628i	0.734931	+	0.678141i	$0.237214\pi$
$11$			4.49828i			1.35628i	−0.734931	+	0.678141i	$0.762786\pi$
$12$	0.735342	+	1.85991i	0.212275	+	0.536910i
$13$			5.55691i			1.54121i	0.637313	+	0.770605i	$0.280046\pi$
$13$			5.55691i			1.54121i	−0.637313	+	0.770605i	$0.719954\pi$
$14$	0.249141	+	1.30777i	0.0665856	+	0.349517i
$15$		0			0
$16$	2.91855	−	2.73534i	0.729636	−	0.683835i
$17$	−7.55691			−1.83282			−0.916410	−	0.400240i	$-0.868927\pi$
$17$	−7.55691			−1.83282			−0.916410	+	0.400240i	$0.868927\pi$
$18$	0.264658	+	1.38923i	0.0623806	+	0.327444i
$19$			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
$22$	6.24914	−	1.19051i	1.33232	−	0.253817i
$23$	1.05863			0.220740			0.110370	−	0.993891i	$-0.464796\pi$
$23$	1.05863			0.220740			0.110370	+	0.993891i	$0.464796\pi$
$24$	2.38923	−	1.51380i	0.487699	−	0.309003i
$25$		0			0
$26$	7.71982	−	1.47068i	1.51398	−	0.288425i
$27$			1.00000i			0.192450i
$28$	1.75086	−	0.692226i	0.330881	−	0.130818i
$29$		−	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	$0.396512\pi$
$32$	−4.57243	−	3.33060i	−0.808299	−	0.588772i
$33$	4.49828			0.783050
$34$	2.00000	+	10.4983i	0.342997	+	1.80044i
$35$		0			0
$36$	1.85991	−	0.735342i	0.309985	−	0.122557i
$37$			7.43965i			1.22307i	0.791217	+	0.611535i	$0.209448\pi$
$37$			7.43965i			1.22307i	−0.791217	+	0.611535i	$0.790552\pi$
$38$	1.47068	−	0.280176i	0.238576	−	0.0454506i
$39$	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	$0.598052\pi$
$42$	1.30777	−	0.249141i	0.201794	−	0.0384432i
$43$			1.88273i			0.287114i	0.989642	+	0.143557i	$0.0458541\pi$
$43$			1.88273i			0.287114i	−0.989642	+	0.143557i	$0.954146\pi$
$44$	−3.30777	−	8.36641i	−0.498666	−	1.26128i
$45$		0			0
$46$	−0.280176	−	1.47068i	−0.0413097	−	0.216840i
$47$	10.0552			1.46670			0.733350	−	0.679851i	$-0.237955\pi$
$47$	10.0552			1.46670			0.733350	+	0.679851i	$0.237955\pi$
$48$	−2.73534	−	2.91855i	−0.394813	−	0.421256i
$49$	−6.11383			−0.873404
$50$		0			0
$51$			7.55691i			1.05818i
$52$	−4.08623	−	10.3354i	−0.566658	−	1.43326i
$53$		−	2.00000i		−	0.274721i	−0.990521	−	0.137361i	$-0.956138\pi$
$53$		−	2.00000i		−	0.274721i	0.990521	−	0.137361i	$-0.0438619\pi$
$54$	1.38923	−	0.264658i	0.189050	−	0.0360154i
$55$		0			0
$56$	−1.42504	−	2.24914i	−0.190429	−	0.300554i
$57$	1.05863			0.140219
$58$	−2.77846	+	0.529317i	−0.364829	+	0.0695027i
$59$		−	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	$0.195366\pi$
$61$			8.99656i			1.15189i	−0.817488	+	0.575946i	$0.804634\pi$
$62$	−0.941367	−	4.94137i	−0.119554	−	0.627554i
$63$	0.941367			0.118601
$64$	−3.41683	+	7.23362i	−0.427103	+	0.904203i
$65$		0			0
$66$	−1.19051	−	6.24914i	−0.146541	−	0.769216i
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	14.0552	−	5.55691i	1.70444	−	0.673875i
$69$		−	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	$0.780345\pi$
$72$	−1.51380	−	2.38923i	−0.178403	−	0.281573i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	10.3354	−	1.96896i	1.20146	−	0.228887i
$75$		0			0
$76$	−0.778457	−	1.96896i	−0.0892952	−	0.225856i
$77$		−	4.23453i		−	0.482570i
$78$	−1.47068	−	7.71982i	−0.166522	−	0.874098i
$79$	11.5569			1.30025			0.650127	−	0.759825i	$-0.274716\pi$
$79$	11.5569			1.30025			0.650127	+	0.759825i	$0.274716\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	1.02760	+	5.39400i	0.113479	+	0.595668i
$83$		−	5.88273i		−	0.645714i	−0.946448	−	0.322857i	$-0.895357\pi$
$83$		−	5.88273i		−	0.645714i	0.946448	−	0.322857i	$-0.104643\pi$
$84$	−0.692226	−	1.75086i	−0.0755281	−	0.191034i
$85$		0			0
$86$	2.61555	−	0.498281i	0.282042	−	0.0537310i
$87$	−2.00000			−0.214423
$88$	−10.7474	+	6.80949i	−1.14568	+	0.725894i
$89$	−4.11727			−0.436429			−0.218215	−	0.975901i	$-0.570023\pi$
$89$	−4.11727			−0.436429			−0.218215	+	0.975901i	$0.570023\pi$
$90$		0			0
$91$		−	5.23109i		−	0.548368i
$92$	−1.96896	+	0.778457i	−0.205279	+	0.0811598i
$93$		−	3.55691i		−	0.368835i
$94$	−2.66119	−	13.9690i	−0.274481	−	1.44079i
$95$		0			0
$96$	−3.33060	+	4.57243i	−0.339927	+	0.466672i
$97$	−17.1138			−1.73765			−0.868823	−	0.495123i	$-0.835123\pi$
$97$	−17.1138			−1.73765			−0.868823	+	0.495123i	$0.835123\pi$
$98$	1.61808	+	8.49351i	0.163450	+	0.857974i
$99$		−	4.49828i		−	0.452094i
$100$		0			0
$101$			2.00000i			0.199007i	0.995037	+	0.0995037i	$0.0317255\pi$
$101$			2.00000i			0.199007i	−0.995037	+	0.0995037i	$0.968274\pi$
$102$	10.4983	−	2.00000i	1.03948	−	0.198030i
$103$	−10.1725			−1.00232			−0.501161	−	0.865354i	$-0.667094\pi$
$103$	−10.1725			−1.00232			−0.501161	+	0.865354i	$0.667094\pi$
$104$	−13.2767	+	8.41205i	−1.30189	+	0.824869i
$105$		0			0
$106$	−2.77846	+	0.529317i	−0.269868	+	0.0514118i
$107$			17.2311i			1.66579i	0.553429	+	0.832896i	$0.313319\pi$
$107$			17.2311i			1.66579i	−0.553429	+	0.832896i	$0.686681\pi$
$108$	−0.735342	−	1.85991i	−0.0707583	−	0.178970i
$109$			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
$112$	−2.74742	+	2.57496i	−0.259607	+	0.243311i
$113$	−15.3224			−1.44141			−0.720704	−	0.693243i	$-0.756181\pi$
$113$	−15.3224			−1.44141			−0.720704	+	0.693243i	$0.756181\pi$
$114$	−0.280176	−	1.47068i	−0.0262409	−	0.137742i
$115$		0			0
$116$	1.47068	+	3.71982i	0.136550	+	0.345377i
$117$		−	5.55691i		−	0.513737i
$118$	−11.8061	+	2.24914i	−1.08684	+	0.207050i
$119$	7.11383			0.652124
$120$		0			0
$121$	−9.23453			−0.839503
$122$	12.4983	−	2.38101i	1.13154	−	0.215567i
$123$			3.88273i			0.350094i
$124$	−6.61555	+	2.61555i	−0.594094	+	0.234883i
$125$		0			0
$126$	−0.249141	−	1.30777i	−0.0221952	−	0.116506i
$127$	18.1725			1.61255			0.806273	−	0.591544i	$-0.201481\pi$
$127$	18.1725			1.61255			0.806273	+	0.591544i	$0.201481\pi$
$128$	10.9534	+	2.83231i	0.968157	+	0.250344i
$129$	1.88273			0.165765
$130$		0			0
$131$		−	6.38101i		−	0.557512i	−0.960362	−	0.278756i	$-0.910078\pi$
$131$		−	6.38101i		−	0.557512i	0.960362	−	0.278756i	$-0.0899220\pi$
$132$	−8.36641	+	3.30777i	−0.728202	+	0.287905i
$133$		−	0.996562i		−	0.0864129i
$134$	5.55691	−	1.05863i	0.480044	−	0.0914520i
$135$		0			0
$136$	−11.4396	−	18.0552i	−0.980942	−	1.54822i
$137$	4.44309			0.379598			0.189799	−	0.981823i	$-0.439216\pi$
$137$	4.44309			0.379598			0.189799	+	0.981823i	$0.439216\pi$
$138$	−1.47068	+	0.280176i	−0.125193	+	0.0238502i
$139$			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
$142$	3.43965	+	18.0552i	0.288649	+	1.51516i
$143$	−24.9966			−2.09032
$144$	−2.91855	+	2.73534i	−0.243212	+	0.227945i
$145$		0			0
$146$	−1.58795	−	8.33537i	−0.131420	−	0.689840i
$147$			6.11383i			0.504260i
$148$	−5.47068	−	13.8371i	−0.449687	−	1.13740i
$149$		−	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	$0.371217\pi$
$152$	−2.52932	+	1.60256i	−0.205155	+	0.129985i
$153$	7.55691			0.610940
$154$	−5.88273	+	1.12070i	−0.474044	+	0.0903089i
$155$		0			0
$156$	−10.3354	+	4.08623i	−0.827492	+	0.327160i
$157$		−	4.32582i		−	0.345238i	−0.984989	−	0.172619i	$-0.944777\pi$
$157$		−	4.32582i		−	0.345238i	0.984989	−	0.172619i	$-0.0552229\pi$
$158$	−3.05863	−	16.0552i	−0.243332	−	1.27728i
$159$	−2.00000			−0.158610
$160$		0			0
$161$	−0.996562			−0.0785401
$162$	−0.264658	−	1.38923i	−0.0207935	−	0.109148i
$163$			6.11727i			0.479141i	0.970879	+	0.239571i	$0.0770067\pi$
$163$			6.11727i			0.479141i	−0.970879	+	0.239571i	$0.922993\pi$
$164$	7.22154	−	2.85514i	0.563908	−	0.222949i
$165$		0			0
$166$	−8.17246	+	1.55691i	−0.634306	+	0.120840i
$167$	6.05520			0.468565			0.234283	−	0.972169i	$-0.424726\pi$
$167$	6.05520			0.468565			0.234283	+	0.972169i	$0.424726\pi$
$168$	−2.24914	+	1.42504i	−0.173525	+	0.109944i
$169$	−17.8793			−1.37533
$170$		0			0
$171$		−	1.05863i		−	0.0809557i
$172$	−1.38445	−	3.50172i	−0.105564	−	0.267004i
$173$		−	16.8793i		−	1.28331i	−0.766994	−	0.641655i	$-0.778248\pi$
$173$		−	16.8793i		−	1.28331i	0.766994	−	0.641655i	$-0.221752\pi$
$174$	0.529317	+	2.77846i	0.0401274	+	0.210634i
$175$		0			0
$176$	12.3043	+	13.1284i	0.927474	+	0.989593i
$177$	−8.49828			−0.638770
$178$	1.08967	+	5.71982i	0.0816741	+	0.428719i
$179$			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	$0.175809\pi$
$181$			14.1173i			1.04933i	−0.851309	+	0.524664i	$0.824191\pi$
$182$	−7.26719	+	1.38445i	−0.538680	+	0.102622i
$183$	8.99656			0.665045
$184$	1.60256	+	2.52932i	0.118142	+	0.186464i
$185$		0			0
$186$	−4.94137	+	0.941367i	−0.362319	+	0.0690244i
$187$		−	33.9931i		−	2.48582i
$188$	−18.7018	+	7.39400i	−1.36397	+	0.539263i
$189$		−	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	$0.593466\pi$
$192$	7.23362	+	3.41683i	0.522042	+	0.246588i
$193$	4.87930			0.351219			0.175610	−	0.984460i	$-0.443810\pi$
$193$	4.87930			0.351219			0.175610	+	0.984460i	$0.443810\pi$
$194$	4.52932	+	23.7750i	0.325186	+	1.70695i
$195$		0			0
$196$	11.3712	−	4.49575i	0.812227	−	0.321125i
$197$			2.88617i			0.205631i	0.994700	+	0.102816i	$0.0327852\pi$
$197$			2.88617i			0.205631i	−0.994700	+	0.102816i	$0.967215\pi$
$198$	−6.24914	+	1.19051i	−0.444107	+	0.0846057i
$199$	−17.6742			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$199$	−17.6742			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	2.77846	−	0.529317i	0.195492	−	0.0372426i
$203$			1.88273i			0.132142i
$204$	−5.55691	−	14.0552i	−0.389062	−	0.984061i
$205$		0			0
$206$	2.69223	+	14.1319i	0.187576	+	0.984614i
$207$	−1.05863			−0.0735801
$208$	15.2001	+	16.2181i	1.05393	+	1.12452i
$209$	−4.76203			−0.329396
$210$		0			0
$211$		−	23.9379i		−	1.64795i	−0.566623	−	0.823977i	$-0.691750\pi$
$211$		−	23.9379i		−	1.64795i	0.566623	−	0.823977i	$-0.308250\pi$
$212$	1.47068	+	3.71982i	0.101007	+	0.255479i
$213$			12.9966i			0.890510i
$214$	23.9379	−	4.56035i	1.63636	−	0.311739i
$215$		0			0
$216$	−2.38923	+	1.51380i	−0.162566	+	0.103001i
$217$	−3.34836			−0.227302
$218$	2.61555	−	0.498281i	0.177147	−	0.0337479i
$219$		−	6.00000i		−	0.405442i
$220$		0			0
$221$		−	41.9931i		−	2.82476i
$222$	−1.96896	−	10.3354i	−0.132148	−	0.693665i
$223$	24.0552			1.61086			0.805428	−	0.592694i	$-0.201936\pi$
$223$	24.0552			1.61086			0.805428	+	0.592694i	$0.201936\pi$
$224$	4.30434	+	3.13531i	0.287596	+	0.209487i
$225$		0			0
$226$	4.05520	+	21.2863i	0.269748	+	1.41594i
$227$		−	11.1138i		−	0.737651i	−0.929499	−	0.368825i	$-0.879760\pi$
$227$		−	11.1138i		−	0.737651i	0.929499	−	0.368825i	$-0.120240\pi$
$228$	−1.96896	+	0.778457i	−0.130398	+	0.0515546i
$229$		−	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
$232$	4.77846	−	3.02760i	0.313721	−	0.198772i
$233$	8.44309			0.553125			0.276562	−	0.960996i	$-0.410805\pi$
$233$	8.44309			0.553125			0.276562	+	0.960996i	$0.410805\pi$
$234$	−7.71982	+	1.47068i	−0.504661	+	0.0961416i
$235$		0			0
$236$	6.24914	+	15.8061i	0.406784	+	1.02889i
$237$		−	11.5569i		−	0.750702i
$238$	−1.88273	−	9.88273i	−0.122039	−	0.640602i
$239$	10.1173			0.654432			0.327216	−	0.944950i	$-0.393890\pi$
$239$	10.1173			0.654432			0.327216	+	0.944950i	$0.393890\pi$
$240$		0			0
$241$	16.8793			1.08729			0.543646	−	0.839315i	$-0.317044\pi$
$241$	16.8793			1.08729			0.543646	+	0.839315i	$0.317044\pi$
$242$	2.44400	+	12.8289i	0.157106	+	0.824671i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.61555	−	16.7328i	−0.423517	−	1.07121i
$245$		0			0
$246$	5.39400	−	1.02760i	0.343909	−	0.0655172i
$247$	−5.88273			−0.374309
$248$	5.38445	+	8.49828i	0.341913	+	0.539641i
$249$	−5.88273			−0.372803
$250$		0			0
$251$			11.8466i			0.747753i	0.927478	+	0.373877i	$0.121972\pi$
$251$			11.8466i			0.747753i	−0.927478	+	0.373877i	$0.878028\pi$
$252$	−1.75086	+	0.692226i	−0.110294	+	0.0436062i
$253$			4.76203i			0.299386i
$254$	−4.80949	−	25.2457i	−0.301774	−	1.58406i
$255$		0			0
$256$	1.03581	−	15.9664i	0.0647382	−	0.997902i
$257$	10.6707			0.665623			0.332811	−	0.942993i	$-0.392003\pi$
$257$	10.6707			0.665623			0.332811	+	0.942993i	$0.392003\pi$
$258$	−0.498281	−	2.61555i	−0.0310216	−	0.162837i
$259$		−	7.00344i		−	0.435172i
$260$		0			0
$261$			2.00000i			0.123797i
$262$	−8.86469	+	1.68879i	−0.547662	+	0.104334i
$263$	1.94480			0.119922			0.0599609	−	0.998201i	$-0.480902\pi$
$263$	1.94480			0.119922			0.0599609	+	0.998201i	$0.480902\pi$
$264$	6.80949	+	10.7474i	0.419095	+	0.661458i
$265$		0			0
$266$	−1.38445	+	0.263748i	−0.0848862	+	0.0161715i
$267$			4.11727i			0.251973i
$268$	−2.94137	−	7.43965i	−0.179673	−	0.454449i
$269$			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	$0.466618\pi$
$272$	−22.0552	+	20.6707i	−1.33729	+	1.25335i
$273$	−5.23109			−0.316600
$274$	−1.17590	−	6.17246i	−0.0710387	−	0.372892i
$275$		0			0
$276$	0.778457	+	1.96896i	0.0468576	+	0.118518i
$277$			18.7880i			1.12886i	0.825480	+	0.564431i	$0.190904\pi$
$277$			18.7880i			1.12886i	−0.825480	+	0.564431i	$0.809096\pi$
$278$	28.0242	−	5.33881i	1.68078	−	0.320200i
$279$	−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	$0.667943\pi$
$282$	−13.9690	+	2.66119i	−0.831840	+	0.158472i
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	24.1725	−	9.55691i	1.43437	−	0.567099i
$285$		0			0
$286$	6.61555	+	34.7259i	0.391186	+	2.05339i
$287$	3.65508			0.215752
$288$	4.57243	+	3.33060i	0.269433	+	0.196257i
$289$	40.1070			2.35923
$290$		0			0
$291$			17.1138i			1.00323i
$292$	−11.1595	+	4.41205i	−0.653059	+	0.258196i
$293$			20.2277i			1.18171i	0.806777	+	0.590856i	$0.201210\pi$
$293$			20.2277i			1.18171i	−0.806777	+	0.590856i	$0.798790\pi$
$294$	8.49351	−	1.61808i	0.495351	−	0.0943681i
$295$		0			0
$296$	−17.7750	+	11.2621i	−1.03315	+	0.654598i
$297$	−4.49828			−0.261017
$298$	−2.77846	+	0.529317i	−0.160952	+	0.0306625i
$299$			5.88273i			0.340207i
$300$		0			0
$301$		−	1.77234i		−	0.102156i
$302$	−2.56035	−	13.4396i	−0.147332	−	0.773365i
$303$	2.00000			0.114897
$304$	2.89572	+	3.08967i	0.166081	+	0.177205i
$305$		0			0
$306$	−2.00000	−	10.4983i	−0.114332	−	0.600147i
$307$		−	8.11039i		−	0.462884i	−0.972849	−	0.231442i	$-0.925656\pi$
$307$		−	8.11039i		−	0.462884i	0.972849	−	0.231442i	$-0.0743444\pi$
$308$	3.11383	+	7.87586i	0.177427	+	0.448769i
$309$			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	$0.140798\pi$
$312$	8.41205	+	13.2767i	0.476239	+	0.751647i
$313$	5.11383			0.289051			0.144525	−	0.989501i	$-0.453834\pi$
$313$	5.11383			0.289051			0.144525	+	0.989501i	$0.453834\pi$
$314$	−6.00955	+	1.14486i	−0.339139	+	0.0646084i
$315$		0			0
$316$	−21.4948	+	8.49828i	−1.20918	+	0.478066i
$317$		−	24.6448i		−	1.38419i	−0.721807	−	0.692094i	$-0.756688\pi$
$317$		−	24.6448i		−	1.38419i	0.721807	−	0.692094i	$-0.243312\pi$
$318$	0.529317	+	2.77846i	0.0296826	+	0.155808i
$319$	8.99656			0.503711
$320$		0			0
$321$	17.2311			0.961746
$322$	0.263748	+	1.38445i	0.0146981	+	0.0771525i
$323$		−	8.00000i		−	0.445132i
$324$	−1.85991	+	0.735342i	−0.103328	+	0.0408523i
$325$		0			0
$326$	8.49828	−	1.61899i	0.470676	−	0.0896673i
$327$	1.88273			0.104115
$328$	−5.87768	−	9.27674i	−0.324540	−	0.512222i
$329$	−9.46563			−0.521857
$330$		0			0
$331$		−	11.0518i		−	0.607460i	−0.952758	−	0.303730i	$-0.901768\pi$
$331$		−	11.0518i		−	0.607460i	0.952758	−	0.303730i	$-0.0982320\pi$
$332$	4.32582	+	10.9414i	0.237410	+	0.600486i
$333$		−	7.43965i		−	0.407690i
$334$	−1.60256	−	8.41205i	−0.0876881	−	0.460287i
$335$		0			0
$336$	2.57496	+	2.74742i	0.140476	+	0.149884i
$337$	19.9931			1.08909			0.544547	−	0.838730i	$-0.316701\pi$
$337$	19.9931			1.08909			0.544547	+	0.838730i	$0.316701\pi$
$338$	4.73190	+	24.8384i	0.257382	+	1.35103i
$339$			15.3224i			0.832198i
$340$		0			0
$341$			16.0000i			0.866449i
$342$	−1.47068	+	0.280176i	−0.0795255	+	0.0151502i
$343$	12.3449			0.666563
$344$	−4.49828	+	2.85008i	−0.242531	+	0.153666i
$345$		0			0
$346$	−23.4492	+	4.46725i	−1.26064	+	0.240161i
$347$			6.87930i			0.369300i	0.982804	+	0.184650i	$0.0591151\pi$
$347$			6.87930i			0.369300i	−0.982804	+	0.184650i	$0.940885\pi$
$348$	3.71982	−	1.47068i	0.199403	−	0.0788369i
$349$		−	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
$352$	14.9820	−	20.5681i	0.798541	−	1.09628i
$353$	3.79145			0.201798			0.100899	−	0.994897i	$-0.467828\pi$
$353$	3.79145			0.201798			0.100899	+	0.994897i	$0.467828\pi$
$354$	2.24914	+	11.8061i	0.119540	+	0.627485i
$355$		0			0
$356$	7.65775	−	3.02760i	0.405860	−	0.160462i
$357$		−	7.11383i		−	0.376504i
$358$	14.7474	−	2.80949i	0.779425	−	0.148486i
$359$	−12.9966			−0.685932			−0.342966	−	0.939348i	$-0.611432\pi$
$359$	−12.9966			−0.685932			−0.342966	+	0.939348i	$0.611432\pi$
$360$		0			0
$361$	17.8793			0.941016
$362$	19.6121	−	3.73625i	1.03079	−	0.196373i
$363$			9.23453i			0.484687i
$364$	3.84664	+	9.72938i	0.201619	+	0.509958i
$365$		0			0
$366$	−2.38101	−	12.4983i	−0.124458	−	0.653296i
$367$	−22.9345			−1.19717			−0.598585	−	0.801059i	$-0.704270\pi$
$367$	−22.9345			−1.19717			−0.598585	+	0.801059i	$0.704270\pi$
$368$	3.08967	−	2.89572i	0.161060	−	0.150950i
$369$	3.88273			0.202127
$370$		0			0
$371$			1.88273i			0.0977467i
$372$	2.61555	+	6.61555i	0.135610	+	0.343000i
$373$		−	15.4396i		−	0.799435i	−0.916638	−	0.399717i	$-0.869108\pi$
$373$		−	15.4396i		−	0.799435i	0.916638	−	0.399717i	$-0.130892\pi$
$374$	−47.2242	+	8.99656i	−2.44191	+	0.465201i
$375$		0			0
$376$	15.2215	+	24.0242i	0.784991	+	1.23895i
$377$	11.1138			0.572391
$378$	−1.30777	+	0.249141i	−0.0672646	+	0.0128144i
$379$		−	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
$382$	2.11727	+	11.1138i	0.108329	+	0.568633i
$383$	−2.94137			−0.150297			−0.0751484	−	0.997172i	$-0.523943\pi$
$383$	−2.94137			−0.150297			−0.0751484	+	0.997172i	$0.523943\pi$
$384$	2.83231	−	10.9534i	0.144536	−	0.558966i
$385$		0			0
$386$	−1.29135	−	6.77846i	−0.0657278	−	0.345014i
$387$		−	1.88273i		−	0.0957047i
$388$	31.8302	−	12.5845i	1.61593	−	0.638882i
$389$			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
$392$	−9.25511	−	14.6073i	−0.467453	−	0.737782i
$393$	−6.38101			−0.321880
$394$	4.00955	−	0.763849i	0.201998	−	0.0384822i
$395$		0			0
$396$	3.30777	+	8.36641i	0.166222	+	0.420428i
$397$			5.32238i			0.267123i	0.991041	+	0.133561i	$0.0426413\pi$
$397$			5.32238i			0.267123i	−0.991041	+	0.133561i	$0.957359\pi$
$398$	4.67762	+	24.5535i	0.234468	+	1.23075i
$399$	−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	$0.444106\pi$
$402$	−1.05863	−	5.55691i	−0.0527998	−	0.277154i
$403$			19.7655i			0.984588i
$404$	−1.47068	−	3.71982i	−0.0731692	−	0.185068i
$405$		0			0
$406$	2.61555	−	0.498281i	0.129807	−	0.0247293i
$407$	−33.4656			−1.65883
$408$	−18.0552	+	11.4396i	−0.893865	+	0.566347i
$409$	16.2277			0.802406			0.401203	−	0.915989i	$-0.368592\pi$
$409$	16.2277			0.802406			0.401203	+	0.915989i	$0.368592\pi$
$410$		0			0
$411$		−	4.44309i		−	0.219161i
$412$	18.9199	−	7.48024i	0.932116	−	0.368525i
$413$			8.00000i			0.393654i
$414$	0.280176	+	1.47068i	0.0137699	+	0.0722801i
$415$		0			0
$416$	18.5078	−	25.4086i	0.907421	−	1.24576i
$417$	20.1725			0.987850
$418$	1.26031	+	6.61555i	0.0616438	+	0.323577i
$419$		−	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	$0.300420\pi$
$421$			33.2311i			1.61958i	−0.586717	+	0.809792i	$0.699580\pi$
$422$	−33.2553	+	6.33537i	−1.61884	+	0.308401i
$423$	−10.0552			−0.488900
$424$	4.77846	−	3.02760i	0.232062	−	0.147033i
$425$		0			0
$426$	18.0552	−	3.43965i	0.874777	−	0.166651i
$427$		−	8.46907i		−	0.409847i
$428$	−12.6707	−	32.0483i	−0.612463	−	1.54911i
$429$			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	$0.601338\pi$
$432$	2.73534	+	2.91855i	0.131604	+	0.140419i
$433$	−20.2277			−0.972079			−0.486040	−	0.873937i	$-0.661559\pi$
$433$	−20.2277			−0.972079			−0.486040	+	0.873937i	$0.661559\pi$
$434$	0.886172	+	4.65164i	0.0425376	+	0.223286i
$435$		0			0
$436$	−1.38445	−	3.50172i	−0.0663033	−	0.167702i
$437$			1.12070i			0.0536106i
$438$	−8.33537	+	1.58795i	−0.398279	+	0.0758752i
$439$	−5.43965			−0.259620			−0.129810	−	0.991539i	$-0.541437\pi$
$439$	−5.43965			−0.259620			−0.129810	+	0.991539i	$0.541437\pi$
$440$		0			0
$441$	6.11383			0.291135
$442$	−58.3380	+	11.1138i	−2.77486	+	0.528631i
$443$			15.3484i			0.729223i	0.931160	+	0.364611i	$0.118798\pi$
$443$			15.3484i			0.729223i	−0.931160	+	0.364611i	$0.881202\pi$
$444$	−13.8371	+	5.47068i	−0.656679	+	0.259627i
$445$		0			0
$446$	−6.36641	−	33.4182i	−0.301458	−	1.58240i
$447$	−2.00000			−0.0945968
$448$	3.21649	−	6.80949i	0.151965	−	0.321718i
$449$	4.22766			0.199515			0.0997577	−	0.995012i	$-0.468193\pi$
$449$	4.22766			0.199515			0.0997577	+	0.995012i	$0.468193\pi$
$450$		0			0
$451$		−	17.4656i		−	0.822424i
$452$	28.4983	−	11.2672i	1.34045	−	0.529964i
$453$		−	9.67418i		−	0.454533i
$454$	−15.4396	+	2.94137i	−0.724619	+	0.138045i
$455$		0			0
$456$	1.60256	+	2.52932i	0.0750466	+	0.118446i
$457$	−2.65164			−0.124038			−0.0620192	−	0.998075i	$-0.519754\pi$
$457$	−2.65164			−0.124038			−0.0620192	+	0.998075i	$0.519754\pi$
$458$	−23.9379	+	4.56035i	−1.11855	+	0.213091i
$459$		−	7.55691i		−	0.352727i
$460$		0			0
$461$		−	10.2345i		−	0.476670i	−0.971183	−	0.238335i	$-0.923398\pi$
$461$		−	10.2345i		−	0.476670i	0.971183	−	0.238335i	$-0.0766016\pi$
$462$	1.12070	+	5.88273i	0.0521399	+	0.273690i
$463$	−19.0586			−0.885730			−0.442865	−	0.896588i	$-0.646038\pi$
$463$	−19.0586			−0.885730			−0.442865	+	0.896588i	$0.646038\pi$
$464$	−5.47068	−	5.83709i	−0.253970	−	0.270980i
$465$		0			0
$466$	−2.23453	−	11.7294i	−0.103513	−	0.543353i
$467$			4.11039i			0.190206i	0.995467	+	0.0951031i	$0.0303181\pi$
$467$			4.11039i			0.190206i	−0.995467	+	0.0951031i	$0.969682\pi$
$468$	4.08623	+	10.3354i	0.188886	+	0.477753i
$469$		−	3.76547i		−	0.173873i
$470$		0			0
$471$	−4.32582			−0.199323
$472$	20.3043	−	12.8647i	0.934583	−	0.592145i
$473$	−8.46907			−0.389408
$474$	−16.0552	+	3.05863i	−0.737440	+	0.140488i
$475$		0			0
$476$	−13.2311	+	5.23109i	−0.606446	+	0.239767i
$477$			2.00000i			0.0915737i
$478$	−2.67762	−	14.0552i	−0.122471	−	0.642870i
$479$	−25.2311			−1.15284			−0.576419	−	0.817154i	$-0.695550\pi$
$479$	−25.2311			−1.15284			−0.576419	+	0.817154i	$0.695550\pi$
$480$		0			0
$481$	−41.3415			−1.88501
$482$	−4.46725	−	23.4492i	−0.203477	−	1.06808i
$483$			0.996562i			0.0453451i
$484$	17.1754	−	6.79054i	0.780701	−	0.308661i
$485$		0			0
$486$	−1.38923	+	0.264658i	−0.0630167	+	0.0120051i
$487$	21.9379			0.994102			0.497051	−	0.867721i	$-0.334416\pi$
$487$	21.9379			0.994102			0.497051	+	0.867721i	$0.334416\pi$
$488$	−21.4948	+	13.6190i	−0.973026	+	0.616502i
$489$	6.11727			0.276632
$490$		0			0
$491$		−	7.50172i		−	0.338548i	−0.985569	−	0.169274i	$-0.945858\pi$
$491$		−	7.50172i		−	0.338548i	0.985569	−	0.169274i	$-0.0541423\pi$
$492$	−2.85514	−	7.22154i	−0.128719	−	0.325572i
$493$			15.1138i			0.680693i
$494$	1.55691	+	8.17246i	0.0700489	+	0.367696i
$495$		0			0
$496$	10.3810	−	9.72938i	0.466121	−	0.436862i
$497$	12.2345			0.548794
$498$	1.55691	+	8.17246i	0.0697670	+	0.366217i
$499$		−	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
$502$	16.4577	−	3.13531i	0.734543	−	0.139936i
$503$	23.9379			1.06734			0.533670	−	0.845693i	$-0.320813\pi$
$503$	23.9379			1.06734			0.533670	+	0.845693i	$0.320813\pi$
$504$	1.42504	+	2.24914i	0.0634763	+	0.100185i
$505$		0			0
$506$	6.61555	−	1.26031i	0.294097	−	0.0560276i
$507$			17.8793i			0.794047i
$508$	−33.7992	+	13.3630i	−1.49960	+	0.592886i
$509$			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
$512$	−22.4552	+	2.78667i	−0.992387	+	0.123155i
$513$	−1.05863			−0.0467398
$514$	−2.82410	−	14.8241i	−0.124566	−	0.653863i
$515$		0			0
$516$	−3.50172	+	1.38445i	−0.154155	+	0.0609471i
$517$			45.2311i			1.98926i
$518$	−9.72938	+	1.85352i	−0.427484	+	0.0814389i
$519$	−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	$0.429703\pi$
$522$	2.77846	−	0.529317i	0.121610	−	0.0231676i
$523$		−	25.7586i		−	1.12634i	−0.826340	−	0.563172i	$-0.809581\pi$
$523$		−	25.7586i		−	1.12634i	0.826340	−	0.563172i	$-0.190419\pi$
$524$	4.69223	+	11.8681i	0.204981	+	0.518461i
$525$		0			0
$526$	−0.514709	−	2.70178i	−0.0224424	−	0.117803i
$527$	−26.8793			−1.17088
$528$	13.1284	−	12.3043i	0.571342	−	0.535477i
$529$	−21.8793			−0.951274
$530$		0			0
$531$			8.49828i			0.368794i
$532$	0.732814	+	1.85352i	0.0317715	+	0.0803602i
$533$		−	21.5760i		−	0.934561i
$534$	5.71982	−	1.08967i	0.247521	−	0.0471546i
$535$		0			0
$536$	−9.55691	+	6.05520i	−0.412796	+	0.261545i
$537$	10.6155			0.458095
$538$	13.5665	−	2.58451i	0.584892	−	0.111426i
$539$		−	27.5017i		−	1.18458i
$540$		0			0
$541$			12.3449i			0.530750i	0.964145	+	0.265375i	$0.0854957\pi$
$541$			12.3449i			0.530750i	−0.964145	+	0.265375i	$0.914504\pi$
$542$	−0.912151	−	4.78801i	−0.0391802	−	0.205663i
$543$	14.1173			0.605830
$544$	34.5535	+	25.1690i	1.48147	+	1.07911i
$545$		0			0
$546$	1.38445	+	7.26719i	0.0592491	+	0.311007i
$547$			19.8759i			0.849830i	0.905233	+	0.424915i	$0.139696\pi$
$547$			19.8759i			0.849830i	−0.905233	+	0.424915i	$0.860304\pi$
$548$	−8.26375	+	3.26719i	−0.353010	+	0.139567i
$549$		−	8.99656i		−	0.383964i
$550$		0			0
$551$	2.11727			0.0901986
$552$	2.52932	−	1.60256i	0.107655	−	0.0682094i
$553$	−10.8793			−0.462635
$554$	26.1008	−	4.97240i	1.10892	−	0.211257i
$555$		0			0
$556$	−14.8337	−	37.5190i	−0.629087	−	1.59116i
$557$		−	3.12070i		−	0.132228i	−0.997812	−	0.0661142i	$-0.978940\pi$
$557$		−	3.12070i		−	0.132228i	0.997812	−	0.0661142i	$-0.0210602\pi$
$558$	0.941367	+	4.94137i	0.0398512	+	0.209185i
$559$	−10.4622			−0.442503
$560$		0			0
$561$	−33.9931			−1.43519
$562$	4.46725	+	23.4492i	0.188439	+	0.989145i
$563$			0.651639i			0.0274633i	0.999906	+	0.0137317i	$0.00437106\pi$
$563$			0.651639i			0.0274633i	−0.999906	+	0.0137317i	$0.995629\pi$
$564$	7.39400	+	18.7018i	0.311344	+	0.787487i
$565$		0			0
$566$	−27.7846	+	5.29317i	−1.16787	+	0.222488i
$567$	−0.941367			−0.0395337
$568$	−19.6742	−	31.0518i	−0.825510	−	1.30290i
$569$	26.9966			1.13175			0.565877	−	0.824489i	$-0.308538\pi$
$569$	26.9966			1.13175			0.565877	+	0.824489i	$0.308538\pi$
$570$		0			0
$571$			14.9414i			0.625277i	0.949872	+	0.312638i	$0.101213\pi$
$571$			14.9414i			0.625277i	−0.949872	+	0.312638i	$0.898787\pi$
$572$	46.4914	−	18.3810i	1.94390	−	0.768549i
$573$			8.00000i			0.334205i
$574$	−0.967346	−	5.07774i	−0.0403763	−	0.211941i
$575$		0			0
$576$	3.41683	−	7.23362i	0.142368	−	0.301401i
$577$	8.87930			0.369650			0.184825	−	0.982771i	$-0.440828\pi$
$577$	8.87930			0.369650			0.184825	+	0.982771i	$0.440828\pi$
$578$	−10.6146	−	55.7177i	−0.441511	−	2.31755i
$579$		−	4.87930i		−	0.202777i
$580$		0			0
$581$			5.53781i			0.229747i
$582$	23.7750	−	4.52932i	0.985506	−	0.187746i
$583$	8.99656			0.372600
$584$	9.08279	+	14.3354i	0.375849	+	0.593202i
$585$		0			0
$586$	28.1008	−	5.35342i	1.16083	−	0.221148i
$587$		−	1.23109i		−	0.0508127i	−0.999677	−	0.0254064i	$-0.991912\pi$
$587$		−	1.23109i		−	0.0508127i	0.999677	−	0.0254064i	$-0.00808797\pi$
$588$	−4.49575	−	11.3712i	−0.185402	−	0.468940i
$589$			3.76547i			0.155153i
$590$		0			0
$591$	2.88617			0.118721
$592$	20.3500	+	21.7129i	0.836379	+	0.892397i
$593$	−3.55691			−0.146065			−0.0730325	−	0.997330i	$-0.523268\pi$
$593$	−3.55691			−0.146065			−0.0730325	+	0.997330i	$0.523268\pi$
$594$	1.19051	+	6.24914i	0.0488471	+	0.256405i
$595$		0			0
$596$	1.47068	+	3.71982i	0.0602415	+	0.152370i
$597$			17.6742i			0.723356i
$598$	8.17246	−	1.55691i	0.334197	−	0.0636670i
$599$	−19.2242			−0.785480			−0.392740	−	0.919649i	$-0.628473\pi$
$599$	−19.2242			−0.785480			−0.392740	+	0.919649i	$0.628473\pi$
$600$		0			0
$601$	−27.7586			−1.13230			−0.566148	−	0.824303i	$-0.691567\pi$
$601$	−27.7586			−1.13230			−0.566148	+	0.824303i	$0.691567\pi$
$602$	−2.46219	+	0.469065i	−0.100351	+	0.0191177i
$603$		−	4.00000i		−	0.162893i
$604$	−17.9931	+	7.11383i	−0.732130	+	0.289458i
$605$		0			0
$606$	−0.529317	−	2.77846i	−0.0215020	−	0.112867i
$607$	−7.16902			−0.290982			−0.145491	−	0.989360i	$-0.546476\pi$
$607$	−7.16902			−0.290982			−0.145491	+	0.989360i	$0.546476\pi$
$608$	3.52588	−	4.84053i	0.142993	−	0.196309i
$609$	1.88273			0.0762922
$610$		0			0
$611$			55.8759i			2.26050i
$612$	−14.0552	+	5.55691i	−0.568148	+	0.224625i
$613$		−	9.55691i		−	0.386000i	−0.981199	−	0.193000i	$-0.938178\pi$
$613$		−	9.55691i		−	0.386000i	0.981199	−	0.193000i	$-0.0618218\pi$
$614$	−11.2672	+	2.14648i	−0.454707	+	0.0866250i
$615$		0			0
$616$	10.1173	−	6.41023i	0.407636	−	0.258276i
$617$	−1.32926			−0.0535139			−0.0267569	−	0.999642i	$-0.508518\pi$
$617$	−1.32926			−0.0535139			−0.0267569	+	0.999642i	$0.508518\pi$
$618$	14.1319	−	2.69223i	0.568467	−	0.108297i
$619$			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
$622$	−8.43621	−	44.2829i	−0.338261	−	1.77558i
$623$	3.87586			0.155283
$624$	16.2181	−	15.2001i	0.649244	−	0.608489i
$625$		0			0
$626$	−1.35342	−	7.10428i	−0.0540934	−	0.283944i
$627$			4.76203i			0.190177i
$628$	3.18096	+	8.04564i	0.126934	+	0.321056i
$629$		−	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	$0.653667\pi$
$632$	17.4948	+	27.6121i	0.695907	+	1.09835i
$633$	−23.9379			−0.951447
$634$	−34.2372	+	6.52244i	−1.35973	+	0.259039i
$635$		0			0
$636$	3.71982	−	1.47068i	0.147501	−	0.0583164i
$637$		−	33.9740i		−	1.34610i
$638$	−2.38101	−	12.4983i	−0.0942653	−	0.494812i
$639$	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	$0.320187\pi$
$642$	−4.56035	−	23.9379i	−0.179983	−	0.944755i
$643$		−	20.3449i		−	0.802325i	−0.916007	−	0.401163i	$-0.868606\pi$
$643$		−	20.3449i		−	0.802325i	0.916007	−	0.401163i	$-0.131394\pi$
$644$	1.85352	−	0.732814i	0.0730388	−	0.0288769i
$645$		0			0
$646$	−11.1138	+	2.11727i	−0.437268	+	0.0833027i
$647$	−37.6965			−1.48200			−0.741002	−	0.671503i	$-0.765649\pi$
$647$	−37.6965			−1.48200			−0.741002	+	0.671503i	$0.765649\pi$
$648$	1.51380	+	2.38923i	0.0594676	+	0.0938578i
$649$	38.2277			1.50057
$650$		0			0
$651$			3.34836i			0.131233i
$652$	−4.49828	−	11.3776i	−0.176166	−	0.445580i
$653$			8.64476i			0.338296i	0.985591	+	0.169148i	$0.0541015\pi$
$653$			8.64476i			0.338296i	−0.985591	+	0.169148i	$0.945898\pi$
$654$	−0.498281	−	2.61555i	−0.0194843	−	0.102276i
$655$		0			0
$656$	−11.3319	+	10.6206i	−0.442438	+	0.414665i
$657$	−6.00000			−0.234082
$658$	2.50516	+	13.1499i	0.0976612	+	0.512637i
$659$			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	$0.188952\pi$
$661$			28.7620i			1.11871i	−0.828927	+	0.559357i	$0.811048\pi$
$662$	−15.3534	+	2.92494i	−0.596728	+	0.113681i
$663$	−41.9931			−1.63088
$664$	14.0552	−	8.90528i	0.545447	−	0.345592i
$665$		0			0
$666$	−10.3354	+	1.96896i	−0.400488	+	0.0762958i
$667$		−	2.11727i		−	0.0819809i
$668$	−11.2621	+	4.45264i	−0.435745	+	0.172278i
$669$		−	24.0552i		−	0.930028i
$670$		0			0
$671$	−40.4691			−1.56229
$672$	3.13531	−	4.30434i	0.120947	−	0.166043i
$673$	18.0000			0.693849			0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000			0.693849			0.346925	+	0.937893i	$0.387226\pi$
$674$	−5.29135	−	27.7750i	−0.203815	−	1.06985i
$675$		0			0
$676$	33.2539	−	13.1474i	1.27900	−	0.505669i
$677$			42.8724i			1.64772i	0.566793	+	0.823860i	$0.308184\pi$
$677$			42.8724i			1.64772i	−0.566793	+	0.823860i	$0.691816\pi$
$678$	21.2863	−	4.05520i	0.817495	−	0.155739i
$679$	16.1104			0.618260
$680$		0			0
$681$	−11.1138			−0.425883
$682$	22.2277	−	4.23453i	0.851141	−	0.162149i
$683$			26.1173i			0.999349i	0.866213	+	0.499675i	$0.166547\pi$
$683$			26.1173i			0.999349i	−0.866213	+	0.499675i	$0.833453\pi$
$684$	0.778457	+	1.96896i	0.0297651	+	0.0752852i
$685$		0			0
$686$	−3.26719	−	17.1499i	−0.124742	−	0.654787i
$687$	−17.2311			−0.657407
$688$	5.14992	+	5.49484i	0.196339	+	0.209489i
$689$	11.1138			0.423403
$690$		0			0
$691$		−	5.29317i		−	0.201362i	−0.994919	−	0.100681i	$-0.967898\pi$
$691$		−	5.29317i		−	0.201362i	0.994919	−	0.100681i	$-0.0321021\pi$
$692$	12.4121	+	31.3940i	0.471835	+	1.19342i
$693$			4.23453i			0.160857i
$694$	9.55691	−	1.82066i	0.362776	−	0.0691114i
$695$		0			0
$696$	−3.02760	−	4.77846i	−0.114761	−	0.181127i
$697$	29.3415			1.11139
$698$	−6.61555	+	1.26031i	−0.250402	+	0.0477035i
$699$		−	8.44309i		−	0.319347i
$700$		0			0
$701$			7.99312i			0.301896i	0.988542	+	0.150948i	$0.0482326\pi$
$701$			7.99312i			0.301896i	−0.988542	+	0.150948i	$0.951767\pi$
$702$	1.47068	+	7.71982i	0.0555074	+	0.291366i
$703$	−7.87586			−0.297044
$704$	−32.5389	−	15.3698i	−1.22635	−	0.579273i
$705$		0			0
$706$	−1.00344	−	5.26719i	−0.0377649	−	0.198233i
$707$		−	1.88273i		−	0.0708075i
$708$	15.8061	−	6.24914i	0.594028	−	0.234857i
$709$		−	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
$712$	−6.23271	−	9.83709i	−0.233581	−	0.368661i
$713$	3.76547			0.141018
$714$	−9.88273	+	1.88273i	−0.369852	+	0.0704595i
$715$		0			0
$716$	−7.80605	−	19.7440i	−0.291726	−	0.737867i
$717$		−	10.1173i		−	0.377836i
$718$	3.43965	+	18.0552i	0.128367	+	0.673814i
$719$	26.8793			1.00243			0.501214	−	0.865323i	$-0.332887\pi$
$719$	26.8793			1.00243			0.501214	+	0.865323i	$0.332887\pi$
$720$		0			0
$721$	9.57602			0.356630
$722$	−4.73190	−	24.8384i	−0.176103	−	0.924391i
$723$		−	16.8793i		−	0.627748i
$724$	−10.3810	−	26.2569i	−0.385807	−	0.975829i
$725$		0			0
$726$	12.8289	−	2.44400i	0.476124	−	0.0907052i
$727$	−41.8138			−1.55079			−0.775394	−	0.631478i	$-0.782449\pi$
$727$	−41.8138			−1.55079			−0.775394	+	0.631478i	$0.782449\pi$
$728$	12.4983	−	7.91883i	0.463217	−	0.293491i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	14.2277i		−	0.526229i
$732$	−16.7328	+	6.61555i	−0.618463	+	0.244518i
$733$		−	30.0844i		−	1.11119i	−0.831452	−	0.555597i	$-0.812490\pi$
$733$		−	30.0844i		−	1.11119i	0.831452	−	0.555597i	$-0.187510\pi$
$734$	6.06980	+	31.8613i	0.224041	+	1.17602i
$735$		0			0
$736$	−4.84053	−	3.52588i	−0.178424	−	0.129966i
$737$	−17.9931			−0.662785
$738$	−1.02760	−	5.39400i	−0.0378264	−	0.198556i
$739$			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
$742$	2.61555	−	0.498281i	0.0960198	−	0.0182925i
$743$	43.2863			1.58802			0.794010	−	0.607905i	$-0.207990\pi$
$743$	43.2863			1.58802			0.794010	+	0.607905i	$0.207990\pi$
$744$	8.49828	−	5.38445i	0.311562	−	0.197404i
$745$		0			0
$746$	−21.4492	+	4.08623i	−0.785311	+	0.149608i
$747$			5.88273i			0.215238i
$748$	24.9966	+	63.2242i	0.913965	+	2.31171i
$749$		−	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	$0.224036\pi$
$752$	29.3465	−	27.5044i	1.07016	−	1.00298i
$753$	11.8466			0.431716
$754$	−2.94137	−	15.4396i	−0.107118	−	0.562279i
$755$		0			0
$756$	0.692226	+	1.75086i	0.0251760	+	0.0636781i
$757$			16.3258i			0.593372i	0.954975	+	0.296686i	$0.0958815\pi$
$757$			16.3258i			0.593372i	−0.954975	+	0.296686i	$0.904119\pi$
$758$	−8.73787	+	1.66463i	−0.317374	+	0.0604620i
$759$	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	$0.135889\pi$
$762$	−25.2457	+	4.80949i	−0.914555	+	0.174230i
$763$		−	1.77234i		−	0.0641631i
$764$	14.8793	−	5.88273i	0.538314	−	0.212830i
$765$		0			0
$766$	0.778457	+	4.08623i	0.0281268	+	0.147642i
$767$	47.2242			1.70517
$768$	−15.9664	−	1.03581i	−0.576139	−	0.0373766i
$769$	−31.3415			−1.13020			−0.565101	−	0.825021i	$-0.691163\pi$
$769$	−31.3415			−1.13020			−0.565101	+	0.825021i	$0.691163\pi$
$770$		0			0
$771$		−	10.6707i		−	0.384297i
$772$	−9.07506	+	3.58795i	−0.326619	+	0.129133i
$773$			9.11383i			0.327802i	0.986477	+	0.163901i	$0.0524077\pi$
$773$			9.11383i			0.327802i	−0.986477	+	0.163901i	$0.947592\pi$
$774$	−2.61555	+	0.498281i	−0.0940139	+	0.0179103i
$775$		0			0
$776$	−25.9069	−	40.8888i	−0.930003	−	1.46782i
$777$	−7.00344			−0.251247
$778$	16.9870	−	3.23615i	0.609014	−	0.116022i
$779$		−	4.11039i		−	0.147270i
$780$		0			0
$781$		−	58.4622i		−	2.09194i
$782$	2.11727	+	11.1138i	0.0757133	+	0.397430i
$783$	2.00000			0.0714742
$784$	−17.8435	+	16.7234i	−0.637267	+	0.597265i
$785$		0			0
$786$	1.68879	+	8.86469i	0.0602371	+	0.316193i
$787$		−	36.2208i		−	1.29113i	−0.763705	−	0.645566i	$-0.776622\pi$
$787$		−	36.2208i		−	1.29113i	0.763705	−	0.645566i	$-0.223378\pi$
$788$	−2.12232	−	5.36802i	−0.0756046	−	0.191228i
$789$		−	1.94480i		−	0.0692369i
$790$		0			0
$791$	14.4240			0.512858
$792$	10.7474	−	6.80949i	0.381893	−	0.241965i
$793$	−49.9931			−1.77531
$794$	7.39400	−	1.40861i	0.262403	−	0.0499898i
$795$		0			0
$796$	32.8724	−	12.9966i	1.16513	−	0.460651i
$797$		−	10.0000i		−	0.354218i	−0.984191	−	0.177109i	$-0.943325\pi$
$797$		−	10.0000i		−	0.354218i	0.984191	−	0.177109i	$-0.0566745\pi$
$798$	0.263748	+	1.38445i	0.00933659	+	0.0490091i
$799$	−75.9862			−2.68820
$800$		0			0
$801$	4.11727			0.145476
$802$	−1.85170	−	9.71982i	−0.0653857	−	0.343219i
$803$			26.9897i			0.952445i
$804$	−7.43965	+	2.94137i	−0.262376	+	0.103734i
$805$		0			0
$806$	27.4588	−	5.23109i	0.967193	−	0.184257i
$807$	9.76547			0.343761
$808$	−4.77846	+	3.02760i	−0.168106	+	0.106511i
$809$	47.5760			1.67268			0.836342	−	0.548208i	$-0.184690\pi$
$809$	47.5760			1.67268			0.836342	+	0.548208i	$0.184690\pi$
$810$		0			0
$811$			20.5174i			0.720463i	0.932863	+	0.360231i	$0.117302\pi$
$811$			20.5174i			0.720463i	−0.932863	+	0.360231i	$0.882698\pi$
$812$	−1.38445	−	3.50172i	−0.0485848	−	0.122886i
$813$		−	3.44652i		−	0.120875i
$814$	8.85696	+	46.4914i	0.310436	+	1.62952i
$815$		0			0
$816$	20.6707	+	22.0552i	0.723621	+	0.772086i
$817$	−1.99312			−0.0697306
$818$	−4.29478	−	22.5439i	−0.150164	−	0.788230i
$819$			5.23109i			0.182789i
$820$		0			0
$821$			44.4622i			1.55174i	0.630892	+	0.775871i	$0.282689\pi$
$821$			44.4622i			1.55174i	−0.630892	+	0.775871i	$0.717311\pi$
$822$	−6.17246	+	1.17590i	−0.215289	+	0.0410142i
$823$	−32.1656			−1.12122			−0.560611	−	0.828079i	$-0.689434\pi$
$823$	−32.1656			−1.12122			−0.560611	+	0.828079i	$0.689434\pi$
$824$	−15.3991	−	24.3043i	−0.536452	−	0.846682i
$825$		0			0
$826$	11.1138	−	2.11727i	0.386700	−	0.0736691i
$827$			20.0000i			0.695468i	0.937593	+	0.347734i	$0.113049\pi$
$827$			20.0000i			0.695468i	−0.937593	+	0.347734i	$0.886951\pi$
$828$	1.96896	−	0.778457i	0.0684262	−	0.0270533i
$829$			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
$832$	−40.1966	−	18.9870i	−1.39357	−	0.658256i
$833$	46.2017			1.60079
$834$	−5.33881	−	28.0242i	−0.184868	−	0.970397i
$835$		0			0
$836$	8.85696	−	3.50172i	0.306324	−	0.121109i
$837$			3.55691i			0.122945i
$838$	−21.6888	+	4.13187i	−0.749227	+	0.142733i
$839$	4.52750			0.156307			0.0781533	−	0.996941i	$-0.475098\pi$
$839$	4.52750			0.156307			0.0781533	+	0.996941i	$0.475098\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	46.1656	−	8.79488i	1.59097	−	0.303092i
$843$			16.8793i			0.581354i
$844$	17.6026	+	44.5224i	0.605905	+	1.53253i
$845$		0			0
$846$	2.66119	+	13.9690i	0.0914936	+	0.480263i
$847$	8.69308			0.298698
$848$	−5.47068	−	5.83709i	−0.187864	−	0.200447i
$849$	−20.0000			−0.686398
$850$		0			0
$851$			7.87586i			0.269981i
$852$	−9.55691	−	24.1725i	−0.327414	−	0.828135i
$853$			50.4293i			1.72667i	0.504633	+	0.863334i	$0.331628\pi$
$853$			50.4293i			1.72667i	−0.504633	+	0.863334i	$0.668372\pi$
$854$	−11.7655	+	2.24141i	−0.402606	+	0.0766994i
$855$		0			0
$856$	−41.1690	+	26.0844i	−1.40713	+	0.891547i
$857$	−26.4362			−0.903044			−0.451522	−	0.892260i	$-0.649119\pi$
$857$	−26.4362			−0.903044			−0.451522	+	0.892260i	$0.649119\pi$
$858$	34.7259	−	6.61555i	1.18552	−	0.225851i
$859$			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
$862$	3.43965	+	18.0552i	0.117155	+	0.614962i
$863$	29.9311			1.01886			0.509432	−	0.860511i	$-0.329855\pi$
$863$	29.9311			1.01886			0.509432	+	0.860511i	$0.329855\pi$
$864$	3.33060	−	4.57243i	0.113309	−	0.155557i
$865$		0			0
$866$	5.35342	+	28.1008i	0.181917	+	0.954905i
$867$		−	40.1070i		−	1.36210i
$868$	6.22766	−	2.46219i	0.211380	−	0.0835722i
$869$			51.9862i			1.76351i
$870$		0			0
$871$	−22.2277			−0.753155
$872$	−4.49828	+	2.85008i	−0.152331	+	0.0965159i
$873$	17.1138			0.579215
$874$	1.55691	−	0.296604i	0.0526634	−	0.0100328i
$875$		0			0
$876$	4.41205	+	11.1595i	0.149069	+	0.377044i
$877$			11.2051i			0.378370i	0.981941	+	0.189185i	$0.0605846\pi$
$877$			11.2051i			0.378370i	−0.981941	+	0.189185i	$0.939415\pi$
$878$	1.43965	+	7.55691i	0.0485858	+	0.255034i
$879$	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	$0.802865\pi$
$882$	−1.61808	−	8.49351i	−0.0544834	−	0.285991i
$883$			50.5726i			1.70190i	0.525244	+	0.850951i	$0.323974\pi$
$883$			50.5726i			1.70190i	−0.525244	+	0.850951i	$0.676026\pi$
$884$	30.8793	+	78.1035i	1.03858	+	2.62691i
$885$		0			0
$886$	21.3224	−	4.06207i	0.716339	−	0.136468i
$887$	48.0483			1.61330			0.806652	−	0.591026i	$-0.201277\pi$
$887$	48.0483			1.61330			0.806652	+	0.591026i	$0.201277\pi$
$888$	11.2621	+	17.7750i	0.377932	+	0.596491i
$889$	−17.1070			−0.573749
$890$		0			0
$891$			4.49828i			0.150698i
$892$	−44.7405	+	17.6888i	−1.49802	+	0.592264i
$893$			10.6448i			0.356213i
$894$	0.529317	+	2.77846i	0.0177030	+	0.0929255i
$895$		0			0
$896$	−10.3112	−	2.66625i	−0.344473	−	0.0890731i
$897$	5.88273			0.196419
$898$	−1.11888	−	5.87318i	−0.0373377	−	0.195991i
$899$		−	7.11383i		−	0.237259i
$900$		0			0
$901$			15.1138i			0.503515i
$902$	−24.2637	+	4.62242i	−0.807894	+	0.153910i
$903$	−1.77234			−0.0589799
$904$	−23.1950	−	36.6087i	−0.771454	−	1.21759i
$905$		0			0
$906$	−13.4396	+	2.56035i	−0.446502	+	0.0850620i
$907$			6.46219i			0.214573i	0.994228	+	0.107287i	$0.0342163\pi$
$907$			6.46219i			0.214573i	−0.994228	+	0.107287i	$0.965784\pi$
$908$	8.17246	+	20.6707i	0.271213	+	0.685983i
$909$		−	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	$0.186110\pi$
$912$	3.08967	−	2.89572i	0.102309	−	0.0958870i
$913$	26.4622			0.875771
$914$	0.701778	+	3.68373i	0.0232128	+	0.121847i
$915$		0			0
$916$	12.6707	+	32.0483i	0.418653	+	1.05891i
$917$			6.00688i			0.198365i
$918$	−10.4983	+	2.00000i	−0.346495	+	0.0660098i
$919$	46.4362			1.53179			0.765895	−	0.642966i	$-0.222296\pi$
$919$	46.4362			1.53179			0.765895	+	0.642966i	$0.222296\pi$
$920$		0			0
$921$	−8.11039			−0.267246
$922$	−14.2181	+	2.70865i	−0.468248	+	0.0892048i
$923$		−	72.2208i		−	2.37718i
$924$	7.87586	−	3.11383i	0.259097	−	0.102437i
$925$		0			0
$926$	5.04403	+	26.4768i	0.165757	+	0.870082i
$927$	10.1725			0.334107
$928$	−6.66119	+	9.14486i	−0.218664	+	0.300195i
$929$	−35.9931			−1.18090			−0.590448	−	0.807076i	$-0.701049\pi$
$929$	−35.9931			−1.18090			−0.590448	+	0.807076i	$0.701049\pi$
$930$		0			0
$931$		−	6.47230i		−	0.212121i
$932$	−15.7034	+	6.20855i	−0.514382	+	0.203368i
$933$		−	31.8759i		−	1.04357i
$934$	5.71027	−	1.08785i	0.186846	−	0.0355955i
$935$		0			0
$936$	13.2767	−	8.41205i	0.433964	−	0.274956i
$937$	−2.70360			−0.0883227			−0.0441613	−	0.999024i	$-0.514062\pi$
$937$	−2.70360			−0.0883227			−0.0441613	+	0.999024i	$0.514062\pi$
$938$	−5.23109	+	0.996562i	−0.170801	+	0.0325389i
$939$		−	5.11383i		−	0.166883i
$940$		0			0
$941$		−	17.7655i		−	0.579138i	−0.957157	−	0.289569i	$-0.906488\pi$
$941$		−	17.7655i		−	0.579138i	0.957157	−	0.289569i	$-0.0935119\pi$
$942$	1.14486	+	6.00955i	0.0373017	+	0.195802i
$943$	−4.11039			−0.133853
$944$	−23.2457	−	24.8026i	−0.756583	−	0.807256i
$945$		0			0
$946$	2.24141	+	11.7655i	0.0728745	+	0.382528i
$947$			26.2277i			0.852284i	0.904656	+	0.426142i	$0.140128\pi$
$947$			26.2277i			0.852284i	−0.904656	+	0.426142i	$0.859872\pi$
$948$	8.49828	+	21.4948i	0.276011	+	0.698120i
$949$			33.3415i			1.08231i
$950$		0			0
$951$	−24.6448			−0.799161
$952$	10.7689	+	16.9966i	0.349022	+	0.550862i
$953$	−9.09472			−0.294607			−0.147304	−	0.989091i	$-0.547059\pi$
$953$	−9.09472			−0.294607			−0.147304	+	0.989091i	$0.547059\pi$
$954$	2.77846	−	0.529317i	0.0899559	−	0.0171373i
$955$		0			0
$956$	−18.8172	+	7.43965i	−0.608593	+	0.240615i
$957$		−	8.99656i		−	0.290818i
$958$	6.67762	+	35.0518i	0.215744	+	1.13247i
$959$	−4.18257			−0.135062
$960$		0			0
$961$	−18.3484			−0.591883
$962$	10.9414	+	57.4328i	0.352764	+	1.85171i
$963$		−	17.2311i		−	0.555264i
$964$	−31.3940	+	12.4121i	−1.01113	+	0.399765i
$965$		0			0
$966$	1.38445	−	0.263748i	0.0445440	−	0.00848597i
$967$	7.47574			0.240404			0.120202	−	0.992749i	$-0.461646\pi$
$967$	7.47574			0.240404			0.120202	+	0.992749i	$0.461646\pi$
$968$	−13.9792	−	22.0634i	−0.449309	−	0.709145i
$969$	−8.00000			−0.256997
$970$		0			0
$971$		−	41.0777i		−	1.31825i	−0.752035	−	0.659124i	$-0.770927\pi$
$971$		−	41.0777i		−	1.31825i	0.752035	−	0.659124i	$-0.229073\pi$
$972$	0.735342	+	1.85991i	0.0235861	+	0.0596567i
$973$		−	18.9897i		−	0.608781i
$974$	−5.80605	−	30.4768i	−0.186038	−	0.976540i
$975$		0			0
$976$	24.6087	+	26.2569i	0.787704	+	0.840462i
$977$	4.20855			0.134644			0.0673218	−	0.997731i	$-0.478555\pi$
$977$	4.20855			0.134644			0.0673218	+	0.997731i	$0.478555\pi$
$978$	−1.61899	−	8.49828i	−0.0517694	−	0.271745i
$979$		−	18.5206i		−	0.591922i
$980$		0			0
$981$		−	1.88273i		−	0.0601111i
$982$	−10.4216	+	1.98539i	−0.332567	+	0.0633564i
$983$	8.35504			0.266484			0.133242	−	0.991084i	$-0.457461\pi$
$983$	8.35504			0.266484			0.133242	+	0.991084i	$0.457461\pi$
$984$	−9.27674	+	5.87768i	−0.295732	+	0.187374i
$985$		0			0
$986$	20.9966	−	4.00000i	0.668667	−	0.127386i
$987$			9.46563i			0.301294i
$988$	10.9414	−	4.32582i	0.348091	−	0.137623i
$989$			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	$0.570903\pi$
$992$	−16.2637	−	11.8466i	−0.516375	−	0.376131i
$993$	−11.0518			−0.350717
$994$	−3.23797	−	16.9966i	−0.102702	−	0.539098i
$995$		0			0
$996$	10.9414	−	4.32582i	0.346690	−	0.137069i
$997$		−	34.8984i		−	1.10524i	−0.833432	−	0.552622i	$-0.813627\pi$
$997$		−	34.8984i		−	1.10524i	0.833432	−	0.552622i	$-0.186373\pi$
$998$	−40.5224	+	7.71982i	−1.28272	+	0.244367i
$999$	−7.43965			−0.235380

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.3	✓	6	40.29	even	2
120.2.k.b.61.4	yes	6	5.4	even	2
360.2.k.f.181.3		6	15.14	odd	2
360.2.k.f.181.4		6	120.29	odd	2
480.2.k.b.241.2		6	20.19	odd	2
480.2.k.b.241.5		6	40.19	odd	2
600.2.d.e.349.5		6	5.2	odd	4
600.2.d.e.349.6		6	40.13	odd	4
600.2.d.f.349.1		6	40.37	odd	4
600.2.d.f.349.2		6	5.3	odd	4
600.2.k.c.301.3		6	1.1	even	1	trivial
600.2.k.c.301.4		6	8.5	even	2	inner
1440.2.k.f.721.2		6	60.59	even	2
1440.2.k.f.721.5		6	120.59	even	2
1800.2.d.q.1549.1		6	120.53	even	4
1800.2.d.q.1549.2		6	15.2	even	4
1800.2.d.r.1549.5		6	15.8	even	4
1800.2.d.r.1549.6		6	120.77	even	4
1800.2.k.p.901.3		6	24.5	odd	2
1800.2.k.p.901.4		6	3.2	odd	2
2400.2.d.e.49.3		6	20.3	even	4
2400.2.d.e.49.4		6	40.27	even	4
2400.2.d.f.49.3		6	40.3	even	4
2400.2.d.f.49.4		6	20.7	even	4
2400.2.k.c.1201.2		6	8.3	odd	2
2400.2.k.c.1201.5		6	4.3	odd	2
3840.2.a.bo.1.2		3	80.59	odd	4
3840.2.a.bp.1.2		3	80.29	even	4
3840.2.a.bq.1.2		3	80.69	even	4
3840.2.a.br.1.2		3	80.19	odd	4
7200.2.d.q.2449.3		6	120.83	odd	4
7200.2.d.q.2449.4		6	60.47	odd	4
7200.2.d.r.2449.3		6	60.23	odd	4
7200.2.d.r.2449.4		6	120.107	odd	4
7200.2.k.p.3601.3		6	24.11	even	2
7200.2.k.p.3601.4		6	12.11	even	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.k (of order \(2\), degree \(1\), minimal)

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

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