LMFDB - Embedded newform 360.2.k.f.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, 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("360.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.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:	$2.87461447277$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.3
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.2.k.f.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264658 - 1.38923i) q^{2} +(-1.85991 + 0.735342i) q^{4} -1.00000i q^{5} +0.941367 q^{7} +(1.51380 + 2.38923i) q^{8} +O(q^{10})$	\(q+(-0.264658 - 1.38923i) q^{2} +(-1.85991 + 0.735342i) q^{4} -1.00000i q^{5} +0.941367 q^{7} +(1.51380 + 2.38923i) q^{8} +(-1.38923 + 0.264658i) q^{10} -4.49828i q^{11} -5.55691i q^{13} +(-0.249141 - 1.30777i) q^{14} +(2.91855 - 2.73534i) q^{16} -7.55691 q^{17} +1.05863i q^{19} +(0.735342 + 1.85991i) q^{20} +(-6.24914 + 1.19051i) q^{22} +1.05863 q^{23} -1.00000 q^{25} +(-7.71982 + 1.47068i) q^{26} +(-1.75086 + 0.692226i) q^{28} +2.00000i q^{29} +3.55691 q^{31} +(-4.57243 - 3.33060i) q^{32} +(2.00000 + 10.4983i) q^{34} -0.941367i q^{35} -7.43965i q^{37} +(1.47068 - 0.280176i) q^{38} +(2.38923 - 1.51380i) q^{40} +3.88273 q^{41} -1.88273i q^{43} +(3.30777 + 8.36641i) q^{44} +(-0.280176 - 1.47068i) q^{46} +10.0552 q^{47} -6.11383 q^{49} +(0.264658 + 1.38923i) q^{50} +(4.08623 + 10.3354i) q^{52} -2.00000i q^{53} -4.49828 q^{55} +(1.42504 + 2.24914i) q^{56} +(2.77846 - 0.529317i) q^{58} +8.49828i q^{59} +8.99656i q^{61} +(-0.941367 - 4.94137i) q^{62} +(-3.41683 + 7.23362i) q^{64} -5.55691 q^{65} -4.00000i q^{67} +(14.0552 - 5.55691i) q^{68} +(-1.30777 + 0.249141i) q^{70} +12.9966 q^{71} -6.00000 q^{73} +(-10.3354 + 1.96896i) q^{74} +(-0.778457 - 1.96896i) q^{76} -4.23453i q^{77} +11.5569 q^{79} +(-2.73534 - 2.91855i) q^{80} +(-1.02760 - 5.39400i) q^{82} -5.88273i q^{83} +7.55691i q^{85} +(-2.61555 + 0.498281i) q^{86} +(10.7474 - 6.80949i) q^{88} +4.11727 q^{89} -5.23109i q^{91} +(-1.96896 + 0.778457i) q^{92} +(-2.66119 - 13.9690i) q^{94} +1.05863 q^{95} +17.1138 q^{97} +(1.61808 + 8.49351i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 8 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 8 * q^8	$ 6 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 8 q^{8} + 16 q^{14} + 10 q^{16} - 12 q^{17} + 4 q^{20} - 20 q^{22} + 8 q^{23} - 6 q^{25} - 28 q^{26} - 28 q^{28} - 12 q^{31} - 12 q^{32} + 12 q^{34} + 8 q^{38} + 6 q^{40} + 20 q^{41} + 4 q^{44} - 20 q^{46} - 8 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{52} + 8 q^{55} - 4 q^{56} - 4 q^{62} + 22 q^{64} + 16 q^{68} + 8 q^{70} + 8 q^{71} - 36 q^{73} - 12 q^{74} + 12 q^{76} + 36 q^{79} - 16 q^{80} + 28 q^{82} + 16 q^{86} + 12 q^{88} + 28 q^{89} + 24 q^{92} + 4 q^{94} + 8 q^{95} + 36 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 8 * q^8 + 16 * q^14 + 10 * q^16 - 12 * q^17 + 4 * q^20 - 20 * q^22 + 8 * q^23 - 6 * q^25 - 28 * q^26 - 28 * q^28 - 12 * q^31 - 12 * q^32 + 12 * q^34 + 8 * q^38 + 6 * q^40 + 20 * q^41 + 4 * q^44 - 20 * q^46 - 8 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^52 + 8 * q^55 - 4 * q^56 - 4 * q^62 + 22 * q^64 + 16 * q^68 + 8 * q^70 + 8 * q^71 - 36 * q^73 - 12 * q^74 + 12 * q^76 + 36 * q^79 - 16 * q^80 + 28 * q^82 + 16 * q^86 + 12 * q^88 + 28 * q^89 + 24 * q^92 + 4 * q^94 + 8 * q^95 + 36 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−1.85991	+	0.735342i	−0.929956	+	0.367671i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	0.941367			0.355803			0.177902	−	0.984048i	$-0.443069\pi$
$7$	0.941367			0.355803			0.177902	+	0.984048i	$0.443069\pi$
$8$	1.51380	+	2.38923i	0.535209	+	0.844720i
$9$		0			0
$10$	−1.38923	+	0.264658i	−0.439313	+	0.0836923i
$11$		−	4.49828i		−	1.35628i	−0.734931	−	0.678141i	$-0.762786\pi$
$11$		−	4.49828i		−	1.35628i	0.734931	−	0.678141i	$-0.237214\pi$
$12$		0			0
$13$		−	5.55691i		−	1.54121i	−0.637313	−	0.770605i	$-0.719954\pi$
$13$		−	5.55691i		−	1.54121i	0.637313	−	0.770605i	$-0.280046\pi$
$14$	−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			0
$19$			1.05863i			0.242867i	0.992600	+	0.121434i	$0.0387491\pi$
$19$			1.05863i			0.242867i	−0.992600	+	0.121434i	$0.961251\pi$
$20$	0.735342	+	1.85991i	0.164427	+	0.415889i
$21$		0			0
$22$	−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	$0.464796\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−7.71982	+	1.47068i	−1.51398	+	0.288425i
$27$		0			0
$28$	−1.75086	+	0.692226i	−0.330881	+	0.130818i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$		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
$33$		0			0
$34$	2.00000	+	10.4983i	0.342997	+	1.80044i
$35$		−	0.941367i		−	0.159120i
$36$		0			0
$37$		−	7.43965i		−	1.22307i	−0.791217	−	0.611535i	$-0.790552\pi$
$37$		−	7.43965i		−	1.22307i	0.791217	−	0.611535i	$-0.209448\pi$
$38$	1.47068	−	0.280176i	0.238576	−	0.0454506i
$39$		0			0
$40$	2.38923	−	1.51380i	0.377770	−	0.239353i
$41$	3.88273			0.606381			0.303191	−	0.952930i	$-0.401948\pi$
$41$	3.88273			0.606381			0.303191	+	0.952930i	$0.401948\pi$
$42$		0			0
$43$		−	1.88273i		−	0.287114i	−0.989642	−	0.143557i	$-0.954146\pi$
$43$		−	1.88273i		−	0.287114i	0.989642	−	0.143557i	$-0.0458541\pi$
$44$	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	$0.237955\pi$
$48$		0			0
$49$	−6.11383			−0.873404
$50$	0.264658	+	1.38923i	0.0374283	+	0.196467i
$51$		0			0
$52$	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	$-0.0438619\pi$
$54$		0			0
$55$	−4.49828			−0.606548
$56$	1.42504	+	2.24914i	0.190429	+	0.300554i
$57$		0			0
$58$	2.77846	−	0.529317i	0.364829	−	0.0695027i
$59$			8.49828i			1.10638i	0.833054	+	0.553191i	$0.186590\pi$
$59$			8.49828i			1.10638i	−0.833054	+	0.553191i	$0.813410\pi$
$60$		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			0
$64$	−3.41683	+	7.23362i	−0.427103	+	0.904203i
$65$	−5.55691			−0.689250
$66$		0			0
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	14.0552	−	5.55691i	1.70444	−	0.673875i
$69$		0			0
$70$	−1.30777	+	0.249141i	−0.156309	+	0.0297780i
$71$	12.9966			1.54241			0.771204	−	0.636588i	$-0.219655\pi$
$71$	12.9966			1.54241			0.771204	+	0.636588i	$0.219655\pi$
$72$		0			0
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−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
$78$		0			0
$79$	11.5569			1.30025			0.650127	−	0.759825i	$-0.274716\pi$
$79$	11.5569			1.30025			0.650127	+	0.759825i	$0.274716\pi$
$80$	−2.73534	−	2.91855i	−0.305821	−	0.326303i
$81$		0			0
$82$	−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			0
$85$			7.55691i			0.819662i
$86$	−2.61555	+	0.498281i	−0.282042	+	0.0537310i
$87$		0			0
$88$	10.7474	−	6.80949i	1.14568	−	0.725894i
$89$	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
$92$	−1.96896	+	0.778457i	−0.205279	+	0.0811598i
$93$		0			0
$94$	−2.66119	−	13.9690i	−0.274481	−	1.44079i
$95$	1.05863			0.108613
$96$		0			0
$97$	17.1138			1.73765			0.868823	−	0.495123i	$-0.164877\pi$
$97$	17.1138			1.73765			0.868823	+	0.495123i	$0.164877\pi$
$98$	1.61808	+	8.49351i	0.163450	+	0.857974i
$99$		0			0
$100$	1.85991	−	0.735342i	0.185991	−	0.0735342i
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$		0			0
$103$	10.1725			1.00232			0.501161	−	0.865354i	$-0.332906\pi$
$103$	10.1725			1.00232			0.501161	+	0.865354i	$0.332906\pi$
$104$	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			0
$109$			1.88273i			0.180333i	0.995927	+	0.0901666i	$0.0287399\pi$
$109$			1.88273i			0.180333i	−0.995927	+	0.0901666i	$0.971260\pi$
$110$	1.19051	+	6.24914i	0.113510	+	0.595832i
$111$		0			0
$112$	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			0
$115$		−	1.05863i		−	0.0987181i
$116$	−1.47068	−	3.71982i	−0.136550	−	0.345377i
$117$		0			0
$118$	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
$123$		0			0
$124$	−6.61555	+	2.61555i	−0.594094	+	0.234883i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−18.1725			−1.61255			−0.806273	−	0.591544i	$-0.798519\pi$
$127$	−18.1725			−1.61255			−0.806273	+	0.591544i	$0.798519\pi$
$128$	10.9534	+	2.83231i	0.968157	+	0.250344i
$129$		0			0
$130$	1.47068	+	7.71982i	0.128987	+	0.677073i
$131$			6.38101i			0.557512i	0.960362	+	0.278756i	$0.0899220\pi$
$131$			6.38101i			0.557512i	−0.960362	+	0.278756i	$0.910078\pi$
$132$		0			0
$133$			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	$0.439216\pi$
$138$		0			0
$139$			20.1725i			1.71101i	0.517798	+	0.855503i	$0.326752\pi$
$139$			20.1725i			1.71101i	−0.517798	+	0.855503i	$0.673248\pi$
$140$	0.692226	+	1.75086i	0.0585038	+	0.147975i
$141$		0			0
$142$	−3.43965	−	18.0552i	−0.288649	−	1.51516i
$143$	−24.9966			−2.09032
$144$		0			0
$145$	2.00000			0.166091
$146$	1.58795	+	8.33537i	0.131420	+	0.689840i
$147$		0			0
$148$	5.47068	+	13.8371i	0.449687	+	1.13740i
$149$			2.00000i			0.163846i	0.996639	+	0.0819232i	$0.0261062\pi$
$149$			2.00000i			0.163846i	−0.996639	+	0.0819232i	$0.973894\pi$
$150$		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
$153$		0			0
$154$	−5.88273	+	1.12070i	−0.474044	+	0.0903089i
$155$		−	3.55691i		−	0.285698i
$156$		0			0
$157$			4.32582i			0.345238i	0.984989	+	0.172619i	$0.0552229\pi$
$157$			4.32582i			0.345238i	−0.984989	+	0.172619i	$0.944777\pi$
$158$	−3.05863	−	16.0552i	−0.243332	−	1.27728i
$159$		0			0
$160$	−3.33060	+	4.57243i	−0.263307	+	0.361482i
$161$	0.996562			0.0785401
$162$		0			0
$163$		−	6.11727i		−	0.479141i	−0.970879	−	0.239571i	$-0.922993\pi$
$163$		−	6.11727i		−	0.479141i	0.970879	−	0.239571i	$-0.0770067\pi$
$164$	−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	$0.424726\pi$
$168$		0			0
$169$	−17.8793			−1.37533
$170$	10.4983	−	2.00000i	0.805181	−	0.153393i
$171$		0			0
$172$	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			0
$175$	−0.941367			−0.0711606
$176$	−12.3043	−	13.1284i	−0.927474	−	0.989593i
$177$		0			0
$178$	−1.08967	−	5.71982i	−0.0816741	−	0.428719i
$179$		−	10.6155i		−	0.793443i	−0.917939	−	0.396722i	$-0.870148\pi$
$179$		−	10.6155i		−	0.793443i	0.917939	−	0.396722i	$-0.129852\pi$
$180$		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
$183$		0			0
$184$	1.60256	+	2.52932i	0.118142	+	0.186464i
$185$	−7.43965			−0.546974
$186$		0			0
$187$			33.9931i			2.48582i
$188$	−18.7018	+	7.39400i	−1.36397	+	0.539263i
$189$		0			0
$190$	−0.280176	−	1.47068i	−0.0203261	−	0.106695i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	−4.87930			−0.351219			−0.175610	−	0.984460i	$-0.556190\pi$
$193$	−4.87930			−0.351219			−0.175610	+	0.984460i	$0.556190\pi$
$194$	−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	$0.967215\pi$
$198$		0			0
$199$	−17.6742			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$199$	−17.6742			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$200$	−1.51380	−	2.38923i	−0.107042	−	0.168944i
$201$		0			0
$202$	−2.77846	+	0.529317i	−0.195492	+	0.0372426i
$203$			1.88273i			0.132142i
$204$		0			0
$205$		−	3.88273i		−	0.271182i
$206$	−2.69223	−	14.1319i	−0.187576	−	0.984614i
$207$		0			0
$208$	−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
$213$		0			0
$214$	23.9379	−	4.56035i	1.63636	−	0.311739i
$215$	−1.88273			−0.128401
$216$		0			0
$217$	3.34836			0.227302
$218$	2.61555	−	0.498281i	0.177147	−	0.0337479i
$219$		0			0
$220$	8.36641	−	3.30777i	0.564063	−	0.223010i
$221$			41.9931i			2.82476i
$222$		0			0
$223$	−24.0552			−1.61086			−0.805428	−	0.592694i	$-0.798064\pi$
$223$	−24.0552			−1.61086			−0.805428	+	0.592694i	$0.798064\pi$
$224$	−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	$-0.120240\pi$
$228$		0			0
$229$		−	17.2311i		−	1.13866i	−0.822108	−	0.569331i	$-0.807202\pi$
$229$		−	17.2311i		−	1.13866i	0.822108	−	0.569331i	$-0.192798\pi$
$230$	−1.47068	+	0.280176i	−0.0969740	+	0.0184743i
$231$		0			0
$232$	−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	$0.410805\pi$
$234$		0			0
$235$		−	10.0552i		−	0.655929i
$236$	−6.24914	−	15.8061i	−0.406784	−	1.02889i
$237$		0			0
$238$	1.88273	+	9.88273i	0.122039	+	0.640602i
$239$	−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	$0.317044\pi$
$242$	2.44400	+	12.8289i	0.157106	+	0.824671i
$243$		0			0
$244$	−6.61555	−	16.7328i	−0.423517	−	1.07121i
$245$			6.11383i			0.390598i
$246$		0			0
$247$	5.88273			0.374309
$248$	5.38445	+	8.49828i	0.341913	+	0.539641i
$249$		0			0
$250$	1.38923	−	0.264658i	0.0878625	−	0.0167385i
$251$		−	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			0
$253$		−	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			0
$259$		−	7.00344i		−	0.435172i
$260$	10.3354	−	4.08623i	0.640973	−	0.253417i
$261$		0			0
$262$	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	$0.480902\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$	1.38445	−	0.263748i	0.0848862	−	0.0161715i
$267$		0			0
$268$	2.94137	+	7.43965i	0.179673	+	0.454449i
$269$		−	9.76547i		−	0.595411i	−0.954658	−	0.297706i	$-0.903779\pi$
$269$		−	9.76547i		−	0.595411i	0.954658	−	0.297706i	$-0.0962214\pi$
$270$		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
$273$		0			0
$274$	−1.17590	−	6.17246i	−0.0710387	−	0.372892i
$275$			4.49828i			0.271257i
$276$		0			0
$277$		−	18.7880i		−	1.12886i	−0.825480	−	0.564431i	$-0.809096\pi$
$277$		−	18.7880i		−	1.12886i	0.825480	−	0.564431i	$-0.190904\pi$
$278$	28.0242	−	5.33881i	1.68078	−	0.320200i
$279$		0			0
$280$	2.24914	−	1.42504i	0.134412	−	0.0851624i
$281$	16.8793			1.00693			0.503467	−	0.864014i	$-0.332057\pi$
$281$	16.8793			1.00693			0.503467	+	0.864014i	$0.332057\pi$
$282$		0			0
$283$			20.0000i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$283$			20.0000i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$284$	−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
$288$		0			0
$289$	40.1070			2.35923
$290$	−0.529317	−	2.77846i	−0.0310825	−	0.163157i
$291$		0			0
$292$	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	$0.798790\pi$
$294$		0			0
$295$	8.49828			0.494789
$296$	17.7750	−	11.2621i	1.03315	−	0.654598i
$297$		0			0
$298$	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
$303$		0			0
$304$	2.89572	+	3.08967i	0.166081	+	0.177205i
$305$	8.99656			0.515142
$306$		0			0
$307$			8.11039i			0.462884i	0.972849	+	0.231442i	$0.0743444\pi$
$307$			8.11039i			0.462884i	−0.972849	+	0.231442i	$0.925656\pi$
$308$	3.11383	+	7.87586i	0.177427	+	0.448769i
$309$		0			0
$310$	−4.94137	+	0.941367i	−0.280651	+	0.0534660i
$311$	−31.8759			−1.80751			−0.903757	−	0.428046i	$-0.859202\pi$
$311$	−31.8759			−1.80751			−0.903757	+	0.428046i	$0.859202\pi$
$312$		0			0
$313$	−5.11383			−0.289051			−0.144525	−	0.989501i	$-0.546166\pi$
$313$	−5.11383			−0.289051			−0.144525	+	0.989501i	$0.546166\pi$
$314$	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			0
$319$	8.99656			0.503711
$320$	7.23362	+	3.41683i	0.404372	+	0.191006i
$321$		0			0
$322$	−0.263748	−	1.38445i	−0.0146981	−	0.0771525i
$323$		−	8.00000i		−	0.445132i
$324$		0			0
$325$			5.55691i			0.308242i
$326$	−8.49828	+	1.61899i	−0.470676	+	0.0896673i
$327$		0			0
$328$	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
$333$		0			0
$334$	−1.60256	−	8.41205i	−0.0876881	−	0.460287i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−19.9931			−1.08909			−0.544547	−	0.838730i	$-0.683299\pi$
$337$	−19.9931			−1.08909			−0.544547	+	0.838730i	$0.683299\pi$
$338$	4.73190	+	24.8384i	0.257382	+	1.35103i
$339$		0			0
$340$	−5.55691	−	14.0552i	−0.301366	−	0.762250i
$341$		−	16.0000i		−	0.866449i
$342$		0			0
$343$	−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	$0.940885\pi$
$348$		0			0
$349$		−	4.76203i		−	0.254906i	−0.991845	−	0.127453i	$-0.959320\pi$
$349$		−	4.76203i		−	0.254906i	0.991845	−	0.127453i	$-0.0406801\pi$
$350$	0.249141	+	1.30777i	0.0133171	+	0.0699034i
$351$		0			0
$352$	−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	$0.467828\pi$
$354$		0			0
$355$		−	12.9966i		−	0.689786i
$356$	−7.65775	+	3.02760i	−0.405860	+	0.160462i
$357$		0			0
$358$	−14.7474	+	2.80949i	−0.779425	+	0.148486i
$359$	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
$362$	19.6121	−	3.73625i	1.03079	−	0.196373i
$363$		0			0
$364$	3.84664	+	9.72938i	0.201619	+	0.509958i
$365$			6.00000i			0.314054i
$366$		0			0
$367$	22.9345			1.19717			0.598585	−	0.801059i	$-0.295730\pi$
$367$	22.9345			1.19717			0.598585	+	0.801059i	$0.295730\pi$
$368$	3.08967	−	2.89572i	0.161060	−	0.150950i
$369$		0			0
$370$	1.96896	+	10.3354i	0.102362	+	0.537310i
$371$		−	1.88273i		−	0.0977467i
$372$		0			0
$373$			15.4396i			0.799435i	0.916638	+	0.399717i	$0.130892\pi$
$373$			15.4396i			0.799435i	−0.916638	+	0.399717i	$0.869108\pi$
$374$	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
$378$		0			0
$379$		−	6.28973i		−	0.323082i	−0.986866	−	0.161541i	$-0.948354\pi$
$379$		−	6.28973i		−	0.323082i	0.986866	−	0.161541i	$-0.0516463\pi$
$380$	−1.96896	+	0.778457i	−0.101006	+	0.0399340i
$381$		0			0
$382$	−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	$0.523943\pi$
$384$		0			0
$385$	−4.23453			−0.215812
$386$	1.29135	+	6.77846i	0.0657278	+	0.345014i
$387$		0			0
$388$	−31.8302	+	12.5845i	−1.61593	+	0.638882i
$389$		−	12.2277i		−	0.619967i	−0.950742	−	0.309983i	$-0.899676\pi$
$389$		−	12.2277i		−	0.619967i	0.950742	−	0.309983i	$-0.100324\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−9.25511	−	14.6073i	−0.467453	−	0.737782i
$393$		0			0
$394$	4.00955	−	0.763849i	0.201998	−	0.0384822i
$395$		−	11.5569i		−	0.581491i
$396$		0			0
$397$		−	5.32238i		−	0.267123i	−0.991041	−	0.133561i	$-0.957359\pi$
$397$		−	5.32238i		−	0.267123i	0.991041	−	0.133561i	$-0.0426413\pi$
$398$	4.67762	+	24.5535i	0.234468	+	1.23075i
$399$		0			0
$400$	−2.91855	+	2.73534i	−0.145927	+	0.136767i
$401$	−6.99656			−0.349392			−0.174696	−	0.984622i	$-0.555894\pi$
$401$	−6.99656			−0.349392			−0.174696	+	0.984622i	$0.555894\pi$
$402$		0			0
$403$		−	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
$408$		0			0
$409$	16.2277			0.802406			0.401203	−	0.915989i	$-0.368592\pi$
$409$	16.2277			0.802406			0.401203	+	0.915989i	$0.368592\pi$
$410$	−5.39400	+	1.02760i	−0.266391	+	0.0507494i
$411$		0			0
$412$	−18.9199	+	7.48024i	−0.932116	+	0.368525i
$413$			8.00000i			0.393654i
$414$		0			0
$415$	−5.88273			−0.288772
$416$	−18.5078	+	25.4086i	−0.907421	+	1.24576i
$417$		0			0
$418$	−1.26031	−	6.61555i	−0.0616438	−	0.323577i
$419$			15.6121i			0.762701i	0.924430	+	0.381351i	$0.124541\pi$
$419$			15.6121i			0.762701i	−0.924430	+	0.381351i	$0.875459\pi$
$420$		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
$423$		0			0
$424$	4.77846	−	3.02760i	0.232062	−	0.147033i
$425$	7.55691			0.366564
$426$		0			0
$427$			8.46907i			0.409847i
$428$	−12.6707	−	32.0483i	−0.612463	−	1.54911i
$429$		0			0
$430$	0.498281	+	2.61555i	0.0240292	+	0.126133i
$431$	12.9966			0.626022			0.313011	−	0.949749i	$-0.398662\pi$
$431$	12.9966			0.626022			0.313011	+	0.949749i	$0.398662\pi$
$432$		0			0
$433$	20.2277			0.972079			0.486040	−	0.873937i	$-0.338441\pi$
$433$	20.2277			0.972079			0.486040	+	0.873937i	$0.338441\pi$
$434$	−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
$438$		0			0
$439$	−5.43965			−0.259620			−0.129810	−	0.991539i	$-0.541437\pi$
$439$	−5.43965			−0.259620			−0.129810	+	0.991539i	$0.541437\pi$
$440$	−6.80949	−	10.7474i	−0.324630	−	0.512363i
$441$		0			0
$442$	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	$0.881202\pi$
$444$		0			0
$445$		−	4.11727i		−	0.195177i
$446$	6.36641	+	33.4182i	0.301458	+	1.58240i
$447$		0			0
$448$	−3.21649	+	6.80949i	−0.151965	+	0.321718i
$449$	−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
$452$	28.4983	−	11.2672i	1.34045	−	0.529964i
$453$		0			0
$454$	−15.4396	+	2.94137i	−0.724619	+	0.138045i
$455$	−5.23109			−0.245238
$456$		0			0
$457$	2.65164			0.124038			0.0620192	−	0.998075i	$-0.480246\pi$
$457$	2.65164			0.124038			0.0620192	+	0.998075i	$0.480246\pi$
$458$	−23.9379	+	4.56035i	−1.11855	+	0.213091i
$459$		0			0
$460$	0.778457	+	1.96896i	0.0362958	+	0.0918034i
$461$			10.2345i			0.476670i	0.971183	+	0.238335i	$0.0766016\pi$
$461$			10.2345i			0.476670i	−0.971183	+	0.238335i	$0.923398\pi$
$462$		0			0
$463$	19.0586			0.885730			0.442865	−	0.896588i	$-0.353962\pi$
$463$	19.0586			0.885730			0.442865	+	0.896588i	$0.353962\pi$
$464$	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	$0.969682\pi$
$468$		0			0
$469$		−	3.76547i		−	0.173873i
$470$	−13.9690	+	2.66119i	−0.644340	+	0.122752i
$471$		0			0
$472$	−20.3043	+	12.8647i	−0.934583	+	0.592145i
$473$	−8.46907			−0.389408
$474$		0			0
$475$		−	1.05863i		−	0.0485734i
$476$	13.2311	−	5.23109i	0.606446	−	0.239767i
$477$		0			0
$478$	2.67762	+	14.0552i	0.122471	+	0.642870i
$479$	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
$482$	−4.46725	−	23.4492i	−0.203477	−	1.06808i
$483$		0			0
$484$	17.1754	−	6.79054i	0.780701	−	0.308661i
$485$		−	17.1138i		−	0.777099i
$486$		0			0
$487$	−21.9379			−0.994102			−0.497051	−	0.867721i	$-0.665584\pi$
$487$	−21.9379			−0.994102			−0.497051	+	0.867721i	$0.665584\pi$
$488$	−21.4948	+	13.6190i	−0.973026	+	0.616502i
$489$		0			0
$490$	8.49351	−	1.61808i	0.383697	−	0.0730972i
$491$			7.50172i			0.338548i	0.985569	+	0.169274i	$0.0541423\pi$
$491$			7.50172i			0.338548i	−0.985569	+	0.169274i	$0.945858\pi$
$492$		0			0
$493$		−	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
$498$		0			0
$499$		−	29.1690i		−	1.30578i	−0.757451	−	0.652892i	$-0.773555\pi$
$499$		−	29.1690i		−	1.30578i	0.757451	−	0.652892i	$-0.226445\pi$
$500$	−0.735342	−	1.85991i	−0.0328855	−	0.0831778i
$501$		0			0
$502$	−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	$0.320813\pi$
$504$		0			0
$505$	−2.00000			−0.0889988
$506$	−6.61555	+	1.26031i	−0.294097	+	0.0560276i
$507$		0			0
$508$	33.7992	−	13.3630i	1.49960	−	0.592886i
$509$		−	28.6967i		−	1.27196i	−0.771706	−	0.635980i	$-0.780596\pi$
$509$		−	28.6967i		−	1.27196i	0.771706	−	0.635980i	$-0.219404\pi$
$510$		0			0
$511$	−5.64820			−0.249862
$512$	−22.4552	+	2.78667i	−0.992387	+	0.123155i
$513$		0			0
$514$	−2.82410	−	14.8241i	−0.124566	−	0.653863i
$515$		−	10.1725i		−	0.448252i
$516$		0			0
$517$		−	45.2311i		−	1.98926i
$518$	−9.72938	+	1.85352i	−0.427484	+	0.0814389i
$519$		0			0
$520$	−8.41205	−	13.2767i	−0.368893	−	0.582223i
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$			25.7586i			1.12634i	0.826340	+	0.563172i	$0.190419\pi$
$523$			25.7586i			1.12634i	−0.826340	+	0.563172i	$0.809581\pi$
$524$	−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
$528$		0			0
$529$	−21.8793			−0.951274
$530$	0.529317	+	2.77846i	0.0229920	+	0.120688i
$531$		0			0
$532$	−0.732814	−	1.85352i	−0.0317715	−	0.0803602i
$533$		−	21.5760i		−	0.934561i
$534$		0			0
$535$	17.2311			0.744965
$536$	9.55691	−	6.05520i	0.412796	−	0.261545i
$537$		0			0
$538$	−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
$543$		0			0
$544$	34.5535	+	25.1690i	1.48147	+	1.07911i
$545$	1.88273			0.0806475
$546$		0			0
$547$		−	19.8759i		−	0.849830i	−0.905233	−	0.424915i	$-0.860304\pi$
$547$		−	19.8759i		−	0.849830i	0.905233	−	0.424915i	$-0.139696\pi$
$548$	−8.26375	+	3.26719i	−0.353010	+	0.139567i
$549$		0			0
$550$	6.24914	−	1.19051i	0.266464	−	0.0507634i
$551$	−2.11727			−0.0901986
$552$		0			0
$553$	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			0
$559$	−10.4622			−0.442503
$560$	−2.57496	−	2.74742i	−0.108812	−	0.116100i
$561$		0			0
$562$	−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	$0.995629\pi$
$564$		0			0
$565$			15.3224i			0.644617i
$566$	27.7846	−	5.29317i	1.16787	−	0.222488i
$567$		0			0
$568$	19.6742	+	31.0518i	0.825510	+	1.30290i
$569$	−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	$0.101213\pi$
$571$			14.9414i			0.625277i	−0.949872	+	0.312638i	$0.898787\pi$
$572$	46.4914	−	18.3810i	1.94390	−	0.768549i
$573$		0			0
$574$	−0.967346	−	5.07774i	−0.0403763	−	0.211941i
$575$	−1.05863			−0.0441481
$576$		0			0
$577$	−8.87930			−0.369650			−0.184825	−	0.982771i	$-0.559172\pi$
$577$	−8.87930			−0.369650			−0.184825	+	0.982771i	$0.559172\pi$
$578$	−10.6146	−	55.7177i	−0.441511	−	2.31755i
$579$		0			0
$580$	−3.71982	+	1.47068i	−0.154457	+	0.0610668i
$581$		−	5.53781i		−	0.229747i
$582$		0			0
$583$	−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	$-0.00808797\pi$
$588$		0			0
$589$			3.76547i			0.155153i
$590$	−2.24914	−	11.8061i	−0.0925957	−	0.486048i
$591$		0			0
$592$	−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	$0.523268\pi$
$594$		0			0
$595$			7.11383i			0.291639i
$596$	−1.47068	−	3.71982i	−0.0602415	−	0.152370i
$597$		0			0
$598$	−8.17246	+	1.55691i	−0.334197	+	0.0636670i
$599$	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	$0.691567\pi$
$602$	−2.46219	+	0.469065i	−0.100351	+	0.0191177i
$603$		0			0
$604$	−17.9931	+	7.11383i	−0.732130	+	0.289458i
$605$			9.23453i			0.375437i
$606$		0			0
$607$	7.16902			0.290982			0.145491	−	0.989360i	$-0.453524\pi$
$607$	7.16902			0.290982			0.145491	+	0.989360i	$0.453524\pi$
$608$	3.52588	−	4.84053i	0.142993	−	0.196309i
$609$		0			0
$610$	−2.38101	−	12.4983i	−0.0964045	−	0.506041i
$611$		−	55.8759i		−	2.26050i
$612$		0			0
$613$			9.55691i			0.386000i	0.981199	+	0.193000i	$0.0618218\pi$
$613$			9.55691i			0.386000i	−0.981199	+	0.193000i	$0.938178\pi$
$614$	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	$0.508518\pi$
$618$		0			0
$619$			28.1725i			1.13235i	0.824286	+	0.566173i	$0.191577\pi$
$619$			28.1725i			1.13235i	−0.824286	+	0.566173i	$0.808423\pi$
$620$	2.61555	+	6.61555i	0.105043	+	0.265687i
$621$		0			0
$622$	8.43621	+	44.2829i	0.338261	+	1.77558i
$623$	3.87586			0.155283
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.35342	+	7.10428i	0.0540934	+	0.283944i
$627$		0			0
$628$	−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
$633$		0			0
$634$	−34.2372	+	6.52244i	−1.35973	+	0.259039i
$635$			18.1725i			0.721152i
$636$		0			0
$637$			33.9740i			1.34610i
$638$	−2.38101	−	12.4983i	−0.0942653	−	0.494812i
$639$		0			0
$640$	2.83231	−	10.9534i	0.111957	−	0.432973i
$641$	−27.1070			−1.07066			−0.535330	−	0.844643i	$-0.679813\pi$
$641$	−27.1070			−1.07066			−0.535330	+	0.844643i	$0.679813\pi$
$642$		0			0
$643$			20.3449i			0.802325i	0.916007	+	0.401163i	$0.131394\pi$
$643$			20.3449i			0.802325i	−0.916007	+	0.401163i	$0.868606\pi$
$644$	−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	$0.765649\pi$
$648$		0			0
$649$	38.2277			1.50057
$650$	7.71982	−	1.47068i	0.302796	−	0.0576849i
$651$		0			0
$652$	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			0
$655$	6.38101			0.249327
$656$	11.3319	−	10.6206i	0.442438	−	0.414665i
$657$		0			0
$658$	−2.50516	−	13.1499i	−0.0976612	−	0.512637i
$659$		−	29.2603i		−	1.13982i	−0.821707	−	0.569910i	$-0.806978\pi$
$659$		−	29.2603i		−	1.13982i	0.821707	−	0.569910i	$-0.193022\pi$
$660$		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
$663$		0			0
$664$	14.0552	−	8.90528i	0.545447	−	0.345592i
$665$	0.996562			0.0386450
$666$		0			0
$667$			2.11727i			0.0819809i
$668$	−11.2621	+	4.45264i	−0.435745	+	0.172278i
$669$		0			0
$670$	1.05863	+	5.55691i	0.0408986	+	0.214682i
$671$	40.4691			1.56229
$672$		0			0
$673$	−18.0000			−0.693849			−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000			−0.693849			−0.346925	+	0.937893i	$0.612774\pi$
$674$	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	$0.691816\pi$
$678$		0			0
$679$	16.1104			0.618260
$680$	−18.0552	+	11.4396i	−0.692385	+	0.438690i
$681$		0			0
$682$	−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			0
$685$		−	4.44309i		−	0.169762i
$686$	3.26719	+	17.1499i	0.124742	+	0.654787i
$687$		0			0
$688$	−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
$693$		0			0
$694$	9.55691	−	1.82066i	0.362776	−	0.0691114i
$695$	20.1725			0.765185
$696$		0			0
$697$	−29.3415			−1.11139
$698$	−6.61555	+	1.26031i	−0.250402	+	0.0477035i
$699$		0			0
$700$	1.75086	−	0.692226i	0.0661763	−	0.0261637i
$701$		−	7.99312i		−	0.301896i	−0.988542	−	0.150948i	$-0.951767\pi$
$701$		−	7.99312i		−	0.301896i	0.988542	−	0.150948i	$-0.0482326\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$		−	28.9966i		−	1.08899i	−0.838764	−	0.544494i	$-0.816722\pi$
$709$		−	28.9966i		−	1.08899i	0.838764	−	0.544494i	$-0.183278\pi$
$710$	−18.0552	+	3.43965i	−0.677599	+	0.129088i
$711$		0			0
$712$	6.23271	+	9.83709i	0.233581	+	0.368661i
$713$	3.76547			0.141018
$714$		0			0
$715$			24.9966i			0.934818i
$716$	7.80605	+	19.7440i	0.291726	+	0.737867i
$717$		0			0
$718$	−3.43965	−	18.0552i	−0.128367	−	0.673814i
$719$	−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
$722$	−4.73190	−	24.8384i	−0.176103	−	0.924391i
$723$		0			0
$724$	−10.3810	−	26.2569i	−0.385807	−	0.975829i
$725$		−	2.00000i		−	0.0742781i
$726$		0			0
$727$	41.8138			1.55079			0.775394	−	0.631478i	$-0.217551\pi$
$727$	41.8138			1.55079			0.775394	+	0.631478i	$0.217551\pi$
$728$	12.4983	−	7.91883i	0.463217	−	0.293491i
$729$		0			0
$730$	8.33537	−	1.58795i	0.308506	−	0.0587727i
$731$			14.2277i			0.526229i
$732$		0			0
$733$			30.0844i			1.11119i	0.831452	+	0.555597i	$0.187510\pi$
$733$			30.0844i			1.11119i	−0.831452	+	0.555597i	$0.812490\pi$
$734$	−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
$738$		0			0
$739$			29.0449i			1.06843i	0.845348	+	0.534217i	$0.179393\pi$
$739$			29.0449i			1.06843i	−0.845348	+	0.534217i	$0.820607\pi$
$740$	13.8371	−	5.47068i	0.508662	−	0.201106i
$741$		0			0
$742$	−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	$0.207990\pi$
$744$		0			0
$745$	2.00000			0.0732743
$746$	21.4492	−	4.08623i	0.785311	−	0.149608i
$747$		0			0
$748$	−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
$753$		0			0
$754$	−2.94137	−	15.4396i	−0.107118	−	0.562279i
$755$		−	9.67418i		−	0.352079i
$756$		0			0
$757$		−	16.3258i		−	0.593372i	−0.954975	−	0.296686i	$-0.904119\pi$
$757$		−	16.3258i		−	0.593372i	0.954975	−	0.296686i	$-0.0958815\pi$
$758$	−8.73787	+	1.66463i	−0.317374	+	0.0604620i
$759$		0			0
$760$	1.60256	+	2.52932i	0.0581309	+	0.0917480i
$761$	−50.2208			−1.82050			−0.910251	−	0.414057i	$-0.864111\pi$
$761$	−50.2208			−1.82050			−0.910251	+	0.414057i	$0.864111\pi$
$762$		0			0
$763$			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
$768$		0			0
$769$	−31.3415			−1.13020			−0.565101	−	0.825021i	$-0.691163\pi$
$769$	−31.3415			−1.13020			−0.565101	+	0.825021i	$0.691163\pi$
$770$	1.12070	+	5.88273i	0.0403874	+	0.211999i
$771$		0			0
$772$	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	$0.947592\pi$
$774$		0			0
$775$	−3.55691			−0.127768
$776$	25.9069	+	40.8888i	0.930003	+	1.46782i
$777$		0			0
$778$	−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
$783$		0			0
$784$	−17.8435	+	16.7234i	−0.637267	+	0.597265i
$785$	4.32582			0.154395
$786$		0			0
$787$			36.2208i			1.29113i	0.763705	+	0.645566i	$0.223378\pi$
$787$			36.2208i			1.29113i	−0.763705	+	0.645566i	$0.776622\pi$
$788$	−2.12232	−	5.36802i	−0.0756046	−	0.191228i
$789$		0			0
$790$	−16.0552	+	3.05863i	−0.571218	+	0.108821i
$791$	−14.4240			−0.512858
$792$		0			0
$793$	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			0
$799$	−75.9862			−2.68820
$800$	4.57243	+	3.33060i	0.161660	+	0.117754i
$801$		0			0
$802$	1.85170	+	9.71982i	0.0653857	+	0.343219i
$803$			26.9897i			0.952445i
$804$		0			0
$805$		−	0.996562i		−	0.0351242i
$806$	−27.4588	+	5.23109i	−0.967193	+	0.184257i
$807$		0			0
$808$	4.77846	−	3.02760i	0.168106	−	0.106511i
$809$	−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	$0.117302\pi$
$811$			20.5174i			0.720463i	−0.932863	+	0.360231i	$0.882698\pi$
$812$	−1.38445	−	3.50172i	−0.0485848	−	0.122886i
$813$		0			0
$814$	8.85696	+	46.4914i	0.310436	+	1.62952i
$815$	−6.11727			−0.214278
$816$		0			0
$817$	1.99312			0.0697306
$818$	−4.29478	−	22.5439i	−0.150164	−	0.788230i
$819$		0			0
$820$	2.85514	+	7.22154i	0.0997057	+	0.252187i
$821$		−	44.4622i		−	1.55174i	−0.630892	−	0.775871i	$-0.717311\pi$
$821$		−	44.4622i		−	1.55174i	0.630892	−	0.775871i	$-0.282689\pi$
$822$		0			0
$823$	32.1656			1.12122			0.560611	−	0.828079i	$-0.310566\pi$
$823$	32.1656			1.12122			0.560611	+	0.828079i	$0.310566\pi$
$824$	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	$0.886951\pi$
$828$		0			0
$829$			33.8827i			1.17680i	0.808571	+	0.588398i	$0.200241\pi$
$829$			33.8827i			1.17680i	−0.808571	+	0.588398i	$0.799759\pi$
$830$	1.55691	+	8.17246i	0.0540413	+	0.283670i
$831$		0			0
$832$	40.1966	+	18.9870i	1.39357	+	0.658256i
$833$	46.2017			1.60079
$834$		0			0
$835$		−	6.05520i		−	0.209549i
$836$	−8.85696	+	3.50172i	−0.306324	+	0.121109i
$837$		0			0
$838$	21.6888	−	4.13187i	0.749227	−	0.142733i
$839$	−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
$842$	46.1656	−	8.79488i	1.59097	−	0.303092i
$843$		0			0
$844$	17.6026	+	44.5224i	0.605905	+	1.53253i
$845$			17.8793i			0.615066i
$846$		0			0
$847$	−8.69308			−0.298698
$848$	−5.47068	−	5.83709i	−0.187864	−	0.200447i
$849$		0			0
$850$	−2.00000	−	10.4983i	−0.0685994	−	0.360088i
$851$		−	7.87586i		−	0.269981i
$852$		0			0
$853$		−	50.4293i		−	1.72667i	−0.504633	−	0.863334i	$-0.668372\pi$
$853$		−	50.4293i		−	1.72667i	0.504633	−	0.863334i	$-0.331628\pi$
$854$	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	$0.649119\pi$
$858$		0			0
$859$			0.406994i			0.0138865i	0.999976	+	0.00694323i	$0.00221012\pi$
$859$			0.406994i			0.0138865i	−0.999976	+	0.00694323i	$0.997790\pi$
$860$	3.50172	−	1.38445i	0.119408	−	0.0472094i
$861$		0			0
$862$	−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	$0.329855\pi$
$864$		0			0
$865$	−16.8793			−0.573913
$866$	−5.35342	−	28.1008i	−0.181917	−	0.954905i
$867$		0			0
$868$	−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
$873$		0			0
$874$	1.55691	−	0.296604i	0.0526634	−	0.0100328i
$875$			0.941367i			0.0318240i
$876$		0			0
$877$		−	11.2051i		−	0.378370i	−0.981941	−	0.189185i	$-0.939415\pi$
$877$		−	11.2051i		−	0.378370i	0.981941	−	0.189185i	$-0.0605846\pi$
$878$	1.43965	+	7.55691i	0.0485858	+	0.255034i
$879$		0			0
$880$	−13.1284	+	12.3043i	−0.442559	+	0.414779i
$881$	48.3380			1.62855			0.814275	−	0.580479i	$-0.197135\pi$
$881$	48.3380			1.62855			0.814275	+	0.580479i	$0.197135\pi$
$882$		0			0
$883$		−	50.5726i		−	1.70190i	−0.525244	−	0.850951i	$-0.676026\pi$
$883$		−	50.5726i		−	1.70190i	0.525244	−	0.850951i	$-0.323974\pi$
$884$	−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	$0.201277\pi$
$888$		0			0
$889$	−17.1070			−0.573749
$890$	−5.71982	+	1.08967i	−0.191729	+	0.0365258i
$891$		0			0
$892$	44.7405	−	17.6888i	1.49802	−	0.592264i
$893$			10.6448i			0.356213i
$894$		0			0
$895$	−10.6155			−0.354839
$896$	10.3112	+	2.66625i	0.344473	+	0.0890731i
$897$		0			0
$898$	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
$903$		0			0
$904$	−23.1950	−	36.6087i	−0.771454	−	1.21759i
$905$	14.1173			0.469274
$906$		0			0
$907$		−	6.46219i		−	0.214573i	−0.994228	−	0.107287i	$-0.965784\pi$
$907$		−	6.46219i		−	0.214573i	0.994228	−	0.107287i	$-0.0342163\pi$
$908$	8.17246	+	20.6707i	0.271213	+	0.685983i
$909$		0			0
$910$	1.38445	+	7.26719i	0.0458942	+	0.240905i
$911$	−50.3380			−1.66777			−0.833887	−	0.551935i	$-0.813890\pi$
$911$	−50.3380			−1.66777			−0.833887	+	0.551935i	$0.813890\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$	46.4362			1.53179			0.765895	−	0.642966i	$-0.222296\pi$
$919$	46.4362			1.53179			0.765895	+	0.642966i	$0.222296\pi$
$920$	2.52932	−	1.60256i	0.0833891	−	0.0528348i
$921$		0			0
$922$	14.2181	−	2.70865i	0.468248	−	0.0892048i
$923$		−	72.2208i		−	2.37718i
$924$		0			0
$925$			7.43965i			0.244614i
$926$	−5.04403	−	26.4768i	−0.165757	−	0.870082i
$927$		0			0
$928$	6.66119	−	9.14486i	0.218664	−	0.300195i
$929$	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
$932$	−15.7034	+	6.20855i	−0.514382	+	0.203368i
$933$		0			0
$934$	5.71027	−	1.08785i	0.186846	−	0.0355955i
$935$	33.9931			1.11169
$936$		0			0
$937$	2.70360			0.0883227			0.0441613	−	0.999024i	$-0.485938\pi$
$937$	2.70360			0.0883227			0.0441613	+	0.999024i	$0.485938\pi$
$938$	−5.23109	+	0.996562i	−0.170801	+	0.0325389i
$939$		0			0
$940$	7.39400	+	18.7018i	0.241166	+	0.609985i
$941$			17.7655i			0.579138i	0.957157	+	0.289569i	$0.0935119\pi$
$941$			17.7655i			0.579138i	−0.957157	+	0.289569i	$0.906488\pi$
$942$		0			0
$943$	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	$0.859872\pi$
$948$		0			0
$949$			33.3415i			1.08231i
$950$	−1.47068	+	0.280176i	−0.0477153	+	0.00909011i
$951$		0			0
$952$	−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	$0.547059\pi$
$954$		0			0
$955$		−	8.00000i		−	0.258874i
$956$	18.8172	−	7.43965i	0.608593	−	0.240615i
$957$		0			0
$958$	−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
$963$		0			0
$964$	−31.3940	+	12.4121i	−1.01113	+	0.399765i
$965$			4.87930i			0.157070i
$966$		0			0
$967$	−7.47574			−0.240404			−0.120202	−	0.992749i	$-0.538354\pi$
$967$	−7.47574			−0.240404			−0.120202	+	0.992749i	$0.538354\pi$
$968$	−13.9792	−	22.0634i	−0.449309	−	0.709145i
$969$		0			0
$970$	−23.7750	+	4.52932i	−0.763370	+	0.145428i
$971$			41.0777i			1.31825i	0.752035	+	0.659124i	$0.229073\pi$
$971$			41.0777i			1.31825i	−0.752035	+	0.659124i	$0.770927\pi$
$972$		0			0
$973$			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	$0.478555\pi$
$978$		0			0
$979$		−	18.5206i		−	0.591922i
$980$	−4.49575	−	11.3712i	−0.143612	−	0.363239i
$981$		0			0
$982$	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	$0.457461\pi$
$984$		0			0
$985$	2.88617			0.0919611
$986$	−20.9966	+	4.00000i	−0.668667	+	0.127386i
$987$		0			0
$988$	−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
$993$		0			0
$994$	−3.23797	−	16.9966i	−0.102702	−	0.539098i
$995$			17.6742i			0.560309i
$996$		0			0
$997$			34.8984i			1.10524i	0.833432	+	0.552622i	$0.186373\pi$
$997$			34.8984i			1.10524i	−0.833432	+	0.552622i	$0.813627\pi$
$998$	−40.5224	+	7.71982i	−1.28272	+	0.244367i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.3	✓	6	24.5	odd	2
120.2.k.b.61.4	yes	6	3.2	odd	2
360.2.k.f.181.3		6	1.1	even	1	trivial
360.2.k.f.181.4		6	8.5	even	2	inner
480.2.k.b.241.2		6	12.11	even	2
480.2.k.b.241.5		6	24.11	even	2
600.2.d.e.349.5		6	15.8	even	4
600.2.d.e.349.6		6	120.77	even	4
600.2.d.f.349.1		6	120.53	even	4
600.2.d.f.349.2		6	15.2	even	4
600.2.k.c.301.3		6	15.14	odd	2
600.2.k.c.301.4		6	120.29	odd	2
1440.2.k.f.721.2		6	4.3	odd	2
1440.2.k.f.721.5		6	8.3	odd	2
1800.2.d.q.1549.1		6	40.37	odd	4
1800.2.d.q.1549.2		6	5.3	odd	4
1800.2.d.r.1549.5		6	5.2	odd	4
1800.2.d.r.1549.6		6	40.13	odd	4
1800.2.k.p.901.3		6	40.29	even	2
1800.2.k.p.901.4		6	5.4	even	2
2400.2.d.e.49.3		6	60.47	odd	4
2400.2.d.e.49.4		6	120.83	odd	4
2400.2.d.f.49.3		6	120.107	odd	4
2400.2.d.f.49.4		6	60.23	odd	4
2400.2.k.c.1201.2		6	120.59	even	2
2400.2.k.c.1201.5		6	60.59	even	2
3840.2.a.bo.1.2		3	48.11	even	4
3840.2.a.bp.1.2		3	48.29	odd	4
3840.2.a.bq.1.2		3	48.5	odd	4
3840.2.a.br.1.2		3	48.35	even	4
7200.2.d.q.2449.3		6	40.27	even	4
7200.2.d.q.2449.4		6	20.3	even	4
7200.2.d.r.2449.3		6	20.7	even	4
7200.2.d.r.2449.4		6	40.3	even	4
7200.2.k.p.3601.3		6	40.19	odd	2
7200.2.k.p.3601.4		6	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.264658 - 1.38923i) q^{2} +(-1.85991 + 0.735342i) q^{4} -1.00000i q^{5} +0.941367 q^{7} +(1.51380 + 2.38923i) q^{8} +O(q^{10})\)	\(q+(-0.264658 - 1.38923i) q^{2} +(-1.85991 + 0.735342i) q^{4} -1.00000i q^{5} +0.941367 q^{7} +(1.51380 + 2.38923i) q^{8} +(-1.38923 + 0.264658i) q^{10} -4.49828i q^{11} -5.55691i q^{13} +(-0.249141 - 1.30777i) q^{14} +(2.91855 - 2.73534i) q^{16} -7.55691 q^{17} +1.05863i q^{19} +(0.735342 + 1.85991i) q^{20} +(-6.24914 + 1.19051i) q^{22} +1.05863 q^{23} -1.00000 q^{25} +(-7.71982 + 1.47068i) q^{26} +(-1.75086 + 0.692226i) q^{28} +2.00000i q^{29} +3.55691 q^{31} +(-4.57243 - 3.33060i) q^{32} +(2.00000 + 10.4983i) q^{34} -0.941367i q^{35} -7.43965i q^{37} +(1.47068 - 0.280176i) q^{38} +(2.38923 - 1.51380i) q^{40} +3.88273 q^{41} -1.88273i q^{43} +(3.30777 + 8.36641i) q^{44} +(-0.280176 - 1.47068i) q^{46} +10.0552 q^{47} -6.11383 q^{49} +(0.264658 + 1.38923i) q^{50} +(4.08623 + 10.3354i) q^{52} -2.00000i q^{53} -4.49828 q^{55} +(1.42504 + 2.24914i) q^{56} +(2.77846 - 0.529317i) q^{58} +8.49828i q^{59} +8.99656i q^{61} +(-0.941367 - 4.94137i) q^{62} +(-3.41683 + 7.23362i) q^{64} -5.55691 q^{65} -4.00000i q^{67} +(14.0552 - 5.55691i) q^{68} +(-1.30777 + 0.249141i) q^{70} +12.9966 q^{71} -6.00000 q^{73} +(-10.3354 + 1.96896i) q^{74} +(-0.778457 - 1.96896i) q^{76} -4.23453i q^{77} +11.5569 q^{79} +(-2.73534 - 2.91855i) q^{80} +(-1.02760 - 5.39400i) q^{82} -5.88273i q^{83} +7.55691i q^{85} +(-2.61555 + 0.498281i) q^{86} +(10.7474 - 6.80949i) q^{88} +4.11727 q^{89} -5.23109i q^{91} +(-1.96896 + 0.778457i) q^{92} +(-2.66119 - 13.9690i) q^{94} +1.05863 q^{95} +17.1138 q^{97} +(1.61808 + 8.49351i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 8 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 8 * q^8	\( 6 q - 2 q^{2} - 2 q^{4} + 4 q^{7} - 8 q^{8} + 16 q^{14} + 10 q^{16} - 12 q^{17} + 4 q^{20} - 20 q^{22} + 8 q^{23} - 6 q^{25} - 28 q^{26} - 28 q^{28} - 12 q^{31} - 12 q^{32} + 12 q^{34} + 8 q^{38} + 6 q^{40} + 20 q^{41} + 4 q^{44} - 20 q^{46} - 8 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{52} + 8 q^{55} - 4 q^{56} - 4 q^{62} + 22 q^{64} + 16 q^{68} + 8 q^{70} + 8 q^{71} - 36 q^{73} - 12 q^{74} + 12 q^{76} + 36 q^{79} - 16 q^{80} + 28 q^{82} + 16 q^{86} + 12 q^{88} + 28 q^{89} + 24 q^{92} + 4 q^{94} + 8 q^{95} + 36 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 - 8 * q^8 + 16 * q^14 + 10 * q^16 - 12 * q^17 + 4 * q^20 - 20 * q^22 + 8 * q^23 - 6 * q^25 - 28 * q^26 - 28 * q^28 - 12 * q^31 - 12 * q^32 + 12 * q^34 + 8 * q^38 + 6 * q^40 + 20 * q^41 + 4 * q^44 - 20 * q^46 - 8 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^52 + 8 * q^55 - 4 * q^56 - 4 * q^62 + 22 * q^64 + 16 * q^68 + 8 * q^70 + 8 * q^71 - 36 * q^73 - 12 * q^74 + 12 * q^76 + 36 * q^79 - 16 * q^80 + 28 * q^82 + 16 * q^86 + 12 * q^88 + 28 * q^89 + 24 * q^92 + 4 * q^94 + 8 * q^95 + 36 * q^97 + 6 * q^98

Introduction

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