LMFDB - Embedded newform 1530.2.m.e.647.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1530,2,Mod(647,1530)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1530.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1530, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,4,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.e.953.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(1.00000 + 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.00000 + 1.00000i) q^{10} -2.82843i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.41421 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +4.00000i q^{19} +(-2.12132 + 0.707107i) q^{20} +(2.00000 + 2.00000i) q^{22} +(5.65685 + 5.65685i) q^{23} +(-4.00000 + 3.00000i) q^{25} -5.65685i q^{26} +(1.00000 - 1.00000i) q^{28} +9.89949 q^{29} +6.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(1.41421 - 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(1.00000 - 2.00000i) q^{40} -5.65685i q^{41} +(1.00000 - 1.00000i) q^{43} -2.82843 q^{44} -8.00000 q^{46} -5.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-6.00000 + 2.00000i) q^{55} +1.41421i q^{56} +(-7.00000 + 7.00000i) q^{58} +1.41421 q^{59} +8.00000 q^{61} +(-4.24264 + 4.24264i) q^{62} +1.00000i q^{64} +(11.3137 + 5.65685i) q^{65} +(9.00000 + 9.00000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(1.00000 + 3.00000i) q^{70} -15.5563i q^{71} +(12.0000 - 12.0000i) q^{73} +4.24264 q^{74} +4.00000 q^{76} +(2.82843 - 2.82843i) q^{77} -8.00000i q^{79} +(0.707107 + 2.12132i) q^{80} +(4.00000 + 4.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-2.00000 - 1.00000i) q^{85} +1.41421i q^{86} +(2.00000 - 2.00000i) q^{88} -7.07107 q^{89} -8.00000 q^{91} +(5.65685 - 5.65685i) q^{92} +(8.48528 - 2.82843i) q^{95} +(10.0000 + 10.0000i) q^{97} +(3.53553 + 3.53553i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{7} + 8 q^{10} - 16 q^{13} - 4 q^{16} + 8 q^{22} - 16 q^{25} + 4 q^{28} + 24 q^{31} - 12 q^{37} + 4 q^{40} + 4 q^{43} - 32 q^{46} + 16 q^{52} - 24 q^{55} - 28 q^{58} + 32 q^{61} + 36 q^{67} + 4 q^{70}+ \cdots + 40 q^{97}+O(q^{100}) $ 4 * q + 4 * q^7 + 8 * q^10 - 16 * q^13 - 4 * q^16 + 8 * q^22 - 16 * q^25 + 4 * q^28 + 24 * q^31 - 12 * q^37 + 4 * q^40 + 4 * q^43 - 32 * q^46 + 16 * q^52 - 24 * q^55 - 28 * q^58 + 32 * q^61 + 36 * q^67 + 4 * q^70 + 48 * q^73 + 16 * q^76 + 16 * q^82 - 8 * q^85 + 8 * q^88 - 32 * q^91 + 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$		−	2.82843i		−	0.852803i	−0.904534	−	0.426401i	$-0.859781\pi$
$11$		−	2.82843i		−	0.852803i	0.904534	−	0.426401i	$-0.140219\pi$
$12$		0			0
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.116171	+	0.993229i	$0.537062\pi$
$13$	−4.00000	+	4.00000i	−1.10940	+	1.10940i	−0.993229	+	0.116171i	$0.962938\pi$
$14$	−1.41421			−0.377964
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	−2.12132	+	0.707107i	−0.474342	+	0.158114i
$21$		0			0
$22$	2.00000	+	2.00000i	0.426401	+	0.426401i
$23$	5.65685	+	5.65685i	1.17954	+	1.17954i	0.979863	+	0.199673i	$0.0639880\pi$
$23$	5.65685	+	5.65685i	1.17954	+	1.17954i	0.199673	+	0.979863i	$0.436012\pi$
$24$		0			0
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$		−	5.65685i		−	1.10940i
$27$		0			0
$28$	1.00000	−	1.00000i	0.188982	−	0.188982i
$29$	9.89949			1.83829			0.919145	−	0.393919i	$-0.128881\pi$
$29$	9.89949			1.83829			0.919145	+	0.393919i	$0.128881\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			1.00000i			0.171499i
$35$	1.41421	−	2.82843i	0.239046	−	0.478091i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−2.82843	−	2.82843i	−0.458831	−	0.458831i
$39$		0			0
$40$	1.00000	−	2.00000i	0.158114	−	0.316228i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	−0.626734	−	0.779233i	$-0.715609\pi$
$43$	1.00000	−	1.00000i	0.152499	−	0.152499i	0.779233	+	0.626734i	$0.215609\pi$
$44$	−2.82843			−0.426401
$45$		0			0
$46$	−8.00000			−1.17954
$47$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$47$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	0.707107	−	4.94975i	0.100000	−	0.700000i
$51$		0			0
$52$	4.00000	+	4.00000i	0.554700	+	0.554700i
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	0.352892	−	0.935664i	$-0.385198\pi$
$53$	−4.24264	−	4.24264i	−0.582772	−	0.582772i	−0.935664	+	0.352892i	$0.885198\pi$
$54$		0			0
$55$	−6.00000	+	2.00000i	−0.809040	+	0.269680i
$56$			1.41421i			0.188982i
$57$		0			0
$58$	−7.00000	+	7.00000i	−0.919145	+	0.919145i
$59$	1.41421			0.184115			0.0920575	−	0.995754i	$-0.470656\pi$
$59$	1.41421			0.184115			0.0920575	+	0.995754i	$0.470656\pi$
$60$		0			0
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−4.24264	+	4.24264i	−0.538816	+	0.538816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	11.3137	+	5.65685i	1.40329	+	0.701646i
$66$		0			0
$67$	9.00000	+	9.00000i	1.09952	+	1.09952i	0.994466	+	0.105059i	$0.0335031\pi$
$67$	9.00000	+	9.00000i	1.09952	+	1.09952i	0.105059	+	0.994466i	$0.466497\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	1.00000	+	3.00000i	0.119523	+	0.358569i
$71$		−	15.5563i		−	1.84620i	−0.384561	−	0.923099i	$-0.625647\pi$
$71$		−	15.5563i		−	1.84620i	0.384561	−	0.923099i	$-0.374353\pi$
$72$		0			0
$73$	12.0000	−	12.0000i	1.40449	−	1.40449i	0.619486	−	0.785007i	$-0.287341\pi$
$73$	12.0000	−	12.0000i	1.40449	−	1.40449i	0.785007	−	0.619486i	$-0.212659\pi$
$74$	4.24264			0.493197
$75$		0			0
$76$	4.00000			0.458831
$77$	2.82843	−	2.82843i	0.322329	−	0.322329i
$78$		0			0
$79$		−	8.00000i		−	0.900070i	−0.893011	−	0.450035i	$-0.851411\pi$
$79$		−	8.00000i		−	0.900070i	0.893011	−	0.450035i	$-0.148589\pi$
$80$	0.707107	+	2.12132i	0.0790569	+	0.237171i
$81$		0			0
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	0.900515	−	0.434825i	$-0.143190\pi$
$83$	4.24264	+	4.24264i	0.465690	+	0.465690i	−0.434825	+	0.900515i	$0.643190\pi$
$84$		0			0
$85$	−2.00000	−	1.00000i	−0.216930	−	0.108465i
$86$			1.41421i			0.152499i
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	−7.07107			−0.749532			−0.374766	−	0.927119i	$-0.622277\pi$
$89$	−7.07107			−0.749532			−0.374766	+	0.927119i	$0.622277\pi$
$90$		0			0
$91$	−8.00000			−0.838628
$92$	5.65685	−	5.65685i	0.589768	−	0.589768i
$93$		0			0
$94$		0			0
$95$	8.48528	−	2.82843i	0.870572	−	0.290191i
$96$		0			0
$97$	10.0000	+	10.0000i	1.01535	+	1.01535i	0.999880	+	0.0154658i	$0.00492310\pi$
$97$	10.0000	+	10.0000i	1.01535	+	1.01535i	0.0154658	+	0.999880i	$0.495077\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$		0			0
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$			11.3137i			1.12576i	0.826540	+	0.562878i	$0.190306\pi$
$101$			11.3137i			1.12576i	−0.826540	+	0.562878i	$0.809694\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$	−5.65685			−0.554700
$105$		0			0
$106$	6.00000			0.582772
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	−0.165848	−	0.986151i	$-0.553036\pi$
$107$	8.48528	−	8.48528i	0.820303	−	0.820303i	0.986151	+	0.165848i	$0.0530362\pi$
$108$		0			0
$109$			18.0000i			1.72409i	0.506834	+	0.862044i	$0.330816\pi$
$109$			18.0000i			1.72409i	−0.506834	+	0.862044i	$0.669184\pi$
$110$	2.82843	−	5.65685i	0.269680	−	0.539360i
$111$		0			0
$112$	−1.00000	−	1.00000i	−0.0944911	−	0.0944911i
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$		0			0
$115$	8.00000	−	16.0000i	0.746004	−	1.49201i
$116$		−	9.89949i		−	0.919145i
$117$		0			0
$118$	−1.00000	+	1.00000i	−0.0920575	+	0.0920575i
$119$	1.41421			0.129641
$120$		0			0
$121$	3.00000			0.272727
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$		0			0
$124$		−	6.00000i		−	0.538816i
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−12.0000	+	4.00000i	−1.05247	+	0.350823i
$131$		−	5.65685i		−	0.494242i	−0.968985	−	0.247121i	$-0.920516\pi$
$131$		−	5.65685i		−	0.494242i	0.968985	−	0.247121i	$-0.0794845\pi$
$132$		0			0
$133$	−4.00000	+	4.00000i	−0.346844	+	0.346844i
$134$	−12.7279			−1.09952
$135$		0			0
$136$	1.00000			0.0857493
$137$	−2.82843	+	2.82843i	−0.241649	+	0.241649i	−0.817532	−	0.575883i	$-0.804658\pi$
$137$	−2.82843	+	2.82843i	−0.241649	+	0.241649i	0.575883	+	0.817532i	$0.304658\pi$
$138$		0			0
$139$			16.0000i			1.35710i	0.734553	+	0.678551i	$0.237392\pi$
$139$			16.0000i			1.35710i	−0.734553	+	0.678551i	$0.762608\pi$
$140$	−2.82843	−	1.41421i	−0.239046	−	0.119523i
$141$		0			0
$142$	11.0000	+	11.0000i	0.923099	+	0.923099i
$143$	11.3137	+	11.3137i	0.946100	+	0.946100i
$144$		0			0
$145$	−7.00000	−	21.0000i	−0.581318	−	1.74396i
$146$			16.9706i			1.40449i
$147$		0			0
$148$	−3.00000	+	3.00000i	−0.246598	+	0.246598i
$149$	−11.3137			−0.926855			−0.463428	−	0.886135i	$-0.653381\pi$
$149$	−11.3137			−0.926855			−0.463428	+	0.886135i	$0.653381\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	−2.82843	+	2.82843i	−0.229416	+	0.229416i
$153$		0			0
$154$			4.00000i			0.322329i
$155$	−4.24264	−	12.7279i	−0.340777	−	1.02233i
$156$		0			0
$157$	8.00000	+	8.00000i	0.638470	+	0.638470i	0.950178	−	0.311708i	$-0.100901\pi$
$157$	8.00000	+	8.00000i	0.638470	+	0.638470i	−0.311708	+	0.950178i	$0.600901\pi$
$158$	5.65685	+	5.65685i	0.450035	+	0.450035i
$159$		0			0
$160$	−2.00000	−	1.00000i	−0.158114	−	0.0790569i
$161$			11.3137i			0.891645i
$162$		0			0
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	−0.901900	−	0.431944i	$-0.857828\pi$
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	0.431944	+	0.901900i	$0.357828\pi$
$164$	−5.65685			−0.441726
$165$		0			0
$166$	−6.00000			−0.465690
$167$	−15.5563	+	15.5563i	−1.20379	+	1.20379i	−0.230781	+	0.973006i	$0.574128\pi$
$167$	−15.5563	+	15.5563i	−1.20379	+	1.20379i	−0.973006	+	0.230781i	$0.925872\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$	2.12132	−	0.707107i	0.162698	−	0.0542326i
$171$		0			0
$172$	−1.00000	−	1.00000i	−0.0762493	−	0.0762493i
$173$	11.3137	+	11.3137i	0.860165	+	0.860165i	0.991357	−	0.131192i	$-0.0418803\pi$
$173$	11.3137	+	11.3137i	0.860165	+	0.860165i	−0.131192	+	0.991357i	$0.541880\pi$
$174$		0			0
$175$	−7.00000	−	1.00000i	−0.529150	−	0.0755929i
$176$			2.82843i			0.213201i
$177$		0			0
$178$	5.00000	−	5.00000i	0.374766	−	0.374766i
$179$	−18.3848			−1.37414			−0.687071	−	0.726590i	$-0.741104\pi$
$179$	−18.3848			−1.37414			−0.687071	+	0.726590i	$0.741104\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	5.65685	−	5.65685i	0.419314	−	0.419314i
$183$		0			0
$184$			8.00000i			0.589768i
$185$	−4.24264	+	8.48528i	−0.311925	+	0.623850i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$		0			0
$189$		0			0
$190$	−4.00000	+	8.00000i	−0.290191	+	0.580381i
$191$		−	14.1421i		−	1.02329i	−0.859197	−	0.511645i	$-0.829036\pi$
$191$		−	14.1421i		−	1.02329i	0.859197	−	0.511645i	$-0.170964\pi$
$192$		0			0
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	0.889271	+	0.457381i	$0.151213\pi$
$194$	−14.1421			−1.01535
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−8.48528	+	8.48528i	−0.604551	+	0.604551i	−0.941517	−	0.336966i	$-0.890599\pi$
$197$	−8.48528	+	8.48528i	−0.604551	+	0.604551i	0.336966	+	0.941517i	$0.390599\pi$
$198$		0			0
$199$		−	14.0000i		−	0.992434i	−0.868199	−	0.496217i	$-0.834722\pi$
$199$		−	14.0000i		−	0.992434i	0.868199	−	0.496217i	$-0.165278\pi$
$200$	−4.94975	−	0.707107i	−0.350000	−	0.0500000i
$201$		0			0
$202$	−8.00000	−	8.00000i	−0.562878	−	0.562878i
$203$	9.89949	+	9.89949i	0.694808	+	0.694808i
$204$		0			0
$205$	−12.0000	+	4.00000i	−0.838116	+	0.279372i
$206$		0			0
$207$		0			0
$208$	4.00000	−	4.00000i	0.277350	−	0.277350i
$209$	11.3137			0.782586
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	−4.24264	+	4.24264i	−0.291386	+	0.291386i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	−2.82843	−	1.41421i	−0.192897	−	0.0964486i
$216$		0			0
$217$	6.00000	+	6.00000i	0.407307	+	0.407307i
$218$	−12.7279	−	12.7279i	−0.862044	−	0.862044i
$219$		0			0
$220$	2.00000	+	6.00000i	0.134840	+	0.404520i
$221$			5.65685i			0.380521i
$222$		0			0
$223$	8.00000	−	8.00000i	0.535720	−	0.535720i	−0.386549	−	0.922269i	$-0.626333\pi$
$223$	8.00000	−	8.00000i	0.535720	−	0.535720i	0.922269	+	0.386549i	$0.126333\pi$
$224$	1.41421			0.0944911
$225$		0			0
$226$	6.00000			0.399114
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	−0.367024	−	0.930212i	$-0.619623\pi$
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	0.930212	+	0.367024i	$0.119623\pi$
$228$		0			0
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$	5.65685	+	16.9706i	0.373002	+	1.11901i
$231$		0			0
$232$	7.00000	+	7.00000i	0.459573	+	0.459573i
$233$	1.41421	+	1.41421i	0.0926482	+	0.0926482i	0.751912	−	0.659264i	$-0.229132\pi$
$233$	1.41421	+	1.41421i	0.0926482	+	0.0926482i	−0.659264	+	0.751912i	$0.729132\pi$
$234$		0			0
$235$		0			0
$236$		−	1.41421i		−	0.0920575i
$237$		0			0
$238$	−1.00000	+	1.00000i	−0.0648204	+	0.0648204i
$239$	28.2843			1.82956			0.914779	−	0.403955i	$-0.132365\pi$
$239$	28.2843			1.82956			0.914779	+	0.403955i	$0.132365\pi$
$240$		0			0
$241$	−14.0000			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$242$	−2.12132	+	2.12132i	−0.136364	+	0.136364i
$243$		0			0
$244$		−	8.00000i		−	0.512148i
$245$	−10.6066	+	3.53553i	−0.677631	+	0.225877i
$246$		0			0
$247$	−16.0000	−	16.0000i	−1.01806	−	1.01806i
$248$	4.24264	+	4.24264i	0.269408	+	0.269408i
$249$		0			0
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$		−	15.5563i		−	0.981908i	−0.871185	−	0.490954i	$-0.836648\pi$
$251$		−	15.5563i		−	0.981908i	0.871185	−	0.490954i	$-0.163352\pi$
$252$		0			0
$253$	16.0000	−	16.0000i	1.00591	−	1.00591i
$254$		0			0
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.41421	+	1.41421i	−0.0882162	+	0.0882162i	−0.749838	−	0.661622i	$-0.769869\pi$
$257$	−1.41421	+	1.41421i	−0.0882162	+	0.0882162i	0.661622	+	0.749838i	$0.269869\pi$
$258$		0			0
$259$		−	6.00000i		−	0.372822i
$260$	5.65685	−	11.3137i	0.350823	−	0.701646i
$261$		0			0
$262$	4.00000	+	4.00000i	0.247121	+	0.247121i
$263$	8.48528	+	8.48528i	0.523225	+	0.523225i	0.918544	−	0.395319i	$-0.129366\pi$
$263$	8.48528	+	8.48528i	0.523225	+	0.523225i	−0.395319	+	0.918544i	$0.629366\pi$
$264$		0			0
$265$	−6.00000	+	12.0000i	−0.368577	+	0.737154i
$266$		−	5.65685i		−	0.346844i
$267$		0			0
$268$	9.00000	−	9.00000i	0.549762	−	0.549762i
$269$	4.24264			0.258678			0.129339	−	0.991600i	$-0.458714\pi$
$269$	4.24264			0.258678			0.129339	+	0.991600i	$0.458714\pi$
$270$		0			0
$271$	−4.00000			−0.242983			−0.121491	−	0.992592i	$-0.538768\pi$
$271$	−4.00000			−0.242983			−0.121491	+	0.992592i	$0.538768\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$		0			0
$274$		−	4.00000i		−	0.241649i
$275$	8.48528	+	11.3137i	0.511682	+	0.682242i
$276$		0			0
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	0.0942828	−	0.995545i	$-0.469944\pi$
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	−0.995545	+	0.0942828i	$0.969944\pi$
$278$	−11.3137	−	11.3137i	−0.678551	−	0.678551i
$279$		0			0
$280$	3.00000	−	1.00000i	0.179284	−	0.0597614i
$281$			15.5563i			0.928014i	0.885832	+	0.464007i	$0.153589\pi$
$281$			15.5563i			0.928014i	−0.885832	+	0.464007i	$0.846411\pi$
$282$		0			0
$283$	−12.0000	+	12.0000i	−0.713326	+	0.713326i	−0.967230	−	0.253904i	$-0.918285\pi$
$283$	−12.0000	+	12.0000i	−0.713326	+	0.713326i	0.253904	+	0.967230i	$0.418285\pi$
$284$	−15.5563			−0.923099
$285$		0			0
$286$	−16.0000			−0.946100
$287$	5.65685	−	5.65685i	0.333914	−	0.333914i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	19.7990	+	9.89949i	1.16264	+	0.581318i
$291$		0			0
$292$	−12.0000	−	12.0000i	−0.702247	−	0.702247i
$293$	21.2132	+	21.2132i	1.23929	+	1.23929i	0.960292	+	0.278996i	$0.0900018\pi$
$293$	21.2132	+	21.2132i	1.23929	+	1.23929i	0.278996	+	0.960292i	$0.409998\pi$
$294$		0			0
$295$	−1.00000	−	3.00000i	−0.0582223	−	0.174667i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	8.00000	−	8.00000i	0.463428	−	0.463428i
$299$	−45.2548			−2.61715
$300$		0			0
$301$	2.00000			0.115278
$302$	−11.3137	+	11.3137i	−0.651031	+	0.651031i
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$	−5.65685	−	16.9706i	−0.323911	−	0.971732i
$306$		0			0
$307$	−7.00000	−	7.00000i	−0.399511	−	0.399511i	0.478549	−	0.878061i	$-0.341163\pi$
$307$	−7.00000	−	7.00000i	−0.399511	−	0.399511i	−0.878061	+	0.478549i	$0.841163\pi$
$308$	−2.82843	−	2.82843i	−0.161165	−	0.161165i
$309$		0			0
$310$	12.0000	+	6.00000i	0.681554	+	0.340777i
$311$		−	21.2132i		−	1.20289i	−0.798914	−	0.601445i	$-0.794592\pi$
$311$		−	21.2132i		−	1.20289i	0.798914	−	0.601445i	$-0.205408\pi$
$312$		0			0
$313$	−6.00000	+	6.00000i	−0.339140	+	0.339140i	−0.856044	−	0.516904i	$-0.827085\pi$
$313$	−6.00000	+	6.00000i	−0.339140	+	0.339140i	0.516904	+	0.856044i	$0.327085\pi$
$314$	−11.3137			−0.638470
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	−0.877227	−	0.480076i	$-0.840609\pi$
$317$	−7.07107	+	7.07107i	−0.397151	+	0.397151i	0.480076	+	0.877227i	$0.340609\pi$
$318$		0			0
$319$		−	28.0000i		−	1.56770i
$320$	2.12132	−	0.707107i	0.118585	−	0.0395285i
$321$		0			0
$322$	−8.00000	−	8.00000i	−0.445823	−	0.445823i
$323$	2.82843	+	2.82843i	0.157378	+	0.157378i
$324$		0			0
$325$	4.00000	−	28.0000i	0.221880	−	1.55316i
$326$		−	8.48528i		−	0.469956i
$327$		0			0
$328$	4.00000	−	4.00000i	0.220863	−	0.220863i
$329$		0			0
$330$		0			0
$331$	−34.0000			−1.86881			−0.934405	−	0.356214i	$-0.884068\pi$
$331$	−34.0000			−1.86881			−0.934405	+	0.356214i	$0.884068\pi$
$332$	4.24264	−	4.24264i	0.232845	−	0.232845i
$333$		0			0
$334$		−	22.0000i		−	1.20379i
$335$	12.7279	−	25.4558i	0.695401	−	1.39080i
$336$		0			0
$337$	4.00000	+	4.00000i	0.217894	+	0.217894i	0.807610	−	0.589716i	$-0.200761\pi$
$337$	4.00000	+	4.00000i	0.217894	+	0.217894i	−0.589716	+	0.807610i	$0.700761\pi$
$338$	13.4350	+	13.4350i	0.730769	+	0.730769i
$339$		0			0
$340$	−1.00000	+	2.00000i	−0.0542326	+	0.108465i
$341$		−	16.9706i		−	0.919007i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	1.41421			0.0762493
$345$		0			0
$346$	−16.0000			−0.860165
$347$	25.4558	−	25.4558i	1.36654	−	1.36654i	0.501223	−	0.865318i	$-0.332883\pi$
$347$	25.4558	−	25.4558i	1.36654	−	1.36654i	0.865318	−	0.501223i	$-0.167117\pi$
$348$		0			0
$349$		−	14.0000i		−	0.749403i	−0.927146	−	0.374701i	$-0.877745\pi$
$349$		−	14.0000i		−	0.749403i	0.927146	−	0.374701i	$-0.122255\pi$
$350$	5.65685	−	4.24264i	0.302372	−	0.226779i
$351$		0			0
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	22.6274	+	22.6274i	1.20434	+	1.20434i	0.972835	+	0.231501i	$0.0743638\pi$
$353$	22.6274	+	22.6274i	1.20434	+	1.20434i	0.231501	+	0.972835i	$0.425636\pi$
$354$		0			0
$355$	−33.0000	+	11.0000i	−1.75146	+	0.583819i
$356$			7.07107i			0.374766i
$357$		0			0
$358$	13.0000	−	13.0000i	0.687071	−	0.687071i
$359$	−36.7696			−1.94062			−0.970311	−	0.241859i	$-0.922243\pi$
$359$	−36.7696			−1.94062			−0.970311	+	0.241859i	$0.922243\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	1.41421	−	1.41421i	0.0743294	−	0.0743294i
$363$		0			0
$364$			8.00000i			0.419314i
$365$	−33.9411	−	16.9706i	−1.77656	−	0.888280i
$366$		0			0
$367$	11.0000	+	11.0000i	0.574195	+	0.574195i	0.933298	−	0.359103i	$-0.116917\pi$
$367$	11.0000	+	11.0000i	0.574195	+	0.574195i	−0.359103	+	0.933298i	$0.616917\pi$
$368$	−5.65685	−	5.65685i	−0.294884	−	0.294884i
$369$		0			0
$370$	−3.00000	−	9.00000i	−0.155963	−	0.467888i
$371$		−	8.48528i		−	0.440534i
$372$		0			0
$373$	18.0000	−	18.0000i	0.932005	−	0.932005i	−0.0658264	−	0.997831i	$-0.520968\pi$
$373$	18.0000	−	18.0000i	0.932005	−	0.932005i	0.997831	+	0.0658264i	$0.0209684\pi$
$374$	2.82843			0.146254
$375$		0			0
$376$		0			0
$377$	−39.5980	+	39.5980i	−2.03940	+	2.03940i
$378$		0			0
$379$			32.0000i			1.64373i	0.569683	+	0.821865i	$0.307066\pi$
$379$			32.0000i			1.64373i	−0.569683	+	0.821865i	$0.692934\pi$
$380$	−2.82843	−	8.48528i	−0.145095	−	0.435286i
$381$		0			0
$382$	10.0000	+	10.0000i	0.511645	+	0.511645i
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	0.456266	−	0.889843i	$-0.349187\pi$
$383$	−8.48528	−	8.48528i	−0.433578	−	0.433578i	−0.889843	+	0.456266i	$0.849187\pi$
$384$		0			0
$385$	−8.00000	−	4.00000i	−0.407718	−	0.203859i
$386$			8.48528i			0.431889i
$387$		0			0
$388$	10.0000	−	10.0000i	0.507673	−	0.507673i
$389$	−5.65685			−0.286814			−0.143407	−	0.989664i	$-0.545806\pi$
$389$	−5.65685			−0.286814			−0.143407	+	0.989664i	$0.545806\pi$
$390$		0			0
$391$	8.00000			0.404577
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$		0			0
$394$		−	12.0000i		−	0.604551i
$395$	−16.9706	+	5.65685i	−0.853882	+	0.284627i
$396$		0			0
$397$	5.00000	+	5.00000i	0.250943	+	0.250943i	0.821357	−	0.570414i	$-0.193217\pi$
$397$	5.00000	+	5.00000i	0.250943	+	0.250943i	−0.570414	+	0.821357i	$0.693217\pi$
$398$	9.89949	+	9.89949i	0.496217	+	0.496217i
$399$		0			0
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$		−	19.7990i		−	0.988714i	−0.869259	−	0.494357i	$-0.835403\pi$
$401$		−	19.7990i		−	0.988714i	0.869259	−	0.494357i	$-0.164597\pi$
$402$		0			0
$403$	−24.0000	+	24.0000i	−1.19553	+	1.19553i
$404$	11.3137			0.562878
$405$		0			0
$406$	−14.0000			−0.694808
$407$	−8.48528	+	8.48528i	−0.420600	+	0.420600i
$408$		0			0
$409$			14.0000i			0.692255i	0.938187	+	0.346128i	$0.112504\pi$
$409$			14.0000i			0.692255i	−0.938187	+	0.346128i	$0.887496\pi$
$410$	5.65685	−	11.3137i	0.279372	−	0.558744i
$411$		0			0
$412$		0			0
$413$	1.41421	+	1.41421i	0.0695889	+	0.0695889i
$414$		0			0
$415$	6.00000	−	12.0000i	0.294528	−	0.589057i
$416$			5.65685i			0.277350i
$417$		0			0
$418$	−8.00000	+	8.00000i	−0.391293	+	0.391293i
$419$	−11.3137			−0.552711			−0.276355	−	0.961056i	$-0.589127\pi$
$419$	−11.3137			−0.552711			−0.276355	+	0.961056i	$0.589127\pi$
$420$		0			0
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$		0			0
$423$		0			0
$424$		−	6.00000i		−	0.291386i
$425$	−0.707107	+	4.94975i	−0.0342997	+	0.240098i
$426$		0			0
$427$	8.00000	+	8.00000i	0.387147	+	0.387147i
$428$	−8.48528	−	8.48528i	−0.410152	−	0.410152i
$429$		0			0
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$		−	4.24264i		−	0.204361i	−0.994766	−	0.102180i	$-0.967418\pi$
$431$		−	4.24264i		−	0.204361i	0.994766	−	0.102180i	$-0.0325819\pi$
$432$		0			0
$433$	−15.0000	+	15.0000i	−0.720854	+	0.720854i	−0.968779	−	0.247925i	$-0.920251\pi$
$433$	−15.0000	+	15.0000i	−0.720854	+	0.720854i	0.247925	+	0.968779i	$0.420251\pi$
$434$	−8.48528			−0.407307
$435$		0			0
$436$	18.0000			0.862044
$437$	−22.6274	+	22.6274i	−1.08242	+	1.08242i
$438$		0			0
$439$		−	8.00000i		−	0.381819i	−0.981608	−	0.190910i	$-0.938856\pi$
$439$		−	8.00000i		−	0.381819i	0.981608	−	0.190910i	$-0.0611437\pi$
$440$	−5.65685	−	2.82843i	−0.269680	−	0.134840i
$441$		0			0
$442$	−4.00000	−	4.00000i	−0.190261	−	0.190261i
$443$	15.5563	+	15.5563i	0.739104	+	0.739104i	0.972405	−	0.233300i	$-0.0749525\pi$
$443$	15.5563	+	15.5563i	0.739104	+	0.739104i	−0.233300	+	0.972405i	$0.574953\pi$
$444$		0			0
$445$	5.00000	+	15.0000i	0.237023	+	0.711068i
$446$			11.3137i			0.535720i
$447$		0			0
$448$	−1.00000	+	1.00000i	−0.0472456	+	0.0472456i
$449$	2.82843			0.133482			0.0667409	−	0.997770i	$-0.478740\pi$
$449$	2.82843			0.133482			0.0667409	+	0.997770i	$0.478740\pi$
$450$		0			0
$451$	−16.0000			−0.753411
$452$	−4.24264	+	4.24264i	−0.199557	+	0.199557i
$453$		0			0
$454$			12.0000i			0.563188i
$455$	5.65685	+	16.9706i	0.265197	+	0.795592i
$456$		0			0
$457$	−9.00000	−	9.00000i	−0.421002	−	0.421002i	0.464546	−	0.885549i	$-0.346217\pi$
$457$	−9.00000	−	9.00000i	−0.421002	−	0.421002i	−0.885549	+	0.464546i	$0.846217\pi$
$458$	−9.89949	−	9.89949i	−0.462573	−	0.462573i
$459$		0			0
$460$	−16.0000	−	8.00000i	−0.746004	−	0.373002i
$461$			8.48528i			0.395199i	0.980283	+	0.197599i	$0.0633145\pi$
$461$			8.48528i			0.395199i	−0.980283	+	0.197599i	$0.936685\pi$
$462$		0			0
$463$	−12.0000	+	12.0000i	−0.557687	+	0.557687i	−0.928648	−	0.370961i	$-0.879028\pi$
$463$	−12.0000	+	12.0000i	−0.557687	+	0.557687i	0.370961	+	0.928648i	$0.379028\pi$
$464$	−9.89949			−0.459573
$465$		0			0
$466$	−2.00000			−0.0926482
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$		0			0
$469$			18.0000i			0.831163i
$470$		0			0
$471$		0			0
$472$	1.00000	+	1.00000i	0.0460287	+	0.0460287i
$473$	−2.82843	−	2.82843i	−0.130051	−	0.130051i
$474$		0			0
$475$	−12.0000	−	16.0000i	−0.550598	−	0.734130i
$476$		−	1.41421i		−	0.0648204i
$477$		0			0
$478$	−20.0000	+	20.0000i	−0.914779	+	0.914779i
$479$	−9.89949			−0.452319			−0.226160	−	0.974090i	$-0.572617\pi$
$479$	−9.89949			−0.452319			−0.226160	+	0.974090i	$0.572617\pi$
$480$		0			0
$481$	24.0000			1.09431
$482$	9.89949	−	9.89949i	0.450910	−	0.450910i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$	14.1421	−	28.2843i	0.642161	−	1.28432i
$486$		0			0
$487$	−17.0000	−	17.0000i	−0.770344	−	0.770344i	0.207823	−	0.978166i	$-0.433362\pi$
$487$	−17.0000	−	17.0000i	−0.770344	−	0.770344i	−0.978166	+	0.207823i	$0.933362\pi$
$488$	5.65685	+	5.65685i	0.256074	+	0.256074i
$489$		0			0
$490$	5.00000	−	10.0000i	0.225877	−	0.451754i
$491$			1.41421i			0.0638226i	0.999491	+	0.0319113i	$0.0101594\pi$
$491$			1.41421i			0.0638226i	−0.999491	+	0.0319113i	$0.989841\pi$
$492$		0			0
$493$	7.00000	−	7.00000i	0.315264	−	0.315264i
$494$	22.6274			1.01806
$495$		0			0
$496$	−6.00000			−0.269408
$497$	15.5563	−	15.5563i	0.697798	−	0.697798i
$498$		0			0
$499$		−	4.00000i		−	0.179065i	−0.995984	−	0.0895323i	$-0.971463\pi$
$499$		−	4.00000i		−	0.179065i	0.995984	−	0.0895323i	$-0.0285372\pi$
$500$	6.36396	−	9.19239i	0.284605	−	0.411096i
$501$		0			0
$502$	11.0000	+	11.0000i	0.490954	+	0.490954i
$503$	−16.9706	−	16.9706i	−0.756680	−	0.756680i	0.219037	−	0.975717i	$-0.429709\pi$
$503$	−16.9706	−	16.9706i	−0.756680	−	0.756680i	−0.975717	+	0.219037i	$0.929709\pi$
$504$		0			0
$505$	24.0000	−	8.00000i	1.06799	−	0.355995i
$506$			22.6274i			1.00591i
$507$		0			0
$508$		0			0
$509$	28.2843			1.25368			0.626839	−	0.779149i	$-0.284348\pi$
$509$	28.2843			1.25368			0.626839	+	0.779149i	$0.284348\pi$
$510$		0			0
$511$	24.0000			1.06170
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	2.00000i		−	0.0882162i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	4.24264	+	4.24264i	0.186411	+	0.186411i
$519$		0			0
$520$	4.00000	+	12.0000i	0.175412	+	0.526235i
$521$		−	19.7990i		−	0.867409i	−0.901055	−	0.433705i	$-0.857206\pi$
$521$		−	19.7990i		−	0.867409i	0.901055	−	0.433705i	$-0.142794\pi$
$522$		0			0
$523$	−15.0000	+	15.0000i	−0.655904	+	0.655904i	−0.954408	−	0.298504i	$-0.903512\pi$
$523$	−15.0000	+	15.0000i	−0.655904	+	0.655904i	0.298504	+	0.954408i	$0.403512\pi$
$524$	−5.65685			−0.247121
$525$		0			0
$526$	−12.0000			−0.523225
$527$	4.24264	−	4.24264i	0.184812	−	0.184812i
$528$		0			0
$529$			41.0000i			1.78261i
$530$	−4.24264	−	12.7279i	−0.184289	−	0.552866i
$531$		0			0
$532$	4.00000	+	4.00000i	0.173422	+	0.173422i
$533$	22.6274	+	22.6274i	0.980102	+	0.980102i
$534$		0			0
$535$	−24.0000	−	12.0000i	−1.03761	−	0.518805i
$536$			12.7279i			0.549762i
$537$		0			0
$538$	−3.00000	+	3.00000i	−0.129339	+	0.129339i
$539$	−14.1421			−0.609145
$540$		0			0
$541$	40.0000			1.71973			0.859867	−	0.510518i	$-0.170546\pi$
$541$	40.0000			1.71973			0.859867	+	0.510518i	$0.170546\pi$
$542$	2.82843	−	2.82843i	0.121491	−	0.121491i
$543$		0			0
$544$		−	1.00000i		−	0.0428746i
$545$	38.1838	−	12.7279i	1.63561	−	0.545204i
$546$		0			0
$547$	−32.0000	−	32.0000i	−1.36822	−	1.36822i	−0.862976	−	0.505246i	$-0.831402\pi$
$547$	−32.0000	−	32.0000i	−1.36822	−	1.36822i	−0.505246	−	0.862976i	$-0.668598\pi$
$548$	2.82843	+	2.82843i	0.120824	+	0.120824i
$549$		0			0
$550$	−14.0000	−	2.00000i	−0.596962	−	0.0852803i
$551$			39.5980i			1.68693i
$552$		0			0
$553$	8.00000	−	8.00000i	0.340195	−	0.340195i
$554$	21.2132			0.901263
$555$		0			0
$556$	16.0000			0.678551
$557$	1.41421	−	1.41421i	0.0599222	−	0.0599222i	−0.676511	−	0.736433i	$-0.736509\pi$
$557$	1.41421	−	1.41421i	0.0599222	−	0.0599222i	0.736433	+	0.676511i	$0.236509\pi$
$558$		0			0
$559$			8.00000i			0.338364i
$560$	−1.41421	+	2.82843i	−0.0597614	+	0.119523i
$561$		0			0
$562$	−11.0000	−	11.0000i	−0.464007	−	0.464007i
$563$	−4.24264	−	4.24264i	−0.178806	−	0.178806i	0.612029	−	0.790835i	$-0.290353\pi$
$563$	−4.24264	−	4.24264i	−0.178806	−	0.178806i	−0.790835	+	0.612029i	$0.790353\pi$
$564$		0			0
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$		−	16.9706i		−	0.713326i
$567$		0			0
$568$	11.0000	−	11.0000i	0.461550	−	0.461550i
$569$	−18.3848			−0.770730			−0.385365	−	0.922764i	$-0.625924\pi$
$569$	−18.3848			−0.770730			−0.385365	+	0.922764i	$0.625924\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	11.3137	−	11.3137i	0.473050	−	0.473050i
$573$		0			0
$574$			8.00000i			0.333914i
$575$	−39.5980	−	5.65685i	−1.65135	−	0.235907i
$576$		0			0
$577$	−9.00000	−	9.00000i	−0.374675	−	0.374675i	0.494502	−	0.869177i	$-0.335351\pi$
$577$	−9.00000	−	9.00000i	−0.374675	−	0.374675i	−0.869177	+	0.494502i	$0.835351\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$	−21.0000	+	7.00000i	−0.871978	+	0.290659i
$581$			8.48528i			0.352029i
$582$		0			0
$583$	−12.0000	+	12.0000i	−0.496989	+	0.496989i
$584$	16.9706			0.702247
$585$		0			0
$586$	−30.0000			−1.23929
$587$	−18.3848	+	18.3848i	−0.758821	+	0.758821i	−0.976108	−	0.217287i	$-0.930279\pi$
$587$	−18.3848	+	18.3848i	−0.758821	+	0.758821i	0.217287	+	0.976108i	$0.430279\pi$
$588$		0			0
$589$			24.0000i			0.988903i
$590$	2.82843	+	1.41421i	0.116445	+	0.0582223i
$591$		0			0
$592$	3.00000	+	3.00000i	0.123299	+	0.123299i
$593$	−32.5269	−	32.5269i	−1.33572	−	1.33572i	−0.900159	−	0.435561i	$-0.856550\pi$
$593$	−32.5269	−	32.5269i	−1.33572	−	1.33572i	−0.435561	−	0.900159i	$-0.643450\pi$
$594$		0			0
$595$	−1.00000	−	3.00000i	−0.0409960	−	0.122988i
$596$			11.3137i			0.463428i
$597$		0			0
$598$	32.0000	−	32.0000i	1.30858	−	1.30858i
$599$	−2.82843			−0.115566			−0.0577832	−	0.998329i	$-0.518403\pi$
$599$	−2.82843			−0.115566			−0.0577832	+	0.998329i	$0.518403\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−1.41421	+	1.41421i	−0.0576390	+	0.0576390i
$603$		0			0
$604$		−	16.0000i		−	0.651031i
$605$	−2.12132	−	6.36396i	−0.0862439	−	0.258732i
$606$		0			0
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	0.333809	−	0.942641i	$-0.391666\pi$
$607$	−15.0000	−	15.0000i	−0.608831	−	0.608831i	−0.942641	+	0.333809i	$0.891666\pi$
$608$	2.82843	+	2.82843i	0.114708	+	0.114708i
$609$		0			0
$610$	16.0000	+	8.00000i	0.647821	+	0.323911i
$611$		0			0
$612$		0			0
$613$	30.0000	−	30.0000i	1.21169	−	1.21169i	0.241218	−	0.970471i	$-0.422453\pi$
$613$	30.0000	−	30.0000i	1.21169	−	1.21169i	0.970471	−	0.241218i	$-0.0775467\pi$
$614$	9.89949			0.399511
$615$		0			0
$616$	4.00000			0.161165
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	−0.990624	−	0.136613i	$-0.956378\pi$
$617$	−21.2132	+	21.2132i	−0.854011	+	0.854011i	0.136613	+	0.990624i	$0.456378\pi$
$618$		0			0
$619$			8.00000i			0.321547i	0.986991	+	0.160774i	$0.0513989\pi$
$619$			8.00000i			0.321547i	−0.986991	+	0.160774i	$0.948601\pi$
$620$	−12.7279	+	4.24264i	−0.511166	+	0.170389i
$621$		0			0
$622$	15.0000	+	15.0000i	0.601445	+	0.601445i
$623$	−7.07107	−	7.07107i	−0.283296	−	0.283296i
$624$		0			0
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$		−	8.48528i		−	0.339140i
$627$		0			0
$628$	8.00000	−	8.00000i	0.319235	−	0.319235i
$629$	−4.24264			−0.169165
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	5.65685	−	5.65685i	0.225018	−	0.225018i
$633$		0			0
$634$		−	10.0000i		−	0.397151i
$635$		0			0
$636$		0			0
$637$	20.0000	+	20.0000i	0.792429	+	0.792429i
$638$	19.7990	+	19.7990i	0.783850	+	0.783850i
$639$		0			0
$640$	−1.00000	+	2.00000i	−0.0395285	+	0.0790569i
$641$		−	2.82843i		−	0.111716i	−0.998439	−	0.0558581i	$-0.982211\pi$
$641$		−	2.82843i		−	0.111716i	0.998439	−	0.0558581i	$-0.0177894\pi$
$642$		0			0
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	−0.481877	−	0.876239i	$-0.660045\pi$
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	0.876239	+	0.481877i	$0.160045\pi$
$644$	11.3137			0.445823
$645$		0			0
$646$	−4.00000			−0.157378
$647$	25.4558	−	25.4558i	1.00077	−	1.00077i	0.000772798	−	1.00000i	$-0.499754\pi$
$647$	25.4558	−	25.4558i	1.00077	−	1.00077i	1.00000		0.000772798i	$-0.000245989\pi$
$648$		0			0
$649$		−	4.00000i		−	0.157014i
$650$	16.9706	+	22.6274i	0.665640	+	0.887520i
$651$		0			0
$652$	6.00000	+	6.00000i	0.234978	+	0.234978i
$653$	−2.82843	−	2.82843i	−0.110685	−	0.110685i	0.649595	−	0.760280i	$-0.274938\pi$
$653$	−2.82843	−	2.82843i	−0.110685	−	0.110685i	−0.760280	+	0.649595i	$0.774938\pi$
$654$		0			0
$655$	−12.0000	+	4.00000i	−0.468879	+	0.156293i
$656$			5.65685i			0.220863i
$657$		0			0
$658$		0			0
$659$	−7.07107			−0.275450			−0.137725	−	0.990471i	$-0.543979\pi$
$659$	−7.07107			−0.275450			−0.137725	+	0.990471i	$0.543979\pi$
$660$		0			0
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	24.0416	−	24.0416i	0.934405	−	0.934405i
$663$		0			0
$664$			6.00000i			0.232845i
$665$	11.3137	+	5.65685i	0.438727	+	0.219363i
$666$		0			0
$667$	56.0000	+	56.0000i	2.16833	+	2.16833i
$668$	15.5563	+	15.5563i	0.601893	+	0.601893i
$669$		0			0
$670$	9.00000	+	27.0000i	0.347700	+	1.04310i
$671$		−	22.6274i		−	0.873522i
$672$		0			0
$673$	2.00000	−	2.00000i	0.0770943	−	0.0770943i	−0.667508	−	0.744602i	$-0.732639\pi$
$673$	2.00000	−	2.00000i	0.0770943	−	0.0770943i	0.744602	+	0.667508i	$0.232639\pi$
$674$	−5.65685			−0.217894
$675$		0			0
$676$	−19.0000			−0.730769
$677$	−12.7279	+	12.7279i	−0.489174	+	0.489174i	−0.908045	−	0.418872i	$-0.862426\pi$
$677$	−12.7279	+	12.7279i	−0.489174	+	0.489174i	0.418872	+	0.908045i	$0.362426\pi$
$678$		0			0
$679$			20.0000i			0.767530i
$680$	−0.707107	−	2.12132i	−0.0271163	−	0.0813489i
$681$		0			0
$682$	12.0000	+	12.0000i	0.459504	+	0.459504i
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	0.650920	−	0.759147i	$-0.274383\pi$
$683$	−2.82843	−	2.82843i	−0.108227	−	0.108227i	−0.759147	+	0.650920i	$0.774383\pi$
$684$		0			0
$685$	8.00000	+	4.00000i	0.305664	+	0.152832i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	−1.00000	+	1.00000i	−0.0381246	+	0.0381246i
$689$	33.9411			1.29305
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	11.3137	−	11.3137i	0.430083	−	0.430083i
$693$		0			0
$694$			36.0000i			1.36654i
$695$	33.9411	−	11.3137i	1.28746	−	0.429153i
$696$		0			0
$697$	−4.00000	−	4.00000i	−0.151511	−	0.151511i
$698$	9.89949	+	9.89949i	0.374701	+	0.374701i
$699$		0			0
$700$	−1.00000	+	7.00000i	−0.0377964	+	0.264575i
$701$		−	2.82843i		−	0.106828i	−0.998572	−	0.0534141i	$-0.982990\pi$
$701$		−	2.82843i		−	0.106828i	0.998572	−	0.0534141i	$-0.0170103\pi$
$702$		0			0
$703$	12.0000	−	12.0000i	0.452589	−	0.452589i
$704$	2.82843			0.106600
$705$		0			0
$706$	−32.0000			−1.20434
$707$	−11.3137	+	11.3137i	−0.425496	+	0.425496i
$708$		0			0
$709$			46.0000i			1.72757i	0.503864	+	0.863783i	$0.331911\pi$
$709$			46.0000i			1.72757i	−0.503864	+	0.863783i	$0.668089\pi$
$710$	15.5563	−	31.1127i	0.583819	−	1.16764i
$711$		0			0
$712$	−5.00000	−	5.00000i	−0.187383	−	0.187383i
$713$	33.9411	+	33.9411i	1.27111	+	1.27111i
$714$		0			0
$715$	16.0000	−	32.0000i	0.598366	−	1.19673i
$716$			18.3848i			0.687071i
$717$		0			0
$718$	26.0000	−	26.0000i	0.970311	−	0.970311i
$719$	52.3259			1.95143			0.975713	−	0.219051i	$-0.0702961\pi$
$719$	52.3259			1.95143			0.975713	+	0.219051i	$0.0702961\pi$
$720$		0			0
$721$		0			0
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$		0			0
$724$			2.00000i			0.0743294i
$725$	−39.5980	+	29.6985i	−1.47063	+	1.10297i
$726$		0			0
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$	−5.65685	−	5.65685i	−0.209657	−	0.209657i
$729$		0			0
$730$	36.0000	−	12.0000i	1.33242	−	0.444140i
$731$		−	1.41421i		−	0.0523066i
$732$		0			0
$733$	22.0000	−	22.0000i	0.812589	−	0.812589i	−0.172433	−	0.985021i	$-0.555163\pi$
$733$	22.0000	−	22.0000i	0.812589	−	0.812589i	0.985021	+	0.172433i	$0.0551627\pi$
$734$	−15.5563			−0.574195
$735$		0			0
$736$	8.00000			0.294884
$737$	25.4558	−	25.4558i	0.937678	−	0.937678i
$738$		0			0
$739$			30.0000i			1.10357i	0.833987	+	0.551784i	$0.186053\pi$
$739$			30.0000i			1.10357i	−0.833987	+	0.551784i	$0.813947\pi$
$740$	8.48528	+	4.24264i	0.311925	+	0.155963i
$741$		0			0
$742$	6.00000	+	6.00000i	0.220267	+	0.220267i
$743$	−12.7279	−	12.7279i	−0.466942	−	0.466942i	0.433980	−	0.900922i	$-0.357109\pi$
$743$	−12.7279	−	12.7279i	−0.466942	−	0.466942i	−0.900922	+	0.433980i	$0.857109\pi$
$744$		0			0
$745$	8.00000	+	24.0000i	0.293097	+	0.879292i
$746$			25.4558i			0.932005i
$747$		0			0
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	16.9706			0.620091
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		0			0
$754$		−	56.0000i		−	2.03940i
$755$	−11.3137	−	33.9411i	−0.411748	−	1.23524i
$756$		0			0
$757$	8.00000	+	8.00000i	0.290765	+	0.290765i	0.837382	−	0.546617i	$-0.184085\pi$
$757$	8.00000	+	8.00000i	0.290765	+	0.290765i	−0.546617	+	0.837382i	$0.684085\pi$
$758$	−22.6274	−	22.6274i	−0.821865	−	0.821865i
$759$		0			0
$760$	8.00000	+	4.00000i	0.290191	+	0.145095i
$761$			15.5563i			0.563917i	0.959427	+	0.281959i	$0.0909841\pi$
$761$			15.5563i			0.563917i	−0.959427	+	0.281959i	$0.909016\pi$
$762$		0			0
$763$	−18.0000	+	18.0000i	−0.651644	+	0.651644i
$764$	−14.1421			−0.511645
$765$		0			0
$766$	12.0000			0.433578
$767$	−5.65685	+	5.65685i	−0.204257	+	0.204257i
$768$		0			0
$769$			30.0000i			1.08183i	0.841078	+	0.540914i	$0.181921\pi$
$769$			30.0000i			1.08183i	−0.841078	+	0.540914i	$0.818079\pi$
$770$	8.48528	−	2.82843i	0.305788	−	0.101929i
$771$		0			0
$772$	−6.00000	−	6.00000i	−0.215945	−	0.215945i
$773$	−9.89949	−	9.89949i	−0.356060	−	0.356060i	0.506298	−	0.862358i	$-0.331013\pi$
$773$	−9.89949	−	9.89949i	−0.356060	−	0.356060i	−0.862358	+	0.506298i	$0.831013\pi$
$774$		0			0
$775$	−24.0000	+	18.0000i	−0.862105	+	0.646579i
$776$			14.1421i			0.507673i
$777$		0			0
$778$	4.00000	−	4.00000i	0.143407	−	0.143407i
$779$	22.6274			0.810711
$780$		0			0
$781$	−44.0000			−1.57444
$782$	−5.65685	+	5.65685i	−0.202289	+	0.202289i
$783$		0			0
$784$			5.00000i			0.178571i
$785$	11.3137	−	22.6274i	0.403804	−	0.807607i
$786$		0			0
$787$	30.0000	+	30.0000i	1.06938	+	1.06938i	0.997406	+	0.0719783i	$0.0229312\pi$
$787$	30.0000	+	30.0000i	1.06938	+	1.06938i	0.0719783	+	0.997406i	$0.477069\pi$
$788$	8.48528	+	8.48528i	0.302276	+	0.302276i
$789$		0			0
$790$	8.00000	−	16.0000i	0.284627	−	0.569254i
$791$		−	8.48528i		−	0.301702i
$792$		0			0
$793$	−32.0000	+	32.0000i	−1.13635	+	1.13635i
$794$	−7.07107			−0.250943
$795$		0			0
$796$	−14.0000			−0.496217
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		0			0
$799$		0			0
$800$	−0.707107	+	4.94975i	−0.0250000	+	0.175000i
$801$		0			0
$802$	14.0000	+	14.0000i	0.494357	+	0.494357i
$803$	−33.9411	−	33.9411i	−1.19776	−	1.19776i
$804$		0			0
$805$	24.0000	−	8.00000i	0.845889	−	0.281963i
$806$		−	33.9411i		−	1.19553i
$807$		0			0
$808$	−8.00000	+	8.00000i	−0.281439	+	0.281439i
$809$	−39.5980			−1.39219			−0.696095	−	0.717949i	$-0.745081\pi$
$809$	−39.5980			−1.39219			−0.696095	+	0.717949i	$0.745081\pi$
$810$		0			0
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$	9.89949	−	9.89949i	0.347404	−	0.347404i
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	16.9706	+	8.48528i	0.594453	+	0.297226i
$816$		0			0
$817$	4.00000	+	4.00000i	0.139942	+	0.139942i
$818$	−9.89949	−	9.89949i	−0.346128	−	0.346128i
$819$		0			0
$820$	4.00000	+	12.0000i	0.139686	+	0.419058i
$821$		−	12.7279i		−	0.444208i	−0.975023	−	0.222104i	$-0.928708\pi$
$821$		−	12.7279i		−	0.444208i	0.975023	−	0.222104i	$-0.0712924\pi$
$822$		0			0
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	−0.918436	−	0.395569i	$-0.870547\pi$
$823$	−15.0000	+	15.0000i	−0.522867	+	0.522867i	0.395569	+	0.918436i	$0.370547\pi$
$824$		0			0
$825$		0			0
$826$	−2.00000			−0.0695889
$827$	−19.7990	+	19.7990i	−0.688478	+	0.688478i	−0.961896	−	0.273417i	$-0.911846\pi$
$827$	−19.7990	+	19.7990i	−0.688478	+	0.688478i	0.273417	+	0.961896i	$0.411846\pi$
$828$		0			0
$829$			2.00000i			0.0694629i	0.999397	+	0.0347314i	$0.0110576\pi$
$829$			2.00000i			0.0694629i	−0.999397	+	0.0347314i	$0.988942\pi$
$830$	4.24264	+	12.7279i	0.147264	+	0.441793i
$831$		0			0
$832$	−4.00000	−	4.00000i	−0.138675	−	0.138675i
$833$	−3.53553	−	3.53553i	−0.122499	−	0.122499i
$834$		0			0
$835$	44.0000	+	22.0000i	1.52268	+	0.761341i
$836$		−	11.3137i		−	0.391293i
$837$		0			0
$838$	8.00000	−	8.00000i	0.276355	−	0.276355i
$839$	32.5269			1.12295			0.561477	−	0.827492i	$-0.310233\pi$
$839$	32.5269			1.12295			0.561477	+	0.827492i	$0.310233\pi$
$840$		0			0
$841$	69.0000			2.37931
$842$	−4.24264	+	4.24264i	−0.146211	+	0.146211i
$843$		0			0
$844$		0			0
$845$	−40.3051	+	13.4350i	−1.38654	+	0.462179i
$846$		0			0
$847$	3.00000	+	3.00000i	0.103081	+	0.103081i
$848$	4.24264	+	4.24264i	0.145693	+	0.145693i
$849$		0			0
$850$	−3.00000	−	4.00000i	−0.102899	−	0.137199i
$851$		−	33.9411i		−	1.16349i
$852$		0			0
$853$	−21.0000	+	21.0000i	−0.719026	+	0.719026i	−0.968406	−	0.249380i	$-0.919773\pi$
$853$	−21.0000	+	21.0000i	−0.719026	+	0.719026i	0.249380	+	0.968406i	$0.419773\pi$
$854$	−11.3137			−0.387147
$855$		0			0
$856$	12.0000			0.410152
$857$	−26.8701	+	26.8701i	−0.917864	+	0.917864i	−0.996874	−	0.0790101i	$-0.974824\pi$
$857$	−26.8701	+	26.8701i	−0.917864	+	0.917864i	0.0790101	+	0.996874i	$0.474824\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−1.41421	+	2.82843i	−0.0482243	+	0.0964486i
$861$		0			0
$862$	3.00000	+	3.00000i	0.102180	+	0.102180i
$863$	−11.3137	−	11.3137i	−0.385123	−	0.385123i	0.487821	−	0.872944i	$-0.337792\pi$
$863$	−11.3137	−	11.3137i	−0.385123	−	0.385123i	−0.872944	+	0.487821i	$0.837792\pi$
$864$		0			0
$865$	16.0000	−	32.0000i	0.544016	−	1.08803i
$866$		−	21.2132i		−	0.720854i
$867$		0			0
$868$	6.00000	−	6.00000i	0.203653	−	0.203653i
$869$	−22.6274			−0.767583
$870$		0			0
$871$	−72.0000			−2.43963
$872$	−12.7279	+	12.7279i	−0.431022	+	0.431022i
$873$		0			0
$874$		−	32.0000i		−	1.08242i
$875$	2.82843	+	15.5563i	0.0956183	+	0.525901i
$876$		0			0
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	0.0846827	−	0.996408i	$-0.473012\pi$
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	−0.996408	+	0.0846827i	$0.973012\pi$
$878$	5.65685	+	5.65685i	0.190910	+	0.190910i
$879$		0			0
$880$	6.00000	−	2.00000i	0.202260	−	0.0674200i
$881$			2.82843i			0.0952921i	0.998864	+	0.0476461i	$0.0151720\pi$
$881$			2.82843i			0.0952921i	−0.998864	+	0.0476461i	$0.984828\pi$
$882$		0			0
$883$	−11.0000	+	11.0000i	−0.370179	+	0.370179i	−0.867543	−	0.497363i	$-0.834302\pi$
$883$	−11.0000	+	11.0000i	−0.370179	+	0.370179i	0.497363	+	0.867543i	$0.334302\pi$
$884$	5.65685			0.190261
$885$		0			0
$886$	−22.0000			−0.739104
$887$	5.65685	−	5.65685i	0.189939	−	0.189939i	−0.605731	−	0.795670i	$-0.707119\pi$
$887$	5.65685	−	5.65685i	0.189939	−	0.189939i	0.795670	+	0.605731i	$0.207119\pi$
$888$		0			0
$889$		0			0
$890$	−14.1421	−	7.07107i	−0.474045	−	0.237023i
$891$		0			0
$892$	−8.00000	−	8.00000i	−0.267860	−	0.267860i
$893$		0			0
$894$		0			0
$895$	13.0000	+	39.0000i	0.434542	+	1.30363i
$896$		−	1.41421i		−	0.0472456i
$897$		0			0
$898$	−2.00000	+	2.00000i	−0.0667409	+	0.0667409i
$899$	59.3970			1.98100
$900$		0			0
$901$	−6.00000			−0.199889
$902$	11.3137	−	11.3137i	0.376705	−	0.376705i
$903$		0			0
$904$		−	6.00000i		−	0.199557i
$905$	1.41421	+	4.24264i	0.0470100	+	0.141030i
$906$		0			0
$907$	−14.0000	−	14.0000i	−0.464862	−	0.464862i	0.435383	−	0.900245i	$-0.356613\pi$
$907$	−14.0000	−	14.0000i	−0.464862	−	0.464862i	−0.900245	+	0.435383i	$0.856613\pi$
$908$	−8.48528	−	8.48528i	−0.281594	−	0.281594i
$909$		0			0
$910$	−16.0000	−	8.00000i	−0.530395	−	0.265197i
$911$			12.7279i			0.421695i	0.977519	+	0.210847i	$0.0676223\pi$
$911$			12.7279i			0.421695i	−0.977519	+	0.210847i	$0.932378\pi$
$912$		0			0
$913$	12.0000	−	12.0000i	0.397142	−	0.397142i
$914$	12.7279			0.421002
$915$		0			0
$916$	14.0000			0.462573
$917$	5.65685	−	5.65685i	0.186806	−	0.186806i
$918$		0			0
$919$		−	52.0000i		−	1.71532i	−0.514216	−	0.857661i	$-0.671917\pi$
$919$		−	52.0000i		−	1.71532i	0.514216	−	0.857661i	$-0.328083\pi$
$920$	16.9706	−	5.65685i	0.559503	−	0.186501i
$921$		0			0
$922$	−6.00000	−	6.00000i	−0.197599	−	0.197599i
$923$	62.2254	+	62.2254i	2.04817	+	2.04817i
$924$		0			0
$925$	21.0000	+	3.00000i	0.690476	+	0.0986394i
$926$		−	16.9706i		−	0.557687i
$927$		0			0
$928$	7.00000	−	7.00000i	0.229786	−	0.229786i
$929$	−5.65685			−0.185595			−0.0927977	−	0.995685i	$-0.529581\pi$
$929$	−5.65685			−0.185595			−0.0927977	+	0.995685i	$0.529581\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$	1.41421	−	1.41421i	0.0463241	−	0.0463241i
$933$		0			0
$934$		−	12.0000i		−	0.392652i
$935$	−2.82843	+	5.65685i	−0.0924995	+	0.184999i
$936$		0			0
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	0.784046	−	0.620703i	$-0.213153\pi$
$937$	5.00000	+	5.00000i	0.163343	+	0.163343i	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−12.7279	−	12.7279i	−0.415581	−	0.415581i
$939$		0			0
$940$		0			0
$941$			18.3848i			0.599327i	0.954045	+	0.299663i	$0.0968743\pi$
$941$			18.3848i			0.599327i	−0.954045	+	0.299663i	$0.903126\pi$
$942$		0			0
$943$	32.0000	−	32.0000i	1.04206	−	1.04206i
$944$	−1.41421			−0.0460287
$945$		0			0
$946$	4.00000			0.130051
$947$	14.1421	−	14.1421i	0.459558	−	0.459558i	−0.438953	−	0.898510i	$-0.644650\pi$
$947$	14.1421	−	14.1421i	0.459558	−	0.459558i	0.898510	+	0.438953i	$0.144650\pi$
$948$		0			0
$949$			96.0000i			3.11629i
$950$	19.7990	+	2.82843i	0.642364	+	0.0917663i
$951$		0			0
$952$	1.00000	+	1.00000i	0.0324102	+	0.0324102i
$953$	25.4558	+	25.4558i	0.824596	+	0.824596i	0.986763	−	0.162168i	$-0.0518485\pi$
$953$	25.4558	+	25.4558i	0.824596	+	0.824596i	−0.162168	+	0.986763i	$0.551849\pi$
$954$		0			0
$955$	−30.0000	+	10.0000i	−0.970777	+	0.323592i
$956$		−	28.2843i		−	0.914779i
$957$		0			0
$958$	7.00000	−	7.00000i	0.226160	−	0.226160i
$959$	−5.65685			−0.182669
$960$		0			0
$961$	5.00000			0.161290
$962$	−16.9706	+	16.9706i	−0.547153	+	0.547153i
$963$		0			0
$964$			14.0000i			0.450910i
$965$	−16.9706	−	8.48528i	−0.546302	−	0.273151i
$966$		0			0
$967$	−2.00000	−	2.00000i	−0.0643157	−	0.0643157i	0.674217	−	0.738533i	$-0.264481\pi$
$967$	−2.00000	−	2.00000i	−0.0643157	−	0.0643157i	−0.738533	+	0.674217i	$0.764481\pi$
$968$	2.12132	+	2.12132i	0.0681818	+	0.0681818i
$969$		0			0
$970$	10.0000	+	30.0000i	0.321081	+	0.963242i
$971$		−	43.8406i		−	1.40691i	−0.710739	−	0.703456i	$-0.751639\pi$
$971$		−	43.8406i		−	1.40691i	0.710739	−	0.703456i	$-0.248361\pi$
$972$		0			0
$973$	−16.0000	+	16.0000i	−0.512936	+	0.512936i
$974$	24.0416			0.770344
$975$		0			0
$976$	−8.00000			−0.256074
$977$	−33.9411	+	33.9411i	−1.08587	+	1.08587i	−0.0899242	+	0.995949i	$0.528662\pi$
$977$	−33.9411	+	33.9411i	−1.08587	+	1.08587i	−0.995949	+	0.0899242i	$0.971338\pi$
$978$		0			0
$979$			20.0000i			0.639203i
$980$	3.53553	+	10.6066i	0.112938	+	0.338815i
$981$		0			0
$982$	−1.00000	−	1.00000i	−0.0319113	−	0.0319113i
$983$	−9.89949	−	9.89949i	−0.315745	−	0.315745i	0.531385	−	0.847130i	$-0.321672\pi$
$983$	−9.89949	−	9.89949i	−0.315745	−	0.315745i	−0.847130	+	0.531385i	$0.821672\pi$
$984$		0			0
$985$	24.0000	+	12.0000i	0.764704	+	0.382352i
$986$			9.89949i			0.315264i
$987$		0			0
$988$	−16.0000	+	16.0000i	−0.509028	+	0.509028i
$989$	11.3137			0.359755
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	4.24264	−	4.24264i	0.134704	−	0.134704i
$993$		0			0
$994$			22.0000i			0.697798i
$995$	−29.6985	+	9.89949i	−0.941505	+	0.313835i
$996$		0			0
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	0.384662	−	0.923057i	$-0.374318\pi$
$997$	−17.0000	−	17.0000i	−0.538395	−	0.538395i	−0.923057	+	0.384662i	$0.874318\pi$
$998$	2.82843	+	2.82843i	0.0895323	+	0.0895323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.e.647.1	✓	4
3.2	odd	2	inner	1530.2.m.e.647.2	yes	4
5.3	odd	4	inner	1530.2.m.e.953.2	yes	4
15.8	even	4	inner	1530.2.m.e.953.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.e.647.1	✓	4	1.1	even	1	trivial
1530.2.m.e.647.2	yes	4	3.2	odd	2	inner
1530.2.m.e.953.1	yes	4	15.8	even	4	inner
1530.2.m.e.953.2	yes	4	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(1.00000 + 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.00000 + 1.00000i) q^{10} -2.82843i q^{11} +(-4.00000 + 4.00000i) q^{13} -1.41421 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +4.00000i q^{19} +(-2.12132 + 0.707107i) q^{20} +(2.00000 + 2.00000i) q^{22} +(5.65685 + 5.65685i) q^{23} +(-4.00000 + 3.00000i) q^{25} -5.65685i q^{26} +(1.00000 - 1.00000i) q^{28} +9.89949 q^{29} +6.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(1.41421 - 2.82843i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(1.00000 - 2.00000i) q^{40} -5.65685i q^{41} +(1.00000 - 1.00000i) q^{43} -2.82843 q^{44} -8.00000 q^{46} -5.00000i q^{49} +(0.707107 - 4.94975i) q^{50} +(4.00000 + 4.00000i) q^{52} +(-4.24264 - 4.24264i) q^{53} +(-6.00000 + 2.00000i) q^{55} +1.41421i q^{56} +(-7.00000 + 7.00000i) q^{58} +1.41421 q^{59} +8.00000 q^{61} +(-4.24264 + 4.24264i) q^{62} +1.00000i q^{64} +(11.3137 + 5.65685i) q^{65} +(9.00000 + 9.00000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(1.00000 + 3.00000i) q^{70} -15.5563i q^{71} +(12.0000 - 12.0000i) q^{73} +4.24264 q^{74} +4.00000 q^{76} +(2.82843 - 2.82843i) q^{77} -8.00000i q^{79} +(0.707107 + 2.12132i) q^{80} +(4.00000 + 4.00000i) q^{82} +(4.24264 + 4.24264i) q^{83} +(-2.00000 - 1.00000i) q^{85} +1.41421i q^{86} +(2.00000 - 2.00000i) q^{88} -7.07107 q^{89} -8.00000 q^{91} +(5.65685 - 5.65685i) q^{92} +(8.48528 - 2.82843i) q^{95} +(10.0000 + 10.0000i) q^{97} +(3.53553 + 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{7} + 8 q^{10} - 16 q^{13} - 4 q^{16} + 8 q^{22} - 16 q^{25} + 4 q^{28} + 24 q^{31} - 12 q^{37} + 4 q^{40} + 4 q^{43} - 32 q^{46} + 16 q^{52} - 24 q^{55} - 28 q^{58} + 32 q^{61} + 36 q^{67} + 4 q^{70}+ \cdots + 40 q^{97}+O(q^{100}) \) 4 * q + 4 * q^7 + 8 * q^10 - 16 * q^13 - 4 * q^16 + 8 * q^22 - 16 * q^25 + 4 * q^28 + 24 * q^31 - 12 * q^37 + 4 * q^40 + 4 * q^43 - 32 * q^46 + 16 * q^52 - 24 * q^55 - 28 * q^58 + 32 * q^61 + 36 * q^67 + 4 * q^70 + 48 * q^73 + 16 * q^76 + 16 * q^82 - 8 * q^85 + 8 * q^88 - 32 * q^91 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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