LMFDB - Embedded newform 1530.2.m.b.647.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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.b.953.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} -2.82843i q^{11} +(4.00000 - 4.00000i) q^{13} +4.24264 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(2.00000 + 2.00000i) q^{22} +(4.24264 + 4.24264i) q^{23} +(-4.00000 - 3.00000i) q^{25} +5.65685i q^{26} +(-3.00000 + 3.00000i) q^{28} +4.24264 q^{29} -8.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(-8.48528 + 4.24264i) q^{35} +(-5.00000 - 5.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} -8.48528i q^{41} +(-3.00000 + 3.00000i) q^{43} -2.82843 q^{44} -6.00000 q^{46} +(2.82843 - 2.82843i) q^{47} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-6.00000 - 2.00000i) q^{55} -4.24264i q^{56} +(-3.00000 + 3.00000i) q^{58} +9.89949 q^{59} -14.0000 q^{61} +(5.65685 - 5.65685i) q^{62} +1.00000i q^{64} +(-5.65685 - 11.3137i) q^{65} +(-5.00000 - 5.00000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(3.00000 - 9.00000i) q^{70} +15.5563i q^{71} +(6.00000 - 6.00000i) q^{73} +7.07107 q^{74} +4.00000 q^{76} +(-8.48528 + 8.48528i) q^{77} +10.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(6.00000 + 6.00000i) q^{82} +(-4.24264 - 4.24264i) q^{83} +(-1.00000 - 2.00000i) q^{85} -4.24264i q^{86} +(2.00000 - 2.00000i) q^{88} -18.3848 q^{89} -24.0000 q^{91} +(4.24264 - 4.24264i) q^{92} +4.00000i q^{94} +(8.48528 + 2.82843i) q^{95} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{7}+O(q^{10}) $ 4 * q - 12 * q^7	$ 4 q - 12 q^{7} + 4 q^{10} + 16 q^{13} - 4 q^{16} + 8 q^{22} - 16 q^{25} - 12 q^{28} - 32 q^{31} - 20 q^{37} + 8 q^{40} - 12 q^{43} - 24 q^{46} - 16 q^{52} - 24 q^{55} - 12 q^{58} - 56 q^{61} - 20 q^{67} + 12 q^{70} + 24 q^{73} + 16 q^{76} + 24 q^{82} - 4 q^{85} + 8 q^{88} - 96 q^{91}+O(q^{100}) $ 4 * q - 12 * q^7 + 4 * q^10 + 16 * q^13 - 4 * q^16 + 8 * q^22 - 16 * q^25 - 12 * q^28 - 32 * q^31 - 20 * q^37 + 8 * q^40 - 12 * q^43 - 24 * q^46 - 16 * q^52 - 24 * q^55 - 12 * q^58 - 56 * q^61 - 20 * q^67 + 12 * q^70 + 24 * q^73 + 16 * q^76 + 24 * q^82 - 4 * q^85 + 8 * q^88 - 96 * q^91

Display 100 coefficients 10 coefficients

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
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−3.00000	−	3.00000i	−1.13389	−	1.13389i	−0.144370	−	0.989524i	$-0.546115\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.00000	+	2.00000i	0.316228	+	0.632456i
$11$		−	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	$-0.462938\pi$
$13$	4.00000	−	4.00000i	1.10940	−	1.10940i	0.993229	−	0.116171i	$-0.0370621\pi$
$14$	4.24264			1.13389
$15$		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
$23$	4.24264	+	4.24264i	0.884652	+	0.884652i	0.994003	−	0.109351i	$-0.0348774\pi$
$23$	4.24264	+	4.24264i	0.884652	+	0.884652i	−0.109351	+	0.994003i	$0.534877\pi$
$24$		0			0
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$			5.65685i			1.10940i
$27$		0			0
$28$	−3.00000	+	3.00000i	−0.566947	+	0.566947i
$29$	4.24264			0.787839			0.393919	−	0.919145i	$-0.371119\pi$
$29$	4.24264			0.787839			0.393919	+	0.919145i	$0.371119\pi$
$30$		0			0
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			1.00000i			0.171499i
$35$	−8.48528	+	4.24264i	−1.43427	+	0.717137i
$36$		0			0
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	0.164399	−	0.986394i	$-0.447432\pi$
$37$	−5.00000	−	5.00000i	−0.821995	−	0.821995i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−2.82843	−	2.82843i	−0.458831	−	0.458831i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$		0			0
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	−0.897833	−	0.440337i	$-0.854859\pi$
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	0.440337	+	0.897833i	$0.354859\pi$
$44$	−2.82843			−0.426401
$45$		0			0
$46$	−6.00000			−0.884652
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	−0.470064	−	0.882632i	$-0.655769\pi$
$47$	2.82843	−	2.82843i	0.412568	−	0.412568i	0.882632	+	0.470064i	$0.155769\pi$
$48$		0			0
$49$			11.0000i			1.57143i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$	−4.00000	−	4.00000i	−0.554700	−	0.554700i
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	0.603276	−	0.797533i	$-0.293862\pi$
$53$	−1.41421	−	1.41421i	−0.194257	−	0.194257i	−0.797533	+	0.603276i	$0.793862\pi$
$54$		0			0
$55$	−6.00000	−	2.00000i	−0.809040	−	0.269680i
$56$		−	4.24264i		−	0.566947i
$57$		0			0
$58$	−3.00000	+	3.00000i	−0.393919	+	0.393919i
$59$	9.89949			1.28880			0.644402	−	0.764687i	$-0.277106\pi$
$59$	9.89949			1.28880			0.644402	+	0.764687i	$0.277106\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	5.65685	−	5.65685i	0.718421	−	0.718421i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.65685	−	11.3137i	−0.701646	−	1.40329i
$66$		0			0
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	3.00000	−	9.00000i	0.358569	−	1.07571i
$71$			15.5563i			1.84620i	0.384561	+	0.923099i	$0.374353\pi$
$71$			15.5563i			1.84620i	−0.384561	+	0.923099i	$0.625647\pi$
$72$		0			0
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	−0.262646	−	0.964892i	$-0.584595\pi$
$73$	6.00000	−	6.00000i	0.702247	−	0.702247i	0.964892	+	0.262646i	$0.0845950\pi$
$74$	7.07107			0.821995
$75$		0			0
$76$	4.00000			0.458831
$77$	−8.48528	+	8.48528i	−0.966988	+	0.966988i
$78$		0			0
$79$			10.0000i			1.12509i	0.826767	+	0.562544i	$0.190177\pi$
$79$			10.0000i			1.12509i	−0.826767	+	0.562544i	$0.809823\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$		0			0
$82$	6.00000	+	6.00000i	0.662589	+	0.662589i
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	0.434825	−	0.900515i	$-0.356810\pi$
$83$	−4.24264	−	4.24264i	−0.465690	−	0.465690i	−0.900515	+	0.434825i	$0.856810\pi$
$84$		0			0
$85$	−1.00000	−	2.00000i	−0.108465	−	0.216930i
$86$		−	4.24264i		−	0.457496i
$87$		0			0
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	−18.3848			−1.94878			−0.974391	−	0.224860i	$-0.927808\pi$
$89$	−18.3848			−1.94878			−0.974391	+	0.224860i	$0.927808\pi$
$90$		0			0
$91$	−24.0000			−2.51588
$92$	4.24264	−	4.24264i	0.442326	−	0.442326i
$93$		0			0
$94$			4.00000i			0.412568i
$95$	8.48528	+	2.82843i	0.870572	+	0.290191i
$96$		0			0
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	−7.77817	−	7.77817i	−0.785714	−	0.785714i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$			16.9706i			1.68863i	0.535844	+	0.844317i	$0.319994\pi$
$101$			16.9706i			1.68863i	−0.535844	+	0.844317i	$0.680006\pi$
$102$		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
$106$	2.00000			0.194257
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	−0.557047	−	0.830481i	$-0.688066\pi$
$107$	2.82843	−	2.82843i	0.273434	−	0.273434i	0.830481	+	0.557047i	$0.188066\pi$
$108$		0			0
$109$		−	16.0000i		−	1.53252i	−0.642529	−	0.766261i	$-0.722115\pi$
$109$		−	16.0000i		−	1.53252i	0.642529	−	0.766261i	$-0.277885\pi$
$110$	5.65685	−	2.82843i	0.539360	−	0.269680i
$111$		0			0
$112$	3.00000	+	3.00000i	0.283473	+	0.283473i
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	0.770490	−	0.637452i	$-0.220012\pi$
$113$	1.41421	+	1.41421i	0.133038	+	0.133038i	−0.637452	+	0.770490i	$0.720012\pi$
$114$		0			0
$115$	12.0000	−	6.00000i	1.11901	−	0.559503i
$116$		−	4.24264i		−	0.393919i
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−4.24264			−0.388922
$120$		0			0
$121$	3.00000			0.272727
$122$	9.89949	−	9.89949i	0.896258	−	0.896258i
$123$		0			0
$124$			8.00000i			0.718421i
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$		0			0
$127$	12.0000	+	12.0000i	1.06483	+	1.06483i	0.997748	+	0.0670802i	$0.0213683\pi$
$127$	12.0000	+	12.0000i	1.06483	+	1.06483i	0.0670802	+	0.997748i	$0.478632\pi$
$128$	−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
$133$	12.0000	−	12.0000i	1.04053	−	1.04053i
$134$	7.07107			0.610847
$135$		0			0
$136$	1.00000			0.0857493
$137$	8.48528	−	8.48528i	0.724947	−	0.724947i	−0.244662	−	0.969608i	$-0.578677\pi$
$137$	8.48528	−	8.48528i	0.724947	−	0.724947i	0.969608	+	0.244662i	$0.0786770\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	4.24264	+	8.48528i	0.358569	+	0.717137i
$141$		0			0
$142$	−11.0000	−	11.0000i	−0.923099	−	0.923099i
$143$	−11.3137	−	11.3137i	−0.946100	−	0.946100i
$144$		0			0
$145$	3.00000	−	9.00000i	0.249136	−	0.747409i
$146$			8.48528i			0.702247i
$147$		0			0
$148$	−5.00000	+	5.00000i	−0.410997	+	0.410997i
$149$	−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
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−2.82843	+	2.82843i	−0.229416	+	0.229416i
$153$		0			0
$154$		−	12.0000i		−	0.966988i
$155$	−5.65685	+	16.9706i	−0.454369	+	1.36311i
$156$		0			0
$157$	−4.00000	−	4.00000i	−0.319235	−	0.319235i	0.529238	−	0.848473i	$-0.322478\pi$
$157$	−4.00000	−	4.00000i	−0.319235	−	0.319235i	−0.848473	+	0.529238i	$0.822478\pi$
$158$	−7.07107	−	7.07107i	−0.562544	−	0.562544i
$159$		0			0
$160$	−1.00000	−	2.00000i	−0.0790569	−	0.158114i
$161$		−	25.4558i		−	2.00620i
$162$		0			0
$163$	10.0000	−	10.0000i	0.783260	−	0.783260i	−0.197119	−	0.980380i	$-0.563159\pi$
$163$	10.0000	−	10.0000i	0.783260	−	0.783260i	0.980380	+	0.197119i	$0.0631586\pi$
$164$	−8.48528			−0.662589
$165$		0			0
$166$	6.00000			0.465690
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	−0.117582	−	0.993063i	$-0.537514\pi$
$167$	11.3137	−	11.3137i	0.875481	−	0.875481i	0.993063	+	0.117582i	$0.0375143\pi$
$168$		0			0
$169$		−	19.0000i		−	1.46154i
$170$	2.12132	+	0.707107i	0.162698	+	0.0542326i
$171$		0			0
$172$	3.00000	+	3.00000i	0.228748	+	0.228748i
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	0.651300	−	0.758820i	$-0.274224\pi$
$173$	−1.41421	−	1.41421i	−0.107521	−	0.107521i	−0.758820	+	0.651300i	$0.774224\pi$
$174$		0			0
$175$	3.00000	+	21.0000i	0.226779	+	1.58745i
$176$			2.82843i			0.213201i
$177$		0			0
$178$	13.0000	−	13.0000i	0.974391	−	0.974391i
$179$	4.24264			0.317110			0.158555	−	0.987350i	$-0.449317\pi$
$179$	4.24264			0.317110			0.158555	+	0.987350i	$0.449317\pi$
$180$		0			0
$181$	4.00000			0.297318			0.148659	−	0.988889i	$-0.452504\pi$
$181$	4.00000			0.297318			0.148659	+	0.988889i	$0.452504\pi$
$182$	16.9706	−	16.9706i	1.25794	−	1.25794i
$183$		0			0
$184$			6.00000i			0.442326i
$185$	−14.1421	+	7.07107i	−1.03975	+	0.519875i
$186$		0			0
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	−2.82843	−	2.82843i	−0.206284	−	0.206284i
$189$		0			0
$190$	−8.00000	+	4.00000i	−0.580381	+	0.290191i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$		0			0
$193$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$193$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$194$		0			0
$195$		0			0
$196$	11.0000			0.785714
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	−0.260235	−	0.965545i	$-0.583800\pi$
$197$	9.89949	−	9.89949i	0.705310	−	0.705310i	0.965545	+	0.260235i	$0.0838002\pi$
$198$		0			0
$199$		−	8.00000i		−	0.567105i	−0.958957	−	0.283552i	$-0.908487\pi$
$199$		−	8.00000i		−	0.567105i	0.958957	−	0.283552i	$-0.0915130\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$		0			0
$202$	−12.0000	−	12.0000i	−0.844317	−	0.844317i
$203$	−12.7279	−	12.7279i	−0.893325	−	0.893325i
$204$		0			0
$205$	−18.0000	−	6.00000i	−1.25717	−	0.419058i
$206$		0			0
$207$		0			0
$208$	−4.00000	+	4.00000i	−0.277350	+	0.277350i
$209$	11.3137			0.782586
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	−1.41421	+	1.41421i	−0.0971286	+	0.0971286i
$213$		0			0
$214$			4.00000i			0.273434i
$215$	4.24264	+	8.48528i	0.289346	+	0.578691i
$216$		0			0
$217$	24.0000	+	24.0000i	1.62923	+	1.62923i
$218$	11.3137	+	11.3137i	0.766261	+	0.766261i
$219$		0			0
$220$	−2.00000	+	6.00000i	−0.134840	+	0.404520i
$221$		−	5.65685i		−	0.380521i
$222$		0			0
$223$	−12.0000	+	12.0000i	−0.803579	+	0.803579i	−0.983653	−	0.180074i	$-0.942366\pi$
$223$	−12.0000	+	12.0000i	−0.803579	+	0.803579i	0.180074	+	0.983653i	$0.442366\pi$
$224$	−4.24264			−0.283473
$225$		0			0
$226$	−2.00000			−0.133038
$227$	−11.3137	+	11.3137i	−0.750917	+	0.750917i	−0.974650	−	0.223733i	$-0.928176\pi$
$227$	−11.3137	+	11.3137i	−0.750917	+	0.750917i	0.223733	+	0.974650i	$0.428176\pi$
$228$		0			0
$229$			22.0000i			1.45380i	0.686743	+	0.726900i	$0.259040\pi$
$229$			22.0000i			1.45380i	−0.686743	+	0.726900i	$0.740960\pi$
$230$	−4.24264	+	12.7279i	−0.279751	+	0.839254i
$231$		0			0
$232$	3.00000	+	3.00000i	0.196960	+	0.196960i
$233$	−1.41421	−	1.41421i	−0.0926482	−	0.0926482i	0.659264	−	0.751912i	$-0.270868\pi$
$233$	−1.41421	−	1.41421i	−0.0926482	−	0.0926482i	−0.751912	+	0.659264i	$0.770868\pi$
$234$		0			0
$235$	−4.00000	−	8.00000i	−0.260931	−	0.521862i
$236$		−	9.89949i		−	0.644402i
$237$		0			0
$238$	3.00000	−	3.00000i	0.194461	−	0.194461i
$239$	−5.65685			−0.365911			−0.182956	−	0.983121i	$-0.558567\pi$
$239$	−5.65685			−0.365911			−0.182956	+	0.983121i	$0.558567\pi$
$240$		0			0
$241$	30.0000			1.93247			0.966235	−	0.257663i	$-0.0829523\pi$
$241$	30.0000			1.93247			0.966235	+	0.257663i	$0.0829523\pi$
$242$	−2.12132	+	2.12132i	−0.136364	+	0.136364i
$243$		0			0
$244$			14.0000i			0.896258i
$245$	23.3345	+	7.77817i	1.49079	+	0.496929i
$246$		0			0
$247$	16.0000	+	16.0000i	1.01806	+	1.01806i
$248$	−5.65685	−	5.65685i	−0.359211	−	0.359211i
$249$		0			0
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$		−	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
$253$	12.0000	−	12.0000i	0.754434	−	0.754434i
$254$	−16.9706			−1.06483
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	−0.826940	−	0.562291i	$-0.809920\pi$
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	0.562291	+	0.826940i	$0.309920\pi$
$258$		0			0
$259$			30.0000i			1.86411i
$260$	−11.3137	+	5.65685i	−0.701646	+	0.350823i
$261$		0			0
$262$	4.00000	+	4.00000i	0.247121	+	0.247121i
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	0.859669	−	0.510852i	$-0.170670\pi$
$263$	5.65685	+	5.65685i	0.348817	+	0.348817i	−0.510852	+	0.859669i	$0.670670\pi$
$264$		0			0
$265$	−4.00000	+	2.00000i	−0.245718	+	0.122859i
$266$			16.9706i			1.04053i
$267$		0			0
$268$	−5.00000	+	5.00000i	−0.305424	+	0.305424i
$269$	−18.3848			−1.12094			−0.560470	−	0.828175i	$-0.689379\pi$
$269$	−18.3848			−1.12094			−0.560470	+	0.828175i	$0.689379\pi$
$270$		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
$274$			12.0000i			0.724947i
$275$	−8.48528	+	11.3137i	−0.511682	+	0.682242i
$276$		0			0
$277$	−7.00000	−	7.00000i	−0.420589	−	0.420589i	0.464817	−	0.885407i	$-0.346120\pi$
$277$	−7.00000	−	7.00000i	−0.420589	−	0.420589i	−0.885407	+	0.464817i	$0.846120\pi$
$278$		0			0
$279$		0			0
$280$	−9.00000	−	3.00000i	−0.537853	−	0.179284i
$281$			26.8701i			1.60293i	0.598040	+	0.801467i	$0.295947\pi$
$281$			26.8701i			1.60293i	−0.598040	+	0.801467i	$0.704053\pi$
$282$		0			0
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.211498	−	0.977378i	$-0.432166\pi$
$283$	20.0000	−	20.0000i	1.18888	−	1.18888i	0.977378	−	0.211498i	$-0.0678343\pi$
$284$	15.5563			0.923099
$285$		0			0
$286$	16.0000			0.946100
$287$	−25.4558	+	25.4558i	−1.50261	+	1.50261i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	4.24264	+	8.48528i	0.249136	+	0.498273i
$291$		0			0
$292$	−6.00000	−	6.00000i	−0.351123	−	0.351123i
$293$	15.5563	+	15.5563i	0.908812	+	0.908812i	0.996176	−	0.0873648i	$-0.0278446\pi$
$293$	15.5563	+	15.5563i	0.908812	+	0.908812i	−0.0873648	+	0.996176i	$0.527845\pi$
$294$		0			0
$295$	7.00000	−	21.0000i	0.407556	−	1.22267i
$296$		−	7.07107i		−	0.410997i
$297$		0			0
$298$	8.00000	−	8.00000i	0.463428	−	0.463428i
$299$	33.9411			1.96287
$300$		0			0
$301$	18.0000			1.03750
$302$		0			0
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$	−9.89949	+	29.6985i	−0.566843	+	1.70053i
$306$		0			0
$307$	−19.0000	−	19.0000i	−1.08439	−	1.08439i	−0.996095	−	0.0882927i	$-0.971859\pi$
$307$	−19.0000	−	19.0000i	−1.08439	−	1.08439i	−0.0882927	−	0.996095i	$-0.528141\pi$
$308$	8.48528	+	8.48528i	0.483494	+	0.483494i
$309$		0			0
$310$	−8.00000	−	16.0000i	−0.454369	−	0.908739i
$311$			9.89949i			0.561349i	0.959803	+	0.280674i	$0.0905581\pi$
$311$			9.89949i			0.561349i	−0.959803	+	0.280674i	$0.909442\pi$
$312$		0			0
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$	5.65685			0.319235
$315$		0			0
$316$	10.0000			0.562544
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	−0.187889	−	0.982190i	$-0.560164\pi$
$317$	14.1421	−	14.1421i	0.794301	−	0.794301i	0.982190	+	0.187889i	$0.0601645\pi$
$318$		0			0
$319$		−	12.0000i		−	0.671871i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$		0			0
$322$	18.0000	+	18.0000i	1.00310	+	1.00310i
$323$	2.82843	+	2.82843i	0.157378	+	0.157378i
$324$		0			0
$325$	−28.0000	+	4.00000i	−1.55316	+	0.221880i
$326$			14.1421i			0.783260i
$327$		0			0
$328$	6.00000	−	6.00000i	0.331295	−	0.331295i
$329$	−16.9706			−0.935617
$330$		0			0
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$	−4.24264	+	4.24264i	−0.232845	+	0.232845i
$333$		0			0
$334$			16.0000i			0.875481i
$335$	−14.1421	+	7.07107i	−0.772667	+	0.386334i
$336$		0			0
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	0.924913	−	0.380178i	$-0.124137\pi$
$337$	10.0000	+	10.0000i	0.544735	+	0.544735i	−0.380178	+	0.924913i	$0.624137\pi$
$338$	13.4350	+	13.4350i	0.730769	+	0.730769i
$339$		0			0
$340$	−2.00000	+	1.00000i	−0.108465	+	0.0542326i
$341$			22.6274i			1.22534i
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	−4.24264			−0.228748
$345$		0			0
$346$	2.00000			0.107521
$347$	11.3137	−	11.3137i	0.607352	−	0.607352i	−0.334901	−	0.942253i	$-0.608703\pi$
$347$	11.3137	−	11.3137i	0.607352	−	0.607352i	0.942253	+	0.334901i	$0.108703\pi$
$348$		0			0
$349$			6.00000i			0.321173i	0.987022	+	0.160586i	$0.0513385\pi$
$349$			6.00000i			0.321173i	−0.987022	+	0.160586i	$0.948662\pi$
$350$	−16.9706	−	12.7279i	−0.907115	−	0.680336i
$351$		0			0
$352$	−2.00000	−	2.00000i	−0.106600	−	0.106600i
$353$	−5.65685	−	5.65685i	−0.301084	−	0.301084i	0.540354	−	0.841438i	$-0.318290\pi$
$353$	−5.65685	−	5.65685i	−0.301084	−	0.301084i	−0.841438	+	0.540354i	$0.818290\pi$
$354$		0			0
$355$	33.0000	+	11.0000i	1.75146	+	0.583819i
$356$			18.3848i			0.974391i
$357$		0			0
$358$	−3.00000	+	3.00000i	−0.158555	+	0.158555i
$359$	2.82843			0.149279			0.0746393	−	0.997211i	$-0.476219\pi$
$359$	2.82843			0.149279			0.0746393	+	0.997211i	$0.476219\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−2.82843	+	2.82843i	−0.148659	+	0.148659i
$363$		0			0
$364$			24.0000i			1.25794i
$365$	−8.48528	−	16.9706i	−0.444140	−	0.888280i
$366$		0			0
$367$	−17.0000	−	17.0000i	−0.887393	−	0.887393i	0.106879	−	0.994272i	$-0.465914\pi$
$367$	−17.0000	−	17.0000i	−0.887393	−	0.887393i	−0.994272	+	0.106879i	$0.965914\pi$
$368$	−4.24264	−	4.24264i	−0.221163	−	0.221163i
$369$		0			0
$370$	5.00000	−	15.0000i	0.259938	−	0.779813i
$371$			8.48528i			0.440534i
$372$		0			0
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	−0.534500	−	0.845168i	$-0.679500\pi$
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	0.845168	+	0.534500i	$0.179500\pi$
$374$	2.82843			0.146254
$375$		0			0
$376$	4.00000			0.206284
$377$	16.9706	−	16.9706i	0.874028	−	0.874028i
$378$		0			0
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$	2.82843	−	8.48528i	0.145095	−	0.435286i
$381$		0			0
$382$	2.00000	+	2.00000i	0.102329	+	0.102329i
$383$	5.65685	+	5.65685i	0.289052	+	0.289052i	0.836705	−	0.547653i	$-0.184479\pi$
$383$	5.65685	+	5.65685i	0.289052	+	0.289052i	−0.547653	+	0.836705i	$0.684479\pi$
$384$		0			0
$385$	12.0000	+	24.0000i	0.611577	+	1.22315i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.3137			0.573628			0.286814	−	0.957986i	$-0.407404\pi$
$389$	11.3137			0.573628			0.286814	+	0.957986i	$0.407404\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	−7.77817	+	7.77817i	−0.392857	+	0.392857i
$393$		0			0
$394$			14.0000i			0.705310i
$395$	21.2132	+	7.07107i	1.06735	+	0.355784i
$396$		0			0
$397$	9.00000	+	9.00000i	0.451697	+	0.451697i	0.895918	−	0.444220i	$-0.146519\pi$
$397$	9.00000	+	9.00000i	0.451697	+	0.451697i	−0.444220	+	0.895918i	$0.646519\pi$
$398$	5.65685	+	5.65685i	0.283552	+	0.283552i
$399$		0			0
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$		−	22.6274i		−	1.12996i	−0.825105	−	0.564980i	$-0.808884\pi$
$401$		−	22.6274i		−	1.12996i	0.825105	−	0.564980i	$-0.191116\pi$
$402$		0			0
$403$	−32.0000	+	32.0000i	−1.59403	+	1.59403i
$404$	16.9706			0.844317
$405$		0			0
$406$	18.0000			0.893325
$407$	−14.1421	+	14.1421i	−0.701000	+	0.701000i
$408$		0			0
$409$			10.0000i			0.494468i	0.968956	+	0.247234i	$0.0795217\pi$
$409$			10.0000i			0.494468i	−0.968956	+	0.247234i	$0.920478\pi$
$410$	16.9706	−	8.48528i	0.838116	−	0.419058i
$411$		0			0
$412$		0			0
$413$	−29.6985	−	29.6985i	−1.46137	−	1.46137i
$414$		0			0
$415$	−12.0000	+	6.00000i	−0.589057	+	0.294528i
$416$		−	5.65685i		−	0.277350i
$417$		0			0
$418$	−8.00000	+	8.00000i	−0.391293	+	0.391293i
$419$	16.9706			0.829066			0.414533	−	0.910034i	$-0.363945\pi$
$419$	16.9706			0.829066			0.414533	+	0.910034i	$0.363945\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	14.1421	−	14.1421i	0.688428	−	0.688428i
$423$		0			0
$424$		−	2.00000i		−	0.0971286i
$425$	−4.94975	+	0.707107i	−0.240098	+	0.0342997i
$426$		0			0
$427$	42.0000	+	42.0000i	2.03252	+	2.03252i
$428$	−2.82843	−	2.82843i	−0.136717	−	0.136717i
$429$		0			0
$430$	−9.00000	−	3.00000i	−0.434019	−	0.144673i
$431$			15.5563i			0.749323i	0.927162	+	0.374661i	$0.122241\pi$
$431$			15.5563i			0.749323i	−0.927162	+	0.374661i	$0.877759\pi$
$432$		0			0
$433$	27.0000	−	27.0000i	1.29754	−	1.29754i	0.367523	−	0.930015i	$-0.380206\pi$
$433$	27.0000	−	27.0000i	1.29754	−	1.29754i	0.930015	−	0.367523i	$-0.119794\pi$
$434$	−33.9411			−1.62923
$435$		0			0
$436$	−16.0000			−0.766261
$437$	−16.9706	+	16.9706i	−0.811812	+	0.811812i
$438$		0			0
$439$			26.0000i			1.24091i	0.784241	+	0.620456i	$0.213053\pi$
$439$			26.0000i			1.24091i	−0.784241	+	0.620456i	$0.786947\pi$
$440$	−2.82843	−	5.65685i	−0.134840	−	0.269680i
$441$		0			0
$442$	4.00000	+	4.00000i	0.190261	+	0.190261i
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	0.800674	−	0.599100i	$-0.204475\pi$
$443$	4.24264	+	4.24264i	0.201574	+	0.201574i	−0.599100	+	0.800674i	$0.704475\pi$
$444$		0			0
$445$	−13.0000	+	39.0000i	−0.616259	+	1.84878i
$446$		−	16.9706i		−	0.803579i
$447$		0			0
$448$	3.00000	−	3.00000i	0.141737	−	0.141737i
$449$	33.9411			1.60178			0.800890	−	0.598811i	$-0.204360\pi$
$449$	33.9411			1.60178			0.800890	+	0.598811i	$0.204360\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	1.41421	−	1.41421i	0.0665190	−	0.0665190i
$453$		0			0
$454$		−	16.0000i		−	0.750917i
$455$	−16.9706	+	50.9117i	−0.795592	+	2.38678i
$456$		0			0
$457$	−11.0000	−	11.0000i	−0.514558	−	0.514558i	0.401361	−	0.915920i	$-0.368537\pi$
$457$	−11.0000	−	11.0000i	−0.514558	−	0.514558i	−0.915920	+	0.401361i	$0.868537\pi$
$458$	−15.5563	−	15.5563i	−0.726900	−	0.726900i
$459$		0			0
$460$	−6.00000	−	12.0000i	−0.279751	−	0.559503i
$461$		−	19.7990i		−	0.922131i	−0.887366	−	0.461065i	$-0.847467\pi$
$461$		−	19.7990i		−	0.922131i	0.887366	−	0.461065i	$-0.152533\pi$
$462$		0			0
$463$	12.0000	−	12.0000i	0.557687	−	0.557687i	−0.370961	−	0.928648i	$-0.620972\pi$
$463$	12.0000	−	12.0000i	0.557687	−	0.557687i	0.928648	+	0.370961i	$0.120972\pi$
$464$	−4.24264			−0.196960
$465$		0			0
$466$	2.00000			0.0926482
$467$	−14.1421	+	14.1421i	−0.654420	+	0.654420i	−0.954054	−	0.299634i	$-0.903135\pi$
$467$	−14.1421	+	14.1421i	−0.654420	+	0.654420i	0.299634	+	0.954054i	$0.403135\pi$
$468$		0			0
$469$			30.0000i			1.38527i
$470$	8.48528	+	2.82843i	0.391397	+	0.130466i
$471$		0			0
$472$	7.00000	+	7.00000i	0.322201	+	0.322201i
$473$	8.48528	+	8.48528i	0.390154	+	0.390154i
$474$		0			0
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$			4.24264i			0.194461i
$477$		0			0
$478$	4.00000	−	4.00000i	0.182956	−	0.182956i
$479$	9.89949			0.452319			0.226160	−	0.974090i	$-0.427383\pi$
$479$	9.89949			0.452319			0.226160	+	0.974090i	$0.427383\pi$
$480$		0			0
$481$	−40.0000			−1.82384
$482$	−21.2132	+	21.2132i	−0.966235	+	0.966235i
$483$		0			0
$484$		−	3.00000i		−	0.136364i
$485$		0			0
$486$		0			0
$487$	5.00000	+	5.00000i	0.226572	+	0.226572i	0.811259	−	0.584687i	$-0.198783\pi$
$487$	5.00000	+	5.00000i	0.226572	+	0.226572i	−0.584687	+	0.811259i	$0.698783\pi$
$488$	−9.89949	−	9.89949i	−0.448129	−	0.448129i
$489$		0			0
$490$	−22.0000	+	11.0000i	−0.993859	+	0.496929i
$491$			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
$493$	3.00000	−	3.00000i	0.135113	−	0.135113i
$494$	−22.6274			−1.01806
$495$		0			0
$496$	8.00000			0.359211
$497$	46.6690	−	46.6690i	2.09339	−	2.09339i
$498$		0			0
$499$		−	40.0000i		−	1.79065i	−0.445418	−	0.895323i	$-0.646945\pi$
$499$		−	40.0000i		−	1.79065i	0.445418	−	0.895323i	$-0.353055\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$		0			0
$502$	11.0000	+	11.0000i	0.490954	+	0.490954i
$503$	−24.0416	−	24.0416i	−1.07196	−	1.07196i	−0.997201	−	0.0747619i	$-0.976180\pi$
$503$	−24.0416	−	24.0416i	−1.07196	−	1.07196i	−0.0747619	−	0.997201i	$-0.523820\pi$
$504$		0			0
$505$	36.0000	+	12.0000i	1.60198	+	0.533993i
$506$			16.9706i			0.754434i
$507$		0			0
$508$	12.0000	−	12.0000i	0.532414	−	0.532414i
$509$	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
$511$	−36.0000			−1.59255
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	6.00000i		−	0.264649i
$515$		0			0
$516$		0			0
$517$	−8.00000	−	8.00000i	−0.351840	−	0.351840i
$518$	−21.2132	−	21.2132i	−0.932055	−	0.932055i
$519$		0			0
$520$	4.00000	−	12.0000i	0.175412	−	0.526235i
$521$		−	5.65685i		−	0.247831i	−0.992293	−	0.123916i	$-0.960455\pi$
$521$		−	5.65685i		−	0.247831i	0.992293	−	0.123916i	$-0.0395452\pi$
$522$		0			0
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	−0.996903	−	0.0786374i	$-0.974943\pi$
$523$	−21.0000	+	21.0000i	−0.918266	+	0.918266i	0.0786374	+	0.996903i	$0.474943\pi$
$524$	−5.65685			−0.247121
$525$		0			0
$526$	−8.00000			−0.348817
$527$	−5.65685	+	5.65685i	−0.246416	+	0.246416i
$528$		0			0
$529$			13.0000i			0.565217i
$530$	1.41421	−	4.24264i	0.0614295	−	0.184289i
$531$		0			0
$532$	−12.0000	−	12.0000i	−0.520266	−	0.520266i
$533$	−33.9411	−	33.9411i	−1.47015	−	1.47015i
$534$		0			0
$535$	−4.00000	−	8.00000i	−0.172935	−	0.345870i
$536$		−	7.07107i		−	0.305424i
$537$		0			0
$538$	13.0000	−	13.0000i	0.560470	−	0.560470i
$539$	31.1127			1.34012
$540$		0			0
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$	2.82843	−	2.82843i	0.121491	−	0.121491i
$543$		0			0
$544$		−	1.00000i		−	0.0428746i
$545$	−33.9411	−	11.3137i	−1.45388	−	0.484626i
$546$		0			0
$547$	16.0000	+	16.0000i	0.684111	+	0.684111i	0.960924	−	0.276813i	$-0.0892783\pi$
$547$	16.0000	+	16.0000i	0.684111	+	0.684111i	−0.276813	+	0.960924i	$0.589278\pi$
$548$	−8.48528	−	8.48528i	−0.362473	−	0.362473i
$549$		0			0
$550$	−2.00000	−	14.0000i	−0.0852803	−	0.596962i
$551$			16.9706i			0.722970i
$552$		0			0
$553$	30.0000	−	30.0000i	1.27573	−	1.27573i
$554$	9.89949			0.420589
$555$		0			0
$556$		0			0
$557$	−12.7279	+	12.7279i	−0.539299	+	0.539299i	−0.923323	−	0.384024i	$-0.874538\pi$
$557$	−12.7279	+	12.7279i	−0.539299	+	0.539299i	0.384024	+	0.923323i	$0.374538\pi$
$558$		0			0
$559$			24.0000i			1.01509i
$560$	8.48528	−	4.24264i	0.358569	−	0.179284i
$561$		0			0
$562$	−19.0000	−	19.0000i	−0.801467	−	0.801467i
$563$	9.89949	+	9.89949i	0.417214	+	0.417214i	0.884242	−	0.467028i	$-0.154675\pi$
$563$	9.89949	+	9.89949i	0.417214	+	0.417214i	−0.467028	+	0.884242i	$0.654675\pi$
$564$		0			0
$565$	4.00000	−	2.00000i	0.168281	−	0.0841406i
$566$			28.2843i			1.18888i
$567$		0			0
$568$	−11.0000	+	11.0000i	−0.461550	+	0.461550i
$569$	35.3553			1.48217			0.741086	−	0.671410i	$-0.234311\pi$
$569$	35.3553			1.48217			0.741086	+	0.671410i	$0.234311\pi$
$570$		0			0
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$	−11.3137	+	11.3137i	−0.473050	+	0.473050i
$573$		0			0
$574$		−	36.0000i		−	1.50261i
$575$	−4.24264	−	29.6985i	−0.176930	−	1.23851i
$576$		0			0
$577$	−21.0000	−	21.0000i	−0.874241	−	0.874241i	0.118690	−	0.992931i	$-0.462131\pi$
$577$	−21.0000	−	21.0000i	−0.874241	−	0.874241i	−0.992931	+	0.118690i	$0.962131\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$	−9.00000	−	3.00000i	−0.373705	−	0.124568i
$581$			25.4558i			1.05609i
$582$		0			0
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	8.48528			0.351123
$585$		0			0
$586$	−22.0000			−0.908812
$587$	4.24264	−	4.24264i	0.175113	−	0.175113i	−0.614109	−	0.789221i	$-0.710484\pi$
$587$	4.24264	−	4.24264i	0.175113	−	0.175113i	0.789221	+	0.614109i	$0.210484\pi$
$588$		0			0
$589$		−	32.0000i		−	1.31854i
$590$	9.89949	+	19.7990i	0.407556	+	0.815112i
$591$		0			0
$592$	5.00000	+	5.00000i	0.205499	+	0.205499i
$593$	−12.7279	−	12.7279i	−0.522673	−	0.522673i	0.395705	−	0.918378i	$-0.370500\pi$
$593$	−12.7279	−	12.7279i	−0.522673	−	0.522673i	−0.918378	+	0.395705i	$0.870500\pi$
$594$		0			0
$595$	−3.00000	+	9.00000i	−0.122988	+	0.368964i
$596$			11.3137i			0.463428i
$597$		0			0
$598$	−24.0000	+	24.0000i	−0.981433	+	0.981433i
$599$	14.1421			0.577832			0.288916	−	0.957354i	$-0.406705\pi$
$599$	14.1421			0.577832			0.288916	+	0.957354i	$0.406705\pi$
$600$		0			0
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$	−12.7279	+	12.7279i	−0.518751	+	0.518751i
$603$		0			0
$604$		0			0
$605$	2.12132	−	6.36396i	0.0862439	−	0.258732i
$606$		0			0
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	0.392218	−	0.919872i	$-0.371708\pi$
$607$	−13.0000	−	13.0000i	−0.527654	−	0.527654i	−0.919872	+	0.392218i	$0.871708\pi$
$608$	2.82843	+	2.82843i	0.114708	+	0.114708i
$609$		0			0
$610$	−14.0000	−	28.0000i	−0.566843	−	1.13369i
$611$		−	22.6274i		−	0.915407i
$612$		0			0
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	−0.475707	−	0.879604i	$-0.657808\pi$
$613$	10.0000	−	10.0000i	0.403896	−	0.403896i	0.879604	+	0.475707i	$0.157808\pi$
$614$	26.8701			1.08439
$615$		0			0
$616$	−12.0000			−0.483494
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	−0.616530	−	0.787332i	$-0.711462\pi$
$617$	4.24264	−	4.24264i	0.170802	−	0.170802i	0.787332	+	0.616530i	$0.211462\pi$
$618$		0			0
$619$		−	16.0000i		−	0.643094i	−0.946894	−	0.321547i	$-0.895797\pi$
$619$		−	16.0000i		−	0.643094i	0.946894	−	0.321547i	$-0.104203\pi$
$620$	16.9706	+	5.65685i	0.681554	+	0.227185i
$621$		0			0
$622$	−7.00000	−	7.00000i	−0.280674	−	0.280674i
$623$	55.1543	+	55.1543i	2.20971	+	2.20971i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		0			0
$627$		0			0
$628$	−4.00000	+	4.00000i	−0.159617	+	0.159617i
$629$	−7.07107			−0.281942
$630$		0			0
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	−7.07107	+	7.07107i	−0.281272	+	0.281272i
$633$		0			0
$634$			20.0000i			0.794301i
$635$	33.9411	−	16.9706i	1.34691	−	0.673456i
$636$		0			0
$637$	44.0000	+	44.0000i	1.74334	+	1.74334i
$638$	8.48528	+	8.48528i	0.335936	+	0.335936i
$639$		0			0
$640$	−2.00000	+	1.00000i	−0.0790569	+	0.0395285i
$641$		−	28.2843i		−	1.11716i	−0.829450	−	0.558581i	$-0.811346\pi$
$641$		−	28.2843i		−	1.11716i	0.829450	−	0.558581i	$-0.188654\pi$
$642$		0			0
$643$	22.0000	−	22.0000i	0.867595	−	0.867595i	−0.124610	−	0.992206i	$-0.539768\pi$
$643$	22.0000	−	22.0000i	0.867595	−	0.867595i	0.992206	+	0.124610i	$0.0397681\pi$
$644$	−25.4558			−1.00310
$645$		0			0
$646$	−4.00000			−0.157378
$647$	−16.9706	+	16.9706i	−0.667182	+	0.667182i	−0.957063	−	0.289881i	$-0.906384\pi$
$647$	−16.9706	+	16.9706i	−0.667182	+	0.667182i	0.289881	+	0.957063i	$0.406384\pi$
$648$		0			0
$649$		−	28.0000i		−	1.09910i
$650$	16.9706	−	22.6274i	0.665640	−	0.887520i
$651$		0			0
$652$	−10.0000	−	10.0000i	−0.391630	−	0.391630i
$653$	−12.7279	−	12.7279i	−0.498082	−	0.498082i	0.412758	−	0.910841i	$-0.364565\pi$
$653$	−12.7279	−	12.7279i	−0.498082	−	0.498082i	−0.910841	+	0.412758i	$0.864565\pi$
$654$		0			0
$655$	−12.0000	−	4.00000i	−0.468879	−	0.156293i
$656$			8.48528i			0.331295i
$657$		0			0
$658$	12.0000	−	12.0000i	0.467809	−	0.467809i
$659$	18.3848			0.716169			0.358085	−	0.933689i	$-0.383430\pi$
$659$	18.3848			0.716169			0.358085	+	0.933689i	$0.383430\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	12.7279	−	12.7279i	0.494685	−	0.494685i
$663$		0			0
$664$		−	6.00000i		−	0.232845i
$665$	−16.9706	−	33.9411i	−0.658090	−	1.31618i
$666$		0			0
$667$	18.0000	+	18.0000i	0.696963	+	0.696963i
$668$	−11.3137	−	11.3137i	−0.437741	−	0.437741i
$669$		0			0
$670$	5.00000	−	15.0000i	0.193167	−	0.579501i
$671$			39.5980i			1.52866i
$672$		0			0
$673$	−20.0000	+	20.0000i	−0.770943	+	0.770943i	−0.978271	−	0.207328i	$-0.933523\pi$
$673$	−20.0000	+	20.0000i	−0.770943	+	0.770943i	0.207328	+	0.978271i	$0.433523\pi$
$674$	−14.1421			−0.544735
$675$		0			0
$676$	−19.0000			−0.730769
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	−0.976492	−	0.215555i	$-0.930844\pi$
$677$	−19.7990	+	19.7990i	−0.760937	+	0.760937i	0.215555	+	0.976492i	$0.430844\pi$
$678$		0			0
$679$		0			0
$680$	0.707107	−	2.12132i	0.0271163	−	0.0813489i
$681$		0			0
$682$	−16.0000	−	16.0000i	−0.612672	−	0.612672i
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	0.525879	−	0.850559i	$-0.323736\pi$
$683$	−8.48528	−	8.48528i	−0.324680	−	0.324680i	−0.850559	+	0.525879i	$0.823736\pi$
$684$		0			0
$685$	−12.0000	−	24.0000i	−0.458496	−	0.916993i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	3.00000	−	3.00000i	0.114374	−	0.114374i
$689$	−11.3137			−0.431018
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	−1.41421	+	1.41421i	−0.0537603	+	0.0537603i
$693$		0			0
$694$			16.0000i			0.607352i
$695$		0			0
$696$		0			0
$697$	−6.00000	−	6.00000i	−0.227266	−	0.227266i
$698$	−4.24264	−	4.24264i	−0.160586	−	0.160586i
$699$		0			0
$700$	21.0000	−	3.00000i	0.793725	−	0.113389i
$701$		−	31.1127i		−	1.17511i	−0.809184	−	0.587555i	$-0.800091\pi$
$701$		−	31.1127i		−	1.17511i	0.809184	−	0.587555i	$-0.199909\pi$
$702$		0			0
$703$	20.0000	−	20.0000i	0.754314	−	0.754314i
$704$	2.82843			0.106600
$705$		0			0
$706$	8.00000			0.301084
$707$	50.9117	−	50.9117i	1.91473	−	1.91473i
$708$		0			0
$709$			28.0000i			1.05156i	0.850620	+	0.525781i	$0.176227\pi$
$709$			28.0000i			1.05156i	−0.850620	+	0.525781i	$0.823773\pi$
$710$	−31.1127	+	15.5563i	−1.16764	+	0.583819i
$711$		0			0
$712$	−13.0000	−	13.0000i	−0.487196	−	0.487196i
$713$	−33.9411	−	33.9411i	−1.27111	−	1.27111i
$714$		0			0
$715$	−32.0000	+	16.0000i	−1.19673	+	0.598366i
$716$		−	4.24264i		−	0.158555i
$717$		0			0
$718$	−2.00000	+	2.00000i	−0.0746393	+	0.0746393i
$719$	−7.07107			−0.263706			−0.131853	−	0.991269i	$-0.542093\pi$
$719$	−7.07107			−0.263706			−0.131853	+	0.991269i	$0.542093\pi$
$720$		0			0
$721$		0			0
$722$	−2.12132	+	2.12132i	−0.0789474	+	0.0789474i
$723$		0			0
$724$		−	4.00000i		−	0.148659i
$725$	−16.9706	−	12.7279i	−0.630271	−	0.472703i
$726$		0			0
$727$	−28.0000	−	28.0000i	−1.03846	−	1.03846i	−0.999230	−	0.0392324i	$-0.987509\pi$
$727$	−28.0000	−	28.0000i	−1.03846	−	1.03846i	−0.0392324	−	0.999230i	$-0.512491\pi$
$728$	−16.9706	−	16.9706i	−0.628971	−	0.628971i
$729$		0			0
$730$	18.0000	+	6.00000i	0.666210	+	0.222070i
$731$			4.24264i			0.156920i
$732$		0			0
$733$	−2.00000	+	2.00000i	−0.0738717	+	0.0738717i	−0.743077	−	0.669206i	$-0.766635\pi$
$733$	−2.00000	+	2.00000i	−0.0738717	+	0.0738717i	0.669206	+	0.743077i	$0.266635\pi$
$734$	24.0416			0.887393
$735$		0			0
$736$	6.00000			0.221163
$737$	−14.1421	+	14.1421i	−0.520932	+	0.520932i
$738$		0			0
$739$			26.0000i			0.956425i	0.878244	+	0.478213i	$0.158715\pi$
$739$			26.0000i			0.956425i	−0.878244	+	0.478213i	$0.841285\pi$
$740$	7.07107	+	14.1421i	0.259938	+	0.519875i
$741$		0			0
$742$	−6.00000	−	6.00000i	−0.220267	−	0.220267i
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	0.323603	−	0.946193i	$-0.395106\pi$
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	−0.946193	+	0.323603i	$0.895106\pi$
$744$		0			0
$745$	−8.00000	+	24.0000i	−0.293097	+	0.879292i
$746$			8.48528i			0.310668i
$747$		0			0
$748$	−2.00000	+	2.00000i	−0.0731272	+	0.0731272i
$749$	−16.9706			−0.620091
$750$		0			0
$751$	18.0000			0.656829			0.328415	−	0.944534i	$-0.393486\pi$
$751$	18.0000			0.656829			0.328415	+	0.944534i	$0.393486\pi$
$752$	−2.82843	+	2.82843i	−0.103142	+	0.103142i
$753$		0			0
$754$			24.0000i			0.874028i
$755$		0			0
$756$		0			0
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$	19.7990	+	19.7990i	0.719132	+	0.719132i
$759$		0			0
$760$	4.00000	+	8.00000i	0.145095	+	0.290191i
$761$		−	9.89949i		−	0.358856i	−0.983771	−	0.179428i	$-0.942575\pi$
$761$		−	9.89949i		−	0.358856i	0.983771	−	0.179428i	$-0.0574248\pi$
$762$		0			0
$763$	−48.0000	+	48.0000i	−1.73772	+	1.73772i
$764$	−2.82843			−0.102329
$765$		0			0
$766$	−8.00000			−0.289052
$767$	39.5980	−	39.5980i	1.42980	−	1.42980i
$768$		0			0
$769$		−	34.0000i		−	1.22607i	−0.790055	−	0.613036i	$-0.789948\pi$
$769$		−	34.0000i		−	1.22607i	0.790055	−	0.613036i	$-0.210052\pi$
$770$	−25.4558	−	8.48528i	−0.917365	−	0.305788i
$771$		0			0
$772$		0			0
$773$	24.0416	+	24.0416i	0.864717	+	0.864717i	0.991882	−	0.127164i	$-0.0405876\pi$
$773$	24.0416	+	24.0416i	0.864717	+	0.864717i	−0.127164	+	0.991882i	$0.540588\pi$
$774$		0			0
$775$	32.0000	+	24.0000i	1.14947	+	0.862105i
$776$		0			0
$777$		0			0
$778$	−8.00000	+	8.00000i	−0.286814	+	0.286814i
$779$	33.9411			1.21607
$780$		0			0
$781$	44.0000			1.57444
$782$	−4.24264	+	4.24264i	−0.151717	+	0.151717i
$783$		0			0
$784$		−	11.0000i		−	0.392857i
$785$	−11.3137	+	5.65685i	−0.403804	+	0.201902i
$786$		0			0
$787$	−38.0000	−	38.0000i	−1.35455	−	1.35455i	−0.880491	−	0.474063i	$-0.842787\pi$
$787$	−38.0000	−	38.0000i	−1.35455	−	1.35455i	−0.474063	−	0.880491i	$-0.657213\pi$
$788$	−9.89949	−	9.89949i	−0.352655	−	0.352655i
$789$		0			0
$790$	−20.0000	+	10.0000i	−0.711568	+	0.355784i
$791$		−	8.48528i		−	0.301702i
$792$		0			0
$793$	−56.0000	+	56.0000i	−1.98862	+	1.98862i
$794$	−12.7279			−0.451697
$795$		0			0
$796$	−8.00000			−0.283552
$797$	35.3553	−	35.3553i	1.25235	−	1.25235i	0.297687	−	0.954664i	$-0.403785\pi$
$797$	35.3553	−	35.3553i	1.25235	−	1.25235i	0.954664	−	0.297687i	$-0.0962151\pi$
$798$		0			0
$799$		−	4.00000i		−	0.141510i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	16.0000	+	16.0000i	0.564980	+	0.564980i
$803$	−16.9706	−	16.9706i	−0.598878	−	0.598878i
$804$		0			0
$805$	−54.0000	−	18.0000i	−1.90325	−	0.634417i
$806$		−	45.2548i		−	1.59403i
$807$		0			0
$808$	−12.0000	+	12.0000i	−0.422159	+	0.422159i
$809$	25.4558			0.894980			0.447490	−	0.894289i	$-0.352318\pi$
$809$	25.4558			0.894980			0.447490	+	0.894289i	$0.352318\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−12.7279	+	12.7279i	−0.446663	+	0.446663i
$813$		0			0
$814$		−	20.0000i		−	0.701000i
$815$	−14.1421	−	28.2843i	−0.495377	−	0.990755i
$816$		0			0
$817$	−12.0000	−	12.0000i	−0.419827	−	0.419827i
$818$	−7.07107	−	7.07107i	−0.247234	−	0.247234i
$819$		0			0
$820$	−6.00000	+	18.0000i	−0.209529	+	0.628587i
$821$			1.41421i			0.0493564i	0.999695	+	0.0246782i	$0.00785611\pi$
$821$			1.41421i			0.0493564i	−0.999695	+	0.0246782i	$0.992144\pi$
$822$		0			0
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	−0.757458	−	0.652884i	$-0.773559\pi$
$823$	−3.00000	+	3.00000i	−0.104573	+	0.104573i	0.652884	+	0.757458i	$0.273559\pi$
$824$		0			0
$825$		0			0
$826$	42.0000			1.46137
$827$	−5.65685	+	5.65685i	−0.196708	+	0.196708i	−0.798587	−	0.601879i	$-0.794419\pi$
$827$	−5.65685	+	5.65685i	−0.196708	+	0.196708i	0.601879	+	0.798587i	$0.294419\pi$
$828$		0			0
$829$		−	46.0000i		−	1.59765i	−0.601566	−	0.798823i	$-0.705456\pi$
$829$		−	46.0000i		−	1.59765i	0.601566	−	0.798823i	$-0.294544\pi$
$830$	4.24264	−	12.7279i	0.147264	−	0.441793i
$831$		0			0
$832$	4.00000	+	4.00000i	0.138675	+	0.138675i
$833$	7.77817	+	7.77817i	0.269498	+	0.269498i
$834$		0			0
$835$	−16.0000	−	32.0000i	−0.553703	−	1.10741i
$836$		−	11.3137i		−	0.391293i
$837$		0			0
$838$	−12.0000	+	12.0000i	−0.414533	+	0.414533i
$839$	−46.6690			−1.61119			−0.805597	−	0.592464i	$-0.798155\pi$
$839$	−46.6690			−1.61119			−0.805597	+	0.592464i	$0.798155\pi$
$840$		0			0
$841$	−11.0000			−0.379310
$842$	−1.41421	+	1.41421i	−0.0487370	+	0.0487370i
$843$		0			0
$844$			20.0000i			0.688428i
$845$	−40.3051	−	13.4350i	−1.38654	−	0.462179i
$846$		0			0
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$	1.41421	+	1.41421i	0.0485643	+	0.0485643i
$849$		0			0
$850$	3.00000	−	4.00000i	0.102899	−	0.137199i
$851$		−	42.4264i		−	1.45436i
$852$		0			0
$853$	21.0000	−	21.0000i	0.719026	−	0.719026i	−0.249380	−	0.968406i	$-0.580227\pi$
$853$	21.0000	−	21.0000i	0.719026	−	0.719026i	0.968406	+	0.249380i	$0.0802267\pi$
$854$	−59.3970			−2.03252
$855$		0			0
$856$	4.00000			0.136717
$857$	−21.2132	+	21.2132i	−0.724629	+	0.724629i	−0.969544	−	0.244915i	$-0.921240\pi$
$857$	−21.2132	+	21.2132i	−0.724629	+	0.724629i	0.244915	+	0.969544i	$0.421240\pi$
$858$		0			0
$859$			34.0000i			1.16007i	0.814593	+	0.580033i	$0.196960\pi$
$859$			34.0000i			1.16007i	−0.814593	+	0.580033i	$0.803040\pi$
$860$	8.48528	−	4.24264i	0.289346	−	0.144673i
$861$		0			0
$862$	−11.0000	−	11.0000i	−0.374661	−	0.374661i
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$		0			0
$865$	−4.00000	+	2.00000i	−0.136004	+	0.0680020i
$866$			38.1838i			1.29754i
$867$		0			0
$868$	24.0000	−	24.0000i	0.814613	−	0.814613i
$869$	28.2843			0.959478
$870$		0			0
$871$	−40.0000			−1.35535
$872$	11.3137	−	11.3137i	0.383131	−	0.383131i
$873$		0			0
$874$		−	24.0000i		−	0.811812i
$875$	46.6690	+	8.48528i	1.57770	+	0.286855i
$876$		0			0
$877$	23.0000	+	23.0000i	0.776655	+	0.776655i	0.979260	−	0.202606i	$-0.0649409\pi$
$877$	23.0000	+	23.0000i	0.776655	+	0.776655i	−0.202606	+	0.979260i	$0.564941\pi$
$878$	−18.3848	−	18.3848i	−0.620456	−	0.620456i
$879$		0			0
$880$	6.00000	+	2.00000i	0.202260	+	0.0674200i
$881$		−	28.2843i		−	0.952921i	−0.879196	−	0.476461i	$-0.841919\pi$
$881$		−	28.2843i		−	0.952921i	0.879196	−	0.476461i	$-0.158081\pi$
$882$		0			0
$883$	−25.0000	+	25.0000i	−0.841317	+	0.841317i	−0.989030	−	0.147713i	$-0.952809\pi$
$883$	−25.0000	+	25.0000i	−0.841317	+	0.841317i	0.147713	+	0.989030i	$0.452809\pi$
$884$	−5.65685			−0.190261
$885$		0			0
$886$	−6.00000			−0.201574
$887$	24.0416	−	24.0416i	0.807239	−	0.807239i	−0.176976	−	0.984215i	$-0.556632\pi$
$887$	24.0416	−	24.0416i	0.807239	−	0.807239i	0.984215	+	0.176976i	$0.0566316\pi$
$888$		0			0
$889$		−	72.0000i		−	2.41480i
$890$	−18.3848	−	36.7696i	−0.616259	−	1.23252i
$891$		0			0
$892$	12.0000	+	12.0000i	0.401790	+	0.401790i
$893$	11.3137	+	11.3137i	0.378599	+	0.378599i
$894$		0			0
$895$	3.00000	−	9.00000i	0.100279	−	0.300837i
$896$			4.24264i			0.141737i
$897$		0			0
$898$	−24.0000	+	24.0000i	−0.800890	+	0.800890i
$899$	−33.9411			−1.13200
$900$		0			0
$901$	−2.00000			−0.0666297
$902$	16.9706	−	16.9706i	0.565058	−	0.565058i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$	2.82843	−	8.48528i	0.0940201	−	0.282060i
$906$		0			0
$907$	30.0000	+	30.0000i	0.996134	+	0.996134i	0.999993	−	0.00385890i	$-0.00122833\pi$
$907$	30.0000	+	30.0000i	0.996134	+	0.996134i	−0.00385890	+	0.999993i	$0.501228\pi$
$908$	11.3137	+	11.3137i	0.375459	+	0.375459i
$909$		0			0
$910$	−24.0000	−	48.0000i	−0.795592	−	1.59118i
$911$		−	35.3553i		−	1.17137i	−0.810537	−	0.585687i	$-0.800825\pi$
$911$		−	35.3553i		−	1.17137i	0.810537	−	0.585687i	$-0.199175\pi$
$912$		0			0
$913$	−12.0000	+	12.0000i	−0.397142	+	0.397142i
$914$	15.5563			0.514558
$915$		0			0
$916$	22.0000			0.726900
$917$	−16.9706	+	16.9706i	−0.560417	+	0.560417i
$918$		0			0
$919$		−	4.00000i		−	0.131948i	−0.997821	−	0.0659739i	$-0.978985\pi$
$919$		−	4.00000i		−	0.131948i	0.997821	−	0.0659739i	$-0.0210154\pi$
$920$	12.7279	+	4.24264i	0.419627	+	0.139876i
$921$		0			0
$922$	14.0000	+	14.0000i	0.461065	+	0.461065i
$923$	62.2254	+	62.2254i	2.04817	+	2.04817i
$924$		0			0
$925$	5.00000	+	35.0000i	0.164399	+	1.15079i
$926$			16.9706i			0.557687i
$927$		0			0
$928$	3.00000	−	3.00000i	0.0984798	−	0.0984798i
$929$	31.1127			1.02077			0.510387	−	0.859945i	$-0.329502\pi$
$929$	31.1127			1.02077			0.510387	+	0.859945i	$0.329502\pi$
$930$		0			0
$931$	−44.0000			−1.44204
$932$	−1.41421	+	1.41421i	−0.0463241	+	0.0463241i
$933$		0			0
$934$		−	20.0000i		−	0.654420i
$935$	−5.65685	+	2.82843i	−0.184999	+	0.0924995i
$936$		0			0
$937$	11.0000	+	11.0000i	0.359354	+	0.359354i	0.863575	−	0.504221i	$-0.168220\pi$
$937$	11.0000	+	11.0000i	0.359354	+	0.359354i	−0.504221	+	0.863575i	$0.668220\pi$
$938$	−21.2132	−	21.2132i	−0.692636	−	0.692636i
$939$		0			0
$940$	−8.00000	+	4.00000i	−0.260931	+	0.130466i
$941$		−	7.07107i		−	0.230510i	−0.993336	−	0.115255i	$-0.963231\pi$
$941$		−	7.07107i		−	0.230510i	0.993336	−	0.115255i	$-0.0367686\pi$
$942$		0			0
$943$	36.0000	−	36.0000i	1.17232	−	1.17232i
$944$	−9.89949			−0.322201
$945$		0			0
$946$	−12.0000			−0.390154
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	−0.751568	−	0.659656i	$-0.770702\pi$
$947$	−2.82843	+	2.82843i	−0.0919115	+	0.0919115i	0.659656	+	0.751568i	$0.270702\pi$
$948$		0			0
$949$		−	48.0000i		−	1.55815i
$950$	2.82843	+	19.7990i	0.0917663	+	0.642364i
$951$		0			0
$952$	−3.00000	−	3.00000i	−0.0972306	−	0.0972306i
$953$	−8.48528	−	8.48528i	−0.274865	−	0.274865i	0.556190	−	0.831055i	$-0.312263\pi$
$953$	−8.48528	−	8.48528i	−0.274865	−	0.274865i	−0.831055	+	0.556190i	$0.812263\pi$
$954$		0			0
$955$	−6.00000	−	2.00000i	−0.194155	−	0.0647185i
$956$			5.65685i			0.182956i
$957$		0			0
$958$	−7.00000	+	7.00000i	−0.226160	+	0.226160i
$959$	−50.9117			−1.64402
$960$		0			0
$961$	33.0000			1.06452
$962$	28.2843	−	28.2843i	0.911922	−	0.911922i
$963$		0			0
$964$		−	30.0000i		−	0.966235i
$965$		0			0
$966$		0			0
$967$	−14.0000	−	14.0000i	−0.450210	−	0.450210i	0.445214	−	0.895424i	$-0.353127\pi$
$967$	−14.0000	−	14.0000i	−0.450210	−	0.450210i	−0.895424	+	0.445214i	$0.853127\pi$
$968$	2.12132	+	2.12132i	0.0681818	+	0.0681818i
$969$		0			0
$970$		0			0
$971$		−	35.3553i		−	1.13461i	−0.823509	−	0.567303i	$-0.807987\pi$
$971$		−	35.3553i		−	1.13461i	0.823509	−	0.567303i	$-0.192013\pi$
$972$		0			0
$973$		0			0
$974$	−7.07107			−0.226572
$975$		0			0
$976$	14.0000			0.448129
$977$	16.9706	−	16.9706i	0.542936	−	0.542936i	−0.381452	−	0.924389i	$-0.624576\pi$
$977$	16.9706	−	16.9706i	0.542936	−	0.542936i	0.924389	+	0.381452i	$0.124576\pi$
$978$		0			0
$979$			52.0000i			1.66193i
$980$	7.77817	−	23.3345i	0.248465	−	0.745394i
$981$		0			0
$982$	−1.00000	−	1.00000i	−0.0319113	−	0.0319113i
$983$	16.9706	+	16.9706i	0.541277	+	0.541277i	0.923903	−	0.382626i	$-0.124980\pi$
$983$	16.9706	+	16.9706i	0.541277	+	0.541277i	−0.382626	+	0.923903i	$0.624980\pi$
$984$		0			0
$985$	−14.0000	−	28.0000i	−0.446077	−	0.892154i
$986$			4.24264i			0.135113i
$987$		0			0
$988$	16.0000	−	16.0000i	0.509028	−	0.509028i
$989$	−25.4558			−0.809449
$990$		0			0
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$	−5.65685	+	5.65685i	−0.179605	+	0.179605i
$993$		0			0
$994$			66.0000i			2.09339i
$995$	−16.9706	−	5.65685i	−0.538003	−	0.179334i
$996$		0			0
$997$	15.0000	+	15.0000i	0.475055	+	0.475055i	0.903546	−	0.428491i	$-0.140955\pi$
$997$	15.0000	+	15.0000i	0.475055	+	0.475055i	−0.428491	+	0.903546i	$0.640955\pi$
$998$	28.2843	+	28.2843i	0.895323	+	0.895323i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.b.647.1	✓	4	1.1	even	1	trivial
1530.2.m.b.647.2	yes	4	3.2	odd	2	inner
1530.2.m.b.953.1	yes	4	15.8	even	4	inner
1530.2.m.b.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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(-3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.00000 + 2.00000i) q^{10} -2.82843i q^{11} +(4.00000 - 4.00000i) q^{13} +4.24264 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +4.00000i q^{19} +(-2.12132 - 0.707107i) q^{20} +(2.00000 + 2.00000i) q^{22} +(4.24264 + 4.24264i) q^{23} +(-4.00000 - 3.00000i) q^{25} +5.65685i q^{26} +(-3.00000 + 3.00000i) q^{28} +4.24264 q^{29} -8.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +1.00000i q^{34} +(-8.48528 + 4.24264i) q^{35} +(-5.00000 - 5.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(2.00000 - 1.00000i) q^{40} -8.48528i q^{41} +(-3.00000 + 3.00000i) q^{43} -2.82843 q^{44} -6.00000 q^{46} +(2.82843 - 2.82843i) q^{47} +11.0000i q^{49} +(4.94975 - 0.707107i) q^{50} +(-4.00000 - 4.00000i) q^{52} +(-1.41421 - 1.41421i) q^{53} +(-6.00000 - 2.00000i) q^{55} -4.24264i q^{56} +(-3.00000 + 3.00000i) q^{58} +9.89949 q^{59} -14.0000 q^{61} +(5.65685 - 5.65685i) q^{62} +1.00000i q^{64} +(-5.65685 - 11.3137i) q^{65} +(-5.00000 - 5.00000i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(3.00000 - 9.00000i) q^{70} +15.5563i q^{71} +(6.00000 - 6.00000i) q^{73} +7.07107 q^{74} +4.00000 q^{76} +(-8.48528 + 8.48528i) q^{77} +10.0000i q^{79} +(-0.707107 + 2.12132i) q^{80} +(6.00000 + 6.00000i) q^{82} +(-4.24264 - 4.24264i) q^{83} +(-1.00000 - 2.00000i) q^{85} -4.24264i q^{86} +(2.00000 - 2.00000i) q^{88} -18.3848 q^{89} -24.0000 q^{91} +(4.24264 - 4.24264i) q^{92} +4.00000i q^{94} +(8.48528 + 2.82843i) q^{95} +(-7.77817 - 7.77817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{7}+O(q^{10}) \) 4 * q - 12 * q^7	\( 4 q - 12 q^{7} + 4 q^{10} + 16 q^{13} - 4 q^{16} + 8 q^{22} - 16 q^{25} - 12 q^{28} - 32 q^{31} - 20 q^{37} + 8 q^{40} - 12 q^{43} - 24 q^{46} - 16 q^{52} - 24 q^{55} - 12 q^{58} - 56 q^{61} - 20 q^{67} + 12 q^{70} + 24 q^{73} + 16 q^{76} + 24 q^{82} - 4 q^{85} + 8 q^{88} - 96 q^{91}+O(q^{100}) \) 4 * q - 12 * q^7 + 4 * q^10 + 16 * q^13 - 4 * q^16 + 8 * q^22 - 16 * q^25 - 12 * q^28 - 32 * q^31 - 20 * q^37 + 8 * q^40 - 12 * q^43 - 24 * q^46 - 16 * q^52 - 24 * q^55 - 12 * q^58 - 56 * q^61 - 20 * q^67 + 12 * q^70 + 24 * q^73 + 16 * q^76 + 24 * q^82 - 4 * q^85 + 8 * q^88 - 96 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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