LMFDB - Embedded newform 1920.2.y.j.1567.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(223,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.223"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$1920 = 2^{7} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1920.y (of order $4$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,16,0,4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256$ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$2^{12}$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1567.2
Root			$-1.40988 + 0.110627i$ of defining polynomial
Character	$\chi$	$=$	1920.1567
Dual form			1920.2.y.j.223.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(-2.06823 + 0.849960i) q^{5} +(2.08016 + 2.08016i) q^{7} +1.00000 q^{9} +(3.33354 - 3.33354i) q^{11} -6.13735i q^{13} +(-2.06823 + 0.849960i) q^{15} +(-2.33136 - 2.33136i) q^{17} +(0.834324 - 0.834324i) q^{19} +(2.08016 + 2.08016i) q^{21} +(-2.95105 + 2.95105i) q^{23} +(3.55514 - 3.51582i) q^{25} +1.00000 q^{27} +(0.576185 + 0.576185i) q^{29} -2.62300i q^{31} +(3.33354 - 3.33354i) q^{33} +(-6.07029 - 2.53419i) q^{35} -2.07309i q^{37} -6.13735i q^{39} +10.8873i q^{41} -5.16088i q^{43} +(-2.06823 + 0.849960i) q^{45} +(8.65772 - 8.65772i) q^{47} +1.65411i q^{49} +(-2.33136 - 2.33136i) q^{51} +1.58490 q^{53} +(-4.06115 + 9.72791i) q^{55} +(0.834324 - 0.834324i) q^{57} +(2.32603 + 2.32603i) q^{59} +(7.22499 - 7.22499i) q^{61} +(2.08016 + 2.08016i) q^{63} +(5.21651 + 12.6934i) q^{65} -0.885549i q^{67} +(-2.95105 + 2.95105i) q^{69} -2.56877 q^{71} +(7.35033 + 7.35033i) q^{73} +(3.55514 - 3.51582i) q^{75} +13.8686 q^{77} +7.72612 q^{79} +1.00000 q^{81} -8.67714 q^{83} +(6.80334 + 2.84022i) q^{85} +(0.576185 + 0.576185i) q^{87} -8.70590 q^{89} +(12.7667 - 12.7667i) q^{91} -2.62300i q^{93} +(-1.01643 + 2.43472i) q^{95} +(11.9985 + 11.9985i) q^{97} +(3.33354 - 3.33354i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100})$ 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$ .

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−2.06823	+	0.849960i	−0.924940	+	0.380114i
$5$	−2.06823	+	0.849960i	−0.924940	+	0.380114i
$6$		0			0
$7$	2.08016	+	2.08016i	0.786226	+	0.786226i	0.980873	−	0.194647i	$-0.0623563\pi$
$7$	2.08016	+	2.08016i	0.786226	+	0.786226i	−0.194647	+	0.980873i	$0.562356\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	3.33354	−	3.33354i	1.00510	−	1.00510i	0.00511408	−	0.999987i	$-0.498372\pi$
$11$	3.33354	−	3.33354i	1.00510	−	1.00510i	0.999987	−	0.00511408i	$-0.00162787\pi$
$12$		0			0
$13$		−	6.13735i		−	1.70220i	−0.525007	−	0.851098i	$-0.675937\pi$
$13$		−	6.13735i		−	1.70220i	0.525007	−	0.851098i	$-0.324063\pi$
$14$		0			0
$15$	−2.06823	+	0.849960i	−0.534014	+	0.219459i
$16$		0			0
$17$	−2.33136	−	2.33136i	−0.565437	−	0.565437i	0.365410	−	0.930847i	$-0.380929\pi$
$17$	−2.33136	−	2.33136i	−0.565437	−	0.565437i	−0.930847	+	0.365410i	$0.880929\pi$
$18$		0			0
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	−0.604897	−	0.796304i	$-0.706786\pi$
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	0.796304	+	0.604897i	$0.206786\pi$
$20$		0			0
$21$	2.08016	+	2.08016i	0.453928	+	0.453928i
$22$		0			0
$23$	−2.95105	+	2.95105i	−0.615336	+	0.615336i	−0.944331	−	0.328996i	$-0.893290\pi$
$23$	−2.95105	+	2.95105i	−0.615336	+	0.615336i	0.328996	+	0.944331i	$0.393290\pi$
$24$		0			0
$25$	3.55514	−	3.51582i	0.711027	−	0.703165i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	0.576185	+	0.576185i	0.106995	+	0.106995i	0.758578	−	0.651583i	$-0.225895\pi$
$29$	0.576185	+	0.576185i	0.106995	+	0.106995i	−0.651583	+	0.758578i	$0.725895\pi$
$30$		0			0
$31$		−	2.62300i		−	0.471106i	−0.971862	−	0.235553i	$-0.924310\pi$
$31$		−	2.62300i		−	0.471106i	0.971862	−	0.235553i	$-0.0756900\pi$
$32$		0			0
$33$	3.33354	−	3.33354i	0.580295	−	0.580295i
$34$		0			0
$35$	−6.07029	−	2.53419i	−1.02607	−	0.428356i
$36$		0			0
$37$		−	2.07309i		−	0.340814i	−0.985374	−	0.170407i	$-0.945492\pi$
$37$		−	2.07309i		−	0.340814i	0.985374	−	0.170407i	$-0.0545083\pi$
$38$		0			0
$39$		−	6.13735i		−	0.982763i
$40$		0			0
$41$			10.8873i			1.70031i	0.526533	+	0.850154i	$0.323492\pi$
$41$			10.8873i			1.70031i	−0.526533	+	0.850154i	$0.676508\pi$
$42$		0			0
$43$		−	5.16088i		−	0.787027i	−0.919319	−	0.393514i	$-0.871259\pi$
$43$		−	5.16088i		−	0.787027i	0.919319	−	0.393514i	$-0.128741\pi$
$44$		0			0
$45$	−2.06823	+	0.849960i	−0.308313	+	0.126705i
$46$		0			0
$47$	8.65772	−	8.65772i	1.26286	−	1.26286i	0.313156	−	0.949702i	$-0.398614\pi$
$47$	8.65772	−	8.65772i	1.26286	−	1.26286i	0.949702	−	0.313156i	$-0.101386\pi$
$48$		0			0
$49$			1.65411i			0.236302i
$50$		0			0
$51$	−2.33136	−	2.33136i	−0.326455	−	0.326455i
$52$		0			0
$53$	1.58490			0.217703			0.108851	−	0.994058i	$-0.465283\pi$
$53$	1.58490			0.217703			0.108851	+	0.994058i	$0.465283\pi$
$54$		0			0
$55$	−4.06115	+	9.72791i	−0.547605	+	1.31171i
$56$		0			0
$57$	0.834324	−	0.834324i	0.110509	−	0.110509i
$58$		0			0
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	0.842118	−	0.539294i	$-0.181309\pi$
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	−0.539294	+	0.842118i	$0.681309\pi$
$60$		0			0
$61$	7.22499	−	7.22499i	0.925065	−	0.925065i	−0.0723167	−	0.997382i	$-0.523039\pi$
$61$	7.22499	−	7.22499i	0.925065	−	0.925065i	0.997382	+	0.0723167i	$0.0230392\pi$
$62$		0			0
$63$	2.08016	+	2.08016i	0.262075	+	0.262075i
$64$		0			0
$65$	5.21651	+	12.6934i	0.647028	+	1.57443i
$66$		0			0
$67$		−	0.885549i		−	0.108187i	−0.998536	−	0.0540935i	$-0.982773\pi$
$67$		−	0.885549i		−	0.108187i	0.998536	−	0.0540935i	$-0.0172269\pi$
$68$		0			0
$69$	−2.95105	+	2.95105i	−0.355264	+	0.355264i
$70$		0			0
$71$	−2.56877			−0.304857			−0.152428	−	0.988315i	$-0.548709\pi$
$71$	−2.56877			−0.304857			−0.152428	+	0.988315i	$0.548709\pi$
$72$		0			0
$73$	7.35033	+	7.35033i	0.860291	+	0.860291i	0.991372	−	0.131081i	$-0.0418447\pi$
$73$	7.35033	+	7.35033i	0.860291	+	0.860291i	−0.131081	+	0.991372i	$0.541845\pi$
$74$		0			0
$75$	3.55514	−	3.51582i	0.410512	−	0.405972i
$76$		0			0
$77$	13.8686			1.58047
$78$		0			0
$79$	7.72612			0.869256			0.434628	−	0.900610i	$-0.356880\pi$
$79$	7.72612			0.869256			0.434628	+	0.900610i	$0.356880\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−8.67714			−0.952440			−0.476220	−	0.879326i	$-0.657993\pi$
$83$	−8.67714			−0.952440			−0.476220	+	0.879326i	$0.657993\pi$
$84$		0			0
$85$	6.80334	+	2.84022i	0.737926	+	0.308065i
$86$		0			0
$87$	0.576185	+	0.576185i	0.0617735	+	0.0617735i
$88$		0			0
$89$	−8.70590			−0.922823			−0.461412	−	0.887186i	$-0.652657\pi$
$89$	−8.70590			−0.922823			−0.461412	+	0.887186i	$0.652657\pi$
$90$		0			0
$91$	12.7667	−	12.7667i	1.33831	−	1.33831i
$92$		0			0
$93$		−	2.62300i		−	0.271993i
$94$		0			0
$95$	−1.01643	+	2.43472i	−0.104284	+	0.249797i
$96$		0			0
$97$	11.9985	+	11.9985i	1.21826	+	1.21826i	0.968240	+	0.250021i	$0.0804375\pi$
$97$	11.9985	+	11.9985i	1.21826	+	1.21826i	0.250021	+	0.968240i	$0.419562\pi$
$98$		0			0
$99$	3.33354	−	3.33354i	0.335034	−	0.335034i
$100$		0			0
$101$	6.69380	+	6.69380i	0.666058	+	0.666058i	0.956801	−	0.290743i	$-0.0939024\pi$
$101$	6.69380	+	6.69380i	0.666058	+	0.666058i	−0.290743	+	0.956801i	$0.593902\pi$
$102$		0			0
$103$	13.4242	−	13.4242i	1.32272	−	1.32272i	0.411158	−	0.911564i	$-0.365124\pi$
$103$	13.4242	−	13.4242i	1.32272	−	1.32272i	0.911564	−	0.411158i	$-0.134876\pi$
$104$		0			0
$105$	−6.07029	−	2.53419i	−0.592400	−	0.247312i
$106$		0			0
$107$	−10.9567			−1.05922			−0.529612	−	0.848240i	$-0.677663\pi$
$107$	−10.9567			−1.05922			−0.529612	+	0.848240i	$0.677663\pi$
$108$		0			0
$109$	−0.643941	−	0.643941i	−0.0616784	−	0.0616784i	0.675595	−	0.737273i	$-0.263887\pi$
$109$	−0.643941	−	0.643941i	−0.0616784	−	0.0616784i	−0.737273	+	0.675595i	$0.763887\pi$
$110$		0			0
$111$		−	2.07309i		−	0.196769i
$112$		0			0
$113$	9.19571	−	9.19571i	0.865060	−	0.865060i	−0.126861	−	0.991921i	$-0.540490\pi$
$113$	9.19571	−	9.19571i	0.865060	−	0.865060i	0.991921	+	0.126861i	$0.0404901\pi$
$114$		0			0
$115$	3.59517	−	8.61171i	0.335251	−	0.803046i
$116$		0			0
$117$		−	6.13735i		−	0.567398i
$118$		0			0
$119$		−	9.69918i		−	0.889122i
$120$		0			0
$121$		−	11.2250i		−	1.02046i
$122$		0			0
$123$			10.8873i			0.981674i
$124$		0			0
$125$	−4.36452	+	10.2932i	−0.390375	+	0.920656i
$126$		0			0
$127$	−4.80716	+	4.80716i	−0.426567	+	0.426567i	−0.887457	−	0.460890i	$-0.847530\pi$
$127$	−4.80716	+	4.80716i	−0.426567	+	0.426567i	0.460890	+	0.887457i	$0.347530\pi$
$128$		0			0
$129$		−	5.16088i		−	0.454391i
$130$		0			0
$131$	−3.53632	−	3.53632i	−0.308970	−	0.308970i	0.535540	−	0.844510i	$-0.320108\pi$
$131$	−3.53632	−	3.53632i	−0.308970	−	0.308970i	−0.844510	+	0.535540i	$0.820108\pi$
$132$		0			0
$133$	3.47105			0.300978
$134$		0			0
$135$	−2.06823	+	0.849960i	−0.178005	+	0.0731529i
$136$		0			0
$137$	7.54548	−	7.54548i	0.644654	−	0.644654i	−0.307042	−	0.951696i	$-0.599339\pi$
$137$	7.54548	−	7.54548i	0.644654	−	0.644654i	0.951696	+	0.307042i	$0.0993392\pi$
$138$		0			0
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	0.576200	−	0.817309i	$-0.304535\pi$
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	−0.817309	+	0.576200i	$0.804535\pi$
$140$		0			0
$141$	8.65772	−	8.65772i	0.729111	−	0.729111i
$142$		0			0
$143$	−20.4591	−	20.4591i	−1.71088	−	1.71088i
$144$		0			0
$145$	−1.68142	−	0.701948i	−0.139634	−	0.0582936i
$146$		0			0
$147$			1.65411i			0.136429i
$148$		0			0
$149$	−3.20287	+	3.20287i	−0.262389	+	0.262389i	−0.826024	−	0.563635i	$-0.809403\pi$
$149$	−3.20287	+	3.20287i	−0.262389	+	0.262389i	0.563635	+	0.826024i	$0.309403\pi$
$150$		0			0
$151$	−8.82773			−0.718390			−0.359195	−	0.933262i	$-0.616949\pi$
$151$	−8.82773			−0.718390			−0.359195	+	0.933262i	$0.616949\pi$
$152$		0			0
$153$	−2.33136	−	2.33136i	−0.188479	−	0.188479i
$154$		0			0
$155$	2.22945	+	5.42497i	0.179074	+	0.435744i
$156$		0			0
$157$	−15.5186			−1.23852			−0.619258	−	0.785187i	$-0.712567\pi$
$157$	−15.5186			−1.23852			−0.619258	+	0.785187i	$0.712567\pi$
$158$		0			0
$159$	1.58490			0.125691
$160$		0			0
$161$	−12.2773			−0.967586
$162$		0			0
$163$	8.65221			0.677694			0.338847	−	0.940842i	$-0.389963\pi$
$163$	8.65221			0.677694			0.338847	+	0.940842i	$0.389963\pi$
$164$		0			0
$165$	−4.06115	+	9.72791i	−0.316160	+	0.757316i
$166$		0			0
$167$	−2.86613	−	2.86613i	−0.221788	−	0.221788i	0.587463	−	0.809251i	$-0.300127\pi$
$167$	−2.86613	−	2.86613i	−0.221788	−	0.221788i	−0.809251	+	0.587463i	$0.800127\pi$
$168$		0			0
$169$	−24.6671			−1.89747
$170$		0			0
$171$	0.834324	−	0.834324i	0.0638024	−	0.0638024i
$172$		0			0
$173$			15.1143i			1.14912i	0.818464	+	0.574558i	$0.194826\pi$
$173$			15.1143i			1.14912i	−0.818464	+	0.574558i	$0.805174\pi$
$174$		0			0
$175$	14.7087	+	0.0817750i	1.11187	+	0.00618161i
$176$		0			0
$177$	2.32603	+	2.32603i	0.174835	+	0.174835i
$178$		0			0
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	−0.997331	−	0.0730070i	$-0.976740\pi$
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	0.0730070	+	0.997331i	$0.476740\pi$
$180$		0			0
$181$	9.58991	+	9.58991i	0.712813	+	0.712813i	0.967123	−	0.254310i	$-0.0818484\pi$
$181$	9.58991	+	9.58991i	0.712813	+	0.712813i	−0.254310	+	0.967123i	$0.581848\pi$
$182$		0			0
$183$	7.22499	−	7.22499i	0.534087	−	0.534087i
$184$		0			0
$185$	1.76205	+	4.28763i	0.129548	+	0.315233i
$186$		0			0
$187$	−15.5434			−1.13664
$188$		0			0
$189$	2.08016	+	2.08016i	0.151309	+	0.151309i
$190$		0			0
$191$		−	14.5044i		−	1.04950i	−0.851257	−	0.524750i	$-0.824159\pi$
$191$		−	14.5044i		−	1.04950i	0.851257	−	0.524750i	$-0.175841\pi$
$192$		0			0
$193$	−1.68153	+	1.68153i	−0.121039	+	0.121039i	−0.765032	−	0.643992i	$-0.777277\pi$
$193$	−1.68153	+	1.68153i	−0.121039	+	0.121039i	0.643992	+	0.765032i	$0.277277\pi$
$194$		0			0
$195$	5.21651	+	12.6934i	0.373562	+	0.908996i
$196$		0			0
$197$		−	8.65121i		−	0.616373i	−0.951326	−	0.308187i	$-0.900278\pi$
$197$		−	8.65121i		−	0.616373i	0.951326	−	0.308187i	$-0.0997221\pi$
$198$		0			0
$199$			22.3275i			1.58275i	0.611328	+	0.791377i	$0.290635\pi$
$199$			22.3275i			1.58275i	−0.611328	+	0.791377i	$0.709365\pi$
$200$		0			0
$201$		−	0.885549i		−	0.0624618i
$202$		0			0
$203$			2.39711i			0.168244i
$204$		0			0
$205$	−9.25376	−	22.5174i	−0.646311	−	1.57268i
$206$		0			0
$207$	−2.95105	+	2.95105i	−0.205112	+	0.205112i
$208$		0			0
$209$		−	5.56251i		−	0.384767i
$210$		0			0
$211$	5.27613	+	5.27613i	0.363224	+	0.363224i	0.864998	−	0.501775i	$-0.167319\pi$
$211$	5.27613	+	5.27613i	0.363224	+	0.363224i	−0.501775	+	0.864998i	$0.667319\pi$
$212$		0			0
$213$	−2.56877			−0.176009
$214$		0			0
$215$	4.38655	+	10.6739i	0.299160	+	0.727953i
$216$		0			0
$217$	5.45626	−	5.45626i	0.370395	−	0.370395i
$218$		0			0
$219$	7.35033	+	7.35033i	0.496689	+	0.496689i
$220$		0			0
$221$	−14.3084	+	14.3084i	−0.962484	+	0.962484i
$222$		0			0
$223$	−13.8202	−	13.8202i	−0.925469	−	0.925469i	0.0719400	−	0.997409i	$-0.477081\pi$
$223$	−13.8202	−	13.8202i	−0.925469	−	0.925469i	−0.997409	+	0.0719400i	$0.977081\pi$
$224$		0			0
$225$	3.55514	−	3.51582i	0.237009	−	0.234388i
$226$		0			0
$227$		−	1.66286i		−	0.110368i	−0.998476	−	0.0551839i	$-0.982425\pi$
$227$		−	1.66286i		−	0.110368i	0.998476	−	0.0551839i	$-0.0175745\pi$
$228$		0			0
$229$	−11.3744	+	11.3744i	−0.751643	+	0.751643i	−0.974786	−	0.223142i	$-0.928368\pi$
$229$	−11.3744	+	11.3744i	−0.751643	+	0.751643i	0.223142	+	0.974786i	$0.428368\pi$
$230$		0			0
$231$	13.8686			0.912486
$232$		0			0
$233$	9.38976	+	9.38976i	0.615143	+	0.615143i	0.944282	−	0.329138i	$-0.106758\pi$
$233$	9.38976	+	9.38976i	0.615143	+	0.615143i	−0.329138	+	0.944282i	$0.606758\pi$
$234$		0			0
$235$	−10.5474	+	25.2649i	−0.688038	+	1.64810i
$236$		0			0
$237$	7.72612			0.501865
$238$		0			0
$239$	−8.88914			−0.574991			−0.287495	−	0.957782i	$-0.592823\pi$
$239$	−8.88914			−0.574991			−0.287495	+	0.957782i	$0.592823\pi$
$240$		0			0
$241$	20.5978			1.32682			0.663411	−	0.748255i	$-0.269108\pi$
$241$	20.5978			1.32682			0.663411	+	0.748255i	$0.269108\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−1.40593	−	3.42109i	−0.0898217	−	0.218565i
$246$		0			0
$247$	−5.12054	−	5.12054i	−0.325812	−	0.325812i
$248$		0			0
$249$	−8.67714			−0.549891
$250$		0			0
$251$	16.8455	−	16.8455i	1.06328	−	1.06328i	0.0654195	−	0.997858i	$-0.479161\pi$
$251$	16.8455	−	16.8455i	1.06328	−	1.06328i	0.997858	−	0.0654195i	$-0.0208386\pi$
$252$		0			0
$253$			19.6749i			1.23695i
$254$		0			0
$255$	6.80334	+	2.84022i	0.426042	+	0.177861i
$256$		0			0
$257$	−14.1500	−	14.1500i	−0.882653	−	0.882653i	0.111151	−	0.993804i	$-0.464546\pi$
$257$	−14.1500	−	14.1500i	−0.882653	−	0.882653i	−0.993804	+	0.111151i	$0.964546\pi$
$258$		0			0
$259$	4.31236	−	4.31236i	0.267957	−	0.267957i
$260$		0			0
$261$	0.576185	+	0.576185i	0.0356650	+	0.0356650i
$262$		0			0
$263$	−11.1204	+	11.1204i	−0.685712	+	0.685712i	−0.961281	−	0.275569i	$-0.911134\pi$
$263$	−11.1204	+	11.1204i	−0.685712	+	0.685712i	0.275569	+	0.961281i	$0.411134\pi$
$264$		0			0
$265$	−3.27794	+	1.34710i	−0.201362	+	0.0827519i
$266$		0			0
$267$	−8.70590			−0.532792
$268$		0			0
$269$	10.2902	+	10.2902i	0.627403	+	0.627403i	0.947414	−	0.320011i	$-0.103687\pi$
$269$	10.2902	+	10.2902i	0.627403	+	0.627403i	−0.320011	+	0.947414i	$0.603687\pi$
$270$		0			0
$271$			21.3325i			1.29586i	0.761702	+	0.647928i	$0.224364\pi$
$271$			21.3325i			1.29586i	−0.761702	+	0.647928i	$0.775636\pi$
$272$		0			0
$273$	12.7667	−	12.7667i	0.772674	−	0.772674i
$274$		0			0
$275$	0.131048	−	23.5713i	0.00790249	−	1.42141i
$276$		0			0
$277$		−	19.0041i		−	1.14184i	−0.821004	−	0.570922i	$-0.806586\pi$
$277$		−	19.0041i		−	1.14184i	0.821004	−	0.570922i	$-0.193414\pi$
$278$		0			0
$279$		−	2.62300i		−	0.157035i
$280$		0			0
$281$		−	3.86317i		−	0.230457i	−0.993339	−	0.115229i	$-0.963240\pi$
$281$		−	3.86317i		−	0.230457i	0.993339	−	0.115229i	$-0.0367600\pi$
$282$		0			0
$283$			5.89151i			0.350214i	0.984549	+	0.175107i	$0.0560271\pi$
$283$			5.89151i			0.350214i	−0.984549	+	0.175107i	$0.943973\pi$
$284$		0			0
$285$	−1.01643	+	2.43472i	−0.0602081	+	0.144220i
$286$		0			0
$287$	−22.6473	+	22.6473i	−1.33683	+	1.33683i
$288$		0			0
$289$		−	6.12955i		−	0.360562i
$290$		0			0
$291$	11.9985	+	11.9985i	0.703364	+	0.703364i
$292$		0			0
$293$	4.49132			0.262386			0.131193	−	0.991357i	$-0.458119\pi$
$293$	4.49132			0.262386			0.131193	+	0.991357i	$0.458119\pi$
$294$		0			0
$295$	−6.78780	−	2.83373i	−0.395201	−	0.164986i
$296$		0			0
$297$	3.33354	−	3.33354i	0.193432	−	0.193432i
$298$		0			0
$299$	18.1116	+	18.1116i	1.04742	+	1.04742i
$300$		0			0
$301$	10.7355	−	10.7355i	0.618781	−	0.618781i
$302$		0			0
$303$	6.69380	+	6.69380i	0.384549	+	0.384549i
$304$		0			0
$305$	−8.80197	+	21.0839i	−0.503999	+	1.20726i
$306$		0			0
$307$			3.84487i			0.219438i	0.993963	+	0.109719i	$0.0349951\pi$
$307$			3.84487i			0.219438i	−0.993963	+	0.109719i	$0.965005\pi$
$308$		0			0
$309$	13.4242	−	13.4242i	0.763674	−	0.763674i
$310$		0			0
$311$	4.07103			0.230847			0.115423	−	0.993316i	$-0.463178\pi$
$311$	4.07103			0.230847			0.115423	+	0.993316i	$0.463178\pi$
$312$		0			0
$313$	−1.37922	−	1.37922i	−0.0779584	−	0.0779584i	0.667052	−	0.745011i	$-0.267556\pi$
$313$	−1.37922	−	1.37922i	−0.0779584	−	0.0779584i	−0.745011	+	0.667052i	$0.767556\pi$
$314$		0			0
$315$	−6.07029	−	2.53419i	−0.342022	−	0.142785i
$316$		0			0
$317$	−9.80915			−0.550937			−0.275468	−	0.961310i	$-0.588833\pi$
$317$	−9.80915			−0.550937			−0.275468	+	0.961310i	$0.588833\pi$
$318$		0			0
$319$	3.84148			0.215081
$320$		0			0
$321$	−10.9567			−0.611543
$322$		0			0
$323$	−3.89021			−0.216457
$324$		0			0
$325$	−21.5778	−	21.8191i	−1.19692	−	1.21031i
$326$		0			0
$327$	−0.643941	−	0.643941i	−0.0356100	−	0.0356100i
$328$		0			0
$329$	36.0188			1.98578
$330$		0			0
$331$	−7.17235	+	7.17235i	−0.394228	+	0.394228i	−0.876191	−	0.481963i	$-0.839924\pi$
$331$	−7.17235	+	7.17235i	−0.394228	+	0.394228i	0.481963	+	0.876191i	$0.339924\pi$
$332$		0			0
$333$		−	2.07309i		−	0.113605i
$334$		0			0
$335$	0.752681	+	1.83152i	0.0411234	+	0.100066i
$336$		0			0
$337$	−25.3587	−	25.3587i	−1.38138	−	1.38138i	−0.842178	−	0.539200i	$-0.818727\pi$
$337$	−25.3587	−	25.3587i	−1.38138	−	1.38138i	−0.539200	−	0.842178i	$-0.681273\pi$
$338$		0			0
$339$	9.19571	−	9.19571i	0.499442	−	0.499442i
$340$		0			0
$341$	−8.74390	−	8.74390i	−0.473509	−	0.473509i
$342$		0			0
$343$	11.1203	−	11.1203i	0.600439	−	0.600439i
$344$		0			0
$345$	3.59517	−	8.61171i	0.193557	−	0.463639i
$346$		0			0
$347$	−8.80549			−0.472704			−0.236352	−	0.971668i	$-0.575952\pi$
$347$	−8.80549			−0.472704			−0.236352	+	0.971668i	$0.575952\pi$
$348$		0			0
$349$	14.8110	+	14.8110i	0.792815	+	0.792815i	0.981951	−	0.189136i	$-0.0605687\pi$
$349$	14.8110	+	14.8110i	0.792815	+	0.792815i	−0.189136	+	0.981951i	$0.560569\pi$
$350$		0			0
$351$		−	6.13735i		−	0.327588i
$352$		0			0
$353$	−21.3226	+	21.3226i	−1.13489	+	1.13489i	−0.145536	+	0.989353i	$0.546491\pi$
$353$	−21.3226	+	21.3226i	−1.13489	+	1.13489i	−0.989353	+	0.145536i	$0.953509\pi$
$354$		0			0
$355$	5.31280	−	2.18335i	0.281974	−	0.115880i
$356$		0			0
$357$		−	9.69918i		−	0.513335i
$358$		0			0
$359$		−	9.38977i		−	0.495573i	−0.968815	−	0.247787i	$-0.920297\pi$
$359$		−	9.38977i		−	0.495573i	0.968815	−	0.247787i	$-0.0797032\pi$
$360$		0			0
$361$			17.6078i			0.926727i
$362$		0			0
$363$		−	11.2250i		−	0.589161i
$364$		0			0
$365$	−21.4496	−	8.95467i	−1.12273	−	0.468709i
$366$		0			0
$367$	0.129655	−	0.129655i	0.00676792	−	0.00676792i	−0.703715	−	0.710483i	$-0.748477\pi$
$367$	0.129655	−	0.129655i	0.00676792	−	0.00676792i	0.710483	+	0.703715i	$0.248477\pi$
$368$		0			0
$369$			10.8873i			0.566770i
$370$		0			0
$371$	3.29684	+	3.29684i	0.171164	+	0.171164i
$372$		0			0
$373$	2.85797			0.147980			0.0739900	−	0.997259i	$-0.476427\pi$
$373$	2.85797			0.147980			0.0739900	+	0.997259i	$0.476427\pi$
$374$		0			0
$375$	−4.36452	+	10.2932i	−0.225383	+	0.531541i
$376$		0			0
$377$	3.53625	−	3.53625i	0.182126	−	0.182126i
$378$		0			0
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	0.215739	−	0.976451i	$-0.430784\pi$
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	−0.976451	+	0.215739i	$0.930784\pi$
$380$		0			0
$381$	−4.80716	+	4.80716i	−0.246278	+	0.246278i
$382$		0			0
$383$	22.2921	+	22.2921i	1.13907	+	1.13907i	0.988616	+	0.150458i	$0.0480749\pi$
$383$	22.2921	+	22.2921i	1.13907	+	1.13907i	0.150458	+	0.988616i	$0.451925\pi$
$384$		0			0
$385$	−28.6834	+	11.7878i	−1.46184	+	0.600759i
$386$		0			0
$387$		−	5.16088i		−	0.262342i
$388$		0			0
$389$	−17.1132	+	17.1132i	−0.867671	+	0.867671i	−0.992214	−	0.124543i	$-0.960254\pi$
$389$	−17.1132	+	17.1132i	−0.867671	+	0.867671i	0.124543	+	0.992214i	$0.460254\pi$
$390$		0			0
$391$	13.7599			0.695867
$392$		0			0
$393$	−3.53632	−	3.53632i	−0.178384	−	0.178384i
$394$		0			0
$395$	−15.9794	+	6.56689i	−0.804009	+	0.330416i
$396$		0			0
$397$	−16.2806			−0.817099			−0.408549	−	0.912736i	$-0.633965\pi$
$397$	−16.2806			−0.817099			−0.408549	+	0.912736i	$0.633965\pi$
$398$		0			0
$399$	3.47105			0.173770
$400$		0			0
$401$	5.13860			0.256609			0.128305	−	0.991735i	$-0.459046\pi$
$401$	5.13860			0.256609			0.128305	+	0.991735i	$0.459046\pi$
$402$		0			0
$403$	−16.0983			−0.801914
$404$		0			0
$405$	−2.06823	+	0.849960i	−0.102771	+	0.0422349i
$406$		0			0
$407$	−6.91074	−	6.91074i	−0.342553	−	0.342553i
$408$		0			0
$409$	−3.88999			−0.192348			−0.0961738	−	0.995365i	$-0.530660\pi$
$409$	−3.88999			−0.192348			−0.0961738	+	0.995365i	$0.530660\pi$
$410$		0			0
$411$	7.54548	−	7.54548i	0.372191	−	0.372191i
$412$		0			0
$413$			9.67703i			0.476176i
$414$		0			0
$415$	17.9463	−	7.37522i	0.880949	−	0.362035i
$416$		0			0
$417$	−2.84263	−	2.84263i	−0.139204	−	0.139204i
$418$		0			0
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	−0.902995	−	0.429650i	$-0.858637\pi$
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	0.429650	+	0.902995i	$0.358637\pi$
$420$		0			0
$421$	19.2867	+	19.2867i	0.939978	+	0.939978i	0.998298	−	0.0583197i	$-0.0185743\pi$
$421$	19.2867	+	19.2867i	0.939978	+	0.939978i	−0.0583197	+	0.998298i	$0.518574\pi$
$422$		0			0
$423$	8.65772	−	8.65772i	0.420953	−	0.420953i
$424$		0			0
$425$	−16.4849	−	0.0916501i	−0.799636	−	0.00444568i
$426$		0			0
$427$	30.0582			1.45462
$428$		0			0
$429$	−20.4591	−	20.4591i	−0.987776	−	0.987776i
$430$		0			0
$431$			4.13031i			0.198950i	0.995040	+	0.0994751i	$0.0317164\pi$
$431$			4.13031i			0.198950i	−0.995040	+	0.0994751i	$0.968284\pi$
$432$		0			0
$433$	13.3312	−	13.3312i	0.640655	−	0.640655i	−0.310062	−	0.950716i	$-0.600350\pi$
$433$	13.3312	−	13.3312i	0.640655	−	0.640655i	0.950716	+	0.310062i	$0.100350\pi$
$434$		0			0
$435$	−1.68142	−	0.701948i	−0.0806178	−	0.0336558i
$436$		0			0
$437$			4.92426i			0.235559i
$438$		0			0
$439$		−	22.0770i		−	1.05368i	−0.849965	−	0.526839i	$-0.823377\pi$
$439$		−	22.0770i		−	1.05368i	0.849965	−	0.526839i	$-0.176623\pi$
$440$		0			0
$441$			1.65411i			0.0787673i
$442$		0			0
$443$		−	8.44869i		−	0.401409i	−0.979652	−	0.200705i	$-0.935677\pi$
$443$		−	8.44869i		−	0.401409i	0.979652	−	0.200705i	$-0.0643231\pi$
$444$		0			0
$445$	18.0058	−	7.39967i	0.853556	−	0.350778i
$446$		0			0
$447$	−3.20287	+	3.20287i	−0.151491	+	0.151491i
$448$		0			0
$449$			12.3249i			0.581648i	0.956777	+	0.290824i	$0.0939293\pi$
$449$			12.3249i			0.581648i	−0.956777	+	0.290824i	$0.906071\pi$
$450$		0			0
$451$	36.2932	+	36.2932i	1.70898	+	1.70898i
$452$		0			0
$453$	−8.82773			−0.414763
$454$		0			0
$455$	−15.5532	+	37.2555i	−0.729146	+	1.74657i
$456$		0			0
$457$	10.5838	−	10.5838i	0.495089	−	0.495089i	−0.414816	−	0.909905i	$-0.636154\pi$
$457$	10.5838	−	10.5838i	0.495089	−	0.495089i	0.909905	+	0.414816i	$0.136154\pi$
$458$		0			0
$459$	−2.33136	−	2.33136i	−0.108818	−	0.108818i
$460$		0			0
$461$	6.77081	−	6.77081i	0.315348	−	0.315348i	−0.531629	−	0.846977i	$-0.678420\pi$
$461$	6.77081	−	6.77081i	0.315348	−	0.315348i	0.846977	+	0.531629i	$0.178420\pi$
$462$		0			0
$463$	11.3573	+	11.3573i	0.527819	+	0.527819i	0.919921	−	0.392103i	$-0.128252\pi$
$463$	11.3573	+	11.3573i	0.527819	+	0.527819i	−0.392103	+	0.919921i	$0.628252\pi$
$464$		0			0
$465$	2.22945	+	5.42497i	0.103388	+	0.251577i
$466$		0			0
$467$			3.11578i			0.144181i	0.997398	+	0.0720906i	$0.0229671\pi$
$467$			3.11578i			0.144181i	−0.997398	+	0.0720906i	$0.977033\pi$
$468$		0			0
$469$	1.84208	−	1.84208i	0.0850594	−	0.0850594i
$470$		0			0
$471$	−15.5186			−0.715058
$472$		0			0
$473$	−17.2040	−	17.2040i	−0.791042	−	0.791042i
$474$		0			0
$475$	0.0327989	−	5.89947i	0.00150492	−	0.270686i
$476$		0			0
$477$	1.58490			0.0725676
$478$		0			0
$479$	15.3508			0.701396			0.350698	−	0.936489i	$-0.385944\pi$
$479$	15.3508			0.701396			0.350698	+	0.936489i	$0.385944\pi$
$480$		0			0
$481$	−12.7233			−0.580132
$482$		0			0
$483$	−12.2773			−0.558636
$484$		0			0
$485$	−35.0138	−	14.6174i	−1.58990	−	0.663740i
$486$		0			0
$487$	−8.51351	−	8.51351i	−0.385784	−	0.385784i	0.487397	−	0.873181i	$-0.337947\pi$
$487$	−8.51351	−	8.51351i	−0.385784	−	0.385784i	−0.873181	+	0.487397i	$0.837947\pi$
$488$		0			0
$489$	8.65221			0.391267
$490$		0			0
$491$	−6.16348	+	6.16348i	−0.278154	+	0.278154i	−0.832372	−	0.554218i	$-0.813017\pi$
$491$	−6.16348	+	6.16348i	−0.278154	+	0.278154i	0.554218	+	0.832372i	$0.313017\pi$
$492$		0			0
$493$		−	2.68659i		−	0.120998i
$494$		0			0
$495$	−4.06115	+	9.72791i	−0.182535	+	0.437237i
$496$		0			0
$497$	−5.34345	−	5.34345i	−0.239686	−	0.239686i
$498$		0			0
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	−0.969627	−	0.244589i	$-0.921347\pi$
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	0.244589	+	0.969627i	$0.421347\pi$
$500$		0			0
$501$	−2.86613	−	2.86613i	−0.128049	−	0.128049i
$502$		0			0
$503$	−8.39462	+	8.39462i	−0.374298	+	0.374298i	−0.869040	−	0.494742i	$-0.835263\pi$
$503$	−8.39462	+	8.39462i	−0.374298	+	0.374298i	0.494742	+	0.869040i	$0.335263\pi$
$504$		0			0
$505$	−19.5338	−	8.15485i	−0.869242	−	0.362886i
$506$		0			0
$507$	−24.6671			−1.09550
$508$		0			0
$509$	−5.50555	−	5.50555i	−0.244029	−	0.244029i	0.574486	−	0.818515i	$-0.305202\pi$
$509$	−5.50555	−	5.50555i	−0.244029	−	0.244029i	−0.818515	+	0.574486i	$0.805202\pi$
$510$		0			0
$511$			30.5797i			1.35277i
$512$		0			0
$513$	0.834324	−	0.834324i	0.0368363	−	0.0368363i
$514$		0			0
$515$	−16.3542	+	39.1742i	−0.720653	+	1.72622i
$516$		0			0
$517$		−	57.7217i		−	2.53860i
$518$		0			0
$519$			15.1143i			0.663442i
$520$		0			0
$521$			39.2289i			1.71865i	0.511430	+	0.859325i	$0.329116\pi$
$521$			39.2289i			1.71865i	−0.511430	+	0.859325i	$0.670884\pi$
$522$		0			0
$523$		−	16.7434i		−	0.732137i	−0.930588	−	0.366068i	$-0.880704\pi$
$523$		−	16.7434i		−	0.732137i	0.930588	−	0.366068i	$-0.119296\pi$
$524$		0			0
$525$	14.7087	+	0.0817750i	0.641941	+	0.00356895i
$526$		0			0
$527$	−6.11516	+	6.11516i	−0.266381	+	0.266381i
$528$		0			0
$529$			5.58265i			0.242724i
$530$		0			0
$531$	2.32603	+	2.32603i	0.100941	+	0.100941i
$532$		0			0
$533$	66.8191			2.89426
$534$		0			0
$535$	22.6610	−	9.31276i	0.979719	−	0.402626i
$536$		0			0
$537$	−12.3666	+	12.3666i	−0.533659	+	0.533659i
$538$		0			0
$539$	5.51406	+	5.51406i	0.237507	+	0.237507i
$540$		0			0
$541$	−3.45427	+	3.45427i	−0.148511	+	0.148511i	−0.777452	−	0.628942i	$-0.783488\pi$
$541$	−3.45427	+	3.45427i	−0.148511	+	0.148511i	0.628942	+	0.777452i	$0.283488\pi$
$542$		0			0
$543$	9.58991	+	9.58991i	0.411543	+	0.411543i
$544$		0			0
$545$	1.87914	+	0.784493i	0.0804936	+	0.0336040i
$546$		0			0
$547$		−	18.1175i		−	0.774647i	−0.921944	−	0.387324i	$-0.873400\pi$
$547$		−	18.1175i		−	0.774647i	0.921944	−	0.387324i	$-0.126600\pi$
$548$		0			0
$549$	7.22499	−	7.22499i	0.308355	−	0.308355i
$550$		0			0
$551$	0.961451			0.0409592
$552$		0			0
$553$	16.0715	+	16.0715i	0.683431	+	0.683431i
$554$		0			0
$555$	1.76205	+	4.28763i	0.0747947	+	0.182000i
$556$		0			0
$557$	−21.1776			−0.897324			−0.448662	−	0.893701i	$-0.648099\pi$
$557$	−21.1776			−0.897324			−0.448662	+	0.893701i	$0.648099\pi$
$558$		0			0
$559$	−31.6742			−1.33967
$560$		0			0
$561$	−15.5434			−0.656241
$562$		0			0
$563$	44.5712			1.87845			0.939226	−	0.343298i	$-0.111544\pi$
$563$	44.5712			1.87845			0.939226	+	0.343298i	$0.111544\pi$
$564$		0			0
$565$	−11.2028	+	26.8348i	−0.471307	+	1.12895i
$566$		0			0
$567$	2.08016	+	2.08016i	0.0873584	+	0.0873584i
$568$		0			0
$569$	−5.14194			−0.215562			−0.107781	−	0.994175i	$-0.534374\pi$
$569$	−5.14194			−0.215562			−0.107781	+	0.994175i	$0.534374\pi$
$570$		0			0
$571$	−17.4873	+	17.4873i	−0.731820	+	0.731820i	−0.970980	−	0.239160i	$-0.923128\pi$
$571$	−17.4873	+	17.4873i	−0.731820	+	0.731820i	0.239160	+	0.970980i	$0.423128\pi$
$572$		0			0
$573$		−	14.5044i		−	0.605929i
$574$		0			0
$575$	−0.116011	+	20.8667i	−0.00483801	+	0.870203i
$576$		0			0
$577$	−2.82131	−	2.82131i	−0.117453	−	0.117453i	0.645938	−	0.763390i	$-0.276467\pi$
$577$	−2.82131	−	2.82131i	−0.117453	−	0.117453i	−0.763390	+	0.645938i	$0.776467\pi$
$578$		0			0
$579$	−1.68153	+	1.68153i	−0.0698822	+	0.0698822i
$580$		0			0
$581$	−18.0498	−	18.0498i	−0.748833	−	0.748833i
$582$		0			0
$583$	5.28334	−	5.28334i	0.218813	−	0.218813i
$584$		0			0
$585$	5.21651	+	12.6934i	0.215676	+	0.524809i
$586$		0			0
$587$	−45.9941			−1.89838			−0.949191	−	0.314702i	$-0.898095\pi$
$587$	−45.9941			−1.89838			−0.949191	+	0.314702i	$0.898095\pi$
$588$		0			0
$589$	−2.18844	−	2.18844i	−0.0901729	−	0.0901729i
$590$		0			0
$591$		−	8.65121i		−	0.355863i
$592$		0			0
$593$	−7.77054	+	7.77054i	−0.319098	+	0.319098i	−0.848421	−	0.529323i	$-0.822446\pi$
$593$	−7.77054	+	7.77054i	−0.319098	+	0.319098i	0.529323	+	0.848421i	$0.322446\pi$
$594$		0			0
$595$	8.24392	+	20.0601i	0.337968	+	0.822385i
$596$		0			0
$597$			22.3275i			0.913804i
$598$		0			0
$599$			16.1877i			0.661413i	0.943734	+	0.330707i	$0.107287\pi$
$599$			16.1877i			0.661413i	−0.943734	+	0.330707i	$0.892713\pi$
$600$		0			0
$601$			14.1986i			0.579174i	0.957152	+	0.289587i	$0.0935180\pi$
$601$			14.1986i			0.579174i	−0.957152	+	0.289587i	$0.906482\pi$
$602$		0			0
$603$		−	0.885549i		−	0.0360623i
$604$		0			0
$605$	9.54082	+	23.2159i	0.387889	+	0.943860i
$606$		0			0
$607$	−22.9646	+	22.9646i	−0.932105	+	0.932105i	−0.997837	−	0.0657320i	$-0.979062\pi$
$607$	−22.9646	+	22.9646i	−0.932105	+	0.932105i	0.0657320	+	0.997837i	$0.479062\pi$
$608$		0			0
$609$			2.39711i			0.0971359i
$610$		0			0
$611$	−53.1355	−	53.1355i	−2.14963	−	2.14963i
$612$		0			0
$613$	−37.1155			−1.49908			−0.749541	−	0.661958i	$-0.769726\pi$
$613$	−37.1155			−1.49908			−0.749541	+	0.661958i	$0.769726\pi$
$614$		0			0
$615$	−9.25376	−	22.5174i	−0.373148	−	0.907989i
$616$		0			0
$617$	−1.45005	+	1.45005i	−0.0583767	+	0.0583767i	−0.735692	−	0.677316i	$-0.763143\pi$
$617$	−1.45005	+	1.45005i	−0.0583767	+	0.0583767i	0.677316	+	0.735692i	$0.263143\pi$
$618$		0			0
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	0.920869	−	0.389872i	$-0.127481\pi$
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	−0.389872	+	0.920869i	$0.627481\pi$
$620$		0			0
$621$	−2.95105	+	2.95105i	−0.118421	+	0.118421i
$622$		0			0
$623$	−18.1096	−	18.1096i	−0.725548	−	0.725548i
$624$		0			0
$625$	0.277973	−	24.9985i	0.0111189	−	0.999938i
$626$		0			0
$627$		−	5.56251i		−	0.222145i
$628$		0			0
$629$	−4.83312	+	4.83312i	−0.192709	+	0.192709i
$630$		0			0
$631$	−11.6636			−0.464322			−0.232161	−	0.972677i	$-0.574580\pi$
$631$	−11.6636			−0.464322			−0.232161	+	0.972677i	$0.574580\pi$
$632$		0			0
$633$	5.27613	+	5.27613i	0.209707	+	0.209707i
$634$		0			0
$635$	5.85641	−	14.0282i	0.232405	−	0.556692i
$636$		0			0
$637$	10.1519			0.402232
$638$		0			0
$639$	−2.56877			−0.101619
$640$		0			0
$641$	−20.8880			−0.825025			−0.412512	−	0.910952i	$-0.635349\pi$
$641$	−20.8880			−0.825025			−0.412512	+	0.910952i	$0.635349\pi$
$642$		0			0
$643$	−36.6130			−1.44388			−0.721939	−	0.691957i	$-0.756749\pi$
$643$	−36.6130			−1.44388			−0.721939	+	0.691957i	$0.756749\pi$
$644$		0			0
$645$	4.38655	+	10.6739i	0.172720	+	0.420284i
$646$		0			0
$647$	−23.8735	−	23.8735i	−0.938562	−	0.938562i	0.0596566	−	0.998219i	$-0.480999\pi$
$647$	−23.8735	−	23.8735i	−0.938562	−	0.938562i	−0.998219	+	0.0596566i	$0.980999\pi$
$648$		0			0
$649$	15.5079			0.608737
$650$		0			0
$651$	5.45626	−	5.45626i	0.213848	−	0.213848i
$652$		0			0
$653$		−	22.3501i		−	0.874627i	−0.899309	−	0.437313i	$-0.855930\pi$
$653$		−	22.3501i		−	0.874627i	0.899309	−	0.437313i	$-0.144070\pi$
$654$		0			0
$655$	10.3197	+	4.30819i	0.403222	+	0.168335i
$656$		0			0
$657$	7.35033	+	7.35033i	0.286764	+	0.286764i
$658$		0			0
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	−0.323967	−	0.946068i	$-0.605017\pi$
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	0.946068	+	0.323967i	$0.105017\pi$
$660$		0			0
$661$	15.1592	+	15.1592i	0.589624	+	0.589624i	0.937530	−	0.347906i	$-0.113107\pi$
$661$	15.1592	+	15.1592i	0.589624	+	0.589624i	−0.347906	+	0.937530i	$0.613107\pi$
$662$		0			0
$663$	−14.3084	+	14.3084i	−0.555691	+	0.555691i
$664$		0			0
$665$	−7.17893	+	2.95026i	−0.278387	+	0.114406i
$666$		0			0
$667$	−3.40070			−0.131676
$668$		0			0
$669$	−13.8202	−	13.8202i	−0.534320	−	0.534320i
$670$		0			0
$671$		−	48.1696i		−	1.85957i
$672$		0			0
$673$	15.2524	−	15.2524i	0.587938	−	0.587938i	−0.349134	−	0.937073i	$-0.613524\pi$
$673$	15.2524	−	15.2524i	0.587938	−	0.587938i	0.937073	+	0.349134i	$0.113524\pi$
$674$		0			0
$675$	3.55514	−	3.51582i	0.136837	−	0.135324i
$676$		0			0
$677$			3.95511i			0.152007i	0.997108	+	0.0760036i	$0.0242161\pi$
$677$			3.95511i			0.152007i	−0.997108	+	0.0760036i	$0.975784\pi$
$678$		0			0
$679$			49.9175i			1.91566i
$680$		0			0
$681$		−	1.66286i		−	0.0637209i
$682$		0			0
$683$		−	50.9345i		−	1.94895i	−0.224490	−	0.974476i	$-0.572072\pi$
$683$		−	50.9345i		−	1.94895i	0.224490	−	0.974476i	$-0.427928\pi$
$684$		0			0
$685$	−9.19242	+	22.0191i	−0.351224	+	0.841308i
$686$		0			0
$687$	−11.3744	+	11.3744i	−0.433962	+	0.433962i
$688$		0			0
$689$		−	9.72710i		−	0.370573i
$690$		0			0
$691$	−13.5869	−	13.5869i	−0.516870	−	0.516870i	0.399753	−	0.916623i	$-0.369096\pi$
$691$	−13.5869	−	13.5869i	−0.516870	−	0.516870i	−0.916623	+	0.399753i	$0.869096\pi$
$692$		0			0
$693$	13.8686			0.526824
$694$		0			0
$695$	8.29534	+	3.46309i	0.314660	+	0.131362i
$696$		0			0
$697$	25.3822	−	25.3822i	0.961418	−	0.961418i
$698$		0			0
$699$	9.38976	+	9.38976i	0.355153	+	0.355153i
$700$		0			0
$701$	0.627254	−	0.627254i	0.0236911	−	0.0236911i	−0.695162	−	0.718853i	$-0.744667\pi$
$701$	0.627254	−	0.627254i	0.0236911	−	0.0236911i	0.718853	+	0.695162i	$0.244667\pi$
$702$		0			0
$703$	−1.72963	−	1.72963i	−0.0652343	−	0.0652343i
$704$		0			0
$705$	−10.5474	+	25.2649i	−0.397239	+	0.951529i
$706$		0			0
$707$			27.8483i			1.04734i
$708$		0			0
$709$	−26.7170	+	26.7170i	−1.00338	+	1.00338i	−0.00338478	+	0.999994i	$0.501077\pi$
$709$	−26.7170	+	26.7170i	−1.00338	+	1.00338i	−0.999994	+	0.00338478i	$0.998923\pi$
$710$		0			0
$711$	7.72612			0.289752
$712$		0			0
$713$	7.74061	+	7.74061i	0.289888	+	0.289888i
$714$		0			0
$715$	59.7036	+	24.9247i	2.23279	+	0.932131i
$716$		0			0
$717$	−8.88914			−0.331971
$718$		0			0
$719$	27.5794			1.02854			0.514269	−	0.857629i	$-0.328063\pi$
$719$	27.5794			1.02854			0.514269	+	0.857629i	$0.328063\pi$
$720$		0			0
$721$	55.8488			2.07992
$722$		0			0
$723$	20.5978			0.766041
$724$		0			0
$725$	4.07418	+	0.0226510i	0.151311	+	0.000841235i
$726$		0			0
$727$	−8.11985	−	8.11985i	−0.301148	−	0.301148i	0.540315	−	0.841463i	$-0.318305\pi$
$727$	−8.11985	−	8.11985i	−0.301148	−	0.301148i	−0.841463	+	0.540315i	$0.818305\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0319	+	12.0319i	−0.445014	+	0.445014i
$732$		0			0
$733$			12.3271i			0.455313i	0.973742	+	0.227656i	$0.0731063\pi$
$733$			12.3271i			0.455313i	−0.973742	+	0.227656i	$0.926894\pi$
$734$		0			0
$735$	−1.40593	−	3.42109i	−0.0518586	−	0.126189i
$736$		0			0
$737$	−2.95201	−	2.95201i	−0.108739	−	0.108739i
$738$		0			0
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	−0.0834496	−	0.996512i	$-0.526594\pi$
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	0.996512	+	0.0834496i	$0.0265938\pi$
$740$		0			0
$741$	−5.12054	−	5.12054i	−0.188108	−	0.188108i
$742$		0			0
$743$	26.8731	−	26.8731i	0.985877	−	0.985877i	−0.0140246	−	0.999902i	$-0.504464\pi$
$743$	26.8731	−	26.8731i	0.985877	−	0.985877i	0.999902	+	0.0140246i	$0.00446431\pi$
$744$		0			0
$745$	3.90195	−	9.34658i	0.142957	−	0.342432i
$746$		0			0
$747$	−8.67714			−0.317480
$748$		0			0
$749$	−22.7917	−	22.7917i	−0.832789	−	0.832789i
$750$		0			0
$751$		−	24.7594i		−	0.903484i	−0.892149	−	0.451742i	$-0.850803\pi$
$751$		−	24.7594i		−	0.903484i	0.892149	−	0.451742i	$-0.149197\pi$
$752$		0			0
$753$	16.8455	−	16.8455i	0.613883	−	0.613883i
$754$		0			0
$755$	18.2578	−	7.50322i	0.664468	−	0.273070i
$756$		0			0
$757$			35.5014i			1.29032i	0.764047	+	0.645160i	$0.223209\pi$
$757$			35.5014i			1.29032i	−0.764047	+	0.645160i	$0.776791\pi$
$758$		0			0
$759$			19.6749i			0.714153i
$760$		0			0
$761$			19.8569i			0.719812i	0.932989	+	0.359906i	$0.117191\pi$
$761$			19.8569i			0.719812i	−0.932989	+	0.359906i	$0.882809\pi$
$762$		0			0
$763$		−	2.67900i		−	0.0969862i
$764$		0			0
$765$	6.80334	+	2.84022i	0.245975	+	0.102688i
$766$		0			0
$767$	14.2757	−	14.2757i	0.515465	−	0.515465i
$768$		0			0
$769$			37.1951i			1.34129i	0.741779	+	0.670644i	$0.233982\pi$
$769$			37.1951i			1.34129i	−0.741779	+	0.670644i	$0.766018\pi$
$770$		0			0
$771$	−14.1500	−	14.1500i	−0.509600	−	0.509600i
$772$		0			0
$773$	−13.2454			−0.476402			−0.238201	−	0.971216i	$-0.576558\pi$
$773$	−13.2454			−0.476402			−0.238201	+	0.971216i	$0.576558\pi$
$774$		0			0
$775$	−9.22202	−	9.32514i	−0.331265	−	0.334969i
$776$		0			0
$777$	4.31236	−	4.31236i	0.154705	−	0.154705i
$778$		0			0
$779$	9.08353	+	9.08353i	0.325451	+	0.325451i
$780$		0			0
$781$	−8.56310	+	8.56310i	−0.306412	+	0.306412i
$782$		0			0
$783$	0.576185	+	0.576185i	0.0205912	+	0.0205912i
$784$		0			0
$785$	32.0959	−	13.1902i	1.14555	−	0.470777i
$786$		0			0
$787$		−	12.0292i		−	0.428794i	−0.976747	−	0.214397i	$-0.931221\pi$
$787$		−	12.0292i		−	0.428794i	0.976747	−	0.214397i	$-0.0687786\pi$
$788$		0			0
$789$	−11.1204	+	11.1204i	−0.395896	+	0.395896i
$790$		0			0
$791$	38.2571			1.36026
$792$		0			0
$793$	−44.3423	−	44.3423i	−1.57464	−	1.57464i
$794$		0			0
$795$	−3.27794	+	1.34710i	−0.116256	+	0.0477768i
$796$		0			0
$797$	45.2714			1.60359			0.801797	−	0.597597i	$-0.203878\pi$
$797$	45.2714			1.60359			0.801797	+	0.597597i	$0.203878\pi$
$798$		0			0
$799$	−40.3685			−1.42813
$800$		0			0
$801$	−8.70590			−0.307608
$802$		0			0
$803$	49.0053			1.72936
$804$		0			0
$805$	25.3922	−	10.4352i	0.894958	−	0.367793i
$806$		0			0
$807$	10.2902	+	10.2902i	0.362231	+	0.362231i
$808$		0			0
$809$	5.16391			0.181553			0.0907767	−	0.995871i	$-0.471065\pi$
$809$	5.16391			0.181553			0.0907767	+	0.995871i	$0.471065\pi$
$810$		0			0
$811$	15.7171	−	15.7171i	0.551903	−	0.551903i	−0.375087	−	0.926990i	$-0.622387\pi$
$811$	15.7171	−	15.7171i	0.551903	−	0.551903i	0.926990	+	0.375087i	$0.122387\pi$
$812$		0			0
$813$			21.3325i			0.748163i
$814$		0			0
$815$	−17.8947	+	7.35404i	−0.626826	+	0.257601i
$816$		0			0
$817$	−4.30585	−	4.30585i	−0.150643	−	0.150643i
$818$		0			0
$819$	12.7667	−	12.7667i	0.446103	−	0.446103i
$820$		0			0
$821$	15.6816	+	15.6816i	0.547293	+	0.547293i	0.925657	−	0.378364i	$-0.123513\pi$
$821$	15.6816	+	15.6816i	0.547293	+	0.547293i	−0.378364	+	0.925657i	$0.623513\pi$
$822$		0			0
$823$	3.65203	−	3.65203i	0.127302	−	0.127302i	−0.640585	−	0.767887i	$-0.721308\pi$
$823$	3.65203	−	3.65203i	0.127302	−	0.127302i	0.767887	+	0.640585i	$0.221308\pi$
$824$		0			0
$825$	0.131048	−	23.5713i	0.00456251	−	0.820649i
$826$		0			0
$827$	14.0926			0.490046			0.245023	−	0.969517i	$-0.421204\pi$
$827$	14.0926			0.490046			0.245023	+	0.969517i	$0.421204\pi$
$828$		0			0
$829$	12.1216	+	12.1216i	0.421000	+	0.421000i	0.885548	−	0.464548i	$-0.153783\pi$
$829$	12.1216	+	12.1216i	0.421000	+	0.421000i	−0.464548	+	0.885548i	$0.653783\pi$
$830$		0			0
$831$		−	19.0041i		−	0.659244i
$832$		0			0
$833$	3.85633	−	3.85633i	0.133614	−	0.133614i
$834$		0			0
$835$	8.36390	+	3.49171i	0.289445	+	0.120836i
$836$		0			0
$837$		−	2.62300i		−	0.0906643i
$838$		0			0
$839$		−	14.6206i		−	0.504759i	−0.967628	−	0.252380i	$-0.918787\pi$
$839$		−	14.6206i		−	0.504759i	0.967628	−	0.252380i	$-0.0812132\pi$
$840$		0			0
$841$		−	28.3360i		−	0.977104i
$842$		0			0
$843$		−	3.86317i		−	0.133054i
$844$		0			0
$845$	51.0172	−	20.9661i	1.75504	−	0.721254i
$846$		0			0
$847$	23.3498	−	23.3498i	0.802309	−	0.802309i
$848$		0			0
$849$			5.89151i			0.202196i
$850$		0			0
$851$	6.11779	+	6.11779i	0.209715	+	0.209715i
$852$		0			0
$853$	−13.7252			−0.469940			−0.234970	−	0.972003i	$-0.575499\pi$
$853$	−13.7252			−0.469940			−0.234970	+	0.972003i	$0.575499\pi$
$854$		0			0
$855$	−1.01643	+	2.43472i	−0.0347612	+	0.0832655i
$856$		0			0
$857$	18.7921	−	18.7921i	0.641927	−	0.641927i	−0.309102	−	0.951029i	$-0.600028\pi$
$857$	18.7921	−	18.7921i	0.641927	−	0.641927i	0.951029	+	0.309102i	$0.100028\pi$
$858$		0			0
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	0.981625	−	0.190822i	$-0.0611152\pi$
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	−0.190822	+	0.981625i	$0.561115\pi$
$860$		0			0
$861$	−22.6473	+	22.6473i	−0.771817	+	0.771817i
$862$		0			0
$863$	8.96863	+	8.96863i	0.305296	+	0.305296i	0.843082	−	0.537786i	$-0.180739\pi$
$863$	8.96863	+	8.96863i	0.305296	+	0.305296i	−0.537786	+	0.843082i	$0.680739\pi$
$864$		0			0
$865$	−12.8465	−	31.2597i	−0.436795	−	1.06286i
$866$		0			0
$867$		−	6.12955i		−	0.208171i
$868$		0			0
$869$	25.7553	−	25.7553i	0.873690	−	0.873690i
$870$		0			0
$871$	−5.43492			−0.184155
$872$		0			0
$873$	11.9985	+	11.9985i	0.406087	+	0.406087i
$874$		0			0
$875$	−30.4905	+	12.3327i	−1.03077	+	0.416921i
$876$		0			0
$877$	47.1944			1.59364			0.796822	−	0.604215i	$-0.206513\pi$
$877$	47.1944			1.59364			0.796822	+	0.604215i	$0.206513\pi$
$878$		0			0
$879$	4.49132			0.151489
$880$		0			0
$881$	51.5667			1.73733			0.868663	−	0.495403i	$-0.164980\pi$
$881$	51.5667			1.73733			0.868663	+	0.495403i	$0.164980\pi$
$882$		0			0
$883$	−33.7083			−1.13438			−0.567188	−	0.823589i	$-0.691969\pi$
$883$	−33.7083			−1.13438			−0.567188	+	0.823589i	$0.691969\pi$
$884$		0			0
$885$	−6.78780	−	2.83373i	−0.228170	−	0.0952548i
$886$		0			0
$887$	−4.91204	−	4.91204i	−0.164930	−	0.164930i	0.619817	−	0.784747i	$-0.287207\pi$
$887$	−4.91204	−	4.91204i	−0.164930	−	0.164930i	−0.784747	+	0.619817i	$0.787207\pi$
$888$		0			0
$889$	−19.9993			−0.670755
$890$		0			0
$891$	3.33354	−	3.33354i	0.111678	−	0.111678i
$892$		0			0
$893$		−	14.4467i		−	0.483440i
$894$		0			0
$895$	15.0659	−	36.0881i	0.503596	−	1.20629i
$896$		0			0
$897$	18.1116	+	18.1116i	0.604729	+	0.604729i
$898$		0			0
$899$	1.51134	−	1.51134i	0.0504059	−	0.0504059i
$900$		0			0
$901$	−3.69497	−	3.69497i	−0.123097	−	0.123097i
$902$		0			0
$903$	10.7355	−	10.7355i	0.357254	−	0.357254i
$904$		0			0
$905$	−27.9852	−	11.6831i	−0.930259	−	0.388359i
$906$		0			0
$907$	−39.4081			−1.30852			−0.654262	−	0.756268i	$-0.727021\pi$
$907$	−39.4081			−1.30852			−0.654262	+	0.756268i	$0.727021\pi$
$908$		0			0
$909$	6.69380	+	6.69380i	0.222019	+	0.222019i
$910$		0			0
$911$		−	7.29607i		−	0.241729i	−0.992669	−	0.120865i	$-0.961433\pi$
$911$		−	7.29607i		−	0.241729i	0.992669	−	0.120865i	$-0.0385667\pi$
$912$		0			0
$913$	−28.9256	+	28.9256i	−0.957298	+	0.957298i
$914$		0			0
$915$	−8.80197	+	21.0839i	−0.290984	+	0.697012i
$916$		0			0
$917$		−	14.7122i		−	0.485840i
$918$		0			0
$919$		−	52.5346i		−	1.73296i	−0.499215	−	0.866478i	$-0.666378\pi$
$919$		−	52.5346i		−	1.73296i	0.499215	−	0.866478i	$-0.333622\pi$
$920$		0			0
$921$			3.84487i			0.126693i
$922$		0			0
$923$			15.7654i			0.518926i
$924$		0			0
$925$	−7.28862	−	7.37012i	−0.239648	−	0.242328i
$926$		0			0
$927$	13.4242	−	13.4242i	0.440907	−	0.440907i
$928$		0			0
$929$		−	48.7878i		−	1.60068i	−0.599549	−	0.800338i	$-0.704654\pi$
$929$		−	48.7878i		−	1.60068i	0.599549	−	0.800338i	$-0.295346\pi$
$930$		0			0
$931$	1.38007	+	1.38007i	0.0452299	+	0.0452299i
$932$		0			0
$933$	4.07103			0.133279
$934$		0			0
$935$	32.1472	−	13.2112i	1.05133	−	0.432054i
$936$		0			0
$937$	−29.3163	+	29.3163i	−0.957722	+	0.957722i	−0.999142	−	0.0414198i	$-0.986812\pi$
$937$	−29.3163	+	29.3163i	−0.957722	+	0.957722i	0.0414198	+	0.999142i	$0.486812\pi$
$938$		0			0
$939$	−1.37922	−	1.37922i	−0.0450093	−	0.0450093i
$940$		0			0
$941$	7.65378	−	7.65378i	0.249506	−	0.249506i	−0.571262	−	0.820768i	$-0.693546\pi$
$941$	7.65378	−	7.65378i	0.249506	−	0.249506i	0.820768	+	0.571262i	$0.193546\pi$
$942$		0			0
$943$	−32.1289	−	32.1289i	−1.04626	−	1.04626i
$944$		0			0
$945$	−6.07029	−	2.53419i	−0.197467	−	0.0824372i
$946$		0			0
$947$			39.6694i			1.28908i	0.764569	+	0.644541i	$0.222952\pi$
$947$			39.6694i			1.28908i	−0.764569	+	0.644541i	$0.777048\pi$
$948$		0			0
$949$	45.1116	−	45.1116i	1.46438	−	1.46438i
$950$		0			0
$951$	−9.80915			−0.318084
$952$		0			0
$953$	8.83095	+	8.83095i	0.286063	+	0.286063i	0.835521	−	0.549458i	$-0.185166\pi$
$953$	8.83095	+	8.83095i	0.286063	+	0.286063i	−0.549458	+	0.835521i	$0.685166\pi$
$954$		0			0
$955$	12.3281	+	29.9983i	0.398929	+	0.970724i
$956$		0			0
$957$	3.84148			0.124177
$958$		0			0
$959$	31.3916			1.01369
$960$		0			0
$961$	24.1198			0.778060
$962$		0			0
$963$	−10.9567			−0.353075
$964$		0			0
$965$	2.04856	−	4.90703i	0.0659455	−	0.157963i
$966$		0			0
$967$	2.42314	+	2.42314i	0.0779231	+	0.0779231i	0.744994	−	0.667071i	$-0.232452\pi$
$967$	2.42314	+	2.42314i	0.0779231	+	0.0779231i	−0.667071	+	0.744994i	$0.732452\pi$
$968$		0			0
$969$	−3.89021			−0.124972
$970$		0			0
$971$	21.9788	−	21.9788i	0.705334	−	0.705334i	−0.260216	−	0.965550i	$-0.583794\pi$
$971$	21.9788	−	21.9788i	0.705334	−	0.705334i	0.965550	+	0.260216i	$0.0837939\pi$
$972$		0			0
$973$		−	11.8263i		−	0.379132i
$974$		0			0
$975$	−21.5778	−	21.8191i	−0.691044	−	0.698771i
$976$		0			0
$977$	32.7193	+	32.7193i	1.04678	+	1.04678i	0.998851	+	0.0479337i	$0.0152636\pi$
$977$	32.7193	+	32.7193i	1.04678	+	1.04678i	0.0479337	+	0.998851i	$0.484736\pi$
$978$		0			0
$979$	−29.0215	+	29.0215i	−0.927531	+	0.927531i
$980$		0			0
$981$	−0.643941	−	0.643941i	−0.0205595	−	0.0205595i
$982$		0			0
$983$	−27.7480	+	27.7480i	−0.885023	+	0.885023i	−0.994040	−	0.109017i	$-0.965230\pi$
$983$	−27.7480	+	27.7480i	−0.885023	+	0.885023i	0.109017	+	0.994040i	$0.465230\pi$
$984$		0			0
$985$	7.35318	+	17.8927i	0.234292	+	0.570108i
$986$		0			0
$987$	36.0188			1.14649
$988$		0			0
$989$	15.2300	+	15.2300i	0.484286	+	0.484286i
$990$		0			0
$991$		−	24.6172i		−	0.781991i	−0.920393	−	0.390996i	$-0.872131\pi$
$991$		−	24.6172i		−	0.781991i	0.920393	−	0.390996i	$-0.127869\pi$
$992$		0			0
$993$	−7.17235	+	7.17235i	−0.227608	+	0.227608i
$994$		0			0
$995$	−18.9775	−	46.1784i	−0.601627	−	1.46395i
$996$		0			0
$997$			36.9465i			1.17011i	0.810995	+	0.585053i	$0.198926\pi$
$997$			36.9465i			1.17011i	−0.810995	+	0.585053i	$0.801074\pi$
$998$		0			0
$999$		−	2.07309i		−	0.0655897i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.j.1567.2		16
4.3	odd	2		1920.2.y.i.1567.2		16
5.3	odd	4		1920.2.bc.j.1183.6		16
8.3	odd	2		240.2.y.e.187.1	yes	16
8.5	even	2		960.2.y.e.847.7		16
16.3	odd	4		1920.2.bc.j.607.6		16
16.5	even	4		240.2.bc.e.67.4	yes	16
16.11	odd	4		960.2.bc.e.367.3		16
16.13	even	4		1920.2.bc.i.607.6		16
20.3	even	4		1920.2.bc.i.1183.6		16
24.11	even	2		720.2.z.f.667.8		16
40.3	even	4		240.2.bc.e.43.4	yes	16
40.13	odd	4		960.2.bc.e.463.3		16
48.5	odd	4		720.2.bd.f.307.5		16
80.3	even	4	inner	1920.2.y.j.223.2		16
80.13	odd	4		1920.2.y.i.223.2		16
80.43	even	4		960.2.y.e.943.7		16
80.53	odd	4		240.2.y.e.163.1	✓	16
120.83	odd	4		720.2.bd.f.523.5		16
240.53	even	4		720.2.z.f.163.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.1	✓	16	80.53	odd	4
240.2.y.e.187.1	yes	16	8.3	odd	2
240.2.bc.e.43.4	yes	16	40.3	even	4
240.2.bc.e.67.4	yes	16	16.5	even	4
720.2.z.f.163.8		16	240.53	even	4
720.2.z.f.667.8		16	24.11	even	2
720.2.bd.f.307.5		16	48.5	odd	4
720.2.bd.f.523.5		16	120.83	odd	4
960.2.y.e.847.7		16	8.5	even	2
960.2.y.e.943.7		16	80.43	even	4
960.2.bc.e.367.3		16	16.11	odd	4
960.2.bc.e.463.3		16	40.13	odd	4
1920.2.y.i.223.2		16	80.13	odd	4
1920.2.y.i.1567.2		16	4.3	odd	2
1920.2.y.j.223.2		16	80.3	even	4	inner
1920.2.y.j.1567.2		16	1.1	even	1	trivial
1920.2.bc.i.607.6		16	16.13	even	4
1920.2.bc.i.1183.6		16	20.3	even	4
1920.2.bc.j.607.6		16	16.3	odd	4
1920.2.bc.j.1183.6		16	5.3	odd	4

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

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Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	1920.2.y.j.1567.2

Level	$1920$
Weight	$2$
Character	1920.1567
Analytic conductor	$15.331$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$