LMFDB - Embedded newform 1197.2.j.a.856.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1197,2,Mod(172,1197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1197.172"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1197, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.a.172.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{4} +(1.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} +(2.50000 - 4.33013i) q^{23} +(0.500000 + 0.866025i) q^{25} +(5.00000 - 1.73205i) q^{28} -2.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(-4.00000 - 3.46410i) q^{35} +(-4.00000 + 6.92820i) q^{37} -6.00000 q^{41} +12.0000 q^{43} +(3.00000 - 5.19615i) q^{44} +(-2.50000 + 4.33013i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{53} -6.00000 q^{55} +(7.00000 + 12.1244i) q^{59} +(6.50000 - 11.2583i) q^{61} -8.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(1.00000 + 1.73205i) q^{67} +(7.00000 - 12.1244i) q^{68} +10.0000 q^{71} +(-0.500000 - 0.866025i) q^{73} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(2.00000 - 3.46410i) q^{79} +(4.00000 + 6.92820i) q^{80} +9.00000 q^{83} -14.0000 q^{85} +(9.00000 - 15.5885i) q^{89} +(1.00000 - 5.19615i) q^{91} +10.0000 q^{92} +(-1.00000 - 1.73205i) q^{95} +6.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} + 2 q^{5} + q^{7} - 3 q^{11} + 4 q^{13} - 4 q^{16} - 7 q^{17} + q^{19} + 8 q^{20} + 5 q^{23} + q^{25} + 10 q^{28} - 4 q^{29} - 10 q^{31} - 8 q^{35} - 8 q^{37} - 12 q^{41} + 24 q^{43} + 6 q^{44}+ \cdots + 12 q^{97}+O(q^{100}) $ 2 * q + 2 * q^4 + 2 * q^5 + q^7 - 3 * q^11 + 4 * q^13 - 4 * q^16 - 7 * q^17 + q^19 + 8 * q^20 + 5 * q^23 + q^25 + 10 * q^28 - 4 * q^29 - 10 * q^31 - 8 * q^35 - 8 * q^37 - 12 * q^41 + 24 * q^43 + 6 * q^44 - 5 * q^47 - 13 * q^49 + 4 * q^52 + 4 * q^53 - 12 * q^55 + 14 * q^59 + 13 * q^61 - 16 * q^64 + 4 * q^65 + 2 * q^67 + 14 * q^68 + 20 * q^71 - q^73 + 4 * q^76 - 15 * q^77 + 4 * q^79 + 8 * q^80 + 18 * q^83 - 28 * q^85 + 18 * q^89 + 2 * q^91 + 20 * q^92 - 2 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	4.00000			0.894427
$21$		0			0
$22$		0			0
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	−0.478407	−	0.878138i	$-0.658786\pi$
$23$	2.50000	−	4.33013i	0.521286	−	0.902894i	0.999694	−	0.0247559i	$-0.00788087\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$	5.00000	−	1.73205i	0.944911	−	0.327327i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.00000	−	3.46410i	−0.676123	−	0.585540i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$		0			0
$46$		0			0
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	−0.988722	−	0.149763i	$-0.952149\pi$
$47$	−2.50000	+	4.33013i	−0.364662	+	0.631614i	0.624059	+	0.781377i	$0.285482\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.812198	+	0.583382i	$0.198271\pi$
$59$	7.00000	+	12.1244i	0.911322	+	1.57846i	0.0991242	+	0.995075i	$0.468396\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	7.00000	−	12.1244i	0.848875	−	1.47029i
$69$		0			0
$70$		0			0
$71$	10.0000			1.18678			0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000			1.18678			0.593391	+	0.804914i	$0.297789\pi$
$72$		0			0
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	0.835281	−	0.549823i	$-0.185305\pi$
$73$	−0.500000	−	0.866025i	−0.0585206	−	0.101361i	−0.893801	+	0.448463i	$0.851972\pi$
$74$		0			0
$75$		0			0
$76$	2.00000			0.229416
$77$	−7.50000	+	2.59808i	−0.854704	+	0.296078i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	4.00000	+	6.92820i	0.447214	+	0.774597i
$81$		0			0
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	−14.0000			−1.51851
$86$		0			0
$87$		0			0
$88$		0			0
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$		0			0
$91$	1.00000	−	5.19615i	0.104828	−	0.544705i
$92$	10.0000			1.04257
$93$		0			0
$94$		0			0
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$		0			0
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$		0			0
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	0.983889	+	0.178782i	$0.0572157\pi$
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	−0.337115	+	0.941464i	$0.609451\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$		0			0
$111$		0			0
$112$	8.00000	+	6.92820i	0.755929	+	0.654654i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$	−5.00000	−	8.66025i	−0.466252	−	0.807573i
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$		0			0
$118$		0			0
$119$	−17.5000	+	6.06218i	−1.60422	+	0.555719i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$	10.0000	−	17.3205i	0.898027	−	1.55543i
$125$	12.0000			1.07331
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$		0			0
$133$	−2.00000	−	1.73205i	−0.173422	−	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$	2.00000	−	10.3923i	0.169031	−	0.878310i
$141$		0			0
$142$		0			0
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$		0			0
$145$	−2.00000	+	3.46410i	−0.166091	+	0.287678i
$146$		0			0
$147$		0			0
$148$	−16.0000			−1.31519
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−20.0000			−1.60644
$156$		0			0
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	0.748852	−	0.662738i	$-0.230606\pi$
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	−0.948373	+	0.317156i	$0.897272\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.0000	−	8.66025i	−0.788110	−	0.682524i
$162$		0			0
$163$	−4.50000	+	7.79423i	−0.352467	+	0.610491i	−0.986681	−	0.162667i	$-0.947991\pi$
$163$	−4.50000	+	7.79423i	−0.352467	+	0.610491i	0.634214	+	0.773158i	$0.281324\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$		0			0
$166$		0			0
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$	12.0000	+	20.7846i	0.914991	+	1.58481i
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	−0.779926	−	0.625871i	$-0.784744\pi$
$173$	2.00000	−	3.46410i	0.152057	−	0.263371i	0.931984	+	0.362500i	$0.118077\pi$
$174$		0			0
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	12.0000			0.904534
$177$		0			0
$178$		0			0
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.00000	+	13.8564i	0.588172	+	1.01874i
$186$		0			0
$187$	−10.5000	+	18.1865i	−0.767836	+	1.32993i
$188$	−10.0000			−0.729325
$189$		0			0
$190$		0			0
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$		0			0
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$		0			0
$195$		0			0
$196$	−2.00000	−	13.8564i	−0.142857	−	0.989743i
$197$	5.00000			0.356235			0.178118	−	0.984009i	$-0.442999\pi$
$197$	5.00000			0.356235			0.178118	+	0.984009i	$0.442999\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.00000	+	5.19615i	−0.0701862	+	0.364698i
$204$		0			0
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$		0			0
$207$		0			0
$208$	−4.00000	+	6.92820i	−0.277350	+	0.480384i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−4.00000	+	6.92820i	−0.274721	+	0.475831i
$213$		0			0
$214$		0			0
$215$	12.0000	−	20.7846i	0.818393	−	1.41750i
$216$		0			0
$217$	−25.0000	+	8.66025i	−1.69711	+	0.587896i
$218$		0			0
$219$		0			0
$220$	−6.00000	−	10.3923i	−0.404520	−	0.700649i
$221$	−7.00000	−	12.1244i	−0.470871	−	0.815572i
$222$		0			0
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	0.982877	−	0.184263i	$-0.0589899\pi$
$227$	5.00000	+	8.66025i	0.331862	+	0.574801i	−0.651015	+	0.759065i	$0.725657\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	−0.882073	−	0.471113i	$-0.843853\pi$
$229$	−0.500000	+	0.866025i	−0.0330409	+	0.0572286i	0.849032	+	0.528341i	$0.177186\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.5000	+	18.1865i	−0.687878	+	1.19144i	0.284645	+	0.958633i	$0.408124\pi$
$233$	−10.5000	+	18.1865i	−0.687878	+	1.19144i	−0.972523	+	0.232806i	$0.925209\pi$
$234$		0			0
$235$	5.00000	+	8.66025i	0.326164	+	0.564933i
$236$	−14.0000	+	24.2487i	−0.911322	+	1.57846i
$237$		0			0
$238$		0			0
$239$	1.00000			0.0646846			0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000			0.0646846			0.0323423	+	0.999477i	$0.489703\pi$
$240$		0			0
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	0.965615	−	0.259975i	$-0.0837143\pi$
$241$	4.00000	+	6.92820i	0.257663	+	0.446285i	−0.707953	+	0.706260i	$0.750381\pi$
$242$		0			0
$243$		0			0
$244$	26.0000			1.66448
$245$	−11.0000	+	8.66025i	−0.702764	+	0.553283i
$246$		0			0
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−16.0000			−1.00991			−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000			−1.00991			−0.504956	+	0.863145i	$0.668491\pi$
$252$		0			0
$253$	−15.0000			−0.943042
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$		0			0
$259$	16.0000	+	13.8564i	0.994192	+	0.860995i
$260$	8.00000			0.496139
$261$		0			0
$262$		0			0
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	0.645128	−	0.764075i	$-0.276804\pi$
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	−0.984272	+	0.176659i	$0.943471\pi$
$264$		0			0
$265$	8.00000			0.491436
$266$		0			0
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	28.0000			1.69775
$273$		0			0
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.0000			1.19310			0.596550	−	0.802576i	$-0.296538\pi$
$281$	20.0000			1.19310			0.596550	+	0.802576i	$0.296538\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	10.0000	+	17.3205i	0.593391	+	1.02778i
$285$		0			0
$286$		0			0
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$		0			0
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$	28.0000			1.63022
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.00000	−	8.66025i	0.289157	−	0.500835i
$300$		0			0
$301$	6.00000	−	31.1769i	0.345834	−	1.79701i
$302$		0			0
$303$		0			0
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	−13.0000	−	22.5167i	−0.744378	−	1.28930i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	−12.0000	−	10.3923i	−0.683763	−	0.592157i
$309$		0			0
$310$		0			0
$311$	2.50000	+	4.33013i	0.141762	+	0.245539i	0.928160	−	0.372181i	$-0.121390\pi$
$311$	2.50000	+	4.33013i	0.141762	+	0.245539i	−0.786398	+	0.617720i	$0.788057\pi$
$312$		0			0
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$		0			0
$315$		0			0
$316$	8.00000			0.450035
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$		0			0
$319$	3.00000	+	5.19615i	0.167968	+	0.290929i
$320$	−8.00000	+	13.8564i	−0.447214	+	0.774597i
$321$		0			0
$322$		0			0
$323$	−7.00000			−0.389490
$324$		0			0
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.0000	+	8.66025i	0.551318	+	0.477455i
$330$		0			0
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	9.00000	+	15.5885i	0.493939	+	0.855528i
$333$		0			0
$334$		0			0
$335$	4.00000			0.218543
$336$		0			0
$337$	12.0000			0.653682			0.326841	−	0.945079i	$-0.394016\pi$
$337$	12.0000			0.653682			0.326841	+	0.945079i	$0.394016\pi$
$338$		0			0
$339$		0			0
$340$	−14.0000	−	24.2487i	−0.759257	−	1.31507i
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	−27.0000			−1.44528			−0.722638	−	0.691226i	$-0.757071\pi$
$349$	−27.0000			−1.44528			−0.722638	+	0.691226i	$0.757071\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$		0			0
$355$	10.0000	−	17.3205i	0.530745	−	0.919277i
$356$	36.0000			1.90800
$357$		0			0
$358$		0			0
$359$	−15.5000	+	26.8468i	−0.818059	+	1.41692i	0.0890519	+	0.996027i	$0.471616\pi$
$359$	−15.5000	+	26.8468i	−0.818059	+	1.41692i	−0.907111	+	0.420892i	$0.861717\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$		0			0
$364$	10.0000	−	3.46410i	0.524142	−	0.181568i
$365$	−2.00000			−0.104685
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	10.0000	+	17.3205i	0.521286	+	0.902894i
$369$		0			0
$370$		0			0
$371$	10.0000	−	3.46410i	0.519174	−	0.179847i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$		0			0
$382$		0			0
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$		0			0
$385$	−3.00000	+	15.5885i	−0.152894	+	0.794461i
$386$		0			0
$387$		0			0
$388$	6.00000	+	10.3923i	0.304604	+	0.527589i
$389$	−14.5000	−	25.1147i	−0.735179	−	1.27337i	−0.954645	−	0.297747i	$-0.903765\pi$
$389$	−14.5000	−	25.1147i	−0.735179	−	1.27337i	0.219465	−	0.975620i	$-0.429569\pi$
$390$		0			0
$391$	−35.0000			−1.77003
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	−0.418634	−	0.908155i	$-0.637491\pi$
$397$	11.5000	−	19.9186i	0.577168	−	0.999685i	0.995802	−	0.0915300i	$-0.0291757\pi$
$398$		0			0
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	−13.0000	+	22.5167i	−0.646774	+	1.12025i
$405$		0			0
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$		0			0
$411$		0			0
$412$	−16.0000			−0.788263
$413$	35.0000	−	12.1244i	1.72224	−	0.596601i
$414$		0			0
$415$	9.00000	−	15.5885i	0.441793	−	0.765207i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	4.00000			0.194948			0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000			0.194948			0.0974740	+	0.995238i	$0.468924\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.50000	−	6.06218i	0.169775	−	0.294059i
$426$		0			0
$427$	−26.0000	−	22.5167i	−1.25823	−	1.08966i
$428$	−36.0000			−1.74013
$429$		0			0
$430$		0			0
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$431$	−3.00000	−	5.19615i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$432$		0			0
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$		0			0
$435$		0			0
$436$	6.00000	−	10.3923i	0.287348	−	0.497701i
$437$	−2.50000	−	4.33013i	−0.119591	−	0.207138i
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.5000	−	18.1865i	0.498870	−	0.864068i	−0.501129	−	0.865373i	$-0.667082\pi$
$443$	10.5000	−	18.1865i	0.498870	−	0.864068i	0.999999	+	0.00130426i	$0.000415158\pi$
$444$		0			0
$445$	−18.0000	−	31.1769i	−0.853282	−	1.47793i
$446$		0			0
$447$		0			0
$448$	−4.00000	+	20.7846i	−0.188982	+	0.981981i
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−12.0000	−	20.7846i	−0.564433	−	0.977626i
$453$		0			0
$454$		0			0
$455$	−8.00000	−	6.92820i	−0.375046	−	0.324799i
$456$		0			0
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	−0.410184	−	0.912003i	$-0.634536\pi$
$457$	12.5000	−	21.6506i	0.584725	−	1.01277i	0.994910	−	0.100771i	$-0.0321310\pi$
$458$		0			0
$459$		0			0
$460$	10.0000	−	17.3205i	0.466252	−	0.807573i
$461$	15.0000			0.698620			0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000			0.698620			0.349310	+	0.937007i	$0.386416\pi$
$462$		0			0
$463$	−9.00000			−0.418265			−0.209133	−	0.977887i	$-0.567064\pi$
$463$	−9.00000			−0.418265			−0.209133	+	0.977887i	$0.567064\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$		0			0
$467$	−2.50000	+	4.33013i	−0.115686	+	0.200374i	−0.918054	−	0.396456i	$-0.870240\pi$
$467$	−2.50000	+	4.33013i	−0.115686	+	0.200374i	0.802368	+	0.596830i	$0.203573\pi$
$468$		0			0
$469$	5.00000	−	1.73205i	0.230879	−	0.0799787i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.0000	−	31.1769i	−0.827641	−	1.43352i
$474$		0			0
$475$	1.00000			0.0458831
$476$	−28.0000	−	24.2487i	−1.28338	−	1.11144i
$477$		0			0
$478$		0			0
$479$	15.5000	+	26.8468i	0.708213	+	1.22666i	0.965519	+	0.260331i	$0.0838317\pi$
$479$	15.5000	+	26.8468i	0.708213	+	1.22666i	−0.257306	+	0.966330i	$0.582835\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$		0			0
$483$		0			0
$484$	4.00000			0.181818
$485$	6.00000	−	10.3923i	0.272446	−	0.471890i
$486$		0			0
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−27.0000			−1.21849			−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000			−1.21849			−0.609246	+	0.792981i	$0.708528\pi$
$492$		0			0
$493$	7.00000	+	12.1244i	0.315264	+	0.546054i
$494$		0			0
$495$		0			0
$496$	40.0000			1.79605
$497$	5.00000	−	25.9808i	0.224281	−	1.16540i
$498$		0			0
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$	12.0000	+	20.7846i	0.536656	+	0.929516i
$501$		0			0
$502$		0			0
$503$	11.0000			0.490466			0.245233	−	0.969464i	$-0.421136\pi$
$503$	11.0000			0.490466			0.245233	+	0.969464i	$0.421136\pi$
$504$		0			0
$505$	26.0000			1.15698
$506$		0			0
$507$		0			0
$508$	16.0000	+	27.7128i	0.709885	+	1.22956i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	−2.50000	+	0.866025i	−0.110593	+	0.0383107i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	15.0000			0.659699
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$		0			0
$523$	−17.0000	+	29.4449i	−0.743358	+	1.28753i	0.207600	+	0.978214i	$0.433435\pi$
$523$	−17.0000	+	29.4449i	−0.743358	+	1.28753i	−0.950958	+	0.309320i	$0.899899\pi$
$524$	2.00000			0.0873704
$525$		0			0
$526$		0			0
$527$	−35.0000	+	60.6218i	−1.52462	+	2.64073i
$528$		0			0
$529$	−1.00000	−	1.73205i	−0.0434783	−	0.0753066i
$530$		0			0
$531$		0			0
$532$	1.00000	−	5.19615i	0.0433555	−	0.225282i
$533$	−12.0000			−0.519778
$534$		0			0
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.00000	+	20.7846i	0.129219	+	0.895257i
$540$		0			0
$541$	7.00000	−	12.1244i	0.300954	−	0.521267i	−0.675399	−	0.737453i	$-0.736028\pi$
$541$	7.00000	−	12.1244i	0.300954	−	0.521267i	0.976352	+	0.216186i	$0.0693618\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−12.0000			−0.514024
$546$		0			0
$547$	−14.0000			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$		0			0
$550$		0			0
$551$	−1.00000	+	1.73205i	−0.0426014	+	0.0737878i
$552$		0			0
$553$	−8.00000	−	6.92820i	−0.340195	−	0.294617i
$554$		0			0
$555$		0			0
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	−5.00000	−	8.66025i	−0.211857	−	0.366947i	0.740439	−	0.672124i	$-0.234618\pi$
$557$	−5.00000	−	8.66025i	−0.211857	−	0.366947i	−0.952296	+	0.305177i	$0.901284\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$	20.0000	−	6.92820i	0.845154	−	0.292770i
$561$		0			0
$562$		0			0
$563$	−5.00000	−	8.66025i	−0.210725	−	0.364986i	0.741217	−	0.671266i	$-0.234249\pi$
$563$	−5.00000	−	8.66025i	−0.210725	−	0.364986i	−0.951942	+	0.306280i	$0.900916\pi$
$564$		0			0
$565$	−12.0000	+	20.7846i	−0.504844	+	0.874415i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.0000	−	17.3205i	0.419222	−	0.726113i	−0.576640	−	0.816999i	$-0.695636\pi$
$569$	10.0000	−	17.3205i	0.419222	−	0.726113i	0.995861	+	0.0908852i	$0.0289696\pi$
$570$		0			0
$571$	−23.5000	−	40.7032i	−0.983444	−	1.70338i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	−23.5000	−	40.7032i	−0.983444	−	1.70338i	−0.334790	−	0.942293i	$-0.608665\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$		0			0
$574$		0			0
$575$	5.00000			0.208514
$576$		0			0
$577$	14.5000	+	25.1147i	0.603643	+	1.04554i	0.992264	+	0.124143i	$0.0396180\pi$
$577$	14.5000	+	25.1147i	0.603643	+	1.04554i	−0.388621	+	0.921397i	$0.627049\pi$
$578$		0			0
$579$		0			0
$580$	−8.00000			−0.332182
$581$	4.50000	−	23.3827i	0.186691	−	0.970077i
$582$		0			0
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.0000			0.619116			0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000			0.619116			0.309558	+	0.950881i	$0.399819\pi$
$588$		0			0
$589$	−10.0000			−0.412043
$590$		0			0
$591$		0			0
$592$	−16.0000	−	27.7128i	−0.657596	−	1.13899i
$593$	3.50000	−	6.06218i	0.143728	−	0.248944i	−0.785170	−	0.619281i	$-0.787424\pi$
$593$	3.50000	−	6.06218i	0.143728	−	0.248944i	0.928898	+	0.370337i	$0.120758\pi$
$594$		0			0
$595$	−7.00000	+	36.3731i	−0.286972	+	1.49115i
$596$	12.0000			0.491539
$597$		0			0
$598$		0			0
$599$	−8.00000	−	13.8564i	−0.326871	−	0.566157i	0.655018	−	0.755613i	$-0.272661\pi$
$599$	−8.00000	−	13.8564i	−0.326871	−	0.566157i	−0.981889	+	0.189456i	$0.939328\pi$
$600$		0			0
$601$	−20.0000			−0.815817			−0.407909	−	0.913023i	$-0.633742\pi$
$601$	−20.0000			−0.815817			−0.407909	+	0.913023i	$0.633742\pi$
$602$		0			0
$603$		0			0
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$		0			0
$607$	9.00000	−	15.5885i	0.365299	−	0.632716i	−0.623525	−	0.781803i	$-0.714300\pi$
$607$	9.00000	−	15.5885i	0.365299	−	0.632716i	0.988824	+	0.149087i	$0.0476335\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.00000	+	8.66025i	−0.202278	+	0.350356i
$612$		0			0
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.863655	+	0.504084i	$0.168170\pi$
$613$	21.5000	+	37.2391i	0.868377	+	1.50407i	0.00472215	+	0.999989i	$0.498497\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.0000			−0.402585			−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000			−0.402585			−0.201292	+	0.979531i	$0.564514\pi$
$618$		0			0
$619$	−19.5000	−	33.7750i	−0.783771	−	1.35753i	−0.929730	−	0.368241i	$-0.879960\pi$
$619$	−19.5000	−	33.7750i	−0.783771	−	1.35753i	0.145959	−	0.989291i	$-0.453373\pi$
$620$	−20.0000	−	34.6410i	−0.803219	−	1.39122i
$621$		0			0
$622$		0			0
$623$	−36.0000	−	31.1769i	−1.44231	−	1.24908i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$		0			0
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	56.0000			2.23287
$630$		0			0
$631$	48.0000			1.91085			0.955425	−	0.295234i	$-0.0953977\pi$
$631$	48.0000			1.91085			0.955425	+	0.295234i	$0.0953977\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.0000	−	27.7128i	0.634941	−	1.09975i
$636$		0			0
$637$	−13.0000	−	5.19615i	−0.515079	−	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	0.999878	+	0.0156233i	$0.00497325\pi$
$641$	13.0000	+	22.5167i	0.513469	+	0.889355i	−0.486409	+	0.873731i	$0.661693\pi$
$642$		0			0
$643$	−9.00000			−0.354925			−0.177463	−	0.984128i	$-0.556789\pi$
$643$	−9.00000			−0.354925			−0.177463	+	0.984128i	$0.556789\pi$
$644$	5.00000	−	25.9808i	0.197028	−	1.02379i
$645$		0			0
$646$		0			0
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$		0			0
$649$	21.0000	−	36.3731i	0.824322	−	1.42777i
$650$		0			0
$651$		0			0
$652$	−18.0000			−0.704934
$653$	−11.5000	+	19.9186i	−0.450030	+	0.779474i	−0.998387	−	0.0567696i	$-0.981920\pi$
$653$	−11.5000	+	19.9186i	−0.450030	+	0.779474i	0.548358	+	0.836244i	$0.315253\pi$
$654$		0			0
$655$	−1.00000	−	1.73205i	−0.0390732	−	0.0676768i
$656$	12.0000	−	20.7846i	0.468521	−	0.811503i
$657$		0			0
$658$		0			0
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$		0			0
$661$	−6.00000	−	10.3923i	−0.233373	−	0.404214i	0.725426	−	0.688301i	$-0.241643\pi$
$661$	−6.00000	−	10.3923i	−0.233373	−	0.404214i	−0.958799	+	0.284087i	$0.908310\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.00000	+	1.73205i	−0.193892	+	0.0671660i
$666$		0			0
$667$	−5.00000	+	8.66025i	−0.193601	+	0.335326i
$668$	−14.0000	−	24.2487i	−0.541676	−	0.938211i
$669$		0			0
$670$		0			0
$671$	−39.0000			−1.50558
$672$		0			0
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$		0			0
$675$		0			0
$676$	−9.00000	−	15.5885i	−0.346154	−	0.599556i
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	−0.957984	−	0.286820i	$-0.907402\pi$
$677$	−6.00000	+	10.3923i	−0.230599	+	0.399409i	0.727386	+	0.686229i	$0.240735\pi$
$678$		0			0
$679$	3.00000	−	15.5885i	0.115129	−	0.598230i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	0.888366	+	0.459136i	$0.151841\pi$
$683$	22.0000	+	38.1051i	0.841807	+	1.45805i	−0.0465592	+	0.998916i	$0.514826\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$		0			0
$687$		0			0
$688$	−24.0000	+	41.5692i	−0.914991	+	1.58481i
$689$	4.00000	+	6.92820i	0.152388	+	0.263944i
$690$		0			0
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	−0.626794	−	0.779185i	$-0.715633\pi$
$691$	9.50000	−	16.4545i	0.361397	−	0.625958i	0.988191	+	0.153227i	$0.0489666\pi$
$692$	8.00000			0.304114
$693$		0			0
$694$		0			0
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$		0			0
$697$	21.0000	+	36.3731i	0.795432	+	1.37773i
$698$		0			0
$699$		0			0
$700$	4.00000	+	3.46410i	0.151186	+	0.130931i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$	12.0000	+	20.7846i	0.452267	+	0.783349i
$705$		0			0
$706$		0			0
$707$	32.5000	−	11.2583i	1.22229	−	0.423413i
$708$		0			0
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−50.0000			−1.87251
$714$		0			0
$715$	−12.0000			−0.448775
$716$	−10.0000	+	17.3205i	−0.373718	+	0.647298i
$717$		0			0
$718$		0			0
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	−0.496527	−	0.868021i	$-0.665392\pi$
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	0.999992	−	0.00400572i	$-0.00127506\pi$
$720$		0			0
$721$	16.0000	+	13.8564i	0.595871	+	0.516040i
$722$		0			0
$723$		0			0
$724$	16.0000	+	27.7128i	0.594635	+	1.02994i
$725$	−1.00000	−	1.73205i	−0.0371391	−	0.0643268i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−42.0000	−	72.7461i	−1.55343	−	2.69061i
$732$		0			0
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	−0.650564	−	0.759452i	$-0.725467\pi$
$733$	9.00000	−	15.5885i	0.332423	−	0.575773i	0.982986	+	0.183679i	$0.0588007\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$		0			0
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	0.945818	+	0.324697i	$0.105262\pi$
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	−0.191714	+	0.981451i	$0.561404\pi$
$740$	−16.0000	+	27.7128i	−0.588172	+	1.01874i
$741$		0			0
$742$		0			0
$743$	44.0000			1.61420			0.807102	−	0.590412i	$-0.201035\pi$
$743$	44.0000			1.61420			0.807102	+	0.590412i	$0.201035\pi$
$744$		0			0
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$		0			0
$747$		0			0
$748$	−42.0000			−1.53567
$749$	36.0000	+	31.1769i	1.31541	+	1.13918i
$750$		0			0
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	−0.277424	−	0.960748i	$-0.589481\pi$
$751$	19.0000	−	32.9090i	0.693320	−	1.20087i	0.970744	−	0.240118i	$-0.0771860\pi$
$752$	−10.0000	−	17.3205i	−0.364662	−	0.631614i
$753$		0			0
$754$		0			0
$755$	16.0000			0.582300
$756$		0			0
$757$	−17.0000			−0.617876			−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000			−0.617876			−0.308938	+	0.951082i	$0.599973\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	−0.761057	−	0.648686i	$-0.775319\pi$
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	0.942306	+	0.334752i	$0.108652\pi$
$762$		0			0
$763$	−15.0000	+	5.19615i	−0.543036	+	0.188113i
$764$	−16.0000			−0.578860
$765$		0			0
$766$		0			0
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$		0			0
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$		0			0
$772$	8.00000	−	13.8564i	0.287926	−	0.498703i
$773$	−18.0000	−	31.1769i	−0.647415	−	1.12136i	−0.983738	−	0.179609i	$-0.942517\pi$
$773$	−18.0000	−	31.1769i	−0.647415	−	1.12136i	0.336323	−	0.941747i	$-0.390817\pi$
$774$		0			0
$775$	5.00000	−	8.66025i	0.179605	−	0.311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.536742	−	0.929665i
$782$		0			0
$783$		0			0
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	5.00000	+	8.66025i	0.178118	+	0.308509i
$789$		0			0
$790$		0			0
$791$	−6.00000	+	31.1769i	−0.213335	+	1.10852i
$792$		0			0
$793$	13.0000	−	22.5167i	0.461644	−	0.799590i
$794$		0			0
$795$		0			0
$796$	−16.0000	+	27.7128i	−0.567105	+	0.982255i
$797$	22.0000			0.779280			0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000			0.779280			0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$	35.0000			1.23821
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.50000	+	2.59808i	−0.0529339	+	0.0916841i
$804$		0			0
$805$	−25.0000	+	8.66025i	−0.881134	+	0.305234i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.0000	−	43.3013i	−0.878953	−	1.52239i	−0.852491	−	0.522742i	$-0.824909\pi$
$809$	−25.0000	−	43.3013i	−0.878953	−	1.52239i	−0.0264621	−	0.999650i	$-0.508424\pi$
$810$		0			0
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$	−10.0000	+	3.46410i	−0.350931	+	0.121566i
$813$		0			0
$814$		0			0
$815$	9.00000	+	15.5885i	0.315256	+	0.546040i
$816$		0			0
$817$	6.00000	−	10.3923i	0.209913	−	0.363581i
$818$		0			0
$819$		0			0
$820$	−24.0000			−0.838116
$821$	−25.5000	+	44.1673i	−0.889956	+	1.54145i	−0.0500305	+	0.998748i	$0.515932\pi$
$821$	−25.5000	+	44.1673i	−0.889956	+	1.54145i	−0.839926	+	0.542702i	$0.817401\pi$
$822$		0			0
$823$	7.50000	+	12.9904i	0.261434	+	0.452816i	0.966623	−	0.256203i	$-0.0824714\pi$
$823$	7.50000	+	12.9904i	0.261434	+	0.452816i	−0.705190	+	0.709019i	$0.749138\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.00000			−0.0695468			−0.0347734	−	0.999395i	$-0.511071\pi$
$827$	−2.00000			−0.0695468			−0.0347734	+	0.999395i	$0.511071\pi$
$828$		0			0
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$		0			0
$831$		0			0
$832$	−16.0000			−0.554700
$833$	7.00000	+	48.4974i	0.242536	+	1.68034i
$834$		0			0
$835$	−14.0000	+	24.2487i	−0.484490	+	0.839161i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$		0			0
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$		0			0
$844$	−8.00000	−	13.8564i	−0.275371	−	0.476957i
$845$	−9.00000	+	15.5885i	−0.309609	+	0.536259i
$846$		0			0
$847$	−4.00000	−	3.46410i	−0.137442	−	0.119028i
$848$	−16.0000			−0.549442
$849$		0			0
$850$		0			0
$851$	20.0000	+	34.6410i	0.685591	+	1.18748i
$852$		0			0
$853$	−5.00000			−0.171197			−0.0855984	−	0.996330i	$-0.527280\pi$
$853$	−5.00000			−0.171197			−0.0855984	+	0.996330i	$0.527280\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$	48.0000			1.63679
$861$		0			0
$862$		0			0
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	−0.949891	−	0.312581i	$-0.898806\pi$
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	0.745649	+	0.666339i	$0.232140\pi$
$864$		0			0
$865$	−4.00000	−	6.92820i	−0.136004	−	0.235566i
$866$		0			0
$867$		0			0
$868$	−40.0000	−	34.6410i	−1.35769	−	1.17579i
$869$	−12.0000			−0.407072
$870$		0			0
$871$	2.00000	+	3.46410i	0.0677674	+	0.117377i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.00000	−	31.1769i	0.202837	−	1.05397i
$876$		0			0
$877$	−18.0000	+	31.1769i	−0.607817	+	1.05277i	0.383783	+	0.923423i	$0.374621\pi$
$877$	−18.0000	+	31.1769i	−0.607817	+	1.05277i	−0.991600	+	0.129346i	$0.958712\pi$
$878$		0			0
$879$		0			0
$880$	12.0000	−	20.7846i	0.404520	−	0.700649i
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$		0			0
$883$	−9.00000			−0.302874			−0.151437	−	0.988467i	$-0.548390\pi$
$883$	−9.00000			−0.302874			−0.151437	+	0.988467i	$0.548390\pi$
$884$	14.0000	−	24.2487i	0.470871	−	0.815572i
$885$		0			0
$886$		0			0
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$		0			0
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$		0			0
$891$		0			0
$892$	2.00000	+	3.46410i	0.0669650	+	0.115987i
$893$	2.50000	+	4.33013i	0.0836593	+	0.144902i
$894$		0			0
$895$	20.0000			0.668526
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$		0			0
$901$	14.0000	−	24.2487i	0.466408	−	0.807842i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	16.0000	−	27.7128i	0.531858	−	0.921205i
$906$		0			0
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	0.882150	−	0.470968i	$-0.156095\pi$
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	−0.848946	+	0.528480i	$0.822762\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$		0			0
$910$		0			0
$911$	50.0000			1.65657			0.828287	−	0.560304i	$-0.189316\pi$
$911$	50.0000			1.65657			0.828287	+	0.560304i	$0.189316\pi$
$912$		0			0
$913$	−13.5000	−	23.3827i	−0.446785	−	0.773854i
$914$		0			0
$915$		0			0
$916$	−2.00000			−0.0660819
$917$	−2.00000	−	1.73205i	−0.0660458	−	0.0571974i
$918$		0			0
$919$	−1.50000	+	2.59808i	−0.0494804	+	0.0857026i	−0.889705	−	0.456536i	$-0.849090\pi$
$919$	−1.50000	+	2.59808i	−0.0494804	+	0.0857026i	0.840224	+	0.542239i	$0.182423\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	20.0000			0.658308
$924$		0			0
$925$	−8.00000			−0.263038
$926$		0			0
$927$		0			0
$928$		0			0
$929$	17.5000	−	30.3109i	0.574156	−	0.994468i	−0.421976	−	0.906607i	$-0.638663\pi$
$929$	17.5000	−	30.3109i	0.574156	−	0.994468i	0.996133	−	0.0878612i	$-0.0280032\pi$
$930$		0			0
$931$	−5.50000	+	4.33013i	−0.180255	+	0.141914i
$932$	−42.0000			−1.37576
$933$		0			0
$934$		0			0
$935$	21.0000	+	36.3731i	0.686773	+	1.18953i
$936$		0			0
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$		0			0
$939$		0			0
$940$	−10.0000	+	17.3205i	−0.326164	+	0.564933i
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	0.989599	+	0.143856i	$0.0459502\pi$
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	−0.370216	+	0.928946i	$0.620716\pi$
$942$		0			0
$943$	−15.0000	+	25.9808i	−0.488467	+	0.846050i
$944$	−56.0000			−1.82264
$945$		0			0
$946$		0			0
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$		0			0
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	1.00000	+	1.73205i	0.0323423	+	0.0560185i
$957$		0			0
$958$		0			0
$959$	−7.50000	+	2.59808i	−0.242188	+	0.0838963i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$		0			0
$963$		0			0
$964$	−8.00000	+	13.8564i	−0.257663	+	0.446285i
$965$	−16.0000			−0.515058
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	−0.973529	−	0.228562i	$-0.926597\pi$
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	0.684706	+	0.728820i	$0.259931\pi$
$972$		0			0
$973$	2.50000	−	12.9904i	0.0801463	−	0.416452i
$974$		0			0
$975$		0			0
$976$	26.0000	+	45.0333i	0.832240	+	1.44148i
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$	−54.0000			−1.72585
$980$	−26.0000	−	10.3923i	−0.830540	−	0.331970i
$981$		0			0
$982$		0			0
$983$	20.0000	+	34.6410i	0.637901	+	1.10488i	0.985893	+	0.167379i	$0.0535304\pi$
$983$	20.0000	+	34.6410i	0.637901	+	1.10488i	−0.347992	+	0.937498i	$0.613136\pi$
$984$		0			0
$985$	5.00000	−	8.66025i	0.159313	−	0.275939i
$986$		0			0
$987$		0			0
$988$	4.00000			0.127257
$989$	30.0000	−	51.9615i	0.953945	−	1.65228i
$990$		0			0
$991$	21.0000	+	36.3731i	0.667087	+	1.15543i	0.978715	+	0.205224i	$0.0657924\pi$
$991$	21.0000	+	36.3731i	0.667087	+	1.15543i	−0.311628	+	0.950204i	$0.600874\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	32.0000			1.01447
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	0.857999	−	0.513651i	$-0.171707\pi$
$997$	−0.500000	−	0.866025i	−0.0158352	−	0.0274273i	−0.873834	+	0.486224i	$0.838374\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.a.856.1		2
3.2	odd	2		399.2.j.b.58.1	✓	2
7.2	even	3		8379.2.a.h.1.1		1
7.4	even	3	inner	1197.2.j.a.172.1		2
7.5	odd	6		8379.2.a.i.1.1		1
21.2	odd	6		2793.2.a.h.1.1		1
21.5	even	6		2793.2.a.g.1.1		1
21.11	odd	6		399.2.j.b.172.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.b.58.1	✓	2	3.2	odd	2
399.2.j.b.172.1	yes	2	21.11	odd	6
1197.2.j.a.172.1		2	7.4	even	3	inner
1197.2.j.a.856.1		2	1.1	even	1	trivial
2793.2.a.g.1.1		1	21.5	even	6
2793.2.a.h.1.1		1	21.2	odd	6
8379.2.a.h.1.1		1	7.2	even	3
8379.2.a.i.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{4} +(1.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(0.500000 - 0.866025i) q^{19} +4.00000 q^{20} +(2.50000 - 4.33013i) q^{23} +(0.500000 + 0.866025i) q^{25} +(5.00000 - 1.73205i) q^{28} -2.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(-4.00000 - 3.46410i) q^{35} +(-4.00000 + 6.92820i) q^{37} -6.00000 q^{41} +12.0000 q^{43} +(3.00000 - 5.19615i) q^{44} +(-2.50000 + 4.33013i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{53} -6.00000 q^{55} +(7.00000 + 12.1244i) q^{59} +(6.50000 - 11.2583i) q^{61} -8.00000 q^{64} +(2.00000 - 3.46410i) q^{65} +(1.00000 + 1.73205i) q^{67} +(7.00000 - 12.1244i) q^{68} +10.0000 q^{71} +(-0.500000 - 0.866025i) q^{73} +2.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(2.00000 - 3.46410i) q^{79} +(4.00000 + 6.92820i) q^{80} +9.00000 q^{83} -14.0000 q^{85} +(9.00000 - 15.5885i) q^{89} +(1.00000 - 5.19615i) q^{91} +10.0000 q^{92} +(-1.00000 - 1.73205i) q^{95} +6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} + 2 q^{5} + q^{7} - 3 q^{11} + 4 q^{13} - 4 q^{16} - 7 q^{17} + q^{19} + 8 q^{20} + 5 q^{23} + q^{25} + 10 q^{28} - 4 q^{29} - 10 q^{31} - 8 q^{35} - 8 q^{37} - 12 q^{41} + 24 q^{43} + 6 q^{44}+ \cdots + 12 q^{97}+O(q^{100}) \) 2 * q + 2 * q^4 + 2 * q^5 + q^7 - 3 * q^11 + 4 * q^13 - 4 * q^16 - 7 * q^17 + q^19 + 8 * q^20 + 5 * q^23 + q^25 + 10 * q^28 - 4 * q^29 - 10 * q^31 - 8 * q^35 - 8 * q^37 - 12 * q^41 + 24 * q^43 + 6 * q^44 - 5 * q^47 - 13 * q^49 + 4 * q^52 + 4 * q^53 - 12 * q^55 + 14 * q^59 + 13 * q^61 - 16 * q^64 + 4 * q^65 + 2 * q^67 + 14 * q^68 + 20 * q^71 - q^73 + 4 * q^76 - 15 * q^77 + 4 * q^79 + 8 * q^80 + 18 * q^83 - 28 * q^85 + 18 * q^89 + 2 * q^91 + 20 * q^92 - 2 * q^95 + 12 * q^97

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