LMFDB - Embedded newform 1197.2.j.a.172.1

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			172.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1197.172
Dual form			1197.2.j.a.856.1

$q$-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 $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		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	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		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	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$		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	0.999694	+	0.0247559i	$0.00788087\pi$
$23$	2.50000	+	4.33013i	0.521286	+	0.902894i	−0.478407	+	0.878138i	$0.658786\pi$
$24$		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	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$		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	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$		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	0.624059	−	0.781377i	$-0.285482\pi$
$47$	−2.50000	−	4.33013i	−0.364662	−	0.631614i	−0.988722	+	0.149763i	$0.952149\pi$
$48$		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	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		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	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.812198	−	0.583382i	$-0.198271\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		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	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	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	−0.893801	−	0.448463i	$-0.851972\pi$
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	0.835281	+	0.549823i	$0.185305\pi$
$74$		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	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	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	0.736644	+	0.676280i	$0.236409\pi$
$89$	9.00000	+	15.5885i	0.953998	+	1.65237i	0.217354	+	0.976093i	$0.430258\pi$
$90$		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	−0.337115	−	0.941464i	$-0.609451\pi$
$101$	6.50000	−	11.2583i	0.646774	−	1.12025i	0.983889	−	0.178782i	$-0.0572157\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	−0.973176	−	0.230063i	$-0.926107\pi$
$109$	−3.00000	+	5.19615i	−0.287348	+	0.497701i	0.685828	+	0.727764i	$0.259440\pi$
$110$		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	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		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	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$		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	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		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	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$		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	0.634214	−	0.773158i	$-0.281324\pi$
$163$	−4.50000	−	7.79423i	−0.352467	−	0.610491i	−0.986681	+	0.162667i	$0.947991\pi$
$164$	−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	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		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	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$		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	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	−0.973315	−	0.229475i	$-0.926299\pi$
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	0.685388	+	0.728178i	$0.259632\pi$
$194$		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	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		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	−0.651015	−	0.759065i	$-0.725657\pi$
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	0.982877	+	0.184263i	$0.0589899\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	−0.972523	−	0.232806i	$-0.925209\pi$
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	0.284645	−	0.958633i	$-0.408124\pi$
$234$		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	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$		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	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$		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	−0.984272	−	0.176659i	$-0.943471\pi$
$263$	−5.50000	+	9.52628i	−0.339145	+	0.587416i	0.645128	+	0.764075i	$0.276804\pi$
$264$		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	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	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	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$		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	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	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	−0.786398	−	0.617720i	$-0.788057\pi$
$311$	2.50000	−	4.33013i	0.141762	−	0.245539i	0.928160	+	0.372181i	$0.121390\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$		0			0
$315$		0			0
$316$	8.00000			0.450035
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$		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	−0.963135	−	0.269019i	$-0.913301\pi$
$331$	−13.0000	−	22.5167i	−0.714545	−	1.23763i	0.248590	−	0.968609i	$-0.420033\pi$
$332$	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	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		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	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$		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	−0.907111	−	0.420892i	$-0.861717\pi$
$359$	−15.5000	−	26.8468i	−0.818059	−	1.41692i	0.0890519	−	0.996027i	$-0.471616\pi$
$360$		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	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	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	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		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	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		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	0.219465	+	0.975620i	$0.429569\pi$
$389$	−14.5000	+	25.1147i	−0.735179	+	1.27337i	−0.954645	+	0.297747i	$0.903765\pi$
$390$		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	0.995802	+	0.0915300i	$0.0291757\pi$
$397$	11.5000	+	19.9186i	0.577168	+	0.999685i	−0.418634	+	0.908155i	$0.637491\pi$
$398$		0			0
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		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	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$		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	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$		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	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	0.999999	−	0.00130426i	$-0.000415158\pi$
$443$	10.5000	+	18.1865i	0.498870	+	0.864068i	−0.501129	+	0.865373i	$0.667082\pi$
$444$		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	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$		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	0.802368	−	0.596830i	$-0.203573\pi$
$467$	−2.50000	−	4.33013i	−0.115686	−	0.200374i	−0.918054	+	0.396456i	$0.870240\pi$
$468$		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	−0.257306	−	0.966330i	$-0.582835\pi$
$479$	15.5000	−	26.8468i	0.708213	−	1.22666i	0.965519	−	0.260331i	$-0.0838317\pi$
$480$		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	−0.887793	−	0.460243i	$-0.847762\pi$
$487$	−1.00000	+	1.73205i	−0.0453143	+	0.0784867i	0.842479	+	0.538730i	$0.181096\pi$
$488$		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	0.968500	−	0.249015i	$-0.0801067\pi$
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	−0.699903	+	0.714238i	$0.746773\pi$
$500$	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	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$		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	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$		0			0
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	−0.950958	−	0.309320i	$-0.899899\pi$
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	0.207600	−	0.978214i	$-0.433435\pi$
$524$	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	0.976352	−	0.216186i	$-0.0693618\pi$
$541$	7.00000	+	12.1244i	0.300954	+	0.521267i	−0.675399	+	0.737453i	$0.736028\pi$
$542$		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	−0.952296	−	0.305177i	$-0.901284\pi$
$557$	−5.00000	+	8.66025i	−0.211857	+	0.366947i	0.740439	+	0.672124i	$0.234618\pi$
$558$		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	−0.951942	−	0.306280i	$-0.900916\pi$
$563$	−5.00000	+	8.66025i	−0.210725	+	0.364986i	0.741217	+	0.671266i	$0.234249\pi$
$564$		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	0.995861	−	0.0908852i	$-0.0289696\pi$
$569$	10.0000	+	17.3205i	0.419222	+	0.726113i	−0.576640	+	0.816999i	$0.695636\pi$
$570$		0			0
$571$	−23.5000	+	40.7032i	−0.983444	+	1.70338i	−0.334790	+	0.942293i	$0.608665\pi$
$571$	−23.5000	+	40.7032i	−0.983444	+	1.70338i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	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	−0.388621	−	0.921397i	$-0.627049\pi$
$577$	14.5000	−	25.1147i	0.603643	−	1.04554i	0.992264	−	0.124143i	$-0.0396180\pi$
$578$		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	0.928898	−	0.370337i	$-0.120758\pi$
$593$	3.50000	+	6.06218i	0.143728	+	0.248944i	−0.785170	+	0.619281i	$0.787424\pi$
$594$		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	−0.981889	−	0.189456i	$-0.939328\pi$
$599$	−8.00000	+	13.8564i	−0.326871	+	0.566157i	0.655018	+	0.755613i	$0.272661\pi$
$600$		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	0.988824	−	0.149087i	$-0.0476335\pi$
$607$	9.00000	+	15.5885i	0.365299	+	0.632716i	−0.623525	+	0.781803i	$0.714300\pi$
$608$		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	0.00472215	−	0.999989i	$-0.498497\pi$
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.863655	−	0.504084i	$-0.168170\pi$
$614$		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	0.145959	+	0.989291i	$0.453373\pi$
$619$	−19.5000	+	33.7750i	−0.783771	+	1.35753i	−0.929730	+	0.368241i	$0.879960\pi$
$620$	−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	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		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	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$		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	0.548358	−	0.836244i	$-0.315253\pi$
$653$	−11.5000	−	19.9186i	−0.450030	−	0.779474i	−0.998387	+	0.0567696i	$0.981920\pi$
$654$		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	−0.958799	−	0.284087i	$-0.908310\pi$
$661$	−6.00000	+	10.3923i	−0.233373	+	0.404214i	0.725426	+	0.688301i	$0.241643\pi$
$662$		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	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$		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	−0.0465592	−	0.998916i	$-0.514826\pi$
$683$	22.0000	−	38.1051i	0.841807	−	1.45805i	0.888366	−	0.459136i	$-0.151841\pi$
$684$		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	0.988191	−	0.153227i	$-0.0489666\pi$
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	−0.626794	+	0.779185i	$0.715633\pi$
$692$	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	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$		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	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$		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	0.982986	−	0.183679i	$-0.0588007\pi$
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	−0.650564	+	0.759452i	$0.725467\pi$
$734$		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	−0.191714	−	0.981451i	$-0.561404\pi$
$739$	20.5000	−	35.5070i	0.754105	−	1.30615i	0.945818	−	0.324697i	$-0.105262\pi$
$740$	−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	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	−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	0.942306	−	0.334752i	$-0.108652\pi$
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	−0.761057	+	0.648686i	$0.775319\pi$
$762$		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	0.336323	+	0.941747i	$0.390817\pi$
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	−0.983738	+	0.179609i	$0.942517\pi$
$774$		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	−0.987367	−	0.158450i	$-0.949350\pi$
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	0.630905	+	0.775860i	$0.282684\pi$
$788$	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	−0.0264621	+	0.999650i	$0.508424\pi$
$809$	−25.0000	+	43.3013i	−0.878953	+	1.52239i	−0.852491	+	0.522742i	$0.824909\pi$
$810$		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	−0.839926	−	0.542702i	$-0.817401\pi$
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.0500305	−	0.998748i	$-0.515932\pi$
$822$		0			0
$823$	7.50000	−	12.9904i	0.261434	−	0.452816i	−0.705190	−	0.709019i	$-0.749138\pi$
$823$	7.50000	−	12.9904i	0.261434	−	0.452816i	0.966623	+	0.256203i	$0.0824714\pi$
$824$		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	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$		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	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	48.0000			1.63679
$861$		0			0
$862$		0			0
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	0.745649	−	0.666339i	$-0.232140\pi$
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	−0.949891	+	0.312581i	$0.898806\pi$
$864$		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	−0.991600	−	0.129346i	$-0.958712\pi$
$877$	−18.0000	−	31.1769i	−0.607817	−	1.05277i	0.383783	−	0.923423i	$-0.374621\pi$
$878$		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	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$		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	−0.848946	−	0.528480i	$-0.822762\pi$
$907$	1.00000	−	1.73205i	0.0332045	−	0.0575118i	0.882150	+	0.470968i	$0.156095\pi$
$908$	−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	0.840224	−	0.542239i	$-0.182423\pi$
$919$	−1.50000	−	2.59808i	−0.0494804	−	0.0857026i	−0.889705	+	0.456536i	$0.849090\pi$
$920$		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	0.996133	+	0.0878612i	$0.0280032\pi$
$929$	17.5000	+	30.3109i	0.574156	+	0.994468i	−0.421976	+	0.906607i	$0.638663\pi$
$930$		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	−0.370216	−	0.928946i	$-0.620716\pi$
$941$	19.0000	−	32.9090i	0.619382	−	1.07280i	0.989599	−	0.143856i	$-0.0459502\pi$
$942$		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	0.602494	−	0.798123i	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$		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	0.684706	−	0.728820i	$-0.259931\pi$
$971$	−9.00000	−	15.5885i	−0.288824	−	0.500257i	−0.973529	+	0.228562i	$0.926597\pi$
$972$		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	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$		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	−0.347992	−	0.937498i	$-0.613136\pi$
$983$	20.0000	−	34.6410i	0.637901	−	1.10488i	0.985893	−	0.167379i	$-0.0535304\pi$
$984$		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	−0.311628	−	0.950204i	$-0.600874\pi$
$991$	21.0000	−	36.3731i	0.667087	−	1.15543i	0.978715	−	0.205224i	$-0.0657924\pi$
$992$		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	−0.873834	−	0.486224i	$-0.838374\pi$
$997$	−0.500000	+	0.866025i	−0.0158352	+	0.0274273i	0.857999	+	0.513651i	$0.171707\pi$
$998$		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.172.1		2
3.2	odd	2		399.2.j.b.172.1	yes	2
7.2	even	3	inner	1197.2.j.a.856.1		2
7.3	odd	6		8379.2.a.i.1.1		1
7.4	even	3		8379.2.a.h.1.1		1
21.2	odd	6		399.2.j.b.58.1	✓	2
21.11	odd	6		2793.2.a.h.1.1		1
21.17	even	6		2793.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.b.58.1	✓	2	21.2	odd	6
399.2.j.b.172.1	yes	2	3.2	odd	2
1197.2.j.a.172.1		2	1.1	even	1	trivial
1197.2.j.a.856.1		2	7.2	even	3	inner
2793.2.a.g.1.1		1	21.17	even	6
2793.2.a.h.1.1		1	21.11	odd	6
8379.2.a.h.1.1		1	7.4	even	3
8379.2.a.i.1.1		1	7.3	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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