LMFDB - Embedded newform 1197.2.j.f.856.2

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 = [4,0,0,-2,0] 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.f.172.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.73205 q^{8} +(-1.50000 - 2.59808i) q^{10} +(-2.59808 - 4.50000i) q^{11} -4.00000 q^{13} +(0.866025 - 4.50000i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.46410 + 6.00000i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.73205 q^{20} -9.00000 q^{22} +(4.33013 - 7.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} +(-3.46410 + 6.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} -3.46410 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.59808 - 4.50000i) q^{32} +12.0000 q^{34} +(0.866025 - 4.50000i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(0.866025 + 1.50000i) q^{38} +(1.50000 - 2.59808i) q^{40} +3.46410 q^{41} -7.00000 q^{43} +(-2.59808 + 4.50000i) q^{44} +(-7.50000 - 12.9904i) q^{46} +(4.33013 - 7.50000i) q^{47} +(5.50000 - 4.33013i) q^{49} +3.46410 q^{50} +(2.00000 + 3.46410i) q^{52} +(1.73205 + 3.00000i) q^{53} -9.00000 q^{55} +(4.33013 - 1.50000i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(3.46410 + 6.00000i) q^{59} +(3.50000 - 6.06218i) q^{61} -3.46410 q^{62} +1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.46410 - 6.00000i) q^{68} +(-6.00000 - 5.19615i) q^{70} +3.46410 q^{71} +(3.50000 + 6.06218i) q^{73} +(6.92820 + 12.0000i) q^{74} +1.00000 q^{76} +(-10.3923 - 9.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(3.00000 - 5.19615i) q^{82} -5.19615 q^{83} +12.0000 q^{85} +(-6.06218 + 10.5000i) q^{86} +(-4.50000 - 7.79423i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-10.0000 + 3.46410i) q^{91} -8.66025 q^{92} +(-7.50000 - 12.9904i) q^{94} +(0.866025 + 1.50000i) q^{95} -10.0000 q^{97} +(-1.73205 - 12.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 10 q^{7} - 6 q^{10} - 16 q^{13} + 10 q^{16} - 2 q^{19} - 36 q^{22} + 4 q^{25} - 8 q^{28} - 4 q^{31} + 48 q^{34} - 16 q^{37} + 6 q^{40} - 28 q^{43} - 30 q^{46} + 22 q^{49} + 8 q^{52} - 36 q^{55}+ \cdots - 40 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 + 10 * q^7 - 6 * q^10 - 16 * q^13 + 10 * q^16 - 2 * q^19 - 36 * q^22 + 4 * q^25 - 8 * q^28 - 4 * q^31 + 48 * q^34 - 16 * q^37 + 6 * q^40 - 28 * q^43 - 30 * q^46 + 22 * q^49 + 8 * q^52 - 36 * q^55 - 12 * q^58 + 14 * q^61 + 4 * q^64 - 16 * q^67 - 24 * q^70 + 14 * q^73 + 4 * q^76 - 16 * q^79 + 12 * q^82 + 48 * q^85 - 18 * q^88 - 40 * q^91 - 30 * q^94 - 40 * 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 $

$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	0.990839	−	0.135045i	$-0.0431180\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	1.73205			0.612372
$9$		0			0
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−2.59808	−	4.50000i	−0.783349	−	1.35680i	−0.929980	−	0.367610i	$-0.880176\pi$
$11$	−2.59808	−	4.50000i	−0.783349	−	1.35680i	0.146631	−	0.989191i	$-0.453157\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	0.866025	−	4.50000i	0.231455	−	1.20268i
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.46410	+	6.00000i	0.840168	+	1.45521i	0.889752	+	0.456444i	$0.150877\pi$
$17$	3.46410	+	6.00000i	0.840168	+	1.45521i	−0.0495842	+	0.998770i	$0.515790\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−1.73205			−0.387298
$21$		0			0
$22$	−9.00000			−1.91881
$23$	4.33013	−	7.50000i	0.902894	−	1.56386i	0.0791743	−	0.996861i	$-0.474772\pi$
$23$	4.33013	−	7.50000i	0.902894	−	1.56386i	0.823720	−	0.566997i	$-0.191895\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−3.46410	+	6.00000i	−0.679366	+	1.17670i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−3.46410			−0.643268			−0.321634	−	0.946864i	$-0.604232\pi$
$29$	−3.46410			−0.643268			−0.321634	+	0.946864i	$0.604232\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−2.59808	−	4.50000i	−0.459279	−	0.795495i
$33$		0			0
$34$	12.0000			2.05798
$35$	0.866025	−	4.50000i	0.146385	−	0.760639i
$36$		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	$0.938240\pi$
$38$	0.866025	+	1.50000i	0.140488	+	0.243332i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	3.46410			0.541002			0.270501	−	0.962720i	$-0.412811\pi$
$41$	3.46410			0.541002			0.270501	+	0.962720i	$0.412811\pi$
$42$		0			0
$43$	−7.00000			−1.06749			−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000			−1.06749			−0.533745	+	0.845645i	$0.679216\pi$
$44$	−2.59808	+	4.50000i	−0.391675	+	0.678401i
$45$		0			0
$46$	−7.50000	−	12.9904i	−1.10581	−	1.91533i
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	−0.355608	−	0.934635i	$-0.615726\pi$
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	0.987222	−	0.159352i	$-0.0509405\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	3.46410			0.489898
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	1.73205	+	3.00000i	0.237915	+	0.412082i	0.960116	−	0.279602i	$-0.0902025\pi$
$53$	1.73205	+	3.00000i	0.237915	+	0.412082i	−0.722200	+	0.691684i	$0.756869\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	4.33013	−	1.50000i	0.578638	−	0.200446i
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	3.46410	+	6.00000i	0.450988	+	0.781133i	0.998448	−	0.0556984i	$-0.0177385\pi$
$59$	3.46410	+	6.00000i	0.450988	+	0.781133i	−0.547460	+	0.836832i	$0.684405\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−3.46410			−0.439941
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.46410	+	6.00000i	−0.429669	+	0.744208i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	3.46410	−	6.00000i	0.420084	−	0.727607i
$69$		0			0
$70$	−6.00000	−	5.19615i	−0.717137	−	0.621059i
$71$	3.46410			0.411113			0.205557	−	0.978645i	$-0.434100\pi$
$71$	3.46410			0.411113			0.205557	+	0.978645i	$0.434100\pi$
$72$		0			0
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	6.92820	+	12.0000i	0.805387	+	1.39497i
$75$		0			0
$76$	1.00000			0.114708
$77$	−10.3923	−	9.00000i	−1.18431	−	1.02565i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	−4.33013	−	7.50000i	−0.484123	−	0.838525i
$81$		0			0
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−5.19615			−0.570352			−0.285176	−	0.958475i	$-0.592052\pi$
$83$	−5.19615			−0.570352			−0.285176	+	0.958475i	$0.592052\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$	−6.06218	+	10.5000i	−0.653701	+	1.13224i
$87$		0			0
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	−0.989126	−	0.147073i	$-0.953015\pi$
$89$	−3.46410	+	6.00000i	−0.367194	+	0.635999i	0.621932	+	0.783072i	$0.286348\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$	−8.66025			−0.902894
$93$		0			0
$94$	−7.50000	−	12.9904i	−0.773566	−	1.33986i
$95$	0.866025	+	1.50000i	0.0888523	+	0.153897i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	−1.73205	−	12.0000i	−0.174964	−	1.21218i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	4.33013	+	7.50000i	0.430864	+	0.746278i	0.996948	−	0.0780696i	$-0.0248756\pi$
$101$	4.33013	+	7.50000i	0.430864	+	0.746278i	−0.566084	+	0.824347i	$0.691542\pi$
$102$		0			0
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	−6.92820			−0.679366
$105$		0			0
$106$	6.00000			0.582772
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.230063	−	0.973176i	$-0.573893\pi$
$110$	−7.79423	+	13.5000i	−0.743151	+	1.28717i
$111$		0			0
$112$	2.50000	−	12.9904i	0.236228	−	1.22748i
$113$	−10.3923			−0.977626			−0.488813	−	0.872389i	$-0.662570\pi$
$113$	−10.3923			−0.977626			−0.488813	+	0.872389i	$0.662570\pi$
$114$		0			0
$115$	−7.50000	−	12.9904i	−0.699379	−	1.21136i
$116$	1.73205	+	3.00000i	0.160817	+	0.278543i
$117$		0			0
$118$	12.0000			1.10469
$119$	13.8564	+	12.0000i	1.27021	+	1.10004i
$120$		0			0
$121$	−8.00000	+	13.8564i	−0.727273	+	1.25967i
$122$	−6.06218	−	10.5000i	−0.548844	−	0.950625i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	12.1244			1.08444
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	6.06218	−	10.5000i	0.535826	−	0.928078i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	−1.73205	+	3.00000i	−0.151330	+	0.262111i	−0.931717	−	0.363186i	$-0.881689\pi$
$131$	−1.73205	+	3.00000i	−0.151330	+	0.262111i	0.780387	+	0.625297i	$0.215022\pi$
$132$		0			0
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	−13.8564			−1.19701
$135$		0			0
$136$	6.00000	+	10.3923i	0.514496	+	0.891133i
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	0.989557	−	0.144142i	$-0.0460423\pi$
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	−0.619609	+	0.784910i	$0.712709\pi$
$138$		0			0
$139$	17.0000			1.44192			0.720961	−	0.692976i	$-0.243701\pi$
$139$	17.0000			1.44192			0.720961	+	0.692976i	$0.243701\pi$
$140$	−4.33013	+	1.50000i	−0.365963	+	0.126773i
$141$		0			0
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$	10.3923	+	18.0000i	0.869048	+	1.50524i
$144$		0			0
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	12.1244			1.00342
$147$		0			0
$148$	8.00000			0.657596
$149$	0.866025	−	1.50000i	0.0709476	−	0.122885i	−0.828369	−	0.560182i	$-0.810731\pi$
$149$	0.866025	−	1.50000i	0.0709476	−	0.122885i	0.899317	+	0.437298i	$0.144064\pi$
$150$		0			0
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.833597	+	0.552372i	$0.186277\pi$
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.0615699	+	0.998103i	$0.480389\pi$
$152$	−0.866025	+	1.50000i	−0.0702439	+	0.121666i
$153$		0			0
$154$	−22.5000	+	7.79423i	−1.81310	+	0.628077i
$155$	−3.46410			−0.278243
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	6.92820	+	12.0000i	0.551178	+	0.954669i
$159$		0			0
$160$	−9.00000			−0.711512
$161$	4.33013	−	22.5000i	0.341262	−	1.77325i
$162$		0			0
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$	−1.73205	−	3.00000i	−0.135250	−	0.234261i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	17.3205			1.34030			0.670151	−	0.742225i	$-0.266230\pi$
$167$	17.3205			1.34030			0.670151	+	0.742225i	$0.266230\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	10.3923	−	18.0000i	0.797053	−	1.38054i
$171$		0			0
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$	3.46410	−	6.00000i	0.263371	−	0.456172i	−0.703765	−	0.710433i	$-0.748499\pi$
$173$	3.46410	−	6.00000i	0.263371	−	0.456172i	0.967135	+	0.254262i	$0.0818324\pi$
$174$		0			0
$175$	4.00000	+	3.46410i	0.302372	+	0.261861i
$176$	−25.9808			−1.95837
$177$		0			0
$178$	6.00000	+	10.3923i	0.449719	+	0.778936i
$179$	5.19615	+	9.00000i	0.388379	+	0.672692i	0.992232	−	0.124404i	$-0.0397019\pi$
$179$	5.19615	+	9.00000i	0.388379	+	0.672692i	−0.603853	+	0.797096i	$0.706369\pi$
$180$		0			0
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$	−3.46410	+	18.0000i	−0.256776	+	1.33425i
$183$		0			0
$184$	7.50000	−	12.9904i	0.552907	−	0.957664i
$185$	6.92820	+	12.0000i	0.509372	+	0.882258i
$186$		0			0
$187$	18.0000	−	31.1769i	1.31629	−	2.27988i
$188$	−8.66025			−0.631614
$189$		0			0
$190$	3.00000			0.217643
$191$	2.59808	−	4.50000i	0.187990	−	0.325609i	−0.756590	−	0.653890i	$-0.773136\pi$
$191$	2.59808	−	4.50000i	0.187990	−	0.325609i	0.944580	+	0.328281i	$0.106469\pi$
$192$		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	$0.926299\pi$
$194$	−8.66025	+	15.0000i	−0.621770	+	1.07694i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−15.5885			−1.11063			−0.555316	−	0.831640i	$-0.687403\pi$
$197$	−15.5885			−1.11063			−0.555316	+	0.831640i	$0.687403\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	1.73205	+	3.00000i	0.122474	+	0.212132i
$201$		0			0
$202$	15.0000			1.05540
$203$	−8.66025	+	3.00000i	−0.607831	+	0.210559i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	12.1244	+	21.0000i	0.844744	+	1.46314i
$207$		0			0
$208$	−10.0000	+	17.3205i	−0.693375	+	1.20096i
$209$	5.19615			0.359425
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	1.73205	−	3.00000i	0.118958	−	0.206041i
$213$		0			0
$214$		0			0
$215$	−6.06218	+	10.5000i	−0.413437	+	0.716094i
$216$		0			0
$217$	−4.00000	−	3.46410i	−0.271538	−	0.235159i
$218$	−34.6410			−2.34619
$219$		0			0
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	−13.8564	−	24.0000i	−0.932083	−	1.61441i
$222$		0			0
$223$	−10.0000			−0.669650			−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000			−0.669650			−0.334825	+	0.942280i	$0.608677\pi$
$224$	−10.3923	−	9.00000i	−0.694365	−	0.601338i
$225$		0			0
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	−0.897173	−	0.441679i	$-0.854383\pi$
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	0.831092	+	0.556136i	$0.187717\pi$
$230$	−25.9808			−1.71312
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.46410	−	6.00000i	0.226941	−	0.393073i	−0.729959	−	0.683491i	$-0.760461\pi$
$233$	3.46410	−	6.00000i	0.226941	−	0.393073i	0.956900	+	0.290418i	$0.0937943\pi$
$234$		0			0
$235$	−7.50000	−	12.9904i	−0.489246	−	0.847399i
$236$	3.46410	−	6.00000i	0.225494	−	0.390567i
$237$		0			0
$238$	30.0000	−	10.3923i	1.94461	−	0.673633i
$239$	10.3923			0.672222			0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923			0.672222			0.336111	+	0.941822i	$0.390888\pi$
$240$		0			0
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$	13.8564	+	24.0000i	0.890724	+	1.54278i
$243$		0			0
$244$	−7.00000			−0.448129
$245$	−1.73205	−	12.0000i	−0.110657	−	0.766652i
$246$		0			0
$247$	2.00000	−	3.46410i	0.127257	−	0.220416i
$248$	−1.73205	−	3.00000i	−0.109985	−	0.190500i
$249$		0			0
$250$	10.5000	−	18.1865i	0.664078	−	1.15022i
$251$	1.73205			0.109326			0.0546630	−	0.998505i	$-0.482592\pi$
$251$	1.73205			0.109326			0.0546630	+	0.998505i	$0.482592\pi$
$252$		0			0
$253$	−45.0000			−2.82913
$254$	17.3205	−	30.0000i	1.08679	−	1.88237i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	12.1244	−	21.0000i	0.756297	−	1.30994i	−0.188431	−	0.982086i	$-0.560340\pi$
$257$	12.1244	−	21.0000i	0.756297	−	1.30994i	0.944727	−	0.327858i	$-0.106327\pi$
$258$		0			0
$259$	−4.00000	+	20.7846i	−0.248548	+	1.29149i
$260$	6.92820			0.429669
$261$		0			0
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	−12.1244	−	21.0000i	−0.747620	−	1.29492i	−0.948961	−	0.315394i	$-0.897863\pi$
$263$	−12.1244	−	21.0000i	−0.747620	−	1.29492i	0.201341	−	0.979521i	$-0.435470\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$	3.46410	+	3.00000i	0.212398	+	0.183942i
$267$		0			0
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	3.46410	+	6.00000i	0.211210	+	0.365826i	0.952093	−	0.305807i	$-0.0989263\pi$
$269$	3.46410	+	6.00000i	0.211210	+	0.365826i	−0.740883	+	0.671634i	$0.765593\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	34.6410			2.10042
$273$		0			0
$274$	15.0000			0.906183
$275$	5.19615	−	9.00000i	0.313340	−	0.542720i
$276$		0			0
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	0.992522	−	0.122068i	$-0.0389525\pi$
$277$	6.50000	+	11.2583i	0.390547	+	0.676448i	−0.601975	+	0.798515i	$0.705619\pi$
$278$	14.7224	−	25.5000i	0.882993	−	1.52939i
$279$		0			0
$280$	1.50000	−	7.79423i	0.0896421	−	0.465794i
$281$	17.3205			1.03325			0.516627	−	0.856210i	$-0.327187\pi$
$281$	17.3205			1.03325			0.516627	+	0.856210i	$0.327187\pi$
$282$		0			0
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$	−1.73205	−	3.00000i	−0.102778	−	0.178017i
$285$		0			0
$286$	36.0000			2.12872
$287$	8.66025	−	3.00000i	0.511199	−	0.177084i
$288$		0			0
$289$	−15.5000	+	26.8468i	−0.911765	+	1.57922i
$290$	5.19615	+	9.00000i	0.305129	+	0.528498i
$291$		0			0
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	−31.1769			−1.82137			−0.910687	−	0.413096i	$-0.864447\pi$
$293$	−31.1769			−1.82137			−0.910687	+	0.413096i	$0.864447\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	−6.92820	+	12.0000i	−0.402694	+	0.697486i
$297$		0			0
$298$	−1.50000	−	2.59808i	−0.0868927	−	0.150503i
$299$	−17.3205	+	30.0000i	−1.00167	+	1.73494i
$300$		0			0
$301$	−17.5000	+	6.06218i	−1.00868	+	0.349418i
$302$	38.1051			2.19270
$303$		0			0
$304$	2.50000	+	4.33013i	0.143385	+	0.248350i
$305$	−6.06218	−	10.5000i	−0.347119	−	0.601228i
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−2.59808	+	13.5000i	−0.148039	+	0.769234i
$309$		0			0
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−15.5885	−	27.0000i	−0.883940	−	1.53103i	−0.846923	−	0.531715i	$-0.821548\pi$
$311$	−15.5885	−	27.0000i	−0.883940	−	1.53103i	−0.0370169	−	0.999315i	$-0.511786\pi$
$312$		0			0
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	0.0863973	+	0.996261i	$0.472465\pi$
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	−0.905986	+	0.423308i	$0.860869\pi$
$314$	22.5167			1.27069
$315$		0			0
$316$	8.00000			0.450035
$317$	1.73205	−	3.00000i	0.0972817	−	0.168497i	−0.813277	−	0.581877i	$-0.802319\pi$
$317$	1.73205	−	3.00000i	0.0972817	−	0.168497i	0.910559	+	0.413380i	$0.135652\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	0.866025	−	1.50000i	0.0484123	−	0.0838525i
$321$		0			0
$322$	−30.0000	−	25.9808i	−1.67183	−	1.44785i
$323$	−6.92820			−0.385496
$324$		0			0
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	9.52628	+	16.5000i	0.527612	+	0.913850i
$327$		0			0
$328$	6.00000			0.331295
$329$	4.33013	−	22.5000i	0.238728	−	1.24047i
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	2.59808	+	4.50000i	0.142588	+	0.246970i
$333$		0			0
$334$	15.0000	−	25.9808i	0.820763	−	1.42160i
$335$	−13.8564			−0.757056
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	2.59808	−	4.50000i	0.141317	−	0.244768i
$339$		0			0
$340$	−6.00000	−	10.3923i	−0.325396	−	0.563602i
$341$	−5.19615	+	9.00000i	−0.281387	+	0.487377i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−12.1244			−0.653701
$345$		0			0
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	0.866025	+	1.50000i	0.0464907	+	0.0805242i	0.888334	−	0.459197i	$-0.151863\pi$
$347$	0.866025	+	1.50000i	0.0464907	+	0.0805242i	−0.841844	+	0.539721i	$0.818530\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	8.66025	−	3.00000i	0.462910	−	0.160357i
$351$		0			0
$352$	−13.5000	+	23.3827i	−0.719552	+	1.24630i
$353$	10.3923	+	18.0000i	0.553127	+	0.958043i	0.998047	+	0.0624731i	$0.0198987\pi$
$353$	10.3923	+	18.0000i	0.553127	+	0.958043i	−0.444920	+	0.895570i	$0.646768\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	6.92820			0.367194
$357$		0			0
$358$	18.0000			0.951330
$359$	−4.33013	+	7.50000i	−0.228535	+	0.395835i	−0.957374	−	0.288850i	$-0.906727\pi$
$359$	−4.33013	+	7.50000i	−0.228535	+	0.395835i	0.728839	+	0.684685i	$0.240060\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	12.1244	−	21.0000i	0.637242	−	1.10374i
$363$		0			0
$364$	8.00000	+	6.92820i	0.419314	+	0.363137i
$365$	12.1244			0.634618
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−21.6506	−	37.5000i	−1.12862	−	1.95482i
$369$		0			0
$370$	24.0000			1.24770
$371$	6.92820	+	6.00000i	0.359694	+	0.311504i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	−31.1769	−	54.0000i	−1.61212	−	2.79227i
$375$		0			0
$376$	7.50000	−	12.9904i	0.386783	−	0.669928i
$377$	13.8564			0.713641
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	0.866025	−	1.50000i	0.0444262	−	0.0769484i
$381$		0			0
$382$	−4.50000	−	7.79423i	−0.230240	−	0.398787i
$383$	−17.3205	+	30.0000i	−0.885037	+	1.53293i	−0.0393649	+	0.999225i	$0.512533\pi$
$383$	−17.3205	+	30.0000i	−0.885037	+	1.53293i	−0.845672	+	0.533703i	$0.820800\pi$
$384$		0			0
$385$	−22.5000	+	7.79423i	−1.14671	+	0.397231i
$386$	−13.8564			−0.705273
$387$		0			0
$388$	5.00000	+	8.66025i	0.253837	+	0.439658i
$389$	−13.8564	−	24.0000i	−0.702548	−	1.21685i	−0.967569	−	0.252606i	$-0.918712\pi$
$389$	−13.8564	−	24.0000i	−0.702548	−	1.21685i	0.265022	−	0.964242i	$-0.414621\pi$
$390$		0			0
$391$	60.0000			3.03433
$392$	9.52628	−	7.50000i	0.481150	−	0.378807i
$393$		0			0
$394$	−13.5000	+	23.3827i	−0.680120	+	1.17800i
$395$	6.92820	+	12.0000i	0.348596	+	0.603786i
$396$		0			0
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	12.1244			0.607739
$399$		0			0
$400$	10.0000			0.500000
$401$	13.8564	−	24.0000i	0.691956	−	1.19850i	−0.279240	−	0.960221i	$-0.590083\pi$
$401$	13.8564	−	24.0000i	0.691956	−	1.19850i	0.971196	−	0.238282i	$-0.0765841\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	4.33013	−	7.50000i	0.215432	−	0.373139i
$405$		0			0
$406$	−3.00000	+	15.5885i	−0.148888	+	0.773642i
$407$	41.5692			2.06051
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$	−5.19615	−	9.00000i	−0.256620	−	0.444478i
$411$		0			0
$412$	14.0000			0.689730
$413$	13.8564	+	12.0000i	0.681829	+	0.590481i
$414$		0			0
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$	10.3923	+	18.0000i	0.509525	+	0.882523i
$417$		0			0
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	−15.5885			−0.761546			−0.380773	−	0.924669i	$-0.624342\pi$
$419$	−15.5885			−0.761546			−0.380773	+	0.924669i	$0.624342\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−3.46410	+	6.00000i	−0.168630	+	0.292075i
$423$		0			0
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−6.92820	+	12.0000i	−0.336067	+	0.582086i
$426$		0			0
$427$	3.50000	−	18.1865i	0.169377	−	0.880108i
$428$		0			0
$429$		0			0
$430$	10.5000	+	18.1865i	0.506355	+	0.877033i
$431$	−19.0526	−	33.0000i	−0.917729	−	1.58955i	−0.802855	−	0.596174i	$-0.796687\pi$
$431$	−19.0526	−	33.0000i	−0.917729	−	1.58955i	−0.114874	−	0.993380i	$-0.536647\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−8.66025	+	3.00000i	−0.415705	+	0.144005i
$435$		0			0
$436$	−10.0000	+	17.3205i	−0.478913	+	0.829502i
$437$	4.33013	+	7.50000i	0.207138	+	0.358774i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$	−15.5885			−0.743151
$441$		0			0
$442$	−48.0000			−2.28313
$443$	1.73205	−	3.00000i	0.0822922	−	0.142534i	−0.821942	−	0.569571i	$-0.807109\pi$
$443$	1.73205	−	3.00000i	0.0822922	−	0.142534i	0.904234	+	0.427037i	$0.140443\pi$
$444$		0			0
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	−20.7846			−0.980886			−0.490443	−	0.871473i	$-0.663165\pi$
$449$	−20.7846			−0.980886			−0.490443	+	0.871473i	$0.663165\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	5.19615	+	9.00000i	0.244406	+	0.423324i
$453$		0			0
$454$		0			0
$455$	−3.46410	+	18.0000i	−0.162400	+	0.843853i
$456$		0			0
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	0.461067	+	0.887365i	$0.347467\pi$
$457$	−11.5000	+	19.9186i	−0.537947	+	0.931752i	−0.999014	+	0.0443868i	$0.985867\pi$
$458$	1.73205	+	3.00000i	0.0809334	+	0.140181i
$459$		0			0
$460$	−7.50000	+	12.9904i	−0.349689	+	0.605680i
$461$	8.66025			0.403348			0.201674	−	0.979453i	$-0.435362\pi$
$461$	8.66025			0.403348			0.201674	+	0.979453i	$0.435362\pi$
$462$		0			0
$463$	−7.00000			−0.325318			−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000			−0.325318			−0.162659	+	0.986682i	$0.552007\pi$
$464$	−8.66025	+	15.0000i	−0.402042	+	0.696358i
$465$		0			0
$466$	−6.00000	−	10.3923i	−0.277945	−	0.481414i
$467$	−18.1865	+	31.5000i	−0.841572	+	1.45765i	0.0469925	+	0.998895i	$0.485036\pi$
$467$	−18.1865	+	31.5000i	−0.841572	+	1.45765i	−0.888565	+	0.458751i	$0.848297\pi$
$468$		0			0
$469$	−16.0000	−	13.8564i	−0.738811	−	0.639829i
$470$	−25.9808			−1.19840
$471$		0			0
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	18.1865	+	31.5000i	0.836218	+	1.44837i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$	3.46410	−	18.0000i	0.158777	−	0.825029i
$477$		0			0
$478$	9.00000	−	15.5885i	0.411650	−	0.712999i
$479$	−11.2583	−	19.5000i	−0.514406	−	0.890978i	−0.999860	−	0.0167156i	$-0.994679\pi$
$479$	−11.2583	−	19.5000i	−0.514406	−	0.890978i	0.485454	−	0.874262i	$-0.338654\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$	48.4974			2.20900
$483$		0			0
$484$	16.0000			0.727273
$485$	−8.66025	+	15.0000i	−0.393242	+	0.681115i
$486$		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	$0.847762\pi$
$488$	6.06218	−	10.5000i	0.274422	−	0.475313i
$489$		0			0
$490$	−19.5000	−	7.79423i	−0.880920	−	0.352107i
$491$	−22.5167			−1.01616			−0.508081	−	0.861309i	$-0.669645\pi$
$491$	−22.5167			−1.01616			−0.508081	+	0.861309i	$0.669645\pi$
$492$		0			0
$493$	−12.0000	−	20.7846i	−0.540453	−	0.936092i
$494$	−3.46410	−	6.00000i	−0.155857	−	0.269953i
$495$		0			0
$496$	−10.0000			−0.449013
$497$	8.66025	−	3.00000i	0.388465	−	0.134568i
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	−6.06218	−	10.5000i	−0.271109	−	0.469574i
$501$		0			0
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	1.73205			0.0772283			0.0386142	−	0.999254i	$-0.487706\pi$
$503$	1.73205			0.0772283			0.0386142	+	0.999254i	$0.487706\pi$
$504$		0			0
$505$	15.0000			0.667491
$506$	−38.9711	+	67.5000i	−1.73248	+	3.00074i
$507$		0			0
$508$	−10.0000	−	17.3205i	−0.443678	−	0.768473i
$509$	−19.0526	+	33.0000i	−0.844490	+	1.46270i	0.0415737	+	0.999135i	$0.486763\pi$
$509$	−19.0526	+	33.0000i	−0.844490	+	1.46270i	−0.886064	+	0.463564i	$0.846570\pi$
$510$		0			0
$511$	14.0000	+	12.1244i	0.619324	+	0.536350i
$512$	−8.66025			−0.382733
$513$		0			0
$514$	−21.0000	−	36.3731i	−0.926270	−	1.60435i
$515$	12.1244	+	21.0000i	0.534263	+	0.925371i
$516$		0			0
$517$	−45.0000			−1.97910
$518$	27.7128	+	24.0000i	1.21763	+	1.05450i
$519$		0			0
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	−1.00000	+	1.73205i	−0.0437269	+	0.0757373i	−0.887061	−	0.461653i	$-0.847256\pi$
$523$	−1.00000	+	1.73205i	−0.0437269	+	0.0757373i	0.843334	+	0.537390i	$0.180590\pi$
$524$	3.46410			0.151330
$525$		0			0
$526$	−42.0000			−1.83129
$527$	6.92820	−	12.0000i	0.301797	−	0.522728i
$528$		0			0
$529$	−26.0000	−	45.0333i	−1.13043	−	1.95797i
$530$	5.19615	−	9.00000i	0.225706	−	0.390935i
$531$		0			0
$532$	2.50000	−	0.866025i	0.108389	−	0.0375470i
$533$	−13.8564			−0.600188
$534$		0			0
$535$		0			0
$536$	−6.92820	−	12.0000i	−0.299253	−	0.518321i
$537$		0			0
$538$	12.0000			0.517357
$539$	−33.7750	−	13.5000i	−1.45479	−	0.581486i
$540$		0			0
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	9.52628	+	16.5000i	0.409189	+	0.708736i
$543$		0			0
$544$	18.0000	−	31.1769i	0.771744	−	1.33670i
$545$	−34.6410			−1.48386
$546$		0			0
$547$	38.0000			1.62476			0.812381	−	0.583127i	$-0.198171\pi$
$547$	38.0000			1.62476			0.812381	+	0.583127i	$0.198171\pi$
$548$	4.33013	−	7.50000i	0.184974	−	0.320384i
$549$		0			0
$550$	−9.00000	−	15.5885i	−0.383761	−	0.664694i
$551$	1.73205	−	3.00000i	0.0737878	−	0.127804i
$552$		0			0
$553$	−4.00000	+	20.7846i	−0.170097	+	0.883852i
$554$	22.5167			0.956641
$555$		0			0
$556$	−8.50000	−	14.7224i	−0.360480	−	0.624370i
$557$	9.52628	+	16.5000i	0.403641	+	0.699127i	0.994162	−	0.107895i	$-0.0344110\pi$
$557$	9.52628	+	16.5000i	0.403641	+	0.699127i	−0.590521	+	0.807022i	$0.701078\pi$
$558$		0			0
$559$	28.0000			1.18427
$560$	−17.3205	−	15.0000i	−0.731925	−	0.633866i
$561$		0			0
$562$	15.0000	−	25.9808i	0.632737	−	1.09593i
$563$	−10.3923	−	18.0000i	−0.437983	−	0.758610i	0.559550	−	0.828796i	$-0.310974\pi$
$563$	−10.3923	−	18.0000i	−0.437983	−	0.758610i	−0.997534	+	0.0701867i	$0.977640\pi$
$564$		0			0
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	53.6936			2.25691
$567$		0			0
$568$	6.00000			0.251754
$569$	−15.5885	+	27.0000i	−0.653502	+	1.13190i	0.328765	+	0.944412i	$0.393368\pi$
$569$	−15.5885	+	27.0000i	−0.653502	+	1.13190i	−0.982267	+	0.187487i	$0.939966\pi$
$570$		0			0
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	0.999638	+	0.0268925i	$0.00856117\pi$
$571$	12.5000	+	21.6506i	0.523109	+	0.906051i	−0.476530	+	0.879158i	$0.658105\pi$
$572$	10.3923	−	18.0000i	0.434524	−	0.752618i
$573$		0			0
$574$	3.00000	−	15.5885i	0.125218	−	0.650650i
$575$	17.3205			0.722315
$576$		0			0
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	0.633062	−	0.774101i	$-0.281798\pi$
$577$	−8.50000	−	14.7224i	−0.353860	−	0.612903i	−0.986922	+	0.161198i	$0.948464\pi$
$578$	26.8468	+	46.5000i	1.11668	+	1.93415i
$579$		0			0
$580$	6.00000			0.249136
$581$	−12.9904	+	4.50000i	−0.538932	+	0.186691i
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$	6.06218	+	10.5000i	0.250855	+	0.434493i
$585$		0			0
$586$	−27.0000	+	46.7654i	−1.11536	+	1.93186i
$587$	3.46410			0.142979			0.0714894	−	0.997441i	$-0.477225\pi$
$587$	3.46410			0.142979			0.0714894	+	0.997441i	$0.477225\pi$
$588$		0			0
$589$	2.00000			0.0824086
$590$	10.3923	−	18.0000i	0.427844	−	0.741048i
$591$		0			0
$592$	20.0000	+	34.6410i	0.821995	+	1.42374i
$593$	4.33013	−	7.50000i	0.177817	−	0.307988i	−0.763316	−	0.646026i	$-0.776430\pi$
$593$	4.33013	−	7.50000i	0.177817	−	0.307988i	0.941133	+	0.338038i	$0.109763\pi$
$594$		0			0
$595$	30.0000	−	10.3923i	1.22988	−	0.426043i
$596$	−1.73205			−0.0709476
$597$		0			0
$598$	30.0000	+	51.9615i	1.22679	+	2.12486i
$599$	−8.66025	−	15.0000i	−0.353848	−	0.612883i	0.633072	−	0.774093i	$-0.281794\pi$
$599$	−8.66025	−	15.0000i	−0.353848	−	0.612883i	−0.986920	+	0.161210i	$0.948460\pi$
$600$		0			0
$601$	−40.0000			−1.63163			−0.815817	−	0.578310i	$-0.803712\pi$
$601$	−40.0000			−1.63163			−0.815817	+	0.578310i	$0.803712\pi$
$602$	−6.06218	+	31.5000i	−0.247076	+	1.28384i
$603$		0			0
$604$	11.0000	−	19.0526i	0.447584	−	0.775238i
$605$	13.8564	+	24.0000i	0.563343	+	0.975739i
$606$		0			0
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	0.588537	+	0.808470i	$0.299704\pi$
$608$	5.19615			0.210732
$609$		0			0
$610$	−21.0000			−0.850265
$611$	−17.3205	+	30.0000i	−0.700713	+	1.21367i
$612$		0			0
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	1.73205	−	3.00000i	0.0698999	−	0.121070i
$615$		0			0
$616$	−18.0000	−	15.5885i	−0.725241	−	0.628077i
$617$	−19.0526			−0.767027			−0.383514	−	0.923535i	$-0.625286\pi$
$617$	−19.0526			−0.767027			−0.383514	+	0.923535i	$0.625286\pi$
$618$		0			0
$619$	−20.5000	−	35.5070i	−0.823965	−	1.42715i	−0.902708	−	0.430254i	$-0.858424\pi$
$619$	−20.5000	−	35.5070i	−0.823965	−	1.42715i	0.0787435	−	0.996895i	$-0.474909\pi$
$620$	1.73205	+	3.00000i	0.0695608	+	0.120483i
$621$		0			0
$622$	−54.0000			−2.16520
$623$	−3.46410	+	18.0000i	−0.138786	+	0.721155i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	25.1147	+	43.5000i	1.00379	+	1.73861i
$627$		0			0
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	−55.4256			−2.20996
$630$		0			0
$631$	−13.0000			−0.517522			−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000			−0.517522			−0.258761	+	0.965941i	$0.583314\pi$
$632$	−6.92820	+	12.0000i	−0.275589	+	0.477334i
$633$		0			0
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	17.3205	−	30.0000i	0.687343	−	1.19051i
$636$		0			0
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$	31.1769			1.23431
$639$		0			0
$640$	−10.5000	−	18.1865i	−0.415049	−	0.718886i
$641$	−6.92820	−	12.0000i	−0.273648	−	0.473972i	0.696145	−	0.717901i	$-0.254897\pi$
$641$	−6.92820	−	12.0000i	−0.273648	−	0.473972i	−0.969793	+	0.243929i	$0.921564\pi$
$642$		0			0
$643$	32.0000			1.26196			0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000			1.26196			0.630978	+	0.775800i	$0.282654\pi$
$644$	−21.6506	+	7.50000i	−0.853155	+	0.295541i
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−12.9904	−	22.5000i	−0.510705	−	0.884566i	−0.999923	−	0.0124050i	$-0.996051\pi$
$647$	−12.9904	−	22.5000i	−0.510705	−	0.884566i	0.489218	−	0.872161i	$-0.337282\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$	−13.8564			−0.543493
$651$		0			0
$652$	11.0000			0.430793
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$	3.00000	+	5.19615i	0.117220	+	0.203030i
$656$	8.66025	−	15.0000i	0.338126	−	0.585652i
$657$		0			0
$658$	−30.0000	−	25.9808i	−1.16952	−	1.01284i
$659$	17.3205			0.674711			0.337356	−	0.941377i	$-0.390468\pi$
$659$	17.3205			0.674711			0.337356	+	0.941377i	$0.390468\pi$
$660$		0			0
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	0.777689	−	0.628649i	$-0.216392\pi$
$661$	−4.00000	−	6.92820i	−0.155582	−	0.269476i	−0.933271	+	0.359174i	$0.883059\pi$
$662$	12.1244	+	21.0000i	0.471226	+	0.816188i
$663$		0			0
$664$	−9.00000			−0.349268
$665$	3.46410	+	3.00000i	0.134332	+	0.116335i
$666$		0			0
$667$	−15.0000	+	25.9808i	−0.580802	+	1.00598i
$668$	−8.66025	−	15.0000i	−0.335075	−	0.580367i
$669$		0			0
$670$	−12.0000	+	20.7846i	−0.463600	+	0.802980i
$671$	−36.3731			−1.40417
$672$		0			0
$673$	−4.00000			−0.154189			−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000			−0.154189			−0.0770943	+	0.997024i	$0.524564\pi$
$674$	12.1244	−	21.0000i	0.467013	−	0.808890i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	10.3923	−	18.0000i	0.399409	−	0.691796i	−0.594244	−	0.804285i	$-0.702549\pi$
$677$	10.3923	−	18.0000i	0.399409	−	0.691796i	0.993653	+	0.112488i	$0.0358821\pi$
$678$		0			0
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$	20.7846			0.797053
$681$		0			0
$682$	9.00000	+	15.5885i	0.344628	+	0.596913i
$683$	−5.19615	−	9.00000i	−0.198825	−	0.344375i	0.749323	−	0.662205i	$-0.230379\pi$
$683$	−5.19615	−	9.00000i	−0.198825	−	0.344375i	−0.948148	+	0.317830i	$0.897046\pi$
$684$		0			0
$685$	15.0000			0.573121
$686$	−14.7224	−	28.5000i	−0.562105	−	1.08814i
$687$		0			0
$688$	−17.5000	+	30.3109i	−0.667181	+	1.15559i
$689$	−6.92820	−	12.0000i	−0.263944	−	0.457164i
$690$		0			0
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	−0.825473	−	0.564441i	$-0.809092\pi$
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	0.901557	+	0.432660i	$0.142425\pi$
$692$	−6.92820			−0.263371
$693$		0			0
$694$	3.00000			0.113878
$695$	14.7224	−	25.5000i	0.558454	−	0.967270i
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−8.66025	+	15.0000i	−0.327795	+	0.567758i
$699$		0			0
$700$	1.00000	−	5.19615i	0.0377964	−	0.196396i
$701$	−1.73205			−0.0654187			−0.0327093	−	0.999465i	$-0.510414\pi$
$701$	−1.73205			−0.0654187			−0.0327093	+	0.999465i	$0.510414\pi$
$702$		0			0
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	−2.59808	−	4.50000i	−0.0979187	−	0.169600i
$705$		0			0
$706$	36.0000			1.35488
$707$	17.3205	+	15.0000i	0.651405	+	0.564133i
$708$		0			0
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$	−5.19615	−	9.00000i	−0.195008	−	0.337764i
$711$		0			0
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	−17.3205			−0.648658
$714$		0			0
$715$	36.0000			1.34632
$716$	5.19615	−	9.00000i	0.194189	−	0.336346i
$717$		0			0
$718$	7.50000	+	12.9904i	0.279898	+	0.484797i
$719$	−1.73205	+	3.00000i	−0.0645946	+	0.111881i	−0.896514	−	0.443015i	$-0.853909\pi$
$719$	−1.73205	+	3.00000i	−0.0645946	+	0.111881i	0.831919	+	0.554896i	$0.187242\pi$
$720$		0			0
$721$	−7.00000	+	36.3731i	−0.260694	+	1.35460i
$722$	−1.73205			−0.0644603
$723$		0			0
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−3.46410	−	6.00000i	−0.128654	−	0.222834i
$726$		0			0
$727$	11.0000			0.407967			0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000			0.407967			0.203984	+	0.978974i	$0.434611\pi$
$728$	−17.3205	+	6.00000i	−0.641941	+	0.222375i
$729$		0			0
$730$	10.5000	−	18.1865i	0.388622	−	0.673114i
$731$	−24.2487	−	42.0000i	−0.896871	−	1.55343i
$732$		0			0
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	−13.8564			−0.511449
$735$		0			0
$736$	−45.0000			−1.65872
$737$	−20.7846	+	36.0000i	−0.765611	+	1.32608i
$738$		0			0
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	−0.994420	−	0.105493i	$-0.966358\pi$
$739$	−16.0000	−	27.7128i	−0.588570	−	1.01943i	0.405851	−	0.913939i	$-0.366975\pi$
$740$	6.92820	−	12.0000i	0.254686	−	0.441129i
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	34.6410			1.27086			0.635428	−	0.772160i	$-0.280824\pi$
$743$	34.6410			1.27086			0.635428	+	0.772160i	$0.280824\pi$
$744$		0			0
$745$	−1.50000	−	2.59808i	−0.0549557	−	0.0951861i
$746$	−3.46410	−	6.00000i	−0.126830	−	0.219676i
$747$		0			0
$748$	−36.0000			−1.31629
$749$		0			0
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	−21.6506	−	37.5000i	−0.789517	−	1.36748i
$753$		0			0
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$	38.1051			1.38679
$756$		0			0
$757$	41.0000			1.49017			0.745085	−	0.666969i	$-0.232409\pi$
$757$	41.0000			1.49017			0.745085	+	0.666969i	$0.232409\pi$
$758$	−13.8564	+	24.0000i	−0.503287	+	0.871719i
$759$		0			0
$760$	1.50000	+	2.59808i	0.0544107	+	0.0942421i
$761$	7.79423	−	13.5000i	0.282541	−	0.489375i	−0.689469	−	0.724315i	$-0.742156\pi$
$761$	7.79423	−	13.5000i	0.282541	−	0.489375i	0.972010	+	0.234940i	$0.0754895\pi$
$762$		0			0
$763$	−40.0000	−	34.6410i	−1.44810	−	1.25409i
$764$	−5.19615			−0.187990
$765$		0			0
$766$	30.0000	+	51.9615i	1.08394	+	1.87745i
$767$	−13.8564	−	24.0000i	−0.500326	−	0.866590i
$768$		0			0
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$	−7.79423	+	40.5000i	−0.280885	+	1.45952i
$771$		0			0
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	17.3205	+	30.0000i	0.622975	+	1.07903i	0.988929	+	0.148392i	$0.0474097\pi$
$773$	17.3205	+	30.0000i	0.622975	+	1.07903i	−0.365953	+	0.930633i	$0.619257\pi$
$774$		0			0
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	−17.3205			−0.621770
$777$		0			0
$778$	−48.0000			−1.72088
$779$	−1.73205	+	3.00000i	−0.0620572	+	0.107486i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	51.9615	−	90.0000i	1.85814	−	3.21839i
$783$		0			0
$784$	−5.00000	−	34.6410i	−0.178571	−	1.23718i
$785$	22.5167			0.803654
$786$		0			0
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	7.79423	+	13.5000i	0.277658	+	0.480918i
$789$		0			0
$790$	24.0000			0.853882
$791$	−25.9808	+	9.00000i	−0.923770	+	0.320003i
$792$		0			0
$793$	−14.0000	+	24.2487i	−0.497155	+	0.861097i
$794$	1.73205	+	3.00000i	0.0614682	+	0.106466i
$795$		0			0
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	60.0000			2.12265
$800$	5.19615	−	9.00000i	0.183712	−	0.318198i
$801$		0			0
$802$	−24.0000	−	41.5692i	−0.847469	−	1.46786i
$803$	18.1865	−	31.5000i	0.641789	−	1.11161i
$804$		0			0
$805$	−30.0000	−	25.9808i	−1.05736	−	0.915702i
$806$	13.8564			0.488071
$807$		0			0
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	2.59808	+	4.50000i	0.0913435	+	0.158212i	0.908077	−	0.418804i	$-0.137551\pi$
$809$	2.59808	+	4.50000i	0.0913435	+	0.158212i	−0.816733	+	0.577016i	$0.804217\pi$
$810$		0			0
$811$	−22.0000			−0.772524			−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000			−0.772524			−0.386262	+	0.922389i	$0.626234\pi$
$812$	6.92820	+	6.00000i	0.243132	+	0.210559i
$813$		0			0
$814$	36.0000	−	62.3538i	1.26180	−	2.18550i
$815$	9.52628	+	16.5000i	0.333691	+	0.577970i
$816$		0			0
$817$	3.50000	−	6.06218i	0.122449	−	0.212089i
$818$	−24.2487			−0.847836
$819$		0			0
$820$	−6.00000			−0.209529
$821$	25.1147	−	43.5000i	0.876510	−	1.51816i	0.0213653	−	0.999772i	$-0.493199\pi$
$821$	25.1147	−	43.5000i	0.876510	−	1.51816i	0.855145	−	0.518389i	$-0.173468\pi$
$822$		0			0
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	−0.963119	−	0.269075i	$-0.913282\pi$
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	0.248534	−	0.968623i	$-0.420051\pi$
$824$	−12.1244	+	21.0000i	−0.422372	+	0.731570i
$825$		0			0
$826$	30.0000	−	10.3923i	1.04383	−	0.361595i
$827$	27.7128			0.963669			0.481834	−	0.876262i	$-0.339971\pi$
$827$	27.7128			0.963669			0.481834	+	0.876262i	$0.339971\pi$
$828$		0			0
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	0.999875	−	0.0158163i	$-0.00503471\pi$
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	−0.513635	+	0.858009i	$0.671701\pi$
$830$	7.79423	+	13.5000i	0.270542	+	0.468592i
$831$		0			0
$832$	−4.00000			−0.138675
$833$	45.0333	+	18.0000i	1.56031	+	0.623663i
$834$		0			0
$835$	15.0000	−	25.9808i	0.519096	−	0.899101i
$836$	−2.59808	−	4.50000i	−0.0898563	−	0.155636i
$837$		0			0
$838$	−13.5000	+	23.3827i	−0.466350	+	0.807741i
$839$	−27.7128			−0.956753			−0.478376	−	0.878155i	$-0.658774\pi$
$839$	−27.7128			−0.956753			−0.478376	+	0.878155i	$0.658774\pi$
$840$		0			0
$841$	−17.0000			−0.586207
$842$	1.73205	−	3.00000i	0.0596904	−	0.103387i
$843$		0			0
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	2.59808	−	4.50000i	0.0893765	−	0.154805i
$846$		0			0
$847$	−8.00000	+	41.5692i	−0.274883	+	1.42834i
$848$	17.3205			0.594789
$849$		0			0
$850$	12.0000	+	20.7846i	0.411597	+	0.712906i
$851$	34.6410	+	60.0000i	1.18748	+	2.05677i
$852$		0			0
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	−24.2487	−	21.0000i	−0.829774	−	0.718605i
$855$		0			0
$856$		0			0
$857$	−17.3205	−	30.0000i	−0.591657	−	1.02478i	−0.994009	−	0.109295i	$-0.965141\pi$
$857$	−17.3205	−	30.0000i	−0.591657	−	1.02478i	0.402352	−	0.915485i	$-0.368193\pi$
$858$		0			0
$859$	18.5000	−	32.0429i	0.631212	−	1.09329i	−0.356092	−	0.934451i	$-0.615891\pi$
$859$	18.5000	−	32.0429i	0.631212	−	1.09329i	0.987304	−	0.158840i	$-0.0507755\pi$
$860$	12.1244			0.413437
$861$		0			0
$862$	−66.0000			−2.24797
$863$	−5.19615	+	9.00000i	−0.176879	+	0.306364i	−0.940810	−	0.338935i	$-0.889933\pi$
$863$	−5.19615	+	9.00000i	−0.176879	+	0.306364i	0.763931	+	0.645298i	$0.223267\pi$
$864$		0			0
$865$	−6.00000	−	10.3923i	−0.204006	−	0.353349i
$866$	−3.46410	+	6.00000i	−0.117715	+	0.203888i
$867$		0			0
$868$	−1.00000	+	5.19615i	−0.0339422	+	0.176369i
$869$	41.5692			1.41014
$870$		0			0
$871$	16.0000	+	27.7128i	0.542139	+	0.939013i
$872$	−17.3205	−	30.0000i	−0.586546	−	1.01593i
$873$		0			0
$874$	15.0000			0.507383
$875$	30.3109	−	10.5000i	1.02470	−	0.354965i
$876$		0			0
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	−0.526767	−	0.850010i	$-0.676596\pi$
$877$	14.0000	−	24.2487i	0.472746	−	0.818821i	0.999514	+	0.0311889i	$0.00992933\pi$
$878$	−24.2487	−	42.0000i	−0.818354	−	1.41743i
$879$		0			0
$880$	−22.5000	+	38.9711i	−0.758475	+	1.31372i
$881$	20.7846			0.700251			0.350126	−	0.936703i	$-0.386139\pi$
$881$	20.7846			0.700251			0.350126	+	0.936703i	$0.386139\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−13.8564	+	24.0000i	−0.466041	+	0.807207i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	1.73205	−	3.00000i	0.0581566	−	0.100730i	−0.835481	−	0.549519i	$-0.814811\pi$
$887$	1.73205	−	3.00000i	0.0581566	−	0.100730i	0.893638	+	0.448789i	$0.148144\pi$
$888$		0			0
$889$	50.0000	−	17.3205i	1.67695	−	0.580911i
$890$	20.7846			0.696702
$891$		0			0
$892$	5.00000	+	8.66025i	0.167412	+	0.289967i
$893$	4.33013	+	7.50000i	0.144902	+	0.250978i
$894$		0			0
$895$	18.0000			0.601674
$896$	6.06218	−	31.5000i	0.202523	−	1.05234i
$897$		0			0
$898$	−18.0000	+	31.1769i	−0.600668	+	1.04039i
$899$	3.46410	+	6.00000i	0.115534	+	0.200111i
$900$		0			0
$901$	−12.0000	+	20.7846i	−0.399778	+	0.692436i
$902$	−31.1769			−1.03808
$903$		0			0
$904$	−18.0000			−0.598671
$905$	12.1244	−	21.0000i	0.403027	−	0.698064i
$906$		0			0
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$		0			0
$909$		0			0
$910$	24.0000	+	20.7846i	0.795592	+	0.689003i
$911$	31.1769			1.03294			0.516469	−	0.856306i	$-0.327246\pi$
$911$	31.1769			1.03294			0.516469	+	0.856306i	$0.327246\pi$
$912$		0			0
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	19.9186	+	34.5000i	0.658848	+	1.14116i
$915$		0			0
$916$	2.00000			0.0660819
$917$	−1.73205	+	9.00000i	−0.0571974	+	0.297206i
$918$		0			0
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	−0.971481	−	0.237119i	$-0.923797\pi$
$919$	−8.50000	+	14.7224i	−0.280389	+	0.485648i	0.691091	+	0.722767i	$0.257130\pi$
$920$	−12.9904	−	22.5000i	−0.428280	−	0.741803i
$921$		0			0
$922$	7.50000	−	12.9904i	0.246999	−	0.427815i
$923$	−13.8564			−0.456089
$924$		0			0
$925$	−16.0000			−0.526077
$926$	−6.06218	+	10.5000i	−0.199216	+	0.345051i
$927$		0			0
$928$	9.00000	+	15.5885i	0.295439	+	0.511716i
$929$	21.6506	−	37.5000i	0.710334	−	1.23034i	−0.254397	−	0.967100i	$-0.581877\pi$
$929$	21.6506	−	37.5000i	0.710334	−	1.23034i	0.964732	−	0.263235i	$-0.0847896\pi$
$930$		0			0
$931$	1.00000	+	6.92820i	0.0327737	+	0.227063i
$932$	−6.92820			−0.226941
$933$		0			0
$934$	31.5000	+	54.5596i	1.03071	+	1.78524i
$935$	−31.1769	−	54.0000i	−1.01959	−	1.76599i
$936$		0			0
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$	−34.6410	+	12.0000i	−1.13107	+	0.391814i
$939$		0			0
$940$	−7.50000	+	12.9904i	−0.244623	+	0.423700i
$941$	1.73205	+	3.00000i	0.0564632	+	0.0977972i	0.892875	−	0.450304i	$-0.148684\pi$
$941$	1.73205	+	3.00000i	0.0564632	+	0.0977972i	−0.836412	+	0.548101i	$0.815351\pi$
$942$		0			0
$943$	15.0000	−	25.9808i	0.488467	−	0.846050i
$944$	34.6410			1.12747
$945$		0			0
$946$	63.0000			2.04831
$947$	8.66025	−	15.0000i	0.281420	−	0.487435i	−0.690314	−	0.723510i	$-0.742528\pi$
$947$	8.66025	−	15.0000i	0.281420	−	0.487435i	0.971735	+	0.236075i	$0.0758611\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	−1.73205	+	3.00000i	−0.0561951	+	0.0973329i
$951$		0			0
$952$	24.0000	+	20.7846i	0.777844	+	0.673633i
$953$	−48.4974			−1.57099			−0.785493	−	0.618871i	$-0.787590\pi$
$953$	−48.4974			−1.57099			−0.785493	+	0.618871i	$0.787590\pi$
$954$		0			0
$955$	−4.50000	−	7.79423i	−0.145617	−	0.252215i
$956$	−5.19615	−	9.00000i	−0.168056	−	0.291081i
$957$		0			0
$958$	−39.0000			−1.26003
$959$	17.3205	+	15.0000i	0.559308	+	0.484375i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−27.7128	−	48.0000i	−0.893497	−	1.54758i
$963$		0			0
$964$	14.0000	−	24.2487i	0.450910	−	0.780998i
$965$	−13.8564			−0.446054
$966$		0			0
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−13.8564	+	24.0000i	−0.445362	+	0.771389i
$969$		0			0
$970$	15.0000	+	25.9808i	0.481621	+	0.834192i
$971$	−6.92820	+	12.0000i	−0.222337	+	0.385098i	−0.955517	−	0.294936i	$-0.904702\pi$
$971$	−6.92820	+	12.0000i	−0.222337	+	0.385098i	0.733180	+	0.680034i	$0.238035\pi$
$972$		0			0
$973$	42.5000	−	14.7224i	1.36249	−	0.471979i
$974$	−3.46410			−0.110997
$975$		0			0
$976$	−17.5000	−	30.3109i	−0.560161	−	0.970228i
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$	36.0000			1.15056
$980$	−9.52628	+	7.50000i	−0.304306	+	0.239579i
$981$		0			0
$982$	−19.5000	+	33.7750i	−0.622270	+	1.07780i
$983$	−22.5167	−	39.0000i	−0.718170	−	1.24391i	−0.961724	−	0.274020i	$-0.911647\pi$
$983$	−22.5167	−	39.0000i	−0.718170	−	1.24391i	0.243554	−	0.969887i	$-0.421687\pi$
$984$		0			0
$985$	−13.5000	+	23.3827i	−0.430146	+	0.745034i
$986$	−41.5692			−1.32383
$987$		0			0
$988$	−4.00000			−0.127257
$989$	−30.3109	+	52.5000i	−0.963830	+	1.66940i
$990$		0			0
$991$	26.0000	+	45.0333i	0.825917	+	1.43053i	0.901216	+	0.433370i	$0.142676\pi$
$991$	26.0000	+	45.0333i	0.825917	+	1.43053i	−0.0752991	+	0.997161i	$0.523991\pi$
$992$	−5.19615	+	9.00000i	−0.164978	+	0.285750i
$993$		0			0
$994$	3.00000	−	15.5885i	0.0951542	−	0.494436i
$995$	12.1244			0.384368
$996$		0			0
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	−0.992558	−	0.121771i	$-0.961143\pi$
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	0.390822	−	0.920466i	$-0.372191\pi$
$998$	4.33013	+	7.50000i	0.137068	+	0.237408i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.f.856.2	yes	4
3.2	odd	2	inner	1197.2.j.f.856.1	yes	4
7.2	even	3		8379.2.a.be.1.1		2
7.4	even	3	inner	1197.2.j.f.172.2	yes	4
7.5	odd	6		8379.2.a.bb.1.1		2
21.2	odd	6		8379.2.a.be.1.2		2
21.5	even	6		8379.2.a.bb.1.2		2
21.11	odd	6	inner	1197.2.j.f.172.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1197.2.j.f.172.1	✓	4	21.11	odd	6	inner
1197.2.j.f.172.2	yes	4	7.4	even	3	inner
1197.2.j.f.856.1	yes	4	3.2	odd	2	inner
1197.2.j.f.856.2	yes	4	1.1	even	1	trivial
8379.2.a.bb.1.1		2	7.5	odd	6
8379.2.a.bb.1.2		2	21.5	even	6
8379.2.a.be.1.1		2	7.2	even	3
8379.2.a.be.1.2		2	21.2	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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.73205 q^{8} +(-1.50000 - 2.59808i) q^{10} +(-2.59808 - 4.50000i) q^{11} -4.00000 q^{13} +(0.866025 - 4.50000i) q^{14} +(2.50000 - 4.33013i) q^{16} +(3.46410 + 6.00000i) q^{17} +(-0.500000 + 0.866025i) q^{19} -1.73205 q^{20} -9.00000 q^{22} +(4.33013 - 7.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} +(-3.46410 + 6.00000i) q^{26} +(-2.00000 - 1.73205i) q^{28} -3.46410 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.59808 - 4.50000i) q^{32} +12.0000 q^{34} +(0.866025 - 4.50000i) q^{35} +(-4.00000 + 6.92820i) q^{37} +(0.866025 + 1.50000i) q^{38} +(1.50000 - 2.59808i) q^{40} +3.46410 q^{41} -7.00000 q^{43} +(-2.59808 + 4.50000i) q^{44} +(-7.50000 - 12.9904i) q^{46} +(4.33013 - 7.50000i) q^{47} +(5.50000 - 4.33013i) q^{49} +3.46410 q^{50} +(2.00000 + 3.46410i) q^{52} +(1.73205 + 3.00000i) q^{53} -9.00000 q^{55} +(4.33013 - 1.50000i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(3.46410 + 6.00000i) q^{59} +(3.50000 - 6.06218i) q^{61} -3.46410 q^{62} +1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +(-4.00000 - 6.92820i) q^{67} +(3.46410 - 6.00000i) q^{68} +(-6.00000 - 5.19615i) q^{70} +3.46410 q^{71} +(3.50000 + 6.06218i) q^{73} +(6.92820 + 12.0000i) q^{74} +1.00000 q^{76} +(-10.3923 - 9.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.33013 - 7.50000i) q^{80} +(3.00000 - 5.19615i) q^{82} -5.19615 q^{83} +12.0000 q^{85} +(-6.06218 + 10.5000i) q^{86} +(-4.50000 - 7.79423i) q^{88} +(-3.46410 + 6.00000i) q^{89} +(-10.0000 + 3.46410i) q^{91} -8.66025 q^{92} +(-7.50000 - 12.9904i) q^{94} +(0.866025 + 1.50000i) q^{95} -10.0000 q^{97} +(-1.73205 - 12.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 10 q^{7} - 6 q^{10} - 16 q^{13} + 10 q^{16} - 2 q^{19} - 36 q^{22} + 4 q^{25} - 8 q^{28} - 4 q^{31} + 48 q^{34} - 16 q^{37} + 6 q^{40} - 28 q^{43} - 30 q^{46} + 22 q^{49} + 8 q^{52} - 36 q^{55}+ \cdots - 40 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 + 10 * q^7 - 6 * q^10 - 16 * q^13 + 10 * q^16 - 2 * q^19 - 36 * q^22 + 4 * q^25 - 8 * q^28 - 4 * q^31 + 48 * q^34 - 16 * q^37 + 6 * q^40 - 28 * q^43 - 30 * q^46 + 22 * q^49 + 8 * q^52 - 36 * q^55 - 12 * q^58 + 14 * q^61 + 4 * q^64 - 16 * q^67 - 24 * q^70 + 14 * q^73 + 4 * q^76 - 16 * q^79 + 12 * q^82 + 48 * q^85 - 18 * q^88 - 40 * q^91 - 30 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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