LMFDB - Embedded newform 819.2.bm.a.550.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(478,819)] 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("819.478"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-2,-3] 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:	$6.53974792554$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.a.478.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.73205i q^{2} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-3.00000 - 3.46410i) q^{14} -5.00000 q^{16} -6.00000 q^{17} +(-1.50000 - 0.866025i) q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} +(-1.00000 + 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} +(2.00000 - 1.73205i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-1.50000 - 0.866025i) q^{31} -5.19615i q^{32} -10.3923i q^{34} +(1.50000 - 4.33013i) q^{35} +(1.50000 - 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(-4.50000 + 2.59808i) q^{44} +(-7.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-3.00000 - 1.73205i) q^{50} +(1.00000 - 3.46410i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 + 7.79423i) q^{55} +(-3.00000 - 3.46410i) q^{56} +(4.50000 + 2.59808i) q^{58} -3.46410i q^{59} +(-3.50000 + 6.06218i) q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-1.50000 - 6.06218i) q^{65} +(7.50000 - 4.33013i) q^{67} +6.00000 q^{68} +(7.50000 + 2.59808i) q^{70} +(-1.50000 + 0.866025i) q^{71} +(7.50000 + 4.33013i) q^{73} +(1.50000 + 0.866025i) q^{76} +(-4.50000 + 12.9904i) q^{77} +(2.50000 + 4.33013i) q^{79} +(7.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(16.5000 - 9.52628i) q^{86} +(4.50000 + 7.79423i) q^{88} +6.92820i q^{89} +(-4.00000 - 8.66025i) q^{91} +(-7.50000 - 12.9904i) q^{94} +3.00000 q^{95} +(-4.50000 + 2.59808i) q^{97} +(12.0000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 3 q^{5} - 4 q^{7} - 3 q^{10} + 9 q^{11} - 2 q^{13} - 6 q^{14} - 10 q^{16} - 12 q^{17} - 3 q^{19} + 3 q^{20} + 9 q^{22} - 2 q^{25} - 12 q^{26} + 4 q^{28} + 3 q^{29} - 3 q^{31} + 3 q^{35}+ \cdots + 24 q^{98}+O(q^{100}) $ 2 * q - 2 * q^4 - 3 * q^5 - 4 * q^7 - 3 * q^10 + 9 * q^11 - 2 * q^13 - 6 * q^14 - 10 * q^16 - 12 * q^17 - 3 * q^19 + 3 * q^20 + 9 * q^22 - 2 * q^25 - 12 * q^26 + 4 * q^28 + 3 * q^29 - 3 * q^31 + 3 * q^35 + 3 * q^38 - 3 * q^40 + 9 * q^41 - 11 * q^43 - 9 * q^44 - 15 * q^47 + 2 * q^49 - 6 * q^50 + 2 * q^52 - 9 * q^53 - 9 * q^55 - 6 * q^56 + 9 * q^58 - 7 * q^61 + 3 * q^62 - 2 * q^64 - 3 * q^65 + 15 * q^67 + 12 * q^68 + 15 * q^70 - 3 * q^71 + 15 * q^73 + 3 * q^76 - 9 * q^77 + 5 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^85 + 33 * q^86 + 9 * q^88 - 8 * q^91 - 15 * q^94 + 6 * q^95 - 9 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.73205i			1.22474i	0.790569	+	0.612372i	$0.209785\pi$
$2$			1.73205i			1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$			1.73205i			0.612372i
$9$		0			0
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.367610	−	0.929980i	$-0.380176\pi$
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.989191	+	0.146631i	$0.0468429\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	−3.00000	−	3.46410i	−0.801784	−	0.925820i
$15$		0			0
$16$	−5.00000			−1.25000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	0.317970	−	0.948101i	$-0.396999\pi$
$19$	−1.50000	−	0.866025i	−0.344124	−	0.198680i	−0.662094	+	0.749421i	$0.730332\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$		0			0
$22$	4.50000	+	7.79423i	0.959403	+	1.66174i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−6.00000	−	1.73205i	−1.17670	−	0.339683i
$27$		0			0
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		−	5.19615i		−	0.918559i
$33$		0			0
$34$		−	10.3923i		−	1.78227i
$35$	1.50000	−	4.33013i	0.253546	−	0.731925i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	4.50000	+	2.59808i	0.702782	+	0.405751i	0.808383	−	0.588657i	$-0.200343\pi$
$41$	4.50000	+	2.59808i	0.702782	+	0.405751i	−0.105601	+	0.994409i	$0.533677\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	−4.50000	+	2.59808i	−0.678401	+	0.391675i
$45$		0			0
$46$		0			0
$47$	−7.50000	+	4.33013i	−1.09399	+	0.631614i	−0.934635	−	0.355608i	$-0.884274\pi$
$47$	−7.50000	+	4.33013i	−1.09399	+	0.631614i	−0.159352	+	0.987222i	$0.550941\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−3.00000	−	1.73205i	−0.424264	−	0.244949i
$51$		0			0
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	−4.50000	+	7.79423i	−0.606780	+	1.05097i
$56$	−3.00000	−	3.46410i	−0.400892	−	0.462910i
$57$		0			0
$58$	4.50000	+	2.59808i	0.590879	+	0.341144i
$59$		−	3.46410i		−	0.450988i	−0.974245	−	0.225494i	$-0.927600\pi$
$59$		−	3.46410i		−	0.450988i	0.974245	−	0.225494i	$-0.0723995\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$	1.50000	−	2.59808i	0.190500	−	0.329956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.50000	−	6.06218i	−0.186052	−	0.751921i
$66$		0			0
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.0338274	−	0.999428i	$-0.489230\pi$
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.882443	+	0.470418i	$0.155897\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$	7.50000	+	2.59808i	0.896421	+	0.310530i
$71$	−1.50000	+	0.866025i	−0.178017	+	0.102778i	−0.586361	−	0.810050i	$-0.699440\pi$
$71$	−1.50000	+	0.866025i	−0.178017	+	0.102778i	0.408344	+	0.912828i	$0.366107\pi$
$72$		0			0
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.869935	−	0.493166i	$-0.164160\pi$
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.00787336	+	0.999969i	$0.497494\pi$
$74$		0			0
$75$		0			0
$76$	1.50000	+	0.866025i	0.172062	+	0.0993399i
$77$	−4.50000	+	12.9904i	−0.512823	+	1.48039i
$78$		0			0
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$	7.50000	−	4.33013i	0.838525	−	0.484123i
$81$		0			0
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	9.00000	−	5.19615i	0.976187	−	0.563602i
$86$	16.5000	−	9.52628i	1.77924	−	1.02725i
$87$		0			0
$88$	4.50000	+	7.79423i	0.479702	+	0.830868i
$89$			6.92820i			0.734388i	0.930144	+	0.367194i	$0.119682\pi$
$89$			6.92820i			0.734388i	−0.930144	+	0.367194i	$0.880318\pi$
$90$		0			0
$91$	−4.00000	−	8.66025i	−0.419314	−	0.907841i
$92$		0			0
$93$		0			0
$94$	−7.50000	−	12.9904i	−0.773566	−	1.33986i
$95$	3.00000			0.307794
$96$		0			0
$97$	−4.50000	+	2.59808i	−0.456906	+	0.263795i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−4.50000	+	2.59808i	−0.456906	+	0.263795i	0.253837	+	0.967247i	$0.418307\pi$
$98$	12.0000	+	1.73205i	1.21218	+	0.174964i
$99$		0			0
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	−13.5000	−	7.79423i	−1.31124	−	0.757042i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−4.50000	−	2.59808i	−0.431022	−	0.248851i	0.268760	−	0.963207i	$-0.413386\pi$
$109$	−4.50000	−	2.59808i	−0.431022	−	0.248851i	−0.699782	+	0.714357i	$0.746719\pi$
$110$	−13.5000	−	7.79423i	−1.28717	−	0.743151i
$111$		0			0
$112$	10.0000	−	8.66025i	0.944911	−	0.818317i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$		0			0
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$		0			0
$118$	6.00000			0.552345
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$	−10.5000	−	6.06218i	−0.950625	−	0.548844i
$123$		0			0
$124$	1.50000	+	0.866025i	0.134704	+	0.0777714i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$		−	12.1244i		−	1.07165i
$129$		0			0
$130$	10.5000	−	2.59808i	0.920911	−	0.227866i
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	0.981824	+	0.189794i	$0.0607819\pi$
$131$	7.50000	+	12.9904i	0.655278	+	1.13497i	−0.326546	+	0.945181i	$0.605885\pi$
$132$		0			0
$133$	4.50000	−	0.866025i	0.390199	−	0.0750939i
$134$	7.50000	+	12.9904i	0.647901	+	1.12220i
$135$		0			0
$136$		−	10.3923i		−	0.891133i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$	−1.50000	+	4.33013i	−0.126773	+	0.365963i
$141$		0			0
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$	4.50000	+	18.1865i	0.376309	+	1.52083i
$144$		0			0
$145$			5.19615i			0.431517i
$146$	−7.50000	+	12.9904i	−0.620704	+	1.07509i
$147$		0			0
$148$		0			0
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.988492	−	0.151272i	$-0.0483370\pi$
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.363241	+	0.931695i	$0.381670\pi$
$150$		0			0
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	0.862159	−	0.506637i	$-0.169112\pi$
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	−0.00768132	+	0.999970i	$0.502445\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$		0			0
$154$	−22.5000	−	7.79423i	−1.81310	−	0.628077i
$155$	3.00000			0.240966
$156$		0			0
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.115050	+	0.993360i	$0.536703\pi$
$157$	−11.5000	+	19.9186i	−0.917800	+	1.58968i	−0.802749	+	0.596316i	$0.796630\pi$
$158$	−7.50000	+	4.33013i	−0.596668	+	0.344486i
$159$		0			0
$160$	4.50000	+	7.79423i	0.355756	+	0.616188i
$161$		0			0
$162$		0			0
$163$	10.5000	+	6.06218i	0.822423	+	0.474826i	0.851251	−	0.524758i	$-0.175844\pi$
$163$	10.5000	+	6.06218i	0.822423	+	0.474826i	−0.0288280	+	0.999584i	$0.509178\pi$
$164$	−4.50000	−	2.59808i	−0.351391	−	0.202876i
$165$		0			0
$166$	−6.00000			−0.465690
$167$	1.50000	+	0.866025i	0.116073	+	0.0670151i	0.556913	−	0.830571i	$-0.311986\pi$
$167$	1.50000	+	0.866025i	0.116073	+	0.0670151i	−0.440839	+	0.897586i	$0.645319\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	9.00000	+	15.5885i	0.690268	+	1.19558i
$171$		0			0
$172$	5.50000	+	9.52628i	0.419371	+	0.726372i
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	−0.426329	−	0.904568i	$-0.640193\pi$
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	0.996544	−	0.0830722i	$-0.0264732\pi$
$174$		0			0
$175$	−1.00000	−	5.19615i	−0.0755929	−	0.392792i
$176$	−22.5000	+	12.9904i	−1.69600	+	0.979187i
$177$		0			0
$178$	−12.0000			−0.899438
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	15.0000	−	6.92820i	1.11187	−	0.513553i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−27.0000	+	15.5885i	−1.97444	+	1.13994i
$188$	7.50000	−	4.33013i	0.546994	−	0.315807i
$189$		0			0
$190$			5.19615i			0.376969i
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$		0			0
$193$	1.50000	−	0.866025i	0.107972	−	0.0623379i	−0.445041	−	0.895510i	$-0.646811\pi$
$193$	1.50000	−	0.866025i	0.107972	−	0.0623379i	0.553014	+	0.833172i	$0.313478\pi$
$194$	−4.50000	−	7.79423i	−0.323081	−	0.559593i
$195$		0			0
$196$	−1.00000	+	6.92820i	−0.0714286	+	0.494872i
$197$	−19.5000	−	11.2583i	−1.38932	−	0.802123i	−0.396079	−	0.918216i	$-0.629629\pi$
$197$	−19.5000	−	11.2583i	−1.38932	−	0.802123i	−0.993238	+	0.116094i	$0.962963\pi$
$198$		0			0
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	−3.00000	−	1.73205i	−0.212132	−	0.122474i
$201$		0			0
$202$	13.5000	−	7.79423i	0.949857	−	0.548400i
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	−9.00000			−0.628587
$206$	−19.5000	+	11.2583i	−1.35863	+	0.784405i
$207$		0			0
$208$	5.00000	−	17.3205i	0.346688	−	1.20096i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$		0			0
$215$	16.5000	+	9.52628i	1.12529	+	0.649687i
$216$		0			0
$217$	4.50000	−	0.866025i	0.305480	−	0.0587896i
$218$	4.50000	−	7.79423i	0.304778	−	0.527892i
$219$		0			0
$220$	4.50000	−	7.79423i	0.303390	−	0.525487i
$221$	6.00000	−	20.7846i	0.403604	−	1.39812i
$222$		0			0
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	0.643046	−	0.765828i	$-0.277671\pi$
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	−0.341703	+	0.939808i	$0.611004\pi$
$224$	9.00000	+	10.3923i	0.601338	+	0.694365i
$225$		0			0
$226$	−22.5000	+	12.9904i	−1.49668	+	0.864107i
$227$		−	17.3205i		−	1.14960i	−0.818293	−	0.574801i	$-0.805079\pi$
$227$		−	17.3205i		−	1.14960i	0.818293	−	0.574801i	$-0.194921\pi$
$228$		0			0
$229$	−10.5000	+	6.06218i	−0.693860	+	0.400600i	−0.805056	−	0.593198i	$-0.797865\pi$
$229$	−10.5000	+	6.06218i	−0.693860	+	0.400600i	0.111197	+	0.993798i	$0.464532\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	+	2.59808i	0.295439	+	0.170572i
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	0.910968	−	0.412477i	$-0.135336\pi$
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	−0.812700	+	0.582683i	$0.802003\pi$
$234$		0			0
$235$	7.50000	−	12.9904i	0.489246	−	0.847399i
$236$			3.46410i			0.225494i
$237$		0			0
$238$	18.0000	+	20.7846i	1.16677	+	1.34727i
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$			6.92820i			0.446285i	0.974786	+	0.223142i	$0.0716315\pi$
$241$			6.92820i			0.446285i	−0.974786	+	0.223142i	$0.928369\pi$
$242$	24.0000	+	13.8564i	1.54278	+	0.890724i
$243$		0			0
$244$	3.50000	−	6.06218i	0.224065	−	0.388091i
$245$	4.50000	+	11.2583i	0.287494	+	0.719268i
$246$		0			0
$247$	4.50000	−	4.33013i	0.286328	−	0.275519i
$248$	1.50000	−	2.59808i	0.0952501	−	0.164978i
$249$		0			0
$250$	21.0000			1.32816
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	−0.814795	+	0.579748i	$0.803151\pi$
$252$		0			0
$253$		0			0
$254$	−19.5000	−	11.2583i	−1.22354	−	0.706410i
$255$		0			0
$256$	19.0000			1.18750
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$		0			0
$259$		0			0
$260$	1.50000	+	6.06218i	0.0930261	+	0.375960i
$261$		0			0
$262$	−22.5000	+	12.9904i	−1.39005	+	0.802548i
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	0.908560	−	0.417755i	$-0.137183\pi$
$263$	1.50000	+	2.59808i	0.0924940	+	0.160204i	−0.816066	+	0.577959i	$0.803849\pi$
$264$		0			0
$265$		−	15.5885i		−	0.957591i
$266$	1.50000	+	7.79423i	0.0919709	+	0.477895i
$267$		0			0
$268$	−7.50000	+	4.33013i	−0.458135	+	0.264505i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$		0			0
$271$		−	17.3205i		−	1.05215i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$		−	17.3205i		−	1.05215i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$		0			0
$275$			10.3923i			0.626680i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	−19.5000	+	11.2583i	−1.16953	+	0.675230i
$279$		0			0
$280$	7.50000	+	2.59808i	0.448211	+	0.155265i
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$		0			0
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	−0.997076	−	0.0764162i	$-0.975652\pi$
$283$	−9.50000	−	16.4545i	−0.564716	−	0.978117i	0.432360	−	0.901701i	$-0.357681\pi$
$284$	1.50000	−	0.866025i	0.0890086	−	0.0513892i
$285$		0			0
$286$	−31.5000	+	7.79423i	−1.86263	+	0.460882i
$287$	−13.5000	+	2.59808i	−0.796880	+	0.153360i
$288$		0			0
$289$	19.0000			1.11765
$290$	−9.00000			−0.528498
$291$		0			0
$292$	−7.50000	−	4.33013i	−0.438904	−	0.253402i
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.331632	−	0.943409i	$-0.392401\pi$
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.982832	+	0.184503i	$0.0590674\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$		0			0
$297$		0			0
$298$	−16.5000	+	28.5788i	−0.955819	+	1.65553i
$299$		0			0
$300$		0			0
$301$	27.5000	+	9.52628i	1.58507	+	0.549086i
$302$	−10.5000	+	18.1865i	−0.604207	+	1.04652i
$303$		0			0
$304$	7.50000	+	4.33013i	0.430155	+	0.248350i
$305$		−	12.1244i		−	0.694239i
$306$		0			0
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$	4.50000	−	12.9904i	0.256411	−	0.740196i
$309$		0			0
$310$			5.19615i			0.295122i
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	−0.996447	−	0.0842210i	$-0.973160\pi$
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	0.571161	+	0.820838i	$0.306493\pi$
$312$		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	$-0.347098\pi$
$314$	−34.5000	−	19.9186i	−1.94695	−	1.12407i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	4.50000	−	2.59808i	0.252745	−	0.145922i	−0.368275	−	0.929717i	$-0.620052\pi$
$317$	4.50000	−	2.59808i	0.252745	−	0.145922i	0.621021	+	0.783794i	$0.286718\pi$
$318$		0			0
$319$		−	15.5885i		−	0.872786i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$		0			0
$322$		0			0
$323$	9.00000	+	5.19615i	0.500773	+	0.289122i
$324$		0			0
$325$	−5.00000	−	5.19615i	−0.277350	−	0.288231i
$326$	−10.5000	+	18.1865i	−0.581541	+	1.00726i
$327$		0			0
$328$	−4.50000	+	7.79423i	−0.248471	+	0.430364i
$329$	7.50000	−	21.6506i	0.413488	−	1.19364i
$330$		0			0
$331$	28.5000	+	16.4545i	1.56650	+	0.904420i	0.996572	+	0.0827265i	$0.0263628\pi$
$331$	28.5000	+	16.4545i	1.56650	+	0.904420i	0.569929	+	0.821694i	$0.306971\pi$
$332$		−	3.46410i		−	0.190117i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	−7.50000	+	12.9904i	−0.409769	+	0.709740i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	12.0000	−	19.0526i	0.652714	−	1.03632i
$339$		0			0
$340$	−9.00000	+	5.19615i	−0.488094	+	0.281801i
$341$	−9.00000			−0.487377
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	16.5000	−	9.52628i	0.889620	−	0.513623i
$345$		0			0
$346$	22.5000	+	12.9904i	1.20961	+	0.698367i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$	−4.50000	−	2.59808i	−0.240879	−	0.139072i	0.374701	−	0.927146i	$-0.377745\pi$
$349$	−4.50000	−	2.59808i	−0.240879	−	0.139072i	−0.615581	+	0.788074i	$0.711079\pi$
$350$	9.00000	−	1.73205i	0.481070	−	0.0925820i
$351$		0			0
$352$	−13.5000	−	23.3827i	−0.719552	−	1.24630i
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	−0.539387	−	0.842058i	$-0.681344\pi$
$353$	−1.50000	+	0.866025i	−0.0798369	+	0.0460939i	0.459550	+	0.888152i	$0.348011\pi$
$354$		0			0
$355$	1.50000	−	2.59808i	0.0796117	−	0.137892i
$356$		−	6.92820i		−	0.367194i
$357$		0			0
$358$	−4.50000	+	2.59808i	−0.237832	+	0.137313i
$359$	16.5000	−	9.52628i	0.870837	−	0.502778i	0.00321050	−	0.999995i	$-0.498978\pi$
$359$	16.5000	−	9.52628i	0.870837	−	0.502778i	0.867626	+	0.497217i	$0.165645\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$			3.46410i			0.182069i
$363$		0			0
$364$	4.00000	+	8.66025i	0.209657	+	0.453921i
$365$	−15.0000			−0.785136
$366$		0			0
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.50000	−	23.3827i	−0.233628	−	1.21397i
$372$		0			0
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	−0.999956	−	0.00933789i	$-0.997028\pi$
$373$	−9.50000	+	16.4545i	−0.491891	+	0.851981i	0.508065	+	0.861319i	$0.330361\pi$
$374$	−27.0000	−	46.7654i	−1.39614	−	2.41818i
$375$		0			0
$376$	−7.50000	−	12.9904i	−0.386783	−	0.669928i
$377$	7.50000	+	7.79423i	0.386270	+	0.401423i
$378$		0			0
$379$	−1.50000	−	0.866025i	−0.0770498	−	0.0444847i	0.460980	−	0.887410i	$-0.347498\pi$
$379$	−1.50000	−	0.866025i	−0.0770498	−	0.0444847i	−0.538030	+	0.842926i	$0.680831\pi$
$380$	−3.00000			−0.153897
$381$		0			0
$382$	−22.5000	−	12.9904i	−1.15120	−	0.664646i
$383$	13.5000	+	7.79423i	0.689818	+	0.398266i	0.803544	−	0.595246i	$-0.202945\pi$
$383$	13.5000	+	7.79423i	0.689818	+	0.398266i	−0.113726	+	0.993512i	$0.536279\pi$
$384$		0			0
$385$	−4.50000	−	23.3827i	−0.229341	−	1.19169i
$386$	1.50000	+	2.59808i	0.0763480	+	0.132239i
$387$		0			0
$388$	4.50000	−	2.59808i	0.228453	−	0.131897i
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		0			0
$391$		0			0
$392$	12.0000	+	1.73205i	0.606092	+	0.0874818i
$393$		0			0
$394$	19.5000	−	33.7750i	0.982396	−	1.70156i
$395$	−7.50000	−	4.33013i	−0.377366	−	0.217872i
$396$		0			0
$397$	31.5000	+	18.1865i	1.58094	+	0.912756i	0.994722	+	0.102602i	$0.0327168\pi$
$397$	31.5000	+	18.1865i	1.58094	+	0.912756i	0.586217	+	0.810154i	$0.300617\pi$
$398$			6.92820i			0.347279i
$399$		0			0
$400$	5.00000	−	8.66025i	0.250000	−	0.433013i
$401$			6.92820i			0.345978i	0.984924	+	0.172989i	$0.0553425\pi$
$401$			6.92820i			0.345978i	−0.984924	+	0.172989i	$0.944657\pi$
$402$		0			0
$403$	4.50000	−	4.33013i	0.224161	−	0.215699i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$	−13.5000	+	2.59808i	−0.669994	+	0.128940i
$407$		0			0
$408$		0			0
$409$		−	6.92820i		−	0.342578i	−0.985221	−	0.171289i	$-0.945207\pi$
$409$		−	6.92820i		−	0.342578i	0.985221	−	0.171289i	$-0.0547931\pi$
$410$		−	15.5885i		−	0.769859i
$411$		0			0
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$	6.00000	+	6.92820i	0.295241	+	0.340915i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	18.0000	+	5.19615i	0.882523	+	0.254762i
$417$		0			0
$418$		−	15.5885i		−	0.762456i
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	−19.5000	−	11.2583i	−0.949245	−	0.548047i
$423$		0			0
$424$	−13.5000	−	7.79423i	−0.655618	−	0.378521i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−3.50000	−	18.1865i	−0.169377	−	0.880108i
$428$		0			0
$429$		0			0
$430$	−16.5000	+	28.5788i	−0.795701	+	1.37819i
$431$	28.5000	−	16.4545i	1.37280	−	0.792585i	0.381517	−	0.924362i	$-0.375402\pi$
$431$	28.5000	−	16.4545i	1.37280	−	0.792585i	0.991279	+	0.131777i	$0.0420683\pi$
$432$		0			0
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$	1.50000	+	7.79423i	0.0720023	+	0.374135i
$435$		0			0
$436$	4.50000	+	2.59808i	0.215511	+	0.124425i
$437$		0			0
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	−13.5000	−	7.79423i	−0.643587	−	0.371575i
$441$		0			0
$442$	36.0000	+	10.3923i	1.71235	+	0.494312i
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$		0			0
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	−1.50000	+	0.866025i	−0.0707894	+	0.0408703i	−0.534977	−	0.844867i	$-0.679680\pi$
$449$	−1.50000	+	0.866025i	−0.0707894	+	0.0408703i	0.464188	+	0.885737i	$0.346346\pi$
$450$		0			0
$451$	27.0000			1.27138
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$		0			0
$454$	30.0000			1.40797
$455$	13.5000	+	9.52628i	0.632890	+	0.446599i
$456$		0			0
$457$		−	34.6410i		−	1.62044i	−0.586127	−	0.810219i	$-0.699348\pi$
$457$		−	34.6410i		−	1.62044i	0.586127	−	0.810219i	$-0.300652\pi$
$458$	−10.5000	−	18.1865i	−0.490633	−	0.849801i
$459$		0			0
$460$		0			0
$461$	−25.5000	+	14.7224i	−1.18765	+	0.685692i	−0.957773	−	0.287527i	$-0.907167\pi$
$461$	−25.5000	+	14.7224i	−1.18765	+	0.685692i	−0.229881	+	0.973219i	$0.573834\pi$
$462$		0			0
$463$			24.2487i			1.12693i	0.826139	+	0.563467i	$0.190533\pi$
$463$			24.2487i			1.12693i	−0.826139	+	0.563467i	$0.809467\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$		0			0
$466$	−4.50000	+	2.59808i	−0.208458	+	0.120354i
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	0.513986	−	0.857798i	$-0.328168\pi$
$467$	−10.5000	−	18.1865i	−0.485882	−	0.841572i	−0.999868	+	0.0162260i	$0.994835\pi$
$468$		0			0
$469$	−7.50000	+	21.6506i	−0.346318	+	0.999733i
$470$	22.5000	+	12.9904i	1.03785	+	0.599202i
$471$		0			0
$472$	6.00000			0.276172
$473$	−49.5000	−	28.5788i	−2.27601	−	1.31406i
$474$		0			0
$475$	3.00000	−	1.73205i	0.137649	−	0.0794719i
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$		0			0
$478$	−18.0000			−0.823301
$479$	−25.5000	+	14.7224i	−1.16512	+	0.672685i	−0.952527	−	0.304455i	$-0.901526\pi$
$479$	−25.5000	+	14.7224i	−1.16512	+	0.672685i	−0.212598	+	0.977140i	$0.568192\pi$
$480$		0			0
$481$		0			0
$482$	−12.0000			−0.546585
$483$		0			0
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$	4.50000	−	7.79423i	0.204334	−	0.353918i
$486$		0			0
$487$			24.2487i			1.09881i	0.835555	+	0.549407i	$0.185146\pi$
$487$			24.2487i			1.09881i	−0.835555	+	0.549407i	$0.814854\pi$
$488$	−10.5000	−	6.06218i	−0.475313	−	0.274422i
$489$		0			0
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$	−9.00000	+	15.5885i	−0.405340	+	0.702069i
$494$	7.50000	+	7.79423i	0.337441	+	0.350679i
$495$		0			0
$496$	7.50000	+	4.33013i	0.336760	+	0.194428i
$497$	1.50000	−	4.33013i	0.0672842	−	0.194233i
$498$		0			0
$499$	1.50000	−	0.866025i	0.0671492	−	0.0387686i	−0.466049	−	0.884759i	$-0.654323\pi$
$499$	1.50000	−	0.866025i	0.0671492	−	0.0387686i	0.533199	+	0.845990i	$0.320990\pi$
$500$			12.1244i			0.542218i
$501$		0			0
$502$	−4.50000	+	2.59808i	−0.200845	+	0.115958i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$		0			0
$505$	13.5000	+	7.79423i	0.600742	+	0.346839i
$506$		0			0
$507$		0			0
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$			6.92820i			0.307087i	0.988142	+	0.153544i	$0.0490686\pi$
$509$			6.92820i			0.307087i	−0.988142	+	0.153544i	$0.950931\pi$
$510$		0			0
$511$	−22.5000	+	4.33013i	−0.995341	+	0.191554i
$512$			8.66025i			0.382733i
$513$		0			0
$514$		−	51.9615i		−	2.29192i
$515$	−19.5000	−	11.2583i	−0.859273	−	0.496101i
$516$		0			0
$517$	−22.5000	+	38.9711i	−0.989549	+	1.71395i
$518$		0			0
$519$		0			0
$520$	10.5000	−	2.59808i	0.460455	−	0.113933i
$521$	19.5000	−	33.7750i	0.854311	−	1.47971i	−0.0229727	−	0.999736i	$-0.507313\pi$
$521$	19.5000	−	33.7750i	0.854311	−	1.47971i	0.877283	−	0.479973i	$-0.159354\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−7.50000	−	12.9904i	−0.327639	−	0.567487i
$525$		0			0
$526$	−4.50000	+	2.59808i	−0.196209	+	0.113282i
$527$	9.00000	+	5.19615i	0.392046	+	0.226348i
$528$		0			0
$529$	−23.0000			−1.00000
$530$	27.0000			1.17281
$531$		0			0
$532$	−4.50000	+	0.866025i	−0.195100	+	0.0375470i
$533$	−13.5000	+	12.9904i	−0.584750	+	0.562676i
$534$		0			0
$535$		0			0
$536$	7.50000	+	12.9904i	0.323951	+	0.561099i
$537$		0			0
$538$			10.3923i			0.448044i
$539$	−13.5000	−	33.7750i	−0.581486	−	1.45479i
$540$		0			0
$541$	−10.5000	+	6.06218i	−0.451430	+	0.260633i	−0.708434	−	0.705777i	$-0.750598\pi$
$541$	−10.5000	+	6.06218i	−0.451430	+	0.260633i	0.257004	+	0.966410i	$0.417265\pi$
$542$	30.0000			1.28861
$543$		0			0
$544$			31.1769i			1.33670i
$545$	9.00000			0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$		0			0
$550$	−18.0000			−0.767523
$551$	−4.50000	+	2.59808i	−0.191706	+	0.110682i
$552$		0			0
$553$	−12.5000	−	4.33013i	−0.531554	−	0.184136i
$554$		−	17.3205i		−	0.735878i
$555$		0			0
$556$	−6.50000	−	11.2583i	−0.275661	−	0.477460i
$557$	−13.5000	+	7.79423i	−0.572013	+	0.330252i	−0.757953	−	0.652309i	$-0.773800\pi$
$557$	−13.5000	+	7.79423i	−0.572013	+	0.330252i	0.185940	+	0.982561i	$0.440467\pi$
$558$		0			0
$559$	38.5000	−	9.52628i	1.62838	−	0.402919i
$560$	−7.50000	+	21.6506i	−0.316933	+	0.914906i
$561$		0			0
$562$	12.0000			0.506189
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$		0			0
$565$	−22.5000	−	12.9904i	−0.946582	−	0.546509i
$566$	28.5000	−	16.4545i	1.19794	−	0.691633i
$567$		0			0
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	−0.518509	−	0.855072i	$-0.673513\pi$
$571$	11.5000	−	19.9186i	0.481260	−	0.833567i	0.999769	+	0.0215055i	$0.00684595\pi$
$572$	−4.50000	−	18.1865i	−0.188154	−	0.760417i
$573$		0			0
$574$	−4.50000	−	23.3827i	−0.187826	−	0.975974i
$575$		0			0
$576$		0			0
$577$	13.5000	+	7.79423i	0.562012	+	0.324478i	0.753953	−	0.656929i	$-0.228145\pi$
$577$	13.5000	+	7.79423i	0.562012	+	0.324478i	−0.191940	+	0.981407i	$0.561478\pi$
$578$			32.9090i			1.36883i
$579$		0			0
$580$		−	5.19615i		−	0.215758i
$581$	−6.00000	−	6.92820i	−0.248922	−	0.287430i
$582$		0			0
$583$			46.7654i			1.93682i
$584$	−7.50000	+	12.9904i	−0.310352	+	0.537546i
$585$		0			0
$586$	22.5000	+	38.9711i	0.929466	+	1.60988i
$587$	13.5000	+	7.79423i	0.557205	+	0.321702i	0.752023	−	0.659137i	$-0.229078\pi$
$587$	13.5000	+	7.79423i	0.557205	+	0.321702i	−0.194818	+	0.980839i	$0.562412\pi$
$588$		0			0
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$	−9.00000	+	5.19615i	−0.370524	+	0.213922i
$591$		0			0
$592$		0			0
$593$	4.50000	−	2.59808i	0.184793	−	0.106690i	−0.404750	−	0.914428i	$-0.632641\pi$
$593$	4.50000	−	2.59808i	0.184793	−	0.106690i	0.589543	+	0.807737i	$0.299308\pi$
$594$		0			0
$595$	−9.00000	+	25.9808i	−0.368964	+	1.06511i
$596$	−16.5000	−	9.52628i	−0.675866	−	0.390212i
$597$		0			0
$598$		0			0
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$		0			0
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$	−16.5000	+	47.6314i	−0.672490	+	1.94131i
$603$		0			0
$604$	−10.5000	−	6.06218i	−0.427239	−	0.246667i
$605$			27.7128i			1.12669i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	−4.50000	+	7.79423i	−0.182499	+	0.316098i
$609$		0			0
$610$	21.0000			0.850265
$611$	−7.50000	−	30.3109i	−0.303418	−	1.22625i
$612$		0			0
$613$	31.5000	−	18.1865i	1.27227	−	0.734547i	0.296858	−	0.954922i	$-0.404061\pi$
$613$	31.5000	−	18.1865i	1.27227	−	0.734547i	0.975415	+	0.220375i	$0.0707280\pi$
$614$	42.0000			1.69498
$615$		0			0
$616$	−22.5000	−	7.79423i	−0.906551	−	0.314038i
$617$	−37.5000	+	21.6506i	−1.50969	+	0.871622i	−0.509757	+	0.860318i	$0.670265\pi$
$617$	−37.5000	+	21.6506i	−1.50969	+	0.871622i	−0.999936	+	0.0113033i	$0.996402\pi$
$618$		0			0
$619$	16.5000	+	9.52628i	0.663191	+	0.382893i	0.793492	−	0.608581i	$-0.208261\pi$
$619$	16.5000	+	9.52628i	0.663191	+	0.382893i	−0.130301	+	0.991475i	$0.541594\pi$
$620$	−3.00000			−0.120483
$621$		0			0
$622$	−22.5000	−	12.9904i	−0.902168	−	0.520867i
$623$	−12.0000	−	13.8564i	−0.480770	−	0.555145i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	28.5000	−	16.4545i	1.13909	−	0.657653i
$627$		0			0
$628$	11.5000	−	19.9186i	0.458900	−	0.794838i
$629$		0			0
$630$		0			0
$631$	−40.5000	+	23.3827i	−1.61228	+	0.930850i	−0.623439	+	0.781872i	$0.714265\pi$
$631$	−40.5000	+	23.3827i	−1.61228	+	0.930850i	−0.988841	+	0.148978i	$0.952402\pi$
$632$	−7.50000	+	4.33013i	−0.298334	+	0.172243i
$633$		0			0
$634$	4.50000	+	7.79423i	0.178718	+	0.309548i
$635$		−	22.5167i		−	0.893546i
$636$		0			0
$637$	23.0000	+	10.3923i	0.911293	+	0.411758i
$638$	27.0000			1.06894
$639$		0			0
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$		0			0
$643$	−4.50000	+	2.59808i	−0.177463	+	0.102458i	−0.586100	−	0.810239i	$-0.699337\pi$
$643$	−4.50000	+	2.59808i	−0.177463	+	0.102458i	0.408637	+	0.912697i	$0.366004\pi$
$644$		0			0
$645$		0			0
$646$	−9.00000	+	15.5885i	−0.354100	+	0.613320i
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	0.763908	−	0.645325i	$-0.223278\pi$
$647$	−4.50000	−	7.79423i	−0.176913	−	0.306423i	−0.940822	+	0.338902i	$0.889945\pi$
$648$		0			0
$649$	−9.00000	−	15.5885i	−0.353281	−	0.611900i
$650$	9.00000	−	8.66025i	0.353009	−	0.339683i
$651$		0			0
$652$	−10.5000	−	6.06218i	−0.411212	−	0.237413i
$653$	30.0000			1.17399			0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000			1.17399			0.586995	+	0.809590i	$0.300311\pi$
$654$		0			0
$655$	−22.5000	−	12.9904i	−0.879148	−	0.507576i
$656$	−22.5000	−	12.9904i	−0.878477	−	0.507189i
$657$		0			0
$658$	37.5000	+	12.9904i	1.46190	+	0.506418i
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	0.974320	−	0.225168i	$-0.0722932\pi$
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	−0.682161	+	0.731202i	$0.738960\pi$
$660$		0			0
$661$	31.5000	−	18.1865i	1.22521	−	0.707374i	0.259184	−	0.965828i	$-0.416546\pi$
$661$	31.5000	−	18.1865i	1.22521	−	0.707374i	0.966024	+	0.258454i	$0.0832129\pi$
$662$	−28.5000	+	49.3634i	−1.10768	+	1.91856i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−6.00000	+	5.19615i	−0.232670	+	0.201498i
$666$		0			0
$667$		0			0
$668$	−1.50000	−	0.866025i	−0.0580367	−	0.0335075i
$669$		0			0
$670$	−22.5000	−	12.9904i	−0.869251	−	0.501862i
$671$			36.3731i			1.40417i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$			38.1051i			1.46775i
$675$		0			0
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	0.999760	+	0.0219013i	$0.00697196\pi$
$677$	13.5000	+	23.3827i	0.518847	+	0.898670i	−0.480913	+	0.876768i	$0.659695\pi$
$678$		0			0
$679$	4.50000	−	12.9904i	0.172694	−	0.498525i
$680$	9.00000	+	15.5885i	0.345134	+	0.597790i
$681$		0			0
$682$		−	15.5885i		−	0.596913i
$683$			24.2487i			0.927851i	0.885874	+	0.463926i	$0.153559\pi$
$683$			24.2487i			0.927851i	−0.885874	+	0.463926i	$0.846441\pi$
$684$		0			0
$685$		0			0
$686$	−27.0000	+	17.3205i	−1.03086	+	0.661300i
$687$		0			0
$688$	27.5000	+	47.6314i	1.04843	+	1.81593i
$689$	−22.5000	−	23.3827i	−0.857182	−	0.890809i
$690$		0			0
$691$			31.1769i			1.18603i	0.805193	+	0.593013i	$0.202062\pi$
$691$			31.1769i			1.18603i	−0.805193	+	0.593013i	$0.797938\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$		0			0
$694$		0			0
$695$	−19.5000	−	11.2583i	−0.739677	−	0.427053i
$696$		0			0
$697$	−27.0000	−	15.5885i	−1.02270	−	0.590455i
$698$	4.50000	−	7.79423i	0.170328	−	0.295016i
$699$		0			0
$700$	1.00000	+	5.19615i	0.0377964	+	0.196396i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$		0			0
$704$	−4.50000	+	2.59808i	−0.169600	+	0.0979187i
$705$		0			0
$706$	−1.50000	−	2.59808i	−0.0564532	−	0.0977799i
$707$	22.5000	+	7.79423i	0.846200	+	0.293132i
$708$		0			0
$709$	−10.5000	−	6.06218i	−0.394336	−	0.227670i	0.289701	−	0.957117i	$-0.406444\pi$
$709$	−10.5000	−	6.06218i	−0.394336	−	0.227670i	−0.684037	+	0.729447i	$0.739777\pi$
$710$	4.50000	+	2.59808i	0.168882	+	0.0975041i
$711$		0			0
$712$	−12.0000			−0.449719
$713$		0			0
$714$		0			0
$715$	−22.5000	−	23.3827i	−0.841452	−	0.874463i
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$		0			0
$718$	16.5000	+	28.5788i	0.615775	+	1.06655i
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	−32.5000	−	11.2583i	−1.21036	−	0.419282i
$722$	24.0000	−	13.8564i	0.893188	−	0.515682i
$723$		0			0
$724$	−2.00000			−0.0743294
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$	15.0000	−	6.92820i	0.555937	−	0.256776i
$729$		0			0
$730$		−	25.9808i		−	0.961591i
$731$	33.0000	+	57.1577i	1.22055	+	2.11405i
$732$		0			0
$733$	43.5000	−	25.1147i	1.60671	−	0.927634i	0.616609	−	0.787269i	$-0.288506\pi$
$733$	43.5000	−	25.1147i	1.60671	−	0.927634i	0.990100	−	0.140365i	$-0.0448275\pi$
$734$	34.5000	−	19.9186i	1.27342	−	0.735208i
$735$		0			0
$736$		0			0
$737$	22.5000	−	38.9711i	0.828798	−	1.43552i
$738$		0			0
$739$	−34.5000	+	19.9186i	−1.26910	+	0.732717i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−34.5000	+	19.9186i	−1.26910	+	0.732717i	−0.294285	+	0.955718i	$0.595081\pi$
$740$		0			0
$741$		0			0
$742$	40.5000	−	7.79423i	1.48680	−	0.286135i
$743$	1.50000	+	0.866025i	0.0550297	+	0.0317714i	0.527262	−	0.849703i	$-0.323218\pi$
$743$	1.50000	+	0.866025i	0.0550297	+	0.0317714i	−0.472233	+	0.881474i	$0.656552\pi$
$744$		0			0
$745$	−33.0000			−1.20903
$746$	−28.5000	−	16.4545i	−1.04346	−	0.602441i
$747$		0			0
$748$	27.0000	−	15.5885i	0.987218	−	0.569970i
$749$		0			0
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$	37.5000	−	21.6506i	1.36748	−	0.789517i
$753$		0			0
$754$	−13.5000	+	12.9904i	−0.491641	+	0.473082i
$755$	−21.0000			−0.764268
$756$		0			0
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	−0.669193	−	0.743089i	$-0.733360\pi$
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	0.978130	+	0.207993i	$0.0666932\pi$
$758$	1.50000	−	2.59808i	0.0544825	−	0.0943664i
$759$		0			0
$760$			5.19615i			0.188484i
$761$	−25.5000	−	14.7224i	−0.924374	−	0.533688i	−0.0393463	−	0.999226i	$-0.512528\pi$
$761$	−25.5000	−	14.7224i	−0.924374	−	0.533688i	−0.885028	+	0.465538i	$0.845861\pi$
$762$		0			0
$763$	13.5000	−	2.59808i	0.488733	−	0.0940567i
$764$	7.50000	−	12.9904i	0.271340	−	0.469975i
$765$		0			0
$766$	−13.5000	+	23.3827i	−0.487775	+	0.844851i
$767$	12.0000	+	3.46410i	0.433295	+	0.125081i
$768$		0			0
$769$	−16.5000	−	9.52628i	−0.595005	−	0.343526i	0.172069	−	0.985085i	$-0.444955\pi$
$769$	−16.5000	−	9.52628i	−0.595005	−	0.343526i	−0.767074	+	0.641558i	$0.778288\pi$
$770$	40.5000	−	7.79423i	1.45952	−	0.280885i
$771$		0			0
$772$	−1.50000	+	0.866025i	−0.0539862	+	0.0311689i
$773$		−	13.8564i		−	0.498380i	−0.968455	−	0.249190i	$-0.919836\pi$
$773$		−	13.8564i		−	0.498380i	0.968455	−	0.249190i	$-0.0801644\pi$
$774$		0			0
$775$	3.00000	−	1.73205i	0.107763	−	0.0622171i
$776$	−4.50000	−	7.79423i	−0.161541	−	0.279797i
$777$		0			0
$778$	4.50000	+	2.59808i	0.161333	+	0.0931455i
$779$	−4.50000	−	7.79423i	−0.161229	−	0.279257i
$780$		0			0
$781$	−4.50000	+	7.79423i	−0.161023	+	0.278899i
$782$		0			0
$783$		0			0
$784$	−5.00000	+	34.6410i	−0.178571	+	1.23718i
$785$		−	39.8372i		−	1.42185i
$786$		0			0
$787$			31.1769i			1.11134i	0.831404	+	0.555668i	$0.187538\pi$
$787$			31.1769i			1.11134i	−0.831404	+	0.555668i	$0.812462\pi$
$788$	19.5000	+	11.2583i	0.694659	+	0.401061i
$789$		0			0
$790$	7.50000	−	12.9904i	0.266838	−	0.462177i
$791$	−37.5000	−	12.9904i	−1.33335	−	0.461885i
$792$		0			0
$793$	−17.5000	−	18.1865i	−0.621443	−	0.645823i
$794$	−31.5000	+	54.5596i	−1.11789	+	1.93625i
$795$		0			0
$796$	−4.00000			−0.141776
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	45.0000	−	25.9808i	1.59199	−	0.919133i
$800$	9.00000	+	5.19615i	0.318198	+	0.183712i
$801$		0			0
$802$	−12.0000			−0.423735
$803$	45.0000			1.58802
$804$		0			0
$805$		0			0
$806$	7.50000	+	7.79423i	0.264176	+	0.274540i
$807$		0			0
$808$	13.5000	−	7.79423i	0.474928	−	0.274200i
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	0.620274	−	0.784385i	$-0.287021\pi$
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	−0.989434	+	0.144981i	$0.953688\pi$
$810$		0			0
$811$			3.46410i			0.121641i	0.998149	+	0.0608205i	$0.0193717\pi$
$811$			3.46410i			0.121641i	−0.998149	+	0.0608205i	$0.980628\pi$
$812$	−1.50000	−	7.79423i	−0.0526397	−	0.273524i
$813$		0			0
$814$		0			0
$815$	−21.0000			−0.735598
$816$		0			0
$817$			19.0526i			0.666565i
$818$	12.0000			0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$		0			0
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$	−19.5000	+	11.2583i	−0.679315	+	0.392203i
$825$		0			0
$826$	−12.0000	+	10.3923i	−0.417533	+	0.361595i
$827$			10.3923i			0.361376i	0.983540	+	0.180688i	$0.0578324\pi$
$827$			10.3923i			0.361376i	−0.983540	+	0.180688i	$0.942168\pi$
$828$		0			0
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	0.798823	−	0.601566i	$-0.205456\pi$
$829$	−3.50000	−	6.06218i	−0.121560	−	0.210548i	−0.920383	+	0.391018i	$0.872123\pi$
$830$	9.00000	−	5.19615i	0.312395	−	0.180361i
$831$		0			0
$832$	1.00000	−	3.46410i	0.0346688	−	0.120096i
$833$	−6.00000	+	41.5692i	−0.207888	+	1.44029i
$834$		0			0
$835$	−3.00000			−0.103819
$836$	9.00000			0.311272
$837$		0			0
$838$	31.5000	+	18.1865i	1.08815	+	0.628243i
$839$	−1.50000	+	0.866025i	−0.0517858	+	0.0298985i	−0.525669	−	0.850689i	$-0.676185\pi$
$839$	−1.50000	+	0.866025i	−0.0517858	+	0.0298985i	0.473884	+	0.880587i	$0.342852\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	22.5000	+	0.866025i	0.774024	+	0.0297922i
$846$		0			0
$847$	8.00000	+	41.5692i	0.274883	+	1.42834i
$848$	22.5000	−	38.9711i	0.772653	−	1.33827i
$849$		0			0
$850$	18.0000	+	10.3923i	0.617395	+	0.356453i
$851$		0			0
$852$		0			0
$853$		−	41.5692i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$853$		−	41.5692i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$854$	31.5000	−	6.06218i	1.07791	−	0.207443i
$855$		0			0
$856$		0			0
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	0.433546	+	0.901131i	$0.357262\pi$
$857$	−16.5000	+	28.5788i	−0.563629	+	0.976235i	−0.997176	+	0.0751033i	$0.976071\pi$
$858$		0			0
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	0.999982	−	0.00607046i	$-0.00193230\pi$
$859$	14.5000	+	25.1147i	0.494734	+	0.856904i	−0.505248	+	0.862974i	$0.668599\pi$
$860$	−16.5000	−	9.52628i	−0.562645	−	0.324843i
$861$		0			0
$862$	28.5000	+	49.3634i	0.970714	+	1.68133i
$863$	−1.50000	+	0.866025i	−0.0510606	+	0.0294798i	−0.525313	−	0.850909i	$-0.676052\pi$
$863$	−1.50000	+	0.866025i	−0.0510606	+	0.0294798i	0.474252	+	0.880389i	$0.342718\pi$
$864$		0			0
$865$			25.9808i			0.883372i
$866$	28.5000	−	16.4545i	0.968469	−	0.559146i
$867$		0			0
$868$	−4.50000	+	0.866025i	−0.152740	+	0.0293948i
$869$	22.5000	+	12.9904i	0.763260	+	0.440668i
$870$		0			0
$871$	7.50000	+	30.3109i	0.254128	+	1.02705i
$872$	4.50000	−	7.79423i	0.152389	−	0.263946i
$873$		0			0
$874$		0			0
$875$	21.0000	+	24.2487i	0.709930	+	0.819756i
$876$		0			0
$877$	1.50000	+	0.866025i	0.0506514	+	0.0292436i	0.525112	−	0.851033i	$-0.324023\pi$
$877$	1.50000	+	0.866025i	0.0506514	+	0.0292436i	−0.474460	+	0.880277i	$0.657357\pi$
$878$			13.8564i			0.467631i
$879$		0			0
$880$	22.5000	−	38.9711i	0.758475	−	1.31372i
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	0.441934	+	0.897048i	$0.354293\pi$
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	−0.997833	+	0.0657979i	$0.979041\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	−6.00000	+	20.7846i	−0.201802	+	0.699062i
$885$		0			0
$886$	−22.5000	+	12.9904i	−0.755902	+	0.436420i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		0			0
$889$	−6.50000	−	33.7750i	−0.218003	−	1.13278i
$890$	18.0000	−	10.3923i	0.603361	−	0.348351i
$891$		0			0
$892$	−4.50000	−	2.59808i	−0.150671	−	0.0869900i
$893$	15.0000			0.501956
$894$		0			0
$895$	−4.50000	−	2.59808i	−0.150418	−	0.0868441i
$896$	21.0000	+	24.2487i	0.701561	+	0.810093i
$897$		0			0
$898$	−1.50000	−	2.59808i	−0.0500556	−	0.0866989i
$899$	−4.50000	+	2.59808i	−0.150083	+	0.0866507i
$900$		0			0
$901$	27.0000	−	46.7654i	0.899500	−	1.55798i
$902$			46.7654i			1.55712i
$903$		0			0
$904$	−22.5000	+	12.9904i	−0.748339	+	0.432054i
$905$	−3.00000	+	1.73205i	−0.0997234	+	0.0575753i
$906$		0			0
$907$	14.5000	+	25.1147i	0.481465	+	0.833921i	0.999774	−	0.0212722i	$-0.00677166\pi$
$907$	14.5000	+	25.1147i	0.481465	+	0.833921i	−0.518309	+	0.855193i	$0.673438\pi$
$908$			17.3205i			0.574801i
$909$		0			0
$910$	−16.5000	+	23.3827i	−0.546970	+	0.775128i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	60.0000			1.98462
$915$		0			0
$916$	10.5000	−	6.06218i	0.346930	−	0.200300i
$917$	−37.5000	−	12.9904i	−1.23836	−	0.428980i
$918$		0			0
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	−0.159492	−	0.987199i	$-0.550986\pi$
$919$	23.5000	−	40.7032i	0.775193	−	1.34267i	0.934686	−	0.355475i	$-0.115681\pi$
$920$		0			0
$921$		0			0
$922$	−25.5000	−	44.1673i	−0.839798	−	1.45457i
$923$	−1.50000	−	6.06218i	−0.0493731	−	0.199539i
$924$		0			0
$925$		0			0
$926$	−42.0000			−1.38021
$927$		0			0
$928$	−13.5000	−	7.79423i	−0.443159	−	0.255858i
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.985108	−	0.171935i	$-0.0550020\pi$
$929$	40.5000	+	23.3827i	1.32876	+	0.767161i	0.343654	+	0.939096i	$0.388335\pi$
$930$		0			0
$931$	−7.50000	+	9.52628i	−0.245803	+	0.312211i
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$		0			0
$934$	31.5000	−	18.1865i	1.03071	−	0.595082i
$935$	27.0000	−	46.7654i	0.882994	−	1.52939i
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	−37.5000	−	12.9904i	−1.22442	−	0.424151i
$939$		0			0
$940$	−7.50000	+	12.9904i	−0.244623	+	0.423700i
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	0.571551	−	0.820566i	$-0.306342\pi$
$941$	4.50000	+	2.59808i	0.146696	+	0.0846949i	−0.424856	+	0.905261i	$0.639675\pi$
$942$		0			0
$943$		0			0
$944$			17.3205i			0.563735i
$945$		0			0
$946$	49.5000	−	85.7365i	1.60938	−	2.78753i
$947$			38.1051i			1.23825i	0.785292	+	0.619125i	$0.212513\pi$
$947$			38.1051i			1.23825i	−0.785292	+	0.619125i	$0.787487\pi$
$948$		0			0
$949$	−22.5000	+	21.6506i	−0.730381	+	0.702809i
$950$	3.00000	+	5.19615i	0.0973329	+	0.168585i
$951$		0			0
$952$	18.0000	+	20.7846i	0.583383	+	0.673633i
$953$	−28.5000	−	49.3634i	−0.923206	−	1.59904i	−0.794422	−	0.607366i	$-0.792226\pi$
$953$	−28.5000	−	49.3634i	−0.923206	−	1.59904i	−0.128784	−	0.991673i	$-0.541107\pi$
$954$		0			0
$955$		−	25.9808i		−	0.840718i
$956$		−	10.3923i		−	0.336111i
$957$		0			0
$958$	−25.5000	−	44.1673i	−0.823868	−	1.42698i
$959$		0			0
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$		0			0
$963$		0			0
$964$		−	6.92820i		−	0.223142i
$965$	−1.50000	+	2.59808i	−0.0482867	+	0.0836350i
$966$		0			0
$967$			10.3923i			0.334194i	0.985940	+	0.167097i	$0.0534393\pi$
$967$			10.3923i			0.334194i	−0.985940	+	0.167097i	$0.946561\pi$
$968$	24.0000	+	13.8564i	0.771389	+	0.445362i
$969$		0			0
$970$	13.5000	+	7.79423i	0.433459	+	0.250258i
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	−0.646899	−	0.762576i	$-0.723934\pi$
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	0.983860	+	0.178942i	$0.0572676\pi$
$972$		0			0
$973$	−32.5000	−	11.2583i	−1.04190	−	0.360925i
$974$	−42.0000			−1.34577
$975$		0			0
$976$	17.5000	−	30.3109i	0.560161	−	0.970228i
$977$	16.5000	−	9.52628i	0.527882	−	0.304773i	−0.212272	−	0.977211i	$-0.568086\pi$
$977$	16.5000	−	9.52628i	0.527882	−	0.304773i	0.740153	+	0.672438i	$0.234753\pi$
$978$		0			0
$979$	18.0000	+	31.1769i	0.575282	+	0.996419i
$980$	−4.50000	−	11.2583i	−0.143747	−	0.359634i
$981$		0			0
$982$	−40.5000	−	23.3827i	−1.29241	−	0.746171i
$983$	31.5000	+	18.1865i	1.00469	+	0.580060i	0.909634	−	0.415411i	$-0.136362\pi$
$983$	31.5000	+	18.1865i	1.00469	+	0.580060i	0.0950602	+	0.995472i	$0.469696\pi$
$984$		0			0
$985$	39.0000			1.24264
$986$	−27.0000	−	15.5885i	−0.859855	−	0.496438i
$987$		0			0
$988$	−4.50000	+	4.33013i	−0.143164	+	0.137760i
$989$		0			0
$990$		0			0
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.770849	−	0.637018i	$-0.780168\pi$
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.166250	−	0.986084i	$-0.553166\pi$
$992$	−4.50000	+	7.79423i	−0.142875	+	0.247467i
$993$		0			0
$994$	7.50000	+	2.59808i	0.237886	+	0.0824060i
$995$	−6.00000	+	3.46410i	−0.190213	+	0.109819i
$996$		0			0
$997$	2.00000			0.0633406			0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000			0.0633406			0.0316703	+	0.999498i	$0.489917\pi$
$998$	1.50000	+	2.59808i	0.0474817	+	0.0822407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.a.550.1		2
3.2	odd	2		91.2.k.a.4.1	✓	2
7.2	even	3		819.2.do.c.667.1		2
13.10	even	6		819.2.do.c.361.1		2
21.2	odd	6		91.2.u.a.30.1	yes	2
21.5	even	6		637.2.u.a.30.1		2
21.11	odd	6		637.2.q.c.589.1		2
21.17	even	6		637.2.q.b.589.1		2
21.20	even	2		637.2.k.b.459.1		2
39.20	even	12		1183.2.e.e.508.1		4
39.23	odd	6		91.2.u.a.88.1	yes	2
39.32	even	12		1183.2.e.e.508.2		4
91.23	even	6	inner	819.2.bm.a.478.1		2
273.23	odd	6		91.2.k.a.23.1	yes	2
273.32	even	12		8281.2.a.s.1.1		2
273.59	odd	12		8281.2.a.w.1.2		2
273.62	even	6		637.2.u.a.361.1		2
273.101	even	6		637.2.q.b.491.1		2
273.137	even	12		8281.2.a.s.1.2		2
273.149	even	12		1183.2.e.e.170.2		4
273.179	odd	6		637.2.q.c.491.1		2
273.227	odd	12		8281.2.a.w.1.1		2
273.254	even	12		1183.2.e.e.170.1		4
273.257	even	6		637.2.k.b.569.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	3.2	odd	2
91.2.k.a.23.1	yes	2	273.23	odd	6
91.2.u.a.30.1	yes	2	21.2	odd	6
91.2.u.a.88.1	yes	2	39.23	odd	6
637.2.k.b.459.1		2	21.20	even	2
637.2.k.b.569.1		2	273.257	even	6
637.2.q.b.491.1		2	273.101	even	6
637.2.q.b.589.1		2	21.17	even	6
637.2.q.c.491.1		2	273.179	odd	6
637.2.q.c.589.1		2	21.11	odd	6
637.2.u.a.30.1		2	21.5	even	6
637.2.u.a.361.1		2	273.62	even	6
819.2.bm.a.478.1		2	91.23	even	6	inner
819.2.bm.a.550.1		2	1.1	even	1	trivial
819.2.do.c.361.1		2	13.10	even	6
819.2.do.c.667.1		2	7.2	even	3
1183.2.e.e.170.1		4	273.254	even	12
1183.2.e.e.170.2		4	273.149	even	12
1183.2.e.e.508.1		4	39.20	even	12
1183.2.e.e.508.2		4	39.32	even	12
8281.2.a.s.1.1		2	273.32	even	12
8281.2.a.s.1.2		2	273.137	even	12
8281.2.a.w.1.1		2	273.227	odd	12
8281.2.a.w.1.2		2	273.59	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-3.00000 - 3.46410i) q^{14} -5.00000 q^{16} -6.00000 q^{17} +(-1.50000 - 0.866025i) q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} +(-1.00000 + 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} +(2.00000 - 1.73205i) q^{28} +(1.50000 - 2.59808i) q^{29} +(-1.50000 - 0.866025i) q^{31} -5.19615i q^{32} -10.3923i q^{34} +(1.50000 - 4.33013i) q^{35} +(1.50000 - 2.59808i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(-4.50000 + 2.59808i) q^{44} +(-7.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-3.00000 - 1.73205i) q^{50} +(1.00000 - 3.46410i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 + 7.79423i) q^{55} +(-3.00000 - 3.46410i) q^{56} +(4.50000 + 2.59808i) q^{58} -3.46410i q^{59} +(-3.50000 + 6.06218i) q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-1.50000 - 6.06218i) q^{65} +(7.50000 - 4.33013i) q^{67} +6.00000 q^{68} +(7.50000 + 2.59808i) q^{70} +(-1.50000 + 0.866025i) q^{71} +(7.50000 + 4.33013i) q^{73} +(1.50000 + 0.866025i) q^{76} +(-4.50000 + 12.9904i) q^{77} +(2.50000 + 4.33013i) q^{79} +(7.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(16.5000 - 9.52628i) q^{86} +(4.50000 + 7.79423i) q^{88} +6.92820i q^{89} +(-4.00000 - 8.66025i) q^{91} +(-7.50000 - 12.9904i) q^{94} +3.00000 q^{95} +(-4.50000 + 2.59808i) q^{97} +(12.0000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 3 q^{5} - 4 q^{7} - 3 q^{10} + 9 q^{11} - 2 q^{13} - 6 q^{14} - 10 q^{16} - 12 q^{17} - 3 q^{19} + 3 q^{20} + 9 q^{22} - 2 q^{25} - 12 q^{26} + 4 q^{28} + 3 q^{29} - 3 q^{31} + 3 q^{35}+ \cdots + 24 q^{98}+O(q^{100}) \) 2 * q - 2 * q^4 - 3 * q^5 - 4 * q^7 - 3 * q^10 + 9 * q^11 - 2 * q^13 - 6 * q^14 - 10 * q^16 - 12 * q^17 - 3 * q^19 + 3 * q^20 + 9 * q^22 - 2 * q^25 - 12 * q^26 + 4 * q^28 + 3 * q^29 - 3 * q^31 + 3 * q^35 + 3 * q^38 - 3 * q^40 + 9 * q^41 - 11 * q^43 - 9 * q^44 - 15 * q^47 + 2 * q^49 - 6 * q^50 + 2 * q^52 - 9 * q^53 - 9 * q^55 - 6 * q^56 + 9 * q^58 - 7 * q^61 + 3 * q^62 - 2 * q^64 - 3 * q^65 + 15 * q^67 + 12 * q^68 + 15 * q^70 - 3 * q^71 + 15 * q^73 + 3 * q^76 - 9 * q^77 + 5 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^85 + 33 * q^86 + 9 * q^88 - 8 * q^91 - 15 * q^94 + 6 * q^95 - 9 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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