LMFDB - Embedded newform 1764.2.x.b.1469.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(293,1764)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1764.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1469.8
Root			$-0.213160 - 1.71888i$ of defining polynomial
Character	$\chi$	$=$	1764.1469
Dual form			1764.2.x.b.293.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.55054 - 0.771901i) q^{3} +(-1.43402 - 2.48379i) q^{5} +(1.80834 - 2.39372i) q^{9} +O(q^{10})$	\(q+(1.55054 - 0.771901i) q^{3} +(-1.43402 - 2.48379i) q^{5} +(1.80834 - 2.39372i) q^{9} +(2.34941 + 1.35643i) q^{11} +(3.18987 - 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +6.44383 q^{17} -3.16234i q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(0.956179 - 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(-8.26739 + 4.77318i) q^{31} +(4.68987 + 0.289688i) q^{33} +3.41279 q^{37} +(3.52443 - 5.31785i) q^{39} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(-8.53870 - 1.05889i) q^{45} +(5.65372 - 9.79254i) q^{47} +(9.99141 - 4.97400i) q^{51} -2.49899i q^{53} -7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(-4.33680 - 7.51156i) q^{59} +(0.566915 + 0.327308i) q^{61} +(-9.14867 - 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} -7.86582i q^{71} +12.7905i q^{73} +(-0.344443 + 5.57633i) q^{75} +(-2.59566 + 4.49581i) q^{79} +(-2.45983 - 8.65732i) q^{81} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-4.95720 - 0.306200i) q^{87} +6.29653 q^{89} +(-9.13448 + 13.7826i) q^{93} +(-7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.55054	−	0.771901i	0.895204	−	0.445657i
$3$	1.55054	−	0.771901i	0.895204	−	0.445657i
$4$		0			0
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	−0.985140	−	0.171753i	$-0.945057\pi$
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	0.343828	−	0.939033i	$-0.388276\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.80834	−	2.39372i	0.602779	−	0.797908i
$10$		0			0
$11$	2.34941	+	1.35643i	0.708373	+	0.408979i	0.810458	−	0.585797i	$-0.199218\pi$
$11$	2.34941	+	1.35643i	0.708373	+	0.408979i	−0.102086	+	0.994776i	$0.532552\pi$
$12$		0			0
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.0125026	−	0.999922i	$-0.496020\pi$
$13$	3.18987	−	1.84167i	0.884712	−	0.510789i	0.872209	+	0.489133i	$0.162687\pi$
$14$		0			0
$15$	−4.14074	−	2.74429i	−1.06913	−	0.708574i
$16$		0			0
$17$	6.44383			1.56286			0.781429	−	0.623994i	$-0.214491\pi$
$17$	6.44383			1.56286			0.781429	+	0.623994i	$0.214491\pi$
$18$		0			0
$19$		−	3.16234i		−	0.725491i	−0.931888	−	0.362746i	$-0.881839\pi$
$19$		−	3.16234i		−	0.725491i	0.931888	−	0.362746i	$-0.118161\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.59068	+	1.49573i	−0.540195	+	0.311882i	−0.745158	−	0.666888i	$-0.767626\pi$
$23$	−2.59068	+	1.49573i	−0.540195	+	0.311882i	0.204963	+	0.978770i	$0.434293\pi$
$24$		0			0
$25$	−1.61282	+	2.79348i	−0.322563	+	0.558696i
$26$		0			0
$27$	0.956179	−	5.10742i	0.184017	−	0.982923i
$28$		0			0
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	0.251383	−	0.967888i	$-0.419115\pi$
$29$	−2.48332	−	1.43375i	−0.461142	−	0.266240i	−0.712524	+	0.701648i	$0.752448\pi$
$30$		0			0
$31$	−8.26739	+	4.77318i	−1.48487	+	0.857289i	−0.999852	−	0.0172169i	$-0.994519\pi$
$31$	−8.26739	+	4.77318i	−1.48487	+	0.857289i	−0.485016	+	0.874506i	$0.661186\pi$
$32$		0			0
$33$	4.68987	+	0.289688i	0.816402	+	0.0504282i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.41279			0.561059			0.280530	−	0.959845i	$-0.409490\pi$
$37$	3.41279			0.561059			0.280530	+	0.959845i	$0.409490\pi$
$38$		0			0
$39$	3.52443	−	5.31785i	0.564361	−	0.851538i
$40$		0			0
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	0.921375	−	0.388674i	$-0.127067\pi$
$41$	0.794538	+	1.37618i	0.124086	+	0.214923i	−0.797289	+	0.603597i	$0.793733\pi$
$42$		0			0
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	0.250131	+	0.968212i	$0.419526\pi$
$43$	−4.67828	+	8.10302i	−0.713431	+	1.23570i	−0.963562	+	0.267487i	$0.913807\pi$
$44$		0			0
$45$	−8.53870	−	1.05889i	−1.27287	−	0.157850i
$46$		0			0
$47$	5.65372	−	9.79254i	0.824680	−	1.42839i	−0.0774831	−	0.996994i	$-0.524688\pi$
$47$	5.65372	−	9.79254i	0.824680	−	1.42839i	0.902163	−	0.431394i	$-0.141978\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	9.99141	−	4.97400i	1.39908	−	0.696499i
$52$		0			0
$53$		−	2.49899i		−	0.343263i	−0.985161	−	0.171632i	$-0.945096\pi$
$53$		−	2.49899i		−	0.343263i	0.985161	−	0.171632i	$-0.0549039\pi$
$54$		0			0
$55$		−	7.78058i		−	1.04913i
$56$		0			0
$57$	−2.44102	−	4.90333i	−0.323320	−	0.649462i
$58$		0			0
$59$	−4.33680	−	7.51156i	−0.564604	−	0.977922i	−0.997086	−	0.0762801i	$-0.975696\pi$
$59$	−4.33680	−	7.51156i	−0.564604	−	0.977922i	0.432483	−	0.901642i	$-0.357638\pi$
$60$		0			0
$61$	0.566915	+	0.327308i	0.0725860	+	0.0419075i	0.535854	−	0.844311i	$-0.319990\pi$
$61$	0.566915	+	0.327308i	0.0725860	+	0.0419075i	−0.463268	+	0.886218i	$0.653323\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.14867	−	5.28199i	−1.13475	−	0.655150i
$66$		0			0
$67$	−3.86146	−	6.68825i	−0.471752	−	0.817099i	0.527725	−	0.849415i	$-0.323045\pi$
$67$	−3.86146	−	6.68825i	−0.471752	−	0.817099i	−0.999478	+	0.0323159i	$0.989712\pi$
$68$		0			0
$69$	−2.86240	+	4.31894i	−0.344592	+	0.519939i
$70$		0			0
$71$		−	7.86582i		−	0.933501i	−0.884389	−	0.466750i	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		0			0
$73$			12.7905i			1.49702i	0.663123	+	0.748510i	$0.269231\pi$
$73$			12.7905i			1.49702i	−0.663123	+	0.748510i	$0.730769\pi$
$74$		0			0
$75$	−0.344443	+	5.57633i	−0.0397729	+	0.643899i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.59566	+	4.49581i	−0.292034	+	0.505819i	−0.974291	−	0.225295i	$-0.927666\pi$
$79$	−2.59566	+	4.49581i	−0.292034	+	0.505819i	0.682256	+	0.731113i	$0.260999\pi$
$80$		0			0
$81$	−2.45983	−	8.65732i	−0.273314	−	0.961925i
$82$		0			0
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.00876173	−	0.999962i	$-0.497211\pi$
$83$	7.92948	−	13.7343i	0.870373	−	1.50753i	0.861611	−	0.507569i	$-0.169456\pi$
$84$		0			0
$85$	−9.24057	−	16.0051i	−1.00228	−	1.73600i
$86$		0			0
$87$	−4.95720	−	0.306200i	−0.531468	−	0.0328281i
$88$		0			0
$89$	6.29653			0.667430			0.333715	−	0.942674i	$-0.391698\pi$
$89$	6.29653			0.667430			0.333715	+	0.942674i	$0.391698\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−9.13448	+	13.7826i	−0.947202	+	1.42919i
$94$		0			0
$95$	−7.85460	+	4.53486i	−0.805865	+	0.465267i
$96$		0			0
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.986942	−	0.161077i	$-0.0514967\pi$
$97$	13.2065	+	7.62477i	1.34092	+	0.774178i	0.353974	+	0.935255i	$0.384830\pi$
$98$		0			0
$99$	7.49544	−	3.17095i	0.753320	−	0.318692i
$100$		0			0
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	−0.766086	−	0.642739i	$-0.777798\pi$
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	0.939671	+	0.342080i	$0.111131\pi$
$102$		0			0
$103$	−2.89161	+	1.66947i	−0.284919	+	0.164498i	−0.635648	−	0.771979i	$-0.719267\pi$
$103$	−2.89161	+	1.66947i	−0.284919	+	0.164498i	0.350729	+	0.936477i	$0.385934\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	3.58853i		−	0.346917i	−0.984841	−	0.173458i	$-0.944506\pi$
$107$		−	3.58853i		−	0.346917i	0.984841	−	0.173458i	$-0.0554942\pi$
$108$		0			0
$109$	−13.7935			−1.32117			−0.660587	−	0.750750i	$-0.729692\pi$
$109$	−13.7935			−1.32117			−0.660587	+	0.750750i	$0.729692\pi$
$110$		0			0
$111$	5.29166	−	2.63434i	0.502262	−	0.250040i
$112$		0			0
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	−0.727586	−	0.686016i	$-0.759358\pi$
$113$	−5.28607	+	3.05191i	−0.497271	+	0.287100i	0.230315	+	0.973116i	$0.426024\pi$
$114$		0			0
$115$	7.43018	+	4.28981i	0.692867	+	0.400027i
$116$		0			0
$117$	1.35991	−	10.9660i	0.125724	−	1.01381i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.82019	−	3.15267i	−0.165472	−	0.286606i
$122$		0			0
$123$	2.29424	+	1.52051i	0.206864	+	0.137100i
$124$		0			0
$125$	−5.08895			−0.455170
$126$		0			0
$127$	−13.3819			−1.18745			−0.593727	−	0.804666i	$-0.702344\pi$
$127$	−13.3819			−1.18745			−0.593727	+	0.804666i	$0.702344\pi$
$128$		0			0
$129$	−0.999123	+	16.1752i	−0.0879679	+	1.42415i
$130$		0			0
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	0.882517	−	0.470280i	$-0.155847\pi$
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	−0.848533	+	0.529142i	$0.822514\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−14.0569	+	4.94918i	−1.20983	+	0.425958i
$136$		0			0
$137$	14.3082	+	8.26083i	1.22243	+	0.705771i	0.965435	−	0.260642i	$-0.0839343\pi$
$137$	14.3082	+	8.26083i	1.22243	+	0.705771i	0.256995	+	0.966413i	$0.417268\pi$
$138$		0			0
$139$	−9.91826	+	5.72631i	−0.841256	+	0.485699i	−0.857691	−	0.514165i	$-0.828102\pi$
$139$	−9.91826	+	5.72631i	−0.841256	+	0.485699i	0.0164348	+	0.999865i	$0.494768\pi$
$140$		0			0
$141$	1.20745	−	19.5478i	0.101685	−	1.64622i
$142$		0			0
$143$	9.99241			0.835607
$144$		0			0
$145$			8.22408i			0.682973i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.24781	−	2.45247i	0.347994	−	0.200914i	−0.315807	−	0.948823i	$-0.602275\pi$
$149$	4.24781	−	2.45247i	0.347994	−	0.200914i	0.663801	+	0.747909i	$0.268942\pi$
$150$		0			0
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	−0.993852	−	0.110712i	$-0.964687\pi$
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	0.592806	+	0.805345i	$0.298020\pi$
$152$		0			0
$153$	11.6526	−	15.4248i	0.942059	−	1.24702i
$154$		0			0
$155$	23.7112	+	13.6897i	1.90453	+	1.09958i
$156$		0			0
$157$	13.3514	−	7.70843i	1.06556	−	0.615200i	0.138593	−	0.990349i	$-0.455742\pi$
$157$	13.3514	−	7.70843i	1.06556	−	0.615200i	0.926964	+	0.375149i	$0.122409\pi$
$158$		0			0
$159$	−1.92898	−	3.87479i	−0.152978	−	0.307291i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	11.4411			0.896133			0.448066	−	0.894000i	$-0.352113\pi$
$163$	11.4411			0.896133			0.448066	+	0.894000i	$0.352113\pi$
$164$		0			0
$165$	−6.00584	−	12.0641i	−0.467554	−	0.939188i
$166$		0			0
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	0.999996	+	0.00264735i	$0.000842678\pi$
$167$	6.49103	+	11.2428i	0.502291	+	0.869993i	−0.497706	+	0.867346i	$0.665824\pi$
$168$		0			0
$169$	0.283528	−	0.491084i	0.0218098	−	0.0377757i
$170$		0			0
$171$	−7.56978	−	5.71858i	−0.578875	−	0.437311i
$172$		0			0
$173$	−9.79984	+	16.9738i	−0.745068	+	1.29050i	0.205095	+	0.978742i	$0.434250\pi$
$173$	−9.79984	+	16.9738i	−0.745068	+	1.29050i	−0.950163	+	0.311754i	$0.899084\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−12.5226	−	8.29938i	−0.941253	−	0.623820i
$178$		0			0
$179$			18.7788i			1.40360i	0.712375	+	0.701799i	$0.247619\pi$
$179$			18.7788i			1.40360i	−0.712375	+	0.701799i	$0.752381\pi$
$180$		0			0
$181$			4.47775i			0.332829i	0.986056	+	0.166414i	$0.0532190\pi$
$181$			4.47775i			0.332829i	−0.986056	+	0.166414i	$0.946781\pi$
$182$		0			0
$183$	1.13167	+	0.0699021i	0.0836556	+	0.00516731i
$184$		0			0
$185$	−4.89400	−	8.47666i	−0.359814	−	0.623217i
$186$		0			0
$187$	15.1392	+	8.74061i	1.10709	+	0.639177i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.90050	+	3.40665i	0.426945	+	0.246497i	0.698044	−	0.716055i	$-0.254054\pi$
$191$	5.90050	+	3.40665i	0.426945	+	0.246497i	−0.271099	+	0.962551i	$0.587387\pi$
$192$		0			0
$193$	7.97694	+	13.8165i	0.574193	+	0.994531i	0.996129	+	0.0879053i	$0.0280173\pi$
$193$	7.97694	+	13.8165i	0.574193	+	0.994531i	−0.421936	+	0.906626i	$0.638649\pi$
$194$		0			0
$195$	−18.2625	−	1.12806i	−1.30781	−	0.0807817i
$196$		0			0
$197$			25.9511i			1.84894i	0.381254	+	0.924470i	$0.375492\pi$
$197$			25.9511i			1.84894i	−0.381254	+	0.924470i	$0.624508\pi$
$198$		0			0
$199$			3.18358i			0.225678i	0.993613	+	0.112839i	$0.0359944\pi$
$199$			3.18358i			0.225678i	−0.993613	+	0.112839i	$0.964006\pi$
$200$		0			0
$201$	−11.1500	−	7.38971i	−0.786461	−	0.521230i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.27876	−	3.94693i	0.159156	−	0.275666i
$206$		0			0
$207$	−1.10446	+	8.90617i	−0.0767654	+	0.619022i
$208$		0			0
$209$	4.28950	−	7.42963i	0.296711	−	0.513918i
$210$		0			0
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	0.864118	−	0.503290i	$-0.167877\pi$
$211$	−0.0552411	−	0.0956804i	−0.00380295	−	0.00658691i	−0.867921	+	0.496703i	$0.834544\pi$
$212$		0			0
$213$	−6.07163	−	12.1963i	−0.416021	−	0.835673i
$214$		0			0
$215$	26.8349			1.83013
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.87304	+	19.8322i	0.667158	+	1.34014i
$220$		0			0
$221$	20.5550	−	11.8674i	1.38268	−	0.798290i
$222$		0			0
$223$	−11.3064	−	6.52775i	−0.757132	−	0.437130i	0.0711331	−	0.997467i	$-0.477339\pi$
$223$	−11.3064	−	6.52775i	−0.757132	−	0.437130i	−0.828265	+	0.560336i	$0.810672\pi$
$224$		0			0
$225$	3.77030	+	8.91219i	0.251353	+	0.594146i
$226$		0			0
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	−0.977829	−	0.209406i	$-0.932847\pi$
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	0.670265	+	0.742122i	$0.266180\pi$
$228$		0			0
$229$	11.6204	−	6.70902i	0.767895	−	0.443344i	−0.0642281	−	0.997935i	$-0.520459\pi$
$229$	11.6204	−	6.70902i	0.767895	−	0.443344i	0.832123	+	0.554591i	$0.187125\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	21.1789i		−	1.38748i	−0.720227	−	0.693738i	$-0.755963\pi$
$233$		−	21.1789i		−	1.38748i	0.720227	−	0.693738i	$-0.244037\pi$
$234$		0			0
$235$	−32.4302			−2.11551
$236$		0			0
$237$	−0.554346	+	8.97452i	−0.0360086	+	0.582958i
$238$		0			0
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	−0.728810	−	0.684716i	$-0.759926\pi$
$239$	−7.73342	+	4.46489i	−0.500233	+	0.288810i	0.228577	+	0.973526i	$0.426593\pi$
$240$		0			0
$241$	15.9430	+	9.20469i	1.02698	+	0.592926i	0.916117	−	0.400910i	$-0.131306\pi$
$241$	15.9430	+	9.20469i	1.02698	+	0.592926i	0.110860	+	0.993836i	$0.464639\pi$
$242$		0			0
$243$	−10.4967	−	11.5248i	−0.673361	−	0.739314i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.82401	−	10.0875i	−0.370573	−	0.641851i
$248$		0			0
$249$	1.69347	−	27.4163i	0.107319	−	1.73743i
$250$		0			0
$251$	6.33194			0.399669			0.199834	−	0.979830i	$-0.435960\pi$
$251$	6.33194			0.399669			0.199834	+	0.979830i	$0.435960\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$	−26.6822	−	17.6838i	−1.67091	−	1.10740i
$256$		0			0
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	−0.999918	−	0.0128120i	$-0.995922\pi$
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	0.488863	−	0.872360i	$-0.337412\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.92268	+	3.35169i	−0.490402	+	0.207465i
$262$		0			0
$263$	10.4663	+	6.04270i	0.645377	+	0.372609i	0.786683	−	0.617357i	$-0.211797\pi$
$263$	10.4663	+	6.04270i	0.645377	+	0.372609i	−0.141306	+	0.989966i	$0.545130\pi$
$264$		0			0
$265$	−6.20698	+	3.58360i	−0.381292	+	0.220139i
$266$		0			0
$267$	9.76300	−	4.86029i	0.597486	−	0.297445i
$268$		0			0
$269$	25.3304			1.54442			0.772212	−	0.635365i	$-0.219150\pi$
$269$	25.3304			1.54442			0.772212	+	0.635365i	$0.219150\pi$
$270$		0			0
$271$			0.225849i			0.0137193i	0.999976	+	0.00685967i	$0.00218352\pi$
$271$			0.225849i			0.0137193i	−0.999976	+	0.00685967i	$0.997816\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.57832	+	4.37534i	−0.456990	+	0.263843i
$276$		0			0
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	−0.376702	−	0.926335i	$-0.622942\pi$
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	0.990580	−	0.136934i	$-0.0437248\pi$
$278$		0			0
$279$	−3.52456	+	28.4214i	−0.211010	+	1.70154i
$280$		0			0
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	0.743004	−	0.669287i	$-0.233400\pi$
$281$	8.96635	+	5.17672i	0.534887	+	0.308817i	−0.208117	+	0.978104i	$0.566733\pi$
$282$		0			0
$283$	−11.8781	+	6.85783i	−0.706080	+	0.407656i	−0.809608	−	0.586971i	$-0.800320\pi$
$283$	−11.8781	+	6.85783i	−0.706080	+	0.407656i	0.103528	+	0.994627i	$0.466987\pi$
$284$		0			0
$285$	−8.67840	+	13.0944i	−0.514064	+	0.775648i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	24.5230			1.44253
$290$		0			0
$291$	26.3627	+	1.62840i	1.54541	+	0.0954582i
$292$		0			0
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	0.716226	−	0.697868i	$-0.245868\pi$
$293$	−4.21527	−	7.30105i	−0.246258	−	0.426532i	−0.962485	+	0.271336i	$0.912535\pi$
$294$		0			0
$295$	−12.4381	+	21.5434i	−0.724175	+	1.25431i
$296$		0			0
$297$	9.17431	−	10.7024i	0.532347	−	0.621017i
$298$		0			0
$299$	−5.50930	+	9.54239i	−0.318611	+	0.551851i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.372569	−	6.03166i	0.0214035	−	0.346510i
$304$		0			0
$305$		−	1.87746i		−	0.107503i
$306$		0			0
$307$		−	5.34345i		−	0.304967i	−0.988306	−	0.152484i	$-0.951273\pi$
$307$		−	5.34345i		−	0.304967i	0.988306	−	0.152484i	$-0.0487271\pi$
$308$		0			0
$309$	−3.19488	+	4.82061i	−0.181751	+	0.274235i
$310$		0			0
$311$	−4.70867	−	8.15565i	−0.267004	−	0.462465i	0.701083	−	0.713080i	$-0.252700\pi$
$311$	−4.70867	−	8.15565i	−0.267004	−	0.462465i	−0.968087	+	0.250615i	$0.919367\pi$
$312$		0			0
$313$	−14.3347	−	8.27614i	−0.810245	−	0.467795i	0.0367961	−	0.999323i	$-0.488285\pi$
$313$	−14.3347	−	8.27614i	−0.810245	−	0.467795i	−0.847041	+	0.531528i	$0.821618\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.9725	+	13.2632i	1.29026	+	0.744934i	0.978701	−	0.205291i	$-0.0658141\pi$
$317$	22.9725	+	13.2632i	1.29026	+	0.744934i	0.311563	+	0.950225i	$0.399147\pi$
$318$		0			0
$319$	−3.88956	−	6.73691i	−0.217773	−	0.377194i
$320$		0			0
$321$	−2.76999	−	5.56416i	−0.154606	−	0.310561i
$322$		0			0
$323$		−	20.3776i		−	1.13384i
$324$		0			0
$325$			11.8811i			0.659046i
$326$		0			0
$327$	−21.3873	+	10.6472i	−1.18272	+	0.588791i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.82000	−	15.2767i	0.484791	−	0.839682i	−0.515056	−	0.857156i	$-0.672229\pi$
$331$	8.82000	−	15.2767i	0.484791	−	0.839682i	0.999847	+	0.0174739i	$0.00556238\pi$
$332$		0			0
$333$	6.17148	−	8.16928i	0.338195	−	0.447674i
$334$		0			0
$335$	−11.0748	+	19.1821i	−0.605081	+	1.04803i
$336$		0			0
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	0.993515	−	0.113697i	$-0.0362694\pi$
$337$	7.31169	+	12.6642i	0.398293	+	0.689864i	−0.595222	+	0.803561i	$0.702936\pi$
$338$		0			0
$339$	−5.84048	+	8.81243i	−0.317211	+	0.478625i
$340$		0			0
$341$	−25.8979			−1.40245
$342$		0			0
$343$		0			0
$344$		0			0
$345$	14.8321	+	0.916160i	0.798533	+	0.0493244i
$346$		0			0
$347$	−1.05563	+	0.609467i	−0.0566691	+	0.0327179i	−0.528067	−	0.849203i	$-0.677083\pi$
$347$	−1.05563	+	0.609467i	−0.0566691	+	0.0327179i	0.471398	+	0.881921i	$0.343750\pi$
$348$		0			0
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	0.757946	−	0.652318i	$-0.226203\pi$
$349$	10.6857	+	6.16942i	0.571995	+	0.330241i	−0.185951	+	0.982559i	$0.559537\pi$
$350$		0			0
$351$	−6.35611	−	18.0530i	−0.339264	−	0.963597i
$352$		0			0
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	−0.400402	−	0.916339i	$-0.631130\pi$
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	0.993774	−	0.111411i	$-0.0355370\pi$
$354$		0			0
$355$	−19.5371	+	11.2797i	−1.03692	+	0.598666i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			12.1035i			0.638796i	0.947621	+	0.319398i	$0.103481\pi$
$359$			12.1035i			0.638796i	−0.947621	+	0.319398i	$0.896519\pi$
$360$		0			0
$361$	8.99958			0.473662
$362$		0			0
$363$	−5.25583	−	3.48333i	−0.275860	−	0.182827i
$364$		0			0
$365$	31.7691	−	18.3419i	1.66287	−	0.960058i
$366$		0			0
$367$	12.7544	+	7.36375i	0.665774	+	0.384385i	0.794473	−	0.607299i	$-0.207747\pi$
$367$	12.7544	+	7.36375i	0.665774	+	0.384385i	−0.128700	+	0.991684i	$0.541080\pi$
$368$		0			0
$369$	4.73099	+	0.586693i	0.246285	+	0.0305420i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	0.959336	−	0.282268i	$-0.0910867\pi$
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	−0.724119	+	0.689675i	$0.757753\pi$
$374$		0			0
$375$	−7.89062	+	3.92817i	−0.407470	+	0.202850i
$376$		0			0
$377$	−10.5620			−0.543970
$378$		0			0
$379$	21.2298			1.09050			0.545250	−	0.838273i	$-0.316435\pi$
$379$	21.2298			1.09050			0.545250	+	0.838273i	$0.316435\pi$
$380$		0			0
$381$	−20.7492	+	10.3295i	−1.06301	+	0.529198i
$382$		0			0
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	0.767579	−	0.640954i	$-0.221461\pi$
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	−0.938872	+	0.344266i	$0.888128\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.9365	+	25.8515i	0.555933	+	1.31411i
$388$		0			0
$389$	6.66661	+	3.84897i	0.338011	+	0.195151i	0.659392	−	0.751799i	$-0.270814\pi$
$389$	6.66661	+	3.84897i	0.338011	+	0.195151i	−0.321381	+	0.946950i	$0.604147\pi$
$390$		0			0
$391$	−16.6939	+	9.63825i	−0.844249	+	0.487427i
$392$		0			0
$393$	1.12314	+	0.744364i	0.0566548	+	0.0375482i
$394$		0			0
$395$	14.8889			0.749141
$396$		0			0
$397$			0.0494341i			0.00248102i	0.999999	+	0.00124051i	$0.000394867\pi$
$397$			0.0494341i			0.00248102i	−0.999999	+	0.00124051i	$0.999605\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.6039	+	10.1636i	−0.879096	+	0.507546i	−0.870360	−	0.492416i	$-0.836114\pi$
$401$	−17.6039	+	10.1636i	−0.879096	+	0.507546i	−0.00873572	+	0.999962i	$0.502781\pi$
$402$		0			0
$403$	−17.5813	+	30.4517i	−0.875786	+	1.51691i
$404$		0			0
$405$	−17.9755	+	18.5245i	−0.893212	+	0.920488i
$406$		0			0
$407$	8.01803	+	4.62921i	0.397439	+	0.229461i
$408$		0			0
$409$	−12.1144	+	6.99428i	−0.599021	+	0.345845i	−0.768656	−	0.639662i	$-0.779074\pi$
$409$	−12.1144	+	6.99428i	−0.599021	+	0.345845i	0.169636	+	0.985507i	$0.445741\pi$
$410$		0			0
$411$	28.5619	+	1.76424i	1.40886	+	0.0870234i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−45.4840			−2.23272
$416$		0			0
$417$	−10.9585	+	16.5348i	−0.536640	+	0.809712i
$418$		0			0
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	−0.999692	−	0.0248344i	$-0.992094\pi$
$419$	−10.6718	−	18.4842i	−0.521353	−	0.903010i	0.478339	−	0.878176i	$-0.341239\pi$
$420$		0			0
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	−0.752823	−	0.658223i	$-0.771309\pi$
$421$	3.97287	−	6.88121i	0.193626	−	0.335370i	0.946449	+	0.322853i	$0.104642\pi$
$422$		0			0
$423$	−13.2168	−	31.2417i	−0.642622	−	1.51902i
$424$		0			0
$425$	−10.3927	+	18.0007i	−0.504121	+	0.873163i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	15.4936	−	7.71315i	0.748039	−	0.372394i
$430$		0			0
$431$			31.9293i			1.53798i	0.639262	+	0.768989i	$0.279240\pi$
$431$			31.9293i			1.53798i	−0.639262	+	0.768989i	$0.720760\pi$
$432$		0			0
$433$			18.5300i			0.890493i	0.895408	+	0.445247i	$0.146884\pi$
$433$			18.5300i			0.890493i	−0.895408	+	0.445247i	$0.853116\pi$
$434$		0			0
$435$	6.34817	+	12.7517i	0.304372	+	0.611400i
$436$		0			0
$437$	4.73002	+	8.19263i	0.226267	+	0.391907i
$438$		0			0
$439$	−1.80316	−	1.04106i	−0.0860603	−	0.0496869i	0.456352	−	0.889799i	$-0.349156\pi$
$439$	−1.80316	−	1.04106i	−0.0860603	−	0.0496869i	−0.542413	+	0.840112i	$0.682489\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.13895	−	1.23493i	−0.101625	−	0.0586731i	0.448326	−	0.893870i	$-0.352020\pi$
$443$	−2.13895	−	1.23493i	−0.101625	−	0.0586731i	−0.549951	+	0.835197i	$0.685354\pi$
$444$		0			0
$445$	−9.02933	−	15.6393i	−0.428031	−	0.741372i
$446$		0			0
$447$	4.69332	−	7.08154i	0.221986	−	0.334945i
$448$		0			0
$449$			37.5094i			1.77018i	0.465424	+	0.885088i	$0.345902\pi$
$449$			37.5094i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$450$		0			0
$451$			4.31094i			0.202994i
$452$		0			0
$453$	−1.05249	+	17.0391i	−0.0494501	+	0.800567i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−2.92345	+	5.06356i	−0.136753	+	0.236864i	−0.926266	−	0.376871i	$-0.877000\pi$
$457$	−2.92345	+	5.06356i	−0.136753	+	0.236864i	0.789513	+	0.613734i	$0.210333\pi$
$458$		0			0
$459$	6.16145	−	32.9113i	0.287592	−	1.53617i
$460$		0			0
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	−0.941299	−	0.337574i	$-0.890394\pi$
$461$	−3.82830	+	6.63081i	−0.178302	+	0.308827i	0.762997	+	0.646402i	$0.223727\pi$
$462$		0			0
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	0.957057	−	0.289901i	$-0.0936225\pi$
$463$	4.89449	+	8.47751i	0.227466	+	0.393983i	−0.729590	+	0.683885i	$0.760289\pi$
$464$		0			0
$465$	47.3321	+	2.92365i	2.19498	+	0.135581i
$466$		0			0
$467$	28.1612			1.30314			0.651572	−	0.758587i	$-0.274110\pi$
$467$	28.1612			1.30314			0.651572	+	0.758587i	$0.274110\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	14.7517	−	22.2582i	0.679723	−	1.02560i
$472$		0			0
$473$	−21.9824	+	12.6915i	−1.01075	+	0.583557i
$474$		0			0
$475$	8.83394	+	5.10028i	0.405329	+	0.234017i
$476$		0			0
$477$	−5.98190	−	4.51903i	−0.273893	−	0.206912i
$478$		0			0
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	−0.299567	−	0.954075i	$-0.596842\pi$
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	0.976037	−	0.217605i	$-0.0698245\pi$
$480$		0			0
$481$	10.8864	−	6.28525i	0.496376	−	0.286583i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	43.7362i		−	1.98596i
$486$		0			0
$487$	29.3403			1.32953			0.664767	−	0.747051i	$-0.268531\pi$
$487$	29.3403			1.32953			0.664767	+	0.747051i	$0.268531\pi$
$488$		0			0
$489$	17.7398	−	8.83136i	0.802221	−	0.399368i
$490$		0			0
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	−0.682075	−	0.731283i	$-0.738922\pi$
$491$	−8.63745	+	4.98683i	−0.389803	+	0.225053i	0.292272	+	0.956335i	$0.405589\pi$
$492$		0			0
$493$	−16.0021	−	9.23883i	−0.720699	−	0.416096i
$494$		0			0
$495$	−18.6246	−	14.0699i	−0.837112	−	0.632396i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	0.997583	−	0.0694898i	$-0.0221371\pi$
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	−0.558971	+	0.829187i	$0.688804\pi$
$500$		0			0
$501$	18.7429	+	12.4219i	0.837372	+	0.554972i
$502$		0			0
$503$	−21.2907			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$503$	−21.2907			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$	0.0605520	−	0.980300i	0.00268921	−	0.0435367i
$508$		0			0
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.702378	−	0.711804i	$-0.747878\pi$
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.265252	−	0.964179i	$-0.585455\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−16.1514	−	3.02376i	−0.713102	−	0.133502i
$514$		0			0
$515$	8.29324	+	4.78810i	0.365444	+	0.210989i
$516$		0			0
$517$	26.5658	−	15.3378i	1.16836	−	0.674554i
$518$		0			0
$519$	−2.09292	+	33.8831i	−0.0918689	+	1.48730i
$520$		0			0
$521$	5.20087			0.227854			0.113927	−	0.993489i	$-0.463657\pi$
$521$	5.20087			0.227854			0.113927	+	0.993489i	$0.463657\pi$
$522$		0			0
$523$			40.0731i			1.75227i	0.482062	+	0.876137i	$0.339888\pi$
$523$			40.0731i			1.75227i	−0.482062	+	0.876137i	$0.660112\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−53.2737	+	30.7576i	−2.32064	+	1.33982i
$528$		0			0
$529$	−7.02557	+	12.1686i	−0.305460	+	0.529072i
$530$		0			0
$531$	−25.8230	−	3.20233i	−1.12062	−	0.138969i
$532$		0			0
$533$	5.06895	+	2.92656i	0.219561	+	0.126763i
$534$		0			0
$535$	−8.91317	+	5.14602i	−0.385350	+	0.222482i
$536$		0			0
$537$	14.4954	+	29.1173i	0.625523	+	1.25651i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.24192			0.354348			0.177174	−	0.984180i	$-0.443305\pi$
$541$	8.24192			0.354348			0.177174	+	0.984180i	$0.443305\pi$
$542$		0			0
$543$	3.45638	+	6.94293i	0.148328	+	0.297950i
$544$		0			0
$545$	19.7801	+	34.2601i	0.847285	+	1.46754i
$546$		0			0
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	−0.915162	−	0.403086i	$-0.867938\pi$
$547$	−2.53756	+	4.39518i	−0.108498	+	0.187925i	0.806664	+	0.591011i	$0.201271\pi$
$548$		0			0
$549$	1.80866	−	0.765153i	0.0771917	−	0.0326559i
$550$		0			0
$551$	−4.53400	+	7.85312i	−0.193155	+	0.334554i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−14.1315	−	9.36570i	−0.599848	−	0.397552i
$556$		0			0
$557$		−	43.4285i		−	1.84012i	−0.391773	−	0.920062i	$-0.628138\pi$
$557$		−	43.4285i		−	1.84012i	0.391773	−	0.920062i	$-0.371862\pi$
$558$		0			0
$559$			34.4635i			1.45765i
$560$		0			0
$561$	30.2208	+	1.86670i	1.27592	+	0.0788122i
$562$		0			0
$563$	−4.99118	−	8.64498i	−0.210353	−	0.364343i	0.741472	−	0.670984i	$-0.234128\pi$
$563$	−4.99118	−	8.64498i	−0.210353	−	0.364343i	−0.951825	+	0.306641i	$0.900795\pi$
$564$		0			0
$565$	15.1606	+	8.75300i	0.637813	+	0.368241i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.0597	+	8.11739i	0.589415	+	0.340299i	0.764866	−	0.644189i	$-0.222805\pi$
$569$	14.0597	+	8.11739i	0.589415	+	0.340299i	−0.175451	+	0.984488i	$0.556138\pi$
$570$		0			0
$571$	6.31028	+	10.9297i	0.264077	+	0.457395i	0.967321	−	0.253553i	$-0.0815994\pi$
$571$	6.31028	+	10.9297i	0.264077	+	0.457395i	−0.703244	+	0.710948i	$0.748266\pi$
$572$		0			0
$573$	11.7785	+	0.727547i	0.492056	+	0.0303937i
$574$		0			0
$575$		−	9.64936i		−	0.402406i
$576$		0			0
$577$		−	4.82678i		−	0.200942i	−0.994940	−	0.100471i	$-0.967965\pi$
$577$		−	4.82678i		−	0.200942i	0.994940	−	0.100471i	$-0.0320349\pi$
$578$		0			0
$579$	23.0335	+	15.2655i	0.957239	+	0.634415i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	3.38971	−	5.87115i	0.140387	−	0.243158i
$584$		0			0
$585$	−29.1875	+	12.3478i	−1.20675	+	0.510518i
$586$		0			0
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	−0.953925	−	0.300044i	$-0.902999\pi$
$587$	−5.26032	+	9.11114i	−0.217117	+	0.376057i	0.736809	+	0.676101i	$0.236332\pi$
$588$		0			0
$589$	15.0944	+	26.1443i	0.621955	+	1.07726i
$590$		0			0
$591$	20.0317	+	40.2382i	0.823994	+	1.65518i
$592$		0			0
$593$	29.4685			1.21013			0.605063	−	0.796178i	$-0.293148\pi$
$593$	29.4685			1.21013			0.605063	+	0.796178i	$0.293148\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.45740	+	4.93625i	0.100575	+	0.202027i
$598$		0			0
$599$	7.11658	−	4.10876i	0.290776	−	0.167879i	−0.347516	−	0.937674i	$-0.612975\pi$
$599$	7.11658	−	4.10876i	0.290776	−	0.167879i	0.638292	+	0.769795i	$0.279641\pi$
$600$		0			0
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.348425	−	0.937337i	$-0.613283\pi$
$601$	−32.7131	−	18.8869i	−1.33439	−	0.770413i	−0.985970	+	0.166924i	$0.946617\pi$
$602$		0			0
$603$	−22.9926	−	2.85133i	−0.936333	−	0.116115i
$604$		0			0
$605$	−5.22038	+	9.04197i	−0.212239	+	0.367608i
$606$		0			0
$607$	−30.8497	+	17.8111i	−1.25215	+	0.722929i	−0.971536	−	0.236892i	$-0.923871\pi$
$607$	−30.8497	+	17.8111i	−1.25215	+	0.722929i	−0.280613	+	0.959821i	$0.590538\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	41.6493i		−	1.68495i
$612$		0			0
$613$	−23.9319			−0.966601			−0.483301	−	0.875455i	$-0.660562\pi$
$613$	−23.9319			−0.966601			−0.483301	+	0.875455i	$0.660562\pi$
$614$		0			0
$615$	0.486667	−	7.87885i	0.0196243	−	0.317706i
$616$		0			0
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	−0.539448	−	0.842019i	$-0.681367\pi$
$617$	−1.98622	+	1.14675i	−0.0799623	+	0.0461663i	0.459486	+	0.888185i	$0.348034\pi$
$618$		0			0
$619$	−9.10806	−	5.25854i	−0.366084	−	0.211359i	0.305662	−	0.952140i	$-0.401122\pi$
$619$	−9.10806	−	5.25854i	−0.366084	−	0.211359i	−0.671746	+	0.740781i	$0.734455\pi$
$620$		0			0
$621$	5.16217	+	14.6619i	0.207151	+	0.588362i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.3617	+	26.6073i	0.614469	+	1.06429i
$626$		0			0
$627$	0.916093	−	14.8310i	0.0365852	−	0.592293i
$628$		0			0
$629$	21.9914			0.876856
$630$		0			0
$631$	−2.02836			−0.0807477			−0.0403739	−	0.999185i	$-0.512855\pi$
$631$	−2.02836			−0.0807477			−0.0403739	+	0.999185i	$0.512855\pi$
$632$		0			0
$633$	−0.159509	−	0.105715i	−0.00633992	−	0.00420181i
$634$		0			0
$635$	19.1899	+	33.2380i	0.761530	+	1.31901i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−18.8286	−	14.2241i	−0.744848	−	0.562695i
$640$		0			0
$641$	−10.7778	−	6.22257i	−0.425698	−	0.245777i	0.271814	−	0.962350i	$-0.412376\pi$
$641$	−10.7778	−	6.22257i	−0.425698	−	0.245777i	−0.697512	+	0.716573i	$0.745710\pi$
$642$		0			0
$643$	12.3358	−	7.12209i	0.486477	−	0.280868i	−0.236635	−	0.971599i	$-0.576044\pi$
$643$	12.3358	−	7.12209i	0.486477	−	0.280868i	0.723112	+	0.690731i	$0.242711\pi$
$644$		0			0
$645$	41.6086	−	20.7139i	1.63834	−	0.815610i
$646$		0			0
$647$	−20.3820			−0.801299			−0.400649	−	0.916231i	$-0.631215\pi$
$647$	−20.3820			−0.801299			−0.400649	+	0.916231i	$0.631215\pi$
$648$		0			0
$649$		−	23.5303i		−	0.923644i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.55335	+	4.36093i	−0.295585	+	0.170656i	−0.640458	−	0.767993i	$-0.721255\pi$
$653$	−7.55335	+	4.36093i	−0.295585	+	0.170656i	0.344873	+	0.938650i	$0.387922\pi$
$654$		0			0
$655$	1.11556	−	1.93221i	0.0435887	−	0.0754978i
$656$		0			0
$657$	30.6170	+	23.1296i	1.19448	+	0.902373i
$658$		0			0
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	0.136864	−	0.990590i	$-0.456298\pi$
$659$	−16.7524	−	9.67200i	−0.652581	−	0.376768i	−0.789444	+	0.613822i	$0.789631\pi$
$660$		0			0
$661$	31.8948	−	18.4145i	1.24056	−	0.716240i	0.271355	−	0.962479i	$-0.412528\pi$
$661$	31.8948	−	18.4145i	1.24056	−	0.716240i	0.969209	+	0.246239i	$0.0791949\pi$
$662$		0			0
$663$	22.7108	−	34.2674i	0.882016	−	1.33083i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.57801			0.332142
$668$		0			0
$669$	−22.5698	−	1.39411i	−0.872598	−	0.0538993i
$670$		0			0
$671$	0.887942	+	1.53796i	0.0342786	+	0.0593723i
$672$		0			0
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	−0.645319	−	0.763913i	$-0.723276\pi$
$673$	8.79204	−	15.2283i	0.338908	−	0.587006i	0.984228	+	0.176907i	$0.0566091\pi$
$674$		0			0
$675$	12.7253	+	10.9084i	0.489798	+	0.419864i
$676$		0			0
$677$	20.4146	−	35.3590i	0.784595	−	1.35896i	−0.144646	−	0.989484i	$-0.546204\pi$
$677$	20.4146	−	35.3590i	0.784595	−	1.35896i	0.929241	−	0.369475i	$-0.120462\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−0.989649	+	16.0218i	−0.0379234	+	0.613958i
$682$		0			0
$683$			9.88755i			0.378337i	0.981945	+	0.189168i	$0.0605792\pi$
$683$			9.88755i			0.378337i	−0.981945	+	0.189168i	$0.939421\pi$
$684$		0			0
$685$		−	47.3847i		−	1.81048i
$686$		0			0
$687$	12.8391	−	19.3724i	0.489843	−	0.739102i
$688$		0			0
$689$	−4.60233	−	7.97148i	−0.175335	−	0.303689i
$690$		0			0
$691$	−37.9217	−	21.8941i	−1.44261	−	0.832891i	−0.444587	−	0.895736i	$-0.646649\pi$
$691$	−37.9217	−	21.8941i	−1.44261	−	0.832891i	−0.998023	+	0.0628444i	$0.979983\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	28.4459	+	16.4233i	1.07902	+	0.622970i
$696$		0			0
$697$	5.11987	+	8.86787i	0.193929	+	0.335894i
$698$		0			0
$699$	−16.3480	−	32.8387i	−0.618339	−	1.24207i
$700$		0			0
$701$		−	29.6742i		−	1.12078i	−0.828229	−	0.560389i	$-0.810651\pi$
$701$		−	29.6742i		−	1.12078i	0.828229	−	0.560389i	$-0.189349\pi$
$702$		0			0
$703$		−	10.7924i		−	0.407044i
$704$		0			0
$705$	−50.2842	+	25.0329i	−1.89381	+	0.942793i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−23.5269	+	40.7498i	−0.883572	+	1.53039i	−0.0362296	+	0.999343i	$0.511535\pi$
$709$	−23.5269	+	40.7498i	−0.883572	+	1.53039i	−0.847342	+	0.531048i	$0.821799\pi$
$710$		0			0
$711$	6.06791	+	14.3432i	0.227564	+	0.537914i
$712$		0			0
$713$	14.2788	−	24.7316i	0.534745	−	0.926206i
$714$		0			0
$715$	−14.3293	−	24.8191i	−0.535885	−	0.928180i
$716$		0			0
$717$	−8.54451	+	12.8924i	−0.319100	+	0.481476i
$718$		0			0
$719$	1.81830			0.0678110			0.0339055	−	0.999425i	$-0.489205\pi$
$719$	1.81830			0.0678110			0.0339055	+	0.999425i	$0.489205\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	31.8253	+	1.96581i	1.18360	+	0.0731093i
$724$		0			0
$725$	8.01029	−	4.62474i	0.297495	−	0.171759i
$726$		0			0
$727$	−21.7854	−	12.5778i	−0.807976	−	0.466485i	0.0382766	−	0.999267i	$-0.487813\pi$
$727$	−21.7854	−	12.5778i	−0.807976	−	0.466485i	−0.846252	+	0.532782i	$0.821147\pi$
$728$		0			0
$729$	−25.1714	−	9.76721i	−0.932276	−	0.361748i
$730$		0			0
$731$	−30.1460	+	52.2145i	−1.11499	+	1.93122i
$732$		0			0
$733$	−3.84543	+	2.22016i	−0.142034	+	0.0820034i	−0.569333	−	0.822107i	$-0.692799\pi$
$733$	−3.84543	+	2.22016i	−0.142034	+	0.0820034i	0.427299	+	0.904110i	$0.359465\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	20.9512i		−	0.771747i
$738$		0			0
$739$	17.9522			0.660381			0.330191	−	0.943914i	$-0.392887\pi$
$739$	17.9522			0.660381			0.330191	+	0.943914i	$0.392887\pi$
$740$		0			0
$741$	−16.8169	−	11.1455i	−0.617783	−	0.409439i
$742$		0			0
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.949106	−	0.314956i	$-0.898010\pi$
$743$	−31.3712	+	18.1122i	−1.15090	+	0.664472i	−0.201793	+	0.979428i	$0.564677\pi$
$744$		0			0
$745$	−12.1829	−	7.03378i	−0.446345	−	0.257698i
$746$		0			0
$747$	−18.5368	−	43.8171i	−0.678228	−	1.60319i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	0.735995	−	0.676986i	$-0.236714\pi$
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	−0.954285	+	0.298897i	$0.903381\pi$
$752$		0			0
$753$	9.81792	−	4.88763i	0.357785	−	0.178115i
$754$		0			0
$755$	28.2682			1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$	−12.5833	+	6.26430i	−0.456744	+	0.227380i
$760$		0			0
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	−0.999390	−	0.0349300i	$-0.988879\pi$
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	0.469445	−	0.882962i	$-0.344454\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−55.0220	−	6.82332i	−1.98932	−	0.246698i
$766$		0			0
$767$	−27.6677	−	15.9740i	−0.999023	−	0.576786i
$768$		0			0
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	−0.415772	−	0.909469i	$-0.636489\pi$
$769$	4.54689	−	2.62515i	0.163965	−	0.0946653i	0.579737	+	0.814804i	$0.303155\pi$
$770$		0			0
$771$	−23.6569	−	15.6787i	−0.851981	−	0.564654i
$772$		0			0
$773$	−31.3657			−1.12815			−0.564073	−	0.825725i	$-0.690766\pi$
$773$	−31.3657			−1.12815			−0.564073	+	0.825725i	$0.690766\pi$
$774$		0			0
$775$		−	30.7930i		−	1.10612i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.35195	−	2.51260i	0.155925	−	0.0900233i
$780$		0			0
$781$	10.6694	−	18.4800i	0.381782	−	0.661266i
$782$		0			0
$783$	−9.69725	+	11.3125i	−0.346551	+	0.404274i
$784$		0			0
$785$	−38.2923	−	22.1081i	−1.36671	−	0.789071i
$786$		0			0
$787$	1.59324	−	0.919855i	0.0567927	−	0.0327893i	−0.471335	−	0.881954i	$-0.656228\pi$
$787$	1.59324	−	0.919855i	0.0567927	−	0.0327893i	0.528128	+	0.849165i	$0.322894\pi$
$788$		0			0
$789$	20.8927	+	1.29052i	0.743800	+	0.0459436i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	2.41118			0.0856236
$794$		0			0
$795$	−6.85798	+	10.3477i	−0.243227	+	0.366995i
$796$		0			0
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	0.956792	−	0.290773i	$-0.0939126\pi$
$797$	6.39659	+	11.0792i	0.226579	+	0.392446i	−0.730213	+	0.683219i	$0.760579\pi$
$798$		0			0
$799$	36.4316	−	63.1015i	1.28886	−	2.23237i
$800$		0			0
$801$	11.3862	−	15.0721i	0.402313	−	0.532548i
$802$		0			0
$803$	−17.3495	+	30.0502i	−0.612250	+	1.06045i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	39.2758	−	19.5526i	1.38257	−	0.688284i
$808$		0			0
$809$		−	14.9206i		−	0.524582i	−0.964989	−	0.262291i	$-0.915522\pi$
$809$		−	14.9206i		−	0.524582i	0.964989	−	0.262291i	$-0.0844780\pi$
$810$		0			0
$811$			37.5478i			1.31848i	0.751933	+	0.659240i	$0.229122\pi$
$811$			37.5478i			1.31848i	−0.751933	+	0.659240i	$0.770878\pi$
$812$		0			0
$813$	0.174333	+	0.350187i	0.00611413	+	0.0122816i
$814$		0			0
$815$	−16.4067	−	28.4172i	−0.574701	−	0.995411i
$816$		0			0
$817$	25.6245	+	14.7943i	0.896489	+	0.517588i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.88164	+	1.66371i	0.100570	+	0.0580640i	0.549441	−	0.835532i	$-0.314841\pi$
$821$	2.88164	+	1.66371i	0.100570	+	0.0580640i	−0.448872	+	0.893596i	$0.648174\pi$
$822$		0			0
$823$	−25.4654	−	44.1073i	−0.887667	−	1.53748i	−0.842626	−	0.538499i	$-0.818992\pi$
$823$	−25.4654	−	44.1073i	−0.887667	−	1.53748i	−0.0450407	−	0.998985i	$-0.514342\pi$
$824$		0			0
$825$	−8.37314	+	12.6338i	−0.291515	+	0.439854i
$826$		0			0
$827$			16.9198i			0.588360i	0.955750	+	0.294180i	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		0			0
$829$		−	5.37475i		−	0.186673i	−0.995635	−	0.0933364i	$-0.970247\pi$
$829$		−	5.37475i		−	0.186673i	0.995635	−	0.0933364i	$-0.0297532\pi$
$830$		0			0
$831$	2.18200	−	35.3253i	0.0756928	−	1.22542i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	18.6165	−	32.2447i	0.644251	−	1.11588i
$836$		0			0
$837$	16.4735	+	46.7890i	0.569408	+	1.61727i
$838$		0			0
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	−0.585026	−	0.811014i	$-0.698916\pi$
$839$	11.8714	−	20.5618i	0.409846	−	0.709874i	0.994872	+	0.101140i	$0.0322492\pi$
$840$		0			0
$841$	−10.3887	−	17.9938i	−0.358232	−	0.620477i
$842$		0			0
$843$	17.8986	+	1.10557i	0.616460	+	0.0380780i
$844$		0			0
$845$	−1.62634			−0.0559476
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−13.1239	+	19.8021i	−0.450411	+	0.679605i
$850$		0			0
$851$	−8.84146	+	5.10462i	−0.303081	+	0.174984i
$852$		0			0
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	0.667077	−	0.744988i	$-0.267545\pi$
$853$	10.3810	+	5.99345i	0.355437	+	0.205212i	−0.311640	+	0.950200i	$0.600878\pi$
$854$		0			0
$855$	−3.34858	+	27.0023i	−0.114519	+	0.923459i
$856$		0			0
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.175884	+	0.984411i	$0.556278\pi$
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.764583	+	0.644526i	$0.777055\pi$
$858$		0			0
$859$	33.8798	−	19.5605i	1.15596	−	0.667395i	0.205630	−	0.978630i	$-0.434076\pi$
$859$	33.8798	−	19.5605i	1.15596	−	0.667395i	0.950333	+	0.311235i	$0.100742\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			45.3011i			1.54207i	0.636794	+	0.771034i	$0.280260\pi$
$863$			45.3011i			1.54207i	−0.636794	+	0.771034i	$0.719740\pi$
$864$		0			0
$865$	56.2126			1.91129
$866$		0			0
$867$	38.0238	−	18.9293i	1.29136	−	0.642873i
$868$		0			0
$869$	−12.1965	+	7.04166i	−0.413738	+	0.238872i
$870$		0			0
$871$	−24.6351	−	14.2231i	−0.834730	−	0.481931i
$872$		0			0
$873$	42.1334	−	17.8245i	1.42600	−	0.603269i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	0.898236	−	0.439512i	$-0.144849\pi$
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	−0.829747	+	0.558139i	$0.811515\pi$
$878$		0			0
$879$	−12.1716	−	8.06680i	−0.410539	−	0.272086i
$880$		0			0
$881$	−54.3727			−1.83186			−0.915931	−	0.401336i	$-0.868546\pi$
$881$	−54.3727			−1.83186			−0.915931	+	0.401336i	$0.868546\pi$
$882$		0			0
$883$	23.1175			0.777965			0.388982	−	0.921245i	$-0.372827\pi$
$883$	23.1175			0.777965			0.388982	+	0.921245i	$0.372827\pi$
$884$		0			0
$885$	−2.65636	+	43.0049i	−0.0892926	+	1.44559i
$886$		0			0
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	0.567629	−	0.823285i	$-0.307861\pi$
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	−0.996800	+	0.0799384i	$0.974528\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	5.96391	−	23.6762i	0.199799	−	0.793181i
$892$		0			0
$893$	−30.9674	−	17.8790i	−1.03628	−	0.598298i
$894$		0			0
$895$	46.6428	−	26.9292i	1.55910	−	0.900144i
$896$		0			0
$897$	−1.17660	+	19.0485i	−0.0392856	+	0.636010i
$898$		0			0
$899$	27.3741			0.912979
$900$		0			0
$901$		−	16.1031i		−	0.536472i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.1218	−	6.42118i	0.369702	−	0.213447i
$906$		0			0
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	−0.375974	−	0.926630i	$-0.622692\pi$
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	0.990472	−	0.137712i	$-0.0439748\pi$
$908$		0			0
$909$	−4.07817	−	9.63991i	−0.135264	−	0.319736i
$910$		0			0
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	0.551476	−	0.834191i	$-0.314065\pi$
$911$	3.16266	+	1.82596i	0.104784	+	0.0604969i	−0.446692	+	0.894688i	$0.647398\pi$
$912$		0			0
$913$	37.2591	−	21.5116i	1.23310	−	0.711929i
$914$		0			0
$915$	−1.44922	−	2.91108i	−0.0479096	−	0.0962373i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−34.7988			−1.14791			−0.573954	−	0.818888i	$-0.694591\pi$
$919$	−34.7988			−1.14791			−0.573954	+	0.818888i	$0.694591\pi$
$920$		0			0
$921$	−4.12462	−	8.28523i	−0.135911	−	0.273008i
$922$		0			0
$923$	−14.4863	−	25.0910i	−0.476822	−	0.825879i
$924$		0			0
$925$	−5.50420	+	9.53356i	−0.180977	+	0.313461i
$926$		0			0
$927$	−1.23275	+	9.94068i	−0.0404889	+	0.326495i
$928$		0			0
$929$	−25.1736	+	43.6019i	−0.825917	+	1.43053i	0.0752987	+	0.997161i	$0.476009\pi$
$929$	−25.1736	+	43.6019i	−0.825917	+	1.43053i	−0.901216	+	0.433370i	$0.857324\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−13.5963	−	9.01103i	−0.445124	−	0.295008i
$934$		0			0
$935$		−	50.1368i		−	1.63965i
$936$		0			0
$937$			6.48087i			0.211721i	0.994381	+	0.105860i	$0.0337596\pi$
$937$			6.48087i			0.211721i	−0.994381	+	0.105860i	$0.966240\pi$
$938$		0			0
$939$	−28.6148	−	1.76751i	−0.933810	−	0.0576804i
$940$		0			0
$941$	0.334024	+	0.578547i	0.0108889	+	0.0188601i	0.871418	−	0.490540i	$-0.163201\pi$
$941$	0.334024	+	0.578547i	0.0108889	+	0.0188601i	−0.860530	+	0.509400i	$0.829867\pi$
$942$		0			0
$943$	−4.11679	−	2.37683i	−0.134061	−	0.0774003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	50.7461	+	29.2983i	1.64903	+	0.952067i	0.977459	+	0.211125i	$0.0677127\pi$
$947$	50.7461	+	29.2983i	1.64903	+	0.952067i	0.671569	+	0.740942i	$0.265621\pi$
$948$		0			0
$949$	23.5560	+	40.8002i	0.764661	+	1.32443i
$950$		0			0
$951$	45.8576	+	2.83257i	1.48703	+	0.0918524i
$952$		0			0
$953$		−	48.3707i		−	1.56688i	−0.621467	−	0.783441i	$-0.713463\pi$
$953$		−	48.3707i		−	1.56688i	0.621467	−	0.783441i	$-0.286537\pi$
$954$		0			0
$955$		−	19.5408i		−	0.632326i
$956$		0			0
$957$	−11.2311	−	7.44348i	−0.363051	−	0.240614i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.0665	−	52.0767i	0.969887	−	1.67989i
$962$		0			0
$963$	−8.58996	−	6.48928i	−0.276808	−	0.209114i
$964$		0			0
$965$	22.8781	−	39.6261i	0.736474	−	1.27561i
$966$		0			0
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	0.969829	−	0.243787i	$-0.0783898\pi$
$967$	8.51390	+	14.7465i	0.273788	+	0.474216i	−0.696040	+	0.718003i	$0.745057\pi$
$968$		0			0
$969$	−15.7295	−	31.5963i	−0.505304	−	1.01502i
$970$		0			0
$971$	27.1302			0.870651			0.435325	−	0.900273i	$-0.356633\pi$
$971$	27.1302			0.870651			0.435325	+	0.900273i	$0.356633\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	9.17105	+	18.4221i	0.293709	+	0.589981i
$976$		0			0
$977$	−5.49838	+	3.17449i	−0.175909	+	0.101561i	−0.585369	−	0.810767i	$-0.699050\pi$
$977$	−5.49838	+	3.17449i	−0.175909	+	0.101561i	0.409460	+	0.912328i	$0.365717\pi$
$978$		0			0
$979$	14.7931	+	8.54080i	0.472789	+	0.272965i
$980$		0			0
$981$	−24.9432	+	33.0177i	−0.796376	+	1.05418i
$982$		0			0
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	−0.980156	−	0.198227i	$-0.936482\pi$
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	0.661748	+	0.749727i	$0.269815\pi$
$984$		0			0
$985$	64.4572	−	37.2144i	2.05378	−	1.18575i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	27.9898i		−	0.890024i
$990$		0			0
$991$	−12.7761			−0.405845			−0.202922	−	0.979195i	$-0.565044\pi$
$991$	−12.7761			−0.405845			−0.202922	+	0.979195i	$0.565044\pi$
$992$		0			0
$993$	1.88366	−	30.4952i	0.0597760	−	0.967737i
$994$		0			0
$995$	7.90734	−	4.56530i	0.250679	−	0.144730i
$996$		0			0
$997$	−17.9846	−	10.3834i	−0.569579	−	0.328847i	0.187402	−	0.982283i	$-0.439993\pi$
$997$	−17.9846	−	10.3834i	−0.569579	−	0.328847i	−0.756981	+	0.653436i	$0.773327\pi$
$998$		0			0
$999$	3.26324	−	17.4305i	0.103244	−	0.551478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.x.b.1469.8		16
3.2	odd	2		5292.2.x.b.4409.8		16
7.2	even	3		1764.2.w.b.1109.4		16
7.3	odd	6		1764.2.bm.a.1685.7		16
7.4	even	3		252.2.bm.a.173.2	yes	16
7.5	odd	6		252.2.w.a.101.5	yes	16
7.6	odd	2		1764.2.x.a.1469.1		16
9.4	even	3		5292.2.x.a.881.1		16
9.5	odd	6		1764.2.x.a.293.1		16
21.2	odd	6		5292.2.w.b.521.8		16
21.5	even	6		756.2.w.a.521.1		16
21.11	odd	6		756.2.bm.a.89.1		16
21.17	even	6		5292.2.bm.a.4625.8		16
21.20	even	2		5292.2.x.a.4409.1		16
28.11	odd	6		1008.2.df.d.929.7		16
28.19	even	6		1008.2.ca.d.353.4		16
63.4	even	3		756.2.w.a.341.1		16
63.5	even	6		252.2.bm.a.185.2	yes	16
63.11	odd	6		2268.2.t.b.2105.8		16
63.13	odd	6		5292.2.x.b.881.8		16
63.23	odd	6		1764.2.bm.a.1697.7		16
63.25	even	3		2268.2.t.a.2105.1		16
63.31	odd	6		5292.2.w.b.1097.8		16
63.32	odd	6		252.2.w.a.5.5	✓	16
63.40	odd	6		756.2.bm.a.17.1		16
63.41	even	6	inner	1764.2.x.b.293.8		16
63.47	even	6		2268.2.t.a.1781.1		16
63.58	even	3		5292.2.bm.a.2285.8		16
63.59	even	6		1764.2.w.b.509.4		16
63.61	odd	6		2268.2.t.b.1781.8		16
84.11	even	6		3024.2.df.d.1601.1		16
84.47	odd	6		3024.2.ca.d.2033.1		16
252.67	odd	6		3024.2.ca.d.2609.1		16
252.95	even	6		1008.2.ca.d.257.4		16
252.103	even	6		3024.2.df.d.17.1		16
252.131	odd	6		1008.2.df.d.689.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	63.32	odd	6
252.2.w.a.101.5	yes	16	7.5	odd	6
252.2.bm.a.173.2	yes	16	7.4	even	3
252.2.bm.a.185.2	yes	16	63.5	even	6
756.2.w.a.341.1		16	63.4	even	3
756.2.w.a.521.1		16	21.5	even	6
756.2.bm.a.17.1		16	63.40	odd	6
756.2.bm.a.89.1		16	21.11	odd	6
1008.2.ca.d.257.4		16	252.95	even	6
1008.2.ca.d.353.4		16	28.19	even	6
1008.2.df.d.689.7		16	252.131	odd	6
1008.2.df.d.929.7		16	28.11	odd	6
1764.2.w.b.509.4		16	63.59	even	6
1764.2.w.b.1109.4		16	7.2	even	3
1764.2.x.a.293.1		16	9.5	odd	6
1764.2.x.a.1469.1		16	7.6	odd	2
1764.2.x.b.293.8		16	63.41	even	6	inner
1764.2.x.b.1469.8		16	1.1	even	1	trivial
1764.2.bm.a.1685.7		16	7.3	odd	6
1764.2.bm.a.1697.7		16	63.23	odd	6
2268.2.t.a.1781.1		16	63.47	even	6
2268.2.t.a.2105.1		16	63.25	even	3
2268.2.t.b.1781.8		16	63.61	odd	6
2268.2.t.b.2105.8		16	63.11	odd	6
3024.2.ca.d.2033.1		16	84.47	odd	6
3024.2.ca.d.2609.1		16	252.67	odd	6
3024.2.df.d.17.1		16	252.103	even	6
3024.2.df.d.1601.1		16	84.11	even	6
5292.2.w.b.521.8		16	21.2	odd	6
5292.2.w.b.1097.8		16	63.31	odd	6
5292.2.x.a.881.1		16	9.4	even	3
5292.2.x.a.4409.1		16	21.20	even	2
5292.2.x.b.881.8		16	63.13	odd	6
5292.2.x.b.4409.8		16	3.2	odd	2
5292.2.bm.a.2285.8		16	63.58	even	3
5292.2.bm.a.4625.8		16	21.17	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.55054 - 0.771901i) q^{3} +(-1.43402 - 2.48379i) q^{5} +(1.80834 - 2.39372i) q^{9} +O(q^{10})\)	\(q+(1.55054 - 0.771901i) q^{3} +(-1.43402 - 2.48379i) q^{5} +(1.80834 - 2.39372i) q^{9} +(2.34941 + 1.35643i) q^{11} +(3.18987 - 1.84167i) q^{13} +(-4.14074 - 2.74429i) q^{15} +6.44383 q^{17} -3.16234i q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(0.956179 - 5.10742i) q^{27} +(-2.48332 - 1.43375i) q^{29} +(-8.26739 + 4.77318i) q^{31} +(4.68987 + 0.289688i) q^{33} +3.41279 q^{37} +(3.52443 - 5.31785i) q^{39} +(0.794538 + 1.37618i) q^{41} +(-4.67828 + 8.10302i) q^{43} +(-8.53870 - 1.05889i) q^{45} +(5.65372 - 9.79254i) q^{47} +(9.99141 - 4.97400i) q^{51} -2.49899i q^{53} -7.78058i q^{55} +(-2.44102 - 4.90333i) q^{57} +(-4.33680 - 7.51156i) q^{59} +(0.566915 + 0.327308i) q^{61} +(-9.14867 - 5.28199i) q^{65} +(-3.86146 - 6.68825i) q^{67} +(-2.86240 + 4.31894i) q^{69} -7.86582i q^{71} +12.7905i q^{73} +(-0.344443 + 5.57633i) q^{75} +(-2.59566 + 4.49581i) q^{79} +(-2.45983 - 8.65732i) q^{81} +(7.92948 - 13.7343i) q^{83} +(-9.24057 - 16.0051i) q^{85} +(-4.95720 - 0.306200i) q^{87} +6.29653 q^{89} +(-9.13448 + 13.7826i) q^{93} +(-7.85460 + 4.53486i) q^{95} +(13.2065 + 7.62477i) q^{97} +(7.49544 - 3.17095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} + 6 q^{11} + 3 q^{13} - 3 q^{15} + 18 q^{17} - 21 q^{23} - 8 q^{25} - 9 q^{27} + 6 q^{29} - 6 q^{31} + 27 q^{33} - 2 q^{37} + 6 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 18 q^{51} + 15 q^{57} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - 21 q^{69} - 42 q^{75} - q^{79} - 18 q^{81} + 6 q^{85} + 51 q^{87} + 42 q^{89} + 48 q^{93} - 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 6 * q^11 + 3 * q^13 - 3 * q^15 + 18 * q^17 - 21 * q^23 - 8 * q^25 - 9 * q^27 + 6 * q^29 - 6 * q^31 + 27 * q^33 - 2 * q^37 + 6 * q^39 + 6 * q^41 - 2 * q^43 - 15 * q^45 - 18 * q^47 + 18 * q^51 + 15 * q^57 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - 21 * q^69 - 42 * q^75 - q^79 - 18 * q^81 + 6 * q^85 + 51 * q^87 + 42 * q^89 + 48 * q^93 - 6 * q^95 + 3 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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