LMFDB - Embedded newform 1764.2.b.j.1567.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1764.1567");

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.b (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.4
Root			$0.0777157 - 1.41208i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.j.1567.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0777157 + 1.41208i) q^{2} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 - 2.79004i) q^{8} +O(q^{10})$	\(q+(0.0777157 + 1.41208i) q^{2} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 - 2.79004i) q^{8} +(0.619848 - 0.0341142i) q^{10} +2.11598i q^{11} +3.84803i q^{13} +(3.90366 - 0.872621i) q^{16} -5.64831i q^{17} +2.97584 q^{19} +(0.0963438 + 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} +4.77038i q^{23} +4.80731 q^{25} +(-5.43371 + 0.299052i) q^{26} -7.02285 q^{29} +7.42528 q^{31} +(1.53558 + 5.44445i) q^{32} +(7.97584 - 0.438962i) q^{34} -5.28670 q^{37} +(0.231269 + 4.20212i) q^{38} +(-1.22472 + 0.203861i) q^{40} +6.81813i q^{41} +4.38646i q^{43} +(-0.464416 - 4.20639i) q^{44} +(-6.73615 + 0.370733i) q^{46} -1.68914 q^{47} +(0.373604 + 6.78829i) q^{50} +(-0.844569 - 7.64957i) q^{52} -10.7120 q^{53} +0.928833 q^{55} +(-0.545785 - 9.91680i) q^{58} +8.11818 q^{59} +6.18674i q^{61} +(0.577061 + 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} +1.68914 q^{65} +7.85056i q^{67} +(1.23970 + 11.2284i) q^{68} +1.16982i q^{71} +10.0348i q^{73} +(-0.410860 - 7.46523i) q^{74} +(-5.91574 + 0.653140i) q^{76} +15.5836i q^{79} +(-0.383048 - 1.71356i) q^{80} +(-9.62772 + 0.529876i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(-6.19401 + 0.340896i) q^{86} +(5.90366 - 0.982694i) q^{88} +10.4187i q^{89} +(-1.04701 - 9.48314i) q^{92} +(-0.131272 - 2.38519i) q^{94} -1.30628i q^{95} -2.22605i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	$ 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 8 q^{10} + 10 q^{16} - 12 q^{19} + 22 q^{20} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 16 q^{29} + 12 q^{31} + 12 q^{32} + 28 q^{34} - 12 q^{37} - 2 q^{38} - 4 q^{40} - 4 q^{44} - 12 q^{46} - 8 q^{47} - 2 q^{50} - 4 q^{52} - 8 q^{53} + 8 q^{55} - 14 q^{58} + 28 q^{59} - 48 q^{62} + 2 q^{64} + 8 q^{65} + 16 q^{68} - 38 q^{74} - 44 q^{76} + 6 q^{80} + 4 q^{82} + 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} + 32 q^{94}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 8 * q^10 + 10 * q^16 - 12 * q^19 + 22 * q^20 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 16 * q^29 + 12 * q^31 + 12 * q^32 + 28 * q^34 - 12 * q^37 - 2 * q^38 - 4 * q^40 - 4 * q^44 - 12 * q^46 - 8 * q^47 - 2 * q^50 - 4 * q^52 - 8 * q^53 + 8 * q^55 - 14 * q^58 + 28 * q^59 - 48 * q^62 + 2 * q^64 + 8 * q^65 + 16 * q^68 - 38 * q^74 - 44 * q^76 + 6 * q^80 + 4 * q^82 + 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 + 32 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.0777157	+	1.41208i	0.0549533	+	0.998489i
$2$	0.0777157	+	1.41208i	0.0549533	+	0.998489i
$3$		0			0
$3$		0			0
$4$	−1.98792	+	0.219481i	−0.993960	+	0.109740i
$5$		−	0.438962i		−	0.196310i	−0.995171	−	0.0981549i	$-0.968706\pi$
$5$		−	0.438962i		−	0.196310i	0.995171	−	0.0981549i	$-0.0312941\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.464416	−	2.79004i	−0.164196	−	0.986428i
$9$		0			0
$10$	0.619848	−	0.0341142i	0.196013	−	0.0107879i
$11$			2.11598i			0.637991i	0.947756	+	0.318995i	$0.103345\pi$
$11$			2.11598i			0.637991i	−0.947756	+	0.318995i	$0.896655\pi$
$12$		0			0
$13$			3.84803i			1.06725i	0.845721	+	0.533625i	$0.179171\pi$
$13$			3.84803i			1.06725i	−0.845721	+	0.533625i	$0.820829\pi$
$14$		0			0
$15$		0			0
$16$	3.90366	−	0.872621i	0.975914	−	0.218155i
$17$		−	5.64831i		−	1.36992i	−0.728583	−	0.684958i	$-0.759821\pi$
$17$		−	5.64831i		−	1.36992i	0.728583	−	0.684958i	$-0.240179\pi$
$18$		0			0
$19$	2.97584			0.682705			0.341352	−	0.939935i	$-0.389115\pi$
$19$	2.97584			0.682705			0.341352	+	0.939935i	$0.389115\pi$
$20$	0.0963438	+	0.872621i	0.0215431	+	0.195124i
$21$		0			0
$22$	−2.98792	+	0.164445i	−0.637027	+	0.0350597i
$23$			4.77038i			0.994694i	0.867552	+	0.497347i	$0.165692\pi$
$23$			4.77038i			0.994694i	−0.867552	+	0.497347i	$0.834308\pi$
$24$		0			0
$25$	4.80731			0.961462
$26$	−5.43371	+	0.299052i	−1.06564	+	0.0586489i
$27$		0			0
$28$		0			0
$29$	−7.02285			−1.30411			−0.652055	−	0.758172i	$-0.726093\pi$
$29$	−7.02285			−1.30411			−0.652055	+	0.758172i	$0.726093\pi$
$30$		0			0
$31$	7.42528			1.33362			0.666810	−	0.745228i	$-0.267659\pi$
$31$	7.42528			1.33362			0.666810	+	0.745228i	$0.267659\pi$
$32$	1.53558	+	5.44445i	0.271455	+	0.962451i
$33$		0			0
$34$	7.97584	−	0.438962i	1.36785	−	0.0752813i
$35$		0			0
$36$		0			0
$37$	−5.28670			−0.869129			−0.434564	−	0.900641i	$-0.643098\pi$
$37$	−5.28670			−0.869129			−0.434564	+	0.900641i	$0.643098\pi$
$38$	0.231269	+	4.20212i	0.0375169	+	0.681673i
$39$		0			0
$40$	−1.22472	+	0.203861i	−0.193645	+	0.0322333i
$41$			6.81813i			1.06481i	0.846489	+	0.532407i	$0.178712\pi$
$41$			6.81813i			1.06481i	−0.846489	+	0.532407i	$0.821288\pi$
$42$		0			0
$43$			4.38646i			0.668928i	0.942408	+	0.334464i	$0.108555\pi$
$43$			4.38646i			0.668928i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	−0.464416	−	4.20639i	−0.0700134	−	0.634138i
$45$		0			0
$46$	−6.73615	+	0.370733i	−0.993190	+	0.0546617i
$47$	−1.68914			−0.246386			−0.123193	−	0.992383i	$-0.539313\pi$
$47$	−1.68914			−0.246386			−0.123193	+	0.992383i	$0.539313\pi$
$48$		0			0
$49$		0			0
$50$	0.373604	+	6.78829i	0.0528355	+	0.960010i
$51$		0			0
$52$	−0.844569	−	7.64957i	−0.117121	−	1.06080i
$53$	−10.7120			−1.47140			−0.735702	−	0.677305i	$-0.763148\pi$
$53$	−10.7120			−1.47140			−0.735702	+	0.677305i	$0.763148\pi$
$54$		0			0
$55$	0.928833			0.125244
$56$		0			0
$57$		0			0
$58$	−0.545785	−	9.91680i	−0.0716651	−	1.30214i
$59$	8.11818			1.05690			0.528448	−	0.848966i	$-0.322774\pi$
$59$	8.11818			1.05690			0.528448	+	0.848966i	$0.322774\pi$
$60$		0			0
$61$			6.18674i			0.792130i	0.918222	+	0.396065i	$0.129625\pi$
$61$			6.18674i			0.792130i	−0.918222	+	0.396065i	$0.870375\pi$
$62$	0.577061	+	10.4851i	0.0732868	+	1.33160i
$63$		0			0
$64$	−7.56863	+	2.59148i	−0.946079	+	0.323935i
$65$	1.68914			0.209512
$66$		0			0
$67$			7.85056i			0.959098i	0.877515	+	0.479549i	$0.159200\pi$
$67$			7.85056i			0.959098i	−0.877515	+	0.479549i	$0.840800\pi$
$68$	1.23970	+	11.2284i	0.150335	+	1.36164i
$69$		0			0
$70$		0			0
$71$			1.16982i			0.138833i	0.997588	+	0.0694163i	$0.0221137\pi$
$71$			1.16982i			0.138833i	−0.997588	+	0.0694163i	$0.977886\pi$
$72$		0			0
$73$			10.0348i			1.17448i	0.809413	+	0.587240i	$0.199786\pi$
$73$			10.0348i			1.17448i	−0.809413	+	0.587240i	$0.800214\pi$
$74$	−0.410860	−	7.46523i	−0.0477615	−	0.867815i
$75$		0			0
$76$	−5.91574	+	0.653140i	−0.678581	+	0.0749203i
$77$		0			0
$78$		0			0
$79$			15.5836i			1.75329i	0.481136	+	0.876646i	$0.340224\pi$
$79$			15.5836i			1.75329i	−0.481136	+	0.876646i	$0.659776\pi$
$80$	−0.383048	−	1.71356i	−0.0428260	−	0.191581i
$81$		0			0
$82$	−9.62772	+	0.529876i	−1.06320	+	0.0585150i
$83$	−5.49645			−0.603314			−0.301657	−	0.953417i	$-0.597540\pi$
$83$	−5.49645			−0.603314			−0.301657	+	0.953417i	$0.597540\pi$
$84$		0			0
$85$	−2.47939			−0.268928
$86$	−6.19401	+	0.340896i	−0.667918	+	0.0367598i
$87$		0			0
$88$	5.90366	−	0.982694i	0.629332	−	0.104756i
$89$			10.4187i			1.10438i	0.833719	+	0.552189i	$0.186207\pi$
$89$			10.4187i			1.10438i	−0.833719	+	0.552189i	$0.813793\pi$
$90$		0			0
$91$		0			0
$92$	−1.04701	−	9.48314i	−0.109158	−	0.988686i
$93$		0			0
$94$	−0.131272	−	2.38519i	−0.0135397	−	0.246014i
$95$		−	1.30628i		−	0.134022i
$96$		0			0
$97$		−	2.22605i		−	0.226021i	−0.993594	−	0.113011i	$-0.963951\pi$
$97$		−	2.22605i		−	0.226021i	0.993594	−	0.113011i	$-0.0360494\pi$
$98$		0			0
$99$		0			0
$100$	−9.55656	+	1.05511i	−0.955656	+	0.105511i
$101$		−	0.767851i		−	0.0764040i	−0.999270	−	0.0382020i	$-0.987837\pi$
$101$		−	0.767851i		−	0.0764040i	0.999270	−	0.0382020i	$-0.0121630\pi$
$102$		0			0
$103$	8.63878			0.851205			0.425602	−	0.904910i	$-0.360062\pi$
$103$	8.63878			0.851205			0.425602	+	0.904910i	$0.360062\pi$
$104$	10.7361	−	1.78709i	1.05277	−	0.175238i
$105$		0			0
$106$	−0.832489	−	15.1261i	−0.0808585	−	1.46918i
$107$		−	2.54433i		−	0.245970i	−0.992409	−	0.122985i	$-0.960753\pi$
$107$		−	2.54433i		−	0.245970i	0.992409	−	0.122985i	$-0.0392467\pi$
$108$		0			0
$109$	−6.80731			−0.652022			−0.326011	−	0.945366i	$-0.605705\pi$
$109$	−6.80731			−0.652022			−0.326011	+	0.945366i	$0.605705\pi$
$110$	0.0721849	+	1.31158i	0.00688256	+	0.125055i
$111$		0			0
$112$		0			0
$113$	−13.6408			−1.28322			−0.641610	−	0.767031i	$-0.721733\pi$
$113$	−13.6408			−1.28322			−0.641610	+	0.767031i	$0.721733\pi$
$114$		0			0
$115$	2.09402			0.195268
$116$	13.9609	−	1.54138i	1.29623	−	0.143114i
$117$		0			0
$118$	0.630909	+	11.4635i	0.0580799	+	1.05530i
$119$		0			0
$120$		0			0
$121$	6.52264			0.592968
$122$	−8.73615	+	0.480806i	−0.790933	+	0.0435302i
$123$		0			0
$124$	−14.7609	+	1.62971i	−1.32557	+	0.146352i
$125$		−	4.30504i		−	0.385054i
$126$		0			0
$127$		−	3.51914i		−	0.312273i	−0.987735	−	0.156137i	$-0.950096\pi$
$127$		−	3.51914i		−	0.312273i	0.987735	−	0.156137i	$-0.0499040\pi$
$128$	−4.24757	−	10.4861i	−0.375436	−	0.926848i
$129$		0			0
$130$	0.131272	+	2.38519i	0.0115134	+	0.209195i
$131$	19.6167			1.71392			0.856958	−	0.515387i	$-0.172352\pi$
$131$	19.6167			1.71392			0.856958	+	0.515387i	$0.172352\pi$
$132$		0			0
$133$		0			0
$134$	−11.0856	+	0.610111i	−0.957649	+	0.0527056i
$135$		0			0
$136$	−15.7590	+	2.62317i	−1.35132	+	0.224935i
$137$	3.37827			0.288625			0.144313	−	0.989532i	$-0.453903\pi$
$137$	3.37827			0.288625			0.144313	+	0.989532i	$0.453903\pi$
$138$		0			0
$139$	−16.4481			−1.39511			−0.697556	−	0.716530i	$-0.745729\pi$
$139$	−16.4481			−1.39511			−0.697556	+	0.716530i	$0.745729\pi$
$140$		0			0
$141$		0			0
$142$	−1.65188	+	0.0909137i	−0.138623	+	0.00762930i
$143$	−8.14233			−0.680896
$144$		0			0
$145$			3.08276i			0.256010i
$146$	−14.1699	+	0.779858i	−1.17271	+	0.0645415i
$147$		0			0
$148$	10.5095	−	1.16033i	0.863879	−	0.0953786i
$149$	−6.47939			−0.530812			−0.265406	−	0.964137i	$-0.585506\pi$
$149$	−6.47939			−0.530812			−0.265406	+	0.964137i	$0.585506\pi$
$150$		0			0
$151$		−	7.76914i		−	0.632244i	−0.948719	−	0.316122i	$-0.897619\pi$
$151$		−	7.76914i		−	0.632244i	0.948719	−	0.316122i	$-0.102381\pi$
$152$	−1.38203	−	8.30271i	−0.112097	−	0.673439i
$153$		0			0
$154$		0			0
$155$		−	3.25942i		−	0.261803i
$156$		0			0
$157$		−	8.46391i		−	0.675493i	−0.941237	−	0.337747i	$-0.890335\pi$
$157$		−	8.46391i		−	0.675493i	0.941237	−	0.337747i	$-0.109665\pi$
$158$	−22.0052	+	1.21109i	−1.75064	+	0.0963492i
$159$		0			0
$160$	2.38990	−	0.674063i	0.188939	−	0.0532893i
$161$		0			0
$162$		0			0
$163$			6.95459i			0.544725i	0.962195	+	0.272363i	$0.0878050\pi$
$163$			6.95459i			0.544725i	−0.962195	+	0.272363i	$0.912195\pi$
$164$	−1.49645	−	13.5539i	−0.116853	−	1.05838i
$165$		0			0
$166$	−0.427160	−	7.76141i	−0.0331541	−	0.602402i
$167$	8.12021			0.628361			0.314180	−	0.949363i	$-0.398270\pi$
$167$	8.12021			0.628361			0.314180	+	0.949363i	$0.398270\pi$
$168$		0			0
$169$	−1.80731			−0.139024
$170$	−0.192688	−	3.50109i	−0.0147785	−	0.268521i
$171$		0			0
$172$	−0.962744	−	8.71993i	−0.0734085	−	0.664888i
$173$			1.41635i			0.107683i	0.998549	+	0.0538417i	$0.0171466\pi$
$173$			1.41635i			0.107683i	−0.998549	+	0.0538417i	$0.982853\pi$
$174$		0			0
$175$		0			0
$176$	1.84645	+	8.26004i	0.139181	+	0.622624i
$177$		0			0
$178$	−14.7120	+	0.809695i	−1.10271	+	0.0606892i
$179$		−	10.7318i		−	0.802132i	−0.916049	−	0.401066i	$-0.868640\pi$
$179$		−	10.7318i		−	0.802132i	0.916049	−	0.401066i	$-0.131360\pi$
$180$		0			0
$181$		−	1.21426i		−	0.0902549i	−0.998981	−	0.0451275i	$-0.985631\pi$
$181$		−	1.21426i		−	0.0902549i	0.998981	−	0.0451275i	$-0.0143694\pi$
$182$		0			0
$183$		0			0
$184$	13.3096	−	2.21544i	0.981193	−	0.163325i
$185$			2.32066i			0.170618i
$186$		0			0
$187$	11.9517			0.873994
$188$	3.35787	−	0.370733i	0.244898	−	0.0270385i
$189$		0			0
$190$	1.84457	−	0.101518i	0.133819	−	0.00736493i
$191$			6.55261i			0.474131i	0.971494	+	0.237065i	$0.0761855\pi$
$191$			6.55261i			0.474131i	−0.971494	+	0.237065i	$0.923814\pi$
$192$		0			0
$193$	−3.23635			−0.232958			−0.116479	−	0.993193i	$-0.537161\pi$
$193$	−3.23635			−0.232958			−0.116479	+	0.993193i	$0.537161\pi$
$194$	3.14335	−	0.172999i	0.225680	−	0.0124206i
$195$		0			0
$196$		0			0
$197$	19.2554			1.37189			0.685947	−	0.727652i	$-0.259388\pi$
$197$	19.2554			1.37189			0.685947	+	0.727652i	$0.259388\pi$
$198$		0			0
$199$	8.62173			0.611178			0.305589	−	0.952164i	$-0.401147\pi$
$199$	8.62173			0.611178			0.305589	+	0.952164i	$0.401147\pi$
$200$	−2.23260	−	13.4126i	−0.157868	−	0.948413i
$201$		0			0
$202$	1.08426	−	0.0596741i	0.0762886	−	0.00419865i
$203$		0			0
$204$		0			0
$205$	2.99290			0.209033
$206$	0.671369	+	12.1986i	0.0467765	+	0.849918i
$207$		0			0
$208$	3.35787	+	15.0214i	0.232826	+	1.04154i
$209$			6.29681i			0.435559i
$210$		0			0
$211$			6.09787i			0.419795i	0.977723	+	0.209897i	$0.0673130\pi$
$211$			6.09787i			0.419795i	−0.977723	+	0.209897i	$0.932687\pi$
$212$	21.2946	−	2.35108i	1.46252	−	0.161473i
$213$		0			0
$214$	3.59279	−	0.197735i	0.245598	−	0.0135169i
$215$	1.92549			0.131317
$216$		0			0
$217$		0			0
$218$	−0.529035	−	9.61245i	−0.0358308	−	0.651037i
$219$		0			0
$220$	−1.84645	+	0.203861i	−0.124487	+	0.0137443i
$221$	21.7348			1.46204
$222$		0			0
$223$	−2.44944			−0.164027			−0.0820134	−	0.996631i	$-0.526135\pi$
$223$	−2.44944			−0.164027			−0.0820134	+	0.996631i	$0.526135\pi$
$224$		0			0
$225$		0			0
$226$	−1.06011	−	19.2619i	−0.0705172	−	1.28128i
$227$	23.2796			1.54512			0.772561	−	0.634941i	$-0.218976\pi$
$227$	23.2796			1.54512			0.772561	+	0.634941i	$0.218976\pi$
$228$		0			0
$229$		−	11.7069i		−	0.773615i	−0.922160	−	0.386808i	$-0.873578\pi$
$229$		−	11.7069i		−	0.773615i	0.922160	−	0.386808i	$-0.126422\pi$
$230$	0.162738	+	2.95691i	0.0107306	+	0.194973i
$231$		0			0
$232$	3.26153	+	19.5940i	0.214130	+	1.28641i
$233$	8.16853			0.535138			0.267569	−	0.963539i	$-0.413780\pi$
$233$	8.16853			0.535138			0.267569	+	0.963539i	$0.413780\pi$
$234$		0			0
$235$			0.741467i			0.0483680i
$236$	−16.1383	+	1.78178i	−1.05051	+	0.115984i
$237$		0			0
$238$		0			0
$239$			18.1984i			1.17716i	0.808439	+	0.588579i	$0.200313\pi$
$239$			18.1984i			1.17716i	−0.808439	+	0.588579i	$0.799687\pi$
$240$		0			0
$241$		−	28.9148i		−	1.86256i	−0.364299	−	0.931282i	$-0.618691\pi$
$241$		−	28.9148i		−	1.86256i	0.364299	−	0.931282i	$-0.381309\pi$
$242$	0.506912	+	9.21047i	0.0325855	+	0.592072i
$243$		0			0
$244$	−1.35787	−	12.2987i	−0.0869288	−	0.787346i
$245$		0			0
$246$		0			0
$247$			11.4511i			0.728617i
$248$	−3.44842	−	20.7168i	−0.218975	−	1.31552i
$249$		0			0
$250$	6.07904	−	0.334569i	0.384472	−	0.0211600i
$251$	−20.3586			−1.28502			−0.642512	−	0.766276i	$-0.722108\pi$
$251$	−20.3586			−1.28502			−0.642512	+	0.766276i	$0.722108\pi$
$252$		0			0
$253$	−10.0940			−0.634605
$254$	4.96929	−	0.273492i	0.311801	−	0.0171604i
$255$		0			0
$256$	14.4771	−	6.81283i	0.904816	−	0.425802i
$257$		−	21.2869i		−	1.32784i	−0.747802	−	0.663922i	$-0.768891\pi$
$257$		−	21.2869i		−	1.32784i	0.747802	−	0.663922i	$-0.231109\pi$
$258$		0			0
$259$		0			0
$260$	−3.35787	+	0.370733i	−0.208246	+	0.0229919i
$261$		0			0
$262$	1.52452	+	27.7002i	0.0941853	+	1.71133i
$263$			20.1796i			1.24433i	0.782887	+	0.622164i	$0.213746\pi$
$263$			20.1796i			1.24433i	−0.782887	+	0.622164i	$0.786254\pi$
$264$		0			0
$265$			4.70215i			0.288851i
$266$		0			0
$267$		0			0
$268$	−1.72305	−	15.6063i	−0.105252	−	0.953306i
$269$			16.3695i			0.998066i	0.866583	+	0.499033i	$0.166311\pi$
$269$			16.3695i			0.998066i	−0.866583	+	0.499033i	$0.833689\pi$
$270$		0			0
$271$	13.4539			0.817268			0.408634	−	0.912698i	$-0.366005\pi$
$271$	13.4539			0.817268			0.408634	+	0.912698i	$0.366005\pi$
$272$	−4.92883	−	22.0490i	−0.298854	−	1.33692i
$273$		0			0
$274$	0.262545	+	4.77038i	0.0158609	+	0.288189i
$275$			10.1722i			0.613404i
$276$		0			0
$277$	2.80731			0.168675			0.0843375	−	0.996437i	$-0.473123\pi$
$277$	2.80731			0.168675			0.0843375	+	0.996437i	$0.473123\pi$
$278$	−1.27828	−	23.2260i	−0.0766660	−	1.39300i
$279$		0			0
$280$		0			0
$281$	25.4502			1.51823			0.759115	−	0.650957i	$-0.225632\pi$
$281$	25.4502			1.51823			0.759115	+	0.650957i	$0.225632\pi$
$282$		0			0
$283$	−4.73949			−0.281733			−0.140867	−	0.990029i	$-0.544989\pi$
$283$	−4.73949			−0.281733			−0.140867	+	0.990029i	$0.544989\pi$
$284$	−0.256754	−	2.32552i	−0.0152356	−	0.137994i
$285$		0			0
$286$	−0.632787	−	11.4976i	−0.0374175	−	0.679867i
$287$		0			0
$288$		0			0
$289$	−14.9034			−0.876668
$290$	−4.35310	+	0.239579i	−0.255623	+	0.0140686i
$291$		0			0
$292$	−2.20244	−	19.9483i	−0.128888	−	1.16739i
$293$			3.22818i			0.188592i	0.995544	+	0.0942960i	$0.0300600\pi$
$293$			3.22818i			0.188592i	−0.995544	+	0.0942960i	$0.969940\pi$
$294$		0			0
$295$		−	3.56357i		−	0.207479i
$296$	2.45523	+	14.7501i	0.142707	+	0.857333i
$297$		0			0
$298$	−0.503550	−	9.14940i	−0.0291699	−	0.530010i
$299$	−18.3566			−1.06159
$300$		0			0
$301$		0			0
$302$	10.9706	−	0.603784i	0.631288	−	0.0347439i
$303$		0			0
$304$	11.6167	−	2.59678i	0.666261	−	0.148936i
$305$	2.71574			0.155503
$306$		0			0
$307$	−5.45523			−0.311347			−0.155673	−	0.987809i	$-0.549755\pi$
$307$	−5.45523			−0.311347			−0.155673	+	0.987809i	$0.549755\pi$
$308$		0			0
$309$		0			0
$310$	4.60255	−	0.253308i	0.261407	−	0.0143869i
$311$	−30.5251			−1.73092			−0.865460	−	0.500979i	$-0.832973\pi$
$311$	−30.5251			−1.73092			−0.865460	+	0.500979i	$0.832973\pi$
$312$		0			0
$313$		−	18.8324i		−	1.06447i	−0.846596	−	0.532235i	$-0.821352\pi$
$313$		−	18.8324i		−	1.06447i	0.846596	−	0.532235i	$-0.178648\pi$
$314$	11.9517	−	0.657778i	0.674472	−	0.0371206i
$315$		0			0
$316$	−3.42030	−	30.9790i	−0.192407	−	1.74270i
$317$	−17.1652			−0.964093			−0.482046	−	0.876146i	$-0.660106\pi$
$317$	−17.1652			−0.964093			−0.482046	+	0.876146i	$0.660106\pi$
$318$		0			0
$319$		−	14.8602i		−	0.832010i
$320$	1.13756	+	3.32234i	0.0635916	+	0.185725i
$321$		0			0
$322$		0			0
$323$		−	16.8085i		−	0.935248i
$324$		0			0
$325$			18.4987i			1.02612i
$326$	−9.82041	+	0.540480i	−0.543902	+	0.0299344i
$327$		0			0
$328$	19.0228	−	3.16645i	1.05036	−	0.174838i
$329$		0			0
$330$		0			0
$331$		−	21.4868i		−	1.18102i	−0.807029	−	0.590511i	$-0.798926\pi$
$331$		−	21.4868i		−	1.18102i	0.807029	−	0.590511i	$-0.201074\pi$
$332$	10.9265	−	1.20637i	0.599670	−	0.0662079i
$333$		0			0
$334$	0.631068	+	11.4664i	0.0345305	+	0.627411i
$335$	3.44610			0.188280
$336$		0			0
$337$	5.91046			0.321964			0.160982	−	0.986957i	$-0.448534\pi$
$337$	5.91046			0.321964			0.160982	+	0.986957i	$0.448534\pi$
$338$	−0.140456	−	2.55206i	−0.00763983	−	0.138814i
$339$		0			0
$340$	4.92883	−	0.544179i	0.267303	−	0.0295123i
$341$			15.7117i			0.850837i
$342$		0			0
$343$		0			0
$344$	12.2384	−	2.03714i	0.659850	−	0.109835i
$345$		0			0
$346$	−2.00000	+	0.110073i	−0.107521	+	0.00591755i
$347$			2.81560i			0.151149i	0.997140	+	0.0755746i	$0.0240791\pi$
$347$			2.81560i			0.151149i	−0.997140	+	0.0755746i	$0.975921\pi$
$348$		0			0
$349$		−	9.54077i		−	0.510705i	−0.966848	−	0.255353i	$-0.917808\pi$
$349$		−	9.54077i		−	0.510705i	0.966848	−	0.255353i	$-0.0821916\pi$
$350$		0			0
$351$		0			0
$352$	−11.5203	+	3.24926i	−0.614035	+	0.173186i
$353$			9.96912i			0.530603i	0.964166	+	0.265301i	$0.0854715\pi$
$353$			9.96912i			0.530603i	−0.964166	+	0.265301i	$0.914529\pi$
$354$		0			0
$355$	0.513508			0.0272542
$356$	−2.28670	−	20.7115i	−0.121195	−	1.09771i
$357$		0			0
$358$	15.1541	−	0.834029i	0.800920	−	0.0440798i
$359$			6.92820i			0.365657i	0.983145	+	0.182828i	$0.0585252\pi$
$359$			6.92820i			0.365657i	−0.983145	+	0.182828i	$0.941475\pi$
$360$		0			0
$361$	−10.1444			−0.533914
$362$	1.71462	−	0.0943667i	0.0901185	−	0.00495980i
$363$		0			0
$364$		0			0
$365$	4.40488			0.230562
$366$		0			0
$367$	17.9047			0.934616			0.467308	−	0.884094i	$-0.345224\pi$
$367$	17.9047			0.934616			0.467308	+	0.884094i	$0.345224\pi$
$368$	4.16274	+	18.6219i	0.216998	+	0.970735i
$369$		0			0
$370$	−3.27695	+	0.180352i	−0.170361	+	0.00937604i
$371$		0			0
$372$		0			0
$373$	14.4743			0.749452			0.374726	−	0.927136i	$-0.377737\pi$
$373$	14.4743			0.749452			0.374726	+	0.927136i	$0.377737\pi$
$374$	0.928833	+	16.8767i	0.0480288	+	0.872673i
$375$		0			0
$376$	0.784463	+	4.71276i	0.0404556	+	0.243042i
$377$		−	27.0241i		−	1.39181i
$378$		0			0
$379$			21.5969i			1.10936i	0.832064	+	0.554679i	$0.187159\pi$
$379$			21.5969i			1.10936i	−0.832064	+	0.554679i	$0.812841\pi$
$380$	0.286704	+	2.59678i	0.0147076	+	0.133212i
$381$		0			0
$382$	−9.25279	+	0.509241i	−0.473414	+	0.0260550i
$383$	0.636338			0.0325154			0.0162577	−	0.999868i	$-0.494825\pi$
$383$	0.636338			0.0325154			0.0162577	+	0.999868i	$0.494825\pi$
$384$		0			0
$385$		0			0
$386$	−0.251515	−	4.56997i	−0.0128018	−	0.232606i
$387$		0			0
$388$	0.488575	+	4.42521i	0.0248037	+	0.224656i
$389$	1.01909			0.0516701			0.0258351	−	0.999666i	$-0.491776\pi$
$389$	1.01909			0.0516701			0.0258351	+	0.999666i	$0.491776\pi$
$390$		0			0
$391$	26.9446			1.36265
$392$		0			0
$393$		0			0
$394$	1.49645	+	27.1902i	0.0753900	+	1.36982i
$395$	6.84061			0.344188
$396$		0			0
$397$			29.7953i			1.49538i	0.664047	+	0.747691i	$0.268838\pi$
$397$			29.7953i			1.49538i	−0.664047	+	0.747691i	$0.731162\pi$
$398$	0.670043	+	12.1745i	0.0335862	+	0.610254i
$399$		0			0
$400$	18.7661	−	4.19496i	0.938305	−	0.209748i
$401$	6.79025			0.339089			0.169545	−	0.985523i	$-0.445770\pi$
$401$	6.79025			0.339089			0.169545	+	0.985523i	$0.445770\pi$
$402$		0			0
$403$			28.5727i			1.42331i
$404$	0.168529	+	1.52643i	0.00838461	+	0.0759426i
$405$		0			0
$406$		0			0
$407$		−	11.1865i		−	0.554496i
$408$		0			0
$409$		−	3.71322i		−	0.183607i	−0.995777	−	0.0918034i	$-0.970737\pi$
$409$		−	3.71322i		−	0.183607i	0.995777	−	0.0918034i	$-0.0292631\pi$
$410$	0.232595	+	4.22620i	0.0114871	+	0.208717i
$411$		0			0
$412$	−17.1732	+	1.89605i	−0.846064	+	0.0934116i
$413$		0			0
$414$		0			0
$415$			2.41273i			0.118436i
$416$	−20.9504	+	5.90897i	−1.02718	+	0.289711i
$417$		0			0
$418$	−8.89158	+	0.489361i	−0.434901	+	0.0239354i
$419$	20.7082			1.01166			0.505832	−	0.862632i	$-0.331186\pi$
$419$	20.7082			1.01166			0.505832	+	0.862632i	$0.331186\pi$
$420$		0			0
$421$	15.6579			0.763118			0.381559	−	0.924344i	$-0.375387\pi$
$421$	15.6579			0.763118			0.381559	+	0.924344i	$0.375387\pi$
$422$	−8.61066	+	0.473900i	−0.419161	+	0.0230691i
$423$		0			0
$424$	4.97482	+	29.8869i	0.241599	+	1.45143i
$425$		−	27.1532i		−	1.31712i
$426$		0			0
$427$		0			0
$428$	0.558433	+	5.05793i	0.0269929	+	0.244484i
$429$		0			0
$430$	0.149641	+	2.71894i	0.00721631	+	0.131119i
$431$		−	11.8614i		−	0.571345i	−0.958327	−	0.285672i	$-0.907783\pi$
$431$		−	11.8614i		−	0.571345i	0.958327	−	0.285672i	$-0.0922169\pi$
$432$		0			0
$433$		−	16.9269i		−	0.813454i	−0.913550	−	0.406727i	$-0.866670\pi$
$433$		−	16.9269i		−	0.813454i	0.913550	−	0.406727i	$-0.133330\pi$
$434$		0			0
$435$		0			0
$436$	13.5324	−	1.49408i	0.648084	−	0.0715532i
$437$			14.1959i			0.679082i
$438$		0			0
$439$	−2.35281			−0.112293			−0.0561467	−	0.998423i	$-0.517881\pi$
$439$	−2.35281			−0.112293			−0.0561467	+	0.998423i	$0.517881\pi$
$440$	−0.431365	−	2.59148i	−0.0205645	−	0.123544i
$441$		0			0
$442$	1.68914	+	30.6913i	0.0803441	+	1.45983i
$443$		−	1.60393i		−	0.0762050i	−0.999274	−	0.0381025i	$-0.987869\pi$
$443$		−	1.60393i		−	0.0762050i	0.999274	−	0.0381025i	$-0.0121313\pi$
$444$		0			0
$445$	4.57341			0.216800
$446$	−0.190360	−	3.45880i	−0.00901381	−	0.163779i
$447$		0			0
$448$		0			0
$449$	−1.35208			−0.0638086			−0.0319043	−	0.999491i	$-0.510157\pi$
$449$	−1.35208			−0.0638086			−0.0319043	+	0.999491i	$0.510157\pi$
$450$		0			0
$451$	−14.4270			−0.679341
$452$	27.1169	−	2.99390i	1.27547	−	0.140821i
$453$		0			0
$454$	1.80919	+	32.8726i	0.0849095	+	1.54279i
$455$		0			0
$456$		0			0
$457$	22.1468			1.03598			0.517992	−	0.855385i	$-0.326680\pi$
$457$	22.1468			1.03598			0.517992	+	0.855385i	$0.326680\pi$
$458$	16.5311	−	0.909811i	0.772446	−	0.0425127i
$459$		0			0
$460$	−4.16274	+	0.459597i	−0.194089	+	0.0214288i
$461$		−	30.7842i		−	1.43376i	−0.697195	−	0.716882i	$-0.745569\pi$
$461$		−	30.7842i		−	1.43376i	0.697195	−	0.716882i	$-0.254431\pi$
$462$		0			0
$463$		−	13.8120i		−	0.641897i	−0.947097	−	0.320948i	$-0.895998\pi$
$463$		−	13.8120i		−	0.641897i	0.947097	−	0.320948i	$-0.104002\pi$
$464$	−27.4148	+	6.12829i	−1.27270	+	0.284499i
$465$		0			0
$466$	0.634823	+	11.5346i	0.0294076	+	0.534329i
$467$	17.0266			0.787897			0.393949	−	0.919132i	$-0.371109\pi$
$467$	17.0266			0.787897			0.393949	+	0.919132i	$0.371109\pi$
$468$		0			0
$469$		0			0
$470$	−1.04701	+	0.0576236i	−0.0482949	+	0.00265798i
$471$		0			0
$472$	−3.77021	−	22.6500i	−0.173538	−	1.04255i
$473$	−9.28164			−0.426770
$474$		0			0
$475$	14.3058			0.656395
$476$		0			0
$477$		0			0
$478$	−25.6976	+	1.41430i	−1.17538	+	0.0646887i
$479$	31.7805			1.45209			0.726045	−	0.687647i	$-0.241356\pi$
$479$	31.7805			1.45209			0.726045	+	0.687647i	$0.241356\pi$
$480$		0			0
$481$		−	20.3434i		−	0.927578i
$482$	40.8299	−	2.24713i	1.85975	−	0.102354i
$483$		0			0
$484$	−12.9665	+	1.43160i	−0.589386	+	0.0650726i
$485$	−0.977151			−0.0443701
$486$		0			0
$487$		−	5.76992i		−	0.261460i	−0.991418	−	0.130730i	$-0.958268\pi$
$487$		−	5.76992i		−	0.261460i	0.991418	−	0.130730i	$-0.0417321\pi$
$488$	17.2612	−	2.87322i	0.781379	−	0.130065i
$489$		0			0
$490$		0			0
$491$			22.6443i			1.02192i	0.859603	+	0.510962i	$0.170711\pi$
$491$			22.6443i			1.02192i	−0.859603	+	0.510962i	$0.829289\pi$
$492$		0			0
$493$			39.6672i			1.78652i
$494$	−16.1699	+	0.889931i	−0.727516	+	0.0400399i
$495$		0			0
$496$	28.9858	−	6.47946i	1.30150	−	0.290936i
$497$		0			0
$498$		0			0
$499$			19.4432i			0.870396i	0.900335	+	0.435198i	$0.143322\pi$
$499$			19.4432i			0.870396i	−0.900335	+	0.435198i	$0.856678\pi$
$500$	0.944874	+	8.55807i	0.0422560	+	0.382729i
$501$		0			0
$502$	−1.58218	−	28.7479i	−0.0706162	−	1.28308i
$503$	−11.7570			−0.524217			−0.262108	−	0.965038i	$-0.584418\pi$
$503$	−11.7570			−0.524217			−0.262108	+	0.965038i	$0.584418\pi$
$504$		0			0
$505$	−0.337057			−0.0149989
$506$	−0.784463	−	14.2535i	−0.0348736	−	0.633646i
$507$		0			0
$508$	0.772384	+	6.99577i	0.0342690	+	0.310387i
$509$			20.1467i			0.892987i	0.894787	+	0.446494i	$0.147327\pi$
$509$			20.1467i			0.892987i	−0.894787	+	0.446494i	$0.852673\pi$
$510$		0			0
$511$		0			0
$512$	10.7453	+	19.9133i	0.474881	+	0.880050i
$513$		0			0
$514$	30.0588	−	1.65433i	1.32584	−	0.0729693i
$515$		−	3.79210i		−	0.167100i
$516$		0			0
$517$		−	3.57417i		−	0.157192i
$518$		0			0
$519$		0			0
$520$	−0.784463	−	4.71276i	−0.0344010	−	0.206668i
$521$		−	35.9071i		−	1.57312i	−0.617515	−	0.786559i	$-0.711860\pi$
$521$		−	35.9071i		−	1.57312i	0.617515	−	0.786559i	$-0.288140\pi$
$522$		0			0
$523$	−45.2961			−1.98066			−0.990330	−	0.138735i	$-0.955697\pi$
$523$	−45.2961			−1.98066			−0.990330	+	0.138735i	$0.955697\pi$
$524$	−38.9964	+	4.30548i	−1.70356	+	0.188086i
$525$		0			0
$526$	−28.4951	+	1.56827i	−1.24245	+	0.0683799i
$527$		−	41.9403i		−	1.82695i
$528$		0			0
$529$	0.243451			0.0105848
$530$	−6.63980	+	0.365431i	−0.288415	+	0.0158733i
$531$		0			0
$532$		0			0
$533$	−26.2364			−1.13642
$534$		0			0
$535$	−1.11687			−0.0482863
$536$	21.9034	−	3.64593i	0.946081	−	0.157480i
$537$		0			0
$538$	−23.1150	+	1.27217i	−0.996558	+	0.0548470i
$539$		0			0
$540$		0			0
$541$	−33.8983			−1.45740			−0.728701	−	0.684832i	$-0.759876\pi$
$541$	−33.8983			−1.45740			−0.728701	+	0.684832i	$0.759876\pi$
$542$	1.04558	+	18.9980i	0.0449115	+	0.816033i
$543$		0			0
$544$	30.7519	−	8.67345i	1.31848	−	0.371871i
$545$			2.98815i			0.127998i
$546$		0			0
$547$		−	7.83251i		−	0.334894i	−0.985881	−	0.167447i	$-0.946448\pi$
$547$		−	7.83251i		−	0.334894i	0.985881	−	0.167447i	$-0.0535523\pi$
$548$	−6.71574	+	0.741467i	−0.286882	+	0.0316739i
$549$		0			0
$550$	−14.3639	+	0.790536i	−0.612477	+	0.0337086i
$551$	−20.8989			−0.890322
$552$		0			0
$553$		0			0
$554$	0.218172	+	3.96414i	0.00926925	+	0.168420i
$555$		0			0
$556$	32.6976	−	3.61005i	1.38669	−	0.153100i
$557$	−15.3940			−0.652266			−0.326133	−	0.945324i	$-0.605746\pi$
$557$	−15.3940			−0.652266			−0.326133	+	0.945324i	$0.605746\pi$
$558$		0			0
$559$	−16.8792			−0.713914
$560$		0			0
$561$		0			0
$562$	1.97788	+	35.9376i	0.0834317	+	1.51594i
$563$	−16.4410			−0.692907			−0.346453	−	0.938067i	$-0.612614\pi$
$563$	−16.4410			−0.692907			−0.346453	+	0.938067i	$0.612614\pi$
$564$		0			0
$565$			5.98780i			0.251909i
$566$	−0.368333	−	6.69252i	−0.0154822	−	0.281308i
$567$		0			0
$568$	3.26385	−	0.543286i	0.136948	−	0.0227958i
$569$	37.2292			1.56073			0.780366	−	0.625323i	$-0.215033\pi$
$569$	37.2292			1.56073			0.780366	+	0.625323i	$0.215033\pi$
$570$		0			0
$571$			20.7454i			0.868166i	0.900873	+	0.434083i	$0.142928\pi$
$571$			20.7454i			0.868166i	−0.900873	+	0.434083i	$0.857072\pi$
$572$	16.1863	−	1.78709i	0.676784	−	0.0747219i
$573$		0			0
$574$		0			0
$575$			22.9327i			0.956361i
$576$		0			0
$577$			15.4211i			0.641988i	0.947081	+	0.320994i	$0.104017\pi$
$577$			15.4211i			0.641988i	−0.947081	+	0.320994i	$0.895983\pi$
$578$	−1.15822	−	21.0447i	−0.0481758	−	0.875344i
$579$		0			0
$580$	−0.676608	−	6.12829i	−0.0280946	−	0.254463i
$581$		0			0
$582$		0			0
$583$		−	22.6663i		−	0.938743i
$584$	27.9974	−	4.66031i	1.15854	−	0.192845i
$585$		0			0
$586$	−4.55843	+	0.250880i	−0.188307	+	0.0103638i
$587$	34.0410			1.40502			0.702512	−	0.711672i	$-0.252062\pi$
$587$	34.0410			1.40502			0.702512	+	0.711672i	$0.252062\pi$
$588$		0			0
$589$	22.0965			0.910469
$590$	5.03203	−	0.276945i	0.207166	−	0.0114017i
$591$		0			0
$592$	−20.6375	+	4.61329i	−0.848195	+	0.189605i
$593$		−	31.8347i		−	1.30729i	−0.756800	−	0.653647i	$-0.773238\pi$
$593$		−	31.8347i		−	1.30729i	0.756800	−	0.653647i	$-0.226762\pi$
$594$		0			0
$595$		0			0
$596$	12.8805	−	1.42210i	0.527606	−	0.0582516i
$597$		0			0
$598$	−1.42659	−	25.9209i	−0.0583377	−	1.05998i
$599$			20.7846i			0.849236i	0.905373	+	0.424618i	$0.139592\pi$
$599$			20.7846i			0.849236i	−0.905373	+	0.424618i	$0.860408\pi$
$600$		0			0
$601$			15.8614i			0.646999i	0.946228	+	0.323499i	$0.104859\pi$
$601$			15.8614i			0.646999i	−0.946228	+	0.323499i	$0.895141\pi$
$602$		0			0
$603$		0			0
$604$	1.70518	+	15.4444i	0.0693827	+	0.628425i
$605$		−	2.86319i		−	0.116405i
$606$		0			0
$607$	−43.4302			−1.76278			−0.881388	−	0.472393i	$-0.843390\pi$
$607$	−43.4302			−1.76278			−0.881388	+	0.472393i	$0.843390\pi$
$608$	4.56965	+	16.2018i	0.185324	+	0.657070i
$609$		0			0
$610$	0.211056	+	3.83484i	0.00854539	+	0.155268i
$611$		−	6.49985i		−	0.262956i
$612$		0			0
$613$	15.5206			0.626871			0.313436	−	0.949609i	$-0.398520\pi$
$613$	15.5206			0.626871			0.313436	+	0.949609i	$0.398520\pi$
$614$	−0.423957	−	7.70321i	−0.0171095	−	0.310876i
$615$		0			0
$616$		0			0
$617$	19.8053			0.797330			0.398665	−	0.917097i	$-0.369474\pi$
$617$	19.8053			0.797330			0.398665	+	0.917097i	$0.369474\pi$
$618$		0			0
$619$	−16.3133			−0.655687			−0.327844	−	0.944732i	$-0.606322\pi$
$619$	−16.3133			−0.655687			−0.327844	+	0.944732i	$0.606322\pi$
$620$	0.715380	+	6.47946i	0.0287303	+	0.260221i
$621$		0			0
$622$	−2.37228	−	43.1038i	−0.0951197	−	1.72830i
$623$		0			0
$624$		0			0
$625$	22.1468			0.885873
$626$	26.5928	−	1.46357i	1.06286	−	0.0584962i
$627$		0			0
$628$	1.85767	+	16.8256i	0.0741289	+	0.671413i
$629$			29.8609i			1.19063i
$630$		0			0
$631$		−	27.3095i		−	1.08717i	−0.839353	−	0.543587i	$-0.817066\pi$
$631$		−	27.3095i		−	1.08717i	0.839353	−	0.543587i	$-0.182934\pi$
$632$	43.4789	−	7.23728i	1.72950	−	0.287884i
$633$		0			0
$634$	−1.33400	−	24.2386i	−0.0529801	−	0.962636i
$635$	−1.54477			−0.0613022
$636$		0			0
$637$		0			0
$638$	20.9837	−	1.15487i	0.830753	−	0.0457217i
$639$		0			0
$640$	−4.60300	+	1.86452i	−0.181949	+	0.0737017i
$641$	−9.79066			−0.386708			−0.193354	−	0.981129i	$-0.561937\pi$
$641$	−9.79066			−0.386708			−0.193354	+	0.981129i	$0.561937\pi$
$642$		0			0
$643$	7.26458			0.286487			0.143244	−	0.989687i	$-0.454247\pi$
$643$	7.26458			0.286487			0.143244	+	0.989687i	$0.454247\pi$
$644$		0			0
$645$		0			0
$646$	23.7348	−	1.30628i	0.933835	−	0.0513949i
$647$	−46.0839			−1.81174			−0.905872	−	0.423551i	$-0.860783\pi$
$647$	−46.0839			−1.81174			−0.905872	+	0.423551i	$0.860783\pi$
$648$		0			0
$649$			17.1779i			0.674290i
$650$	−26.1215	+	1.43764i	−1.02457	+	0.0563887i
$651$		0			0
$652$	−1.52640	−	13.8252i	−0.0597784	−	0.541435i
$653$	6.77981			0.265314			0.132657	−	0.991162i	$-0.457649\pi$
$653$	6.77981			0.265314			0.132657	+	0.991162i	$0.457649\pi$
$654$		0			0
$655$		−	8.61097i		−	0.336458i
$656$	5.94965	+	26.6156i	0.232295	+	1.03917i
$657$		0			0
$658$		0			0
$659$		−	29.3184i		−	1.14208i	−0.820921	−	0.571041i	$-0.806540\pi$
$659$		−	29.3184i		−	1.14208i	0.820921	−	0.571041i	$-0.193460\pi$
$660$		0			0
$661$		−	30.5780i		−	1.18935i	−0.803967	−	0.594674i	$-0.797281\pi$
$661$		−	30.5780i		−	1.18935i	0.803967	−	0.594674i	$-0.202719\pi$
$662$	30.3410	−	1.66986i	1.17924	−	0.0649011i
$663$		0			0
$664$	2.55264	+	15.3353i	0.0990617	+	0.595125i
$665$		0			0
$666$		0			0
$667$		−	33.5017i		−	1.29719i
$668$	−16.1423	+	1.78223i	−0.624566	+	0.0689566i
$669$		0			0
$670$	0.267816	+	4.86615i	0.0103466	+	0.187996i
$671$	−13.0910			−0.505372
$672$		0			0
$673$	−6.37827			−0.245864			−0.122932	−	0.992415i	$-0.539230\pi$
$673$	−6.37827			−0.245864			−0.122932	+	0.992415i	$0.539230\pi$
$674$	0.459336	+	8.34603i	0.0176930	+	0.321477i
$675$		0			0
$676$	3.59279	−	0.396671i	0.138184	−	0.0152566i
$677$			12.4960i			0.480261i	0.970741	+	0.240131i	$0.0771903\pi$
$677$			12.4960i			0.480261i	−0.970741	+	0.240131i	$0.922810\pi$
$678$		0			0
$679$		0			0
$680$	1.15147	+	6.91760i	0.0441569	+	0.265278i
$681$		0			0
$682$	−22.1862	+	1.22105i	−0.849552	+	0.0467563i
$683$		−	45.2547i		−	1.73162i	−0.500371	−	0.865811i	$-0.666803\pi$
$683$		−	45.2547i		−	1.73162i	0.500371	−	0.865811i	$-0.333197\pi$
$684$		0			0
$685$		−	1.48293i		−	0.0566600i
$686$		0			0
$687$		0			0
$688$	3.82772	+	17.1232i	0.145930	+	0.652817i
$689$		−	41.2200i		−	1.57036i
$690$		0			0
$691$	−10.5931			−0.402980			−0.201490	−	0.979491i	$-0.564578\pi$
$691$	−10.5931			−0.402980			−0.201490	+	0.979491i	$0.564578\pi$
$692$	−0.310863	−	2.81560i	−0.0118172	−	0.107033i
$693$		0			0
$694$	−3.97584	+	0.218816i	−0.150921	+	0.00830615i
$695$			7.22010i			0.273874i
$696$		0			0
$697$	38.5109			1.45870
$698$	13.4723	−	0.741467i	0.509934	−	0.0280649i
$699$		0			0
$700$		0			0
$701$	−29.6566			−1.12011			−0.560057	−	0.828454i	$-0.689221\pi$
$701$	−29.6566			−1.12011			−0.560057	+	0.828454i	$0.689221\pi$
$702$		0			0
$703$	−15.7324			−0.593358
$704$	−5.48351	−	16.0151i	−0.206668	−	0.603590i
$705$		0			0
$706$	−14.0772	+	0.774757i	−0.529801	+	0.0291584i
$707$		0			0
$708$		0			0
$709$	−35.7011			−1.34078			−0.670392	−	0.742007i	$-0.733874\pi$
$709$	−35.7011			−1.34078			−0.670392	+	0.742007i	$0.733874\pi$
$710$	0.0399076	+	0.725113i	0.00149771	+	0.0272130i
$711$		0			0
$712$	29.0685	−	4.83861i	1.08939	−	0.181335i
$713$			35.4214i			1.32654i
$714$		0			0
$715$			3.57417i			0.133667i
$716$	2.35543	+	21.3340i	0.0880264	+	0.797288i
$717$		0			0
$718$	−9.78315	+	0.538430i	−0.365104	+	0.0200940i
$719$	12.8089			0.477693			0.238846	−	0.971057i	$-0.423231\pi$
$719$	12.8089			0.477693			0.238846	+	0.971057i	$0.423231\pi$
$720$		0			0
$721$		0			0
$722$	−0.788376	−	14.3246i	−0.0293403	−	0.533107i
$723$		0			0
$724$	0.266506	+	2.41384i	0.00990462	+	0.0897098i
$725$	−33.7610			−1.25385
$726$		0			0
$727$	−19.3286			−0.716860			−0.358430	−	0.933557i	$-0.616688\pi$
$727$	−19.3286			−0.716860			−0.358430	+	0.933557i	$0.616688\pi$
$728$		0			0
$729$		0			0
$730$	0.342328	+	6.22003i	0.0126701	+	0.230214i
$731$	24.7761			0.916375
$732$		0			0
$733$		−	37.6903i		−	1.39212i	−0.717983	−	0.696061i	$-0.754934\pi$
$733$		−	37.6903i		−	1.39212i	0.717983	−	0.696061i	$-0.245066\pi$
$734$	1.39147	+	25.2828i	0.0513602	+	0.933204i
$735$		0			0
$736$	−25.9721	+	7.32532i	−0.957344	+	0.270015i
$737$	−16.6116			−0.611896
$738$		0			0
$739$		−	13.8647i		−	0.510023i	−0.966938	−	0.255011i	$-0.917921\pi$
$739$		−	13.8647i		−	0.510023i	0.966938	−	0.255011i	$-0.0820792\pi$
$740$	−0.509341	−	4.61329i	−0.0187237	−	0.169588i
$741$		0			0
$742$		0			0
$743$		−	18.9927i		−	0.696773i	−0.937351	−	0.348387i	$-0.886730\pi$
$743$		−	18.9927i		−	0.696773i	0.937351	−	0.348387i	$-0.113270\pi$
$744$		0			0
$745$			2.84421i			0.104204i
$746$	1.12488	+	20.4389i	0.0411849	+	0.748320i
$747$		0			0
$748$	−23.7590	+	2.62317i	−0.868715	+	0.0959125i
$749$		0			0
$750$		0			0
$751$		−	29.1987i		−	1.06547i	−0.846281	−	0.532737i	$-0.821164\pi$
$751$		−	29.1987i		−	1.06547i	0.846281	−	0.532737i	$-0.178836\pi$
$752$	−6.59381	+	1.47398i	−0.240452	+	0.0537504i
$753$		0			0
$754$	38.1601	−	2.10020i	1.38971	−	0.0764847i
$755$	−3.41036			−0.124116
$756$		0			0
$757$	−10.8022			−0.392614			−0.196307	−	0.980542i	$-0.562895\pi$
$757$	−10.8022			−0.392614			−0.196307	+	0.980542i	$0.562895\pi$
$758$	−30.4965	+	1.67842i	−1.10768	+	0.0609628i
$759$		0			0
$760$	−3.64457	+	0.606658i	−0.132203	+	0.0220058i
$761$			0.234595i			0.00850407i	0.999991	+	0.00425204i	$0.00135347\pi$
$761$			0.234595i			0.00850407i	−0.999991	+	0.00425204i	$0.998647\pi$
$762$		0			0
$763$		0			0
$764$	−1.43817	−	13.0261i	−0.0520313	−	0.471267i
$765$		0			0
$766$	0.0494535	+	0.898559i	0.00178683	+	0.0324662i
$767$			31.2390i			1.12797i
$768$		0			0
$769$			34.8540i			1.25687i	0.777863	+	0.628434i	$0.216304\pi$
$769$			34.8540i			1.25687i	−0.777863	+	0.628434i	$0.783696\pi$
$770$		0			0
$771$		0			0
$772$	6.43361	−	0.710317i	0.231551	−	0.0255649i
$773$			19.6717i			0.707540i	0.935332	+	0.353770i	$0.115100\pi$
$773$			19.6717i			0.707540i	−0.935332	+	0.353770i	$0.884900\pi$
$774$		0			0
$775$	35.6957			1.28223
$776$	−6.21076	+	1.03381i	−0.222953	+	0.0371118i
$777$		0			0
$778$	0.0791996	+	1.43904i	0.00283944	+	0.0515920i
$779$			20.2897i			0.726953i
$780$		0			0
$781$	−2.47532			−0.0885739
$782$	2.09402	+	38.0478i	0.0748819	+	1.36059i
$783$		0			0
$784$		0			0
$785$	−3.71533			−0.132606
$786$		0			0
$787$	−38.9562			−1.38864			−0.694319	−	0.719668i	$-0.744294\pi$
$787$	−38.9562			−1.38864			−0.694319	+	0.719668i	$0.744294\pi$
$788$	−38.2783	+	4.22620i	−1.36361	+	0.150552i
$789$		0			0
$790$	0.531622	+	9.65946i	0.0189143	+	0.343668i
$791$		0			0
$792$		0			0
$793$	−23.8067			−0.845402
$794$	−42.0732	+	2.31556i	−1.49312	+	0.0821762i
$795$		0			0
$796$	−17.1393	+	1.89230i	−0.607487	+	0.0670710i
$797$		−	20.4557i		−	0.724579i	−0.932066	−	0.362289i	$-0.881995\pi$
$797$		−	20.4557i		−	0.724579i	0.932066	−	0.362289i	$-0.118005\pi$
$798$		0			0
$799$			9.54077i			0.337528i
$800$	7.38203	+	26.1731i	0.260994	+	0.925361i
$801$		0			0
$802$	0.527709	+	9.58836i	0.0186341	+	0.338577i
$803$	−21.2333			−0.749308
$804$		0			0
$805$		0			0
$806$	−40.3468	+	2.22055i	−1.42116	+	0.0782154i
$807$		0			0
$808$	−2.14233	+	0.356603i	−0.0753670	+	0.0125452i
$809$	48.9300			1.72029			0.860143	−	0.510053i	$-0.170374\pi$
$809$	48.9300			1.72029			0.860143	+	0.510053i	$0.170374\pi$
$810$		0			0
$811$	51.9424			1.82394			0.911972	−	0.410253i	$-0.134560\pi$
$811$	51.9424			1.82394			0.911972	+	0.410253i	$0.134560\pi$
$812$		0			0
$813$		0			0
$814$	15.7963	−	0.869369i	0.553658	−	0.0304714i
$815$	3.05280			0.106935
$816$		0			0
$817$			13.0534i			0.456681i
$818$	5.24335	−	0.288575i	0.183329	−	0.0100898i
$819$		0			0
$820$	−5.94965	+	0.656884i	−0.207771	+	0.0229394i
$821$	−31.4645			−1.09812			−0.549059	−	0.835784i	$-0.685014\pi$
$821$	−31.4645			−1.09812			−0.549059	+	0.835784i	$0.685014\pi$
$822$		0			0
$823$		−	41.5119i		−	1.44701i	−0.690317	−	0.723507i	$-0.742529\pi$
$823$		−	41.5119i		−	1.44701i	0.690317	−	0.723507i	$-0.257471\pi$
$824$	−4.01199	−	24.1025i	−0.139764	−	0.839652i
$825$		0			0
$826$		0			0
$827$		−	38.6850i		−	1.34521i	−0.740003	−	0.672604i	$-0.765176\pi$
$827$		−	38.6850i		−	1.34521i	0.740003	−	0.672604i	$-0.234824\pi$
$828$		0			0
$829$		−	10.3289i		−	0.358737i	−0.983782	−	0.179369i	$-0.942595\pi$
$829$		−	10.3289i		−	0.358737i	0.983782	−	0.179369i	$-0.0574054\pi$
$830$	−3.40696	+	0.187507i	−0.118257	+	0.00650847i
$831$		0			0
$832$	−9.97209	−	29.1243i	−0.345720	−	1.00970i
$833$		0			0
$834$		0			0
$835$		−	3.56446i		−	0.123353i
$836$	−1.38203	−	12.5176i	−0.0477985	−	0.432929i
$837$		0			0
$838$	1.60935	+	29.2416i	0.0555942	+	1.01013i
$839$	−10.4794			−0.361789			−0.180894	−	0.983503i	$-0.557899\pi$
$839$	−10.4794			−0.361789			−0.180894	+	0.983503i	$0.557899\pi$
$840$		0			0
$841$	20.3204			0.700704
$842$	1.21686	+	22.1101i	0.0419359	+	0.761965i
$843$		0			0
$844$	−1.33837	−	12.1221i	−0.0460685	−	0.417259i
$845$			0.793341i			0.0272918i
$846$		0			0
$847$		0			0
$848$	−41.8159	+	9.34751i	−1.43596	+	0.320995i
$849$		0			0
$850$	38.3424	−	2.11023i	1.31513	−	0.0723802i
$851$		−	25.2196i		−	0.864517i
$852$		0			0
$853$			25.5157i			0.873642i	0.899548	+	0.436821i	$0.143896\pi$
$853$			25.5157i			0.873642i	−0.899548	+	0.436821i	$0.856104\pi$
$854$		0			0
$855$		0			0
$856$	−7.09879	+	1.18163i	−0.242632	+	0.0403873i
$857$		−	11.5450i		−	0.394370i	−0.980366	−	0.197185i	$-0.936820\pi$
$857$		−	11.5450i		−	0.394370i	0.980366	−	0.197185i	$-0.0631800\pi$
$858$		0			0
$859$	32.9105			1.12289			0.561445	−	0.827514i	$-0.310246\pi$
$859$	32.9105			1.12289			0.561445	+	0.827514i	$0.310246\pi$
$860$	−3.82772	+	0.422608i	−0.130524	+	0.0144108i
$861$		0			0
$862$	16.7492	−	0.921819i	0.570481	−	0.0313973i
$863$		−	57.2818i		−	1.94990i	−0.222432	−	0.974948i	$-0.571400\pi$
$863$		−	57.2818i		−	1.94990i	0.222432	−	0.974948i	$-0.428600\pi$
$864$		0			0
$865$	0.621725			0.0211393
$866$	23.9020	−	1.31548i	0.812224	−	0.0447019i
$867$		0			0
$868$		0			0
$869$	−32.9745			−1.11858
$870$		0			0
$871$	−30.2092			−1.02360
$872$	3.16143	+	18.9927i	0.107059	+	0.643173i
$873$		0			0
$874$	−20.0457	+	1.10324i	−0.678056	+	0.0373178i
$875$		0			0
$876$		0			0
$877$	34.0431			1.14955			0.574777	−	0.818310i	$-0.305089\pi$
$877$	34.0431			1.14955			0.574777	+	0.818310i	$0.305089\pi$
$878$	−0.182850	−	3.32234i	−0.00617089	−	0.112124i
$879$		0			0
$880$	3.62584	−	0.810520i	0.122227	−	0.0273226i
$881$			23.4638i			0.790514i	0.918571	+	0.395257i	$0.129344\pi$
$881$			23.4638i			0.790514i	−0.918571	+	0.395257i	$0.870656\pi$
$882$		0			0
$883$		−	8.14468i		−	0.274090i	−0.990565	−	0.137045i	$-0.956239\pi$
$883$		−	8.14468i		−	0.274090i	0.990565	−	0.137045i	$-0.0437606\pi$
$884$	−43.2071	+	4.77038i	−1.45321	+	0.160445i
$885$		0			0
$886$	2.26487	−	0.124651i	0.0760899	−	0.00418772i
$887$	−29.2217			−0.981170			−0.490585	−	0.871393i	$-0.663217\pi$
$887$	−29.2217			−0.981170			−0.490585	+	0.871393i	$0.663217\pi$
$888$		0			0
$889$		0			0
$890$	0.355425	+	6.45800i	0.0119139	+	0.216473i
$891$		0			0
$892$	4.86930	−	0.537606i	0.163036	−	0.0180004i
$893$	−5.02660			−0.168209
$894$		0			0
$895$	−4.71085			−0.157466
$896$		0			0
$897$		0			0
$898$	−0.105078	−	1.90924i	−0.00350649	−	0.0637122i
$899$	−52.1466			−1.73919
$900$		0			0
$901$			60.5046i			2.01570i
$902$	−1.12120	−	20.3720i	−0.0373320	−	0.678314i
$903$		0			0
$904$	6.33502	+	38.0584i	0.210700	+	1.26580i
$905$	−0.533012			−0.0177179
$906$		0			0
$907$		−	56.1181i		−	1.86337i	−0.363265	−	0.931686i	$-0.618338\pi$
$907$		−	56.1181i		−	1.86337i	0.363265	−	0.931686i	$-0.381662\pi$
$908$	−46.2780	+	5.10943i	−1.53579	+	0.169562i
$909$		0			0
$910$		0			0
$911$			43.1536i			1.42974i	0.699256	+	0.714871i	$0.253515\pi$
$911$			43.1536i			1.42974i	−0.699256	+	0.714871i	$0.746485\pi$
$912$		0			0
$913$		−	11.6304i		−	0.384909i
$914$	1.72115	+	31.2730i	0.0569307	+	1.03442i
$915$		0			0
$916$	2.56945	+	23.2724i	0.0848969	+	0.768943i
$917$		0			0
$918$		0			0
$919$		−	38.5228i		−	1.27075i	−0.772203	−	0.635375i	$-0.780845\pi$
$919$		−	38.5228i		−	1.27075i	0.772203	−	0.635375i	$-0.219155\pi$
$920$	−0.972496	−	5.84239i	−0.0320622	−	0.192618i
$921$		0			0
$922$	43.4697	−	2.39242i	1.43160	−	0.0787900i
$923$	−4.50151			−0.148169
$924$		0			0
$925$	−25.4148			−0.835635
$926$	19.5036	−	1.07341i	0.640927	−	0.0352743i
$927$		0			0
$928$	−10.7842	−	38.2355i	−0.354008	−	1.25514i
$929$			47.6930i			1.56476i	0.622803	+	0.782379i	$0.285994\pi$
$929$			47.6930i			1.56476i	−0.622803	+	0.782379i	$0.714006\pi$
$930$		0			0
$931$		0			0
$932$	−16.2384	+	1.79284i	−0.531906	+	0.0587263i
$933$		0			0
$934$	1.32323	+	24.0429i	0.0432975	+	0.786707i
$935$		−	5.24633i		−	0.171573i
$936$		0			0
$937$		−	6.18932i		−	0.202196i	−0.994876	−	0.101098i	$-0.967764\pi$
$937$		−	6.18932i		−	0.202196i	0.994876	−	0.101098i	$-0.0322356\pi$
$938$		0			0
$939$		0			0
$940$	−0.162738	−	1.47398i	−0.00530792	−	0.0480758i
$941$		−	7.30986i		−	0.238295i	−0.992877	−	0.119147i	$-0.961984\pi$
$941$		−	7.30986i		−	0.238295i	0.992877	−	0.119147i	$-0.0380161\pi$
$942$		0			0
$943$	−32.5251			−1.05916
$944$	31.6906	−	7.08409i	1.03144	−	0.230568i
$945$		0			0
$946$	−0.721329	−	13.1064i	−0.0234524	−	0.426125i
$947$			15.2196i			0.494569i	0.968943	+	0.247285i	$0.0795382\pi$
$947$			15.2196i			0.494569i	−0.968943	+	0.247285i	$0.920462\pi$
$948$		0			0
$949$	−38.6140			−1.25346
$950$	1.11178	+	20.2009i	0.0360711	+	0.655403i
$951$		0			0
$952$		0			0
$953$	−17.5899			−0.569792			−0.284896	−	0.958558i	$-0.591959\pi$
$953$	−17.5899			−0.569792			−0.284896	+	0.958558i	$0.591959\pi$
$954$		0			0
$955$	2.87635			0.0930764
$956$	−3.99421	−	36.1770i	−0.129182	−	1.17005i
$957$		0			0
$958$	2.46985	+	44.8765i	0.0797971	+	1.44990i
$959$		0			0
$960$		0			0
$961$	24.1348			0.778543
$962$	28.7264	−	1.58100i	0.926177	−	0.0509735i
$963$		0			0
$964$	6.34624	+	57.4803i	0.204399	+	1.85131i
$965$			1.42063i			0.0457318i
$966$		0			0
$967$			15.0905i			0.485279i	0.970117	+	0.242640i	$0.0780132\pi$
$967$			15.0905i			0.485279i	−0.970117	+	0.242640i	$0.921987\pi$
$968$	−3.02922	−	18.1984i	−0.0973629	−	0.584920i
$969$		0			0
$970$	−0.0759399	−	1.37981i	−0.00243828	−	0.0443031i
$971$	−44.9320			−1.44194			−0.720968	−	0.692968i	$-0.756303\pi$
$971$	−44.9320			−1.44194			−0.720968	+	0.692968i	$0.756303\pi$
$972$		0			0
$973$		0			0
$974$	8.14757	−	0.448413i	0.261065	−	0.0143681i
$975$		0			0
$976$	5.39868	+	24.1509i	0.172807	+	0.773051i
$977$	−12.0824			−0.386551			−0.193276	−	0.981144i	$-0.561911\pi$
$977$	−12.0824			−0.386551			−0.193276	+	0.981144i	$0.561911\pi$
$978$		0			0
$979$	−22.0457			−0.704584
$980$		0			0
$981$		0			0
$982$	−31.9755	+	1.75982i	−1.02038	+	0.0561581i
$983$	17.3495			0.553362			0.276681	−	0.960962i	$-0.410765\pi$
$983$	17.3495			0.553362			0.276681	+	0.960962i	$0.410765\pi$
$984$		0			0
$985$		−	8.45241i		−	0.269316i
$986$	−56.0131	+	3.08276i	−1.78382	+	0.0981752i
$987$		0			0
$988$	−2.51330	−	22.7639i	−0.0799588	−	0.724216i
$989$	−20.9251			−0.665379
$990$		0			0
$991$			49.0905i			1.55941i	0.626147	+	0.779705i	$0.284631\pi$
$991$			49.0905i			1.55941i	−0.626147	+	0.779705i	$0.715369\pi$
$992$	11.4021	+	40.4265i	0.362018	+	1.28354i
$993$		0			0
$994$		0			0
$995$		−	3.78461i		−	0.119980i
$996$		0			0
$997$		−	9.09953i		−	0.288185i	−0.989564	−	0.144093i	$-0.953974\pi$
$997$		−	9.09953i		−	0.288185i	0.989564	−	0.144093i	$-0.0460263\pi$
$998$	−27.4552	+	1.51104i	−0.869081	+	0.0478311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.j.1567.4		8
3.2	odd	2		588.2.b.a.391.5		8
4.3	odd	2		1764.2.b.i.1567.3		8
7.2	even	3		252.2.bf.f.199.4		8
7.3	odd	6		252.2.bf.g.19.1		8
7.6	odd	2		1764.2.b.i.1567.4		8
12.11	even	2		588.2.b.b.391.6		8
21.2	odd	6		84.2.o.b.31.1	yes	8
21.5	even	6		588.2.o.b.31.1		8
21.11	odd	6		588.2.o.d.19.4		8
21.17	even	6		84.2.o.a.19.4	✓	8
21.20	even	2		588.2.b.b.391.5		8
28.3	even	6		252.2.bf.f.19.4		8
28.23	odd	6		252.2.bf.g.199.1		8
28.27	even	2	inner	1764.2.b.j.1567.3		8
84.11	even	6		588.2.o.b.19.1		8
84.23	even	6		84.2.o.a.31.4	yes	8
84.47	odd	6		588.2.o.d.31.4		8
84.59	odd	6		84.2.o.b.19.1	yes	8
84.83	odd	2		588.2.b.a.391.6		8
168.59	odd	6		1344.2.bl.i.1279.3		8
168.101	even	6		1344.2.bl.j.1279.3		8
168.107	even	6		1344.2.bl.j.703.3		8
168.149	odd	6		1344.2.bl.i.703.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.4	✓	8	21.17	even	6
84.2.o.a.31.4	yes	8	84.23	even	6
84.2.o.b.19.1	yes	8	84.59	odd	6
84.2.o.b.31.1	yes	8	21.2	odd	6
252.2.bf.f.19.4		8	28.3	even	6
252.2.bf.f.199.4		8	7.2	even	3
252.2.bf.g.19.1		8	7.3	odd	6
252.2.bf.g.199.1		8	28.23	odd	6
588.2.b.a.391.5		8	3.2	odd	2
588.2.b.a.391.6		8	84.83	odd	2
588.2.b.b.391.5		8	21.20	even	2
588.2.b.b.391.6		8	12.11	even	2
588.2.o.b.19.1		8	84.11	even	6
588.2.o.b.31.1		8	21.5	even	6
588.2.o.d.19.4		8	21.11	odd	6
588.2.o.d.31.4		8	84.47	odd	6
1344.2.bl.i.703.3		8	168.149	odd	6
1344.2.bl.i.1279.3		8	168.59	odd	6
1344.2.bl.j.703.3		8	168.107	even	6
1344.2.bl.j.1279.3		8	168.101	even	6
1764.2.b.i.1567.3		8	4.3	odd	2
1764.2.b.i.1567.4		8	7.6	odd	2
1764.2.b.j.1567.3		8	28.27	even	2	inner
1764.2.b.j.1567.4		8	1.1	even	1	trivial

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0777157 + 1.41208i) q^{2} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 - 2.79004i) q^{8} +O(q^{10})\)	\(q+(0.0777157 + 1.41208i) q^{2} +(-1.98792 + 0.219481i) q^{4} -0.438962i q^{5} +(-0.464416 - 2.79004i) q^{8} +(0.619848 - 0.0341142i) q^{10} +2.11598i q^{11} +3.84803i q^{13} +(3.90366 - 0.872621i) q^{16} -5.64831i q^{17} +2.97584 q^{19} +(0.0963438 + 0.872621i) q^{20} +(-2.98792 + 0.164445i) q^{22} +4.77038i q^{23} +4.80731 q^{25} +(-5.43371 + 0.299052i) q^{26} -7.02285 q^{29} +7.42528 q^{31} +(1.53558 + 5.44445i) q^{32} +(7.97584 - 0.438962i) q^{34} -5.28670 q^{37} +(0.231269 + 4.20212i) q^{38} +(-1.22472 + 0.203861i) q^{40} +6.81813i q^{41} +4.38646i q^{43} +(-0.464416 - 4.20639i) q^{44} +(-6.73615 + 0.370733i) q^{46} -1.68914 q^{47} +(0.373604 + 6.78829i) q^{50} +(-0.844569 - 7.64957i) q^{52} -10.7120 q^{53} +0.928833 q^{55} +(-0.545785 - 9.91680i) q^{58} +8.11818 q^{59} +6.18674i q^{61} +(0.577061 + 10.4851i) q^{62} +(-7.56863 + 2.59148i) q^{64} +1.68914 q^{65} +7.85056i q^{67} +(1.23970 + 11.2284i) q^{68} +1.16982i q^{71} +10.0348i q^{73} +(-0.410860 - 7.46523i) q^{74} +(-5.91574 + 0.653140i) q^{76} +15.5836i q^{79} +(-0.383048 - 1.71356i) q^{80} +(-9.62772 + 0.529876i) q^{82} -5.49645 q^{83} -2.47939 q^{85} +(-6.19401 + 0.340896i) q^{86} +(5.90366 - 0.982694i) q^{88} +10.4187i q^{89} +(-1.04701 - 9.48314i) q^{92} +(-0.131272 - 2.38519i) q^{94} -1.30628i q^{95} -2.22605i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8	\( 8 q + 2 q^{2} + 2 q^{4} - 4 q^{8} + 8 q^{10} + 10 q^{16} - 12 q^{19} + 22 q^{20} - 6 q^{22} - 4 q^{25} - 6 q^{26} + 16 q^{29} + 12 q^{31} + 12 q^{32} + 28 q^{34} - 12 q^{37} - 2 q^{38} - 4 q^{40} - 4 q^{44} - 12 q^{46} - 8 q^{47} - 2 q^{50} - 4 q^{52} - 8 q^{53} + 8 q^{55} - 14 q^{58} + 28 q^{59} - 48 q^{62} + 2 q^{64} + 8 q^{65} + 16 q^{68} - 38 q^{74} - 44 q^{76} + 6 q^{80} + 4 q^{82} + 4 q^{83} - 32 q^{85} - 6 q^{86} + 26 q^{88} + 28 q^{92} + 32 q^{94}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^4 - 4 * q^8 + 8 * q^10 + 10 * q^16 - 12 * q^19 + 22 * q^20 - 6 * q^22 - 4 * q^25 - 6 * q^26 + 16 * q^29 + 12 * q^31 + 12 * q^32 + 28 * q^34 - 12 * q^37 - 2 * q^38 - 4 * q^40 - 4 * q^44 - 12 * q^46 - 8 * q^47 - 2 * q^50 - 4 * q^52 - 8 * q^53 + 8 * q^55 - 14 * q^58 + 28 * q^59 - 48 * q^62 + 2 * q^64 + 8 * q^65 + 16 * q^68 - 38 * q^74 - 44 * q^76 + 6 * q^80 + 4 * q^82 + 4 * q^83 - 32 * q^85 - 6 * q^86 + 26 * q^88 + 28 * q^92 + 32 * q^94

Introduction

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