LMFDB - Embedded newform 1638.2.p.h.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$-1.38232 + 0.298668i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.h.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.75410 - 3.03819i) q^{5} +(1.12588 + 2.39424i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.75410 - 3.03819i) q^{5} +(1.12588 + 2.39424i) q^{7} -1.00000 q^{8} -3.50820 q^{10} +6.40782 q^{11} +(-0.213022 + 3.59925i) q^{13} +(2.63641 + 0.222079i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.33890 + 4.05110i) q^{17} +5.23821 q^{19} +(-1.75410 + 3.03819i) q^{20} +(3.20391 - 5.54934i) q^{22} +(-1.08480 + 1.87894i) q^{23} +(-3.65372 + 6.32843i) q^{25} +(3.01053 + 1.98411i) q^{26} +(1.51053 - 2.17216i) q^{28} +(1.23033 + 2.13099i) q^{29} +(4.46035 - 7.72555i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.67781 q^{34} +(5.29925 - 7.62037i) q^{35} +(-1.94981 + 3.37717i) q^{37} +(2.61911 - 4.53642i) q^{38} +(1.75410 + 3.03819i) q^{40} +(-5.09300 - 8.82134i) q^{41} +(-1.19338 + 2.06699i) q^{43} +(-3.20391 - 5.54934i) q^{44} +(1.08480 + 1.87894i) q^{46} +(2.44070 + 4.22742i) q^{47} +(-4.46478 + 5.39126i) q^{49} +(3.65372 + 6.32843i) q^{50} +(3.22356 - 1.61514i) q^{52} +(1.05395 - 1.82549i) q^{53} +(-11.2399 - 19.4682i) q^{55} +(-1.12588 - 2.39424i) q^{56} +2.46066 q^{58} +(-5.89729 - 10.2144i) q^{59} +9.35561 q^{61} +(-4.46035 - 7.72555i) q^{62} +1.00000 q^{64} +(11.3089 - 5.66624i) q^{65} +7.28922 q^{67} +(2.33890 - 4.05110i) q^{68} +(-3.94981 - 8.39947i) q^{70} +(-2.79339 + 4.83829i) q^{71} +(4.23175 - 7.32961i) q^{73} +(1.94981 + 3.37717i) q^{74} +(-2.61911 - 4.53642i) q^{76} +(7.21444 + 15.3419i) q^{77} +(0.893764 + 1.54804i) q^{79} +3.50820 q^{80} -10.1860 q^{82} +2.59218 q^{83} +(8.20533 - 14.2121i) q^{85} +(1.19338 + 2.06699i) q^{86} -6.40782 q^{88} +(3.50376 - 6.06869i) q^{89} +(-8.85732 + 3.54230i) q^{91} +2.16961 q^{92} +4.88140 q^{94} +(-9.18834 - 15.9147i) q^{95} +(-4.92513 + 8.53057i) q^{97} +(2.43658 + 6.56225i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 3 q^{13} - 3 q^{14} - 4 q^{16} + 2 q^{17} + 8 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 2 q^{29} + 14 q^{31} + 4 q^{32} + 4 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} + 4 q^{46} - 7 q^{47} - 7 q^{49} - 2 q^{50} + 9 q^{52} + q^{53} - 25 q^{55} + 3 q^{56} - 4 q^{58} - 16 q^{59} + 8 q^{61} - 14 q^{62} + 8 q^{64} - q^{65} - 38 q^{67} + 2 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} + 6 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} + 4 q^{80} - 24 q^{82} + 64 q^{83} + 15 q^{85} - 8 q^{88} + 11 q^{89} - 20 q^{91} + 8 q^{92} - 14 q^{94} - 28 q^{95} + 11 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 - 4 * q^10 + 8 * q^11 + 3 * q^13 - 3 * q^14 - 4 * q^16 + 2 * q^17 + 8 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 2 * q^29 + 14 * q^31 + 4 * q^32 + 4 * q^34 + 4 * q^35 - 6 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 7 * q^49 - 2 * q^50 + 9 * q^52 + q^53 - 25 * q^55 + 3 * q^56 - 4 * q^58 - 16 * q^59 + 8 * q^61 - 14 * q^62 + 8 * q^64 - q^65 - 38 * q^67 + 2 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 + 6 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 + 4 * q^80 - 24 * q^82 + 64 * q^83 + 15 * q^85 - 8 * q^88 + 11 * q^89 - 20 * q^91 + 8 * q^92 - 14 * q^94 - 28 * q^95 + 11 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.75410	−	3.03819i	−0.784457	−	1.35872i	−0.929323	−	0.369268i	$-0.879609\pi$
$5$	−1.75410	−	3.03819i	−0.784457	−	1.35872i	0.144866	−	0.989451i	$-0.453725\pi$
$6$		0			0
$7$	1.12588	+	2.39424i	0.425543	+	0.904938i
$7$	1.12588	+	2.39424i	0.425543	+	0.904938i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−3.50820			−1.10939
$11$	6.40782			1.93203			0.966015	−	0.258485i	$-0.0832231\pi$
$11$	6.40782			1.93203			0.966015	+	0.258485i	$0.0832231\pi$
$12$		0			0
$13$	−0.213022	+	3.59925i	−0.0590817	+	0.998253i
$13$	−0.213022	+	3.59925i	−0.0590817	+	0.998253i
$14$	2.63641	+	0.222079i	0.704611	+	0.0593532i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.33890	+	4.05110i	0.567267	+	0.982536i	0.996835	+	0.0795010i	$0.0253327\pi$
$17$	2.33890	+	4.05110i	0.567267	+	0.982536i	−0.429567	+	0.903035i	$0.641334\pi$
$18$		0			0
$19$	5.23821			1.20173			0.600864	−	0.799351i	$-0.294823\pi$
$19$	5.23821			1.20173			0.600864	+	0.799351i	$0.294823\pi$
$20$	−1.75410	+	3.03819i	−0.392228	+	0.679359i
$21$		0			0
$22$	3.20391	−	5.54934i	0.683076	−	1.18312i
$23$	−1.08480	+	1.87894i	−0.226197	+	0.391785i	−0.956678	−	0.291148i	$-0.905963\pi$
$23$	−1.08480	+	1.87894i	−0.226197	+	0.391785i	0.730481	+	0.682933i	$0.239296\pi$
$24$		0			0
$25$	−3.65372	+	6.32843i	−0.730745	+	1.26569i
$26$	3.01053	+	1.98411i	0.590414	+	0.389116i
$27$		0			0
$28$	1.51053	−	2.17216i	0.285464	−	0.410500i
$29$	1.23033	+	2.13099i	0.228467	+	0.395716i	0.957354	−	0.288918i	$-0.0932955\pi$
$29$	1.23033	+	2.13099i	0.228467	+	0.395716i	−0.728887	+	0.684634i	$0.759962\pi$
$30$		0			0
$31$	4.46035	−	7.72555i	0.801102	−	1.38755i	−0.117790	−	0.993039i	$-0.537581\pi$
$31$	4.46035	−	7.72555i	0.801102	−	1.38755i	0.918892	−	0.394510i	$-0.129086\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	4.67781			0.802237
$35$	5.29925	−	7.62037i	0.895737	−	1.28808i
$36$		0			0
$37$	−1.94981	+	3.37717i	−0.320547	+	0.555204i	−0.980601	−	0.196014i	$-0.937200\pi$
$37$	−1.94981	+	3.37717i	−0.320547	+	0.555204i	0.660054	+	0.751218i	$0.270533\pi$
$38$	2.61911	−	4.53642i	0.424875	−	0.735905i
$39$		0			0
$40$	1.75410	+	3.03819i	0.277347	+	0.480380i
$41$	−5.09300	−	8.82134i	−0.795393	−	1.37766i	−0.922589	−	0.385784i	$-0.873931\pi$
$41$	−5.09300	−	8.82134i	−0.795393	−	1.37766i	0.127196	−	0.991878i	$-0.459402\pi$
$42$		0			0
$43$	−1.19338	+	2.06699i	−0.181988	+	0.315213i	−0.942558	−	0.334044i	$-0.891587\pi$
$43$	−1.19338	+	2.06699i	−0.181988	+	0.315213i	0.760569	+	0.649257i	$0.224920\pi$
$44$	−3.20391	−	5.54934i	−0.483008	−	0.836594i
$45$		0			0
$46$	1.08480	+	1.87894i	0.159946	+	0.277034i
$47$	2.44070	+	4.22742i	0.356013	+	0.616632i	0.987291	−	0.158924i	$-0.0508026\pi$
$47$	2.44070	+	4.22742i	0.356013	+	0.616632i	−0.631278	+	0.775557i	$0.717469\pi$
$48$		0			0
$49$	−4.46478	+	5.39126i	−0.637826	+	0.770180i
$50$	3.65372	+	6.32843i	0.516714	+	0.894976i
$51$		0			0
$52$	3.22356	−	1.61514i	0.447027	−	0.223980i
$53$	1.05395	−	1.82549i	0.144771	−	0.250750i	−0.784517	−	0.620108i	$-0.787089\pi$
$53$	1.05395	−	1.82549i	0.144771	−	0.250750i	0.929287	+	0.369358i	$0.120422\pi$
$54$		0			0
$55$	−11.2399	−	19.4682i	−1.51559	−	2.62509i
$56$	−1.12588	−	2.39424i	−0.150452	−	0.319944i
$57$		0			0
$58$	2.46066			0.323101
$59$	−5.89729	−	10.2144i	−0.767761	−	1.32980i	−0.938774	−	0.344533i	$-0.888037\pi$
$59$	−5.89729	−	10.2144i	−0.767761	−	1.32980i	0.171013	−	0.985269i	$-0.445296\pi$
$60$		0			0
$61$	9.35561			1.19786			0.598932	−	0.800800i	$-0.295592\pi$
$61$	9.35561			1.19786			0.598932	+	0.800800i	$0.295592\pi$
$62$	−4.46035	−	7.72555i	−0.566464	−	0.981145i
$63$		0			0
$64$	1.00000			0.125000
$65$	11.3089	−	5.66624i	1.40269	−	0.702811i
$66$		0			0
$67$	7.28922			0.890520			0.445260	−	0.895401i	$-0.353111\pi$
$67$	7.28922			0.890520			0.445260	+	0.895401i	$0.353111\pi$
$68$	2.33890	−	4.05110i	0.283634	−	0.491268i
$69$		0			0
$70$	−3.94981	−	8.39947i	−0.472093	−	1.00393i
$71$	−2.79339	+	4.83829i	−0.331514	+	0.574199i	−0.982809	−	0.184625i	$-0.940893\pi$
$71$	−2.79339	+	4.83829i	−0.331514	+	0.574199i	0.651295	+	0.758825i	$0.274226\pi$
$72$		0			0
$73$	4.23175	−	7.32961i	0.495289	−	0.857866i	−0.504696	−	0.863297i	$-0.668395\pi$
$73$	4.23175	−	7.32961i	0.495289	−	0.857866i	0.999985	+	0.00543110i	$0.00172878\pi$
$74$	1.94981	+	3.37717i	0.226661	+	0.392588i
$75$		0			0
$76$	−2.61911	−	4.53642i	−0.300432	−	0.520364i
$77$	7.21444	+	15.3419i	0.822162	+	1.74837i
$78$		0			0
$79$	0.893764	+	1.54804i	0.100556	+	0.174169i	0.911914	−	0.410381i	$-0.134604\pi$
$79$	0.893764	+	1.54804i	0.100556	+	0.174169i	−0.811358	+	0.584550i	$0.801271\pi$
$80$	3.50820			0.392228
$81$		0			0
$82$	−10.1860			−1.12486
$83$	2.59218			0.284529			0.142264	−	0.989829i	$-0.454562\pi$
$83$	2.59218			0.284529			0.142264	+	0.989829i	$0.454562\pi$
$84$		0			0
$85$	8.20533	−	14.2121i	0.889993	−	1.54151i
$86$	1.19338	+	2.06699i	0.128685	+	0.222889i
$87$		0			0
$88$	−6.40782			−0.683076
$89$	3.50376	−	6.06869i	0.371398	−	0.643280i	−0.618383	−	0.785877i	$-0.712212\pi$
$89$	3.50376	−	6.06869i	0.371398	−	0.643280i	0.989781	+	0.142597i	$0.0455453\pi$
$90$		0			0
$91$	−8.85732	+	3.54230i	−0.928499	+	0.371334i
$92$	2.16961			0.226197
$93$		0			0
$94$	4.88140			0.503478
$95$	−9.18834	−	15.9147i	−0.942704	−	1.63281i
$96$		0			0
$97$	−4.92513	+	8.53057i	−0.500071	+	0.866149i	0.499929	+	0.866066i	$0.333359\pi$
$97$	−4.92513	+	8.53057i	−0.500071	+	0.866149i	−1.00000		8.21569e-5i	$0.999974\pi$
$98$	2.43658	+	6.56225i	0.246132	+	0.662887i
$99$		0			0
$100$	7.30745			0.730745
$101$	−13.8203			−1.37517			−0.687586	−	0.726103i	$-0.741330\pi$
$101$	−13.8203			−1.37517			−0.687586	+	0.726103i	$0.741330\pi$
$102$		0			0
$103$	−6.56658	−	11.3737i	−0.647025	−	1.12068i	−0.983830	−	0.179105i	$-0.942680\pi$
$103$	−6.56658	−	11.3737i	−0.647025	−	1.12068i	0.336805	−	0.941574i	$-0.390654\pi$
$104$	0.213022	−	3.59925i	0.0208885	−	0.352936i
$105$		0			0
$106$	−1.05395	−	1.82549i	−0.102368	−	0.177307i
$107$	−4.88232	+	8.45642i	−0.471991	+	0.817513i	−0.999486	−	0.0320452i	$-0.989798\pi$
$107$	−4.88232	+	8.45642i	−0.471991	+	0.817513i	0.527495	+	0.849558i	$0.323131\pi$
$108$		0			0
$109$	1.14786	−	1.98816i	0.109945	−	0.190431i	−0.805803	−	0.592184i	$-0.798266\pi$
$109$	1.14786	−	1.98816i	0.109945	−	0.190431i	0.915748	+	0.401753i	$0.131599\pi$
$110$	−22.4799			−2.14337
$111$		0			0
$112$	−2.63641	−	0.222079i	−0.249118	−	0.0209845i
$113$	−1.96268	+	3.39947i	−0.184634	+	0.319795i	−0.943453	−	0.331506i	$-0.892443\pi$
$113$	−1.96268	+	3.39947i	−0.184634	+	0.319795i	0.758819	+	0.651301i	$0.225777\pi$
$114$		0			0
$115$	7.61142			0.709768
$116$	1.23033	−	2.13099i	0.114233	−	0.197858i
$117$		0			0
$118$	−11.7946			−1.08578
$119$	−7.06598	+	10.1610i	−0.647738	+	0.931453i
$120$		0			0
$121$	30.0602			2.73274
$122$	4.67781	−	8.10220i	0.423509	−	0.733539i
$123$		0			0
$124$	−8.92069			−0.801102
$125$	8.09497			0.724036
$126$		0			0
$127$	3.51196	+	6.08289i	0.311636	+	0.539769i	0.978717	−	0.205216i	$-0.0657898\pi$
$127$	3.51196	+	6.08289i	0.311636	+	0.539769i	−0.667081	+	0.744985i	$0.732457\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.747323	−	12.6269i	0.0655446	−	1.10745i
$131$	4.56251	+	7.90250i	0.398628	+	0.690444i	0.993557	−	0.113334i	$-0.0361531\pi$
$131$	4.56251	+	7.90250i	0.398628	+	0.690444i	−0.594929	+	0.803778i	$0.702820\pi$
$132$		0			0
$133$	5.89760	+	12.5415i	0.511387	+	1.08749i
$134$	3.64461	−	6.31265i	0.314846	−	0.545330i
$135$		0			0
$136$	−2.33890	−	4.05110i	−0.200559	−	0.347379i
$137$	7.53370	+	13.0488i	0.643648	+	1.11483i	0.984612	+	0.174754i	$0.0559131\pi$
$137$	7.53370	+	13.0488i	0.643648	+	1.11483i	−0.340964	+	0.940076i	$0.610754\pi$
$138$		0			0
$139$	7.02519	−	12.1680i	0.595869	−	1.03208i	−0.397555	−	0.917578i	$-0.630141\pi$
$139$	7.02519	−	12.1680i	0.595869	−	1.03208i	0.993424	−	0.114497i	$-0.0365255\pi$
$140$	−9.24906	−	0.779098i	−0.781688	−	0.0658458i
$141$		0			0
$142$	2.79339	+	4.83829i	0.234416	+	0.406020i
$143$	−1.36501	+	23.0634i	−0.114148	+	1.92866i
$144$		0			0
$145$	4.31624	−	7.47595i	0.358444	−	0.620844i
$146$	−4.23175	−	7.32961i	−0.350222	−	0.606603i
$147$		0			0
$148$	3.89962			0.320547
$149$	−1.22934			−0.100711			−0.0503555	−	0.998731i	$-0.516035\pi$
$149$	−1.22934			−0.100711			−0.0503555	+	0.998731i	$0.516035\pi$
$150$		0			0
$151$	8.17245	−	14.1551i	0.665065	−	1.15193i	−0.314203	−	0.949356i	$-0.601737\pi$
$151$	8.17245	−	14.1551i	0.665065	−	1.15193i	0.979268	−	0.202570i	$-0.0649294\pi$
$152$	−5.23821			−0.424875
$153$		0			0
$154$	16.8937	+	1.42304i	1.36133	+	0.114672i
$155$	−31.2955			−2.51372
$156$		0			0
$157$	−7.98494	+	13.8303i	−0.637267	+	1.10378i	0.348763	+	0.937211i	$0.386602\pi$
$157$	−7.98494	+	13.8303i	−0.637267	+	1.10378i	−0.986030	+	0.166568i	$0.946731\pi$
$158$	1.78753			0.142208
$159$		0			0
$160$	1.75410	−	3.03819i	0.138674	−	0.240190i
$161$	−5.71999	−	0.481825i	−0.450798	−	0.0379731i
$162$		0			0
$163$	7.78633			0.609872			0.304936	−	0.952373i	$-0.401365\pi$
$163$	7.78633			0.609872			0.304936	+	0.952373i	$0.401365\pi$
$164$	−5.09300	+	8.82134i	−0.397697	+	0.688831i
$165$		0			0
$166$	1.29609	−	2.24489i	0.100596	−	0.174237i
$167$	−3.32333	−	5.75618i	−0.257167	−	0.445427i	0.708315	−	0.705897i	$-0.249456\pi$
$167$	−3.32333	−	5.75618i	−0.257167	−	0.445427i	−0.965482	+	0.260470i	$0.916122\pi$
$168$		0			0
$169$	−12.9092	−	1.53344i	−0.993019	−	0.117957i
$170$	−8.20533	−	14.2121i	−0.629320	−	1.09001i
$171$		0			0
$172$	2.38675			0.181988
$173$	14.6067			1.11053			0.555265	−	0.831673i	$-0.312617\pi$
$173$	14.6067			1.11053			0.555265	+	0.831673i	$0.312617\pi$
$174$		0			0
$175$	−19.2655	−	1.62283i	−1.45633	−	0.122675i
$176$	−3.20391	+	5.54934i	−0.241504	+	0.418297i
$177$		0			0
$178$	−3.50376	−	6.06869i	−0.262618	−	0.454867i
$179$	14.1285			1.05601			0.528006	−	0.849240i	$-0.322940\pi$
$179$	14.1285			1.05601			0.528006	+	0.849240i	$0.322940\pi$
$180$		0			0
$181$	−13.6453			−1.01425			−0.507124	−	0.861873i	$-0.669291\pi$
$181$	−13.6453			−1.01425			−0.507124	+	0.861873i	$0.669291\pi$
$182$	−1.36093	+	9.44181i	−0.100879	+	0.699874i
$183$		0			0
$184$	1.08480	−	1.87894i	0.0799729	−	0.138517i
$185$	13.6807			1.00582
$186$		0			0
$187$	14.9873	+	25.9587i	1.09598	+	1.89829i
$188$	2.44070	−	4.22742i	0.178006	−	0.308316i
$189$		0			0
$190$	−18.3767			−1.33318
$191$	2.43145			0.175933			0.0879666	−	0.996123i	$-0.471963\pi$
$191$	2.43145			0.175933			0.0879666	+	0.996123i	$0.471963\pi$
$192$		0			0
$193$	3.51754			0.253198			0.126599	−	0.991954i	$-0.459594\pi$
$193$	3.51754			0.253198			0.126599	+	0.991954i	$0.459594\pi$
$194$	4.92513	+	8.53057i	0.353604	+	0.612460i
$195$		0			0
$196$	6.90136	+	1.17099i	0.492954	+	0.0836418i
$197$	−1.15702	−	2.00402i	−0.0824345	−	0.142781i	0.821861	−	0.569689i	$-0.192936\pi$
$197$	−1.15702	−	2.00402i	−0.0824345	−	0.142781i	−0.904295	+	0.426908i	$0.859603\pi$
$198$		0			0
$199$	−2.84733	−	4.93173i	−0.201842	−	0.349601i	0.747280	−	0.664509i	$-0.231359\pi$
$199$	−2.84733	−	4.93173i	−0.201842	−	0.349601i	−0.949122	+	0.314909i	$0.898026\pi$
$200$	3.65372	−	6.32843i	0.258357	−	0.447488i
$201$		0			0
$202$	−6.91016	+	11.9687i	−0.486197	+	0.842118i
$203$	−3.71691	+	5.34495i	−0.260876	+	0.375142i
$204$		0			0
$205$	−17.8673	+	30.9470i	−1.24790	+	2.16143i
$206$	−13.1332			−0.915031
$207$		0			0
$208$	−3.01053	−	1.98411i	−0.208743	−	0.137573i
$209$	33.5655			2.32178
$210$		0			0
$211$	0.291966	+	0.505700i	0.0200998	+	0.0348139i	0.875900	−	0.482492i	$-0.160268\pi$
$211$	0.291966	+	0.505700i	0.0200998	+	0.0348139i	−0.855801	+	0.517306i	$0.826935\pi$
$212$	−2.10789			−0.144771
$213$		0			0
$214$	4.88232	+	8.45642i	0.333748	+	0.578069i
$215$	8.37320			0.571048
$216$		0			0
$217$	23.5186	+	1.98110i	1.59655	+	0.134486i
$218$	−1.14786	−	1.98816i	−0.0777430	−	0.134655i
$219$		0			0
$220$	−11.2399	+	19.4682i	−0.757797	+	1.31254i
$221$	−15.0792	+	7.55533i	−1.01433	+	0.508227i
$222$		0			0
$223$	−7.25749	−	12.5703i	−0.485998	−	0.841773i	0.513873	−	0.857866i	$-0.328210\pi$
$223$	−7.25749	−	12.5703i	−0.485998	−	0.841773i	−0.999870	+	0.0160938i	$0.994877\pi$
$224$	−1.51053	+	2.17216i	−0.100927	+	0.145134i
$225$		0			0
$226$	1.96268	+	3.39947i	0.130556	+	0.226129i
$227$	10.1232	+	17.5339i	0.671899	+	1.16376i	0.977365	+	0.211560i	$0.0678545\pi$
$227$	10.1232	+	17.5339i	0.671899	+	1.16376i	−0.305466	+	0.952203i	$0.598812\pi$
$228$		0			0
$229$	−0.668929	−	1.15862i	−0.0442041	−	0.0765637i	0.843077	−	0.537793i	$-0.180742\pi$
$229$	−0.668929	−	1.15862i	−0.0442041	−	0.0765637i	−0.887281	+	0.461229i	$0.847409\pi$
$230$	3.80571	−	6.59168i	0.250941	−	0.434643i
$231$		0			0
$232$	−1.23033	−	2.13099i	−0.0807752	−	0.139907i
$233$	−6.97568	−	12.0822i	−0.456992	−	0.791534i	0.541808	−	0.840502i	$-0.317740\pi$
$233$	−6.97568	−	12.0822i	−0.456992	−	0.791534i	−0.998800	+	0.0489686i	$0.984407\pi$
$234$		0			0
$235$	8.56246	−	14.8306i	0.558553	−	0.967443i
$236$	−5.89729	+	10.2144i	−0.383881	+	0.664901i
$237$		0			0
$238$	5.26665	+	11.1998i	0.341386	+	0.725975i
$239$	−9.05495			−0.585716			−0.292858	−	0.956156i	$-0.594606\pi$
$239$	−9.05495			−0.585716			−0.292858	+	0.956156i	$0.594606\pi$
$240$		0			0
$241$	−10.0551	−	17.4159i	−0.647705	−	1.12186i	−0.983670	−	0.179983i	$-0.942396\pi$
$241$	−10.0551	−	17.4159i	−0.647705	−	1.12186i	0.335965	−	0.941875i	$-0.390938\pi$
$242$	15.0301	−	26.0329i	0.966171	−	1.67346i
$243$		0			0
$244$	−4.67781	−	8.10220i	−0.299466	−	0.518690i
$245$	24.2113	+	4.10805i	1.54681	+	0.262454i
$246$		0			0
$247$	−1.11585	+	18.8536i	−0.0710001	+	1.19963i
$248$	−4.46035	+	7.72555i	−0.283232	+	0.490573i
$249$		0			0
$250$	4.04749	−	7.01045i	0.255986	−	0.443380i
$251$	−4.09035	+	7.08469i	−0.258181	+	0.447182i	−0.965755	−	0.259457i	$-0.916456\pi$
$251$	−4.09035	+	7.08469i	−0.258181	+	0.447182i	0.707574	+	0.706639i	$0.249790\pi$
$252$		0			0
$253$	−6.95123	+	12.0399i	−0.437020	+	0.756941i
$254$	7.02391			0.440719
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.87696	−	8.44715i	0.304217	−	0.526919i	−0.672870	−	0.739761i	$-0.734939\pi$
$257$	4.87696	−	8.44715i	0.304217	−	0.526919i	0.977087	+	0.212842i	$0.0682720\pi$
$258$		0			0
$259$	−10.2810	−	0.866025i	−0.638832	−	0.0538122i
$260$	−10.5615	−	6.96065i	−0.654999	−	0.431681i
$261$		0			0
$262$	9.12502			0.563745
$263$	2.94716			0.181730			0.0908648	−	0.995863i	$-0.471037\pi$
$263$	2.94716			0.181730			0.0908648	+	0.995863i	$0.471037\pi$
$264$		0			0
$265$	−7.39490			−0.454265
$266$	13.8101	+	1.16330i	0.846751	+	0.0713264i
$267$		0			0
$268$	−3.64461	−	6.31265i	−0.222630	−	0.385607i
$269$	−11.9676	−	20.7285i	−0.729679	−	1.26384i	−0.957019	−	0.290026i	$-0.906336\pi$
$269$	−11.9676	−	20.7285i	−0.729679	−	1.26384i	0.227340	−	0.973816i	$-0.426997\pi$
$270$		0			0
$271$	−9.68335	+	16.7721i	−0.588222	+	1.01883i	0.406244	+	0.913765i	$0.366838\pi$
$271$	−9.68335	+	16.7721i	−0.588222	+	1.01883i	−0.994465	+	0.105065i	$0.966495\pi$
$272$	−4.67781			−0.283634
$273$		0			0
$274$	15.0674			0.910255
$275$	−23.4124	+	40.5515i	−1.41182	+	2.44535i
$276$		0			0
$277$	−1.21710	−	2.10807i	−0.0731282	−	0.126662i	0.827143	−	0.561992i	$-0.189965\pi$
$277$	−1.21710	−	2.10807i	−0.0731282	−	0.126662i	−0.900271	+	0.435330i	$0.856632\pi$
$278$	−7.02519	−	12.1680i	−0.421343	−	0.729787i
$279$		0			0
$280$	−5.29925	+	7.62037i	−0.316691	+	0.455404i
$281$	2.80329			0.167230			0.0836152	−	0.996498i	$-0.473353\pi$
$281$	2.80329			0.167230			0.0836152	+	0.996498i	$0.473353\pi$
$282$		0			0
$283$	−16.9541			−1.00782			−0.503909	−	0.863757i	$-0.668105\pi$
$283$	−16.9541			−1.00782			−0.503909	+	0.863757i	$0.668105\pi$
$284$	5.58678			0.331514
$285$		0			0
$286$	19.2910	+	12.7138i	1.14070	+	0.751784i
$287$	15.3863	−	22.1257i	0.908224	−	1.30604i
$288$		0			0
$289$	−2.44094	+	4.22782i	−0.143584	+	0.248696i
$290$	−4.31624	−	7.47595i	−0.253458	−	0.439003i
$291$		0			0
$292$	−8.46350			−0.495289
$293$	−2.84568	+	4.92886i	−0.166246	+	0.287947i	−0.937097	−	0.349069i	$-0.886498\pi$
$293$	−2.84568	+	4.92886i	−0.166246	+	0.287947i	0.770851	+	0.637016i	$0.219831\pi$
$294$		0			0
$295$	−20.6888	+	35.8341i	−1.20455	+	2.08634i
$296$	1.94981	−	3.37717i	0.113331	−	0.196294i
$297$		0			0
$298$	−0.614668	+	1.06464i	−0.0356067	+	0.0616727i
$299$	−6.53168	−	4.30474i	−0.377737	−	0.248950i
$300$		0			0
$301$	−6.29247	−	0.530048i	−0.362692	−	0.0305515i
$302$	−8.17245	−	14.1551i	−0.470272	−	0.814535i
$303$		0			0
$304$	−2.61911	+	4.53642i	−0.150216	+	0.260182i
$305$	−16.4107	−	28.4241i	−0.939672	−	1.62756i
$306$		0			0
$307$	3.48603			0.198958			0.0994791	−	0.995040i	$-0.468282\pi$
$307$	3.48603			0.198958			0.0994791	+	0.995040i	$0.468282\pi$
$308$	9.67923	−	13.9188i	0.551525	−	0.793099i
$309$		0			0
$310$	−15.6478	+	27.1027i	−0.888734	+	1.53933i
$311$	−12.0016	+	20.7873i	−0.680546	+	1.17874i	0.294268	+	0.955723i	$0.404924\pi$
$311$	−12.0016	+	20.7873i	−0.680546	+	1.17874i	−0.974814	+	0.223018i	$0.928409\pi$
$312$		0			0
$313$	−8.77758	−	15.2032i	−0.496138	−	0.859337i	0.503852	−	0.863790i	$-0.331916\pi$
$313$	−8.77758	−	15.2032i	−0.496138	−	0.859337i	−0.999990	+	0.00445337i	$0.998582\pi$
$314$	7.98494	+	13.8303i	0.450616	+	0.780490i
$315$		0			0
$316$	0.893764	−	1.54804i	0.0502781	−	0.0870843i
$317$	1.42018	+	2.45983i	0.0797655	+	0.138158i	0.903149	−	0.429328i	$-0.141250\pi$
$317$	1.42018	+	2.45983i	0.0797655	+	0.138158i	−0.823383	+	0.567486i	$0.807916\pi$
$318$		0			0
$319$	7.88374	+	13.6550i	0.441405	+	0.764535i
$320$	−1.75410	−	3.03819i	−0.0980571	−	0.169840i
$321$		0			0
$322$	−3.27727	+	4.71274i	−0.182635	+	0.262631i
$323$	12.2517	+	21.2205i	0.681701	+	1.18074i
$324$		0			0
$325$	−21.9993	−	14.4988i	−1.22030	−	0.804247i
$326$	3.89316	−	6.74316i	0.215622	−	0.373469i
$327$		0			0
$328$	5.09300	+	8.82134i	0.281214	+	0.487077i
$329$	−7.37352	+	10.6032i	−0.406515	+	0.584573i
$330$		0			0
$331$	−18.8749			−1.03746			−0.518729	−	0.854939i	$-0.673595\pi$
$331$	−18.8749			−1.03746			−0.518729	+	0.854939i	$0.673595\pi$
$332$	−1.29609	−	2.24489i	−0.0711321	−	0.123204i
$333$		0			0
$334$	−6.64666			−0.363689
$335$	−12.7860	−	22.1460i	−0.698575	−	1.20997i
$336$		0			0
$337$	10.9560			0.596813			0.298407	−	0.954439i	$-0.403545\pi$
$337$	10.9560			0.596813			0.298407	+	0.954439i	$0.403545\pi$
$338$	−7.78262	+	10.4130i	−0.423319	+	0.566393i
$339$		0			0
$340$	−16.4107			−0.889993
$341$	28.5811	−	49.5039i	1.54775	−	2.68079i
$342$		0			0
$343$	−17.9348	−	4.61985i	−0.968388	−	0.249449i
$344$	1.19338	−	2.06699i	0.0643426	−	0.111445i
$345$		0			0
$346$	7.30337	−	12.6498i	0.392632	−	0.680058i
$347$	−16.0515	−	27.8020i	−0.861688	−	1.49249i	−0.870299	−	0.492524i	$-0.836074\pi$
$347$	−16.0515	−	27.8020i	−0.861688	−	1.49249i	0.00861062	−	0.999963i	$-0.497259\pi$
$348$		0			0
$349$	−9.04373	−	15.6642i	−0.484100	−	0.838485i	0.515734	−	0.856749i	$-0.327519\pi$
$349$	−9.04373	−	15.6642i	−0.484100	−	0.838485i	−0.999833	+	0.0182638i	$0.994186\pi$
$350$	−11.0381	+	15.8730i	−0.590013	+	0.848445i
$351$		0			0
$352$	3.20391	+	5.54934i	0.170769	+	0.295781i
$353$	27.4645			1.46179			0.730894	−	0.682491i	$-0.239103\pi$
$353$	27.4645			1.46179			0.730894	+	0.682491i	$0.239103\pi$
$354$		0			0
$355$	19.5995			1.04023
$356$	−7.00752			−0.371398
$357$		0			0
$358$	7.06425	−	12.2356i	0.373357	−	0.646673i
$359$	10.8390	+	18.7738i	0.572063	+	0.990842i	0.996354	+	0.0853162i	$0.0271900\pi$
$359$	10.8390	+	18.7738i	0.572063	+	0.990842i	−0.424291	+	0.905526i	$0.639477\pi$
$360$		0			0
$361$	8.43886			0.444151
$362$	−6.82265	+	11.8172i	−0.358591	+	0.621097i
$363$		0			0
$364$	7.49638	+	5.89951i	0.392917	+	0.309218i
$365$	−29.6916			−1.55413
$366$		0			0
$367$	15.3217			0.799788			0.399894	−	0.916561i	$-0.369047\pi$
$367$	15.3217			0.799788			0.399894	+	0.916561i	$0.369047\pi$
$368$	−1.08480	−	1.87894i	−0.0565494	−	0.0979463i
$369$		0			0
$370$	6.84033	−	11.8478i	0.355612	−	0.615937i
$371$	5.55728	+	0.468119i	0.288520	+	0.0243035i
$372$		0			0
$373$	−33.3585			−1.72724			−0.863618	−	0.504147i	$-0.831807\pi$
$373$	−33.3585			−1.72724			−0.863618	+	0.504147i	$0.831807\pi$
$374$	29.9745			1.54995
$375$		0			0
$376$	−2.44070	−	4.22742i	−0.125870	−	0.218012i
$377$	−7.93208	+	3.97432i	−0.408523	+	0.204688i
$378$		0			0
$379$	8.43868	+	14.6162i	0.433466	+	0.750785i	0.997169	−	0.0751926i	$-0.0239571\pi$
$379$	8.43868	+	14.6162i	0.433466	+	0.750785i	−0.563703	+	0.825977i	$0.690624\pi$
$380$	−9.18834	+	15.9147i	−0.471352	+	0.816405i
$381$		0			0
$382$	1.21572	−	2.10569i	0.0622018	−	0.107737i
$383$	−21.5866			−1.10302			−0.551512	−	0.834167i	$-0.685949\pi$
$383$	−21.5866			−1.10302			−0.551512	+	0.834167i	$0.685949\pi$
$384$		0			0
$385$	33.9566	−	48.8300i	1.73059	−	2.48861i
$386$	1.75877	−	3.04628i	0.0895191	−	0.155052i
$387$		0			0
$388$	9.85026			0.500071
$389$	−8.68908	+	15.0499i	−0.440554	+	0.763062i	−0.997731	−	0.0673322i	$-0.978551\pi$
$389$	−8.68908	+	15.0499i	−0.440554	+	0.763062i	0.557177	+	0.830394i	$0.311885\pi$
$390$		0			0
$391$	−10.1490			−0.513258
$392$	4.46478	−	5.39126i	0.225506	−	0.272300i
$393$		0			0
$394$	−2.31405			−0.116580
$395$	3.13550	−	5.43084i	0.157764	−	0.273255i
$396$		0			0
$397$	5.87435			0.294825			0.147413	−	0.989075i	$-0.452905\pi$
$397$	5.87435			0.294825			0.147413	+	0.989075i	$0.452905\pi$
$398$	−5.69467			−0.285448
$399$		0			0
$400$	−3.65372	−	6.32843i	−0.182686	−	0.316422i
$401$	−6.98855	+	12.1045i	−0.348992	+	0.604471i	−0.986071	−	0.166327i	$-0.946809\pi$
$401$	−6.98855	+	12.1045i	−0.348992	+	0.604471i	0.637079	+	0.770799i	$0.280143\pi$
$402$		0			0
$403$	26.8560	+	17.6996i	1.33779	+	0.881681i
$404$	6.91016	+	11.9687i	0.343793	+	0.595467i
$405$		0			0
$406$	2.77041	+	5.89142i	0.137493	+	0.292386i
$407$	−12.4940	+	21.6403i	−0.619307	+	1.07267i
$408$		0			0
$409$	18.7448	+	32.4670i	0.926873	+	1.60539i	0.788521	+	0.615008i	$0.210847\pi$
$409$	18.7448	+	32.4670i	0.926873	+	1.60539i	0.138352	+	0.990383i	$0.455819\pi$
$410$	17.8673	+	30.9470i	0.882401	+	1.52836i
$411$		0			0
$412$	−6.56658	+	11.3737i	−0.323512	+	0.560340i
$413$	17.8161	−	25.6197i	0.876673	−	1.26066i
$414$		0			0
$415$	−4.54694	−	7.87553i	−0.223200	−	0.386594i
$416$	−3.22356	+	1.61514i	−0.158048	+	0.0791889i
$417$		0			0
$418$	16.7828	−	29.0686i	0.820872	−	1.42179i
$419$	16.9548	+	29.3665i	0.828294	+	1.43465i	0.899375	+	0.437177i	$0.144022\pi$
$419$	16.9548	+	29.3665i	0.828294	+	1.43465i	−0.0710814	+	0.997471i	$0.522645\pi$
$420$		0			0
$421$	−10.5503			−0.514192			−0.257096	−	0.966386i	$-0.582766\pi$
$421$	−10.5503			−0.514192			−0.257096	+	0.966386i	$0.582766\pi$
$422$	0.583933			0.0284254
$423$		0			0
$424$	−1.05395	+	1.82549i	−0.0511842	+	0.0886536i
$425$	−34.1828			−1.65811
$426$		0			0
$427$	10.5333	+	22.3996i	0.509742	+	1.08399i
$428$	9.76463			0.471991
$429$		0			0
$430$	4.18660	−	7.25141i	0.201896	−	0.349694i
$431$	25.6086			1.23352			0.616761	−	0.787151i	$-0.288445\pi$
$431$	25.6086			1.23352			0.616761	+	0.787151i	$0.288445\pi$
$432$		0			0
$433$	3.68968	−	6.39071i	0.177315	−	0.307118i	−0.763645	−	0.645636i	$-0.776592\pi$
$433$	3.68968	−	6.39071i	0.177315	−	0.307118i	0.940960	+	0.338518i	$0.109926\pi$
$434$	13.4750	−	19.3772i	0.646821	−	0.930135i
$435$		0			0
$436$	−2.29572			−0.109945
$437$	−5.68244	+	9.84227i	−0.271828	+	0.470820i
$438$		0			0
$439$	11.5255	−	19.9628i	0.550082	−	0.952771i	−0.448186	−	0.893941i	$-0.647930\pi$
$439$	11.5255	−	19.9628i	0.550082	−	0.952771i	0.998268	−	0.0588301i	$-0.0187370\pi$
$440$	11.2399	+	19.4682i	0.535844	+	0.928108i
$441$		0			0
$442$	−0.996476	+	16.8366i	−0.0473975	+	0.800836i
$443$	−9.05605	−	15.6855i	−0.430266	−	0.745242i	0.566630	−	0.823972i	$-0.308247\pi$
$443$	−9.05605	−	15.6855i	−0.430266	−	0.745242i	−0.996896	+	0.0787300i	$0.974914\pi$
$444$		0			0
$445$	−24.5837			−1.16538
$446$	−14.5150			−0.687304
$447$		0			0
$448$	1.12588	+	2.39424i	0.0531929	+	0.113117i
$449$	9.23084	−	15.9883i	0.435630	−	0.754534i	−0.561717	−	0.827330i	$-0.689859\pi$
$449$	9.23084	−	15.9883i	0.435630	−	0.754534i	0.997347	+	0.0727961i	$0.0231922\pi$
$450$		0			0
$451$	−32.6350	−	56.5256i	−1.53672	−	2.66168i
$452$	3.92536			0.184634
$453$		0			0
$454$	20.2464			0.950209
$455$	26.2988	+	20.6966i	1.23291	+	0.970274i
$456$		0			0
$457$	8.90233	−	15.4193i	0.416433	−	0.721283i	−0.579145	−	0.815225i	$-0.696613\pi$
$457$	8.90233	−	15.4193i	0.416433	−	0.721283i	0.995578	+	0.0939414i	$0.0299466\pi$
$458$	−1.33786			−0.0625140
$459$		0			0
$460$	−3.80571	−	6.59168i	−0.177442	−	0.307339i
$461$	2.51030	−	4.34797i	0.116916	−	0.202505i	−0.801628	−	0.597823i	$-0.796032\pi$
$461$	2.51030	−	4.34797i	0.116916	−	0.202505i	0.918544	+	0.395318i	$0.129366\pi$
$462$		0			0
$463$	−25.0075			−1.16220			−0.581099	−	0.813833i	$-0.697377\pi$
$463$	−25.0075			−1.16220			−0.581099	+	0.813833i	$0.697377\pi$
$464$	−2.46066			−0.114233
$465$		0			0
$466$	−13.9514			−0.646284
$467$	−12.9128	−	22.3656i	−0.597532	−	1.03496i	−0.993184	−	0.116555i	$-0.962815\pi$
$467$	−12.9128	−	22.3656i	−0.597532	−	1.03496i	0.395653	−	0.918400i	$-0.370518\pi$
$468$		0			0
$469$	8.20680	+	17.4522i	0.378955	+	0.805866i
$470$	−8.56246	−	14.8306i	−0.394957	−	0.684085i
$471$		0			0
$472$	5.89729	+	10.2144i	0.271445	+	0.470156i
$473$	−7.64695	+	13.2449i	−0.351607	+	0.609001i
$474$		0			0
$475$	−19.1390	+	33.1497i	−0.878156	+	1.52101i
$476$	12.3326	+	1.03884i	0.565265	+	0.0476153i
$477$		0			0
$478$	−4.52748	+	7.84182i	−0.207082	+	0.358677i
$479$	−23.1137			−1.05609			−0.528047	−	0.849215i	$-0.677075\pi$
$479$	−23.1137			−1.05609			−0.528047	+	0.849215i	$0.677075\pi$
$480$		0			0
$481$	−11.7399	−	7.73728i	−0.535296	−	0.352790i
$482$	−20.1102			−0.915993
$483$		0			0
$484$	−15.0301	−	26.0329i	−0.683186	−	1.18331i
$485$	34.5566			1.56914
$486$		0			0
$487$	8.13701	+	14.0937i	0.368723	+	0.638647i	0.989366	−	0.145446i	$-0.0464617\pi$
$487$	8.13701	+	14.0937i	0.368723	+	0.638647i	−0.620643	+	0.784093i	$0.713128\pi$
$488$	−9.35561			−0.423509
$489$		0			0
$490$	15.6633	−	18.9136i	0.707598	−	0.854430i
$491$	19.0299	+	32.9608i	0.858809	+	1.48750i	0.873065	+	0.487603i	$0.162129\pi$
$491$	19.0299	+	32.9608i	0.858809	+	1.48750i	−0.0142561	+	0.999898i	$0.504538\pi$
$492$		0			0
$493$	−5.75525	+	9.96838i	−0.259203	+	0.448953i
$494$	15.7698	+	10.3932i	0.709517	+	0.467611i
$495$		0			0
$496$	4.46035	+	7.72555i	0.200275	+	0.346887i
$497$	−14.7291	−	1.24071i	−0.660689	−	0.0556533i
$498$		0			0
$499$	17.1178	+	29.6489i	0.766297	+	1.32727i	0.939558	+	0.342389i	$0.111236\pi$
$499$	17.1178	+	29.6489i	0.766297	+	1.32727i	−0.173261	+	0.984876i	$0.555430\pi$
$500$	−4.04749	−	7.01045i	−0.181009	−	0.313517i
$501$		0			0
$502$	4.09035	+	7.08469i	0.182561	+	0.316205i
$503$	1.12053	−	1.94081i	0.0499619	−	0.0865365i	−0.839963	−	0.542644i	$-0.817423\pi$
$503$	1.12053	−	1.94081i	0.0499619	−	0.0865365i	0.889925	+	0.456107i	$0.150757\pi$
$504$		0			0
$505$	24.2422	+	41.9887i	1.07876	+	1.86847i
$506$	6.95123	+	12.0399i	0.309020	+	0.535238i
$507$		0			0
$508$	3.51196	−	6.08289i	0.155818	−	0.269884i
$509$	−12.9164	+	22.3718i	−0.572509	+	0.991614i	0.423799	+	0.905756i	$0.360696\pi$
$509$	−12.9164	+	22.3718i	−0.572509	+	0.991614i	−0.996307	+	0.0858576i	$0.972637\pi$
$510$		0			0
$511$	22.3133	+	1.87957i	0.987083	+	0.0831472i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−4.87696	−	8.44715i	−0.215114	−	0.372588i
$515$	−23.0369	+	39.9010i	−1.01513	+	1.75825i
$516$		0			0
$517$	15.6396	+	27.0885i	0.687828	+	1.19135i
$518$	−5.89051	+	8.47062i	−0.258814	+	0.372178i
$519$		0			0
$520$	−11.3089	+	5.66624i	−0.495927	+	0.248481i
$521$	12.1715	−	21.0817i	0.533245	−	0.923607i	−0.466001	−	0.884784i	$-0.654306\pi$
$521$	12.1715	−	21.0817i	0.533245	−	0.923607i	0.999246	−	0.0388230i	$-0.0123609\pi$
$522$		0			0
$523$	−4.44354	+	7.69644i	−0.194303	+	0.336542i	−0.946672	−	0.322200i	$-0.895578\pi$
$523$	−4.44354	+	7.69644i	−0.194303	+	0.336542i	0.752369	+	0.658742i	$0.228911\pi$
$524$	4.56251	−	7.90250i	0.199314	−	0.345222i
$525$		0			0
$526$	1.47358	−	2.55232i	0.0642511	−	0.111286i
$527$	41.7293			1.81776
$528$		0			0
$529$	9.14640	+	15.8420i	0.397669	+	0.688784i
$530$	−3.69745	+	6.40417i	−0.160607	+	0.278180i
$531$		0			0
$532$	7.91249	−	11.3782i	0.343050	−	0.493310i
$533$	32.8351	−	16.4519i	1.42225	−	0.712609i
$534$		0			0
$535$	34.2563			1.48103
$536$	−7.28922			−0.314846
$537$		0			0
$538$	−23.9353			−1.03192
$539$	−28.6095	+	34.5462i	−1.23230	+	1.48801i
$540$		0			0
$541$	8.01702	+	13.8859i	0.344679	+	0.597001i	0.985295	−	0.170860i	$-0.0546545\pi$
$541$	8.01702	+	13.8859i	0.344679	+	0.597001i	−0.640617	+	0.767861i	$0.721321\pi$
$542$	9.68335	+	16.7721i	0.415936	+	0.720422i
$543$		0			0
$544$	−2.33890	+	4.05110i	−0.100280	+	0.173689i
$545$	−8.05385			−0.344989
$546$		0			0
$547$	−10.3955			−0.444481			−0.222240	−	0.974992i	$-0.571337\pi$
$547$	−10.3955			−0.444481			−0.222240	+	0.974992i	$0.571337\pi$
$548$	7.53370	−	13.0488i	0.321824	−	0.557415i
$549$		0			0
$550$	23.4124	+	40.5515i	0.998308	+	1.72912i
$551$	6.44473	+	11.1626i	0.274555	+	0.475543i
$552$		0			0
$553$	−2.70012	+	3.88280i	−0.114821	+	0.165113i
$554$	−2.43419			−0.103419
$555$		0			0
$556$	−14.0504			−0.595869
$557$	−32.3902			−1.37242			−0.686209	−	0.727404i	$-0.740726\pi$
$557$	−32.3902			−1.37242			−0.686209	+	0.727404i	$0.740726\pi$
$558$		0			0
$559$	−7.18540	−	4.73558i	−0.303910	−	0.200294i
$560$	3.94981	+	8.39947i	0.166910	+	0.354942i
$561$		0			0
$562$	1.40165	−	2.42772i	0.0591248	−	0.102407i
$563$	−1.21655	−	2.10712i	−0.0512713	−	0.0888045i	0.839251	−	0.543745i	$-0.182994\pi$
$563$	−1.21655	−	2.10712i	−0.0512713	−	0.0888045i	−0.890522	+	0.454940i	$0.849661\pi$
$564$		0			0
$565$	13.7710			0.579348
$566$	−8.47705	+	14.6827i	−0.356317	+	0.617159i
$567$		0			0
$568$	2.79339	−	4.83829i	0.117208	−	0.203010i
$569$	−3.97033	+	6.87681i	−0.166445	+	0.288291i	−0.937167	−	0.348880i	$-0.886562\pi$
$569$	−3.97033	+	6.87681i	−0.166445	+	0.288291i	0.770723	+	0.637171i	$0.219895\pi$
$570$		0			0
$571$	18.0463	−	31.2571i	0.755214	−	1.30807i	−0.190054	−	0.981774i	$-0.560866\pi$
$571$	18.0463	−	31.2571i	0.755214	−	1.30807i	0.945268	−	0.326295i	$-0.105800\pi$
$572$	20.6560	−	10.3496i	0.863669	−	0.432737i
$573$		0			0
$574$	−11.4682	−	24.3878i	−0.478675	−	1.01793i
$575$	−7.92715	−	13.7302i	−0.330585	−	0.572590i
$576$		0			0
$577$	−16.3980	+	28.4021i	−0.682657	+	1.18240i	0.291510	+	0.956568i	$0.405842\pi$
$577$	−16.3980	+	28.4021i	−0.682657	+	1.18240i	−0.974167	+	0.225829i	$0.927491\pi$
$578$	2.44094	+	4.22782i	0.101530	+	0.175854i
$579$		0			0
$580$	−8.63248			−0.358444
$581$	2.91848	+	6.20630i	0.121079	+	0.257481i
$582$		0			0
$583$	6.75350	−	11.6974i	0.279701	−	0.484457i
$584$	−4.23175	+	7.32961i	−0.175111	+	0.303301i
$585$		0			0
$586$	2.84568	+	4.92886i	0.117554	+	0.203609i
$587$	−10.9482	−	18.9629i	−0.451881	−	0.782681i	0.546622	−	0.837380i	$-0.315914\pi$
$587$	−10.9482	−	18.9629i	−0.451881	−	0.782681i	−0.998503	+	0.0546984i	$0.982580\pi$
$588$		0			0
$589$	23.3642	−	40.4680i	0.962707	−	1.66746i
$590$	20.6888	+	35.8341i	0.851746	+	1.47527i
$591$		0			0
$592$	−1.94981	−	3.37717i	−0.0801368	−	0.138801i
$593$	−3.25002	−	5.62921i	−0.133463	−	0.231164i	0.791547	−	0.611109i	$-0.209276\pi$
$593$	−3.25002	−	5.62921i	−0.133463	−	0.231164i	−0.925009	+	0.379945i	$0.875943\pi$
$594$		0			0
$595$	43.2653	+	3.64447i	1.77370	+	0.149409i
$596$	0.614668	+	1.06464i	0.0251778	+	0.0436092i
$597$		0			0
$598$	−6.99386	+	3.50423i	−0.286000	+	0.143299i
$599$	−1.40105	+	2.42668i	−0.0572452	+	0.0991516i	−0.893228	−	0.449604i	$-0.851565\pi$
$599$	−1.40105	+	2.42668i	−0.0572452	+	0.0991516i	0.835983	+	0.548756i	$0.184898\pi$
$600$		0			0
$601$	−11.8591	−	20.5405i	−0.483741	−	0.837864i	0.516085	−	0.856538i	$-0.327389\pi$
$601$	−11.8591	−	20.5405i	−0.483741	−	0.837864i	−0.999826	+	0.0186737i	$0.994056\pi$
$602$	−3.60527	+	5.18442i	−0.146940	+	0.211301i
$603$		0			0
$604$	−16.3449			−0.665065
$605$	−52.7285	−	91.3284i	−2.14372	−	3.71303i
$606$		0			0
$607$	−11.8430			−0.480694			−0.240347	−	0.970687i	$-0.577261\pi$
$607$	−11.8430			−0.480694			−0.240347	+	0.970687i	$0.577261\pi$
$608$	2.61911	+	4.53642i	0.106219	+	0.183976i
$609$		0			0
$610$	−32.8213			−1.32890
$611$	−15.7355	+	7.88417i	−0.636589	+	0.318959i
$612$		0			0
$613$	−16.1979			−0.654227			−0.327114	−	0.944985i	$-0.606076\pi$
$613$	−16.1979			−0.654227			−0.327114	+	0.944985i	$0.606076\pi$
$614$	1.74302	−	3.01899i	0.0703424	−	0.121837i
$615$		0			0
$616$	−7.21444	−	15.3419i	−0.290678	−	0.618142i
$617$	22.0973	−	38.2737i	0.889606	−	1.54084i	0.0492637	−	0.998786i	$-0.484313\pi$
$617$	22.0973	−	38.2737i	0.889606	−	1.54084i	0.840342	−	0.542057i	$-0.182354\pi$
$618$		0			0
$619$	−17.0272	+	29.4920i	−0.684383	+	1.18539i	0.289248	+	0.957254i	$0.406595\pi$
$619$	−17.0272	+	29.4920i	−0.684383	+	1.18539i	−0.973630	+	0.228131i	$0.926738\pi$
$620$	15.6478	+	27.1027i	0.628430	+	1.08847i
$621$		0			0
$622$	12.0016	+	20.7873i	0.481219	+	0.833496i
$623$	18.4747	+	1.55622i	0.740174	+	0.0623488i
$624$		0			0
$625$	4.06923	+	7.04812i	0.162769	+	0.281925i
$626$	−17.5552			−0.701646
$627$		0			0
$628$	15.9699			0.637267
$629$	−18.2417			−0.727344
$630$		0			0
$631$	−0.712707	+	1.23444i	−0.0283724	+	0.0491424i	−0.879863	−	0.475227i	$-0.842366\pi$
$631$	−0.712707	+	1.23444i	−0.0283724	+	0.0491424i	0.851491	+	0.524370i	$0.175699\pi$
$632$	−0.893764	−	1.54804i	−0.0355520	−	0.0615779i
$633$		0			0
$634$	2.84037			0.112805
$635$	12.3206	−	21.3400i	0.488929	−	0.846850i
$636$		0			0
$637$	−18.4534	−	17.2183i	−0.731151	−	0.682216i
$638$	15.7675			0.624240
$639$		0			0
$640$	−3.50820			−0.138674
$641$	−11.6001	−	20.0919i	−0.458175	−	0.793582i	0.540690	−	0.841222i	$-0.318163\pi$
$641$	−11.6001	−	20.0919i	−0.458175	−	0.793582i	−0.998865	+	0.0476400i	$0.984830\pi$
$642$		0			0
$643$	3.41821	−	5.92052i	0.134801	−	0.233482i	−0.790720	−	0.612178i	$-0.790294\pi$
$643$	3.41821	−	5.92052i	0.134801	−	0.233482i	0.925521	+	0.378695i	$0.123627\pi$
$644$	2.44272	+	5.19457i	0.0962567	+	0.204695i
$645$		0			0
$646$	24.5033			0.964071
$647$	42.5965			1.67464			0.837320	−	0.546713i	$-0.184121\pi$
$647$	42.5965			1.67464			0.837320	+	0.546713i	$0.184121\pi$
$648$		0			0
$649$	−37.7888	−	65.4521i	−1.48334	−	2.56922i
$650$	−23.5560	+	11.8026i	−0.923941	+	0.462935i
$651$		0			0
$652$	−3.89316	−	6.74316i	−0.152468	−	0.264082i
$653$	−19.7223	+	34.1601i	−0.771794	+	1.33679i	0.164784	+	0.986330i	$0.447307\pi$
$653$	−19.7223	+	34.1601i	−0.771794	+	1.33679i	−0.936579	+	0.350457i	$0.886026\pi$
$654$		0			0
$655$	16.0062	−	27.7235i	0.625413	−	1.08325i
$656$	10.1860			0.397697
$657$		0			0
$658$	5.49588	+	11.6873i	0.214252	+	0.455617i
$659$	−0.667872	+	1.15679i	−0.0260166	+	0.0450621i	−0.878741	−	0.477300i	$-0.841616\pi$
$659$	−0.667872	+	1.15679i	−0.0260166	+	0.0450621i	0.852724	+	0.522362i	$0.174949\pi$
$660$		0			0
$661$	−12.8932			−0.501488			−0.250744	−	0.968053i	$-0.580675\pi$
$661$	−12.8932			−0.501488			−0.250744	+	0.968053i	$0.580675\pi$
$662$	−9.43745	+	16.3461i	−0.366797	+	0.635311i
$663$		0			0
$664$	−2.59218			−0.100596
$665$	27.7586	−	39.9171i	1.07643	−	1.54792i
$666$		0			0
$667$	−5.33867			−0.206714
$668$	−3.32333	+	5.75618i	−0.128584	+	0.222713i
$669$		0			0
$670$	−25.5720			−0.987934
$671$	59.9491			2.31431
$672$		0			0
$673$	−13.8759	−	24.0338i	−0.534877	−	0.926434i	−0.999169	−	0.0407519i	$-0.987025\pi$
$673$	−13.8759	−	24.0338i	−0.534877	−	0.926434i	0.464292	−	0.885682i	$-0.346309\pi$
$674$	5.47802	−	9.48821i	0.211005	−	0.365472i
$675$		0			0
$676$	5.12662	+	11.9465i	0.197178	+	0.459479i
$677$	1.50219	+	2.60188i	0.0577340	+	0.0999982i	0.893448	−	0.449167i	$-0.148279\pi$
$677$	1.50219	+	2.60188i	0.0577340	+	0.0999982i	−0.835714	+	0.549165i	$0.814946\pi$
$678$		0			0
$679$	−25.9694	−	2.18754i	−0.996613	−	0.0839500i
$680$	−8.20533	+	14.2121i	−0.314660	+	0.545007i
$681$		0			0
$682$	−28.5811	−	49.5039i	−1.09443	−	1.89560i
$683$	−7.43467	−	12.8772i	−0.284480	−	0.492733i	0.688003	−	0.725708i	$-0.258487\pi$
$683$	−7.43467	−	12.8772i	−0.284480	−	0.492733i	−0.972483	+	0.232974i	$0.925154\pi$
$684$		0			0
$685$	26.4297	−	45.7776i	1.00983	−	1.74907i
$686$	−12.9683	+	13.2221i	−0.495132	+	0.504821i
$687$		0			0
$688$	−1.19338	−	2.06699i	−0.0454971	−	0.0788033i
$689$	6.34588	+	4.18229i	0.241759	+	0.159333i
$690$		0			0
$691$	−4.19053	+	7.25822i	−0.159415	+	0.276116i	−0.934658	−	0.355548i	$-0.884294\pi$
$691$	−4.19053	+	7.25822i	−0.159415	+	0.276116i	0.775243	+	0.631664i	$0.217628\pi$
$692$	−7.30337	−	12.6498i	−0.277633	−	0.480874i
$693$		0			0
$694$	−32.1029			−1.21861
$695$	−49.2915			−1.86973
$696$		0			0
$697$	23.8241	−	41.2645i	0.902401	−	1.56300i
$698$	−18.0875			−0.684620
$699$		0			0
$700$	8.22731	+	17.4958i	0.310963	+	0.661279i
$701$	−39.2809			−1.48362			−0.741809	−	0.670611i	$-0.766032\pi$
$701$	−39.2809			−1.48362			−0.741809	+	0.670611i	$0.766032\pi$
$702$		0			0
$703$	−10.2135	+	17.6904i	−0.385211	+	0.667204i
$704$	6.40782			0.241504
$705$		0			0
$706$	13.7323	−	23.7850i	0.516820	−	0.895159i
$707$	−15.5600	−	33.0892i	−0.585195	−	1.24445i
$708$		0			0
$709$	19.3204			0.725592			0.362796	−	0.931869i	$-0.381822\pi$
$709$	19.3204			0.725592			0.362796	+	0.931869i	$0.381822\pi$
$710$	9.79976	−	16.9737i	0.367778	−	0.637011i
$711$		0			0
$712$	−3.50376	+	6.06869i	−0.131309	+	0.227434i
$713$	9.67721	+	16.7614i	0.362414	+	0.627720i
$714$		0			0
$715$	72.4652	−	36.3083i	2.71004	−	1.35785i
$716$	−7.06425	−	12.2356i	−0.264003	−	0.457267i
$717$		0			0
$718$	21.6781			0.809019
$719$	28.4410			1.06067			0.530335	−	0.847788i	$-0.322066\pi$
$719$	28.4410			1.06067			0.530335	+	0.847788i	$0.322066\pi$
$720$		0			0
$721$	19.8381	−	28.5274i	0.738809	−	1.06241i
$722$	4.21943	−	7.30827i	0.157031	−	0.271986i
$723$		0			0
$724$	6.82265	+	11.8172i	0.253562	+	0.439182i
$725$	−17.9811			−0.667803
$726$		0			0
$727$	−48.4057			−1.79527			−0.897634	−	0.440741i	$-0.854716\pi$
$727$	−48.4057			−1.79527			−0.897634	+	0.440741i	$0.854716\pi$
$728$	8.85732	−	3.54230i	0.328274	−	0.131287i
$729$		0			0
$730$	−14.8458	+	25.7137i	−0.549468	+	0.951707i
$731$	−11.1648			−0.412944
$732$		0			0
$733$	−3.69118	−	6.39332i	−0.136337	−	0.236143i	0.789770	−	0.613403i	$-0.210200\pi$
$733$	−3.69118	−	6.39332i	−0.136337	−	0.236143i	−0.926107	+	0.377260i	$0.876866\pi$
$734$	7.66086	−	13.2690i	0.282768	−	0.489768i
$735$		0			0
$736$	−2.16961			−0.0799729
$737$	46.7080			1.72051
$738$		0			0
$739$	4.82426			0.177463			0.0887316	−	0.996056i	$-0.471719\pi$
$739$	4.82426			0.177463			0.0887316	+	0.996056i	$0.471719\pi$
$740$	−6.84033	−	11.8478i	−0.251455	−	0.435533i
$741$		0			0
$742$	3.18404	−	4.57868i	0.116890	−	0.168089i
$743$	−17.8556	−	30.9268i	−0.655059	−	1.13460i	−0.981879	−	0.189509i	$-0.939310\pi$
$743$	−17.8556	−	30.9268i	−0.655059	−	1.13460i	0.326820	−	0.945087i	$-0.394023\pi$
$744$		0			0
$745$	2.15637	+	3.73495i	0.0790035	+	0.136838i
$746$	−16.6792	+	28.8893i	−0.610670	+	1.05771i
$747$		0			0
$748$	14.9873	−	25.9587i	0.547989	−	0.949145i
$749$	−25.7436	−	2.16852i	−0.940651	−	0.0792361i
$750$		0			0
$751$	−6.54845	+	11.3422i	−0.238956	+	0.413885i	−0.960415	−	0.278573i	$-0.910139\pi$
$751$	−6.54845	+	11.3422i	−0.238956	+	0.413885i	0.721459	+	0.692457i	$0.243472\pi$
$752$	−4.88140			−0.178006
$753$		0			0
$754$	−0.524175	+	8.85654i	−0.0190893	+	0.322536i
$755$	−57.3411			−2.08686
$756$		0			0
$757$	−22.0344	−	38.1646i	−0.800852	−	1.38712i	−0.919056	−	0.394127i	$-0.871047\pi$
$757$	−22.0344	−	38.1646i	−0.800852	−	1.38712i	0.118204	−	0.992989i	$-0.462286\pi$
$758$	16.8774			0.613013
$759$		0			0
$760$	9.18834	+	15.9147i	0.333296	+	0.577286i
$761$	8.61142			0.312164			0.156082	−	0.987744i	$-0.450114\pi$
$761$	8.61142			0.312164			0.156082	+	0.987744i	$0.450114\pi$
$762$		0			0
$763$	6.05248	+	0.509833i	0.219115	+	0.0184572i
$764$	−1.21572	−	2.10569i	−0.0439833	−	0.0761814i
$765$		0			0
$766$	−10.7933	+	18.6945i	−0.389978	+	0.675461i
$767$	38.0205	−	19.0499i	1.37284	−	0.687853i
$768$		0			0
$769$	−3.20391	−	5.54934i	−0.115536	−	0.200114i	0.802458	−	0.596709i	$-0.203525\pi$
$769$	−3.20391	−	5.54934i	−0.115536	−	0.200114i	−0.917994	+	0.396595i	$0.870192\pi$
$770$	−25.3097	−	53.8223i	−0.912098	−	1.93962i
$771$		0			0
$772$	−1.75877	−	3.04628i	−0.0632996	−	0.109638i
$773$	6.29082	+	10.8960i	0.226265	+	0.391902i	0.956698	−	0.291082i	$-0.0940151\pi$
$773$	6.29082	+	10.8960i	0.226265	+	0.391902i	−0.730433	+	0.682984i	$0.760682\pi$
$774$		0			0
$775$	32.5937	+	56.4540i	1.17080	+	2.02789i
$776$	4.92513	−	8.53057i	0.176802	−	0.306230i
$777$		0			0
$778$	8.68908	+	15.0499i	0.311519	+	0.539566i
$779$	−26.6782	−	46.2080i	−0.955846	−	1.65557i
$780$		0			0
$781$	−17.8995	+	31.0029i	−0.640496	+	1.10937i
$782$	−5.07451	+	8.78930i	−0.181464	+	0.314305i
$783$		0			0
$784$	−2.43658	−	6.56225i	−0.0870206	−	0.234366i
$785$	56.0255			1.99963
$786$		0			0
$787$	9.60693	+	16.6397i	0.342450	+	0.593141i	0.984887	−	0.173198i	$-0.0554099\pi$
$787$	9.60693	+	16.6397i	0.342450	+	0.593141i	−0.642437	+	0.766338i	$0.722077\pi$
$788$	−1.15702	+	2.00402i	−0.0412172	+	0.0713904i
$789$		0			0
$790$	−3.13550	−	5.43084i	−0.111556	−	0.193221i
$791$	−10.3489	−	0.871742i	−0.367964	−	0.0309956i
$792$		0			0
$793$	−1.99295	+	33.6732i	−0.0707718	+	1.19577i
$794$	2.93718	−	5.08734i	0.104237	−	0.180543i
$795$		0			0
$796$	−2.84733	+	4.93173i	−0.100921	+	0.174800i
$797$	8.43333	−	14.6070i	0.298724	−	0.517405i	−0.677120	−	0.735872i	$-0.736772\pi$
$797$	8.43333	−	14.6070i	0.298724	−	0.517405i	0.975844	+	0.218467i	$0.0701058\pi$
$798$		0			0
$799$	−11.4171	+	19.7750i	−0.403909	+	0.699591i
$800$	−7.30745			−0.258357
$801$		0			0
$802$	6.98855	+	12.1045i	0.246774	+	0.427426i
$803$	27.1163	−	46.9668i	0.956914	−	1.65742i
$804$		0			0
$805$	8.56955	+	18.2236i	0.302037	+	0.642296i
$806$	28.7563	−	14.4082i	1.01290	−	0.507507i
$807$		0			0
$808$	13.8203			0.486197
$809$	−8.76049			−0.308002			−0.154001	−	0.988071i	$-0.549216\pi$
$809$	−8.76049			−0.308002			−0.154001	+	0.988071i	$0.549216\pi$
$810$		0			0
$811$	−32.7259			−1.14916			−0.574581	−	0.818448i	$-0.694835\pi$
$811$	−32.7259			−1.14916			−0.574581	+	0.818448i	$0.694835\pi$
$812$	6.48732	+	0.546462i	0.227660	+	0.0191770i
$813$		0			0
$814$	12.4940	+	21.6403i	0.437916	+	0.758493i
$815$	−13.6580	−	23.6563i	−0.478418	−	0.828645i
$816$		0			0
$817$	−6.25116	+	10.8273i	−0.218701	+	0.378800i
$818$	37.4897			1.31080
$819$		0			0
$820$	35.7345			1.24790
$821$	7.34756	−	12.7263i	0.256432	−	0.444152i	−0.708852	−	0.705357i	$-0.750787\pi$
$821$	7.34756	−	12.7263i	0.256432	−	0.444152i	0.965283	+	0.261205i	$0.0841198\pi$
$822$		0			0
$823$	−20.6994	−	35.8525i	−0.721537	−	1.24974i	−0.960384	−	0.278682i	$-0.910103\pi$
$823$	−20.6994	−	35.8525i	−0.721537	−	1.24974i	0.238846	−	0.971057i	$-0.423231\pi$
$824$	6.56658	+	11.3737i	0.228758	+	0.396220i
$825$		0			0
$826$	−13.2793	−	28.2391i	−0.462046	−	0.982563i
$827$	−37.8157			−1.31498			−0.657491	−	0.753462i	$-0.728382\pi$
$827$	−37.8157			−1.31498			−0.657491	+	0.753462i	$0.728382\pi$
$828$		0			0
$829$	34.4239			1.19559			0.597796	−	0.801648i	$-0.296043\pi$
$829$	34.4239			1.19559			0.597796	+	0.801648i	$0.296043\pi$
$830$	−9.09387			−0.315653
$831$		0			0
$832$	−0.213022	+	3.59925i	−0.00738521	+	0.124782i
$833$	−32.2832	−	5.47764i	−1.11855	−	0.189789i
$834$		0			0
$835$	−11.6589	+	20.1938i	−0.403473	+	0.698836i
$836$	−16.7828	−	29.0686i	−0.580444	−	1.00536i
$837$		0			0
$838$	33.9095			1.17138
$839$	0.709771	−	1.22936i	0.0245040	−	0.0424422i	−0.853513	−	0.521071i	$-0.825533\pi$
$839$	0.709771	−	1.22936i	0.0245040	−	0.0424422i	0.878017	+	0.478629i	$0.158866\pi$
$840$		0			0
$841$	11.4726	−	19.8711i	0.395606	−	0.685210i
$842$	−5.27517	+	9.13685i	−0.181794	+	0.314877i
$843$		0			0
$844$	0.291966	−	0.505700i	0.0100499	−	0.0174069i
$845$	17.9852	+	41.9105i	0.618710	+	1.44177i
$846$		0			0
$847$	33.8442	+	71.9713i	1.16290	+	2.47296i
$848$	1.05395	+	1.82549i	0.0361927	+	0.0626875i
$849$		0			0
$850$	−17.0914	+	29.6032i	−0.586230	+	1.01538i
$851$	−4.23033	−	7.32715i	−0.145014	−	0.251171i
$852$		0			0
$853$	36.8892			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$853$	36.8892			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$854$	24.6653	+	2.07769i	0.844028	+	0.0710970i
$855$		0			0
$856$	4.88232	−	8.45642i	0.166874	−	0.289034i
$857$	−13.9245	+	24.1180i	−0.475653	+	0.823855i	−0.999611	−	0.0278890i	$-0.991121\pi$
$857$	−13.9245	+	24.1180i	−0.475653	+	0.823855i	0.523958	+	0.851744i	$0.324455\pi$
$858$		0			0
$859$	−25.2862	−	43.7970i	−0.862754	−	1.49433i	−0.869260	−	0.494355i	$-0.835404\pi$
$859$	−25.2862	−	43.7970i	−0.862754	−	1.49433i	0.00650572	−	0.999979i	$-0.497929\pi$
$860$	−4.18660	−	7.25141i	−0.142762	−	0.247271i
$861$		0			0
$862$	12.8043	−	22.1777i	0.436116	−	0.755375i
$863$	−14.5501	−	25.2016i	−0.495293	−	0.857872i	0.504693	−	0.863299i	$-0.331606\pi$
$863$	−14.5501	−	25.2016i	−0.495293	−	0.857872i	−0.999985	+	0.00542701i	$0.998273\pi$
$864$		0			0
$865$	−25.6217	−	44.3780i	−0.871163	−	1.50890i
$866$	−3.68968	−	6.39071i	−0.125380	−	0.217165i
$867$		0			0
$868$	−10.0436	−	21.3583i	−0.340903	−	0.724948i
$869$	5.72708	+	9.91959i	0.194278	+	0.336499i
$870$		0			0
$871$	−1.55277	+	26.2358i	−0.0526135	+	0.888965i
$872$	−1.14786	+	1.98816i	−0.0388715	+	0.0673275i
$873$		0			0
$874$	5.68244	+	9.84227i	0.192211	+	0.332920i
$875$	9.11398	+	19.3813i	0.308109	+	0.655208i
$876$		0			0
$877$	1.11266			0.0375720			0.0187860	−	0.999824i	$-0.494020\pi$
$877$	1.11266			0.0375720			0.0187860	+	0.999824i	$0.494020\pi$
$878$	−11.5255	−	19.9628i	−0.388967	−	0.673711i
$879$		0			0
$880$	22.4799			0.757797
$881$	8.14254	+	14.1033i	0.274329	+	0.475152i	0.969966	−	0.243242i	$-0.0782109\pi$
$881$	8.14254	+	14.1033i	0.274329	+	0.475152i	−0.695636	+	0.718394i	$0.744878\pi$
$882$		0			0
$883$	−37.0876			−1.24810			−0.624048	−	0.781386i	$-0.714513\pi$
$883$	−37.0876			−1.24810			−0.624048	+	0.781386i	$0.714513\pi$
$884$	14.0827	+	9.28128i	0.473652	+	0.312163i
$885$		0			0
$886$	−18.1121			−0.608488
$887$	−10.8028	+	18.7110i	−0.362722	+	0.628252i	−0.988408	−	0.151823i	$-0.951486\pi$
$887$	−10.8028	+	18.7110i	−0.362722	+	0.628252i	0.625686	+	0.780075i	$0.284819\pi$
$888$		0			0
$889$	−10.6099	+	15.2571i	−0.355843	+	0.511706i
$890$	−12.2919	+	21.2902i	−0.412025	+	0.713647i
$891$		0			0
$892$	−7.25749	+	12.5703i	−0.242999	+	0.420886i
$893$	12.7849	+	22.1441i	0.427831	+	0.741024i
$894$		0			0
$895$	−24.7828	−	42.9250i	−0.828396	−	1.43482i
$896$	2.63641	+	0.222079i	0.0880764	+	0.00741914i
$897$		0			0
$898$	−9.23084	−	15.9883i	−0.308037	−	0.533536i
$899$	21.9508			0.732100
$900$		0			0
$901$	9.86031			0.328495
$902$	−65.2701			−2.17326
$903$		0			0
$904$	1.96268	−	3.39947i	0.0652778	−	0.113065i
$905$	23.9352	+	41.4570i	0.795633	+	1.37808i
$906$		0			0
$907$	−29.0539			−0.964720			−0.482360	−	0.875973i	$-0.660220\pi$
$907$	−29.0539			−0.964720			−0.482360	+	0.875973i	$0.660220\pi$
$908$	10.1232	−	17.5339i	0.335950	−	0.581882i
$909$		0			0
$910$	31.0732	−	12.4271i	1.03007	−	0.411954i
$911$	22.2791			0.738141			0.369071	−	0.929401i	$-0.379676\pi$
$911$	22.2791			0.738141			0.369071	+	0.929401i	$0.379676\pi$
$912$		0			0
$913$	16.6102			0.549718
$914$	−8.90233	−	15.4193i	−0.294463	−	0.510024i
$915$		0			0
$916$	−0.668929	+	1.15862i	−0.0221020	+	0.0382819i
$917$	−13.7836	+	19.8210i	−0.455176	+	0.654548i
$918$		0			0
$919$	−35.1435			−1.15928			−0.579639	−	0.814873i	$-0.696806\pi$
$919$	−35.1435			−1.15928			−0.579639	+	0.814873i	$0.696806\pi$
$920$	−7.61142			−0.250941
$921$		0			0
$922$	−2.51030	−	4.34797i	−0.0826723	−	0.143193i
$923$	−16.8192	−	11.0848i	−0.553610	−	0.364860i
$924$		0			0
$925$	−14.2481	−	24.6785i	−0.468476	−	0.811425i
$926$	−12.5038	+	21.6571i	−0.410899	+	0.711698i
$927$		0			0
$928$	−1.23033	+	2.13099i	−0.0403876	+	0.0699533i
$929$	36.7445			1.20555			0.602774	−	0.797912i	$-0.294062\pi$
$929$	36.7445			1.20555			0.602774	+	0.797912i	$0.294062\pi$
$930$		0			0
$931$	−23.3875	+	28.2406i	−0.766494	+	0.925547i
$932$	−6.97568	+	12.0822i	−0.228496	+	0.395767i
$933$		0			0
$934$	−25.8255			−0.845037
$935$	52.5783	−	91.0683i	1.71949	−	2.97825i
$936$		0			0
$937$	18.5284			0.605295			0.302647	−	0.953103i	$-0.402130\pi$
$937$	18.5284			0.605295			0.302647	+	0.953103i	$0.402130\pi$
$938$	19.2174	+	1.61878i	0.627471	+	0.0528552i
$939$		0			0
$940$	−17.1249			−0.558553
$941$	−22.5985	+	39.1417i	−0.736689	+	1.27598i	0.217290	+	0.976107i	$0.430278\pi$
$941$	−22.5985	+	39.1417i	−0.736689	+	1.27598i	−0.953979	+	0.299875i	$0.903055\pi$
$942$		0			0
$943$	22.0996			0.719664
$944$	11.7946			0.383881
$945$		0			0
$946$	7.64695	+	13.2449i	0.248624	+	0.430629i
$947$	14.4333	−	24.9993i	0.469020	−	0.812367i	−0.530353	−	0.847777i	$-0.677941\pi$
$947$	14.4333	−	24.9993i	0.469020	−	0.812367i	0.999373	+	0.0354104i	$0.0112738\pi$
$948$		0			0
$949$	25.4797	+	16.7925i	0.827105	+	0.545108i
$950$	19.1390	+	33.1497i	0.620950	+	1.07552i
$951$		0			0
$952$	7.06598	−	10.1610i	0.229010	−	0.329318i
$953$	−8.36687	+	14.4919i	−0.271030	+	0.469437i	−0.969126	−	0.246567i	$-0.920697\pi$
$953$	−8.36687	+	14.4919i	−0.271030	+	0.469437i	0.698096	+	0.716004i	$0.254031\pi$
$954$		0			0
$955$	−4.26500	−	7.38719i	−0.138012	−	0.239044i
$956$	4.52748	+	7.84182i	0.146429	+	0.253623i
$957$		0			0
$958$	−11.5569	+	20.0171i	−0.373386	+	0.646723i
$959$	−22.7598	+	32.7288i	−0.734953	+	1.05687i
$960$		0			0
$961$	−24.2894	−	42.0704i	−0.783528	−	1.35711i
$962$	−12.5707	+	6.29845i	−0.405294	+	0.203070i
$963$		0			0
$964$	−10.0551	+	17.4159i	−0.323852	+	0.560929i
$965$	−6.17012	−	10.6870i	−0.198623	−	0.344025i
$966$		0			0
$967$	−3.01759			−0.0970392			−0.0485196	−	0.998822i	$-0.515450\pi$
$967$	−3.01759			−0.0970392			−0.0485196	+	0.998822i	$0.515450\pi$
$968$	−30.0602			−0.966171
$969$		0			0
$970$	17.2783	−	29.9269i	0.554774	−	0.960896i
$971$	−25.6802			−0.824116			−0.412058	−	0.911158i	$-0.635190\pi$
$971$	−25.6802			−0.824116			−0.412058	+	0.911158i	$0.635190\pi$
$972$		0			0
$973$	37.0426	+	3.12030i	1.18753	+	0.100032i
$974$	16.2740			0.521453
$975$		0			0
$976$	−4.67781	+	8.10220i	−0.149733	+	0.259345i
$977$	40.6502			1.30052			0.650258	−	0.759713i	$-0.274661\pi$
$977$	40.6502			1.30052			0.650258	+	0.759713i	$0.274661\pi$
$978$		0			0
$979$	22.4515	−	38.8871i	0.717552	−	1.24284i
$980$	−8.54799	−	23.0217i	−0.273056	−	0.735400i
$981$		0			0
$982$	38.0599			1.21454
$983$	2.39794	−	4.15335i	0.0764823	−	0.132471i	−0.825248	−	0.564771i	$-0.808964\pi$
$983$	2.39794	−	4.15335i	0.0764823	−	0.132471i	0.901730	+	0.432300i	$0.142298\pi$
$984$		0			0
$985$	−4.05906	+	7.03051i	−0.129333	+	0.224011i
$986$	5.75525	+	9.96838i	0.183284	+	0.317458i
$987$		0			0
$988$	16.8857	−	8.46047i	0.537205	−	0.269163i
$989$	−2.58916	−	4.48456i	−0.0823306	−	0.142601i
$990$		0			0
$991$	−39.1431			−1.24342			−0.621710	−	0.783247i	$-0.713562\pi$
$991$	−39.1431			−1.24342			−0.621710	+	0.783247i	$0.713562\pi$
$992$	8.92069			0.283232
$993$		0			0
$994$	−8.43901	+	12.1354i	−0.267669	+	0.384911i
$995$	−9.98901	+	17.3015i	−0.316673	+	0.548494i
$996$		0			0
$997$	28.7246	+	49.7524i	0.909716	+	1.57567i	0.814459	+	0.580221i	$0.197034\pi$
$997$	28.7246	+	49.7524i	0.909716	+	1.57567i	0.0952567	+	0.995453i	$0.469633\pi$
$998$	34.2356			1.08371
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.h.991.1		8
3.2	odd	2		546.2.k.c.445.4	yes	8
7.2	even	3		1638.2.m.h.289.1		8
13.9	even	3		1638.2.m.h.1621.1		8
21.2	odd	6		546.2.j.c.289.4	✓	8
39.35	odd	6		546.2.j.c.529.4	yes	8
91.9	even	3	inner	1638.2.p.h.919.1		8
273.191	odd	6		546.2.k.c.373.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.4	✓	8	21.2	odd	6
546.2.j.c.529.4	yes	8	39.35	odd	6
546.2.k.c.373.4	yes	8	273.191	odd	6
546.2.k.c.445.4	yes	8	3.2	odd	2
1638.2.m.h.289.1		8	7.2	even	3
1638.2.m.h.1621.1		8	13.9	even	3
1638.2.p.h.919.1		8	91.9	even	3	inner
1638.2.p.h.991.1		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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.75410 - 3.03819i) q^{5} +(1.12588 + 2.39424i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.75410 - 3.03819i) q^{5} +(1.12588 + 2.39424i) q^{7} -1.00000 q^{8} -3.50820 q^{10} +6.40782 q^{11} +(-0.213022 + 3.59925i) q^{13} +(2.63641 + 0.222079i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.33890 + 4.05110i) q^{17} +5.23821 q^{19} +(-1.75410 + 3.03819i) q^{20} +(3.20391 - 5.54934i) q^{22} +(-1.08480 + 1.87894i) q^{23} +(-3.65372 + 6.32843i) q^{25} +(3.01053 + 1.98411i) q^{26} +(1.51053 - 2.17216i) q^{28} +(1.23033 + 2.13099i) q^{29} +(4.46035 - 7.72555i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.67781 q^{34} +(5.29925 - 7.62037i) q^{35} +(-1.94981 + 3.37717i) q^{37} +(2.61911 - 4.53642i) q^{38} +(1.75410 + 3.03819i) q^{40} +(-5.09300 - 8.82134i) q^{41} +(-1.19338 + 2.06699i) q^{43} +(-3.20391 - 5.54934i) q^{44} +(1.08480 + 1.87894i) q^{46} +(2.44070 + 4.22742i) q^{47} +(-4.46478 + 5.39126i) q^{49} +(3.65372 + 6.32843i) q^{50} +(3.22356 - 1.61514i) q^{52} +(1.05395 - 1.82549i) q^{53} +(-11.2399 - 19.4682i) q^{55} +(-1.12588 - 2.39424i) q^{56} +2.46066 q^{58} +(-5.89729 - 10.2144i) q^{59} +9.35561 q^{61} +(-4.46035 - 7.72555i) q^{62} +1.00000 q^{64} +(11.3089 - 5.66624i) q^{65} +7.28922 q^{67} +(2.33890 - 4.05110i) q^{68} +(-3.94981 - 8.39947i) q^{70} +(-2.79339 + 4.83829i) q^{71} +(4.23175 - 7.32961i) q^{73} +(1.94981 + 3.37717i) q^{74} +(-2.61911 - 4.53642i) q^{76} +(7.21444 + 15.3419i) q^{77} +(0.893764 + 1.54804i) q^{79} +3.50820 q^{80} -10.1860 q^{82} +2.59218 q^{83} +(8.20533 - 14.2121i) q^{85} +(1.19338 + 2.06699i) q^{86} -6.40782 q^{88} +(3.50376 - 6.06869i) q^{89} +(-8.85732 + 3.54230i) q^{91} +2.16961 q^{92} +4.88140 q^{94} +(-9.18834 - 15.9147i) q^{95} +(-4.92513 + 8.53057i) q^{97} +(2.43658 + 6.56225i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} - 4 q^{10} + 8 q^{11} + 3 q^{13} - 3 q^{14} - 4 q^{16} + 2 q^{17} + 8 q^{19} - 2 q^{20} + 4 q^{22} - 4 q^{23} + 2 q^{25} + 12 q^{26} - 2 q^{29} + 14 q^{31} + 4 q^{32} + 4 q^{34} + 4 q^{35} - 6 q^{37} + 4 q^{38} + 2 q^{40} - 12 q^{41} - 4 q^{44} + 4 q^{46} - 7 q^{47} - 7 q^{49} - 2 q^{50} + 9 q^{52} + q^{53} - 25 q^{55} + 3 q^{56} - 4 q^{58} - 16 q^{59} + 8 q^{61} - 14 q^{62} + 8 q^{64} - q^{65} - 38 q^{67} + 2 q^{68} - 22 q^{70} - 20 q^{71} - 7 q^{73} + 6 q^{74} - 4 q^{76} + 24 q^{77} + 24 q^{79} + 4 q^{80} - 24 q^{82} + 64 q^{83} + 15 q^{85} - 8 q^{88} + 11 q^{89} - 20 q^{91} + 8 q^{92} - 14 q^{94} - 28 q^{95} + 11 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 - 4 * q^10 + 8 * q^11 + 3 * q^13 - 3 * q^14 - 4 * q^16 + 2 * q^17 + 8 * q^19 - 2 * q^20 + 4 * q^22 - 4 * q^23 + 2 * q^25 + 12 * q^26 - 2 * q^29 + 14 * q^31 + 4 * q^32 + 4 * q^34 + 4 * q^35 - 6 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 7 * q^49 - 2 * q^50 + 9 * q^52 + q^53 - 25 * q^55 + 3 * q^56 - 4 * q^58 - 16 * q^59 + 8 * q^61 - 14 * q^62 + 8 * q^64 - q^65 - 38 * q^67 + 2 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 + 6 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 + 4 * q^80 - 24 * q^82 + 64 * q^83 + 15 * q^85 - 8 * q^88 + 11 * q^89 - 20 * q^91 + 8 * q^92 - 14 * q^94 - 28 * q^95 + 11 * q^97 - 2 * q^98

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