LMFDB - Embedded newform 1323.2.g.d.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (of order $3$, degree $2$, not 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.d.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 - 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +2.94356 q^{8} +O(q^{10})$	\(q+(0.673648 - 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +2.94356 q^{8} +(-1.70574 + 2.95442i) q^{10} -0.467911 q^{11} +(-2.91147 + 5.04282i) q^{13} +(1.79813 - 3.11446i) q^{16} +(1.93969 - 3.35965i) q^{17} +(1.09240 + 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +0.106067 q^{23} +1.41147 q^{25} +(3.92262 + 6.79417i) q^{26} +(4.39053 + 7.60462i) q^{29} +(3.84002 + 6.65111i) q^{31} +(0.520945 + 0.902302i) q^{32} +(-2.61334 - 4.52644i) q^{34} +(3.84002 + 6.65111i) q^{37} +2.94356 q^{38} -7.45336 q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(-0.0432332 - 0.0748822i) q^{44} +(0.0714517 - 0.123758i) q^{46} +(-2.66637 + 4.61830i) q^{47} +(0.950837 - 1.64690i) q^{50} -1.07604 q^{52} +(-0.358441 + 0.620838i) q^{53} +1.18479 q^{55} +11.8307 q^{58} +(0.368241 + 0.637812i) q^{59} +(-0.479055 + 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(7.37211 - 12.7689i) q^{65} +(4.81908 + 8.34689i) q^{67} +0.716881 q^{68} -13.2344 q^{71} +(5.13429 - 8.89284i) q^{73} +10.3473 q^{74} +(-0.201867 + 0.349643i) q^{76} +(6.31908 - 10.9450i) q^{79} +(-4.55303 + 7.88609i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} -1.65270 q^{86} -1.37733 q^{88} +(-4.05690 - 7.02676i) q^{89} +(0.00980018 + 0.0169744i) q^{92} +(3.59240 + 6.22221i) q^{94} +(-2.76604 - 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8} - 12 q^{11} + 3 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{31} - 9 q^{34} + 3 q^{37} - 12 q^{38} - 18 q^{40} + 3 q^{43} + 15 q^{44} + 3 q^{47} - 6 q^{50} - 42 q^{52} + 6 q^{53} - 18 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 12 q^{68} - 18 q^{71} + 21 q^{73} + 60 q^{74} - 15 q^{76} + 21 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} + 12 q^{89} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8 - 12 * q^11 + 3 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^31 - 9 * q^34 + 3 * q^37 - 12 * q^38 - 18 * q^40 + 3 * q^43 + 15 * q^44 + 3 * q^47 - 6 * q^50 - 42 * q^52 + 6 * q^53 - 18 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 12 * q^68 - 18 * q^71 + 21 * q^73 + 60 * q^74 - 15 * q^76 + 21 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 + 12 * q^89 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.673648	−	1.16679i	0.476341	−	0.825047i	−0.523291	−	0.852154i	$-0.675296\pi$
$2$	0.673648	−	1.16679i	0.476341	−	0.825047i	0.999633	+	0.0271067i	$0.00862938\pi$
$3$		0			0
$3$		0			0
$4$	0.0923963	+	0.160035i	0.0461981	+	0.0800175i
$5$	−2.53209			−1.13238			−0.566192	−	0.824273i	$-0.691584\pi$
$5$	−2.53209			−1.13238			−0.566192	+	0.824273i	$0.691584\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.94356			1.04071
$9$		0			0
$10$	−1.70574	+	2.95442i	−0.539401	+	0.934271i
$11$	−0.467911			−0.141081			−0.0705403	−	0.997509i	$-0.522472\pi$
$11$	−0.467911			−0.141081			−0.0705403	+	0.997509i	$0.522472\pi$
$12$		0			0
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	0.107094	+	0.994249i	$0.465845\pi$
$13$	−2.91147	+	5.04282i	−0.807498	+	1.39863i	−0.914592	+	0.404378i	$0.867488\pi$
$14$		0			0
$15$		0			0
$16$	1.79813	−	3.11446i	0.449533	−	0.778615i
$17$	1.93969	−	3.35965i	0.470445	−	0.814834i	−0.528984	−	0.848632i	$-0.677427\pi$
$17$	1.93969	−	3.35965i	0.470445	−	0.814834i	0.999429	+	0.0337978i	$0.0107602\pi$
$18$		0			0
$19$	1.09240	+	1.89209i	0.250613	+	0.434074i	0.963695	−	0.267007i	$-0.0860345\pi$
$19$	1.09240	+	1.89209i	0.250613	+	0.434074i	−0.713082	+	0.701081i	$0.752701\pi$
$20$	−0.233956	−	0.405223i	−0.0523141	−	0.0906106i
$21$		0			0
$22$	−0.315207	+	0.545955i	−0.0672025	+	0.116398i
$23$	0.106067			0.0221165			0.0110582	−	0.999939i	$-0.496480\pi$
$23$	0.106067			0.0221165			0.0110582	+	0.999939i	$0.496480\pi$
$24$		0			0
$25$	1.41147			0.282295
$26$	3.92262	+	6.79417i	0.769289	+	1.33245i
$27$		0			0
$28$		0			0
$29$	4.39053	+	7.60462i	0.815301	+	1.41214i	0.909112	+	0.416552i	$0.136762\pi$
$29$	4.39053	+	7.60462i	0.815301	+	1.41214i	−0.0938108	+	0.995590i	$0.529905\pi$
$30$		0			0
$31$	3.84002	+	6.65111i	0.689688	+	1.19458i	0.971939	+	0.235235i	$0.0755858\pi$
$31$	3.84002	+	6.65111i	0.689688	+	1.19458i	−0.282250	+	0.959341i	$0.591081\pi$
$32$	0.520945	+	0.902302i	0.0920909	+	0.159506i
$33$		0			0
$34$	−2.61334	−	4.52644i	−0.448184	−	0.776278i
$35$		0			0
$36$		0			0
$37$	3.84002	+	6.65111i	0.631296	+	1.09344i	0.987287	+	0.158947i	$0.0508099\pi$
$37$	3.84002	+	6.65111i	0.631296	+	1.09344i	−0.355991	+	0.934489i	$0.615857\pi$
$38$	2.94356			0.477509
$39$		0			0
$40$	−7.45336			−1.17848
$41$	−1.11334	+	1.92836i	−0.173875	+	0.301160i	−0.939771	−	0.341804i	$-0.888962\pi$
$41$	−1.11334	+	1.92836i	−0.173875	+	0.301160i	0.765897	+	0.642964i	$0.222295\pi$
$42$		0			0
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	0.815462	−	0.578811i	$-0.196483\pi$
$43$	−0.613341	−	1.06234i	−0.0935336	−	0.162005i	−0.908996	+	0.416806i	$0.863150\pi$
$44$	−0.0432332	−	0.0748822i	−0.00651766	−	0.0112889i
$45$		0			0
$46$	0.0714517	−	0.123758i	0.0105350	−	0.0182471i
$47$	−2.66637	+	4.61830i	−0.388931	+	0.673648i	−0.992306	−	0.123810i	$-0.960489\pi$
$47$	−2.66637	+	4.61830i	−0.388931	+	0.673648i	0.603375	+	0.797457i	$0.293822\pi$
$48$		0			0
$49$		0			0
$50$	0.950837	−	1.64690i	0.134469	−	0.232907i
$51$		0			0
$52$	−1.07604			−0.149220
$53$	−0.358441	+	0.620838i	−0.0492356	+	0.0852786i	−0.889593	−	0.456754i	$-0.849012\pi$
$53$	−0.358441	+	0.620838i	−0.0492356	+	0.0852786i	0.840357	+	0.542033i	$0.182345\pi$
$54$		0			0
$55$	1.18479			0.159757
$56$		0			0
$57$		0			0
$58$	11.8307			1.55345
$59$	0.368241	+	0.637812i	0.0479409	+	0.0830360i	0.889000	−	0.457907i	$-0.151401\pi$
$59$	0.368241	+	0.637812i	0.0479409	+	0.0830360i	−0.841059	+	0.540943i	$0.818067\pi$
$60$		0			0
$61$	−0.479055	+	0.829748i	−0.0613368	+	0.106238i	−0.895063	−	0.445939i	$-0.852870\pi$
$61$	−0.479055	+	0.829748i	−0.0613368	+	0.106238i	0.833726	+	0.552178i	$0.186203\pi$
$62$	10.3473			1.31411
$63$		0			0
$64$	8.59627			1.07453
$65$	7.37211	−	12.7689i	0.914398	−	1.58378i
$66$		0			0
$67$	4.81908	+	8.34689i	0.588744	+	1.01973i	0.994397	+	0.105708i	$0.0337107\pi$
$67$	4.81908	+	8.34689i	0.588744	+	1.01973i	−0.405653	+	0.914027i	$0.632956\pi$
$68$	0.716881			0.0869346
$69$		0			0
$70$		0			0
$71$	−13.2344			−1.57064			−0.785318	−	0.619092i	$-0.787501\pi$
$71$	−13.2344			−1.57064			−0.785318	+	0.619092i	$0.787501\pi$
$72$		0			0
$73$	5.13429	−	8.89284i	0.600923	−	1.04083i	−0.391759	−	0.920068i	$-0.628133\pi$
$73$	5.13429	−	8.89284i	0.600923	−	1.04083i	0.992682	−	0.120761i	$-0.0385334\pi$
$74$	10.3473			1.20285
$75$		0			0
$76$	−0.201867	+	0.349643i	−0.0231557	+	0.0401068i
$77$		0			0
$78$		0			0
$79$	6.31908	−	10.9450i	0.710952	−	1.23140i	−0.253548	−	0.967323i	$-0.581598\pi$
$79$	6.31908	−	10.9450i	0.710952	−	1.23140i	0.964500	−	0.264082i	$-0.0850689\pi$
$80$	−4.55303	+	7.88609i	−0.509045	+	0.881691i
$81$		0			0
$82$	1.50000	+	2.59808i	0.165647	+	0.286910i
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	0.781286	−	0.624173i	$-0.214564\pi$
$83$	−1.36571	−	2.36549i	−0.149907	−	0.259646i	−0.931193	+	0.364527i	$0.881231\pi$
$84$		0			0
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$	−1.65270			−0.178216
$87$		0			0
$88$	−1.37733			−0.146823
$89$	−4.05690	−	7.02676i	−0.430031	−	0.744835i	0.566845	−	0.823825i	$-0.308164\pi$
$89$	−4.05690	−	7.02676i	−0.430031	−	0.744835i	−0.996875	+	0.0789894i	$0.974831\pi$
$90$		0			0
$91$		0			0
$92$	0.00980018	+	0.0169744i	0.00102174	+	0.00176970i
$93$		0			0
$94$	3.59240	+	6.22221i	0.370527	+	0.641772i
$95$	−2.76604	−	4.79093i	−0.283790	−	0.491539i
$96$		0			0
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	0.971629	+	0.236511i	$0.0760039\pi$
$97$	6.80200	+	11.7814i	0.690639	+	1.19622i	−0.280990	+	0.959711i	$0.590663\pi$
$98$		0			0
$99$		0			0
$100$	0.130415	+	0.225885i	0.0130415	+	0.0225885i
$101$	9.57398			0.952646			0.476323	−	0.879270i	$-0.341969\pi$
$101$	9.57398			0.952646			0.476323	+	0.879270i	$0.341969\pi$
$102$		0			0
$103$	3.04189			0.299726			0.149863	−	0.988707i	$-0.452117\pi$
$103$	3.04189			0.299726			0.149863	+	0.988707i	$0.452117\pi$
$104$	−8.57011	+	14.8439i	−0.840368	+	1.45556i
$105$		0			0
$106$	0.482926	+	0.836452i	0.0469059	+	0.0812434i
$107$	−3.25877	−	5.64436i	−0.315037	−	0.545660i	0.664408	−	0.747370i	$-0.268684\pi$
$107$	−3.25877	−	5.64436i	−0.315037	−	0.545660i	−0.979445	+	0.201709i	$0.935350\pi$
$108$		0			0
$109$	−5.31908	+	9.21291i	−0.509475	+	0.882437i	0.490465	+	0.871461i	$0.336827\pi$
$109$	−5.31908	+	9.21291i	−0.509475	+	0.882437i	−0.999940	+	0.0109759i	$0.996506\pi$
$110$	0.798133	−	1.38241i	0.0760990	−	0.131807i
$111$		0			0
$112$		0			0
$113$	2.58853	−	4.48346i	0.243508	−	0.421768i	−0.718203	−	0.695834i	$-0.755035\pi$
$113$	2.58853	−	4.48346i	0.243508	−	0.421768i	0.961711	+	0.274065i	$0.0883684\pi$
$114$		0			0
$115$	−0.268571			−0.0250443
$116$	−0.811337	+	1.40528i	−0.0753308	+	0.130477i
$117$		0			0
$118$	0.992259			0.0913449
$119$		0			0
$120$		0			0
$121$	−10.7811			−0.980096
$122$	0.645430	+	1.11792i	0.0584345	+	0.101211i
$123$		0			0
$124$	−0.709607	+	1.22908i	−0.0637246	+	0.110374i
$125$	9.08647			0.812718
$126$		0			0
$127$	−8.88207			−0.788157			−0.394078	−	0.919077i	$-0.628936\pi$
$127$	−8.88207			−0.788157			−0.394078	+	0.919077i	$0.628936\pi$
$128$	4.74897	−	8.22546i	0.419754	−	0.727035i
$129$		0			0
$130$	−9.93242	−	17.2035i	−0.871131	−	1.50884i
$131$	−11.3628			−0.992771			−0.496385	−	0.868102i	$-0.665340\pi$
$131$	−11.3628			−0.992771			−0.496385	+	0.868102i	$0.665340\pi$
$132$		0			0
$133$		0			0
$134$	12.9855			1.12177
$135$		0			0
$136$	5.70961	−	9.88933i	0.489595	−	0.848003i
$137$	5.72462			0.489087			0.244544	−	0.969638i	$-0.421362\pi$
$137$	5.72462			0.489087			0.244544	+	0.969638i	$0.421362\pi$
$138$		0			0
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	−0.845768	−	0.533551i	$-0.820857\pi$
$139$	0.461981	−	0.800175i	0.0391847	−	0.0678700i	0.884953	+	0.465681i	$0.154191\pi$
$140$		0			0
$141$		0			0
$142$	−8.91534	+	15.4418i	−0.748159	+	1.29585i
$143$	1.36231	−	2.35959i	0.113922	−	0.197319i
$144$		0			0
$145$	−11.1172	−	19.2556i	−0.923234	−	1.59909i
$146$	−6.91740	−	11.9813i	−0.572488	−	0.991579i
$147$		0			0
$148$	−0.709607	+	1.22908i	−0.0583294	+	0.101029i
$149$	−8.72462			−0.714749			−0.357374	−	0.933961i	$-0.616328\pi$
$149$	−8.72462			−0.714749			−0.357374	+	0.933961i	$0.616328\pi$
$150$		0			0
$151$	18.4270			1.49956			0.749782	−	0.661685i	$-0.230158\pi$
$151$	18.4270			1.49956			0.749782	+	0.661685i	$0.230158\pi$
$152$	3.21554	+	5.56947i	0.260815	+	0.451744i
$153$		0			0
$154$		0			0
$155$	−9.72328	−	16.8412i	−0.780992	−	1.35272i
$156$		0			0
$157$	−2.46198	−	4.26428i	−0.196488	−	0.340326i	0.750900	−	0.660416i	$-0.229620\pi$
$157$	−2.46198	−	4.26428i	−0.196488	−	0.340326i	−0.947387	+	0.320090i	$0.896287\pi$
$158$	−8.51367	−	14.7461i	−0.677311	−	1.17314i
$159$		0			0
$160$	−1.31908	−	2.28471i	−0.104282	−	0.180622i
$161$		0			0
$162$		0			0
$163$	−3.81908	−	6.61484i	−0.299133	−	0.518114i	0.676805	−	0.736163i	$-0.263364\pi$
$163$	−3.81908	−	6.61484i	−0.299133	−	0.518114i	−0.975938	+	0.218049i	$0.930031\pi$
$164$	−0.411474			−0.0321307
$165$		0			0
$166$	−3.68004			−0.285627
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	−0.954446	−	0.298385i	$-0.903552\pi$
$167$	−2.82770	+	4.89771i	−0.218814	+	0.378996i	0.735632	+	0.677382i	$0.236885\pi$
$168$		0			0
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$	6.61721	+	11.4613i	0.507517	+	0.879045i
$171$		0			0
$172$	0.113341	−	0.196312i	0.00864215	−	0.0149687i
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	−0.118071	−	0.993005i	$-0.537671\pi$
$173$	10.5346	−	18.2465i	0.800932	−	1.38725i	0.919003	−	0.394250i	$-0.128995\pi$
$174$		0			0
$175$		0			0
$176$	−0.841367	+	1.45729i	−0.0634204	+	0.109847i
$177$		0			0
$178$	−10.9317			−0.819366
$179$	−2.56031	+	4.43458i	−0.191366	+	0.331456i	−0.945703	−	0.325031i	$-0.894625\pi$
$179$	−2.56031	+	4.43458i	−0.191366	+	0.331456i	0.754337	+	0.656487i	$0.227959\pi$
$180$		0			0
$181$	−0.319955			−0.0237821			−0.0118910	−	0.999929i	$-0.503785\pi$
$181$	−0.319955			−0.0237821			−0.0118910	+	0.999929i	$0.503785\pi$
$182$		0			0
$183$		0			0
$184$	0.312214			0.0230168
$185$	−9.72328	−	16.8412i	−0.714870	−	1.23819i
$186$		0			0
$187$	−0.907604	+	1.57202i	−0.0663706	+	0.114957i
$188$	−0.985452			−0.0718715
$189$		0			0
$190$	−7.45336			−0.540724
$191$	−7.78359	+	13.4816i	−0.563200	+	0.975492i	0.434014	+	0.900906i	$0.357097\pi$
$191$	−7.78359	+	13.4816i	−0.563200	+	0.975492i	−0.997215	+	0.0745858i	$0.976237\pi$
$192$		0			0
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	0.736576	−	0.676355i	$-0.236441\pi$
$193$	−3.02094	−	5.23243i	−0.217452	−	0.376639i	−0.954028	+	0.299716i	$0.903108\pi$
$194$	18.3286			1.31592
$195$		0			0
$196$		0			0
$197$	−25.2344			−1.79788			−0.898939	−	0.438074i	$-0.855661\pi$
$197$	−25.2344			−1.79788			−0.898939	+	0.438074i	$0.855661\pi$
$198$		0			0
$199$	−1.52094	+	2.63435i	−0.107817	+	0.186744i	−0.914886	−	0.403713i	$-0.867719\pi$
$199$	−1.52094	+	2.63435i	−0.107817	+	0.186744i	0.807069	+	0.590458i	$0.201053\pi$
$200$	4.15476			0.293786
$201$		0			0
$202$	6.44949	−	11.1708i	0.453785	−	0.785978i
$203$		0			0
$204$		0			0
$205$	2.81908	−	4.88279i	0.196893	−	0.341029i
$206$	2.04916	−	3.54925i	0.142772	−	0.247288i
$207$		0			0
$208$	10.4704	+	18.1353i	0.725994	+	1.25746i
$209$	−0.511144	−	0.885328i	−0.0353566	−	0.0612394i
$210$		0			0
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	−0.756775	−	0.653676i	$-0.773226\pi$
$211$	2.72668	−	4.72275i	0.187713	−	0.325128i	0.944487	+	0.328548i	$0.106559\pi$
$212$	−0.132474			−0.00909837
$213$		0			0
$214$	−8.78106			−0.600261
$215$	1.55303	+	2.68993i	0.105916	+	0.183452i
$216$		0			0
$217$		0			0
$218$	7.16637	+	12.4125i	0.485368	+	0.840682i
$219$		0			0
$220$	0.109470	+	0.189608i	0.00738049	+	0.0127834i
$221$	11.2947	+	19.5630i	0.759766	+	1.31595i
$222$		0			0
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	0.524395	−	0.851475i	$-0.324291\pi$
$223$	−7.09627	−	12.2911i	−0.475201	−	0.823073i	−0.999597	+	0.0284023i	$0.990958\pi$
$224$		0			0
$225$		0			0
$226$	−3.48751	−	6.04055i	−0.231986	−	0.401811i
$227$	2.89393			0.192077			0.0960385	−	0.995378i	$-0.469383\pi$
$227$	2.89393			0.192077			0.0960385	+	0.995378i	$0.469383\pi$
$228$		0			0
$229$	9.16756			0.605809			0.302905	−	0.953021i	$-0.402044\pi$
$229$	9.16756			0.605809			0.302905	+	0.953021i	$0.402044\pi$
$230$	−0.180922	+	0.313366i	−0.0119297	+	0.0206628i
$231$		0			0
$232$	12.9238	+	22.3847i	0.848489	+	1.46963i
$233$	6.63563	+	11.4932i	0.434715	+	0.752948i	0.997272	−	0.0738103i	$-0.0235159\pi$
$233$	6.63563	+	11.4932i	0.434715	+	0.752948i	−0.562558	+	0.826758i	$0.690183\pi$
$234$		0			0
$235$	6.75150	−	11.6939i	0.440419	−	0.762828i
$236$	−0.0680482	+	0.117863i	−0.00442956	+	0.00767222i
$237$		0			0
$238$		0			0
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	−0.669571	−	0.742748i	$-0.733522\pi$
$239$	4.76857	−	8.25941i	0.308453	−	0.534257i	0.978024	+	0.208491i	$0.0668553\pi$
$240$		0			0
$241$	−8.95811			−0.577043			−0.288521	−	0.957473i	$-0.593164\pi$
$241$	−8.95811			−0.577043			−0.288521	+	0.957473i	$0.593164\pi$
$242$	−7.26264	+	12.5793i	−0.466860	+	0.808626i
$243$		0			0
$244$	−0.177052			−0.0113346
$245$		0			0
$246$		0			0
$247$	−12.7219			−0.809477
$248$	11.3033	+	19.5780i	0.717763	+	1.24320i
$249$		0			0
$250$	6.12108	−	10.6020i	0.387131	−	0.670531i
$251$	24.9982			1.57788			0.788938	−	0.614473i	$-0.210631\pi$
$251$	24.9982			1.57788			0.788938	+	0.614473i	$0.210631\pi$
$252$		0			0
$253$	−0.0496299			−0.00312020
$254$	−5.98339	+	10.3635i	−0.375431	+	0.650266i
$255$		0			0
$256$	2.19800	+	3.80704i	0.137375	+	0.237940i
$257$	−10.8520			−0.676932			−0.338466	−	0.940979i	$-0.609908\pi$
$257$	−10.8520			−0.676932			−0.338466	+	0.940979i	$0.609908\pi$
$258$		0			0
$259$		0			0
$260$	2.72462			0.168974
$261$		0			0
$262$	−7.65451	+	13.2580i	−0.472897	+	0.819082i
$263$	−26.0874			−1.60862			−0.804309	−	0.594211i	$-0.797464\pi$
$263$	−26.0874			−1.60862			−0.804309	+	0.594211i	$0.797464\pi$
$264$		0			0
$265$	0.907604	−	1.57202i	0.0557537	−	0.0965682i
$266$		0			0
$267$		0			0
$268$	−0.890530	+	1.54244i	−0.0543978	+	0.0942197i
$269$	−3.81655	+	6.61046i	−0.232699	+	0.403047i	−0.958602	−	0.284751i	$-0.908089\pi$
$269$	−3.81655	+	6.61046i	−0.232699	+	0.403047i	0.725902	+	0.687798i	$0.241422\pi$
$270$		0			0
$271$	−1.70187	−	2.94772i	−0.103381	−	0.179061i	0.809695	−	0.586852i	$-0.199633\pi$
$271$	−1.70187	−	2.94772i	−0.103381	−	0.179061i	−0.913076	+	0.407790i	$0.866299\pi$
$272$	−6.97565	−	12.0822i	−0.422961	−	0.732590i
$273$		0			0
$274$	3.85638	−	6.67945i	0.232973	−	0.403520i
$275$	−0.660444			−0.0398263
$276$		0			0
$277$	−5.72193			−0.343798			−0.171899	−	0.985115i	$-0.554990\pi$
$277$	−5.72193			−0.343798			−0.171899	+	0.985115i	$0.554990\pi$
$278$	−0.622426	−	1.07807i	−0.0373306	−	0.0646585i
$279$		0			0
$280$		0			0
$281$	14.1887	+	24.5755i	0.846425	+	1.46605i	0.884378	+	0.466771i	$0.154583\pi$
$281$	14.1887	+	24.5755i	0.846425	+	1.46605i	−0.0379535	+	0.999280i	$0.512084\pi$
$282$		0			0
$283$	−2.28564	−	3.95885i	−0.135867	−	0.235329i	0.790061	−	0.613028i	$-0.210049\pi$
$283$	−2.28564	−	3.95885i	−0.135867	−	0.235329i	−0.925929	+	0.377699i	$0.876715\pi$
$284$	−1.22281	−	2.11797i	−0.0725605	−	0.125678i
$285$		0			0
$286$	−1.83544	−	3.17907i	−0.108532	−	0.187982i
$287$		0			0
$288$		0			0
$289$	0.975185	+	1.68907i	0.0573638	+	0.0993571i
$290$	−29.9564			−1.75910
$291$		0			0
$292$	1.89756			0.111046
$293$	2.16385	−	3.74789i	0.126413	−	0.218954i	−0.795871	−	0.605466i	$-0.792987\pi$
$293$	2.16385	−	3.74789i	0.126413	−	0.218954i	0.922285	+	0.386512i	$0.126320\pi$
$294$		0			0
$295$	−0.932419	−	1.61500i	−0.0542875	−	0.0940287i
$296$	11.3033	+	19.5780i	0.656994	+	1.13795i
$297$		0			0
$298$	−5.87733	+	10.1798i	−0.340464	+	0.589702i
$299$	−0.308811	+	0.534876i	−0.0178590	+	0.0309327i
$300$		0			0
$301$		0			0
$302$	12.4133	−	21.5004i	0.714304	−	1.23721i
$303$		0			0
$304$	7.85710			0.450635
$305$	1.21301	−	2.10100i	0.0694568	−	0.120303i
$306$		0			0
$307$	12.3773			0.706411			0.353206	−	0.935546i	$-0.385092\pi$
$307$	12.3773			0.706411			0.353206	+	0.935546i	$0.385092\pi$
$308$		0			0
$309$		0			0
$310$	−26.2003			−1.48808
$311$	−10.9927	−	19.0400i	−0.623340	−	1.07966i	−0.988859	−	0.148853i	$-0.952442\pi$
$311$	−10.9927	−	19.0400i	−0.623340	−	1.07966i	0.365519	−	0.930804i	$-0.380892\pi$
$312$		0			0
$313$	6.94491	−	12.0289i	0.392549	−	0.679915i	−0.600236	−	0.799823i	$-0.704927\pi$
$313$	6.94491	−	12.0289i	0.392549	−	0.679915i	0.992785	+	0.119908i	$0.0382599\pi$
$314$	−6.63404			−0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	−3.09105	+	5.35386i	−0.173611	+	0.300703i	−0.939680	−	0.342056i	$-0.888877\pi$
$317$	−3.09105	+	5.35386i	−0.173611	+	0.300703i	0.766069	+	0.642759i	$0.222210\pi$
$318$		0			0
$319$	−2.05438	−	3.55829i	−0.115023	−	0.199226i
$320$	−21.7665			−1.21678
$321$		0			0
$322$		0			0
$323$	8.47565			0.471598
$324$		0			0
$325$	−4.10947	+	7.11781i	−0.227952	+	0.394825i
$326$	−10.2909			−0.569958
$327$		0			0
$328$	−3.27719	+	5.67626i	−0.180952	+	0.313419i
$329$		0			0
$330$		0			0
$331$	−5.36571	+	9.29369i	−0.294926	+	0.510827i	−0.974968	−	0.222346i	$-0.928628\pi$
$331$	−5.36571	+	9.29369i	−0.294926	+	0.510827i	0.680041	+	0.733174i	$0.261962\pi$
$332$	0.252374	−	0.437124i	0.0138508	−	0.0239903i
$333$		0			0
$334$	3.80974	+	6.59867i	0.208460	+	0.361063i
$335$	−12.2023	−	21.1351i	−0.666685	−	1.15473i
$336$		0			0
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	−0.493518	−	0.869735i	$-0.664289\pi$
$337$	9.29726	−	16.1033i	0.506454	−	0.877204i	0.999972	−	0.00746831i	$-0.00237726\pi$
$338$	−28.1676			−1.53211
$339$		0			0
$340$	−1.81521			−0.0984434
$341$	−1.79679	−	3.11213i	−0.0973016	−	0.168531i
$342$		0			0
$343$		0			0
$344$	−1.80541	−	3.12706i	−0.0973410	−	0.168600i
$345$		0			0
$346$	−14.1932	−	24.5834i	−0.763034	−	1.32161i
$347$	−10.2062	−	17.6777i	−0.547898	−	0.948987i	−0.998418	−	0.0562207i	$-0.982095\pi$
$347$	−10.2062	−	17.6777i	−0.547898	−	0.948987i	0.450521	−	0.892766i	$-0.351238\pi$
$348$		0			0
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	0.909750	−	0.415157i	$-0.136274\pi$
$349$	1.78106	+	3.08489i	0.0953379	+	0.165130i	−0.814412	+	0.580288i	$0.802940\pi$
$350$		0			0
$351$		0			0
$352$	−0.243756	−	0.422197i	−0.0129922	−	0.0225032i
$353$	−10.0223			−0.533433			−0.266716	−	0.963775i	$-0.585939\pi$
$353$	−10.0223			−0.533433			−0.266716	+	0.963775i	$0.585939\pi$
$354$		0			0
$355$	33.5107			1.77857
$356$	0.749686	−	1.29849i	0.0397333	−	0.0688200i
$357$		0			0
$358$	3.44949	+	5.97470i	0.182311	+	0.315773i
$359$	4.74035	+	8.21053i	0.250186	+	0.433335i	0.963577	−	0.267431i	$-0.0861748\pi$
$359$	4.74035	+	8.21053i	0.250186	+	0.433335i	−0.713391	+	0.700766i	$0.752841\pi$
$360$		0			0
$361$	7.11334	−	12.3207i	0.374386	−	0.648456i
$362$	−0.215537	+	0.373321i	−0.0113284	+	0.0196213i
$363$		0			0
$364$		0			0
$365$	−13.0005	+	22.5175i	−0.680476	+	1.17862i
$366$		0			0
$367$	16.1334			0.842157			0.421079	−	0.907024i	$-0.361652\pi$
$367$	16.1334			0.842157			0.421079	+	0.907024i	$0.361652\pi$
$368$	0.190722	−	0.330341i	0.00994209	−	0.0172202i
$369$		0			0
$370$	−26.2003			−1.36209
$371$		0			0
$372$		0			0
$373$	14.0496			0.727462			0.363731	−	0.931504i	$-0.381503\pi$
$373$	14.0496			0.727462			0.363731	+	0.931504i	$0.381503\pi$
$374$	1.22281	+	2.11797i	0.0632301	+	0.109518i
$375$		0			0
$376$	−7.84864	+	13.5942i	−0.404763	+	0.701070i
$377$	−51.1317			−2.63341
$378$		0			0
$379$	16.0574			0.824812			0.412406	−	0.911000i	$-0.364689\pi$
$379$	16.0574			0.824812			0.412406	+	0.911000i	$0.364689\pi$
$380$	0.511144	−	0.885328i	0.0262212	−	0.0454164i
$381$		0			0
$382$	10.4868	+	18.1637i	0.536551	+	0.929334i
$383$	32.0205			1.63617			0.818086	−	0.575095i	$-0.195035\pi$
$383$	32.0205			1.63617			0.818086	+	0.575095i	$0.195035\pi$
$384$		0			0
$385$		0			0
$386$	−8.14022			−0.414326
$387$		0			0
$388$	−1.25696	+	2.17712i	−0.0638124	+	0.110526i
$389$	30.0428			1.52323			0.761616	−	0.648029i	$-0.224406\pi$
$389$	30.0428			1.52323			0.761616	+	0.648029i	$0.224406\pi$
$390$		0			0
$391$	0.205737	−	0.356347i	0.0104046	−	0.0180212i
$392$		0			0
$393$		0			0
$394$	−16.9991	+	29.4433i	−0.856403	+	1.48333i
$395$	−16.0005	+	27.7136i	−0.805071	+	1.39442i
$396$		0			0
$397$	6.15998	+	10.6694i	0.309160	+	0.535482i	0.978179	−	0.207764i	$-0.0666187\pi$
$397$	6.15998	+	10.6694i	0.309160	+	0.535482i	−0.669019	+	0.743246i	$0.733285\pi$
$398$	2.04916	+	3.54925i	0.102715	+	0.177908i
$399$		0			0
$400$	2.53802	−	4.39598i	0.126901	−	0.219799i
$401$	−20.9760			−1.04749			−0.523745	−	0.851875i	$-0.675465\pi$
$401$	−20.9760			−1.04749			−0.523745	+	0.851875i	$0.675465\pi$
$402$		0			0
$403$	−44.7205			−2.22769
$404$	0.884600	+	1.53217i	0.0440105	+	0.0762284i
$405$		0			0
$406$		0			0
$407$	−1.79679	−	3.11213i	−0.0890635	−	0.154263i
$408$		0			0
$409$	−12.8307	−	22.2234i	−0.634437	−	1.09888i	−0.986634	−	0.162951i	$-0.947899\pi$
$409$	−12.8307	−	22.2234i	−0.634437	−	1.09888i	0.352197	−	0.935926i	$-0.385435\pi$
$410$	−3.79813	−	6.57856i	−0.187576	−	0.324892i
$411$		0			0
$412$	0.281059	+	0.486809i	0.0138468	+	0.0239833i
$413$		0			0
$414$		0			0
$415$	3.45811	+	5.98962i	0.169752	+	0.294019i
$416$	−6.06687			−0.297453
$417$		0			0
$418$	−1.37733			−0.0673672
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	−0.883532	−	0.468370i	$-0.844841\pi$
$419$	−0.739885	+	1.28152i	−0.0361458	+	0.0626063i	0.847387	+	0.530976i	$0.178175\pi$
$420$		0			0
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	0.660965	−	0.750417i	$-0.270147\pi$
$421$	−6.55350	−	11.3510i	−0.319398	−	0.553214i	−0.980363	+	0.197203i	$0.936814\pi$
$422$	−3.67365	−	6.36295i	−0.178830	−	0.309743i
$423$		0			0
$424$	−1.05509	+	1.82747i	−0.0512398	+	0.0887500i
$425$	2.73783	−	4.74205i	0.132804	−	0.230023i
$426$		0			0
$427$		0			0
$428$	0.602196	−	1.04303i	0.0291083	−	0.0504170i
$429$		0			0
$430$	4.18479			0.201809
$431$	8.86349	−	15.3520i	0.426939	−	0.739481i	−0.569660	−	0.821881i	$-0.692925\pi$
$431$	8.86349	−	15.3520i	0.426939	−	0.739481i	0.996599	+	0.0823997i	$0.0262584\pi$
$432$		0			0
$433$	−5.83843			−0.280577			−0.140289	−	0.990111i	$-0.544803\pi$
$433$	−5.83843			−0.280577			−0.140289	+	0.990111i	$0.544803\pi$
$434$		0			0
$435$		0			0
$436$	−1.96585			−0.0941472
$437$	0.115867	+	0.200688i	0.00554267	+	0.00960019i
$438$		0			0
$439$	−14.9277	+	25.8555i	−0.712459	+	1.23401i	0.251473	+	0.967864i	$0.419085\pi$
$439$	−14.9277	+	25.8555i	−0.712459	+	1.23401i	−0.963931	+	0.266151i	$0.914248\pi$
$440$	3.48751			0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	5.33275	−	9.23659i	0.253367	−	0.438844i	−0.711084	−	0.703107i	$-0.751795\pi$
$443$	5.33275	−	9.23659i	0.253367	−	0.438844i	0.964451	+	0.264263i	$0.0851288\pi$
$444$		0			0
$445$	10.2724	+	17.7924i	0.486960	+	0.843440i
$446$	−19.1215			−0.905432
$447$		0			0
$448$		0			0
$449$	−3.55438			−0.167741			−0.0838707	−	0.996477i	$-0.526728\pi$
$449$	−3.55438			−0.167741			−0.0838707	+	0.996477i	$0.526728\pi$
$450$		0			0
$451$	0.520945	−	0.902302i	0.0245303	−	0.0424878i
$452$	0.956680			0.0449985
$453$		0			0
$454$	1.94949	−	3.37662i	0.0914942	−	0.158473i
$455$		0			0
$456$		0			0
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	−0.918772	−	0.394789i	$-0.870818\pi$
$457$	−2.51161	+	4.35024i	−0.117488	+	0.203496i	0.801283	+	0.598285i	$0.204151\pi$
$458$	6.17571	−	10.6966i	0.288572	−	0.499821i
$459$		0			0
$460$	−0.0248149	−	0.0429807i	−0.00115700	−	0.00200399i
$461$	9.23055	+	15.9878i	0.429910	+	0.744625i	0.996865	−	0.0791233i	$-0.0252121\pi$
$461$	9.23055	+	15.9878i	0.429910	+	0.744625i	−0.566955	+	0.823749i	$0.691879\pi$
$462$		0			0
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	−0.651897	−	0.758307i	$-0.726027\pi$
$463$	7.11721	−	12.3274i	0.330765	−	0.572902i	0.982662	+	0.185406i	$0.0593600\pi$
$464$	31.5790			1.46602
$465$		0			0
$466$	17.8803			0.828290
$467$	−1.68433	−	2.91734i	−0.0779413	−	0.134998i	0.824420	−	0.565978i	$-0.191501\pi$
$467$	−1.68433	−	2.91734i	−0.0779413	−	0.134998i	−0.902362	+	0.430980i	$0.858168\pi$
$468$		0			0
$469$		0			0
$470$	−9.09627	−	15.7552i	−0.419579	−	0.726733i
$471$		0			0
$472$	1.08394	+	1.87744i	0.0498924	+	0.0864162i
$473$	0.286989	+	0.497079i	0.0131958	+	0.0228557i
$474$		0			0
$475$	1.54189	+	2.67063i	0.0707467	+	0.122537i
$476$		0			0
$477$		0			0
$478$	−6.42468	−	11.1279i	−0.293858	−	0.508977i
$479$	36.7665			1.67990			0.839952	−	0.542660i	$-0.182583\pi$
$479$	36.7665			1.67990			0.839952	+	0.542660i	$0.182583\pi$
$480$		0			0
$481$	−44.7205			−2.03908
$482$	−6.03462	+	10.4523i	−0.274869	+	0.476087i
$483$		0			0
$484$	−0.996130	−	1.72535i	−0.0452786	−	0.0784249i
$485$	−17.2233	−	29.8316i	−0.782069	−	1.35458i
$486$		0			0
$487$	18.7087	−	32.4045i	0.847773	−	1.46839i	−0.0354172	−	0.999373i	$-0.511276\pi$
$487$	18.7087	−	32.4045i	0.847773	−	1.46839i	0.883191	−	0.469014i	$-0.155391\pi$
$488$	−1.41013	+	2.44242i	−0.0638336	+	0.110563i
$489$		0			0
$490$		0			0
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	0.390734	+	0.920504i	$0.372221\pi$
$491$	−13.3353	+	23.0974i	−0.601813	+	1.04237i	−0.992547	+	0.121866i	$0.961112\pi$
$492$		0			0
$493$	34.0651			1.53422
$494$	−8.57011	+	14.8439i	−0.385587	+	0.667857i
$495$		0			0
$496$	27.6195			1.24015
$497$		0			0
$498$		0			0
$499$	33.7452			1.51064			0.755320	−	0.655356i	$-0.227481\pi$
$499$	33.7452			1.51064			0.755320	+	0.655356i	$0.227481\pi$
$500$	0.839556	+	1.45415i	0.0375461	+	0.0650317i
$501$		0			0
$502$	16.8400	−	29.1678i	0.751607	−	1.30182i
$503$	32.0401			1.42860			0.714299	−	0.699840i	$-0.246745\pi$
$503$	32.0401			1.42860			0.714299	+	0.699840i	$0.246745\pi$
$504$		0			0
$505$	−24.2422			−1.07876
$506$	−0.0334331	+	0.0579078i	−0.00148628	+	0.00257431i
$507$		0			0
$508$	−0.820670	−	1.42144i	−0.0364114	−	0.0630663i
$509$	7.93851			0.351868			0.175934	−	0.984402i	$-0.443705\pi$
$509$	7.93851			0.351868			0.175934	+	0.984402i	$0.443705\pi$
$510$		0			0
$511$		0			0
$512$	24.9186			1.10126
$513$		0			0
$514$	−7.31046	+	12.6621i	−0.322451	+	0.558501i
$515$	−7.70233			−0.339405
$516$		0			0
$517$	1.24763	−	2.16095i	0.0548705	−	0.0950386i
$518$		0			0
$519$		0			0
$520$	21.7003	−	37.5860i	0.951620	−	1.64825i
$521$	−7.33750	+	12.7089i	−0.321462	+	0.556788i	−0.980790	−	0.195067i	$-0.937507\pi$
$521$	−7.33750	+	12.7089i	−0.321462	+	0.556788i	0.659328	+	0.751855i	$0.270841\pi$
$522$		0			0
$523$	−14.1716	−	24.5459i	−0.619680	−	1.07332i	−0.989544	−	0.144232i	$-0.953929\pi$
$523$	−14.1716	−	24.5459i	−0.619680	−	1.07332i	0.369864	−	0.929086i	$-0.379404\pi$
$524$	−1.04988	−	1.81844i	−0.0458641	−	0.0794390i
$525$		0			0
$526$	−17.5737	+	30.4386i	−0.766251	+	1.32719i
$527$	29.7939			1.29784
$528$		0			0
$529$	−22.9887			−0.999511
$530$	−1.22281	−	2.11797i	−0.0531155	−	0.0919988i
$531$		0			0
$532$		0			0
$533$	−6.48293	−	11.2288i	−0.280807	−	0.486371i
$534$		0			0
$535$	8.25150	+	14.2920i	0.356743	+	0.617898i
$536$	14.1853	+	24.5696i	0.612710	+	1.06124i
$537$		0			0
$538$	5.14203	+	8.90625i	0.221688	+	0.383976i
$539$		0			0
$540$		0			0
$541$	−5.64290	−	9.77380i	−0.242607	−	0.420208i	0.718849	−	0.695166i	$-0.244669\pi$
$541$	−5.64290	−	9.77380i	−0.242607	−	0.420208i	−0.961456	+	0.274958i	$0.911336\pi$
$542$	−4.58584			−0.196979
$543$		0			0
$544$	4.04189			0.173295
$545$	13.4684	−	23.3279i	0.576922	−	0.999258i
$546$		0			0
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	0.988519	+	0.151099i	$0.0482812\pi$
$547$	14.6202	+	25.3229i	0.625115	+	1.08273i	−0.363404	+	0.931632i	$0.618385\pi$
$548$	0.528934	+	0.916140i	0.0225949	+	0.0391356i
$549$		0			0
$550$	−0.444907	+	0.770602i	−0.0189709	+	0.0328586i
$551$	−9.59240	+	16.6145i	−0.408650	+	0.707802i
$552$		0			0
$553$		0			0
$554$	−3.85457	+	6.67631i	−0.163765	+	0.283649i
$555$		0			0
$556$	0.170741			0.00724105
$557$	−0.387841	+	0.671761i	−0.0164334	+	0.0284634i	−0.874125	−	0.485701i	$-0.838564\pi$
$557$	−0.387841	+	0.671761i	−0.0164334	+	0.0284634i	0.857692	+	0.514164i	$0.171898\pi$
$558$		0			0
$559$	7.14290			0.302113
$560$		0			0
$561$		0			0
$562$	38.2327			1.61275
$563$	12.4761	+	21.6093i	0.525806	+	0.910722i	0.999548	+	0.0300588i	$0.00956944\pi$
$563$	12.4761	+	21.6093i	0.525806	+	0.910722i	−0.473742	+	0.880663i	$0.657097\pi$
$564$		0			0
$565$	−6.55438	+	11.3525i	−0.275745	+	0.477604i
$566$	−6.15888			−0.258877
$567$		0			0
$568$	−38.9564			−1.63457
$569$	−12.4017	+	21.4803i	−0.519905	+	0.900502i	0.479827	+	0.877363i	$0.340699\pi$
$569$	−12.4017	+	21.4803i	−0.519905	+	0.900502i	−0.999732	+	0.0231391i	$0.992634\pi$
$570$		0			0
$571$	−4.39827	−	7.61803i	−0.184062	−	0.318805i	0.759198	−	0.650860i	$-0.225591\pi$
$571$	−4.39827	−	7.61803i	−0.184062	−	0.318805i	−0.943260	+	0.332055i	$0.892258\pi$
$572$	0.503490			0.0210520
$573$		0			0
$574$		0			0
$575$	0.149711			0.00624336
$576$		0			0
$577$	6.43717	−	11.1495i	0.267983	−	0.464160i	−0.700358	−	0.713792i	$-0.746976\pi$
$577$	6.43717	−	11.1495i	0.267983	−	0.464160i	0.968341	+	0.249632i	$0.0803096\pi$
$578$	2.62773			0.109299
$579$		0			0
$580$	2.05438	−	3.55829i	0.0853034	−	0.147750i
$581$		0			0
$582$		0			0
$583$	0.167718	−	0.290497i	0.00694619	−	0.0120311i
$584$	15.1131	−	26.1766i	0.625384	−	1.08320i
$585$		0			0
$586$	−2.91534	−	5.04952i	−0.120432	−	0.208594i
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.790190	+	0.612861i	$0.209982\pi$
$587$	22.4315	+	38.8526i	0.925849	+	1.60362i	0.135658	+	0.990756i	$0.456685\pi$
$588$		0			0
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$	−2.51249			−0.103438
$591$		0			0
$592$	27.6195			1.13515
$593$	1.88026	+	3.25671i	0.0772131	+	0.133737i	0.902047	−	0.431639i	$-0.142064\pi$
$593$	1.88026	+	3.25671i	0.0772131	+	0.133737i	−0.824833	+	0.565376i	$0.808731\pi$
$594$		0			0
$595$		0			0
$596$	−0.806123	−	1.39625i	−0.0330201	−	0.0571924i
$597$		0			0
$598$	0.416060	+	0.720637i	0.0170139	+	0.0294690i
$599$	−1.84524	−	3.19604i	−0.0753943	−	0.130587i	0.825863	−	0.563870i	$-0.190688\pi$
$599$	−1.84524	−	3.19604i	−0.0753943	−	0.130587i	−0.901258	+	0.433283i	$0.857355\pi$
$600$		0			0
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	0.998107	−	0.0615091i	$-0.0195913\pi$
$601$	10.9285	+	18.9288i	0.445785	+	0.772122i	−0.552322	+	0.833631i	$0.686258\pi$
$602$		0			0
$603$		0			0
$604$	1.70258	+	2.94896i	0.0692771	+	0.119991i
$605$	27.2986			1.10985
$606$		0			0
$607$	24.3946			0.990145			0.495072	−	0.868852i	$-0.335142\pi$
$607$	24.3946			0.990145			0.495072	+	0.868852i	$0.335142\pi$
$608$	−1.13816	+	1.97134i	−0.0461583	+	0.0799485i
$609$		0			0
$610$	−1.63429	−	2.83067i	−0.0661703	−	0.114610i
$611$	−15.5262	−	26.8921i	−0.628121	−	1.08794i
$612$		0			0
$613$	−21.0107	+	36.3917i	−0.848616	+	1.46985i	0.0338284	+	0.999428i	$0.489230\pi$
$613$	−21.0107	+	36.3917i	−0.848616	+	1.46985i	−0.882444	+	0.470418i	$0.844103\pi$
$614$	8.33796	−	14.4418i	0.336493	−	0.582823i
$615$		0			0
$616$		0			0
$617$	23.2049	−	40.1920i	0.934192	−	1.61807i	0.158125	−	0.987419i	$-0.449455\pi$
$617$	23.2049	−	40.1920i	0.934192	−	1.61807i	0.776068	−	0.630650i	$-0.217212\pi$
$618$		0			0
$619$	−27.2094			−1.09364			−0.546820	−	0.837250i	$-0.684162\pi$
$619$	−27.2094			−1.09364			−0.546820	+	0.837250i	$0.684162\pi$
$620$	1.79679	−	3.11213i	0.0721608	−	0.124986i
$621$		0			0
$622$	−29.6209			−1.18769
$623$		0			0
$624$		0			0
$625$	−30.0651			−1.20260
$626$	−9.35685	−	16.2065i	−0.373975	−	0.647743i
$627$		0			0
$628$	0.454956	−	0.788006i	0.0181547	−	0.0314449i
$629$	29.7939			1.18796
$630$		0			0
$631$	−29.6023			−1.17845			−0.589224	−	0.807970i	$-0.700566\pi$
$631$	−29.6023			−1.17845			−0.589224	+	0.807970i	$0.700566\pi$
$632$	18.6006	−	32.2172i	0.739892	−	1.28153i
$633$		0			0
$634$	4.16456	+	7.21324i	0.165396	+	0.286474i
$635$	22.4902			0.892496
$636$		0			0
$637$		0			0
$638$	−5.53571			−0.219161
$639$		0			0
$640$	−12.0248	+	20.8276i	−0.475323	+	0.823283i
$641$	0.279000			0.0110198			0.00550991	−	0.999985i	$-0.498246\pi$
$641$	0.279000			0.0110198			0.00550991	+	0.999985i	$0.498246\pi$
$642$		0			0
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	−0.628181	−	0.778067i	$-0.716200\pi$
$643$	9.12196	−	15.7997i	0.359735	−	0.623079i	0.987916	+	0.154988i	$0.0495338\pi$
$644$		0			0
$645$		0			0
$646$	5.70961	−	9.88933i	0.224642	−	0.389090i
$647$	11.2285	−	19.4483i	0.441438	−	0.764592i	−0.556359	−	0.830942i	$-0.687802\pi$
$647$	11.2285	−	19.4483i	0.441438	−	0.764592i	0.997796	+	0.0663498i	$0.0211353\pi$
$648$		0			0
$649$	−0.172304	−	0.298439i	−0.00676352	−	0.0117148i
$650$	5.53667	+	9.58980i	0.217166	+	0.376143i
$651$		0			0
$652$	0.705737	−	1.22237i	0.0276388	−	0.0478718i
$653$	50.5313			1.97744			0.988721	−	0.149771i	$-0.0478538\pi$
$653$	50.5313			1.97744			0.988721	+	0.149771i	$0.0478538\pi$
$654$		0			0
$655$	28.7716			1.12420
$656$	4.00387	+	6.93491i	0.156325	+	0.270763i
$657$		0			0
$658$		0			0
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	0.838824	−	0.544403i	$-0.183244\pi$
$659$	−1.33631	−	2.31456i	−0.0520554	−	0.0901626i	−0.890879	+	0.454241i	$0.849911\pi$
$660$		0			0
$661$	17.3050	+	29.9731i	0.673086	+	1.16582i	0.977024	+	0.213128i	$0.0683651\pi$
$661$	17.3050	+	29.9731i	0.673086	+	1.16582i	−0.303938	+	0.952692i	$0.598302\pi$
$662$	7.22921	+	12.5214i	0.280971	+	0.486656i
$663$		0			0
$664$	−4.02007	−	6.96296i	−0.156009	−	0.270215i
$665$		0			0
$666$		0			0
$667$	0.465690	+	0.806598i	0.0180316	+	0.0312316i
$668$	−1.04507			−0.0404351
$669$		0			0
$670$	−32.8803			−1.27028
$671$	0.224155	−	0.388249i	0.00865342	−	0.0149882i
$672$		0			0
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	0.661869	−	0.749619i	$-0.269763\pi$
$673$	−8.25624	−	14.3002i	−0.318255	−	0.551234i	−0.980124	+	0.198386i	$0.936430\pi$
$674$	−12.5262	−	21.6959i	−0.482490	−	0.835697i
$675$		0			0
$676$	1.93170	−	3.34581i	0.0742963	−	0.128685i
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	0.0482766	+	0.998834i	$0.484627\pi$
$677$	−21.8790	+	37.8955i	−0.840877	+	1.45644i	−0.889154	+	0.457608i	$0.848706\pi$
$678$		0			0
$679$		0			0
$680$	−14.4572	+	25.0407i	−0.554410	+	0.960266i
$681$		0			0
$682$	−4.84161			−0.185395
$683$	14.1206	−	24.4576i	0.540310	−	0.935845i	−0.458576	−	0.888655i	$-0.651640\pi$
$683$	14.1206	−	24.4576i	0.540310	−	0.935845i	0.998886	−	0.0471895i	$-0.0150265\pi$
$684$		0			0
$685$	−14.4953			−0.553835
$686$		0			0
$687$		0			0
$688$	−4.41147			−0.168186
$689$	−2.08718	−	3.61510i	−0.0795153	−	0.137725i
$690$		0			0
$691$	14.5326	−	25.1711i	0.552844	−	0.957555i	−0.445223	−	0.895420i	$-0.646876\pi$
$691$	14.5326	−	25.1711i	0.552844	−	0.957555i	0.998068	−	0.0621351i	$-0.0197910\pi$
$692$	3.89344			0.148006
$693$		0			0
$694$	−27.5016			−1.04395
$695$	−1.16978	+	2.02611i	−0.0443722	+	0.0768549i
$696$		0			0
$697$	4.31908	+	7.48086i	0.163597	+	0.283358i
$698$	4.79923			0.181654
$699$		0			0
$700$		0			0
$701$	1.10876			0.0418771			0.0209386	−	0.999781i	$-0.493335\pi$
$701$	1.10876			0.0418771			0.0209386	+	0.999781i	$0.493335\pi$
$702$		0			0
$703$	−8.38965	+	14.5313i	−0.316422	+	0.548059i
$704$	−4.02229			−0.151596
$705$		0			0
$706$	−6.75150	+	11.6939i	−0.254096	+	0.440107i
$707$		0			0
$708$		0			0
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	−0.638874	−	0.769311i	$-0.720600\pi$
$709$	9.23442	−	15.9945i	0.346806	−	0.600686i	0.985680	+	0.168626i	$0.0539329\pi$
$710$	22.5744	−	39.1001i	0.847204	−	1.46740i
$711$		0			0
$712$	−11.9418	−	20.6837i	−0.447536	−	0.775155i
$713$	0.407299	+	0.705463i	0.0152535	+	0.0264198i
$714$		0			0
$715$	−3.44949	+	5.97470i	−0.129004	+	0.223441i
$716$	−0.946251			−0.0353631
$717$		0			0
$718$	12.7733			0.476696
$719$	−16.8885	−	29.2517i	−0.629834	−	1.09090i	−0.987585	−	0.157087i	$-0.949790\pi$
$719$	−16.8885	−	29.2517i	−0.629834	−	1.09090i	0.357751	−	0.933817i	$-0.383544\pi$
$720$		0			0
$721$		0			0
$722$	−9.58378	−	16.5996i	−0.356671	−	0.617773i
$723$		0			0
$724$	−0.0295627	−	0.0512040i	−0.00109869	−	0.00190298i
$725$	6.19712	+	10.7337i	0.230155	+	0.398641i
$726$		0			0
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	0.667095	−	0.744973i	$-0.267538\pi$
$727$	−8.40214	−	14.5529i	−0.311618	−	0.539738i	−0.978713	+	0.205234i	$0.934204\pi$
$728$		0			0
$729$		0			0
$730$	17.5155	+	30.3377i	0.648277	+	1.12285i
$731$	−4.75877			−0.176009
$732$		0			0
$733$	−13.6364			−0.503672			−0.251836	−	0.967770i	$-0.581034\pi$
$733$	−13.6364			−0.503672			−0.251836	+	0.967770i	$0.581034\pi$
$734$	10.8682	−	18.8243i	0.401154	−	0.694819i
$735$		0			0
$736$	0.0552549	+	0.0957044i	0.00203672	+	0.00352771i
$737$	−2.25490	−	3.90560i	−0.0830603	−	0.143865i
$738$		0			0
$739$	16.0209	−	27.7491i	0.589340	−	1.02077i	−0.404979	−	0.914326i	$-0.632721\pi$
$739$	16.0209	−	27.7491i	0.589340	−	1.02077i	0.994319	−	0.106441i	$-0.0339455\pi$
$740$	1.79679	−	3.11213i	0.0660513	−	0.114404i
$741$		0			0
$742$		0			0
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	−0.370507	−	0.928830i	$-0.620816\pi$
$743$	16.8764	−	29.2309i	0.619137	−	1.07238i	0.989644	−	0.143547i	$-0.0458507\pi$
$744$		0			0
$745$	22.0915			0.809371
$746$	9.46451	−	16.3930i	0.346520	−	0.600191i
$747$		0			0
$748$	−0.335437			−0.0122648
$749$		0			0
$750$		0			0
$751$	26.1165			0.953004			0.476502	−	0.879173i	$-0.341904\pi$
$751$	26.1165			0.953004			0.476502	+	0.879173i	$0.341904\pi$
$752$	9.58899	+	16.6086i	0.349675	+	0.605654i
$753$		0			0
$754$	−34.4447	+	59.6600i	−1.25440	+	2.17269i
$755$	−46.6587			−1.69808
$756$		0			0
$757$	35.6536			1.29585			0.647927	−	0.761703i	$-0.275636\pi$
$757$	35.6536			1.29585			0.647927	+	0.761703i	$0.275636\pi$
$758$	10.8170	−	18.7356i	0.392892	−	0.680509i
$759$		0			0
$760$	−8.14203	−	14.1024i	−0.295342	−	0.511548i
$761$	−40.7648			−1.47772			−0.738861	−	0.673858i	$-0.764636\pi$
$761$	−40.7648			−1.47772			−0.738861	+	0.673858i	$0.764636\pi$
$762$		0			0
$763$		0			0
$764$	−2.87670			−0.104075
$765$		0			0
$766$	21.5706	−	37.3613i	0.779377	−	1.34992i
$767$	−4.28850			−0.154849
$768$		0			0
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	0.253639	+	0.967299i	$0.418373\pi$
$769$	−19.7135	+	34.1447i	−0.710886	+	1.23129i	−0.964525	+	0.263992i	$0.914961\pi$
$770$		0			0
$771$		0			0
$772$	0.558248	−	0.966914i	0.0200918	−	0.0348000i
$773$	12.4513	−	21.5663i	0.447842	−	0.775686i	−0.550403	−	0.834899i	$-0.685526\pi$
$773$	12.4513	−	21.5663i	0.447842	−	0.775686i	0.998245	+	0.0592135i	$0.0188593\pi$
$774$		0			0
$775$	5.42009	+	9.38788i	0.194695	+	0.337222i
$776$	20.0221	+	34.6793i	0.718752	+	1.24492i
$777$		0			0
$778$	20.2383	−	35.0538i	0.725578	−	1.25674i
$779$	−4.86484			−0.174301
$780$		0			0
$781$	6.19253			0.221586
$782$	−0.277189	−	0.480105i	−0.00991225	−	0.0171685i
$783$		0			0
$784$		0			0
$785$	6.23396	+	10.7975i	0.222499	+	0.385380i
$786$		0			0
$787$	15.3525	+	26.5913i	0.547258	+	0.947879i	0.998461	+	0.0554572i	$0.0176616\pi$
$787$	15.3525	+	26.5913i	0.547258	+	0.947879i	−0.451203	+	0.892421i	$0.649005\pi$
$788$	−2.33157	−	4.03839i	−0.0830586	−	0.143862i
$789$		0			0
$790$	21.5574	+	37.3385i	0.766977	+	1.32844i
$791$		0			0
$792$		0			0
$793$	−2.78952	−	4.83158i	−0.0990586	−	0.171575i
$794$	16.5986			0.589063
$795$		0			0
$796$	−0.562118			−0.0199238
$797$	−5.50686	+	9.53817i	−0.195063	+	0.337859i	−0.946921	−	0.321466i	$-0.895825\pi$
$797$	−5.50686	+	9.53817i	−0.195063	+	0.337859i	0.751858	+	0.659325i	$0.229158\pi$
$798$		0			0
$799$	10.3439	+	17.9161i	0.365941	+	0.633828i
$800$	0.735300	+	1.27358i	0.0259968	+	0.0450277i
$801$		0			0
$802$	−14.1304	+	24.4746i	−0.498962	+	0.864228i
$803$	−2.40239	+	4.16106i	−0.0847785	+	0.146841i
$804$		0			0
$805$		0			0
$806$	−30.1259	+	52.1796i	−1.06114	+	1.83795i
$807$		0			0
$808$	28.1816			0.991425
$809$	8.49407	−	14.7122i	0.298636	−	0.517252i	−0.677188	−	0.735810i	$-0.736802\pi$
$809$	8.49407	−	14.7122i	0.298636	−	0.517252i	0.975824	+	0.218558i	$0.0701352\pi$
$810$		0			0
$811$	37.9796			1.33364			0.666822	−	0.745217i	$-0.267654\pi$
$811$	37.9796			1.33364			0.666822	+	0.745217i	$0.267654\pi$
$812$		0			0
$813$		0			0
$814$	−4.84161			−0.169699
$815$	9.67024	+	16.7494i	0.338734	+	0.586704i
$816$		0			0
$817$	1.34002	−	2.32099i	0.0468814	−	0.0812011i
$818$	−34.5735			−1.20883
$819$		0			0
$820$	1.04189			0.0363843
$821$	4.13934	−	7.16954i	0.144464	−	0.250219i	−0.784709	−	0.619864i	$-0.787188\pi$
$821$	4.13934	−	7.16954i	0.144464	−	0.250219i	0.929173	+	0.369646i	$0.120521\pi$
$822$		0			0
$823$	−27.2763	−	47.2440i	−0.950792	−	1.64682i	−0.743716	−	0.668496i	$-0.766938\pi$
$823$	−27.2763	−	47.2440i	−0.950792	−	1.64682i	−0.207077	−	0.978325i	$-0.566395\pi$
$824$	8.95399			0.311927
$825$		0			0
$826$		0			0
$827$	31.8708			1.10826			0.554129	−	0.832431i	$-0.313052\pi$
$827$	31.8708			1.10826			0.554129	+	0.832431i	$0.313052\pi$
$828$		0			0
$829$	0.176174	−	0.305143i	0.00611879	−	0.0105981i	−0.862950	−	0.505290i	$-0.831386\pi$
$829$	0.176174	−	0.305143i	0.00611879	−	0.0105981i	0.869069	+	0.494692i	$0.164719\pi$
$830$	9.31820			0.323439
$831$		0			0
$832$	−25.0278	+	43.3494i	−0.867683	+	1.50287i
$833$		0			0
$834$		0			0
$835$	7.15998	−	12.4014i	0.247781	−	0.429170i
$836$	0.0944557	−	0.163602i	0.00326682	−	0.00565829i
$837$		0			0
$838$	0.996845	+	1.72659i	0.0344354	+	0.0596439i
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	0.997030	−	0.0770182i	$-0.0245399\pi$
$839$	12.5077	+	21.6640i	0.431815	+	0.747926i	−0.565215	+	0.824944i	$0.691207\pi$
$840$		0			0
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$	−17.6590			−0.608570
$843$		0			0
$844$	1.00774			0.0346879
$845$	26.4688	+	45.8454i	0.910556	+	1.57713i
$846$		0			0
$847$		0			0
$848$	1.28905	+	2.23270i	0.0442661	+	0.0766711i
$849$		0			0
$850$	−3.68866	−	6.38895i	−0.126520	−	0.219139i
$851$	0.407299	+	0.705463i	0.0139620	+	0.0241829i
$852$		0			0
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	−0.977640	−	0.210286i	$-0.932560\pi$
$853$	−19.5954	−	33.9402i	−0.670933	−	1.16209i	0.306706	−	0.951804i	$-0.400773\pi$
$854$		0			0
$855$		0			0
$856$	−9.59240	−	16.6145i	−0.327861	−	0.567873i
$857$	−16.4074			−0.560465			−0.280232	−	0.959932i	$-0.590411\pi$
$857$	−16.4074			−0.560465			−0.280232	+	0.959932i	$0.590411\pi$
$858$		0			0
$859$	−26.8324			−0.915511			−0.457756	−	0.889078i	$-0.651347\pi$
$859$	−26.8324			−0.915511			−0.457756	+	0.889078i	$0.651347\pi$
$860$	−0.286989	+	0.497079i	−0.00978624	+	0.0169503i
$861$		0			0
$862$	−11.9418	−	20.6837i	−0.406738	−	0.704490i
$863$	7.25284	+	12.5623i	0.246890	+	0.427625i	0.962661	−	0.270709i	$-0.0872582\pi$
$863$	7.25284	+	12.5623i	0.246890	+	0.427625i	−0.715772	+	0.698334i	$0.753925\pi$
$864$		0			0
$865$	−26.6746	+	46.2017i	−0.906963	+	1.57091i
$866$	−3.93305	+	6.81224i	−0.133650	+	0.231489i
$867$		0			0
$868$		0			0
$869$	−2.95677	+	5.12127i	−0.100301	+	0.173727i
$870$		0			0
$871$	−56.1225			−1.90164
$872$	−15.6570	+	27.1188i	−0.530214	+	0.918358i
$873$		0			0
$874$	0.312214			0.0105608
$875$		0			0
$876$		0			0
$877$	18.9145			0.638696			0.319348	−	0.947637i	$-0.396536\pi$
$877$	18.9145			0.638696			0.319348	+	0.947637i	$0.396536\pi$
$878$	20.1120	+	34.8350i	0.678747	+	1.17562i
$879$		0			0
$880$	2.13041	−	3.68999i	0.0718163	−	0.124389i
$881$	−53.8976			−1.81585			−0.907927	−	0.419128i	$-0.862336\pi$
$881$	−53.8976			−1.81585			−0.907927	+	0.419128i	$0.862336\pi$
$882$		0			0
$883$	43.4252			1.46137			0.730687	−	0.682712i	$-0.239200\pi$
$883$	43.4252			1.46137			0.730687	+	0.682712i	$0.239200\pi$
$884$	−2.08718	+	3.61510i	−0.0701995	+	0.121589i
$885$		0			0
$886$	−7.18479	−	12.4444i	−0.241378	−	0.418079i
$887$	38.9600			1.30815			0.654074	−	0.756431i	$-0.273058\pi$
$887$	38.9600			1.30815			0.654074	+	0.756431i	$0.273058\pi$
$888$		0			0
$889$		0			0
$890$	27.6800			0.927837
$891$		0			0
$892$	1.31134	−	2.27130i	0.0439068	−	0.0760488i
$893$	−11.6509			−0.389884
$894$		0			0
$895$	6.48293	−	11.2288i	0.216700	−	0.375336i
$896$		0			0
$897$		0			0
$898$	−2.39440	+	4.14722i	−0.0799022	+	0.138395i
$899$	−33.7195	+	58.4038i	−1.12461	+	1.94788i
$900$		0			0
$901$	1.39053	+	2.40847i	0.0463253	+	0.0802377i
$902$	−0.701867	−	1.21567i	−0.0233696	−	0.0404773i
$903$		0			0
$904$	7.61949	−	13.1973i	0.253420	−	0.438937i
$905$	0.810155			0.0269305
$906$		0			0
$907$	34.5276			1.14647			0.573236	−	0.819390i	$-0.305688\pi$
$907$	34.5276			1.14647			0.573236	+	0.819390i	$0.305688\pi$
$908$	0.267389	+	0.463131i	0.00887360	+	0.0153695i
$909$		0			0
$910$		0			0
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	0.937157	+	0.348907i	$0.113447\pi$
$911$	23.2631	+	40.2929i	0.770741	+	1.33496i	−0.166416	+	0.986056i	$0.553220\pi$
$912$		0			0
$913$	0.639033	+	1.10684i	0.0211489	+	0.0366310i
$914$	3.38388	+	5.86106i	0.111929	+	0.193867i
$915$		0			0
$916$	0.847048	+	1.46713i	0.0279873	+	0.0484753i
$917$		0			0
$918$		0			0
$919$	4.97818	+	8.62246i	0.164215	+	0.284429i	0.936376	−	0.350998i	$-0.114158\pi$
$919$	4.97818	+	8.62246i	0.164215	+	0.284429i	−0.772161	+	0.635427i	$0.780824\pi$
$920$	−0.790555			−0.0260638
$921$		0			0
$922$	24.8726			0.819135
$923$	38.5317	−	66.7388i	1.26829	−	2.19674i
$924$		0			0
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$	−9.58899	−	16.6086i	−0.315114	−	0.545793i
$927$		0			0
$928$	−4.57444	+	7.92317i	−0.150164	+	0.260091i
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	−0.782239	−	0.622978i	$-0.785923\pi$
$929$	4.52300	−	7.83407i	0.148395	−	0.257028i	0.930634	+	0.365950i	$0.119256\pi$
$930$		0			0
$931$		0			0
$932$	−1.22621	+	2.12387i	−0.0401660	+	0.0695696i
$933$		0			0
$934$	−4.53857			−0.148507
$935$	2.29813	−	3.98048i	0.0751570	−	0.130176i
$936$		0			0
$937$	−24.3928			−0.796878			−0.398439	−	0.917195i	$-0.630448\pi$
$937$	−24.3928			−0.796878			−0.398439	+	0.917195i	$0.630448\pi$
$938$		0			0
$939$		0			0
$940$	2.49525			0.0813862
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.694220	−	0.719763i	$-0.744251\pi$
$941$	−29.7690	−	51.5615i	−0.970443	−	1.68086i	−0.276223	−	0.961094i	$-0.589083\pi$
$942$		0			0
$943$	−0.118089	+	0.204535i	−0.00384549	+	0.00666059i
$944$	2.64858			0.0862041
$945$		0			0
$946$	0.773318			0.0251428
$947$	4.32429	−	7.48989i	0.140521	−	0.243389i	−0.787172	−	0.616733i	$-0.788456\pi$
$947$	4.32429	−	7.48989i	0.140521	−	0.243389i	0.927693	+	0.373344i	$0.121789\pi$
$948$		0			0
$949$	29.8967	+	51.7826i	0.970487	+	1.68093i
$950$	4.15476			0.134798
$951$		0			0
$952$		0			0
$953$	−3.78249			−0.122527			−0.0612634	−	0.998122i	$-0.519513\pi$
$953$	−3.78249			−0.122527			−0.0612634	+	0.998122i	$0.519513\pi$
$954$		0			0
$955$	19.7087	−	34.1365i	0.637760	−	1.10463i
$956$	1.76239			0.0569998
$957$		0			0
$958$	24.7677	−	42.8989i	0.800208	−	1.38600i
$959$		0			0
$960$		0			0
$961$	−13.9915	+	24.2341i	−0.451340	+	0.781744i
$962$	−30.1259	+	52.1796i	−0.971298	+	1.68234i
$963$		0			0
$964$	−0.827696	−	1.43361i	−0.0266583	−	0.0461735i
$965$	7.64930	+	13.2490i	0.246240	+	0.426500i
$966$		0			0
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	−0.469613	−	0.882872i	$-0.655607\pi$
$967$	16.4745	−	28.5346i	0.529783	−	0.917611i	0.999396	−	0.0347392i	$-0.0110601\pi$
$968$	−31.7347			−1.01999
$969$		0			0
$970$	−46.4097			−1.49013
$971$	−27.7285	−	48.0272i	−0.889850	−	1.54126i	−0.840052	−	0.542506i	$-0.817476\pi$
$971$	−27.7285	−	48.0272i	−0.889850	−	1.54126i	−0.0497974	−	0.998759i	$-0.515858\pi$
$972$		0			0
$973$		0			0
$974$	−25.2062	−	43.6584i	−0.807659	−	1.39891i
$975$		0			0
$976$	1.72281	+	2.98400i	0.0551458	+	0.0955154i
$977$	28.2743	+	48.9724i	0.904573	+	1.56677i	0.821489	+	0.570225i	$0.193144\pi$
$977$	28.2743	+	48.9724i	0.904573	+	1.56677i	0.0830847	+	0.996542i	$0.473523\pi$
$978$		0			0
$979$	1.89827	+	3.28790i	0.0606690	+	0.105082i
$980$		0			0
$981$		0			0
$982$	17.9666	+	31.1190i	0.573336	+	0.993047i
$983$	−28.9973			−0.924871			−0.462435	−	0.886653i	$-0.653024\pi$
$983$	−28.9973			−0.924871			−0.462435	+	0.886653i	$0.653024\pi$
$984$		0			0
$985$	63.8958			2.03589
$986$	22.9479	−	39.7469i	0.730810	−	1.26580i
$987$		0			0
$988$	−1.17546	−	2.03596i	−0.0373963	−	0.0647724i
$989$	−0.0650551	−	0.112679i	−0.00206863	−	0.00358298i
$990$		0			0
$991$	−3.40461	+	5.89696i	−0.108151	+	0.187323i	−0.915021	−	0.403406i	$-0.867826\pi$
$991$	−3.40461	+	5.89696i	−0.108151	+	0.187323i	0.806870	+	0.590729i	$0.201160\pi$
$992$	−4.00088	+	6.92972i	−0.127028	+	0.220019i
$993$		0			0
$994$		0			0
$995$	3.85117	−	6.67042i	0.122090	−	0.211466i
$996$		0			0
$997$	−38.9377			−1.23317			−0.616585	−	0.787289i	$-0.711484\pi$
$997$	−38.9377			−1.23317			−0.616585	+	0.787289i	$0.711484\pi$
$998$	22.7324	−	39.3736i	0.719580	−	1.24635i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.g.d.361.2		6
3.2	odd	2		441.2.g.c.67.2		6
7.2	even	3		1323.2.h.c.226.2		6
7.3	odd	6		1323.2.f.d.442.2		6
7.4	even	3		189.2.f.b.64.2		6
7.5	odd	6		1323.2.h.b.226.2		6
7.6	odd	2		1323.2.g.e.361.2		6
9.2	odd	6		441.2.h.d.214.2		6
9.7	even	3		1323.2.h.c.802.2		6
21.2	odd	6		441.2.h.d.373.2		6
21.5	even	6		441.2.h.e.373.2		6
21.11	odd	6		63.2.f.a.22.2	✓	6
21.17	even	6		441.2.f.c.148.2		6
21.20	even	2		441.2.g.b.67.2		6
28.11	odd	6		3024.2.r.k.1009.3		6
63.2	odd	6		441.2.g.c.79.2		6
63.4	even	3		567.2.a.c.1.2		3
63.11	odd	6		63.2.f.a.43.2	yes	6
63.16	even	3	inner	1323.2.g.d.667.2		6
63.20	even	6		441.2.h.e.214.2		6
63.25	even	3		189.2.f.b.127.2		6
63.31	odd	6		3969.2.a.l.1.2		3
63.32	odd	6		567.2.a.h.1.2		3
63.34	odd	6		1323.2.h.b.802.2		6
63.38	even	6		441.2.f.c.295.2		6
63.47	even	6		441.2.g.b.79.2		6
63.52	odd	6		1323.2.f.d.883.2		6
63.59	even	6		3969.2.a.q.1.2		3
63.61	odd	6		1323.2.g.e.667.2		6
84.11	even	6		1008.2.r.h.337.1		6
252.11	even	6		1008.2.r.h.673.1		6
252.67	odd	6		9072.2.a.bs.1.1		3
252.95	even	6		9072.2.a.ca.1.3		3
252.151	odd	6		3024.2.r.k.2017.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.2	✓	6	21.11	odd	6
63.2.f.a.43.2	yes	6	63.11	odd	6
189.2.f.b.64.2		6	7.4	even	3
189.2.f.b.127.2		6	63.25	even	3
441.2.f.c.148.2		6	21.17	even	6
441.2.f.c.295.2		6	63.38	even	6
441.2.g.b.67.2		6	21.20	even	2
441.2.g.b.79.2		6	63.47	even	6
441.2.g.c.67.2		6	3.2	odd	2
441.2.g.c.79.2		6	63.2	odd	6
441.2.h.d.214.2		6	9.2	odd	6
441.2.h.d.373.2		6	21.2	odd	6
441.2.h.e.214.2		6	63.20	even	6
441.2.h.e.373.2		6	21.5	even	6
567.2.a.c.1.2		3	63.4	even	3
567.2.a.h.1.2		3	63.32	odd	6
1008.2.r.h.337.1		6	84.11	even	6
1008.2.r.h.673.1		6	252.11	even	6
1323.2.f.d.442.2		6	7.3	odd	6
1323.2.f.d.883.2		6	63.52	odd	6
1323.2.g.d.361.2		6	1.1	even	1	trivial
1323.2.g.d.667.2		6	63.16	even	3	inner
1323.2.g.e.361.2		6	7.6	odd	2
1323.2.g.e.667.2		6	63.61	odd	6
1323.2.h.b.226.2		6	7.5	odd	6
1323.2.h.b.802.2		6	63.34	odd	6
1323.2.h.c.226.2		6	7.2	even	3
1323.2.h.c.802.2		6	9.7	even	3
3024.2.r.k.1009.3		6	28.11	odd	6
3024.2.r.k.2017.3		6	252.151	odd	6
3969.2.a.l.1.2		3	63.31	odd	6
3969.2.a.q.1.2		3	63.59	even	6
9072.2.a.bs.1.1		3	252.67	odd	6
9072.2.a.ca.1.3		3	252.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.673648 - 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +2.94356 q^{8} +O(q^{10})\)	\(q+(0.673648 - 1.16679i) q^{2} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +2.94356 q^{8} +(-1.70574 + 2.95442i) q^{10} -0.467911 q^{11} +(-2.91147 + 5.04282i) q^{13} +(1.79813 - 3.11446i) q^{16} +(1.93969 - 3.35965i) q^{17} +(1.09240 + 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +0.106067 q^{23} +1.41147 q^{25} +(3.92262 + 6.79417i) q^{26} +(4.39053 + 7.60462i) q^{29} +(3.84002 + 6.65111i) q^{31} +(0.520945 + 0.902302i) q^{32} +(-2.61334 - 4.52644i) q^{34} +(3.84002 + 6.65111i) q^{37} +2.94356 q^{38} -7.45336 q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(-0.0432332 - 0.0748822i) q^{44} +(0.0714517 - 0.123758i) q^{46} +(-2.66637 + 4.61830i) q^{47} +(0.950837 - 1.64690i) q^{50} -1.07604 q^{52} +(-0.358441 + 0.620838i) q^{53} +1.18479 q^{55} +11.8307 q^{58} +(0.368241 + 0.637812i) q^{59} +(-0.479055 + 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(7.37211 - 12.7689i) q^{65} +(4.81908 + 8.34689i) q^{67} +0.716881 q^{68} -13.2344 q^{71} +(5.13429 - 8.89284i) q^{73} +10.3473 q^{74} +(-0.201867 + 0.349643i) q^{76} +(6.31908 - 10.9450i) q^{79} +(-4.55303 + 7.88609i) q^{80} +(1.50000 + 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} -1.65270 q^{86} -1.37733 q^{88} +(-4.05690 - 7.02676i) q^{89} +(0.00980018 + 0.0169744i) q^{92} +(3.59240 + 6.22221i) q^{94} +(-2.76604 - 4.79093i) q^{95} +(6.80200 + 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8} - 12 q^{11} + 3 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{31} - 9 q^{34} + 3 q^{37} - 12 q^{38} - 18 q^{40} + 3 q^{43} + 15 q^{44} + 3 q^{47} - 6 q^{50} - 42 q^{52} + 6 q^{53} - 18 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 12 q^{68} - 18 q^{71} + 21 q^{73} + 60 q^{74} - 15 q^{76} + 21 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} + 12 q^{89} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8 - 12 * q^11 + 3 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^31 - 9 * q^34 + 3 * q^37 - 12 * q^38 - 18 * q^40 + 3 * q^43 + 15 * q^44 + 3 * q^47 - 6 * q^50 - 42 * q^52 + 6 * q^53 - 18 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 12 * q^68 - 18 * q^71 + 21 * q^73 + 60 * q^74 - 15 * q^76 + 21 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 + 12 * q^89 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97

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