LMFDB - Embedded newform 1323.2.f.d.442.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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			442.2
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.d.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +O(q^{10})$	\(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +2.94356 q^{8} -3.41147 q^{10} +(0.233956 + 0.405223i) q^{11} +(2.91147 - 5.04282i) q^{13} +(1.79813 + 3.11446i) q^{16} +3.87939 q^{17} +2.18479 q^{19} +(0.233956 + 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} +7.84524 q^{26} +(4.39053 + 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(0.520945 - 0.902302i) q^{32} +(2.61334 + 4.52644i) q^{34} -7.68004 q^{37} +(1.47178 + 2.54920i) q^{38} +(-3.72668 + 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +0.0864665 q^{44} -0.142903 q^{46} +(2.66637 + 4.61830i) q^{47} +(0.950837 - 1.64690i) q^{50} +(-0.538019 - 0.931876i) q^{52} +0.716881 q^{53} -1.18479 q^{55} +(-5.91534 + 10.2457i) q^{58} +(-0.368241 + 0.637812i) q^{59} +(0.479055 + 0.829748i) q^{61} -10.3473 q^{62} +8.59627 q^{64} +(7.37211 + 12.7689i) q^{65} +(4.81908 - 8.34689i) q^{67} +(0.358441 - 0.620838i) q^{68} -13.2344 q^{71} +10.2686 q^{73} +(-5.17365 - 8.96102i) q^{74} +(0.201867 - 0.349643i) q^{76} +(6.31908 + 10.9450i) q^{79} -9.10607 q^{80} +3.00000 q^{82} +(1.36571 + 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 - 1.43128i) q^{86} +(0.688663 + 1.19280i) q^{88} -8.11381 q^{89} +(0.00980018 + 0.0169744i) q^{92} +(-3.59240 + 6.22221i) q^{94} +(-2.76604 + 4.79093i) q^{95} +(-6.80200 - 11.7814i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} - 3 q^{16} + 12 q^{17} + 6 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 6 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} - 6 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} - 30 q^{44} - 3 q^{47} - 6 q^{50} - 21 q^{52} - 12 q^{53} + 9 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 6 q^{68} - 18 q^{71} + 42 q^{73} - 30 q^{74} + 15 q^{76} + 21 q^{79} - 30 q^{80} + 18 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 24 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 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 - 3 * q^16 + 12 * q^17 + 6 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 6 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 - 6 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 - 30 * q^44 - 3 * q^47 - 6 * q^50 - 21 * q^52 - 12 * q^53 + 9 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 6 * q^68 - 18 * q^71 + 42 * q^73 - 30 * q^74 + 15 * q^76 + 21 * q^79 - 30 * q^80 + 18 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 24 * 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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.673648	+	1.16679i	0.476341	+	0.825047i	0.999633	−	0.0271067i	$-0.00862938\pi$
$2$	0.673648	+	1.16679i	0.476341	+	0.825047i	−0.523291	+	0.852154i	$0.675296\pi$
$3$		0			0
$3$		0			0
$4$	0.0923963	−	0.160035i	0.0461981	−	0.0800175i
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	0.430745	+	0.902473i	$0.358251\pi$
$5$	−1.26604	+	2.19285i	−0.566192	+	0.980674i	−0.996938	+	0.0782003i	$0.975083\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.94356			1.04071
$9$		0			0
$10$	−3.41147			−1.07880
$11$	0.233956	+	0.405223i	0.0705403	+	0.122179i	0.899138	−	0.437665i	$-0.144194\pi$
$11$	0.233956	+	0.405223i	0.0705403	+	0.122179i	−0.828598	+	0.559844i	$0.810861\pi$
$12$		0			0
$13$	2.91147	−	5.04282i	0.807498	−	1.39863i	−0.107094	−	0.994249i	$-0.534155\pi$
$13$	2.91147	−	5.04282i	0.807498	−	1.39863i	0.914592	−	0.404378i	$-0.132512\pi$
$14$		0			0
$15$		0			0
$16$	1.79813	+	3.11446i	0.449533	+	0.778615i
$17$	3.87939			0.940889			0.470445	−	0.882430i	$-0.344094\pi$
$17$	3.87939			0.940889			0.470445	+	0.882430i	$0.344094\pi$
$18$		0			0
$19$	2.18479			0.501226			0.250613	−	0.968087i	$-0.419368\pi$
$19$	2.18479			0.501226			0.250613	+	0.968087i	$0.419368\pi$
$20$	0.233956	+	0.405223i	0.0523141	+	0.0906106i
$21$		0			0
$22$	−0.315207	+	0.545955i	−0.0672025	+	0.116398i
$23$	−0.0530334	+	0.0918566i	−0.0110582	+	0.0191534i	−0.871502	−	0.490393i	$-0.836853\pi$
$23$	−0.0530334	+	0.0918566i	−0.0110582	+	0.0191534i	0.860443	+	0.509546i	$0.170187\pi$
$24$		0			0
$25$	−0.705737	−	1.22237i	−0.141147	−	0.244474i
$26$	7.84524			1.53858
$27$		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	0.282250	+	0.959341i	$0.408919\pi$
$31$	−3.84002	+	6.65111i	−0.689688	+	1.19458i	−0.971939	+	0.235235i	$0.924414\pi$
$32$	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
$37$	−7.68004			−1.26259			−0.631296	−	0.775542i	$-0.717477\pi$
$37$	−7.68004			−1.26259			−0.631296	+	0.775542i	$0.717477\pi$
$38$	1.47178	+	2.54920i	0.238754	+	0.413535i
$39$		0			0
$40$	−3.72668	+	6.45480i	−0.589240	+	1.02059i
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	−0.765897	−	0.642964i	$-0.777705\pi$
$41$	1.11334	−	1.92836i	0.173875	−	0.301160i	0.939771	+	0.341804i	$0.111038\pi$
$42$		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	$0.863150\pi$
$44$	0.0864665			0.0130353
$45$		0			0
$46$	−0.142903			−0.0210700
$47$	2.66637	+	4.61830i	0.388931	+	0.673648i	0.992306	−	0.123810i	$-0.0395112\pi$
$47$	2.66637	+	4.61830i	0.388931	+	0.673648i	−0.603375	+	0.797457i	$0.706178\pi$
$48$		0			0
$49$		0			0
$50$	0.950837	−	1.64690i	0.134469	−	0.232907i
$51$		0			0
$52$	−0.538019	−	0.931876i	−0.0746098	−	0.129228i
$53$	0.716881			0.0984712			0.0492356	−	0.998787i	$-0.484321\pi$
$53$	0.716881			0.0984712			0.0492356	+	0.998787i	$0.484321\pi$
$54$		0			0
$55$	−1.18479			−0.159757
$56$		0			0
$57$		0			0
$58$	−5.91534	+	10.2457i	−0.776723	+	1.34532i
$59$	−0.368241	+	0.637812i	−0.0479409	+	0.0830360i	−0.889000	−	0.457907i	$-0.848599\pi$
$59$	−0.368241	+	0.637812i	−0.0479409	+	0.0830360i	0.841059	+	0.540943i	$0.181933\pi$
$60$		0			0
$61$	0.479055	+	0.829748i	0.0613368	+	0.106238i	0.895063	−	0.445939i	$-0.147130\pi$
$61$	0.479055	+	0.829748i	0.0613368	+	0.106238i	−0.833726	+	0.552178i	$0.813797\pi$
$62$	−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	−0.405653	−	0.914027i	$-0.632956\pi$
$67$	4.81908	−	8.34689i	0.588744	−	1.01973i	0.994397	−	0.105708i	$-0.0337107\pi$
$68$	0.358441	−	0.620838i	0.0434673	−	0.0752876i
$69$		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
$73$	10.2686			1.20185			0.600923	−	0.799307i	$-0.294800\pi$
$73$	10.2686			1.20185			0.600923	+	0.799307i	$0.294800\pi$
$74$	−5.17365	−	8.96102i	−0.601424	−	1.04170i
$75$		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	0.964500	+	0.264082i	$0.0850689\pi$
$79$	6.31908	+	10.9450i	0.710952	+	1.23140i	−0.253548	+	0.967323i	$0.581598\pi$
$80$	−9.10607			−1.01809
$81$		0			0
$82$	3.00000			0.331295
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	0.931193	−	0.364527i	$-0.118769\pi$
$83$	1.36571	+	2.36549i	0.149907	+	0.259646i	−0.781286	+	0.624173i	$0.785436\pi$
$84$		0			0
$85$	−4.91147	+	8.50692i	−0.532724	+	0.922705i
$86$	0.826352	−	1.43128i	0.0891078	−	0.154339i
$87$		0			0
$88$	0.688663	+	1.19280i	0.0734117	+	0.127153i
$89$	−8.11381			−0.860062			−0.430031	−	0.902814i	$-0.641497\pi$
$89$	−8.11381			−0.860062			−0.430031	+	0.902814i	$0.641497\pi$
$90$		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	$-0.923996\pi$
$97$	−6.80200	−	11.7814i	−0.690639	−	1.19622i	0.280990	−	0.959711i	$-0.409337\pi$
$98$		0			0
$99$		0			0
$100$	−0.260830			−0.0260830
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	0.999632	−	0.0271271i	$-0.00863590\pi$
$101$	4.78699	+	8.29131i	0.476323	+	0.825016i	−0.523309	+	0.852143i	$0.675303\pi$
$102$		0			0
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	−0.781314	−	0.624139i	$-0.785450\pi$
$103$	1.52094	−	2.63435i	0.149863	−	0.259571i	0.931177	+	0.364568i	$0.118783\pi$
$104$	8.57011	−	14.8439i	0.840368	−	1.45556i
$105$		0			0
$106$	0.482926	+	0.836452i	0.0469059	+	0.0812434i
$107$	6.51754			0.630074			0.315037	−	0.949079i	$-0.397983\pi$
$107$	6.51754			0.630074			0.315037	+	0.949079i	$0.397983\pi$
$108$		0			0
$109$	10.6382			1.01895			0.509475	−	0.860485i	$-0.329840\pi$
$109$	10.6382			1.01895			0.509475	+	0.860485i	$0.329840\pi$
$110$	−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
$115$	−0.134285	−	0.232589i	−0.0125222	−	0.0216890i
$116$	1.62267			0.150662
$117$		0			0
$118$	−0.992259			−0.0913449
$119$		0			0
$120$		0			0
$121$	5.39053	−	9.33667i	0.490048	−	0.848788i
$122$	−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
$131$	−5.68139	+	9.84045i	−0.496385	+	0.859764i	−0.999991	−	0.00416893i	$-0.998673\pi$
$131$	−5.68139	+	9.84045i	−0.496385	+	0.859764i	0.503606	+	0.863933i	$0.332006\pi$
$132$		0			0
$133$		0			0
$134$	12.9855			1.12177
$135$		0			0
$136$	11.4192			0.979190
$137$	−2.86231	−	4.95767i	−0.244544	−	0.423562i	0.717459	−	0.696600i	$-0.245305\pi$
$137$	−2.86231	−	4.95767i	−0.244544	−	0.423562i	−0.962003	+	0.273038i	$0.911972\pi$
$138$		0			0
$139$	−0.461981	+	0.800175i	−0.0391847	+	0.0678700i	−0.884953	−	0.465681i	$-0.845809\pi$
$139$	−0.461981	+	0.800175i	−0.0391847	+	0.0678700i	0.845768	+	0.533551i	$0.179143\pi$
$140$		0			0
$141$		0			0
$142$	−8.91534	−	15.4418i	−0.748159	−	1.29585i
$143$	2.72462			0.227844
$144$		0			0
$145$	−22.2344			−1.84647
$146$	6.91740	+	11.9813i	0.572488	+	0.991579i
$147$		0			0
$148$	−0.709607	+	1.22908i	−0.0583294	+	0.101029i
$149$	4.36231	−	7.55574i	0.357374	−	0.618991i	−0.630147	−	0.776476i	$-0.717005\pi$
$149$	4.36231	−	7.55574i	0.357374	−	0.618991i	0.987521	+	0.157485i	$0.0503387\pi$
$150$		0			0
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	−0.947927	−	0.318488i	$-0.896825\pi$
$151$	−9.21348	−	15.9582i	−0.749782	−	1.29866i	0.198145	−	0.980173i	$-0.436508\pi$
$152$	6.43107			0.521629
$153$		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	$-0.770380\pi$
$157$	2.46198	−	4.26428i	0.196488	−	0.340326i	0.947387	+	0.320090i	$0.103713\pi$
$158$	−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
$163$	7.63816			0.598267			0.299133	−	0.954211i	$-0.403302\pi$
$163$	7.63816			0.598267			0.299133	+	0.954211i	$0.403302\pi$
$164$	−0.205737	−	0.356347i	−0.0160654	−	0.0278260i
$165$		0			0
$166$	−1.84002	+	3.18701i	−0.142813	+	0.247360i
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	−0.735632	−	0.677382i	$-0.763115\pi$
$167$	2.82770	−	4.89771i	0.218814	−	0.378996i	0.954446	+	0.298385i	$0.0964480\pi$
$168$		0			0
$169$	−10.4534	−	18.1058i	−0.804105	−	1.39275i
$170$	−13.2344			−1.01503
$171$		0			0
$172$	−0.226682			−0.0172843
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	−0.919003	−	0.394250i	$-0.871005\pi$
$173$	−10.5346	−	18.2465i	−0.800932	−	1.38725i	0.118071	−	0.993005i	$-0.462329\pi$
$174$		0			0
$175$		0			0
$176$	−0.841367	+	1.45729i	−0.0634204	+	0.109847i
$177$		0			0
$178$	−5.46585	−	9.46713i	−0.409683	−	0.709592i
$179$	5.12061			0.382733			0.191366	−	0.981519i	$-0.438708\pi$
$179$	5.12061			0.382733			0.191366	+	0.981519i	$0.438708\pi$
$180$		0			0
$181$	0.319955			0.0237821			0.0118910	−	0.999929i	$-0.496215\pi$
$181$	0.319955			0.0237821			0.0118910	+	0.999929i	$0.496215\pi$
$182$		0			0
$183$		0			0
$184$	−0.156107	+	0.270386i	−0.0115084	+	0.0199331i
$185$	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	−0.997215	−	0.0745858i	$-0.976237\pi$
$191$	−7.78359	−	13.4816i	−0.563200	−	0.975492i	0.434014	−	0.900906i	$-0.357097\pi$
$192$		0			0
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	−0.954028	−	0.299716i	$-0.903108\pi$
$193$	−3.02094	+	5.23243i	−0.217452	+	0.376639i	0.736576	+	0.676355i	$0.236441\pi$
$194$	9.16431	−	15.8731i	0.657959	−	1.13962i
$195$		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
$199$	−3.04189			−0.215634			−0.107817	−	0.994171i	$-0.534386\pi$
$199$	−3.04189			−0.215634			−0.107817	+	0.994171i	$0.534386\pi$
$200$	−2.07738	−	3.59813i	−0.146893	−	0.254426i
$201$		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
$206$	4.09833			0.285544
$207$		0			0
$208$	20.9409			1.45199
$209$	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	$0.106559\pi$
$212$	0.0662372	−	0.114726i	0.00454919	−	0.00787942i
$213$		0			0
$214$	4.39053	+	7.60462i	0.300130	+	0.519841i
$215$	3.10607			0.211832
$216$		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	0.999597	−	0.0284023i	$-0.00904195\pi$
$223$	7.09627	+	12.2911i	0.475201	+	0.823073i	−0.524395	+	0.851475i	$0.675709\pi$
$224$		0			0
$225$		0			0
$226$	6.97502			0.463972
$227$	1.44697	+	2.50622i	0.0960385	+	0.166344i	0.910042	−	0.414517i	$-0.136049\pi$
$227$	1.44697	+	2.50622i	0.0960385	+	0.166344i	−0.814003	+	0.580861i	$0.802716\pi$
$228$		0			0
$229$	4.58378	−	7.93934i	0.302905	−	0.524646i	−0.673888	−	0.738834i	$-0.735377\pi$
$229$	4.58378	−	7.93934i	0.302905	−	0.524646i	0.976793	+	0.214187i	$0.0687103\pi$
$230$	0.180922	−	0.313366i	0.0119297	−	0.0206628i
$231$		0			0
$232$	12.9238	+	22.3847i	0.848489	+	1.46963i
$233$	−13.2713			−0.869429			−0.434715	−	0.900568i	$-0.643151\pi$
$233$	−13.2713			−0.869429			−0.434715	+	0.900568i	$0.643151\pi$
$234$		0			0
$235$	−13.5030			−0.880838
$236$	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
$241$	−4.47906	−	7.75795i	−0.288521	−	0.499734i	0.684936	−	0.728604i	$-0.259830\pi$
$241$	−4.47906	−	7.75795i	−0.288521	−	0.499734i	−0.973457	+	0.228870i	$0.926497\pi$
$242$	14.5253			0.933720
$243$		0			0
$244$	0.177052			0.0113346
$245$		0			0
$246$		0			0
$247$	6.36097	−	11.0175i	0.404739	−	0.701028i
$248$	−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	$-0.789369\pi$
$251$	−24.9982			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$252$		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
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	−0.984144	−	0.177369i	$-0.943241\pi$
$257$	−5.42602	+	9.39815i	−0.338466	+	0.586240i	0.645678	+	0.763609i	$0.276575\pi$
$258$		0			0
$259$		0			0
$260$	2.72462			0.168974
$261$		0			0
$262$	−15.3090			−0.945795
$263$	13.0437	+	22.5924i	0.804309	+	1.39310i	0.916757	+	0.399446i	$0.130798\pi$
$263$	13.0437	+	22.5924i	0.804309	+	1.39310i	−0.112448	+	0.993658i	$0.535869\pi$
$264$		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
$269$	−7.63310			−0.465399			−0.232699	−	0.972549i	$-0.574756\pi$
$269$	−7.63310			−0.465399			−0.232699	+	0.972549i	$0.574756\pi$
$270$		0			0
$271$	−3.40373			−0.206762			−0.103381	−	0.994642i	$-0.532966\pi$
$271$	−3.40373			−0.206762			−0.103381	+	0.994642i	$0.532966\pi$
$272$	6.97565	+	12.0822i	0.422961	+	0.732590i
$273$		0			0
$274$	3.85638	−	6.67945i	0.232973	−	0.403520i
$275$	0.330222	−	0.571962i	0.0199131	−	0.0344906i
$276$		0			0
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	0.939084	−	0.343689i	$-0.111676\pi$
$277$	2.86097	+	4.95534i	0.171899	+	0.297738i	−0.767185	+	0.641426i	$0.778343\pi$
$278$	−1.24485			−0.0746612
$279$		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	$-0.789951\pi$
$283$	2.28564	−	3.95885i	0.135867	−	0.235329i	0.925929	+	0.377699i	$0.123285\pi$
$284$	−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
$289$	−1.95037			−0.114728
$290$	−14.9782	−	25.9430i	−0.879549	−	1.52342i
$291$		0			0
$292$	0.948778	−	1.64333i	0.0555230	−	0.0961687i
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	−0.922285	−	0.386512i	$-0.873680\pi$
$293$	−2.16385	+	3.74789i	−0.126413	+	0.218954i	0.795871	+	0.605466i	$0.207013\pi$
$294$		0			0
$295$	−0.932419	−	1.61500i	−0.0542875	−	0.0940287i
$296$	−22.6067			−1.31399
$297$		0			0
$298$	11.7547			0.680929
$299$	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
$304$	3.92855	+	6.80445i	0.225318	+	0.390262i
$305$	−2.42602			−0.138914
$306$		0			0
$307$	−12.3773			−0.706411			−0.353206	−	0.935546i	$-0.614908\pi$
$307$	−12.3773			−0.706411			−0.353206	+	0.935546i	$0.614908\pi$
$308$		0			0
$309$		0			0
$310$	13.1001	−	22.6901i	0.744038	−	1.28871i
$311$	10.9927	−	19.0400i	0.623340	−	1.07966i	−0.365519	−	0.930804i	$-0.619108\pi$
$311$	10.9927	−	19.0400i	0.623340	−	1.07966i	0.988859	−	0.148853i	$-0.0475582\pi$
$312$		0			0
$313$	−6.94491	−	12.0289i	−0.392549	−	0.679915i	0.600236	−	0.799823i	$-0.295073\pi$
$313$	−6.94491	−	12.0289i	−0.392549	−	0.679915i	−0.992785	+	0.119908i	$0.961740\pi$
$314$	6.63404			0.374380
$315$		0			0
$316$	2.33544			0.131379
$317$	−3.09105	−	5.35386i	−0.173611	−	0.300703i	0.766069	−	0.642759i	$-0.222210\pi$
$317$	−3.09105	−	5.35386i	−0.173611	−	0.300703i	−0.939680	+	0.342056i	$0.888877\pi$
$318$		0			0
$319$	−2.05438	+	3.55829i	−0.115023	+	0.199226i
$320$	−10.8833	+	18.8504i	−0.608392	+	1.05377i
$321$		0			0
$322$		0			0
$323$	8.47565			0.471598
$324$		0			0
$325$	−8.21894			−0.455905
$326$	5.14543	+	8.91215i	0.284979	+	0.493598i
$327$		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	0.680041	−	0.733174i	$-0.261962\pi$
$331$	−5.36571	−	9.29369i	−0.294926	−	0.510827i	−0.974968	+	0.222346i	$0.928628\pi$
$332$	0.504748			0.0277016
$333$		0			0
$334$	7.61949			0.416920
$335$	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	$-0.00237726\pi$
$338$	14.0838	−	24.3938i	0.766057	−	1.32685i
$339$		0			0
$340$	0.907604	+	1.57202i	0.0492217	+	0.0852545i
$341$	−3.59358			−0.194603
$342$		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	0.450521	+	0.892766i	$0.351238\pi$
$347$	−10.2062	+	17.6777i	−0.547898	+	0.948987i	−0.998418	+	0.0562207i	$0.982095\pi$
$348$		0			0
$349$	−1.78106	−	3.08489i	−0.0953379	−	0.165130i	0.814412	−	0.580288i	$-0.197060\pi$
$349$	−1.78106	−	3.08489i	−0.0953379	−	0.165130i	−0.909750	+	0.415157i	$0.863726\pi$
$350$		0			0
$351$		0			0
$352$	0.487511			0.0259844
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	0.701296	−	0.712871i	$-0.252605\pi$
$353$	−5.01114	−	8.67956i	−0.266716	−	0.461966i	−0.968012	+	0.250904i	$0.919272\pi$
$354$		0			0
$355$	16.7554	−	29.0211i	0.889283	−	1.54028i
$356$	−0.749686	+	1.29849i	−0.0397333	+	0.0688200i
$357$		0			0
$358$	3.44949	+	5.97470i	0.182311	+	0.315773i
$359$	−9.48070			−0.500372			−0.250186	−	0.968198i	$-0.580492\pi$
$359$	−9.48070			−0.500372			−0.250186	+	0.968198i	$0.580492\pi$
$360$		0			0
$361$	−14.2267			−0.748773
$362$	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
$367$	8.06670	+	13.9719i	0.421079	+	0.729329i	0.996045	−	0.0888474i	$-0.0283183\pi$
$367$	8.06670	+	13.9719i	0.421079	+	0.729329i	−0.574967	+	0.818177i	$0.694985\pi$
$368$	−0.381445			−0.0198842
$369$		0			0
$370$	26.2003			1.36209
$371$		0			0
$372$		0			0
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	−0.988572	−	0.150752i	$-0.951831\pi$
$373$	−7.02481	+	12.1673i	−0.363731	+	0.630001i	0.624841	+	0.780752i	$0.285164\pi$
$374$	−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
$383$	16.0103	−	27.7306i	0.818086	−	1.41697i	−0.0890039	−	0.996031i	$-0.528368\pi$
$383$	16.0103	−	27.7306i	0.818086	−	1.41697i	0.907090	−	0.420936i	$-0.138298\pi$
$384$		0			0
$385$		0			0
$386$	−8.14022			−0.414326
$387$		0			0
$388$	−2.51392			−0.127625
$389$	−15.0214	−	26.0178i	−0.761616	−	1.31916i	−0.942017	−	0.335564i	$-0.891073\pi$
$389$	−15.0214	−	26.0178i	−0.761616	−	1.31916i	0.180402	−	0.983593i	$-0.442260\pi$
$390$		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
$395$	−32.0009			−1.61014
$396$		0			0
$397$	12.3200			0.618321			0.309160	−	0.951010i	$-0.399952\pi$
$397$	12.3200			0.618321			0.309160	+	0.951010i	$0.399952\pi$
$398$	−2.04916	−	3.54925i	−0.102715	−	0.177908i
$399$		0			0
$400$	2.53802	−	4.39598i	0.126901	−	0.219799i
$401$	10.4880	−	18.1657i	0.523745	−	0.907152i	−0.475873	−	0.879514i	$-0.657868\pi$
$401$	10.4880	−	18.1657i	0.523745	−	0.907152i	0.999618	−	0.0276385i	$-0.00879873\pi$
$402$		0			0
$403$	22.3603	+	38.7291i	1.11384	+	1.92923i
$404$	1.76920			0.0880210
$405$		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	−0.352197	−	0.935926i	$-0.614565\pi$
$409$	12.8307	−	22.2234i	0.634437	−	1.09888i	0.986634	−	0.162951i	$-0.0521012\pi$
$410$	−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
$415$	−6.91622			−0.339504
$416$	−3.03343	−	5.25406i	−0.148726	−	0.257601i
$417$		0			0
$418$	−0.688663	+	1.19280i	−0.0336836	+	0.0583417i
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	−0.847387	−	0.530976i	$-0.821825\pi$
$419$	0.739885	−	1.28152i	0.0361458	−	0.0626063i	0.883532	+	0.468370i	$0.155159\pi$
$420$		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	$0.936814\pi$
$422$	7.34730			0.357661
$423$		0			0
$424$	2.11019			0.102480
$425$	−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
$430$	2.09240	+	3.62414i	0.100904	+	0.174771i
$431$	−17.7270			−0.853879			−0.426939	−	0.904280i	$-0.640408\pi$
$431$	−17.7270			−0.853879			−0.426939	+	0.904280i	$0.640408\pi$
$432$		0			0
$433$	5.83843			0.280577			0.140289	−	0.990111i	$-0.455197\pi$
$433$	5.83843			0.280577			0.140289	+	0.990111i	$0.455197\pi$
$434$		0			0
$435$		0			0
$436$	0.982926	−	1.70248i	0.0470736	−	0.0815339i
$437$	−0.115867	+	0.200688i	−0.00554267	+	0.00960019i
$438$		0			0
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	0.963931	+	0.266151i	$0.0857518\pi$
$439$	14.9277	+	25.8555i	0.712459	+	1.23401i	−0.251473	+	0.967864i	$0.580915\pi$
$440$	−3.48751			−0.166261
$441$		0			0
$442$	30.4347			1.44763
$443$	5.33275	+	9.23659i	0.253367	+	0.438844i	0.964451	−	0.264263i	$-0.0851288\pi$
$443$	5.33275	+	9.23659i	0.253367	+	0.438844i	−0.711084	+	0.703107i	$0.751795\pi$
$444$		0			0
$445$	10.2724	−	17.7924i	0.486960	−	0.843440i
$446$	−9.56077	+	16.5597i	−0.452716	+	0.784127i
$447$		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
$451$	1.04189			0.0490606
$452$	−0.478340	−	0.828510i	−0.0224992	−	0.0389698i
$453$		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	0.801283	−	0.598285i	$-0.204151\pi$
$457$	−2.51161	−	4.35024i	−0.117488	−	0.203496i	−0.918772	+	0.394789i	$0.870818\pi$
$458$	12.3514			0.577144
$459$		0			0
$460$	−0.0496299			−0.00231400
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	0.566955	−	0.823749i	$-0.308121\pi$
$461$	−9.23055	−	15.9878i	−0.429910	−	0.744625i	−0.996865	+	0.0791233i	$0.974788\pi$
$462$		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	$0.0593600\pi$
$464$	−15.7895	+	27.3482i	−0.733010	+	1.26961i
$465$		0			0
$466$	−8.94016	−	15.4848i	−0.414145	−	0.717320i
$467$	−3.36865			−0.155883			−0.0779413	−	0.996958i	$-0.524835\pi$
$467$	−3.36865			−0.155883			−0.0779413	+	0.996958i	$0.524835\pi$
$468$		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
$478$	12.8494			0.587716
$479$	18.3833	+	31.8407i	0.839952	+	1.45484i	0.889934	+	0.456090i	$0.150751\pi$
$479$	18.3833	+	31.8407i	0.839952	+	1.45484i	−0.0499812	+	0.998750i	$0.515916\pi$
$480$		0			0
$481$	−22.3603	+	38.7291i	−1.01954	+	1.76589i
$482$	6.03462	−	10.4523i	0.274869	−	0.476087i
$483$		0			0
$484$	−0.996130	−	1.72535i	−0.0452786	−	0.0784249i
$485$	34.4466			1.56414
$486$		0			0
$487$	−37.4175			−1.69555			−0.847773	−	0.530358i	$-0.822057\pi$
$487$	−37.4175			−1.69555			−0.847773	+	0.530358i	$0.822057\pi$
$488$	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
$493$	17.0326	+	29.5013i	0.767108	+	1.32867i
$494$	17.1402			0.771175
$495$		0			0
$496$	−27.6195			−1.24015
$497$		0			0
$498$		0			0
$499$	−16.8726	+	29.2242i	−0.755320	+	1.30825i	0.189895	+	0.981804i	$0.439185\pi$
$499$	−16.8726	+	29.2242i	−0.755320	+	1.30825i	−0.945215	+	0.326449i	$0.894148\pi$
$500$	−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	$-0.753255\pi$
$503$	−32.0401			−1.42860			−0.714299	+	0.699840i	$0.753255\pi$
$504$		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
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	−0.764550	−	0.644564i	$-0.777039\pi$
$509$	3.96926	−	6.87495i	0.175934	−	0.304727i	0.940484	+	0.339838i	$0.110372\pi$
$510$		0			0
$511$		0			0
$512$	24.9186			1.10126
$513$		0			0
$514$	−14.6209			−0.644901
$515$	3.85117	+	6.67042i	0.169703	+	0.293934i
$516$		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
$521$	−14.6750			−0.642923			−0.321462	−	0.946923i	$-0.604174\pi$
$521$	−14.6750			−0.642923			−0.321462	+	0.946923i	$0.604174\pi$
$522$		0			0
$523$	−28.3432			−1.23936			−0.619680	−	0.784854i	$-0.712738\pi$
$523$	−28.3432			−1.23936			−0.619680	+	0.784854i	$0.712738\pi$
$524$	1.04988	+	1.81844i	0.0458641	+	0.0794390i
$525$		0			0
$526$	−17.5737	+	30.4386i	−0.766251	+	1.32719i
$527$	−14.8969	+	25.8022i	−0.648920	+	1.12396i
$528$		0			0
$529$	11.4944	+	19.9088i	0.499755	+	0.865602i
$530$	−2.44562			−0.106231
$531$		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
$541$	11.2858			0.485215			0.242607	−	0.970125i	$-0.421997\pi$
$541$	11.2858			0.485215			0.242607	+	0.970125i	$0.421997\pi$
$542$	−2.29292	−	3.97145i	−0.0984893	−	0.170588i
$543$		0			0
$544$	2.02094	−	3.50038i	0.0866473	−	0.150077i
$545$	−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	$0.618385\pi$
$548$	−1.05787			−0.0451899
$549$		0			0
$550$	0.889814			0.0379418
$551$	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
$556$	0.0853707	+	0.147866i	0.00362052	+	0.00627093i
$557$	0.775682			0.0328667			0.0164334	−	0.999865i	$-0.494769\pi$
$557$	0.775682			0.0328667			0.0164334	+	0.999865i	$0.494769\pi$
$558$		0			0
$559$	−7.14290			−0.302113
$560$		0			0
$561$		0			0
$562$	−19.1163	+	33.1105i	−0.806374	+	1.39668i
$563$	−12.4761	+	21.6093i	−0.525806	+	0.910722i	0.473742	+	0.880663i	$0.342903\pi$
$563$	−12.4761	+	21.6093i	−0.525806	+	0.910722i	−0.999548	+	0.0300588i	$0.990431\pi$
$564$		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	−0.999732	−	0.0231391i	$-0.992634\pi$
$569$	−12.4017	−	21.4803i	−0.519905	−	0.900502i	0.479827	−	0.877363i	$-0.340699\pi$
$570$		0			0
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	−0.943260	−	0.332055i	$-0.892258\pi$
$571$	−4.39827	+	7.61803i	−0.184062	+	0.318805i	0.759198	+	0.650860i	$0.225591\pi$
$572$	0.251745	−	0.436035i	0.0105260	−	0.0182315i
$573$		0			0
$574$		0			0
$575$	0.149711			0.00624336
$576$		0			0
$577$	12.8743			0.535965			0.267983	−	0.963424i	$-0.413643\pi$
$577$	12.8743			0.535965			0.267983	+	0.963424i	$0.413643\pi$
$578$	−1.31386	−	2.27568i	−0.0546495	−	0.0946557i
$579$		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
$584$	30.2262			1.25077
$585$		0			0
$586$	−5.83069			−0.240864
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.790190	−	0.612861i	$-0.790018\pi$
$587$	−22.4315	−	38.8526i	−0.925849	−	1.60362i	−0.135658	−	0.990756i	$-0.543315\pi$
$588$		0			0
$589$	−8.38965	+	14.5313i	−0.345690	+	0.598752i
$590$	1.25624	−	2.17588i	0.0517188	−	0.0895795i
$591$		0			0
$592$	−13.8097	−	23.9192i	−0.567577	−	0.983072i
$593$	3.76053			0.154426			0.0772131	−	0.997015i	$-0.475398\pi$
$593$	3.76053			0.154426			0.0772131	+	0.997015i	$0.475398\pi$
$594$		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	−0.901258	−	0.433283i	$-0.857355\pi$
$599$	−1.84524	+	3.19604i	−0.0753943	+	0.130587i	0.825863	+	0.563870i	$0.190688\pi$
$600$		0			0
$601$	−10.9285	−	18.9288i	−0.445785	−	0.772122i	0.552322	−	0.833631i	$-0.313742\pi$
$601$	−10.9285	−	18.9288i	−0.445785	−	0.772122i	−0.998107	+	0.0615091i	$0.980409\pi$
$602$		0			0
$603$		0			0
$604$	−3.40516			−0.138554
$605$	13.6493	+	23.6413i	0.554923	+	0.961155i
$606$		0			0
$607$	12.1973	−	21.1263i	0.495072	−	0.857490i	−0.504911	−	0.863171i	$-0.668475\pi$
$607$	12.1973	−	21.1263i	0.495072	−	0.857490i	0.999984	+	0.00568063i	$0.00180821\pi$
$608$	1.13816	−	1.97134i	0.0461583	−	0.0799485i
$609$		0			0
$610$	−1.63429	−	2.83067i	−0.0661703	−	0.114610i
$611$	31.0523			1.25624
$612$		0			0
$613$	42.0215			1.69723			0.848616	−	0.529010i	$-0.177437\pi$
$613$	42.0215			1.69723			0.848616	+	0.529010i	$0.177437\pi$
$614$	−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
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	−0.998490	−	0.0549349i	$-0.982505\pi$
$619$	−13.6047	−	23.5641i	−0.546820	−	0.947120i	0.451670	−	0.892185i	$-0.350828\pi$
$620$	−3.59358			−0.144322
$621$		0			0
$622$	29.6209			1.18769
$623$		0			0
$624$		0			0
$625$	15.0326	−	26.0372i	0.601302	−	1.04149i
$626$	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
$635$	11.2451	−	19.4771i	0.446248	−	0.772925i
$636$		0			0
$637$		0			0
$638$	−5.53571			−0.219161
$639$		0			0
$640$	−24.0496			−0.950645
$641$	−0.139500	−	0.241621i	−0.00550991	−	0.00954345i	0.863257	−	0.504764i	$-0.168421\pi$
$641$	−0.139500	−	0.241621i	−0.00550991	−	0.00954345i	−0.868767	+	0.495221i	$0.835087\pi$
$642$		0			0
$643$	−9.12196	+	15.7997i	−0.359735	+	0.623079i	−0.987916	−	0.154988i	$-0.950466\pi$
$643$	−9.12196	+	15.7997i	−0.359735	+	0.623079i	0.628181	+	0.778067i	$0.283800\pi$
$644$		0			0
$645$		0			0
$646$	5.70961	+	9.88933i	0.224642	+	0.389090i
$647$	22.4570			0.882875			0.441438	−	0.897292i	$-0.354469\pi$
$647$	22.4570			0.882875			0.441438	+	0.897292i	$0.354469\pi$
$648$		0			0
$649$	−0.344608			−0.0135270
$650$	−5.53667	−	9.58980i	−0.217166	−	0.376143i
$651$		0			0
$652$	0.705737	−	1.22237i	0.0276388	−	0.0478718i
$653$	−25.2656	+	43.7614i	−0.988721	+	1.71251i	−0.364655	+	0.931143i	$0.618813\pi$
$653$	−25.2656	+	43.7614i	−0.988721	+	1.71251i	−0.624066	+	0.781372i	$0.714520\pi$
$654$		0			0
$655$	−14.3858	−	24.9169i	−0.562099	−	0.973584i
$656$	8.00774			0.312650
$657$		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	0.303938	+	0.952692i	$0.401698\pi$
$661$	−17.3050	+	29.9731i	−0.673086	+	1.16582i	−0.977024	+	0.213128i	$0.931635\pi$
$662$	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
$667$	−0.931379			−0.0360631
$668$	−0.522537	−	0.905061i	−0.0202176	−	0.0350179i
$669$		0			0
$670$	−16.4402	+	28.4752i	−0.635139	+	1.10009i
$671$	−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	$0.936430\pi$
$674$	25.0523			0.964979
$675$		0			0
$676$	−3.86341			−0.148593
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	0.889154	+	0.457608i	$0.151294\pi$
$677$	21.8790	+	37.8955i	0.840877	+	1.45644i	−0.0482766	+	0.998834i	$0.515373\pi$
$678$		0			0
$679$		0			0
$680$	−14.4572	+	25.0407i	−0.554410	+	0.960266i
$681$		0			0
$682$	−2.42081	−	4.19296i	−0.0926975	−	0.160557i
$683$	−28.2412			−1.08062			−0.540310	−	0.841466i	$-0.681693\pi$
$683$	−28.2412			−1.08062			−0.540310	+	0.841466i	$0.681693\pi$
$684$		0			0
$685$	14.4953			0.553835
$686$		0			0
$687$		0			0
$688$	2.20574	−	3.82045i	0.0840929	−	0.145653i
$689$	2.08718	−	3.61510i	0.0795153	−	0.137725i
$690$		0			0
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	−0.998068	−	0.0621351i	$-0.980209\pi$
$691$	−14.5326	−	25.1711i	−0.552844	−	0.957555i	0.445223	−	0.895420i	$-0.353124\pi$
$692$	−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
$698$	2.39961	−	4.15625i	0.0908268	−	0.157317i
$699$		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
$703$	−16.7793			−0.632843
$704$	2.01114	+	3.48340i	0.0757979	+	0.131286i
$705$		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	0.985680	−	0.168626i	$-0.0539329\pi$
$709$	9.23442	+	15.9945i	0.346806	+	0.600686i	−0.638874	+	0.769311i	$0.720600\pi$
$710$	45.1489			1.69441
$711$		0			0
$712$	−23.8835			−0.895072
$713$	−0.407299	−	0.705463i	−0.0152535	−	0.0264198i
$714$		0			0
$715$	−3.44949	+	5.97470i	−0.129004	+	0.223441i
$716$	0.473126	−	0.819478i	0.0176815	−	0.0306253i
$717$		0			0
$718$	−6.38666	−	11.0620i	−0.238348	−	0.412831i
$719$	−33.7769			−1.25967			−0.629834	−	0.776730i	$-0.716877\pi$
$719$	−33.7769			−1.25967			−0.629834	+	0.776730i	$0.716877\pi$
$720$		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	0.978713	−	0.205234i	$-0.0657957\pi$
$727$	8.40214	+	14.5529i	0.311618	+	0.539738i	−0.667095	+	0.744973i	$0.732462\pi$
$728$		0			0
$729$		0			0
$730$	−35.0310			−1.29655
$731$	−2.37939	−	4.12122i	−0.0880047	−	0.152429i
$732$		0			0
$733$	−6.81820	+	11.8095i	−0.251836	+	0.436193i	−0.964031	−	0.265789i	$-0.914368\pi$
$733$	−6.81820	+	11.8095i	−0.251836	+	0.436193i	0.712195	+	0.701981i	$0.247701\pi$
$734$	−10.8682	+	18.8243i	−0.401154	+	0.694819i
$735$		0			0
$736$	0.0552549	+	0.0957044i	0.00203672	+	0.00352771i
$737$	4.50980			0.166121
$738$		0			0
$739$	−32.0419			−1.17868			−0.589340	−	0.807885i	$-0.700612\pi$
$739$	−32.0419			−1.17868			−0.589340	+	0.807885i	$0.700612\pi$
$740$	−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
$745$	11.0458	+	19.1318i	0.404685	+	0.700936i
$746$	−18.9290			−0.693040
$747$		0			0
$748$	0.335437			0.0122648
$749$		0			0
$750$		0			0
$751$	−13.0582	+	22.6175i	−0.476502	+	0.825326i	−0.999637	−	0.0269236i	$-0.991429\pi$
$751$	−13.0582	+	22.6175i	−0.476502	+	0.825326i	0.523135	+	0.852250i	$0.324762\pi$
$752$	−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
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	0.214148	+	0.976801i	$0.431302\pi$
$761$	−20.3824	+	35.3033i	−0.738861	+	1.27974i	−0.953009	+	0.302943i	$0.902031\pi$
$762$		0			0
$763$		0			0
$764$	−2.87670			−0.104075
$765$		0			0
$766$	43.1411			1.55875
$767$	2.14425	+	3.71395i	0.0774243	+	0.134103i
$768$		0			0
$769$	19.7135	−	34.1447i	0.710886	−	1.23129i	−0.253639	−	0.967299i	$-0.581627\pi$
$769$	19.7135	−	34.1447i	0.710886	−	1.23129i	0.964525	−	0.263992i	$-0.0850392\pi$
$770$		0			0
$771$		0			0
$772$	0.558248	+	0.966914i	0.0200918	+	0.0348000i
$773$	24.9026			0.895685			0.447842	−	0.894113i	$-0.352193\pi$
$773$	24.9026			0.895685			0.447842	+	0.894113i	$0.352193\pi$
$774$		0			0
$775$	10.8402			0.389391
$776$	−20.0221	−	34.6793i	−0.718752	−	1.24492i
$777$		0			0
$778$	20.2383	−	35.0538i	0.725578	−	1.25674i
$779$	2.43242	−	4.21307i	0.0871504	−	0.150949i
$780$		0			0
$781$	−3.09627	−	5.36289i	−0.110793	−	0.191899i
$782$	−0.554378			−0.0198245
$783$		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	0.451203	+	0.892421i	$0.350995\pi$
$787$	−15.3525	+	26.5913i	−0.547258	+	0.947879i	−0.998461	+	0.0554572i	$0.982338\pi$
$788$	−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
$793$	5.57903			0.198117
$794$	8.29932	+	14.3748i	0.294532	+	0.510144i
$795$		0			0
$796$	−0.281059	+	0.486809i	−0.00996188	+	0.0172545i
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	−0.751858	−	0.659325i	$-0.770842\pi$
$797$	5.50686	−	9.53817i	0.195063	−	0.337859i	0.946921	+	0.321466i	$0.104175\pi$
$798$		0			0
$799$	10.3439	+	17.9161i	0.365941	+	0.633828i
$800$	−1.47060			−0.0519935
$801$		0			0
$802$	28.2608			0.997925
$803$	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
$808$	14.0908	+	24.4060i	0.495713	+	0.858600i
$809$	−16.9881			−0.597271			−0.298636	−	0.954367i	$-0.596532\pi$
$809$	−16.9881			−0.597271			−0.298636	+	0.954367i	$0.596532\pi$
$810$		0			0
$811$	−37.9796			−1.33364			−0.666822	−	0.745217i	$-0.732346\pi$
$811$	−37.9796			−1.33364			−0.666822	+	0.745217i	$0.732346\pi$
$812$		0			0
$813$		0			0
$814$	2.42081	−	4.19296i	0.0848493	−	0.146963i
$815$	−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	0.929173	−	0.369646i	$-0.120521\pi$
$821$	4.13934	+	7.16954i	0.144464	+	0.250219i	−0.784709	+	0.619864i	$0.787188\pi$
$822$		0			0
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.207077	+	0.978325i	$0.566395\pi$
$823$	−27.2763	+	47.2440i	−0.950792	+	1.64682i	−0.743716	+	0.668496i	$0.766938\pi$
$824$	4.47700	−	7.75438i	0.155964	−	0.270137i
$825$		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
$829$	0.352349			0.0122376			0.00611879	−	0.999981i	$-0.498052\pi$
$829$	0.352349			0.0122376			0.00611879	+	0.999981i	$0.498052\pi$
$830$	−4.65910	−	8.06980i	−0.161720	−	0.280107i
$831$		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
$836$	0.188911			0.00653363
$837$		0			0
$838$	1.99369			0.0688709
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	0.565215	−	0.824944i	$-0.308793\pi$
$839$	−12.5077	−	21.6640i	−0.431815	−	0.747926i	−0.997030	+	0.0770182i	$0.975460\pi$
$840$		0			0
$841$	−24.0535	+	41.6619i	−0.829431	+	1.43662i
$842$	8.82951	−	15.2932i	0.304285	−	0.527037i
$843$		0			0
$844$	−0.503870	−	0.872729i	−0.0173439	−	0.0300406i
$845$	52.9377			1.82111
$846$		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	$0.0674397\pi$
$853$	19.5954	+	33.9402i	0.670933	+	1.16209i	−0.306706	+	0.951804i	$0.599227\pi$
$854$		0			0
$855$		0			0
$856$	19.1848			0.655723
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	0.691210	−	0.722654i	$-0.257078\pi$
$857$	−8.20368	−	14.2092i	−0.280232	−	0.485377i	−0.971442	+	0.237278i	$0.923745\pi$
$858$		0			0
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	−0.998842	−	0.0481111i	$-0.984680\pi$
$859$	−13.4162	+	23.2376i	−0.457756	+	0.792856i	0.541086	+	0.840967i	$0.318013\pi$
$860$	0.286989	−	0.497079i	0.00978624	−	0.0169503i
$861$		0			0
$862$	−11.9418	−	20.6837i	−0.406738	−	0.704490i
$863$	−14.5057			−0.493779			−0.246890	−	0.969044i	$-0.579408\pi$
$863$	−14.5057			−0.493779			−0.246890	+	0.969044i	$0.579408\pi$
$864$		0			0
$865$	53.3492			1.81393
$866$	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
$871$	−28.0612	−	48.6035i	−0.950819	−	1.64687i
$872$	31.3141			1.06043
$873$		0			0
$874$	−0.312214			−0.0105608
$875$		0			0
$876$		0			0
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	−0.980352	−	0.197255i	$-0.936797\pi$
$877$	−9.45723	+	16.3804i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270131\pi$
$878$	−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	$-0.137664\pi$
$881$	53.8976			1.81585			0.907927	+	0.419128i	$0.137664\pi$
$882$		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
$887$	19.4800	−	33.7403i	0.654074	−	1.13289i	−0.328051	−	0.944660i	$-0.606392\pi$
$887$	19.4800	−	33.7403i	0.654074	−	1.13289i	0.982125	−	0.188229i	$-0.0602749\pi$
$888$		0			0
$889$		0			0
$890$	27.6800			0.927837
$891$		0			0
$892$	2.62267			0.0878136
$893$	5.82547	+	10.0900i	0.194942	+	0.337650i
$894$		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
$899$	−67.4389			−2.24921
$900$		0			0
$901$	2.78106			0.0926505
$902$	0.701867	+	1.21567i	0.0233696	+	0.0404773i
$903$		0			0
$904$	7.61949	−	13.1973i	0.253420	−	0.438937i
$905$	−0.405078	+	0.701615i	−0.0134652	+	0.0233225i
$906$		0			0
$907$	−17.2638	−	29.9018i	−0.573236	−	0.992874i	−0.996231	−	0.0867416i	$-0.972355\pi$
$907$	−17.2638	−	29.9018i	−0.573236	−	0.992874i	0.422995	−	0.906132i	$-0.360979\pi$
$908$	0.534777			0.0177472
$909$		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
$919$	−9.95636			−0.328430			−0.164215	−	0.986425i	$-0.552509\pi$
$919$	−9.95636			−0.328430			−0.164215	+	0.986425i	$0.552509\pi$
$920$	−0.395277	−	0.684640i	−0.0130319	−	0.0225719i
$921$		0			0
$922$	12.4363	−	21.5403i	0.409567	−	0.709391i
$923$	−38.5317	+	66.7388i	−1.26829	+	2.19674i
$924$		0			0
$925$	5.42009	+	9.38788i	0.178212	+	0.308671i
$926$	19.1780			0.630228
$927$		0			0
$928$	9.14889			0.300327
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	0.782239	−	0.622978i	$-0.214077\pi$
$929$	−4.52300	−	7.83407i	−0.148395	−	0.257028i	−0.930634	+	0.365950i	$0.880744\pi$
$930$		0			0
$931$		0			0
$932$	−1.22621	+	2.12387i	−0.0401660	+	0.0695696i
$933$		0			0
$934$	−2.26929	−	3.93052i	−0.0742533	−	0.128610i
$935$	−4.59627			−0.150314
$936$		0			0
$937$	24.3928			0.796878			0.398439	−	0.917195i	$-0.369552\pi$
$937$	24.3928			0.796878			0.398439	+	0.917195i	$0.369552\pi$
$938$		0			0
$939$		0			0
$940$	−1.24763	+	2.16095i	−0.0406931	+	0.0704825i
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.276223	−	0.961094i	$-0.410917\pi$
$941$	29.7690	−	51.5615i	0.970443	−	1.68086i	0.694220	−	0.719763i	$-0.255749\pi$
$942$		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	0.927693	−	0.373344i	$-0.121789\pi$
$947$	4.32429	+	7.48989i	0.140521	+	0.243389i	−0.787172	+	0.616733i	$0.788456\pi$
$948$		0			0
$949$	29.8967	−	51.7826i	0.970487	−	1.68093i
$950$	2.07738	−	3.59813i	0.0673992	−	0.116739i
$951$		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
$955$	39.4175			1.27552
$956$	−0.881196	−	1.52628i	−0.0284999	−	0.0493633i
$957$		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
$962$	−60.2518			−1.94260
$963$		0			0
$964$	−1.65539			−0.0533166
$965$	−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	$-0.0110601\pi$
$968$	15.8674	−	27.4831i	0.509996	−	0.883340i
$969$		0			0
$970$	23.2049	+	40.1920i	0.745063	+	1.29049i
$971$	−55.4570			−1.77970			−0.889850	−	0.456254i	$-0.849191\pi$
$971$	−55.4570			−1.77970			−0.889850	+	0.456254i	$0.849191\pi$
$972$		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	0.0830847	−	0.996542i	$-0.473523\pi$
$977$	28.2743	−	48.9724i	0.904573	−	1.56677i	0.821489	−	0.570225i	$-0.193144\pi$
$978$		0			0
$979$	−1.89827	−	3.28790i	−0.0606690	−	0.105082i
$980$		0			0
$981$		0			0
$982$	−35.9331			−1.14667
$983$	−14.4987	−	25.1124i	−0.462435	−	0.800961i	0.536646	−	0.843807i	$-0.319691\pi$
$983$	−14.4987	−	25.1124i	−0.462435	−	0.800961i	−0.999082	+	0.0428458i	$0.986358\pi$
$984$		0			0
$985$	31.9479	−	55.3354i	1.01794	−	1.76313i
$986$	−22.9479	+	39.7469i	−0.730810	+	1.26580i
$987$		0			0
$988$	−1.17546	−	2.03596i	−0.0373963	−	0.0647724i
$989$	0.130110			0.00413726
$990$		0			0
$991$	6.80922			0.216302			0.108151	−	0.994134i	$-0.465507\pi$
$991$	6.80922			0.216302			0.108151	+	0.994134i	$0.465507\pi$
$992$	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
$997$	−19.4688	−	33.7210i	−0.616585	−	1.06796i	−0.990104	−	0.140333i	$-0.955183\pi$
$997$	−19.4688	−	33.7210i	−0.616585	−	1.06796i	0.373520	−	0.927622i	$-0.378151\pi$
$998$	−45.4647			−1.43916
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.d.442.2		6
3.2	odd	2		441.2.f.c.148.2		6
7.2	even	3		1323.2.g.e.361.2		6
7.3	odd	6		1323.2.h.c.226.2		6
7.4	even	3		1323.2.h.b.226.2		6
7.5	odd	6		1323.2.g.d.361.2		6
7.6	odd	2		189.2.f.b.64.2		6
9.2	odd	6		441.2.f.c.295.2		6
9.4	even	3		3969.2.a.l.1.2		3
9.5	odd	6		3969.2.a.q.1.2		3
9.7	even	3	inner	1323.2.f.d.883.2		6
21.2	odd	6		441.2.g.b.67.2		6
21.5	even	6		441.2.g.c.67.2		6
21.11	odd	6		441.2.h.e.373.2		6
21.17	even	6		441.2.h.d.373.2		6
21.20	even	2		63.2.f.a.22.2	✓	6
28.27	even	2		3024.2.r.k.1009.3		6
63.2	odd	6		441.2.h.e.214.2		6
63.11	odd	6		441.2.g.b.79.2		6
63.13	odd	6		567.2.a.c.1.2		3
63.16	even	3		1323.2.h.b.802.2		6
63.20	even	6		63.2.f.a.43.2	yes	6
63.25	even	3		1323.2.g.e.667.2		6
63.34	odd	6		189.2.f.b.127.2		6
63.38	even	6		441.2.g.c.79.2		6
63.41	even	6		567.2.a.h.1.2		3
63.47	even	6		441.2.h.d.214.2		6
63.52	odd	6		1323.2.g.d.667.2		6
63.61	odd	6		1323.2.h.c.802.2		6
84.83	odd	2		1008.2.r.h.337.1		6
252.83	odd	6		1008.2.r.h.673.1		6
252.139	even	6		9072.2.a.bs.1.1		3
252.167	odd	6		9072.2.a.ca.1.3		3
252.223	even	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	21.20	even	2
63.2.f.a.43.2	yes	6	63.20	even	6
189.2.f.b.64.2		6	7.6	odd	2
189.2.f.b.127.2		6	63.34	odd	6
441.2.f.c.148.2		6	3.2	odd	2
441.2.f.c.295.2		6	9.2	odd	6
441.2.g.b.67.2		6	21.2	odd	6
441.2.g.b.79.2		6	63.11	odd	6
441.2.g.c.67.2		6	21.5	even	6
441.2.g.c.79.2		6	63.38	even	6
441.2.h.d.214.2		6	63.47	even	6
441.2.h.d.373.2		6	21.17	even	6
441.2.h.e.214.2		6	63.2	odd	6
441.2.h.e.373.2		6	21.11	odd	6
567.2.a.c.1.2		3	63.13	odd	6
567.2.a.h.1.2		3	63.41	even	6
1008.2.r.h.337.1		6	84.83	odd	2
1008.2.r.h.673.1		6	252.83	odd	6
1323.2.f.d.442.2		6	1.1	even	1	trivial
1323.2.f.d.883.2		6	9.7	even	3	inner
1323.2.g.d.361.2		6	7.5	odd	6
1323.2.g.d.667.2		6	63.52	odd	6
1323.2.g.e.361.2		6	7.2	even	3
1323.2.g.e.667.2		6	63.25	even	3
1323.2.h.b.226.2		6	7.4	even	3
1323.2.h.b.802.2		6	63.16	even	3
1323.2.h.c.226.2		6	7.3	odd	6
1323.2.h.c.802.2		6	63.61	odd	6
3024.2.r.k.1009.3		6	28.27	even	2
3024.2.r.k.2017.3		6	252.223	even	6
3969.2.a.l.1.2		3	9.4	even	3
3969.2.a.q.1.2		3	9.5	odd	6
9072.2.a.bs.1.1		3	252.139	even	6
9072.2.a.ca.1.3		3	252.167	odd	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +2.94356 q^{8} +O(q^{10})\)	\(q+(0.673648 + 1.16679i) q^{2} +(0.0923963 - 0.160035i) q^{4} +(-1.26604 + 2.19285i) q^{5} +2.94356 q^{8} -3.41147 q^{10} +(0.233956 + 0.405223i) q^{11} +(2.91147 - 5.04282i) q^{13} +(1.79813 + 3.11446i) q^{16} +3.87939 q^{17} +2.18479 q^{19} +(0.233956 + 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(-0.0530334 + 0.0918566i) q^{23} +(-0.705737 - 1.22237i) q^{25} +7.84524 q^{26} +(4.39053 + 7.60462i) q^{29} +(-3.84002 + 6.65111i) q^{31} +(0.520945 - 0.902302i) q^{32} +(2.61334 + 4.52644i) q^{34} -7.68004 q^{37} +(1.47178 + 2.54920i) q^{38} +(-3.72668 + 6.45480i) q^{40} +(1.11334 - 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +0.0864665 q^{44} -0.142903 q^{46} +(2.66637 + 4.61830i) q^{47} +(0.950837 - 1.64690i) q^{50} +(-0.538019 - 0.931876i) q^{52} +0.716881 q^{53} -1.18479 q^{55} +(-5.91534 + 10.2457i) q^{58} +(-0.368241 + 0.637812i) q^{59} +(0.479055 + 0.829748i) q^{61} -10.3473 q^{62} +8.59627 q^{64} +(7.37211 + 12.7689i) q^{65} +(4.81908 - 8.34689i) q^{67} +(0.358441 - 0.620838i) q^{68} -13.2344 q^{71} +10.2686 q^{73} +(-5.17365 - 8.96102i) q^{74} +(0.201867 - 0.349643i) q^{76} +(6.31908 + 10.9450i) q^{79} -9.10607 q^{80} +3.00000 q^{82} +(1.36571 + 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(0.826352 - 1.43128i) q^{86} +(0.688663 + 1.19280i) q^{88} -8.11381 q^{89} +(0.00980018 + 0.0169744i) q^{92} +(-3.59240 + 6.22221i) q^{94} +(-2.76604 + 4.79093i) q^{95} +(-6.80200 - 11.7814i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} - 3 q^{16} + 12 q^{17} + 6 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 6 q^{26} + 9 q^{29} - 3 q^{31} + 9 q^{34} - 6 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} - 30 q^{44} - 3 q^{47} - 6 q^{50} - 21 q^{52} - 12 q^{53} + 9 q^{58} + 3 q^{59} + 6 q^{61} - 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 6 q^{68} - 18 q^{71} + 42 q^{73} - 30 q^{74} + 15 q^{76} + 21 q^{79} - 30 q^{80} + 18 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 24 q^{89} + 3 q^{92} - 18 q^{94} - 12 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 - 3 * q^16 + 12 * q^17 + 6 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 - 6 * q^26 + 9 * q^29 - 3 * q^31 + 9 * q^34 - 6 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 - 30 * q^44 - 3 * q^47 - 6 * q^50 - 21 * q^52 - 12 * q^53 + 9 * q^58 + 3 * q^59 + 6 * q^61 - 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 6 * q^68 - 18 * q^71 + 42 * q^73 - 30 * q^74 + 15 * q^76 + 21 * q^79 - 30 * q^80 + 18 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 + 24 * q^89 + 3 * q^92 - 18 * q^94 - 12 * q^95 - 3 * q^97

Introduction

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