LMFDB - Embedded newform 1323.2.h.b.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.3
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1323.226
Dual form			1323.2.h.b.802.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.879385 q^{2} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +O(q^{10})$	\(q+0.879385 q^{2} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +(-0.592396 - 1.02606i) q^{10} +(0.826352 - 1.43128i) q^{11} +(-1.68479 + 2.91815i) q^{13} -0.0418891 q^{16} +(-0.233956 - 0.405223i) q^{17} +(-1.61334 + 2.79439i) q^{19} +(0.826352 + 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(4.47178 + 7.74535i) q^{23} +(1.59240 - 2.75811i) q^{25} +(-1.48158 + 2.56617i) q^{26} +(3.13429 + 5.42874i) q^{29} -9.23442 q^{31} +5.63816 q^{32} +(-0.205737 - 0.356347i) q^{34} +(-4.61721 + 7.99724i) q^{37} +(-1.41875 + 2.45734i) q^{38} +(1.91147 + 3.31077i) q^{40} +(-1.70574 + 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(-1.01367 + 1.75573i) q^{44} +(3.93242 + 6.81115i) q^{46} +9.35504 q^{47} +(1.40033 - 2.42544i) q^{50} +(2.06670 - 3.57964i) q^{52} +(-0.286989 - 0.497079i) q^{53} -2.22668 q^{55} +(2.75624 + 4.77396i) q^{58} -10.3969 q^{59} -7.63816 q^{61} -8.12061 q^{62} +5.04189 q^{64} +4.53983 q^{65} +0.596267 q^{67} +(0.286989 + 0.497079i) q^{68} +0.554378 q^{71} +(1.02481 + 1.77503i) q^{73} +(-4.06031 + 7.03266i) q^{74} +(1.97906 - 3.42782i) q^{76} -2.40373 q^{79} +(0.0282185 + 0.0488759i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(1.93969 + 3.35965i) q^{86} +(-2.34477 + 4.06126i) q^{88} +(-4.54323 + 7.86911i) q^{89} +(-5.48545 - 9.50108i) q^{92} +8.22668 q^{94} +4.34730 q^{95} +(-0.949493 - 1.64457i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^5 - 12 * q^8	$ 6 q - 6 q^{2} + 6 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 3 q^{26} + 9 q^{29} + 6 q^{31} + 9 q^{34} + 3 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} + 15 q^{44} + 6 q^{47} - 6 q^{50} - 21 q^{52} + 6 q^{53} + 9 q^{58} - 6 q^{59} - 12 q^{61} - 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} - 6 q^{68} - 18 q^{71} - 21 q^{73} - 30 q^{74} + 15 q^{76} - 42 q^{79} + 15 q^{80} - 9 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} - 12 q^{89} + 3 q^{92} + 36 q^{94} + 24 q^{95} - 3 q^{97}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 3 * q^26 + 9 * q^29 + 6 * q^31 + 9 * q^34 + 3 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 + 15 * q^44 + 6 * q^47 - 6 * q^50 - 21 * q^52 + 6 * q^53 + 9 * q^58 - 6 * q^59 - 12 * q^61 - 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 - 6 * q^68 - 18 * q^71 - 21 * q^73 - 30 * q^74 + 15 * q^76 - 42 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 12 * q^89 + 3 * q^92 + 36 * q^94 + 24 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.879385			0.621819			0.310910	−	0.950439i	$-0.399366\pi$
$2$	0.879385			0.621819			0.310910	+	0.950439i	$0.399366\pi$
$3$		0			0
$3$		0			0
$4$	−1.22668			−0.613341
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	0.675158	−	0.737673i	$-0.264075\pi$
$5$	−0.673648	−	1.16679i	−0.301265	−	0.521806i	−0.976423	+	0.215867i	$0.930742\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.83750			−1.00321
$9$		0			0
$10$	−0.592396	−	1.02606i	−0.187332	−	0.324469i
$11$	0.826352	−	1.43128i	0.249154	−	0.431548i	−0.714137	−	0.700006i	$-0.753181\pi$
$11$	0.826352	−	1.43128i	0.249154	−	0.431548i	0.963291	+	0.268458i	$0.0865140\pi$
$12$		0			0
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	−0.999301	−	0.0373813i	$-0.988098\pi$
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	0.532024	+	0.846729i	$0.321432\pi$
$14$		0			0
$15$		0			0
$16$	−0.0418891			−0.0104723
$17$	−0.233956	−	0.405223i	−0.0567426	−	0.0982810i	0.836259	−	0.548335i	$-0.184738\pi$
$17$	−0.233956	−	0.405223i	−0.0567426	−	0.0982810i	−0.893001	+	0.450054i	$0.851405\pi$
$18$		0			0
$19$	−1.61334	+	2.79439i	−0.370126	+	0.641077i	−0.989585	−	0.143953i	$-0.954019\pi$
$19$	−1.61334	+	2.79439i	−0.370126	+	0.641077i	0.619459	+	0.785029i	$0.287352\pi$
$20$	0.826352	+	1.43128i	0.184778	+	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	4.47178	+	7.74535i	0.932431	+	1.61502i	0.779152	+	0.626835i	$0.215650\pi$
$23$	4.47178	+	7.74535i	0.932431	+	1.61502i	0.153279	+	0.988183i	$0.451017\pi$
$24$		0			0
$25$	1.59240	−	2.75811i	0.318479	−	0.551622i
$26$	−1.48158	+	2.56617i	−0.290562	+	0.503268i
$27$		0			0
$28$		0			0
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	0.995239	+	0.0974595i	$0.0310717\pi$
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	−0.413217	+	0.910632i	$0.635595\pi$
$30$		0			0
$31$	−9.23442			−1.65855			−0.829276	−	0.558840i	$-0.811247\pi$
$31$	−9.23442			−1.65855			−0.829276	+	0.558840i	$0.811247\pi$
$32$	5.63816			0.996695
$33$		0			0
$34$	−0.205737	−	0.356347i	−0.0352836	−	0.0611130i
$35$		0			0
$36$		0			0
$37$	−4.61721	+	7.99724i	−0.759065	+	1.31474i	0.184263	+	0.982877i	$0.441010\pi$
$37$	−4.61721	+	7.99724i	−0.759065	+	1.31474i	−0.943328	+	0.331862i	$0.892323\pi$
$38$	−1.41875	+	2.45734i	−0.230151	+	0.398634i
$39$		0			0
$40$	1.91147	+	3.31077i	0.302231	+	0.523479i
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	−0.967927	−	0.251231i	$-0.919165\pi$
$41$	−1.70574	+	2.95442i	−0.266391	+	0.461403i	0.701536	+	0.712634i	$0.252498\pi$
$42$		0			0
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	−1.01367	+	1.75573i	−0.152817	+	0.264686i
$45$		0			0
$46$	3.93242	+	6.81115i	0.579803	+	1.00425i
$47$	9.35504			1.36457			0.682286	−	0.731085i	$-0.260986\pi$
$47$	9.35504			1.36457			0.682286	+	0.731085i	$0.260986\pi$
$48$		0			0
$49$		0			0
$50$	1.40033	−	2.42544i	0.198037	−	0.343009i
$51$		0			0
$52$	2.06670	−	3.57964i	0.286600	−	0.496406i
$53$	−0.286989	−	0.497079i	−0.0394210	−	0.0682791i	0.845642	−	0.533751i	$-0.179218\pi$
$53$	−0.286989	−	0.497079i	−0.0394210	−	0.0682791i	−0.885063	+	0.465472i	$0.845885\pi$
$54$		0			0
$55$	−2.22668			−0.300246
$56$		0			0
$57$		0			0
$58$	2.75624	+	4.77396i	0.361913	+	0.626851i
$59$	−10.3969			−1.35356			−0.676782	−	0.736183i	$-0.736626\pi$
$59$	−10.3969			−1.35356			−0.676782	+	0.736183i	$0.736626\pi$
$60$		0			0
$61$	−7.63816			−0.977966			−0.488983	−	0.872293i	$-0.662632\pi$
$61$	−7.63816			−0.977966			−0.488983	+	0.872293i	$0.662632\pi$
$62$	−8.12061			−1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	4.53983			0.563097
$66$		0			0
$67$	0.596267			0.0728456			0.0364228	−	0.999336i	$-0.488404\pi$
$67$	0.596267			0.0728456			0.0364228	+	0.999336i	$0.488404\pi$
$68$	0.286989	+	0.497079i	0.0348025	+	0.0602797i
$69$		0			0
$70$		0			0
$71$	0.554378			0.0657925			0.0328963	−	0.999459i	$-0.489527\pi$
$71$	0.554378			0.0657925			0.0328963	+	0.999459i	$0.489527\pi$
$72$		0			0
$73$	1.02481	+	1.77503i	0.119946	+	0.207752i	0.919746	−	0.392514i	$-0.128395\pi$
$73$	1.02481	+	1.77503i	0.119946	+	0.207752i	−0.799800	+	0.600266i	$0.795061\pi$
$74$	−4.06031	+	7.03266i	−0.472001	+	0.817530i
$75$		0			0
$76$	1.97906	−	3.42782i	0.227013	−	0.393198i
$77$		0			0
$78$		0			0
$79$	−2.40373			−0.270441			−0.135221	−	0.990816i	$-0.543174\pi$
$79$	−2.40373			−0.270441			−0.135221	+	0.990816i	$0.543174\pi$
$80$	0.0282185	+	0.0488759i	0.00315492	+	0.00546449i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	0.901187	+	0.433431i	$0.142697\pi$
$83$	7.52481	+	13.0334i	0.825956	+	1.43060i	−0.0752309	+	0.997166i	$0.523969\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	1.93969	+	3.35965i	0.209162	+	0.362280i
$87$		0			0
$88$	−2.34477	+	4.06126i	−0.249953	+	0.432932i
$89$	−4.54323	+	7.86911i	−0.481582	+	0.834124i	−0.999777	−	0.0211385i	$-0.993271\pi$
$89$	−4.54323	+	7.86911i	−0.481582	+	0.834124i	0.518195	+	0.855263i	$0.326604\pi$
$90$		0			0
$91$		0			0
$92$	−5.48545	−	9.50108i	−0.571898	−	0.990556i
$93$		0			0
$94$	8.22668			0.848517
$95$	4.34730			0.446023
$96$		0			0
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	0.813788	−	0.581161i	$-0.197402\pi$
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	−0.910195	+	0.414181i	$0.864068\pi$
$98$		0			0
$99$		0			0
$100$	−1.95336	+	3.38332i	−0.195336	+	0.338332i
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	−0.820372	−	0.571830i	$-0.806234\pi$
$101$	0.854570	−	1.48016i	0.0850329	−	0.147281i	0.905405	+	0.424548i	$0.139567\pi$
$102$		0			0
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	0.762381	−	0.647128i	$-0.224030\pi$
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	−0.941620	+	0.336677i	$0.890697\pi$
$104$	4.78059	−	8.28023i	0.468776	−	0.811943i
$105$		0			0
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	3.56418	−	6.17334i	0.344562	−	0.596799i	−0.640712	−	0.767781i	$-0.721361\pi$
$107$	3.56418	−	6.17334i	0.344562	−	0.596799i	0.985274	+	0.170982i	$0.0546941\pi$
$108$		0			0
$109$	−0.201867	−	0.349643i	−0.0193353	−	0.0334898i	0.856196	−	0.516651i	$-0.172822\pi$
$109$	−0.201867	−	0.349643i	−0.0193353	−	0.0334898i	−0.875531	+	0.483162i	$0.839488\pi$
$110$	−1.95811			−0.186699
$111$		0			0
$112$		0			0
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	−0.300320	−	0.953839i	$-0.597093\pi$
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	0.976208	−	0.216835i	$-0.0695732\pi$
$114$		0			0
$115$	6.02481	−	10.4353i	0.561817	−	0.973095i
$116$	−3.84477	−	6.65934i	−0.356978	−	0.618304i
$117$		0			0
$118$	−9.14290			−0.841672
$119$		0			0
$120$		0			0
$121$	4.13429	+	7.16079i	0.375844	+	0.650981i
$122$	−6.71688			−0.608118
$123$		0			0
$124$	11.3277			1.01726
$125$	−11.0273			−0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	−6.84255			−0.604802
$129$		0			0
$130$	3.99226			0.350144
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	0.979013	−	0.203797i	$-0.0653284\pi$
$131$	3.58260	+	6.20524i	0.313013	+	0.542154i	−0.666000	+	0.745952i	$0.731995\pi$
$132$		0			0
$133$		0			0
$134$	0.524348			0.0452968
$135$		0			0
$136$	0.663848	+	1.14982i	0.0569245	+	0.0985961i
$137$	1.28446	−	2.22475i	0.109739	−	0.190074i	−0.805925	−	0.592017i	$-0.798332\pi$
$137$	1.28446	−	2.22475i	0.109739	−	0.190074i	0.915665	+	0.401943i	$0.131665\pi$
$138$		0			0
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$		0			0
$142$	0.487511			0.0409111
$143$	2.78446	+	4.82283i	0.232848	+	0.403305i
$144$		0			0
$145$	4.22281	−	7.31412i	0.350685	−	0.607405i
$146$	0.901207	+	1.56094i	0.0745844	+	0.129184i
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	0.215537	+	0.373321i	0.0176575	+	0.0305837i	0.874719	−	0.484630i	$-0.161046\pi$
$149$	0.215537	+	0.373321i	0.0176575	+	0.0305837i	−0.857062	+	0.515214i	$0.827712\pi$
$150$		0			0
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	−0.811375	−	0.584526i	$-0.801280\pi$
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	0.911902	+	0.410408i	$0.134614\pi$
$152$	4.57785	−	7.92907i	0.371313	−	0.643132i
$153$		0			0
$154$		0			0
$155$	6.22075	+	10.7747i	0.499663	+	0.865441i
$156$		0			0
$157$	−10.1334			−0.808734			−0.404367	−	0.914597i	$-0.632508\pi$
$157$	−10.1334			−0.808734			−0.404367	+	0.914597i	$0.632508\pi$
$158$	−2.11381			−0.168166
$159$		0			0
$160$	−3.79813	−	6.57856i	−0.300269	−	0.520081i
$161$		0			0
$162$		0			0
$163$	1.29813	−	2.24843i	0.101678	−	0.176111i	−0.810698	−	0.585464i	$-0.800912\pi$
$163$	1.29813	−	2.24843i	0.101678	−	0.176111i	0.912376	+	0.409353i	$0.134246\pi$
$164$	2.09240	−	3.62414i	0.163389	−	0.282998i
$165$		0			0
$166$	6.61721	+	11.4613i	0.513595	+	0.889573i
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.0656422	−	0.997843i	$-0.479090\pi$
$167$	11.5915	−	20.0771i	0.896979	−	1.55361i	0.831337	−	0.555769i	$-0.187576\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	−0.277189	+	0.480105i	−0.0212594	+	0.0368224i
$171$		0			0
$172$	−2.70574	−	4.68647i	−0.206311	−	0.357340i
$173$	−4.75196			−0.361285			−0.180643	−	0.983549i	$-0.557818\pi$
$173$	−4.75196			−0.361285			−0.180643	+	0.983549i	$0.557818\pi$
$174$		0			0
$175$		0			0
$176$	−0.0346151	+	0.0599551i	−0.00260921	+	0.00451929i
$177$		0			0
$178$	−3.99525	+	6.91998i	−0.299457	+	0.518674i
$179$	−4.26604	−	7.38901i	−0.318859	−	0.552280i	0.661391	−	0.750041i	$-0.269966\pi$
$179$	−4.26604	−	7.38901i	−0.318859	−	0.552280i	−0.980250	+	0.197761i	$0.936633\pi$
$180$		0			0
$181$	17.2344			1.28102			0.640512	−	0.767948i	$-0.278722\pi$
$181$	17.2344			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$182$		0			0
$183$		0			0
$184$	−12.6887	−	21.9774i	−0.935421	−	1.62020i
$185$	12.4415			0.914718
$186$		0			0
$187$	−0.773318			−0.0565506
$188$	−11.4757			−0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	−12.9094			−0.934092			−0.467046	−	0.884233i	$-0.654682\pi$
$191$	−12.9094			−0.934092			−0.467046	+	0.884233i	$0.654682\pi$
$192$		0			0
$193$	−0.638156			−0.0459355			−0.0229677	−	0.999736i	$-0.507311\pi$
$193$	−0.638156			−0.0459355			−0.0229677	+	0.999736i	$0.507311\pi$
$194$	−0.834970	−	1.44621i	−0.0599473	−	0.103832i
$195$		0			0
$196$		0			0
$197$	−11.4456			−0.815467			−0.407733	−	0.913101i	$-0.633681\pi$
$197$	−11.4456			−0.815467			−0.407733	+	0.913101i	$0.633681\pi$
$198$		0			0
$199$	−1.81908	−	3.15074i	−0.128951	−	0.223350i	0.794319	−	0.607500i	$-0.207828\pi$
$199$	−1.81908	−	3.15074i	−0.128951	−	0.223350i	−0.923270	+	0.384151i	$0.874494\pi$
$200$	−4.51842	+	7.82613i	−0.319500	+	0.553391i
$201$		0			0
$202$	0.751497	−	1.30163i	0.0528751	−	0.0915824i
$203$		0			0
$204$		0			0
$205$	4.59627			0.321017
$206$	−1.59967	−	2.77071i	−0.111454	−	0.193045i
$207$		0			0
$208$	0.0705744	−	0.122238i	0.00489345	−	0.00847571i
$209$	2.66637	+	4.61830i	0.184437	+	0.319454i
$210$		0			0
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	0.352044	+	0.609758i	0.0241785	+	0.0418784i
$213$		0			0
$214$	3.13429	−	5.42874i	0.214255	−	0.371101i
$215$	2.97178	−	5.14728i	0.202674	−	0.351041i
$216$		0			0
$217$		0			0
$218$	−0.177519	−	0.307471i	−0.0120231	−	0.0208246i
$219$		0			0
$220$	2.73143			0.184153
$221$	1.57667			0.106058
$222$		0			0
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	0.959905	−	0.280327i	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$		0			0
$226$	6.31820	−	10.9434i	0.420280	−	0.727947i
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	−0.596913	−	0.802306i	$-0.703606\pi$
$227$	5.97178	−	10.3434i	0.396361	−	0.686517i	0.993274	+	0.115789i	$0.0369395\pi$
$228$		0			0
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	−0.995484	−	0.0949315i	$-0.969737\pi$
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	0.415529	−	0.909580i	$-0.363597\pi$
$230$	5.29813	−	9.17664i	0.349349	−	0.605089i
$231$		0			0
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	8.12701	−	14.0764i	0.532418	−	0.922175i	−0.466865	−	0.884328i	$-0.654617\pi$
$233$	8.12701	−	14.0764i	0.532418	−	0.922175i	0.999284	−	0.0378470i	$-0.0120499\pi$
$234$		0			0
$235$	−6.30200	−	10.9154i	−0.411097	−	0.712042i
$236$	12.7537			0.830196
$237$		0			0
$238$		0			0
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	−0.999910	−	0.0134062i	$-0.995733\pi$
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	0.511565	+	0.859244i	$0.329066\pi$
$240$		0			0
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	0.496320	+	0.868140i	$0.334684\pi$
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	−0.999991	+	0.00424420i	$0.998649\pi$
$242$	3.63563	+	6.29710i	0.233707	+	0.404793i
$243$		0			0
$244$	9.36959			0.599826
$245$		0			0
$246$		0			0
$247$	−5.43629	−	9.41593i	−0.345903	−	0.599121i
$248$	26.2026			1.66387
$249$		0			0
$250$	−9.69728			−0.613310
$251$	19.0651			1.20338			0.601690	−	0.798730i	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	−18.2662			−1.14612
$255$		0			0
$256$	−16.1010			−1.00631
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	−0.898776	−	0.438409i	$-0.855542\pi$
$257$	−13.2909	−	23.0204i	−0.829061	−	1.43598i	0.0697146	−	0.997567i	$-0.477791\pi$
$258$		0			0
$259$		0			0
$260$	−5.56893			−0.345370
$261$		0			0
$262$	3.15048	+	5.45680i	0.194637	+	0.337122i
$263$	−0.367059	+	0.635765i	−0.0226338	+	0.0392029i	−0.877120	−	0.480270i	$-0.840539\pi$
$263$	−0.367059	+	0.635765i	−0.0226338	+	0.0392029i	0.854487	+	0.519473i	$0.173872\pi$
$264$		0			0
$265$	−0.386659	+	0.669713i	−0.0237523	+	0.0411402i
$266$		0			0
$267$		0			0
$268$	−0.731429			−0.0446792
$269$	10.4251	+	18.0569i	0.635632	+	1.10095i	0.986381	+	0.164478i	$0.0525939\pi$
$269$	10.4251	+	18.0569i	0.635632	+	1.10095i	−0.350749	+	0.936470i	$0.614073\pi$
$270$		0			0
$271$	3.47906	−	6.02590i	0.211338	−	0.366047i	−0.740796	−	0.671730i	$-0.765551\pi$
$271$	3.47906	−	6.02590i	0.211338	−	0.366047i	0.952133	+	0.305683i	$0.0988847\pi$
$272$	0.00980018	+	0.0169744i	0.000594223	+	0.00102922i
$273$		0			0
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	−2.63176	−	4.55834i	−0.158701	−	0.274878i
$276$		0			0
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	0.462138	+	0.886808i	$0.347083\pi$
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	−0.999067	+	0.0431811i	$0.986251\pi$
$278$	−2.69681	+	4.67102i	−0.161744	+	0.280149i
$279$		0			0
$280$		0			0
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	0.979159	+	0.203095i	$0.0651001\pi$
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	−0.313694	+	0.949524i	$0.601567\pi$
$282$		0			0
$283$	18.5945			1.10533			0.552665	−	0.833404i	$-0.313611\pi$
$283$	18.5945			1.10533			0.552665	+	0.833404i	$0.313611\pi$
$284$	−0.680045			−0.0403532
$285$		0			0
$286$	2.44862	+	4.24113i	0.144790	+	0.250783i
$287$		0			0
$288$		0			0
$289$	8.39053	−	14.5328i	0.493561	−	0.854872i
$290$	3.71348	−	6.43193i	0.218063	−	0.377696i
$291$		0			0
$292$	−1.25712	−	2.17740i	−0.0735675	−	0.127423i
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	−0.991406	−	0.130822i	$-0.958238\pi$
$293$	−6.54576	+	11.3376i	−0.382407	+	0.662349i	0.608998	+	0.793171i	$0.291572\pi$
$294$		0			0
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	13.1013	−	22.6922i	0.761499	−	1.31895i
$297$		0			0
$298$	0.189540	+	0.328293i	0.0109798	+	0.0190175i
$299$	−30.1361			−1.74282
$300$		0			0
$301$		0			0
$302$	1.08630	−	1.88153i	0.0625098	−	0.108270i
$303$		0			0
$304$	0.0675813	−	0.117054i	0.00387606	−	0.00671353i
$305$	5.14543	+	8.91215i	0.294626	+	0.510308i
$306$		0			0
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$		0			0
$310$	5.47044	+	9.47508i	0.310700	+	0.538148i
$311$	−9.52435			−0.540076			−0.270038	−	0.962850i	$-0.587036\pi$
$311$	−9.52435			−0.540076			−0.270038	+	0.962850i	$0.587036\pi$
$312$		0			0
$313$	17.6287			0.996431			0.498215	−	0.867053i	$-0.333989\pi$
$313$	17.6287			0.996431			0.498215	+	0.867053i	$0.333989\pi$
$314$	−8.91117			−0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	−8.07697			−0.453648			−0.226824	−	0.973936i	$-0.572834\pi$
$317$	−8.07697			−0.453648			−0.226824	+	0.973936i	$0.572834\pi$
$318$		0			0
$319$	10.3601			0.580054
$320$	−3.39646	−	5.88284i	−0.189868	−	0.328861i
$321$		0			0
$322$		0			0
$323$	1.50980			0.0840075
$324$		0			0
$325$	5.36571	+	9.29369i	0.297636	+	0.515521i
$326$	1.14156	−	1.97724i	0.0632251	−	0.109509i
$327$		0			0
$328$	4.84002	−	8.38316i	0.267246	−	0.462883i
$329$		0			0
$330$		0			0
$331$	23.0496			1.26692			0.633461	−	0.773775i	$-0.281634\pi$
$331$	23.0496			1.26692			0.633461	+	0.773775i	$0.281634\pi$
$332$	−9.23055	−	15.9878i	−0.506592	−	0.877444i
$333$		0			0
$334$	10.1934	−	17.6555i	0.557759	−	0.966066i
$335$	−0.401674	−	0.695720i	−0.0219458	−	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	0.723689	+	1.25347i	0.0393635	+	0.0681795i
$339$		0			0
$340$	0.386659	−	0.669713i	0.0209695	−	0.0363203i
$341$	−7.63088	+	13.2171i	−0.413235	+	0.715745i
$342$		0			0
$343$		0			0
$344$	−6.25877	−	10.8405i	−0.337450	−	0.584481i
$345$		0			0
$346$	−4.17881			−0.224654
$347$	−12.9463			−0.694991			−0.347496	−	0.937682i	$-0.612968\pi$
$347$	−12.9463			−0.694991			−0.347496	+	0.937682i	$0.612968\pi$
$348$		0			0
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	0.884938	−	0.465710i	$-0.154201\pi$
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	−0.845785	+	0.533524i	$0.820868\pi$
$350$		0			0
$351$		0			0
$352$	4.65910	−	8.06980i	0.248331	−	0.430122i
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	−0.991267	−	0.131873i	$-0.957901\pi$
$353$	−7.16637	+	12.4125i	−0.381428	+	0.660652i	0.609839	+	0.792525i	$0.291234\pi$
$354$		0			0
$355$	−0.373455	−	0.646844i	−0.0198210	−	0.0343309i
$356$	5.57310	−	9.65289i	0.295374	−	0.511602i
$357$		0			0
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	−10.4684	+	18.1318i	−0.552500	+	0.956958i	0.445593	+	0.895235i	$0.352993\pi$
$359$	−10.4684	+	18.1318i	−0.552500	+	0.956958i	−0.998093	+	0.0617224i	$0.980341\pi$
$360$		0			0
$361$	4.29426	+	7.43788i	0.226014	+	0.391467i
$362$	15.1557			0.796566
$363$		0			0
$364$		0			0
$365$	1.38073	−	2.39149i	0.0722707	−	0.125176i
$366$		0			0
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	−0.979373	−	0.202063i	$-0.935236\pi$
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	0.664678	+	0.747130i	$0.268569\pi$
$368$	−0.187319	−	0.324446i	−0.00976466	−	0.0169129i
$369$		0			0
$370$	10.9409			0.568789
$371$		0			0
$372$		0			0
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	0.875959	−	0.482386i	$-0.160230\pi$
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	−0.855738	+	0.517410i	$0.826896\pi$
$374$	−0.680045			−0.0351643
$375$		0			0
$376$	−26.5449			−1.36895
$377$	−21.1225			−1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	−5.33275			−0.273564
$381$		0			0
$382$	−11.3523			−0.580837
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	0.750182	−	0.661232i	$-0.229966\pi$
$383$	−3.86618	−	6.69642i	−0.197553	−	0.342171i	−0.947734	+	0.319061i	$0.896633\pi$
$384$		0			0
$385$		0			0
$386$	−0.561185			−0.0285636
$387$		0			0
$388$	1.16473	+	2.01736i	0.0591300	+	0.102416i
$389$	2.69981	−	4.67620i	0.136886	−	0.237093i	−0.789431	−	0.613840i	$-0.789624\pi$
$389$	2.69981	−	4.67620i	0.136886	−	0.237093i	0.926316	+	0.376747i	$0.122957\pi$
$390$		0			0
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$		0			0
$394$	−10.0651			−0.507073
$395$	1.61927	+	2.80466i	0.0814743	+	0.141118i
$396$		0			0
$397$	−14.6172	+	25.3178i	−0.733617	+	1.27066i	0.221711	+	0.975112i	$0.428836\pi$
$397$	−14.6172	+	25.3178i	−0.733617	+	1.27066i	−0.955328	+	0.295549i	$0.904497\pi$
$398$	−1.59967	−	2.77071i	−0.0801842	−	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	−13.6989	−	23.7272i	−0.684092	−	1.18488i	−0.973721	−	0.227743i	$-0.926865\pi$
$401$	−13.6989	−	23.7272i	−0.684092	−	1.18488i	0.289629	−	0.957139i	$-0.406468\pi$
$402$		0			0
$403$	15.5581	−	26.9474i	0.775003	−	1.34235i
$404$	−1.04829	+	1.81568i	−0.0521542	+	0.0903337i
$405$		0			0
$406$		0			0
$407$	7.63088	+	13.2171i	0.378249	+	0.655146i
$408$		0			0
$409$	9.02498			0.446256			0.223128	−	0.974789i	$-0.428373\pi$
$409$	9.02498			0.446256			0.223128	+	0.974789i	$0.428373\pi$
$410$	4.04189			0.199615
$411$		0			0
$412$	2.23143	+	3.86495i	0.109935	+	0.190412i
$413$		0			0
$414$		0			0
$415$	10.1382	−	17.5598i	0.497662	−	0.861977i
$416$	−9.49912	+	16.4530i	−0.465733	+	0.806673i
$417$		0			0
$418$	2.34477	+	4.06126i	0.114686	+	0.198643i
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	−0.868158	−	0.496287i	$-0.834696\pi$
$419$	−0.0876485	+	0.151812i	−0.00428191	+	0.00741649i	0.863877	+	0.503704i	$0.168030\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	−2.56031	+	4.43458i	−0.124634	+	0.215872i
$423$		0			0
$424$	0.814330	+	1.41046i	0.0395474	+	0.0684980i
$425$	−1.49020			−0.0722853
$426$		0			0
$427$		0			0
$428$	−4.37211	+	7.57272i	−0.211334	+	0.366041i
$429$		0			0
$430$	2.61334	−	4.52644i	0.126026	−	0.218284i
$431$	−14.6596	−	25.3911i	−0.706126	−	1.22305i	−0.966283	−	0.257481i	$-0.917108\pi$
$431$	−14.6596	−	25.3911i	−0.706126	−	1.22305i	0.260157	−	0.965566i	$-0.416226\pi$
$432$		0			0
$433$	−19.6554			−0.944578			−0.472289	−	0.881444i	$-0.656572\pi$
$433$	−19.6554			−0.944578			−0.472289	+	0.881444i	$0.656572\pi$
$434$		0			0
$435$		0			0
$436$	0.247626	+	0.428901i	0.0118591	+	0.0205406i
$437$	−28.8580			−1.38047
$438$		0			0
$439$	21.9299			1.04666			0.523330	−	0.852130i	$-0.324690\pi$
$439$	21.9299			1.04666			0.523330	+	0.852130i	$0.324690\pi$
$440$	6.31820			0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	18.7101			0.888942			0.444471	−	0.895793i	$-0.353392\pi$
$443$	18.7101			0.888942			0.444471	+	0.895793i	$0.353392\pi$
$444$		0			0
$445$	12.2422			0.580334
$446$	3.11468	+	5.39479i	0.147485	+	0.255451i
$447$		0			0
$448$		0			0
$449$	−6.68004			−0.315251			−0.157625	−	0.987499i	$-0.550384\pi$
$449$	−6.68004			−0.315251			−0.157625	+	0.987499i	$0.550384\pi$
$450$		0			0
$451$	2.81908	+	4.88279i	0.132745	+	0.229921i
$452$	−8.81345	+	15.2653i	−0.414550	+	0.718022i
$453$		0			0
$454$	5.25150	−	9.09586i	0.246465	−	0.426890i
$455$		0			0
$456$		0			0
$457$	−19.4287			−0.908837			−0.454418	−	0.890788i	$-0.650153\pi$
$457$	−19.4287			−0.908837			−0.454418	+	0.890788i	$0.650153\pi$
$458$	−7.71776	−	13.3676i	−0.360627	−	0.624625i
$459$		0			0
$460$	−7.39053	+	12.8008i	−0.344585	+	0.596839i
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	0.877052	−	0.480395i	$-0.159507\pi$
$461$	0.482926	+	0.836452i	0.0224921	+	0.0389575i	−0.854560	+	0.519352i	$0.826173\pi$
$462$		0			0
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	−0.131292	−	0.227405i	−0.00609509	−	0.0105570i
$465$		0			0
$466$	7.14677	−	12.3786i	0.331068	−	0.573426i
$467$	17.1074	−	29.6309i	0.791637	−	1.37115i	−0.133317	−	0.991074i	$-0.542563\pi$
$467$	17.1074	−	29.6309i	0.791637	−	1.37115i	0.924953	−	0.380081i	$-0.124104\pi$
$468$		0			0
$469$		0			0
$470$	−5.54189	−	9.59883i	−0.255628	−	0.442761i
$471$		0			0
$472$	29.5012			1.35790
$473$	7.29086			0.335234
$474$		0			0
$475$	5.13816	+	8.89955i	0.235755	+	0.408339i
$476$		0			0
$477$		0			0
$478$	−6.63903	+	11.4991i	−0.303662	+	0.525959i
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	−0.502125	−	0.864795i	$-0.667448\pi$
$479$	10.8965	−	18.8732i	0.497872	−	0.862339i	0.999997	+	0.00245553i	$0.000781622\pi$
$480$		0			0
$481$	−15.5581	−	26.9474i	−0.709388	−	1.22870i
$482$	−6.87598	+	11.9095i	−0.313192	+	0.542465i
$483$		0			0
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	−1.27925	+	2.21572i	−0.0580877	+	0.100611i
$486$		0			0
$487$	−9.69640	−	16.7947i	−0.439386	−	0.761039i	0.558256	−	0.829669i	$-0.311471\pi$
$487$	−9.69640	−	16.7947i	−0.439386	−	0.761039i	−0.997642	+	0.0686297i	$0.978137\pi$
$488$	21.6732			0.981101
$489$		0			0
$490$		0			0
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	−0.403987	−	0.914765i	$-0.632376\pi$
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	0.994203	−	0.107519i	$-0.0342908\pi$
$492$		0			0
$493$	1.46657	−	2.54017i	0.0660509	−	0.114403i
$494$	−4.78059	−	8.28023i	−0.215089	−	0.372545i
$495$		0			0
$496$	0.386821			0.0173688
$497$		0			0
$498$		0			0
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	0.980510	−	0.196470i	$-0.0629479\pi$
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	−0.660403	+	0.750911i	$0.729615\pi$
$500$	13.5270			0.604947
$501$		0			0
$502$	16.7656			0.748284
$503$	18.7033			0.833937			0.416969	−	0.908921i	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	12.9982			0.577842
$507$		0			0
$508$	25.4801			1.13050
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	0.996807	+	0.0798442i	$0.0254423\pi$
$509$	12.8045	+	22.1781i	0.567551	+	0.983027i	−0.429257	+	0.903183i	$0.641224\pi$
$510$		0			0
$511$		0			0
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	−11.6878	−	20.2438i	−0.515526	−	0.892917i
$515$	−2.45084	+	4.24497i	−0.107997	+	0.187056i
$516$		0			0
$517$	7.73055	−	13.3897i	0.339989	−	0.588879i
$518$		0			0
$519$		0			0
$520$	−12.8817			−0.564902
$521$	10.6061	+	18.3702i	0.464660	+	0.804815i	0.999186	−	0.0403370i	$-0.0128431\pi$
$521$	10.6061	+	18.3702i	0.464660	+	0.804815i	−0.534526	+	0.845152i	$0.679510\pi$
$522$		0			0
$523$	10.4029	−	18.0183i	0.454885	−	0.787884i	−0.543796	−	0.839217i	$-0.683014\pi$
$523$	10.4029	−	18.0183i	0.454885	−	0.787884i	0.998682	+	0.0513330i	$0.0163470\pi$
$524$	−4.39470	−	7.61185i	−0.191984	−	0.332525i
$525$		0			0
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	2.16044	+	3.74200i	0.0941104	+	0.163004i
$528$		0			0
$529$	−28.4937	+	49.3525i	−1.23885	+	2.14576i
$530$	−0.340022	+	0.588936i	−0.0147696	+	0.0255817i
$531$		0			0
$532$		0			0
$533$	−5.74763	−	9.95518i	−0.248957	−	0.431207i
$534$		0			0
$535$	−9.60401			−0.415217
$536$	−1.69190			−0.0730791
$537$		0			0
$538$	9.16772	+	15.8790i	0.395248	+	0.684590i
$539$		0			0
$540$		0			0
$541$	−13.3648	+	23.1486i	−0.574599	+	0.995235i	0.421486	+	0.906835i	$0.361509\pi$
$541$	−13.3648	+	23.1486i	−0.574599	+	0.995235i	−0.996085	+	0.0884001i	$0.971825\pi$
$542$	3.05943	−	5.29909i	0.131414	−	0.227615i
$543$		0			0
$544$	−1.31908	−	2.28471i	−0.0565550	−	0.0979561i
$545$	−0.271974	+	0.471073i	−0.0116501	+	0.0201786i
$546$		0			0
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	−1.57563	+	2.72907i	−0.0673074	+	0.116580i
$549$		0			0
$550$	−2.31433	−	4.00854i	−0.0986834	−	0.170925i
$551$	−20.2267			−0.861686
$552$		0			0
$553$		0			0
$554$	−7.85844	+	13.6112i	−0.333873	+	0.578285i
$555$		0			0
$556$	3.76187	−	6.51575i	0.159539	−	0.276329i
$557$	16.1694	+	28.0062i	0.685118	+	1.18666i	0.973400	+	0.229114i	$0.0735827\pi$
$557$	16.1694	+	28.0062i	0.685118	+	1.18666i	−0.288282	+	0.957546i	$0.593084\pi$
$558$		0			0
$559$	−14.8648			−0.628716
$560$		0			0
$561$		0			0
$562$	9.80974	+	16.9910i	0.413799	+	0.716721i
$563$	−17.7419			−0.747730			−0.373865	−	0.927483i	$-0.621968\pi$
$563$	−17.7419			−0.747730			−0.373865	+	0.927483i	$0.621968\pi$
$564$		0			0
$565$	−19.3601			−0.814485
$566$	16.3517			0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	26.6013			1.11519			0.557593	−	0.830115i	$-0.311725\pi$
$569$	26.6013			1.11519			0.557593	+	0.830115i	$0.311725\pi$
$570$		0			0
$571$	−10.0172			−0.419208			−0.209604	−	0.977786i	$-0.567218\pi$
$571$	−10.0172			−0.419208			−0.209604	+	0.977786i	$0.567218\pi$
$572$	−3.41565	−	5.91608i	−0.142815	−	0.247364i
$573$		0			0
$574$		0			0
$575$	28.4834			1.18784
$576$		0			0
$577$	−16.4572	−	28.5048i	−0.685124	−	1.18667i	−0.973398	−	0.229121i	$-0.926415\pi$
$577$	−16.4572	−	28.5048i	−0.685124	−	1.18667i	0.288274	−	0.957548i	$-0.406918\pi$
$578$	7.37851	−	12.7800i	0.306905	−	0.531576i
$579$		0			0
$580$	−5.18004	+	8.97210i	−0.215090	+	0.372546i
$581$		0			0
$582$		0			0
$583$	−0.948615			−0.0392876
$584$	−2.90791	−	5.03665i	−0.120330	−	0.208418i
$585$		0			0
$586$	−5.75624	+	9.97011i	−0.237788	+	0.411861i
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	0.978592	−	0.205808i	$-0.0659821\pi$
$587$	7.53643	+	13.0535i	0.311062	+	0.538774i	−0.667531	+	0.744582i	$0.732649\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	6.15910	+	10.6679i	0.253566	+	0.439189i
$591$		0			0
$592$	0.193411	−	0.334997i	0.00794913	−	0.0137683i
$593$	−20.5005	+	35.5079i	−0.841853	+	1.45813i	0.0464729	+	0.998920i	$0.485202\pi$
$593$	−20.5005	+	35.5079i	−0.841853	+	1.45813i	−0.888326	+	0.459213i	$0.848131\pi$
$594$		0			0
$595$		0			0
$596$	−0.264396	−	0.457947i	−0.0108301	−	0.0187582i
$597$		0			0
$598$	−26.5012			−1.08372
$599$	−6.07367			−0.248164			−0.124082	−	0.992272i	$-0.539599\pi$
$599$	−6.07367			−0.248164			−0.124082	+	0.992272i	$0.539599\pi$
$600$		0			0
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	0.685110	−	0.728440i	$-0.259754\pi$
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	−0.973402	+	0.229102i	$0.926421\pi$
$602$		0			0
$603$		0			0
$604$	−1.51532	+	2.62461i	−0.0616575	+	0.106794i
$605$	5.57011	−	9.64771i	0.226457	−	0.392235i
$606$		0			0
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.773986	+	0.633203i	$0.218260\pi$
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.161377	+	0.986893i	$0.448406\pi$
$608$	−9.09627	+	15.7552i	−0.368902	+	0.638958i
$609$		0			0
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	−15.7613	+	27.2994i	−0.637634	+	1.10441i
$612$		0			0
$613$	13.2469	+	22.9443i	0.535038	+	0.926712i	0.999162	+	0.0409421i	$0.0130359\pi$
$613$	13.2469	+	22.9443i	0.535038	+	0.926712i	−0.464124	+	0.885770i	$0.653631\pi$
$614$	−5.54933			−0.223953
$615$		0			0
$616$		0			0
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	−0.887781	−	0.460266i	$-0.847754\pi$
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	0.842492	+	0.538708i	$0.181087\pi$
$618$		0			0
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	−0.797090	−	0.603861i	$-0.793628\pi$
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	0.921504	+	0.388369i	$0.126962\pi$
$620$	−7.63088	−	13.2171i	−0.306464	−	0.530811i
$621$		0			0
$622$	−8.37557			−0.335830
$623$		0			0
$624$		0			0
$625$	−0.533433	−	0.923933i	−0.0213373	−	0.0369573i
$626$	15.5024			0.619600
$627$		0			0
$628$	12.4305			0.496030
$629$	4.32089			0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	6.82058			0.271308
$633$		0			0
$634$	−7.10277			−0.282087
$635$	13.9927	+	24.2361i	0.555284	+	0.961781i
$636$		0			0
$637$		0			0
$638$	9.11051			0.360689
$639$		0			0
$640$	4.60947	+	7.98384i	0.182205	+	0.315589i
$641$	2.44444	−	4.23389i	0.0965496	−	0.167229i	−0.813705	−	0.581278i	$-0.802553\pi$
$641$	2.44444	−	4.23389i	0.0965496	−	0.167229i	0.910254	+	0.414050i	$0.135886\pi$
$642$		0			0
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$		0			0
$646$	1.32770			0.0522375
$647$	1.14038	+	1.97519i	0.0448329	+	0.0776528i	0.887571	−	0.460671i	$-0.152391\pi$
$647$	1.14038	+	1.97519i	0.0448329	+	0.0776528i	−0.842738	+	0.538324i	$0.819058\pi$
$648$		0			0
$649$	−8.59152	+	14.8809i	−0.337247	+	0.584128i
$650$	4.71853	+	8.17273i	0.185076	+	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	11.7396	+	20.3336i	0.459407	+	0.795717i	0.998930	−	0.0462542i	$-0.0147284\pi$
$653$	11.7396	+	20.3336i	0.459407	+	0.795717i	−0.539522	+	0.841971i	$0.681395\pi$
$654$		0			0
$655$	4.82682	−	8.36030i	0.188599	−	0.326664i
$656$	0.0714517	−	0.123758i	0.00278972	−	0.00483194i
$657$		0			0
$658$		0			0
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.776101	−	0.630609i	$-0.782805\pi$
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.158073	−	0.987427i	$-0.550528\pi$
$660$		0			0
$661$	−29.3090			−1.13999			−0.569995	−	0.821648i	$-0.693055\pi$
$661$	−29.3090			−1.13999			−0.569995	+	0.821648i	$0.693055\pi$
$662$	20.2695			0.787797
$663$		0			0
$664$	−21.3516	−	36.9821i	−0.828604	−	1.43518i
$665$		0			0
$666$		0			0
$667$	−28.0317	+	48.5523i	−1.08539	+	1.87995i
$668$	−14.2191	+	24.6282i	−0.550154	+	0.952894i
$669$		0			0
$670$	−0.353226	−	0.611806i	−0.0136463	−	0.0236361i
$671$	−6.31180	+	10.9324i	−0.243664	+	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	−12.7613	+	22.1032i	−0.491547	+	0.851384i
$675$		0			0
$676$	−1.00950	−	1.74850i	−0.0388267	−	0.0672499i
$677$	35.8907			1.37939			0.689697	−	0.724098i	$-0.257744\pi$
$677$	35.8907			1.37939			0.689697	+	0.724098i	$0.257744\pi$
$678$		0			0
$679$		0			0
$680$	0.894400	−	1.54915i	0.0342987	−	0.0594070i
$681$		0			0
$682$	−6.71048	+	11.6229i	−0.256958	+	0.445064i
$683$	17.5321	+	30.3665i	0.670847	+	1.16194i	0.977664	+	0.210172i	$0.0674025\pi$
$683$	17.5321	+	30.3665i	0.670847	+	1.16194i	−0.306818	+	0.951768i	$0.599264\pi$
$684$		0			0
$685$	−3.46110			−0.132242
$686$		0			0
$687$		0			0
$688$	−0.0923963	−	0.160035i	−0.00352257	−	0.00610128i
$689$	1.93407			0.0736821
$690$		0			0
$691$	−2.06687			−0.0786273			−0.0393136	−	0.999227i	$-0.512517\pi$
$691$	−2.06687			−0.0786273			−0.0393136	+	0.999227i	$0.512517\pi$
$692$	5.82915			0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	8.26352			0.313453
$696$		0			0
$697$	1.59627			0.0604629
$698$	0.643208	+	1.11407i	0.0243458	+	0.0421681i
$699$		0			0
$700$		0			0
$701$	7.36009			0.277987			0.138993	−	0.990293i	$-0.455613\pi$
$701$	7.36009			0.277987			0.138993	+	0.990293i	$0.455613\pi$
$702$		0			0
$703$	−14.8983	−	25.8046i	−0.561899	−	0.973237i
$704$	4.16637	−	7.21637i	0.157026	−	0.271977i
$705$		0			0
$706$	−6.30200	+	10.9154i	−0.237179	+	0.410806i
$707$		0			0
$708$		0			0
$709$	9.10876			0.342086			0.171043	−	0.985264i	$-0.445286\pi$
$709$	9.10876			0.342086			0.171043	+	0.985264i	$0.445286\pi$
$710$	−0.328411	−	0.568825i	−0.0123251	−	0.0213476i
$711$		0			0
$712$	12.8914	−	22.3286i	0.483126	−	0.836799i
$713$	−41.2943	−	71.5239i	−1.54648	−	2.67859i
$714$		0			0
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	5.23308	+	9.06396i	0.195569	+	0.338736i
$717$		0			0
$718$	−9.20574	+	15.9448i	−0.343555	+	0.595055i
$719$	12.9768	−	22.4765i	0.483954	−	0.838233i	−0.515876	−	0.856663i	$-0.672533\pi$
$719$	12.9768	−	22.4765i	0.483954	−	0.838233i	0.999830	+	0.0184300i	$0.00586678\pi$
$720$		0			0
$721$		0			0
$722$	3.77631	+	6.54076i	0.140540	+	0.243422i
$723$		0			0
$724$	−21.1411			−0.785705
$725$	19.9641			0.741448
$726$		0			0
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	0.756311	−	0.654213i	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$		0			0
$730$	1.21419	−	2.10304i	0.0449393	−	0.0778372i
$731$	1.03209	−	1.78763i	0.0381732	−	0.0661179i
$732$		0			0
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	0.947372	+	0.320135i	$0.103728\pi$
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	−0.196441	+	0.980516i	$0.562938\pi$
$734$	−5.30154	+	9.18253i	−0.195683	+	0.338933i
$735$		0			0
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	0.492726	−	0.853427i	0.0181498	−	0.0314364i
$738$		0			0
$739$	12.6809	+	21.9640i	0.466475	+	0.807959i	0.999267	−	0.0382877i	$-0.0121903\pi$
$739$	12.6809	+	21.9640i	0.466475	+	0.807959i	−0.532791	+	0.846247i	$0.678857\pi$
$740$	−15.2618			−0.561034
$741$		0			0
$742$		0			0
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	−0.995076	−	0.0991184i	$-0.968398\pi$
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	0.583377	+	0.812202i	$0.301731\pi$
$744$		0			0
$745$	0.290393	−	0.502975i	0.0106392	−	0.0184276i
$746$	0.343426	+	0.594831i	0.0125737	+	0.0217783i
$747$		0			0
$748$	0.948615			0.0346848
$749$		0			0
$750$		0			0
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	0.555978	−	0.831197i	$-0.312344\pi$
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	−0.997827	+	0.0658924i	$0.979011\pi$
$752$	−0.391874			−0.0142902
$753$		0			0
$754$	−18.5748			−0.676454
$755$	−3.32863			−0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	−6.08883			−0.221156
$759$		0			0
$760$	−12.3354			−0.447453
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	0.982744	−	0.184970i	$-0.0592188\pi$
$761$	9.13610	+	15.8242i	0.331183	+	0.573626i	−0.651561	+	0.758596i	$0.725886\pi$
$762$		0			0
$763$		0			0
$764$	15.8357			0.572917
$765$		0			0
$766$	−3.39986	−	5.88874i	−0.122842	−	0.212769i
$767$	17.5167	−	30.3398i	0.632490	−	1.09550i
$768$		0			0
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	−0.649217	−	0.760604i	$-0.724903\pi$
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	0.983310	+	0.181936i	$0.0582365\pi$
$770$		0			0
$771$		0			0
$772$	0.782814			0.0281741
$773$	1.48040	+	2.56413i	0.0532463	+	0.0922253i	0.891420	−	0.453178i	$-0.149710\pi$
$773$	1.48040	+	2.56413i	0.0532463	+	0.0922253i	−0.838174	+	0.545403i	$0.816376\pi$
$774$		0			0
$775$	−14.7049	+	25.4696i	−0.528214	+	0.914894i
$776$	2.69418	+	4.66646i	0.0967155	+	0.167516i
$777$		0			0
$778$	2.37417	−	4.11218i	0.0851181	−	0.147429i
$779$	−5.50387	−	9.53298i	−0.197197	−	0.341555i
$780$		0			0
$781$	0.458111	−	0.793471i	0.0163925	−	0.0283926i
$782$	1.84002	−	3.18701i	0.0657991	−	0.113967i
$783$		0			0
$784$		0			0
$785$	6.82635	+	11.8236i	0.243643	+	0.422002i
$786$		0			0
$787$	33.4020			1.19065			0.595326	−	0.803484i	$-0.297023\pi$
$787$	33.4020			1.19065			0.595326	+	0.803484i	$0.297023\pi$
$788$	14.0401			0.500159
$789$		0			0
$790$	1.42396	+	2.46638i	0.0506623	+	0.0877497i
$791$		0			0
$792$		0			0
$793$	12.8687	−	22.2893i	0.456981	−	0.791515i
$794$	−12.8542	+	22.2641i	−0.456177	+	0.790122i
$795$		0			0
$796$	2.23143	+	3.86495i	0.0790909	+	0.136989i
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.0162779	+	0.999868i	$0.505182\pi$
$797$	−24.6755	+	42.7391i	−0.874050	+	1.51390i	−0.857772	+	0.514031i	$0.828152\pi$
$798$		0			0
$799$	−2.18866	−	3.79088i	−0.0774293	−	0.134112i
$800$	8.97818	−	15.5507i	0.317427	−	0.549799i
$801$		0			0
$802$	−12.0466	−	20.8654i	−0.425382	−	0.736782i
$803$	3.38743			0.119540
$804$		0			0
$805$		0			0
$806$	13.6816	−	23.6971i	0.481912	−	0.834696i
$807$		0			0
$808$	−2.42484	+	4.19995i	−0.0853056	+	0.147754i
$809$	9.91400	+	17.1716i	0.348558	+	0.603720i	0.985993	−	0.166784i	$-0.0533382\pi$
$809$	9.91400	+	17.1716i	0.348558	+	0.603720i	−0.637436	+	0.770503i	$0.720005\pi$
$810$		0			0
$811$	23.8557			0.837686			0.418843	−	0.908059i	$-0.362436\pi$
$811$	23.8557			0.837686			0.418843	+	0.908059i	$0.362436\pi$
$812$		0			0
$813$		0			0
$814$	6.71048	+	11.6229i	0.235202	+	0.407382i
$815$	−3.49794			−0.122528
$816$		0			0
$817$	−14.2344			−0.497999
$818$	7.93643			0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	50.9427			1.77791			0.888957	−	0.457991i	$-0.151431\pi$
$821$	50.9427			1.77791			0.888957	+	0.457991i	$0.151431\pi$
$822$		0			0
$823$	13.6149			0.474587			0.237293	−	0.971438i	$-0.423740\pi$
$823$	13.6149			0.474587			0.237293	+	0.971438i	$0.423740\pi$
$824$	5.16163	+	8.94020i	0.179814	+	0.311447i
$825$		0			0
$826$		0			0
$827$	−36.2158			−1.25935			−0.629673	−	0.776861i	$-0.716811\pi$
$827$	−36.2158			−1.25935			−0.629673	+	0.776861i	$0.716811\pi$
$828$		0			0
$829$	12.6630	+	21.9329i	0.439803	+	0.761761i	0.997674	−	0.0681664i	$-0.0217149\pi$
$829$	12.6630	+	21.9329i	0.439803	+	0.761761i	−0.557871	+	0.829928i	$0.688382\pi$
$830$	8.91534	−	15.4418i	0.309456	−	0.535994i
$831$		0			0
$832$	−8.49454	+	14.7130i	−0.294495	+	0.510080i
$833$		0			0
$834$		0			0
$835$	−31.2344			−1.08091
$836$	−3.27079	−	5.66518i	−0.113123	−	0.195934i
$837$		0			0
$838$	−0.0770768	+	0.133501i	−0.00266257	+	0.00461171i
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	0.780960	−	0.624582i	$-0.214730\pi$
$839$	−4.35710	−	7.54671i	−0.150424	−	0.260541i	−0.931383	+	0.364040i	$0.881397\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$	10.8626	+	18.8146i	0.374350	+	0.648394i
$843$		0			0
$844$	3.57145	−	6.18594i	0.122934	−	0.212929i
$845$	1.10876	−	1.92042i	0.0381423	−	0.0660645i
$846$		0			0
$847$		0			0
$848$	0.0120217	+	0.0208222i	0.000412827	+	0.000715037i
$849$		0			0
$850$	−1.31046			−0.0449484
$851$	−82.5886			−2.83110
$852$		0			0
$853$	−5.99067	−	10.3761i	−0.205117	−	0.355272i	0.745053	−	0.667005i	$-0.232424\pi$
$853$	−5.99067	−	10.3761i	−0.205117	−	0.355272i	−0.950170	+	0.311733i	$0.899091\pi$
$854$		0			0
$855$		0			0
$856$	−10.1133	+	17.5168i	−0.345667	+	0.598713i
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	−0.916183	−	0.400760i	$-0.868746\pi$
$857$	−3.25015	+	5.62943i	−0.111023	+	0.192298i	0.805160	+	0.593058i	$0.202079\pi$
$858$		0			0
$859$	−26.7763	−	46.3779i	−0.913596	−	1.58239i	−0.808944	−	0.587886i	$-0.799960\pi$
$859$	−26.7763	−	46.3779i	−0.913596	−	1.58239i	−0.104652	−	0.994509i	$-0.533373\pi$
$860$	−3.64543	+	6.31407i	−0.124308	+	0.215308i
$861$		0			0
$862$	−12.8914	−	22.3286i	−0.439083	−	0.760514i
$863$	1.84982	−	3.20399i	0.0629687	−	0.109065i	−0.832822	−	0.553540i	$-0.813277\pi$
$863$	1.84982	−	3.20399i	0.0629687	−	0.109065i	0.895791	+	0.444475i	$0.146610\pi$
$864$		0			0
$865$	3.20115	+	5.54456i	0.108842	+	0.188521i
$866$	−17.2847			−0.587357
$867$		0			0
$868$		0			0
$869$	−1.98633	+	3.44042i	−0.0673816	+	0.116708i
$870$		0			0
$871$	−1.00459	+	1.73999i	−0.0340391	+	0.0589574i
$872$	0.572796	+	0.992112i	0.0193973	+	0.0335971i
$873$		0			0
$874$	−25.3773			−0.858401
$875$		0			0
$876$		0			0
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	0.948217	−	0.317622i	$-0.102884\pi$
$877$	5.89440	+	10.2094i	0.199040	+	0.344747i	−0.749178	+	0.662369i	$0.769551\pi$
$878$	19.2849			0.650833
$879$		0			0
$880$	0.0932736			0.00314425
$881$	49.4858			1.66722			0.833609	−	0.552355i	$-0.186271\pi$
$881$	49.4858			1.66722			0.833609	+	0.552355i	$0.186271\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	−1.93407			−0.0650497
$885$		0			0
$886$	16.4534			0.552762
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	0.748849	−	0.662741i	$-0.230607\pi$
$887$	−5.94238	−	10.2925i	−0.199526	−	0.345589i	−0.948375	+	0.317152i	$0.897273\pi$
$888$		0			0
$889$		0			0
$890$	10.7656			0.360863
$891$		0			0
$892$	−4.34477	−	7.52536i	−0.145474	−	0.251968i
$893$	−15.0929	+	26.1416i	−0.505063	+	0.874795i
$894$		0			0
$895$	−5.74763	+	9.95518i	−0.192122	+	0.332765i
$896$		0			0
$897$		0			0
$898$	−5.87433			−0.196029
$899$	−28.9433	−	50.1313i	−0.965314	−	1.67197i
$900$		0			0
$901$	−0.134285	+	0.232589i	−0.00447369	+	0.00774866i
$902$	2.47906	+	4.29385i	0.0825435	+	0.142970i
$903$		0			0
$904$	−20.3868	+	35.3110i	−0.678056	+	1.17443i
$905$	−11.6099	−	20.1090i	−0.385927	−	0.668446i
$906$		0			0
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	−0.565032	−	0.825069i	$-0.691136\pi$
$907$	13.0107	−	22.5353i	0.432014	−	0.748271i	0.997047	+	0.0767980i	$0.0244697\pi$
$908$	−7.32547	+	12.6881i	−0.243104	+	0.421069i
$909$		0			0
$910$		0			0
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	0.830688	−	0.556738i	$-0.187947\pi$
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	−0.897493	+	0.441028i	$0.854614\pi$
$912$		0			0
$913$	24.8726			0.823162
$914$	−17.0853			−0.565132
$915$		0			0
$916$	10.7657	+	18.6468i	0.355710	+	0.616108i
$917$		0			0
$918$		0			0
$919$	−13.7135	+	23.7524i	−0.452366	+	0.783521i	−0.998532	−	0.0541559i	$-0.982753\pi$
$919$	−13.7135	+	23.7524i	−0.452366	+	0.783521i	0.546167	+	0.837677i	$0.316087\pi$
$920$	−17.0954	+	29.6101i	−0.563618	+	0.976216i
$921$		0			0
$922$	0.424678	+	0.735564i	0.0139860	+	0.0242245i
$923$	−0.934011	+	1.61775i	−0.0307434	+	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$	0.195937	−	0.339373i	0.00643889	−	0.0111525i
$927$		0			0
$928$	17.6716	+	30.6081i	0.580098	+	1.00476i
$929$	7.67675			0.251866			0.125933	−	0.992039i	$-0.459808\pi$
$929$	7.67675			0.251866			0.125933	+	0.992039i	$0.459808\pi$
$930$		0			0
$931$		0			0
$932$	−9.96926	+	17.2673i	−0.326554	+	0.565608i
$933$		0			0
$934$	15.0440	−	26.0570i	0.492255	−	0.852610i
$935$	0.520945	+	0.902302i	0.0170367	+	0.0295084i
$936$		0			0
$937$	2.02465			0.0661425			0.0330713	−	0.999453i	$-0.489471\pi$
$937$	2.02465			0.0661425			0.0330713	+	0.999453i	$0.489471\pi$
$938$		0			0
$939$		0			0
$940$	7.73055	+	13.3897i	0.252143	+	0.436724i
$941$	−6.13928			−0.200135			−0.100067	−	0.994981i	$-0.531906\pi$
$941$	−6.13928			−0.200135			−0.100067	+	0.994981i	$0.531906\pi$
$942$		0			0
$943$	−30.5107			−0.993566
$944$	0.435518			0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	−5.56448			−0.180821			−0.0904107	−	0.995905i	$-0.528818\pi$
$947$	−5.56448			−0.180821			−0.0904107	+	0.995905i	$0.528818\pi$
$948$		0			0
$949$	−6.90640			−0.224191
$950$	4.51842	+	7.82613i	0.146597	+	0.253913i
$951$		0			0
$952$		0			0
$953$	8.72018			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$953$	8.72018			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$954$		0			0
$955$	8.69640	+	15.0626i	0.281409	+	0.487415i
$956$	9.26099	−	16.0405i	0.299522	−	0.518787i
$957$		0			0
$958$	9.58219	−	16.5968i	0.309586	−	0.536219i
$959$		0			0
$960$		0			0
$961$	54.2746			1.75079
$962$	−13.6816	−	23.6971i	−0.441111	−	0.764027i
$963$		0			0
$964$	9.59152	−	16.6130i	0.308922	−	0.535069i
$965$	0.429892	+	0.744596i	0.0138387	+	0.0239694i
$966$		0			0
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.143670	−	0.989626i	$-0.454110\pi$
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.785206	−	0.619235i	$-0.212557\pi$
$968$	−11.7310	−	20.3187i	−0.377049	−	0.653068i
$969$		0			0
$970$	−1.12495	+	1.94847i	−0.0361200	+	0.0625617i
$971$	15.3596	−	26.6036i	0.492914	−	0.853752i	−0.507053	−	0.861915i	$-0.669265\pi$
$971$	15.3596	−	26.6036i	0.492914	−	0.853752i	0.999967	+	0.00816326i	$0.00259847\pi$
$972$		0			0
$973$		0			0
$974$	−8.52687	−	14.7690i	−0.273219	−	0.473229i
$975$		0			0
$976$	0.319955			0.0102415
$977$	−10.3000			−0.329527			−0.164764	−	0.986333i	$-0.552686\pi$
$977$	−10.3000			−0.329527			−0.164764	+	0.986333i	$0.552686\pi$
$978$		0			0
$979$	7.50862	+	13.0053i	0.239976	+	0.415651i
$980$		0			0
$981$		0			0
$982$	11.5009	−	19.9201i	0.367008	−	0.635676i
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	−0.954326	−	0.298767i	$-0.903425\pi$
$983$	−6.84817	+	11.8614i	−0.218423	+	0.378319i	0.735903	+	0.677087i	$0.236758\pi$
$984$		0			0
$985$	7.71032	+	13.3547i	0.245671	+	0.425515i
$986$	1.28968	−	2.23379i	0.0410717	−	0.0711383i
$987$		0			0
$988$	6.66860	+	11.5503i	0.212156	+	0.367465i
$989$	−19.7271	+	34.1684i	−0.627287	+	1.08649i
$990$		0			0
$991$	−28.9907	−	50.2133i	−0.920919	−	1.59508i	−0.797997	−	0.602662i	$-0.794107\pi$
$991$	−28.9907	−	50.2133i	−0.920919	−	1.59508i	−0.122922	−	0.992416i	$-0.539227\pi$
$992$	−52.0651			−1.65307
$993$		0			0
$994$		0			0
$995$	−2.45084	+	4.24497i	−0.0776968	+	0.134575i
$996$		0			0
$997$	8.10876	−	14.0448i	0.256807	−	0.444803i	−0.708578	−	0.705633i	$-0.750663\pi$
$997$	8.10876	−	14.0448i	0.256807	−	0.444803i	0.965385	+	0.260830i	$0.0839962\pi$
$998$	6.28817	+	10.8914i	0.199049	+	0.344762i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.h.b.226.3		6
3.2	odd	2		441.2.h.e.373.1		6
7.2	even	3		1323.2.f.d.442.1		6
7.3	odd	6		1323.2.g.d.361.1		6
7.4	even	3		1323.2.g.e.361.1		6
7.5	odd	6		189.2.f.b.64.1		6
7.6	odd	2		1323.2.h.c.226.3		6
9.2	odd	6		441.2.g.b.79.3		6
9.7	even	3		1323.2.g.e.667.1		6
21.2	odd	6		441.2.f.c.148.3		6
21.5	even	6		63.2.f.a.22.3	✓	6
21.11	odd	6		441.2.g.b.67.3		6
21.17	even	6		441.2.g.c.67.3		6
21.20	even	2		441.2.h.d.373.1		6
28.19	even	6		3024.2.r.k.1009.2		6
63.2	odd	6		441.2.f.c.295.3		6
63.5	even	6		567.2.a.h.1.1		3
63.11	odd	6		441.2.h.e.214.1		6
63.16	even	3		1323.2.f.d.883.1		6
63.20	even	6		441.2.g.c.79.3		6
63.23	odd	6		3969.2.a.q.1.1		3
63.25	even	3	inner	1323.2.h.b.802.3		6
63.34	odd	6		1323.2.g.d.667.1		6
63.38	even	6		441.2.h.d.214.1		6
63.40	odd	6		567.2.a.c.1.3		3
63.47	even	6		63.2.f.a.43.3	yes	6
63.52	odd	6		1323.2.h.c.802.3		6
63.58	even	3		3969.2.a.l.1.3		3
63.61	odd	6		189.2.f.b.127.1		6
84.47	odd	6		1008.2.r.h.337.2		6
252.47	odd	6		1008.2.r.h.673.2		6
252.103	even	6		9072.2.a.bs.1.2		3
252.131	odd	6		9072.2.a.ca.1.2		3
252.187	even	6		3024.2.r.k.2017.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	21.5	even	6
63.2.f.a.43.3	yes	6	63.47	even	6
189.2.f.b.64.1		6	7.5	odd	6
189.2.f.b.127.1		6	63.61	odd	6
441.2.f.c.148.3		6	21.2	odd	6
441.2.f.c.295.3		6	63.2	odd	6
441.2.g.b.67.3		6	21.11	odd	6
441.2.g.b.79.3		6	9.2	odd	6
441.2.g.c.67.3		6	21.17	even	6
441.2.g.c.79.3		6	63.20	even	6
441.2.h.d.214.1		6	63.38	even	6
441.2.h.d.373.1		6	21.20	even	2
441.2.h.e.214.1		6	63.11	odd	6
441.2.h.e.373.1		6	3.2	odd	2
567.2.a.c.1.3		3	63.40	odd	6
567.2.a.h.1.1		3	63.5	even	6
1008.2.r.h.337.2		6	84.47	odd	6
1008.2.r.h.673.2		6	252.47	odd	6
1323.2.f.d.442.1		6	7.2	even	3
1323.2.f.d.883.1		6	63.16	even	3
1323.2.g.d.361.1		6	7.3	odd	6
1323.2.g.d.667.1		6	63.34	odd	6
1323.2.g.e.361.1		6	7.4	even	3
1323.2.g.e.667.1		6	9.7	even	3
1323.2.h.b.226.3		6	1.1	even	1	trivial
1323.2.h.b.802.3		6	63.25	even	3	inner
1323.2.h.c.226.3		6	7.6	odd	2
1323.2.h.c.802.3		6	63.52	odd	6
3024.2.r.k.1009.2		6	28.19	even	6
3024.2.r.k.2017.2		6	252.187	even	6
3969.2.a.l.1.3		3	63.58	even	3
3969.2.a.q.1.1		3	63.23	odd	6
9072.2.a.bs.1.2		3	252.103	even	6
9072.2.a.ca.1.2		3	252.131	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.879385 q^{2} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +O(q^{10})\)	\(q+0.879385 q^{2} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} -2.83750 q^{8} +(-0.592396 - 1.02606i) q^{10} +(0.826352 - 1.43128i) q^{11} +(-1.68479 + 2.91815i) q^{13} -0.0418891 q^{16} +(-0.233956 - 0.405223i) q^{17} +(-1.61334 + 2.79439i) q^{19} +(0.826352 + 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(4.47178 + 7.74535i) q^{23} +(1.59240 - 2.75811i) q^{25} +(-1.48158 + 2.56617i) q^{26} +(3.13429 + 5.42874i) q^{29} -9.23442 q^{31} +5.63816 q^{32} +(-0.205737 - 0.356347i) q^{34} +(-4.61721 + 7.99724i) q^{37} +(-1.41875 + 2.45734i) q^{38} +(1.91147 + 3.31077i) q^{40} +(-1.70574 + 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(-1.01367 + 1.75573i) q^{44} +(3.93242 + 6.81115i) q^{46} +9.35504 q^{47} +(1.40033 - 2.42544i) q^{50} +(2.06670 - 3.57964i) q^{52} +(-0.286989 - 0.497079i) q^{53} -2.22668 q^{55} +(2.75624 + 4.77396i) q^{58} -10.3969 q^{59} -7.63816 q^{61} -8.12061 q^{62} +5.04189 q^{64} +4.53983 q^{65} +0.596267 q^{67} +(0.286989 + 0.497079i) q^{68} +0.554378 q^{71} +(1.02481 + 1.77503i) q^{73} +(-4.06031 + 7.03266i) q^{74} +(1.97906 - 3.42782i) q^{76} -2.40373 q^{79} +(0.0282185 + 0.0488759i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(1.93969 + 3.35965i) q^{86} +(-2.34477 + 4.06126i) q^{88} +(-4.54323 + 7.86911i) q^{89} +(-5.48545 - 9.50108i) q^{92} +8.22668 q^{94} +4.34730 q^{95} +(-0.949493 - 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 3 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^5 - 12 * q^8	\( 6 q - 6 q^{2} + 6 q^{4} - 3 q^{5} - 12 q^{8} + 6 q^{11} - 3 q^{13} + 6 q^{16} - 6 q^{17} - 3 q^{19} + 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 3 q^{26} + 9 q^{29} + 6 q^{31} + 9 q^{34} + 3 q^{37} - 6 q^{38} - 9 q^{40} + 3 q^{43} + 15 q^{44} + 6 q^{47} - 6 q^{50} - 21 q^{52} + 6 q^{53} + 9 q^{58} - 6 q^{59} - 12 q^{61} - 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} - 6 q^{68} - 18 q^{71} - 21 q^{73} - 30 q^{74} + 15 q^{76} - 42 q^{79} + 15 q^{80} - 9 q^{82} + 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} - 12 q^{89} + 3 q^{92} + 36 q^{94} + 24 q^{95} - 3 q^{97}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 3 * q^5 - 12 * q^8 + 6 * q^11 - 3 * q^13 + 6 * q^16 - 6 * q^17 - 3 * q^19 + 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 3 * q^26 + 9 * q^29 + 6 * q^31 + 9 * q^34 + 3 * q^37 - 6 * q^38 - 9 * q^40 + 3 * q^43 + 15 * q^44 + 6 * q^47 - 6 * q^50 - 21 * q^52 + 6 * q^53 + 9 * q^58 - 6 * q^59 - 12 * q^61 - 60 * q^62 + 24 * q^64 - 30 * q^65 - 24 * q^67 - 6 * q^68 - 18 * q^71 - 21 * q^73 - 30 * q^74 + 15 * q^76 - 42 * q^79 + 15 * q^80 - 9 * q^82 + 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 12 * q^89 + 3 * q^92 + 36 * q^94 + 24 * q^95 - 3 * q^97

Introduction

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