LMFDB - Embedded newform 1323.2.g.d.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	1323.667
Dual form			1323.2.g.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +O(q^{10})$	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +(0.592396 + 1.02606i) q^{10} -1.65270 q^{11} +(1.68479 + 2.91815i) q^{13} +(0.0209445 + 0.0362770i) q^{16} +(0.233956 + 0.405223i) q^{17} +(1.61334 - 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} -8.94356 q^{23} -3.18479 q^{25} +(1.48158 - 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +(-4.61721 + 7.99724i) q^{31} +(-2.81908 + 4.88279i) q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 + 7.99724i) q^{37} -2.83750 q^{38} +3.82295 q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 + 1.75573i) q^{44} +(3.93242 + 6.81115i) q^{46} +(4.67752 + 8.10170i) q^{47} +(1.40033 + 2.42544i) q^{50} +4.13341 q^{52} +(-0.286989 - 0.497079i) q^{53} +2.22668 q^{55} -5.51249 q^{58} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(-2.26991 - 3.93161i) q^{65} +(-0.298133 + 0.516382i) q^{67} +0.573978 q^{68} +0.554378 q^{71} +(-1.02481 - 1.77503i) q^{73} +8.12061 q^{74} +(-1.97906 - 3.42782i) q^{76} +(1.20187 + 2.08169i) q^{79} +(-0.0282185 - 0.0488759i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} -3.87939 q^{86} +4.68954 q^{88} +(4.54323 - 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} +(4.11334 - 7.12452i) q^{94} +(-2.17365 + 3.76487i) q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8} - 12 q^{11} + 3 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{31} - 9 q^{34} + 3 q^{37} - 12 q^{38} - 18 q^{40} + 3 q^{43} + 15 q^{44} + 3 q^{47} - 6 q^{50} - 42 q^{52} + 6 q^{53} - 18 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 12 q^{68} - 18 q^{71} + 21 q^{73} + 60 q^{74} - 15 q^{76} + 21 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} + 12 q^{89} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8 - 12 * q^11 + 3 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^31 - 9 * q^34 + 3 * q^37 - 12 * q^38 - 18 * q^40 + 3 * q^43 + 15 * q^44 + 3 * q^47 - 6 * q^50 - 42 * q^52 + 6 * q^53 - 18 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 12 * q^68 - 18 * q^71 + 21 * q^73 + 60 * q^74 - 15 * q^76 + 21 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 + 12 * q^89 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.439693	−	0.761570i	−0.310910	−	0.538511i	0.667650	−	0.744475i	$-0.267300\pi$
$2$	−0.439693	−	0.761570i	−0.310910	−	0.538511i	−0.978560	+	0.205964i	$0.933967\pi$
$3$		0			0
$3$		0			0
$4$	0.613341	−	1.06234i	0.306670	−	0.531169i
$5$	−1.34730			−0.602529			−0.301265	−	0.953541i	$-0.597409\pi$
$5$	−1.34730			−0.602529			−0.301265	+	0.953541i	$0.597409\pi$
$6$		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
$11$	−1.65270			−0.498309			−0.249154	−	0.968464i	$-0.580153\pi$
$11$	−1.65270			−0.498309			−0.249154	+	0.968464i	$0.580153\pi$
$12$		0			0
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	0.999301	−	0.0373813i	$-0.0119016\pi$
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	−0.532024	+	0.846729i	$0.678568\pi$
$14$		0			0
$15$		0			0
$16$	0.0209445	+	0.0362770i	0.00523613	+	0.00906925i
$17$	0.233956	+	0.405223i	0.0567426	+	0.0982810i	0.893001	−	0.450054i	$-0.148595\pi$
$17$	0.233956	+	0.405223i	0.0567426	+	0.0982810i	−0.836259	+	0.548335i	$0.815262\pi$
$18$		0			0
$19$	1.61334	−	2.79439i	0.370126	−	0.641077i	−0.619459	−	0.785029i	$-0.712648\pi$
$19$	1.61334	−	2.79439i	0.370126	−	0.641077i	0.989585	+	0.143953i	$0.0459813\pi$
$20$	−0.826352	+	1.43128i	−0.184778	+	0.320045i
$21$		0			0
$22$	0.726682	+	1.25865i	0.154929	+	0.268345i
$23$	−8.94356			−1.86486			−0.932431	−	0.361348i	$-0.882317\pi$
$23$	−8.94356			−1.86486			−0.932431	+	0.361348i	$0.882317\pi$
$24$		0			0
$25$	−3.18479			−0.636959
$26$	1.48158	−	2.56617i	0.290562	−	0.503268i
$27$		0			0
$28$		0			0
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	−0.413217	−	0.910632i	$-0.635595\pi$
$29$	3.13429	−	5.42874i	0.582022	−	1.00809i	0.995239	−	0.0974595i	$-0.0310717\pi$
$30$		0			0
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	0.0693317	+	0.997594i	$0.477913\pi$
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	−0.898607	+	0.438754i	$0.855420\pi$
$32$	−2.81908	+	4.88279i	−0.498347	+	0.863163i
$33$		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	$0.892323\pi$
$38$	−2.83750			−0.460303
$39$		0			0
$40$	3.82295			0.604461
$41$	1.70574	+	2.95442i	0.266391	+	0.461403i	0.967927	−	0.251231i	$-0.0808353\pi$
$41$	1.70574	+	2.95442i	0.266391	+	0.461403i	−0.701536	+	0.712634i	$0.747502\pi$
$42$		0			0
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	−0.647376	−	0.762171i	$-0.724133\pi$
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	0.983747	+	0.179558i	$0.0574668\pi$
$44$	−1.01367	+	1.75573i	−0.152817	+	0.264686i
$45$		0			0
$46$	3.93242	+	6.81115i	0.579803	+	1.00425i
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	0.974281	+	0.225335i	$0.0723475\pi$
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	−0.291995	+	0.956420i	$0.594319\pi$
$48$		0			0
$49$		0			0
$50$	1.40033	+	2.42544i	0.198037	+	0.343009i
$51$		0			0
$52$	4.13341			0.573201
$53$	−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
$58$	−5.51249			−0.723825
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	0.299162	+	0.954202i	$0.403293\pi$
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	−0.975945	+	0.218019i	$0.930041\pi$
$60$		0			0
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	0.510937	−	0.859618i	$-0.329299\pi$
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	−0.999920	+	0.0126752i	$0.995965\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	−2.26991	−	3.93161i	−0.281548	−	0.487656i
$66$		0			0
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	−0.883662	−	0.468125i	$-0.844930\pi$
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	0.847239	+	0.531211i	$0.178263\pi$
$68$	0.573978			0.0696051
$69$		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	0.799800	−	0.600266i	$-0.204939\pi$
$73$	−1.02481	−	1.77503i	−0.119946	−	0.207752i	−0.919746	+	0.392514i	$0.871605\pi$
$74$	8.12061			0.944002
$75$		0			0
$76$	−1.97906	−	3.42782i	−0.227013	−	0.393198i
$77$		0			0
$78$		0			0
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	0.925682	−	0.378303i	$-0.123492\pi$
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	−0.790461	+	0.612512i	$0.790159\pi$
$80$	−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	0.0752309	+	0.997166i	$0.476031\pi$
$83$	−7.52481	+	13.0334i	−0.825956	+	1.43060i	−0.901187	+	0.433431i	$0.857303\pi$
$84$		0			0
$85$	−0.315207	−	0.545955i	−0.0341891	−	0.0592172i
$86$	−3.87939			−0.418325
$87$		0			0
$88$	4.68954			0.499907
$89$	4.54323	−	7.86911i	0.481582	−	0.834124i	−0.518195	−	0.855263i	$-0.673396\pi$
$89$	4.54323	−	7.86911i	0.481582	−	0.834124i	0.999777	+	0.0211385i	$0.00672911\pi$
$90$		0			0
$91$		0			0
$92$	−5.48545	+	9.50108i	−0.571898	+	0.990556i
$93$		0			0
$94$	4.11334	−	7.12452i	0.424259	−	0.734838i
$95$	−2.17365	+	3.76487i	−0.223012	+	0.386267i
$96$		0			0
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	−0.813788	−	0.581161i	$-0.802598\pi$
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	0.910195	+	0.414181i	$0.135932\pi$
$98$		0			0
$99$		0			0
$100$	−1.95336	+	3.38332i	−0.195336	+	0.338332i
$101$	1.70914			0.170066			0.0850329	−	0.996378i	$-0.472900\pi$
$101$	1.70914			0.170066			0.0850329	+	0.996378i	$0.472900\pi$
$102$		0			0
$103$	−3.63816			−0.358478			−0.179239	−	0.983806i	$-0.557364\pi$
$103$	−3.63816			−0.358478			−0.179239	+	0.983806i	$0.557364\pi$
$104$	−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	$0.839488\pi$
$110$	−0.979055	−	1.69577i	−0.0933493	−	0.161686i
$111$		0			0
$112$		0			0
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	0.976208	+	0.216835i	$0.0695732\pi$
$113$	7.18479	+	12.4444i	0.675888	+	1.17067i	−0.300320	+	0.953839i	$0.597093\pi$
$114$		0			0
$115$	12.0496			1.12363
$116$	−3.84477	−	6.65934i	−0.356978	−	0.618304i
$117$		0			0
$118$	9.14290			0.841672
$119$		0			0
$120$		0			0
$121$	−8.26857			−0.751688
$122$	−3.35844	+	5.81699i	−0.304059	+	0.526646i
$123$		0			0
$124$	5.66385	+	9.81007i	0.508629	+	0.880971i
$125$	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	$0.873108\pi$
$128$	3.42127	+	5.92582i	0.302401	+	0.523774i
$129$		0			0
$130$	−1.99613	+	3.45740i	−0.175072	+	0.303234i
$131$	7.16519			0.626026			0.313013	−	0.949749i	$-0.398662\pi$
$131$	7.16519			0.626026			0.313013	+	0.949749i	$0.398662\pi$
$132$		0			0
$133$		0			0
$134$	0.524348			0.0452968
$135$		0			0
$136$	−0.663848	−	1.14982i	−0.0569245	−	0.0985961i
$137$	−2.56893			−0.219478			−0.109739	−	0.993960i	$-0.535002\pi$
$137$	−2.56893			−0.219478			−0.109739	+	0.993960i	$0.535002\pi$
$138$		0			0
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	0.966272	−	0.257523i	$-0.0829064\pi$
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	−0.706158	+	0.708055i	$0.749573\pi$
$140$		0			0
$141$		0			0
$142$	−0.243756	−	0.422197i	−0.0204555	−	0.0354300i
$143$	−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
$149$	−0.431074			−0.0353150			−0.0176575	−	0.999844i	$-0.505621\pi$
$149$	−0.431074			−0.0353150			−0.0176575	+	0.999844i	$0.505621\pi$
$150$		0			0
$151$	−2.47060			−0.201055			−0.100527	−	0.994934i	$-0.532053\pi$
$151$	−2.47060			−0.201055			−0.100527	+	0.994934i	$0.532053\pi$
$152$	−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
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	−0.994248	−	0.107106i	$-0.965841\pi$
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	0.589881	+	0.807491i	$0.299175\pi$
$158$	1.05690	−	1.83061i	0.0840828	−	0.145636i
$159$		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	$0.134246\pi$
$164$	4.18479			0.326777
$165$		0			0
$166$	13.2344			1.02719
$167$	−11.5915	−	20.0771i	−0.896979	−	1.55361i	−0.831337	−	0.555769i	$-0.812424\pi$
$167$	−11.5915	−	20.0771i	−0.896979	−	1.55361i	−0.0656422	−	0.997843i	$-0.520910\pi$
$168$		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
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	0.761457	−	0.648215i	$-0.224484\pi$
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	−0.942100	+	0.335333i	$0.891151\pi$
$174$		0			0
$175$		0			0
$176$	−0.0346151	−	0.0599551i	−0.00260921	−	0.00451929i
$177$		0			0
$178$	−7.99050			−0.598914
$179$	−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	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		0			0
$183$		0			0
$184$	25.3773			1.87084
$185$	6.22075	−	10.7747i	0.457359	−	0.792169i
$186$		0			0
$187$	−0.386659	−	0.669713i	−0.0282753	−	0.0489743i
$188$	11.4757			0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	0.999291	−	0.0376425i	$-0.0119848\pi$
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	−0.532245	+	0.846590i	$0.678651\pi$
$192$		0			0
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$	−1.66994			−0.119895
$195$		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	0.923270	−	0.384151i	$-0.125506\pi$
$199$	1.81908	+	3.15074i	0.128951	+	0.223350i	−0.794319	+	0.607500i	$0.792172\pi$
$200$	9.03684			0.639001
$201$		0			0
$202$	−0.751497	−	1.30163i	−0.0528751	−	0.0915824i
$203$		0			0
$204$		0			0
$205$	−2.29813	−	3.98048i	−0.160509	−	0.278009i
$206$	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	0.748234	−	0.663435i	$-0.230902\pi$
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	−0.948668	+	0.316273i	$0.897569\pi$
$212$	−0.704088			−0.0483570
$213$		0			0
$214$	−6.26857			−0.428511
$215$	−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
$220$	1.36571	−	2.36549i	0.0920765	−	0.159481i
$221$	−0.788333	+	1.36543i	−0.0530290	+	0.0918490i
$222$		0			0
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	−0.959905	−	0.280327i	$-0.909557\pi$
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	0.722722	+	0.691139i	$0.242891\pi$
$224$		0			0
$225$		0			0
$226$	6.31820	−	10.9434i	0.420280	−	0.727947i
$227$	11.9436			0.792722			0.396361	−	0.918095i	$-0.370273\pi$
$227$	11.9436			0.792722			0.396361	+	0.918095i	$0.370273\pi$
$228$		0			0
$229$	−17.5526			−1.15991			−0.579955	−	0.814649i	$-0.696930\pi$
$229$	−17.5526			−1.15991			−0.579955	+	0.814649i	$0.696930\pi$
$230$	−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
$236$	6.37686	+	11.0450i	0.415098	+	0.718971i
$237$		0			0
$238$		0			0
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	0.511565	−	0.859244i	$-0.329066\pi$
$239$	−7.54963	−	13.0763i	−0.488345	−	0.845838i	−0.999910	+	0.0134062i	$0.995733\pi$
$240$		0			0
$241$	−15.6382			−1.00734			−0.503671	−	0.863896i	$-0.668018\pi$
$241$	−15.6382			−1.00734			−0.503671	+	0.863896i	$0.668018\pi$
$242$	3.63563	+	6.29710i	0.233707	+	0.404793i
$243$		0			0
$244$	−9.36959			−0.599826
$245$		0			0
$246$		0			0
$247$	10.8726			0.691806
$248$	13.1013	−	22.6922i	0.831935	−	1.44095i
$249$		0			0
$250$	−4.84864	−	8.39809i	−0.306655	−	0.531142i
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	9.13310	+	15.8190i	0.573062	+	0.992572i
$255$		0			0
$256$	8.05051	−	13.9439i	0.503157	−	0.871493i
$257$	−26.5817			−1.65812			−0.829061	−	0.559158i	$-0.811124\pi$
$257$	−26.5817			−1.65812			−0.829061	+	0.559158i	$0.811124\pi$
$258$		0			0
$259$		0			0
$260$	−5.56893			−0.345370
$261$		0			0
$262$	−3.15048	−	5.45680i	−0.194637	−	0.337122i
$263$	0.734118			0.0452676			0.0226338	−	0.999744i	$-0.492795\pi$
$263$	0.734118			0.0452676			0.0226338	+	0.999744i	$0.492795\pi$
$264$		0			0
$265$	0.386659	+	0.669713i	0.0237523	+	0.0411402i
$266$		0			0
$267$		0			0
$268$	0.365715	+	0.633436i	0.0223396	+	0.0386933i
$269$	−10.4251	−	18.0569i	−0.635632	−	1.10095i	−0.986381	−	0.164478i	$-0.947406\pi$
$269$	−10.4251	−	18.0569i	−0.635632	−	1.10095i	0.350749	−	0.936470i	$-0.385927\pi$
$270$		0			0
$271$	−3.47906	+	6.02590i	−0.211338	+	0.366047i	−0.952133	−	0.305683i	$-0.901115\pi$
$271$	−3.47906	+	6.02590i	−0.211338	+	0.366047i	0.740796	+	0.671730i	$0.234449\pi$
$272$	−0.00980018	+	0.0169744i	−0.000594223	+	0.00102922i
$273$		0			0
$274$	1.12954	+	1.95642i	0.0682379	+	0.118191i
$275$	5.26352			0.317402
$276$		0			0
$277$	17.8726			1.07386			0.536930	−	0.843627i	$-0.319584\pi$
$277$	17.8726			1.07386			0.536930	+	0.843627i	$0.319584\pi$
$278$	2.69681	−	4.67102i	0.161744	−	0.280149i
$279$		0			0
$280$		0			0
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	−0.313694	−	0.949524i	$-0.601567\pi$
$281$	11.1552	−	19.3214i	0.665465	−	1.15262i	0.979159	−	0.203095i	$-0.0651001\pi$
$282$		0			0
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	−0.445417	−	0.895323i	$-0.646944\pi$
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	0.998081	−	0.0619196i	$-0.0197222\pi$
$284$	0.340022	−	0.588936i	0.0201766	−	0.0349469i
$285$		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
$290$	7.42696			0.436126
$291$		0			0
$292$	−2.51424			−0.147135
$293$	6.54576	+	11.3376i	0.382407	+	0.662349i	0.991406	−	0.130822i	$-0.0417618\pi$
$293$	6.54576	+	11.3376i	0.382407	+	0.662349i	−0.608998	+	0.793171i	$0.708428\pi$
$294$		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
$299$	−15.0680	−	26.0986i	−0.871408	−	1.50932i
$300$		0			0
$301$		0			0
$302$	1.08630	+	1.88153i	0.0625098	+	0.108270i
$303$		0			0
$304$	0.135163			0.00775211
$305$	5.14543	+	8.91215i	0.294626	+	0.510308i
$306$		0			0
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$		0			0
$309$		0			0
$310$	−10.9409			−0.621400
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	−0.968871	−	0.247565i	$-0.920370\pi$
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	0.698833	+	0.715285i	$0.253703\pi$
$312$		0			0
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	0.999998	−	0.00205946i	$-0.000655547\pi$
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	−0.501782	+	0.864994i	$0.667322\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	0.956865	−	0.290533i	$-0.0938325\pi$
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	−0.730041	+	0.683403i	$0.760499\pi$
$318$		0			0
$319$	−5.18004	+	8.97210i	−0.290027	+	0.502341i
$320$	−6.79292			−0.379736
$321$		0			0
$322$		0			0
$323$	1.50980			0.0840075
$324$		0			0
$325$	−5.36571	−	9.29369i	−0.297636	−	0.515521i
$326$	−2.28312			−0.126450
$327$		0			0
$328$	−4.84002	−	8.38316i	−0.267246	−	0.462883i
$329$		0			0
$330$		0			0
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	−0.986839	−	0.161706i	$-0.948300\pi$
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	0.353378	−	0.935481i	$-0.385033\pi$
$332$	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	−0.925659	−	0.378359i	$-0.876489\pi$
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	0.135161	−	0.990824i	$-0.456845\pi$
$338$	−1.44738			−0.0787269
$339$		0			0
$340$	−0.773318			−0.0419391
$341$	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
$346$	−2.08940	+	3.61895i	−0.112327	+	0.194556i
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	−0.638308	−	0.769781i	$-0.720365\pi$
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	0.985804	+	0.167901i	$0.0536988\pi$
$348$		0			0
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	−0.884938	−	0.465710i	$-0.845799\pi$
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	0.845785	+	0.533524i	$0.179132\pi$
$350$		0			0
$351$		0			0
$352$	4.65910	−	8.06980i	0.248331	−	0.430122i
$353$	−14.3327			−0.762855			−0.381428	−	0.924399i	$-0.624567\pi$
$353$	−14.3327			−0.762855			−0.381428	+	0.924399i	$0.624567\pi$
$354$		0			0
$355$	−0.746911			−0.0396419
$356$	−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
$362$	7.57785	+	13.1252i	0.398283	+	0.689846i
$363$		0			0
$364$		0			0
$365$	1.38073	+	2.39149i	0.0722707	+	0.125176i
$366$		0			0
$367$	−12.0574			−0.629390			−0.314695	−	0.949193i	$-0.601902\pi$
$367$	−12.0574			−0.629390			−0.314695	+	0.949193i	$0.601902\pi$
$368$	−0.187319	−	0.324446i	−0.00976466	−	0.0169129i
$369$		0			0
$370$	−10.9409			−0.568789
$371$		0			0
$372$		0			0
$373$	−0.781059			−0.0404417			−0.0202209	−	0.999796i	$-0.506437\pi$
$373$	−0.781059			−0.0404417			−0.0202209	+	0.999796i	$0.506437\pi$
$374$	−0.340022	+	0.588936i	−0.0175821	+	0.0304532i
$375$		0			0
$376$	−13.2724	−	22.9885i	−0.684474	−	1.18554i
$377$	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	$0.556908\pi$
$380$	2.66637	+	4.61830i	0.136782	+	0.236914i
$381$		0			0
$382$	5.67617	−	9.83142i	0.290418	−	0.503019i
$383$	−7.73236			−0.395105			−0.197553	−	0.980292i	$-0.563299\pi$
$383$	−7.73236			−0.395105			−0.197553	+	0.980292i	$0.563299\pi$
$384$		0			0
$385$		0			0
$386$	−0.561185			−0.0285636
$387$		0			0
$388$	−1.16473	−	2.01736i	−0.0591300	−	0.102416i
$389$	−5.39961			−0.273771			−0.136886	−	0.990587i	$-0.543709\pi$
$389$	−5.39961			−0.273771			−0.136886	+	0.990587i	$0.543709\pi$
$390$		0			0
$391$	−2.09240	−	3.62414i	−0.105817	−	0.183280i
$392$		0			0
$393$		0			0
$394$	5.03256	+	8.71664i	0.253536	+	0.439138i
$395$	−1.61927	−	2.80466i	−0.0814743	−	0.141118i
$396$		0			0
$397$	14.6172	−	25.3178i	0.733617	−	1.27066i	−0.221711	−	0.975112i	$-0.571164\pi$
$397$	14.6172	−	25.3178i	0.733617	−	1.27066i	0.955328	−	0.295549i	$-0.0955026\pi$
$398$	1.59967	−	2.77071i	0.0801842	−	0.138883i
$399$		0			0
$400$	−0.0667040	−	0.115535i	−0.00333520	−	0.00577674i
$401$	27.3979			1.36818			0.684092	−	0.729396i	$-0.260199\pi$
$401$	27.3979			1.36818			0.684092	+	0.729396i	$0.260199\pi$
$402$		0			0
$403$	−31.1162			−1.55001
$404$	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
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	−0.732628	−	0.680629i	$-0.761706\pi$
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	0.955756	+	0.294160i	$0.0950398\pi$
$410$	−2.02094	+	3.50038i	−0.0998073	+	0.172871i
$411$		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
$416$	−18.9982			−0.931466
$417$		0			0
$418$	4.68954			0.229373
$419$	0.0876485	+	0.151812i	0.00428191	+	0.00741649i	0.868158	−	0.496287i	$-0.165304\pi$
$419$	0.0876485	+	0.151812i	0.00428191	+	0.00741649i	−0.863877	+	0.503704i	$0.831970\pi$
$420$		0			0
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	−0.390490	−	0.920607i	$-0.627694\pi$
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	0.992514	−	0.122130i	$-0.0389724\pi$
$422$	−2.56031	+	4.43458i	−0.124634	+	0.215872i
$423$		0			0
$424$	0.814330	+	1.41046i	0.0395474	+	0.0684980i
$425$	−0.745100	−	1.29055i	−0.0361427	−	0.0626009i
$426$		0			0
$427$		0			0
$428$	−4.37211	−	7.57272i	−0.211334	−	0.366041i
$429$		0			0
$430$	5.22668			0.252053
$431$	−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	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		0			0
$435$		0			0
$436$	−0.495252			−0.0237183
$437$	−14.4290	+	24.9918i	−0.690233	+	1.19552i
$438$		0			0
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	0.999631	+	0.0271516i	$0.00864370\pi$
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	−0.476302	+	0.879282i	$0.658023\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	0.553544	−	0.832820i	$-0.313275\pi$
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	−0.998015	+	0.0629732i	$0.979942\pi$
$444$		0			0
$445$	−6.12108	+	10.6020i	−0.290167	+	0.502584i
$446$	6.22937			0.294969
$447$		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
$452$	17.6269			0.829100
$453$		0			0
$454$	−5.25150	−	9.09586i	−0.246465	−	0.426890i
$455$		0			0
$456$		0			0
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$	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	$-0.840493\pi$
$461$	−0.482926	+	0.836452i	−0.0224921	+	0.0389575i	0.854560	+	0.519352i	$0.173827\pi$
$462$		0			0
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	0.871156	−	0.491006i	$-0.163371\pi$
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	−0.860802	+	0.508941i	$0.830037\pi$
$464$	0.262585			0.0121902
$465$		0			0
$466$	−14.2935			−0.662136
$467$	−17.1074	+	29.6309i	−0.791637	+	1.37115i	0.133317	+	0.991074i	$0.457437\pi$
$467$	−17.1074	+	29.6309i	−0.791637	+	1.37115i	−0.924953	+	0.380081i	$0.875896\pi$
$468$		0			0
$469$		0			0
$470$	−5.54189	+	9.59883i	−0.255628	+	0.442761i
$471$		0			0
$472$	14.7506	−	25.5488i	0.678952	−	1.17598i
$473$	−3.64543	+	6.31407i	−0.167617	+	0.290321i
$474$		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
$479$	21.7929			0.995744			0.497872	−	0.867251i	$-0.334115\pi$
$479$	21.7929			0.995744			0.497872	+	0.867251i	$0.334115\pi$
$480$		0			0
$481$	−31.1162			−1.41878
$482$	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	$0.978137\pi$
$488$	10.8366	+	18.7696i	0.490551	+	0.849659i
$489$		0			0
$490$		0			0
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	0.994203	+	0.107519i	$0.0342908\pi$
$491$	13.0783	+	22.6523i	0.590216	+	1.02228i	−0.403987	+	0.914765i	$0.632376\pi$
$492$		0			0
$493$	2.93313			0.132102
$494$	−4.78059	−	8.28023i	−0.215089	−	0.372545i
$495$		0			0
$496$	−0.386821			−0.0173688
$497$		0			0
$498$		0			0
$499$	−14.3013			−0.640214			−0.320107	−	0.947381i	$-0.603719\pi$
$499$	−14.3013			−0.640214			−0.320107	+	0.947381i	$0.603719\pi$
$500$	6.76352	−	11.7148i	0.302474	−	0.523900i
$501$		0			0
$502$	8.38279	+	14.5194i	0.374142	+	0.648033i
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	−6.49912	−	11.2568i	−0.288921	−	0.500426i
$507$		0			0
$508$	−12.7400	+	22.0664i	−0.565248	+	0.979039i
$509$	25.6091			1.13510			0.567551	−	0.823338i	$-0.307891\pi$
$509$	25.6091			1.13510			0.567551	+	0.823338i	$0.307891\pi$
$510$		0			0
$511$		0			0
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	11.6878	+	20.2438i	0.515526	+	0.892917i
$515$	4.90167			0.215994
$516$		0			0
$517$	−7.73055	−	13.3897i	−0.339989	−	0.588879i
$518$		0			0
$519$		0			0
$520$	6.44087	+	11.1559i	0.282451	+	0.489220i
$521$	−10.6061	−	18.3702i	−0.464660	−	0.804815i	0.534526	−	0.845152i	$-0.320490\pi$
$521$	−10.6061	−	18.3702i	−0.464660	−	0.804815i	−0.999186	+	0.0403370i	$0.987157\pi$
$522$		0			0
$523$	−10.4029	+	18.0183i	−0.454885	+	0.787884i	−0.998682	−	0.0513330i	$-0.983653\pi$
$523$	−10.4029	+	18.0183i	−0.454885	+	0.787884i	0.543796	+	0.839217i	$0.316986\pi$
$524$	4.39470	−	7.61185i	0.191984	−	0.332525i
$525$		0			0
$526$	−0.322786	−	0.559082i	−0.0140741	−	0.0243771i
$527$	−4.32089			−0.188221
$528$		0			0
$529$	56.9873			2.47771
$530$	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
$535$	−4.80200	+	8.31731i	−0.207609	+	0.359589i
$536$	0.845952	−	1.46523i	0.0365396	−	0.0632884i
$537$		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	$0.971825\pi$
$542$	6.11886			0.262828
$543$		0			0
$544$	−2.63816			−0.113110
$545$	0.271974	+	0.471073i	0.0116501	+	0.0201786i
$546$		0			0
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	0.142523	+	0.989792i	$0.454479\pi$
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	−0.928446	+	0.371467i	$0.878855\pi$
$548$	−1.57563	+	2.72907i	−0.0673074	+	0.116580i
$549$		0			0
$550$	−2.31433	−	4.00854i	−0.0986834	−	0.170925i
$551$	−10.1133	−	17.5168i	−0.430843	−	0.746242i
$552$		0			0
$553$		0			0
$554$	−7.85844	−	13.6112i	−0.333873	−	0.578285i
$555$		0			0
$556$	7.52374			0.319078
$557$	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
$562$	−19.6195			−0.827598
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	−0.990156	−	0.139965i	$-0.955301\pi$
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	0.616291	+	0.787518i	$0.288634\pi$
$564$		0			0
$565$	−9.68004	−	16.7663i	−0.407243	−	0.705365i
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	−0.997697	−	0.0678320i	$-0.978392\pi$
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	0.440104	−	0.897947i	$-0.354942\pi$
$570$		0			0
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	−0.741986	−	0.670416i	$-0.766116\pi$
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	0.951590	+	0.307371i	$0.0994491\pi$
$572$	−6.83130			−0.285631
$573$		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	$0.0735852\pi$
$577$	16.4572	+	28.5048i	0.685124	+	1.18667i	−0.288274	+	0.957548i	$0.593082\pi$
$578$	−14.7570			−0.613811
$579$		0			0
$580$	5.18004	+	8.97210i	0.215090	+	0.372546i
$581$		0			0
$582$		0			0
$583$	0.474308	+	0.821525i	0.0196438	+	0.0340241i
$584$	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	$-0.934018\pi$
$587$	−7.53643	+	13.0535i	−0.311062	+	0.538774i	0.667531	+	0.744582i	$0.267351\pi$
$588$		0			0
$589$	14.8983	+	25.8046i	0.613873	+	1.06326i
$590$	−12.3182			−0.507132
$591$		0			0
$592$	−0.386821			−0.0158983
$593$	20.5005	−	35.5079i	0.841853	−	1.45813i	−0.0464729	−	0.998920i	$-0.514798\pi$
$593$	20.5005	−	35.5079i	0.841853	−	1.45813i	0.888326	−	0.459213i	$-0.151869\pi$
$594$		0			0
$595$		0			0
$596$	−0.264396	+	0.457947i	−0.0108301	+	0.0187582i
$597$		0			0
$598$	−13.2506	+	22.9507i	−0.541858	+	0.938526i
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	−0.797292	−	0.603594i	$-0.793735\pi$
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	0.921374	+	0.388678i	$0.127068\pi$
$600$		0			0
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	−0.685110	−	0.728440i	$-0.740246\pi$
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	0.973402	+	0.229102i	$0.0735791\pi$
$602$		0			0
$603$		0			0
$604$	−1.51532	+	2.62461i	−0.0616575	+	0.106794i
$605$	11.1402			0.452914
$606$		0			0
$607$	46.0898			1.87073			0.935363	−	0.353689i	$-0.115073\pi$
$607$	46.0898			1.87073			0.935363	+	0.353689i	$0.115073\pi$
$608$	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	$0.653631\pi$
$614$	−2.77466	−	4.80586i	−0.111976	−	0.193949i
$615$		0			0
$616$		0			0
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	0.842492	−	0.538708i	$-0.181087\pi$
$617$	−1.12495	−	1.94847i	−0.0452889	−	0.0784426i	−0.887781	+	0.460266i	$0.847754\pi$
$618$		0			0
$619$	6.19078			0.248828			0.124414	−	0.992230i	$-0.460295\pi$
$619$	6.19078			0.248828			0.124414	+	0.992230i	$0.460295\pi$
$620$	−7.63088	−	13.2171i	−0.306464	−	0.530811i
$621$		0			0
$622$	8.37557			0.335830
$623$		0			0
$624$		0			0
$625$	1.06687			0.0426746
$626$	7.75119	−	13.4255i	0.309800	−	0.536589i
$627$		0			0
$628$	6.21523	+	10.7651i	0.248015	+	0.429574i
$629$	−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	$0.325623\pi$
$632$	−3.41029	−	5.90680i	−0.135654	−	0.234960i
$633$		0			0
$634$	3.55138	−	6.15118i	0.141043	−	0.244295i
$635$	27.9855			1.11057
$636$		0			0
$637$		0			0
$638$	9.11051			0.360689
$639$		0			0
$640$	−4.60947	−	7.98384i	−0.182205	−	0.315589i
$641$	−4.88888			−0.193099			−0.0965496	−	0.995328i	$-0.530781\pi$
$641$	−4.88888			−0.193099			−0.0965496	+	0.995328i	$0.530781\pi$
$642$		0			0
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	0.922218	+	0.386671i	$0.126375\pi$
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	−0.126242	+	0.992000i	$0.540291\pi$
$644$		0			0
$645$		0			0
$646$	−0.663848	−	1.14982i	−0.0261188	−	0.0452390i
$647$	−1.14038	−	1.97519i	−0.0448329	−	0.0776528i	0.842738	−	0.538324i	$-0.180942\pi$
$647$	−1.14038	−	1.97519i	−0.0448329	−	0.0776528i	−0.887571	+	0.460671i	$0.847609\pi$
$648$		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
$653$	−23.4793			−0.918815			−0.459407	−	0.888226i	$-0.651938\pi$
$653$	−23.4793			−0.918815			−0.459407	+	0.888226i	$0.651938\pi$
$654$		0			0
$655$	−9.65364			−0.377199
$656$	−0.0714517	+	0.123758i	−0.00278972	+	0.00483194i
$657$		0			0
$658$		0			0
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.158073	+	0.987427i	$0.550528\pi$
$659$	−23.9812	+	41.5366i	−0.934174	+	1.61804i	−0.776101	+	0.630609i	$0.782805\pi$
$660$		0			0
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	0.426571	+	0.904454i	$0.359721\pi$
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	−0.996566	+	0.0828055i	$0.973612\pi$
$662$	−10.1348	+	17.5539i	−0.393898	+	0.682252i
$663$		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
$668$	−28.4382			−1.10031
$669$		0			0
$670$	−0.706452			−0.0272926
$671$	6.31180	+	10.9324i	0.243664	+	0.422039i
$672$		0			0
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	0.492719	+	0.870189i	$0.336003\pi$
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	−0.999965	+	0.00838731i	$0.997330\pi$
$674$	−12.7613	+	22.1032i	−0.491547	+	0.851384i
$675$		0			0
$676$	−1.00950	−	1.74850i	−0.0388267	−	0.0672499i
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	0.971936	+	0.235246i	$0.0755895\pi$
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	−0.282239	+	0.959344i	$0.591077\pi$
$678$		0			0
$679$		0			0
$680$	0.894400	+	1.54915i	0.0342987	+	0.0594070i
$681$		0			0
$682$	−13.4210			−0.513915
$683$	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
$688$	0.184793			0.00704515
$689$	0.967034	−	1.67495i	0.0368411	−	0.0638106i
$690$		0			0
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	0.845699	−	0.533660i	$-0.179184\pi$
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	−0.885013	+	0.465567i	$0.845850\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	−4.13176	−	7.15642i	−0.156727	−	0.271458i
$696$		0			0
$697$	−0.798133	+	1.38241i	−0.0302315	+	0.0523624i
$698$	1.28642			0.0486916
$699$		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
$704$	−8.33275			−0.314052
$705$		0			0
$706$	6.30200	+	10.9154i	0.237179	+	0.410806i
$707$		0			0
$708$		0			0
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$	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
$716$	−10.4662			−0.391139
$717$		0			0
$718$	18.4115			0.687110
$719$	−12.9768	+	22.4765i	−0.483954	+	0.838233i	−0.999830	−	0.0184300i	$-0.994133\pi$
$719$	−12.9768	+	22.4765i	−0.483954	+	0.838233i	0.515876	+	0.856663i	$0.327467\pi$
$720$		0			0
$721$		0			0
$722$	3.77631	−	6.54076i	0.140540	−	0.243422i
$723$		0			0
$724$	−10.5706	+	18.3088i	−0.392852	+	0.680440i
$725$	−9.98205	+	17.2894i	−0.370724	+	0.642113i
$726$		0			0
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	−0.756311	−	0.654213i	$-0.773000\pi$
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	0.944720	+	0.327878i	$0.106333\pi$
$728$		0			0
$729$		0			0
$730$	1.21419	−	2.10304i	0.0449393	−	0.0778372i
$731$	2.06418			0.0763464
$732$		0			0
$733$	40.6614			1.50186			0.750931	−	0.660381i	$-0.229605\pi$
$733$	40.6614			1.50186			0.750931	+	0.660381i	$0.229605\pi$
$734$	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	$0.678857\pi$
$740$	−7.63088	−	13.2171i	−0.280517	−	0.485869i
$741$		0			0
$742$		0			0
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	0.583377	−	0.812202i	$-0.301731\pi$
$743$	−11.2221	−	19.4372i	−0.411699	−	0.713083i	−0.995076	+	0.0991184i	$0.968398\pi$
$744$		0			0
$745$	0.580785			0.0212783
$746$	0.343426	+	0.594831i	0.0125737	+	0.0217783i
$747$		0			0
$748$	−0.948615			−0.0346848
$749$		0			0
$750$		0			0
$751$	24.2172			0.883698			0.441849	−	0.897090i	$-0.354323\pi$
$751$	24.2172			0.883698			0.441849	+	0.897090i	$0.354323\pi$
$752$	−0.195937	+	0.339373i	−0.00714508	+	0.0123756i
$753$		0			0
$754$	−9.28740	−	16.0862i	−0.338227	−	0.585827i
$755$	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	$0.447012\pi$
$758$	3.04442	+	5.27308i	0.110578	+	0.191527i
$759$		0			0
$760$	6.16772	−	10.6828i	0.223727	−	0.387506i
$761$	18.2722			0.662366			0.331183	−	0.943566i	$-0.392552\pi$
$761$	18.2722			0.662366			0.331183	+	0.943566i	$0.392552\pi$
$762$		0			0
$763$		0			0
$764$	15.8357			0.572917
$765$		0			0
$766$	3.39986	+	5.88874i	0.122842	+	0.212769i
$767$	−35.0333			−1.26498
$768$		0			0
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	0.649217	−	0.760604i	$-0.275097\pi$
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	−0.983310	+	0.181936i	$0.941764\pi$
$770$		0			0
$771$		0			0
$772$	−0.391407	−	0.677937i	−0.0140870	−	0.0243995i
$773$	−1.48040	−	2.56413i	−0.0532463	−	0.0922253i	0.838174	−	0.545403i	$-0.183624\pi$
$773$	−1.48040	−	2.56413i	−0.0532463	−	0.0922253i	−0.891420	+	0.453178i	$0.850290\pi$
$774$		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
$779$	11.0077			0.394393
$780$		0			0
$781$	−0.916222			−0.0327850
$782$	−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
$787$	16.7010	−	28.9270i	0.595326	−	1.03113i	−0.398175	−	0.917310i	$-0.630356\pi$
$787$	16.7010	−	28.9270i	0.595326	−	1.03113i	0.993501	−	0.113825i	$-0.0363104\pi$
$788$	−7.02007	+	12.1591i	−0.250080	+	0.433150i
$789$		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
$794$	−25.7083			−0.912354
$795$		0			0
$796$	4.46286			0.158182
$797$	24.6755	+	42.7391i	0.874050	+	1.51390i	0.857772	+	0.514031i	$0.171848\pi$
$797$	24.6755	+	42.7391i	0.874050	+	1.51390i	0.0162779	+	0.999868i	$0.494818\pi$
$798$		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
$803$	1.69372	+	2.93360i	0.0597699	+	0.103525i
$804$		0			0
$805$		0			0
$806$	13.6816	+	23.6971i	0.481912	+	0.834696i
$807$		0			0
$808$	−4.84968			−0.170611
$809$	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	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$		0			0
$813$		0			0
$814$	−13.4210			−0.470405
$815$	−1.74897	+	3.02931i	−0.0612638	+	0.106112i
$816$		0			0
$817$	−7.11721	−	12.3274i	−0.249000	−	0.431280i
$818$	−7.93643			−0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.841110	−	0.540864i	$-0.818097\pi$
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.0478469	−	0.998855i	$-0.515236\pi$
$822$		0			0
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	−0.959937	−	0.280217i	$-0.909594\pi$
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	0.722643	+	0.691221i	$0.242927\pi$
$824$	10.3233			0.359628
$825$		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	0.557871	−	0.829928i	$-0.311618\pi$
$829$	−12.6630	−	21.9329i	−0.439803	−	0.761761i	−0.997674	+	0.0681664i	$0.978285\pi$
$830$	−17.8307			−0.618912
$831$		0			0
$832$	8.49454	+	14.7130i	0.294495	+	0.510080i
$833$		0			0
$834$		0			0
$835$	15.6172	+	27.0498i	0.540456	+	0.936097i
$836$	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	$-0.785270\pi$
$839$	4.35710	−	7.54671i	0.150424	−	0.260541i	0.931383	+	0.364040i	$0.118603\pi$
$840$		0			0
$841$	−5.14749	−	8.91571i	−0.177500	−	0.307438i
$842$	−21.7252			−0.748701
$843$		0			0
$844$	−7.14290			−0.245869
$845$	−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
$850$	−0.655230	+	1.13489i	−0.0224742	+	0.0389265i
$851$	41.2943	−	71.5239i	1.41555	−	2.45181i
$852$		0			0
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	−0.745053	−	0.667005i	$-0.767576\pi$
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	0.950170	+	0.311733i	$0.100909\pi$
$854$		0			0
$855$		0			0
$856$	−10.1133	+	17.5168i	−0.345667	+	0.598713i
$857$	−6.50030			−0.222046			−0.111023	−	0.993818i	$-0.535413\pi$
$857$	−6.50030			−0.222046			−0.111023	+	0.993818i	$0.535413\pi$
$858$		0			0
$859$	−53.5526			−1.82719			−0.913596	−	0.406623i	$-0.866706\pi$
$859$	−53.5526			−1.82719			−0.913596	+	0.406623i	$0.866706\pi$
$860$	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
$866$	−8.64233	−	14.9690i	−0.293678	−	0.508666i
$867$		0			0
$868$		0			0
$869$	−1.98633	−	3.44042i	−0.0673816	−	0.116708i
$870$		0			0
$871$	−2.00917			−0.0680782
$872$	0.572796	+	0.992112i	0.0193973	+	0.0335971i
$873$		0			0
$874$	25.3773			0.858401
$875$		0			0
$876$		0			0
$877$	−11.7888			−0.398079			−0.199040	−	0.979991i	$-0.563782\pi$
$877$	−11.7888			−0.398079			−0.199040	+	0.979991i	$0.563782\pi$
$878$	9.64244	−	16.7012i	0.325416	−	0.563638i
$879$		0			0
$880$	0.0466368	+	0.0807773i	0.00157213	+	0.00272300i
$881$	−49.4858			−1.66722			−0.833609	−	0.552355i	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	0.967034	+	1.67495i	0.0325249	+	0.0563347i
$885$		0			0
$886$	−8.22668	+	14.2490i	−0.276381	+	0.478706i
$887$	−11.8848			−0.399051			−0.199526	−	0.979893i	$-0.563940\pi$
$887$	−11.8848			−0.399051			−0.199526	+	0.979893i	$0.563940\pi$
$888$		0			0
$889$		0			0
$890$	10.7656			0.360863
$891$		0			0
$892$	4.34477	+	7.52536i	0.145474	+	0.251968i
$893$	30.1857			1.01013
$894$		0			0
$895$	5.74763	+	9.95518i	0.192122	+	0.332765i
$896$		0			0
$897$		0			0
$898$	2.93717	+	5.08732i	0.0980145	+	0.169766i
$899$	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
$905$	23.2199			0.771855
$906$		0			0
$907$	−26.0215			−0.864029			−0.432014	−	0.901867i	$-0.642197\pi$
$907$	−26.0215			−0.864029			−0.432014	+	0.901867i	$0.642197\pi$
$908$	7.32547	−	12.6881i	0.243104	−	0.421069i
$909$		0			0
$910$		0			0
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	−0.897493	−	0.441028i	$-0.854614\pi$
$911$	−2.01636	+	3.49244i	−0.0668050	+	0.115710i	0.830688	+	0.556738i	$0.187947\pi$
$912$		0			0
$913$	12.4363	−	21.5403i	0.411581	−	0.712879i
$914$	8.54266	−	14.7963i	0.282566	−	0.489419i
$915$		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	$0.316087\pi$
$920$	−34.1908			−1.12724
$921$		0			0
$922$	0.849356			0.0279720
$923$	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
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	0.922097	−	0.386958i	$-0.126474\pi$
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	−0.796164	+	0.605081i	$0.793141\pi$
$930$		0			0
$931$		0			0
$932$	−9.96926	−	17.2673i	−0.326554	−	0.565608i
$933$		0			0
$934$	30.0880			0.984510
$935$	0.520945	+	0.902302i	0.0170367	+	0.0295084i
$936$		0			0
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$		0			0
$939$		0			0
$940$	−15.4611			−0.504286
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	−0.911712	−	0.410829i	$-0.865239\pi$
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	0.811645	+	0.584151i	$0.198573\pi$
$942$		0			0
$943$	−15.2554	−	26.4231i	−0.496783	−	0.860454i
$944$	−0.435518			−0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	0.907684	−	0.419654i	$-0.137849\pi$
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	−0.817273	+	0.576250i	$0.804515\pi$
$948$		0			0
$949$	3.45320	−	5.98112i	0.112096	−	0.194155i
$950$	9.03684			0.293194
$951$		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
$956$	−18.5220			−0.599044
$957$		0			0
$958$	−9.58219	−	16.5968i	−0.309586	−	0.536219i
$959$		0			0
$960$		0			0
$961$	−27.1373	−	47.0031i	−0.875396	−	1.51623i
$962$	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	0.785206	+	0.619235i	$0.212557\pi$
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.143670	+	0.989626i	$0.454110\pi$
$968$	23.4620			0.754098
$969$		0			0
$970$	2.24990			0.0722401
$971$	−15.3596	+	26.6036i	−0.492914	+	0.853752i	−0.999967	−	0.00816326i	$-0.997402\pi$
$971$	−15.3596	+	26.6036i	−0.492914	+	0.853752i	0.507053	+	0.861915i	$0.330735\pi$
$972$		0			0
$973$		0			0
$974$	−8.52687	+	14.7690i	−0.273219	+	0.473229i
$975$		0			0
$976$	0.159978	−	0.277089i	0.00512076	−	0.00886941i
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	−0.771808	−	0.635856i	$-0.780647\pi$
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	0.936571	+	0.350477i	$0.113981\pi$
$978$		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
$983$	−13.6963			−0.436846			−0.218423	−	0.975854i	$-0.570091\pi$
$983$	−13.6963			−0.436846			−0.218423	+	0.975854i	$0.570091\pi$
$984$		0			0
$985$	15.4206			0.491343
$986$	−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	$-0.539227\pi$
$992$	−26.0326	−	45.0897i	−0.826534	−	1.43160i
$993$		0			0
$994$		0			0
$995$	−2.45084	−	4.24497i	−0.0776968	−	0.134575i
$996$		0			0
$997$	16.2175			0.513614			0.256807	−	0.966463i	$-0.417330\pi$
$997$	16.2175			0.513614			0.256807	+	0.966463i	$0.417330\pi$
$998$	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.g.d.667.1		6
3.2	odd	2		441.2.g.c.79.3		6
7.2	even	3		189.2.f.b.127.1		6
7.3	odd	6		1323.2.h.b.802.3		6
7.4	even	3		1323.2.h.c.802.3		6
7.5	odd	6		1323.2.f.d.883.1		6
7.6	odd	2		1323.2.g.e.667.1		6
9.4	even	3		1323.2.h.c.226.3		6
9.5	odd	6		441.2.h.d.373.1		6
21.2	odd	6		63.2.f.a.43.3	yes	6
21.5	even	6		441.2.f.c.295.3		6
21.11	odd	6		441.2.h.d.214.1		6
21.17	even	6		441.2.h.e.214.1		6
21.20	even	2		441.2.g.b.79.3		6
28.23	odd	6		3024.2.r.k.2017.2		6
63.2	odd	6		567.2.a.h.1.1		3
63.4	even	3	inner	1323.2.g.d.361.1		6
63.5	even	6		441.2.f.c.148.3		6
63.13	odd	6		1323.2.h.b.226.3		6
63.16	even	3		567.2.a.c.1.3		3
63.23	odd	6		63.2.f.a.22.3	✓	6
63.31	odd	6		1323.2.g.e.361.1		6
63.32	odd	6		441.2.g.c.67.3		6
63.40	odd	6		1323.2.f.d.442.1		6
63.41	even	6		441.2.h.e.373.1		6
63.47	even	6		3969.2.a.q.1.1		3
63.58	even	3		189.2.f.b.64.1		6
63.59	even	6		441.2.g.b.67.3		6
63.61	odd	6		3969.2.a.l.1.3		3
84.23	even	6		1008.2.r.h.673.2		6
252.23	even	6		1008.2.r.h.337.2		6
252.79	odd	6		9072.2.a.bs.1.2		3
252.191	even	6		9072.2.a.ca.1.2		3
252.247	odd	6		3024.2.r.k.1009.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	63.23	odd	6
63.2.f.a.43.3	yes	6	21.2	odd	6
189.2.f.b.64.1		6	63.58	even	3
189.2.f.b.127.1		6	7.2	even	3
441.2.f.c.148.3		6	63.5	even	6
441.2.f.c.295.3		6	21.5	even	6
441.2.g.b.67.3		6	63.59	even	6
441.2.g.b.79.3		6	21.20	even	2
441.2.g.c.67.3		6	63.32	odd	6
441.2.g.c.79.3		6	3.2	odd	2
441.2.h.d.214.1		6	21.11	odd	6
441.2.h.d.373.1		6	9.5	odd	6
441.2.h.e.214.1		6	21.17	even	6
441.2.h.e.373.1		6	63.41	even	6
567.2.a.c.1.3		3	63.16	even	3
567.2.a.h.1.1		3	63.2	odd	6
1008.2.r.h.337.2		6	252.23	even	6
1008.2.r.h.673.2		6	84.23	even	6
1323.2.f.d.442.1		6	63.40	odd	6
1323.2.f.d.883.1		6	7.5	odd	6
1323.2.g.d.361.1		6	63.4	even	3	inner
1323.2.g.d.667.1		6	1.1	even	1	trivial
1323.2.g.e.361.1		6	63.31	odd	6
1323.2.g.e.667.1		6	7.6	odd	2
1323.2.h.b.226.3		6	63.13	odd	6
1323.2.h.b.802.3		6	7.3	odd	6
1323.2.h.c.226.3		6	9.4	even	3
1323.2.h.c.802.3		6	7.4	even	3
3024.2.r.k.1009.2		6	252.247	odd	6
3024.2.r.k.2017.2		6	28.23	odd	6
3969.2.a.l.1.3		3	63.61	odd	6
3969.2.a.q.1.1		3	63.47	even	6
9072.2.a.bs.1.2		3	252.79	odd	6
9072.2.a.ca.1.2		3	252.191	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +O(q^{10})\)	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} -1.34730 q^{5} -2.83750 q^{8} +(0.592396 + 1.02606i) q^{10} -1.65270 q^{11} +(1.68479 + 2.91815i) q^{13} +(0.0209445 + 0.0362770i) q^{16} +(0.233956 + 0.405223i) q^{17} +(1.61334 - 2.79439i) q^{19} +(-0.826352 + 1.43128i) q^{20} +(0.726682 + 1.25865i) q^{22} -8.94356 q^{23} -3.18479 q^{25} +(1.48158 - 2.56617i) q^{26} +(3.13429 - 5.42874i) q^{29} +(-4.61721 + 7.99724i) q^{31} +(-2.81908 + 4.88279i) q^{32} +(0.205737 - 0.356347i) q^{34} +(-4.61721 + 7.99724i) q^{37} -2.83750 q^{38} +3.82295 q^{40} +(1.70574 + 2.95442i) q^{41} +(2.20574 - 3.82045i) q^{43} +(-1.01367 + 1.75573i) q^{44} +(3.93242 + 6.81115i) q^{46} +(4.67752 + 8.10170i) q^{47} +(1.40033 + 2.42544i) q^{50} +4.13341 q^{52} +(-0.286989 - 0.497079i) q^{53} +2.22668 q^{55} -5.51249 q^{58} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(-2.26991 - 3.93161i) q^{65} +(-0.298133 + 0.516382i) q^{67} +0.573978 q^{68} +0.554378 q^{71} +(-1.02481 - 1.77503i) q^{73} +8.12061 q^{74} +(-1.97906 - 3.42782i) q^{76} +(1.20187 + 2.08169i) q^{79} +(-0.0282185 - 0.0488759i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-7.52481 + 13.0334i) q^{83} +(-0.315207 - 0.545955i) q^{85} -3.87939 q^{86} +4.68954 q^{88} +(4.54323 - 7.86911i) q^{89} +(-5.48545 + 9.50108i) q^{92} +(4.11334 - 7.12452i) q^{94} +(-2.17365 + 3.76487i) q^{95} +(0.949493 - 1.64457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{8} - 12 q^{11} + 3 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} - 24 q^{23} - 12 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{31} - 9 q^{34} + 3 q^{37} - 12 q^{38} - 18 q^{40} + 3 q^{43} + 15 q^{44} + 3 q^{47} - 6 q^{50} - 42 q^{52} + 6 q^{53} - 18 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} - 12 q^{68} - 18 q^{71} + 21 q^{73} + 60 q^{74} - 15 q^{76} + 21 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} - 12 q^{86} + 54 q^{88} + 12 q^{89} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^8 - 12 * q^11 + 3 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^19 - 6 * q^20 - 9 * q^22 - 24 * q^23 - 12 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^31 - 9 * q^34 + 3 * q^37 - 12 * q^38 - 18 * q^40 + 3 * q^43 + 15 * q^44 + 3 * q^47 - 6 * q^50 - 42 * q^52 + 6 * q^53 - 18 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 - 12 * q^68 - 18 * q^71 + 21 * q^73 + 60 * q^74 - 15 * q^76 + 21 * q^79 - 15 * q^80 + 9 * q^82 - 18 * q^83 - 9 * q^85 - 12 * q^86 + 54 * q^88 + 12 * q^89 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97

Introduction

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