LMFDB - Embedded newform 513.2.h.c.235.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.13
Character	$\chi$	$=$	513.235
Dual form			513.2.h.c.334.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02031 q^{2} +2.08166 q^{4} +(-2.09369 + 3.62638i) q^{5} +(-0.976107 + 1.69067i) q^{7} +0.164982 q^{8} +O(q^{10})$	\(q+2.02031 q^{2} +2.08166 q^{4} +(-2.09369 + 3.62638i) q^{5} +(-0.976107 + 1.69067i) q^{7} +0.164982 q^{8} +(-4.22991 + 7.32643i) q^{10} +(0.669450 - 1.15952i) q^{11} +1.95110 q^{13} +(-1.97204 + 3.41568i) q^{14} -3.83001 q^{16} +(3.34047 + 5.78587i) q^{17} +(4.11317 + 1.44285i) q^{19} +(-4.35836 + 7.54890i) q^{20} +(1.35250 - 2.34260i) q^{22} +1.97253 q^{23} +(-6.26710 - 10.8549i) q^{25} +3.94183 q^{26} +(-2.03192 + 3.51940i) q^{28} +(-2.95031 - 5.11009i) q^{29} +(-0.385886 - 0.668373i) q^{31} -8.06778 q^{32} +(6.74880 + 11.6893i) q^{34} +(-4.08734 - 7.07948i) q^{35} +2.26011 q^{37} +(8.30989 + 2.91500i) q^{38} +(-0.345421 + 0.598288i) q^{40} +(3.79845 - 6.57911i) q^{41} +7.95603 q^{43} +(1.39357 - 2.41373i) q^{44} +3.98513 q^{46} +(-0.553869 - 0.959330i) q^{47} +(1.59443 + 2.76163i) q^{49} +(-12.6615 - 21.9304i) q^{50} +4.06153 q^{52} +(-3.75226 + 6.49910i) q^{53} +(2.80325 + 4.85537i) q^{55} +(-0.161040 + 0.278929i) q^{56} +(-5.96055 - 10.3240i) q^{58} +(0.506996 - 0.878143i) q^{59} +(-0.166041 - 0.287591i) q^{61} +(-0.779609 - 1.35032i) q^{62} -8.63941 q^{64} +(-4.08500 + 7.07543i) q^{65} +12.9089 q^{67} +(6.95373 + 12.0442i) q^{68} +(-8.25770 - 14.3028i) q^{70} +(-1.81291 - 3.14004i) q^{71} +(-2.48182 - 4.29864i) q^{73} +4.56613 q^{74} +(8.56223 + 3.00352i) q^{76} +(1.30691 + 2.26363i) q^{77} +5.17682 q^{79} +(8.01886 - 13.8891i) q^{80} +(7.67406 - 13.2919i) q^{82} +(-6.30706 + 10.9242i) q^{83} -27.9757 q^{85} +16.0737 q^{86} +(0.110447 - 0.191300i) q^{88} +(-0.569098 + 0.985707i) q^{89} +(-1.90448 + 3.29866i) q^{91} +4.10614 q^{92} +(-1.11899 - 1.93815i) q^{94} +(-13.8440 + 11.8951i) q^{95} -3.75873 q^{97} +(3.22125 + 5.57936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.02031			1.42858			0.714288	−	0.699852i	$-0.246751\pi$
$2$	2.02031			1.42858			0.714288	+	0.699852i	$0.246751\pi$
$3$		0			0
$3$		0			0
$4$	2.08166			1.04083
$5$	−2.09369	+	3.62638i	−0.936328	+	1.62177i	−0.164079	+	0.986447i	$0.552465\pi$
$5$	−2.09369	+	3.62638i	−0.936328	+	1.62177i	−0.772249	+	0.635321i	$0.780868\pi$
$6$		0			0
$7$	−0.976107	+	1.69067i	−0.368934	+	0.639012i	−0.989399	−	0.145222i	$-0.953610\pi$
$7$	−0.976107	+	1.69067i	−0.368934	+	0.639012i	0.620465	+	0.784234i	$0.286944\pi$
$8$	0.164982			0.0583299
$9$		0			0
$10$	−4.22991	+	7.32643i	−1.33762	+	2.31682i
$11$	0.669450	−	1.15952i	0.201847	−	0.349609i	−0.747277	−	0.664513i	$-0.768639\pi$
$11$	0.669450	−	1.15952i	0.201847	−	0.349609i	0.949124	+	0.314904i	$0.101972\pi$
$12$		0			0
$13$	1.95110			0.541138			0.270569	−	0.962701i	$-0.412788\pi$
$13$	1.95110			0.541138			0.270569	+	0.962701i	$0.412788\pi$
$14$	−1.97204	+	3.41568i	−0.527050	+	0.912878i
$15$		0			0
$16$	−3.83001			−0.957502
$17$	3.34047	+	5.78587i	0.810184	+	1.40328i	0.912735	+	0.408551i	$0.133966\pi$
$17$	3.34047	+	5.78587i	0.810184	+	1.40328i	−0.102552	+	0.994728i	$0.532701\pi$
$18$		0			0
$19$	4.11317	+	1.44285i	0.943626	+	0.331012i
$19$	4.11317	+	1.44285i	0.943626	+	0.331012i
$20$	−4.35836	+	7.54890i	−0.974559	+	1.68799i
$21$		0			0
$22$	1.35250	−	2.34260i	0.288354	−	0.499443i
$23$	1.97253			0.411301			0.205651	−	0.978625i	$-0.434069\pi$
$23$	1.97253			0.411301			0.205651	+	0.978625i	$0.434069\pi$
$24$		0			0
$25$	−6.26710	−	10.8549i	−1.25342	−	2.17099i
$26$	3.94183			0.773056
$27$		0			0
$28$	−2.03192	+	3.51940i	−0.383998	+	0.665103i
$29$	−2.95031	−	5.11009i	−0.547859	−	0.948920i	−0.998421	−	0.0561744i	$-0.982110\pi$
$29$	−2.95031	−	5.11009i	−0.547859	−	0.948920i	0.450562	−	0.892745i	$-0.351224\pi$
$30$		0			0
$31$	−0.385886	−	0.668373i	−0.0693071	−	0.120043i	0.829289	−	0.558819i	$-0.188746\pi$
$31$	−0.385886	−	0.668373i	−0.0693071	−	0.120043i	−0.898596	+	0.438776i	$0.855412\pi$
$32$	−8.06778			−1.42619
$33$		0			0
$34$	6.74880	+	11.6893i	1.15741	+	2.00469i
$35$	−4.08734	−	7.07948i	−0.690886	−	1.19665i
$36$		0			0
$37$	2.26011			0.371560			0.185780	−	0.982591i	$-0.440519\pi$
$37$	2.26011			0.371560			0.185780	+	0.982591i	$0.440519\pi$
$38$	8.30989	+	2.91500i	1.34804	+	0.472876i
$39$		0			0
$40$	−0.345421	+	0.598288i	−0.0546159	+	0.0945976i
$41$	3.79845	−	6.57911i	0.593219	−	1.02749i	−0.400577	−	0.916263i	$-0.631190\pi$
$41$	3.79845	−	6.57911i	0.593219	−	1.02749i	0.993796	−	0.111222i	$-0.0354764\pi$
$42$		0			0
$43$	7.95603			1.21328			0.606642	−	0.794975i	$-0.292516\pi$
$43$	7.95603			1.21328			0.606642	+	0.794975i	$0.292516\pi$
$44$	1.39357	−	2.41373i	0.210088	−	0.363884i
$45$		0			0
$46$	3.98513			0.587576
$47$	−0.553869	−	0.959330i	−0.0807902	−	0.139933i	0.822799	−	0.568332i	$-0.192411\pi$
$47$	−0.553869	−	0.959330i	−0.0807902	−	0.139933i	−0.903590	+	0.428399i	$0.859078\pi$
$48$		0			0
$49$	1.59443	+	2.76163i	0.227776	+	0.394519i
$50$	−12.6615	−	21.9304i	−1.79061	−	3.10142i
$51$		0			0
$52$	4.06153			0.563233
$53$	−3.75226	+	6.49910i	−0.515412	+	0.892721i	0.484427	+	0.874831i	$0.339028\pi$
$53$	−3.75226	+	6.49910i	−0.515412	+	0.892721i	−0.999840	+	0.0178892i	$0.994305\pi$
$54$		0			0
$55$	2.80325	+	4.85537i	0.377990	+	0.654697i
$56$	−0.161040	+	0.278929i	−0.0215199	+	0.0372735i
$57$		0			0
$58$	−5.96055	−	10.3240i	−0.782658	−	1.35560i
$59$	0.506996	−	0.878143i	0.0660053	−	0.114325i	−0.831134	−	0.556072i	$-0.812308\pi$
$59$	0.506996	−	0.878143i	0.0660053	−	0.114325i	0.897139	+	0.441747i	$0.145641\pi$
$60$		0			0
$61$	−0.166041	−	0.287591i	−0.0212593	−	0.0368222i	0.855200	−	0.518298i	$-0.173434\pi$
$61$	−0.166041	−	0.287591i	−0.0212593	−	0.0368222i	−0.876459	+	0.481476i	$0.840101\pi$
$62$	−0.779609	−	1.35032i	−0.0990105	−	0.171491i
$63$		0			0
$64$	−8.63941			−1.07993
$65$	−4.08500	+	7.07543i	−0.506682	+	0.877599i
$66$		0			0
$67$	12.9089			1.57708			0.788539	−	0.614984i	$-0.210838\pi$
$67$	12.9089			1.57708			0.788539	+	0.614984i	$0.210838\pi$
$68$	6.95373	+	12.0442i	0.843264	+	1.46058i
$69$		0			0
$70$	−8.25770	−	14.3028i	−0.986984	−	1.70951i
$71$	−1.81291	−	3.14004i	−0.215152	−	0.372655i	0.738167	−	0.674618i	$-0.235691\pi$
$71$	−1.81291	−	3.14004i	−0.215152	−	0.372655i	−0.953320	+	0.301963i	$0.902358\pi$
$72$		0			0
$73$	−2.48182	−	4.29864i	−0.290475	−	0.503118i	0.683447	−	0.730000i	$-0.260480\pi$
$73$	−2.48182	−	4.29864i	−0.290475	−	0.503118i	−0.973922	+	0.226882i	$0.927147\pi$
$74$	4.56613			0.530801
$75$		0			0
$76$	8.56223	+	3.00352i	0.982156	+	0.344528i
$77$	1.30691	+	2.26363i	0.148936	+	0.257965i
$78$		0			0
$79$	5.17682			0.582438			0.291219	−	0.956656i	$-0.405939\pi$
$79$	5.17682			0.582438			0.291219	+	0.956656i	$0.405939\pi$
$80$	8.01886	−	13.8891i	0.896536	−	1.55285i
$81$		0			0
$82$	7.67406	−	13.2919i	0.847458	−	1.46784i
$83$	−6.30706	+	10.9242i	−0.692290	+	1.19908i	0.278796	+	0.960350i	$0.410065\pi$
$83$	−6.30706	+	10.9242i	−0.692290	+	1.19908i	−0.971086	+	0.238731i	$0.923269\pi$
$84$		0			0
$85$	−27.9757			−3.03439
$86$	16.0737			1.73327
$87$		0			0
$88$	0.110447	−	0.191300i	0.0117737	−	0.0203927i
$89$	−0.569098	+	0.985707i	−0.0603243	+	0.104485i	−0.894610	−	0.446847i	$-0.852547\pi$
$89$	−0.569098	+	0.985707i	−0.0603243	+	0.104485i	0.834286	+	0.551332i	$0.185880\pi$
$90$		0			0
$91$	−1.90448	+	3.29866i	−0.199644	+	0.345793i
$92$	4.10614			0.428095
$93$		0			0
$94$	−1.11899	−	1.93815i	−0.115415	−	0.199904i
$95$	−13.8440	+	11.8951i	−1.42037	+	1.22041i
$96$		0			0
$97$	−3.75873			−0.381641			−0.190821	−	0.981625i	$-0.561115\pi$
$97$	−3.75873			−0.381641			−0.190821	+	0.981625i	$0.561115\pi$
$98$	3.22125	+	5.57936i	0.325395	+	0.563601i
$99$		0			0
$100$	−13.0460	−	22.5963i	−1.30460	−	2.25963i
$101$	−4.14343	−	7.17663i	−0.412287	−	0.714102i	0.582853	−	0.812578i	$-0.301937\pi$
$101$	−4.14343	−	7.17663i	−0.412287	−	0.714102i	−0.995139	+	0.0984762i	$0.968603\pi$
$102$		0			0
$103$	1.96614	+	3.40546i	0.193730	+	0.335550i	0.946483	−	0.322752i	$-0.104608\pi$
$103$	1.96614	+	3.40546i	0.193730	+	0.335550i	−0.752754	+	0.658302i	$0.771275\pi$
$104$	0.321896			0.0315645
$105$		0			0
$106$	−7.58074	+	13.1302i	−0.736306	+	1.27532i
$107$	0.188538			0.0182266			0.00911332	−	0.999958i	$-0.497099\pi$
$107$	0.188538			0.0182266			0.00911332	+	0.999958i	$0.497099\pi$
$108$		0			0
$109$	−1.08750	−	1.88361i	−0.104164	−	0.180417i	0.809233	−	0.587488i	$-0.199883\pi$
$109$	−1.08750	−	1.88361i	−0.104164	−	0.180417i	−0.913396	+	0.407072i	$0.866550\pi$
$110$	5.66343	+	9.80936i	0.539987	+	0.935285i
$111$		0			0
$112$	3.73850	−	6.47527i	0.353255	−	0.611855i
$113$	−6.33171	−	10.9669i	−0.595638	−	1.03167i	−0.993457	−	0.114211i	$-0.963566\pi$
$113$	−6.33171	−	10.9669i	−0.595638	−	1.03167i	0.397819	−	0.917464i	$-0.369767\pi$
$114$		0			0
$115$	−4.12988	+	7.15316i	−0.385113	+	0.667035i
$116$	−6.14155	−	10.6375i	−0.570228	−	0.987665i
$117$		0			0
$118$	1.02429	−	1.77412i	0.0942936	−	0.163321i
$119$	−13.0426			−1.19562
$120$		0			0
$121$	4.60367	+	7.97379i	0.418516	+	0.724890i
$122$	−0.335454	−	0.581023i	−0.0303706	−	0.0526033i
$123$		0			0
$124$	−0.803283	−	1.39133i	−0.0721370	−	0.124945i
$125$	31.5486			2.82179
$126$		0			0
$127$	−2.35619	+	4.08103i	−0.209078	+	0.362133i	−0.951424	−	0.307883i	$-0.900379\pi$
$127$	−2.35619	+	4.08103i	−0.209078	+	0.362133i	0.742347	+	0.670016i	$0.233713\pi$
$128$	−1.31876			−0.116563
$129$		0			0
$130$	−8.25298	+	14.2946i	−0.723834	+	1.25372i
$131$	9.45102	−	16.3697i	0.825740	−	1.43022i	−0.0756127	−	0.997137i	$-0.524091\pi$
$131$	9.45102	−	16.3697i	0.825740	−	1.43022i	0.901353	−	0.433086i	$-0.142575\pi$
$132$		0			0
$133$	−6.45427	+	5.54563i	−0.559656	+	0.480867i
$134$	26.0801			2.25298
$135$		0			0
$136$	0.551117	+	0.954564i	0.0472579	+	0.0818531i
$137$	2.83481	+	4.91003i	0.242194	+	0.419492i	0.961339	−	0.275368i	$-0.0887996\pi$
$137$	2.83481	+	4.91003i	0.242194	+	0.419492i	−0.719145	+	0.694860i	$0.755466\pi$
$138$		0			0
$139$	−7.16307			−0.607564			−0.303782	−	0.952742i	$-0.598249\pi$
$139$	−7.16307			−0.607564			−0.303782	+	0.952742i	$0.598249\pi$
$140$	−8.50845	−	14.7371i	−0.719095	−	1.24551i
$141$		0			0
$142$	−3.66263	−	6.34387i	−0.307361	−	0.532366i
$143$	1.30616	−	2.26234i	0.109227	−	0.189187i
$144$		0			0
$145$	24.7082			2.05190
$146$	−5.01405	−	8.68460i	−0.414966	−	0.718742i
$147$		0			0
$148$	4.70478			0.386731
$149$	−9.01546	+	15.6152i	−0.738576	+	1.27925i	0.214561	+	0.976711i	$0.431168\pi$
$149$	−9.01546	+	15.6152i	−0.738576	+	1.27925i	−0.953137	+	0.302540i	$0.902165\pi$
$150$		0			0
$151$	−3.24064	+	5.61296i	−0.263720	+	0.456776i	−0.967227	−	0.253911i	$-0.918283\pi$
$151$	−3.24064	+	5.61296i	−0.263720	+	0.456776i	0.703508	+	0.710688i	$0.251616\pi$
$152$	0.678599	+	0.238044i	0.0550416	+	0.0193079i
$153$		0			0
$154$	2.64037	+	4.57325i	0.212767	+	0.368523i
$155$	3.23170			0.259577
$156$		0			0
$157$	0.136893	−	0.237105i	0.0109252	−	0.0189231i	−0.860511	−	0.509432i	$-0.829856\pi$
$157$	0.136893	−	0.237105i	0.0109252	−	0.0189231i	0.871436	+	0.490509i	$0.163189\pi$
$158$	10.4588			0.832057
$159$		0			0
$160$	16.8914	−	29.2568i	1.33539	−	2.31296i
$161$	−1.92540	+	3.33490i	−0.151743	+	0.262827i
$162$		0			0
$163$	−8.01750			−0.627979			−0.313989	−	0.949426i	$-0.601666\pi$
$163$	−8.01750			−0.627979			−0.313989	+	0.949426i	$0.601666\pi$
$164$	7.90709	−	13.6955i	0.617440	−	1.06944i
$165$		0			0
$166$	−12.7422	+	22.0702i	−0.988989	+	1.71298i
$167$	20.7469			1.60545			0.802724	−	0.596351i	$-0.203383\pi$
$167$	20.7469			1.60545			0.802724	+	0.596351i	$0.203383\pi$
$168$		0			0
$169$	−9.19321			−0.707170
$170$	−56.5196			−4.33486
$171$		0			0
$172$	16.5618			1.26282
$173$	17.8905			1.36019			0.680095	−	0.733124i	$-0.261938\pi$
$173$	17.8905			1.36019			0.680095	+	0.733124i	$0.261938\pi$
$174$		0			0
$175$	24.4694			1.84972
$176$	−2.56400	+	4.44098i	−0.193269	+	0.334751i
$177$		0			0
$178$	−1.14976	+	1.99144i	−0.0861778	+	0.149264i
$179$	−0.212492			−0.0158824			−0.00794121	−	0.999968i	$-0.502528\pi$
$179$	−0.212492			−0.0158824			−0.00794121	+	0.999968i	$0.502528\pi$
$180$		0			0
$181$	7.99132	−	13.8414i	0.593990	−	1.02882i	−0.399698	−	0.916647i	$-0.630885\pi$
$181$	7.99132	−	13.8414i	0.593990	−	1.02882i	0.993689	−	0.112174i	$-0.0357815\pi$
$182$	−3.84765	+	6.66432i	−0.285207	+	0.493992i
$183$		0			0
$184$	0.325432			0.0239912
$185$	−4.73198	+	8.19602i	−0.347902	+	0.602583i
$186$		0			0
$187$	8.94512			0.654132
$188$	−1.15297	−	1.99700i	−0.0840889	−	0.145646i
$189$		0			0
$190$	−27.9693	+	24.0317i	−2.02911	+	1.74344i
$191$	−6.86947	+	11.8983i	−0.497057	+	0.860928i	−0.999994	−	0.00339491i	$-0.998919\pi$
$191$	−6.86947	+	11.8983i	−0.497057	+	0.860928i	0.502937	+	0.864323i	$0.332253\pi$
$192$		0			0
$193$	7.24295	−	12.5452i	0.521359	−	0.903021i	−0.478332	−	0.878179i	$-0.658759\pi$
$193$	7.24295	−	12.5452i	0.521359	−	0.903021i	0.999691	−	0.0248416i	$-0.00790813\pi$
$194$	−7.59381			−0.545203
$195$		0			0
$196$	3.31906	+	5.74879i	0.237076	+	0.410628i
$197$	−16.6680			−1.18755			−0.593774	−	0.804632i	$-0.702363\pi$
$197$	−16.6680			−1.18755			−0.593774	+	0.804632i	$0.702363\pi$
$198$		0			0
$199$	−4.99765	+	8.65619i	−0.354274	+	0.613621i	−0.986993	−	0.160760i	$-0.948605\pi$
$199$	−4.99765	+	8.65619i	−0.354274	+	0.613621i	0.632719	+	0.774381i	$0.281939\pi$
$200$	−1.03396	−	1.79087i	−0.0731119	−	0.126634i
$201$		0			0
$202$	−8.37102	−	14.4990i	−0.588983	−	1.02015i
$203$	11.5193			0.808495
$204$		0			0
$205$	15.9056	+	27.5493i	1.11089	+	1.92413i
$206$	3.97222	+	6.88009i	0.276758	+	0.479359i
$207$		0			0
$208$	−7.47273			−0.518140
$209$	4.42658	−	3.80340i	0.306193	−	0.263087i
$210$		0			0
$211$	−1.02198	+	1.77012i	−0.0703559	+	0.121860i	−0.899057	−	0.437831i	$-0.855747\pi$
$211$	−1.02198	+	1.77012i	−0.0703559	+	0.121860i	0.828701	+	0.559691i	$0.189080\pi$
$212$	−7.81093	+	13.5289i	−0.536457	+	0.929171i
$213$		0			0
$214$	0.380905			0.0260381
$215$	−16.6575	+	28.8516i	−1.13603	+	1.96766i
$216$		0			0
$217$	1.50666			0.102279
$218$	−2.19709	−	3.80547i	−0.148806	−	0.257739i
$219$		0			0
$220$	5.83541	+	10.1072i	0.393423	+	0.681429i
$221$	6.51759	+	11.2888i	0.438421	+	0.759367i
$222$		0			0
$223$	−26.2506			−1.75787			−0.878937	−	0.476939i	$-0.841746\pi$
$223$	−26.2506			−1.75787			−0.878937	+	0.476939i	$0.841746\pi$
$224$	7.87501	−	13.6399i	0.526171	−	0.911356i
$225$		0			0
$226$	−12.7920	−	22.1565i	−0.850914	−	1.47383i
$227$	12.4225	−	21.5163i	0.824508	−	1.42809i	−0.0777867	−	0.996970i	$-0.524785\pi$
$227$	12.4225	−	21.5163i	0.824508	−	1.42809i	0.902295	−	0.431120i	$-0.141881\pi$
$228$		0			0
$229$	−13.6496	−	23.6419i	−0.901993	−	1.56230i	−0.824903	−	0.565274i	$-0.808771\pi$
$229$	−13.6496	−	23.6419i	−0.901993	−	1.56230i	−0.0770898	−	0.997024i	$-0.524563\pi$
$230$	−8.34364	+	14.4516i	−0.550163	+	0.952911i
$231$		0			0
$232$	−0.486748	−	0.843072i	−0.0319566	−	0.0553504i
$233$	−8.88155	−	15.3833i	−0.581850	−	1.00779i	−0.995260	−	0.0972483i	$-0.968996\pi$
$233$	−8.88155	−	15.3833i	−0.581850	−	1.00779i	0.413411	−	0.910545i	$-0.364337\pi$
$234$		0			0
$235$	4.63853			0.302584
$236$	1.05539	−	1.82800i	0.0687003	−	0.118992i
$237$		0			0
$238$	−26.3502			−1.70803
$239$	−5.94744	−	10.3013i	−0.384708	−	0.666334i	0.607021	−	0.794686i	$-0.292365\pi$
$239$	−5.94744	−	10.3013i	−0.384708	−	0.666334i	−0.991729	+	0.128352i	$0.959031\pi$
$240$		0			0
$241$	0.969666	+	1.67951i	0.0624616	+	0.108187i	0.895565	−	0.444930i	$-0.146772\pi$
$241$	0.969666	+	1.67951i	0.0624616	+	0.108187i	−0.833104	+	0.553117i	$0.813438\pi$
$242$	9.30086	+	16.1096i	0.597882	+	1.03556i
$243$		0			0
$244$	−0.345640	−	0.598666i	−0.0221273	−	0.0383257i
$245$	−13.3530			−0.853091
$246$		0			0
$247$	8.02521	+	2.81514i	0.510632	+	0.179123i
$248$	−0.0636641	−	0.110270i	−0.00404268	−	0.00700212i
$249$		0			0
$250$	63.7380			4.03115
$251$	8.69809	−	15.0655i	0.549019	−	0.950928i	−0.449323	−	0.893369i	$-0.648335\pi$
$251$	8.69809	−	15.0655i	0.549019	−	0.950928i	0.998342	−	0.0575591i	$-0.0183318\pi$
$252$		0			0
$253$	1.32051	−	2.28719i	0.0830199	−	0.143795i
$254$	−4.76023	+	8.24496i	−0.298684	+	0.517335i
$255$		0			0
$256$	14.6145			0.913408
$257$	28.1812			1.75789			0.878946	−	0.476921i	$-0.158247\pi$
$257$	28.1812			1.75789			0.878946	+	0.476921i	$0.158247\pi$
$258$		0			0
$259$	−2.20611	+	3.82109i	−0.137081	+	0.237431i
$260$	−8.50359	+	14.7287i	−0.527371	+	0.913433i
$261$		0			0
$262$	19.0940	−	33.0718i	1.17963	−	2.04318i
$263$	1.19859			0.0739085			0.0369542	−	0.999317i	$-0.488234\pi$
$263$	1.19859			0.0739085			0.0369542	+	0.999317i	$0.488234\pi$
$264$		0			0
$265$	−15.7122	−	27.2143i	−0.965190	−	1.67176i
$266$	−13.0396	+	11.2039i	−0.799512	+	0.686955i
$267$		0			0
$268$	26.8721			1.64147
$269$	−3.49711	−	6.05717i	−0.213222	−	0.369312i	0.739499	−	0.673158i	$-0.235063\pi$
$269$	−3.49711	−	6.05717i	−0.213222	−	0.369312i	−0.952721	+	0.303846i	$0.901729\pi$
$270$		0			0
$271$	6.19864	+	10.7364i	0.376541	+	0.652188i	0.990556	−	0.137106i	$-0.0437801\pi$
$271$	6.19864	+	10.7364i	0.376541	+	0.652188i	−0.614016	+	0.789294i	$0.710447\pi$
$272$	−12.7940	−	22.1599i	−0.775752	−	1.34364i
$273$		0			0
$274$	5.72720	+	9.91980i	0.345993	+	0.599277i
$275$	−16.7821			−1.01200
$276$		0			0
$277$	9.75455	−	16.8954i	0.586094	−	1.01514i	−0.408644	−	0.912694i	$-0.633998\pi$
$277$	9.75455	−	16.8954i	0.586094	−	1.01514i	0.994738	−	0.102451i	$-0.0326684\pi$
$278$	−14.4716			−0.867952
$279$		0			0
$280$	−0.674337	−	1.16799i	−0.0402993	−	0.0698005i
$281$	−12.0748	−	20.9141i	−0.720321	−	1.24763i	−0.960871	−	0.276996i	$-0.910661\pi$
$281$	−12.0748	−	20.9141i	−0.720321	−	1.24763i	0.240550	−	0.970637i	$-0.422672\pi$
$282$		0			0
$283$	−10.6040	+	18.3667i	−0.630344	+	1.09179i	0.357137	+	0.934052i	$0.383753\pi$
$283$	−10.6040	+	18.3667i	−0.630344	+	1.09179i	−0.987481	+	0.157736i	$0.949580\pi$
$284$	−3.77386	−	6.53651i	−0.223937	−	0.387870i
$285$		0			0
$286$	2.63886	−	4.57064i	0.156039	−	0.270268i
$287$	7.41539	+	12.8438i	0.437717	+	0.758148i
$288$		0			0
$289$	−13.8175	+	23.9326i	−0.812795	+	1.40780i
$290$	49.9182			2.93130
$291$		0			0
$292$	−5.16631	−	8.94832i	−0.302336	−	0.523661i
$293$	−7.84223	−	13.5831i	−0.458148	−	0.793535i	0.540715	−	0.841206i	$-0.318154\pi$
$293$	−7.84223	−	13.5831i	−0.458148	−	0.793535i	−0.998863	+	0.0476705i	$0.984820\pi$
$294$		0			0
$295$	2.12299	+	3.67712i	0.123605	+	0.214090i
$296$	0.372877			0.0216730
$297$		0			0
$298$	−18.2141	+	31.5477i	−1.05511	+	1.82751i
$299$	3.84861			0.222571
$300$		0			0
$301$	−7.76594	+	13.4510i	−0.447621	+	0.775303i
$302$	−6.54711	+	11.3399i	−0.376744	+	0.652540i
$303$		0			0
$304$	−15.7535	−	5.52612i	−0.903524	−	0.316945i
$305$	1.39055			0.0796228
$306$		0			0
$307$	8.67805	+	15.0308i	0.495283	+	0.857855i	0.999985	−	0.00543863i	$-0.00173118\pi$
$307$	8.67805	+	15.0308i	0.495283	+	0.857855i	−0.504703	+	0.863293i	$0.668398\pi$
$308$	2.72054	+	4.71212i	0.155017	+	0.268498i
$309$		0			0
$310$	6.52905			0.370825
$311$	9.13185	+	15.8168i	0.517820	+	0.896890i	0.999786	+	0.0207003i	$0.00658957\pi$
$311$	9.13185	+	15.8168i	0.517820	+	0.896890i	−0.481966	+	0.876190i	$0.660077\pi$
$312$		0			0
$313$	4.90896	+	8.50257i	0.277471	+	0.480594i	0.970756	−	0.240070i	$-0.0771704\pi$
$313$	4.90896	+	8.50257i	0.277471	+	0.480594i	−0.693285	+	0.720664i	$0.743837\pi$
$314$	0.276566	−	0.479027i	0.0156075	−	0.0270330i
$315$		0			0
$316$	10.7764			0.606220
$317$	−5.67689	−	9.83266i	−0.318846	−	0.552257i	0.661402	−	0.750032i	$-0.269962\pi$
$317$	−5.67689	−	9.83266i	−0.318846	−	0.552257i	−0.980247	+	0.197775i	$0.936629\pi$
$318$		0			0
$319$	−7.90035			−0.442334
$320$	18.0883	−	31.3298i	1.01117	−	1.75139i
$321$		0			0
$322$	−3.88991	+	6.73753i	−0.216776	+	0.375468i
$323$	5.39181	+	28.6181i	0.300008	+	1.59235i
$324$		0			0
$325$	−12.2277	−	21.1791i	−0.678273	−	1.17480i
$326$	−16.1978			−0.897116
$327$		0			0
$328$	0.626676	−	1.08543i	0.0346024	−	0.0599331i
$329$	2.16254			0.119225
$330$		0			0
$331$	2.31414	−	4.00820i	0.127196	−	0.220311i	−0.795393	−	0.606094i	$-0.792735\pi$
$331$	2.31414	−	4.00820i	0.127196	−	0.220311i	0.922589	+	0.385783i	$0.126069\pi$
$332$	−13.1292	+	22.7404i	−0.720557	+	1.24804i
$333$		0			0
$334$	41.9153			2.29350
$335$	−27.0274	+	46.8128i	−1.47666	+	2.55765i
$336$		0			0
$337$	7.33227	−	12.6999i	0.399414	−	0.691806i	−0.594239	−	0.804288i	$-0.702547\pi$
$337$	7.33227	−	12.6999i	0.399414	−	0.691806i	0.993654	+	0.112482i	$0.0358802\pi$
$338$	−18.5732			−1.01025
$339$		0			0
$340$	−58.2359			−3.15829
$341$	−1.03332			−0.0559577
$342$		0			0
$343$	−19.8908			−1.07400
$344$	1.31260			0.0707707
$345$		0			0
$346$	36.1444			1.94314
$347$	15.0595	−	26.0837i	0.808434	−	1.40025i	−0.105514	−	0.994418i	$-0.533649\pi$
$347$	15.0595	−	26.0837i	0.808434	−	1.40025i	0.913948	−	0.405831i	$-0.133018\pi$
$348$		0			0
$349$	1.39279	−	2.41239i	0.0745545	−	0.129132i	−0.826338	−	0.563175i	$-0.809580\pi$
$349$	1.39279	−	2.41239i	0.0745545	−	0.129132i	0.900892	+	0.434042i	$0.142913\pi$
$350$	49.4359			2.64246
$351$		0			0
$352$	−5.40098	+	9.35476i	−0.287873	+	0.498611i
$353$	−5.04882	+	8.74482i	−0.268722	+	0.465440i	−0.968532	−	0.248889i	$-0.919935\pi$
$353$	−5.04882	+	8.74482i	−0.268722	+	0.465440i	0.699810	+	0.714329i	$0.253268\pi$
$354$		0			0
$355$	15.1827			0.805812
$356$	−1.18467	+	2.05191i	−0.0627874	+	0.108751i
$357$		0			0
$358$	−0.429301			−0.0226893
$359$	3.12391	+	5.41076i	0.164873	+	0.285569i	0.936610	−	0.350373i	$-0.113945\pi$
$359$	3.12391	+	5.41076i	0.164873	+	0.285569i	−0.771737	+	0.635942i	$0.780612\pi$
$360$		0			0
$361$	14.8364	+	11.8694i	0.780862	+	0.624704i
$362$	16.1450	−	27.9639i	0.848560	−	1.46975i
$363$		0			0
$364$	−3.96449	+	6.86669i	−0.207796	+	0.359912i
$365$	20.7847			1.08792
$366$		0			0
$367$	−1.44516	−	2.50309i	−0.0754366	−	0.130660i	0.825839	−	0.563905i	$-0.190702\pi$
$367$	−1.44516	−	2.50309i	−0.0754366	−	0.130660i	−0.901276	+	0.433245i	$0.857368\pi$
$368$	−7.55482			−0.393822
$369$		0			0
$370$	−9.56007	+	16.5585i	−0.497004	+	0.860837i
$371$	−7.32521	−	12.6876i	−0.380306	−	0.658710i
$372$		0			0
$373$	−7.36377	−	12.7544i	−0.381282	−	0.660399i	0.609964	−	0.792429i	$-0.291184\pi$
$373$	−7.36377	−	12.7544i	−0.381282	−	0.660399i	−0.991246	+	0.132030i	$0.957851\pi$
$374$	18.0719			0.934478
$375$		0			0
$376$	−0.0913784	−	0.158272i	−0.00471248	−	0.00816226i
$377$	−5.75635	−	9.97029i	−0.296467	−	0.513496i
$378$		0			0
$379$	11.7601			0.604077			0.302038	−	0.953296i	$-0.402333\pi$
$379$	11.7601			0.604077			0.302038	+	0.953296i	$0.402333\pi$
$380$	−28.8186	+	24.7615i	−1.47836	+	1.27024i
$381$		0			0
$382$	−13.8785	+	24.0382i	−0.710084	+	1.22990i
$383$	−15.4531	+	26.7656i	−0.789619	+	1.36766i	0.136582	+	0.990629i	$0.456388\pi$
$383$	−15.4531	+	26.7656i	−0.789619	+	1.36766i	−0.926200	+	0.377031i	$0.876945\pi$
$384$		0			0
$385$	−10.9451			−0.557813
$386$	14.6330	−	25.3451i	0.744801	−	1.29003i
$387$		0			0
$388$	−7.82440			−0.397224
$389$	7.08875	+	12.2781i	0.359414	+	0.622523i	0.987863	−	0.155327i	$-0.0496432\pi$
$389$	7.08875	+	12.2781i	0.359414	+	0.622523i	−0.628449	+	0.777851i	$0.716310\pi$
$390$		0			0
$391$	6.58919	+	11.4128i	0.333230	+	0.577171i
$392$	0.263052	+	0.455620i	0.0132861	+	0.0230123i
$393$		0			0
$394$	−33.6746			−1.69650
$395$	−10.8387	+	18.7731i	−0.545353	+	0.944579i
$396$		0			0
$397$	−3.48803	−	6.04144i	−0.175059	−	0.303211i	0.765123	−	0.643885i	$-0.222678\pi$
$397$	−3.48803	−	6.04144i	−0.175059	−	0.303211i	−0.940182	+	0.340673i	$0.889345\pi$
$398$	−10.0968	+	17.4882i	−0.506108	+	0.876604i
$399$		0			0
$400$	24.0030	+	41.5745i	1.20015	+	2.07872i
$401$	8.39419	−	14.5392i	0.419186	−	0.726051i	−0.576672	−	0.816976i	$-0.695649\pi$
$401$	8.39419	−	14.5392i	0.419186	−	0.726051i	0.995858	+	0.0909249i	$0.0289823\pi$
$402$		0			0
$403$	−0.752901	−	1.30406i	−0.0375047	−	0.0649600i
$404$	−8.62522	−	14.9393i	−0.429121	−	0.743259i
$405$		0			0
$406$	23.2725			1.15500
$407$	1.51303	−	2.62065i	0.0749982	−	0.129901i
$408$		0			0
$409$	13.4002			0.662595			0.331298	−	0.943526i	$-0.392514\pi$
$409$	13.4002			0.662595			0.331298	+	0.943526i	$0.392514\pi$
$410$	32.1343	+	55.6582i	1.58700	+	2.74876i
$411$		0			0
$412$	4.09284	+	7.08901i	0.201640	+	0.349251i
$413$	0.989765	+	1.71432i	0.0487032	+	0.0843563i
$414$		0			0
$415$	−26.4101	−	45.7436i	−1.29642	−	2.24547i
$416$	−15.7410			−0.771768
$417$		0			0
$418$	8.94307	−	7.68405i	0.437420	−	0.375839i
$419$	−5.28778	−	9.15870i	−0.258325	−	0.447432i	0.707468	−	0.706745i	$-0.249837\pi$
$419$	−5.28778	−	9.15870i	−0.258325	−	0.447432i	−0.965793	+	0.259313i	$0.916504\pi$
$420$		0			0
$421$	−19.2670			−0.939014			−0.469507	−	0.882929i	$-0.655568\pi$
$421$	−19.2670			−0.939014			−0.469507	+	0.882929i	$0.655568\pi$
$422$	−2.06472	+	3.57619i	−0.100509	+	0.174086i
$423$		0			0
$424$	−0.619055	+	1.07223i	−0.0300640	+	0.0520723i
$425$	41.8702	−	72.5212i	2.03100	−	3.51780i
$426$		0			0
$427$	0.648293			0.0313731
$428$	0.392472			0.0189708
$429$		0			0
$430$	−33.6533	+	58.2893i	−1.62291	+	2.81096i
$431$	−13.7684	+	23.8476i	−0.663203	+	1.14870i	0.316567	+	0.948570i	$0.397470\pi$
$431$	−13.7684	+	23.8476i	−0.663203	+	1.14870i	−0.979769	+	0.200130i	$0.935863\pi$
$432$		0			0
$433$	−10.9652	+	18.9923i	−0.526954	+	0.912711i	0.472552	+	0.881303i	$0.343333\pi$
$433$	−10.9652	+	18.9923i	−0.526954	+	0.912711i	−0.999507	+	0.0314088i	$0.990001\pi$
$434$	3.04393			0.146113
$435$		0			0
$436$	−2.26381	−	3.92103i	−0.108417	−	0.187783i
$437$	8.11337	+	2.84607i	0.388115	+	0.136146i
$438$		0			0
$439$	−14.2229			−0.678820			−0.339410	−	0.940638i	$-0.610227\pi$
$439$	−14.2229			−0.678820			−0.339410	+	0.940638i	$0.610227\pi$
$440$	0.462485	+	0.801047i	0.0220481	+	0.0381884i
$441$		0			0
$442$	13.1676	+	22.8069i	0.626318	+	1.08481i
$443$	7.11660	+	12.3263i	0.338120	+	0.585641i	0.984079	−	0.177731i	$-0.0568757\pi$
$443$	7.11660	+	12.3263i	0.338120	+	0.585641i	−0.645959	+	0.763372i	$0.723542\pi$
$444$		0			0
$445$	−2.38303	−	4.12753i	−0.112967	−	0.195664i
$446$	−53.0345			−2.51126
$447$		0			0
$448$	8.43299	−	14.6064i	0.398421	−	0.690086i
$449$	−3.11473			−0.146993			−0.0734966	−	0.997295i	$-0.523416\pi$
$449$	−3.11473			−0.146993			−0.0734966	+	0.997295i	$0.523416\pi$
$450$		0			0
$451$	−5.08575	−	8.80878i	−0.239479	−	0.414789i
$452$	−13.1805	−	22.8293i	−0.619958	−	1.07380i
$453$		0			0
$454$	25.0973	−	43.4697i	1.17787	−	2.04014i
$455$	−7.97480	−	13.8128i	−0.373864	−	0.647552i
$456$		0			0
$457$	5.77896	−	10.0095i	0.270329	−	0.468223i	−0.698617	−	0.715495i	$-0.746201\pi$
$457$	5.77896	−	10.0095i	0.270329	−	0.468223i	0.968946	+	0.247273i	$0.0795344\pi$
$458$	−27.5765	−	47.7639i	−1.28857	−	2.23186i
$459$		0			0
$460$	−8.59701	+	14.8905i	−0.400838	+	0.694271i
$461$	5.52503			0.257326			0.128663	−	0.991688i	$-0.458931\pi$
$461$	5.52503			0.257326			0.128663	+	0.991688i	$0.458931\pi$
$462$		0			0
$463$	−6.11457	−	10.5907i	−0.284168	−	0.492193i	0.688239	−	0.725484i	$-0.258384\pi$
$463$	−6.11457	−	10.5907i	−0.284168	−	0.492193i	−0.972407	+	0.233291i	$0.925051\pi$
$464$	11.2997	+	19.5717i	0.524576	+	0.908592i
$465$		0			0
$466$	−17.9435	−	31.0791i	−0.831217	−	1.43971i
$467$	−2.22377			−0.102904			−0.0514518	−	0.998675i	$-0.516385\pi$
$467$	−2.22377			−0.102904			−0.0514518	+	0.998675i	$0.516385\pi$
$468$		0			0
$469$	−12.6005	+	21.8247i	−0.581838	+	1.00777i
$470$	9.37128			0.432265
$471$		0			0
$472$	0.0836452	−	0.144878i	0.00385008	−	0.00666854i
$473$	5.32617	−	9.22519i	0.244897	−	0.424175i
$474$		0			0
$475$	−10.1156	−	53.6907i	−0.464137	−	2.46350i
$476$	−27.1504			−1.24443
$477$		0			0
$478$	−12.0157	−	20.8118i	−0.549585	−	0.951909i
$479$	6.95882	+	12.0530i	0.317957	+	0.550717i	0.980062	−	0.198694i	$-0.0636700\pi$
$479$	6.95882	+	12.0530i	0.317957	+	0.550717i	−0.662105	+	0.749411i	$0.730337\pi$
$480$		0			0
$481$	4.40970			0.201065
$482$	1.95903	+	3.39313i	0.0892312	+	0.154553i
$483$		0			0
$484$	9.58329	+	16.5987i	0.435604	+	0.754488i
$485$	7.86962	−	13.6306i	0.357341	−	0.618933i
$486$		0			0
$487$	−24.5312			−1.11161			−0.555807	−	0.831312i	$-0.687590\pi$
$487$	−24.5312			−1.11161			−0.555807	+	0.831312i	$0.687590\pi$
$488$	−0.0273937	−	0.0474472i	−0.00124005	−	0.00214784i
$489$		0			0
$490$	−26.9772			−1.21871
$491$	8.70193	−	15.0722i	0.392712	−	0.680198i	−0.600094	−	0.799930i	$-0.704870\pi$
$491$	8.70193	−	15.0722i	0.392712	−	0.680198i	0.992806	+	0.119732i	$0.0382034\pi$
$492$		0			0
$493$	19.7109	−	34.1402i	0.887733	−	1.53760i
$494$	16.2134	+	5.68746i	0.729477	+	0.255891i
$495$		0			0
$496$	1.47795	+	2.55988i	0.0663617	+	0.114942i
$497$	7.07836			0.317508
$498$		0			0
$499$	19.2038	−	33.2619i	0.859678	−	1.48901i	−0.0125579	−	0.999921i	$-0.503997\pi$
$499$	19.2038	−	33.2619i	0.859678	−	1.48901i	0.872236	−	0.489085i	$-0.162669\pi$
$500$	65.6735			2.93701
$501$		0			0
$502$	17.5729	−	30.4371i	0.784315	−	1.35847i
$503$	0.757962	−	1.31283i	0.0337958	−	0.0585361i	−0.848633	−	0.528982i	$-0.822574\pi$
$503$	0.757962	−	1.31283i	0.0337958	−	0.0585361i	0.882429	+	0.470446i	$0.155907\pi$
$504$		0			0
$505$	34.7003			1.54414
$506$	2.66785	−	4.62085i	0.118600	−	0.205422i
$507$		0			0
$508$	−4.90478	+	8.49533i	−0.217615	+	0.376919i
$509$	−1.21524			−0.0538644			−0.0269322	−	0.999637i	$-0.508574\pi$
$509$	−1.21524			−0.0538644			−0.0269322	+	0.999637i	$0.508574\pi$
$510$		0			0
$511$	9.69009			0.428665
$512$	32.1634			1.42144
$513$		0			0
$514$	56.9348			2.51128
$515$	−16.4660			−0.725579
$516$		0			0
$517$	−1.48315			−0.0652290
$518$	−4.45703	+	7.71980i	−0.195831	+	0.339189i
$519$		0			0
$520$	−0.673952	+	1.16732i	−0.0295547	+	0.0511903i
$521$	11.3543			0.497443			0.248721	−	0.968575i	$-0.419990\pi$
$521$	11.3543			0.497443			0.248721	+	0.968575i	$0.419990\pi$
$522$		0			0
$523$	−2.83152	+	4.90434i	−0.123814	+	0.214452i	−0.921269	−	0.388927i	$-0.872846\pi$
$523$	−2.83152	+	4.90434i	−0.123814	+	0.214452i	0.797455	+	0.603379i	$0.206179\pi$
$524$	19.6738	−	34.0761i	0.859455	−	1.48862i
$525$		0			0
$526$	2.42153			0.105584
$527$	2.57808	−	4.46537i	0.112303	−	0.194514i
$528$		0			0
$529$	−19.1091			−0.830831
$530$	−31.7435	−	54.9813i	−1.37885	−	2.38824i
$531$		0			0
$532$	−13.4356	+	11.5441i	−0.582508	+	0.500501i
$533$	7.41116	−	12.8365i	0.321013	−	0.556011i
$534$		0			0
$535$	−0.394740	+	0.683710i	−0.0170661	+	0.0295594i
$536$	2.12974			0.0919908
$537$		0			0
$538$	−7.06525	−	12.2374i	−0.304604	−	0.527590i
$539$	4.26957			0.183903
$540$		0			0
$541$	21.0798	−	36.5114i	0.906293	−	1.56975i	0.0871219	−	0.996198i	$-0.472233\pi$
$541$	21.0798	−	36.5114i	0.906293	−	1.56975i	0.819172	−	0.573549i	$-0.194434\pi$
$542$	12.5232	+	21.6908i	0.537917	+	0.931700i
$543$		0			0
$544$	−26.9502	−	46.6791i	−1.15548	−	2.00135i
$545$	9.10756			0.390125
$546$		0			0
$547$	−5.23919	−	9.07454i	−0.224011	−	0.387999i	0.732011	−	0.681293i	$-0.238582\pi$
$547$	−5.23919	−	9.07454i	−0.224011	−	0.387999i	−0.956022	+	0.293294i	$0.905249\pi$
$548$	5.90111	+	10.2210i	0.252083	+	0.436621i
$549$		0			0
$550$	−33.9050			−1.44571
$551$	−4.76205	−	25.2755i	−0.202870	−	1.07677i
$552$		0			0
$553$	−5.05313	+	8.75228i	−0.214881	+	0.372185i
$554$	19.7072	−	34.1339i	0.837280	−	1.45021i
$555$		0			0
$556$	−14.9111			−0.632371
$557$	18.3181	−	31.7279i	0.776164	−	1.34436i	−0.157973	−	0.987443i	$-0.550496\pi$
$557$	18.3181	−	31.7279i	0.776164	−	1.34436i	0.934138	−	0.356913i	$-0.116171\pi$
$558$		0			0
$559$	15.5230			0.656553
$560$	15.6545	+	27.1144i	0.661525	+	1.14579i
$561$		0			0
$562$	−24.3948	−	42.2531i	−1.02903	−	1.78234i
$563$	−4.29307	−	7.43582i	−0.180931	−	0.313382i	0.761267	−	0.648439i	$-0.224578\pi$
$563$	−4.29307	−	7.43582i	−0.180931	−	0.313382i	−0.942198	+	0.335057i	$0.891245\pi$
$564$		0			0
$565$	53.0267			2.23085
$566$	−21.4235	+	37.1065i	−0.900495	+	1.55970i
$567$		0			0
$568$	−0.299097	−	0.518050i	−0.0125498	−	0.0217369i
$569$	2.90516	−	5.03189i	0.121791	−	0.210948i	−0.798683	−	0.601752i	$-0.794470\pi$
$569$	2.90516	−	5.03189i	0.121791	−	0.210948i	0.920474	+	0.390804i	$0.127803\pi$
$570$		0			0
$571$	4.11198	+	7.12216i	0.172081	+	0.298053i	0.939147	−	0.343515i	$-0.111618\pi$
$571$	4.11198	+	7.12216i	0.172081	+	0.298053i	−0.767066	+	0.641568i	$0.778284\pi$
$572$	2.71899	−	4.70943i	0.113687	−	0.196911i
$573$		0			0
$574$	14.9814	+	25.9486i	0.625312	+	1.08307i
$575$	−12.3621	−	21.4117i	−0.515534	−	0.892930i
$576$		0			0
$577$	−24.3169			−1.01232			−0.506162	−	0.862438i	$-0.668936\pi$
$577$	−24.3169			−1.01232			−0.506162	+	0.862438i	$0.668936\pi$
$578$	−27.9157	+	48.3514i	−1.16114	+	2.01115i
$579$		0			0
$580$	51.4341			2.13568
$581$	−12.3127	−	21.3263i	−0.510818	−	0.884763i
$582$		0			0
$583$	5.02390	+	8.70165i	0.208069	+	0.360386i
$584$	−0.409456	−	0.709198i	−0.0169434	−	0.0293468i
$585$		0			0
$586$	−15.8437	−	27.4422i	−0.654499	−	1.13363i
$587$	1.21589			0.0501851			0.0250925	−	0.999685i	$-0.492012\pi$
$587$	1.21589			0.0501851			0.0250925	+	0.999685i	$0.492012\pi$
$588$		0			0
$589$	−0.622852	−	3.30591i	−0.0256642	−	0.136218i
$590$	4.28910	+	7.42894i	0.176579	+	0.305845i
$591$		0			0
$592$	−8.65624			−0.355769
$593$	−5.40934	+	9.36925i	−0.222135	+	0.384749i	−0.955456	−	0.295134i	$-0.904636\pi$
$593$	−5.40934	+	9.36925i	−0.222135	+	0.384749i	0.733321	+	0.679882i	$0.237969\pi$
$594$		0			0
$595$	27.3073	−	47.2976i	1.11949	−	1.93901i
$596$	−18.7671	+	32.5056i	−0.768732	+	1.33148i
$597$		0			0
$598$	7.77539			0.317959
$599$	−45.8655			−1.87401			−0.937007	−	0.349310i	$-0.886416\pi$
$599$	−45.8655			−1.87401			−0.937007	+	0.349310i	$0.886416\pi$
$600$		0			0
$601$	−14.2594	+	24.6980i	−0.581652	+	1.00745i	0.413632	+	0.910444i	$0.364260\pi$
$601$	−14.2594	+	24.6980i	−0.581652	+	1.00745i	−0.995284	+	0.0970064i	$0.969073\pi$
$602$	−15.6896	+	27.1752i	−0.639461	+	1.10758i
$603$		0			0
$604$	−6.74593	+	11.6843i	−0.274488	+	0.475427i
$605$	−38.5547			−1.56747
$606$		0			0
$607$	14.8706	+	25.7567i	0.603580	+	1.04543i	0.992274	+	0.124065i	$0.0395931\pi$
$607$	14.8706	+	25.7567i	0.603580	+	1.04543i	−0.388694	+	0.921367i	$0.627074\pi$
$608$	−33.1842	−	11.6406i	−1.34580	−	0.472088i
$609$		0			0
$610$	2.80935			0.113747
$611$	−1.08065	−	1.87175i	−0.0437186	−	0.0757228i
$612$		0			0
$613$	−15.9215	−	27.5769i	−0.643065	−	1.11382i	−0.984745	−	0.174005i	$-0.944329\pi$
$613$	−15.9215	−	27.5769i	−0.643065	−	1.11382i	0.341680	−	0.939816i	$-0.389004\pi$
$614$	17.5324	+	30.3670i	0.707549	+	1.22551i
$615$		0			0
$616$	0.215617	+	0.373459i	0.00868744	+	0.0150471i
$617$	−33.8268			−1.36181			−0.680907	−	0.732370i	$-0.738414\pi$
$617$	−33.8268			−1.36181			−0.680907	+	0.732370i	$0.738414\pi$
$618$		0			0
$619$	−2.12694	+	3.68397i	−0.0854890	+	0.148071i	−0.905599	−	0.424134i	$-0.860579\pi$
$619$	−2.12694	+	3.68397i	−0.0854890	+	0.148071i	0.820111	+	0.572205i	$0.193912\pi$
$620$	6.72731			0.270175
$621$		0			0
$622$	18.4492	+	31.9549i	0.739745	+	1.28128i
$623$	−1.11100	−	1.92431i	−0.0445113	−	0.0770959i
$624$		0			0
$625$	−34.7176	+	60.1327i	−1.38870	+	2.40531i
$626$	9.91764	+	17.1778i	0.396388	+	0.686565i
$627$		0			0
$628$	0.284964	−	0.493573i	0.0113713	−	0.0196957i
$629$	7.54983	+	13.0767i	0.301032	+	0.521402i
$630$		0			0
$631$	−14.9006	+	25.8087i	−0.593185	+	1.02743i	0.400615	+	0.916246i	$0.368796\pi$
$631$	−14.9006	+	25.8087i	−0.593185	+	1.02743i	−0.993800	+	0.111180i	$0.964537\pi$
$632$	0.854082			0.0339736
$633$		0			0
$634$	−11.4691	−	19.8650i	−0.455496	−	0.788941i
$635$	−9.86626	−	17.0889i	−0.391531	−	0.678151i
$636$		0			0
$637$	3.11089	+	5.38822i	0.123258	+	0.213489i
$638$	−15.9612			−0.631909
$639$		0			0
$640$	2.76107	−	4.78231i	0.109141	−	0.189037i
$641$	−14.7532			−0.582718			−0.291359	−	0.956614i	$-0.594107\pi$
$641$	−14.7532			−0.582718			−0.291359	+	0.956614i	$0.594107\pi$
$642$		0			0
$643$	−14.4049	+	24.9501i	−0.568076	+	0.983936i	0.428681	+	0.903456i	$0.358979\pi$
$643$	−14.4049	+	24.9501i	−0.568076	+	0.983936i	−0.996756	+	0.0804797i	$0.974355\pi$
$644$	−4.00804	+	6.94212i	−0.157939	+	0.273558i
$645$		0			0
$646$	10.8931	+	57.8174i	0.428585	+	2.27480i
$647$	−6.79304			−0.267062			−0.133531	−	0.991045i	$-0.542632\pi$
$647$	−6.79304			−0.267062			−0.133531	+	0.991045i	$0.542632\pi$
$648$		0			0
$649$	−0.678817	−	1.17575i	−0.0266459	−	0.0461521i
$650$	−24.7038	−	42.7883i	−0.968965	−	1.67830i
$651$		0			0
$652$	−16.6897			−0.653620
$653$	−1.09463	−	1.89596i	−0.0428363	−	0.0741946i	0.843812	−	0.536638i	$-0.180306\pi$
$653$	−1.09463	−	1.89596i	−0.0428363	−	0.0741946i	−0.886649	+	0.462444i	$0.846973\pi$
$654$		0			0
$655$	39.5751	+	68.5461i	1.54633	+	2.67832i
$656$	−14.5481	+	25.1981i	−0.568008	+	0.983819i
$657$		0			0
$658$	4.36901			0.170322
$659$	13.6061	+	23.5665i	0.530019	+	0.918020i	0.999387	+	0.0350171i	$0.0111486\pi$
$659$	13.6061	+	23.5665i	0.530019	+	0.918020i	−0.469368	+	0.883003i	$0.655518\pi$
$660$		0			0
$661$	−2.60228			−0.101217			−0.0506086	−	0.998719i	$-0.516116\pi$
$661$	−2.60228			−0.101217			−0.0506086	+	0.998719i	$0.516116\pi$
$662$	4.67528	−	8.09782i	0.181710	−	0.314731i
$663$		0			0
$664$	−1.04055	+	1.80229i	−0.0403812	+	0.0699423i
$665$	−6.59731	−	35.0165i	−0.255833	−	1.35788i
$666$		0			0
$667$	−5.81958	−	10.0798i	−0.225335	−	0.390292i
$668$	43.1881			1.67100
$669$		0			0
$670$	−54.6037	+	94.5764i	−2.10953	+	3.65381i
$671$	−0.444624			−0.0171645
$672$		0			0
$673$	15.2685	−	26.4458i	0.588558	−	1.01941i	−0.405863	−	0.913934i	$-0.633029\pi$
$673$	15.2685	−	26.4458i	0.588558	−	1.01941i	0.994422	−	0.105479i	$-0.0336375\pi$
$674$	14.8135	−	25.6577i	0.570594	−	0.988298i
$675$		0			0
$676$	−19.1372			−0.736044
$677$	8.89435	−	15.4055i	0.341838	−	0.592080i	−0.642936	−	0.765920i	$-0.722284\pi$
$677$	8.89435	−	15.4055i	0.341838	−	0.592080i	0.984774	+	0.173839i	$0.0556174\pi$
$678$		0			0
$679$	3.66892	−	6.35476i	0.140800	−	0.243873i
$680$	−4.61548			−0.176996
$681$		0			0
$682$	−2.08764			−0.0799398
$683$	35.2754			1.34978			0.674888	−	0.737920i	$-0.264192\pi$
$683$	35.2754			1.34978			0.674888	+	0.737920i	$0.264192\pi$
$684$		0			0
$685$	−23.7409			−0.907092
$686$	−40.1857			−1.53430
$687$		0			0
$688$	−30.4717			−1.16172
$689$	−7.32103	+	12.6804i	−0.278909	+	0.483085i
$690$		0			0
$691$	1.14295	−	1.97964i	0.0434797	−	0.0753090i	−0.843467	−	0.537182i	$-0.819489\pi$
$691$	1.14295	−	1.97964i	0.0434797	−	0.0753090i	0.886946	+	0.461873i	$0.152822\pi$
$692$	37.2420			1.41573
$693$		0			0
$694$	30.4248	−	52.6973i	1.15491	−	2.00036i
$695$	14.9973	−	25.9761i	0.568879	−	0.985328i
$696$		0			0
$697$	50.7545			1.92246
$698$	2.81388	−	4.87377i	0.106507	−	0.184475i
$699$		0			0
$700$	50.9371			1.92524
$701$	1.58169	+	2.73956i	0.0597395	+	0.103472i	0.894348	−	0.447371i	$-0.147640\pi$
$701$	1.58169	+	2.73956i	0.0597395	+	0.103472i	−0.834609	+	0.550843i	$0.814306\pi$
$702$		0			0
$703$	9.29622	+	3.26100i	0.350614	+	0.122991i
$704$	−5.78366	+	10.0176i	−0.217980	+	0.377552i
$705$		0			0
$706$	−10.2002	+	17.6673i	−0.383890	+	0.664916i
$707$	16.1777			0.608426
$708$		0			0
$709$	6.79804	+	11.7746i	0.255306	+	0.442203i	0.964979	−	0.262329i	$-0.0844905\pi$
$709$	6.79804	+	11.7746i	0.255306	+	0.442203i	−0.709673	+	0.704531i	$0.751157\pi$
$710$	30.6737			1.15116
$711$		0			0
$712$	−0.0938909	+	0.162624i	−0.00351871	+	0.00609458i
$713$	−0.761172	−	1.31839i	−0.0285061	−	0.0493740i
$714$		0			0
$715$	5.46941	+	9.47330i	0.204544	+	0.354281i
$716$	−0.442337			−0.0165309
$717$		0			0
$718$	6.31126	+	10.9314i	0.235534	+	0.407957i
$719$	19.2497	+	33.3414i	0.717891	+	1.24342i	0.961834	+	0.273634i	$0.0882257\pi$
$719$	19.2497	+	33.3414i	0.717891	+	1.24342i	−0.243943	+	0.969790i	$0.578441\pi$
$720$		0			0
$721$	−7.67666			−0.285894
$722$	29.9741	+	23.9798i	1.11552	+	0.892437i
$723$		0			0
$724$	16.6352	−	28.8131i	0.618243	−	1.07083i
$725$	−36.9798	+	64.0509i	−1.37339	+	2.37879i
$726$		0			0
$727$	51.8485			1.92296			0.961478	−	0.274882i	$-0.0886387\pi$
$727$	51.8485			1.92296			0.961478	+	0.274882i	$0.0886387\pi$
$728$	−0.314205	+	0.544219i	−0.0116452	+	0.0201701i
$729$		0			0
$730$	41.9916			1.55418
$731$	26.5769	+	46.0325i	0.982982	+	1.70258i
$732$		0			0
$733$	12.1069	+	20.9698i	0.447179	+	0.774536i	0.998201	−	0.0599543i	$-0.0190955\pi$
$733$	12.1069	+	20.9698i	0.447179	+	0.774536i	−0.551023	+	0.834490i	$0.685762\pi$
$734$	−2.91967	−	5.05701i	−0.107767	−	0.186658i
$735$		0			0
$736$	−15.9140			−0.586596
$737$	8.64190	−	14.9682i	0.318328	−	0.551361i
$738$		0			0
$739$	−5.83272	−	10.1026i	−0.214560	−	0.371629i	0.738576	−	0.674170i	$-0.235498\pi$
$739$	−5.83272	−	10.1026i	−0.214560	−	0.371629i	−0.953136	+	0.302541i	$0.902165\pi$
$740$	−9.85037	+	17.0613i	−0.362107	+	0.627187i
$741$		0			0
$742$	−14.7992	−	25.6330i	−0.543296	−	0.941017i
$743$	−8.04284	+	13.9306i	−0.295063	+	0.511065i	−0.975000	−	0.222207i	$-0.928674\pi$
$743$	−8.04284	+	13.9306i	−0.295063	+	0.511065i	0.679936	+	0.733271i	$0.262007\pi$
$744$		0			0
$745$	−37.7512	−	65.3870i	−1.38310	−	2.39560i
$746$	−14.8771	−	25.7679i	−0.544690	−	0.943431i
$747$		0			0
$748$	18.6207			0.680841
$749$	−0.184033	+	0.318755i	−0.00672442	+	0.0116470i
$750$		0			0
$751$	−23.1339			−0.844168			−0.422084	−	0.906557i	$-0.638701\pi$
$751$	−23.1339			−0.844168			−0.422084	+	0.906557i	$0.638701\pi$
$752$	2.12132	+	3.67424i	0.0773567	+	0.133986i
$753$		0			0
$754$	−11.6296	−	20.1431i	−0.423526	−	0.733568i
$755$	−13.5698	−	23.5036i	−0.493857	−	0.855385i
$756$		0			0
$757$	3.49346	+	6.05085i	0.126972	+	0.219922i	0.922502	−	0.385992i	$-0.126141\pi$
$757$	3.49346	+	6.05085i	0.126972	+	0.219922i	−0.795530	+	0.605914i	$0.792807\pi$
$758$	23.7591			0.862970
$759$		0			0
$760$	−2.28402	+	1.96247i	−0.0828500	+	0.0711862i
$761$	6.33130	+	10.9661i	0.229510	+	0.397522i	0.957663	−	0.287892i	$-0.0929545\pi$
$761$	6.33130	+	10.9661i	0.229510	+	0.397522i	−0.728153	+	0.685414i	$0.759621\pi$
$762$		0			0
$763$	4.24607			0.153718
$764$	−14.2999	+	24.7682i	−0.517352	+	0.896080i
$765$		0			0
$766$	−31.2202	+	54.0749i	−1.12803	+	1.95381i
$767$	0.989200	−	1.71334i	0.0357179	−	0.0618653i
$768$		0			0
$769$	−29.3862			−1.05969			−0.529847	−	0.848093i	$-0.677751\pi$
$769$	−29.3862			−1.05969			−0.529847	+	0.848093i	$0.677751\pi$
$770$	−22.1125			−0.796878
$771$		0			0
$772$	15.0774	−	26.1148i	0.542647	−	0.939892i
$773$	−15.3004	+	26.5010i	−0.550316	+	0.953176i	0.447935	+	0.894066i	$0.352159\pi$
$773$	−15.3004	+	26.5010i	−0.550316	+	0.953176i	−0.998252	+	0.0591096i	$0.981174\pi$
$774$		0			0
$775$	−4.83677	+	8.37753i	−0.173742	+	0.300930i
$776$	−0.620122			−0.0222611
$777$		0			0
$778$	14.3215	+	24.8056i	0.513451	+	0.889322i
$779$	25.1164	−	21.5804i	0.899887	−	0.773199i
$780$		0			0
$781$	−4.85460			−0.173711
$782$	13.3122	+	23.0574i	0.476044	+	0.824533i
$783$		0			0
$784$	−6.10668	−	10.5771i	−0.218096	−	0.377753i
$785$	0.573223	+	0.992851i	0.0204592	+	0.0354364i
$786$		0			0
$787$	1.32618	+	2.29700i	0.0472731	+	0.0818794i	0.888694	−	0.458501i	$-0.151614\pi$
$787$	1.32618	+	2.29700i	0.0472731	+	0.0818794i	−0.841421	+	0.540381i	$0.818280\pi$
$788$	−34.6972			−1.23604
$789$		0			0
$790$	−21.8975	+	37.9276i	−0.779079	+	1.34940i
$791$	24.7217			0.879003
$792$		0			0
$793$	−0.323962	−	0.561118i	−0.0115042	−	0.0199259i
$794$	−7.04690	−	12.2056i	−0.250085	−	0.433160i
$795$		0			0
$796$	−10.4034	+	18.0193i	−0.368739	+	0.638675i
$797$	−4.98622	−	8.63638i	−0.176621	−	0.305916i	0.764100	−	0.645098i	$-0.223183\pi$
$797$	−4.98622	−	8.63638i	−0.176621	−	0.305916i	−0.940721	+	0.339181i	$0.889850\pi$
$798$		0			0
$799$	3.70037	−	6.40923i	0.130910	−	0.226742i
$800$	50.5616	+	87.5752i	1.78762	+	3.09625i
$801$		0			0
$802$	16.9589	−	29.3736i	0.598839	−	1.03722i
$803$	−6.64582			−0.234526
$804$		0			0
$805$	−8.06240	−	13.9645i	−0.284162	−	0.492184i
$806$	−1.52110	−	2.63461i	−0.0535783	−	0.0928003i
$807$		0			0
$808$	−0.683591	−	1.18401i	−0.0240487	−	0.0416535i
$809$	−35.7179			−1.25578			−0.627888	−	0.778304i	$-0.716080\pi$
$809$	−35.7179			−1.25578			−0.627888	+	0.778304i	$0.716080\pi$
$810$		0			0
$811$	0.139604	−	0.241802i	0.00490217	−	0.00849080i	−0.863564	−	0.504239i	$-0.831773\pi$
$811$	0.139604	−	0.241802i	0.00490217	−	0.00849080i	0.868466	+	0.495749i	$0.165106\pi$
$812$	23.9792			0.841506
$813$		0			0
$814$	3.05679	−	5.29452i	0.107141	−	0.185573i
$815$	16.7862	−	29.0745i	0.587994	−	1.01844i
$816$		0			0
$817$	32.7245	+	11.4793i	1.14489	+	0.401612i
$818$	27.0725			0.946568
$819$		0			0
$820$	33.1101	+	57.3483i	1.15625	+	2.00269i
$821$	19.9193	+	34.5012i	0.695188	+	1.20410i	0.970117	+	0.242637i	$0.0780124\pi$
$821$	19.9193	+	34.5012i	0.695188	+	1.20410i	−0.274929	+	0.961465i	$0.588654\pi$
$822$		0			0
$823$	−35.2960			−1.23034			−0.615171	−	0.788394i	$-0.710913\pi$
$823$	−35.2960			−1.23034			−0.615171	+	0.788394i	$0.710913\pi$
$824$	0.324378	+	0.561839i	0.0113002	+	0.0195726i
$825$		0			0
$826$	1.99963	+	3.46347i	0.0695762	+	0.120509i
$827$	3.59739	−	6.23087i	0.125094	−	0.216669i	−0.796676	−	0.604407i	$-0.793410\pi$
$827$	3.59739	−	6.23087i	0.125094	−	0.216669i	0.921770	+	0.387738i	$0.126744\pi$
$828$		0			0
$829$	23.9258			0.830976			0.415488	−	0.909599i	$-0.363611\pi$
$829$	23.9258			0.830976			0.415488	+	0.909599i	$0.363611\pi$
$830$	−53.3567	−	92.4165i	−1.85204	−	3.20782i
$831$		0			0
$832$	−16.8563			−0.584389
$833$	−10.6523	+	18.4503i	−0.369080	+	0.639266i
$834$		0			0
$835$	−43.4377	+	75.2364i	−1.50323	+	2.60366i
$836$	9.21464	−	7.91739i	0.318695	−	0.273829i
$837$		0			0
$838$	−10.6830	−	18.5034i	−0.369037	−	0.639190i
$839$	−10.6726			−0.368461			−0.184230	−	0.982883i	$-0.558979\pi$
$839$	−10.6726			−0.368461			−0.184230	+	0.982883i	$0.558979\pi$
$840$		0			0
$841$	−2.90867	+	5.03796i	−0.100299	+	0.173723i
$842$	−38.9253			−1.34145
$843$		0			0
$844$	−2.12741	+	3.68479i	−0.0732286	+	0.126836i
$845$	19.2478	−	33.3381i	0.662143	−	1.14687i
$846$		0			0
$847$	−17.9747			−0.617618
$848$	14.3712	−	24.8916i	0.493509	−	0.854782i
$849$		0			0
$850$	84.5908	−	146.516i	2.90144	−	5.02544i
$851$	4.45814			0.152823
$852$		0			0
$853$	32.2062			1.10272			0.551359	−	0.834268i	$-0.314109\pi$
$853$	32.2062			1.10272			0.551359	+	0.834268i	$0.314109\pi$
$854$	1.30975			0.0448189
$855$		0			0
$856$	0.0311053			0.00106316
$857$	−21.6897			−0.740906			−0.370453	−	0.928851i	$-0.620798\pi$
$857$	−21.6897			−0.740906			−0.370453	+	0.928851i	$0.620798\pi$
$858$		0			0
$859$	21.5980			0.736914			0.368457	−	0.929645i	$-0.379886\pi$
$859$	21.5980			0.736914			0.368457	+	0.929645i	$0.379886\pi$
$860$	−34.6753	+	60.0593i	−1.18242	+	2.04800i
$861$		0			0
$862$	−27.8166	+	48.1797i	−0.947436	+	1.64101i
$863$	38.7369			1.31862			0.659309	−	0.751872i	$-0.270849\pi$
$863$	38.7369			1.31862			0.659309	+	0.751872i	$0.270849\pi$
$864$		0			0
$865$	−37.4572	+	64.8778i	−1.27358	+	2.20591i
$866$	−22.1531	+	38.3704i	−0.752794	+	1.30388i
$867$		0			0
$868$	3.13636			0.106455
$869$	3.46563	−	6.00264i	0.117563	−	0.203626i
$870$		0			0
$871$	25.1866			0.853416
$872$	−0.179418	−	0.310761i	−0.00607585	−	0.0105237i
$873$		0			0
$874$	16.3915	+	5.74994i	0.554452	+	0.194495i
$875$	−30.7948	+	53.3382i	−1.04106	+	1.80316i
$876$		0			0
$877$	−24.2248	+	41.9586i	−0.818014	+	1.41684i	0.0891294	+	0.996020i	$0.471592\pi$
$877$	−24.2248	+	41.9586i	−0.818014	+	1.41684i	−0.907143	+	0.420822i	$0.861742\pi$
$878$	−28.7346			−0.969747
$879$		0			0
$880$	−10.7365	−	18.5961i	−0.361926	−	0.626874i
$881$	−40.7710			−1.37361			−0.686804	−	0.726842i	$-0.740987\pi$
$881$	−40.7710			−1.37361			−0.686804	+	0.726842i	$0.740987\pi$
$882$		0			0
$883$	13.5637	−	23.4930i	0.456455	−	0.790604i	−0.542315	−	0.840175i	$-0.682452\pi$
$883$	13.5637	−	23.4930i	0.456455	−	0.790604i	0.998771	+	0.0495713i	$0.0157855\pi$
$884$	13.5674	+	23.4995i	0.456322	+	0.790373i
$885$		0			0
$886$	14.3778	+	24.9030i	0.483030	+	0.836633i
$887$	41.5865			1.39634			0.698169	−	0.715933i	$-0.253999\pi$
$887$	41.5865			1.39634			0.698169	+	0.715933i	$0.253999\pi$
$888$		0			0
$889$	−4.59978	−	7.96705i	−0.154272	−	0.267206i
$890$	−4.81447	−	8.33891i	−0.161381	−	0.279521i
$891$		0			0
$892$	−54.6450			−1.82965
$893$	−0.893993	−	4.74504i	−0.0299163	−	0.158787i
$894$		0			0
$895$	0.444894	−	0.770578i	0.0148712	−	0.0257576i
$896$	1.28725	−	2.22958i	0.0430039	−	0.0744849i
$897$		0			0
$898$	−6.29272			−0.209991
$899$	−2.27696	+	3.94382i	−0.0759410	+	0.131534i
$900$		0			0
$901$	−50.1373			−1.67031
$902$	−10.2748	−	17.7965i	−0.342114	−	0.592558i
$903$		0			0
$904$	−1.04462	−	1.80933i	−0.0347435	−	0.0601775i
$905$	33.4627	+	57.9592i	1.11234	+	1.92663i
$906$		0			0
$907$	−18.6864			−0.620472			−0.310236	−	0.950660i	$-0.600408\pi$
$907$	−18.6864			−0.620472			−0.310236	+	0.950660i	$0.600408\pi$
$908$	25.8594	−	44.7897i	0.858173	−	1.48640i
$909$		0			0
$910$	−16.1116	−	27.9061i	−0.534094	−	0.925078i
$911$	1.65127	−	2.86008i	0.0547090	−	0.0947587i	−0.837374	−	0.546631i	$-0.815910\pi$
$911$	1.65127	−	2.86008i	0.0547090	−	0.0947587i	0.892083	+	0.451872i	$0.149244\pi$
$912$		0			0
$913$	8.44453	+	14.6264i	0.279473	+	0.484062i
$914$	11.6753	−	20.2222i	0.386185	−	0.668892i
$915$		0			0
$916$	−28.4139	−	49.2143i	−0.938822	−	1.62609i
$917$	18.4504	+	31.9571i	0.609287	+	1.05532i
$918$		0			0
$919$	11.0557			0.364695			0.182348	−	0.983234i	$-0.441630\pi$
$919$	11.0557			0.364695			0.182348	+	0.983234i	$0.441630\pi$
$920$	−0.681355	+	1.18014i	−0.0224636	+	0.0389081i
$921$		0			0
$922$	11.1623			0.367611
$923$	−3.53716	−	6.12654i	−0.116427	−	0.201657i
$924$		0			0
$925$	−14.1643	−	24.5333i	−0.465720	−	0.806651i
$926$	−12.3533	−	21.3966i	−0.405956	−	0.703136i
$927$		0			0
$928$	23.8024	+	41.2270i	0.781354	+	1.35334i
$929$	26.4813			0.868822			0.434411	−	0.900715i	$-0.356957\pi$
$929$	26.4813			0.868822			0.434411	+	0.900715i	$0.356957\pi$
$930$		0			0
$931$	2.57355	+	13.6596i	0.0843446	+	0.447675i
$932$	−18.4884	−	32.0228i	−0.605607	−	1.04894i
$933$		0			0
$934$	−4.49270			−0.147006
$935$	−18.7283	+	32.4384i	−0.612482	+	1.06085i
$936$		0			0
$937$	−2.52504	+	4.37349i	−0.0824894	+	0.142876i	−0.904319	−	0.426858i	$-0.859620\pi$
$937$	−2.52504	+	4.37349i	−0.0824894	+	0.142876i	0.821829	+	0.569734i	$0.192954\pi$
$938$	−25.4570	+	44.0928i	−0.831199	+	1.43968i
$939$		0			0
$940$	9.65585			0.314939
$941$	−5.88984			−0.192003			−0.0960016	−	0.995381i	$-0.530605\pi$
$941$	−5.88984			−0.192003			−0.0960016	+	0.995381i	$0.530605\pi$
$942$		0			0
$943$	7.49257	−	12.9775i	0.243992	−	0.422606i
$944$	−1.94180	+	3.36330i	−0.0632002	+	0.109466i
$945$		0			0
$946$	10.7605	−	18.6378i	0.349855	−	0.605966i
$947$	−45.8461			−1.48980			−0.744899	−	0.667177i	$-0.767502\pi$
$947$	−45.8461			−1.48980			−0.744899	+	0.667177i	$0.767502\pi$
$948$		0			0
$949$	−4.84228	−	8.38708i	−0.157187	−	0.272256i
$950$	−20.4367	−	108.472i	−0.663056	−	3.51930i
$951$		0			0
$952$	−2.15180			−0.0697402
$953$	10.9280	+	18.9279i	0.353993	+	0.613134i	0.986945	−	0.161057i	$-0.0514904\pi$
$953$	10.9280	+	18.9279i	0.353993	+	0.613134i	−0.632952	+	0.774191i	$0.718157\pi$
$954$		0			0
$955$	−28.7651	−	49.8226i	−0.930817	−	1.61222i
$956$	−12.3806	−	21.4438i	−0.400416	−	0.693541i
$957$		0			0
$958$	14.0590	+	24.3509i	0.454225	+	0.786741i
$959$	−11.0683			−0.357414
$960$		0			0
$961$	15.2022	−	26.3310i	0.490393	−	0.849386i
$962$	8.90897			0.287237
$963$		0			0
$964$	2.01852	+	3.49617i	0.0650120	+	0.112604i
$965$	30.3290	+	52.5314i	0.976326	+	1.69105i
$966$		0			0
$967$	16.4138	−	28.4296i	0.527833	−	0.914233i	−0.471641	−	0.881791i	$-0.656338\pi$
$967$	16.4138	−	28.4296i	0.527833	−	0.914233i	0.999474	−	0.0324422i	$-0.0103285\pi$
$968$	0.759523	+	1.31553i	0.0244120	+	0.0422828i
$969$		0			0
$970$	15.8991	−	27.5380i	0.510489	−	0.884193i
$971$	−10.5807	−	18.3264i	−0.339552	−	0.588121i	0.644797	−	0.764354i	$-0.276942\pi$
$971$	−10.5807	−	18.3264i	−0.339552	−	0.588121i	−0.984348	+	0.176233i	$0.943609\pi$
$972$		0			0
$973$	6.99193	−	12.1104i	0.224151	−	0.388241i
$974$	−49.5606			−1.58802
$975$		0			0
$976$	0.635937	+	1.10147i	0.0203558	+	0.0352573i
$977$	25.9506	+	44.9478i	0.830234	+	1.43801i	0.897853	+	0.440296i	$0.145126\pi$
$977$	25.9506	+	44.9478i	0.830234	+	1.43801i	−0.0676189	+	0.997711i	$0.521540\pi$
$978$		0			0
$979$	0.761966	+	1.31976i	0.0243525	+	0.0421798i
$980$	−27.7964			−0.887924
$981$		0			0
$982$	17.5806	−	30.4505i	0.561020	−	0.971715i
$983$	0.610142			0.0194605			0.00973025	−	0.999953i	$-0.496903\pi$
$983$	0.610142			0.0194605			0.00973025	+	0.999953i	$0.496903\pi$
$984$		0			0
$985$	34.8978	−	60.4447i	1.11194	−	1.92593i
$986$	39.8221	−	68.9739i	1.26819	−	2.19658i
$987$		0			0
$988$	16.7058	+	5.86017i	0.531481	+	0.186437i
$989$	15.6935			0.499025
$990$		0			0
$991$	25.6460	+	44.4202i	0.814673	+	1.41106i	0.909562	+	0.415568i	$0.136417\pi$
$991$	25.6460	+	44.4202i	0.814673	+	1.41106i	−0.0948888	+	0.995488i	$0.530250\pi$
$992$	3.11324	+	5.39229i	0.0988454	+	0.171205i
$993$		0			0
$994$	14.3005			0.453584
$995$	−20.9271	−	36.2468i	−0.663434	−	1.14910i
$996$		0			0
$997$	2.21044	+	3.82860i	0.0700054	+	0.121253i	0.898903	−	0.438147i	$-0.144365\pi$
$997$	2.21044	+	3.82860i	0.0700054	+	0.121253i	−0.828898	+	0.559400i	$0.811032\pi$
$998$	38.7976	−	67.1994i	1.22812	−	2.12716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.235.13		32
3.2	odd	2		171.2.h.c.7.4	yes	32
9.4	even	3		513.2.g.c.64.4		32
9.5	odd	6		171.2.g.c.121.13	yes	32
19.11	even	3		513.2.g.c.505.4		32
57.11	odd	6		171.2.g.c.106.13	✓	32
171.49	even	3	inner	513.2.h.c.334.13		32
171.68	odd	6		171.2.h.c.49.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.13	✓	32	57.11	odd	6
171.2.g.c.121.13	yes	32	9.5	odd	6
171.2.h.c.7.4	yes	32	3.2	odd	2
171.2.h.c.49.4	yes	32	171.68	odd	6
513.2.g.c.64.4		32	9.4	even	3
513.2.g.c.505.4		32	19.11	even	3
513.2.h.c.235.13		32	1.1	even	1	trivial
513.2.h.c.334.13		32	171.49	even	3	inner

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.02031 q^{2} +2.08166 q^{4} +(-2.09369 + 3.62638i) q^{5} +(-0.976107 + 1.69067i) q^{7} +0.164982 q^{8} +O(q^{10})\)	\(q+2.02031 q^{2} +2.08166 q^{4} +(-2.09369 + 3.62638i) q^{5} +(-0.976107 + 1.69067i) q^{7} +0.164982 q^{8} +(-4.22991 + 7.32643i) q^{10} +(0.669450 - 1.15952i) q^{11} +1.95110 q^{13} +(-1.97204 + 3.41568i) q^{14} -3.83001 q^{16} +(3.34047 + 5.78587i) q^{17} +(4.11317 + 1.44285i) q^{19} +(-4.35836 + 7.54890i) q^{20} +(1.35250 - 2.34260i) q^{22} +1.97253 q^{23} +(-6.26710 - 10.8549i) q^{25} +3.94183 q^{26} +(-2.03192 + 3.51940i) q^{28} +(-2.95031 - 5.11009i) q^{29} +(-0.385886 - 0.668373i) q^{31} -8.06778 q^{32} +(6.74880 + 11.6893i) q^{34} +(-4.08734 - 7.07948i) q^{35} +2.26011 q^{37} +(8.30989 + 2.91500i) q^{38} +(-0.345421 + 0.598288i) q^{40} +(3.79845 - 6.57911i) q^{41} +7.95603 q^{43} +(1.39357 - 2.41373i) q^{44} +3.98513 q^{46} +(-0.553869 - 0.959330i) q^{47} +(1.59443 + 2.76163i) q^{49} +(-12.6615 - 21.9304i) q^{50} +4.06153 q^{52} +(-3.75226 + 6.49910i) q^{53} +(2.80325 + 4.85537i) q^{55} +(-0.161040 + 0.278929i) q^{56} +(-5.96055 - 10.3240i) q^{58} +(0.506996 - 0.878143i) q^{59} +(-0.166041 - 0.287591i) q^{61} +(-0.779609 - 1.35032i) q^{62} -8.63941 q^{64} +(-4.08500 + 7.07543i) q^{65} +12.9089 q^{67} +(6.95373 + 12.0442i) q^{68} +(-8.25770 - 14.3028i) q^{70} +(-1.81291 - 3.14004i) q^{71} +(-2.48182 - 4.29864i) q^{73} +4.56613 q^{74} +(8.56223 + 3.00352i) q^{76} +(1.30691 + 2.26363i) q^{77} +5.17682 q^{79} +(8.01886 - 13.8891i) q^{80} +(7.67406 - 13.2919i) q^{82} +(-6.30706 + 10.9242i) q^{83} -27.9757 q^{85} +16.0737 q^{86} +(0.110447 - 0.191300i) q^{88} +(-0.569098 + 0.985707i) q^{89} +(-1.90448 + 3.29866i) q^{91} +4.10614 q^{92} +(-1.11899 - 1.93815i) q^{94} +(-13.8440 + 11.8951i) q^{95} -3.75873 q^{97} +(3.22125 + 5.57936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

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