LMFDB - Embedded newform 144.3.m.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (of order $4$, degree $2$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.1
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12457 + 1.65389i) q^{2} +(-1.47068 - 3.71982i) q^{4} +(0.0586332 - 0.0586332i) q^{5} +4.61555 q^{7} +(7.80605 + 1.75086i) q^{8} +O(q^{10})$	\(q+(-1.12457 + 1.65389i) q^{2} +(-1.47068 - 3.71982i) q^{4} +(0.0586332 - 0.0586332i) q^{5} +4.61555 q^{7} +(7.80605 + 1.75086i) q^{8} +(0.0310355 + 0.162910i) q^{10} +(5.36641 + 5.36641i) q^{11} +(11.0552 + 11.0552i) q^{13} +(-5.19051 + 7.63359i) q^{14} +(-11.6742 + 10.9414i) q^{16} +12.8793 q^{17} +(2.63359 - 2.63359i) q^{19} +(-0.304336 - 0.131874i) q^{20} +(-14.9103 + 2.84053i) q^{22} -16.3810 q^{23} +24.9931i q^{25} +(-30.7164 + 5.85170i) q^{26} +(-6.78801 - 17.1690i) q^{28} +(26.0518 + 26.0518i) q^{29} -20.2345i q^{31} +(-4.96735 - 31.6121i) q^{32} +(-14.4837 + 21.3009i) q^{34} +(0.270624 - 0.270624i) q^{35} +(41.2829 - 41.2829i) q^{37} +(1.39400 + 7.31733i) q^{38} +(0.560352 - 0.355035i) q^{40} +3.29640i q^{41} +(-0.786951 - 0.786951i) q^{43} +(12.0698 - 27.8544i) q^{44} +(18.4216 - 27.0923i) q^{46} -79.7517i q^{47} -27.6967 q^{49} +(-41.3358 - 28.1065i) q^{50} +(24.8647 - 57.3821i) q^{52} +(-1.06207 + 1.06207i) q^{53} +0.629299 q^{55} +(36.0292 + 8.08117i) q^{56} +(-72.3837 + 13.7896i) q^{58} +(-32.5163 - 32.5163i) q^{59} +(15.2897 + 15.2897i) q^{61} +(33.4656 + 22.7552i) q^{62} +(57.8690 + 27.3346i) q^{64} +1.29640 q^{65} +(-60.0631 + 60.0631i) q^{67} +(-18.9414 - 47.9087i) q^{68} +(0.143246 + 0.751918i) q^{70} -56.3535 q^{71} +9.70663i q^{73} +(21.8517 + 114.703i) q^{74} +(-13.6697 - 5.92332i) q^{76} +(24.7689 + 24.7689i) q^{77} -84.4278i q^{79} +(-0.0429672 + 1.32602i) q^{80} +(-5.45188 - 3.70704i) q^{82} +(-26.7577 + 26.7577i) q^{83} +(0.755154 - 0.755154i) q^{85} +(2.18651 - 0.416546i) q^{86} +(32.4946 + 51.2863i) q^{88} +115.555i q^{89} +(51.0258 + 51.0258i) q^{91} +(24.0913 + 60.9345i) q^{92} +(131.900 + 89.6864i) q^{94} -0.308832i q^{95} -146.245 q^{97} +(31.1469 - 45.8072i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8	$ 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} + 36 q^{10} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 40 q^{16} + 4 q^{17} + 30 q^{19} + 84 q^{20} - 52 q^{22} - 60 q^{23} - 96 q^{26} + 56 q^{28} + 18 q^{29} - 8 q^{32} - 76 q^{34} + 100 q^{35} + 46 q^{37} - 40 q^{38} + 40 q^{40} - 114 q^{43} - 20 q^{44} + 28 q^{46} - 46 q^{49} - 46 q^{50} + 100 q^{52} - 78 q^{53} + 252 q^{55} + 168 q^{56} - 176 q^{58} - 206 q^{59} + 30 q^{61} + 144 q^{62} + 64 q^{64} - 12 q^{65} - 226 q^{67} - 112 q^{68} - 16 q^{70} + 260 q^{71} + 92 q^{74} - 188 q^{76} + 212 q^{77} - 232 q^{80} + 304 q^{82} - 318 q^{83} - 212 q^{85} - 268 q^{86} - 8 q^{88} + 188 q^{91} + 168 q^{92} + 48 q^{94} - 4 q^{97} - 10 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 + 36 * q^10 + 18 * q^11 - 2 * q^13 - 12 * q^14 - 40 * q^16 + 4 * q^17 + 30 * q^19 + 84 * q^20 - 52 * q^22 - 60 * q^23 - 96 * q^26 + 56 * q^28 + 18 * q^29 - 8 * q^32 - 76 * q^34 + 100 * q^35 + 46 * q^37 - 40 * q^38 + 40 * q^40 - 114 * q^43 - 20 * q^44 + 28 * q^46 - 46 * q^49 - 46 * q^50 + 100 * q^52 - 78 * q^53 + 252 * q^55 + 168 * q^56 - 176 * q^58 - 206 * q^59 + 30 * q^61 + 144 * q^62 + 64 * q^64 - 12 * q^65 - 226 * q^67 - 112 * q^68 - 16 * q^70 + 260 * q^71 + 92 * q^74 - 188 * q^76 + 212 * q^77 - 232 * q^80 + 304 * q^82 - 318 * q^83 - 212 * q^85 - 268 * q^86 - 8 * q^88 + 188 * q^91 + 168 * q^92 + 48 * q^94 - 4 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.12457	+	1.65389i	−0.562285	+	0.826943i
$2$	−1.12457	+	1.65389i	−0.562285	+	0.826943i
$3$		0			0
$3$		0			0
$4$	−1.47068	−	3.71982i	−0.367671	−	0.929956i
$5$	0.0586332	−	0.0586332i	0.0117266	−	0.0117266i	−0.701219	−	0.712946i	$-0.747361\pi$
$5$	0.0586332	−	0.0586332i	0.0117266	−	0.0117266i	0.712946	+	0.701219i	$0.247361\pi$
$6$		0			0
$7$	4.61555			0.659364			0.329682	−	0.944092i	$-0.393058\pi$
$7$	4.61555			0.659364			0.329682	+	0.944092i	$0.393058\pi$
$8$	7.80605	+	1.75086i	0.975757	+	0.218857i
$9$		0			0
$10$	0.0310355	+	0.162910i	0.00310355	+	0.0162910i
$11$	5.36641	+	5.36641i	0.487855	+	0.487855i	0.907629	−	0.419774i	$-0.137891\pi$
$11$	5.36641	+	5.36641i	0.487855	+	0.487855i	−0.419774	+	0.907629i	$0.637891\pi$
$12$		0			0
$13$	11.0552	+	11.0552i	0.850400	+	0.850400i	0.990182	−	0.139783i	$-0.0446404\pi$
$13$	11.0552	+	11.0552i	0.850400	+	0.850400i	−0.139783	+	0.990182i	$0.544640\pi$
$14$	−5.19051	+	7.63359i	−0.370751	+	0.545257i
$15$		0			0
$16$	−11.6742	+	10.9414i	−0.729636	+	0.683835i
$17$	12.8793			0.757606			0.378803	−	0.925477i	$-0.376336\pi$
$17$	12.8793			0.757606			0.378803	+	0.925477i	$0.376336\pi$
$18$		0			0
$19$	2.63359	−	2.63359i	0.138610	−	0.138610i	−0.634397	−	0.773007i	$-0.718752\pi$
$19$	2.63359	−	2.63359i	0.138610	−	0.138610i	0.773007	+	0.634397i	$0.218752\pi$
$20$	−0.304336	−	0.131874i	−0.0152168	−	0.00659371i
$21$		0			0
$22$	−14.9103	+	2.84053i	−0.677742	+	0.129115i
$23$	−16.3810			−0.712218			−0.356109	−	0.934444i	$-0.615897\pi$
$23$	−16.3810			−0.712218			−0.356109	+	0.934444i	$0.615897\pi$
$24$		0			0
$25$			24.9931i			0.999725i
$26$	−30.7164	+	5.85170i	−1.18140	+	0.225065i
$27$		0			0
$28$	−6.78801	−	17.1690i	−0.242429	−	0.613179i
$29$	26.0518	+	26.0518i	0.898336	+	0.898336i	0.995289	−	0.0969525i	$-0.0309095\pi$
$29$	26.0518	+	26.0518i	0.898336	+	0.898336i	−0.0969525	+	0.995289i	$0.530910\pi$
$30$		0			0
$31$		−	20.2345i		−	0.652727i	−0.945244	−	0.326363i	$-0.894177\pi$
$31$		−	20.2345i		−	0.652727i	0.945244	−	0.326363i	$-0.105823\pi$
$32$	−4.96735	−	31.6121i	−0.155230	−	0.987878i
$33$		0			0
$34$	−14.4837	+	21.3009i	−0.425990	+	0.626497i
$35$	0.270624	−	0.270624i	0.00773212	−	0.00773212i
$36$		0			0
$37$	41.2829	−	41.2829i	1.11575	−	1.11575i	0.123395	−	0.992358i	$-0.460622\pi$
$37$	41.2829	−	41.2829i	1.11575	−	1.11575i	0.992358	−	0.123395i	$-0.0393783\pi$
$38$	1.39400	+	7.31733i	0.0366843	+	0.192561i
$39$		0			0
$40$	0.560352	−	0.355035i	0.0140088	−	0.00887588i
$41$			3.29640i			0.0804001i	0.999192	+	0.0402000i	$0.0127995\pi$
$41$			3.29640i			0.0804001i	−0.999192	+	0.0402000i	$0.987200\pi$
$42$		0			0
$43$	−0.786951	−	0.786951i	−0.0183012	−	0.0183012i	0.697897	−	0.716198i	$-0.254119\pi$
$43$	−0.786951	−	0.786951i	−0.0183012	−	0.0183012i	−0.716198	+	0.697897i	$0.754119\pi$
$44$	12.0698	−	27.8544i	0.274314	−	0.633054i
$45$		0			0
$46$	18.4216	−	27.0923i	0.400470	−	0.588964i
$47$		−	79.7517i		−	1.69685i	−0.529320	−	0.848423i	$-0.677553\pi$
$47$		−	79.7517i		−	1.69685i	0.529320	−	0.848423i	$-0.322447\pi$
$48$		0			0
$49$	−27.6967			−0.565239
$50$	−41.3358	−	28.1065i	−0.826716	−	0.562130i
$51$		0			0
$52$	24.8647	−	57.3821i	0.478167	−	1.10350i
$53$	−1.06207	+	1.06207i	−0.0200391	+	0.0200391i	−0.717055	−	0.697016i	$-0.754511\pi$
$53$	−1.06207	+	1.06207i	−0.0200391	+	0.0200391i	0.697016	+	0.717055i	$0.254511\pi$
$54$		0			0
$55$	0.629299			0.0114418
$56$	36.0292	+	8.08117i	0.643379	+	0.144307i
$57$		0			0
$58$	−72.3837	+	13.7896i	−1.24799	+	0.237752i
$59$	−32.5163	−	32.5163i	−0.551124	−	0.551124i	0.375641	−	0.926765i	$-0.377423\pi$
$59$	−32.5163	−	32.5163i	−0.551124	−	0.551124i	−0.926765	+	0.375641i	$0.877423\pi$
$60$		0			0
$61$	15.2897	+	15.2897i	0.250651	+	0.250651i	0.821238	−	0.570586i	$-0.193284\pi$
$61$	15.2897	+	15.2897i	0.250651	+	0.250651i	−0.570586	+	0.821238i	$0.693284\pi$
$62$	33.4656	+	22.7552i	0.539768	+	0.367019i
$63$		0			0
$64$	57.8690	+	27.3346i	0.904203	+	0.427103i
$65$	1.29640			0.0199446
$66$		0			0
$67$	−60.0631	+	60.0631i	−0.896465	+	0.896465i	−0.995122	−	0.0986569i	$-0.968545\pi$
$67$	−60.0631	+	60.0631i	−0.896465	+	0.896465i	0.0986569	+	0.995122i	$0.468545\pi$
$68$	−18.9414	−	47.9087i	−0.278550	−	0.704540i
$69$		0			0
$70$	0.143246	+	0.751918i	0.00204637	+	0.0107417i
$71$	−56.3535			−0.793711			−0.396856	−	0.917881i	$-0.629899\pi$
$71$	−56.3535			−0.793711			−0.396856	+	0.917881i	$0.629899\pi$
$72$		0			0
$73$			9.70663i			0.132968i	0.997788	+	0.0664838i	$0.0211781\pi$
$73$			9.70663i			0.132968i	−0.997788	+	0.0664838i	$0.978822\pi$
$74$	21.8517	+	114.703i	0.295293	+	1.55004i
$75$		0			0
$76$	−13.6697	−	5.92332i	−0.179864	−	0.0779384i
$77$	24.7689	+	24.7689i	0.321674	+	0.321674i
$78$		0			0
$79$		−	84.4278i		−	1.06871i	−0.845261	−	0.534353i	$-0.820555\pi$
$79$		−	84.4278i		−	1.06871i	0.845261	−	0.534353i	$-0.179445\pi$
$80$	−0.0429672	+	1.32602i	−0.000537090	+	0.0165753i
$81$		0			0
$82$	−5.45188	−	3.70704i	−0.0664863	−	0.0452078i
$83$	−26.7577	+	26.7577i	−0.322382	+	0.322382i	−0.849680	−	0.527298i	$-0.823205\pi$
$83$	−26.7577	+	26.7577i	−0.322382	+	0.322382i	0.527298	+	0.849680i	$0.323205\pi$
$84$		0			0
$85$	0.755154	−	0.755154i	0.00888416	−	0.00888416i
$86$	2.18651	−	0.416546i	0.0254245	−	0.00484356i
$87$		0			0
$88$	32.4946	+	51.2863i	0.369257	+	0.582799i
$89$			115.555i			1.29838i	0.760628	+	0.649188i	$0.224891\pi$
$89$			115.555i			1.29838i	−0.760628	+	0.649188i	$0.775109\pi$
$90$		0			0
$91$	51.0258	+	51.0258i	0.560723	+	0.560723i
$92$	24.0913	+	60.9345i	0.261862	+	0.662331i
$93$		0			0
$94$	131.900	+	89.6864i	1.40319	+	0.954111i
$95$		−	0.308832i		−	0.00325086i
$96$		0			0
$97$	−146.245			−1.50768			−0.753841	−	0.657056i	$-0.771801\pi$
$97$	−146.245			−1.50768			−0.753841	+	0.657056i	$0.771801\pi$
$98$	31.1469	−	45.8072i	0.317826	−	0.467421i
$99$		0			0
$100$	92.9700	−	36.7570i	0.929700	−	0.367570i
$101$	53.8554	−	53.8554i	0.533222	−	0.533222i	−0.388308	−	0.921530i	$-0.626940\pi$
$101$	53.8554	−	53.8554i	0.533222	−	0.533222i	0.921530	+	0.388308i	$0.126940\pi$
$102$		0			0
$103$	−158.184			−1.53577			−0.767885	−	0.640588i	$-0.778691\pi$
$103$	−158.184			−1.53577			−0.767885	+	0.640588i	$0.778691\pi$
$104$	66.9414	+	105.654i	0.643667	+	1.01590i
$105$		0			0
$106$	−0.562172	−	2.95092i	−0.00530351	−	0.0278389i
$107$	57.6009	+	57.6009i	0.538327	+	0.538327i	0.923037	−	0.384711i	$-0.125699\pi$
$107$	57.6009	+	57.6009i	0.538327	+	0.538327i	−0.384711	+	0.923037i	$0.625699\pi$
$108$		0			0
$109$	56.8795	+	56.8795i	0.521830	+	0.521830i	0.918124	−	0.396294i	$-0.129704\pi$
$109$	56.8795	+	56.8795i	0.521830	+	0.521830i	−0.396294	+	0.918124i	$0.629704\pi$
$110$	−0.707691	+	1.04079i	−0.00643355	+	0.00946172i
$111$		0			0
$112$	−53.8827	+	50.5004i	−0.481096	+	0.450896i
$113$	−135.731			−1.20116			−0.600580	−	0.799565i	$-0.705064\pi$
$113$	−135.731			−1.20116			−0.600580	+	0.799565i	$0.705064\pi$
$114$		0			0
$115$	−0.960471	+	0.960471i	−0.00835192	+	0.00835192i
$116$	58.5941	−	135.222i	0.505121	−	1.16571i
$117$		0			0
$118$	90.3452	−	17.2114i	0.765637	−	0.145860i
$119$	59.4450			0.499538
$120$		0			0
$121$		−	63.4034i		−	0.523995i
$122$	−42.4819	+	8.09311i	−0.348212	+	0.0663369i
$123$		0			0
$124$	−75.2689	+	29.7586i	−0.607007	+	0.239989i
$125$	2.93125	+	2.93125i	0.0234500	+	0.0234500i
$126$		0			0
$127$		−	166.552i		−	1.31144i	−0.755006	−	0.655718i	$-0.772366\pi$
$127$		−	166.552i		−	1.31144i	0.755006	−	0.655718i	$-0.227634\pi$
$128$	−110.286	+	64.9691i	−0.861610	+	0.507571i
$129$		0			0
$130$	−1.45790	+	2.14410i	−0.0112146	+	0.0164931i
$131$	−22.2547	+	22.2547i	−0.169883	+	0.169883i	−0.786928	−	0.617045i	$-0.788330\pi$
$131$	−22.2547	+	22.2547i	−0.169883	+	0.169883i	0.617045	+	0.786928i	$0.288330\pi$
$132$		0			0
$133$	12.1555	−	12.1555i	0.0913945	−	0.0913945i
$134$	−31.7924	−	166.883i	−0.237257	−	1.24539i
$135$		0			0
$136$	100.536	+	22.5498i	0.739239	+	0.165808i
$137$		−	174.890i		−	1.27657i	−0.769800	−	0.638285i	$-0.779644\pi$
$137$		−	174.890i		−	1.27657i	0.769800	−	0.638285i	$-0.220356\pi$
$138$		0			0
$139$	99.8891	+	99.8891i	0.718627	+	0.718627i	0.968324	−	0.249697i	$-0.0803310\pi$
$139$	99.8891	+	99.8891i	0.718627	+	0.718627i	−0.249697	+	0.968324i	$0.580331\pi$
$140$	−1.40468	−	0.608672i	−0.0100334	−	0.00434766i
$141$		0			0
$142$	63.3735	−	93.2023i	0.446292	−	0.656354i
$143$			118.653i			0.829744i
$144$		0			0
$145$	3.05499			0.0210689
$146$	−16.0537	−	10.9158i	−0.109957	−	0.0747657i
$147$		0			0
$148$	−214.279	−	92.8509i	−1.44783	−	0.627371i
$149$	74.8860	−	74.8860i	0.502590	−	0.502590i	−0.409652	−	0.912242i	$-0.634350\pi$
$149$	74.8860	−	74.8860i	0.502590	−	0.502590i	0.912242	+	0.409652i	$0.134350\pi$
$150$		0			0
$151$	70.0357			0.463813			0.231906	−	0.972738i	$-0.425504\pi$
$151$	70.0357			0.463813			0.231906	+	0.972738i	$0.425504\pi$
$152$	25.1690	−	15.9469i	0.165586	−	0.104914i
$153$		0			0
$154$	−68.8193	+	13.1106i	−0.446879	+	0.0851337i
$155$	−1.18641	−	1.18641i	−0.00765429	−	0.00765429i
$156$		0			0
$157$	−29.5307	−	29.5307i	−0.188094	−	0.188094i	0.606778	−	0.794872i	$-0.292462\pi$
$157$	−29.5307	−	29.5307i	−0.188094	−	0.188094i	−0.794872	+	0.606778i	$0.792462\pi$
$158$	139.634	+	94.9450i	0.883760	+	0.600918i
$159$		0			0
$160$	−2.14477	−	1.56227i	−0.0134048	−	0.00976417i
$161$	−75.6074			−0.469611
$162$		0			0
$163$	47.7990	−	47.7990i	0.293245	−	0.293245i	−0.545116	−	0.838361i	$-0.683514\pi$
$163$	47.7990	−	47.7990i	0.293245	−	0.293245i	0.838361	+	0.545116i	$0.183514\pi$
$164$	12.2620	−	4.84796i	0.0747685	−	0.0295608i
$165$		0			0
$166$	−14.1633	−	74.3452i	−0.0853212	−	0.447863i
$167$	156.268			0.935734			0.467867	−	0.883799i	$-0.345023\pi$
$167$	156.268			0.935734			0.467867	+	0.883799i	$0.345023\pi$
$168$		0			0
$169$			75.4347i			0.446359i
$170$	0.399715	+	2.09816i	0.00235127	+	0.0123421i
$171$		0			0
$172$	−1.76996	+	4.08467i	−0.0102905	+	0.0237481i
$173$	−190.103	−	190.103i	−1.09886	−	1.09886i	−0.994544	−	0.104319i	$-0.966734\pi$
$173$	−190.103	−	190.103i	−1.09886	−	1.09886i	−0.104319	−	0.994544i	$-0.533266\pi$
$174$		0			0
$175$			115.357i			0.659183i
$176$	−121.364	−	3.93258i	−0.689569	−	0.0223442i
$177$		0			0
$178$	−191.116	−	129.950i	−1.07368	−	0.730057i
$179$	−54.2749	+	54.2749i	−0.303212	+	0.303212i	−0.842269	−	0.539057i	$-0.818781\pi$
$179$	−54.2749	+	54.2749i	−0.303212	+	0.303212i	0.539057	+	0.842269i	$0.318781\pi$
$180$		0			0
$181$	19.7343	−	19.7343i	0.109029	−	0.109029i	−0.650487	−	0.759517i	$-0.725435\pi$
$181$	19.7343	−	19.7343i	0.109029	−	0.109029i	0.759517	+	0.650487i	$0.225435\pi$
$182$	−141.773	+	27.0088i	−0.778972	+	0.148400i
$183$		0			0
$184$	−127.871	−	28.6809i	−0.694952	−	0.155874i
$185$		−	4.84109i		−	0.0261680i
$186$		0			0
$187$	69.1155	+	69.1155i	0.369602	+	0.369602i
$188$	−296.662	+	117.290i	−1.57799	+	0.623880i
$189$		0			0
$190$	0.510773	+	0.347303i	0.00268828	+	0.00182791i
$191$		−	166.552i		−	0.872002i	−0.899946	−	0.436001i	$-0.856394\pi$
$191$		−	166.552i		−	0.872002i	0.899946	−	0.436001i	$-0.143606\pi$
$192$		0			0
$193$	2.18257			0.0113087			0.00565434	−	0.999984i	$-0.498200\pi$
$193$	2.18257			0.0113087			0.00565434	+	0.999984i	$0.498200\pi$
$194$	164.463	−	241.873i	0.847748	−	1.24677i
$195$		0			0
$196$	40.7331	+	103.027i	0.207822	+	0.525648i
$197$	−67.4310	+	67.4310i	−0.342290	+	0.342290i	−0.857227	−	0.514938i	$-0.827815\pi$
$197$	−67.4310	+	67.4310i	−0.342290	+	0.342290i	0.514938	+	0.857227i	$0.327815\pi$
$198$		0			0
$199$	222.906			1.12013			0.560065	−	0.828449i	$-0.310776\pi$
$199$	222.906			1.12013			0.560065	+	0.828449i	$0.310776\pi$
$200$	−43.7594	+	195.098i	−0.218797	+	0.975488i
$201$		0			0
$202$	28.5066	+	149.635i	0.141122	+	0.740767i
$203$	120.243	+	120.243i	0.592331	+	0.592331i
$204$		0			0
$205$	0.193278	+	0.193278i	0.000942822	+	0.000942822i
$206$	177.889	−	261.619i	0.863541	−	1.26999i
$207$		0			0
$208$	−250.019	−	8.10140i	−1.20202	−	0.0389490i
$209$	28.2659			0.135243
$210$		0			0
$211$	−147.118	+	147.118i	−0.697240	+	0.697240i	−0.963814	−	0.266574i	$-0.914108\pi$
$211$	−147.118	+	147.118i	−0.697240	+	0.697240i	0.266574	+	0.963814i	$0.414108\pi$
$212$	5.51269	+	2.38875i	0.0260032	+	0.0112677i
$213$		0			0
$214$	−160.042	+	30.4891i	−0.747859	+	0.142473i
$215$	−0.0922828			−0.000429223
$216$		0			0
$217$		−	93.3934i		−	0.430385i
$218$	−158.037	+	30.1073i	−0.724941	+	0.138107i
$219$		0			0
$220$	−0.925499	−	2.34088i	−0.00420681	−	0.0106404i
$221$	142.383	+	142.383i	0.644268	+	0.644268i
$222$		0			0
$223$			60.7036i			0.272213i	0.990694	+	0.136107i	$0.0434590\pi$
$223$			60.7036i			0.272213i	−0.990694	+	0.136107i	$0.956541\pi$
$224$	−22.9270	−	145.907i	−0.102353	−	0.651371i
$225$		0			0
$226$	152.639	−	224.484i	0.675394	−	0.993291i
$227$	225.526	−	225.526i	0.993505	−	0.993505i	−0.00647371	−	0.999979i	$-0.502061\pi$
$227$	225.526	−	225.526i	0.993505	−	0.993505i	0.999979	+	0.00647371i	$0.00206066\pi$
$228$		0			0
$229$	227.796	−	227.796i	0.994743	−	0.994743i	−0.00524305	−	0.999986i	$-0.501669\pi$
$229$	227.796	−	227.796i	0.994743	−	0.994743i	0.999986	+	0.00524305i	$0.00166892\pi$
$230$	−0.508393	−	2.66863i	−0.00221040	−	0.0116027i
$231$		0			0
$232$	157.748	+	248.974i	0.679950	+	1.07317i
$233$			121.053i			0.519540i	0.965671	+	0.259770i	$0.0836467\pi$
$233$			121.053i			0.519540i	−0.965671	+	0.259770i	$0.916353\pi$
$234$		0			0
$235$	−4.67610	−	4.67610i	−0.0198983	−	0.0198983i
$236$	−73.1338	+	168.776i	−0.309889	+	0.715154i
$237$		0			0
$238$	−66.8501	+	98.3153i	−0.280883	+	0.413090i
$239$			221.393i			0.926332i	0.886271	+	0.463166i	$0.153287\pi$
$239$			221.393i			0.926332i	−0.886271	+	0.463166i	$0.846713\pi$
$240$		0			0
$241$	84.2667			0.349654			0.174827	−	0.984599i	$-0.444063\pi$
$241$	84.2667			0.349654			0.174827	+	0.984599i	$0.444063\pi$
$242$	104.862	+	71.3015i	0.433314	+	0.294634i
$243$		0			0
$244$	34.3887	−	79.3614i	0.140937	−	0.325252i
$245$	−1.62395	+	1.62395i	−0.00662835	+	0.00662835i
$246$		0			0
$247$	58.2298			0.235748
$248$	35.4278	−	157.952i	0.142854	−	0.636903i
$249$		0			0
$250$	−8.14437	+	1.55156i	−0.0325775	+	0.00620625i
$251$	176.615	+	176.615i	0.703646	+	0.703646i	0.965191	−	0.261545i	$-0.0842321\pi$
$251$	176.615	+	176.615i	0.703646	+	0.703646i	−0.261545	+	0.965191i	$0.584232\pi$
$252$		0			0
$253$	−87.9072	−	87.9072i	−0.347459	−	0.347459i
$254$	275.459	+	187.300i	1.08448	+	0.737401i
$255$		0			0
$256$	16.5730	−	255.463i	0.0647382	−	0.997902i
$257$	163.001			0.634244			0.317122	−	0.948385i	$-0.397283\pi$
$257$	163.001			0.634244			0.317122	+	0.948385i	$0.397283\pi$
$258$		0			0
$259$	190.543	−	190.543i	0.735687	−	0.735687i
$260$	−1.90660	−	4.82239i	−0.00733307	−	0.0185476i
$261$		0			0
$262$	−11.7798	−	61.8337i	−0.0449610	−	0.236007i
$263$	−175.001			−0.665404			−0.332702	−	0.943032i	$-0.607960\pi$
$263$	−175.001			−0.665404			−0.332702	+	0.943032i	$0.607960\pi$
$264$		0			0
$265$			0.124545i			0.000469982i
$266$	6.43409	+	33.7735i	0.0241883	+	0.126968i
$267$		0			0
$268$	311.758	+	135.090i	1.16328	+	0.504069i
$269$	−29.7489	−	29.7489i	−0.110591	−	0.110591i	0.649646	−	0.760237i	$-0.274917\pi$
$269$	−29.7489	−	29.7489i	−0.110591	−	0.110591i	−0.760237	+	0.649646i	$0.774917\pi$
$270$		0			0
$271$			275.891i			1.01805i	0.860753	+	0.509024i	$0.169993\pi$
$271$			275.891i			1.01805i	−0.860753	+	0.509024i	$0.830007\pi$
$272$	−150.355	+	140.917i	−0.552777	+	0.518078i
$273$		0			0
$274$	289.248	+	196.676i	1.05565	+	0.717796i
$275$	−134.123	+	134.123i	−0.487721	+	0.487721i
$276$		0			0
$277$	−278.337	+	278.337i	−1.00483	+	1.00483i	−0.00484003	+	0.999988i	$0.501541\pi$
$277$	−278.337	+	278.337i	−1.00483	+	1.00483i	−0.999988	+	0.00484003i	$0.998459\pi$
$278$	−277.538	+	52.8730i	−0.998337	+	0.190191i
$279$		0			0
$280$	2.58633	−	1.63868i	0.00923690	−	0.00585244i
$281$		−	202.356i		−	0.720128i	−0.932928	−	0.360064i	$-0.882755\pi$
$281$		−	202.356i		−	0.720128i	0.932928	−	0.360064i	$-0.117245\pi$
$282$		0			0
$283$	−292.256	−	292.256i	−1.03271	−	1.03271i	−0.999447	−	0.0332615i	$-0.989411\pi$
$283$	−292.256	−	292.256i	−1.03271	−	1.03271i	−0.0332615	−	0.999447i	$-0.510589\pi$
$284$	82.8782	+	209.625i	0.291825	+	0.738117i
$285$		0			0
$286$	−196.239	−	133.434i	−0.686151	−	0.466553i
$287$			15.2147i			0.0530129i
$288$		0			0
$289$	−123.124			−0.426034
$290$	−3.43556	+	5.05261i	−0.0118467	+	0.0174228i
$291$		0			0
$292$	36.1070	−	14.2754i	0.123654	−	0.0488883i
$293$	−331.170	+	331.170i	−1.13027	+	1.13027i	−0.140141	+	0.990132i	$0.544756\pi$
$293$	−331.170	+	331.170i	−1.13027	+	1.13027i	−0.990132	+	0.140141i	$0.955244\pi$
$294$		0			0
$295$	−3.81307			−0.0129257
$296$	394.537	−	249.976i	1.33289	−	0.844513i
$297$		0			0
$298$	39.6384	+	208.067i	0.133015	+	0.698213i
$299$	−181.095	−	181.095i	−0.605670	−	0.605670i
$300$		0			0
$301$	−3.63221	−	3.63221i	−0.0120671	−	0.0120671i
$302$	−78.7601	+	115.831i	−0.260795	+	0.383547i
$303$		0			0
$304$	−1.92993	+	59.5602i	−0.00634846	+	0.195922i
$305$	1.79297			0.00587859
$306$		0			0
$307$	23.7513	−	23.7513i	0.0773656	−	0.0773656i	−0.667365	−	0.744731i	$-0.732578\pi$
$307$	23.7513	−	23.7513i	0.0773656	−	0.0773656i	0.744731	+	0.667365i	$0.232578\pi$
$308$	55.7087	−	128.563i	0.180873	−	0.417413i
$309$		0			0
$310$	3.29640	−	0.627989i	0.0106336	−	0.00202577i
$311$	157.757			0.507258			0.253629	−	0.967302i	$-0.418376\pi$
$311$	157.757			0.507258			0.253629	+	0.967302i	$0.418376\pi$
$312$		0			0
$313$			58.5936i			0.187200i	0.995610	+	0.0936000i	$0.0298375\pi$
$313$			58.5936i			0.187200i	−0.995610	+	0.0936000i	$0.970163\pi$
$314$	82.0499	−	15.6311i	0.261305	−	0.0497806i
$315$		0			0
$316$	−314.057	+	124.167i	−0.993850	+	0.392932i
$317$	−27.0040	−	27.0040i	−0.0851863	−	0.0851863i	0.663230	−	0.748416i	$-0.269185\pi$
$317$	−27.0040	−	27.0040i	−0.0851863	−	0.0851863i	−0.748416	+	0.663230i	$0.769185\pi$
$318$		0			0
$319$			279.609i			0.876516i
$320$	4.99576	−	1.79033i	0.0156117	−	0.00559477i
$321$		0			0
$322$	85.0258	−	125.046i	0.264055	−	0.388342i
$323$	33.9188	−	33.9188i	0.105012	−	0.105012i
$324$		0			0
$325$	−276.304	+	276.304i	−0.850166	+	0.850166i
$326$	25.3008	+	132.807i	0.0776098	+	0.407385i
$327$		0			0
$328$	−5.77154	+	25.7319i	−0.0175961	+	0.0784509i
$329$		−	368.098i		−	1.11884i
$330$		0			0
$331$	−182.195	−	182.195i	−0.550437	−	0.550437i	0.376130	−	0.926567i	$-0.377255\pi$
$331$	−182.195	−	182.195i	−0.550437	−	0.550437i	−0.926567	+	0.376130i	$0.877255\pi$
$332$	138.886	+	60.1819i	0.418332	+	0.181271i
$333$		0			0
$334$	−175.734	+	258.449i	−0.526149	+	0.773799i
$335$			7.04338i			0.0210250i
$336$		0			0
$337$	510.137			1.51376			0.756881	−	0.653553i	$-0.226722\pi$
$337$	510.137			1.51376			0.756881	+	0.653553i	$0.226722\pi$
$338$	−124.760	−	84.8316i	−0.369114	−	0.250981i
$339$		0			0
$340$	−3.91963	−	1.69845i	−0.0115283	−	0.00499543i
$341$	108.587	−	108.587i	0.318436	−	0.318436i
$342$		0			0
$343$	−353.997			−1.03206
$344$	−4.76514	−	7.52082i	−0.0138522	−	0.0218629i
$345$		0			0
$346$	528.194	−	100.625i	1.52657	−	0.290823i
$347$	−432.614	−	432.614i	−1.24673	−	1.24673i	−0.957157	−	0.289570i	$-0.906488\pi$
$347$	−432.614	−	432.614i	−1.24673	−	1.24673i	−0.289570	−	0.957157i	$-0.593512\pi$
$348$		0			0
$349$	−148.839	−	148.839i	−0.426472	−	0.426472i	0.460953	−	0.887425i	$-0.347508\pi$
$349$	−148.839	−	148.839i	−0.426472	−	0.426472i	−0.887425	+	0.460953i	$0.847508\pi$
$350$	−190.787	−	129.727i	−0.545107	−	0.370649i
$351$		0			0
$352$	142.987	−	196.300i	0.406212	−	0.557671i
$353$	268.587			0.760869			0.380434	−	0.924808i	$-0.375774\pi$
$353$	268.587			0.760869			0.380434	+	0.924808i	$0.375774\pi$
$354$		0			0
$355$	−3.30418	+	3.30418i	−0.00930756	+	0.00930756i
$356$	429.846	−	169.945i	1.20743	−	0.477375i
$357$		0			0
$358$	−28.7286	−	150.801i	−0.0802475	−	0.421231i
$359$	−628.520			−1.75075			−0.875376	−	0.483442i	$-0.839386\pi$
$359$	−628.520			−1.75075			−0.875376	+	0.483442i	$0.839386\pi$
$360$		0			0
$361$			347.128i			0.961574i
$362$	10.4457	+	54.8310i	0.0288556	+	0.151467i
$363$		0			0
$364$	114.764	−	264.850i	0.315286	−	0.727609i
$365$	0.569131	+	0.569131i	0.00155926	+	0.00155926i
$366$		0			0
$367$		−	396.386i		−	1.08007i	−0.841643	−	0.540035i	$-0.818411\pi$
$367$		−	396.386i		−	1.08007i	0.841643	−	0.540035i	$-0.181589\pi$
$368$	191.235	−	179.231i	0.519660	−	0.487040i
$369$		0			0
$370$	8.00661	+	5.44414i	0.0216395	+	0.0147139i
$371$	−4.90204	+	4.90204i	−0.0132130	+	0.0132130i
$372$		0			0
$373$	134.275	−	134.275i	0.359987	−	0.359987i	−0.503821	−	0.863808i	$-0.668073\pi$
$373$	134.275	−	134.275i	0.359987	−	0.359987i	0.863808	+	0.503821i	$0.168073\pi$
$374$	−192.035	+	36.5840i	−0.513461	+	0.0978182i
$375$		0			0
$376$	139.634	−	622.546i	0.371367	−	1.65571i
$377$			576.015i			1.52789i
$378$		0			0
$379$	−350.491	−	350.491i	−0.924777	−	0.924777i	0.0725851	−	0.997362i	$-0.476875\pi$
$379$	−350.491	−	350.491i	−0.924777	−	0.924777i	−0.997362	+	0.0725851i	$0.976875\pi$
$380$	−1.14880	+	0.454194i	−0.00302316	+	0.00119525i
$381$		0			0
$382$	275.459	+	187.300i	0.721096	+	0.490314i
$383$		−	403.778i		−	1.05425i	−0.849787	−	0.527126i	$-0.823270\pi$
$383$		−	403.778i		−	1.05425i	0.849787	−	0.527126i	$-0.176730\pi$
$384$		0			0
$385$	2.90456			0.00754431
$386$	−2.45446	+	3.60973i	−0.00635870	+	0.00935163i
$387$		0			0
$388$	215.080	+	544.007i	0.554331	+	1.40208i
$389$	125.310	−	125.310i	0.322134	−	0.322134i	−0.527452	−	0.849585i	$-0.676852\pi$
$389$	125.310	−	125.310i	0.322134	−	0.322134i	0.849585	+	0.527452i	$0.176852\pi$
$390$		0			0
$391$	−210.976			−0.539580
$392$	−216.202	−	48.4931i	−0.551536	−	0.123707i
$393$		0			0
$394$	−35.6924	−	187.354i	−0.0905898	−	0.475518i
$395$	−4.95027	−	4.95027i	−0.0125323	−	0.0125323i
$396$		0			0
$397$	−69.8722	−	69.8722i	−0.176001	−	0.176001i	0.613609	−	0.789610i	$-0.289717\pi$
$397$	−69.8722	−	69.8722i	−0.176001	−	0.176001i	−0.789610	+	0.613609i	$0.789717\pi$
$398$	−250.673	+	368.661i	−0.629832	+	0.926284i
$399$		0			0
$400$	−273.459	−	291.774i	−0.683647	−	0.729436i
$401$	−11.3010			−0.0281821			−0.0140911	−	0.999901i	$-0.504485\pi$
$401$	−11.3010			−0.0281821			−0.0140911	+	0.999901i	$0.504485\pi$
$402$		0			0
$403$	223.697	−	223.697i	0.555079	−	0.555079i
$404$	−279.537	−	121.128i	−0.691923	−	0.299823i
$405$		0			0
$406$	−334.090	+	63.6467i	−0.822883	+	0.156765i
$407$	443.081			1.08865
$408$		0			0
$409$		−	614.595i		−	1.50268i	−0.659917	−	0.751339i	$-0.729408\pi$
$409$		−	614.595i		−	1.50268i	0.659917	−	0.751339i	$-0.270592\pi$
$410$	−0.537016	+	0.102305i	−0.00130979	+	0.000249526i
$411$		0			0
$412$	232.639	+	588.418i	0.564658	+	1.42820i
$413$	−150.081	−	150.081i	−0.363391	−	0.363391i
$414$		0			0
$415$			3.13778i			0.00756092i
$416$	294.563	−	404.393i	0.708084	−	0.972099i
$417$		0			0
$418$	−31.7870	+	46.7485i	−0.0760453	+	0.111839i
$419$	−78.7092	+	78.7092i	−0.187850	+	0.187850i	−0.794766	−	0.606916i	$-0.792406\pi$
$419$	−78.7092	+	78.7092i	−0.187850	+	0.187850i	0.606916	+	0.794766i	$0.292406\pi$
$420$		0			0
$421$	−374.618	+	374.618i	−0.889829	+	0.889829i	−0.994506	−	0.104678i	$-0.966619\pi$
$421$	−374.618	+	374.618i	−0.889829	+	0.889829i	0.104678	+	0.994506i	$0.466619\pi$
$422$	−77.8718	−	408.760i	−0.184530	−	0.968626i
$423$		0			0
$424$	−10.1501	+	6.43105i	−0.0239390	+	0.0151676i
$425$			321.894i			0.757397i
$426$		0			0
$427$	70.5705	+	70.5705i	0.165270	+	0.165270i
$428$	129.553	−	298.978i	0.302693	−	0.698547i
$429$		0			0
$430$	0.103779	−	0.152625i	0.000241345	−	0.000354943i
$431$			616.593i			1.43061i	0.698813	+	0.715305i	$0.253712\pi$
$431$			616.593i			1.43061i	−0.698813	+	0.715305i	$0.746288\pi$
$432$		0			0
$433$	219.246			0.506342			0.253171	−	0.967422i	$-0.418526\pi$
$433$	219.246			0.506342			0.253171	+	0.967422i	$0.418526\pi$
$434$	154.462	+	105.027i	0.355904	+	0.241999i
$435$		0			0
$436$	127.930	−	295.233i	0.293417	−	0.677141i
$437$	−43.1409	+	43.1409i	−0.0987207	+	0.0987207i
$438$		0			0
$439$	575.292			1.31046			0.655231	−	0.755429i	$-0.272571\pi$
$439$	575.292			1.31046			0.655231	+	0.755429i	$0.272571\pi$
$440$	4.91234	+	1.10181i	0.0111644	+	0.00250412i
$441$		0			0
$442$	−395.605	+	75.3658i	−0.895035	+	0.170511i
$443$	−371.895	−	371.895i	−0.839492	−	0.839492i	0.149300	−	0.988792i	$-0.452298\pi$
$443$	−371.895	−	371.895i	−0.839492	−	0.839492i	−0.988792	+	0.149300i	$0.952298\pi$
$444$		0			0
$445$	6.77538	+	6.77538i	0.0152256	+	0.0152256i
$446$	−100.397	−	68.2655i	−0.225105	−	0.153062i
$447$		0			0
$448$	267.097	+	126.164i	0.596199	+	0.281616i
$449$	498.135			1.10943			0.554716	−	0.832040i	$-0.312827\pi$
$449$	498.135			1.10943			0.554716	+	0.832040i	$0.312827\pi$
$450$		0			0
$451$	−17.6898	+	17.6898i	−0.0392236	+	0.0392236i
$452$	199.617	+	504.896i	0.441632	+	1.11703i
$453$		0			0
$454$	119.374	+	626.614i	0.262939	+	1.38021i
$455$	5.98361			0.0131508
$456$		0			0
$457$			61.1711i			0.133854i	0.997758	+	0.0669268i	$0.0213194\pi$
$457$			61.1711i			0.133854i	−0.997758	+	0.0669268i	$0.978681\pi$
$458$	120.576	+	632.922i	0.263267	+	1.38193i
$459$		0			0
$460$	4.98533	+	2.16023i	0.0108377	+	0.00469616i
$461$	443.183	+	443.183i	0.961352	+	0.961352i	0.999280	−	0.0379287i	$-0.0120760\pi$
$461$	443.183	+	443.183i	0.961352	+	0.961352i	−0.0379287	+	0.999280i	$0.512076\pi$
$462$		0			0
$463$			706.883i			1.52675i	0.645958	+	0.763373i	$0.276458\pi$
$463$			706.883i			1.52675i	−0.645958	+	0.763373i	$0.723542\pi$
$464$	−589.175	−	19.0911i	−1.26977	−	0.0411446i
$465$		0			0
$466$	−200.208	−	136.132i	−0.429630	−	0.292129i
$467$	406.857	−	406.857i	0.871214	−	0.871214i	−0.121391	−	0.992605i	$-0.538735\pi$
$467$	406.857	−	406.857i	0.871214	−	0.871214i	0.992605	+	0.121391i	$0.0387355\pi$
$468$		0			0
$469$	−277.224	+	277.224i	−0.591096	+	0.591096i
$470$	12.9923	−	2.47513i	0.0276433	−	0.00526624i
$471$		0			0
$472$	−196.893	−	310.756i	−0.417146	−	0.658381i
$473$		−	8.44620i		−	0.0178567i
$474$		0			0
$475$	65.8217	+	65.8217i	0.138572	+	0.138572i
$476$	−87.4248	−	221.125i	−0.183665	−	0.464548i
$477$		0			0
$478$	−366.160	−	248.972i	−0.766024	−	0.520863i
$479$			133.063i			0.277793i	0.990307	+	0.138896i	$0.0443555\pi$
$479$			133.063i			0.277793i	−0.990307	+	0.138896i	$0.955645\pi$
$480$		0			0
$481$	912.780			1.89767
$482$	−94.7638	+	139.368i	−0.196605	+	0.289144i
$483$		0			0
$484$	−235.849	+	93.2463i	−0.487292	+	0.192658i
$485$	−8.57482	+	8.57482i	−0.0176800	+	0.0176800i
$486$		0			0
$487$	−208.075			−0.427259			−0.213629	−	0.976915i	$-0.568529\pi$
$487$	−208.075			−0.427259			−0.213629	+	0.976915i	$0.568529\pi$
$488$	92.5823	+	146.123i	0.189718	+	0.299432i
$489$		0			0
$490$	−0.859582	−	4.51207i	−0.00175425	−	0.00920830i
$491$	98.9374	+	98.9374i	0.201502	+	0.201502i	0.800643	−	0.599141i	$-0.204491\pi$
$491$	98.9374	+	98.9374i	0.201502	+	0.201502i	−0.599141	+	0.800643i	$0.704491\pi$
$492$		0			0
$493$	335.528	+	335.528i	0.680585	+	0.680585i
$494$	−65.4835	+	96.3055i	−0.132558	+	0.194950i
$495$		0			0
$496$	221.393	+	236.222i	0.446358	+	0.476253i
$497$	−260.102			−0.523345
$498$		0			0
$499$	−287.076	+	287.076i	−0.575304	+	0.575304i	−0.933606	−	0.358302i	$-0.883356\pi$
$499$	−287.076	+	287.076i	−0.575304	+	0.575304i	0.358302	+	0.933606i	$0.383356\pi$
$500$	6.59280	−	15.2147i	0.0131856	−	0.0304294i
$501$		0			0
$502$	−490.717	+	93.4853i	−0.977525	+	0.186226i
$503$	78.7359			0.156533			0.0782663	−	0.996932i	$-0.475062\pi$
$503$	78.7359			0.156533			0.0782663	+	0.996932i	$0.475062\pi$
$504$		0			0
$505$		−	6.31543i		−	0.0125058i
$506$	244.246	−	46.5307i	0.482700	−	0.0919580i
$507$		0			0
$508$	−619.545	+	244.946i	−1.21958	+	0.482177i
$509$	242.477	+	242.477i	0.476378	+	0.476378i	0.903971	−	0.427593i	$-0.140638\pi$
$509$	242.477	+	242.477i	0.476378	+	0.476378i	−0.427593	+	0.903971i	$0.640638\pi$
$510$		0			0
$511$			44.8014i			0.0876740i
$512$	403.869	+	314.696i	0.788807	+	0.614640i
$513$		0			0
$514$	−183.306	+	269.585i	−0.356626	+	0.524484i
$515$	−9.27484	+	9.27484i	−0.0180094	+	0.0180094i
$516$		0			0
$517$	427.980	−	427.980i	0.827815	−	0.827815i
$518$	100.858	+	529.415i	0.194706	+	1.02204i
$519$		0			0
$520$	10.1198	+	2.26982i	0.0194611	+	0.00436503i
$521$			561.306i			1.07736i	0.842510	+	0.538681i	$0.181077\pi$
$521$			561.306i			1.07736i	−0.842510	+	0.538681i	$0.818923\pi$
$522$		0			0
$523$	396.152	+	396.152i	0.757460	+	0.757460i	0.975859	−	0.218399i	$-0.0700836\pi$
$523$	396.152	+	396.152i	0.757460	+	0.757460i	−0.218399	+	0.975859i	$0.570084\pi$
$524$	115.513	+	50.0539i	0.220445	+	0.0955228i
$525$		0			0
$526$	196.801	−	289.432i	0.374147	−	0.550252i
$527$		−	260.607i		−	0.494510i
$528$		0			0
$529$	−260.662			−0.492745
$530$	−0.205984	−	0.140060i	−0.000388648	−	0.000264264i
$531$		0			0
$532$	−63.0931	−	27.3394i	−0.118596	−	0.0513898i
$533$	−36.4424	+	36.4424i	−0.0683722	+	0.0683722i
$534$		0			0
$535$	6.75465			0.0126255
$536$	−574.018	+	363.694i	−1.07093	+	0.678534i
$537$		0			0
$538$	82.6560	−	15.7466i	0.153636	−	0.0292687i
$539$	−148.632	−	148.632i	−0.275755	−	0.275755i
$540$		0			0
$541$	−22.5728	−	22.5728i	−0.0417242	−	0.0417242i	0.685937	−	0.727661i	$-0.259393\pi$
$541$	−22.5728	−	22.5728i	−0.0417242	−	0.0417242i	−0.727661	+	0.685937i	$0.759393\pi$
$542$	−456.292	−	310.259i	−0.841867	−	0.572433i
$543$		0			0
$544$	−63.9759	−	407.142i	−0.117603	−	0.748422i
$545$	6.67005			0.0122386
$546$		0			0
$547$	601.634	−	601.634i	1.09988	−	1.09988i	0.105456	−	0.994424i	$-0.466370\pi$
$547$	601.634	−	601.634i	1.09988	−	1.09988i	0.994424	−	0.105456i	$-0.0336302\pi$
$548$	−650.560	+	257.208i	−1.18715	+	0.469357i
$549$		0			0
$550$	−70.9937	−	372.656i	−0.129079	−	0.677556i
$551$	137.219			0.249037
$552$		0			0
$553$		−	389.681i		−	0.704666i
$554$	−147.329	−	773.349i	−0.265936	−	1.39594i
$555$		0			0
$556$	224.665	−	518.475i	0.404073	−	0.932510i
$557$	−502.883	−	502.883i	−0.902841	−	0.902841i	0.0928399	−	0.995681i	$-0.470406\pi$
$557$	−502.883	−	502.883i	−0.902841	−	0.902841i	−0.995681	+	0.0928399i	$0.970406\pi$
$558$		0			0
$559$		−	17.3998i		−	0.0311266i
$560$	−0.198317	+	6.12031i	−0.000354138	+	0.0109291i
$561$		0			0
$562$	334.674	+	227.564i	0.595505	+	0.404917i
$563$	−655.972	+	655.972i	−1.16514	+	1.16514i	−0.181802	+	0.983335i	$0.558193\pi$
$563$	−655.972	+	655.972i	−1.16514	+	1.16514i	−0.983335	+	0.181802i	$0.941807\pi$
$564$		0			0
$565$	−7.95834	+	7.95834i	−0.0140856	+	0.0140856i
$566$	812.022	−	154.696i	1.43467	−	0.273315i
$567$		0			0
$568$	−439.899	−	98.6671i	−0.774469	−	0.173710i
$569$		−	649.911i		−	1.14220i	−0.820881	−	0.571099i	$-0.806517\pi$
$569$		−	649.911i		−	1.14220i	0.820881	−	0.571099i	$-0.193483\pi$
$570$		0			0
$571$	269.718	+	269.718i	0.472360	+	0.472360i	0.902678	−	0.430317i	$-0.141598\pi$
$571$	269.718	+	269.718i	0.472360	+	0.472360i	−0.430317	+	0.902678i	$0.641598\pi$
$572$	441.370	−	174.502i	0.771625	−	0.305073i
$573$		0			0
$574$	−25.1634	−	17.1100i	−0.0438387	−	0.0298084i
$575$		−	409.413i		−	0.712022i
$576$		0			0
$577$	−142.675			−0.247271			−0.123635	−	0.992328i	$-0.539455\pi$
$577$	−142.675			−0.247271			−0.123635	+	0.992328i	$0.539455\pi$
$578$	138.461	−	203.633i	0.239552	−	0.352306i
$579$		0			0
$580$	−4.49293	−	11.3640i	−0.00774643	−	0.0195932i
$581$	−123.502	+	123.502i	−0.212567	+	0.212567i
$582$		0			0
$583$	−11.3990			−0.0195523
$584$	−16.9949	+	75.7705i	−0.0291009	+	0.129744i
$585$		0			0
$586$	−175.294	−	920.141i	−0.299136	−	1.57021i
$587$	687.876	+	687.876i	1.17185	+	1.17185i	0.981768	+	0.190082i	$0.0608753\pi$
$587$	687.876	+	687.876i	1.17185	+	1.17185i	0.190082	+	0.981768i	$0.439125\pi$
$588$		0			0
$589$	−53.2895	−	53.2895i	−0.0904746	−	0.0904746i
$590$	4.28807	−	6.30639i	0.00726791	−	0.0106888i
$591$		0			0
$592$	−30.2526	+	933.634i	−0.0511024	+	1.57708i
$593$	58.8678			0.0992711			0.0496355	−	0.998767i	$-0.484194\pi$
$593$	58.8678			0.0992711			0.0496355	+	0.998767i	$0.484194\pi$
$594$		0			0
$595$	3.48545	−	3.48545i	0.00585790	−	0.00585790i
$596$	−388.696	−	168.429i	−0.652175	−	0.282599i
$597$		0			0
$598$	503.166	−	95.8568i	0.841414	−	0.160296i
$599$	670.449			1.11928			0.559641	−	0.828735i	$-0.310939\pi$
$599$	670.449			1.11928			0.559641	+	0.828735i	$0.310939\pi$
$600$		0			0
$601$			910.721i			1.51534i	0.652636	+	0.757671i	$0.273663\pi$
$601$			910.721i			1.51534i	−0.652636	+	0.757671i	$0.726337\pi$
$602$	10.0919	−	1.92259i	0.0167640	−	0.00319367i
$603$		0			0
$604$	−103.000	−	260.520i	−0.170530	−	0.431325i
$605$	−3.71754	−	3.71754i	−0.00614469	−	0.00614469i
$606$		0			0
$607$		−	761.794i		−	1.25501i	−0.778611	−	0.627507i	$-0.784075\pi$
$607$		−	761.794i		−	1.25501i	0.778611	−	0.627507i	$-0.215925\pi$
$608$	−96.3354	−	70.1715i	−0.158446	−	0.115414i
$609$		0			0
$610$	−2.01632	+	2.96537i	−0.00330544	+	0.00486126i
$611$	881.671	−	881.671i	1.44300	−	1.44300i
$612$		0			0
$613$	273.397	−	273.397i	0.445999	−	0.445999i	−0.448023	−	0.894022i	$-0.647872\pi$
$613$	273.397	−	273.397i	0.445999	−	0.445999i	0.894022	+	0.448023i	$0.147872\pi$
$614$	12.5719	+	65.9918i	0.0204755	+	0.107479i
$615$		0			0
$616$	149.981	+	236.714i	0.243475	+	0.384276i
$617$		−	1088.68i		−	1.76448i	−0.470804	−	0.882238i	$-0.656036\pi$
$617$		−	1088.68i		−	1.76448i	0.470804	−	0.882238i	$-0.343964\pi$
$618$		0			0
$619$	−129.299	−	129.299i	−0.208884	−	0.208884i	0.594909	−	0.803793i	$-0.297188\pi$
$619$	−129.299	−	129.299i	−0.208884	−	0.208884i	−0.803793	+	0.594909i	$0.797188\pi$
$620$	−2.66841	+	6.15809i	−0.00430389	+	0.00993241i
$621$		0			0
$622$	−177.409	+	260.913i	−0.285224	+	0.419474i
$623$			533.351i			0.856102i
$624$		0			0
$625$	−624.484			−0.999175
$626$	−96.9072	−	65.8926i	−0.154804	−	0.105260i
$627$		0			0
$628$	−66.4188	+	153.279i	−0.105762	+	0.244076i
$629$	531.694	−	531.694i	0.845301	−	0.845301i
$630$		0			0
$631$	455.029			0.721123			0.360562	−	0.932735i	$-0.382585\pi$
$631$	455.029			0.721123			0.360562	+	0.932735i	$0.382585\pi$
$632$	147.821	−	659.048i	0.233894	−	1.04280i
$633$		0			0
$634$	75.0296	−	14.2937i	0.118343	−	0.0225452i
$635$	−9.76549	−	9.76549i	−0.0153787	−	0.0153787i
$636$		0			0
$637$	−306.193	−	306.193i	−0.480679	−	0.480679i
$638$	−462.441	−	314.440i	−0.724829	−	0.492852i
$639$		0			0
$640$	−2.65708	+	10.2758i	−0.00415169	+	0.0160559i
$641$	−798.626			−1.24591			−0.622953	−	0.782259i	$-0.714067\pi$
$641$	−798.626			−1.24591			−0.622953	+	0.782259i	$0.714067\pi$
$642$		0			0
$643$	−305.718	+	305.718i	−0.475455	+	0.475455i	−0.903675	−	0.428219i	$-0.859141\pi$
$643$	−305.718	+	305.718i	−0.475455	+	0.475455i	0.428219	+	0.903675i	$0.359141\pi$
$644$	111.194	+	281.246i	0.172662	+	0.436717i
$645$		0			0
$646$	17.9538	+	94.2420i	0.0277923	+	0.145885i
$647$	−1161.90			−1.79583			−0.897916	−	0.440167i	$-0.854919\pi$
$647$	−1161.90			−1.79583			−0.897916	+	0.440167i	$0.854919\pi$
$648$		0			0
$649$		−	348.992i		−	0.537738i
$650$	−146.252	−	767.698i	−0.225003	−	1.18107i
$651$		0			0
$652$	−248.101	−	107.507i	−0.380523	−	0.164887i
$653$	−77.5410	−	77.5410i	−0.118746	−	0.118746i	0.645237	−	0.763983i	$-0.276759\pi$
$653$	−77.5410	−	77.5410i	−0.118746	−	0.118746i	−0.763983	+	0.645237i	$0.776759\pi$
$654$		0			0
$655$			2.60973i			0.00398431i
$656$	−36.0671	−	38.4828i	−0.0549804	−	0.0586628i
$657$		0			0
$658$	608.792	+	413.952i	0.925216	+	0.629106i
$659$	−836.993	+	836.993i	−1.27010	+	1.27010i	−0.324059	+	0.946037i	$0.605048\pi$
$659$	−836.993	+	836.993i	−1.27010	+	1.27010i	−0.946037	+	0.324059i	$0.894952\pi$
$660$		0			0
$661$	121.071	−	121.071i	0.183164	−	0.183164i	−0.609569	−	0.792733i	$-0.708658\pi$
$661$	121.071	−	121.071i	0.183164	−	0.183164i	0.792733	+	0.609569i	$0.208658\pi$
$662$	506.220	−	96.4386i	0.764682	−	0.145678i
$663$		0			0
$664$	−255.721	+	162.023i	−0.385123	+	0.244011i
$665$		−	1.42543i		−	0.00214350i
$666$		0			0
$667$	−426.754	−	426.754i	−0.639811	−	0.639811i
$668$	−229.820	−	581.288i	−0.344042	−	0.870191i
$669$		0			0
$670$	−11.6490	−	7.92078i	−0.0173865	−	0.0118221i
$671$			164.102i			0.244563i
$672$		0			0
$673$	−954.371			−1.41808			−0.709042	−	0.705166i	$-0.750872\pi$
$673$	−954.371			−1.41808			−0.709042	+	0.705166i	$0.750872\pi$
$674$	−573.685	+	843.710i	−0.851165	+	1.25179i
$675$		0			0
$676$	280.604	−	110.941i	0.415094	−	0.164113i
$677$	−245.475	+	245.475i	−0.362593	+	0.362593i	−0.864767	−	0.502174i	$-0.832534\pi$
$677$	−245.475	+	245.475i	−0.362593	+	0.362593i	0.502174	+	0.864767i	$0.332534\pi$
$678$		0			0
$679$	−675.002			−0.994112
$680$	7.21694	−	4.57260i	0.0106131	−	0.00672442i
$681$		0			0
$682$	57.4768	+	301.704i	0.0842768	+	0.442381i
$683$	911.271	+	911.271i	1.33422	+	1.33422i	0.901556	+	0.432663i	$0.142426\pi$
$683$	911.271	+	911.271i	1.33422	+	1.33422i	0.432663	+	0.901556i	$0.357574\pi$
$684$		0			0
$685$	−10.2544	−	10.2544i	−0.0149699	−	0.0149699i
$686$	398.095	−	585.472i	0.580313	−	0.853457i
$687$		0			0
$688$	17.7973	+	0.576688i	0.0258682	+	0.000838210i
$689$	−23.4828			−0.0340824
$690$		0			0
$691$	−476.155	+	476.155i	−0.689081	+	0.689081i	−0.962029	−	0.272947i	$-0.912001\pi$
$691$	−476.155	+	476.155i	−0.689081	+	0.689081i	0.272947	+	0.962029i	$0.412001\pi$
$692$	−427.569	+	986.733i	−0.617874	+	1.42591i
$693$		0			0
$694$	1202.00	−	228.990i	1.73199	−	0.329957i
$695$	11.7136			0.0168541
$696$		0			0
$697$			42.4553i			0.0609115i
$698$	413.542	−	78.7828i	0.592467	−	0.112869i
$699$		0			0
$700$	429.108	−	169.654i	0.613011	−	0.242362i
$701$	−934.966	−	934.966i	−1.33376	−	1.33376i	−0.901978	−	0.431782i	$-0.857885\pi$
$701$	−934.966	−	934.966i	−1.33376	−	1.33376i	−0.431782	−	0.901978i	$-0.642115\pi$
$702$		0			0
$703$		−	217.444i		−	0.309309i
$704$	163.860	+	457.237i	0.232755	+	0.649485i
$705$		0			0
$706$	−302.045	+	444.212i	−0.427825	+	0.629196i
$707$	248.572	−	248.572i	0.351587	−	0.351587i
$708$		0			0
$709$	5.89548	−	5.89548i	0.00831520	−	0.00831520i	−0.702937	−	0.711252i	$-0.748128\pi$
$709$	5.89548	−	5.89548i	0.00831520	−	0.00831520i	0.711252	+	0.702937i	$0.248128\pi$
$710$	−1.74896	−	9.18053i	−0.00246332	−	0.0129303i
$711$		0			0
$712$	−202.321	+	902.032i	−0.284159	+	1.26690i
$713$			331.462i			0.464884i
$714$		0			0
$715$	6.95702	+	6.95702i	0.00973010	+	0.00973010i
$716$	281.714	+	122.072i	0.393456	+	0.170492i
$717$		0			0
$718$	706.815	−	1039.50i	0.984422	−	1.44777i
$719$			19.5965i			0.0272552i	0.999907	+	0.0136276i	$0.00433793\pi$
$719$			19.5965i			0.0272552i	−0.999907	+	0.0136276i	$0.995662\pi$
$720$		0			0
$721$	−730.107			−1.01263
$722$	−574.111	−	390.370i	−0.795168	−	0.540679i
$723$		0			0
$724$	−102.431	−	44.3853i	−0.141480	−	0.0613057i
$725$	−651.115	+	651.115i	−0.898089	+	0.898089i
$726$		0			0
$727$	741.995			1.02063			0.510313	−	0.859989i	$-0.329530\pi$
$727$	741.995			1.02063			0.510313	+	0.859989i	$0.329530\pi$
$728$	308.971	+	487.649i	0.424411	+	0.669848i
$729$		0			0
$730$	−1.58130	+	0.301250i	−0.00216617	+	0.000412672i
$731$	−10.1354	−	10.1354i	−0.0138651	−	0.0138651i
$732$		0			0
$733$	349.267	+	349.267i	0.476490	+	0.476490i	0.904007	−	0.427517i	$-0.140612\pi$
$733$	349.267	+	349.267i	0.476490	+	0.476490i	−0.427517	+	0.904007i	$0.640612\pi$
$734$	655.577	+	445.764i	0.893157	+	0.607307i
$735$		0			0
$736$	81.3702	+	517.838i	0.110557	+	0.703585i
$737$	−644.646			−0.874690
$738$		0			0
$739$	−358.932	+	358.932i	−0.485700	+	0.485700i	−0.906946	−	0.421246i	$-0.861593\pi$
$739$	−358.932	+	358.932i	−0.485700	+	0.485700i	0.421246	+	0.906946i	$0.361593\pi$
$740$	−18.0080	+	7.11971i	−0.0243351	+	0.00962123i
$741$		0			0
$742$	−2.59473	−	13.6201i	−0.00349694	−	0.0183559i
$743$	856.214			1.15237			0.576187	−	0.817318i	$-0.304540\pi$
$743$	856.214			1.15237			0.576187	+	0.817318i	$0.304540\pi$
$744$		0			0
$745$		−	8.78160i		−	0.0117874i
$746$	71.0741	+	373.078i	0.0952736	+	0.500104i
$747$		0			0
$748$	155.451	−	358.745i	0.207822	−	0.479605i
$749$	265.860	+	265.860i	0.354953	+	0.354953i
$750$		0			0
$751$			442.218i			0.588839i	0.955676	+	0.294420i	$0.0951264\pi$
$751$			442.218i			0.588839i	−0.955676	+	0.294420i	$0.904874\pi$
$752$	872.593	+	931.036i	1.16036	+	1.23808i
$753$		0			0
$754$	−952.663	−	647.769i	−1.26348	−	0.859110i
$755$	4.10641	−	4.10641i	0.00543896	−	0.00543896i
$756$		0			0
$757$	489.198	−	489.198i	0.646233	−	0.646233i	−0.305848	−	0.952080i	$-0.598940\pi$
$757$	489.198	−	489.198i	0.646233	−	0.646233i	0.952080	+	0.305848i	$0.0989399\pi$
$758$	973.823	−	185.520i	1.28473	−	0.244750i
$759$		0			0
$760$	0.540721	−	2.41076i	0.000711475	−	0.00317205i
$761$		−	404.015i		−	0.530899i	−0.964125	−	0.265450i	$-0.914480\pi$
$761$		−	404.015i		−	0.530899i	0.964125	−	0.265450i	$-0.0855204\pi$
$762$		0			0
$763$	262.530	+	262.530i	0.344076	+	0.344076i
$764$	−619.545	+	244.946i	−0.810923	+	0.320610i
$765$		0			0
$766$	667.804	+	454.077i	0.871807	+	0.592790i
$767$		−	718.949i		−	0.937352i
$768$		0			0
$769$	−387.336			−0.503688			−0.251844	−	0.967768i	$-0.581037\pi$
$769$	−387.336			−0.503688			−0.251844	+	0.967768i	$0.581037\pi$
$770$	−3.26638	+	4.80381i	−0.00424205	+	0.00623872i
$771$		0			0
$772$	−3.20987	−	8.11879i	−0.00415787	−	0.0105166i
$773$	960.396	−	960.396i	1.24243	−	1.24243i	0.283436	−	0.958991i	$-0.408526\pi$
$773$	960.396	−	960.396i	1.24243	−	1.24243i	0.958991	−	0.283436i	$-0.0914745\pi$
$774$		0			0
$775$	505.724			0.652547
$776$	−1141.60	−	256.055i	−1.47113	−	0.329968i
$777$		0			0
$778$	66.3286	+	348.168i	0.0852553	+	0.447517i
$779$	8.68138	+	8.68138i	0.0111443	+	0.0111443i
$780$		0			0
$781$	−302.416	−	302.416i	−0.387216	−	0.387216i
$782$	237.257	−	348.930i	0.303398	−	0.446202i
$783$		0			0
$784$	323.337	−	303.040i	0.412419	−	0.386531i
$785$	−3.46296			−0.00441141
$786$		0			0
$787$	−298.374	+	298.374i	−0.379129	+	0.379129i	−0.870788	−	0.491659i	$-0.836391\pi$
$787$	−298.374	+	298.374i	−0.379129	+	0.379129i	0.491659	+	0.870788i	$0.336391\pi$
$788$	350.001	+	151.662i	0.444164	+	0.192464i
$789$		0			0
$790$	13.7541	−	2.62026i	0.0174103	−	0.00331678i
$791$	−626.473			−0.792002
$792$		0			0
$793$			338.062i			0.426308i
$794$	194.137	−	36.9845i	0.244505	−	0.0465800i
$795$		0			0
$796$	−327.824	−	829.171i	−0.411839	−	1.04167i
$797$	870.093	+	870.093i	1.09171	+	1.09171i	0.995346	+	0.0963642i	$0.0307214\pi$
$797$	870.093	+	870.093i	1.09171	+	1.09171i	0.0963642	+	0.995346i	$0.469279\pi$
$798$		0			0
$799$		−	1027.15i		−	1.28554i
$800$	790.085	−	124.150i	0.987607	−	0.155187i
$801$		0			0
$802$	12.7088	−	18.6906i	0.0158464	−	0.0233050i
$803$	−52.0897	+	52.0897i	−0.0648689	+	0.0648689i
$804$		0			0
$805$	−4.43310	+	4.43310i	−0.00550695	+	0.00550695i
$806$	118.406	+	621.532i	0.146906	+	0.771131i
$807$		0			0
$808$	514.692	−	326.105i	0.636995	−	0.403595i
$809$			107.642i			0.133055i	0.997785	+	0.0665277i	$0.0211921\pi$
$809$			107.642i			0.133055i	−0.997785	+	0.0665277i	$0.978808\pi$
$810$		0			0
$811$	829.739	+	829.739i	1.02311	+	1.02311i	0.999727	+	0.0233795i	$0.00744260\pi$
$811$	829.739	+	829.739i	1.02311	+	1.02311i	0.0233795	+	0.999727i	$0.492557\pi$
$812$	270.444	−	624.123i	0.333059	−	0.768624i
$813$		0			0
$814$	−498.276	+	732.806i	−0.612133	+	0.900253i
$815$		−	5.60521i		−	0.00687756i
$816$		0			0
$817$	−4.14502			−0.00507346
$818$	1016.47	+	691.155i	1.24263	+	0.844933i
$819$		0			0
$820$	0.434710	−	1.00321i	0.000530135	−	0.00122343i
$821$	−506.899	+	506.899i	−0.617416	+	0.617416i	−0.944868	−	0.327452i	$-0.893810\pi$
$821$	−506.899	+	506.899i	−0.617416	+	0.617416i	0.327452	+	0.944868i	$0.393810\pi$
$822$		0			0
$823$	−927.304			−1.12674			−0.563368	−	0.826206i	$-0.690495\pi$
$823$	−927.304			−1.12674			−0.563368	+	0.826206i	$0.690495\pi$
$824$	−1234.80	−	276.958i	−1.49854	−	0.336115i
$825$		0			0
$826$	416.993	−	79.4402i	0.504834	−	0.0961745i
$827$	19.4711	+	19.4711i	0.0235443	+	0.0235443i	0.718781	−	0.695237i	$-0.244700\pi$
$827$	19.4711	+	19.4711i	0.0235443	+	0.0235443i	−0.695237	+	0.718781i	$0.744700\pi$
$828$		0			0
$829$	409.028	+	409.028i	0.493400	+	0.493400i	0.909376	−	0.415976i	$-0.136560\pi$
$829$	409.028	+	409.028i	0.493400	+	0.493400i	−0.415976	+	0.909376i	$0.636560\pi$
$830$	−5.18953	−	3.52866i	−0.00625245	−	0.00425139i
$831$		0			0
$832$	337.563	+	941.942i	0.405725	+	1.13214i
$833$	−356.714			−0.428228
$834$		0			0
$835$	9.16246	−	9.16246i	0.0109730	−	0.0109730i
$836$	−41.5701	−	105.144i	−0.0497250	−	0.125770i
$837$		0			0
$838$	−41.6621	−	218.690i	−0.0497161	−	0.260967i
$839$	−634.212			−0.755914			−0.377957	−	0.925823i	$-0.623373\pi$
$839$	−634.212			−0.755914			−0.377957	+	0.925823i	$0.623373\pi$
$840$		0			0
$841$			516.388i			0.614017i
$842$	−198.291	−	1040.86i	−0.235501	−	1.23618i
$843$		0			0
$844$	763.616	+	330.888i	0.904758	+	0.392048i
$845$	4.42297	+	4.42297i	0.00523429	+	0.00523429i
$846$		0			0
$847$		−	292.641i		−	0.345503i
$848$	0.778300	−	24.0193i	0.000917807	−	0.0283247i
$849$		0			0
$850$	−532.376	−	361.992i	−0.626325	−	0.425873i
$851$	−676.255	+	676.255i	−0.794659	+	0.794659i
$852$		0			0
$853$	687.203	−	687.203i	0.805630	−	0.805630i	−0.178339	−	0.983969i	$-0.557072\pi$
$853$	687.203	−	687.203i	0.805630	−	0.805630i	0.983969	+	0.178339i	$0.0570723\pi$
$854$	−196.077	+	37.3541i	−0.229598	+	0.0437402i
$855$		0			0
$856$	348.785	+	550.487i	0.407459	+	0.643093i
$857$			995.675i			1.16181i	0.813970	+	0.580907i	$0.197302\pi$
$857$			995.675i			1.16181i	−0.813970	+	0.580907i	$0.802698\pi$
$858$		0			0
$859$	430.241	+	430.241i	0.500863	+	0.500863i	0.911706	−	0.410843i	$-0.134766\pi$
$859$	430.241	+	430.241i	0.500863	+	0.500863i	−0.410843	+	0.911706i	$0.634766\pi$
$860$	0.135719	+	0.343276i	0.000157813	+	0.000399158i
$861$		0			0
$862$	−1019.77	−	693.402i	−1.18303	−	0.804411i
$863$		−	1014.03i		−	1.17501i	−0.809222	−	0.587503i	$-0.800111\pi$
$863$		−	1014.03i		−	1.17501i	0.809222	−	0.587503i	$-0.199889\pi$
$864$		0			0
$865$	−22.2927			−0.0257719
$866$	−246.558	+	362.608i	−0.284709	+	0.418716i
$867$		0			0
$868$	−347.407	+	137.352i	−0.400239	+	0.158240i
$869$	453.074	−	453.074i	0.521374	−	0.521374i
$870$		0			0
$871$	−1328.02			−1.52471
$872$	344.416	+	543.592i	0.394973	+	0.623386i
$873$		0			0
$874$	−22.8352	−	119.865i	−0.0261272	−	0.137146i
$875$	13.5293	+	13.5293i	0.0154621	+	0.0154621i
$876$		0			0
$877$	−544.315	−	544.315i	−0.620656	−	0.620656i	0.325043	−	0.945699i	$-0.394621\pi$
$877$	−544.315	−	544.315i	−0.620656	−	0.620656i	−0.945699	+	0.325043i	$0.894621\pi$
$878$	−646.957	+	951.469i	−0.736853	+	1.08368i
$879$		0			0
$880$	−7.34655	+	6.88539i	−0.00834835	+	0.00782431i
$881$	645.905			0.733150			0.366575	−	0.930388i	$-0.380530\pi$
$881$	645.905			0.733150			0.366575	+	0.930388i	$0.380530\pi$
$882$		0			0
$883$	586.952	−	586.952i	0.664725	−	0.664725i	−0.291765	−	0.956490i	$-0.594243\pi$
$883$	586.952	−	586.952i	0.664725	−	0.664725i	0.956490	+	0.291765i	$0.0942425\pi$
$884$	320.240	−	739.041i	0.362262	−	0.836019i
$885$		0			0
$886$	1033.29	−	196.850i	1.16625	−	0.222178i
$887$	1221.93			1.37759			0.688797	−	0.724955i	$-0.258139\pi$
$887$	1221.93			1.37759			0.688797	+	0.724955i	$0.258139\pi$
$888$		0			0
$889$		−	768.730i		−	0.864713i
$890$	−18.8251	+	3.58632i	−0.0211518	+	0.00402957i
$891$		0			0
$892$	225.807	−	89.2758i	0.253147	−	0.100085i
$893$	−210.034	−	210.034i	−0.235200	−	0.235200i
$894$		0			0
$895$			6.36462i			0.00711131i
$896$	−509.031	+	299.868i	−0.568115	+	0.334674i
$897$		0			0
$898$	−560.188	+	823.859i	−0.623817	+	0.917438i
$899$	527.145	−	527.145i	0.586368	−	0.586368i
$900$		0			0
$901$	−13.6787	+	13.6787i	−0.0151817	+	0.0151817i
$902$	−9.36352	−	49.1504i	−0.0103808	−	0.0544905i
$903$		0			0
$904$	−1059.52	−	237.646i	−1.17204	−	0.262883i
$905$		−	2.31417i		−	0.00255710i
$906$		0			0
$907$	310.014	+	310.014i	0.341801	+	0.341801i	0.857044	−	0.515243i	$-0.172298\pi$
$907$	310.014	+	310.014i	0.341801	+	0.341801i	−0.515243	+	0.857044i	$0.672298\pi$
$908$	−1170.59	−	507.239i	−1.28920	−	0.558633i
$909$		0			0
$910$	−6.72898	+	9.89621i	−0.00739449	+	0.0108750i
$911$			1044.12i			1.14612i	0.819513	+	0.573060i	$0.194244\pi$
$911$			1044.12i			1.14612i	−0.819513	+	0.573060i	$0.805756\pi$
$912$		0			0
$913$	−287.186			−0.314552
$914$	−101.170	−	68.7911i	−0.110689	−	0.0752638i
$915$		0			0
$916$	−1182.38	−	512.346i	−1.29081	−	0.559329i
$917$	−102.718	+	102.718i	−0.112015	+	0.112015i
$918$		0			0
$919$	188.522			0.205138			0.102569	−	0.994726i	$-0.467294\pi$
$919$	188.522			0.205138			0.102569	+	0.994726i	$0.467294\pi$
$920$	−9.17914	+	5.81584i	−0.00997732	+	0.00632156i
$921$		0			0
$922$	−1231.37	+	234.584i	−1.33554	+	0.254430i
$923$	−622.999	−	622.999i	−0.674972	−	0.674972i
$924$		0			0
$925$	1031.79	+	1031.79i	1.11545	+	1.11545i
$926$	−1169.10	−	794.940i	−1.26253	−	0.858466i
$927$		0			0
$928$	694.143	−	952.959i	0.747999	−	1.02690i
$929$	220.366			0.237208			0.118604	−	0.992942i	$-0.462158\pi$
$929$	220.366			0.237208			0.118604	+	0.992942i	$0.462158\pi$
$930$		0			0
$931$	−72.9419	+	72.9419i	−0.0783479	+	0.0783479i
$932$	450.295	−	178.030i	0.483149	−	0.191020i
$933$		0			0
$934$	215.356	+	1130.43i	0.230574	+	1.21032i
$935$	8.10493			0.00866837
$936$		0			0
$937$		−	558.321i		−	0.595860i	−0.954588	−	0.297930i	$-0.903704\pi$
$937$		−	558.321i		−	0.595860i	0.954588	−	0.297930i	$-0.0962962\pi$
$938$	−146.739	−	770.256i	−0.156439	−	0.821168i
$939$		0			0
$940$	−10.5172	+	24.2713i	−0.0111885	+	0.0258205i
$941$	794.760	+	794.760i	0.844591	+	0.844591i	0.989452	−	0.144861i	$-0.0462736\pi$
$941$	794.760	+	794.760i	0.844591	+	0.844591i	−0.144861	+	0.989452i	$0.546274\pi$
$942$		0			0
$943$		−	53.9984i		−	0.0572624i
$944$	735.375	+	23.8284i	0.778998	+	0.0252420i
$945$		0			0
$946$	13.9691	+	9.49834i	0.0147664	+	0.0100405i
$947$	44.9362	−	44.9362i	0.0474511	−	0.0474511i	−0.682983	−	0.730434i	$-0.739318\pi$
$947$	44.9362	−	44.9362i	0.0474511	−	0.0474511i	0.730434	+	0.682983i	$0.239318\pi$
$948$		0			0
$949$	−107.309	+	107.309i	−0.113076	+	0.113076i
$950$	−182.883	+	34.8405i	−0.192508	+	0.0366742i
$951$		0			0
$952$	464.031	+	104.080i	0.487427	+	0.109328i
$953$			304.232i			0.319236i	0.987179	+	0.159618i	$0.0510262\pi$
$953$			304.232i			0.319236i	−0.987179	+	0.159618i	$0.948974\pi$
$954$		0			0
$955$	−9.76549	−	9.76549i	−0.0102256	−	0.0102256i
$956$	823.545	−	325.600i	0.861448	−	0.340585i
$957$		0			0
$958$	−220.071	−	149.638i	−0.229719	−	0.156199i
$959$		−	807.213i		−	0.841724i
$960$		0			0
$961$	551.564			0.573948
$962$	−1026.49	+	1509.63i	−1.06703	+	1.56927i
$963$		0			0
$964$	−123.930	−	313.457i	−0.128558	−	0.325163i
$965$	0.127971	−	0.127971i	0.000132613	−	0.000132613i
$966$		0			0
$967$	834.409			0.862884			0.431442	−	0.902141i	$-0.358005\pi$
$967$	834.409			0.862884			0.431442	+	0.902141i	$0.358005\pi$
$968$	111.010	−	494.930i	0.114680	−	0.511291i
$969$		0			0
$970$	−4.53879	−	23.8248i	−0.00467917	−	0.0245616i
$971$	−211.499	−	211.499i	−0.217816	−	0.217816i	0.589761	−	0.807577i	$-0.299222\pi$
$971$	−211.499	−	211.499i	−0.217816	−	0.217816i	−0.807577	+	0.589761i	$0.799222\pi$
$972$		0			0
$973$	461.043	+	461.043i	0.473837	+	0.473837i
$974$	233.995	−	344.133i	0.240241	−	0.353319i
$975$		0			0
$976$	−345.786	−	11.2045i	−0.354288	−	0.0114800i
$977$	−891.561			−0.912549			−0.456275	−	0.889839i	$-0.650817\pi$
$977$	−891.561			−0.912549			−0.456275	+	0.889839i	$0.650817\pi$
$978$		0			0
$979$	−620.117	+	620.117i	−0.633419	+	0.633419i
$980$	8.42911	+	3.65248i	0.00860113	+	0.00372702i
$981$		0			0
$982$	−274.893	+	52.3692i	−0.279932	+	0.0533291i
$983$	181.589			0.184730			0.0923648	−	0.995725i	$-0.470557\pi$
$983$	181.589			0.184730			0.0923648	+	0.995725i	$0.470557\pi$
$984$		0			0
$985$			7.90739i			0.00802781i
$986$	−932.251	+	177.601i	−0.945488	+	0.180122i
$987$		0			0
$988$	−85.6376	−	216.605i	−0.0866777	−	0.219235i
$989$	12.8911	+	12.8911i	0.0130344	+	0.0130344i
$990$		0			0
$991$		−	1140.89i		−	1.15125i	−0.817715	−	0.575624i	$-0.804759\pi$
$991$		−	1140.89i		−	1.15125i	0.817715	−	0.575624i	$-0.195241\pi$
$992$	−639.656	+	100.512i	−0.644815	+	0.101323i
$993$		0			0
$994$	292.503	−	430.180i	0.294269	−	0.432776i
$995$	13.0697	−	13.0697i	0.0131354	−	0.0131354i
$996$		0			0
$997$	−742.946	+	742.946i	−0.745182	+	0.745182i	−0.973570	−	0.228388i	$-0.926654\pi$
$997$	−742.946	+	742.946i	−0.745182	+	0.745182i	0.228388	+	0.973570i	$0.426654\pi$
$998$	−151.954	−	797.630i	−0.152259	−	0.799228i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.a.19.1		6
3.2	odd	2		16.3.f.a.3.3	✓	6
4.3	odd	2		576.3.m.a.559.2		6
8.3	odd	2		1152.3.m.b.991.2		6
8.5	even	2		1152.3.m.a.991.2		6
12.11	even	2		64.3.f.a.47.3		6
15.2	even	4		400.3.k.d.99.3		6
15.8	even	4		400.3.k.c.99.1		6
15.14	odd	2		400.3.r.c.51.1		6
16.3	odd	4		1152.3.m.a.415.2		6
16.5	even	4		576.3.m.a.271.2		6
16.11	odd	4	inner	144.3.m.a.91.1		6
16.13	even	4		1152.3.m.b.415.2		6
24.5	odd	2		128.3.f.b.95.3		6
24.11	even	2		128.3.f.a.95.1		6
48.5	odd	4		64.3.f.a.15.3		6
48.11	even	4		16.3.f.a.11.3	yes	6
48.29	odd	4		128.3.f.a.31.1		6
48.35	even	4		128.3.f.b.31.3		6
96.5	odd	8		1024.3.c.j.1023.1		12
96.11	even	8		1024.3.c.j.1023.2		12
96.29	odd	8		1024.3.d.k.511.1		12
96.35	even	8		1024.3.d.k.511.11		12
96.53	odd	8		1024.3.c.j.1023.12		12
96.59	even	8		1024.3.c.j.1023.11		12
96.77	odd	8		1024.3.d.k.511.12		12
96.83	even	8		1024.3.d.k.511.2		12
240.59	even	4		400.3.r.c.251.1		6
240.107	odd	4		400.3.k.c.299.1		6
240.203	odd	4		400.3.k.d.299.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.3	✓	6	3.2	odd	2
16.3.f.a.11.3	yes	6	48.11	even	4
64.3.f.a.15.3		6	48.5	odd	4
64.3.f.a.47.3		6	12.11	even	2
128.3.f.a.31.1		6	48.29	odd	4
128.3.f.a.95.1		6	24.11	even	2
128.3.f.b.31.3		6	48.35	even	4
128.3.f.b.95.3		6	24.5	odd	2
144.3.m.a.19.1		6	1.1	even	1	trivial
144.3.m.a.91.1		6	16.11	odd	4	inner
400.3.k.c.99.1		6	15.8	even	4
400.3.k.c.299.1		6	240.107	odd	4
400.3.k.d.99.3		6	15.2	even	4
400.3.k.d.299.3		6	240.203	odd	4
400.3.r.c.51.1		6	15.14	odd	2
400.3.r.c.251.1		6	240.59	even	4
576.3.m.a.271.2		6	16.5	even	4
576.3.m.a.559.2		6	4.3	odd	2
1024.3.c.j.1023.1		12	96.5	odd	8
1024.3.c.j.1023.2		12	96.11	even	8
1024.3.c.j.1023.11		12	96.59	even	8
1024.3.c.j.1023.12		12	96.53	odd	8
1024.3.d.k.511.1		12	96.29	odd	8
1024.3.d.k.511.2		12	96.83	even	8
1024.3.d.k.511.11		12	96.35	even	8
1024.3.d.k.511.12		12	96.77	odd	8
1152.3.m.a.415.2		6	16.3	odd	4
1152.3.m.a.991.2		6	8.5	even	2
1152.3.m.b.415.2		6	16.13	even	4
1152.3.m.b.991.2		6	8.3	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12457 + 1.65389i) q^{2} +(-1.47068 - 3.71982i) q^{4} +(0.0586332 - 0.0586332i) q^{5} +4.61555 q^{7} +(7.80605 + 1.75086i) q^{8} +O(q^{10})\)	\(q+(-1.12457 + 1.65389i) q^{2} +(-1.47068 - 3.71982i) q^{4} +(0.0586332 - 0.0586332i) q^{5} +4.61555 q^{7} +(7.80605 + 1.75086i) q^{8} +(0.0310355 + 0.162910i) q^{10} +(5.36641 + 5.36641i) q^{11} +(11.0552 + 11.0552i) q^{13} +(-5.19051 + 7.63359i) q^{14} +(-11.6742 + 10.9414i) q^{16} +12.8793 q^{17} +(2.63359 - 2.63359i) q^{19} +(-0.304336 - 0.131874i) q^{20} +(-14.9103 + 2.84053i) q^{22} -16.3810 q^{23} +24.9931i q^{25} +(-30.7164 + 5.85170i) q^{26} +(-6.78801 - 17.1690i) q^{28} +(26.0518 + 26.0518i) q^{29} -20.2345i q^{31} +(-4.96735 - 31.6121i) q^{32} +(-14.4837 + 21.3009i) q^{34} +(0.270624 - 0.270624i) q^{35} +(41.2829 - 41.2829i) q^{37} +(1.39400 + 7.31733i) q^{38} +(0.560352 - 0.355035i) q^{40} +3.29640i q^{41} +(-0.786951 - 0.786951i) q^{43} +(12.0698 - 27.8544i) q^{44} +(18.4216 - 27.0923i) q^{46} -79.7517i q^{47} -27.6967 q^{49} +(-41.3358 - 28.1065i) q^{50} +(24.8647 - 57.3821i) q^{52} +(-1.06207 + 1.06207i) q^{53} +0.629299 q^{55} +(36.0292 + 8.08117i) q^{56} +(-72.3837 + 13.7896i) q^{58} +(-32.5163 - 32.5163i) q^{59} +(15.2897 + 15.2897i) q^{61} +(33.4656 + 22.7552i) q^{62} +(57.8690 + 27.3346i) q^{64} +1.29640 q^{65} +(-60.0631 + 60.0631i) q^{67} +(-18.9414 - 47.9087i) q^{68} +(0.143246 + 0.751918i) q^{70} -56.3535 q^{71} +9.70663i q^{73} +(21.8517 + 114.703i) q^{74} +(-13.6697 - 5.92332i) q^{76} +(24.7689 + 24.7689i) q^{77} -84.4278i q^{79} +(-0.0429672 + 1.32602i) q^{80} +(-5.45188 - 3.70704i) q^{82} +(-26.7577 + 26.7577i) q^{83} +(0.755154 - 0.755154i) q^{85} +(2.18651 - 0.416546i) q^{86} +(32.4946 + 51.2863i) q^{88} +115.555i q^{89} +(51.0258 + 51.0258i) q^{91} +(24.0913 + 60.9345i) q^{92} +(131.900 + 89.6864i) q^{94} -0.308832i q^{95} -146.245 q^{97} +(31.1469 - 45.8072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8	\( 6 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} + 36 q^{10} + 18 q^{11} - 2 q^{13} - 12 q^{14} - 40 q^{16} + 4 q^{17} + 30 q^{19} + 84 q^{20} - 52 q^{22} - 60 q^{23} - 96 q^{26} + 56 q^{28} + 18 q^{29} - 8 q^{32} - 76 q^{34} + 100 q^{35} + 46 q^{37} - 40 q^{38} + 40 q^{40} - 114 q^{43} - 20 q^{44} + 28 q^{46} - 46 q^{49} - 46 q^{50} + 100 q^{52} - 78 q^{53} + 252 q^{55} + 168 q^{56} - 176 q^{58} - 206 q^{59} + 30 q^{61} + 144 q^{62} + 64 q^{64} - 12 q^{65} - 226 q^{67} - 112 q^{68} - 16 q^{70} + 260 q^{71} + 92 q^{74} - 188 q^{76} + 212 q^{77} - 232 q^{80} + 304 q^{82} - 318 q^{83} - 212 q^{85} - 268 q^{86} - 8 q^{88} + 188 q^{91} + 168 q^{92} + 48 q^{94} - 4 q^{97} - 10 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 8 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 + 36 * q^10 + 18 * q^11 - 2 * q^13 - 12 * q^14 - 40 * q^16 + 4 * q^17 + 30 * q^19 + 84 * q^20 - 52 * q^22 - 60 * q^23 - 96 * q^26 + 56 * q^28 + 18 * q^29 - 8 * q^32 - 76 * q^34 + 100 * q^35 + 46 * q^37 - 40 * q^38 + 40 * q^40 - 114 * q^43 - 20 * q^44 + 28 * q^46 - 46 * q^49 - 46 * q^50 + 100 * q^52 - 78 * q^53 + 252 * q^55 + 168 * q^56 - 176 * q^58 - 206 * q^59 + 30 * q^61 + 144 * q^62 + 64 * q^64 - 12 * q^65 - 226 * q^67 - 112 * q^68 - 16 * q^70 + 260 * q^71 + 92 * q^74 - 188 * q^76 + 212 * q^77 - 232 * q^80 + 304 * q^82 - 318 * q^83 - 212 * q^85 - 268 * q^86 - 8 * q^88 + 188 * q^91 + 168 * q^92 + 48 * q^94 - 4 * q^97 - 10 * q^98

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