LMFDB - Embedded newform 441.3.m.d.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(19,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("441.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.m (of order $6$, 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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.325
Dual form			441.3.m.d.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-6.00000 + 3.46410i) q^{5} +7.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-6.00000 + 3.46410i) q^{5} +7.00000 q^{8} +(-6.00000 - 3.46410i) q^{10} +(5.00000 - 8.66025i) q^{11} -6.92820i q^{13} +(-2.50000 - 4.33013i) q^{16} +(18.0000 - 10.3923i) q^{19} +20.7846i q^{20} +10.0000 q^{22} +(-7.00000 - 12.1244i) q^{23} +(11.5000 - 19.9186i) q^{25} +(6.00000 - 3.46410i) q^{26} +38.0000 q^{29} +(24.0000 + 13.8564i) q^{31} +(16.5000 - 28.5788i) q^{32} +(-13.0000 - 22.5167i) q^{37} +(18.0000 + 10.3923i) q^{38} +(-42.0000 + 24.2487i) q^{40} -69.2820i q^{41} +26.0000 q^{43} +(-15.0000 - 25.9808i) q^{44} +(7.00000 - 12.1244i) q^{46} +(24.0000 - 13.8564i) q^{47} +23.0000 q^{50} +(-18.0000 - 10.3923i) q^{52} +(5.00000 - 8.66025i) q^{53} +69.2820i q^{55} +(19.0000 + 32.9090i) q^{58} +(-66.0000 - 38.1051i) q^{59} +(-30.0000 + 17.3205i) q^{61} +27.7128i q^{62} +13.0000 q^{64} +(24.0000 + 41.5692i) q^{65} +(-37.0000 + 64.0859i) q^{67} +62.0000 q^{71} +(-36.0000 - 20.7846i) q^{73} +(13.0000 - 22.5167i) q^{74} -62.3538i q^{76} +(23.0000 + 39.8372i) q^{79} +(30.0000 + 17.3205i) q^{80} +(60.0000 - 34.6410i) q^{82} +90.0666i q^{83} +(13.0000 + 22.5167i) q^{86} +(35.0000 - 60.6218i) q^{88} +(-36.0000 + 20.7846i) q^{89} -42.0000 q^{92} +(24.0000 + 13.8564i) q^{94} +(-72.0000 + 124.708i) q^{95} -55.4256i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{4} - 12 q^{5} + 14 q^{8}+O(q^{10}) $ 2 * q + q^2 + 3 * q^4 - 12 * q^5 + 14 * q^8	$ 2 q + q^{2} + 3 q^{4} - 12 q^{5} + 14 q^{8} - 12 q^{10} + 10 q^{11} - 5 q^{16} + 36 q^{19} + 20 q^{22} - 14 q^{23} + 23 q^{25} + 12 q^{26} + 76 q^{29} + 48 q^{31} + 33 q^{32} - 26 q^{37} + 36 q^{38} - 84 q^{40} + 52 q^{43} - 30 q^{44} + 14 q^{46} + 48 q^{47} + 46 q^{50} - 36 q^{52} + 10 q^{53} + 38 q^{58} - 132 q^{59} - 60 q^{61} + 26 q^{64} + 48 q^{65} - 74 q^{67} + 124 q^{71} - 72 q^{73} + 26 q^{74} + 46 q^{79} + 60 q^{80} + 120 q^{82} + 26 q^{86} + 70 q^{88} - 72 q^{89} - 84 q^{92} + 48 q^{94} - 144 q^{95}+O(q^{100}) $ 2 * q + q^2 + 3 * q^4 - 12 * q^5 + 14 * q^8 - 12 * q^10 + 10 * q^11 - 5 * q^16 + 36 * q^19 + 20 * q^22 - 14 * q^23 + 23 * q^25 + 12 * q^26 + 76 * q^29 + 48 * q^31 + 33 * q^32 - 26 * q^37 + 36 * q^38 - 84 * q^40 + 52 * q^43 - 30 * q^44 + 14 * q^46 + 48 * q^47 + 46 * q^50 - 36 * q^52 + 10 * q^53 + 38 * q^58 - 132 * q^59 - 60 * q^61 + 26 * q^64 + 48 * q^65 - 74 * q^67 + 124 * q^71 - 72 * q^73 + 26 * q^74 + 46 * q^79 + 60 * q^80 + 120 * q^82 + 26 * q^86 + 70 * q^88 - 72 * q^89 - 84 * q^92 + 48 * q^94 - 144 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.250000	+	0.433013i	0.963525	−	0.267617i	$-0.0862360\pi$
$2$	0.500000	+	0.866025i	0.250000	+	0.433013i	−0.713525	+	0.700629i	$0.752903\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	−	2.59808i	0.375000	−	0.649519i
$5$	−6.00000	+	3.46410i	−1.20000	+	0.692820i	−0.960555	−	0.278090i	$-0.910299\pi$
$5$	−6.00000	+	3.46410i	−1.20000	+	0.692820i	−0.239445	+	0.970910i	$0.576965\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	7.00000			0.875000
$9$		0			0
$10$	−6.00000	−	3.46410i	−0.600000	−	0.346410i
$11$	5.00000	−	8.66025i	0.454545	−	0.787296i	−0.544116	−	0.839010i	$-0.683135\pi$
$11$	5.00000	−	8.66025i	0.454545	−	0.787296i	0.998662	+	0.0517139i	$0.0164684\pi$
$12$		0			0
$13$		−	6.92820i		−	0.532939i	−0.963843	−	0.266469i	$-0.914143\pi$
$13$		−	6.92820i		−	0.532939i	0.963843	−	0.266469i	$-0.0858571\pi$
$14$		0			0
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	18.0000	−	10.3923i	0.947368	−	0.546963i	0.0551060	−	0.998481i	$-0.482450\pi$
$19$	18.0000	−	10.3923i	0.947368	−	0.546963i	0.892262	+	0.451517i	$0.149117\pi$
$20$			20.7846i			1.03923i
$21$		0			0
$22$	10.0000			0.454545
$23$	−7.00000	−	12.1244i	−0.304348	−	0.527146i	0.672768	−	0.739853i	$-0.265105\pi$
$23$	−7.00000	−	12.1244i	−0.304348	−	0.527146i	−0.977116	+	0.212708i	$0.931772\pi$
$24$		0			0
$25$	11.5000	−	19.9186i	0.460000	−	0.796743i
$26$	6.00000	−	3.46410i	0.230769	−	0.133235i
$27$		0			0
$28$		0			0
$29$	38.0000			1.31034			0.655172	−	0.755479i	$-0.272596\pi$
$29$	38.0000			1.31034			0.655172	+	0.755479i	$0.272596\pi$
$30$		0			0
$31$	24.0000	+	13.8564i	0.774194	+	0.446981i	0.834369	−	0.551207i	$-0.185833\pi$
$31$	24.0000	+	13.8564i	0.774194	+	0.446981i	−0.0601750	+	0.998188i	$0.519166\pi$
$32$	16.5000	−	28.5788i	0.515625	−	0.893089i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−13.0000	−	22.5167i	−0.351351	−	0.608558i	0.635135	−	0.772401i	$-0.280944\pi$
$37$	−13.0000	−	22.5167i	−0.351351	−	0.608558i	−0.986486	+	0.163843i	$0.947611\pi$
$38$	18.0000	+	10.3923i	0.473684	+	0.273482i
$39$		0			0
$40$	−42.0000	+	24.2487i	−1.05000	+	0.606218i
$41$		−	69.2820i		−	1.68981i	−0.534920	−	0.844903i	$-0.679658\pi$
$41$		−	69.2820i		−	1.68981i	0.534920	−	0.844903i	$-0.320342\pi$
$42$		0			0
$43$	26.0000			0.604651			0.302326	−	0.953205i	$-0.402237\pi$
$43$	26.0000			0.604651			0.302326	+	0.953205i	$0.402237\pi$
$44$	−15.0000	−	25.9808i	−0.340909	−	0.590472i
$45$		0			0
$46$	7.00000	−	12.1244i	0.152174	−	0.263573i
$47$	24.0000	−	13.8564i	0.510638	−	0.294817i	−0.222458	−	0.974942i	$-0.571408\pi$
$47$	24.0000	−	13.8564i	0.510638	−	0.294817i	0.733096	+	0.680125i	$0.238075\pi$
$48$		0			0
$49$		0			0
$50$	23.0000			0.460000
$51$		0			0
$52$	−18.0000	−	10.3923i	−0.346154	−	0.199852i
$53$	5.00000	−	8.66025i	0.0943396	−	0.163401i	−0.814993	−	0.579471i	$-0.803259\pi$
$53$	5.00000	−	8.66025i	0.0943396	−	0.163401i	0.909333	+	0.416070i	$0.136593\pi$
$54$		0			0
$55$			69.2820i			1.25967i
$56$		0			0
$57$		0			0
$58$	19.0000	+	32.9090i	0.327586	+	0.567396i
$59$	−66.0000	−	38.1051i	−1.11864	−	0.645849i	−0.177590	−	0.984105i	$-0.556830\pi$
$59$	−66.0000	−	38.1051i	−1.11864	−	0.645849i	−0.941054	+	0.338255i	$0.890163\pi$
$60$		0			0
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	−0.725322	−	0.688409i	$-0.758309\pi$
$61$	−30.0000	+	17.3205i	−0.491803	+	0.283943i	0.233519	+	0.972352i	$0.424976\pi$
$62$			27.7128i			0.446981i
$63$		0			0
$64$	13.0000			0.203125
$65$	24.0000	+	41.5692i	0.369231	+	0.639526i
$66$		0			0
$67$	−37.0000	+	64.0859i	−0.552239	+	0.956506i	0.445874	+	0.895096i	$0.352893\pi$
$67$	−37.0000	+	64.0859i	−0.552239	+	0.956506i	−0.998113	+	0.0614098i	$0.980440\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	62.0000			0.873239			0.436620	−	0.899646i	$-0.356176\pi$
$71$	62.0000			0.873239			0.436620	+	0.899646i	$0.356176\pi$
$72$		0			0
$73$	−36.0000	−	20.7846i	−0.493151	−	0.284721i	0.232730	−	0.972541i	$-0.425234\pi$
$73$	−36.0000	−	20.7846i	−0.493151	−	0.284721i	−0.725881	+	0.687821i	$0.758568\pi$
$74$	13.0000	−	22.5167i	0.175676	−	0.304279i
$75$		0			0
$76$		−	62.3538i		−	0.820445i
$77$		0			0
$78$		0			0
$79$	23.0000	+	39.8372i	0.291139	+	0.504268i	0.974079	−	0.226206i	$-0.0726324\pi$
$79$	23.0000	+	39.8372i	0.291139	+	0.504268i	−0.682940	+	0.730474i	$0.739299\pi$
$80$	30.0000	+	17.3205i	0.375000	+	0.216506i
$81$		0			0
$82$	60.0000	−	34.6410i	0.731707	−	0.422451i
$83$			90.0666i			1.08514i	0.840011	+	0.542570i	$0.182549\pi$
$83$			90.0666i			1.08514i	−0.840011	+	0.542570i	$0.817451\pi$
$84$		0			0
$85$		0			0
$86$	13.0000	+	22.5167i	0.151163	+	0.261822i
$87$		0			0
$88$	35.0000	−	60.6218i	0.397727	−	0.688884i
$89$	−36.0000	+	20.7846i	−0.404494	+	0.233535i	−0.688421	−	0.725311i	$-0.741696\pi$
$89$	−36.0000	+	20.7846i	−0.404494	+	0.233535i	0.283927	+	0.958846i	$0.408363\pi$
$90$		0			0
$91$		0			0
$92$	−42.0000			−0.456522
$93$		0			0
$94$	24.0000	+	13.8564i	0.255319	+	0.147409i
$95$	−72.0000	+	124.708i	−0.757895	+	1.31271i
$96$		0			0
$97$		−	55.4256i		−	0.571398i	−0.958319	−	0.285699i	$-0.907774\pi$
$97$		−	55.4256i		−	0.571398i	0.958319	−	0.285699i	$-0.0922258\pi$
$98$		0			0
$99$		0			0
$100$	−34.5000	−	59.7558i	−0.345000	−	0.597558i
$101$	102.000	+	58.8897i	1.00990	+	0.583067i	0.911163	−	0.412047i	$-0.135186\pi$
$101$	102.000	+	58.8897i	1.00990	+	0.583067i	0.0987383	+	0.995113i	$0.468519\pi$
$102$		0			0
$103$	84.0000	−	48.4974i	0.815534	−	0.470849i	−0.0333400	−	0.999444i	$-0.510614\pi$
$103$	84.0000	−	48.4974i	0.815534	−	0.470849i	0.848874	+	0.528595i	$0.177281\pi$
$104$		−	48.4974i		−	0.466321i
$105$		0			0
$106$	10.0000			0.0943396
$107$	5.00000	+	8.66025i	0.0467290	+	0.0809370i	0.888444	−	0.458985i	$-0.151787\pi$
$107$	5.00000	+	8.66025i	0.0467290	+	0.0809370i	−0.841715	+	0.539922i	$0.818454\pi$
$108$		0			0
$109$	−37.0000	+	64.0859i	−0.339450	+	0.587944i	−0.984329	−	0.176340i	$-0.943574\pi$
$109$	−37.0000	+	64.0859i	−0.339450	+	0.587944i	0.644880	+	0.764284i	$0.276907\pi$
$110$	−60.0000	+	34.6410i	−0.545455	+	0.314918i
$111$		0			0
$112$		0			0
$113$	−178.000			−1.57522			−0.787611	−	0.616173i	$-0.788682\pi$
$113$	−178.000			−1.57522			−0.787611	+	0.616173i	$0.788682\pi$
$114$		0			0
$115$	84.0000	+	48.4974i	0.730435	+	0.421717i
$116$	57.0000	−	98.7269i	0.491379	−	0.851094i
$117$		0			0
$118$		−	76.2102i		−	0.645849i
$119$		0			0
$120$		0			0
$121$	10.5000	+	18.1865i	0.0867769	+	0.150302i
$122$	−30.0000	−	17.3205i	−0.245902	−	0.141971i
$123$		0			0
$124$	72.0000	−	41.5692i	0.580645	−	0.335236i
$125$		−	13.8564i		−	0.110851i
$126$		0			0
$127$	−190.000			−1.49606			−0.748031	−	0.663663i	$-0.769001\pi$
$127$	−190.000			−1.49606			−0.748031	+	0.663663i	$0.769001\pi$
$128$	−59.5000	−	103.057i	−0.464844	−	0.805133i
$129$		0			0
$130$	−24.0000	+	41.5692i	−0.184615	+	0.319763i
$131$	−42.0000	+	24.2487i	−0.320611	+	0.185105i	−0.651665	−	0.758507i	$-0.725929\pi$
$131$	−42.0000	+	24.2487i	−0.320611	+	0.185105i	0.331054	+	0.943612i	$0.392596\pi$
$132$		0			0
$133$		0			0
$134$	−74.0000			−0.552239
$135$		0			0
$136$		0			0
$137$	−103.000	+	178.401i	−0.751825	+	1.30220i	0.195113	+	0.980781i	$0.437493\pi$
$137$	−103.000	+	178.401i	−0.751825	+	1.30220i	−0.946937	+	0.321418i	$0.895841\pi$
$138$		0			0
$139$			117.779i			0.847334i	0.905818	+	0.423667i	$0.139257\pi$
$139$			117.779i			0.847334i	−0.905818	+	0.423667i	$0.860743\pi$
$140$		0			0
$141$		0			0
$142$	31.0000	+	53.6936i	0.218310	+	0.378124i
$143$	−60.0000	−	34.6410i	−0.419580	−	0.242245i
$144$		0			0
$145$	−228.000	+	131.636i	−1.57241	+	0.907834i
$146$		−	41.5692i		−	0.284721i
$147$		0			0
$148$	−78.0000			−0.527027
$149$	53.0000	+	91.7987i	0.355705	+	0.616099i	0.987238	−	0.159250i	$-0.0509076\pi$
$149$	53.0000	+	91.7987i	0.355705	+	0.616099i	−0.631534	+	0.775349i	$0.717574\pi$
$150$		0			0
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	−0.779761	−	0.626077i	$-0.784660\pi$
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	0.932079	+	0.362255i	$0.117993\pi$
$152$	126.000	−	72.7461i	0.828947	−	0.478593i
$153$		0			0
$154$		0			0
$155$	−192.000			−1.23871
$156$		0			0
$157$	−210.000	−	121.244i	−1.33758	−	0.772252i	−0.351132	−	0.936326i	$-0.614203\pi$
$157$	−210.000	−	121.244i	−1.33758	−	0.772252i	−0.986448	+	0.164074i	$0.947536\pi$
$158$	−23.0000	+	39.8372i	−0.145570	+	0.252134i
$159$		0			0
$160$			228.631i			1.42894i
$161$		0			0
$162$		0			0
$163$	−85.0000	−	147.224i	−0.521472	−	0.903217i	−0.999688	−	0.0249743i	$-0.992050\pi$
$163$	−85.0000	−	147.224i	−0.521472	−	0.903217i	0.478216	−	0.878242i	$-0.341284\pi$
$164$	−180.000	−	103.923i	−1.09756	−	0.633677i
$165$		0			0
$166$	−78.0000	+	45.0333i	−0.469880	+	0.271285i
$167$			96.9948i			0.580807i	0.956904	+	0.290404i	$0.0937896\pi$
$167$			96.9948i			0.580807i	−0.956904	+	0.290404i	$0.906210\pi$
$168$		0			0
$169$	121.000			0.715976
$170$		0			0
$171$		0			0
$172$	39.0000	−	67.5500i	0.226744	−	0.392732i
$173$	150.000	−	86.6025i	0.867052	−	0.500593i	0.000684548	−	1.00000i	$-0.499782\pi$
$173$	150.000	−	86.6025i	0.867052	−	0.500593i	0.866367	+	0.499407i	$0.166449\pi$
$174$		0			0
$175$		0			0
$176$	−50.0000			−0.284091
$177$		0			0
$178$	−36.0000	−	20.7846i	−0.202247	−	0.116767i
$179$	−19.0000	+	32.9090i	−0.106145	+	0.183849i	−0.914206	−	0.405251i	$-0.867184\pi$
$179$	−19.0000	+	32.9090i	−0.106145	+	0.183849i	0.808060	+	0.589100i	$0.200518\pi$
$180$		0			0
$181$		−	187.061i		−	1.03349i	−0.856140	−	0.516744i	$-0.827144\pi$
$181$		−	187.061i		−	1.03349i	0.856140	−	0.516744i	$-0.172856\pi$
$182$		0			0
$183$		0			0
$184$	−49.0000	−	84.8705i	−0.266304	−	0.461253i
$185$	156.000	+	90.0666i	0.843243	+	0.486847i
$186$		0			0
$187$		0			0
$188$		−	83.1384i		−	0.442226i
$189$		0			0
$190$	−144.000			−0.757895
$191$	41.0000	+	71.0141i	0.214660	+	0.371801i	0.953167	−	0.302444i	$-0.0978024\pi$
$191$	41.0000	+	71.0141i	0.214660	+	0.371801i	−0.738508	+	0.674245i	$0.764469\pi$
$192$		0			0
$193$	−25.0000	+	43.3013i	−0.129534	+	0.224359i	−0.923496	−	0.383608i	$-0.874681\pi$
$193$	−25.0000	+	43.3013i	−0.129534	+	0.224359i	0.793962	+	0.607967i	$0.208015\pi$
$194$	48.0000	−	27.7128i	0.247423	−	0.142850i
$195$		0			0
$196$		0			0
$197$	278.000			1.41117			0.705584	−	0.708627i	$-0.250685\pi$
$197$	278.000			1.41117			0.705584	+	0.708627i	$0.250685\pi$
$198$		0			0
$199$	252.000	+	145.492i	1.26633	+	0.731117i	0.974292	−	0.225289i	$-0.0723327\pi$
$199$	252.000	+	145.492i	1.26633	+	0.731117i	0.292040	+	0.956406i	$0.405666\pi$
$200$	80.5000	−	139.430i	0.402500	−	0.697150i
$201$		0			0
$202$			117.779i			0.583067i
$203$		0			0
$204$		0			0
$205$	240.000	+	415.692i	1.17073	+	2.02777i
$206$	84.0000	+	48.4974i	0.407767	+	0.235424i
$207$		0			0
$208$	−30.0000	+	17.3205i	−0.144231	+	0.0832717i
$209$		−	207.846i		−	0.994479i
$210$		0			0
$211$	74.0000			0.350711			0.175355	−	0.984505i	$-0.443893\pi$
$211$	74.0000			0.350711			0.175355	+	0.984505i	$0.443893\pi$
$212$	−15.0000	−	25.9808i	−0.0707547	−	0.122551i
$213$		0			0
$214$	−5.00000	+	8.66025i	−0.0233645	+	0.0404685i
$215$	−156.000	+	90.0666i	−0.725581	+	0.418915i
$216$		0			0
$217$		0			0
$218$	−74.0000			−0.339450
$219$		0			0
$220$	180.000	+	103.923i	0.818182	+	0.472377i
$221$		0			0
$222$		0			0
$223$		−	304.841i		−	1.36700i	−0.729951	−	0.683500i	$-0.760457\pi$
$223$		−	304.841i		−	1.36700i	0.729951	−	0.683500i	$-0.239543\pi$
$224$		0			0
$225$		0			0
$226$	−89.0000	−	154.153i	−0.393805	−	0.682091i
$227$	−6.00000	−	3.46410i	−0.0264317	−	0.0152604i	0.486726	−	0.873555i	$-0.338191\pi$
$227$	−6.00000	−	3.46410i	−0.0264317	−	0.0152604i	−0.513158	+	0.858294i	$0.671524\pi$
$228$		0			0
$229$	246.000	−	142.028i	1.07424	−	0.620210i	0.144900	−	0.989446i	$-0.453714\pi$
$229$	246.000	−	142.028i	1.07424	−	0.620210i	0.929336	+	0.369236i	$0.120381\pi$
$230$			96.9948i			0.421717i
$231$		0			0
$232$	266.000			1.14655
$233$	89.0000	+	154.153i	0.381974	+	0.661599i	0.991344	−	0.131287i	$-0.0419110\pi$
$233$	89.0000	+	154.153i	0.381974	+	0.661599i	−0.609370	+	0.792886i	$0.708578\pi$
$234$		0			0
$235$	−96.0000	+	166.277i	−0.408511	+	0.707561i
$236$	−198.000	+	114.315i	−0.838983	+	0.484387i
$237$		0			0
$238$		0			0
$239$	−34.0000			−0.142259			−0.0711297	−	0.997467i	$-0.522660\pi$
$239$	−34.0000			−0.142259			−0.0711297	+	0.997467i	$0.522660\pi$
$240$		0			0
$241$	−168.000	−	96.9948i	−0.697095	−	0.402468i	0.109169	−	0.994023i	$-0.465181\pi$
$241$	−168.000	−	96.9948i	−0.697095	−	0.402468i	−0.806265	+	0.591555i	$0.798514\pi$
$242$	−10.5000	+	18.1865i	−0.0433884	+	0.0751510i
$243$		0			0
$244$			103.923i			0.425914i
$245$		0			0
$246$		0			0
$247$	−72.0000	−	124.708i	−0.291498	−	0.504889i
$248$	168.000	+	96.9948i	0.677419	+	0.391108i
$249$		0			0
$250$	12.0000	−	6.92820i	0.0480000	−	0.0277128i
$251$			187.061i			0.745265i	0.927979	+	0.372632i	$0.121545\pi$
$251$			187.061i			0.745265i	−0.927979	+	0.372632i	$0.878455\pi$
$252$		0			0
$253$	−140.000			−0.553360
$254$	−95.0000	−	164.545i	−0.374016	−	0.647814i
$255$		0			0
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	120.000	−	69.2820i	0.466926	−	0.269580i	−0.248026	−	0.968753i	$-0.579782\pi$
$257$	120.000	−	69.2820i	0.466926	−	0.269580i	0.714952	+	0.699173i	$0.246449\pi$
$258$		0			0
$259$		0			0
$260$	144.000			0.553846
$261$		0			0
$262$	−42.0000	−	24.2487i	−0.160305	−	0.0925523i
$263$	−31.0000	+	53.6936i	−0.117871	+	0.204158i	−0.918924	−	0.394435i	$-0.870940\pi$
$263$	−31.0000	+	53.6936i	−0.117871	+	0.204158i	0.801053	+	0.598594i	$0.204274\pi$
$264$		0			0
$265$			69.2820i			0.261442i
$266$		0			0
$267$		0			0
$268$	111.000	+	192.258i	0.414179	+	0.717379i
$269$	−198.000	−	114.315i	−0.736059	−	0.424964i	0.0845754	−	0.996417i	$-0.473047\pi$
$269$	−198.000	−	114.315i	−0.736059	−	0.424964i	−0.820635	+	0.571453i	$0.806380\pi$
$270$		0			0
$271$	288.000	−	166.277i	1.06273	−	0.613568i	0.136544	−	0.990634i	$-0.456400\pi$
$271$	288.000	−	166.277i	1.06273	−	0.613568i	0.926186	+	0.377066i	$0.123067\pi$
$272$		0			0
$273$		0			0
$274$	−206.000			−0.751825
$275$	−115.000	−	199.186i	−0.418182	−	0.724312i
$276$		0			0
$277$	−13.0000	+	22.5167i	−0.0469314	+	0.0812876i	−0.888537	−	0.458805i	$-0.848278\pi$
$277$	−13.0000	+	22.5167i	−0.0469314	+	0.0812876i	0.841605	+	0.540093i	$0.181611\pi$
$278$	−102.000	+	58.8897i	−0.366906	+	0.211834i
$279$		0			0
$280$		0			0
$281$	494.000			1.75801			0.879004	−	0.476815i	$-0.158209\pi$
$281$	494.000			1.75801			0.879004	+	0.476815i	$0.158209\pi$
$282$		0			0
$283$	−174.000	−	100.459i	−0.614841	−	0.354979i	0.160017	−	0.987114i	$-0.448845\pi$
$283$	−174.000	−	100.459i	−0.614841	−	0.354979i	−0.774858	+	0.632136i	$0.782179\pi$
$284$	93.0000	−	161.081i	0.327465	−	0.567186i
$285$		0			0
$286$		−	69.2820i		−	0.242245i
$287$		0			0
$288$		0			0
$289$	−144.500	−	250.281i	−0.500000	−	0.866025i
$290$	−228.000	−	131.636i	−0.786207	−	0.453917i
$291$		0			0
$292$	−108.000	+	62.3538i	−0.369863	+	0.213541i
$293$			491.902i			1.67885i	0.543477	+	0.839424i	$0.317107\pi$
$293$			491.902i			1.67885i	−0.543477	+	0.839424i	$0.682893\pi$
$294$		0			0
$295$	528.000			1.78983
$296$	−91.0000	−	157.617i	−0.307432	−	0.532489i
$297$		0			0
$298$	−53.0000	+	91.7987i	−0.177852	+	0.308049i
$299$	−84.0000	+	48.4974i	−0.280936	+	0.162199i
$300$		0			0
$301$		0			0
$302$	46.0000			0.152318
$303$		0			0
$304$	−90.0000	−	51.9615i	−0.296053	−	0.170926i
$305$	120.000	−	207.846i	0.393443	−	0.681463i
$306$		0			0
$307$			20.7846i			0.0677023i	0.999427	+	0.0338512i	$0.0107772\pi$
$307$			20.7846i			0.0677023i	−0.999427	+	0.0338512i	$0.989223\pi$
$308$		0			0
$309$		0			0
$310$	−96.0000	−	166.277i	−0.309677	−	0.536377i
$311$	−12.0000	−	6.92820i	−0.0385852	−	0.0222772i	0.480583	−	0.876949i	$-0.340425\pi$
$311$	−12.0000	−	6.92820i	−0.0385852	−	0.0222772i	−0.519169	+	0.854672i	$0.673758\pi$
$312$		0			0
$313$	−228.000	+	131.636i	−0.728435	+	0.420562i	−0.817849	−	0.575433i	$-0.804834\pi$
$313$	−228.000	+	131.636i	−0.728435	+	0.420562i	0.0894147	+	0.995994i	$0.471500\pi$
$314$		−	242.487i		−	0.772252i
$315$		0			0
$316$	138.000			0.436709
$317$	125.000	+	216.506i	0.394322	+	0.682985i	0.993014	−	0.117994i	$-0.0376462\pi$
$317$	125.000	+	216.506i	0.394322	+	0.682985i	−0.598693	+	0.800979i	$0.704313\pi$
$318$		0			0
$319$	190.000	−	329.090i	0.595611	−	1.03163i
$320$	−78.0000	+	45.0333i	−0.243750	+	0.140729i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−138.000	−	79.6743i	−0.424615	−	0.245152i
$326$	85.0000	−	147.224i	0.260736	−	0.451608i
$327$		0			0
$328$		−	484.974i		−	1.47858i
$329$		0			0
$330$		0			0
$331$	323.000	+	559.452i	0.975831	+	1.69019i	0.677166	+	0.735831i	$0.263208\pi$
$331$	323.000	+	559.452i	0.975831	+	1.69019i	0.298665	+	0.954358i	$0.403459\pi$
$332$	234.000	+	135.100i	0.704819	+	0.406928i
$333$		0			0
$334$	−84.0000	+	48.4974i	−0.251497	+	0.145202i
$335$		−	512.687i		−	1.53041i
$336$		0			0
$337$	146.000			0.433234			0.216617	−	0.976257i	$-0.430498\pi$
$337$	146.000			0.433234			0.216617	+	0.976257i	$0.430498\pi$
$338$	60.5000	+	104.789i	0.178994	+	0.310027i
$339$		0			0
$340$		0			0
$341$	240.000	−	138.564i	0.703812	−	0.406346i
$342$		0			0
$343$		0			0
$344$	182.000			0.529070
$345$		0			0
$346$	150.000	+	86.6025i	0.433526	+	0.250296i
$347$	53.0000	−	91.7987i	0.152738	−	0.264550i	−0.779495	−	0.626408i	$-0.784524\pi$
$347$	53.0000	−	91.7987i	0.152738	−	0.264550i	0.932233	+	0.361859i	$0.117858\pi$
$348$		0			0
$349$			630.466i			1.80649i	0.429121	+	0.903247i	$0.358823\pi$
$349$			630.466i			1.80649i	−0.429121	+	0.903247i	$0.641177\pi$
$350$		0			0
$351$		0			0
$352$	−165.000	−	285.788i	−0.468750	−	0.811899i
$353$	264.000	+	152.420i	0.747875	+	0.431786i	0.824926	−	0.565241i	$-0.191217\pi$
$353$	264.000	+	152.420i	0.747875	+	0.431786i	−0.0770504	+	0.997027i	$0.524550\pi$
$354$		0			0
$355$	−372.000	+	214.774i	−1.04789	+	0.604998i
$356$			124.708i			0.350302i
$357$		0			0
$358$	−38.0000			−0.106145
$359$	−247.000	−	427.817i	−0.688022	−	1.19169i	−0.972477	−	0.233000i	$-0.925146\pi$
$359$	−247.000	−	427.817i	−0.688022	−	1.19169i	0.284454	−	0.958690i	$-0.408188\pi$
$360$		0			0
$361$	35.5000	−	61.4878i	0.0983380	−	0.170326i
$362$	162.000	−	93.5307i	0.447514	−	0.258372i
$363$		0			0
$364$		0			0
$365$	288.000			0.789041
$366$		0			0
$367$	480.000	+	277.128i	1.30790	+	0.755118i	0.981746	−	0.190198i	$-0.0609131\pi$
$367$	480.000	+	277.128i	1.30790	+	0.755118i	0.326156	+	0.945316i	$0.394246\pi$
$368$	−35.0000	+	60.6218i	−0.0951087	+	0.164733i
$369$		0			0
$370$			180.133i			0.486847i
$371$		0			0
$372$		0			0
$373$	−109.000	−	188.794i	−0.292225	−	0.506149i	0.682110	−	0.731249i	$-0.261062\pi$
$373$	−109.000	−	188.794i	−0.292225	−	0.506149i	−0.974336	+	0.225100i	$0.927729\pi$
$374$		0			0
$375$		0			0
$376$	168.000	−	96.9948i	0.446809	−	0.257965i
$377$		−	263.272i		−	0.698333i
$378$		0			0
$379$	−550.000			−1.45119			−0.725594	−	0.688123i	$-0.758435\pi$
$379$	−550.000			−1.45119			−0.725594	+	0.688123i	$0.758435\pi$
$380$	216.000	+	374.123i	0.568421	+	0.984534i
$381$		0			0
$382$	−41.0000	+	71.0141i	−0.107330	+	0.185901i
$383$	48.0000	−	27.7128i	0.125326	−	0.0723572i	−0.436026	−	0.899934i	$-0.643615\pi$
$383$	48.0000	−	27.7128i	0.125326	−	0.0723572i	0.561353	+	0.827577i	$0.310281\pi$
$384$		0			0
$385$		0			0
$386$	−50.0000			−0.129534
$387$		0			0
$388$	−144.000	−	83.1384i	−0.371134	−	0.214274i
$389$	197.000	−	341.214i	0.506427	−	0.877157i	−0.493546	−	0.869720i	$-0.664299\pi$
$389$	197.000	−	341.214i	0.506427	−	0.877157i	0.999972	−	0.00743692i	$-0.00236727\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	139.000	+	240.755i	0.352792	+	0.611053i
$395$	−276.000	−	159.349i	−0.698734	−	0.403414i
$396$		0			0
$397$	90.0000	−	51.9615i	0.226700	−	0.130885i	−0.382349	−	0.924018i	$-0.624885\pi$
$397$	90.0000	−	51.9615i	0.226700	−	0.130885i	0.609049	+	0.793133i	$0.291551\pi$
$398$			290.985i			0.731117i
$399$		0			0
$400$	−115.000			−0.287500
$401$	89.0000	+	154.153i	0.221945	+	0.384420i	0.955399	−	0.295319i	$-0.0954261\pi$
$401$	89.0000	+	154.153i	0.221945	+	0.384420i	−0.733453	+	0.679740i	$0.762093\pi$
$402$		0			0
$403$	96.0000	−	166.277i	0.238213	−	0.412598i
$404$	306.000	−	176.669i	0.757426	−	0.437300i
$405$		0			0
$406$		0			0
$407$	−260.000			−0.638821
$408$		0			0
$409$	564.000	+	325.626i	1.37897	+	0.796150i	0.992036	−	0.125956i	$-0.0401997\pi$
$409$	564.000	+	325.626i	1.37897	+	0.796150i	0.386937	+	0.922106i	$0.373533\pi$
$410$	−240.000	+	415.692i	−0.585366	+	1.01388i
$411$		0			0
$412$		−	290.985i		−	0.706273i
$413$		0			0
$414$		0			0
$415$	−312.000	−	540.400i	−0.751807	−	1.30217i
$416$	−198.000	−	114.315i	−0.475962	−	0.274797i
$417$		0			0
$418$	180.000	−	103.923i	0.430622	−	0.248620i
$419$		−	713.605i		−	1.70311i	−0.524262	−	0.851557i	$-0.675659\pi$
$419$		−	713.605i		−	1.70311i	0.524262	−	0.851557i	$-0.324341\pi$
$420$		0			0
$421$	602.000			1.42993			0.714964	−	0.699161i	$-0.246443\pi$
$421$	602.000			1.42993			0.714964	+	0.699161i	$0.246443\pi$
$422$	37.0000	+	64.0859i	0.0876777	+	0.151862i
$423$		0			0
$424$	35.0000	−	60.6218i	0.0825472	−	0.142976i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	30.0000			0.0700935
$429$		0			0
$430$	−156.000	−	90.0666i	−0.362791	−	0.209457i
$431$	17.0000	−	29.4449i	0.0394432	−	0.0683175i	−0.845630	−	0.533770i	$-0.820775\pi$
$431$	17.0000	−	29.4449i	0.0394432	−	0.0683175i	0.885073	+	0.465452i	$0.154108\pi$
$432$		0			0
$433$			415.692i			0.960028i	0.877261	+	0.480014i	$0.159368\pi$
$433$			415.692i			0.960028i	−0.877261	+	0.480014i	$0.840632\pi$
$434$		0			0
$435$		0			0
$436$	111.000	+	192.258i	0.254587	+	0.440958i
$437$	−252.000	−	145.492i	−0.576659	−	0.332934i
$438$		0			0
$439$	−84.0000	+	48.4974i	−0.191344	+	0.110472i	−0.592612	−	0.805488i	$-0.701903\pi$
$439$	−84.0000	+	48.4974i	−0.191344	+	0.110472i	0.401268	+	0.915961i	$0.368570\pi$
$440$			484.974i			1.10221i
$441$		0			0
$442$		0			0
$443$	−235.000	−	407.032i	−0.530474	−	0.918808i	−0.999368	−	0.0355534i	$-0.988681\pi$
$443$	−235.000	−	407.032i	−0.530474	−	0.918808i	0.468894	−	0.883255i	$-0.344653\pi$
$444$		0			0
$445$	144.000	−	249.415i	0.323596	−	0.560484i
$446$	264.000	−	152.420i	0.591928	−	0.341750i
$447$		0			0
$448$		0			0
$449$	−514.000			−1.14477			−0.572383	−	0.819986i	$-0.693981\pi$
$449$	−514.000			−1.14477			−0.572383	+	0.819986i	$0.693981\pi$
$450$		0			0
$451$	−600.000	−	346.410i	−1.33038	−	0.768093i
$452$	−267.000	+	462.458i	−0.590708	+	1.02314i
$453$		0			0
$454$		−	6.92820i		−	0.0152604i
$455$		0			0
$456$		0			0
$457$	239.000	+	413.960i	0.522976	+	0.905821i	0.999643	+	0.0267367i	$0.00851158\pi$
$457$	239.000	+	413.960i	0.522976	+	0.905821i	−0.476667	+	0.879084i	$0.658155\pi$
$458$	246.000	+	142.028i	0.537118	+	0.310105i
$459$		0			0
$460$	252.000	−	145.492i	0.547826	−	0.316288i
$461$			672.036i			1.45778i	0.684632	+	0.728889i	$0.259963\pi$
$461$			672.036i			1.45778i	−0.684632	+	0.728889i	$0.740037\pi$
$462$		0			0
$463$	−430.000			−0.928726			−0.464363	−	0.885645i	$-0.653717\pi$
$463$	−430.000			−0.928726			−0.464363	+	0.885645i	$0.653717\pi$
$464$	−95.0000	−	164.545i	−0.204741	−	0.354622i
$465$		0			0
$466$	−89.0000	+	154.153i	−0.190987	+	0.330799i
$467$	−738.000	+	426.084i	−1.58030	+	0.912387i	−0.585485	+	0.810683i	$0.699096\pi$
$467$	−738.000	+	426.084i	−1.58030	+	0.912387i	−0.994815	+	0.101703i	$0.967571\pi$
$468$		0			0
$469$		0			0
$470$	−192.000			−0.408511
$471$		0			0
$472$	−462.000	−	266.736i	−0.978814	−	0.565118i
$473$	130.000	−	225.167i	0.274841	−	0.476039i
$474$		0			0
$475$		−	478.046i		−	1.00641i
$476$		0			0
$477$		0			0
$478$	−17.0000	−	29.4449i	−0.0355649	−	0.0616001i
$479$	336.000	+	193.990i	0.701461	+	0.404989i	0.807891	−	0.589331i	$-0.200609\pi$
$479$	336.000	+	193.990i	0.701461	+	0.404989i	−0.106430	+	0.994320i	$0.533942\pi$
$480$		0			0
$481$	−156.000	+	90.0666i	−0.324324	+	0.187249i
$482$		−	193.990i		−	0.402468i
$483$		0			0
$484$	63.0000			0.130165
$485$	192.000	+	332.554i	0.395876	+	0.685678i
$486$		0			0
$487$	−409.000	+	708.409i	−0.839836	+	1.45464i	0.0501959	+	0.998739i	$0.484015\pi$
$487$	−409.000	+	708.409i	−0.839836	+	1.45464i	−0.890032	+	0.455899i	$0.849318\pi$
$488$	−210.000	+	121.244i	−0.430328	+	0.248450i
$489$		0			0
$490$		0			0
$491$	−490.000			−0.997963			−0.498982	−	0.866613i	$-0.666293\pi$
$491$	−490.000			−0.997963			−0.498982	+	0.866613i	$0.666293\pi$
$492$		0			0
$493$		0			0
$494$	72.0000	−	124.708i	0.145749	−	0.252445i
$495$		0			0
$496$		−	138.564i		−	0.279363i
$497$		0			0
$498$		0			0
$499$	−277.000	−	479.778i	−0.555110	−	0.961479i	−0.997895	−	0.0648512i	$-0.979343\pi$
$499$	−277.000	−	479.778i	−0.555110	−	0.961479i	0.442785	−	0.896628i	$-0.353991\pi$
$500$	−36.0000	−	20.7846i	−0.0720000	−	0.0415692i
$501$		0			0
$502$	−162.000	+	93.5307i	−0.322709	+	0.186316i
$503$			290.985i			0.578498i	0.957254	+	0.289249i	$0.0934056\pi$
$503$			290.985i			0.578498i	−0.957254	+	0.289249i	$0.906594\pi$
$504$		0			0
$505$	−816.000			−1.61584
$506$	−70.0000	−	121.244i	−0.138340	−	0.239612i
$507$		0			0
$508$	−285.000	+	493.634i	−0.561024	+	0.971721i
$509$	−834.000	+	481.510i	−1.63851	+	0.945992i	−0.657159	+	0.753752i	$0.728242\pi$
$509$	−834.000	+	481.510i	−1.63851	+	0.945992i	−0.981348	+	0.192240i	$0.938425\pi$
$510$		0			0
$511$		0			0
$512$	−305.000			−0.595703
$513$		0			0
$514$	120.000	+	69.2820i	0.233463	+	0.134790i
$515$	−336.000	+	581.969i	−0.652427	+	1.13004i
$516$		0			0
$517$		−	277.128i		−	0.536031i
$518$		0			0
$519$		0			0
$520$	168.000	+	290.985i	0.323077	+	0.559586i
$521$	108.000	+	62.3538i	0.207294	+	0.119681i	0.600053	−	0.799960i	$-0.295146\pi$
$521$	108.000	+	62.3538i	0.207294	+	0.119681i	−0.392759	+	0.919641i	$0.628479\pi$
$522$		0			0
$523$	54.0000	−	31.1769i	0.103250	−	0.0596117i	−0.447486	−	0.894291i	$-0.647680\pi$
$523$	54.0000	−	31.1769i	0.103250	−	0.0596117i	0.550736	+	0.834679i	$0.314347\pi$
$524$			145.492i			0.277657i
$525$		0			0
$526$	−62.0000			−0.117871
$527$		0			0
$528$		0			0
$529$	166.500	−	288.386i	0.314745	−	0.545154i
$530$	−60.0000	+	34.6410i	−0.113208	+	0.0653604i
$531$		0			0
$532$		0			0
$533$	−480.000			−0.900563
$534$		0			0
$535$	−60.0000	−	34.6410i	−0.112150	−	0.0647496i
$536$	−259.000	+	448.601i	−0.483209	+	0.836942i
$537$		0			0
$538$		−	228.631i		−	0.424964i
$539$		0			0
$540$		0			0
$541$	59.0000	+	102.191i	0.109057	+	0.188893i	0.915389	−	0.402571i	$-0.131883\pi$
$541$	59.0000	+	102.191i	0.109057	+	0.188893i	−0.806331	+	0.591464i	$0.798550\pi$
$542$	288.000	+	166.277i	0.531365	+	0.306784i
$543$		0			0
$544$		0			0
$545$		−	512.687i		−	0.940710i
$546$		0			0
$547$	−406.000			−0.742230			−0.371115	−	0.928587i	$-0.621024\pi$
$547$	−406.000			−0.742230			−0.371115	+	0.928587i	$0.621024\pi$
$548$	309.000	+	535.204i	0.563869	+	0.976649i
$549$		0			0
$550$	115.000	−	199.186i	0.209091	−	0.362156i
$551$	684.000	−	394.908i	1.24138	−	0.716711i
$552$		0			0
$553$		0			0
$554$	−26.0000			−0.0469314
$555$		0			0
$556$	306.000	+	176.669i	0.550360	+	0.317750i
$557$	−499.000	+	864.293i	−0.895871	+	1.55169i	−0.0631475	+	0.998004i	$0.520114\pi$
$557$	−499.000	+	864.293i	−0.895871	+	1.55169i	−0.832723	+	0.553689i	$0.813219\pi$
$558$		0			0
$559$		−	180.133i		−	0.322242i
$560$		0			0
$561$		0			0
$562$	247.000	+	427.817i	0.439502	+	0.761239i
$563$	−318.000	−	183.597i	−0.564831	−	0.326105i	0.190251	−	0.981735i	$-0.439070\pi$
$563$	−318.000	−	183.597i	−0.564831	−	0.326105i	−0.755082	+	0.655630i	$0.772403\pi$
$564$		0			0
$565$	1068.00	−	616.610i	1.89027	−	1.09135i
$566$		−	200.918i		−	0.354979i
$567$		0			0
$568$	434.000			0.764085
$569$	−31.0000	−	53.6936i	−0.0544815	−	0.0943648i	0.837498	−	0.546440i	$-0.184017\pi$
$569$	−31.0000	−	53.6936i	−0.0544815	−	0.0943648i	−0.891980	+	0.452075i	$0.850684\pi$
$570$		0			0
$571$	−205.000	+	355.070i	−0.359019	+	0.621840i	−0.987797	−	0.155745i	$-0.950222\pi$
$571$	−205.000	+	355.070i	−0.359019	+	0.621840i	0.628778	+	0.777585i	$0.283555\pi$
$572$	−180.000	+	103.923i	−0.314685	+	0.181684i
$573$		0			0
$574$		0			0
$575$	−322.000			−0.560000
$576$		0			0
$577$	720.000	+	415.692i	1.24783	+	0.720437i	0.970677	−	0.240388i	$-0.0772746\pi$
$577$	720.000	+	415.692i	1.24783	+	0.720437i	0.277157	+	0.960825i	$0.410608\pi$
$578$	144.500	−	250.281i	0.250000	−	0.433013i
$579$		0			0
$580$			789.815i			1.36175i
$581$		0			0
$582$		0			0
$583$	−50.0000	−	86.6025i	−0.0857633	−	0.148546i
$584$	−252.000	−	145.492i	−0.431507	−	0.249131i
$585$		0			0
$586$	−426.000	+	245.951i	−0.726962	+	0.419712i
$587$			547.328i			0.932416i	0.884675	+	0.466208i	$0.154380\pi$
$587$			547.328i			0.932416i	−0.884675	+	0.466208i	$0.845620\pi$
$588$		0			0
$589$	576.000			0.977929
$590$	264.000	+	457.261i	0.447458	+	0.775019i
$591$		0			0
$592$	−65.0000	+	112.583i	−0.109797	+	0.190174i
$593$	864.000	−	498.831i	1.45700	−	0.841198i	0.458136	−	0.888882i	$-0.348517\pi$
$593$	864.000	−	498.831i	1.45700	−	0.841198i	0.998862	+	0.0476838i	$0.0151840\pi$
$594$		0			0
$595$		0			0
$596$	318.000			0.533557
$597$		0			0
$598$	−84.0000	−	48.4974i	−0.140468	−	0.0810994i
$599$	593.000	−	1027.11i	0.989983	−	1.71470i	0.372722	−	0.927943i	$-0.378424\pi$
$599$	593.000	−	1027.11i	0.989983	−	1.71470i	0.617261	−	0.786758i	$-0.288242\pi$
$600$		0			0
$601$			401.836i			0.668612i	0.942465	+	0.334306i	$0.108502\pi$
$601$			401.836i			0.668612i	−0.942465	+	0.334306i	$0.891498\pi$
$602$		0			0
$603$		0			0
$604$	−69.0000	−	119.512i	−0.114238	−	0.197867i
$605$	−126.000	−	72.7461i	−0.208264	−	0.120242i
$606$		0			0
$607$	120.000	−	69.2820i	0.197694	−	0.114138i	−0.397886	−	0.917435i	$-0.630256\pi$
$607$	120.000	−	69.2820i	0.197694	−	0.114138i	0.595579	+	0.803297i	$0.296923\pi$
$608$		−	685.892i		−	1.12811i
$609$		0			0
$610$	240.000			0.393443
$611$	−96.0000	−	166.277i	−0.157119	−	0.272139i
$612$		0			0
$613$	−13.0000	+	22.5167i	−0.0212072	+	0.0367319i	−0.876434	−	0.481522i	$-0.840084\pi$
$613$	−13.0000	+	22.5167i	−0.0212072	+	0.0367319i	0.855227	+	0.518254i	$0.173418\pi$
$614$	−18.0000	+	10.3923i	−0.0293160	+	0.0169256i
$615$		0			0
$616$		0			0
$617$	734.000			1.18963			0.594814	−	0.803864i	$-0.297226\pi$
$617$	734.000			1.18963			0.594814	+	0.803864i	$0.297226\pi$
$618$		0			0
$619$	−726.000	−	419.156i	−1.17286	−	0.677151i	−0.218508	−	0.975835i	$-0.570119\pi$
$619$	−726.000	−	419.156i	−1.17286	−	0.677151i	−0.954352	+	0.298685i	$0.903452\pi$
$620$	−288.000	+	498.831i	−0.464516	+	0.804566i
$621$		0			0
$622$		−	13.8564i		−	0.0222772i
$623$		0			0
$624$		0			0
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$	−228.000	−	131.636i	−0.364217	−	0.210281i
$627$		0			0
$628$	−630.000	+	363.731i	−1.00318	+	0.579189i
$629$		0			0
$630$		0			0
$631$	−286.000			−0.453249			−0.226624	−	0.973982i	$-0.572769\pi$
$631$	−286.000			−0.453249			−0.226624	+	0.973982i	$0.572769\pi$
$632$	161.000	+	278.860i	0.254747	+	0.441234i
$633$		0			0
$634$	−125.000	+	216.506i	−0.197161	+	0.341493i
$635$	1140.00	−	658.179i	1.79528	−	1.03650i
$636$		0			0
$637$		0			0
$638$	380.000			0.595611
$639$		0			0
$640$	714.000	+	412.228i	1.11563	+	0.644106i
$641$	329.000	−	569.845i	0.513261	−	0.888993i	−0.486621	−	0.873613i	$-0.661771\pi$
$641$	329.000	−	569.845i	0.513261	−	0.888993i	0.999882	−	0.0153802i	$-0.00489587\pi$
$642$		0			0
$643$			325.626i			0.506416i	0.967412	+	0.253208i	$0.0814857\pi$
$643$			325.626i			0.506416i	−0.967412	+	0.253208i	$0.918514\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	396.000	+	228.631i	0.612056	+	0.353370i	0.773770	−	0.633467i	$-0.218369\pi$
$647$	396.000	+	228.631i	0.612056	+	0.353370i	−0.161714	+	0.986838i	$0.551702\pi$
$648$		0			0
$649$	−660.000	+	381.051i	−1.01695	+	0.587136i
$650$		−	159.349i		−	0.245152i
$651$		0			0
$652$	−510.000			−0.782209
$653$	−307.000	−	531.740i	−0.470138	−	0.814303i	0.529279	−	0.848448i	$-0.322462\pi$
$653$	−307.000	−	531.740i	−0.470138	−	0.814303i	−0.999417	+	0.0341452i	$0.989129\pi$
$654$		0			0
$655$	168.000	−	290.985i	0.256489	−	0.444251i
$656$	−300.000	+	173.205i	−0.457317	+	0.264032i
$657$		0			0
$658$		0			0
$659$	−442.000			−0.670713			−0.335357	−	0.942091i	$-0.608857\pi$
$659$	−442.000			−0.670713			−0.335357	+	0.942091i	$0.608857\pi$
$660$		0			0
$661$	−30.0000	−	17.3205i	−0.0453858	−	0.0262035i	0.477135	−	0.878830i	$-0.341675\pi$
$661$	−30.0000	−	17.3205i	−0.0453858	−	0.0262035i	−0.522521	+	0.852626i	$0.675008\pi$
$662$	−323.000	+	559.452i	−0.487915	+	0.845094i
$663$		0			0
$664$			630.466i			0.949498i
$665$		0			0
$666$		0			0
$667$	−266.000	−	460.726i	−0.398801	−	0.690743i
$668$	252.000	+	145.492i	0.377246	+	0.217803i
$669$		0			0
$670$	444.000	−	256.344i	0.662687	−	0.382602i
$671$			346.410i			0.516260i
$672$		0			0
$673$	386.000			0.573551			0.286776	−	0.957998i	$-0.407417\pi$
$673$	386.000			0.573551			0.286776	+	0.957998i	$0.407417\pi$
$674$	73.0000	+	126.440i	0.108309	+	0.187596i
$675$		0			0
$676$	181.500	−	314.367i	0.268491	−	0.465040i
$677$	−678.000	+	391.443i	−1.00148	+	0.578203i	−0.908685	−	0.417482i	$-0.862913\pi$
$677$	−678.000	+	391.443i	−1.00148	+	0.578203i	−0.0927921	+	0.995686i	$0.529579\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	240.000	+	138.564i	0.351906	+	0.203173i
$683$	149.000	−	258.076i	0.218155	−	0.377856i	−0.736089	−	0.676885i	$-0.763329\pi$
$683$	149.000	−	258.076i	0.218155	−	0.377856i	0.954244	+	0.299029i	$0.0966628\pi$
$684$		0			0
$685$		−	1427.21i		−	2.08352i
$686$		0			0
$687$		0			0
$688$	−65.0000	−	112.583i	−0.0944767	−	0.163639i
$689$	−60.0000	−	34.6410i	−0.0870827	−	0.0502772i
$690$		0			0
$691$	−750.000	+	433.013i	−1.08538	+	0.626646i	−0.932344	−	0.361574i	$-0.882240\pi$
$691$	−750.000	+	433.013i	−1.08538	+	0.626646i	−0.153040	+	0.988220i	$0.548906\pi$
$692$		−	519.615i		−	0.750889i
$693$		0			0
$694$	106.000			0.152738
$695$	−408.000	−	706.677i	−0.587050	−	1.01680i
$696$		0			0
$697$		0			0
$698$	−546.000	+	315.233i	−0.782235	+	0.451624i
$699$		0			0
$700$		0			0
$701$	−154.000			−0.219686			−0.109843	−	0.993949i	$-0.535035\pi$
$701$	−154.000			−0.219686			−0.109843	+	0.993949i	$0.535035\pi$
$702$		0			0
$703$	−468.000	−	270.200i	−0.665718	−	0.384353i
$704$	65.0000	−	112.583i	0.0923295	−	0.159919i
$705$		0			0
$706$			304.841i			0.431786i
$707$		0			0
$708$		0			0
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	−0.988023	−	0.154306i	$-0.950686\pi$
$709$	−445.000	−	770.763i	−0.627645	−	1.08711i	0.360379	−	0.932806i	$-0.382648\pi$
$710$	−372.000	−	214.774i	−0.523944	−	0.302499i
$711$		0			0
$712$	−252.000	+	145.492i	−0.353933	+	0.204343i
$713$		−	387.979i		−	0.544151i
$714$		0			0
$715$	480.000			0.671329
$716$	57.0000	+	98.7269i	0.0796089	+	0.137887i
$717$		0			0
$718$	247.000	−	427.817i	0.344011	−	0.595845i
$719$	72.0000	−	41.5692i	0.100139	−	0.0578153i	−0.449094	−	0.893484i	$-0.648253\pi$
$719$	72.0000	−	41.5692i	0.100139	−	0.0578153i	0.549233	+	0.835669i	$0.314920\pi$
$720$		0			0
$721$		0			0
$722$	71.0000			0.0983380
$723$		0			0
$724$	−486.000	−	280.592i	−0.671271	−	0.387558i
$725$	437.000	−	756.906i	0.602759	−	1.04401i
$726$		0			0
$727$			235.559i			0.324015i	0.986790	+	0.162008i	$0.0517969\pi$
$727$			235.559i			0.324015i	−0.986790	+	0.162008i	$0.948203\pi$
$728$		0			0
$729$		0			0
$730$	144.000	+	249.415i	0.197260	+	0.341665i
$731$		0			0
$732$		0			0
$733$	66.0000	−	38.1051i	0.0900409	−	0.0519852i	−0.454303	−	0.890847i	$-0.650112\pi$
$733$	66.0000	−	38.1051i	0.0900409	−	0.0519852i	0.544344	+	0.838862i	$0.316778\pi$
$734$			554.256i			0.755118i
$735$		0			0
$736$	−462.000			−0.627717
$737$	370.000	+	640.859i	0.502035	+	0.869551i
$738$		0			0
$739$	491.000	−	850.437i	0.664411	−	1.15079i	−0.315033	−	0.949081i	$-0.602016\pi$
$739$	491.000	−	850.437i	0.664411	−	1.15079i	0.979445	−	0.201714i	$-0.0646510\pi$
$740$	468.000	−	270.200i	0.632432	−	0.365135i
$741$		0			0
$742$		0			0
$743$	686.000			0.923284			0.461642	−	0.887066i	$-0.347260\pi$
$743$	686.000			0.923284			0.461642	+	0.887066i	$0.347260\pi$
$744$		0			0
$745$	−636.000	−	367.195i	−0.853691	−	0.492879i
$746$	109.000	−	188.794i	0.146113	−	0.253074i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−145.000	−	251.147i	−0.193076	−	0.334417i	0.753192	−	0.657801i	$-0.228513\pi$
$751$	−145.000	−	251.147i	−0.193076	−	0.334417i	−0.946268	+	0.323383i	$0.895180\pi$
$752$	−120.000	−	69.2820i	−0.159574	−	0.0921304i
$753$		0			0
$754$	228.000	−	131.636i	0.302387	−	0.174583i
$755$			318.697i			0.422116i
$756$		0			0
$757$	−358.000			−0.472919			−0.236460	−	0.971641i	$-0.575987\pi$
$757$	−358.000			−0.472919			−0.236460	+	0.971641i	$0.575987\pi$
$758$	−275.000	−	476.314i	−0.362797	−	0.628383i
$759$		0			0
$760$	−504.000	+	872.954i	−0.663158	+	1.14862i
$761$	−564.000	+	325.626i	−0.741130	+	0.427892i	−0.822480	−	0.568794i	$-0.807410\pi$
$761$	−564.000	+	325.626i	−0.741130	+	0.427892i	0.0813500	+	0.996686i	$0.474077\pi$
$762$		0			0
$763$		0			0
$764$	246.000			0.321990
$765$		0			0
$766$	48.0000	+	27.7128i	0.0626632	+	0.0361786i
$767$	−264.000	+	457.261i	−0.344198	+	0.596169i
$768$		0			0
$769$		−	775.959i		−	1.00905i	−0.863397	−	0.504525i	$-0.831668\pi$
$769$		−	775.959i		−	1.00905i	0.863397	−	0.504525i	$-0.168332\pi$
$770$		0			0
$771$		0			0
$772$	75.0000	+	129.904i	0.0971503	+	0.168269i
$773$	198.000	+	114.315i	0.256145	+	0.147885i	0.622575	−	0.782560i	$-0.286087\pi$
$773$	198.000	+	114.315i	0.256145	+	0.147885i	−0.366430	+	0.930446i	$0.619420\pi$
$774$		0			0
$775$	552.000	−	318.697i	0.712258	−	0.411222i
$776$		−	387.979i		−	0.499973i
$777$		0			0
$778$	394.000			0.506427
$779$	−720.000	−	1247.08i	−0.924262	−	1.60087i
$780$		0			0
$781$	310.000	−	536.936i	0.396927	−	0.687498i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1680.00			2.14013
$786$		0			0
$787$	−66.0000	−	38.1051i	−0.0838628	−	0.0484182i	0.457482	−	0.889219i	$-0.348751\pi$
$787$	−66.0000	−	38.1051i	−0.0838628	−	0.0484182i	−0.541345	+	0.840801i	$0.682085\pi$
$788$	417.000	−	722.265i	0.529188	−	0.916580i
$789$		0			0
$790$		−	318.697i		−	0.403414i
$791$		0			0
$792$		0			0
$793$	120.000	+	207.846i	0.151324	+	0.262101i
$794$	90.0000	+	51.9615i	0.113350	+	0.0654427i
$795$		0			0
$796$	756.000	−	436.477i	0.949749	−	0.548338i
$797$			866.025i			1.08661i	0.839537	+	0.543303i	$0.182827\pi$
$797$			866.025i			1.08661i	−0.839537	+	0.543303i	$0.817173\pi$
$798$		0			0
$799$		0			0
$800$	−379.500	−	657.313i	−0.474375	−	0.821642i
$801$		0			0
$802$	−89.0000	+	154.153i	−0.110973	+	0.192210i
$803$	−360.000	+	207.846i	−0.448319	+	0.258837i
$804$		0			0
$805$		0			0
$806$	192.000			0.238213
$807$		0			0
$808$	714.000	+	412.228i	0.883663	+	0.510183i
$809$	401.000	−	694.552i	0.495674	−	0.858532i	−0.504314	−	0.863520i	$-0.668255\pi$
$809$	401.000	−	694.552i	0.495674	−	0.858532i	0.999988	+	0.00498843i	$0.00158787\pi$
$810$		0			0
$811$			893.738i			1.10202i	0.834499	+	0.551010i	$0.185757\pi$
$811$			893.738i			1.10202i	−0.834499	+	0.551010i	$0.814243\pi$
$812$		0			0
$813$		0			0
$814$	−130.000	−	225.167i	−0.159705	−	0.276617i
$815$	1020.00	+	588.897i	1.25153	+	0.722573i
$816$		0			0
$817$	468.000	−	270.200i	0.572827	−	0.330722i
$818$			651.251i			0.796150i
$819$		0			0
$820$	1440.00			1.75610
$821$	725.000	+	1255.74i	0.883069	+	1.52952i	0.847911	+	0.530139i	$0.177860\pi$
$821$	725.000	+	1255.74i	0.883069	+	1.52952i	0.0351589	+	0.999382i	$0.488806\pi$
$822$		0			0
$823$	623.000	−	1079.07i	0.756987	−	1.31114i	−0.187394	−	0.982285i	$-0.560004\pi$
$823$	623.000	−	1079.07i	0.756987	−	1.31114i	0.944381	−	0.328854i	$-0.106663\pi$
$824$	588.000	−	339.482i	0.713592	−	0.411993i
$825$		0			0
$826$		0			0
$827$	−586.000			−0.708585			−0.354293	−	0.935135i	$-0.615278\pi$
$827$	−586.000			−0.708585			−0.354293	+	0.935135i	$0.615278\pi$
$828$		0			0
$829$	702.000	+	405.300i	0.846803	+	0.488902i	0.859571	−	0.511016i	$-0.170731\pi$
$829$	702.000	+	405.300i	0.846803	+	0.488902i	−0.0127676	+	0.999918i	$0.504064\pi$
$830$	312.000	−	540.400i	0.375904	−	0.651084i
$831$		0			0
$832$		−	90.0666i		−	0.108253i
$833$		0			0
$834$		0			0
$835$	−336.000	−	581.969i	−0.402395	−	0.696969i
$836$	−540.000	−	311.769i	−0.645933	−	0.372930i
$837$		0			0
$838$	618.000	−	356.802i	0.737470	−	0.425779i
$839$		−	13.8564i		−	0.0165154i	−0.999966	−	0.00825769i	$-0.997371\pi$
$839$		−	13.8564i		−	0.0165154i	0.999966	−	0.00825769i	$-0.00262853\pi$
$840$		0			0
$841$	603.000			0.717004
$842$	301.000	+	521.347i	0.357482	+	0.619177i
$843$		0			0
$844$	111.000	−	192.258i	0.131517	−	0.227793i
$845$	−726.000	+	419.156i	−0.859172	+	0.496043i
$846$		0			0
$847$		0			0
$848$	−50.0000			−0.0589623
$849$		0			0
$850$		0			0
$851$	−182.000	+	315.233i	−0.213866	+	0.370427i
$852$		0			0
$853$		−	242.487i		−	0.284276i	−0.989847	−	0.142138i	$-0.954602\pi$
$853$		−	242.487i		−	0.284276i	0.989847	−	0.142138i	$-0.0453976\pi$
$854$		0			0
$855$		0			0
$856$	35.0000	+	60.6218i	0.0408879	+	0.0708198i
$857$	−1212.00	−	699.749i	−1.41424	−	0.816509i	−0.418452	−	0.908239i	$-0.637427\pi$
$857$	−1212.00	−	699.749i	−1.41424	−	0.816509i	−0.995784	+	0.0917297i	$0.970760\pi$
$858$		0			0
$859$	−258.000	+	148.956i	−0.300349	+	0.173407i	−0.642600	−	0.766202i	$-0.722144\pi$
$859$	−258.000	+	148.956i	−0.300349	+	0.173407i	0.342251	+	0.939609i	$0.388811\pi$
$860$			540.400i			0.628372i
$861$		0			0
$862$	34.0000			0.0394432
$863$	−535.000	−	926.647i	−0.619930	−	1.07375i	−0.989498	−	0.144547i	$-0.953827\pi$
$863$	−535.000	−	926.647i	−0.619930	−	1.07375i	0.369567	−	0.929204i	$-0.379506\pi$
$864$		0			0
$865$	−600.000	+	1039.23i	−0.693642	+	1.20142i
$866$	−360.000	+	207.846i	−0.415704	+	0.240007i
$867$		0			0
$868$		0			0
$869$	460.000			0.529344
$870$		0			0
$871$	444.000	+	256.344i	0.509759	+	0.294309i
$872$	−259.000	+	448.601i	−0.297018	+	0.514451i
$873$		0			0
$874$		−	290.985i		−	0.332934i
$875$		0			0
$876$		0			0
$877$	251.000	+	434.745i	0.286203	+	0.495718i	0.972900	−	0.231225i	$-0.0742735\pi$
$877$	251.000	+	434.745i	0.286203	+	0.495718i	−0.686697	+	0.726944i	$0.740940\pi$
$878$	−84.0000	−	48.4974i	−0.0956720	−	0.0552362i
$879$		0			0
$880$	300.000	−	173.205i	0.340909	−	0.196824i
$881$		−	997.661i		−	1.13242i	−0.824261	−	0.566210i	$-0.808409\pi$
$881$		−	997.661i		−	1.13242i	0.824261	−	0.566210i	$-0.191591\pi$
$882$		0			0
$883$	−118.000			−0.133635			−0.0668177	−	0.997765i	$-0.521285\pi$
$883$	−118.000			−0.133635			−0.0668177	+	0.997765i	$0.521285\pi$
$884$		0			0
$885$		0			0
$886$	235.000	−	407.032i	0.265237	−	0.459404i
$887$	444.000	−	256.344i	0.500564	−	0.289001i	−0.228383	−	0.973571i	$-0.573344\pi$
$887$	444.000	−	256.344i	0.500564	−	0.289001i	0.728946	+	0.684571i	$0.240010\pi$
$888$		0			0
$889$		0			0
$890$	288.000			0.323596
$891$		0			0
$892$	−792.000	−	457.261i	−0.887892	−	0.512625i
$893$	288.000	−	498.831i	0.322508	−	0.558601i
$894$		0			0
$895$		−	263.272i		−	0.294158i
$896$		0			0
$897$		0			0
$898$	−257.000	−	445.137i	−0.286192	−	0.495698i
$899$	912.000	+	526.543i	1.01446	+	0.585699i
$900$		0			0
$901$		0			0
$902$		−	692.820i		−	0.768093i
$903$		0			0
$904$	−1246.00			−1.37832
$905$	648.000	+	1122.37i	0.716022	+	1.24019i
$906$		0			0
$907$	−733.000	+	1269.59i	−0.808159	+	1.39977i	0.105979	+	0.994368i	$0.466202\pi$
$907$	−733.000	+	1269.59i	−0.808159	+	1.39977i	−0.914138	+	0.405404i	$0.867131\pi$
$908$	−18.0000	+	10.3923i	−0.0198238	+	0.0114453i
$909$		0			0
$910$		0			0
$911$	542.000			0.594951			0.297475	−	0.954730i	$-0.403855\pi$
$911$	542.000			0.594951			0.297475	+	0.954730i	$0.403855\pi$
$912$		0			0
$913$	780.000	+	450.333i	0.854326	+	0.493246i
$914$	−239.000	+	413.960i	−0.261488	+	0.452910i
$915$		0			0
$916$		−	852.169i		−	0.930315i
$917$		0			0
$918$		0			0
$919$	815.000	+	1411.62i	0.886834	+	1.53604i	0.843598	+	0.536976i	$0.180433\pi$
$919$	815.000	+	1411.62i	0.886834	+	1.53604i	0.0432359	+	0.999065i	$0.486233\pi$
$920$	588.000	+	339.482i	0.639130	+	0.369002i
$921$		0			0
$922$	−582.000	+	336.018i	−0.631236	+	0.364445i
$923$		−	429.549i		−	0.465383i
$924$		0			0
$925$	−598.000			−0.646486
$926$	−215.000	−	372.391i	−0.232181	−	0.402150i
$927$		0			0
$928$	627.000	−	1086.00i	0.675647	−	1.17025i
$929$	168.000	−	96.9948i	0.180840	−	0.104408i	−0.406847	−	0.913496i	$-0.633372\pi$
$929$	168.000	−	96.9948i	0.180840	−	0.104408i	0.587687	+	0.809088i	$0.300039\pi$
$930$		0			0
$931$		0			0
$932$	534.000			0.572961
$933$		0			0
$934$	−738.000	−	426.084i	−0.790150	−	0.456193i
$935$		0			0
$936$		0			0
$937$			1205.51i			1.28656i	0.765631	+	0.643280i	$0.222427\pi$
$937$			1205.51i			1.28656i	−0.765631	+	0.643280i	$0.777573\pi$
$938$		0			0
$939$		0			0
$940$	288.000	+	498.831i	0.306383	+	0.530671i
$941$	762.000	+	439.941i	0.809777	+	0.467525i	0.846878	−	0.531787i	$-0.178479\pi$
$941$	762.000	+	439.941i	0.809777	+	0.467525i	−0.0371015	+	0.999312i	$0.511812\pi$
$942$		0			0
$943$	−840.000	+	484.974i	−0.890774	+	0.514289i
$944$			381.051i			0.403656i
$945$		0			0
$946$	260.000			0.274841
$947$	701.000	+	1214.17i	0.740232	+	1.28212i	0.952389	+	0.304884i	$0.0986178\pi$
$947$	701.000	+	1214.17i	0.740232	+	1.28212i	−0.212157	+	0.977236i	$0.568049\pi$
$948$		0			0
$949$	−144.000	+	249.415i	−0.151739	+	0.262819i
$950$	414.000	−	239.023i	0.435789	−	0.251603i
$951$		0			0
$952$		0			0
$953$	110.000			0.115425			0.0577125	−	0.998333i	$-0.481619\pi$
$953$	110.000			0.115425			0.0577125	+	0.998333i	$0.481619\pi$
$954$		0			0
$955$	−492.000	−	284.056i	−0.515183	−	0.297441i
$956$	−51.0000	+	88.3346i	−0.0533473	+	0.0924002i
$957$		0			0
$958$			387.979i			0.404989i
$959$		0			0
$960$		0			0
$961$	−96.5000	−	167.143i	−0.100416	−	0.173926i
$962$	−156.000	−	90.0666i	−0.162162	−	0.0936244i
$963$		0			0
$964$	−504.000	+	290.985i	−0.522822	+	0.301851i
$965$		−	346.410i		−	0.358974i
$966$		0			0
$967$	1202.00			1.24302			0.621510	−	0.783406i	$-0.286520\pi$
$967$	1202.00			1.24302			0.621510	+	0.783406i	$0.286520\pi$
$968$	73.5000	+	127.306i	0.0759298	+	0.131514i
$969$		0			0
$970$	−192.000	+	332.554i	−0.197938	+	0.342839i
$971$	234.000	−	135.100i	0.240989	−	0.139135i	−0.374642	−	0.927169i	$-0.622235\pi$
$971$	234.000	−	135.100i	0.240989	−	0.139135i	0.615631	+	0.788035i	$0.288901\pi$
$972$		0			0
$973$		0			0
$974$	−818.000			−0.839836
$975$		0			0
$976$	150.000	+	86.6025i	0.153689	+	0.0887321i
$977$	−655.000	+	1134.49i	−0.670420	+	1.16120i	0.307366	+	0.951592i	$0.400553\pi$
$977$	−655.000	+	1134.49i	−0.670420	+	1.16120i	−0.977785	+	0.209609i	$0.932781\pi$
$978$		0			0
$979$			415.692i			0.424609i
$980$		0			0
$981$		0			0
$982$	−245.000	−	424.352i	−0.249491	−	0.432131i
$983$	−1356.00	−	782.887i	−1.37945	−	0.796426i	−0.387357	−	0.921930i	$-0.626612\pi$
$983$	−1356.00	−	782.887i	−1.37945	−	0.796426i	−0.992093	+	0.125503i	$0.959945\pi$
$984$		0			0
$985$	−1668.00	+	963.020i	−1.69340	+	0.977686i
$986$		0			0
$987$		0			0
$988$	−432.000			−0.437247
$989$	−182.000	−	315.233i	−0.184024	−	0.318739i
$990$		0			0
$991$	−409.000	+	708.409i	−0.412714	+	0.714842i	−0.995186	−	0.0980091i	$-0.968753\pi$
$991$	−409.000	+	708.409i	−0.412714	+	0.714842i	0.582471	+	0.812851i	$0.302086\pi$
$992$	792.000	−	457.261i	0.798387	−	0.460949i
$993$		0			0
$994$		0			0
$995$	−2016.00			−2.02613
$996$		0			0
$997$	−150.000	−	86.6025i	−0.150451	−	0.0868631i	0.422884	−	0.906184i	$-0.361018\pi$
$997$	−150.000	−	86.6025i	−0.150451	−	0.0868631i	−0.573336	+	0.819320i	$0.694351\pi$
$998$	277.000	−	479.778i	0.277555	−	0.480740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.m.d.325.1		2
3.2	odd	2		147.3.f.d.31.1		2
7.2	even	3		441.3.m.f.19.1		2
7.3	odd	6		63.3.d.b.55.2		2
7.4	even	3		63.3.d.b.55.1		2
7.5	odd	6	inner	441.3.m.d.19.1		2
7.6	odd	2		441.3.m.f.325.1		2
21.2	odd	6		147.3.f.b.19.1		2
21.5	even	6		147.3.f.d.19.1		2
21.11	odd	6		21.3.d.a.13.1	✓	2
21.17	even	6		21.3.d.a.13.2	yes	2
21.20	even	2		147.3.f.b.31.1		2
28.3	even	6		1008.3.f.d.433.2		2
28.11	odd	6		1008.3.f.d.433.1		2
84.11	even	6		336.3.f.a.97.2		2
84.59	odd	6		336.3.f.a.97.1		2
105.17	odd	12		525.3.e.a.349.4		4
105.32	even	12		525.3.e.a.349.3		4
105.38	odd	12		525.3.e.a.349.1		4
105.53	even	12		525.3.e.a.349.2		4
105.59	even	6		525.3.h.a.76.1		2
105.74	odd	6		525.3.h.a.76.2		2
168.11	even	6		1344.3.f.b.769.1		2
168.53	odd	6		1344.3.f.c.769.2		2
168.59	odd	6		1344.3.f.b.769.2		2
168.101	even	6		1344.3.f.c.769.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.d.a.13.1	✓	2	21.11	odd	6
21.3.d.a.13.2	yes	2	21.17	even	6
63.3.d.b.55.1		2	7.4	even	3
63.3.d.b.55.2		2	7.3	odd	6
147.3.f.b.19.1		2	21.2	odd	6
147.3.f.b.31.1		2	21.20	even	2
147.3.f.d.19.1		2	21.5	even	6
147.3.f.d.31.1		2	3.2	odd	2
336.3.f.a.97.1		2	84.59	odd	6
336.3.f.a.97.2		2	84.11	even	6
441.3.m.d.19.1		2	7.5	odd	6	inner
441.3.m.d.325.1		2	1.1	even	1	trivial
441.3.m.f.19.1		2	7.2	even	3
441.3.m.f.325.1		2	7.6	odd	2
525.3.e.a.349.1		4	105.38	odd	12
525.3.e.a.349.2		4	105.53	even	12
525.3.e.a.349.3		4	105.32	even	12
525.3.e.a.349.4		4	105.17	odd	12
525.3.h.a.76.1		2	105.59	even	6
525.3.h.a.76.2		2	105.74	odd	6
1008.3.f.d.433.1		2	28.11	odd	6
1008.3.f.d.433.2		2	28.3	even	6
1344.3.f.b.769.1		2	168.11	even	6
1344.3.f.b.769.2		2	168.59	odd	6
1344.3.f.c.769.1		2	168.101	even	6
1344.3.f.c.769.2		2	168.53	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-6.00000 + 3.46410i) q^{5} +7.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{4} +(-6.00000 + 3.46410i) q^{5} +7.00000 q^{8} +(-6.00000 - 3.46410i) q^{10} +(5.00000 - 8.66025i) q^{11} -6.92820i q^{13} +(-2.50000 - 4.33013i) q^{16} +(18.0000 - 10.3923i) q^{19} +20.7846i q^{20} +10.0000 q^{22} +(-7.00000 - 12.1244i) q^{23} +(11.5000 - 19.9186i) q^{25} +(6.00000 - 3.46410i) q^{26} +38.0000 q^{29} +(24.0000 + 13.8564i) q^{31} +(16.5000 - 28.5788i) q^{32} +(-13.0000 - 22.5167i) q^{37} +(18.0000 + 10.3923i) q^{38} +(-42.0000 + 24.2487i) q^{40} -69.2820i q^{41} +26.0000 q^{43} +(-15.0000 - 25.9808i) q^{44} +(7.00000 - 12.1244i) q^{46} +(24.0000 - 13.8564i) q^{47} +23.0000 q^{50} +(-18.0000 - 10.3923i) q^{52} +(5.00000 - 8.66025i) q^{53} +69.2820i q^{55} +(19.0000 + 32.9090i) q^{58} +(-66.0000 - 38.1051i) q^{59} +(-30.0000 + 17.3205i) q^{61} +27.7128i q^{62} +13.0000 q^{64} +(24.0000 + 41.5692i) q^{65} +(-37.0000 + 64.0859i) q^{67} +62.0000 q^{71} +(-36.0000 - 20.7846i) q^{73} +(13.0000 - 22.5167i) q^{74} -62.3538i q^{76} +(23.0000 + 39.8372i) q^{79} +(30.0000 + 17.3205i) q^{80} +(60.0000 - 34.6410i) q^{82} +90.0666i q^{83} +(13.0000 + 22.5167i) q^{86} +(35.0000 - 60.6218i) q^{88} +(-36.0000 + 20.7846i) q^{89} -42.0000 q^{92} +(24.0000 + 13.8564i) q^{94} +(-72.0000 + 124.708i) q^{95} -55.4256i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{4} - 12 q^{5} + 14 q^{8}+O(q^{10}) \) 2 * q + q^2 + 3 * q^4 - 12 * q^5 + 14 * q^8	\( 2 q + q^{2} + 3 q^{4} - 12 q^{5} + 14 q^{8} - 12 q^{10} + 10 q^{11} - 5 q^{16} + 36 q^{19} + 20 q^{22} - 14 q^{23} + 23 q^{25} + 12 q^{26} + 76 q^{29} + 48 q^{31} + 33 q^{32} - 26 q^{37} + 36 q^{38} - 84 q^{40} + 52 q^{43} - 30 q^{44} + 14 q^{46} + 48 q^{47} + 46 q^{50} - 36 q^{52} + 10 q^{53} + 38 q^{58} - 132 q^{59} - 60 q^{61} + 26 q^{64} + 48 q^{65} - 74 q^{67} + 124 q^{71} - 72 q^{73} + 26 q^{74} + 46 q^{79} + 60 q^{80} + 120 q^{82} + 26 q^{86} + 70 q^{88} - 72 q^{89} - 84 q^{92} + 48 q^{94} - 144 q^{95}+O(q^{100}) \) 2 * q + q^2 + 3 * q^4 - 12 * q^5 + 14 * q^8 - 12 * q^10 + 10 * q^11 - 5 * q^16 + 36 * q^19 + 20 * q^22 - 14 * q^23 + 23 * q^25 + 12 * q^26 + 76 * q^29 + 48 * q^31 + 33 * q^32 - 26 * q^37 + 36 * q^38 - 84 * q^40 + 52 * q^43 - 30 * q^44 + 14 * q^46 + 48 * q^47 + 46 * q^50 - 36 * q^52 + 10 * q^53 + 38 * q^58 - 132 * q^59 - 60 * q^61 + 26 * q^64 + 48 * q^65 - 74 * q^67 + 124 * q^71 - 72 * q^73 + 26 * q^74 + 46 * q^79 + 60 * q^80 + 120 * q^82 + 26 * q^86 + 70 * q^88 - 72 * q^89 - 84 * q^92 + 48 * q^94 - 144 * q^95

Introduction

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