LMFDB - Embedded newform 441.3.m.d.19.1

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			19.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.19
Dual form			441.3.m.d.325.1

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	−0.713525	−	0.700629i	$-0.752903\pi$
$2$	0.500000	−	0.866025i	0.250000	−	0.433013i	0.963525	+	0.267617i	$0.0862360\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	2.59808i	0.375000	+	0.649519i
$5$	−6.00000	−	3.46410i	−1.20000	−	0.692820i	−0.239445	−	0.970910i	$-0.576965\pi$
$5$	−6.00000	−	3.46410i	−1.20000	−	0.692820i	−0.960555	+	0.278090i	$0.910299\pi$
$6$		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	0.998662	−	0.0517139i	$-0.0164684\pi$
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	−0.544116	+	0.839010i	$0.683135\pi$
$12$		0			0
$13$			6.92820i			0.532939i	0.963843	+	0.266469i	$0.0858571\pi$
$13$			6.92820i			0.532939i	−0.963843	+	0.266469i	$0.914143\pi$
$14$		0			0
$15$		0			0
$16$	−2.50000	+	4.33013i	−0.156250	+	0.270633i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		0			0
$19$	18.0000	+	10.3923i	0.947368	+	0.546963i	0.892262	−	0.451517i	$-0.149117\pi$
$19$	18.0000	+	10.3923i	0.947368	+	0.546963i	0.0551060	+	0.998481i	$0.482450\pi$
$20$		−	20.7846i		−	1.03923i
$21$		0			0
$22$	10.0000			0.454545
$23$	−7.00000	+	12.1244i	−0.304348	+	0.527146i	−0.977116	−	0.212708i	$-0.931772\pi$
$23$	−7.00000	+	12.1244i	−0.304348	+	0.527146i	0.672768	+	0.739853i	$0.265105\pi$
$24$		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	−0.0601750	−	0.998188i	$-0.519166\pi$
$31$	24.0000	−	13.8564i	0.774194	−	0.446981i	0.834369	+	0.551207i	$0.185833\pi$
$32$	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	−0.986486	−	0.163843i	$-0.947611\pi$
$37$	−13.0000	+	22.5167i	−0.351351	+	0.608558i	0.635135	+	0.772401i	$0.280944\pi$
$38$	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	$0.320342\pi$
$41$			69.2820i			1.68981i	−0.534920	+	0.844903i	$0.679658\pi$
$42$		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	0.733096	−	0.680125i	$-0.238075\pi$
$47$	24.0000	+	13.8564i	0.510638	+	0.294817i	−0.222458	+	0.974942i	$0.571408\pi$
$48$		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	0.909333	−	0.416070i	$-0.136593\pi$
$53$	5.00000	+	8.66025i	0.0943396	+	0.163401i	−0.814993	+	0.579471i	$0.803259\pi$
$54$		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	−0.941054	−	0.338255i	$-0.890163\pi$
$59$	−66.0000	+	38.1051i	−1.11864	+	0.645849i	−0.177590	+	0.984105i	$0.556830\pi$
$60$		0			0
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	0.233519	−	0.972352i	$-0.424976\pi$
$61$	−30.0000	−	17.3205i	−0.491803	−	0.283943i	−0.725322	+	0.688409i	$0.758309\pi$
$62$		−	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	−0.998113	−	0.0614098i	$-0.980440\pi$
$67$	−37.0000	−	64.0859i	−0.552239	−	0.956506i	0.445874	−	0.895096i	$-0.352893\pi$
$68$		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	−0.725881	−	0.687821i	$-0.758568\pi$
$73$	−36.0000	+	20.7846i	−0.493151	+	0.284721i	0.232730	+	0.972541i	$0.425234\pi$
$74$	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	−0.682940	−	0.730474i	$-0.739299\pi$
$79$	23.0000	−	39.8372i	0.291139	−	0.504268i	0.974079	+	0.226206i	$0.0726324\pi$
$80$	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	$-0.817451\pi$
$83$		−	90.0666i		−	1.08514i	0.840011	−	0.542570i	$-0.182549\pi$
$84$		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	0.283927	−	0.958846i	$-0.408363\pi$
$89$	−36.0000	−	20.7846i	−0.404494	−	0.233535i	−0.688421	+	0.725311i	$0.741696\pi$
$90$		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	$0.0922258\pi$
$97$			55.4256i			0.571398i	−0.958319	+	0.285699i	$0.907774\pi$
$98$		0			0
$99$		0			0
$100$	−34.5000	+	59.7558i	−0.345000	+	0.597558i
$101$	102.000	−	58.8897i	1.00990	−	0.583067i	0.0987383	−	0.995113i	$-0.468519\pi$
$101$	102.000	−	58.8897i	1.00990	−	0.583067i	0.911163	+	0.412047i	$0.135186\pi$
$102$		0			0
$103$	84.0000	+	48.4974i	0.815534	+	0.470849i	0.848874	−	0.528595i	$-0.177281\pi$
$103$	84.0000	+	48.4974i	0.815534	+	0.470849i	−0.0333400	+	0.999444i	$0.510614\pi$
$104$			48.4974i			0.466321i
$105$		0			0
$106$	10.0000			0.0943396
$107$	5.00000	−	8.66025i	0.0467290	−	0.0809370i	−0.841715	−	0.539922i	$-0.818454\pi$
$107$	5.00000	−	8.66025i	0.0467290	−	0.0809370i	0.888444	+	0.458985i	$0.151787\pi$
$108$		0			0
$109$	−37.0000	−	64.0859i	−0.339450	−	0.587944i	0.644880	−	0.764284i	$-0.276907\pi$
$109$	−37.0000	−	64.0859i	−0.339450	−	0.587944i	−0.984329	+	0.176340i	$0.943574\pi$
$110$	−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	0.331054	−	0.943612i	$-0.392596\pi$
$131$	−42.0000	−	24.2487i	−0.320611	−	0.185105i	−0.651665	+	0.758507i	$0.725929\pi$
$132$		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	−0.946937	−	0.321418i	$-0.895841\pi$
$137$	−103.000	−	178.401i	−0.751825	−	1.30220i	0.195113	−	0.980781i	$-0.437493\pi$
$138$		0			0
$139$		−	117.779i		−	0.847334i	−0.905818	−	0.423667i	$-0.860743\pi$
$139$		−	117.779i		−	0.847334i	0.905818	−	0.423667i	$-0.139257\pi$
$140$		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	−0.631534	−	0.775349i	$-0.717574\pi$
$149$	53.0000	−	91.7987i	0.355705	−	0.616099i	0.987238	+	0.159250i	$0.0509076\pi$
$150$		0			0
$151$	23.0000	+	39.8372i	0.152318	+	0.263822i	0.932079	−	0.362255i	$-0.117993\pi$
$151$	23.0000	+	39.8372i	0.152318	+	0.263822i	−0.779761	+	0.626077i	$0.784660\pi$
$152$	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	−0.986448	−	0.164074i	$-0.947536\pi$
$157$	−210.000	+	121.244i	−1.33758	+	0.772252i	−0.351132	+	0.936326i	$0.614203\pi$
$158$	−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	0.478216	+	0.878242i	$0.341284\pi$
$163$	−85.0000	+	147.224i	−0.521472	+	0.903217i	−0.999688	+	0.0249743i	$0.992050\pi$
$164$	−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	$-0.906210\pi$
$167$		−	96.9948i		−	0.580807i	0.956904	−	0.290404i	$-0.0937896\pi$
$168$		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	0.866367	−	0.499407i	$-0.166449\pi$
$173$	150.000	+	86.6025i	0.867052	+	0.500593i	0.000684548		1.00000i	$0.499782\pi$
$174$		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	0.808060	−	0.589100i	$-0.200518\pi$
$179$	−19.0000	−	32.9090i	−0.106145	−	0.183849i	−0.914206	+	0.405251i	$0.867184\pi$
$180$		0			0
$181$			187.061i			1.03349i	0.856140	+	0.516744i	$0.172856\pi$
$181$			187.061i			1.03349i	−0.856140	+	0.516744i	$0.827144\pi$
$182$		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	−0.738508	−	0.674245i	$-0.764469\pi$
$191$	41.0000	−	71.0141i	0.214660	−	0.371801i	0.953167	+	0.302444i	$0.0978024\pi$
$192$		0			0
$193$	−25.0000	−	43.3013i	−0.129534	−	0.224359i	0.793962	−	0.607967i	$-0.208015\pi$
$193$	−25.0000	−	43.3013i	−0.129534	−	0.224359i	−0.923496	+	0.383608i	$0.874681\pi$
$194$	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	0.292040	−	0.956406i	$-0.405666\pi$
$199$	252.000	−	145.492i	1.26633	−	0.731117i	0.974292	+	0.225289i	$0.0723327\pi$
$200$	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	$0.239543\pi$
$223$			304.841i			1.36700i	−0.729951	+	0.683500i	$0.760457\pi$
$224$		0			0
$225$		0			0
$226$	−89.0000	+	154.153i	−0.393805	+	0.682091i
$227$	−6.00000	+	3.46410i	−0.0264317	+	0.0152604i	−0.513158	−	0.858294i	$-0.671524\pi$
$227$	−6.00000	+	3.46410i	−0.0264317	+	0.0152604i	0.486726	+	0.873555i	$0.338191\pi$
$228$		0			0
$229$	246.000	+	142.028i	1.07424	+	0.620210i	0.929336	−	0.369236i	$-0.120381\pi$
$229$	246.000	+	142.028i	1.07424	+	0.620210i	0.144900	+	0.989446i	$0.453714\pi$
$230$		−	96.9948i		−	0.421717i
$231$		0			0
$232$	266.000			1.14655
$233$	89.0000	−	154.153i	0.381974	−	0.661599i	−0.609370	−	0.792886i	$-0.708578\pi$
$233$	89.0000	−	154.153i	0.381974	−	0.661599i	0.991344	+	0.131287i	$0.0419110\pi$
$234$		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	−0.806265	−	0.591555i	$-0.798514\pi$
$241$	−168.000	+	96.9948i	−0.697095	+	0.402468i	0.109169	+	0.994023i	$0.465181\pi$
$242$	−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	$-0.878455\pi$
$251$		−	187.061i		−	0.745265i	0.927979	−	0.372632i	$-0.121545\pi$
$252$		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	0.714952	−	0.699173i	$-0.246449\pi$
$257$	120.000	+	69.2820i	0.466926	+	0.269580i	−0.248026	+	0.968753i	$0.579782\pi$
$258$		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	0.801053	−	0.598594i	$-0.204274\pi$
$263$	−31.0000	−	53.6936i	−0.117871	−	0.204158i	−0.918924	+	0.394435i	$0.870940\pi$
$264$		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	−0.820635	−	0.571453i	$-0.806380\pi$
$269$	−198.000	+	114.315i	−0.736059	+	0.424964i	0.0845754	+	0.996417i	$0.473047\pi$
$270$		0			0
$271$	288.000	+	166.277i	1.06273	+	0.613568i	0.926186	−	0.377066i	$-0.123067\pi$
$271$	288.000	+	166.277i	1.06273	+	0.613568i	0.136544	+	0.990634i	$0.456400\pi$
$272$		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	0.841605	−	0.540093i	$-0.181611\pi$
$277$	−13.0000	−	22.5167i	−0.0469314	−	0.0812876i	−0.888537	+	0.458805i	$0.848278\pi$
$278$	−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	−0.774858	−	0.632136i	$-0.782179\pi$
$283$	−174.000	+	100.459i	−0.614841	+	0.354979i	0.160017	+	0.987114i	$0.448845\pi$
$284$	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	$-0.682893\pi$
$293$		−	491.902i		−	1.67885i	0.543477	−	0.839424i	$-0.317107\pi$
$294$		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	$-0.989223\pi$
$307$		−	20.7846i		−	0.0677023i	0.999427	−	0.0338512i	$-0.0107772\pi$
$308$		0			0
$309$		0			0
$310$	−96.0000	+	166.277i	−0.309677	+	0.536377i
$311$	−12.0000	+	6.92820i	−0.0385852	+	0.0222772i	−0.519169	−	0.854672i	$-0.673758\pi$
$311$	−12.0000	+	6.92820i	−0.0385852	+	0.0222772i	0.480583	+	0.876949i	$0.340425\pi$
$312$		0			0
$313$	−228.000	−	131.636i	−0.728435	−	0.420562i	0.0894147	−	0.995994i	$-0.471500\pi$
$313$	−228.000	−	131.636i	−0.728435	−	0.420562i	−0.817849	+	0.575433i	$0.804834\pi$
$314$			242.487i			0.772252i
$315$		0			0
$316$	138.000			0.436709
$317$	125.000	−	216.506i	0.394322	−	0.682985i	−0.598693	−	0.800979i	$-0.704313\pi$
$317$	125.000	−	216.506i	0.394322	−	0.682985i	0.993014	+	0.117994i	$0.0376462\pi$
$318$		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	0.298665	−	0.954358i	$-0.403459\pi$
$331$	323.000	−	559.452i	0.975831	−	1.69019i	0.677166	−	0.735831i	$-0.263208\pi$
$332$	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	0.932233	−	0.361859i	$-0.117858\pi$
$347$	53.0000	+	91.7987i	0.152738	+	0.264550i	−0.779495	+	0.626408i	$0.784524\pi$
$348$		0			0
$349$		−	630.466i		−	1.80649i	−0.429121	−	0.903247i	$-0.641177\pi$
$349$		−	630.466i		−	1.80649i	0.429121	−	0.903247i	$-0.358823\pi$
$350$		0			0
$351$		0			0
$352$	−165.000	+	285.788i	−0.468750	+	0.811899i
$353$	264.000	−	152.420i	0.747875	−	0.431786i	−0.0770504	−	0.997027i	$-0.524550\pi$
$353$	264.000	−	152.420i	0.747875	−	0.431786i	0.824926	+	0.565241i	$0.191217\pi$
$354$		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	0.284454	+	0.958690i	$0.408188\pi$
$359$	−247.000	+	427.817i	−0.688022	+	1.19169i	−0.972477	+	0.233000i	$0.925146\pi$
$360$		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	0.326156	−	0.945316i	$-0.394246\pi$
$367$	480.000	−	277.128i	1.30790	−	0.755118i	0.981746	+	0.190198i	$0.0609131\pi$
$368$	−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	−0.974336	−	0.225100i	$-0.927729\pi$
$373$	−109.000	+	188.794i	−0.292225	+	0.506149i	0.682110	+	0.731249i	$0.261062\pi$
$374$		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	0.561353	−	0.827577i	$-0.310281\pi$
$383$	48.0000	+	27.7128i	0.125326	+	0.0723572i	−0.436026	+	0.899934i	$0.643615\pi$
$384$		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	0.999972	+	0.00743692i	$0.00236727\pi$
$389$	197.000	+	341.214i	0.506427	+	0.877157i	−0.493546	+	0.869720i	$0.664299\pi$
$390$		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	0.609049	−	0.793133i	$-0.291551\pi$
$397$	90.0000	+	51.9615i	0.226700	+	0.130885i	−0.382349	+	0.924018i	$0.624885\pi$
$398$		−	290.985i		−	0.731117i
$399$		0			0
$400$	−115.000			−0.287500
$401$	89.0000	−	154.153i	0.221945	−	0.384420i	−0.733453	−	0.679740i	$-0.762093\pi$
$401$	89.0000	−	154.153i	0.221945	−	0.384420i	0.955399	+	0.295319i	$0.0954261\pi$
$402$		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	0.386937	−	0.922106i	$-0.373533\pi$
$409$	564.000	−	325.626i	1.37897	−	0.796150i	0.992036	+	0.125956i	$0.0401997\pi$
$410$	−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	$0.324341\pi$
$419$			713.605i			1.70311i	−0.524262	+	0.851557i	$0.675659\pi$
$420$		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	0.885073	−	0.465452i	$-0.154108\pi$
$431$	17.0000	+	29.4449i	0.0394432	+	0.0683175i	−0.845630	+	0.533770i	$0.820775\pi$
$432$		0			0
$433$		−	415.692i		−	0.960028i	−0.877261	−	0.480014i	$-0.840632\pi$
$433$		−	415.692i		−	0.960028i	0.877261	−	0.480014i	$-0.159368\pi$
$434$		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	0.401268	−	0.915961i	$-0.368570\pi$
$439$	−84.0000	−	48.4974i	−0.191344	−	0.110472i	−0.592612	+	0.805488i	$0.701903\pi$
$440$		−	484.974i		−	1.10221i
$441$		0			0
$442$		0			0
$443$	−235.000	+	407.032i	−0.530474	+	0.918808i	0.468894	+	0.883255i	$0.344653\pi$
$443$	−235.000	+	407.032i	−0.530474	+	0.918808i	−0.999368	+	0.0355534i	$0.988681\pi$
$444$		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	−0.476667	−	0.879084i	$-0.658155\pi$
$457$	239.000	−	413.960i	0.522976	−	0.905821i	0.999643	−	0.0267367i	$-0.00851158\pi$
$458$	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	$-0.740037\pi$
$461$		−	672.036i		−	1.45778i	0.684632	−	0.728889i	$-0.259963\pi$
$462$		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	−0.994815	−	0.101703i	$-0.967571\pi$
$467$	−738.000	−	426.084i	−1.58030	−	0.912387i	−0.585485	−	0.810683i	$-0.699096\pi$
$468$		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	−0.106430	−	0.994320i	$-0.533942\pi$
$479$	336.000	−	193.990i	0.701461	−	0.404989i	0.807891	+	0.589331i	$0.200609\pi$
$480$		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	−0.890032	−	0.455899i	$-0.849318\pi$
$487$	−409.000	−	708.409i	−0.839836	−	1.45464i	0.0501959	−	0.998739i	$-0.484015\pi$
$488$	−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	0.442785	+	0.896628i	$0.353991\pi$
$499$	−277.000	+	479.778i	−0.555110	+	0.961479i	−0.997895	+	0.0648512i	$0.979343\pi$
$500$	−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	$-0.906594\pi$
$503$		−	290.985i		−	0.578498i	0.957254	−	0.289249i	$-0.0934056\pi$
$504$		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	−0.981348	−	0.192240i	$-0.938425\pi$
$509$	−834.000	−	481.510i	−1.63851	−	0.945992i	−0.657159	−	0.753752i	$-0.728242\pi$
$510$		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	−0.392759	−	0.919641i	$-0.628479\pi$
$521$	108.000	−	62.3538i	0.207294	−	0.119681i	0.600053	+	0.799960i	$0.295146\pi$
$522$		0			0
$523$	54.0000	+	31.1769i	0.103250	+	0.0596117i	0.550736	−	0.834679i	$-0.314347\pi$
$523$	54.0000	+	31.1769i	0.103250	+	0.0596117i	−0.447486	+	0.894291i	$0.647680\pi$
$524$		−	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	−0.806331	−	0.591464i	$-0.798550\pi$
$541$	59.0000	−	102.191i	0.109057	−	0.188893i	0.915389	+	0.402571i	$0.131883\pi$
$542$	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	−0.832723	−	0.553689i	$-0.813219\pi$
$557$	−499.000	−	864.293i	−0.895871	−	1.55169i	−0.0631475	−	0.998004i	$-0.520114\pi$
$558$		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	−0.755082	−	0.655630i	$-0.772403\pi$
$563$	−318.000	+	183.597i	−0.564831	+	0.326105i	0.190251	+	0.981735i	$0.439070\pi$
$564$		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	−0.891980	−	0.452075i	$-0.850684\pi$
$569$	−31.0000	+	53.6936i	−0.0544815	+	0.0943648i	0.837498	+	0.546440i	$0.184017\pi$
$570$		0			0
$571$	−205.000	−	355.070i	−0.359019	−	0.621840i	0.628778	−	0.777585i	$-0.283555\pi$
$571$	−205.000	−	355.070i	−0.359019	−	0.621840i	−0.987797	+	0.155745i	$0.950222\pi$
$572$	−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	0.277157	−	0.960825i	$-0.410608\pi$
$577$	720.000	−	415.692i	1.24783	−	0.720437i	0.970677	+	0.240388i	$0.0772746\pi$
$578$	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	$-0.845620\pi$
$587$		−	547.328i		−	0.932416i	0.884675	−	0.466208i	$-0.154380\pi$
$588$		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	0.998862	−	0.0476838i	$-0.0151840\pi$
$593$	864.000	+	498.831i	1.45700	+	0.841198i	0.458136	+	0.888882i	$0.348517\pi$
$594$		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	0.617261	+	0.786758i	$0.288242\pi$
$599$	593.000	+	1027.11i	0.989983	+	1.71470i	0.372722	+	0.927943i	$0.378424\pi$
$600$		0			0
$601$		−	401.836i		−	0.668612i	−0.942465	−	0.334306i	$-0.891498\pi$
$601$		−	401.836i		−	0.668612i	0.942465	−	0.334306i	$-0.108502\pi$
$602$		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	0.595579	−	0.803297i	$-0.296923\pi$
$607$	120.000	+	69.2820i	0.197694	+	0.114138i	−0.397886	+	0.917435i	$0.630256\pi$
$608$			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	0.855227	−	0.518254i	$-0.173418\pi$
$613$	−13.0000	−	22.5167i	−0.0212072	−	0.0367319i	−0.876434	+	0.481522i	$0.840084\pi$
$614$	−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	−0.954352	−	0.298685i	$-0.903452\pi$
$619$	−726.000	+	419.156i	−1.17286	+	0.677151i	−0.218508	+	0.975835i	$0.570119\pi$
$620$	−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	0.999882	+	0.0153802i	$0.00489587\pi$
$641$	329.000	+	569.845i	0.513261	+	0.888993i	−0.486621	+	0.873613i	$0.661771\pi$
$642$		0			0
$643$		−	325.626i		−	0.506416i	−0.967412	−	0.253208i	$-0.918514\pi$
$643$		−	325.626i		−	0.506416i	0.967412	−	0.253208i	$-0.0814857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	396.000	−	228.631i	0.612056	−	0.353370i	−0.161714	−	0.986838i	$-0.551702\pi$
$647$	396.000	−	228.631i	0.612056	−	0.353370i	0.773770	+	0.633467i	$0.218369\pi$
$648$		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	−0.999417	−	0.0341452i	$-0.989129\pi$
$653$	−307.000	+	531.740i	−0.470138	+	0.814303i	0.529279	+	0.848448i	$0.322462\pi$
$654$		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	−0.522521	−	0.852626i	$-0.675008\pi$
$661$	−30.0000	+	17.3205i	−0.0453858	+	0.0262035i	0.477135	+	0.878830i	$0.341675\pi$
$662$	−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	−0.0927921	−	0.995686i	$-0.529579\pi$
$677$	−678.000	−	391.443i	−1.00148	−	0.578203i	−0.908685	+	0.417482i	$0.862913\pi$
$678$		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	0.954244	−	0.299029i	$-0.0966628\pi$
$683$	149.000	+	258.076i	0.218155	+	0.377856i	−0.736089	+	0.676885i	$0.763329\pi$
$684$		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	−0.153040	−	0.988220i	$-0.548906\pi$
$691$	−750.000	−	433.013i	−1.08538	−	0.626646i	−0.932344	+	0.361574i	$0.882240\pi$
$692$			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	0.360379	+	0.932806i	$0.382648\pi$
$709$	−445.000	+	770.763i	−0.627645	+	1.08711i	−0.988023	+	0.154306i	$0.950686\pi$
$710$	−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	0.549233	−	0.835669i	$-0.314920\pi$
$719$	72.0000	+	41.5692i	0.100139	+	0.0578153i	−0.449094	+	0.893484i	$0.648253\pi$
$720$		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	$-0.948203\pi$
$727$		−	235.559i		−	0.324015i	0.986790	−	0.162008i	$-0.0517969\pi$
$728$		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	0.544344	−	0.838862i	$-0.316778\pi$
$733$	66.0000	+	38.1051i	0.0900409	+	0.0519852i	−0.454303	+	0.890847i	$0.650112\pi$
$734$		−	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	0.979445	+	0.201714i	$0.0646510\pi$
$739$	491.000	+	850.437i	0.664411	+	1.15079i	−0.315033	+	0.949081i	$0.602016\pi$
$740$	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	−0.946268	−	0.323383i	$-0.895180\pi$
$751$	−145.000	+	251.147i	−0.193076	+	0.334417i	0.753192	+	0.657801i	$0.228513\pi$
$752$	−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	0.0813500	−	0.996686i	$-0.474077\pi$
$761$	−564.000	−	325.626i	−0.741130	−	0.427892i	−0.822480	+	0.568794i	$0.807410\pi$
$762$		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	$0.168332\pi$
$769$			775.959i			1.00905i	−0.863397	+	0.504525i	$0.831668\pi$
$770$		0			0
$771$		0			0
$772$	75.0000	−	129.904i	0.0971503	−	0.168269i
$773$	198.000	−	114.315i	0.256145	−	0.147885i	−0.366430	−	0.930446i	$-0.619420\pi$
$773$	198.000	−	114.315i	0.256145	−	0.147885i	0.622575	+	0.782560i	$0.286087\pi$
$774$		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	−0.541345	−	0.840801i	$-0.682085\pi$
$787$	−66.0000	+	38.1051i	−0.0838628	+	0.0484182i	0.457482	+	0.889219i	$0.348751\pi$
$788$	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	$-0.817173\pi$
$797$		−	866.025i		−	1.08661i	0.839537	−	0.543303i	$-0.182827\pi$
$798$		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	0.999988	−	0.00498843i	$-0.00158787\pi$
$809$	401.000	+	694.552i	0.495674	+	0.858532i	−0.504314	+	0.863520i	$0.668255\pi$
$810$		0			0
$811$		−	893.738i		−	1.10202i	−0.834499	−	0.551010i	$-0.814243\pi$
$811$		−	893.738i		−	1.10202i	0.834499	−	0.551010i	$-0.185757\pi$
$812$		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	0.0351589	−	0.999382i	$-0.488806\pi$
$821$	725.000	−	1255.74i	0.883069	−	1.52952i	0.847911	−	0.530139i	$-0.177860\pi$
$822$		0			0
$823$	623.000	+	1079.07i	0.756987	+	1.31114i	0.944381	+	0.328854i	$0.106663\pi$
$823$	623.000	+	1079.07i	0.756987	+	1.31114i	−0.187394	+	0.982285i	$0.560004\pi$
$824$	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	−0.0127676	−	0.999918i	$-0.504064\pi$
$829$	702.000	−	405.300i	0.846803	−	0.488902i	0.859571	+	0.511016i	$0.170731\pi$
$830$	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	$0.00262853\pi$
$839$			13.8564i			0.0165154i	−0.999966	+	0.00825769i	$0.997371\pi$
$840$		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	$0.0453976\pi$
$853$			242.487i			0.284276i	−0.989847	+	0.142138i	$0.954602\pi$
$854$		0			0
$855$		0			0
$856$	35.0000	−	60.6218i	0.0408879	−	0.0708198i
$857$	−1212.00	+	699.749i	−1.41424	+	0.816509i	−0.995784	−	0.0917297i	$-0.970760\pi$
$857$	−1212.00	+	699.749i	−1.41424	+	0.816509i	−0.418452	+	0.908239i	$0.637427\pi$
$858$		0			0
$859$	−258.000	−	148.956i	−0.300349	−	0.173407i	0.342251	−	0.939609i	$-0.388811\pi$
$859$	−258.000	−	148.956i	−0.300349	−	0.173407i	−0.642600	+	0.766202i	$0.722144\pi$
$860$		−	540.400i		−	0.628372i
$861$		0			0
$862$	34.0000			0.0394432
$863$	−535.000	+	926.647i	−0.619930	+	1.07375i	0.369567	+	0.929204i	$0.379506\pi$
$863$	−535.000	+	926.647i	−0.619930	+	1.07375i	−0.989498	+	0.144547i	$0.953827\pi$
$864$		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	−0.686697	−	0.726944i	$-0.740940\pi$
$877$	251.000	−	434.745i	0.286203	−	0.495718i	0.972900	+	0.231225i	$0.0742735\pi$
$878$	−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	$0.191591\pi$
$881$			997.661i			1.13242i	−0.824261	+	0.566210i	$0.808409\pi$
$882$		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	0.728946	−	0.684571i	$-0.240010\pi$
$887$	444.000	+	256.344i	0.500564	+	0.289001i	−0.228383	+	0.973571i	$0.573344\pi$
$888$		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	−0.914138	−	0.405404i	$-0.867131\pi$
$907$	−733.000	−	1269.59i	−0.808159	−	1.39977i	0.105979	−	0.994368i	$-0.466202\pi$
$908$	−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	0.0432359	−	0.999065i	$-0.486233\pi$
$919$	815.000	−	1411.62i	0.886834	−	1.53604i	0.843598	−	0.536976i	$-0.180433\pi$
$920$	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	0.587687	−	0.809088i	$-0.300039\pi$
$929$	168.000	+	96.9948i	0.180840	+	0.104408i	−0.406847	+	0.913496i	$0.633372\pi$
$930$		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	$-0.777573\pi$
$937$		−	1205.51i		−	1.28656i	0.765631	−	0.643280i	$-0.222427\pi$
$938$		0			0
$939$		0			0
$940$	288.000	−	498.831i	0.306383	−	0.530671i
$941$	762.000	−	439.941i	0.809777	−	0.467525i	−0.0371015	−	0.999312i	$-0.511812\pi$
$941$	762.000	−	439.941i	0.809777	−	0.467525i	0.846878	+	0.531787i	$0.178479\pi$
$942$		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	−0.212157	−	0.977236i	$-0.568049\pi$
$947$	701.000	−	1214.17i	0.740232	−	1.28212i	0.952389	−	0.304884i	$-0.0986178\pi$
$948$		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	0.615631	−	0.788035i	$-0.288901\pi$
$971$	234.000	+	135.100i	0.240989	+	0.139135i	−0.374642	+	0.927169i	$0.622235\pi$
$972$		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	−0.977785	−	0.209609i	$-0.932781\pi$
$977$	−655.000	−	1134.49i	−0.670420	−	1.16120i	0.307366	−	0.951592i	$-0.400553\pi$
$978$		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	−0.992093	−	0.125503i	$-0.959945\pi$
$983$	−1356.00	+	782.887i	−1.37945	+	0.796426i	−0.387357	+	0.921930i	$0.626612\pi$
$984$		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	0.582471	−	0.812851i	$-0.302086\pi$
$991$	−409.000	−	708.409i	−0.412714	−	0.714842i	−0.995186	+	0.0980091i	$0.968753\pi$
$992$	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	−0.573336	−	0.819320i	$-0.694351\pi$
$997$	−150.000	+	86.6025i	−0.150451	+	0.0868631i	0.422884	+	0.906184i	$0.361018\pi$
$998$	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.19.1		2
3.2	odd	2		147.3.f.d.19.1		2
7.2	even	3		63.3.d.b.55.2		2
7.3	odd	6	inner	441.3.m.d.325.1		2
7.4	even	3		441.3.m.f.325.1		2
7.5	odd	6		63.3.d.b.55.1		2
7.6	odd	2		441.3.m.f.19.1		2
21.2	odd	6		21.3.d.a.13.2	yes	2
21.5	even	6		21.3.d.a.13.1	✓	2
21.11	odd	6		147.3.f.b.31.1		2
21.17	even	6		147.3.f.d.31.1		2
21.20	even	2		147.3.f.b.19.1		2
28.19	even	6		1008.3.f.d.433.1		2
28.23	odd	6		1008.3.f.d.433.2		2
84.23	even	6		336.3.f.a.97.1		2
84.47	odd	6		336.3.f.a.97.2		2
105.2	even	12		525.3.e.a.349.4		4
105.23	even	12		525.3.e.a.349.1		4
105.44	odd	6		525.3.h.a.76.1		2
105.47	odd	12		525.3.e.a.349.3		4
105.68	odd	12		525.3.e.a.349.2		4
105.89	even	6		525.3.h.a.76.2		2
168.5	even	6		1344.3.f.c.769.2		2
168.107	even	6		1344.3.f.b.769.2		2
168.131	odd	6		1344.3.f.b.769.1		2
168.149	odd	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	21.5	even	6
21.3.d.a.13.2	yes	2	21.2	odd	6
63.3.d.b.55.1		2	7.5	odd	6
63.3.d.b.55.2		2	7.2	even	3
147.3.f.b.19.1		2	21.20	even	2
147.3.f.b.31.1		2	21.11	odd	6
147.3.f.d.19.1		2	3.2	odd	2
147.3.f.d.31.1		2	21.17	even	6
336.3.f.a.97.1		2	84.23	even	6
336.3.f.a.97.2		2	84.47	odd	6
441.3.m.d.19.1		2	1.1	even	1	trivial
441.3.m.d.325.1		2	7.3	odd	6	inner
441.3.m.f.19.1		2	7.6	odd	2
441.3.m.f.325.1		2	7.4	even	3
525.3.e.a.349.1		4	105.23	even	12
525.3.e.a.349.2		4	105.68	odd	12
525.3.e.a.349.3		4	105.47	odd	12
525.3.e.a.349.4		4	105.2	even	12
525.3.h.a.76.1		2	105.44	odd	6
525.3.h.a.76.2		2	105.89	even	6
1008.3.f.d.433.1		2	28.19	even	6
1008.3.f.d.433.2		2	28.23	odd	6
1344.3.f.b.769.1		2	168.131	odd	6
1344.3.f.b.769.2		2	168.107	even	6
1344.3.f.c.769.1		2	168.149	odd	6
1344.3.f.c.769.2		2	168.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

L-functions

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