LMFDB - Embedded newform 441.3.j.b.275.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(263,441)]

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([1, 4]))

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

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

chi := DirichletCharacter("441.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.j (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.275
Dual form			441.3.j.b.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-3.00000 - 5.19615i) q^{10} +(1.50000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +(-2.00000 + 3.46410i) q^{13} -10.3923i q^{15} -11.0000 q^{16} +(-13.5000 + 7.79423i) q^{17} +(-13.5000 + 7.79423i) q^{18} +(5.50000 - 9.52628i) q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +(24.0000 - 13.8564i) q^{23} +(-22.5000 - 12.9904i) q^{24} +(-6.50000 + 11.2583i) q^{25} +(6.00000 + 3.46410i) q^{26} -27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} -18.0000 q^{30} -32.0000 q^{31} -15.5885i q^{32} +(4.50000 - 2.59808i) q^{33} +(13.5000 + 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 - 29.4449i) q^{37} +(-16.5000 - 9.52628i) q^{38} +(6.00000 + 10.3923i) q^{39} +(-15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(1.50000 + 0.866025i) q^{44} +(-27.0000 - 15.5885i) q^{45} +(-24.0000 - 41.5692i) q^{46} +48.4974i q^{47} +(-16.5000 + 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +46.7654i q^{51} +(-2.00000 + 3.46410i) q^{52} +46.7654i q^{54} +6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +(-39.0000 - 67.5500i) q^{58} +50.2295i q^{59} -10.3923i q^{60} -56.0000 q^{61} +55.4256i q^{62} -71.0000 q^{64} +13.8564i q^{65} +(-4.50000 - 7.79423i) q^{66} -31.0000 q^{67} +(-13.5000 + 7.79423i) q^{68} -83.1384i q^{69} -31.1769i q^{71} +(-67.5000 + 38.9711i) q^{72} +(32.5000 + 56.2917i) q^{73} +(-51.0000 - 29.4449i) q^{74} +(19.5000 + 33.7750i) q^{75} +(5.50000 - 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +38.0000 q^{79} +(-33.0000 + 19.0526i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(10.5000 - 18.1865i) q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 - 52.8275i) q^{86} -135.100i q^{87} +(7.50000 - 12.9904i) q^{88} +(108.000 + 62.3538i) q^{89} +(-27.0000 + 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 + 83.1384i) q^{93} +84.0000 q^{94} -38.1051i q^{95} +(-40.5000 - 23.3827i) q^{96} +(-57.5000 - 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + 2 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^9	$ 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9} - 6 q^{10} + 3 q^{11} + 3 q^{12} - 4 q^{13} - 22 q^{16} - 27 q^{17} - 27 q^{18} + 11 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 45 q^{24} - 13 q^{25} + 12 q^{26} - 54 q^{27} + 78 q^{29} - 36 q^{30} - 64 q^{31} + 9 q^{33} + 27 q^{34} - 9 q^{36} + 34 q^{37} - 33 q^{38} + 12 q^{39} - 30 q^{40} + 21 q^{41} + 61 q^{43} + 3 q^{44} - 54 q^{45} - 48 q^{46} - 33 q^{48} + 39 q^{50} - 4 q^{52} + 12 q^{55} - 33 q^{57} - 78 q^{58} - 112 q^{61} - 142 q^{64} - 9 q^{66} - 62 q^{67} - 27 q^{68} - 135 q^{72} + 65 q^{73} - 102 q^{74} + 39 q^{75} + 11 q^{76} + 36 q^{78} + 76 q^{79} - 66 q^{80} - 81 q^{81} + 21 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} + 216 q^{89} - 54 q^{90} + 48 q^{92} - 96 q^{93} + 168 q^{94} - 81 q^{96} - 115 q^{97}+O(q^{100}) $ 2 * q + 3 * q^3 + 2 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^9 - 6 * q^10 + 3 * q^11 + 3 * q^12 - 4 * q^13 - 22 * q^16 - 27 * q^17 - 27 * q^18 + 11 * q^19 + 6 * q^20 + 3 * q^22 + 48 * q^23 - 45 * q^24 - 13 * q^25 + 12 * q^26 - 54 * q^27 + 78 * q^29 - 36 * q^30 - 64 * q^31 + 9 * q^33 + 27 * q^34 - 9 * q^36 + 34 * q^37 - 33 * q^38 + 12 * q^39 - 30 * q^40 + 21 * q^41 + 61 * q^43 + 3 * q^44 - 54 * q^45 - 48 * q^46 - 33 * q^48 + 39 * q^50 - 4 * q^52 + 12 * q^55 - 33 * q^57 - 78 * q^58 - 112 * q^61 - 142 * q^64 - 9 * q^66 - 62 * q^67 - 27 * q^68 - 135 * q^72 + 65 * q^73 - 102 * q^74 + 39 * q^75 + 11 * q^76 + 36 * q^78 + 76 * q^79 - 66 * q^80 - 81 * q^81 + 21 * q^82 + 84 * q^83 - 54 * q^85 + 183 * q^86 + 15 * q^88 + 216 * q^89 - 54 * q^90 + 48 * q^92 - 96 * q^93 + 168 * q^94 - 81 * q^96 - 115 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.73205i		−	0.866025i	−0.901388	−	0.433013i	$-0.857451\pi$
$2$		−	1.73205i		−	0.866025i	0.901388	−	0.433013i	$-0.142549\pi$
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$4$	1.00000			0.250000
$5$	3.00000	−	1.73205i	0.600000	−	0.346410i	−0.169042	−	0.985609i	$-0.554067\pi$
$5$	3.00000	−	1.73205i	0.600000	−	0.346410i	0.769042	+	0.639199i	$0.220734\pi$
$6$	−4.50000	−	2.59808i	−0.750000	−	0.433013i
$7$		0			0
$7$		0			0
$8$		−	8.66025i		−	1.08253i
$9$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$10$	−3.00000	−	5.19615i	−0.300000	−	0.519615i
$11$	1.50000	+	0.866025i	0.136364	+	0.0787296i	0.566630	−	0.823972i	$-0.308247\pi$
$11$	1.50000	+	0.866025i	0.136364	+	0.0787296i	−0.430266	+	0.902702i	$0.641580\pi$
$12$	1.50000	−	2.59808i	0.125000	−	0.216506i
$13$	−2.00000	+	3.46410i	−0.153846	+	0.266469i	−0.932638	−	0.360813i	$-0.882499\pi$
$13$	−2.00000	+	3.46410i	−0.153846	+	0.266469i	0.778792	+	0.627282i	$0.215833\pi$
$14$		0			0
$15$		−	10.3923i		−	0.692820i
$16$	−11.0000			−0.687500
$17$	−13.5000	+	7.79423i	−0.794118	+	0.458484i	−0.841410	−	0.540397i	$-0.818274\pi$
$17$	−13.5000	+	7.79423i	−0.794118	+	0.458484i	0.0472925	+	0.998881i	$0.484941\pi$
$18$	−13.5000	+	7.79423i	−0.750000	+	0.433013i
$19$	5.50000	−	9.52628i	0.289474	−	0.501383i	−0.684211	−	0.729285i	$-0.739853\pi$
$19$	5.50000	−	9.52628i	0.289474	−	0.501383i	0.973684	+	0.227901i	$0.0731864\pi$
$20$	3.00000	−	1.73205i	0.150000	−	0.0866025i
$21$		0			0
$22$	1.50000	−	2.59808i	0.0681818	−	0.118094i
$23$	24.0000	−	13.8564i	1.04348	−	0.602452i	0.122662	−	0.992449i	$-0.460857\pi$
$23$	24.0000	−	13.8564i	1.04348	−	0.602452i	0.920817	+	0.389996i	$0.127524\pi$
$24$	−22.5000	−	12.9904i	−0.937500	−	0.541266i
$25$	−6.50000	+	11.2583i	−0.260000	+	0.450333i
$26$	6.00000	+	3.46410i	0.230769	+	0.133235i
$27$	−27.0000			−1.00000
$28$		0			0
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.357316	−	0.933984i	$-0.383692\pi$
$29$	39.0000	−	22.5167i	1.34483	−	0.776437i	0.987511	+	0.157547i	$0.0503586\pi$
$30$	−18.0000			−0.600000
$31$	−32.0000			−1.03226			−0.516129	−	0.856511i	$-0.672628\pi$
$31$	−32.0000			−1.03226			−0.516129	+	0.856511i	$0.672628\pi$
$32$		−	15.5885i		−	0.487139i
$33$	4.50000	−	2.59808i	0.136364	−	0.0787296i
$34$	13.5000	+	23.3827i	0.397059	+	0.687726i
$35$		0			0
$36$	−4.50000	−	7.79423i	−0.125000	−	0.216506i
$37$	17.0000	−	29.4449i	0.459459	−	0.795807i	−0.539473	−	0.842003i	$-0.681376\pi$
$37$	17.0000	−	29.4449i	0.459459	−	0.795807i	0.998932	+	0.0461958i	$0.0147098\pi$
$38$	−16.5000	−	9.52628i	−0.434211	−	0.250692i
$39$	6.00000	+	10.3923i	0.153846	+	0.266469i
$40$	−15.0000	−	25.9808i	−0.375000	−	0.649519i
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	0.622553	−	0.782578i	$-0.286095\pi$
$41$	10.5000	+	6.06218i	0.256098	+	0.147858i	−0.366456	+	0.930436i	$0.619429\pi$
$42$		0			0
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	0.965116	+	0.261822i	$0.0843232\pi$
$43$	30.5000	+	52.8275i	0.709302	+	1.22855i	−0.255814	+	0.966726i	$0.582343\pi$
$44$	1.50000	+	0.866025i	0.0340909	+	0.0196824i
$45$	−27.0000	−	15.5885i	−0.600000	−	0.346410i
$46$	−24.0000	−	41.5692i	−0.521739	−	0.903679i
$47$			48.4974i			1.03186i	0.856631	+	0.515930i	$0.172554\pi$
$47$			48.4974i			1.03186i	−0.856631	+	0.515930i	$0.827446\pi$
$48$	−16.5000	+	28.5788i	−0.343750	+	0.595392i
$49$		0			0
$50$	19.5000	+	11.2583i	0.390000	+	0.225167i
$51$			46.7654i			0.916968i
$52$	−2.00000	+	3.46410i	−0.0384615	+	0.0666173i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$			46.7654i			0.866025i
$55$	6.00000			0.109091
$56$		0			0
$57$	−16.5000	−	28.5788i	−0.289474	−	0.501383i
$58$	−39.0000	−	67.5500i	−0.672414	−	1.16465i
$59$			50.2295i			0.851347i	0.904877	+	0.425674i	$0.139963\pi$
$59$			50.2295i			0.851347i	−0.904877	+	0.425674i	$0.860037\pi$
$60$		−	10.3923i		−	0.173205i
$61$	−56.0000			−0.918033			−0.459016	−	0.888428i	$-0.651798\pi$
$61$	−56.0000			−0.918033			−0.459016	+	0.888428i	$0.651798\pi$
$62$			55.4256i			0.893962i
$63$		0			0
$64$	−71.0000			−1.10938
$65$			13.8564i			0.213175i
$66$	−4.50000	−	7.79423i	−0.0681818	−	0.118094i
$67$	−31.0000			−0.462687			−0.231343	−	0.972872i	$-0.574312\pi$
$67$	−31.0000			−0.462687			−0.231343	+	0.972872i	$0.574312\pi$
$68$	−13.5000	+	7.79423i	−0.198529	+	0.114621i
$69$		−	83.1384i		−	1.20490i
$70$		0			0
$71$		−	31.1769i		−	0.439111i	−0.975600	−	0.219556i	$-0.929539\pi$
$71$		−	31.1769i		−	0.439111i	0.975600	−	0.219556i	$-0.0704608\pi$
$72$	−67.5000	+	38.9711i	−0.937500	+	0.541266i
$73$	32.5000	+	56.2917i	0.445205	+	0.771119i	0.998067	−	0.0621550i	$-0.0197973\pi$
$73$	32.5000	+	56.2917i	0.445205	+	0.771119i	−0.552861	+	0.833273i	$0.686464\pi$
$74$	−51.0000	−	29.4449i	−0.689189	−	0.397904i
$75$	19.5000	+	33.7750i	0.260000	+	0.450333i
$76$	5.50000	−	9.52628i	0.0723684	−	0.125346i
$77$		0			0
$78$	18.0000	−	10.3923i	0.230769	−	0.133235i
$79$	38.0000			0.481013			0.240506	−	0.970648i	$-0.422687\pi$
$79$	38.0000			0.481013			0.240506	+	0.970648i	$0.422687\pi$
$80$	−33.0000	+	19.0526i	−0.412500	+	0.238157i
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$	10.5000	−	18.1865i	0.128049	−	0.221787i
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	−0.225174	−	0.974319i	$-0.572295\pi$
$83$	42.0000	−	24.2487i	0.506024	−	0.292153i	0.731198	+	0.682165i	$0.238962\pi$
$84$		0			0
$85$	−27.0000	+	46.7654i	−0.317647	+	0.550181i
$86$	91.5000	−	52.8275i	1.06395	−	0.614274i
$87$		−	135.100i		−	1.55287i
$88$	7.50000	−	12.9904i	0.0852273	−	0.147618i
$89$	108.000	+	62.3538i	1.21348	+	0.700605i	0.963516	−	0.267650i	$-0.0862469\pi$
$89$	108.000	+	62.3538i	1.21348	+	0.700605i	0.249967	+	0.968254i	$0.419580\pi$
$90$	−27.0000	+	46.7654i	−0.300000	+	0.519615i
$91$		0			0
$92$	24.0000	−	13.8564i	0.260870	−	0.150613i
$93$	−48.0000	+	83.1384i	−0.516129	+	0.893962i
$94$	84.0000			0.893617
$95$		−	38.1051i		−	0.401107i
$96$	−40.5000	−	23.3827i	−0.421875	−	0.243570i
$97$	−57.5000	−	99.5929i	−0.592784	−	1.02673i	−0.993856	−	0.110685i	$-0.964696\pi$
$97$	−57.5000	−	99.5929i	−0.592784	−	1.02673i	0.401072	−	0.916047i	$-0.368638\pi$
$98$		0			0
$99$		−	15.5885i		−	0.157459i
$100$	−6.50000	+	11.2583i	−0.0650000	+	0.112583i
$101$	39.0000	+	22.5167i	0.386139	+	0.222937i	0.680486	−	0.732761i	$-0.261769\pi$
$101$	39.0000	+	22.5167i	0.386139	+	0.222937i	−0.294347	+	0.955699i	$0.595102\pi$
$102$	81.0000			0.794118
$103$	−20.0000	−	34.6410i	−0.194175	−	0.336321i	0.752455	−	0.658644i	$-0.228870\pi$
$103$	−20.0000	−	34.6410i	−0.194175	−	0.336321i	−0.946630	+	0.322323i	$0.895536\pi$
$104$	30.0000	+	17.3205i	0.288462	+	0.166543i
$105$		0			0
$106$		0			0
$107$	121.500	+	70.1481i	1.13551	+	0.655589i	0.945316	−	0.326156i	$-0.105754\pi$
$107$	121.500	+	70.1481i	1.13551	+	0.655589i	0.190198	+	0.981746i	$0.439087\pi$
$108$	−27.0000			−0.250000
$109$	26.0000	+	45.0333i	0.238532	+	0.413150i	0.960293	−	0.278992i	$-0.0900004\pi$
$109$	26.0000	+	45.0333i	0.238532	+	0.413150i	−0.721761	+	0.692142i	$0.756667\pi$
$110$		−	10.3923i		−	0.0944755i
$111$	−51.0000	−	88.3346i	−0.459459	−	0.795807i
$112$		0			0
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	0.113446	−	0.993544i	$-0.463811\pi$
$113$	−78.0000	−	45.0333i	−0.690265	−	0.398525i	−0.803711	+	0.595019i	$0.797144\pi$
$114$	−49.5000	+	28.5788i	−0.434211	+	0.250692i
$115$	48.0000	−	83.1384i	0.417391	−	0.722943i
$116$	39.0000	−	22.5167i	0.336207	−	0.194109i
$117$	36.0000			0.307692
$118$	87.0000			0.737288
$119$		0			0
$120$	−90.0000			−0.750000
$121$	−59.0000	−	102.191i	−0.487603	−	0.844554i
$122$			96.9948i			0.795040i
$123$	31.5000	−	18.1865i	0.256098	−	0.147858i
$124$	−32.0000			−0.258065
$125$			131.636i			1.05309i
$126$		0			0
$127$	−16.0000			−0.125984			−0.0629921	−	0.998014i	$-0.520064\pi$
$127$	−16.0000			−0.125984			−0.0629921	+	0.998014i	$0.520064\pi$
$128$			60.6218i			0.473608i
$129$	183.000			1.41860
$130$	24.0000			0.184615
$131$	138.000	−	79.6743i	1.05344	−	0.608201i	0.129826	−	0.991537i	$-0.458558\pi$
$131$	138.000	−	79.6743i	1.05344	−	0.608201i	0.923609	+	0.383336i	$0.125225\pi$
$132$	4.50000	−	2.59808i	0.0340909	−	0.0196824i
$133$		0			0
$134$			53.6936i			0.400698i
$135$	−81.0000	+	46.7654i	−0.600000	+	0.346410i
$136$	67.5000	+	116.913i	0.496324	+	0.859658i
$137$	163.500	+	94.3968i	1.19343	+	0.689028i	0.959083	−	0.283125i	$-0.0913712\pi$
$137$	163.500	+	94.3968i	1.19343	+	0.689028i	0.234348	+	0.972153i	$0.424705\pi$
$138$	−144.000			−1.04348
$139$	2.50000	−	4.33013i	0.0179856	−	0.0311520i	−0.856893	−	0.515495i	$-0.827608\pi$
$139$	2.50000	−	4.33013i	0.0179856	−	0.0311520i	0.874878	+	0.484343i	$0.160941\pi$
$140$		0			0
$141$	126.000	+	72.7461i	0.893617	+	0.515930i
$142$	−54.0000			−0.380282
$143$	−6.00000	+	3.46410i	−0.0419580	+	0.0242245i
$144$	49.5000	+	85.7365i	0.343750	+	0.595392i
$145$	78.0000	−	135.100i	0.537931	−	0.931724i
$146$	97.5000	−	56.2917i	0.667808	−	0.385559i
$147$		0			0
$148$	17.0000	−	29.4449i	0.114865	−	0.198952i
$149$	132.000	−	76.2102i	0.885906	−	0.511478i	0.0133049	−	0.999911i	$-0.495765\pi$
$149$	132.000	−	76.2102i	0.885906	−	0.511478i	0.872601	+	0.488433i	$0.162431\pi$
$150$	58.5000	−	33.7750i	0.390000	−	0.225167i
$151$	−10.0000	+	17.3205i	−0.0662252	+	0.114705i	−0.897237	−	0.441550i	$-0.854429\pi$
$151$	−10.0000	+	17.3205i	−0.0662252	+	0.114705i	0.831012	+	0.556255i	$0.187762\pi$
$152$	−82.5000	−	47.6314i	−0.542763	−	0.313364i
$153$	121.500	+	70.1481i	0.794118	+	0.458484i
$154$		0			0
$155$	−96.0000	+	55.4256i	−0.619355	+	0.357585i
$156$	6.00000	+	10.3923i	0.0384615	+	0.0666173i
$157$	40.0000			0.254777			0.127389	−	0.991853i	$-0.459340\pi$
$157$	40.0000			0.254777			0.127389	+	0.991853i	$0.459340\pi$
$158$		−	65.8179i		−	0.416569i
$159$		0			0
$160$	−27.0000	−	46.7654i	−0.168750	−	0.292284i
$161$		0			0
$162$	121.500	+	70.1481i	0.750000	+	0.433013i
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	−0.656390	−	0.754422i	$-0.727917\pi$
$163$	53.0000	−	91.7987i	0.325153	−	0.563182i	0.981543	+	0.191240i	$0.0612507\pi$
$164$	10.5000	+	6.06218i	0.0640244	+	0.0369645i
$165$	9.00000	−	15.5885i	0.0545455	−	0.0944755i
$166$	−42.0000	−	72.7461i	−0.253012	−	0.438230i
$167$	−165.000	−	95.2628i	−0.988024	−	0.570436i	−0.0833409	−	0.996521i	$-0.526559\pi$
$167$	−165.000	−	95.2628i	−0.988024	−	0.570436i	−0.904683	+	0.426085i	$0.859892\pi$
$168$		0			0
$169$	76.5000	+	132.502i	0.452663	+	0.784035i
$170$	81.0000	+	46.7654i	0.476471	+	0.275090i
$171$	−99.0000			−0.578947
$172$	30.5000	+	52.8275i	0.177326	+	0.307137i
$173$		−	232.095i		−	1.34159i	−0.741644	−	0.670794i	$-0.765953\pi$
$173$		−	232.095i		−	1.34159i	0.741644	−	0.670794i	$-0.234047\pi$
$174$	−234.000			−1.34483
$175$		0			0
$176$	−16.5000	−	9.52628i	−0.0937500	−	0.0541266i
$177$	130.500	+	75.3442i	0.737288	+	0.425674i
$178$	108.000	−	187.061i	0.606742	−	1.05091i
$179$	54.0000	−	31.1769i	0.301676	−	0.174173i	−0.341520	−	0.939875i	$-0.610942\pi$
$179$	54.0000	−	31.1769i	0.301676	−	0.174173i	0.643196	+	0.765702i	$0.277608\pi$
$180$	−27.0000	−	15.5885i	−0.150000	−	0.0866025i
$181$	232.000			1.28177			0.640884	−	0.767638i	$-0.278568\pi$
$181$	232.000			1.28177			0.640884	+	0.767638i	$0.278568\pi$
$182$		0			0
$183$	−84.0000	+	145.492i	−0.459016	+	0.795040i
$184$	−120.000	−	207.846i	−0.652174	−	1.12960i
$185$		−	117.779i		−	0.636646i
$186$	144.000	+	83.1384i	0.774194	+	0.446981i
$187$	−27.0000			−0.144385
$188$			48.4974i			0.257965i
$189$		0			0
$190$	−66.0000			−0.347368
$191$			232.095i			1.21516i	0.794260	+	0.607578i	$0.207859\pi$
$191$			232.095i			1.21516i	−0.794260	+	0.607578i	$0.792141\pi$
$192$	−106.500	+	184.463i	−0.554688	+	0.960747i
$193$	−265.000			−1.37306			−0.686528	−	0.727103i	$-0.740866\pi$
$193$	−265.000			−1.37306			−0.686528	+	0.727103i	$0.740866\pi$
$194$	−172.500	+	99.5929i	−0.889175	+	0.513366i
$195$	36.0000	+	20.7846i	0.184615	+	0.106588i
$196$		0			0
$197$			124.708i			0.633034i	0.948587	+	0.316517i	$0.102513\pi$
$197$			124.708i			0.633034i	−0.948587	+	0.316517i	$0.897487\pi$
$198$	−27.0000			−0.136364
$199$	145.000	+	251.147i	0.728643	+	1.26205i	0.957457	+	0.288577i	$0.0931821\pi$
$199$	145.000	+	251.147i	0.728643	+	1.26205i	−0.228814	+	0.973470i	$0.573485\pi$
$200$	97.5000	+	56.2917i	0.487500	+	0.281458i
$201$	−46.5000	+	80.5404i	−0.231343	+	0.400698i
$202$	39.0000	−	67.5500i	0.193069	−	0.334406i
$203$		0			0
$204$			46.7654i			0.229242i
$205$	42.0000			0.204878
$206$	−60.0000	+	34.6410i	−0.291262	+	0.168160i
$207$	−216.000	−	124.708i	−1.04348	−	0.602452i
$208$	22.0000	−	38.1051i	0.105769	−	0.183198i
$209$	16.5000	−	9.52628i	0.0789474	−	0.0455803i
$210$		0			0
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	−0.732893	−	0.680344i	$-0.761830\pi$
$211$	47.0000	−	81.4064i	0.222749	−	0.385812i	0.955642	+	0.294532i	$0.0951637\pi$
$212$		0			0
$213$	−81.0000	−	46.7654i	−0.380282	−	0.219556i
$214$	121.500	−	210.444i	0.567757	−	0.983384i
$215$	183.000	+	105.655i	0.851163	+	0.491419i
$216$			233.827i			1.08253i
$217$		0			0
$218$	78.0000	−	45.0333i	0.357798	−	0.206575i
$219$	195.000			0.890411
$220$	6.00000			0.0272727
$221$		−	62.3538i		−	0.282144i
$222$	−153.000	+	88.3346i	−0.689189	+	0.397904i
$223$	−26.0000	−	45.0333i	−0.116592	−	0.201943i	0.801823	−	0.597562i	$-0.203864\pi$
$223$	−26.0000	−	45.0333i	−0.116592	−	0.201943i	−0.918415	+	0.395618i	$0.870530\pi$
$224$		0			0
$225$	117.000			0.520000
$226$	−78.0000	+	135.100i	−0.345133	+	0.597787i
$227$	−163.500	−	94.3968i	−0.720264	−	0.415845i	0.0945856	−	0.995517i	$-0.469847\pi$
$227$	−163.500	−	94.3968i	−0.720264	−	0.415845i	−0.814850	+	0.579672i	$0.803181\pi$
$228$	−16.5000	−	28.5788i	−0.0723684	−	0.125346i
$229$	133.000	+	230.363i	0.580786	+	1.00595i	0.995386	+	0.0959473i	$0.0305880\pi$
$229$	133.000	+	230.363i	0.580786	+	1.00595i	−0.414600	+	0.910004i	$0.636079\pi$
$230$	−144.000	−	83.1384i	−0.626087	−	0.361471i
$231$		0			0
$232$	−195.000	−	337.750i	−0.840517	−	1.45582i
$233$	−175.500	−	101.325i	−0.753219	−	0.434871i	0.0736369	−	0.997285i	$-0.476539\pi$
$233$	−175.500	−	101.325i	−0.753219	−	0.434871i	−0.826856	+	0.562414i	$0.809873\pi$
$234$		−	62.3538i		−	0.266469i
$235$	84.0000	+	145.492i	0.357447	+	0.619116i
$236$			50.2295i			0.212837i
$237$	57.0000	−	98.7269i	0.240506	−	0.416569i
$238$		0			0
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.457252	−	0.889337i	$-0.651166\pi$
$239$	−348.000	−	200.918i	−1.45607	−	0.840661i	−0.998815	+	0.0486764i	$0.984500\pi$
$240$			114.315i			0.476314i
$241$	59.5000	−	103.057i	0.246888	−	0.427623i	−0.715773	−	0.698333i	$-0.753925\pi$
$241$	59.5000	−	103.057i	0.246888	−	0.427623i	0.962661	+	0.270711i	$0.0872587\pi$
$242$	−177.000	+	102.191i	−0.731405	+	0.422277i
$243$	121.500	+	210.444i	0.500000	+	0.866025i
$244$	−56.0000			−0.229508
$245$		0			0
$246$	−31.5000	−	54.5596i	−0.128049	−	0.221787i
$247$	22.0000	+	38.1051i	0.0890688	+	0.154272i
$248$			277.128i			1.11745i
$249$		−	145.492i		−	0.584306i
$250$	228.000			0.912000
$251$			389.711i			1.55264i	0.630342	+	0.776318i	$0.282915\pi$
$251$			389.711i			1.55264i	−0.630342	+	0.776318i	$0.717085\pi$
$252$		0			0
$253$	48.0000			0.189723
$254$			27.7128i			0.109106i
$255$	81.0000	+	140.296i	0.317647	+	0.550181i
$256$	−179.000			−0.699219
$257$	151.500	−	87.4686i	0.589494	−	0.340345i	−0.175403	−	0.984497i	$-0.556123\pi$
$257$	151.500	−	87.4686i	0.589494	−	0.340345i	0.764897	+	0.644152i	$0.222790\pi$
$258$		−	316.965i		−	1.22855i
$259$		0			0
$260$			13.8564i			0.0532939i
$261$	−351.000	−	202.650i	−1.34483	−	0.776437i
$262$	−138.000	−	239.023i	−0.526718	−	0.912302i
$263$	−39.0000	−	22.5167i	−0.148289	−	0.0856147i	0.424020	−	0.905653i	$-0.360619\pi$
$263$	−39.0000	−	22.5167i	−0.148289	−	0.0856147i	−0.572309	+	0.820038i	$0.693952\pi$
$264$	−22.5000	−	38.9711i	−0.0852273	−	0.147618i
$265$		0			0
$266$		0			0
$267$	324.000	−	187.061i	1.21348	−	0.700605i
$268$	−31.0000			−0.115672
$269$	162.000	−	93.5307i	0.602230	−	0.347698i	−0.167688	−	0.985840i	$-0.553630\pi$
$269$	162.000	−	93.5307i	0.602230	−	0.347698i	0.769919	+	0.638142i	$0.220297\pi$
$270$	81.0000	+	140.296i	0.300000	+	0.519615i
$271$	−134.000	+	232.095i	−0.494465	+	0.856438i	−0.999980	−	0.00637958i	$-0.997969\pi$
$271$	−134.000	+	232.095i	−0.494465	+	0.856438i	0.505515	+	0.862818i	$0.331303\pi$
$272$	148.500	−	85.7365i	0.545956	−	0.315208i
$273$		0			0
$274$	163.500	−	283.190i	0.596715	−	1.03354i
$275$	−19.5000	+	11.2583i	−0.0709091	+	0.0409394i
$276$		−	83.1384i		−	0.301226i
$277$	−28.0000	+	48.4974i	−0.101083	+	0.175081i	−0.912131	−	0.409899i	$-0.865564\pi$
$277$	−28.0000	+	48.4974i	−0.101083	+	0.175081i	0.811048	+	0.584979i	$0.198897\pi$
$278$	−7.50000	−	4.33013i	−0.0269784	−	0.0155760i
$279$	144.000	+	249.415i	0.516129	+	0.893962i
$280$		0			0
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	−0.572868	−	0.819648i	$-0.694169\pi$
$281$	−42.0000	+	24.2487i	−0.149466	+	0.0862943i	0.423402	+	0.905942i	$0.360836\pi$
$282$	126.000	−	218.238i	0.446809	−	0.773895i
$283$	−374.000			−1.32155			−0.660777	−	0.750582i	$-0.729773\pi$
$283$	−374.000			−1.32155			−0.660777	+	0.750582i	$0.729773\pi$
$284$		−	31.1769i		−	0.109778i
$285$	−99.0000	−	57.1577i	−0.347368	−	0.200553i
$286$	6.00000	+	10.3923i	0.0209790	+	0.0363367i
$287$		0			0
$288$	−121.500	+	70.1481i	−0.421875	+	0.243570i
$289$	−23.0000	+	39.8372i	−0.0795848	+	0.137845i
$290$	−234.000	−	135.100i	−0.806897	−	0.465862i
$291$	−345.000			−1.18557
$292$	32.5000	+	56.2917i	0.111301	+	0.192780i
$293$	−219.000	−	126.440i	−0.747440	−	0.431535i	0.0773280	−	0.997006i	$-0.475361\pi$
$293$	−219.000	−	126.440i	−0.747440	−	0.431535i	−0.824768	+	0.565471i	$0.808694\pi$
$294$		0			0
$295$	87.0000	+	150.688i	0.294915	+	0.510808i
$296$	−255.000	−	147.224i	−0.861486	−	0.497379i
$297$	−40.5000	−	23.3827i	−0.136364	−	0.0787296i
$298$	−132.000	−	228.631i	−0.442953	−	0.767217i
$299$			110.851i			0.370740i
$300$	19.5000	+	33.7750i	0.0650000	+	0.112583i
$301$		0			0
$302$	30.0000	+	17.3205i	0.0993377	+	0.0573527i
$303$	117.000	−	67.5500i	0.386139	−	0.222937i
$304$	−60.5000	+	104.789i	−0.199013	+	0.344701i
$305$	−168.000	+	96.9948i	−0.550820	+	0.318016i
$306$	121.500	−	210.444i	0.397059	−	0.687726i
$307$	−533.000			−1.73616			−0.868078	−	0.496428i	$-0.834645\pi$
$307$	−533.000			−1.73616			−0.868078	+	0.496428i	$0.834645\pi$
$308$		0			0
$309$	−120.000			−0.388350
$310$	96.0000	+	166.277i	0.309677	+	0.536377i
$311$		−	245.951i		−	0.790840i	−0.918500	−	0.395420i	$-0.870599\pi$
$311$		−	245.951i		−	0.790840i	0.918500	−	0.395420i	$-0.129401\pi$
$312$	90.0000	−	51.9615i	0.288462	−	0.166543i
$313$	−155.000			−0.495208			−0.247604	−	0.968861i	$-0.579643\pi$
$313$	−155.000			−0.495208			−0.247604	+	0.968861i	$0.579643\pi$
$314$		−	69.2820i		−	0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$		−	48.4974i		−	0.152989i	−0.997070	−	0.0764944i	$-0.975627\pi$
$317$		−	48.4974i		−	0.152989i	0.997070	−	0.0764944i	$-0.0243727\pi$
$318$		0			0
$319$	78.0000			0.244514
$320$	−213.000	+	122.976i	−0.665625	+	0.384299i
$321$	364.500	−	210.444i	1.13551	−	0.655589i
$322$		0			0
$323$			171.473i			0.530876i
$324$	−40.5000	+	70.1481i	−0.125000	+	0.216506i
$325$	−26.0000	−	45.0333i	−0.0800000	−	0.138564i
$326$	−159.000	−	91.7987i	−0.487730	−	0.281591i
$327$	156.000			0.477064
$328$	52.5000	−	90.9327i	0.160061	−	0.277234i
$329$		0			0
$330$	−27.0000	−	15.5885i	−0.0818182	−	0.0472377i
$331$	2.00000			0.00604230			0.00302115	−	0.999995i	$-0.499038\pi$
$331$	2.00000			0.00604230			0.00302115	+	0.999995i	$0.499038\pi$
$332$	42.0000	−	24.2487i	0.126506	−	0.0730383i
$333$	−306.000			−0.918919
$334$	−165.000	+	285.788i	−0.494012	+	0.855654i
$335$	−93.0000	+	53.6936i	−0.277612	+	0.160279i
$336$		0			0
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	−0.917477	−	0.397789i	$-0.869778\pi$
$337$	−38.5000	+	66.6840i	−0.114243	+	0.197875i	0.803234	+	0.595664i	$0.203111\pi$
$338$	229.500	−	132.502i	0.678994	−	0.392017i
$339$	−234.000	+	135.100i	−0.690265	+	0.398525i
$340$	−27.0000	+	46.7654i	−0.0794118	+	0.137545i
$341$	−48.0000	−	27.7128i	−0.140762	−	0.0812692i
$342$			171.473i			0.501383i
$343$		0			0
$344$	457.500	−	264.138i	1.32994	−	0.767842i
$345$	−144.000	−	249.415i	−0.417391	−	0.722943i
$346$	−402.000			−1.16185
$347$		−	112.583i		−	0.324448i	−0.986754	−	0.162224i	$-0.948133\pi$
$347$		−	112.583i		−	0.324448i	0.986754	−	0.162224i	$-0.0518666\pi$
$348$		−	135.100i		−	0.388218i
$349$	208.000	+	360.267i	0.595989	+	1.03228i	0.993407	+	0.114645i	$0.0365730\pi$
$349$	208.000	+	360.267i	0.595989	+	1.03228i	−0.397418	+	0.917638i	$0.630094\pi$
$350$		0			0
$351$	54.0000	−	93.5307i	0.153846	−	0.266469i
$352$	13.5000	−	23.3827i	0.0383523	−	0.0664281i
$353$	−1.50000	−	0.866025i	−0.00424929	−	0.00245333i	0.497874	−	0.867249i	$-0.334114\pi$
$353$	−1.50000	−	0.866025i	−0.00424929	−	0.00245333i	−0.502123	+	0.864796i	$0.667448\pi$
$354$	130.500	−	226.033i	0.368644	−	0.638510i
$355$	−54.0000	−	93.5307i	−0.152113	−	0.263467i
$356$	108.000	+	62.3538i	0.303371	+	0.175151i
$357$		0			0
$358$	−54.0000	−	93.5307i	−0.150838	−	0.261259i
$359$	−513.000	−	296.181i	−1.42897	−	0.825016i	−0.431930	−	0.901907i	$-0.642167\pi$
$359$	−513.000	−	296.181i	−1.42897	−	0.825016i	−0.997039	+	0.0768913i	$0.975501\pi$
$360$	−135.000	+	233.827i	−0.375000	+	0.649519i
$361$	120.000	+	207.846i	0.332410	+	0.575751i
$362$		−	401.836i		−	1.11004i
$363$	−354.000			−0.975207
$364$		0			0
$365$	195.000	+	112.583i	0.534247	+	0.308447i
$366$	252.000	+	145.492i	0.688525	+	0.397520i
$367$	−179.000	+	310.037i	−0.487738	+	0.844788i	−0.999901	−	0.0141011i	$-0.995511\pi$
$367$	−179.000	+	310.037i	−0.487738	+	0.844788i	0.512162	+	0.858889i	$0.328845\pi$
$368$	−264.000	+	152.420i	−0.717391	+	0.414186i
$369$		−	109.119i		−	0.295716i
$370$	−204.000			−0.551351
$371$		0			0
$372$	−48.0000	+	83.1384i	−0.129032	+	0.223490i
$373$	290.000	+	502.295i	0.777480	+	1.34663i	0.933390	+	0.358863i	$0.116836\pi$
$373$	290.000	+	502.295i	0.777480	+	1.34663i	−0.155910	+	0.987771i	$0.549831\pi$
$374$			46.7654i			0.125041i
$375$	342.000	+	197.454i	0.912000	+	0.526543i
$376$	420.000			1.11702
$377$			180.133i			0.477807i
$378$		0			0
$379$	83.0000			0.218997			0.109499	−	0.993987i	$-0.465075\pi$
$379$	83.0000			0.218997			0.109499	+	0.993987i	$0.465075\pi$
$380$		−	38.1051i		−	0.100277i
$381$	−24.0000	+	41.5692i	−0.0629921	+	0.109106i
$382$	402.000			1.05236
$383$	−483.000	+	278.860i	−1.26110	+	0.728094i	−0.973287	−	0.229593i	$-0.926260\pi$
$383$	−483.000	+	278.860i	−1.26110	+	0.728094i	−0.287810	+	0.957688i	$0.592927\pi$
$384$	157.500	+	90.9327i	0.410156	+	0.236804i
$385$		0			0
$386$			458.993i			1.18910i
$387$	274.500	−	475.448i	0.709302	−	1.22855i
$388$	−57.5000	−	99.5929i	−0.148196	−	0.256683i
$389$	447.000	+	258.076i	1.14910	+	0.663433i	0.948668	−	0.316274i	$-0.102432\pi$
$389$	447.000	+	258.076i	1.14910	+	0.663433i	0.200432	+	0.979708i	$0.435765\pi$
$390$	36.0000	−	62.3538i	0.0923077	−	0.159882i
$391$	−216.000	+	374.123i	−0.552430	+	0.956836i
$392$		0			0
$393$		−	478.046i		−	1.21640i
$394$	216.000			0.548223
$395$	114.000	−	65.8179i	0.288608	−	0.166628i
$396$		−	15.5885i		−	0.0393648i
$397$	181.000	−	313.501i	0.455919	−	0.789676i	−0.542821	−	0.839848i	$-0.682644\pi$
$397$	181.000	−	313.501i	0.455919	−	0.789676i	0.998741	+	0.0501728i	$0.0159772\pi$
$398$	435.000	−	251.147i	1.09296	−	0.631024i
$399$		0			0
$400$	71.5000	−	123.842i	0.178750	−	0.309604i
$401$	−340.500	+	196.588i	−0.849127	+	0.490244i	−0.860356	−	0.509693i	$-0.829759\pi$
$401$	−340.500	+	196.588i	−0.849127	+	0.490244i	0.0112291	+	0.999937i	$0.496426\pi$
$402$	139.500	+	80.5404i	0.347015	+	0.200349i
$403$	64.0000	−	110.851i	0.158809	−	0.275065i
$404$	39.0000	+	22.5167i	0.0965347	+	0.0557343i
$405$			280.592i			0.692820i
$406$		0			0
$407$	51.0000	−	29.4449i	0.125307	−	0.0723461i
$408$	405.000			0.992647
$409$	−221.000			−0.540342			−0.270171	−	0.962812i	$-0.587080\pi$
$409$	−221.000			−0.540342			−0.270171	+	0.962812i	$0.587080\pi$
$410$		−	72.7461i		−	0.177430i
$411$	490.500	−	283.190i	1.19343	−	0.689028i
$412$	−20.0000	−	34.6410i	−0.0485437	−	0.0840801i
$413$		0			0
$414$	−216.000	+	374.123i	−0.521739	+	0.903679i
$415$	84.0000	−	145.492i	0.202410	−	0.350584i
$416$	54.0000	+	31.1769i	0.129808	+	0.0749445i
$417$	−7.50000	−	12.9904i	−0.0179856	−	0.0311520i
$418$	−16.5000	−	28.5788i	−0.0394737	−	0.0683704i
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.987401	−	0.158236i	$-0.949419\pi$
$419$	−678.000	−	391.443i	−1.61814	−	0.934233i	−0.630737	−	0.775997i	$-0.717247\pi$
$420$		0			0
$421$	341.000	+	590.629i	0.809976	+	1.40292i	0.912880	+	0.408229i	$0.133853\pi$
$421$	341.000	+	590.629i	0.809976	+	1.40292i	−0.102903	+	0.994691i	$0.532813\pi$
$422$	−141.000	−	81.4064i	−0.334123	−	0.192906i
$423$	378.000	−	218.238i	0.893617	−	0.515930i
$424$		0			0
$425$		−	202.650i		−	0.476823i
$426$	−81.0000	+	140.296i	−0.190141	+	0.329334i
$427$		0			0
$428$	121.500	+	70.1481i	0.283879	+	0.163897i
$429$			20.7846i			0.0484490i
$430$	183.000	−	316.965i	0.425581	−	0.737129i
$431$	−243.000	+	140.296i	−0.563805	+	0.325513i	−0.754671	−	0.656103i	$-0.772204\pi$
$431$	−243.000	+	140.296i	−0.563805	+	0.325513i	0.190866	+	0.981616i	$0.438870\pi$
$432$	297.000			0.687500
$433$	295.000			0.681293			0.340647	−	0.940191i	$-0.389354\pi$
$433$	295.000			0.681293			0.340647	+	0.940191i	$0.389354\pi$
$434$		0			0
$435$	−234.000	−	405.300i	−0.537931	−	0.931724i
$436$	26.0000	+	45.0333i	0.0596330	+	0.103287i
$437$		−	304.841i		−	0.697577i
$438$		−	337.750i		−	0.771119i
$439$	−812.000			−1.84966			−0.924829	−	0.380383i	$-0.875792\pi$
$439$	−812.000			−1.84966			−0.924829	+	0.380383i	$0.875792\pi$
$440$		−	51.9615i		−	0.118094i
$441$		0			0
$442$	−108.000			−0.244344
$443$			91.7987i			0.207221i	0.994618	+	0.103610i	$0.0330395\pi$
$443$			91.7987i			0.207221i	−0.994618	+	0.103610i	$0.966961\pi$
$444$	−51.0000	−	88.3346i	−0.114865	−	0.198952i
$445$	432.000			0.970787
$446$	−78.0000	+	45.0333i	−0.174888	+	0.100972i
$447$		−	457.261i		−	1.02296i
$448$		0			0
$449$		−	639.127i		−	1.42344i	−0.702461	−	0.711722i	$-0.747915\pi$
$449$		−	639.127i		−	1.42344i	0.702461	−	0.711722i	$-0.252085\pi$
$450$		−	202.650i		−	0.450333i
$451$	10.5000	+	18.1865i	0.0232816	+	0.0403249i
$452$	−78.0000	−	45.0333i	−0.172566	−	0.0996312i
$453$	30.0000	+	51.9615i	0.0662252	+	0.114705i
$454$	−163.500	+	283.190i	−0.360132	+	0.623767i
$455$		0			0
$456$	−247.500	+	142.894i	−0.542763	+	0.313364i
$457$	65.0000			0.142232			0.0711160	−	0.997468i	$-0.477344\pi$
$457$	65.0000			0.142232			0.0711160	+	0.997468i	$0.477344\pi$
$458$	399.000	−	230.363i	0.871179	−	0.502975i
$459$	364.500	−	210.444i	0.794118	−	0.458484i
$460$	48.0000	−	83.1384i	0.104348	−	0.180736i
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.496753	−	0.867892i	$-0.334525\pi$
$461$	690.000	−	398.372i	1.49675	−	0.864147i	0.999993	+	0.00374501i	$0.00119208\pi$
$462$		0			0
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	0.131660	+	0.991295i	$0.457969\pi$
$463$	−367.000	+	635.663i	−0.792657	+	1.37292i	−0.924317	+	0.381627i	$0.875364\pi$
$464$	−429.000	+	247.683i	−0.924569	+	0.533800i
$465$			332.554i			0.715169i
$466$	−175.500	+	303.975i	−0.376609	+	0.652307i
$467$	−175.500	−	101.325i	−0.375803	−	0.216970i	0.300188	−	0.953880i	$-0.402951\pi$
$467$	−175.500	−	101.325i	−0.375803	−	0.216970i	−0.675991	+	0.736910i	$0.736284\pi$
$468$	36.0000			0.0769231
$469$		0			0
$470$	252.000	−	145.492i	0.536170	−	0.309558i
$471$	60.0000	−	103.923i	0.127389	−	0.220643i
$472$	435.000			0.921610
$473$			105.655i			0.223372i
$474$	−171.000	−	98.7269i	−0.360759	−	0.208285i
$475$	71.5000	+	123.842i	0.150526	+	0.260719i
$476$		0			0
$477$		0			0
$478$	−348.000	+	602.754i	−0.728033	+	1.26099i
$479$	525.000	+	303.109i	1.09603	+	0.632795i	0.935176	−	0.354183i	$-0.115241\pi$
$479$	525.000	+	303.109i	1.09603	+	0.632795i	0.160857	+	0.986978i	$0.448574\pi$
$480$	−162.000			−0.337500
$481$	68.0000	+	117.779i	0.141372	+	0.244864i
$482$	−178.500	−	103.057i	−0.370332	−	0.213811i
$483$		0			0
$484$	−59.0000	−	102.191i	−0.121901	−	0.211138i
$485$	−345.000	−	199.186i	−0.711340	−	0.410692i
$486$	364.500	−	210.444i	0.750000	−	0.433013i
$487$	53.0000	+	91.7987i	0.108830	+	0.188498i	0.915296	−	0.402781i	$-0.131956\pi$
$487$	53.0000	+	91.7987i	0.108830	+	0.188498i	−0.806467	+	0.591279i	$0.798623\pi$
$488$			484.974i			0.993800i
$489$	−159.000	−	275.396i	−0.325153	−	0.563182i
$490$		0			0
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	0.282891	−	0.959152i	$-0.408707\pi$
$491$	−199.500	−	115.181i	−0.406314	−	0.234585i	−0.689205	+	0.724567i	$0.742040\pi$
$492$	31.5000	−	18.1865i	0.0640244	−	0.0369645i
$493$	−351.000	+	607.950i	−0.711968	+	1.23316i
$494$	66.0000	−	38.1051i	0.133603	−	0.0771359i
$495$	−27.0000	−	46.7654i	−0.0545455	−	0.0944755i
$496$	352.000			0.709677
$497$		0			0
$498$	−252.000			−0.506024
$499$	393.500	+	681.562i	0.788577	+	1.36586i	0.926839	+	0.375460i	$0.122515\pi$
$499$	393.500	+	681.562i	0.788577	+	1.36586i	−0.138261	+	0.990396i	$0.544151\pi$
$500$			131.636i			0.263272i
$501$	−495.000	+	285.788i	−0.988024	+	0.570436i
$502$	675.000			1.34462
$503$		−	623.538i		−	1.23964i	−0.784745	−	0.619819i	$-0.787206\pi$
$503$		−	623.538i		−	1.23964i	0.784745	−	0.619819i	$-0.212794\pi$
$504$		0			0
$505$	156.000			0.308911
$506$		−	83.1384i		−	0.164305i
$507$	459.000			0.905325
$508$	−16.0000			−0.0314961
$509$	−186.000	+	107.387i	−0.365422	+	0.210977i	−0.671457	−	0.741044i	$-0.734331\pi$
$509$	−186.000	+	107.387i	−0.365422	+	0.210977i	0.306034	+	0.952020i	$0.400998\pi$
$510$	243.000	−	140.296i	0.476471	−	0.275090i
$511$		0			0
$512$			552.524i			1.07915i
$513$	−148.500	+	257.210i	−0.289474	+	0.501383i
$514$	−151.500	−	262.406i	−0.294747	−	0.510517i
$515$	−120.000	−	69.2820i	−0.233010	−	0.134528i
$516$	183.000			0.354651
$517$	−42.0000	+	72.7461i	−0.0812379	+	0.140708i
$518$		0			0
$519$	−603.000	−	348.142i	−1.16185	−	0.670794i
$520$	120.000			0.230769
$521$	175.500	−	101.325i	0.336852	−	0.194482i	−0.322027	−	0.946730i	$-0.604364\pi$
$521$	175.500	−	101.325i	0.336852	−	0.194482i	0.658879	+	0.752249i	$0.271031\pi$
$522$	−351.000	+	607.950i	−0.672414	+	1.16465i
$523$	−125.000	+	216.506i	−0.239006	+	0.413970i	−0.960429	−	0.278524i	$-0.910155\pi$
$523$	−125.000	+	216.506i	−0.239006	+	0.413970i	0.721424	+	0.692494i	$0.243488\pi$
$524$	138.000	−	79.6743i	0.263359	−	0.152050i
$525$		0			0
$526$	−39.0000	+	67.5500i	−0.0741445	+	0.128422i
$527$	432.000	−	249.415i	0.819734	−	0.473274i
$528$	−49.5000	+	28.5788i	−0.0937500	+	0.0541266i
$529$	119.500	−	206.980i	0.225898	−	0.391267i
$530$		0			0
$531$	391.500	−	226.033i	0.737288	−	0.425674i
$532$		0			0
$533$	−42.0000	+	24.2487i	−0.0787992	+	0.0454948i
$534$	−324.000	−	561.184i	−0.606742	−	1.05091i
$535$	486.000			0.908411
$536$			268.468i			0.500873i
$537$		−	187.061i		−	0.348345i
$538$	−162.000	−	280.592i	−0.301115	−	0.521547i
$539$		0			0
$540$	−81.0000	+	46.7654i	−0.150000	+	0.0866025i
$541$	−325.000	+	562.917i	−0.600739	+	1.04051i	0.391970	+	0.919978i	$0.371794\pi$
$541$	−325.000	+	562.917i	−0.600739	+	1.04051i	−0.992709	+	0.120533i	$0.961540\pi$
$542$	402.000	+	232.095i	0.741697	+	0.428219i
$543$	348.000	−	602.754i	0.640884	−	1.11004i
$544$	121.500	+	210.444i	0.223346	+	0.386846i
$545$	156.000	+	90.0666i	0.286239	+	0.165260i
$546$		0			0
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	−0.996618	−	0.0821692i	$-0.973815\pi$
$547$	−311.500	−	539.534i	−0.569470	−	0.986351i	0.427149	−	0.904181i	$-0.359518\pi$
$548$	163.500	+	94.3968i	0.298358	+	0.172257i
$549$	252.000	+	436.477i	0.459016	+	0.795040i
$550$	19.5000	+	33.7750i	0.0354545	+	0.0614091i
$551$		−	495.367i		−	0.899032i
$552$	−720.000			−1.30435
$553$		0			0
$554$	84.0000	+	48.4974i	0.151625	+	0.0875405i
$555$	−306.000	−	176.669i	−0.551351	−	0.318323i
$556$	2.50000	−	4.33013i	0.00449640	−	0.00778800i
$557$	459.000	−	265.004i	0.824057	−	0.475770i	−0.0277562	−	0.999615i	$-0.508836\pi$
$557$	459.000	−	265.004i	0.824057	−	0.475770i	0.851814	+	0.523845i	$0.175503\pi$
$558$	432.000	−	249.415i	0.774194	−	0.446981i
$559$	−244.000			−0.436494
$560$		0			0
$561$	−40.5000	+	70.1481i	−0.0721925	+	0.125041i
$562$	42.0000	+	72.7461i	0.0747331	+	0.129442i
$563$			112.583i			0.199970i	0.994989	+	0.0999852i	$0.0318795\pi$
$563$			112.583i			0.199970i	−0.994989	+	0.0999852i	$0.968120\pi$
$564$	126.000	+	72.7461i	0.223404	+	0.128983i
$565$	−312.000			−0.552212
$566$			647.787i			1.14450i
$567$		0			0
$568$	−270.000			−0.475352
$569$			652.983i			1.14760i	0.818996	+	0.573799i	$0.194531\pi$
$569$			652.983i			1.14760i	−0.818996	+	0.573799i	$0.805469\pi$
$570$	−99.0000	+	171.473i	−0.173684	+	0.300830i
$571$	545.000			0.954466			0.477233	−	0.878777i	$-0.341640\pi$
$571$	545.000			0.954466			0.477233	+	0.878777i	$0.341640\pi$
$572$	−6.00000	+	3.46410i	−0.0104895	+	0.00605612i
$573$	603.000	+	348.142i	1.05236	+	0.607578i
$574$		0			0
$575$			360.267i			0.626551i
$576$	319.500	+	553.390i	0.554688	+	0.960747i
$577$	−435.500	−	754.308i	−0.754766	−	1.30729i	−0.945491	−	0.325650i	$-0.894417\pi$
$577$	−435.500	−	754.308i	−0.754766	−	1.30729i	0.190725	−	0.981644i	$-0.438916\pi$
$578$	69.0000	+	39.8372i	0.119377	+	0.0689224i
$579$	−397.500	+	688.490i	−0.686528	+	1.18910i
$580$	78.0000	−	135.100i	0.134483	−	0.232931i
$581$		0			0
$582$			597.558i			1.02673i
$583$		0			0
$584$	487.500	−	281.458i	0.834760	−	0.481949i
$585$	108.000	−	62.3538i	0.184615	−	0.106588i
$586$	−219.000	+	379.319i	−0.373720	+	0.647302i
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	−0.498722	−	0.866762i	$-0.666197\pi$
$587$	1.50000	−	0.866025i	0.00255537	−	0.00147534i	0.501277	+	0.865287i	$0.332864\pi$
$588$		0			0
$589$	−176.000	+	304.841i	−0.298812	+	0.517557i
$590$	261.000	−	150.688i	0.442373	−	0.255404i
$591$	324.000	+	187.061i	0.548223	+	0.316517i
$592$	−187.000	+	323.894i	−0.315878	+	0.547117i
$593$	162.000	+	93.5307i	0.273187	+	0.157725i	0.630335	−	0.776323i	$-0.282917\pi$
$593$	162.000	+	93.5307i	0.273187	+	0.157725i	−0.357148	+	0.934048i	$0.616251\pi$
$594$	−40.5000	+	70.1481i	−0.0681818	+	0.118094i
$595$		0			0
$596$	132.000	−	76.2102i	0.221477	−	0.127870i
$597$	870.000			1.45729
$598$	192.000			0.321070
$599$		−	564.649i		−	0.942652i	−0.881959	−	0.471326i	$-0.843776\pi$
$599$		−	564.649i		−	0.942652i	0.881959	−	0.471326i	$-0.156224\pi$
$600$	292.500	−	168.875i	0.487500	−	0.281458i
$601$	230.500	+	399.238i	0.383527	+	0.664289i	0.991564	−	0.129620i	$-0.0413758\pi$
$601$	230.500	+	399.238i	0.383527	+	0.664289i	−0.608036	+	0.793909i	$0.708042\pi$
$602$		0			0
$603$	139.500	+	241.621i	0.231343	+	0.400698i
$604$	−10.0000	+	17.3205i	−0.0165563	+	0.0286763i
$605$	−354.000	−	204.382i	−0.585124	−	0.337821i
$606$	−117.000	−	202.650i	−0.193069	−	0.334406i
$607$	−56.0000	−	96.9948i	−0.0922570	−	0.159794i	0.816204	−	0.577765i	$-0.196075\pi$
$607$	−56.0000	−	96.9948i	−0.0922570	−	0.159794i	−0.908461	+	0.417971i	$0.862741\pi$
$608$	−148.500	−	85.7365i	−0.244243	−	0.141014i
$609$		0			0
$610$	168.000	+	290.985i	0.275410	+	0.477024i
$611$	−168.000	−	96.9948i	−0.274959	−	0.158748i
$612$	121.500	+	70.1481i	0.198529	+	0.114621i
$613$	−451.000	−	781.155i	−0.735726	−	1.27431i	−0.954404	−	0.298518i	$-0.903508\pi$
$613$	−451.000	−	781.155i	−0.735726	−	1.27431i	0.218678	−	0.975797i	$-0.429826\pi$
$614$			923.183i			1.50356i
$615$	63.0000	−	109.119i	0.102439	−	0.177430i
$616$		0			0
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	0.229665	−	0.973270i	$-0.426237\pi$
$617$	−307.500	−	177.535i	−0.498379	−	0.287739i	−0.728044	+	0.685530i	$0.759570\pi$
$618$			207.846i			0.336321i
$619$	−399.500	+	691.954i	−0.645396	+	1.11786i	0.338814	+	0.940853i	$0.389974\pi$
$619$	−399.500	+	691.954i	−0.645396	+	1.11786i	−0.984210	+	0.177005i	$0.943359\pi$
$620$	−96.0000	+	55.4256i	−0.154839	+	0.0893962i
$621$	−648.000	+	374.123i	−1.04348	+	0.602452i
$622$	−426.000			−0.684887
$623$		0			0
$624$	−66.0000	−	114.315i	−0.105769	−	0.183198i
$625$	65.5000	+	113.449i	0.104800	+	0.181519i
$626$			268.468i			0.428862i
$627$		−	57.1577i		−	0.0911606i
$628$	40.0000			0.0636943
$629$			530.008i			0.842619i
$630$		0			0
$631$	830.000			1.31537			0.657686	−	0.753292i	$-0.271535\pi$
$631$	830.000			1.31537			0.657686	+	0.753292i	$0.271535\pi$
$632$		−	329.090i		−	0.520711i
$633$	−141.000	−	244.219i	−0.222749	−	0.385812i
$634$	−84.0000			−0.132492
$635$	−48.0000	+	27.7128i	−0.0755906	+	0.0436422i
$636$		0			0
$637$		0			0
$638$		−	135.100i		−	0.211755i
$639$	−243.000	+	140.296i	−0.380282	+	0.219556i
$640$	105.000	+	181.865i	0.164062	+	0.284165i
$641$	325.500	+	187.928i	0.507800	+	0.293179i	0.731929	−	0.681381i	$-0.238620\pi$
$641$	325.500	+	187.928i	0.507800	+	0.293179i	−0.224129	+	0.974560i	$0.571954\pi$
$642$	−364.500	−	631.333i	−0.567757	−	0.983384i
$643$	−6.50000	+	11.2583i	−0.0101089	+	0.0175091i	−0.871036	−	0.491220i	$-0.836551\pi$
$643$	−6.50000	+	11.2583i	−0.0101089	+	0.0175091i	0.860927	+	0.508729i	$0.169884\pi$
$644$		0			0
$645$	549.000	−	316.965i	0.851163	−	0.491419i
$646$	297.000			0.459752
$647$	−405.000	+	233.827i	−0.625966	+	0.361402i	−0.779188	−	0.626790i	$-0.784368\pi$
$647$	−405.000	+	233.827i	−0.625966	+	0.361402i	0.153222	+	0.988192i	$0.451035\pi$
$648$	607.500	+	350.740i	0.937500	+	0.541266i
$649$	−43.5000	+	75.3442i	−0.0670262	+	0.116093i
$650$	−78.0000	+	45.0333i	−0.120000	+	0.0692820i
$651$		0			0
$652$	53.0000	−	91.7987i	0.0812883	−	0.140796i
$653$	−327.000	+	188.794i	−0.500766	+	0.289117i	−0.729030	−	0.684482i	$-0.760028\pi$
$653$	−327.000	+	188.794i	−0.500766	+	0.289117i	0.228264	+	0.973599i	$0.426695\pi$
$654$		−	270.200i		−	0.413150i
$655$	276.000	−	478.046i	0.421374	−	0.729841i
$656$	−115.500	−	66.6840i	−0.176067	−	0.101652i
$657$	292.500	−	506.625i	0.445205	−	0.771119i
$658$		0			0
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.979162	−	0.203082i	$-0.934904\pi$
$659$	−852.000	+	491.902i	−1.29287	+	0.746438i	−0.313706	+	0.949520i	$0.601571\pi$
$660$	9.00000	−	15.5885i	0.0136364	−	0.0236189i
$661$	382.000			0.577912			0.288956	−	0.957342i	$-0.406692\pi$
$661$	382.000			0.577912			0.288956	+	0.957342i	$0.406692\pi$
$662$		−	3.46410i		−	0.00523278i
$663$	−162.000	−	93.5307i	−0.244344	−	0.141072i
$664$	−210.000	−	363.731i	−0.316265	−	0.547787i
$665$		0			0
$666$			530.008i			0.795807i
$667$	624.000	−	1080.80i	0.935532	−	1.62039i
$668$	−165.000	−	95.2628i	−0.247006	−	0.142609i
$669$	−156.000			−0.233184
$670$	93.0000	+	161.081i	0.138806	+	0.240419i
$671$	−84.0000	−	48.4974i	−0.125186	−	0.0722763i
$672$		0			0
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	0.567401	−	0.823441i	$-0.307949\pi$
$673$	−289.000	−	500.563i	−0.429421	−	0.743778i	−0.996822	+	0.0796633i	$0.974615\pi$
$674$	115.500	+	66.6840i	0.171365	+	0.0989376i
$675$	175.500	−	303.975i	0.260000	−	0.450333i
$676$	76.5000	+	132.502i	0.113166	+	0.196009i
$677$		−	699.749i		−	1.03360i	−0.856106	−	0.516801i	$-0.827123\pi$
$677$		−	699.749i		−	1.03360i	0.856106	−	0.516801i	$-0.172877\pi$
$678$	234.000	+	405.300i	0.345133	+	0.597787i
$679$		0			0
$680$	405.000	+	233.827i	0.595588	+	0.343863i
$681$	−490.500	+	283.190i	−0.720264	+	0.415845i
$682$	−48.0000	+	83.1384i	−0.0703812	+	0.121904i
$683$	−904.500	+	522.213i	−1.32430	+	0.764588i	−0.984412	−	0.175877i	$-0.943724\pi$
$683$	−904.500	+	522.213i	−1.32430	+	0.764588i	−0.339892	+	0.940464i	$0.610391\pi$
$684$	−99.0000			−0.144737
$685$	654.000			0.954745
$686$		0			0
$687$	798.000			1.16157
$688$	−335.500	−	581.103i	−0.487645	−	0.844627i
$689$		0			0
$690$	−432.000	+	249.415i	−0.626087	+	0.361471i
$691$	−182.000			−0.263386			−0.131693	−	0.991291i	$-0.542041\pi$
$691$	−182.000			−0.263386			−0.131693	+	0.991291i	$0.542041\pi$
$692$		−	232.095i		−	0.335397i
$693$		0			0
$694$	−195.000			−0.280980
$695$		−	17.3205i		−	0.0249216i
$696$	−1170.00			−1.68103
$697$	−189.000			−0.271162
$698$	624.000	−	360.267i	0.893983	−	0.516141i
$699$	−526.500	+	303.975i	−0.753219	+	0.434871i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−162.000	−	93.5307i	−0.230769	−	0.133235i
$703$	−187.000	−	323.894i	−0.266003	−	0.460730i
$704$	−106.500	−	61.4878i	−0.151278	−	0.0873406i
$705$	504.000			0.714894
$706$	−1.50000	+	2.59808i	−0.00212465	+	0.00367999i
$707$		0			0
$708$	130.500	+	75.3442i	0.184322	+	0.106418i
$709$	−700.000			−0.987306			−0.493653	−	0.869659i	$-0.664339\pi$
$709$	−700.000			−0.987306			−0.493653	+	0.869659i	$0.664339\pi$
$710$	−162.000	+	93.5307i	−0.228169	+	0.131733i
$711$	−171.000	−	296.181i	−0.240506	−	0.416569i
$712$	540.000	−	935.307i	0.758427	−	1.31363i
$713$	−768.000	+	443.405i	−1.07714	+	0.621886i
$714$		0			0
$715$	−12.0000	+	20.7846i	−0.0167832	+	0.0290694i
$716$	54.0000	−	31.1769i	0.0754190	−	0.0435432i
$717$	−1044.00	+	602.754i	−1.45607	+	0.840661i
$718$	−513.000	+	888.542i	−0.714485	+	1.23752i
$719$	−513.000	−	296.181i	−0.713491	−	0.411934i	0.0988613	−	0.995101i	$-0.468480\pi$
$719$	−513.000	−	296.181i	−0.713491	−	0.411934i	−0.812352	+	0.583167i	$0.801813\pi$
$720$	297.000	+	171.473i	0.412500	+	0.238157i
$721$		0			0
$722$	360.000	−	207.846i	0.498615	−	0.287875i
$723$	−178.500	−	309.171i	−0.246888	−	0.427623i
$724$	232.000			0.320442
$725$			585.433i			0.807494i
$726$			613.146i			0.844554i
$727$	−332.000	−	575.041i	−0.456671	−	0.790978i	0.542111	−	0.840307i	$-0.317625\pi$
$727$	−332.000	−	575.041i	−0.456671	−	0.790978i	−0.998783	+	0.0493289i	$0.984292\pi$
$728$		0			0
$729$	729.000			1.00000
$730$	195.000	−	337.750i	0.267123	−	0.462671i
$731$	−823.500	−	475.448i	−1.12654	−	0.650408i
$732$	−84.0000	+	145.492i	−0.114754	+	0.198760i
$733$	−335.000	−	580.237i	−0.457026	−	0.791592i	0.541776	−	0.840523i	$-0.317752\pi$
$733$	−335.000	−	580.237i	−0.457026	−	0.791592i	−0.998802	+	0.0489306i	$0.984419\pi$
$734$	537.000	+	310.037i	0.731608	+	0.422394i
$735$		0			0
$736$	−216.000	−	374.123i	−0.293478	−	0.508319i
$737$	−46.5000	−	26.8468i	−0.0630936	−	0.0364271i
$738$	−189.000			−0.256098
$739$	−158.500	−	274.530i	−0.214479	−	0.371489i	0.738632	−	0.674109i	$-0.235472\pi$
$739$	−158.500	−	274.530i	−0.214479	−	0.371489i	−0.953111	+	0.302620i	$0.902139\pi$
$740$		−	117.779i		−	0.159161i
$741$	132.000			0.178138
$742$		0			0
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	0.0930168	−	0.995665i	$-0.470349\pi$
$743$	−537.000	−	310.037i	−0.722746	−	0.417277i	−0.815762	+	0.578387i	$0.803682\pi$
$744$	720.000	+	415.692i	0.967742	+	0.558726i
$745$	264.000	−	457.261i	0.354362	−	0.613774i
$746$	870.000	−	502.295i	1.16622	−	0.673317i
$747$	−378.000	−	218.238i	−0.506024	−	0.292153i
$748$	−27.0000			−0.0360963
$749$		0			0
$750$	342.000	−	592.361i	0.456000	−	0.789815i
$751$	−655.000	−	1134.49i	−0.872170	−	1.51064i	−0.859747	−	0.510721i	$-0.829379\pi$
$751$	−655.000	−	1134.49i	−0.872170	−	1.51064i	−0.0124237	−	0.999923i	$-0.503955\pi$
$752$		−	533.472i		−	0.709404i
$753$	1012.50	+	584.567i	1.34462	+	0.776318i
$754$	312.000			0.413793
$755$			69.2820i			0.0917643i
$756$		0			0
$757$	218.000			0.287979			0.143989	−	0.989579i	$-0.454007\pi$
$757$	218.000			0.287979			0.143989	+	0.989579i	$0.454007\pi$
$758$		−	143.760i		−	0.189657i
$759$	72.0000	−	124.708i	0.0948617	−	0.164305i
$760$	−330.000			−0.434211
$761$	570.000	−	329.090i	0.749014	−	0.432444i	−0.0763232	−	0.997083i	$-0.524318\pi$
$761$	570.000	−	329.090i	0.749014	−	0.432444i	0.825338	+	0.564639i	$0.190985\pi$
$762$	72.0000	+	41.5692i	0.0944882	+	0.0545528i
$763$		0			0
$764$			232.095i			0.303789i
$765$	486.000			0.635294
$766$	483.000	+	836.581i	0.630548	+	1.09214i
$767$	−174.000	−	100.459i	−0.226858	−	0.130976i
$768$	−268.500	+	465.056i	−0.349609	+	0.605541i
$769$	511.000	−	885.078i	0.664499	−	1.15095i	−0.314921	−	0.949118i	$-0.601978\pi$
$769$	511.000	−	885.078i	0.664499	−	1.15095i	0.979421	−	0.201829i	$-0.0646885\pi$
$770$		0			0
$771$		−	524.811i		−	0.680689i
$772$	−265.000			−0.343264
$773$	−1026.00	+	592.361i	−1.32730	+	0.766315i	−0.984881	−	0.173234i	$-0.944578\pi$
$773$	−1026.00	+	592.361i	−1.32730	+	0.766315i	−0.342416	+	0.939549i	$0.611245\pi$
$774$	−823.500	−	475.448i	−1.06395	−	0.614274i
$775$	208.000	−	360.267i	0.268387	−	0.464860i
$776$	−862.500	+	497.965i	−1.11147	+	0.641707i
$777$		0			0
$778$	447.000	−	774.227i	0.574550	−	0.995150i
$779$	115.500	−	66.6840i	0.148267	−	0.0856020i
$780$	36.0000	+	20.7846i	0.0461538	+	0.0266469i
$781$	27.0000	−	46.7654i	0.0345711	−	0.0598788i
$782$	648.000	+	374.123i	0.828645	+	0.478418i
$783$	−1053.00	+	607.950i	−1.34483	+	0.776437i
$784$		0			0
$785$	120.000	−	69.2820i	0.152866	−	0.0882574i
$786$	−828.000			−1.05344
$787$	130.000			0.165184			0.0825921	−	0.996583i	$-0.473680\pi$
$787$	130.000			0.165184			0.0825921	+	0.996583i	$0.473680\pi$
$788$			124.708i			0.158258i
$789$	−117.000	+	67.5500i	−0.148289	+	0.0856147i
$790$	−114.000	−	197.454i	−0.144304	−	0.249942i
$791$		0			0
$792$	−135.000			−0.170455
$793$	112.000	−	193.990i	0.141236	−	0.244628i
$794$	−543.000	−	313.501i	−0.683879	−	0.394838i
$795$		0			0
$796$	145.000	+	251.147i	0.182161	+	0.315512i
$797$	−273.000	−	157.617i	−0.342535	−	0.197762i	0.318858	−	0.947803i	$-0.396701\pi$
$797$	−273.000	−	157.617i	−0.342535	−	0.197762i	−0.661392	+	0.750040i	$0.730034\pi$
$798$		0			0
$799$	−378.000	−	654.715i	−0.473091	−	0.819418i
$800$	175.500	+	101.325i	0.219375	+	0.126656i
$801$		−	1122.37i		−	1.40121i
$802$	340.500	+	589.763i	0.424564	+	0.735366i
$803$			112.583i			0.140203i
$804$	−46.5000	+	80.5404i	−0.0578358	+	0.100175i
$805$		0			0
$806$	−192.000	−	110.851i	−0.238213	−	0.137533i
$807$		−	561.184i		−	0.695396i
$808$	195.000	−	337.750i	0.241337	−	0.418007i
$809$	−121.500	+	70.1481i	−0.150185	+	0.0867096i	−0.573210	−	0.819409i	$-0.694302\pi$
$809$	−121.500	+	70.1481i	−0.150185	+	0.0867096i	0.423024	+	0.906118i	$0.360969\pi$
$810$	486.000			0.600000
$811$	−299.000			−0.368681			−0.184340	−	0.982862i	$-0.559015\pi$
$811$	−299.000			−0.368681			−0.184340	+	0.982862i	$0.559015\pi$
$812$		0			0
$813$	402.000	+	696.284i	0.494465	+	0.856438i
$814$	−51.0000	−	88.3346i	−0.0626536	−	0.108519i
$815$		−	367.195i		−	0.450546i
$816$		−	514.419i		−	0.630416i
$817$	671.000			0.821297
$818$			382.783i			0.467950i
$819$		0			0
$820$	42.0000			0.0512195
$821$			606.218i			0.738390i	0.929352	+	0.369195i	$0.120366\pi$
$821$			606.218i			0.738390i	−0.929352	+	0.369195i	$0.879634\pi$
$822$	−490.500	−	849.571i	−0.596715	−	1.03354i
$823$	−814.000			−0.989064			−0.494532	−	0.869159i	$-0.664661\pi$
$823$	−814.000			−0.989064			−0.494532	+	0.869159i	$0.664661\pi$
$824$	−300.000	+	173.205i	−0.364078	+	0.210200i
$825$			67.5500i			0.0818788i
$826$		0			0
$827$		−	1434.14i		−	1.73415i	−0.498182	−	0.867073i	$-0.665999\pi$
$827$		−	1434.14i		−	1.73415i	0.498182	−	0.867073i	$-0.334001\pi$
$828$	−216.000	−	124.708i	−0.260870	−	0.150613i
$829$	−359.000	−	621.806i	−0.433052	−	0.750068i	0.564083	−	0.825718i	$-0.309230\pi$
$829$	−359.000	−	621.806i	−0.433052	−	0.750068i	−0.997134	+	0.0756506i	$0.975897\pi$
$830$	−252.000	−	145.492i	−0.303614	−	0.175292i
$831$	84.0000	+	145.492i	0.101083	+	0.175081i
$832$	142.000	−	245.951i	0.170673	−	0.295614i
$833$		0			0
$834$	−22.5000	+	12.9904i	−0.0269784	+	0.0155760i
$835$	−660.000			−0.790419
$836$	16.5000	−	9.52628i	0.0197368	−	0.0113951i
$837$	864.000			1.03226
$838$	−678.000	+	1174.33i	−0.809069	+	1.40135i
$839$	690.000	−	398.372i	0.822408	−	0.474817i	−0.0288384	−	0.999584i	$-0.509181\pi$
$839$	690.000	−	398.372i	0.822408	−	0.474817i	0.851246	+	0.524767i	$0.175847\pi$
$840$		0			0
$841$	593.500	−	1027.97i	0.705707	−	1.22232i
$842$	1023.00	−	590.629i	1.21496	−	0.701460i
$843$			145.492i			0.172589i
$844$	47.0000	−	81.4064i	0.0556872	−	0.0964531i
$845$	459.000	+	265.004i	0.543195	+	0.313614i
$846$	−378.000	−	654.715i	−0.446809	−	0.773895i
$847$		0			0
$848$		0			0
$849$	−561.000	+	971.681i	−0.660777	+	1.14450i
$850$	−351.000			−0.412941
$851$		−	942.236i		−	1.10721i
$852$	−81.0000	−	46.7654i	−0.0950704	−	0.0548889i
$853$	712.000	+	1233.22i	0.834701	+	1.44574i	0.894274	+	0.447521i	$0.147693\pi$
$853$	712.000	+	1233.22i	0.834701	+	1.44574i	−0.0595725	+	0.998224i	$0.518974\pi$
$854$		0			0
$855$	−297.000	+	171.473i	−0.347368	+	0.200553i
$856$	607.500	−	1052.22i	0.709696	−	1.22923i
$857$	606.000	+	349.874i	0.707118	+	0.408255i	0.809993	−	0.586440i	$-0.199471\pi$
$857$	606.000	+	349.874i	0.707118	+	0.408255i	−0.102875	+	0.994694i	$0.532804\pi$
$858$	36.0000			0.0419580
$859$	155.500	+	269.334i	0.181024	+	0.313544i	0.942230	−	0.334968i	$-0.108725\pi$
$859$	155.500	+	269.334i	0.181024	+	0.313544i	−0.761205	+	0.648511i	$0.775392\pi$
$860$	183.000	+	105.655i	0.212791	+	0.122855i
$861$		0			0
$862$	243.000	+	420.888i	0.281903	+	0.488270i
$863$	891.000	+	514.419i	1.03244	+	0.596082i	0.917684	−	0.397311i	$-0.130056\pi$
$863$	891.000	+	514.419i	1.03244	+	0.596082i	0.114761	+	0.993393i	$0.463390\pi$
$864$			420.888i			0.487139i
$865$	−402.000	−	696.284i	−0.464740	−	0.804953i
$866$		−	510.955i		−	0.590017i
$867$	69.0000	+	119.512i	0.0795848	+	0.137845i
$868$		0			0
$869$	57.0000	+	32.9090i	0.0655926	+	0.0378699i
$870$	−702.000	+	405.300i	−0.806897	+	0.465862i
$871$	62.0000	−	107.387i	0.0711825	−	0.123292i
$872$	390.000	−	225.167i	0.447248	−	0.258219i
$873$	−517.500	+	896.336i	−0.592784	+	1.02673i
$874$	−528.000			−0.604119
$875$		0			0
$876$	195.000			0.222603
$877$	−52.0000	−	90.0666i	−0.0592930	−	0.102699i	0.834855	−	0.550470i	$-0.185551\pi$
$877$	−52.0000	−	90.0666i	−0.0592930	−	0.102699i	−0.894148	+	0.447771i	$0.852218\pi$
$878$			1406.43i			1.60185i
$879$	−657.000	+	379.319i	−0.747440	+	0.431535i
$880$	−66.0000			−0.0750000
$881$		−	62.3538i		−	0.0707762i	−0.999374	−	0.0353881i	$-0.988733\pi$
$881$		−	62.3538i		−	0.0707762i	0.999374	−	0.0353881i	$-0.0112667\pi$
$882$		0			0
$883$	119.000			0.134768			0.0673839	−	0.997727i	$-0.478535\pi$
$883$	119.000			0.134768			0.0673839	+	0.997727i	$0.478535\pi$
$884$		−	62.3538i		−	0.0705360i
$885$	522.000			0.589831
$886$	159.000			0.179458
$887$	1029.00	−	594.093i	1.16009	−	0.669778i	0.208765	−	0.977966i	$-0.433056\pi$
$887$	1029.00	−	594.093i	1.16009	−	0.669778i	0.951326	+	0.308188i	$0.0997224\pi$
$888$	−765.000	+	441.673i	−0.861486	+	0.497379i
$889$		0			0
$890$		−	748.246i		−	0.840726i
$891$	−121.500	+	70.1481i	−0.136364	+	0.0787296i
$892$	−26.0000	−	45.0333i	−0.0291480	−	0.0504858i
$893$	462.000	+	266.736i	0.517357	+	0.298696i
$894$	−792.000			−0.885906
$895$	108.000	−	187.061i	0.120670	−	0.209007i
$896$		0			0
$897$	288.000	+	166.277i	0.321070	+	0.185370i
$898$	−1107.00			−1.23274
$899$	−1248.00	+	720.533i	−1.38821	+	0.801483i
$900$	117.000			0.130000
$901$		0			0
$902$	31.5000	−	18.1865i	0.0349224	−	0.0201625i
$903$		0			0
$904$	−390.000	+	675.500i	−0.431416	+	0.747234i
$905$	696.000	−	401.836i	0.769061	−	0.444017i
$906$	90.0000	−	51.9615i	0.0993377	−	0.0573527i
$907$	−347.500	+	601.888i	−0.383131	+	0.663603i	−0.991508	−	0.130046i	$-0.958488\pi$
$907$	−347.500	+	601.888i	−0.383131	+	0.663603i	0.608377	+	0.793648i	$0.291821\pi$
$908$	−163.500	−	94.3968i	−0.180066	−	0.103961i
$909$		−	405.300i		−	0.445874i
$910$		0			0
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.668110	+	0.744062i	$0.732897\pi$
$911$	−1500.00	+	866.025i	−1.64654	+	0.950632i	−0.978432	+	0.206569i	$0.933770\pi$
$912$	181.500	+	314.367i	0.199013	+	0.344701i
$913$	84.0000			0.0920044
$914$		−	112.583i		−	0.123176i
$915$			581.969i			0.636032i
$916$	133.000	+	230.363i	0.145197	+	0.251488i
$917$		0			0
$918$	−364.500	−	631.333i	−0.397059	−	0.687726i
$919$	−28.0000	+	48.4974i	−0.0304679	+	0.0527720i	−0.880857	−	0.473382i	$-0.843033\pi$
$919$	−28.0000	+	48.4974i	−0.0304679	+	0.0527720i	0.850389	+	0.526154i	$0.176366\pi$
$920$	−720.000	−	415.692i	−0.782609	−	0.451839i
$921$	−799.500	+	1384.77i	−0.868078	+	1.50356i
$922$	−690.000	−	1195.12i	−0.748373	−	1.29622i
$923$	108.000	+	62.3538i	0.117010	+	0.0675556i
$924$		0			0
$925$	221.000	+	382.783i	0.238919	+	0.413820i
$926$	1101.00	+	635.663i	1.18898	+	0.686461i
$927$	−180.000	+	311.769i	−0.194175	+	0.336321i
$928$	−351.000	−	607.950i	−0.378233	−	0.655118i
$929$			796.743i			0.857635i	0.903391	+	0.428818i	$0.141070\pi$
$929$			796.743i			0.857635i	−0.903391	+	0.428818i	$0.858930\pi$
$930$	576.000			0.619355
$931$		0			0
$932$	−175.500	−	101.325i	−0.188305	−	0.108718i
$933$	−639.000	−	368.927i	−0.684887	−	0.395420i
$934$	−175.500	+	303.975i	−0.187901	+	0.325455i
$935$	−81.0000	+	46.7654i	−0.0866310	+	0.0500164i
$936$		−	311.769i		−	0.333087i
$937$	−470.000			−0.501601			−0.250800	−	0.968039i	$-0.580694\pi$
$937$	−470.000			−0.501601			−0.250800	+	0.968039i	$0.580694\pi$
$938$		0			0
$939$	−232.500	+	402.702i	−0.247604	+	0.428862i
$940$	84.0000	+	145.492i	0.0893617	+	0.154779i
$941$		−	401.836i		−	0.427031i	−0.976940	−	0.213515i	$-0.931509\pi$
$941$		−	401.836i		−	0.427031i	0.976940	−	0.213515i	$-0.0684913\pi$
$942$	−180.000	−	103.923i	−0.191083	−	0.110322i
$943$	336.000			0.356310
$944$		−	552.524i		−	0.585301i
$945$		0			0
$946$	183.000			0.193446
$947$		−	1.73205i		−	0.00182899i	−1.00000		0.000914494i	$-0.999709\pi$
$947$		−	1.73205i		−	0.00182899i	1.00000		0.000914494i	$-0.000291092\pi$
$948$	57.0000	−	98.7269i	0.0601266	−	0.104142i
$949$	−260.000			−0.273973
$950$	214.500	−	123.842i	0.225789	−	0.130360i
$951$	−126.000	−	72.7461i	−0.132492	−	0.0764944i
$952$		0			0
$953$			826.188i			0.866934i	0.901169	+	0.433467i	$0.142710\pi$
$953$			826.188i			0.866934i	−0.901169	+	0.433467i	$0.857290\pi$
$954$		0			0
$955$	402.000	+	696.284i	0.420942	+	0.729094i
$956$	−348.000	−	200.918i	−0.364017	−	0.210165i
$957$	117.000	−	202.650i	0.122257	−	0.211755i
$958$	525.000	−	909.327i	0.548017	−	0.949193i
$959$		0			0
$960$			737.854i			0.768598i
$961$	63.0000			0.0655567
$962$	204.000	−	117.779i	0.212058	−	0.122432i
$963$		−	1262.67i		−	1.31118i
$964$	59.5000	−	103.057i	0.0617220	−	0.106906i
$965$	−795.000	+	458.993i	−0.823834	+	0.475641i
$966$		0			0
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	0.367695	+	0.929946i	$0.380147\pi$
$967$	−601.000	+	1040.96i	−0.621510	+	1.07649i	−0.989205	+	0.146540i	$0.953186\pi$
$968$	−885.000	+	510.955i	−0.914256	+	0.527846i
$969$	445.500	+	257.210i	0.459752	+	0.265438i
$970$	−345.000	+	597.558i	−0.355670	+	0.616039i
$971$	−162.000	−	93.5307i	−0.166838	−	0.0963241i	0.414256	−	0.910160i	$-0.364042\pi$
$971$	−162.000	−	93.5307i	−0.166838	−	0.0963241i	−0.581094	+	0.813836i	$0.697375\pi$
$972$	121.500	+	210.444i	0.125000	+	0.216506i
$973$		0			0
$974$	159.000	−	91.7987i	0.163244	−	0.0942492i
$975$	−156.000			−0.160000
$976$	616.000			0.631148
$977$			417.424i			0.427251i	0.976916	+	0.213626i	$0.0685272\pi$
$977$			417.424i			0.427251i	−0.976916	+	0.213626i	$0.931473\pi$
$978$	−477.000	+	275.396i	−0.487730	+	0.281591i
$979$	108.000	+	187.061i	0.110317	+	0.191074i
$980$		0			0
$981$	234.000	−	405.300i	0.238532	−	0.413150i
$982$	−199.500	+	345.544i	−0.203157	+	0.351878i
$983$	1011.00	+	583.701i	1.02848	+	0.593796i	0.916550	−	0.399920i	$-0.130962\pi$
$983$	1011.00	+	583.701i	1.02848	+	0.593796i	0.111934	+	0.993716i	$0.464295\pi$
$984$	−157.500	−	272.798i	−0.160061	−	0.277234i
$985$	216.000	+	374.123i	0.219289	+	0.379820i
$986$	1053.00	+	607.950i	1.06795	+	0.616582i
$987$		0			0
$988$	22.0000	+	38.1051i	0.0222672	+	0.0385679i
$989$	1464.00	+	845.241i	1.48028	+	0.854642i
$990$	−81.0000	+	46.7654i	−0.0818182	+	0.0472377i
$991$	710.000	+	1229.76i	0.716448	+	1.24092i	0.962398	+	0.271642i	$0.0875666\pi$
$991$	710.000	+	1229.76i	0.716448	+	1.24092i	−0.245950	+	0.969282i	$0.579100\pi$
$992$			498.831i			0.502853i
$993$	3.00000	−	5.19615i	0.00302115	−	0.00523278i
$994$		0			0
$995$	870.000	+	502.295i	0.874372	+	0.504819i
$996$		−	145.492i		−	0.146077i
$997$	262.000	−	453.797i	0.262788	−	0.455163i	−0.704193	−	0.710008i	$-0.748691\pi$
$997$	262.000	−	453.797i	0.262788	−	0.455163i	0.966982	+	0.254845i	$0.0820246\pi$
$998$	1180.50	−	681.562i	1.18287	−	0.682928i
$999$	−459.000	+	795.011i	−0.459459	+	0.795807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.j.b.275.1		2
7.2	even	3		441.3.r.a.50.1		2
7.3	odd	6		441.3.n.b.410.1		2
7.4	even	3		441.3.n.a.410.1		2
7.5	odd	6		9.3.d.a.5.1	yes	2
7.6	odd	2		441.3.j.a.275.1		2
9.2	odd	6		441.3.n.a.128.1		2
21.5	even	6		27.3.d.a.17.1		2
28.19	even	6		144.3.q.a.113.1		2
35.12	even	12		225.3.i.a.149.1		4
35.19	odd	6		225.3.j.a.176.1		2
35.33	even	12		225.3.i.a.149.2		4
56.5	odd	6		576.3.q.b.257.1		2
56.19	even	6		576.3.q.a.257.1		2
63.2	odd	6		441.3.r.a.344.1		2
63.5	even	6		81.3.b.a.80.2		2
63.11	odd	6	inner	441.3.j.b.263.1		2
63.20	even	6		441.3.n.b.128.1		2
63.38	even	6		441.3.j.a.263.1		2
63.40	odd	6		81.3.b.a.80.1		2
63.47	even	6		9.3.d.a.2.1	✓	2
63.61	odd	6		27.3.d.a.8.1		2
84.47	odd	6		432.3.q.a.17.1		2
105.47	odd	12		675.3.i.a.449.2		4
105.68	odd	12		675.3.i.a.449.1		4
105.89	even	6		675.3.j.a.476.1		2
168.5	even	6		1728.3.q.a.449.1		2
168.131	odd	6		1728.3.q.b.449.1		2
252.47	odd	6		144.3.q.a.65.1		2
252.103	even	6		1296.3.e.a.161.1		2
252.131	odd	6		1296.3.e.a.161.2		2
252.187	even	6		432.3.q.a.305.1		2
315.47	odd	12		225.3.i.a.74.2		4
315.124	odd	6		675.3.j.a.251.1		2
315.173	odd	12		225.3.i.a.74.1		4
315.187	even	12		675.3.i.a.224.1		4
315.299	even	6		225.3.j.a.101.1		2
315.313	even	12		675.3.i.a.224.2		4
504.61	odd	6		1728.3.q.a.1601.1		2
504.173	even	6		576.3.q.b.65.1		2
504.187	even	6		1728.3.q.b.1601.1		2
504.299	odd	6		576.3.q.a.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	63.47	even	6
9.3.d.a.5.1	yes	2	7.5	odd	6
27.3.d.a.8.1		2	63.61	odd	6
27.3.d.a.17.1		2	21.5	even	6
81.3.b.a.80.1		2	63.40	odd	6
81.3.b.a.80.2		2	63.5	even	6
144.3.q.a.65.1		2	252.47	odd	6
144.3.q.a.113.1		2	28.19	even	6
225.3.i.a.74.1		4	315.173	odd	12
225.3.i.a.74.2		4	315.47	odd	12
225.3.i.a.149.1		4	35.12	even	12
225.3.i.a.149.2		4	35.33	even	12
225.3.j.a.101.1		2	315.299	even	6
225.3.j.a.176.1		2	35.19	odd	6
432.3.q.a.17.1		2	84.47	odd	6
432.3.q.a.305.1		2	252.187	even	6
441.3.j.a.263.1		2	63.38	even	6
441.3.j.a.275.1		2	7.6	odd	2
441.3.j.b.263.1		2	63.11	odd	6	inner
441.3.j.b.275.1		2	1.1	even	1	trivial
441.3.n.a.128.1		2	9.2	odd	6
441.3.n.a.410.1		2	7.4	even	3
441.3.n.b.128.1		2	63.20	even	6
441.3.n.b.410.1		2	7.3	odd	6
441.3.r.a.50.1		2	7.2	even	3
441.3.r.a.344.1		2	63.2	odd	6
576.3.q.a.65.1		2	504.299	odd	6
576.3.q.a.257.1		2	56.19	even	6
576.3.q.b.65.1		2	504.173	even	6
576.3.q.b.257.1		2	56.5	odd	6
675.3.i.a.224.1		4	315.187	even	12
675.3.i.a.224.2		4	315.313	even	12
675.3.i.a.449.1		4	105.68	odd	12
675.3.i.a.449.2		4	105.47	odd	12
675.3.j.a.251.1		2	315.124	odd	6
675.3.j.a.476.1		2	105.89	even	6
1296.3.e.a.161.1		2	252.103	even	6
1296.3.e.a.161.2		2	252.131	odd	6
1728.3.q.a.449.1		2	168.5	even	6
1728.3.q.a.1601.1		2	504.61	odd	6
1728.3.q.b.449.1		2	168.131	odd	6
1728.3.q.b.1601.1		2	504.187	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.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q-1.73205i q^{2} +(1.50000 - 2.59808i) q^{3} +1.00000 q^{4} +(3.00000 - 1.73205i) q^{5} +(-4.50000 - 2.59808i) q^{6} -8.66025i q^{8} +(-4.50000 - 7.79423i) q^{9} +(-3.00000 - 5.19615i) q^{10} +(1.50000 + 0.866025i) q^{11} +(1.50000 - 2.59808i) q^{12} +(-2.00000 + 3.46410i) q^{13} -10.3923i q^{15} -11.0000 q^{16} +(-13.5000 + 7.79423i) q^{17} +(-13.5000 + 7.79423i) q^{18} +(5.50000 - 9.52628i) q^{19} +(3.00000 - 1.73205i) q^{20} +(1.50000 - 2.59808i) q^{22} +(24.0000 - 13.8564i) q^{23} +(-22.5000 - 12.9904i) q^{24} +(-6.50000 + 11.2583i) q^{25} +(6.00000 + 3.46410i) q^{26} -27.0000 q^{27} +(39.0000 - 22.5167i) q^{29} -18.0000 q^{30} -32.0000 q^{31} -15.5885i q^{32} +(4.50000 - 2.59808i) q^{33} +(13.5000 + 23.3827i) q^{34} +(-4.50000 - 7.79423i) q^{36} +(17.0000 - 29.4449i) q^{37} +(-16.5000 - 9.52628i) q^{38} +(6.00000 + 10.3923i) q^{39} +(-15.0000 - 25.9808i) q^{40} +(10.5000 + 6.06218i) q^{41} +(30.5000 + 52.8275i) q^{43} +(1.50000 + 0.866025i) q^{44} +(-27.0000 - 15.5885i) q^{45} +(-24.0000 - 41.5692i) q^{46} +48.4974i q^{47} +(-16.5000 + 28.5788i) q^{48} +(19.5000 + 11.2583i) q^{50} +46.7654i q^{51} +(-2.00000 + 3.46410i) q^{52} +46.7654i q^{54} +6.00000 q^{55} +(-16.5000 - 28.5788i) q^{57} +(-39.0000 - 67.5500i) q^{58} +50.2295i q^{59} -10.3923i q^{60} -56.0000 q^{61} +55.4256i q^{62} -71.0000 q^{64} +13.8564i q^{65} +(-4.50000 - 7.79423i) q^{66} -31.0000 q^{67} +(-13.5000 + 7.79423i) q^{68} -83.1384i q^{69} -31.1769i q^{71} +(-67.5000 + 38.9711i) q^{72} +(32.5000 + 56.2917i) q^{73} +(-51.0000 - 29.4449i) q^{74} +(19.5000 + 33.7750i) q^{75} +(5.50000 - 9.52628i) q^{76} +(18.0000 - 10.3923i) q^{78} +38.0000 q^{79} +(-33.0000 + 19.0526i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(10.5000 - 18.1865i) q^{82} +(42.0000 - 24.2487i) q^{83} +(-27.0000 + 46.7654i) q^{85} +(91.5000 - 52.8275i) q^{86} -135.100i q^{87} +(7.50000 - 12.9904i) q^{88} +(108.000 + 62.3538i) q^{89} +(-27.0000 + 46.7654i) q^{90} +(24.0000 - 13.8564i) q^{92} +(-48.0000 + 83.1384i) q^{93} +84.0000 q^{94} -38.1051i q^{95} +(-40.5000 - 23.3827i) q^{96} +(-57.5000 - 99.5929i) q^{97} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + 2 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^9	\( 2 q + 3 q^{3} + 2 q^{4} + 6 q^{5} - 9 q^{6} - 9 q^{9} - 6 q^{10} + 3 q^{11} + 3 q^{12} - 4 q^{13} - 22 q^{16} - 27 q^{17} - 27 q^{18} + 11 q^{19} + 6 q^{20} + 3 q^{22} + 48 q^{23} - 45 q^{24} - 13 q^{25} + 12 q^{26} - 54 q^{27} + 78 q^{29} - 36 q^{30} - 64 q^{31} + 9 q^{33} + 27 q^{34} - 9 q^{36} + 34 q^{37} - 33 q^{38} + 12 q^{39} - 30 q^{40} + 21 q^{41} + 61 q^{43} + 3 q^{44} - 54 q^{45} - 48 q^{46} - 33 q^{48} + 39 q^{50} - 4 q^{52} + 12 q^{55} - 33 q^{57} - 78 q^{58} - 112 q^{61} - 142 q^{64} - 9 q^{66} - 62 q^{67} - 27 q^{68} - 135 q^{72} + 65 q^{73} - 102 q^{74} + 39 q^{75} + 11 q^{76} + 36 q^{78} + 76 q^{79} - 66 q^{80} - 81 q^{81} + 21 q^{82} + 84 q^{83} - 54 q^{85} + 183 q^{86} + 15 q^{88} + 216 q^{89} - 54 q^{90} + 48 q^{92} - 96 q^{93} + 168 q^{94} - 81 q^{96} - 115 q^{97}+O(q^{100}) \) 2 * q + 3 * q^3 + 2 * q^4 + 6 * q^5 - 9 * q^6 - 9 * q^9 - 6 * q^10 + 3 * q^11 + 3 * q^12 - 4 * q^13 - 22 * q^16 - 27 * q^17 - 27 * q^18 + 11 * q^19 + 6 * q^20 + 3 * q^22 + 48 * q^23 - 45 * q^24 - 13 * q^25 + 12 * q^26 - 54 * q^27 + 78 * q^29 - 36 * q^30 - 64 * q^31 + 9 * q^33 + 27 * q^34 - 9 * q^36 + 34 * q^37 - 33 * q^38 + 12 * q^39 - 30 * q^40 + 21 * q^41 + 61 * q^43 + 3 * q^44 - 54 * q^45 - 48 * q^46 - 33 * q^48 + 39 * q^50 - 4 * q^52 + 12 * q^55 - 33 * q^57 - 78 * q^58 - 112 * q^61 - 142 * q^64 - 9 * q^66 - 62 * q^67 - 27 * q^68 - 135 * q^72 + 65 * q^73 - 102 * q^74 + 39 * q^75 + 11 * q^76 + 36 * q^78 + 76 * q^79 - 66 * q^80 - 81 * q^81 + 21 * q^82 + 84 * q^83 - 54 * q^85 + 183 * q^86 + 15 * q^88 + 216 * q^89 - 54 * q^90 + 48 * q^92 - 96 * q^93 + 168 * q^94 - 81 * q^96 - 115 * q^97

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