LMFDB - Embedded newform 441.3.n.b.128.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(128,441)]

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, 2]))

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

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

chi := DirichletCharacter("441.128");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.n (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 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			128.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	441.128
Dual form			441.3.n.b.410.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(4.50000 - 2.59808i) q^{6} +8.66025i q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(4.50000 - 2.59808i) q^{6} +8.66025i q^{8} +9.00000 q^{9} +(3.00000 + 5.19615i) q^{10} +1.73205i q^{11} +(-1.50000 + 2.59808i) q^{12} +(2.00000 + 3.46410i) q^{13} +10.3923i q^{15} +(5.50000 + 9.52628i) 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} -27.7128i q^{23} +25.9808i q^{24} +13.0000 q^{25} +(6.00000 + 3.46410i) q^{26} +27.0000 q^{27} +(39.0000 + 22.5167i) q^{29} +(9.00000 + 15.5885i) q^{30} +(-16.0000 + 27.7128i) q^{31} +(-13.5000 - 7.79423i) q^{32} +5.19615i q^{33} +(-13.5000 + 23.3827i) q^{34} +(-4.50000 + 7.79423i) q^{36} +(17.0000 - 29.4449i) q^{37} +19.0526i q^{38} +(6.00000 + 10.3923i) q^{39} -30.0000 q^{40} +(-10.5000 + 6.06218i) q^{41} +(30.5000 - 52.8275i) q^{43} +(-1.50000 - 0.866025i) q^{44} +31.1769i q^{45} +(-24.0000 - 41.5692i) q^{46} +(42.0000 - 24.2487i) q^{47} +(16.5000 + 28.5788i) q^{48} +(19.5000 - 11.2583i) q^{50} +(-40.5000 + 23.3827i) q^{51} -4.00000 q^{52} +(40.5000 - 23.3827i) q^{54} -6.00000 q^{55} +(-16.5000 + 28.5788i) q^{57} +78.0000 q^{58} +(-43.5000 - 25.1147i) q^{59} +(-9.00000 - 5.19615i) q^{60} +(-28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 + 6.92820i) q^{65} +(4.50000 + 7.79423i) q^{66} +(15.5000 - 26.8468i) q^{67} -15.5885i q^{68} -83.1384i q^{69} +31.1769i q^{71} +77.9423i q^{72} +(-32.5000 - 56.2917i) q^{73} -58.8897i q^{74} +39.0000 q^{75} +(-5.50000 - 9.52628i) q^{76} +(18.0000 + 10.3923i) q^{78} +(-19.0000 - 32.9090i) q^{79} +(-33.0000 + 19.0526i) q^{80} +81.0000 q^{81} +(-10.5000 + 18.1865i) q^{82} +(-42.0000 - 24.2487i) q^{83} +(-27.0000 - 46.7654i) q^{85} -105.655i q^{86} +(117.000 + 67.5500i) q^{87} -15.0000 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} +(42.0000 - 72.7461i) q^{94} +(-33.0000 - 19.0526i) 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^{2} + 6 q^{3} - q^{4} + 9 q^{6} + 18 q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 6 * q^3 - q^4 + 9 * q^6 + 18 * q^9	$ 2 q + 3 q^{2} + 6 q^{3} - q^{4} + 9 q^{6} + 18 q^{9} + 6 q^{10} - 3 q^{12} + 4 q^{13} + 11 q^{16} - 27 q^{17} + 27 q^{18} - 11 q^{19} - 6 q^{20} + 3 q^{22} + 26 q^{25} + 12 q^{26} + 54 q^{27} + 78 q^{29} + 18 q^{30} - 32 q^{31} - 27 q^{32} - 27 q^{34} - 9 q^{36} + 34 q^{37} + 12 q^{39} - 60 q^{40} - 21 q^{41} + 61 q^{43} - 3 q^{44} - 48 q^{46} + 84 q^{47} + 33 q^{48} + 39 q^{50} - 81 q^{51} - 8 q^{52} + 81 q^{54} - 12 q^{55} - 33 q^{57} + 156 q^{58} - 87 q^{59} - 18 q^{60} - 56 q^{61} - 142 q^{64} - 24 q^{65} + 9 q^{66} + 31 q^{67} - 65 q^{73} + 78 q^{75} - 11 q^{76} + 36 q^{78} - 38 q^{79} - 66 q^{80} + 162 q^{81} - 21 q^{82} - 84 q^{83} - 54 q^{85} + 234 q^{87} - 30 q^{88} + 216 q^{89} + 54 q^{90} + 48 q^{92} - 96 q^{93} + 84 q^{94} - 66 q^{95} - 81 q^{96} + 115 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 + 6 * q^3 - q^4 + 9 * q^6 + 18 * q^9 + 6 * q^10 - 3 * q^12 + 4 * q^13 + 11 * q^16 - 27 * q^17 + 27 * q^18 - 11 * q^19 - 6 * q^20 + 3 * q^22 + 26 * q^25 + 12 * q^26 + 54 * q^27 + 78 * q^29 + 18 * q^30 - 32 * q^31 - 27 * q^32 - 27 * q^34 - 9 * q^36 + 34 * q^37 + 12 * q^39 - 60 * q^40 - 21 * q^41 + 61 * q^43 - 3 * q^44 - 48 * q^46 + 84 * q^47 + 33 * q^48 + 39 * q^50 - 81 * q^51 - 8 * q^52 + 81 * q^54 - 12 * q^55 - 33 * q^57 + 156 * q^58 - 87 * q^59 - 18 * q^60 - 56 * q^61 - 142 * q^64 - 24 * q^65 + 9 * q^66 + 31 * q^67 - 65 * q^73 + 78 * q^75 - 11 * q^76 + 36 * q^78 - 38 * q^79 - 66 * q^80 + 162 * q^81 - 21 * q^82 - 84 * q^83 - 54 * q^85 + 234 * q^87 - 30 * q^88 + 216 * q^89 + 54 * q^90 + 48 * q^92 - 96 * q^93 + 84 * q^94 - 66 * q^95 - 81 * q^96 + 115 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.50000	−	0.866025i	0.750000	−	0.433013i	−0.0756939	−	0.997131i	$-0.524117\pi$
$2$	1.50000	−	0.866025i	0.750000	−	0.433013i	0.825694	+	0.564118i	$0.190784\pi$
$3$	3.00000			1.00000
$3$	3.00000			1.00000
$4$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$5$			3.46410i			0.692820i	0.938083	+	0.346410i	$0.112599\pi$
$5$			3.46410i			0.692820i	−0.938083	+	0.346410i	$0.887401\pi$
$6$	4.50000	−	2.59808i	0.750000	−	0.433013i
$7$		0			0
$7$		0			0
$8$			8.66025i			1.08253i
$9$	9.00000			1.00000
$10$	3.00000	+	5.19615i	0.300000	+	0.519615i
$11$			1.73205i			0.157459i	0.996896	+	0.0787296i	$0.0250864\pi$
$11$			1.73205i			0.157459i	−0.996896	+	0.0787296i	$0.974914\pi$
$12$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$13$	2.00000	+	3.46410i	0.153846	+	0.266469i	0.932638	−	0.360813i	$-0.117501\pi$
$13$	2.00000	+	3.46410i	0.153846	+	0.266469i	−0.778792	+	0.627282i	$0.784167\pi$
$14$		0			0
$15$			10.3923i			0.692820i
$16$	5.50000	+	9.52628i	0.343750	+	0.595392i
$17$	−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	−0.973684	−	0.227901i	$-0.926814\pi$
$19$	−5.50000	+	9.52628i	−0.289474	+	0.501383i	0.684211	+	0.729285i	$0.260147\pi$
$20$	−3.00000	−	1.73205i	−0.150000	−	0.0866025i
$21$		0			0
$22$	1.50000	+	2.59808i	0.0681818	+	0.118094i
$23$		−	27.7128i		−	1.20490i	−0.798155	−	0.602452i	$-0.794190\pi$
$23$		−	27.7128i		−	1.20490i	0.798155	−	0.602452i	$-0.205810\pi$
$24$			25.9808i			1.08253i
$25$	13.0000			0.520000
$26$	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	0.987511	−	0.157547i	$-0.0503586\pi$
$29$	39.0000	+	22.5167i	1.34483	+	0.776437i	0.357316	+	0.933984i	$0.383692\pi$
$30$	9.00000	+	15.5885i	0.300000	+	0.519615i
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	0.483696	+	0.875236i	$0.339294\pi$
$31$	−16.0000	+	27.7128i	−0.516129	+	0.893962i	−0.999825	+	0.0187254i	$0.994039\pi$
$32$	−13.5000	−	7.79423i	−0.421875	−	0.243570i
$33$			5.19615i			0.157459i
$34$	−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	$0.0147098\pi$
$38$			19.0526i			0.501383i
$39$	6.00000	+	10.3923i	0.153846	+	0.266469i
$40$	−30.0000			−0.750000
$41$	−10.5000	+	6.06218i	−0.256098	+	0.147858i	−0.622553	−	0.782578i	$-0.713905\pi$
$41$	−10.5000	+	6.06218i	−0.256098	+	0.147858i	0.366456	+	0.930436i	$0.380571\pi$
$42$		0			0
$43$	30.5000	−	52.8275i	0.709302	−	1.22855i	−0.255814	−	0.966726i	$-0.582343\pi$
$43$	30.5000	−	52.8275i	0.709302	−	1.22855i	0.965116	−	0.261822i	$-0.0843232\pi$
$44$	−1.50000	−	0.866025i	−0.0340909	−	0.0196824i
$45$			31.1769i			0.692820i
$46$	−24.0000	−	41.5692i	−0.521739	−	0.903679i
$47$	42.0000	−	24.2487i	0.893617	−	0.515930i	0.0184931	−	0.999829i	$-0.494113\pi$
$47$	42.0000	−	24.2487i	0.893617	−	0.515930i	0.875124	+	0.483899i	$0.160780\pi$
$48$	16.5000	+	28.5788i	0.343750	+	0.595392i
$49$		0			0
$50$	19.5000	−	11.2583i	0.390000	−	0.225167i
$51$	−40.5000	+	23.3827i	−0.794118	+	0.458484i
$52$	−4.00000			−0.0769231
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	40.5000	−	23.3827i	0.750000	−	0.433013i
$55$	−6.00000			−0.109091
$56$		0			0
$57$	−16.5000	+	28.5788i	−0.289474	+	0.501383i
$58$	78.0000			1.34483
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	0.0837943	−	0.996483i	$-0.473296\pi$
$59$	−43.5000	−	25.1147i	−0.737288	−	0.425674i	−0.821082	+	0.570810i	$0.806629\pi$
$60$	−9.00000	−	5.19615i	−0.150000	−	0.0866025i
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	0.539893	−	0.841734i	$-0.318465\pi$
$61$	−28.0000	−	48.4974i	−0.459016	−	0.795040i	−0.998909	+	0.0466940i	$0.985131\pi$
$62$			55.4256i			0.893962i
$63$		0			0
$64$	−71.0000			−1.10938
$65$	−12.0000	+	6.92820i	−0.184615	+	0.106588i
$66$	4.50000	+	7.79423i	0.0681818	+	0.118094i
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	−0.726860	−	0.686785i	$-0.759021\pi$
$67$	15.5000	−	26.8468i	0.231343	−	0.400698i	0.958204	+	0.286087i	$0.0923546\pi$
$68$		−	15.5885i		−	0.229242i
$69$		−	83.1384i		−	1.20490i
$70$		0			0
$71$			31.1769i			0.439111i	0.975600	+	0.219556i	$0.0704608\pi$
$71$			31.1769i			0.439111i	−0.975600	+	0.219556i	$0.929539\pi$
$72$			77.9423i			1.08253i
$73$	−32.5000	−	56.2917i	−0.445205	−	0.771119i	0.552861	−	0.833273i	$-0.313536\pi$
$73$	−32.5000	−	56.2917i	−0.445205	−	0.771119i	−0.998067	+	0.0621550i	$0.980203\pi$
$74$		−	58.8897i		−	0.795807i
$75$	39.0000			0.520000
$76$	−5.50000	−	9.52628i	−0.0723684	−	0.125346i
$77$		0			0
$78$	18.0000	+	10.3923i	0.230769	+	0.133235i
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	0.720352	−	0.693608i	$-0.243980\pi$
$79$	−19.0000	−	32.9090i	−0.240506	−	0.416569i	−0.960859	+	0.277039i	$0.910647\pi$
$80$	−33.0000	+	19.0526i	−0.412500	+	0.238157i
$81$	81.0000			1.00000
$82$	−10.5000	+	18.1865i	−0.128049	+	0.221787i
$83$	−42.0000	−	24.2487i	−0.506024	−	0.292153i	0.225174	−	0.974319i	$-0.427705\pi$
$83$	−42.0000	−	24.2487i	−0.506024	−	0.292153i	−0.731198	+	0.682165i	$0.761038\pi$
$84$		0			0
$85$	−27.0000	−	46.7654i	−0.317647	−	0.550181i
$86$		−	105.655i		−	1.22855i
$87$	117.000	+	67.5500i	1.34483	+	0.776437i
$88$	−15.0000			−0.170455
$89$	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
$94$	42.0000	−	72.7461i	0.446809	−	0.773895i
$95$	−33.0000	−	19.0526i	−0.347368	−	0.200553i
$96$	−40.5000	−	23.3827i	−0.421875	−	0.243570i
$97$	57.5000	−	99.5929i	0.592784	−	1.02673i	−0.401072	−	0.916047i	$-0.631362\pi$
$97$	57.5000	−	99.5929i	0.592784	−	1.02673i	0.993856	−	0.110685i	$-0.0353044\pi$
$98$		0			0
$99$			15.5885i			0.157459i
$100$	−6.50000	+	11.2583i	−0.0650000	+	0.112583i
$101$		−	45.0333i		−	0.445874i	−0.974833	−	0.222937i	$-0.928436\pi$
$101$		−	45.0333i		−	0.445874i	0.974833	−	0.222937i	$-0.0715645\pi$
$102$	−40.5000	+	70.1481i	−0.397059	+	0.687726i
$103$	−40.0000			−0.388350			−0.194175	−	0.980967i	$-0.562203\pi$
$103$	−40.0000			−0.388350			−0.194175	+	0.980967i	$0.562203\pi$
$104$	−30.0000	+	17.3205i	−0.288462	+	0.166543i
$105$		0			0
$106$		0			0
$107$	−121.500	−	70.1481i	−1.13551	−	0.655589i	−0.190198	−	0.981746i	$-0.560913\pi$
$107$	−121.500	−	70.1481i	−1.13551	−	0.655589i	−0.945316	+	0.326156i	$0.894246\pi$
$108$	−13.5000	+	23.3827i	−0.125000	+	0.216506i
$109$	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	$0.756667\pi$
$110$	−9.00000	+	5.19615i	−0.0818182	+	0.0472377i
$111$	51.0000	−	88.3346i	0.459459	−	0.795807i
$112$		0			0
$113$	−78.0000	+	45.0333i	−0.690265	+	0.398525i	−0.803711	−	0.595019i	$-0.797144\pi$
$113$	−78.0000	+	45.0333i	−0.690265	+	0.398525i	0.113446	+	0.993544i	$0.463811\pi$
$114$			57.1577i			0.501383i
$115$	96.0000			0.834783
$116$	−39.0000	+	22.5167i	−0.336207	+	0.194109i
$117$	18.0000	+	31.1769i	0.153846	+	0.266469i
$118$	−87.0000			−0.737288
$119$		0			0
$120$	−90.0000			−0.750000
$121$	118.000			0.975207
$122$	−84.0000	−	48.4974i	−0.688525	−	0.397520i
$123$	−31.5000	+	18.1865i	−0.256098	+	0.147858i
$124$	−16.0000	−	27.7128i	−0.129032	−	0.223490i
$125$			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	$0.520064\pi$
$128$	−52.5000	+	30.3109i	−0.410156	+	0.236804i
$129$	91.5000	−	158.483i	0.709302	−	1.22855i
$130$	−12.0000	+	20.7846i	−0.0923077	+	0.159882i
$131$			159.349i			1.21640i	0.793783	+	0.608201i	$0.208109\pi$
$131$			159.349i			1.21640i	−0.793783	+	0.608201i	$0.791891\pi$
$132$	−4.50000	−	2.59808i	−0.0340909	−	0.0196824i
$133$		0			0
$134$		−	53.6936i		−	0.400698i
$135$			93.5307i			0.692820i
$136$	−67.5000	−	116.913i	−0.496324	−	0.859658i
$137$			188.794i			1.37806i	0.724735	+	0.689028i	$0.241962\pi$
$137$			188.794i			1.37806i	−0.724735	+	0.689028i	$0.758038\pi$
$138$	−72.0000	−	124.708i	−0.521739	−	0.903679i
$139$	−2.50000	−	4.33013i	−0.0179856	−	0.0311520i	0.856893	−	0.515495i	$-0.172392\pi$
$139$	−2.50000	−	4.33013i	−0.0179856	−	0.0311520i	−0.874878	+	0.484343i	$0.839059\pi$
$140$		0			0
$141$	126.000	−	72.7461i	0.893617	−	0.515930i
$142$	27.0000	+	46.7654i	0.190141	+	0.329334i
$143$	−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
$149$		−	152.420i		−	1.02296i	−0.859296	−	0.511478i	$-0.829098\pi$
$149$		−	152.420i		−	1.02296i	0.859296	−	0.511478i	$-0.170902\pi$
$150$	58.5000	−	33.7750i	0.390000	−	0.225167i
$151$	20.0000			0.132450			0.0662252	−	0.997805i	$-0.478904\pi$
$151$	20.0000			0.132450			0.0662252	+	0.997805i	$0.478904\pi$
$152$	−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
$156$	−12.0000			−0.0769231
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	−0.795276	−	0.606248i	$-0.792674\pi$
$157$	20.0000	−	34.6410i	0.127389	−	0.220643i	0.922664	+	0.385605i	$0.126007\pi$
$158$	−57.0000	−	32.9090i	−0.360759	−	0.208285i
$159$		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	$0.0612507\pi$
$164$		−	12.1244i		−	0.0739290i
$165$	−18.0000			−0.109091
$166$	−84.0000			−0.506024
$167$	165.000	−	95.2628i	0.988024	−	0.570436i	0.0833409	−	0.996521i	$-0.473441\pi$
$167$	165.000	−	95.2628i	0.988024	−	0.570436i	0.904683	+	0.426085i	$0.140108\pi$
$168$		0			0
$169$	76.5000	−	132.502i	0.452663	−	0.784035i
$170$	−81.0000	−	46.7654i	−0.476471	−	0.275090i
$171$	−49.5000	+	85.7365i	−0.289474	+	0.501383i
$172$	30.5000	+	52.8275i	0.177326	+	0.307137i
$173$	−201.000	+	116.047i	−1.16185	+	0.670794i	−0.951747	−	0.306885i	$-0.900713\pi$
$173$	−201.000	+	116.047i	−1.16185	+	0.670794i	−0.210103	+	0.977679i	$0.567380\pi$
$174$	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
$178$	216.000			1.21348
$179$	−54.0000	+	31.1769i	−0.301676	+	0.174173i	−0.643196	−	0.765702i	$-0.722392\pi$
$179$	−54.0000	+	31.1769i	−0.301676	+	0.174173i	0.341520	+	0.939875i	$0.389058\pi$
$180$	−27.0000	−	15.5885i	−0.150000	−	0.0866025i
$181$	−232.000			−1.28177			−0.640884	−	0.767638i	$-0.721432\pi$
$181$	−232.000			−1.28177			−0.640884	+	0.767638i	$0.721432\pi$
$182$		0			0
$183$	−84.0000	−	145.492i	−0.459016	−	0.795040i
$184$	240.000			1.30435
$185$	102.000	+	58.8897i	0.551351	+	0.318323i
$186$			166.277i			0.893962i
$187$	−13.5000	−	23.3827i	−0.0721925	−	0.125041i
$188$			48.4974i			0.257965i
$189$		0			0
$190$	−66.0000			−0.347368
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.923308	−	0.384060i	$-0.874525\pi$
$191$	−201.000	+	116.047i	−1.05236	+	0.607578i	−0.129048	+	0.991638i	$0.541192\pi$
$192$	−213.000			−1.10938
$193$	132.500	−	229.497i	0.686528	−	1.18910i	−0.286425	−	0.958103i	$-0.592467\pi$
$193$	132.500	−	229.497i	0.686528	−	1.18910i	0.972954	−	0.231000i	$-0.0741996\pi$
$194$		−	199.186i		−	1.02673i
$195$	−36.0000	+	20.7846i	−0.184615	+	0.106588i
$196$		0			0
$197$		−	124.708i		−	0.633034i	−0.948587	−	0.316517i	$-0.897487\pi$
$197$		−	124.708i		−	0.633034i	0.948587	−	0.316517i	$-0.102513\pi$
$198$	13.5000	+	23.3827i	0.0681818	+	0.118094i
$199$	−145.000	−	251.147i	−0.728643	−	1.26205i	−0.957457	−	0.288577i	$-0.906818\pi$
$199$	−145.000	−	251.147i	−0.728643	−	1.26205i	0.228814	−	0.973470i	$-0.426515\pi$
$200$			112.583i			0.562917i
$201$	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
$205$	−21.0000	−	36.3731i	−0.102439	−	0.177430i
$206$	−60.0000	+	34.6410i	−0.291262	+	0.168160i
$207$		−	249.415i		−	1.20490i
$208$	−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	0.955642	−	0.294532i	$-0.0951637\pi$
$211$	47.0000	+	81.4064i	0.222749	+	0.385812i	−0.732893	+	0.680344i	$0.761830\pi$
$212$		0			0
$213$			93.5307i			0.439111i
$214$	−243.000			−1.13551
$215$	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
$219$	−97.5000	−	168.875i	−0.445205	−	0.771119i
$220$	3.00000	−	5.19615i	0.0136364	−	0.0236189i
$221$	−54.0000	−	31.1769i	−0.244344	−	0.141072i
$222$		−	176.669i		−	0.795807i
$223$	26.0000	−	45.0333i	0.116592	−	0.201943i	−0.801823	−	0.597562i	$-0.796136\pi$
$223$	26.0000	−	45.0333i	0.116592	−	0.201943i	0.918415	+	0.395618i	$0.129470\pi$
$224$		0			0
$225$	117.000			0.520000
$226$	−78.0000	+	135.100i	−0.345133	+	0.597787i
$227$			188.794i			0.831690i	0.909436	+	0.415845i	$0.136514\pi$
$227$			188.794i			0.831690i	−0.909436	+	0.415845i	$0.863486\pi$
$228$	−16.5000	−	28.5788i	−0.0723684	−	0.125346i
$229$	266.000			1.16157			0.580786	−	0.814056i	$-0.302745\pi$
$229$	266.000			1.16157			0.580786	+	0.814056i	$0.302745\pi$
$230$	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	0.826856	−	0.562414i	$-0.190127\pi$
$233$	175.500	+	101.325i	0.753219	+	0.434871i	−0.0736369	+	0.997285i	$0.523461\pi$
$234$	54.0000	+	31.1769i	0.230769	+	0.133235i
$235$	84.0000	+	145.492i	0.357447	+	0.619116i
$236$	43.5000	−	25.1147i	0.184322	−	0.106418i
$237$	−57.0000	−	98.7269i	−0.240506	−	0.416569i
$238$		0			0
$239$	−348.000	+	200.918i	−1.45607	+	0.840661i	−0.998815	−	0.0486764i	$-0.984500\pi$
$239$	−348.000	+	200.918i	−1.45607	+	0.840661i	−0.457252	+	0.889337i	$0.651166\pi$
$240$	−99.0000	+	57.1577i	−0.412500	+	0.238157i
$241$	119.000			0.493776			0.246888	−	0.969044i	$-0.420592\pi$
$241$	119.000			0.493776			0.246888	+	0.969044i	$0.420592\pi$
$242$	177.000	−	102.191i	0.731405	−	0.422277i
$243$	243.000			1.00000
$244$	56.0000			0.229508
$245$		0			0
$246$	−31.5000	+	54.5596i	−0.128049	+	0.221787i
$247$	−44.0000			−0.178138
$248$	−240.000	−	138.564i	−0.967742	−	0.558726i
$249$	−126.000	−	72.7461i	−0.506024	−	0.292153i
$250$	114.000	+	197.454i	0.456000	+	0.789815i
$251$			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
$254$	−24.0000	+	13.8564i	−0.0944882	+	0.0545528i
$255$	−81.0000	−	140.296i	−0.317647	−	0.550181i
$256$	89.5000	−	155.019i	0.349609	−	0.605541i
$257$			174.937i			0.680689i	0.940301	+	0.340345i	$0.110544\pi$
$257$			174.937i			0.680689i	−0.940301	+	0.340345i	$0.889456\pi$
$258$		−	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
$263$		−	45.0333i		−	0.171229i	−0.996328	−	0.0856147i	$-0.972715\pi$
$263$		−	45.0333i		−	0.171229i	0.996328	−	0.0856147i	$-0.0272854\pi$
$264$	−45.0000			−0.170455
$265$		0			0
$266$		0			0
$267$	324.000	+	187.061i	1.21348	+	0.700605i
$268$	15.5000	+	26.8468i	0.0578358	+	0.100175i
$269$	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	−0.505515	−	0.862818i	$-0.668697\pi$
$271$	134.000	−	232.095i	0.494465	−	0.856438i	0.999980	+	0.00637958i	$0.00203070\pi$
$272$	−148.500	−	85.7365i	−0.545956	−	0.315208i
$273$		0			0
$274$	163.500	+	283.190i	0.596715	+	1.03354i
$275$			22.5167i			0.0818788i
$276$	72.0000	+	41.5692i	0.260870	+	0.150613i
$277$	56.0000			0.202166			0.101083	−	0.994878i	$-0.467769\pi$
$277$	56.0000			0.202166			0.101083	+	0.994878i	$0.467769\pi$
$278$	−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	0.423402	−	0.905942i	$-0.360836\pi$
$281$	−42.0000	−	24.2487i	−0.149466	−	0.0862943i	−0.572868	+	0.819648i	$0.694169\pi$
$282$	126.000	−	218.238i	0.446809	−	0.773895i
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	0.319634	+	0.947541i	$0.396440\pi$
$283$	−187.000	+	323.894i	−0.660777	+	1.14450i	−0.980412	+	0.196959i	$0.936893\pi$
$284$	−27.0000	−	15.5885i	−0.0950704	−	0.0548889i
$285$	−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
$290$			270.200i			0.931724i
$291$	172.500	−	298.779i	0.592784	−	1.02673i
$292$	65.0000			0.222603
$293$	219.000	−	126.440i	0.747440	−	0.431535i	−0.0773280	−	0.997006i	$-0.524639\pi$
$293$	219.000	−	126.440i	0.747440	−	0.431535i	0.824768	+	0.565471i	$0.191306\pi$
$294$		0			0
$295$	87.0000	−	150.688i	0.294915	−	0.510808i
$296$	255.000	+	147.224i	0.861486	+	0.497379i
$297$			46.7654i			0.157459i
$298$	−132.000	−	228.631i	−0.442953	−	0.767217i
$299$	96.0000	−	55.4256i	0.321070	−	0.185370i
$300$	−19.5000	+	33.7750i	−0.0650000	+	0.112583i
$301$		0			0
$302$	30.0000	−	17.3205i	0.0993377	−	0.0573527i
$303$		−	135.100i		−	0.445874i
$304$	−121.000			−0.398026
$305$	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	$-0.165355\pi$
$307$	533.000			1.73616			0.868078	+	0.496428i	$0.165355\pi$
$308$		0			0
$309$	−120.000			−0.388350
$310$	−192.000			−0.619355
$311$	213.000	+	122.976i	0.684887	+	0.395420i	0.801694	−	0.597735i	$-0.203932\pi$
$311$	213.000	+	122.976i	0.684887	+	0.395420i	−0.116806	+	0.993155i	$0.537266\pi$
$312$	−90.0000	+	51.9615i	−0.288462	+	0.166543i
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	0.715257	−	0.698862i	$-0.246310\pi$
$313$	−77.5000	−	134.234i	−0.247604	−	0.428862i	−0.962860	+	0.269999i	$0.912976\pi$
$314$		−	69.2820i		−	0.220643i
$315$		0			0
$316$	38.0000			0.120253
$317$	42.0000	−	24.2487i	0.132492	−	0.0764944i	−0.432289	−	0.901735i	$-0.642294\pi$
$317$	42.0000	−	24.2487i	0.132492	−	0.0764944i	0.564781	+	0.825241i	$0.308961\pi$
$318$		0			0
$319$	−39.0000	+	67.5500i	−0.122257	+	0.211755i
$320$		−	245.951i		−	0.768598i
$321$	−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
$326$		−	183.597i		−	0.563182i
$327$	78.0000	+	135.100i	0.238532	+	0.413150i
$328$	−52.5000	−	90.9327i	−0.160061	−	0.277234i
$329$		0			0
$330$	−27.0000	+	15.5885i	−0.0818182	+	0.0472377i
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	0.864511	−	0.502614i	$-0.167628\pi$
$331$	−1.00000	−	1.73205i	−0.00302115	−	0.00523278i	−0.867532	+	0.497381i	$0.834295\pi$
$332$	42.0000	−	24.2487i	0.126506	−	0.0730383i
$333$	153.000	−	265.004i	0.459459	−	0.795807i
$334$	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	0.803234	−	0.595664i	$-0.203111\pi$
$337$	−38.5000	−	66.6840i	−0.114243	−	0.197875i	−0.917477	+	0.397789i	$0.869778\pi$
$338$		−	265.004i		−	0.784035i
$339$	−234.000	+	135.100i	−0.690265	+	0.398525i
$340$	54.0000			0.158824
$341$	−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
$345$	288.000			0.834783
$346$	−201.000	+	348.142i	−0.580925	+	1.00619i
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	0.352887	−	0.935666i	$-0.385200\pi$
$347$	−97.5000	−	56.2917i	−0.280980	−	0.162224i	−0.633867	+	0.773442i	$0.718533\pi$
$348$	−117.000	+	67.5500i	−0.336207	+	0.194109i
$349$	−208.000	+	360.267i	−0.595989	+	1.03228i	0.397418	+	0.917638i	$0.369906\pi$
$349$	−208.000	+	360.267i	−0.595989	+	1.03228i	−0.993407	+	0.114645i	$0.963427\pi$
$350$		0			0
$351$	54.0000	+	93.5307i	0.153846	+	0.266469i
$352$	13.5000	−	23.3827i	0.0383523	−	0.0664281i
$353$			1.73205i			0.00490666i	0.999997	+	0.00245333i	$0.000780920\pi$
$353$			1.73205i			0.00490666i	−0.999997	+	0.00245333i	$0.999219\pi$
$354$	−261.000			−0.737288
$355$	−108.000			−0.304225
$356$	−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	0.997039	−	0.0768913i	$-0.0244995\pi$
$359$	513.000	+	296.181i	1.42897	+	0.825016i	0.431930	+	0.901907i	$0.357833\pi$
$360$	−270.000			−0.750000
$361$	120.000	+	207.846i	0.332410	+	0.575751i
$362$	−348.000	+	200.918i	−0.961326	+	0.555022i
$363$	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
$367$	−358.000			−0.975477			−0.487738	−	0.872990i	$-0.662178\pi$
$367$	−358.000			−0.975477			−0.487738	+	0.872990i	$0.662178\pi$
$368$	264.000	−	152.420i	0.717391	−	0.414186i
$369$	−94.5000	+	54.5596i	−0.256098	+	0.147858i
$370$	204.000			0.551351
$371$		0			0
$372$	−48.0000	−	83.1384i	−0.129032	−	0.223490i
$373$	−580.000			−1.55496			−0.777480	−	0.628908i	$-0.783502\pi$
$373$	−580.000			−1.55496			−0.777480	+	0.628908i	$0.783502\pi$
$374$	−40.5000	−	23.3827i	−0.108289	−	0.0625206i
$375$			394.908i			1.05309i
$376$	210.000	+	363.731i	0.558511	+	0.967369i
$377$			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	$0.465075\pi$
$380$	33.0000	−	19.0526i	0.0868421	−	0.0501383i
$381$	−48.0000			−0.125984
$382$	−201.000	+	348.142i	−0.526178	+	0.911367i
$383$		−	557.720i		−	1.45619i	−0.685477	−	0.728094i	$-0.740406\pi$
$383$		−	557.720i		−	1.45619i	0.685477	−	0.728094i	$-0.259594\pi$
$384$	−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
$389$			516.151i			1.32687i	0.748235	+	0.663433i	$0.230901\pi$
$389$			516.151i			1.32687i	−0.748235	+	0.663433i	$0.769099\pi$
$390$	−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
$394$	−108.000	−	187.061i	−0.274112	−	0.474775i
$395$	114.000	−	65.8179i	0.288608	−	0.166628i
$396$	−13.5000	−	7.79423i	−0.0340909	−	0.0196824i
$397$	−181.000	+	313.501i	−0.455919	+	0.789676i	−0.998741	−	0.0501728i	$-0.984023\pi$
$397$	−181.000	+	313.501i	−0.455919	+	0.789676i	0.542821	+	0.839848i	$0.317356\pi$
$398$	−435.000	−	251.147i	−1.09296	−	0.631024i
$399$		0			0
$400$	71.5000	+	123.842i	0.178750	+	0.309604i
$401$			393.176i			0.980488i	0.871585	+	0.490244i	$0.163092\pi$
$401$			393.176i			0.980488i	−0.871585	+	0.490244i	$0.836908\pi$
$402$		−	161.081i		−	0.400698i
$403$	−128.000			−0.317618
$404$	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
$408$	−202.500	−	350.740i	−0.496324	−	0.859658i
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	−0.968905	−	0.247431i	$-0.920414\pi$
$409$	−110.500	+	191.392i	−0.270171	+	0.467950i	0.698734	+	0.715381i	$0.253747\pi$
$410$	−63.0000	−	36.3731i	−0.153659	−	0.0887148i
$411$			566.381i			1.37806i
$412$	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
$416$		−	62.3538i		−	0.149889i
$417$	−7.50000	−	12.9904i	−0.0179856	−	0.0311520i
$418$	−33.0000			−0.0789474
$419$	678.000	−	391.443i	1.61814	−	0.934233i	0.630737	−	0.775997i	$-0.282753\pi$
$419$	678.000	−	391.443i	1.61814	−	0.934233i	0.987401	−	0.158236i	$-0.0505807\pi$
$420$		0			0
$421$	341.000	−	590.629i	0.809976	−	1.40292i	−0.102903	−	0.994691i	$-0.532813\pi$
$421$	341.000	−	590.629i	0.809976	−	1.40292i	0.912880	−	0.408229i	$-0.133853\pi$
$422$	141.000	+	81.4064i	0.334123	+	0.192906i
$423$	378.000	−	218.238i	0.893617	−	0.515930i
$424$		0			0
$425$	−175.500	+	101.325i	−0.412941	+	0.238412i
$426$	81.0000	+	140.296i	0.190141	+	0.329334i
$427$		0			0
$428$	121.500	−	70.1481i	0.283879	−	0.163897i
$429$	−18.0000	+	10.3923i	−0.0419580	+	0.0242245i
$430$	366.000			0.851163
$431$	243.000	−	140.296i	0.563805	−	0.325513i	−0.190866	−	0.981616i	$-0.561130\pi$
$431$	243.000	−	140.296i	0.563805	−	0.325513i	0.754671	+	0.656103i	$0.227796\pi$
$432$	148.500	+	257.210i	0.343750	+	0.595392i
$433$	−295.000			−0.681293			−0.340647	−	0.940191i	$-0.610646\pi$
$433$	−295.000			−0.681293			−0.340647	+	0.940191i	$0.610646\pi$
$434$		0			0
$435$	−234.000	+	405.300i	−0.537931	+	0.931724i
$436$	−52.0000			−0.119266
$437$	264.000	+	152.420i	0.604119	+	0.348788i
$438$	−292.500	−	168.875i	−0.667808	−	0.385559i
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.791836	−	0.610734i	$-0.790874\pi$
$439$	−406.000	−	703.213i	−0.924829	−	1.60185i	−0.132993	−	0.991117i	$-0.542459\pi$
$440$		−	51.9615i		−	0.118094i
$441$		0			0
$442$	−108.000			−0.244344
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	−0.587038	−	0.809559i	$-0.699706\pi$
$443$	−79.5000	+	45.8993i	−0.179458	+	0.103610i	0.407580	+	0.913170i	$0.366373\pi$
$444$	51.0000	+	88.3346i	0.114865	+	0.198952i
$445$	−216.000	+	374.123i	−0.485393	+	0.840726i
$446$		−	90.0666i		−	0.201943i
$447$		−	457.261i		−	1.02296i
$448$		0			0
$449$			639.127i			1.42344i	0.702461	+	0.711722i	$0.252085\pi$
$449$			639.127i			1.42344i	−0.702461	+	0.711722i	$0.747915\pi$
$450$	175.500	−	101.325i	0.390000	−	0.225167i
$451$	−10.5000	−	18.1865i	−0.0232816	−	0.0403249i
$452$		−	90.0666i		−	0.199262i
$453$	60.0000			0.132450
$454$	163.500	+	283.190i	0.360132	+	0.623767i
$455$		0			0
$456$	−247.500	−	142.894i	−0.542763	−	0.313364i
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	0.828275	−	0.560322i	$-0.189323\pi$
$457$	−32.5000	−	56.2917i	−0.0711160	−	0.123176i	−0.899391	+	0.437146i	$0.855989\pi$
$458$	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	$-0.665475\pi$
$461$	−690.000	−	398.372i	−1.49675	−	0.864147i	−0.999993	+	0.00374501i	$0.998808\pi$
$462$		0			0
$463$	−367.000	−	635.663i	−0.792657	−	1.37292i	−0.924317	−	0.381627i	$-0.875364\pi$
$463$	−367.000	−	635.663i	−0.792657	−	1.37292i	0.131660	−	0.991295i	$-0.457969\pi$
$464$			495.367i			1.06760i
$465$	−288.000	−	166.277i	−0.619355	−	0.357585i
$466$	351.000			0.753219
$467$	−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
$472$	217.500	−	376.721i	0.460805	−	0.798138i
$473$	91.5000	+	52.8275i	0.193446	+	0.111686i
$474$	−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
$479$		−	606.218i		−	1.26559i	−0.774319	−	0.632795i	$-0.781908\pi$
$479$		−	606.218i		−	1.26559i	0.774319	−	0.632795i	$-0.218092\pi$
$480$	81.0000	−	140.296i	0.168750	−	0.292284i
$481$	136.000			0.282744
$482$	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	$0.798623\pi$
$488$	420.000	−	242.487i	0.860656	−	0.496900i
$489$	159.000	−	275.396i	0.325153	−	0.563182i
$490$		0			0
$491$	−199.500	+	115.181i	−0.406314	+	0.234585i	−0.689205	−	0.724567i	$-0.742040\pi$
$491$	−199.500	+	115.181i	−0.406314	+	0.234585i	0.282891	+	0.959152i	$0.408707\pi$
$492$		−	36.3731i		−	0.0739290i
$493$	−702.000			−1.42394
$494$	−66.0000	+	38.1051i	−0.133603	+	0.0771359i
$495$	−54.0000			−0.109091
$496$	−352.000			−0.709677
$497$		0			0
$498$	−252.000			−0.506024
$499$	−787.000			−1.57715			−0.788577	−	0.614936i	$-0.789182\pi$
$499$	−787.000			−1.57715			−0.788577	+	0.614936i	$0.789182\pi$
$500$	−114.000	−	65.8179i	−0.228000	−	0.131636i
$501$	495.000	−	285.788i	0.988024	−	0.570436i
$502$	337.500	+	584.567i	0.672311	+	1.16448i
$503$		−	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
$506$	72.0000	−	41.5692i	0.142292	−	0.0821526i
$507$	229.500	−	397.506i	0.452663	−	0.784035i
$508$	8.00000	−	13.8564i	0.0157480	−	0.0272764i
$509$		−	214.774i		−	0.421953i	−0.977491	−	0.210977i	$-0.932336\pi$
$509$		−	214.774i		−	0.421953i	0.977491	−	0.210977i	$-0.0676644\pi$
$510$	−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
$515$		−	138.564i		−	0.269056i
$516$	91.5000	+	158.483i	0.177326	+	0.307137i
$517$	42.0000	+	72.7461i	0.0812379	+	0.140708i
$518$		0			0
$519$	−603.000	+	348.142i	−1.16185	+	0.670794i
$520$	−60.0000	−	103.923i	−0.115385	−	0.199852i
$521$	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	$0.271031\pi$
$522$	702.000			1.34483
$523$	125.000	−	216.506i	0.239006	−	0.413970i	−0.721424	−	0.692494i	$-0.756512\pi$
$523$	125.000	−	216.506i	0.239006	−	0.413970i	0.960429	+	0.278524i	$0.0898452\pi$
$524$	−138.000	−	79.6743i	−0.263359	−	0.152050i
$525$		0			0
$526$	−39.0000	−	67.5500i	−0.0741445	−	0.128422i
$527$		−	498.831i		−	0.946548i
$528$	−49.5000	+	28.5788i	−0.0937500	+	0.0541266i
$529$	−239.000			−0.451796
$530$		0			0
$531$	−391.500	−	226.033i	−0.737288	−	0.425674i
$532$		0			0
$533$	−42.0000	−	24.2487i	−0.0787992	−	0.0454948i
$534$	648.000			1.21348
$535$	243.000	−	420.888i	0.454206	−	0.786707i
$536$	232.500	+	134.234i	0.433769	+	0.250436i
$537$	−162.000	+	93.5307i	−0.301676	+	0.174173i
$538$	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	$0.961540\pi$
$542$		−	464.190i		−	0.856438i
$543$	−696.000			−1.28177
$544$	243.000			0.446691
$545$	−156.000	+	90.0666i	−0.286239	+	0.165260i
$546$		0			0
$547$	−311.500	+	539.534i	−0.569470	+	0.986351i	0.427149	+	0.904181i	$0.359518\pi$
$547$	−311.500	+	539.534i	−0.569470	+	0.986351i	−0.996618	+	0.0821692i	$0.973815\pi$
$548$	−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
$551$	−429.000	+	247.683i	−0.778584	+	0.449516i
$552$	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
$556$	5.00000			0.00899281
$557$	−459.000	+	265.004i	−0.824057	+	0.475770i	−0.851814	−	0.523845i	$-0.824497\pi$
$557$	−459.000	+	265.004i	−0.824057	+	0.475770i	0.0277562	+	0.999615i	$0.491164\pi$
$558$			498.831i			0.893962i
$559$	244.000			0.436494
$560$		0			0
$561$	−40.5000	−	70.1481i	−0.0721925	−	0.125041i
$562$	−84.0000			−0.149466
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	0.410905	−	0.911678i	$-0.365213\pi$
$563$	−97.5000	−	56.2917i	−0.173179	−	0.0999852i	−0.584084	+	0.811693i	$0.698546\pi$
$564$			145.492i			0.257965i
$565$	−156.000	−	270.200i	−0.276106	−	0.478230i
$566$			647.787i			1.14450i
$567$		0			0
$568$	−270.000			−0.475352
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.906423	−	0.422372i	$-0.861198\pi$
$569$	−565.500	+	326.492i	−0.993849	+	0.573799i	−0.0874263	+	0.996171i	$0.527864\pi$
$570$	−198.000			−0.347368
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	−0.999660	−	0.0260926i	$-0.991694\pi$
$571$	−272.500	+	471.984i	−0.477233	+	0.826592i	0.522427	+	0.852684i	$0.325027\pi$
$572$		−	6.92820i		−	0.0121122i
$573$	−603.000	+	348.142i	−1.05236	+	0.607578i
$574$		0			0
$575$		−	360.267i		−	0.626551i
$576$	−639.000			−1.10938
$577$	435.500	+	754.308i	0.754766	+	1.30729i	0.945491	+	0.325650i	$0.105583\pi$
$577$	435.500	+	754.308i	0.754766	+	1.30729i	−0.190725	+	0.981644i	$0.561084\pi$
$578$			79.6743i			0.137845i
$579$	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	$-0.333803\pi$
$587$	−1.50000	−	0.866025i	−0.00255537	−	0.00147534i	−0.501277	+	0.865287i	$0.667136\pi$
$588$		0			0
$589$	−176.000	−	304.841i	−0.298812	−	0.517557i
$590$		−	301.377i		−	0.510808i
$591$		−	374.123i		−	0.633034i
$592$	374.000			0.631757
$593$	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
$597$	−435.000	−	753.442i	−0.728643	−	1.26205i
$598$	96.0000	−	166.277i	0.160535	−	0.278055i
$599$	−489.000	−	282.324i	−0.816361	−	0.471326i	0.0327992	−	0.999462i	$-0.489558\pi$
$599$	−489.000	−	282.324i	−0.816361	−	0.471326i	−0.849160	+	0.528136i	$0.822891\pi$
$600$			337.750i			0.562917i
$601$	−230.500	+	399.238i	−0.383527	+	0.664289i	−0.991564	−	0.129620i	$-0.958624\pi$
$601$	−230.500	+	399.238i	−0.383527	+	0.664289i	0.608036	+	0.793909i	$0.291958\pi$
$602$		0			0
$603$	139.500	−	241.621i	0.231343	−	0.400698i
$604$	−10.0000	+	17.3205i	−0.0165563	+	0.0286763i
$605$			408.764i			0.675643i
$606$	−117.000	−	202.650i	−0.193069	−	0.334406i
$607$	−112.000			−0.184514			−0.0922570	−	0.995735i	$-0.529408\pi$
$607$	−112.000			−0.184514			−0.0922570	+	0.995735i	$0.529408\pi$
$608$	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
$612$		−	140.296i		−	0.229242i
$613$	−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	$-0.429826\pi$
$614$	799.500	−	461.592i	1.30212	−	0.751778i
$615$	−63.0000	−	109.119i	−0.102439	−	0.177430i
$616$		0			0
$617$	−307.500	+	177.535i	−0.498379	+	0.287739i	−0.728044	−	0.685530i	$-0.759570\pi$
$617$	−307.500	+	177.535i	−0.498379	+	0.287739i	0.229665	+	0.973270i	$0.426237\pi$
$618$	−180.000	+	103.923i	−0.291262	+	0.168160i
$619$	−799.000			−1.29079			−0.645396	−	0.763848i	$-0.723308\pi$
$619$	−799.000			−1.29079			−0.645396	+	0.763848i	$0.723308\pi$
$620$	96.0000	−	55.4256i	0.154839	−	0.0893962i
$621$		−	748.246i		−	1.20490i
$622$	426.000			0.684887
$623$		0			0
$624$	−66.0000	+	114.315i	−0.105769	+	0.183198i
$625$	−131.000			−0.209600
$626$	−232.500	−	134.234i	−0.371406	−	0.214431i
$627$	−49.5000	−	28.5788i	−0.0789474	−	0.0455803i
$628$	20.0000	+	34.6410i	0.0318471	+	0.0551609i
$629$			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	$0.271535\pi$
$632$	285.000	−	164.545i	0.450949	−	0.260356i
$633$	141.000	+	244.219i	0.222749	+	0.385812i
$634$	42.0000	−	72.7461i	0.0662461	−	0.114742i
$635$		−	55.4256i		−	0.0872845i
$636$		0			0
$637$		0			0
$638$			135.100i			0.211755i
$639$			280.592i			0.439111i
$640$	−105.000	−	181.865i	−0.164062	−	0.284165i
$641$			375.855i			0.586357i	0.956058	+	0.293179i	$0.0947131\pi$
$641$			375.855i			0.586357i	−0.956058	+	0.293179i	$0.905287\pi$
$642$	−729.000			−1.13551
$643$	6.50000	+	11.2583i	0.0101089	+	0.0175091i	0.871036	−	0.491220i	$-0.163449\pi$
$643$	6.50000	+	11.2583i	0.0101089	+	0.0175091i	−0.860927	+	0.508729i	$0.830116\pi$
$644$		0			0
$645$	549.000	+	316.965i	0.851163	+	0.491419i
$646$	−148.500	−	257.210i	−0.229876	−	0.398157i
$647$	−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	$0.451035\pi$
$648$			701.481i			1.08253i
$649$	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
$653$			377.587i			0.578234i	0.957294	+	0.289117i	$0.0933617\pi$
$653$			377.587i			0.578234i	−0.957294	+	0.289117i	$0.906638\pi$
$654$	234.000	+	135.100i	0.357798	+	0.206575i
$655$	−552.000			−0.842748
$656$	−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	−0.313706	−	0.949520i	$-0.601571\pi$
$659$	−852.000	−	491.902i	−1.29287	−	0.746438i	−0.979162	+	0.203082i	$0.934904\pi$
$660$	9.00000	−	15.5885i	0.0136364	−	0.0236189i
$661$	191.000	−	330.822i	0.288956	−	0.500487i	−0.684605	−	0.728915i	$-0.740025\pi$
$661$	191.000	−	330.822i	0.288956	−	0.500487i	0.973561	+	0.228428i	$0.0733585\pi$
$662$	−3.00000	−	1.73205i	−0.00453172	−	0.00261639i
$663$	−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
$668$			190.526i			0.285218i
$669$	78.0000	−	135.100i	0.116592	−	0.201943i
$670$	186.000			0.277612
$671$	84.0000	−	48.4974i	0.125186	−	0.0722763i
$672$		0			0
$673$	−289.000	+	500.563i	−0.429421	+	0.743778i	−0.996822	−	0.0796633i	$-0.974615\pi$
$673$	−289.000	+	500.563i	−0.429421	+	0.743778i	0.567401	+	0.823441i	$0.307949\pi$
$674$	−115.500	−	66.6840i	−0.171365	−	0.0989376i
$675$	351.000			0.520000
$676$	76.5000	+	132.502i	0.113166	+	0.196009i
$677$	−606.000	+	349.874i	−0.895126	+	0.516801i	−0.875616	−	0.483009i	$-0.839544\pi$
$677$	−606.000	+	349.874i	−0.895126	+	0.516801i	−0.0195100	+	0.999810i	$0.506211\pi$
$678$	−234.000	+	405.300i	−0.345133	+	0.597787i
$679$		0			0
$680$	405.000	−	233.827i	0.595588	−	0.343863i
$681$			566.381i			0.831690i
$682$	−96.0000			−0.140762
$683$	904.500	−	522.213i	1.32430	−	0.764588i	0.339892	−	0.940464i	$-0.389609\pi$
$683$	904.500	−	522.213i	1.32430	−	0.764588i	0.984412	+	0.175877i	$0.0562760\pi$
$684$	−49.5000	−	85.7365i	−0.0723684	−	0.125346i
$685$	−654.000			−0.954745
$686$		0			0
$687$	798.000			1.16157
$688$	671.000			0.975291
$689$		0			0
$690$	432.000	−	249.415i	0.626087	−	0.361471i
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	0.792636	−	0.609695i	$-0.208708\pi$
$691$	−91.0000	−	157.617i	−0.131693	−	0.228099i	−0.924329	+	0.381596i	$0.875375\pi$
$692$		−	232.095i		−	0.335397i
$693$		0			0
$694$	−195.000			−0.280980
$695$	15.0000	−	8.66025i	0.0215827	−	0.0124608i
$696$	−585.000	+	1013.25i	−0.840517	+	1.45582i
$697$	94.5000	−	163.679i	0.135581	−	0.234833i
$698$			720.533i			1.03228i
$699$	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
$704$		−	122.976i		−	0.174681i
$705$	252.000	+	436.477i	0.357447	+	0.619116i
$706$	1.50000	+	2.59808i	0.00212465	+	0.00367999i
$707$		0			0
$708$	130.500	−	75.3442i	0.184322	−	0.106418i
$709$	350.000	+	606.218i	0.493653	+	0.855032i	0.999973	−	0.00731341i	$-0.00232795\pi$
$709$	350.000	+	606.218i	0.493653	+	0.855032i	−0.506320	+	0.862346i	$0.668995\pi$
$710$	−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
$716$		−	62.3538i		−	0.0870864i
$717$	−1044.00	+	602.754i	−1.45607	+	0.840661i
$718$	1026.00			1.42897
$719$	−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
$723$	357.000			0.493776
$724$	116.000	−	200.918i	0.160221	−	0.277511i
$725$	507.000	+	292.717i	0.699310	+	0.403747i
$726$	531.000	−	306.573i	0.731405	−	0.422277i
$727$	332.000	−	575.041i	0.456671	−	0.790978i	−0.542111	−	0.840307i	$-0.682375\pi$
$727$	332.000	−	575.041i	0.456671	−	0.790978i	0.998783	+	0.0493289i	$0.0157082\pi$
$728$		0			0
$729$	729.000			1.00000
$730$	195.000	−	337.750i	0.267123	−	0.462671i
$731$			950.896i			1.30082i
$732$	168.000			0.229508
$733$	−670.000			−0.914052			−0.457026	−	0.889453i	$-0.651085\pi$
$733$	−670.000			−0.914052			−0.457026	+	0.889453i	$0.651085\pi$
$734$	−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
$738$	−94.5000	+	163.679i	−0.128049	+	0.221787i
$739$	−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	$0.902139\pi$
$740$	−102.000	+	58.8897i	−0.137838	+	0.0795807i
$741$	−132.000			−0.178138
$742$		0			0
$743$	−537.000	+	310.037i	−0.722746	+	0.417277i	−0.815762	−	0.578387i	$-0.803682\pi$
$743$	−537.000	+	310.037i	−0.722746	+	0.417277i	0.0930168	+	0.995665i	$0.470349\pi$
$744$	−720.000	−	415.692i	−0.967742	−	0.558726i
$745$	528.000			0.708725
$746$	−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
$751$	1310.00			1.74434			0.872170	−	0.489202i	$-0.162712\pi$
$751$	1310.00			1.74434			0.872170	+	0.489202i	$0.162712\pi$
$752$	462.000	+	266.736i	0.614362	+	0.354702i
$753$			1169.13i			1.55264i
$754$	156.000	+	270.200i	0.206897	+	0.358355i
$755$			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	$0.454007\pi$
$758$	124.500	−	71.8801i	0.164248	−	0.0948286i
$759$	144.000			0.189723
$760$	165.000	−	285.788i	0.217105	−	0.376037i
$761$			658.179i			0.864887i	0.901661	+	0.432444i	$0.142349\pi$
$761$			658.179i			0.864887i	−0.901661	+	0.432444i	$0.857651\pi$
$762$	−72.0000	+	41.5692i	−0.0944882	+	0.0545528i
$763$		0			0
$764$		−	232.095i		−	0.303789i
$765$	−243.000	−	420.888i	−0.317647	−	0.550181i
$766$	−483.000	−	836.581i	−0.630548	−	1.09214i
$767$		−	200.918i		−	0.261953i
$768$	268.500	−	465.056i	0.349609	−	0.605541i
$769$	−511.000	−	885.078i	−0.664499	−	1.15095i	−0.979421	−	0.201829i	$-0.935312\pi$
$769$	−511.000	−	885.078i	−0.664499	−	1.15095i	0.314921	−	0.949118i	$-0.398022\pi$
$770$		0			0
$771$			524.811i			0.680689i
$772$	132.500	+	229.497i	0.171632	+	0.297276i
$773$	−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	$0.611245\pi$
$774$		−	950.896i		−	1.22855i
$775$	−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
$779$		−	133.368i		−	0.171204i
$780$		−	41.5692i		−	0.0532939i
$781$	−54.0000			−0.0691421
$782$	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
$786$	414.000	+	717.069i	0.526718	+	0.912302i
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	−0.821771	−	0.569819i	$-0.807013\pi$
$787$	65.0000	−	112.583i	0.0825921	−	0.143054i	0.904363	+	0.426765i	$0.140347\pi$
$788$	108.000	+	62.3538i	0.137056	+	0.0791292i
$789$		−	135.100i		−	0.171229i
$790$	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
$794$			627.002i			0.789676i
$795$		0			0
$796$	290.000			0.364322
$797$	273.000	−	157.617i	0.342535	−	0.197762i	−0.318858	−	0.947803i	$-0.603299\pi$
$797$	273.000	−	157.617i	0.342535	−	0.197762i	0.661392	+	0.750040i	$0.269966\pi$
$798$		0			0
$799$	−378.000	+	654.715i	−0.473091	+	0.819418i
$800$	−175.500	−	101.325i	−0.219375	−	0.126656i
$801$	972.000	+	561.184i	1.21348	+	0.700605i
$802$	340.500	+	589.763i	0.424564	+	0.735366i
$803$	97.5000	−	56.2917i	0.121420	−	0.0701017i
$804$	46.5000	+	80.5404i	0.0578358	+	0.100175i
$805$		0			0
$806$	−192.000	+	110.851i	−0.238213	+	0.137533i
$807$	486.000	−	280.592i	0.602230	−	0.347698i
$808$	390.000			0.482673
$809$	121.500	−	70.1481i	0.150185	−	0.0867096i	−0.423024	−	0.906118i	$-0.639031\pi$
$809$	121.500	−	70.1481i	0.150185	−	0.0867096i	0.573210	+	0.819409i	$0.305698\pi$
$810$	243.000	+	420.888i	0.300000	+	0.519615i
$811$	299.000			0.368681			0.184340	−	0.982862i	$-0.440985\pi$
$811$	299.000			0.368681			0.184340	+	0.982862i	$0.440985\pi$
$812$		0			0
$813$	402.000	−	696.284i	0.494465	−	0.856438i
$814$	102.000			0.125307
$815$	318.000	+	183.597i	0.390184	+	0.225273i
$816$	−445.500	−	257.210i	−0.545956	−	0.315208i
$817$	335.500	+	581.103i	0.410649	+	0.711264i
$818$			382.783i			0.467950i
$819$		0			0
$820$	42.0000			0.0512195
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	−0.784408	−	0.620245i	$-0.787033\pi$
$821$	−525.000	+	303.109i	−0.639464	+	0.369195i	0.144944	+	0.989440i	$0.453700\pi$
$822$	490.500	+	849.571i	0.596715	+	1.03354i
$823$	407.000	−	704.945i	0.494532	−	0.856555i	−0.505448	−	0.862857i	$-0.668673\pi$
$823$	407.000	−	704.945i	0.494532	−	0.856555i	0.999980	+	0.00630221i	$0.00200607\pi$
$824$		−	346.410i		−	0.420401i
$825$			67.5500i			0.0818788i
$826$		0			0
$827$			1434.14i			1.73415i	0.498182	+	0.867073i	$0.334001\pi$
$827$			1434.14i			1.73415i	−0.498182	+	0.867073i	$0.665999\pi$
$828$	216.000	+	124.708i	0.260870	+	0.150613i
$829$	359.000	+	621.806i	0.433052	+	0.750068i	0.997134	−	0.0756506i	$-0.0241034\pi$
$829$	359.000	+	621.806i	0.433052	+	0.750068i	−0.564083	+	0.825718i	$0.690770\pi$
$830$		−	290.985i		−	0.350584i
$831$	168.000			0.202166
$832$	−142.000	−	245.951i	−0.170673	−	0.295614i
$833$		0			0
$834$	−22.5000	−	12.9904i	−0.0269784	−	0.0155760i
$835$	330.000	+	571.577i	0.395210	+	0.684523i
$836$	16.5000	−	9.52628i	0.0197368	−	0.0113951i
$837$	−432.000	+	748.246i	−0.516129	+	0.893962i
$838$	678.000	−	1174.33i	0.809069	−	1.40135i
$839$	−690.000	−	398.372i	−0.822408	−	0.474817i	0.0288384	−	0.999584i	$-0.490819\pi$
$839$	−690.000	−	398.372i	−0.822408	−	0.474817i	−0.851246	+	0.524767i	$0.824153\pi$
$840$		0			0
$841$	593.500	+	1027.97i	0.705707	+	1.22232i
$842$		−	1181.26i		−	1.40292i
$843$	−126.000	−	72.7461i	−0.149466	−	0.0862943i
$844$	−94.0000			−0.111374
$845$	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
$850$	−175.500	+	303.975i	−0.206471	+	0.357618i
$851$	−816.000	−	471.118i	−0.958872	−	0.553605i
$852$	−81.0000	−	46.7654i	−0.0950704	−	0.0548889i
$853$	−712.000	+	1233.22i	−0.834701	+	1.44574i	0.0595725	+	0.998224i	$0.481026\pi$
$853$	−712.000	+	1233.22i	−0.834701	+	1.44574i	−0.894274	+	0.447521i	$0.852307\pi$
$854$		0			0
$855$	−297.000	−	171.473i	−0.347368	−	0.200553i
$856$	607.500	−	1052.22i	0.709696	−	1.22923i
$857$		−	699.749i		−	0.816509i	−0.912868	−	0.408255i	$-0.866138\pi$
$857$		−	699.749i		−	0.816509i	0.912868	−	0.408255i	$-0.133862\pi$
$858$	−18.0000	+	31.1769i	−0.0209790	+	0.0363367i
$859$	311.000			0.362049			0.181024	−	0.983479i	$-0.442059\pi$
$859$	311.000			0.362049			0.181024	+	0.983479i	$0.442059\pi$
$860$	−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	−0.114761	−	0.993393i	$-0.536610\pi$
$863$	−891.000	−	514.419i	−1.03244	−	0.596082i	−0.917684	+	0.397311i	$0.869944\pi$
$864$	−364.500	−	210.444i	−0.421875	−	0.243570i
$865$	−402.000	−	696.284i	−0.464740	−	0.804953i
$866$	−442.500	+	255.477i	−0.510970	+	0.295009i
$867$	−69.0000	+	119.512i	−0.0795848	+	0.137845i
$868$		0			0
$869$	57.0000	−	32.9090i	0.0655926	−	0.0378699i
$870$			810.600i			0.931724i
$871$	124.000			0.142365
$872$	−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
$877$	104.000			0.118586			0.0592930	−	0.998241i	$-0.481115\pi$
$877$	104.000			0.118586			0.0592930	+	0.998241i	$0.481115\pi$
$878$	−1218.00	−	703.213i	−1.38724	−	0.800926i
$879$	657.000	−	379.319i	0.747440	−	0.431535i
$880$	−33.0000	−	57.1577i	−0.0375000	−	0.0649519i
$881$		−	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	$0.478535\pi$
$884$	54.0000	−	31.1769i	0.0610860	−	0.0352680i
$885$	261.000	−	452.065i	0.294915	−	0.510808i
$886$	−79.5000	+	137.698i	−0.0897291	+	0.155415i
$887$			1188.19i			1.33956i	0.742561	+	0.669778i	$0.233611\pi$
$887$			1188.19i			1.33956i	−0.742561	+	0.669778i	$0.766389\pi$
$888$	765.000	+	441.673i	0.861486	+	0.497379i
$889$		0			0
$890$			748.246i			0.840726i
$891$			140.296i			0.157459i
$892$	26.0000	+	45.0333i	0.0291480	+	0.0504858i
$893$			533.472i			0.597393i
$894$	−396.000	−	685.892i	−0.442953	−	0.767217i
$895$	−108.000	−	187.061i	−0.120670	−	0.209007i
$896$		0			0
$897$	288.000	−	166.277i	0.321070	−	0.185370i
$898$	553.500	+	958.690i	0.616370	+	1.06758i
$899$	−1248.00	+	720.533i	−1.38821	+	0.801483i
$900$	−58.5000	+	101.325i	−0.0650000	+	0.112583i
$901$		0			0
$902$	−31.5000	−	18.1865i	−0.0349224	−	0.0201625i
$903$		0			0
$904$	−390.000	−	675.500i	−0.431416	−	0.747234i
$905$		−	803.672i		−	0.888035i
$906$	90.0000	−	51.9615i	0.0993377	−	0.0573527i
$907$	695.000			0.766262			0.383131	−	0.923694i	$-0.374846\pi$
$907$	695.000			0.766262			0.383131	+	0.923694i	$0.374846\pi$
$908$	−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	−0.978432	−	0.206569i	$-0.933770\pi$
$911$	−1500.00	−	866.025i	−1.64654	−	0.950632i	−0.668110	−	0.744062i	$-0.732897\pi$
$912$	−363.000			−0.398026
$913$	42.0000	−	72.7461i	0.0460022	−	0.0796781i
$914$	−97.5000	−	56.2917i	−0.106674	−	0.0615882i
$915$	504.000	−	290.985i	0.550820	−	0.318016i
$916$	−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	$0.176366\pi$
$920$			831.384i			0.903679i
$921$	1599.00			1.73616
$922$	−1380.00			−1.49675
$923$	−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
$927$	−360.000			−0.388350
$928$	−351.000	−	607.950i	−0.378233	−	0.655118i
$929$	690.000	−	398.372i	0.742734	−	0.428818i	−0.0803285	−	0.996768i	$-0.525597\pi$
$929$	690.000	−	398.372i	0.742734	−	0.428818i	0.823063	+	0.567951i	$0.192264\pi$
$930$	−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
$934$	−351.000			−0.375803
$935$	81.0000	−	46.7654i	0.0866310	−	0.0500164i
$936$	−270.000	+	155.885i	−0.288462	+	0.166543i
$937$	470.000			0.501601			0.250800	−	0.968039i	$-0.419306\pi$
$937$	470.000			0.501601			0.250800	+	0.968039i	$0.419306\pi$
$938$		0			0
$939$	−232.500	−	402.702i	−0.247604	−	0.428862i
$940$	−168.000			−0.178723
$941$	348.000	+	200.918i	0.369819	+	0.213515i	0.673380	−	0.739297i	$-0.264842\pi$
$941$	348.000	+	200.918i	0.369819	+	0.213515i	−0.303560	+	0.952812i	$0.598175\pi$
$942$		−	207.846i		−	0.220643i
$943$	168.000	+	290.985i	0.178155	+	0.308573i
$944$		−	552.524i		−	0.585301i
$945$		0			0
$946$	183.000			0.193446
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	−0.499208	−	0.866482i	$-0.666376\pi$
$947$	1.50000	−	0.866025i	0.00158395	−	0.000914494i	0.500792	+	0.865568i	$0.333042\pi$
$948$	114.000			0.120253
$949$	130.000	−	225.167i	0.136986	−	0.237267i
$950$			247.683i			0.260719i
$951$	126.000	−	72.7461i	0.132492	−	0.0764944i
$952$		0			0
$953$		−	826.188i		−	0.866934i	−0.901169	−	0.433467i	$-0.857290\pi$
$953$		−	826.188i		−	0.866934i	0.901169	−	0.433467i	$-0.142710\pi$
$954$		0			0
$955$	−402.000	−	696.284i	−0.420942	−	0.729094i
$956$		−	401.836i		−	0.420330i
$957$	−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
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$	204.000	−	117.779i	0.212058	−	0.122432i
$963$	−1093.50	−	631.333i	−1.13551	−	0.655589i
$964$	−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	−0.989205	−	0.146540i	$-0.953186\pi$
$967$	−601.000	−	1040.96i	−0.621510	−	1.07649i	0.367695	−	0.929946i	$-0.380147\pi$
$968$			1021.91i			1.05569i
$969$		−	514.419i		−	0.530876i
$970$	690.000			0.711340
$971$	−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
$975$	78.0000	+	135.100i	0.0800000	+	0.138564i
$976$	308.000	−	533.472i	0.315574	−	0.546590i
$977$	361.500	+	208.712i	0.370010	+	0.213626i	0.673463	−	0.739221i	$-0.264806\pi$
$977$	361.500	+	208.712i	0.370010	+	0.213626i	−0.303453	+	0.952847i	$0.598139\pi$
$978$		−	550.792i		−	0.563182i
$979$	−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
$983$		−	1167.40i		−	1.18759i	−0.804616	−	0.593796i	$-0.797629\pi$
$983$		−	1167.40i		−	1.18759i	0.804616	−	0.593796i	$-0.202371\pi$
$984$	−157.500	−	272.798i	−0.160061	−	0.277234i
$985$	432.000			0.438579
$986$	−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	$0.579100\pi$
$992$	432.000	−	249.415i	0.435484	−	0.251427i
$993$	−3.00000	−	5.19615i	−0.00302115	−	0.00523278i
$994$		0			0
$995$	870.000	−	502.295i	0.874372	−	0.504819i
$996$	126.000	−	72.7461i	0.126506	−	0.0730383i
$997$	524.000			0.525577			0.262788	−	0.964853i	$-0.415358\pi$
$997$	524.000			0.525577			0.262788	+	0.964853i	$0.415358\pi$
$998$	−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.n.b.128.1		2
7.2	even	3		9.3.d.a.2.1	✓	2
7.3	odd	6		441.3.j.b.263.1		2
7.4	even	3		441.3.j.a.263.1		2
7.5	odd	6		441.3.r.a.344.1		2
7.6	odd	2		441.3.n.a.128.1		2
9.5	odd	6		441.3.j.a.275.1		2
21.2	odd	6		27.3.d.a.8.1		2
28.23	odd	6		144.3.q.a.65.1		2
35.2	odd	12		225.3.i.a.74.2		4
35.9	even	6		225.3.j.a.101.1		2
35.23	odd	12		225.3.i.a.74.1		4
56.37	even	6		576.3.q.b.65.1		2
56.51	odd	6		576.3.q.a.65.1		2
63.2	odd	6		81.3.b.a.80.1		2
63.5	even	6		441.3.r.a.50.1		2
63.16	even	3		81.3.b.a.80.2		2
63.23	odd	6		9.3.d.a.5.1	yes	2
63.32	odd	6	inner	441.3.n.b.410.1		2
63.41	even	6		441.3.j.b.275.1		2
63.58	even	3		27.3.d.a.17.1		2
63.59	even	6		441.3.n.a.410.1		2
84.23	even	6		432.3.q.a.305.1		2
105.2	even	12		675.3.i.a.224.1		4
105.23	even	12		675.3.i.a.224.2		4
105.44	odd	6		675.3.j.a.251.1		2
168.107	even	6		1728.3.q.b.1601.1		2
168.149	odd	6		1728.3.q.a.1601.1		2
252.23	even	6		144.3.q.a.113.1		2
252.79	odd	6		1296.3.e.a.161.2		2
252.191	even	6		1296.3.e.a.161.1		2
252.247	odd	6		432.3.q.a.17.1		2
315.23	even	12		225.3.i.a.149.2		4
315.58	odd	12		675.3.i.a.449.1		4
315.149	odd	6		225.3.j.a.176.1		2
315.184	even	6		675.3.j.a.476.1		2
315.212	even	12		225.3.i.a.149.1		4
315.247	odd	12		675.3.i.a.449.2		4
504.149	odd	6		576.3.q.b.257.1		2
504.275	even	6		576.3.q.a.257.1		2
504.373	even	6		1728.3.q.a.449.1		2
504.499	odd	6		1728.3.q.b.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.3.d.a.2.1	✓	2	7.2	even	3
9.3.d.a.5.1	yes	2	63.23	odd	6
27.3.d.a.8.1		2	21.2	odd	6
27.3.d.a.17.1		2	63.58	even	3
81.3.b.a.80.1		2	63.2	odd	6
81.3.b.a.80.2		2	63.16	even	3
144.3.q.a.65.1		2	28.23	odd	6
144.3.q.a.113.1		2	252.23	even	6
225.3.i.a.74.1		4	35.23	odd	12
225.3.i.a.74.2		4	35.2	odd	12
225.3.i.a.149.1		4	315.212	even	12
225.3.i.a.149.2		4	315.23	even	12
225.3.j.a.101.1		2	35.9	even	6
225.3.j.a.176.1		2	315.149	odd	6
432.3.q.a.17.1		2	252.247	odd	6
432.3.q.a.305.1		2	84.23	even	6
441.3.j.a.263.1		2	7.4	even	3
441.3.j.a.275.1		2	9.5	odd	6
441.3.j.b.263.1		2	7.3	odd	6
441.3.j.b.275.1		2	63.41	even	6
441.3.n.a.128.1		2	7.6	odd	2
441.3.n.a.410.1		2	63.59	even	6
441.3.n.b.128.1		2	1.1	even	1	trivial
441.3.n.b.410.1		2	63.32	odd	6	inner
441.3.r.a.50.1		2	63.5	even	6
441.3.r.a.344.1		2	7.5	odd	6
576.3.q.a.65.1		2	56.51	odd	6
576.3.q.a.257.1		2	504.275	even	6
576.3.q.b.65.1		2	56.37	even	6
576.3.q.b.257.1		2	504.149	odd	6
675.3.i.a.224.1		4	105.2	even	12
675.3.i.a.224.2		4	105.23	even	12
675.3.i.a.449.1		4	315.58	odd	12
675.3.i.a.449.2		4	315.247	odd	12
675.3.j.a.251.1		2	105.44	odd	6
675.3.j.a.476.1		2	315.184	even	6
1296.3.e.a.161.1		2	252.191	even	6
1296.3.e.a.161.2		2	252.79	odd	6
1728.3.q.a.449.1		2	504.373	even	6
1728.3.q.a.1601.1		2	168.149	odd	6
1728.3.q.b.449.1		2	504.499	odd	6
1728.3.q.b.1601.1		2	168.107	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.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(4.50000 - 2.59808i) q^{6} +8.66025i q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{2} +3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(4.50000 - 2.59808i) q^{6} +8.66025i q^{8} +9.00000 q^{9} +(3.00000 + 5.19615i) q^{10} +1.73205i q^{11} +(-1.50000 + 2.59808i) q^{12} +(2.00000 + 3.46410i) q^{13} +10.3923i q^{15} +(5.50000 + 9.52628i) 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} -27.7128i q^{23} +25.9808i q^{24} +13.0000 q^{25} +(6.00000 + 3.46410i) q^{26} +27.0000 q^{27} +(39.0000 + 22.5167i) q^{29} +(9.00000 + 15.5885i) q^{30} +(-16.0000 + 27.7128i) q^{31} +(-13.5000 - 7.79423i) q^{32} +5.19615i q^{33} +(-13.5000 + 23.3827i) q^{34} +(-4.50000 + 7.79423i) q^{36} +(17.0000 - 29.4449i) q^{37} +19.0526i q^{38} +(6.00000 + 10.3923i) q^{39} -30.0000 q^{40} +(-10.5000 + 6.06218i) q^{41} +(30.5000 - 52.8275i) q^{43} +(-1.50000 - 0.866025i) q^{44} +31.1769i q^{45} +(-24.0000 - 41.5692i) q^{46} +(42.0000 - 24.2487i) q^{47} +(16.5000 + 28.5788i) q^{48} +(19.5000 - 11.2583i) q^{50} +(-40.5000 + 23.3827i) q^{51} -4.00000 q^{52} +(40.5000 - 23.3827i) q^{54} -6.00000 q^{55} +(-16.5000 + 28.5788i) q^{57} +78.0000 q^{58} +(-43.5000 - 25.1147i) q^{59} +(-9.00000 - 5.19615i) q^{60} +(-28.0000 - 48.4974i) q^{61} +55.4256i q^{62} -71.0000 q^{64} +(-12.0000 + 6.92820i) q^{65} +(4.50000 + 7.79423i) q^{66} +(15.5000 - 26.8468i) q^{67} -15.5885i q^{68} -83.1384i q^{69} +31.1769i q^{71} +77.9423i q^{72} +(-32.5000 - 56.2917i) q^{73} -58.8897i q^{74} +39.0000 q^{75} +(-5.50000 - 9.52628i) q^{76} +(18.0000 + 10.3923i) q^{78} +(-19.0000 - 32.9090i) q^{79} +(-33.0000 + 19.0526i) q^{80} +81.0000 q^{81} +(-10.5000 + 18.1865i) q^{82} +(-42.0000 - 24.2487i) q^{83} +(-27.0000 - 46.7654i) q^{85} -105.655i q^{86} +(117.000 + 67.5500i) q^{87} -15.0000 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} +(42.0000 - 72.7461i) q^{94} +(-33.0000 - 19.0526i) q^{95} +(-40.5000 - 23.3827i) q^{96} +(57.5000 - 99.5929i) q^{97} +15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 6 q^{3} - q^{4} + 9 q^{6} + 18 q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 6 * q^3 - q^4 + 9 * q^6 + 18 * q^9	\( 2 q + 3 q^{2} + 6 q^{3} - q^{4} + 9 q^{6} + 18 q^{9} + 6 q^{10} - 3 q^{12} + 4 q^{13} + 11 q^{16} - 27 q^{17} + 27 q^{18} - 11 q^{19} - 6 q^{20} + 3 q^{22} + 26 q^{25} + 12 q^{26} + 54 q^{27} + 78 q^{29} + 18 q^{30} - 32 q^{31} - 27 q^{32} - 27 q^{34} - 9 q^{36} + 34 q^{37} + 12 q^{39} - 60 q^{40} - 21 q^{41} + 61 q^{43} - 3 q^{44} - 48 q^{46} + 84 q^{47} + 33 q^{48} + 39 q^{50} - 81 q^{51} - 8 q^{52} + 81 q^{54} - 12 q^{55} - 33 q^{57} + 156 q^{58} - 87 q^{59} - 18 q^{60} - 56 q^{61} - 142 q^{64} - 24 q^{65} + 9 q^{66} + 31 q^{67} - 65 q^{73} + 78 q^{75} - 11 q^{76} + 36 q^{78} - 38 q^{79} - 66 q^{80} + 162 q^{81} - 21 q^{82} - 84 q^{83} - 54 q^{85} + 234 q^{87} - 30 q^{88} + 216 q^{89} + 54 q^{90} + 48 q^{92} - 96 q^{93} + 84 q^{94} - 66 q^{95} - 81 q^{96} + 115 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 + 6 * q^3 - q^4 + 9 * q^6 + 18 * q^9 + 6 * q^10 - 3 * q^12 + 4 * q^13 + 11 * q^16 - 27 * q^17 + 27 * q^18 - 11 * q^19 - 6 * q^20 + 3 * q^22 + 26 * q^25 + 12 * q^26 + 54 * q^27 + 78 * q^29 + 18 * q^30 - 32 * q^31 - 27 * q^32 - 27 * q^34 - 9 * q^36 + 34 * q^37 + 12 * q^39 - 60 * q^40 - 21 * q^41 + 61 * q^43 - 3 * q^44 - 48 * q^46 + 84 * q^47 + 33 * q^48 + 39 * q^50 - 81 * q^51 - 8 * q^52 + 81 * q^54 - 12 * q^55 - 33 * q^57 + 156 * q^58 - 87 * q^59 - 18 * q^60 - 56 * q^61 - 142 * q^64 - 24 * q^65 + 9 * q^66 + 31 * q^67 - 65 * q^73 + 78 * q^75 - 11 * q^76 + 36 * q^78 - 38 * q^79 - 66 * q^80 + 162 * q^81 - 21 * q^82 - 84 * q^83 - 54 * q^85 + 234 * q^87 - 30 * q^88 + 216 * q^89 + 54 * q^90 + 48 * q^92 - 96 * q^93 + 84 * q^94 - 66 * q^95 - 81 * q^96 + 115 * q^97

Introduction

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