LMFDB - Embedded newform 1050.2.u.a.899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(299,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1050.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.u (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:	$8.38429221223$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			899.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.899
Dual form			1050.2.u.a.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(1.50000 - 0.866025i) q^{12} +3.46410 q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(-0.866025 + 4.50000i) q^{21} +3.00000i q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-1.73205 - 3.00000i) q^{26} -5.19615i q^{27} +(2.59808 + 0.500000i) q^{28} +3.00000i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.59808 + 4.50000i) q^{33} +3.46410i q^{34} -3.00000 q^{36} +(-1.73205 + 1.00000i) q^{37} +(3.00000 + 1.73205i) q^{38} +(-5.19615 - 3.00000i) q^{39} +6.92820 q^{41} +(4.33013 - 1.50000i) q^{42} +8.00000i q^{43} +(2.59808 - 1.50000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-6.00000 + 3.46410i) q^{47} +1.73205i q^{48} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-1.73205 + 3.00000i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-0.866025 - 2.50000i) q^{56} +6.00000 q^{57} +(2.59808 - 1.50000i) q^{58} +(0.866025 - 1.50000i) q^{59} +1.73205i q^{62} +(5.19615 - 6.00000i) q^{63} +1.00000 q^{64} +(2.59808 - 4.50000i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(3.00000 - 1.73205i) q^{68} +10.3923i q^{69} +12.0000i q^{71} +(1.50000 + 2.59808i) q^{72} +(3.46410 - 6.00000i) q^{73} +(1.73205 + 1.00000i) q^{74} -3.46410i q^{76} +(-1.50000 + 7.79423i) q^{77} +6.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.46410 - 6.00000i) q^{82} +8.66025i q^{83} +(-3.46410 - 3.00000i) q^{84} +(6.92820 - 4.00000i) q^{86} +(2.59808 - 4.50000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(6.00000 + 3.46410i) q^{94} +(1.50000 - 0.866025i) q^{96} -5.19615 q^{97} +(6.50000 + 2.59808i) q^{98} -9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 4 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9} + 6 q^{12} - 2 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{31} - 2 q^{32} - 12 q^{36} + 12 q^{38} - 12 q^{46} - 24 q^{47} - 22 q^{49} + 12 q^{51} - 18 q^{53} - 18 q^{54} + 24 q^{57} + 4 q^{64} + 12 q^{68} + 6 q^{72} - 6 q^{77} - 2 q^{79} - 18 q^{81} - 12 q^{91} + 24 q^{92} + 6 q^{93} + 24 q^{94} + 6 q^{96} + 26 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 4 * q^8 + 6 * q^9 + 6 * q^12 - 2 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 - 12 * q^23 - 6 * q^24 - 6 * q^31 - 2 * q^32 - 12 * q^36 + 12 * q^38 - 12 * q^46 - 24 * q^47 - 22 * q^49 + 12 * q^51 - 18 * q^53 - 18 * q^54 + 24 * q^57 + 4 * q^64 + 12 * q^68 + 6 * q^72 - 6 * q^77 - 2 * q^79 - 18 * q^81 - 12 * q^91 + 24 * q^92 + 6 * q^93 + 24 * q^94 + 6 * q^96 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			1.73205i			0.707107i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$	1.00000			0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	3.46410			0.960769			0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410			0.960769			0.480384	+	0.877058i	$0.340497\pi$
$14$	−1.73205	+	2.00000i	−0.462910	+	0.534522i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	−	1.73205i	−0.727607	−	0.420084i	0.0899392	−	0.995947i	$-0.471333\pi$
$17$	−3.00000	−	1.73205i	−0.727607	−	0.420084i	−0.817546	+	0.575863i	$0.804666\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$			3.00000i			0.639602i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	−1.73205	−	3.00000i	−0.339683	−	0.588348i
$27$		−	5.19615i		−	1.00000i
$28$	2.59808	+	0.500000i	0.490990	+	0.0944911i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.59808	+	4.50000i	0.452267	+	0.783349i
$34$			3.46410i			0.594089i
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−1.73205	+	1.00000i	−0.284747	+	0.164399i	−0.635571	−	0.772043i	$-0.719235\pi$
$37$	−1.73205	+	1.00000i	−0.284747	+	0.164399i	0.350823	+	0.936442i	$0.385902\pi$
$38$	3.00000	+	1.73205i	0.486664	+	0.280976i
$39$	−5.19615	−	3.00000i	−0.832050	−	0.480384i
$40$		0			0
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$	4.33013	−	1.50000i	0.668153	−	0.231455i
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	2.59808	−	1.50000i	0.391675	−	0.226134i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.869069	−	0.494690i	$-0.835282\pi$
$47$	−6.00000	+	3.46410i	−0.875190	+	0.505291i	−0.00612051	+	0.999981i	$0.501948\pi$
$48$			1.73205i			0.250000i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	3.00000	+	5.19615i	0.420084	+	0.727607i
$52$	−1.73205	+	3.00000i	−0.240192	+	0.416025i
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	−0.866025	−	2.50000i	−0.115728	−	0.334077i
$57$	6.00000			0.794719
$58$	2.59808	−	1.50000i	0.341144	−	0.196960i
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	−0.804130	−	0.594454i	$-0.797368\pi$
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	0.916877	+	0.399170i	$0.130702\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$			1.73205i			0.219971i
$63$	5.19615	−	6.00000i	0.654654	−	0.755929i
$64$	1.00000			0.125000
$65$		0			0
$66$	2.59808	−	4.50000i	0.319801	−	0.553912i
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	0.390453	−	0.920623i	$-0.372318\pi$
$67$	−1.73205	−	1.00000i	−0.211604	−	0.122169i	−0.602056	+	0.798454i	$0.705652\pi$
$68$	3.00000	−	1.73205i	0.363803	−	0.210042i
$69$			10.3923i			1.25109i
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	3.46410	−	6.00000i	0.405442	−	0.702247i	−0.588930	−	0.808184i	$-0.700451\pi$
$73$	3.46410	−	6.00000i	0.405442	−	0.702247i	0.994373	+	0.105937i	$0.0337841\pi$
$74$	1.73205	+	1.00000i	0.201347	+	0.116248i
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$			6.00000i			0.679366i
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.46410	−	6.00000i	−0.382546	−	0.662589i
$83$			8.66025i			0.950586i	0.879827	+	0.475293i	$0.157658\pi$
$83$			8.66025i			0.950586i	−0.879827	+	0.475293i	$0.842342\pi$
$84$	−3.46410	−	3.00000i	−0.377964	−	0.327327i
$85$		0			0
$86$	6.92820	−	4.00000i	0.747087	−	0.431331i
$87$	2.59808	−	4.50000i	0.278543	−	0.482451i
$88$	−2.59808	−	1.50000i	−0.276956	−	0.159901i
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		0			0
$91$	−3.00000	−	8.66025i	−0.314485	−	0.907841i
$92$	6.00000			0.625543
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	6.00000	+	3.46410i	0.618853	+	0.357295i
$95$		0			0
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−5.19615			−0.527589			−0.263795	−	0.964579i	$-0.584974\pi$
$97$	−5.19615			−0.527589			−0.263795	+	0.964579i	$0.584974\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$		−	9.00000i		−	0.904534i
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	1.73205	+	3.00000i	0.170664	+	0.295599i	0.938652	−	0.344865i	$-0.112075\pi$
$103$	1.73205	+	3.00000i	0.170664	+	0.295599i	−0.767988	+	0.640464i	$0.778742\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	9.00000			0.874157
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$	4.50000	+	2.59808i	0.433013	+	0.250000i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	−3.00000	−	5.19615i	−0.280976	−	0.486664i
$115$		0			0
$116$	−2.59808	−	1.50000i	−0.241225	−	0.139272i
$117$	5.19615	+	9.00000i	0.480384	+	0.832050i
$118$	−1.73205			−0.159448
$119$	−1.73205	+	9.00000i	−0.158777	+	0.825029i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$	−10.3923	−	6.00000i	−0.937043	−	0.541002i
$124$	1.50000	−	0.866025i	0.134704	−	0.0777714i
$125$		0			0
$126$	−7.79423	−	1.50000i	−0.694365	−	0.133631i
$127$			11.0000i			0.976092i	0.872818	+	0.488046i	$0.162290\pi$
$127$			11.0000i			0.976092i	−0.872818	+	0.488046i	$0.837710\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.92820	−	12.0000i	0.609994	−	1.05654i
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$	−5.19615			−0.452267
$133$	6.92820	+	6.00000i	0.600751	+	0.520266i
$134$			2.00000i			0.172774i
$135$		0			0
$136$	−3.00000	−	1.73205i	−0.257248	−	0.148522i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	9.00000	−	5.19615i	0.766131	−	0.442326i
$139$		−	17.3205i		−	1.46911i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$		−	17.3205i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$	10.3923	−	6.00000i	0.872103	−	0.503509i
$143$	−9.00000	−	5.19615i	−0.752618	−	0.434524i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	−6.92820			−0.573382
$147$	12.0000	−	1.73205i	0.989743	−	0.142857i
$148$		−	2.00000i		−	0.164399i
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.300750	−	0.953703i	$-0.402763\pi$
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.976306	+	0.216394i	$0.0694297\pi$
$150$		0			0
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	−0.972567	−	0.232623i	$-0.925269\pi$
$151$	−3.50000	+	6.06218i	−0.284826	+	0.493333i	0.687741	+	0.725956i	$0.258602\pi$
$152$	−3.00000	+	1.73205i	−0.243332	+	0.140488i
$153$		−	10.3923i		−	0.840168i
$154$	7.50000	−	2.59808i	0.604367	−	0.209359i
$155$		0			0
$156$	5.19615	−	3.00000i	0.416025	−	0.240192i
$157$	10.3923	−	18.0000i	0.829396	−	1.43656i	−0.0691164	−	0.997609i	$-0.522018\pi$
$157$	10.3923	−	18.0000i	0.829396	−	1.43656i	0.898513	−	0.438948i	$-0.144649\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$		0			0
$161$	−10.3923	+	12.0000i	−0.819028	+	0.945732i
$162$	9.00000			0.707107
$163$	−12.1244	+	7.00000i	−0.949653	+	0.548282i	−0.892973	−	0.450110i	$-0.851385\pi$
$163$	−12.1244	+	7.00000i	−0.949653	+	0.548282i	−0.0566798	+	0.998392i	$0.518051\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$		0			0
$166$	7.50000	−	4.33013i	0.582113	−	0.336083i
$167$		−	17.3205i		−	1.34030i	−0.742225	−	0.670151i	$-0.766230\pi$
$167$		−	17.3205i		−	1.34030i	0.742225	−	0.670151i	$-0.233770\pi$
$168$	−0.866025	+	4.50000i	−0.0668153	+	0.347183i
$169$	−1.00000			−0.0769231
$170$		0			0
$171$	−9.00000	−	5.19615i	−0.688247	−	0.397360i
$172$	−6.92820	−	4.00000i	−0.528271	−	0.304997i
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$	−5.19615			−0.393919
$175$		0			0
$176$			3.00000i			0.226134i
$177$	−2.59808	+	1.50000i	−0.195283	+	0.112747i
$178$	5.19615	−	9.00000i	0.389468	−	0.674579i
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	0.0585225	−	0.998286i	$-0.481361\pi$
$179$	−10.3923	−	6.00000i	−0.776757	−	0.448461i	−0.835280	+	0.549825i	$0.814694\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−6.00000	+	6.92820i	−0.444750	+	0.513553i
$183$		0			0
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	5.19615	+	9.00000i	0.379980	+	0.658145i
$188$		−	6.92820i		−	0.505291i
$189$	−12.9904	+	4.50000i	−0.944911	+	0.327327i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$	2.59808	+	4.50000i	0.186531	+	0.323081i
$195$		0			0
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−7.79423	+	4.50000i	−0.553912	+	0.319801i
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	0.145848	−	0.989307i	$-0.453409\pi$
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	−0.783841	+	0.620962i	$0.786742\pi$
$200$		0			0
$201$	1.73205	+	3.00000i	0.122169	+	0.211604i
$202$		0			0
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$	−6.00000			−0.420084
$205$		0			0
$206$	1.73205	−	3.00000i	0.120678	−	0.209020i
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$	−1.73205	−	3.00000i	−0.120096	−	0.208013i
$209$	10.3923			0.718851
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	10.3923	−	18.0000i	0.712069	−	1.23334i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$		0			0
$216$		−	5.19615i		−	0.353553i
$217$	−0.866025	+	4.50000i	−0.0587896	+	0.305480i
$218$	2.00000			0.135457
$219$	−10.3923	+	6.00000i	−0.702247	+	0.405442i
$220$		0			0
$221$	−10.3923	−	6.00000i	−0.699062	−	0.403604i
$222$	−1.73205	−	3.00000i	−0.116248	−	0.201347i
$223$	−25.9808			−1.73980			−0.869900	−	0.493228i	$-0.835817\pi$
$223$	−25.9808			−1.73980			−0.869900	+	0.493228i	$0.835817\pi$
$224$	2.59808	+	0.500000i	0.173591	+	0.0334077i
$225$		0			0
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	4.50000	+	2.59808i	0.298675	+	0.172440i	0.641848	−	0.766832i	$-0.278168\pi$
$227$	4.50000	+	2.59808i	0.298675	+	0.172440i	−0.343172	+	0.939272i	$0.611501\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	−0.0480291	−	0.998846i	$-0.515294\pi$
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	0.841011	+	0.541017i	$0.181961\pi$
$230$		0			0
$231$	9.00000	−	10.3923i	0.592157	−	0.683763i
$232$			3.00000i			0.196960i
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$	5.19615	−	9.00000i	0.339683	−	0.588348i
$235$		0			0
$236$	0.866025	+	1.50000i	0.0563735	+	0.0976417i
$237$			1.73205i			0.112509i
$238$	8.66025	−	3.00000i	0.561361	−	0.194461i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$		0			0
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$		0			0
$246$			12.0000i			0.765092i
$247$	−10.3923	+	6.00000i	−0.661247	+	0.381771i
$248$	−1.50000	−	0.866025i	−0.0952501	−	0.0549927i
$249$	7.50000	−	12.9904i	0.475293	−	0.823232i
$250$		0			0
$251$	19.0526			1.20259			0.601293	−	0.799028i	$-0.294652\pi$
$251$	19.0526			1.20259			0.601293	+	0.799028i	$0.294652\pi$
$252$	2.59808	+	7.50000i	0.163663	+	0.472456i
$253$			18.0000i			1.13165i
$254$	9.52628	−	5.50000i	0.597732	−	0.345101i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.00000	+	5.19615i	−0.561405	+	0.324127i	−0.753709	−	0.657208i	$-0.771737\pi$
$257$	−9.00000	+	5.19615i	−0.561405	+	0.324127i	0.192304	+	0.981335i	$0.438404\pi$
$258$	−13.8564			−0.862662
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$		0			0
$261$	−7.79423	+	4.50000i	−0.482451	+	0.278543i
$262$	−2.59808	+	4.50000i	−0.160510	+	0.278011i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	2.59808	+	4.50000i	0.159901	+	0.276956i
$265$		0			0
$266$	1.73205	−	9.00000i	0.106199	−	0.551825i
$267$		−	18.0000i		−	1.10158i
$268$	1.73205	−	1.00000i	0.105802	−	0.0610847i
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.0671428	+	0.997743i	$0.521388\pi$
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.830500	+	0.557019i	$0.811945\pi$
$270$		0			0
$271$	4.50000	−	2.59808i	0.273356	−	0.157822i	−0.357056	−	0.934083i	$-0.616219\pi$
$271$	4.50000	−	2.59808i	0.273356	−	0.157822i	0.630412	+	0.776261i	$0.282886\pi$
$272$			3.46410i			0.210042i
$273$	−3.00000	+	15.5885i	−0.181568	+	0.943456i
$274$	18.0000			1.08742
$275$		0			0
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	−6.92820	−	4.00000i	−0.416275	−	0.240337i	0.277207	−	0.960810i	$-0.410591\pi$
$277$	−6.92820	−	4.00000i	−0.416275	−	0.240337i	−0.693482	+	0.720473i	$0.743925\pi$
$278$	−15.0000	+	8.66025i	−0.899640	+	0.519408i
$279$		−	5.19615i		−	0.311086i
$280$		0			0
$281$		−	30.0000i		−	1.78965i	−0.446417	−	0.894825i	$-0.647300\pi$
$281$		−	30.0000i		−	1.78965i	0.446417	−	0.894825i	$-0.352700\pi$
$282$	−6.00000	−	10.3923i	−0.357295	−	0.618853i
$283$	13.8564	−	24.0000i	0.823678	−	1.42665i	−0.0792477	−	0.996855i	$-0.525252\pi$
$283$	13.8564	−	24.0000i	0.823678	−	1.42665i	0.902926	−	0.429797i	$-0.141415\pi$
$284$	−10.3923	−	6.00000i	−0.616670	−	0.356034i
$285$		0			0
$286$			10.3923i			0.614510i
$287$	−6.00000	−	17.3205i	−0.354169	−	1.02240i
$288$	−3.00000			−0.176777
$289$	−2.50000	−	4.33013i	−0.147059	−	0.254713i
$290$		0			0
$291$	7.79423	+	4.50000i	0.456906	+	0.263795i
$292$	3.46410	+	6.00000i	0.202721	+	0.351123i
$293$			19.0526i			1.11306i	0.830827	+	0.556531i	$0.187868\pi$
$293$			19.0526i			1.11306i	−0.830827	+	0.556531i	$0.812132\pi$
$294$	−7.50000	−	9.52628i	−0.437409	−	0.555584i
$295$		0			0
$296$	−1.73205	+	1.00000i	−0.100673	+	0.0581238i
$297$	−7.79423	+	13.5000i	−0.452267	+	0.783349i
$298$	−15.5885	−	9.00000i	−0.903015	−	0.521356i
$299$	−10.3923	−	18.0000i	−0.601003	−	1.04097i
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$	7.00000			0.402805
$303$		0			0
$304$	3.00000	+	1.73205i	0.172062	+	0.0993399i
$305$		0			0
$306$	−9.00000	+	5.19615i	−0.514496	+	0.297044i
$307$	24.2487			1.38395			0.691974	−	0.721923i	$-0.256741\pi$
$307$	24.2487			1.38395			0.691974	+	0.721923i	$0.256741\pi$
$308$	−6.00000	−	5.19615i	−0.341882	−	0.296078i
$309$		−	6.00000i		−	0.341328i
$310$		0			0
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	−0.992826	−	0.119570i	$-0.961848\pi$
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	0.599963	+	0.800027i	$0.295182\pi$
$312$	−5.19615	−	3.00000i	−0.294174	−	0.169842i
$313$	−0.866025	−	1.50000i	−0.0489506	−	0.0847850i	0.840512	−	0.541793i	$-0.182254\pi$
$313$	−0.866025	−	1.50000i	−0.0489506	−	0.0847850i	−0.889463	+	0.457008i	$0.848921\pi$
$314$	−20.7846			−1.17294
$315$		0			0
$316$	1.00000			0.0562544
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$	−13.5000	−	7.79423i	−0.757042	−	0.437079i
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		−	5.19615i		−	0.290021i
$322$	15.5885	+	3.00000i	0.868711	+	0.167183i
$323$	12.0000			0.667698
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	12.1244	+	7.00000i	0.671506	+	0.387694i
$327$	3.00000	−	1.73205i	0.165900	−	0.0957826i
$328$	6.92820			0.382546
$329$	13.8564	+	12.0000i	0.763928	+	0.661581i
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	−7.50000	−	4.33013i	−0.411616	−	0.237647i
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	−15.0000	+	8.66025i	−0.820763	+	0.473868i
$335$		0			0
$336$	4.33013	−	1.50000i	0.236228	−	0.0818317i
$337$			13.0000i			0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$			13.0000i			0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$	0.500000	+	0.866025i	0.0271964	+	0.0471056i
$339$	18.0000	+	10.3923i	0.977626	+	0.564433i
$340$		0			0
$341$	2.59808	+	4.50000i	0.140694	+	0.243689i
$342$			10.3923i			0.561951i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$			8.00000i			0.431331i
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	2.59808	+	4.50000i	0.139272	+	0.241225i
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$	2.59808	−	1.50000i	0.138478	−	0.0799503i
$353$	30.0000	+	17.3205i	1.59674	+	0.921878i	0.992110	+	0.125370i	$0.0400119\pi$
$353$	30.0000	+	17.3205i	1.59674	+	0.921878i	0.604629	+	0.796507i	$0.293321\pi$
$354$	2.59808	+	1.50000i	0.138086	+	0.0797241i
$355$		0			0
$356$	−10.3923			−0.550791
$357$	10.3923	−	12.0000i	0.550019	−	0.635107i
$358$			12.0000i			0.634220i
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	−0.356572	−	0.934268i	$-0.616054\pi$
$359$	5.19615	−	3.00000i	0.274242	−	0.158334i	0.630814	+	0.775934i	$0.282721\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	6.00000	−	3.46410i	0.315353	−	0.182069i
$363$			3.46410i			0.181818i
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$		0			0
$366$		0			0
$367$	11.2583	−	19.5000i	0.587680	−	1.01789i	−0.406855	−	0.913493i	$-0.633375\pi$
$367$	11.2583	−	19.5000i	0.587680	−	1.01789i	0.994535	−	0.104399i	$-0.0332919\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	10.3923	+	18.0000i	0.541002	+	0.937043i
$370$		0			0
$371$	23.3827	+	4.50000i	1.21397	+	0.233628i
$372$	−3.00000			−0.155543
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.997490	−	0.0708063i	$-0.977443\pi$
$373$	−27.7128	+	16.0000i	−1.43492	+	0.828449i	−0.437425	+	0.899255i	$0.644109\pi$
$374$	5.19615	−	9.00000i	0.268687	−	0.465379i
$375$		0			0
$376$	−6.00000	+	3.46410i	−0.309426	+	0.178647i
$377$			10.3923i			0.535231i
$378$	10.3923	+	9.00000i	0.534522	+	0.462910i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	9.52628	−	16.5000i	0.488046	−	0.845321i
$382$		0			0
$383$	3.00000	−	1.73205i	0.153293	−	0.0885037i	−0.421392	−	0.906879i	$-0.638458\pi$
$383$	3.00000	−	1.73205i	0.153293	−	0.0885037i	0.574684	+	0.818375i	$0.305125\pi$
$384$			1.73205i			0.0883883i
$385$		0			0
$386$			23.0000i			1.17067i
$387$	−20.7846	+	12.0000i	−1.05654	+	0.609994i
$388$	2.59808	−	4.50000i	0.131897	−	0.228453i
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	0.840091	−	0.542445i	$-0.182501\pi$
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	−0.0497253	+	0.998763i	$0.515835\pi$
$390$		0			0
$391$			20.7846i			1.05112i
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$			9.00000i			0.453990i
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$		0			0
$396$	7.79423	+	4.50000i	0.391675	+	0.226134i
$397$	−13.8564	−	24.0000i	−0.695433	−	1.20453i	−0.970034	−	0.242967i	$-0.921879\pi$
$397$	−13.8564	−	24.0000i	−0.695433	−	1.20453i	0.274601	−	0.961558i	$-0.411454\pi$
$398$			10.3923i			0.520919i
$399$	−5.19615	−	15.0000i	−0.260133	−	0.750939i
$400$		0			0
$401$	10.3923	−	6.00000i	0.518967	−	0.299626i	−0.217545	−	0.976050i	$-0.569805\pi$
$401$	10.3923	−	6.00000i	0.518967	−	0.299626i	0.736512	+	0.676425i	$0.236472\pi$
$402$	1.73205	−	3.00000i	0.0863868	−	0.149626i
$403$	−5.19615	−	3.00000i	−0.258839	−	0.149441i
$404$		0			0
$405$		0			0
$406$	−6.00000	−	5.19615i	−0.297775	−	0.257881i
$407$	6.00000			0.297409
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	0.302979	−	0.952997i	$-0.402019\pi$
$409$	−7.50000	−	4.33013i	−0.370851	−	0.214111i	−0.673830	+	0.738886i	$0.735352\pi$
$410$		0			0
$411$	27.0000	−	15.5885i	1.33181	−	0.768922i
$412$	−3.46410			−0.170664
$413$	−4.50000	−	0.866025i	−0.221431	−	0.0426143i
$414$	−18.0000			−0.884652
$415$		0			0
$416$	−1.73205	+	3.00000i	−0.0849208	+	0.147087i
$417$	−15.0000	+	25.9808i	−0.734553	+	1.27228i
$418$	−5.19615	−	9.00000i	−0.254152	−	0.440204i
$419$	−24.2487			−1.18463			−0.592314	−	0.805708i	$-0.701785\pi$
$419$	−24.2487			−1.18463			−0.592314	+	0.805708i	$0.701785\pi$
$420$		0			0
$421$	32.0000			1.55958			0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000			1.55958			0.779792	+	0.626038i	$0.215325\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	−18.0000	−	10.3923i	−0.875190	−	0.505291i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$		0			0
$426$	−20.7846			−1.00702
$427$		0			0
$428$	−3.00000			−0.145010
$429$	9.00000	+	15.5885i	0.434524	+	0.752618i
$430$		0			0
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.0925683	−	0.995706i	$-0.529508\pi$
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.908591	+	0.417687i	$0.862841\pi$
$432$	−4.50000	+	2.59808i	−0.216506	+	0.125000i
$433$	34.6410			1.66474			0.832370	−	0.554220i	$-0.186983\pi$
$433$	34.6410			1.66474			0.832370	+	0.554220i	$0.186983\pi$
$434$	4.33013	−	1.50000i	0.207853	−	0.0720023i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	18.0000	+	10.3923i	0.861057	+	0.497131i
$438$	10.3923	+	6.00000i	0.496564	+	0.286691i
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.503421	+	0.864041i	$0.667925\pi$
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.999992	+	0.00395451i	$0.998741\pi$
$440$		0			0
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$			12.0000i			0.570782i
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$	−1.73205	+	3.00000i	−0.0821995	+	0.142374i
$445$		0			0
$446$	12.9904	+	22.5000i	0.615112	+	1.06541i
$447$	−31.1769			−1.47462
$448$	−0.866025	−	2.50000i	−0.0409159	−	0.118114i
$449$		−	30.0000i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$		−	30.0000i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$450$		0			0
$451$	−18.0000	−	10.3923i	−0.847587	−	0.489355i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$	10.5000	−	6.06218i	0.493333	−	0.284826i
$454$		−	5.19615i		−	0.243868i
$455$		0			0
$456$	6.00000			0.280976
$457$	−4.33013	+	2.50000i	−0.202555	+	0.116945i	−0.597847	−	0.801611i	$-0.703977\pi$
$457$	−4.33013	+	2.50000i	−0.202555	+	0.116945i	0.395292	+	0.918556i	$0.370643\pi$
$458$	−12.0000	−	6.92820i	−0.560723	−	0.323734i
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	−13.8564			−0.645357			−0.322679	−	0.946509i	$-0.604583\pi$
$461$	−13.8564			−0.645357			−0.322679	+	0.946509i	$0.604583\pi$
$462$	−13.5000	−	2.59808i	−0.628077	−	0.120873i
$463$			4.00000i			0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$			4.00000i			0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	2.59808	−	1.50000i	0.120613	−	0.0696358i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$	27.0000	−	15.5885i	1.24941	−	0.721348i	0.278419	−	0.960460i	$-0.410190\pi$
$467$	27.0000	−	15.5885i	1.24941	−	0.721348i	0.970992	+	0.239112i	$0.0768563\pi$
$468$	−10.3923			−0.480384
$469$	−1.00000	+	5.19615i	−0.0461757	+	0.239936i
$470$		0			0
$471$	−31.1769	+	18.0000i	−1.43656	+	0.829396i
$472$	0.866025	−	1.50000i	0.0398621	−	0.0690431i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$	1.50000	−	0.866025i	0.0688973	−	0.0397779i
$475$		0			0
$476$	−6.92820	−	6.00000i	−0.317554	−	0.275010i
$477$	−27.0000			−1.23625
$478$	5.19615	−	3.00000i	0.237666	−	0.137217i
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	−0.775969	−	0.630771i	$-0.782739\pi$
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	0.934248	+	0.356624i	$0.116072\pi$
$480$		0			0
$481$	−6.00000	+	3.46410i	−0.273576	+	0.157949i
$482$			25.9808i			1.18339i
$483$	25.9808	−	9.00000i	1.18217	−	0.409514i
$484$	2.00000			0.0909091
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−0.866025	−	0.500000i	−0.0392434	−	0.0226572i	0.480250	−	0.877132i	$-0.340546\pi$
$487$	−0.866025	−	0.500000i	−0.0392434	−	0.0226572i	−0.519493	+	0.854475i	$0.673879\pi$
$488$		0			0
$489$	24.2487			1.09656
$490$		0			0
$491$		−	33.0000i		−	1.48927i	−0.667472	−	0.744635i	$-0.732624\pi$
$491$		−	33.0000i		−	1.48927i	0.667472	−	0.744635i	$-0.267376\pi$
$492$	10.3923	−	6.00000i	0.468521	−	0.270501i
$493$	5.19615	−	9.00000i	0.234023	−	0.405340i
$494$	10.3923	+	6.00000i	0.467572	+	0.269953i
$495$		0			0
$496$			1.73205i			0.0777714i
$497$	30.0000	−	10.3923i	1.34568	−	0.466159i
$498$	−15.0000			−0.672166
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$		0			0
$501$	−15.0000	+	25.9808i	−0.670151	+	1.16073i
$502$	−9.52628	−	16.5000i	−0.425179	−	0.736431i
$503$		−	38.1051i		−	1.69902i	−0.527570	−	0.849512i	$-0.676897\pi$
$503$		−	38.1051i		−	1.69902i	0.527570	−	0.849512i	$-0.323103\pi$
$504$	5.19615	−	6.00000i	0.231455	−	0.267261i
$505$		0			0
$506$	15.5885	−	9.00000i	0.692991	−	0.400099i
$507$	1.50000	+	0.866025i	0.0666173	+	0.0384615i
$508$	−9.52628	−	5.50000i	−0.422660	−	0.244023i
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	0.573914	−	0.818916i	$-0.305424\pi$
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	−0.996159	+	0.0875661i	$0.972091\pi$
$510$		0			0
$511$	−18.0000	−	3.46410i	−0.796273	−	0.153243i
$512$	1.00000			0.0441942
$513$	9.00000	+	15.5885i	0.397360	+	0.688247i
$514$	9.00000	+	5.19615i	0.396973	+	0.229192i
$515$		0			0
$516$	6.92820	+	12.0000i	0.304997	+	0.528271i
$517$	20.7846			0.914106
$518$	1.00000	−	5.19615i	0.0439375	−	0.228306i
$519$		0			0
$520$		0			0
$521$	−13.8564	+	24.0000i	−0.607060	+	1.05146i	0.384662	+	0.923057i	$0.374318\pi$
$521$	−13.8564	+	24.0000i	−0.607060	+	1.05146i	−0.991722	+	0.128402i	$0.959015\pi$
$522$	7.79423	+	4.50000i	0.341144	+	0.196960i
$523$	19.0526	+	33.0000i	0.833110	+	1.44299i	0.895560	+	0.444941i	$0.146775\pi$
$523$	19.0526	+	33.0000i	0.833110	+	1.44299i	−0.0624496	+	0.998048i	$0.519891\pi$
$524$	5.19615			0.226995
$525$		0			0
$526$		0			0
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	2.59808	−	4.50000i	0.113067	−	0.195837i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	5.19615			0.225494
$532$	−8.66025	+	3.00000i	−0.375470	+	0.130066i
$533$	24.0000			1.03956
$534$	−15.5885	+	9.00000i	−0.674579	+	0.389468i
$535$		0			0
$536$	−1.73205	−	1.00000i	−0.0748132	−	0.0431934i
$537$	10.3923	+	18.0000i	0.448461	+	0.776757i
$538$	29.4449			1.26946
$539$	20.7846	−	3.00000i	0.895257	−	0.129219i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	−4.50000	−	2.59808i	−0.193292	−	0.111597i
$543$	6.00000	−	10.3923i	0.257485	−	0.445976i
$544$	3.00000	−	1.73205i	0.128624	−	0.0742611i
$545$		0			0
$546$	15.0000	−	5.19615i	0.641941	−	0.222375i
$547$			2.00000i			0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$			2.00000i			0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$		0			0
$550$		0			0
$551$	−5.19615	−	9.00000i	−0.221364	−	0.383413i
$552$			10.3923i			0.442326i
$553$	−1.73205	+	2.00000i	−0.0736543	+	0.0850487i
$554$			8.00000i			0.339887i
$555$		0			0
$556$	15.0000	+	8.66025i	0.636142	+	0.367277i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$	−4.50000	+	2.59808i	−0.190500	+	0.109985i
$559$			27.7128i			1.17213i
$560$		0			0
$561$		−	18.0000i		−	0.759961i
$562$	−25.9808	+	15.0000i	−1.09593	+	0.632737i
$563$	22.5000	+	12.9904i	0.948262	+	0.547479i	0.892541	−	0.450967i	$-0.148921\pi$
$563$	22.5000	+	12.9904i	0.948262	+	0.547479i	0.0557214	+	0.998446i	$0.482254\pi$
$564$	−6.00000	+	10.3923i	−0.252646	+	0.437595i
$565$		0			0
$566$	−27.7128			−1.16486
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$			12.0000i			0.503509i
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	−0.604947	−	0.796266i	$-0.706806\pi$
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	0.387113	+	0.922032i	$0.373472\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	9.00000	−	5.19615i	0.376309	−	0.217262i
$573$		0			0
$574$	−12.0000	+	13.8564i	−0.500870	+	0.578355i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	0.866025	−	1.50000i	0.0360531	−	0.0624458i	−0.847436	−	0.530898i	$-0.821855\pi$
$577$	0.866025	−	1.50000i	0.0360531	−	0.0624458i	0.883489	+	0.468452i	$0.155188\pi$
$578$	−2.50000	+	4.33013i	−0.103986	+	0.180110i
$579$	19.9186	+	34.5000i	0.827788	+	1.43377i
$580$		0			0
$581$	21.6506	−	7.50000i	0.898220	−	0.311152i
$582$		−	9.00000i		−	0.373062i
$583$	23.3827	−	13.5000i	0.968412	−	0.559113i
$584$	3.46410	−	6.00000i	0.143346	−	0.248282i
$585$		0			0
$586$	16.5000	−	9.52628i	0.681609	−	0.393527i
$587$		−	15.5885i		−	0.643404i	−0.946841	−	0.321702i	$-0.895745\pi$
$587$		−	15.5885i		−	0.643404i	0.946841	−	0.321702i	$-0.104255\pi$
$588$	−4.50000	+	11.2583i	−0.185577	+	0.464286i
$589$	6.00000			0.247226
$590$		0			0
$591$	27.0000	+	15.5885i	1.11063	+	0.641223i
$592$	1.73205	+	1.00000i	0.0711868	+	0.0410997i
$593$	−33.0000	+	19.0526i	−1.35515	+	0.782395i	−0.988965	−	0.148148i	$-0.952669\pi$
$593$	−33.0000	+	19.0526i	−1.35515	+	0.782395i	−0.366182	+	0.930543i	$0.619335\pi$
$594$	15.5885			0.639602
$595$		0			0
$596$			18.0000i			0.737309i
$597$	9.00000	+	15.5885i	0.368345	+	0.637993i
$598$	−10.3923	+	18.0000i	−0.424973	+	0.736075i
$599$	−25.9808	−	15.0000i	−1.06155	−	0.612883i	−0.135686	−	0.990752i	$-0.543324\pi$
$599$	−25.9808	−	15.0000i	−1.06155	−	0.612883i	−0.925859	+	0.377869i	$0.876657\pi$
$600$		0			0
$601$		−	29.4449i		−	1.20108i	−0.799594	−	0.600541i	$-0.794952\pi$
$601$		−	29.4449i		−	1.20108i	0.799594	−	0.600541i	$-0.205048\pi$
$602$	−16.0000	−	13.8564i	−0.652111	−	0.564745i
$603$		−	6.00000i		−	0.244339i
$604$	−3.50000	−	6.06218i	−0.142413	−	0.246667i
$605$		0			0
$606$		0			0
$607$	11.2583	+	19.5000i	0.456962	+	0.791481i	0.998799	−	0.0490029i	$-0.0156044\pi$
$607$	11.2583	+	19.5000i	0.456962	+	0.791481i	−0.541837	+	0.840484i	$0.682271\pi$
$608$		−	3.46410i		−	0.140488i
$609$	−13.5000	−	2.59808i	−0.547048	−	0.105279i
$610$		0			0
$611$	−20.7846	+	12.0000i	−0.840855	+	0.485468i
$612$	9.00000	+	5.19615i	0.363803	+	0.210042i
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	0.534570	−	0.845124i	$-0.320473\pi$
$613$	1.73205	+	1.00000i	0.0699569	+	0.0403896i	−0.464614	+	0.885514i	$0.653807\pi$
$614$	−12.1244	−	21.0000i	−0.489299	−	0.847491i
$615$		0			0
$616$	−1.50000	+	7.79423i	−0.0604367	+	0.314038i
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$	−5.19615	+	3.00000i	−0.209020	+	0.120678i
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	0.374550	−	0.927207i	$-0.377797\pi$
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	−0.615710	+	0.787973i	$0.711131\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$	13.8564			0.555591
$623$	18.0000	−	20.7846i	0.721155	−	0.832718i
$624$			6.00000i			0.240192i
$625$		0			0
$626$	−0.866025	+	1.50000i	−0.0346133	+	0.0599521i
$627$	−15.5885	−	9.00000i	−0.622543	−	0.359425i
$628$	10.3923	+	18.0000i	0.414698	+	0.718278i
$629$	6.92820			0.276246
$630$		0			0
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	−0.500000	−	0.866025i	−0.0198889	−	0.0344486i
$633$	−6.00000	−	3.46410i	−0.238479	−	0.137686i
$634$	7.50000	−	12.9904i	0.297863	−	0.515914i
$635$		0			0
$636$			15.5885i			0.618123i
$637$	−19.0526	+	15.0000i	−0.754890	+	0.594322i
$638$	−9.00000			−0.356313
$639$	−31.1769	+	18.0000i	−1.23334	+	0.712069i
$640$		0			0
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	0.850741	−	0.525584i	$-0.176153\pi$
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	−0.0297987	+	0.999556i	$0.509487\pi$
$642$	−4.50000	+	2.59808i	−0.177601	+	0.102538i
$643$	−17.3205			−0.683054			−0.341527	−	0.939872i	$-0.610944\pi$
$643$	−17.3205			−0.683054			−0.341527	+	0.939872i	$0.610944\pi$
$644$	−5.19615	−	15.0000i	−0.204757	−	0.591083i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$647$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−4.50000	+	2.59808i	−0.176640	+	0.101983i
$650$		0			0
$651$	5.19615	−	6.00000i	0.203653	−	0.235159i
$652$		−	14.0000i		−	0.548282i
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	0.835182	−	0.549973i	$-0.185362\pi$
$653$	−1.50000	−	2.59808i	−0.0586995	−	0.101671i	−0.893882	+	0.448303i	$0.852029\pi$
$654$	−3.00000	−	1.73205i	−0.117309	−	0.0677285i
$655$		0			0
$656$	−3.46410	−	6.00000i	−0.135250	−	0.234261i
$657$	20.7846			0.810885
$658$	3.46410	−	18.0000i	0.135045	−	0.701713i
$659$			12.0000i			0.467454i	0.972302	+	0.233727i	$0.0750921\pi$
$659$			12.0000i			0.467454i	−0.972302	+	0.233727i	$0.924908\pi$
$660$		0			0
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	0.378754	−	0.925497i	$-0.376353\pi$
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	−0.612127	+	0.790759i	$0.709686\pi$
$662$	4.00000	−	6.92820i	0.155464	−	0.269272i
$663$	10.3923	+	18.0000i	0.403604	+	0.699062i
$664$			8.66025i			0.336083i
$665$		0			0
$666$			6.00000i			0.232495i
$667$	15.5885	−	9.00000i	0.603587	−	0.348481i
$668$	15.0000	+	8.66025i	0.580367	+	0.335075i
$669$	38.9711	+	22.5000i	1.50671	+	0.869900i
$670$		0			0
$671$		0			0
$672$	−3.46410	−	3.00000i	−0.133631	−	0.115728i
$673$			41.0000i			1.58043i	0.612827	+	0.790217i	$0.290032\pi$
$673$			41.0000i			1.58043i	−0.612827	+	0.790217i	$0.709968\pi$
$674$	11.2583	−	6.50000i	0.433655	−	0.250371i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	4.50000	−	2.59808i	0.172949	−	0.0998522i	−0.411027	−	0.911623i	$-0.634830\pi$
$677$	4.50000	−	2.59808i	0.172949	−	0.0998522i	0.583976	+	0.811771i	$0.301496\pi$
$678$		−	20.7846i		−	0.798228i
$679$	4.50000	+	12.9904i	0.172694	+	0.498525i
$680$		0			0
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$	2.59808	−	4.50000i	0.0994855	−	0.172314i
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	−0.993940	−	0.109926i	$-0.964939\pi$
$683$	−10.5000	+	18.1865i	−0.401771	+	0.695888i	0.592168	+	0.805814i	$0.298272\pi$
$684$	9.00000	−	5.19615i	0.344124	−	0.198680i
$685$		0			0
$686$	0.866025	−	18.5000i	0.0330650	−	0.706333i
$687$	−24.0000			−0.915657
$688$	6.92820	−	4.00000i	0.264135	−	0.152499i
$689$	−15.5885	+	27.0000i	−0.593873	+	1.02862i
$690$		0			0
$691$	−6.00000	+	3.46410i	−0.228251	+	0.131781i	−0.609765	−	0.792582i	$-0.708736\pi$
$691$	−6.00000	+	3.46410i	−0.228251	+	0.131781i	0.381514	+	0.924363i	$0.375403\pi$
$692$		0			0
$693$	−22.5000	+	7.79423i	−0.854704	+	0.296078i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	2.59808	−	4.50000i	0.0984798	−	0.170572i
$697$	−20.7846	−	12.0000i	−0.787273	−	0.454532i
$698$	−9.00000	+	5.19615i	−0.340655	+	0.196677i
$699$			31.1769i			1.17922i
$700$		0			0
$701$			3.00000i			0.113308i	0.998394	+	0.0566542i	$0.0180433\pi$
$701$			3.00000i			0.113308i	−0.998394	+	0.0566542i	$0.981957\pi$
$702$	−15.5885	+	9.00000i	−0.588348	+	0.339683i
$703$	3.46410	−	6.00000i	0.130651	−	0.226294i
$704$	−2.59808	−	1.50000i	−0.0979187	−	0.0565334i
$705$		0			0
$706$		−	34.6410i		−	1.30373i
$707$		0			0
$708$		−	3.00000i		−	0.112747i
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$	1.50000	−	2.59808i	0.0562544	−	0.0974355i
$712$	5.19615	+	9.00000i	0.194734	+	0.337289i
$713$			10.3923i			0.389195i
$714$	−15.5885	−	3.00000i	−0.583383	−	0.112272i
$715$		0			0
$716$	10.3923	−	6.00000i	0.388379	−	0.224231i
$717$	5.19615	−	9.00000i	0.194054	−	0.336111i
$718$	−5.19615	−	3.00000i	−0.193919	−	0.111959i
$719$	−22.5167	−	39.0000i	−0.839730	−	1.45445i	−0.890121	−	0.455725i	$-0.849380\pi$
$719$	−22.5167	−	39.0000i	−0.839730	−	1.45445i	0.0503909	−	0.998730i	$-0.483953\pi$
$720$		0			0
$721$	6.00000	−	6.92820i	0.223452	−	0.258020i
$722$	7.00000			0.260513
$723$	22.5000	+	38.9711i	0.836784	+	1.44935i
$724$	−6.00000	−	3.46410i	−0.222988	−	0.128742i
$725$		0			0
$726$	3.00000	−	1.73205i	0.111340	−	0.0642824i
$727$	−29.4449			−1.09205			−0.546025	−	0.837769i	$-0.683860\pi$
$727$	−29.4449			−1.09205			−0.546025	+	0.837769i	$0.683860\pi$
$728$	−3.00000	−	8.66025i	−0.111187	−	0.320970i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	13.8564	−	24.0000i	0.512498	−	0.887672i
$732$		0			0
$733$	−17.3205	−	30.0000i	−0.639748	−	1.10808i	−0.985488	−	0.169745i	$-0.945706\pi$
$733$	−17.3205	−	30.0000i	−0.639748	−	1.10808i	0.345740	−	0.938330i	$-0.387628\pi$
$734$	−22.5167			−0.831105
$735$		0			0
$736$	6.00000			0.221163
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$	10.3923	−	18.0000i	0.382546	−	0.662589i
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	−0.943215	−	0.332184i	$-0.892215\pi$
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	0.759287	+	0.650756i	$0.225548\pi$
$740$		0			0
$741$	20.7846			0.763542
$742$	−7.79423	−	22.5000i	−0.286135	−	0.826001i
$743$	18.0000			0.660356			0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000			0.660356			0.330178	+	0.943919i	$0.392891\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$		0			0
$746$	27.7128	+	16.0000i	1.01464	+	0.585802i
$747$	−22.5000	+	12.9904i	−0.823232	+	0.475293i
$748$	−10.3923			−0.379980
$749$	5.19615	−	6.00000i	0.189863	−	0.219235i
$750$		0			0
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	0.948753	−	0.316017i	$-0.102346\pi$
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	6.00000	+	3.46410i	0.218797	+	0.126323i
$753$	−28.5788	−	16.5000i	−1.04147	−	0.601293i
$754$	9.00000	−	5.19615i	0.327761	−	0.189233i
$755$		0			0
$756$	2.59808	−	13.5000i	0.0944911	−	0.490990i
$757$			4.00000i			0.145382i	0.997354	+	0.0726912i	$0.0231588\pi$
$757$			4.00000i			0.145382i	−0.997354	+	0.0726912i	$0.976841\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$	15.5885	−	27.0000i	0.565825	−	0.980038i
$760$		0			0
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	0.665276	−	0.746597i	$-0.268314\pi$
$761$	−8.66025	−	15.0000i	−0.313934	−	0.543750i	−0.979210	+	0.202848i	$0.934980\pi$
$762$	−19.0526			−0.690201
$763$	5.19615	+	1.00000i	0.188113	+	0.0362024i
$764$		0			0
$765$		0			0
$766$	−3.00000	−	1.73205i	−0.108394	−	0.0625815i
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$		−	19.0526i		−	0.687053i	−0.939143	−	0.343526i	$-0.888379\pi$
$769$		−	19.0526i		−	0.687053i	0.939143	−	0.343526i	$-0.111621\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	19.9186	−	11.5000i	0.716886	−	0.413894i
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	0.00186926	−	0.999998i	$-0.499405\pi$
$773$	−24.0000	−	13.8564i	−0.863220	−	0.498380i	−0.865089	+	0.501618i	$0.832738\pi$
$774$	20.7846	+	12.0000i	0.747087	+	0.431331i
$775$		0			0
$776$	−5.19615			−0.186531
$777$	−3.00000	−	8.66025i	−0.107624	−	0.310685i
$778$		−	18.0000i		−	0.645331i
$779$	−20.7846	+	12.0000i	−0.744686	+	0.429945i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$	18.0000	−	10.3923i	0.643679	−	0.371628i
$783$	15.5885			0.557086
$784$	6.50000	+	2.59808i	0.232143	+	0.0927884i
$785$		0			0
$786$	7.79423	−	4.50000i	0.278011	−	0.160510i
$787$	−20.7846	+	36.0000i	−0.740891	+	1.28326i	0.211199	+	0.977443i	$0.432263\pi$
$787$	−20.7846	+	36.0000i	−0.740891	+	1.28326i	−0.952090	+	0.305818i	$0.901070\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$		0			0
$791$	10.3923	+	30.0000i	0.369508	+	1.06668i
$792$		−	9.00000i		−	0.319801i
$793$		0			0
$794$	−13.8564	+	24.0000i	−0.491745	+	0.851728i
$795$		0			0
$796$	9.00000	−	5.19615i	0.318997	−	0.184173i
$797$		−	25.9808i		−	0.920286i	−0.887845	−	0.460143i	$-0.847798\pi$
$797$		−	25.9808i		−	0.920286i	0.887845	−	0.460143i	$-0.152202\pi$
$798$	−10.3923	+	12.0000i	−0.367884	+	0.424795i
$799$	24.0000			0.849059
$800$		0			0
$801$	−15.5885	+	27.0000i	−0.550791	+	0.953998i
$802$	−10.3923	−	6.00000i	−0.366965	−	0.211867i
$803$	−18.0000	+	10.3923i	−0.635206	+	0.366736i
$804$	−3.46410			−0.122169
$805$		0			0
$806$			6.00000i			0.211341i
$807$	44.1673	−	25.5000i	1.55476	−	0.897643i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$			31.1769i			1.09477i	0.836881	+	0.547385i	$0.184377\pi$
$811$			31.1769i			1.09477i	−0.836881	+	0.547385i	$0.815623\pi$
$812$	−1.50000	+	7.79423i	−0.0526397	+	0.273524i
$813$	−9.00000			−0.315644
$814$	−3.00000	−	5.19615i	−0.105150	−	0.182125i
$815$		0			0
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	−13.8564	−	24.0000i	−0.484774	−	0.839654i
$818$			8.66025i			0.302799i
$819$	18.0000	−	20.7846i	0.628971	−	0.726273i
$820$		0			0
$821$	−2.59808	+	1.50000i	−0.0906735	+	0.0523504i	−0.544651	−	0.838663i	$-0.683338\pi$
$821$	−2.59808	+	1.50000i	−0.0906735	+	0.0523504i	0.453978	+	0.891013i	$0.350005\pi$
$822$	−27.0000	−	15.5885i	−0.941733	−	0.543710i
$823$	6.92820	+	4.00000i	0.241502	+	0.139431i	0.615867	−	0.787850i	$-0.288806\pi$
$823$	6.92820	+	4.00000i	0.241502	+	0.139431i	−0.374365	+	0.927281i	$0.622139\pi$
$824$	1.73205	+	3.00000i	0.0603388	+	0.104510i
$825$		0			0
$826$	1.50000	+	4.33013i	0.0521917	+	0.150664i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$	9.00000	+	15.5885i	0.312772	+	0.541736i
$829$	15.0000	+	8.66025i	0.520972	+	0.300783i	0.737332	−	0.675530i	$-0.236085\pi$
$829$	15.0000	+	8.66025i	0.520972	+	0.300783i	−0.216361	+	0.976314i	$0.569419\pi$
$830$		0			0
$831$	6.92820	+	12.0000i	0.240337	+	0.416275i
$832$	3.46410			0.120096
$833$	24.0000	−	3.46410i	0.831551	−	0.120024i
$834$	30.0000			1.03882
$835$		0			0
$836$	−5.19615	+	9.00000i	−0.179713	+	0.311272i
$837$	−4.50000	+	7.79423i	−0.155543	+	0.269408i
$838$	12.1244	+	21.0000i	0.418829	+	0.725433i
$839$	−3.46410			−0.119594			−0.0597970	−	0.998211i	$-0.519045\pi$
$839$	−3.46410			−0.119594			−0.0597970	+	0.998211i	$0.519045\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−16.0000	−	27.7128i	−0.551396	−	0.955047i
$843$	−25.9808	+	45.0000i	−0.894825	+	1.54988i
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$		0			0
$846$			20.7846i			0.714590i
$847$	−3.46410	+	4.00000i	−0.119028	+	0.137442i
$848$	9.00000			0.309061
$849$	−41.5692	+	24.0000i	−1.42665	+	0.823678i
$850$		0			0
$851$	10.3923	+	6.00000i	0.356244	+	0.205677i
$852$	10.3923	+	18.0000i	0.356034	+	0.616670i
$853$	−24.2487			−0.830260			−0.415130	−	0.909762i	$-0.636264\pi$
$853$	−24.2487			−0.830260			−0.415130	+	0.909762i	$0.636264\pi$
$854$		0			0
$855$		0			0
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	−12.0000	−	6.92820i	−0.409912	−	0.236663i	0.280840	−	0.959755i	$-0.409387\pi$
$857$	−12.0000	−	6.92820i	−0.409912	−	0.236663i	−0.690752	+	0.723092i	$0.742720\pi$
$858$	9.00000	−	15.5885i	0.307255	−	0.532181i
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	−0.160437	−	0.987046i	$-0.551290\pi$
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	0.774589	+	0.632465i	$0.217957\pi$
$860$		0			0
$861$	−6.00000	+	31.1769i	−0.204479	+	1.06251i
$862$			24.0000i			0.817443i
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.800799	−	0.598933i	$-0.795592\pi$
$863$	−27.0000	−	46.7654i	−0.919091	−	1.59191i	−0.118291	−	0.992979i	$-0.537742\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$		0			0
$866$	−17.3205	−	30.0000i	−0.588575	−	1.01944i
$867$			8.66025i			0.294118i
$868$	−3.46410	−	3.00000i	−0.117579	−	0.101827i
$869$			3.00000i			0.101768i
$870$		0			0
$871$	−6.00000	−	3.46410i	−0.203302	−	0.117377i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$	−7.79423	−	13.5000i	−0.263795	−	0.456906i
$874$		−	20.7846i		−	0.703050i
$875$		0			0
$876$		−	12.0000i		−	0.405442i
$877$	38.1051	−	22.0000i	1.28672	−	0.742887i	0.308651	−	0.951175i	$-0.400123\pi$
$877$	38.1051	−	22.0000i	1.28672	−	0.742887i	0.978068	+	0.208288i	$0.0667892\pi$
$878$	31.5000	+	18.1865i	1.06307	+	0.613766i
$879$	16.5000	−	28.5788i	0.556531	−	0.963940i
$880$		0			0
$881$	10.3923			0.350126			0.175063	−	0.984557i	$-0.443987\pi$
$881$	10.3923			0.350126			0.175063	+	0.984557i	$0.443987\pi$
$882$	3.00000	+	20.7846i	0.101015	+	0.699854i
$883$		−	52.0000i		−	1.74994i	−0.484178	−	0.874970i	$-0.660881\pi$
$883$		−	52.0000i		−	1.74994i	0.484178	−	0.874970i	$-0.339119\pi$
$884$	10.3923	−	6.00000i	0.349531	−	0.201802i
$885$		0			0
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	21.0000	−	12.1244i	0.705111	−	0.407096i	−0.104137	−	0.994563i	$-0.533208\pi$
$887$	21.0000	−	12.1244i	0.705111	−	0.407096i	0.809248	+	0.587467i	$0.199875\pi$
$888$	3.46410			0.116248
$889$	27.5000	−	9.52628i	0.922320	−	0.319501i
$890$		0			0
$891$	23.3827	−	13.5000i	0.783349	−	0.452267i
$892$	12.9904	−	22.5000i	0.434950	−	0.753356i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$	15.5885	+	27.0000i	0.521356	+	0.903015i
$895$		0			0
$896$	−1.73205	+	2.00000i	−0.0578638	+	0.0668153i
$897$			36.0000i			1.20201i
$898$	−25.9808	+	15.0000i	−0.866989	+	0.500556i
$899$	2.59808	−	4.50000i	0.0866507	−	0.150083i
$900$		0			0
$901$	27.0000	−	15.5885i	0.899500	−	0.519327i
$902$			20.7846i			0.692052i
$903$	−36.0000	−	6.92820i	−1.19800	−	0.230556i
$904$	−12.0000			−0.399114
$905$		0			0
$906$	−10.5000	−	6.06218i	−0.348839	−	0.201402i
$907$	22.5167	+	13.0000i	0.747653	+	0.431658i	0.824845	−	0.565358i	$-0.191262\pi$
$907$	22.5167	+	13.0000i	0.747653	+	0.431658i	−0.0771920	+	0.997016i	$0.524595\pi$
$908$	−4.50000	+	2.59808i	−0.149338	+	0.0862202i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$	12.9904	−	22.5000i	0.429919	−	0.744641i
$914$	4.33013	+	2.50000i	0.143228	+	0.0826927i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	−9.00000	+	10.3923i	−0.297206	+	0.343184i
$918$	18.0000			0.594089
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	0.652616	−	0.757689i	$-0.273671\pi$
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$920$		0			0
$921$	−36.3731	−	21.0000i	−1.19853	−	0.691974i
$922$	6.92820	+	12.0000i	0.228168	+	0.395199i
$923$			41.5692i			1.36827i
$924$	4.50000	+	12.9904i	0.148039	+	0.427352i
$925$		0			0
$926$	3.46410	−	2.00000i	0.113837	−	0.0657241i
$927$	−5.19615	+	9.00000i	−0.170664	+	0.295599i
$928$	−2.59808	−	1.50000i	−0.0852860	−	0.0492399i
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	−0.922474	−	0.386060i	$-0.873836\pi$
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	0.126899	−	0.991916i	$-0.459497\pi$
$930$		0			0
$931$	9.00000	−	22.5167i	0.294963	−	0.737954i
$932$	18.0000			0.589610
$933$	20.7846	−	12.0000i	0.680458	−	0.392862i
$934$	−27.0000	−	15.5885i	−0.883467	−	0.510070i
$935$		0			0
$936$	5.19615	+	9.00000i	0.169842	+	0.294174i
$937$	−22.5167			−0.735587			−0.367794	−	0.929907i	$-0.619887\pi$
$937$	−22.5167			−0.735587			−0.367794	+	0.929907i	$0.619887\pi$
$938$	5.00000	−	1.73205i	0.163256	−	0.0565535i
$939$			3.00000i			0.0979013i
$940$		0			0
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	0.462693	+	0.886518i	$0.346883\pi$
$941$	−16.4545	+	28.5000i	−0.536401	+	0.929073i	−0.999094	+	0.0425550i	$0.986450\pi$
$942$	31.1769	+	18.0000i	1.01580	+	0.586472i
$943$	−20.7846	−	36.0000i	−0.676840	−	1.17232i
$944$	−1.73205			−0.0563735
$945$		0			0
$946$	−24.0000			−0.780307
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$	−1.50000	−	0.866025i	−0.0487177	−	0.0281272i
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$		0			0
$951$		−	25.9808i		−	0.842484i
$952$	−1.73205	+	9.00000i	−0.0561361	+	0.291692i
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$	13.5000	+	23.3827i	0.437079	+	0.757042i
$955$		0			0
$956$	−5.19615	−	3.00000i	−0.168056	−	0.0970269i
$957$	−13.5000	+	7.79423i	−0.436393	+	0.251952i
$958$	−6.92820			−0.223840
$959$	46.7654	+	9.00000i	1.51013	+	0.290625i
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$	6.00000	+	3.46410i	0.193448	+	0.111687i
$963$	−4.50000	+	7.79423i	−0.145010	+	0.251166i
$964$	22.5000	−	12.9904i	0.724676	−	0.418392i
$965$		0			0
$966$	−20.7846	−	18.0000i	−0.668734	−	0.579141i
$967$		−	7.00000i		−	0.225105i	−0.993646	−	0.112552i	$-0.964097\pi$
$967$		−	7.00000i		−	0.225105i	0.993646	−	0.112552i	$-0.0359026\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$		0			0
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	0.927103	−	0.374806i	$-0.122291\pi$
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	−0.788143	+	0.615492i	$0.788957\pi$
$972$			15.5885i			0.500000i
$973$	−43.3013	+	15.0000i	−1.38817	+	0.480878i
$974$			1.00000i			0.0320421i
$975$		0			0
$976$		0			0
$977$	12.0000	−	20.7846i	0.383914	−	0.664959i	−0.607704	−	0.794164i	$-0.707909\pi$
$977$	12.0000	−	20.7846i	0.383914	−	0.664959i	0.991618	+	0.129205i	$0.0412426\pi$
$978$	−12.1244	−	21.0000i	−0.387694	−	0.671506i
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$	−6.00000			−0.191565
$982$	−28.5788	+	16.5000i	−0.911987	+	0.526536i
$983$	−12.0000	−	6.92820i	−0.382741	−	0.220975i	0.296269	−	0.955104i	$-0.404257\pi$
$983$	−12.0000	−	6.92820i	−0.382741	−	0.220975i	−0.679010	+	0.734129i	$0.737591\pi$
$984$	−10.3923	−	6.00000i	−0.331295	−	0.191273i
$985$		0			0
$986$	−10.3923			−0.330958
$987$	−10.3923	−	30.0000i	−0.330791	−	0.954911i
$988$		−	12.0000i		−	0.381771i
$989$	41.5692	−	24.0000i	1.32182	−	0.763156i
$990$		0			0
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	−0.202988	−	0.979181i	$-0.565065\pi$
$991$	23.5000	−	40.7032i	0.746502	−	1.29298i	0.949490	−	0.313798i	$-0.101602\pi$
$992$	1.50000	−	0.866025i	0.0476250	−	0.0274963i
$993$		−	13.8564i		−	0.439720i
$994$	−24.0000	−	20.7846i	−0.761234	−	0.659248i
$995$		0			0
$996$	7.50000	+	12.9904i	0.237647	+	0.411616i
$997$	−8.66025	+	15.0000i	−0.274273	+	0.475055i	−0.969951	−	0.243299i	$-0.921771\pi$
$997$	−8.66025	+	15.0000i	−0.274273	+	0.475055i	0.695678	+	0.718353i	$0.255104\pi$
$998$	11.0000	−	19.0526i	0.348199	−	0.603098i
$999$	5.19615	+	9.00000i	0.164399	+	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.u.a.899.1		4
3.2	odd	2		1050.2.u.d.899.1		4
5.2	odd	4		1050.2.s.b.101.2		4
5.3	odd	4		42.2.f.a.17.1	yes	4
5.4	even	2		1050.2.u.d.899.2		4
7.5	odd	6	inner	1050.2.u.a.299.2		4
15.2	even	4		1050.2.s.b.101.1		4
15.8	even	4		42.2.f.a.17.2	yes	4
15.14	odd	2	inner	1050.2.u.a.899.2		4
20.3	even	4		336.2.bc.e.17.1		4
21.5	even	6		1050.2.u.d.299.2		4
35.3	even	12		294.2.d.a.293.2		4
35.12	even	12		1050.2.s.b.551.1		4
35.13	even	4		294.2.f.a.227.1		4
35.18	odd	12		294.2.d.a.293.1		4
35.19	odd	6		1050.2.u.d.299.1		4
35.23	odd	12		294.2.f.a.215.2		4
35.33	even	12		42.2.f.a.5.2	yes	4
45.13	odd	12		1134.2.l.c.269.1		4
45.23	even	12		1134.2.l.c.269.2		4
45.38	even	12		1134.2.t.d.1025.1		4
45.43	odd	12		1134.2.t.d.1025.2		4
60.23	odd	4		336.2.bc.e.17.2		4
105.23	even	12		294.2.f.a.215.1		4
105.38	odd	12		294.2.d.a.293.3		4
105.47	odd	12		1050.2.s.b.551.2		4
105.53	even	12		294.2.d.a.293.4		4
105.68	odd	12		42.2.f.a.5.1	✓	4
105.83	odd	4		294.2.f.a.227.2		4
105.89	even	6	inner	1050.2.u.a.299.1		4
140.3	odd	12		2352.2.k.e.881.1		4
140.103	odd	12		336.2.bc.e.257.2		4
140.123	even	12		2352.2.k.e.881.3		4
315.68	odd	12		1134.2.t.d.593.2		4
315.103	even	12		1134.2.t.d.593.1		4
315.173	odd	12		1134.2.l.c.215.2		4
315.313	even	12		1134.2.l.c.215.1		4
420.143	even	12		2352.2.k.e.881.4		4
420.263	odd	12		2352.2.k.e.881.2		4
420.383	even	12		336.2.bc.e.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.f.a.5.1	✓	4	105.68	odd	12
42.2.f.a.5.2	yes	4	35.33	even	12
42.2.f.a.17.1	yes	4	5.3	odd	4
42.2.f.a.17.2	yes	4	15.8	even	4
294.2.d.a.293.1		4	35.18	odd	12
294.2.d.a.293.2		4	35.3	even	12
294.2.d.a.293.3		4	105.38	odd	12
294.2.d.a.293.4		4	105.53	even	12
294.2.f.a.215.1		4	105.23	even	12
294.2.f.a.215.2		4	35.23	odd	12
294.2.f.a.227.1		4	35.13	even	4
294.2.f.a.227.2		4	105.83	odd	4
336.2.bc.e.17.1		4	20.3	even	4
336.2.bc.e.17.2		4	60.23	odd	4
336.2.bc.e.257.1		4	420.383	even	12
336.2.bc.e.257.2		4	140.103	odd	12
1050.2.s.b.101.1		4	15.2	even	4
1050.2.s.b.101.2		4	5.2	odd	4
1050.2.s.b.551.1		4	35.12	even	12
1050.2.s.b.551.2		4	105.47	odd	12
1050.2.u.a.299.1		4	105.89	even	6	inner
1050.2.u.a.299.2		4	7.5	odd	6	inner
1050.2.u.a.899.1		4	1.1	even	1	trivial
1050.2.u.a.899.2		4	15.14	odd	2	inner
1050.2.u.d.299.1		4	35.19	odd	6
1050.2.u.d.299.2		4	21.5	even	6
1050.2.u.d.899.1		4	3.2	odd	2
1050.2.u.d.899.2		4	5.4	even	2
1134.2.l.c.215.1		4	315.313	even	12
1134.2.l.c.215.2		4	315.173	odd	12
1134.2.l.c.269.1		4	45.13	odd	12
1134.2.l.c.269.2		4	45.23	even	12
1134.2.t.d.593.1		4	315.103	even	12
1134.2.t.d.593.2		4	315.68	odd	12
1134.2.t.d.1025.1		4	45.38	even	12
1134.2.t.d.1025.2		4	45.43	odd	12
2352.2.k.e.881.1		4	140.3	odd	12
2352.2.k.e.881.2		4	420.263	odd	12
2352.2.k.e.881.3		4	140.123	even	12
2352.2.k.e.881.4		4	420.143	even	12

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205i q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +(1.50000 - 0.866025i) q^{12} +3.46410 q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 1.73205i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-3.00000 + 1.73205i) q^{19} +(-0.866025 + 4.50000i) q^{21} +3.00000i q^{22} +(-3.00000 - 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(-1.73205 - 3.00000i) q^{26} -5.19615i q^{27} +(2.59808 + 0.500000i) q^{28} +3.00000i q^{29} +(-1.50000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.59808 + 4.50000i) q^{33} +3.46410i q^{34} -3.00000 q^{36} +(-1.73205 + 1.00000i) q^{37} +(3.00000 + 1.73205i) q^{38} +(-5.19615 - 3.00000i) q^{39} +6.92820 q^{41} +(4.33013 - 1.50000i) q^{42} +8.00000i q^{43} +(2.59808 - 1.50000i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(-6.00000 + 3.46410i) q^{47} +1.73205i q^{48} +(-5.50000 + 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{51} +(-1.73205 + 3.00000i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(-0.866025 - 2.50000i) q^{56} +6.00000 q^{57} +(2.59808 - 1.50000i) q^{58} +(0.866025 - 1.50000i) q^{59} +1.73205i q^{62} +(5.19615 - 6.00000i) q^{63} +1.00000 q^{64} +(2.59808 - 4.50000i) q^{66} +(-1.73205 - 1.00000i) q^{67} +(3.00000 - 1.73205i) q^{68} +10.3923i q^{69} +12.0000i q^{71} +(1.50000 + 2.59808i) q^{72} +(3.46410 - 6.00000i) q^{73} +(1.73205 + 1.00000i) q^{74} -3.46410i q^{76} +(-1.50000 + 7.79423i) q^{77} +6.00000i q^{78} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-3.46410 - 6.00000i) q^{82} +8.66025i q^{83} +(-3.46410 - 3.00000i) q^{84} +(6.92820 - 4.00000i) q^{86} +(2.59808 - 4.50000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(5.19615 + 9.00000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +6.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(6.00000 + 3.46410i) q^{94} +(1.50000 - 0.866025i) q^{96} -5.19615 q^{97} +(6.50000 + 2.59808i) q^{98} -9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 4 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} + 4 q^{8} + 6 q^{9} + 6 q^{12} - 2 q^{16} - 12 q^{17} + 6 q^{18} - 12 q^{19} - 12 q^{23} - 6 q^{24} - 6 q^{31} - 2 q^{32} - 12 q^{36} + 12 q^{38} - 12 q^{46} - 24 q^{47} - 22 q^{49} + 12 q^{51} - 18 q^{53} - 18 q^{54} + 24 q^{57} + 4 q^{64} + 12 q^{68} + 6 q^{72} - 6 q^{77} - 2 q^{79} - 18 q^{81} - 12 q^{91} + 24 q^{92} + 6 q^{93} + 24 q^{94} + 6 q^{96} + 26 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 + 4 * q^8 + 6 * q^9 + 6 * q^12 - 2 * q^16 - 12 * q^17 + 6 * q^18 - 12 * q^19 - 12 * q^23 - 6 * q^24 - 6 * q^31 - 2 * q^32 - 12 * q^36 + 12 * q^38 - 12 * q^46 - 24 * q^47 - 22 * q^49 + 12 * q^51 - 18 * q^53 - 18 * q^54 + 24 * q^57 + 4 * q^64 + 12 * q^68 + 6 * q^72 - 6 * q^77 - 2 * q^79 - 18 * q^81 - 12 * q^91 + 24 * q^92 + 6 * q^93 + 24 * q^94 + 6 * q^96 + 26 * q^98

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