LMFDB - Embedded newform 975.2.bb.d.874.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(724,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("975.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bb (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:	$7.78541419707$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			874.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.874
Dual form			975.2.bb.d.724.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -1.00000i q^{12} +(-0.866025 - 3.50000i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +1.00000i q^{18} +(-3.00000 + 5.19615i) q^{19} -2.00000 q^{21} +(-1.73205 - 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.50000 + 2.59808i) q^{24} +(2.50000 + 2.59808i) q^{26} +1.00000i q^{27} +(-1.73205 + 1.00000i) q^{28} +(-0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(4.33013 + 2.50000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +7.00000 q^{34} +(0.500000 + 0.866025i) q^{36} +(-0.866025 + 0.500000i) q^{37} -6.00000i q^{38} +(2.50000 + 2.59808i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(1.73205 - 1.00000i) q^{42} +(-5.19615 - 3.00000i) q^{43} -2.00000 q^{44} +(3.00000 - 5.19615i) q^{46} -6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +7.00000 q^{51} +(3.46410 + 1.00000i) q^{52} -9.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{56} -6.00000i q^{57} +(0.866025 + 0.500000i) q^{58} +(-0.500000 + 0.866025i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(1.73205 - 1.00000i) q^{63} -7.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(6.06218 - 3.50000i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +11.0000i q^{73} +(0.500000 - 0.866025i) q^{74} +(-3.00000 - 5.19615i) q^{76} +4.00000i q^{77} +(-3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} -14.0000i q^{83} +(1.00000 - 1.73205i) q^{84} +6.00000 q^{86} +(0.866025 + 0.500000i) q^{87} +(5.19615 - 3.00000i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(2.00000 - 6.92820i) q^{91} -6.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} -5.00000 q^{96} +(-1.73205 - 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^4 + 2 * q^6 + 2 * q^9	$ 4 q - 2 q^{4} + 2 q^{6} + 2 q^{9} + 4 q^{11} - 8 q^{14} + 2 q^{16} - 12 q^{19} - 8 q^{21} + 6 q^{24} + 10 q^{26} - 2 q^{29} + 16 q^{31} + 28 q^{34} + 2 q^{36} + 10 q^{39} - 18 q^{41} - 8 q^{44} + 12 q^{46} - 6 q^{49} + 28 q^{51} - 2 q^{54} + 12 q^{56} - 2 q^{61} - 28 q^{64} + 8 q^{66} + 12 q^{69} - 12 q^{71} + 2 q^{74} - 12 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} + 24 q^{86} - 28 q^{89} + 8 q^{91} + 12 q^{94} - 20 q^{96} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 2 * q^6 + 2 * q^9 + 4 * q^11 - 8 * q^14 + 2 * q^16 - 12 * q^19 - 8 * q^21 + 6 * q^24 + 10 * q^26 - 2 * q^29 + 16 * q^31 + 28 * q^34 + 2 * q^36 + 10 * q^39 - 18 * q^41 - 8 * q^44 + 12 * q^46 - 6 * q^49 + 28 * q^51 - 2 * q^54 + 12 * q^56 - 2 * q^61 - 28 * q^64 + 8 * q^66 + 12 * q^69 - 12 * q^71 + 2 * q^74 - 12 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 + 24 * q^86 - 28 * q^89 + 8 * q^91 + 12 * q^94 - 20 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$		−	3.00000i		−	1.06066i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$13$	−0.866025	−	3.50000i	−0.240192	−	0.970725i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.470850	−	0.882213i	$-0.656053\pi$
$17$	−6.06218	−	3.50000i	−1.47029	−	0.848875i	−0.999444	+	0.0333386i	$0.989386\pi$
$18$			1.00000i			0.235702i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$	−1.73205	−	1.00000i	−0.369274	−	0.213201i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$		0			0
$26$	2.50000	+	2.59808i	0.490290	+	0.509525i
$27$			1.00000i			0.192450i
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$	7.00000			1.20049
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$	−0.866025	+	0.500000i	−0.142374	+	0.0821995i	0.427121	+	0.904194i	$0.359528\pi$
$38$		−	6.00000i		−	0.973329i
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$	1.73205	−	1.00000i	0.267261	−	0.154303i
$43$	−5.19615	−	3.00000i	−0.792406	−	0.457496i	0.0484030	−	0.998828i	$-0.484587\pi$
$43$	−5.19615	−	3.00000i	−0.792406	−	0.457496i	−0.840809	+	0.541332i	$0.817920\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$		0			0
$51$	7.00000			0.980196
$52$	3.46410	+	1.00000i	0.480384	+	0.138675i
$53$		−	9.00000i		−	1.23625i	−0.786082	−	0.618123i	$-0.787894\pi$
$53$		−	9.00000i		−	1.23625i	0.786082	−	0.618123i	$-0.212106\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	3.00000	−	5.19615i	0.400892	−	0.694365i
$57$		−	6.00000i		−	0.794719i
$58$	0.866025	+	0.500000i	0.113715	+	0.0656532i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	−3.46410	+	2.00000i	−0.439941	+	0.254000i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	2.00000			0.246183
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	6.06218	−	3.50000i	0.735147	−	0.424437i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$			11.0000i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$73$			11.0000i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−3.00000	−	5.19615i	−0.344124	−	0.596040i
$77$			4.00000i			0.455842i
$78$	−3.46410	−	1.00000i	−0.392232	−	0.113228i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.79423	+	4.50000i	0.860729	+	0.496942i
$83$		−	14.0000i		−	1.53670i	−0.640030	−	0.768350i	$-0.721078\pi$
$83$		−	14.0000i		−	1.53670i	0.640030	−	0.768350i	$-0.278922\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$		0			0
$86$	6.00000			0.646997
$87$	0.866025	+	0.500000i	0.0928477	+	0.0536056i
$88$	5.19615	−	3.00000i	0.553912	−	0.319801i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$		0			0
$91$	2.00000	−	6.92820i	0.209657	−	0.726273i
$92$		−	6.00000i		−	0.625543i
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$		0			0
$96$	−5.00000			−0.510310
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	2.00000			0.201008
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	−6.06218	+	3.50000i	−0.600245	+	0.346552i
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$	−10.5000	+	2.59808i	−1.02961	+	0.254762i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	−0.227345	−	0.973814i	$-0.573004\pi$
$107$	5.19615	−	3.00000i	0.502331	−	0.290021i	0.729676	+	0.683793i	$0.239671\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$			2.00000i			0.188982i
$113$	12.9904	+	7.50000i	1.22203	+	0.705541i	0.965351	−	0.260955i	$-0.0840376\pi$
$113$	12.9904	+	7.50000i	1.22203	+	0.705541i	0.256681	+	0.966496i	$0.417371\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$		0			0
$116$	1.00000			0.0928477
$117$	−3.46410	−	1.00000i	−0.320256	−	0.0924500i
$118$		0			0
$119$	−7.00000	−	12.1244i	−0.641689	−	1.11144i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		−	1.00000i		−	0.0905357i
$123$	7.79423	+	4.50000i	0.702782	+	0.405751i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−17.3205	+	10.0000i	−1.53695	+	0.887357i	−0.537931	+	0.842989i	$0.680794\pi$
$127$	−17.3205	+	10.0000i	−1.53695	+	0.887357i	−0.999015	+	0.0443678i	$0.985873\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	6.00000			0.528271
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	1.73205	−	1.00000i	0.150756	−	0.0870388i
$133$	−10.3923	+	6.00000i	−0.901127	+	0.520266i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		0			0
$136$	−10.5000	+	18.1865i	−0.900368	+	1.55948i
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	0.384893	−	0.922961i	$-0.374238\pi$
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	−0.606861	+	0.794808i	$0.707572\pi$
$138$			6.00000i			0.510754i
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$		0			0
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$		−	6.00000i		−	0.503509i
$143$	5.19615	−	5.00000i	0.434524	−	0.418121i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$	2.59808	+	1.50000i	0.214286	+	0.123718i
$148$		−	1.00000i		−	0.0821995i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	15.5885	+	9.00000i	1.26439	+	0.729996i
$153$	−6.06218	+	3.50000i	−0.490098	+	0.282958i
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$		0			0
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$			3.00000i			0.239426i	0.992809	+	0.119713i	$0.0381975\pi$
$157$			3.00000i			0.239426i	−0.992809	+	0.119713i	$0.961803\pi$
$158$	−3.46410	+	2.00000i	−0.275589	+	0.159111i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.928793	−	0.370599i	$-0.879152\pi$
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.143448	+	0.989658i	$0.545819\pi$
$168$			6.00000i			0.462910i
$169$	−11.5000	+	6.06218i	−0.884615	+	0.466321i
$170$		0			0
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$	5.19615	−	3.00000i	0.396203	−	0.228748i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$	−1.00000			−0.0758098
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	12.1244	+	7.00000i	0.908759	+	0.524672i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	1.73205	+	7.00000i	0.128388	+	0.518875i
$183$		−	1.00000i		−	0.0739221i
$184$	9.00000	+	15.5885i	0.663489	+	1.14920i
$185$		0			0
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$		−	14.0000i		−	1.02378i
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$		0			0
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	−0.784552	−	0.620063i	$-0.787107\pi$
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	0.929267	+	0.369410i	$0.120440\pi$
$192$	6.06218	−	3.50000i	0.437500	−	0.252591i
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	−0.753563	−	0.657376i	$-0.771667\pi$
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	0.192522	+	0.981293i	$0.438333\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	−1.73205	+	1.00000i	−0.123091	+	0.0710669i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$		0			0
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	2.59808	+	1.50000i	0.182800	+	0.105540i
$203$		−	2.00000i		−	0.140372i
$204$	−3.50000	+	6.06218i	−0.245049	+	0.424437i
$205$		0			0
$206$	−3.00000	−	5.19615i	−0.209020	−	0.362033i
$207$			6.00000i			0.417029i
$208$	2.59808	−	2.50000i	0.180144	−	0.173344i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	7.79423	+	4.50000i	0.535310	+	0.309061i
$213$		−	6.00000i		−	0.411113i
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$		0			0
$216$	3.00000			0.204124
$217$	6.92820	+	4.00000i	0.470317	+	0.271538i
$218$	−1.73205	+	1.00000i	−0.117309	+	0.0677285i
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	−7.00000	+	24.2487i	−0.470871	+	1.63114i
$222$			1.00000i			0.0671156i
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.0417488	−	0.999128i	$-0.486707\pi$
$223$	13.8564	−	8.00000i	0.927894	−	0.535720i	0.886145	+	0.463409i	$0.153374\pi$
$224$	5.00000	+	8.66025i	0.334077	+	0.578638i
$225$		0			0
$226$	−15.0000			−0.997785
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	0.0403978	−	0.999184i	$-0.487137\pi$
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	−0.845120	+	0.534577i	$0.820471\pi$
$228$	5.19615	+	3.00000i	0.344124	+	0.198680i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$		0			0
$237$	−3.46410	+	2.00000i	−0.225018	+	0.129914i
$238$	12.1244	+	7.00000i	0.785905	+	0.453743i
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$		0			0
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	−0.956456	−	0.291877i	$-0.905720\pi$
$241$	−3.50000	+	6.06218i	−0.225455	+	0.390499i	0.731001	+	0.682376i	$0.239053\pi$
$242$			7.00000i			0.449977i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−0.500000	−	0.866025i	−0.0320092	−	0.0554416i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	20.7846	+	6.00000i	1.32249	+	0.381771i
$248$		−	12.0000i		−	0.762001i
$249$	7.00000	+	12.1244i	0.443607	+	0.768350i
$250$		0			0
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$			2.00000i			0.125988i
$253$	−10.3923	−	6.00000i	−0.653359	−	0.377217i
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	6.06218	−	3.50000i	0.378148	−	0.218324i	−0.298864	−	0.954296i	$-0.596608\pi$
$257$	6.06218	−	3.50000i	0.378148	−	0.218324i	0.677012	+	0.735972i	$0.263274\pi$
$258$	−5.19615	+	3.00000i	−0.323498	+	0.186772i
$259$	−2.00000			−0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	6.92820	−	4.00000i	0.428026	−	0.247121i
$263$	−25.9808	+	15.0000i	−1.60204	+	0.924940i	−0.610964	+	0.791658i	$0.709218\pi$
$263$	−25.9808	+	15.0000i	−1.60204	+	0.924940i	−0.991078	+	0.133281i	$0.957449\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		0			0
$266$	6.00000	−	10.3923i	0.367884	−	0.637193i
$267$	12.1244	+	7.00000i	0.741999	+	0.428393i
$268$			2.00000i			0.122169i
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	−0.996586	−	0.0825561i	$-0.973692\pi$
$269$	−7.00000	+	12.1244i	−0.426798	+	0.739235i	0.569789	+	0.821791i	$0.307025\pi$
$270$		0			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$		−	7.00000i		−	0.424437i
$273$	1.73205	+	7.00000i	0.104828	+	0.423659i
$274$	3.00000			0.181237
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−26.8468	−	15.5000i	−1.61307	−	0.931305i	−0.988654	−	0.150210i	$-0.952005\pi$
$277$	−26.8468	−	15.5000i	−1.61307	−	0.931305i	−0.624413	−	0.781094i	$-0.714662\pi$
$278$			12.0000i			0.719712i
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	−19.0000			−1.13344			−0.566722	−	0.823909i	$-0.691789\pi$
$281$	−19.0000			−1.13344			−0.566722	+	0.823909i	$0.691789\pi$
$282$	−5.19615	−	3.00000i	−0.309426	−	0.178647i
$283$	−15.5885	+	9.00000i	−0.926638	+	0.534994i	−0.885747	−	0.464169i	$-0.846353\pi$
$283$	−15.5885	+	9.00000i	−0.926638	+	0.534994i	−0.0408910	+	0.999164i	$0.513020\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$	−2.00000	+	6.92820i	−0.118262	+	0.409673i
$287$		−	18.0000i		−	1.06251i
$288$	4.33013	−	2.50000i	0.255155	−	0.147314i
$289$	16.0000	+	27.7128i	0.941176	+	1.63017i
$290$		0			0
$291$	2.00000			0.117242
$292$	−9.52628	−	5.50000i	−0.557483	−	0.321863i
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	0.710084	−	0.704117i	$-0.248657\pi$
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	−0.254741	+	0.967009i	$0.581990\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$			3.00000i			0.173785i
$299$	15.0000	+	15.5885i	0.867472	+	0.901504i
$300$		0			0
$301$	−6.00000	−	10.3923i	−0.345834	−	0.599002i
$302$	1.73205	−	1.00000i	0.0996683	−	0.0575435i
$303$	2.59808	+	1.50000i	0.149256	+	0.0861727i
$304$	−6.00000			−0.344124
$305$		0			0
$306$	3.50000	−	6.06218i	0.200082	−	0.346552i
$307$		−	14.0000i		−	0.799022i	−0.916728	−	0.399511i	$-0.869180\pi$
$307$		−	14.0000i		−	0.799022i	0.916728	−	0.399511i	$-0.130820\pi$
$308$	−3.46410	−	2.00000i	−0.197386	−	0.113961i
$309$	−3.00000	−	5.19615i	−0.170664	−	0.295599i
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	7.79423	−	7.50000i	0.441261	−	0.424604i
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−1.50000	−	2.59808i	−0.0846499	−	0.146618i
$315$		0			0
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$			25.0000i			1.40414i	0.712108	+	0.702070i	$0.247741\pi$
$317$			25.0000i			1.40414i	−0.712108	+	0.702070i	$0.752259\pi$
$318$	−7.79423	−	4.50000i	−0.437079	−	0.252347i
$319$	1.00000	−	1.73205i	0.0559893	−	0.0969762i
$320$		0			0
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	10.3923	−	6.00000i	0.579141	−	0.334367i
$323$	36.3731	−	21.0000i	2.02385	−	1.16847i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−4.00000			−0.221540
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$	−23.3827	+	13.5000i	−1.29109	+	0.745413i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	12.1244	+	7.00000i	0.665410	+	0.384175i
$333$			1.00000i			0.0547997i
$334$	8.00000	−	13.8564i	0.437741	−	0.758189i
$335$		0			0
$336$	−1.00000	−	1.73205i	−0.0545545	−	0.0944911i
$337$			33.0000i			1.79762i	0.438334	+	0.898812i	$0.355569\pi$
$337$			33.0000i			1.79762i	−0.438334	+	0.898812i	$0.644431\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$	−15.0000			−0.814688
$340$		0			0
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−5.19615	−	3.00000i	−0.280976	−	0.162221i
$343$		−	20.0000i		−	1.07990i
$344$	−9.00000	+	15.5885i	−0.485247	+	0.840473i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	15.5885	+	9.00000i	0.836832	+	0.483145i	0.856186	−	0.516667i	$-0.172828\pi$
$347$	15.5885	+	9.00000i	0.836832	+	0.483145i	−0.0193540	+	0.999813i	$0.506161\pi$
$348$	−0.866025	+	0.500000i	−0.0464238	+	0.0268028i
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	0.274011	−	0.961727i	$-0.411649\pi$
$350$		0			0
$351$	3.50000	−	0.866025i	0.186816	−	0.0462250i
$352$			10.0000i			0.533002i
$353$	−9.52628	+	5.50000i	−0.507033	+	0.292735i	−0.731613	−	0.681720i	$-0.761232\pi$
$353$	−9.52628	+	5.50000i	−0.507033	+	0.292735i	0.224580	+	0.974456i	$0.427899\pi$
$354$		0			0
$355$		0			0
$356$	14.0000			0.741999
$357$	12.1244	+	7.00000i	0.641689	+	0.370479i
$358$	1.73205	+	1.00000i	0.0915417	+	0.0528516i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	6.06218	−	3.50000i	0.318621	−	0.183956i
$363$			7.00000i			0.367405i
$364$	5.00000	+	5.19615i	0.262071	+	0.272352i
$365$		0			0
$366$	0.500000	+	0.866025i	0.0261354	+	0.0452679i
$367$	−8.66025	+	5.00000i	−0.452062	+	0.260998i	−0.708700	−	0.705509i	$-0.750718\pi$
$367$	−8.66025	+	5.00000i	−0.452062	+	0.260998i	0.256639	+	0.966507i	$0.417385\pi$
$368$	−5.19615	−	3.00000i	−0.270868	−	0.156386i
$369$	−9.00000			−0.468521
$370$		0			0
$371$	9.00000	−	15.5885i	0.467257	−	0.809312i
$372$		−	4.00000i		−	0.207390i
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	0.725923	−	0.687776i	$-0.241413\pi$
$373$	9.52628	+	5.50000i	0.493252	+	0.284779i	−0.232671	+	0.972556i	$0.574746\pi$
$374$	7.00000	+	12.1244i	0.361961	+	0.626936i
$375$		0			0
$376$	−18.0000			−0.928279
$377$	−2.59808	+	2.50000i	−0.133808	+	0.128757i
$378$		−	2.00000i		−	0.102869i
$379$	−18.0000	−	31.1769i	−0.924598	−	1.60145i	−0.792207	−	0.610253i	$-0.791068\pi$
$379$	−18.0000	−	31.1769i	−0.924598	−	1.60145i	−0.132391	−	0.991198i	$-0.542266\pi$
$380$		0			0
$381$	10.0000	−	17.3205i	0.512316	−	0.887357i
$382$			4.00000i			0.204658i
$383$	−6.92820	−	4.00000i	−0.354015	−	0.204390i	0.312437	−	0.949938i	$-0.398855\pi$
$383$	−6.92820	−	4.00000i	−0.354015	−	0.204390i	−0.666452	+	0.745548i	$0.732188\pi$
$384$	1.50000	−	2.59808i	0.0765466	−	0.132583i
$385$		0			0
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	−5.19615	+	3.00000i	−0.264135	+	0.152499i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−19.0000			−0.963338			−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000			−0.963338			−0.481669	+	0.876353i	$0.659969\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	−7.79423	+	4.50000i	−0.393668	+	0.227284i
$393$	6.92820	−	4.00000i	0.349482	−	0.201773i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	−29.4449	−	17.0000i	−1.47780	−	0.853206i	−0.478110	−	0.878300i	$-0.658678\pi$
$397$	−29.4449	−	17.0000i	−1.47780	−	0.853206i	−0.999685	+	0.0250943i	$0.992011\pi$
$398$			14.0000i			0.701757i
$399$	6.00000	−	10.3923i	0.300376	−	0.520266i
$400$		0			0
$401$	−0.500000	−	0.866025i	−0.0249688	−	0.0432472i	0.853271	−	0.521468i	$-0.174615\pi$
$401$	−0.500000	−	0.866025i	−0.0249688	−	0.0432472i	−0.878240	+	0.478220i	$0.841282\pi$
$402$		−	2.00000i		−	0.0997509i
$403$	−3.46410	−	14.0000i	−0.172559	−	0.697390i
$404$	3.00000			0.149256
$405$		0			0
$406$	1.00000	+	1.73205i	0.0496292	+	0.0859602i
$407$	−1.73205	−	1.00000i	−0.0858546	−	0.0495682i
$408$		−	21.0000i		−	1.03965i
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$		0			0
$411$	3.00000			0.147979
$412$	−5.19615	−	3.00000i	−0.255996	−	0.147799i
$413$		0			0
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	5.00000	−	17.3205i	0.245145	−	0.849208i
$417$			12.0000i			0.587643i
$418$	10.3923	−	6.00000i	0.508304	−	0.293470i
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	0.992559	−	0.121768i	$-0.0388562\pi$
$419$	8.00000	+	13.8564i	0.390826	+	0.676930i	−0.601733	+	0.798697i	$0.705523\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−6.92820	−	4.00000i	−0.337260	−	0.194717i
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$	−27.0000			−1.31124
$425$		0			0
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	−1.73205	+	1.00000i	−0.0838198	+	0.0483934i
$428$			6.00000i			0.290021i
$429$	−2.00000	+	6.92820i	−0.0965609	+	0.334497i
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−16.4545	−	9.50000i	−0.790752	−	0.456541i	0.0494752	−	0.998775i	$-0.484245\pi$
$433$	−16.4545	−	9.50000i	−0.790752	−	0.456541i	−0.840227	+	0.542234i	$0.817578\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$		−	36.0000i		−	1.72211i
$438$	9.52628	+	5.50000i	0.455183	+	0.262800i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−6.06218	−	24.5000i	−0.288348	−	1.16535i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$	0.500000	+	0.866025i	0.0237289	+	0.0410997i
$445$		0			0
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$			3.00000i			0.141895i
$448$	−12.1244	−	7.00000i	−0.572822	−	0.330719i
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	−0.115833	−	0.993269i	$-0.536954\pi$
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	0.918112	−	0.396320i	$-0.129713\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−12.9904	+	7.50000i	−0.611016	+	0.352770i
$453$	1.73205	−	1.00000i	0.0813788	−	0.0469841i
$454$	14.0000			0.657053
$455$		0			0
$456$	−18.0000			−0.842927
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	−0.213006	−	0.977051i	$-0.568325\pi$
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	0.739648	+	0.672994i	$0.234992\pi$
$458$	−19.0526	+	11.0000i	−0.890268	+	0.513996i
$459$	3.50000	−	6.06218i	0.163366	−	0.282958i
$460$		0			0
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	−0.997871	−	0.0652135i	$-0.979227\pi$
$461$	−9.50000	+	16.4545i	−0.442459	+	0.766362i	0.555412	+	0.831575i	$0.312560\pi$
$462$	3.46410	+	2.00000i	0.161165	+	0.0930484i
$463$		−	26.0000i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$		−	26.0000i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$		−	6.00000i		−	0.277647i	−0.990317	−	0.138823i	$-0.955668\pi$
$467$		−	6.00000i		−	0.277647i	0.990317	−	0.138823i	$-0.0443321\pi$
$468$	2.59808	−	2.50000i	0.120096	−	0.115563i
$469$	4.00000			0.184703
$470$		0			0
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$		0			0
$473$		−	12.0000i		−	0.551761i
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$		0			0
$476$	14.0000			0.641689
$477$	−7.79423	−	4.50000i	−0.356873	−	0.206041i
$478$	25.9808	−	15.0000i	1.18833	−	0.686084i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	2.50000	+	2.59808i	0.113990	+	0.118462i
$482$		−	7.00000i		−	0.318841i
$483$	10.3923	−	6.00000i	0.472866	−	0.273009i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	0.809719	−	0.586817i	$-0.199619\pi$
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	−0.103339	+	0.994646i	$0.532953\pi$
$488$	2.59808	+	1.50000i	0.117609	+	0.0679018i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	0.790358	−	0.612646i	$-0.209895\pi$
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	−0.925746	+	0.378147i	$0.876561\pi$
$492$	−7.79423	+	4.50000i	−0.351391	+	0.202876i
$493$			7.00000i			0.315264i
$494$	−21.0000	+	5.19615i	−0.944835	+	0.233786i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−10.3923	+	6.00000i	−0.466159	+	0.269137i
$498$	−12.1244	−	7.00000i	−0.543305	−	0.313678i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$		0			0
$501$	8.00000	−	13.8564i	0.357414	−	0.619059i
$502$		−	12.0000i		−	0.535586i
$503$	1.73205	+	1.00000i	0.0772283	+	0.0445878i	0.538117	−	0.842870i	$-0.319136\pi$
$503$	1.73205	+	1.00000i	0.0772283	+	0.0445878i	−0.460889	+	0.887458i	$0.652469\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$		0			0
$506$	12.0000			0.533465
$507$	6.92820	−	11.0000i	0.307692	−	0.488527i
$508$		−	20.0000i		−	0.887357i
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	0.933108	−	0.359596i	$-0.117085\pi$
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	−0.777973	+	0.628297i	$0.783752\pi$
$510$		0			0
$511$	−11.0000	+	19.0526i	−0.486611	+	0.842836i
$512$			11.0000i			0.486136i
$513$	−5.19615	−	3.00000i	−0.229416	−	0.132453i
$514$	−3.50000	+	6.06218i	−0.154378	+	0.267391i
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	10.3923	−	6.00000i	0.457053	−	0.263880i
$518$	1.73205	−	1.00000i	0.0761019	−	0.0439375i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	0.866025	−	0.500000i	0.0379049	−	0.0218844i
$523$	12.1244	−	7.00000i	0.530161	−	0.306089i	−0.210921	−	0.977503i	$-0.567646\pi$
$523$	12.1244	−	7.00000i	0.530161	−	0.306089i	0.741082	+	0.671414i	$0.234313\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$		0			0
$526$	15.0000	−	25.9808i	0.654031	−	1.13282i
$527$	−24.2487	−	14.0000i	−1.05629	−	0.609850i
$528$		−	2.00000i		−	0.0870388i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$		−	12.0000i		−	0.520266i
$533$	−23.3827	+	22.5000i	−1.01282	+	0.974583i
$534$	−14.0000			−0.605839
$535$		0			0
$536$	−3.00000	−	5.19615i	−0.129580	−	0.224440i
$537$	1.73205	+	1.00000i	0.0747435	+	0.0431532i
$538$		−	14.0000i		−	0.603583i
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$		0			0
$541$	45.0000			1.93470			0.967351	−	0.253442i	$-0.0815627\pi$
$541$	45.0000			1.93470			0.967351	+	0.253442i	$0.0815627\pi$
$542$		0			0
$543$	6.06218	−	3.50000i	0.260153	−	0.150199i
$544$	−17.5000	−	30.3109i	−0.750306	−	1.29957i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$			26.0000i			1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$			26.0000i			1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	2.59808	−	1.50000i	0.110984	−	0.0640768i
$549$	0.500000	+	0.866025i	0.0213395	+	0.0369611i
$550$		0			0
$551$	6.00000			0.255609
$552$	−15.5885	−	9.00000i	−0.663489	−	0.383065i
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$	31.0000			1.31706
$555$		0			0
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	7.79423	−	4.50000i	0.330252	−	0.190671i	−0.325701	−	0.945473i	$-0.605600\pi$
$557$	7.79423	−	4.50000i	0.330252	−	0.190671i	0.655953	+	0.754802i	$0.272267\pi$
$558$			4.00000i			0.169334i
$559$	−6.00000	+	20.7846i	−0.253773	+	0.879095i
$560$		0			0
$561$	7.00000	+	12.1244i	0.295540	+	0.511891i
$562$	16.4545	−	9.50000i	0.694090	−	0.400733i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	9.00000	−	15.5885i	0.378298	−	0.655232i
$567$		−	2.00000i		−	0.0839921i
$568$	15.5885	+	9.00000i	0.654077	+	0.377632i
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	0.999018	−	0.0443003i	$-0.0141058\pi$
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	−0.537874	+	0.843025i	$0.680772\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	1.73205	+	7.00000i	0.0724207	+	0.292685i
$573$			4.00000i			0.167102i
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	−27.7128	−	16.0000i	−1.15270	−	0.665512i
$579$	4.50000	−	7.79423i	0.187014	−	0.323917i
$580$		0			0
$581$	14.0000	−	24.2487i	0.580818	−	1.00601i
$582$	−1.73205	+	1.00000i	−0.0717958	+	0.0414513i
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$	33.0000			1.36555
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	−0.757914	−	0.652355i	$-0.773781\pi$
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	0.185999	+	0.982550i	$0.440448\pi$
$588$	−2.59808	+	1.50000i	−0.107143	+	0.0618590i
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	−0.866025	−	0.500000i	−0.0355934	−	0.0205499i
$593$			13.0000i			0.533846i	0.963718	+	0.266923i	$0.0860069\pi$
$593$			13.0000i			0.533846i	−0.963718	+	0.266923i	$0.913993\pi$
$594$	1.00000	−	1.73205i	0.0410305	−	0.0710669i
$595$		0			0
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$			14.0000i			0.572982i
$598$	−20.7846	−	6.00000i	−0.849946	−	0.245358i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$		0			0
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$	10.3923	+	6.00000i	0.423559	+	0.244542i
$603$		−	2.00000i		−	0.0814463i
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$		0			0
$606$	−3.00000			−0.121867
$607$	6.92820	+	4.00000i	0.281207	+	0.162355i	0.633970	−	0.773358i	$-0.281424\pi$
$607$	6.92820	+	4.00000i	0.281207	+	0.162355i	−0.352763	+	0.935713i	$0.614758\pi$
$608$	−25.9808	+	15.0000i	−1.05366	+	0.608330i
$609$	1.00000	+	1.73205i	0.0405220	+	0.0701862i
$610$		0			0
$611$	−21.0000	+	5.19615i	−0.849569	+	0.210214i
$612$		−	7.00000i		−	0.282958i
$613$	−19.9186	+	11.5000i	−0.804504	+	0.464481i	−0.845044	−	0.534697i	$-0.820426\pi$
$613$	−19.9186	+	11.5000i	−0.804504	+	0.464481i	0.0405396	+	0.999178i	$0.487092\pi$
$614$	7.00000	+	12.1244i	0.282497	+	0.489299i
$615$		0			0
$616$	12.0000			0.483494
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	0.709199	−	0.705008i	$-0.249057\pi$
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	−0.255956	+	0.966689i	$0.582390\pi$
$618$	5.19615	+	3.00000i	0.209020	+	0.120678i
$619$	24.0000			0.964641			0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000			0.964641			0.482321	+	0.875995i	$0.339794\pi$
$620$		0			0
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	−15.5885	+	9.00000i	−0.625040	+	0.360867i
$623$		−	28.0000i		−	1.12180i
$624$	−1.00000	+	3.46410i	−0.0400320	+	0.138675i
$625$		0			0
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	10.3923	−	6.00000i	0.415029	−	0.239617i
$628$	−2.59808	−	1.50000i	−0.103675	−	0.0598565i
$629$	7.00000			0.279108
$630$		0			0
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	−0.993491	−	0.113913i	$-0.963661\pi$
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	0.595397	+	0.803432i	$0.296995\pi$
$632$		−	12.0000i		−	0.477334i
$633$	−6.92820	−	4.00000i	−0.275371	−	0.158986i
$634$	−12.5000	−	21.6506i	−0.496438	−	0.859857i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	−7.79423	+	7.50000i	−0.308819	+	0.297161i
$638$			2.00000i			0.0791808i
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	15.5000	−	26.8468i	0.612213	−	1.06038i	−0.378653	−	0.925539i	$-0.623613\pi$
$641$	15.5000	−	26.8468i	0.612213	−	1.06038i	0.990867	−	0.134846i	$-0.0430539\pi$
$642$		−	6.00000i		−	0.236801i
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	0.747686	−	0.664052i	$-0.231165\pi$
$643$	13.8564	+	8.00000i	0.546443	+	0.315489i	−0.201243	+	0.979541i	$0.564498\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$		0			0
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$	27.7128	−	16.0000i	1.08950	−	0.629025i	0.156059	−	0.987748i	$-0.450121\pi$
$647$	27.7128	−	16.0000i	1.08950	−	0.629025i	0.933444	+	0.358723i	$0.116788\pi$
$648$	−2.59808	+	1.50000i	−0.102062	+	0.0589256i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	−0.598213	−	0.801337i	$-0.704122\pi$
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	0.394872	+	0.918736i	$0.370789\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	9.52628	+	5.50000i	0.371656	+	0.214575i
$658$			12.0000i			0.467809i
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	−0.933357	−	0.358951i	$-0.883135\pi$
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	0.777539	+	0.628835i	$0.216468\pi$
$660$		0			0
$661$	−22.5000	−	38.9711i	−0.875149	−	1.51580i	−0.856604	−	0.515974i	$-0.827430\pi$
$661$	−22.5000	−	38.9711i	−0.875149	−	1.51580i	−0.0185442	−	0.999828i	$-0.505903\pi$
$662$			4.00000i			0.155464i
$663$	−6.06218	−	24.5000i	−0.235435	−	0.951501i
$664$	−42.0000			−1.62992
$665$		0			0
$666$	−0.500000	−	0.866025i	−0.0193746	−	0.0335578i
$667$	5.19615	+	3.00000i	0.201196	+	0.116160i
$668$		−	16.0000i		−	0.619059i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	−8.66025	−	5.00000i	−0.334077	−	0.192879i
$673$	−25.1147	+	14.5000i	−0.968102	+	0.558934i	−0.898657	−	0.438652i	$-0.855456\pi$
$673$	−25.1147	+	14.5000i	−0.968102	+	0.558934i	−0.0694449	+	0.997586i	$0.522123\pi$
$674$	−16.5000	−	28.5788i	−0.635556	−	1.10082i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$		−	34.0000i		−	1.30673i	−0.757045	−	0.653363i	$-0.773358\pi$
$677$		−	34.0000i		−	1.30673i	0.757045	−	0.653363i	$-0.226642\pi$
$678$	12.9904	−	7.50000i	0.498893	−	0.288036i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$		0			0
$681$	14.0000			0.536481
$682$	−6.92820	−	4.00000i	−0.265295	−	0.153168i
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	0.841825	−	0.539750i	$-0.181481\pi$
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	−0.0465244	+	0.998917i	$0.514815\pi$
$684$	−6.00000			−0.229416
$685$		0			0
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−19.0526	+	11.0000i	−0.726900	+	0.419676i
$688$		−	6.00000i		−	0.228748i
$689$	−31.5000	+	7.79423i	−1.20005	+	0.296936i
$690$		0			0
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	−0.920348	−	0.391102i	$-0.872094\pi$
$691$	−21.0000	−	36.3731i	−0.798878	−	1.38370i	0.121470	−	0.992595i	$-0.461239\pi$
$692$	−5.19615	+	3.00000i	−0.197528	+	0.114043i
$693$	3.46410	+	2.00000i	0.131590	+	0.0759737i
$694$	−18.0000			−0.683271
$695$		0			0
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$			63.0000i			2.38630i
$698$	22.5167	+	13.0000i	0.852268	+	0.492057i
$699$	−5.00000	−	8.66025i	−0.189117	−	0.327561i
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	−2.59808	+	2.50000i	−0.0980581	+	0.0943564i
$703$		−	6.00000i		−	0.226294i
$704$	−7.00000	−	12.1244i	−0.263822	−	0.456954i
$705$		0			0
$706$	5.50000	−	9.52628i	0.206995	−	0.358526i
$707$		−	6.00000i		−	0.225653i
$708$		0			0
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−36.3731	+	21.0000i	−1.36314	+	0.787008i
$713$	−20.7846	+	12.0000i	−0.778390	+	0.449404i
$714$	−14.0000			−0.523937
$715$		0			0
$716$	2.00000			0.0747435
$717$	25.9808	−	15.0000i	0.970269	−	0.560185i
$718$	−15.5885	+	9.00000i	−0.581756	+	0.335877i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		0			0
$721$	−6.00000	+	10.3923i	−0.223452	+	0.387030i
$722$	14.7224	+	8.50000i	0.547912	+	0.316337i
$723$		−	7.00000i		−	0.260333i
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$		0			0
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$		−	14.0000i		−	0.519231i	−0.965712	−	0.259616i	$-0.916404\pi$
$727$		−	14.0000i		−	0.519231i	0.965712	−	0.259616i	$-0.0835959\pi$
$728$	−20.7846	−	6.00000i	−0.770329	−	0.222375i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	21.0000	+	36.3731i	0.776713	+	1.34531i
$732$	0.866025	+	0.500000i	0.0320092	+	0.0184805i
$733$		−	15.0000i		−	0.554038i	−0.960864	−	0.277019i	$-0.910654\pi$
$733$		−	15.0000i		−	0.554038i	0.960864	−	0.277019i	$-0.0893464\pi$
$734$	5.00000	−	8.66025i	0.184553	−	0.319656i
$735$		0			0
$736$	−30.0000			−1.10581
$737$	3.46410	+	2.00000i	0.127602	+	0.0736709i
$738$	7.79423	−	4.50000i	0.286910	−	0.165647i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	−21.0000	+	5.19615i	−0.771454	+	0.190885i
$742$			18.0000i			0.660801i
$743$	−31.1769	+	18.0000i	−1.14377	+	0.660356i	−0.947361	−	0.320166i	$-0.896261\pi$
$743$	−31.1769	+	18.0000i	−1.14377	+	0.660356i	−0.196409	+	0.980522i	$0.562928\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$		0			0
$746$	−11.0000			−0.402739
$747$	−12.1244	−	7.00000i	−0.443607	−	0.256117i
$748$	12.1244	+	7.00000i	0.443310	+	0.255945i
$749$	12.0000			0.438470
$750$		0			0
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	0.989423	+	0.145062i	$0.0463382\pi$
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	−0.369084	+	0.929396i	$0.620328\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$		−	12.0000i		−	0.437304i
$754$	1.00000	−	3.46410i	0.0364179	−	0.126155i
$755$		0			0
$756$	−1.00000	−	1.73205i	−0.0363696	−	0.0629941i
$757$	43.3013	−	25.0000i	1.57381	−	0.908640i	0.578116	−	0.815955i	$-0.303788\pi$
$757$	43.3013	−	25.0000i	1.57381	−	0.908640i	0.995695	−	0.0926859i	$-0.0295452\pi$
$758$	31.1769	+	18.0000i	1.13240	+	0.653789i
$759$	12.0000			0.435572
$760$		0			0
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.0870179	+	0.996207i	$0.527734\pi$
$761$	−25.0000	+	43.3013i	−0.906249	+	1.56967i	−0.819231	+	0.573463i	$0.805600\pi$
$762$			20.0000i			0.724524i
$763$	3.46410	+	2.00000i	0.125409	+	0.0724049i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$		0			0
$766$	8.00000			0.289052
$767$		0			0
$768$			17.0000i			0.613435i
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$		0			0
$771$	−3.50000	+	6.06218i	−0.126049	+	0.218324i
$772$		−	9.00000i		−	0.323917i
$773$	12.1244	+	7.00000i	0.436083	+	0.251773i	0.701935	−	0.712241i	$-0.252320\pi$
$773$	12.1244	+	7.00000i	0.436083	+	0.251773i	−0.265852	+	0.964014i	$0.585653\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$		0			0
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$	1.73205	−	1.00000i	0.0621370	−	0.0358748i
$778$	16.4545	−	9.50000i	0.589922	−	0.340592i
$779$	54.0000			1.93475
$780$		0			0
$781$	−12.0000			−0.429394
$782$	−36.3731	+	21.0000i	−1.30070	+	0.750958i
$783$	0.866025	−	0.500000i	0.0309492	−	0.0178685i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	−4.00000	+	6.92820i	−0.142675	+	0.247121i
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$		−	6.00000i		−	0.213741i
$789$	15.0000	−	25.9808i	0.534014	−	0.924940i
$790$		0			0
$791$	15.0000	+	25.9808i	0.533339	+	0.923770i
$792$		−	6.00000i		−	0.213201i
$793$	3.46410	+	1.00000i	0.123014	+	0.0355110i
$794$	34.0000			1.20661
$795$		0			0
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−1.73205	−	1.00000i	−0.0613524	−	0.0354218i	0.469010	−	0.883193i	$-0.344611\pi$
$797$	−1.73205	−	1.00000i	−0.0613524	−	0.0354218i	−0.530362	+	0.847771i	$0.677944\pi$
$798$			12.0000i			0.424795i
$799$	−21.0000	+	36.3731i	−0.742927	+	1.28679i
$800$		0			0
$801$	−14.0000			−0.494666
$802$	0.866025	+	0.500000i	0.0305804	+	0.0176556i
$803$	−19.0526	+	11.0000i	−0.672350	+	0.388182i
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$		0			0
$806$	10.0000	+	10.3923i	0.352235	+	0.366053i
$807$		−	14.0000i		−	0.492823i
$808$	−7.79423	+	4.50000i	−0.274200	+	0.158309i
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	1.73205	+	1.00000i	0.0607831	+	0.0350931i
$813$		0			0
$814$	2.00000			0.0701000
$815$		0			0
$816$	3.50000	+	6.06218i	0.122525	+	0.212219i
$817$	31.1769	−	18.0000i	1.09074	−	0.629740i
$818$			7.00000i			0.244749i
$819$	−5.00000	−	5.19615i	−0.174714	−	0.181568i
$820$		0			0
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.859396	−	0.511311i	$-0.829160\pi$
$821$	−25.0000	−	43.3013i	−0.872506	−	1.51122i	−0.0131101	−	0.999914i	$-0.504173\pi$
$822$	−2.59808	+	1.50000i	−0.0906183	+	0.0523185i
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	0.816409	−	0.577474i	$-0.195962\pi$
$823$	20.7846	+	12.0000i	0.724506	+	0.418294i	−0.0919029	+	0.995768i	$0.529295\pi$
$824$	18.0000			0.627060
$825$		0			0
$826$		0			0
$827$		−	16.0000i		−	0.556375i	−0.960527	−	0.278187i	$-0.910266\pi$
$827$		−	16.0000i		−	0.556375i	0.960527	−	0.278187i	$-0.0897336\pi$
$828$	−5.19615	−	3.00000i	−0.180579	−	0.104257i
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	0.975035	−	0.222049i	$-0.0712747\pi$
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	−0.679818	+	0.733381i	$0.737941\pi$
$830$		0			0
$831$	31.0000			1.07538
$832$	6.06218	+	24.5000i	0.210168	+	0.849385i
$833$			21.0000i			0.727607i
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$			4.00000i			0.138260i
$838$	−13.8564	−	8.00000i	−0.478662	−	0.276355i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	16.4545	−	9.50000i	0.567059	−	0.327392i
$843$	16.4545	−	9.50000i	0.566722	−	0.327197i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	6.00000			0.206284
$847$	12.1244	−	7.00000i	0.416598	−	0.240523i
$848$	7.79423	−	4.50000i	0.267655	−	0.154531i
$849$	9.00000	−	15.5885i	0.308879	−	0.534994i
$850$		0			0
$851$	3.00000	−	5.19615i	0.102839	−	0.178122i
$852$	5.19615	+	3.00000i	0.178017	+	0.102778i
$853$			21.0000i			0.719026i	0.933140	+	0.359513i	$0.117057\pi$
$853$			21.0000i			0.719026i	−0.933140	+	0.359513i	$0.882943\pi$
$854$	1.00000	−	1.73205i	0.0342193	−	0.0592696i
$855$		0			0
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$			31.0000i			1.05894i	0.848329	+	0.529470i	$0.177609\pi$
$857$			31.0000i			1.05894i	−0.848329	+	0.529470i	$0.822391\pi$
$858$	−1.73205	−	7.00000i	−0.0591312	−	0.238976i
$859$	−34.0000			−1.16007			−0.580033	−	0.814593i	$-0.696960\pi$
$859$	−34.0000			−1.16007			−0.580033	+	0.814593i	$0.696960\pi$
$860$		0			0
$861$	9.00000	+	15.5885i	0.306719	+	0.531253i
$862$	−25.9808	−	15.0000i	−0.884908	−	0.510902i
$863$			10.0000i			0.340404i	0.985409	+	0.170202i	$0.0544420\pi$
$863$			10.0000i			0.340404i	−0.985409	+	0.170202i	$0.945558\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$		0			0
$866$	19.0000			0.645646
$867$	−27.7128	−	16.0000i	−0.941176	−	0.543388i
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$		0			0
$871$	−5.00000	−	5.19615i	−0.169419	−	0.176065i
$872$		−	6.00000i		−	0.203186i
$873$	−1.73205	+	1.00000i	−0.0586210	+	0.0338449i
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$		0			0
$876$	11.0000			0.371656
$877$	14.7224	+	8.50000i	0.497141	+	0.287025i	0.727532	−	0.686074i	$-0.240667\pi$
$877$	14.7224	+	8.50000i	0.497141	+	0.287025i	−0.230391	+	0.973098i	$0.574001\pi$
$878$	−12.1244	−	7.00000i	−0.409177	−	0.236239i
$879$	−9.00000			−0.303562
$880$		0			0
$881$	−18.5000	−	32.0429i	−0.623281	−	1.07955i	−0.988871	−	0.148778i	$-0.952466\pi$
$881$	−18.5000	−	32.0429i	−0.623281	−	1.07955i	0.365590	−	0.930776i	$-0.380867\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$			16.0000i			0.538443i	0.963078	+	0.269221i	$0.0867663\pi$
$883$			16.0000i			0.538443i	−0.963078	+	0.269221i	$0.913234\pi$
$884$	−17.5000	−	18.1865i	−0.588589	−	0.611679i
$885$		0			0
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$	−2.59808	−	1.50000i	−0.0871857	−	0.0503367i
$889$	−40.0000			−1.34156
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$			16.0000i			0.535720i
$893$	31.1769	+	18.0000i	1.04330	+	0.602347i
$894$	−1.50000	−	2.59808i	−0.0501675	−	0.0868927i
$895$		0			0
$896$	−6.00000			−0.200446
$897$	−20.7846	−	6.00000i	−0.693978	−	0.200334i
$898$			34.0000i			1.13459i
$899$	−2.00000	−	3.46410i	−0.0667037	−	0.115534i
$900$		0			0
$901$	−31.5000	+	54.5596i	−1.04942	+	1.81764i
$902$			18.0000i			0.599334i
$903$	10.3923	+	6.00000i	0.345834	+	0.199667i
$904$	22.5000	−	38.9711i	0.748339	−	1.29616i
$905$		0			0
$906$	−1.00000	+	1.73205i	−0.0332228	+	0.0575435i
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	−0.662512	−	0.749051i	$-0.730510\pi$
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	0.317441	+	0.948278i	$0.397176\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	5.19615	−	3.00000i	0.172062	−	0.0993399i
$913$	24.2487	−	14.0000i	0.802515	−	0.463332i
$914$	−6.50000	+	11.2583i	−0.215001	+	0.372392i
$915$		0			0
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$	−13.8564	−	8.00000i	−0.457579	−	0.264183i
$918$			7.00000i			0.231034i
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	−0.597365	−	0.801970i	$-0.703786\pi$
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	0.993208	+	0.116348i	$0.0371189\pi$
$920$		0			0
$921$	7.00000	+	12.1244i	0.230658	+	0.399511i
$922$		−	19.0000i		−	0.625732i
$923$	20.7846	+	6.00000i	0.684134	+	0.197492i
$924$	4.00000			0.131590
$925$		0			0
$926$	13.0000	+	22.5167i	0.427207	+	0.739943i
$927$	5.19615	+	3.00000i	0.170664	+	0.0985329i
$928$		−	5.00000i		−	0.164133i
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$	−8.66025	−	5.00000i	−0.283676	−	0.163780i
$933$	−15.5885	+	9.00000i	−0.510343	+	0.294647i
$934$	3.00000	+	5.19615i	0.0981630	+	0.170023i
$935$		0			0
$936$	−3.00000	+	10.3923i	−0.0980581	+	0.339683i
$937$			49.0000i			1.60076i	0.599493	+	0.800380i	$0.295369\pi$
$937$			49.0000i			1.60076i	−0.599493	+	0.800380i	$0.704631\pi$
$938$	−3.46410	+	2.00000i	−0.113107	+	0.0653023i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$		0			0
$941$	−38.0000			−1.23876			−0.619382	−	0.785090i	$-0.712617\pi$
$941$	−38.0000			−1.23876			−0.619382	+	0.785090i	$0.712617\pi$
$942$	2.59808	+	1.50000i	0.0846499	+	0.0488726i
$943$	46.7654	+	27.0000i	1.52289	+	0.879241i
$944$		0			0
$945$		0			0
$946$	6.00000	+	10.3923i	0.195077	+	0.337883i
$947$	41.5692	−	24.0000i	1.35082	−	0.779895i	0.362454	−	0.932002i	$-0.381939\pi$
$947$	41.5692	−	24.0000i	1.35082	−	0.779895i	0.988364	+	0.152106i	$0.0486057\pi$
$948$		−	4.00000i		−	0.129914i
$949$	38.5000	−	9.52628i	1.24976	−	0.309236i
$950$		0			0
$951$	−12.5000	−	21.6506i	−0.405340	−	0.702070i
$952$	−36.3731	+	21.0000i	−1.17886	+	0.680614i
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	0.413473	−	0.910516i	$-0.364315\pi$
$953$	−5.19615	−	3.00000i	−0.168320	−	0.0971795i	−0.581793	+	0.813337i	$0.697649\pi$
$954$	9.00000			0.291386
$955$		0			0
$956$	15.0000	−	25.9808i	0.485135	−	0.840278i
$957$			2.00000i			0.0646508i
$958$	−20.7846	−	12.0000i	−0.671520	−	0.387702i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−3.46410	−	1.00000i	−0.111687	−	0.0322413i
$963$		−	6.00000i		−	0.193347i
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$		0			0
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$		−	2.00000i		−	0.0643157i	−0.999483	−	0.0321578i	$-0.989762\pi$
$967$		−	2.00000i		−	0.0643157i	0.999483	−	0.0321578i	$-0.0102379\pi$
$968$	−18.1865	−	10.5000i	−0.584537	−	0.337483i
$969$	−21.0000	+	36.3731i	−0.674617	+	1.16847i
$970$		0			0
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	20.7846	−	12.0000i	0.666324	−	0.384702i
$974$	−18.0000			−0.576757
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	−28.5788	+	16.5000i	−0.914318	+	0.527882i	−0.881818	−	0.471590i	$-0.843680\pi$
$977$	−28.5788	+	16.5000i	−0.914318	+	0.527882i	−0.0325001	+	0.999472i	$0.510347\pi$
$978$	3.46410	−	2.00000i	0.110770	−	0.0639529i
$979$	14.0000	−	24.2487i	0.447442	−	0.774992i
$980$		0			0
$981$	1.00000	−	1.73205i	0.0319275	−	0.0553001i
$982$	5.19615	+	3.00000i	0.165816	+	0.0957338i
$983$			4.00000i			0.127580i	0.997963	+	0.0637901i	$0.0203188\pi$
$983$			4.00000i			0.127580i	−0.997963	+	0.0637901i	$0.979681\pi$
$984$	13.5000	−	23.3827i	0.430364	−	0.745413i
$985$		0			0
$986$	−3.50000	−	6.06218i	−0.111463	−	0.193059i
$987$			12.0000i			0.381964i
$988$	−15.5885	+	15.0000i	−0.495935	+	0.477214i
$989$	36.0000			1.14473
$990$		0			0
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	0.881471	−	0.472237i	$-0.156554\pi$
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	−0.849705	+	0.527258i	$0.823220\pi$
$992$	17.3205	+	10.0000i	0.549927	+	0.317500i
$993$			4.00000i			0.126936i
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$		0			0
$996$	−14.0000			−0.443607
$997$	−30.3109	−	17.5000i	−0.959955	−	0.554231i	−0.0637961	−	0.997963i	$-0.520321\pi$
$997$	−30.3109	−	17.5000i	−0.959955	−	0.554231i	−0.896159	+	0.443732i	$0.853654\pi$
$998$	20.7846	−	12.0000i	0.657925	−	0.379853i
$999$	−0.500000	−	0.866025i	−0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bb.d.874.1		4
5.2	odd	4		39.2.e.a.16.1	✓	2
5.3	odd	4		975.2.i.f.601.1		2
5.4	even	2	inner	975.2.bb.d.874.2		4
13.9	even	3	inner	975.2.bb.d.724.2		4
15.2	even	4		117.2.g.b.55.1		2
20.7	even	4		624.2.q.c.289.1		2
60.47	odd	4		1872.2.t.j.289.1		2
65.2	even	12		507.2.b.b.337.1		2
65.7	even	12		507.2.j.d.316.1		4
65.9	even	6	inner	975.2.bb.d.724.1		4
65.12	odd	4		507.2.e.c.484.1		2
65.17	odd	12		507.2.e.c.22.1		2
65.22	odd	12		39.2.e.a.22.1	yes	2
65.32	even	12		507.2.j.d.316.2		4
65.37	even	12		507.2.b.b.337.2		2
65.42	odd	12		507.2.a.c.1.1		1
65.47	even	4		507.2.j.d.361.2		4
65.48	odd	12		975.2.i.f.451.1		2
65.57	even	4		507.2.j.d.361.1		4
65.62	odd	12		507.2.a.b.1.1		1
195.2	odd	12		1521.2.b.c.1351.2		2
195.62	even	12		1521.2.a.d.1.1		1
195.107	even	12		1521.2.a.a.1.1		1
195.152	even	12		117.2.g.b.100.1		2
195.167	odd	12		1521.2.b.c.1351.1		2
260.87	even	12		624.2.q.c.529.1		2
260.107	even	12		8112.2.a.w.1.1		1
260.127	even	12		8112.2.a.bc.1.1		1
780.347	odd	12		1872.2.t.j.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.a.16.1	✓	2	5.2	odd	4
39.2.e.a.22.1	yes	2	65.22	odd	12
117.2.g.b.55.1		2	15.2	even	4
117.2.g.b.100.1		2	195.152	even	12
507.2.a.b.1.1		1	65.62	odd	12
507.2.a.c.1.1		1	65.42	odd	12
507.2.b.b.337.1		2	65.2	even	12
507.2.b.b.337.2		2	65.37	even	12
507.2.e.c.22.1		2	65.17	odd	12
507.2.e.c.484.1		2	65.12	odd	4
507.2.j.d.316.1		4	65.7	even	12
507.2.j.d.316.2		4	65.32	even	12
507.2.j.d.361.1		4	65.57	even	4
507.2.j.d.361.2		4	65.47	even	4
624.2.q.c.289.1		2	20.7	even	4
624.2.q.c.529.1		2	260.87	even	12
975.2.i.f.451.1		2	65.48	odd	12
975.2.i.f.601.1		2	5.3	odd	4
975.2.bb.d.724.1		4	65.9	even	6	inner
975.2.bb.d.724.2		4	13.9	even	3	inner
975.2.bb.d.874.1		4	1.1	even	1	trivial
975.2.bb.d.874.2		4	5.4	even	2	inner
1521.2.a.a.1.1		1	195.107	even	12
1521.2.a.d.1.1		1	195.62	even	12
1521.2.b.c.1351.1		2	195.167	odd	12
1521.2.b.c.1351.2		2	195.2	odd	12
1872.2.t.j.289.1		2	60.47	odd	4
1872.2.t.j.1153.1		2	780.347	odd	12
8112.2.a.w.1.1		1	260.107	even	12
8112.2.a.bc.1.1		1	260.127	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(1.73205 + 1.00000i) q^{7} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -1.00000i q^{12} +(-0.866025 - 3.50000i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{16} +(-6.06218 - 3.50000i) q^{17} +1.00000i q^{18} +(-3.00000 + 5.19615i) q^{19} -2.00000 q^{21} +(-1.73205 - 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(1.50000 + 2.59808i) q^{24} +(2.50000 + 2.59808i) q^{26} +1.00000i q^{27} +(-1.73205 + 1.00000i) q^{28} +(-0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(4.33013 + 2.50000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +7.00000 q^{34} +(0.500000 + 0.866025i) q^{36} +(-0.866025 + 0.500000i) q^{37} -6.00000i q^{38} +(2.50000 + 2.59808i) q^{39} +(-4.50000 - 7.79423i) q^{41} +(1.73205 - 1.00000i) q^{42} +(-5.19615 - 3.00000i) q^{43} -2.00000 q^{44} +(3.00000 - 5.19615i) q^{46} -6.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +7.00000 q^{51} +(3.46410 + 1.00000i) q^{52} -9.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{56} -6.00000i q^{57} +(0.866025 + 0.500000i) q^{58} +(-0.500000 + 0.866025i) q^{61} +(-3.46410 + 2.00000i) q^{62} +(1.73205 - 1.00000i) q^{63} -7.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(6.06218 - 3.50000i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +11.0000i q^{73} +(0.500000 - 0.866025i) q^{74} +(-3.00000 - 5.19615i) q^{76} +4.00000i q^{77} +(-3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} -14.0000i q^{83} +(1.00000 - 1.73205i) q^{84} +6.00000 q^{86} +(0.866025 + 0.500000i) q^{87} +(5.19615 - 3.00000i) q^{88} +(-7.00000 - 12.1244i) q^{89} +(2.00000 - 6.92820i) q^{91} -6.00000i q^{92} +(-3.46410 + 2.00000i) q^{93} +(3.00000 + 5.19615i) q^{94} -5.00000 q^{96} +(-1.73205 - 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^4 + 2 * q^6 + 2 * q^9	\( 4 q - 2 q^{4} + 2 q^{6} + 2 q^{9} + 4 q^{11} - 8 q^{14} + 2 q^{16} - 12 q^{19} - 8 q^{21} + 6 q^{24} + 10 q^{26} - 2 q^{29} + 16 q^{31} + 28 q^{34} + 2 q^{36} + 10 q^{39} - 18 q^{41} - 8 q^{44} + 12 q^{46} - 6 q^{49} + 28 q^{51} - 2 q^{54} + 12 q^{56} - 2 q^{61} - 28 q^{64} + 8 q^{66} + 12 q^{69} - 12 q^{71} + 2 q^{74} - 12 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} + 24 q^{86} - 28 q^{89} + 8 q^{91} + 12 q^{94} - 20 q^{96} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 2 * q^6 + 2 * q^9 + 4 * q^11 - 8 * q^14 + 2 * q^16 - 12 * q^19 - 8 * q^21 + 6 * q^24 + 10 * q^26 - 2 * q^29 + 16 * q^31 + 28 * q^34 + 2 * q^36 + 10 * q^39 - 18 * q^41 - 8 * q^44 + 12 * q^46 - 6 * q^49 + 28 * q^51 - 2 * q^54 + 12 * q^56 - 2 * q^61 - 28 * q^64 + 8 * q^66 + 12 * q^69 - 12 * q^71 + 2 * q^74 - 12 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 + 24 * q^86 - 28 * q^89 + 8 * q^91 + 12 * q^94 - 20 * q^96 + 8 * q^99

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