LMFDB - Embedded newform 975.2.i.f.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(451,975)]

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, 0, 4]))

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

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

chi := DirichletCharacter("975.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.i (of order $3$, degree $2$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	975.451
Dual form			975.2.i.f.601.1

$q$-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} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} -1.00000 q^{18} +(3.00000 + 5.19615i) q^{19} -2.00000 q^{21} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{33} -7.00000 q^{34} +(0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} +6.00000 q^{38} +(-2.50000 + 2.59808i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(3.00000 + 5.19615i) q^{43} +2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +7.00000 q^{51} +(1.00000 + 3.46410i) q^{52} +9.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{61} +(2.00000 - 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +7.00000 q^{64} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-3.00000 + 5.19615i) q^{76} +4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +14.0000 q^{83} +(-1.00000 - 1.73205i) q^{84} +6.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(3.00000 - 5.19615i) q^{88} +(7.00000 - 12.1244i) q^{89} +(2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} -5.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} + 6 q^{8} - q^{9} + 2 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} + q^{16} - 7 q^{17} - 2 q^{18} + 6 q^{19} - 4 q^{21} - 2 q^{22} - 6 q^{23} - 3 q^{24} + 5 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 + q^4 + q^6 + 2 * q^7 + 6 * q^8 - q^9 + 2 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 + q^16 - 7 * q^17 - 2 * q^18 + 6 * q^19 - 4 * q^21 - 2 * q^22 - 6 * q^23 - 3 * q^24 + 5 * q^26 + 2 * q^27 - 2 * q^28 + q^29 + 8 * q^31 + 5 * q^32 + 2 * q^33 - 14 * q^34 + q^36 + q^37 + 12 * q^38 - 5 * q^39 - 9 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 + 6 * q^46 - 12 * q^47 + q^48 + 3 * q^49 + 14 * q^51 + 2 * q^52 + 18 * q^53 + q^54 + 6 * q^56 - 12 * q^57 - q^58 - q^61 + 4 * q^62 + 2 * q^63 + 14 * q^64 + 4 * q^66 - 2 * q^67 + 7 * q^68 - 6 * q^69 - 6 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 6 * q^76 + 8 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 9 * q^82 + 28 * q^83 - 2 * q^84 + 12 * q^86 + q^87 + 6 * q^88 + 14 * q^89 + 4 * q^91 - 12 * q^92 - 4 * q^93 - 6 * q^94 - 10 * q^96 - 2 * q^97 - 3 * q^98 - 4 * q^99

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	3.00000			1.06066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.00000			−0.288675
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	2.00000			0.534522
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$	−1.00000			−0.235702
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$		0			0
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$	1.00000			0.192450
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	−7.00000			−1.20049
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	6.00000			0.973329
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	0.998828	−	0.0484030i	$-0.0154132\pi$
$43$	3.00000	+	5.19615i	0.457496	+	0.792406i	−0.541332	+	0.840809i	$0.682080\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	7.00000			0.980196
$52$	1.00000	+	3.46410i	0.138675	+	0.480384i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$	−6.00000			−0.794719
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$	2.00000			0.246183
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	3.50000	−	6.06218i	0.424437	−	0.735147i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	4.00000			0.455842
$78$	1.00000	+	3.46410i	0.113228	+	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$		0			0
$86$	6.00000			0.646997
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$		0			0
$91$	2.00000	+	6.92820i	0.209657	+	0.726273i
$92$	−6.00000			−0.625543
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	−5.00000			−0.510310
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$	3.50000	−	6.06218i	0.346552	−	0.600245i
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$	10.5000	+	2.59808i	1.02961	+	0.254762i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$	2.00000			0.188982
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$		0			0
$116$	1.00000			0.0928477
$117$	−1.00000	−	3.46410i	−0.0924500	−	0.320256i
$118$		0			0
$119$	7.00000	−	12.1244i	0.641689	−	1.11144i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.00000			−0.0905357
$123$	−4.50000	−	7.79423i	−0.405751	−	0.702782i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	10.0000	−	17.3205i	0.887357	−	1.53695i	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	10.0000	−	17.3205i	0.887357	−	1.53695i	0.842989	−	0.537931i	$-0.180794\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−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	$0.613642\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$		0			0
$136$	−10.5000	−	18.1865i	−0.900368	−	1.55948i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	−6.00000			−0.510754
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$		0			0
$141$	3.00000	−	5.19615i	0.252646	−	0.437595i
$142$	−6.00000			−0.503509
$143$	5.00000	−	5.19615i	0.418121	−	0.434524i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$	1.00000			0.0821995
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	9.00000	+	15.5885i	0.729996	+	1.26439i
$153$	−3.50000	+	6.06218i	−0.282958	+	0.490098i
$154$	2.00000	−	3.46410i	0.161165	−	0.279145i
$155$		0			0
$156$	−3.50000	−	0.866025i	−0.280224	−	0.0693375i
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	−4.50000	+	7.79423i	−0.356873	+	0.618123i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−9.00000			−0.702782
$165$		0			0
$166$	7.00000	−	12.1244i	0.543305	−	0.941033i
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	−0.370599	−	0.928793i	$-0.620848\pi$
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	0.989658	−	0.143448i	$-0.0458190\pi$
$168$	−6.00000			−0.462910
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	−3.00000	+	5.19615i	−0.228748	+	0.396203i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	1.00000			0.0758098
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	−0.826231	−	0.563331i	$-0.809520\pi$
$179$	1.00000	−	1.73205i	0.0747435	−	0.129460i	0.900975	+	0.433872i	$0.142853\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	7.00000	+	1.73205i	0.518875	+	0.128388i
$183$	1.00000			0.0739221
$184$	−9.00000	+	15.5885i	−0.663489	+	1.14920i
$185$		0			0
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−14.0000			−1.02378
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	1.00000	+	1.73205i	0.0727393	+	0.125988i
$190$		0			0
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$	−3.50000	+	6.06218i	−0.252591	+	0.437500i
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	−0.981293	−	0.192522i	$-0.938333\pi$
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	0.657376	+	0.753563i	$0.271667\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$	−1.00000	+	1.73205i	−0.0710669	+	0.123091i
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$		0			0
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	2.00000			0.140372
$204$	3.50000	+	6.06218i	0.245049	+	0.424437i
$205$		0			0
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	6.00000			0.417029
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	12.0000			0.830057
$210$		0			0
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	6.00000			0.411113
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	3.00000			0.204124
$217$	4.00000	+	6.92820i	0.271538	+	0.470317i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	5.50000	−	9.52628i	0.371656	−	0.643726i
$220$		0			0
$221$	−7.00000	−	24.2487i	−0.470871	−	1.63114i
$222$	1.00000			0.0671156
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	−5.00000	+	8.66025i	−0.334077	+	0.578638i
$225$		0			0
$226$	−15.0000			−0.997785
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$	−3.00000	−	5.19615i	−0.198680	−	0.344124i
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	−2.00000	+	3.46410i	−0.131590	+	0.227921i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$	−3.50000	−	0.866025i	−0.228802	−	0.0566139i
$235$		0			0
$236$		0			0
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	−7.00000	−	12.1244i	−0.453743	−	0.785905i
$239$	30.0000			1.94054			0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000			1.94054			0.970269	+	0.242028i	$0.0778125\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	7.00000			0.449977
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	6.00000	+	20.7846i	0.381771	+	1.32249i
$248$	12.0000			0.762001
$249$	−7.00000	+	12.1244i	−0.443607	+	0.768350i
$250$		0			0
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$	2.00000			0.125988
$253$	6.00000	+	10.3923i	0.377217	+	0.653359i
$254$	−10.0000	−	17.3205i	−0.627456	−	1.08679i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−3.50000	+	6.06218i	−0.218324	+	0.378148i	−0.954296	−	0.298864i	$-0.903392\pi$
$257$	−3.50000	+	6.06218i	−0.218324	+	0.378148i	0.735972	+	0.677012i	$0.236726\pi$
$258$	−3.00000	+	5.19615i	−0.186772	+	0.323498i
$259$	2.00000			0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	−4.00000	+	6.92820i	−0.247121	+	0.428026i
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	6.00000	+	10.3923i	0.367884	+	0.637193i
$267$	7.00000	+	12.1244i	0.428393	+	0.741999i
$268$	−2.00000			−0.122169
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−7.00000			−0.424437
$273$	−7.00000	−	1.73205i	−0.423659	−	0.104828i
$274$	−3.00000			−0.181237
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−15.5000	−	26.8468i	−0.931305	−	1.61307i	−0.150210	−	0.988654i	$-0.547995\pi$
$278$	−12.0000			−0.719712
$279$	−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	$0.691789\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	0.464169	+	0.885747i	$0.346353\pi$
$283$	−9.00000	+	15.5885i	−0.534994	+	0.926638i	−0.999164	+	0.0408910i	$0.986980\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$	−18.0000			−1.06251
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$		0			0
$291$	2.00000			0.117242
$292$	−5.50000	−	9.52628i	−0.321863	−	0.557483i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$	−3.00000			−0.173785
$299$	−15.0000	+	15.5885i	−0.867472	+	0.901504i
$300$		0			0
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$	−1.00000	+	1.73205i	−0.0575435	+	0.0996683i
$303$	−1.50000	−	2.59808i	−0.0861727	−	0.149256i
$304$	6.00000			0.344124
$305$		0			0
$306$	3.50000	+	6.06218i	0.200082	+	0.346552i
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$	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	$0.329518\pi$
$312$	−7.50000	+	7.79423i	−0.424604	+	0.441261i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$		0			0
$316$	−2.00000	−	3.46410i	−0.112509	−	0.194871i
$317$	25.0000			1.40414			0.702070	−	0.712108i	$-0.252259\pi$
$317$	25.0000			1.40414			0.702070	+	0.712108i	$0.252259\pi$
$318$	4.50000	+	7.79423i	0.252347	+	0.437079i
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$		0			0
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	−6.00000	+	10.3923i	−0.334367	+	0.579141i
$323$	21.0000	−	36.3731i	1.16847	−	2.02385i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−4.00000			−0.221540
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−13.5000	+	23.3827i	−0.745413	+	1.29109i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	7.00000	+	12.1244i	0.384175	+	0.665410i
$333$	−1.00000			−0.0547997
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	33.0000			1.79762			0.898812	−	0.438334i	$-0.144431\pi$
$337$	33.0000			1.79762			0.898812	+	0.438334i	$0.144431\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$	15.0000			0.814688
$340$		0			0
$341$	4.00000	−	6.92820i	0.216612	−	0.375183i
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	20.0000			1.07990
$344$	9.00000	+	15.5885i	0.485247	+	0.840473i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$	−0.500000	+	0.866025i	−0.0268028	+	0.0464238i
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$		0			0
$351$	3.50000	+	0.866025i	0.186816	+	0.0462250i
$352$	10.0000			0.533002
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$354$		0			0
$355$		0			0
$356$	14.0000			0.741999
$357$	7.00000	+	12.1244i	0.370479	+	0.641689i
$358$	−1.00000	−	1.73205i	−0.0528516	−	0.0915417i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$	−7.00000			−0.367405
$364$	−5.00000	+	5.19615i	−0.262071	+	0.272352i
$365$		0			0
$366$	0.500000	−	0.866025i	0.0261354	−	0.0452679i
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	9.00000			0.468521
$370$		0			0
$371$	9.00000	+	15.5885i	0.467257	+	0.809312i
$372$	−4.00000			−0.207390
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$	−7.00000	+	12.1244i	−0.361961	+	0.626936i
$375$		0			0
$376$	−18.0000			−0.928279
$377$	2.50000	−	2.59808i	0.128757	−	0.133808i
$378$	2.00000			0.102869
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.132391	−	0.991198i	$-0.457734\pi$
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.792207	−	0.610253i	$-0.208932\pi$
$380$		0			0
$381$	10.0000	+	17.3205i	0.512316	+	0.887357i
$382$	4.00000			0.204658
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$	−1.50000	−	2.59808i	−0.0765466	−	0.132583i
$385$		0			0
$386$	4.50000	+	7.79423i	0.229044	+	0.396716i
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	−14.0000			−0.701757
$399$	−6.00000	−	10.3923i	−0.300376	−	0.520266i
$400$		0			0
$401$	−0.500000	+	0.866025i	−0.0249688	+	0.0432472i	−0.878240	−	0.478220i	$-0.841282\pi$
$401$	−0.500000	+	0.866025i	−0.0249688	+	0.0432472i	0.853271	+	0.521468i	$0.174615\pi$
$402$	−2.00000			−0.0997509
$403$	14.0000	+	3.46410i	0.697390	+	0.172559i
$404$	−3.00000			−0.149256
$405$		0			0
$406$	1.00000	−	1.73205i	0.0496292	−	0.0859602i
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$	21.0000			1.03965
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	0.766426	−	0.642333i	$-0.222033\pi$
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	3.00000			0.147979
$412$	−3.00000	−	5.19615i	−0.147799	−	0.255996i
$413$		0			0
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$		0			0
$416$	5.00000	+	17.3205i	0.245145	+	0.849208i
$417$	12.0000			0.587643
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	−0.992559	−	0.121768i	$-0.961144\pi$
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	0.601733	+	0.798697i	$0.294477\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	27.0000			1.31124
$425$		0			0
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	1.00000	−	1.73205i	0.0483934	−	0.0838198i
$428$	−6.00000			−0.290021
$429$	2.00000	+	6.92820i	0.0965609	+	0.334497i
$430$		0			0
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	0.998775	−	0.0494752i	$-0.0157549\pi$
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	−0.542234	+	0.840227i	$0.682422\pi$
$434$	8.00000			0.384012
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−36.0000			−1.72211
$438$	−5.50000	−	9.52628i	−0.262800	−	0.455183i
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−24.5000	−	6.06218i	−1.16535	−	0.288348i
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$	−0.500000	+	0.866025i	−0.0237289	+	0.0410997i
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	3.00000			0.141895
$448$	7.00000	+	12.1244i	0.330719	+	0.572822i
$449$	−17.0000	−	29.4449i	−0.802280	−	1.38959i	−0.918112	−	0.396320i	$-0.870287\pi$
$449$	−17.0000	−	29.4449i	−0.802280	−	1.38959i	0.115833	−	0.993269i	$-0.463046\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$	1.00000	−	1.73205i	0.0469841	−	0.0813788i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	−0.977051	−	0.213006i	$-0.931675\pi$
$457$	−6.50000	+	11.2583i	−0.304057	+	0.526642i	0.672994	+	0.739648i	$0.265008\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$	−3.50000	−	6.06218i	−0.163366	−	0.282958i
$460$		0			0
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	0.555412	−	0.831575i	$-0.312560\pi$
$461$	−9.50000	−	16.4545i	−0.442459	−	0.766362i	−0.997871	+	0.0652135i	$0.979227\pi$
$462$	2.00000	+	3.46410i	0.0930484	+	0.161165i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$	2.50000	−	2.59808i	0.115563	−	0.120096i
$469$	−4.00000			−0.184703
$470$		0			0
$471$	−1.50000	+	2.59808i	−0.0691164	+	0.119713i
$472$		0			0
$473$	12.0000			0.551761
$474$	−2.00000	−	3.46410i	−0.0918630	−	0.159111i
$475$		0			0
$476$	14.0000			0.641689
$477$	−4.50000	−	7.79423i	−0.206041	−	0.356873i
$478$	15.0000	−	25.9808i	0.686084	−	1.18833i
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	2.50000	−	2.59808i	0.113990	−	0.118462i
$482$	−7.00000			−0.318841
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	0.994646	−	0.103339i	$-0.0329526\pi$
$487$	9.00000	+	15.5885i	0.407829	+	0.706380i	−0.586817	+	0.809719i	$0.699619\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$	4.00000			0.180886
$490$		0			0
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	−0.925746	−	0.378147i	$-0.876561\pi$
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	0.790358	+	0.612646i	$0.209895\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$	−7.00000			−0.315264
$494$	21.0000	+	5.19615i	0.944835	+	0.233786i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$	7.00000	+	12.1244i	0.313678	+	0.543305i
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$		0			0
$501$	8.00000	+	13.8564i	0.357414	+	0.619059i
$502$	−12.0000			−0.535586
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	0.842870	−	0.538117i	$-0.180864\pi$
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	−0.887458	+	0.460889i	$0.847531\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$		0			0
$506$	12.0000			0.533465
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$	20.0000			0.887357
$509$	−3.50000	+	6.06218i	−0.155135	+	0.268701i	−0.933108	−	0.359596i	$-0.882915\pi$
$509$	−3.50000	+	6.06218i	−0.155135	+	0.268701i	0.777973	+	0.628297i	$0.216248\pi$
$510$		0			0
$511$	−11.0000	−	19.0526i	−0.486611	−	0.842836i
$512$	11.0000			0.486136
$513$	3.00000	+	5.19615i	0.132453	+	0.229416i
$514$	3.50000	+	6.06218i	0.154378	+	0.267391i
$515$		0			0
$516$	−3.00000	−	5.19615i	−0.132068	−	0.228748i
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	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	$0.520933\pi$
$522$	−0.500000	+	0.866025i	−0.0218844	+	0.0379049i
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	−0.671414	−	0.741082i	$-0.734313\pi$
$523$	7.00000	−	12.1244i	0.306089	−	0.530161i	0.977503	+	0.210921i	$0.0676463\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$		0			0
$526$	15.0000	+	25.9808i	0.654031	+	1.13282i
$527$	−14.0000	−	24.2487i	−0.609850	−	1.05629i
$528$	2.00000			0.0870388
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$		0			0
$532$	−12.0000			−0.520266
$533$	−22.5000	+	23.3827i	−0.974583	+	1.01282i
$534$	14.0000			0.605839
$535$		0			0
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$	1.00000	+	1.73205i	0.0431532	+	0.0747435i
$538$	14.0000			0.603583
$539$	−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
$543$	3.50000	−	6.06218i	0.150199	−	0.260153i
$544$	17.5000	−	30.3109i	0.750306	−	1.29957i
$545$		0			0
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$	26.0000			1.11168			0.555840	−	0.831289i	$-0.312397\pi$
$547$	26.0000			1.11168			0.555840	+	0.831289i	$0.312397\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	−0.500000	+	0.866025i	−0.0213395	+	0.0369611i
$550$		0			0
$551$	6.00000			0.255609
$552$	−9.00000	−	15.5885i	−0.383065	−	0.663489i
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$	−31.0000			−1.31706
$555$		0			0
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$	−4.00000			−0.169334
$559$	6.00000	+	20.7846i	0.253773	+	0.879095i
$560$		0			0
$561$	7.00000	−	12.1244i	0.295540	−	0.511891i
$562$	−9.50000	+	16.4545i	−0.400733	+	0.694090i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	6.00000			0.252646
$565$		0			0
$566$	9.00000	+	15.5885i	0.378298	+	0.655232i
$567$	−2.00000			−0.0839921
$568$	−9.00000	−	15.5885i	−0.377632	−	0.654077i
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	7.00000	+	1.73205i	0.292685	+	0.0724207i
$573$	−4.00000			−0.167102
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$		0			0
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	16.0000	+	27.7128i	0.665512	+	1.15270i
$579$	−4.50000	−	7.79423i	−0.187014	−	0.323917i
$580$		0			0
$581$	14.0000	+	24.2487i	0.580818	+	1.00601i
$582$	1.00000	−	1.73205i	0.0414513	−	0.0717958i
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$	−33.0000			−1.36555
$585$		0			0
$586$	−9.00000			−0.371787
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	−0.652355	−	0.757914i	$-0.726219\pi$
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	0.982550	+	0.185999i	$0.0595520\pi$
$588$	−1.50000	+	2.59808i	−0.0618590	+	0.107143i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−0.500000	−	0.866025i	−0.0205499	−	0.0355934i
$593$	−13.0000			−0.533846			−0.266923	−	0.963718i	$-0.586007\pi$
$593$	−13.0000			−0.533846			−0.266923	+	0.963718i	$0.586007\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$		0			0
$596$	1.50000	−	2.59808i	0.0614424	−	0.106421i
$597$	14.0000			0.572982
$598$	6.00000	+	20.7846i	0.245358	+	0.849946i
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$		0			0
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$	6.00000	+	10.3923i	0.244542	+	0.423559i
$603$	2.00000			0.0814463
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$		0			0
$606$	−3.00000			−0.121867
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$608$	−15.0000	+	25.9808i	−0.608330	+	1.05366i
$609$	−1.00000	+	1.73205i	−0.0405220	+	0.0701862i
$610$		0			0
$611$	−21.0000	−	5.19615i	−0.849569	−	0.210214i
$612$	−7.00000			−0.282958
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	−0.999178	−	0.0405396i	$-0.987092\pi$
$613$	−11.5000	+	19.9186i	−0.464481	+	0.804504i	0.534697	+	0.845044i	$0.320426\pi$
$614$	−7.00000	+	12.1244i	−0.282497	+	0.489299i
$615$		0			0
$616$	12.0000			0.483494
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	0.966689	−	0.255956i	$-0.0823901\pi$
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	−0.705008	+	0.709199i	$0.749057\pi$
$618$	−3.00000	−	5.19615i	−0.120678	−	0.209020i
$619$	−24.0000			−0.964641			−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000			−0.964641			−0.482321	+	0.875995i	$0.660206\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	9.00000	−	15.5885i	0.360867	−	0.625040i
$623$	28.0000			1.12180
$624$	1.00000	+	3.46410i	0.0400320	+	0.138675i
$625$		0			0
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$	1.50000	+	2.59808i	0.0598565	+	0.103675i
$629$	−7.00000			−0.279108
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$	−12.0000			−0.477334
$633$	4.00000	+	6.92820i	0.158986	+	0.275371i
$634$	12.5000	−	21.6506i	0.496438	−	0.859857i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	7.50000	−	7.79423i	0.297161	−	0.308819i
$638$	−2.00000			−0.0791808
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$	−6.00000			−0.236801
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	0.664052	−	0.747686i	$-0.268835\pi$
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	−0.979541	+	0.201243i	$0.935502\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	0.358723	+	0.933444i	$0.383212\pi$
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	−0.987748	+	0.156059i	$0.950121\pi$
$648$	−1.50000	+	2.59808i	−0.0589256	+	0.102062i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$		0			0
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	5.50000	+	9.52628i	0.214575	+	0.371656i
$658$	−12.0000			−0.467809
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	0.933357	−	0.358951i	$-0.116865\pi$
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	−0.777539	+	0.628835i	$0.783532\pi$
$660$		0			0
$661$	−22.5000	+	38.9711i	−0.875149	+	1.51580i	−0.0185442	+	0.999828i	$0.505903\pi$
$661$	−22.5000	+	38.9711i	−0.875149	+	1.51580i	−0.856604	+	0.515974i	$0.827430\pi$
$662$	4.00000			0.155464
$663$	24.5000	+	6.06218i	0.951501	+	0.235435i
$664$	42.0000			1.62992
$665$		0			0
$666$	−0.500000	+	0.866025i	−0.0193746	+	0.0335578i
$667$	3.00000	+	5.19615i	0.116160	+	0.201196i
$668$	16.0000			0.619059
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	−5.00000	−	8.66025i	−0.192879	−	0.334077i
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	0.438652	+	0.898657i	$0.355456\pi$
$673$	−14.5000	+	25.1147i	−0.558934	+	0.968102i	−0.997586	+	0.0694449i	$0.977877\pi$
$674$	16.5000	−	28.5788i	0.635556	−	1.10082i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−34.0000			−1.30673			−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000			−1.30673			−0.653363	+	0.757045i	$0.726642\pi$
$678$	7.50000	−	12.9904i	0.288036	−	0.498893i
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$		0			0
$681$	14.0000			0.536481
$682$	−4.00000	−	6.92820i	−0.153168	−	0.265295i
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$	6.00000			0.229416
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	11.0000	−	19.0526i	0.419676	−	0.726900i
$688$	6.00000			0.228748
$689$	31.5000	+	7.79423i	1.20005	+	0.296936i
$690$		0			0
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	−2.00000	−	3.46410i	−0.0759737	−	0.131590i
$694$	18.0000			0.683271
$695$		0			0
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$	63.0000			2.38630
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	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	$0.487975\pi$
$702$	2.50000	−	2.59808i	0.0943564	−	0.0980581i
$703$	6.00000			0.226294
$704$	7.00000	−	12.1244i	0.263822	−	0.456954i
$705$		0			0
$706$	5.50000	+	9.52628i	0.206995	+	0.358526i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$		0			0
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	21.0000	−	36.3731i	0.787008	−	1.36314i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$	14.0000			0.523937
$715$		0			0
$716$	2.00000			0.0747435
$717$	−15.0000	+	25.9808i	−0.560185	+	0.970269i
$718$	−9.00000	+	15.5885i	−0.335877	+	0.581756i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		0			0
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	7.00000			0.260333
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$		0			0
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$	6.00000	+	20.7846i	0.222375	+	0.770329i
$729$	1.00000			0.0370370
$730$		0			0
$731$	21.0000	−	36.3731i	0.776713	−	1.34531i
$732$	0.500000	+	0.866025i	0.0184805	+	0.0320092i
$733$	15.0000			0.554038			0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000			0.554038			0.277019	+	0.960864i	$0.410654\pi$
$734$	−5.00000	−	8.66025i	−0.184553	−	0.319656i
$735$		0			0
$736$	−30.0000			−1.10581
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	4.50000	−	7.79423i	0.165647	−	0.286910i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	−21.0000	−	5.19615i	−0.771454	−	0.190885i
$742$	18.0000			0.660801
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$		0			0
$746$	−11.0000			−0.402739
$747$	−7.00000	−	12.1244i	−0.256117	−	0.443607i
$748$	−7.00000	−	12.1244i	−0.255945	−	0.443310i
$749$	−12.0000			−0.438470
$750$		0			0
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	12.0000			0.437304
$754$	−1.00000	−	3.46410i	−0.0364179	−	0.126155i
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	−25.0000	+	43.3013i	−0.908640	+	1.57381i	−0.0926859	+	0.995695i	$0.529545\pi$
$757$	−25.0000	+	43.3013i	−0.908640	+	1.57381i	−0.815955	+	0.578116i	$0.803788\pi$
$758$	−18.0000	−	31.1769i	−0.653789	−	1.13240i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.819231	−	0.573463i	$-0.805600\pi$
$761$	−25.0000	−	43.3013i	−0.906249	−	1.56967i	−0.0870179	−	0.996207i	$-0.527734\pi$
$762$	20.0000			0.724524
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$		0			0
$766$	8.00000			0.289052
$767$		0			0
$768$	−17.0000			−0.613435
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	0.457938	+	0.888984i	$0.348588\pi$
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	−0.998852	+	0.0479061i	$0.984745\pi$
$770$		0			0
$771$	−3.50000	−	6.06218i	−0.126049	−	0.218324i
$772$	−9.00000			−0.323917
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$		0			0
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$	9.50000	−	16.4545i	0.340592	−	0.589922i
$779$	−54.0000			−1.93475
$780$		0			0
$781$	−12.0000			−0.429394
$782$	21.0000	−	36.3731i	0.750958	−	1.30070i
$783$	0.500000	−	0.866025i	0.0178685	−	0.0309492i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$		0			0
$786$	−4.00000	−	6.92820i	−0.142675	−	0.247121i
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	6.00000			0.213741
$789$	−15.0000	−	25.9808i	−0.534014	−	0.924940i
$790$		0			0
$791$	15.0000	−	25.9808i	0.533339	−	0.923770i
$792$	−6.00000			−0.213201
$793$	−1.00000	−	3.46410i	−0.0355110	−	0.123014i
$794$	−34.0000			−1.20661
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	0.847771	−	0.530362i	$-0.177944\pi$
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	−0.883193	+	0.469010i	$0.844611\pi$
$798$	−12.0000			−0.424795
$799$	21.0000	+	36.3731i	0.742927	+	1.28679i
$800$		0			0
$801$	−14.0000			−0.494666
$802$	0.500000	+	0.866025i	0.0176556	+	0.0305804i
$803$	−11.0000	+	19.0526i	−0.388182	+	0.672350i
$804$	1.00000	−	1.73205i	0.0352673	−	0.0610847i
$805$		0			0
$806$	10.0000	−	10.3923i	0.352235	−	0.366053i
$807$	−14.0000			−0.492823
$808$	−4.50000	+	7.79423i	−0.158309	+	0.274200i
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	0.415357	+	0.909659i	$0.363657\pi$
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	−0.995466	+	0.0951198i	$0.969677\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	1.00000	+	1.73205i	0.0350931	+	0.0607831i
$813$		0			0
$814$	−2.00000			−0.0701000
$815$		0			0
$816$	3.50000	−	6.06218i	0.122525	−	0.212219i
$817$	−18.0000	+	31.1769i	−0.629740	+	1.09074i
$818$	−7.00000			−0.244749
$819$	5.00000	−	5.19615i	0.174714	−	0.181568i
$820$		0			0
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.0131101	+	0.999914i	$0.504173\pi$
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.859396	+	0.511311i	$0.829160\pi$
$822$	1.50000	−	2.59808i	0.0523185	−	0.0906183i
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$	−18.0000			−0.627060
$825$		0			0
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$	3.00000	+	5.19615i	0.104257	+	0.180579i
$829$	−8.50000	+	14.7224i	−0.295217	+	0.511331i	−0.975035	−	0.222049i	$-0.928725\pi$
$829$	−8.50000	+	14.7224i	−0.295217	+	0.511331i	0.679818	+	0.733381i	$0.262059\pi$
$830$		0			0
$831$	31.0000			1.07538
$832$	24.5000	+	6.06218i	0.849385	+	0.210168i
$833$	−21.0000			−0.727607
$834$	6.00000	−	10.3923i	0.207763	−	0.359856i
$835$		0			0
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	4.00000			0.138260
$838$	8.00000	+	13.8564i	0.276355	+	0.478662i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−9.50000	+	16.4545i	−0.327392	+	0.567059i
$843$	9.50000	−	16.4545i	0.327197	−	0.566722i
$844$	8.00000			0.275371
$845$		0			0
$846$	6.00000			0.206284
$847$	−7.00000	+	12.1244i	−0.240523	+	0.416598i
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$	−9.00000	−	15.5885i	−0.308879	−	0.534994i
$850$		0			0
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	−21.0000			−0.719026			−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000			−0.719026			−0.359513	+	0.933140i	$0.617057\pi$
$854$	−1.00000	−	1.73205i	−0.0342193	−	0.0592696i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	31.0000			1.05894			0.529470	−	0.848329i	$-0.322391\pi$
$857$	31.0000			1.05894			0.529470	+	0.848329i	$0.322391\pi$
$858$	7.00000	+	1.73205i	0.238976	+	0.0591312i
$859$	34.0000			1.16007			0.580033	−	0.814593i	$-0.303040\pi$
$859$	34.0000			1.16007			0.580033	+	0.814593i	$0.303040\pi$
$860$		0			0
$861$	9.00000	−	15.5885i	0.306719	−	0.531253i
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	−10.0000			−0.340404			−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000			−0.340404			−0.170202	+	0.985409i	$0.554442\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	19.0000			0.645646
$867$	−16.0000	−	27.7128i	−0.543388	−	0.941176i
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	−4.00000	+	6.92820i	−0.135691	+	0.235023i
$870$		0			0
$871$	−5.00000	+	5.19615i	−0.169419	+	0.176065i
$872$	−6.00000			−0.203186
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$	−18.0000	+	31.1769i	−0.608859	+	1.05457i
$875$		0			0
$876$	11.0000			0.371656
$877$	8.50000	+	14.7224i	0.287025	+	0.497141i	0.973098	−	0.230391i	$-0.0740005\pi$
$877$	8.50000	+	14.7224i	0.287025	+	0.497141i	−0.686074	+	0.727532i	$0.740667\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$	9.00000			0.303562
$880$		0			0
$881$	−18.5000	+	32.0429i	−0.623281	+	1.07955i	0.365590	+	0.930776i	$0.380867\pi$
$881$	−18.5000	+	32.0429i	−0.623281	+	1.07955i	−0.988871	+	0.148778i	$0.952466\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$	17.5000	−	18.1865i	0.588589	−	0.611679i
$885$		0			0
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	1.50000	+	2.59808i	0.0503367	+	0.0871857i
$889$	40.0000			1.34156
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	16.0000			0.535720
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$	1.50000	−	2.59808i	0.0501675	−	0.0868927i
$895$		0			0
$896$	−6.00000			−0.200446
$897$	−6.00000	−	20.7846i	−0.200334	−	0.693978i
$898$	−34.0000			−1.13459
$899$	2.00000	−	3.46410i	0.0667037	−	0.115534i
$900$		0			0
$901$	−31.5000	−	54.5596i	−1.04942	−	1.81764i
$902$	18.0000			0.599334
$903$	−6.00000	−	10.3923i	−0.199667	−	0.345834i
$904$	−22.5000	−	38.9711i	−0.748339	−	1.29616i
$905$		0			0
$906$	−1.00000	−	1.73205i	−0.0332228	−	0.0575435i
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	7.00000	−	12.1244i	0.232303	−	0.402361i
$909$	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	$0.730560\pi$
$912$	−3.00000	+	5.19615i	−0.0993399	+	0.172062i
$913$	14.0000	−	24.2487i	0.463332	−	0.802515i
$914$	6.50000	+	11.2583i	0.215001	+	0.372392i
$915$		0			0
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$	−8.00000	−	13.8564i	−0.264183	−	0.457579i
$918$	−7.00000			−0.231034
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$		0			0
$921$	7.00000	−	12.1244i	0.230658	−	0.399511i
$922$	−19.0000			−0.625732
$923$	−6.00000	−	20.7846i	−0.197492	−	0.684134i
$924$	−4.00000			−0.131590
$925$		0			0
$926$	13.0000	−	22.5167i	0.427207	−	0.739943i
$927$	3.00000	+	5.19615i	0.0985329	+	0.170664i
$928$	5.00000			0.164133
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	0.997905	−	0.0646999i	$-0.0206090\pi$
$929$	13.5000	+	23.3827i	0.442921	+	0.767161i	−0.554984	+	0.831861i	$0.687276\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$	−5.00000	−	8.66025i	−0.163780	−	0.283676i
$933$	−9.00000	+	15.5885i	−0.294647	+	0.510343i
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$		0			0
$936$	−3.00000	−	10.3923i	−0.0980581	−	0.339683i
$937$	49.0000			1.60076			0.800380	−	0.599493i	$-0.204631\pi$
$937$	49.0000			1.60076			0.800380	+	0.599493i	$0.204631\pi$
$938$	−2.00000	+	3.46410i	−0.0653023	+	0.113107i
$939$	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	$0.712617\pi$
$942$	1.50000	+	2.59808i	0.0488726	+	0.0846499i
$943$	−27.0000	−	46.7654i	−0.879241	−	1.52289i
$944$		0			0
$945$		0			0
$946$	6.00000	−	10.3923i	0.195077	−	0.337883i
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	4.00000			0.129914
$949$	−38.5000	−	9.52628i	−1.24976	−	0.309236i
$950$		0			0
$951$	−12.5000	+	21.6506i	−0.405340	+	0.702070i
$952$	21.0000	−	36.3731i	0.680614	−	1.17886i
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$	−9.00000			−0.291386
$955$		0			0
$956$	15.0000	+	25.9808i	0.485135	+	0.840278i
$957$	2.00000			0.0646508
$958$	12.0000	+	20.7846i	0.387702	+	0.671520i
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−1.00000	−	3.46410i	−0.0322413	−	0.111687i
$963$	6.00000			0.193347
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$		0			0
$966$	−6.00000	−	10.3923i	−0.193047	−	0.334367i
$967$	−2.00000			−0.0643157			−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000			−0.0643157			−0.0321578	+	0.999483i	$0.510238\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$	21.0000	+	36.3731i	0.674617	+	1.16847i
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	12.0000	−	20.7846i	0.384702	−	0.666324i
$974$	18.0000			0.576757
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	16.5000	−	28.5788i	0.527882	−	0.914318i	−0.471590	−	0.881818i	$-0.656320\pi$
$977$	16.5000	−	28.5788i	0.527882	−	0.914318i	0.999472	−	0.0325001i	$-0.0103469\pi$
$978$	2.00000	−	3.46410i	0.0639529	−	0.110770i
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$		0			0
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−4.00000			−0.127580			−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000			−0.127580			−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−13.5000	−	23.3827i	−0.430364	−	0.745413i
$985$		0			0
$986$	−3.50000	+	6.06218i	−0.111463	+	0.193059i
$987$	12.0000			0.381964
$988$	−15.0000	+	15.5885i	−0.477214	+	0.495935i
$989$	−36.0000			−1.14473
$990$		0			0
$991$	1.00000	−	1.73205i	0.0317660	−	0.0550204i	−0.849705	−	0.527258i	$-0.823220\pi$
$991$	1.00000	−	1.73205i	0.0317660	−	0.0550204i	0.881471	+	0.472237i	$0.156554\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$	−4.00000			−0.126936
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$		0			0
$996$	−14.0000			−0.443607
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$	12.0000	−	20.7846i	0.379853	−	0.657925i
$999$	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.i.f.451.1		2
5.2	odd	4		975.2.bb.d.724.2		4
5.3	odd	4		975.2.bb.d.724.1		4
5.4	even	2		39.2.e.a.22.1	yes	2
13.3	even	3	inner	975.2.i.f.601.1		2
15.14	odd	2		117.2.g.b.100.1		2
20.19	odd	2		624.2.q.c.529.1		2
60.59	even	2		1872.2.t.j.1153.1		2
65.3	odd	12		975.2.bb.d.874.2		4
65.4	even	6		507.2.a.b.1.1		1
65.9	even	6		507.2.a.c.1.1		1
65.19	odd	12		507.2.b.b.337.1		2
65.24	odd	12		507.2.j.d.361.2		4
65.29	even	6		39.2.e.a.16.1	✓	2
65.34	odd	4		507.2.j.d.316.1		4
65.42	odd	12		975.2.bb.d.874.1		4
65.44	odd	4		507.2.j.d.316.2		4
65.49	even	6		507.2.e.c.484.1		2
65.54	odd	12		507.2.j.d.361.1		4
65.59	odd	12		507.2.b.b.337.2		2
65.64	even	2		507.2.e.c.22.1		2
195.29	odd	6		117.2.g.b.55.1		2
195.59	even	12		1521.2.b.c.1351.1		2
195.74	odd	6		1521.2.a.a.1.1		1
195.134	odd	6		1521.2.a.d.1.1		1
195.149	even	12		1521.2.b.c.1351.2		2
260.139	odd	6		8112.2.a.w.1.1		1
260.159	odd	6		624.2.q.c.289.1		2
260.199	odd	6		8112.2.a.bc.1.1		1
780.419	even	6		1872.2.t.j.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.a.16.1	✓	2	65.29	even	6
39.2.e.a.22.1	yes	2	5.4	even	2
117.2.g.b.55.1		2	195.29	odd	6
117.2.g.b.100.1		2	15.14	odd	2
507.2.a.b.1.1		1	65.4	even	6
507.2.a.c.1.1		1	65.9	even	6
507.2.b.b.337.1		2	65.19	odd	12
507.2.b.b.337.2		2	65.59	odd	12
507.2.e.c.22.1		2	65.64	even	2
507.2.e.c.484.1		2	65.49	even	6
507.2.j.d.316.1		4	65.34	odd	4
507.2.j.d.316.2		4	65.44	odd	4
507.2.j.d.361.1		4	65.54	odd	12
507.2.j.d.361.2		4	65.24	odd	12
624.2.q.c.289.1		2	260.159	odd	6
624.2.q.c.529.1		2	20.19	odd	2
975.2.i.f.451.1		2	1.1	even	1	trivial
975.2.i.f.601.1		2	13.3	even	3	inner
975.2.bb.d.724.1		4	5.3	odd	4
975.2.bb.d.724.2		4	5.2	odd	4
975.2.bb.d.874.1		4	65.42	odd	12
975.2.bb.d.874.2		4	65.3	odd	12
1521.2.a.a.1.1		1	195.74	odd	6
1521.2.a.d.1.1		1	195.134	odd	6
1521.2.b.c.1351.1		2	195.59	even	12
1521.2.b.c.1351.2		2	195.149	even	12
1872.2.t.j.289.1		2	780.419	even	6
1872.2.t.j.1153.1		2	60.59	even	2
8112.2.a.w.1.1		1	260.139	odd	6
8112.2.a.bc.1.1		1	260.199	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} -1.00000 q^{18} +(3.00000 + 5.19615i) q^{19} -2.00000 q^{21} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} +4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} +(1.00000 + 1.73205i) q^{33} -7.00000 q^{34} +(0.500000 - 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} +6.00000 q^{38} +(-2.50000 + 2.59808i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(3.00000 + 5.19615i) q^{43} +2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +7.00000 q^{51} +(1.00000 + 3.46410i) q^{52} +9.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{56} -6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{61} +(2.00000 - 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +7.00000 q^{64} +2.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(-3.00000 + 5.19615i) q^{76} +4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +14.0000 q^{83} +(-1.00000 - 1.73205i) q^{84} +6.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(3.00000 - 5.19615i) q^{88} +(7.00000 - 12.1244i) q^{89} +(2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} -5.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} + 6 q^{8} - q^{9} + 2 q^{11} - 2 q^{12} + 7 q^{13} + 4 q^{14} + q^{16} - 7 q^{17} - 2 q^{18} + 6 q^{19} - 4 q^{21} - 2 q^{22} - 6 q^{23} - 3 q^{24} + 5 q^{26}+ \cdots - 4 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 + q^4 + q^6 + 2 * q^7 + 6 * q^8 - q^9 + 2 * q^11 - 2 * q^12 + 7 * q^13 + 4 * q^14 + q^16 - 7 * q^17 - 2 * q^18 + 6 * q^19 - 4 * q^21 - 2 * q^22 - 6 * q^23 - 3 * q^24 + 5 * q^26 + 2 * q^27 - 2 * q^28 + q^29 + 8 * q^31 + 5 * q^32 + 2 * q^33 - 14 * q^34 + q^36 + q^37 + 12 * q^38 - 5 * q^39 - 9 * q^41 - 2 * q^42 + 6 * q^43 + 4 * q^44 + 6 * q^46 - 12 * q^47 + q^48 + 3 * q^49 + 14 * q^51 + 2 * q^52 + 18 * q^53 + q^54 + 6 * q^56 - 12 * q^57 - q^58 - q^61 + 4 * q^62 + 2 * q^63 + 14 * q^64 + 4 * q^66 - 2 * q^67 + 7 * q^68 - 6 * q^69 - 6 * q^71 - 3 * q^72 - 22 * q^73 - q^74 - 6 * q^76 + 8 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 9 * q^82 + 28 * q^83 - 2 * q^84 + 12 * q^86 + q^87 + 6 * q^88 + 14 * q^89 + 4 * q^91 - 12 * q^92 - 4 * q^93 - 6 * q^94 - 10 * q^96 - 2 * q^97 - 3 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more