LMFDB - Embedded newform 1089.2.e.c.727.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1089,2,Mod(364,1089)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1089.364"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1089, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,-3,1,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.69570878012$
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 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.c.364.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(2.00000 - 3.46410i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -1.00000 q^{10} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -6.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +6.92820i q^{21} +(2.00000 + 3.46410i) q^{23} +(-4.50000 + 2.59808i) q^{24} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +5.19615i q^{27} +4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(1.50000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(2.50000 + 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{34} -4.00000 q^{35} +3.00000 q^{36} +3.00000 q^{37} +(-3.00000 + 5.19615i) q^{38} +(3.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(6.00000 + 3.46410i) q^{42} +(3.00000 - 5.19615i) q^{43} -3.00000 q^{45} +4.00000 q^{46} +(3.50000 - 6.06218i) q^{47} +1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(6.00000 - 3.46410i) q^{51} +(1.00000 - 1.73205i) q^{52} -9.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +(6.00000 - 10.3923i) q^{56} +(9.00000 - 5.19615i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(3.50000 + 6.06218i) q^{59} +1.73205i q^{60} -7.00000 q^{62} +(-6.00000 - 10.3923i) q^{63} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-6.00000 - 3.46410i) q^{69} +(-2.00000 + 3.46410i) q^{70} +9.00000 q^{71} +(4.50000 - 7.79423i) q^{72} -4.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +6.92820i q^{75} +(-3.00000 - 5.19615i) q^{76} +(3.00000 - 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} +10.3923i q^{87} +6.00000 q^{89} +(-1.50000 + 2.59808i) q^{90} -8.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +(10.5000 + 6.06218i) q^{93} +(-3.50000 - 6.06218i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-7.50000 - 4.33013i) q^{96} +(9.50000 - 16.4545i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} + q^{4} - q^{5} + 4 q^{7} + 6 q^{8} + 3 q^{9} - 2 q^{10} - 3 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} + q^{16} - 8 q^{17} - 3 q^{18} - 12 q^{19} + q^{20} + 4 q^{23} - 9 q^{24}+ \cdots - 18 q^{98}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 + q^4 - q^5 + 4 * q^7 + 6 * q^8 + 3 * q^9 - 2 * q^10 - 3 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 + q^16 - 8 * q^17 - 3 * q^18 - 12 * q^19 + q^20 + 4 * q^23 - 9 * q^24 + 4 * q^25 - 4 * q^26 + 8 * q^28 + 6 * q^29 + 3 * q^30 - 7 * q^31 + 5 * q^32 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^39 - 3 * q^40 - 2 * q^41 + 12 * q^42 + 6 * q^43 - 6 * q^45 + 8 * q^46 + 7 * q^47 - 9 * q^49 - 4 * q^50 + 12 * q^51 + 2 * q^52 - 18 * q^53 + 9 * q^54 + 12 * q^56 + 18 * q^57 - 6 * q^58 + 7 * q^59 - 14 * q^62 - 12 * q^63 + 14 * q^64 - 2 * q^65 - 11 * q^67 - 4 * q^68 - 12 * q^69 - 4 * q^70 + 18 * q^71 + 9 * q^72 - 8 * q^73 + 3 * q^74 - 6 * q^76 + 6 * q^78 + 8 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 - 12 * q^83 - 12 * q^84 + 4 * q^85 - 6 * q^86 + 12 * q^89 - 3 * q^90 - 16 * q^91 - 4 * q^92 + 21 * q^93 - 7 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 - 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	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	$0.0516399\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$			1.73205i			0.707107i
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	3.00000			1.06066
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$	1.50000	+	0.866025i	0.387298	+	0.223607i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$			6.92820i			1.51186i
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	−4.50000	+	2.59808i	−0.918559	+	0.530330i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−2.00000			−0.392232
$27$			5.19615i			1.00000i
$28$	4.00000			0.755929
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$	1.50000	−	0.866025i	0.273861	−	0.158114i
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		0			0
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	−4.00000			−0.676123
$36$	3.00000			0.500000
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$	3.00000	+	1.73205i	0.480384	+	0.277350i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$	6.00000	+	3.46410i	0.925820	+	0.534522i
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$	4.00000			0.589768
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$			1.73205i			0.250000i
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	6.00000	−	3.46410i	0.840168	−	0.485071i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$		0			0
$56$	6.00000	−	10.3923i	0.801784	−	1.38873i
$57$	9.00000	−	5.19615i	1.19208	−	0.688247i
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$			1.73205i			0.223607i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	−7.00000			−0.889001
$63$	−6.00000	−	10.3923i	−0.755929	−	1.30931i
$64$	7.00000			0.875000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−6.00000	−	3.46410i	−0.722315	−	0.417029i
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$	4.50000	−	7.79423i	0.530330	−	0.918559i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$			6.92820i			0.800000i
$76$	−3.00000	−	5.19615i	−0.344124	−	0.596040i
$77$		0			0
$78$	3.00000	−	1.73205i	0.339683	−	0.196116i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−2.00000			−0.220863
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	−6.00000	+	3.46410i	−0.654654	+	0.377964i
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$	−3.00000	−	5.19615i	−0.323498	−	0.560316i
$87$			10.3923i			1.11417i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.50000	+	2.59808i	−0.158114	+	0.273861i
$91$	−8.00000			−0.838628
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$	10.5000	+	6.06218i	1.08880	+	0.628619i
$94$	−3.50000	−	6.06218i	−0.360997	−	0.625266i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	−7.50000	−	4.33013i	−0.765466	−	0.441942i
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.253837	−	0.967247i	$-0.418307\pi$
$97$	9.50000	−	16.4545i	0.964579	−	1.67070i	0.710742	−	0.703452i	$-0.248359\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	4.00000			0.400000
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	−0.948207	−	0.317653i	$-0.897105\pi$
$101$	−2.00000	+	3.46410i	−0.199007	+	0.344691i	0.749199	+	0.662344i	$0.230438\pi$
$102$		−	6.92820i		−	0.685994i
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$	6.00000	−	3.46410i	0.585540	−	0.338062i
$106$	−4.50000	+	7.79423i	−0.437079	+	0.757042i
$107$	18.0000			1.74013			0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000			1.74013			0.870063	+	0.492941i	$0.164078\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	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
$111$	−4.50000	+	2.59808i	−0.427121	+	0.246598i
$112$	−2.00000	−	3.46410i	−0.188982	−	0.327327i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		−	10.3923i		−	0.973329i
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	6.00000			0.557086
$117$	−6.00000			−0.554700
$118$	7.00000			0.644402
$119$	−8.00000	+	13.8564i	−0.733359	+	1.27021i
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$		0			0
$122$		0			0
$123$	3.00000	+	1.73205i	0.270501	+	0.156174i
$124$	3.50000	−	6.06218i	0.314309	−	0.544400i
$125$	−9.00000			−0.804984
$126$	−12.0000			−1.06904
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$			10.3923i			0.914991i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−12.0000	+	20.7846i	−1.04053	+	1.80225i
$134$	−11.0000			−0.950255
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$	−12.0000			−1.02899
$137$	−2.50000	+	4.33013i	−0.213589	+	0.369948i	−0.952835	−	0.303488i	$-0.901849\pi$
$137$	−2.50000	+	4.33013i	−0.213589	+	0.369948i	0.739246	+	0.673436i	$0.235182\pi$
$138$	−6.00000	+	3.46410i	−0.510754	+	0.294884i
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−2.00000	−	3.46410i	−0.169031	−	0.292770i
$141$			12.1244i			1.02105i
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$		0			0
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−6.00000			−0.498273
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$	13.5000	+	7.79423i	1.11346	+	0.642857i
$148$	1.50000	+	2.59808i	0.123299	+	0.213561i
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$	6.00000	+	3.46410i	0.489898	+	0.282843i
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	0.331842	+	0.943335i	$0.392330\pi$
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	−0.982873	+	0.184284i	$0.941004\pi$
$152$	−18.0000			−1.45999
$153$	−6.00000	+	10.3923i	−0.485071	+	0.840168i
$154$		0			0
$155$	−3.50000	+	6.06218i	−0.281127	+	0.486926i
$156$			3.46410i			0.277350i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$	2.50000	−	4.33013i	0.197642	−	0.342327i
$161$	16.0000			1.26098
$162$	−9.00000			−0.707107
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$			20.7846i			1.60357i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	4.00000			0.306786
$171$	−9.00000	+	15.5885i	−0.688247	+	1.19208i
$172$	6.00000			0.457496
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	9.00000	+	5.19615i	0.682288	+	0.393919i
$175$	−8.00000	−	13.8564i	−0.604743	−	1.04745i
$176$		0			0
$177$	−10.5000	−	6.06218i	−0.789228	−	0.455661i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$		0			0
$184$	6.00000	+	10.3923i	0.442326	+	0.766131i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$	10.5000	−	6.06218i	0.769897	−	0.444500i
$187$		0			0
$188$	7.00000			0.510527
$189$	18.0000	+	10.3923i	1.30931	+	0.755929i
$190$	6.00000			0.435286
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	−0.529101	−	0.848559i	$-0.677471\pi$
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	0.999424	+	0.0339349i	$0.0108039\pi$
$192$	−10.5000	+	6.06218i	−0.757772	+	0.437500i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	−9.50000	−	16.4545i	−0.682060	−	1.18136i
$195$		−	3.46410i		−	0.248069i
$196$	4.50000	−	7.79423i	0.321429	−	0.556731i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	6.00000	−	10.3923i	0.424264	−	0.734847i
$201$	16.5000	+	9.52628i	1.16382	+	0.671932i
$202$	2.00000	+	3.46410i	0.140720	+	0.243733i
$203$	−12.0000	−	20.7846i	−0.842235	−	1.45879i
$204$	6.00000	+	3.46410i	0.420084	+	0.242536i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	13.0000			0.905753
$207$	12.0000			0.834058
$208$	−2.00000			−0.138675
$209$		0			0
$210$		−	6.92820i		−	0.478091i
$211$	3.00000	+	5.19615i	0.206529	+	0.357718i	0.950619	−	0.310361i	$-0.100450\pi$
$211$	3.00000	+	5.19615i	0.206529	+	0.357718i	−0.744090	+	0.668079i	$0.767117\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	−13.5000	+	7.79423i	−0.925005	+	0.534052i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	−6.00000			−0.409197
$216$			15.5885i			1.06066i
$217$	−28.0000			−1.90076
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$		0			0
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$			5.19615i			0.348743i
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	20.0000			1.33631
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$	15.0000			0.997785
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$	9.00000	+	5.19615i	0.596040	+	0.344124i
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$	−2.00000	−	3.46410i	−0.131876	−	0.228416i
$231$		0			0
$232$	9.00000	−	15.5885i	0.590879	−	1.02343i
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	−7.00000			−0.456630
$236$	−3.50000	+	6.06218i	−0.227831	+	0.394614i
$237$			13.8564i			0.900070i
$238$	8.00000	+	13.8564i	0.518563	+	0.898177i
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	0.946590	−	0.322440i	$-0.104503\pi$
$239$	3.00000	+	5.19615i	0.194054	+	0.336111i	−0.752536	+	0.658551i	$0.771170\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$	−4.50000	+	7.79423i	−0.287494	+	0.497955i
$246$	3.00000	−	1.73205i	0.191273	−	0.110432i
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	−10.5000	−	18.1865i	−0.666751	−	1.15485i
$249$		−	20.7846i		−	1.31717i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	28.0000			1.76734			0.883672	−	0.468106i	$-0.155064\pi$
$251$	28.0000			1.76734			0.883672	+	0.468106i	$0.155064\pi$
$252$	6.00000	−	10.3923i	0.377964	−	0.654654i
$253$		0			0
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$	−6.00000	−	3.46410i	−0.375735	−	0.216930i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−11.0000	−	19.0526i	−0.686161	−	1.18847i	−0.973070	−	0.230508i	$-0.925961\pi$
$257$	−11.0000	−	19.0526i	−0.686161	−	1.18847i	0.286909	−	0.957958i	$-0.407372\pi$
$258$	9.00000	+	5.19615i	0.560316	+	0.323498i
$259$	6.00000	−	10.3923i	0.372822	−	0.645746i
$260$	−2.00000			−0.124035
$261$	−9.00000	−	15.5885i	−0.557086	−	0.964901i
$262$	−6.00000			−0.370681
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	4.50000	+	7.79423i	0.276433	+	0.478796i
$266$	12.0000	+	20.7846i	0.735767	+	1.27439i
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	5.50000	−	9.52628i	0.335966	−	0.581910i
$269$	−17.0000			−1.03651			−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000			−1.03651			−0.518254	+	0.855227i	$0.673418\pi$
$270$		−	5.19615i		−	0.316228i
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	12.0000	−	6.92820i	0.726273	−	0.419314i
$274$	2.50000	+	4.33013i	0.151031	+	0.261593i
$275$		0			0
$276$		−	6.92820i		−	0.417029i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−2.00000			−0.119952
$279$	−21.0000			−1.25724
$280$	−12.0000			−0.717137
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	−0.762561	−	0.646916i	$-0.776058\pi$
$281$	3.00000	−	5.19615i	0.178965	−	0.309976i	0.941526	+	0.336939i	$0.109392\pi$
$282$	10.5000	+	6.06218i	0.625266	+	0.360997i
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$	4.50000	+	7.79423i	0.267026	+	0.462502i
$285$	−9.00000	−	5.19615i	−0.533114	−	0.307794i
$286$		0			0
$287$	−8.00000			−0.472225
$288$	15.0000			0.883883
$289$	−1.00000			−0.0588235
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$			32.9090i			1.92916i
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$	13.5000	−	7.79423i	0.787336	−	0.454569i
$295$	3.50000	−	6.06218i	0.203778	−	0.352954i
$296$	9.00000			0.523114
$297$		0			0
$298$	−4.00000			−0.231714
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$	−6.00000	+	3.46410i	−0.346410	+	0.200000i
$301$	−12.0000	−	20.7846i	−0.691669	−	1.19800i
$302$	8.00000	+	13.8564i	0.460348	+	0.797347i
$303$		−	6.92820i		−	0.398015i
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$		0			0
$306$	6.00000	+	10.3923i	0.342997	+	0.594089i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	−19.5000	−	11.2583i	−1.10932	−	0.640464i
$310$	3.50000	+	6.06218i	0.198787	+	0.344309i
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	0.993490	+	0.113917i	$0.0363399\pi$
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	−0.398090	+	0.917346i	$0.630327\pi$
$312$	9.00000	+	5.19615i	0.509525	+	0.294174i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	7.00000			0.395033
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$	8.00000			0.450035
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	0.372061	+	0.928208i	$0.378651\pi$
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	−0.989882	+	0.141890i	$0.954682\pi$
$318$		−	15.5885i		−	0.874157i
$319$		0			0
$320$	−3.50000	−	6.06218i	−0.195656	−	0.338886i
$321$	−27.0000	+	15.5885i	−1.50699	+	0.870063i
$322$	8.00000	−	13.8564i	0.445823	−	0.772187i
$323$	24.0000			1.33540
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−8.00000			−0.443760
$326$	−5.50000	+	9.52628i	−0.304617	+	0.527612i
$327$	−3.00000	+	1.73205i	−0.165900	+	0.0957826i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−14.0000	−	24.2487i	−0.771845	−	1.33687i
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	0.851957	+	0.523612i	$0.175416\pi$
$332$	−12.0000			−0.658586
$333$	4.50000	−	7.79423i	0.246598	−	0.427121i
$334$	12.0000			0.656611
$335$	−5.50000	+	9.52628i	−0.300497	+	0.520476i
$336$	6.00000	+	3.46410i	0.327327	+	0.188982i
$337$	−11.0000	−	19.0526i	−0.599208	−	1.03786i	−0.992938	−	0.118633i	$-0.962149\pi$
$337$	−11.0000	−	19.0526i	−0.599208	−	1.03786i	0.393730	−	0.919226i	$-0.371184\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−22.5000	−	12.9904i	−1.22203	−	0.705541i
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$		0			0
$342$	9.00000	+	15.5885i	0.486664	+	0.842927i
$343$	−8.00000			−0.431959
$344$	9.00000	−	15.5885i	0.485247	−	0.840473i
$345$			6.92820i			0.373002i
$346$		0			0
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$	−9.00000	+	5.19615i	−0.482451	+	0.278543i
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	−0.114747	−	0.993395i	$-0.536606\pi$
$349$	15.0000	−	25.9808i	0.802932	−	1.39072i	0.917679	−	0.397324i	$-0.130061\pi$
$350$	−16.0000			−0.855236
$351$	9.00000	−	5.19615i	0.480384	−	0.277350i
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	−10.5000	+	6.06218i	−0.558069	+	0.322201i
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$		−	27.7128i		−	1.46672i
$358$	−4.50000	+	7.79423i	−0.237832	+	0.411938i
$359$	32.0000			1.68890			0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000			1.68890			0.844448	+	0.535638i	$0.179929\pi$
$360$	−9.00000			−0.474342
$361$	17.0000			0.894737
$362$	3.50000	−	6.06218i	0.183956	−	0.318621i
$363$		0			0
$364$	−4.00000	−	6.92820i	−0.209657	−	0.363137i
$365$	2.00000	+	3.46410i	0.104685	+	0.181319i
$366$		0			0
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	−0.686018	−	0.727585i	$-0.740643\pi$
$367$	5.50000	−	9.52628i	0.287098	−	0.497268i	0.973116	+	0.230317i	$0.0739762\pi$
$368$	4.00000			0.208514
$369$	−6.00000			−0.312348
$370$	−3.00000			−0.155963
$371$	−18.0000	+	31.1769i	−0.934513	+	1.61862i
$372$			12.1244i			0.628619i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$	13.5000	−	7.79423i	0.697137	−	0.402492i
$376$	10.5000	−	18.1865i	0.541496	−	0.937899i
$377$	−12.0000			−0.618031
$378$	18.0000	−	10.3923i	0.925820	−	0.534522i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$	3.00000	−	1.73205i	0.153695	−	0.0887357i
$382$	−6.50000	−	11.2583i	−0.332569	−	0.576026i
$383$	−14.5000	−	25.1147i	−0.740915	−	1.28330i	−0.952079	−	0.305852i	$-0.901059\pi$
$383$	−14.5000	−	25.1147i	−0.740915	−	1.28330i	0.211164	−	0.977451i	$-0.432275\pi$
$384$		−	5.19615i		−	0.265165i
$385$		0			0
$386$	4.00000			0.203595
$387$	−9.00000	−	15.5885i	−0.457496	−	0.792406i
$388$	19.0000			0.964579
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$	−3.00000	−	1.73205i	−0.151911	−	0.0877058i
$391$	−8.00000	−	13.8564i	−0.404577	−	0.700749i
$392$	−13.5000	−	23.3827i	−0.681853	−	1.18100i
$393$	9.00000	+	5.19615i	0.453990	+	0.262111i
$394$	−8.00000	+	13.8564i	−0.403034	+	0.698076i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	−1.50000	+	2.59808i	−0.0751882	+	0.130230i
$399$		−	41.5692i		−	2.08106i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−8.50000	−	14.7224i	−0.424470	−	0.735203i	0.571901	−	0.820323i	$-0.306206\pi$
$401$	−8.50000	−	14.7224i	−0.424470	−	0.735203i	−0.996371	+	0.0851195i	$0.972873\pi$
$402$	16.5000	−	9.52628i	0.822945	−	0.475128i
$403$	−7.00000	+	12.1244i	−0.348695	+	0.603957i
$404$	−4.00000			−0.199007
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$	−24.0000			−1.19110
$407$		0			0
$408$	18.0000	−	10.3923i	0.891133	−	0.514496i
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$		−	8.66025i		−	0.427179i
$412$	−6.50000	+	11.2583i	−0.320232	+	0.554658i
$413$	28.0000			1.37779
$414$	6.00000	−	10.3923i	0.294884	−	0.510754i
$415$	12.0000			0.589057
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$	3.00000	+	1.73205i	0.146911	+	0.0848189i
$418$		0			0
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	0.798476	−	0.602027i	$-0.205640\pi$
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	−0.920609	+	0.390487i	$0.872307\pi$
$420$	6.00000	+	3.46410i	0.292770	+	0.169031i
$421$	−6.50000	+	11.2583i	−0.316791	+	0.548697i	−0.979817	−	0.199899i	$-0.935939\pi$
$421$	−6.50000	+	11.2583i	−0.316791	+	0.548697i	0.663026	+	0.748596i	$0.269272\pi$
$422$	6.00000			0.292075
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$	−27.0000			−1.31124
$425$	−8.00000	+	13.8564i	−0.388057	+	0.672134i
$426$			15.5885i			0.755263i
$427$		0			0
$428$	9.00000	+	15.5885i	0.435031	+	0.753497i
$429$		0			0
$430$	−3.00000	+	5.19615i	−0.144673	+	0.250581i
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−14.0000	+	24.2487i	−0.672022	+	1.16398i
$435$	9.00000	−	5.19615i	0.431517	−	0.249136i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		−	6.92820i		−	0.331042i
$439$	−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
$441$	−27.0000			−1.28571
$442$	8.00000			0.380521
$443$	−0.500000	+	0.866025i	−0.0237557	+	0.0411461i	−0.877659	−	0.479286i	$-0.840896\pi$
$443$	−0.500000	+	0.866025i	−0.0237557	+	0.0411461i	0.853903	+	0.520432i	$0.174229\pi$
$444$	−4.50000	−	2.59808i	−0.213561	−	0.123299i
$445$	−3.00000	−	5.19615i	−0.142214	−	0.246321i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	6.00000	+	3.46410i	0.283790	+	0.163846i
$448$	14.0000	−	24.2487i	0.661438	−	1.14564i
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$	−12.0000			−0.565685
$451$		0			0
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$		−	27.7128i		−	1.30206i
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	4.00000	+	6.92820i	0.187523	+	0.324799i
$456$	27.0000	−	15.5885i	1.26439	−	0.729996i
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	−0.927622	−	0.373519i	$-0.878151\pi$
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	0.787288	+	0.616585i	$0.211484\pi$
$458$	6.00000			0.280362
$459$		−	20.7846i		−	0.970143i
$460$	4.00000			0.186501
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	−0.971248	−	0.238071i	$-0.923485\pi$
$461$	−6.00000	+	10.3923i	−0.279448	+	0.484018i	0.691800	+	0.722089i	$0.256818\pi$
$462$		0			0
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	0.943878	−	0.330294i	$-0.107148\pi$
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	−0.757982	+	0.652275i	$0.773815\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		−	12.1244i		−	0.562254i
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$	−44.0000			−2.03173
$470$	−3.50000	+	6.06218i	−0.161443	+	0.279627i
$471$	−10.5000	−	6.06218i	−0.483814	−	0.279330i
$472$	10.5000	+	18.1865i	0.483302	+	0.837103i
$473$		0			0
$474$	12.0000	+	6.92820i	0.551178	+	0.318223i
$475$	−12.0000	+	20.7846i	−0.550598	+	0.953663i
$476$	−16.0000			−0.733359
$477$	−13.5000	+	23.3827i	−0.618123	+	1.07062i
$478$	6.00000			0.274434
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$			8.66025i			0.395285i
$481$	−3.00000	−	5.19615i	−0.136788	−	0.236924i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$	−24.0000	+	13.8564i	−1.09204	+	0.630488i
$484$		0			0
$485$	−19.0000			−0.862746
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	−37.0000			−1.67663			−0.838315	−	0.545186i	$-0.816459\pi$
$487$	−37.0000			−1.67663			−0.838315	+	0.545186i	$0.816459\pi$
$488$		0			0
$489$	16.5000	−	9.52628i	0.746156	−	0.430793i
$490$	4.50000	+	7.79423i	0.203289	+	0.352107i
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	0.761539	−	0.648119i	$-0.224444\pi$
$491$	−4.00000	−	6.92820i	−0.180517	−	0.312665i	−0.942057	+	0.335453i	$0.891111\pi$
$492$			3.46410i			0.156174i
$493$	−12.0000	+	20.7846i	−0.540453	+	0.936092i
$494$	12.0000			0.539906
$495$		0			0
$496$	−7.00000			−0.314309
$497$	18.0000	−	31.1769i	0.807410	−	1.39848i
$498$	−18.0000	−	10.3923i	−0.806599	−	0.465690i
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$	−18.0000	−	10.3923i	−0.804181	−	0.464294i
$502$	14.0000	−	24.2487i	0.624851	−	1.08227i
$503$	14.0000			0.624229			0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000			0.624229			0.312115	+	0.950044i	$0.398963\pi$
$504$	−18.0000	−	31.1769i	−0.801784	−	1.38873i
$505$	4.00000			0.177998
$506$		0			0
$507$			15.5885i			0.692308i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$	−6.00000	+	3.46410i	−0.265684	+	0.153393i
$511$	−8.00000	+	13.8564i	−0.353899	+	0.612971i
$512$	11.0000			0.486136
$513$		−	31.1769i		−	1.37649i
$514$	−22.0000			−0.970378
$515$	6.50000	−	11.2583i	0.286424	−	0.496101i
$516$	−9.00000	+	5.19615i	−0.396203	+	0.228748i
$517$		0			0
$518$	−6.00000	−	10.3923i	−0.263625	−	0.456612i
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−18.0000			−0.787839
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	3.00000	−	5.19615i	0.131056	−	0.226995i
$525$	24.0000	+	13.8564i	1.04745	+	0.604743i
$526$	8.00000	+	13.8564i	0.348817	+	0.604168i
$527$	14.0000	+	24.2487i	0.609850	+	1.05629i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	9.00000			0.390935
$531$	21.0000			0.911322
$532$	−24.0000			−1.04053
$533$	−2.00000	+	3.46410i	−0.0866296	+	0.150047i
$534$			10.3923i			0.449719i
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$	−16.5000	−	28.5788i	−0.712691	−	1.23442i
$537$	13.5000	−	7.79423i	0.582568	−	0.336346i
$538$	−8.50000	+	14.7224i	−0.366461	+	0.634729i
$539$		0			0
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	11.0000	−	19.0526i	0.472490	−	0.818377i
$543$	−10.5000	+	6.06218i	−0.450598	+	0.260153i
$544$	−10.0000	−	17.3205i	−0.428746	−	0.742611i
$545$	−1.00000	−	1.73205i	−0.0428353	−	0.0741929i
$546$		−	13.8564i		−	0.592999i
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	−0.999424	−	0.0339321i	$-0.989197\pi$
$547$	−11.0000	+	19.0526i	−0.470326	+	0.814629i	0.529098	+	0.848561i	$0.322530\pi$
$548$	−5.00000			−0.213589
$549$		0			0
$550$		0			0
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$	−18.0000	−	10.3923i	−0.766131	−	0.442326i
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$	4.50000	+	2.59808i	0.191014	+	0.110282i
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	−40.0000			−1.69485			−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000			−1.69485			−0.847427	+	0.530912i	$0.821850\pi$
$558$	−10.5000	+	18.1865i	−0.444500	+	0.769897i
$559$	−12.0000			−0.507546
$560$	−2.00000	+	3.46410i	−0.0845154	+	0.146385i
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	−7.00000	−	12.1244i	−0.295015	−	0.510981i	0.679974	−	0.733237i	$-0.261991\pi$
$563$	−7.00000	−	12.1244i	−0.295015	−	0.510981i	−0.974988	+	0.222256i	$0.928658\pi$
$564$	−10.5000	+	6.06218i	−0.442130	+	0.255264i
$565$	7.50000	−	12.9904i	0.315527	−	0.546509i
$566$	28.0000			1.17693
$567$	−36.0000			−1.51186
$568$	27.0000			1.13289
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	−9.00000	+	5.19615i	−0.376969	+	0.217643i
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$			22.5167i			0.940647i
$574$	−4.00000	+	6.92820i	−0.166957	+	0.289178i
$575$	16.0000			0.667246
$576$	10.5000	−	18.1865i	0.437500	−	0.757772i
$577$	−3.00000			−0.124892			−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000			−0.124892			−0.0624458	+	0.998048i	$0.519890\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	−6.00000	−	3.46410i	−0.249351	−	0.143963i
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	24.0000	+	41.5692i	0.995688	+	1.72458i
$582$	28.5000	+	16.4545i	1.18136	+	0.682060i
$583$		0			0
$584$	−12.0000			−0.496564
$585$	3.00000	+	5.19615i	0.124035	+	0.214834i
$586$	12.0000			0.495715
$587$	2.50000	−	4.33013i	0.103186	−	0.178723i	−0.809810	−	0.586693i	$-0.800430\pi$
$587$	2.50000	−	4.33013i	0.103186	−	0.178723i	0.912996	+	0.407969i	$0.133763\pi$
$588$			15.5885i			0.642857i
$589$	21.0000	+	36.3731i	0.865290	+	1.49873i
$590$	−3.50000	−	6.06218i	−0.144093	−	0.249576i
$591$	24.0000	−	13.8564i	0.987228	−	0.569976i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	2.00000	−	3.46410i	0.0819232	−	0.141895i
$597$	4.50000	−	2.59808i	0.184173	−	0.106332i
$598$	−4.00000	−	6.92820i	−0.163572	−	0.283315i
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	0.822270	−	0.569097i	$-0.192707\pi$
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	−0.903988	+	0.427558i	$0.859374\pi$
$600$			20.7846i			0.848528i
$601$	1.00000	−	1.73205i	0.0407909	−	0.0706518i	−0.844909	−	0.534910i	$-0.820346\pi$
$601$	1.00000	−	1.73205i	0.0407909	−	0.0706518i	0.885700	+	0.464258i	$0.153679\pi$
$602$	−24.0000			−0.978167
$603$	−33.0000			−1.34386
$604$	−16.0000			−0.651031
$605$		0			0
$606$	−6.00000	−	3.46410i	−0.243733	−	0.140720i
$607$	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
$609$	36.0000	+	20.7846i	1.45879	+	0.842235i
$610$		0			0
$611$	−14.0000			−0.566379
$612$	−12.0000			−0.485071
$613$	16.0000			0.646234			0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000			0.646234			0.323117	+	0.946359i	$0.395269\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		−	3.46410i		−	0.139686i
$616$		0			0
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	0.976575	−	0.215177i	$-0.0690329\pi$
$617$	7.50000	+	12.9904i	0.301939	+	0.522973i	−0.674636	+	0.738150i	$0.735700\pi$
$618$	−19.5000	+	11.2583i	−0.784405	+	0.452876i
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	−0.497579	−	0.867419i	$-0.665777\pi$
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	0.999996	−	0.00279365i	$-0.000889247\pi$
$620$	−7.00000			−0.281127
$621$	−18.0000	+	10.3923i	−0.722315	+	0.417029i
$622$	21.0000			0.842023
$623$	12.0000	−	20.7846i	0.480770	−	0.832718i
$624$	3.00000	−	1.73205i	0.120096	−	0.0693375i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	7.00000	+	12.1244i	0.279776	+	0.484587i
$627$		0			0
$628$	−3.50000	+	6.06218i	−0.139665	+	0.241907i
$629$	−12.0000			−0.478471
$630$	6.00000	+	10.3923i	0.239046	+	0.414039i
$631$	37.0000			1.47295			0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000			1.47295			0.736473	+	0.676467i	$0.236490\pi$
$632$	12.0000	−	20.7846i	0.477334	−	0.826767i
$633$	−9.00000	−	5.19615i	−0.357718	−	0.206529i
$634$	11.0000	+	19.0526i	0.436866	+	0.756674i
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$	13.5000	+	7.79423i	0.535310	+	0.309061i
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$		0			0
$639$	13.5000	−	23.3827i	0.534052	−	0.925005i
$640$	3.00000			0.118585
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$			31.1769i			1.23045i
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	0.979541	−	0.201243i	$-0.0644981\pi$
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	−0.664052	+	0.747686i	$0.731165\pi$
$644$	8.00000	+	13.8564i	0.315244	+	0.546019i
$645$	9.00000	−	5.19615i	0.354375	−	0.204598i
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−13.5000	−	23.3827i	−0.530330	−	0.918559i
$649$		0			0
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$	42.0000	−	24.2487i	1.64611	−	0.950382i
$652$	−5.50000	−	9.52628i	−0.215397	−	0.373078i
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	−0.991803	−	0.127780i	$-0.959215\pi$
$653$	−15.5000	−	26.8468i	−0.606562	−	1.05060i	0.385241	−	0.922816i	$-0.374118\pi$
$654$			3.46410i			0.135457i
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−2.00000			−0.0780869
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$	−28.0000			−1.09155
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	−0.317803	−	0.948157i	$-0.602945\pi$
$659$	17.0000	−	29.4449i	0.662226	−	1.14701i	0.980029	−	0.198852i	$-0.0637214\pi$
$660$		0			0
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	−24.5000	−	42.4352i	−0.952940	−	1.65054i	−0.213925	−	0.976850i	$-0.568625\pi$
$662$	0.500000	+	0.866025i	0.0194331	+	0.0336590i
$663$	−12.0000	−	6.92820i	−0.466041	−	0.269069i
$664$	−18.0000	+	31.1769i	−0.698535	+	1.20990i
$665$	24.0000			0.930680
$666$	−4.50000	−	7.79423i	−0.174371	−	0.302020i
$667$	24.0000			0.929284
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$		−	27.7128i		−	1.07144i
$670$	5.50000	+	9.52628i	0.212484	+	0.368032i
$671$		0			0
$672$	−30.0000	+	17.3205i	−1.15728	+	0.668153i
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	−0.996328	−	0.0856156i	$-0.972714\pi$
$673$	−11.0000	+	19.0526i	−0.424019	+	0.734422i	0.572309	+	0.820038i	$0.306048\pi$
$674$	−22.0000			−0.847408
$675$	18.0000	+	10.3923i	0.692820	+	0.400000i
$676$	9.00000			0.346154
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$	−22.5000	+	12.9904i	−0.864107	+	0.498893i
$679$	−38.0000	−	65.8179i	−1.45831	−	2.52586i
$680$	6.00000	+	10.3923i	0.230089	+	0.398527i
$681$		−	31.1769i		−	1.19470i
$682$		0			0
$683$	5.00000			0.191320			0.0956598	−	0.995414i	$-0.469504\pi$
$683$	5.00000			0.191320			0.0956598	+	0.995414i	$0.469504\pi$
$684$	−18.0000			−0.688247
$685$	5.00000			0.191040
$686$	−4.00000	+	6.92820i	−0.152721	+	0.264520i
$687$	−9.00000	−	5.19615i	−0.343371	−	0.198246i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	9.00000	+	15.5885i	0.342873	+	0.593873i
$690$	6.00000	+	3.46410i	0.228416	+	0.131876i
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	0.313355	+	0.949636i	$0.398547\pi$
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	−0.979086	+	0.203445i	$0.934786\pi$
$692$		0			0
$693$		0			0
$694$	4.00000			0.151838
$695$	−1.00000	+	1.73205i	−0.0379322	+	0.0657004i
$696$			31.1769i			1.18176i
$697$	4.00000	+	6.92820i	0.151511	+	0.262424i
$698$	−15.0000	−	25.9808i	−0.567758	−	0.983386i
$699$	36.0000	−	20.7846i	1.36165	−	0.786146i
$700$	8.00000	−	13.8564i	0.302372	−	0.523723i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		−	10.3923i		−	0.392232i
$703$	−18.0000			−0.678883
$704$		0			0
$705$	10.5000	−	6.06218i	0.395453	−	0.228315i
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	8.00000	+	13.8564i	0.300871	+	0.521124i
$708$		−	12.1244i		−	0.455661i
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	−0.717769	−	0.696281i	$-0.754837\pi$
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	0.961882	+	0.273466i	$0.0881700\pi$
$710$	−9.00000			−0.337764
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$	18.0000			0.674579
$713$	14.0000	−	24.2487i	0.524304	−	0.908121i
$714$	−24.0000	−	13.8564i	−0.898177	−	0.518563i
$715$		0			0
$716$	−4.50000	−	7.79423i	−0.168173	−	0.291284i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	16.0000	−	27.7128i	0.597115	−	1.03423i
$719$	−15.0000			−0.559406			−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000			−0.559406			−0.279703	+	0.960087i	$0.590236\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	52.0000			1.93658
$722$	8.50000	−	14.7224i	0.316337	−	0.547912i
$723$			17.3205i			0.644157i
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−12.0000	−	20.7846i	−0.445669	−	0.771921i
$726$		0			0
$727$	16.5000	−	28.5788i	0.611951	−	1.05993i	−0.378960	−	0.925413i	$-0.623718\pi$
$727$	16.5000	−	28.5788i	0.611951	−	1.05993i	0.990911	−	0.134517i	$-0.0429484\pi$
$728$	−24.0000			−0.889499
$729$	−27.0000			−1.00000
$730$	4.00000			0.148047
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$		0			0
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	0.805289	−	0.592883i	$-0.202010\pi$
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	−0.916096	+	0.400959i	$0.868677\pi$
$734$	−5.50000	−	9.52628i	−0.203009	−	0.351621i
$735$		−	15.5885i		−	0.574989i
$736$	−10.0000	+	17.3205i	−0.368605	+	0.638442i
$737$		0			0
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	16.0000			0.588570			0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000			0.588570			0.294285	+	0.955718i	$0.404919\pi$
$740$	1.50000	−	2.59808i	0.0551411	−	0.0955072i
$741$	−18.0000	−	10.3923i	−0.661247	−	0.381771i
$742$	18.0000	+	31.1769i	0.660801	+	1.14454i
$743$	−25.0000	−	43.3013i	−0.917161	−	1.58857i	−0.803706	−	0.595026i	$-0.797142\pi$
$743$	−25.0000	−	43.3013i	−0.917161	−	1.58857i	−0.113455	−	0.993543i	$-0.536192\pi$
$744$	31.5000	+	18.1865i	1.15485	+	0.666751i
$745$	−2.00000	+	3.46410i	−0.0732743	+	0.126915i
$746$	10.0000			0.366126
$747$	18.0000	+	31.1769i	0.658586	+	1.14070i
$748$		0			0
$749$	36.0000	−	62.3538i	1.31541	−	2.27836i
$750$		−	15.5885i		−	0.569210i
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	0.948753	−	0.316017i	$-0.102346\pi$
$751$	5.50000	+	9.52628i	0.200698	+	0.347619i	−0.748056	+	0.663636i	$0.769012\pi$
$752$	−3.50000	−	6.06218i	−0.127632	−	0.221065i
$753$	−42.0000	+	24.2487i	−1.53057	+	0.883672i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	16.0000			0.582300
$756$			20.7846i			0.755929i
$757$	−19.0000			−0.690567			−0.345283	−	0.938498i	$-0.612217\pi$
$757$	−19.0000			−0.690567			−0.345283	+	0.938498i	$0.612217\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$		0			0
$760$	9.00000	+	15.5885i	0.326464	+	0.565453i
$761$	18.0000	+	31.1769i	0.652499	+	1.13016i	0.982514	+	0.186187i	$0.0596129\pi$
$761$	18.0000	+	31.1769i	0.652499	+	1.13016i	−0.330015	+	0.943976i	$0.607054\pi$
$762$		−	3.46410i		−	0.125491i
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$	13.0000			0.470323
$765$	12.0000			0.433861
$766$	−29.0000			−1.04781
$767$	7.00000	−	12.1244i	0.252755	−	0.437785i
$768$	−25.5000	−	14.7224i	−0.920152	−	0.531250i
$769$	−8.00000	−	13.8564i	−0.288487	−	0.499675i	0.684962	−	0.728579i	$-0.259819\pi$
$769$	−8.00000	−	13.8564i	−0.288487	−	0.499675i	−0.973449	+	0.228904i	$0.926486\pi$
$770$		0			0
$771$	33.0000	+	19.0526i	1.18847	+	0.686161i
$772$	−2.00000	+	3.46410i	−0.0719816	+	0.124676i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	−18.0000			−0.646997
$775$	−28.0000			−1.00579
$776$	28.5000	−	49.3634i	1.02309	−	1.77204i
$777$			20.7846i			0.745644i
$778$	16.5000	+	28.5788i	0.591554	+	1.02460i
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$	3.00000	−	1.73205i	0.107417	−	0.0620174i
$781$		0			0
$782$	−16.0000			−0.572159
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	−9.00000			−0.321429
$785$	3.50000	−	6.06218i	0.124920	−	0.216368i
$786$	9.00000	−	5.19615i	0.321019	−	0.185341i
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	0.713871	−	0.700278i	$-0.246941\pi$
$787$	−7.00000	−	12.1244i	−0.249523	−	0.432187i	−0.963394	+	0.268091i	$0.913607\pi$
$788$	−8.00000	−	13.8564i	−0.284988	−	0.493614i
$789$		−	27.7128i		−	0.986602i
$790$	−4.00000	+	6.92820i	−0.142314	+	0.246494i
$791$	60.0000			2.13335
$792$		0			0
$793$		0			0
$794$	6.50000	−	11.2583i	0.230676	−	0.399543i
$795$	−13.5000	−	7.79423i	−0.478796	−	0.276433i
$796$	−1.50000	−	2.59808i	−0.0531661	−	0.0920864i
$797$	−2.50000	−	4.33013i	−0.0885545	−	0.153381i	0.818346	−	0.574726i	$-0.194891\pi$
$797$	−2.50000	−	4.33013i	−0.0885545	−	0.153381i	−0.906900	+	0.421345i	$0.861558\pi$
$798$	−36.0000	−	20.7846i	−1.27439	−	0.735767i
$799$	−14.0000	+	24.2487i	−0.495284	+	0.857858i
$800$	20.0000			0.707107
$801$	9.00000	−	15.5885i	0.317999	−	0.550791i
$802$	−17.0000			−0.600291
$803$		0			0
$804$			19.0526i			0.671932i
$805$	−8.00000	−	13.8564i	−0.281963	−	0.488374i
$806$	7.00000	+	12.1244i	0.246564	+	0.427062i
$807$	25.5000	−	14.7224i	0.897643	−	0.518254i
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$	4.50000	+	7.79423i	0.158114	+	0.273861i
$811$	14.0000			0.491606			0.245803	−	0.969320i	$-0.420948\pi$
$811$	14.0000			0.491606			0.245803	+	0.969320i	$0.420948\pi$
$812$	12.0000	−	20.7846i	0.421117	−	0.729397i
$813$	−33.0000	+	19.0526i	−1.15736	+	0.668202i
$814$		0			0
$815$	5.50000	+	9.52628i	0.192657	+	0.333691i
$816$		−	6.92820i		−	0.242536i
$817$	−18.0000	+	31.1769i	−0.629740	+	1.09074i
$818$		0			0
$819$	−12.0000	+	20.7846i	−0.419314	+	0.726273i
$820$	−2.00000			−0.0698430
$821$	−10.0000	+	17.3205i	−0.349002	+	0.604490i	−0.986073	−	0.166316i	$-0.946813\pi$
$821$	−10.0000	+	17.3205i	−0.349002	+	0.604490i	0.637070	+	0.770806i	$0.280146\pi$
$822$	−7.50000	−	4.33013i	−0.261593	−	0.151031i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	19.5000	+	33.7750i	0.679315	+	1.17661i
$825$		0			0
$826$	14.0000	−	24.2487i	0.487122	−	0.843721i
$827$	40.0000			1.39094			0.695468	−	0.718557i	$-0.255197\pi$
$827$	40.0000			1.39094			0.695468	+	0.718557i	$0.255197\pi$
$828$	6.00000	+	10.3923i	0.208514	+	0.361158i
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		−	3.46410i		−	0.120168i
$832$	−7.00000	−	12.1244i	−0.242681	−	0.420336i
$833$	18.0000	+	31.1769i	0.623663	+	1.08022i
$834$	3.00000	−	1.73205i	0.103882	−	0.0599760i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$	31.5000	−	18.1865i	1.08880	−	0.628619i
$838$	−5.00000			−0.172722
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	−0.970435	−	0.241363i	$-0.922405\pi$
$839$	−8.00000	+	13.8564i	−0.276191	+	0.478376i	0.694244	+	0.719740i	$0.255739\pi$
$840$	18.0000	−	10.3923i	0.621059	−	0.358569i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	6.50000	+	11.2583i	0.224005	+	0.387988i
$843$			10.3923i			0.357930i
$844$	−3.00000	+	5.19615i	−0.103264	+	0.178859i
$845$	−9.00000			−0.309609
$846$	−21.0000			−0.721995
$847$		0			0
$848$	−4.50000	+	7.79423i	−0.154531	+	0.267655i
$849$	−42.0000	−	24.2487i	−1.44144	−	0.832214i
$850$	8.00000	+	13.8564i	0.274398	+	0.475271i
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−13.5000	−	7.79423i	−0.462502	−	0.267026i
$853$	1.00000	−	1.73205i	0.0342393	−	0.0593043i	−0.848398	−	0.529359i	$-0.822432\pi$
$853$	1.00000	−	1.73205i	0.0342393	−	0.0593043i	0.882637	+	0.470055i	$0.155766\pi$
$854$		0			0
$855$	18.0000			0.615587
$856$	54.0000			1.84568
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	−0.334328	−	0.942457i	$-0.608509\pi$
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	0.983355	−	0.181692i	$-0.0581574\pi$
$858$		0			0
$859$	−7.50000	−	12.9904i	−0.255897	−	0.443226i	0.709242	−	0.704965i	$-0.249037\pi$
$859$	−7.50000	−	12.9904i	−0.255897	−	0.443226i	−0.965139	+	0.261739i	$0.915704\pi$
$860$	−3.00000	−	5.19615i	−0.102299	−	0.177187i
$861$	12.0000	−	6.92820i	0.408959	−	0.236113i
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−22.5000	+	12.9904i	−0.765466	+	0.441942i
$865$		0			0
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$	1.50000	−	0.866025i	0.0509427	−	0.0294118i
$868$	−14.0000	−	24.2487i	−0.475191	−	0.823055i
$869$		0			0
$870$		−	10.3923i		−	0.352332i
$871$	−11.0000	+	19.0526i	−0.372721	+	0.645571i
$872$	6.00000			0.203186
$873$	−28.5000	−	49.3634i	−0.964579	−	1.67070i
$874$	−24.0000			−0.811812
$875$	−18.0000	+	31.1769i	−0.608511	+	1.05397i
$876$	6.00000	+	3.46410i	0.202721	+	0.117041i
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	0.673109	−	0.739543i	$-0.264958\pi$
$877$	−9.00000	−	15.5885i	−0.303908	−	0.526385i	−0.977018	+	0.213158i	$0.931625\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$	−18.0000	−	10.3923i	−0.607125	−	0.350524i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	−13.5000	+	23.3827i	−0.454569	+	0.787336i
$883$	−5.00000			−0.168263			−0.0841317	−	0.996455i	$-0.526812\pi$
$883$	−5.00000			−0.168263			−0.0841317	+	0.996455i	$0.526812\pi$
$884$	−4.00000	+	6.92820i	−0.134535	+	0.233021i
$885$			12.1244i			0.407556i
$886$	0.500000	+	0.866025i	0.0167978	+	0.0290947i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$	−13.5000	+	7.79423i	−0.453030	+	0.261557i
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$	−6.00000			−0.201120
$891$		0			0
$892$	−16.0000			−0.535720
$893$	−21.0000	+	36.3731i	−0.702738	+	1.21718i
$894$	6.00000	−	3.46410i	0.200670	−	0.115857i
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	6.00000	+	10.3923i	0.200446	+	0.347183i
$897$			13.8564i			0.462652i
$898$	11.5000	−	19.9186i	0.383760	−	0.664692i
$899$	−42.0000			−1.40078
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	36.0000			1.19933
$902$		0			0
$903$	36.0000	+	20.7846i	1.19800	+	0.691669i
$904$	22.5000	+	38.9711i	0.748339	+	1.29616i
$905$	−3.50000	−	6.06218i	−0.116344	−	0.201514i
$906$	−24.0000	−	13.8564i	−0.797347	−	0.460348i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−18.0000			−0.597351
$909$	6.00000	+	10.3923i	0.199007	+	0.344691i
$910$	8.00000			0.265197
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	−0.998208	−	0.0598468i	$-0.980939\pi$
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	0.550933	+	0.834550i	$0.314272\pi$
$912$		−	10.3923i		−	0.344124i
$913$		0			0
$914$	3.00000	+	5.19615i	0.0992312	+	0.171873i
$915$		0			0
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	−24.0000			−0.792550
$918$	−18.0000	−	10.3923i	−0.594089	−	0.342997i
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$	6.00000	−	10.3923i	0.197814	−	0.342624i
$921$	−42.0000	+	24.2487i	−1.38395	+	0.799022i
$922$	6.00000	+	10.3923i	0.197599	+	0.342252i
$923$	−9.00000	−	15.5885i	−0.296239	−	0.513100i
$924$		0			0
$925$	6.00000	−	10.3923i	0.197279	−	0.341697i
$926$	8.00000			0.262896
$927$	39.0000			1.28093
$928$	30.0000			0.984798
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$	−10.5000	−	6.06218i	−0.344309	−	0.198787i
$931$	27.0000	+	46.7654i	0.884889	+	1.53267i
$932$	−12.0000	−	20.7846i	−0.393073	−	0.680823i
$933$	−31.5000	−	18.1865i	−1.03126	−	0.595400i
$934$	13.5000	−	23.3827i	0.441733	−	0.765105i
$935$		0			0
$936$	−18.0000			−0.588348
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$	−22.0000	+	38.1051i	−0.718325	+	1.24418i
$939$		−	24.2487i		−	0.791327i
$940$	−3.50000	−	6.06218i	−0.114157	−	0.197726i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	−10.5000	+	6.06218i	−0.342108	+	0.197516i
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$	7.00000			0.227831
$945$		−	20.7846i		−	0.676123i
$946$		0			0
$947$	−7.50000	+	12.9904i	−0.243717	+	0.422131i	−0.961770	−	0.273858i	$-0.911700\pi$
$947$	−7.50000	+	12.9904i	−0.243717	+	0.422131i	0.718053	+	0.695988i	$0.245034\pi$
$948$	−12.0000	+	6.92820i	−0.389742	+	0.225018i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	12.0000	+	20.7846i	0.389331	+	0.674342i
$951$		−	38.1051i		−	1.23564i
$952$	−24.0000	+	41.5692i	−0.777844	+	1.34727i
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$	13.5000	+	23.3827i	0.437079	+	0.757042i
$955$	−13.0000			−0.420670
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		0			0
$958$	2.00000	+	3.46410i	0.0646171	+	0.111920i
$959$	10.0000	+	17.3205i	0.322917	+	0.559308i
$960$	10.5000	+	6.06218i	0.338886	+	0.195656i
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	−6.00000			−0.193448
$963$	27.0000	−	46.7654i	0.870063	−	1.50699i
$964$	10.0000			0.322078
$965$	2.00000	−	3.46410i	0.0643823	−	0.111513i
$966$			27.7128i			0.891645i
$967$	−25.0000	−	43.3013i	−0.803946	−	1.39247i	−0.917000	−	0.398886i	$-0.869397\pi$
$967$	−25.0000	−	43.3013i	−0.803946	−	1.39247i	0.113055	−	0.993589i	$-0.463936\pi$
$968$		0			0
$969$	−36.0000	+	20.7846i	−1.15649	+	0.667698i
$970$	−9.50000	+	16.4545i	−0.305027	+	0.528322i
$971$	20.0000			0.641831			0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000			0.641831			0.320915	+	0.947108i	$0.396010\pi$
$972$			15.5885i			0.500000i
$973$	−8.00000			−0.256468
$974$	−18.5000	+	32.0429i	−0.592778	+	1.02672i
$975$	12.0000	−	6.92820i	0.384308	−	0.221880i
$976$		0			0
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$		−	19.0526i		−	0.609234i
$979$		0			0
$980$	−9.00000			−0.287494
$981$	3.00000	−	5.19615i	0.0957826	−	0.165900i
$982$	−8.00000			−0.255290
$983$	−1.50000	+	2.59808i	−0.0478426	+	0.0828658i	−0.888955	−	0.457995i	$-0.848568\pi$
$983$	−1.50000	+	2.59808i	−0.0478426	+	0.0828658i	0.841112	+	0.540860i	$0.181901\pi$
$984$	9.00000	+	5.19615i	0.286910	+	0.165647i
$985$	8.00000	+	13.8564i	0.254901	+	0.441502i
$986$	12.0000	+	20.7846i	0.382158	+	0.661917i
$987$	42.0000	+	24.2487i	1.33687	+	0.771845i
$988$	−6.00000	+	10.3923i	−0.190885	+	0.330623i
$989$	24.0000			0.763156
$990$		0			0
$991$	−44.0000			−1.39771			−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000			−1.39771			−0.698853	+	0.715265i	$0.746306\pi$
$992$	17.5000	−	30.3109i	0.555626	−	0.962372i
$993$		−	1.73205i		−	0.0549650i
$994$	−18.0000	−	31.1769i	−0.570925	−	0.988872i
$995$	1.50000	+	2.59808i	0.0475532	+	0.0823646i
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	−2.00000	+	3.46410i	−0.0633406	+	0.109709i	−0.895957	−	0.444141i	$-0.853509\pi$
$997$	−2.00000	+	3.46410i	−0.0633406	+	0.109709i	0.832616	+	0.553851i	$0.186842\pi$
$998$	25.0000			0.791361
$999$			15.5885i			0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.c.727.1		2
9.2	odd	6		9801.2.a.i.1.1		1
9.4	even	3	inner	1089.2.e.c.364.1		2
9.7	even	3		9801.2.a.c.1.1		1
11.10	odd	2		99.2.e.a.34.1	✓	2
33.32	even	2		297.2.e.c.100.1		2
99.32	even	6		297.2.e.c.199.1		2
99.43	odd	6		891.2.a.g.1.1		1
99.65	even	6		891.2.a.c.1.1		1
99.76	odd	6		99.2.e.a.67.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.a.34.1	✓	2	11.10	odd	2
99.2.e.a.67.1	yes	2	99.76	odd	6
297.2.e.c.100.1		2	33.32	even	2
297.2.e.c.199.1		2	99.32	even	6
891.2.a.c.1.1		1	99.65	even	6
891.2.a.g.1.1		1	99.43	odd	6
1089.2.e.c.364.1		2	9.4	even	3	inner
1089.2.e.c.727.1		2	1.1	even	1	trivial
9801.2.a.c.1.1		1	9.7	even	3
9801.2.a.i.1.1		1	9.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(2.00000 - 3.46410i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} -1.00000 q^{10} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(1.50000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -6.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +6.92820i q^{21} +(2.00000 + 3.46410i) q^{23} +(-4.50000 + 2.59808i) q^{24} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +5.19615i q^{27} +4.00000 q^{28} +(3.00000 - 5.19615i) q^{29} +(1.50000 - 0.866025i) q^{30} +(-3.50000 - 6.06218i) q^{31} +(2.50000 + 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{34} -4.00000 q^{35} +3.00000 q^{36} +3.00000 q^{37} +(-3.00000 + 5.19615i) q^{38} +(3.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(6.00000 + 3.46410i) q^{42} +(3.00000 - 5.19615i) q^{43} -3.00000 q^{45} +4.00000 q^{46} +(3.50000 - 6.06218i) q^{47} +1.73205i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(6.00000 - 3.46410i) q^{51} +(1.00000 - 1.73205i) q^{52} -9.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +(6.00000 - 10.3923i) q^{56} +(9.00000 - 5.19615i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(3.50000 + 6.06218i) q^{59} +1.73205i q^{60} -7.00000 q^{62} +(-6.00000 - 10.3923i) q^{63} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-6.00000 - 3.46410i) q^{69} +(-2.00000 + 3.46410i) q^{70} +9.00000 q^{71} +(4.50000 - 7.79423i) q^{72} -4.00000 q^{73} +(1.50000 - 2.59808i) q^{74} +6.92820i q^{75} +(-3.00000 - 5.19615i) q^{76} +(3.00000 - 1.73205i) q^{78} +(4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -2.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(2.00000 + 3.46410i) q^{85} +(-3.00000 - 5.19615i) q^{86} +10.3923i q^{87} +6.00000 q^{89} +(-1.50000 + 2.59808i) q^{90} -8.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +(10.5000 + 6.06218i) q^{93} +(-3.50000 - 6.06218i) q^{94} +(3.00000 + 5.19615i) q^{95} +(-7.50000 - 4.33013i) q^{96} +(9.50000 - 16.4545i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} + q^{4} - q^{5} + 4 q^{7} + 6 q^{8} + 3 q^{9} - 2 q^{10} - 3 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} + q^{16} - 8 q^{17} - 3 q^{18} - 12 q^{19} + q^{20} + 4 q^{23} - 9 q^{24}+ \cdots - 18 q^{98}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 + q^4 - q^5 + 4 * q^7 + 6 * q^8 + 3 * q^9 - 2 * q^10 - 3 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 + q^16 - 8 * q^17 - 3 * q^18 - 12 * q^19 + q^20 + 4 * q^23 - 9 * q^24 + 4 * q^25 - 4 * q^26 + 8 * q^28 + 6 * q^29 + 3 * q^30 - 7 * q^31 + 5 * q^32 - 4 * q^34 - 8 * q^35 + 6 * q^36 + 6 * q^37 - 6 * q^38 + 6 * q^39 - 3 * q^40 - 2 * q^41 + 12 * q^42 + 6 * q^43 - 6 * q^45 + 8 * q^46 + 7 * q^47 - 9 * q^49 - 4 * q^50 + 12 * q^51 + 2 * q^52 - 18 * q^53 + 9 * q^54 + 12 * q^56 + 18 * q^57 - 6 * q^58 + 7 * q^59 - 14 * q^62 - 12 * q^63 + 14 * q^64 - 2 * q^65 - 11 * q^67 - 4 * q^68 - 12 * q^69 - 4 * q^70 + 18 * q^71 + 9 * q^72 - 8 * q^73 + 3 * q^74 - 6 * q^76 + 6 * q^78 + 8 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 - 12 * q^83 - 12 * q^84 + 4 * q^85 - 6 * q^86 + 12 * q^89 - 3 * q^90 - 16 * q^91 - 4 * q^92 + 21 * q^93 - 7 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more