LMFDB - Embedded newform 798.2.k.a.463.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(463,798)] 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("798.463"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,-1,-1,-3,-1,2,2,-1,-3,-6,2,-2,-1,-3,-1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$1$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			463.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	798.463
Dual form			798.2.k.a.505.1

$q$-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} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +3.00000 q^{20} +(-0.500000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +3.00000 q^{30} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +5.00000 q^{37} +(4.00000 + 1.73205i) q^{38} +2.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} +3.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +1.00000 q^{49} +4.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.50000 + 7.79423i) q^{55} +1.00000 q^{56} +(4.00000 + 1.73205i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(1.50000 - 2.59808i) q^{66} +(-4.00000 + 6.92820i) q^{67} +3.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(-2.50000 - 4.33013i) q^{74} +4.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -3.00000 q^{77} +(-1.00000 - 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +1.00000 q^{84} +(-4.50000 + 7.79423i) q^{85} +(5.00000 - 8.66025i) q^{86} -3.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(-1.00000 + 1.73205i) q^{91} +(2.00000 + 3.46410i) q^{93} +(12.0000 + 5.19615i) q^{95} +1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 6 q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - 3 q^{17} + 2 q^{18} - 7 q^{19} + 6 q^{20} - q^{21}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - q^9 - 3 * q^10 - 6 * q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - 3 * q^17 + 2 * q^18 - 7 * q^19 + 6 * q^20 - q^21 + 3 * q^22 - q^24 - 4 * q^25 + 4 * q^26 + 2 * q^27 - q^28 + 6 * q^30 - 8 * q^31 - q^32 + 3 * q^33 - 3 * q^34 - 3 * q^35 - q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 3 * q^40 + 3 * q^41 - q^42 + 10 * q^43 + 3 * q^44 + 6 * q^45 - q^48 + 2 * q^49 + 8 * q^50 - 3 * q^51 - 2 * q^52 - 12 * q^53 - q^54 + 9 * q^55 + 2 * q^56 + 8 * q^57 - 6 * q^59 - 3 * q^60 - 8 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 12 * q^65 + 3 * q^66 - 8 * q^67 + 6 * q^68 - 3 * q^70 - q^72 - 14 * q^73 - 5 * q^74 + 8 * q^75 - q^76 - 6 * q^77 - 2 * q^78 + 4 * q^79 - 3 * q^80 - q^81 + 3 * q^82 + 2 * q^84 - 9 * q^85 + 10 * q^86 - 6 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 + 4 * q^93 + 24 * q^95 + 2 * q^96 - 8 * q^97 - q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−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
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000			0.288675
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−1.50000	+	2.59808i	−0.387298	+	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	1.00000			0.235702
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$	3.00000			0.670820
$21$	−0.500000	−	0.866025i	−0.109109	−	0.188982i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	2.00000			0.392232
$27$	1.00000			0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	3.00000			0.547723
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	4.00000	+	1.73205i	0.648886	+	0.280976i
$39$	2.00000			0.320256
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	0.941562	+	0.336840i	$0.109358\pi$
$43$	5.00000	+	8.66025i	0.762493	+	1.32068i	−0.179069	+	0.983836i	$0.557309\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	3.00000			0.447214
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.00000			0.142857
$50$	4.00000			0.565685
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	4.50000	+	7.79423i	0.606780	+	1.05097i
$56$	1.00000			0.133631
$57$	4.00000	+	1.73205i	0.529813	+	0.229416i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	6.00000			0.744208
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	3.00000			0.363803
$69$		0			0
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	−0.906208	−	0.422833i	$-0.861036\pi$
$73$	−7.00000	−	12.1244i	−0.819288	−	1.41905i	0.0869195	−	0.996215i	$-0.472298\pi$
$74$	−2.50000	−	4.33013i	−0.290619	−	0.503367i
$75$	4.00000			0.461880
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	−3.00000			−0.341882
$78$	−1.00000	−	1.73205i	−0.113228	−	0.196116i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	1.00000			0.109109
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$		0			0
$88$	−3.00000			−0.319801
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	12.0000	+	5.19615i	1.23117	+	0.533114i
$96$	1.00000			0.102062
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	3.00000			0.297044
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$	−1.50000	+	2.59808i	−0.146385	+	0.253546i
$106$	12.0000			1.16554
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$	−2.50000	−	4.33013i	−0.237289	−	0.410997i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$	−0.500000	−	4.33013i	−0.0468293	−	0.405554i
$115$		0			0
$116$		0			0
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−2.00000			−0.181818
$122$	8.00000			0.724286
$123$	1.50000	−	2.59808i	0.135250	−	0.234261i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−3.00000			−0.268328
$126$	1.00000			0.0890871
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−3.00000			−0.261116
$133$	−3.50000	+	2.59808i	−0.303488	+	0.225282i
$134$	8.00000			0.691095
$135$	−1.50000	−	2.59808i	−0.129099	−	0.223607i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	3.00000			0.253546
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−7.00000	+	12.1244i	−0.579324	+	1.00342i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−2.50000	+	4.33013i	−0.205499	+	0.355934i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−2.00000	−	3.46410i	−0.163299	−	0.282843i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−3.50000	+	2.59808i	−0.283887	+	0.210732i
$153$	3.00000			0.242536
$154$	1.50000	+	2.59808i	0.120873	+	0.209359i
$155$	6.00000	+	10.3923i	0.481932	+	0.834730i
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	12.0000			0.951662
$160$	3.00000			0.237171
$161$		0			0
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−22.0000			−1.72317			−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000			−1.72317			−0.861586	+	0.507611i	$0.830529\pi$
$164$	−3.00000			−0.234261
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$		0			0
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	9.00000			0.690268
$171$	−0.500000	−	4.33013i	−0.0382360	−	0.331133i
$172$	−10.0000			−0.762493
$173$	−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	$0.906580\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−3.00000			−0.224860
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	8.00000	−	13.8564i	0.594635	−	1.02994i	−0.398963	−	0.916967i	$-0.630630\pi$
$181$	8.00000	−	13.8564i	0.594635	−	1.02994i	0.993598	−	0.112972i	$-0.0360369\pi$
$182$	2.00000			0.148250
$183$	8.00000			0.591377
$184$		0			0
$185$	−7.50000	−	12.9904i	−0.551411	−	0.955072i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$	1.00000			0.0727393
$190$	−1.50000	−	12.9904i	−0.108821	−	0.942421i
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	−4.00000	+	6.92820i	−0.287183	+	0.497416i
$195$	−3.00000	−	5.19615i	−0.214834	−	0.372104i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−3.00000			−0.213201
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$	8.00000			0.564276
$202$	−3.00000			−0.211079
$203$		0			0
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	0.500000	+	0.866025i	0.0348367	+	0.0603388i
$207$		0			0
$208$	2.00000			0.138675
$209$	10.5000	−	7.79423i	0.726300	−	0.539138i
$210$	3.00000			0.207020
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	15.0000	−	25.9808i	1.02299	−	1.77187i
$216$	1.00000			0.0680414
$217$	−4.00000			−0.271538
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	−9.00000			−0.606780
$221$	6.00000			0.403604
$222$	−2.50000	+	4.33013i	−0.167789	+	0.290619i
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	−3.50000	+	2.59808i	−0.231793	+	0.172062i
$229$	−28.0000			−1.85029			−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000			−1.85029			−0.925146	+	0.379611i	$0.876058\pi$
$230$		0			0
$231$	1.50000	+	2.59808i	0.0986928	+	0.170941i
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$		0			0
$236$	6.00000			0.390567
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$	3.00000			0.193649
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−3.00000			−0.191273
$247$	−1.00000	−	8.66025i	−0.0636285	−	0.551039i
$248$	−4.00000			−0.254000
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$	−0.500000	−	0.866025i	−0.0314970	−	0.0545545i
$253$		0			0
$254$	2.00000			0.125491
$255$	9.00000			0.563602
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$	−10.0000			−0.622573
$259$	5.00000			0.310685
$260$	−3.00000	+	5.19615i	−0.186052	+	0.322252i
$261$		0			0
$262$		0			0
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$	36.0000			2.21146
$266$	4.00000	+	1.73205i	0.245256	+	0.106199i
$267$	−3.00000			−0.183597
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$	−1.50000	+	2.59808i	−0.0912871	+	0.158114i
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	2.00000			0.121046
$274$	6.00000			0.362473
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$		0			0
$277$	−19.0000			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$277$	−19.0000			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$278$	5.00000			0.299880
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	−12.0000	+	20.7846i	−0.715860	+	1.23991i	0.246767	+	0.969075i	$0.420632\pi$
$281$	−12.0000	+	20.7846i	−0.715860	+	1.23991i	−0.962627	+	0.270831i	$0.912702\pi$
$282$		0			0
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.797283	+	0.603606i	$0.206270\pi$
$283$	15.5000	+	26.8468i	0.921379	+	1.59588i	0.124096	+	0.992270i	$0.460397\pi$
$284$		0			0
$285$	−1.50000	−	12.9904i	−0.0888523	−	0.769484i
$286$	−6.00000			−0.354787
$287$	1.50000	+	2.59808i	0.0885422	+	0.153360i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	14.0000			0.819288
$293$	−27.0000			−1.57736			−0.788678	−	0.614806i	$-0.789234\pi$
$293$	−27.0000			−1.57736			−0.788678	+	0.614806i	$0.789234\pi$
$294$	−0.500000	+	0.866025i	−0.0291606	+	0.0505076i
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	5.00000			0.290619
$297$	−3.00000			−0.174078
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$	−2.00000	+	3.46410i	−0.115470	+	0.200000i
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$	−4.00000	−	6.92820i	−0.230174	−	0.398673i
$303$	−3.00000			−0.172345
$304$	4.00000	+	1.73205i	0.229416	+	0.0993399i
$305$	24.0000			1.37424
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$	0.500000	+	0.866025i	0.0284440	+	0.0492665i
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	2.00000			0.113228
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	−0.956647	−	0.291250i	$-0.905929\pi$
$313$	−4.00000	+	6.92820i	−0.226093	+	0.391605i	0.730554	+	0.682855i	$0.239262\pi$
$314$	−7.00000	+	12.1244i	−0.395033	+	0.684217i
$315$	3.00000			0.169031
$316$	−4.00000			−0.225018
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	0.302777	+	0.953062i	$0.402086\pi$
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	−0.976764	+	0.214318i	$0.931247\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$		0			0
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	12.0000	+	5.19615i	0.667698	+	0.289122i
$324$	1.00000			0.0555556
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	11.0000	+	19.0526i	0.609234	+	1.05522i
$327$	−5.50000	+	9.52628i	−0.304151	+	0.526804i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$		0			0
$330$	−9.00000			−0.495434
$331$	32.0000			1.75888			0.879440	−	0.476011i	$-0.157918\pi$
$331$	32.0000			1.75888			0.879440	+	0.476011i	$0.157918\pi$
$332$		0			0
$333$	−2.50000	+	4.33013i	−0.136999	+	0.237289i
$334$	6.00000			0.328305
$335$	24.0000			1.31126
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	0.609936	−	0.792451i	$-0.291195\pi$
$337$	−7.00000	−	12.1244i	−0.381314	−	0.660456i	−0.991250	+	0.131995i	$0.957862\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	12.0000			0.649836
$342$	−3.50000	+	2.59808i	−0.189258	+	0.140488i
$343$	1.00000			0.0539949
$344$	5.00000	+	8.66025i	0.269582	+	0.466930i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	20.0000			1.07058			0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000			1.07058			0.535288	+	0.844670i	$0.320203\pi$
$350$	4.00000			0.213809
$351$	−1.00000	+	1.73205i	−0.0533761	+	0.0924500i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−33.0000			−1.75641			−0.878206	−	0.478282i	$-0.841260\pi$
$353$	−33.0000			−1.75641			−0.878206	+	0.478282i	$0.841260\pi$
$354$	6.00000			0.318896
$355$		0			0
$356$	1.50000	+	2.59808i	0.0794998	+	0.137698i
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$	1.50000	+	2.59808i	0.0792775	+	0.137313i
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	3.00000			0.158114
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	−16.0000			−0.840941
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	−21.0000	+	36.3731i	−1.09919	+	1.90385i
$366$	−4.00000	−	6.92820i	−0.209083	−	0.362143i
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	−0.852680	−	0.522433i	$-0.825025\pi$
$367$	0.500000	−	0.866025i	0.0260998	−	0.0452062i	0.878780	+	0.477227i	$0.158358\pi$
$368$		0			0
$369$	−3.00000			−0.156174
$370$	−7.50000	+	12.9904i	−0.389906	+	0.675338i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$	−4.00000			−0.207390
$373$	23.0000			1.19089			0.595447	−	0.803394i	$-0.296975\pi$
$373$	23.0000			1.19089			0.595447	+	0.803394i	$0.296975\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$		0			0
$378$	−0.500000	−	0.866025i	−0.0257172	−	0.0445435i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−10.5000	+	7.79423i	−0.538639	+	0.399835i
$381$	2.00000			0.102463
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	4.50000	+	7.79423i	0.229341	+	0.397231i
$386$	0.500000	−	0.866025i	0.0254493	−	0.0440795i
$387$	−10.0000			−0.508329
$388$	8.00000			0.406138
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$		0			0
$392$	1.00000			0.0505076
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	6.00000	−	10.3923i	0.301893	−	0.522894i
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	8.00000			0.401004
$399$	4.00000	+	1.73205i	0.200250	+	0.0867110i
$400$	4.00000			0.200000
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.828932	+	0.559350i	$0.188949\pi$
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.0699455	+	0.997551i	$0.477717\pi$
$402$	−4.00000	−	6.92820i	−0.199502	−	0.345547i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	−1.50000	+	2.59808i	−0.0745356	+	0.129099i
$406$		0			0
$407$	−15.0000			−0.743522
$408$	−1.50000	+	2.59808i	−0.0742611	+	0.128624i
$409$	20.0000	−	34.6410i	0.988936	−	1.71289i	0.366002	−	0.930614i	$-0.380726\pi$
$409$	20.0000	−	34.6410i	0.988936	−	1.71289i	0.622935	−	0.782274i	$-0.285940\pi$
$410$	−9.00000			−0.444478
$411$	6.00000			0.295958
$412$	0.500000	−	0.866025i	0.0246332	−	0.0426660i
$413$	−3.00000	−	5.19615i	−0.147620	−	0.255686i
$414$		0			0
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	5.00000			0.244851
$418$	−12.0000	−	5.19615i	−0.586939	−	0.254152i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$	−1.50000	−	2.59808i	−0.0731925	−	0.126773i
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	0.999109	−	0.0422075i	$-0.0134391\pi$
$421$	9.50000	+	16.4545i	0.463002	+	0.801942i	−0.536107	+	0.844150i	$0.680106\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	12.0000			0.582086
$426$		0			0
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$	−6.00000			−0.289683
$430$	−30.0000			−1.44673
$431$	16.5000	−	28.5788i	0.794777	−	1.37659i	−0.128204	−	0.991748i	$-0.540921\pi$
$431$	16.5000	−	28.5788i	0.794777	−	1.37659i	0.922981	−	0.384846i	$-0.125746\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	−0.607238	−	0.794520i	$-0.707723\pi$
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	0.991693	+	0.128624i	$0.0410559\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	11.0000			0.526804
$437$		0			0
$438$	14.0000			0.668946
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	−0.998353	−	0.0573756i	$-0.981727\pi$
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	0.449488	−	0.893287i	$-0.351607\pi$
$440$	4.50000	+	7.79423i	0.214529	+	0.371575i
$441$	−0.500000	+	0.866025i	−0.0238095	+	0.0412393i
$442$	−3.00000	−	5.19615i	−0.142695	−	0.247156i
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	5.00000			0.237289
$445$	−9.00000			−0.426641
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$	−9.00000	+	15.5885i	−0.425685	+	0.737309i
$448$	1.00000			0.0472456
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−2.00000	+	3.46410i	−0.0942809	+	0.163299i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	6.00000			0.281284
$456$	4.00000	+	1.73205i	0.187317	+	0.0811107i
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	14.0000	+	24.2487i	0.654177	+	1.13307i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$		0			0
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	0.986127	−	0.165992i	$-0.0530827\pi$
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	−0.636817	+	0.771015i	$0.719749\pi$
$462$	1.50000	−	2.59808i	0.0697863	−	0.120873i
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	6.00000	−	10.3923i	0.278243	−	0.481932i
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	2.00000			0.0924500
$469$	−4.00000	+	6.92820i	−0.184703	+	0.319915i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−15.0000	−	25.9808i	−0.689701	−	1.19460i
$474$	−4.00000			−0.183726
$475$	−2.00000	−	17.3205i	−0.0917663	−	0.794719i
$476$	3.00000			0.137505
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$	−1.50000	−	2.59808i	−0.0684653	−	0.118585i
$481$	−5.00000	+	8.66025i	−0.227980	+	0.394874i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−12.0000	+	20.7846i	−0.544892	+	0.943781i
$486$	1.00000			0.0453609
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$	11.0000	+	19.0526i	0.497437	+	0.861586i
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$	1.50000	+	2.59808i	0.0676252	+	0.117130i
$493$		0			0
$494$	−7.00000	+	5.19615i	−0.314945	+	0.233786i
$495$	−9.00000			−0.404520
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$		0			0
$498$		0			0
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	0.550572	−	0.834788i	$-0.314410\pi$
$499$	−10.0000	−	17.3205i	−0.447661	−	0.775372i	−0.998233	+	0.0594153i	$0.981076\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	6.00000			0.268060
$502$	6.00000			0.267793
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.164124	−	0.986440i	$-0.447520\pi$
$503$	21.0000	−	36.3731i	0.936344	−	1.62179i	0.772220	−	0.635355i	$-0.219146\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	−9.00000			−0.400495
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$	−4.50000	−	7.79423i	−0.199263	−	0.345134i
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	1.00000			0.0441942
$513$	−3.50000	+	2.59808i	−0.154529	+	0.114708i
$514$	−15.0000			−0.661622
$515$	1.50000	+	2.59808i	0.0660979	+	0.114485i
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$		0			0
$518$	−2.50000	−	4.33013i	−0.109844	−	0.190255i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$	6.00000			0.263117
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$		0			0
$525$	4.00000			0.174574
$526$	10.5000	−	18.1865i	0.457822	−	0.792971i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	1.50000	−	2.59808i	0.0652791	−	0.113067i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−18.0000	−	31.1769i	−0.781870	−	1.35424i
$531$	6.00000			0.260378
$532$	−0.500000	−	4.33013i	−0.0216777	−	0.187735i
$533$	−6.00000			−0.259889
$534$	1.50000	+	2.59808i	0.0649113	+	0.112430i
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	1.50000	+	2.59808i	0.0647298	+	0.112115i
$538$	−7.50000	+	12.9904i	−0.323348	+	0.560055i
$539$	−3.00000			−0.129219
$540$	3.00000			0.129099
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	−0.312507	−	0.949915i	$-0.601169\pi$
$541$	15.5000	−	26.8468i	0.666397	−	1.15423i	0.978905	−	0.204318i	$-0.0654977\pi$
$542$	12.5000	−	21.6506i	0.536921	−	0.929974i
$543$	−16.0000			−0.686626
$544$	3.00000			0.128624
$545$	−16.5000	+	28.5788i	−0.706782	+	1.22418i
$546$	−1.00000	−	1.73205i	−0.0427960	−	0.0741249i
$547$	5.00000	−	8.66025i	0.213785	−	0.370286i	−0.739111	−	0.673583i	$-0.764754\pi$
$547$	5.00000	−	8.66025i	0.213785	−	0.370286i	0.952896	+	0.303298i	$0.0980876\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	−12.0000			−0.511682
$551$		0			0
$552$		0			0
$553$	2.00000	+	3.46410i	0.0850487	+	0.147309i
$554$	9.50000	+	16.4545i	0.403616	+	0.699084i
$555$	−7.50000	+	12.9904i	−0.318357	+	0.551411i
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	−0.710457	−	0.703740i	$-0.751512\pi$
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	0.964686	+	0.263404i	$0.0848453\pi$
$558$	−4.00000			−0.169334
$559$	−20.0000			−0.845910
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$	4.50000	−	7.79423i	0.189990	−	0.329073i
$562$	24.0000			1.01238
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$		0			0
$565$	−18.0000	−	31.1769i	−0.757266	−	1.31162i
$566$	15.5000	−	26.8468i	0.651514	−	1.12845i
$567$	−0.500000	−	0.866025i	−0.0209980	−	0.0363696i
$568$		0			0
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$	−10.5000	+	7.79423i	−0.439797	+	0.326464i
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	6.00000	+	10.3923i	0.250654	+	0.434145i
$574$	1.50000	−	2.59808i	0.0626088	−	0.108442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−8.00000			−0.332756
$579$	0.500000	−	0.866025i	0.0207793	−	0.0359908i
$580$		0			0
$581$		0			0
$582$	8.00000			0.331611
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	13.5000	+	23.3827i	0.557680	+	0.965930i
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.865286	−	0.501278i	$-0.832863\pi$
$587$	−21.0000	−	36.3731i	−0.866763	−	1.50128i	−0.00147660	−	0.999999i	$-0.500470\pi$
$588$	1.00000			0.0412393
$589$	14.0000	−	10.3923i	0.576860	−	0.428207i
$590$	18.0000			0.741048
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$	−2.50000	−	4.33013i	−0.102749	−	0.177967i
$593$	−7.50000	+	12.9904i	−0.307988	+	0.533451i	−0.977922	−	0.208970i	$-0.932989\pi$
$593$	−7.50000	+	12.9904i	−0.307988	+	0.533451i	0.669934	+	0.742421i	$0.266322\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$	−4.50000	+	7.79423i	−0.184482	+	0.319532i
$596$	18.0000			0.737309
$597$	8.00000			0.327418
$598$		0			0
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	−0.833753	−	0.552137i	$-0.813812\pi$
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	0.895042	+	0.445983i	$0.147146\pi$
$600$	4.00000			0.163299
$601$	44.0000			1.79480			0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000			1.79480			0.897399	+	0.441221i	$0.145454\pi$
$602$	5.00000	−	8.66025i	0.203785	−	0.352966i
$603$	−4.00000	−	6.92820i	−0.162893	−	0.282138i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$	1.50000	+	2.59808i	0.0609333	+	0.105540i
$607$	−40.0000			−1.62355			−0.811775	−	0.583970i	$-0.801498\pi$
$607$	−40.0000			−1.62355			−0.811775	+	0.583970i	$0.801498\pi$
$608$	−0.500000	−	4.33013i	−0.0202777	−	0.175610i
$609$		0			0
$610$	−12.0000	−	20.7846i	−0.485866	−	0.841544i
$611$		0			0
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	0.928010	−	0.372554i	$-0.121518\pi$
$613$	3.50000	+	6.06218i	0.141364	+	0.244849i	−0.786647	+	0.617403i	$0.788185\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$	−9.00000			−0.362915
$616$	−3.00000			−0.120873
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	−0.388351	−	0.921512i	$-0.626955\pi$
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	0.992228	−	0.124434i	$-0.0397116\pi$
$618$	0.500000	−	0.866025i	0.0201129	−	0.0348367i
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$	−12.0000			−0.481932
$621$		0			0
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$	1.50000	−	2.59808i	0.0600962	−	0.104090i
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	8.00000			0.319744
$627$	−12.0000	−	5.19615i	−0.479234	−	0.207514i
$628$	14.0000			0.558661
$629$	−7.50000	−	12.9904i	−0.299045	−	0.517960i
$630$	−1.50000	−	2.59808i	−0.0597614	−	0.103510i
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	−0.559625	−	0.828746i	$-0.689055\pi$
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	0.997528	+	0.0702759i	$0.0223880\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	24.0000			0.953162
$635$	6.00000			0.238103
$636$	−6.00000	+	10.3923i	−0.237915	+	0.412082i
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$		0			0
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$		0			0
$645$	−30.0000			−1.18125
$646$	−1.50000	−	12.9904i	−0.0590167	−	0.511100i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	9.00000	+	15.5885i	0.353281	+	0.611900i
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$	2.00000	+	3.46410i	0.0783862	+	0.135769i
$652$	11.0000	−	19.0526i	0.430793	−	0.746156i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	11.0000			0.430134
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	14.0000			0.546192
$658$		0			0
$659$	4.50000	−	7.79423i	0.175295	−	0.303620i	−0.764968	−	0.644068i	$-0.777245\pi$
$659$	4.50000	−	7.79423i	0.175295	−	0.303620i	0.940263	+	0.340448i	$0.110579\pi$
$660$	4.50000	+	7.79423i	0.175162	+	0.303390i
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−16.0000	−	27.7128i	−0.621858	−	1.07709i
$663$	−3.00000	−	5.19615i	−0.116510	−	0.201802i
$664$		0			0
$665$	12.0000	+	5.19615i	0.465340	+	0.201498i
$666$	5.00000			0.193746
$667$		0			0
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	0.500000	−	0.866025i	0.0193311	−	0.0334825i
$670$	−12.0000	−	20.7846i	−0.463600	−	0.802980i
$671$	12.0000	−	20.7846i	0.463255	−	0.802381i
$672$	1.00000			0.0385758
$673$	5.00000			0.192736			0.0963679	−	0.995346i	$-0.469277\pi$
$673$	5.00000			0.192736			0.0963679	+	0.995346i	$0.469277\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	−9.00000			−0.346154
$677$	−3.00000			−0.115299			−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000			−0.115299			−0.0576497	+	0.998337i	$0.518361\pi$
$678$	−6.00000	+	10.3923i	−0.230429	+	0.399114i
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−15.0000			−0.573959			−0.286980	−	0.957937i	$-0.592651\pi$
$683$	−15.0000			−0.573959			−0.286980	+	0.957937i	$0.592651\pi$
$684$	4.00000	+	1.73205i	0.152944	+	0.0662266i
$685$	18.0000			0.687745
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	14.0000	+	24.2487i	0.534133	+	0.925146i
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	−19.0000			−0.722794			−0.361397	−	0.932412i	$-0.617700\pi$
$691$	−19.0000			−0.722794			−0.361397	+	0.932412i	$0.617700\pi$
$692$	6.00000			0.228086
$693$	1.50000	−	2.59808i	0.0569803	−	0.0986928i
$694$	6.00000	−	10.3923i	0.227757	−	0.394486i
$695$	15.0000			0.568982
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$	−10.0000	−	17.3205i	−0.378506	−	0.655591i
$699$	−12.0000	+	20.7846i	−0.453882	+	0.786146i
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	−0.996904	−	0.0786236i	$-0.974947\pi$
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	0.430362	−	0.902656i	$-0.358386\pi$
$702$	2.00000			0.0754851
$703$	−17.5000	+	12.9904i	−0.660025	+	0.489942i
$704$	−3.00000			−0.113067
$705$		0			0
$706$	16.5000	+	28.5788i	0.620986	+	1.07558i
$707$	1.50000	−	2.59808i	0.0564133	−	0.0977107i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	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	$0.0881700\pi$
$710$		0			0
$711$	−4.00000			−0.150012
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$		0			0
$714$	3.00000			0.112272
$715$	−18.0000			−0.673162
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	7.50000	+	12.9904i	0.280093	+	0.485135i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	−1.00000			−0.0372419
$722$	−18.5000	+	4.33013i	−0.688499	+	0.161151i
$723$	−28.0000			−1.04133
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$		0			0
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	−1.00000	+	1.73205i	−0.0370625	+	0.0641941i
$729$	1.00000			0.0370370
$730$	42.0000			1.55449
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$	−4.00000	+	6.92820i	−0.147844	+	0.256074i
$733$	−22.0000			−0.812589			−0.406294	−	0.913742i	$-0.633179\pi$
$733$	−22.0000			−0.812589			−0.406294	+	0.913742i	$0.633179\pi$
$734$	−1.00000			−0.0369107
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$		0			0
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	0.708072	−	0.706140i	$-0.249565\pi$
$739$	−7.00000	−	12.1244i	−0.257499	−	0.446002i	−0.965571	+	0.260138i	$0.916232\pi$
$740$	15.0000			0.551411
$741$	−7.00000	+	5.19615i	−0.257151	+	0.190885i
$742$	12.0000			0.440534
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	−0.992000	−	0.126239i	$-0.959709\pi$
$743$	−16.5000	−	28.5788i	−0.605326	−	1.04846i	0.386674	−	0.922217i	$-0.373624\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	−27.0000	+	46.7654i	−0.989203	+	1.71335i
$746$	−11.5000	−	19.9186i	−0.421045	−	0.729271i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	−12.0000			−0.438470
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	−0.760263	−	0.649616i	$-0.774930\pi$
$751$	5.00000	−	8.66025i	0.182453	−	0.316017i	0.942715	+	0.333599i	$0.108263\pi$
$752$		0			0
$753$	6.00000			0.218652
$754$		0			0
$755$	−12.0000	−	20.7846i	−0.436725	−	0.756429i
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	−5.50000	−	9.52628i	−0.199901	−	0.346239i	0.748595	−	0.663027i	$-0.230729\pi$
$757$	−5.50000	−	9.52628i	−0.199901	−	0.346239i	−0.948496	+	0.316789i	$0.897395\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$		0			0
$760$	12.0000	+	5.19615i	0.435286	+	0.188484i
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$	−1.00000	−	1.73205i	−0.0362262	−	0.0627456i
$763$	−5.50000	−	9.52628i	−0.199113	−	0.344874i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	6.00000	−	10.3923i	0.216789	−	0.375489i
$767$	12.0000			0.433295
$768$	1.00000			0.0360844
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	−0.988061	−	0.154062i	$-0.950765\pi$
$769$	−10.0000	+	17.3205i	−0.360609	+	0.624593i	0.627452	+	0.778655i	$0.284098\pi$
$770$	4.50000	−	7.79423i	0.162169	−	0.280885i
$771$	−15.0000			−0.540212
$772$	−1.00000			−0.0359908
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	−0.266621	−	0.963802i	$-0.585907\pi$
$773$	19.5000	−	33.7750i	0.701366	−	1.21480i	0.967987	−	0.251000i	$-0.0807596\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	−4.00000	−	6.92820i	−0.143592	−	0.248708i
$777$	−2.50000	−	4.33013i	−0.0896870	−	0.155342i
$778$		0			0
$779$	−12.0000	−	5.19615i	−0.429945	−	0.186171i
$780$	6.00000			0.214834
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$		0			0
$787$	23.0000			0.819861			0.409931	−	0.912117i	$-0.365553\pi$
$787$	23.0000			0.819861			0.409931	+	0.912117i	$0.365553\pi$
$788$	6.00000	−	10.3923i	0.213741	−	0.370211i
$789$	10.5000	−	18.1865i	0.373810	−	0.647458i
$790$	−12.0000			−0.426941
$791$	12.0000			0.426671
$792$	1.50000	−	2.59808i	0.0533002	−	0.0923186i
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	−18.0000	−	31.1769i	−0.638394	−	1.10573i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−15.0000			−0.531327			−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000			−0.531327			−0.265664	+	0.964066i	$0.585591\pi$
$798$	−0.500000	−	4.33013i	−0.0176998	−	0.153285i
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	1.50000	+	2.59808i	0.0529999	+	0.0917985i
$802$	18.0000	−	31.1769i	0.635602	−	1.10090i
$803$	21.0000	+	36.3731i	0.741074	+	1.28358i
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$	−8.00000			−0.281788
$807$	−7.50000	+	12.9904i	−0.264013	+	0.457283i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	−12.0000			−0.421898			−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000			−0.421898			−0.210949	+	0.977497i	$0.567655\pi$
$810$	3.00000			0.105409
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	−0.798009	−	0.602645i	$-0.794113\pi$
$811$	3.50000	−	6.06218i	0.122902	−	0.212872i	0.920911	+	0.389774i	$0.127447\pi$
$812$		0			0
$813$	12.5000	−	21.6506i	0.438394	−	0.759321i
$814$	7.50000	+	12.9904i	0.262875	+	0.455313i
$815$	33.0000	+	57.1577i	1.15594	+	2.00215i
$816$	3.00000			0.105021
$817$	−40.0000	−	17.3205i	−1.39942	−	0.605968i
$818$	−40.0000			−1.39857
$819$	−1.00000	−	1.73205i	−0.0349428	−	0.0605228i
$820$	4.50000	+	7.79423i	0.157147	+	0.272186i
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	0.0542853	+	0.998525i	$0.482712\pi$
$821$	−24.0000	+	41.5692i	−0.837606	+	1.45078i	−0.891891	+	0.452250i	$0.850621\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−1.00000			−0.0348367
$825$	−12.0000			−0.417786
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−10.5000	+	18.1865i	−0.365121	+	0.632408i	−0.988796	−	0.149276i	$-0.952306\pi$
$827$	−10.5000	+	18.1865i	−0.365121	+	0.632408i	0.623675	+	0.781684i	$0.285639\pi$
$828$		0			0
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$		0			0
$831$	9.50000	+	16.4545i	0.329551	+	0.570800i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−1.50000	−	2.59808i	−0.0519719	−	0.0900180i
$834$	−2.50000	−	4.33013i	−0.0865679	−	0.149940i
$835$	18.0000			0.622916
$836$	1.50000	+	12.9904i	0.0518786	+	0.449282i
$837$	−4.00000			−0.138260
$838$	3.00000	+	5.19615i	0.103633	+	0.179498i
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$	−1.50000	+	2.59808i	−0.0517549	+	0.0896421i
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	9.50000	−	16.4545i	0.327392	−	0.567059i
$843$	24.0000			0.826604
$844$	20.0000			0.688428
$845$	13.5000	−	23.3827i	0.464414	−	0.804389i
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	12.0000			0.412082
$849$	15.5000	−	26.8468i	0.531959	−	0.921379i
$850$	−6.00000	−	10.3923i	−0.205798	−	0.356453i
$851$		0			0
$852$		0			0
$853$	−10.0000	−	17.3205i	−0.342393	−	0.593043i	0.642483	−	0.766300i	$-0.277904\pi$
$853$	−10.0000	−	17.3205i	−0.342393	−	0.593043i	−0.984877	+	0.173257i	$0.944571\pi$
$854$	8.00000			0.273754
$855$	−10.5000	+	7.79423i	−0.359092	+	0.266557i
$856$	−12.0000			−0.410152
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	0.978984	+	0.203938i	$0.0653741\pi$
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	−0.312877	+	0.949794i	$0.601293\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	−0.657201	−	0.753715i	$-0.728260\pi$
$859$	9.50000	−	16.4545i	0.324136	−	0.561420i	0.981337	+	0.192295i	$0.0615932\pi$
$860$	15.0000	+	25.9808i	0.511496	+	0.885937i
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	−33.0000			−1.12398
$863$	15.0000			0.510606			0.255303	−	0.966861i	$-0.417825\pi$
$863$	15.0000			0.510606			0.255303	+	0.966861i	$0.417825\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$	−16.0000			−0.543702
$867$	−8.00000			−0.271694
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	−5.50000	−	9.52628i	−0.186254	−	0.322601i
$873$	8.00000			0.270759
$874$		0			0
$875$	−3.00000			−0.101419
$876$	−7.00000	−	12.1244i	−0.236508	−	0.409644i
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$	−11.5000	+	19.9186i	−0.388106	+	0.672220i
$879$	13.5000	+	23.3827i	0.455344	+	0.788678i
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	39.0000			1.31394			0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000			1.31394			0.656972	+	0.753915i	$0.271837\pi$
$882$	1.00000			0.0336718
$883$	23.0000	−	39.8372i	0.774012	−	1.34063i	−0.161337	−	0.986899i	$-0.551581\pi$
$883$	23.0000	−	39.8372i	0.774012	−	1.34063i	0.935348	−	0.353728i	$-0.115086\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$	18.0000			0.605063
$886$	36.0000			1.20944
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	−0.674441	−	0.738328i	$-0.735615\pi$
$887$	9.00000	−	15.5885i	0.302190	−	0.523409i	0.976632	+	0.214919i	$0.0689488\pi$
$888$	−2.50000	−	4.33013i	−0.0838945	−	0.145310i
$889$	−1.00000	+	1.73205i	−0.0335389	+	0.0580911i
$890$	4.50000	+	7.79423i	0.150840	+	0.261263i
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	−1.00000			−0.0334825
$893$		0			0
$894$	18.0000			0.602010
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$		0			0
$900$	4.00000			0.133333
$901$	36.0000			1.19933
$902$	−4.50000	+	7.79423i	−0.149834	+	0.259519i
$903$	5.00000	−	8.66025i	0.166390	−	0.288195i
$904$	12.0000			0.399114
$905$	−48.0000			−1.59557
$906$	−4.00000	+	6.92820i	−0.132891	+	0.230174i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	1.50000	+	2.59808i	0.0497519	+	0.0861727i
$910$	−3.00000	−	5.19615i	−0.0994490	−	0.172251i
$911$	−15.0000			−0.496972			−0.248486	−	0.968635i	$-0.579933\pi$
$911$	−15.0000			−0.496972			−0.248486	+	0.968635i	$0.579933\pi$
$912$	−0.500000	−	4.33013i	−0.0165567	−	0.143385i
$913$		0			0
$914$	−14.5000	−	25.1147i	−0.479617	−	0.830722i
$915$	−12.0000	−	20.7846i	−0.396708	−	0.687118i
$916$	14.0000	−	24.2487i	0.462573	−	0.801200i
$917$		0			0
$918$	−1.50000	+	2.59808i	−0.0495074	+	0.0857493i
$919$	−46.0000			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$920$		0			0
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	7.50000	−	12.9904i	0.246999	−	0.427815i
$923$		0			0
$924$	−3.00000			−0.0986928
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$	0.500000	−	0.866025i	0.0164222	−	0.0284440i
$928$		0			0
$929$	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	$0.687276\pi$
$930$	−12.0000			−0.393496
$931$	−3.50000	+	2.59808i	−0.114708	+	0.0851485i
$932$	24.0000			0.786146
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	13.5000	−	23.3827i	0.441497	−	0.764696i
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$	−7.00000	+	12.1244i	−0.228680	+	0.396085i	−0.957417	−	0.288708i	$-0.906774\pi$
$937$	−7.00000	+	12.1244i	−0.228680	+	0.396085i	0.728737	+	0.684794i	$0.240108\pi$
$938$	8.00000			0.261209
$939$	8.00000			0.261070
$940$		0			0
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	−0.461133	−	0.887331i	$-0.652557\pi$
$941$	16.5000	−	28.5788i	0.537885	−	0.931644i	0.999018	−	0.0443125i	$-0.0141097\pi$
$942$	14.0000			0.456145
$943$		0			0
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$	−1.50000	−	2.59808i	−0.0487950	−	0.0845154i
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$	2.00000	+	3.46410i	0.0649570	+	0.112509i
$949$	28.0000			0.908918
$950$	−14.0000	+	10.3923i	−0.454220	+	0.337171i
$951$	24.0000			0.778253
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	0.995112	+	0.0987513i	$0.0314848\pi$
$953$	18.0000	+	31.1769i	0.583077	+	1.00992i	−0.412035	+	0.911168i	$0.635182\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$	18.0000	+	31.1769i	0.582466	+	1.00886i
$956$	7.50000	−	12.9904i	0.242567	−	0.420139i
$957$		0			0
$958$	30.0000			0.969256
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$	−1.50000	+	2.59808i	−0.0484123	+	0.0838525i
$961$	−15.0000			−0.483871
$962$	10.0000			0.322413
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	14.0000	+	24.2487i	0.450910	+	0.780998i
$965$	1.50000	−	2.59808i	0.0482867	−	0.0836350i
$966$		0			0
$967$	5.00000	+	8.66025i	0.160789	+	0.278495i	0.935152	−	0.354247i	$-0.115263\pi$
$967$	5.00000	+	8.66025i	0.160789	+	0.278495i	−0.774363	+	0.632742i	$0.781929\pi$
$968$	−2.00000			−0.0642824
$969$	−1.50000	−	12.9904i	−0.0481869	−	0.417311i
$970$	24.0000			0.770594
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	0.991783	−	0.127933i	$-0.0408342\pi$
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	−0.606685	+	0.794943i	$0.707501\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−2.50000	+	4.33013i	−0.0801463	+	0.138817i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$	−4.00000	+	6.92820i	−0.128103	+	0.221880i
$976$	8.00000			0.256074
$977$	12.0000			0.383914			0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000			0.383914			0.191957	+	0.981403i	$0.438517\pi$
$978$	11.0000	−	19.0526i	0.351741	−	0.609234i
$979$	−4.50000	+	7.79423i	−0.143821	+	0.249105i
$980$	3.00000			0.0958315
$981$	11.0000			0.351203
$982$	16.5000	−	28.5788i	0.526536	−	0.911987i
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$	18.0000	+	31.1769i	0.573528	+	0.993379i
$986$		0			0
$987$		0			0
$988$	8.00000	+	3.46410i	0.254514	+	0.110208i
$989$		0			0
$990$	4.50000	+	7.79423i	0.143019	+	0.247717i
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−16.0000	−	27.7128i	−0.507745	−	0.879440i
$994$		0			0
$995$	24.0000			0.760851
$996$		0			0
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	−0.832616	−	0.553851i	$-0.813158\pi$
$997$	2.00000	−	3.46410i	0.0633406	−	0.109709i	0.895957	+	0.444141i	$0.146491\pi$
$998$	−10.0000	+	17.3205i	−0.316544	+	0.548271i
$999$	5.00000			0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.k.a.463.1	✓	2
3.2	odd	2		2394.2.o.j.1261.1		2
19.11	even	3	inner	798.2.k.a.505.1	yes	2
57.11	odd	6		2394.2.o.j.505.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.a.463.1	✓	2	1.1	even	1	trivial
798.2.k.a.505.1	yes	2	19.11	even	3	inner
2394.2.o.j.505.1		2	57.11	odd	6
2394.2.o.j.1261.1		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.k (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} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{6} +1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} -3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +1.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +3.00000 q^{20} +(-0.500000 - 0.866025i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +2.00000 q^{26} +1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +3.00000 q^{30} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 - 2.59808i) q^{35} +(-0.500000 - 0.866025i) q^{36} +5.00000 q^{37} +(4.00000 + 1.73205i) q^{38} +2.00000 q^{39} +(-1.50000 - 2.59808i) q^{40} +(1.50000 + 2.59808i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(5.00000 + 8.66025i) q^{43} +(1.50000 - 2.59808i) q^{44} +3.00000 q^{45} +(-0.500000 + 0.866025i) q^{48} +1.00000 q^{49} +4.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.50000 + 7.79423i) q^{55} +1.00000 q^{56} +(4.00000 + 1.73205i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(-1.50000 - 2.59808i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(1.50000 - 2.59808i) q^{66} +(-4.00000 + 6.92820i) q^{67} +3.00000 q^{68} +(-1.50000 + 2.59808i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-7.00000 - 12.1244i) q^{73} +(-2.50000 - 4.33013i) q^{74} +4.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -3.00000 q^{77} +(-1.00000 - 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +1.00000 q^{84} +(-4.50000 + 7.79423i) q^{85} +(5.00000 - 8.66025i) q^{86} -3.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(-1.00000 + 1.73205i) q^{91} +(2.00000 + 3.46410i) q^{93} +(12.0000 + 5.19615i) q^{95} +1.00000 q^{96} +(-4.00000 - 6.92820i) q^{97} +(-0.500000 - 0.866025i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{8} - q^{9} - 3 q^{10} - 6 q^{11} + 2 q^{12} - 2 q^{13} - q^{14} - 3 q^{15} - q^{16} - 3 q^{17} + 2 q^{18} - 7 q^{19} + 6 q^{20} - q^{21}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - 3 * q^5 - q^6 + 2 * q^7 + 2 * q^8 - q^9 - 3 * q^10 - 6 * q^11 + 2 * q^12 - 2 * q^13 - q^14 - 3 * q^15 - q^16 - 3 * q^17 + 2 * q^18 - 7 * q^19 + 6 * q^20 - q^21 + 3 * q^22 - q^24 - 4 * q^25 + 4 * q^26 + 2 * q^27 - q^28 + 6 * q^30 - 8 * q^31 - q^32 + 3 * q^33 - 3 * q^34 - 3 * q^35 - q^36 + 10 * q^37 + 8 * q^38 + 4 * q^39 - 3 * q^40 + 3 * q^41 - q^42 + 10 * q^43 + 3 * q^44 + 6 * q^45 - q^48 + 2 * q^49 + 8 * q^50 - 3 * q^51 - 2 * q^52 - 12 * q^53 - q^54 + 9 * q^55 + 2 * q^56 + 8 * q^57 - 6 * q^59 - 3 * q^60 - 8 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 12 * q^65 + 3 * q^66 - 8 * q^67 + 6 * q^68 - 3 * q^70 - q^72 - 14 * q^73 - 5 * q^74 + 8 * q^75 - q^76 - 6 * q^77 - 2 * q^78 + 4 * q^79 - 3 * q^80 - q^81 + 3 * q^82 + 2 * q^84 - 9 * q^85 + 10 * q^86 - 6 * q^88 + 3 * q^89 - 3 * q^90 - 2 * q^91 + 4 * q^93 + 24 * q^95 + 2 * q^96 - 8 * q^97 - q^98 + 3 * q^99

Introduction

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