LMFDB - Embedded newform 1470.2.i.f.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1470,2,Mod(361,1470)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1470, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1470.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,1,-1,-1,-2,0,2,-1,-1,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.f.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +2.00000 q^{41} -12.0000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{46} +(4.00000 - 6.92820i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.00000 q^{55} +4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(1.00000 - 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} +8.00000 q^{69} +8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 + 12.1244i) q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +12.0000 q^{83} +2.00000 q^{85} +(6.00000 - 10.3923i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-1.00000 + 1.73205i) q^{89} +1.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(4.00000 + 6.92820i) q^{94} +(2.00000 + 3.46410i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9} - q^{10} - 4 q^{11} + q^{12} - 4 q^{13} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + 2 q^{20} + 8 q^{22} + 8 q^{23} + q^{24}+ \cdots + 8 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^8 - q^9 - q^10 - 4 * q^11 + q^12 - 4 * q^13 - 2 * q^15 - q^16 - 2 * q^17 - q^18 + 4 * q^19 + 2 * q^20 + 8 * q^22 + 8 * q^23 + q^24 - q^25 + 2 * q^26 - 2 * q^27 + 12 * q^29 + q^30 + 8 * q^31 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 2 * q^37 + 4 * q^38 - 2 * q^39 - q^40 + 4 * q^41 - 24 * q^43 - 4 * q^44 - q^45 + 8 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 + q^54 + 8 * q^55 + 8 * q^57 - 6 * q^58 - 4 * q^59 + q^60 + 2 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^66 - 12 * q^67 - 2 * q^68 + 16 * q^69 + 16 * q^71 - q^72 + 14 * q^73 + 2 * q^74 + q^75 - 8 * q^76 + 4 * q^78 - q^80 - q^81 - 2 * q^82 + 24 * q^83 + 4 * q^85 + 12 * q^86 + 6 * q^87 - 4 * q^88 - 2 * q^89 + 2 * q^90 - 16 * q^92 - 8 * q^93 + 8 * q^94 + 4 * q^95 + q^96 + 20 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	4.00000			0.852803
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	−12.0000			−1.82998			−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000			−1.82998			−0.914991	+	0.403473i	$0.867803\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	4.00000			0.539360
$56$		0			0
$57$	4.00000			0.529813
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	2.00000	+	3.46410i	0.246183	+	0.426401i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	8.00000			0.963087
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	2.00000			0.226455
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	6.00000	−	10.3923i	0.646997	−	1.12063i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	1.00000	+	1.73205i	0.0990148	+	0.171499i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.261861	−	0.965106i	$-0.415664\pi$
$107$	10.0000	−	17.3205i	0.966736	−	1.67444i	0.704875	−	0.709331i	$-0.251003\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$	2.00000			0.189832
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$	4.00000			0.368230
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	12.0000			1.03664
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−14.0000			−1.15865
$147$		0			0
$148$	−2.00000			−0.164399
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$	2.00000			0.161690
$154$		0			0
$155$	−8.00000			−0.642575
$156$	−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	$-0.355351\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	1.00000			0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−16.0000			−1.23812			−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000			−1.23812			−0.619059	+	0.785345i	$0.712486\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−1.00000	+	1.73205i	−0.0766965	+	0.132842i
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	6.00000	+	10.3923i	0.457496	+	0.792406i
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	0.467093	+	0.884208i	$0.345301\pi$
$173$	−7.00000	+	12.1244i	−0.532200	+	0.921798i	−0.999293	+	0.0375896i	$0.988032\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$	4.00000			0.301511
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−1.00000	−	1.73205i	−0.0749532	−	0.129823i
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−4.00000			−0.290191
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	0.995610	−	0.0935936i	$-0.0298354\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−5.00000	+	8.66025i	−0.358979	+	0.621770i
$195$	2.00000			0.143223
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	6.00000			0.422159
$203$		0			0
$204$	−2.00000			−0.140028
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	4.00000	+	6.92820i	0.278019	+	0.481543i
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	−16.0000			−1.10674
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$	10.0000	+	17.3205i	0.683586	+	1.18401i
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−2.00000			−0.135457
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	7.00000	−	12.1244i	0.465633	−	0.806500i
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	−0.0137585	−	0.999905i	$-0.504380\pi$
$229$	13.0000	−	22.5167i	0.859064	−	1.48794i	0.872823	−	0.488037i	$-0.162287\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	6.00000			0.393919
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	−0.982027	−	0.188739i	$-0.939560\pi$
$233$	−5.00000	+	8.66025i	−0.327561	+	0.567352i	0.654466	+	0.756091i	$0.272893\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	−2.50000	−	4.33013i	−0.160706	−	0.278351i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−2.00000			−0.127515
$247$	−4.00000	+	6.92820i	−0.254514	+	0.440831i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$		0			0
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	12.0000			0.747087
$259$		0			0
$260$	−2.00000			−0.124035
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	6.00000			0.368577
$266$		0			0
$267$	−2.00000			−0.122398
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.807535	−	0.589819i	$-0.799199\pi$
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.107031	−	0.994256i	$-0.534134\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	0.575408	−	0.817867i	$-0.304843\pi$
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	−0.995997	+	0.0893846i	$0.971510\pi$
$278$	−10.0000	+	17.3205i	−0.599760	+	1.03882i
$279$	−8.00000			−0.478947
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$	−4.00000	−	6.92820i	−0.237356	−	0.411113i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	−8.00000			−0.473050
$287$		0			0
$288$	1.00000			0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	4.00000			0.232889
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−8.00000	+	13.8564i	−0.462652	+	0.801337i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	8.00000			0.460348
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$	−1.00000	−	1.73205i	−0.0566139	−	0.0980581i
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.240640	+	0.970614i	$0.577357\pi$
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.720257	+	0.693708i	$0.755976\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$		0			0
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	−12.0000	−	20.7846i	−0.671871	−	1.16371i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	20.0000			1.11629
$322$		0			0
$323$	−8.00000			−0.445132
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000	+	1.73205i	0.0554700	+	0.0960769i
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$	2.00000			0.110432
$329$		0			0
$330$	−4.00000			−0.220193
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$	8.00000	−	13.8564i	0.437741	−	0.758189i
$335$	12.0000			0.655630
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−7.00000	−	12.1244i	−0.380188	−	0.658505i
$340$	−1.00000	−	1.73205i	−0.0542326	−	0.0939336i
$341$	16.0000	−	27.7128i	0.866449	−	1.50073i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	−12.0000			−0.646997
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	2.00000			0.106000
$357$		0			0
$358$	−20.0000			−1.05703
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	−0.740951	−	0.671559i	$-0.765625\pi$
$359$	4.00000	−	6.92820i	0.211112	−	0.365657i	0.952063	+	0.305903i	$0.0989582\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	−5.00000			−0.262432
$364$		0			0
$365$	−14.0000			−0.732793
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	0.893873	+	0.448320i	$0.147978\pi$
$367$	16.0000	+	27.7128i	0.835193	+	1.44660i	−0.0586798	+	0.998277i	$0.518689\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	−2.00000			−0.103975
$371$		0			0
$372$	8.00000			0.414781
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$		0			0
$382$	8.00000	+	13.8564i	0.409316	+	0.708955i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−14.0000			−0.712581
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	−12.0000			−0.605320
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$		0			0
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$	−16.0000			−0.802008
$399$		0			0
$400$	1.00000			0.0500000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−8.00000			−0.396545
$408$	1.00000	−	1.73205i	0.0495074	−	0.0857493i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	−1.00000	−	1.73205i	−0.0493865	−	0.0855399i
$411$	5.00000	−	8.66025i	0.246632	−	0.427179i
$412$	8.00000			0.394132
$413$		0			0
$414$	−8.00000			−0.393179
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	10.0000	+	17.3205i	0.489702	+	0.848189i
$418$	8.00000	−	13.8564i	0.391293	−	0.677739i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	−10.0000	+	17.3205i	−0.486792	+	0.843149i
$423$	4.00000	+	6.92820i	0.194487	+	0.336861i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	−8.00000			−0.387601
$427$		0			0
$428$	−20.0000			−0.966736
$429$	−4.00000	+	6.92820i	−0.193122	+	0.334497i
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−6.00000			−0.288342			−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000			−0.288342			−0.144171	+	0.989553i	$0.546051\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−16.0000	−	27.7128i	−0.765384	−	1.32568i
$438$	−7.00000	−	12.1244i	−0.334473	−	0.579324i
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$	−4.00000			−0.190261
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	−0.814595	−	0.580030i	$-0.803041\pi$
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	0.909618	+	0.415445i	$0.136374\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	−1.00000	−	1.73205i	−0.0474045	−	0.0821071i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$	7.00000	+	12.1244i	0.329252	+	0.570282i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	12.0000			0.563188
$455$		0			0
$456$	4.00000			0.187317
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.841316	−	0.540544i	$-0.181781\pi$
$458$	13.0000	+	22.5167i	0.607450	+	1.05213i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	−34.0000			−1.58354			−0.791769	−	0.610821i	$-0.790840\pi$
$461$	−34.0000			−1.58354			−0.791769	+	0.610821i	$0.790840\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	−0.536352	−	0.843995i	$-0.680198\pi$
$467$	10.0000	−	17.3205i	0.462745	−	0.801498i	0.999097	+	0.0424970i	$0.0135313\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	−8.00000			−0.369012
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	24.0000	+	41.5692i	1.10352	+	1.91135i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$	8.00000	−	13.8564i	0.365911	−	0.633777i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	18.0000			0.819878
$483$		0			0
$484$	5.00000			0.227273
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	12.0000	+	20.7846i	0.543772	+	0.941841i	0.998683	+	0.0513038i	$0.0163377\pi$
$487$	12.0000	+	20.7846i	0.543772	+	0.941841i	−0.454911	+	0.890537i	$0.650329\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$	1.00000	−	1.73205i	0.0450835	−	0.0780869i
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$	−2.00000	+	3.46410i	−0.0898933	+	0.155700i
$496$	−8.00000			−0.359211
$497$		0			0
$498$	−12.0000			−0.537733
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−8.00000	−	13.8564i	−0.357414	−	0.619059i
$502$	−2.00000	+	3.46410i	−0.0892644	+	0.154610i
$503$	16.0000			0.713405			0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000			0.713405			0.356702	+	0.934218i	$0.383901\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	16.0000	−	27.7128i	0.711287	−	1.23198i
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$		0			0
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	−0.978421	−	0.206623i	$-0.933753\pi$
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	0.668151	+	0.744026i	$0.267086\pi$
$510$	−2.00000			−0.0885615
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$	−1.00000	−	1.73205i	−0.0441081	−	0.0763975i
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−6.00000	+	10.3923i	−0.264135	+	0.457496i
$517$	−32.0000			−1.40736
$518$		0			0
$519$	−14.0000			−0.614532
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	0.981347	+	0.192244i	$0.0615766\pi$
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	−0.378695	−	0.925521i	$-0.623627\pi$
$523$	14.0000	−	24.2487i	0.612177	−	1.06032i	0.990873	−	0.134801i	$-0.0430394\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	24.0000			1.04645
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	4.00000			0.173585
$532$		0			0
$533$	−4.00000			−0.173259
$534$	1.00000	−	1.73205i	0.0432742	−	0.0749532i
$535$	10.0000	+	17.3205i	0.432338	+	0.748831i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−10.0000	+	17.3205i	−0.431532	+	0.747435i
$538$	30.0000			1.29339
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	−0.976352	−	0.216186i	$-0.930638\pi$
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	0.675399	+	0.737453i	$0.263972\pi$
$542$	12.0000	+	20.7846i	0.515444	+	0.892775i
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$	8.00000			0.340503
$553$		0			0
$554$	14.0000			0.594803
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	24.0000			1.01509
$560$		0			0
$561$	−8.00000			−0.337760
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−4.00000	−	6.92820i	−0.168430	−	0.291730i
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	20.0000			0.840663
$567$		0			0
$568$	8.00000			0.335673
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	0.995788	−	0.0916910i	$-0.0292272\pi$
$571$	10.0000	+	17.3205i	0.418487	+	0.724841i	−0.577301	+	0.816532i	$0.695894\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$	16.0000			0.668410
$574$		0			0
$575$	−8.00000			−0.333623
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	−0.998836	−	0.0482425i	$-0.984638\pi$
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	0.457639	−	0.889138i	$-0.348695\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$	6.00000			0.249136
$581$		0			0
$582$	−10.0000			−0.414513
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	32.0000			1.31854
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−18.0000			−0.737309
$597$	−8.00000	+	13.8564i	−0.327418	+	0.567105i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	−4.00000	−	6.92820i	−0.163436	−	0.283079i	0.772663	−	0.634816i	$-0.218924\pi$
$599$	−4.00000	−	6.92820i	−0.163436	−	0.283079i	−0.936099	+	0.351738i	$0.885591\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$607$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$	−1.00000	−	1.73205i	−0.0404226	−	0.0700140i
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	0.972924	+	0.231127i	$0.0742412\pi$
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	−0.286300	+	0.958140i	$0.592425\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$	−2.00000			−0.0806478
$616$		0			0
$617$	10.0000			0.402585			0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000			0.402585			0.201292	+	0.979531i	$0.435486\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.846566	+	0.532284i	$0.178666\pi$
$619$	22.0000	+	38.1051i	0.884255	+	1.53157i	0.0376891	+	0.999290i	$0.488000\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$	−4.00000	+	6.92820i	−0.160514	+	0.278019i
$622$	8.00000			0.320771
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.0000	−	29.4449i	−0.679457	−	1.17685i
$627$	−8.00000	−	13.8564i	−0.319489	−	0.553372i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	−4.00000			−0.159490
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	10.0000	+	17.3205i	0.397464	+	0.688428i
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$		0			0
$636$	−6.00000			−0.237915
$637$		0			0
$638$	24.0000			0.950169
$639$	−4.00000	+	6.92820i	−0.158238	+	0.274075i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−10.0000	+	17.3205i	−0.394669	+	0.683586i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$	12.0000			0.472500
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498790\pi$
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	12.0000			0.469956
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	−0.313953	−	0.949439i	$-0.601653\pi$
$653$	17.0000	−	29.4449i	0.665261	−	1.15227i	0.979214	−	0.202828i	$-0.0650132\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	−14.0000			−0.546192
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$	−2.00000	+	3.46410i	−0.0776736	+	0.134535i
$664$	12.0000			0.465690
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	24.0000	−	41.5692i	0.929284	−	1.60957i
$668$	8.00000	+	13.8564i	0.309529	+	0.536120i
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	2.00000			0.0770943			0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000			0.0770943			0.0385472	+	0.999257i	$0.487727\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$	14.0000			0.537667
$679$		0			0
$680$	2.00000			0.0766965
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$	16.0000	+	27.7128i	0.612672	+	1.06118i
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	10.0000			0.382080
$686$		0			0
$687$	26.0000			0.991962
$688$	6.00000	−	10.3923i	0.228748	−	0.396203i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	14.0000			0.532200
$693$		0			0
$694$	12.0000			0.455514
$695$	−10.0000	+	17.3205i	−0.379322	+	0.657004i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	17.0000	−	29.4449i	0.643459	−	1.11450i
$699$	−10.0000			−0.378235
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	−1.00000	+	1.73205i	−0.0377426	+	0.0653720i
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	18.0000			0.677439
$707$		0			0
$708$	−4.00000			−0.150329
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$		0			0
$712$	−1.00000	+	1.73205i	−0.0374766	+	0.0649113i
$713$	64.0000			2.39682
$714$		0			0
$715$	−8.00000			−0.299183
$716$	10.0000	−	17.3205i	0.373718	−	0.647298i
$717$	−8.00000	−	13.8564i	−0.298765	−	0.517477i
$718$	4.00000	+	6.92820i	0.149279	+	0.258558i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	−3.00000			−0.111648
$723$	9.00000	−	15.5885i	0.334714	−	0.579741i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	2.50000	−	4.33013i	0.0927837	−	0.160706i
$727$	−24.0000			−0.890111			−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000			−0.890111			−0.445055	+	0.895503i	$0.646816\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	7.00000	−	12.1244i	0.259082	−	0.448743i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−1.00000	−	1.73205i	−0.0369611	−	0.0640184i
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−8.00000			−0.294884
$737$	−24.0000	+	41.5692i	−0.884051	+	1.53122i
$738$	−1.00000	−	1.73205i	−0.0368105	−	0.0637577i
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	−0.980052	−	0.198741i	$-0.936315\pi$
$739$	−18.0000	−	31.1769i	−0.662141	−	1.14686i	0.317911	−	0.948120i	$-0.397019\pi$
$740$	1.00000	−	1.73205i	0.0367607	−	0.0636715i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$	−7.00000	−	12.1244i	−0.256288	−	0.443904i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	8.00000			0.292509
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	2.00000	+	3.46410i	0.0728841	+	0.126239i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$	8.00000			0.291150
$756$		0			0
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−16.0000	−	27.7128i	−0.580763	−	1.00591i
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	−0.883581	−	0.468278i	$-0.844875\pi$
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	0.847331	+	0.531065i	$0.178208\pi$
$762$		0			0
$763$		0			0
$764$	−16.0000			−0.578860
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	0.999314	−	0.0370420i	$-0.0117935\pi$
$773$	13.0000	+	22.5167i	0.467578	+	0.809868i	−0.531736	+	0.846910i	$0.678460\pi$
$774$	6.00000	+	10.3923i	0.215666	+	0.373544i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	10.0000			0.358979
$777$		0			0
$778$	−18.0000			−0.645331
$779$	4.00000	−	6.92820i	0.143315	−	0.248229i
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	−6.00000			−0.214423
$784$		0			0
$785$	14.0000			0.499681
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$		0			0
$792$	4.00000			0.142134
$793$	−2.00000	+	3.46410i	−0.0710221	+	0.123014i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−1.00000	−	1.73205i	−0.0353333	−	0.0611990i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	28.0000	−	48.4974i	0.988099	−	1.71144i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	16.0000			0.563576
$807$	15.0000	−	25.9808i	0.528025	−	0.914566i
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	19.0000	+	32.9090i	0.668004	+	1.15702i	0.978461	+	0.206430i	$0.0661846\pi$
$809$	19.0000	+	32.9090i	0.668004	+	1.15702i	−0.310457	+	0.950587i	$0.600482\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	36.0000			1.26413			0.632065	−	0.774915i	$-0.282207\pi$
$811$	36.0000			1.26413			0.632065	+	0.774915i	$0.282207\pi$
$812$		0			0
$813$	24.0000			0.841717
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	−6.00000	−	10.3923i	−0.210171	−	0.364027i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	−24.0000	+	41.5692i	−0.839654	+	1.45432i
$818$	10.0000			0.349642
$819$		0			0
$820$	2.00000			0.0698430
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$	−4.00000			−0.139262
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	7.00000	−	12.1244i	0.242827	−	0.420589i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	−20.0000			−0.692543
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$	8.00000	+	13.8564i	0.276686	+	0.479234i
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$	5.00000	+	8.66025i	0.172209	+	0.298275i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	−8.00000			−0.275046
$847$		0			0
$848$	6.00000			0.206041
$849$	10.0000	−	17.3205i	0.343199	−	0.594438i
$850$	−1.00000	−	1.73205i	−0.0342997	−	0.0594089i
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$	4.00000	−	6.92820i	0.137038	−	0.237356i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$	10.0000	−	17.3205i	0.341793	−	0.592003i
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	0.990439	−	0.137948i	$-0.0440508\pi$
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	−0.614687	+	0.788771i	$0.710717\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	14.0000	−	24.2487i	0.477674	−	0.827355i	−0.521999	−	0.852946i	$-0.674813\pi$
$859$	14.0000	−	24.2487i	0.477674	−	0.827355i	0.999672	+	0.0255910i	$0.00814674\pi$
$860$	−12.0000			−0.409197
$861$		0			0
$862$		0			0
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−7.00000	−	12.1244i	−0.238007	−	0.412240i
$866$	3.00000	−	5.19615i	0.101944	−	0.176572i
$867$	13.0000			0.441503
$868$		0			0
$869$		0			0
$870$	3.00000	−	5.19615i	0.101710	−	0.176166i
$871$	12.0000	+	20.7846i	0.406604	+	0.704260i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$	32.0000			1.08242
$875$		0			0
$876$	14.0000			0.473016
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	28.0000			0.942275			0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000			0.942275			0.471138	+	0.882060i	$0.343844\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$	2.00000			0.0671156
$889$		0			0
$890$	2.00000			0.0670402
$891$	−2.00000	+	3.46410i	−0.0670025	+	0.116052i
$892$		0			0
$893$	−16.0000	−	27.7128i	−0.535420	−	0.927374i
$894$	−9.00000	+	15.5885i	−0.301005	+	0.521356i
$895$	−20.0000			−0.668526
$896$		0			0
$897$	−16.0000			−0.534224
$898$	7.00000	−	12.1244i	0.233593	−	0.404595i
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$	8.00000			0.266371
$903$		0			0
$904$	−14.0000			−0.465633
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	−6.00000	+	10.3923i	−0.199117	+	0.344881i
$909$	6.00000			0.199007
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−24.0000	−	41.5692i	−0.794284	−	1.37574i
$914$	19.0000	+	32.9090i	0.628464	+	1.08853i
$915$	−1.00000	+	1.73205i	−0.0330590	+	0.0572598i
$916$	−26.0000			−0.859064
$917$		0			0
$918$	−2.00000			−0.0660098
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$	4.00000	+	6.92820i	0.131876	+	0.228416i
$921$	−2.00000	−	3.46410i	−0.0659022	−	0.114146i
$922$	17.0000	−	29.4449i	0.559865	−	0.969715i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	8.00000	−	13.8564i	0.262896	−	0.455350i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−5.00000	+	8.66025i	−0.164045	+	0.284134i	−0.936316	−	0.351160i	$-0.885787\pi$
$929$	−5.00000	+	8.66025i	−0.164045	+	0.284134i	0.772271	+	0.635293i	$0.219121\pi$
$930$	8.00000			0.262330
$931$		0			0
$932$	10.0000			0.327561
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$	−4.00000	−	6.92820i	−0.130814	−	0.226576i
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$		0			0
$939$	−34.0000			−1.10955
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	4.00000			0.130189
$945$		0			0
$946$	−48.0000			−1.56061
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$	−14.0000			−0.453981
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$	12.0000	−	20.7846i	0.387905	−	0.671871i
$958$		0			0
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−2.00000	−	3.46410i	−0.0644826	−	0.111687i
$963$	10.0000	+	17.3205i	0.322245	+	0.558146i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$	−14.0000			−0.450676
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	−4.00000	−	6.92820i	−0.128499	−	0.222566i
$970$	−5.00000	−	8.66025i	−0.160540	−	0.278064i
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−24.0000			−0.769010
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−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	$0.926302\pi$
$978$	6.00000	−	10.3923i	0.191859	−	0.332309i
$979$	8.00000			0.255681
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	−16.0000	−	27.7128i	−0.510321	−	0.883901i	−0.999928	−	0.0119587i	$-0.996193\pi$
$983$	−16.0000	−	27.7128i	−0.510321	−	0.883901i	0.489608	−	0.871943i	$-0.337140\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$	−3.00000	+	5.19615i	−0.0955879	+	0.165563i
$986$	12.0000			0.382158
$987$		0			0
$988$	8.00000			0.254514
$989$	−48.0000	+	83.1384i	−1.52631	+	2.64365i
$990$	−2.00000	−	3.46410i	−0.0635642	−	0.110096i
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	0.999954	+	0.00956046i	$0.00304324\pi$
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	−0.491698	+	0.870766i	$0.663623\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	−28.0000			−0.888553
$994$		0			0
$995$	−16.0000			−0.507234
$996$	6.00000	−	10.3923i	0.190117	−	0.329293i
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	−0.992558	−	0.121771i	$-0.961143\pi$
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	0.390822	−	0.920466i	$-0.372191\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.f.961.1		2
7.2	even	3		210.2.a.c.1.1	✓	1
7.3	odd	6		1470.2.i.b.361.1		2
7.4	even	3	inner	1470.2.i.f.361.1		2
7.5	odd	6		1470.2.a.q.1.1		1
7.6	odd	2		1470.2.i.b.961.1		2
21.2	odd	6		630.2.a.b.1.1		1
21.5	even	6		4410.2.a.l.1.1		1
28.23	odd	6		1680.2.a.q.1.1		1
35.2	odd	12		1050.2.g.d.799.2		2
35.9	even	6		1050.2.a.h.1.1		1
35.19	odd	6		7350.2.a.p.1.1		1
35.23	odd	12		1050.2.g.d.799.1		2
56.37	even	6		6720.2.a.bp.1.1		1
56.51	odd	6		6720.2.a.k.1.1		1
84.23	even	6		5040.2.a.i.1.1		1
105.2	even	12		3150.2.g.e.2899.1		2
105.23	even	12		3150.2.g.e.2899.2		2
105.44	odd	6		3150.2.a.w.1.1		1
140.79	odd	6		8400.2.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.c.1.1	✓	1	7.2	even	3
630.2.a.b.1.1		1	21.2	odd	6
1050.2.a.h.1.1		1	35.9	even	6
1050.2.g.d.799.1		2	35.23	odd	12
1050.2.g.d.799.2		2	35.2	odd	12
1470.2.a.q.1.1		1	7.5	odd	6
1470.2.i.b.361.1		2	7.3	odd	6
1470.2.i.b.961.1		2	7.6	odd	2
1470.2.i.f.361.1		2	7.4	even	3	inner
1470.2.i.f.961.1		2	1.1	even	1	trivial
1680.2.a.q.1.1		1	28.23	odd	6
3150.2.a.w.1.1		1	105.44	odd	6
3150.2.g.e.2899.1		2	105.2	even	12
3150.2.g.e.2899.2		2	105.23	even	12
4410.2.a.l.1.1		1	21.5	even	6
5040.2.a.i.1.1		1	84.23	even	6
6720.2.a.k.1.1		1	56.51	odd	6
6720.2.a.bp.1.1		1	56.37	even	6
7350.2.a.p.1.1		1	35.19	odd	6
8400.2.a.p.1.1		1	140.79	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +6.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} +2.00000 q^{41} -12.0000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{46} +(4.00000 - 6.92820i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.00000 q^{55} +4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(1.00000 - 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} +8.00000 q^{69} +8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 + 12.1244i) q^{73} +(1.00000 + 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +12.0000 q^{83} +2.00000 q^{85} +(6.00000 - 10.3923i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-1.00000 + 1.73205i) q^{89} +1.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(4.00000 + 6.92820i) q^{94} +(2.00000 + 3.46410i) q^{95} +(0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9} - q^{10} - 4 q^{11} + q^{12} - 4 q^{13} - 2 q^{15} - q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + 2 q^{20} + 8 q^{22} + 8 q^{23} + q^{24}+ \cdots + 8 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^8 - q^9 - q^10 - 4 * q^11 + q^12 - 4 * q^13 - 2 * q^15 - q^16 - 2 * q^17 - q^18 + 4 * q^19 + 2 * q^20 + 8 * q^22 + 8 * q^23 + q^24 - q^25 + 2 * q^26 - 2 * q^27 + 12 * q^29 + q^30 + 8 * q^31 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 2 * q^37 + 4 * q^38 - 2 * q^39 - q^40 + 4 * q^41 - 24 * q^43 - 4 * q^44 - q^45 + 8 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 + q^54 + 8 * q^55 + 8 * q^57 - 6 * q^58 - 4 * q^59 + q^60 + 2 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^66 - 12 * q^67 - 2 * q^68 + 16 * q^69 + 16 * q^71 - q^72 + 14 * q^73 + 2 * q^74 + q^75 - 8 * q^76 + 4 * q^78 - q^80 - q^81 - 2 * q^82 + 24 * q^83 + 4 * q^85 + 12 * q^86 + 6 * q^87 - 4 * q^88 - 2 * q^89 + 2 * q^90 - 16 * q^92 - 8 * q^93 + 8 * q^94 + 4 * q^95 + q^96 + 20 * q^97 + 8 * q^99

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