LMFDB - Embedded newform 1470.2.i.n.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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.n.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +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} +10.0000 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} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +2.00000 q^{41} +8.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(2.00000 - 3.46410i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.00000 q^{55} +(5.00000 - 8.66025i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-3.00000 + 5.19615i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -2.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +4.00000 q^{83} +6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-5.00000 - 8.66025i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(7.00000 - 12.1244i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(0.500000 - 0.866025i) q^{96} -2.00000 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}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9	$ 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} - 6 q^{17} + q^{18} + 2 q^{20} + 8 q^{22} + 8 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + 20 q^{29} + q^{30} - 8 q^{31} + q^{32} + 4 q^{33} - 12 q^{34} + 2 q^{36} - 2 q^{37} - 2 q^{39} + q^{40} + 4 q^{41} + 16 q^{43} + 4 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} - 2 q^{50} - 6 q^{51} - 2 q^{52} - 10 q^{53} + q^{54} - 8 q^{55} + 10 q^{58} + 4 q^{59} - q^{60} - 6 q^{61} - 16 q^{62} + 2 q^{64} - 2 q^{65} - 4 q^{66} - 6 q^{68} - 16 q^{69} - 24 q^{71} + q^{72} - 6 q^{73} + 2 q^{74} - q^{75} - 4 q^{78} + 8 q^{79} - q^{80} - q^{81} + 2 q^{82} + 8 q^{83} + 12 q^{85} + 8 q^{86} - 10 q^{87} - 4 q^{88} + 14 q^{89} - 2 q^{90} - 16 q^{92} - 8 q^{93} - 4 q^{94} + q^{96} - 4 q^{97} - 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 - 6 * q^17 + q^18 + 2 * q^20 + 8 * q^22 + 8 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + 20 * q^29 + q^30 - 8 * q^31 + q^32 + 4 * q^33 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 2 * q^39 + q^40 + 4 * q^41 + 16 * q^43 + 4 * q^44 - q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 - 2 * q^50 - 6 * q^51 - 2 * q^52 - 10 * q^53 + q^54 - 8 * q^55 + 10 * q^58 + 4 * q^59 - q^60 - 6 * q^61 - 16 * q^62 + 2 * q^64 - 2 * q^65 - 4 * q^66 - 6 * q^68 - 16 * q^69 - 24 * q^71 + q^72 - 6 * q^73 + 2 * q^74 - q^75 - 4 * q^78 + 8 * q^79 - q^80 - q^81 + 2 * q^82 + 8 * q^83 + 12 * q^85 + 8 * q^86 - 10 * q^87 - 4 * q^88 + 14 * q^89 - 2 * q^90 - 16 * q^92 - 8 * q^93 - 4 * q^94 + q^96 - 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

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	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	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
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	−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
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	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
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	−0.682489	−	0.730896i	$-0.739102\pi$
$47$	2.00000	−	3.46410i	0.291730	−	0.505291i	0.974219	+	0.225605i	$0.0724358\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	−0.972867	−	0.231367i	$-0.925680\pi$
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	0.286064	−	0.958211i	$-0.407653\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−4.00000			−0.539360
$56$		0			0
$57$		0			0
$58$	5.00000	−	8.66025i	0.656532	−	1.13715i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	−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
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−3.00000	−	5.19615i	−0.351123	−	0.608164i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$	−2.00000			−0.226455
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−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
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−5.00000	−	8.66025i	−0.536056	−	0.928477i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		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	$0.929823\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−10.0000			−0.971286
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$	2.00000			0.189832
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−5.00000	−	8.66025i	−0.464238	−	0.804084i
$117$	−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
$122$	3.00000	+	5.19615i	0.271607	+	0.470438i
$123$	−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
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−5.00000	+	8.66025i	−0.415227	+	0.719195i
$146$	−6.00000			−0.496564
$147$		0			0
$148$	2.00000			0.164399
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	8.00000			0.642575
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	3.00000	−	5.19615i	0.230089	−	0.398527i
$171$		0			0
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$	−10.0000			−0.758098
$175$		0			0
$176$	−4.00000			−0.301511
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	6.00000			0.443533
$184$	−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
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	−4.00000			−0.291730
$189$		0			0
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	2.00000			0.143223
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	0.880616	+	0.473831i	$0.157129\pi$
$199$	12.0000	+	20.7846i	0.850657	+	1.47338i	−0.0299585	+	0.999551i	$0.509538\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−6.00000			−0.422159
$203$		0			0
$204$	6.00000			0.420084
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	4.00000	+	6.92820i	0.278019	+	0.481543i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$		0			0
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	18.0000			1.21911
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	−0.315906	+	0.948790i	$0.602309\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	−10.0000			−0.656532
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	2.00000	+	3.46410i	0.130466	+	0.225973i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	6.00000			0.384111
$245$		0			0
$246$	−2.00000			−0.127515
$247$		0			0
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$	32.0000			2.01182
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$	−8.00000			−0.498058
$259$		0			0
$260$	2.00000			0.124035
$261$	−5.00000	+	8.66025i	−0.309492	+	0.536056i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$	10.0000			0.614295
$266$		0			0
$267$	−14.0000			−0.856786
$268$		0			0
$269$	1.00000	+	1.73205i	0.0609711	+	0.105605i	0.894900	−	0.446267i	$-0.147247\pi$
$269$	1.00000	+	1.73205i	0.0609711	+	0.105605i	−0.833929	+	0.551872i	$0.813914\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	−0.718580	−	0.695444i	$-0.755208\pi$
$271$	4.00000	−	6.92820i	0.242983	−	0.420858i	0.961563	+	0.274586i	$0.0885408\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	8.00000	−	13.8564i	0.479808	−	0.831052i
$279$	8.00000			0.478947
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	8.00000			0.473050
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−3.00000	+	5.19615i	−0.175562	+	0.304082i
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		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
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	1.00000			0.0577350
$301$		0			0
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−8.00000			−0.450035
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	−0.0453045	−	0.998973i	$-0.514426\pi$
$317$	15.0000	−	25.9808i	0.842484	−	1.45922i	0.887788	−	0.460252i	$-0.152241\pi$
$318$	5.00000	+	8.66025i	0.280386	+	0.485643i
$319$	20.0000	+	34.6410i	1.11979	+	1.93952i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−4.00000			−0.223258
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	8.00000	+	13.8564i	0.443079	+	0.767435i
$327$	9.00000	−	15.5885i	0.497701	−	0.862044i
$328$	−2.00000			−0.110432
$329$		0			0
$330$	4.00000			0.220193
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	−2.00000	−	3.46410i	−0.109764	−	0.190117i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$		0			0
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	16.0000	−	27.7128i	0.866449	−	1.50073i
$342$		0			0
$343$		0			0
$344$	−8.00000			−0.431331
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	−0.999072	−	0.0430610i	$-0.986289\pi$
$347$	−10.0000	−	17.3205i	−0.536828	−	0.929814i	0.462244	−	0.886753i	$-0.347044\pi$
$348$	−5.00000	+	8.66025i	−0.268028	+	0.464238i
$349$	−18.0000			−0.963518			−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000			−0.963518			−0.481759	+	0.876304i	$0.660002\pi$
$350$		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	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$	−14.0000			−0.741999
$357$		0			0
$358$	4.00000			0.211407
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	−0.471696	−	0.881761i	$-0.656358\pi$
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	0.999476	−	0.0323801i	$-0.0103087\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−9.00000	+	15.5885i	−0.473029	+	0.819311i
$363$	5.00000			0.262432
$364$		0			0
$365$	6.00000			0.314054
$366$	3.00000	−	5.19615i	0.156813	−	0.271607i
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$	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
$373$	15.0000	−	25.9808i	0.776671	−	1.34523i	−0.157180	−	0.987570i	$-0.550240\pi$
$373$	15.0000	−	25.9808i	0.776671	−	1.34523i	0.933851	−	0.357663i	$-0.116426\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−2.00000	+	3.46410i	−0.103142	+	0.178647i
$377$	20.0000			1.03005
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	0.247451	+	0.968900i	$0.420407\pi$
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	−0.962818	+	0.270151i	$0.912926\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−10.0000			−0.508987
$387$	−4.00000	+	6.92820i	−0.203331	+	0.352180i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	−48.0000			−2.42746
$392$		0			0
$393$	−4.00000			−0.201773
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	−0.635161	−	0.772380i	$-0.719066\pi$
$397$	7.00000	−	12.1244i	0.351320	−	0.608504i	0.986481	+	0.163876i	$0.0523996\pi$
$398$	24.0000			1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	0.0332161	+	0.999448i	$0.489425\pi$
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	−0.882156	+	0.470958i	$0.843908\pi$
$402$		0			0
$403$	−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
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	16.0000			0.788263
$413$		0			0
$414$	8.00000			0.393179
$415$	−2.00000	+	3.46410i	−0.0981761	+	0.170046i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−8.00000	−	13.8564i	−0.391762	−	0.678551i
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$	2.00000	+	3.46410i	0.0972433	+	0.168430i
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	12.0000			0.581402
$427$		0			0
$428$	−4.00000			−0.193347
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	18.0000	+	31.1769i	0.867029	+	1.50174i	0.865018	+	0.501741i	$0.167307\pi$
$431$	18.0000	+	31.1769i	0.867029	+	1.50174i	0.00201168	+	0.999998i	$0.499360\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	10.0000			0.479463
$436$	9.00000	−	15.5885i	0.431022	−	0.746552i
$437$		0			0
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	−0.177325	−	0.984152i	$-0.556744\pi$
$439$	16.0000	−	27.7128i	0.763638	−	1.32266i	0.940963	−	0.338508i	$-0.109922\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$	12.0000	−	20.7846i	0.568216	−	0.984180i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$		0			0
$454$	20.0000			0.938647
$455$		0			0
$456$		0			0
$457$	3.00000	−	5.19615i	0.140334	−	0.243066i	−0.787288	−	0.616585i	$-0.788516\pi$
$457$	3.00000	−	5.19615i	0.140334	−	0.243066i	0.927622	+	0.373519i	$0.121849\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	−5.00000	+	8.66025i	−0.232119	+	0.402042i
$465$	−4.00000	−	6.92820i	−0.185496	−	0.321288i
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$	4.00000			0.184506
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	16.0000	+	27.7128i	0.735681	+	1.27424i
$474$	−4.00000	+	6.92820i	−0.183726	+	0.318223i
$475$		0			0
$476$		0			0
$477$	10.0000			0.457869
$478$	−6.00000	+	10.3923i	−0.274434	+	0.475333i
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−14.0000			−0.637683
$483$		0			0
$484$	5.00000			0.227273
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$	16.0000			0.723545
$490$		0			0
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$	−30.0000	−	51.9615i	−1.35113	−	2.34023i
$494$		0			0
$495$	2.00000	−	3.46410i	0.0898933	−	0.155700i
$496$	8.00000			0.359211
$497$		0			0
$498$	−4.00000			−0.179244
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		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
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	−0.843012	−	0.537895i	$-0.819220\pi$
$509$	1.00000	−	1.73205i	0.0443242	−	0.0767718i	0.887336	+	0.461123i	$0.152553\pi$
$510$	−6.00000			−0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	7.00000	+	12.1244i	0.308757	+	0.534782i
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	16.0000			0.703679
$518$		0			0
$519$	−18.0000			−0.790112
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	5.00000	+	8.66025i	0.218844	+	0.379049i
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	0.378695	+	0.925521i	$0.376373\pi$
$523$	−14.0000	+	24.2487i	−0.612177	+	1.06032i	−0.990873	+	0.134801i	$0.956961\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$		0			0
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	5.00000	−	8.66025i	0.217186	−	0.376177i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	4.00000			0.173259
$534$	−7.00000	+	12.1244i	−0.302920	+	0.524672i
$535$	2.00000	+	3.46410i	0.0864675	+	0.149766i
$536$		0			0
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$	2.00000			0.0862261
$539$		0			0
$540$	1.00000			0.0430331
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−4.00000	−	6.92820i	−0.171815	−	0.297592i
$543$	9.00000	+	15.5885i	0.386227	+	0.668965i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−18.0000			−0.771035
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$		0			0
$552$	8.00000			0.340503
$553$		0			0
$554$	22.0000			0.934690
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	16.0000			0.676728
$560$		0			0
$561$	−24.0000			−1.01328
$562$	−11.0000	+	19.0526i	−0.464007	+	0.803684i
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$	2.00000	+	3.46410i	0.0842152	+	0.145865i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	28.0000			1.17693
$567$		0			0
$568$	12.0000			0.503509
$569$	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	$0.126528\pi$
$570$		0			0
$571$	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
$573$	12.0000			0.501307
$574$		0			0
$575$	−8.00000			−0.333623
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	−5.00000	+	8.66025i	−0.207793	+	0.359908i
$580$	10.0000			0.415227
$581$		0			0
$582$	2.00000			0.0829027
$583$	20.0000	−	34.6410i	0.828315	−	1.43468i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	15.0000	−	25.9808i	0.619644	−	1.07326i
$587$	−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
$589$		0			0
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	11.0000	+	19.0526i	0.452480	+	0.783718i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−19.0000	+	32.9090i	−0.780236	+	1.35141i	0.151567	+	0.988447i	$0.451568\pi$
$593$	−19.0000	+	32.9090i	−0.780236	+	1.35141i	−0.931804	+	0.362962i	$0.881765\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−6.00000			−0.245770
$597$	12.0000	−	20.7846i	0.491127	−	0.850657i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	−10.0000	−	17.3205i	−0.408589	−	0.707697i	0.586143	−	0.810208i	$-0.300646\pi$
$599$	−10.0000	−	17.3205i	−0.408589	−	0.707697i	−0.994732	+	0.102511i	$0.967312\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$		0			0
$609$		0			0
$610$	−6.00000			−0.242933
$611$	4.00000	−	6.92820i	0.161823	−	0.280285i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	0.972056	−	0.234751i	$-0.0754275\pi$
$613$	7.00000	+	12.1244i	0.282727	+	0.489698i	−0.689328	+	0.724449i	$0.742094\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	2.00000			0.0806478
$616$		0			0
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	0.935146	−	0.354262i	$-0.115268\pi$
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	−0.774373	+	0.632730i	$0.781934\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$		0			0
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$		0			0
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$	12.0000			0.478471
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$	10.0000			0.396526
$637$		0			0
$638$	40.0000			1.58362
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	0.919171	−	0.393860i	$-0.128860\pi$
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	−0.800678	+	0.599095i	$0.795527\pi$
$642$	−2.00000	+	3.46410i	−0.0789337	+	0.136717i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	0.998246	+	0.0592060i	$0.0188569\pi$
$647$	14.0000	+	24.2487i	0.550397	+	0.953315i	−0.447849	+	0.894109i	$0.647810\pi$
$648$	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
$652$	16.0000			0.626608
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	−0.695934	−	0.718106i	$-0.745009\pi$
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	0.969865	+	0.243643i	$0.0783426\pi$
$654$	−9.00000	−	15.5885i	−0.351928	−	0.609557i
$655$	2.00000	+	3.46410i	0.0781465	+	0.135354i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	6.00000			0.234082
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	−4.00000			−0.155230
$665$		0			0
$666$	−2.00000			−0.0774984
$667$	40.0000	−	69.2820i	1.54881	−	2.68261i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	−12.0000	−	20.7846i	−0.463947	−	0.803579i
$670$		0			0
$671$	−24.0000			−0.926510
$672$		0			0
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$	−3.00000	+	5.19615i	−0.115556	+	0.200148i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	−0.996209	−	0.0869952i	$-0.972274\pi$
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	0.573444	+	0.819244i	$0.305607\pi$
$678$	−6.00000			−0.230429
$679$		0			0
$680$	−6.00000			−0.230089
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$	−16.0000	−	27.7128i	−0.612672	−	1.06118i
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	−0.999129	−	0.0417198i	$-0.986716\pi$
$683$	−14.0000	−	24.2487i	−0.535695	−	0.927851i	0.463434	−	0.886131i	$-0.346617\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$		0			0
$687$	22.0000			0.839352
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−10.0000	−	17.3205i	−0.380970	−	0.659859i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−20.0000			−0.759190
$695$	−8.00000	+	13.8564i	−0.303457	+	0.525603i
$696$	5.00000	+	8.66025i	0.189525	+	0.328266i
$697$	−6.00000	−	10.3923i	−0.227266	−	0.393637i
$698$	−9.00000	+	15.5885i	−0.340655	+	0.590032i
$699$	−18.0000			−0.680823
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$		0			0
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$	2.00000	−	3.46410i	0.0753244	−	0.130466i
$706$	18.0000			0.677439
$707$		0			0
$708$	−4.00000			−0.150329
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−7.00000	+	12.1244i	−0.262336	+	0.454379i
$713$	−64.0000			−2.39682
$714$		0			0
$715$	−8.00000			−0.299183
$716$	2.00000	−	3.46410i	0.0747435	−	0.129460i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$	−10.0000	−	17.3205i	−0.373197	−	0.646396i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	19.0000			0.707107
$723$	−7.00000	+	12.1244i	−0.260333	+	0.450910i
$724$	9.00000	+	15.5885i	0.334482	+	0.579340i
$725$	−5.00000	−	8.66025i	−0.185695	−	0.321634i
$726$	2.50000	−	4.33013i	0.0927837	−	0.160706i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$	−3.00000	−	5.19615i	−0.110883	−	0.192055i
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$	16.0000			0.590571
$735$		0			0
$736$	8.00000			0.294884
$737$		0			0
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	0.900464	−	0.434930i	$-0.143227\pi$
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	−0.826893	+	0.562360i	$0.809894\pi$
$740$	−1.00000	+	1.73205i	−0.0367607	+	0.0636715i
$741$		0			0
$742$		0			0
$743$	−8.00000			−0.293492			−0.146746	−	0.989174i	$-0.546880\pi$
$743$	−8.00000			−0.293492			−0.146746	+	0.989174i	$0.546880\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$	−15.0000	−	25.9808i	−0.549189	−	0.951223i
$747$	−2.00000	+	3.46410i	−0.0731762	+	0.126745i
$748$	−24.0000			−0.877527
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	2.00000	+	3.46410i	0.0729325	+	0.126323i
$753$	−10.0000	−	17.3205i	−0.364420	−	0.631194i
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$		0			0
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−16.0000	−	27.7128i	−0.580763	−	1.00591i
$760$		0			0
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	−16.0000			−0.579619
$763$		0			0
$764$	12.0000			0.434145
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$	14.0000	+	24.2487i	0.505841	+	0.876142i
$767$	4.00000	+	6.92820i	0.144432	+	0.250163i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−5.00000	+	8.66025i	−0.179954	+	0.311689i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$	2.00000			0.0717958
$777$		0			0
$778$	−10.0000			−0.358517
$779$		0			0
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	−24.0000	−	41.5692i	−0.858788	−	1.48746i
$782$	−24.0000	+	41.5692i	−0.858238	+	1.48651i
$783$	10.0000			0.357371
$784$		0			0
$785$	10.0000			0.356915
$786$	−2.00000	+	3.46410i	−0.0713376	+	0.123560i
$787$	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	$0.810621\pi$
$788$	11.0000	+	19.0526i	0.391859	+	0.678719i
$789$		0			0
$790$	8.00000			0.284627
$791$		0			0
$792$	4.00000			0.142134
$793$	−6.00000	+	10.3923i	−0.213066	+	0.369042i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	−5.00000	−	8.66025i	−0.177332	−	0.307148i
$796$	12.0000	−	20.7846i	0.425329	−	0.736691i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	7.00000	+	12.1244i	0.247333	+	0.428393i
$802$	17.0000	+	29.4449i	0.600291	+	1.03973i
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$		0			0
$805$		0			0
$806$	−16.0000			−0.563576
$807$	1.00000	−	1.73205i	0.0352017	−	0.0609711i
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−8.00000			−0.280572
$814$	−4.00000	+	6.92820i	−0.140200	+	0.242833i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$		0			0
$818$	26.0000			0.909069
$819$		0			0
$820$	2.00000			0.0698430
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	3.00000	+	5.19615i	0.104637	+	0.181237i
$823$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$823$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$	−4.00000			−0.139262
$826$		0			0
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$	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	$0.632290\pi$
$830$	2.00000	+	3.46410i	0.0694210	+	0.120241i
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−16.0000			−0.554035
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$		0			0
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$	−14.0000	+	24.2487i	−0.483622	+	0.837658i
$839$	−8.00000			−0.276191			−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000			−0.276191			−0.138095	+	0.990419i	$0.544098\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$	−13.0000	+	22.5167i	−0.448010	+	0.775975i
$843$	11.0000	+	19.0526i	0.378860	+	0.656205i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	4.00000			0.137523
$847$		0			0
$848$	10.0000			0.343401
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$	8.00000	+	13.8564i	0.274236	+	0.474991i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	−22.0000			−0.753266			−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000			−0.753266			−0.376633	+	0.926363i	$0.622918\pi$
$854$		0			0
$855$		0			0
$856$	−2.00000	+	3.46410i	−0.0683586	+	0.118401i
$857$	−19.0000	−	32.9090i	−0.649028	−	1.12415i	−0.983355	−	0.181692i	$-0.941843\pi$
$857$	−19.0000	−	32.9090i	−0.649028	−	1.12415i	0.334328	−	0.942457i	$-0.391491\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	12.0000	−	20.7846i	0.409435	−	0.709162i	−0.585392	−	0.810751i	$-0.699059\pi$
$859$	12.0000	−	20.7846i	0.409435	−	0.709162i	0.994826	+	0.101589i	$0.0323926\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	36.0000			1.22616
$863$	4.00000	−	6.92820i	0.136162	−	0.235839i	−0.789879	−	0.613263i	$-0.789857\pi$
$863$	4.00000	−	6.92820i	0.136162	−	0.235839i	0.926041	+	0.377424i	$0.123190\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$	19.0000			0.645274
$868$		0			0
$869$	32.0000			1.08553
$870$	5.00000	−	8.66025i	0.169516	−	0.293610i
$871$		0			0
$872$	−9.00000	−	15.5885i	−0.304778	−	0.527892i
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$		0			0
$875$		0			0
$876$	6.00000			0.202721
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	−15.0000	−	25.9808i	−0.505937	−	0.876309i
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	48.0000			1.61533			0.807664	−	0.589643i	$-0.200731\pi$
$883$	48.0000			1.61533			0.807664	+	0.589643i	$0.200731\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	−0.647865	−	0.761755i	$-0.724338\pi$
$887$	10.0000	−	17.3205i	0.335767	−	0.581566i	0.983632	+	0.180190i	$0.0576711\pi$
$888$	−2.00000			−0.0671156
$889$		0			0
$890$	14.0000			0.469281
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	−12.0000	−	20.7846i	−0.401790	−	0.695920i
$893$		0			0
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	−4.00000			−0.133705
$896$		0			0
$897$	−16.0000			−0.534224
$898$	13.0000	−	22.5167i	0.433816	−	0.751391i
$899$	−40.0000	−	69.2820i	−1.33407	−	2.31069i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−30.0000	+	51.9615i	−0.999445	+	1.73109i
$902$	8.00000			0.266371
$903$		0			0
$904$	−6.00000			−0.199557
$905$	9.00000	−	15.5885i	0.299170	−	0.518178i
$906$		0			0
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	0.791944	−	0.610594i	$-0.209069\pi$
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	−0.924762	+	0.380547i	$0.875736\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	6.00000			0.199007
$910$		0			0
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$		0			0
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$	−3.00000	−	5.19615i	−0.0992312	−	0.171873i
$915$	−3.00000	+	5.19615i	−0.0991769	+	0.171780i
$916$	22.0000			0.726900
$917$		0			0
$918$	−6.00000			−0.198030
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	−0.597365	−	0.801970i	$-0.703786\pi$
$919$	12.0000	−	20.7846i	0.395843	−	0.685621i	0.993208	+	0.116348i	$0.0371189\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	−9.00000	+	15.5885i	−0.296399	+	0.513378i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	2.00000			0.0657596
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	−8.00000	−	13.8564i	−0.262754	−	0.455104i
$928$	5.00000	+	8.66025i	0.164133	+	0.284287i
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$	−8.00000			−0.262330
$931$		0			0
$932$	−18.0000			−0.589610
$933$		0			0
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	12.0000	+	20.7846i	0.392442	+	0.679729i
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$		0			0
$939$	6.00000			0.195803
$940$	2.00000	−	3.46410i	0.0652328	−	0.112987i
$941$	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	$0.738549\pi$
$942$	5.00000	+	8.66025i	0.162909	+	0.282166i
$943$	8.00000	−	13.8564i	0.260516	−	0.451227i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	32.0000			1.04041
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	0.0408333	+	0.999166i	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$		0			0
$951$	−30.0000			−0.972817
$952$		0			0
$953$	−50.0000			−1.61966			−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000			−1.61966			−0.809829	+	0.586665i	$0.800440\pi$
$954$	5.00000	−	8.66025i	0.161881	−	0.280386i
$955$	−6.00000	−	10.3923i	−0.194155	−	0.336287i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	20.0000	−	34.6410i	0.646508	−	1.11979i
$958$	−8.00000			−0.258468
$959$		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
$963$	2.00000	+	3.46410i	0.0644491	+	0.111629i
$964$	−7.00000	+	12.1244i	−0.225455	+	0.390499i
$965$	10.0000			0.321911
$966$		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
$969$		0			0
$970$	−1.00000	−	1.73205i	−0.0321081	−	0.0556128i
$971$	−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
$974$	−8.00000			−0.256337
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	8.00000	−	13.8564i	0.255812	−	0.443079i
$979$	56.0000			1.78977
$980$		0			0
$981$	−18.0000			−0.574696
$982$	10.0000	−	17.3205i	0.319113	−	0.552720i
$983$	14.0000	+	24.2487i	0.446531	+	0.773414i	0.998157	−	0.0606773i	$-0.0193260\pi$
$983$	14.0000	+	24.2487i	0.446531	+	0.773414i	−0.551627	+	0.834091i	$0.685993\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$	11.0000	−	19.0526i	0.350489	−	0.607065i
$986$	−60.0000			−1.91079
$987$		0			0
$988$		0			0
$989$	32.0000	−	55.4256i	1.01754	−	1.76243i
$990$	−2.00000	−	3.46410i	−0.0635642	−	0.110096i
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	0.710530	−	0.703667i	$-0.248455\pi$
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	−0.964658	+	0.263504i	$0.915122\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	20.0000			0.634681
$994$		0			0
$995$	−24.0000			−0.760851
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$	14.0000	+	24.2487i	0.443162	+	0.767580i
$999$	−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.n.961.1		2
7.2	even	3		1470.2.a.g.1.1		1
7.3	odd	6		1470.2.i.t.361.1		2
7.4	even	3	inner	1470.2.i.n.361.1		2
7.5	odd	6		210.2.a.a.1.1	✓	1
7.6	odd	2		1470.2.i.t.961.1		2
21.2	odd	6		4410.2.a.bc.1.1		1
21.5	even	6		630.2.a.i.1.1		1
28.19	even	6		1680.2.a.o.1.1		1
35.9	even	6		7350.2.a.bo.1.1		1
35.12	even	12		1050.2.g.f.799.1		2
35.19	odd	6		1050.2.a.q.1.1		1
35.33	even	12		1050.2.g.f.799.2		2
56.5	odd	6		6720.2.a.cg.1.1		1
56.19	even	6		6720.2.a.z.1.1		1
84.47	odd	6		5040.2.a.bg.1.1		1
105.47	odd	12		3150.2.g.t.2899.2		2
105.68	odd	12		3150.2.g.t.2899.1		2
105.89	even	6		3150.2.a.t.1.1		1
140.19	even	6		8400.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.a.1.1	✓	1	7.5	odd	6
630.2.a.i.1.1		1	21.5	even	6
1050.2.a.q.1.1		1	35.19	odd	6
1050.2.g.f.799.1		2	35.12	even	12
1050.2.g.f.799.2		2	35.33	even	12
1470.2.a.g.1.1		1	7.2	even	3
1470.2.i.n.361.1		2	7.4	even	3	inner
1470.2.i.n.961.1		2	1.1	even	1	trivial
1470.2.i.t.361.1		2	7.3	odd	6
1470.2.i.t.961.1		2	7.6	odd	2
1680.2.a.o.1.1		1	28.19	even	6
3150.2.a.t.1.1		1	105.89	even	6
3150.2.g.t.2899.1		2	105.68	odd	12
3150.2.g.t.2899.2		2	105.47	odd	12
4410.2.a.bc.1.1		1	21.2	odd	6
5040.2.a.bg.1.1		1	84.47	odd	6
6720.2.a.z.1.1		1	56.19	even	6
6720.2.a.cg.1.1		1	56.5	odd	6
7350.2.a.bo.1.1		1	35.9	even	6
8400.2.a.m.1.1		1	140.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +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} +10.0000 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} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +2.00000 q^{41} +8.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(2.00000 - 3.46410i) q^{47} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.00000 q^{55} +(5.00000 - 8.66025i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-3.00000 + 5.19615i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-3.00000 + 5.19615i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -2.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +4.00000 q^{83} +6.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-5.00000 - 8.66025i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(7.00000 - 12.1244i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(0.500000 - 0.866025i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - q^5 - 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - q^{5} - 2 q^{6} - 2 q^{8} - q^{9} + q^{10} + 4 q^{11} - q^{12} + 4 q^{13} + 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 2 q^{20} + 8 q^{22} + 8 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + 20 q^{29} + q^{30} - 8 q^{31} + q^{32} + 4 q^{33} - 12 q^{34} + 2 q^{36} - 2 q^{37} - 2 q^{39} + q^{40} + 4 q^{41} + 16 q^{43} + 4 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} - 2 q^{50} - 6 q^{51} - 2 q^{52} - 10 q^{53} + q^{54} - 8 q^{55} + 10 q^{58} + 4 q^{59} - q^{60} - 6 q^{61} - 16 q^{62} + 2 q^{64} - 2 q^{65} - 4 q^{66} - 6 q^{68} - 16 q^{69} - 24 q^{71} + q^{72} - 6 q^{73} + 2 q^{74} - q^{75} - 4 q^{78} + 8 q^{79} - q^{80} - q^{81} + 2 q^{82} + 8 q^{83} + 12 q^{85} + 8 q^{86} - 10 q^{87} - 4 q^{88} + 14 q^{89} - 2 q^{90} - 16 q^{92} - 8 q^{93} - 4 q^{94} + q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 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 - 6 * q^17 + q^18 + 2 * q^20 + 8 * q^22 + 8 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + 20 * q^29 + q^30 - 8 * q^31 + q^32 + 4 * q^33 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 2 * q^39 + q^40 + 4 * q^41 + 16 * q^43 + 4 * q^44 - q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 - 2 * q^50 - 6 * q^51 - 2 * q^52 - 10 * q^53 + q^54 - 8 * q^55 + 10 * q^58 + 4 * q^59 - q^60 - 6 * q^61 - 16 * q^62 + 2 * q^64 - 2 * q^65 - 4 * q^66 - 6 * q^68 - 16 * q^69 - 24 * q^71 + q^72 - 6 * q^73 + 2 * q^74 - q^75 - 4 * q^78 + 8 * q^79 - q^80 - q^81 + 2 * q^82 + 8 * q^83 + 12 * q^85 + 8 * q^86 - 10 * q^87 - 4 * q^88 + 14 * q^89 - 2 * q^90 - 16 * q^92 - 8 * q^93 - 4 * q^94 + q^96 - 4 * q^97 - 8 * q^99

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