LMFDB - Embedded newform 1470.2.i.t.361.1

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			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.361
Dual form			1470.2.i.t.961.1

$q$-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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	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
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	4.00000			0.852803
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−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	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	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	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		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	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		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	$-0.260898\pi$
$47$	−2.00000	−	3.46410i	−0.291730	−	0.505291i	−0.974219	+	0.225605i	$0.927564\pi$
$48$	−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	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$	−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	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	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	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	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	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$	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	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$	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	$-0.570452\pi$
$83$	−4.00000			−0.439057			−0.219529	+	0.975606i	$0.570452\pi$
$84$		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	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	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	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		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	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−10.0000			−0.971286
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$	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	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	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	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$	4.00000	+	6.92820i	0.340503	+	0.589768i
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		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	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$		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	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	−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	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$	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	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		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	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$	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	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		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	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	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	0.0299585	+	0.999551i	$0.490462\pi$
$199$	−12.0000	+	20.7846i	−0.850657	+	1.47338i	−0.880616	+	0.473831i	$0.842871\pi$
$200$	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	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$		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	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$		0			0
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	−10.0000			−0.656532
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	0.994283	+	0.106773i	$0.0340517\pi$
$233$	9.00000	+	15.5885i	0.589610	+	1.02123i	−0.404674	+	0.914461i	$0.632615\pi$
$234$	−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	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$	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	$-0.717435\pi$
$251$	−20.0000			−1.26239			−0.631194	+	0.775625i	$0.717435\pi$
$252$		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	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$	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	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	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	$-0.852753\pi$
$269$	−1.00000	+	1.73205i	−0.0609711	+	0.105605i	0.833929	+	0.551872i	$0.186086\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$	−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	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	−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	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	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	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		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	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$	−8.00000			−0.450035
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$	−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	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	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	0.462244	+	0.886753i	$0.347044\pi$
$347$	−10.0000	+	17.3205i	−0.536828	+	0.929814i	−0.999072	+	0.0430610i	$0.986289\pi$
$348$	5.00000	+	8.66025i	0.268028	+	0.464238i
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		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	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	−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	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$	−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	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	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	0.933851	+	0.357663i	$0.116426\pi$
$373$	15.0000	+	25.9808i	0.776671	+	1.34523i	−0.157180	+	0.987570i	$0.550240\pi$
$374$	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	0.962818	+	0.270151i	$0.0870736\pi$
$383$	14.0000	+	24.2487i	0.715367	+	1.23905i	−0.247451	+	0.968900i	$0.579593\pi$
$384$	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	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$	−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	$-0.280934\pi$
$397$	−7.00000	−	12.1244i	−0.351320	−	0.608504i	−0.986481	+	0.163876i	$0.947600\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	−17.0000	−	29.4449i	−0.848939	−	1.47041i	−0.882156	−	0.470958i	$-0.843908\pi$
$401$	−17.0000	−	29.4449i	−0.848939	−	1.47041i	0.0332161	−	0.999448i	$-0.489425\pi$
$402$		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	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	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	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		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	0.00201168	−	0.999998i	$-0.499360\pi$
$431$	18.0000	−	31.1769i	0.867029	−	1.50174i	0.865018	−	0.501741i	$-0.167307\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$		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	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$	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	0.927622	−	0.373519i	$-0.121849\pi$
$457$	3.00000	+	5.19615i	0.140334	+	0.243066i	−0.787288	+	0.616585i	$0.788516\pi$
$458$	−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	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		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	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$	−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	$-0.774829\pi$
$479$	4.00000	−	6.92820i	0.182765	−	0.316558i	0.942821	+	0.333300i	$0.108162\pi$
$480$	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	−0.942309	−	0.334744i	$-0.891350\pi$
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	0.761052	+	0.648691i	$0.224683\pi$
$488$	−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	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$	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	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		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	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$	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	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	5.00000	−	8.66025i	0.218844	−	0.379049i
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$	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	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	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	−0.991254	−	0.131965i	$-0.957871\pi$
$557$	−9.00000	+	15.5885i	−0.381342	+	0.660504i	0.609912	+	0.792469i	$0.291205\pi$
$558$	−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	$-0.860196\pi$
$563$	−2.00000	+	3.46410i	−0.0842900	+	0.145994i	0.820798	+	0.571218i	$0.193529\pi$
$564$	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	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$	−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	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	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	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		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	0.931804	+	0.362962i	$0.118235\pi$
$593$	19.0000	+	32.9090i	0.780236	+	1.35141i	−0.151567	+	0.988447i	$0.548432\pi$
$594$	−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	−0.994732	−	0.102511i	$-0.967312\pi$
$599$	−10.0000	+	17.3205i	−0.408589	+	0.707697i	0.586143	+	0.810208i	$0.300646\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		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	0.911621	+	0.411033i	$0.134832\pi$
$607$	20.0000	+	34.6410i	0.811775	+	1.40604i	−0.0998457	+	0.995003i	$0.531835\pi$
$608$		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	−0.689328	−	0.724449i	$-0.742094\pi$
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	0.972056	+	0.234751i	$0.0754275\pi$
$614$	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	$-0.884732\pi$
$619$	−4.00000	+	6.92820i	−0.160774	+	0.278468i	0.774373	+	0.632730i	$0.218066\pi$
$620$	−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	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$	2.00000	+	3.46410i	0.0789337	+	0.136717i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	−14.0000	+	24.2487i	−0.550397	+	0.953315i	0.447849	+	0.894109i	$0.352190\pi$
$647$	−14.0000	+	24.2487i	−0.550397	+	0.953315i	−0.998246	+	0.0592060i	$0.981143\pi$
$648$	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	0.969865	−	0.243643i	$-0.0783426\pi$
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	−0.695934	+	0.718106i	$0.745009\pi$
$654$	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	−0.411636	−	0.911348i	$-0.635043\pi$
$661$	15.0000	−	25.9808i	0.583432	−	1.01053i	0.995069	−	0.0991864i	$-0.0316240\pi$
$662$	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	$-0.0277265\pi$
$677$	11.0000	+	19.0526i	0.422764	+	0.732249i	−0.573444	+	0.819244i	$0.694393\pi$
$678$	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	0.463434	+	0.886131i	$0.346617\pi$
$683$	−14.0000	+	24.2487i	−0.535695	+	0.927851i	−0.999129	+	0.0417198i	$0.986716\pi$
$684$		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	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	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	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$	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	$-0.214328\pi$
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	−0.930923	+	0.365216i	$0.880995\pi$
$720$	−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	$-0.595887\pi$
$727$	−16.0000			−0.593407			−0.296704	+	0.954970i	$0.595887\pi$
$728$		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	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	−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	−0.826893	−	0.562360i	$-0.809894\pi$
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	0.900464	+	0.434930i	$0.143227\pi$
$740$	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	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−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	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$	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	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$		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	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	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	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	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	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		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	0.214930	+	0.976629i	$0.431048\pi$
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	−0.953251	+	0.302180i	$0.902286\pi$
$810$	−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	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$	−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	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$	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	$-0.455902\pi$
$839$	8.00000			0.276191			0.138095	+	0.990419i	$0.455902\pi$
$840$		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	$-0.377082\pi$
$853$	22.0000			0.753266			0.376633	+	0.926363i	$0.377082\pi$
$854$		0			0
$855$		0			0
$856$	−2.00000	−	3.46410i	−0.0683586	−	0.118401i
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	−0.334328	−	0.942457i	$-0.608509\pi$
$857$	19.0000	−	32.9090i	0.649028	−	1.12415i	0.983355	−	0.181692i	$-0.0581574\pi$
$858$	−4.00000	+	6.92820i	−0.136558	+	0.236525i
$859$	−12.0000	−	20.7846i	−0.409435	−	0.709162i	0.585392	−	0.810751i	$-0.300941\pi$
$859$	−12.0000	−	20.7846i	−0.409435	−	0.709162i	−0.994826	+	0.101589i	$0.967607\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	36.0000			1.22616
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	0.926041	−	0.377424i	$-0.123190\pi$
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	−0.789879	+	0.613263i	$0.789857\pi$
$864$	−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	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	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	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		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	$-0.275662\pi$
$887$	−10.0000	−	17.3205i	−0.335767	−	0.581566i	−0.983632	+	0.180190i	$0.942329\pi$
$888$	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	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−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	0.993208	−	0.116348i	$-0.0371189\pi$
$919$	12.0000	+	20.7846i	0.395843	+	0.685621i	−0.597365	+	0.801970i	$0.703786\pi$
$920$	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	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$	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	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		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	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	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	−0.885720	−	0.464220i	$-0.846335\pi$
$947$	−26.0000	−	45.0333i	−0.844886	−	1.46339i	0.0408333	−	0.999166i	$-0.486999\pi$
$948$	−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	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$	−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	−0.910017	−	0.414572i	$-0.863931\pi$
$977$	−3.00000	+	5.19615i	−0.0959785	+	0.166240i	0.814038	+	0.580812i	$0.197265\pi$
$978$	−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	$-0.980674\pi$
$983$	−14.0000	+	24.2487i	−0.446531	+	0.773414i	0.551627	+	0.834091i	$0.314007\pi$
$984$	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	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	−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	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	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.t.361.1		2
7.2	even	3	inner	1470.2.i.t.961.1		2
7.3	odd	6		1470.2.a.g.1.1		1
7.4	even	3		210.2.a.a.1.1	✓	1
7.5	odd	6		1470.2.i.n.961.1		2
7.6	odd	2		1470.2.i.n.361.1		2
21.11	odd	6		630.2.a.i.1.1		1
21.17	even	6		4410.2.a.bc.1.1		1
28.11	odd	6		1680.2.a.o.1.1		1
35.4	even	6		1050.2.a.q.1.1		1
35.18	odd	12		1050.2.g.f.799.2		2
35.24	odd	6		7350.2.a.bo.1.1		1
35.32	odd	12		1050.2.g.f.799.1		2
56.11	odd	6		6720.2.a.z.1.1		1
56.53	even	6		6720.2.a.cg.1.1		1
84.11	even	6		5040.2.a.bg.1.1		1
105.32	even	12		3150.2.g.t.2899.2		2
105.53	even	12		3150.2.g.t.2899.1		2
105.74	odd	6		3150.2.a.t.1.1		1
140.39	odd	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	7.4	even	3
630.2.a.i.1.1		1	21.11	odd	6
1050.2.a.q.1.1		1	35.4	even	6
1050.2.g.f.799.1		2	35.32	odd	12
1050.2.g.f.799.2		2	35.18	odd	12
1470.2.a.g.1.1		1	7.3	odd	6
1470.2.i.n.361.1		2	7.6	odd	2
1470.2.i.n.961.1		2	7.5	odd	6
1470.2.i.t.361.1		2	1.1	even	1	trivial
1470.2.i.t.961.1		2	7.2	even	3	inner
1680.2.a.o.1.1		1	28.11	odd	6
3150.2.a.t.1.1		1	105.74	odd	6
3150.2.g.t.2899.1		2	105.53	even	12
3150.2.g.t.2899.2		2	105.32	even	12
4410.2.a.bc.1.1		1	21.17	even	6
5040.2.a.bg.1.1		1	84.11	even	6
6720.2.a.z.1.1		1	56.11	odd	6
6720.2.a.cg.1.1		1	56.53	even	6
7350.2.a.bo.1.1		1	35.24	odd	6
8400.2.a.m.1.1		1	140.39	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
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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