LMFDB - Embedded newform 1470.2.i.g.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:	yes
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.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{20} +2.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(1.00000 + 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} -2.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-5.00000 + 8.66025i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(1.00000 + 1.73205i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.00000 q^{55} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +16.0000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-1.00000 - 1.73205i) q^{88} +(-7.00000 + 12.1244i) q^{89} +1.00000 q^{90} +8.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-5.00000 - 8.66025i) q^{94} +(0.500000 - 0.866025i) q^{96} +6.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} + 2 q^{20} + 4 q^{22} - 8 q^{23} + q^{24} - q^{25} - 2 q^{26} - 2 q^{27} + q^{30} + 2 q^{31} - q^{32} + 2 q^{33} - 8 q^{34} + 2 q^{36} - 8 q^{37} + 2 q^{39} - q^{40} - 4 q^{41} - 4 q^{43} - 2 q^{44} - q^{45} - 8 q^{46} - 10 q^{47} - 2 q^{48} + 2 q^{50} - 4 q^{51} - 2 q^{52} + 2 q^{53} + q^{54} + 4 q^{55} - 4 q^{59} + q^{60} + 10 q^{61} - 4 q^{62} + 2 q^{64} - 2 q^{65} + 2 q^{66} - 2 q^{67} + 4 q^{68} - 16 q^{69} - 24 q^{71} - q^{72} - 10 q^{73} - 8 q^{74} + q^{75} - 4 q^{78} - 16 q^{79} - q^{80} - q^{81} + 2 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} - 2 q^{88} - 14 q^{89} + 2 q^{90} + 16 q^{92} - 2 q^{93} - 10 q^{94} + q^{96} + 12 q^{97} + 4 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 - 2 * q^11 + q^12 + 4 * q^13 - 2 * q^15 - q^16 + 4 * q^17 - q^18 + 2 * q^20 + 4 * q^22 - 8 * q^23 + q^24 - q^25 - 2 * q^26 - 2 * q^27 + q^30 + 2 * q^31 - q^32 + 2 * q^33 - 8 * q^34 + 2 * q^36 - 8 * q^37 + 2 * q^39 - q^40 - 4 * q^41 - 4 * q^43 - 2 * q^44 - q^45 - 8 * q^46 - 10 * q^47 - 2 * q^48 + 2 * q^50 - 4 * q^51 - 2 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 4 * q^59 + q^60 + 10 * q^61 - 4 * q^62 + 2 * q^64 - 2 * q^65 + 2 * q^66 - 2 * q^67 + 4 * q^68 - 16 * q^69 - 24 * q^71 - q^72 - 10 * q^73 - 8 * q^74 + q^75 - 4 * q^78 - 16 * q^79 - q^80 - q^81 + 2 * q^82 + 32 * q^83 - 8 * q^85 + 2 * q^86 - 2 * q^88 - 14 * q^89 + 2 * q^90 + 16 * q^92 - 2 * q^93 - 10 * q^94 + q^96 + 12 * q^97 + 4 * 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
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	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
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	−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
$22$	2.00000			0.426401
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$	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
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	1.00000			0.166667
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		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
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	0.227844	+	0.973698i	$0.426832\pi$
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	−0.957169	+	0.289530i	$0.906501\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.00000			0.269680
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	−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
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.0726692	+	0.997356i	$0.523152\pi$
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.827401	+	0.561611i	$0.810182\pi$
$80$	−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
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$		0			0
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	8.00000			0.834058
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	−5.00000	−	8.66025i	−0.515711	−	0.893237i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	0.969664	+	0.244443i	$0.0786053\pi$
$101$	7.00000	+	12.1244i	0.696526	+	1.20642i	−0.273138	+	0.961975i	$0.588061\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$	10.0000	−	17.3205i	0.985329	−	1.70664i	0.344865	−	0.938652i	$-0.387925\pi$
$103$	10.0000	−	17.3205i	0.985329	−	1.70664i	0.640464	−	0.767988i	$-0.278742\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	−8.00000			−0.759326
$112$		0			0
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	4.00000			0.368230
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.00000	−	1.73205i	−0.0880451	−	0.152499i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−2.00000			−0.174078
$133$		0			0
$134$	2.00000			0.172774
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	−10.0000			−0.842152
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$		0			0
$148$	8.00000			0.657596
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	−0.326411	−	0.945228i	$-0.605840\pi$
$149$	8.00000	−	13.8564i	0.655386	−	1.13516i	0.981797	−	0.189933i	$-0.0608272\pi$
$150$	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
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−2.00000			−0.160644
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$	−1.00000	+	1.73205i	−0.0793052	+	0.137361i
$160$	1.00000			0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	−0.601035	−	0.799223i	$-0.705245\pi$
$163$	5.00000	−	8.66025i	0.391630	−	0.678323i	0.992665	+	0.120900i	$0.0385779\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	1.00000	+	1.73205i	0.0778499	+	0.134840i
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	2.00000	−	3.46410i	0.153393	−	0.265684i
$171$		0			0
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$	2.00000			0.150756
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	0.900975	−	0.433872i	$-0.142853\pi$
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	−0.826231	+	0.563331i	$0.809520\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	10.0000			0.729325
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	−3.00000	+	5.19615i	−0.215387	+	0.373062i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.00000	+	1.73205i	−0.0710669	+	0.123091i
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−14.0000			−0.985037
$203$		0			0
$204$	4.00000			0.280056
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	10.0000	+	17.3205i	0.696733	+	1.20678i
$207$	−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	$0.543966\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	−6.00000	−	10.3923i	−0.411113	−	0.712069i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−2.00000			−0.135457
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	4.00000	−	6.92820i	0.268462	−	0.464991i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	7.00000	−	12.1244i	0.465633	−	0.806500i
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$		0			0
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	−0.540301	−	0.841472i	$-0.681690\pi$
$233$	7.00000	−	12.1244i	0.458585	−	0.794293i	0.998886	+	0.0471787i	$0.0150230\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$	−5.00000	−	8.66025i	−0.326164	−	0.564933i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	−16.0000			−1.03931
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	0.984496	+	0.175409i	$0.0561248\pi$
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	2.00000			0.127515
$247$		0			0
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	8.00000	+	13.8564i	0.506979	+	0.878114i
$250$	−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
$253$	16.0000			1.00591
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$	−2.00000	−	3.46410i	−0.125245	−	0.216930i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	2.00000			0.124515
$259$		0			0
$260$	2.00000			0.124035
$261$		0			0
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	−2.00000			−0.122859
$266$		0			0
$267$	−14.0000			−0.856786
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$	−4.00000			−0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	−2.00000			−0.119737
$280$		0			0
$281$	14.0000			0.835170			0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000			0.835170			0.417585	+	0.908638i	$0.362877\pi$
$282$	5.00000	−	8.66025i	0.297746	−	0.515711i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	4.00000			0.236525
$287$		0			0
$288$	1.00000			0.0589256
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	−5.00000	+	8.66025i	−0.292603	+	0.506803i
$293$	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
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$	8.00000	+	13.8564i	0.463428	+	0.802680i
$299$	−8.00000	+	13.8564i	−0.462652	+	0.801337i
$300$	−1.00000			−0.0577350
$301$		0			0
$302$		0			0
$303$	−7.00000	+	12.1244i	−0.402139	+	0.696526i
$304$		0			0
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	−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
$309$	20.0000			1.13776
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	10.0000	+	17.3205i	0.567048	+	0.982156i	0.996856	+	0.0792356i	$0.0252479\pi$
$311$	10.0000	+	17.3205i	0.567048	+	0.982156i	−0.429808	+	0.902920i	$0.641419\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	16.0000			0.900070
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	−1.00000	−	1.73205i	−0.0560772	−	0.0971286i
$319$		0			0
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−12.0000			−0.669775
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$	−2.00000			−0.110432
$329$		0			0
$330$	−2.00000			−0.110096
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	−8.00000	−	13.8564i	−0.439057	−	0.760469i
$333$	−4.00000	−	6.92820i	−0.219199	−	0.379663i
$334$	−9.00000	+	15.5885i	−0.492458	+	0.852962i
$335$	2.00000			0.109272
$336$		0			0
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	−7.00000	−	12.1244i	−0.380188	−	0.658505i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$		0			0
$344$	−2.00000			−0.107833
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$	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
$358$	−2.00000			−0.105703
$359$	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
$362$	11.0000	−	19.0526i	0.578147	−	1.00138i
$363$	7.00000			0.367405
$364$		0			0
$365$	10.0000			0.523424
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	−4.00000	−	6.92820i	−0.208514	−	0.361158i
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$	8.00000			0.415900
$371$		0			0
$372$	2.00000			0.103695
$373$	18.0000	−	31.1769i	0.932005	−	1.61428i	0.152115	−	0.988363i	$-0.451392\pi$
$373$	18.0000	−	31.1769i	0.932005	−	1.61428i	0.779890	−	0.625917i	$-0.215275\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−5.00000	+	8.66025i	−0.257855	+	0.446619i
$377$		0			0
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$	−6.00000	−	10.3923i	−0.307389	−	0.532414i
$382$		0			0
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	−0.987573	−	0.157159i	$-0.949767\pi$
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	0.629890	+	0.776684i	$0.283100\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−18.0000			−0.916176
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$	−3.00000	−	5.19615i	−0.152302	−	0.263795i
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	−32.0000			−1.61831
$392$		0			0
$393$	−12.0000			−0.605320
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−8.00000	−	13.8564i	−0.402524	−	0.697191i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	−0.636609	−	0.771187i	$-0.719663\pi$
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	0.986172	+	0.165726i	$0.0529966\pi$
$402$	1.00000	+	1.73205i	0.0498755	+	0.0863868i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	7.00000	−	12.1244i	0.348263	−	0.603209i
$405$	1.00000			0.0496904
$406$		0			0
$407$	16.0000			0.793091
$408$	−2.00000	+	3.46410i	−0.0990148	+	0.171499i
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	0.925256	+	0.379344i	$0.123850\pi$
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	−0.134107	+	0.990967i	$0.542817\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	−20.0000			−0.985329
$413$		0			0
$414$	8.00000			0.393179
$415$	−8.00000	+	13.8564i	−0.392705	+	0.680184i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$		0			0
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$		0			0
$421$	38.0000			1.85201			0.926003	−	0.377515i	$-0.123221\pi$
$421$	38.0000			1.85201			0.926003	+	0.377515i	$0.123221\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	−5.00000	−	8.66025i	−0.243108	−	0.421076i
$424$	1.00000	+	1.73205i	0.0485643	+	0.0841158i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	12.0000			0.581402
$427$		0			0
$428$	12.0000			0.580042
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	38.0000			1.82616			0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000			1.82616			0.913082	+	0.407777i	$0.133696\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	5.00000	+	8.66025i	0.238909	+	0.413803i
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	−0.368945	−	0.929451i	$-0.620281\pi$
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	0.989401	−	0.145210i	$-0.0463858\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−8.00000			−0.380521
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	0.314082	+	0.949396i	$0.398303\pi$
$443$	−14.0000	+	24.2487i	−0.665160	+	1.15209i	−0.979242	+	0.202695i	$0.935030\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	16.0000			0.756774
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	7.00000	+	12.1244i	0.329252	+	0.570282i
$453$		0			0
$454$	−12.0000			−0.563188
$455$		0			0
$456$		0			0
$457$	21.0000	−	36.3731i	0.982339	−	1.70146i	0.329125	−	0.944286i	$-0.393246\pi$
$457$	21.0000	−	36.3731i	0.982339	−	1.70146i	0.653213	−	0.757174i	$-0.273421\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	−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
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$	−1.00000	−	1.73205i	−0.0463739	−	0.0803219i
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	−0.943610	−	0.331061i	$-0.892594\pi$
$467$	−4.00000	+	6.92820i	−0.185098	+	0.320599i	0.758512	+	0.651660i	$0.225927\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$	10.0000			0.461266
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$	8.00000	−	13.8564i	0.367452	−	0.636446i
$475$		0			0
$476$		0			0
$477$	−2.00000			−0.0915737
$478$	4.00000	−	6.92820i	0.182956	−	0.316889i
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−20.0000			−0.910975
$483$		0			0
$484$	−7.00000			−0.318182
$485$	−3.00000	+	5.19615i	−0.136223	+	0.235945i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	−0.986642	−	0.162905i	$-0.947914\pi$
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	0.352241	−	0.935909i	$-0.385420\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$	10.0000			0.452216
$490$		0			0
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$		0			0
$494$		0			0
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$	−16.0000			−0.716977
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.0619186	+	0.998081i	$0.519722\pi$
$499$	−20.0000	+	34.6410i	−0.895323	+	1.55074i	−0.833404	+	0.552664i	$0.813611\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$	−8.00000	+	13.8564i	−0.355643	+	0.615992i
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$	4.00000			0.177123
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−6.00000	−	10.3923i	−0.264649	−	0.458385i
$515$	10.0000	+	17.3205i	0.440653	+	0.763233i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	20.0000			0.879599
$518$		0			0
$519$	6.00000			0.263371
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$		0			0
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	1.00000	+	1.73205i	0.0435194	+	0.0753778i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	1.00000	−	1.73205i	0.0434372	−	0.0752355i
$531$	4.00000			0.173585
$532$		0			0
$533$	−4.00000			−0.173259
$534$	7.00000	−	12.1244i	0.302920	−	0.524672i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$	−1.00000	+	1.73205i	−0.0431532	+	0.0747435i
$538$	−10.0000			−0.431131
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	−0.886721	−	0.462304i	$-0.847023\pi$
$541$	−1.00000	+	1.73205i	−0.0429934	+	0.0744667i	0.843728	+	0.536771i	$0.180356\pi$
$542$	7.00000	+	12.1244i	0.300676	+	0.520786i
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−14.0000			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$548$	1.00000	−	1.73205i	0.0427179	−	0.0739895i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$	−1.00000	−	1.73205i	−0.0426401	−	0.0738549i
$551$		0			0
$552$	−8.00000			−0.340503
$553$		0			0
$554$	−28.0000			−1.18961
$555$	4.00000	−	6.92820i	0.169791	−	0.294086i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	0.350824	−	0.936442i	$-0.385902\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	8.00000			0.337760
$562$	−7.00000	+	12.1244i	−0.295277	+	0.511435i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	5.00000	+	8.66025i	0.210538	+	0.364662i
$565$	7.00000	−	12.1244i	0.294492	−	0.510075i
$566$	4.00000			0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	0.921869	−	0.387503i	$-0.126662\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$		0			0
$575$	8.00000			0.333623
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	−9.00000	+	15.5885i	−0.374027	+	0.647834i
$580$		0			0
$581$		0			0
$582$	−6.00000			−0.248708
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−15.0000	+	25.9808i	−0.619644	+	1.07326i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$		0			0
$589$		0			0
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	−0.584310	−	0.811530i	$-0.698635\pi$
$593$	10.0000	−	17.3205i	0.410651	−	0.711268i	0.994961	+	0.100262i	$0.0319682\pi$
$594$	−2.00000			−0.0820610
$595$		0			0
$596$	−16.0000			−0.655386
$597$	5.00000	−	8.66025i	0.204636	−	0.354441i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	−0.982208	−	0.187799i	$-0.939865\pi$
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	0.328465	−	0.944516i	$-0.393469\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	4.00000			0.163163			0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000			0.163163			0.0815817	+	0.996667i	$0.474003\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$		0			0
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	−7.00000	−	12.1244i	−0.284356	−	0.492518i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$		0			0
$609$		0			0
$610$	−10.0000			−0.404888
$611$	−10.0000	+	17.3205i	−0.404557	+	0.700713i
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	4.00000	+	6.92820i	0.161558	+	0.279827i	0.935428	−	0.353518i	$-0.115015\pi$
$613$	4.00000	+	6.92820i	0.161558	+	0.279827i	−0.773869	+	0.633345i	$0.781681\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$	2.00000			0.0806478
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−10.0000	+	17.3205i	−0.402259	+	0.696733i
$619$	12.0000	+	20.7846i	0.482321	+	0.835404i	0.999794	−	0.0202954i	$-0.00646066\pi$
$619$	12.0000	+	20.7846i	0.482321	+	0.835404i	−0.517473	+	0.855699i	$0.673127\pi$
$620$	1.00000	+	1.73205i	0.0401610	+	0.0695608i
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$	−20.0000			−0.801927
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	−32.0000			−1.27592
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	6.00000	−	10.3923i	0.238103	−	0.412406i
$636$	2.00000			0.0793052
$637$		0			0
$638$		0			0
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	−36.0000			−1.41970			−0.709851	−	0.704352i	$-0.751238\pi$
$643$	−36.0000			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$644$		0			0
$645$	2.00000			0.0787499
$646$		0			0
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	2.00000			0.0784465
$651$		0			0
$652$	−10.0000			−0.391630
$653$	−1.00000	+	1.73205i	−0.0391330	+	0.0677804i	−0.884929	−	0.465727i	$-0.845793\pi$
$653$	−1.00000	+	1.73205i	−0.0391330	+	0.0677804i	0.845796	+	0.533507i	$0.179126\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	10.0000			0.390137
$658$		0			0
$659$	−34.0000			−1.32445			−0.662226	−	0.749304i	$-0.730388\pi$
$659$	−34.0000			−1.32445			−0.662226	+	0.749304i	$0.730388\pi$
$660$	1.00000	−	1.73205i	0.0389249	−	0.0674200i
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	0.999979	+	0.00652642i	$0.00207744\pi$
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	−0.494337	+	0.869270i	$0.664589\pi$
$662$	2.00000	+	3.46410i	0.0777322	+	0.134636i
$663$	−4.00000	+	6.92820i	−0.155347	+	0.269069i
$664$	16.0000			0.620920
$665$		0			0
$666$	8.00000			0.309994
$667$		0			0
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	−20.0000			−0.772091
$672$		0			0
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$	1.00000	−	1.73205i	0.0385186	−	0.0667161i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−13.0000	+	22.5167i	−0.499631	+	0.865386i	−1.00000		0.000426509i	$-0.999864\pi$
$677$	−13.0000	+	22.5167i	−0.499631	+	0.865386i	0.500369	+	0.865812i	$0.333198\pi$
$678$	14.0000			0.537667
$679$		0			0
$680$	−4.00000			−0.153393
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$		0			0
$687$	−10.0000			−0.381524
$688$	1.00000	−	1.73205i	0.0381246	−	0.0660338i
$689$	2.00000	+	3.46410i	0.0761939	+	0.131972i
$690$	4.00000	+	6.92820i	0.152277	+	0.263752i
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−4.00000			−0.151838
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$		0			0
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	14.0000			0.529529
$700$		0			0
$701$	16.0000			0.604312			0.302156	−	0.953259i	$-0.402294\pi$
$701$	16.0000			0.604312			0.302156	+	0.953259i	$0.402294\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$		0			0
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	5.00000	−	8.66025i	0.188311	−	0.326164i
$706$	24.0000			0.903252
$707$		0			0
$708$	−4.00000			−0.150329
$709$	−21.0000	+	36.3731i	−0.788672	+	1.36602i	0.138109	+	0.990417i	$0.455897\pi$
$709$	−21.0000	+	36.3731i	−0.788672	+	1.36602i	−0.926781	+	0.375602i	$0.877436\pi$
$710$	6.00000	+	10.3923i	0.225176	+	0.390016i
$711$	−8.00000	−	13.8564i	−0.300023	−	0.519656i
$712$	−7.00000	+	12.1244i	−0.262336	+	0.454379i
$713$	−16.0000			−0.599205
$714$		0			0
$715$	4.00000			0.149592
$716$	1.00000	−	1.73205i	0.0373718	−	0.0647298i
$717$	−4.00000	−	6.92820i	−0.149383	−	0.258738i
$718$	10.0000	+	17.3205i	0.373197	+	0.646396i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	−19.0000			−0.707107
$723$	−10.0000	+	17.3205i	−0.371904	+	0.644157i
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$		0			0
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−5.00000	−	8.66025i	−0.184805	−	0.320092i
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	8.00000			0.294884
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	−24.0000	−	41.5692i	−0.882854	−	1.52915i	−0.848153	−	0.529751i	$-0.822285\pi$
$739$	−24.0000	−	41.5692i	−0.882854	−	1.52915i	−0.0347009	−	0.999398i	$-0.511048\pi$
$740$	−4.00000	+	6.92820i	−0.147043	+	0.254686i
$741$		0			0
$742$		0			0
$743$	−48.0000			−1.76095			−0.880475	−	0.474093i	$-0.842776\pi$
$743$	−48.0000			−1.76095			−0.880475	+	0.474093i	$0.842776\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$	8.00000	+	13.8564i	0.293097	+	0.507659i
$746$	18.0000	+	31.1769i	0.659027	+	1.14147i
$747$	−8.00000	+	13.8564i	−0.292705	+	0.506979i
$748$	−8.00000			−0.292509
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	−0.783769	−	0.621052i	$-0.786706\pi$
$751$	4.00000	−	6.92820i	0.145962	−	0.252814i	0.929731	+	0.368238i	$0.120039\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$	−10.0000	−	17.3205i	−0.364420	−	0.631194i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−20.0000			−0.726912			−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000			−0.726912			−0.363456	+	0.931611i	$0.618403\pi$
$758$	−4.00000	+	6.92820i	−0.145287	+	0.251644i
$759$	8.00000	+	13.8564i	0.290382	+	0.502956i
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$	12.0000			0.434714
$763$		0			0
$764$		0			0
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−7.00000	−	12.1244i	−0.252920	−	0.438071i
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	16.0000			0.576975			0.288487	−	0.957484i	$-0.406848\pi$
$769$	16.0000			0.576975			0.288487	+	0.957484i	$0.406848\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	9.00000	−	15.5885i	0.323917	−	0.561041i
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	1.00000	−	1.73205i	0.0359211	−	0.0622171i
$776$	6.00000			0.215387
$777$		0			0
$778$	−24.0000			−0.860442
$779$		0			0
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$	16.0000	−	27.7128i	0.572159	−	0.991008i
$783$		0			0
$784$		0			0
$785$	−10.0000			−0.356915
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	0.952925	−	0.303207i	$-0.0980575\pi$
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	−0.739048	+	0.673653i	$0.764724\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		0			0
$790$	16.0000			0.569254
$791$		0			0
$792$	2.00000			0.0710669
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−7.00000	−	12.1244i	−0.248421	−	0.430277i
$795$	−1.00000	−	1.73205i	−0.0354663	−	0.0614295i
$796$	−5.00000	+	8.66025i	−0.177220	+	0.306955i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$		0			0
$799$	−40.0000			−1.41510
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−7.00000	−	12.1244i	−0.247333	−	0.428393i
$802$	7.00000	+	12.1244i	0.247179	+	0.428126i
$803$	−10.0000	+	17.3205i	−0.352892	+	0.611227i
$804$	−2.00000			−0.0705346
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$	7.00000	+	12.1244i	0.246259	+	0.426533i
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$	14.0000			0.491001
$814$	−8.00000	+	13.8564i	−0.280400	+	0.485667i
$815$	5.00000	+	8.66025i	0.175142	+	0.303355i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$		0			0
$818$	−32.0000			−1.11885
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	−0.995819	−	0.0913446i	$-0.970884\pi$
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	0.577016	+	0.816733i	$0.304217\pi$
$822$	−1.00000	−	1.73205i	−0.0348790	−	0.0604122i
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$	10.0000	−	17.3205i	0.348367	−	0.603388i
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$	−4.00000	+	6.92820i	−0.139010	+	0.240772i
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$	−8.00000	−	13.8564i	−0.277684	−	0.480963i
$831$	−14.0000	+	24.2487i	−0.485655	+	0.841178i
$832$	2.00000			0.0693375
$833$		0			0
$834$	4.00000			0.138509
$835$	−9.00000	+	15.5885i	−0.311458	+	0.539461i
$836$		0			0
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	−18.0000	+	31.1769i	−0.621800	+	1.07699i
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−19.0000	+	32.9090i	−0.654783	+	1.13412i
$843$	7.00000	+	12.1244i	0.241093	+	0.417585i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$	10.0000			0.343807
$847$		0			0
$848$	−2.00000			−0.0686803
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	2.00000	+	3.46410i	0.0685994	+	0.118818i
$851$	−32.0000	−	55.4256i	−1.09695	−	1.89997i
$852$	−6.00000	+	10.3923i	−0.205557	+	0.356034i
$853$	38.0000			1.30110			0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000			1.30110			0.650548	+	0.759465i	$0.274539\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	12.0000			0.408722
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−19.0000	+	32.9090i	−0.645646	+	1.11829i
$867$	1.00000			0.0339618
$868$		0			0
$869$	32.0000			1.08553
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$	−10.0000			−0.337869
$877$	−6.00000	+	10.3923i	−0.202606	+	0.350923i	−0.949367	−	0.314169i	$-0.898274\pi$
$877$	−6.00000	+	10.3923i	−0.202606	+	0.350923i	0.746762	+	0.665092i	$0.231608\pi$
$878$	13.0000	+	22.5167i	0.438729	+	0.759900i
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$		0			0
$883$	34.0000			1.14419			0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000			1.14419			0.572096	+	0.820187i	$0.306131\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$	−14.0000	−	24.2487i	−0.470339	−	0.814651i
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	−0.848749	−	0.528796i	$-0.822644\pi$
$887$	1.00000	−	1.73205i	0.0335767	−	0.0581566i	0.882325	+	0.470640i	$0.155977\pi$
$888$	−8.00000			−0.268462
$889$		0			0
$890$	14.0000			0.469281
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$		0			0
$894$	−8.00000	+	13.8564i	−0.267560	+	0.463428i
$895$	−2.00000			−0.0668526
$896$		0			0
$897$	−16.0000			−0.534224
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$		0			0
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−4.00000	+	6.92820i	−0.133259	+	0.230812i
$902$	−4.00000			−0.133185
$903$		0			0
$904$	−14.0000			−0.465633
$905$	11.0000	−	19.0526i	0.365652	−	0.633328i
$906$		0			0
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	−14.0000			−0.464351
$910$		0			0
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$	−16.0000	−	27.7128i	−0.529523	−	0.917160i
$914$	21.0000	+	36.3731i	0.694618	+	1.20311i
$915$	−5.00000	+	8.66025i	−0.165295	+	0.286299i
$916$	10.0000			0.330409
$917$		0			0
$918$	4.00000			0.132020
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.129893	+	0.991528i	$0.541463\pi$
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.793742	+	0.608254i	$0.791870\pi$
$920$	−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
$925$	8.00000			0.263038
$926$	−8.00000	+	13.8564i	−0.262896	+	0.455350i
$927$	10.0000	+	17.3205i	0.328443	+	0.568880i
$928$		0			0
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	−0.507825	−	0.861460i	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$	2.00000			0.0655826
$931$		0			0
$932$	−14.0000			−0.458585
$933$	−10.0000	+	17.3205i	−0.327385	+	0.567048i
$934$	−4.00000	−	6.92820i	−0.130884	−	0.226698i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	−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
$939$	26.0000			0.848478
$940$	−5.00000	+	8.66025i	−0.163082	+	0.282466i
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	−0.909345	−	0.416044i	$-0.863416\pi$
$941$	−25.0000	−	43.3013i	−0.814977	−	1.41158i	0.0943679	−	0.995537i	$-0.469917\pi$
$942$	−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
$946$	−4.00000			−0.130051
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$	8.00000	+	13.8564i	0.259828	+	0.450035i
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$		0			0
$951$	−6.00000			−0.194563
$952$		0			0
$953$	−58.0000			−1.87880			−0.939402	−	0.342817i	$-0.888619\pi$
$953$	−58.0000			−1.87880			−0.939402	+	0.342817i	$0.888619\pi$
$954$	1.00000	−	1.73205i	0.0323762	−	0.0560772i
$955$		0			0
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$		0			0
$958$	4.00000			0.129234
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−8.00000	−	13.8564i	−0.257930	−	0.446748i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	10.0000	−	17.3205i	0.322078	−	0.557856i
$965$	−18.0000			−0.579441
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$		0			0
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	−0.659762	−	0.751475i	$-0.729343\pi$
$971$	10.0000	−	17.3205i	0.320915	−	0.555842i	0.980677	+	0.195633i	$0.0626762\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	28.0000			0.897178
$975$	1.00000	−	1.73205i	0.0320256	−	0.0554700i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$	−5.00000	+	8.66025i	−0.159882	+	0.276924i
$979$	28.0000			0.894884
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−3.00000	+	5.19615i	−0.0957338	+	0.165816i
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	0.955341	+	0.295506i	$0.0954882\pi$
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	−0.221755	+	0.975102i	$0.571178\pi$
$984$	−1.00000	−	1.73205i	−0.0318788	−	0.0552158i
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	0.991233	−	0.132125i	$-0.0421802\pi$
$991$	12.0000	+	20.7846i	0.381193	+	0.660245i	−0.610040	+	0.792370i	$0.708847\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	4.00000			0.126936
$994$		0			0
$995$	10.0000			0.317021
$996$	8.00000	−	13.8564i	0.253490	−	0.439057i
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	0.814602	−	0.580020i	$-0.196955\pi$
$997$	−3.00000	−	5.19615i	−0.0950110	−	0.164564i	−0.909613	+	0.415456i	$0.863622\pi$
$998$	−20.0000	−	34.6410i	−0.633089	−	1.09654i
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.g.961.1		2
7.2	even	3		1470.2.a.n.1.1	✓	1
7.3	odd	6		1470.2.i.c.361.1		2
7.4	even	3	inner	1470.2.i.g.361.1		2
7.5	odd	6		1470.2.a.p.1.1	yes	1
7.6	odd	2		1470.2.i.c.961.1		2
21.2	odd	6		4410.2.a.e.1.1		1
21.5	even	6		4410.2.a.n.1.1		1
35.9	even	6		7350.2.a.bh.1.1		1
35.19	odd	6		7350.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.n.1.1	✓	1	7.2	even	3
1470.2.a.p.1.1	yes	1	7.5	odd	6
1470.2.i.c.361.1		2	7.3	odd	6
1470.2.i.c.961.1		2	7.6	odd	2
1470.2.i.g.361.1		2	7.4	even	3	inner
1470.2.i.g.961.1		2	1.1	even	1	trivial
4410.2.a.e.1.1		1	21.2	odd	6
4410.2.a.n.1.1		1	21.5	even	6
7350.2.a.o.1.1		1	35.19	odd	6
7350.2.a.bh.1.1		1	35.9	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{20} +2.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -4.00000 q^{34} +1.00000 q^{36} +(-4.00000 + 6.92820i) q^{37} +(1.00000 + 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} -2.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-5.00000 + 8.66025i) q^{47} -1.00000 q^{48} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(1.00000 + 1.73205i) q^{53} +(0.500000 - 0.866025i) q^{54} +2.00000 q^{55} +(-2.00000 - 3.46410i) q^{59} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{69} -12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(0.500000 - 0.866025i) q^{75} -2.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +16.0000 q^{83} -4.00000 q^{85} +(1.00000 - 1.73205i) q^{86} +(-1.00000 - 1.73205i) q^{88} +(-7.00000 + 12.1244i) q^{89} +1.00000 q^{90} +8.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-5.00000 - 8.66025i) q^{94} +(0.500000 - 0.866025i) q^{96} +6.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{8} - q^{9} - q^{10} - 2 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} - q^{16} + 4 q^{17} - q^{18} + 2 q^{20} + 4 q^{22} - 8 q^{23} + q^{24} - q^{25} - 2 q^{26} - 2 q^{27} + q^{30} + 2 q^{31} - q^{32} + 2 q^{33} - 8 q^{34} + 2 q^{36} - 8 q^{37} + 2 q^{39} - q^{40} - 4 q^{41} - 4 q^{43} - 2 q^{44} - q^{45} - 8 q^{46} - 10 q^{47} - 2 q^{48} + 2 q^{50} - 4 q^{51} - 2 q^{52} + 2 q^{53} + q^{54} + 4 q^{55} - 4 q^{59} + q^{60} + 10 q^{61} - 4 q^{62} + 2 q^{64} - 2 q^{65} + 2 q^{66} - 2 q^{67} + 4 q^{68} - 16 q^{69} - 24 q^{71} - q^{72} - 10 q^{73} - 8 q^{74} + q^{75} - 4 q^{78} - 16 q^{79} - q^{80} - q^{81} + 2 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} - 2 q^{88} - 14 q^{89} + 2 q^{90} + 16 q^{92} - 2 q^{93} - 10 q^{94} + q^{96} + 12 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 + 2 * q^8 - q^9 - q^10 - 2 * q^11 + q^12 + 4 * q^13 - 2 * q^15 - q^16 + 4 * q^17 - q^18 + 2 * q^20 + 4 * q^22 - 8 * q^23 + q^24 - q^25 - 2 * q^26 - 2 * q^27 + q^30 + 2 * q^31 - q^32 + 2 * q^33 - 8 * q^34 + 2 * q^36 - 8 * q^37 + 2 * q^39 - q^40 - 4 * q^41 - 4 * q^43 - 2 * q^44 - q^45 - 8 * q^46 - 10 * q^47 - 2 * q^48 + 2 * q^50 - 4 * q^51 - 2 * q^52 + 2 * q^53 + q^54 + 4 * q^55 - 4 * q^59 + q^60 + 10 * q^61 - 4 * q^62 + 2 * q^64 - 2 * q^65 + 2 * q^66 - 2 * q^67 + 4 * q^68 - 16 * q^69 - 24 * q^71 - q^72 - 10 * q^73 - 8 * q^74 + q^75 - 4 * q^78 - 16 * q^79 - q^80 - q^81 + 2 * q^82 + 32 * q^83 - 8 * q^85 + 2 * q^86 - 2 * q^88 - 14 * q^89 + 2 * q^90 + 16 * q^92 - 2 * q^93 - 10 * q^94 + q^96 + 12 * q^97 + 4 * q^99

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