LMFDB - Embedded newform 1470.2.i.a.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.a.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} +(-0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} -4.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{46} +1.00000 q^{48} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{52} +(5.00000 - 8.66025i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} -8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-5.00000 - 8.66025i) q^{89} +1.00000 q^{90} -8.00000 q^{92} +(-2.00000 + 3.46410i) q^{95} +(-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} - q^{10} + 4 q^{11} - q^{12} - 4 q^{13} + 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + 2 q^{20} - 8 q^{22} + 8 q^{23} - q^{24}+ \cdots - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^5 + 2 * q^6 + 2 * q^8 - q^9 - q^10 + 4 * q^11 - q^12 - 4 * q^13 + 2 * q^15 - q^16 - 2 * q^17 - q^18 - 4 * q^19 + 2 * q^20 - 8 * q^22 + 8 * q^23 - q^24 - q^25 + 2 * q^26 + 2 * q^27 - 4 * q^29 - q^30 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 - q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - q^45 + 8 * q^46 + 2 * q^48 + 2 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 2 * q^58 - 12 * q^59 - q^60 - 14 * q^61 + 2 * q^64 + 2 * q^65 + 4 * q^66 + 12 * q^67 - 2 * q^68 - 16 * q^69 - 16 * q^71 - q^72 - 10 * q^73 - 6 * q^74 - q^75 + 8 * q^76 - 4 * q^78 - 16 * q^79 - q^80 - q^81 + 6 * q^82 - 24 * q^83 + 4 * q^85 + 4 * q^86 + 2 * q^87 + 4 * q^88 - 10 * q^89 + 2 * q^90 - 16 * q^92 - 4 * q^95 - q^96 + 4 * q^97 - 8 * q^99

Character values

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

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

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
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	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
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.00000	+	3.46410i	0.348155	+	0.603023i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	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
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	1.00000			0.141421
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−4.00000			−0.539360
$56$		0			0
$57$	4.00000			0.529813
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	2.00000	−	3.46410i	0.246183	−	0.426401i
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	−8.00000			−0.963087
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	4.00000			0.458831
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−8.00000			−0.834058
$93$		0			0
$94$		0			0
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	−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	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−10.0000			−0.971286
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$	6.00000			0.569495
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	12.0000			1.10469
$119$		0			0
$120$	1.00000			0.0912871
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.858137	−	0.513421i	$-0.828378\pi$
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.0155672	−	0.999879i	$-0.504955\pi$
$132$	−4.00000			−0.348155
$133$		0			0
$134$	−12.0000			−1.03664
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	−0.996621	−	0.0821359i	$-0.973826\pi$
$137$	−5.00000	+	8.66025i	−0.427179	+	0.739895i	0.569442	+	0.822031i	$0.307159\pi$
$138$	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
$141$		0			0
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$	10.0000			0.827606
$147$		0			0
$148$	6.00000			0.493197
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$	2.00000			0.161690
$154$		0			0
$155$		0			0
$156$	1.00000	+	1.73205i	0.0800641	+	0.138675i
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	9.00000	−	15.5885i	0.718278	−	1.24409i	0.961681	−	0.274169i	$-0.0884028\pi$
$158$	−8.00000	+	13.8564i	−0.636446	+	1.10236i
$159$	5.00000	+	8.66025i	0.396526	+	0.686803i
$160$	1.00000			0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$	2.00000	−	3.46410i	0.155700	−	0.269680i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	−2.00000			−0.151620
$175$		0			0
$176$	−4.00000			−0.301511
$177$	−6.00000	−	10.3923i	−0.450988	−	0.781133i
$178$	−5.00000	+	8.66025i	−0.374766	+	0.649113i
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	−0.931038	−	0.364922i	$-0.881096\pi$
$179$	−2.00000	+	3.46410i	−0.149487	+	0.258919i	0.781551	+	0.623841i	$0.214429\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$	4.00000	+	6.92820i	0.294884	+	0.510754i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$		0			0
$189$		0			0
$190$	4.00000			0.290191
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$	6.00000			0.422159
$203$		0			0
$204$	2.00000			0.140028
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	4.00000	−	6.92820i	0.278019	−	0.481543i
$208$	1.00000	+	1.73205i	0.0693375	+	0.120096i
$209$	−16.0000			−1.10674
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	4.00000	−	6.92820i	0.274075	−	0.474713i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	1.00000			0.0680414
$217$		0			0
$218$	14.0000			0.948200
$219$	−5.00000	−	8.66025i	−0.337869	−	0.585206i
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	2.00000	−	3.46410i	0.134535	−	0.233021i
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	−8.00000			−0.527504
$231$		0			0
$232$	−2.00000			−0.131306
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	0.960746	+	0.277429i	$0.0894825\pi$
$233$	11.0000	+	19.0526i	0.720634	+	1.24817i	−0.240112	+	0.970745i	$0.577184\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	16.0000			1.03931
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−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
$244$	14.0000			0.896258
$245$		0			0
$246$	−6.00000			−0.382546
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$		0			0
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	32.0000			2.01182
$254$	8.00000	+	13.8564i	0.501965	+	0.869428i
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$	−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	$0.689499\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	−2.00000			−0.124035
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	−10.0000	+	17.3205i	−0.617802	+	1.07006i
$263$	−4.00000	+	6.92820i	−0.246651	+	0.427211i	−0.962594	−	0.270947i	$-0.912663\pi$
$263$	−4.00000	+	6.92820i	−0.246651	+	0.427211i	0.715944	+	0.698158i	$0.245997\pi$
$264$	2.00000	+	3.46410i	0.123091	+	0.213201i
$265$	−10.0000			−0.614295
$266$		0			0
$267$	10.0000			0.611990
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	10.0000			0.604122
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$	4.00000	−	6.92820i	0.240772	−	0.417029i
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	0.319447	+	0.947604i	$0.396503\pi$
$277$	−11.0000	+	19.0526i	−0.660926	+	1.14476i	−0.980373	+	0.197153i	$0.936830\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−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	$0.853740\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$	8.00000			0.473050
$287$		0			0
$288$	1.00000			0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	−1.00000	+	1.73205i	−0.0586210	+	0.101535i
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	−3.00000	−	5.19615i	−0.174371	−	0.302020i
$297$	2.00000	−	3.46410i	0.116052	−	0.201008i
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	−8.00000	−	13.8564i	−0.462652	−	0.801337i
$300$	1.00000			0.0577350
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−7.00000	+	12.1244i	−0.400819	+	0.694239i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$	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
$309$	−8.00000			−0.455104
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$	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	$0.779095\pi$
$314$	−18.0000			−1.01580
$315$		0			0
$316$	16.0000			0.900070
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	0.892741	−	0.450570i	$-0.148779\pi$
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	−0.836576	+	0.547852i	$0.815446\pi$
$318$	5.00000	−	8.66025i	0.280386	−	0.485643i
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	12.0000			0.669775
$322$		0			0
$323$	8.00000			0.445132
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	−10.0000	+	17.3205i	−0.553849	+	0.959294i
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	−6.00000			−0.331295
$329$		0			0
$330$	−4.00000			−0.220193
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	−12.0000			−0.655630
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$		0			0
$342$	4.00000			0.216295
$343$		0			0
$344$	−4.00000			−0.215666
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	1.00000	+	1.73205i	0.0536056	+	0.0928477i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	−0.617388	−	0.786659i	$-0.711809\pi$
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	0.989960	+	0.141344i	$0.0451425\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	10.0000			0.529999
$357$		0			0
$358$	4.00000			0.211407
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−3.00000	−	5.19615i	−0.157676	−	0.273104i
$363$	5.00000			0.262432
$364$		0			0
$365$	10.0000			0.523424
$366$	−7.00000	−	12.1244i	−0.365896	−	0.633750i
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	4.00000			0.206010
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	8.00000	−	13.8564i	0.409316	−	0.708955i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	2.00000			0.101797
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$	−16.0000			−0.809155
$392$		0			0
$393$	20.0000			1.00887
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−8.00000	+	13.8564i	−0.402524	+	0.697191i
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	−15.0000	−	25.9808i	−0.752828	−	1.30394i	−0.946447	−	0.322860i	$-0.895356\pi$
$397$	−15.0000	−	25.9808i	−0.752828	−	1.30394i	0.193618	−	0.981077i	$-0.437978\pi$
$398$	−24.0000			−1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	0.986172	−	0.165726i	$-0.0529966\pi$
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	−0.636609	+	0.771187i	$0.719663\pi$
$402$	6.00000	−	10.3923i	0.299253	−	0.518321i
$403$		0			0
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−24.0000			−1.18964
$408$	−1.00000	−	1.73205i	−0.0495074	−	0.0857493i
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.173064	−	0.984911i	$-0.444633\pi$
$409$	19.0000	−	32.9090i	0.939490	−	1.62724i	0.766426	−	0.642333i	$-0.222033\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	−5.00000	−	8.66025i	−0.246632	−	0.427179i
$412$	−8.00000			−0.394132
$413$		0			0
$414$	−8.00000			−0.393179
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$	8.00000	+	13.8564i	0.391293	+	0.677739i
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	6.00000	+	10.3923i	0.292075	+	0.505889i
$423$		0			0
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−8.00000			−0.387601
$427$		0			0
$428$	12.0000			0.580042
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	16.0000	−	27.7128i	0.765384	−	1.32568i
$438$	−5.00000	+	8.66025i	−0.238909	+	0.413803i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	−4.00000			−0.190693
$441$		0			0
$442$	−4.00000			−0.190261
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	−5.00000	+	8.66025i	−0.237023	+	0.410535i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	−10.0000			−0.472984
$448$		0			0
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	−0.500000	−	0.866025i	−0.0235702	−	0.0408248i
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	4.00000			0.187729
$455$		0			0
$456$	4.00000			0.187317
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	4.00000	+	6.92820i	0.186501	+	0.323029i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	11.0000	−	19.0526i	0.509565	−	0.882593i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$		0			0
$471$	9.00000	+	15.5885i	0.414698	+	0.718278i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−8.00000	+	13.8564i	−0.367840	+	0.637118i
$474$	−8.00000	−	13.8564i	−0.367452	−	0.636446i
$475$	4.00000			0.183533
$476$		0			0
$477$	−10.0000			−0.457869
$478$		0			0
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	0.225372	+	0.974273i	$0.427640\pi$
$479$	−16.0000	+	27.7128i	−0.731059	+	1.26623i	−0.956431	+	0.291958i	$0.905693\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	−14.0000			−0.637683
$483$		0			0
$484$	5.00000			0.227273
$485$	−1.00000	−	1.73205i	−0.0454077	−	0.0786484i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	−0.761052	−	0.648691i	$-0.775317\pi$
$487$	4.00000	−	6.92820i	0.181257	−	0.313947i	0.942309	+	0.334744i	$0.108650\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$	20.0000			0.904431
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	3.00000	+	5.19615i	0.135250	+	0.234261i
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$	4.00000	−	6.92820i	0.179969	−	0.311715i
$495$	2.00000	+	3.46410i	0.0898933	+	0.155700i
$496$		0			0
$497$		0			0
$498$	−12.0000			−0.537733
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	0.968500	−	0.249015i	$-0.0801067\pi$
$499$	6.00000	+	10.3923i	0.268597	+	0.465223i	−0.699903	+	0.714238i	$0.746773\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	4.00000	−	6.92820i	0.178707	−	0.309529i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	40.0000			1.78351			0.891756	−	0.452517i	$-0.149474\pi$
$503$	40.0000			1.78351			0.891756	+	0.452517i	$0.149474\pi$
$504$		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
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$	2.00000			0.0885615
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	7.00000	−	12.1244i	0.308757	−	0.534782i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	−18.0000			−0.790112
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	20.0000			0.873704
$525$		0			0
$526$	8.00000			0.348817
$527$		0			0
$528$	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
$531$	12.0000			0.520756
$532$		0			0
$533$	12.0000			0.519778
$534$	−5.00000	−	8.66025i	−0.216371	−	0.374766i
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−2.00000	−	3.46410i	−0.0863064	−	0.149487i
$538$	−18.0000			−0.776035
$539$		0			0
$540$	1.00000			0.0430331
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	−3.00000	+	5.19615i	−0.128742	+	0.222988i
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	14.0000			0.599694
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	−	8.66025i	−0.213589	−	0.369948i
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$	4.00000	+	6.92820i	0.170406	+	0.295151i
$552$	−8.00000			−0.340503
$553$		0			0
$554$	22.0000			0.934690
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	−0.996082	−	0.0884397i	$-0.971812\pi$
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	0.574632	+	0.818412i	$0.305145\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	28.0000			1.17693
$567$		0			0
$568$	−8.00000			−0.335673
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	−0.998608	−	0.0527519i	$-0.983201\pi$
$569$	−13.0000	−	22.5167i	−0.544988	−	0.943948i	0.453619	−	0.891196i	$-0.350133\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	0.408883	+	0.912587i	$0.365918\pi$
$571$	−14.0000	+	24.2487i	−0.585882	+	1.01478i	−0.994765	+	0.102190i	$0.967415\pi$
$572$	−4.00000	−	6.92820i	−0.167248	−	0.289683i
$573$	−16.0000			−0.668410
$574$		0			0
$575$	−8.00000			−0.333623
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−17.0000	+	29.4449i	−0.707719	+	1.22581i	0.257982	+	0.966150i	$0.416942\pi$
$577$	−17.0000	+	29.4449i	−0.707719	+	1.22581i	−0.965701	+	0.259656i	$0.916391\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	−1.00000	−	1.73205i	−0.0415586	−	0.0719816i
$580$	−2.00000			−0.0830455
$581$		0			0
$582$	2.00000			0.0829027
$583$	−20.0000	−	34.6410i	−0.828315	−	1.43468i
$584$	−5.00000	+	8.66025i	−0.206901	+	0.358364i
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$		0			0
$590$	−6.00000	−	10.3923i	−0.247016	−	0.427844i
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	0.990212	+	0.139569i	$0.0445716\pi$
$593$	15.0000	+	25.9808i	0.615976	+	1.06690i	−0.374236	+	0.927333i	$0.622095\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−10.0000			−0.409616
$597$	12.0000	+	20.7846i	0.491127	+	0.850657i
$598$	−8.00000	+	13.8564i	−0.327144	+	0.566631i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	−2.50000	+	4.33013i	−0.101639	+	0.176045i
$606$	−3.00000	+	5.19615i	−0.121867	+	0.211079i
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	14.0000			0.566843
$611$		0			0
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	−3.00000	+	5.19615i	−0.121169	+	0.209871i	−0.920229	−	0.391381i	$-0.871998\pi$
$613$	−3.00000	+	5.19615i	−0.121169	+	0.209871i	0.799060	+	0.601251i	$0.205331\pi$
$614$	−10.0000	−	17.3205i	−0.403567	−	0.698999i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	4.00000	+	6.92820i	0.160904	+	0.278693i
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$		0			0
$621$	4.00000	+	6.92820i	0.160514	+	0.278019i
$622$	−8.00000			−0.320771
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	8.00000	−	13.8564i	0.319489	−	0.553372i
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	12.0000			0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−8.00000	−	13.8564i	−0.318223	−	0.551178i
$633$	6.00000	−	10.3923i	0.238479	−	0.413057i
$634$	1.00000	−	1.73205i	0.0397151	−	0.0687885i
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$	−10.0000			−0.396526
$637$		0			0
$638$	8.00000			0.316723
$639$	4.00000	+	6.92820i	0.158238	+	0.274075i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	0.306031	+	0.952022i	$0.400999\pi$
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	−0.977490	+	0.210981i	$0.932334\pi$
$642$	−6.00000	−	10.3923i	−0.236801	−	0.410152i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	−4.00000	−	6.92820i	−0.157378	−	0.272587i
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	24.0000	+	41.5692i	0.942082	+	1.63173i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	20.0000			0.783260
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	0.695934	−	0.718106i	$-0.254991\pi$
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	−0.969865	+	0.243643i	$0.921657\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	−10.0000	+	17.3205i	−0.390732	+	0.676768i
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$	10.0000			0.390137
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	2.00000	+	3.46410i	0.0778499	+	0.134840i
$661$	−19.0000	+	32.9090i	−0.739014	+	1.28001i	0.213925	+	0.976850i	$0.431375\pi$
$661$	−19.0000	+	32.9090i	−0.739014	+	1.28001i	−0.952940	+	0.303160i	$0.901958\pi$
$662$	−6.00000	+	10.3923i	−0.233197	+	0.403908i
$663$	2.00000	+	3.46410i	0.0776736	+	0.134535i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	6.00000			0.232495
$667$	−8.00000	−	13.8564i	−0.309761	−	0.536522i
$668$	4.00000	−	6.92820i	0.154765	−	0.268060i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	−56.0000			−2.16186
$672$		0			0
$673$	−30.0000			−1.15642			−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000			−1.15642			−0.578208	+	0.815890i	$0.696248\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$	−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	$-0.000135762\pi$
$677$	13.0000	+	22.5167i	0.499631	+	0.865386i	−0.500369	+	0.865812i	$0.666802\pi$
$678$	18.0000			0.691286
$679$		0			0
$680$	2.00000			0.0766965
$681$	−2.00000	−	3.46410i	−0.0766402	−	0.132745i
$682$		0			0
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−2.00000	−	3.46410i	−0.0764719	−	0.132453i
$685$	10.0000			0.382080
$686$		0			0
$687$	−10.0000			−0.381524
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$	4.00000	−	6.92820i	0.152277	−	0.263752i
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	−0.973515	−	0.228625i	$-0.926577\pi$
$691$	−18.0000	−	31.1769i	−0.684752	−	1.18603i	0.288762	−	0.957401i	$-0.406756\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−4.00000			−0.151838
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$	1.00000	−	1.73205i	0.0379049	−	0.0656532i
$697$	6.00000	−	10.3923i	0.227266	−	0.393637i
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$	−22.0000			−0.832116
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	1.00000	+	1.73205i	0.0377426	+	0.0653720i
$703$	−12.0000	+	20.7846i	−0.452589	+	0.783906i
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$		0			0
$706$	−14.0000			−0.526897
$707$		0			0
$708$	12.0000			0.450988
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$	−8.00000	+	13.8564i	−0.300023	+	0.519656i
$712$	−5.00000	−	8.66025i	−0.187383	−	0.324557i
$713$		0			0
$714$		0			0
$715$	8.00000			0.299183
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	0.975759	−	0.218850i	$-0.0702305\pi$
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	−0.677409	+	0.735607i	$0.736897\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	−3.00000			−0.111648
$723$	7.00000	+	12.1244i	0.260333	+	0.450910i
$724$	−3.00000	+	5.19615i	−0.111494	+	0.193113i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	−2.50000	−	4.33013i	−0.0927837	−	0.160706i
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		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
$732$	−7.00000	+	12.1244i	−0.258727	+	0.448129i
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	−0.881633	−	0.471935i	$-0.843556\pi$
$733$	−23.0000	−	39.8372i	−0.849524	−	1.47142i	0.0321090	−	0.999484i	$-0.489778\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−8.00000			−0.294884
$737$	−24.0000	−	41.5692i	−0.884051	−	1.53122i
$738$	3.00000	−	5.19615i	0.110432	−	0.191273i
$739$	14.0000	−	24.2487i	0.514998	−	0.892003i	−0.484850	−	0.874597i	$-0.661126\pi$
$739$	14.0000	−	24.2487i	0.514998	−	0.892003i	0.999849	−	0.0174060i	$-0.00554079\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$	6.00000	+	10.3923i	0.219529	+	0.380235i
$748$	−8.00000			−0.292509
$749$		0			0
$750$	1.00000			0.0365148
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	0.682341	−	0.731034i	$-0.260962\pi$
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	−0.974265	+	0.225407i	$0.927629\pi$
$752$		0			0
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	−2.00000	−	3.46410i	−0.0728357	−	0.126155i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$	−16.0000	+	27.7128i	−0.580763	+	1.00591i
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	0.761057	−	0.648686i	$-0.224681\pi$
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	−0.942306	+	0.334752i	$0.891348\pi$
$762$	−16.0000			−0.579619
$763$		0			0
$764$	−16.0000			−0.578860
$765$	−1.00000	−	1.73205i	−0.0361551	−	0.0626224i
$766$	−8.00000	+	13.8564i	−0.289052	+	0.500652i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	13.0000	−	22.5167i	0.467578	−	0.809868i	−0.531736	−	0.846910i	$-0.678460\pi$
$773$	13.0000	−	22.5167i	0.467578	−	0.809868i	0.999314	+	0.0370420i	$0.0117935\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$		0			0
$776$	2.00000			0.0717958
$777$		0			0
$778$	−26.0000			−0.932145
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$	1.00000	−	1.73205i	0.0358057	−	0.0620174i
$781$	−16.0000	+	27.7128i	−0.572525	+	0.991642i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	−18.0000			−0.642448
$786$	−10.0000	−	17.3205i	−0.356688	−	0.617802i
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	−0.987367	−	0.158450i	$-0.949350\pi$
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	0.630905	+	0.775860i	$0.282684\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$	−4.00000	−	6.92820i	−0.142404	−	0.246651i
$790$	16.0000			0.569254
$791$		0			0
$792$	−4.00000			−0.142134
$793$	14.0000	+	24.2487i	0.497155	+	0.861097i
$794$	−15.0000	+	25.9808i	−0.532330	+	0.922023i
$795$	5.00000	−	8.66025i	0.177332	−	0.307148i
$796$	12.0000	+	20.7846i	0.425329	+	0.736691i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−5.00000	+	8.66025i	−0.176666	+	0.305995i
$802$	7.00000	−	12.1244i	0.247179	−	0.428126i
$803$	20.0000	+	34.6410i	0.705785	+	1.22245i
$804$	−12.0000			−0.423207
$805$		0			0
$806$		0			0
$807$	9.00000	+	15.5885i	0.316815	+	0.548740i
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	11.0000	−	19.0526i	0.386739	−	0.669852i	−0.605269	−	0.796021i	$-0.706935\pi$
$809$	11.0000	−	19.0526i	0.386739	−	0.669852i	0.992009	+	0.126168i	$0.0402680\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	−10.0000	+	17.3205i	−0.350285	+	0.606711i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	−38.0000			−1.32864
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	0.607714	−	0.794156i	$-0.292087\pi$
$821$	−11.0000	−	19.0526i	−0.383903	−	0.664939i	−0.991616	+	0.129217i	$0.958754\pi$
$822$	−5.00000	+	8.66025i	−0.174395	+	0.302061i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$	−4.00000			−0.139262
$826$		0			0
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$	4.00000	+	6.92820i	0.139010	+	0.240772i
$829$	9.00000	−	15.5885i	0.312583	−	0.541409i	−0.666338	−	0.745650i	$-0.732139\pi$
$829$	9.00000	−	15.5885i	0.312583	−	0.541409i	0.978921	+	0.204240i	$0.0654725\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	−11.0000	−	19.0526i	−0.381586	−	0.660926i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	−4.00000			−0.138509
$835$	4.00000	+	6.92820i	0.138426	+	0.239760i
$836$	8.00000	−	13.8564i	0.276686	−	0.479234i
$837$		0			0
$838$	−10.0000	−	17.3205i	−0.345444	−	0.598327i
$839$	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
$841$	−25.0000			−0.862069
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$	−10.0000			−0.343401
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$	−1.00000	+	1.73205i	−0.0342997	+	0.0594089i
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$	4.00000	+	6.92820i	0.137038	+	0.237356i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	−0.614687	−	0.788771i	$-0.710717\pi$
$857$	11.0000	−	19.0526i	0.375753	−	0.650823i	0.990439	+	0.137948i	$0.0440508\pi$
$858$	−4.00000	+	6.92820i	−0.136558	+	0.236525i
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	−4.00000			−0.136399
$861$		0			0
$862$		0			0
$863$	−16.0000	−	27.7128i	−0.544646	−	0.943355i	−0.998629	−	0.0523446i	$-0.983331\pi$
$863$	−16.0000	−	27.7128i	−0.544646	−	0.943355i	0.453983	−	0.891010i	$-0.350003\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	−13.0000			−0.441503
$868$		0			0
$869$	−64.0000			−2.17105
$870$	1.00000	+	1.73205i	0.0339032	+	0.0587220i
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	−32.0000			−1.08242
$875$		0			0
$876$	10.0000			0.337869
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	2.00000	+	3.46410i	0.0672673	+	0.116510i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	18.0000	−	31.1769i	0.604722	−	1.04741i
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$	6.00000			0.201347
$889$		0			0
$890$	10.0000			0.335201
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$		0			0
$894$	5.00000	+	8.66025i	0.167225	+	0.289642i
$895$	4.00000			0.133705
$896$		0			0
$897$	16.0000			0.534224
$898$	−1.00000	−	1.73205i	−0.0333704	−	0.0577993i
$899$		0			0
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$	24.0000			0.799113
$903$		0			0
$904$	18.0000			0.598671
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$	6.00000			0.199007
$910$		0			0
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−24.0000	+	41.5692i	−0.794284	+	1.37574i
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$	−7.00000	−	12.1244i	−0.231413	−	0.400819i
$916$	−10.0000			−0.330409
$917$		0			0
$918$	2.00000			0.0660098
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	0.924427	−	0.381358i	$-0.124544\pi$
$919$	4.00000	+	6.92820i	0.131948	+	0.228540i	−0.792480	+	0.609898i	$0.791210\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$	−10.0000	+	17.3205i	−0.329511	+	0.570730i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$	16.0000			0.526646
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	0.957708	−	0.287742i	$-0.0929044\pi$
$929$	7.00000	+	12.1244i	0.229663	+	0.397787i	−0.728046	+	0.685529i	$0.759571\pi$
$930$		0			0
$931$		0			0
$932$	−22.0000			−0.720634
$933$	4.00000	+	6.92820i	0.130954	+	0.226819i
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	10.0000			0.326686			0.163343	−	0.986569i	$-0.447772\pi$
$937$	10.0000			0.326686			0.163343	+	0.986569i	$0.447772\pi$
$938$		0			0
$939$	−6.00000			−0.195803
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$	9.00000	−	15.5885i	0.293236	−	0.507899i
$943$	−24.0000	−	41.5692i	−0.781548	−	1.35368i
$944$	12.0000			0.390567
$945$		0			0
$946$	16.0000			0.520205
$947$	−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	$-0.486999\pi$
$948$	−8.00000	+	13.8564i	−0.259828	+	0.450035i
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$	5.00000	+	8.66025i	0.161881	+	0.280386i
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$		0			0
$957$	−4.00000	−	6.92820i	−0.129302	−	0.223957i
$958$	32.0000			1.03387
$959$		0			0
$960$	1.00000			0.0322749
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	6.00000	−	10.3923i	0.193448	−	0.335061i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	7.00000	+	12.1244i	0.225455	+	0.390499i
$965$	2.00000			0.0643823
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$	−4.00000	+	6.92820i	−0.128499	+	0.222566i
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	0.549058	−	0.835784i	$-0.314987\pi$
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	−0.998339	+	0.0576061i	$0.981653\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	−8.00000			−0.256337
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$	−7.00000	+	12.1244i	−0.224065	+	0.388091i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	−10.0000	−	17.3205i	−0.319765	−	0.553849i
$979$	−40.0000			−1.27841
$980$		0			0
$981$	14.0000			0.446986
$982$	18.0000	+	31.1769i	0.574403	+	0.994895i
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	−4.00000			−0.127386
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−16.0000	−	27.7128i	−0.508770	−	0.881216i
$990$	2.00000	−	3.46410i	0.0635642	−	0.110096i
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$		0			0
$993$	12.0000			0.380808
$994$		0			0
$995$	−24.0000			−0.760851
$996$	6.00000	+	10.3923i	0.190117	+	0.329293i
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	−0.985961	−	0.166978i	$-0.946599\pi$
$997$	−11.0000	+	19.0526i	−0.348373	+	0.603401i	0.637587	+	0.770378i	$0.279933\pi$
$998$	6.00000	−	10.3923i	0.189927	−	0.328963i
$999$	−3.00000	−	5.19615i	−0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.a.361.1		2
7.2	even	3	inner	1470.2.i.a.961.1		2
7.3	odd	6		1470.2.a.j.1.1		1
7.4	even	3		210.2.a.e.1.1	✓	1
7.5	odd	6		1470.2.i.j.961.1		2
7.6	odd	2		1470.2.i.j.361.1		2
21.11	odd	6		630.2.a.a.1.1		1
21.17	even	6		4410.2.a.t.1.1		1
28.11	odd	6		1680.2.a.j.1.1		1
35.4	even	6		1050.2.a.c.1.1		1
35.18	odd	12		1050.2.g.g.799.1		2
35.24	odd	6		7350.2.a.w.1.1		1
35.32	odd	12		1050.2.g.g.799.2		2
56.11	odd	6		6720.2.a.bq.1.1		1
56.53	even	6		6720.2.a.j.1.1		1
84.11	even	6		5040.2.a.k.1.1		1
105.32	even	12		3150.2.g.q.2899.1		2
105.53	even	12		3150.2.g.q.2899.2		2
105.74	odd	6		3150.2.a.bp.1.1		1
140.39	odd	6		8400.2.a.ce.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.e.1.1	✓	1	7.4	even	3
630.2.a.a.1.1		1	21.11	odd	6
1050.2.a.c.1.1		1	35.4	even	6
1050.2.g.g.799.1		2	35.18	odd	12
1050.2.g.g.799.2		2	35.32	odd	12
1470.2.a.j.1.1		1	7.3	odd	6
1470.2.i.a.361.1		2	1.1	even	1	trivial
1470.2.i.a.961.1		2	7.2	even	3	inner
1470.2.i.j.361.1		2	7.6	odd	2
1470.2.i.j.961.1		2	7.5	odd	6
1680.2.a.j.1.1		1	28.11	odd	6
3150.2.a.bp.1.1		1	105.74	odd	6
3150.2.g.q.2899.1		2	105.32	even	12
3150.2.g.q.2899.2		2	105.53	even	12
4410.2.a.t.1.1		1	21.17	even	6
5040.2.a.k.1.1		1	84.11	even	6
6720.2.a.j.1.1		1	56.53	even	6
6720.2.a.bq.1.1		1	56.11	odd	6
7350.2.a.w.1.1		1	35.24	odd	6
8400.2.a.ce.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} +(-0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-0.500000 - 0.866025i) q^{12} -2.00000 q^{13} +1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} -4.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.500000 + 0.866025i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(1.00000 - 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{46} +1.00000 q^{48} +1.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{52} +(5.00000 - 8.66025i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{55} +4.00000 q^{57} +(1.00000 + 1.73205i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{69} -8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-5.00000 + 8.66025i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.00000 - 3.46410i) q^{88} +(-5.00000 - 8.66025i) q^{89} +1.00000 q^{90} -8.00000 q^{92} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{5} + 2 q^{6} + 2 q^{8} - q^{9} - q^{10} + 4 q^{11} - q^{12} - 4 q^{13} + 2 q^{15} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + 2 q^{20} - 8 q^{22} + 8 q^{23} - q^{24}+ \cdots - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^5 + 2 * q^6 + 2 * q^8 - q^9 - q^10 + 4 * q^11 - q^12 - 4 * q^13 + 2 * q^15 - q^16 - 2 * q^17 - q^18 - 4 * q^19 + 2 * q^20 - 8 * q^22 + 8 * q^23 - q^24 - q^25 + 2 * q^26 + 2 * q^27 - 4 * q^29 - q^30 - q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 - q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - q^45 + 8 * q^46 + 2 * q^48 + 2 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 - q^54 - 8 * q^55 + 8 * q^57 + 2 * q^58 - 12 * q^59 - q^60 - 14 * q^61 + 2 * q^64 + 2 * q^65 + 4 * q^66 + 12 * q^67 - 2 * q^68 - 16 * q^69 - 16 * q^71 - q^72 - 10 * q^73 - 6 * q^74 - q^75 + 8 * q^76 - 4 * q^78 - 16 * q^79 - q^80 - q^81 + 6 * q^82 - 24 * q^83 + 4 * q^85 + 4 * q^86 + 2 * q^87 + 4 * q^88 - 10 * q^89 + 2 * q^90 - 16 * q^92 - 4 * q^95 - q^96 + 4 * q^97 - 8 * q^99

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