LMFDB - Embedded newform 1470.2.i.o.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1470.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
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.o.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} - 12 q^{29} - q^{30} - 8 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} - 2 q^{37} - 4 q^{38} - 2 q^{39} - q^{40} - 12 q^{41} - 8 q^{43} + q^{45} + 2 q^{48} - 2 q^{50} - 6 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} - 8 q^{57} - 6 q^{58} + q^{60} + 10 q^{61} - 16 q^{62} + 2 q^{64} + 2 q^{65} + 4 q^{67} - 6 q^{68} + q^{72} - 2 q^{73} + 2 q^{74} - q^{75} - 8 q^{76} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} - 12 q^{85} - 4 q^{86} + 6 q^{87} - 18 q^{89} + 2 q^{90} - 8 q^{93} - 4 q^{95} + q^{96} + 4 q^{97}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^8 - q^9 - q^10 - q^12 + 4 * q^13 - 2 * q^15 - q^16 - 6 * q^17 + q^18 + 4 * q^19 - 2 * q^20 + q^24 - q^25 + 2 * q^26 + 2 * q^27 - 12 * q^29 - q^30 - 8 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 4 * q^38 - 2 * q^39 - q^40 - 12 * q^41 - 8 * q^43 + q^45 + 2 * q^48 - 2 * q^50 - 6 * q^51 - 2 * q^52 + 6 * q^53 + q^54 - 8 * q^57 - 6 * q^58 + q^60 + 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^67 - 6 * q^68 + q^72 - 2 * q^73 + 2 * q^74 - q^75 - 8 * q^76 - 4 * q^78 - 8 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 - 12 * q^85 - 4 * q^86 + 6 * q^87 - 18 * q^89 + 2 * q^90 - 8 * q^93 - 4 * q^95 + q^96 + 4 * q^97

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
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−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	$0.598656\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	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	$-0.0544754\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	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	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.217354	+	0.976093i	$0.569742\pi$
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.736644	+	0.676280i	$0.763591\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$		0			0
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$		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
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$		0			0
$119$		0			0
$120$	1.00000			0.0912871
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−5.00000	−	8.66025i	−0.452679	−	0.784063i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	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
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$	4.00000			0.345547
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		0			0
$139$	−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
$142$		0			0
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	2.00000			0.164399
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	6.00000			0.485071
$154$		0			0
$155$	−8.00000			−0.642575
$156$	−1.00000	+	1.73205i	−0.0800641	+	0.138675i
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−3.00000	+	5.19615i	−0.230089	+	0.398527i
$171$	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	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$		0			0
$177$		0			0
$178$	9.00000	+	15.5885i	0.674579	+	1.16840i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	1.00000	+	1.73205i	0.0735215	+	0.127343i
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	−4.00000			−0.290191
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.00454614	−	0.999990i	$-0.498553\pi$
$191$	12.0000	−	20.7846i	0.868290	−	1.50392i	0.863743	−	0.503932i	$-0.168114\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	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	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$	−18.0000			−1.26648
$203$		0			0
$204$	6.00000			0.420084
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$		0			0
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$		0			0
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−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
$218$	10.0000			0.677285
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	1.00000	−	1.73205i	0.0671156	−	0.116248i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	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	$0.702957\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$		0			0
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$	−5.50000	−	9.52628i	−0.353553	−	0.612372i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−10.0000			−0.640184
$245$		0			0
$246$	6.00000			0.382546
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	3.00000	+	5.19615i	0.187867	+	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$	−2.00000			−0.124035
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	18.0000			1.10158
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	6.00000			0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	8.00000			0.478947
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$		0			0
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$		0			0
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$	−1.00000	−	1.73205i	−0.0586210	−	0.101535i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$		0			0
$300$	1.00000			0.0577350
$301$		0			0
$302$	−8.00000			−0.460348
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	−0.892903	−	0.450250i	$-0.851335\pi$
$313$	−1.00000	+	1.73205i	−0.0565233	+	0.0979013i	0.836379	+	0.548151i	$0.184668\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$		0			0
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−12.0000			−0.669775
$322$		0			0
$323$	−24.0000			−1.33540
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	5.00000	−	8.66025i	0.276501	−	0.478913i
$328$	6.00000			0.331295
$329$		0			0
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$	4.00000			0.218543
$336$		0			0
$337$	26.0000			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$		0			0
$342$	4.00000			0.216295
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	9.00000	+	15.5885i	0.483843	+	0.838041i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$		0			0
$356$	18.0000			0.953998
$357$		0			0
$358$	−24.0000			−1.26844
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	−2.00000			−0.104685
$366$	−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	$0.572483\pi$
$368$		0			0
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$	2.00000			0.103975
$371$		0			0
$372$	8.00000			0.414781
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	0.303902	+	0.952703i	$0.401711\pi$
$373$	−13.0000	+	22.5167i	−0.673114	+	1.16587i	−0.977016	+	0.213165i	$0.931623\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	−4.00000			−0.205466			−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000			−0.205466			−0.102733	+	0.994709i	$0.532759\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$	−10.0000	−	17.3205i	−0.512316	−	0.887357i
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	22.0000			1.11977
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$		0			0
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	1.00000			0.0500000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−2.00000	−	3.46410i	−0.0997509	−	0.172774i
$403$	−8.00000	−	13.8564i	−0.398508	−	0.690237i
$404$	−9.00000	+	15.5885i	−0.447767	+	0.775555i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$		0			0
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	−0.984803	−	0.173675i	$-0.944436\pi$
$409$	−13.0000	−	22.5167i	−0.642809	−	1.11338i	0.341994	−	0.939702i	$-0.388898\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	−4.00000			−0.197066
$413$		0			0
$414$		0			0
$415$	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
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$		0			0
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.00000	+	3.46410i	0.0964486	+	0.167054i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$		0			0
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	10.0000	−	17.3205i	0.473514	−	0.820150i
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$		0			0
$452$	9.00000	+	15.5885i	0.423324	+	0.733219i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	12.0000			0.563188
$455$		0			0
$456$	4.00000			0.187317
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	0.383437	+	0.923567i	$0.374740\pi$
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	−0.991551	+	0.129718i	$0.958593\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	−9.00000	−	15.5885i	−0.416917	−	0.722121i
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$		0			0
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$		0			0
$473$		0			0
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−6.00000			−0.274721
$478$	12.0000	−	20.7846i	0.548867	−	0.950666i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	−11.0000			−0.500000
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	0.986642	+	0.162905i	$0.0520863\pi$
$487$	14.0000	+	24.2487i	0.634401	+	1.09881i	−0.352241	+	0.935909i	$0.614580\pi$
$488$	−5.00000	+	8.66025i	−0.226339	+	0.392031i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$	−12.0000			−0.537733
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$		0			0
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	−18.0000			−0.800989
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−10.0000	−	17.3205i	−0.443678	−	0.768473i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$	6.00000			0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	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
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	−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	$0.310721\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.0000	+	41.5692i	−1.04546	+	1.81078i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$		0			0
$532$		0			0
$533$	−12.0000			−0.519778
$534$	9.00000	−	15.5885i	0.389468	−	0.674579i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	6.00000			0.258678
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	−7.00000	−	12.1244i	−0.300399	−	0.520306i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	10.0000			0.428353
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	5.00000	+	8.66025i	0.213395	+	0.369611i
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		0			0
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	1.00000	−	1.73205i	0.0424476	−	0.0735215i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	4.00000	−	6.92820i	0.169334	−	0.293294i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	−9.00000	+	15.5885i	−0.378633	+	0.655811i
$566$	28.0000			1.17693
$567$		0			0
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	0.844459	−	0.535620i	$-0.179922\pi$
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	−0.886090	+	0.463513i	$0.846589\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	11.0000	−	19.0526i	0.457144	−	0.791797i
$580$	6.00000			0.249136
$581$		0			0
$582$	−2.00000			−0.0829027
$583$		0			0
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−32.0000			−1.31854
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	0.374236	+	0.927333i	$0.377905\pi$
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	−0.822578	−	0.568652i	$-0.807465\pi$
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	0.903756	+	0.428048i	$0.140799\pi$
$608$	4.00000			0.162221
$609$		0			0
$610$	−10.0000			−0.404888
$611$		0			0
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$	6.00000			0.241943
$616$		0			0
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$	−2.00000	+	3.46410i	−0.0804518	+	0.139347i
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.846566	−	0.532284i	$-0.821334\pi$
$619$	−22.0000	−	38.1051i	−0.884255	−	1.53157i	−0.0376891	−	0.999290i	$-0.512000\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.00000	+	1.73205i	0.0399680	+	0.0692267i
$627$		0			0
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	12.0000			0.478471
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	10.0000	−	17.3205i	0.396838	−	0.687343i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		0			0
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	−5.00000	−	8.66025i	−0.195515	−	0.338643i
$655$		0			0
$656$	3.00000	−	5.19615i	0.117130	−	0.202876i
$657$	2.00000			0.0780274
$658$		0			0
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	−14.0000	−	24.2487i	−0.544125	−	0.942453i
$663$	−6.00000	+	10.3923i	−0.233021	+	0.403604i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	−2.00000			−0.0774984
$667$		0			0
$668$		0			0
$669$	−10.0000	−	17.3205i	−0.386622	−	0.669650i
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$		0			0
$672$		0			0
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	13.0000	−	22.5167i	0.500741	−	0.867309i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	18.0000			0.691286
$679$		0			0
$680$	6.00000			0.230089
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$		0			0
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	−6.00000			−0.229248
$686$		0			0
$687$	−10.0000			−0.381524
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−2.00000	+	3.46410i	−0.0758643	+	0.131401i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	−18.0000			−0.680823
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	4.00000	+	6.92820i	0.150863	+	0.261302i
$704$		0			0
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$	−4.00000	−	6.92820i	−0.150012	−	0.259828i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$	−12.0000	−	20.7846i	−0.448148	−	0.776215i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	3.00000			0.111648
$723$	−1.00000	+	1.73205i	−0.0371904	+	0.0644157i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.00000	+	1.73205i	−0.0370117	+	0.0641061i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	5.00000	+	8.66025i	0.184805	+	0.320092i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.731072	+	0.682300i	$0.239020\pi$
$739$	26.0000	+	45.0333i	0.956425	+	1.65658i	0.225354	+	0.974277i	$0.427646\pi$
$740$	1.00000	−	1.73205i	0.0367607	−	0.0636715i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$		0			0
$750$	1.00000			0.0365148
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$		0			0
$753$	12.0000	+	20.7846i	0.437304	+	0.757433i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−8.00000			−0.291150
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−2.00000	+	3.46410i	−0.0726433	+	0.125822i
$759$		0			0
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	−20.0000			−0.724524
$763$		0			0
$764$	−24.0000			−0.868290
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$		0			0
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	2.00000			0.0721218			0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000			0.0721218			0.0360609	+	0.999350i	$0.488519\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	11.0000	−	19.0526i	0.395899	−	0.685717i
$773$	−21.0000	−	36.3731i	−0.755318	−	1.30825i	−0.945216	−	0.326445i	$-0.894149\pi$
$773$	−21.0000	−	36.3731i	−0.755318	−	1.30825i	0.189899	−	0.981804i	$-0.439184\pi$
$774$	−2.00000	−	3.46410i	−0.0718885	−	0.124515i
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	6.00000			0.215110
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$	1.00000	+	1.73205i	0.0358057	+	0.0620174i
$781$		0			0
$782$		0			0
$783$	−6.00000			−0.214423
$784$		0			0
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$		0			0
$790$	8.00000			0.284627
$791$		0			0
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−16.0000			−0.563576
$807$	3.00000	−	5.19615i	0.105605	−	0.182913i
$808$	9.00000	+	15.5885i	0.316619	+	0.548400i
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.746968	+	0.664860i	$0.231509\pi$
$809$	27.0000	+	46.7654i	0.949269	+	1.64418i	0.202301	+	0.979323i	$0.435158\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	−26.0000			−0.909069
$819$		0			0
$820$	6.00000			0.209529
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	3.00000	+	5.19615i	0.104637	+	0.181237i
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	0.637419	−	0.770517i	$-0.280002\pi$
$823$	−10.0000	−	17.3205i	−0.348578	−	0.603755i	−0.985997	+	0.166762i	$0.946669\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	2.00000			0.0693375
$833$		0			0
$834$	4.00000			0.138509
$835$		0			0
$836$		0			0
$837$	−4.00000	−	6.92820i	−0.138260	−	0.239474i
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	−9.00000	−	15.5885i	−0.309976	−	0.536895i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$	−6.00000			−0.206041
$849$	14.0000	−	24.2487i	0.480479	−	0.832214i
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$		0			0
$852$		0			0
$853$	−46.0000			−1.57501			−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−46.0000			−1.57501			−0.787505	+	0.616308i	$0.788628\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	0.977800	−	0.209539i	$-0.0671963\pi$
$857$	9.00000	+	15.5885i	0.307434	+	0.532492i	−0.670366	+	0.742030i	$0.733863\pi$
$858$		0			0
$859$	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	$0.144929\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	−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
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	19.0000			0.645274
$868$		0			0
$869$		0			0
$870$	3.00000	−	5.19615i	0.101710	−	0.176166i
$871$	4.00000	+	6.92820i	0.135535	+	0.234753i
$872$	−5.00000	−	8.66025i	−0.169321	−	0.293273i
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$		0			0
$875$		0			0
$876$	2.00000			0.0675737
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	−0.882415	−	0.470471i	$-0.844084\pi$
$877$	−1.00000	+	1.73205i	−0.0337676	+	0.0584872i	0.848648	+	0.528958i	$0.177417\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$		0			0
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	6.00000	+	10.3923i	0.201574	+	0.349136i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	−2.00000			−0.0671156
$889$		0			0
$890$	18.0000			0.603361
$891$		0			0
$892$	−10.0000	−	17.3205i	−0.334825	−	0.579934i
$893$		0			0
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	−24.0000			−0.802232
$896$		0			0
$897$		0			0
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	18.0000			0.598671
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$	6.00000	−	10.3923i	0.199117	−	0.344881i
$909$	18.0000			0.597022
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$		0			0
$914$	13.0000	+	22.5167i	0.430002	+	0.744785i
$915$	−5.00000	+	8.66025i	−0.165295	+	0.286299i
$916$	−10.0000			−0.330409
$917$		0			0
$918$	−6.00000			−0.198030
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$		0			0
$924$		0			0
$925$	2.00000			0.0657596
$926$	−2.00000	+	3.46410i	−0.0657241	+	0.113837i
$927$	2.00000	+	3.46410i	0.0656886	+	0.113776i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$	8.00000			0.262330
$931$		0			0
$932$	−18.0000			−0.589610
$933$		0			0
$934$	−18.0000	−	31.1769i	−0.588978	−	1.02014i
$935$		0			0
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$		0			0
$939$	2.00000			0.0652675
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$	1.00000	+	1.73205i	0.0325818	+	0.0564333i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	0.409964	+	0.912102i	$0.365541\pi$
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	−0.994885	+	0.101012i	$0.967792\pi$
$948$	−4.00000	−	6.92820i	−0.129914	−	0.225018i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$	18.0000			0.583690
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	24.0000			0.775405
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	2.00000	+	3.46410i	0.0644826	+	0.111687i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−1.00000	+	1.73205i	−0.0322078	+	0.0557856i
$965$	22.0000			0.708205
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	−1.00000	−	1.73205i	−0.0321081	−	0.0556128i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$	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
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$	−2.00000	+	3.46410i	−0.0639529	+	0.110770i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	12.0000	−	20.7846i	0.382935	−	0.663264i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	−3.00000	+	5.19615i	−0.0955879	+	0.165563i
$986$	36.0000			1.14647
$987$		0			0
$988$	−8.00000			−0.254514
$989$		0			0
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	−28.0000			−0.888553
$994$		0			0
$995$	−8.00000			−0.253617
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.o.961.1		2
7.2	even	3		30.2.a.a.1.1	✓	1
7.3	odd	6		1470.2.i.q.361.1		2
7.4	even	3	inner	1470.2.i.o.361.1		2
7.5	odd	6		1470.2.a.d.1.1		1
7.6	odd	2		1470.2.i.q.961.1		2
21.2	odd	6		90.2.a.c.1.1		1
21.5	even	6		4410.2.a.z.1.1		1
28.23	odd	6		240.2.a.b.1.1		1
35.2	odd	12		150.2.c.a.49.1		2
35.9	even	6		150.2.a.b.1.1		1
35.19	odd	6		7350.2.a.ct.1.1		1
35.23	odd	12		150.2.c.a.49.2		2
56.37	even	6		960.2.a.e.1.1		1
56.51	odd	6		960.2.a.p.1.1		1
63.2	odd	6		810.2.e.b.271.1		2
63.16	even	3		810.2.e.l.271.1		2
63.23	odd	6		810.2.e.b.541.1		2
63.58	even	3		810.2.e.l.541.1		2
77.65	odd	6		3630.2.a.w.1.1		1
84.23	even	6		720.2.a.j.1.1		1
91.44	odd	12		5070.2.b.k.1351.2		2
91.51	even	6		5070.2.a.w.1.1		1
91.86	odd	12		5070.2.b.k.1351.1		2
105.2	even	12		450.2.c.b.199.2		2
105.23	even	12		450.2.c.b.199.1		2
105.44	odd	6		450.2.a.d.1.1		1
112.37	even	12		3840.2.k.y.1921.1		2
112.51	odd	12		3840.2.k.f.1921.1		2
112.93	even	12		3840.2.k.y.1921.2		2
112.107	odd	12		3840.2.k.f.1921.2		2
119.16	even	6		8670.2.a.g.1.1		1
140.23	even	12		1200.2.f.e.49.1		2
140.79	odd	6		1200.2.a.k.1.1		1
140.107	even	12		1200.2.f.e.49.2		2
168.107	even	6		2880.2.a.q.1.1		1
168.149	odd	6		2880.2.a.a.1.1		1
280.37	odd	12		4800.2.f.p.3649.2		2
280.93	odd	12		4800.2.f.p.3649.1		2
280.107	even	12		4800.2.f.w.3649.1		2
280.149	even	6		4800.2.a.cq.1.1		1
280.163	even	12		4800.2.f.w.3649.2		2
280.219	odd	6		4800.2.a.d.1.1		1
420.23	odd	12		3600.2.f.i.2449.1		2
420.107	odd	12		3600.2.f.i.2449.2		2
420.359	even	6		3600.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.a.a.1.1	✓	1	7.2	even	3
90.2.a.c.1.1		1	21.2	odd	6
150.2.a.b.1.1		1	35.9	even	6
150.2.c.a.49.1		2	35.2	odd	12
150.2.c.a.49.2		2	35.23	odd	12
240.2.a.b.1.1		1	28.23	odd	6
450.2.a.d.1.1		1	105.44	odd	6
450.2.c.b.199.1		2	105.23	even	12
450.2.c.b.199.2		2	105.2	even	12
720.2.a.j.1.1		1	84.23	even	6
810.2.e.b.271.1		2	63.2	odd	6
810.2.e.b.541.1		2	63.23	odd	6
810.2.e.l.271.1		2	63.16	even	3
810.2.e.l.541.1		2	63.58	even	3
960.2.a.e.1.1		1	56.37	even	6
960.2.a.p.1.1		1	56.51	odd	6
1200.2.a.k.1.1		1	140.79	odd	6
1200.2.f.e.49.1		2	140.23	even	12
1200.2.f.e.49.2		2	140.107	even	12
1470.2.a.d.1.1		1	7.5	odd	6
1470.2.i.o.361.1		2	7.4	even	3	inner
1470.2.i.o.961.1		2	1.1	even	1	trivial
1470.2.i.q.361.1		2	7.3	odd	6
1470.2.i.q.961.1		2	7.6	odd	2
2880.2.a.a.1.1		1	168.149	odd	6
2880.2.a.q.1.1		1	168.107	even	6
3600.2.a.f.1.1		1	420.359	even	6
3600.2.f.i.2449.1		2	420.23	odd	12
3600.2.f.i.2449.2		2	420.107	odd	12
3630.2.a.w.1.1		1	77.65	odd	6
3840.2.k.f.1921.1		2	112.51	odd	12
3840.2.k.f.1921.2		2	112.107	odd	12
3840.2.k.y.1921.1		2	112.37	even	12
3840.2.k.y.1921.2		2	112.93	even	12
4410.2.a.z.1.1		1	21.5	even	6
4800.2.a.d.1.1		1	280.219	odd	6
4800.2.a.cq.1.1		1	280.149	even	6
4800.2.f.p.3649.1		2	280.93	odd	12
4800.2.f.p.3649.2		2	280.37	odd	12
4800.2.f.w.3649.1		2	280.107	even	12
4800.2.f.w.3649.2		2	280.163	even	12
5070.2.a.w.1.1		1	91.51	even	6
5070.2.b.k.1351.1		2	91.86	odd	12
5070.2.b.k.1351.2		2	91.44	odd	12
7350.2.a.ct.1.1		1	35.19	odd	6
8670.2.a.g.1.1		1	119.16	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(-0.500000 + 0.866025i) q^{40} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +1.00000 q^{48} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(0.500000 + 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} -6.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +(-9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-4.00000 + 6.92820i) q^{93} +(-2.00000 - 3.46410i) q^{95} +(0.500000 - 0.866025i) q^{96} +2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} - 2 q^{8} - q^{9} - q^{10} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - 2 q^{20} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} - 12 q^{29} - q^{30} - 8 q^{31} + q^{32} - 12 q^{34} + 2 q^{36} - 2 q^{37} - 4 q^{38} - 2 q^{39} - q^{40} - 12 q^{41} - 8 q^{43} + q^{45} + 2 q^{48} - 2 q^{50} - 6 q^{51} - 2 q^{52} + 6 q^{53} + q^{54} - 8 q^{57} - 6 q^{58} + q^{60} + 10 q^{61} - 16 q^{62} + 2 q^{64} + 2 q^{65} + 4 q^{67} - 6 q^{68} + q^{72} - 2 q^{73} + 2 q^{74} - q^{75} - 8 q^{76} - 4 q^{78} - 8 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} - 12 q^{85} - 4 q^{86} + 6 q^{87} - 18 q^{89} + 2 q^{90} - 8 q^{93} - 4 q^{95} + q^{96} + 4 q^{97}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 - 2 * q^8 - q^9 - q^10 - q^12 + 4 * q^13 - 2 * q^15 - q^16 - 6 * q^17 + q^18 + 4 * q^19 - 2 * q^20 + q^24 - q^25 + 2 * q^26 + 2 * q^27 - 12 * q^29 - q^30 - 8 * q^31 + q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 - 4 * q^38 - 2 * q^39 - q^40 - 12 * q^41 - 8 * q^43 + q^45 + 2 * q^48 - 2 * q^50 - 6 * q^51 - 2 * q^52 + 6 * q^53 + q^54 - 8 * q^57 - 6 * q^58 + q^60 + 10 * q^61 - 16 * q^62 + 2 * q^64 + 2 * q^65 + 4 * q^67 - 6 * q^68 + q^72 - 2 * q^73 + 2 * q^74 - q^75 - 8 * q^76 - 4 * q^78 - 8 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 - 12 * q^85 - 4 * q^86 + 6 * q^87 - 18 * q^89 + 2 * q^90 - 8 * q^93 - 4 * q^95 + q^96 + 4 * q^97

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