LMFDB - Embedded newform 1470.2.i.d.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.d.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -1.00000 q^{20} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +6.00000 q^{41} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(6.00000 + 10.3923i) q^{47} +1.00000 q^{48} +1.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(8.00000 + 13.8564i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +12.0000 q^{83} +6.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} -1.00000 q^{90} +(2.00000 + 3.46410i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{31} - q^{32} - 12 q^{34} + 2 q^{36} - 2 q^{37} + 4 q^{38} - 2 q^{39} + q^{40} + 12 q^{41} + 16 q^{43} + q^{45} + 12 q^{47} + 2 q^{48} + 2 q^{50} + 6 q^{51} - 2 q^{52} - 6 q^{53} - q^{54} - 8 q^{57} + 6 q^{58} + 12 q^{59} + q^{60} - 2 q^{61} - 8 q^{62} + 2 q^{64} + 2 q^{65} - 8 q^{67} + 6 q^{68} - q^{72} - 14 q^{73} - 2 q^{74} - q^{75} - 8 q^{76} + 4 q^{78} + 16 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} + 12 q^{85} - 8 q^{86} + 6 q^{87} - 6 q^{89} - 2 q^{90} + 4 q^{93} + 12 q^{94} - 4 q^{95} - q^{96} + 28 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 + 4 * q^31 - q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 + 4 * q^38 - 2 * q^39 + q^40 + 12 * q^41 + 16 * q^43 + q^45 + 12 * q^47 + 2 * q^48 + 2 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - q^54 - 8 * q^57 + 6 * q^58 + 12 * q^59 + q^60 - 2 * q^61 - 8 * q^62 + 2 * q^64 + 2 * q^65 - 8 * q^67 + 6 * q^68 - q^72 - 14 * q^73 - 2 * q^74 - q^75 - 8 * q^76 + 4 * q^78 + 16 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 + 12 * q^85 - 8 * q^86 + 6 * q^87 - 6 * q^89 - 2 * q^90 + 4 * q^93 + 12 * q^94 - 4 * q^95 - q^96 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−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	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−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
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−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	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	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	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$	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	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	−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
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	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
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	−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
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$	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
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	3.00000	−	5.19615i	0.297044	−	0.514496i
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	−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	$0.932756\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$		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
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−1.00000	−	1.73205i	−0.0924500	−	0.160128i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−1.00000	+	1.73205i	−0.0905357	+	0.156813i
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$	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	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		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
$141$	−12.0000			−1.01058
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$	14.0000			1.15865
$147$		0			0
$148$	2.00000			0.164399
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−6.00000			−0.485071
$154$		0			0
$155$	4.00000			0.321288
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	8.00000	−	13.8564i	0.636446	−	1.10236i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−3.00000	−	5.19615i	−0.230089	−	0.398527i
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$		0			0
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$		0			0
$188$	−12.0000			−0.875190
$189$		0			0
$190$	4.00000			0.290191
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$	−6.00000			−0.422159
$203$		0			0
$204$	−6.00000			−0.420084
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	8.00000	−	13.8564i	0.557386	−	0.965422i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	−28.0000			−1.92760			−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000			−1.92760			−0.963800	+	0.266627i	$0.914091\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$	1.00000			0.0680414
$217$		0			0
$218$	14.0000			0.948200
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	−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
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	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
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.00000			0.128037
$245$		0			0
$246$	6.00000			0.382546
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−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
$253$		0			0
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$	−3.00000	+	5.19615i	−0.187867	+	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	8.00000			0.498058
$259$		0			0
$260$	−2.00000			−0.124035
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$	6.00000			0.367194
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	0.449622	+	0.893219i	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−6.00000			−0.362473
$275$		0			0
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$		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
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	−7.00000	−	12.1244i	−0.409644	−	0.709524i
$293$	−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
$295$	12.0000			0.698667
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$		0			0
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$	1.00000			0.0577350
$301$		0			0
$302$	−16.0000			−0.920697
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	−0.887788	−	0.460252i	$-0.847759\pi$
$317$	−15.0000	−	25.9808i	−0.842484	−	1.45922i	0.0453045	−	0.998973i	$-0.485574\pi$
$318$	−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
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$	−7.00000	−	12.1244i	−0.387101	−	0.670478i
$328$	6.00000			0.331295
$329$		0			0
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−1.00000	+	1.73205i	−0.0547997	+	0.0949158i
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$	−8.00000			−0.437087
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	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
$344$	8.00000			0.431331
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	6.00000	−	10.3923i	0.318896	−	0.552345i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	−14.0000			−0.732793
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$		0			0
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$	−2.00000			−0.103975
$371$		0			0
$372$	−4.00000			−0.207390
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	−12.0000			−0.618031
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$		0			0
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−22.0000			−1.11977
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−7.00000	+	12.1244i	−0.355371	+	0.615521i
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$	1.00000	+	1.73205i	0.0506370	+	0.0877058i
$391$		0			0
$392$		0			0
$393$	12.0000			0.605320
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−8.00000	+	13.8564i	−0.402524	+	0.697191i
$396$		0			0
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−4.00000			−0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	−4.00000	+	6.92820i	−0.199502	+	0.345547i
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$		0			0
$408$	3.00000	+	5.19615i	0.148522	+	0.257248i
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	3.00000	+	5.19615i	0.147979	+	0.256307i
$412$	−16.0000			−0.788263
$413$		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
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	14.0000	+	24.2487i	0.681509	+	1.18041i
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$	−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
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$	−7.00000	+	12.1244i	−0.334473	+	0.579324i
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	−1.00000	+	1.73205i	−0.0474579	+	0.0821995i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	18.0000			0.851371
$448$		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
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	−4.00000			−0.187317
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$	−1.00000	+	1.73205i	−0.0467269	+	0.0809334i
$459$	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
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	3.00000	+	5.19615i	0.139272	+	0.241225i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$	12.0000			0.553519
$471$	−1.00000	−	1.73205i	−0.0460776	−	0.0798087i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$		0			0
$474$	8.00000	+	13.8564i	0.367452	+	0.636446i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	26.0000			1.18427
$483$		0			0
$484$	−11.0000			−0.500000
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	−16.0000			−0.723545
$490$		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
$496$	−4.00000			−0.179605
$497$		0			0
$498$	12.0000			0.537733
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	4.50000	−	7.79423i	0.199852	−	0.346154i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$	6.00000			0.265684
$511$		0			0
$512$	1.00000			0.0441942
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$		0			0
$518$		0			0
$519$	−6.00000			−0.263371
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$		0			0
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	12.0000			0.519778
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$		0			0
$538$	18.0000			0.776035
$539$		0			0
$540$	−1.00000			−0.0430331
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$	−14.0000			−0.599694
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$		0			0
$553$		0			0
$554$	−22.0000			−0.934690
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$	2.00000	+	3.46410i	0.0846668	+	0.146647i
$559$	16.0000			0.676728
$560$		0			0
$561$		0			0
$562$	15.0000	+	25.9808i	0.632737	+	1.09593i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$	20.0000			0.840663
$567$		0			0
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	−0.257982	−	0.966150i	$-0.583058\pi$
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	0.965701	−	0.259656i	$-0.0836092\pi$
$578$	−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
$582$	14.0000			0.580319
$583$		0			0
$584$	−7.00000	+	12.1244i	−0.289662	+	0.501709i
$585$	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
$589$	16.0000			0.659269
$590$	−6.00000	−	10.3923i	−0.247016	−	0.427844i
$591$	9.00000	−	15.5885i	0.370211	−	0.641223i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	−0.869638	−	0.493689i	$-0.835648\pi$
$593$	−21.0000	−	36.3731i	−0.862367	−	1.49366i	0.00727173	−	0.999974i	$-0.497685\pi$
$594$		0			0
$595$		0			0
$596$	18.0000			0.737309
$597$	2.00000	+	3.46410i	0.0818546	+	0.141776i
$598$		0			0
$599$	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
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$	3.00000	−	5.19615i	0.121867	−	0.211079i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	−2.00000			−0.0809776
$611$	12.0000	+	20.7846i	0.485468	+	0.840855i
$612$	3.00000	−	5.19615i	0.121268	−	0.210042i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−10.0000	−	17.3205i	−0.403567	−	0.698999i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$	8.00000	+	13.8564i	0.321807	+	0.557386i
$619$	14.0000	−	24.2487i	0.562708	−	0.974638i	−0.434551	−	0.900647i	$-0.643093\pi$
$619$	14.0000	−	24.2487i	0.562708	−	0.974638i	0.997259	−	0.0739910i	$-0.0235736\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	2.00000			0.0800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	5.00000	−	8.66025i	0.199840	−	0.346133i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	8.00000	+	13.8564i	0.318223	+	0.551178i
$633$	14.0000	−	24.2487i	0.556450	−	0.963800i
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	−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
$645$	−8.00000			−0.315000
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$		0			0
$650$	2.00000			0.0784465
$651$		0			0
$652$	−16.0000			−0.626608
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	0.904345	+	0.426801i	$0.140360\pi$
$653$	21.0000	+	36.3731i	0.821794	+	1.42339i	−0.0825519	+	0.996587i	$0.526307\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	14.0000			0.546192
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	0.494337	+	0.869270i	$0.335411\pi$
$661$	−13.0000	+	22.5167i	−0.505641	+	0.875797i	−0.999979	+	0.00652642i	$0.997923\pi$
$662$	2.00000	−	3.46410i	0.0777322	−	0.134636i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	12.0000			0.465690
$665$		0			0
$666$	2.00000			0.0774984
$667$		0			0
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$		0			0
$672$		0			0
$673$	50.0000			1.92736			0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000			1.92736			0.963679	+	0.267063i	$0.0860531\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	0.995877	+	0.0907112i	$0.0289140\pi$
$677$	15.0000	+	25.9808i	0.576497	+	0.998522i	−0.419380	+	0.907811i	$0.637753\pi$
$678$	18.0000			0.691286
$679$		0			0
$680$	6.00000			0.230089
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$	2.00000	+	3.46410i	0.0764719	+	0.132453i
$685$	6.00000			0.229248
$686$		0			0
$687$	2.00000			0.0763048
$688$	−4.00000	−	6.92820i	−0.152499	−	0.264135i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$	−6.00000			−0.228086
$693$		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
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	−6.00000			−0.226941
$700$		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
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$	18.0000			0.677439
$707$		0			0
$708$	−12.0000			−0.450988
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	0.704118	−	0.710083i	$-0.251342\pi$
$709$	−7.00000	−	12.1244i	−0.262891	−	0.455340i	−0.967009	+	0.254743i	$0.918009\pi$
$710$		0			0
$711$	8.00000	−	13.8564i	0.300023	−	0.519656i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−3.00000			−0.111648
$723$	−13.0000	−	22.5167i	−0.483475	−	0.837404i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	5.50000	+	9.52628i	0.204124	+	0.353553i
$727$	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
$730$	7.00000	+	12.1244i	0.259082	+	0.448743i
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	0.846967	−	0.531646i	$-0.178426\pi$
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	−0.883902	+	0.467671i	$0.845093\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	0.104078	+	0.994569i	$0.466811\pi$
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	−0.913361	+	0.407150i	$0.866523\pi$
$740$	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	$0.645106\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−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	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	16.0000			0.582300
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$		0			0
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$		0			0
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$	18.0000	−	31.1769i	0.650366	−	1.12647i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	11.0000	+	19.0526i	0.395899	+	0.685717i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	14.0000			0.502571
$777$		0			0
$778$	−30.0000			−1.07555
$779$	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
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$		0			0
$790$	16.0000			0.569254
$791$		0			0
$792$		0			0
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$	72.0000			2.54718
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	8.00000			0.282138
$805$		0			0
$806$	−8.00000			−0.281788
$807$	−9.00000	−	15.5885i	−0.316815	−	0.548740i
$808$	3.00000	−	5.19615i	0.105540	−	0.182800i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	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
$813$	20.0000			0.701431
$814$		0			0
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	−22.0000			−0.769212
$819$		0			0
$820$	−6.00000			−0.209529
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	3.00000	−	5.19615i	0.104637	−	0.181237i
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	−0.927281	−	0.374365i	$-0.877861\pi$
$823$	−4.00000	+	6.92820i	−0.139431	+	0.241502i	0.787850	+	0.615867i	$0.211194\pi$
$824$	8.00000	+	13.8564i	0.278693	+	0.482711i
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	0.920383	−	0.391018i	$-0.127877\pi$
$830$	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
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$	2.00000	−	3.46410i	0.0691301	−	0.119737i
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$	15.0000	−	25.9808i	0.516627	−	0.894825i
$844$	14.0000	−	24.2487i	0.481900	−	0.834675i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$	−12.0000			−0.412568
$847$		0			0
$848$	6.00000			0.206041
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	3.00000	−	5.19615i	0.102899	−	0.178227i
$851$		0			0
$852$		0			0
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		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	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	24.0000			0.817443
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	0.907905	+	0.419176i	$0.137681\pi$
$863$	24.0000	+	41.5692i	0.816970	+	1.41503i	−0.0909355	+	0.995857i	$0.528986\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	17.0000	+	29.4449i	0.577684	+	1.00058i
$867$	19.0000			0.645274
$868$		0			0
$869$		0			0
$870$	−3.00000	−	5.19615i	−0.101710	−	0.176166i
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	−7.00000	−	12.1244i	−0.236914	−	0.410347i
$874$		0			0
$875$		0			0
$876$	14.0000			0.473016
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	−0.886323	−	0.463068i	$-0.846749\pi$
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	0.0421327	−	0.999112i	$-0.486585\pi$
$878$	14.0000	−	24.2487i	0.472477	−	0.818354i
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$		0			0
$881$	−42.0000			−1.41502			−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000			−1.41502			−0.707508	+	0.706705i	$0.750181\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$	−6.00000	+	10.3923i	−0.201688	+	0.349334i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	2.00000			0.0671156
$889$		0			0
$890$	−6.00000			−0.201120
$891$		0			0
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	−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
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	8.00000	−	13.8564i	0.265782	−	0.460348i
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	−0.702094	−	0.712084i	$-0.747752\pi$
$907$	8.00000	−	13.8564i	0.265636	−	0.460094i	0.967730	+	0.251990i	$0.0810849\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	−6.00000			−0.199007
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$		0			0
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$	1.00000	+	1.73205i	0.0330590	+	0.0572598i
$916$	2.00000			0.0660819
$917$		0			0
$918$	−6.00000			−0.198030
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		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
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$	8.00000	−	13.8564i	0.262754	−	0.455104i
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.844746	−	0.535167i	$-0.820249\pi$
$929$	−27.0000	−	46.7654i	−0.885841	−	1.53432i	−0.0410949	−	0.999155i	$-0.513085\pi$
$930$	4.00000			0.131165
$931$		0			0
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$	−1.00000	−	1.73205i	−0.0326860	−	0.0566139i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$	−10.0000			−0.326338
$940$	−6.00000	−	10.3923i	−0.195698	−	0.338960i
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	−1.00000	+	1.73205i	−0.0325818	+	0.0564333i
$943$		0			0
$944$	−12.0000			−0.390567
$945$		0			0
$946$		0			0
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	0.994885	+	0.101012i	$0.0322080\pi$
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	−0.409964	+	0.912102i	$0.634459\pi$
$948$	8.00000	−	13.8564i	0.259828	−	0.450035i
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$	30.0000			0.972817
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	−24.0000			−0.775405
$959$		0			0
$960$	−1.00000			−0.0322749
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−2.00000	+	3.46410i	−0.0644826	+	0.111687i
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$	−13.0000	−	22.5167i	−0.418702	−	0.725213i
$965$	22.0000			0.708205
$966$		0			0
$967$	56.0000			1.80084			0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000			1.80084			0.900419	+	0.435023i	$0.143260\pi$
$968$	5.50000	+	9.52628i	0.176777	+	0.306186i
$969$	−12.0000	+	20.7846i	−0.385496	+	0.667698i
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	1.00000			0.0320750
$973$		0			0
$974$	−16.0000			−0.512673
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−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	$0.259636\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$		0			0
$980$		0			0
$981$	14.0000			0.446986
$982$	−12.0000	−	20.7846i	−0.382935	−	0.663264i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	36.0000			1.14647
$987$		0			0
$988$	−8.00000			−0.254514
$989$		0			0
$990$		0			0
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.0489218	+	0.998803i	$0.515578\pi$
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.840528	+	0.541769i	$0.817755\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−4.00000			−0.126936
$994$		0			0
$995$	4.00000			0.126809
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	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.d.361.1		2
7.2	even	3	inner	1470.2.i.d.961.1		2
7.3	odd	6		1470.2.a.m.1.1		1
7.4	even	3		210.2.a.d.1.1	✓	1
7.5	odd	6		1470.2.i.h.961.1		2
7.6	odd	2		1470.2.i.h.361.1		2
21.11	odd	6		630.2.a.f.1.1		1
21.17	even	6		4410.2.a.f.1.1		1
28.11	odd	6		1680.2.a.b.1.1		1
35.4	even	6		1050.2.a.a.1.1		1
35.18	odd	12		1050.2.g.h.799.1		2
35.24	odd	6		7350.2.a.bd.1.1		1
35.32	odd	12		1050.2.g.h.799.2		2
56.11	odd	6		6720.2.a.cc.1.1		1
56.53	even	6		6720.2.a.bb.1.1		1
84.11	even	6		5040.2.a.ba.1.1		1
105.32	even	12		3150.2.g.o.2899.1		2
105.53	even	12		3150.2.g.o.2899.2		2
105.74	odd	6		3150.2.a.ba.1.1		1
140.39	odd	6		8400.2.a.cn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.d.1.1	✓	1	7.4	even	3
630.2.a.f.1.1		1	21.11	odd	6
1050.2.a.a.1.1		1	35.4	even	6
1050.2.g.h.799.1		2	35.18	odd	12
1050.2.g.h.799.2		2	35.32	odd	12
1470.2.a.m.1.1		1	7.3	odd	6
1470.2.i.d.361.1		2	1.1	even	1	trivial
1470.2.i.d.961.1		2	7.2	even	3	inner
1470.2.i.h.361.1		2	7.6	odd	2
1470.2.i.h.961.1		2	7.5	odd	6
1680.2.a.b.1.1		1	28.11	odd	6
3150.2.a.ba.1.1		1	105.74	odd	6
3150.2.g.o.2899.1		2	105.32	even	12
3150.2.g.o.2899.2		2	105.53	even	12
4410.2.a.f.1.1		1	21.17	even	6
5040.2.a.ba.1.1		1	84.11	even	6
6720.2.a.bb.1.1		1	56.53	even	6
6720.2.a.cc.1.1		1	56.11	odd	6
7350.2.a.bd.1.1		1	35.24	odd	6
8400.2.a.cn.1.1		1	140.39	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} -1.00000 q^{20} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -6.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +6.00000 q^{41} +8.00000 q^{43} +(0.500000 - 0.866025i) q^{45} +(6.00000 + 10.3923i) q^{47} +1.00000 q^{48} +1.00000 q^{50} +(3.00000 + 5.19615i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-1.00000 - 1.73205i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(3.00000 + 5.19615i) q^{68} +(-0.500000 - 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(8.00000 + 13.8564i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +12.0000 q^{83} +6.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{89} -1.00000 q^{90} +(2.00000 + 3.46410i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + q^5 + 2 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} + 2 q^{6} + 2 q^{8} - q^{9} + q^{10} - q^{12} + 4 q^{13} - 2 q^{15} - q^{16} + 6 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} - q^{24} - q^{25} - 2 q^{26} + 2 q^{27} - 12 q^{29} + q^{30} + 4 q^{31} - q^{32} - 12 q^{34} + 2 q^{36} - 2 q^{37} + 4 q^{38} - 2 q^{39} + q^{40} + 12 q^{41} + 16 q^{43} + q^{45} + 12 q^{47} + 2 q^{48} + 2 q^{50} + 6 q^{51} - 2 q^{52} - 6 q^{53} - q^{54} - 8 q^{57} + 6 q^{58} + 12 q^{59} + q^{60} - 2 q^{61} - 8 q^{62} + 2 q^{64} + 2 q^{65} - 8 q^{67} + 6 q^{68} - q^{72} - 14 q^{73} - 2 q^{74} - q^{75} - 8 q^{76} + 4 q^{78} + 16 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} + 12 q^{85} - 8 q^{86} + 6 q^{87} - 6 q^{89} - 2 q^{90} + 4 q^{93} + 12 q^{94} - 4 q^{95} - q^{96} + 28 q^{97}+O(q^{100}) \) 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 + 4 * q^31 - q^32 - 12 * q^34 + 2 * q^36 - 2 * q^37 + 4 * q^38 - 2 * q^39 + q^40 + 12 * q^41 + 16 * q^43 + q^45 + 12 * q^47 + 2 * q^48 + 2 * q^50 + 6 * q^51 - 2 * q^52 - 6 * q^53 - q^54 - 8 * q^57 + 6 * q^58 + 12 * q^59 + q^60 - 2 * q^61 - 8 * q^62 + 2 * q^64 + 2 * q^65 - 8 * q^67 + 6 * q^68 - q^72 - 14 * q^73 - 2 * q^74 - q^75 - 8 * q^76 + 4 * q^78 + 16 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 + 12 * q^85 - 8 * q^86 + 6 * q^87 - 6 * q^89 - 2 * q^90 + 4 * q^93 + 12 * q^94 - 4 * q^95 - q^96 + 28 * q^97

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