LMFDB - Embedded newform 1470.2.i.r.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1470.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.r.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(0.500000 - 0.866025i) q^{12} -6.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} -1.00000 q^{20} -6.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(-0.500000 + 0.866025i) q^{40} +10.0000 q^{41} -6.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.00000 + 1.73205i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(3.00000 + 5.19615i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} -4.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(2.00000 + 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -6.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +8.00000 q^{83} +(-3.00000 + 5.19615i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-1.00000 + 1.73205i) q^{93} +(1.00000 + 1.73205i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} -2.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} - q^{10} - 6 q^{11} + q^{12} - 12 q^{13} + 2 q^{15} - q^{16} + q^{18} - 4 q^{19} - 2 q^{20} - 12 q^{22} - q^{24} - q^{25} - 6 q^{26} - 2 q^{27} - 16 q^{29} + q^{30} + 2 q^{31} + q^{32} + 6 q^{33} + 2 q^{36} - 4 q^{37} + 4 q^{38} - 6 q^{39} - q^{40} + 20 q^{41} - 12 q^{43} - 6 q^{44} + q^{45} - 2 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{52} - 10 q^{53} - q^{54} - 12 q^{55} - 8 q^{57} - 8 q^{58} - 4 q^{59} - q^{60} + 14 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 6 q^{66} - 14 q^{67} + 16 q^{71} + q^{72} + 6 q^{73} + 4 q^{74} + q^{75} + 8 q^{76} - 12 q^{78} + 8 q^{79} + q^{80} - q^{81} + 10 q^{82} + 16 q^{83} - 6 q^{86} - 8 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{90} - 2 q^{93} + 2 q^{94} + 4 q^{95} - q^{96} - 4 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 - q^10 - 6 * q^11 + q^12 - 12 * q^13 + 2 * q^15 - q^16 + q^18 - 4 * q^19 - 2 * q^20 - 12 * q^22 - q^24 - q^25 - 6 * q^26 - 2 * q^27 - 16 * q^29 + q^30 + 2 * q^31 + q^32 + 6 * q^33 + 2 * q^36 - 4 * q^37 + 4 * q^38 - 6 * q^39 - q^40 + 20 * q^41 - 12 * q^43 - 6 * q^44 + q^45 - 2 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^52 - 10 * q^53 - q^54 - 12 * q^55 - 8 * q^57 - 8 * q^58 - 4 * q^59 - q^60 + 14 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 6 * q^66 - 14 * q^67 + 16 * q^71 + q^72 + 6 * q^73 + 4 * q^74 + q^75 + 8 * q^76 - 12 * q^78 + 8 * q^79 + q^80 - q^81 + 10 * q^82 + 16 * q^83 - 6 * q^86 - 8 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^90 - 2 * q^93 + 2 * q^94 + 4 * q^95 - q^96 - 4 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−6.00000			−1.66410			−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000			−1.66410			−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−6.00000			−1.27920
$23$		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
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	−0.929695	−	0.368329i	$-0.879930\pi$
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	0.783830	+	0.620975i	$0.213263\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$		0			0
$52$	3.00000	+	5.19615i	0.416025	+	0.720577i
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	−0.972867	−	0.231367i	$-0.925680\pi$
$53$	−5.00000	−	8.66025i	−0.686803	−	1.18958i	0.286064	−	0.958211i	$-0.407653\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−6.00000			−0.809040
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	4.00000			0.458831
$77$		0			0
$78$	−6.00000			−0.679366
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−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
$93$	−1.00000	+	1.73205i	−0.103695	+	0.179605i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	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	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$		0			0
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	0.402874	+	0.915255i	$0.368011\pi$
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	−0.994071	+	0.108729i	$0.965322\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	−10.0000			−0.971286
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	−0.946357	−	0.323122i	$-0.895268\pi$
$107$	−2.00000	+	3.46410i	−0.193347	+	0.334887i	0.753010	+	0.658009i	$0.228601\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	−4.00000			−0.379663
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$		0			0
$116$	4.00000	+	6.92820i	0.371391	+	0.643268i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−1.00000			−0.0912871
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.00000	−	5.19615i	−0.264135	−	0.457496i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	−14.0000			−1.20942
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$	4.00000	−	6.92820i	0.335673	−	0.581402i
$143$	18.0000	+	31.1769i	1.50524	+	2.60714i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.00000	+	6.92820i	−0.332182	+	0.575356i
$146$	6.00000			0.496564
$147$		0			0
$148$	4.00000			0.328798
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$		0			0
$154$		0			0
$155$	2.00000			0.160644
$156$	−3.00000	+	5.19615i	−0.240192	+	0.416025i
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	5.00000	−	8.66025i	0.396526	−	0.686803i
$160$	1.00000			0.0790569
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$	−8.00000			−0.606478
$175$		0			0
$176$	6.00000			0.452267
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	9.00000	+	15.5885i	0.674579	+	1.16840i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$	2.00000	+	3.46410i	0.147043	+	0.254686i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$		0			0
$188$	2.00000			0.145865
$189$		0			0
$190$	4.00000			0.290191
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	−0.235983	−	0.971757i	$-0.575831\pi$
$191$	10.0000	−	17.3205i	0.723575	−	1.25327i	0.959558	−	0.281511i	$-0.0908356\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−11.0000	−	19.0526i	−0.791797	−	1.37143i	−0.924853	−	0.380325i	$-0.875812\pi$
$193$	−11.0000	−	19.0526i	−0.791797	−	1.37143i	0.133056	−	0.991109i	$-0.457521\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	−6.00000			−0.429669
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	−0.985873	−	0.167497i	$-0.946431\pi$
$199$	−9.00000	−	15.5885i	−0.637993	−	1.10504i	0.347879	−	0.937539i	$-0.386902\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	7.00000	−	12.1244i	0.493742	−	0.855186i
$202$	−14.0000			−0.985037
$203$		0			0
$204$		0			0
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$	6.00000	+	10.3923i	0.418040	+	0.724066i
$207$		0			0
$208$	3.00000	−	5.19615i	0.208013	−	0.360288i
$209$	24.0000			1.66011
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−3.00000	+	5.19615i	−0.204598	+	0.354375i
$216$	1.00000			0.0680414
$217$		0			0
$218$	−6.00000			−0.406371
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$		0			0
$222$	−2.00000	+	3.46410i	−0.134231	+	0.232495i
$223$	−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
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	−0.315906	+	0.948790i	$0.602309\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$	8.00000			0.525226
$233$	5.00000	−	8.66025i	0.327561	−	0.567352i	−0.654466	−	0.756091i	$-0.727107\pi$
$233$	5.00000	−	8.66025i	0.327561	−	0.567352i	0.982027	+	0.188739i	$0.0604400\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	1.00000	+	1.73205i	0.0652328	+	0.112987i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	8.00000			0.519656
$238$		0			0
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.825131	−	0.564942i	$-0.808899\pi$
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.0766885	−	0.997055i	$-0.524435\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−14.0000			−0.896258
$245$		0			0
$246$	10.0000			0.637577
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	4.00000	+	6.92820i	0.253490	+	0.439057i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$		0			0
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	−0.963391	−	0.268101i	$-0.913604\pi$
$257$	−4.00000	+	6.92820i	−0.249513	+	0.432169i	0.713878	+	0.700270i	$0.246937\pi$
$258$	−6.00000			−0.373544
$259$		0			0
$260$	6.00000			0.372104
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	16.0000	+	27.7128i	0.986602	+	1.70885i	0.634588	+	0.772851i	$0.281170\pi$
$263$	16.0000	+	27.7128i	0.986602	+	1.70885i	0.352014	+	0.935995i	$0.385497\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$	−10.0000			−0.614295
$266$		0			0
$267$	−18.0000			−1.10158
$268$	−7.00000	+	12.1244i	−0.427593	+	0.740613i
$269$	11.0000	+	19.0526i	0.670682	+	1.16166i	0.977711	+	0.209955i	$0.0673317\pi$
$269$	11.0000	+	19.0526i	0.670682	+	1.16166i	−0.307029	+	0.951700i	$0.599335\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	0.451786	+	0.892126i	$0.350787\pi$
$271$	−9.00000	+	15.5885i	−0.546711	+	0.946931i	−0.998497	+	0.0548050i	$0.982546\pi$
$272$		0			0
$273$		0			0
$274$	−10.0000			−0.604122
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$		0			0
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	0.960810	−	0.277207i	$-0.0894088\pi$
$277$	4.00000	+	6.92820i	0.240337	+	0.416275i	−0.720473	+	0.693482i	$0.756075\pi$
$278$	−4.00000	+	6.92820i	−0.239904	+	0.415526i
$279$	−2.00000			−0.119737
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	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	$0.520407\pi$
$284$	−4.00000	−	6.92820i	−0.237356	−	0.411113i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	36.0000			2.12872
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	4.00000	+	6.92820i	0.234888	+	0.406838i
$291$	−1.00000	−	1.73205i	−0.0586210	−	0.101535i
$292$	3.00000	−	5.19615i	0.175562	−	0.304082i
$293$	−22.0000			−1.28525			−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000			−1.28525			−0.642627	+	0.766179i	$0.722155\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	3.00000	+	5.19615i	0.174078	+	0.301511i
$298$		0			0
$299$		0			0
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	8.00000			0.460348
$303$	7.00000	−	12.1244i	0.402139	−	0.696526i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	−7.00000	−	12.1244i	−0.400819	−	0.694239i
$306$		0			0
$307$	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
$309$	−12.0000			−0.682656
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	3.00000	+	5.19615i	0.169842	+	0.294174i
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	−0.971589	−	0.236675i	$-0.923942\pi$
$317$	−5.00000	+	8.66025i	−0.280828	+	0.486408i	0.690761	+	0.723083i	$0.257276\pi$
$318$	−5.00000	−	8.66025i	−0.280386	−	0.485643i
$319$	24.0000	+	41.5692i	1.34374	+	2.32743i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−4.00000			−0.223258
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.00000	+	5.19615i	0.166410	+	0.288231i
$326$	1.00000	+	1.73205i	0.0553849	+	0.0959294i
$327$	3.00000	−	5.19615i	0.165900	−	0.287348i
$328$	−10.0000			−0.552158
$329$		0			0
$330$	−6.00000			−0.330289
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	−4.00000	−	6.92820i	−0.219529	−	0.380235i
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$	9.00000	−	15.5885i	0.492458	−	0.852962i
$335$	−14.0000			−0.764902
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$	11.5000	−	19.9186i	0.625518	−	1.08343i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−4.00000			−0.216295
$343$		0			0
$344$	6.00000			0.323498
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$	−4.00000	+	6.92820i	−0.214423	+	0.371391i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	6.00000			0.320256
$352$	3.00000	−	5.19615i	0.159901	−	0.276956i
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	0.914329	−	0.404971i	$-0.132718\pi$
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	−0.807880	+	0.589347i	$0.799385\pi$
$354$	−2.00000	−	3.46410i	−0.106299	−	0.184115i
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	18.0000			0.953998
$357$		0			0
$358$	−2.00000			−0.105703
$359$	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
$362$	−5.00000	+	8.66025i	−0.262794	+	0.455173i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	6.00000			0.314054
$366$	7.00000	−	12.1244i	0.365896	−	0.633750i
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	0.809093	−	0.587680i	$-0.199959\pi$
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	−0.913493	+	0.406855i	$0.866625\pi$
$368$		0			0
$369$	−5.00000	+	8.66025i	−0.260290	+	0.450835i
$370$	4.00000			0.207950
$371$		0			0
$372$	2.00000			0.103695
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	−0.743691	−	0.668523i	$-0.766927\pi$
$373$	4.00000	−	6.92820i	0.207112	−	0.358729i	0.950804	+	0.309794i	$0.100260\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	1.00000	−	1.73205i	0.0515711	−	0.0893237i
$377$	48.0000			2.47213
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	−0.987573	−	0.157159i	$-0.949767\pi$
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	0.629890	+	0.776684i	$0.283100\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−22.0000			−1.11977
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	−0.991500	−	0.130105i	$-0.958469\pi$
$389$	−12.0000	−	20.7846i	−0.608424	−	1.05382i	0.383076	−	0.923717i	$-0.374865\pi$
$390$	−3.00000	+	5.19615i	−0.151911	+	0.263117i
$391$		0			0
$392$		0			0
$393$	12.0000			0.605320
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−18.0000			−0.902258
$399$		0			0
$400$	1.00000			0.0500000
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	−0.889914	−	0.456129i	$-0.849236\pi$
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	0.839976	+	0.542623i	$0.182569\pi$
$402$	−7.00000	−	12.1244i	−0.349128	−	0.604708i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−7.00000	+	12.1244i	−0.348263	+	0.603209i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−8.00000	−	13.8564i	−0.395575	−	0.685155i	0.597600	−	0.801795i	$-0.296121\pi$
$409$	−8.00000	−	13.8564i	−0.395575	−	0.685155i	−0.993174	+	0.116639i	$0.962788\pi$
$410$	−5.00000	−	8.66025i	−0.246932	−	0.427699i
$411$	5.00000	−	8.66025i	0.246632	−	0.427179i
$412$	12.0000			0.591198
$413$		0			0
$414$		0			0
$415$	4.00000	−	6.92820i	0.196352	−	0.340092i
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$	−4.00000	−	6.92820i	−0.195881	−	0.339276i
$418$	12.0000	−	20.7846i	0.586939	−	1.01661i
$419$	−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
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	6.00000	−	10.3923i	0.292075	−	0.505889i
$423$	−1.00000	−	1.73205i	−0.0486217	−	0.0842152i
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$		0			0
$426$	8.00000			0.387601
$427$		0			0
$428$	4.00000			0.193347
$429$	−18.0000	+	31.1769i	−0.869048	+	1.50524i
$430$	3.00000	+	5.19615i	0.144673	+	0.250581i
$431$		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
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$		0			0
$435$	−8.00000			−0.383571
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$		0			0
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$		0			0
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$		0			0
$448$		0			0
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	−30.0000	−	51.9615i	−1.41264	−	2.44677i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	20.0000			0.938647
$455$		0			0
$456$	4.00000			0.187317
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$458$	7.00000	+	12.1244i	0.327089	+	0.566534i
$459$		0			0
$460$		0			0
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$	1.00000	+	1.73205i	0.0463739	+	0.0803219i
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$	−6.00000			−0.277350
$469$		0			0
$470$	2.00000			0.0922531
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	18.0000	+	31.1769i	0.827641	+	1.43352i
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	4.00000			0.183533
$476$		0			0
$477$	10.0000			0.457869
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	−0.903859	−	0.427830i	$-0.859278\pi$
$479$	−18.0000	−	31.1769i	−0.822441	−	1.42451i	0.0814184	−	0.996680i	$-0.474055\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	12.0000	−	20.7846i	0.547153	−	0.947697i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	25.0000			1.13636
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	0.697459	−	0.716625i	$-0.254314\pi$
$487$	−6.00000	−	10.3923i	−0.271886	−	0.470920i	−0.969345	+	0.245705i	$0.920981\pi$
$488$	−7.00000	+	12.1244i	−0.316875	+	0.548844i
$489$	−2.00000			−0.0904431
$490$		0			0
$491$	−22.0000			−0.992846			−0.496423	−	0.868081i	$-0.665354\pi$
$491$	−22.0000			−0.992846			−0.496423	+	0.868081i	$0.665354\pi$
$492$	5.00000	−	8.66025i	0.225417	−	0.390434i
$493$		0			0
$494$	−12.0000	−	20.7846i	−0.539906	−	0.935144i
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$	−2.00000			−0.0898027
$497$		0			0
$498$	8.00000			0.358489
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	10.0000	−	17.3205i	0.446322	−	0.773052i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−14.0000			−0.622992
$506$		0			0
$507$	11.5000	+	19.9186i	0.510733	+	0.884615i
$508$	−2.00000	−	3.46410i	−0.0887357	−	0.153695i
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	−0.192599	−	0.981278i	$-0.561692\pi$
$509$	17.0000	−	29.4449i	0.753512	−	1.30512i	0.946111	−	0.323843i	$-0.104975\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	4.00000	+	6.92820i	0.176432	+	0.305590i
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	12.0000			0.527759
$518$		0			0
$519$	−6.00000			−0.263371
$520$	3.00000	−	5.19615i	0.131559	−	0.227866i
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	0.843288	−	0.537461i	$-0.180617\pi$
$521$	−1.00000	−	1.73205i	−0.0438108	−	0.0758825i	−0.887099	+	0.461579i	$0.847283\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.244507	+	0.969648i	$0.578626\pi$
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.717486	+	0.696573i	$0.754707\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	32.0000			1.39527
$527$		0			0
$528$	3.00000	+	5.19615i	0.130558	+	0.226134i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−5.00000	+	8.66025i	−0.217186	+	0.376177i
$531$	4.00000			0.173585
$532$		0			0
$533$	−60.0000			−2.59889
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	2.00000	+	3.46410i	0.0864675	+	0.149766i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$	1.00000	−	1.73205i	0.0431532	−	0.0747435i
$538$	22.0000			0.948487
$539$		0			0
$540$	1.00000			0.0430331
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	−0.992036	−	0.125952i	$-0.959801\pi$
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	0.605096	+	0.796152i	$0.293135\pi$
$542$	9.00000	+	15.5885i	0.386583	+	0.669582i
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$		0			0
$545$	−6.00000			−0.257012
$546$		0			0
$547$	30.0000			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	3.00000	+	5.19615i	0.127920	+	0.221565i
$551$	16.0000	−	27.7128i	0.681623	−	1.18061i
$552$		0			0
$553$		0			0
$554$	8.00000			0.339887
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	0.844062	−	0.536246i	$-0.180158\pi$
$557$	−1.00000	−	1.73205i	−0.0423714	−	0.0733893i	−0.886433	+	0.462856i	$0.846825\pi$
$558$	−1.00000	+	1.73205i	−0.0423334	+	0.0733236i
$559$	36.0000			1.52264
$560$		0			0
$561$		0			0
$562$	3.00000	−	5.19615i	0.126547	−	0.219186i
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	0.999978	+	0.00664037i	$0.00211371\pi$
$563$	12.0000	+	20.7846i	0.505740	+	0.875967i	−0.494238	+	0.869326i	$0.664553\pi$
$564$	1.00000	+	1.73205i	0.0421076	+	0.0729325i
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$	28.0000			1.17693
$567$		0			0
$568$	−8.00000			−0.335673
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	0.453619	+	0.891196i	$0.350133\pi$
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	−0.998608	+	0.0527519i	$0.983201\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	18.0000	−	31.1769i	0.752618	−	1.30357i
$573$	20.0000			0.835512
$574$		0			0
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	0.682730	−	0.730670i	$-0.260792\pi$
$577$	−7.00000	−	12.1244i	−0.291414	−	0.504744i	−0.974144	+	0.225927i	$0.927459\pi$
$578$	−8.50000	−	14.7224i	−0.353553	−	0.612372i
$579$	11.0000	−	19.0526i	0.457144	−	0.791797i
$580$	8.00000			0.332182
$581$		0			0
$582$	−2.00000			−0.0829027
$583$	−30.0000	+	51.9615i	−1.24247	+	2.15203i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	−11.0000	+	19.0526i	−0.454406	+	0.787054i
$587$	−32.0000			−1.32078			−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000			−1.32078			−0.660391	+	0.750922i	$0.729609\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	−8.00000	+	13.8564i	−0.328521	+	0.569014i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$	−8.00000	+	13.8564i	−0.328521	+	0.569014i	0.653698	+	0.756756i	$0.273217\pi$
$594$	6.00000			0.246183
$595$		0			0
$596$		0			0
$597$	9.00000	−	15.5885i	0.368345	−	0.637993i
$598$		0			0
$599$	−22.0000	−	38.1051i	−0.898896	−	1.55693i	−0.828908	−	0.559385i	$-0.811037\pi$
$599$	−22.0000	−	38.1051i	−0.898896	−	1.55693i	−0.0699877	−	0.997548i	$-0.522296\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−12.0000			−0.489490			−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000			−0.489490			−0.244745	+	0.969587i	$0.578704\pi$
$602$		0			0
$603$	14.0000			0.570124
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	12.5000	+	21.6506i	0.508197	+	0.880223i
$606$	−7.00000	−	12.1244i	−0.284356	−	0.492518i
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	0.0998457	+	0.995003i	$0.468165\pi$
$607$	−20.0000	+	34.6410i	−0.811775	+	1.40604i	−0.911621	+	0.411033i	$0.865168\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	−14.0000			−0.566843
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$		0			0
$613$	−18.0000	−	31.1769i	−0.727013	−	1.25922i	−0.958140	−	0.286300i	$-0.907575\pi$
$613$	−18.0000	−	31.1769i	−0.727013	−	1.25922i	0.231127	−	0.972924i	$-0.425759\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$	10.0000			0.403239
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$	−6.00000	+	10.3923i	−0.241355	+	0.418040i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$		0			0
$622$	−12.0000			−0.481156
$623$		0			0
$624$	6.00000			0.240192
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.0000	−	22.5167i	−0.519584	−	0.899947i
$627$	12.0000	+	20.7846i	0.479234	+	0.830057i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$		0			0
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$	5.00000	+	8.66025i	0.198575	+	0.343943i
$635$	2.00000	−	3.46410i	0.0793676	−	0.137469i
$636$	−10.0000			−0.396526
$637$		0			0
$638$	48.0000			1.90034
$639$	−4.00000	+	6.92820i	−0.158238	+	0.274075i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	−2.00000	+	3.46410i	−0.0789337	+	0.136717i
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	−23.0000	−	39.8372i	−0.904223	−	1.56616i	−0.821956	−	0.569550i	$-0.807117\pi$
$647$	−23.0000	−	39.8372i	−0.904223	−	1.56616i	−0.0822669	−	0.996610i	$-0.526216\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−12.0000	+	20.7846i	−0.471041	+	0.815867i
$650$	6.00000			0.235339
$651$		0			0
$652$	2.00000			0.0783260
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	−6.00000			−0.234082
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	0.636200	−	0.771524i	$-0.280505\pi$
$661$	−9.00000	−	15.5885i	−0.350059	−	0.606321i	−0.986260	+	0.165203i	$0.947172\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$		0			0
$664$	−8.00000			−0.310460
$665$		0			0
$666$	−4.00000			−0.154997
$667$		0			0
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$	−7.00000	+	12.1244i	−0.270434	+	0.468405i
$671$	−84.0000			−3.24278
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	−13.0000	+	22.5167i	−0.500741	+	0.867309i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	−0.996209	−	0.0869952i	$-0.972274\pi$
$677$	−11.0000	+	19.0526i	−0.422764	+	0.732249i	0.573444	+	0.819244i	$0.305607\pi$
$678$	6.00000			0.230429
$679$		0			0
$680$		0			0
$681$	−10.0000	+	17.3205i	−0.383201	+	0.663723i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	−10.0000			−0.382080
$686$		0			0
$687$	−14.0000			−0.534133
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	30.0000	+	51.9615i	1.14291	+	1.97958i
$690$		0			0
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	28.0000			1.06287
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$	4.00000	+	6.92820i	0.151620	+	0.262613i
$697$		0			0
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	10.0000			0.378235
$700$		0			0
$701$	24.0000			0.906467			0.453234	−	0.891392i	$-0.350270\pi$
$701$	24.0000			0.906467			0.453234	+	0.891392i	$0.350270\pi$
$702$	3.00000	−	5.19615i	0.113228	−	0.196116i
$703$	−8.00000	−	13.8564i	−0.301726	−	0.522604i
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$	−1.00000	+	1.73205i	−0.0376622	+	0.0652328i
$706$	4.00000			0.150542
$707$		0			0
$708$	−4.00000			−0.150329
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	−0.884192	−	0.467123i	$-0.845291\pi$
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	0.846637	+	0.532172i	$0.178624\pi$
$710$	−4.00000	−	6.92820i	−0.150117	−	0.260011i
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$		0			0
$714$		0			0
$715$	36.0000			1.34632
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	−2.00000	−	3.46410i	−0.0746914	−	0.129369i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	−0.975759	−	0.218850i	$-0.929769\pi$
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	0.677409	+	0.735607i	$0.263103\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	3.00000			0.111648
$723$	14.0000	−	24.2487i	0.520666	−	0.901819i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$	−12.5000	+	21.6506i	−0.463919	+	0.803530i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$		0			0
$732$	−7.00000	−	12.1244i	−0.258727	−	0.448129i
$733$	−23.0000	+	39.8372i	−0.849524	+	1.47142i	0.0321090	+	0.999484i	$0.489778\pi$
$733$	−23.0000	+	39.8372i	−0.849524	+	1.47142i	−0.881633	+	0.471935i	$0.843556\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$		0			0
$737$	−42.0000	+	72.7461i	−1.54709	+	2.67964i
$738$	5.00000	+	8.66025i	0.184053	+	0.318788i
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	24.0000			0.881662
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$		0			0
$746$	−4.00000	−	6.92820i	−0.146450	−	0.253660i
$747$	−4.00000	+	6.92820i	−0.146352	+	0.253490i
$748$		0			0
$749$		0			0
$750$	−1.00000			−0.0365148
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	0.227153	+	0.973859i	$0.427058\pi$
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	−0.956963	+	0.290209i	$0.906275\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	10.0000	+	17.3205i	0.364420	+	0.631194i
$754$	24.0000	−	41.5692i	0.874028	−	1.51386i
$755$	8.00000			0.291150
$756$		0			0
$757$	−40.0000			−1.45382			−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000			−1.45382			−0.726912	+	0.686730i	$0.759045\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$		0			0
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$	4.00000			0.144905
$763$		0			0
$764$	−20.0000			−0.723575
$765$		0			0
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	−8.00000			−0.288113
$772$	−11.0000	+	19.0526i	−0.395899	+	0.685717i
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	0.531736	−	0.846910i	$-0.321540\pi$
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	−0.999314	+	0.0370420i	$0.988206\pi$
$774$	−3.00000	−	5.19615i	−0.107833	−	0.186772i
$775$	1.00000	−	1.73205i	0.0359211	−	0.0622171i
$776$	2.00000			0.0717958
$777$		0			0
$778$	−24.0000			−0.860442
$779$	−20.0000	+	34.6410i	−0.716574	+	1.24114i
$780$	3.00000	+	5.19615i	0.107417	+	0.186052i
$781$	−24.0000	−	41.5692i	−0.858788	−	1.48746i
$782$		0			0
$783$	8.00000			0.285897
$784$		0			0
$785$	−14.0000			−0.499681
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$	−16.0000	+	27.7128i	−0.569615	+	0.986602i
$790$	−8.00000			−0.284627
$791$		0			0
$792$	−6.00000			−0.213201
$793$	−42.0000	+	72.7461i	−1.49146	+	2.58329i
$794$	7.00000	+	12.1244i	0.248421	+	0.430277i
$795$	−5.00000	−	8.66025i	−0.177332	−	0.307148i
$796$	−9.00000	+	15.5885i	−0.318997	+	0.552518i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$	1.00000	+	1.73205i	0.0353112	+	0.0611608i
$803$	18.0000	−	31.1769i	0.635206	−	1.10021i
$804$	−14.0000			−0.493742
$805$		0			0
$806$	−12.0000			−0.422682
$807$	−11.0000	+	19.0526i	−0.387218	+	0.670682i
$808$	7.00000	+	12.1244i	0.246259	+	0.426533i
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	0.979739	−	0.200279i	$-0.0641847\pi$
$809$	9.00000	+	15.5885i	0.316423	+	0.548061i	−0.663316	+	0.748340i	$0.730851\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$	−18.0000			−0.631288
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$		0			0
$817$	12.0000	−	20.7846i	0.419827	−	0.727161i
$818$	−16.0000			−0.559427
$819$		0			0
$820$	−10.0000			−0.349215
$821$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$821$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$822$	−5.00000	−	8.66025i	−0.174395	−	0.302061i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	6.00000	−	10.3923i	0.209020	−	0.362033i
$825$	−6.00000			−0.208893
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	11.0000	+	19.0526i	0.382046	+	0.661723i	0.991355	−	0.131210i	$-0.0418863\pi$
$829$	11.0000	+	19.0526i	0.382046	+	0.661723i	−0.609309	+	0.792933i	$0.708553\pi$
$830$	−4.00000	−	6.92820i	−0.138842	−	0.240481i
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$	−6.00000			−0.208013
$833$		0			0
$834$	−8.00000			−0.277017
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	−12.0000	−	20.7846i	−0.415029	−	0.718851i
$837$	−1.00000	−	1.73205i	−0.0345651	−	0.0598684i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	44.0000			1.51905			0.759524	−	0.650479i	$-0.225432\pi$
$839$	44.0000			1.51905			0.759524	+	0.650479i	$0.225432\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$	−6.00000	−	10.3923i	−0.206529	−	0.357718i
$845$	11.5000	−	19.9186i	0.395612	−	0.685220i
$846$	−2.00000			−0.0687614
$847$		0			0
$848$	10.0000			0.343401
$849$	−14.0000	+	24.2487i	−0.480479	+	0.832214i
$850$		0			0
$851$		0			0
$852$	4.00000	−	6.92820i	0.137038	−	0.237356i
$853$	22.0000			0.753266			0.376633	−	0.926363i	$-0.377082\pi$
$853$	22.0000			0.753266			0.376633	+	0.926363i	$0.377082\pi$
$854$		0			0
$855$	−4.00000			−0.136797
$856$	2.00000	−	3.46410i	0.0683586	−	0.118401i
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$	18.0000	+	31.1769i	0.614510	+	1.06436i
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	−0.696661	−	0.717400i	$-0.745332\pi$
$859$	8.00000	−	13.8564i	0.272956	−	0.472774i	0.969618	+	0.244626i	$0.0786652\pi$
$860$	6.00000			0.204598
$861$		0			0
$862$		0			0
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	−0.453983	−	0.891010i	$-0.649997\pi$
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	0.998629	−	0.0523446i	$-0.0166694\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−9.00000	+	15.5885i	−0.305832	+	0.529717i
$867$	17.0000			0.577350
$868$		0			0
$869$	−48.0000			−1.62829
$870$	−4.00000	+	6.92820i	−0.135613	+	0.234888i
$871$	42.0000	+	72.7461i	1.42312	+	2.46491i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$		0			0
$875$		0			0
$876$	6.00000			0.202721
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$	−11.0000	−	19.0526i	−0.371021	−	0.642627i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	14.0000			0.471138			0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000			0.471138			0.235569	+	0.971858i	$0.424305\pi$
$884$		0			0
$885$	−2.00000	−	3.46410i	−0.0672293	−	0.116445i
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	13.0000	−	22.5167i	0.436497	−	0.756035i	−0.560919	−	0.827871i	$-0.689552\pi$
$887$	13.0000	−	22.5167i	0.436497	−	0.756035i	0.997417	+	0.0718351i	$0.0228855\pi$
$888$	4.00000			0.134231
$889$		0			0
$890$	18.0000			0.603361
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$	−4.00000	−	6.92820i	−0.133855	−	0.231843i
$894$		0			0
$895$	−2.00000			−0.0668526
$896$		0			0
$897$		0			0
$898$	−5.00000	+	8.66025i	−0.166852	+	0.288996i
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$		0			0
$902$	−60.0000			−1.99778
$903$		0			0
$904$	−6.00000			−0.199557
$905$	−5.00000	+	8.66025i	−0.166206	+	0.287877i
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	14.0000			0.464351
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	−24.0000	−	41.5692i	−0.794284	−	1.37574i
$914$	19.0000	+	32.9090i	0.628464	+	1.08853i
$915$	7.00000	−	12.1244i	0.231413	−	0.400819i
$916$	14.0000			0.462573
$917$		0			0
$918$		0			0
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$		0			0
$921$	10.0000	+	17.3205i	0.329511	+	0.570730i
$922$	1.00000	−	1.73205i	0.0329332	−	0.0570421i
$923$	−48.0000			−1.57994
$924$		0			0
$925$	4.00000			0.131519
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	−4.00000	−	6.92820i	−0.131306	−	0.227429i
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$	2.00000			0.0655826
$931$		0			0
$932$	−10.0000			−0.327561
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$	−3.00000	+	5.19615i	−0.0980581	+	0.169842i
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$		0			0
$939$	26.0000			0.848478
$940$	1.00000	−	1.73205i	0.0326164	−	0.0564933i
$941$	1.00000	+	1.73205i	0.0325991	+	0.0564632i	0.881865	−	0.471503i	$-0.156288\pi$
$941$	1.00000	+	1.73205i	0.0325991	+	0.0564632i	−0.849266	+	0.527966i	$0.822955\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$		0			0
$944$	4.00000			0.130189
$945$		0			0
$946$	36.0000			1.17046
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	−0.152106	−	0.988364i	$-0.548606\pi$
$947$	24.0000	−	41.5692i	0.779895	−	1.35082i	0.932002	−	0.362454i	$-0.118061\pi$
$948$	−4.00000	−	6.92820i	−0.129914	−	0.225018i
$949$	−18.0000	−	31.1769i	−0.584305	−	1.01205i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$	−10.0000			−0.324272
$952$		0			0
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	5.00000	−	8.66025i	0.161881	−	0.280386i
$955$	−10.0000	−	17.3205i	−0.323592	−	0.560478i
$956$	2.00000	+	3.46410i	0.0646846	+	0.112037i
$957$	−24.0000	+	41.5692i	−0.775810	+	1.34374i
$958$	−36.0000			−1.16311
$959$		0			0
$960$	1.00000			0.0322749
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−12.0000	−	20.7846i	−0.386896	−	0.670123i
$963$	−2.00000	−	3.46410i	−0.0644491	−	0.111629i
$964$	−14.0000	+	24.2487i	−0.450910	+	0.780998i
$965$	−22.0000			−0.708205
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$		0			0
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	−2.00000	+	3.46410i	−0.0641831	+	0.111168i	−0.896331	−	0.443385i	$-0.853777\pi$
$971$	−2.00000	+	3.46410i	−0.0641831	+	0.111168i	0.832148	+	0.554553i	$0.187111\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−12.0000			−0.384505
$975$	−3.00000	+	5.19615i	−0.0960769	+	0.166410i
$976$	7.00000	+	12.1244i	0.224065	+	0.388091i
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$	−1.00000	+	1.73205i	−0.0319765	+	0.0553849i
$979$	108.000			3.45169
$980$		0			0
$981$	6.00000			0.191565
$982$	−11.0000	+	19.0526i	−0.351024	+	0.607992i
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	−0.977961	−	0.208788i	$-0.933048\pi$
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	0.308165	−	0.951333i	$-0.400285\pi$
$984$	−5.00000	−	8.66025i	−0.159394	−	0.276079i
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$		0			0
$987$		0			0
$988$	−24.0000			−0.763542
$989$		0			0
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	20.0000			0.634681
$994$		0			0
$995$	−18.0000			−0.570638
$996$	4.00000	−	6.92820i	0.126745	−	0.219529i
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	0.979265	+	0.202586i	$0.0649345\pi$
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	−0.314188	+	0.949361i	$0.601732\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	2.00000	−	3.46410i	0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.r.961.1		2
7.2	even	3		1470.2.a.c.1.1	✓	1
7.3	odd	6		1470.2.i.k.361.1		2
7.4	even	3	inner	1470.2.i.r.361.1		2
7.5	odd	6		1470.2.a.i.1.1	yes	1
7.6	odd	2		1470.2.i.k.961.1		2
21.2	odd	6		4410.2.a.be.1.1		1
21.5	even	6		4410.2.a.v.1.1		1
35.9	even	6		7350.2.a.da.1.1		1
35.19	odd	6		7350.2.a.cf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.a.c.1.1	✓	1	7.2	even	3
1470.2.a.i.1.1	yes	1	7.5	odd	6
1470.2.i.k.361.1		2	7.3	odd	6
1470.2.i.k.961.1		2	7.6	odd	2
1470.2.i.r.361.1		2	7.4	even	3	inner
1470.2.i.r.961.1		2	1.1	even	1	trivial
4410.2.a.v.1.1		1	21.5	even	6
4410.2.a.be.1.1		1	21.2	odd	6
7350.2.a.cf.1.1		1	35.19	odd	6
7350.2.a.da.1.1		1	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(0.500000 - 0.866025i) q^{12} -6.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} -1.00000 q^{20} -6.00000 q^{22} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} -8.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(-3.00000 - 5.19615i) q^{39} +(-0.500000 + 0.866025i) q^{40} +10.0000 q^{41} -6.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.00000 + 1.73205i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(3.00000 + 5.19615i) q^{52} +(-5.00000 - 8.66025i) q^{53} +(-0.500000 + 0.866025i) q^{54} -6.00000 q^{55} -4.00000 q^{57} +(-4.00000 + 6.92820i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(-7.00000 - 12.1244i) q^{67} +8.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(2.00000 + 3.46410i) q^{74} +(0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -6.00000 q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +8.00000 q^{83} +(-3.00000 + 5.19615i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-1.00000 + 1.73205i) q^{93} +(1.00000 + 1.73205i) q^{94} +(2.00000 + 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} -2.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{8} - q^{9} - q^{10} - 6 q^{11} + q^{12} - 12 q^{13} + 2 q^{15} - q^{16} + q^{18} - 4 q^{19} - 2 q^{20} - 12 q^{22} - q^{24} - q^{25} - 6 q^{26} - 2 q^{27} - 16 q^{29} + q^{30} + 2 q^{31} + q^{32} + 6 q^{33} + 2 q^{36} - 4 q^{37} + 4 q^{38} - 6 q^{39} - q^{40} + 20 q^{41} - 12 q^{43} - 6 q^{44} + q^{45} - 2 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{52} - 10 q^{53} - q^{54} - 12 q^{55} - 8 q^{57} - 8 q^{58} - 4 q^{59} - q^{60} + 14 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 6 q^{66} - 14 q^{67} + 16 q^{71} + q^{72} + 6 q^{73} + 4 q^{74} + q^{75} + 8 q^{76} - 12 q^{78} + 8 q^{79} + q^{80} - q^{81} + 10 q^{82} + 16 q^{83} - 6 q^{86} - 8 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{90} - 2 q^{93} + 2 q^{94} + 4 q^{95} - q^{96} - 4 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^8 - q^9 - q^10 - 6 * q^11 + q^12 - 12 * q^13 + 2 * q^15 - q^16 + q^18 - 4 * q^19 - 2 * q^20 - 12 * q^22 - q^24 - q^25 - 6 * q^26 - 2 * q^27 - 16 * q^29 + q^30 + 2 * q^31 + q^32 + 6 * q^33 + 2 * q^36 - 4 * q^37 + 4 * q^38 - 6 * q^39 - q^40 + 20 * q^41 - 12 * q^43 - 6 * q^44 + q^45 - 2 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^52 - 10 * q^53 - q^54 - 12 * q^55 - 8 * q^57 - 8 * q^58 - 4 * q^59 - q^60 + 14 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 6 * q^66 - 14 * q^67 + 16 * q^71 + q^72 + 6 * q^73 + 4 * q^74 + q^75 + 8 * q^76 - 12 * q^78 + 8 * q^79 + q^80 - q^81 + 10 * q^82 + 16 * q^83 - 6 * q^86 - 8 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^90 - 2 * q^93 + 2 * q^94 + 4 * q^95 - q^96 - 4 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more