LMFDB - Embedded newform 882.2.e.b.655.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$7.04280545828$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(3.50000 + 6.06218i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(4.50000 - 2.59808i) q^{30} +2.00000 q^{31} -1.00000 q^{32} -10.3923i q^{33} +(3.00000 - 5.19615i) q^{34} +(1.50000 + 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(-3.50000 - 6.06218i) q^{38} +3.46410i q^{39} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(3.00000 + 5.19615i) q^{44} +9.00000 q^{45} +(1.50000 - 2.59808i) q^{46} +(-1.50000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(9.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +5.19615i q^{54} +18.0000 q^{55} -12.1244i q^{57} +(3.00000 - 5.19615i) q^{58} +(-4.50000 + 2.59808i) q^{60} +5.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} +10.3923i q^{66} +8.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(4.50000 - 2.59808i) q^{69} +3.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.92820i q^{75} +(3.50000 + 6.06218i) q^{76} -3.46410i q^{78} +5.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(1.00000 - 1.73205i) q^{86} +(9.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{88} -9.00000 q^{90} +(-1.50000 + 2.59808i) q^{92} +(-3.00000 - 1.73205i) q^{93} +21.0000 q^{95} +(1.50000 + 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} - 3 q^{10} + 6 q^{11} - 3 q^{12} - 2 q^{13} - 9 q^{15} + 2 q^{16} - 6 q^{17} - 3 q^{18} + 7 q^{19} + 3 q^{20} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} - 6 q^{29} + 9 q^{30} + 4 q^{31} - 2 q^{32} + 6 q^{34} + 3 q^{36} - 2 q^{37} - 7 q^{38} - 3 q^{40} - 2 q^{43} + 6 q^{44} + 18 q^{45} + 3 q^{46} - 3 q^{48} + 4 q^{50} + 18 q^{51} - 2 q^{52} - 6 q^{53} + 36 q^{55} + 6 q^{58} - 9 q^{60} + 10 q^{61} - 4 q^{62} + 2 q^{64} - 12 q^{65} + 16 q^{67} - 6 q^{68} + 9 q^{69} + 6 q^{71} - 3 q^{72} - 2 q^{73} + 2 q^{74} + 7 q^{76} + 10 q^{79} + 3 q^{80} - 9 q^{81} - 12 q^{83} + 18 q^{85} + 2 q^{86} + 18 q^{87} - 6 q^{88} - 18 q^{90} - 3 q^{92} - 6 q^{93} + 42 q^{95} + 3 q^{96} - 2 q^{97} - 18 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 - 3 * q^10 + 6 * q^11 - 3 * q^12 - 2 * q^13 - 9 * q^15 + 2 * q^16 - 6 * q^17 - 3 * q^18 + 7 * q^19 + 3 * q^20 - 6 * q^22 - 3 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 - 6 * q^29 + 9 * q^30 + 4 * q^31 - 2 * q^32 + 6 * q^34 + 3 * q^36 - 2 * q^37 - 7 * q^38 - 3 * q^40 - 2 * q^43 + 6 * q^44 + 18 * q^45 + 3 * q^46 - 3 * q^48 + 4 * q^50 + 18 * q^51 - 2 * q^52 - 6 * q^53 + 36 * q^55 + 6 * q^58 - 9 * q^60 + 10 * q^61 - 4 * q^62 + 2 * q^64 - 12 * q^65 + 16 * q^67 - 6 * q^68 + 9 * q^69 + 6 * q^71 - 3 * q^72 - 2 * q^73 + 2 * q^74 + 7 * q^76 + 10 * q^79 + 3 * q^80 - 9 * q^81 - 12 * q^83 + 18 * q^85 + 2 * q^86 + 18 * q^87 - 6 * q^88 - 18 * q^90 - 3 * q^92 - 6 * q^93 + 42 * q^95 + 3 * q^96 - 2 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	1.00000			0.500000
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$	1.00000			0.250000
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	4.50000	−	2.59808i	0.821584	−	0.474342i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000			−0.176777
$33$		−	10.3923i		−	1.80907i
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−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	$0.885902\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$			3.46410i			0.554700i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	3.00000	+	5.19615i	0.452267	+	0.783349i
$45$	9.00000			1.34164
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$		0			0
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	9.00000	−	5.19615i	1.26025	−	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	$0.301865\pi$
$54$			5.19615i			0.707107i
$55$	18.0000			2.42712
$56$		0			0
$57$		−	12.1244i		−	1.60591i
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−4.50000	+	2.59808i	−0.580948	+	0.335410i
$61$	5.00000			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000			−0.744208
$66$			10.3923i			1.27920i
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$			6.92820i			0.800000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$		0			0
$78$		−	3.46410i		−	0.392232i
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$		0			0
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	9.00000	−	5.19615i	0.964901	−	0.557086i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−9.00000			−0.948683
$91$		0			0
$92$	−1.50000	+	2.59808i	−0.156386	+	0.270868i
$93$	−3.00000	−	1.73205i	−0.311086	−	0.179605i
$94$		0			0
$95$	21.0000			2.15455
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	−9.00000	+	15.5885i	−0.904534	+	1.56670i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	−0.507300	−	0.861770i	$-0.669356\pi$
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	0.999964	+	0.00844953i	$0.00268960\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$		−	5.19615i		−	0.500000i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	−18.0000			−1.71623
$111$			3.46410i			0.328798i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$			12.1244i			1.13555i
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$		0			0
$119$		0			0
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−5.00000			−0.452679
$123$		0			0
$124$	2.00000			0.179605
$125$	3.00000			0.268328
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	−1.00000			−0.0883883
$129$	3.00000	−	1.73205i	0.264135	−	0.152499i
$130$	6.00000			0.526235
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$		−	10.3923i		−	0.904534i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	−13.5000	−	7.79423i	−1.16190	−	0.670820i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	−4.50000	+	2.59808i	−0.383065	+	0.221163i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000			−0.251754
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		−	6.92820i		−	0.565685i
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.162758	−	0.986666i	$-0.552039\pi$
$152$	−3.50000	−	6.06218i	−0.283887	−	0.491708i
$153$	−18.0000			−1.45521
$154$		0			0
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$			3.46410i			0.277350i
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−5.00000			−0.397779
$159$	9.00000	−	5.19615i	0.713746	−	0.412082i
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$		0			0
$165$	−27.0000	−	15.5885i	−2.10195	−	1.21356i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−9.00000	−	15.5885i	−0.690268	−	1.19558i
$171$	−10.5000	+	18.1865i	−0.802955	+	1.39076i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	−9.00000	+	5.19615i	−0.682288	+	0.393919i
$175$		0			0
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$		0			0
$178$		0			0
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	0.304446	+	0.952529i	$0.401529\pi$
$179$	−9.00000	+	15.5885i	−0.672692	+	1.16514i	−0.977138	+	0.212607i	$0.931805\pi$
$180$	9.00000			0.670820
$181$	−25.0000			−1.85824			−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$		0			0
$183$	−7.50000	−	4.33013i	−0.554416	−	0.320092i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−6.00000			−0.441129
$186$	3.00000	+	1.73205i	0.219971	+	0.127000i
$187$	−36.0000			−2.63258
$188$		0			0
$189$		0			0
$190$	−21.0000			−1.52350
$191$	−9.00000			−0.651217			−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000			−0.651217			−0.325609	+	0.945505i	$0.605569\pi$
$192$	−1.50000	−	0.866025i	−0.108253	−	0.0625000i
$193$	17.0000			1.22369			0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000			1.22369			0.611843	+	0.790979i	$0.290428\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	9.00000	+	5.19615i	0.644503	+	0.372104i
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	−12.0000	−	6.92820i	−0.846415	−	0.488678i
$202$	4.50000	+	7.79423i	0.316619	+	0.548400i
$203$		0			0
$204$	9.00000	−	5.19615i	0.630126	−	0.363803i
$205$		0			0
$206$	−5.00000	+	8.66025i	−0.348367	+	0.603388i
$207$	−9.00000			−0.625543
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−21.0000	+	36.3731i	−1.45260	+	2.51598i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	−4.50000	−	2.59808i	−0.308335	−	0.178017i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	3.00000	+	5.19615i	0.204598	+	0.354375i
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−5.00000	+	8.66025i	−0.338643	+	0.586546i
$219$	3.00000	−	1.73205i	0.202721	−	0.117041i
$220$	18.0000			1.21356
$221$	12.0000			0.807207
$222$		−	3.46410i		−	0.232495i
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$		0			0
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		−	12.1244i		−	0.802955i
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	0.882073	+	0.471113i	$0.156147\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$		0			0
$236$		0			0
$237$	−7.50000	−	4.33013i	−0.487177	−	0.281272i
$238$		0			0
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$	−4.50000	+	2.59808i	−0.290474	+	0.167705i
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	12.5000	−	21.6506i	0.803530	−	1.39176i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	5.00000			0.320092
$245$		0			0
$246$		0			0
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$	−2.00000			−0.127000
$249$	18.0000	−	10.3923i	1.14070	−	0.658586i
$250$	−3.00000			−0.189737
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	−17.0000			−1.06667
$255$		−	31.1769i		−	1.95237i
$256$	1.00000			0.0625000
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$	−3.00000	+	1.73205i	−0.186772	+	0.107833i
$259$		0			0
$260$	−6.00000			−0.372104
$261$	−18.0000			−1.11417
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	0.983728	+	0.179664i	$0.0575011\pi$
$263$	10.5000	+	18.1865i	0.647458	+	1.12143i	−0.336270	+	0.941766i	$0.609166\pi$
$264$			10.3923i			0.639602i
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$	8.00000			0.488678
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	13.5000	+	7.79423i	0.821584	+	0.474342i
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	3.00000	+	5.19615i	0.181237	+	0.313911i
$275$	12.0000	−	20.7846i	0.723627	−	1.25336i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	2.50000	+	4.33013i	0.149940	+	0.259704i
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$		0			0
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	−0.110717	−	0.993852i	$-0.535315\pi$
$281$	13.5000	−	23.3827i	0.805342	−	1.39489i	0.916060	−	0.401042i	$-0.131352\pi$
$282$		0			0
$283$	−19.0000			−1.12943			−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000			−1.12943			−0.564716	+	0.825285i	$0.691014\pi$
$284$	3.00000			0.178017
$285$	−31.5000	−	18.1865i	−1.86590	−	1.07728i
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−9.00000	−	15.5885i	−0.528498	−	0.915386i
$291$	3.00000	−	1.73205i	0.175863	−	0.101535i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	0.906509	−	0.422186i	$-0.138737\pi$
$293$	1.50000	+	2.59808i	0.0876309	+	0.151781i	−0.818878	+	0.573967i	$0.805404\pi$
$294$		0			0
$295$		0			0
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	27.0000	−	15.5885i	1.56670	−	0.904534i
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	6.00000			0.346989
$300$			6.92820i			0.400000i
$301$		0			0
$302$	11.5000	+	19.9186i	0.661751	+	1.14619i
$303$			15.5885i			0.895533i
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	7.50000	−	12.9904i	0.429449	−	0.743827i
$306$	18.0000			1.02899
$307$	−25.0000			−1.42683			−0.713413	−	0.700744i	$-0.752851\pi$
$307$	−25.0000			−1.42683			−0.713413	+	0.700744i	$0.752851\pi$
$308$		0			0
$309$	−15.0000	+	8.66025i	−0.853320	+	0.492665i
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		−	3.46410i		−	0.196116i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	13.0000			0.733632
$315$		0			0
$316$	5.00000			0.281272
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$	−9.00000	+	5.19615i	−0.504695	+	0.291386i
$319$	−36.0000			−2.01561
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$		−	20.7846i		−	1.16008i
$322$		0			0
$323$	−42.0000			−2.33694
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	1.00000	+	1.73205i	0.0553849	+	0.0959294i
$327$	−15.0000	+	8.66025i	−0.829502	+	0.478913i
$328$		0			0
$329$		0			0
$330$	27.0000	+	15.5885i	1.48630	+	0.858116i
$331$	26.0000			1.42909			0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000			1.42909			0.714545	+	0.699590i	$0.246634\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$		0			0
$335$	12.0000	−	20.7846i	0.655630	−	1.13558i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$			25.9808i			1.41108i
$340$	9.00000	+	15.5885i	0.488094	+	0.845403i
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	10.5000	−	18.1865i	0.567775	−	0.983415i
$343$		0			0
$344$	1.00000	−	1.73205i	0.0539164	−	0.0933859i
$345$		−	15.5885i		−	0.839254i
$346$	6.00000			0.322562
$347$	−24.0000			−1.28839			−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000			−1.28839			−0.644194	+	0.764862i	$0.722807\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$		0			0
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	4.50000	−	7.79423i	0.238835	−	0.413675i
$356$		0			0
$357$		0			0
$358$	9.00000	−	15.5885i	0.475665	−	0.823876i
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	0.902891	−	0.429870i	$-0.141441\pi$
$359$	1.50000	+	2.59808i	0.0791670	+	0.137121i	−0.823724	+	0.566991i	$0.808107\pi$
$360$	−9.00000			−0.474342
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	25.0000			1.31397
$363$	37.5000	−	21.6506i	1.96824	−	1.13636i
$364$		0			0
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$	7.50000	+	4.33013i	0.392031	+	0.226339i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$	−3.00000	−	1.73205i	−0.155543	−	0.0898027i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	36.0000			1.86152
$375$	−4.50000	−	2.59808i	−0.232379	−	0.134164i
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	21.0000			1.07728
$381$	−25.5000	−	14.7224i	−1.30640	−	0.754253i
$382$	9.00000			0.460480
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	−0.539076	−	0.842257i	$-0.681226\pi$
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	0.998954	+	0.0457244i	$0.0145596\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$		0			0
$386$	−17.0000			−0.865277
$387$	−6.00000			−0.304997
$388$	−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	$-0.374865\pi$
$390$	−9.00000	−	5.19615i	−0.455733	−	0.263117i
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$	−13.5000	+	7.79423i	−0.680985	+	0.393167i
$394$	−18.0000			−0.906827
$395$	7.50000	−	12.9904i	0.377366	−	0.653617i
$396$	−9.00000	+	15.5885i	−0.452267	+	0.783349i
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$	12.0000	+	6.92820i	0.598506	+	0.345547i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−4.50000	−	7.79423i	−0.223883	−	0.387777i
$405$	13.5000	+	23.3827i	0.670820	+	1.16190i
$406$		0			0
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	−9.00000	+	5.19615i	−0.445566	+	0.257248i
$409$	32.0000			1.58230			0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000			1.58230			0.791149	+	0.611623i	$0.209483\pi$
$410$		0			0
$411$			10.3923i			0.512615i
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$		0			0
$414$	9.00000			0.442326
$415$	18.0000	+	31.1769i	0.883585	+	1.53041i
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$			8.66025i			0.424094i
$418$	21.0000	−	36.3731i	1.02714	−	1.77906i
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	0.622601	−	0.782540i	$-0.286076\pi$
$419$	−7.50000	−	12.9904i	−0.366399	−	0.634622i	−0.989000	+	0.147918i	$0.952743\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	24.0000			1.16417
$426$	4.50000	+	2.59808i	0.218026	+	0.125877i
$427$		0			0
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	−18.0000	+	10.3923i	−0.869048	+	0.501745i
$430$	−3.00000	−	5.19615i	−0.144673	−	0.250581i
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		−	5.19615i		−	0.250000i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		−	31.1769i		−	1.49482i
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−21.0000			−1.00457
$438$	−3.00000	+	1.73205i	−0.143346	+	0.0827606i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	−18.0000			−0.858116
$441$		0			0
$442$	−12.0000			−0.570782
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$			3.46410i			0.164399i
$445$		0			0
$446$	−14.0000	+	24.2487i	−0.662919	+	1.14821i
$447$	−9.00000	+	5.19615i	−0.425685	+	0.245770i
$448$		0			0
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$	−6.00000	+	10.3923i	−0.282843	+	0.489898i
$451$		0			0
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$			39.8372i			1.87171i
$454$	−7.50000	−	12.9904i	−0.351992	−	0.609669i
$455$		0			0
$456$			12.1244i			0.567775i
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	−0.500000	+	0.866025i	−0.0233635	+	0.0404667i
$459$	27.0000	+	15.5885i	1.26025	+	0.727607i
$460$	4.50000	+	7.79423i	0.209814	+	0.363408i
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	−0.169904	−	0.985461i	$-0.554346\pi$
$461$	16.5000	−	28.5788i	0.768482	−	1.33105i	0.938386	−	0.345589i	$-0.112321\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−9.00000	+	5.19615i	−0.417365	+	0.240966i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−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	$0.922888\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$		0			0
$470$		0			0
$471$	19.5000	+	11.2583i	0.898513	+	0.518756i
$472$		0			0
$473$	−12.0000			−0.551761
$474$	7.50000	+	4.33013i	0.344486	+	0.198889i
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$		0			0
$477$	−18.0000			−0.824163
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$	4.50000	−	2.59808i	0.205396	−	0.118585i
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	0.324316	+	0.945949i	$0.394866\pi$
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	−0.981374	+	0.192109i	$0.938467\pi$
$488$	−5.00000			−0.226339
$489$			3.46410i			0.156652i
$490$		0			0
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	0.588292	−	0.808649i	$-0.299801\pi$
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	−0.994456	+	0.105151i	$0.966467\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	−7.00000	+	12.1244i	−0.314945	+	0.545501i
$495$	27.0000	+	46.7654i	1.21356	+	2.10195i
$496$	2.00000			0.0898027
$497$		0			0
$498$	−18.0000	+	10.3923i	−0.806599	+	0.465690i
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	3.00000			0.134164
$501$		0			0
$502$	−3.00000			−0.133897
$503$	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
$505$	−27.0000			−1.20148
$506$	18.0000			0.800198
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	17.0000			0.754253
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$			31.1769i			1.38054i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	31.5000	−	18.1865i	1.39076	−	0.802955i
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	−15.0000	−	25.9808i	−0.660979	−	1.14485i
$516$	3.00000	−	1.73205i	0.132068	−	0.0762493i
$517$		0			0
$518$		0			0
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$	6.00000			0.263117
$521$	−12.0000	+	20.7846i	−0.525730	+	0.910590i	0.473821	+	0.880621i	$0.342874\pi$
$521$	−12.0000	+	20.7846i	−0.525730	+	0.910590i	−0.999551	+	0.0299693i	$0.990459\pi$
$522$	18.0000			0.787839
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	0.972421	−	0.233233i	$-0.0749303\pi$
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	−0.688196	+	0.725525i	$0.741597\pi$
$524$	4.50000	−	7.79423i	0.196583	−	0.340492i
$525$		0			0
$526$	−10.5000	−	18.1865i	−0.457822	−	0.792971i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		−	10.3923i		−	0.452267i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	36.0000			1.55642
$536$	−8.00000			−0.345547
$537$	27.0000	−	15.5885i	1.16514	−	0.672692i
$538$	−4.50000	+	7.79423i	−0.194009	+	0.336033i
$539$		0			0
$540$	−13.5000	−	7.79423i	−0.580948	−	0.335410i
$541$	−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	$-0.470961\pi$
$542$	−14.0000	−	24.2487i	−0.601351	−	1.04157i
$543$	37.5000	+	21.6506i	1.60928	+	0.929118i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−15.0000	−	25.9808i	−0.642529	−	1.11289i
$546$		0			0
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	0.289605	+	0.957146i	$0.406476\pi$
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	−0.973715	+	0.227768i	$0.926857\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	7.50000	+	12.9904i	0.320092	+	0.554416i
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	−42.0000			−1.78926
$552$	−4.50000	+	2.59808i	−0.191533	+	0.110581i
$553$		0			0
$554$	−8.00000	−	13.8564i	−0.339887	−	0.588702i
$555$	9.00000	+	5.19615i	0.382029	+	0.220564i
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$	−3.00000	−	5.19615i	−0.127000	−	0.219971i
$559$	4.00000			0.169182
$560$		0			0
$561$	54.0000	+	31.1769i	2.27988	+	1.31629i
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−33.0000			−1.39078			−0.695392	−	0.718631i	$-0.744769\pi$
$563$	−33.0000			−1.39078			−0.695392	+	0.718631i	$0.744769\pi$
$564$		0			0
$565$	−45.0000			−1.89316
$566$	19.0000			0.798630
$567$		0			0
$568$	−3.00000			−0.125877
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$	31.5000	+	18.1865i	1.31939	+	0.761750i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$	13.5000	+	7.79423i	0.563971	+	0.325609i
$574$		0			0
$575$	12.0000			0.500435
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	2.00000	−	3.46410i	0.0832611	−	0.144212i	−0.821388	−	0.570370i	$-0.806800\pi$
$577$	2.00000	−	3.46410i	0.0832611	−	0.144212i	0.904649	+	0.426158i	$0.140133\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	−25.5000	−	14.7224i	−1.05974	−	0.611843i
$580$	9.00000	+	15.5885i	0.373705	+	0.647275i
$581$		0			0
$582$	−3.00000	+	1.73205i	−0.124354	+	0.0717958i
$583$	−36.0000			−1.49097
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$	−9.00000	−	15.5885i	−0.372104	−	0.644503i
$586$	−1.50000	−	2.59808i	−0.0619644	−	0.107326i
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	−0.833408	−	0.552658i	$-0.813614\pi$
$587$	1.50000	−	2.59808i	0.0619116	−	0.107234i	0.895320	+	0.445424i	$0.146947\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$		0			0
$591$	−27.0000	−	15.5885i	−1.11063	−	0.641223i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$	−27.0000	+	15.5885i	−1.10782	+	0.639602i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	21.0000	−	12.1244i	0.859473	−	0.496217i
$598$	−6.00000			−0.245358
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		−	6.92820i		−	0.282843i
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	−0.972739	−	0.231903i	$-0.925505\pi$
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	0.687203	+	0.726465i	$0.258838\pi$
$602$		0			0
$603$	12.0000	+	20.7846i	0.488678	+	0.846415i
$604$	−11.5000	−	19.9186i	−0.467928	−	0.810476i
$605$	37.5000	+	64.9519i	1.52459	+	2.64067i
$606$		−	15.5885i		−	0.633238i
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$		0			0
$610$	−7.50000	+	12.9904i	−0.303666	+	0.525965i
$611$		0			0
$612$	−18.0000			−0.727607
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$	25.0000			1.00892
$615$		0			0
$616$		0			0
$617$	−21.0000	−	36.3731i	−0.845428	−	1.46432i	−0.885249	−	0.465118i	$-0.846012\pi$
$617$	−21.0000	−	36.3731i	−0.845428	−	1.46432i	0.0398207	−	0.999207i	$-0.487321\pi$
$618$	15.0000	−	8.66025i	0.603388	−	0.348367i
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	0.927752	−	0.373198i	$-0.121739\pi$
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	−0.787075	+	0.616858i	$0.788405\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$	−12.0000			−0.481156
$623$		0			0
$624$			3.46410i			0.138675i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	10.0000			0.399680
$627$	63.0000	−	36.3731i	2.51598	−	1.45260i
$628$	−13.0000			−0.518756
$629$	12.0000			0.478471
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−5.00000			−0.198889
$633$			13.8564i			0.550743i
$634$	−18.0000			−0.714871
$635$	25.5000	−	44.1673i	1.01194	−	1.75273i
$636$	9.00000	−	5.19615i	0.356873	−	0.206041i
$637$		0			0
$638$	36.0000			1.42525
$639$	4.50000	+	7.79423i	0.178017	+	0.308335i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	−0.999247	−	0.0387913i	$-0.987649\pi$
$641$	−13.5000	−	23.3827i	−0.533218	−	0.923561i	0.466029	−	0.884769i	$-0.345684\pi$
$642$			20.7846i			0.820303i
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$		0			0
$645$		−	10.3923i		−	0.409197i
$646$	42.0000			1.65247
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$		0			0
$650$	4.00000	−	6.92820i	0.156893	−	0.271746i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	−0.262515	−	0.964928i	$-0.584552\pi$
$653$	18.0000	−	31.1769i	0.704394	−	1.22005i	0.966910	−	0.255119i	$-0.0821147\pi$
$654$	15.0000	−	8.66025i	0.586546	−	0.338643i
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		0			0
$659$	−21.0000	+	36.3731i	−0.818044	+	1.41689i	0.0890776	+	0.996025i	$0.471608\pi$
$659$	−21.0000	+	36.3731i	−0.818044	+	1.41689i	−0.907122	+	0.420869i	$0.861725\pi$
$660$	−27.0000	−	15.5885i	−1.05097	−	0.606780i
$661$	5.00000			0.194477			0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000			0.194477			0.0972387	+	0.995261i	$0.468999\pi$
$662$	−26.0000			−1.01052
$663$	−18.0000	−	10.3923i	−0.699062	−	0.403604i
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$	−3.00000	+	5.19615i	−0.116248	+	0.201347i
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$		0			0
$669$	−42.0000	+	24.2487i	−1.62381	+	0.937509i
$670$	−12.0000	+	20.7846i	−0.463600	+	0.802980i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$		0			0
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	0.963679	−	0.267063i	$-0.0860531\pi$
$674$	−11.0000	−	19.0526i	−0.423704	−	0.733877i
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	42.0000			1.61419			0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000			1.61419			0.807096	+	0.590421i	$0.201038\pi$
$678$		−	25.9808i		−	0.997785i
$679$		0			0
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$		−	25.9808i		−	0.995585i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	−0.802905	−	0.596107i	$-0.796713\pi$
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	0.917697	+	0.397282i	$0.130047\pi$
$684$	−10.5000	+	18.1865i	−0.401478	+	0.695379i
$685$	−18.0000			−0.687745
$686$		0			0
$687$	−1.50000	+	0.866025i	−0.0572286	+	0.0330409i
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	12.0000			0.457164
$690$			15.5885i			0.593442i
$691$	47.0000			1.78796			0.893982	−	0.448103i	$-0.147900\pi$
$691$	47.0000			1.78796			0.893982	+	0.448103i	$0.147900\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	24.0000			0.911028
$695$	−15.0000			−0.568982
$696$	−9.00000	+	5.19615i	−0.341144	+	0.196960i
$697$		0			0
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$			15.5885i			0.589610i
$700$		0			0
$701$	−18.0000			−0.679851			−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000			−0.679851			−0.339925	+	0.940452i	$0.610402\pi$
$702$	9.00000	−	5.19615i	0.339683	−	0.196116i
$703$	7.00000	−	12.1244i	0.264010	−	0.457279i
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$		0			0
$708$		0			0
$709$	−52.0000			−1.95290			−0.976450	−	0.215742i	$-0.930783\pi$
$709$	−52.0000			−1.95290			−0.976450	+	0.215742i	$0.930783\pi$
$710$	−4.50000	+	7.79423i	−0.168882	+	0.292512i
$711$	7.50000	+	12.9904i	0.281272	+	0.487177i
$712$		0			0
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	−18.0000	−	31.1769i	−0.673162	−	1.16595i
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$		−	25.9808i		−	0.970269i
$718$	−1.50000	−	2.59808i	−0.0559795	−	0.0969593i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$	9.00000			0.335410
$721$		0			0
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$			13.8564i			0.515325i
$724$	−25.0000			−0.929118
$725$	24.0000			0.891338
$726$	−37.5000	+	21.6506i	−1.39176	+	0.803530i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$	−7.50000	−	4.33013i	−0.277208	−	0.160046i
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	0.463566	+	0.886062i	$0.346570\pi$
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	−0.999136	+	0.0415715i	$0.986764\pi$
$734$	4.00000	+	6.92820i	0.147643	+	0.255725i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$		0			0
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	−6.00000			−0.220564
$741$	−21.0000	+	12.1244i	−0.771454	+	0.445399i
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	3.00000	+	1.73205i	0.109985	+	0.0635001i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	7.00000	−	12.1244i	0.256288	−	0.443904i
$747$	−36.0000			−1.31717
$748$	−36.0000			−1.31629
$749$		0			0
$750$	4.50000	+	2.59808i	0.164317	+	0.0948683i
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$	−4.50000	−	2.59808i	−0.163989	−	0.0946792i
$754$	−12.0000			−0.437014
$755$	−69.0000			−2.51117
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−2.00000			−0.0726433
$759$	27.0000	+	15.5885i	0.980038	+	0.565825i
$760$	−21.0000			−0.761750
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$	25.5000	+	14.7224i	0.923768	+	0.533337i
$763$		0			0
$764$	−9.00000			−0.325609
$765$	−27.0000	+	46.7654i	−0.976187	+	1.69081i
$766$	−9.00000	+	15.5885i	−0.325183	+	0.563234i
$767$		0			0
$768$	−1.50000	−	0.866025i	−0.0541266	−	0.0312500i
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$	27.0000	−	15.5885i	0.972381	−	0.561405i
$772$	17.0000			0.611843
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.113480	−	0.993540i	$-0.463800\pi$
$773$	25.5000	−	44.1673i	0.917171	−	1.58859i	0.803691	−	0.595047i	$-0.202867\pi$
$774$	6.00000			0.215666
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	1.00000	−	1.73205i	0.0358979	−	0.0621770i
$777$		0			0
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$		0			0
$780$	9.00000	+	5.19615i	0.322252	+	0.186052i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	9.00000	+	15.5885i	0.321839	+	0.557442i
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$		0			0
$785$	−19.5000	+	33.7750i	−0.695985	+	1.20548i
$786$	13.5000	−	7.79423i	0.481529	−	0.278011i
$787$	20.0000			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$788$	18.0000			0.641223
$789$		−	36.3731i		−	1.29492i
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$		0			0
$792$	9.00000	−	15.5885i	0.319801	−	0.553912i
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	13.0000	+	22.5167i	0.461353	+	0.799086i
$795$		−	31.1769i		−	1.10573i
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$		0			0
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$	−12.0000			−0.423471
$804$	−12.0000	−	6.92820i	−0.423207	−	0.244339i
$805$		0			0
$806$	2.00000	+	3.46410i	0.0704470	+	0.122018i
$807$	−13.5000	+	7.79423i	−0.475223	+	0.274370i
$808$	4.50000	+	7.79423i	0.158309	+	0.274200i
$809$	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	$-0.0101559\pi$
$810$	−13.5000	−	23.3827i	−0.474342	−	0.821584i
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$		−	48.4974i		−	1.70088i
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−6.00000			−0.210171
$816$	9.00000	−	5.19615i	0.315063	−	0.181902i
$817$	−14.0000			−0.489798
$818$	−32.0000			−1.11885
$819$		0			0
$820$		0			0
$821$	−24.0000			−0.837606			−0.418803	−	0.908077i	$-0.637550\pi$
$821$	−24.0000			−0.837606			−0.418803	+	0.908077i	$0.637550\pi$
$822$		−	10.3923i		−	0.362473i
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$	−5.00000	+	8.66025i	−0.174183	+	0.301694i
$825$	−36.0000	+	20.7846i	−1.25336	+	0.723627i
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−9.00000			−0.312772
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	−18.0000	−	31.1769i	−0.624789	−	1.08217i
$831$		−	27.7128i		−	0.961347i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$		−	8.66025i		−	0.299880i
$835$		0			0
$836$	−21.0000	+	36.3731i	−0.726300	+	1.25799i
$837$		−	10.3923i		−	0.359211i
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−5.00000	+	8.66025i	−0.172311	+	0.298452i
$843$	−40.5000	+	23.3827i	−1.39489	+	0.805342i
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	−13.5000	−	23.3827i	−0.464414	−	0.804389i
$846$		0			0
$847$		0			0
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	28.5000	+	16.4545i	0.978117	+	0.564716i
$850$	−24.0000			−0.823193
$851$	6.00000			0.205677
$852$	−4.50000	−	2.59808i	−0.154167	−	0.0890086i
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	0.393753	+	0.919216i	$0.371177\pi$
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	−0.992941	+	0.118609i	$0.962157\pi$
$854$		0			0
$855$	31.5000	+	54.5596i	1.07728	+	1.86590i
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−27.0000	−	46.7654i	−0.922302	−	1.59747i	−0.795843	−	0.605503i	$-0.792972\pi$
$857$	−27.0000	−	46.7654i	−0.922302	−	1.59747i	−0.126459	−	0.991972i	$-0.540361\pi$
$858$	18.0000	−	10.3923i	0.614510	−	0.354787i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	3.00000	+	5.19615i	0.102299	+	0.177187i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−4.50000	−	7.79423i	−0.153182	−	0.265319i	0.779214	−	0.626758i	$-0.215619\pi$
$863$	−4.50000	−	7.79423i	−0.153182	−	0.265319i	−0.932395	+	0.361440i	$0.882285\pi$
$864$			5.19615i			0.176777i
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$	−14.0000			−0.475739
$867$			32.9090i			1.11765i
$868$		0			0
$869$	15.0000	+	25.9808i	0.508840	+	0.881337i
$870$			31.1769i			1.05700i
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	−5.00000	+	8.66025i	−0.169321	+	0.293273i
$873$	−6.00000			−0.203069
$874$	21.0000			0.710336
$875$		0			0
$876$	3.00000	−	1.73205i	0.101361	−	0.0585206i
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−8.00000			−0.269987
$879$		−	5.19615i		−	0.175262i
$880$	18.0000			0.606780
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	12.0000			0.403604
$885$		0			0
$886$	−18.0000			−0.604722
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		−	3.46410i		−	0.116248i
$889$		0			0
$890$		0			0
$891$	−54.0000			−1.80907
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$		0			0
$894$	9.00000	−	5.19615i	0.301005	−	0.173785i
$895$	27.0000	+	46.7654i	0.902510	+	1.56319i
$896$		0			0
$897$	−9.00000	−	5.19615i	−0.300501	−	0.173494i
$898$	−33.0000			−1.10122
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$	−37.5000	+	64.9519i	−1.24654	+	2.15907i
$906$		−	39.8372i		−	1.32350i
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	−0.999334	−	0.0364935i	$-0.988381\pi$
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	0.468063	−	0.883695i	$-0.344952\pi$
$908$	7.50000	+	12.9904i	0.248896	+	0.431101i
$909$	13.5000	−	23.3827i	0.447767	−	0.775555i
$910$		0			0
$911$	−7.50000	+	12.9904i	−0.248486	+	0.430391i	−0.963106	−	0.269122i	$-0.913266\pi$
$911$	−7.50000	+	12.9904i	−0.248486	+	0.430391i	0.714620	+	0.699513i	$0.246600\pi$
$912$		−	12.1244i		−	0.401478i
$913$	−72.0000			−2.38285
$914$	−29.0000			−0.959235
$915$	−22.5000	+	12.9904i	−0.743827	+	0.429449i
$916$	0.500000	−	0.866025i	0.0165205	−	0.0286143i
$917$		0			0
$918$	−27.0000	−	15.5885i	−0.891133	−	0.514496i
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$	37.5000	+	21.6506i	1.23567	+	0.713413i
$922$	−16.5000	+	28.5788i	−0.543399	+	0.941194i
$923$	−3.00000	−	5.19615i	−0.0987462	−	0.171033i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	−6.50000	−	11.2583i	−0.213603	−	0.369972i
$927$	30.0000			0.985329
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$	9.00000	−	5.19615i	0.295122	−	0.170389i
$931$		0			0
$932$	−4.50000	−	7.79423i	−0.147402	−	0.255308i
$933$	−18.0000	−	10.3923i	−0.589294	−	0.340229i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−54.0000	+	93.5307i	−1.76599	+	3.05878i
$936$	−3.00000	+	5.19615i	−0.0980581	+	0.169842i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$	15.0000	+	8.66025i	0.489506	+	0.282617i
$940$		0			0
$941$	21.0000			0.684580			0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000			0.684580			0.342290	+	0.939594i	$0.388797\pi$
$942$	−19.5000	−	11.2583i	−0.635344	−	0.366816i
$943$		0			0
$944$		0			0
$945$		0			0
$946$	12.0000			0.390154
$947$	−24.0000			−0.779895			−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000			−0.779895			−0.389948	+	0.920837i	$0.627507\pi$
$948$	−7.50000	−	4.33013i	−0.243589	−	0.140636i
$949$	4.00000			0.129845
$950$	−14.0000	+	24.2487i	−0.454220	+	0.786732i
$951$	−27.0000	−	15.5885i	−0.875535	−	0.505490i
$952$		0			0
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$	18.0000			0.582772
$955$	−13.5000	+	23.3827i	−0.436850	+	0.756646i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	54.0000	+	31.1769i	1.74557	+	1.00781i
$958$	−3.00000	−	5.19615i	−0.0969256	−	0.167880i
$959$		0			0
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	−27.0000			−0.870968
$962$	2.00000	−	3.46410i	0.0644826	−	0.111687i
$963$	−18.0000	+	31.1769i	−0.580042	+	1.00466i
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	25.5000	−	44.1673i	0.820874	−	1.42180i
$966$		0			0
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	0.696374	−	0.717679i	$-0.254796\pi$
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	−0.969715	+	0.244238i	$0.921462\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$	63.0000	+	36.3731i	2.02385	+	1.16847i
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$		0			0
$974$	14.5000	−	25.1147i	0.464610	−	0.804728i
$975$	12.0000	−	6.92820i	0.384308	−	0.221880i
$976$	5.00000			0.160046
$977$	6.00000			0.191957			0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000			0.191957			0.0959785	+	0.995383i	$0.469402\pi$
$978$		−	3.46410i		−	0.110770i
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$	9.00000	+	15.5885i	0.287202	+	0.497448i
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$	−27.0000	−	46.7654i	−0.858116	−	1.48630i
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	−2.00000			−0.0635001
$993$	−39.0000	−	22.5167i	−1.23763	−	0.714545i
$994$		0			0
$995$	21.0000	+	36.3731i	0.665745	+	1.15310i
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	27.5000	+	47.6314i	0.870934	+	1.50850i	0.861032	+	0.508551i	$0.169818\pi$
$997$	27.5000	+	47.6314i	0.870934	+	1.50850i	0.00990158	+	0.999951i	$0.496848\pi$
$998$	16.0000	−	27.7128i	0.506471	−	0.877234i
$999$	−9.00000	+	5.19615i	−0.284747	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.b.655.1		2
3.2	odd	2		2646.2.e.f.2125.1		2
7.2	even	3		882.2.h.j.79.1		2
7.3	odd	6		882.2.f.h.295.1		2
7.4	even	3		126.2.f.a.43.1	✓	2
7.5	odd	6		882.2.h.f.79.1		2
7.6	odd	2		882.2.e.d.655.1		2
9.4	even	3		882.2.h.j.67.1		2
9.5	odd	6		2646.2.h.e.361.1		2
21.2	odd	6		2646.2.h.e.667.1		2
21.5	even	6		2646.2.h.a.667.1		2
21.11	odd	6		378.2.f.a.127.1		2
21.17	even	6		2646.2.f.c.883.1		2
21.20	even	2		2646.2.e.j.2125.1		2
28.11	odd	6		1008.2.r.d.673.1		2
63.4	even	3		126.2.f.a.85.1	yes	2
63.5	even	6		2646.2.e.j.1549.1		2
63.11	odd	6		1134.2.a.h.1.1		1
63.13	odd	6		882.2.h.f.67.1		2
63.23	odd	6		2646.2.e.f.1549.1		2
63.25	even	3		1134.2.a.a.1.1		1
63.31	odd	6		882.2.f.h.589.1		2
63.32	odd	6		378.2.f.a.253.1		2
63.38	even	6		7938.2.a.u.1.1		1
63.40	odd	6		882.2.e.d.373.1		2
63.41	even	6		2646.2.h.a.361.1		2
63.52	odd	6		7938.2.a.l.1.1		1
63.58	even	3	inner	882.2.e.b.373.1		2
63.59	even	6		2646.2.f.c.1765.1		2
84.11	even	6		3024.2.r.a.2017.1		2
252.11	even	6		9072.2.a.w.1.1		1
252.67	odd	6		1008.2.r.d.337.1		2
252.95	even	6		3024.2.r.a.1009.1		2
252.151	odd	6		9072.2.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	7.4	even	3
126.2.f.a.85.1	yes	2	63.4	even	3
378.2.f.a.127.1		2	21.11	odd	6
378.2.f.a.253.1		2	63.32	odd	6
882.2.e.b.373.1		2	63.58	even	3	inner
882.2.e.b.655.1		2	1.1	even	1	trivial
882.2.e.d.373.1		2	63.40	odd	6
882.2.e.d.655.1		2	7.6	odd	2
882.2.f.h.295.1		2	7.3	odd	6
882.2.f.h.589.1		2	63.31	odd	6
882.2.h.f.67.1		2	63.13	odd	6
882.2.h.f.79.1		2	7.5	odd	6
882.2.h.j.67.1		2	9.4	even	3
882.2.h.j.79.1		2	7.2	even	3
1008.2.r.d.337.1		2	252.67	odd	6
1008.2.r.d.673.1		2	28.11	odd	6
1134.2.a.a.1.1		1	63.25	even	3
1134.2.a.h.1.1		1	63.11	odd	6
2646.2.e.f.1549.1		2	63.23	odd	6
2646.2.e.f.2125.1		2	3.2	odd	2
2646.2.e.j.1549.1		2	63.5	even	6
2646.2.e.j.2125.1		2	21.20	even	2
2646.2.f.c.883.1		2	21.17	even	6
2646.2.f.c.1765.1		2	63.59	even	6
2646.2.h.a.361.1		2	63.41	even	6
2646.2.h.a.667.1		2	21.5	even	6
2646.2.h.e.361.1		2	9.5	odd	6
2646.2.h.e.667.1		2	21.2	odd	6
3024.2.r.a.1009.1		2	252.95	even	6
3024.2.r.a.2017.1		2	84.11	even	6
7938.2.a.l.1.1		1	63.52	odd	6
7938.2.a.u.1.1		1	63.38	even	6
9072.2.a.c.1.1		1	252.151	odd	6
9072.2.a.w.1.1		1	252.11	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.50000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +(1.50000 + 0.866025i) q^{6} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(3.00000 + 5.19615i) q^{11} +(-1.50000 - 0.866025i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(-4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(3.50000 + 6.06218i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(1.50000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(4.50000 - 2.59808i) q^{30} +2.00000 q^{31} -1.00000 q^{32} -10.3923i q^{33} +(3.00000 - 5.19615i) q^{34} +(1.50000 + 2.59808i) q^{36} +(-1.00000 - 1.73205i) q^{37} +(-3.50000 - 6.06218i) q^{38} +3.46410i q^{39} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(3.00000 + 5.19615i) q^{44} +9.00000 q^{45} +(1.50000 - 2.59808i) q^{46} +(-1.50000 - 0.866025i) q^{48} +(2.00000 + 3.46410i) q^{50} +(9.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +5.19615i q^{54} +18.0000 q^{55} -12.1244i q^{57} +(3.00000 - 5.19615i) q^{58} +(-4.50000 + 2.59808i) q^{60} +5.00000 q^{61} -2.00000 q^{62} +1.00000 q^{64} -6.00000 q^{65} +10.3923i q^{66} +8.00000 q^{67} +(-3.00000 + 5.19615i) q^{68} +(4.50000 - 2.59808i) q^{69} +3.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.92820i q^{75} +(3.50000 + 6.06218i) q^{76} -3.46410i q^{78} +5.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(1.00000 - 1.73205i) q^{86} +(9.00000 - 5.19615i) q^{87} +(-3.00000 - 5.19615i) q^{88} -9.00000 q^{90} +(-1.50000 + 2.59808i) q^{92} +(-3.00000 - 1.73205i) q^{93} +21.0000 q^{95} +(1.50000 + 0.866025i) q^{96} +(-1.00000 + 1.73205i) q^{97} +(-9.00000 + 15.5885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} + 2 q^{4} + 3 q^{5} + 3 q^{6} - 2 q^{8} + 3 q^{9} - 3 q^{10} + 6 q^{11} - 3 q^{12} - 2 q^{13} - 9 q^{15} + 2 q^{16} - 6 q^{17} - 3 q^{18} + 7 q^{19} + 3 q^{20} - 6 q^{22} - 3 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} - 6 q^{29} + 9 q^{30} + 4 q^{31} - 2 q^{32} + 6 q^{34} + 3 q^{36} - 2 q^{37} - 7 q^{38} - 3 q^{40} - 2 q^{43} + 6 q^{44} + 18 q^{45} + 3 q^{46} - 3 q^{48} + 4 q^{50} + 18 q^{51} - 2 q^{52} - 6 q^{53} + 36 q^{55} + 6 q^{58} - 9 q^{60} + 10 q^{61} - 4 q^{62} + 2 q^{64} - 12 q^{65} + 16 q^{67} - 6 q^{68} + 9 q^{69} + 6 q^{71} - 3 q^{72} - 2 q^{73} + 2 q^{74} + 7 q^{76} + 10 q^{79} + 3 q^{80} - 9 q^{81} - 12 q^{83} + 18 q^{85} + 2 q^{86} + 18 q^{87} - 6 q^{88} - 18 q^{90} - 3 q^{92} - 6 q^{93} + 42 q^{95} + 3 q^{96} - 2 q^{97} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 + 2 * q^4 + 3 * q^5 + 3 * q^6 - 2 * q^8 + 3 * q^9 - 3 * q^10 + 6 * q^11 - 3 * q^12 - 2 * q^13 - 9 * q^15 + 2 * q^16 - 6 * q^17 - 3 * q^18 + 7 * q^19 + 3 * q^20 - 6 * q^22 - 3 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 - 6 * q^29 + 9 * q^30 + 4 * q^31 - 2 * q^32 + 6 * q^34 + 3 * q^36 - 2 * q^37 - 7 * q^38 - 3 * q^40 - 2 * q^43 + 6 * q^44 + 18 * q^45 + 3 * q^46 - 3 * q^48 + 4 * q^50 + 18 * q^51 - 2 * q^52 - 6 * q^53 + 36 * q^55 + 6 * q^58 - 9 * q^60 + 10 * q^61 - 4 * q^62 + 2 * q^64 - 12 * q^65 + 16 * q^67 - 6 * q^68 + 9 * q^69 + 6 * q^71 - 3 * q^72 - 2 * q^73 + 2 * q^74 + 7 * q^76 + 10 * q^79 + 3 * q^80 - 9 * q^81 - 12 * q^83 + 18 * q^85 + 2 * q^86 + 18 * q^87 - 6 * q^88 - 18 * q^90 - 3 * q^92 - 6 * q^93 + 42 * q^95 + 3 * q^96 - 2 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more