LMFDB - Embedded newform 1014.2.e.e.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.e.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +1.00000 q^{12} +2.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(1.00000 - 1.73205i) q^{20} -2.00000 q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(5.00000 + 8.66025i) q^{29} +(-1.00000 + 1.73205i) q^{30} -10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +(-2.00000 + 3.46410i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 - 6.92820i) q^{37} -6.00000 q^{38} +2.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(2.00000 - 3.46410i) q^{43} +(1.00000 - 1.73205i) q^{45} +(-2.00000 + 3.46410i) q^{46} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +2.00000 q^{51} -6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +6.00000 q^{57} +(-5.00000 + 8.66025i) q^{58} +(-2.00000 + 3.46410i) q^{59} -2.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-5.00000 - 8.66025i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(2.00000 - 3.46410i) q^{69} -4.00000 q^{70} +(0.500000 - 0.866025i) q^{72} -4.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-3.00000 - 5.19615i) q^{76} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +4.00000 q^{83} +(1.00000 - 1.73205i) q^{84} +(2.00000 - 3.46410i) q^{85} +4.00000 q^{86} +(5.00000 - 8.66025i) q^{87} +(3.00000 + 5.19615i) q^{89} +2.00000 q^{90} -4.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(6.00000 - 10.3923i) q^{95} -1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 4 q^{21} + 4 q^{23} + q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} + 10 q^{29} - 2 q^{30} - 20 q^{31} + q^{32} - 4 q^{34} - 4 q^{35} - q^{36} - 8 q^{37} - 12 q^{38} + 4 q^{40} + 10 q^{41} - 2 q^{42} + 4 q^{43} + 2 q^{45} - 4 q^{46} - 24 q^{47} - q^{48} + 3 q^{49} - q^{50} + 4 q^{51} - 12 q^{53} + q^{54} - 2 q^{56} + 12 q^{57} - 10 q^{58} - 4 q^{59} - 4 q^{60} - 2 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{67} - 2 q^{68} + 4 q^{69} - 8 q^{70} + q^{72} - 8 q^{73} + 8 q^{74} + q^{75} - 6 q^{76} + 2 q^{80} - q^{81} - 10 q^{82} + 8 q^{83} + 2 q^{84} + 4 q^{85} + 8 q^{86} + 10 q^{87} + 6 q^{89} + 4 q^{90} - 8 q^{92} + 10 q^{93} - 12 q^{94} + 12 q^{95} - 2 q^{96} - 12 q^{97} - 3 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + 2 * q^7 - 2 * q^8 - q^9 - 2 * q^10 + 2 * q^12 + 4 * q^14 + 2 * q^15 - q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 4 * q^21 + 4 * q^23 + q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 + 10 * q^29 - 2 * q^30 - 20 * q^31 + q^32 - 4 * q^34 - 4 * q^35 - q^36 - 8 * q^37 - 12 * q^38 + 4 * q^40 + 10 * q^41 - 2 * q^42 + 4 * q^43 + 2 * q^45 - 4 * q^46 - 24 * q^47 - q^48 + 3 * q^49 - q^50 + 4 * q^51 - 12 * q^53 + q^54 - 2 * q^56 + 12 * q^57 - 10 * q^58 - 4 * q^59 - 4 * q^60 - 2 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^67 - 2 * q^68 + 4 * q^69 - 8 * q^70 + q^72 - 8 * q^73 + 8 * q^74 + q^75 - 6 * q^76 + 2 * q^80 - q^81 - 10 * q^82 + 8 * q^83 + 2 * q^84 + 4 * q^85 + 8 * q^86 + 10 * q^87 + 6 * q^89 + 4 * q^90 - 8 * q^92 + 10 * q^93 - 12 * q^94 + 12 * q^95 - 2 * q^96 - 12 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	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
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$	−2.00000			−0.436436
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.785872	+	0.618389i	$0.212214\pi$
$29$	5.00000	+	8.66025i	0.928477	+	1.60817i	0.142605	+	0.989780i	$0.454452\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−2.00000	+	3.46410i	−0.338062	+	0.585540i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	2.00000			0.316228
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	0.931436	+	0.363905i	$0.118557\pi$
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	−0.150567	+	0.988600i	$0.548110\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$		0			0
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	2.00000			0.280056
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$	6.00000			0.794719
$58$	−5.00000	+	8.66025i	−0.656532	+	1.13715i
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−2.00000			−0.258199
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	−5.00000	−	8.66025i	−0.635001	−	1.09985i
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	2.00000	−	3.46410i	0.240772	−	0.417029i
$70$	−4.00000			−0.478091
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−3.00000	−	5.19615i	−0.344124	−	0.596040i
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	4.00000			0.439057			0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000			0.439057			0.219529	+	0.975606i	$0.429548\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	4.00000			0.431331
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	−4.00000			−0.417029
$93$	5.00000	+	8.66025i	0.518476	+	0.898027i
$94$	−6.00000	−	10.3923i	−0.618853	−	1.07188i
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$	−1.00000			−0.102062
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	0.382164	+	0.924095i	$0.375179\pi$
$97$	−6.00000	+	10.3923i	−0.609208	+	1.05518i	−0.991371	+	0.131084i	$0.958154\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	1.00000	+	1.73205i	0.0990148	+	0.171499i
$103$	16.0000			1.57653			0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000			1.57653			0.788263	+	0.615338i	$0.210980\pi$
$104$		0			0
$105$	4.00000			0.390360
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$		0			0
$111$	−4.00000	+	6.92820i	−0.379663	+	0.657596i
$112$	−2.00000			−0.188982
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	0.322498	+	0.946570i	$0.395477\pi$
$113$	−7.00000	+	12.1244i	−0.658505	+	1.14056i	−0.981003	+	0.193993i	$0.937856\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	−10.0000			−0.928477
$117$		0			0
$118$	−4.00000			−0.368230
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−2.00000			−0.181071
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	12.0000			1.07331
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.00000			−0.352180
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$	6.00000	+	10.3923i	0.520266	+	0.901127i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−2.00000			−0.172133
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	4.00000			0.340503
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	−2.00000	−	3.46410i	−0.169031	−	0.292770i
$141$	6.00000	+	10.3923i	0.505291	+	0.875190i
$142$		0			0
$143$		0			0
$144$	1.00000			0.0833333
$145$	−10.0000	−	17.3205i	−0.830455	−	1.43839i
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	8.00000			0.657596
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	7.00000	−	12.1244i	0.573462	−	0.993266i	0.996207	−	0.0870170i	$-0.0277334\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$		0			0
$155$	20.0000			1.60644
$156$		0			0
$157$	−2.00000			−0.159617			−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000			−0.159617			−0.0798087	+	0.996810i	$0.525431\pi$
$158$		0			0
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$	8.00000			0.630488
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	−0.450110	−	0.892973i	$-0.648615\pi$
$163$	7.00000	−	12.1244i	0.548282	−	0.949653i	0.998392	−	0.0566798i	$-0.0180514\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	2.00000	+	3.46410i	0.155230	+	0.268866i
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	0.999169	−	0.0407502i	$-0.0129748\pi$
$167$	6.00000	+	10.3923i	0.464294	+	0.804181i	−0.534875	+	0.844931i	$0.679641\pi$
$168$	2.00000			0.154303
$169$		0			0
$170$	4.00000			0.306786
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−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	$0.239913\pi$
$174$	10.0000			0.758098
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$		0			0
$177$	4.00000			0.300658
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$	8.00000	+	13.8564i	0.588172	+	1.01874i
$186$	−5.00000	+	8.66025i	−0.366618	+	0.635001i
$187$		0			0
$188$	6.00000	−	10.3923i	0.437595	−	0.757937i
$189$	1.00000	−	1.73205i	0.0727393	−	0.125988i
$190$	12.0000			0.870572
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−8.00000	−	13.8564i	−0.575853	−	0.997406i	−0.995948	−	0.0899262i	$-0.971337\pi$
$193$	−8.00000	−	13.8564i	−0.575853	−	0.997406i	0.420096	−	0.907480i	$-0.361996\pi$
$194$	−12.0000			−0.861550
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	−0.929762	−	0.368161i	$-0.879988\pi$
$197$	−11.0000	−	19.0526i	−0.783718	−	1.35744i	0.146045	−	0.989278i	$-0.453346\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	1.00000			0.0707107
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$	−1.00000	+	1.73205i	−0.0703598	+	0.121867i
$203$	20.0000			1.40372
$204$	−1.00000	+	1.73205i	−0.0700140	+	0.121268i
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	−4.00000			−0.278019
$208$		0			0
$209$		0			0
$210$	2.00000	+	3.46410i	0.138013	+	0.239046i
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	4.00000	−	6.92820i	0.273434	−	0.473602i
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	−1.00000			−0.0680414
$217$	−10.0000	+	17.3205i	−0.678844	+	1.17579i
$218$	−2.00000	−	3.46410i	−0.135457	−	0.234619i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$		0			0
$222$	−8.00000			−0.536925
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	0.530607	−	0.847618i	$-0.321964\pi$
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	−0.999362	+	0.0357107i	$0.988630\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$	−14.0000			−0.931266
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	4.00000			0.264327			0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000			0.264327			0.132164	+	0.991228i	$0.457808\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$		0			0
$232$	−5.00000	−	8.66025i	−0.328266	−	0.568574i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	24.0000			1.56559
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$		0			0
$238$	−2.00000	+	3.46410i	−0.129641	+	0.224544i
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	−10.0000	+	17.3205i	−0.644157	+	1.11571i	0.340339	+	0.940303i	$0.389458\pi$
$241$	−10.0000	+	17.3205i	−0.644157	+	1.11571i	−0.984496	+	0.175409i	$0.943875\pi$
$242$	11.0000			0.707107
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.00000	−	1.73205i	−0.0640184	−	0.110883i
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$	10.0000			0.637577
$247$		0			0
$248$	10.0000			0.635001
$249$	−2.00000	−	3.46410i	−0.126745	−	0.219529i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.0364441	+	0.999336i	$0.511603\pi$
$251$	−14.0000	+	24.2487i	−0.883672	+	1.53057i	−0.847228	+	0.531229i	$0.821730\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	−4.00000			−0.250490
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	−2.00000	−	3.46410i	−0.124515	−	0.215666i
$259$	−16.0000			−0.994192
$260$		0			0
$261$	−10.0000			−0.618984
$262$	−4.00000	−	6.92820i	−0.247121	−	0.428026i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	−6.00000	+	10.3923i	−0.367884	+	0.637193i
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	2.00000			0.122169
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	0.976977	−	0.213343i	$-0.0684351\pi$
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	−0.673249	+	0.739416i	$0.735102\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	2.00000			0.120824
$275$		0			0
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	20.0000			1.19952
$279$	5.00000	−	8.66025i	0.299342	−	0.518476i
$280$	2.00000	−	3.46410i	0.119523	−	0.207020i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−6.00000	+	10.3923i	−0.357295	+	0.618853i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$		0			0
$285$	−12.0000			−0.710819
$286$		0			0
$287$	20.0000			1.18056
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	10.0000	−	17.3205i	0.587220	−	1.01710i
$291$	12.0000			0.703452
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	7.00000	−	12.1244i	0.408944	−	0.708312i	−0.585827	−	0.810436i	$-0.699230\pi$
$293$	7.00000	−	12.1244i	0.408944	−	0.708312i	0.994772	+	0.102123i	$0.0325637\pi$
$294$	3.00000			0.174964
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$		0			0
$298$	14.0000			0.810998
$299$		0			0
$300$	−1.00000			−0.0577350
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	1.00000	−	1.73205i	0.0574485	−	0.0995037i
$304$	6.00000			0.344124
$305$	2.00000	−	3.46410i	0.114520	−	0.198354i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$		0			0
$309$	−8.00000	−	13.8564i	−0.455104	−	0.788263i
$310$	10.0000	+	17.3205i	0.567962	+	0.983739i
$311$	28.0000			1.58773			0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000			1.58773			0.793867	+	0.608091i	$0.208065\pi$
$312$		0			0
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	−1.00000	−	1.73205i	−0.0564333	−	0.0977453i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$		0			0
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$		0			0
$320$	−2.00000			−0.111803
$321$	−4.00000	+	6.92820i	−0.223258	+	0.386695i
$322$	4.00000	+	6.92820i	0.222911	+	0.386094i
$323$	−6.00000	−	10.3923i	−0.333849	−	0.578243i
$324$	1.00000			0.0555556
$325$		0			0
$326$	14.0000			0.775388
$327$	2.00000	+	3.46410i	0.110600	+	0.191565i
$328$	−5.00000	−	8.66025i	−0.276079	−	0.478183i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	−0.970091	−	0.242742i	$-0.921953\pi$
$331$	−5.00000	+	8.66025i	−0.274825	+	0.476011i	0.695266	+	0.718752i	$0.255287\pi$
$332$	−2.00000	+	3.46410i	−0.109764	+	0.190117i
$333$	8.00000			0.438397
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	14.0000			0.760376
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$		0			0
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$	20.0000			1.07990
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$	−6.00000			−0.322562
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	5.00000	+	8.66025i	0.268028	+	0.464238i
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$	−2.00000			−0.106904
$351$		0			0
$352$		0			0
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	0.971208	+	0.238233i	$0.0765683\pi$
$353$	13.0000	+	22.5167i	0.691920	+	1.19844i	−0.279288	+	0.960207i	$0.590098\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$	−6.00000			−0.317999
$357$	2.00000	−	3.46410i	0.105851	−	0.183340i
$358$		0			0
$359$	4.00000			0.211112			0.105556	−	0.994413i	$-0.466338\pi$
$359$	4.00000			0.211112			0.105556	+	0.994413i	$0.466338\pi$
$360$	−1.00000	+	1.73205i	−0.0527046	+	0.0912871i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−11.0000	−	19.0526i	−0.578147	−	1.00138i
$363$	−11.0000			−0.577350
$364$		0			0
$365$	8.00000			0.418739
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−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	$0.900289\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	−10.0000			−0.520579
$370$	−8.00000	+	13.8564i	−0.415900	+	0.720360i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$	−10.0000			−0.518476
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$		0			0
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$	12.0000			0.618853
$377$		0			0
$378$	2.00000			0.102869
$379$	17.0000	+	29.4449i	0.873231	+	1.51248i	0.858635	+	0.512588i	$0.171313\pi$
$379$	17.0000	+	29.4449i	0.873231	+	1.51248i	0.0145964	+	0.999893i	$0.495354\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$	4.00000	−	6.92820i	0.204926	−	0.354943i
$382$	−12.0000			−0.613973
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	−0.912589	−	0.408879i	$-0.865920\pi$
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	0.810394	+	0.585886i	$0.199253\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	8.00000	−	13.8564i	0.407189	−	0.705273i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−1.50000	−	2.59808i	−0.0757614	−	0.131223i
$393$	4.00000	+	6.92820i	0.201773	+	0.349482i
$394$	11.0000	−	19.0526i	0.554172	−	0.959854i
$395$		0			0
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$		0			0
$399$	6.00000	−	10.3923i	0.300376	−	0.520266i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$	−2.00000			−0.0997509
$403$		0			0
$404$	−2.00000			−0.0995037
$405$	1.00000	+	1.73205i	0.0496904	+	0.0860663i
$406$	10.0000	+	17.3205i	0.496292	+	0.859602i
$407$		0			0
$408$	−2.00000			−0.0990148
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	10.0000	−	17.3205i	0.493865	−	0.855399i
$411$	−2.00000			−0.0986527
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$	4.00000	+	6.92820i	0.196827	+	0.340915i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	−8.00000			−0.392705
$416$		0			0
$417$	−20.0000			−0.979404
$418$		0			0
$419$	−20.0000	−	34.6410i	−0.977064	−	1.69232i	−0.672949	−	0.739689i	$-0.734973\pi$
$419$	−20.0000	−	34.6410i	−0.977064	−	1.69232i	−0.304115	−	0.952635i	$-0.598361\pi$
$420$	−2.00000	+	3.46410i	−0.0975900	+	0.169031i
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	6.00000	−	10.3923i	0.292075	−	0.505889i
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$	6.00000			0.291386
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	2.00000	+	3.46410i	0.0967868	+	0.167640i
$428$	8.00000			0.386695
$429$		0			0
$430$	−8.00000			−0.385794
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	0.518096	−	0.855323i	$-0.326641\pi$
$431$	−10.0000	−	17.3205i	−0.481683	−	0.834300i	−0.999779	+	0.0210230i	$0.993308\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	0.363851	+	0.931457i	$0.381462\pi$
$433$	−13.0000	+	22.5167i	−0.624740	+	1.08208i	−0.988591	+	0.150624i	$0.951872\pi$
$434$	−20.0000			−0.960031
$435$	−10.0000	+	17.3205i	−0.479463	+	0.830455i
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	−24.0000			−1.14808
$438$	−2.00000	+	3.46410i	−0.0955637	+	0.165521i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−16.0000			−0.760183			−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000			−0.760183			−0.380091	+	0.924949i	$0.624107\pi$
$444$	−4.00000	−	6.92820i	−0.189832	−	0.328798i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	7.00000	−	12.1244i	0.331460	−	0.574105i
$447$	−14.0000			−0.662177
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	3.00000	−	5.19615i	0.141579	−	0.245222i	−0.786513	−	0.617574i	$-0.788115\pi$
$449$	3.00000	−	5.19615i	0.141579	−	0.245222i	0.928091	+	0.372353i	$0.121449\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	−7.00000	−	12.1244i	−0.329252	−	0.570282i
$453$	−5.00000	−	8.66025i	−0.234920	−	0.406894i
$454$	8.00000			0.375459
$455$		0			0
$456$	−6.00000			−0.280976
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	0.981921	+	0.189292i	$0.0606194\pi$
$457$	14.0000	+	24.2487i	0.654892	+	1.13431i	−0.327028	+	0.945015i	$0.606047\pi$
$458$	2.00000	+	3.46410i	0.0934539	+	0.161867i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	8.00000			0.373002
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	6.00000			0.278844			0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000			0.278844			0.139422	+	0.990233i	$0.455476\pi$
$464$	5.00000	−	8.66025i	0.232119	−	0.402042i
$465$	−10.0000	−	17.3205i	−0.463739	−	0.803219i
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	12.0000	+	20.7846i	0.553519	+	0.958723i
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$		0			0
$474$		0			0
$475$	3.00000	−	5.19615i	0.137649	−	0.238416i
$476$	−4.00000			−0.183340
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	8.00000	+	13.8564i	0.365911	+	0.633777i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$	2.00000			0.0912871
$481$		0			0
$482$	−20.0000			−0.910975
$483$	−4.00000	−	6.92820i	−0.182006	−	0.315244i
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	12.0000	−	20.7846i	0.544892	−	0.943781i
$486$	−1.00000			−0.0453609
$487$	9.00000	−	15.5885i	0.407829	−	0.706380i	−0.586817	−	0.809719i	$-0.699619\pi$
$487$	9.00000	−	15.5885i	0.407829	−	0.706380i	0.994646	+	0.103339i	$0.0329526\pi$
$488$	1.00000	−	1.73205i	0.0452679	−	0.0784063i
$489$	−14.0000			−0.633102
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	−0.987181	−	0.159603i	$-0.948978\pi$
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	0.355370	−	0.934726i	$-0.384355\pi$
$492$	5.00000	+	8.66025i	0.225417	+	0.390434i
$493$	−20.0000			−0.900755
$494$		0			0
$495$		0			0
$496$	5.00000	+	8.66025i	0.224507	+	0.388857i
$497$		0			0
$498$	2.00000	−	3.46410i	0.0896221	−	0.155230i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	−28.0000			−1.24970
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	−2.00000	−	3.46410i	−0.0889988	−	0.154150i
$506$		0			0
$507$		0			0
$508$	−8.00000			−0.354943
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$	−2.00000	−	3.46410i	−0.0885615	−	0.153393i
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$	−1.00000			−0.0441942
$513$	−3.00000	+	5.19615i	−0.132453	+	0.229416i
$514$	−9.00000	+	15.5885i	−0.396973	+	0.687577i
$515$	−32.0000			−1.41009
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$		0			0
$518$	−8.00000	−	13.8564i	−0.351500	−	0.608816i
$519$	6.00000			0.263371
$520$		0			0
$521$	−18.0000			−0.788594			−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000			−0.788594			−0.394297	+	0.918983i	$0.629012\pi$
$522$	−5.00000	−	8.66025i	−0.218844	−	0.379049i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	2.00000			0.0872872
$526$	12.0000	−	20.7846i	0.523225	−	0.906252i
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	6.00000	+	10.3923i	0.260623	+	0.451413i
$531$	−2.00000	−	3.46410i	−0.0867926	−	0.150329i
$532$	−12.0000			−0.520266
$533$		0			0
$534$	6.00000			0.259645
$535$	8.00000	+	13.8564i	0.345870	+	0.599065i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$	10.0000			0.431131
$539$		0			0
$540$	1.00000	−	1.73205i	0.0430331	−	0.0745356i
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$	−5.00000	+	8.66025i	−0.214768	+	0.371990i
$543$	11.0000	+	19.0526i	0.472055	+	0.817624i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	8.00000			0.342682
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$	−60.0000			−2.55609
$552$	−2.00000	+	3.46410i	−0.0851257	+	0.147442i
$553$		0			0
$554$	−2.00000			−0.0849719
$555$	8.00000	−	13.8564i	0.339581	−	0.588172i
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	10.0000			0.423334
$559$		0			0
$560$	4.00000			0.169031
$561$		0			0
$562$	−5.00000	−	8.66025i	−0.210912	−	0.365311i
$563$	−8.00000	+	13.8564i	−0.337160	+	0.583978i	−0.983897	−	0.178735i	$-0.942800\pi$
$563$	−8.00000	+	13.8564i	−0.337160	+	0.583978i	0.646737	+	0.762713i	$0.276133\pi$
$564$	−12.0000			−0.505291
$565$	14.0000	−	24.2487i	0.588984	−	1.02015i
$566$	−2.00000	+	3.46410i	−0.0840663	+	0.145607i
$567$	−2.00000			−0.0839921
$568$		0			0
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$	−6.00000	−	10.3923i	−0.251312	−	0.435286i
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$		0			0
$573$	12.0000			0.501307
$574$	10.0000	+	17.3205i	0.417392	+	0.722944i
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−8.00000			−0.333044			−0.166522	−	0.986038i	$-0.553254\pi$
$577$	−8.00000			−0.333044			−0.166522	+	0.986038i	$0.553254\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$	−8.00000	+	13.8564i	−0.332469	+	0.575853i
$580$	20.0000			0.830455
$581$	4.00000	−	6.92820i	0.165948	−	0.287430i
$582$	6.00000	+	10.3923i	0.248708	+	0.430775i
$583$		0			0
$584$	4.00000			0.165521
$585$		0			0
$586$	14.0000			0.578335
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	30.0000	−	51.9615i	1.23613	−	2.14104i
$590$	8.00000			0.329355
$591$	−11.0000	+	19.0526i	−0.452480	+	0.783718i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$	−4.00000	−	6.92820i	−0.163984	−	0.284029i
$596$	7.00000	+	12.1244i	0.286731	+	0.496633i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	0.549602	−	0.835426i	$-0.314779\pi$
$601$	−11.0000	−	19.0526i	−0.448699	−	0.777170i	−0.998302	+	0.0582563i	$0.981446\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	2.00000			0.0814463
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$	−11.0000	+	19.0526i	−0.447214	+	0.774597i
$606$	2.00000			0.0812444
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	3.00000	+	5.19615i	0.121666	+	0.210732i
$609$	−10.0000	−	17.3205i	−0.405220	−	0.701862i
$610$	4.00000			0.161955
$611$		0			0
$612$	2.00000			0.0808452
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$	−10.0000	+	17.3205i	−0.403239	+	0.698430i
$616$		0			0
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	−0.997899	−	0.0647859i	$-0.979364\pi$
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	0.555056	+	0.831813i	$0.312697\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	−26.0000			−1.04503			−0.522514	−	0.852631i	$-0.675006\pi$
$619$	−26.0000			−1.04503			−0.522514	+	0.852631i	$0.675006\pi$
$620$	−10.0000	+	17.3205i	−0.401610	+	0.695608i
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$	14.0000	+	24.2487i	0.561349	+	0.972285i
$623$	12.0000			0.480770
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−13.0000	−	22.5167i	−0.519584	−	0.899947i
$627$		0			0
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	16.0000			0.637962
$630$	2.00000	−	3.46410i	0.0796819	−	0.138013i
$631$	−5.00000	+	8.66025i	−0.199047	+	0.344759i	−0.948220	−	0.317615i	$-0.897118\pi$
$631$	−5.00000	+	8.66025i	−0.199047	+	0.344759i	0.749173	+	0.662375i	$0.230451\pi$
$632$		0			0
$633$	−6.00000	+	10.3923i	−0.238479	+	0.413057i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$	−6.00000			−0.237915
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$	−8.00000			−0.315735
$643$	3.00000	−	5.19615i	0.118308	−	0.204916i	−0.800789	−	0.598947i	$-0.795586\pi$
$643$	3.00000	−	5.19615i	0.118308	−	0.204916i	0.919097	+	0.394030i	$0.128920\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$	8.00000			0.315000
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	−16.0000	−	27.7128i	−0.629025	−	1.08950i	−0.987748	−	0.156059i	$-0.950121\pi$
$647$	−16.0000	−	27.7128i	−0.629025	−	1.08950i	0.358723	−	0.933444i	$-0.383212\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$		0			0
$650$		0			0
$651$	20.0000			0.783862
$652$	7.00000	+	12.1244i	0.274141	+	0.474826i
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	0.999949	+	0.0101092i	$0.00321793\pi$
$653$	13.0000	+	22.5167i	0.508729	+	0.881145i	−0.491220	+	0.871036i	$0.663449\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	16.0000			0.625172
$656$	5.00000	−	8.66025i	0.195217	−	0.338126i
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$	−24.0000			−0.935617
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	−10.0000			−0.388661
$663$		0			0
$664$	−4.00000			−0.155230
$665$	−12.0000	−	20.7846i	−0.465340	−	0.805993i
$666$	4.00000	+	6.92820i	0.154997	+	0.268462i
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$	−12.0000			−0.464294
$669$	−7.00000	+	12.1244i	−0.270636	+	0.468755i
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$		0			0
$672$	−1.00000	+	1.73205i	−0.0385758	+	0.0668153i
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	0.802395	−	0.596794i	$-0.203559\pi$
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	−0.918036	+	0.396497i	$0.870226\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$	7.00000	+	12.1244i	0.268833	+	0.465633i
$679$	12.0000	+	20.7846i	0.460518	+	0.797640i
$680$	−2.00000	+	3.46410i	−0.0766965	+	0.132842i
$681$	−8.00000			−0.306561
$682$		0			0
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	6.00000			0.229416
$685$	−2.00000	+	3.46410i	−0.0764161	+	0.132357i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	−2.00000	−	3.46410i	−0.0763048	−	0.132164i
$688$	−4.00000			−0.152499
$689$		0			0
$690$	−8.00000			−0.304555
$691$	−5.00000	−	8.66025i	−0.190209	−	0.329452i	0.755110	−	0.655598i	$-0.227583\pi$
$691$	−5.00000	−	8.66025i	−0.190209	−	0.329452i	−0.945319	+	0.326146i	$0.894250\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$		0			0
$694$	12.0000			0.455514
$695$	−20.0000	+	34.6410i	−0.758643	+	1.31401i
$696$	−5.00000	+	8.66025i	−0.189525	+	0.328266i
$697$	−20.0000			−0.757554
$698$	−8.00000	+	13.8564i	−0.302804	+	0.524473i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	−22.0000			−0.830929			−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000			−0.830929			−0.415464	+	0.909610i	$0.636381\pi$
$702$		0			0
$703$	48.0000			1.81035
$704$		0			0
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$	−13.0000	+	22.5167i	−0.489261	+	0.847426i
$707$	4.00000			0.150435
$708$	−2.00000	+	3.46410i	−0.0751646	+	0.130189i
$709$	18.0000	−	31.1769i	0.676004	−	1.17087i	−0.300170	−	0.953886i	$-0.597043\pi$
$709$	18.0000	−	31.1769i	0.676004	−	1.17087i	0.976174	−	0.216988i	$-0.0696232\pi$
$710$		0			0
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−20.0000	−	34.6410i	−0.749006	−	1.29732i
$714$	4.00000			0.149696
$715$		0			0
$716$		0			0
$717$	−8.00000	−	13.8564i	−0.298765	−	0.517477i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$	−2.00000			−0.0745356
$721$	16.0000	−	27.7128i	0.595871	−	1.03208i
$722$	8.50000	−	14.7224i	0.316337	−	0.547912i
$723$	20.0000			0.743808
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	−5.00000	−	8.66025i	−0.185695	−	0.321634i
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	4.00000	+	6.92820i	0.148047	+	0.256424i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	44.0000			1.62518			0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000			1.62518			0.812589	+	0.582838i	$0.198058\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$	4.00000			0.147442
$737$		0			0
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	13.0000	+	22.5167i	0.478213	+	0.828289i	0.999688	−	0.0249776i	$-0.00795146\pi$
$739$	13.0000	+	22.5167i	0.478213	+	0.828289i	−0.521475	+	0.853266i	$0.674618\pi$
$740$	−16.0000			−0.588172
$741$		0			0
$742$	−12.0000			−0.440534
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	0.974633	−	0.223810i	$-0.0718494\pi$
$743$	8.00000	+	13.8564i	0.293492	+	0.508342i	−0.681141	+	0.732152i	$0.738516\pi$
$744$	−5.00000	−	8.66025i	−0.183309	−	0.317500i
$745$	−14.0000	+	24.2487i	−0.512920	+	0.888404i
$746$	6.00000			0.219676
$747$	−2.00000	+	3.46410i	−0.0731762	+	0.126745i
$748$		0			0
$749$	−16.0000			−0.584627
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	6.00000	+	10.3923i	0.218797	+	0.378968i
$753$	28.0000			1.02038
$754$		0			0
$755$	−20.0000			−0.727875
$756$	1.00000	+	1.73205i	0.0363696	+	0.0629941i
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	0.993701	−	0.112062i	$-0.0357456\pi$
$757$	11.0000	+	19.0526i	0.399802	+	0.692477i	−0.593899	+	0.804539i	$0.702412\pi$
$758$	−17.0000	+	29.4449i	−0.617468	+	1.06949i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$	8.00000			0.289809
$763$	−4.00000	+	6.92820i	−0.144810	+	0.250818i
$764$	−6.00000	−	10.3923i	−0.217072	−	0.375980i
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	−4.00000			−0.144526
$767$		0			0
$768$	1.00000			0.0360844
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	0.997107	−	0.0760054i	$-0.0242166\pi$
$769$	12.0000	+	20.7846i	0.432731	+	0.749512i	−0.564376	+	0.825518i	$0.690883\pi$
$770$		0			0
$771$	9.00000	−	15.5885i	0.324127	−	0.561405i
$772$	16.0000			0.575853
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	10.0000			0.359211
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$	8.00000	+	13.8564i	0.286998	+	0.497096i
$778$	−15.0000	−	25.9808i	−0.537776	−	0.931455i
$779$	−60.0000			−2.14972
$780$		0			0
$781$		0			0
$782$	−4.00000	−	6.92820i	−0.143040	−	0.247752i
$783$	5.00000	+	8.66025i	0.178685	+	0.309492i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	4.00000			0.142766
$786$	−4.00000	+	6.92820i	−0.142675	+	0.247121i
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	0.298521	+	0.954403i	$0.403507\pi$
$787$	−19.0000	+	32.9090i	−0.677277	+	1.17308i	−0.975798	+	0.218675i	$0.929827\pi$
$788$	22.0000			0.783718
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$	14.0000	+	24.2487i	0.497783	+	0.862185i
$792$		0			0
$793$		0			0
$794$	−8.00000			−0.283909
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$		0			0
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$	12.0000			0.424795
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−6.00000			−0.212000
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$		0			0
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$	−16.0000			−0.563926
$806$		0			0
$807$	−10.0000			−0.352017
$808$	−1.00000	−	1.73205i	−0.0351799	−	0.0609333i
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.852491	+	0.522742i	$0.175091\pi$
$809$	25.0000	+	43.3013i	0.878953	+	1.52239i	0.0264621	+	0.999650i	$0.491576\pi$
$810$	−1.00000	+	1.73205i	−0.0351364	+	0.0608581i
$811$	−10.0000			−0.351147			−0.175574	−	0.984466i	$-0.556178\pi$
$811$	−10.0000			−0.351147			−0.175574	+	0.984466i	$0.556178\pi$
$812$	−10.0000	+	17.3205i	−0.350931	+	0.607831i
$813$	5.00000	−	8.66025i	0.175358	−	0.303728i
$814$		0			0
$815$	−14.0000	+	24.2487i	−0.490399	+	0.849395i
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	12.0000	+	20.7846i	0.419827	+	0.727161i
$818$	4.00000			0.139857
$819$		0			0
$820$	20.0000			0.698430
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	−1.00000	−	1.73205i	−0.0348790	−	0.0604122i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	−16.0000			−0.557386
$825$		0			0
$826$	−4.00000	+	6.92820i	−0.139178	+	0.241063i
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−15.0000	−	25.9808i	−0.520972	−	0.902349i	−0.999703	−	0.0243876i	$-0.992236\pi$
$829$	−15.0000	−	25.9808i	−0.520972	−	0.902349i	0.478731	−	0.877962i	$-0.341097\pi$
$830$	−4.00000	−	6.92820i	−0.138842	−	0.240481i
$831$	2.00000			0.0693792
$832$		0			0
$833$	−6.00000			−0.207888
$834$	−10.0000	−	17.3205i	−0.346272	−	0.599760i
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$		0			0
$837$	−10.0000			−0.345651
$838$	20.0000	−	34.6410i	0.690889	−	1.19665i
$839$	8.00000	−	13.8564i	0.276191	−	0.478376i	−0.694244	−	0.719740i	$-0.744261\pi$
$839$	8.00000	−	13.8564i	0.276191	−	0.478376i	0.970435	+	0.241363i	$0.0775945\pi$
$840$	−4.00000			−0.138013
$841$	−35.5000	+	61.4878i	−1.22414	+	2.12027i
$842$	−10.0000	−	17.3205i	−0.344623	−	0.596904i
$843$	5.00000	+	8.66025i	0.172209	+	0.298275i
$844$	12.0000			0.413057
$845$		0			0
$846$	12.0000			0.412568
$847$	−11.0000	−	19.0526i	−0.377964	−	0.654654i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	2.00000			0.0685994
$851$	16.0000	−	27.7128i	0.548473	−	0.949983i
$852$		0			0
$853$	56.0000			1.91740			0.958702	−	0.284413i	$-0.0917988\pi$
$853$	56.0000			1.91740			0.958702	+	0.284413i	$0.0917988\pi$
$854$	−2.00000	+	3.46410i	−0.0684386	+	0.118539i
$855$	6.00000	+	10.3923i	0.205196	+	0.355409i
$856$	4.00000	+	6.92820i	0.136717	+	0.236801i
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$	−10.0000	−	17.3205i	−0.340799	−	0.590281i
$862$	10.0000	−	17.3205i	0.340601	−	0.589939i
$863$	44.0000			1.49778			0.748889	−	0.662696i	$-0.230588\pi$
$863$	44.0000			1.49778			0.748889	+	0.662696i	$0.230588\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$	−26.0000			−0.883516
$867$	6.50000	−	11.2583i	0.220752	−	0.382353i
$868$	−10.0000	−	17.3205i	−0.339422	−	0.587896i
$869$		0			0
$870$	−20.0000			−0.678064
$871$		0			0
$872$	4.00000			0.135457
$873$	−6.00000	−	10.3923i	−0.203069	−	0.351726i
$874$	−12.0000	−	20.7846i	−0.405906	−	0.703050i
$875$	12.0000	−	20.7846i	0.405674	−	0.702648i
$876$	−4.00000			−0.135147
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	−0.790554	−	0.612392i	$-0.790207\pi$
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	0.925624	+	0.378444i	$0.123541\pi$
$878$		0			0
$879$	−14.0000			−0.472208
$880$		0			0
$881$	21.0000	+	36.3731i	0.707508	+	1.22544i	0.965779	+	0.259367i	$0.0835140\pi$
$881$	21.0000	+	36.3731i	0.707508	+	1.22544i	−0.258271	+	0.966073i	$0.583153\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	36.0000			1.21150			0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000			1.21150			0.605748	+	0.795656i	$0.292874\pi$
$884$		0			0
$885$	−8.00000			−0.268917
$886$	−8.00000	−	13.8564i	−0.268765	−	0.465515i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	4.00000	−	6.92820i	0.134231	−	0.232495i
$889$	16.0000			0.536623
$890$	6.00000	−	10.3923i	0.201120	−	0.348351i
$891$		0			0
$892$	14.0000			0.468755
$893$	36.0000	−	62.3538i	1.20469	−	2.08659i
$894$	−7.00000	−	12.1244i	−0.234115	−	0.405499i
$895$		0			0
$896$	2.00000			0.0668153
$897$		0			0
$898$	6.00000			0.200223
$899$	−50.0000	−	86.6025i	−1.66759	−	2.88836i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		0			0
$903$	−4.00000	+	6.92820i	−0.133112	+	0.230556i
$904$	7.00000	−	12.1244i	0.232817	−	0.403250i
$905$	44.0000			1.46261
$906$	5.00000	−	8.66025i	0.166114	−	0.287718i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	4.00000	+	6.92820i	0.132745	+	0.229920i
$909$	−2.00000			−0.0663358
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$		0			0
$914$	−14.0000	+	24.2487i	−0.463079	+	0.802076i
$915$	−4.00000			−0.132236
$916$	−2.00000	+	3.46410i	−0.0660819	+	0.114457i
$917$	−8.00000	+	13.8564i	−0.264183	+	0.457579i
$918$	−2.00000			−0.0660098
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$	4.00000	+	6.92820i	0.131876	+	0.228416i
$921$	1.00000	+	1.73205i	0.0329511	+	0.0570730i
$922$	−30.0000			−0.987997
$923$		0			0
$924$		0			0
$925$	4.00000	+	6.92820i	0.131519	+	0.227798i
$926$	3.00000	+	5.19615i	0.0985861	+	0.170756i
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$	10.0000			0.328266
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$	10.0000	−	17.3205i	0.327913	−	0.567962i
$931$	−18.0000			−0.589926
$932$	−3.00000	+	5.19615i	−0.0982683	+	0.170206i
$933$	−14.0000	−	24.2487i	−0.458339	−	0.793867i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$	13.0000	+	22.5167i	0.424239	+	0.734803i
$940$	−12.0000	+	20.7846i	−0.391397	+	0.677919i
$941$	10.0000			0.325991			0.162995	−	0.986627i	$-0.447884\pi$
$941$	10.0000			0.325991			0.162995	+	0.986627i	$0.447884\pi$
$942$	−1.00000	+	1.73205i	−0.0325818	+	0.0564333i
$943$	−20.0000	+	34.6410i	−0.651290	+	1.12807i
$944$	4.00000			0.130189
$945$	−2.00000	+	3.46410i	−0.0650600	+	0.112687i
$946$		0			0
$947$	26.0000	+	45.0333i	0.844886	+	1.46339i	0.885720	+	0.464220i	$0.153665\pi$
$947$	26.0000	+	45.0333i	0.844886	+	1.46339i	−0.0408333	+	0.999166i	$0.513001\pi$
$948$		0			0
$949$		0			0
$950$	6.00000			0.194666
$951$	9.00000	+	15.5885i	0.291845	+	0.505490i
$952$	−2.00000	−	3.46410i	−0.0648204	−	0.112272i
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$	6.00000			0.194257
$955$	12.0000	−	20.7846i	0.388311	−	0.672574i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	−2.00000	−	3.46410i	−0.0645834	−	0.111862i
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	69.0000			2.22581
$962$		0			0
$963$	8.00000			0.257796
$964$	−10.0000	−	17.3205i	−0.322078	−	0.557856i
$965$	16.0000	+	27.7128i	0.515058	+	0.892107i
$966$	4.00000	−	6.92820i	0.128698	−	0.222911i
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$	24.0000			0.770594
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−20.0000	−	34.6410i	−0.641171	−	1.11054i
$974$	18.0000			0.576757
$975$		0			0
$976$	2.00000			0.0640184
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	−7.00000	−	12.1244i	−0.223835	−	0.387694i
$979$		0			0
$980$	6.00000			0.191663
$981$	2.00000	−	3.46410i	0.0638551	−	0.110600i
$982$	14.0000	−	24.2487i	0.446758	−	0.773807i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$	−5.00000	+	8.66025i	−0.159394	+	0.276079i
$985$	22.0000	+	38.1051i	0.700978	+	1.21413i
$986$	−10.0000	−	17.3205i	−0.318465	−	0.551597i
$987$	24.0000			0.763928
$988$		0			0
$989$	16.0000			0.508770
$990$		0			0
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	−5.00000	+	8.66025i	−0.158750	+	0.274963i
$993$	10.0000			0.317340
$994$		0			0
$995$		0			0
$996$	4.00000			0.126745
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$	−7.00000	−	12.1244i	−0.221581	−	0.383790i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.e.991.1		2
13.2	odd	12		78.2.b.a.25.2	yes	2
13.3	even	3		1014.2.a.b.1.1		1
13.4	even	6		1014.2.e.b.529.1		2
13.5	odd	4		1014.2.i.c.361.2		4
13.6	odd	12		1014.2.i.c.823.1		4
13.7	odd	12		1014.2.i.c.823.2		4
13.8	odd	4		1014.2.i.c.361.1		4
13.9	even	3	inner	1014.2.e.e.529.1		2
13.10	even	6		1014.2.a.g.1.1		1
13.11	odd	12		78.2.b.a.25.1	✓	2
13.12	even	2		1014.2.e.b.991.1		2
39.2	even	12		234.2.b.a.181.1		2
39.11	even	12		234.2.b.a.181.2		2
39.23	odd	6		3042.2.a.c.1.1		1
39.29	odd	6		3042.2.a.n.1.1		1
52.3	odd	6		8112.2.a.g.1.1		1
52.11	even	12		624.2.c.a.337.1		2
52.15	even	12		624.2.c.a.337.2		2
52.23	odd	6		8112.2.a.j.1.1		1
65.2	even	12		1950.2.f.d.649.1		2
65.24	odd	12		1950.2.b.c.1351.2		2
65.28	even	12		1950.2.f.g.649.2		2
65.37	even	12		1950.2.f.g.649.1		2
65.54	odd	12		1950.2.b.c.1351.1		2
65.63	even	12		1950.2.f.d.649.2		2
91.41	even	12		3822.2.c.d.883.2		2
91.76	even	12		3822.2.c.d.883.1		2
104.11	even	12		2496.2.c.m.961.2		2
104.37	odd	12		2496.2.c.f.961.2		2
104.67	even	12		2496.2.c.m.961.1		2
104.93	odd	12		2496.2.c.f.961.1		2
156.11	odd	12		1872.2.c.b.1585.2		2
156.119	odd	12		1872.2.c.b.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.b.a.25.1	✓	2	13.11	odd	12
78.2.b.a.25.2	yes	2	13.2	odd	12
234.2.b.a.181.1		2	39.2	even	12
234.2.b.a.181.2		2	39.11	even	12
624.2.c.a.337.1		2	52.11	even	12
624.2.c.a.337.2		2	52.15	even	12
1014.2.a.b.1.1		1	13.3	even	3
1014.2.a.g.1.1		1	13.10	even	6
1014.2.e.b.529.1		2	13.4	even	6
1014.2.e.b.991.1		2	13.12	even	2
1014.2.e.e.529.1		2	13.9	even	3	inner
1014.2.e.e.991.1		2	1.1	even	1	trivial
1014.2.i.c.361.1		4	13.8	odd	4
1014.2.i.c.361.2		4	13.5	odd	4
1014.2.i.c.823.1		4	13.6	odd	12
1014.2.i.c.823.2		4	13.7	odd	12
1872.2.c.b.1585.1		2	156.119	odd	12
1872.2.c.b.1585.2		2	156.11	odd	12
1950.2.b.c.1351.1		2	65.54	odd	12
1950.2.b.c.1351.2		2	65.24	odd	12
1950.2.f.d.649.1		2	65.2	even	12
1950.2.f.d.649.2		2	65.63	even	12
1950.2.f.g.649.1		2	65.37	even	12
1950.2.f.g.649.2		2	65.28	even	12
2496.2.c.f.961.1		2	104.93	odd	12
2496.2.c.f.961.2		2	104.37	odd	12
2496.2.c.m.961.1		2	104.67	even	12
2496.2.c.m.961.2		2	104.11	even	12
3042.2.a.c.1.1		1	39.23	odd	6
3042.2.a.n.1.1		1	39.29	odd	6
3822.2.c.d.883.1		2	91.76	even	12
3822.2.c.d.883.2		2	91.41	even	12
8112.2.a.g.1.1		1	52.3	odd	6
8112.2.a.j.1.1		1	52.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +1.00000 q^{12} +2.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(1.00000 - 1.73205i) q^{20} -2.00000 q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(5.00000 + 8.66025i) q^{29} +(-1.00000 + 1.73205i) q^{30} -10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} -2.00000 q^{34} +(-2.00000 + 3.46410i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 - 6.92820i) q^{37} -6.00000 q^{38} +2.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(2.00000 - 3.46410i) q^{43} +(1.00000 - 1.73205i) q^{45} +(-2.00000 + 3.46410i) q^{46} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +2.00000 q^{51} -6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{56} +6.00000 q^{57} +(-5.00000 + 8.66025i) q^{58} +(-2.00000 + 3.46410i) q^{59} -2.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(-5.00000 - 8.66025i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{67} +(-1.00000 - 1.73205i) q^{68} +(2.00000 - 3.46410i) q^{69} -4.00000 q^{70} +(0.500000 - 0.866025i) q^{72} -4.00000 q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-3.00000 - 5.19615i) q^{76} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} +4.00000 q^{83} +(1.00000 - 1.73205i) q^{84} +(2.00000 - 3.46410i) q^{85} +4.00000 q^{86} +(5.00000 - 8.66025i) q^{87} +(3.00000 + 5.19615i) q^{89} +2.00000 q^{90} -4.00000 q^{92} +(5.00000 + 8.66025i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(6.00000 - 10.3923i) q^{95} -1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(-1.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} + 2 q^{12} + 4 q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 2 q^{20} - 4 q^{21} + 4 q^{23} + q^{24} - 2 q^{25} + 2 q^{27} + 2 q^{28} + 10 q^{29} - 2 q^{30} - 20 q^{31} + q^{32} - 4 q^{34} - 4 q^{35} - q^{36} - 8 q^{37} - 12 q^{38} + 4 q^{40} + 10 q^{41} - 2 q^{42} + 4 q^{43} + 2 q^{45} - 4 q^{46} - 24 q^{47} - q^{48} + 3 q^{49} - q^{50} + 4 q^{51} - 12 q^{53} + q^{54} - 2 q^{56} + 12 q^{57} - 10 q^{58} - 4 q^{59} - 4 q^{60} - 2 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{67} - 2 q^{68} + 4 q^{69} - 8 q^{70} + q^{72} - 8 q^{73} + 8 q^{74} + q^{75} - 6 q^{76} + 2 q^{80} - q^{81} - 10 q^{82} + 8 q^{83} + 2 q^{84} + 4 q^{85} + 8 q^{86} + 10 q^{87} + 6 q^{89} + 4 q^{90} - 8 q^{92} + 10 q^{93} - 12 q^{94} + 12 q^{95} - 2 q^{96} - 12 q^{97} - 3 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + 2 * q^7 - 2 * q^8 - q^9 - 2 * q^10 + 2 * q^12 + 4 * q^14 + 2 * q^15 - q^16 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 2 * q^20 - 4 * q^21 + 4 * q^23 + q^24 - 2 * q^25 + 2 * q^27 + 2 * q^28 + 10 * q^29 - 2 * q^30 - 20 * q^31 + q^32 - 4 * q^34 - 4 * q^35 - q^36 - 8 * q^37 - 12 * q^38 + 4 * q^40 + 10 * q^41 - 2 * q^42 + 4 * q^43 + 2 * q^45 - 4 * q^46 - 24 * q^47 - q^48 + 3 * q^49 - q^50 + 4 * q^51 - 12 * q^53 + q^54 - 2 * q^56 + 12 * q^57 - 10 * q^58 - 4 * q^59 - 4 * q^60 - 2 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^67 - 2 * q^68 + 4 * q^69 - 8 * q^70 + q^72 - 8 * q^73 + 8 * q^74 + q^75 - 6 * q^76 + 2 * q^80 - q^81 - 10 * q^82 + 8 * q^83 + 2 * q^84 + 4 * q^85 + 8 * q^86 + 10 * q^87 + 6 * q^89 + 4 * q^90 - 8 * q^92 + 10 * q^93 - 12 * q^94 + 12 * q^95 - 2 * q^96 - 12 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more