LMFDB - Embedded newform 637.2.u.a.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, 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:	$5.08647060876$
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 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} -3.00000 q^{10} -5.19615i q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 - 3.46410i) q^{13} +(1.50000 + 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(3.00000 - 1.73205i) q^{18} -1.73205i q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} -1.73205i q^{24} +(-1.00000 - 1.73205i) q^{25} +(1.50000 + 6.06218i) q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -3.00000 q^{30} +(-1.50000 + 0.866025i) q^{31} +(-4.50000 - 2.59808i) q^{32} -5.19615i q^{33} +10.3923i q^{34} +(-1.00000 + 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(1.00000 - 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(-4.50000 - 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} +(7.50000 + 4.33013i) q^{47} +(2.50000 + 4.33013i) q^{48} +(3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-2.50000 - 2.59808i) q^{52} +(4.50000 + 7.79423i) q^{53} +(7.50000 - 4.33013i) q^{54} +(4.50000 - 7.79423i) q^{55} -1.73205i q^{57} -5.19615i q^{58} +(3.00000 + 1.73205i) q^{59} +(1.50000 - 0.866025i) q^{60} -7.00000 q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(4.50000 - 4.33013i) q^{65} +(4.50000 + 7.79423i) q^{66} +8.66025i q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.50000 - 0.866025i) q^{71} +3.46410i q^{72} +(7.50000 - 4.33013i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 0.866025i) q^{76} +(1.50000 + 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +8.66025i q^{80} +1.00000 q^{81} -9.00000 q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(16.5000 + 9.52628i) q^{86} +(-1.50000 + 2.59808i) q^{87} -9.00000 q^{88} +(6.00000 - 3.46410i) q^{89} +6.00000 q^{90} +(-1.50000 + 0.866025i) q^{93} -15.0000 q^{94} +(1.50000 - 2.59808i) q^{95} +(-4.50000 - 2.59808i) q^{96} +(4.50000 - 2.59808i) q^{97} +10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 4 * q^9	$ 2 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{9} - 6 q^{10} + q^{12} + 2 q^{13} + 3 q^{15} + 5 q^{16} + 6 q^{17} + 6 q^{18} + 3 q^{20} + 9 q^{22} - 2 q^{25} + 3 q^{26} - 10 q^{27} - 3 q^{29} - 6 q^{30} - 3 q^{31} - 9 q^{32} - 2 q^{36} + 3 q^{38} + 2 q^{39} + 3 q^{40} + 9 q^{41} - 11 q^{43} - 9 q^{44} - 6 q^{45} + 15 q^{47} + 5 q^{48} + 6 q^{50} + 6 q^{51} - 5 q^{52} + 9 q^{53} + 15 q^{54} + 9 q^{55} + 6 q^{59} + 3 q^{60} - 14 q^{61} + 3 q^{62} - 2 q^{64} + 9 q^{65} + 9 q^{66} - 6 q^{68} + 3 q^{71} + 15 q^{73} - 2 q^{75} - 3 q^{76} + 3 q^{78} + 5 q^{79} + 2 q^{81} - 18 q^{82} + 18 q^{85} + 33 q^{86} - 3 q^{87} - 18 q^{88} + 12 q^{89} + 12 q^{90} - 3 q^{93} - 30 q^{94} + 3 q^{95} - 9 q^{96} + 9 q^{97}+O(q^{100}) $ 2 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 4 * q^9 - 6 * q^10 + q^12 + 2 * q^13 + 3 * q^15 + 5 * q^16 + 6 * q^17 + 6 * q^18 + 3 * q^20 + 9 * q^22 - 2 * q^25 + 3 * q^26 - 10 * q^27 - 3 * q^29 - 6 * q^30 - 3 * q^31 - 9 * q^32 - 2 * q^36 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 9 * q^41 - 11 * q^43 - 9 * q^44 - 6 * q^45 + 15 * q^47 + 5 * q^48 + 6 * q^50 + 6 * q^51 - 5 * q^52 + 9 * q^53 + 15 * q^54 + 9 * q^55 + 6 * q^59 + 3 * q^60 - 14 * q^61 + 3 * q^62 - 2 * q^64 + 9 * q^65 + 9 * q^66 - 6 * q^68 + 3 * q^71 + 15 * q^73 - 2 * q^75 - 3 * q^76 + 3 * q^78 + 5 * q^79 + 2 * q^81 - 18 * q^82 + 18 * q^85 + 33 * q^86 - 3 * q^87 - 18 * q^88 + 12 * q^89 + 12 * q^90 - 3 * q^93 - 30 * q^94 + 3 * q^95 - 9 * q^96 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	1.00000			0.577350			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	−2.00000			−0.666667
$10$	−3.00000			−0.948683
$11$		−	5.19615i		−	1.56670i	−0.621582	−	0.783349i	$-0.713510\pi$
$11$		−	5.19615i		−	1.56670i	0.621582	−	0.783349i	$-0.286490\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		0			0
$15$	1.50000	+	0.866025i	0.387298	+	0.223607i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	3.00000	−	1.73205i	0.707107	−	0.408248i
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$		0			0
$22$	4.50000	+	7.79423i	0.959403	+	1.66174i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	1.50000	+	6.06218i	0.294174	+	1.18889i
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	−3.00000			−0.547723
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−1.50000	+	0.866025i	−0.269408	+	0.155543i	0.359211	+	0.933257i	$0.383046\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$		−	5.19615i		−	0.904534i
$34$			10.3923i			1.78227i
$35$		0			0
$36$	−1.00000	+	1.73205i	−0.166667	+	0.288675i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$	1.00000	−	3.46410i	0.160128	−	0.554700i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	4.50000	+	2.59808i	0.702782	+	0.405751i	0.808383	−	0.588657i	$-0.200343\pi$
$41$	4.50000	+	2.59808i	0.702782	+	0.405751i	−0.105601	+	0.994409i	$0.533677\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	−4.50000	−	2.59808i	−0.678401	−	0.391675i
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$		0			0
$47$	7.50000	+	4.33013i	1.09399	+	0.631614i	0.934635	−	0.355608i	$-0.115726\pi$
$47$	7.50000	+	4.33013i	1.09399	+	0.631614i	0.159352	+	0.987222i	$0.449059\pi$
$48$	2.50000	+	4.33013i	0.360844	+	0.625000i
$49$		0			0
$50$	3.00000	+	1.73205i	0.424264	+	0.244949i
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	7.50000	−	4.33013i	1.02062	−	0.589256i
$55$	4.50000	−	7.79423i	0.606780	−	1.05097i
$56$		0			0
$57$		−	1.73205i		−	0.229416i
$58$		−	5.19615i		−	0.682288i
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	0.682406	−	0.730974i	$-0.260934\pi$
$59$	3.00000	+	1.73205i	0.390567	+	0.225494i	−0.291839	+	0.956467i	$0.594267\pi$
$60$	1.50000	−	0.866025i	0.193649	−	0.111803i
$61$	−7.00000			−0.896258			−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000			−0.896258			−0.448129	+	0.893969i	$0.647910\pi$
$62$	1.50000	−	2.59808i	0.190500	−	0.329956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.50000	−	4.33013i	0.558156	−	0.537086i
$66$	4.50000	+	7.79423i	0.553912	+	0.959403i
$67$			8.66025i			1.05802i	0.848616	+	0.529009i	$0.177436\pi$
$67$			8.66025i			1.05802i	−0.848616	+	0.529009i	$0.822564\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	1.50000	−	0.866025i	0.178017	−	0.102778i	−0.408344	−	0.912828i	$-0.633893\pi$
$71$	1.50000	−	0.866025i	0.178017	−	0.102778i	0.586361	+	0.810050i	$0.300560\pi$
$72$			3.46410i			0.408248i
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.00787336	−	0.999969i	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$		0			0
$75$	−1.00000	−	1.73205i	−0.115470	−	0.200000i
$76$	−1.50000	−	0.866025i	−0.172062	−	0.0993399i
$77$		0			0
$78$	1.50000	+	6.06218i	0.169842	+	0.686406i
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$			8.66025i			0.968246i
$81$	1.00000			0.111111
$82$	−9.00000			−0.993884
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	9.00000	−	5.19615i	0.976187	−	0.563602i
$86$	16.5000	+	9.52628i	1.77924	+	1.02725i
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−9.00000			−0.959403
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$		0			0
$93$	−1.50000	+	0.866025i	−0.155543	+	0.0898027i
$94$	−15.0000			−1.54713
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$	−4.50000	−	2.59808i	−0.459279	−	0.265165i
$97$	4.50000	−	2.59808i	0.456906	−	0.263795i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	4.50000	−	2.59808i	0.456906	−	0.263795i	0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$			10.3923i			1.04447i
$100$	−2.00000			−0.200000
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$			10.3923i			1.02899i
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	−13.5000	−	7.79423i	−1.31124	−	0.757042i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	4.50000	−	2.59808i	0.431022	−	0.248851i	−0.268760	−	0.963207i	$-0.586614\pi$
$109$	4.50000	−	2.59808i	0.431022	−	0.248851i	0.699782	+	0.714357i	$0.253281\pi$
$110$			15.5885i			1.48630i
$111$		0			0
$112$		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	$-0.415962\pi$
$114$	1.50000	+	2.59808i	0.140488	+	0.243332i
$115$		0			0
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	−2.00000	+	6.92820i	−0.184900	+	0.640513i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	1.50000	−	2.59808i	0.136931	−	0.237171i
$121$	−16.0000			−1.45455
$122$	10.5000	−	6.06218i	0.950625	−	0.548844i
$123$	4.50000	+	2.59808i	0.405751	+	0.234261i
$124$			1.73205i			0.155543i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	−5.50000	−	9.52628i	−0.484248	−	0.838742i
$130$	−3.00000	+	10.3923i	−0.263117	+	0.911465i
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$	−4.50000	−	2.59808i	−0.391675	−	0.226134i
$133$		0			0
$134$	−7.50000	−	12.9904i	−0.647901	−	1.12220i
$135$	−7.50000	−	4.33013i	−0.645497	−	0.372678i
$136$	−9.00000	−	5.19615i	−0.771744	−	0.445566i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	−6.50000	−	11.2583i	−0.551323	−	0.954919i	−0.998179	−	0.0603135i	$-0.980790\pi$
$139$	−6.50000	−	11.2583i	−0.551323	−	0.954919i	0.446857	−	0.894606i	$-0.352543\pi$
$140$		0			0
$141$	7.50000	+	4.33013i	0.631614	+	0.364662i
$142$	−1.50000	+	2.59808i	−0.125877	+	0.218026i
$143$	−18.0000	−	5.19615i	−1.50524	−	0.434524i
$144$	−5.00000	−	8.66025i	−0.416667	−	0.721688i
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	−7.50000	+	12.9904i	−0.620704	+	1.07509i
$147$		0			0
$148$		0			0
$149$			19.0526i			1.56085i	0.625252	+	0.780423i	$0.284996\pi$
$149$			19.0526i			1.56085i	−0.625252	+	0.780423i	$0.715004\pi$
$150$	3.00000	+	1.73205i	0.244949	+	0.141421i
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	−0.862159	−	0.506637i	$-0.830888\pi$
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	0.00768132	+	0.999970i	$0.497555\pi$
$152$	−3.00000			−0.243332
$153$	−6.00000	+	10.3923i	−0.485071	+	0.840168i
$154$		0			0
$155$	−3.00000			−0.240966
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.802749	+	0.596316i	$0.203370\pi$
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.115050	+	0.993360i	$0.463297\pi$
$158$			8.66025i			0.688973i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$	−4.50000	−	7.79423i	−0.355756	−	0.616188i
$161$		0			0
$162$	−1.50000	+	0.866025i	−0.117851	+	0.0680414i
$163$		−	12.1244i		−	0.949653i	−0.880079	−	0.474826i	$-0.842511\pi$
$163$		−	12.1244i		−	0.949653i	0.880079	−	0.474826i	$-0.157489\pi$
$164$	4.50000	−	2.59808i	0.351391	−	0.202876i
$165$	4.50000	−	7.79423i	0.350325	−	0.606780i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	1.50000	+	0.866025i	0.116073	+	0.0670151i	0.556913	−	0.830571i	$-0.311986\pi$
$167$	1.50000	+	0.866025i	0.116073	+	0.0670151i	−0.440839	+	0.897586i	$0.645319\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−9.00000	+	15.5885i	−0.690268	+	1.19558i
$171$			3.46410i			0.264906i
$172$	−11.0000			−0.838742
$173$	−15.0000			−1.14043			−0.570214	−	0.821496i	$-0.693140\pi$
$173$	−15.0000			−1.14043			−0.570214	+	0.821496i	$0.693140\pi$
$174$		−	5.19615i		−	0.393919i
$175$		0			0
$176$	22.5000	−	12.9904i	1.69600	−	0.979187i
$177$	3.00000	+	1.73205i	0.225494	+	0.130189i
$178$	−6.00000	+	10.3923i	−0.449719	+	0.778936i
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$	−3.00000	+	1.73205i	−0.223607	+	0.129099i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$		0			0
$185$		0			0
$186$	1.50000	−	2.59808i	0.109985	−	0.190500i
$187$	−27.0000	−	15.5885i	−1.97444	−	1.13994i
$188$	7.50000	−	4.33013i	0.546994	−	0.315807i
$189$		0			0
$190$			5.19615i			0.376969i
$191$	−15.0000			−1.08536			−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000			−1.08536			−0.542681	+	0.839939i	$0.682591\pi$
$192$	−1.00000			−0.0721688
$193$			1.73205i			0.124676i	0.998055	+	0.0623379i	$0.0198556\pi$
$193$			1.73205i			0.124676i	−0.998055	+	0.0623379i	$0.980144\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$	4.50000	−	4.33013i	0.322252	−	0.310087i
$196$		0			0
$197$	19.5000	+	11.2583i	1.38932	+	0.802123i	0.993238	−	0.116094i	$-0.0370372\pi$
$197$	19.5000	+	11.2583i	1.38932	+	0.802123i	0.396079	+	0.918216i	$0.370371\pi$
$198$	−9.00000	−	15.5885i	−0.639602	−	1.10782i
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−3.00000	+	1.73205i	−0.212132	+	0.122474i
$201$			8.66025i			0.610847i
$202$	−13.5000	+	7.79423i	−0.949857	+	0.548400i
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		−	22.5167i		−	1.56881i
$207$		0			0
$208$	17.5000	−	4.33013i	1.21341	−	0.300240i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	9.00000			0.618123
$213$	1.50000	−	0.866025i	0.102778	−	0.0593391i
$214$		0			0
$215$		−	19.0526i		−	1.29937i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−4.50000	+	7.79423i	−0.304778	+	0.527892i
$219$	7.50000	−	4.33013i	0.506803	−	0.292603i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	−15.0000	−	15.5885i	−1.00901	−	1.04859i
$222$		0			0
$223$	−4.50000	−	2.59808i	−0.301342	−	0.173980i	0.341703	−	0.939808i	$-0.388996\pi$
$223$	−4.50000	−	2.59808i	−0.301342	−	0.173980i	−0.643046	+	0.765828i	$0.722329\pi$
$224$		0			0
$225$	2.00000	+	3.46410i	0.133333	+	0.230940i
$226$	22.5000	+	12.9904i	1.49668	+	0.864107i
$227$	15.0000	+	8.66025i	0.995585	+	0.574801i	0.906939	−	0.421262i	$-0.138413\pi$
$227$	15.0000	+	8.66025i	0.995585	+	0.574801i	0.0886460	+	0.996063i	$0.471746\pi$
$228$	−1.50000	−	0.866025i	−0.0993399	−	0.0573539i
$229$	−10.5000	−	6.06218i	−0.693860	−	0.400600i	0.111197	−	0.993798i	$-0.464532\pi$
$229$	−10.5000	−	6.06218i	−0.693860	−	0.400600i	−0.805056	+	0.593198i	$0.797865\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	+	2.59808i	0.295439	+	0.170572i
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−3.00000	−	12.1244i	−0.196116	−	0.792594i
$235$	7.50000	+	12.9904i	0.489246	+	0.847399i
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$	2.50000	−	4.33013i	0.162392	−	0.281272i
$238$		0			0
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$			8.66025i			0.559017i
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	0.680640	−	0.732618i	$-0.261702\pi$
$241$	6.00000	+	3.46410i	0.386494	+	0.223142i	−0.294146	+	0.955761i	$0.595035\pi$
$242$	24.0000	−	13.8564i	1.54278	−	0.890724i
$243$	16.0000			1.02640
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	−6.00000	−	1.73205i	−0.381771	−	0.110208i
$248$	1.50000	+	2.59808i	0.0952501	+	0.164978i
$249$			3.46410i			0.219529i
$250$	10.5000	+	18.1865i	0.664078	+	1.15022i
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	0.909475	−	0.415759i	$-0.136484\pi$
$251$	1.50000	+	2.59808i	0.0946792	+	0.163989i	−0.814795	+	0.579748i	$0.803151\pi$
$252$		0			0
$253$		0			0
$254$		−	22.5167i		−	1.41282i
$255$	9.00000	−	5.19615i	0.563602	−	0.325396i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$	16.5000	+	9.52628i	1.02725	+	0.593080i
$259$		0			0
$260$	−1.50000	−	6.06218i	−0.0930261	−	0.375960i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$			25.9808i			1.60510i
$263$	3.00000			0.184988			0.0924940	−	0.995713i	$-0.470516\pi$
$263$	3.00000			0.184988			0.0924940	+	0.995713i	$0.470516\pi$
$264$	−9.00000			−0.553912
$265$			15.5885i			0.957591i
$266$		0			0
$267$	6.00000	−	3.46410i	0.367194	−	0.212000i
$268$	7.50000	+	4.33013i	0.458135	+	0.264505i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$	15.0000			0.912871
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	15.0000	−	8.66025i	0.911185	−	0.526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$		0			0
$275$	−9.00000	+	5.19615i	−0.542720	+	0.313340i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	19.5000	+	11.2583i	1.16953	+	0.675230i
$279$	3.00000	−	1.73205i	0.179605	−	0.103695i
$280$		0			0
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$	−15.0000			−0.893237
$283$	−19.0000			−1.12943			−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000			−1.12943			−0.564716	+	0.825285i	$0.691014\pi$
$284$		−	1.73205i		−	0.102778i
$285$	1.50000	−	2.59808i	0.0888523	−	0.153897i
$286$	31.5000	−	7.79423i	1.86263	−	0.460882i
$287$		0			0
$288$	9.00000	+	5.19615i	0.530330	+	0.306186i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	4.50000	−	2.59808i	0.263795	−	0.152302i
$292$		−	8.66025i		−	0.506803i
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.331632	−	0.943409i	$-0.392401\pi$
$293$	22.5000	−	12.9904i	1.31446	−	0.758906i	0.982832	+	0.184503i	$0.0590674\pi$
$294$		0			0
$295$	3.00000	+	5.19615i	0.174667	+	0.302532i
$296$		0			0
$297$			25.9808i			1.50756i
$298$	−16.5000	−	28.5788i	−0.955819	−	1.65553i
$299$		0			0
$300$	−2.00000			−0.115470
$301$		0			0
$302$	10.5000	−	18.1865i	0.604207	−	1.04652i
$303$	9.00000			0.517036
$304$	7.50000	−	4.33013i	0.430155	−	0.248350i
$305$	−10.5000	−	6.06218i	−0.601228	−	0.347119i
$306$		−	20.7846i		−	1.18818i
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$	−6.50000	+	11.2583i	−0.369772	+	0.640464i
$310$	4.50000	−	2.59808i	0.255583	−	0.147561i
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$312$	−6.00000	−	1.73205i	−0.339683	−	0.0980581i
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	−34.5000	−	19.9186i	−1.94695	−	1.12407i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	4.50000	+	2.59808i	0.252745	+	0.145922i	0.621021	−	0.783794i	$-0.286718\pi$
$317$	4.50000	+	2.59808i	0.252745	+	0.145922i	−0.368275	+	0.929717i	$0.620052\pi$
$318$	−13.5000	−	7.79423i	−0.757042	−	0.437079i
$319$	13.5000	+	7.79423i	0.755855	+	0.436393i
$320$	−1.50000	−	0.866025i	−0.0838525	−	0.0484123i
$321$		0			0
$322$		0			0
$323$	−9.00000	−	5.19615i	−0.500773	−	0.289122i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−7.00000	+	1.73205i	−0.388290	+	0.0960769i
$326$	10.5000	+	18.1865i	0.581541	+	1.00726i
$327$	4.50000	−	2.59808i	0.248851	−	0.143674i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$			15.5885i			0.858116i
$331$		−	32.9090i		−	1.80884i	−0.426643	−	0.904420i	$-0.640304\pi$
$331$		−	32.9090i		−	1.80884i	0.426643	−	0.904420i	$-0.359696\pi$
$332$	3.00000	+	1.73205i	0.164646	+	0.0950586i
$333$		0			0
$334$	−3.00000			−0.164153
$335$	−7.50000	+	12.9904i	−0.409769	+	0.709740i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	22.5000	+	0.866025i	1.22384	+	0.0471056i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$		−	10.3923i		−	0.563602i
$341$	4.50000	+	7.79423i	0.243689	+	0.422081i
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$		0			0
$344$	−16.5000	+	9.52628i	−0.889620	+	0.513623i
$345$		0			0
$346$	22.5000	−	12.9904i	1.20961	−	0.698367i
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	4.50000	+	2.59808i	0.240879	+	0.139072i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	4.50000	+	2.59808i	0.240879	+	0.139072i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−5.00000	+	17.3205i	−0.266880	+	0.924500i
$352$	−13.5000	+	23.3827i	−0.719552	+	1.24630i
$353$		−	1.73205i		−	0.0921878i	−0.998937	−	0.0460939i	$-0.985323\pi$
$353$		−	1.73205i		−	0.0921878i	0.998937	−	0.0460939i	$-0.0146773\pi$
$354$	−6.00000			−0.318896
$355$	3.00000			0.159223
$356$		−	6.92820i		−	0.367194i
$357$		0			0
$358$	−4.50000	+	2.59808i	−0.237832	+	0.137313i
$359$	16.5000	+	9.52628i	0.870837	+	0.502778i	0.867626	−	0.497217i	$-0.165645\pi$
$359$	16.5000	+	9.52628i	0.870837	+	0.502778i	0.00321050	+	0.999995i	$0.498978\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	16.0000			0.842105
$362$	3.00000	−	1.73205i	0.157676	−	0.0910346i
$363$	−16.0000			−0.839782
$364$		0			0
$365$	15.0000			0.785136
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$	−23.0000			−1.20059			−0.600295	−	0.799779i	$-0.704950\pi$
$367$	−23.0000			−1.20059			−0.600295	+	0.799779i	$0.704950\pi$
$368$		0			0
$369$	−9.00000	−	5.19615i	−0.468521	−	0.270501i
$370$		0			0
$371$		0			0
$372$			1.73205i			0.0898027i
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	54.0000			2.79227
$375$		−	12.1244i		−	0.626099i
$376$	7.50000	−	12.9904i	0.386783	−	0.669928i
$377$	7.50000	+	7.79423i	0.386270	+	0.401423i
$378$		0			0
$379$	−1.50000	−	0.866025i	−0.0770498	−	0.0444847i	0.460980	−	0.887410i	$-0.347498\pi$
$379$	−1.50000	−	0.866025i	−0.0770498	−	0.0444847i	−0.538030	+	0.842926i	$0.680831\pi$
$380$	−1.50000	−	2.59808i	−0.0769484	−	0.133278i
$381$	−6.50000	+	11.2583i	−0.333005	+	0.576782i
$382$	22.5000	−	12.9904i	1.15120	−	0.664646i
$383$		−	15.5885i		−	0.796533i	−0.917270	−	0.398266i	$-0.869612\pi$
$383$		−	15.5885i		−	0.796533i	0.917270	−	0.398266i	$-0.130388\pi$
$384$	10.5000	−	6.06218i	0.535826	−	0.309359i
$385$		0			0
$386$	−1.50000	−	2.59808i	−0.0763480	−	0.132239i
$387$	11.0000	+	19.0526i	0.559161	+	0.968496i
$388$		−	5.19615i		−	0.263795i
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	0.825491	−	0.564416i	$-0.190898\pi$
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	−0.901544	+	0.432688i	$0.857565\pi$
$390$	−3.00000	+	10.3923i	−0.151911	+	0.526235i
$391$		0			0
$392$		0			0
$393$	7.50000	−	12.9904i	0.378325	−	0.655278i
$394$	−39.0000			−1.96479
$395$	7.50000	−	4.33013i	0.377366	−	0.217872i
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$			36.3731i			1.82551i	0.408505	+	0.912756i	$0.366050\pi$
$397$			36.3731i			1.82551i	−0.408505	+	0.912756i	$0.633950\pi$
$398$			6.92820i			0.347279i
$399$		0			0
$400$	5.00000	−	8.66025i	0.250000	−	0.433013i
$401$	−6.00000	+	3.46410i	−0.299626	+	0.172989i	−0.642275	−	0.766475i	$-0.722009\pi$
$401$	−6.00000	+	3.46410i	−0.299626	+	0.172989i	0.342649	+	0.939463i	$0.388676\pi$
$402$	−7.50000	−	12.9904i	−0.374066	−	0.647901i
$403$	1.50000	+	6.06218i	0.0747203	+	0.301979i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	1.50000	+	0.866025i	0.0745356	+	0.0430331i
$406$		0			0
$407$		0			0
$408$	−9.00000	−	5.19615i	−0.445566	−	0.257248i
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	0.344270	−	0.938871i	$-0.388126\pi$
$409$	−6.00000	−	3.46410i	−0.296681	−	0.171289i	−0.640951	+	0.767582i	$0.721460\pi$
$410$	−13.5000	−	7.79423i	−0.666717	−	0.384930i
$411$		0			0
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$		0			0
$414$		0			0
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	−13.5000	+	12.9904i	−0.661892	+	0.636906i
$417$	−6.50000	−	11.2583i	−0.318306	−	0.551323i
$418$	13.5000	−	7.79423i	0.660307	−	0.381228i
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		−	22.5167i		−	1.09609i
$423$	−15.0000	−	8.66025i	−0.729325	−	0.421076i
$424$	13.5000	−	7.79423i	0.655618	−	0.378521i
$425$	−12.0000			−0.582086
$426$	−1.50000	+	2.59808i	−0.0726752	+	0.125877i
$427$		0			0
$428$		0			0
$429$	−18.0000	−	5.19615i	−0.869048	−	0.250873i
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$		−	32.9090i		−	1.58517i	−0.609762	−	0.792585i	$-0.708735\pi$
$431$		−	32.9090i		−	1.58517i	0.609762	−	0.792585i	$-0.291265\pi$
$432$	−12.5000	−	21.6506i	−0.601407	−	1.04167i
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	0.998775	−	0.0494752i	$-0.0157549\pi$
$433$	9.50000	+	16.4545i	0.456541	+	0.790752i	−0.542234	+	0.840227i	$0.682422\pi$
$434$		0			0
$435$	−4.50000	+	2.59808i	−0.215758	+	0.124568i
$436$		−	5.19615i		−	0.248851i
$437$		0			0
$438$	−7.50000	+	12.9904i	−0.358364	+	0.620704i
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$	−13.5000	−	7.79423i	−0.643587	−	0.371575i
$441$		0			0
$442$	36.0000	+	10.3923i	1.71235	+	0.494312i
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	−0.987346	−	0.158583i	$-0.949307\pi$
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	0.631010	+	0.775775i	$0.282641\pi$
$444$		0			0
$445$	12.0000			0.568855
$446$	9.00000			0.426162
$447$			19.0526i			0.901155i
$448$		0			0
$449$	1.50000	−	0.866025i	0.0707894	−	0.0408703i	−0.464188	−	0.885737i	$-0.653654\pi$
$449$	1.50000	−	0.866025i	0.0707894	−	0.0408703i	0.534977	+	0.844867i	$0.320320\pi$
$450$	−6.00000	−	3.46410i	−0.282843	−	0.163299i
$451$	13.5000	−	23.3827i	0.635690	−	1.10105i
$452$	−15.0000			−0.705541
$453$	−10.5000	+	6.06218i	−0.493333	+	0.284826i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	−3.00000			−0.140488
$457$	−30.0000	+	17.3205i	−1.40334	+	0.810219i	−0.994734	−	0.102491i	$-0.967319\pi$
$457$	−30.0000	+	17.3205i	−1.40334	+	0.810219i	−0.408607	+	0.912710i	$0.633985\pi$
$458$	21.0000			0.981266
$459$	−15.0000	+	25.9808i	−0.700140	+	1.21268i
$460$		0			0
$461$	−25.5000	+	14.7224i	−1.18765	+	0.685692i	−0.957773	−	0.287527i	$-0.907167\pi$
$461$	−25.5000	+	14.7224i	−1.18765	+	0.685692i	−0.229881	+	0.973219i	$0.573834\pi$
$462$		0			0
$463$			24.2487i			1.12693i	0.826139	+	0.563467i	$0.190533\pi$
$463$			24.2487i			1.12693i	−0.826139	+	0.563467i	$0.809467\pi$
$464$	−15.0000			−0.696358
$465$	−3.00000			−0.139122
$466$		−	5.19615i		−	0.240707i
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	−0.999868	−	0.0162260i	$-0.994835\pi$
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	0.513986	+	0.857798i	$0.328168\pi$
$468$	5.00000	+	5.19615i	0.231125	+	0.240192i
$469$		0			0
$470$	−22.5000	−	12.9904i	−1.03785	−	0.599202i
$471$	11.5000	+	19.9186i	0.529892	+	0.917800i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	−49.5000	+	28.5788i	−2.27601	+	1.31406i
$474$			8.66025i			0.397779i
$475$	−3.00000	+	1.73205i	−0.137649	+	0.0794719i
$476$		0			0
$477$	−9.00000	−	15.5885i	−0.412082	−	0.713746i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$		−	29.4449i		−	1.34537i	−0.739929	−	0.672685i	$-0.765141\pi$
$479$		−	29.4449i		−	1.34537i	0.739929	−	0.672685i	$-0.234859\pi$
$480$	−4.50000	−	7.79423i	−0.205396	−	0.355756i
$481$		0			0
$482$	−12.0000			−0.546585
$483$		0			0
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$	9.00000			0.408669
$486$	−24.0000	+	13.8564i	−1.08866	+	0.628539i
$487$	−21.0000	−	12.1244i	−0.951601	−	0.549407i	−0.0580230	−	0.998315i	$-0.518480\pi$
$487$	−21.0000	−	12.1244i	−0.951601	−	0.549407i	−0.893578	+	0.448908i	$0.851813\pi$
$488$			12.1244i			0.548844i
$489$		−	12.1244i		−	0.548282i
$490$		0			0
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	−0.382118	−	0.924113i	$-0.624805\pi$
$491$	13.5000	−	23.3827i	0.609246	−	1.05525i	0.991365	−	0.131132i	$-0.0418613\pi$
$492$	4.50000	−	2.59808i	0.202876	−	0.117130i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	10.5000	−	2.59808i	0.472417	−	0.116893i
$495$	−9.00000	+	15.5885i	−0.404520	+	0.700649i
$496$	−7.50000	−	4.33013i	−0.336760	−	0.194428i
$497$		0			0
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$	−1.50000	−	0.866025i	−0.0671492	−	0.0387686i	0.466049	−	0.884759i	$-0.345677\pi$
$499$	−1.50000	−	0.866025i	−0.0671492	−	0.0387686i	−0.533199	+	0.845990i	$0.679010\pi$
$500$	−10.5000	−	6.06218i	−0.469574	−	0.271109i
$501$	1.50000	+	0.866025i	0.0670151	+	0.0386912i
$502$	−4.50000	−	2.59808i	−0.200845	−	0.115958i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$		0			0
$505$	13.5000	+	7.79423i	0.600742	+	0.346839i
$506$		0			0
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	−0.361098	−	0.932528i	$-0.617598\pi$
$509$	6.00000	−	3.46410i	0.265945	−	0.153544i	0.627044	+	0.778984i	$0.284265\pi$
$510$	−9.00000	+	15.5885i	−0.398527	+	0.690268i
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$			8.66025i			0.382360i
$514$	−45.0000	−	25.9808i	−1.98486	−	1.14596i
$515$	−19.5000	+	11.2583i	−0.859273	+	0.496101i
$516$	−11.0000			−0.484248
$517$	22.5000	−	38.9711i	0.989549	−	1.71395i
$518$		0			0
$519$	−15.0000			−0.658427
$520$	−7.50000	−	7.79423i	−0.328897	−	0.341800i
$521$	19.5000	+	33.7750i	0.854311	+	1.47971i	0.877283	+	0.479973i	$0.159354\pi$
$521$	19.5000	+	33.7750i	0.854311	+	1.47971i	−0.0229727	+	0.999736i	$0.507313\pi$
$522$			10.3923i			0.454859i
$523$	−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	$0.861206\pi$
$524$	−7.50000	−	12.9904i	−0.327639	−	0.567487i
$525$		0			0
$526$	−4.50000	+	2.59808i	−0.196209	+	0.113282i
$527$			10.3923i			0.452696i
$528$	22.5000	−	12.9904i	0.979187	−	0.565334i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	−13.5000	−	23.3827i	−0.586403	−	1.01568i
$531$	−6.00000	−	3.46410i	−0.260378	−	0.150329i
$532$		0			0
$533$	13.5000	−	12.9904i	0.584750	−	0.562676i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$	15.0000			0.647901
$537$	3.00000			0.129460
$538$		−	10.3923i		−	0.448044i
$539$		0			0
$540$	−7.50000	+	4.33013i	−0.322749	+	0.186339i
$541$	10.5000	+	6.06218i	0.451430	+	0.260633i	0.708434	−	0.705777i	$-0.249402\pi$
$541$	10.5000	+	6.06218i	0.451430	+	0.260633i	−0.257004	+	0.966410i	$0.582735\pi$
$542$	−15.0000	+	25.9808i	−0.644305	+	1.11597i
$543$	−2.00000			−0.0858282
$544$	−27.0000	+	15.5885i	−1.15762	+	0.668350i
$545$	9.00000			0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	14.0000			0.597505
$550$	9.00000	−	15.5885i	0.383761	−	0.664694i
$551$	4.50000	+	2.59808i	0.191706	+	0.110682i
$552$		0			0
$553$		0			0
$554$			17.3205i			0.735878i
$555$		0			0
$556$	−13.0000			−0.551323
$557$			15.5885i			0.660504i	0.943893	+	0.330252i	$0.107134\pi$
$557$			15.5885i			0.660504i	−0.943893	+	0.330252i	$0.892866\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$	−38.5000	+	9.52628i	−1.62838	+	0.402919i
$560$		0			0
$561$	−27.0000	−	15.5885i	−1.13994	−	0.658145i
$562$	−6.00000	−	10.3923i	−0.253095	−	0.438373i
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$	7.50000	−	4.33013i	0.315807	−	0.182331i
$565$		−	25.9808i		−	1.09302i
$566$	28.5000	−	16.4545i	1.19794	−	0.691633i
$567$		0			0
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$			5.19615i			0.217643i
$571$	11.5000	+	19.9186i	0.481260	+	0.833567i	0.999769	−	0.0215055i	$-0.00684595\pi$
$571$	11.5000	+	19.9186i	0.481260	+	0.833567i	−0.518509	+	0.855072i	$0.673513\pi$
$572$	−13.5000	+	12.9904i	−0.564463	+	0.543155i
$573$	−15.0000			−0.626634
$574$		0			0
$575$		0			0
$576$	2.00000			0.0833333
$577$	13.5000	−	7.79423i	0.562012	−	0.324478i	−0.191940	−	0.981407i	$-0.561478\pi$
$577$	13.5000	−	7.79423i	0.562012	−	0.324478i	0.753953	+	0.656929i	$0.228145\pi$
$578$	28.5000	+	16.4545i	1.18544	+	0.684416i
$579$			1.73205i			0.0719816i
$580$			5.19615i			0.215758i
$581$		0			0
$582$	−4.50000	+	7.79423i	−0.186531	+	0.323081i
$583$	40.5000	−	23.3827i	1.67734	−	0.968412i
$584$	−7.50000	−	12.9904i	−0.310352	−	0.537546i
$585$	−9.00000	+	8.66025i	−0.372104	+	0.358057i
$586$	−22.5000	+	38.9711i	−0.929466	+	1.60988i
$587$	13.5000	+	7.79423i	0.557205	+	0.321702i	0.752023	−	0.659137i	$-0.229078\pi$
$587$	13.5000	+	7.79423i	0.557205	+	0.321702i	−0.194818	+	0.980839i	$0.562412\pi$
$588$		0			0
$589$	1.50000	+	2.59808i	0.0618064	+	0.107052i
$590$	−9.00000	−	5.19615i	−0.370524	−	0.213922i
$591$	19.5000	+	11.2583i	0.802123	+	0.463106i
$592$		0			0
$593$	−4.50000	−	2.59808i	−0.184793	−	0.106690i	0.404750	−	0.914428i	$-0.367359\pi$
$593$	−4.50000	−	2.59808i	−0.184793	−	0.106690i	−0.589543	+	0.807737i	$0.700692\pi$
$594$	−22.5000	−	38.9711i	−0.923186	−	1.59901i
$595$		0			0
$596$	16.5000	+	9.52628i	0.675866	+	0.390212i
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$		0			0
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	0.759328	−	0.650708i	$-0.225528\pi$
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	−0.943193	+	0.332244i	$0.892194\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$		0			0
$603$		−	17.3205i		−	0.705346i
$604$			12.1244i			0.493333i
$605$	−24.0000	−	13.8564i	−0.975739	−	0.563343i
$606$	−13.5000	+	7.79423i	−0.548400	+	0.316619i
$607$	43.0000			1.74532			0.872658	−	0.488332i	$-0.162394\pi$
$607$	43.0000			1.74532			0.872658	+	0.488332i	$0.162394\pi$
$608$	−4.50000	+	7.79423i	−0.182499	+	0.316098i
$609$		0			0
$610$	21.0000			0.850265
$611$	22.5000	−	21.6506i	0.910253	−	0.875891i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$			36.3731i			1.46909i	0.678558	+	0.734547i	$0.262605\pi$
$613$			36.3731i			1.46909i	−0.678558	+	0.734547i	$0.737395\pi$
$614$	−21.0000	−	36.3731i	−0.847491	−	1.46790i
$615$	4.50000	+	7.79423i	0.181458	+	0.314294i
$616$		0			0
$617$	37.5000	−	21.6506i	1.50969	−	0.871622i	0.509757	−	0.860318i	$-0.329735\pi$
$617$	37.5000	−	21.6506i	1.50969	−	0.871622i	0.999936	−	0.0113033i	$-0.00359804\pi$
$618$		−	22.5167i		−	0.905753i
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	−0.130301	−	0.991475i	$-0.541594\pi$
$619$	16.5000	−	9.52628i	0.663191	−	0.382893i	0.793492	+	0.608581i	$0.208261\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$		0			0
$622$	22.5000	+	12.9904i	0.902168	+	0.520867i
$623$		0			0
$624$	17.5000	−	4.33013i	0.700561	−	0.173344i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$			32.9090i			1.31531i
$627$	−9.00000			−0.359425
$628$	23.0000			0.917800
$629$		0			0
$630$		0			0
$631$	−40.5000	+	23.3827i	−1.61228	+	0.930850i	−0.623439	+	0.781872i	$0.714265\pi$
$631$	−40.5000	+	23.3827i	−1.61228	+	0.930850i	−0.988841	+	0.148978i	$0.952402\pi$
$632$	−7.50000	−	4.33013i	−0.298334	−	0.172243i
$633$	−6.50000	+	11.2583i	−0.258352	+	0.447478i
$634$	−9.00000			−0.357436
$635$	−19.5000	+	11.2583i	−0.773834	+	0.446773i
$636$	9.00000			0.356873
$637$		0			0
$638$	−27.0000			−1.06894
$639$	−3.00000	+	1.73205i	−0.118678	+	0.0685189i
$640$	21.0000			0.830098
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	4.50000	−	2.59808i	0.177463	−	0.102458i	−0.408637	−	0.912697i	$-0.633996\pi$
$643$	4.50000	−	2.59808i	0.177463	−	0.102458i	0.586100	+	0.810239i	$0.300663\pi$
$644$		0			0
$645$		−	19.0526i		−	0.750194i
$646$	18.0000			0.708201
$647$	9.00000			0.353827			0.176913	−	0.984226i	$-0.443389\pi$
$647$	9.00000			0.353827			0.176913	+	0.984226i	$0.443389\pi$
$648$		−	1.73205i		−	0.0680414i
$649$	9.00000	−	15.5885i	0.353281	−	0.611900i
$650$	9.00000	−	8.66025i	0.353009	−	0.339683i
$651$		0			0
$652$	−10.5000	−	6.06218i	−0.411212	−	0.237413i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$	−4.50000	+	7.79423i	−0.175964	+	0.304778i
$655$	22.5000	−	12.9904i	0.879148	−	0.507576i
$656$			25.9808i			1.01438i
$657$	−15.0000	+	8.66025i	−0.585206	+	0.337869i
$658$		0			0
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$	−4.50000	−	7.79423i	−0.175162	−	0.303390i
$661$		−	36.3731i		−	1.41475i	−0.706839	−	0.707374i	$-0.749880\pi$
$661$		−	36.3731i		−	1.41475i	0.706839	−	0.707374i	$-0.250120\pi$
$662$	28.5000	+	49.3634i	1.10768	+	1.91856i
$663$	−15.0000	−	15.5885i	−0.582552	−	0.605406i
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.50000	−	0.866025i	0.0580367	−	0.0335075i
$669$	−4.50000	−	2.59808i	−0.173980	−	0.100447i
$670$		−	25.9808i		−	1.00372i
$671$			36.3731i			1.40417i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−33.0000	+	19.0526i	−1.27111	+	0.733877i
$675$	5.00000	+	8.66025i	0.192450	+	0.333333i
$676$	−11.5000	+	6.06218i	−0.442308	+	0.233161i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$	22.5000	+	12.9904i	0.864107	+	0.498893i
$679$		0			0
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$	15.0000	+	8.66025i	0.574801	+	0.331862i
$682$	−13.5000	−	7.79423i	−0.516942	−	0.298456i
$683$	21.0000	+	12.1244i	0.803543	+	0.463926i	0.844708	−	0.535227i	$-0.179774\pi$
$683$	21.0000	+	12.1244i	0.803543	+	0.463926i	−0.0411658	+	0.999152i	$0.513107\pi$
$684$	3.00000	+	1.73205i	0.114708	+	0.0662266i
$685$		0			0
$686$		0			0
$687$	−10.5000	−	6.06218i	−0.400600	−	0.231287i
$688$	27.5000	−	47.6314i	1.04843	−	1.81593i
$689$	31.5000	−	7.79423i	1.20005	−	0.296936i
$690$		0			0
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.916161	−	0.400811i	$-0.868728\pi$
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.110968	+	0.993824i	$0.535395\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$		0			0
$694$		0			0
$695$		−	22.5167i		−	0.854106i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	27.0000	−	15.5885i	1.02270	−	0.590455i
$698$	−9.00000			−0.340655
$699$	−1.50000	+	2.59808i	−0.0567352	+	0.0982683i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	−7.50000	−	30.3109i	−0.283069	−	1.14401i
$703$		0			0
$704$			5.19615i			0.195837i
$705$	7.50000	+	12.9904i	0.282466	+	0.489246i
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$		0			0
$708$	3.00000	−	1.73205i	0.112747	−	0.0650945i
$709$			12.1244i			0.455340i	0.973738	+	0.227670i	$0.0731107\pi$
$709$			12.1244i			0.455340i	−0.973738	+	0.227670i	$0.926889\pi$
$710$	−4.50000	+	2.59808i	−0.168882	+	0.0975041i
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$	−6.00000	−	10.3923i	−0.224860	−	0.389468i
$713$		0			0
$714$		0			0
$715$	−22.5000	−	23.3827i	−0.841452	−	0.874463i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$		−	10.3923i		−	0.388108i
$718$	−33.0000			−1.23155
$719$	15.0000			0.559406			0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000			0.559406			0.279703	+	0.960087i	$0.409764\pi$
$720$		−	17.3205i		−	0.645497i
$721$		0			0
$722$	−24.0000	+	13.8564i	−0.893188	+	0.515682i
$723$	6.00000	+	3.46410i	0.223142	+	0.128831i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	6.00000			0.222834
$726$	24.0000	−	13.8564i	0.890724	−	0.514259i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−22.5000	+	12.9904i	−0.832762	+	0.480796i
$731$	−66.0000			−2.44110
$732$	−3.50000	+	6.06218i	−0.129364	+	0.224065i
$733$	43.5000	+	25.1147i	1.60671	+	0.927634i	0.990100	+	0.140365i	$0.0448275\pi$
$733$	43.5000	+	25.1147i	1.60671	+	0.927634i	0.616609	+	0.787269i	$0.288506\pi$
$734$	34.5000	−	19.9186i	1.27342	−	0.735208i
$735$		0			0
$736$		0			0
$737$	45.0000			1.65760
$738$	18.0000			0.662589
$739$		−	39.8372i		−	1.46543i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$		−	39.8372i		−	1.46543i	0.680534	−	0.732717i	$-0.261748\pi$
$740$		0			0
$741$	−6.00000	−	1.73205i	−0.220416	−	0.0636285i
$742$		0			0
$743$	−1.50000	−	0.866025i	−0.0550297	−	0.0317714i	0.472233	−	0.881474i	$-0.343448\pi$
$743$	−1.50000	−	0.866025i	−0.0550297	−	0.0317714i	−0.527262	+	0.849703i	$0.676782\pi$
$744$	1.50000	+	2.59808i	0.0549927	+	0.0952501i
$745$	−16.5000	+	28.5788i	−0.604513	+	1.04705i
$746$	−28.5000	+	16.4545i	−1.04346	+	0.602441i
$747$		−	6.92820i		−	0.253490i
$748$	−27.0000	+	15.5885i	−0.987218	+	0.569970i
$749$		0			0
$750$	10.5000	+	18.1865i	0.383406	+	0.664078i
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	0.623856	−	0.781540i	$-0.285565\pi$
$751$	−10.0000	−	17.3205i	−0.364905	−	0.632034i	−0.988761	+	0.149505i	$0.952232\pi$
$752$			43.3013i			1.57903i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	−18.0000	−	5.19615i	−0.655521	−	0.189233i
$755$	−21.0000			−0.764268
$756$		0			0
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	−0.669193	−	0.743089i	$-0.733360\pi$
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	0.978130	+	0.207993i	$0.0666932\pi$
$758$	3.00000			0.108965
$759$		0			0
$760$	−4.50000	−	2.59808i	−0.163232	−	0.0942421i
$761$			29.4449i			1.06738i	0.845682	+	0.533688i	$0.179194\pi$
$761$			29.4449i			1.06738i	−0.845682	+	0.533688i	$0.820806\pi$
$762$		−	22.5167i		−	0.815693i
$763$		0			0
$764$	−7.50000	+	12.9904i	−0.271340	+	0.469975i
$765$	−18.0000	+	10.3923i	−0.650791	+	0.375735i
$766$	13.5000	+	23.3827i	0.487775	+	0.844851i
$767$	9.00000	−	8.66025i	0.324971	−	0.312704i
$768$	−9.50000	+	16.4545i	−0.342802	+	0.593750i
$769$	16.5000	+	9.52628i	0.595005	+	0.343526i	0.767074	−	0.641558i	$-0.221712\pi$
$769$	16.5000	+	9.52628i	0.595005	+	0.343526i	−0.172069	+	0.985085i	$0.555045\pi$
$770$		0			0
$771$	15.0000	+	25.9808i	0.540212	+	0.935674i
$772$	1.50000	+	0.866025i	0.0539862	+	0.0311689i
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	0.700032	−	0.714111i	$-0.253169\pi$
$773$	12.0000	+	6.92820i	0.431610	+	0.249190i	−0.268422	+	0.963301i	$0.586502\pi$
$774$	−33.0000	−	19.0526i	−1.18616	−	0.684830i
$775$	3.00000	+	1.73205i	0.107763	+	0.0622171i
$776$	−4.50000	−	7.79423i	−0.161541	−	0.279797i
$777$		0			0
$778$	4.50000	+	2.59808i	0.161333	+	0.0931455i
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$	−1.50000	−	6.06218i	−0.0537086	−	0.217061i
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$		0			0
$783$	7.50000	−	12.9904i	0.268028	−	0.464238i
$784$		0			0
$785$			39.8372i			1.42185i
$786$			25.9808i			0.926703i
$787$	27.0000	+	15.5885i	0.962446	+	0.555668i	0.896925	−	0.442183i	$-0.145796\pi$
$787$	27.0000	+	15.5885i	0.962446	+	0.555668i	0.0655211	+	0.997851i	$0.479129\pi$
$788$	19.5000	−	11.2583i	0.694659	−	0.401061i
$789$	3.00000			0.106803
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$		0			0
$792$	18.0000			0.639602
$793$	−7.00000	+	24.2487i	−0.248577	+	0.861097i
$794$	−31.5000	−	54.5596i	−1.11789	−	1.93625i
$795$			15.5885i			0.552866i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	−0.994943	−	0.100446i	$-0.967973\pi$
$797$	−16.5000	−	28.5788i	−0.584460	−	1.01231i	0.410483	−	0.911868i	$-0.365360\pi$
$798$		0			0
$799$	45.0000	−	25.9808i	1.59199	−	0.919133i
$800$			10.3923i			0.367423i
$801$	−12.0000	+	6.92820i	−0.423999	+	0.244796i
$802$	6.00000	−	10.3923i	0.211867	−	0.366965i
$803$	−22.5000	−	38.9711i	−0.794008	−	1.37526i
$804$	7.50000	+	4.33013i	0.264505	+	0.152712i
$805$		0			0
$806$	−7.50000	−	7.79423i	−0.264176	−	0.274540i
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$		−	15.5885i		−	0.548400i
$809$	−21.0000			−0.738321			−0.369160	−	0.929366i	$-0.620355\pi$
$809$	−21.0000			−0.738321			−0.369160	+	0.929366i	$0.620355\pi$
$810$	−3.00000			−0.105409
$811$		−	3.46410i		−	0.121641i	−0.998149	−	0.0608205i	$-0.980628\pi$
$811$		−	3.46410i		−	0.121641i	0.998149	−	0.0608205i	$-0.0193717\pi$
$812$		0			0
$813$	15.0000	−	8.66025i	0.526073	−	0.303728i
$814$		0			0
$815$	10.5000	−	18.1865i	0.367799	−	0.637046i
$816$	30.0000			1.05021
$817$	−16.5000	+	9.52628i	−0.577262	+	0.333282i
$818$	12.0000			0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	19.5000	+	11.2583i	0.679315	+	0.392203i
$825$	−9.00000	+	5.19615i	−0.313340	+	0.180907i
$826$		0			0
$827$		−	10.3923i		−	0.361376i	−0.983540	−	0.180688i	$-0.942168\pi$
$827$		−	10.3923i		−	0.361376i	0.983540	−	0.180688i	$-0.0578324\pi$
$828$		0			0
$829$	−7.00000			−0.243120			−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000			−0.243120			−0.121560	+	0.992584i	$0.538790\pi$
$830$		−	10.3923i		−	0.360722i
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$		0			0
$834$	19.5000	+	11.2583i	0.675230	+	0.389844i
$835$	1.50000	+	2.59808i	0.0519096	+	0.0899101i
$836$	−4.50000	+	7.79423i	−0.155636	+	0.269569i
$837$	7.50000	−	4.33013i	0.259238	−	0.149671i
$838$			36.3731i			1.25649i
$839$	−1.50000	+	0.866025i	−0.0517858	+	0.0298985i	−0.525669	−	0.850689i	$-0.676185\pi$
$839$	−1.50000	+	0.866025i	−0.0517858	+	0.0298985i	0.473884	+	0.880587i	$0.342852\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$			6.92820i			0.238620i
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	−10.5000	−	19.9186i	−0.361211	−	0.685220i
$846$	30.0000			1.03142
$847$		0			0
$848$	−22.5000	+	38.9711i	−0.772653	+	1.33827i
$849$	−19.0000			−0.652078
$850$	18.0000	−	10.3923i	0.617395	−	0.356453i
$851$		0			0
$852$		−	1.73205i		−	0.0593391i
$853$			41.5692i			1.42330i	0.702533	+	0.711651i	$0.252052\pi$
$853$			41.5692i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$854$		0			0
$855$	−3.00000	+	5.19615i	−0.102598	+	0.177705i
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$	31.5000	−	7.79423i	1.07539	−	0.266091i
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$	−16.5000	−	9.52628i	−0.562645	−	0.324843i
$861$		0			0
$862$	28.5000	+	49.3634i	0.970714	+	1.68133i
$863$	−1.50000	−	0.866025i	−0.0510606	−	0.0294798i	0.474252	−	0.880389i	$-0.342718\pi$
$863$	−1.50000	−	0.866025i	−0.0510606	−	0.0294798i	−0.525313	+	0.850909i	$0.676052\pi$
$864$	22.5000	+	12.9904i	0.765466	+	0.441942i
$865$	−22.5000	−	12.9904i	−0.765023	−	0.441686i
$866$	−28.5000	−	16.4545i	−0.968469	−	0.559146i
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$		0			0
$869$	−22.5000	−	12.9904i	−0.763260	−	0.440668i
$870$	4.50000	−	7.79423i	0.152564	−	0.264249i
$871$	30.0000	+	8.66025i	1.01651	+	0.293442i
$872$	−4.50000	−	7.79423i	−0.152389	−	0.263946i
$873$	−9.00000	+	5.19615i	−0.304604	+	0.175863i
$874$		0			0
$875$		0			0
$876$		−	8.66025i		−	0.292603i
$877$		−	1.73205i		−	0.0584872i	−0.999572	−	0.0292436i	$-0.990690\pi$
$877$		−	1.73205i		−	0.0584872i	0.999572	−	0.0292436i	$-0.00930985\pi$
$878$	−12.0000	−	6.92820i	−0.404980	−	0.233816i
$879$	22.5000	−	12.9904i	0.758906	−	0.438155i
$880$	45.0000			1.51695
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	0.441934	+	0.897048i	$0.354293\pi$
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	−0.997833	+	0.0657979i	$0.979041\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	−21.0000	+	5.19615i	−0.706306	+	0.174766i
$885$	3.00000	+	5.19615i	0.100844	+	0.174667i
$886$		−	25.9808i		−	0.872841i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$		0			0
$890$	−18.0000	+	10.3923i	−0.603361	+	0.348351i
$891$		−	5.19615i		−	0.174078i
$892$	−4.50000	+	2.59808i	−0.150671	+	0.0869900i
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$	−16.5000	−	28.5788i	−0.551843	−	0.955819i
$895$	4.50000	+	2.59808i	0.150418	+	0.0868441i
$896$		0			0
$897$		0			0
$898$	−1.50000	+	2.59808i	−0.0500556	+	0.0866989i
$899$		−	5.19615i		−	0.173301i
$900$	4.00000			0.133333
$901$	54.0000			1.79900
$902$			46.7654i			1.55712i
$903$		0			0
$904$	−22.5000	+	12.9904i	−0.748339	+	0.432054i
$905$	−3.00000	−	1.73205i	−0.0997234	−	0.0575753i
$906$	10.5000	−	18.1865i	0.348839	−	0.604207i
$907$	−29.0000			−0.962929			−0.481465	−	0.876466i	$-0.659895\pi$
$907$	−29.0000			−0.962929			−0.481465	+	0.876466i	$0.659895\pi$
$908$	15.0000	−	8.66025i	0.497792	−	0.287401i
$909$	−18.0000			−0.597022
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	7.50000	−	4.33013i	0.248350	−	0.143385i
$913$	18.0000			0.595713
$914$	30.0000	−	51.9615i	0.992312	−	1.71873i
$915$	−10.5000	−	6.06218i	−0.347119	−	0.200409i
$916$	−10.5000	+	6.06218i	−0.346930	+	0.200300i
$917$		0			0
$918$		−	51.9615i		−	1.71499i
$919$	−47.0000			−1.55039			−0.775193	−	0.631724i	$-0.782348\pi$
$919$	−47.0000			−1.55039			−0.775193	+	0.631724i	$0.782348\pi$
$920$		0			0
$921$			24.2487i			0.799022i
$922$	25.5000	−	44.1673i	0.839798	−	1.45457i
$923$	−1.50000	−	6.06218i	−0.0493731	−	0.199539i
$924$		0			0
$925$		0			0
$926$	−21.0000	−	36.3731i	−0.690103	−	1.19529i
$927$	13.0000	−	22.5167i	0.426976	−	0.739544i
$928$	13.5000	−	7.79423i	0.443159	−	0.255858i
$929$		−	46.7654i		−	1.53432i	−0.641455	−	0.767161i	$-0.721669\pi$
$929$		−	46.7654i		−	1.53432i	0.641455	−	0.767161i	$-0.278331\pi$
$930$	4.50000	−	2.59808i	0.147561	−	0.0851943i
$931$		0			0
$932$	1.50000	+	2.59808i	0.0491341	+	0.0851028i
$933$	−7.50000	−	12.9904i	−0.245539	−	0.425286i
$934$		−	36.3731i		−	1.19016i
$935$	−27.0000	−	46.7654i	−0.882994	−	1.52939i
$936$	12.0000	+	3.46410i	0.392232	+	0.113228i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$	9.50000	−	16.4545i	0.310021	−	0.536972i
$940$	15.0000			0.489246
$941$	−4.50000	+	2.59808i	−0.146696	+	0.0846949i	−0.571551	−	0.820566i	$-0.693658\pi$
$941$	−4.50000	+	2.59808i	−0.146696	+	0.0846949i	0.424856	+	0.905261i	$0.360325\pi$
$942$	−34.5000	−	19.9186i	−1.12407	−	0.648983i
$943$		0			0
$944$			17.3205i			0.563735i
$945$		0			0
$946$	49.5000	−	85.7365i	1.60938	−	2.78753i
$947$	−33.0000	+	19.0526i	−1.07236	+	0.619125i	−0.928824	−	0.370521i	$-0.879179\pi$
$947$	−33.0000	+	19.0526i	−1.07236	+	0.619125i	−0.143532	+	0.989646i	$0.545846\pi$
$948$	−2.50000	−	4.33013i	−0.0811962	−	0.140636i
$949$	−7.50000	−	30.3109i	−0.243460	−	0.983933i
$950$	3.00000	−	5.19615i	0.0973329	−	0.168585i
$951$	4.50000	+	2.59808i	0.145922	+	0.0842484i
$952$		0			0
$953$	28.5000	+	49.3634i	0.923206	+	1.59904i	0.794422	+	0.607366i	$0.207774\pi$
$953$	28.5000	+	49.3634i	0.923206	+	1.59904i	0.128784	+	0.991673i	$0.458893\pi$
$954$	27.0000	+	15.5885i	0.874157	+	0.504695i
$955$	−22.5000	−	12.9904i	−0.728083	−	0.420359i
$956$	−9.00000	−	5.19615i	−0.291081	−	0.168056i
$957$	13.5000	+	7.79423i	0.436393	+	0.251952i
$958$	25.5000	+	44.1673i	0.823868	+	1.42698i
$959$		0			0
$960$	−1.50000	−	0.866025i	−0.0484123	−	0.0279508i
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$		0			0
$964$	6.00000	−	3.46410i	0.193247	−	0.111571i
$965$	−1.50000	+	2.59808i	−0.0482867	+	0.0836350i
$966$		0			0
$967$			10.3923i			0.334194i	0.985940	+	0.167097i	$0.0534393\pi$
$967$			10.3923i			0.334194i	−0.985940	+	0.167097i	$0.946561\pi$
$968$			27.7128i			0.890724i
$969$	−9.00000	−	5.19615i	−0.289122	−	0.166924i
$970$	−13.5000	+	7.79423i	−0.433459	+	0.250258i
$971$	−21.0000			−0.673922			−0.336961	−	0.941519i	$-0.609399\pi$
$971$	−21.0000			−0.673922			−0.336961	+	0.941519i	$0.609399\pi$
$972$	8.00000	−	13.8564i	0.256600	−	0.444444i
$973$		0			0
$974$	42.0000			1.34577
$975$	−7.00000	+	1.73205i	−0.224179	+	0.0554700i
$976$	−17.5000	−	30.3109i	−0.560161	−	0.970228i
$977$		−	19.0526i		−	0.609545i	−0.952425	−	0.304773i	$-0.901420\pi$
$977$		−	19.0526i		−	0.609545i	0.952425	−	0.304773i	$-0.0985805\pi$
$978$	10.5000	+	18.1865i	0.335753	+	0.581541i
$979$	−18.0000	−	31.1769i	−0.575282	−	0.996419i
$980$		0			0
$981$	−9.00000	+	5.19615i	−0.287348	+	0.165900i
$982$			46.7654i			1.49234i
$983$	−31.5000	+	18.1865i	−1.00469	+	0.580060i	−0.909634	−	0.415411i	$-0.863638\pi$
$983$	−31.5000	+	18.1865i	−1.00469	+	0.580060i	−0.0950602	+	0.995472i	$0.530304\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	19.5000	+	33.7750i	0.621322	+	1.07616i
$986$	−27.0000	−	15.5885i	−0.859855	−	0.496438i
$987$		0			0
$988$	−4.50000	+	4.33013i	−0.143164	+	0.137760i
$989$		0			0
$990$		−	31.1769i		−	0.990867i
$991$	59.0000			1.87420			0.937098	−	0.349065i	$-0.113501\pi$
$991$	59.0000			1.87420			0.937098	+	0.349065i	$0.113501\pi$
$992$	9.00000			0.285750
$993$		−	32.9090i		−	1.04433i
$994$		0			0
$995$	6.00000	−	3.46410i	0.190213	−	0.109819i
$996$	3.00000	+	1.73205i	0.0950586	+	0.0548821i
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	−0.849756	−	0.527176i	$-0.823251\pi$
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	0.881426	+	0.472322i	$0.156584\pi$
$998$	3.00000			0.0949633
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.a.30.1		2
7.2	even	3		637.2.q.b.589.1		2
7.3	odd	6		91.2.k.a.4.1	✓	2
7.4	even	3		637.2.k.b.459.1		2
7.5	odd	6		637.2.q.c.589.1		2
7.6	odd	2		91.2.u.a.30.1	yes	2
13.10	even	6		637.2.k.b.569.1		2
21.17	even	6		819.2.bm.a.550.1		2
21.20	even	2		819.2.do.c.667.1		2
91.6	even	12		1183.2.e.e.170.2		4
91.10	odd	6		91.2.u.a.88.1	yes	2
91.19	even	12		8281.2.a.s.1.1		2
91.20	even	12		1183.2.e.e.170.1		4
91.23	even	6		637.2.q.b.491.1		2
91.33	even	12		8281.2.a.s.1.2		2
91.45	even	12		1183.2.e.e.508.2		4
91.58	odd	12		8281.2.a.w.1.1		2
91.59	even	12		1183.2.e.e.508.1		4
91.62	odd	6		91.2.k.a.23.1	yes	2
91.72	odd	12		8281.2.a.w.1.2		2
91.75	odd	6		637.2.q.c.491.1		2
91.88	even	6	inner	637.2.u.a.361.1		2
273.62	even	6		819.2.bm.a.478.1		2
273.101	even	6		819.2.do.c.361.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	7.3	odd	6
91.2.k.a.23.1	yes	2	91.62	odd	6
91.2.u.a.30.1	yes	2	7.6	odd	2
91.2.u.a.88.1	yes	2	91.10	odd	6
637.2.k.b.459.1		2	7.4	even	3
637.2.k.b.569.1		2	13.10	even	6
637.2.q.b.491.1		2	91.23	even	6
637.2.q.b.589.1		2	7.2	even	3
637.2.q.c.491.1		2	91.75	odd	6
637.2.q.c.589.1		2	7.5	odd	6
637.2.u.a.30.1		2	1.1	even	1	trivial
637.2.u.a.361.1		2	91.88	even	6	inner
819.2.bm.a.478.1		2	273.62	even	6
819.2.bm.a.550.1		2	21.17	even	6
819.2.do.c.361.1		2	273.101	even	6
819.2.do.c.667.1		2	21.20	even	2
1183.2.e.e.170.1		4	91.20	even	12
1183.2.e.e.170.2		4	91.6	even	12
1183.2.e.e.508.1		4	91.59	even	12
1183.2.e.e.508.2		4	91.45	even	12
8281.2.a.s.1.1		2	91.19	even	12
8281.2.a.s.1.2		2	91.33	even	12
8281.2.a.w.1.1		2	91.58	odd	12
8281.2.a.w.1.2		2	91.72	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} -3.00000 q^{10} -5.19615i q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 - 3.46410i) q^{13} +(1.50000 + 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(3.00000 - 1.73205i) q^{18} -1.73205i q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} -1.73205i q^{24} +(-1.00000 - 1.73205i) q^{25} +(1.50000 + 6.06218i) q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -3.00000 q^{30} +(-1.50000 + 0.866025i) q^{31} +(-4.50000 - 2.59808i) q^{32} -5.19615i q^{33} +10.3923i q^{34} +(-1.00000 + 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(1.00000 - 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(-4.50000 - 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} +(7.50000 + 4.33013i) q^{47} +(2.50000 + 4.33013i) q^{48} +(3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-2.50000 - 2.59808i) q^{52} +(4.50000 + 7.79423i) q^{53} +(7.50000 - 4.33013i) q^{54} +(4.50000 - 7.79423i) q^{55} -1.73205i q^{57} -5.19615i q^{58} +(3.00000 + 1.73205i) q^{59} +(1.50000 - 0.866025i) q^{60} -7.00000 q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(4.50000 - 4.33013i) q^{65} +(4.50000 + 7.79423i) q^{66} +8.66025i q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.50000 - 0.866025i) q^{71} +3.46410i q^{72} +(7.50000 - 4.33013i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 0.866025i) q^{76} +(1.50000 + 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +8.66025i q^{80} +1.00000 q^{81} -9.00000 q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(16.5000 + 9.52628i) q^{86} +(-1.50000 + 2.59808i) q^{87} -9.00000 q^{88} +(6.00000 - 3.46410i) q^{89} +6.00000 q^{90} +(-1.50000 + 0.866025i) q^{93} -15.0000 q^{94} +(1.50000 - 2.59808i) q^{95} +(-4.50000 - 2.59808i) q^{96} +(4.50000 - 2.59808i) q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 4 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 3 q^{6} - 4 q^{9} - 6 q^{10} + q^{12} + 2 q^{13} + 3 q^{15} + 5 q^{16} + 6 q^{17} + 6 q^{18} + 3 q^{20} + 9 q^{22} - 2 q^{25} + 3 q^{26} - 10 q^{27} - 3 q^{29} - 6 q^{30} - 3 q^{31} - 9 q^{32} - 2 q^{36} + 3 q^{38} + 2 q^{39} + 3 q^{40} + 9 q^{41} - 11 q^{43} - 9 q^{44} - 6 q^{45} + 15 q^{47} + 5 q^{48} + 6 q^{50} + 6 q^{51} - 5 q^{52} + 9 q^{53} + 15 q^{54} + 9 q^{55} + 6 q^{59} + 3 q^{60} - 14 q^{61} + 3 q^{62} - 2 q^{64} + 9 q^{65} + 9 q^{66} - 6 q^{68} + 3 q^{71} + 15 q^{73} - 2 q^{75} - 3 q^{76} + 3 q^{78} + 5 q^{79} + 2 q^{81} - 18 q^{82} + 18 q^{85} + 33 q^{86} - 3 q^{87} - 18 q^{88} + 12 q^{89} + 12 q^{90} - 3 q^{93} - 30 q^{94} + 3 q^{95} - 9 q^{96} + 9 q^{97}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 - 3 * q^6 - 4 * q^9 - 6 * q^10 + q^12 + 2 * q^13 + 3 * q^15 + 5 * q^16 + 6 * q^17 + 6 * q^18 + 3 * q^20 + 9 * q^22 - 2 * q^25 + 3 * q^26 - 10 * q^27 - 3 * q^29 - 6 * q^30 - 3 * q^31 - 9 * q^32 - 2 * q^36 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 9 * q^41 - 11 * q^43 - 9 * q^44 - 6 * q^45 + 15 * q^47 + 5 * q^48 + 6 * q^50 + 6 * q^51 - 5 * q^52 + 9 * q^53 + 15 * q^54 + 9 * q^55 + 6 * q^59 + 3 * q^60 - 14 * q^61 + 3 * q^62 - 2 * q^64 + 9 * q^65 + 9 * q^66 - 6 * q^68 + 3 * q^71 + 15 * q^73 - 2 * q^75 - 3 * q^76 + 3 * q^78 + 5 * q^79 + 2 * q^81 - 18 * q^82 + 18 * q^85 + 33 * q^86 - 3 * q^87 - 18 * q^88 + 12 * q^89 + 12 * q^90 - 3 * q^93 - 30 * q^94 + 3 * q^95 - 9 * q^96 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more