LMFDB - Embedded newform 198.2.e.b.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, degree $2$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	198.67
Dual form			198.2.e.b.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.73205i q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.73205i q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -3.00000 q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(2.00000 - 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +2.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} -3.46410i q^{21} +(0.500000 - 0.866025i) q^{22} +(-1.50000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +4.00000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(-4.50000 - 2.59808i) q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.73205i q^{33} +(3.00000 + 5.19615i) q^{34} +6.00000 q^{35} -3.00000 q^{36} -7.00000 q^{37} +(1.00000 + 1.73205i) q^{38} +(6.00000 - 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-6.00000 + 10.3923i) q^{41} +(3.00000 - 1.73205i) q^{42} +(-4.00000 - 6.92820i) q^{43} +1.00000 q^{44} -9.00000 q^{45} +(-4.50000 - 7.79423i) q^{47} -1.73205i q^{48} +(1.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} +(9.00000 + 5.19615i) q^{51} +(2.00000 + 3.46410i) q^{52} +9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(1.00000 + 1.73205i) q^{56} +(3.00000 + 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} -5.19615i q^{60} +(-4.00000 - 6.92820i) q^{61} +1.00000 q^{62} +(3.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(1.50000 - 0.866025i) q^{66} +(3.50000 - 6.06218i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{70} -15.0000 q^{71} +(-1.50000 - 2.59808i) q^{72} -10.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} -6.92820i q^{75} +(-1.00000 + 1.73205i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(6.00000 + 3.46410i) q^{78} +(5.00000 + 8.66025i) q^{79} +3.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{82} +(3.00000 + 1.73205i) q^{84} +(-9.00000 + 15.5885i) q^{85} +(4.00000 - 6.92820i) q^{86} +(0.500000 + 0.866025i) q^{88} -6.00000 q^{89} +(-4.50000 - 7.79423i) q^{90} -8.00000 q^{91} +(1.50000 - 0.866025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(1.50000 - 0.866025i) q^{96} +(9.50000 + 16.4545i) q^{97} +3.00000 q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 - 2 * q^7 - 2 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} - q^{11} - 3 q^{12} + 4 q^{13} + 2 q^{14} - 9 q^{15} - q^{16} + 12 q^{17} - 3 q^{18} + 4 q^{19} - 3 q^{20} + q^{22} - 3 q^{24} - 4 q^{25} + 8 q^{26} + 4 q^{28} - 9 q^{30} + q^{31} + q^{32} + 6 q^{34} + 12 q^{35} - 6 q^{36} - 14 q^{37} + 2 q^{38} + 12 q^{39} + 3 q^{40} - 12 q^{41} + 6 q^{42} - 8 q^{43} + 2 q^{44} - 18 q^{45} - 9 q^{47} + 3 q^{49} + 4 q^{50} + 18 q^{51} + 4 q^{52} + 18 q^{53} - 9 q^{54} + 6 q^{55} + 2 q^{56} + 6 q^{57} + 9 q^{59} - 8 q^{61} + 2 q^{62} + 6 q^{63} + 2 q^{64} + 12 q^{65} + 3 q^{66} + 7 q^{67} - 6 q^{68} + 6 q^{70} - 30 q^{71} - 3 q^{72} - 20 q^{73} - 7 q^{74} - 2 q^{76} - 2 q^{77} + 12 q^{78} + 10 q^{79} + 6 q^{80} - 9 q^{81} - 24 q^{82} + 6 q^{84} - 18 q^{85} + 8 q^{86} + q^{88} - 12 q^{89} - 9 q^{90} - 16 q^{91} + 3 q^{93} + 9 q^{94} - 6 q^{95} + 3 q^{96} + 19 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 - 2 * q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 - q^11 - 3 * q^12 + 4 * q^13 + 2 * q^14 - 9 * q^15 - q^16 + 12 * q^17 - 3 * q^18 + 4 * q^19 - 3 * q^20 + q^22 - 3 * q^24 - 4 * q^25 + 8 * q^26 + 4 * q^28 - 9 * q^30 + q^31 + q^32 + 6 * q^34 + 12 * q^35 - 6 * q^36 - 14 * q^37 + 2 * q^38 + 12 * q^39 + 3 * q^40 - 12 * q^41 + 6 * q^42 - 8 * q^43 + 2 * q^44 - 18 * q^45 - 9 * q^47 + 3 * q^49 + 4 * q^50 + 18 * q^51 + 4 * q^52 + 18 * q^53 - 9 * q^54 + 6 * q^55 + 2 * q^56 + 6 * q^57 + 9 * q^59 - 8 * q^61 + 2 * q^62 + 6 * q^63 + 2 * q^64 + 12 * q^65 + 3 * q^66 + 7 * q^67 - 6 * q^68 + 6 * q^70 - 30 * q^71 - 3 * q^72 - 20 * q^73 - 7 * q^74 - 2 * q^76 - 2 * q^77 + 12 * q^78 + 10 * q^79 + 6 * q^80 - 9 * q^81 - 24 * q^82 + 6 * q^84 - 18 * q^85 + 8 * q^86 + q^88 - 12 * q^89 - 9 * q^90 - 16 * q^91 + 3 * q^93 + 9 * q^94 - 6 * q^95 + 3 * q^96 + 19 * q^97 + 6 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$			1.73205i			0.707107i
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−3.00000			−0.948683
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$	−4.50000	+	2.59808i	−1.16190	+	0.670820i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		−	3.46410i		−	0.755929i
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	4.00000			0.784465
$27$			5.19615i			1.00000i
$28$	2.00000			0.377964
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−4.50000	−	2.59808i	−0.821584	−	0.474342i
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		−	1.73205i		−	0.301511i
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	6.00000			1.01419
$36$	−3.00000			−0.500000
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	6.00000	−	3.46410i	0.960769	−	0.554700i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−6.00000	+	10.3923i	−0.937043	+	1.62301i	−0.166092	+	0.986110i	$0.553115\pi$
$41$	−6.00000	+	10.3923i	−0.937043	+	1.62301i	−0.770950	+	0.636895i	$0.780218\pi$
$42$	3.00000	−	1.73205i	0.462910	−	0.267261i
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	1.00000			0.150756
$45$	−9.00000			−1.34164
$46$		0			0
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$		−	1.73205i		−	0.250000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	3.00000			0.404520
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	3.00000	+	1.73205i	0.397360	+	0.229416i
$58$		0			0
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		−	5.19615i		−	0.670820i
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	1.00000			0.127000
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$	1.00000			0.125000
$65$	6.00000	+	10.3923i	0.744208	+	1.28901i
$66$	1.50000	−	0.866025i	0.184637	−	0.106600i
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$	3.00000	+	5.19615i	0.358569	+	0.621059i
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		−	6.92820i		−	0.800000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−1.00000	+	1.73205i	−0.113961	+	0.197386i
$78$	6.00000	+	3.46410i	0.679366	+	0.392232i
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	3.00000			0.335410
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−12.0000			−1.32518
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$	3.00000	+	1.73205i	0.327327	+	0.188982i
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−4.50000	−	7.79423i	−0.474342	−	0.821584i
$91$	−8.00000			−0.838628
$92$		0			0
$93$	1.50000	−	0.866025i	0.155543	−	0.0898027i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.710742	+	0.703452i	$0.248359\pi$
$97$	9.50000	+	16.4545i	0.964579	+	1.67070i	0.253837	+	0.967247i	$0.418307\pi$
$98$	3.00000			0.303046
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	4.00000			0.400000
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$			10.3923i			1.02899i
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	0.456862	+	0.889538i	$0.348973\pi$
$103$	−5.50000	+	9.52628i	−0.541931	+	0.938652i	−0.998793	+	0.0491146i	$0.984360\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	9.00000	+	5.19615i	0.878310	+	0.507093i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	−10.5000	−	6.06218i	−0.996616	−	0.575396i
$112$	−1.00000	+	1.73205i	−0.0944911	+	0.163663i
$113$	−10.5000	+	18.1865i	−0.987757	+	1.71085i	−0.358778	+	0.933423i	$0.616806\pi$
$113$	−10.5000	+	18.1865i	−0.987757	+	1.71085i	−0.628979	+	0.777422i	$0.716527\pi$
$114$			3.46410i			0.324443i
$115$		0			0
$116$		0			0
$117$	12.0000			1.10940
$118$	9.00000			0.828517
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$	4.50000	−	2.59808i	0.410792	−	0.237171i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	4.00000	−	6.92820i	0.362143	−	0.627250i
$123$	−18.0000	+	10.3923i	−1.62301	+	0.937043i
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$	−3.00000			−0.268328
$126$	6.00000			0.534522
$127$	14.0000			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		−	13.8564i		−	1.21999i
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	1.50000	+	0.866025i	0.130558	+	0.0753778i
$133$	−2.00000	−	3.46410i	−0.173422	−	0.300376i
$134$	7.00000			0.604708
$135$	−13.5000	−	7.79423i	−1.16190	−	0.670820i
$136$	−6.00000			−0.514496
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$	−3.00000	+	5.19615i	−0.253546	+	0.439155i
$141$		−	15.5885i		−	1.31278i
$142$	−7.50000	−	12.9904i	−0.629386	−	1.09013i
$143$	−4.00000			−0.334497
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$		0			0
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$	4.50000	−	2.59808i	0.371154	−	0.214286i
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$	6.00000	−	3.46410i	0.489898	−	0.282843i
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$	−2.00000			−0.162221
$153$	9.00000	+	15.5885i	0.727607	+	1.26025i
$154$	−2.00000			−0.161165
$155$	1.50000	+	2.59808i	0.120483	+	0.208683i
$156$			6.92820i			0.554700i
$157$	−5.50000	+	9.52628i	−0.438948	+	0.760280i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−5.50000	+	9.52628i	−0.438948	+	0.760280i	0.558661	+	0.829396i	$0.311315\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	13.5000	+	7.79423i	1.07062	+	0.618123i
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$		0			0
$162$	−9.00000			−0.707107
$163$	23.0000			1.80150			0.900750	−	0.434339i	$-0.143018\pi$
$163$	23.0000			1.80150			0.900750	+	0.434339i	$0.143018\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$	4.50000	+	2.59808i	0.350325	+	0.202260i
$166$		0			0
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$			3.46410i			0.267261i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−18.0000			−1.38054
$171$	3.00000	+	5.19615i	0.229416	+	0.397360i
$172$	8.00000			0.609994
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$	−0.500000	+	0.866025i	−0.0376889	+	0.0652791i
$177$	13.5000	−	7.79423i	1.01472	−	0.585850i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−3.00000			−0.224231			−0.112115	−	0.993695i	$-0.535763\pi$
$179$	−3.00000			−0.224231			−0.112115	+	0.993695i	$0.535763\pi$
$180$	4.50000	−	7.79423i	0.335410	−	0.580948i
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$	−4.00000	−	6.92820i	−0.296500	−	0.513553i
$183$		−	13.8564i		−	1.02430i
$184$		0			0
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$	1.50000	+	0.866025i	0.109985	+	0.0635001i
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	9.00000			0.656392
$189$	9.00000	−	5.19615i	0.654654	−	0.377964i
$190$	−6.00000			−0.435286
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$	−9.50000	+	16.4545i	−0.682060	+	1.18136i
$195$			20.7846i			1.48842i
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	3.00000			0.213201
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	10.5000	−	6.06218i	0.740613	−	0.427593i
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$		0			0
$204$	−9.00000	+	5.19615i	−0.630126	+	0.363803i
$205$	−18.0000	−	31.1769i	−1.25717	−	2.17749i
$206$	−11.0000			−0.766406
$207$		0			0
$208$	−4.00000			−0.277350
$209$	−1.00000	−	1.73205i	−0.0691714	−	0.119808i
$210$			10.3923i			0.717137i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−4.50000	+	7.79423i	−0.309061	+	0.535310i
$213$	−22.5000	−	12.9904i	−1.54167	−	0.890086i
$214$		0			0
$215$	24.0000			1.63679
$216$		−	5.19615i		−	0.353553i
$217$	−2.00000			−0.135769
$218$	7.00000	+	12.1244i	0.474100	+	0.821165i
$219$	−15.0000	−	8.66025i	−1.01361	−	0.585206i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	12.0000	−	20.7846i	0.807207	−	1.39812i
$222$		−	12.1244i		−	0.813733i
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	−2.00000			−0.133631
$225$	6.00000	−	10.3923i	0.400000	−	0.692820i
$226$	−21.0000			−1.39690
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	−3.00000	+	1.73205i	−0.198680	+	0.114708i
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$	−3.00000	+	1.73205i	−0.197386	+	0.113961i
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$	27.0000			1.76129
$236$	4.50000	+	7.79423i	0.292925	+	0.507361i
$237$			17.3205i			1.12509i
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	−0.157893	−	0.987456i	$-0.550470\pi$
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	0.934109	−	0.356988i	$-0.116196\pi$
$240$	4.50000	+	2.59808i	0.290474	+	0.167705i
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−1.00000			−0.0642824
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	8.00000			0.512148
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$	−18.0000	−	10.3923i	−1.14764	−	0.662589i
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	−0.500000	+	0.866025i	−0.0317500	+	0.0549927i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	3.00000	+	5.19615i	0.188982	+	0.327327i
$253$		0			0
$254$	7.00000	+	12.1244i	0.439219	+	0.760750i
$255$	−27.0000	+	15.5885i	−1.69081	+	0.976187i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	12.0000	−	6.92820i	0.747087	−	0.431331i
$259$	7.00000	+	12.1244i	0.434959	+	0.753371i
$260$	−12.0000			−0.744208
$261$		0			0
$262$		0			0
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$			1.73205i			0.106600i
$265$	−13.5000	+	23.3827i	−0.829298	+	1.43639i
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		−	15.5885i		−	0.948683i
$271$	−22.0000			−1.33640			−0.668202	−	0.743980i	$-0.732936\pi$
$271$	−22.0000			−1.33640			−0.668202	+	0.743980i	$0.732936\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$	−12.0000	−	6.92820i	−0.726273	−	0.419314i
$274$	−1.50000	+	2.59808i	−0.0906183	+	0.156956i
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	16.0000			0.959616
$279$	3.00000			0.179605
$280$	−6.00000			−0.358569
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$	13.5000	−	7.79423i	0.803913	−	0.464140i
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	−0.678280	−	0.734804i	$-0.737274\pi$
$283$	5.00000	−	8.66025i	0.297219	−	0.514799i	0.975499	+	0.220005i	$0.0706075\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$	−9.00000	+	5.19615i	−0.533114	+	0.307794i
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	24.0000			1.41668
$288$	3.00000			0.176777
$289$	19.0000			1.11765
$290$		0			0
$291$			32.9090i			1.92916i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	4.50000	+	2.59808i	0.262445	+	0.151523i
$295$	13.5000	+	23.3827i	0.786000	+	1.36139i
$296$	7.00000			0.406867
$297$	4.50000	−	2.59808i	0.261116	−	0.150756i
$298$	−12.0000			−0.695141
$299$		0			0
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	1.00000	−	1.73205i	0.0575435	−	0.0996683i
$303$		−	20.7846i		−	1.19404i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	24.0000			1.37424
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−1.00000	−	1.73205i	−0.0569803	−	0.0986928i
$309$	−16.5000	+	9.52628i	−0.938652	+	0.541931i
$310$	−1.50000	+	2.59808i	−0.0851943	+	0.147561i
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	−0.996447	−	0.0842210i	$-0.973160\pi$
$311$	−7.50000	+	12.9904i	−0.425286	+	0.736617i	0.571161	+	0.820838i	$0.306493\pi$
$312$	−6.00000	+	3.46410i	−0.339683	+	0.196116i
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	−11.0000			−0.620766
$315$	9.00000	+	15.5885i	0.507093	+	0.878310i
$316$	−10.0000			−0.562544
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$			15.5885i			0.874157i
$319$		0			0
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−16.0000			−0.887520
$326$	11.5000	+	19.9186i	0.636926	+	1.10319i
$327$	21.0000	+	12.1244i	1.16130	+	0.670478i
$328$	6.00000	−	10.3923i	0.331295	−	0.573819i
$329$	−9.00000	+	15.5885i	−0.496186	+	0.859419i
$330$			5.19615i			0.286039i
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	0.879440	−	0.476011i	$-0.157918\pi$
$331$	0.500000	+	0.866025i	0.0274825	+	0.0476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$		0			0
$333$	−10.5000	−	18.1865i	−0.575396	−	0.996616i
$334$	12.0000			0.656611
$335$	10.5000	+	18.1865i	0.573676	+	0.993636i
$336$	−3.00000	+	1.73205i	−0.163663	+	0.0944911i
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	−0.806397	−	0.591375i	$-0.798585\pi$
$337$	2.00000	−	3.46410i	0.108947	−	0.188702i	0.915344	+	0.402673i	$0.131919\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	−31.5000	+	18.1865i	−1.71085	+	0.987757i
$340$	−9.00000	−	15.5885i	−0.488094	−	0.845403i
$341$	−1.00000			−0.0541530
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$	−20.0000			−1.07990
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	−0.774197	−	0.632945i	$-0.781846\pi$
$347$	3.00000	−	5.19615i	0.161048	−	0.278944i	0.935245	+	0.354001i	$0.115179\pi$
$348$		0			0
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	0.738883	−	0.673833i	$-0.235353\pi$
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	−0.952998	+	0.302975i	$0.902020\pi$
$350$	−8.00000			−0.427618
$351$	18.0000	+	10.3923i	0.960769	+	0.554700i
$352$	−1.00000			−0.0533002
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	13.5000	+	7.79423i	0.717517	+	0.414259i
$355$	22.5000	−	38.9711i	1.19418	−	2.06837i
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$		−	20.7846i		−	1.10004i
$358$	−1.50000	−	2.59808i	−0.0792775	−	0.137313i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$	9.00000			0.474342
$361$	−15.0000			−0.789474
$362$	2.50000	+	4.33013i	0.131397	+	0.227586i
$363$	−1.50000	+	0.866025i	−0.0787296	+	0.0454545i
$364$	4.00000	−	6.92820i	0.209657	−	0.363137i
$365$	15.0000	−	25.9808i	0.785136	−	1.35990i
$366$	12.0000	−	6.92820i	0.627250	−	0.362143i
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	0.942799	−	0.333363i	$-0.108183\pi$
$367$	3.50000	+	6.06218i	0.182699	+	0.316443i	−0.760100	+	0.649806i	$0.774850\pi$
$368$		0			0
$369$	−36.0000			−1.87409
$370$	21.0000			1.09174
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$			1.73205i			0.0898027i
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	−0.427051	−	0.904227i	$-0.640448\pi$
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	0.996610	−	0.0822766i	$-0.0262191\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$	−4.50000	−	2.59808i	−0.232379	−	0.134164i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$		0			0
$378$	9.00000	+	5.19615i	0.462910	+	0.267261i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	21.0000	+	12.1244i	1.07586	+	0.621150i
$382$	1.50000	−	2.59808i	0.0767467	−	0.132929i
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$			1.73205i			0.0883883i
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$	4.00000			0.203595
$387$	12.0000	−	20.7846i	0.609994	−	1.05654i
$388$	−19.0000			−0.964579
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$	−18.0000	+	10.3923i	−0.911465	+	0.526235i
$391$		0			0
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−30.0000			−1.50946
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−1.00000			−0.0501886			−0.0250943	−	0.999685i	$-0.507989\pi$
$397$	−1.00000			−0.0501886			−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−3.50000	−	6.06218i	−0.175439	−	0.303870i
$399$		−	6.92820i		−	0.346844i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	10.5000	+	6.06218i	0.523692	+	0.302354i
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	12.0000			0.597022
$405$	−13.5000	−	23.3827i	−0.670820	−	1.16190i
$406$		0			0
$407$	3.50000	+	6.06218i	0.173489	+	0.300491i
$408$	−9.00000	−	5.19615i	−0.445566	−	0.257248i
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$	18.0000	−	31.1769i	0.888957	−	1.53972i
$411$			5.19615i			0.256307i
$412$	−5.50000	−	9.52628i	−0.270966	−	0.469326i
$413$	−18.0000			−0.885722
$414$		0			0
$415$		0			0
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	24.0000	−	13.8564i	1.17529	−	0.678551i
$418$	1.00000	−	1.73205i	0.0489116	−	0.0847174i
$419$	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	$-0.00478389\pi$
$420$	−9.00000	+	5.19615i	−0.439155	+	0.253546i
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	0.979817	−	0.199899i	$-0.0640614\pi$
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	−0.663026	+	0.748596i	$0.730728\pi$
$422$	−14.0000			−0.681509
$423$	13.5000	−	23.3827i	0.656392	−	1.13691i
$424$	−9.00000			−0.437079
$425$	−12.0000	−	20.7846i	−0.582086	−	1.00820i
$426$		−	25.9808i		−	1.25877i
$427$	−8.00000	+	13.8564i	−0.387147	+	0.670559i
$428$		0			0
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	−1.00000	−	1.73205i	−0.0480015	−	0.0831411i
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$		0			0
$438$		−	17.3205i		−	0.827606i
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$	−3.00000			−0.143019
$441$	9.00000			0.428571
$442$	24.0000			1.14156
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	0.828190	−	0.560448i	$-0.189371\pi$
$443$	−1.50000	−	2.59808i	−0.0712672	−	0.123438i	−0.899457	+	0.437009i	$0.856038\pi$
$444$	10.5000	−	6.06218i	0.498308	−	0.287698i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	−18.0000	+	10.3923i	−0.851371	+	0.491539i
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	27.0000			1.27421			0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000			1.27421			0.637104	+	0.770778i	$0.280132\pi$
$450$	12.0000			0.565685
$451$	12.0000			0.565058
$452$	−10.5000	−	18.1865i	−0.493878	−	0.855423i
$453$		−	3.46410i		−	0.162758i
$454$		0			0
$455$	12.0000	−	20.7846i	0.562569	−	0.974398i
$456$	−3.00000	−	1.73205i	−0.140488	−	0.0811107i
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−14.0000			−0.654177
$459$			31.1769i			1.45521i
$460$		0			0
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	0.787668	−	0.616100i	$-0.211288\pi$
$461$	−3.00000	−	5.19615i	−0.139724	−	0.242009i	−0.927392	+	0.374091i	$0.877955\pi$
$462$	−3.00000	−	1.73205i	−0.139573	−	0.0805823i
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$		0			0
$465$			5.19615i			0.240966i
$466$	9.00000	+	15.5885i	0.416917	+	0.722121i
$467$	−15.0000			−0.694117			−0.347059	−	0.937843i	$-0.612820\pi$
$467$	−15.0000			−0.694117			−0.347059	+	0.937843i	$0.612820\pi$
$468$	−6.00000	+	10.3923i	−0.277350	+	0.480384i
$469$	−14.0000			−0.646460
$470$	13.5000	+	23.3827i	0.622709	+	1.07856i
$471$	−16.5000	+	9.52628i	−0.760280	+	0.438948i
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$	−15.0000	+	8.66025i	−0.688973	+	0.397779i
$475$	−4.00000	−	6.92820i	−0.183533	−	0.317888i
$476$	12.0000			0.550019
$477$	13.5000	+	23.3827i	0.618123	+	1.07062i
$478$	24.0000			1.09773
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$			5.19615i			0.237171i
$481$	−14.0000	+	24.2487i	−0.638345	+	1.10565i
$482$	7.00000	−	12.1244i	0.318841	−	0.552249i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.0227273	−	0.0393648i
$485$	−57.0000			−2.58824
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	11.0000			0.498458			0.249229	−	0.968445i	$-0.419823\pi$
$487$	11.0000			0.498458			0.249229	+	0.968445i	$0.419823\pi$
$488$	4.00000	+	6.92820i	0.181071	+	0.313625i
$489$	34.5000	+	19.9186i	1.56014	+	0.900750i
$490$	−4.50000	+	7.79423i	−0.203289	+	0.352107i
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$		−	20.7846i		−	0.937043i
$493$		0			0
$494$	8.00000			0.359937
$495$	4.50000	+	7.79423i	0.202260	+	0.350325i
$496$	−1.00000			−0.0449013
$497$	15.0000	+	25.9808i	0.672842	+	1.16540i
$498$		0			0
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	18.0000	−	10.3923i	0.804181	−	0.464294i
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$	18.0000			0.802580			0.401290	−	0.915951i	$-0.368562\pi$
$503$	18.0000			0.802580			0.401290	+	0.915951i	$0.368562\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$	36.0000			1.60198
$506$		0			0
$507$		−	5.19615i		−	0.230769i
$508$	−7.00000	+	12.1244i	−0.310575	+	0.537931i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	−27.0000	−	15.5885i	−1.19558	−	0.690268i
$511$	10.0000	+	17.3205i	0.442374	+	0.766214i
$512$	−1.00000			−0.0441942
$513$			10.3923i			0.458831i
$514$	18.0000			0.793946
$515$	−16.5000	−	28.5788i	−0.727077	−	1.25933i
$516$	12.0000	+	6.92820i	0.528271	+	0.304997i
$517$	−4.50000	+	7.79423i	−0.197910	+	0.342790i
$518$	−7.00000	+	12.1244i	−0.307562	+	0.532714i
$519$		−	10.3923i		−	0.456172i
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$		0			0
$523$	−34.0000			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$524$		0			0
$525$	−12.0000	+	6.92820i	−0.523723	+	0.302372i
$526$	−9.00000	+	15.5885i	−0.392419	+	0.679689i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$	−1.50000	+	0.866025i	−0.0652791	+	0.0376889i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−27.0000			−1.17281
$531$	27.0000			1.17170
$532$	4.00000			0.173422
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		−	10.3923i		−	0.449719i
$535$		0			0
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$	−4.50000	−	2.59808i	−0.194189	−	0.112115i
$538$	−1.50000	−	2.59808i	−0.0646696	−	0.112011i
$539$	−3.00000			−0.129219
$540$	13.5000	−	7.79423i	0.580948	−	0.335410i
$541$	8.00000			0.343947			0.171973	−	0.985102i	$-0.444986\pi$
$541$	8.00000			0.343947			0.171973	+	0.985102i	$0.444986\pi$
$542$	−11.0000	−	19.0526i	−0.472490	−	0.818377i
$543$	7.50000	+	4.33013i	0.321856	+	0.185824i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	−21.0000	+	36.3731i	−0.899541	+	1.55805i
$546$		−	13.8564i		−	0.592999i
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	0.843855	−	0.536571i	$-0.180281\pi$
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	−0.886612	+	0.462514i	$0.846947\pi$
$548$	−3.00000			−0.128154
$549$	12.0000	−	20.7846i	0.512148	−	0.887066i
$550$	−4.00000			−0.170561
$551$		0			0
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$	31.5000	−	18.1865i	1.33710	−	0.771975i
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$	1.50000	+	2.59808i	0.0635001	+	0.109985i
$559$	−32.0000			−1.35346
$560$	−3.00000	−	5.19615i	−0.126773	−	0.219578i
$561$		−	10.3923i		−	0.438763i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	13.5000	+	7.79423i	0.568453	+	0.328196i
$565$	−31.5000	−	54.5596i	−1.32521	−	2.29534i
$566$	10.0000			0.420331
$567$	18.0000			0.755929
$568$	15.0000			0.629386
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$	−9.00000	−	5.19615i	−0.376969	−	0.217643i
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	0.454634	+	0.890678i	$0.349770\pi$
$571$	−13.0000	+	22.5167i	−0.544033	+	0.942293i	−0.998667	+	0.0516146i	$0.983563\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$		−	5.19615i		−	0.217072i
$574$	12.0000	+	20.7846i	0.500870	+	0.867533i
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−43.0000			−1.79011			−0.895057	−	0.445952i	$-0.852865\pi$
$577$	−43.0000			−1.79011			−0.895057	+	0.445952i	$0.852865\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	6.00000	−	3.46410i	0.249351	−	0.143963i
$580$		0			0
$581$		0			0
$582$	−28.5000	+	16.4545i	−1.18136	+	0.682060i
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	10.0000			0.413803
$585$	−18.0000	+	31.1769i	−0.744208	+	1.28901i
$586$	−18.0000			−0.743573
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	0.895320	−	0.445424i	$-0.146947\pi$
$587$	1.50000	+	2.59808i	0.0619116	+	0.107234i	−0.833408	+	0.552658i	$0.813614\pi$
$588$			5.19615i			0.214286i
$589$	1.00000	−	1.73205i	0.0412043	−	0.0713679i
$590$	−13.5000	+	23.3827i	−0.555786	+	0.962650i
$591$	−9.00000	−	5.19615i	−0.370211	−	0.213741i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−36.0000			−1.47834			−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000			−1.47834			−0.739171	+	0.673517i	$0.764783\pi$
$594$	4.50000	+	2.59808i	0.184637	+	0.106600i
$595$	36.0000			1.47586
$596$	−6.00000	−	10.3923i	−0.245770	−	0.425685i
$597$	−10.5000	−	6.06218i	−0.429736	−	0.248108i
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$			6.92820i			0.282843i
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	0.998302	−	0.0582563i	$-0.0185541\pi$
$601$	11.0000	+	19.0526i	0.448699	+	0.777170i	−0.549602	+	0.835426i	$0.685221\pi$
$602$	−16.0000			−0.652111
$603$	21.0000			0.855186
$604$	2.00000			0.0813788
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$	18.0000	−	10.3923i	0.731200	−	0.422159i
$607$	−19.0000	+	32.9090i	−0.771186	+	1.33573i	0.165727	+	0.986172i	$0.447003\pi$
$607$	−19.0000	+	32.9090i	−0.771186	+	1.33573i	−0.936913	+	0.349562i	$0.886330\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$		0			0
$610$	12.0000	+	20.7846i	0.485866	+	0.841544i
$611$	−36.0000			−1.45640
$612$	−18.0000			−0.727607
$613$	44.0000			1.77714			0.888572	−	0.458738i	$-0.151698\pi$
$613$	44.0000			1.77714			0.888572	+	0.458738i	$0.151698\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		−	62.3538i		−	2.51435i
$616$	1.00000	−	1.73205i	0.0402911	−	0.0697863i
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	−0.996204	−	0.0870504i	$-0.972256\pi$
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	0.573490	+	0.819213i	$0.305589\pi$
$618$	−16.5000	−	9.52628i	−0.663727	−	0.383203i
$619$	21.5000	+	37.2391i	0.864158	+	1.49677i	0.867881	+	0.496772i	$0.165482\pi$
$619$	21.5000	+	37.2391i	0.864158	+	1.49677i	−0.00372288	+	0.999993i	$0.501185\pi$
$620$	−3.00000			−0.120483
$621$		0			0
$622$	−15.0000			−0.601445
$623$	6.00000	+	10.3923i	0.240385	+	0.416359i
$624$	−6.00000	−	3.46410i	−0.240192	−	0.138675i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		−	3.46410i		−	0.138343i
$628$	−5.50000	−	9.52628i	−0.219474	−	0.380140i
$629$	−42.0000			−1.67465
$630$	−9.00000	+	15.5885i	−0.358569	+	0.621059i
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	−21.0000	+	12.1244i	−0.834675	+	0.481900i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−21.0000	+	36.3731i	−0.833360	+	1.44342i
$636$	−13.5000	+	7.79423i	−0.535310	+	0.309061i
$637$	−6.00000	−	10.3923i	−0.237729	−	0.411758i
$638$		0			0
$639$	−22.5000	−	38.9711i	−0.890086	−	1.54167i
$640$	−3.00000			−0.118585
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	0.800678	−	0.599095i	$-0.204473\pi$
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	−0.919171	+	0.393860i	$0.871140\pi$
$642$		0			0
$643$	20.0000	−	34.6410i	0.788723	−	1.36611i	−0.138027	−	0.990429i	$-0.544076\pi$
$643$	20.0000	−	34.6410i	0.788723	−	1.36611i	0.926750	−	0.375680i	$-0.122591\pi$
$644$		0			0
$645$	36.0000	+	20.7846i	1.41750	+	0.818393i
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	36.0000			1.41531			0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000			1.41531			0.707653	+	0.706560i	$0.249754\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−9.00000			−0.353281
$650$	−8.00000	−	13.8564i	−0.313786	−	0.543493i
$651$	−3.00000	−	1.73205i	−0.117579	−	0.0678844i
$652$	−11.5000	+	19.9186i	−0.450375	+	0.780072i
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$			24.2487i			0.948200i
$655$		0			0
$656$	12.0000			0.468521
$657$	−15.0000	−	25.9808i	−0.585206	−	1.01361i
$658$	−18.0000			−0.701713
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	−4.50000	+	2.59808i	−0.175162	+	0.101130i
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$	−0.500000	+	0.866025i	−0.0194331	+	0.0336590i
$663$	36.0000	−	20.7846i	1.39812	−	0.807207i
$664$		0			0
$665$	12.0000			0.465340
$666$	10.5000	−	18.1865i	0.406867	−	0.704714i
$667$		0			0
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$			27.7128i			1.07144i
$670$	−10.5000	+	18.1865i	−0.405650	+	0.702607i
$671$	−4.00000	+	6.92820i	−0.154418	+	0.267460i
$672$	−3.00000	−	1.73205i	−0.115728	−	0.0668153i
$673$	23.0000	+	39.8372i	0.886585	+	1.53561i	0.843886	+	0.536522i	$0.180262\pi$
$673$	23.0000	+	39.8372i	0.886585	+	1.53561i	0.0426985	+	0.999088i	$0.486405\pi$
$674$	4.00000			0.154074
$675$	18.0000	−	10.3923i	0.692820	−	0.400000i
$676$	3.00000			0.115385
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$	−31.5000	−	18.1865i	−1.20975	−	0.698450i
$679$	19.0000	−	32.9090i	0.729153	−	1.26293i
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$		0			0
$682$	−0.500000	−	0.866025i	−0.0191460	−	0.0331618i
$683$	39.0000			1.49229			0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000			1.49229			0.746147	+	0.665782i	$0.231902\pi$
$684$	−6.00000			−0.229416
$685$	−9.00000			−0.343872
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−21.0000	+	12.1244i	−0.801200	+	0.462573i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$		0			0
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	−0.998159	−	0.0606524i	$-0.980682\pi$
$691$	−14.5000	−	25.1147i	−0.551606	−	0.955410i	0.446553	−	0.894757i	$-0.352651\pi$
$692$	6.00000			0.228086
$693$	−6.00000			−0.227921
$694$	6.00000			0.227757
$695$	24.0000	+	41.5692i	0.910372	+	1.57681i
$696$		0			0
$697$	−36.0000	+	62.3538i	−1.36360	+	2.36182i
$698$	4.00000	−	6.92820i	0.151402	−	0.262236i
$699$	27.0000	+	15.5885i	1.02123	+	0.589610i
$700$	−4.00000	−	6.92820i	−0.151186	−	0.261861i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$			20.7846i			0.784465i
$703$	−14.0000			−0.528020
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	40.5000	+	23.3827i	1.52532	+	0.880643i
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$	−12.0000	+	20.7846i	−0.451306	+	0.781686i
$708$			15.5885i			0.585850i
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	0.987421	−	0.158114i	$-0.0505412\pi$
$709$	9.50000	+	16.4545i	0.356780	+	0.617961i	−0.630641	+	0.776075i	$0.717208\pi$
$710$	45.0000			1.68882
$711$	−15.0000	+	25.9808i	−0.562544	+	0.974355i
$712$	6.00000			0.224860
$713$		0			0
$714$	18.0000	−	10.3923i	0.673633	−	0.388922i
$715$	6.00000	−	10.3923i	0.224387	−	0.388650i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	36.0000	−	20.7846i	1.34444	−	0.776215i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	33.0000			1.23069			0.615346	−	0.788257i	$-0.289016\pi$
$719$	33.0000			1.23069			0.615346	+	0.788257i	$0.289016\pi$
$720$	4.50000	+	7.79423i	0.167705	+	0.290474i
$721$	22.0000			0.819323
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$		−	24.2487i		−	0.901819i
$724$	−2.50000	+	4.33013i	−0.0929118	+	0.160928i
$725$		0			0
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$	18.5000	+	32.0429i	0.686127	+	1.18841i	0.973081	+	0.230463i	$0.0740239\pi$
$727$	18.5000	+	32.0429i	0.686127	+	1.18841i	−0.286954	+	0.957944i	$0.592643\pi$
$728$	8.00000			0.296500
$729$	−27.0000			−1.00000
$730$	30.0000			1.11035
$731$	−24.0000	−	41.5692i	−0.887672	−	1.53749i
$732$	12.0000	+	6.92820i	0.443533	+	0.256074i
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	−3.50000	+	6.06218i	−0.129187	+	0.223759i
$735$			15.5885i			0.574989i
$736$		0			0
$737$	−7.00000			−0.257848
$738$	−18.0000	−	31.1769i	−0.662589	−	1.14764i
$739$	−28.0000			−1.03000			−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000			−1.03000			−0.514998	+	0.857191i	$0.672207\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$	12.0000	−	6.92820i	0.440831	−	0.254514i
$742$	9.00000	−	15.5885i	0.330400	−	0.572270i
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	−0.166920	−	0.985970i	$-0.553382\pi$
$743$	21.0000	−	36.3731i	0.770415	−	1.33440i	0.937336	−	0.348428i	$-0.113284\pi$
$744$	−1.50000	+	0.866025i	−0.0549927	+	0.0317500i
$745$	−18.0000	−	31.1769i	−0.659469	−	1.14223i
$746$	22.0000			0.805477
$747$		0			0
$748$	6.00000			0.219382
$749$		0			0
$750$		−	5.19615i		−	0.189737i
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	−0.638994	−	0.769212i	$-0.720649\pi$
$751$	9.50000	−	16.4545i	0.346660	−	0.600433i	0.985654	+	0.168779i	$0.0539825\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−36.0000	−	20.7846i	−1.31191	−	0.757433i
$754$		0			0
$755$	6.00000			0.218362
$756$			10.3923i			0.377964i
$757$	35.0000			1.27210			0.636048	−	0.771649i	$-0.280568\pi$
$757$	35.0000			1.27210			0.636048	+	0.771649i	$0.280568\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$			24.2487i			0.878438i
$763$	−14.0000	−	24.2487i	−0.506834	−	0.877862i
$764$	3.00000			0.108536
$765$	−54.0000			−1.95237
$766$	−21.0000			−0.758761
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$	2.00000	−	3.46410i	0.0721218	−	0.124919i	−0.827709	−	0.561157i	$-0.810356\pi$
$769$	2.00000	−	3.46410i	0.0721218	−	0.124919i	0.899831	+	0.436239i	$0.143690\pi$
$770$	3.00000	−	5.19615i	0.108112	−	0.187256i
$771$	27.0000	−	15.5885i	0.972381	−	0.561405i
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$	24.0000			0.862662
$775$	−4.00000			−0.143684
$776$	−9.50000	−	16.4545i	−0.341030	−	0.590682i
$777$			24.2487i			0.869918i
$778$	−4.50000	+	7.79423i	−0.161333	+	0.279437i
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$	−18.0000	−	10.3923i	−0.644503	−	0.372104i
$781$	7.50000	+	12.9904i	0.268371	+	0.464832i
$782$		0			0
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−16.5000	−	28.5788i	−0.588910	−	1.02002i
$786$		0			0
$787$	5.00000	−	8.66025i	0.178231	−	0.308705i	−0.763044	−	0.646347i	$-0.776296\pi$
$787$	5.00000	−	8.66025i	0.178231	−	0.308705i	0.941275	+	0.337642i	$0.109629\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$			31.1769i			1.10993i
$790$	−15.0000	−	25.9808i	−0.533676	−	0.924354i
$791$	42.0000			1.49335
$792$	−1.50000	+	2.59808i	−0.0533002	+	0.0923186i
$793$	−32.0000			−1.13635
$794$	−0.500000	−	0.866025i	−0.0177443	−	0.0307341i
$795$	−40.5000	+	23.3827i	−1.43639	+	0.829298i
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$	6.00000	−	3.46410i	0.212398	−	0.122628i
$799$	−27.0000	−	46.7654i	−0.955191	−	1.65444i
$800$	−4.00000			−0.141421
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$	3.00000			0.105934
$803$	5.00000	+	8.66025i	0.176446	+	0.305614i
$804$			12.1244i			0.427593i
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$	−4.50000	−	2.59808i	−0.158408	−	0.0914566i
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	−36.0000			−1.26569			−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000			−1.26569			−0.632846	+	0.774277i	$0.718114\pi$
$810$	13.5000	−	23.3827i	0.474342	−	0.821584i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$	−33.0000	−	19.0526i	−1.15736	−	0.668202i
$814$	−3.50000	+	6.06218i	−0.122675	+	0.212479i
$815$	−34.5000	+	59.7558i	−1.20848	+	2.09315i
$816$		−	10.3923i		−	0.363803i
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	22.0000			0.769212
$819$	−12.0000	−	20.7846i	−0.419314	−	0.726273i
$820$	36.0000			1.25717
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	0.808915	−	0.587925i	$-0.200055\pi$
$821$	−3.00000	−	5.19615i	−0.104701	−	0.181347i	−0.913616	+	0.406578i	$0.866722\pi$
$822$	−4.50000	+	2.59808i	−0.156956	+	0.0906183i
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	5.50000	−	9.52628i	0.191602	−	0.331864i
$825$	−6.00000	+	3.46410i	−0.208893	+	0.120605i
$826$	−9.00000	−	15.5885i	−0.313150	−	0.542392i
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−25.0000			−0.868286			−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000			−0.868286			−0.434143	+	0.900844i	$0.642949\pi$
$830$		0			0
$831$		−	3.46410i		−	0.120168i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	9.00000	−	15.5885i	0.311832	−	0.540108i
$834$	24.0000	+	13.8564i	0.831052	+	0.479808i
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$	2.00000			0.0691714
$837$	4.50000	+	2.59808i	0.155543	+	0.0898027i
$838$	21.0000			0.725433
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	0.899158	+	0.437623i	$0.144180\pi$
$839$	24.0000	+	41.5692i	0.828572	+	1.43513i	−0.0705865	+	0.997506i	$0.522487\pi$
$840$	−9.00000	−	5.19615i	−0.310530	−	0.179284i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−6.50000	+	11.2583i	−0.224005	+	0.387988i
$843$			10.3923i			0.357930i
$844$	−7.00000	−	12.1244i	−0.240950	−	0.417338i
$845$	9.00000			0.309609
$846$	27.0000			0.928279
$847$	2.00000			0.0687208
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	15.0000	−	8.66025i	0.514799	−	0.297219i
$850$	12.0000	−	20.7846i	0.411597	−	0.712906i
$851$		0			0
$852$	22.5000	−	12.9904i	0.770837	−	0.445043i
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	0.720946	−	0.692992i	$-0.243708\pi$
$853$	−7.00000	−	12.1244i	−0.239675	−	0.415130i	−0.960621	+	0.277862i	$0.910374\pi$
$854$	−16.0000			−0.547509
$855$	−18.0000			−0.615587
$856$		0			0
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$		−	6.92820i		−	0.236525i
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	−0.470581	−	0.882357i	$-0.655956\pi$
$859$	15.5000	−	26.8468i	0.528853	−	0.916001i	0.999434	−	0.0336436i	$-0.0107111\pi$
$860$	−12.0000	+	20.7846i	−0.409197	+	0.708749i
$861$	36.0000	+	20.7846i	1.22688	+	0.708338i
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	18.0000			0.612018
$866$	13.0000	+	22.5167i	0.441758	+	0.765147i
$867$	28.5000	+	16.4545i	0.967911	+	0.558824i
$868$	1.00000	−	1.73205i	0.0339422	−	0.0587896i
$869$	5.00000	−	8.66025i	0.169613	−	0.293779i
$870$		0			0
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$	−14.0000			−0.474100
$873$	−28.5000	+	49.3634i	−0.964579	+	1.67070i
$874$		0			0
$875$	3.00000	+	5.19615i	0.101419	+	0.175662i
$876$	15.0000	−	8.66025i	0.506803	−	0.292603i
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$	−27.0000	+	15.5885i	−0.910687	+	0.525786i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$	4.50000	+	7.79423i	0.151523	+	0.262445i
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$			46.7654i			1.57200i
$886$	1.50000	−	2.59808i	0.0503935	−	0.0872841i
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	−0.496340	−	0.868128i	$-0.665323\pi$
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	0.999991	−	0.00422062i	$-0.00134347\pi$
$888$	10.5000	+	6.06218i	0.352357	+	0.203433i
$889$	−14.0000	−	24.2487i	−0.469545	−	0.813276i
$890$	18.0000			0.603361
$891$	9.00000			0.301511
$892$	−16.0000			−0.535720
$893$	−9.00000	−	15.5885i	−0.301174	−	0.521648i
$894$	−18.0000	−	10.3923i	−0.602010	−	0.347571i
$895$	4.50000	−	7.79423i	0.150418	−	0.260532i
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$		0			0
$898$	13.5000	+	23.3827i	0.450501	+	0.780290i
$899$		0			0
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	54.0000			1.79900
$902$	6.00000	+	10.3923i	0.199778	+	0.346026i
$903$	−24.0000	+	13.8564i	−0.798670	+	0.461112i
$904$	10.5000	−	18.1865i	0.349225	−	0.604875i
$905$	−7.50000	+	12.9904i	−0.249308	+	0.431815i
$906$	3.00000	−	1.73205i	0.0996683	−	0.0575435i
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	−0.956671	−	0.291172i	$-0.905955\pi$
$907$	−22.0000	−	38.1051i	−0.730498	−	1.26526i	0.226173	−	0.974087i	$-0.427379\pi$
$908$		0			0
$909$	18.0000	−	31.1769i	0.597022	−	1.03407i
$910$	24.0000			0.795592
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	0.714620	−	0.699513i	$-0.246600\pi$
$911$	−7.50000	−	12.9904i	−0.248486	−	0.430391i	−0.963106	+	0.269122i	$0.913266\pi$
$912$		−	3.46410i		−	0.114708i
$913$		0			0
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$	36.0000	+	20.7846i	1.19012	+	0.687118i
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$		0			0
$918$	−27.0000	+	15.5885i	−0.891133	+	0.514496i
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$	3.00000	+	1.73205i	0.0988534	+	0.0570730i
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	−30.0000	+	51.9615i	−0.987462	+	1.71033i
$924$		−	3.46410i		−	0.113961i
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$	4.00000			0.131448
$927$	−33.0000			−1.08386
$928$		0			0
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	−0.953305	−	0.302010i	$-0.902342\pi$
$929$	−22.5000	−	38.9711i	−0.738201	−	1.27860i	0.215104	−	0.976591i	$-0.430991\pi$
$930$	−4.50000	+	2.59808i	−0.147561	+	0.0851943i
$931$	3.00000	−	5.19615i	0.0983210	−	0.170297i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$	−22.5000	+	12.9904i	−0.736617	+	0.425286i
$934$	−7.50000	−	12.9904i	−0.245407	−	0.425058i
$935$	18.0000			0.588663
$936$	−12.0000			−0.392232
$937$	−4.00000			−0.130674			−0.0653372	−	0.997863i	$-0.520812\pi$
$937$	−4.00000			−0.130674			−0.0653372	+	0.997863i	$0.520812\pi$
$938$	−7.00000	−	12.1244i	−0.228558	−	0.395874i
$939$		−	24.2487i		−	0.791327i
$940$	−13.5000	+	23.3827i	−0.440321	+	0.762659i
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	−16.5000	−	9.52628i	−0.537599	−	0.310383i
$943$		0			0
$944$	−9.00000			−0.292925
$945$			31.1769i			1.01419i
$946$	−8.00000			−0.260102
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$	−15.0000	−	8.66025i	−0.487177	−	0.281272i
$949$	−20.0000	+	34.6410i	−0.649227	+	1.12449i
$950$	4.00000	−	6.92820i	0.129777	−	0.224781i
$951$			31.1769i			1.01098i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$	−13.5000	+	23.3827i	−0.437079	+	0.757042i
$955$	9.00000			0.291233
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$	−4.50000	+	2.59808i	−0.145237	+	0.0838525i
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	−28.0000			−0.902756
$963$		0			0
$964$	14.0000			0.450910
$965$	6.00000	+	10.3923i	0.193147	+	0.334540i
$966$		0			0
$967$	−25.0000	+	43.3013i	−0.803946	+	1.39247i	0.113055	+	0.993589i	$0.463936\pi$
$967$	−25.0000	+	43.3013i	−0.803946	+	1.39247i	−0.917000	+	0.398886i	$0.869397\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	18.0000	+	10.3923i	0.578243	+	0.333849i
$970$	−28.5000	−	49.3634i	−0.915080	−	1.58496i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$		−	15.5885i		−	0.500000i
$973$	−32.0000			−1.02587
$974$	5.50000	+	9.52628i	0.176231	+	0.305242i
$975$	−24.0000	−	13.8564i	−0.768615	−	0.443760i
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$			39.8372i			1.27385i
$979$	3.00000	+	5.19615i	0.0958804	+	0.166070i
$980$	−9.00000			−0.287494
$981$	21.0000	+	36.3731i	0.670478	+	1.16130i
$982$	−12.0000			−0.382935
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$	18.0000	−	10.3923i	0.573819	−	0.331295i
$985$	9.00000	−	15.5885i	0.286764	−	0.496690i
$986$		0			0
$987$	−27.0000	+	15.5885i	−0.859419	+	0.496186i
$988$	4.00000	+	6.92820i	0.127257	+	0.220416i
$989$		0			0
$990$	−4.50000	+	7.79423i	−0.143019	+	0.247717i
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	−0.500000	−	0.866025i	−0.0158750	−	0.0274963i
$993$			1.73205i			0.0549650i
$994$	−15.0000	+	25.9808i	−0.475771	+	0.824060i
$995$	10.5000	−	18.1865i	0.332872	−	0.576552i
$996$		0			0
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$	−5.00000			−0.158272
$999$		−	36.3731i		−	1.15079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.e.b.67.1	✓	2
3.2	odd	2		594.2.e.b.199.1		2
9.2	odd	6		594.2.e.b.397.1		2
9.4	even	3		1782.2.a.e.1.1		1
9.5	odd	6		1782.2.a.h.1.1		1
9.7	even	3	inner	198.2.e.b.133.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.e.b.67.1	✓	2	1.1	even	1	trivial
198.2.e.b.133.1	yes	2	9.7	even	3	inner
594.2.e.b.199.1		2	3.2	odd	2
594.2.e.b.397.1		2	9.2	odd	6
1782.2.a.e.1.1		1	9.4	even	3
1782.2.a.h.1.1		1	9.5	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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.73205i q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +1.73205i q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -3.00000 q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.50000 + 0.866025i) q^{12} +(2.00000 - 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-4.50000 + 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +2.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} -3.46410i q^{21} +(0.500000 - 0.866025i) q^{22} +(-1.50000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} +4.00000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(-4.50000 - 2.59808i) q^{30} +(0.500000 - 0.866025i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.73205i q^{33} +(3.00000 + 5.19615i) q^{34} +6.00000 q^{35} -3.00000 q^{36} -7.00000 q^{37} +(1.00000 + 1.73205i) q^{38} +(6.00000 - 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-6.00000 + 10.3923i) q^{41} +(3.00000 - 1.73205i) q^{42} +(-4.00000 - 6.92820i) q^{43} +1.00000 q^{44} -9.00000 q^{45} +(-4.50000 - 7.79423i) q^{47} -1.73205i q^{48} +(1.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} +(9.00000 + 5.19615i) q^{51} +(2.00000 + 3.46410i) q^{52} +9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(1.00000 + 1.73205i) q^{56} +(3.00000 + 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} -5.19615i q^{60} +(-4.00000 - 6.92820i) q^{61} +1.00000 q^{62} +(3.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(6.00000 + 10.3923i) q^{65} +(1.50000 - 0.866025i) q^{66} +(3.50000 - 6.06218i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{70} -15.0000 q^{71} +(-1.50000 - 2.59808i) q^{72} -10.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} -6.92820i q^{75} +(-1.00000 + 1.73205i) q^{76} +(-1.00000 + 1.73205i) q^{77} +(6.00000 + 3.46410i) q^{78} +(5.00000 + 8.66025i) q^{79} +3.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{82} +(3.00000 + 1.73205i) q^{84} +(-9.00000 + 15.5885i) q^{85} +(4.00000 - 6.92820i) q^{86} +(0.500000 + 0.866025i) q^{88} -6.00000 q^{89} +(-4.50000 - 7.79423i) q^{90} -8.00000 q^{91} +(1.50000 - 0.866025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(1.50000 - 0.866025i) q^{96} +(9.50000 + 16.4545i) q^{97} +3.00000 q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 - 2 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} - 2 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} - q^{11} - 3 q^{12} + 4 q^{13} + 2 q^{14} - 9 q^{15} - q^{16} + 12 q^{17} - 3 q^{18} + 4 q^{19} - 3 q^{20} + q^{22} - 3 q^{24} - 4 q^{25} + 8 q^{26} + 4 q^{28} - 9 q^{30} + q^{31} + q^{32} + 6 q^{34} + 12 q^{35} - 6 q^{36} - 14 q^{37} + 2 q^{38} + 12 q^{39} + 3 q^{40} - 12 q^{41} + 6 q^{42} - 8 q^{43} + 2 q^{44} - 18 q^{45} - 9 q^{47} + 3 q^{49} + 4 q^{50} + 18 q^{51} + 4 q^{52} + 18 q^{53} - 9 q^{54} + 6 q^{55} + 2 q^{56} + 6 q^{57} + 9 q^{59} - 8 q^{61} + 2 q^{62} + 6 q^{63} + 2 q^{64} + 12 q^{65} + 3 q^{66} + 7 q^{67} - 6 q^{68} + 6 q^{70} - 30 q^{71} - 3 q^{72} - 20 q^{73} - 7 q^{74} - 2 q^{76} - 2 q^{77} + 12 q^{78} + 10 q^{79} + 6 q^{80} - 9 q^{81} - 24 q^{82} + 6 q^{84} - 18 q^{85} + 8 q^{86} + q^{88} - 12 q^{89} - 9 q^{90} - 16 q^{91} + 3 q^{93} + 9 q^{94} - 6 q^{95} + 3 q^{96} + 19 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 - 2 * q^7 - 2 * q^8 + 3 * q^9 - 6 * q^10 - q^11 - 3 * q^12 + 4 * q^13 + 2 * q^14 - 9 * q^15 - q^16 + 12 * q^17 - 3 * q^18 + 4 * q^19 - 3 * q^20 + q^22 - 3 * q^24 - 4 * q^25 + 8 * q^26 + 4 * q^28 - 9 * q^30 + q^31 + q^32 + 6 * q^34 + 12 * q^35 - 6 * q^36 - 14 * q^37 + 2 * q^38 + 12 * q^39 + 3 * q^40 - 12 * q^41 + 6 * q^42 - 8 * q^43 + 2 * q^44 - 18 * q^45 - 9 * q^47 + 3 * q^49 + 4 * q^50 + 18 * q^51 + 4 * q^52 + 18 * q^53 - 9 * q^54 + 6 * q^55 + 2 * q^56 + 6 * q^57 + 9 * q^59 - 8 * q^61 + 2 * q^62 + 6 * q^63 + 2 * q^64 + 12 * q^65 + 3 * q^66 + 7 * q^67 - 6 * q^68 + 6 * q^70 - 30 * q^71 - 3 * q^72 - 20 * q^73 - 7 * q^74 - 2 * q^76 - 2 * q^77 + 12 * q^78 + 10 * q^79 + 6 * q^80 - 9 * q^81 - 24 * q^82 + 6 * q^84 - 18 * q^85 + 8 * q^86 + q^88 - 12 * q^89 - 9 * q^90 - 16 * q^91 + 3 * q^93 + 9 * q^94 - 6 * q^95 + 3 * q^96 + 19 * q^97 + 6 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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