LMFDB - Embedded newform 74.2.c.a.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.c (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:	$0.590892974957$
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			63.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.2.c.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-1.00000 - 1.73205i) q^{12} +(3.00000 - 5.19615i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -6.00000 q^{23} +(1.00000 - 1.73205i) q^{24} +(2.00000 + 3.46410i) q^{25} +6.00000 q^{26} -4.00000 q^{27} -9.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} -2.00000 q^{38} +(6.00000 + 10.3923i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} -8.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +2.00000 q^{48} +(3.50000 + 6.06218i) q^{49} +(-2.00000 + 3.46410i) q^{50} +6.00000 q^{51} +(3.00000 + 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-2.00000 - 3.46410i) q^{57} +(-4.50000 - 7.79423i) q^{58} +(-4.00000 - 6.92820i) q^{59} -2.00000 q^{60} +(2.50000 - 4.33013i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -4.00000 q^{66} +(3.00000 - 5.19615i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(5.00000 - 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-3.00000 + 5.19615i) q^{79} -1.00000 q^{80} +(5.50000 - 9.52628i) q^{81} -3.00000 q^{82} +(-1.00000 - 1.73205i) q^{83} -3.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(9.00000 - 15.5885i) q^{87} -2.00000 q^{88} +(6.50000 + 11.2583i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(3.00000 - 5.19615i) q^{92} +(-10.0000 + 17.3205i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.00000 + 1.73205i) q^{95} +(1.00000 + 1.73205i) q^{96} +3.00000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} + 2 q^{24} + 4 q^{25} + 12 q^{26} - 8 q^{27} - 18 q^{29} - 2 q^{30} + 20 q^{31} + q^{32} - 4 q^{33} + 3 q^{34} + 2 q^{36} - q^{37} - 4 q^{38} + 12 q^{39} - q^{40} - 3 q^{41} - 16 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{46} + 4 q^{47} + 4 q^{48} + 7 q^{49} - 4 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} - 4 q^{54} + 2 q^{55} - 4 q^{57} - 9 q^{58} - 8 q^{59} - 4 q^{60} + 5 q^{61} + 10 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{66} + 6 q^{67} + 6 q^{68} + 12 q^{69} + q^{72} - 4 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 12 q^{78} - 6 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 2 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{87} - 4 q^{88} + 13 q^{89} - q^{90} + 6 q^{92} - 20 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 6 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 + q^20 + 2 * q^22 - 12 * q^23 + 2 * q^24 + 4 * q^25 + 12 * q^26 - 8 * q^27 - 18 * q^29 - 2 * q^30 + 20 * q^31 + q^32 - 4 * q^33 + 3 * q^34 + 2 * q^36 - q^37 - 4 * q^38 + 12 * q^39 - q^40 - 3 * q^41 - 16 * q^43 - 2 * q^44 - 2 * q^45 - 6 * q^46 + 4 * q^47 + 4 * q^48 + 7 * q^49 - 4 * q^50 + 12 * q^51 + 6 * q^52 + 6 * q^53 - 4 * q^54 + 2 * q^55 - 4 * q^57 - 9 * q^58 - 8 * q^59 - 4 * q^60 + 5 * q^61 + 10 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^66 + 6 * q^67 + 6 * q^68 + 12 * q^69 + q^72 - 4 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 12 * q^78 - 6 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 2 * q^83 - 6 * q^85 - 8 * q^86 + 18 * q^87 - 4 * q^88 + 13 * q^89 - q^90 + 6 * q^92 - 20 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 6 * q^97 - 7 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	−2.00000			−0.816497
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	0.896410	−	0.443227i	$-0.146166\pi$
$14$		0			0
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	1.00000	−	1.73205i	0.204124	−	0.353553i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	6.00000			1.17670
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$	1.00000			0.166667
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	−2.00000			−0.324443
$39$	6.00000	+	10.3923i	0.960769	+	1.66410i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.00000			−0.149071
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	2.00000			0.288675
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	6.00000			0.840168
$52$	3.00000	+	5.19615i	0.416025	+	0.720577i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−2.00000	−	3.46410i	−0.272166	−	0.471405i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$		0			0
$57$	−2.00000	−	3.46410i	−0.264906	−	0.458831i
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$	−2.00000			−0.258199
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	5.00000	+	8.66025i	0.635001	+	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$	−4.00000			−0.492366
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	−0.622509	−	0.782613i	$-0.713886\pi$
$67$	3.00000	−	5.19615i	0.366508	−	0.634811i	0.989017	+	0.147802i	$0.0472198\pi$
$68$	3.00000			0.363803
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$		0			0
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	5.00000	−	3.46410i	0.581238	−	0.402694i
$75$	−8.00000			−0.923760
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$		0			0
$78$	−6.00000	+	10.3923i	−0.679366	+	1.17670i
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	−0.983967	−	0.178352i	$-0.942924\pi$
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	0.646440	+	0.762964i	$0.276257\pi$
$80$	−1.00000			−0.111803
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000			−0.331295
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$	−4.00000	−	6.92820i	−0.431331	−	0.747087i
$87$	9.00000	−	15.5885i	0.964901	−	1.67126i
$88$	−2.00000			−0.213201
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	0.972162	+	0.234309i	$0.0752827\pi$
$89$	6.50000	+	11.2583i	0.688999	+	1.19338i	−0.283164	+	0.959072i	$0.591384\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$		0			0
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	−10.0000	+	17.3205i	−1.03695	+	1.79605i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	1.00000	+	1.73205i	0.102062	+	0.176777i
$97$	3.00000			0.304604			0.152302	−	0.988334i	$-0.451331\pi$
$97$	3.00000			0.304604			0.152302	+	0.988334i	$0.451331\pi$
$98$	−3.50000	+	6.06218i	−0.353553	+	0.612372i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	−4.00000			−0.400000
$101$	7.00000			0.696526			0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000			0.696526			0.348263	+	0.937397i	$0.386772\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	−0.992003	−	0.126217i	$-0.959717\pi$
$107$	−4.00000	+	6.92820i	−0.386695	+	0.669775i	0.605308	+	0.795991i	$0.293050\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	0.989002	+	0.147901i	$0.0472517\pi$
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	−0.366415	+	0.930451i	$0.619415\pi$
$110$	2.00000			0.190693
$111$	11.0000	+	5.19615i	1.04407	+	0.493197i
$112$		0			0
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	0.999425	−	0.0338931i	$-0.0107906\pi$
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	−0.529065	+	0.848581i	$0.677457\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$	−6.00000			−0.554700
$118$	4.00000	−	6.92820i	0.368230	−	0.637793i
$119$		0			0
$120$	−1.00000	−	1.73205i	−0.0912871	−	0.158114i
$121$	−7.00000			−0.636364
$122$	5.00000			0.452679
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	9.00000			0.804984
$126$		0			0
$127$	7.00000	+	12.1244i	0.621150	+	1.07586i	0.989272	+	0.146085i	$0.0466674\pi$
$127$	7.00000	+	12.1244i	0.621150	+	1.07586i	−0.368122	+	0.929777i	$0.619999\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.00000	−	13.8564i	0.704361	−	1.21999i
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	−2.00000	−	3.46410i	−0.174078	−	0.301511i
$133$		0			0
$134$	6.00000			0.518321
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−21.0000			−1.79415			−0.897076	−	0.441877i	$-0.854313\pi$
$137$	−21.0000			−1.79415			−0.897076	+	0.441877i	$0.854313\pi$
$138$	12.0000			1.02151
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	−0.993724	−	0.111856i	$-0.964321\pi$
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	0.399992	−	0.916519i	$-0.369013\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$		0			0
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	−14.0000			−1.15470
$148$	5.50000	+	2.59808i	0.452097	+	0.213561i
$149$	−9.00000			−0.737309			−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000			−0.737309			−0.368654	+	0.929567i	$0.620181\pi$
$150$	−4.00000	−	6.92820i	−0.326599	−	0.565685i
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$		0			0
$155$	5.00000	−	8.66025i	0.401610	−	0.695608i
$156$	−12.0000			−0.960769
$157$	8.50000	+	14.7224i	0.678374	+	1.17498i	0.975470	+	0.220131i	$0.0706483\pi$
$157$	8.50000	+	14.7224i	0.678374	+	1.17498i	−0.297097	+	0.954847i	$0.596018\pi$
$158$	−6.00000			−0.477334
$159$	−12.0000			−0.951662
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	11.0000			0.864242
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$	10.0000	−	17.3205i	0.773823	−	1.34030i	−0.161630	−	0.986851i	$-0.551675\pi$
$167$	10.0000	−	17.3205i	0.773823	−	1.34030i	0.935454	−	0.353450i	$-0.114991\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	−1.50000	−	2.59808i	−0.115045	−	0.199263i
$171$	2.00000			0.152944
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	−3.50000	−	6.06218i	−0.266100	−	0.460899i	0.701751	−	0.712422i	$-0.252402\pi$
$173$	−3.50000	−	6.06218i	−0.266100	−	0.460899i	−0.967851	+	0.251523i	$0.919068\pi$
$174$	18.0000			1.36458
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	16.0000			1.20263
$178$	−6.50000	+	11.2583i	−0.487196	+	0.843848i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	−0.994757	−	0.102268i	$-0.967390\pi$
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	0.585945	+	0.810351i	$0.300723\pi$
$182$		0			0
$183$	5.00000	+	8.66025i	0.369611	+	0.640184i
$184$	6.00000			0.442326
$185$	−5.50000	−	2.59808i	−0.404368	−	0.191014i
$186$	−20.0000			−1.46647
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$		0			0
$190$	−1.00000	+	1.73205i	−0.0725476	+	0.125656i
$191$	22.0000			1.59186			0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000			1.59186			0.795932	+	0.605386i	$0.206981\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	1.50000	+	2.59808i	0.107694	+	0.186531i
$195$	12.0000			0.859338
$196$	−7.00000			−0.500000
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	0.980614	−	0.195947i	$-0.0627782\pi$
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	−0.660003	+	0.751263i	$0.729445\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	−20.0000			−1.41776			−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000			−1.41776			−0.708881	+	0.705328i	$0.750800\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$	3.50000	+	6.06218i	0.246259	+	0.426533i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−6.00000			−0.416025
$209$	−2.00000	+	3.46410i	−0.138343	+	0.239617i
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	−8.00000			−0.546869
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$	4.00000			0.272166
$217$		0			0
$218$	−6.50000	+	11.2583i	−0.440236	+	0.762510i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	−18.0000			−1.21081
$222$	1.00000	+	12.1244i	0.0671156	+	0.813733i
$223$	2.00000			0.133930			0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000			0.133930			0.0669650	+	0.997755i	$0.478668\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−5.00000	+	8.66025i	−0.332595	+	0.576072i
$227$	−15.0000	+	25.9808i	−0.995585	+	1.72440i	−0.416503	+	0.909134i	$0.636745\pi$
$227$	−15.0000	+	25.9808i	−0.995585	+	1.72440i	−0.579082	+	0.815270i	$0.696589\pi$
$228$	4.00000			0.264906
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	−0.435653	−	0.900115i	$-0.643482\pi$
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	0.997349	−	0.0727709i	$-0.0231842\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$	9.00000			0.590879
$233$	−1.00000			−0.0655122			−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000			−0.0655122			−0.0327561	+	0.999463i	$0.510428\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$	8.00000			0.520756
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$		0			0
$239$	−2.00000	−	3.46410i	−0.129369	−	0.224074i	0.794063	−	0.607835i	$-0.207962\pi$
$239$	−2.00000	−	3.46410i	−0.129369	−	0.224074i	−0.923432	+	0.383761i	$0.874629\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	2.50000	+	4.33013i	0.160046	+	0.277208i
$245$	7.00000			0.447214
$246$	3.00000	−	5.19615i	0.191273	−	0.331295i
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	−10.0000			−0.635001
$249$	4.00000			0.253490
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	−7.00000	+	12.1244i	−0.439219	+	0.760750i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	−0.993882	−	0.110450i	$-0.964771\pi$
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	0.401288	−	0.915952i	$-0.368563\pi$
$258$	16.0000			0.996116
$259$		0			0
$260$	6.00000			0.372104
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$	7.00000	−	12.1244i	0.432461	−	0.749045i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	6.00000			0.368577
$266$		0			0
$267$	−26.0000			−1.59117
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$	−4.00000			−0.243432
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$		0			0
$274$	−10.5000	−	18.1865i	−0.634328	−	1.09869i
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	10.5000	−	18.1865i	0.630884	−	1.09272i	−0.356488	−	0.934300i	$-0.616026\pi$
$277$	10.5000	−	18.1865i	0.630884	−	1.09272i	0.987371	−	0.158423i	$-0.0506409\pi$
$278$	7.00000	−	12.1244i	0.419832	−	0.727171i
$279$	−5.00000	−	8.66025i	−0.299342	−	0.518476i
$280$		0			0
$281$	4.50000	+	7.79423i	0.268447	+	0.464965i	0.968461	−	0.249165i	$-0.0801561\pi$
$281$	4.50000	+	7.79423i	0.268447	+	0.464965i	−0.700014	+	0.714130i	$0.746823\pi$
$282$	−4.00000			−0.238197
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$	12.0000			0.709575
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000			−0.528498
$291$	−3.00000	+	5.19615i	−0.175863	+	0.304604i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	−0.949964	−	0.312358i	$-0.898881\pi$
$293$	−3.50000	+	6.06218i	−0.204472	+	0.354156i	0.745492	+	0.666514i	$0.232214\pi$
$294$	−7.00000	−	12.1244i	−0.408248	−	0.707107i
$295$	−8.00000			−0.465778
$296$	0.500000	+	6.06218i	0.0290619	+	0.352357i
$297$	−8.00000			−0.464207
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	−18.0000	+	31.1769i	−1.04097	+	1.80301i
$300$	4.00000	−	6.92820i	0.230940	−	0.400000i
$301$		0			0
$302$	−6.00000			−0.345261
$303$	−7.00000	+	12.1244i	−0.402139	+	0.696526i
$304$	2.00000			0.114708
$305$	−2.50000	−	4.33013i	−0.143150	−	0.247942i
$306$	−3.00000			−0.171499
$307$	32.0000			1.82634			0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000			1.82634			0.913168	+	0.407583i	$0.133628\pi$
$308$		0			0
$309$	8.00000	−	13.8564i	0.455104	−	0.788263i
$310$	10.0000			0.567962
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$	−6.00000	−	10.3923i	−0.339683	−	0.588348i
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$	−8.50000	+	14.7224i	−0.479683	+	0.830835i
$315$		0			0
$316$	−3.00000	−	5.19615i	−0.168763	−	0.292306i
$317$	−3.50000	−	6.06218i	−0.196580	−	0.340486i	0.750838	−	0.660487i	$-0.229650\pi$
$317$	−3.50000	−	6.06218i	−0.196580	−	0.340486i	−0.947417	+	0.320001i	$0.896317\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$	−18.0000			−1.00781
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−8.00000	−	13.8564i	−0.446516	−	0.773389i
$322$		0			0
$323$	6.00000			0.333849
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	24.0000			1.33128
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−26.0000			−1.43780
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$		0			0
$330$	−2.00000	+	3.46410i	−0.110096	+	0.190693i
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$	2.00000			0.109764
$333$	−5.00000	+	3.46410i	−0.273998	+	0.189832i
$334$	20.0000			1.09435
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$		0			0
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	−0.994728	−	0.102552i	$-0.967299\pi$
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	0.586177	+	0.810183i	$0.300632\pi$
$338$	11.5000	−	19.9186i	0.625518	−	1.08343i
$339$	−20.0000			−1.08625
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	20.0000			1.08306
$342$	1.00000	+	1.73205i	0.0540738	+	0.0936586i
$343$		0			0
$344$	8.00000			0.431331
$345$	−6.00000	−	10.3923i	−0.323029	−	0.559503i
$346$	3.50000	−	6.06218i	0.188161	−	0.325905i
$347$	−6.00000			−0.322097			−0.161048	−	0.986947i	$-0.551488\pi$
$347$	−6.00000			−0.322097			−0.161048	+	0.986947i	$0.551488\pi$
$348$	9.00000	+	15.5885i	0.482451	+	0.835629i
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	−0.999951	−	0.00987003i	$-0.996858\pi$
$349$	−9.50000	−	16.4545i	−0.508523	−	0.880788i	0.491428	−	0.870918i	$-0.336475\pi$
$350$		0			0
$351$	−12.0000	+	20.7846i	−0.640513	+	1.10940i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$	8.00000	+	13.8564i	0.425195	+	0.736460i
$355$		0			0
$356$	−13.0000			−0.688999
$357$		0			0
$358$	12.0000	+	20.7846i	0.634220	+	1.09850i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	1.00000			0.0527046
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−11.0000			−0.578147
$363$	7.00000	−	12.1244i	0.367405	−	0.636364i
$364$		0			0
$365$	−1.00000	+	1.73205i	−0.0523424	+	0.0906597i
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	3.00000			0.156174
$370$	−0.500000	−	6.06218i	−0.0259938	−	0.315158i
$371$		0			0
$372$	−10.0000	−	17.3205i	−0.518476	−	0.898027i
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.230291	−	0.973122i	$-0.426032\pi$
$373$	18.5000	−	32.0429i	0.957894	−	1.65912i	0.727603	−	0.685999i	$-0.240634\pi$
$374$	3.00000	−	5.19615i	0.155126	−	0.268687i
$375$	−9.00000	+	15.5885i	−0.464758	+	0.804984i
$376$	−2.00000			−0.103142
$377$	−27.0000	+	46.7654i	−1.39057	+	2.40854i
$378$		0			0
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	0.999874	+	0.0158521i	$0.00504609\pi$
$379$	10.0000	+	17.3205i	0.513665	+	0.889695i	−0.486209	+	0.873843i	$0.661621\pi$
$380$	−2.00000			−0.102598
$381$	−28.0000			−1.43448
$382$	11.0000	+	19.0526i	0.562809	+	0.974814i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	5.50000	+	9.52628i	0.279943	+	0.484875i
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	−1.50000	+	2.59808i	−0.0761510	+	0.131897i
$389$	−5.50000	+	9.52628i	−0.278861	+	0.483002i	−0.971102	−	0.238665i	$-0.923290\pi$
$389$	−5.50000	+	9.52628i	−0.278861	+	0.483002i	0.692241	+	0.721666i	$0.256624\pi$
$390$	6.00000	+	10.3923i	0.303822	+	0.526235i
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	−3.50000	−	6.06218i	−0.176777	−	0.306186i
$393$	28.0000			1.41241
$394$	−4.50000	+	7.79423i	−0.226707	+	0.392668i
$395$	3.00000	+	5.19615i	0.150946	+	0.261447i
$396$	2.00000			0.100504
$397$	−25.0000			−1.25471			−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000			−1.25471			−0.627357	+	0.778732i	$0.715863\pi$
$398$	−10.0000	−	17.3205i	−0.501255	−	0.868199i
$399$		0			0
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	−6.00000	+	10.3923i	−0.299253	+	0.518321i
$403$	30.0000	−	51.9615i	1.49441	−	2.58839i
$404$	−3.50000	+	6.06218i	−0.174132	+	0.301605i
$405$	−5.50000	−	9.52628i	−0.273297	−	0.473365i
$406$		0			0
$407$	−1.00000	−	12.1244i	−0.0495682	−	0.600982i
$408$	−6.00000			−0.297044
$409$	10.5000	+	18.1865i	0.519192	+	0.899266i	0.999751	+	0.0223042i	$0.00710022\pi$
$409$	10.5000	+	18.1865i	0.519192	+	0.899266i	−0.480560	+	0.876962i	$0.659566\pi$
$410$	−1.50000	+	2.59808i	−0.0740797	+	0.128310i
$411$	21.0000	−	36.3731i	1.03585	−	1.79415i
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$		0			0
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	−2.00000			−0.0981761
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$	28.0000			1.37117
$418$	−4.00000			−0.195646
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	0.910735	−	0.412991i	$-0.135516\pi$
$419$	2.00000	+	3.46410i	0.0977064	+	0.169232i	−0.813029	+	0.582224i	$0.802183\pi$
$420$		0			0
$421$	−25.0000			−1.21843			−0.609213	−	0.793007i	$-0.708514\pi$
$421$	−25.0000			−1.21843			−0.609213	+	0.793007i	$0.708514\pi$
$422$	−6.00000	−	10.3923i	−0.292075	−	0.505889i
$423$	−1.00000	−	1.73205i	−0.0486217	−	0.0842152i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$		0			0
$428$	−4.00000	−	6.92820i	−0.193347	−	0.334887i
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$	−8.00000			−0.385794
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	−0.840936	−	0.541135i	$-0.817995\pi$
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	0.889104	+	0.457705i	$0.151328\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	−9.00000			−0.432512			−0.216256	−	0.976337i	$-0.569385\pi$
$433$	−9.00000			−0.432512			−0.216256	+	0.976337i	$0.569385\pi$
$434$		0			0
$435$	−9.00000	−	15.5885i	−0.431517	−	0.747409i
$436$	−13.0000			−0.622587
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$	4.00000			0.191127
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	−1.00000	+	1.73205i	−0.0476731	+	0.0825723i
$441$	3.50000	−	6.06218i	0.166667	−	0.288675i
$442$	−9.00000	−	15.5885i	−0.428086	−	0.741467i
$443$	24.0000			1.14027			0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000			1.14027			0.570137	+	0.821549i	$0.306890\pi$
$444$	−10.0000	+	6.92820i	−0.474579	+	0.328798i
$445$	13.0000			0.616259
$446$	1.00000	+	1.73205i	0.0473514	+	0.0820150i
$447$	9.00000	−	15.5885i	0.425685	−	0.737309i
$448$		0			0
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	−0.115833	−	0.993269i	$-0.536954\pi$
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	0.918112	−	0.396320i	$-0.129713\pi$
$450$	4.00000			0.188562
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	−10.0000			−0.470360
$453$	−6.00000	−	10.3923i	−0.281905	−	0.488273i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	2.00000	+	3.46410i	0.0936586	+	0.162221i
$457$	−13.5000	+	23.3827i	−0.631503	+	1.09380i	0.355741	+	0.934585i	$0.384228\pi$
$457$	−13.5000	+	23.3827i	−0.631503	+	1.09380i	−0.987245	+	0.159211i	$0.949105\pi$
$458$	17.0000			0.794358
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	−0.991977	−	0.126419i	$-0.959652\pi$
$461$	−13.0000	−	22.5167i	−0.605470	−	1.04871i	0.386507	−	0.922287i	$-0.373682\pi$
$462$		0			0
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	−0.534450	−	0.845200i	$-0.679481\pi$
$463$	10.0000	−	17.3205i	0.464739	−	0.804952i	0.999190	+	0.0402476i	$0.0128147\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$	10.0000	+	17.3205i	0.463739	+	0.803219i
$466$	−0.500000	−	0.866025i	−0.0231621	−	0.0401179i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$	3.00000	−	5.19615i	0.138675	−	0.240192i
$469$		0			0
$470$	2.00000			0.0922531
$471$	−34.0000			−1.56664
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$	−16.0000			−0.735681
$474$	6.00000	−	10.3923i	0.275589	−	0.477334i
$475$	−8.00000			−0.367065
$476$		0			0
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	2.00000	−	3.46410i	0.0914779	−	0.158444i
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	−0.956431	−	0.291958i	$-0.905693\pi$
$479$	−16.0000	−	27.7128i	−0.731059	−	1.26623i	0.225372	−	0.974273i	$-0.427640\pi$
$480$	2.00000			0.0912871
$481$	−33.0000	−	15.5885i	−1.50467	−	0.710772i
$482$	10.0000			0.455488
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$	−5.00000	+	8.66025i	−0.226805	+	0.392837i
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	8.00000			0.361773
$490$	3.50000	+	6.06218i	0.158114	+	0.273861i
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$	6.00000			0.270501
$493$	13.5000	+	23.3827i	0.608009	+	1.05310i
$494$	−6.00000	+	10.3923i	−0.269953	+	0.467572i
$495$	−2.00000			−0.0898933
$496$	−5.00000	−	8.66025i	−0.224507	−	0.388857i
$497$		0			0
$498$	2.00000	+	3.46410i	0.0896221	+	0.155230i
$499$	−15.0000	+	25.9808i	−0.671492	+	1.16306i	0.305989	+	0.952035i	$0.401013\pi$
$499$	−15.0000	+	25.9808i	−0.671492	+	1.16306i	−0.977481	+	0.211024i	$0.932320\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	20.0000	+	34.6410i	0.893534	+	1.54765i
$502$	10.0000	+	17.3205i	0.446322	+	0.773052i
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	0.666705	−	0.745321i	$-0.267704\pi$
$503$	−7.00000	−	12.1244i	−0.312115	−	0.540598i	−0.978820	+	0.204723i	$0.934371\pi$
$504$		0			0
$505$	3.50000	−	6.06218i	0.155748	−	0.269763i
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$	46.0000			2.04293
$508$	−14.0000			−0.621150
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	0.948353	−	0.317217i	$-0.102748\pi$
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	−0.748894	+	0.662690i	$0.769415\pi$
$510$	6.00000			0.265684
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	4.00000	−	6.92820i	0.176604	−	0.305888i
$514$	9.50000	−	16.4545i	0.419027	−	0.725776i
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$	8.00000	+	13.8564i	0.352180	+	0.609994i
$517$	4.00000			0.175920
$518$		0			0
$519$	14.0000			0.614532
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	0.324185	+	0.945994i	$0.394910\pi$
$521$	−15.0000	+	25.9808i	−0.657162	+	1.13824i	−0.981347	+	0.192244i	$0.938423\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	−0.924132	−	0.382073i	$-0.875210\pi$
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	0.792951	+	0.609285i	$0.208544\pi$
$524$	14.0000			0.611593
$525$		0			0
$526$	24.0000			1.04645
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$	4.00000			0.174078
$529$	13.0000			0.565217
$530$	3.00000	+	5.19615i	0.130312	+	0.225706i
$531$	−4.00000	+	6.92820i	−0.173585	+	0.300658i
$532$		0			0
$533$	9.00000	+	15.5885i	0.389833	+	0.675211i
$534$	−13.0000	−	22.5167i	−0.562565	−	0.974391i
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$	−24.0000	+	41.5692i	−1.03568	+	1.79384i
$538$	1.00000	+	1.73205i	0.0431131	+	0.0746740i
$539$	7.00000	+	12.1244i	0.301511	+	0.522233i
$540$	−2.00000	−	3.46410i	−0.0860663	−	0.149071i
$541$	−9.00000			−0.386940			−0.193470	−	0.981106i	$-0.561974\pi$
$541$	−9.00000			−0.386940			−0.193470	+	0.981106i	$0.561974\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$	−11.0000	−	19.0526i	−0.472055	−	0.817624i
$544$	−3.00000			−0.128624
$545$	13.0000			0.556859
$546$		0			0
$547$	−6.00000			−0.256541			−0.128271	−	0.991739i	$-0.540943\pi$
$547$	−6.00000			−0.256541			−0.128271	+	0.991739i	$0.540943\pi$
$548$	10.5000	−	18.1865i	0.448538	−	0.776890i
$549$	−5.00000			−0.213395
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$	−6.00000	+	10.3923i	−0.255377	+	0.442326i
$553$		0			0
$554$	21.0000			0.892205
$555$	10.0000	−	6.92820i	0.424476	−	0.294086i
$556$	14.0000			0.593732
$557$	−17.5000	−	30.3109i	−0.741499	−	1.28431i	−0.951813	−	0.306680i	$-0.900782\pi$
$557$	−17.5000	−	30.3109i	−0.741499	−	1.28431i	0.210314	−	0.977634i	$-0.432551\pi$
$558$	5.00000	−	8.66025i	0.211667	−	0.366618i
$559$	−24.0000	+	41.5692i	−1.01509	+	1.75819i
$560$		0			0
$561$	12.0000			0.506640
$562$	−4.50000	+	7.79423i	−0.189821	+	0.328780i
$563$	10.0000			0.421450			0.210725	−	0.977545i	$-0.432418\pi$
$563$	10.0000			0.421450			0.210725	+	0.977545i	$0.432418\pi$
$564$	−2.00000	−	3.46410i	−0.0842152	−	0.145865i
$565$	10.0000			0.420703
$566$	−4.00000			−0.168133
$567$		0			0
$568$		0			0
$569$	11.0000			0.461144			0.230572	−	0.973055i	$-0.425940\pi$
$569$	11.0000			0.461144			0.230572	+	0.973055i	$0.425940\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	0.613933	−	0.789359i	$-0.289587\pi$
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	−0.990571	+	0.137002i	$0.956253\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$	−22.0000	+	38.1051i	−0.919063	+	1.59186i
$574$		0			0
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	8.00000			0.332756
$579$	−11.0000	+	19.0526i	−0.457144	+	0.791797i
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$		0			0
$582$	−6.00000			−0.248708
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$	2.00000			0.0827606
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	−7.00000			−0.289167
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	0.370531	+	0.928820i	$0.379176\pi$
$587$	−15.0000	+	25.9808i	−0.619116	+	1.07234i	−0.989647	+	0.143521i	$0.954158\pi$
$588$	7.00000	−	12.1244i	0.288675	−	0.500000i
$589$	−10.0000	+	17.3205i	−0.412043	+	0.713679i
$590$	−4.00000	−	6.92820i	−0.164677	−	0.285230i
$591$	−18.0000			−0.740421
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	19.0000			0.780236			0.390118	−	0.920765i	$-0.372434\pi$
$593$	19.0000			0.780236			0.390118	+	0.920765i	$0.372434\pi$
$594$	−4.00000	−	6.92820i	−0.164122	−	0.284268i
$595$		0			0
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$	20.0000	−	34.6410i	0.818546	−	1.41776i
$598$	−36.0000			−1.47215
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	−0.949908	−	0.312531i	$-0.898823\pi$
$599$	−5.00000	+	8.66025i	−0.204294	+	0.353848i	0.745613	+	0.666379i	$0.232157\pi$
$600$	8.00000			0.326599
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$		0			0
$603$	−6.00000			−0.244339
$604$	−3.00000	−	5.19615i	−0.122068	−	0.211428i
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	−14.0000			−0.568711
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	0.746532	−	0.665350i	$-0.231718\pi$
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	−0.949476	+	0.313841i	$0.898384\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$		0			0
$610$	2.50000	−	4.33013i	0.101222	−	0.175322i
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	16.0000	+	27.7128i	0.645707	+	1.11840i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−7.00000	−	12.1244i	−0.281809	−	0.488108i	0.690021	−	0.723789i	$-0.257601\pi$
$617$	−7.00000	−	12.1244i	−0.281809	−	0.488108i	−0.971830	+	0.235681i	$0.924268\pi$
$618$	16.0000			0.643614
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	5.00000	+	8.66025i	0.200805	+	0.347804i
$621$	24.0000			0.963087
$622$	−6.00000	+	10.3923i	−0.240578	+	0.416693i
$623$		0			0
$624$	6.00000	−	10.3923i	0.240192	−	0.416025i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	9.50000	−	16.4545i	0.379696	−	0.657653i
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$	−17.0000			−0.678374
$629$	−15.0000	+	10.3923i	−0.598089	+	0.414368i
$630$		0			0
$631$	−5.00000	−	8.66025i	−0.199047	−	0.344759i	0.749173	−	0.662375i	$-0.230451\pi$
$631$	−5.00000	−	8.66025i	−0.199047	−	0.344759i	−0.948220	+	0.317615i	$0.897118\pi$
$632$	3.00000	−	5.19615i	0.119334	−	0.206692i
$633$	12.0000	−	20.7846i	0.476957	−	0.826114i
$634$	3.50000	−	6.06218i	0.139003	−	0.240760i
$635$	14.0000			0.555573
$636$	6.00000	−	10.3923i	0.237915	−	0.412082i
$637$	42.0000			1.66410
$638$	−9.00000	−	15.5885i	−0.356313	−	0.617153i
$639$		0			0
$640$	1.00000			0.0395285
$641$	−9.50000	−	16.4545i	−0.375227	−	0.649913i	0.615134	−	0.788423i	$-0.289102\pi$
$641$	−9.50000	−	16.4545i	−0.375227	−	0.649913i	−0.990361	+	0.138510i	$0.955769\pi$
$642$	8.00000	−	13.8564i	0.315735	−	0.546869i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$		0			0
$645$	−8.00000	−	13.8564i	−0.315000	−	0.545595i
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	−2.00000	+	3.46410i	−0.0786281	+	0.136188i	−0.902658	−	0.430358i	$-0.858387\pi$
$647$	−2.00000	+	3.46410i	−0.0786281	+	0.136188i	0.824030	+	0.566546i	$0.191721\pi$
$648$	−5.50000	+	9.52628i	−0.216060	+	0.374228i
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$	12.0000	+	20.7846i	0.470679	+	0.815239i
$651$		0			0
$652$	4.00000			0.156652
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	−0.974634	−	0.223803i	$-0.928153\pi$
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	0.681137	+	0.732156i	$0.261486\pi$
$654$	−13.0000	−	22.5167i	−0.508340	−	0.880471i
$655$	−14.0000			−0.547025
$656$	3.00000			0.117130
$657$	1.00000	+	1.73205i	0.0390137	+	0.0675737i
$658$		0			0
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	−0.602844	−	0.797859i	$-0.705966\pi$
$659$	10.0000	−	17.3205i	0.389545	−	0.674711i	0.992388	+	0.123148i	$0.0392990\pi$
$660$	−4.00000			−0.155700
$661$	−13.5000	+	23.3827i	−0.525089	+	0.909481i	0.474484	+	0.880264i	$0.342635\pi$
$661$	−13.5000	+	23.3827i	−0.525089	+	0.909481i	−0.999573	+	0.0292169i	$0.990699\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$	18.0000	−	31.1769i	0.699062	−	1.21081i
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$	−5.50000	−	2.59808i	−0.213121	−	0.100673i
$667$	54.0000			2.09089
$668$	10.0000	+	17.3205i	0.386912	+	0.670151i
$669$	−2.00000	+	3.46410i	−0.0773245	+	0.133930i
$670$	3.00000	−	5.19615i	0.115900	−	0.200745i
$671$	5.00000	−	8.66025i	0.193023	−	0.334325i
$672$		0			0
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	−0.846108	−	0.533011i	$-0.821060\pi$
$673$	1.00000	−	1.73205i	0.0385472	−	0.0667657i	0.884655	+	0.466246i	$0.154394\pi$
$674$	−15.0000			−0.577778
$675$	−8.00000	−	13.8564i	−0.307920	−	0.533333i
$676$	23.0000			0.884615
$677$	47.0000			1.80636			0.903178	−	0.429265i	$-0.141228\pi$
$677$	47.0000			1.80636			0.903178	+	0.429265i	$0.141228\pi$
$678$	−10.0000	−	17.3205i	−0.384048	−	0.665190i
$679$		0			0
$680$	3.00000			0.115045
$681$	−30.0000	−	51.9615i	−1.14960	−	1.99117i
$682$	10.0000	+	17.3205i	0.382920	+	0.663237i
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$	−10.5000	+	18.1865i	−0.401184	+	0.694872i
$686$		0			0
$687$	17.0000	+	29.4449i	0.648590	+	1.12339i
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	36.0000			1.37149
$690$	6.00000	−	10.3923i	0.228416	−	0.395628i
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$	7.00000			0.266100
$693$		0			0
$694$	−3.00000	−	5.19615i	−0.113878	−	0.197243i
$695$	−14.0000			−0.531050
$696$	−9.00000	+	15.5885i	−0.341144	+	0.590879i
$697$	9.00000			0.340899
$698$	9.50000	−	16.4545i	0.359580	−	0.622811i
$699$	1.00000	−	1.73205i	0.0378235	−	0.0655122i
$700$		0			0
$701$	1.00000	+	1.73205i	0.0377695	+	0.0654187i	0.884292	−	0.466934i	$-0.154641\pi$
$701$	1.00000	+	1.73205i	0.0377695	+	0.0654187i	−0.846523	+	0.532353i	$0.821308\pi$
$702$	−24.0000			−0.905822
$703$	11.0000	+	5.19615i	0.414873	+	0.195977i
$704$	2.00000			0.0753778
$705$	2.00000	+	3.46410i	0.0753244	+	0.130466i
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$		0			0
$708$	−8.00000	+	13.8564i	−0.300658	+	0.520756i
$709$	−6.00000			−0.225335			−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000			−0.225335			−0.112667	+	0.993633i	$0.535939\pi$
$710$		0			0
$711$	6.00000			0.225018
$712$	−6.50000	−	11.2583i	−0.243598	−	0.421924i
$713$	−60.0000			−2.24702
$714$		0			0
$715$	−6.00000	−	10.3923i	−0.224387	−	0.388650i
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$	8.00000			0.298765
$718$	8.00000	+	13.8564i	0.298557	+	0.517116i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$		0			0
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	10.0000	+	17.3205i	0.371904	+	0.644157i
$724$	−5.50000	−	9.52628i	−0.204406	−	0.354041i
$725$	−18.0000	−	31.1769i	−0.668503	−	1.15788i
$726$	14.0000			0.519589
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−2.00000			−0.0740233
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−10.0000			−0.369611
$733$	−13.0000	+	22.5167i	−0.480166	+	0.831672i	−0.999741	−	0.0227529i	$-0.992757\pi$
$733$	−13.0000	+	22.5167i	−0.480166	+	0.831672i	0.519575	+	0.854425i	$0.326090\pi$
$734$	4.00000			0.147643
$735$	−7.00000	+	12.1244i	−0.258199	+	0.447214i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	34.0000			1.25071			0.625355	−	0.780340i	$-0.284954\pi$
$739$	34.0000			1.25071			0.625355	+	0.780340i	$0.284954\pi$
$740$	5.00000	−	3.46410i	0.183804	−	0.127343i
$741$	−24.0000			−0.881662
$742$		0			0
$743$	−9.00000	+	15.5885i	−0.330178	+	0.571885i	−0.982547	−	0.186017i	$-0.940442\pi$
$743$	−9.00000	+	15.5885i	−0.330178	+	0.571885i	0.652369	+	0.757902i	$0.273775\pi$
$744$	10.0000	−	17.3205i	0.366618	−	0.635001i
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$	37.0000			1.35467
$747$	−1.00000	+	1.73205i	−0.0365881	+	0.0633724i
$748$	6.00000			0.219382
$749$		0			0
$750$	−18.0000			−0.657267
$751$	−4.00000			−0.145962			−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000			−0.145962			−0.0729810	+	0.997333i	$0.523251\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	−20.0000	+	34.6410i	−0.728841	+	1.26239i
$754$	−54.0000			−1.96656
$755$	3.00000	+	5.19615i	0.109181	+	0.189107i
$756$		0			0
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$	12.0000	−	20.7846i	0.435572	−	0.754434i
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	6.50000	+	11.2583i	0.235625	+	0.408114i	0.959454	−	0.281865i	$-0.0909530\pi$
$761$	6.50000	+	11.2583i	0.235625	+	0.408114i	−0.723829	+	0.689979i	$0.757620\pi$
$762$	−14.0000	−	24.2487i	−0.507166	−	0.878438i
$763$		0			0
$764$	−11.0000	+	19.0526i	−0.397966	+	0.689297i
$765$	1.50000	+	2.59808i	0.0542326	+	0.0939336i
$766$	−8.00000			−0.289052
$767$	−48.0000			−1.73318
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	38.0000			1.36854
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	−11.5000	+	19.9186i	−0.413626	+	0.716422i	−0.995283	−	0.0970125i	$-0.969071\pi$
$773$	−11.5000	+	19.9186i	−0.413626	+	0.716422i	0.581657	+	0.813434i	$0.302405\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$	20.0000	+	34.6410i	0.718421	+	1.24434i
$776$	−3.00000			−0.107694
$777$		0			0
$778$	−11.0000			−0.394369
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$	−6.00000	+	10.3923i	−0.214834	+	0.372104i
$781$		0			0
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$	36.0000			1.28654
$784$	3.50000	−	6.06218i	0.125000	−	0.216506i
$785$	17.0000			0.606756
$786$	14.0000	+	24.2487i	0.499363	+	0.864923i
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	−9.00000			−0.320612
$789$	24.0000	+	41.5692i	0.854423	+	1.47990i
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$		0			0
$792$	1.00000	+	1.73205i	0.0355335	+	0.0615457i
$793$	−15.0000	−	25.9808i	−0.532666	−	0.922604i
$794$	−12.5000	−	21.6506i	−0.443608	−	0.768352i
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	−3.00000	−	5.19615i	−0.106132	−	0.183827i
$800$	4.00000			0.141421
$801$	6.50000	−	11.2583i	0.229666	−	0.397794i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	−4.00000			−0.141157
$804$	−12.0000			−0.423207
$805$		0			0
$806$	60.0000			2.11341
$807$	−2.00000	+	3.46410i	−0.0704033	+	0.121942i
$808$	−7.00000			−0.246259
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.202301	−	0.979323i	$-0.435158\pi$
$809$	27.0000	−	46.7654i	0.949269	−	1.64418i	0.746968	−	0.664860i	$-0.231509\pi$
$810$	5.50000	−	9.52628i	0.193250	−	0.334719i
$811$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$811$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$812$		0			0
$813$	12.0000			0.420858
$814$	10.0000	−	6.92820i	0.350500	−	0.242833i
$815$	−4.00000			−0.140114
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	−10.5000	+	18.1865i	−0.367124	+	0.635877i
$819$		0			0
$820$	−3.00000			−0.104765
$821$	23.0000	−	39.8372i	0.802706	−	1.39033i	−0.115124	−	0.993351i	$-0.536726\pi$
$821$	23.0000	−	39.8372i	0.802706	−	1.39033i	0.917829	−	0.396976i	$-0.129940\pi$
$822$	42.0000			1.46492
$823$	27.0000	+	46.7654i	0.941161	+	1.63014i	0.763261	+	0.646090i	$0.223597\pi$
$823$	27.0000	+	46.7654i	0.941161	+	1.63014i	0.177899	+	0.984049i	$0.443070\pi$
$824$	8.00000			0.278693
$825$	−16.0000			−0.557048
$826$		0			0
$827$	−4.00000	+	6.92820i	−0.139094	+	0.240917i	−0.927154	−	0.374681i	$-0.877752\pi$
$827$	−4.00000	+	6.92820i	−0.139094	+	0.240917i	0.788060	+	0.615598i	$0.211086\pi$
$828$	−6.00000			−0.208514
$829$	−25.0000	−	43.3013i	−0.868286	−	1.50392i	−0.863747	−	0.503926i	$-0.831889\pi$
$829$	−25.0000	−	43.3013i	−0.868286	−	1.50392i	−0.00453881	−	0.999990i	$-0.501445\pi$
$830$	−1.00000	−	1.73205i	−0.0347105	−	0.0601204i
$831$	21.0000	+	36.3731i	0.728482	+	1.26177i
$832$	3.00000	−	5.19615i	0.104006	−	0.180144i
$833$	10.5000	−	18.1865i	0.363803	−	0.630126i
$834$	14.0000	+	24.2487i	0.484780	+	0.839664i
$835$	−10.0000	−	17.3205i	−0.346064	−	0.599401i
$836$	−2.00000	−	3.46410i	−0.0691714	−	0.119808i
$837$	−40.0000			−1.38260
$838$	−2.00000	+	3.46410i	−0.0690889	+	0.119665i
$839$	7.00000	+	12.1244i	0.241667	+	0.418579i	0.961189	−	0.275890i	$-0.0889726\pi$
$839$	7.00000	+	12.1244i	0.241667	+	0.418579i	−0.719522	+	0.694469i	$0.755639\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−12.5000	−	21.6506i	−0.430778	−	0.746130i
$843$	−18.0000			−0.619953
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	−23.0000			−0.791224
$846$	1.00000	−	1.73205i	0.0343807	−	0.0595491i
$847$		0			0
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	−4.00000	−	6.92820i	−0.137280	−	0.237775i
$850$	12.0000			0.411597
$851$	3.00000	+	36.3731i	0.102839	+	1.24685i
$852$		0			0
$853$	−11.5000	−	19.9186i	−0.393753	−	0.681999i	0.599189	−	0.800608i	$-0.295490\pi$
$853$	−11.5000	−	19.9186i	−0.393753	−	0.681999i	−0.992941	+	0.118609i	$0.962157\pi$
$854$		0			0
$855$	1.00000	−	1.73205i	0.0341993	−	0.0592349i
$856$	4.00000	−	6.92820i	0.136717	−	0.236801i
$857$	−5.00000			−0.170797			−0.0853984	−	0.996347i	$-0.527216\pi$
$857$	−5.00000			−0.170797			−0.0853984	+	0.996347i	$0.527216\pi$
$858$	−12.0000	+	20.7846i	−0.409673	+	0.709575i
$859$	−32.0000			−1.09183			−0.545913	−	0.837842i	$-0.683817\pi$
$859$	−32.0000			−1.09183			−0.545913	+	0.837842i	$0.683817\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$		0			0
$862$	2.00000			0.0681203
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	−2.00000	+	3.46410i	−0.0680414	+	0.117851i
$865$	−7.00000			−0.238007
$866$	−4.50000	−	7.79423i	−0.152916	−	0.264859i
$867$	8.00000	+	13.8564i	0.271694	+	0.470588i
$868$		0			0
$869$	−6.00000	+	10.3923i	−0.203536	+	0.352535i
$870$	9.00000	−	15.5885i	0.305129	−	0.528498i
$871$	−18.0000	−	31.1769i	−0.609907	−	1.05639i
$872$	−6.50000	−	11.2583i	−0.220118	−	0.381255i
$873$	−1.50000	−	2.59808i	−0.0507673	−	0.0879316i
$874$	12.0000			0.405906
$875$		0			0
$876$	2.00000	+	3.46410i	0.0675737	+	0.117041i
$877$	−5.00000			−0.168838			−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000			−0.168838			−0.0844190	+	0.996430i	$0.526903\pi$
$878$	8.00000			0.269987
$879$	−7.00000	−	12.1244i	−0.236104	−	0.408944i
$880$	−2.00000			−0.0674200
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	0.0136556	+	0.999907i	$0.495653\pi$
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	−0.872772	+	0.488127i	$0.837680\pi$
$882$	7.00000			0.235702
$883$	−23.0000	+	39.8372i	−0.774012	+	1.34063i	0.161337	+	0.986899i	$0.448419\pi$
$883$	−23.0000	+	39.8372i	−0.774012	+	1.34063i	−0.935348	+	0.353728i	$0.884914\pi$
$884$	9.00000	−	15.5885i	0.302703	−	0.524297i
$885$	8.00000	−	13.8564i	0.268917	−	0.465778i
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	−14.0000			−0.470074			−0.235037	−	0.971986i	$-0.575521\pi$
$887$	−14.0000			−0.470074			−0.235037	+	0.971986i	$0.575521\pi$
$888$	−11.0000	−	5.19615i	−0.369136	−	0.174371i
$889$		0			0
$890$	6.50000	+	11.2583i	0.217880	+	0.377380i
$891$	11.0000	−	19.0526i	0.368514	−	0.638285i
$892$	−1.00000	+	1.73205i	−0.0334825	+	0.0579934i
$893$	−2.00000	+	3.46410i	−0.0669274	+	0.115922i
$894$	18.0000			0.602010
$895$	12.0000	−	20.7846i	0.401116	−	0.694753i
$896$		0			0
$897$	−36.0000	−	62.3538i	−1.20201	−	2.08193i
$898$	34.0000			1.13459
$899$	−90.0000			−3.00167
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$	−6.00000			−0.199778
$903$		0			0
$904$	−5.00000	−	8.66025i	−0.166298	−	0.288036i
$905$	5.50000	+	9.52628i	0.182826	+	0.316664i
$906$	6.00000	−	10.3923i	0.199337	−	0.345261i
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	−0.958523	−	0.285015i	$-0.908001\pi$
$907$	−7.00000	+	12.1244i	−0.232431	+	0.402583i	0.726092	+	0.687598i	$0.241335\pi$
$908$	−15.0000	−	25.9808i	−0.497792	−	0.862202i
$909$	−3.50000	−	6.06218i	−0.116088	−	0.201070i
$910$		0			0
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−2.00000	−	3.46410i	−0.0661903	−	0.114645i
$914$	−27.0000			−0.893081
$915$	10.0000			0.330590
$916$	8.50000	+	14.7224i	0.280848	+	0.486443i
$917$		0			0
$918$	−6.00000	+	10.3923i	−0.198030	+	0.342997i
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	−32.0000	+	55.4256i	−1.05444	+	1.82634i
$922$	13.0000	−	22.5167i	0.428132	−	0.741547i
$923$		0			0
$924$		0			0
$925$	20.0000	−	13.8564i	0.657596	−	0.455596i
$926$	20.0000			0.657241
$927$	4.00000	+	6.92820i	0.131377	+	0.227552i
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	24.5000	−	42.4352i	0.803819	−	1.39226i	−0.113267	−	0.993565i	$-0.536131\pi$
$929$	24.5000	−	42.4352i	0.803819	−	1.39226i	0.917086	−	0.398691i	$-0.130535\pi$
$930$	−10.0000	+	17.3205i	−0.327913	+	0.567962i
$931$	−14.0000			−0.458831
$932$	0.500000	−	0.866025i	0.0163780	−	0.0283676i
$933$	−24.0000			−0.785725
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	−6.00000			−0.196221
$936$	6.00000			0.196116
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	0.874077	−	0.485787i	$-0.161467\pi$
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	−0.857743	+	0.514079i	$0.828134\pi$
$938$		0			0
$939$	38.0000			1.24008
$940$	1.00000	+	1.73205i	0.0326164	+	0.0564933i
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	0.717496	−	0.696563i	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$	−17.0000	−	29.4449i	−0.553890	−	0.959366i
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$	−4.00000	+	6.92820i	−0.130189	+	0.225494i
$945$		0			0
$946$	−8.00000	−	13.8564i	−0.260102	−	0.450511i
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	0.602494	−	0.798123i	$-0.294174\pi$
$947$	−12.0000	−	20.7846i	−0.389948	−	0.675409i	−0.992442	+	0.122714i	$0.960840\pi$
$948$	12.0000			0.389742
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$	14.0000			0.453981
$952$		0			0
$953$	−5.00000	−	8.66025i	−0.161966	−	0.280533i	0.773608	−	0.633665i	$-0.218450\pi$
$953$	−5.00000	−	8.66025i	−0.161966	−	0.280533i	−0.935574	+	0.353132i	$0.885117\pi$
$954$	6.00000			0.194257
$955$	11.0000	−	19.0526i	0.355952	−	0.616526i
$956$	4.00000			0.129369
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$	16.0000	−	27.7128i	0.516937	−	0.895360i
$959$		0			0
$960$	1.00000	+	1.73205i	0.0322749	+	0.0559017i
$961$	69.0000			2.22581
$962$	−3.00000	−	36.3731i	−0.0967239	−	1.17271i
$963$	8.00000			0.257796
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	5.50000	−	9.52628i	0.177051	−	0.306662i
$966$		0			0
$967$	−10.0000	+	17.3205i	−0.321578	+	0.556990i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−10.0000	+	17.3205i	−0.321578	+	0.556990i	0.659236	+	0.751936i	$0.270880\pi$
$968$	7.00000			0.224989
$969$	−6.00000	+	10.3923i	−0.192748	+	0.333849i
$970$	3.00000			0.0963242
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	−1.00000	−	1.73205i	−0.0320421	−	0.0554985i
$975$	−24.0000	+	41.5692i	−0.768615	+	1.33128i
$976$	−5.00000			−0.160046
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$	4.00000	+	6.92820i	0.127906	+	0.221540i
$979$	13.0000	+	22.5167i	0.415482	+	0.719636i
$980$	−3.50000	+	6.06218i	−0.111803	+	0.193649i
$981$	6.50000	−	11.2583i	0.207529	−	0.359451i
$982$	−9.00000	−	15.5885i	−0.287202	−	0.497448i
$983$	27.0000	+	46.7654i	0.861166	+	1.49158i	0.870804	+	0.491630i	$0.163599\pi$
$983$	27.0000	+	46.7654i	0.861166	+	1.49158i	−0.00963785	+	0.999954i	$0.503068\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	9.00000			0.286764
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$		0			0
$988$	−12.0000			−0.381771
$989$	48.0000			1.52631
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$	−40.0000			−1.26936
$994$		0			0
$995$	−10.0000	+	17.3205i	−0.317021	+	0.549097i
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	0.999592	−	0.0285686i	$-0.00909491\pi$
$997$	15.0000	+	25.9808i	0.475055	+	0.822819i	−0.524537	+	0.851388i	$0.675762\pi$
$998$	−30.0000			−0.949633
$999$	2.00000	+	24.2487i	0.0632772	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.c.a.63.1	yes	2
3.2	odd	2		666.2.f.b.433.1		2
4.3	odd	2		592.2.i.d.433.1		2
37.10	even	3	inner	74.2.c.a.47.1	✓	2
37.11	even	6		2738.2.a.d.1.1		1
37.26	even	3		2738.2.a.b.1.1		1
111.47	odd	6		666.2.f.b.343.1		2
148.47	odd	6		592.2.i.d.417.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.c.a.47.1	✓	2	37.10	even	3	inner
74.2.c.a.63.1	yes	2	1.1	even	1	trivial
592.2.i.d.417.1		2	148.47	odd	6
592.2.i.d.433.1		2	4.3	odd	2
666.2.f.b.343.1		2	111.47	odd	6
666.2.f.b.433.1		2	3.2	odd	2
2738.2.a.b.1.1		1	37.26	even	3
2738.2.a.d.1.1		1	37.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +2.00000 q^{11} +(-1.00000 - 1.73205i) q^{12} +(3.00000 - 5.19615i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} -6.00000 q^{23} +(1.00000 - 1.73205i) q^{24} +(2.00000 + 3.46410i) q^{25} +6.00000 q^{26} -4.00000 q^{27} -9.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +10.0000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} -2.00000 q^{38} +(6.00000 + 10.3923i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-1.50000 + 2.59808i) q^{41} -8.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +2.00000 q^{48} +(3.50000 + 6.06218i) q^{49} +(-2.00000 + 3.46410i) q^{50} +6.00000 q^{51} +(3.00000 + 5.19615i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-2.00000 - 3.46410i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-2.00000 - 3.46410i) q^{57} +(-4.50000 - 7.79423i) q^{58} +(-4.00000 - 6.92820i) q^{59} -2.00000 q^{60} +(2.50000 - 4.33013i) q^{61} +(5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -4.00000 q^{66} +(3.00000 - 5.19615i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(5.00000 - 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-3.00000 + 5.19615i) q^{79} -1.00000 q^{80} +(5.50000 - 9.52628i) q^{81} -3.00000 q^{82} +(-1.00000 - 1.73205i) q^{83} -3.00000 q^{85} +(-4.00000 - 6.92820i) q^{86} +(9.00000 - 15.5885i) q^{87} -2.00000 q^{88} +(6.50000 + 11.2583i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(3.00000 - 5.19615i) q^{92} +(-10.0000 + 17.3205i) q^{93} +(1.00000 + 1.73205i) q^{94} +(1.00000 + 1.73205i) q^{95} +(1.00000 + 1.73205i) q^{96} +3.00000 q^{97} +(-3.50000 + 6.06218i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 6 q^{13} + 2 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + q^{20} + 2 q^{22} - 12 q^{23} + 2 q^{24} + 4 q^{25} + 12 q^{26} - 8 q^{27} - 18 q^{29} - 2 q^{30} + 20 q^{31} + q^{32} - 4 q^{33} + 3 q^{34} + 2 q^{36} - q^{37} - 4 q^{38} + 12 q^{39} - q^{40} - 3 q^{41} - 16 q^{43} - 2 q^{44} - 2 q^{45} - 6 q^{46} + 4 q^{47} + 4 q^{48} + 7 q^{49} - 4 q^{50} + 12 q^{51} + 6 q^{52} + 6 q^{53} - 4 q^{54} + 2 q^{55} - 4 q^{57} - 9 q^{58} - 8 q^{59} - 4 q^{60} + 5 q^{61} + 10 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{66} + 6 q^{67} + 6 q^{68} + 12 q^{69} + q^{72} - 4 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 12 q^{78} - 6 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 2 q^{83} - 6 q^{85} - 8 q^{86} + 18 q^{87} - 4 q^{88} + 13 q^{89} - q^{90} + 6 q^{92} - 20 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 6 q^{97} - 7 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 + q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 6 * q^13 + 2 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 + q^20 + 2 * q^22 - 12 * q^23 + 2 * q^24 + 4 * q^25 + 12 * q^26 - 8 * q^27 - 18 * q^29 - 2 * q^30 + 20 * q^31 + q^32 - 4 * q^33 + 3 * q^34 + 2 * q^36 - q^37 - 4 * q^38 + 12 * q^39 - q^40 - 3 * q^41 - 16 * q^43 - 2 * q^44 - 2 * q^45 - 6 * q^46 + 4 * q^47 + 4 * q^48 + 7 * q^49 - 4 * q^50 + 12 * q^51 + 6 * q^52 + 6 * q^53 - 4 * q^54 + 2 * q^55 - 4 * q^57 - 9 * q^58 - 8 * q^59 - 4 * q^60 + 5 * q^61 + 10 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^66 + 6 * q^67 + 6 * q^68 + 12 * q^69 + q^72 - 4 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 12 * q^78 - 6 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 2 * q^83 - 6 * q^85 - 8 * q^86 + 18 * q^87 - 4 * q^88 + 13 * q^89 - q^90 + 6 * q^92 - 20 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 6 * q^97 - 7 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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