LMFDB - Embedded newform 735.2.i.i.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(226,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("735.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	735.361
Dual form			735.2.i.i.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11803 - 1.93649i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.23607 q^{6} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.11803 - 1.93649i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.23607 q^{6} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.11803 + 1.93649i) q^{10} +(1.23607 - 2.14093i) q^{11} +(-1.50000 - 2.59808i) q^{12} +4.47214 q^{13} +1.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.11803 + 1.93649i) q^{18} +(3.23607 + 5.60503i) q^{19} +3.00000 q^{20} -5.52786 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-5.00000 - 8.66025i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.11803 - 1.93649i) q^{30} +(5.23607 - 9.06914i) q^{31} +(3.35410 - 5.80948i) q^{32} +(1.23607 + 2.14093i) q^{33} +4.47214 q^{34} +3.00000 q^{36} +(-5.47214 - 9.47802i) q^{37} +(7.23607 - 12.5332i) q^{38} +(-2.23607 + 3.87298i) q^{39} +(-1.11803 - 1.93649i) q^{40} +2.00000 q^{41} -8.94427 q^{43} +(3.70820 + 6.42280i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.47214 + 7.74597i) q^{46} +(-2.47214 - 4.28187i) q^{47} -1.00000 q^{48} +2.23607 q^{50} +(-1.00000 - 1.73205i) q^{51} +(-6.70820 + 11.6190i) q^{52} +(6.23607 - 10.8012i) q^{53} +(-1.11803 - 1.93649i) q^{54} -2.47214 q^{55} -6.47214 q^{57} +(2.23607 + 3.87298i) q^{58} +(4.47214 - 7.74597i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(-1.00000 - 1.73205i) q^{61} -23.4164 q^{62} -13.0000 q^{64} +(-2.23607 - 3.87298i) q^{65} +(2.76393 - 4.78727i) q^{66} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +4.00000 q^{69} +14.4721 q^{71} +(-1.11803 - 1.93649i) q^{72} +(-1.76393 + 3.05522i) q^{73} +(-12.2361 + 21.1935i) q^{74} +(-0.500000 - 0.866025i) q^{75} -19.4164 q^{76} +10.0000 q^{78} +(2.47214 + 4.28187i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.23607 - 3.87298i) q^{82} -0.944272 q^{83} +2.00000 q^{85} +(10.0000 + 17.3205i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.76393 - 4.78727i) q^{88} +(-1.00000 - 1.73205i) q^{89} +2.23607 q^{90} +12.0000 q^{92} +(5.23607 + 9.06914i) q^{93} +(-5.52786 + 9.57454i) q^{94} +(3.23607 - 5.60503i) q^{95} +(3.35410 + 5.80948i) q^{96} +0.472136 q^{97} -2.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 6 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 6 * q^4 - 2 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} - 6 q^{4} - 2 q^{5} - 2 q^{9} - 4 q^{11} - 6 q^{12} + 4 q^{15} + 2 q^{16} - 4 q^{17} + 4 q^{19} + 12 q^{20} - 40 q^{22} - 8 q^{23} - 2 q^{25} - 20 q^{26} + 4 q^{27} - 8 q^{29} + 12 q^{31} - 4 q^{33} + 12 q^{36} - 4 q^{37} + 20 q^{38} + 8 q^{41} - 12 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} - 4 q^{51} + 16 q^{53} + 8 q^{55} - 8 q^{57} - 6 q^{60} - 4 q^{61} - 40 q^{62} - 52 q^{64} + 20 q^{66} + 8 q^{67} - 12 q^{68} + 16 q^{69} + 40 q^{71} - 16 q^{73} - 40 q^{74} - 2 q^{75} - 24 q^{76} + 40 q^{78} - 8 q^{79} + 2 q^{80} - 2 q^{81} + 32 q^{83} + 8 q^{85} + 40 q^{86} + 4 q^{87} + 20 q^{88} - 4 q^{89} + 48 q^{92} + 12 q^{93} - 40 q^{94} + 4 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 6 * q^4 - 2 * q^5 - 2 * q^9 - 4 * q^11 - 6 * q^12 + 4 * q^15 + 2 * q^16 - 4 * q^17 + 4 * q^19 + 12 * q^20 - 40 * q^22 - 8 * q^23 - 2 * q^25 - 20 * q^26 + 4 * q^27 - 8 * q^29 + 12 * q^31 - 4 * q^33 + 12 * q^36 - 4 * q^37 + 20 * q^38 + 8 * q^41 - 12 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 - 4 * q^51 + 16 * q^53 + 8 * q^55 - 8 * q^57 - 6 * q^60 - 4 * q^61 - 40 * q^62 - 52 * q^64 + 20 * q^66 + 8 * q^67 - 12 * q^68 + 16 * q^69 + 40 * q^71 - 16 * q^73 - 40 * q^74 - 2 * q^75 - 24 * q^76 + 40 * q^78 - 8 * q^79 + 2 * q^80 - 2 * q^81 + 32 * q^83 + 8 * q^85 + 40 * q^86 + 4 * q^87 + 20 * q^88 - 4 * q^89 + 48 * q^92 + 12 * q^93 - 40 * q^94 + 4 * q^95 - 16 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.11803	−	1.93649i	−0.790569	−	1.36931i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.11803	−	1.93649i	−0.790569	−	1.36931i	0.135045	−	0.990839i	$-0.456882\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.50000	+	2.59808i	−0.750000	+	1.29904i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.23607			0.912871
$7$		0			0
$7$		0			0
$8$	2.23607			0.790569
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.11803	+	1.93649i	−0.353553	+	0.612372i
$11$	1.23607	−	2.14093i	0.372689	−	0.645515i	−0.617290	−	0.786736i	$-0.711769\pi$
$11$	1.23607	−	2.14093i	0.372689	−	0.645515i	0.989978	+	0.141221i	$0.0451027\pi$
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	4.47214			1.24035			0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214			1.24035			0.620174	+	0.784465i	$0.287062\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−1.11803	+	1.93649i	−0.263523	+	0.456435i
$19$	3.23607	+	5.60503i	0.742405	+	1.28588i	0.951397	+	0.307966i	$0.0996482\pi$
$19$	3.23607	+	5.60503i	0.742405	+	1.28588i	−0.208993	+	0.977917i	$0.567018\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	−5.52786			−1.17854
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−1.11803	+	1.93649i	−0.228218	+	0.395285i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−5.00000	−	8.66025i	−0.980581	−	1.69842i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−1.11803	−	1.93649i	−0.204124	−	0.353553i
$31$	5.23607	−	9.06914i	0.940426	−	1.62886i	0.175764	−	0.984432i	$-0.443760\pi$
$31$	5.23607	−	9.06914i	0.940426	−	1.62886i	0.764661	−	0.644433i	$-0.222906\pi$
$32$	3.35410	−	5.80948i	0.592927	−	1.02698i
$33$	1.23607	+	2.14093i	0.215172	+	0.372689i
$34$	4.47214			0.766965
$35$		0			0
$36$	3.00000			0.500000
$37$	−5.47214	−	9.47802i	−0.899614	−	1.55818i	−0.827989	−	0.560745i	$-0.810515\pi$
$37$	−5.47214	−	9.47802i	−0.899614	−	1.55818i	−0.0716249	−	0.997432i	$-0.522818\pi$
$38$	7.23607	−	12.5332i	1.17385	−	2.03316i
$39$	−2.23607	+	3.87298i	−0.358057	+	0.620174i
$40$	−1.11803	−	1.93649i	−0.176777	−	0.306186i
$41$	2.00000			0.312348			0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000			0.312348			0.156174	+	0.987730i	$0.450084\pi$
$42$		0			0
$43$	−8.94427			−1.36399			−0.681994	−	0.731357i	$-0.738887\pi$
$43$	−8.94427			−1.36399			−0.681994	+	0.731357i	$0.738887\pi$
$44$	3.70820	+	6.42280i	0.559033	+	0.968273i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−4.47214	+	7.74597i	−0.659380	+	1.14208i
$47$	−2.47214	−	4.28187i	−0.360598	−	0.624574i	0.627461	−	0.778648i	$-0.284094\pi$
$47$	−2.47214	−	4.28187i	−0.360598	−	0.624574i	−0.988059	+	0.154074i	$0.950761\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	2.23607			0.316228
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	−6.70820	+	11.6190i	−0.930261	+	1.61126i
$53$	6.23607	−	10.8012i	0.856590	−	1.48366i	−0.0185724	−	0.999828i	$-0.505912\pi$
$53$	6.23607	−	10.8012i	0.856590	−	1.48366i	0.875162	−	0.483830i	$-0.160755\pi$
$54$	−1.11803	−	1.93649i	−0.152145	−	0.263523i
$55$	−2.47214			−0.333343
$56$		0			0
$57$	−6.47214			−0.857255
$58$	2.23607	+	3.87298i	0.293610	+	0.508548i
$59$	4.47214	−	7.74597i	0.582223	−	1.00844i	−0.412993	−	0.910734i	$-0.635517\pi$
$59$	4.47214	−	7.74597i	0.582223	−	1.00844i	0.995215	−	0.0977047i	$-0.0311501\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−23.4164			−2.97389
$63$		0			0
$64$	−13.0000			−1.62500
$65$	−2.23607	−	3.87298i	−0.277350	−	0.480384i
$66$	2.76393	−	4.78727i	0.340217	−	0.589272i
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	4.00000			0.481543
$70$		0			0
$71$	14.4721			1.71753			0.858763	−	0.512373i	$-0.171233\pi$
$71$	14.4721			1.71753			0.858763	+	0.512373i	$0.171233\pi$
$72$	−1.11803	−	1.93649i	−0.131762	−	0.228218i
$73$	−1.76393	+	3.05522i	−0.206453	+	0.357586i	−0.950595	−	0.310435i	$-0.899525\pi$
$73$	−1.76393	+	3.05522i	−0.206453	+	0.357586i	0.744142	+	0.668022i	$0.232859\pi$
$74$	−12.2361	+	21.1935i	−1.42241	+	2.46369i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−19.4164			−2.22721
$77$		0			0
$78$	10.0000			1.13228
$79$	2.47214	+	4.28187i	0.278137	+	0.481747i	0.970922	−	0.239397i	$-0.0769497\pi$
$79$	2.47214	+	4.28187i	0.278137	+	0.481747i	−0.692785	+	0.721144i	$0.743616\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.23607	−	3.87298i	−0.246932	−	0.427699i
$83$	−0.944272			−0.103647			−0.0518237	−	0.998656i	$-0.516503\pi$
$83$	−0.944272			−0.103647			−0.0518237	+	0.998656i	$0.516503\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	10.0000	+	17.3205i	1.07833	+	1.86772i
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$	2.76393	−	4.78727i	0.294636	−	0.510325i
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	0.808146	−	0.588982i	$-0.200471\pi$
$89$	−1.00000	−	1.73205i	−0.106000	−	0.183597i	−0.914146	+	0.405385i	$0.867138\pi$
$90$	2.23607			0.235702
$91$		0			0
$92$	12.0000			1.25109
$93$	5.23607	+	9.06914i	0.542955	+	0.940426i
$94$	−5.52786	+	9.57454i	−0.570156	+	0.987539i
$95$	3.23607	−	5.60503i	0.332014	−	0.575064i
$96$	3.35410	+	5.80948i	0.342327	+	0.592927i
$97$	0.472136			0.0479381			0.0239691	−	0.999713i	$-0.492370\pi$
$97$	0.472136			0.0479381			0.0239691	+	0.999713i	$0.492370\pi$
$98$		0			0
$99$	−2.47214			−0.248459
$100$	−1.50000	−	2.59808i	−0.150000	−	0.259808i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	−2.23607	+	3.87298i	−0.221404	+	0.383482i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	10.0000			0.980581
$105$		0			0
$106$	−27.8885			−2.70877
$107$	−2.47214	−	4.28187i	−0.238990	−	0.413944i	0.721434	−	0.692483i	$-0.243483\pi$
$107$	−2.47214	−	4.28187i	−0.238990	−	0.413944i	−0.960425	+	0.278539i	$0.910150\pi$
$108$	−1.50000	+	2.59808i	−0.144338	+	0.250000i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	2.76393	+	4.78727i	0.263531	+	0.456448i
$111$	10.9443			1.03878
$112$		0			0
$113$	−8.47214			−0.796992			−0.398496	−	0.917170i	$-0.630468\pi$
$113$	−8.47214			−0.796992			−0.398496	+	0.917170i	$0.630468\pi$
$114$	7.23607	+	12.5332i	0.677720	+	1.17385i
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−2.23607	−	3.87298i	−0.206725	−	0.358057i
$118$	−20.0000			−1.84115
$119$		0			0
$120$	2.23607			0.204124
$121$	2.44427	+	4.23360i	0.222207	+	0.384873i
$122$	−2.23607	+	3.87298i	−0.202444	+	0.350643i
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$	15.7082	+	27.2074i	1.41064	+	2.44330i
$125$	1.00000			0.0894427
$126$		0			0
$127$	12.9443			1.14862			0.574309	−	0.818638i	$-0.305271\pi$
$127$	12.9443			1.14862			0.574309	+	0.818638i	$0.305271\pi$
$128$	7.82624	+	13.5554i	0.691748	+	1.19814i
$129$	4.47214	−	7.74597i	0.393750	−	0.681994i
$130$	−5.00000	+	8.66025i	−0.438529	+	0.759555i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$	−7.41641			−0.645515
$133$		0			0
$134$	−8.94427			−0.772667
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−2.23607	+	3.87298i	−0.191741	+	0.332106i
$137$	−6.23607	+	10.8012i	−0.532783	+	0.922808i	0.466484	+	0.884530i	$0.345521\pi$
$137$	−6.23607	+	10.8012i	−0.532783	+	0.922808i	−0.999267	+	0.0382780i	$0.987813\pi$
$138$	−4.47214	−	7.74597i	−0.380693	−	0.659380i
$139$	19.4164			1.64688			0.823439	−	0.567405i	$-0.192052\pi$
$139$	19.4164			1.64688			0.823439	+	0.567405i	$0.192052\pi$
$140$		0			0
$141$	4.94427			0.416383
$142$	−16.1803	−	28.0252i	−1.35782	−	2.35182i
$143$	5.52786	−	9.57454i	0.462263	−	0.800663i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$	7.88854			0.652861
$147$		0			0
$148$	32.8328			2.69884
$149$	−1.47214	−	2.54981i	−0.120602	−	0.208889i	0.799403	−	0.600795i	$-0.205149\pi$
$149$	−1.47214	−	2.54981i	−0.120602	−	0.208889i	−0.920005	+	0.391906i	$0.871816\pi$
$150$	−1.11803	+	1.93649i	−0.0912871	+	0.158114i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	7.23607	+	12.5332i	0.586923	+	1.01658i
$153$	2.00000			0.161690
$154$		0			0
$155$	−10.4721			−0.841142
$156$	−6.70820	−	11.6190i	−0.537086	−	0.930261i
$157$	4.23607	−	7.33708i	0.338075	−	0.585563i	−0.645996	−	0.763341i	$-0.723558\pi$
$157$	4.23607	−	7.33708i	0.338075	−	0.585563i	0.984071	+	0.177778i	$0.0568909\pi$
$158$	5.52786	−	9.57454i	0.439773	−	0.761710i
$159$	6.23607	+	10.8012i	0.494552	+	0.856590i
$160$	−6.70820			−0.530330
$161$		0			0
$162$	2.23607			0.175682
$163$	−0.472136	−	0.817763i	−0.0369805	−	0.0640522i	0.846943	−	0.531684i	$-0.178441\pi$
$163$	−0.472136	−	0.817763i	−0.0369805	−	0.0640522i	−0.883923	+	0.467632i	$0.845107\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	1.23607	−	2.14093i	0.0962278	−	0.166671i
$166$	1.05573	+	1.82857i	0.0819404	+	0.141925i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	7.00000			0.538462
$170$	−2.23607	−	3.87298i	−0.171499	−	0.297044i
$171$	3.23607	−	5.60503i	0.247468	−	0.428628i
$172$	13.4164	−	23.2379i	1.02299	−	1.77187i
$173$	7.47214	+	12.9421i	0.568096	+	0.983971i	0.996754	+	0.0805044i	$0.0256531\pi$
$173$	7.47214	+	12.9421i	0.568096	+	0.983971i	−0.428658	+	0.903467i	$0.641014\pi$
$174$	−4.47214			−0.339032
$175$		0			0
$176$	2.47214			0.186344
$177$	4.47214	+	7.74597i	0.336146	+	0.582223i
$178$	−2.23607	+	3.87298i	−0.167600	+	0.290292i
$179$	1.23607	−	2.14093i	0.0923881	−	0.160021i	−0.816127	−	0.577872i	$-0.803883\pi$
$179$	1.23607	−	2.14093i	0.0923881	−	0.160021i	0.908516	+	0.417851i	$0.137217\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−18.9443			−1.40812			−0.704058	−	0.710142i	$-0.748631\pi$
$181$	−18.9443			−1.40812			−0.704058	+	0.710142i	$0.748631\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$	−4.47214	−	7.74597i	−0.329690	−	0.571040i
$185$	−5.47214	+	9.47802i	−0.402319	+	0.696838i
$186$	11.7082	−	20.2792i	0.858487	−	1.48694i
$187$	2.47214	+	4.28187i	0.180780	+	0.313121i
$188$	14.8328			1.08179
$189$		0			0
$190$	−14.4721			−1.04992
$191$	−13.7082	−	23.7433i	−0.991891	−	1.71801i	−0.606011	−	0.795456i	$-0.707231\pi$
$191$	−13.7082	−	23.7433i	−0.991891	−	1.71801i	−0.385880	−	0.922549i	$-0.626102\pi$
$192$	6.50000	−	11.2583i	0.469097	−	0.812500i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−0.527864	−	0.914287i	−0.0378984	−	0.0656420i
$195$	4.47214			0.320256
$196$		0			0
$197$	24.4721			1.74357			0.871784	−	0.489891i	$-0.162963\pi$
$197$	24.4721			1.74357			0.871784	+	0.489891i	$0.162963\pi$
$198$	2.76393	+	4.78727i	0.196424	+	0.340217i
$199$	0.291796	−	0.505406i	0.0206849	−	0.0358273i	−0.855498	−	0.517807i	$-0.826749\pi$
$199$	0.291796	−	0.505406i	0.0206849	−	0.0358273i	0.876183	+	0.481979i	$0.160082\pi$
$200$	−1.11803	+	1.93649i	−0.0790569	+	0.136931i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	31.3050			2.20261
$203$		0			0
$204$	6.00000			0.420084
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$		0			0
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$	2.23607	+	3.87298i	0.155043	+	0.268543i
$209$	16.0000			1.10674
$210$		0			0
$211$	0.944272			0.0650064			0.0325032	−	0.999472i	$-0.489652\pi$
$211$	0.944272			0.0650064			0.0325032	+	0.999472i	$0.489652\pi$
$212$	18.7082	+	32.4036i	1.28488	+	2.22549i
$213$	−7.23607	+	12.5332i	−0.495807	+	0.858763i
$214$	−5.52786	+	9.57454i	−0.377877	+	0.654502i
$215$	4.47214	+	7.74597i	0.304997	+	0.528271i
$216$	2.23607			0.152145
$217$		0			0
$218$	−4.47214			−0.302891
$219$	−1.76393	−	3.05522i	−0.119195	−	0.206453i
$220$	3.70820	−	6.42280i	0.250007	−	0.433025i
$221$	−4.47214	+	7.74597i	−0.300828	+	0.521050i
$222$	−12.2361	−	21.1935i	−0.821231	−	1.42241i
$223$	−4.94427			−0.331093			−0.165546	−	0.986202i	$-0.552939\pi$
$223$	−4.94427			−0.331093			−0.165546	+	0.986202i	$0.552939\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	9.47214	+	16.4062i	0.630077	+	1.09133i
$227$	−8.47214	+	14.6742i	−0.562315	+	0.973959i	0.434978	+	0.900441i	$0.356756\pi$
$227$	−8.47214	+	14.6742i	−0.562315	+	0.973959i	−0.997294	+	0.0735180i	$0.976577\pi$
$228$	9.70820	−	16.8151i	0.642942	−	1.11361i
$229$	−5.94427	−	10.2958i	−0.392809	−	0.680364i	0.600010	−	0.799992i	$-0.295163\pi$
$229$	−5.94427	−	10.2958i	−0.392809	−	0.680364i	−0.992819	+	0.119628i	$0.961830\pi$
$230$	8.94427			0.589768
$231$		0			0
$232$	−4.47214			−0.293610
$233$	−8.70820	−	15.0831i	−0.570493	−	0.988124i	−0.996515	−	0.0834107i	$-0.973419\pi$
$233$	−8.70820	−	15.0831i	−0.570493	−	0.988124i	0.426022	−	0.904713i	$-0.359915\pi$
$234$	−5.00000	+	8.66025i	−0.326860	+	0.566139i
$235$	−2.47214	+	4.28187i	−0.161264	+	0.279318i
$236$	13.4164	+	23.2379i	0.873334	+	1.51266i
$237$	−4.94427			−0.321165
$238$		0			0
$239$	−1.52786			−0.0988293			−0.0494147	−	0.998778i	$-0.515736\pi$
$239$	−1.52786			−0.0988293			−0.0494147	+	0.998778i	$0.515736\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−0.527864	+	0.914287i	−0.0340027	+	0.0588944i	−0.882526	−	0.470264i	$-0.844159\pi$
$241$	−0.527864	+	0.914287i	−0.0340027	+	0.0588944i	0.848523	+	0.529158i	$0.177492\pi$
$242$	5.46556	−	9.46662i	0.351339	−	0.608538i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.00000			0.384111
$245$		0			0
$246$	4.47214			0.285133
$247$	14.4721	+	25.0665i	0.920840	+	1.59494i
$248$	11.7082	−	20.2792i	0.743472	−	1.28773i
$249$	0.472136	−	0.817763i	0.0299204	−	0.0518237i
$250$	−1.11803	−	1.93649i	−0.0707107	−	0.122474i
$251$	0.944272			0.0596019			0.0298010	−	0.999556i	$-0.490513\pi$
$251$	0.944272			0.0596019			0.0298010	+	0.999556i	$0.490513\pi$
$252$		0			0
$253$	−9.88854			−0.621687
$254$	−14.4721	−	25.0665i	−0.908063	−	1.57281i
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$	4.50000	−	7.79423i	0.281250	−	0.487139i
$257$	0.527864	+	0.914287i	0.0329273	+	0.0570317i	0.882019	−	0.471213i	$-0.156184\pi$
$257$	0.527864	+	0.914287i	0.0329273	+	0.0570317i	−0.849092	+	0.528245i	$0.822850\pi$
$258$	−20.0000			−1.24515
$259$		0			0
$260$	13.4164			0.832050
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	4.47214	−	7.74597i	0.276289	−	0.478547i
$263$	−12.4721	+	21.6024i	−0.769065	+	1.33206i	0.169006	+	0.985615i	$0.445944\pi$
$263$	−12.4721	+	21.6024i	−0.769065	+	1.33206i	−0.938071	+	0.346444i	$0.887389\pi$
$264$	2.76393	+	4.78727i	0.170108	+	0.294636i
$265$	−12.4721			−0.766157
$266$		0			0
$267$	2.00000			0.122398
$268$	6.00000	+	10.3923i	0.366508	+	0.634811i
$269$	−11.9443	+	20.6881i	−0.728255	+	1.26137i	0.229365	+	0.973340i	$0.426335\pi$
$269$	−11.9443	+	20.6881i	−0.728255	+	1.26137i	−0.957620	+	0.288034i	$0.906998\pi$
$270$	−1.11803	+	1.93649i	−0.0680414	+	0.117851i
$271$	−5.23607	−	9.06914i	−0.318068	−	0.550911i	0.662017	−	0.749489i	$-0.269701\pi$
$271$	−5.23607	−	9.06914i	−0.318068	−	0.550911i	−0.980085	+	0.198578i	$0.936368\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	27.8885			1.68481
$275$	1.23607	+	2.14093i	0.0745377	+	0.129103i
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	−0.527864	+	0.914287i	−0.0317163	+	0.0549342i	−0.881448	−	0.472281i	$-0.843431\pi$
$277$	−0.527864	+	0.914287i	−0.0317163	+	0.0549342i	0.849732	+	0.527216i	$0.176764\pi$
$278$	−21.7082	−	37.5997i	−1.30197	−	2.25508i
$279$	−10.4721			−0.626950
$280$		0			0
$281$	6.94427			0.414261			0.207130	−	0.978313i	$-0.433588\pi$
$281$	6.94427			0.414261			0.207130	+	0.978313i	$0.433588\pi$
$282$	−5.52786	−	9.57454i	−0.329180	−	0.570156i
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	−0.630738	−	0.775996i	$-0.717248\pi$
$283$	6.00000	−	10.3923i	0.356663	−	0.617758i	0.987401	+	0.158237i	$0.0505811\pi$
$284$	−21.7082	+	37.5997i	−1.28814	+	2.23113i
$285$	3.23607	+	5.60503i	0.191688	+	0.332014i
$286$	−24.7214			−1.46180
$287$		0			0
$288$	−6.70820			−0.395285
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	2.23607	−	3.87298i	0.131306	−	0.227429i
$291$	−0.236068	+	0.408882i	−0.0138385	+	0.0239691i
$292$	−5.29180	−	9.16566i	−0.309679	−	0.536380i
$293$	−22.9443			−1.34042			−0.670209	−	0.742172i	$-0.733796\pi$
$293$	−22.9443			−1.34042			−0.670209	+	0.742172i	$0.733796\pi$
$294$		0			0
$295$	−8.94427			−0.520756
$296$	−12.2361	−	21.1935i	−0.711207	−	1.23185i
$297$	1.23607	−	2.14093i	0.0717239	−	0.124230i
$298$	−3.29180	+	5.70156i	−0.190689	+	0.330282i
$299$	−8.94427	−	15.4919i	−0.517261	−	0.895922i
$300$	3.00000			0.173205
$301$		0			0
$302$	−35.7771			−2.05874
$303$	−7.00000	−	12.1244i	−0.402139	−	0.696526i
$304$	−3.23607	+	5.60503i	−0.185601	+	0.321471i
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$	−2.23607	−	3.87298i	−0.127827	−	0.221404i
$307$	32.9443			1.88023			0.940114	−	0.340859i	$-0.110718\pi$
$307$	32.9443			1.88023			0.940114	+	0.340859i	$0.110718\pi$
$308$		0			0
$309$		0			0
$310$	11.7082	+	20.2792i	0.664981	+	1.15178i
$311$	−4.94427	+	8.56373i	−0.280364	+	0.485605i	−0.971474	−	0.237145i	$-0.923788\pi$
$311$	−4.94427	+	8.56373i	−0.280364	+	0.485605i	0.691110	+	0.722749i	$0.257122\pi$
$312$	−5.00000	+	8.66025i	−0.283069	+	0.490290i
$313$	4.70820	+	8.15485i	0.266123	+	0.460939i	0.967857	−	0.251500i	$-0.0809238\pi$
$313$	4.70820	+	8.15485i	0.266123	+	0.460939i	−0.701734	+	0.712439i	$0.747590\pi$
$314$	−18.9443			−1.06909
$315$		0			0
$316$	−14.8328			−0.834411
$317$	15.1803	+	26.2931i	0.852613	+	1.47677i	0.878842	+	0.477113i	$0.158317\pi$
$317$	15.1803	+	26.2931i	0.852613	+	1.47677i	−0.0262292	+	0.999656i	$0.508350\pi$
$318$	13.9443	−	24.1522i	0.781956	−	1.35439i
$319$	−2.47214	+	4.28187i	−0.138413	+	0.239738i
$320$	6.50000	+	11.2583i	0.363361	+	0.629360i
$321$	4.94427			0.275962
$322$		0			0
$323$	−12.9443			−0.720239
$324$	−1.50000	−	2.59808i	−0.0833333	−	0.144338i
$325$	−2.23607	+	3.87298i	−0.124035	+	0.214834i
$326$	−1.05573	+	1.82857i	−0.0584714	+	0.101275i
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	4.47214			0.246932
$329$		0			0
$330$	−5.52786			−0.304299
$331$	8.47214	+	14.6742i	0.465671	+	0.806565i	0.999232	−	0.0391964i	$-0.0124798\pi$
$331$	8.47214	+	14.6742i	0.465671	+	0.806565i	−0.533561	+	0.845762i	$0.679146\pi$
$332$	1.41641	−	2.45329i	0.0777355	−	0.134642i
$333$	−5.47214	+	9.47802i	−0.299871	+	0.519392i
$334$	−8.94427	−	15.4919i	−0.489409	−	0.847681i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	11.8885			0.647610			0.323805	−	0.946124i	$-0.395038\pi$
$337$	11.8885			0.647610			0.323805	+	0.946124i	$0.395038\pi$
$338$	−7.82624	−	13.5554i	−0.425691	−	0.737319i
$339$	4.23607	−	7.33708i	0.230072	−	0.398496i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−12.9443	−	22.4201i	−0.700972	−	1.21412i
$342$	−14.4721			−0.782563
$343$		0			0
$344$	−20.0000			−1.07833
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$	16.7082	−	28.9395i	0.898239	−	1.55579i
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	−0.738458	−	0.674299i	$-0.764446\pi$
$347$	4.00000	−	6.92820i	0.214731	−	0.371925i	0.953189	+	0.302374i	$0.0977791\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−23.8885			−1.27872			−0.639362	−	0.768906i	$-0.720802\pi$
$349$	−23.8885			−1.27872			−0.639362	+	0.768906i	$0.720802\pi$
$350$		0			0
$351$	4.47214			0.238705
$352$	−8.29180	−	14.3618i	−0.441954	−	0.765487i
$353$	−13.9443	+	24.1522i	−0.742179	+	1.28549i	0.209323	+	0.977847i	$0.432874\pi$
$353$	−13.9443	+	24.1522i	−0.742179	+	1.28549i	−0.951501	+	0.307645i	$0.900459\pi$
$354$	10.0000	−	17.3205i	0.531494	−	0.920575i
$355$	−7.23607	−	12.5332i	−0.384051	−	0.665195i
$356$	6.00000			0.317999
$357$		0			0
$358$	−5.52786			−0.292157
$359$	−4.76393	−	8.25137i	−0.251431	−	0.435491i	0.712489	−	0.701683i	$-0.247568\pi$
$359$	−4.76393	−	8.25137i	−0.251431	−	0.435491i	−0.963920	+	0.266192i	$0.914234\pi$
$360$	−1.11803	+	1.93649i	−0.0589256	+	0.102062i
$361$	−11.4443	+	19.8221i	−0.602330	+	1.04327i
$362$	21.1803	+	36.6854i	1.11321	+	1.92814i
$363$	−4.88854			−0.256582
$364$		0			0
$365$	3.52786			0.184657
$366$	−2.23607	−	3.87298i	−0.116881	−	0.202444i
$367$	10.4721	−	18.1383i	0.546641	−	0.946810i	−0.451861	−	0.892089i	$-0.649240\pi$
$367$	10.4721	−	18.1383i	0.546641	−	0.946810i	0.998502	−	0.0547215i	$-0.0174271\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	−1.00000	−	1.73205i	−0.0520579	−	0.0901670i
$370$	24.4721			1.27225
$371$		0			0
$372$	−31.4164			−1.62886
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	0.777847	−	0.628454i	$-0.216312\pi$
$373$	−3.00000	−	5.19615i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$374$	5.52786	−	9.57454i	0.285839	−	0.495088i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−5.52786	−	9.57454i	−0.285078	−	0.493769i
$377$	−8.94427			−0.460653
$378$		0			0
$379$	−2.11146			−0.108458			−0.0542291	−	0.998529i	$-0.517270\pi$
$379$	−2.11146			−0.108458			−0.0542291	+	0.998529i	$0.517270\pi$
$380$	9.70820	+	16.8151i	0.498020	+	0.862597i
$381$	−6.47214	+	11.2101i	−0.331578	+	0.574309i
$382$	−30.6525	+	53.0916i	−1.56832	+	2.71640i
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	0.745548	−	0.666452i	$-0.232188\pi$
$383$	−4.00000	−	6.92820i	−0.204390	−	0.354015i	−0.949938	+	0.312437i	$0.898855\pi$
$384$	−15.6525			−0.798762
$385$		0			0
$386$	−31.3050			−1.59338
$387$	4.47214	+	7.74597i	0.227331	+	0.393750i
$388$	−0.708204	+	1.22665i	−0.0359536	+	0.0622735i
$389$	−5.47214	+	9.47802i	−0.277448	+	0.480555i	−0.970750	−	0.240093i	$-0.922822\pi$
$389$	−5.47214	+	9.47802i	−0.277448	+	0.480555i	0.693302	+	0.720648i	$0.256155\pi$
$390$	−5.00000	−	8.66025i	−0.253185	−	0.438529i
$391$	8.00000			0.404577
$392$		0			0
$393$	−4.00000			−0.201773
$394$	−27.3607	−	47.3901i	−1.37841	−	2.38748i
$395$	2.47214	−	4.28187i	0.124387	−	0.215444i
$396$	3.70820	−	6.42280i	0.186344	−	0.322758i
$397$	6.70820	+	11.6190i	0.336675	+	0.583138i	0.983805	−	0.179241i	$-0.0573643\pi$
$397$	6.70820	+	11.6190i	0.336675	+	0.583138i	−0.647130	+	0.762380i	$0.724031\pi$
$398$	−1.30495			−0.0654113
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	0.713751	−	0.700399i	$-0.246995\pi$
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	−0.963439	+	0.267927i	$0.913661\pi$
$402$	4.47214	−	7.74597i	0.223050	−	0.386334i
$403$	23.4164	−	40.5584i	1.16645	−	2.02036i
$404$	−21.0000	−	36.3731i	−1.04479	−	1.80963i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−27.0557			−1.34110
$408$	−2.23607	−	3.87298i	−0.110702	−	0.191741i
$409$	−11.9443	+	20.6881i	−0.590606	+	1.02296i	0.403545	+	0.914960i	$0.367778\pi$
$409$	−11.9443	+	20.6881i	−0.590606	+	1.02296i	−0.994151	+	0.108000i	$0.965555\pi$
$410$	−2.23607	+	3.87298i	−0.110432	+	0.191273i
$411$	−6.23607	−	10.8012i	−0.307603	−	0.532783i
$412$		0			0
$413$		0			0
$414$	8.94427			0.439587
$415$	0.472136	+	0.817763i	0.0231762	+	0.0401424i
$416$	15.0000	−	25.9808i	0.735436	−	1.27381i
$417$	−9.70820	+	16.8151i	−0.475413	+	0.823439i
$418$	−17.8885	−	30.9839i	−0.874957	−	1.51547i
$419$	−5.88854			−0.287674			−0.143837	−	0.989601i	$-0.545944\pi$
$419$	−5.88854			−0.287674			−0.143837	+	0.989601i	$0.545944\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−1.05573	−	1.82857i	−0.0513920	−	0.0890136i
$423$	−2.47214	+	4.28187i	−0.120199	+	0.208191i
$424$	13.9443	−	24.1522i	0.677194	−	1.17293i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	32.3607			1.56788
$427$		0			0
$428$	14.8328			0.716971
$429$	5.52786	+	9.57454i	0.266888	+	0.462263i
$430$	10.0000	−	17.3205i	0.482243	−	0.835269i
$431$	4.76393	−	8.25137i	0.229471	−	0.397455i	−0.728181	−	0.685385i	$-0.759634\pi$
$431$	4.76393	−	8.25137i	0.229471	−	0.397455i	0.957651	+	0.287930i	$0.0929672\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−7.52786			−0.361766			−0.180883	−	0.983505i	$-0.557896\pi$
$433$	−7.52786			−0.361766			−0.180883	+	0.983505i	$0.557896\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	12.9443	−	22.4201i	0.619208	−	1.07250i
$438$	−3.94427	+	6.83168i	−0.188465	+	0.326430i
$439$	5.23607	+	9.06914i	0.249904	+	0.432846i	0.963499	−	0.267712i	$-0.0862676\pi$
$439$	5.23607	+	9.06914i	0.249904	+	0.432846i	−0.713595	+	0.700558i	$0.752934\pi$
$440$	−5.52786			−0.263531
$441$		0			0
$442$	20.0000			0.951303
$443$	4.00000	+	6.92820i	0.190046	+	0.329169i	0.945265	−	0.326303i	$-0.105803\pi$
$443$	4.00000	+	6.92820i	0.190046	+	0.329169i	−0.755219	+	0.655472i	$0.772470\pi$
$444$	−16.4164	+	28.4341i	−0.779088	+	1.34942i
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$	5.52786	+	9.57454i	0.261752	+	0.453368i
$447$	2.94427			0.139259
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.11803	−	1.93649i	−0.0527046	−	0.0912871i
$451$	2.47214	−	4.28187i	0.116408	−	0.201625i
$452$	12.7082	−	22.0113i	0.597744	−	1.03532i
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$	37.8885			1.77820
$455$		0			0
$456$	−14.4721			−0.677720
$457$	5.47214	+	9.47802i	0.255976	+	0.443363i	0.965160	−	0.261660i	$-0.0842699\pi$
$457$	5.47214	+	9.47802i	0.255976	+	0.443363i	−0.709184	+	0.705023i	$0.750937\pi$
$458$	−13.2918	+	23.0221i	−0.621085	+	1.07575i
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$	−6.00000	−	10.3923i	−0.279751	−	0.484544i
$461$	31.8885			1.48520			0.742599	−	0.669737i	$-0.233593\pi$
$461$	31.8885			1.48520			0.742599	+	0.669737i	$0.233593\pi$
$462$		0			0
$463$	3.05573			0.142012			0.0710059	−	0.997476i	$-0.477379\pi$
$463$	3.05573			0.142012			0.0710059	+	0.997476i	$0.477379\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$	5.23607	−	9.06914i	0.242817	−	0.420571i
$466$	−19.4721	+	33.7267i	−0.902029	+	1.56236i
$467$	4.47214	+	7.74597i	0.206946	+	0.358441i	0.950751	−	0.309956i	$-0.100314\pi$
$467$	4.47214	+	7.74597i	0.206946	+	0.358441i	−0.743805	+	0.668397i	$0.766981\pi$
$468$	13.4164			0.620174
$469$		0			0
$470$	11.0557			0.509963
$471$	4.23607	+	7.33708i	0.195188	+	0.338075i
$472$	10.0000	−	17.3205i	0.460287	−	0.797241i
$473$	−11.0557	+	19.1491i	−0.508343	+	0.880476i
$474$	5.52786	+	9.57454i	0.253903	+	0.439773i
$475$	−6.47214			−0.296962
$476$		0			0
$477$	−12.4721			−0.571060
$478$	1.70820	+	2.95870i	0.0781314	+	0.135328i
$479$	8.94427	−	15.4919i	0.408674	−	0.707845i	−0.586067	−	0.810262i	$-0.699325\pi$
$479$	8.94427	−	15.4919i	0.408674	−	0.707845i	0.994741	+	0.102418i	$0.0326579\pi$
$480$	3.35410	−	5.80948i	0.153093	−	0.265165i
$481$	−24.4721	−	42.3870i	−1.11583	−	1.93268i
$482$	2.36068			0.107526
$483$		0			0
$484$	−14.6656			−0.666620
$485$	−0.236068	−	0.408882i	−0.0107193	−	0.0185664i
$486$	−1.11803	+	1.93649i	−0.0507151	+	0.0878410i
$487$	1.52786	−	2.64634i	0.0692341	−	0.119917i	−0.829330	−	0.558759i	$-0.811278\pi$
$487$	1.52786	−	2.64634i	0.0692341	−	0.119917i	0.898564	+	0.438842i	$0.144611\pi$
$488$	−2.23607	−	3.87298i	−0.101222	−	0.175322i
$489$	0.944272			0.0427015
$490$		0			0
$491$	41.3050			1.86407			0.932033	−	0.362373i	$-0.118033\pi$
$491$	41.3050			1.86407			0.932033	+	0.362373i	$0.118033\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$	32.3607	−	56.0503i	1.45598	−	2.52182i
$495$	1.23607	+	2.14093i	0.0555571	+	0.0962278i
$496$	10.4721			0.470213
$497$		0			0
$498$	−2.11146			−0.0946166
$499$	−10.9443	−	18.9560i	−0.489933	−	0.848589i	0.510000	−	0.860174i	$-0.329645\pi$
$499$	−10.9443	−	18.9560i	−0.489933	−	0.848589i	−0.999933	+	0.0115857i	$0.996312\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$	−1.05573	−	1.82857i	−0.0471195	−	0.0816133i
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	14.0000			0.622992
$506$	11.0557	+	19.1491i	0.491487	+	0.851281i
$507$	−3.50000	+	6.06218i	−0.155440	+	0.269231i
$508$	−19.4164	+	33.6302i	−0.861464	+	1.49210i
$509$	5.94427	+	10.2958i	0.263475	+	0.456352i	0.967163	−	0.254157i	$-0.0817979\pi$
$509$	5.94427	+	10.2958i	0.263475	+	0.456352i	−0.703688	+	0.710509i	$0.748465\pi$
$510$	4.47214			0.198030
$511$		0			0
$512$	11.1803			0.494106
$513$	3.23607	+	5.60503i	0.142876	+	0.247468i
$514$	1.18034	−	2.04441i	0.0520626	−	0.0901750i
$515$		0			0
$516$	13.4164	+	23.2379i	0.590624	+	1.02299i
$517$	−12.2229			−0.537563
$518$		0			0
$519$	−14.9443			−0.655981
$520$	−5.00000	−	8.66025i	−0.219265	−	0.379777i
$521$	7.94427	−	13.7599i	0.348045	−	0.602831i	−0.637857	−	0.770155i	$-0.720179\pi$
$521$	7.94427	−	13.7599i	0.348045	−	0.602831i	0.985902	+	0.167323i	$0.0535123\pi$
$522$	2.23607	−	3.87298i	0.0978700	−	0.169516i
$523$	4.47214	+	7.74597i	0.195553	+	0.338707i	0.947082	−	0.320993i	$-0.104017\pi$
$523$	4.47214	+	7.74597i	0.195553	+	0.338707i	−0.751529	+	0.659700i	$0.770683\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	55.7771			2.43200
$527$	10.4721	+	18.1383i	0.456173	+	0.790116i
$528$	−1.23607	+	2.14093i	−0.0537930	+	0.0931721i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	13.9443	+	24.1522i	0.605700	+	1.04910i
$531$	−8.94427			−0.388148
$532$		0			0
$533$	8.94427			0.387419
$534$	−2.23607	−	3.87298i	−0.0967641	−	0.167600i
$535$	−2.47214	+	4.28187i	−0.106880	+	0.185121i
$536$	4.47214	−	7.74597i	0.193167	−	0.334575i
$537$	1.23607	+	2.14093i	0.0533403	+	0.0923881i
$538$	53.4164			2.30294
$539$		0			0
$540$	3.00000			0.129099
$541$	−11.9443	−	20.6881i	−0.513524	−	0.889450i	−0.999877	−	0.0156876i	$-0.995006\pi$
$541$	−11.9443	−	20.6881i	−0.513524	−	0.889450i	0.486353	−	0.873763i	$-0.338327\pi$
$542$	−11.7082	+	20.2792i	−0.502910	+	0.871066i
$543$	9.47214	−	16.4062i	0.406488	−	0.704058i
$544$	6.70820	+	11.6190i	0.287612	+	0.498158i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−29.8885			−1.27794			−0.638971	−	0.769231i	$-0.720640\pi$
$547$	−29.8885			−1.27794			−0.638971	+	0.769231i	$0.720640\pi$
$548$	−18.7082	−	32.4036i	−0.799175	−	1.38421i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	2.76393	−	4.78727i	0.117854	−	0.204130i
$551$	−6.47214	−	11.2101i	−0.275722	−	0.477565i
$552$	8.94427			0.380693
$553$		0			0
$554$	2.36068			0.100296
$555$	−5.47214	−	9.47802i	−0.232279	−	0.402319i
$556$	−29.1246	+	50.4453i	−1.23516	+	2.13936i
$557$	−5.76393	+	9.98342i	−0.244226	+	0.423011i	−0.961914	−	0.273354i	$-0.911867\pi$
$557$	−5.76393	+	9.98342i	−0.244226	+	0.423011i	0.717688	+	0.696365i	$0.245200\pi$
$558$	11.7082	+	20.2792i	0.495648	+	0.858487i
$559$	−40.0000			−1.69182
$560$		0			0
$561$	−4.94427			−0.208747
$562$	−7.76393	−	13.4475i	−0.327502	−	0.567250i
$563$	−10.9443	+	18.9560i	−0.461246	+	0.798902i	−0.999023	−	0.0441853i	$-0.985931\pi$
$563$	−10.9443	+	18.9560i	−0.461246	+	0.798902i	0.537777	+	0.843087i	$0.319264\pi$
$564$	−7.41641	+	12.8456i	−0.312287	+	0.540897i
$565$	4.23607	+	7.33708i	0.178213	+	0.308673i
$566$	−26.8328			−1.12787
$567$		0			0
$568$	32.3607			1.35782
$569$	2.05573	+	3.56063i	0.0861806	+	0.149269i	0.905894	−	0.423505i	$-0.139200\pi$
$569$	2.05573	+	3.56063i	0.0861806	+	0.149269i	−0.819713	+	0.572774i	$0.805867\pi$
$570$	7.23607	−	12.5332i	0.303086	−	0.524960i
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	16.5836	+	28.7236i	0.693395	+	1.20100i
$573$	27.4164			1.14534
$574$		0			0
$575$	4.00000			0.166812
$576$	6.50000	+	11.2583i	0.270833	+	0.469097i
$577$	−17.1803	+	29.7572i	−0.715227	+	1.23881i	0.247645	+	0.968851i	$0.420343\pi$
$577$	−17.1803	+	29.7572i	−0.715227	+	1.23881i	−0.962872	+	0.269959i	$0.912990\pi$
$578$	14.5344	−	25.1744i	0.604553	−	1.04712i
$579$	7.00000	+	12.1244i	0.290910	+	0.503871i
$580$	−6.00000			−0.249136
$581$		0			0
$582$	1.05573			0.0437613
$583$	−15.4164	−	26.7020i	−0.638482	−	1.10588i
$584$	−3.94427	+	6.83168i	−0.163215	+	0.282697i
$585$	−2.23607	+	3.87298i	−0.0924500	+	0.160128i
$586$	25.6525	+	44.4314i	1.05969	+	1.83544i
$587$	4.00000			0.165098			0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000			0.165098			0.0825488	+	0.996587i	$0.473694\pi$
$588$		0			0
$589$	67.7771			2.79271
$590$	10.0000	+	17.3205i	0.411693	+	0.713074i
$591$	−12.2361	+	21.1935i	−0.503325	+	0.871784i
$592$	5.47214	−	9.47802i	0.224903	−	0.389544i
$593$	−5.94427	−	10.2958i	−0.244102	−	0.422797i	0.717777	−	0.696273i	$-0.245160\pi$
$593$	−5.94427	−	10.2958i	−0.244102	−	0.422797i	−0.961879	+	0.273476i	$0.911827\pi$
$594$	−5.52786			−0.226811
$595$		0			0
$596$	8.83282			0.361806
$597$	0.291796	+	0.505406i	0.0119424	+	0.0206849i
$598$	−20.0000	+	34.6410i	−0.817861	+	1.41658i
$599$	16.1803	−	28.0252i	0.661111	−	1.14508i	−0.319213	−	0.947683i	$-0.603419\pi$
$599$	16.1803	−	28.0252i	0.661111	−	1.14508i	0.980324	−	0.197395i	$-0.0632480\pi$
$600$	−1.11803	−	1.93649i	−0.0456435	−	0.0790569i
$601$	−21.0557			−0.858881			−0.429441	−	0.903095i	$-0.641289\pi$
$601$	−21.0557			−0.858881			−0.429441	+	0.903095i	$0.641289\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	24.0000	+	41.5692i	0.976546	+	1.69143i
$605$	2.44427	−	4.23360i	0.0993738	−	0.172120i
$606$	−15.6525	+	27.1109i	−0.635838	+	1.10130i
$607$	−7.41641	−	12.8456i	−0.301023	−	0.521387i	0.675345	−	0.737502i	$-0.263995\pi$
$607$	−7.41641	−	12.8456i	−0.301023	−	0.521387i	−0.976368	+	0.216115i	$0.930661\pi$
$608$	43.4164			1.76077
$609$		0			0
$610$	4.47214			0.181071
$611$	−11.0557	−	19.1491i	−0.447267	−	0.774689i
$612$	−3.00000	+	5.19615i	−0.121268	+	0.210042i
$613$	−5.47214	+	9.47802i	−0.221017	+	0.382814i	−0.955117	−	0.296228i	$-0.904271\pi$
$613$	−5.47214	+	9.47802i	−0.221017	+	0.382814i	0.734100	+	0.679042i	$0.237604\pi$
$614$	−36.8328	−	63.7963i	−1.48645	−	2.57461i
$615$	2.00000			0.0806478
$616$		0			0
$617$	7.52786			0.303060			0.151530	−	0.988453i	$-0.451580\pi$
$617$	7.52786			0.303060			0.151530	+	0.988453i	$0.451580\pi$
$618$		0			0
$619$	6.29180	−	10.8977i	0.252889	−	0.438016i	−0.711431	−	0.702756i	$-0.751953\pi$
$619$	6.29180	−	10.8977i	0.252889	−	0.438016i	0.964320	+	0.264740i	$0.0852860\pi$
$620$	15.7082	−	27.2074i	0.630857	−	1.09268i
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	22.1115			0.886589
$623$		0			0
$624$	−4.47214			−0.179029
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.5279	−	18.2348i	0.420778	−	0.728809i
$627$	−8.00000	+	13.8564i	−0.319489	+	0.553372i
$628$	12.7082	+	22.0113i	0.507113	+	0.878345i
$629$	21.8885			0.872753
$630$		0			0
$631$	−22.8328			−0.908960			−0.454480	−	0.890757i	$-0.650175\pi$
$631$	−22.8328			−0.908960			−0.454480	+	0.890757i	$0.650175\pi$
$632$	5.52786	+	9.57454i	0.219887	+	0.380855i
$633$	−0.472136	+	0.817763i	−0.0187657	+	0.0325032i
$634$	33.9443	−	58.7932i	1.34810	−	2.33498i
$635$	−6.47214	−	11.2101i	−0.256839	−	0.444858i
$636$	−37.4164			−1.48366
$637$		0			0
$638$	11.0557			0.437700
$639$	−7.23607	−	12.5332i	−0.286254	−	0.495807i
$640$	7.82624	−	13.5554i	0.309359	−	0.535826i
$641$	18.4164	−	31.8982i	0.727404	−	1.25990i	−0.230572	−	0.973055i	$-0.574060\pi$
$641$	18.4164	−	31.8982i	0.727404	−	1.25990i	0.957977	−	0.286846i	$-0.0926068\pi$
$642$	−5.52786	−	9.57454i	−0.218167	−	0.377877i
$643$	32.9443			1.29920			0.649598	−	0.760278i	$-0.274937\pi$
$643$	32.9443			1.29920			0.649598	+	0.760278i	$0.274937\pi$
$644$		0			0
$645$	−8.94427			−0.352180
$646$	14.4721	+	25.0665i	0.569399	+	0.986227i
$647$	16.9443	−	29.3483i	0.666148	−	1.15380i	−0.312825	−	0.949811i	$-0.601275\pi$
$647$	16.9443	−	29.3483i	0.666148	−	1.15380i	0.978973	−	0.203991i	$-0.0653915\pi$
$648$	−1.11803	+	1.93649i	−0.0439205	+	0.0760726i
$649$	−11.0557	−	19.1491i	−0.433975	−	0.751667i
$650$	10.0000			0.392232
$651$		0			0
$652$	2.83282			0.110942
$653$	24.7082	+	42.7959i	0.966907	+	1.67473i	0.704403	+	0.709801i	$0.251215\pi$
$653$	24.7082	+	42.7959i	0.966907	+	1.67473i	0.262504	+	0.964931i	$0.415452\pi$
$654$	2.23607	−	3.87298i	0.0874372	−	0.151446i
$655$	2.00000	−	3.46410i	0.0781465	−	0.135354i
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$	3.52786			0.137635
$658$		0			0
$659$	−41.3050			−1.60901			−0.804506	−	0.593944i	$-0.797570\pi$
$659$	−41.3050			−1.60901			−0.804506	+	0.593944i	$0.797570\pi$
$660$	3.70820	+	6.42280i	0.144342	+	0.250007i
$661$	−0.0557281	+	0.0965239i	−0.00216757	+	0.00375434i	−0.867107	−	0.498122i	$-0.834023\pi$
$661$	−0.0557281	+	0.0965239i	−0.00216757	+	0.00375434i	0.864940	+	0.501876i	$0.167357\pi$
$662$	18.9443	−	32.8124i	0.736290	−	1.27529i
$663$	−4.47214	−	7.74597i	−0.173683	−	0.300828i
$664$	−2.11146			−0.0819404
$665$		0			0
$666$	24.4721			0.948276
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−12.0000	+	20.7846i	−0.464294	+	0.804181i
$669$	2.47214	−	4.28187i	0.0955783	−	0.165546i
$670$	4.47214	+	7.74597i	0.172774	+	0.299253i
$671$	−4.94427			−0.190872
$672$		0			0
$673$	−44.8328			−1.72818			−0.864089	−	0.503339i	$-0.832105\pi$
$673$	−44.8328			−1.72818			−0.864089	+	0.503339i	$0.832105\pi$
$674$	−13.2918	−	23.0221i	−0.511981	−	0.886777i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−10.5000	+	18.1865i	−0.403846	+	0.699482i
$677$	19.4721	+	33.7267i	0.748375	+	1.29622i	0.948601	+	0.316474i	$0.102499\pi$
$677$	19.4721	+	33.7267i	0.748375	+	1.29622i	−0.200226	+	0.979750i	$0.564168\pi$
$678$	−18.9443			−0.727550
$679$		0			0
$680$	4.47214			0.171499
$681$	−8.47214	−	14.6742i	−0.324653	−	0.562315i
$682$	−28.9443	+	50.1329i	−1.10833	+	1.91969i
$683$	−16.9443	+	29.3483i	−0.648355	+	1.12298i	0.335161	+	0.942161i	$0.391209\pi$
$683$	−16.9443	+	29.3483i	−0.648355	+	1.12298i	−0.983516	+	0.180822i	$0.942124\pi$
$684$	9.70820	+	16.8151i	0.371202	+	0.642942i
$685$	12.4721			0.476536
$686$		0			0
$687$	11.8885			0.453576
$688$	−4.47214	−	7.74597i	−0.170499	−	0.295312i
$689$	27.8885	−	48.3044i	1.06247	−	1.84025i
$690$	−4.47214	+	7.74597i	−0.170251	+	0.294884i
$691$	−0.180340	−	0.312358i	−0.00686045	−	0.0118827i	0.862575	−	0.505930i	$-0.168850\pi$
$691$	−0.180340	−	0.312358i	−0.00686045	−	0.0118827i	−0.869435	+	0.494047i	$0.835517\pi$
$692$	−44.8328			−1.70429
$693$		0			0
$694$	−17.8885			−0.679040
$695$	−9.70820	−	16.8151i	−0.368253	−	0.637833i
$696$	2.23607	−	3.87298i	0.0847579	−	0.146805i
$697$	−2.00000	+	3.46410i	−0.0757554	+	0.131212i
$698$	26.7082	+	46.2600i	1.01092	+	1.75097i
$699$	17.4164			0.658749
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	−5.00000	−	8.66025i	−0.188713	−	0.326860i
$703$	35.4164	−	61.3430i	1.33576	−	2.31360i
$704$	−16.0689	+	27.8321i	−0.605619	+	1.04896i
$705$	−2.47214	−	4.28187i	−0.0931060	−	0.161264i
$706$	62.3607			2.34698
$707$		0			0
$708$	−26.8328			−1.00844
$709$	22.8885	+	39.6441i	0.859597	+	1.48887i	0.872313	+	0.488947i	$0.162619\pi$
$709$	22.8885	+	39.6441i	0.859597	+	1.48887i	−0.0127162	+	0.999919i	$0.504048\pi$
$710$	−16.1803	+	28.0252i	−0.607237	+	1.05177i
$711$	2.47214	−	4.28187i	0.0927123	−	0.160582i
$712$	−2.23607	−	3.87298i	−0.0838002	−	0.145146i
$713$	−41.8885			−1.56874
$714$		0			0
$715$	−11.0557			−0.413461
$716$	3.70820	+	6.42280i	0.138582	+	0.240031i
$717$	0.763932	−	1.32317i	0.0285296	−	0.0494147i
$718$	−10.6525	+	18.4506i	−0.397547	+	0.688571i
$719$	23.4164	+	40.5584i	0.873285	+	1.51257i	0.858579	+	0.512682i	$0.171348\pi$
$719$	23.4164	+	40.5584i	0.873285	+	1.51257i	0.0147058	+	0.999892i	$0.495319\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	51.1803			1.90474
$723$	−0.527864	−	0.914287i	−0.0196315	−	0.0340027i
$724$	28.4164	−	49.2187i	1.05609	−	1.82920i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	5.46556	+	9.46662i	0.202846	+	0.351339i
$727$	−14.8328			−0.550119			−0.275059	−	0.961427i	$-0.588698\pi$
$727$	−14.8328			−0.550119			−0.275059	+	0.961427i	$0.588698\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−3.94427	−	6.83168i	−0.145984	−	0.252852i
$731$	8.94427	−	15.4919i	0.330816	−	0.572990i
$732$	−3.00000	+	5.19615i	−0.110883	+	0.192055i
$733$	18.7082	+	32.4036i	0.691003	+	1.19685i	0.971510	+	0.237001i	$0.0761643\pi$
$733$	18.7082	+	32.4036i	0.691003	+	1.19685i	−0.280506	+	0.959852i	$0.590502\pi$
$734$	−46.8328			−1.72863
$735$		0			0
$736$	−26.8328			−0.989071
$737$	−4.94427	−	8.56373i	−0.182125	−	0.315449i
$738$	−2.23607	+	3.87298i	−0.0823108	+	0.142566i
$739$	−14.9443	+	25.8842i	−0.549734	+	0.952167i	0.448559	+	0.893753i	$0.351938\pi$
$739$	−14.9443	+	25.8842i	−0.549734	+	0.952167i	−0.998292	+	0.0584136i	$0.981396\pi$
$740$	−16.4164	−	28.4341i	−0.603479	−	1.04526i
$741$	−28.9443			−1.06329
$742$		0			0
$743$	−18.8328			−0.690909			−0.345455	−	0.938436i	$-0.612275\pi$
$743$	−18.8328			−0.690909			−0.345455	+	0.938436i	$0.612275\pi$
$744$	11.7082	+	20.2792i	0.429244	+	0.743472i
$745$	−1.47214	+	2.54981i	−0.0539349	+	0.0934180i
$746$	−6.70820	+	11.6190i	−0.245605	+	0.425400i
$747$	0.472136	+	0.817763i	0.0172746	+	0.0299204i
$748$	−14.8328			−0.542341
$749$		0			0
$750$	2.23607			0.0816497
$751$	1.52786	+	2.64634i	0.0557526	+	0.0965663i	0.892555	−	0.450939i	$-0.148911\pi$
$751$	1.52786	+	2.64634i	0.0557526	+	0.0965663i	−0.836802	+	0.547505i	$0.815578\pi$
$752$	2.47214	−	4.28187i	0.0901495	−	0.156144i
$753$	−0.472136	+	0.817763i	−0.0172056	+	0.0298010i
$754$	10.0000	+	17.3205i	0.364179	+	0.630776i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	−3.88854			−0.141332			−0.0706658	−	0.997500i	$-0.522512\pi$
$757$	−3.88854			−0.141332			−0.0706658	+	0.997500i	$0.522512\pi$
$758$	2.36068	+	4.08882i	0.0857438	+	0.148513i
$759$	4.94427	−	8.56373i	0.179466	−	0.310844i
$760$	7.23607	−	12.5332i	0.262480	−	0.454628i
$761$	3.94427	+	6.83168i	0.142980	+	0.247648i	0.928617	−	0.371039i	$-0.120998\pi$
$761$	3.94427	+	6.83168i	0.142980	+	0.247648i	−0.785638	+	0.618687i	$0.787665\pi$
$762$	28.9443			1.04854
$763$		0			0
$764$	82.2492			2.97567
$765$	−1.00000	−	1.73205i	−0.0361551	−	0.0626224i
$766$	−8.94427	+	15.4919i	−0.323170	+	0.559746i
$767$	20.0000	−	34.6410i	0.722158	−	1.25081i
$768$	4.50000	+	7.79423i	0.162380	+	0.281250i
$769$	−0.832816			−0.0300321			−0.0150161	−	0.999887i	$-0.504780\pi$
$769$	−0.832816			−0.0300321			−0.0150161	+	0.999887i	$0.504780\pi$
$770$		0			0
$771$	−1.05573			−0.0380211
$772$	21.0000	+	36.3731i	0.755807	+	1.30910i
$773$	−12.5279	+	21.6989i	−0.450596	+	0.780455i	−0.998423	−	0.0561365i	$-0.982122\pi$
$773$	−12.5279	+	21.6989i	−0.450596	+	0.780455i	0.547827	+	0.836592i	$0.315455\pi$
$774$	10.0000	−	17.3205i	0.359443	−	0.622573i
$775$	5.23607	+	9.06914i	0.188085	+	0.325773i
$776$	1.05573			0.0378984
$777$		0			0
$778$	24.4721			0.877369
$779$	6.47214	+	11.2101i	0.231888	+	0.401642i
$780$	−6.70820	+	11.6190i	−0.240192	+	0.416025i
$781$	17.8885	−	30.9839i	0.640102	−	1.10869i
$782$	−8.94427	−	15.4919i	−0.319847	−	0.553990i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	−8.47214			−0.302383
$786$	4.47214	+	7.74597i	0.159516	+	0.276289i
$787$	24.4721	−	42.3870i	0.872337	−	1.51093i	0.0127652	−	0.999919i	$-0.495937\pi$
$787$	24.4721	−	42.3870i	0.872337	−	1.51093i	0.859572	−	0.511014i	$-0.170730\pi$
$788$	−36.7082	+	63.5805i	−1.30768	+	2.26496i
$789$	−12.4721	−	21.6024i	−0.444020	−	0.769065i
$790$	−11.0557			−0.393345
$791$		0			0
$792$	−5.52786			−0.196424
$793$	−4.47214	−	7.74597i	−0.158810	−	0.275067i
$794$	15.0000	−	25.9808i	0.532330	−	0.922023i
$795$	6.23607	−	10.8012i	0.221171	−	0.383079i
$796$	0.875388	+	1.51622i	0.0310273	+	0.0537409i
$797$	1.05573			0.0373958			0.0186979	−	0.999825i	$-0.494048\pi$
$797$	1.05573			0.0373958			0.0186979	+	0.999825i	$0.494048\pi$
$798$		0			0
$799$	9.88854			0.349832
$800$	3.35410	+	5.80948i	0.118585	+	0.205396i
$801$	−1.00000	+	1.73205i	−0.0353333	+	0.0611990i
$802$	−11.1803	+	19.3649i	−0.394792	+	0.683799i
$803$	4.36068	+	7.55292i	0.153885	+	0.266537i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	−104.721			−3.68865
$807$	−11.9443	−	20.6881i	−0.420458	−	0.728255i
$808$	−15.6525	+	27.1109i	−0.550652	+	0.953758i
$809$	−10.5279	+	18.2348i	−0.370140	+	0.641101i	−0.989587	−	0.143937i	$-0.954024\pi$
$809$	−10.5279	+	18.2348i	−0.370140	+	0.641101i	0.619447	+	0.785039i	$0.287357\pi$
$810$	−1.11803	−	1.93649i	−0.0392837	−	0.0680414i
$811$	−28.5836			−1.00371			−0.501853	−	0.864953i	$-0.667348\pi$
$811$	−28.5836			−1.00371			−0.501853	+	0.864953i	$0.667348\pi$
$812$		0			0
$813$	10.4721			0.367274
$814$	30.2492	+	52.3932i	1.06023	+	1.83638i
$815$	−0.472136	+	0.817763i	−0.0165382	+	0.0286450i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	−28.9443	−	50.1329i	−1.01263	−	1.75393i
$818$	53.4164			1.86766
$819$		0			0
$820$	6.00000			0.209529
$821$	18.8885	+	32.7159i	0.659215	+	1.14179i	0.980819	+	0.194919i	$0.0624445\pi$
$821$	18.8885	+	32.7159i	0.659215	+	1.14179i	−0.321605	+	0.946874i	$0.604222\pi$
$822$	−13.9443	+	24.1522i	−0.486362	+	0.842404i
$823$	−13.5279	+	23.4309i	−0.471552	+	0.816751i	−0.999470	−	0.0325435i	$-0.989639\pi$
$823$	−13.5279	+	23.4309i	−0.471552	+	0.816751i	0.527919	+	0.849295i	$0.322973\pi$
$824$		0			0
$825$	−2.47214			−0.0860687
$826$		0			0
$827$	−4.94427			−0.171929			−0.0859646	−	0.996298i	$-0.527397\pi$
$827$	−4.94427			−0.171929			−0.0859646	+	0.996298i	$0.527397\pi$
$828$	−6.00000	−	10.3923i	−0.208514	−	0.361158i
$829$	−15.4721	+	26.7985i	−0.537369	+	0.930751i	0.461675	+	0.887049i	$0.347249\pi$
$829$	−15.4721	+	26.7985i	−0.537369	+	0.930751i	−0.999045	+	0.0437022i	$0.986085\pi$
$830$	1.05573	−	1.82857i	0.0366449	−	0.0634708i
$831$	−0.527864	−	0.914287i	−0.0183114	−	0.0317163i
$832$	−58.1378			−2.01556
$833$		0			0
$834$	43.4164			1.50339
$835$	−4.00000	−	6.92820i	−0.138426	−	0.239760i
$836$	−24.0000	+	41.5692i	−0.830057	+	1.43770i
$837$	5.23607	−	9.06914i	0.180985	−	0.313475i
$838$	6.58359	+	11.4031i	0.227426	+	0.393914i
$839$	−1.16718			−0.0402957			−0.0201478	−	0.999797i	$-0.506414\pi$
$839$	−1.16718			−0.0402957			−0.0201478	+	0.999797i	$0.506414\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−24.5967	−	42.6028i	−0.847660	−	1.46819i
$843$	−3.47214	+	6.01392i	−0.119587	+	0.207130i
$844$	−1.41641	+	2.45329i	−0.0487548	+	0.0844457i
$845$	−3.50000	−	6.06218i	−0.120404	−	0.208545i
$846$	11.0557			0.380104
$847$		0			0
$848$	12.4721			0.428295
$849$	6.00000	+	10.3923i	0.205919	+	0.356663i
$850$	−2.23607	+	3.87298i	−0.0766965	+	0.132842i
$851$	−21.8885	+	37.9121i	−0.750330	+	1.29961i
$852$	−21.7082	−	37.5997i	−0.743711	−	1.28814i
$853$	−31.3050			−1.07186			−0.535931	−	0.844262i	$-0.680039\pi$
$853$	−31.3050			−1.07186			−0.535931	+	0.844262i	$0.680039\pi$
$854$		0			0
$855$	−6.47214			−0.221342
$856$	−5.52786	−	9.57454i	−0.188939	−	0.327251i
$857$	−8.41641	+	14.5776i	−0.287499	+	0.497963i	−0.973212	−	0.229909i	$-0.926157\pi$
$857$	−8.41641	+	14.5776i	−0.287499	+	0.497963i	0.685713	+	0.727872i	$0.259490\pi$
$858$	12.3607	−	21.4093i	0.421987	−	0.730902i
$859$	20.7639	+	35.9642i	0.708456	+	1.22708i	0.965430	+	0.260664i	$0.0839414\pi$
$859$	20.7639	+	35.9642i	0.708456	+	1.22708i	−0.256973	+	0.966418i	$0.582725\pi$
$860$	−26.8328			−0.914991
$861$		0			0
$862$	−21.3050			−0.725650
$863$	6.94427	+	12.0278i	0.236386	+	0.409432i	0.959675	−	0.281114i	$-0.0907038\pi$
$863$	6.94427	+	12.0278i	0.236386	+	0.409432i	−0.723289	+	0.690546i	$0.757370\pi$
$864$	3.35410	−	5.80948i	0.114109	−	0.197642i
$865$	7.47214	−	12.9421i	0.254060	−	0.440045i
$866$	8.41641	+	14.5776i	0.286001	+	0.495369i
$867$	−13.0000			−0.441503
$868$		0			0
$869$	12.2229			0.414634
$870$	2.23607	+	3.87298i	0.0758098	+	0.131306i
$871$	8.94427	−	15.4919i	0.303065	−	0.524924i
$872$	2.23607	−	3.87298i	0.0757228	−	0.131156i
$873$	−0.236068	−	0.408882i	−0.00798969	−	0.0138385i
$874$	−57.8885			−1.95811
$875$		0			0
$876$	10.5836			0.357586
$877$	1.58359	+	2.74286i	0.0534741	+	0.0926199i	0.891523	−	0.452975i	$-0.149637\pi$
$877$	1.58359	+	2.74286i	0.0534741	+	0.0926199i	−0.838049	+	0.545595i	$0.816304\pi$
$878$	11.7082	−	20.2792i	0.395133	−	0.684390i
$879$	11.4721	−	19.8703i	0.386946	−	0.670209i
$880$	−1.23607	−	2.14093i	−0.0416678	−	0.0721708i
$881$	−7.88854			−0.265772			−0.132886	−	0.991131i	$-0.542424\pi$
$881$	−7.88854			−0.265772			−0.132886	+	0.991131i	$0.542424\pi$
$882$		0			0
$883$	−2.11146			−0.0710562			−0.0355281	−	0.999369i	$-0.511311\pi$
$883$	−2.11146			−0.0710562			−0.0355281	+	0.999369i	$0.511311\pi$
$884$	−13.4164	−	23.2379i	−0.451243	−	0.781575i
$885$	4.47214	−	7.74597i	0.150329	−	0.260378i
$886$	8.94427	−	15.4919i	0.300489	−	0.520462i
$887$	11.4164	+	19.7738i	0.383325	+	0.663939i	0.991535	−	0.129837i	$-0.0414454\pi$
$887$	11.4164	+	19.7738i	0.383325	+	0.663939i	−0.608210	+	0.793776i	$0.708112\pi$
$888$	24.4721			0.821231
$889$		0			0
$890$	4.47214			0.149906
$891$	1.23607	+	2.14093i	0.0414098	+	0.0717239i
$892$	7.41641	−	12.8456i	0.248320	−	0.430102i
$893$	16.0000	−	27.7128i	0.535420	−	0.927374i
$894$	−3.29180	−	5.70156i	−0.110094	−	0.190689i
$895$	−2.47214			−0.0826344
$896$		0			0
$897$	17.8885			0.597281
$898$	15.6525	+	27.1109i	0.522330	+	0.904702i
$899$	−10.4721	+	18.1383i	−0.349265	+	0.604945i
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$	12.4721	+	21.6024i	0.415507	+	0.719679i
$902$	−11.0557			−0.368115
$903$		0			0
$904$	−18.9443			−0.630077
$905$	9.47214	+	16.4062i	0.314864	+	0.545361i
$906$	17.8885	−	30.9839i	0.594307	−	1.02937i
$907$	−9.05573	+	15.6850i	−0.300691	+	0.520811i	−0.976293	−	0.216455i	$-0.930550\pi$
$907$	−9.05573	+	15.6850i	−0.300691	+	0.520811i	0.675602	+	0.737267i	$0.263884\pi$
$908$	−25.4164	−	44.0225i	−0.843473	−	1.46094i
$909$	14.0000			0.464351
$910$		0			0
$911$	−34.2492			−1.13473			−0.567364	−	0.823467i	$-0.692037\pi$
$911$	−34.2492			−1.13473			−0.567364	+	0.823467i	$0.692037\pi$
$912$	−3.23607	−	5.60503i	−0.107157	−	0.185601i
$913$	−1.16718	+	2.02162i	−0.0386282	+	0.0669059i
$914$	12.2361	−	21.1935i	0.404733	−	0.701018i
$915$	−1.00000	−	1.73205i	−0.0330590	−	0.0572598i
$916$	35.6656			1.17843
$917$		0			0
$918$	4.47214			0.147602
$919$	26.4721	+	45.8511i	0.873235	+	1.51249i	0.858631	+	0.512594i	$0.171316\pi$
$919$	26.4721	+	45.8511i	0.873235	+	1.51249i	0.0146043	+	0.999893i	$0.495351\pi$
$920$	−4.47214	+	7.74597i	−0.147442	+	0.255377i
$921$	−16.4721	+	28.5306i	−0.542775	+	0.940114i
$922$	−35.6525	−	61.7519i	−1.17415	−	2.03369i
$923$	64.7214			2.13033
$924$		0			0
$925$	10.9443			0.359845
$926$	−3.41641	−	5.91739i	−0.112270	−	0.194458i
$927$		0			0
$928$	−6.70820	+	11.6190i	−0.220208	+	0.381411i
$929$	−25.9443	−	44.9368i	−0.851204	−	1.47433i	−0.880122	−	0.474747i	$-0.842540\pi$
$929$	−25.9443	−	44.9368i	−0.851204	−	1.47433i	0.0289185	−	0.999582i	$-0.490794\pi$
$930$	−23.4164			−0.767854
$931$		0			0
$932$	52.2492			1.71148
$933$	−4.94427	−	8.56373i	−0.161868	−	0.280364i
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	2.47214	−	4.28187i	0.0808475	−	0.140032i
$936$	−5.00000	−	8.66025i	−0.163430	−	0.283069i
$937$	43.5279			1.42199			0.710997	−	0.703195i	$-0.248244\pi$
$937$	43.5279			1.42199			0.710997	+	0.703195i	$0.248244\pi$
$938$		0			0
$939$	−9.41641			−0.307293
$940$	−7.41641	−	12.8456i	−0.241897	−	0.418977i
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$	9.47214	−	16.4062i	0.308619	−	0.534544i
$943$	−4.00000	−	6.92820i	−0.130258	−	0.225613i
$944$	8.94427			0.291111
$945$		0			0
$946$	49.4427			1.60752
$947$	−8.94427	−	15.4919i	−0.290650	−	0.503420i	0.683314	−	0.730125i	$-0.260538\pi$
$947$	−8.94427	−	15.4919i	−0.290650	−	0.503420i	−0.973964	+	0.226705i	$0.927205\pi$
$948$	7.41641	−	12.8456i	0.240874	−	0.417206i
$949$	−7.88854	+	13.6634i	−0.256073	+	0.443531i
$950$	7.23607	+	12.5332i	0.234769	+	0.406632i
$951$	−30.3607			−0.984512
$952$		0			0
$953$	−6.58359			−0.213263			−0.106632	−	0.994299i	$-0.534007\pi$
$953$	−6.58359			−0.213263			−0.106632	+	0.994299i	$0.534007\pi$
$954$	13.9443	+	24.1522i	0.451462	+	0.781956i
$955$	−13.7082	+	23.7433i	−0.443587	+	0.768315i
$956$	2.29180	−	3.96951i	0.0741220	−	0.128383i
$957$	−2.47214	−	4.28187i	−0.0799128	−	0.138413i
$958$	−40.0000			−1.29234
$959$		0			0
$960$	−13.0000			−0.419573
$961$	−39.3328	−	68.1264i	−1.26880	−	2.19763i
$962$	−54.7214	+	94.7802i	−1.76429	+	3.05584i
$963$	−2.47214	+	4.28187i	−0.0796635	+	0.137981i
$964$	−1.58359	−	2.74286i	−0.0510041	−	0.0883416i
$965$	−14.0000			−0.450676
$966$		0			0
$967$	−9.88854			−0.317994			−0.158997	−	0.987279i	$-0.550826\pi$
$967$	−9.88854			−0.317994			−0.158997	+	0.987279i	$0.550826\pi$
$968$	5.46556	+	9.46662i	0.175670	+	0.304269i
$969$	6.47214	−	11.2101i	0.207915	−	0.360119i
$970$	−0.527864	+	0.914287i	−0.0169487	+	0.0293560i
$971$	11.5279	+	19.9668i	0.369947	+	0.640767i	0.989557	−	0.144143i	$-0.0460426\pi$
$971$	11.5279	+	19.9668i	0.369947	+	0.640767i	−0.619610	+	0.784910i	$0.712709\pi$
$972$	3.00000			0.0962250
$973$		0			0
$974$	−6.83282			−0.218938
$975$	−2.23607	−	3.87298i	−0.0716115	−	0.124035i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−28.7082	+	49.7241i	−0.918457	+	1.59081i	−0.116697	+	0.993168i	$0.537231\pi$
$977$	−28.7082	+	49.7241i	−0.918457	+	1.59081i	−0.801760	+	0.597646i	$0.796103\pi$
$978$	−1.05573	−	1.82857i	−0.0337585	−	0.0584714i
$979$	−4.94427			−0.158020
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−46.1803	−	79.9867i	−1.47367	−	2.55248i
$983$	15.4164	−	26.7020i	0.491707	−	0.851662i	−0.508247	−	0.861211i	$-0.669706\pi$
$983$	15.4164	−	26.7020i	0.491707	−	0.851662i	0.999954	+	0.00954955i	$0.00303976\pi$
$984$	−2.23607	+	3.87298i	−0.0712832	+	0.123466i
$985$	−12.2361	−	21.1935i	−0.389874	−	0.675281i
$986$	−8.94427			−0.284844
$987$		0			0
$988$	−86.8328			−2.76252
$989$	17.8885	+	30.9839i	0.568823	+	0.985230i
$990$	2.76393	−	4.78727i	0.0878435	−	0.152149i
$991$	6.47214	−	11.2101i	0.205594	−	0.356100i	−0.744728	−	0.667368i	$-0.767421\pi$
$991$	6.47214	−	11.2101i	0.205594	−	0.356100i	0.950322	+	0.311269i	$0.100754\pi$
$992$	−35.1246	−	60.8376i	−1.11521	−	1.93160i
$993$	−16.9443			−0.537710
$994$		0			0
$995$	−0.583592			−0.0185011
$996$	1.41641	+	2.45329i	0.0448806	+	0.0777355i
$997$	10.7082	−	18.5472i	0.339132	−	0.587394i	−0.645138	−	0.764066i	$-0.723200\pi$
$997$	10.7082	−	18.5472i	0.339132	−	0.587394i	0.984270	+	0.176672i	$0.0565333\pi$
$998$	−24.4721	+	42.3870i	−0.774652	+	1.34174i
$999$	−5.47214	−	9.47802i	−0.173131	−	0.299871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.i.361.1		4
7.2	even	3	inner	735.2.i.i.226.1		4
7.3	odd	6		105.2.a.b.1.2	✓	2
7.4	even	3		735.2.a.k.1.2		2
7.5	odd	6		735.2.i.k.226.1		4
7.6	odd	2		735.2.i.k.361.1		4
21.11	odd	6		2205.2.a.w.1.1		2
21.17	even	6		315.2.a.d.1.1		2
28.3	even	6		1680.2.a.v.1.2		2
35.3	even	12		525.2.d.c.274.1		4
35.4	even	6		3675.2.a.y.1.1		2
35.17	even	12		525.2.d.c.274.4		4
35.24	odd	6		525.2.a.g.1.1		2
56.3	even	6		6720.2.a.cs.1.1		2
56.45	odd	6		6720.2.a.cx.1.2		2
84.59	odd	6		5040.2.a.bw.1.1		2
105.17	odd	12		1575.2.d.d.1324.2		4
105.38	odd	12		1575.2.d.d.1324.3		4
105.59	even	6		1575.2.a.r.1.2		2
140.59	even	6		8400.2.a.cx.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.a.b.1.2	✓	2	7.3	odd	6
315.2.a.d.1.1		2	21.17	even	6
525.2.a.g.1.1		2	35.24	odd	6
525.2.d.c.274.1		4	35.3	even	12
525.2.d.c.274.4		4	35.17	even	12
735.2.a.k.1.2		2	7.4	even	3
735.2.i.i.226.1		4	7.2	even	3	inner
735.2.i.i.361.1		4	1.1	even	1	trivial
735.2.i.k.226.1		4	7.5	odd	6
735.2.i.k.361.1		4	7.6	odd	2
1575.2.a.r.1.2		2	105.59	even	6
1575.2.d.d.1324.2		4	105.17	odd	12
1575.2.d.d.1324.3		4	105.38	odd	12
1680.2.a.v.1.2		2	28.3	even	6
2205.2.a.w.1.1		2	21.11	odd	6
3675.2.a.y.1.1		2	35.4	even	6
5040.2.a.bw.1.1		2	84.59	odd	6
6720.2.a.cs.1.1		2	56.3	even	6
6720.2.a.cx.1.2		2	56.45	odd	6
8400.2.a.cx.1.2		2	140.59	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11803 - 1.93649i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.23607 q^{6} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.11803 - 1.93649i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.23607 q^{6} +2.23607 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.11803 + 1.93649i) q^{10} +(1.23607 - 2.14093i) q^{11} +(-1.50000 - 2.59808i) q^{12} +4.47214 q^{13} +1.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.11803 + 1.93649i) q^{18} +(3.23607 + 5.60503i) q^{19} +3.00000 q^{20} -5.52786 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-5.00000 - 8.66025i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.11803 - 1.93649i) q^{30} +(5.23607 - 9.06914i) q^{31} +(3.35410 - 5.80948i) q^{32} +(1.23607 + 2.14093i) q^{33} +4.47214 q^{34} +3.00000 q^{36} +(-5.47214 - 9.47802i) q^{37} +(7.23607 - 12.5332i) q^{38} +(-2.23607 + 3.87298i) q^{39} +(-1.11803 - 1.93649i) q^{40} +2.00000 q^{41} -8.94427 q^{43} +(3.70820 + 6.42280i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-4.47214 + 7.74597i) q^{46} +(-2.47214 - 4.28187i) q^{47} -1.00000 q^{48} +2.23607 q^{50} +(-1.00000 - 1.73205i) q^{51} +(-6.70820 + 11.6190i) q^{52} +(6.23607 - 10.8012i) q^{53} +(-1.11803 - 1.93649i) q^{54} -2.47214 q^{55} -6.47214 q^{57} +(2.23607 + 3.87298i) q^{58} +(4.47214 - 7.74597i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(-1.00000 - 1.73205i) q^{61} -23.4164 q^{62} -13.0000 q^{64} +(-2.23607 - 3.87298i) q^{65} +(2.76393 - 4.78727i) q^{66} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +4.00000 q^{69} +14.4721 q^{71} +(-1.11803 - 1.93649i) q^{72} +(-1.76393 + 3.05522i) q^{73} +(-12.2361 + 21.1935i) q^{74} +(-0.500000 - 0.866025i) q^{75} -19.4164 q^{76} +10.0000 q^{78} +(2.47214 + 4.28187i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.23607 - 3.87298i) q^{82} -0.944272 q^{83} +2.00000 q^{85} +(10.0000 + 17.3205i) q^{86} +(1.00000 - 1.73205i) q^{87} +(2.76393 - 4.78727i) q^{88} +(-1.00000 - 1.73205i) q^{89} +2.23607 q^{90} +12.0000 q^{92} +(5.23607 + 9.06914i) q^{93} +(-5.52786 + 9.57454i) q^{94} +(3.23607 - 5.60503i) q^{95} +(3.35410 + 5.80948i) q^{96} +0.472136 q^{97} -2.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 6 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 6 * q^4 - 2 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} - 6 q^{4} - 2 q^{5} - 2 q^{9} - 4 q^{11} - 6 q^{12} + 4 q^{15} + 2 q^{16} - 4 q^{17} + 4 q^{19} + 12 q^{20} - 40 q^{22} - 8 q^{23} - 2 q^{25} - 20 q^{26} + 4 q^{27} - 8 q^{29} + 12 q^{31} - 4 q^{33} + 12 q^{36} - 4 q^{37} + 20 q^{38} + 8 q^{41} - 12 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} - 4 q^{51} + 16 q^{53} + 8 q^{55} - 8 q^{57} - 6 q^{60} - 4 q^{61} - 40 q^{62} - 52 q^{64} + 20 q^{66} + 8 q^{67} - 12 q^{68} + 16 q^{69} + 40 q^{71} - 16 q^{73} - 40 q^{74} - 2 q^{75} - 24 q^{76} + 40 q^{78} - 8 q^{79} + 2 q^{80} - 2 q^{81} + 32 q^{83} + 8 q^{85} + 40 q^{86} + 4 q^{87} + 20 q^{88} - 4 q^{89} + 48 q^{92} + 12 q^{93} - 40 q^{94} + 4 q^{95} - 16 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 6 * q^4 - 2 * q^5 - 2 * q^9 - 4 * q^11 - 6 * q^12 + 4 * q^15 + 2 * q^16 - 4 * q^17 + 4 * q^19 + 12 * q^20 - 40 * q^22 - 8 * q^23 - 2 * q^25 - 20 * q^26 + 4 * q^27 - 8 * q^29 + 12 * q^31 - 4 * q^33 + 12 * q^36 - 4 * q^37 + 20 * q^38 + 8 * q^41 - 12 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 - 4 * q^51 + 16 * q^53 + 8 * q^55 - 8 * q^57 - 6 * q^60 - 4 * q^61 - 40 * q^62 - 52 * q^64 + 20 * q^66 + 8 * q^67 - 12 * q^68 + 16 * q^69 + 40 * q^71 - 16 * q^73 - 40 * q^74 - 2 * q^75 - 24 * q^76 + 40 * q^78 - 8 * q^79 + 2 * q^80 - 2 * q^81 + 32 * q^83 + 8 * q^85 + 40 * q^86 + 4 * q^87 + 20 * q^88 - 4 * q^89 + 48 * q^92 + 12 * q^93 - 40 * q^94 + 4 * q^95 - 16 * q^97 + 8 * q^99

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