LMFDB - Embedded newform 735.2.i.k.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.k.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	$-0.712938\pi$
$13$	−4.47214			−1.24035			−0.620174	+	0.784465i	$0.712938\pi$
$14$		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	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−1.11803	+	1.93649i	−0.263523	+	0.456435i
$19$	−3.23607	−	5.60503i	−0.742405	−	1.28588i	−0.951397	−	0.307966i	$-0.900352\pi$
$19$	−3.23607	−	5.60503i	−0.742405	−	1.28588i	0.208993	−	0.977917i	$-0.432982\pi$
$20$	−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	$0.556240\pi$
$31$	−5.23607	+	9.06914i	−0.940426	+	1.62886i	−0.764661	+	0.644433i	$0.777094\pi$
$32$	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	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		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	0.988059	−	0.154074i	$-0.0492393\pi$
$47$	2.47214	+	4.28187i	0.360598	+	0.624574i	−0.627461	+	0.778648i	$0.715906\pi$
$48$	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	$0.364483\pi$
$59$	−4.47214	+	7.74597i	−0.582223	+	1.00844i	−0.995215	+	0.0977047i	$0.968850\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	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	−0.744142	−	0.668022i	$-0.767141\pi$
$73$	1.76393	−	3.05522i	0.206453	−	0.357586i	0.950595	+	0.310435i	$0.100475\pi$
$74$	−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	$-0.483497\pi$
$83$	0.944272			0.103647			0.0518237	+	0.998656i	$0.483497\pi$
$84$		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	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	−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	$-0.507630\pi$
$97$	−0.472136			−0.0479381			−0.0239691	+	0.999713i	$0.507630\pi$
$98$		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	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$	−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	0.765331	−	0.643637i	$-0.222575\pi$
$131$	−2.00000	−	3.46410i	−0.174741	−	0.302660i	−0.940072	+	0.340977i	$0.889242\pi$
$132$	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	$-0.807948\pi$
$139$	−19.4164			−1.64688			−0.823439	+	0.567405i	$0.807948\pi$
$140$		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	−0.984071	−	0.177778i	$-0.943109\pi$
$157$	−4.23607	+	7.33708i	−0.338075	+	0.585563i	0.645996	+	0.763341i	$0.276442\pi$
$158$	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	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		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	$-0.974347\pi$
$173$	−7.47214	−	12.9421i	−0.568096	−	0.983971i	0.428658	−	0.903467i	$-0.358986\pi$
$174$	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	$-0.251369\pi$
$181$	18.9443			1.40812			0.704058	+	0.710142i	$0.251369\pi$
$182$		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	−0.876183	−	0.481979i	$-0.839918\pi$
$199$	−0.291796	+	0.505406i	−0.0206849	+	0.0358273i	0.855498	+	0.517807i	$0.173251\pi$
$200$	−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	$-0.447061\pi$
$223$	4.94427			0.331093			0.165546	+	0.986202i	$0.447061\pi$
$224$		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	$-0.643244\pi$
$227$	8.47214	−	14.6742i	0.562315	−	0.973959i	0.997294	−	0.0735180i	$-0.0234226\pi$
$228$	9.70820	−	16.8151i	0.642942	−	1.11361i
$229$	5.94427	+	10.2958i	0.392809	+	0.680364i	0.992819	−	0.119628i	$-0.0381702\pi$
$229$	5.94427	+	10.2958i	0.392809	+	0.680364i	−0.600010	+	0.799992i	$0.704837\pi$
$230$	−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	−0.848523	−	0.529158i	$-0.822508\pi$
$241$	0.527864	−	0.914287i	0.0340027	−	0.0588944i	0.882526	+	0.470264i	$0.155841\pi$
$242$	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	$-0.509487\pi$
$251$	−0.944272			−0.0596019			−0.0298010	+	0.999556i	$0.509487\pi$
$252$		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	0.849092	−	0.528245i	$-0.177150\pi$
$257$	−0.527864	−	0.914287i	−0.0329273	−	0.0570317i	−0.882019	+	0.471213i	$0.843816\pi$
$258$	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	$-0.573665\pi$
$269$	11.9443	−	20.6881i	0.728255	−	1.26137i	0.957620	−	0.288034i	$-0.0930017\pi$
$270$	−1.11803	+	1.93649i	−0.0680414	+	0.117851i
$271$	5.23607	+	9.06914i	0.318068	+	0.550911i	0.980085	−	0.198578i	$-0.0636325\pi$
$271$	5.23607	+	9.06914i	0.318068	+	0.550911i	−0.662017	+	0.749489i	$0.730299\pi$
$272$	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	−0.987401	−	0.158237i	$-0.949419\pi$
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	0.630738	+	0.775996i	$0.282752\pi$
$284$	−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	$-0.266204\pi$
$293$	22.9443			1.34042			0.670209	+	0.742172i	$0.266204\pi$
$294$		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	$-0.889282\pi$
$307$	−32.9443			−1.88023			−0.940114	+	0.340859i	$0.889282\pi$
$308$		0			0
$309$		0			0
$310$	11.7082	+	20.2792i	0.664981	+	1.15178i
$311$	4.94427	−	8.56373i	0.280364	−	0.485605i	−0.691110	−	0.722749i	$-0.742878\pi$
$311$	4.94427	−	8.56373i	0.280364	−	0.485605i	0.971474	+	0.237145i	$0.0762115\pi$
$312$	−5.00000	+	8.66025i	−0.283069	+	0.490290i
$313$	−4.70820	−	8.15485i	−0.266123	−	0.460939i	0.701734	−	0.712439i	$-0.252410\pi$
$313$	−4.70820	−	8.15485i	−0.266123	−	0.460939i	−0.967857	+	0.251500i	$0.919076\pi$
$314$	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	$-0.279198\pi$
$349$	23.8885			1.27872			0.639362	+	0.768906i	$0.279198\pi$
$350$		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	$-0.567126\pi$
$353$	13.9443	−	24.1522i	0.742179	−	1.28549i	0.951501	−	0.307645i	$-0.0995408\pi$
$354$	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	$0.350760\pi$
$367$	−10.4721	+	18.1383i	−0.546641	+	0.946810i	−0.998502	+	0.0547215i	$0.982573\pi$
$368$	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	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$	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	0.647130	−	0.762380i	$-0.275969\pi$
$397$	−6.70820	−	11.6190i	−0.336675	−	0.583138i	−0.983805	+	0.179241i	$0.942636\pi$
$398$	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	$-0.632222\pi$
$409$	11.9443	−	20.6881i	0.590606	−	1.02296i	0.994151	−	0.108000i	$-0.0344447\pi$
$410$	−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	$-0.454056\pi$
$419$	5.88854			0.287674			0.143837	+	0.989601i	$0.454056\pi$
$420$		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	$-0.442104\pi$
$433$	7.52786			0.361766			0.180883	+	0.983505i	$0.442104\pi$
$434$		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	0.713595	−	0.700558i	$-0.247066\pi$
$439$	−5.23607	−	9.06914i	−0.249904	−	0.432846i	−0.963499	+	0.267712i	$0.913732\pi$
$440$	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	$-0.766407\pi$
$461$	−31.8885			−1.48520			−0.742599	+	0.669737i	$0.766407\pi$
$462$		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	0.743805	−	0.668397i	$-0.233019\pi$
$467$	−4.47214	−	7.74597i	−0.206946	−	0.358441i	−0.950751	+	0.309956i	$0.899686\pi$
$468$	−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	−0.994741	−	0.102418i	$-0.967342\pi$
$479$	−8.94427	+	15.4919i	−0.408674	+	0.707845i	0.586067	+	0.810262i	$0.300675\pi$
$480$	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	$-0.247152\pi$
$503$	32.0000			1.42681			0.713405	+	0.700752i	$0.247152\pi$
$504$		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	0.703688	−	0.710509i	$-0.251535\pi$
$509$	−5.94427	−	10.2958i	−0.263475	−	0.456352i	−0.967163	+	0.254157i	$0.918202\pi$
$510$	−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	−0.985902	−	0.167323i	$-0.946488\pi$
$521$	−7.94427	+	13.7599i	−0.348045	+	0.602831i	0.637857	+	0.770155i	$0.279821\pi$
$522$	2.23607	−	3.87298i	0.0978700	−	0.169516i
$523$	−4.47214	−	7.74597i	−0.195553	−	0.338707i	0.751529	−	0.659700i	$-0.229317\pi$
$523$	−4.47214	−	7.74597i	−0.195553	−	0.338707i	−0.947082	+	0.320993i	$0.895983\pi$
$524$	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	−0.537777	−	0.843087i	$-0.680736\pi$
$563$	10.9443	−	18.9560i	0.461246	−	0.798902i	0.999023	+	0.0441853i	$0.0140692\pi$
$564$	−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	$-0.579657\pi$
$577$	17.1803	−	29.7572i	0.715227	−	1.23881i	0.962872	−	0.269959i	$-0.0870100\pi$
$578$	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	$-0.526306\pi$
$587$	−4.00000			−0.165098			−0.0825488	+	0.996587i	$0.526306\pi$
$588$		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	0.961879	−	0.273476i	$-0.0881735\pi$
$593$	5.94427	+	10.2958i	0.244102	+	0.422797i	−0.717777	+	0.696273i	$0.754840\pi$
$594$	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	$-0.358711\pi$
$601$	21.0557			0.858881			0.429441	+	0.903095i	$0.358711\pi$
$602$		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	0.976368	−	0.216115i	$-0.0693387\pi$
$607$	7.41641	+	12.8456i	0.301023	+	0.521387i	−0.675345	+	0.737502i	$0.736005\pi$
$608$	−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	−0.964320	−	0.264740i	$-0.914714\pi$
$619$	−6.29180	+	10.8977i	−0.252889	+	0.438016i	0.711431	+	0.702756i	$0.248047\pi$
$620$	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	$-0.725063\pi$
$643$	−32.9443			−1.29920			−0.649598	+	0.760278i	$0.725063\pi$
$644$		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	$0.398725\pi$
$647$	−16.9443	+	29.3483i	−0.666148	+	1.15380i	−0.978973	+	0.203991i	$0.934609\pi$
$648$	−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	−0.864940	−	0.501876i	$-0.832643\pi$
$661$	0.0557281	−	0.0965239i	0.00216757	−	0.00375434i	0.867107	+	0.498122i	$0.165977\pi$
$662$	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	$-0.897501\pi$
$677$	−19.4721	−	33.7267i	−0.748375	−	1.29622i	0.200226	−	0.979750i	$-0.435832\pi$
$678$	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	0.869435	−	0.494047i	$-0.164483\pi$
$691$	0.180340	+	0.312358i	0.00686045	+	0.0118827i	−0.862575	+	0.505930i	$0.831150\pi$
$692$	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	$-0.828652\pi$
$719$	−23.4164	−	40.5584i	−0.873285	−	1.51257i	−0.0147058	−	0.999892i	$-0.504681\pi$
$720$	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	$-0.411302\pi$
$727$	14.8328			0.550119			0.275059	+	0.961427i	$0.411302\pi$
$728$		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	$-0.923836\pi$
$733$	−18.7082	−	32.4036i	−0.691003	−	1.19685i	0.280506	−	0.959852i	$-0.409498\pi$
$734$	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	0.785638	−	0.618687i	$-0.212335\pi$
$761$	−3.94427	−	6.83168i	−0.142980	−	0.247648i	−0.928617	+	0.371039i	$0.879002\pi$
$762$	−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	$-0.495220\pi$
$769$	0.832816			0.0300321			0.0150161	+	0.999887i	$0.495220\pi$
$770$		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	−0.547827	−	0.836592i	$-0.684545\pi$
$773$	12.5279	−	21.6989i	0.450596	−	0.780455i	0.998423	+	0.0561365i	$0.0178782\pi$
$774$	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	$0.504063\pi$
$787$	−24.4721	+	42.3870i	−0.872337	+	1.51093i	−0.859572	+	0.511014i	$0.829270\pi$
$788$	−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	$-0.505952\pi$
$797$	−1.05573			−0.0373958			−0.0186979	+	0.999825i	$0.505952\pi$
$798$		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	$-0.332652\pi$
$811$	28.5836			1.00371			0.501853	+	0.864953i	$0.332652\pi$
$812$		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	$-0.652751\pi$
$829$	15.4721	−	26.7985i	0.537369	−	0.930751i	0.999045	−	0.0437022i	$-0.0139153\pi$
$830$	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	$-0.493586\pi$
$839$	1.16718			0.0402957			0.0201478	+	0.999797i	$0.493586\pi$
$840$		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	$-0.319961\pi$
$853$	31.3050			1.07186			0.535931	+	0.844262i	$0.319961\pi$
$854$		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	−0.685713	−	0.727872i	$-0.740510\pi$
$857$	8.41641	−	14.5776i	0.287499	−	0.497963i	0.973212	+	0.229909i	$0.0738429\pi$
$858$	12.3607	−	21.4093i	0.421987	−	0.730902i
$859$	−20.7639	−	35.9642i	−0.708456	−	1.22708i	−0.965430	−	0.260664i	$-0.916059\pi$
$859$	−20.7639	−	35.9642i	−0.708456	−	1.22708i	0.256973	−	0.966418i	$-0.417275\pi$
$860$	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	$-0.457576\pi$
$881$	7.88854			0.265772			0.132886	+	0.991131i	$0.457576\pi$
$882$		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	0.608210	−	0.793776i	$-0.291888\pi$
$887$	−11.4164	−	19.7738i	−0.383325	−	0.663939i	−0.991535	+	0.129837i	$0.958555\pi$
$888$	−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	$0.157460\pi$
$929$	25.9443	+	44.9368i	0.851204	+	1.47433i	−0.0289185	+	0.999582i	$0.509206\pi$
$930$	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	$-0.751756\pi$
$937$	−43.5279			−1.42199			−0.710997	+	0.703195i	$0.751756\pi$
$938$		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	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$	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	0.619610	−	0.784910i	$-0.287291\pi$
$971$	−11.5279	−	19.9668i	−0.369947	−	0.640767i	−0.989557	+	0.144143i	$0.953957\pi$
$972$	−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	−0.999954	−	0.00954955i	$-0.996960\pi$
$983$	−15.4164	+	26.7020i	−0.491707	+	0.851662i	0.508247	+	0.861211i	$0.330294\pi$
$984$	−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	−0.984270	−	0.176672i	$-0.943467\pi$
$997$	−10.7082	+	18.5472i	−0.339132	+	0.587394i	0.645138	+	0.764066i	$0.276800\pi$
$998$	−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.k.361.1		4
7.2	even	3	inner	735.2.i.k.226.1		4
7.3	odd	6		735.2.a.k.1.2		2
7.4	even	3		105.2.a.b.1.2	✓	2
7.5	odd	6		735.2.i.i.226.1		4
7.6	odd	2		735.2.i.i.361.1		4
21.11	odd	6		315.2.a.d.1.1		2
21.17	even	6		2205.2.a.w.1.1		2
28.11	odd	6		1680.2.a.v.1.2		2
35.4	even	6		525.2.a.g.1.1		2
35.18	odd	12		525.2.d.c.274.1		4
35.24	odd	6		3675.2.a.y.1.1		2
35.32	odd	12		525.2.d.c.274.4		4
56.11	odd	6		6720.2.a.cs.1.1		2
56.53	even	6		6720.2.a.cx.1.2		2
84.11	even	6		5040.2.a.bw.1.1		2
105.32	even	12		1575.2.d.d.1324.2		4
105.53	even	12		1575.2.d.d.1324.3		4
105.74	odd	6		1575.2.a.r.1.2		2
140.39	odd	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	7.4	even	3
315.2.a.d.1.1		2	21.11	odd	6
525.2.a.g.1.1		2	35.4	even	6
525.2.d.c.274.1		4	35.18	odd	12
525.2.d.c.274.4		4	35.32	odd	12
735.2.a.k.1.2		2	7.3	odd	6
735.2.i.i.226.1		4	7.5	odd	6
735.2.i.i.361.1		4	7.6	odd	2
735.2.i.k.226.1		4	7.2	even	3	inner
735.2.i.k.361.1		4	1.1	even	1	trivial
1575.2.a.r.1.2		2	105.74	odd	6
1575.2.d.d.1324.2		4	105.32	even	12
1575.2.d.d.1324.3		4	105.53	even	12
1680.2.a.v.1.2		2	28.11	odd	6
2205.2.a.w.1.1		2	21.17	even	6
3675.2.a.y.1.1		2	35.24	odd	6
5040.2.a.bw.1.1		2	84.11	even	6
6720.2.a.cs.1.1		2	56.11	odd	6
6720.2.a.cx.1.2		2	56.53	even	6
8400.2.a.cx.1.2		2	140.39	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
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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