LMFDB - Embedded newform 735.2.i.i.226.2

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			226.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	735.226
Dual form			735.2.i.i.361.2

$q$-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} +(-3.23607 - 5.60503i) 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} +(-1.23607 + 2.14093i) q^{19} +3.00000 q^{20} -14.4721 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} +(0.763932 + 1.32317i) q^{31} +(-3.35410 - 5.80948i) q^{32} +(-3.23607 + 5.60503i) q^{33} -4.47214 q^{34} +3.00000 q^{36} +(3.47214 - 6.01392i) q^{37} +(2.76393 + 4.78727i) q^{38} +(2.23607 + 3.87298i) q^{39} +(1.11803 - 1.93649i) q^{40} +2.00000 q^{41} +8.94427 q^{43} +(-9.70820 + 16.8151i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(4.47214 + 7.74597i) q^{46} +(6.47214 - 11.2101i) q^{47} -1.00000 q^{48} -2.23607 q^{50} +(-1.00000 + 1.73205i) q^{51} +(6.70820 + 11.6190i) q^{52} +(1.76393 + 3.05522i) q^{53} +(1.11803 - 1.93649i) q^{54} +6.47214 q^{55} +2.47214 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} +3.41641 q^{62} -13.0000 q^{64} +(2.23607 - 3.87298i) q^{65} +(7.23607 + 12.5332i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +4.00000 q^{69} +5.52786 q^{71} +(1.11803 - 1.93649i) q^{72} +(-6.23607 - 10.8012i) q^{73} +(-7.76393 - 13.4475i) q^{74} +(-0.500000 + 0.866025i) q^{75} +7.41641 q^{76} +10.0000 q^{78} +(-6.47214 + 11.2101i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.23607 - 3.87298i) q^{82} +16.9443 q^{83} +2.00000 q^{85} +(10.0000 - 17.3205i) q^{86} +(1.00000 + 1.73205i) q^{87} +(7.23607 + 12.5332i) q^{88} +(-1.00000 + 1.73205i) q^{89} -2.23607 q^{90} +12.0000 q^{92} +(0.763932 - 1.32317i) q^{93} +(-14.4721 - 25.0665i) q^{94} +(-1.23607 - 2.14093i) q^{95} +(-3.35410 + 5.80948i) q^{96} -8.47214 q^{97} +6.47214 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	1.11803	−	1.93649i	0.790569	−	1.36931i	0.925615	−	0.378467i	$-0.123549\pi$
$3$	−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
$11$	−3.23607	−	5.60503i	−0.975711	−	1.68998i	−0.677568	−	0.735460i	$-0.736966\pi$
$11$	−3.23607	−	5.60503i	−0.975711	−	1.68998i	−0.298143	−	0.954521i	$-0.596367\pi$
$12$	−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	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	1.11803	+	1.93649i	0.263523	+	0.456435i
$19$	−1.23607	+	2.14093i	−0.283573	+	0.491164i	−0.972262	−	0.233893i	$-0.924853\pi$
$19$	−1.23607	+	2.14093i	−0.283573	+	0.491164i	0.688689	+	0.725057i	$0.258187\pi$
$20$	3.00000			0.670820
$21$		0			0
$22$	−14.4721			−3.08547
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	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
$31$	0.763932	+	1.32317i	0.137206	+	0.237648i	0.926438	−	0.376447i	$-0.122854\pi$
$31$	0.763932	+	1.32317i	0.137206	+	0.237648i	−0.789232	+	0.614095i	$0.789521\pi$
$32$	−3.35410	−	5.80948i	−0.592927	−	1.02698i
$33$	−3.23607	+	5.60503i	−0.563327	+	0.975711i
$34$	−4.47214			−0.766965
$35$		0			0
$36$	3.00000			0.500000
$37$	3.47214	−	6.01392i	0.570816	−	0.988682i	−0.425667	−	0.904880i	$-0.639960\pi$
$37$	3.47214	−	6.01392i	0.570816	−	0.988682i	0.996482	−	0.0838017i	$-0.0267062\pi$
$38$	2.76393	+	4.78727i	0.448369	+	0.776598i
$39$	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	$-0.261113\pi$
$43$	8.94427			1.36399			0.681994	+	0.731357i	$0.261113\pi$
$44$	−9.70820	+	16.8151i	−1.46357	+	2.53497i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	4.47214	+	7.74597i	0.659380	+	1.14208i
$47$	6.47214	−	11.2101i	0.944058	−	1.63516i	0.186432	−	0.982468i	$-0.440308\pi$
$47$	6.47214	−	11.2101i	0.944058	−	1.63516i	0.757626	−	0.652689i	$-0.226359\pi$
$48$	−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
$53$	1.76393	+	3.05522i	0.242295	+	0.419667i	0.961368	−	0.275268i	$-0.0887666\pi$
$53$	1.76393	+	3.05522i	0.242295	+	0.419667i	−0.719073	+	0.694935i	$0.755433\pi$
$54$	1.11803	−	1.93649i	0.152145	−	0.263523i
$55$	6.47214			0.872703
$56$		0			0
$57$	2.47214			0.327442
$58$	−2.23607	+	3.87298i	−0.293610	+	0.508548i
$59$	−4.47214	−	7.74597i	−0.582223	−	1.00844i	−0.995215	−	0.0977047i	$-0.968850\pi$
$59$	−4.47214	−	7.74597i	−0.582223	−	1.00844i	0.412993	−	0.910734i	$-0.364483\pi$
$60$	−1.50000	−	2.59808i	−0.193649	−	0.335410i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	3.41641			0.433884
$63$		0			0
$64$	−13.0000			−1.62500
$65$	2.23607	−	3.87298i	0.277350	−	0.480384i
$66$	7.23607	+	12.5332i	0.890698	+	1.54273i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	4.00000			0.481543
$70$		0			0
$71$	5.52786			0.656037			0.328018	−	0.944671i	$-0.393619\pi$
$71$	5.52786			0.656037			0.328018	+	0.944671i	$0.393619\pi$
$72$	1.11803	−	1.93649i	0.131762	−	0.228218i
$73$	−6.23607	−	10.8012i	−0.729877	−	1.26418i	−0.956935	−	0.290302i	$-0.906244\pi$
$73$	−6.23607	−	10.8012i	−0.729877	−	1.26418i	0.227058	−	0.973881i	$-0.427089\pi$
$74$	−7.76393	−	13.4475i	−0.902539	−	1.56324i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	7.41641			0.850720
$77$		0			0
$78$	10.0000			1.13228
$79$	−6.47214	+	11.2101i	−0.728172	+	1.26123i	0.229483	+	0.973313i	$0.426297\pi$
$79$	−6.47214	+	11.2101i	−0.728172	+	1.26123i	−0.957655	+	0.287918i	$0.907037\pi$
$80$	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
$83$	16.9443			1.85988			0.929938	−	0.367717i	$-0.119860\pi$
$83$	16.9443			1.85988			0.929938	+	0.367717i	$0.119860\pi$
$84$		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
$88$	7.23607	+	12.5332i	0.771367	+	1.33605i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	−2.23607			−0.235702
$91$		0			0
$92$	12.0000			1.25109
$93$	0.763932	−	1.32317i	0.0792161	−	0.137206i
$94$	−14.4721	−	25.0665i	−1.49269	−	2.58541i
$95$	−1.23607	−	2.14093i	−0.126818	−	0.219655i
$96$	−3.35410	+	5.80948i	−0.342327	+	0.592927i
$97$	−8.47214			−0.860215			−0.430108	−	0.902778i	$-0.641524\pi$
$97$	−8.47214			−0.860215			−0.430108	+	0.902778i	$0.641524\pi$
$98$		0			0
$99$	6.47214			0.650474
$100$	−1.50000	+	2.59808i	−0.150000	+	0.259808i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$	2.23607	+	3.87298i	0.221404	+	0.383482i
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	10.0000			0.980581
$105$		0			0
$106$	7.88854			0.766203
$107$	6.47214	−	11.2101i	0.625685	−	1.08372i	−0.362723	−	0.931897i	$-0.618153\pi$
$107$	6.47214	−	11.2101i	0.625685	−	1.08372i	0.988408	−	0.151821i	$-0.0485138\pi$
$108$	−1.50000	−	2.59808i	−0.144338	−	0.250000i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	7.23607	−	12.5332i	0.689932	−	1.19500i
$111$	−6.94427			−0.659121
$112$		0			0
$113$	0.472136			0.0444148			0.0222074	−	0.999753i	$-0.492931\pi$
$113$	0.472136			0.0444148			0.0222074	+	0.999753i	$0.492931\pi$
$114$	2.76393	−	4.78727i	0.258866	−	0.448369i
$115$	−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
$121$	−15.4443	+	26.7503i	−1.40402	+	2.43184i
$122$	2.23607	+	3.87298i	0.202444	+	0.350643i
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	2.29180	−	3.96951i	0.205809	−	0.356472i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.94427			−0.438733			−0.219367	−	0.975643i	$-0.570399\pi$
$127$	−4.94427			−0.438733			−0.219367	+	0.975643i	$0.570399\pi$
$128$	−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	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$	19.4164			1.68998
$133$		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
$137$	−1.76393	−	3.05522i	−0.150703	−	0.261025i	0.780783	−	0.624802i	$-0.214820\pi$
$137$	−1.76393	−	3.05522i	−0.150703	−	0.261025i	−0.931486	+	0.363777i	$0.881487\pi$
$138$	4.47214	−	7.74597i	0.380693	−	0.659380i
$139$	−7.41641			−0.629052			−0.314526	−	0.949249i	$-0.601845\pi$
$139$	−7.41641			−0.629052			−0.314526	+	0.949249i	$0.601845\pi$
$140$		0			0
$141$	−12.9443			−1.09010
$142$	6.18034	−	10.7047i	0.518643	−	0.898315i
$143$	14.4721	+	25.0665i	1.21022	+	2.09616i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	−27.8885			−2.30807
$147$		0			0
$148$	−20.8328			−1.71245
$149$	7.47214	−	12.9421i	0.612141	−	1.06026i	−0.378738	−	0.925504i	$-0.623642\pi$
$149$	7.47214	−	12.9421i	0.612141	−	1.06026i	0.990879	−	0.134756i	$-0.0430249\pi$
$150$	1.11803	+	1.93649i	0.0912871	+	0.158114i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	2.76393	−	4.78727i	0.224184	−	0.388299i
$153$	2.00000			0.161690
$154$		0			0
$155$	−1.52786			−0.122721
$156$	6.70820	−	11.6190i	0.537086	−	0.930261i
$157$	−0.236068	−	0.408882i	−0.0188403	−	0.0326323i	0.856452	−	0.516227i	$-0.172664\pi$
$157$	−0.236068	−	0.408882i	−0.0188403	−	0.0326323i	−0.875292	+	0.483595i	$0.839331\pi$
$158$	14.4721	+	25.0665i	1.15134	+	1.99418i
$159$	1.76393	−	3.05522i	0.139889	−	0.242295i
$160$	6.70820			0.530330
$161$		0			0
$162$	−2.23607			−0.175682
$163$	8.47214	−	14.6742i	0.663589	−	1.14937i	−0.316077	−	0.948734i	$-0.602366\pi$
$163$	8.47214	−	14.6742i	0.663589	−	1.14937i	0.979666	−	0.200636i	$-0.0643009\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$	−3.23607	−	5.60503i	−0.251928	−	0.436351i
$166$	18.9443	−	32.8124i	1.47036	−	2.54674i
$167$	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
$171$	−1.23607	−	2.14093i	−0.0945245	−	0.163721i
$172$	−13.4164	−	23.2379i	−1.02299	−	1.77187i
$173$	−1.47214	+	2.54981i	−0.111924	+	0.193859i	−0.916546	−	0.399929i	$-0.869035\pi$
$173$	−1.47214	+	2.54981i	−0.111924	+	0.193859i	0.804622	+	0.593788i	$0.202368\pi$
$174$	4.47214			0.339032
$175$		0			0
$176$	−6.47214			−0.487856
$177$	−4.47214	+	7.74597i	−0.336146	+	0.582223i
$178$	2.23607	+	3.87298i	0.167600	+	0.290292i
$179$	−3.23607	−	5.60503i	−0.241875	−	0.418940i	0.719373	−	0.694624i	$-0.244429\pi$
$179$	−3.23607	−	5.60503i	−0.241875	−	0.418940i	−0.961248	+	0.275684i	$0.911096\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	−1.05573			−0.0784717			−0.0392358	−	0.999230i	$-0.512492\pi$
$181$	−1.05573			−0.0784717			−0.0392358	+	0.999230i	$0.512492\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$	4.47214	−	7.74597i	0.329690	−	0.571040i
$185$	3.47214	+	6.01392i	0.255277	+	0.442152i
$186$	−1.70820	−	2.95870i	−0.125252	−	0.216942i
$187$	−6.47214	+	11.2101i	−0.473289	+	0.819761i
$188$	−38.8328			−2.83217
$189$		0			0
$190$	−5.52786			−0.401033
$191$	−0.291796	+	0.505406i	−0.0211136	+	0.0365699i	−0.876389	−	0.481604i	$-0.840055\pi$
$191$	−0.291796	+	0.505406i	−0.0211136	+	0.0365699i	0.855276	+	0.518173i	$0.173388\pi$
$192$	6.50000	+	11.2583i	0.469097	+	0.812500i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	−9.47214	+	16.4062i	−0.680060	+	1.17790i
$195$	−4.47214			−0.320256
$196$		0			0
$197$	15.5279			1.10631			0.553157	−	0.833077i	$-0.313423\pi$
$197$	15.5279			1.10631			0.553157	+	0.833077i	$0.313423\pi$
$198$	7.23607	−	12.5332i	0.514245	−	0.890698i
$199$	13.7082	+	23.7433i	0.971749	+	1.68312i	0.690272	+	0.723550i	$0.257491\pi$
$199$	13.7082	+	23.7433i	0.971749	+	1.68312i	0.281477	+	0.959568i	$0.409176\pi$
$200$	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
$211$	−16.9443			−1.16649			−0.583246	−	0.812296i	$-0.698218\pi$
$211$	−16.9443			−1.16649			−0.583246	+	0.812296i	$0.698218\pi$
$212$	5.29180	−	9.16566i	0.363442	−	0.629500i
$213$	−2.76393	−	4.78727i	−0.189382	−	0.328018i
$214$	−14.4721	−	25.0665i	−0.989295	−	1.71351i
$215$	−4.47214	+	7.74597i	−0.304997	+	0.528271i
$216$	−2.23607			−0.152145
$217$		0			0
$218$	4.47214			0.302891
$219$	−6.23607	+	10.8012i	−0.421394	+	0.729877i
$220$	−9.70820	−	16.8151i	−0.654527	−	1.13367i
$221$	4.47214	+	7.74597i	0.300828	+	0.521050i
$222$	−7.76393	+	13.4475i	−0.521081	+	0.902539i
$223$	12.9443			0.866813			0.433406	−	0.901199i	$-0.357312\pi$
$223$	12.9443			0.866813			0.433406	+	0.901199i	$0.357312\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	0.527864	−	0.914287i	0.0351130	−	0.0608175i
$227$	0.472136	+	0.817763i	0.0313368	+	0.0542769i	0.881268	−	0.472616i	$-0.156690\pi$
$227$	0.472136	+	0.817763i	0.0313368	+	0.0542769i	−0.849932	+	0.526893i	$0.823357\pi$
$228$	−3.70820	−	6.42280i	−0.245582	−	0.425360i
$229$	11.9443	−	20.6881i	0.789300	−	1.36711i	−0.137097	−	0.990558i	$-0.543777\pi$
$229$	11.9443	−	20.6881i	0.789300	−	1.36711i	0.926396	−	0.376550i	$-0.122890\pi$
$230$	−8.94427			−0.589768
$231$		0			0
$232$	4.47214			0.293610
$233$	4.70820	−	8.15485i	0.308445	−	0.534242i	−0.669578	−	0.742742i	$-0.733525\pi$
$233$	4.70820	−	8.15485i	0.308445	−	0.534242i	0.978022	+	0.208500i	$0.0668582\pi$
$234$	−5.00000	−	8.66025i	−0.326860	−	0.566139i
$235$	6.47214	+	11.2101i	0.422196	+	0.731264i
$236$	−13.4164	+	23.2379i	−0.873334	+	1.51266i
$237$	12.9443			0.840821
$238$		0			0
$239$	−10.4721			−0.677386			−0.338693	−	0.940897i	$-0.609985\pi$
$239$	−10.4721			−0.677386			−0.338693	+	0.940897i	$0.609985\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−9.47214	−	16.4062i	−0.610154	−	1.05682i	−0.991214	−	0.132267i	$-0.957774\pi$
$241$	−9.47214	−	16.4062i	−0.610154	−	1.05682i	0.381060	−	0.924550i	$-0.375559\pi$
$242$	34.5344	+	59.8154i	2.21996	+	3.84508i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	6.00000			0.384111
$245$		0			0
$246$	−4.47214			−0.285133
$247$	5.52786	−	9.57454i	0.351730	−	0.609213i
$248$	−1.70820	−	2.95870i	−0.108471	−	0.187877i
$249$	−8.47214	−	14.6742i	−0.536900	−	0.929938i
$250$	1.11803	−	1.93649i	0.0707107	−	0.122474i
$251$	−16.9443			−1.06951			−0.534756	−	0.845006i	$-0.679597\pi$
$251$	−16.9443			−1.06951			−0.534756	+	0.845006i	$0.679597\pi$
$252$		0			0
$253$	25.8885			1.62760
$254$	−5.52786	+	9.57454i	−0.346849	+	0.600760i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	9.47214	−	16.4062i	0.590856	−	1.02339i	−0.403262	−	0.915085i	$-0.632124\pi$
$257$	9.47214	−	16.4062i	0.590856	−	1.02339i	0.994117	−	0.108307i	$-0.0345430\pi$
$258$	−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
$263$	−3.52786	−	6.11044i	−0.217537	−	0.376786i	0.736517	−	0.676419i	$-0.236469\pi$
$263$	−3.52786	−	6.11044i	−0.217537	−	0.376786i	−0.954055	+	0.299633i	$0.903136\pi$
$264$	7.23607	−	12.5332i	0.445349	−	0.771367i
$265$	−3.52786			−0.216715
$266$		0			0
$267$	2.00000			0.122398
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	5.94427	+	10.2958i	0.362429	+	0.627745i	0.988360	−	0.152133i	$-0.0486143\pi$
$269$	5.94427	+	10.2958i	0.362429	+	0.627745i	−0.625931	+	0.779878i	$0.715281\pi$
$270$	1.11803	+	1.93649i	0.0680414	+	0.117851i
$271$	−0.763932	+	1.32317i	−0.0464056	+	0.0803768i	−0.888295	−	0.459273i	$-0.848110\pi$
$271$	−0.763932	+	1.32317i	−0.0464056	+	0.0803768i	0.841890	+	0.539650i	$0.181443\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	−7.88854			−0.476564
$275$	−3.23607	+	5.60503i	−0.195142	+	0.337996i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	−9.47214	−	16.4062i	−0.569125	−	0.985754i	−0.996653	−	0.0817518i	$-0.973949\pi$
$277$	−9.47214	−	16.4062i	−0.569125	−	0.985754i	0.427527	−	0.904002i	$-0.359385\pi$
$278$	−8.29180	+	14.3618i	−0.497309	+	0.861364i
$279$	−1.52786			−0.0914708
$280$		0			0
$281$	−10.9443			−0.652881			−0.326440	−	0.945218i	$-0.605849\pi$
$281$	−10.9443			−0.652881			−0.326440	+	0.945218i	$0.605849\pi$
$282$	−14.4721	+	25.0665i	−0.861803	+	1.49269i
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	0.987401	−	0.158237i	$-0.0505811\pi$
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	−0.630738	+	0.775996i	$0.717248\pi$
$284$	−8.29180	−	14.3618i	−0.492028	−	0.852217i
$285$	−1.23607	+	2.14093i	−0.0732183	+	0.126818i
$286$	64.7214			3.82705
$287$		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
$291$	4.23607	+	7.33708i	0.248323	+	0.430108i
$292$	−18.7082	+	32.4036i	−1.09481	+	1.89627i
$293$	−5.05573			−0.295359			−0.147679	−	0.989035i	$-0.547180\pi$
$293$	−5.05573			−0.295359			−0.147679	+	0.989035i	$0.547180\pi$
$294$		0			0
$295$	8.94427			0.520756
$296$	−7.76393	+	13.4475i	−0.451269	+	0.781621i
$297$	−3.23607	−	5.60503i	−0.187776	−	0.325237i
$298$	−16.7082	−	28.9395i	−0.967880	−	1.67642i
$299$	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
$304$	1.23607	+	2.14093i	0.0708934	+	0.122791i
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$	2.23607	−	3.87298i	0.127827	−	0.221404i
$307$	15.0557			0.859276			0.429638	−	0.903001i	$-0.358641\pi$
$307$	15.0557			0.859276			0.429638	+	0.903001i	$0.358641\pi$
$308$		0			0
$309$		0			0
$310$	−1.70820	+	2.95870i	−0.0970195	+	0.168043i
$311$	12.9443	+	22.4201i	0.734002	+	1.27133i	0.955160	+	0.296091i	$0.0956832\pi$
$311$	12.9443	+	22.4201i	0.734002	+	1.27133i	−0.221157	+	0.975238i	$0.570983\pi$
$312$	−5.00000	−	8.66025i	−0.283069	−	0.490290i
$313$	−8.70820	+	15.0831i	−0.492217	+	0.852544i	−0.999960	−	0.00896408i	$-0.997147\pi$
$313$	−8.70820	+	15.0831i	−0.492217	+	0.852544i	0.507743	+	0.861509i	$0.330480\pi$
$314$	−1.05573			−0.0595782
$315$		0			0
$316$	38.8328			2.18452
$317$	−7.18034	+	12.4367i	−0.403288	+	0.698515i	−0.994121	−	0.108279i	$-0.965466\pi$
$317$	−7.18034	+	12.4367i	−0.403288	+	0.698515i	0.590832	+	0.806794i	$0.298799\pi$
$318$	−3.94427	−	6.83168i	−0.221184	−	0.383102i
$319$	6.47214	+	11.2101i	0.362370	+	0.627643i
$320$	6.50000	−	11.2583i	0.363361	−	0.629360i
$321$	−12.9443			−0.722479
$322$		0			0
$323$	4.94427			0.275107
$324$	−1.50000	+	2.59808i	−0.0833333	+	0.144338i
$325$	2.23607	+	3.87298i	0.124035	+	0.214834i
$326$	−18.9443	−	32.8124i	−1.04923	−	1.81731i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−4.47214			−0.246932
$329$		0			0
$330$	−14.4721			−0.796665
$331$	−0.472136	+	0.817763i	−0.0259509	+	0.0449483i	−0.878709	−	0.477357i	$-0.841595\pi$
$331$	−0.472136	+	0.817763i	−0.0259509	+	0.0449483i	0.852758	+	0.522306i	$0.174928\pi$
$332$	−25.4164	−	44.0225i	−1.39491	−	2.41605i
$333$	3.47214	+	6.01392i	0.190272	+	0.329561i
$334$	8.94427	−	15.4919i	0.489409	−	0.847681i
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−23.8885			−1.30129			−0.650646	−	0.759381i	$-0.725502\pi$
$337$	−23.8885			−1.30129			−0.650646	+	0.759381i	$0.725502\pi$
$338$	7.82624	−	13.5554i	0.425691	−	0.737319i
$339$	−0.236068	−	0.408882i	−0.0128215	−	0.0222074i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	4.94427	−	8.56373i	0.267747	−	0.463752i
$342$	−5.52786			−0.298913
$343$		0			0
$344$	−20.0000			−1.07833
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$	3.29180	+	5.70156i	0.176968	+	0.306518i
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	0.953189	−	0.302374i	$-0.0977791\pi$
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	−0.738458	+	0.674299i	$0.764446\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	11.8885			0.636379			0.318190	−	0.948027i	$-0.396925\pi$
$349$	11.8885			0.636379			0.318190	+	0.948027i	$0.396925\pi$
$350$		0			0
$351$	−4.47214			−0.238705
$352$	−21.7082	+	37.5997i	−1.15705	+	2.00407i
$353$	3.94427	+	6.83168i	0.209932	+	0.363614i	0.951693	−	0.307051i	$-0.0993423\pi$
$353$	3.94427	+	6.83168i	0.209932	+	0.363614i	−0.741761	+	0.670665i	$0.766009\pi$
$354$	10.0000	+	17.3205i	0.531494	+	0.920575i
$355$	−2.76393	+	4.78727i	−0.146694	+	0.254082i
$356$	6.00000			0.317999
$357$		0			0
$358$	−14.4721			−0.764876
$359$	−9.23607	+	15.9973i	−0.487461	+	0.844307i	−0.999896	−	0.0144187i	$-0.995410\pi$
$359$	−9.23607	+	15.9973i	−0.487461	+	0.844307i	0.512435	+	0.858726i	$0.328744\pi$
$360$	1.11803	+	1.93649i	0.0589256	+	0.102062i
$361$	6.44427	+	11.1618i	0.339172	+	0.587463i
$362$	−1.18034	+	2.04441i	−0.0620373	+	0.107452i
$363$	30.8885			1.62123
$364$		0			0
$365$	12.4721			0.652821
$366$	2.23607	−	3.87298i	0.116881	−	0.202444i
$367$	1.52786	+	2.64634i	0.0797539	+	0.138138i	0.903144	−	0.429338i	$-0.141253\pi$
$367$	1.52786	+	2.64634i	0.0797539	+	0.138138i	−0.823390	+	0.567476i	$0.807920\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	15.5279			0.807255
$371$		0			0
$372$	−4.58359			−0.237648
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	14.4721	+	25.0665i	0.748336	+	1.29616i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−14.4721	+	25.0665i	−0.746343	+	1.29270i
$377$	8.94427			0.460653
$378$		0			0
$379$	−37.8885			−1.94620			−0.973102	−	0.230375i	$-0.926005\pi$
$379$	−37.8885			−1.94620			−0.973102	+	0.230375i	$0.926005\pi$
$380$	−3.70820	+	6.42280i	−0.190227	+	0.329483i
$381$	2.47214	+	4.28187i	0.126651	+	0.219367i
$382$	0.652476	+	1.13012i	0.0333836	+	0.0578220i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	15.6525			0.798762
$385$		0			0
$386$	31.3050			1.59338
$387$	−4.47214	+	7.74597i	−0.227331	+	0.393750i
$388$	12.7082	+	22.0113i	0.645161	+	1.11745i
$389$	3.47214	+	6.01392i	0.176044	+	0.304918i	0.940522	−	0.339732i	$-0.110336\pi$
$389$	3.47214	+	6.01392i	0.176044	+	0.304918i	−0.764478	+	0.644650i	$0.777003\pi$
$390$	−5.00000	+	8.66025i	−0.253185	+	0.438529i
$391$	8.00000			0.404577
$392$		0			0
$393$	−4.00000			−0.201773
$394$	17.3607	−	30.0696i	0.874618	−	1.51488i
$395$	−6.47214	−	11.2101i	−0.325649	−	0.564040i
$396$	−9.70820	−	16.8151i	−0.487856	−	0.844991i
$397$	−6.70820	+	11.6190i	−0.336675	+	0.583138i	−0.983805	−	0.179241i	$-0.942636\pi$
$397$	−6.70820	+	11.6190i	−0.336675	+	0.583138i	0.647130	+	0.762380i	$0.275969\pi$
$398$	61.3050			3.07294
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	−0.963439	−	0.267927i	$-0.913661\pi$
$401$	−5.00000	+	8.66025i	−0.249688	+	0.432472i	0.713751	+	0.700399i	$0.246995\pi$
$402$	−4.47214	−	7.74597i	−0.223050	−	0.386334i
$403$	−3.41641	−	5.91739i	−0.170183	−	0.294766i
$404$	−21.0000	+	36.3731i	−1.04479	+	1.80963i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−44.9443			−2.22780
$408$	2.23607	−	3.87298i	0.110702	−	0.191741i
$409$	5.94427	+	10.2958i	0.293925	+	0.509094i	0.974734	−	0.223367i	$-0.0717050\pi$
$409$	5.94427	+	10.2958i	0.293925	+	0.509094i	−0.680809	+	0.732461i	$0.738372\pi$
$410$	2.23607	+	3.87298i	0.110432	+	0.191273i
$411$	−1.76393	+	3.05522i	−0.0870084	+	0.150703i
$412$		0			0
$413$		0			0
$414$	−8.94427			−0.439587
$415$	−8.47214	+	14.6742i	−0.415881	+	0.720327i
$416$	15.0000	+	25.9808i	0.735436	+	1.27381i
$417$	3.70820	+	6.42280i	0.181592	+	0.314526i
$418$	17.8885	−	30.9839i	0.874957	−	1.51547i
$419$	29.8885			1.46015			0.730075	−	0.683367i	$-0.239485\pi$
$419$	29.8885			1.46015			0.730075	+	0.683367i	$0.239485\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	−18.9443	+	32.8124i	−0.922193	+	1.59728i
$423$	6.47214	+	11.2101i	0.314686	+	0.545052i
$424$	−3.94427	−	6.83168i	−0.191551	−	0.331776i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	−12.3607			−0.598877
$427$		0			0
$428$	−38.8328			−1.87705
$429$	14.4721	−	25.0665i	0.698721	−	1.21022i
$430$	10.0000	+	17.3205i	0.482243	+	0.835269i
$431$	9.23607	+	15.9973i	0.444886	+	0.770565i	0.998044	−	0.0625113i	$-0.0199110\pi$
$431$	9.23607	+	15.9973i	0.444886	+	0.770565i	−0.553159	+	0.833076i	$0.686578\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−16.4721			−0.791600			−0.395800	−	0.918337i	$-0.629533\pi$
$433$	−16.4721			−0.791600			−0.395800	+	0.918337i	$0.629533\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$	3.00000	−	5.19615i	0.143674	−	0.248851i
$437$	−4.94427	−	8.56373i	−0.236517	−	0.409659i
$438$	13.9443	+	24.1522i	0.666283	+	1.15404i
$439$	0.763932	−	1.32317i	0.0364605	−	0.0631514i	−0.847219	−	0.531243i	$-0.821725\pi$
$439$	0.763932	−	1.32317i	0.0364605	−	0.0631514i	0.883680	+	0.468092i	$0.155058\pi$
$440$	−14.4721			−0.689932
$441$		0			0
$442$	20.0000			0.951303
$443$	4.00000	−	6.92820i	0.190046	−	0.329169i	−0.755219	−	0.655472i	$-0.772470\pi$
$443$	4.00000	−	6.92820i	0.190046	−	0.329169i	0.945265	+	0.326303i	$0.105803\pi$
$444$	10.4164	+	18.0417i	0.494341	+	0.856223i
$445$	−1.00000	−	1.73205i	−0.0474045	−	0.0821071i
$446$	14.4721	−	25.0665i	0.685275	−	1.18693i
$447$	−14.9443			−0.706840
$448$		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
$451$	−6.47214	−	11.2101i	−0.304761	−	0.527862i
$452$	−0.708204	−	1.22665i	−0.0333111	−	0.0576965i
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$	2.11146			0.0990955
$455$		0			0
$456$	−5.52786			−0.258866
$457$	−3.47214	+	6.01392i	−0.162420	+	0.281319i	−0.935736	−	0.352701i	$-0.885263\pi$
$457$	−3.47214	+	6.01392i	−0.162420	+	0.281319i	0.773316	+	0.634020i	$0.218597\pi$
$458$	−26.7082	−	46.2600i	−1.24799	−	2.16159i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−6.00000	+	10.3923i	−0.279751	+	0.484544i
$461$	−3.88854			−0.181108			−0.0905538	−	0.995892i	$-0.528864\pi$
$461$	−3.88854			−0.181108			−0.0905538	+	0.995892i	$0.528864\pi$
$462$		0			0
$463$	20.9443			0.973363			0.486681	−	0.873580i	$-0.338207\pi$
$463$	20.9443			0.973363			0.486681	+	0.873580i	$0.338207\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	0.763932	+	1.32317i	0.0354265	+	0.0613605i
$466$	−10.5279	−	18.2348i	−0.487694	−	0.844711i
$467$	−4.47214	+	7.74597i	−0.206946	+	0.358441i	−0.950751	−	0.309956i	$-0.899686\pi$
$467$	−4.47214	+	7.74597i	−0.206946	+	0.358441i	0.743805	+	0.668397i	$0.233019\pi$
$468$	−13.4164			−0.620174
$469$		0			0
$470$	28.9443			1.33510
$471$	−0.236068	+	0.408882i	−0.0108774	+	0.0188403i
$472$	10.0000	+	17.3205i	0.460287	+	0.797241i
$473$	−28.9443	−	50.1329i	−1.33086	−	2.30512i
$474$	14.4721	−	25.0665i	0.664727	−	1.15134i
$475$	2.47214			0.113429
$476$		0			0
$477$	−3.52786			−0.161530
$478$	−11.7082	+	20.2792i	−0.535521	+	0.927549i
$479$	−8.94427	−	15.4919i	−0.408674	−	0.707845i	0.586067	−	0.810262i	$-0.300675\pi$
$479$	−8.94427	−	15.4919i	−0.408674	−	0.707845i	−0.994741	+	0.102418i	$0.967342\pi$
$480$	−3.35410	−	5.80948i	−0.153093	−	0.265165i
$481$	−15.5279	+	26.8950i	−0.708010	+	1.22631i
$482$	−42.3607			−1.92948
$483$		0			0
$484$	92.6656			4.21207
$485$	4.23607	−	7.33708i	0.192350	−	0.333160i
$486$	1.11803	+	1.93649i	0.0507151	+	0.0878410i
$487$	10.4721	+	18.1383i	0.474538	+	0.821924i	0.999575	−	0.0291558i	$-0.00928189\pi$
$487$	10.4721	+	18.1383i	0.474538	+	0.821924i	−0.525037	+	0.851079i	$0.675949\pi$
$488$	2.23607	−	3.87298i	0.101222	−	0.175322i
$489$	−16.9443			−0.766246
$490$		0			0
$491$	−21.3050			−0.961479			−0.480740	−	0.876863i	$-0.659632\pi$
$491$	−21.3050			−0.961479			−0.480740	+	0.876863i	$0.659632\pi$
$492$	−3.00000	+	5.19615i	−0.135250	+	0.234261i
$493$	2.00000	+	3.46410i	0.0900755	+	0.156015i
$494$	−12.3607	−	21.4093i	−0.556133	−	0.963251i
$495$	−3.23607	+	5.60503i	−0.145450	+	0.251928i
$496$	1.52786			0.0686031
$497$		0			0
$498$	−37.8885			−1.69783
$499$	6.94427	−	12.0278i	0.310868	−	0.538440i	−0.667682	−	0.744446i	$-0.732714\pi$
$499$	6.94427	−	12.0278i	0.310868	−	0.538440i	0.978551	+	0.206007i	$0.0660469\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$	−18.9443	+	32.8124i	−0.845524	+	1.46449i
$503$	−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
$506$	28.9443	−	50.1329i	1.28673	−	2.22868i
$507$	−3.50000	−	6.06218i	−0.155440	−	0.269231i
$508$	7.41641	+	12.8456i	0.329050	+	0.569931i
$509$	−11.9443	+	20.6881i	−0.529421	+	0.916983i	0.469991	+	0.882671i	$0.344257\pi$
$509$	−11.9443	+	20.6881i	−0.529421	+	0.916983i	−0.999411	+	0.0343119i	$0.989076\pi$
$510$	−4.47214			−0.198030
$511$		0			0
$512$	−11.1803			−0.494106
$513$	−1.23607	+	2.14093i	−0.0545737	+	0.0945245i
$514$	−21.1803	−	36.6854i	−0.934225	−	1.61812i
$515$		0			0
$516$	−13.4164	+	23.2379i	−0.590624	+	1.02299i
$517$	−83.7771			−3.68451
$518$		0			0
$519$	2.94427			0.129239
$520$	−5.00000	+	8.66025i	−0.219265	+	0.379777i
$521$	−9.94427	−	17.2240i	−0.435666	−	0.754596i	0.561683	−	0.827352i	$-0.310154\pi$
$521$	−9.94427	−	17.2240i	−0.435666	−	0.754596i	−0.997350	+	0.0727559i	$0.976821\pi$
$522$	−2.23607	−	3.87298i	−0.0978700	−	0.169516i
$523$	−4.47214	+	7.74597i	−0.195553	+	0.338707i	−0.947082	−	0.320993i	$-0.895983\pi$
$523$	−4.47214	+	7.74597i	−0.195553	+	0.338707i	0.751529	+	0.659700i	$0.229317\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−15.7771			−0.687914
$527$	1.52786	−	2.64634i	0.0665548	−	0.115276i
$528$	3.23607	+	5.60503i	0.140832	+	0.243928i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−3.94427	+	6.83168i	−0.171328	+	0.296749i
$531$	8.94427			0.388148
$532$		0			0
$533$	−8.94427			−0.387419
$534$	2.23607	−	3.87298i	0.0967641	−	0.167600i
$535$	6.47214	+	11.2101i	0.279815	+	0.484654i
$536$	−4.47214	−	7.74597i	−0.193167	−	0.334575i
$537$	−3.23607	+	5.60503i	−0.139647	+	0.241875i
$538$	26.5836			1.14610
$539$		0			0
$540$	3.00000			0.129099
$541$	5.94427	−	10.2958i	0.255564	−	0.442650i	−0.709484	−	0.704721i	$-0.751072\pi$
$541$	5.94427	−	10.2958i	0.255564	−	0.442650i	0.965049	+	0.262071i	$0.0844054\pi$
$542$	1.70820	+	2.95870i	0.0733736	+	0.127087i
$543$	0.527864	+	0.914287i	0.0226528	+	0.0392358i
$544$	−6.70820	+	11.6190i	−0.287612	+	0.498158i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	5.88854			0.251776			0.125888	−	0.992044i	$-0.459822\pi$
$547$	5.88854			0.251776			0.125888	+	0.992044i	$0.459822\pi$
$548$	−5.29180	+	9.16566i	−0.226054	+	0.391538i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	7.23607	+	12.5332i	0.308547	+	0.534419i
$551$	2.47214	−	4.28187i	0.105317	−	0.182414i
$552$	−8.94427			−0.380693
$553$		0			0
$554$	−42.3607			−1.79973
$555$	3.47214	−	6.01392i	0.147384	−	0.255277i
$556$	11.1246	+	19.2684i	0.471789	+	0.817162i
$557$	−10.2361	−	17.7294i	−0.433716	−	0.751218i	0.563474	−	0.826134i	$-0.309465\pi$
$557$	−10.2361	−	17.7294i	−0.433716	−	0.751218i	−0.997190	+	0.0749156i	$0.976131\pi$
$558$	−1.70820	+	2.95870i	−0.0723140	+	0.125252i
$559$	−40.0000			−1.69182
$560$		0			0
$561$	12.9443			0.546508
$562$	−12.2361	+	21.1935i	−0.516147	+	0.893993i
$563$	6.94427	+	12.0278i	0.292666	+	0.506913i	0.974439	−	0.224651i	$-0.0721242\pi$
$563$	6.94427	+	12.0278i	0.292666	+	0.506913i	−0.681773	+	0.731564i	$0.738791\pi$
$564$	19.4164	+	33.6302i	0.817578	+	1.41609i
$565$	−0.236068	+	0.408882i	−0.00993145	+	0.0172018i
$566$	26.8328			1.12787
$567$		0			0
$568$	−12.3607			−0.518643
$569$	19.9443	−	34.5445i	0.836107	−	1.44818i	−0.0570183	−	0.998373i	$-0.518159\pi$
$569$	19.9443	−	34.5445i	0.836107	−	1.44818i	0.893126	−	0.449807i	$-0.148507\pi$
$570$	2.76393	+	4.78727i	0.115768	+	0.200517i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	43.4164	−	75.1994i	1.81533	−	3.14425i
$573$	0.583592			0.0243799
$574$		0			0
$575$	4.00000			0.166812
$576$	6.50000	−	11.2583i	0.270833	−	0.469097i
$577$	5.18034	+	8.97261i	0.215660	+	0.373535i	0.953477	−	0.301467i	$-0.0974763\pi$
$577$	5.18034	+	8.97261i	0.215660	+	0.373535i	−0.737816	+	0.675002i	$0.764143\pi$
$578$	−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
$582$	18.9443			0.785265
$583$	11.4164	−	19.7738i	0.472819	−	0.818947i
$584$	13.9443	+	24.1522i	0.577018	+	0.999425i
$585$	2.23607	+	3.87298i	0.0924500	+	0.160128i
$586$	−5.65248	+	9.79038i	−0.233502	+	0.404437i
$587$	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
$589$	−3.77709			−0.155632
$590$	10.0000	−	17.3205i	0.411693	−	0.713074i
$591$	−7.76393	−	13.4475i	−0.319365	−	0.553157i
$592$	−3.47214	−	6.01392i	−0.142704	−	0.247170i
$593$	11.9443	−	20.6881i	0.490492	−	0.849558i	−0.509448	−	0.860502i	$-0.670150\pi$
$593$	11.9443	−	20.6881i	0.490492	−	0.849558i	0.999940	+	0.0109438i	$0.00348359\pi$
$594$	−14.4721			−0.593799
$595$		0			0
$596$	−44.8328			−1.83642
$597$	13.7082	−	23.7433i	0.561039	−	0.971749i
$598$	−20.0000	−	34.6410i	−0.817861	−	1.41658i
$599$	−6.18034	−	10.7047i	−0.252522	−	0.437381i	0.711698	−	0.702486i	$-0.247927\pi$
$599$	−6.18034	−	10.7047i	−0.252522	−	0.437381i	−0.964219	+	0.265105i	$0.914593\pi$
$600$	1.11803	−	1.93649i	0.0456435	−	0.0790569i
$601$	−38.9443			−1.58857			−0.794285	−	0.607545i	$-0.792154\pi$
$601$	−38.9443			−1.58857			−0.794285	+	0.607545i	$0.792154\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$	24.0000	−	41.5692i	0.976546	−	1.69143i
$605$	−15.4443	−	26.7503i	−0.627899	−	1.08755i
$606$	15.6525	+	27.1109i	0.635838	+	1.10130i
$607$	19.4164	−	33.6302i	0.788088	−	1.36501i	−0.139049	−	0.990285i	$-0.544405\pi$
$607$	19.4164	−	33.6302i	0.788088	−	1.36501i	0.927137	−	0.374722i	$-0.122262\pi$
$608$	16.5836			0.672553
$609$		0			0
$610$	−4.47214			−0.181071
$611$	−28.9443	+	50.1329i	−1.17096	+	2.02816i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	3.47214	+	6.01392i	0.140238	+	0.242900i	0.927586	−	0.373609i	$-0.121880\pi$
$613$	3.47214	+	6.01392i	0.140238	+	0.242900i	−0.787348	+	0.616509i	$0.788546\pi$
$614$	16.8328	−	29.1553i	0.679317	−	1.17661i
$615$	2.00000			0.0806478
$616$		0			0
$617$	16.4721			0.663143			0.331572	−	0.943430i	$-0.392421\pi$
$617$	16.4721			0.663143			0.331572	+	0.943430i	$0.392421\pi$
$618$		0			0
$619$	19.7082	+	34.1356i	0.792140	+	1.37203i	0.924640	+	0.380843i	$0.124366\pi$
$619$	19.7082	+	34.1356i	0.792140	+	1.37203i	−0.132500	+	0.991183i	$0.542300\pi$
$620$	2.29180	+	3.96951i	0.0920407	+	0.159419i
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	57.8885			2.32112
$623$		0			0
$624$	4.47214			0.179029
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	19.4721	+	33.7267i	0.778263	+	1.34799i
$627$	−8.00000	−	13.8564i	−0.319489	−	0.553372i
$628$	−0.708204	+	1.22665i	−0.0282604	+	0.0489485i
$629$	−13.8885			−0.553773
$630$		0			0
$631$	30.8328			1.22744			0.613718	−	0.789526i	$-0.289673\pi$
$631$	30.8328			1.22744			0.613718	+	0.789526i	$0.289673\pi$
$632$	14.4721	−	25.0665i	0.575671	−	0.997091i
$633$	8.47214	+	14.6742i	0.336737	+	0.583246i
$634$	16.0557	+	27.8093i	0.637654	+	1.10445i
$635$	2.47214	−	4.28187i	0.0981037	−	0.169921i
$636$	−10.5836			−0.419667
$637$		0			0
$638$	28.9443			1.14591
$639$	−2.76393	+	4.78727i	−0.109339	+	0.189382i
$640$	−7.82624	−	13.5554i	−0.309359	−	0.535826i
$641$	−8.41641	−	14.5776i	−0.332428	−	0.575782i	0.650559	−	0.759455i	$-0.274535\pi$
$641$	−8.41641	−	14.5776i	−0.332428	−	0.575782i	−0.982987	+	0.183673i	$0.941201\pi$
$642$	−14.4721	+	25.0665i	−0.571170	+	0.989295i
$643$	15.0557			0.593740			0.296870	−	0.954918i	$-0.404057\pi$
$643$	15.0557			0.593740			0.296870	+	0.954918i	$0.404057\pi$
$644$		0			0
$645$	8.94427			0.352180
$646$	5.52786	−	9.57454i	0.217491	−	0.376705i
$647$	−0.944272	−	1.63553i	−0.0371232	−	0.0642992i	0.846867	−	0.531805i	$-0.178486\pi$
$647$	−0.944272	−	1.63553i	−0.0371232	−	0.0642992i	−0.883990	+	0.467506i	$0.845153\pi$
$648$	1.11803	+	1.93649i	0.0439205	+	0.0760726i
$649$	−28.9443	+	50.1329i	−1.13616	+	1.96789i
$650$	10.0000			0.392232
$651$		0			0
$652$	−50.8328			−1.99077
$653$	11.2918	−	19.5580i	0.441882	−	0.765362i	−0.555947	−	0.831218i	$-0.687644\pi$
$653$	11.2918	−	19.5580i	0.441882	−	0.765362i	0.997829	+	0.0658554i	$0.0209776\pi$
$654$	−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
$657$	12.4721			0.486584
$658$		0			0
$659$	21.3050			0.829923			0.414962	−	0.909839i	$-0.363795\pi$
$659$	21.3050			0.829923			0.414962	+	0.909839i	$0.363795\pi$
$660$	−9.70820	+	16.8151i	−0.377891	+	0.654527i
$661$	−17.9443	−	31.0804i	−0.697951	−	1.20889i	−0.969176	−	0.246371i	$-0.920762\pi$
$661$	−17.9443	−	31.0804i	−0.697951	−	1.20889i	0.271224	−	0.962516i	$-0.412571\pi$
$662$	1.05573	+	1.82857i	0.0410320	+	0.0710696i
$663$	4.47214	−	7.74597i	0.173683	−	0.300828i
$664$	−37.8885			−1.47036
$665$		0			0
$666$	15.5279			0.601693
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$	−6.47214	−	11.2101i	−0.250227	−	0.433406i
$670$	−4.47214	+	7.74597i	−0.172774	+	0.299253i
$671$	12.9443			0.499708
$672$		0			0
$673$	8.83282			0.340480			0.170240	−	0.985403i	$-0.445546\pi$
$673$	8.83282			0.340480			0.170240	+	0.985403i	$0.445546\pi$
$674$	−26.7082	+	46.2600i	−1.02876	+	1.78187i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−10.5000	−	18.1865i	−0.403846	−	0.699482i
$677$	10.5279	−	18.2348i	0.404619	−	0.700820i	−0.589658	−	0.807653i	$-0.700738\pi$
$677$	10.5279	−	18.2348i	0.404619	−	0.700820i	0.994277	+	0.106833i	$0.0340709\pi$
$678$	−1.05573			−0.0405450
$679$		0			0
$680$	−4.47214			−0.171499
$681$	0.472136	−	0.817763i	0.0180923	−	0.0313368i
$682$	−11.0557	−	19.1491i	−0.423346	−	0.733256i
$683$	0.944272	+	1.63553i	0.0361316	+	0.0625817i	0.883526	−	0.468383i	$-0.155163\pi$
$683$	0.944272	+	1.63553i	0.0361316	+	0.0625817i	−0.847394	+	0.530964i	$0.821830\pi$
$684$	−3.70820	+	6.42280i	−0.141787	+	0.245582i
$685$	3.52786			0.134793
$686$		0			0
$687$	−23.8885			−0.911405
$688$	4.47214	−	7.74597i	0.170499	−	0.295312i
$689$	−7.88854	−	13.6634i	−0.300530	−	0.520533i
$690$	4.47214	+	7.74597i	0.170251	+	0.294884i
$691$	22.1803	−	38.4175i	0.843780	−	1.46147i	−0.0428967	−	0.999080i	$-0.513659\pi$
$691$	22.1803	−	38.4175i	0.843780	−	1.46147i	0.886677	−	0.462390i	$-0.153008\pi$
$692$	8.83282			0.335773
$693$		0			0
$694$	17.8885			0.679040
$695$	3.70820	−	6.42280i	0.140660	−	0.243631i
$696$	−2.23607	−	3.87298i	−0.0847579	−	0.146805i
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	13.2918	−	23.0221i	0.503102	−	0.871398i
$699$	−9.41641			−0.356161
$700$		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
$703$	8.58359	+	14.8672i	0.323736	+	0.560728i
$704$	42.0689	+	72.8654i	1.58553	+	2.74622i
$705$	6.47214	−	11.2101i	0.243755	−	0.422196i
$706$	17.6393			0.663865
$707$		0			0
$708$	26.8328			1.00844
$709$	−12.8885	+	22.3236i	−0.484039	+	0.838381i	−0.999832	−	0.0183327i	$-0.994164\pi$
$709$	−12.8885	+	22.3236i	−0.484039	+	0.838381i	0.515793	+	0.856714i	$0.327498\pi$
$710$	6.18034	+	10.7047i	0.231944	+	0.401739i
$711$	−6.47214	−	11.2101i	−0.242724	−	0.420410i
$712$	2.23607	−	3.87298i	0.0838002	−	0.145146i
$713$	−6.11146			−0.228876
$714$		0			0
$715$	−28.9443			−1.08245
$716$	−9.70820	+	16.8151i	−0.362813	+	0.628410i
$717$	5.23607	+	9.06914i	0.195545	+	0.338693i
$718$	20.6525	+	35.7711i	0.770744	+	1.33497i
$719$	−3.41641	+	5.91739i	−0.127411	+	0.220681i	−0.922673	−	0.385584i	$-0.874000\pi$
$719$	−3.41641	+	5.91739i	−0.127411	+	0.220681i	0.795262	+	0.606266i	$0.207333\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	28.8197			1.07256
$723$	−9.47214	+	16.4062i	−0.352273	+	0.610154i
$724$	1.58359	+	2.74286i	0.0588537	+	0.101938i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	34.5344	−	59.8154i	1.28169	−	2.21996i
$727$	38.8328			1.44023			0.720115	−	0.693855i	$-0.244089\pi$
$727$	38.8328			1.44023			0.720115	+	0.693855i	$0.244089\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	13.9443	−	24.1522i	0.516101	−	0.893913i
$731$	−8.94427	−	15.4919i	−0.330816	−	0.572990i
$732$	−3.00000	−	5.19615i	−0.110883	−	0.192055i
$733$	5.29180	−	9.16566i	0.195457	−	0.338541i	−0.751593	−	0.659627i	$-0.770714\pi$
$733$	5.29180	−	9.16566i	0.195457	−	0.338541i	0.947050	+	0.321085i	$0.104048\pi$
$734$	6.83282			0.252204
$735$		0			0
$736$	26.8328			0.989071
$737$	12.9443	−	22.4201i	0.476808	−	0.825856i
$738$	2.23607	+	3.87298i	0.0823108	+	0.142566i
$739$	2.94427	+	5.09963i	0.108307	+	0.187593i	0.915084	−	0.403262i	$-0.132124\pi$
$739$	2.94427	+	5.09963i	0.108307	+	0.187593i	−0.806778	+	0.590855i	$0.798790\pi$
$740$	10.4164	−	18.0417i	0.382915	−	0.663228i
$741$	−11.0557			−0.406142
$742$		0			0
$743$	34.8328			1.27789			0.638946	−	0.769252i	$-0.279371\pi$
$743$	34.8328			1.27789			0.638946	+	0.769252i	$0.279371\pi$
$744$	−1.70820	+	2.95870i	−0.0626258	+	0.108471i
$745$	7.47214	+	12.9421i	0.273758	+	0.474163i
$746$	6.70820	+	11.6190i	0.245605	+	0.425400i
$747$	−8.47214	+	14.6742i	−0.309979	+	0.536900i
$748$	38.8328			1.41987
$749$		0			0
$750$	−2.23607			−0.0816497
$751$	10.4721	−	18.1383i	0.382134	−	0.661875i	−0.609233	−	0.792991i	$-0.708523\pi$
$751$	10.4721	−	18.1383i	0.382134	−	0.661875i	0.991367	+	0.131116i	$0.0418561\pi$
$752$	−6.47214	−	11.2101i	−0.236015	−	0.408789i
$753$	8.47214	+	14.6742i	0.308742	+	0.534756i
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	31.8885			1.15901			0.579504	−	0.814969i	$-0.303246\pi$
$757$	31.8885			1.15901			0.579504	+	0.814969i	$0.303246\pi$
$758$	−42.3607	+	73.3708i	−1.53861	+	2.66495i
$759$	−12.9443	−	22.4201i	−0.469847	−	0.813799i
$760$	2.76393	+	4.78727i	0.100258	+	0.173653i
$761$	−13.9443	+	24.1522i	−0.505479	+	0.875516i	0.494500	+	0.869177i	$0.335351\pi$
$761$	−13.9443	+	24.1522i	−0.505479	+	0.875516i	−0.999980	+	0.00633874i	$0.997982\pi$
$762$	11.0557			0.400507
$763$		0			0
$764$	1.75078			0.0633409
$765$	−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
$769$	52.8328			1.90520			0.952600	−	0.304226i	$-0.0983976\pi$
$769$	52.8328			1.90520			0.952600	+	0.304226i	$0.0983976\pi$
$770$		0			0
$771$	−18.9443			−0.682261
$772$	21.0000	−	36.3731i	0.755807	−	1.30910i
$773$	−21.4721	−	37.1908i	−0.772299	−	1.33766i	−0.936300	−	0.351201i	$-0.885773\pi$
$773$	−21.4721	−	37.1908i	−0.772299	−	1.33766i	0.164001	−	0.986460i	$-0.447560\pi$
$774$	10.0000	+	17.3205i	0.359443	+	0.622573i
$775$	0.763932	−	1.32317i	0.0274412	−	0.0475296i
$776$	18.9443			0.680060
$777$		0			0
$778$	15.5279			0.556701
$779$	−2.47214	+	4.28187i	−0.0885735	+	0.153414i
$780$	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
$785$	0.472136			0.0168513
$786$	−4.47214	+	7.74597i	−0.159516	+	0.276289i
$787$	15.5279	+	26.8950i	0.553509	+	0.958705i	0.998018	+	0.0629307i	$0.0200447\pi$
$787$	15.5279	+	26.8950i	0.553509	+	0.958705i	−0.444509	+	0.895774i	$0.646622\pi$
$788$	−23.2918	−	40.3426i	−0.829736	−	1.43714i
$789$	−3.52786	+	6.11044i	−0.125595	+	0.217537i
$790$	−28.9443			−1.02979
$791$		0			0
$792$	−14.4721			−0.514245
$793$	4.47214	−	7.74597i	0.158810	−	0.275067i
$794$	15.0000	+	25.9808i	0.532330	+	0.922023i
$795$	1.76393	+	3.05522i	0.0625602	+	0.108357i
$796$	41.1246	−	71.2299i	1.45762	−	2.52468i
$797$	18.9443			0.671041			0.335520	−	0.942033i	$-0.391088\pi$
$797$	18.9443			0.671041			0.335520	+	0.942033i	$0.391088\pi$
$798$		0			0
$799$	−25.8885			−0.915871
$800$	−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
$803$	−40.3607	+	69.9067i	−1.42430	+	2.46696i
$804$	−12.0000			−0.423207
$805$		0			0
$806$	−15.2786			−0.538167
$807$	5.94427	−	10.2958i	0.209248	−	0.362429i
$808$	15.6525	+	27.1109i	0.550652	+	0.953758i
$809$	−19.4721	−	33.7267i	−0.684604	−	1.18577i	−0.973561	−	0.228427i	$-0.926642\pi$
$809$	−19.4721	−	33.7267i	−0.684604	−	1.18577i	0.288957	−	0.957342i	$-0.406691\pi$
$810$	1.11803	−	1.93649i	0.0392837	−	0.0680414i
$811$	−55.4164			−1.94593			−0.972967	−	0.230946i	$-0.925818\pi$
$811$	−55.4164			−1.94593			−0.972967	+	0.230946i	$0.925818\pi$
$812$		0			0
$813$	1.52786			0.0535845
$814$	−50.2492	+	87.0342i	−1.76123	+	3.05055i
$815$	8.47214	+	14.6742i	0.296766	+	0.514014i
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	−11.0557	+	19.1491i	−0.386791	+	0.669942i
$818$	26.5836			0.929474
$819$		0			0
$820$	6.00000			0.209529
$821$	−16.8885	+	29.2518i	−0.589414	+	1.02090i	0.404895	+	0.914363i	$0.367308\pi$
$821$	−16.8885	+	29.2518i	−0.589414	+	1.02090i	−0.994309	+	0.106532i	$0.966025\pi$
$822$	3.94427	+	6.83168i	0.137572	+	0.238282i
$823$	−22.4721	−	38.9229i	−0.783329	−	1.35677i	−0.929992	−	0.367580i	$-0.880186\pi$
$823$	−22.4721	−	38.9229i	−0.783329	−	1.35677i	0.146663	−	0.989187i	$-0.453147\pi$
$824$		0			0
$825$	6.47214			0.225331
$826$		0			0
$827$	12.9443			0.450116			0.225058	−	0.974345i	$-0.427743\pi$
$827$	12.9443			0.450116			0.225058	+	0.974345i	$0.427743\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−6.52786	−	11.3066i	−0.226722	−	0.392694i	0.730113	−	0.683327i	$-0.239468\pi$
$829$	−6.52786	−	11.3066i	−0.226722	−	0.392694i	−0.956835	+	0.290633i	$0.906134\pi$
$830$	18.9443	+	32.8124i	0.657565	+	1.13894i
$831$	−9.47214	+	16.4062i	−0.328585	+	0.569125i
$832$	58.1378			2.01556
$833$		0			0
$834$	16.5836			0.574243
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	−24.0000	−	41.5692i	−0.830057	−	1.43770i
$837$	0.763932	+	1.32317i	0.0264054	+	0.0457354i
$838$	33.4164	−	57.8789i	1.15435	−	1.99939i
$839$	−54.8328			−1.89304			−0.946520	−	0.322647i	$-0.895427\pi$
$839$	−54.8328			−1.89304			−0.946520	+	0.322647i	$0.895427\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	24.5967	−	42.6028i	0.847660	−	1.46819i
$843$	5.47214	+	9.47802i	0.188470	+	0.326440i
$844$	25.4164	+	44.0225i	0.874869	+	1.51532i
$845$	−3.50000	+	6.06218i	−0.120404	+	0.208545i
$846$	28.9443			0.995125
$847$		0			0
$848$	3.52786			0.121147
$849$	6.00000	−	10.3923i	0.205919	−	0.356663i
$850$	2.23607	+	3.87298i	0.0766965	+	0.132842i
$851$	13.8885	+	24.0557i	0.476093	+	0.824618i
$852$	−8.29180	+	14.3618i	−0.284072	+	0.492028i
$853$	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
$855$	2.47214			0.0845453
$856$	−14.4721	+	25.0665i	−0.494647	+	0.856754i
$857$	18.4164	+	31.8982i	0.629093	+	1.08962i	0.987734	+	0.156145i	$0.0499067\pi$
$857$	18.4164	+	31.8982i	0.629093	+	1.08962i	−0.358642	+	0.933475i	$0.616760\pi$
$858$	−32.3607	−	56.0503i	−1.10478	−	1.91353i
$859$	25.2361	−	43.7102i	0.861044	−	1.49137i	−0.00987923	−	0.999951i	$-0.503145\pi$
$859$	25.2361	−	43.7102i	0.861044	−	1.49137i	0.870923	−	0.491420i	$-0.163522\pi$
$860$	26.8328			0.914991
$861$		0			0
$862$	41.3050			1.40685
$863$	−10.9443	+	18.9560i	−0.372547	+	0.645271i	−0.989957	−	0.141371i	$-0.954849\pi$
$863$	−10.9443	+	18.9560i	−0.372547	+	0.645271i	0.617409	+	0.786642i	$0.288182\pi$
$864$	−3.35410	−	5.80948i	−0.114109	−	0.197642i
$865$	−1.47214	−	2.54981i	−0.0500541	−	0.0866963i
$866$	−18.4164	+	31.8982i	−0.625815	+	1.08394i
$867$	−13.0000			−0.441503
$868$		0			0
$869$	83.7771			2.84194
$870$	−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
$873$	4.23607	−	7.33708i	0.143369	−	0.248323i
$874$	−22.1115			−0.747931
$875$		0			0
$876$	37.4164			1.26418
$877$	28.4164	−	49.2187i	0.959554	−	1.66200i	0.235969	−	0.971761i	$-0.424174\pi$
$877$	28.4164	−	49.2187i	0.959554	−	1.66200i	0.723585	−	0.690236i	$-0.242493\pi$
$878$	−1.70820	−	2.95870i	−0.0576491	−	0.0998512i
$879$	2.52786	+	4.37839i	0.0852627	+	0.147679i
$880$	3.23607	−	5.60503i	0.109088	−	0.188946i
$881$	27.8885			0.939589			0.469794	−	0.882776i	$-0.344328\pi$
$881$	27.8885			0.939589			0.469794	+	0.882776i	$0.344328\pi$
$882$		0			0
$883$	−37.8885			−1.27505			−0.637526	−	0.770429i	$-0.720042\pi$
$883$	−37.8885			−1.27505			−0.637526	+	0.770429i	$0.720042\pi$
$884$	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
$887$	−15.4164	+	26.7020i	−0.517632	+	0.896565i	0.482158	+	0.876084i	$0.339853\pi$
$887$	−15.4164	+	26.7020i	−0.517632	+	0.896565i	−0.999790	+	0.0204812i	$0.993480\pi$
$888$	15.5279			0.521081
$889$		0			0
$890$	−4.47214			−0.149906
$891$	−3.23607	+	5.60503i	−0.108412	+	0.187776i
$892$	−19.4164	−	33.6302i	−0.650109	−	1.12602i
$893$	16.0000	+	27.7128i	0.535420	+	0.927374i
$894$	−16.7082	+	28.9395i	−0.558806	+	0.967880i
$895$	6.47214			0.216340
$896$		0			0
$897$	−17.8885			−0.597281
$898$	−15.6525	+	27.1109i	−0.522330	+	0.904702i
$899$	−1.52786	−	2.64634i	−0.0509571	−	0.0882603i
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	3.52786	−	6.11044i	0.117530	−	0.203568i
$902$	−28.9443			−0.963739
$903$		0			0
$904$	−1.05573			−0.0351130
$905$	0.527864	−	0.914287i	0.0175468	−	0.0303919i
$906$	−17.8885	−	30.9839i	−0.594307	−	1.02937i
$907$	−26.9443	−	46.6688i	−0.894670	−	1.54961i	−0.834213	−	0.551443i	$-0.814077\pi$
$907$	−26.9443	−	46.6688i	−0.894670	−	1.54961i	−0.0604572	−	0.998171i	$-0.519256\pi$
$908$	1.41641	−	2.45329i	0.0470051	−	0.0814153i
$909$	14.0000			0.464351
$910$		0			0
$911$	46.2492			1.53231			0.766153	−	0.642659i	$-0.222169\pi$
$911$	46.2492			1.53231			0.766153	+	0.642659i	$0.222169\pi$
$912$	1.23607	−	2.14093i	0.0409303	−	0.0708934i
$913$	−54.8328	−	94.9732i	−1.81470	−	3.14315i
$914$	7.76393	+	13.4475i	0.256808	+	0.444805i
$915$	−1.00000	+	1.73205i	−0.0330590	+	0.0572598i
$916$	−71.6656			−2.36790
$917$		0			0
$918$	−4.47214			−0.147602
$919$	17.5279	−	30.3592i	0.578191	−	1.00146i	−0.417496	−	0.908679i	$-0.637092\pi$
$919$	17.5279	−	30.3592i	0.578191	−	1.00146i	0.995687	−	0.0927772i	$-0.0295744\pi$
$920$	4.47214	+	7.74597i	0.147442	+	0.255377i
$921$	−7.52786	−	13.0386i	−0.248052	−	0.429638i
$922$	−4.34752	+	7.53013i	−0.143178	+	0.247992i
$923$	−24.7214			−0.813713
$924$		0			0
$925$	−6.94427			−0.228326
$926$	23.4164	−	40.5584i	0.769511	−	1.33283i
$927$		0			0
$928$	6.70820	+	11.6190i	0.220208	+	0.381411i
$929$	−8.05573	+	13.9529i	−0.264300	+	0.457781i	−0.967380	−	0.253330i	$-0.918474\pi$
$929$	−8.05573	+	13.9529i	−0.264300	+	0.457781i	0.703080	+	0.711111i	$0.251808\pi$
$930$	3.41641			0.112028
$931$		0			0
$932$	−28.2492			−0.925334
$933$	12.9443	−	22.4201i	0.423776	−	0.734002i
$934$	10.0000	+	17.3205i	0.327210	+	0.566744i
$935$	−6.47214	−	11.2101i	−0.211661	−	0.366608i
$936$	−5.00000	+	8.66025i	−0.163430	+	0.283069i
$937$	52.4721			1.71419			0.857095	−	0.515158i	$-0.172267\pi$
$937$	52.4721			1.71419			0.857095	+	0.515158i	$0.172267\pi$
$938$		0			0
$939$	17.4164			0.568363
$940$	19.4164	−	33.6302i	0.633293	−	1.09690i
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	0.510934	−	0.859620i	$-0.329300\pi$
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	−0.999920	+	0.0126715i	$0.995966\pi$
$942$	0.527864	+	0.914287i	0.0171987	+	0.0297891i
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$	−8.94427			−0.291111
$945$		0			0
$946$	−129.443			−4.20855
$947$	8.94427	−	15.4919i	0.290650	−	0.503420i	−0.683314	−	0.730125i	$-0.739462\pi$
$947$	8.94427	−	15.4919i	0.290650	−	0.503420i	0.973964	+	0.226705i	$0.0727952\pi$
$948$	−19.4164	−	33.6302i	−0.630616	−	1.09226i
$949$	27.8885	+	48.3044i	0.905300	+	1.56803i
$950$	2.76393	−	4.78727i	0.0896738	−	0.155320i
$951$	14.3607			0.465677
$952$		0			0
$953$	−33.4164			−1.08246			−0.541232	−	0.840873i	$-0.682042\pi$
$953$	−33.4164			−1.08246			−0.541232	+	0.840873i	$0.682042\pi$
$954$	−3.94427	+	6.83168i	−0.127701	+	0.221184i
$955$	−0.291796	−	0.505406i	−0.00944230	−	0.0163545i
$956$	15.7082	+	27.2074i	0.508040	+	0.879950i
$957$	6.47214	−	11.2101i	0.209214	−	0.362370i
$958$	−40.0000			−1.29234
$959$		0			0
$960$	−13.0000			−0.419573
$961$	14.3328	−	24.8252i	0.462349	−	0.800812i
$962$	34.7214	+	60.1392i	1.11946	+	1.93896i
$963$	6.47214	+	11.2101i	0.208562	+	0.361239i
$964$	−28.4164	+	49.2187i	−0.915231	+	1.58523i
$965$	−14.0000			−0.450676
$966$		0			0
$967$	25.8885			0.832519			0.416260	−	0.909246i	$-0.363341\pi$
$967$	25.8885			0.832519			0.416260	+	0.909246i	$0.363341\pi$
$968$	34.5344	−	59.8154i	1.10998	−	1.92254i
$969$	−2.47214	−	4.28187i	−0.0794164	−	0.137553i
$970$	−9.47214	−	16.4062i	−0.304132	−	0.526772i
$971$	20.4721	−	35.4588i	0.656982	−	1.13793i	−0.324411	−	0.945916i	$-0.605166\pi$
$971$	20.4721	−	35.4588i	0.656982	−	1.13793i	0.981393	−	0.192010i	$-0.0615006\pi$
$972$	3.00000			0.0962250
$973$		0			0
$974$	46.8328			1.50062
$975$	2.23607	−	3.87298i	0.0716115	−	0.124035i
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−15.2918	−	26.4862i	−0.489228	−	0.847368i	0.510695	−	0.859762i	$-0.329388\pi$
$977$	−15.2918	−	26.4862i	−0.489228	−	0.847368i	−0.999923	+	0.0123942i	$0.996055\pi$
$978$	−18.9443	+	32.8124i	−0.605771	+	1.04923i
$979$	12.9443			0.413701
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−23.8197	+	41.2569i	−0.760116	+	1.31656i
$983$	−11.4164	−	19.7738i	−0.364127	−	0.630686i	0.624509	−	0.781018i	$-0.285299\pi$
$983$	−11.4164	−	19.7738i	−0.364127	−	0.630686i	−0.988636	+	0.150332i	$0.951966\pi$
$984$	2.23607	+	3.87298i	0.0712832	+	0.123466i
$985$	−7.76393	+	13.4475i	−0.247379	+	0.428474i
$986$	8.94427			0.284844
$987$		0			0
$988$	−33.1672			−1.05519
$989$	−17.8885	+	30.9839i	−0.568823	+	0.985230i
$990$	7.23607	+	12.5332i	0.229977	+	0.398332i
$991$	−2.47214	−	4.28187i	−0.0785300	−	0.136018i	0.824086	−	0.566465i	$-0.191689\pi$
$991$	−2.47214	−	4.28187i	−0.0785300	−	0.136018i	−0.902616	+	0.430447i	$0.858356\pi$
$992$	5.12461	−	8.87609i	0.162707	−	0.281816i
$993$	0.944272			0.0299656
$994$		0			0
$995$	−27.4164			−0.869159
$996$	−25.4164	+	44.0225i	−0.805350	+	1.39491i
$997$	−2.70820	−	4.69075i	−0.0857697	−	0.148557i	0.819949	−	0.572436i	$-0.194002\pi$
$997$	−2.70820	−	4.69075i	−0.0857697	−	0.148557i	−0.905719	+	0.423879i	$0.860668\pi$
$998$	−15.5279	−	26.8950i	−0.491526	−	0.851348i
$999$	3.47214	−	6.01392i	0.109854	−	0.190272i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.i.226.2		4
7.2	even	3		735.2.a.k.1.1		2
7.3	odd	6		735.2.i.k.361.2		4
7.4	even	3	inner	735.2.i.i.361.2		4
7.5	odd	6		105.2.a.b.1.1	✓	2
7.6	odd	2		735.2.i.k.226.2		4
21.2	odd	6		2205.2.a.w.1.2		2
21.5	even	6		315.2.a.d.1.2		2
28.19	even	6		1680.2.a.v.1.1		2
35.9	even	6		3675.2.a.y.1.2		2
35.12	even	12		525.2.d.c.274.2		4
35.19	odd	6		525.2.a.g.1.2		2
35.33	even	12		525.2.d.c.274.3		4
56.5	odd	6		6720.2.a.cx.1.1		2
56.19	even	6		6720.2.a.cs.1.2		2
84.47	odd	6		5040.2.a.bw.1.2		2
105.47	odd	12		1575.2.d.d.1324.4		4
105.68	odd	12		1575.2.d.d.1324.1		4
105.89	even	6		1575.2.a.r.1.1		2
140.19	even	6		8400.2.a.cx.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.a.b.1.1	✓	2	7.5	odd	6
315.2.a.d.1.2		2	21.5	even	6
525.2.a.g.1.2		2	35.19	odd	6
525.2.d.c.274.2		4	35.12	even	12
525.2.d.c.274.3		4	35.33	even	12
735.2.a.k.1.1		2	7.2	even	3
735.2.i.i.226.2		4	1.1	even	1	trivial
735.2.i.i.361.2		4	7.4	even	3	inner
735.2.i.k.226.2		4	7.6	odd	2
735.2.i.k.361.2		4	7.3	odd	6
1575.2.a.r.1.1		2	105.89	even	6
1575.2.d.d.1324.1		4	105.68	odd	12
1575.2.d.d.1324.4		4	105.47	odd	12
1680.2.a.v.1.1		2	28.19	even	6
2205.2.a.w.1.2		2	21.2	odd	6
3675.2.a.y.1.2		2	35.9	even	6
5040.2.a.bw.1.2		2	84.47	odd	6
6720.2.a.cs.1.2		2	56.19	even	6
6720.2.a.cx.1.1		2	56.5	odd	6
8400.2.a.cx.1.1		2	140.19	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} +(-3.23607 - 5.60503i) 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} +(-1.23607 + 2.14093i) q^{19} +3.00000 q^{20} -14.4721 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} +(0.763932 + 1.32317i) q^{31} +(-3.35410 - 5.80948i) q^{32} +(-3.23607 + 5.60503i) q^{33} -4.47214 q^{34} +3.00000 q^{36} +(3.47214 - 6.01392i) q^{37} +(2.76393 + 4.78727i) q^{38} +(2.23607 + 3.87298i) q^{39} +(1.11803 - 1.93649i) q^{40} +2.00000 q^{41} +8.94427 q^{43} +(-9.70820 + 16.8151i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(4.47214 + 7.74597i) q^{46} +(6.47214 - 11.2101i) q^{47} -1.00000 q^{48} -2.23607 q^{50} +(-1.00000 + 1.73205i) q^{51} +(6.70820 + 11.6190i) q^{52} +(1.76393 + 3.05522i) q^{53} +(1.11803 - 1.93649i) q^{54} +6.47214 q^{55} +2.47214 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} +3.41641 q^{62} -13.0000 q^{64} +(2.23607 - 3.87298i) q^{65} +(7.23607 + 12.5332i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +4.00000 q^{69} +5.52786 q^{71} +(1.11803 - 1.93649i) q^{72} +(-6.23607 - 10.8012i) q^{73} +(-7.76393 - 13.4475i) q^{74} +(-0.500000 + 0.866025i) q^{75} +7.41641 q^{76} +10.0000 q^{78} +(-6.47214 + 11.2101i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.23607 - 3.87298i) q^{82} +16.9443 q^{83} +2.00000 q^{85} +(10.0000 - 17.3205i) q^{86} +(1.00000 + 1.73205i) q^{87} +(7.23607 + 12.5332i) q^{88} +(-1.00000 + 1.73205i) q^{89} -2.23607 q^{90} +12.0000 q^{92} +(0.763932 - 1.32317i) q^{93} +(-14.4721 - 25.0665i) q^{94} +(-1.23607 - 2.14093i) q^{95} +(-3.35410 + 5.80948i) q^{96} -8.47214 q^{97} +6.47214 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

Introduction

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